LMFDB - Embedded newform 2001.2.a.l.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 $ x^11 - 2x^10 - 18x^9 + 30x^8 + 124x^7 - 152x^6 - 408x^5 + 285x^4 + 634x^3 - 93x^2 - 369x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.24285$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24285 q^{2} -1.00000 q^{3} +3.03039 q^{4} +3.33222 q^{5} -2.24285 q^{6} +0.336371 q^{7} +2.31101 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.24285 q^{2} -1.00000 q^{3} +3.03039 q^{4} +3.33222 q^{5} -2.24285 q^{6} +0.336371 q^{7} +2.31101 q^{8} +1.00000 q^{9} +7.47368 q^{10} +5.35570 q^{11} -3.03039 q^{12} -2.46960 q^{13} +0.754431 q^{14} -3.33222 q^{15} -0.877521 q^{16} +3.61233 q^{17} +2.24285 q^{18} -5.53686 q^{19} +10.0979 q^{20} -0.336371 q^{21} +12.0120 q^{22} +1.00000 q^{23} -2.31101 q^{24} +6.10369 q^{25} -5.53895 q^{26} -1.00000 q^{27} +1.01934 q^{28} -1.00000 q^{29} -7.47368 q^{30} +8.47832 q^{31} -6.59017 q^{32} -5.35570 q^{33} +8.10192 q^{34} +1.12086 q^{35} +3.03039 q^{36} +9.55887 q^{37} -12.4184 q^{38} +2.46960 q^{39} +7.70079 q^{40} -11.0317 q^{41} -0.754431 q^{42} +3.41828 q^{43} +16.2299 q^{44} +3.33222 q^{45} +2.24285 q^{46} -9.57079 q^{47} +0.877521 q^{48} -6.88685 q^{49} +13.6897 q^{50} -3.61233 q^{51} -7.48385 q^{52} -6.66459 q^{53} -2.24285 q^{54} +17.8464 q^{55} +0.777358 q^{56} +5.53686 q^{57} -2.24285 q^{58} -1.21308 q^{59} -10.0979 q^{60} +7.12445 q^{61} +19.0156 q^{62} +0.336371 q^{63} -13.0257 q^{64} -8.22926 q^{65} -12.0120 q^{66} +5.16723 q^{67} +10.9468 q^{68} -1.00000 q^{69} +2.51393 q^{70} +2.09303 q^{71} +2.31101 q^{72} -10.2973 q^{73} +21.4391 q^{74} -6.10369 q^{75} -16.7788 q^{76} +1.80150 q^{77} +5.53895 q^{78} -3.62841 q^{79} -2.92409 q^{80} +1.00000 q^{81} -24.7426 q^{82} +12.6742 q^{83} -1.01934 q^{84} +12.0371 q^{85} +7.66669 q^{86} +1.00000 q^{87} +12.3771 q^{88} +11.8040 q^{89} +7.47368 q^{90} -0.830703 q^{91} +3.03039 q^{92} -8.47832 q^{93} -21.4659 q^{94} -18.4500 q^{95} +6.59017 q^{96} -3.01739 q^{97} -15.4462 q^{98} +5.35570 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * 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 $

$2$	2.24285	1.58594	0.792968	−	0.609263i	$-0.208535\pi$
$2$	2.24285	1.58594	0.792968	+	0.609263i	$0.208535\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.03039	1.51519
$5$	3.33222	1.49021	0.745107	−	0.666945i	$-0.232398\pi$
$5$	3.33222	1.49021	0.745107	+	0.666945i	$0.232398\pi$
$6$	−2.24285	−0.915641
$7$	0.336371	0.127136	0.0635682	−	0.997977i	$-0.479752\pi$
$7$	0.336371	0.127136	0.0635682	+	0.997977i	$0.479752\pi$
$8$	2.31101	0.817066
$9$	1.00000	0.333333
$10$	7.47368	2.36338
$11$	5.35570	1.61480	0.807402	−	0.590001i	$-0.200873\pi$
$11$	5.35570	1.61480	0.807402	+	0.590001i	$0.200873\pi$
$12$	−3.03039	−0.874798
$13$	−2.46960	−0.684944	−0.342472	−	0.939528i	$-0.611264\pi$
$13$	−2.46960	−0.684944	−0.342472	+	0.939528i	$0.611264\pi$
$14$	0.754431	0.201630
$15$	−3.33222	−0.860376
$16$	−0.877521	−0.219380
$17$	3.61233	0.876118	0.438059	−	0.898946i	$-0.355666\pi$
$17$	3.61233	0.876118	0.438059	+	0.898946i	$0.355666\pi$
$18$	2.24285	0.528645
$19$	−5.53686	−1.27024	−0.635121	−	0.772413i	$-0.719050\pi$
$19$	−5.53686	−1.27024	−0.635121	+	0.772413i	$0.719050\pi$
$20$	10.0979	2.25796
$21$	−0.336371	−0.0734022
$22$	12.0120	2.56098
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.31101	−0.471733
$25$	6.10369	1.22074
$26$	−5.53895	−1.08628
$27$	−1.00000	−0.192450
$28$	1.01934	0.192636
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−7.47368	−1.36450
$31$	8.47832	1.52275	0.761376	−	0.648311i	$-0.224524\pi$
$31$	8.47832	1.52275	0.761376	+	0.648311i	$0.224524\pi$
$32$	−6.59017	−1.16499
$33$	−5.35570	−0.932308
$34$	8.10192	1.38947
$35$	1.12086	0.189460
$36$	3.03039	0.505065
$37$	9.55887	1.57147	0.785734	−	0.618565i	$-0.212285\pi$
$37$	9.55887	1.57147	0.785734	+	0.618565i	$0.212285\pi$
$38$	−12.4184	−2.01452
$39$	2.46960	0.395453
$40$	7.70079	1.21760
$41$	−11.0317	−1.72287	−0.861434	−	0.507870i	$-0.830433\pi$
$41$	−11.0317	−1.72287	−0.861434	+	0.507870i	$0.830433\pi$
$42$	−0.754431	−0.116411
$43$	3.41828	0.521282	0.260641	−	0.965436i	$-0.416066\pi$
$43$	3.41828	0.521282	0.260641	+	0.965436i	$0.416066\pi$
$44$	16.2299	2.44674
$45$	3.33222	0.496738
$46$	2.24285	0.330691
$47$	−9.57079	−1.39604	−0.698022	−	0.716077i	$-0.745936\pi$
$47$	−9.57079	−1.39604	−0.698022	+	0.716077i	$0.745936\pi$
$48$	0.877521	0.126659
$49$	−6.88685	−0.983836
$50$	13.6897	1.93601
$51$	−3.61233	−0.505827
$52$	−7.48385	−1.03782
$53$	−6.66459	−0.915452	−0.457726	−	0.889093i	$-0.651336\pi$
$53$	−6.66459	−0.915452	−0.457726	+	0.889093i	$0.651336\pi$
$54$	−2.24285	−0.305214
$55$	17.8464	2.40640
$56$	0.777358	0.103879
$57$	5.53686	0.733375
$58$	−2.24285	−0.294501
$59$	−1.21308	−0.157930	−0.0789650	−	0.996877i	$-0.525162\pi$
$59$	−1.21308	−0.157930	−0.0789650	+	0.996877i	$0.525162\pi$
$60$	−10.0979	−1.30364
$61$	7.12445	0.912193	0.456096	−	0.889930i	$-0.349247\pi$
$61$	7.12445	0.912193	0.456096	+	0.889930i	$0.349247\pi$
$62$	19.0156	2.41499
$63$	0.336371	0.0423788
$64$	−13.0257	−1.62822
$65$	−8.22926	−1.02071
$66$	−12.0120	−1.47858
$67$	5.16723	0.631278	0.315639	−	0.948879i	$-0.397781\pi$
$67$	5.16723	0.631278	0.315639	+	0.948879i	$0.397781\pi$
$68$	10.9468	1.32749
$69$	−1.00000	−0.120386
$70$	2.51393	0.300472
$71$	2.09303	0.248397	0.124199	−	0.992257i	$-0.460364\pi$
$71$	2.09303	0.248397	0.124199	+	0.992257i	$0.460364\pi$
$72$	2.31101	0.272355
$73$	−10.2973	−1.20520	−0.602602	−	0.798042i	$-0.705869\pi$
