LMFDB - Embedded newform 1441.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47542 q^{2} +2.04682 q^{3} +4.12769 q^{4} -2.23639 q^{5} -5.06674 q^{6} +4.08338 q^{7} -5.26693 q^{8} +1.18947 q^{9} +O(q^{10})$	\(q-2.47542 q^{2} +2.04682 q^{3} +4.12769 q^{4} -2.23639 q^{5} -5.06674 q^{6} +4.08338 q^{7} -5.26693 q^{8} +1.18947 q^{9} +5.53600 q^{10} -1.00000 q^{11} +8.44865 q^{12} +1.53641 q^{13} -10.1081 q^{14} -4.57749 q^{15} +4.78247 q^{16} -7.14724 q^{17} -2.94444 q^{18} -5.68052 q^{19} -9.23114 q^{20} +8.35795 q^{21} +2.47542 q^{22} -2.93915 q^{23} -10.7805 q^{24} +0.00144703 q^{25} -3.80326 q^{26} -3.70582 q^{27} +16.8550 q^{28} +1.35285 q^{29} +11.3312 q^{30} -9.40542 q^{31} -1.30475 q^{32} -2.04682 q^{33} +17.6924 q^{34} -9.13204 q^{35} +4.90978 q^{36} +5.39967 q^{37} +14.0617 q^{38} +3.14476 q^{39} +11.7789 q^{40} +5.65939 q^{41} -20.6894 q^{42} -11.8818 q^{43} -4.12769 q^{44} -2.66013 q^{45} +7.27564 q^{46} -3.65479 q^{47} +9.78886 q^{48} +9.67401 q^{49} -0.00358201 q^{50} -14.6291 q^{51} +6.34183 q^{52} -7.19224 q^{53} +9.17346 q^{54} +2.23639 q^{55} -21.5069 q^{56} -11.6270 q^{57} -3.34887 q^{58} -2.49802 q^{59} -18.8945 q^{60} +10.5940 q^{61} +23.2823 q^{62} +4.85708 q^{63} -6.33515 q^{64} -3.43601 q^{65} +5.06674 q^{66} +0.701669 q^{67} -29.5016 q^{68} -6.01592 q^{69} +22.6056 q^{70} -7.26543 q^{71} -6.26488 q^{72} -0.169718 q^{73} -13.3664 q^{74} +0.00296182 q^{75} -23.4475 q^{76} -4.08338 q^{77} -7.78458 q^{78} +15.9250 q^{79} -10.6955 q^{80} -11.1536 q^{81} -14.0094 q^{82} +2.69054 q^{83} +34.4991 q^{84} +15.9840 q^{85} +29.4124 q^{86} +2.76904 q^{87} +5.26693 q^{88} +2.02463 q^{89} +6.58493 q^{90} +6.27375 q^{91} -12.1319 q^{92} -19.2512 q^{93} +9.04714 q^{94} +12.7039 q^{95} -2.67058 q^{96} -15.5614 q^{97} -23.9472 q^{98} -1.18947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.47542	−1.75038	−0.875192	−	0.483775i	$-0.839265\pi$
$2$	−2.47542	−1.75038	−0.875192	+	0.483775i	$0.839265\pi$
$3$	2.04682	1.18173	0.590866	−	0.806770i	$-0.298786\pi$
$3$	2.04682	1.18173	0.590866	+	0.806770i	$0.298786\pi$
$4$	4.12769	2.06385
$5$	−2.23639	−1.00014	−0.500072	−	0.865984i	$-0.666693\pi$
$5$	−2.23639	−1.00014	−0.500072	+	0.865984i	$0.666693\pi$
$6$	−5.06674	−2.06849
$7$	4.08338	1.54337	0.771687	−	0.636003i	$-0.219413\pi$
$7$	4.08338	1.54337	0.771687	+	0.636003i	$0.219413\pi$
$8$	−5.26693	−1.86214
$9$	1.18947	0.396491
$10$	5.53600	1.75064
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	8.44865	2.43891
$13$	1.53641	0.426123	0.213062	−	0.977039i	$-0.431656\pi$
$13$	1.53641	0.426123	0.213062	+	0.977039i	$0.431656\pi$
$14$	−10.1081	−2.70150
$15$	−4.57749	−1.18190
$16$	4.78247	1.19562
$17$	−7.14724	−1.73346	−0.866730	−	0.498778i	$-0.833782\pi$
$17$	−7.14724	−1.73346	−0.866730	+	0.498778i	$0.833782\pi$
$18$	−2.94444	−0.694012
$19$	−5.68052	−1.30320	−0.651601	−	0.758562i	$-0.725902\pi$
$19$	−5.68052	−1.30320	−0.651601	+	0.758562i	$0.725902\pi$
$20$	−9.23114	−2.06415
$21$	8.35795	1.82385
$22$	2.47542	0.527761
$23$	−2.93915	−0.612856	−0.306428	−	0.951894i	$-0.599134\pi$
$23$	−2.93915	−0.612856	−0.306428	+	0.951894i	$0.599134\pi$
$24$	−10.7805	−2.20055
$25$	0.00144703	0.000289407 0
$26$	−3.80326	−0.745880
$27$	−3.70582	−0.713186
$28$	16.8550	3.18529
$29$	1.35285	0.251218	0.125609	−	0.992080i	$-0.459912\pi$
$29$	1.35285	0.251218	0.125609	+	0.992080i	$0.459912\pi$
$30$	11.3312	2.06879
$31$	−9.40542	−1.68926	−0.844632	−	0.535348i	$-0.820180\pi$
$31$	−9.40542	−1.68926	−0.844632	+	0.535348i	$0.820180\pi$
$32$	−1.30475	−0.230649
$33$	−2.04682	−0.356306
$34$	17.6924	3.03422
$35$	−9.13204	−1.54360
$36$	4.90978	0.818297
$37$	5.39967	0.887700	0.443850	−	0.896101i	$-0.353612\pi$
$37$	5.39967	0.887700	0.443850	+	0.896101i	$0.353612\pi$
$38$	14.0617	2.28110
$39$	3.14476	0.503564
$40$	11.7789	1.86241
$41$	5.65939	0.883848	0.441924	−	0.897052i	$-0.354296\pi$
$41$	5.65939	0.883848	0.441924	+	0.897052i	$0.354296\pi$
$42$	−20.6894	−3.19245
$43$	−11.8818	−1.81195	−0.905977	−	0.423326i	$-0.860862\pi$
$43$	−11.8818	−1.81195	−0.905977	+	0.423326i	$0.860862\pi$
$44$	−4.12769	−0.622273
$45$	−2.66013	−0.396549
$46$	7.27564	1.07273
$47$	−3.65479	−0.533106	−0.266553	−	0.963820i	$-0.585885\pi$
$47$	−3.65479	−0.533106	−0.266553	+	0.963820i	$0.585885\pi$
$48$	9.78886	1.41290
$49$	9.67401	1.38200
$50$	−0.00358201	−0.000506573 0
$51$	−14.6291	−2.04849
$52$	6.34183	0.879454
$53$	−7.19224	−0.987930	−0.493965	−	0.869482i	$-0.664453\pi$
$53$	−7.19224	−0.987930	−0.493965	+	0.869482i	$0.664453\pi$
$54$	9.17346	1.24835
$55$	2.23639	0.301555
$56$	−21.5069	−2.87398
$57$	−11.6270	−1.54003
$58$	−3.34887	−0.439728
$59$	−2.49802	−0.325214	−0.162607	−	0.986691i	$-0.551990\pi$
$59$	−2.49802	−0.325214	−0.162607	+	0.986691i	$0.551990\pi$
$60$	−18.8945	−2.43927
$61$	10.5940	1.35642	0.678212	−	0.734867i	$-0.262755\pi$
$61$	10.5940	1.35642	0.678212	+	0.734867i	$0.262755\pi$
$62$	23.2823	2.95686
$63$	4.85708	0.611934
$64$	−6.33515	−0.791893
$65$	−3.43601	−0.426185
$66$	5.06674	0.623672
$67$	0.701669	0.0857225	0.0428613	−	0.999081i	$-0.486353\pi$
$67$	0.701669	0.0857225	0.0428613	+	0.999081i	$0.486353\pi$
$68$	−29.5016	−3.57760
$69$	−6.01592	−0.724232
$70$	22.6056	2.70189
$71$	−7.26543	−0.862247	−0.431124	−	0.902293i	$-0.641883\pi$
$71$	−7.26543	−0.862247	−0.431124	+	0.902293i	$0.641883\pi$
$72$	−6.26488	−0.738323
$73$	−0.169718	−0.0198640	−0.00993199	−	0.999951i	$-0.503162\pi$
$73$	−0.169718	−0.0198640	−0.00993199	+	0.999951i	$0.503162\pi$
$74$	−13.3664	−1.55382
$75$	0.00296182	0.000342001 0
