LMFDB - Embedded newform 2001.2.a.k.1.4

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			1.4
Root			$-0.473620$ 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)

$f(q)$	$=$	$q+0.161383 q^{2} -1.00000 q^{3} -1.97396 q^{4} +2.08087 q^{5} -0.161383 q^{6} +3.66994 q^{7} -0.641331 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.161383 q^{2} -1.00000 q^{3} -1.97396 q^{4} +2.08087 q^{5} -0.161383 q^{6} +3.66994 q^{7} -0.641331 q^{8} +1.00000 q^{9} +0.335818 q^{10} +3.77836 q^{11} +1.97396 q^{12} +3.51085 q^{13} +0.592268 q^{14} -2.08087 q^{15} +3.84441 q^{16} +3.02517 q^{17} +0.161383 q^{18} -1.97558 q^{19} -4.10754 q^{20} -3.66994 q^{21} +0.609764 q^{22} -1.00000 q^{23} +0.641331 q^{24} -0.669990 q^{25} +0.566593 q^{26} -1.00000 q^{27} -7.24430 q^{28} +1.00000 q^{29} -0.335818 q^{30} -3.58155 q^{31} +1.90309 q^{32} -3.77836 q^{33} +0.488212 q^{34} +7.63666 q^{35} -1.97396 q^{36} +5.34560 q^{37} -0.318827 q^{38} -3.51085 q^{39} -1.33452 q^{40} -12.0312 q^{41} -0.592268 q^{42} +3.68702 q^{43} -7.45831 q^{44} +2.08087 q^{45} -0.161383 q^{46} -0.138067 q^{47} -3.84441 q^{48} +6.46848 q^{49} -0.108125 q^{50} -3.02517 q^{51} -6.93026 q^{52} +3.01823 q^{53} -0.161383 q^{54} +7.86226 q^{55} -2.35365 q^{56} +1.97558 q^{57} +0.161383 q^{58} +9.43156 q^{59} +4.10754 q^{60} -10.8624 q^{61} -0.578003 q^{62} +3.66994 q^{63} -7.38169 q^{64} +7.30561 q^{65} -0.609764 q^{66} +4.57266 q^{67} -5.97155 q^{68} +1.00000 q^{69} +1.23243 q^{70} -3.28228 q^{71} -0.641331 q^{72} +1.53135 q^{73} +0.862691 q^{74} +0.669990 q^{75} +3.89971 q^{76} +13.8664 q^{77} -0.566593 q^{78} +7.31941 q^{79} +7.99971 q^{80} +1.00000 q^{81} -1.94164 q^{82} +5.82693 q^{83} +7.24430 q^{84} +6.29498 q^{85} +0.595024 q^{86} -1.00000 q^{87} -2.42318 q^{88} +6.06380 q^{89} +0.335818 q^{90} +12.8846 q^{91} +1.97396 q^{92} +3.58155 q^{93} -0.0222817 q^{94} -4.11093 q^{95} -1.90309 q^{96} -13.5506 q^{97} +1.04391 q^{98} +3.77836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.161383	0.114115	0.0570577	−	0.998371i	$-0.481828\pi$
$2$	0.161383	0.114115	0.0570577	+	0.998371i	$0.481828\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97396	−0.986978
$5$	2.08087	0.930592	0.465296	−	0.885155i	$-0.345948\pi$
$5$	2.08087	0.930592	0.465296	+	0.885155i	$0.345948\pi$
$6$	−0.161383	−0.0658845
$7$	3.66994	1.38711	0.693554	−	0.720405i	$-0.256044\pi$
$7$	3.66994	1.38711	0.693554	+	0.720405i	$0.256044\pi$
$8$	−0.641331	−0.226745
$9$	1.00000	0.333333
$10$	0.335818	0.106195
$11$	3.77836	1.13922	0.569609	−	0.821916i	$-0.307095\pi$
$11$	3.77836	1.13922	0.569609	+	0.821916i	$0.307095\pi$
$12$	1.97396	0.569832
$13$	3.51085	0.973735	0.486867	−	0.873476i	$-0.338140\pi$
$13$	3.51085	0.973735	0.486867	+	0.873476i	$0.338140\pi$
$14$	0.592268	0.158290
$15$	−2.08087	−0.537278
$16$	3.84441	0.961103
$17$	3.02517	0.733712	0.366856	−	0.930278i	$-0.380434\pi$
$17$	3.02517	0.733712	0.366856	+	0.930278i	$0.380434\pi$
$18$	0.161383	0.0380384
$19$	−1.97558	−0.453230	−0.226615	−	0.973984i	$-0.572766\pi$
$19$	−1.97558	−0.453230	−0.226615	+	0.973984i	$0.572766\pi$
$20$	−4.10754	−0.918474
$21$	−3.66994	−0.800847
$22$	0.609764	0.130002
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.641331	0.130911
$25$	−0.669990	−0.133998
$26$	0.566593	0.111118
$27$	−1.00000	−0.192450
$28$	−7.24430	−1.36904
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.335818	−0.0613116
$31$	−3.58155	−0.643266	−0.321633	−	0.946864i	$-0.604232\pi$
$31$	−3.58155	−0.643266	−0.321633	+	0.946864i	$0.604232\pi$
$32$	1.90309	0.336421
$33$	−3.77836	−0.657728
$34$	0.488212	0.0837277
$35$	7.63666	1.29083
$36$	−1.97396	−0.328993
$37$	5.34560	0.878811	0.439406	−	0.898289i	$-0.355189\pi$
$37$	5.34560	0.878811	0.439406	+	0.898289i	$0.355189\pi$
$38$	−0.318827	−0.0517205
$39$	−3.51085	−0.562186
$40$	−1.33452	−0.211007
$41$	−12.0312	−1.87896	−0.939480	−	0.342604i	$-0.888691\pi$
$41$	−12.0312	−1.87896	−0.939480	+	0.342604i	$0.888691\pi$
$42$	−0.592268	−0.0913890
$43$	3.68702	0.562266	0.281133	−	0.959669i	$-0.409290\pi$
$43$	3.68702	0.562266	0.281133	+	0.959669i	$0.409290\pi$
$44$	−7.45831	−1.12438
