LMFDB - Embedded newform 1441.2.a.e.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.67300 q^{2} -1.49184 q^{3} +0.798939 q^{4} -1.12664 q^{5} -2.49585 q^{6} -0.438386 q^{7} -2.00938 q^{8} -0.774411 q^{9} +O(q^{10})$	\(q+1.67300 q^{2} -1.49184 q^{3} +0.798939 q^{4} -1.12664 q^{5} -2.49585 q^{6} -0.438386 q^{7} -2.00938 q^{8} -0.774411 q^{9} -1.88488 q^{10} +1.00000 q^{11} -1.19189 q^{12} +6.70892 q^{13} -0.733421 q^{14} +1.68077 q^{15} -4.95957 q^{16} +0.414914 q^{17} -1.29559 q^{18} +5.91492 q^{19} -0.900119 q^{20} +0.654002 q^{21} +1.67300 q^{22} -8.48053 q^{23} +2.99767 q^{24} -3.73068 q^{25} +11.2240 q^{26} +5.63082 q^{27} -0.350244 q^{28} +6.46992 q^{29} +2.81194 q^{30} +8.15693 q^{31} -4.27863 q^{32} -1.49184 q^{33} +0.694152 q^{34} +0.493904 q^{35} -0.618707 q^{36} -0.0703706 q^{37} +9.89568 q^{38} -10.0086 q^{39} +2.26385 q^{40} +10.4191 q^{41} +1.09415 q^{42} +4.47503 q^{43} +0.798939 q^{44} +0.872485 q^{45} -14.1880 q^{46} +4.80516 q^{47} +7.39890 q^{48} -6.80782 q^{49} -6.24143 q^{50} -0.618985 q^{51} +5.36002 q^{52} +14.4201 q^{53} +9.42038 q^{54} -1.12664 q^{55} +0.880883 q^{56} -8.82412 q^{57} +10.8242 q^{58} +3.77174 q^{59} +1.34283 q^{60} -11.5149 q^{61} +13.6466 q^{62} +0.339491 q^{63} +2.76100 q^{64} -7.55856 q^{65} -2.49585 q^{66} +4.98056 q^{67} +0.331491 q^{68} +12.6516 q^{69} +0.826304 q^{70} +12.8793 q^{71} +1.55609 q^{72} -14.2632 q^{73} -0.117730 q^{74} +5.56557 q^{75} +4.72566 q^{76} -0.438386 q^{77} -16.7445 q^{78} -2.49267 q^{79} +5.58767 q^{80} -6.07705 q^{81} +17.4312 q^{82} +9.29253 q^{83} +0.522508 q^{84} -0.467460 q^{85} +7.48674 q^{86} -9.65210 q^{87} -2.00938 q^{88} -0.995685 q^{89} +1.45967 q^{90} -2.94109 q^{91} -6.77543 q^{92} -12.1688 q^{93} +8.03904 q^{94} -6.66400 q^{95} +6.38303 q^{96} -0.687320 q^{97} -11.3895 q^{98} -0.774411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.67300	1.18299	0.591496	−	0.806308i	$-0.298538\pi$
$2$	1.67300	1.18299	0.591496	+	0.806308i	$0.298538\pi$
$3$	−1.49184	−0.861315	−0.430657	−	0.902516i	$-0.641718\pi$
$3$	−1.49184	−0.861315	−0.430657	+	0.902516i	$0.641718\pi$
$4$	0.798939	0.399470
$5$	−1.12664	−0.503850	−0.251925	−	0.967747i	$-0.581064\pi$
$5$	−1.12664	−0.503850	−0.251925	+	0.967747i	$0.581064\pi$
$6$	−2.49585	−1.01893
$7$	−0.438386	−0.165694	−0.0828471	−	0.996562i	$-0.526401\pi$
$7$	−0.438386	−0.165694	−0.0828471	+	0.996562i	$0.526401\pi$
$8$	−2.00938	−0.710423
$9$	−0.774411	−0.258137
$10$	−1.88488	−0.596051
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.19189	−0.344069
$13$	6.70892	1.86072	0.930359	−	0.366649i	$-0.119495\pi$
$13$	6.70892	1.86072	0.930359	+	0.366649i	$0.119495\pi$
$14$	−0.733421	−0.196015
$15$	1.68077	0.433973
$16$	−4.95957	−1.23989
$17$	0.414914	0.100631	0.0503157	−	0.998733i	$-0.483977\pi$
$17$	0.414914	0.100631	0.0503157	+	0.998733i	$0.483977\pi$
$18$	−1.29559	−0.305374
$19$	5.91492	1.35698	0.678488	−	0.734612i	$-0.262636\pi$
$19$	5.91492	1.35698	0.678488	+	0.734612i	$0.262636\pi$
$20$	−0.900119	−0.201273
$21$	0.654002	0.142715
$22$	1.67300	0.356685
$23$	−8.48053	−1.76831	−0.884157	−	0.467191i	$-0.845266\pi$
$23$	−8.48053	−1.76831	−0.884157	+	0.467191i	$0.845266\pi$
$24$	2.99767	0.611897
$25$	−3.73068	−0.746135
$26$	11.2240	2.20122
$27$	5.63082	1.08365
$28$	−0.350244	−0.0661898
$29$	6.46992	1.20143	0.600717	−	0.799461i	$-0.294882\pi$
$29$	6.46992	1.20143	0.600717	+	0.799461i	$0.294882\pi$
$30$	2.81194	0.513387
$31$	8.15693	1.46503	0.732514	−	0.680752i	$-0.238347\pi$
$31$	8.15693	1.46503	0.732514	+	0.680752i	$0.238347\pi$
$32$	−4.27863	−0.756361
$33$	−1.49184	−0.259696
$34$	0.694152	0.119046
$35$	0.493904	0.0834851
$36$	−0.618707	−0.103118
$37$	−0.0703706	−0.0115689	−0.00578443	−	0.999983i	$-0.501841\pi$
$37$	−0.0703706	−0.0115689	−0.00578443	+	0.999983i	$0.501841\pi$
$38$	9.89568	1.60529
$39$	−10.0086	−1.60266
$40$	2.26385	0.357947
$41$	10.4191	1.62719	0.813595	−	0.581432i	$-0.197507\pi$
$41$	10.4191	1.62719	0.813595	+	0.581432i	$0.197507\pi$
$42$	1.09415	0.168831
$43$	4.47503	0.682436	0.341218	−	0.939984i	$-0.389161\pi$
$43$	4.47503	0.682436	0.341218	+	0.939984i	$0.389161\pi$
$44$	0.798939	0.120445
$45$	0.872485	0.130062
$46$	−14.1880	−2.09190
$47$	4.80516	0.700904	0.350452	−	0.936581i	$-0.386028\pi$
$47$	4.80516	0.700904	0.350452	+	0.936581i	$0.386028\pi$
$48$	7.39890	1.06794
$49$	−6.80782	−0.972545
$50$	−6.24143	−0.882672
$51$	−0.618985	−0.0866753
$52$	5.36002	0.743300
$53$	14.4201	1.98075	0.990374	−	0.138418i	$-0.0442016\pi$
$53$	14.4201	1.98075	0.990374	+	0.138418i	$0.0442016\pi$
$54$	9.42038	1.28195
$55$	−1.12664	−0.151917
$56$	0.880883	0.117713
$57$	−8.82412	−1.16878
$58$	10.8242	1.42129
$59$	3.77174	0.491038	0.245519	−	0.969392i	$-0.421042\pi$
$59$	3.77174	0.491038	0.245519	+	0.969392i	$0.421042\pi$
$60$	1.34283	0.173359
$61$	−11.5149	−1.47433	−0.737164	−	0.675714i	$-0.763835\pi$
$61$	−11.5149	−1.47433	−0.737164	+	0.675714i	$0.763835\pi$
$62$	13.6466	1.73312
$63$	0.339491	0.0427718
$64$	2.76100	0.345124
$65$	−7.55856	−0.937523
$66$	−2.49585	−0.307218
$67$	4.98056	0.608473	0.304236	−	0.952597i	$-0.401599\pi$
$67$	4.98056	0.608473	0.304236	+	0.952597i	$0.401599\pi$
$68$	0.331491	0.0401992
$69$	12.6516	1.52307
$70$	0.826304	0.0987622
$71$	12.8793	1.52850	0.764248	−	0.644923i	$-0.223110\pi$
$71$	12.8793	1.52850	0.764248	+	0.644923i	$0.223110\pi$
$72$	1.55609	0.183386
$73$	−14.2632	−1.66939	−0.834693	−	0.550716i	$-0.814355\pi$
$73$	−14.2632	−1.66939	−0.834693	+	0.550716i	$0.814355\pi$
$74$	−0.117730	−0.0136859
$75$	5.56557	0.642657
