LMFDB - Embedded newform 2001.2.a.k.1.5

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 $ x^10 - x^9 - 17x^8 + 23x^7 + 69x^6 - 88x^5 - 106x^4 + 101x^3 + 60x^2 - 23x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.78422$ 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)

$f(q)$	$=$	$q+0.611391 q^{2} -1.00000 q^{3} -1.62620 q^{4} +0.834863 q^{5} -0.611391 q^{6} -0.685491 q^{7} -2.21703 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.611391 q^{2} -1.00000 q^{3} -1.62620 q^{4} +0.834863 q^{5} -0.611391 q^{6} -0.685491 q^{7} -2.21703 q^{8} +1.00000 q^{9} +0.510427 q^{10} -4.30989 q^{11} +1.62620 q^{12} -6.93620 q^{13} -0.419103 q^{14} -0.834863 q^{15} +1.89693 q^{16} +4.35585 q^{17} +0.611391 q^{18} +5.00543 q^{19} -1.35766 q^{20} +0.685491 q^{21} -2.63503 q^{22} -1.00000 q^{23} +2.21703 q^{24} -4.30300 q^{25} -4.24072 q^{26} -1.00000 q^{27} +1.11475 q^{28} +1.00000 q^{29} -0.510427 q^{30} +9.44967 q^{31} +5.59382 q^{32} +4.30989 q^{33} +2.66313 q^{34} -0.572291 q^{35} -1.62620 q^{36} +7.15237 q^{37} +3.06027 q^{38} +6.93620 q^{39} -1.85091 q^{40} -3.83893 q^{41} +0.419103 q^{42} -7.88050 q^{43} +7.00875 q^{44} +0.834863 q^{45} -0.611391 q^{46} +6.51919 q^{47} -1.89693 q^{48} -6.53010 q^{49} -2.63082 q^{50} -4.35585 q^{51} +11.2797 q^{52} -5.81406 q^{53} -0.611391 q^{54} -3.59817 q^{55} +1.51975 q^{56} -5.00543 q^{57} +0.611391 q^{58} +12.3793 q^{59} +1.35766 q^{60} +14.2688 q^{61} +5.77744 q^{62} -0.685491 q^{63} -0.373862 q^{64} -5.79077 q^{65} +2.63503 q^{66} +5.19008 q^{67} -7.08350 q^{68} +1.00000 q^{69} -0.349893 q^{70} -9.86256 q^{71} -2.21703 q^{72} +10.3402 q^{73} +4.37289 q^{74} +4.30300 q^{75} -8.13983 q^{76} +2.95439 q^{77} +4.24072 q^{78} -0.255706 q^{79} +1.58368 q^{80} +1.00000 q^{81} -2.34709 q^{82} +3.16558 q^{83} -1.11475 q^{84} +3.63654 q^{85} -4.81806 q^{86} -1.00000 q^{87} +9.55514 q^{88} +11.3236 q^{89} +0.510427 q^{90} +4.75470 q^{91} +1.62620 q^{92} -9.44967 q^{93} +3.98577 q^{94} +4.17884 q^{95} -5.59382 q^{96} +5.84187 q^{97} -3.99244 q^{98} -4.30989 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * 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 $

$2$	0.611391	0.432318	0.216159	−	0.976358i	$-0.430647\pi$
$2$	0.611391	0.432318	0.216159	+	0.976358i	$0.430647\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.62620	−0.813101
$5$	0.834863	0.373362	0.186681	−	0.982421i	$-0.440227\pi$
$5$	0.834863	0.373362	0.186681	+	0.982421i	$0.440227\pi$
$6$	−0.611391	−0.249599
$7$	−0.685491	−0.259091	−0.129546	−	0.991573i	$-0.541352\pi$
$7$	−0.685491	−0.259091	−0.129546	+	0.991573i	$0.541352\pi$
$8$	−2.21703	−0.783837
$9$	1.00000	0.333333
$10$	0.510427	0.161411
$11$	−4.30989	−1.29948	−0.649741	−	0.760156i	$-0.725122\pi$
$11$	−4.30989	−1.29948	−0.649741	+	0.760156i	$0.725122\pi$
$12$	1.62620	0.469444
$13$	−6.93620	−1.92375	−0.961877	−	0.273482i	$-0.911825\pi$
$13$	−6.93620	−1.92375	−0.961877	+	0.273482i	$0.911825\pi$
$14$	−0.419103	−0.112010
$15$	−0.834863	−0.215561
$16$	1.89693	0.474234
$17$	4.35585	1.05645	0.528225	−	0.849105i	$-0.322858\pi$
$17$	4.35585	1.05645	0.528225	+	0.849105i	$0.322858\pi$
$18$	0.611391	0.144106
$19$	5.00543	1.14832	0.574162	−	0.818742i	$-0.305328\pi$
$19$	5.00543	1.14832	0.574162	+	0.818742i	$0.305328\pi$
$20$	−1.35766	−0.303581
$21$	0.685491	0.149586
$22$	−2.63503	−0.561790
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.21703	0.452548
$25$	−4.30300	−0.860601
$26$	−4.24072	−0.831674
$27$	−1.00000	−0.192450
$28$	1.11475	0.210667
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.510427	−0.0931908
$31$	9.44967	1.69721	0.848606	−	0.529026i	$-0.177442\pi$
$31$	9.44967	1.69721	0.848606	+	0.529026i	$0.177442\pi$
$32$	5.59382	0.988857
$33$	4.30989	0.750256
$34$	2.66313	0.456723
$35$	−0.572291	−0.0967348
$36$	−1.62620	−0.271034
$37$	7.15237	1.17584	0.587921	−	0.808918i	$-0.299946\pi$
$37$	7.15237	1.17584	0.587921	+	0.808918i	$0.299946\pi$
$38$	3.06027	0.496441
$39$	6.93620	1.11068
$40$	−1.85091	−0.292655
$41$	−3.83893	−0.599540	−0.299770	−	0.954011i	$-0.596910\pi$
$41$	−3.83893	−0.599540	−0.299770	+	0.954011i	$0.596910\pi$
$42$	0.419103	0.0646689
$43$	−7.88050	−1.20176	−0.600882	−	0.799337i	$-0.705184\pi$
$43$	−7.88050	−1.20176	−0.600882	+	0.799337i	$0.705184\pi$
$44$	7.00875	1.05661
$45$	0.834863	0.124454
$46$	−0.611391	−0.0901446
$47$	6.51919	0.950922	0.475461	−	0.879737i	$-0.342281\pi$
$47$	6.51919	0.950922	0.475461	+	0.879737i	$0.342281\pi$
$48$	−1.89693	−0.273799
$49$	−6.53010	−0.932872
$50$	−2.63082	−0.372054
$51$	−4.35585	−0.609942
$52$	11.2797	1.56421
$53$	−5.81406	−0.798623	−0.399312	−	0.916815i	$-0.630751\pi$
$53$	−5.81406	−0.798623	−0.399312	+	0.916815i	$0.630751\pi$
$54$	−0.611391	−0.0831997
$55$	−3.59817	−0.485177
$56$	1.51975	0.203085
$57$	−5.00543	−0.662985
$58$	0.611391	0.0802795
$59$	12.3793	1.61165	0.805826	−	0.592152i	$-0.201722\pi$
$59$	12.3793	1.61165	0.805826	+	0.592152i	$0.201722\pi$
$60$	1.35766	0.175273
$61$	14.2688	1.82693	0.913465	−	0.406916i	$-0.133396\pi$
$61$	14.2688	1.82693	0.913465	+	0.406916i	$0.133396\pi$
$62$	5.77744	0.733736
$63$	−0.685491	−0.0863637
$64$	−0.373862	−0.0467327
$65$	−5.79077	−0.718257
$66$	2.63503	0.324349
$67$	5.19008	0.634069	0.317035	−	0.948414i	$-0.397313\pi$
$67$	5.19008	0.634069	0.317035	+	0.948414i	$0.397313\pi$
$68$	−7.08350	−0.859000
$69$	1.00000	0.120386
$70$	−0.349893	−0.0418202
$71$	−9.86256	−1.17047	−0.585235	−	0.810864i	$-0.698998\pi$
$71$	−9.86256	−1.17047	−0.585235	+	0.810864i	$0.698998\pi$
$72$	−2.21703	−0.261279
$73$	10.3402	1.21023	0.605113	−	0.796140i	$-0.293128\pi$
