LMFDB - Embedded newform 1441.2.a.d.1.12

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			1.12
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.265643 q^{2} -2.11945 q^{3} -1.92943 q^{4} +2.15570 q^{5} +0.563016 q^{6} -4.44888 q^{7} +1.04383 q^{8} +1.49206 q^{9} +O(q^{10})$	\(q-0.265643 q^{2} -2.11945 q^{3} -1.92943 q^{4} +2.15570 q^{5} +0.563016 q^{6} -4.44888 q^{7} +1.04383 q^{8} +1.49206 q^{9} -0.572646 q^{10} -1.00000 q^{11} +4.08933 q^{12} +5.07313 q^{13} +1.18181 q^{14} -4.56889 q^{15} +3.58158 q^{16} +3.31284 q^{17} -0.396354 q^{18} +3.75957 q^{19} -4.15928 q^{20} +9.42917 q^{21} +0.265643 q^{22} -1.96478 q^{23} -2.21233 q^{24} -0.352960 q^{25} -1.34764 q^{26} +3.19600 q^{27} +8.58383 q^{28} -2.10371 q^{29} +1.21369 q^{30} -5.72997 q^{31} -3.03907 q^{32} +2.11945 q^{33} -0.880032 q^{34} -9.59046 q^{35} -2.87883 q^{36} +2.73849 q^{37} -0.998703 q^{38} -10.7522 q^{39} +2.25018 q^{40} +0.563090 q^{41} -2.50479 q^{42} -12.0123 q^{43} +1.92943 q^{44} +3.21643 q^{45} +0.521930 q^{46} +6.72427 q^{47} -7.59098 q^{48} +12.7926 q^{49} +0.0937612 q^{50} -7.02139 q^{51} -9.78828 q^{52} +8.79541 q^{53} -0.848996 q^{54} -2.15570 q^{55} -4.64386 q^{56} -7.96821 q^{57} +0.558834 q^{58} -4.15057 q^{59} +8.81537 q^{60} -1.81657 q^{61} +1.52213 q^{62} -6.63799 q^{63} -6.35586 q^{64} +10.9362 q^{65} -0.563016 q^{66} -8.21913 q^{67} -6.39190 q^{68} +4.16425 q^{69} +2.54764 q^{70} +6.12397 q^{71} +1.55745 q^{72} -15.4026 q^{73} -0.727461 q^{74} +0.748080 q^{75} -7.25384 q^{76} +4.44888 q^{77} +2.85626 q^{78} +12.9950 q^{79} +7.72082 q^{80} -11.2499 q^{81} -0.149581 q^{82} -16.0358 q^{83} -18.1930 q^{84} +7.14148 q^{85} +3.19098 q^{86} +4.45869 q^{87} -1.04383 q^{88} -15.2228 q^{89} -0.854421 q^{90} -22.5698 q^{91} +3.79091 q^{92} +12.1444 q^{93} -1.78626 q^{94} +8.10450 q^{95} +6.44116 q^{96} -10.6652 q^{97} -3.39825 q^{98} -1.49206 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.265643	−0.187838	−0.0939189	−	0.995580i	$-0.529939\pi$
$2$	−0.265643	−0.187838	−0.0939189	+	0.995580i	$0.529939\pi$
$3$	−2.11945	−1.22366	−0.611832	−	0.790988i	$-0.709567\pi$
$3$	−2.11945	−1.22366	−0.611832	+	0.790988i	$0.709567\pi$
$4$	−1.92943	−0.964717
$5$	2.15570	0.964058	0.482029	−	0.876155i	$-0.339900\pi$
$5$	2.15570	0.964058	0.482029	+	0.876155i	$0.339900\pi$
$6$	0.563016	0.229850
$7$	−4.44888	−1.68152	−0.840760	−	0.541408i	$-0.817891\pi$
$7$	−4.44888	−1.68152	−0.840760	+	0.541408i	$0.817891\pi$
$8$	1.04383	0.369048
$9$	1.49206	0.497352
$10$	−0.572646	−0.181087
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.08933	1.18049
$13$	5.07313	1.40703	0.703517	−	0.710678i	$-0.251612\pi$
$13$	5.07313	1.40703	0.703517	+	0.710678i	$0.251612\pi$
$14$	1.18181	0.315853
$15$	−4.56889	−1.17968
$16$	3.58158	0.895396
$17$	3.31284	0.803481	0.401741	−	0.915753i	$-0.368405\pi$
$17$	3.31284	0.803481	0.401741	+	0.915753i	$0.368405\pi$
$18$	−0.396354	−0.0934216
$19$	3.75957	0.862504	0.431252	−	0.902231i	$-0.358072\pi$
$19$	3.75957	0.862504	0.431252	+	0.902231i	$0.358072\pi$
$20$	−4.15928	−0.930043
$21$	9.42917	2.05761
$22$	0.265643	0.0566353
$23$	−1.96478	−0.409685	−0.204843	−	0.978795i	$-0.565668\pi$
$23$	−1.96478	−0.409685	−0.204843	+	0.978795i	$0.565668\pi$
$24$	−2.21233	−0.451591
$25$	−0.352960	−0.0705919
$26$	−1.34764	−0.264294
$27$	3.19600	0.615071
$28$	8.58383	1.62219
$29$	−2.10371	−0.390648	−0.195324	−	0.980739i	$-0.562576\pi$
$29$	−2.10371	−0.390648	−0.195324	+	0.980739i	$0.562576\pi$
$30$	1.21369	0.221589
$31$	−5.72997	−1.02913	−0.514567	−	0.857450i	$-0.672047\pi$
$31$	−5.72997	−1.02913	−0.514567	+	0.857450i	$0.672047\pi$
$32$	−3.03907	−0.537238
$33$	2.11945	0.368948
$34$	−0.880032	−0.150924
$35$	−9.59046	−1.62108
$36$	−2.87883	−0.479804
$37$	2.73849	0.450205	0.225103	−	0.974335i	$-0.427728\pi$
$37$	2.73849	0.450205	0.225103	+	0.974335i	$0.427728\pi$
$38$	−0.998703	−0.162011
$39$	−10.7522	−1.72174
$40$	2.25018	0.355784
$41$	0.563090	0.0879399	0.0439700	−	0.999033i	$-0.485999\pi$
$41$	0.563090	0.0879399	0.0439700	+	0.999033i	$0.485999\pi$
$42$	−2.50479	−0.386498
$43$	−12.0123	−1.83186	−0.915930	−	0.401338i	$-0.868545\pi$
$43$	−12.0123	−1.83186	−0.915930	+	0.401338i	$0.868545\pi$
$44$	1.92943	0.290873
$45$	3.21643	0.479477
$46$	0.521930	0.0769544
$47$	6.72427	0.980836	0.490418	−	0.871487i	$-0.336844\pi$
$47$	6.72427	0.980836	0.490418	+	0.871487i	$0.336844\pi$
$48$	−7.59098	−1.09566
$49$	12.7926	1.82751
$50$	0.0937612	0.0132598
$51$	−7.02139	−0.983191
$52$	−9.78828	−1.35739
$53$	8.79541	1.20814	0.604071	−	0.796930i	$-0.293544\pi$
$53$	8.79541	1.20814	0.604071	+	0.796930i	$0.293544\pi$
$54$	−0.848996	−0.115534
$55$	−2.15570	−0.290674
$56$	−4.64386	−0.620562
$57$	−7.96821	−1.05541
$58$	0.558834	0.0733785
$59$	−4.15057	−0.540358	−0.270179	−	0.962810i	$-0.587083\pi$
$59$	−4.15057	−0.540358	−0.270179	+	0.962810i	$0.587083\pi$
$60$	8.81537	1.13806
$61$	−1.81657	−0.232588	−0.116294	−	0.993215i	$-0.537102\pi$
$61$	−1.81657	−0.232588	−0.116294	+	0.993215i	$0.537102\pi$
$62$	1.52213	0.193310
$63$	−6.63799	−0.836308
$64$	−6.35586	−0.794482
$65$	10.9362	1.35646
$66$	−0.563016	−0.0693025
$67$	−8.21913	−1.00413	−0.502063	−	0.864831i	$-0.667426\pi$
$67$	−8.21913	−1.00413	−0.502063	+	0.864831i	$0.667426\pi$
$68$	−6.39190	−0.775132
$69$	4.16425	0.501317
$70$	2.54764	0.304501
$71$	6.12397	0.726782	0.363391	−	0.931637i	$-0.381619\pi$
$71$	6.12397	0.726782	0.363391	+	0.931637i	$0.381619\pi$
$72$	1.55745	0.183547
$73$	−15.4026	−1.80274	−0.901371	−	0.433048i	$-0.857438\pi$
$73$	−15.4026	−1.80274	−0.901371	+	0.433048i	$0.857438\pi$