$76$	−23.4475	−2.68961
$77$	−4.08338	−0.465345
$78$	−7.78458	−0.881430
$79$	15.9250	1.79170	0.895852	−	0.444353i	$-0.146566\pi$
$79$	15.9250	1.79170	0.895852	+	0.444353i	$0.146566\pi$
$80$	−10.6955	−1.19579
$81$	−11.1536	−1.23929
$82$	−14.0094	−1.54707
$83$	2.69054	0.295325	0.147662	−	0.989038i	$-0.452825\pi$
$83$	2.69054	0.295325	0.147662	+	0.989038i	$0.452825\pi$
$84$	34.4991	3.76416
$85$	15.9840	1.73371
$86$	29.4124	3.17162
$87$	2.76904	0.296872
$88$	5.26693	0.561457
$89$	2.02463	0.214610	0.107305	−	0.994226i	$-0.465778\pi$
$89$	2.02463	0.214610	0.107305	+	0.994226i	$0.465778\pi$
$90$	6.58493	0.694113
$91$	6.27375	0.657668
$92$	−12.1319	−1.26484
$93$	−19.2512	−1.99626
$94$	9.04714	0.933141
$95$	12.7039	1.30339
$96$	−2.67058	−0.272565
$97$	−15.5614	−1.58002	−0.790009	−	0.613095i	$-0.789924\pi$
$97$	−15.5614	−1.58002	−0.790009	+	0.613095i	$0.789924\pi$
$98$	−23.9472	−2.41904
$99$	−1.18947	−0.119547
$100$	0.00597291	0.000597291 0
$101$	7.45137	0.741439	0.370720	−	0.928745i	$-0.379111\pi$
$101$	7.45137	0.741439	0.370720	+	0.928745i	$0.379111\pi$
$102$	36.2132	3.58564
$103$	7.30934	0.720211	0.360105	−	0.932912i	$-0.382741\pi$
$103$	7.30934	0.720211	0.360105	+	0.932912i	$0.382741\pi$
$104$	−8.09217	−0.793502
$105$	−18.6917	−1.82412
$106$	17.8038	1.72926
$107$	12.6022	1.21830	0.609151	−	0.793054i	$-0.291510\pi$
$107$	12.6022	1.21830	0.609151	+	0.793054i	$0.291510\pi$
$108$	−15.2965	−1.47191
$109$	−9.91702	−0.949878	−0.474939	−	0.880019i	$-0.657530\pi$
$109$	−9.91702	−0.949878	−0.474939	+	0.880019i	$0.657530\pi$
$110$	−5.53600	−0.527837
$111$	11.0521	1.04902
$112$	19.5287	1.84528
$113$	14.9866	1.40982	0.704910	−	0.709297i	$-0.250987\pi$
$113$	14.9866	1.40982	0.704910	+	0.709297i	$0.250987\pi$
$114$	28.7817	2.69565
$115$	6.57310	0.612945
$116$	5.58415	0.518475
$117$	1.82752	0.168954
$118$	6.18363	0.569250
$119$	−29.1849	−2.67538
$120$	24.1093	2.20087
$121$	1.00000	0.0909091
$122$	−26.2246	−2.37426
$123$	11.5838	1.04447
$124$	−38.8227	−3.48638
$125$	11.1787	0.999855
$126$	−12.0233	−1.07112
$127$	3.56323	0.316185	0.158093	−	0.987424i	$-0.449466\pi$
$127$	3.56323	0.316185	0.158093	+	0.987424i	$0.449466\pi$
$128$	18.2916	1.61677
$129$	−24.3199	−2.14125
$130$	8.50557	0.745988
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−8.44865	−0.735360
$133$	−23.1957	−2.01133
$134$	−1.73692	−0.150047
$135$	8.28767	0.713289
$136$	37.6440	3.22795
$137$	−14.0948	−1.20420	−0.602100	−	0.798421i	$-0.705669\pi$
$137$	−14.0948	−1.20420	−0.602100	+	0.798421i	$0.705669\pi$
$138$	14.8919	1.26768
$139$	−6.01080	−0.509830	−0.254915	−	0.966963i	$-0.582047\pi$
$139$	−6.01080	−0.509830	−0.254915	+	0.966963i	$0.582047\pi$
$140$	−37.6943	−3.18575
$141$	−7.48070	−0.629989
$142$	17.9850	1.50926
$143$	−1.53641	−0.128481
$144$	5.68862	0.474052
$145$	−3.02550	−0.251254
$146$	0.420123	0.0347696
$147$	19.8010	1.63316
$148$	22.2882	1.83208
$149$	−0.526950	−0.0431694	−0.0215847	−	0.999767i	$-0.506871\pi$
$149$	−0.526950	−0.0431694	−0.0215847	+	0.999767i	$0.506871\pi$
$150$	−0.00733173	−0.000598634 0
$151$	3.21376	0.261532	0.130766	−	0.991413i	$-0.458256\pi$
$151$	3.21376	0.261532	0.130766	+	0.991413i	$0.458256\pi$
$152$	29.9189	2.42674
$153$	−8.50145	−0.687302
$154$	10.1081	0.814532
$155$	21.0342	1.68951
$156$	12.9806	1.03928
$157$	−8.28731	−0.661400	−0.330700	−	0.943736i	$-0.607285\pi$
$157$	−8.28731	−0.661400	−0.330700	+	0.943736i	$0.607285\pi$
$158$	−39.4211	−3.13617
$159$	−14.7212	−1.16747
$160$	2.91792	0.230682
$161$	−12.0017	−0.945866
$162$	27.6098	2.16923
$163$	−19.8495	−1.55473	−0.777365	−	0.629050i	$-0.783444\pi$
$163$	−19.8495	−1.55473	−0.777365	+	0.629050i	$0.783444\pi$
$164$	23.3602	1.82413
$165$	4.57749	0.356357
$166$	−6.66020	−0.516932
$167$	−14.8122	−1.14620	−0.573102	−	0.819484i	$-0.694260\pi$
$167$	−14.8122	−1.14620	−0.573102	+	0.819484i	$0.694260\pi$
$168$	−44.0208	−3.39628
$169$	−10.6394	−0.818419
$170$	−39.5671	−3.03466
$171$	−6.75683	−0.516708
$172$	−49.0444	−3.73960
$173$	14.5825	1.10869	0.554343	−	0.832289i	$-0.312970\pi$
$173$	14.5825	1.10869	0.554343	+	0.832289i	$0.312970\pi$
$174$	−6.85453	−0.519641
$175$	0.00590879	0.000446663 0
$176$	−4.78247	−0.360492
$177$	−5.11299	−0.384316
$178$	−5.01180	−0.375650
$179$	−11.7279	−0.876584	−0.438292	−	0.898833i	$-0.644416\pi$
$179$	−11.7279	−0.876584	−0.438292	+	0.898833i	$0.644416\pi$
$180$	−10.9802	−0.818416
$181$	−19.3607	−1.43907	−0.719533	−	0.694458i	$-0.755644\pi$
$181$	−19.3607	−1.43907	−0.719533	+	0.694458i	$0.755644\pi$
$182$	−15.5302	−1.15117
$183$	21.6840	1.60293
$184$	15.4803	1.14122
$185$	−12.0758	−0.887828
$186$	47.6548	3.49422
$187$	7.14724	0.522658
$188$	−15.0859	−1.10025
$189$	−15.1323	−1.10071
$190$	−31.4474	−2.28143
$191$	7.15373	0.517626	0.258813	−	0.965928i	$-0.416669\pi$
$191$	7.15373	0.517626	0.258813	+	0.965928i	$0.416669\pi$
$192$	−12.9669	−0.935806
$193$	5.42441	0.390458	0.195229	−	0.980758i	$-0.437455\pi$
$193$	5.42441	0.390458	0.195229	+	0.980758i	$0.437455\pi$
$194$	38.5209	2.76564
$195$	−7.03290	−0.503637
$196$	39.9314	2.85224
$197$	5.32416	0.379331	0.189665	−	0.981849i	$-0.439260\pi$
$197$	5.32416	0.379331	0.189665	+	0.981849i	$0.439260\pi$
$198$	2.94444	0.209253
$199$	−16.5582	−1.17378	−0.586891	−	0.809666i	$-0.699648\pi$
$199$	−16.5582	−1.17378	−0.586891	+	0.809666i	$0.699648\pi$
$200$	−0.00762142	−0.000538916 0
$201$	1.43619	0.101301
$202$	−18.4453	−1.29780
$203$	5.52421	0.387723
$204$	−60.3845	−4.22776
$205$	−12.6566	−0.883976
$206$	−18.0937	−1.26065
$207$	−3.49605	−0.242992