$73$	10.3402	1.21023	0.605113	+	0.796140i	$0.293128\pi$
$74$	4.37289	0.508339
$75$	4.30300	0.496868
$76$	−8.13983	−0.933703
$77$	2.95439	0.336684
$78$	4.24072	0.480167
$79$	−0.255706	−0.0287692	−0.0143846	−	0.999897i	$-0.504579\pi$
$79$	−0.255706	−0.0287692	−0.0143846	+	0.999897i	$0.504579\pi$
$80$	1.58368	0.177061
$81$	1.00000	0.111111
$82$	−2.34709	−0.259192
$83$	3.16558	0.347467	0.173734	−	0.984793i	$-0.444417\pi$
$83$	3.16558	0.347467	0.173734	+	0.984793i	$0.444417\pi$
$84$	−1.11475	−0.121629
$85$	3.63654	0.394438
$86$	−4.81806	−0.519545
$87$	−1.00000	−0.107211
$88$	9.55514	1.01858
$89$	11.3236	1.20030	0.600148	−	0.799889i	$-0.295108\pi$
$89$	11.3236	1.20030	0.600148	+	0.799889i	$0.295108\pi$
$90$	0.510427	0.0538038
$91$	4.75470	0.498428
$92$	1.62620	0.169543
$93$	−9.44967	−0.979886
$94$	3.98577	0.411101
$95$	4.17884	0.428740
$96$	−5.59382	−0.570917
$97$	5.84187	0.593152	0.296576	−	0.955009i	$-0.404155\pi$
$97$	5.84187	0.593152	0.296576	+	0.955009i	$0.404155\pi$
$98$	−3.99244	−0.403298
$99$	−4.30989	−0.433160
$100$	6.99755	0.699755
$101$	12.7292	1.26660	0.633302	−	0.773905i	$-0.281699\pi$
$101$	12.7292	1.26660	0.633302	+	0.773905i	$0.281699\pi$
$102$	−2.66313	−0.263689
$103$	−15.6336	−1.54042	−0.770212	−	0.637788i	$-0.779850\pi$
$103$	−15.6336	−1.54042	−0.770212	+	0.637788i	$0.779850\pi$
$104$	15.3777	1.50791
$105$	0.572291	0.0558499
$106$	−3.55466	−0.345259
$107$	4.65571	0.450084	0.225042	−	0.974349i	$-0.427748\pi$
$107$	4.65571	0.450084	0.225042	+	0.974349i	$0.427748\pi$
$108$	1.62620	0.156481
$109$	−4.75799	−0.455732	−0.227866	−	0.973692i	$-0.573175\pi$
$109$	−4.75799	−0.455732	−0.227866	+	0.973692i	$0.573175\pi$
$110$	−2.19989	−0.209751
$111$	−7.15237	−0.678873
$112$	−1.30033	−0.122870
$113$	−10.5909	−0.996306	−0.498153	−	0.867089i	$-0.665988\pi$
$113$	−10.5909	−0.996306	−0.498153	+	0.867089i	$0.665988\pi$
$114$	−3.06027	−0.286621
$115$	−0.834863	−0.0778514
$116$	−1.62620	−0.150989
$117$	−6.93620	−0.641251
$118$	7.56861	0.696747
$119$	−2.98590	−0.273717
$120$	1.85091	0.168964
$121$	7.57516	0.688651
$122$	8.72380	0.789816
$123$	3.83893	0.346145
$124$	−15.3671	−1.38000
$125$	−7.76673	−0.694678
$126$	−0.419103	−0.0373366
$127$	8.28369	0.735058	0.367529	−	0.930012i	$-0.380204\pi$
$127$	8.28369	0.735058	0.367529	+	0.930012i	$0.380204\pi$
$128$	−11.4162	−1.00906
$129$	7.88050	0.693839
$130$	−3.54042	−0.310516
$131$	1.34215	0.117264	0.0586320	−	0.998280i	$-0.481326\pi$
$131$	1.34215	0.117264	0.0586320	+	0.998280i	$0.481326\pi$
$132$	−7.00875	−0.610034
$133$	−3.43117	−0.297521
$134$	3.17317	0.274120
$135$	−0.834863	−0.0718535
$136$	−9.65704	−0.828084
$137$	2.09029	0.178585	0.0892926	−	0.996005i	$-0.471539\pi$
$137$	2.09029	0.178585	0.0892926	+	0.996005i	$0.471539\pi$
$138$	0.611391	0.0520450
$139$	3.71254	0.314893	0.157447	−	0.987528i	$-0.449674\pi$
$139$	3.71254	0.314893	0.157447	+	0.987528i	$0.449674\pi$
$140$	0.930660	0.0786551
$141$	−6.51919	−0.549015
$142$	−6.02988	−0.506016
$143$	29.8942	2.49988
$144$	1.89693	0.158078
$145$	0.834863	0.0693316
$146$	6.32189	0.523203
$147$	6.53010	0.538594
$148$	−11.6312	−0.956079
$149$	0.963445	0.0789285	0.0394642	−	0.999221i	$-0.487435\pi$
$149$	0.963445	0.0789285	0.0394642	+	0.999221i	$0.487435\pi$
$150$	2.63082	0.214805
$151$	21.5727	1.75556	0.877779	−	0.479065i	$-0.159024\pi$
$151$	21.5727	1.75556	0.877779	+	0.479065i	$0.159024\pi$
$152$	−11.0972	−0.900098
$153$	4.35585	0.352150
$154$	1.80629	0.145555
$155$	7.88918	0.633674
$156$	−11.2797	−0.903095
$157$	−9.60822	−0.766820	−0.383410	−	0.923578i	$-0.625250\pi$
$157$	−9.60822	−0.766820	−0.383410	+	0.923578i	$0.625250\pi$
$158$	−0.156336	−0.0124375
$159$	5.81406	0.461085
$160$	4.67007	0.369202
$161$	0.685491	0.0540242
$162$	0.611391	0.0480354
$163$	22.2529	1.74298	0.871489	−	0.490415i	$-0.163155\pi$
$163$	22.2529	1.74298	0.871489	+	0.490415i	$0.163155\pi$
$164$	6.24288	0.487487
$165$	3.59817	0.280117
$166$	1.93540	0.150216
$167$	17.6567	1.36632	0.683158	−	0.730270i	$-0.260606\pi$
$167$	17.6567	1.36632	0.683158	+	0.730270i	$0.260606\pi$
$168$	−1.51975	−0.117251
$169$	35.1108	2.70083
$170$	2.22335	0.170523
$171$	5.00543	0.382775
$172$	12.8153	0.977156
$173$	5.17476	0.393430	0.196715	−	0.980461i	$-0.436973\pi$
$173$	5.17476	0.393430	0.196715	+	0.980461i	$0.436973\pi$
$174$	−0.611391	−0.0463494
$175$	2.94967	0.222974
$176$	−8.17558	−0.616258
$177$	−12.3793	−0.930488
$178$	6.92312	0.518910
$179$	−3.93984	−0.294477	−0.147239	−	0.989101i	$-0.547039\pi$
$179$	−3.93984	−0.294477	−0.147239	+	0.989101i	$0.547039\pi$
$180$	−1.35766	−0.101194
$181$	4.69684	0.349114	0.174557	−	0.984647i	$-0.444151\pi$
$181$	4.69684	0.349114	0.174557	+	0.984647i	$0.444151\pi$
$182$	2.90698	0.215480
$183$	−14.2688	−1.05478
$184$	2.21703	0.163441
$185$	5.97125	0.439015
$186$	−5.77744	−0.423623
$187$	−18.7733	−1.37284
$188$	−10.6015	−0.773195
$189$	0.685491	0.0498621
$190$	2.55491	0.185352
$191$	18.7144	1.35413	0.677064	−	0.735924i	$-0.263252\pi$
$191$	18.7144	1.35413	0.677064	+	0.735924i	$0.263252\pi$
$192$	0.373862	0.0269812
$193$	−23.7007	−1.70602	−0.853008	−	0.521898i	$-0.825224\pi$
$193$	−23.7007	−1.70602	−0.853008	+	0.521898i	$0.825224\pi$
$194$	3.57167	0.256431
$195$	5.79077	0.414686
$196$	10.6193	0.758519
$197$	−21.4337	−1.52709	−0.763544	−	0.645756i	$-0.776542\pi$
$197$	−21.4337	−1.52709	−0.763544	+	0.645756i	$0.776542\pi$
$198$	−2.63503	−0.187263
$199$	−2.13493	−0.151341	−0.0756707	−	0.997133i	$-0.524110\pi$
$199$	−2.13493	−0.151341	−0.0756707	+	0.997133i	$0.524110\pi$
$200$	9.53987	0.674571
$201$	−5.19008	−0.366080
$202$	7.78252	0.547576
