LMFDB - Embedded newform 1441.2.a.c.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.78830 q^{2} -0.518611 q^{3} +5.77463 q^{4} -0.346547 q^{5} +1.44605 q^{6} +3.25187 q^{7} -10.5248 q^{8} -2.73104 q^{9} +O(q^{10})$	\(q-2.78830 q^{2} -0.518611 q^{3} +5.77463 q^{4} -0.346547 q^{5} +1.44605 q^{6} +3.25187 q^{7} -10.5248 q^{8} -2.73104 q^{9} +0.966278 q^{10} +1.00000 q^{11} -2.99479 q^{12} -1.09715 q^{13} -9.06719 q^{14} +0.179723 q^{15} +17.7971 q^{16} +2.36128 q^{17} +7.61497 q^{18} +2.68319 q^{19} -2.00118 q^{20} -1.68646 q^{21} -2.78830 q^{22} -4.44527 q^{23} +5.45829 q^{24} -4.87991 q^{25} +3.05918 q^{26} +2.97218 q^{27} +18.7783 q^{28} -10.0939 q^{29} -0.501123 q^{30} -5.30514 q^{31} -28.5741 q^{32} -0.518611 q^{33} -6.58396 q^{34} -1.12693 q^{35} -15.7708 q^{36} +7.22400 q^{37} -7.48155 q^{38} +0.568994 q^{39} +3.64734 q^{40} -5.64960 q^{41} +4.70235 q^{42} -6.57558 q^{43} +5.77463 q^{44} +0.946435 q^{45} +12.3948 q^{46} +12.1120 q^{47} -9.22978 q^{48} +3.57464 q^{49} +13.6067 q^{50} -1.22459 q^{51} -6.33563 q^{52} +2.35724 q^{53} -8.28735 q^{54} -0.346547 q^{55} -34.2253 q^{56} -1.39153 q^{57} +28.1448 q^{58} -5.75015 q^{59} +1.03784 q^{60} -11.9507 q^{61} +14.7923 q^{62} -8.88099 q^{63} +44.0789 q^{64} +0.380214 q^{65} +1.44605 q^{66} +14.3325 q^{67} +13.6355 q^{68} +2.30537 q^{69} +3.14221 q^{70} +3.26351 q^{71} +28.7437 q^{72} -6.82510 q^{73} -20.1427 q^{74} +2.53077 q^{75} +15.4944 q^{76} +3.25187 q^{77} -1.58653 q^{78} +2.76132 q^{79} -6.16753 q^{80} +6.65172 q^{81} +15.7528 q^{82} +4.68744 q^{83} -9.73866 q^{84} -0.818294 q^{85} +18.3347 q^{86} +5.23481 q^{87} -10.5248 q^{88} +9.75197 q^{89} -2.63895 q^{90} -3.56778 q^{91} -25.6698 q^{92} +2.75131 q^{93} -33.7721 q^{94} -0.929853 q^{95} +14.8188 q^{96} -9.08439 q^{97} -9.96719 q^{98} -2.73104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * 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 $

$2$	−2.78830	−1.97163	−0.985814	−	0.167843i	$-0.946320\pi$
$2$	−2.78830	−1.97163	−0.985814	+	0.167843i	$0.946320\pi$
$3$	−0.518611	−0.299420	−0.149710	−	0.988730i	$-0.547834\pi$
$3$	−0.518611	−0.299420	−0.149710	+	0.988730i	$0.547834\pi$
$4$	5.77463	2.88732
$5$	−0.346547	−0.154981	−0.0774903	−	0.996993i	$-0.524691\pi$
$5$	−0.346547	−0.154981	−0.0774903	+	0.996993i	$0.524691\pi$
$6$	1.44605	0.590346
$7$	3.25187	1.22909	0.614545	−	0.788882i	$-0.289340\pi$
$7$	3.25187	1.22909	0.614545	+	0.788882i	$0.289340\pi$
$8$	−10.5248	−3.72108
$9$	−2.73104	−0.910347
$10$	0.966278	0.305564
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.99479	−0.864521
$13$	−1.09715	−0.304294	−0.152147	−	0.988358i	$-0.548619\pi$
$13$	−1.09715	−0.304294	−0.152147	+	0.988358i	$0.548619\pi$
$14$	−9.06719	−2.42331
$15$	0.179723	0.0464044
$16$	17.7971	4.44927
$17$	2.36128	0.572694	0.286347	−	0.958126i	$-0.407559\pi$
$17$	2.36128	0.572694	0.286347	+	0.958126i	$0.407559\pi$
$18$	7.61497	1.79487
$19$	2.68319	0.615567	0.307783	−	0.951456i	$-0.400413\pi$
$19$	2.68319	0.615567	0.307783	+	0.951456i	$0.400413\pi$
$20$	−2.00118	−0.447478
$21$	−1.68646	−0.368015
$22$	−2.78830	−0.594468
$23$	−4.44527	−0.926904	−0.463452	−	0.886122i	$-0.653389\pi$
$23$	−4.44527	−0.926904	−0.463452	+	0.886122i	$0.653389\pi$
$24$	5.45829	1.11417
$25$	−4.87991	−0.975981
$26$	3.05918	0.599955
$27$	2.97218	0.571997
$28$	18.7783	3.54877
$29$	−10.0939	−1.87439	−0.937194	−	0.348807i	$-0.886587\pi$
$29$	−10.0939	−1.87439	−0.937194	+	0.348807i	$0.886587\pi$
$30$	−0.501123	−0.0914921
$31$	−5.30514	−0.952831	−0.476416	−	0.879220i	$-0.658064\pi$
$31$	−5.30514	−0.952831	−0.476416	+	0.879220i	$0.658064\pi$
$32$	−28.5741	−5.05123
$33$	−0.518611	−0.0902787
$34$	−6.58396	−1.12914
$35$	−1.12693	−0.190485
$36$	−15.7708	−2.62846
$37$	7.22400	1.18762	0.593809	−	0.804606i	$-0.297623\pi$
$37$	7.22400	1.18762	0.593809	+	0.804606i	$0.297623\pi$
$38$	−7.48155	−1.21367
$39$	0.568994	0.0911120
$40$	3.64734	0.576696
$41$	−5.64960	−0.882319	−0.441159	−	0.897429i	$-0.645433\pi$
$41$	−5.64960	−0.882319	−0.441159	+	0.897429i	$0.645433\pi$
$42$	4.70235	0.725588
$43$	−6.57558	−1.00277	−0.501384	−	0.865225i	$-0.667175\pi$
$43$	−6.57558	−1.00277	−0.501384	+	0.865225i	$0.667175\pi$
$44$	5.77463	0.870558
$45$	0.946435	0.141086
$46$	12.3948	1.82751
$47$	12.1120	1.76672	0.883362	−	0.468691i	$-0.155274\pi$
$47$	12.1120	1.76672	0.883362	+	0.468691i	$0.155274\pi$
$48$	−9.22978	−1.33220
$49$	3.57464	0.510663
$50$	13.6067	1.92427
$51$	−1.22459	−0.171476
$52$	−6.33563	−0.878594
$53$	2.35724	0.323792	0.161896	−	0.986808i	$-0.448239\pi$
$53$	2.35724	0.323792	0.161896	+	0.986808i	$0.448239\pi$
$54$	−8.28735	−1.12777
$55$	−0.346547	−0.0467284
$56$	−34.2253	−4.57355
$57$	−1.39153	−0.184313
$58$	28.1448	3.69560
$59$	−5.75015	−0.748605	−0.374303	−	0.927307i	$-0.622118\pi$
$59$	−5.75015	−0.748605	−0.374303	+	0.927307i	$0.622118\pi$
$60$	1.03784	0.133984
$61$	−11.9507	−1.53013	−0.765063	−	0.643955i	$-0.777292\pi$
$61$	−11.9507	−1.53013	−0.765063	+	0.643955i	$0.777292\pi$
$62$	14.7923	1.87863
$63$	−8.88099	−1.11890
$64$	44.0789	5.50987
$65$	0.380214	0.0471597
$66$	1.44605	0.177996
$67$	14.3325	1.75100	0.875498	−	0.483221i	$-0.160533\pi$
$67$	14.3325	1.75100	0.875498	+	0.483221i	$0.160533\pi$
$68$	13.6355	1.65355
$69$	2.30537	0.277534
$70$	3.14221	0.375566
$71$	3.26351	0.387307	0.193654	−	0.981070i	$-0.437966\pi$
$71$	3.26351	0.387307	0.193654	+	0.981070i	$0.437966\pi$
$72$	28.7437	3.38748
$73$	−6.82510	−0.798818	−0.399409	−	0.916773i	$-0.630785\pi$