$45$	2.08087	0.310197
$46$	−0.161383	−0.0237947
$47$	−0.138067	−0.0201392	−0.0100696	−	0.999949i	$-0.503205\pi$
$47$	−0.138067	−0.0201392	−0.0100696	+	0.999949i	$0.503205\pi$
$48$	−3.84441	−0.554893
$49$	6.46848	0.924068
$50$	−0.108125	−0.0152912
$51$	−3.02517	−0.423609
$52$	−6.93026	−0.961054
$53$	3.01823	0.414586	0.207293	−	0.978279i	$-0.433535\pi$
$53$	3.01823	0.414586	0.207293	+	0.978279i	$0.433535\pi$
$54$	−0.161383	−0.0219615
$55$	7.86226	1.06015
$56$	−2.35365	−0.314519
$57$	1.97558	0.261672
$58$	0.161383	0.0211907
$59$	9.43156	1.22788	0.613942	−	0.789351i	$-0.289583\pi$
$59$	9.43156	1.22788	0.613942	+	0.789351i	$0.289583\pi$
$60$	4.10754	0.530281
$61$	−10.8624	−1.39079	−0.695394	−	0.718628i	$-0.744770\pi$
$61$	−10.8624	−1.39079	−0.695394	+	0.718628i	$0.744770\pi$
$62$	−0.578003	−0.0734065
$63$	3.66994	0.462369
$64$	−7.38169	−0.922712
$65$	7.30561	0.906150
$66$	−0.609764	−0.0750568
$67$	4.57266	0.558639	0.279320	−	0.960198i	$-0.409891\pi$
$67$	4.57266	0.558639	0.279320	+	0.960198i	$0.409891\pi$
$68$	−5.97155	−0.724157
$69$	1.00000	0.120386
$70$	1.23243	0.147304
$71$	−3.28228	−0.389535	−0.194768	−	0.980849i	$-0.562395\pi$
$71$	−3.28228	−0.389535	−0.194768	+	0.980849i	$0.562395\pi$
$72$	−0.641331	−0.0755815
$73$	1.53135	0.179231	0.0896153	−	0.995976i	$-0.471436\pi$
$73$	1.53135	0.179231	0.0896153	+	0.995976i	$0.471436\pi$
$74$	0.862691	0.100286
$75$	0.669990	0.0773638
$76$	3.89971	0.447328
$77$	13.8664	1.58022
$78$	−0.566593	−0.0641540
$79$	7.31941	0.823498	0.411749	−	0.911297i	$-0.364918\pi$
$79$	7.31941	0.823498	0.411749	+	0.911297i	$0.364918\pi$
$80$	7.99971	0.894395
$81$	1.00000	0.111111
$82$	−1.94164	−0.214418
$83$	5.82693	0.639588	0.319794	−	0.947487i	$-0.396386\pi$
$83$	5.82693	0.639588	0.319794	+	0.947487i	$0.396386\pi$
$84$	7.24430	0.790418
$85$	6.29498	0.682786
$86$	0.595024	0.0641631
$87$	−1.00000	−0.107211
$88$	−2.42318	−0.258311
$89$	6.06380	0.642761	0.321381	−	0.946950i	$-0.395853\pi$
$89$	6.06380	0.642761	0.321381	+	0.946950i	$0.395853\pi$
$90$	0.335818	0.0353983
$91$	12.8846	1.35067
$92$	1.97396	0.205799
$93$	3.58155	0.371390
$94$	−0.0222817	−0.00229819
$95$	−4.11093	−0.421772
$96$	−1.90309	−0.194233
$97$	−13.5506	−1.37585	−0.687926	−	0.725781i	$-0.741479\pi$
$97$	−13.5506	−1.37585	−0.687926	+	0.725781i	$0.741479\pi$
$98$	1.04391	0.105450
$99$	3.77836	0.379739
$100$	1.32253	0.132253
$101$	−5.39674	−0.536996	−0.268498	−	0.963280i	$-0.586527\pi$
$101$	−5.39674	−0.536996	−0.268498	+	0.963280i	$0.586527\pi$
$102$	−0.488212	−0.0483402
$103$	7.28928	0.718234	0.359117	−	0.933293i	$-0.383078\pi$
$103$	7.28928	0.718234	0.359117	+	0.933293i	$0.383078\pi$
$104$	−2.25162	−0.220789
$105$	−7.63666	−0.745262
$106$	0.487093	0.0473106
$107$	−5.92929	−0.573207	−0.286603	−	0.958049i	$-0.592526\pi$
$107$	−5.92929	−0.573207	−0.286603	+	0.958049i	$0.592526\pi$
$108$	1.97396	0.189944
$109$	16.9282	1.62143	0.810715	−	0.585441i	$-0.199078\pi$
$109$	16.9282	1.62143	0.810715	+	0.585441i	$0.199078\pi$
$110$	1.26884	0.120979
$111$	−5.34560	−0.507382
$112$	14.1088	1.33315
$113$	6.48668	0.610215	0.305108	−	0.952318i	$-0.401308\pi$
$113$	6.48668	0.610215	0.305108	+	0.952318i	$0.401308\pi$
$114$	0.318827	0.0298608
$115$	−2.08087	−0.194042
$116$	−1.97396	−0.183277
$117$	3.51085	0.324578
$118$	1.52210	0.140120
$119$	11.1022	1.01774
$120$	1.33452	0.121825
$121$	3.27598	0.297816
$122$	−1.75301	−0.158710
$123$	12.0312	1.08482
$124$	7.06982	0.634889
$125$	−11.7985	−1.05529
$126$	0.592268	0.0527634
$127$	8.62092	0.764983	0.382492	−	0.923959i	$-0.375066\pi$
$127$	8.62092	0.764983	0.382492	+	0.923959i	$0.375066\pi$
$128$	−4.99746	−0.441717
$129$	−3.68702	−0.324624
$130$	1.17901	0.103406
$131$	−4.57907	−0.400075	−0.200037	−	0.979788i	$-0.564106\pi$
$131$	−4.57907	−0.400075	−0.200037	+	0.979788i	$0.564106\pi$
$132$	7.45831	0.649162
$133$	−7.25028	−0.628679
$134$	0.737952	0.0637493
$135$	−2.08087	−0.179093
$136$	−1.94013	−0.166365
$137$	−0.365639	−0.0312387	−0.0156193	−	0.999878i	$-0.504972\pi$
$137$	−0.365639	−0.0312387	−0.0156193	+	0.999878i	$0.504972\pi$
$138$	0.161383	0.0137379
$139$	−12.2183	−1.03634	−0.518172	−	0.855277i	$-0.673387\pi$