$73$	−10.2973	−1.20520	−0.602602	+	0.798042i	$0.705869\pi$
$74$	21.4391	2.49225
$75$	−6.10369	−0.704793
$76$	−16.7788	−1.92466
$77$	1.80150	0.205300
$78$	5.53895	0.627163
$79$	−3.62841	−0.408229	−0.204114	−	0.978947i	$-0.565431\pi$
$79$	−3.62841	−0.408229	−0.204114	+	0.978947i	$0.565431\pi$
$80$	−2.92409	−0.326924
$81$	1.00000	0.111111
$82$	−24.7426	−2.73236
$83$	12.6742	1.39117	0.695587	−	0.718442i	$-0.255144\pi$
$83$	12.6742	1.39117	0.695587	+	0.718442i	$0.255144\pi$
$84$	−1.01934	−0.111219
$85$	12.0371	1.30560
$86$	7.66669	0.826721
$87$	1.00000	0.107211
$88$	12.3771	1.31940
$89$	11.8040	1.25122	0.625611	−	0.780135i	$-0.284850\pi$
$89$	11.8040	1.25122	0.625611	+	0.780135i	$0.284850\pi$
$90$	7.47368	0.787795
$91$	−0.830703	−0.0870814
$92$	3.03039	0.315940
$93$	−8.47832	−0.879161
$94$	−21.4659	−2.21404
$95$	−18.4500	−1.89293
$96$	6.59017	0.672607
$97$	−3.01739	−0.306369	−0.153185	−	0.988198i	$-0.548953\pi$
$97$	−3.01739	−0.306369	−0.153185	+	0.988198i	$0.548953\pi$
$98$	−15.4462	−1.56030
$99$	5.35570	0.538268
$100$	18.4966	1.84966
$101$	−16.5824	−1.65001	−0.825007	−	0.565122i	$-0.808829\pi$
$101$	−16.5824	−1.65001	−0.825007	+	0.565122i	$0.808829\pi$
$102$	−8.10192	−0.802210
$103$	6.41290	0.631882	0.315941	−	0.948779i	$-0.397680\pi$
$103$	6.41290	0.631882	0.315941	+	0.948779i	$0.397680\pi$
$104$	−5.70728	−0.559644
$105$	−1.12086	−0.109385
$106$	−14.9477	−1.45185
$107$	13.1923	1.27535	0.637673	−	0.770307i	$-0.279897\pi$
$107$	13.1923	1.27535	0.637673	+	0.770307i	$0.279897\pi$
$108$	−3.03039	−0.291599
$109$	−10.5087	−1.00655	−0.503274	−	0.864127i	$-0.667871\pi$
$109$	−10.5087	−1.00655	−0.503274	+	0.864127i	$0.667871\pi$
$110$	40.0268	3.81640
$111$	−9.55887	−0.907287
$112$	−0.295173	−0.0278912
$113$	3.10892	0.292462	0.146231	−	0.989250i	$-0.453286\pi$
$113$	3.10892	0.292462	0.146231	+	0.989250i	$0.453286\pi$
$114$	12.4184	1.16309
$115$	3.33222	0.310731
$116$	−3.03039	−0.281365
$117$	−2.46960	−0.228315
$118$	−2.72077	−0.250467
$119$	1.21508	0.111387
$120$	−7.70079	−0.702983
$121$	17.6835	1.60759
$122$	15.9791	1.44668
$123$	11.0317	0.994698
$124$	25.6926	2.30726
$125$	3.67774	0.328947
$126$	0.754431	0.0672101
$127$	14.8180	1.31489	0.657443	−	0.753504i	$-0.271638\pi$
$127$	14.8180	1.31489	0.657443	+	0.753504i	$0.271638\pi$
$128$	−16.0345	−1.41726
$129$	−3.41828	−0.300963
$130$	−18.4570	−1.61879
$131$	2.63363	0.230102	0.115051	−	0.993360i	$-0.463297\pi$
$131$	2.63363	0.230102	0.115051	+	0.993360i	$0.463297\pi$
$132$	−16.2299	−1.41263
$133$	−1.86244	−0.161494
$134$	11.5893	1.00117
$135$	−3.33222	−0.286792
$136$	8.34813	0.715846
$137$	−11.2822	−0.963901	−0.481951	−	0.876198i	$-0.660072\pi$
$137$	−11.2822	−0.963901	−0.481951	+	0.876198i	$0.660072\pi$
$138$	−2.24285	−0.190924
$139$	3.55731	0.301727	0.150863	−	0.988555i	$-0.451795\pi$
$139$	3.55731	0.301727	0.150863	+	0.988555i	$0.451795\pi$
$140$	3.39665	0.287069
$141$	9.57079	0.806006
$142$	4.69437	0.393942
$143$	−13.2264	−1.10605
$144$	−0.877521	−0.0731268
$145$	−3.33222	−0.276726
$146$	−23.0952	−1.91138
$147$	6.88685	0.568018
$148$	28.9671	2.38108
$149$	14.5948	1.19565	0.597827	−	0.801625i	$-0.296031\pi$
$149$	14.5948	1.19565	0.597827	+	0.801625i	$0.296031\pi$
$150$	−13.6897	−1.11776
$151$	18.5847	1.51240	0.756202	−	0.654338i	$-0.227053\pi$
$151$	18.5847	1.51240	0.756202	+	0.654338i	$0.227053\pi$
$152$	−12.7957	−1.03787
$153$	3.61233	0.292039
$154$	4.04051	0.325593
$155$	28.2516	2.26923
$156$	7.48385	0.599188
$157$	−9.26130	−0.739132	−0.369566	−	0.929204i	$-0.620494\pi$
$157$	−9.26130	−0.739132	−0.369566	+	0.929204i	$0.620494\pi$
$158$	−8.13800	−0.647425
$159$	6.66459	0.528536
$160$	−21.9599	−1.73608
$161$	0.336371	0.0265098
$162$	2.24285	0.176215
$163$	−21.2102	−1.66131	−0.830655	−	0.556788i	$-0.812034\pi$
$163$	−21.2102	−1.66131	−0.830655	+	0.556788i	$0.812034\pi$
$164$	−33.4304	−2.61048
$165$	−17.8464	−1.38934
$166$	28.4264	2.20631
$167$	−21.3627	−1.65310	−0.826549	−	0.562865i	$-0.809699\pi$
$167$	−21.3627	−1.65310	−0.826549	+	0.562865i	$0.809699\pi$
$168$	−0.777358	−0.0599744
$169$	−6.90107	−0.530851
$170$	26.9974	2.07060
$171$	−5.53686	−0.423414
$172$	10.3587	0.789844
$173$	−10.6746	−0.811578	−0.405789	−	0.913967i	$-0.633003\pi$
$173$	−10.6746	−0.811578	−0.405789	+	0.913967i	$0.633003\pi$
$174$	2.24285	0.170030
$175$	2.05311	0.155200
$176$	−4.69974	−0.354256
$177$	1.21308	0.0911810
$178$	26.4746	1.98436
$179$	−2.48471	−0.185716	−0.0928579	−	0.995679i	$-0.529600\pi$
$179$	−2.48471	−0.185716	−0.0928579	+	0.995679i	$0.529600\pi$
$180$	10.0979	0.752655
$181$	−10.3160	−0.766784	−0.383392	−	0.923586i	$-0.625244\pi$
$181$	−10.3160	−0.766784	−0.383392	+	0.923586i	$0.625244\pi$
$182$	−1.86315	−0.138106
$183$	−7.12445	−0.526655
$184$	2.31101	0.170370
$185$	31.8522	2.34182
$186$	−19.0156	−1.39429
$187$	19.3466	1.41476
$188$	−29.0032	−2.11528
$189$	−0.336371	−0.0244674
$190$	−41.3807	−3.00207
$191$	−21.4183	−1.54977	−0.774886	−	0.632101i	$-0.782193\pi$
$191$	−21.4183	−1.54977	−0.774886	+	0.632101i	$0.782193\pi$
$192$	13.0257	0.940052
$193$	−13.7870	−0.992409	−0.496204	−	0.868206i	$-0.665273\pi$
$193$	−13.7870	−0.992409	−0.496204	+	0.868206i	$0.665273\pi$
$194$	−6.76756	−0.485882
$195$	8.22926	0.589309
$196$	−20.8698	−1.49070
$197$	−15.4879	−1.10347	−0.551735	−	0.834019i	$-0.686034\pi$
$197$	−15.4879	−1.10347	−0.551735	+	0.834019i	$0.686034\pi$
$198$	12.0120	0.853659
$199$	4.97074	0.352367	0.176183	−	0.984357i	$-0.443625\pi$
$199$	4.97074	0.352367	0.176183	+	0.984357i	$0.443625\pi$
$200$	14.1057	0.997423
$201$	−5.16723	−0.364468
