LMFDB - Embedded newform 1441.2.a.e.1.11

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:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-0.574950 q^{2} +1.45629 q^{3} -1.66943 q^{4} -2.31674 q^{5} -0.837294 q^{6} -3.08132 q^{7} +2.10974 q^{8} -0.879222 q^{9} +O(q^{10})$	\(q-0.574950 q^{2} +1.45629 q^{3} -1.66943 q^{4} -2.31674 q^{5} -0.837294 q^{6} -3.08132 q^{7} +2.10974 q^{8} -0.879222 q^{9} +1.33201 q^{10} +1.00000 q^{11} -2.43118 q^{12} -0.647487 q^{13} +1.77160 q^{14} -3.37384 q^{15} +2.12587 q^{16} +5.50931 q^{17} +0.505509 q^{18} -2.59130 q^{19} +3.86764 q^{20} -4.48729 q^{21} -0.574950 q^{22} -3.99022 q^{23} +3.07239 q^{24} +0.367289 q^{25} +0.372273 q^{26} -5.64927 q^{27} +5.14405 q^{28} -1.55883 q^{29} +1.93979 q^{30} +6.06469 q^{31} -5.44175 q^{32} +1.45629 q^{33} -3.16758 q^{34} +7.13862 q^{35} +1.46780 q^{36} +9.24956 q^{37} +1.48987 q^{38} -0.942927 q^{39} -4.88772 q^{40} -10.1000 q^{41} +2.57997 q^{42} +9.39576 q^{43} -1.66943 q^{44} +2.03693 q^{45} +2.29418 q^{46} +4.79830 q^{47} +3.09588 q^{48} +2.49452 q^{49} -0.211173 q^{50} +8.02315 q^{51} +1.08093 q^{52} +13.1785 q^{53} +3.24805 q^{54} -2.31674 q^{55} -6.50078 q^{56} -3.77368 q^{57} +0.896253 q^{58} -5.95888 q^{59} +5.63240 q^{60} +11.3635 q^{61} -3.48690 q^{62} +2.70916 q^{63} -1.12300 q^{64} +1.50006 q^{65} -0.837294 q^{66} +11.8075 q^{67} -9.19742 q^{68} -5.81091 q^{69} -4.10435 q^{70} +14.0984 q^{71} -1.85493 q^{72} +1.41174 q^{73} -5.31804 q^{74} +0.534878 q^{75} +4.32599 q^{76} -3.08132 q^{77} +0.542136 q^{78} +14.2436 q^{79} -4.92508 q^{80} -5.58930 q^{81} +5.80699 q^{82} +6.00638 q^{83} +7.49122 q^{84} -12.7636 q^{85} -5.40210 q^{86} -2.27011 q^{87} +2.10974 q^{88} +4.01206 q^{89} -1.17113 q^{90} +1.99511 q^{91} +6.66140 q^{92} +8.83195 q^{93} -2.75878 q^{94} +6.00336 q^{95} -7.92476 q^{96} -16.7207 q^{97} -1.43423 q^{98} -0.879222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * 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 $

$2$	−0.574950	−0.406551	−0.203276	−	0.979122i	$-0.565159\pi$
$2$	−0.574950	−0.406551	−0.203276	+	0.979122i	$0.565159\pi$
$3$	1.45629	0.840789	0.420394	−	0.907341i	$-0.361892\pi$
$3$	1.45629	0.840789	0.420394	+	0.907341i	$0.361892\pi$
$4$	−1.66943	−0.834716
$5$	−2.31674	−1.03608	−0.518039	−	0.855357i	$-0.673338\pi$
$5$	−2.31674	−1.03608	−0.518039	+	0.855357i	$0.673338\pi$
$6$	−0.837294	−0.341824
$7$	−3.08132	−1.16463	−0.582314	−	0.812964i	$-0.697853\pi$
$7$	−3.08132	−1.16463	−0.582314	+	0.812964i	$0.697853\pi$
$8$	2.10974	0.745906
$9$	−0.879222	−0.293074
$10$	1.33201	0.421219
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.43118	−0.701820
$13$	−0.647487	−0.179580	−0.0897902	−	0.995961i	$-0.528620\pi$
$13$	−0.647487	−0.179580	−0.0897902	+	0.995961i	$0.528620\pi$
$14$	1.77160	0.473481
$15$	−3.37384	−0.871123
$16$	2.12587	0.531467
$17$	5.50931	1.33620	0.668102	−	0.744070i	$-0.267107\pi$
$17$	5.50931	1.33620	0.668102	+	0.744070i	$0.267107\pi$
$18$	0.505509	0.119150
$19$	−2.59130	−0.594484	−0.297242	−	0.954802i	$-0.596067\pi$
$19$	−2.59130	−0.594484	−0.297242	+	0.954802i	$0.596067\pi$
$20$	3.86764	0.864831
$21$	−4.48729	−0.979207
$22$	−0.574950	−0.122580
$23$	−3.99022	−0.832018	−0.416009	−	0.909361i	$-0.636571\pi$
$23$	−3.99022	−0.832018	−0.416009	+	0.909361i	$0.636571\pi$
$24$	3.07239	0.627150
$25$	0.367289	0.0734577
$26$	0.372273	0.0730087
$27$	−5.64927	−1.08720
$28$	5.14405	0.972134
$29$	−1.55883	−0.289468	−0.144734	−	0.989471i	$-0.546233\pi$
$29$	−1.55883	−0.289468	−0.144734	+	0.989471i	$0.546233\pi$
$30$	1.93979	0.354156
$31$	6.06469	1.08925	0.544626	−	0.838679i	$-0.316672\pi$
$31$	6.06469	1.08925	0.544626	+	0.838679i	$0.316672\pi$
$32$	−5.44175	−0.961975
$33$	1.45629	0.253507
$34$	−3.16758	−0.543236
$35$	7.13862	1.20665
$36$	1.46780	0.244634
$37$	9.24956	1.52062	0.760309	−	0.649561i	$-0.225047\pi$
$37$	9.24956	1.52062	0.760309	+	0.649561i	$0.225047\pi$
$38$	1.48987	0.241688
$39$	−0.942927	−0.150989
$40$	−4.88772	−0.772817
$41$	−10.1000	−1.57735	−0.788676	−	0.614809i	$-0.789233\pi$
$41$	−10.1000	−1.57735	−0.788676	+	0.614809i	$0.789233\pi$
$42$	2.57997	0.398098
$43$	9.39576	1.43284	0.716420	−	0.697669i	$-0.245779\pi$
$43$	9.39576	1.43284	0.716420	+	0.697669i	$0.245779\pi$
$44$	−1.66943	−0.251676
$45$	2.03693	0.303648
$46$	2.29418	0.338258
$47$	4.79830	0.699904	0.349952	−	0.936768i	$-0.386198\pi$
$47$	4.79830	0.699904	0.349952	+	0.936768i	$0.386198\pi$
$48$	3.09588	0.446851
$49$	2.49452	0.356360
$50$	−0.211173	−0.0298643
$51$	8.02315	1.12347
$52$	1.08093	0.149899
$53$	13.1785	1.81020	0.905102	−	0.425195i	$-0.139795\pi$
$53$	13.1785	1.81020	0.905102	+	0.425195i	$0.139795\pi$
$54$	3.24805	0.442003
$55$	−2.31674	−0.312389
$56$	−6.50078	−0.868704
$57$	−3.77368	−0.499836
$58$	0.896253	0.117684
$59$	−5.95888	−0.775780	−0.387890	−	0.921706i	$-0.626796\pi$
$59$	−5.95888	−0.775780	−0.387890	+	0.921706i	$0.626796\pi$
$60$	5.63240	0.727140
$61$	11.3635	1.45494	0.727472	−	0.686137i	$-0.240695\pi$
$61$	11.3635	1.45494	0.727472	+	0.686137i	$0.240695\pi$
$62$	−3.48690	−0.442837
$63$	2.70916	0.341323
$64$	−1.12300	−0.140375
$65$	1.50006	0.186059
$66$	−0.837294	−0.103064
$67$	11.8075	1.44252	0.721260	−	0.692665i	$-0.243563\pi$
$67$	11.8075	1.44252	0.721260	+	0.692665i	$0.243563\pi$
$68$	−9.19742	−1.11535
$69$	−5.81091	−0.699551
$70$	−4.10435	−0.490564
$71$	14.0984	1.67318	0.836589	−	0.547831i	$-0.184546\pi$
$71$	14.0984	1.67318	0.836589	+	0.547831i	$0.184546\pi$
$72$	−1.85493	−0.218606
$73$	1.41174	0.165232	0.0826161	−	0.996581i	$-0.473672\pi$