$76$	4.72566	0.542070
$77$	−0.438386	−0.0499587
$78$	−16.7445	−1.89594
$79$	−2.49267	−0.280447	−0.140224	−	0.990120i	$-0.544782\pi$
$79$	−2.49267	−0.280447	−0.140224	+	0.990120i	$0.544782\pi$
$80$	5.58767	0.624721
$81$	−6.07705	−0.675228
$82$	17.4312	1.92495
$83$	9.29253	1.01999	0.509994	−	0.860178i	$-0.329648\pi$
$83$	9.29253	1.01999	0.509994	+	0.860178i	$0.329648\pi$
$84$	0.522508	0.0570103
$85$	−0.467460	−0.0507031
$86$	7.48674	0.807316
$87$	−9.65210	−1.03481
$88$	−2.00938	−0.214200
$89$	−0.995685	−0.105542	−0.0527712	−	0.998607i	$-0.516805\pi$
$89$	−0.995685	−0.105542	−0.0527712	+	0.998607i	$0.516805\pi$
$90$	1.45967	0.153863
$91$	−2.94109	−0.308310
$92$	−6.77543	−0.706387
$93$	−12.1688	−1.26185
$94$	8.03904	0.829164
$95$	−6.66400	−0.683712
$96$	6.38303	0.651465
$97$	−0.687320	−0.0697868	−0.0348934	−	0.999391i	$-0.511109\pi$
$97$	−0.687320	−0.0697868	−0.0348934	+	0.999391i	$0.511109\pi$
$98$	−11.3895	−1.15051
$99$	−0.774411	−0.0778313
$100$	−2.98058	−0.298058
$101$	−8.55380	−0.851134	−0.425567	−	0.904927i	$-0.639925\pi$
$101$	−8.55380	−0.851134	−0.425567	+	0.904927i	$0.639925\pi$
$102$	−1.03556	−0.102536
$103$	−12.6617	−1.24760	−0.623800	−	0.781584i	$-0.714412\pi$
$103$	−12.6617	−1.24760	−0.623800	+	0.781584i	$0.714412\pi$
$104$	−13.4808	−1.32190
$105$	−0.736827	−0.0719069
$106$	24.1248	2.34321
$107$	5.66098	0.547268	0.273634	−	0.961834i	$-0.411774\pi$
$107$	5.66098	0.547268	0.273634	+	0.961834i	$0.411774\pi$
$108$	4.49868	0.432886
$109$	−4.31049	−0.412870	−0.206435	−	0.978460i	$-0.566186\pi$
$109$	−4.31049	−0.412870	−0.206435	+	0.978460i	$0.566186\pi$
$110$	−1.88488	−0.179716
$111$	0.104982	0.00996443
$112$	2.17421	0.205443
$113$	−10.2048	−0.959988	−0.479994	−	0.877272i	$-0.659361\pi$
$113$	−10.2048	−0.959988	−0.479994	+	0.877272i	$0.659361\pi$
$114$	−14.7628	−1.38266
$115$	9.55453	0.890965
$116$	5.16907	0.479937
$117$	−5.19546	−0.480321
$118$	6.31013	0.580894
$119$	−0.181892	−0.0166740
$120$	−3.37731	−0.308305
$121$	1.00000	0.0909091
$122$	−19.2644	−1.74412
$123$	−15.5436	−1.40152
$124$	6.51689	0.585234
$125$	9.83635	0.879790
$126$	0.567969	0.0505987
$127$	−17.4598	−1.54931	−0.774655	−	0.632385i	$-0.782076\pi$
$127$	−17.4598	−1.54931	−0.774655	+	0.632385i	$0.782076\pi$
$128$	13.1764	1.16464
$129$	−6.67603	−0.587792
$130$	−12.6455	−1.10908
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−1.19189	−0.103741
$133$	−2.59302	−0.224843
$134$	8.33250	0.719818
$135$	−6.34392	−0.545998
$136$	−0.833719	−0.0714908
$137$	14.3718	1.22787	0.613935	−	0.789357i	$-0.289586\pi$
$137$	14.3718	1.22787	0.613935	+	0.789357i	$0.289586\pi$
$138$	21.1662	1.80178
$139$	8.98666	0.762239	0.381119	−	0.924526i	$-0.375539\pi$
$139$	8.98666	0.762239	0.381119	+	0.924526i	$0.375539\pi$
$140$	0.394599	0.0333497
$141$	−7.16853	−0.603699
$142$	21.5472	1.80820
$143$	6.70892	0.561028
$144$	3.84075	0.320063
$145$	−7.28930	−0.605343
$146$	−23.8624	−1.97487
$147$	10.1562	0.837668
$148$	−0.0562218	−0.00462141
$149$	10.6003	0.868409	0.434205	−	0.900814i	$-0.357029\pi$
$149$	10.6003	0.868409	0.434205	+	0.900814i	$0.357029\pi$
$150$	9.31122	0.760258
$151$	−5.17506	−0.421140	−0.210570	−	0.977579i	$-0.567532\pi$
$151$	−5.17506	−0.421140	−0.210570	+	0.977579i	$0.567532\pi$
$152$	−11.8853	−0.964026
$153$	−0.321314	−0.0259767
$154$	−0.733421	−0.0591007
$155$	−9.18994	−0.738154
$156$	−7.99629	−0.640216
$157$	7.40190	0.590736	0.295368	−	0.955384i	$-0.404558\pi$
$157$	7.40190	0.590736	0.295368	+	0.955384i	$0.404558\pi$
$158$	−4.17024	−0.331767
$159$	−21.5124	−1.70605
$160$	4.82048	0.381093
$161$	3.71775	0.292999
$162$	−10.1669	−0.798789
$163$	−22.5380	−1.76531	−0.882657	−	0.470018i	$-0.844247\pi$
$163$	−22.5380	−1.76531	−0.882657	+	0.470018i	$0.844247\pi$
$164$	8.32423	0.650013
$165$	1.68077	0.130848
$166$	15.5464	1.20664
$167$	−6.28473	−0.486327	−0.243163	−	0.969985i	$-0.578185\pi$
$167$	−6.28473	−0.486327	−0.243163	+	0.969985i	$0.578185\pi$
$168$	−1.31414	−0.101388
$169$	32.0096	2.46228
$170$	−0.782061	−0.0599814
$171$	−4.58058	−0.350286
$172$	3.57528	0.272612
$173$	9.52170	0.723921	0.361961	−	0.932193i	$-0.382107\pi$
$173$	9.52170	0.723921	0.361961	+	0.932193i	$0.382107\pi$
$174$	−16.1480	−1.22418
$175$	1.63548	0.123630
$176$	−4.95957	−0.373842
$177$	−5.62683	−0.422939
$178$	−1.66578	−0.124856
$179$	11.7859	0.880917	0.440458	−	0.897773i	$-0.354816\pi$
$179$	11.7859	0.880917	0.440458	+	0.897773i	$0.354816\pi$
$180$	0.697062	0.0519560
$181$	18.2939	1.35978	0.679888	−	0.733316i	$-0.262028\pi$
$181$	18.2939	1.35978	0.679888	+	0.733316i	$0.262028\pi$
$182$	−4.92046	−0.364729
$183$	17.1783	1.26986
$184$	17.0406	1.25625
$185$	0.0792826	0.00582897
$186$	−20.3585	−1.49276
$187$	0.414914	0.0303415
$188$	3.83903	0.279990
$189$	−2.46847	−0.179555
$190$	−11.1489	−0.808826
$191$	3.21927	0.232938	0.116469	−	0.993194i	$-0.462842\pi$
$191$	3.21927	0.232938	0.116469	+	0.993194i	$0.462842\pi$
$192$	−4.11897	−0.297261
$193$	−16.5162	−1.18886	−0.594430	−	0.804147i	$-0.702622\pi$
$193$	−16.5162	−1.18886	−0.594430	+	0.804147i	$0.702622\pi$
$194$	−1.14989	−0.0825572
$195$	11.2762	0.807503
$196$	−5.43903	−0.388502
$197$	−19.8232	−1.41235	−0.706173	−	0.708039i	$-0.749580\pi$
$197$	−19.8232	−1.41235	−0.706173	+	0.708039i	$0.749580\pi$
$198$	−1.29559	−0.0920737
$199$	9.36808	0.664086	0.332043	−	0.943264i	$-0.392262\pi$
$199$	9.36808	0.664086	0.332043	+	0.943264i	$0.392262\pi$
$200$	7.49634	0.530071
$201$	−7.43021	−0.524086
$202$	−14.3105	−1.00689
$203$	−2.83632	−0.199071
$204$	−0.494531	−0.0346241
$205$	−11.7386	−0.819860
$206$	−21.1831	−1.47590