$139$	−12.2183	−1.03634	−0.518172	+	0.855277i	$0.673387\pi$
$140$	−15.0744	−1.27402
$141$	0.138067	0.0116273
$142$	−0.529706	−0.0444519
$143$	13.2652	1.10930
$144$	3.84441	0.320368
$145$	2.08087	0.172807
$146$	0.247134	0.0204530
$147$	−6.46848	−0.533511
$148$	−10.5520	−0.867367
$149$	2.72205	0.222999	0.111499	−	0.993764i	$-0.464435\pi$
$149$	2.72205	0.222999	0.111499	+	0.993764i	$0.464435\pi$
$150$	0.108125	0.00882840
$151$	−14.3704	−1.16945	−0.584724	−	0.811232i	$-0.698797\pi$
$151$	−14.3704	−1.16945	−0.584724	+	0.811232i	$0.698797\pi$
$152$	1.26700	0.102767
$153$	3.02517	0.244571
$154$	2.23780	0.180327
$155$	−7.45273	−0.598618
$156$	6.93026	0.554865
$157$	−9.48437	−0.756936	−0.378468	−	0.925614i	$-0.623549\pi$
$157$	−9.48437	−0.756936	−0.378468	+	0.925614i	$0.623549\pi$
$158$	1.18123	0.0939738
$159$	−3.01823	−0.239361
$160$	3.96007	0.313071
$161$	−3.66994	−0.289232
$162$	0.161383	0.0126795
$163$	20.6148	1.61468	0.807339	−	0.590088i	$-0.200907\pi$
$163$	20.6148	1.61468	0.807339	+	0.590088i	$0.200907\pi$
$164$	23.7491	1.85449
$165$	−7.86226	−0.612076
$166$	0.940370	0.0729869
$167$	13.3426	1.03248	0.516241	−	0.856443i	$-0.327331\pi$
$167$	13.3426	1.03248	0.516241	+	0.856443i	$0.327331\pi$
$168$	2.35365	0.181588
$169$	−0.673934	−0.0518411
$170$	1.01591	0.0779164
$171$	−1.97558	−0.151077
$172$	−7.27802	−0.554944
$173$	9.60604	0.730334	0.365167	−	0.930942i	$-0.381012\pi$
$173$	9.60604	0.730334	0.365167	+	0.930942i	$0.381012\pi$
$174$	−0.161383	−0.0122344
$175$	−2.45883	−0.185870
$176$	14.5256	1.09490
$177$	−9.43156	−0.708920
$178$	0.978597	0.0733489
$179$	10.3216	0.771473	0.385737	−	0.922609i	$-0.373947\pi$
$179$	10.3216	0.771473	0.385737	+	0.922609i	$0.373947\pi$
$180$	−4.10754	−0.306158
$181$	9.34390	0.694527	0.347263	−	0.937768i	$-0.387111\pi$
$181$	9.34390	0.694527	0.347263	+	0.937768i	$0.387111\pi$
$182$	2.07936	0.154133
$183$	10.8624	0.802972
$184$	0.641331	0.0472795
$185$	11.1235	0.817815
$186$	0.578003	0.0423812
$187$	11.4302	0.835857
$188$	0.272538	0.0198769
$189$	−3.66994	−0.266949
$190$	−0.663436	−0.0481307
$191$	−0.626325	−0.0453193	−0.0226597	−	0.999743i	$-0.507213\pi$
$191$	−0.626325	−0.0453193	−0.0226597	+	0.999743i	$0.507213\pi$
$192$	7.38169	0.532728
$193$	−0.516976	−0.0372128	−0.0186064	−	0.999827i	$-0.505923\pi$
$193$	−0.516976	−0.0372128	−0.0186064	+	0.999827i	$0.505923\pi$
$194$	−2.18684	−0.157006
$195$	−7.30561	−0.523166
$196$	−12.7685	−0.912035
$197$	−0.0598105	−0.00426132	−0.00213066	−	0.999998i	$-0.500678\pi$
$197$	−0.0598105	−0.00426132	−0.00213066	+	0.999998i	$0.500678\pi$
$198$	0.609764	0.0433341
$199$	−5.54830	−0.393308	−0.196654	−	0.980473i	$-0.563008\pi$
$199$	−5.54830	−0.393308	−0.196654	+	0.980473i	$0.563008\pi$
$200$	0.429685	0.0303833
$201$	−4.57266	−0.322531
$202$	−0.870945	−0.0612795
$203$	3.66994	0.257579
$204$	5.97155	0.418092
$205$	−25.0354	−1.74855
$206$	1.17637	0.0819615
$207$	−1.00000	−0.0695048
$208$	13.4971	0.935859
$209$	−7.46446	−0.516328
$210$	−1.23243	−0.0850458
$211$	−10.0930	−0.694833	−0.347416	−	0.937711i	$-0.612941\pi$
$211$	−10.0930	−0.694833	−0.347416	+	0.937711i	$0.612941\pi$
$212$	−5.95785	−0.409187
$213$	3.28228	0.224898
$214$	−0.956890	−0.0654117
$215$	7.67220	0.523240
$216$	0.641331	0.0436370
$217$	−13.1441	−0.892279
$218$	2.73194	0.185030
$219$	−1.53135	−0.103479
$220$	−15.5198	−1.04634
$221$	10.6209	0.714440
$222$	−0.862691	−0.0579000
$223$	−2.65301	−0.177659	−0.0888293	−	0.996047i	$-0.528313\pi$
$223$	−2.65301	−0.177659	−0.0888293	+	0.996047i	$0.528313\pi$
$224$	6.98422	0.466653
$225$	−0.669990	−0.0446660
$226$	1.04684	0.0696349
$227$	−2.02512	−0.134412	−0.0672059	−	0.997739i	$-0.521408\pi$
$227$	−2.02512	−0.134412	−0.0672059	+	0.997739i	$0.521408\pi$
$228$	−3.89971	−0.258265
$229$	−1.74269	−0.115160	−0.0575800	−	0.998341i	$-0.518338\pi$
$229$	−1.74269	−0.115160	−0.0575800	+	0.998341i	$0.518338\pi$
$230$	−0.335818	−0.0221432
$231$	−13.8664	−0.912339
$232$	−0.641331	−0.0421054
$233$	10.8194	0.708802	0.354401	−	0.935093i	$-0.384685\pi$
$233$	10.8194	0.708802	0.354401	+	0.935093i	$0.384685\pi$
$234$	0.566593	0.0370394