$73$	1.41174	0.165232	0.0826161	+	0.996581i	$0.473672\pi$
$74$	−5.31804	−0.618210
$75$	0.534878	0.0617624
$76$	4.32599	0.496225
$77$	−3.08132	−0.351149
$78$	0.542136	0.0613849
$79$	14.2436	1.60253	0.801264	−	0.598311i	$-0.204161\pi$
$79$	14.2436	1.60253	0.801264	+	0.598311i	$0.204161\pi$
$80$	−4.92508	−0.550641
$81$	−5.58930	−0.621033
$82$	5.80699	0.641274
$83$	6.00638	0.659286	0.329643	−	0.944106i	$-0.393072\pi$
$83$	6.00638	0.659286	0.329643	+	0.944106i	$0.393072\pi$
$84$	7.49122	0.817360
$85$	−12.7636	−1.38441
$86$	−5.40210	−0.582523
$87$	−2.27011	−0.243382
$88$	2.10974	0.224899
$89$	4.01206	0.425277	0.212639	−	0.977131i	$-0.431794\pi$
$89$	4.01206	0.425277	0.212639	+	0.977131i	$0.431794\pi$
$90$	−1.17113	−0.123448
$91$	1.99511	0.209145
$92$	6.66140	0.694498
$93$	8.83195	0.915830
$94$	−2.75878	−0.284547
$95$	6.00336	0.615932
$96$	−7.92476	−0.808818
$97$	−16.7207	−1.69773	−0.848865	−	0.528609i	$-0.822714\pi$
$97$	−16.7207	−1.69773	−0.848865	+	0.528609i	$0.822714\pi$
$98$	−1.43423	−0.144879
$99$	−0.879222	−0.0883652
$100$	−0.613164	−0.0613164
$101$	3.56497	0.354728	0.177364	−	0.984145i	$-0.443243\pi$
$101$	3.56497	0.354728	0.177364	+	0.984145i	$0.443243\pi$
$102$	−4.61291	−0.456746
$103$	−17.1958	−1.69435	−0.847176	−	0.531313i	$-0.821699\pi$
$103$	−17.1958	−1.69435	−0.847176	+	0.531313i	$0.821699\pi$
$104$	−1.36603	−0.133950
$105$	10.3959	1.01453
$106$	−7.57697	−0.735941
$107$	2.74343	0.265217	0.132608	−	0.991169i	$-0.457665\pi$
$107$	2.74343	0.265217	0.132608	+	0.991169i	$0.457665\pi$
$108$	9.43107	0.907505
$109$	−4.29294	−0.411189	−0.205595	−	0.978637i	$-0.565913\pi$
$109$	−4.29294	−0.411189	−0.205595	+	0.978637i	$0.565913\pi$
$110$	1.33201	0.127002
$111$	13.4700	1.27852
$112$	−6.55047	−0.618962
$113$	−7.32619	−0.689190	−0.344595	−	0.938752i	$-0.611984\pi$
$113$	−7.32619	−0.689190	−0.344595	+	0.938752i	$0.611984\pi$
$114$	2.16968	0.203209
$115$	9.24430	0.862035
$116$	2.60237	0.241624
$117$	0.569285	0.0526304
$118$	3.42606	0.315394
$119$	−16.9759	−1.55618
$120$	−7.11794	−0.649776
$121$	1.00000	0.0909091
$122$	−6.53344	−0.591509
$123$	−14.7085	−1.32622
$124$	−10.1246	−0.909215
$125$	10.7328	0.959970
$126$	−1.55763	−0.138765
$127$	2.62693	0.233103	0.116551	−	0.993185i	$-0.462816\pi$
$127$	2.62693	0.233103	0.116551	+	0.993185i	$0.462816\pi$
$128$	11.5292	1.01904
$129$	13.6829	1.20472
$130$	−0.862459	−0.0756427
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−2.43118	−0.211607
$133$	7.98461	0.692353
$134$	−6.78874	−0.586458
$135$	13.0879	1.12643
$136$	11.6232	0.996683
$137$	5.67780	0.485087	0.242544	−	0.970140i	$-0.422018\pi$
$137$	5.67780	0.485087	0.242544	+	0.970140i	$0.422018\pi$
$138$	3.34098	0.284403
$139$	−12.9048	−1.09457	−0.547287	−	0.836945i	$-0.684339\pi$
$139$	−12.9048	−1.09457	−0.547287	+	0.836945i	$0.684339\pi$
$140$	−11.9174	−1.00721
$141$	6.98771	0.588471
$142$	−8.10591	−0.680233
$143$	−0.647487	−0.0541455
$144$	−1.86911	−0.155759
$145$	3.61142	0.299912
$146$	−0.811683	−0.0671754
$147$	3.63274	0.299624
$148$	−15.4415	−1.26928
$149$	11.0916	0.908657	0.454328	−	0.890834i	$-0.349879\pi$
$149$	11.0916	0.908657	0.454328	+	0.890834i	$0.349879\pi$
$150$	−0.307529	−0.0251096
$151$	−20.9885	−1.70802	−0.854009	−	0.520259i	$-0.825836\pi$
$151$	−20.9885	−1.70802	−0.854009	+	0.520259i	$0.825836\pi$
$152$	−5.46696	−0.443429
$153$	−4.84391	−0.391607
$154$	1.77160	0.142760
$155$	−14.0503	−1.12855
$156$	1.57415	0.126033
$157$	−10.7303	−0.856374	−0.428187	−	0.903690i	$-0.640848\pi$
$157$	−10.7303	−0.856374	−0.428187	+	0.903690i	$0.640848\pi$
$158$	−8.18935	−0.651510
$159$	19.1917	1.52200
$160$	12.6071	0.996681
$161$	12.2951	0.968992
$162$	3.21357	0.252482
$163$	−7.86078	−0.615704	−0.307852	−	0.951434i	$-0.599610\pi$
$163$	−7.86078	−0.615704	−0.307852	+	0.951434i	$0.599610\pi$
$164$	16.8612	1.31664
$165$	−3.37384	−0.262653
$166$	−3.45337	−0.268034
$167$	0.638935	0.0494423	0.0247211	−	0.999694i	$-0.492130\pi$
$167$	0.638935	0.0494423	0.0247211	+	0.999694i	$0.492130\pi$
$168$	−9.46702	−0.730396
$169$	−12.5808	−0.967751
$170$	7.33846	0.562834
$171$	2.27833	0.174228
$172$	−15.6856	−1.19601
$173$	−9.44525	−0.718109	−0.359055	−	0.933317i	$-0.616901\pi$
$173$	−9.44525	−0.718109	−0.359055	+	0.933317i	$0.616901\pi$
$174$	1.30520	0.0989472
$175$	−1.13173	−0.0855510
$176$	2.12587	0.160243
$177$	−8.67785	−0.652267
$178$	−2.30673	−0.172897
$179$	−18.7896	−1.40440	−0.702200	−	0.711980i	$-0.747799\pi$
$179$	−18.7896	−1.40440	−0.702200	+	0.711980i	$0.747799\pi$
$180$	−3.40052	−0.253460
$181$	−20.7901	−1.54532	−0.772658	−	0.634822i	$-0.781073\pi$
$181$	−20.7901	−1.54532	−0.772658	+	0.634822i	$0.781073\pi$
$182$	−1.14709	−0.0850280
$183$	16.5485	1.22330
$184$	−8.41832	−0.620607
$185$	−21.4288	−1.57548
$186$	−5.07793	−0.372332
$187$	5.50931	0.402881
$188$	−8.01043	−0.584221
$189$	17.4072	1.26619
$190$	−3.45164	−0.250408
$191$	18.2637	1.32151	0.660757	−	0.750600i	$-0.270235\pi$
$191$	18.2637	1.32151	0.660757	+	0.750600i	$0.270235\pi$
$192$	−1.63541	−0.118026
$193$	21.4712	1.54553	0.772766	−	0.634691i	$-0.218873\pi$
$193$	21.4712	1.54553	0.772766	+	0.634691i	$0.218873\pi$
$194$	9.61358	0.690215
$195$	2.18452	0.156437
$196$	−4.16443	−0.297459
$197$	15.7540	1.12243	0.561214	−	0.827670i	$-0.310334\pi$
$197$	15.7540	1.12243	0.561214	+	0.827670i	$0.310334\pi$
$198$	0.505509	0.0359250
$199$	−17.2946	−1.22598	−0.612991	−	0.790090i	$-0.710034\pi$
$199$	−17.2946	−1.22598	−0.612991	+	0.790090i	$0.710034\pi$
$200$	0.774884	0.0547926
$201$	17.1952	1.21285
$202$	−2.04968	−0.144215
$203$	4.80327	0.337123