$74$	−0.727461	−0.0845656
$75$	0.748080	0.0863808
$76$	−7.25384	−0.832072
$77$	4.44888	0.506997
$78$	2.85626	0.323407
$79$	12.9950	1.46205	0.731026	−	0.682349i	$-0.239042\pi$
$79$	12.9950	1.46205	0.731026	+	0.682349i	$0.239042\pi$
$80$	7.72082	0.863213
$81$	−11.2499	−1.24999
$82$	−0.149581	−0.0165185
$83$	−16.0358	−1.76015	−0.880076	−	0.474833i	$-0.842509\pi$
$83$	−16.0358	−1.76015	−0.880076	+	0.474833i	$0.842509\pi$
$84$	−18.1930	−1.98502
$85$	7.14148	0.774603
$86$	3.19098	0.344093
$87$	4.45869	0.478022
$88$	−1.04383	−0.111272
$89$	−15.2228	−1.61361	−0.806805	−	0.590818i	$-0.798805\pi$
$89$	−15.2228	−1.61361	−0.806805	+	0.590818i	$0.798805\pi$
$90$	−0.854421	−0.0900639
$91$	−22.5698	−2.36596
$92$	3.79091	0.395230
$93$	12.1444	1.25931
$94$	−1.78626	−0.184238
$95$	8.10450	0.831504
$96$	6.44116	0.657398
$97$	−10.6652	−1.08289	−0.541444	−	0.840737i	$-0.682122\pi$
$97$	−10.6652	−1.08289	−0.541444	+	0.840737i	$0.682122\pi$
$98$	−3.39825	−0.343275
$99$	−1.49206	−0.149957
$100$	0.681012	0.0681012
$101$	5.84463	0.581562	0.290781	−	0.956790i	$-0.406085\pi$
$101$	5.84463	0.581562	0.290781	+	0.956790i	$0.406085\pi$
$102$	1.86518	0.184680
$103$	−5.75551	−0.567108	−0.283554	−	0.958956i	$-0.591513\pi$
$103$	−5.75551	−0.567108	−0.283554	+	0.958956i	$0.591513\pi$
$104$	5.29547	0.519264
$105$	20.3265	1.98366
$106$	−2.33644	−0.226935
$107$	13.1013	1.26655	0.633277	−	0.773925i	$-0.281709\pi$
$107$	13.1013	1.26655	0.633277	+	0.773925i	$0.281709\pi$
$108$	−6.16648	−0.593370
$109$	−14.9897	−1.43575	−0.717876	−	0.696171i	$-0.754886\pi$
$109$	−14.9897	−1.43575	−0.717876	+	0.696171i	$0.754886\pi$
$110$	0.572646	0.0545997
$111$	−5.80409	−0.550900
$112$	−15.9340	−1.50563
$113$	1.52572	0.143528	0.0717638	−	0.997422i	$-0.477137\pi$
$113$	1.52572	0.143528	0.0717638	+	0.997422i	$0.477137\pi$
$114$	2.11670	0.198247
$115$	−4.23548	−0.394960
$116$	4.05896	0.376865
$117$	7.56941	0.699792
$118$	1.10257	0.101500
$119$	−14.7384	−1.35107
$120$	−4.76913	−0.435360
$121$	1.00000	0.0909091
$122$	0.482560	0.0436889
$123$	−1.19344	−0.107609
$124$	11.0556	0.992823
$125$	−11.5394	−1.03211
$126$	1.76333	0.157090
$127$	17.9786	1.59535	0.797673	−	0.603090i	$-0.206064\pi$
$127$	17.9786	1.59535	0.797673	+	0.603090i	$0.206064\pi$
$128$	7.76654	0.686471
$129$	25.4595	2.24158
$130$	−2.90511	−0.254795
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−4.08933	−0.355931
$133$	−16.7259	−1.45032
$134$	2.18335	0.188613
$135$	6.88963	0.592965
$136$	3.45803	0.296523
$137$	0.846801	0.0723471	0.0361735	−	0.999346i	$-0.488483\pi$
$137$	0.846801	0.0723471	0.0361735	+	0.999346i	$0.488483\pi$
$138$	−1.10620	−0.0941663
$139$	−12.8522	−1.09011	−0.545054	−	0.838401i	$-0.683491\pi$
$139$	−12.8522	−1.09011	−0.545054	+	0.838401i	$0.683491\pi$
$140$	18.5041	1.56389
$141$	−14.2517	−1.20021
$142$	−1.62679	−0.136517
$143$	−5.07313	−0.424237
$144$	5.34393	0.445327
$145$	−4.53496	−0.376608
$146$	4.09160	0.338623
$147$	−27.1132	−2.23626
$148$	−5.28374	−0.434321
$149$	−20.4511	−1.67542	−0.837709	−	0.546116i	$-0.816106\pi$
$149$	−20.4511	−1.67542	−0.837709	+	0.546116i	$0.816106\pi$
$150$	−0.198722	−0.0162256
$151$	−20.5551	−1.67275	−0.836375	−	0.548158i	$-0.815329\pi$
$151$	−20.5551	−1.67275	−0.836375	+	0.548158i	$0.815329\pi$
$152$	3.92434	0.318306
$153$	4.94295	0.399613
$154$	−1.18181	−0.0952333
$155$	−12.3521	−0.992145
$156$	20.7457	1.66099
$157$	−15.0061	−1.19762	−0.598809	−	0.800892i	$-0.704359\pi$
$157$	−15.0061	−1.19762	−0.598809	+	0.800892i	$0.704359\pi$
$158$	−3.45203	−0.274629
$159$	−18.6414	−1.47836
$160$	−6.55133	−0.517928
$161$	8.74108	0.688893
$162$	2.98847	0.234796
$163$	−0.694867	−0.0544262	−0.0272131	−	0.999630i	$-0.508663\pi$
$163$	−0.694867	−0.0544262	−0.0272131	+	0.999630i	$0.508663\pi$
$164$	−1.08645	−0.0848371
$165$	4.56889	0.355688
$166$	4.25978	0.330623
$167$	23.2526	1.79934	0.899669	−	0.436573i	$-0.143808\pi$
$167$	23.2526	1.79934	0.899669	+	0.436573i	$0.143808\pi$
$168$	9.84242	0.759359
$169$	12.7367	0.979745
$170$	−1.89708	−0.145500
$171$	5.60949	0.428969
$172$	23.1770	1.76723
$173$	−11.6771	−0.887793	−0.443897	−	0.896078i	$-0.646404\pi$
$173$	−11.6771	−0.887793	−0.443897	+	0.896078i	$0.646404\pi$
$174$	−1.18442	−0.0897906
$175$	1.57028	0.118702
$176$	−3.58158	−0.269972
$177$	8.79691	0.661217
$178$	4.04382	0.303097
$179$	0.837653	0.0626091	0.0313046	−	0.999510i	$-0.490034\pi$
$179$	0.837653	0.0626091	0.0313046	+	0.999510i	$0.490034\pi$
$180$	−6.20588	−0.462559
$181$	10.5028	0.780666	0.390333	−	0.920674i	$-0.372360\pi$
$181$	10.5028	0.780666	0.390333	+	0.920674i	$0.372360\pi$
$182$	5.99550	0.444416
$183$	3.85013	0.284610
$184$	−2.05089	−0.151194
$185$	5.90337	0.434024
$186$	−3.22607	−0.236547
$187$	−3.31284	−0.242259
$188$	−12.9740	−0.946229
$189$	−14.2187	−1.03425
$190$	−2.15290	−0.156188
$191$	−4.46995	−0.323435	−0.161717	−	0.986837i	$-0.551703\pi$
$191$	−4.46995	−0.323435	−0.161717	+	0.986837i	$0.551703\pi$
$192$	13.4709	0.972179
$193$	−5.85549	−0.421488	−0.210744	−	0.977541i	$-0.567589\pi$
$193$	−5.85549	−0.421488	−0.210744	+	0.977541i	$0.567589\pi$
$194$	2.83314	0.203407
$195$	−23.1786	−1.65985
$196$	−24.6824	−1.76303
$197$	17.0053	1.21158	0.605788	−	0.795626i	$-0.292858\pi$
$197$	17.0053	1.21158	0.605788	+	0.795626i	$0.292858\pi$
$198$	0.396354	0.0281677
$199$	19.1471	1.35730	0.678650	−	0.734461i	$-0.262565\pi$
$199$	19.1471	1.35730	0.678650	+	0.734461i	$0.262565\pi$
$200$	−0.368429	−0.0260518
$201$	17.4200	1.22871
$202$	−1.55258	−0.109239
$203$	9.35914	0.656883
$204$	13.5473	0.948501
$205$	1.21385	0.0847792