$202$	−37.1920	−2.61682
$203$	−0.336371	−0.0236086
$204$	−10.9468	−0.766427
$205$	−36.7602	−2.56744
$206$	14.3832	1.00212
$207$	1.00000	0.0695048
$208$	2.16713	0.150263
$209$	−29.6537	−2.05119
$210$	−2.51393	−0.173478
$211$	−26.1099	−1.79748	−0.898739	−	0.438484i	$-0.855516\pi$
$211$	−26.1099	−1.79748	−0.898739	+	0.438484i	$0.855516\pi$
$212$	−20.1963	−1.38709
$213$	−2.09303	−0.143412
$214$	29.5883	2.02262
$215$	11.3905	0.776823
$216$	−2.31101	−0.157244
$217$	2.85186	0.193597
$218$	−23.5694	−1.59632
$219$	10.2973	0.695824
$220$	54.0814	3.64617
$221$	−8.92101	−0.600092
$222$	−21.4391	−1.43890
$223$	−8.28206	−0.554608	−0.277304	−	0.960782i	$-0.589441\pi$
$223$	−8.28206	−0.554608	−0.277304	+	0.960782i	$0.589441\pi$
$224$	−2.21675	−0.148113
$225$	6.10369	0.406913
$226$	6.97284	0.463826
$227$	−15.0362	−0.997985	−0.498992	−	0.866606i	$-0.666296\pi$
$227$	−15.0362	−0.997985	−0.498992	+	0.866606i	$0.666296\pi$
$228$	16.7788	1.11121
$229$	−9.35622	−0.618277	−0.309138	−	0.951017i	$-0.600041\pi$
$229$	−9.35622	−0.618277	−0.309138	+	0.951017i	$0.600041\pi$
$230$	7.47368	0.492800
$231$	−1.80150	−0.118530
$232$	−2.31101	−0.151725
$233$	1.51916	0.0995233	0.0497616	−	0.998761i	$-0.484154\pi$
$233$	1.51916	0.0995233	0.0497616	+	0.998761i	$0.484154\pi$
$234$	−5.53895	−0.362093
$235$	−31.8920	−2.08040
$236$	−3.67612	−0.239295
$237$	3.62841	0.235691
$238$	2.72525	0.176652
$239$	−13.1287	−0.849225	−0.424612	−	0.905375i	$-0.639590\pi$
$239$	−13.1287	−0.849225	−0.424612	+	0.905375i	$0.639590\pi$
$240$	2.92409	0.188749
$241$	26.0253	1.67644	0.838218	−	0.545335i	$-0.183598\pi$
$241$	26.0253	1.67644	0.838218	+	0.545335i	$0.183598\pi$
$242$	39.6616	2.54954
$243$	−1.00000	−0.0641500
$244$	21.5899	1.38215
$245$	−22.9485	−1.46613
$246$	24.7426	1.57753
$247$	13.6738	0.870045
$248$	19.5935	1.24419
$249$	−12.6742	−0.803195
$250$	8.24863	0.521689
$251$	24.1425	1.52386	0.761932	−	0.647657i	$-0.224251\pi$
$251$	24.1425	1.52386	0.761932	+	0.647657i	$0.224251\pi$
$252$	1.01934	0.0642121
$253$	5.35570	0.336710
$254$	33.2346	2.08533
$255$	−12.0371	−0.753791
$256$	−9.91149	−0.619468
$257$	23.1679	1.44518	0.722588	−	0.691279i	$-0.242952\pi$
$257$	23.1679	1.44518	0.722588	+	0.691279i	$0.242952\pi$
$258$	−7.66669	−0.477308
$259$	3.21533	0.199791
$260$	−24.9378	−1.54658
$261$	−1.00000	−0.0618984
$262$	5.90685	0.364927
$263$	11.8107	0.728277	0.364138	−	0.931345i	$-0.381364\pi$
$263$	11.8107	0.728277	0.364138	+	0.931345i	$0.381364\pi$
$264$	−12.3771	−0.761757
$265$	−22.2079	−1.36422
$266$	−4.17718	−0.256119
$267$	−11.8040	−0.722393
$268$	15.6587	0.956508
$269$	−8.58123	−0.523207	−0.261603	−	0.965175i	$-0.584251\pi$
$269$	−8.58123	−0.523207	−0.261603	+	0.965175i	$0.584251\pi$
$270$	−7.47368	−0.454834
$271$	−11.0288	−0.669952	−0.334976	−	0.942227i	$-0.608728\pi$
$271$	−11.0288	−0.669952	−0.334976	+	0.942227i	$0.608728\pi$
$272$	−3.16990	−0.192203
$273$	0.830703	0.0502764
$274$	−25.3043	−1.52869
$275$	32.6895	1.97125
$276$	−3.03039	−0.182408
$277$	9.78001	0.587624	0.293812	−	0.955863i	$-0.405076\pi$
$277$	9.78001	0.587624	0.293812	+	0.955863i	$0.405076\pi$
$278$	7.97851	0.478520
$279$	8.47832	0.507584
$280$	2.59033	0.154802
$281$	−2.79284	−0.166607	−0.0833034	−	0.996524i	$-0.526547\pi$
$281$	−2.79284	−0.166607	−0.0833034	+	0.996524i	$0.526547\pi$
$282$	21.4659	1.27827
$283$	−22.6337	−1.34544	−0.672718	−	0.739899i	$-0.734873\pi$
$283$	−22.6337	−1.34544	−0.672718	+	0.739899i	$0.734873\pi$
$284$	6.34270	0.376370
$285$	18.4500	1.09289
$286$	−29.6650	−1.75413
$287$	−3.71076	−0.219039
$288$	−6.59017	−0.388330
$289$	−3.95108	−0.232417
$290$	−7.47368	−0.438870
$291$	3.01739	0.176882
$292$	−31.2047	−1.82612
$293$	26.9534	1.57463	0.787316	−	0.616550i	$-0.211470\pi$
$293$	26.9534	1.57463	0.787316	+	0.616550i	$0.211470\pi$
$294$	15.4462	0.900841
$295$	−4.04226	−0.235350
$296$	22.0906	1.28399
$297$	−5.35570	−0.310769
$298$	32.7340	1.89623
$299$	−2.46960	−0.142821
$300$	−18.4966	−1.06790
$301$	1.14981	0.0662740
$302$	41.6828	2.39858
$303$	16.5824	0.952636
$304$	4.85871	0.278666
$305$	23.7402	1.35936
$306$	8.10192	0.463156
$307$	10.5081	0.599727	0.299863	−	0.953982i	$-0.403059\pi$
$307$	10.5081	0.599727	0.299863	+	0.953982i	$0.403059\pi$
$308$	5.45926	0.311070
$309$	−6.41290	−0.364817
$310$	63.3643	3.59885
$311$	31.8702	1.80719	0.903596	−	0.428385i	$-0.140917\pi$
$311$	31.8702	1.80719	0.903596	+	0.428385i	$0.140917\pi$
$312$	5.70728	0.323111
$313$	−21.3092	−1.20446	−0.602232	−	0.798321i	$-0.705722\pi$
$313$	−21.3092	−1.20446	−0.602232	+	0.798321i	$0.705722\pi$
$314$	−20.7717	−1.17222
$315$	1.12086	0.0631535
$316$	−10.9955	−0.618546
$317$	13.6193	0.764935	0.382467	−	0.923969i	$-0.375074\pi$
$317$	13.6193	0.764935	0.382467	+	0.923969i	$0.375074\pi$
$318$	14.9477	0.838225
$319$	−5.35570	−0.299862
$320$	−43.4046	−2.42639
$321$	−13.1923	−0.736321
$322$	0.754431	0.0420428
$323$	−20.0009	−1.11288
$324$	3.03039	0.168355
$325$	−15.0737	−0.836138
$326$	−47.5713	−2.63473
$327$	10.5087	0.581131
$328$	−25.4945	−1.40770
$329$	−3.21934	−0.177488
$330$	−40.0268	−2.20340
$331$	−8.92149	−0.490370	−0.245185	−	0.969476i	$-0.578849\pi$
$331$	−8.92149	−0.490370	−0.245185	+	0.969476i	$0.578849\pi$
$332$	38.4078	2.10790
$333$	9.55887	0.523823
$334$	−47.9135	−2.62171
$335$	17.2183	0.940739
$336$	0.295173	0.0161030
$337$	6.68953	0.364402	0.182201	−	0.983261i	$-0.441678\pi$
$337$	6.68953	0.364402	0.182201	+	0.983261i	$0.441678\pi$
$338$	−15.4781	−0.841896
$339$	−3.10892	−0.168853
$340$	36.4770	1.97824
$341$	45.4074	2.45895
$342$	−12.4184	−0.671508