$204$	−13.3941	−0.937775
$205$	23.3990	1.63426
$206$	9.88672	0.688841
$207$	3.50829	0.243843
$208$	−1.37647	−0.0954411
$209$	−2.59130	−0.179244
$210$	−5.97712	−0.412460
$211$	−3.52806	−0.242882	−0.121441	−	0.992599i	$-0.538751\pi$
$211$	−3.52806	−0.242882	−0.121441	+	0.992599i	$0.538751\pi$
$212$	−22.0006	−1.51101
$213$	20.5314	1.40679
$214$	−1.57733	−0.107824
$215$	−21.7675	−1.48453
$216$	−11.9185	−0.810951
$217$	−18.6873	−1.26857
$218$	2.46823	0.167170
$219$	2.05591	0.138925
$220$	3.86764	0.260756
$221$	−3.56720	−0.239956
$222$	−7.74460	−0.519784
$223$	14.7611	0.988476	0.494238	−	0.869327i	$-0.335447\pi$
$223$	14.7611	0.988476	0.494238	+	0.869327i	$0.335447\pi$
$224$	16.7678	1.12034
$225$	−0.322928	−0.0215286
$226$	4.21219	0.280191
$227$	20.3995	1.35397	0.676983	−	0.735999i	$-0.263287\pi$
$227$	20.3995	1.35397	0.676983	+	0.735999i	$0.263287\pi$
$228$	6.29990	0.417221
$229$	26.2767	1.73642	0.868208	−	0.496201i	$-0.165272\pi$
$229$	26.2767	1.73642	0.868208	+	0.496201i	$0.165272\pi$
$230$	−5.31501	−0.350462
$231$	−4.48729	−0.295242
$232$	−3.28874	−0.215916
$233$	7.63505	0.500189	0.250094	−	0.968221i	$-0.419538\pi$
$233$	7.63505	0.500189	0.250094	+	0.968221i	$0.419538\pi$
$234$	−0.327310	−0.0213970
$235$	−11.1164	−0.725155
$236$	9.94795	0.647556
$237$	20.7428	1.34739
$238$	9.76032	0.632668
$239$	13.4729	0.871491	0.435746	−	0.900070i	$-0.356485\pi$
$239$	13.4729	0.871491	0.435746	+	0.900070i	$0.356485\pi$
$240$	−7.17235	−0.462973
$241$	8.72667	0.562134	0.281067	−	0.959688i	$-0.409312\pi$
$241$	8.72667	0.562134	0.281067	+	0.959688i	$0.409312\pi$
$242$	−0.574950	−0.0369592
$243$	8.80817	0.565044
$244$	−18.9706	−1.21447
$245$	−5.77916	−0.369217
$246$	8.45665	0.539176
$247$	1.67783	0.106758
$248$	12.7949	0.812479
$249$	8.74703	0.554320
$250$	−6.17082	−0.390277
$251$	26.5054	1.67301	0.836503	−	0.547962i	$-0.184596\pi$
$251$	26.5054	1.67301	0.836503	+	0.547962i	$0.184596\pi$
$252$	−4.52277	−0.284907
$253$	−3.99022	−0.250863
$254$	−1.51036	−0.0947682
$255$	−18.5876	−1.16400
$256$	−4.38270	−0.273919
$257$	−15.1713	−0.946362	−0.473181	−	0.880965i	$-0.656894\pi$
$257$	−15.1713	−0.946362	−0.473181	+	0.880965i	$0.656894\pi$
$258$	−7.86701	−0.489779
$259$	−28.5008	−1.77096
$260$	−2.50425	−0.155307
$261$	1.37056	0.0848357
$262$	0.574950	0.0355206
$263$	−13.6733	−0.843134	−0.421567	−	0.906797i	$-0.638520\pi$
$263$	−13.6733	−0.843134	−0.421567	+	0.906797i	$0.638520\pi$
$264$	3.07239	0.189093
$265$	−30.5311	−1.87551
$266$	−4.59075	−0.281477
$267$	5.84271	0.357568
$268$	−19.7119	−1.20409
$269$	10.0773	0.614423	0.307211	−	0.951641i	$-0.400604\pi$
$269$	10.0773	0.614423	0.307211	+	0.951641i	$0.400604\pi$
$270$	−7.52489	−0.457950
$271$	19.9695	1.21306	0.606532	−	0.795059i	$-0.292560\pi$
$271$	19.9695	1.21306	0.606532	+	0.795059i	$0.292560\pi$
$272$	11.7121	0.710148
$273$	2.90546	0.175846
$274$	−3.26446	−0.197213
$275$	0.367289	0.0221483
$276$	9.70092	0.583927
$277$	−9.00719	−0.541190	−0.270595	−	0.962693i	$-0.587220\pi$
$277$	−9.00719	−0.541190	−0.270595	+	0.962693i	$0.587220\pi$
$278$	7.41964	0.445000
$279$	−5.33222	−0.319231
$280$	15.0606	0.900045
$281$	7.93534	0.473383	0.236691	−	0.971585i	$-0.423937\pi$
$281$	7.93534	0.473383	0.236691	+	0.971585i	$0.423937\pi$
$282$	−4.01759	−0.239244
$283$	20.7077	1.23094	0.615471	−	0.788159i	$-0.288966\pi$
$283$	20.7077	1.23094	0.615471	+	0.788159i	$0.288966\pi$
$284$	−23.5364	−1.39663
$285$	8.74263	0.517869
$286$	0.372273	0.0220129
$287$	31.1213	1.83703
$288$	4.78451	0.281930
$289$	13.3525	0.785442
$290$	−2.07639	−0.121930
$291$	−24.3502	−1.42743
$292$	−2.35681	−0.137922
$293$	9.13987	0.533957	0.266978	−	0.963702i	$-0.413975\pi$
$293$	9.13987	0.533957	0.266978	+	0.963702i	$0.413975\pi$
$294$	−2.08865	−0.121812
$295$	13.8052	0.803769
$296$	19.5142	1.13424
$297$	−5.64927	−0.327804
$298$	−6.37710	−0.369416
$299$	2.58361	0.149414
$300$	−0.892943	−0.0515541
$301$	−28.9513	−1.66873
$302$	12.0673	0.694397
$303$	5.19163	0.298251
$304$	−5.50875	−0.315949
$305$	−26.3262	−1.50744
$306$	2.78501	0.159208
$307$	−17.2030	−0.981827	−0.490914	−	0.871208i	$-0.663337\pi$
$307$	−17.2030	−0.981827	−0.490914	+	0.871208i	$0.663337\pi$
$308$	5.14405	0.293110
$309$	−25.0420	−1.42459
$310$	8.07824	0.458813
$311$	32.1005	1.82025	0.910127	−	0.414330i	$-0.135984\pi$
$311$	32.1005	1.82025	0.910127	+	0.414330i	$0.135984\pi$
$312$	−1.98933	−0.112624
$313$	4.47358	0.252862	0.126431	−	0.991975i	$-0.459648\pi$
$313$	4.47358	0.252862	0.126431	+	0.991975i	$0.459648\pi$
$314$	6.16941	0.348160
$315$	−6.27643	−0.353637
$316$	−23.7787	−1.33766
$317$	−12.3609	−0.694257	−0.347128	−	0.937818i	$-0.612843\pi$
$317$	−12.3609	−0.694257	−0.347128	+	0.937818i	$0.612843\pi$
$318$	−11.0343	−0.618771
$319$	−1.55883	−0.0872780
$320$	2.60170	0.145439
$321$	3.99522	0.222991
$322$	−7.06909	−0.393945
$323$	−14.2763	−0.794352
$324$	9.33096	0.518387
$325$	−0.237814	−0.0131916
$326$	4.51956	0.250315
$327$	−6.25176	−0.345723
$328$	−21.3083	−1.17656
$329$	−14.7851	−0.815128
$330$	1.93979	0.106782
$331$	−21.6296	−1.18887	−0.594436	−	0.804143i	$-0.702625\pi$
$331$	−21.6296	−1.18887	−0.594436	+	0.804143i	$0.702625\pi$
$332$	−10.0272	−0.550317
$333$	−8.13242	−0.445654
$334$	−0.367356	−0.0201008
$335$	−27.3550	−1.49456
$336$	−9.53938	−0.520416
$337$	13.5896	0.740273	0.370136	−	0.928977i	$-0.379311\pi$
$337$	13.5896	0.740273	0.370136	+	0.928977i	$0.379311\pi$
$338$	7.23331	0.393440
$339$	−10.6690	−0.579463
$340$	21.3080	1.15559
$341$	6.06469	0.328422
$342$	−1.30992	−0.0708326
$343$	13.8828	0.749602
$344$	19.8226	1.06876