$207$	6.56742	0.456467
$208$	−33.2734	−2.30709
$209$	5.91492	0.409144
$210$	−1.23271	−0.0850653
$211$	5.10895	0.351715	0.175857	−	0.984416i	$-0.443730\pi$
$211$	5.10895	0.351715	0.175857	+	0.984416i	$0.443730\pi$
$212$	11.5208	0.791248
$213$	−19.2139	−1.31652
$214$	9.47084	0.647413
$215$	−5.04176	−0.343845
$216$	−11.3145	−0.769851
$217$	−3.57588	−0.242747
$218$	−7.21147	−0.488422
$219$	21.2785	1.43787
$220$	−0.900119	−0.0606860
$221$	2.78362	0.187247
$222$	0.175635	0.0117878
$223$	4.23090	0.283322	0.141661	−	0.989915i	$-0.454756\pi$
$223$	4.23090	0.283322	0.141661	+	0.989915i	$0.454756\pi$
$224$	1.87569	0.125325
$225$	2.88908	0.192605
$226$	−17.0727	−1.13566
$227$	24.8258	1.64775	0.823873	−	0.566775i	$-0.191809\pi$
$227$	24.8258	1.64775	0.823873	+	0.566775i	$0.191809\pi$
$228$	−7.04993	−0.466893
$229$	−23.3519	−1.54314	−0.771568	−	0.636147i	$-0.780527\pi$
$229$	−23.3519	−1.54314	−0.771568	+	0.636147i	$0.780527\pi$
$230$	15.9848	1.05400
$231$	0.654002	0.0430302
$232$	−13.0005	−0.853526
$233$	20.4182	1.33764	0.668820	−	0.743424i	$-0.266800\pi$
$233$	20.4182	1.33764	0.668820	+	0.743424i	$0.266800\pi$
$234$	−8.69202	−0.568215
$235$	−5.41370	−0.353151
$236$	3.01339	0.196155
$237$	3.71866	0.241553
$238$	−0.304306	−0.0197253
$239$	10.9109	0.705767	0.352883	−	0.935667i	$-0.385201\pi$
$239$	10.9109	0.705767	0.352883	+	0.935667i	$0.385201\pi$
$240$	−8.33591	−0.538081
$241$	2.19603	0.141459	0.0707293	−	0.997496i	$-0.477467\pi$
$241$	2.19603	0.141459	0.0707293	+	0.997496i	$0.477467\pi$
$242$	1.67300	0.107545
$243$	−7.82647	−0.502068
$244$	−9.19968	−0.588949
$245$	7.66998	0.490017
$246$	−26.0046	−1.65799
$247$	39.6827	2.52495
$248$	−16.3904	−1.04079
$249$	−13.8630	−0.878531
$250$	16.4563	1.04078
$251$	1.53382	0.0968140	0.0484070	−	0.998828i	$-0.484586\pi$
$251$	1.53382	0.0968140	0.0484070	+	0.998828i	$0.484586\pi$
$252$	0.271233	0.0170860
$253$	−8.48053	−0.533166
$254$	−29.2103	−1.83282
$255$	0.697375	0.0436713
$256$	16.5222	1.03264
$257$	11.1972	0.698461	0.349230	−	0.937037i	$-0.386443\pi$
$257$	11.1972	0.698461	0.349230	+	0.937037i	$0.386443\pi$
$258$	−11.1690	−0.695353
$259$	0.0308495	0.00191689
$260$	−6.03882	−0.374512
$261$	−5.01038	−0.310135
$262$	−1.67300	−0.103358
$263$	−8.27309	−0.510140	−0.255070	−	0.966923i	$-0.582099\pi$
$263$	−8.27309	−0.510140	−0.255070	+	0.966923i	$0.582099\pi$
$264$	2.99767	0.184494
$265$	−16.2463	−0.998000
$266$	−4.33813	−0.265988
$267$	1.48540	0.0909052
$268$	3.97917	0.243066
$269$	−4.50079	−0.274418	−0.137209	−	0.990542i	$-0.543813\pi$
$269$	−4.50079	−0.274418	−0.137209	+	0.990542i	$0.543813\pi$
$270$	−10.6134	−0.645911
$271$	18.0644	1.09734	0.548668	−	0.836041i	$-0.315135\pi$
$271$	18.0644	1.09734	0.548668	+	0.836041i	$0.315135\pi$
$272$	−2.05780	−0.124772
$273$	4.38764	0.265552
$274$	24.0441	1.45256
$275$	−3.73068	−0.224968
$276$	10.1079	0.608422
$277$	19.2745	1.15809	0.579046	−	0.815295i	$-0.303425\pi$
$277$	19.2745	1.15809	0.579046	+	0.815295i	$0.303425\pi$
$278$	15.0347	0.901722
$279$	−6.31681	−0.378178
$280$	−0.992441	−0.0593097
$281$	−25.8344	−1.54115	−0.770575	−	0.637350i	$-0.780031\pi$
$281$	−25.8344	−1.54115	−0.770575	+	0.637350i	$0.780031\pi$
$282$	−11.9930	−0.714171
$283$	−2.86159	−0.170104	−0.0850519	−	0.996377i	$-0.527106\pi$
$283$	−2.86159	−0.170104	−0.0850519	+	0.996377i	$0.527106\pi$
$284$	10.2898	0.610587
$285$	9.94163	0.588891
$286$	11.2240	0.663691
$287$	−4.56759	−0.269616
$288$	3.31342	0.195245
$289$	−16.8278	−0.989873
$290$	−12.1950	−0.716116
$291$	1.02537	0.0601084
$292$	−11.3955	−0.666868
$293$	2.62110	0.153126	0.0765632	−	0.997065i	$-0.475605\pi$
$293$	2.62110	0.153126	0.0765632	+	0.997065i	$0.475605\pi$
$294$	16.9913	0.990954
$295$	−4.24940	−0.247410
$296$	0.141401	0.00821878
$297$	5.63082	0.326733
$298$	17.7343	1.02732
$299$	−56.8952	−3.29033
$300$	4.44655	0.256722
$301$	−1.96179	−0.113076
$302$	−8.65789	−0.498206
$303$	12.7609	0.733095
$304$	−29.3355	−1.68251
$305$	12.9731	0.742840
$306$	−0.537559	−0.0307302
$307$	−4.23317	−0.241600	−0.120800	−	0.992677i	$-0.538546\pi$
$307$	−4.23317	−0.241600	−0.120800	+	0.992677i	$0.538546\pi$
$308$	−0.350244	−0.0199570
$309$	18.8893	1.07458
$310$	−15.3748	−0.873230
$311$	−20.0593	−1.13746	−0.568728	−	0.822525i	$-0.692564\pi$
$311$	−20.0593	−1.13746	−0.568728	+	0.822525i	$0.692564\pi$
$312$	20.1111	1.13857
$313$	−24.5329	−1.38668	−0.693340	−	0.720610i	$-0.743862\pi$
$313$	−24.5329	−1.38668	−0.693340	+	0.720610i	$0.743862\pi$
$314$	12.3834	0.698835
$315$	−0.382485	−0.0215506
$316$	−1.99149	−0.112030
$317$	14.9160	0.837768	0.418884	−	0.908040i	$-0.362421\pi$
$317$	14.9160	0.837768	0.418884	+	0.908040i	$0.362421\pi$
$318$	−35.9904	−2.01824
$319$	6.46992	0.362246
$320$	−3.11066	−0.173891
$321$	−8.44528	−0.471370
$322$	6.21980	0.346616
$323$	2.45418	0.136554
$324$	−4.85520	−0.269733
$325$	−25.0288	−1.38835
$326$	−37.7062	−2.08835
$327$	6.43057	0.355611
$328$	−20.9359	−1.15599
$329$	−2.10651	−0.116136
$330$	2.81194	0.154792
$331$	22.9280	1.26024	0.630118	−	0.776500i	$-0.283007\pi$
$331$	22.9280	1.26024	0.630118	+	0.776500i	$0.283007\pi$
$332$	7.42417	0.407454
$333$	0.0544958	0.00298635
$334$	−10.5144	−0.575321
$335$	−5.61132	−0.306579
$336$	−3.24357	−0.176951
$337$	6.15588	0.335332	0.167666	−	0.985844i	$-0.446377\pi$
$337$	6.15588	0.335332	0.167666	+	0.985844i	$0.446377\pi$
$338$	53.5521	2.91285
$339$	15.2240	0.826852
$340$	−0.373472	−0.0202544
$341$	8.15693	0.441722
$342$	−7.66333	−0.414385
$343$	6.05315	0.326839
$344$	−8.99203	−0.484818
$345$	−14.2538	−0.767401