$208$	7.34783	0.509481
$209$	5.68052	0.392930
$210$	46.2696	3.19291
$211$	−3.68684	−0.253813	−0.126906	−	0.991915i	$-0.540505\pi$
$211$	−3.68684	−0.253813	−0.126906	+	0.991915i	$0.540505\pi$
$212$	−29.6874	−2.03894
$213$	−14.8710	−1.01895
$214$	−31.1957	−2.13250
$215$	26.5723	1.81222
$216$	19.5183	1.32805
$217$	−38.4059	−2.60716
$218$	24.5488	1.66265
$219$	−0.347382	−0.0234739
$220$	9.23114	0.622363
$221$	−10.9811	−0.738668
$222$	−27.3587	−1.83619
$223$	11.9883	0.802795	0.401397	−	0.915904i	$-0.368525\pi$
$223$	11.9883	0.802795	0.401397	+	0.915904i	$0.368525\pi$
$224$	−5.32778	−0.355977
$225$	0.00172121	0.000114747 0
$226$	−37.0981	−2.46773
$227$	−16.7999	−1.11505	−0.557524	−	0.830161i	$-0.688248\pi$
$227$	−16.7999	−1.11505	−0.557524	+	0.830161i	$0.688248\pi$
$228$	−47.9927	−3.17840
$229$	20.7546	1.37150	0.685751	−	0.727837i	$-0.259474\pi$
$229$	20.7546	1.37150	0.685751	+	0.727837i	$0.259474\pi$
$230$	−16.2712	−1.07289
$231$	−8.35795	−0.549913
$232$	−7.12537	−0.467803
$233$	2.26221	0.148203	0.0741013	−	0.997251i	$-0.476391\pi$
$233$	2.26221	0.148203	0.0741013	+	0.997251i	$0.476391\pi$
$234$	−4.52387	−0.295735
$235$	8.17355	0.533183
$236$	−10.3110	−0.671192
$237$	32.5956	2.11731
$238$	72.2449	4.68294
$239$	−20.4942	−1.32566	−0.662831	−	0.748769i	$-0.730645\pi$
$239$	−20.4942	−1.32566	−0.662831	+	0.748769i	$0.730645\pi$
$240$	−21.8917	−1.41310
$241$	−4.30603	−0.277376	−0.138688	−	0.990336i	$-0.544289\pi$
$241$	−4.30603	−0.277376	−0.138688	+	0.990336i	$0.544289\pi$
$242$	−2.47542	−0.159126
$243$	−11.7119	−0.751318
$244$	43.7288	2.79945
$245$	−21.6349	−1.38220
$246$	−28.6746	−1.82823
$247$	−8.72761	−0.555325
$248$	49.5377	3.14565
$249$	5.50705	0.348995
$250$	−27.6720	−1.75013
$251$	−13.6304	−0.860345	−0.430172	−	0.902747i	$-0.641547\pi$
$251$	−13.6304	−0.860345	−0.430172	+	0.902747i	$0.641547\pi$
$252$	20.0485	1.26294
$253$	2.93915	0.184783
$254$	−8.82047	−0.553446
$255$	32.7164	2.04878
$256$	−32.6091	−2.03807
$257$	24.4671	1.52622	0.763108	−	0.646271i	$-0.223672\pi$
$257$	24.4671	1.52622	0.763108	+	0.646271i	$0.223672\pi$
$258$	60.2018	3.74800
$259$	22.0489	1.37005
$260$	−14.1828	−0.879581
$261$	1.60918	0.0996057
$262$	2.47542	0.152932
$263$	10.3518	0.638320	0.319160	−	0.947701i	$-0.396599\pi$
$263$	10.3518	0.638320	0.319160	+	0.947701i	$0.396599\pi$
$264$	10.7805	0.663492
$265$	16.0847	0.988073
$266$	57.4192	3.52059
$267$	4.14405	0.253612
$268$	2.89627	0.176918
$269$	9.76549	0.595413	0.297706	−	0.954657i	$-0.403778\pi$
$269$	9.76549	0.595413	0.297706	+	0.954657i	$0.403778\pi$
$270$	−20.5154	−1.24853
$271$	−10.0724	−0.611857	−0.305928	−	0.952055i	$-0.598967\pi$
$271$	−10.0724	−0.611857	−0.305928	+	0.952055i	$0.598967\pi$
$272$	−34.1815	−2.07255
$273$	12.8412	0.777187
$274$	34.8905	2.10781
$275$	−0.00144703	−8.72594e−5 0
$276$	−24.8319	−1.49470
$277$	−1.05121	−0.0631614	−0.0315807	−	0.999501i	$-0.510054\pi$
$277$	−1.05121	−0.0631614	−0.0315807	+	0.999501i	$0.510054\pi$
$278$	14.8793	0.892398
$279$	−11.1875	−0.669778
$280$	48.0978	2.87440
$281$	0.910283	0.0543029	0.0271515	−	0.999631i	$-0.491356\pi$
$281$	0.910283	0.0543029	0.0271515	+	0.999631i	$0.491356\pi$
$282$	18.5179	1.10272
$283$	9.34923	0.555754	0.277877	−	0.960617i	$-0.410369\pi$
$283$	9.34923	0.555754	0.277877	+	0.960617i	$0.410369\pi$
$284$	−29.9895	−1.77955
$285$	26.0025	1.54026
$286$	3.80326	0.224891
$287$	23.1095	1.36411
$288$	−1.55196	−0.0914502
$289$	34.0830	2.00488
$290$	7.48938	0.439792
$291$	−31.8513	−1.86716
$292$	−0.700544	−0.0409962
$293$	−10.5233	−0.614776	−0.307388	−	0.951584i	$-0.599455\pi$
$293$	−10.5233	−0.614776	−0.307388	+	0.951584i	$0.599455\pi$
$294$	−49.0157	−2.85865
$295$	5.58654	0.325261
$296$	−28.4397	−1.65302
$297$	3.70582	0.215034
$298$	1.30442	0.0755631
$299$	−4.51575	−0.261152
$300$	0.0122255	0.000705838 0
$301$	−48.5179	−2.79652
$302$	−7.95540	−0.457782
$303$	15.2516	0.876183
$304$	−27.1669	−1.55813
$305$	−23.6923	−1.35662
$306$	21.0447	1.20304
$307$	34.0733	1.94467	0.972334	−	0.233595i	$-0.0750488\pi$
$307$	34.0733	1.94467	0.972334	+	0.233595i	$0.0750488\pi$
$308$	−16.8550	−0.960400
$309$	14.9609	0.851096
$310$	−52.0684	−2.95729
$311$	20.0547	1.13720	0.568598	−	0.822615i	$-0.307486\pi$
$311$	20.0547	1.13720	0.568598	+	0.822615i	$0.307486\pi$
$312$	−16.5632	−0.937707
$313$	29.3676	1.65996	0.829979	−	0.557795i	$-0.188353\pi$
$313$	29.3676	1.65996	0.829979	+	0.557795i	$0.188353\pi$
$314$	20.5146	1.15770
$315$	−10.8623	−0.612023
$316$	65.7336	3.69780
$317$	21.1885	1.19006	0.595032	−	0.803702i	$-0.297139\pi$
$317$	21.1885	1.19006	0.595032	+	0.803702i	$0.297139\pi$
$318$	36.4412	2.04352
$319$	−1.35285	−0.0757451
$320$	14.1679	0.792008
$321$	25.7945	1.43971
$322$	29.7092	1.65563
$323$	40.6000	2.25905
$324$	−46.0385	−2.55770
$325$	0.00222324	0.000123323 0
$326$	49.1357	2.72138
$327$	−20.2984	−1.12250
$328$	−29.8076	−1.64585
$329$	−14.9239	−0.822782
$330$	−11.3312	−0.623762
$331$	−18.1998	−1.00035	−0.500174	−	0.865925i	$-0.666731\pi$
$331$	−18.1998	−1.00035	−0.500174	+	0.865925i	$0.666731\pi$
$332$	11.1057	0.609505
$333$	6.42276	0.351965
$334$	36.6665	2.00630
$335$	−1.56921	−0.0857349
$336$	39.9716	2.18063
$337$	−20.9512	−1.14128	−0.570641	−	0.821200i	$-0.693305\pi$
$337$	−20.9512	−1.14128	−0.570641	+	0.821200i	$0.693305\pi$
$338$	26.3371	1.43255
$339$	30.6749	1.66603
$340$	65.9772	3.57811
$341$	9.40542	0.509332
$342$	16.7260	0.904438
$343$	10.9190	0.589572
$344$	62.5805	3.37412
$345$	13.4540	0.724337
$346$	−36.0977	−1.94063