$206$	1.52891	0.106524
$207$	−2.93157	−0.203758
$208$	18.1698	1.25985
$209$	−3.75957	−0.260055
$210$	−5.39958	−0.372607
$211$	11.1820	0.769799	0.384899	−	0.922959i	$-0.374236\pi$
$211$	11.1820	0.769799	0.384899	+	0.922959i	$0.374236\pi$
$212$	−16.9702	−1.16552
$213$	−12.9794	−0.889336
$214$	−3.48028	−0.237907
$215$	−25.8949	−1.76602
$216$	3.33607	0.226991
$217$	25.4920	1.73051
$218$	3.98191	0.269689
$219$	32.6451	2.20595
$220$	4.15928	0.280419
$221$	16.8065	1.13053
$222$	1.54182	0.103480
$223$	−4.45648	−0.298428	−0.149214	−	0.988805i	$-0.547674\pi$
$223$	−4.45648	−0.298428	−0.149214	+	0.988805i	$0.547674\pi$
$224$	13.5205	0.903376
$225$	−0.526636	−0.0351091
$226$	−0.405296	−0.0269599
$227$	−17.0982	−1.13485	−0.567423	−	0.823426i	$-0.692060\pi$
$227$	−17.0982	−1.13485	−0.567423	+	0.823426i	$0.692060\pi$
$228$	15.3741	1.01818
$229$	0.393088	0.0259760	0.0129880	−	0.999916i	$-0.495866\pi$
$229$	0.393088	0.0259760	0.0129880	+	0.999916i	$0.495866\pi$
$230$	1.12512	0.0741885
$231$	−9.42917	−0.620394
$232$	−2.19590	−0.144168
$233$	18.0650	1.18348	0.591740	−	0.806129i	$-0.298441\pi$
$233$	18.0650	1.18348	0.591740	+	0.806129i	$0.298441\pi$
$234$	−2.01076	−0.131447
$235$	14.4955	0.945583
$236$	8.00825	0.521293
$237$	−27.5422	−1.78906
$238$	3.91516	0.253782
$239$	−27.6147	−1.78625	−0.893124	−	0.449811i	$-0.851491\pi$
$239$	−27.6147	−1.78625	−0.893124	+	0.449811i	$0.851491\pi$
$240$	−16.3639	−1.05628
$241$	−6.95841	−0.448231	−0.224115	−	0.974563i	$-0.571949\pi$
$241$	−6.95841	−0.448231	−0.224115	+	0.974563i	$0.571949\pi$
$242$	−0.265643	−0.0170762
$243$	14.2556	0.914499
$244$	3.50496	0.224382
$245$	27.5769	1.76182
$246$	0.317029	0.0202130
$247$	19.0728	1.21357
$248$	−5.98110	−0.379800
$249$	33.9869	2.15383
$250$	3.06535	0.193870
$251$	−25.3436	−1.59967	−0.799837	−	0.600218i	$-0.795081\pi$
$251$	−25.3436	−1.59967	−0.799837	+	0.600218i	$0.795081\pi$
$252$	12.8076	0.806801
$253$	1.96478	0.123525
$254$	−4.77590	−0.299666
$255$	−15.1360	−0.947853
$256$	10.6486	0.665537
$257$	10.0015	0.623879	0.311939	−	0.950102i	$-0.399021\pi$
$257$	10.0015	0.623879	0.311939	+	0.950102i	$0.399021\pi$
$258$	−6.76312	−0.421054
$259$	−12.1832	−0.757029
$260$	−21.1006	−1.30860
$261$	−3.13885	−0.194290
$262$	0.265643	0.0164115
$263$	13.9603	0.860827	0.430413	−	0.902632i	$-0.358368\pi$
$263$	13.9603	0.860827	0.430413	+	0.902632i	$0.358368\pi$
$264$	2.21233	0.136160
$265$	18.9603	1.16472
$266$	4.44311	0.272425
$267$	32.2638	1.97452
$268$	15.8583	0.968698
$269$	2.15502	0.131394	0.0656971	−	0.997840i	$-0.479073\pi$
$269$	2.15502	0.131394	0.0656971	+	0.997840i	$0.479073\pi$
$270$	−1.83018	−0.111381
$271$	−5.42144	−0.329329	−0.164664	−	0.986350i	$-0.552654\pi$
$271$	−5.42144	−0.329329	−0.164664	+	0.986350i	$0.552654\pi$
$272$	11.8652	0.719434
$273$	47.8355	2.89513
$274$	−0.224947	−0.0135895
$275$	0.352960	0.0212843
$276$	−8.03464	−0.483629
$277$	−2.45672	−0.147610	−0.0738049	−	0.997273i	$-0.523514\pi$
$277$	−2.45672	−0.147610	−0.0738049	+	0.997273i	$0.523514\pi$
$278$	3.41409	0.204763
$279$	−8.54945	−0.511842
$280$	−10.0108	−0.598258
$281$	15.5561	0.927999	0.464000	−	0.885835i	$-0.346414\pi$
$281$	15.5561	0.927999	0.464000	+	0.885835i	$0.346414\pi$
$282$	3.78588	0.225446
$283$	17.2786	1.02711	0.513554	−	0.858057i	$-0.328328\pi$
$283$	17.2786	1.02711	0.513554	+	0.858057i	$0.328328\pi$
$284$	−11.8158	−0.701138
$285$	−17.1771	−1.01748
$286$	1.34764	0.0796877
$287$	−2.50512	−0.147873
$288$	−4.53447	−0.267196
$289$	−6.02510	−0.354418
$290$	1.20468	0.0707412
$291$	22.6043	1.32509
$292$	29.7184	1.73914
$293$	11.1648	0.652256	0.326128	−	0.945326i	$-0.394256\pi$
$293$	11.1648	0.652256	0.326128	+	0.945326i	$0.394256\pi$
$294$	7.20242	0.420054
$295$	−8.94738	−0.520937
$296$	2.85851	0.166148
$297$	−3.19600	−0.185451
$298$	5.43269	0.314707
$299$	−9.96759	−0.576441
$300$	−1.44337	−0.0833330
$301$	53.4414	3.08031
$302$	5.46031	0.314206
$303$	−12.3874	−0.711637
$304$	13.4652	0.772283
$305$	−3.91599	−0.224229
$306$	−1.31306	−0.0750625
$307$	18.5411	1.05820	0.529098	−	0.848561i	$-0.322530\pi$
$307$	18.5411	1.05820	0.529098	+	0.848561i	$0.322530\pi$
$308$	−8.58383	−0.489109
$309$	12.1985	0.693949
$310$	3.28125	0.186362
$311$	−24.8560	−1.40946	−0.704729	−	0.709477i	$-0.748931\pi$
$311$	−24.8560	−1.40946	−0.704729	+	0.709477i	$0.748931\pi$
$312$	−11.2235	−0.635404
$313$	−1.40113	−0.0791967	−0.0395983	−	0.999216i	$-0.512608\pi$
$313$	−1.40113	−0.0791967	−0.0395983	+	0.999216i	$0.512608\pi$
$314$	3.98627	0.224958
$315$	−14.3095	−0.806250
$316$	−25.0730	−1.41047
$317$	−12.7633	−0.716860	−0.358430	−	0.933557i	$-0.616688\pi$
$317$	−12.7633	−0.716860	−0.358430	+	0.933557i	$0.616688\pi$
$318$	4.95196	0.277692
$319$	2.10371	0.117785
$320$	−13.7013	−0.765927
$321$	−27.7676	−1.54984
$322$	−2.32201	−0.129400
$323$	12.4548	0.693006
$324$	21.7060	1.20589
$325$	−1.79061	−0.0993253
$326$	0.184586	0.0102233
$327$	31.7699	1.75688
$328$	0.587768	0.0324541
$329$	−29.9155	−1.64930
$330$	−1.21369	−0.0668116
$331$	−2.29308	−0.126039	−0.0630196	−	0.998012i	$-0.520073\pi$
$331$	−2.29308	−0.126039	−0.0630196	+	0.998012i	$0.520073\pi$
$332$	30.9399	1.69805
$333$	4.08599	0.223911
$334$	−6.17688	−0.337984
$335$	−17.7180	−0.968036
$336$	33.7714	1.84238
$337$	−6.47900	−0.352934	−0.176467	−	0.984307i	$-0.556467\pi$
$337$	−6.47900	−0.352934	−0.176467	+	0.984307i	$0.556467\pi$
$338$	−3.38341	−0.184033
$339$	−3.23368	−0.175629
$340$	−13.7790	−0.747272
$341$	5.72997	0.310296
$342$	−1.49012	−0.0805766
$343$	−25.7704	−1.39147
$344$	−12.5388	−0.676045