$235$	−0.287299	−0.0187413
$236$	−18.6175	−1.21189
$237$	−7.31941	−0.475447
$238$	1.79171	0.116139
$239$	13.5515	0.876572	0.438286	−	0.898836i	$-0.355586\pi$
$239$	13.5515	0.876572	0.438286	+	0.898836i	$0.355586\pi$
$240$	−7.99971	−0.516379
$241$	−17.0852	−1.10055	−0.550277	−	0.834982i	$-0.685478\pi$
$241$	−17.0852	−1.10055	−0.550277	+	0.834982i	$0.685478\pi$
$242$	0.528689	0.0339854
$243$	−1.00000	−0.0641500
$244$	21.4419	1.37268
$245$	13.4600	0.859931
$246$	1.94164	0.123794
$247$	−6.93598	−0.441326
$248$	2.29696	0.145857
$249$	−5.82693	−0.369267
$250$	−1.90408	−0.120425
$251$	14.0710	0.888151	0.444076	−	0.895989i	$-0.353532\pi$
$251$	14.0710	0.888151	0.444076	+	0.895989i	$0.353532\pi$
$252$	−7.24430	−0.456348
$253$	−3.77836	−0.237543
$254$	1.39127	0.0872963
$255$	−6.29498	−0.394207
$256$	13.9569	0.872305
$257$	2.08470	0.130040	0.0650201	−	0.997884i	$-0.479289\pi$
$257$	2.08470	0.130040	0.0650201	+	0.997884i	$0.479289\pi$
$258$	−0.595024	−0.0370446
$259$	19.6180	1.21901
$260$	−14.4210	−0.894350
$261$	1.00000	0.0618984
$262$	−0.738986	−0.0456547
$263$	−22.5597	−1.39109	−0.695545	−	0.718483i	$-0.744837\pi$
$263$	−22.5597	−1.39109	−0.695545	+	0.718483i	$0.744837\pi$
$264$	2.42318	0.149136
$265$	6.28054	0.385810
$266$	−1.17008	−0.0717419
$267$	−6.06380	−0.371098
$268$	−9.02623	−0.551365
$269$	21.7650	1.32704	0.663518	−	0.748160i	$-0.269062\pi$
$269$	21.7650	1.32704	0.663518	+	0.748160i	$0.269062\pi$
$270$	−0.335818	−0.0204372
$271$	−19.0602	−1.15782	−0.578911	−	0.815391i	$-0.696522\pi$
$271$	−19.0602	−1.15782	−0.578911	+	0.815391i	$0.696522\pi$
$272$	11.6300	0.705172
$273$	−12.8846	−0.779812
$274$	−0.0590081	−0.00356481
$275$	−2.53146	−0.152653
$276$	−1.97396	−0.118818
$277$	−5.11613	−0.307399	−0.153699	−	0.988118i	$-0.549119\pi$
$277$	−5.11613	−0.307399	−0.153699	+	0.988118i	$0.549119\pi$
$278$	−1.97183	−0.118263
$279$	−3.58155	−0.214422
$280$	−4.89763	−0.292689
$281$	−7.01306	−0.418364	−0.209182	−	0.977877i	$-0.567080\pi$
$281$	−7.01306	−0.418364	−0.209182	+	0.977877i	$0.567080\pi$
$282$	0.0222817	0.00132686
$283$	−18.5054	−1.10003	−0.550014	−	0.835155i	$-0.685378\pi$
$283$	−18.5054	−1.10003	−0.550014	+	0.835155i	$0.685378\pi$
$284$	6.47907	0.384462
$285$	4.11093	0.243510
$286$	2.14079	0.126588
$287$	−44.1539	−2.60632
$288$	1.90309	0.112140
$289$	−7.84835	−0.461667
$290$	0.335818	0.0197199
$291$	13.5506	0.794348
$292$	−3.02281	−0.176897
$293$	7.86714	0.459603	0.229802	−	0.973237i	$-0.426192\pi$
$293$	7.86714	0.459603	0.229802	+	0.973237i	$0.426192\pi$
$294$	−1.04391	−0.0608818
$295$	19.6258	1.14266
$296$	−3.42830	−0.199266
$297$	−3.77836	−0.219243
$298$	0.439294	0.0254476
$299$	−3.51085	−0.203038
$300$	−1.32253	−0.0763564
$301$	13.5312	0.779923
$302$	−2.31915	−0.133452
$303$	5.39674	0.310035
$304$	−7.59496	−0.435601
$305$	−22.6032	−1.29426
$306$	0.488212	0.0279092
$307$	−1.52335	−0.0869424	−0.0434712	−	0.999055i	$-0.513842\pi$
$307$	−1.52335	−0.0869424	−0.0434712	+	0.999055i	$0.513842\pi$
$308$	−27.3716	−1.55964
$309$	−7.28928	−0.414673
$310$	−1.20275	−0.0683115
$311$	15.6060	0.884936	0.442468	−	0.896784i	$-0.354103\pi$
$311$	15.6060	0.884936	0.442468	+	0.896784i	$0.354103\pi$
$312$	2.25162	0.127473
$313$	−8.42755	−0.476353	−0.238177	−	0.971222i	$-0.576550\pi$
$313$	−8.42755	−0.476353	−0.238177	+	0.971222i	$0.576550\pi$
$314$	−1.53062	−0.0863780
$315$	7.63666	0.430277
$316$	−14.4482	−0.812774
$317$	−8.28338	−0.465241	−0.232621	−	0.972568i	$-0.574730\pi$
$317$	−8.28338	−0.465241	−0.232621	+	0.972568i	$0.574730\pi$
$318$	−0.487093	−0.0273148
$319$	3.77836	0.211547
$320$	−15.3603	−0.858668
$321$	5.92929	0.330941
$322$	−0.592268	−0.0330058
$323$	−5.97648	−0.332540
$324$	−1.97396	−0.109664
$325$	−2.35224	−0.130479
$326$	3.32689	0.184259
$327$	−16.9282	−0.936133
$328$	7.71599	0.426044
$329$	−0.506698	−0.0279352
$330$	−1.26884	−0.0698473
$331$	−21.2067	−1.16563	−0.582814	−	0.812605i	$-0.698048\pi$
$331$	−21.2067	−1.16563	−0.582814	+	0.812605i	$0.698048\pi$
$332$	−11.5021	−0.631260
$333$	5.34560	0.292937
$334$	2.15328	0.117822
$335$	9.51510	0.519865
$336$	−14.1088	−0.769696
$337$	−13.8277	−0.753242	−0.376621	−	0.926367i	$-0.622914\pi$