$347$	−30.2380	−1.62326	−0.811630	−	0.584172i	$-0.801419\pi$
$347$	−30.2380	−1.62326	−0.811630	+	0.584172i	$0.801419\pi$
$348$	11.4298	0.612699
$349$	−35.9435	−1.92401	−0.962007	−	0.273025i	$-0.911976\pi$
$349$	−35.9435	−1.92401	−0.962007	+	0.273025i	$0.911976\pi$
$350$	−0.0146267	−0.000781831 0
$351$	−5.69366	−0.303905
$352$	1.30475	0.0695432
$353$	−19.7463	−1.05099	−0.525494	−	0.850797i	$-0.676119\pi$
$353$	−19.7463	−1.05099	−0.525494	+	0.850797i	$0.676119\pi$
$354$	12.6568	0.672701
$355$	16.2483	0.862372
$356$	8.35704	0.442922
$357$	−59.7363	−3.16158
$358$	29.0314	1.53436
$359$	−35.8656	−1.89292	−0.946458	−	0.322828i	$-0.895367\pi$
$359$	−35.8656	−1.89292	−0.946458	+	0.322828i	$0.895367\pi$
$360$	14.0107	0.738430
$361$	13.2683	0.698333
$362$	47.9257	2.51892
$363$	2.04682	0.107430
$364$	25.8961	1.35733
$365$	0.379556	0.0198669
$366$	−53.6770	−2.80574
$367$	26.0772	1.36122	0.680609	−	0.732647i	$-0.261715\pi$
$367$	26.0772	1.36122	0.680609	+	0.732647i	$0.261715\pi$
$368$	−14.0564	−0.732741
$369$	6.73170	0.350438
$370$	29.8926	1.55404
$371$	−29.3687	−1.52474
$372$	−79.4631	−4.11997
$373$	−0.958724	−0.0496409	−0.0248204	−	0.999692i	$-0.507901\pi$
$373$	−0.958724	−0.0496409	−0.0248204	+	0.999692i	$0.507901\pi$
$374$	−17.6924	−0.914852
$375$	22.8808	1.18156
$376$	19.2495	0.992719
$377$	2.07853	0.107050
$378$	37.4587	1.92667
$379$	24.5096	1.25897	0.629486	−	0.777011i	$-0.283265\pi$
$379$	24.5096	1.25897	0.629486	+	0.777011i	$0.283265\pi$
$380$	52.4377	2.69000
$381$	7.29328	0.373646
$382$	−17.7085	−0.906044
$383$	−20.0441	−1.02420	−0.512102	−	0.858924i	$-0.671133\pi$
$383$	−20.0441	−1.02420	−0.512102	+	0.858924i	$0.671133\pi$
$384$	37.4397	1.91059
$385$	9.13204	0.465412
$386$	−13.4277	−0.683452
$387$	−14.1331	−0.718424
$388$	−64.2326	−3.26092
$389$	−8.55487	−0.433749	−0.216874	−	0.976199i	$-0.569586\pi$
$389$	−8.55487	−0.433749	−0.216874	+	0.976199i	$0.569586\pi$
$390$	17.4094	0.881558
$391$	21.0068	1.06236
$392$	−50.9524	−2.57348
$393$	−2.04682	−0.103248
$394$	−13.1795	−0.663975
$395$	−35.6146	−1.79196
$396$	−4.90978	−0.246726
$397$	−29.9543	−1.50337	−0.751683	−	0.659525i	$-0.770757\pi$
$397$	−29.9543	−1.50337	−0.751683	+	0.659525i	$0.770757\pi$
$398$	40.9886	2.05457
$399$	−47.4775	−2.37685
$400$	0.00692039	0.000346020 0
$401$	−5.84555	−0.291913	−0.145956	−	0.989291i	$-0.546626\pi$
$401$	−5.84555	−0.291913	−0.145956	+	0.989291i	$0.546626\pi$
$402$	−3.55517	−0.177316
$403$	−14.4506	−0.719835
$404$	30.7570	1.53022
$405$	24.9438	1.23947
$406$	−13.6747	−0.678665
$407$	−5.39967	−0.267651
$408$	77.0505	3.81457
$409$	17.3295	0.856889	0.428445	−	0.903568i	$-0.359062\pi$
$409$	17.3295	0.856889	0.428445	+	0.903568i	$0.359062\pi$
$410$	31.3304	1.54730
$411$	−28.8495	−1.42304
$412$	30.1707	1.48640
$413$	−10.2004	−0.501927
$414$	8.65418	0.425330
$415$	−6.01709	−0.295368
$416$	−2.00463	−0.0982849
$417$	−12.3030	−0.602482
$418$	−14.0617	−0.687779
$419$	40.7072	1.98868	0.994339	−	0.106257i	$-0.0338866\pi$
$419$	40.7072	1.98868	0.994339	+	0.106257i	$0.0338866\pi$
$420$	−77.1534	−3.76470
$421$	−0.837798	−0.0408318	−0.0204159	−	0.999792i	$-0.506499\pi$
$421$	−0.837798	−0.0408318	−0.0204159	+	0.999792i	$0.506499\pi$
$422$	9.12648	0.444270
$423$	−4.34728	−0.211372
$424$	37.8810	1.83967
$425$	−0.0103423	−0.000501675 0
$426$	36.8120	1.78355
$427$	43.2594	2.09347
$428$	52.0181	2.51439
$429$	−3.14476	−0.151830
$430$	−65.7776	−3.17208
$431$	−28.0111	−1.34925	−0.674624	−	0.738161i	$-0.735694\pi$
$431$	−28.0111	−1.34925	−0.674624	+	0.738161i	$0.735694\pi$
$432$	−17.7230	−0.852697
$433$	29.4669	1.41609	0.708044	−	0.706169i	$-0.249578\pi$
$433$	29.4669	1.41609	0.708044	+	0.706169i	$0.249578\pi$
$434$	95.0707	4.56354
$435$	−6.19266	−0.296915
$436$	−40.9344	−1.96040
$437$	16.6959	0.798675
$438$	0.859916	0.0410884
$439$	7.58551	0.362036	0.181018	−	0.983480i	$-0.442061\pi$
$439$	7.58551	0.362036	0.181018	+	0.983480i	$0.442061\pi$
$440$	−11.7789	−0.561538
$441$	11.5070	0.547952
$442$	27.1828	1.29295
$443$	−9.20068	−0.437137	−0.218569	−	0.975822i	$-0.570139\pi$
$443$	−9.20068	−0.437137	−0.218569	+	0.975822i	$0.570139\pi$
$444$	45.6199	2.16502
$445$	−4.52786	−0.214641
$446$	−29.6760	−1.40520
$447$	−1.07857	−0.0510147
$448$	−25.8688	−1.22219
$449$	34.4465	1.62563	0.812816	−	0.582520i	$-0.197933\pi$
$449$	34.4465	1.62563	0.812816	+	0.582520i	$0.197933\pi$
$450$	−0.00426071	−0.000200852 0
$451$	−5.65939	−0.266490
$452$	61.8600	2.90965
$453$	6.57799	0.309061
$454$	41.5867	1.95176
$455$	−14.0306	−0.657763
$456$	61.2387	2.86776
$457$	−38.1493	−1.78455	−0.892274	−	0.451495i	$-0.850891\pi$
$457$	−38.1493	−1.78455	−0.892274	+	0.451495i	$0.850891\pi$
$458$	−51.3763	−2.40065
$459$	26.4864	1.23628
$460$	27.1317	1.26502
$461$	−10.0760	−0.469285	−0.234643	−	0.972082i	$-0.575392\pi$
$461$	−10.0760	−0.469285	−0.234643	+	0.972082i	$0.575392\pi$
$462$	20.6894	0.962559
$463$	36.5276	1.69758	0.848792	−	0.528727i	$-0.177331\pi$
$463$	36.5276	1.69758	0.848792	+	0.528727i	$0.177331\pi$
$464$	6.46996	0.300361
$465$	43.0532	1.99655
$466$	−5.59993	−0.259412
$467$	14.4590	0.669084	0.334542	−	0.942381i	$-0.391418\pi$
$467$	14.4590	0.669084	0.334542	+	0.942381i	$0.391418\pi$
$468$	7.54344	0.348696
$469$	2.86518	0.132302
$470$	−20.2329	−0.933276
$471$	−16.9626	−0.781597
$472$	13.1569	0.605594
$473$	11.8818	0.546325
$474$	−80.6878	−3.70611
$475$	−0.00821990	−0.000377155 0
$476$	−120.466	−5.52157
$477$	−8.55498	−0.391706
$478$	50.7318	2.32042
$479$	10.5823	0.483518	0.241759	−	0.970336i	$-0.422276\pi$
$479$	10.5823	0.483518	0.241759	+	0.970336i	$0.422276\pi$