$345$	8.97687	0.483298
$346$	3.10194	0.166761
$347$	−6.14372	−0.329812	−0.164906	−	0.986309i	$-0.552732\pi$
$347$	−6.14372	−0.329812	−0.164906	+	0.986309i	$0.552732\pi$
$348$	−8.60275	−0.461156
$349$	−23.8846	−1.27851	−0.639257	−	0.768993i	$-0.720758\pi$
$349$	−23.8846	−1.27851	−0.639257	+	0.768993i	$0.720758\pi$
$350$	−0.417133	−0.0222967
$351$	16.2138	0.865427
$352$	3.03907	0.161983
$353$	8.73559	0.464948	0.232474	−	0.972603i	$-0.425318\pi$
$353$	8.73559	0.464948	0.232474	+	0.972603i	$0.425318\pi$
$354$	−2.33684	−0.124202
$355$	13.2014	0.700660
$356$	29.3713	1.55668
$357$	31.2373	1.65325
$358$	−0.222517	−0.0117604
$359$	−8.34774	−0.440577	−0.220288	−	0.975435i	$-0.570700\pi$
$359$	−8.34774	−0.440577	−0.220288	+	0.975435i	$0.570700\pi$
$360$	3.35739	0.176950
$361$	−4.86564	−0.256086
$362$	−2.78999	−0.146639
$363$	−2.11945	−0.111242
$364$	43.5469	2.28248
$365$	−33.2034	−1.73795
$366$	−1.02276	−0.0534605
$367$	−30.1523	−1.57394	−0.786970	−	0.616992i	$-0.788351\pi$
$367$	−30.1523	−1.57394	−0.786970	+	0.616992i	$0.788351\pi$
$368$	−7.03702	−0.366830
$369$	0.840163	0.0437371
$370$	−1.56819	−0.0815262
$371$	−39.1297	−2.03152
$372$	−23.4318	−1.21488
$373$	16.1367	0.835528	0.417764	−	0.908556i	$-0.362814\pi$
$373$	16.1367	0.835528	0.417764	+	0.908556i	$0.362814\pi$
$374$	0.880032	0.0455054
$375$	24.4571	1.26296
$376$	7.01897	0.361976
$377$	−10.6724	−0.549655
$378$	3.77708	0.194272
$379$	−20.2345	−1.03938	−0.519689	−	0.854356i	$-0.673952\pi$
$379$	−20.2345	−1.03938	−0.519689	+	0.854356i	$0.673952\pi$
$380$	−15.6371	−0.802166
$381$	−38.1048	−1.95217
$382$	1.18741	0.0607533
$383$	15.4956	0.791786	0.395893	−	0.918297i	$-0.370435\pi$
$383$	15.4956	0.791786	0.395893	+	0.918297i	$0.370435\pi$
$384$	−16.4608	−0.840010
$385$	9.59046	0.488775
$386$	1.55547	0.0791713
$387$	−17.9231	−0.911080
$388$	20.5778	1.04468
$389$	−24.4943	−1.24191	−0.620954	−	0.783847i	$-0.713255\pi$
$389$	−24.4943	−1.24191	−0.620954	+	0.783847i	$0.713255\pi$
$390$	6.15723	0.311783
$391$	−6.50900	−0.329174
$392$	13.3532	0.674439
$393$	2.11945	0.106912
$394$	−4.51733	−0.227580
$395$	28.0133	1.40950
$396$	2.87883	0.144666
$397$	7.54435	0.378640	0.189320	−	0.981915i	$-0.439372\pi$
$397$	7.54435	0.378640	0.189320	+	0.981915i	$0.439372\pi$
$398$	−5.08629	−0.254953
$399$	35.4496	1.77470
$400$	−1.26415	−0.0632077
$401$	−27.7877	−1.38765	−0.693825	−	0.720143i	$-0.744076\pi$
$401$	−27.7877	−1.38765	−0.693825	+	0.720143i	$0.744076\pi$
$402$	−4.62750	−0.230799
$403$	−29.0689	−1.44803
$404$	−11.2768	−0.561043
$405$	−24.2515	−1.20507
$406$	−2.48619	−0.123387
$407$	−2.73849	−0.135742
$408$	−7.32911	−0.362845
$409$	0.801496	0.0396314	0.0198157	−	0.999804i	$-0.493692\pi$
$409$	0.801496	0.0396314	0.0198157	+	0.999804i	$0.493692\pi$
$410$	−0.322452	−0.0159247
$411$	−1.79475	−0.0885285
$412$	11.1049	0.547098
$413$	18.4654	0.908623
$414$	0.778750	0.0382735
$415$	−34.5683	−1.69689
$416$	−15.4176	−0.755912
$417$	27.2395	1.33392
$418$	0.998703	0.0488481
$419$	19.1743	0.936727	0.468364	−	0.883536i	$-0.344844\pi$
$419$	19.1743	0.936727	0.468364	+	0.883536i	$0.344844\pi$
$420$	−39.2186	−1.91367
$421$	−12.6214	−0.615129	−0.307564	−	0.951527i	$-0.599514\pi$
$421$	−12.6214	−0.615129	−0.307564	+	0.951527i	$0.599514\pi$
$422$	−2.97041	−0.144597
$423$	10.0330	0.487821
$424$	9.18088	0.445863
$425$	−1.16930	−0.0567193
$426$	3.44789	0.167051
$427$	8.08172	0.391102
$428$	−25.2782	−1.22187
$429$	10.7522	0.519123
$430$	6.87880	0.331725
$431$	0.411574	0.0198248	0.00991240	−	0.999951i	$-0.496845\pi$
$431$	0.411574	0.0198248	0.00991240	+	0.999951i	$0.496845\pi$
$432$	11.4468	0.550732
$433$	−13.3185	−0.640048	−0.320024	−	0.947409i	$-0.603691\pi$
$433$	−13.3185	−0.640048	−0.320024	+	0.947409i	$0.603691\pi$
$434$	−6.77177	−0.325055
$435$	9.61160	0.460841
$436$	28.9216	1.38510
$437$	−7.38673	−0.353355
$438$	−8.67193	−0.414361
$439$	5.07237	0.242091	0.121045	−	0.992647i	$-0.461375\pi$
$439$	5.07237	0.242091	0.121045	+	0.992647i	$0.461375\pi$
$440$	−2.25018	−0.107273
$441$	19.0872	0.908916
$442$	−4.46452	−0.212356
$443$	−28.7719	−1.36699	−0.683497	−	0.729953i	$-0.739542\pi$
$443$	−28.7719	−1.36699	−0.683497	+	0.729953i	$0.739542\pi$
$444$	11.1986	0.531463
$445$	−32.8157	−1.55561
$446$	1.18383	0.0560561
$447$	43.3450	2.05015
$448$	28.2765	1.33594
$449$	−30.0357	−1.41747	−0.708737	−	0.705473i	$-0.750735\pi$
$449$	−30.0357	−1.41747	−0.708737	+	0.705473i	$0.750735\pi$
$450$	0.139897	0.00659482
$451$	−0.563090	−0.0265149
$452$	−2.94377	−0.138463
$453$	43.5654	2.04688
$454$	4.54201	0.213167
$455$	−48.6537	−2.28092
$456$	−8.31742	−0.389499
$457$	−11.8240	−0.553103	−0.276551	−	0.960999i	$-0.589192\pi$
$457$	−11.8240	−0.553103	−0.276551	+	0.960999i	$0.589192\pi$
$458$	−0.104421	−0.00487927
$459$	10.5878	0.494198
$460$	8.17207	0.381025
$461$	−38.5963	−1.79761	−0.898804	−	0.438351i	$-0.855563\pi$
$461$	−38.5963	−1.79761	−0.898804	+	0.438351i	$0.855563\pi$
$462$	2.50479	0.116534
$463$	5.48357	0.254843	0.127422	−	0.991849i	$-0.459330\pi$
$463$	5.48357	0.254843	0.127422	+	0.991849i	$0.459330\pi$
$464$	−7.53459	−0.349785
$465$	26.1796	1.21405
$466$	−4.79885	−0.222302
$467$	−3.05855	−0.141533	−0.0707663	−	0.997493i	$-0.522544\pi$
$467$	−3.05855	−0.141533	−0.0707663	+	0.997493i	$0.522544\pi$
$468$	−14.6047	−0.675101
$469$	36.5659	1.68846
$470$	−3.85063	−0.177616
$471$	31.8047	1.46548
$472$	−4.33247	−0.199418
$473$	12.0123	0.552327
$474$	7.31640	0.336053
$475$	−1.32698	−0.0608859
$476$	28.4368	1.30340
$477$	13.1233	0.600873
$478$	7.33565	0.335525
$479$	−5.72742	−0.261693	−0.130846	−	0.991403i	$-0.541769\pi$