$73$	−6.82510	−0.798818	−0.399409	+	0.916773i	$0.630785\pi$
$74$	−20.1427	−2.34154
$75$	2.53077	0.292229
$76$	15.4944	1.77733
$77$	3.25187	0.370585
$78$	−1.58653	−0.179639
$79$	2.76132	0.310673	0.155337	−	0.987862i	$-0.450354\pi$
$79$	2.76132	0.310673	0.155337	+	0.987862i	$0.450354\pi$
$80$	−6.16753	−0.689551
$81$	6.65172	0.739080
$82$	15.7528	1.73960
$83$	4.68744	0.514514	0.257257	−	0.966343i	$-0.417181\pi$
$83$	4.68744	0.514514	0.257257	+	0.966343i	$0.417181\pi$
$84$	−9.73866	−1.06257
$85$	−0.818294	−0.0887565
$86$	18.3347	1.97708
$87$	5.23481	0.561230
$88$	−10.5248	−1.12195
$89$	9.75197	1.03371	0.516854	−	0.856074i	$-0.327103\pi$
$89$	9.75197	1.03371	0.516854	+	0.856074i	$0.327103\pi$
$90$	−2.63895	−0.278169
$91$	−3.56778	−0.374005
$92$	−25.6698	−2.67626
$93$	2.75131	0.285297
$94$	−33.7721	−3.48332
$95$	−0.929853	−0.0954009
$96$	14.8188	1.51244
$97$	−9.08439	−0.922380	−0.461190	−	0.887301i	$-0.652577\pi$
$97$	−9.08439	−0.922380	−0.461190	+	0.887301i	$0.652577\pi$
$98$	−9.96719	−1.00684
$99$	−2.73104	−0.274480
$100$	−28.1796	−2.81796
$101$	−14.5981	−1.45257	−0.726284	−	0.687395i	$-0.758754\pi$
$101$	−14.5981	−1.45257	−0.726284	+	0.687395i	$0.758754\pi$
$102$	3.41452	0.338087
$103$	−14.2708	−1.40615	−0.703073	−	0.711118i	$-0.748189\pi$
$103$	−14.2708	−1.40615	−0.703073	+	0.711118i	$0.748189\pi$
$104$	11.5473	1.13230
$105$	0.584436	0.0570352
$106$	−6.57270	−0.638398
$107$	−5.24914	−0.507454	−0.253727	−	0.967276i	$-0.581656\pi$
$107$	−5.24914	−0.507454	−0.253727	+	0.967276i	$0.581656\pi$
$108$	17.1633	1.65154
$109$	−9.07604	−0.869327	−0.434664	−	0.900593i	$-0.643133\pi$
$109$	−9.07604	−0.869327	−0.434664	+	0.900593i	$0.643133\pi$
$110$	0.966278	0.0921310
$111$	−3.74645	−0.355597
$112$	57.8738	5.46856
$113$	−12.3114	−1.15816	−0.579079	−	0.815271i	$-0.696588\pi$
$113$	−12.3114	−1.15816	−0.579079	+	0.815271i	$0.696588\pi$
$114$	3.88002	0.363397
$115$	1.54050	0.143652
$116$	−58.2885	−5.41195
$117$	2.99636	0.277014
$118$	16.0331	1.47597
$119$	7.67856	0.703893
$120$	−1.89155	−0.172674
$121$	1.00000	0.0909091
$122$	33.3221	3.01684
$123$	2.92995	0.264184
$124$	−30.6352	−2.75112
$125$	3.42385	0.306239
$126$	24.7629	2.20605
$127$	8.08051	0.717030	0.358515	−	0.933524i	$-0.383283\pi$
$127$	8.08051	0.717030	0.358515	+	0.933524i	$0.383283\pi$
$128$	−65.7573	−5.81217
$129$	3.41017	0.300249
$130$	−1.06015	−0.0929814
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.99479	−0.260663
$133$	8.72539	0.756587
$134$	−39.9634	−3.45231
$135$	−1.03000	−0.0886484
$136$	−24.8520	−2.13104
$137$	14.3263	1.22398	0.611990	−	0.790865i	$-0.290369\pi$
$137$	14.3263	1.22398	0.611990	+	0.790865i	$0.290369\pi$
$138$	−6.42807	−0.547194
$139$	18.2883	1.55120	0.775598	−	0.631228i	$-0.217449\pi$
$139$	18.2883	1.55120	0.775598	+	0.631228i	$0.217449\pi$
$140$	−6.50758	−0.549991
$141$	−6.28145	−0.528993
$142$	−9.09965	−0.763626
$143$	−1.09715	−0.0917482
$144$	−48.6046	−4.05038
$145$	3.49801	0.290494
$146$	19.0304	1.57497
$147$	−1.85385	−0.152903
$148$	41.7159	3.42903
$149$	−22.4051	−1.83549	−0.917747	−	0.397165i	$-0.869994\pi$
$149$	−22.4051	−1.83549	−0.917747	+	0.397165i	$0.869994\pi$
$150$	−7.05657	−0.576166
$151$	−5.29878	−0.431209	−0.215604	−	0.976481i	$-0.569172\pi$
$151$	−5.29878	−0.431209	−0.215604	+	0.976481i	$0.569172\pi$
$152$	−28.2401	−2.29057
$153$	−6.44875	−0.521351
$154$	−9.06719	−0.730655
$155$	1.83848	0.147670
$156$	3.28573	0.263069
$157$	1.81799	0.145091	0.0725457	−	0.997365i	$-0.476888\pi$
$157$	1.81799	0.145091	0.0725457	+	0.997365i	$0.476888\pi$
$158$	−7.69940	−0.612532
$159$	−1.22249	−0.0969500
$160$	9.90226	0.782842
$161$	−14.4554	−1.13925
$162$	−18.5470	−1.45719
$163$	−6.65388	−0.521172	−0.260586	−	0.965451i	$-0.583916\pi$
$163$	−6.65388	−0.521172	−0.260586	+	0.965451i	$0.583916\pi$
$164$	−32.6243	−2.54753
$165$	0.179723	0.0139914
$166$	−13.0700	−1.01443
$167$	−15.0408	−1.16389	−0.581945	−	0.813228i	$-0.697708\pi$
$167$	−15.0408	−1.16389	−0.581945	+	0.813228i	$0.697708\pi$
$168$	17.7496	1.36941
$169$	−11.7963	−0.907405
$170$	2.28165	0.174995
$171$	−7.32791	−0.560379
$172$	−37.9716	−2.89530
$173$	−1.74110	−0.132373	−0.0661867	−	0.997807i	$-0.521083\pi$
$173$	−1.74110	−0.132373	−0.0661867	+	0.997807i	$0.521083\pi$
$174$	−14.5962	−1.10654
$175$	−15.8688	−1.19957
$176$	17.7971	1.34151
$177$	2.98209	0.224148
$178$	−27.1915	−2.03809
$179$	−12.4139	−0.927861	−0.463931	−	0.885871i	$-0.653561\pi$
$179$	−12.4139	−0.927861	−0.463931	+	0.885871i	$0.653561\pi$
$180$	5.46531	0.407360
$181$	14.3657	1.06779	0.533896	−	0.845550i	$-0.320727\pi$
$181$	14.3657	1.06779	0.533896	+	0.845550i	$0.320727\pi$
$182$	9.94806	0.737399
$183$	6.19775	0.458151
$184$	46.7857	3.44909
$185$	−2.50346	−0.184058
$186$	−7.67147	−0.562500
$187$	2.36128	0.172674
$188$	69.9426	5.10109
$189$	9.66515	0.703036
$190$	2.59271	0.188095
$191$	1.16691	0.0844344	0.0422172	−	0.999108i	$-0.486558\pi$
$191$	1.16691	0.0844344	0.0422172	+	0.999108i	$0.486558\pi$
$192$	−22.8598	−1.64977
$193$	−15.8923	−1.14395	−0.571975	−	0.820271i	$-0.693823\pi$
$193$	−15.8923	−1.14395	−0.571975	+	0.820271i	$0.693823\pi$
$194$	25.3300	1.81859
$195$	−0.197183	−0.0141206
$196$	20.6422	1.47445
$197$	−1.15353	−0.0821855	−0.0410927	−	0.999155i	$-0.513084\pi$
$197$	−1.15353	−0.0821855	−0.0410927	+	0.999155i	$0.513084\pi$
$198$	7.61497	0.541172
$199$	−2.10238	−0.149034	−0.0745169	−	0.997220i	$-0.523741\pi$
$199$	−2.10238	−0.149034	−0.0745169	+	0.997220i	$0.523741\pi$
$200$	51.3601	3.63171
$201$	−7.43301	−0.524284
$202$	40.7040	2.86392