$345$	13.4624	0.724790
$346$	5.43055	0.291948
$347$	−21.4802	−1.15312	−0.576559	−	0.817056i	$-0.695605\pi$
$347$	−21.4802	−1.15312	−0.576559	+	0.817056i	$0.695605\pi$
$348$	3.78980	0.203155
$349$	−1.28702	−0.0688926	−0.0344463	−	0.999407i	$-0.510967\pi$
$349$	−1.28702	−0.0688926	−0.0344463	+	0.999407i	$0.510967\pi$
$350$	0.650690	0.0347809
$351$	3.65783	0.195240
$352$	−5.44175	−0.290046
$353$	−5.58544	−0.297283	−0.148642	−	0.988891i	$-0.547490\pi$
$353$	−5.58544	−0.297283	−0.148642	+	0.988891i	$0.547490\pi$
$354$	4.98933	0.265180
$355$	−32.6624	−1.73354
$356$	−6.69785	−0.354986
$357$	−24.7219	−1.30842
$358$	10.8031	0.570961
$359$	−19.7317	−1.04140	−0.520700	−	0.853740i	$-0.674329\pi$
$359$	−19.7317	−1.04140	−0.520700	+	0.853740i	$0.674329\pi$
$360$	4.29740	0.226493
$361$	−12.2852	−0.646589
$362$	11.9533	0.628250
$363$	1.45629	0.0764353
$364$	−3.33070	−0.174576
$365$	−3.27065	−0.171193
$366$	−9.51457	−0.497335
$367$	−27.6393	−1.44276	−0.721380	−	0.692540i	$-0.756492\pi$
$367$	−27.6393	−1.44276	−0.721380	+	0.692540i	$0.756492\pi$
$368$	−8.48267	−0.442190
$369$	8.88013	0.462281
$370$	12.3205	0.640513
$371$	−40.6071	−2.10821
$372$	−14.7443	−0.764458
$373$	29.4424	1.52447	0.762234	−	0.647301i	$-0.224102\pi$
$373$	29.4424	1.52447	0.762234	+	0.647301i	$0.224102\pi$
$374$	−3.16758	−0.163792
$375$	15.6300	0.807132
$376$	10.1232	0.522063
$377$	1.00932	0.0519829
$378$	−10.0083	−0.514770
$379$	−11.5312	−0.592316	−0.296158	−	0.955139i	$-0.595705\pi$
$379$	−11.5312	−0.592316	−0.296158	+	0.955139i	$0.595705\pi$
$380$	−10.0222	−0.514128
$381$	3.82558	0.195990
$382$	−10.5007	−0.537263
$383$	9.68692	0.494979	0.247489	−	0.968891i	$-0.420394\pi$
$383$	9.68692	0.494979	0.247489	+	0.968891i	$0.420394\pi$
$384$	16.7898	0.856801
$385$	7.13862	0.363818
$386$	−12.3449	−0.628338
$387$	−8.26096	−0.419928
$388$	27.9141	1.41712
$389$	−25.9390	−1.31516	−0.657581	−	0.753384i	$-0.728420\pi$
$389$	−25.9390	−1.31516	−0.657581	+	0.753384i	$0.728420\pi$
$390$	−1.25599	−0.0635995
$391$	−21.9833	−1.11175
$392$	5.26279	0.265811
$393$	−1.45629	−0.0734601
$394$	−9.05779	−0.456325
$395$	−32.9987	−1.66034
$396$	1.46780	0.0737598
$397$	29.5082	1.48097	0.740487	−	0.672070i	$-0.234595\pi$
$397$	29.5082	1.48097	0.740487	+	0.672070i	$0.234595\pi$
$398$	9.94354	0.498425
$399$	11.6279	0.582123
$400$	0.780807	0.0390404
$401$	26.9195	1.34430	0.672148	−	0.740417i	$-0.265372\pi$
$401$	26.9195	1.34430	0.672148	+	0.740417i	$0.265372\pi$
$402$	−9.88637	−0.493087
$403$	−3.92681	−0.195608
$404$	−5.95148	−0.296097
$405$	12.9490	0.643439
$406$	−2.76164	−0.137058
$407$	9.24956	0.458484
$408$	16.9268	0.838000
$409$	11.4338	0.565365	0.282683	−	0.959213i	$-0.408776\pi$
$409$	11.4338	0.565365	0.282683	+	0.959213i	$0.408776\pi$
$410$	−13.4533	−0.664410
$411$	8.26852	0.407856
$412$	28.7072	1.41430
$413$	18.3612	0.903496
$414$	−2.01709	−0.0991346
$415$	−13.9152	−0.683072
$416$	3.52346	0.172752
$417$	−18.7932	−0.920305
$418$	1.48987	0.0728718
$419$	−13.7970	−0.674027	−0.337013	−	0.941500i	$-0.609417\pi$
$419$	−13.7970	−0.674027	−0.337013	+	0.941500i	$0.609417\pi$
$420$	−17.3552	−0.846848
$421$	14.9873	0.730438	0.365219	−	0.930922i	$-0.380994\pi$
$421$	14.9873	0.730438	0.365219	+	0.930922i	$0.380994\pi$
$422$	2.02846	0.0987438
$423$	−4.21877	−0.205124
$424$	27.8032	1.35024
$425$	2.02351	0.0981545
$426$	−11.8045	−0.571932
$427$	−35.0145	−1.69447
$428$	−4.57996	−0.221381
$429$	−0.942927	−0.0455250
$430$	12.5153	0.603539
$431$	34.9943	1.68562	0.842808	−	0.538214i	$-0.180901\pi$
$431$	34.9943	1.68562	0.842808	+	0.538214i	$0.180901\pi$
$432$	−12.0096	−0.577812
$433$	−11.6354	−0.559161	−0.279580	−	0.960122i	$-0.590195\pi$
$433$	−11.6354	−0.559161	−0.279580	+	0.960122i	$0.590195\pi$
$434$	10.7442	0.515740
$435$	5.25927	0.252162
$436$	7.16678	0.343226
$437$	10.3398	0.494621
$438$	−1.18205	−0.0564803
$439$	27.4480	1.31002	0.655011	−	0.755619i	$-0.272664\pi$
$439$	27.4480	1.31002	0.655011	+	0.755619i	$0.272664\pi$
$440$	−4.88772	−0.233013
$441$	−2.19324	−0.104440
$442$	2.05097	0.0975545
$443$	35.3389	1.67900	0.839502	−	0.543357i	$-0.182847\pi$
$443$	35.3389	1.67900	0.839502	+	0.543357i	$0.182847\pi$
$444$	−22.4873	−1.06720
$445$	−9.29489	−0.440620
$446$	−8.48690	−0.401866
$447$	16.1525	0.763988
$448$	3.46032	0.163485
$449$	−17.9902	−0.849012	−0.424506	−	0.905425i	$-0.639552\pi$
$449$	−17.9902	−0.849012	−0.424506	+	0.905425i	$0.639552\pi$
$450$	0.185668	0.00875247
$451$	−10.1000	−0.475590
$452$	12.2306	0.575278
$453$	−30.5653	−1.43608
$454$	−11.7287	−0.550456
$455$	−4.62216	−0.216690
$456$	−7.96148	−0.372830
$457$	5.39734	0.252477	0.126239	−	0.992000i	$-0.459710\pi$
$457$	5.39734	0.252477	0.126239	+	0.992000i	$0.459710\pi$
$458$	−15.1078	−0.705942
$459$	−31.1236	−1.45272
$460$	−15.4327	−0.719555
$461$	−23.9443	−1.11520	−0.557599	−	0.830111i	$-0.688277\pi$
$461$	−23.9443	−1.11520	−0.557599	+	0.830111i	$0.688277\pi$
$462$	2.57997	0.120031
$463$	17.2907	0.803566	0.401783	−	0.915735i	$-0.368391\pi$
$463$	17.2907	0.803566	0.401783	+	0.915735i	$0.368391\pi$
$464$	−3.31388	−0.153843
$465$	−20.4613	−0.948872
$466$	−4.38977	−0.203352
$467$	−12.4475	−0.576000	−0.288000	−	0.957630i	$-0.592990\pi$
$467$	−12.4475	−0.576000	−0.288000	+	0.957630i	$0.592990\pi$
$468$	−0.950382	−0.0439314
$469$	−36.3828	−1.68000
$470$	6.39139	0.294813
$471$	−15.6265	−0.720030
$472$	−12.5717	−0.578659
$473$	9.39576	0.432018
$474$	−11.9261	−0.547782
$475$	−0.951754	−0.0436695
$476$	28.3402	1.29897
$477$	−11.5868	−0.530524
$478$	−7.74626	−0.354306