$479$	−5.72742	−0.261693	−0.130846	+	0.991403i	$0.541769\pi$
$480$	13.8852	0.633770
$481$	13.8927	0.633455
$482$	1.84845	0.0841947
$483$	−18.5263	−0.842974
$484$	−1.92943	−0.0877015
$485$	−22.9910	−1.04397
$486$	−3.78691	−0.171778
$487$	10.5241	0.476894	0.238447	−	0.971156i	$-0.423362\pi$
$487$	10.5241	0.476894	0.238447	+	0.971156i	$0.423362\pi$
$488$	−1.89619	−0.0858363
$489$	1.47273	0.0665993
$490$	−7.32561	−0.330937
$491$	−1.98550	−0.0896045	−0.0448022	−	0.998996i	$-0.514266\pi$
$491$	−1.98550	−0.0896045	−0.0448022	+	0.998996i	$0.514266\pi$
$492$	2.30266	0.103812
$493$	−6.96924	−0.313879
$494$	−5.06655	−0.227955
$495$	−3.21643	−0.144568
$496$	−20.5224	−0.921482
$497$	−27.2448	−1.22210
$498$	−9.02839	−0.404572
$499$	−12.1595	−0.544335	−0.272167	−	0.962250i	$-0.587740\pi$
$499$	−12.1595	−0.544335	−0.272167	+	0.962250i	$0.587740\pi$
$500$	22.2645	0.995697
$501$	−49.2826	−2.20178
$502$	6.73235	0.300479
$503$	19.6508	0.876184	0.438092	−	0.898930i	$-0.355654\pi$
$503$	19.6508	0.876184	0.438092	+	0.898930i	$0.355654\pi$
$504$	−6.92891	−0.308638
$505$	12.5993	0.560660
$506$	−0.521930	−0.0232026
$507$	−26.9947	−1.19888
$508$	−34.6886	−1.53906
$509$	−32.6470	−1.44705	−0.723527	−	0.690296i	$-0.757480\pi$
$509$	−32.6470	−1.44705	−0.723527	+	0.690296i	$0.757480\pi$
$510$	4.02077	0.178043
$511$	68.5245	3.03135
$512$	−18.3618	−0.811484
$513$	12.0156	0.530502
$514$	−2.65684	−0.117188
$515$	−12.4072	−0.546725
$516$	−49.1223	−2.16249
$517$	−6.72427	−0.295733
$518$	3.23639	0.142199
$519$	24.7490	1.08636
$520$	11.4154	0.500600
$521$	19.8000	0.867455	0.433728	−	0.901044i	$-0.357198\pi$
$521$	19.8000	0.867455	0.433728	+	0.901044i	$0.357198\pi$
$522$	0.833813	0.0364950
$523$	9.54737	0.417477	0.208739	−	0.977971i	$-0.433064\pi$
$523$	9.54737	0.417477	0.208739	+	0.977971i	$0.433064\pi$
$524$	1.92943	0.0842877
$525$	−3.32812	−0.145251
$526$	−3.70844	−0.161696
$527$	−18.9825	−0.826890
$528$	7.59098	0.330355
$529$	−19.1396	−0.832158
$530$	−5.03666	−0.218778
$531$	−6.19289	−0.268748
$532$	32.2715	1.39915
$533$	2.85663	0.123735
$534$	−8.57066	−0.370889
$535$	28.2425	1.22103
$536$	−8.57934	−0.370571
$537$	−1.77536	−0.0766125
$538$	−0.572467	−0.0246808
$539$	−12.7926	−0.551015
$540$	−13.2931	−0.572043
$541$	15.1943	0.653255	0.326628	−	0.945153i	$-0.394088\pi$
$541$	15.1943	0.653255	0.326628	+	0.945153i	$0.394088\pi$
$542$	1.44017	0.0618605
$543$	−22.2601	−0.955273
$544$	−10.0680	−0.431660
$545$	−32.3133	−1.38415
$546$	−12.7072	−0.543816
$547$	8.99092	0.384424	0.192212	−	0.981353i	$-0.438434\pi$
$547$	8.99092	0.384424	0.192212	+	0.981353i	$0.438434\pi$
$548$	−1.63385	−0.0697945
$549$	−2.71043	−0.115678
$550$	−0.0937612	−0.00399799
$551$	−7.90902	−0.336936
$552$	4.34675	0.185010
$553$	−57.8133	−2.45847
$554$	0.652609	0.0277267
$555$	−12.5119	−0.531100
$556$	24.7974	1.05164
$557$	20.2558	0.858267	0.429133	−	0.903241i	$-0.358819\pi$
$557$	20.2558	0.858267	0.429133	+	0.903241i	$0.358819\pi$
$558$	2.27110	0.0961434
$559$	−60.9400	−2.57749
$560$	−34.3490	−1.45151
$561$	7.02139	0.296443
$562$	−4.13237	−0.174313
$563$	−12.5797	−0.530173	−0.265086	−	0.964225i	$-0.585400\pi$
$563$	−12.5797	−0.530173	−0.265086	+	0.964225i	$0.585400\pi$
$564$	27.4978	1.15787
$565$	3.28899	0.138369
$566$	−4.58995	−0.192930
$567$	50.0497	2.10189
$568$	6.39236	0.268217
$569$	17.5551	0.735948	0.367974	−	0.929836i	$-0.380051\pi$
$569$	17.5551	0.735948	0.367974	+	0.929836i	$0.380051\pi$
$570$	4.56296	0.191122
$571$	44.7538	1.87289	0.936445	−	0.350815i	$-0.114096\pi$
$571$	44.7538	1.87289	0.936445	+	0.350815i	$0.114096\pi$
$572$	9.78828	0.409268
$573$	9.47383	0.395775
$574$	0.665468	0.0277761
$575$	0.693488	0.0289205
$576$	−9.48330	−0.395138
$577$	42.3908	1.76475	0.882376	−	0.470545i	$-0.155943\pi$
$577$	42.3908	1.76475	0.882376	+	0.470545i	$0.155943\pi$
$578$	1.60053	0.0665731
$579$	12.4104	0.515759
$580$	8.74990	0.363320
$581$	71.3412	2.95973
$582$	−6.00468	−0.248902
$583$	−8.79541	−0.364269
$584$	−16.0777	−0.665299
$585$	16.3174	0.674640
$586$	−2.96585	−0.122518
$587$	−25.3070	−1.04453	−0.522265	−	0.852783i	$-0.674913\pi$
$587$	−25.3070	−1.04453	−0.522265	+	0.852783i	$0.674913\pi$
$588$	52.3131	2.15735
$589$	−21.5422	−0.887632
$590$	2.37681	0.0978516
$591$	−36.0418	−1.48256
$592$	9.80814	0.403112
$593$	−36.0058	−1.47858	−0.739291	−	0.673386i	$-0.764839\pi$
$593$	−36.0058	−1.47858	−0.739291	+	0.673386i	$0.764839\pi$
$594$	0.848996	0.0348347
$595$	−31.7716	−1.30251
$596$	39.4590	1.61631
$597$	−40.5812	−1.66088
$598$	2.64782	0.108277
$599$	−21.4999	−0.878461	−0.439230	−	0.898374i	$-0.644749\pi$
$599$	−21.4999	−0.878461	−0.439230	+	0.898374i	$0.644749\pi$
$600$	0.780865	0.0318787
$601$	41.8588	1.70745	0.853727	−	0.520720i	$-0.174336\pi$
$601$	41.8588	1.70745	0.853727	+	0.520720i	$0.174336\pi$
$602$	−14.1963	−0.578599
$603$	−12.2634	−0.499405
$604$	39.6597	1.61373
$605$	2.15570	0.0876416
$606$	3.29062	0.133672
$607$	−7.12032	−0.289005	−0.144502	−	0.989504i	$-0.546158\pi$
$607$	−7.12032	−0.289005	−0.144502	+	0.989504i	$0.546158\pi$
$608$	−11.4256	−0.463370
$609$	−19.8362	−0.803803
$610$	1.04025	0.0421186
$611$	34.1131	1.38007
$612$	−9.53709	−0.385514
$613$	−14.5567	−0.587938	−0.293969	−	0.955815i	$-0.594976\pi$
$613$	−14.5567	−0.587938	−0.293969	+	0.955815i	$0.594976\pi$
$614$	−4.92531	−0.198769
$615$	−2.57270	−0.103741
$616$	4.64386	0.187106
$617$	−45.5814	−1.83504	−0.917519	−	0.397691i	$-0.869812\pi$
$617$	−45.5814	−1.83504	−0.917519	+	0.397691i	$0.869812\pi$
$618$	−3.24045	−0.130350
$619$	31.0894	1.24959	0.624795	−	0.780789i	$-0.285183\pi$