$480$	5.97247	0.272605
$481$	8.29610	0.378270
$482$	10.6592	0.485515
$483$	−24.5653	−1.11776
$484$	4.12769	0.187622
$485$	34.8013	1.58025
$486$	28.9918	1.31510
$487$	−9.80624	−0.444363	−0.222182	−	0.975005i	$-0.571318\pi$
$487$	−9.80624	−0.444363	−0.222182	+	0.975005i	$0.571318\pi$
$488$	−55.7979	−2.52585
$489$	−40.6283	−1.83727
$490$	53.5554	2.41939
$491$	11.8518	0.534864	0.267432	−	0.963577i	$-0.413825\pi$
$491$	11.8518	0.534864	0.267432	+	0.963577i	$0.413825\pi$
$492$	47.8142	2.15563
$493$	−9.66914	−0.435476
$494$	21.6045	0.972032
$495$	2.66013	0.119564
$496$	−44.9811	−2.01971
$497$	−29.6675	−1.33077
$498$	−13.6322	−0.610875
$499$	21.1263	0.945743	0.472872	−	0.881131i	$-0.343217\pi$
$499$	21.1263	0.945743	0.472872	+	0.881131i	$0.343217\pi$
$500$	46.1423	2.06355
$501$	−30.3180	−1.35451
$502$	33.7410	1.50593
$503$	20.1228	0.897229	0.448615	−	0.893725i	$-0.351918\pi$
$503$	20.1228	0.897229	0.448615	+	0.893725i	$0.351918\pi$
$504$	−25.5819	−1.13951
$505$	−16.6642	−0.741546
$506$	−7.27564	−0.323441
$507$	−21.7770	−0.967152
$508$	14.7079	0.652558
$509$	19.3165	0.856190	0.428095	−	0.903734i	$-0.359185\pi$
$509$	19.3165	0.856190	0.428095	+	0.903734i	$0.359185\pi$
$510$	−80.9868	−3.58616
$511$	−0.693023	−0.0306576
$512$	44.1380	1.95064
$513$	21.0510	0.929424
$514$	−60.5663	−2.67147
$515$	−16.3465	−0.720315
$516$	−100.385	−4.41920
$517$	3.65479	0.160738
$518$	−54.5802	−2.39812
$519$	29.8477	1.31017
$520$	18.0973	0.793617
$521$	−22.7586	−0.997071	−0.498535	−	0.866869i	$-0.666129\pi$
$521$	−22.7586	−0.997071	−0.498535	+	0.866869i	$0.666129\pi$
$522$	−3.98339	−0.174348
$523$	−2.69397	−0.117799	−0.0588995	−	0.998264i	$-0.518759\pi$
$523$	−2.69397	−0.117799	−0.0588995	+	0.998264i	$0.518759\pi$
$524$	−4.12769	−0.180319
$525$	0.0120942	0.000527836 0
$526$	−25.6251	−1.11731
$527$	67.2228	2.92827
$528$	−9.78886	−0.426005
$529$	−14.3614	−0.624407
$530$	−39.8163	−1.72951
$531$	−2.97132	−0.128944
$532$	−95.7449	−4.15107
$533$	8.69514	0.376628
$534$	−10.2583	−0.443918
$535$	−28.1835	−1.21848
$536$	−3.69564	−0.159627
$537$	−24.0049	−1.03589
$538$	−24.1737	−1.04220
$539$	−9.67401	−0.416689
$540$	34.2090	1.47212
$541$	−1.78123	−0.0765811	−0.0382906	−	0.999267i	$-0.512191\pi$
$541$	−1.78123	−0.0765811	−0.0382906	+	0.999267i	$0.512191\pi$
$542$	24.9335	1.07098
$543$	−39.6278	−1.70059
$544$	9.32534	0.399820
$545$	22.1783	0.950015
$546$	−31.7874	−1.36038
$547$	29.8802	1.27759	0.638794	−	0.769378i	$-0.279434\pi$
$547$	29.8802	1.27759	0.638794	+	0.769378i	$0.279434\pi$
$548$	−58.1790	−2.48529
$549$	12.6013	0.537810
$550$	0.00358201	0.000152737 0
$551$	−7.68489	−0.327388
$552$	31.6854	1.34862
$553$	65.0279	2.76527
$554$	2.60220	0.110557
$555$	−24.7169	−1.04918
$556$	−24.8108	−1.05221
$557$	35.0609	1.48558	0.742788	−	0.669526i	$-0.233503\pi$
$557$	35.0609	1.48558	0.742788	+	0.669526i	$0.233503\pi$
$558$	27.6937	1.17237
$559$	−18.2553	−0.772116
$560$	−43.6737	−1.84555
$561$	14.6291	0.617642
$562$	−2.25333	−0.0950510
$563$	27.5102	1.15942	0.579708	−	0.814825i	$-0.303167\pi$
$563$	27.5102	1.15942	0.579708	+	0.814825i	$0.303167\pi$
$564$	−30.8781	−1.30020
$565$	−33.5159	−1.41002
$566$	−23.1433	−0.972783
$567$	−45.5443	−1.91268
$568$	38.2665	1.60563
$569$	16.7451	0.701992	0.350996	−	0.936377i	$-0.385843\pi$
$569$	16.7451	0.701992	0.350996	+	0.936377i	$0.385843\pi$
$570$	−64.3672	−2.69604
$571$	−35.3621	−1.47986	−0.739929	−	0.672685i	$-0.765141\pi$
$571$	−35.3621	−1.47986	−0.739929	+	0.672685i	$0.765141\pi$
$572$	−6.34183	−0.265165
$573$	14.6424	0.611695
$574$	−57.2056	−2.38771
$575$	−0.00425305	−0.000177365 0
$576$	−7.53549	−0.313979
$577$	−22.4718	−0.935512	−0.467756	−	0.883858i	$-0.654937\pi$
$577$	−22.4718	−0.935512	−0.467756	+	0.883858i	$0.654937\pi$
$578$	−84.3697	−3.50932
$579$	11.1028	0.461417
$580$	−12.4883	−0.518550
$581$	10.9865	0.455797
$582$	78.8454	3.26825
$583$	7.19224	0.297872
$584$	0.893893	0.0369896
$585$	−4.08705	−0.168979
$586$	26.0495	1.07610
$587$	−17.3806	−0.717376	−0.358688	−	0.933458i	$-0.616776\pi$
$587$	−17.3806	−0.717376	−0.358688	+	0.933458i	$0.616776\pi$
$588$	81.7323	3.37059
$589$	53.4277	2.20145
$590$	−13.8290	−0.569332
$591$	10.8976	0.448267
$592$	25.8237	1.06135
$593$	19.5324	0.802099	0.401049	−	0.916056i	$-0.368646\pi$
$593$	19.5324	0.802099	0.401049	+	0.916056i	$0.368646\pi$
$594$	−9.17346	−0.376392
$595$	65.2689	2.67576
$596$	−2.17509	−0.0890950
$597$	−33.8917	−1.38710
$598$	11.1784	0.457117
$599$	−11.1811	−0.456846	−0.228423	−	0.973562i	$-0.573357\pi$
$599$	−11.1811	−0.456846	−0.228423	+	0.973562i	$0.573357\pi$
$600$	−0.0155997	−0.000636855 0
$601$	5.09932	0.208006	0.104003	−	0.994577i	$-0.466835\pi$
$601$	5.09932	0.208006	0.104003	+	0.994577i	$0.466835\pi$
$602$	120.102	4.89499
$603$	0.834617	0.0339882
$604$	13.2654	0.539762
$605$	−2.23639	−0.0909222
$606$	−37.7541	−1.53366
$607$	15.1525	0.615019	0.307510	−	0.951545i	$-0.400504\pi$
$607$	15.1525	0.615019	0.307510	+	0.951545i	$0.400504\pi$
$608$	7.41164	0.300582
$609$	11.3071	0.458185
$610$	58.6485	2.37461
$611$	−5.61526	−0.227169
$612$	−35.0914	−1.41849
$613$	34.3885	1.38894	0.694470	−	0.719522i	$-0.255639\pi$
$613$	34.3885	1.38894	0.694470	+	0.719522i	$0.255639\pi$
$614$	−84.3458	−3.40392
$615$	−25.9058	−1.04462
$616$	21.5069	0.866538
$617$	−41.4379	−1.66823	−0.834113	−	0.551594i	$-0.814020\pi$
$617$	−41.4379	−1.66823	−0.834113	+	0.551594i	$0.814020\pi$
$618$	−37.0345	−1.48975
$619$	35.2839	1.41818	0.709090	−	0.705118i	$-0.249106\pi$