$203$	−32.8240	−2.30379
$204$	−7.07153	−0.495106
$205$	1.95785	0.136742
$206$	39.7914	2.77240
$207$	12.1402	0.843804
$208$	−19.5261	−1.35389
$209$	2.68319	0.185600
$210$	−1.62959	−0.112452
$211$	−11.7566	−0.809361	−0.404680	−	0.914458i	$-0.632617\pi$
$211$	−11.7566	−0.809361	−0.404680	+	0.914458i	$0.632617\pi$
$212$	13.6122	0.934890
$213$	−1.69249	−0.115968
$214$	14.6362	1.00051
$215$	2.27875	0.155409
$216$	−31.2817	−2.12845
$217$	−17.2516	−1.17112
$218$	25.3068	1.71399
$219$	3.53958	0.239182
$220$	−2.00118	−0.134920
$221$	−2.59067	−0.174268
$222$	10.4462	0.701105
$223$	−29.3592	−1.96604	−0.983020	−	0.183499i	$-0.941258\pi$
$223$	−29.3592	−1.96604	−0.983020	+	0.183499i	$0.941258\pi$
$224$	−92.9191	−6.20842
$225$	13.3272	0.888482
$226$	34.3279	2.28346
$227$	−11.3500	−0.753326	−0.376663	−	0.926350i	$-0.622928\pi$
$227$	−11.3500	−0.753326	−0.376663	+	0.926350i	$0.622928\pi$
$228$	−8.03560	−0.532170
$229$	−27.9435	−1.84656	−0.923279	−	0.384131i	$-0.874501\pi$
$229$	−27.9435	−1.84656	−0.923279	+	0.384131i	$0.874501\pi$
$230$	−4.29537	−0.283228
$231$	−1.68646	−0.110961
$232$	106.236	6.97476
$233$	10.1185	0.662885	0.331443	−	0.943475i	$-0.392465\pi$
$233$	10.1185	0.662885	0.331443	+	0.943475i	$0.392465\pi$
$234$	−8.35476	−0.546168
$235$	−4.19740	−0.273808
$236$	−33.2050	−2.16146
$237$	−1.43205	−0.0930219
$238$	−21.4102	−1.38781
$239$	2.11412	0.136751	0.0683756	−	0.997660i	$-0.478218\pi$
$239$	2.11412	0.136751	0.0683756	+	0.997660i	$0.478218\pi$
$240$	3.19855	0.206466
$241$	−9.01077	−0.580435	−0.290217	−	0.956961i	$-0.593728\pi$
$241$	−9.01077	−0.580435	−0.290217	+	0.956961i	$0.593728\pi$
$242$	−2.78830	−0.179239
$243$	−12.3662	−0.793293
$244$	−69.0107	−4.41796
$245$	−1.23878	−0.0791429
$246$	−8.16958	−0.520873
$247$	−2.94386	−0.187313
$248$	55.8356	3.54556
$249$	−2.43096	−0.154056
$250$	−9.54674	−0.603789
$251$	3.99311	0.252043	0.126022	−	0.992028i	$-0.459779\pi$
$251$	3.99311	0.252043	0.126022	+	0.992028i	$0.459779\pi$
$252$	−51.2844	−3.23061
$253$	−4.44527	−0.279472
$254$	−22.5309	−1.41372
$255$	0.424377	0.0265755
$256$	95.1933	5.94958
$257$	−13.4169	−0.836923	−0.418462	−	0.908235i	$-0.637431\pi$
$257$	−13.4169	−0.836923	−0.418462	+	0.908235i	$0.637431\pi$
$258$	−9.50859	−0.591979
$259$	23.4915	1.45969
$260$	2.19559	0.136165
$261$	27.5668	1.70634
$262$	−2.78830	−0.172262
$263$	19.1764	1.18247	0.591233	−	0.806501i	$-0.298641\pi$
$263$	19.1764	1.18247	0.591233	+	0.806501i	$0.298641\pi$
$264$	5.45829	0.335934
$265$	−0.816896	−0.0501815
$266$	−24.3290	−1.49171
$267$	−5.05749	−0.309513
$268$	82.7650	5.05568
$269$	−15.8518	−0.966503	−0.483251	−	0.875482i	$-0.660544\pi$
$269$	−15.8518	−0.966503	−0.483251	+	0.875482i	$0.660544\pi$
$270$	2.87196	0.174782
$271$	−6.54458	−0.397555	−0.198777	−	0.980045i	$-0.563697\pi$
$271$	−6.54458	−0.397555	−0.198777	+	0.980045i	$0.563697\pi$
$272$	42.0239	2.54807
$273$	1.85029	0.111985
$274$	−39.9461	−2.41323
$275$	−4.87991	−0.294269
$276$	13.3127	0.801328
$277$	7.19384	0.432236	0.216118	−	0.976367i	$-0.430660\pi$
$277$	7.19384	0.432236	0.216118	+	0.976367i	$0.430660\pi$
$278$	−50.9934	−3.05838
$279$	14.4886	0.867407
$280$	11.8607	0.708811
$281$	2.78859	0.166353	0.0831767	−	0.996535i	$-0.473493\pi$
$281$	2.78859	0.166353	0.0831767	+	0.996535i	$0.473493\pi$
$282$	17.5146	1.04298
$283$	20.4020	1.21277	0.606386	−	0.795171i	$-0.292619\pi$
$283$	20.4020	1.21277	0.606386	+	0.795171i	$0.292619\pi$
$284$	18.8456	1.11828
$285$	0.482232	0.0285650
$286$	3.05918	0.180893
$287$	−18.3717	−1.08445
$288$	78.0370	4.59837
$289$	−11.4244	−0.672022
$290$	−9.75351	−0.572746
$291$	4.71127	0.276179
$292$	−39.4124	−2.30644
$293$	25.3062	1.47841	0.739203	−	0.673482i	$-0.235202\pi$
$293$	25.3062	1.47841	0.739203	+	0.673482i	$0.235202\pi$
$294$	5.16910	0.301468
$295$	1.99270	0.116019
$296$	−76.0312	−4.41923
$297$	2.97218	0.172464
$298$	62.4721	3.61891
$299$	4.87713	0.282052
$300$	14.6143	0.843756
$301$	−21.3829	−1.23249
$302$	14.7746	0.850183
$303$	7.57075	0.434928
$304$	47.7530	2.73882
$305$	4.14147	0.237140
$306$	17.9811	1.02791
$307$	−30.0065	−1.71256	−0.856281	−	0.516510i	$-0.827231\pi$
$307$	−30.0065	−1.71256	−0.856281	+	0.516510i	$0.827231\pi$
$308$	18.7783	1.06999
$309$	7.40101	0.421029
$310$	−5.12624	−0.291151
$311$	−7.58565	−0.430143	−0.215071	−	0.976598i	$-0.568998\pi$
$311$	−7.58565	−0.430143	−0.215071	+	0.976598i	$0.568998\pi$
$312$	−5.98855	−0.339035
$313$	29.0392	1.64139	0.820695	−	0.571366i	$-0.193586\pi$
$313$	29.0392	1.64139	0.820695	+	0.571366i	$0.193586\pi$
$314$	−5.06911	−0.286066
$315$	3.07768	0.173408
$316$	15.9456	0.897011
$317$	6.32692	0.355355	0.177678	−	0.984089i	$-0.443142\pi$
$317$	6.32692	0.355355	0.177678	+	0.984089i	$0.443142\pi$
$318$	3.40868	0.191149
$319$	−10.0939	−0.565150
$320$	−15.2754	−0.853922
$321$	2.72227	0.151942
$322$	40.3062	2.24617
$323$	6.33576	0.352531
$324$	38.4112	2.13396
$325$	5.35398	0.296986
$326$	18.5530	1.02756
$327$	4.70694	0.260294
$328$	59.4609	3.28318
$329$	39.3868	2.17146
$330$	−0.501123	−0.0275859
$331$	−23.5959	−1.29695	−0.648473	−	0.761238i	$-0.724592\pi$
$331$	−23.5959	−1.29695	−0.648473	+	0.761238i	$0.724592\pi$
$332$	27.0682	1.48556
$333$	−19.7290	−1.08115
$334$	41.9382	2.29476
$335$	−4.96690	−0.271370
$336$	−30.0140	−1.63740
$337$	4.37708	0.238435	0.119217	−	0.992868i	$-0.461961\pi$
$337$	4.37708	0.238435	0.119217	+	0.992868i	$0.461961\pi$
$338$	32.8916	1.78906
$339$	6.38483	0.346776
$340$	−4.72535	−0.256268
$341$	−5.30514	−0.287289
$342$	20.4324	1.10486