$619$	31.0894	1.24959	0.624795	+	0.780789i	$0.285183\pi$
$620$	23.8326	0.957139
$621$	−6.27945	−0.251986
$622$	6.60283	0.264749
$623$	67.7243	2.71332
$624$	−38.5100	−1.54164
$625$	−23.1106	−0.924425
$626$	0.372201	0.0148761
$627$	7.96821	0.318220
$628$	28.9533	1.15536
$629$	9.07218	0.361732
$630$	3.80122	0.151444
$631$	−22.7800	−0.906859	−0.453430	−	0.891292i	$-0.649800\pi$
$631$	−22.7800	−0.906859	−0.453430	+	0.891292i	$0.649800\pi$
$632$	13.5645	0.539568
$633$	−23.6996	−0.941975
$634$	3.39049	0.134653
$635$	38.7565	1.53801
$636$	35.9674	1.42620
$637$	64.8984	2.57137
$638$	−0.558834	−0.0221245
$639$	9.13732	0.361467
$640$	16.7423	0.661798
$641$	41.1745	1.62629	0.813147	−	0.582058i	$-0.197752\pi$
$641$	41.1745	1.62629	0.813147	+	0.582058i	$0.197752\pi$
$642$	7.37626	0.291118
$643$	−7.58192	−0.299002	−0.149501	−	0.988762i	$-0.547767\pi$
$643$	−7.58192	−0.299002	−0.149501	+	0.988762i	$0.547767\pi$
$644$	−16.8653	−0.664587
$645$	54.8829	2.16101
$646$	−3.30854	−0.130173
$647$	15.2817	0.600785	0.300393	−	0.953816i	$-0.402882\pi$
$647$	15.2817	0.600785	0.300393	+	0.953816i	$0.402882\pi$
$648$	−11.7430	−0.461308
$649$	4.15057	0.162924
$650$	0.475663	0.0186571
$651$	−54.0289	−2.11756
$652$	1.34070	0.0525059
$653$	−2.50117	−0.0978785	−0.0489392	−	0.998802i	$-0.515584\pi$
$653$	−2.50117	−0.0978785	−0.0489392	+	0.998802i	$0.515584\pi$
$654$	−8.43944	−0.330008
$655$	−2.15570	−0.0842301
$656$	2.01675	0.0787410
$657$	−22.9816	−0.896598
$658$	7.94684	0.309800
$659$	7.90064	0.307765	0.153883	−	0.988089i	$-0.450822\pi$
$659$	7.90064	0.307765	0.153883	+	0.988089i	$0.450822\pi$
$660$	−8.81537	−0.343138
$661$	25.8256	1.00450	0.502250	−	0.864722i	$-0.332506\pi$
$661$	25.8256	1.00450	0.502250	+	0.864722i	$0.332506\pi$
$662$	0.609141	0.0236749
$663$	−35.6204	−1.38338
$664$	−16.7385	−0.649581
$665$	−36.0560	−1.39819
$666$	−1.08541	−0.0420589
$667$	4.13332	0.160043
$668$	−44.8643	−1.73585
$669$	9.44527	0.365175
$670$	4.70665	0.181834
$671$	1.81657	0.0701280
$672$	−28.6560	−1.10543
$673$	−5.72375	−0.220634	−0.110317	−	0.993896i	$-0.535187\pi$
$673$	−5.72375	−0.220634	−0.110317	+	0.993896i	$0.535187\pi$
$674$	1.72110	0.0662943
$675$	−1.12806	−0.0434191
$676$	−24.5746	−0.945177
$677$	32.6830	1.25611	0.628055	−	0.778169i	$-0.283851\pi$
$677$	32.6830	1.25611	0.628055	+	0.778169i	$0.283851\pi$
$678$	0.859004	0.0329899
$679$	47.4482	1.82090
$680$	7.45447	0.285866
$681$	36.2387	1.38867
$682$	−1.52213	−0.0582853
$683$	−13.2167	−0.505724	−0.252862	−	0.967502i	$-0.581372\pi$
$683$	−13.2167	−0.505724	−0.252862	+	0.967502i	$0.581372\pi$
$684$	−10.8231	−0.413833
$685$	1.82545	0.0697468
$686$	6.84573	0.261371
$687$	−0.833129	−0.0317859
$688$	−43.0231	−1.64024
$689$	44.6203	1.69990
$690$	−2.38464	−0.0907818
$691$	−2.73678	−0.104112	−0.0520560	−	0.998644i	$-0.516577\pi$
$691$	−2.73678	−0.104112	−0.0520560	+	0.998644i	$0.516577\pi$
$692$	22.5302	0.856469
$693$	6.63799	0.252156
$694$	1.63204	0.0619513
$695$	−27.7054	−1.05093
$696$	4.65410	0.176413
$697$	1.86543	0.0706581
$698$	6.34478	0.240154
$699$	−38.2879	−1.44818
$700$	−3.02974	−0.114514
$701$	−1.44707	−0.0546552	−0.0273276	−	0.999627i	$-0.508700\pi$
$701$	−1.44707	−0.0546552	−0.0273276	+	0.999627i	$0.508700\pi$
$702$	−4.30707	−0.162560
$703$	10.2956	0.388304
$704$	6.35586	0.239545
$705$	−30.7225	−1.15708
$706$	−2.32055	−0.0873349
$707$	−26.0021	−0.977909
$708$	−16.9731	−0.637887
$709$	−35.4051	−1.32967	−0.664834	−	0.746991i	$-0.731498\pi$
$709$	−35.4051	−1.32967	−0.664834	+	0.746991i	$0.731498\pi$
$710$	−3.50687	−0.131610
$711$	19.3893	0.727155
$712$	−15.8899	−0.595500
$713$	11.2581	0.421621
$714$	−8.29797	−0.310544
$715$	−10.9362	−0.408989
$716$	−1.61620	−0.0604001
$717$	58.5280	2.18577
$718$	2.21752	0.0827570
$719$	27.6003	1.02932	0.514658	−	0.857395i	$-0.327919\pi$
$719$	27.6003	1.02932	0.514658	+	0.857395i	$0.327919\pi$
$720$	11.5199	0.429321
$721$	25.6056	0.953603
$722$	1.29252	0.0481027
$723$	14.7480	0.548483
$724$	−20.2644	−0.753122
$725$	0.742523	0.0275766
$726$	0.563016	0.0208955
$727$	19.8827	0.737409	0.368704	−	0.929547i	$-0.379802\pi$
$727$	19.8827	0.737409	0.368704	+	0.929547i	$0.379802\pi$
$728$	−23.5589	−0.873152
$729$	3.53574	0.130953
$730$	8.82026	0.326452
$731$	−39.7948	−1.47187
$732$	−7.42857	−0.274568
$733$	12.2775	0.453479	0.226739	−	0.973955i	$-0.427193\pi$
$733$	12.2775	0.453479	0.226739	+	0.973955i	$0.427193\pi$
$734$	8.00975	0.295645
$735$	−58.4478	−2.15588
$736$	5.97111	0.220098
$737$	8.21913	0.302755
$738$	−0.223183	−0.00821549
$739$	−31.6291	−1.16350	−0.581748	−	0.813369i	$-0.697631\pi$
$739$	−31.6291	−1.16350	−0.581748	+	0.813369i	$0.697631\pi$
$740$	−11.3902	−0.418711
$741$	−40.4238	−1.48501
$742$	10.3945	0.381596
$743$	−30.3728	−1.11427	−0.557134	−	0.830422i	$-0.688099\pi$
$743$	−30.3728	−1.11427	−0.557134	+	0.830422i	$0.688099\pi$
$744$	12.6766	0.464748
$745$	−44.0864	−1.61520
$746$	−4.28661	−0.156944
$747$	−23.9263	−0.875416
$748$	6.39190	0.233711
$749$	−58.2863	−2.12974
$750$	−6.49685	−0.237232
$751$	42.2085	1.54021	0.770106	−	0.637916i	$-0.220203\pi$
$751$	42.2085	1.54021	0.770106	+	0.637916i	$0.220203\pi$
$752$	24.0835	0.878237
$753$	53.7144	1.95746
$754$	2.83504	0.103246
$755$	−44.3106	−1.61263
$756$	27.4339	0.997763
$757$	42.2429	1.53535	0.767673	−	0.640842i	$-0.221415\pi$
$757$	42.2429	1.53535	0.767673	+	0.640842i	$0.221415\pi$
$758$	5.37516	0.195234
$759$	−4.16425	−0.151153
$760$	8.45969	0.306865
$761$	−45.7649	−1.65897	−0.829487	−	0.558526i	$-0.811367\pi$
$761$	−45.7649	−1.65897	−0.829487	+	0.558526i	$0.811367\pi$