$343$	−4.67114	−0.252218
$344$	7.89968	0.425922
$345$	−3.33222	−0.179401
$346$	−23.9416	−1.28711
$347$	−10.4807	−0.562635	−0.281317	−	0.959615i	$-0.590771\pi$
$347$	−10.4807	−0.562635	−0.281317	+	0.959615i	$0.590771\pi$
$348$	3.03039	0.162446
$349$	−21.7281	−1.16308	−0.581538	−	0.813519i	$-0.697549\pi$
$349$	−21.7281	−1.16308	−0.581538	+	0.813519i	$0.697549\pi$
$350$	4.60482	0.246138
$351$	2.46960	0.131818
$352$	−35.2950	−1.88123
$353$	−24.6326	−1.31106	−0.655530	−	0.755169i	$-0.727555\pi$
$353$	−24.6326	−1.31106	−0.655530	+	0.755169i	$0.727555\pi$
$354$	2.72077	0.144607
$355$	6.97445	0.370165
$356$	35.7707	1.89584
$357$	−1.21508	−0.0643091
$358$	−5.57284	−0.294534
$359$	−5.00818	−0.264322	−0.132161	−	0.991228i	$-0.542192\pi$
$359$	−5.00818	−0.264322	−0.132161	+	0.991228i	$0.542192\pi$
$360$	7.70079	0.405868
$361$	11.6568	0.613515
$362$	−23.1373	−1.21607
$363$	−17.6835	−0.928145
$364$	−2.51735	−0.131945
$365$	−34.3127	−1.79601
$366$	−15.9791	−0.835241
$367$	−5.98074	−0.312192	−0.156096	−	0.987742i	$-0.549891\pi$
$367$	−5.98074	−0.312192	−0.156096	+	0.987742i	$0.549891\pi$
$368$	−0.877521	−0.0457440
$369$	−11.0317	−0.574289
$370$	71.4399	3.71398
$371$	−2.24178	−0.116387
$372$	−25.6926	−1.33210
$373$	25.9060	1.34136	0.670680	−	0.741747i	$-0.266002\pi$
$373$	25.9060	1.34136	0.670680	+	0.741747i	$0.266002\pi$
$374$	43.3915	2.24372
$375$	−3.67774	−0.189918
$376$	−22.1182	−1.14066
$377$	2.46960	0.127191
$378$	−0.754431	−0.0388038
$379$	34.7368	1.78431	0.892155	−	0.451729i	$-0.149193\pi$
$379$	34.7368	1.78431	0.892155	+	0.451729i	$0.149193\pi$
$380$	−55.9107	−2.86816
$381$	−14.8180	−0.759150
$382$	−48.0380	−2.45784
$383$	−22.0435	−1.12637	−0.563184	−	0.826331i	$-0.690424\pi$
$383$	−22.0435	−1.12637	−0.563184	+	0.826331i	$0.690424\pi$
$384$	16.0345	0.818256
$385$	6.00301	0.305942
$386$	−30.9222	−1.57390
$387$	3.41828	0.173761
$388$	−9.14386	−0.464209
$389$	−10.7238	−0.543716	−0.271858	−	0.962337i	$-0.587638\pi$
$389$	−10.7238	−0.543716	−0.271858	+	0.962337i	$0.587638\pi$
$390$	18.4570	0.934607
$391$	3.61233	0.182683
$392$	−15.9156	−0.803859
$393$	−2.63363	−0.132849
$394$	−34.7372	−1.75003
$395$	−12.0907	−0.608348
$396$	16.2299	0.815581
$397$	−7.85754	−0.394358	−0.197179	−	0.980367i	$-0.563178\pi$
$397$	−7.85754	−0.394358	−0.197179	+	0.980367i	$0.563178\pi$
$398$	11.1486	0.558831
$399$	1.86244	0.0932386
$400$	−5.35612	−0.267806
$401$	15.0606	0.752089	0.376044	−	0.926602i	$-0.377284\pi$
$401$	15.0606	0.752089	0.376044	+	0.926602i	$0.377284\pi$
$402$	−11.5893	−0.578023
$403$	−20.9381	−1.04300
$404$	−50.2512	−2.50009
$405$	3.33222	0.165579
$406$	−0.754431	−0.0374418
$407$	51.1944	2.53761
$408$	−8.34813	−0.413294
$409$	29.3347	1.45051	0.725253	−	0.688483i	$-0.241723\pi$
$409$	29.3347	1.45051	0.725253	+	0.688483i	$0.241723\pi$
$410$	−82.4476	−4.07180
$411$	11.2822	0.556509
$412$	19.4336	0.957424
$413$	−0.408047	−0.0200787
$414$	2.24285	0.110230
$415$	42.2332	2.07315
$416$	16.2751	0.797952
$417$	−3.55731	−0.174202
$418$	−66.5090	−3.25306
$419$	−28.4982	−1.39223	−0.696114	−	0.717931i	$-0.745089\pi$
$419$	−28.4982	−1.39223	−0.696114	+	0.717931i	$0.745089\pi$
$420$	−3.39665	−0.165740
$421$	13.1838	0.642540	0.321270	−	0.946988i	$-0.395890\pi$
$421$	13.1838	0.642540	0.321270	+	0.946988i	$0.395890\pi$
$422$	−58.5606	−2.85069
$423$	−9.57079	−0.465348
$424$	−15.4019	−0.747984
$425$	22.0485	1.06951
$426$	−4.69437	−0.227443
$427$	2.39646	0.115973
$428$	39.9777	1.93240
$429$	13.2264	0.638579
$430$	25.5471	1.23199
$431$	21.0595	1.01440	0.507200	−	0.861829i	$-0.330681\pi$
$431$	21.0595	1.01440	0.507200	+	0.861829i	$0.330681\pi$
$432$	0.877521	0.0422198
$433$	−29.6426	−1.42453	−0.712267	−	0.701909i	$-0.752331\pi$
$433$	−29.6426	−1.42453	−0.712267	+	0.701909i	$0.752331\pi$
$434$	6.39631	0.307033
$435$	3.33222	0.159768
$436$	−31.8454	−1.52512
$437$	−5.53686	−0.264864
$438$	23.0952	1.10353
$439$	18.1064	0.864171	0.432086	−	0.901833i	$-0.357778\pi$
$439$	18.1064	0.864171	0.432086	+	0.901833i	$0.357778\pi$
$440$	41.2432	1.96619
$441$	−6.88685	−0.327945
$442$	−20.0085	−0.951708
$443$	20.7008	0.983527	0.491763	−	0.870729i	$-0.336353\pi$
$443$	20.7008	0.983527	0.491763	+	0.870729i	$0.336353\pi$
$444$	−28.9671	−1.37472
$445$	39.3335	1.86459
$446$	−18.5754	−0.879573
$447$	−14.5948	−0.690311
$448$	−4.38149	−0.207006
$449$	−13.6101	−0.642301	−0.321150	−	0.947028i	$-0.604069\pi$
$449$	−13.6101	−0.642301	−0.321150	+	0.947028i	$0.604069\pi$
$450$	13.6897	0.645338
$451$	−59.0827	−2.78209
$452$	9.42122	0.443137
$453$	−18.5847	−0.873187
$454$	−33.7239	−1.58274
$455$	−2.76809	−0.129770
$456$	12.7957	0.599215
$457$	4.36067	0.203984	0.101992	−	0.994785i	$-0.467478\pi$
$457$	4.36067	0.203984	0.101992	+	0.994785i	$0.467478\pi$
$458$	−20.9846	−0.980548
$459$	−3.61233	−0.168609
$460$	10.0979	0.470818
$461$	1.61989	0.0754459	0.0377230	−	0.999288i	$-0.487990\pi$
$461$	1.61989	0.0754459	0.0377230	+	0.999288i	$0.487990\pi$
$462$	−4.04051	−0.187981
$463$	−0.152373	−0.00708136	−0.00354068	−	0.999994i	$-0.501127\pi$
$463$	−0.152373	−0.00708136	−0.00354068	+	0.999994i	$0.501127\pi$
$464$	0.877521	0.0407379
$465$	−28.2516	−1.31014
$466$	3.40725	0.157838
$467$	25.7057	1.18952	0.594758	−	0.803904i	$-0.297248\pi$
$467$	25.7057	1.18952	0.594758	+	0.803904i	$0.297248\pi$
$468$	−7.48385	−0.345941
$469$	1.73811	0.0802584
$470$	−71.5290	−3.29939
$471$	9.26130	0.426738
$472$	−2.80345	−0.129039
$473$	18.3073	0.841769
$474$	8.13800	0.373791
$475$	−33.7953	−1.55063
$476$	3.68218	0.168772
$477$	−6.66459	−0.305151
$478$	−29.4457	−1.34682