$337$	−13.8277	−0.753242	−0.376621	+	0.926367i	$0.622914\pi$
$338$	−0.108762	−0.00591587
$339$	−6.48668	−0.352308
$340$	−12.4260	−0.673895
$341$	−13.5324	−0.732819
$342$	−0.318827	−0.0172402
$343$	−1.95065	−0.105325
$344$	−2.36460	−0.127491
$345$	2.08087	0.112030
$346$	1.55026	0.0833423
$347$	33.5066	1.79873	0.899365	−	0.437198i	$-0.144029\pi$
$347$	33.5066	1.79873	0.899365	+	0.437198i	$0.144029\pi$
$348$	1.97396	0.105815
$349$	−20.9451	−1.12117	−0.560584	−	0.828098i	$-0.689423\pi$
$349$	−20.9451	−1.12117	−0.560584	+	0.828098i	$0.689423\pi$
$350$	−0.396814	−0.0212106
$351$	−3.51085	−0.187395
$352$	7.19054	0.383257
$353$	33.6831	1.79277	0.896386	−	0.443275i	$-0.146183\pi$
$353$	33.6831	1.79277	0.896386	+	0.443275i	$0.146183\pi$
$354$	−1.52210	−0.0808986
$355$	−6.82999	−0.362498
$356$	−11.9697	−0.634391
$357$	−11.1022	−0.587591
$358$	1.66574	0.0880370
$359$	−1.33233	−0.0703176	−0.0351588	−	0.999382i	$-0.511194\pi$
$359$	−1.33233	−0.0703176	−0.0351588	+	0.999382i	$0.511194\pi$
$360$	−1.33452	−0.0703356
$361$	−15.0971	−0.794583
$362$	1.50795	0.0792562
$363$	−3.27598	−0.171944
$364$	−25.4337	−1.33309
$365$	3.18653	0.166791
$366$	1.75301	0.0916314
$367$	14.0175	0.731708	0.365854	−	0.930672i	$-0.380777\pi$
$367$	14.0175	0.731708	0.365854	+	0.930672i	$0.380777\pi$
$368$	−3.84441	−0.200404
$369$	−12.0312	−0.626320
$370$	1.79515	0.0933252
$371$	11.0767	0.575075
$372$	−7.06982	−0.366553
$373$	−17.5045	−0.906347	−0.453173	−	0.891422i	$-0.649708\pi$
$373$	−17.5045	−0.906347	−0.453173	+	0.891422i	$0.649708\pi$
$374$	1.84464	0.0953841
$375$	11.7985	0.609272
$376$	0.0885467	0.00456645
$377$	3.51085	0.180818
$378$	−0.592268	−0.0304630
$379$	−26.0033	−1.33570	−0.667851	−	0.744295i	$-0.732786\pi$
$379$	−26.0033	−1.33570	−0.667851	+	0.744295i	$0.732786\pi$
$380$	8.11479	0.416280
$381$	−8.62092	−0.441663
$382$	−0.101079	−0.00517163
$383$	−19.8921	−1.01644	−0.508219	−	0.861228i	$-0.669696\pi$
$383$	−19.8921	−1.01644	−0.508219	+	0.861228i	$0.669696\pi$
$384$	4.99746	0.255025
$385$	28.8540	1.47054
$386$	−0.0834314	−0.00424655
$387$	3.68702	0.187422
$388$	26.7482	1.35793
$389$	−6.92622	−0.351173	−0.175587	−	0.984464i	$-0.556182\pi$
$389$	−6.92622	−0.351173	−0.175587	+	0.984464i	$0.556182\pi$
$390$	−1.17901	−0.0597012
$391$	−3.02517	−0.152989
$392$	−4.14843	−0.209528
$393$	4.57907	0.230983
$394$	−0.00965242	−0.000486282 0
$395$	15.2307	0.766341
$396$	−7.45831	−0.374794
$397$	−23.2007	−1.16441	−0.582205	−	0.813042i	$-0.697810\pi$
$397$	−23.2007	−1.16441	−0.582205	+	0.813042i	$0.697810\pi$
$398$	−0.895403	−0.0448825
$399$	7.25028	0.362968
$400$	−2.57572	−0.128786
$401$	12.9918	0.648778	0.324389	−	0.945924i	$-0.394841\pi$
$401$	12.9918	0.648778	0.324389	+	0.945924i	$0.394841\pi$
$402$	−0.737952	−0.0368057
$403$	−12.5743	−0.626370
$404$	10.6529	0.530003
$405$	2.08087	0.103399
$406$	0.592268	0.0293938
$407$	20.1976	1.00116
$408$	1.94013	0.0960510
$409$	−32.0911	−1.58680	−0.793402	−	0.608699i	$-0.791692\pi$
$409$	−32.0911	−1.58680	−0.793402	+	0.608699i	$0.791692\pi$
$410$	−4.04029	−0.199536
$411$	0.365639	0.0180357
$412$	−14.3887	−0.708881
$413$	34.6133	1.70321
$414$	−0.161383	−0.00793156
$415$	12.1251	0.595196
$416$	6.68145	0.327585
$417$	12.2183	0.598333
$418$	−1.20464	−0.0589209
$419$	28.0069	1.36823	0.684113	−	0.729376i	$-0.260189\pi$
$419$	28.0069	1.36823	0.684113	+	0.729376i	$0.260189\pi$
$420$	15.0744	0.735557
$421$	−23.7699	−1.15847	−0.579237	−	0.815159i	$-0.696650\pi$
$421$	−23.7699	−1.15847	−0.579237	+	0.815159i	$0.696650\pi$
$422$	−1.62885	−0.0792911
$423$	−0.138067	−0.00671305
$424$	−1.93568	−0.0940051
$425$	−2.02683	−0.0983159
$426$	0.529706	0.0256643
$427$	−39.8644	−1.92917
$428$	11.7042	0.565742
$429$	−13.2652	−0.640452
$430$	1.23817	0.0597097
$431$	3.63777	0.175225	0.0876126	−	0.996155i	$-0.472076\pi$
$431$	3.63777	0.175225	0.0876126	+	0.996155i	$0.472076\pi$
$432$	−3.84441	−0.184964
$433$	39.2350	1.88552	0.942758	−	0.333478i	$-0.108222\pi$
$433$	39.2350	1.88552	0.942758	+	0.333478i	$0.108222\pi$
$434$	−2.12124	−0.101823
$435$	−2.08087	−0.0997700
$436$	−33.4156	−1.60032
$437$	1.97558	0.0945050