$762$	10.1223	0.366691
$763$	66.6874	2.41425
$764$	8.62448	0.312023
$765$	10.6555	0.385251
$766$	−4.11628	−0.148727
$767$	−21.0564	−0.760302
$768$	−22.5691	−0.814393
$769$	−45.2753	−1.63267	−0.816334	−	0.577581i	$-0.803997\pi$
$769$	−45.2753	−1.63267	−0.816334	+	0.577581i	$0.803997\pi$
$770$	−2.54764	−0.0918104
$771$	−21.1977	−0.763418
$772$	11.2978	0.406616
$773$	27.3722	0.984508	0.492254	−	0.870452i	$-0.336173\pi$
$773$	27.3722	0.984508	0.492254	+	0.870452i	$0.336173\pi$
$774$	4.76113	0.171135
$775$	2.02245	0.0726486
$776$	−11.1326	−0.399638
$777$	25.8217	0.926349
$778$	6.50672	0.233277
$779$	2.11698	0.0758486
$780$	44.7216	1.60129
$781$	−6.12397	−0.219133
$782$	1.72907	0.0618314
$783$	−6.72345	−0.240277
$784$	45.8176	1.63634
$785$	−32.3487	−1.15457
$786$	−0.563016	−0.0200821
$787$	32.8721	1.17176	0.585881	−	0.810397i	$-0.300748\pi$
$787$	32.8721	1.17176	0.585881	+	0.810397i	$0.300748\pi$
$788$	−32.8106	−1.16883
$789$	−29.5880	−1.05336
$790$	−7.44154	−0.264758
$791$	−6.78774	−0.241344
$792$	−1.55745	−0.0553415
$793$	−9.21572	−0.327260
$794$	−2.00410	−0.0711229
$795$	−40.1853	−1.42522
$796$	−36.9430	−1.30941
$797$	−43.1730	−1.52927	−0.764633	−	0.644466i	$-0.777080\pi$
$797$	−43.1730	−1.52927	−0.764633	+	0.644466i	$0.777080\pi$
$798$	−9.41694	−0.333356
$799$	22.2764	0.788084
$800$	1.07267	0.0379246
$801$	−22.7132	−0.802533
$802$	7.38160	0.260653
$803$	15.4026	0.543547
$804$	−33.6108	−1.18536
$805$	18.8431	0.664133
$806$	7.72196	0.271994
$807$	−4.56746	−0.160782
$808$	6.10078	0.214625
$809$	7.64287	0.268709	0.134355	−	0.990933i	$-0.457104\pi$
$809$	7.64287	0.268709	0.134355	+	0.990933i	$0.457104\pi$
$810$	6.44223	0.226357
$811$	−49.0903	−1.72379	−0.861897	−	0.507083i	$-0.830724\pi$
$811$	−49.0903	−1.72379	−0.861897	+	0.507083i	$0.830724\pi$
$812$	−18.0578	−0.633706
$813$	11.4905	0.402988
$814$	0.727461	0.0254975
$815$	−1.49792	−0.0524700
$816$	−25.1477	−0.880345
$817$	−45.1611	−1.57999
$818$	−0.212912	−0.00744428
$819$	−33.6754	−1.17671
$820$	−2.34205	−0.0817879
$821$	−8.12240	−0.283474	−0.141737	−	0.989904i	$-0.545269\pi$
$821$	−8.12240	−0.283474	−0.141737	+	0.989904i	$0.545269\pi$
$822$	0.476763	0.0166290
$823$	−40.1658	−1.40009	−0.700045	−	0.714099i	$-0.746837\pi$
$823$	−40.1658	−1.40009	−0.700045	+	0.714099i	$0.746837\pi$
$824$	−6.00776	−0.209290
$825$	−0.748080	−0.0260448
$826$	−4.90520	−0.170674
$827$	15.6530	0.544307	0.272154	−	0.962254i	$-0.412264\pi$
$827$	15.6530	0.544307	0.272154	+	0.962254i	$0.412264\pi$
$828$	5.65626	0.196569
$829$	−34.7378	−1.20649	−0.603246	−	0.797555i	$-0.706126\pi$
$829$	−34.7378	−1.20649	−0.603246	+	0.797555i	$0.706126\pi$
$830$	9.18281	0.318740
$831$	5.20688	0.180625
$832$	−32.2441	−1.11786
$833$	42.3797	1.46837
$834$	−7.23598	−0.250562
$835$	50.1256	1.73467
$836$	7.25384	0.250879
$837$	−18.3130	−0.632991
$838$	−5.09352	−0.175953
$839$	−48.3675	−1.66983	−0.834916	−	0.550378i	$-0.814484\pi$
$839$	−48.3675	−1.66983	−0.834916	+	0.550378i	$0.814484\pi$
$840$	21.2173	0.732066
$841$	−24.5744	−0.847394
$842$	3.35278	0.115544
$843$	−32.9703	−1.13556
$844$	−21.5749	−0.742638
$845$	27.4565	0.944532
$846$	−2.66520	−0.0916313
$847$	−4.44888	−0.152865
$848$	31.5015	1.08177
$849$	−36.6212	−1.25684
$850$	0.310616	0.0106540
$851$	−5.38054	−0.184442
$852$	25.0430	0.857958
$853$	−6.10821	−0.209141	−0.104571	−	0.994517i	$-0.533347\pi$
$853$	−6.10821	−0.209141	−0.104571	+	0.994517i	$0.533347\pi$
$854$	−2.14685	−0.0734637
$855$	12.0924	0.413551
$856$	13.6755	0.467420
$857$	6.35415	0.217054	0.108527	−	0.994094i	$-0.465387\pi$
$857$	6.35415	0.217054	0.108527	+	0.994094i	$0.465387\pi$
$858$	−2.85626	−0.0975110
$859$	8.49761	0.289935	0.144967	−	0.989436i	$-0.453692\pi$
$859$	8.49761	0.289935	0.144967	+	0.989436i	$0.453692\pi$
$860$	49.9625	1.70371
$861$	5.30948	0.180946
$862$	−0.109332	−0.00372385
$863$	−33.6884	−1.14677	−0.573384	−	0.819287i	$-0.694370\pi$
$863$	−33.6884	−1.14677	−0.573384	+	0.819287i	$0.694370\pi$
$864$	−9.71290	−0.330439
$865$	−25.1723	−0.855884
$866$	3.53798	0.120225
$867$	12.7699	0.433688
$868$	−49.1851	−1.66945
$869$	−12.9950	−0.440825
$870$	−2.55325	−0.0865634
$871$	−41.6967	−1.41284
$872$	−15.6466	−0.529862
$873$	−15.9131	−0.538577
$874$	1.96223	0.0663735
$875$	51.3373	1.73552
$876$	−62.9865	−2.12812
$877$	39.1972	1.32360	0.661798	−	0.749683i	$-0.269794\pi$
$877$	39.1972	1.32360	0.661798	+	0.749683i	$0.269794\pi$
$878$	−1.34744	−0.0454738
$879$	−23.6632	−0.798141
$880$	−7.72082	−0.260269
$881$	20.3933	0.687067	0.343534	−	0.939140i	$-0.388376\pi$
$881$	20.3933	0.687067	0.343534	+	0.939140i	$0.388376\pi$
$882$	−5.07039	−0.170729
$883$	−12.4010	−0.417327	−0.208663	−	0.977988i	$-0.566911\pi$
$883$	−12.4010	−0.417327	−0.208663	+	0.977988i	$0.566911\pi$
$884$	−32.4270	−1.09064
$885$	18.9635	0.637451
$886$	7.64305	0.256773
$887$	34.6720	1.16417	0.582086	−	0.813127i	$-0.302237\pi$
$887$	34.6720	1.16417	0.582086	+	0.813127i	$0.302237\pi$
$888$	−6.05846	−0.203309
$889$	−79.9849	−2.68261
$890$	8.71726	0.292203
$891$	11.2499	0.376887
$892$	8.59848	0.287898
$893$	25.2804	0.845975
$894$	−11.5143	−0.385096
$895$	1.80573	0.0603588
$896$	−34.5524	−1.15432
$897$	21.1258	0.705370
$898$	7.97878	0.266255
$899$	12.0542	0.402029
$900$	1.01611	0.0338703
$901$	29.1378	0.970720
$902$	0.149581	0.00498050
$903$	−113.266	−3.76926
$904$	1.59258	0.0529686
$905$	22.6409	0.752608
$906$	−11.5728	−0.384482
$907$	−30.0433	−0.997573	−0.498786	−	0.866725i	$-0.666221\pi$
$907$	−30.0433	−0.997573	−0.498786	+	0.866725i	$0.666221\pi$
$908$	32.9898	1.09481