$479$	−3.12639	−0.142848	−0.0714242	−	0.997446i	$-0.522754\pi$
$479$	−3.12639	−0.142848	−0.0714242	+	0.997446i	$0.522754\pi$
$480$	18.3596	0.837998
$481$	−5.98897	−0.273073
$482$	−5.01740	−0.228536
$483$	17.9053	0.814717
$484$	−1.66943	−0.0758833
$485$	38.7375	1.75898
$486$	−5.06426	−0.229720
$487$	5.01242	0.227134	0.113567	−	0.993530i	$-0.463772\pi$
$487$	5.01242	0.227134	0.113567	+	0.993530i	$0.463772\pi$
$488$	23.9740	1.08525
$489$	−11.4476	−0.517677
$490$	3.32273	0.150106
$491$	32.2030	1.45330	0.726651	−	0.687006i	$-0.241076\pi$
$491$	32.2030	1.45330	0.726651	+	0.687006i	$0.241076\pi$
$492$	24.5548	1.10702
$493$	−8.58811	−0.386789
$494$	−0.964669	−0.0434025
$495$	2.03693	0.0915532
$496$	12.8927	0.578901
$497$	−43.4418	−1.94863
$498$	−5.02911	−0.225360
$499$	−36.0722	−1.61481	−0.807407	−	0.589994i	$-0.799130\pi$
$499$	−36.0722	−1.61481	−0.807407	+	0.589994i	$0.799130\pi$
$500$	−17.9177	−0.801302
$501$	0.930474	0.0415705
$502$	−15.2393	−0.680163
$503$	18.3217	0.816924	0.408462	−	0.912775i	$-0.366065\pi$
$503$	18.3217	0.816924	0.408462	+	0.912775i	$0.366065\pi$
$504$	5.71563	0.254595
$505$	−8.25911	−0.367526
$506$	2.29418	0.101989
$507$	−18.3212	−0.813674
$508$	−4.38549	−0.194575
$509$	19.4456	0.861912	0.430956	−	0.902373i	$-0.358176\pi$
$509$	19.4456	0.861912	0.430956	+	0.902373i	$0.358176\pi$
$510$	10.6869	0.473225
$511$	−4.35003	−0.192434
$512$	−20.5385	−0.907682
$513$	14.6389	0.646325
$514$	8.72277	0.384745
$515$	39.8382	1.75548
$516$	−22.8427	−1.00560
$517$	4.79830	0.211029
$518$	16.3866	0.719985
$519$	−13.7550	−0.603778
$520$	3.16474	0.138783
$521$	−22.4153	−0.982031	−0.491016	−	0.871151i	$-0.663374\pi$
$521$	−22.4153	−0.982031	−0.491016	+	0.871151i	$0.663374\pi$
$522$	−0.788005	−0.0344901
$523$	30.7511	1.34465	0.672326	−	0.740255i	$-0.265295\pi$
$523$	30.7511	1.34465	0.672326	+	0.740255i	$0.265295\pi$
$524$	1.66943	0.0729295
$525$	−1.64813	−0.0719303
$526$	7.86149	0.342777
$527$	33.4123	1.45546
$528$	3.09588	0.134731
$529$	−7.07817	−0.307747
$530$	17.5539	0.762492
$531$	5.23918	0.227361
$532$	−13.3298	−0.577918
$533$	6.53960	0.283262
$534$	−3.35927	−0.145370
$535$	−6.35581	−0.274785
$536$	24.9108	1.07598
$537$	−27.3631	−1.18080
$538$	−5.79394	−0.249794
$539$	2.49452	0.107447
$540$	−21.8493	−0.940246
$541$	17.3342	0.745255	0.372628	−	0.927981i	$-0.378457\pi$
$541$	17.3342	0.745255	0.372628	+	0.927981i	$0.378457\pi$
$542$	−11.4815	−0.493172
$543$	−30.2764	−1.29928
$544$	−29.9803	−1.28539
$545$	9.94564	0.426024
$546$	−1.67049	−0.0714906
$547$	37.9199	1.62134	0.810668	−	0.585506i	$-0.199104\pi$
$547$	37.9199	1.62134	0.810668	+	0.585506i	$0.199104\pi$
$548$	−9.47871	−0.404910
$549$	−9.99102	−0.426407
$550$	−0.211173	−0.00900444
$551$	4.03940	0.172084
$552$	−12.2595	−0.521800
$553$	−43.8890	−1.86635
$554$	5.17869	0.220021
$555$	−31.2066	−1.32465
$556$	21.5437	0.913658
$557$	24.7825	1.05007	0.525035	−	0.851081i	$-0.324052\pi$
$557$	24.7825	1.05007	0.525035	+	0.851081i	$0.324052\pi$
$558$	3.06576	0.129784
$559$	−6.08363	−0.257310
$560$	15.1758	0.641293
$561$	8.02315	0.338738
$562$	−4.56243	−0.192454
$563$	−8.06237	−0.339788	−0.169894	−	0.985462i	$-0.554343\pi$
$563$	−8.06237	−0.339788	−0.169894	+	0.985462i	$0.554343\pi$
$564$	−11.6655	−0.491206
$565$	16.9729	0.714054
$566$	−11.9059	−0.500441
$567$	17.2224	0.723273
$568$	29.7441	1.24803
$569$	3.55307	0.148953	0.0744763	−	0.997223i	$-0.476271\pi$
$569$	3.55307	0.148953	0.0744763	+	0.997223i	$0.476271\pi$
$570$	−5.02658	−0.210540
$571$	−1.02329	−0.0428233	−0.0214116	−	0.999771i	$-0.506816\pi$
$571$	−1.02329	−0.0428233	−0.0214116	+	0.999771i	$0.506816\pi$
$572$	1.08093	0.0451962
$573$	26.5972	1.11111
$574$	−17.8932	−0.746847
$575$	−1.46556	−0.0611181
$576$	0.987366	0.0411402
$577$	−14.7881	−0.615637	−0.307819	−	0.951445i	$-0.599599\pi$
$577$	−14.7881	−0.615637	−0.307819	+	0.951445i	$0.599599\pi$
$578$	−7.67703	−0.319322
$579$	31.2683	1.29947
$580$	−6.02901	−0.250341
$581$	−18.5076	−0.767823
$582$	14.0001	0.580325
$583$	13.1785	0.545797
$584$	2.97842	0.123248
$585$	−1.31889	−0.0545292
$586$	−5.25497	−0.217081
$587$	34.3262	1.41679	0.708397	−	0.705815i	$-0.249419\pi$
$587$	34.3262	1.41679	0.708397	+	0.705815i	$0.249419\pi$
$588$	−6.06462	−0.250101
$589$	−15.7154	−0.647543
$590$	−7.93729	−0.326773
$591$	22.9424	0.943726
$592$	19.6633	0.808159
$593$	−27.7463	−1.13940	−0.569701	−	0.821852i	$-0.692941\pi$
$593$	−27.7463	−1.13940	−0.569701	+	0.821852i	$0.692941\pi$
$594$	3.24805	0.133269
$595$	39.3289	1.61233
$596$	−18.5166	−0.758470
$597$	−25.1860	−1.03079
$598$	−1.48545	−0.0607445
$599$	44.1134	1.80243	0.901213	−	0.433377i	$-0.142678\pi$
$599$	44.1134	1.80243	0.901213	+	0.433377i	$0.142678\pi$
$600$	1.12846	0.0460690
$601$	26.3041	1.07297	0.536484	−	0.843910i	$-0.319752\pi$
$601$	26.3041	1.07297	0.536484	+	0.843910i	$0.319752\pi$
$602$	16.6456	0.678423
$603$	−10.3814	−0.422765
$604$	35.0388	1.42571
$605$	−2.31674	−0.0941889
$606$	−2.98493	−0.121254
$607$	−31.2098	−1.26677	−0.633383	−	0.773838i	$-0.718334\pi$
$607$	−31.2098	−1.26677	−0.633383	+	0.773838i	$0.718334\pi$
$608$	14.1012	0.571879
$609$	6.99494	0.283449
$610$	15.1363	0.612850
$611$	−3.10683	−0.125689
$612$	8.08658	0.326881
$613$	−19.1976	−0.775385	−0.387692	−	0.921789i	$-0.626728\pi$
$613$	−19.1976	−0.775385	−0.387692	+	0.921789i	$0.626728\pi$
$614$	9.89087	0.399163
$615$	34.0758	1.37407
$616$	−6.50078	−0.261924
$617$	−31.1009	−1.25207	−0.626037	−	0.779794i	$-0.715324\pi$
$617$	−31.1009	−1.25207	−0.626037	+	0.779794i	$0.715324\pi$
$618$	14.3979	0.579170
$619$	−23.7528	−0.954704	−0.477352	−	0.878712i	$-0.658403\pi$