$203$	−0.685491	−0.0481120
$204$	7.08350	0.495944
$205$	−3.20498	−0.223846
$206$	−9.55824	−0.665954
$207$	−1.00000	−0.0695048
$208$	−13.1575	−0.912309
$209$	−21.5728	−1.49222
$210$	0.349893	0.0241449
$211$	0.324360	0.0223299	0.0111649	−	0.999938i	$-0.496446\pi$
$211$	0.324360	0.0223299	0.0111649	+	0.999938i	$0.496446\pi$
$212$	9.45484	0.649361
$213$	9.86256	0.675771
$214$	2.84646	0.194580
$215$	−6.57914	−0.448693
$216$	2.21703	0.150849
$217$	−6.47767	−0.439733
$218$	−2.90899	−0.197021
$219$	−10.3402	−0.698724
$220$	5.85135	0.394498
$221$	−30.2131	−2.03235
$222$	−4.37289	−0.293489
$223$	−10.7572	−0.720354	−0.360177	−	0.932884i	$-0.617284\pi$
$223$	−10.7572	−0.720354	−0.360177	+	0.932884i	$0.617284\pi$
$224$	−3.83451	−0.256204
$225$	−4.30300	−0.286867
$226$	−6.47516	−0.430721
$227$	18.4688	1.22582	0.612908	−	0.790154i	$-0.290000\pi$
$227$	18.4688	1.22582	0.612908	+	0.790154i	$0.290000\pi$
$228$	8.13983	0.539074
$229$	−21.7562	−1.43769	−0.718846	−	0.695169i	$-0.755330\pi$
$229$	−21.7562	−1.43769	−0.718846	+	0.695169i	$0.755330\pi$
$230$	−0.510427	−0.0336566
$231$	−2.95439	−0.194385
$232$	−2.21703	−0.145555
$233$	5.18209	0.339490	0.169745	−	0.985488i	$-0.445706\pi$
$233$	5.18209	0.339490	0.169745	+	0.985488i	$0.445706\pi$
$234$	−4.24072	−0.277225
$235$	5.44263	0.355038
$236$	−20.1313	−1.31044
$237$	0.255706	0.0166099
$238$	−1.82555	−0.118333
$239$	2.60340	0.168400	0.0841999	−	0.996449i	$-0.473167\pi$
$239$	2.60340	0.168400	0.0841999	+	0.996449i	$0.473167\pi$
$240$	−1.58368	−0.102226
$241$	4.88851	0.314896	0.157448	−	0.987527i	$-0.449673\pi$
$241$	4.88851	0.314896	0.157448	+	0.987527i	$0.449673\pi$
$242$	4.63138	0.297717
$243$	−1.00000	−0.0641500
$244$	−23.2039	−1.48548
$245$	−5.45174	−0.348299
$246$	2.34709	0.149645
$247$	−34.7186	−2.20909
$248$	−20.9502	−1.33034
$249$	−3.16558	−0.200610
$250$	−4.74851	−0.300322
$251$	12.7129	0.802432	0.401216	−	0.915984i	$-0.368588\pi$
$251$	12.7129	0.802432	0.401216	+	0.915984i	$0.368588\pi$
$252$	1.11475	0.0702224
$253$	4.30989	0.270961
$254$	5.06457	0.317779
$255$	−3.63654	−0.227729
$256$	−6.23204	−0.389503
$257$	16.1859	1.00965	0.504825	−	0.863222i	$-0.331557\pi$
$257$	16.1859	1.00965	0.504825	+	0.863222i	$0.331557\pi$
$258$	4.81806	0.299959
$259$	−4.90289	−0.304651
$260$	9.41696	0.584015
$261$	1.00000	0.0618984
$262$	0.820577	0.0506954
$263$	12.8887	0.794749	0.397374	−	0.917657i	$-0.369921\pi$
$263$	12.8887	0.794749	0.397374	+	0.917657i	$0.369921\pi$
$264$	−9.55514	−0.588078
$265$	−4.85395	−0.298176
$266$	−2.09779	−0.128624
$267$	−11.3236	−0.692991
$268$	−8.44011	−0.515562
$269$	−1.11547	−0.0680112	−0.0340056	−	0.999422i	$-0.510826\pi$
$269$	−1.11547	−0.0680112	−0.0340056	+	0.999422i	$0.510826\pi$
$270$	−0.510427	−0.0310636
$271$	−5.92399	−0.359857	−0.179928	−	0.983680i	$-0.557587\pi$
$271$	−5.92399	−0.359857	−0.179928	+	0.983680i	$0.557587\pi$
$272$	8.26277	0.501004
$273$	−4.75470	−0.287767
$274$	1.27798	0.0772057
$275$	18.5455	1.11833
$276$	−1.62620	−0.0978858
$277$	−25.0512	−1.50518	−0.752589	−	0.658491i	$-0.771195\pi$
$277$	−25.0512	−1.50518	−0.752589	+	0.658491i	$0.771195\pi$
$278$	2.26981	0.136134
$279$	9.44967	0.565737
$280$	1.26878	0.0758243
$281$	−16.4921	−0.983834	−0.491917	−	0.870642i	$-0.663704\pi$
$281$	−16.4921	−0.983834	−0.491917	+	0.870642i	$0.663704\pi$
$282$	−3.98577	−0.237349
$283$	−26.8068	−1.59350	−0.796751	−	0.604308i	$-0.793450\pi$
$283$	−26.8068	−1.59350	−0.796751	+	0.604308i	$0.793450\pi$
$284$	16.0385	0.951710
$285$	−4.17884	−0.247533
$286$	18.2771	1.08075
$287$	2.63155	0.155336
$288$	5.59382	0.329619
$289$	1.97346	0.116086
$290$	0.510427	0.0299733
$291$	−5.84187	−0.342457
$292$	−16.8152	−0.984036
$293$	−11.2496	−0.657210	−0.328605	−	0.944467i	$-0.606579\pi$
$293$	−11.2496	−0.657210	−0.328605	+	0.944467i	$0.606579\pi$
$294$	3.99244	0.232844
$295$	10.3350	0.601730
$296$	−15.8570	−0.921669
$297$	4.30989	0.250085
$298$	0.589041	0.0341222
$299$	6.93620	0.401131
$300$	−6.99755	−0.404004
$301$	5.40201	0.311367
$302$	13.1893	0.758960
$303$	−12.7292	−0.731274
$304$	9.49497	0.544574
$305$	11.9125	0.682107
$306$	2.66313	0.152241
$307$	−3.26882	−0.186562	−0.0932808	−	0.995640i	$-0.529735\pi$
$307$	−3.26882	−0.186562	−0.0932808	+	0.995640i	$0.529735\pi$
$308$	−4.80443	−0.273758
$309$	15.6336	0.889365
$310$	4.82337	0.273949
$311$	−6.84083	−0.387908	−0.193954	−	0.981011i	$-0.562131\pi$
$311$	−6.84083	−0.387908	−0.193954	+	0.981011i	$0.562131\pi$
$312$	−15.3777	−0.870592
$313$	−10.8195	−0.611552	−0.305776	−	0.952103i	$-0.598916\pi$
$313$	−10.8195	−0.611552	−0.305776	+	0.952103i	$0.598916\pi$
$314$	−5.87438	−0.331510
$315$	−0.572291	−0.0322449
$316$	0.415830	0.0233923
$317$	21.5866	1.21242	0.606212	−	0.795303i	$-0.292688\pi$
$317$	21.5866	1.21242	0.606212	+	0.795303i	$0.292688\pi$
$318$	3.55466	0.199336
$319$	−4.30989	−0.241308
$320$	−0.312123	−0.0174482
$321$	−4.65571	−0.259856
$322$	0.419103	0.0233557
$323$	21.8029	1.21315
$324$	−1.62620	−0.0903445
$325$	29.8465	1.65558
$326$	13.6052	0.753522
$327$	4.75799	0.263117
$328$	8.51101	0.469942
$329$	−4.46884	−0.246375
$330$	2.19989	0.121100
$331$	−26.1848	−1.43925	−0.719624	−	0.694364i	$-0.755686\pi$
$331$	−26.1848	−1.43925	−0.719624	+	0.694364i	$0.755686\pi$
$332$	−5.14786	−0.282526
$333$	7.15237	0.391948
$334$	10.7951	0.590684
$335$	4.33300	0.236737
$336$	1.30033	0.0709389
$337$	−4.93868	−0.269027	−0.134513	−	0.990912i	$-0.542947\pi$
$337$	−4.93868	−0.269027	−0.134513	+	0.990912i	$0.542947\pi$
$338$	21.4664	1.16762
$339$	10.5909	0.575218
$340$	−5.91375	−0.320718
$341$	−40.7271	−2.20549
$342$	3.06027	0.165480