$909$	8.72052	0.289242
$910$	12.9245	0.428443
$911$	32.2300	1.06783	0.533914	−	0.845539i	$-0.320721\pi$
$911$	32.2300	1.06783	0.533914	+	0.845539i	$0.320721\pi$
$912$	−28.5388	−0.945014
$913$	16.0358	0.530706
$914$	3.14096	0.103894
$915$	8.29972	0.274380
$916$	−0.758437	−0.0250595
$917$	4.44888	0.146915
$918$	−2.81259	−0.0928292
$919$	−31.7512	−1.04737	−0.523687	−	0.851911i	$-0.675444\pi$
$919$	−31.7512	−1.04737	−0.523687	+	0.851911i	$0.675444\pi$
$920$	−4.42110	−0.145759
$921$	−39.2969	−1.29488
$922$	10.2528	0.337659
$923$	31.0677	1.02261
$924$	18.1930	0.598505
$925$	−0.966578	−0.0317809
$926$	−1.45667	−0.0478692
$927$	−8.58756	−0.282052
$928$	6.39332	0.209871
$929$	18.7774	0.616067	0.308034	−	0.951375i	$-0.400329\pi$
$929$	18.7774	0.616067	0.308034	+	0.951375i	$0.400329\pi$
$930$	−6.95443	−0.228045
$931$	48.0945	1.57623
$932$	−34.8553	−1.14172
$933$	52.6811	1.72470
$934$	0.812481	0.0265852
$935$	−7.14148	−0.233552
$936$	7.90115	0.258257
$937$	−45.9639	−1.50158	−0.750788	−	0.660543i	$-0.770326\pi$
$937$	−45.9639	−1.50158	−0.750788	+	0.660543i	$0.770326\pi$
$938$	−9.71348	−0.317156
$939$	2.96963	0.0969101
$940$	−27.9681	−0.912220
$941$	12.1677	0.396656	0.198328	−	0.980136i	$-0.436449\pi$
$941$	12.1677	0.396656	0.198328	+	0.980136i	$0.436449\pi$
$942$	−8.44869	−0.275273
$943$	−1.10635	−0.0360277
$944$	−14.8656	−0.483834
$945$	−30.6511	−0.997082
$946$	−3.19098	−0.103748
$947$	−47.1566	−1.53239	−0.766193	−	0.642611i	$-0.777851\pi$
$947$	−47.1566	−1.53239	−0.766193	+	0.642611i	$0.777851\pi$
$948$	53.1409	1.72594
$949$	−78.1396	−2.53652
$950$	0.352502	0.0114367
$951$	27.0512	0.877195
$952$	−15.3844	−0.498610
$953$	0.795485	0.0257683	0.0128841	−	0.999917i	$-0.495899\pi$
$953$	0.795485	0.0257683	0.0128841	+	0.999917i	$0.495899\pi$
$954$	−3.48610	−0.112867
$955$	−9.63588	−0.311810
$956$	53.2808	1.72322
$957$	−4.45869	−0.144129
$958$	1.52145	0.0491558
$959$	−3.76732	−0.121653
$960$	29.0392	0.937237
$961$	1.83261	0.0591165
$962$	−3.69051	−0.118987
$963$	19.5479	0.629924
$964$	13.4258	0.432416
$965$	−12.6227	−0.406339
$966$	4.92137	0.158342
$967$	0.481648	0.0154888	0.00774438	−	0.999970i	$-0.497535\pi$
$967$	0.481648	0.0154888	0.00774438	+	0.999970i	$0.497535\pi$
$968$	1.04383	0.0335498
$969$	−26.3974	−0.848006
$970$	6.10739	0.196096
$971$	18.0929	0.580630	0.290315	−	0.956931i	$-0.406240\pi$
$971$	18.0929	0.580630	0.290315	+	0.956931i	$0.406240\pi$
$972$	−27.5053	−0.882233
$973$	57.1778	1.83304
$974$	−2.79566	−0.0895787
$975$	3.79511	0.121541
$976$	−6.50621	−0.208259
$977$	47.6594	1.52476	0.762379	−	0.647131i	$-0.224031\pi$
$977$	47.6594	1.52476	0.762379	+	0.647131i	$0.224031\pi$
$978$	−0.391221	−0.0125099
$979$	15.2228	0.486522
$980$	−53.2078	−1.69966
$981$	−22.3655	−0.714075
$982$	0.527435	0.0168311
$983$	−12.8634	−0.410279	−0.205139	−	0.978733i	$-0.565765\pi$
$983$	−12.8634	−0.410279	−0.205139	+	0.978733i	$0.565765\pi$
$984$	−1.24574	−0.0397129
$985$	36.6583	1.16803
$986$	1.85133	0.0589583
$987$	63.4044	2.01818
$988$	−36.7997	−1.17075
$989$	23.6015	0.750486
$990$	0.854421	0.0271553
$991$	12.5497	0.398655	0.199327	−	0.979933i	$-0.436124\pi$
$991$	12.5497	0.398655	0.199327	+	0.979933i	$0.436124\pi$
$992$	17.4138	0.552889
$993$	4.86007	0.154230
$994$	7.23739	0.229556
$995$	41.2754	1.30852
$996$	−65.5755	−2.07784
$997$	18.8507	0.597009	0.298504	−	0.954408i	$-0.403512\pi$
$997$	18.8507	0.597009	0.298504	+	0.954408i	$0.403512\pi$
$998$	3.23009	0.102247
$999$	8.75224	0.276909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.d.1.12	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.d.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-0.265643 q^{2} -2.11945 q^{3} -1.92943 q^{4} +2.15570 q^{5} +0.563016 q^{6} -4.44888 q^{7} +1.04383 q^{8} +1.49206 q^{9} +O(q^{10})\)	\(q-0.265643 q^{2} -2.11945 q^{3} -1.92943 q^{4} +2.15570 q^{5} +0.563016 q^{6} -4.44888 q^{7} +1.04383 q^{8} +1.49206 q^{9} -0.572646 q^{10} -1.00000 q^{11} +4.08933 q^{12} +5.07313 q^{13} +1.18181 q^{14} -4.56889 q^{15} +3.58158 q^{16} +3.31284 q^{17} -0.396354 q^{18} +3.75957 q^{19} -4.15928 q^{20} +9.42917 q^{21} +0.265643 q^{22} -1.96478 q^{23} -2.21233 q^{24} -0.352960 q^{25} -1.34764 q^{26} +3.19600 q^{27} +8.58383 q^{28} -2.10371 q^{29} +1.21369 q^{30} -5.72997 q^{31} -3.03907 q^{32} +2.11945 q^{33} -0.880032 q^{34} -9.59046 q^{35} -2.87883 q^{36} +2.73849 q^{37} -0.998703 q^{38} -10.7522 q^{39} +2.25018 q^{40} +0.563090 q^{41} -2.50479 q^{42} -12.0123 q^{43} +1.92943 q^{44} +3.21643 q^{45} +0.521930 q^{46} +6.72427 q^{47} -7.59098 q^{48} +12.7926 q^{49} +0.0937612 q^{50} -7.02139 q^{51} -9.78828 q^{52} +8.79541 q^{53} -0.848996 q^{54} -2.15570 q^{55} -4.64386 q^{56} -7.96821 q^{57} +0.558834 q^{58} -4.15057 q^{59} +8.81537 q^{60} -1.81657 q^{61} +1.52213 q^{62} -6.63799 q^{63} -6.35586 q^{64} +10.9362 q^{65} -0.563016 q^{66} -8.21913 q^{67} -6.39190 q^{68} +4.16425 q^{69} +2.54764 q^{70} +6.12397 q^{71} +1.55745 q^{72} -15.4026 q^{73} -0.727461 q^{74} +0.748080 q^{75} -7.25384 q^{76} +4.44888 q^{77} +2.85626 q^{78} +12.9950 q^{79} +7.72082 q^{80} -11.2499 q^{81} -0.149581 q^{82} -16.0358 q^{83} -18.1930 q^{84} +7.14148 q^{85} +3.19098 q^{86} +4.45869 q^{87} -1.04383 q^{88} -15.2228 q^{89} -0.854421 q^{90} -22.5698 q^{91} +3.79091 q^{92} +12.1444 q^{93} -1.78626 q^{94} +8.10450 q^{95} +6.44116 q^{96} -10.6652 q^{97} -3.39825 q^{98} -1.49206 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 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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