$479$	5.89195	0.269210	0.134605	−	0.990899i	$-0.457023\pi$
$479$	5.89195	0.269210	0.134605	+	0.990899i	$0.457023\pi$
$480$	21.9599	1.00233
$481$	−23.6066	−1.07637
$482$	58.3709	2.65872
$483$	−0.336371	−0.0153054
$484$	53.5880	2.43582
$485$	−10.0546	−0.456556
$486$	−2.24285	−0.101738
$487$	−31.3733	−1.42166	−0.710831	−	0.703363i	$-0.751681\pi$
$487$	−31.3733	−1.42166	−0.710831	+	0.703363i	$0.751681\pi$
$488$	16.4647	0.745321
$489$	21.2102	0.959158
$490$	−51.4701	−2.32518
$491$	2.87963	0.129956	0.0649778	−	0.997887i	$-0.479302\pi$
$491$	2.87963	0.129956	0.0649778	+	0.997887i	$0.479302\pi$
$492$	33.4304	1.50716
$493$	−3.61233	−0.162691
$494$	30.6684	1.37984
$495$	17.8464	0.802135
$496$	−7.43991	−0.334062
$497$	0.704036	0.0315804
$498$	−28.4264	−1.27382
$499$	43.8494	1.96297	0.981484	−	0.191542i	$-0.0613489\pi$
$499$	43.8494	1.96297	0.981484	+	0.191542i	$0.0613489\pi$
$500$	11.1450	0.498419
$501$	21.3627	0.954416
$502$	54.1482	2.41675
$503$	−41.9172	−1.86900	−0.934498	−	0.355969i	$-0.884151\pi$
$503$	−41.9172	−1.86900	−0.934498	+	0.355969i	$0.884151\pi$
$504$	0.777358	0.0346263
$505$	−55.2563	−2.45887
$506$	12.0120	0.534001
$507$	6.90107	0.306487
$508$	44.9044	1.99231
$509$	−15.4761	−0.685966	−0.342983	−	0.939342i	$-0.611437\pi$
$509$	−15.4761	−0.685966	−0.342983	+	0.939342i	$0.611437\pi$
$510$	−26.9974	−1.19546
$511$	−3.46370	−0.153225
$512$	9.83894	0.434824
$513$	5.53686	0.244458
$514$	51.9623	2.29196
$515$	21.3692	0.941640
$516$	−10.3587	−0.456017
$517$	−51.2583	−2.25434
$518$	7.21151	0.316856
$519$	10.6746	0.468565
$520$	−19.0179	−0.833990
$521$	1.20679	0.0528705	0.0264352	−	0.999651i	$-0.491584\pi$
$521$	1.20679	0.0528705	0.0264352	+	0.999651i	$0.491584\pi$
$522$	−2.24285	−0.0981670
$523$	−8.84819	−0.386905	−0.193452	−	0.981110i	$-0.561968\pi$
$523$	−8.84819	−0.386905	−0.193452	+	0.981110i	$0.561968\pi$
$524$	7.98094	0.348649
$525$	−2.05311	−0.0896049
$526$	26.4896	1.15500
$527$	30.6265	1.33411
$528$	4.69974	0.204530
$529$	1.00000	0.0434783
$530$	−49.8090	−2.16357
$531$	−1.21308	−0.0526434
$532$	−5.64392	−0.244695
$533$	27.2440	1.18007
$534$	−26.4746	−1.14567
$535$	43.9596	1.90054
$536$	11.9415	0.515795
$537$	2.48471	0.107223
$538$	−19.2464	−0.829772
$539$	−36.8839	−1.58870
$540$	−10.0979	−0.434545
$541$	22.1794	0.953567	0.476783	−	0.879021i	$-0.341803\pi$
$541$	22.1794	0.953567	0.476783	+	0.879021i	$0.341803\pi$
$542$	−24.7360	−1.06250
$543$	10.3160	0.442703
$544$	−23.8059	−1.02067
$545$	−35.0172	−1.49997
$546$	1.86315	0.0797353
$547$	22.7728	0.973697	0.486848	−	0.873486i	$-0.338146\pi$
$547$	22.7728	0.973697	0.486848	+	0.873486i	$0.338146\pi$
$548$	−34.1894	−1.46050
$549$	7.12445	0.304064
$550$	73.3178	3.12628
$551$	5.53686	0.235878
$552$	−2.31101	−0.0983631
$553$	−1.22049	−0.0519007
$554$	21.9351	0.931934
$555$	−31.8522	−1.35205
$556$	10.7800	0.457175
$557$	0.846399	0.0358631	0.0179315	−	0.999839i	$-0.494292\pi$
$557$	0.846399	0.0358631	0.0179315	+	0.999839i	$0.494292\pi$
$558$	19.0156	0.804996
$559$	−8.44179	−0.357049
$560$	−0.983582	−0.0415639
$561$	−19.3466	−0.816812
$562$	−6.26393	−0.264228
$563$	−40.0831	−1.68930	−0.844650	−	0.535318i	$-0.820192\pi$
$563$	−40.0831	−1.68930	−0.844650	+	0.535318i	$0.820192\pi$
$564$	29.0032	1.22126
$565$	10.3596	0.435831
$566$	−50.7641	−2.13378
$567$	0.336371	0.0141263
$568$	4.83702	0.202957
$569$	23.3038	0.976945	0.488472	−	0.872579i	$-0.337554\pi$
$569$	23.3038	0.976945	0.488472	+	0.872579i	$0.337554\pi$
$570$	41.3807	1.73325
$571$	−0.411433	−0.0172179	−0.00860896	−	0.999963i	$-0.502740\pi$
$571$	−0.411433	−0.0172179	−0.00860896	+	0.999963i	$0.502740\pi$
$572$	−40.0813	−1.67588
$573$	21.4183	0.894761
$574$	−8.32269	−0.347382
$575$	6.10369	0.254541
$576$	−13.0257	−0.542739
$577$	−13.5456	−0.563910	−0.281955	−	0.959428i	$-0.590983\pi$
$577$	−13.5456	−0.563910	−0.281955	+	0.959428i	$0.590983\pi$
$578$	−8.86169	−0.368598
$579$	13.7870	0.572968
$580$	−10.0979	−0.419293
$581$	4.26324	0.176869
$582$	6.76756	0.280524
$583$	−35.6936	−1.47828
$584$	−23.7971	−0.984730
$585$	−8.22926	−0.340238
$586$	60.4524	2.49727
$587$	33.9417	1.40092	0.700461	−	0.713690i	$-0.252978\pi$
$587$	33.9417	1.40092	0.700461	+	0.713690i	$0.252978\pi$
$588$	20.8698	0.860658
$589$	−46.9433	−1.93426
$590$	−9.06620	−0.373250
$591$	15.4879	0.637089
$592$	−8.38811	−0.344749
$593$	−35.4814	−1.45705	−0.728524	−	0.685021i	$-0.759793\pi$
$593$	−35.4814	−1.45705	−0.728524	+	0.685021i	$0.759793\pi$
$594$	−12.0120	−0.492860
$595$	4.04893	0.165990
$596$	44.2280	1.81165
$597$	−4.97074	−0.203439
$598$	−5.53895	−0.226505
$599$	39.5554	1.61619	0.808094	−	0.589054i	$-0.200499\pi$
$599$	39.5554	1.61619	0.808094	+	0.589054i	$0.200499\pi$
$600$	−14.1057	−0.575862
$601$	15.7875	0.643984	0.321992	−	0.946742i	$-0.395648\pi$
$601$	15.7875	0.643984	0.321992	+	0.946742i	$0.395648\pi$
$602$	2.57886	0.105106
$603$	5.16723	0.210426
$604$	56.3190	2.29159
$605$	58.9254	2.39566
$606$	37.1920	1.51082
$607$	23.3376	0.947244	0.473622	−	0.880728i	$-0.342946\pi$
$607$	23.3376	0.947244	0.473622	+	0.880728i	$0.342946\pi$
$608$	36.4888	1.47982
$609$	0.336371	0.0136305
$610$	53.2459	2.15586
$611$	23.6360	0.956212
$612$	10.9468	0.442497
$613$	−37.7636	−1.52526	−0.762628	−	0.646837i	$-0.776091\pi$
$613$	−37.7636	−1.52526	−0.762628	+	0.646837i	$0.776091\pi$
$614$	23.5680	0.951129
$615$	36.7602	1.48231
$616$	4.16329	0.167744
$617$	−19.3263	−0.778046	−0.389023	−	0.921228i	$-0.627187\pi$
$617$	−19.3263	−0.778046	−0.389023	+	0.921228i	$0.627187\pi$
$618$	−14.3832	−0.578577