$438$	−0.247134	−0.0118085
$439$	28.2038	1.34609	0.673046	−	0.739601i	$-0.264986\pi$
$439$	28.2038	1.34609	0.673046	+	0.739601i	$0.264986\pi$
$440$	−5.04231	−0.240383
$441$	6.46848	0.308023
$442$	1.71404	0.0815286
$443$	−24.3212	−1.15553	−0.577767	−	0.816202i	$-0.696076\pi$
$443$	−24.3212	−1.15553	−0.577767	+	0.816202i	$0.696076\pi$
$444$	10.5520	0.500775
$445$	12.6180	0.598149
$446$	−0.428152	−0.0202736
$447$	−2.72205	−0.128748
$448$	−27.0904	−1.27990
$449$	40.9877	1.93433	0.967164	−	0.254152i	$-0.0817962\pi$
$449$	40.9877	1.93433	0.967164	+	0.254152i	$0.0817962\pi$
$450$	−0.108125	−0.00509708
$451$	−45.4582	−2.14054
$452$	−12.8044	−0.602269
$453$	14.3704	0.675181
$454$	−0.326821	−0.0153384
$455$	26.8112	1.25693
$456$	−1.26700	−0.0593328
$457$	9.80944	0.458866	0.229433	−	0.973324i	$-0.426313\pi$
$457$	9.80944	0.458866	0.229433	+	0.973324i	$0.426313\pi$
$458$	−0.281241	−0.0131415
$459$	−3.02517	−0.141203
$460$	4.10754	0.191515
$461$	−24.6215	−1.14674	−0.573369	−	0.819297i	$-0.694364\pi$
$461$	−24.6215	−1.14674	−0.573369	+	0.819297i	$0.694364\pi$
$462$	−2.23780	−0.104112
$463$	10.1126	0.469972	0.234986	−	0.971999i	$-0.424495\pi$
$463$	10.1126	0.469972	0.234986	+	0.971999i	$0.424495\pi$
$464$	3.84441	0.178472
$465$	7.45273	0.345612
$466$	1.74607	0.0808852
$467$	0.219921	0.0101767	0.00508836	−	0.999987i	$-0.498380\pi$
$467$	0.219921	0.0101767	0.00508836	+	0.999987i	$0.498380\pi$
$468$	−6.93026	−0.320351
$469$	16.7814	0.774893
$470$	−0.0463654	−0.00213867
$471$	9.48437	0.437017
$472$	−6.04875	−0.278416
$473$	13.9309	0.640543
$474$	−1.18123	−0.0542558
$475$	1.32362	0.0607319
$476$	−21.9152	−1.00448
$477$	3.01823	0.138195
$478$	2.18698	0.100030
$479$	−16.9614	−0.774984	−0.387492	−	0.921873i	$-0.626659\pi$
$479$	−16.9614	−0.774984	−0.387492	+	0.921873i	$0.626659\pi$
$480$	−3.96007	−0.180752
$481$	18.7676	0.855729
$482$	−2.75727	−0.125590
$483$	3.66994	0.166988
$484$	−6.46664	−0.293938
$485$	−28.1969	−1.28036
$486$	−0.161383	−0.00732050
$487$	28.0531	1.27121	0.635603	−	0.772016i	$-0.280752\pi$
$487$	28.0531	1.27121	0.635603	+	0.772016i	$0.280752\pi$
$488$	6.96639	0.315354
$489$	−20.6148	−0.932235
$490$	2.17223	0.0981313
$491$	37.9620	1.71320	0.856601	−	0.515980i	$-0.172572\pi$
$491$	37.9620	1.71320	0.856601	+	0.515980i	$0.172572\pi$
$492$	−23.7491	−1.07069
$493$	3.02517	0.136247
$494$	−1.11935	−0.0503620
$495$	7.86226	0.353382
$496$	−13.7690	−0.618244
$497$	−12.0458	−0.540327
$498$	−0.940370	−0.0421390
$499$	5.03700	0.225487	0.112744	−	0.993624i	$-0.464036\pi$
$499$	5.03700	0.225487	0.112744	+	0.993624i	$0.464036\pi$
$500$	23.2897	1.04155
$501$	−13.3426	−0.596104
$502$	2.27082	0.101352
$503$	−19.3933	−0.864706	−0.432353	−	0.901704i	$-0.642317\pi$
$503$	−19.3933	−0.864706	−0.432353	+	0.901704i	$0.642317\pi$
$504$	−2.35365	−0.104840
$505$	−11.2299	−0.499724
$506$	−0.609764	−0.0271073
$507$	0.673934	0.0299305
$508$	−17.0173	−0.755021
$509$	−26.5066	−1.17488	−0.587442	−	0.809266i	$-0.699865\pi$
$509$	−26.5066	−1.17488	−0.587442	+	0.809266i	$0.699865\pi$
$510$	−1.01591	−0.0449850
$511$	5.61996	0.248612
$512$	12.2473	0.541260
$513$	1.97558	0.0872242
$514$	0.336436	0.0148396
$515$	15.1680	0.668383
$516$	7.27802	0.320397
$517$	−0.521667	−0.0229429
$518$	3.16603	0.139107
$519$	−9.60604	−0.421658
$520$	−4.68531	−0.205465
$521$	−14.1503	−0.619936	−0.309968	−	0.950747i	$-0.600318\pi$
$521$	−14.1503	−0.619936	−0.309968	+	0.950747i	$0.600318\pi$
$522$	0.161383	0.00706356
$523$	−2.42020	−0.105828	−0.0529139	−	0.998599i	$-0.516851\pi$
$523$	−2.42020	−0.105828	−0.0529139	+	0.998599i	$0.516851\pi$
$524$	9.03887	0.394865
$525$	2.45883	0.107312
$526$	−3.64076	−0.158745
$527$	−10.8348	−0.471971
$528$	−14.5256	−0.632144
$529$	1.00000	0.0434783
$530$	1.01358	0.0440269
$531$	9.43156	0.409295
$532$	14.3117	0.620492
$533$	−42.2398	−1.82961
$534$	−0.978597	−0.0423480
$535$	−12.3381	−0.533422
$536$	−2.93259	−0.126668
$537$	−10.3216	−0.445410
$538$	3.51251	0.151435
$539$	24.4402	1.05271
$540$	4.10754	0.176760
$541$	21.1409	0.908919	0.454459	−	0.890768i	$-0.349833\pi$
$541$	21.1409	0.908919	0.454459	+	0.890768i	$0.349833\pi$