$619$	35.2839	1.41818	0.709090	+	0.705118i	$0.249106\pi$
$620$	86.8227	3.48688
$621$	10.8920	0.437080
$622$	−49.6437	−1.99053
$623$	8.26733	0.331224
$624$	15.0397	0.602070
$625$	−25.0072	−1.00029
$626$	−72.6972	−2.90556
$627$	11.6270	0.464338
$628$	−34.2075	−1.36503
$629$	−38.5927	−1.53879
$630$	26.8888	1.07128
$631$	−25.1873	−1.00269	−0.501346	−	0.865247i	$-0.667162\pi$
$631$	−25.1873	−1.00269	−0.501346	+	0.865247i	$0.667162\pi$
$632$	−83.8759	−3.33641
$633$	−7.54631	−0.299939
$634$	−52.4504	−2.08307
$635$	−7.96877	−0.316231
$636$	−60.7647	−2.40948
$637$	14.8633	0.588903
$638$	3.34887	0.132583
$639$	−8.64203	−0.341874
$640$	−40.9072	−1.61700
$641$	−42.0474	−1.66077	−0.830386	−	0.557188i	$-0.811880\pi$
$641$	−42.0474	−1.66077	−0.830386	+	0.557188i	$0.811880\pi$
$642$	−63.8521	−2.52004
$643$	−15.5260	−0.612286	−0.306143	−	0.951986i	$-0.599039\pi$
$643$	−15.5260	−0.612286	−0.306143	+	0.951986i	$0.599039\pi$
$644$	−49.5393	−1.95212
$645$	54.3888	2.14156
$646$	−100.502	−3.95420
$647$	−27.6742	−1.08799	−0.543993	−	0.839090i	$-0.683088\pi$
$647$	−27.6742	−1.08799	−0.543993	+	0.839090i	$0.683088\pi$
$648$	58.7451	2.30773
$649$	2.49802	0.0980557
$650$	−0.00550344	−0.000215863 0
$651$	−78.6100	−3.08097
$652$	−81.9325	−3.20872
$653$	−21.8880	−0.856543	−0.428271	−	0.903650i	$-0.640877\pi$
$653$	−21.8880	−0.856543	−0.428271	+	0.903650i	$0.640877\pi$
$654$	50.2469	1.96481
$655$	2.23639	0.0873830
$656$	27.0659	1.05674
$657$	−0.201875	−0.00787590
$658$	36.9429	1.44019
$659$	−25.0969	−0.977635	−0.488817	−	0.872386i	$-0.662572\pi$
$659$	−25.0969	−0.977635	−0.488817	+	0.872386i	$0.662572\pi$
$660$	18.8945	0.735467
$661$	−4.92309	−0.191486	−0.0957430	−	0.995406i	$-0.530523\pi$
$661$	−4.92309	−0.191486	−0.0957430	+	0.995406i	$0.530523\pi$
$662$	45.0520	1.75100
$663$	−22.4763	−0.872908
$664$	−14.1709	−0.549937
$665$	51.8748	2.01162
$666$	−15.8990	−0.616074
$667$	−3.97624	−0.153960
$668$	−61.1404	−2.36559
$669$	24.5379	0.948689
$670$	3.88444	0.150069
$671$	−10.5940	−0.408977
$672$	−10.9050	−0.420670
$673$	28.2896	1.09048	0.545242	−	0.838279i	$-0.316438\pi$
$673$	28.2896	1.09048	0.545242	+	0.838279i	$0.316438\pi$
$674$	51.8629	1.99768
$675$	−0.00536245	−0.000206401 0
$676$	−43.9164	−1.68909
$677$	−15.9438	−0.612769	−0.306385	−	0.951908i	$-0.599119\pi$
$677$	−15.9438	−0.612769	−0.306385	+	0.951908i	$0.599119\pi$
$678$	−75.9331	−2.91619
$679$	−63.5431	−2.43856
$680$	−84.1868	−3.22842
$681$	−34.3863	−1.31769
$682$	−23.2823	−0.891527
$683$	2.32216	0.0888550	0.0444275	−	0.999013i	$-0.485854\pi$
$683$	2.32216	0.0888550	0.0444275	+	0.999013i	$0.485854\pi$
$684$	−27.8901	−1.06641
$685$	31.5215	1.20437
$686$	−27.0291	−1.03198
$687$	42.4809	1.62075
$688$	−56.8243	−2.16640
$689$	−11.0502	−0.420980
$690$	−33.3042	−1.26787
$691$	2.66193	0.101265	0.0506323	−	0.998717i	$-0.483876\pi$
$691$	2.66193	0.101265	0.0506323	+	0.998717i	$0.483876\pi$
$692$	60.1920	2.28816
$693$	−4.85708	−0.184505
$694$	74.8517	2.84133
$695$	13.4425	0.509904
$696$	−14.5844	−0.552818
$697$	−40.4490	−1.53212
$698$	88.9753	3.36776
$699$	4.63035	0.175136
$700$	0.0243897	0.000921843 0
$701$	10.7625	0.406495	0.203247	−	0.979127i	$-0.434850\pi$
$701$	10.7625	0.406495	0.203247	+	0.979127i	$0.434850\pi$
$702$	14.0942	0.531951
$703$	−30.6729	−1.15685
$704$	6.33515	0.238765
$705$	16.7298	0.630080
$706$	48.8803	1.83963
$707$	30.4268	1.14432
$708$	−21.1049	−0.793169
$709$	−45.3024	−1.70137	−0.850683	−	0.525679i	$-0.823811\pi$
$709$	−45.3024	−1.70137	−0.850683	+	0.525679i	$0.823811\pi$
$710$	−40.2214	−1.50948
$711$	18.9424	0.710395
$712$	−10.6636	−0.399634
$713$	27.6440	1.03528
$714$	147.872	5.53398
$715$	3.43601	0.128500
$716$	−48.4092	−1.80914
$717$	−41.9480	−1.56658
$718$	88.7824	3.31333
$719$	−25.1628	−0.938416	−0.469208	−	0.883088i	$-0.655460\pi$
$719$	−25.1628	−0.938416	−0.469208	+	0.883088i	$0.655460\pi$
$720$	−12.7220	−0.474120
$721$	29.8468	1.11155
$722$	−32.8447	−1.22235
$723$	−8.81368	−0.327784
$724$	−79.9148	−2.97001
$725$	0.00195762	7.27041e−5 0
$726$	−5.06674	−0.188044
$727$	−22.6608	−0.840443	−0.420221	−	0.907422i	$-0.638048\pi$
$727$	−22.6608	−0.840443	−0.420221	+	0.907422i	$0.638048\pi$
$728$	−33.0434	−1.22467
$729$	9.48857	0.351429
$730$	−0.939559	−0.0347746
$731$	84.9219	3.14095
$732$	89.5050	3.30820
$733$	18.0152	0.665406	0.332703	−	0.943032i	$-0.392039\pi$
$733$	18.0152	0.665406	0.332703	+	0.943032i	$0.392039\pi$
$734$	−64.5519	−2.38265
$735$	−44.2827	−1.63339
$736$	3.83485	0.141355
$737$	−0.701669	−0.0258463
$738$	−16.6638	−0.613402
$739$	7.88353	0.290000	0.145000	−	0.989432i	$-0.453682\pi$
$739$	7.88353	0.290000	0.145000	+	0.989432i	$0.453682\pi$
$740$	−49.8451	−1.83234
$741$	−17.8638	−0.656245
$742$	72.6997	2.66889
$743$	10.6495	0.390692	0.195346	−	0.980734i	$-0.437417\pi$
$743$	10.6495	0.390692	0.195346	+	0.980734i	$0.437417\pi$
$744$	101.395	3.71731
$745$	1.17847	0.0431757
$746$	2.37324	0.0868906
$747$	3.20032	0.117094
$748$	29.5016	1.07869
$749$	51.4597	1.88030
$750$	−56.6396	−2.06819
$751$	−31.6752	−1.15585	−0.577923	−	0.816092i	$-0.696136\pi$
$751$	−31.6752	−1.15585	−0.577923	+	0.816092i	$0.696136\pi$
$752$	−17.4789	−0.637391
$753$	−27.8990	−1.01670
$754$	−5.14524	−0.187378
$755$	−7.18723	−0.261570
$756$	−62.4615	−2.27170
$757$	10.9963	0.399669	0.199835	−	0.979830i	$-0.435960\pi$
$757$	10.9963	0.399669	0.199835	+	0.979830i	$0.435960\pi$
$758$	−60.6715	−2.20369
$759$	6.01592	0.218364
$760$	−66.9104	−2.42710
$761$	28.3464	1.02756	0.513779	−	0.857923i	$-0.328245\pi$
$761$	28.3464	1.02756	0.513779	+	0.857923i	$0.328245\pi$