$346$	15.9298	0.856393
$347$	9.08529	0.487724	0.243862	−	0.969810i	$-0.421586\pi$
$347$	9.08529	0.487724	0.243862	+	0.969810i	$0.421586\pi$
$348$	−7.71144	−0.413376
$349$	−11.2493	−0.602163	−0.301082	−	0.953598i	$-0.597348\pi$
$349$	−11.2493	−0.602163	−0.301082	+	0.953598i	$0.597348\pi$
$350$	2.73616	0.146254
$351$	37.7767	2.01637
$352$	−4.27863	−0.228052
$353$	−10.3092	−0.548701	−0.274351	−	0.961630i	$-0.588463\pi$
$353$	−10.3092	−0.548701	−0.274351	+	0.961630i	$0.588463\pi$
$354$	−9.41371	−0.500333
$355$	−14.5104	−0.770133
$356$	−0.795492	−0.0421610
$357$	0.271354	0.0143616
$358$	19.7178	1.04212
$359$	−4.91736	−0.259528	−0.129764	−	0.991545i	$-0.541422\pi$
$359$	−4.91736	−0.259528	−0.129764	+	0.991545i	$0.541422\pi$
$360$	−1.75315	−0.0923993
$361$	15.9863	0.841383
$362$	30.6058	1.60860
$363$	−1.49184	−0.0783013
$364$	−2.34976	−0.123161
$365$	16.0696	0.841120
$366$	28.7394	1.50223
$367$	13.3846	0.698672	0.349336	−	0.936998i	$-0.386407\pi$
$367$	13.3846	0.698672	0.349336	+	0.936998i	$0.386407\pi$
$368$	42.0598	2.19252
$369$	−8.06867	−0.420038
$370$	0.132640	0.00689563
$371$	−6.32155	−0.328199
$372$	−9.72216	−0.504070
$373$	−18.1922	−0.941955	−0.470977	−	0.882145i	$-0.656099\pi$
$373$	−18.1922	−0.941955	−0.470977	+	0.882145i	$0.656099\pi$
$374$	0.694152	0.0358937
$375$	−14.6743	−0.757776
$376$	−9.65538	−0.497938
$377$	43.4062	2.23553
$378$	−4.12976	−0.212412
$379$	11.4612	0.588724	0.294362	−	0.955694i	$-0.404893\pi$
$379$	11.4612	0.588724	0.294362	+	0.955694i	$0.404893\pi$
$380$	−5.32413	−0.273122
$381$	26.0473	1.33444
$382$	5.38584	0.275564
$383$	21.9494	1.12156	0.560782	−	0.827963i	$-0.310500\pi$
$383$	21.9494	1.12156	0.560782	+	0.827963i	$0.310500\pi$
$384$	−19.6571	−1.00312
$385$	0.493904	0.0251717
$386$	−27.6316	−1.40641
$387$	−3.46551	−0.176162
$388$	−0.549127	−0.0278777
$389$	22.4303	1.13726	0.568631	−	0.822592i	$-0.307473\pi$
$389$	22.4303	1.13726	0.568631	+	0.822592i	$0.307473\pi$
$390$	18.8651	0.955269
$391$	−3.51869	−0.177948
$392$	13.6795	0.690918
$393$	1.49184	0.0752534
$394$	−33.1643	−1.67079
$395$	2.80835	0.141303
$396$	−0.618707	−0.0310912
$397$	−1.61878	−0.0812443	−0.0406221	−	0.999175i	$-0.512934\pi$
$397$	−1.61878	−0.0812443	−0.0406221	+	0.999175i	$0.512934\pi$
$398$	15.6728	0.785608
$399$	3.86837	0.193661
$400$	18.5026	0.925128
$401$	−23.5568	−1.17637	−0.588185	−	0.808726i	$-0.700157\pi$
$401$	−23.5568	−1.17637	−0.588185	+	0.808726i	$0.700157\pi$
$402$	−12.4308	−0.619990
$403$	54.7241	2.72600
$404$	−6.83396	−0.340002
$405$	6.84667	0.340214
$406$	−4.74518	−0.235499
$407$	−0.0703706	−0.00348814
$408$	1.24378	0.0615761
$409$	−15.0212	−0.742749	−0.371375	−	0.928483i	$-0.621113\pi$
$409$	−15.0212	−0.742749	−0.371375	+	0.928483i	$0.621113\pi$
$410$	−19.6387	−0.969888
$411$	−21.4405	−1.05758
$412$	−10.1160	−0.498378
$413$	−1.65348	−0.0813623
$414$	10.9873	0.539997
$415$	−10.4694	−0.513921
$416$	−28.7049	−1.40738
$417$	−13.4067	−0.656528
$418$	9.89568	0.484013
$419$	−10.8982	−0.532412	−0.266206	−	0.963916i	$-0.585770\pi$
$419$	−10.8982	−0.532412	−0.266206	+	0.963916i	$0.585770\pi$
$420$	−0.588680	−0.0287246
$421$	−23.0149	−1.12168	−0.560840	−	0.827924i	$-0.689522\pi$
$421$	−23.0149	−1.12168	−0.560840	+	0.827924i	$0.689522\pi$
$422$	8.54729	0.416075
$423$	−3.72117	−0.180929
$424$	−28.9754	−1.40717
$425$	−1.54791	−0.0750846
$426$	−32.1449	−1.55743
$427$	5.04795	0.244288
$428$	4.52278	0.218617
$429$	−10.0086	−0.483222
$430$	−8.43488	−0.406766
$431$	13.4907	0.649826	0.324913	−	0.945744i	$-0.394665\pi$
$431$	13.4907	0.649826	0.324913	+	0.945744i	$0.394665\pi$
$432$	−27.9265	−1.34361
$433$	13.7959	0.662986	0.331493	−	0.943458i	$-0.392448\pi$
$433$	13.7959	0.662986	0.331493	+	0.943458i	$0.392448\pi$
$434$	−5.98246	−0.287167
$435$	10.8745	0.521391
$436$	−3.44382	−0.164929
$437$	−50.1617	−2.39956
$438$	35.5989	1.70098
$439$	−0.877639	−0.0418874	−0.0209437	−	0.999781i	$-0.506667\pi$
$439$	−0.877639	−0.0418874	−0.0209437	+	0.999781i	$0.506667\pi$
$440$	2.26385	0.107925
$441$	5.27205	0.251050
$442$	4.65701	0.221511
$443$	−8.61049	−0.409097	−0.204548	−	0.978856i	$-0.565573\pi$
$443$	−8.61049	−0.409097	−0.204548	+	0.978856i	$0.565573\pi$
$444$	0.0838740	0.00398049
$445$	1.12178	0.0531776
$446$	7.07830	0.335167
$447$	−15.8139	−0.747974
$448$	−1.21038	−0.0571851
$449$	9.07390	0.428224	0.214112	−	0.976809i	$-0.431314\pi$
$449$	9.07390	0.428224	0.214112	+	0.976809i	$0.431314\pi$
$450$	4.83343	0.227850
$451$	10.4191	0.490616
$452$	−8.15302	−0.383486
$453$	7.72036	0.362734
$454$	41.5336	1.94927
$455$	3.31356	0.155342
$456$	17.7310	0.830330
$457$	−2.53270	−0.118475	−0.0592375	−	0.998244i	$-0.518867\pi$
$457$	−2.53270	−0.118475	−0.0592375	+	0.998244i	$0.518867\pi$
$458$	−39.0678	−1.82552
$459$	2.33630	0.109049
$460$	7.63349	0.355913
$461$	−29.7019	−1.38336	−0.691678	−	0.722206i	$-0.743128\pi$
$461$	−29.7019	−1.38336	−0.691678	+	0.722206i	$0.743128\pi$
$462$	1.09415	0.0509043
$463$	3.11272	0.144660	0.0723301	−	0.997381i	$-0.476956\pi$
$463$	3.11272	0.144660	0.0723301	+	0.997381i	$0.476956\pi$
$464$	−32.0881	−1.48965
$465$	13.7099	0.635783
$466$	34.1597	1.58242
$467$	24.5855	1.13768	0.568840	−	0.822448i	$-0.307392\pi$
$467$	24.5855	1.13768	0.568840	+	0.822448i	$0.307392\pi$
$468$	−4.15086	−0.191873
$469$	−2.18341	−0.100820
$470$	−9.05713	−0.417774
$471$	−11.0424	−0.508809
$472$	−7.57885	−0.348845
$473$	4.47503	0.205762
$474$	6.22133	0.285755
$475$	−22.0666	−1.01249
$476$	−0.145321	−0.00666077
$477$	−11.1671	−0.511304
$478$	18.2540	0.834917
$479$	21.1814	0.967801	0.483900	−	0.875123i	$-0.339220\pi$