$343$	9.27476	0.500790
$344$	17.4713	0.941988
$345$	0.834863	0.0449475
$346$	3.16380	0.170087
$347$	−23.6045	−1.26716	−0.633579	−	0.773678i	$-0.718415\pi$
$347$	−23.6045	−1.26716	−0.633579	+	0.773678i	$0.718415\pi$
$348$	1.62620	0.0871736
$349$	−11.7720	−0.630141	−0.315070	−	0.949068i	$-0.602028\pi$
$349$	−11.7720	−0.630141	−0.315070	+	0.949068i	$0.602028\pi$
$350$	1.80340	0.0963958
$351$	6.93620	0.370227
$352$	−24.1088	−1.28500
$353$	17.0723	0.908669	0.454334	−	0.890831i	$-0.349877\pi$
$353$	17.0723	0.908669	0.454334	+	0.890831i	$0.349877\pi$
$354$	−7.56861	−0.402267
$355$	−8.23388	−0.437009
$356$	−18.4144	−0.975961
$357$	2.98590	0.158030
$358$	−2.40878	−0.127308
$359$	33.2963	1.75731	0.878655	−	0.477456i	$-0.158441\pi$
$359$	33.2963	1.75731	0.878655	+	0.477456i	$0.158441\pi$
$360$	−1.85091	−0.0975516
$361$	6.05430	0.318647
$362$	2.87160	0.150928
$363$	−7.57516	−0.397593
$364$	−7.73210	−0.405272
$365$	8.63263	0.451852
$366$	−8.72380	−0.456000
$367$	−17.4010	−0.908327	−0.454163	−	0.890918i	$-0.650062\pi$
$367$	−17.4010	−0.908327	−0.454163	+	0.890918i	$0.650062\pi$
$368$	−1.89693	−0.0988846
$369$	−3.83893	−0.199847
$370$	3.65077	0.189794
$371$	3.98549	0.206916
$372$	15.3671	0.796746
$373$	−27.0425	−1.40021	−0.700104	−	0.714041i	$-0.746863\pi$
$373$	−27.0425	−1.40021	−0.700104	+	0.714041i	$0.746863\pi$
$374$	−11.4778	−0.593502
$375$	7.76673	0.401072
$376$	−14.4532	−0.745367
$377$	−6.93620	−0.357232
$378$	0.419103	0.0215563
$379$	−5.91128	−0.303642	−0.151821	−	0.988408i	$-0.548514\pi$
$379$	−5.91128	−0.303642	−0.151821	+	0.988408i	$0.548514\pi$
$380$	−6.79564	−0.348609
$381$	−8.28369	−0.424386
$382$	11.4418	0.585414
$383$	33.5241	1.71300	0.856502	−	0.516144i	$-0.172633\pi$
$383$	33.5241	1.71300	0.856502	+	0.516144i	$0.172633\pi$
$384$	11.4162	0.582581
$385$	2.46651	0.125705
$386$	−14.4904	−0.737542
$387$	−7.88050	−0.400588
$388$	−9.50006	−0.482293
$389$	−36.5143	−1.85135	−0.925674	−	0.378321i	$-0.876501\pi$
$389$	−36.5143	−1.85135	−0.925674	+	0.378321i	$0.876501\pi$
$390$	3.54042	0.179276
$391$	−4.35585	−0.220285
$392$	14.4774	0.731219
$393$	−1.34215	−0.0677024
$394$	−13.1044	−0.660188
$395$	−0.213480	−0.0107413
$396$	7.00875	0.352203
$397$	6.90723	0.346664	0.173332	−	0.984863i	$-0.444547\pi$
$397$	6.90723	0.346664	0.173332	+	0.984863i	$0.444547\pi$
$398$	−1.30528	−0.0654276
$399$	3.43117	0.171774
$400$	−8.16252	−0.408126
$401$	17.0761	0.852739	0.426370	−	0.904549i	$-0.359792\pi$
$401$	17.0761	0.852739	0.426370	+	0.904549i	$0.359792\pi$
$402$	−3.17317	−0.158263
$403$	−65.5448	−3.26502
$404$	−20.7003	−1.02988
$405$	0.834863	0.0414847
$406$	−0.419103	−0.0207997
$407$	−30.8260	−1.52799
$408$	9.65704	0.478095
$409$	19.7240	0.975291	0.487646	−	0.873042i	$-0.337856\pi$
$409$	19.7240	0.975291	0.487646	+	0.873042i	$0.337856\pi$
$410$	−1.95950	−0.0967726
$411$	−2.09029	−0.103106
$412$	25.4234	1.25252
$413$	−8.48592	−0.417565
$414$	−0.611391	−0.0300482
$415$	2.64282	0.129731
$416$	−38.7998	−1.90232
$417$	−3.71254	−0.181804
$418$	−13.1894	−0.645116
$419$	−8.17325	−0.399289	−0.199645	−	0.979868i	$-0.563979\pi$
$419$	−8.17325	−0.399289	−0.199645	+	0.979868i	$0.563979\pi$
$420$	−0.930660	−0.0454116
$421$	−19.2844	−0.939865	−0.469932	−	0.882702i	$-0.655722\pi$
$421$	−19.2844	−0.939865	−0.469932	+	0.882702i	$0.655722\pi$
$422$	0.198311	0.00965361
$423$	6.51919	0.316974
$424$	12.8899	0.625990
$425$	−18.7433	−0.909182
$426$	6.02988	0.292148
$427$	−9.78112	−0.473342
$428$	−7.57112	−0.365964
$429$	−29.8942	−1.44331
$430$	−4.02242	−0.193978
$431$	38.4805	1.85354	0.926771	−	0.375627i	$-0.122573\pi$
$431$	38.4805	1.85354	0.926771	+	0.375627i	$0.122573\pi$
$432$	−1.89693	−0.0912663
$433$	−6.78157	−0.325902	−0.162951	−	0.986634i	$-0.552101\pi$
$433$	−6.78157	−0.325902	−0.162951	+	0.986634i	$0.552101\pi$
$434$	−3.96038	−0.190104
$435$	−0.834863	−0.0400286
$436$	7.73744	0.370556
$437$	−5.00543	−0.239442
$438$	−6.32189	−0.302071
$439$	25.2260	1.20397	0.601985	−	0.798508i	$-0.294377\pi$
$439$	25.2260	1.20397	0.601985	+	0.798508i	$0.294377\pi$
$440$	7.97723	0.380299
$441$	−6.53010	−0.310957
$442$	−18.4720	−0.878622
$443$	2.71891	0.129180	0.0645898	−	0.997912i	$-0.479426\pi$
$443$	2.71891	0.129180	0.0645898	+	0.997912i	$0.479426\pi$
$444$	11.6312	0.551992
$445$	9.45362	0.448145
$446$	−6.57684	−0.311422
$447$	−0.963445	−0.0455694
$448$	0.256279	0.0121080
$449$	1.22087	0.0576166	0.0288083	−	0.999585i	$-0.490829\pi$
$449$	1.22087	0.0576166	0.0288083	+	0.999585i	$0.490829\pi$
$450$	−2.63082	−0.124018
$451$	16.5454	0.779091
$452$	17.2229	0.810097
$453$	−21.5727	−1.01357
$454$	11.2916	0.529943
$455$	3.96952	0.186094
$456$	11.0972	0.519672
$457$	37.0693	1.73403	0.867014	−	0.498284i	$-0.166036\pi$
$457$	37.0693	1.73403	0.867014	+	0.498284i	$0.166036\pi$
$458$	−13.3016	−0.621541
$459$	−4.35585	−0.203314
$460$	1.35766	0.0633010
$461$	32.1018	1.49513	0.747566	−	0.664188i	$-0.231222\pi$
$461$	32.1018	1.49513	0.747566	+	0.664188i	$0.231222\pi$
$462$	−1.80629	−0.0840361
$463$	17.4487	0.810911	0.405456	−	0.914115i	$-0.367113\pi$
$463$	17.4487	0.810911	0.405456	+	0.914115i	$0.367113\pi$
$464$	1.89693	0.0880630
$465$	−7.88918	−0.365852
$466$	3.16828	0.146768
$467$	18.3114	0.847353	0.423676	−	0.905814i	$-0.360739\pi$
$467$	18.3114	0.847353	0.423676	+	0.905814i	$0.360739\pi$
$468$	11.2797	0.521402
$469$	−3.55775	−0.164282
$470$	3.32757	0.153489
$471$	9.60822	0.442724
$472$	−27.4453	−1.26327
$473$	33.9641	1.56167
$474$	0.156336	0.00718077
$475$	−21.5384	−0.988248
$476$	4.85567	0.222559
$477$	−5.81406	−0.266208
$478$	1.59169	0.0728024