$343$	−11.1388	−0.601439
$344$	69.2068	3.73138
$345$	−0.798919	−0.0430124
$346$	4.85472	0.260991
$347$	−15.5276	−0.833563	−0.416781	−	0.909007i	$-0.636842\pi$
$347$	−15.5276	−0.833563	−0.416781	+	0.909007i	$0.636842\pi$
$348$	30.2291	1.62045
$349$	13.6472	0.730517	0.365259	−	0.930906i	$-0.380981\pi$
$349$	13.6472	0.730517	0.365259	+	0.930906i	$0.380981\pi$
$350$	44.2470	2.36510
$351$	−3.26093	−0.174056
$352$	−28.5741	−1.52300
$353$	21.0612	1.12098	0.560488	−	0.828163i	$-0.310614\pi$
$353$	21.0612	1.12098	0.560488	+	0.828163i	$0.310614\pi$
$354$	−8.31497	−0.441936
$355$	−1.13096	−0.0600251
$356$	56.3140	2.98464
$357$	−3.98219	−0.210760
$358$	34.6138	1.82940
$359$	4.07521	0.215081	0.107541	−	0.994201i	$-0.465702\pi$
$359$	4.07521	0.215081	0.107541	+	0.994201i	$0.465702\pi$
$360$	−9.96105	−0.524993
$361$	−11.8005	−0.621078
$362$	−40.0558	−2.10529
$363$	−0.518611	−0.0272200
$364$	−20.6026	−1.07987
$365$	2.36522	0.123801
$366$	−17.2812	−0.903303
$367$	7.31301	0.381736	0.190868	−	0.981616i	$-0.438870\pi$
$367$	7.31301	0.381736	0.190868	+	0.981616i	$0.438870\pi$
$368$	−79.1130	−4.12405
$369$	15.4293	0.803217
$370$	6.98039	0.362893
$371$	7.66544	0.397970
$372$	15.8878	0.823743
$373$	33.6568	1.74268	0.871340	−	0.490679i	$-0.163251\pi$
$373$	33.6568	1.74268	0.871340	+	0.490679i	$0.163251\pi$
$374$	−6.58396	−0.340448
$375$	−1.77565	−0.0916941
$376$	−127.477	−6.57413
$377$	11.0745	0.570366
$378$	−26.9494	−1.38613
$379$	14.5706	0.748440	0.374220	−	0.927340i	$-0.377910\pi$
$379$	14.5706	0.748440	0.374220	+	0.927340i	$0.377910\pi$
$380$	−5.36956	−0.275452
$381$	−4.19065	−0.214693
$382$	−3.25369	−0.166473
$383$	−13.8951	−0.710008	−0.355004	−	0.934865i	$-0.615521\pi$
$383$	−13.8951	−0.710008	−0.355004	+	0.934865i	$0.615521\pi$
$384$	34.1025	1.74028
$385$	−1.12693	−0.0574334
$386$	44.3124	2.25544
$387$	17.9582	0.912866
$388$	−52.4590	−2.66320
$389$	0.795676	0.0403424	0.0201712	−	0.999797i	$-0.493579\pi$
$389$	0.795676	0.0403424	0.0201712	+	0.999797i	$0.493579\pi$
$390$	0.549807	0.0278405
$391$	−10.4965	−0.530832
$392$	−37.6224	−1.90022
$393$	−0.518611	−0.0261605
$394$	3.21638	0.162039
$395$	−0.956929	−0.0481483
$396$	−15.7708	−0.792510
$397$	−27.6499	−1.38771	−0.693854	−	0.720116i	$-0.744089\pi$
$397$	−27.6499	−1.38771	−0.693854	+	0.720116i	$0.744089\pi$
$398$	5.86207	0.293839
$399$	−4.52509	−0.226538
$400$	−86.8481	−4.34241
$401$	−4.35007	−0.217232	−0.108616	−	0.994084i	$-0.534642\pi$
$401$	−4.35007	−0.217232	−0.108616	+	0.994084i	$0.534642\pi$
$402$	20.7255	1.03369
$403$	5.82053	0.289941
$404$	−84.2988	−4.19402
$405$	−2.30513	−0.114543
$406$	91.5232	4.54222
$407$	7.22400	0.358080
$408$	12.8885	0.638078
$409$	−10.2939	−0.509000	−0.254500	−	0.967073i	$-0.581911\pi$
$409$	−10.2939	−0.509000	−0.254500	+	0.967073i	$0.581911\pi$
$410$	−5.45908	−0.269605
$411$	−7.42980	−0.366485
$412$	−82.4087	−4.05999
$413$	−18.6987	−0.920104
$414$	−33.8506	−1.66367
$415$	−1.62442	−0.0797396
$416$	31.3500	1.53706
$417$	−9.48453	−0.464460
$418$	−7.48155	−0.365935
$419$	17.4695	0.853443	0.426721	−	0.904383i	$-0.359668\pi$
$419$	17.4695	0.853443	0.426721	+	0.904383i	$0.359668\pi$
$420$	3.37490	0.164678
$421$	39.8660	1.94295	0.971475	−	0.237141i	$-0.0762105\pi$
$421$	39.8660	1.94295	0.971475	+	0.237141i	$0.0762105\pi$
$422$	32.7811	1.59576
$423$	−33.0785	−1.60833
$424$	−24.8095	−1.20486
$425$	−11.5228	−0.558939
$426$	4.71918	0.228645
$427$	−38.8620	−1.88066
$428$	−30.3119	−1.46518
$429$	0.568994	0.0274713
$430$	−6.35384	−0.306409
$431$	−8.39873	−0.404553	−0.202276	−	0.979328i	$-0.564834\pi$
$431$	−8.39873	−0.404553	−0.202276	+	0.979328i	$0.564834\pi$
$432$	52.8962	2.54497
$433$	−6.71118	−0.322519	−0.161259	−	0.986912i	$-0.551556\pi$
$433$	−6.71118	−0.322519	−0.161259	+	0.986912i	$0.551556\pi$
$434$	48.1027	2.30900
$435$	−1.81411	−0.0869798
$436$	−52.4108	−2.51002
$437$	−11.9275	−0.570571
$438$	−9.86941	−0.471578
$439$	−4.25933	−0.203287	−0.101643	−	0.994821i	$-0.532410\pi$
$439$	−4.25933	−0.203287	−0.101643	+	0.994821i	$0.532410\pi$
$440$	3.64734	0.173880
$441$	−9.76250	−0.464881
$442$	7.22358	0.343591
$443$	24.9756	1.18663	0.593314	−	0.804971i	$-0.297819\pi$
$443$	24.9756	1.18663	0.593314	+	0.804971i	$0.297819\pi$
$444$	−21.6344	−1.02672
$445$	−3.37952	−0.160205
$446$	81.8624	3.87630
$447$	11.6195	0.549585
$448$	143.339	6.77212
$449$	24.0965	1.13719	0.568593	−	0.822619i	$-0.307488\pi$
$449$	24.0965	1.13719	0.568593	+	0.822619i	$0.307488\pi$
$450$	−37.1603	−1.75176
$451$	−5.64960	−0.266029
$452$	−71.0938	−3.34397
$453$	2.74801	0.129113
$454$	31.6472	1.48528
$455$	1.23641	0.0579636
$456$	14.6456	0.685845
$457$	−20.8723	−0.976365	−0.488183	−	0.872741i	$-0.662340\pi$
$457$	−20.8723	−0.976365	−0.488183	+	0.872741i	$0.662340\pi$
$458$	77.9149	3.64072
$459$	7.01815	0.327579
$460$	8.89580	0.414769
$461$	−2.39503	−0.111548	−0.0557738	−	0.998443i	$-0.517763\pi$
$461$	−2.39503	−0.111548	−0.0557738	+	0.998443i	$0.517763\pi$
$462$	4.70235	0.218773
$463$	−11.5556	−0.537036	−0.268518	−	0.963275i	$-0.586534\pi$
$463$	−11.5556	−0.537036	−0.268518	+	0.963275i	$0.586534\pi$
$464$	−179.642	−8.33967
$465$	−0.953457	−0.0442155
$466$	−28.2135	−1.30696
$467$	14.1978	0.656995	0.328497	−	0.944505i	$-0.393458\pi$
$467$	14.1978	0.656995	0.328497	+	0.944505i	$0.393458\pi$
$468$	17.3029	0.799826
$469$	46.6075	2.15213
$470$	11.7036	0.539847
$471$	−0.942831	−0.0434433
$472$	60.5192	2.78562
$473$	−6.57558	−0.302346
$474$	3.99300	0.183405
$475$	−13.0937	−0.600781
$476$	44.3409	2.03236