$619$	40.2999	1.61979	0.809894	−	0.586576i	$-0.199524\pi$
$619$	40.2999	1.61979	0.809894	+	0.586576i	$0.199524\pi$
$620$	85.6134	3.43832
$621$	−1.00000	−0.0401286
$622$	71.4801	2.86609
$623$	3.97053	0.159076
$624$	−2.16713	−0.0867546
$625$	−18.2634	−0.730537
$626$	−47.7933	−1.91020
$627$	29.6537	1.18426
$628$	−28.0653	−1.11993
$629$	34.5298	1.37679
$630$	2.51393	0.100157
$631$	−4.24160	−0.168855	−0.0844276	−	0.996430i	$-0.526906\pi$
$631$	−4.24160	−0.168855	−0.0844276	+	0.996430i	$0.526906\pi$
$632$	−8.38530	−0.333549
$633$	26.1099	1.03777
$634$	30.5460	1.21314
$635$	49.3769	1.95946
$636$	20.1963	0.800835
$637$	17.0078	0.673873
$638$	−12.0120	−0.475562
$639$	2.09303	0.0827991
$640$	−53.4304	−2.11202
$641$	14.6358	0.578080	0.289040	−	0.957317i	$-0.406664\pi$
$641$	14.6358	0.578080	0.289040	+	0.957317i	$0.406664\pi$
$642$	−29.5883	−1.16776
$643$	−7.97033	−0.314319	−0.157159	−	0.987573i	$-0.550234\pi$
$643$	−7.97033	−0.314319	−0.157159	+	0.987573i	$0.550234\pi$
$644$	1.01934	0.0401675
$645$	−11.3905	−0.448499
$646$	−44.8592	−1.76496
$647$	−0.258751	−0.0101726	−0.00508628	−	0.999987i	$-0.501619\pi$
$647$	−0.258751	−0.0101726	−0.00508628	+	0.999987i	$0.501619\pi$
$648$	2.31101	0.0907851
$649$	−6.49691	−0.255026
$650$	−33.8081	−1.32606
$651$	−2.85186	−0.111773
$652$	−64.2751	−2.51721
$653$	25.8829	1.01288	0.506438	−	0.862276i	$-0.330962\pi$
$653$	25.8829	1.01288	0.506438	+	0.862276i	$0.330962\pi$
$654$	23.5694	0.921637
$655$	8.77585	0.342901
$656$	9.68058	0.377963
$657$	−10.2973	−0.401734
$658$	−7.22051	−0.281485
$659$	−2.80499	−0.109267	−0.0546335	−	0.998506i	$-0.517399\pi$
$659$	−2.80499	−0.109267	−0.0546335	+	0.998506i	$0.517399\pi$
$660$	−54.0814	−2.10512
$661$	33.3102	1.29562	0.647809	−	0.761803i	$-0.275685\pi$
$661$	33.3102	1.29562	0.647809	+	0.761803i	$0.275685\pi$
$662$	−20.0096	−0.777695
$663$	8.92101	0.346463
$664$	29.2902	1.13668
$665$	−6.20606	−0.240661
$666$	21.4391	0.830749
$667$	−1.00000	−0.0387202
$668$	−64.7374	−2.50476
$669$	8.28206	0.320203
$670$	38.6182	1.49195
$671$	38.1564	1.47301
$672$	2.21675	0.0855128
$673$	−0.265368	−0.0102292	−0.00511459	−	0.999987i	$-0.501628\pi$
$673$	−0.265368	−0.0102292	−0.00511459	+	0.999987i	$0.501628\pi$
$674$	15.0036	0.577918
$675$	−6.10369	−0.234931
$676$	−20.9129	−0.804343
$677$	16.0535	0.616987	0.308494	−	0.951226i	$-0.400175\pi$
$677$	16.0535	0.616987	0.308494	+	0.951226i	$0.400175\pi$
$678$	−6.97284	−0.267790
$679$	−1.01496	−0.0389507
$680$	27.8178	1.06676
$681$	15.0362	0.576187
$682$	101.842	3.89973
$683$	32.7737	1.25405	0.627025	−	0.778999i	$-0.284272\pi$
$683$	32.7737	1.25405	0.627025	+	0.778999i	$0.284272\pi$
$684$	−16.7788	−0.641555
$685$	−37.5947	−1.43642
$686$	−10.4767	−0.400001
$687$	9.35622	0.356962
$688$	−2.99961	−0.114359
$689$	16.4589	0.627034
$690$	−7.47368	−0.284518
$691$	45.9477	1.74793	0.873966	−	0.485986i	$-0.161540\pi$
$691$	45.9477	1.74793	0.873966	+	0.485986i	$0.161540\pi$
$692$	−32.3483	−1.22970
$693$	1.80150	0.0684335
$694$	−23.5067	−0.892303
$695$	11.8537	0.449638
$696$	2.31101	0.0875986
$697$	−39.8503	−1.50944
$698$	−48.7328	−1.84457
$699$	−1.51916	−0.0574598
$700$	6.22171	0.235159
$701$	−11.1726	−0.421984	−0.210992	−	0.977488i	$-0.567669\pi$
$701$	−11.1726	−0.421984	−0.210992	+	0.977488i	$0.567669\pi$
$702$	5.53895	0.209054
$703$	−52.9261	−1.99614
$704$	−69.7620	−2.62925
$705$	31.8920	1.20112
$706$	−55.2473	−2.07926
$707$	−5.57786	−0.209777
$708$	3.67612	0.138157
$709$	−0.376876	−0.0141539	−0.00707693	−	0.999975i	$-0.502253\pi$
$709$	−0.376876	−0.0141539	−0.00707693	+	0.999975i	$0.502253\pi$
$710$	15.6427	0.587059
$711$	−3.62841	−0.136076
$712$	27.2792	1.02233
$713$	8.47832	0.317516
$714$	−2.72525	−0.101990
$715$	−44.0734	−1.64825
$716$	−7.52963	−0.281396
$717$	13.1287	0.490300
$718$	−11.2326	−0.419198
$719$	33.2548	1.24020	0.620098	−	0.784525i	$-0.287093\pi$
$719$	33.2548	1.24020	0.620098	+	0.784525i	$0.287093\pi$
$720$	−2.92409	−0.108975
$721$	2.15712	0.0803352
$722$	26.1444	0.972995
$723$	−26.0253	−0.967891
$724$	−31.2616	−1.16183
$725$	−6.10369	−0.226685
$726$	−39.6616	−1.47198
$727$	−10.5234	−0.390293	−0.195146	−	0.980774i	$-0.562518\pi$
$727$	−10.5234	−0.390293	−0.195146	+	0.980774i	$0.562518\pi$
$728$	−1.91976	−0.0711512
$729$	1.00000	0.0370370
$730$	−76.9584	−2.84836
$731$	12.3479	0.456705
$732$	−21.5899	−0.797984
$733$	−17.1253	−0.632536	−0.316268	−	0.948670i	$-0.602430\pi$
$733$	−17.1253	−0.632536	−0.316268	+	0.948670i	$0.602430\pi$
$734$	−13.4139	−0.495117
$735$	22.9485	0.846469
$736$	−6.59017	−0.242917
$737$	27.6741	1.01939
$738$	−24.7426	−0.910786
$739$	20.9535	0.770788	0.385394	−	0.922752i	$-0.374065\pi$
$739$	20.9535	0.770788	0.385394	+	0.922752i	$0.374065\pi$
$740$	96.5247	3.54832
$741$	−13.6738	−0.502321
$742$	−5.02798	−0.184583
$743$	15.7655	0.578381	0.289190	−	0.957272i	$-0.406614\pi$
$743$	15.7655	0.578381	0.289190	+	0.957272i	$0.406614\pi$
$744$	−19.5935	−0.718332
$745$	48.6332	1.78178
$746$	58.1033	2.12731
$747$	12.6742	0.463725
$748$	58.6276	2.14364
$749$	4.43750	0.162143
$750$	−8.24863	−0.301197
$751$	40.8709	1.49140	0.745700	−	0.666282i	$-0.232115\pi$
$751$	40.8709	1.49140	0.745700	+	0.666282i	$0.232115\pi$
$752$	8.39858	0.306265
$753$	−24.1425	−0.879803
$754$	5.53895	0.201717
$755$	61.9284	2.25381
$756$	−1.01934	−0.0370729
$757$	37.3932	1.35908	0.679539	−	0.733639i	$-0.262180\pi$
$757$	37.3932	1.35908	0.679539	+	0.733639i	$0.262180\pi$
$758$	77.9096	2.82980
$759$	−5.35570	−0.194400
$760$	−42.6382	−1.54665
$761$	−12.0596	−0.437161	−0.218581	−	0.975819i	$-0.570143\pi$