$479$	−3.40517	−0.155586	−0.0777931	−	0.996970i	$-0.524787\pi$
$479$	−3.40517	−0.155586	−0.0777931	+	0.996970i	$0.524787\pi$
$480$	−4.67007	−0.213159
$481$	−49.6103	−2.26203
$482$	2.98879	0.136136
$483$	−0.685491	−0.0311909
$484$	−12.3187	−0.559943
$485$	4.87716	0.221461
$486$	−0.611391	−0.0277332
$487$	−28.7100	−1.30097	−0.650487	−	0.759518i	$-0.725435\pi$
$487$	−28.7100	−1.30097	−0.650487	+	0.759518i	$0.725435\pi$
$488$	−31.6343	−1.43202
$489$	−22.2529	−1.00631
$490$	−3.33314	−0.150576
$491$	14.5823	0.658089	0.329045	−	0.944314i	$-0.393273\pi$
$491$	14.5823	0.658089	0.329045	+	0.944314i	$0.393273\pi$
$492$	−6.24288	−0.281451
$493$	4.35585	0.196178
$494$	−21.2266	−0.955032
$495$	−3.59817	−0.161726
$496$	17.9254	0.804875
$497$	6.76069	0.303259
$498$	−1.93540	−0.0867275
$499$	23.7734	1.06425	0.532123	−	0.846667i	$-0.321395\pi$
$499$	23.7734	1.06425	0.532123	+	0.846667i	$0.321395\pi$
$500$	12.6303	0.564843
$501$	−17.6567	−0.788843
$502$	7.77255	0.346906
$503$	41.4368	1.84758	0.923788	−	0.382904i	$-0.125076\pi$
$503$	41.4368	1.84758	0.923788	+	0.382904i	$0.125076\pi$
$504$	1.51975	0.0676951
$505$	10.6271	0.472902
$506$	2.63503	0.117141
$507$	−35.1108	−1.55933
$508$	−13.4709	−0.597677
$509$	4.51731	0.200226	0.100113	−	0.994976i	$-0.468080\pi$
$509$	4.51731	0.200226	0.100113	+	0.994976i	$0.468080\pi$
$510$	−2.22335	−0.0984514
$511$	−7.08809	−0.313559
$512$	19.0222	0.840671
$513$	−5.00543	−0.220995
$514$	9.89592	0.436490
$515$	−13.0519	−0.575136
$516$	−12.8153	−0.564161
$517$	−28.0970	−1.23570
$518$	−2.99758	−0.131706
$519$	−5.17476	−0.227147
$520$	12.8383	0.562996
$521$	−19.6782	−0.862119	−0.431059	−	0.902324i	$-0.641860\pi$
$521$	−19.6782	−0.862119	−0.431059	+	0.902324i	$0.641860\pi$
$522$	0.611391	0.0267598
$523$	23.9065	1.04536	0.522678	−	0.852530i	$-0.324933\pi$
$523$	23.9065	1.04536	0.522678	+	0.852530i	$0.324933\pi$
$524$	−2.18260	−0.0953475
$525$	−2.94967	−0.128734
$526$	7.88000	0.343584
$527$	41.1614	1.79302
$528$	8.17558	0.355797
$529$	1.00000	0.0434783
$530$	−2.96766	−0.128907
$531$	12.3793	0.537217
$532$	5.57978	0.241914
$533$	26.6276	1.15337
$534$	−6.92312	−0.299593
$535$	3.88688	0.168044
$536$	−11.5065	−0.497007
$537$	3.93984	0.170016
$538$	−0.681986	−0.0294025
$539$	28.1440	1.21225
$540$	1.35766	0.0584242
$541$	−21.9779	−0.944902	−0.472451	−	0.881357i	$-0.656631\pi$
$541$	−21.9779	−0.944902	−0.472451	+	0.881357i	$0.656631\pi$
$542$	−3.62187	−0.155573
$543$	−4.69684	−0.201561
$544$	24.3659	1.04468
$545$	−3.97227	−0.170153
$546$	−2.90698	−0.124407
$547$	−27.7223	−1.18532	−0.592659	−	0.805453i	$-0.701922\pi$
$547$	−27.7223	−1.18532	−0.592659	+	0.805453i	$0.701922\pi$
$548$	−3.39923	−0.145208
$549$	14.2688	0.608977
$550$	11.3385	0.483477
$551$	5.00543	0.213238
$552$	−2.21703	−0.0943629
$553$	0.175284	0.00745385
$554$	−15.3160	−0.650716
$555$	−5.97125	−0.253465
$556$	−6.03733	−0.256040
$557$	4.05940	0.172002	0.0860012	−	0.996295i	$-0.472591\pi$
$557$	4.05940	0.172002	0.0860012	+	0.996295i	$0.472591\pi$
$558$	5.77744	0.244579
$559$	54.6607	2.31190
$560$	−1.08560	−0.0458749
$561$	18.7733	0.792608
$562$	−10.0831	−0.425329
$563$	−8.97405	−0.378211	−0.189106	−	0.981957i	$-0.560559\pi$
$563$	−8.97405	−0.378211	−0.189106	+	0.981957i	$0.560559\pi$
$564$	10.6015	0.446404
$565$	−8.84193	−0.371983
$566$	−16.3895	−0.688900
$567$	−0.685491	−0.0287879
$568$	21.8655	0.917458
$569$	−13.0274	−0.546137	−0.273069	−	0.961995i	$-0.588039\pi$
$569$	−13.0274	−0.546137	−0.273069	+	0.961995i	$0.588039\pi$
$570$	−2.55491	−0.107013
$571$	−8.27190	−0.346168	−0.173084	−	0.984907i	$-0.555373\pi$
$571$	−8.27190	−0.346168	−0.173084	+	0.984907i	$0.555373\pi$
$572$	−48.6141	−2.03266
$573$	−18.7144	−0.781806
$574$	1.60891	0.0671545
$575$	4.30300	0.179448
$576$	−0.373862	−0.0155776
$577$	27.0737	1.12709	0.563547	−	0.826084i	$-0.309436\pi$
$577$	27.0737	1.12709	0.563547	+	0.826084i	$0.309436\pi$
$578$	1.20656	0.0501862
$579$	23.7007	0.984969
$580$	−1.35766	−0.0563736
$581$	−2.16997	−0.0900256
$582$	−3.57167	−0.148050
$583$	25.0580	1.03780
$584$	−22.9244	−0.948620
$585$	−5.79077	−0.239419
$586$	−6.87792	−0.284124
$587$	17.0434	0.703458	0.351729	−	0.936102i	$-0.385594\pi$
$587$	17.0434	0.703458	0.351729	+	0.936102i	$0.385594\pi$
$588$	−10.6193	−0.437931
$589$	47.2997	1.94895
$590$	6.31875	0.260139
$591$	21.4337	0.881664
$592$	13.5676	0.557624
$593$	14.4296	0.592554	0.296277	−	0.955102i	$-0.404255\pi$
$593$	14.4296	0.592554	0.296277	+	0.955102i	$0.404255\pi$
$594$	2.63503	0.108116
$595$	−2.49281	−0.102195
$596$	−1.56676	−0.0641768
$597$	2.13493	0.0873769
$598$	4.24072	0.173416
$599$	26.5520	1.08488	0.542442	−	0.840093i	$-0.317500\pi$
$599$	26.5520	1.08488	0.542442	+	0.840093i	$0.317500\pi$
$600$	−9.53987	−0.389464
$601$	−0.281069	−0.0114651	−0.00573253	−	0.999984i	$-0.501825\pi$
$601$	−0.281069	−0.0114651	−0.00573253	+	0.999984i	$0.501825\pi$
$602$	3.30274	0.134610
$603$	5.19008	0.211356
$604$	−35.0815	−1.42745
$605$	6.32422	0.257116
$606$	−7.78252	−0.316143
$607$	36.7176	1.49032	0.745161	−	0.666885i	$-0.232373\pi$
$607$	36.7176	1.49032	0.745161	+	0.666885i	$0.232373\pi$
$608$	27.9995	1.13553
$609$	0.685491	0.0277775
$610$	7.28318	0.294887
$611$	−45.2184	−1.82934
$612$	−7.08350	−0.286333
$613$	26.1991	1.05817	0.529085	−	0.848569i	$-0.322535\pi$
$613$	26.1991	1.05817	0.529085	+	0.848569i	$0.322535\pi$
$614$	−1.99853	−0.0806541
$615$	3.20498	0.129237
$616$	−6.54996	−0.263905
$617$	−7.82574	−0.315052	−0.157526	−	0.987515i	$-0.550352\pi$
$617$	−7.82574	−0.315052	−0.157526	+	0.987515i	$0.550352\pi$
$618$	9.55824	0.384489
$619$	−5.62966	−0.226275	−0.113137	−	0.993579i	$-0.536090\pi$