$477$	−6.43773	−0.294763
$478$	−5.89481	−0.269622
$479$	−32.0497	−1.46439	−0.732194	−	0.681097i	$-0.761503\pi$
$479$	−32.0497	−1.46439	−0.732194	+	0.681097i	$0.761503\pi$
$480$	−5.13542	−0.234399
$481$	−7.92580	−0.361386
$482$	25.1247	1.14440
$483$	7.49676	0.341114
$484$	5.77463	0.262483
$485$	3.14817	0.142951
$486$	34.4807	1.56408
$487$	7.49720	0.339731	0.169865	−	0.985467i	$-0.445667\pi$
$487$	7.49720	0.339731	0.169865	+	0.985467i	$0.445667\pi$
$488$	125.779	5.69373
$489$	3.45078	0.156050
$490$	3.45410	0.156040
$491$	7.89500	0.356296	0.178148	−	0.984004i	$-0.442989\pi$
$491$	7.89500	0.356296	0.178148	+	0.984004i	$0.442989\pi$
$492$	16.9194	0.762783
$493$	−23.8345	−1.07345
$494$	8.20838	0.369312
$495$	0.946435	0.0425391
$496$	−94.4160	−4.23941
$497$	10.6125	0.476036
$498$	6.77825	0.303741
$499$	23.0394	1.03138	0.515692	−	0.856774i	$-0.327535\pi$
$499$	23.0394	1.03138	0.515692	+	0.856774i	$0.327535\pi$
$500$	19.7715	0.884208
$501$	7.80031	0.348492
$502$	−11.1340	−0.496935
$503$	27.7631	1.23789	0.618947	−	0.785433i	$-0.287560\pi$
$503$	27.7631	1.23789	0.618947	+	0.785433i	$0.287560\pi$
$504$	93.4707	4.16352
$505$	5.05894	0.225120
$506$	12.3948	0.551015
$507$	6.11768	0.271696
$508$	46.6620	2.07029
$509$	−22.3664	−0.991375	−0.495688	−	0.868501i	$-0.665084\pi$
$509$	−22.3664	−0.991375	−0.495688	+	0.868501i	$0.665084\pi$
$510$	−1.18329	−0.0523970
$511$	−22.1943	−0.981819
$512$	−133.913	−5.91818
$513$	7.97494	0.352102
$514$	37.4104	1.65010
$515$	4.94551	0.217925
$516$	19.6925	0.866913
$517$	12.1120	0.532687
$518$	−65.5014	−2.87797
$519$	0.902955	0.0396353
$520$	−4.00168	−0.175485
$521$	13.5691	0.594473	0.297236	−	0.954804i	$-0.403935\pi$
$521$	13.5691	0.594473	0.297236	+	0.954804i	$0.403935\pi$
$522$	−76.8647	−3.36428
$523$	−25.9224	−1.13351	−0.566754	−	0.823887i	$-0.691801\pi$
$523$	−25.9224	−1.13351	−0.566754	+	0.823887i	$0.691801\pi$
$524$	5.77463	0.252266
$525$	8.22974	0.359175
$526$	−53.4695	−2.33138
$527$	−12.5269	−0.545681
$528$	−9.22978	−0.401674
$529$	−3.23953	−0.140849
$530$	2.27775	0.0989392
$531$	15.7039	0.681491
$532$	50.3859	2.18451
$533$	6.19845	0.268485
$534$	14.1018	0.610245
$535$	1.81908	0.0786455
$536$	−150.847	−6.51560
$537$	6.43801	0.277821
$538$	44.1997	1.90558
$539$	3.57464	0.153971
$540$	−5.94788	−0.255956
$541$	20.8947	0.898332	0.449166	−	0.893448i	$-0.351721\pi$
$541$	20.8947	0.898332	0.449166	+	0.893448i	$0.351721\pi$
$542$	18.2483	0.783830
$543$	−7.45020	−0.319719
$544$	−67.4713	−2.89281
$545$	3.14528	0.134729
$546$	−5.15918	−0.220792
$547$	−1.87632	−0.0802256	−0.0401128	−	0.999195i	$-0.512772\pi$
$547$	−1.87632	−0.0802256	−0.0401128	+	0.999195i	$0.512772\pi$
$548$	82.7292	3.53402
$549$	32.6378	1.39295
$550$	13.6067	0.580190
$551$	−27.0839	−1.15381
$552$	−24.2636	−1.03273
$553$	8.97946	0.381845
$554$	−20.0586	−0.852208
$555$	1.29832	0.0551107
$556$	105.608	4.47879
$557$	10.1483	0.429997	0.214999	−	0.976614i	$-0.431025\pi$
$557$	10.1483	0.429997	0.214999	+	0.976614i	$0.431025\pi$
$558$	−40.3985	−1.71020
$559$	7.21439	0.305136
$560$	−20.0560	−0.847521
$561$	−1.22459	−0.0517021
$562$	−7.77543	−0.327987
$563$	0.339639	0.0143141	0.00715705	−	0.999974i	$-0.497722\pi$
$563$	0.339639	0.0143141	0.00715705	+	0.999974i	$0.497722\pi$
$564$	−36.2730	−1.52737
$565$	4.26648	0.179492
$566$	−56.8869	−2.39113
$567$	21.6305	0.908396
$568$	−34.3478	−1.44120
$569$	−14.5347	−0.609326	−0.304663	−	0.952460i	$-0.598544\pi$
$569$	−14.5347	−0.609326	−0.304663	+	0.952460i	$0.598544\pi$
$570$	−1.34461	−0.0563195
$571$	−38.3435	−1.60463	−0.802313	−	0.596904i	$-0.796397\pi$
$571$	−38.3435	−1.60463	−0.802313	+	0.596904i	$0.796397\pi$
$572$	−6.33563	−0.264906
$573$	−0.605171	−0.0252814
$574$	51.2260	2.13813
$575$	21.6925	0.904641
$576$	−120.381	−5.01589
$577$	17.7719	0.739855	0.369928	−	0.929061i	$-0.379382\pi$
$577$	17.7719	0.739855	0.369928	+	0.929061i	$0.379382\pi$
$578$	31.8546	1.32498
$579$	8.24191	0.342522
$580$	20.1997	0.838747
$581$	15.2429	0.632384
$582$	−13.1364	−0.544523
$583$	2.35724	0.0976270
$584$	71.8329	2.97247
$585$	−1.03838	−0.0429317
$586$	−70.5615	−2.91487
$587$	−29.3725	−1.21233	−0.606166	−	0.795339i	$-0.707293\pi$
$587$	−29.3725	−1.21233	−0.606166	+	0.795339i	$0.707293\pi$
$588$	−10.7053	−0.441479
$589$	−14.2347	−0.586531
$590$	−5.55624	−0.228747
$591$	0.598233	0.0246080
$592$	128.566	5.28404
$593$	−39.1998	−1.60974	−0.804871	−	0.593450i	$-0.797765\pi$
$593$	−39.1998	−1.60974	−0.804871	+	0.593450i	$0.797765\pi$
$594$	−8.28735	−0.340034
$595$	−2.66098	−0.109090
$596$	−129.381	−5.29965
$597$	1.09032	0.0446238
$598$	−13.5989	−0.556101
$599$	−36.3657	−1.48586	−0.742931	−	0.669368i	$-0.766565\pi$
$599$	−36.3657	−1.48586	−0.742931	+	0.669368i	$0.766565\pi$
$600$	−26.6359	−1.08741
$601$	3.28956	0.134184	0.0670919	−	0.997747i	$-0.478628\pi$
$601$	3.28956	0.134184	0.0670919	+	0.997747i	$0.478628\pi$
$602$	59.6221	2.43001
$603$	−39.1427	−1.59402
$604$	−30.5985	−1.24504
$605$	−0.346547	−0.0140891
$606$	−21.1096	−0.857517
$607$	20.9307	0.849551	0.424776	−	0.905299i	$-0.360353\pi$
$607$	20.9307	0.849551	0.424776	+	0.905299i	$0.360353\pi$
$608$	−76.6697	−3.10937
$609$	17.0229	0.689803
$610$	−11.5477	−0.467552
$611$	−13.2887	−0.537604
$612$	−37.2391	−1.50530
$613$	−25.6077	−1.03429	−0.517144	−	0.855899i	$-0.673005\pi$
$613$	−25.6077	−1.03429	−0.517144	+	0.855899i	$0.673005\pi$
$614$	83.6672	3.37654
$615$	−1.01536	−0.0409434
$616$	−34.2253	−1.37898
$617$	7.54214	0.303635	0.151818	−	0.988409i	$-0.451487\pi$