$479$	21.1814	0.967801	0.483900	+	0.875123i	$0.339220\pi$
$480$	−7.19139	−0.328241
$481$	−0.472111	−0.0215264
$482$	3.67396	0.167344
$483$	−5.54628	−0.252365
$484$	0.798939	0.0363154
$485$	0.774364	0.0351621
$486$	−13.0937	−0.593942
$487$	14.5726	0.660348	0.330174	−	0.943920i	$-0.392893\pi$
$487$	14.5726	0.660348	0.330174	+	0.943920i	$0.392893\pi$
$488$	23.1377	1.04740
$489$	33.6231	1.52049
$490$	12.8319	0.579686
$491$	26.7337	1.20648	0.603238	−	0.797562i	$-0.293877\pi$
$491$	26.7337	1.20648	0.603238	+	0.797562i	$0.293877\pi$
$492$	−12.4184	−0.559866
$493$	2.68446	0.120902
$494$	66.3893	2.98700
$495$	0.872485	0.0392153
$496$	−40.4549	−1.81648
$497$	−5.64612	−0.253263
$498$	−23.1928	−1.03929
$499$	9.76923	0.437331	0.218665	−	0.975800i	$-0.429830\pi$
$499$	9.76923	0.437331	0.218665	+	0.975800i	$0.429830\pi$
$500$	7.85865	0.351449
$501$	9.37581	0.418880
$502$	2.56609	0.114530
$503$	−35.2664	−1.57245	−0.786225	−	0.617940i	$-0.787967\pi$
$503$	−35.2664	−1.57245	−0.786225	+	0.617940i	$0.787967\pi$
$504$	−0.682166	−0.0303861
$505$	9.63707	0.428844
$506$	−14.1880	−0.630732
$507$	−47.7532	−2.12079
$508$	−13.9493	−0.618902
$509$	37.0984	1.64436	0.822180	−	0.569228i	$-0.192758\pi$
$509$	37.0984	1.64436	0.822180	+	0.569228i	$0.192758\pi$
$510$	1.16671	0.0516628
$511$	6.25280	0.276608
$512$	1.28884	0.0569591
$513$	33.3059	1.47049
$514$	18.7329	0.826273
$515$	14.2653	0.628603
$516$	−5.33374	−0.234805
$517$	4.80516	0.211331
$518$	0.0516113	0.00226767
$519$	−14.2049	−0.623524
$520$	15.1880	0.666038
$521$	−24.6016	−1.07782	−0.538908	−	0.842365i	$-0.681163\pi$
$521$	−24.6016	−1.07782	−0.538908	+	0.842365i	$0.681163\pi$
$522$	−8.38238	−0.366887
$523$	−0.682719	−0.0298532	−0.0149266	−	0.999889i	$-0.504751\pi$
$523$	−0.682719	−0.0298532	−0.0149266	+	0.999889i	$0.504751\pi$
$524$	−0.798939	−0.0349018
$525$	−2.43987	−0.106485
$526$	−13.8409	−0.603492
$527$	3.38442	0.147428
$528$	7.39890	0.321996
$529$	48.9194	2.12693
$530$	−27.1800	−1.18063
$531$	−2.92088	−0.126755
$532$	−2.07166	−0.0898180
$533$	69.9009	3.02774
$534$	2.48508	0.107540
$535$	−6.37790	−0.275741
$536$	−10.0078	−0.432273
$537$	−17.5826	−0.758747
$538$	−7.52983	−0.324634
$539$	−6.80782	−0.293233
$540$	−5.06841	−0.218110
$541$	32.5375	1.39889	0.699447	−	0.714684i	$-0.253429\pi$
$541$	32.5375	1.39889	0.699447	+	0.714684i	$0.253429\pi$
$542$	30.2218	1.29814
$543$	−27.2916	−1.17119
$544$	−1.77526	−0.0761137
$545$	4.85639	0.208025
$546$	7.34054	0.314146
$547$	42.0304	1.79709	0.898545	−	0.438881i	$-0.144625\pi$
$547$	42.0304	1.79709	0.898545	+	0.438881i	$0.144625\pi$
$548$	11.4822	0.490497
$549$	8.91724	0.380579
$550$	−6.24143	−0.266136
$551$	38.2691	1.63032
$552$	−25.4219	−1.08203
$553$	1.09275	0.0464685
$554$	32.2463	1.37001
$555$	−0.118277	−0.00502058
$556$	7.17980	0.304491
$557$	−26.9423	−1.14158	−0.570790	−	0.821096i	$-0.693363\pi$
$557$	−26.9423	−1.14158	−0.570790	+	0.821096i	$0.693363\pi$
$558$	−10.5681	−0.447381
$559$	30.0226	1.26982
$560$	−2.44956	−0.103513
$561$	−0.618985	−0.0261336
$562$	−43.2210	−1.82317
$563$	0.439366	0.0185171	0.00925854	−	0.999957i	$-0.497053\pi$
$563$	0.439366	0.0185171	0.00925854	+	0.999957i	$0.497053\pi$
$564$	−5.72722	−0.241159
$565$	11.4972	0.483690
$566$	−4.78745	−0.201231
$567$	2.66409	0.111881
$568$	−25.8795	−1.08588
$569$	17.7019	0.742101	0.371051	−	0.928613i	$-0.378998\pi$
$569$	17.7019	0.742101	0.371051	+	0.928613i	$0.378998\pi$
$570$	16.6324	0.696654
$571$	−3.44776	−0.144284	−0.0721421	−	0.997394i	$-0.522984\pi$
$571$	−3.44776	−0.144284	−0.0721421	+	0.997394i	$0.522984\pi$
$572$	5.36002	0.224114
$573$	−4.80263	−0.200633
$574$	−7.64159	−0.318954
$575$	31.6381	1.31940
$576$	−2.13815	−0.0890894
$577$	21.3780	0.889976	0.444988	−	0.895537i	$-0.353208\pi$
$577$	21.3780	0.889976	0.444988	+	0.895537i	$0.353208\pi$
$578$	−28.1530	−1.17101
$579$	24.6395	1.02398
$580$	−5.82370	−0.241816
$581$	−4.07372	−0.169006
$582$	1.71545	0.0711077
$583$	14.4201	0.597218
$584$	28.6602	1.18597
$585$	5.85343	0.242010
$586$	4.38511	0.181147
$587$	−30.7139	−1.26770	−0.633848	−	0.773457i	$-0.718526\pi$
$587$	−30.7139	−1.26770	−0.633848	+	0.773457i	$0.718526\pi$
$588$	8.11417	0.334623
$589$	48.2476	1.98801
$590$	−7.10926	−0.292684
$591$	29.5731	1.21648
$592$	0.349008	0.0143442
$593$	−4.55398	−0.187009	−0.0935047	−	0.995619i	$-0.529807\pi$
$593$	−4.55398	−0.187009	−0.0935047	+	0.995619i	$0.529807\pi$
$594$	9.42038	0.386523
$595$	0.204928	0.00840122
$596$	8.46898	0.346903
$597$	−13.9757	−0.571987
$598$	−95.1858	−3.89244
$599$	17.1227	0.699616	0.349808	−	0.936821i	$-0.386247\pi$
$599$	17.1227	0.699616	0.349808	+	0.936821i	$0.386247\pi$
$600$	−11.1833	−0.456558
$601$	−2.42972	−0.0991102	−0.0495551	−	0.998771i	$-0.515780\pi$
$601$	−2.42972	−0.0991102	−0.0495551	+	0.998771i	$0.515780\pi$
$602$	−3.28208	−0.133768
$603$	−3.85700	−0.157069
$604$	−4.13456	−0.168233
$605$	−1.12664	−0.0458046
$606$	21.3490	0.867245
$607$	0.497658	0.0201993	0.0100997	−	0.999949i	$-0.496785\pi$
$607$	0.497658	0.0201993	0.0100997	+	0.999949i	$0.496785\pi$
$608$	−25.3077	−1.02636
$609$	4.23134	0.171463
$610$	21.7041	0.878774
$611$	32.2374	1.30419
$612$	−0.256710	−0.0103769
$613$	2.51525	0.101590	0.0507949	−	0.998709i	$-0.483825\pi$
$613$	2.51525	0.101590	0.0507949	+	0.998709i	$0.483825\pi$
$614$	−7.08211	−0.285811
$615$	17.5121	0.706157
$616$	0.880883	0.0354918
$617$	−44.5175	−1.79221	−0.896103	−	0.443847i	$-0.853613\pi$
$617$	−44.5175	−1.79221	−0.896103	+	0.443847i	$0.853613\pi$
$618$	31.6019	1.27121