$619$	−5.62966	−0.226275	−0.113137	+	0.993579i	$0.536090\pi$
$620$	−12.8294	−0.515241
$621$	1.00000	0.0401286
$622$	−4.18242	−0.167700
$623$	−7.76220	−0.310986
$624$	13.1575	0.526722
$625$	15.0309	0.601235
$626$	−6.61492	−0.264385
$627$	21.5728	0.861537
$628$	15.6249	0.623502
$629$	31.1547	1.24222
$630$	−0.349893	−0.0139401
$631$	−11.4063	−0.454078	−0.227039	−	0.973886i	$-0.572904\pi$
$631$	−11.4063	−0.454078	−0.227039	+	0.973886i	$0.572904\pi$
$632$	0.566908	0.0225504
$633$	−0.324360	−0.0128921
$634$	13.1978	0.524153
$635$	6.91574	0.274443
$636$	−9.45484	−0.374909
$637$	45.2941	1.79462
$638$	−2.63503	−0.104322
$639$	−9.86256	−0.390157
$640$	−9.53097	−0.376745
$641$	25.2121	0.995818	0.497909	−	0.867229i	$-0.334101\pi$
$641$	25.2121	0.995818	0.497909	+	0.867229i	$0.334101\pi$
$642$	−2.84646	−0.112341
$643$	−4.38300	−0.172849	−0.0864243	−	0.996258i	$-0.527544\pi$
$643$	−4.38300	−0.172849	−0.0864243	+	0.996258i	$0.527544\pi$
$644$	−1.11475	−0.0439272
$645$	6.57914	0.259053
$646$	13.3301	0.524465
$647$	2.22353	0.0874162	0.0437081	−	0.999044i	$-0.486083\pi$
$647$	2.22353	0.0874162	0.0437081	+	0.999044i	$0.486083\pi$
$648$	−2.21703	−0.0870930
$649$	−53.3536	−2.09431
$650$	18.2479	0.715740
$651$	6.47767	0.253880
$652$	−36.1876	−1.41722
$653$	−14.2881	−0.559137	−0.279568	−	0.960126i	$-0.590191\pi$
$653$	−14.2881	−0.559137	−0.279568	+	0.960126i	$0.590191\pi$
$654$	2.90899	0.113750
$655$	1.12051	0.0437819
$656$	−7.28220	−0.284322
$657$	10.3402	0.403409
$658$	−2.73221	−0.106513
$659$	−15.4293	−0.601040	−0.300520	−	0.953776i	$-0.597160\pi$
$659$	−15.4293	−0.601040	−0.300520	+	0.953776i	$0.597160\pi$
$660$	−5.85135	−0.227763
$661$	31.7825	1.23620	0.618098	−	0.786101i	$-0.287903\pi$
$661$	31.7825	1.23620	0.618098	+	0.786101i	$0.287903\pi$
$662$	−16.0092	−0.622214
$663$	30.2131	1.17338
$664$	−7.01816	−0.272357
$665$	−2.86456	−0.111083
$666$	4.37289	0.169446
$667$	−1.00000	−0.0387202
$668$	−28.7134	−1.11095
$669$	10.7572	0.415897
$670$	2.64916	0.102346
$671$	−61.4969	−2.37406
$672$	3.83451	0.147919
$673$	−0.00588219	−0.000226742 0	−0.000113371	−	1.00000i	$-0.500036\pi$
$673$	−0.00588219	−0.000226742 0	−0.000113371		1.00000i	$0.500036\pi$
$674$	−3.01946	−0.116305
$675$	4.30300	0.165623
$676$	−57.0972	−2.19605
$677$	−27.8314	−1.06965	−0.534824	−	0.844964i	$-0.679622\pi$
$677$	−27.8314	−1.06965	−0.534824	+	0.844964i	$0.679622\pi$
$678$	6.47516	0.248677
$679$	−4.00455	−0.153681
$680$	−8.06230	−0.309175
$681$	−18.4688	−0.707725
$682$	−24.9001	−0.953476
$683$	5.92751	0.226810	0.113405	−	0.993549i	$-0.463824\pi$
$683$	5.92751	0.226810	0.113405	+	0.993549i	$0.463824\pi$
$684$	−8.13983	−0.311234
$685$	1.74510	0.0666769
$686$	5.67050	0.216501
$687$	21.7562	0.830052
$688$	−14.9488	−0.569917
$689$	40.3275	1.53635
$690$	0.510427	0.0194316
$691$	25.7814	0.980771	0.490386	−	0.871506i	$-0.336856\pi$
$691$	25.7814	0.980771	0.490386	+	0.871506i	$0.336856\pi$
$692$	−8.41520	−0.319898
$693$	2.95439	0.112228
$694$	−14.4316	−0.547816
$695$	3.09946	0.117569
$696$	2.21703	0.0840361
$697$	−16.7218	−0.633384
$698$	−7.19729	−0.272422
$699$	−5.18209	−0.196005
$700$	−4.79676	−0.181300
$701$	2.22483	0.0840307	0.0420154	−	0.999117i	$-0.486622\pi$
$701$	2.22483	0.0840307	0.0420154	+	0.999117i	$0.486622\pi$
$702$	4.24072	0.160056
$703$	35.8007	1.35025
$704$	1.61130	0.0607283
$705$	−5.44263	−0.204981
$706$	10.4379	0.392834
$707$	−8.72575	−0.328166
$708$	20.1313	0.756580
$709$	25.5951	0.961243	0.480621	−	0.876928i	$-0.340411\pi$
$709$	25.5951	0.961243	0.480621	+	0.876928i	$0.340411\pi$
$710$	−5.03412	−0.188927
$711$	−0.255706	−0.00958974
$712$	−25.1046	−0.940836
$713$	−9.44967	−0.353893
$714$	1.82555	0.0683195
$715$	24.9576	0.933361
$716$	6.40697	0.239440
$717$	−2.60340	−0.0972257
$718$	20.3570	0.759718
$719$	7.78746	0.290423	0.145212	−	0.989401i	$-0.453614\pi$
$719$	7.78746	0.290423	0.145212	+	0.989401i	$0.453614\pi$
$720$	1.58368	0.0590203
$721$	10.7167	0.399110
$722$	3.70154	0.137757
$723$	−4.88851	−0.181806
$724$	−7.63801	−0.283864
$725$	−4.30300	−0.159810
$726$	−4.63138	−0.171887
$727$	27.2912	1.01217	0.506087	−	0.862482i	$-0.331092\pi$
$727$	27.2912	1.01217	0.506087	+	0.862482i	$0.331092\pi$
$728$	−10.5413	−0.390686
$729$	1.00000	0.0370370
$730$	5.27791	0.195344
$731$	−34.3263	−1.26960
$732$	23.2039	0.857642
$733$	4.37066	0.161434	0.0807171	−	0.996737i	$-0.474279\pi$
$733$	4.37066	0.161434	0.0807171	+	0.996737i	$0.474279\pi$
$734$	−10.6388	−0.392686
$735$	5.45174	0.201090
$736$	−5.59382	−0.206191
$737$	−22.3687	−0.823961
$738$	−2.34709	−0.0863975
$739$	−9.64767	−0.354895	−0.177448	−	0.984130i	$-0.556784\pi$
$739$	−9.64767	−0.354895	−0.177448	+	0.984130i	$0.556784\pi$
$740$	−9.71046	−0.356963
$741$	34.7186	1.27542
$742$	2.43669	0.0894537
$743$	0.995847	0.0365341	0.0182670	−	0.999833i	$-0.494185\pi$
$743$	0.995847	0.0365341	0.0182670	+	0.999833i	$0.494185\pi$
$744$	20.9502	0.768070
$745$	0.804344	0.0294689
$746$	−16.5335	−0.605336
$747$	3.16558	0.115822
$748$	30.5291	1.11625
$749$	−3.19145	−0.116613
$750$	4.74851	0.173391
$751$	4.60712	0.168116	0.0840581	−	0.996461i	$-0.473212\pi$
$751$	4.60712	0.168116	0.0840581	+	0.996461i	$0.473212\pi$
$752$	12.3665	0.450959
$753$	−12.7129	−0.463284
$754$	−4.24072	−0.154438
$755$	18.0102	0.655459
$756$	−1.11475	−0.0405429
$757$	−15.3820	−0.559069	−0.279535	−	0.960136i	$-0.590180\pi$
$757$	−15.3820	−0.559069	−0.279535	+	0.960136i	$0.590180\pi$
$758$	−3.61410	−0.131270
$759$	−4.30989	−0.156439
$760$	−9.26460	−0.336063
$761$	10.2638	0.372062	0.186031	−	0.982544i	$-0.440438\pi$