$617$	7.54214	0.303635	0.151818	+	0.988409i	$0.451487\pi$
$618$	−20.6363	−0.830112
$619$	38.6024	1.55156	0.775780	−	0.631003i	$-0.217357\pi$
$619$	38.6024	1.55156	0.775780	+	0.631003i	$0.217357\pi$
$620$	10.6165	0.426371
$621$	−13.2122	−0.530186
$622$	21.1511	0.848081
$623$	31.7121	1.27052
$624$	10.1264	0.405382
$625$	23.2130	0.928520
$626$	−80.9699	−3.23621
$627$	−1.39153	−0.0555725
$628$	10.4982	0.418925
$629$	17.0579	0.680142
$630$	−8.58150	−0.341895
$631$	21.4976	0.855806	0.427903	−	0.903825i	$-0.359252\pi$
$631$	21.4976	0.855806	0.427903	+	0.903825i	$0.359252\pi$
$632$	−29.0624	−1.15604
$633$	6.09713	0.242339
$634$	−17.6414	−0.700629
$635$	−2.80028	−0.111126
$636$	−7.05944	−0.279925
$637$	−3.92192	−0.155392
$638$	28.1448	1.11426
$639$	−8.91278	−0.352584
$640$	22.7880	0.900774
$641$	5.33056	0.210545	0.105272	−	0.994443i	$-0.466429\pi$
$641$	5.33056	0.210545	0.105272	+	0.994443i	$0.466429\pi$
$642$	−7.59050	−0.299573
$643$	−2.37394	−0.0936191	−0.0468096	−	0.998904i	$-0.514905\pi$
$643$	−2.37394	−0.0936191	−0.0468096	+	0.998904i	$0.514905\pi$
$644$	−83.4748	−3.28937
$645$	−1.18179	−0.0465328
$646$	−17.6660	−0.695060
$647$	−13.5529	−0.532821	−0.266411	−	0.963860i	$-0.585838\pi$
$647$	−13.5529	−0.532821	−0.266411	+	0.963860i	$0.585838\pi$
$648$	−70.0081	−2.75018
$649$	−5.75015	−0.225713
$650$	−14.9285	−0.585545
$651$	8.94688	0.350656
$652$	−38.4237	−1.50479
$653$	33.2105	1.29963	0.649813	−	0.760094i	$-0.274847\pi$
$653$	33.2105	1.29963	0.649813	+	0.760094i	$0.274847\pi$
$654$	−13.1244	−0.513204
$655$	−0.346547	−0.0135407
$656$	−100.546	−3.92568
$657$	18.6396	0.727202
$658$	−109.822	−4.28132
$659$	−28.5940	−1.11387	−0.556933	−	0.830558i	$-0.688022\pi$
$659$	−28.5940	−1.11387	−0.556933	+	0.830558i	$0.688022\pi$
$660$	1.03784	0.0403977
$661$	19.4259	0.755578	0.377789	−	0.925892i	$-0.376684\pi$
$661$	19.4259	0.755578	0.377789	+	0.925892i	$0.376684\pi$
$662$	65.7924	2.55709
$663$	1.34355	0.0521793
$664$	−49.3344	−1.91455
$665$	−3.02376	−0.117256
$666$	55.0105	2.13162
$667$	44.8701	1.73738
$668$	−86.8549	−3.36052
$669$	15.2260	0.588673
$670$	13.8492	0.535041
$671$	−11.9507	−0.461350
$672$	48.1889	1.85893
$673$	−1.47945	−0.0570285	−0.0285143	−	0.999593i	$-0.509078\pi$
$673$	−1.47945	−0.0570285	−0.0285143	+	0.999593i	$0.509078\pi$
$674$	−12.2046	−0.470105
$675$	−14.5040	−0.558258
$676$	−68.1191	−2.61996
$677$	19.5854	0.752728	0.376364	−	0.926472i	$-0.377174\pi$
$677$	19.5854	0.752728	0.376364	+	0.926472i	$0.377174\pi$
$678$	−17.8028	−0.683714
$679$	−29.5412	−1.13369
$680$	8.61239	0.330270
$681$	5.88624	0.225561
$682$	14.7923	0.566428
$683$	51.7437	1.97992	0.989960	−	0.141350i	$-0.0451444\pi$
$683$	51.7437	1.97992	0.989960	+	0.141350i	$0.0451444\pi$
$684$	−42.3160	−1.61799
$685$	−4.96475	−0.189693
$686$	31.0584	1.18581
$687$	14.4918	0.552897
$688$	−117.026	−4.46158
$689$	−2.58625	−0.0985281
$690$	2.22763	0.0848044
$691$	−15.6154	−0.594038	−0.297019	−	0.954872i	$-0.595992\pi$
$691$	−15.6154	−0.594038	−0.297019	+	0.954872i	$0.595992\pi$
$692$	−10.0542	−0.382204
$693$	−8.88099	−0.337361
$694$	43.2955	1.64348
$695$	−6.33777	−0.240405
$696$	−55.0954	−2.08838
$697$	−13.3403	−0.505299
$698$	−38.0525	−1.44031
$699$	−5.24757	−0.198481
$700$	−91.6365	−3.46353
$701$	52.5155	1.98348	0.991742	−	0.128249i	$-0.0409358\pi$
$701$	52.5155	1.98348	0.991742	+	0.128249i	$0.0409358\pi$
$702$	9.09246	0.343173
$703$	19.3834	0.731058
$704$	44.0789	1.66129
$705$	2.17682	0.0819837
$706$	−58.7251	−2.21015
$707$	−47.4712	−1.78534
$708$	17.2205	0.647185
$709$	31.0565	1.16635	0.583175	−	0.812347i	$-0.301810\pi$
$709$	31.0565	1.16635	0.583175	+	0.812347i	$0.301810\pi$
$710$	3.15346	0.118347
$711$	−7.54129	−0.282820
$712$	−102.638	−3.84651
$713$	23.5828	0.883183
$714$	11.1036	0.415540
$715$	0.380214	0.0142192
$716$	−71.6859	−2.67903
$717$	−1.09641	−0.0409461
$718$	−11.3629	−0.424060
$719$	34.8736	1.30056	0.650282	−	0.759693i	$-0.274651\pi$
$719$	34.8736	1.30056	0.650282	+	0.759693i	$0.274651\pi$
$720$	16.8438	0.627731
$721$	−46.4068	−1.72828
$722$	32.9033	1.22453
$723$	4.67309	0.173794
$724$	82.9564	3.08305
$725$	49.2572	1.82937
$726$	1.44605	0.0536678
$727$	−32.6953	−1.21260	−0.606301	−	0.795235i	$-0.707347\pi$
$727$	−32.6953	−1.21260	−0.606301	+	0.795235i	$0.707347\pi$
$728$	37.5502	1.39170
$729$	−13.5419	−0.501552
$730$	−6.59495	−0.244090
$731$	−15.5268	−0.574279
$732$	35.7897	1.32283
$733$	27.0808	1.00025	0.500126	−	0.865953i	$-0.333287\pi$
$733$	27.0808	1.00025	0.500126	+	0.865953i	$0.333287\pi$
$734$	−20.3909	−0.752641
$735$	0.642447	0.0236970
$736$	127.020	4.68200
$737$	14.3325	0.527945
$738$	−43.0215	−1.58364
$739$	13.9214	0.512107	0.256053	−	0.966663i	$-0.417578\pi$
$739$	13.9214	0.512107	0.256053	+	0.966663i	$0.417578\pi$
$740$	−14.4565	−0.531433
$741$	1.52672	0.0560855
$742$	−21.3736	−0.784648
$743$	2.06461	0.0757431	0.0378715	−	0.999283i	$-0.487942\pi$
$743$	2.06461	0.0757431	0.0378715	+	0.999283i	$0.487942\pi$
$744$	−28.9570	−1.06161
$745$	7.76441	0.284466
$746$	−93.8452	−3.43592
$747$	−12.8016	−0.468386
$748$	13.6355	0.498564
$749$	−17.0695	−0.623707
$750$	4.95105	0.180787
$751$	−36.3281	−1.32563	−0.662815	−	0.748783i	$-0.730638\pi$
$751$	−36.3281	−1.32563	−0.662815	+	0.748783i	$0.730638\pi$
$752$	215.559	7.86064
$753$	−2.07087	−0.0754669
$754$	−30.8791	−1.12455
$755$	1.83628	0.0668290
$756$	55.8127	2.02989
$757$	48.4791	1.76200	0.881001	−	0.473114i	$-0.156870\pi$
$757$	48.4791	1.76200	0.881001	+	0.473114i	$0.156870\pi$
$758$	−40.6272	−1.47565