$542$	−3.07600	−0.132125
$543$	−9.34390	−0.400985
$544$	5.75716	0.246836
$545$	35.2254	1.50889
$546$	−2.07936	−0.0889886
$547$	19.9428	0.852692	0.426346	−	0.904560i	$-0.359801\pi$
$547$	19.9428	0.852692	0.426346	+	0.904560i	$0.359801\pi$
$548$	0.721755	0.0308319
$549$	−10.8624	−0.463596
$550$	−0.408536	−0.0174200
$551$	−1.97558	−0.0841627
$552$	−0.641331	−0.0272968
$553$	26.8618	1.14228
$554$	−0.825660	−0.0350789
$555$	−11.1235	−0.472166
$556$	24.1184	1.02285
$557$	11.3239	0.479809	0.239904	−	0.970797i	$-0.422884\pi$
$557$	11.3239	0.479809	0.239904	+	0.970797i	$0.422884\pi$
$558$	−0.578003	−0.0244688
$559$	12.9446	0.547497
$560$	29.3585	1.24062
$561$	−11.4302	−0.482582
$562$	−1.13179	−0.0477418
$563$	−5.82702	−0.245580	−0.122790	−	0.992433i	$-0.539184\pi$
$563$	−5.82702	−0.245580	−0.122790	+	0.992433i	$0.539184\pi$
$564$	−0.272538	−0.0114759
$565$	13.4979	0.567862
$566$	−2.98646	−0.125530
$567$	3.66994	0.154123
$568$	2.10503	0.0883250
$569$	−17.5619	−0.736235	−0.368117	−	0.929779i	$-0.619998\pi$
$569$	−17.5619	−0.736235	−0.368117	+	0.929779i	$0.619998\pi$
$570$	0.663436	0.0277883
$571$	−5.56698	−0.232971	−0.116485	−	0.993192i	$-0.537163\pi$
$571$	−5.56698	−0.232971	−0.116485	+	0.993192i	$0.537163\pi$
$572$	−26.1850	−1.09485
$573$	0.626325	0.0261651
$574$	−7.12570	−0.297421
$575$	0.669990	0.0279405
$576$	−7.38169	−0.307571
$577$	14.3262	0.596407	0.298203	−	0.954502i	$-0.403613\pi$
$577$	14.3262	0.596407	0.298203	+	0.954502i	$0.403613\pi$
$578$	−1.26659	−0.0526833
$579$	0.516976	0.0214848
$580$	−4.10754	−0.170556
$581$	21.3845	0.887178
$582$	2.18684	0.0906473
$583$	11.4040	0.472303
$584$	−0.982100	−0.0406396
$585$	7.30561	0.302050
$586$	1.26963	0.0524478
$587$	41.9005	1.72942	0.864709	−	0.502272i	$-0.167503\pi$
$587$	41.9005	1.72942	0.864709	+	0.502272i	$0.167503\pi$
$588$	12.7685	0.526564
$589$	7.07565	0.291547
$590$	3.16728	0.130395
$591$	0.0598105	0.00246027
$592$	20.5507	0.844628
$593$	−42.7475	−1.75543	−0.877714	−	0.479185i	$-0.840932\pi$
$593$	−42.7475	−1.75543	−0.877714	+	0.479185i	$0.840932\pi$
$594$	−0.609764	−0.0250189
$595$	23.1022	0.947098
$596$	−5.37320	−0.220095
$597$	5.54830	0.227077
$598$	−0.566593	−0.0231697
$599$	5.56292	0.227295	0.113647	−	0.993521i	$-0.463747\pi$
$599$	5.56292	0.227295	0.113647	+	0.993521i	$0.463747\pi$
$600$	−0.429685	−0.0175418
$601$	11.5568	0.471413	0.235706	−	0.971824i	$-0.424260\pi$
$601$	11.5568	0.471413	0.235706	+	0.971824i	$0.424260\pi$
$602$	2.18371	0.0890012
$603$	4.57266	0.186213
$604$	28.3666	1.15422
$605$	6.81688	0.277146
$606$	0.870945	0.0353797
$607$	−1.34211	−0.0544745	−0.0272372	−	0.999629i	$-0.508671\pi$
$607$	−1.34211	−0.0544745	−0.0272372	+	0.999629i	$0.508671\pi$
$608$	−3.75971	−0.152476
$609$	−3.66994	−0.148714
$610$	−3.64779	−0.147695
$611$	−0.484733	−0.0196102
$612$	−5.97155	−0.241386
$613$	−33.3794	−1.34818	−0.674090	−	0.738649i	$-0.735464\pi$
$613$	−33.3794	−1.34818	−0.674090	+	0.738649i	$0.735464\pi$
$614$	−0.245844	−0.00992147
$615$	25.0354	1.00952
$616$	−8.89292	−0.358306
$617$	−35.6912	−1.43687	−0.718436	−	0.695593i	$-0.755142\pi$
$617$	−35.6912	−1.43687	−0.718436	+	0.695593i	$0.755142\pi$
$618$	−1.17637	−0.0473205
$619$	−37.9577	−1.52565	−0.762825	−	0.646605i	$-0.776188\pi$
$619$	−37.9577	−1.52565	−0.762825	+	0.646605i	$0.776188\pi$
$620$	14.7114	0.590823
$621$	1.00000	0.0401286
$622$	2.51855	0.100985
$623$	22.2538	0.891579
$624$	−13.4971	−0.540318
$625$	−21.2012	−0.848046
$626$	−1.36007	−0.0543592
$627$	7.46446	0.298102
$628$	18.7217	0.747078
$629$	16.1713	0.644794
$630$	1.23243	0.0491012
$631$	33.9249	1.35053	0.675264	−	0.737576i	$-0.264030\pi$
$631$	33.9249	1.35053	0.675264	+	0.737576i	$0.264030\pi$
$632$	−4.69416	−0.186724
$633$	10.0930	0.401162
$634$	−1.33680	−0.0530912
$635$	17.9390	0.711888
$636$	5.95785	0.236244
$637$	22.7099	0.899797
$638$	0.609764	0.0241408
$639$	−3.28228	−0.129845
$640$	−10.3990	−0.411058
$641$	−33.6357	−1.32853	−0.664266	−	0.747496i	$-0.731256\pi$
$641$	−33.6357	−1.32853	−0.664266	+	0.747496i	$0.731256\pi$
$642$	0.956890	0.0377654
$643$	−9.50885	−0.374992	−0.187496	−	0.982265i	$-0.560037\pi$