$761$	10.2638	0.372062	0.186031	+	0.982544i	$0.440438\pi$
$762$	−5.06457	−0.183470
$763$	3.26156	0.118076
$764$	−30.4334	−1.10104
$765$	3.63654	0.131479
$766$	20.4963	0.740563
$767$	−85.8655	−3.10042
$768$	6.23204	0.224879
$769$	−37.4723	−1.35128	−0.675642	−	0.737230i	$-0.736133\pi$
$769$	−37.4723	−1.35128	−0.675642	+	0.737230i	$0.736133\pi$
$770$	1.50800	0.0543446
$771$	−16.1859	−0.582922
$772$	38.5422	1.38716
$773$	24.8016	0.892053	0.446026	−	0.895020i	$-0.352839\pi$
$773$	24.8016	0.892053	0.446026	+	0.895020i	$0.352839\pi$
$774$	−4.81806	−0.173182
$775$	−40.6620	−1.46062
$776$	−12.9516	−0.464935
$777$	4.90289	0.175890
$778$	−22.3245	−0.800372
$779$	−19.2155	−0.688467
$780$	−9.41696	−0.337181
$781$	42.5066	1.52100
$782$	−2.66313	−0.0952333
$783$	−1.00000	−0.0357371
$784$	−12.3872	−0.442399
$785$	−8.02155	−0.286301
$786$	−0.820577	−0.0292690
$787$	−11.3807	−0.405677	−0.202839	−	0.979212i	$-0.565017\pi$
$787$	−11.3807	−0.405677	−0.202839	+	0.979212i	$0.565017\pi$
$788$	34.8555	1.24168
$789$	−12.8887	−0.458848
$790$	−0.130520	−0.00464368
$791$	7.25995	0.258134
$792$	9.55514	0.339527
$793$	−98.9711	−3.51457
$794$	4.22301	0.149869
$795$	4.85395	0.172152
$796$	3.47183	0.123056
$797$	17.9080	0.634333	0.317167	−	0.948370i	$-0.397269\pi$
$797$	17.9080	0.634333	0.317167	+	0.948370i	$0.397269\pi$
$798$	2.09779	0.0742609
$799$	28.3966	1.00460
$800$	−24.0702	−0.851011
$801$	11.3236	0.400099
$802$	10.4402	0.368655
$803$	−44.5650	−1.57267
$804$	8.44011	0.297660
$805$	0.572291	0.0201706
$806$	−40.0735	−1.41153
$807$	1.11547	0.0392663
$808$	−28.2210	−0.992810
$809$	31.3051	1.10063	0.550314	−	0.834958i	$-0.314508\pi$
$809$	31.3051	1.10063	0.550314	+	0.834958i	$0.314508\pi$
$810$	0.510427	0.0179346
$811$	34.5718	1.21398	0.606990	−	0.794709i	$-0.292377\pi$
$811$	34.5718	1.21398	0.606990	+	0.794709i	$0.292377\pi$
$812$	1.11475	0.0391199
$813$	5.92399	0.207763
$814$	−18.8467	−0.660576
$815$	18.5781	0.650762
$816$	−8.26277	−0.289255
$817$	−39.4453	−1.38002
$818$	12.0591	0.421636
$819$	4.75470	0.166143
$820$	5.21195	0.182009
$821$	−3.89321	−0.135874	−0.0679369	−	0.997690i	$-0.521642\pi$
$821$	−3.89321	−0.135874	−0.0679369	+	0.997690i	$0.521642\pi$
$822$	−1.27798	−0.0445747
$823$	8.32208	0.290089	0.145045	−	0.989425i	$-0.453667\pi$
$823$	8.32208	0.290089	0.145045	+	0.989425i	$0.453667\pi$
$824$	34.6601	1.20744
$825$	−18.5455	−0.645671
$826$	−5.18821	−0.180521
$827$	−38.7597	−1.34781	−0.673904	−	0.738819i	$-0.735384\pi$
$827$	−38.7597	−1.34781	−0.673904	+	0.738819i	$0.735384\pi$
$828$	1.62620	0.0565144
$829$	−16.5657	−0.575352	−0.287676	−	0.957728i	$-0.592883\pi$
$829$	−16.5657	−0.575352	−0.287676	+	0.957728i	$0.592883\pi$
$830$	1.61580	0.0560851
$831$	25.0512	0.869015
$832$	2.59318	0.0899023
$833$	−28.4442	−0.985532
$834$	−2.26981	−0.0785971
$835$	14.7409	0.510131
$836$	35.0818	1.21333
$837$	−9.44967	−0.326629
$838$	−4.99705	−0.172620
$839$	−35.5005	−1.22561	−0.612807	−	0.790233i	$-0.709960\pi$
$839$	−35.5005	−1.22561	−0.612807	+	0.790233i	$0.709960\pi$
$840$	−1.26878	−0.0437772
$841$	1.00000	0.0344828
$842$	−11.7903	−0.406321
$843$	16.4921	0.568017
$844$	−0.527475	−0.0181564
$845$	29.3127	1.00839
$846$	3.98577	0.137034
$847$	−5.19270	−0.178423
$848$	−11.0289	−0.378734
$849$	26.8068	0.920009
$850$	−11.4595	−0.393056
$851$	−7.15237	−0.245180
$852$	−16.0385	−0.549470
$853$	0.569695	0.0195060	0.00975299	−	0.999952i	$-0.496895\pi$
$853$	0.569695	0.0195060	0.00975299	+	0.999952i	$0.496895\pi$
$854$	−5.98009	−0.204634
$855$	4.17884	0.142913
$856$	−10.3218	−0.352793
$857$	−42.6670	−1.45748	−0.728739	−	0.684792i	$-0.759893\pi$
$857$	−42.6670	−1.45748	−0.728739	+	0.684792i	$0.759893\pi$
$858$	−18.2771	−0.623969
$859$	10.0786	0.343877	0.171939	−	0.985108i	$-0.444997\pi$
$859$	10.0786	0.343877	0.171939	+	0.985108i	$0.444997\pi$
$860$	10.6990	0.364833
$861$	−2.63155	−0.0896831
$862$	23.5266	0.801320
$863$	39.0533	1.32939	0.664695	−	0.747115i	$-0.268561\pi$
$863$	39.0533	1.32939	0.664695	+	0.747115i	$0.268561\pi$
$864$	−5.59382	−0.190306
$865$	4.32022	0.146892
$866$	−4.14619	−0.140893
$867$	−1.97346	−0.0670223
$868$	10.5340	0.357547
$869$	1.10207	0.0373851
$870$	−0.510427	−0.0173051
$871$	−35.9994	−1.21979
$872$	10.5486	0.357220
$873$	5.84187	0.197717
$874$	−3.06027	−0.103515
$875$	5.32402	0.179985
$876$	16.8152	0.568133
$877$	13.8533	0.467794	0.233897	−	0.972261i	$-0.424852\pi$
$877$	13.8533	0.467794	0.233897	+	0.972261i	$0.424852\pi$
$878$	15.4229	0.520498
$879$	11.2496	0.379441
$880$	−6.82549	−0.230087
$881$	40.8796	1.37727	0.688635	−	0.725108i	$-0.258210\pi$
$881$	40.8796	1.37727	0.688635	+	0.725108i	$0.258210\pi$
$882$	−3.99244	−0.134433
$883$	7.40254	0.249115	0.124558	−	0.992212i	$-0.460249\pi$
$883$	7.40254	0.249115	0.124558	+	0.992212i	$0.460249\pi$
$884$	49.1325	1.65251
$885$	−10.3350	−0.347409
$886$	1.66232	0.0558467
$887$	24.3437	0.817380	0.408690	−	0.912673i	$-0.365986\pi$
$887$	24.3437	0.817380	0.408690	+	0.912673i	$0.365986\pi$
$888$	15.8570	0.532126
$889$	−5.67839	−0.190447
$890$	5.77986	0.193741
$891$	−4.30989	−0.144387
$892$	17.4934	0.585721
$893$	32.6313	1.09197
$894$	−0.589041	−0.0197005
$895$	−3.28922	−0.109947
$896$	7.82571	0.261439
$897$	−6.93620	−0.231593
$898$	0.746430	0.0249087
$899$	9.44967	0.315164
$900$	6.99755	0.233252
$901$	−25.3252	−0.843705
$902$	10.1157	0.336816
$903$	−5.40201	−0.179768
$904$	23.4802	0.780941
$905$	3.92122	0.130346
$906$	−13.1893	−0.438186
$907$	−29.8887	−0.992439	−0.496219	−	0.868197i	$-0.665279\pi$
$907$	−29.8887	−0.992439	−0.496219	+	0.868197i	$0.665279\pi$
$908$	−30.0340	−0.996712
$909$	12.7292	0.422201