$619$	−23.7528	−0.954704	−0.477352	+	0.878712i	$0.658403\pi$
$620$	23.4561	0.942018
$621$	22.5418	0.904571
$622$	−18.4562	−0.740026
$623$	−12.3624	−0.495290
$624$	−2.00454	−0.0802458
$625$	−26.7015	−1.06806
$626$	−2.57209	−0.102801
$627$	−3.77368	−0.150706
$628$	17.9136	0.714829
$629$	50.9587	2.03186
$630$	3.60864	0.143772
$631$	−6.46886	−0.257521	−0.128761	−	0.991676i	$-0.541100\pi$
$631$	−6.46886	−0.257521	−0.128761	+	0.991676i	$0.541100\pi$
$632$	30.0503	1.19533
$633$	−5.13787	−0.204212
$634$	7.10690	0.282251
$635$	−6.08593	−0.241513
$636$	−32.0392	−1.27044
$637$	−1.61517	−0.0639953
$638$	0.896253	0.0354830
$639$	−12.3957	−0.490365
$640$	−26.7101	−1.05581
$641$	36.9458	1.45927	0.729636	−	0.683836i	$-0.239689\pi$
$641$	36.9458	1.45927	0.729636	+	0.683836i	$0.239689\pi$
$642$	−2.29705	−0.0906575
$643$	6.10420	0.240726	0.120363	−	0.992730i	$-0.461594\pi$
$643$	6.10420	0.240726	0.120363	+	0.992730i	$0.461594\pi$
$644$	−20.5259	−0.808833
$645$	−31.6998	−1.24818
$646$	8.20814	0.322945
$647$	19.0863	0.750358	0.375179	−	0.926952i	$-0.377581\pi$
$647$	19.0863	0.750358	0.375179	+	0.926952i	$0.377581\pi$
$648$	−11.7920	−0.463233
$649$	−5.95888	−0.233906
$650$	0.136732	0.00536305
$651$	−27.2140	−1.06660
$652$	13.1230	0.513938
$653$	9.26968	0.362751	0.181375	−	0.983414i	$-0.441945\pi$
$653$	9.26968	0.362751	0.181375	+	0.983414i	$0.441945\pi$
$654$	3.59445	0.140554
$655$	2.31674	0.0905226
$656$	−21.4712	−0.838310
$657$	−1.24124	−0.0484253
$658$	8.50069	0.331391
$659$	45.0627	1.75539	0.877696	−	0.479218i	$-0.159080\pi$
$659$	45.0627	1.75539	0.877696	+	0.479218i	$0.159080\pi$
$660$	5.63240	0.219241
$661$	28.8633	1.12265	0.561326	−	0.827595i	$-0.310291\pi$
$661$	28.8633	1.12265	0.561326	+	0.827595i	$0.310291\pi$
$662$	12.4360	0.483337
$663$	−5.19488	−0.201752
$664$	12.6719	0.491765
$665$	−18.4983	−0.717332
$666$	4.67574	0.181181
$667$	6.22009	0.240843
$668$	−1.06666	−0.0412703
$669$	21.4964	0.831099
$670$	15.7278	0.607616
$671$	11.3635	0.438682
$672$	24.4187	0.941972
$673$	20.7145	0.798487	0.399243	−	0.916845i	$-0.369273\pi$
$673$	20.7145	0.798487	0.399243	+	0.916845i	$0.369273\pi$
$674$	−7.81335	−0.300959
$675$	−2.07491	−0.0798634
$676$	21.0027	0.807797
$677$	−30.9798	−1.19065	−0.595326	−	0.803485i	$-0.702977\pi$
$677$	−30.9798	−1.19065	−0.595326	+	0.803485i	$0.702977\pi$
$678$	6.13417	0.235581
$679$	51.5218	1.97723
$680$	−26.9280	−1.03264
$681$	29.7076	1.13840
$682$	−3.48690	−0.133520
$683$	−19.5130	−0.746645	−0.373323	−	0.927702i	$-0.621782\pi$
$683$	−19.5130	−0.746645	−0.373323	+	0.927702i	$0.621782\pi$
$684$	−3.80351	−0.145431
$685$	−13.1540	−0.502588
$686$	−7.98193	−0.304751
$687$	38.2665	1.45996
$688$	19.9741	0.761507
$689$	−8.53289	−0.325077
$690$	−7.74019	−0.294664
$691$	−28.9739	−1.10222	−0.551109	−	0.834433i	$-0.685795\pi$
$691$	−28.9739	−1.10222	−0.551109	+	0.834433i	$0.685795\pi$
$692$	15.7682	0.599417
$693$	2.70916	0.102913
$694$	12.3501	0.468802
$695$	29.8971	1.13406
$696$	−4.78935	−0.181540
$697$	−55.6439	−2.10766
$698$	0.739973	0.0280084
$699$	11.1188	0.420553
$700$	1.88935	0.0714108
$701$	0.254074	0.00959624	0.00479812	−	0.999988i	$-0.498473\pi$
$701$	0.254074	0.00959624	0.00479812	+	0.999988i	$0.498473\pi$
$702$	−2.10307	−0.0793752
$703$	−23.9684	−0.903984
$704$	−1.12300	−0.0423246
$705$	−16.1887	−0.609702
$706$	3.21135	0.120861
$707$	−10.9848	−0.413126
$708$	14.4871	0.544458
$709$	−12.2192	−0.458903	−0.229452	−	0.973320i	$-0.573693\pi$
$709$	−12.2192	−0.458903	−0.229452	+	0.973320i	$0.573693\pi$
$710$	18.7793	0.704774
$711$	−12.5233	−0.469659
$712$	8.46440	0.317217
$713$	−24.1994	−0.906276
$714$	14.2139	0.531940
$715$	1.50006	0.0560990
$716$	31.3679	1.17228
$717$	19.6205	0.732740
$718$	11.3448	0.423382
$719$	−21.6389	−0.806995	−0.403497	−	0.914981i	$-0.632206\pi$
$719$	−21.6389	−0.806995	−0.403497	+	0.914981i	$0.632206\pi$
$720$	4.33025	0.161379
$721$	52.9857	1.97329
$722$	7.06337	0.262871
$723$	12.7086	0.472636
$724$	34.7077	1.28990
$725$	−0.572542	−0.0212637
$726$	−0.837294	−0.0310749
$727$	−24.8593	−0.921982	−0.460991	−	0.887405i	$-0.652506\pi$
$727$	−24.8593	−0.921982	−0.460991	+	0.887405i	$0.652506\pi$
$728$	4.20917	0.156002
$729$	29.5951	1.09612
$730$	1.88046	0.0695989
$731$	51.7642	1.91457
$732$	−27.6266	−1.02111
$733$	−20.5139	−0.757699	−0.378850	−	0.925458i	$-0.623680\pi$
$733$	−20.5139	−0.757699	−0.378850	+	0.925458i	$0.623680\pi$
$734$	15.8912	0.586556
$735$	−8.41612	−0.310433
$736$	21.7138	0.800380
$737$	11.8075	0.434936
$738$	−5.10563	−0.187941
$739$	−6.69111	−0.246136	−0.123068	−	0.992398i	$-0.539273\pi$
$739$	−6.69111	−0.246136	−0.123068	+	0.992398i	$0.539273\pi$
$740$	35.7740	1.31508
$741$	2.44340	0.0897607
$742$	23.3471	0.857097
$743$	−24.6279	−0.903510	−0.451755	−	0.892142i	$-0.649202\pi$
$743$	−24.6279	−0.903510	−0.451755	+	0.892142i	$0.649202\pi$
$744$	18.6331	0.683123
$745$	−25.6963	−0.941439
$746$	−16.9279	−0.619775
$747$	−5.28094	−0.193220
$748$	−9.19742	−0.336291
$749$	−8.45337	−0.308879
$750$	−8.98650	−0.328141
$751$	−15.0866	−0.550520	−0.275260	−	0.961370i	$-0.588764\pi$
$751$	−15.0866	−0.550520	−0.275260	+	0.961370i	$0.588764\pi$
$752$	10.2005	0.371976
$753$	38.5995	1.40665
$754$	−0.580311	−0.0211337
$755$	48.6248	1.76964
$756$	−29.0601	−1.05691
$757$	−20.9486	−0.761391	−0.380696	−	0.924700i	$-0.624315\pi$
$757$	−20.9486	−0.761391	−0.380696	+	0.924700i	$0.624315\pi$
$758$	6.62984	0.240807
$759$	−5.81091	−0.210923
$760$	12.6655	0.459427
$761$	24.5687	0.890616	0.445308	−	0.895378i	$-0.353094\pi$