$619$	−40.2898	−1.61938	−0.809692	−	0.586855i	$-0.800366\pi$
$619$	−40.2898	−1.61938	−0.809692	+	0.586855i	$0.800366\pi$
$620$	−7.34220	−0.294870
$621$	−47.7524	−1.91624
$622$	−33.5592	−1.34560
$623$	0.436494	0.0174878
$624$	49.6386	1.98713
$625$	7.57132	0.302853
$626$	−41.0436	−1.64043
$627$	−8.82412	−0.352401
$628$	5.91366	0.235981
$629$	−0.0291977	−0.00116419
$630$	−0.639899	−0.0254942
$631$	−13.3359	−0.530893	−0.265447	−	0.964126i	$-0.585519\pi$
$631$	−13.3359	−0.530893	−0.265447	+	0.964126i	$0.585519\pi$
$632$	5.00871	0.199236
$633$	−7.62174	−0.302937
$634$	24.9546	0.991073
$635$	19.6710	0.780620
$636$	−17.1871	−0.681514
$637$	−45.6731	−1.80963
$638$	10.8242	0.428534
$639$	−9.97390	−0.394561
$640$	−14.8451	−0.586804
$641$	−17.4992	−0.691177	−0.345588	−	0.938386i	$-0.612321\pi$
$641$	−17.4992	−0.691177	−0.345588	+	0.938386i	$0.612321\pi$
$642$	−14.1290	−0.557626
$643$	0.425674	0.0167869	0.00839347	−	0.999965i	$-0.497328\pi$
$643$	0.425674	0.0167869	0.00839347	+	0.999965i	$0.497328\pi$
$644$	2.97025	0.117044
$645$	7.52150	0.296159
$646$	4.10585	0.161543
$647$	19.5613	0.769032	0.384516	−	0.923118i	$-0.374368\pi$
$647$	19.5613	0.769032	0.384516	+	0.923118i	$0.374368\pi$
$648$	12.2111	0.479697
$649$	3.77174	0.148054
$650$	−41.8732	−1.64240
$651$	5.33464	0.209081
$652$	−18.0065	−0.705189
$653$	−35.4134	−1.38583	−0.692917	−	0.721018i	$-0.743675\pi$
$653$	−35.4134	−1.38583	−0.692917	+	0.721018i	$0.743675\pi$
$654$	10.7584	0.420685
$655$	1.12664	0.0440216
$656$	−51.6743	−2.01754
$657$	11.0456	0.430930
$658$	−3.52420	−0.137388
$659$	32.2081	1.25465	0.627325	−	0.778758i	$-0.284150\pi$
$659$	32.2081	1.25465	0.627325	+	0.778758i	$0.284150\pi$
$660$	1.34283	0.0522698
$661$	6.82312	0.265389	0.132694	−	0.991157i	$-0.457637\pi$
$661$	6.82312	0.265389	0.132694	+	0.991157i	$0.457637\pi$
$662$	38.3586	1.49085
$663$	−4.15272	−0.161278
$664$	−18.6722	−0.724623
$665$	2.92141	0.113287
$666$	0.0911717	0.00353283
$667$	−54.8684	−2.12451
$668$	−5.02111	−0.194273
$669$	−6.31182	−0.244029
$670$	−9.38775	−0.362680
$671$	−11.5149	−0.444526
$672$	−2.79823	−0.107944
$673$	−50.9412	−1.96364	−0.981819	−	0.189818i	$-0.939210\pi$
$673$	−50.9412	−1.96364	−0.981819	+	0.189818i	$0.939210\pi$
$674$	10.2988	0.396695
$675$	−21.0068	−0.808551
$676$	25.5737	0.983604
$677$	−27.1128	−1.04203	−0.521015	−	0.853548i	$-0.674446\pi$
$677$	−27.1128	−1.04203	−0.521015	+	0.853548i	$0.674446\pi$
$678$	25.4697	0.978159
$679$	0.301311	0.0115633
$680$	0.939303	0.0360206
$681$	−37.0361	−1.41923
$682$	13.6466	0.522554
$683$	19.8345	0.758947	0.379474	−	0.925203i	$-0.376105\pi$
$683$	19.8345	0.758947	0.379474	+	0.925203i	$0.376105\pi$
$684$	−3.65960	−0.139928
$685$	−16.1919	−0.618662
$686$	10.1269	0.386648
$687$	34.8373	1.32912
$688$	−22.1942	−0.846147
$689$	96.7430	3.68562
$690$	−23.8467	−0.907829
$691$	−4.42320	−0.168266	−0.0841332	−	0.996455i	$-0.526812\pi$
$691$	−4.42320	−0.168266	−0.0841332	+	0.996455i	$0.526812\pi$
$692$	7.60726	0.289184
$693$	0.339491	0.0128962
$694$	15.1997	0.576974
$695$	−10.1248	−0.384054
$696$	19.3947	0.735155
$697$	4.32303	0.163746
$698$	−18.8202	−0.712354
$699$	−30.4607	−1.15213
$700$	1.30665	0.0493865
$701$	−48.2511	−1.82242	−0.911210	−	0.411941i	$-0.864851\pi$
$701$	−48.2511	−1.82242	−0.911210	+	0.411941i	$0.864851\pi$
$702$	63.2005	2.38535
$703$	−0.416237	−0.0156987
$704$	2.76100	0.104059
$705$	8.07637	0.304174
$706$	−17.2473	−0.649109
$707$	3.74986	0.141028
$708$	−4.49550	−0.168951
$709$	−39.4113	−1.48012	−0.740062	−	0.672539i	$-0.765204\pi$
$709$	−39.4113	−1.48012	−0.740062	+	0.672539i	$0.765204\pi$
$710$	−24.2760	−0.911060
$711$	1.93035	0.0723938
$712$	2.00071	0.0749797
$713$	−69.1751	−2.59063
$714$	0.453977	0.0169897
$715$	−7.55856	−0.282674
$716$	9.41619	0.351899
$717$	−16.2773	−0.607887
$718$	−8.22676	−0.307020
$719$	−30.2623	−1.12859	−0.564296	−	0.825572i	$-0.690852\pi$
$719$	−30.2623	−1.12859	−0.564296	+	0.825572i	$0.690852\pi$
$720$	−4.32715	−0.161264
$721$	5.55073	0.206720
$722$	26.7451	0.995349
$723$	−3.27612	−0.121840
$724$	14.6157	0.543189
$725$	−24.1372	−0.896433
$726$	−2.49585	−0.0926298
$727$	24.6084	0.912675	0.456338	−	0.889807i	$-0.349161\pi$
$727$	24.6084	0.912675	0.456338	+	0.889807i	$0.349161\pi$
$728$	5.90977	0.219031
$729$	29.9070	1.10767
$730$	26.8844	0.995038
$731$	1.85675	0.0686744
$732$	13.7245	0.507270
$733$	36.7955	1.35907	0.679537	−	0.733641i	$-0.262181\pi$
$733$	36.7955	1.35907	0.679537	+	0.733641i	$0.262181\pi$
$734$	22.3925	0.826523
$735$	−11.4424	−0.422059
$736$	36.2850	1.33748
$737$	4.98056	0.183461
$738$	−13.4989	−0.496902
$739$	20.3502	0.748594	0.374297	−	0.927309i	$-0.377884\pi$
$739$	20.3502	0.748594	0.374297	+	0.927309i	$0.377884\pi$
$740$	0.0633420	0.00232850
$741$	−59.2003	−2.17478
$742$	−10.5760	−0.388256
$743$	−15.4255	−0.565907	−0.282954	−	0.959134i	$-0.591314\pi$
$743$	−15.4255	−0.565907	−0.282954	+	0.959134i	$0.591314\pi$
$744$	24.4518	0.896446
$745$	−11.9427	−0.437548
$746$	−30.4356	−1.11432
$747$	−7.19624	−0.263297
$748$	0.331491	0.0121205
$749$	−2.48169	−0.0906791
$750$	−24.5501	−0.896443
$751$	−32.0431	−1.16927	−0.584635	−	0.811297i	$-0.698762\pi$
$751$	−32.0431	−1.16927	−0.584635	+	0.811297i	$0.698762\pi$
$752$	−23.8315	−0.869047
$753$	−2.28822	−0.0833873
$754$	72.6187	2.64462
$755$	5.83044	0.212192
$756$	−1.97216	−0.0717267
$757$	−4.48845	−0.163136	−0.0815678	−	0.996668i	$-0.525993\pi$
$757$	−4.48845	−0.163136	−0.0815678	+	0.996668i	$0.525993\pi$
$758$	19.1747	0.696455
$759$	12.6516	0.459224
$760$	13.3905	0.485725
$761$	−29.9584	−1.08599	−0.542996	−	0.839735i	$-0.682710\pi$