$910$	2.42693	0.0804519
$911$	43.4237	1.43869	0.719345	−	0.694653i	$-0.244442\pi$
$911$	43.4237	1.43869	0.719345	+	0.694653i	$0.244442\pi$
$912$	−9.49497	−0.314410
$913$	−13.6433	−0.451527
$914$	22.6638	0.749652
$915$	−11.9125	−0.393814
$916$	35.3800	1.16899
$917$	−0.920031	−0.0303821
$918$	−2.66313	−0.0878963
$919$	−9.90012	−0.326575	−0.163287	−	0.986579i	$-0.552210\pi$
$919$	−9.90012	−0.326575	−0.163287	+	0.986579i	$0.552210\pi$
$920$	1.85091	0.0610228
$921$	3.26882	0.107711
$922$	19.6268	0.646373
$923$	68.4086	2.25170
$924$	4.80443	0.158054
$925$	−30.7767	−1.01193
$926$	10.6680	0.350572
$927$	−15.6336	−0.513475
$928$	5.59382	0.183626
$929$	−32.1938	−1.05624	−0.528122	−	0.849168i	$-0.677104\pi$
$929$	−32.1938	−1.05624	−0.528122	+	0.849168i	$0.677104\pi$
$930$	−4.82337	−0.158165
$931$	−32.6860	−1.07124
$932$	−8.42713	−0.276040
$933$	6.84083	0.223959
$934$	11.1954	0.366326
$935$	−15.6731	−0.512565
$936$	15.3777	0.502637
$937$	−10.2659	−0.335372	−0.167686	−	0.985840i	$-0.553629\pi$
$937$	−10.2659	−0.335372	−0.167686	+	0.985840i	$0.553629\pi$
$938$	−2.17518	−0.0710220
$939$	10.8195	0.353080
$940$	−8.85081	−0.288682
$941$	32.3494	1.05456	0.527279	−	0.849692i	$-0.323212\pi$
$941$	32.3494	1.05456	0.527279	+	0.849692i	$0.323212\pi$
$942$	5.87438	0.191398
$943$	3.83893	0.125013
$944$	23.4828	0.764300
$945$	0.572291	0.0186166
$946$	20.7653	0.675139
$947$	−42.5434	−1.38247	−0.691237	−	0.722628i	$-0.742934\pi$
$947$	−42.5434	−1.38247	−0.691237	+	0.722628i	$0.742934\pi$
$948$	−0.415830	−0.0135055
$949$	−71.7215	−2.32818
$950$	−13.1684	−0.427238
$951$	−21.5866	−0.699993
$952$	6.61981	0.214549
$953$	−11.4943	−0.372338	−0.186169	−	0.982518i	$-0.559607\pi$
$953$	−11.4943	−0.372338	−0.186169	+	0.982518i	$0.559607\pi$
$954$	−3.55466	−0.115086
$955$	15.6240	0.505580
$956$	−4.23365	−0.136926
$957$	4.30989	0.139319
$958$	−2.08189	−0.0672628
$959$	−1.43287	−0.0462698
$960$	0.312123	0.0100737
$961$	58.2964	1.88053
$962$	−30.3312	−0.977919
$963$	4.65571	0.150028
$964$	−7.94970	−0.256043
$965$	−19.7869	−0.636961
$966$	−0.419103	−0.0134844
$967$	16.6068	0.534037	0.267019	−	0.963691i	$-0.413961\pi$
$967$	16.6068	0.534037	0.267019	+	0.963691i	$0.413961\pi$
$968$	−16.7943	−0.539790
$969$	−21.8029	−0.700410
$970$	2.98185	0.0957415
$971$	15.8282	0.507953	0.253976	−	0.967210i	$-0.418261\pi$
$971$	15.8282	0.507953	0.253976	+	0.967210i	$0.418261\pi$
$972$	1.62620	0.0521604
$973$	−2.54491	−0.0815860
$974$	−17.5530	−0.562435
$975$	−29.8465	−0.955852
$976$	27.0670	0.866392
$977$	21.2614	0.680213	0.340106	−	0.940387i	$-0.389537\pi$
$977$	21.2614	0.680213	0.340106	+	0.940387i	$0.389537\pi$
$978$	−13.6052	−0.435046
$979$	−48.8033	−1.55976
$980$	8.86563	0.283202
$981$	−4.75799	−0.151911
$982$	8.91547	0.284504
$983$	50.5034	1.61081	0.805404	−	0.592727i	$-0.201949\pi$
$983$	50.5034	1.61081	0.805404	+	0.592727i	$0.201949\pi$
$984$	−8.51101	−0.271321
$985$	−17.8942	−0.570156
$986$	2.66313	0.0848113
$987$	4.46884	0.142245
$988$	56.4595	1.79622
$989$	7.88050	0.250585
$990$	−2.19989	−0.0699170
$991$	18.7508	0.595640	0.297820	−	0.954622i	$-0.403741\pi$
$991$	18.7508	0.595640	0.297820	+	0.954622i	$0.403741\pi$
$992$	52.8598	1.67830
$993$	26.1848	0.830951
$994$	4.13342	0.131104
$995$	−1.78238	−0.0565051
$996$	5.14786	0.163116
$997$	6.97463	0.220889	0.110444	−	0.993882i	$-0.464773\pi$
$997$	6.97463	0.220889	0.110444	+	0.993882i	$0.464773\pi$
$998$	14.5349	0.460093
$999$	−7.15237	−0.226291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.k.1.5	✓	10
3.2	odd	2		6003.2.a.k.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.k.1.5	✓	10	1.1	even	1	trivial
6003.2.a.k.1.6		10	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)

\(f(q)\)	\(=\)	\(q+0.611391 q^{2} -1.00000 q^{3} -1.62620 q^{4} +0.834863 q^{5} -0.611391 q^{6} -0.685491 q^{7} -2.21703 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.611391 q^{2} -1.00000 q^{3} -1.62620 q^{4} +0.834863 q^{5} -0.611391 q^{6} -0.685491 q^{7} -2.21703 q^{8} +1.00000 q^{9} +0.510427 q^{10} -4.30989 q^{11} +1.62620 q^{12} -6.93620 q^{13} -0.419103 q^{14} -0.834863 q^{15} +1.89693 q^{16} +4.35585 q^{17} +0.611391 q^{18} +5.00543 q^{19} -1.35766 q^{20} +0.685491 q^{21} -2.63503 q^{22} -1.00000 q^{23} +2.21703 q^{24} -4.30300 q^{25} -4.24072 q^{26} -1.00000 q^{27} +1.11475 q^{28} +1.00000 q^{29} -0.510427 q^{30} +9.44967 q^{31} +5.59382 q^{32} +4.30989 q^{33} +2.66313 q^{34} -0.572291 q^{35} -1.62620 q^{36} +7.15237 q^{37} +3.06027 q^{38} +6.93620 q^{39} -1.85091 q^{40} -3.83893 q^{41} +0.419103 q^{42} -7.88050 q^{43} +7.00875 q^{44} +0.834863 q^{45} -0.611391 q^{46} +6.51919 q^{47} -1.89693 q^{48} -6.53010 q^{49} -2.63082 q^{50} -4.35585 q^{51} +11.2797 q^{52} -5.81406 q^{53} -0.611391 q^{54} -3.59817 q^{55} +1.51975 q^{56} -5.00543 q^{57} +0.611391 q^{58} +12.3793 q^{59} +1.35766 q^{60} +14.2688 q^{61} +5.77744 q^{62} -0.685491 q^{63} -0.373862 q^{64} -5.79077 q^{65} +2.63503 q^{66} +5.19008 q^{67} -7.08350 q^{68} +1.00000 q^{69} -0.349893 q^{70} -9.86256 q^{71} -2.21703 q^{72} +10.3402 q^{73} +4.37289 q^{74} +4.30300 q^{75} -8.13983 q^{76} +2.95439 q^{77} +4.24072 q^{78} -0.255706 q^{79} +1.58368 q^{80} +1.00000 q^{81} -2.34709 q^{82} +3.16558 q^{83} -1.11475 q^{84} +3.63654 q^{85} -4.81806 q^{86} -1.00000 q^{87} +9.55514 q^{88} +11.3236 q^{89} +0.510427 q^{90} +4.75470 q^{91} +1.62620 q^{92} -9.44967 q^{93} +3.98577 q^{94} +4.17884 q^{95} -5.59382 q^{96} +5.84187 q^{97} -3.99244 q^{98} -4.30989 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * q^99

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