$761$	24.5687	0.890616	0.445308	+	0.895378i	$0.353094\pi$
$762$	−2.19952	−0.0796801
$763$	13.2279	0.478883
$764$	−30.4900	−1.10309
$765$	11.2221	0.405735
$766$	−5.56950	−0.201234
$767$	3.85829	0.139315
$768$	−6.38248	−0.230308
$769$	14.3369	0.517001	0.258500	−	0.966011i	$-0.416772\pi$
$769$	14.3369	0.517001	0.258500	+	0.966011i	$0.416772\pi$
$770$	−4.10435	−0.147910
$771$	−22.0939	−0.795691
$772$	−35.8447	−1.29008
$773$	9.87454	0.355163	0.177581	−	0.984106i	$-0.443173\pi$
$773$	9.87454	0.355163	0.177581	+	0.984106i	$0.443173\pi$
$774$	4.74964	0.170722
$775$	2.22749	0.0800139
$776$	−35.2764	−1.26635
$777$	−41.5055	−1.48900
$778$	14.9137	0.534681
$779$	26.1720	0.937711
$780$	−3.64691	−0.130580
$781$	14.0984	0.504482
$782$	12.6393	0.451982
$783$	8.80628	0.314711
$784$	5.30302	0.189394
$785$	24.8594	0.887271
$786$	0.837294	0.0298653
$787$	50.9338	1.81559	0.907797	−	0.419410i	$-0.137763\pi$
$787$	50.9338	1.81559	0.907797	+	0.419410i	$0.137763\pi$
$788$	−26.3003	−0.936909
$789$	−19.9123	−0.708897
$790$	18.9726	0.675015
$791$	22.5743	0.802650
$792$	−1.85493	−0.0659121
$793$	−7.35770	−0.261280
$794$	−16.9658	−0.602092
$795$	−44.4621	−1.57691
$796$	28.8722	1.02335
$797$	17.7461	0.628600	0.314300	−	0.949324i	$-0.398230\pi$
$797$	17.7461	0.628600	0.314300	+	0.949324i	$0.398230\pi$
$798$	−6.68546	−0.236663
$799$	26.4353	0.935214
$800$	−1.99869	−0.0706645
$801$	−3.52749	−0.124638
$802$	−15.4774	−0.546525
$803$	1.41174	0.0498194
$804$	−28.7062	−1.01239
$805$	−28.4846	−1.00395
$806$	2.25772	0.0795248
$807$	14.6754	0.516600
$808$	7.52117	0.264594
$809$	15.8165	0.556078	0.278039	−	0.960570i	$-0.410316\pi$
$809$	15.8165	0.556078	0.278039	+	0.960570i	$0.410316\pi$
$810$	−7.44501	−0.261591
$811$	−15.2098	−0.534088	−0.267044	−	0.963684i	$-0.586047\pi$
$811$	−15.2098	−0.534088	−0.267044	+	0.963684i	$0.586047\pi$
$812$	−8.01873	−0.281402
$813$	29.0814	1.01993
$814$	−5.31804	−0.186397
$815$	18.2114	0.637917
$816$	17.0562	0.597085
$817$	−24.3472	−0.851801
$818$	−6.57387	−0.229850
$819$	−1.75415	−0.0612949
$820$	−39.0631	−1.36414
$821$	−7.45121	−0.260049	−0.130024	−	0.991511i	$-0.541506\pi$
$821$	−7.45121	−0.260049	−0.130024	+	0.991511i	$0.541506\pi$
$822$	−4.75399	−0.165814
$823$	27.3420	0.953082	0.476541	−	0.879152i	$-0.341890\pi$
$823$	27.3420	0.953082	0.476541	+	0.879152i	$0.341890\pi$
$824$	−36.2787	−1.26383
$825$	0.534878	0.0186221
$826$	−10.5568	−0.367317
$827$	50.4490	1.75428	0.877142	−	0.480231i	$-0.159447\pi$
$827$	50.4490	1.75428	0.877142	+	0.480231i	$0.159447\pi$
$828$	−5.85685	−0.203540
$829$	18.3753	0.638199	0.319100	−	0.947721i	$-0.396620\pi$
$829$	18.3753	0.638199	0.319100	+	0.947721i	$0.396620\pi$
$830$	8.00057	0.277704
$831$	−13.1171	−0.455026
$832$	0.727127	0.0252086
$833$	13.7431	0.476170
$834$	10.8051	0.374151
$835$	−1.48025	−0.0512261
$836$	4.32599	0.149618
$837$	−34.2611	−1.18424
$838$	7.93258	0.274026
$839$	−0.526422	−0.0181741	−0.00908705	−	0.999959i	$-0.502893\pi$
$839$	−0.526422	−0.0181741	−0.00908705	+	0.999959i	$0.502893\pi$
$840$	21.9326	0.756748
$841$	−26.5700	−0.916208
$842$	−8.61697	−0.296961
$843$	11.5561	0.398015
$844$	5.88985	0.202737
$845$	29.1464	1.00267
$846$	2.42558	0.0833933
$847$	−3.08132	−0.105875
$848$	28.0157	0.962063
$849$	30.1563	1.03496
$850$	−1.16342	−0.0399049
$851$	−36.9078	−1.26518
$852$	−34.2758	−1.17427
$853$	−30.2714	−1.03647	−0.518236	−	0.855237i	$-0.673411\pi$
$853$	−30.2714	−1.03647	−0.518236	+	0.855237i	$0.673411\pi$
$854$	20.1316	0.688889
$855$	−5.27829	−0.180514
$856$	5.78792	0.197827
$857$	−20.3070	−0.693674	−0.346837	−	0.937925i	$-0.612744\pi$
$857$	−20.3070	−0.693674	−0.346837	+	0.937925i	$0.612744\pi$
$858$	0.542136	0.0185082
$859$	48.3761	1.65057	0.825285	−	0.564716i	$-0.191014\pi$
$859$	48.3761	1.65057	0.825285	+	0.564716i	$0.191014\pi$
$860$	36.3394	1.23916
$861$	45.3215	1.54455
$862$	−20.1200	−0.685289
$863$	22.1806	0.755037	0.377519	−	0.926002i	$-0.376777\pi$
$863$	22.1806	0.755037	0.377519	+	0.926002i	$0.376777\pi$
$864$	30.7419	1.04586
$865$	21.8822	0.744017
$866$	6.68976	0.227327
$867$	19.4451	0.660391
$868$	31.1971	1.05890
$869$	14.2436	0.483180
$870$	−3.02382	−0.102517
$871$	−7.64522	−0.259048
$872$	−9.05700	−0.306709
$873$	14.7012	0.497561
$874$	−5.94489	−0.201089
$875$	−33.0711	−1.11801
$876$	−3.43220	−0.115963
$877$	−31.7614	−1.07251	−0.536253	−	0.844057i	$-0.680161\pi$
$877$	−31.7614	−1.07251	−0.536253	+	0.844057i	$0.680161\pi$
$878$	−15.7812	−0.532591
$879$	13.3103	0.448945
$880$	−4.92508	−0.166025
$881$	−20.8663	−0.703003	−0.351502	−	0.936187i	$-0.614329\pi$
$881$	−20.8663	−0.703003	−0.351502	+	0.936187i	$0.614329\pi$
$882$	1.26100	0.0424602
$883$	−23.8273	−0.801854	−0.400927	−	0.916110i	$-0.631312\pi$
$883$	−23.8273	−0.801854	−0.400927	+	0.916110i	$0.631312\pi$
$884$	5.95521	0.200295
$885$	20.1043	0.675800
$886$	−20.3181	−0.682601
$887$	19.9372	0.669427	0.334714	−	0.942320i	$-0.391360\pi$
$887$	19.9372	0.669427	0.334714	+	0.942320i	$0.391360\pi$
$888$	28.4183	0.953655
$889$	−8.09442	−0.271478
$890$	5.34410	0.179135
$891$	−5.58930	−0.187249
$892$	−24.6426	−0.825097
$893$	−12.4338	−0.416082
$894$	−9.28690	−0.310600
$895$	43.5306	1.45507
$896$	−35.5250	−1.18681
$897$	3.76248	0.125626
$898$	10.3435	0.345167
$899$	−9.45386	−0.315304
$900$	0.539107	0.0179702
$901$	72.6044	2.41880
$902$	5.80699	0.193352
$903$	−42.1615	−1.40305
$904$	−15.4564	−0.514071
$905$	48.1653	1.60107
$906$	17.5735	0.583841
$907$	8.70745	0.289126	0.144563	−	0.989496i	$-0.453822\pi$
$907$	8.70745	0.289126	0.144563	+	0.989496i	$0.453822\pi$