$761$	−12.0596	−0.437161	−0.218581	+	0.975819i	$0.570143\pi$
$762$	−33.2346	−1.20396
$763$	−3.53482	−0.127969
$764$	−64.9057	−2.34820
$765$	12.0371	0.435201
$766$	−49.4402	−1.78635
$767$	2.99583	0.108173
$768$	9.91149	0.357650
$769$	27.8157	1.00306	0.501531	−	0.865140i	$-0.332770\pi$
$769$	27.8157	1.00306	0.501531	+	0.865140i	$0.332770\pi$
$770$	13.4639	0.485204
$771$	−23.1679	−0.834373
$772$	−41.7799	−1.50369
$773$	−12.1443	−0.436801	−0.218401	−	0.975859i	$-0.570084\pi$
$773$	−12.1443	−0.436801	−0.218401	+	0.975859i	$0.570084\pi$
$774$	7.66669	0.275574
$775$	51.7491	1.85888
$776$	−6.97321	−0.250324
$777$	−3.21533	−0.115349
$778$	−24.0518	−0.862299
$779$	61.0811	2.18846
$780$	24.9378	0.892918
$781$	11.2097	0.401113
$782$	8.10192	0.289724
$783$	1.00000	0.0357371
$784$	6.04336	0.215834
$785$	−30.8607	−1.10147
$786$	−5.90685	−0.210690
$787$	−18.7378	−0.667929	−0.333964	−	0.942586i	$-0.608387\pi$
$787$	−18.7378	−0.667929	−0.333964	+	0.942586i	$0.608387\pi$
$788$	−46.9345	−1.67197
$789$	−11.8107	−0.420471
$790$	−27.1176	−0.964801
$791$	1.04575	0.0371826
$792$	12.3771	0.439800
$793$	−17.5946	−0.624801
$794$	−17.6233	−0.625427
$795$	22.2079	0.787632
$796$	15.0633	0.533904
$797$	26.9033	0.952964	0.476482	−	0.879184i	$-0.341912\pi$
$797$	26.9033	0.952964	0.476482	+	0.879184i	$0.341912\pi$
$798$	4.17718	0.147871
$799$	−34.5728	−1.22310
$800$	−40.2244	−1.42215
$801$	11.8040	0.417074
$802$	33.7786	1.19277
$803$	−55.1490	−1.94617
$804$	−15.6587	−0.552240
$805$	1.12086	0.0395052
$806$	−46.9610	−1.65413
$807$	8.58123	0.302073
$808$	−38.3222	−1.34817
$809$	−25.3753	−0.892147	−0.446073	−	0.894996i	$-0.647178\pi$
$809$	−25.3753	−0.892147	−0.446073	+	0.894996i	$0.647178\pi$
$810$	7.47368	0.262598
$811$	−26.9252	−0.945471	−0.472736	−	0.881204i	$-0.656733\pi$
$811$	−26.9252	−0.945471	−0.472736	+	0.881204i	$0.656733\pi$
$812$	−1.01934	−0.0357717
$813$	11.0288	0.386797
$814$	114.822	4.02449
$815$	−70.6770	−2.47571
$816$	3.16990	0.110969
$817$	−18.9265	−0.662155
$818$	65.7933	2.30041
$819$	−0.830703	−0.0290271
$820$	−111.398	−3.89017
$821$	−24.9489	−0.870722	−0.435361	−	0.900256i	$-0.643379\pi$
$821$	−24.9489	−0.870722	−0.435361	+	0.900256i	$0.643379\pi$
$822$	25.3043	0.882587
$823$	21.2224	0.739765	0.369882	−	0.929079i	$-0.379398\pi$
$823$	21.2224	0.739765	0.369882	+	0.929079i	$0.379398\pi$
$824$	14.8203	0.516289
$825$	−32.6895	−1.13810
$826$	−0.915189	−0.0318435
$827$	13.9717	0.485844	0.242922	−	0.970046i	$-0.421894\pi$
$827$	13.9717	0.485844	0.242922	+	0.970046i	$0.421894\pi$
$828$	3.03039	0.105313
$829$	5.62458	0.195350	0.0976748	−	0.995218i	$-0.468859\pi$
$829$	5.62458	0.195350	0.0976748	+	0.995218i	$0.468859\pi$
$830$	94.7229	3.28788
$831$	−9.78001	−0.339265
$832$	32.1684	1.11524
$833$	−24.8776	−0.861957
$834$	−7.97851	−0.276273
$835$	−71.1853	−2.46347
$836$	−89.8624	−3.10796
$837$	−8.47832	−0.293054
$838$	−63.9173	−2.20799
$839$	47.4932	1.63965	0.819824	−	0.572616i	$-0.194071\pi$
$839$	47.4932	1.63965	0.819824	+	0.572616i	$0.194071\pi$
$840$	−2.59033	−0.0893748
$841$	1.00000	0.0344828
$842$	29.5693	1.01903
$843$	2.79284	0.0961905
$844$	−79.1231	−2.72353
$845$	−22.9959	−0.791082
$846$	−21.4659	−0.738012
$847$	5.94823	0.204384
$848$	5.84832	0.200832
$849$	22.6337	0.776788
$850$	49.4516	1.69618
$851$	9.55887	0.327674
$852$	−6.34270	−0.217297
$853$	−10.5035	−0.359634	−0.179817	−	0.983700i	$-0.557550\pi$
$853$	−10.5035	−0.359634	−0.179817	+	0.983700i	$0.557550\pi$
$854$	5.37491	0.183926
$855$	−18.4500	−0.630978
$856$	30.4875	1.04204
$857$	−21.3106	−0.727956	−0.363978	−	0.931407i	$-0.618582\pi$
$857$	−21.3106	−0.727956	−0.363978	+	0.931407i	$0.618582\pi$
$858$	29.6650	1.01275
$859$	−21.9655	−0.749452	−0.374726	−	0.927136i	$-0.622263\pi$
$859$	−21.9655	−0.749452	−0.374726	+	0.927136i	$0.622263\pi$
$860$	34.5175	1.17704
$861$	3.71076	0.126462
$862$	47.2333	1.60877
$863$	50.0442	1.70353	0.851763	−	0.523928i	$-0.175534\pi$
$863$	50.0442	1.70353	0.851763	+	0.523928i	$0.175534\pi$
$864$	6.59017	0.224202
$865$	−35.5702	−1.20942
$866$	−66.4841	−2.25922
$867$	3.95108	0.134186
$868$	8.64226	0.293337
$869$	−19.4327	−0.659209
$870$	7.47368	0.253381
$871$	−12.7610	−0.432390
$872$	−24.2857	−0.822416
$873$	−3.01739	−0.102123
$874$	−12.4184	−0.420057
$875$	1.23709	0.0418211
$876$	31.2047	1.05431
$877$	−26.3344	−0.889248	−0.444624	−	0.895717i	$-0.646663\pi$
$877$	−26.3344	−0.889248	−0.444624	+	0.895717i	$0.646663\pi$
$878$	40.6100	1.37052
$879$	−26.9534	−0.909114
$880$	−15.6606	−0.527918
$881$	53.3563	1.79762	0.898809	−	0.438340i	$-0.144433\pi$
$881$	53.3563	1.79762	0.898809	+	0.438340i	$0.144433\pi$
$882$	−15.4462	−0.520101
$883$	2.46924	0.0830966	0.0415483	−	0.999136i	$-0.486771\pi$
$883$	2.46924	0.0830966	0.0415483	+	0.999136i	$0.486771\pi$
$884$	−27.0341	−0.909256
$885$	4.04226	0.135879
$886$	46.4289	1.55981
$887$	53.9526	1.81155	0.905776	−	0.423757i	$-0.139289\pi$
$887$	53.9526	1.81155	0.905776	+	0.423757i	$0.139289\pi$
$888$	−22.0906	−0.741313
$889$	4.98436	0.167170
$890$	88.2193	2.95712
$891$	5.35570	0.179423
$892$	−25.0979	−0.840339
$893$	52.9921	1.77331
$894$	−32.7340	−1.09479
$895$	−8.27960	−0.276756
$896$	−5.39354	−0.180186
$897$	2.46960	0.0824576
$898$	−30.5255	−1.01865
$899$	−8.47832	−0.282768
$900$	18.4966	0.616552
$901$	−24.0747	−0.802044
$902$	−132.514	−4.41222
$903$	−1.14981	−0.0382633
$904$	7.18474	0.238961
$905$	−34.3753	−1.14267
$906$	−41.6828	−1.38482
$907$	4.54378	0.150874	0.0754368	−	0.997151i	$-0.475965\pi$
$907$	4.54378	0.150874	0.0754368	+	0.997151i	$0.475965\pi$
$908$	−45.5654	−1.51214