$759$	2.30537	0.0836796
$760$	9.78652	0.354994
$761$	17.7784	0.644467	0.322233	−	0.946660i	$-0.395566\pi$
$761$	17.7784	0.644467	0.322233	+	0.946660i	$0.395566\pi$
$762$	11.6848	0.423295
$763$	−29.5141	−1.06848
$764$	6.73845	0.243789
$765$	2.23480	0.0807992
$766$	38.7438	1.39987
$767$	6.30877	0.227796
$768$	−49.3683	−1.78143
$769$	23.4236	0.844678	0.422339	−	0.906438i	$-0.361209\pi$
$769$	23.4236	0.844678	0.422339	+	0.906438i	$0.361209\pi$
$770$	3.14221	0.113237
$771$	6.95816	0.250592
$772$	−91.7720	−3.30294
$773$	16.2206	0.583415	0.291707	−	0.956508i	$-0.405777\pi$
$773$	16.2206	0.583415	0.291707	+	0.956508i	$0.405777\pi$
$774$	−50.0729	−1.79983
$775$	25.8886	0.929945
$776$	95.6115	3.43225
$777$	−12.1830	−0.437061
$778$	−2.21859	−0.0795402
$779$	−15.1590	−0.543126
$780$	−1.13866	−0.0407706
$781$	3.26351	0.116778
$782$	29.2675	1.04660
$783$	−30.0009	−1.07214
$784$	63.6183	2.27208
$785$	−0.630019	−0.0224864
$786$	1.44605	0.0515787
$787$	−1.47460	−0.0525638	−0.0262819	−	0.999655i	$-0.508367\pi$
$787$	−1.47460	−0.0525638	−0.0262819	+	0.999655i	$0.508367\pi$
$788$	−6.66120	−0.237295
$789$	−9.94509	−0.354054
$790$	2.66821	0.0949305
$791$	−40.0350	−1.42348
$792$	28.7437	1.02136
$793$	13.1117	0.465609
$794$	77.0962	2.73604
$795$	0.423651	0.0150254
$796$	−12.1405	−0.430307
$797$	9.01138	0.319199	0.159600	−	0.987182i	$-0.448980\pi$
$797$	9.01138	0.319199	0.159600	+	0.987182i	$0.448980\pi$
$798$	12.6173	0.446648
$799$	28.5999	1.01179
$800$	139.439	4.92990
$801$	−26.6331	−0.941033
$802$	12.1293	0.428301
$803$	−6.82510	−0.240853
$804$	−42.9229	−1.51377
$805$	5.00949	0.176561
$806$	−16.2294	−0.571656
$807$	8.22094	0.289391
$808$	153.642	5.40512
$809$	−21.1395	−0.743224	−0.371612	−	0.928388i	$-0.621195\pi$
$809$	−21.1395	−0.743224	−0.371612	+	0.928388i	$0.621195\pi$
$810$	6.42741	0.225836
$811$	46.1221	1.61957	0.809784	−	0.586728i	$-0.199584\pi$
$811$	46.1221	1.61957	0.809784	+	0.586728i	$0.199584\pi$
$812$	−189.546	−6.65178
$813$	3.39409	0.119036
$814$	−20.1427	−0.706001
$815$	2.30588	0.0807715
$816$	−21.7941	−0.762945
$817$	−17.6436	−0.617270
$818$	28.7025	1.00356
$819$	9.74377	0.340475
$820$	11.3059	0.394818
$821$	−6.76831	−0.236216	−0.118108	−	0.993001i	$-0.537683\pi$
$821$	−6.76831	−0.236216	−0.118108	+	0.993001i	$0.537683\pi$
$822$	20.7165	0.722572
$823$	−35.7114	−1.24482	−0.622411	−	0.782691i	$-0.713847\pi$
$823$	−35.7114	−1.24482	−0.622411	+	0.782691i	$0.713847\pi$
$824$	150.198	5.23238
$825$	2.53077	0.0881103
$826$	52.1377	1.81410
$827$	23.3360	0.811472	0.405736	−	0.913990i	$-0.367015\pi$
$827$	23.3360	0.811472	0.405736	+	0.913990i	$0.367015\pi$
$828$	70.1054	2.43633
$829$	−13.0852	−0.454467	−0.227234	−	0.973840i	$-0.572968\pi$
$829$	−13.0852	−0.454467	−0.227234	+	0.973840i	$0.572968\pi$
$830$	4.52937	0.157217
$831$	−3.73081	−0.129420
$832$	−48.3611	−1.67662
$833$	8.44073	0.292454
$834$	26.4457	0.915741
$835$	5.21233	0.180380
$836$	15.4944	0.535887
$837$	−15.7678	−0.545017
$838$	−48.7104	−1.68267
$839$	34.8466	1.20304	0.601519	−	0.798859i	$-0.294563\pi$
$839$	34.8466	1.20304	0.601519	+	0.798859i	$0.294563\pi$
$840$	−6.15108	−0.212233
$841$	72.8867	2.51333
$842$	−111.158	−3.83077
$843$	−1.44619	−0.0498096
$844$	−67.8903	−2.33688
$845$	4.08796	0.140630
$846$	92.2329	3.17103
$847$	3.25187	0.111735
$848$	41.9521	1.44064
$849$	−10.5807	−0.363129
$850$	32.1291	1.10202
$851$	−32.1127	−1.10081
$852$	−9.77352	−0.334835
$853$	21.5308	0.737200	0.368600	−	0.929588i	$-0.379837\pi$
$853$	21.5308	0.737200	0.368600	+	0.929588i	$0.379837\pi$
$854$	108.359	3.70797
$855$	2.53947	0.0868479
$856$	55.2462	1.88828
$857$	−43.7482	−1.49441	−0.747206	−	0.664593i	$-0.768605\pi$
$857$	−43.7482	−1.49441	−0.747206	+	0.664593i	$0.768605\pi$
$858$	−1.58653	−0.0541632
$859$	5.34278	0.182293	0.0911466	−	0.995837i	$-0.470947\pi$
$859$	5.34278	0.182293	0.0911466	+	0.995837i	$0.470947\pi$
$860$	13.1589	0.448716
$861$	9.52780	0.324706
$862$	23.4182	0.797627
$863$	6.02403	0.205060	0.102530	−	0.994730i	$-0.467306\pi$
$863$	6.02403	0.205060	0.102530	+	0.994730i	$0.467306\pi$
$864$	−84.9274	−2.88929
$865$	0.603374	0.0205153
$866$	18.7128	0.635887
$867$	5.92481	0.201217
$868$	−99.6217	−3.38138
$869$	2.76132	0.0936715
$870$	5.05828	0.171492
$871$	−15.7249	−0.532818
$872$	95.5236	3.23484
$873$	24.8099	0.839686
$874$	33.2576	1.12495
$875$	11.1339	0.376395
$876$	20.4397	0.690595
$877$	1.21981	0.0411900	0.0205950	−	0.999788i	$-0.493444\pi$
$877$	1.21981	0.0411900	0.0205950	+	0.999788i	$0.493444\pi$
$878$	11.8763	0.400805
$879$	−13.1241	−0.442665
$880$	−6.16753	−0.207907
$881$	−3.53887	−0.119228	−0.0596138	−	0.998222i	$-0.518987\pi$
$881$	−3.53887	−0.119228	−0.0596138	+	0.998222i	$0.518987\pi$
$882$	27.2208	0.916572
$883$	−47.9516	−1.61370	−0.806850	−	0.590756i	$-0.798830\pi$
$883$	−47.9516	−1.61370	−0.806850	+	0.590756i	$0.798830\pi$
$884$	−14.9602	−0.503165
$885$	−1.03344	−0.0347386
$886$	−69.6396	−2.33959
$887$	−29.5586	−0.992481	−0.496240	−	0.868185i	$-0.665287\pi$
$887$	−29.5586	−0.992481	−0.496240	+	0.868185i	$0.665287\pi$
$888$	39.4307	1.32321
$889$	26.2768	0.881294
$890$	9.42312	0.315864
$891$	6.65172	0.222841
$892$	−169.539	−5.67658
$893$	32.4990	1.08754
$894$	−32.3988	−1.08358
$895$	4.30202	0.143801
$896$	−213.834	−7.14369
$897$	−2.52933	−0.0844520
$898$	−67.1885	−2.24211
$899$	53.5495	1.78598
$900$	76.9598	2.56533
$901$	5.56610	0.185434
$902$	15.7528	0.524510
$903$	11.0894	0.369033
$904$	129.575	4.30960
$905$	−4.97838	−0.165487
$906$	−7.66228	−0.254562