$908$	−34.0557	−1.13018
$909$	−3.13440	−0.103962
$910$	2.65751	0.0880956
$911$	−55.2942	−1.83198	−0.915989	−	0.401204i	$-0.868592\pi$
$911$	−55.2942	−1.83198	−0.915989	+	0.401204i	$0.868592\pi$
$912$	−8.02234	−0.265646
$913$	6.00638	0.198782
$914$	−3.10320	−0.102645
$915$	−38.3386	−1.26744
$916$	−43.8672	−1.44941
$917$	3.08132	0.101754
$918$	17.8945	0.590607
$919$	39.4401	1.30101	0.650504	−	0.759503i	$-0.274558\pi$
$919$	39.4401	1.30101	0.650504	+	0.759503i	$0.274558\pi$
$920$	19.5031	0.642997
$921$	−25.0525	−0.825509
$922$	13.7668	0.453385
$923$	−9.12855	−0.300470
$924$	7.49122	0.246443
$925$	3.39726	0.111701
$926$	−9.94128	−0.326691
$927$	15.1189	0.496571
$928$	8.48279	0.278461
$929$	−5.91398	−0.194031	−0.0970156	−	0.995283i	$-0.530930\pi$
$929$	−5.91398	−0.194031	−0.0970156	+	0.995283i	$0.530930\pi$
$930$	11.7643	0.385765
$931$	−6.46404	−0.211850
$932$	−12.7462	−0.417516
$933$	46.7476	1.53045
$934$	7.15667	0.234174
$935$	−12.7636	−0.417416
$936$	1.20104	0.0392573
$937$	41.4747	1.35492	0.677460	−	0.735560i	$-0.263081\pi$
$937$	41.4747	1.35492	0.677460	+	0.735560i	$0.263081\pi$
$938$	20.9183	0.683006
$939$	6.51482	0.212603
$940$	18.5581	0.605298
$941$	13.5359	0.441259	0.220630	−	0.975358i	$-0.429189\pi$
$941$	13.5359	0.441259	0.220630	+	0.975358i	$0.429189\pi$
$942$	8.98445	0.292729
$943$	40.3011	1.31238
$944$	−12.6678	−0.412301
$945$	−40.3280	−1.31187
$946$	−5.40210	−0.175637
$947$	16.7930	0.545699	0.272849	−	0.962057i	$-0.412034\pi$
$947$	16.7930	0.545699	0.272849	+	0.962057i	$0.412034\pi$
$948$	−34.6286	−1.12469
$949$	−0.914086	−0.0296725
$950$	0.547211	0.0177539
$951$	−18.0010	−0.583723
$952$	−35.8148	−1.16077
$953$	−41.0383	−1.32936	−0.664681	−	0.747127i	$-0.731432\pi$
$953$	−41.0383	−1.32936	−0.664681	+	0.747127i	$0.731432\pi$
$954$	6.66184	0.215685
$955$	−42.3122	−1.36919
$956$	−22.4921	−0.727448
$957$	−2.27011	−0.0733824
$958$	1.79752	0.0580752
$959$	−17.4951	−0.564947
$960$	3.78882	0.122284
$961$	5.78052	0.186468
$962$	3.44336	0.111018
$963$	−2.41208	−0.0777282
$964$	−14.5686	−0.469223
$965$	−49.7432	−1.60129
$966$	−10.2946	−0.331224
$967$	−55.9305	−1.79860	−0.899302	−	0.437329i	$-0.855925\pi$
$967$	−55.9305	−1.79860	−0.899302	+	0.437329i	$0.855925\pi$
$968$	2.10974	0.0678097
$969$	−20.7904	−0.667883
$970$	−22.2722	−0.715116
$971$	−2.88580	−0.0926098	−0.0463049	−	0.998927i	$-0.514745\pi$
$971$	−2.88580	−0.0926098	−0.0463049	+	0.998927i	$0.514745\pi$
$972$	−14.7046	−0.471652
$973$	39.7639	1.27477
$974$	−2.88189	−0.0923417
$975$	−0.346327	−0.0110913
$976$	24.1572	0.773255
$977$	−23.1140	−0.739483	−0.369742	−	0.929135i	$-0.620554\pi$
$977$	−23.1140	−0.739483	−0.369742	+	0.929135i	$0.620554\pi$
$978$	6.58178	0.210462
$979$	4.01206	0.128226
$980$	9.64791	0.308191
$981$	3.77445	0.120509
$982$	−18.5151	−0.590842
$983$	8.22556	0.262355	0.131177	−	0.991359i	$-0.458124\pi$
$983$	8.22556	0.262355	0.131177	+	0.991359i	$0.458124\pi$
$984$	−31.0311	−0.989236
$985$	−36.4980	−1.16292
$986$	4.93773	0.157250
$987$	−21.5314	−0.685351
$988$	−2.80102	−0.0891124
$989$	−37.4911	−1.19215
$990$	−1.17113	−0.0372211
$991$	−43.8732	−1.39368	−0.696839	−	0.717227i	$-0.745411\pi$
$991$	−43.8732	−1.39368	−0.696839	+	0.717227i	$0.745411\pi$
$992$	−33.0026	−1.04783
$993$	−31.4990	−0.999590
$994$	24.9769	0.792218
$995$	40.0671	1.27021
$996$	−14.6026	−0.462700
$997$	−45.9987	−1.45679	−0.728396	−	0.685156i	$-0.759734\pi$
$997$	−45.9987	−1.45679	−0.728396	+	0.685156i	$0.759734\pi$
$998$	20.7397	0.656505
$999$	−52.2533	−1.65322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.11	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.11	✓	28	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)

\(f(q)\)	\(=\)	\(q-0.574950 q^{2} +1.45629 q^{3} -1.66943 q^{4} -2.31674 q^{5} -0.837294 q^{6} -3.08132 q^{7} +2.10974 q^{8} -0.879222 q^{9} +O(q^{10})\)	\(q-0.574950 q^{2} +1.45629 q^{3} -1.66943 q^{4} -2.31674 q^{5} -0.837294 q^{6} -3.08132 q^{7} +2.10974 q^{8} -0.879222 q^{9} +1.33201 q^{10} +1.00000 q^{11} -2.43118 q^{12} -0.647487 q^{13} +1.77160 q^{14} -3.37384 q^{15} +2.12587 q^{16} +5.50931 q^{17} +0.505509 q^{18} -2.59130 q^{19} +3.86764 q^{20} -4.48729 q^{21} -0.574950 q^{22} -3.99022 q^{23} +3.07239 q^{24} +0.367289 q^{25} +0.372273 q^{26} -5.64927 q^{27} +5.14405 q^{28} -1.55883 q^{29} +1.93979 q^{30} +6.06469 q^{31} -5.44175 q^{32} +1.45629 q^{33} -3.16758 q^{34} +7.13862 q^{35} +1.46780 q^{36} +9.24956 q^{37} +1.48987 q^{38} -0.942927 q^{39} -4.88772 q^{40} -10.1000 q^{41} +2.57997 q^{42} +9.39576 q^{43} -1.66943 q^{44} +2.03693 q^{45} +2.29418 q^{46} +4.79830 q^{47} +3.09588 q^{48} +2.49452 q^{49} -0.211173 q^{50} +8.02315 q^{51} +1.08093 q^{52} +13.1785 q^{53} +3.24805 q^{54} -2.31674 q^{55} -6.50078 q^{56} -3.77368 q^{57} +0.896253 q^{58} -5.95888 q^{59} +5.63240 q^{60} +11.3635 q^{61} -3.48690 q^{62} +2.70916 q^{63} -1.12300 q^{64} +1.50006 q^{65} -0.837294 q^{66} +11.8075 q^{67} -9.19742 q^{68} -5.81091 q^{69} -4.10435 q^{70} +14.0984 q^{71} -1.85493 q^{72} +1.41174 q^{73} -5.31804 q^{74} +0.534878 q^{75} +4.32599 q^{76} -3.08132 q^{77} +0.542136 q^{78} +14.2436 q^{79} -4.92508 q^{80} -5.58930 q^{81} +5.80699 q^{82} +6.00638 q^{83} +7.49122 q^{84} -12.7636 q^{85} -5.40210 q^{86} -2.27011 q^{87} +2.10974 q^{88} +4.01206 q^{89} -1.17113 q^{90} +1.99511 q^{91} +6.66140 q^{92} +8.83195 q^{93} -2.75878 q^{94} +6.00336 q^{95} -7.92476 q^{96} -16.7207 q^{97} -1.43423 q^{98} -0.879222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * q^99

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