$762$	−18.0539	−0.654025
$763$	−40.4950	−1.46602
$764$	29.5284	1.06830
$765$	19.0126	0.687401
$766$	49.6175	1.79275
$767$	−3.83798	−0.138581
$768$	−66.7450	−2.40845
$769$	−3.16152	−0.114007	−0.0570037	−	0.998374i	$-0.518155\pi$
$769$	−3.16152	−0.114007	−0.0570037	+	0.998374i	$0.518155\pi$
$770$	−22.6056	−0.814650
$771$	50.0798	1.80358
$772$	22.3903	0.805845
$773$	29.7840	1.07126	0.535628	−	0.844454i	$-0.320075\pi$
$773$	29.7840	1.07126	0.535628	+	0.844454i	$0.320075\pi$
$774$	34.9852	1.25752
$775$	−0.0136100	−0.000488884 0
$776$	81.9607	2.94222
$777$	45.1301	1.61903
$778$	21.1769	0.759228
$779$	−32.1483	−1.15183
$780$	−29.0297	−1.03943
$781$	7.26543	0.259977
$782$	−52.0007	−1.85954
$783$	−5.01342	−0.179165
$784$	46.2657	1.65235
$785$	18.5337	0.661495
$786$	5.06674	0.180724
$787$	47.2118	1.68292	0.841459	−	0.540320i	$-0.181697\pi$
$787$	47.2118	1.68292	0.841459	+	0.540320i	$0.181697\pi$
$788$	21.9765	0.782881
$789$	21.1883	0.754324
$790$	88.1609	3.13662
$791$	61.1960	2.17588
$792$	6.26488	0.222613
$793$	16.2767	0.578004
$794$	74.1495	2.63147
$795$	32.9224	1.16764
$796$	−68.3473	−2.42251
$797$	−4.64933	−0.164688	−0.0823438	−	0.996604i	$-0.526241\pi$
$797$	−4.64933	−0.164688	−0.0823438	+	0.996604i	$0.526241\pi$
$798$	117.527	4.16040
$799$	26.1217	0.924119
$800$	−0.00188801	−6.67513e−5 0
$801$	2.40824	0.0850910
$802$	14.4702	0.510960
$803$	0.169718	0.00598922
$804$	5.92815	0.209070
$805$	26.8405	0.946003
$806$	35.7712	1.25999
$807$	19.9882	0.703618
$808$	−39.2459	−1.38066
$809$	19.9137	0.700130	0.350065	−	0.936725i	$-0.386159\pi$
$809$	19.9137	0.700130	0.350065	+	0.936725i	$0.386159\pi$
$810$	−61.7462	−2.16954
$811$	−35.3358	−1.24081	−0.620404	−	0.784282i	$-0.713031\pi$
$811$	−35.3358	−1.24081	−0.620404	+	0.784282i	$0.713031\pi$
$812$	22.8022	0.800201
$813$	−20.6165	−0.723051
$814$	13.3664	0.468493
$815$	44.3912	1.55495
$816$	−69.9633	−2.44921
$817$	67.4947	2.36134
$818$	−42.8978	−1.49989
$819$	7.46246	0.260759
$820$	−52.2426	−1.82439
$821$	7.60758	0.265506	0.132753	−	0.991149i	$-0.457618\pi$
$821$	7.60758	0.265506	0.132753	+	0.991149i	$0.457618\pi$
$822$	71.4146	2.49087
$823$	−43.2855	−1.50884	−0.754420	−	0.656392i	$-0.772082\pi$
$823$	−43.2855	−1.50884	−0.754420	+	0.656392i	$0.772082\pi$
$824$	−38.4978	−1.34113
$825$	−0.00296182	−0.000103117 0
$826$	25.2501	0.878565
$827$	6.37604	0.221717	0.110858	−	0.993836i	$-0.464640\pi$
$827$	6.37604	0.221717	0.110858	+	0.993836i	$0.464640\pi$
$828$	−14.4306	−0.501498
$829$	33.6993	1.17043	0.585213	−	0.810880i	$-0.301011\pi$
$829$	33.6993	1.17043	0.585213	+	0.810880i	$0.301011\pi$
$830$	14.8948	0.517007
$831$	−2.15165	−0.0746398
$832$	−9.73338	−0.337444
$833$	−69.1425	−2.39565
$834$	30.4552	1.05458
$835$	33.1260	1.14637
$836$	23.4475	0.810947
$837$	34.8548	1.20476
$838$	−100.767	−3.48095
$839$	−16.2288	−0.560280	−0.280140	−	0.959959i	$-0.590381\pi$
$839$	−16.2288	−0.560280	−0.280140	+	0.959959i	$0.590381\pi$
$840$	98.4476	3.39677
$841$	−27.1698	−0.936890
$842$	2.07390	0.0714713
$843$	1.86319	0.0641715
$844$	−15.2182	−0.523831
$845$	23.7940	0.818537
$846$	10.7613	0.369982
$847$	4.08338	0.140307
$848$	−34.3967	−1.18119
$849$	19.1362	0.656753
$850$	0.0256015	0.000878124 0
$851$	−15.8705	−0.544032
$852$	−61.3830	−2.10295
$853$	−35.8347	−1.22696	−0.613478	−	0.789712i	$-0.710230\pi$
$853$	−35.8347	−1.22696	−0.613478	+	0.789712i	$0.710230\pi$
$854$	−107.085	−3.66438
$855$	15.1109	0.516783
$856$	−66.3750	−2.26865
$857$	−6.78075	−0.231626	−0.115813	−	0.993271i	$-0.536947\pi$
$857$	−6.78075	−0.231626	−0.115813	+	0.993271i	$0.536947\pi$
$858$	7.78458	0.265761
$859$	−41.4982	−1.41590	−0.707950	−	0.706262i	$-0.750380\pi$
$859$	−41.4982	−1.41590	−0.707950	+	0.706262i	$0.750380\pi$
$860$	109.682	3.74014
$861$	47.3009	1.61201
$862$	69.3392	2.36170
$863$	29.6213	1.00832	0.504160	−	0.863610i	$-0.331802\pi$
$863$	29.6213	1.00832	0.504160	+	0.863610i	$0.331802\pi$
$864$	4.83516	0.164495
$865$	−32.6121	−1.10885
$866$	−72.9428	−2.47870
$867$	69.7618	2.36924
$868$	−158.528	−5.38079
$869$	−15.9250	−0.540219
$870$	15.3294	0.519716
$871$	1.07805	0.0365284
$872$	52.2322	1.76881
$873$	−18.5098	−0.626463
$874$	−41.3294	−1.39799
$875$	45.6470	1.54315
$876$	−1.43389	−0.0484466
$877$	−5.56313	−0.187854	−0.0939268	−	0.995579i	$-0.529942\pi$
$877$	−5.56313	−0.187854	−0.0939268	+	0.995579i	$0.529942\pi$
$878$	−18.7773	−0.633703
$879$	−21.5393	−0.726501
$880$	10.6955	0.360544
$881$	0.759863	0.0256004	0.0128002	−	0.999918i	$-0.495925\pi$
$881$	0.759863	0.0256004	0.0128002	+	0.999918i	$0.495925\pi$
$882$	−28.4846	−0.959126
$883$	57.8555	1.94699	0.973496	−	0.228703i	$-0.0734486\pi$
$883$	57.8555	1.94699	0.973496	+	0.228703i	$0.0734486\pi$
$884$	−45.3266	−1.52450
$885$	11.4346	0.384371
$886$	22.7755	0.765159
$887$	−20.3111	−0.681981	−0.340991	−	0.940067i	$-0.610762\pi$
$887$	−20.3111	−0.681981	−0.340991	+	0.940067i	$0.610762\pi$
$888$	−58.2109	−1.95343
$889$	14.5500	0.487992
$890$	11.2083	0.375705
$891$	11.1536	0.373659
$892$	49.4840	1.65685
$893$	20.7611	0.694745
$894$	2.66992	0.0892953
$895$	26.2282	0.876711
$896$	74.6917	2.49527
$897$	−9.24292	−0.308612
$898$	−85.2696	−2.84548
$899$	−12.7241	−0.424373
$900$	0.00710462	0.000236821 0
$901$	51.4046	1.71254
$902$	14.0094	0.466461
$903$	−99.3074	−3.30474
$904$	−78.9333	−2.62528
$905$	43.2980	1.43927
$906$	−16.2833	−0.540976
$907$	21.4335	0.711686	0.355843	−	0.934546i	$-0.384194\pi$
$907$	21.4335	0.711686	0.355843	+	0.934546i	$0.384194\pi$
$908$	−69.3448	−2.30129