$907$	−19.2962	−0.640721	−0.320360	−	0.947296i	$-0.603804\pi$
$907$	−19.2962	−0.640721	−0.320360	+	0.947296i	$0.603804\pi$
$908$	−65.5420	−2.17509
$909$	39.8681	1.32234
$910$	−3.44747	−0.114283
$911$	−6.89259	−0.228362	−0.114181	−	0.993460i	$-0.536424\pi$
$911$	−6.89259	−0.228362	−0.114181	+	0.993460i	$0.536424\pi$
$912$	−24.7653	−0.820060
$913$	4.68744	0.155132
$914$	58.1983	1.92503
$915$	−2.14781	−0.0710045
$916$	−161.363	−5.33159
$917$	3.25187	0.107386
$918$	−19.5687	−0.645864
$919$	−37.9682	−1.25246	−0.626228	−	0.779640i	$-0.715402\pi$
$919$	−37.9682	−1.25246	−0.626228	+	0.779640i	$0.715402\pi$
$920$	−16.2134	−0.534541
$921$	15.5617	0.512776
$922$	6.67806	0.219930
$923$	−3.58056	−0.117855
$924$	−9.73866	−0.320378
$925$	−35.2524	−1.15909
$926$	32.2206	1.05883
$927$	38.9742	1.28008
$928$	288.423	9.46796
$929$	−51.6127	−1.69336	−0.846678	−	0.532105i	$-0.821401\pi$
$929$	−51.6127	−1.69336	−0.846678	+	0.532105i	$0.821401\pi$
$930$	2.65853	0.0871765
$931$	9.59146	0.314347
$932$	58.4306	1.91396
$933$	3.93401	0.128794
$934$	−39.5877	−1.29535
$935$	−0.818294	−0.0267611
$936$	−31.5361	−1.03079
$937$	57.1363	1.86656	0.933281	−	0.359148i	$-0.116933\pi$
$937$	57.1363	1.86656	0.933281	+	0.359148i	$0.116933\pi$
$938$	−129.956	−4.24320
$939$	−15.0600	−0.491466
$940$	−24.2384	−0.790570
$941$	−1.40676	−0.0458590	−0.0229295	−	0.999737i	$-0.507299\pi$
$941$	−1.40676	−0.0458590	−0.0229295	+	0.999737i	$0.507299\pi$
$942$	2.62890	0.0856541
$943$	25.1140	0.817825
$944$	−102.336	−3.33075
$945$	−3.34943	−0.108957
$946$	18.3347	0.596113
$947$	3.76555	0.122364	0.0611820	−	0.998127i	$-0.480513\pi$
$947$	3.76555	0.122364	0.0611820	+	0.998127i	$0.480513\pi$
$948$	−8.26958	−0.268584
$949$	7.48815	0.243076
$950$	36.5093	1.18452
$951$	−3.28122	−0.106401
$952$	−80.8154	−2.61924
$953$	−36.0223	−1.16688	−0.583438	−	0.812158i	$-0.698293\pi$
$953$	−36.0223	−1.16688	−0.583438	+	0.812158i	$0.698293\pi$
$954$	17.9503	0.581164
$955$	−0.404388	−0.0130857
$956$	12.2083	0.394844
$957$	5.23481	0.169217
$958$	89.3642	2.88723
$959$	46.5873	1.50438
$960$	7.92201	0.255682
$961$	−2.85551	−0.0921131
$962$	22.0995	0.712518
$963$	14.3356	0.461959
$964$	−52.0338	−1.67590
$965$	5.50742	0.177290
$966$	−20.9032	−0.672550
$967$	18.1512	0.583704	0.291852	−	0.956464i	$-0.405729\pi$
$967$	18.1512	0.583704	0.291852	+	0.956464i	$0.405729\pi$
$968$	−10.5248	−0.338280
$969$	−3.28580	−0.105555
$970$	−8.77805	−0.281846
$971$	38.5138	1.23597	0.617984	−	0.786191i	$-0.287950\pi$
$971$	38.5138	1.23597	0.617984	+	0.786191i	$0.287950\pi$
$972$	−71.4103	−2.29049
$973$	59.4712	1.90656
$974$	−20.9045	−0.669822
$975$	−2.77664	−0.0889236
$976$	−212.687	−6.80795
$977$	26.8641	0.859459	0.429729	−	0.902958i	$-0.358609\pi$
$977$	26.8641	0.859459	0.429729	+	0.902958i	$0.358609\pi$
$978$	−9.62181	−0.307672
$979$	9.75197	0.311674
$980$	−7.15351	−0.228511
$981$	24.7871	0.791390
$982$	−22.0136	−0.702483
$983$	39.6723	1.26535	0.632676	−	0.774417i	$-0.281957\pi$
$983$	39.6723	1.26535	0.632676	+	0.774417i	$0.281957\pi$
$984$	−30.8371	−0.983052
$985$	0.399752	0.0127372
$986$	66.4578	2.11645
$987$	−20.4264	−0.650181
$988$	−16.9997	−0.540833
$989$	29.2303	0.929469
$990$	−2.63895	−0.0838712
$991$	−38.1571	−1.21210	−0.606050	−	0.795427i	$-0.707247\pi$
$991$	−38.1571	−1.21210	−0.606050	+	0.795427i	$0.707247\pi$
$992$	151.589	4.81297
$993$	12.2371	0.388332
$994$	−29.5909	−0.938565
$995$	0.728574	0.0230973
$996$	−14.0379	−0.444808
$997$	41.1658	1.30374	0.651868	−	0.758333i	$-0.273986\pi$
$997$	41.1658	1.30374	0.651868	+	0.758333i	$0.273986\pi$
$998$	−64.2407	−2.03350
$999$	21.4711	0.679314

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.78830 q^{2} -0.518611 q^{3} +5.77463 q^{4} -0.346547 q^{5} +1.44605 q^{6} +3.25187 q^{7} -10.5248 q^{8} -2.73104 q^{9} +O(q^{10})\)	\(q-2.78830 q^{2} -0.518611 q^{3} +5.77463 q^{4} -0.346547 q^{5} +1.44605 q^{6} +3.25187 q^{7} -10.5248 q^{8} -2.73104 q^{9} +0.966278 q^{10} +1.00000 q^{11} -2.99479 q^{12} -1.09715 q^{13} -9.06719 q^{14} +0.179723 q^{15} +17.7971 q^{16} +2.36128 q^{17} +7.61497 q^{18} +2.68319 q^{19} -2.00118 q^{20} -1.68646 q^{21} -2.78830 q^{22} -4.44527 q^{23} +5.45829 q^{24} -4.87991 q^{25} +3.05918 q^{26} +2.97218 q^{27} +18.7783 q^{28} -10.0939 q^{29} -0.501123 q^{30} -5.30514 q^{31} -28.5741 q^{32} -0.518611 q^{33} -6.58396 q^{34} -1.12693 q^{35} -15.7708 q^{36} +7.22400 q^{37} -7.48155 q^{38} +0.568994 q^{39} +3.64734 q^{40} -5.64960 q^{41} +4.70235 q^{42} -6.57558 q^{43} +5.77463 q^{44} +0.946435 q^{45} +12.3948 q^{46} +12.1120 q^{47} -9.22978 q^{48} +3.57464 q^{49} +13.6067 q^{50} -1.22459 q^{51} -6.33563 q^{52} +2.35724 q^{53} -8.28735 q^{54} -0.346547 q^{55} -34.2253 q^{56} -1.39153 q^{57} +28.1448 q^{58} -5.75015 q^{59} +1.03784 q^{60} -11.9507 q^{61} +14.7923 q^{62} -8.88099 q^{63} +44.0789 q^{64} +0.380214 q^{65} +1.44605 q^{66} +14.3325 q^{67} +13.6355 q^{68} +2.30537 q^{69} +3.14221 q^{70} +3.26351 q^{71} +28.7437 q^{72} -6.82510 q^{73} -20.1427 q^{74} +2.53077 q^{75} +15.4944 q^{76} +3.25187 q^{77} -1.58653 q^{78} +2.76132 q^{79} -6.16753 q^{80} +6.65172 q^{81} +15.7528 q^{82} +4.68744 q^{83} -9.73866 q^{84} -0.818294 q^{85} +18.3347 q^{86} +5.23481 q^{87} -10.5248 q^{88} +9.75197 q^{89} -2.63895 q^{90} -3.56778 q^{91} -25.6698 q^{92} +2.75131 q^{93} -33.7721 q^{94} -0.929853 q^{95} +14.8188 q^{96} -9.08439 q^{97} -9.96719 q^{98} -2.73104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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