$761$	−29.9584	−1.08599	−0.542996	+	0.839735i	$0.682710\pi$
$762$	43.5772	1.57863
$763$	1.88966	0.0684103
$764$	2.57200	0.0930516
$765$	0.362006	0.0130884
$766$	36.7215	1.32680
$767$	25.3043	0.913685
$768$	−24.6485	−0.889424
$769$	−12.9497	−0.466979	−0.233489	−	0.972359i	$-0.575014\pi$
$769$	−12.9497	−0.466979	−0.233489	+	0.972359i	$0.575014\pi$
$770$	0.826304	0.0297779
$771$	−16.7044	−0.601594
$772$	−13.1954	−0.474914
$773$	−31.2913	−1.12547	−0.562734	−	0.826638i	$-0.690251\pi$
$773$	−31.2913	−1.12547	−0.562734	+	0.826638i	$0.690251\pi$
$774$	−5.79781	−0.208398
$775$	−30.4308	−1.09311
$776$	1.38109	0.0495781
$777$	−0.0460225	−0.00165105
$778$	37.5260	1.34537
$779$	61.6282	2.20806
$780$	9.00896	0.322573
$781$	12.8793	0.460859
$782$	−5.88678	−0.210511
$783$	36.4310	1.30194
$784$	33.7639	1.20585
$785$	−8.33929	−0.297642
$786$	2.49585	0.0890242
$787$	16.8323	0.600006	0.300003	−	0.953938i	$-0.403012\pi$
$787$	16.8323	0.600006	0.300003	+	0.953938i	$0.403012\pi$
$788$	−15.8376	−0.564190
$789$	12.3421	0.439391
$790$	4.69837	0.167161
$791$	4.47364	0.159064
$792$	1.55609	0.0552931
$793$	−77.2523	−2.74331
$794$	−2.70822	−0.0961113
$795$	24.2368	0.859592
$796$	7.48453	0.265282
$797$	14.3051	0.506712	0.253356	−	0.967373i	$-0.418466\pi$
$797$	14.3051	0.506712	0.253356	+	0.967373i	$0.418466\pi$
$798$	6.47179	0.229099
$799$	1.99373	0.0705329
$800$	15.9622	0.564348
$801$	0.771070	0.0272444
$802$	−39.4106	−1.39164
$803$	−14.2632	−0.503339
$804$	−5.93628	−0.209357
$805$	−4.18857	−0.147628
$806$	91.5537	3.22484
$807$	6.71446	0.236360
$808$	17.1878	0.604665
$809$	22.1051	0.777176	0.388588	−	0.921412i	$-0.372963\pi$
$809$	22.1051	0.777176	0.388588	+	0.921412i	$0.372963\pi$
$810$	11.4545	0.402470
$811$	−27.9604	−0.981823	−0.490911	−	0.871210i	$-0.663336\pi$
$811$	−27.9604	−0.981823	−0.490911	+	0.871210i	$0.663336\pi$
$812$	−2.26605	−0.0795227
$813$	−26.9492	−0.945151
$814$	−0.117730	−0.00412644
$815$	25.3923	0.889453
$816$	3.06990	0.107468
$817$	26.4694	0.926048
$818$	−25.1305	−0.878666
$819$	2.27762	0.0795864
$820$	−9.37843	−0.327509
$821$	−12.7474	−0.444887	−0.222443	−	0.974946i	$-0.571403\pi$
$821$	−12.7474	−0.444887	−0.222443	+	0.974946i	$0.571403\pi$
$822$	−35.8700	−1.25111
$823$	1.59217	0.0554994	0.0277497	−	0.999615i	$-0.491166\pi$
$823$	1.59217	0.0554994	0.0277497	+	0.999615i	$0.491166\pi$
$824$	25.4422	0.886323
$825$	5.56557	0.193768
$826$	−2.76627	−0.0962509
$827$	−16.1370	−0.561140	−0.280570	−	0.959834i	$-0.590524\pi$
$827$	−16.1370	−0.561140	−0.280570	+	0.959834i	$0.590524\pi$
$828$	5.24697	0.182345
$829$	−14.6192	−0.507746	−0.253873	−	0.967238i	$-0.581705\pi$
$829$	−14.6192	−0.507746	−0.253873	+	0.967238i	$0.581705\pi$
$830$	−17.5153	−0.607964
$831$	−28.7545	−0.997482
$832$	18.5233	0.642180
$833$	−2.82466	−0.0978686
$834$	−22.4294	−0.776667
$835$	7.08064	0.245036
$836$	4.72566	0.163440
$837$	45.9302	1.58758
$838$	−18.2327	−0.629839
$839$	−47.0443	−1.62415	−0.812075	−	0.583554i	$-0.801662\pi$
$839$	−47.0443	−1.62415	−0.812075	+	0.583554i	$0.801662\pi$
$840$	1.48056	0.0510843
$841$	12.8599	0.443445
$842$	−38.5041	−1.32694
$843$	38.5408	1.32741
$844$	4.08174	0.140499
$845$	−36.0634	−1.24062
$846$	−6.22552	−0.214038
$847$	−0.438386	−0.0150631
$848$	−71.5174	−2.45592
$849$	4.26904	0.146513
$850$	−2.58966	−0.0888245
$851$	0.596780	0.0204574
$852$	−15.3507	−0.525908
$853$	−40.2114	−1.37681	−0.688407	−	0.725325i	$-0.741690\pi$
$853$	−40.2114	−1.37681	−0.688407	+	0.725325i	$0.741690\pi$
$854$	8.44524	0.288990
$855$	5.16068	0.176492
$856$	−11.3751	−0.388791
$857$	15.4113	0.526439	0.263219	−	0.964736i	$-0.415216\pi$
$857$	15.4113	0.526439	0.263219	+	0.964736i	$0.415216\pi$
$858$	−16.7445	−0.571647
$859$	18.7549	0.639908	0.319954	−	0.947433i	$-0.396333\pi$
$859$	18.7549	0.639908	0.319954	+	0.947433i	$0.396333\pi$
$860$	−4.02806	−0.137356
$861$	6.81411	0.232224
$862$	22.5701	0.768739
$863$	14.2988	0.486738	0.243369	−	0.969934i	$-0.421747\pi$
$863$	14.2988	0.486738	0.243369	+	0.969934i	$0.421747\pi$
$864$	−24.0922	−0.819632
$865$	−10.7276	−0.364748
$866$	23.0805	0.784308
$867$	25.1045	0.852592
$868$	−2.85691	−0.0969699
$869$	−2.49267	−0.0845580
$870$	18.1930	0.616801
$871$	33.4142	1.13220
$872$	8.66141	0.293312
$873$	0.532268	0.0180146
$874$	−83.9206	−2.83866
$875$	−4.31212	−0.145776
$876$	17.0002	0.574384
$877$	−20.5122	−0.692646	−0.346323	−	0.938115i	$-0.612570\pi$
$877$	−20.5122	−0.692646	−0.346323	+	0.938115i	$0.612570\pi$
$878$	−1.46829	−0.0495525
$879$	−3.91027	−0.131890
$880$	5.58767	0.188360
$881$	37.4254	1.26089	0.630446	−	0.776233i	$-0.282872\pi$
$881$	37.4254	1.26089	0.630446	+	0.776233i	$0.282872\pi$
$882$	8.82016	0.296990
$883$	5.24347	0.176457	0.0882284	−	0.996100i	$-0.471879\pi$
$883$	5.24347	0.176457	0.0882284	+	0.996100i	$0.471879\pi$
$884$	2.22394	0.0747993
$885$	6.33943	0.213098
$886$	−14.4054	−0.483958
$887$	−28.8778	−0.969623	−0.484812	−	0.874619i	$-0.661112\pi$
$887$	−28.8778	−0.969623	−0.484812	+	0.874619i	$0.661112\pi$
$888$	−0.210948	−0.00707896
$889$	7.65414	0.256712
$890$	1.87674	0.0629086
$891$	−6.07705	−0.203589
$892$	3.38023	0.113178
$893$	28.4221	0.951110
$894$	−26.4568	−0.884847
$895$	−13.2785	−0.443850
$896$	−5.77635	−0.192974
$897$	84.8786	2.83401
$898$	15.1807	0.506585
$899$	52.7747	1.76013
$900$	2.30820	0.0769399
$901$	5.98308	0.199325
$902$	17.4312	0.580395
$903$	2.92668	0.0973937
$904$	20.5053	0.681997
$905$	−20.6107	−0.685123
$906$	12.9162	0.429112
$907$	−40.2902	−1.33781	−0.668907	−	0.743346i	$-0.733238\pi$