$909$	−16.5824	−0.550005
$910$	−6.20841	−0.205807
$911$	−14.6485	−0.485327	−0.242664	−	0.970110i	$-0.578021\pi$
$911$	−14.6485	−0.485327	−0.242664	+	0.970110i	$0.578021\pi$
$912$	−4.85871	−0.160888
$913$	67.8792	2.24647
$914$	9.78035	0.323505
$915$	−23.7402	−0.784828
$916$	−28.3530	−0.936809
$917$	0.885879	0.0292543
$918$	−8.10192	−0.267403
$919$	14.7669	0.487114	0.243557	−	0.969887i	$-0.421686\pi$
$919$	14.7669	0.487114	0.243557	+	0.969887i	$0.421686\pi$
$920$	7.70079	0.253888
$921$	−10.5081	−0.346252
$922$	3.63318	0.119652
$923$	−5.16896	−0.170138
$924$	−5.45926	−0.179596
$925$	58.3444	1.91835
$926$	−0.341750	−0.0112306
$927$	6.41290	0.210627
$928$	6.59017	0.216333
$929$	−27.7957	−0.911947	−0.455973	−	0.889993i	$-0.650709\pi$
$929$	−27.7957	−0.911947	−0.455973	+	0.889993i	$0.650709\pi$
$930$	−63.3643	−2.07780
$931$	38.1315	1.24971
$932$	4.60364	0.150797
$933$	−31.8702	−1.04338
$934$	57.6541	1.88650
$935$	64.4670	2.10830
$936$	−5.70728	−0.186548
$937$	7.42265	0.242487	0.121244	−	0.992623i	$-0.461312\pi$
$937$	7.42265	0.242487	0.121244	+	0.992623i	$0.461312\pi$
$938$	3.89832	0.127285
$939$	21.3092	0.695398
$940$	−96.6451	−3.15222
$941$	42.6205	1.38939	0.694695	−	0.719305i	$-0.255539\pi$
$941$	42.6205	1.38939	0.694695	+	0.719305i	$0.255539\pi$
$942$	20.7717	0.676780
$943$	−11.0317	−0.359243
$944$	1.06451	0.0346468
$945$	−1.12086	−0.0364617
$946$	41.0605	1.33499
$947$	18.8970	0.614069	0.307035	−	0.951698i	$-0.400663\pi$
$947$	18.8970	0.614069	0.307035	+	0.951698i	$0.400663\pi$
$948$	10.9955	0.357117
$949$	25.4301	0.825497
$950$	−75.7978	−2.45920
$951$	−13.6193	−0.441635
$952$	2.80807	0.0910101
$953$	−4.93984	−0.160017	−0.0800086	−	0.996794i	$-0.525495\pi$
$953$	−4.93984	−0.160017	−0.0800086	+	0.996794i	$0.525495\pi$
$954$	−14.9477	−0.483950
$955$	−71.3704	−2.30949
$956$	−39.7851	−1.28674
$957$	5.35570	0.173125
$958$	13.2148	0.426950
$959$	−3.79500	−0.122547
$960$	43.4046	1.40088
$961$	40.8820	1.31877
$962$	−52.9461	−1.70705
$963$	13.1923	0.425115
$964$	78.8667	2.54013
$965$	−45.9413	−1.47890
$966$	−0.754431	−0.0242734
$967$	35.7015	1.14808	0.574041	−	0.818827i	$-0.305375\pi$
$967$	35.7015	1.14808	0.574041	+	0.818827i	$0.305375\pi$
$968$	40.8668	1.31351
$969$	20.0009	0.642523
$970$	−22.5510	−0.724069
$971$	57.8911	1.85781	0.928906	−	0.370315i	$-0.120750\pi$
$971$	57.8911	1.85781	0.928906	+	0.370315i	$0.120750\pi$
$972$	−3.03039	−0.0971998
$973$	1.19658	0.0383605
$974$	−70.3658	−2.25467
$975$	15.0737	0.482744
$976$	−6.25186	−0.200117
$977$	−24.1856	−0.773766	−0.386883	−	0.922129i	$-0.626448\pi$
$977$	−24.1856	−0.773766	−0.386883	+	0.922129i	$0.626448\pi$
$978$	47.5713	1.52116
$979$	63.2187	2.02048
$980$	−69.5429	−2.22147
$981$	−10.5087	−0.335516
$982$	6.45858	0.206101
$983$	−30.1771	−0.962500	−0.481250	−	0.876583i	$-0.659817\pi$
$983$	−30.1771	−0.962500	−0.481250	+	0.876583i	$0.659817\pi$
$984$	25.4945	0.812733
$985$	−51.6092	−1.64441
$986$	−8.10192	−0.258018
$987$	3.21934	0.102473
$988$	41.4370	1.31829
$989$	3.41828	0.108695
$990$	40.0268	1.27213
$991$	24.1655	0.767642	0.383821	−	0.923407i	$-0.374608\pi$
$991$	24.1655	0.767642	0.383821	+	0.923407i	$0.374608\pi$
$992$	−55.8736	−1.77399
$993$	8.92149	0.283115
$994$	1.57905	0.0500844
$995$	16.5636	0.525102
$996$	−38.4078	−1.21700
$997$	−33.3183	−1.05520	−0.527600	−	0.849493i	$-0.676908\pi$
$997$	−33.3183	−1.05520	−0.527600	+	0.849493i	$0.676908\pi$
$998$	98.3478	3.11314
$999$	−9.55887	−0.302429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.9	✓	11
3.2	odd	2		6003.2.a.m.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.9	✓	11	1.1	even	1	trivial
6003.2.a.m.1.3		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24285 q^{2} -1.00000 q^{3} +3.03039 q^{4} +3.33222 q^{5} -2.24285 q^{6} +0.336371 q^{7} +2.31101 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.24285 q^{2} -1.00000 q^{3} +3.03039 q^{4} +3.33222 q^{5} -2.24285 q^{6} +0.336371 q^{7} +2.31101 q^{8} +1.00000 q^{9} +7.47368 q^{10} +5.35570 q^{11} -3.03039 q^{12} -2.46960 q^{13} +0.754431 q^{14} -3.33222 q^{15} -0.877521 q^{16} +3.61233 q^{17} +2.24285 q^{18} -5.53686 q^{19} +10.0979 q^{20} -0.336371 q^{21} +12.0120 q^{22} +1.00000 q^{23} -2.31101 q^{24} +6.10369 q^{25} -5.53895 q^{26} -1.00000 q^{27} +1.01934 q^{28} -1.00000 q^{29} -7.47368 q^{30} +8.47832 q^{31} -6.59017 q^{32} -5.35570 q^{33} +8.10192 q^{34} +1.12086 q^{35} +3.03039 q^{36} +9.55887 q^{37} -12.4184 q^{38} +2.46960 q^{39} +7.70079 q^{40} -11.0317 q^{41} -0.754431 q^{42} +3.41828 q^{43} +16.2299 q^{44} +3.33222 q^{45} +2.24285 q^{46} -9.57079 q^{47} +0.877521 q^{48} -6.88685 q^{49} +13.6897 q^{50} -3.61233 q^{51} -7.48385 q^{52} -6.66459 q^{53} -2.24285 q^{54} +17.8464 q^{55} +0.777358 q^{56} +5.53686 q^{57} -2.24285 q^{58} -1.21308 q^{59} -10.0979 q^{60} +7.12445 q^{61} +19.0156 q^{62} +0.336371 q^{63} -13.0257 q^{64} -8.22926 q^{65} -12.0120 q^{66} +5.16723 q^{67} +10.9468 q^{68} -1.00000 q^{69} +2.51393 q^{70} +2.09303 q^{71} +2.31101 q^{72} -10.2973 q^{73} +21.4391 q^{74} -6.10369 q^{75} -16.7788 q^{76} +1.80150 q^{77} +5.53895 q^{78} -3.62841 q^{79} -2.92409 q^{80} +1.00000 q^{81} -24.7426 q^{82} +12.6742 q^{83} -1.01934 q^{84} +12.0371 q^{85} +7.66669 q^{86} +1.00000 q^{87} +12.3771 q^{88} +11.8040 q^{89} +7.47368 q^{90} -0.830703 q^{91} +3.03039 q^{92} -8.47832 q^{93} -21.4659 q^{94} -18.4500 q^{95} +6.59017 q^{96} -3.01739 q^{97} -15.4462 q^{98} +5.35570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

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