$909$	8.86321	0.293974
$910$	34.7315	1.15134
$911$	−45.2553	−1.49938	−0.749688	−	0.661792i	$-0.769796\pi$
$911$	−45.2553	−1.49938	−0.749688	+	0.661792i	$0.769796\pi$
$912$	−55.6058	−1.84129
$913$	−2.69054	−0.0890438
$914$	94.4354	3.12364
$915$	−48.4940	−1.60316
$916$	85.6685	2.83057
$917$	−4.08338	−0.134845
$918$	−65.5649	−2.16396
$919$	−37.6134	−1.24075	−0.620375	−	0.784305i	$-0.713020\pi$
$919$	−37.6134	−1.24075	−0.620375	+	0.784305i	$0.713020\pi$
$920$	−34.6201	−1.14139
$921$	69.7420	2.29808
$922$	24.9423	0.821430
$923$	−11.1627	−0.367424
$924$	−34.4991	−1.13494
$925$	0.00781349	0.000256906 0
$926$	−90.4212	−2.97142
$927$	8.69427	0.285557
$928$	−1.76513	−0.0579431
$929$	−21.4915	−0.705115	−0.352557	−	0.935790i	$-0.614688\pi$
$929$	−21.4915	−0.705115	−0.352557	+	0.935790i	$0.614688\pi$
$930$	−106.575	−3.49472
$931$	−54.9534	−1.80103
$932$	9.33773	0.305868
$933$	41.0483	1.34386
$934$	−35.7922	−1.17116
$935$	−15.9840	−0.522734
$936$	−9.62542	−0.314617
$937$	−3.00384	−0.0981312	−0.0490656	−	0.998796i	$-0.515624\pi$
$937$	−3.00384	−0.0981312	−0.0490656	+	0.998796i	$0.515624\pi$
$938$	−7.09253	−0.231579
$939$	60.1103	1.96163
$940$	33.7379	1.10041
$941$	−5.64458	−0.184008	−0.0920041	−	0.995759i	$-0.529327\pi$
$941$	−5.64458	−0.184008	−0.0920041	+	0.995759i	$0.529327\pi$
$942$	41.9896	1.36810
$943$	−16.6338	−0.541672
$944$	−11.9467	−0.388831
$945$	33.8417	1.10087
$946$	−29.4124	−0.956279
$947$	4.89322	0.159008	0.0795041	−	0.996835i	$-0.474666\pi$
$947$	4.89322	0.159008	0.0795041	+	0.996835i	$0.474666\pi$
$948$	134.545	4.36981
$949$	−0.260756	−0.00846451
$950$	0.0203477	0.000660166 0
$951$	43.3690	1.40634
$952$	153.715	4.98193
$953$	4.20546	0.136228	0.0681142	−	0.997678i	$-0.478302\pi$
$953$	4.20546	0.136228	0.0681142	+	0.997678i	$0.478302\pi$
$954$	21.1771	0.685635
$955$	−15.9985	−0.517700
$956$	−84.5940	−2.73596
$957$	−2.76904	−0.0895104
$958$	−26.1956	−0.846342
$959$	−57.5545	−1.85853
$960$	28.9991	0.935941
$961$	57.4619	1.85361
$962$	−20.5363	−0.662117
$963$	14.9900	0.483046
$964$	−17.7740	−0.572461
$965$	−12.1311	−0.390514
$966$	60.8094	1.95651
$967$	−44.3237	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$967$	−44.3237	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$968$	−5.26693	−0.169286
$969$	83.1010	2.66959
$970$	−86.1478	−2.76604
$971$	34.8494	1.11837	0.559186	−	0.829042i	$-0.311114\pi$
$971$	34.8494	1.11837	0.559186	+	0.829042i	$0.311114\pi$
$972$	−48.3431	−1.55061
$973$	−24.5444	−0.786858
$974$	24.2745	0.777806
$975$	0.00455056	0.000145735 0
$976$	50.6655	1.62176
$977$	−9.41151	−0.301101	−0.150550	−	0.988602i	$-0.548105\pi$
$977$	−9.41151	−0.301101	−0.150550	+	0.988602i	$0.548105\pi$
$978$	100.572	3.21594
$979$	−2.02463	−0.0647074
$980$	−89.3022	−2.85265
$981$	−11.7960	−0.376618
$982$	−29.3382	−0.936218
$983$	−26.4075	−0.842267	−0.421134	−	0.906999i	$-0.638368\pi$
$983$	−26.4075	−0.842267	−0.421134	+	0.906999i	$0.638368\pi$
$984$	−61.0109	−1.94495
$985$	−11.9069	−0.379386
$986$	23.9352	0.762251
$987$	−30.5466	−0.972308
$988$	−36.0249	−1.14610
$989$	34.9224	1.11047
$990$	−6.58493	−0.209283
$991$	−58.2438	−1.85017	−0.925087	−	0.379755i	$-0.876008\pi$
$991$	−58.2438	−1.85017	−0.925087	+	0.379755i	$0.876008\pi$
$992$	12.2717	0.389626
$993$	−37.2516	−1.18214
$994$	73.4395	2.32936
$995$	37.0307	1.17395
$996$	22.7314	0.720272
$997$	12.9566	0.410340	0.205170	−	0.978726i	$-0.434225\pi$
$997$	12.9566	0.410340	0.205170	+	0.978726i	$0.434225\pi$
$998$	−52.2964	−1.65541
$999$	−20.0102	−0.633095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.d.1.3	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.d.1.3	✓	23	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47542 q^{2} +2.04682 q^{3} +4.12769 q^{4} -2.23639 q^{5} -5.06674 q^{6} +4.08338 q^{7} -5.26693 q^{8} +1.18947 q^{9} +O(q^{10})\)	\(q-2.47542 q^{2} +2.04682 q^{3} +4.12769 q^{4} -2.23639 q^{5} -5.06674 q^{6} +4.08338 q^{7} -5.26693 q^{8} +1.18947 q^{9} +5.53600 q^{10} -1.00000 q^{11} +8.44865 q^{12} +1.53641 q^{13} -10.1081 q^{14} -4.57749 q^{15} +4.78247 q^{16} -7.14724 q^{17} -2.94444 q^{18} -5.68052 q^{19} -9.23114 q^{20} +8.35795 q^{21} +2.47542 q^{22} -2.93915 q^{23} -10.7805 q^{24} +0.00144703 q^{25} -3.80326 q^{26} -3.70582 q^{27} +16.8550 q^{28} +1.35285 q^{29} +11.3312 q^{30} -9.40542 q^{31} -1.30475 q^{32} -2.04682 q^{33} +17.6924 q^{34} -9.13204 q^{35} +4.90978 q^{36} +5.39967 q^{37} +14.0617 q^{38} +3.14476 q^{39} +11.7789 q^{40} +5.65939 q^{41} -20.6894 q^{42} -11.8818 q^{43} -4.12769 q^{44} -2.66013 q^{45} +7.27564 q^{46} -3.65479 q^{47} +9.78886 q^{48} +9.67401 q^{49} -0.00358201 q^{50} -14.6291 q^{51} +6.34183 q^{52} -7.19224 q^{53} +9.17346 q^{54} +2.23639 q^{55} -21.5069 q^{56} -11.6270 q^{57} -3.34887 q^{58} -2.49802 q^{59} -18.8945 q^{60} +10.5940 q^{61} +23.2823 q^{62} +4.85708 q^{63} -6.33515 q^{64} -3.43601 q^{65} +5.06674 q^{66} +0.701669 q^{67} -29.5016 q^{68} -6.01592 q^{69} +22.6056 q^{70} -7.26543 q^{71} -6.26488 q^{72} -0.169718 q^{73} -13.3664 q^{74} +0.00296182 q^{75} -23.4475 q^{76} -4.08338 q^{77} -7.78458 q^{78} +15.9250 q^{79} -10.6955 q^{80} -11.1536 q^{81} -14.0094 q^{82} +2.69054 q^{83} +34.4991 q^{84} +15.9840 q^{85} +29.4124 q^{86} +2.76904 q^{87} +5.26693 q^{88} +2.02463 q^{89} +6.58493 q^{90} +6.27375 q^{91} -12.1319 q^{92} -19.2512 q^{93} +9.04714 q^{94} +12.7039 q^{95} -2.67058 q^{96} -15.5614 q^{97} -23.9472 q^{98} -1.18947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

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