$907$	−40.2902	−1.33781	−0.668907	+	0.743346i	$0.733238\pi$
$908$	19.8343	0.658224
$909$	6.62416	0.219709
$910$	5.54360	0.183769
$911$	34.6795	1.14898	0.574492	−	0.818510i	$-0.305200\pi$
$911$	34.6795	1.14898	0.574492	+	0.818510i	$0.305200\pi$
$912$	43.7639	1.44917
$913$	9.29253	0.307538
$914$	−4.23722	−0.140155
$915$	−19.3539	−0.639819
$916$	−18.6567	−0.616435
$917$	0.438386	0.0144768
$918$	3.90864	0.129005
$919$	34.1412	1.12621	0.563106	−	0.826384i	$-0.309606\pi$
$919$	34.1412	1.12621	0.563106	+	0.826384i	$0.309606\pi$
$920$	−19.1987	−0.632961
$921$	6.31522	0.208094
$922$	−49.6914	−1.63650
$923$	86.4064	2.84410
$924$	0.522508	0.0171892
$925$	0.262530	0.00863193
$926$	5.20759	0.171132
$927$	9.80540	0.322052
$928$	−27.6824	−0.908719
$929$	20.8883	0.685323	0.342662	−	0.939459i	$-0.388672\pi$
$929$	20.8883	0.685323	0.342662	+	0.939459i	$0.388672\pi$
$930$	22.9368	0.752126
$931$	−40.2677	−1.31972
$932$	16.3129	0.534347
$933$	29.9252	0.979708
$934$	41.1316	1.34587
$935$	−0.467460	−0.0152876
$936$	10.4396	0.341231
$937$	53.8849	1.76034	0.880171	−	0.474656i	$-0.157427\pi$
$937$	53.8849	1.76034	0.880171	+	0.474656i	$0.157427\pi$
$938$	−3.65285	−0.119270
$939$	36.5992	1.19437
$940$	−4.32521	−0.141073
$941$	−23.1601	−0.754998	−0.377499	−	0.926010i	$-0.623216\pi$
$941$	−23.1601	−0.754998	−0.377499	+	0.926010i	$0.623216\pi$
$942$	−18.4741	−0.601917
$943$	−88.3595	−2.87738
$944$	−18.7062	−0.608836
$945$	2.78109	0.0904688
$946$	7.48674	0.243415
$947$	−20.2719	−0.658747	−0.329374	−	0.944200i	$-0.606838\pi$
$947$	−20.2719	−0.658747	−0.329374	+	0.944200i	$0.606838\pi$
$948$	2.97099	0.0964931
$949$	−95.6909	−3.10626
$950$	−36.9176	−1.19776
$951$	−22.2524	−0.721582
$952$	0.365491	0.0118456
$953$	−39.5410	−1.28086	−0.640430	−	0.768017i	$-0.721244\pi$
$953$	−39.5410	−1.28086	−0.640430	+	0.768017i	$0.721244\pi$
$954$	−18.6825	−0.604869
$955$	−3.62697	−0.117366
$956$	8.71714	0.281932
$957$	−9.65210	−0.312008
$958$	35.4365	1.14490
$959$	−6.30042	−0.203451
$960$	4.64060	0.149775
$961$	35.5354	1.14630
$962$	−0.789843	−0.0254656
$963$	−4.38393	−0.141270
$964$	1.75449	0.0565084
$965$	18.6078	0.599007
$966$	−9.27895	−0.298545
$967$	−61.1084	−1.96511	−0.982557	−	0.185964i	$-0.940459\pi$
$967$	−61.1084	−1.96511	−0.982557	+	0.185964i	$0.940459\pi$
$968$	−2.00938	−0.0645839
$969$	−3.66125	−0.117616
$970$	1.29551	0.0415964
$971$	−29.6739	−0.952280	−0.476140	−	0.879370i	$-0.657964\pi$
$971$	−29.6739	−0.952280	−0.476140	+	0.879370i	$0.657964\pi$
$972$	−6.25287	−0.200561
$973$	−3.93963	−0.126299
$974$	24.3800	0.781186
$975$	37.3390	1.19580
$976$	57.1088	1.82801
$977$	−55.2813	−1.76861	−0.884303	−	0.466913i	$-0.845366\pi$
$977$	−55.2813	−1.76861	−0.884303	+	0.466913i	$0.845366\pi$
$978$	56.2516	1.79873
$979$	−0.995685	−0.0318222
$980$	6.12785	0.195747
$981$	3.33809	0.106577
$982$	44.7256	1.42725
$983$	55.5192	1.77079	0.885394	−	0.464842i	$-0.153889\pi$
$983$	55.5192	1.77079	0.885394	+	0.464842i	$0.153889\pi$
$984$	31.2331	0.995674
$985$	22.3337	0.711611
$986$	4.49111	0.143026
$987$	3.14258	0.100029
$988$	31.7041	1.00864
$989$	−37.9506	−1.20676
$990$	1.45967	0.0463914
$991$	38.2171	1.21401	0.607003	−	0.794700i	$-0.292372\pi$
$991$	38.2171	1.21401	0.607003	+	0.794700i	$0.292372\pi$
$992$	−34.9004	−1.10809
$993$	−34.2049	−1.08546
$994$	−9.44597	−0.299608
$995$	−10.5545	−0.334600
$996$	−11.0757	−0.350946
$997$	17.5447	0.555646	0.277823	−	0.960632i	$-0.410387\pi$
$997$	17.5447	0.555646	0.277823	+	0.960632i	$0.410387\pi$
$998$	16.3439	0.517359
$999$	−0.396244	−0.0125366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.20	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+1.67300 q^{2} -1.49184 q^{3} +0.798939 q^{4} -1.12664 q^{5} -2.49585 q^{6} -0.438386 q^{7} -2.00938 q^{8} -0.774411 q^{9} +O(q^{10})\)	\(q+1.67300 q^{2} -1.49184 q^{3} +0.798939 q^{4} -1.12664 q^{5} -2.49585 q^{6} -0.438386 q^{7} -2.00938 q^{8} -0.774411 q^{9} -1.88488 q^{10} +1.00000 q^{11} -1.19189 q^{12} +6.70892 q^{13} -0.733421 q^{14} +1.68077 q^{15} -4.95957 q^{16} +0.414914 q^{17} -1.29559 q^{18} +5.91492 q^{19} -0.900119 q^{20} +0.654002 q^{21} +1.67300 q^{22} -8.48053 q^{23} +2.99767 q^{24} -3.73068 q^{25} +11.2240 q^{26} +5.63082 q^{27} -0.350244 q^{28} +6.46992 q^{29} +2.81194 q^{30} +8.15693 q^{31} -4.27863 q^{32} -1.49184 q^{33} +0.694152 q^{34} +0.493904 q^{35} -0.618707 q^{36} -0.0703706 q^{37} +9.89568 q^{38} -10.0086 q^{39} +2.26385 q^{40} +10.4191 q^{41} +1.09415 q^{42} +4.47503 q^{43} +0.798939 q^{44} +0.872485 q^{45} -14.1880 q^{46} +4.80516 q^{47} +7.39890 q^{48} -6.80782 q^{49} -6.24143 q^{50} -0.618985 q^{51} +5.36002 q^{52} +14.4201 q^{53} +9.42038 q^{54} -1.12664 q^{55} +0.880883 q^{56} -8.82412 q^{57} +10.8242 q^{58} +3.77174 q^{59} +1.34283 q^{60} -11.5149 q^{61} +13.6466 q^{62} +0.339491 q^{63} +2.76100 q^{64} -7.55856 q^{65} -2.49585 q^{66} +4.98056 q^{67} +0.331491 q^{68} +12.6516 q^{69} +0.826304 q^{70} +12.8793 q^{71} +1.55609 q^{72} -14.2632 q^{73} -0.117730 q^{74} +5.56557 q^{75} +4.72566 q^{76} -0.438386 q^{77} -16.7445 q^{78} -2.49267 q^{79} +5.58767 q^{80} -6.07705 q^{81} +17.4312 q^{82} +9.29253 q^{83} +0.522508 q^{84} -0.467460 q^{85} +7.48674 q^{86} -9.65210 q^{87} -2.00938 q^{88} -0.995685 q^{89} +1.45967 q^{90} -2.94109 q^{91} -6.77543 q^{92} -12.1688 q^{93} +8.03904 q^{94} -6.66400 q^{95} +6.38303 q^{96} -0.687320 q^{97} -11.3895 q^{98} -0.774411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 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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