$643$	−9.50885	−0.374992	−0.187496	+	0.982265i	$0.560037\pi$
$644$	7.24430	0.285466
$645$	−7.67220	−0.302093
$646$	−0.964505	−0.0379479
$647$	32.0048	1.25824	0.629120	−	0.777309i	$-0.283416\pi$
$647$	32.0048	1.25824	0.629120	+	0.777309i	$0.283416\pi$
$648$	−0.641331	−0.0251938
$649$	35.6358	1.39883
$650$	−0.379612	−0.0148896
$651$	13.1441	0.515157
$652$	−40.6927	−1.59365
$653$	−37.8578	−1.48149	−0.740745	−	0.671786i	$-0.765527\pi$
$653$	−37.8578	−1.48149	−0.740745	+	0.671786i	$0.765527\pi$
$654$	−2.73194	−0.106827
$655$	−9.52843	−0.372307
$656$	−46.2529	−1.80587
$657$	1.53135	0.0597435
$658$	−0.0817727	−0.00318783
$659$	19.1091	0.744383	0.372192	−	0.928156i	$-0.378606\pi$
$659$	19.1091	0.744383	0.372192	+	0.928156i	$0.378606\pi$
$660$	15.5198	0.604105
$661$	−42.2818	−1.64457	−0.822286	−	0.569074i	$-0.807302\pi$
$661$	−42.2818	−1.64457	−0.822286	+	0.569074i	$0.807302\pi$
$662$	−3.42242	−0.133016
$663$	−10.6209	−0.412482
$664$	−3.73699	−0.145023
$665$	−15.0869	−0.585044
$666$	0.862691	0.0334286
$667$	−1.00000	−0.0387202
$668$	−26.3377	−1.01904
$669$	2.65301	0.102571
$670$	1.53558	0.0593246
$671$	−41.0420	−1.58441
$672$	−6.98422	−0.269422
$673$	31.7136	1.22247	0.611234	−	0.791450i	$-0.290673\pi$
$673$	31.7136	1.22247	0.611234	+	0.791450i	$0.290673\pi$
$674$	−2.23156	−0.0859565
$675$	0.669990	0.0257879
$676$	1.33032	0.0511660
$677$	−6.06261	−0.233005	−0.116502	−	0.993190i	$-0.537168\pi$
$677$	−6.06261	−0.233005	−0.116502	+	0.993190i	$0.537168\pi$
$678$	−1.04684	−0.0402037
$679$	−49.7298	−1.90845
$680$	−4.03716	−0.154818
$681$	2.02512	0.0776027
$682$	−2.18390	−0.0836259
$683$	25.3602	0.970379	0.485190	−	0.874409i	$-0.338751\pi$
$683$	25.3602	0.970379	0.485190	+	0.874409i	$0.338751\pi$
$684$	3.89971	0.149109
$685$	−0.760847	−0.0290705
$686$	−0.314803	−0.0120192
$687$	1.74269	0.0664877
$688$	14.1744	0.540395
$689$	10.5966	0.403697
$690$	0.335818	0.0127844
$691$	−32.7346	−1.24528	−0.622642	−	0.782507i	$-0.713941\pi$
$691$	−32.7346	−1.24528	−0.622642	+	0.782507i	$0.713941\pi$
$692$	−18.9619	−0.720823
$693$	13.8664	0.526739
$694$	5.40742	0.205263
$695$	−25.4247	−0.964413
$696$	0.641331	0.0243096
$697$	−36.3965	−1.37861
$698$	−3.38020	−0.127942
$699$	−10.8194	−0.409227
$700$	4.85361	0.183449
$701$	−2.21763	−0.0837587	−0.0418793	−	0.999123i	$-0.513335\pi$
$701$	−2.21763	−0.0837587	−0.0418793	+	0.999123i	$0.513335\pi$
$702$	−0.566593	−0.0213847
$703$	−10.5607	−0.398304
$704$	−27.8907	−1.05117
$705$	0.287299	0.0108203
$706$	5.43590	0.204583
$707$	−19.8057	−0.744871
$708$	18.6175	0.699688
$709$	−21.0149	−0.789232	−0.394616	−	0.918846i	$-0.629122\pi$
$709$	−21.0149	−0.789232	−0.394616	+	0.918846i	$0.629122\pi$
$710$	−1.10225	−0.0413666
$711$	7.31941	0.274499
$712$	−3.88890	−0.145743
$713$	3.58155	0.134130
$714$	−1.79171	−0.0670531
$715$	27.6032	1.03230
$716$	−20.3744	−0.761427
$717$	−13.5515	−0.506089
$718$	−0.215016	−0.00802432
$719$	29.7877	1.11089	0.555447	−	0.831552i	$-0.312547\pi$
$719$	29.7877	1.11089	0.555447	+	0.831552i	$0.312547\pi$
$720$	7.99971	0.298132
$721$	26.7512	0.996268
$722$	−2.43642	−0.0906741
$723$	17.0852	0.635406
$724$	−18.4444	−0.685482
$725$	−0.669990	−0.0248828
$726$	−0.528689	−0.0196215
$727$	52.4598	1.94563	0.972813	−	0.231590i	$-0.0743928\pi$
$727$	52.4598	1.94563	0.972813	+	0.231590i	$0.0743928\pi$
$728$	−8.26330	−0.306258
$729$	1.00000	0.0370370
$730$	0.514253	0.0190334
$731$	11.1539	0.412541
$732$	−21.4419	−0.792516
$733$	43.1979	1.59555	0.797776	−	0.602954i	$-0.206010\pi$
$733$	43.1979	1.59555	0.797776	+	0.602954i	$0.206010\pi$
$734$	2.26219	0.0834991
$735$	−13.4600	−0.496481
$736$	−1.90309	−0.0701487
$737$	17.2771	0.636412
$738$	−1.94164	−0.0714727
$739$	−7.29686	−0.268419	−0.134210	−	0.990953i	$-0.542850\pi$
$739$	−7.29686	−0.268419	−0.134210	+	0.990953i	$0.542850\pi$
$740$	−21.9573	−0.807165
$741$	6.93598	0.254800
$742$	1.78760	0.0656249
$743$	−30.7316	−1.12743	−0.563716	−	0.825969i	$-0.690629\pi$
$743$	−30.7316	−1.12743	−0.563716	+	0.825969i	$0.690629\pi$
$744$	−2.29696	−0.0842106
$745$	5.66422	0.207521
$746$	−2.82493	−0.103428
$747$	5.82693	0.213196
$748$	−22.5626	−0.824972
$749$	−21.7602	−0.795099
$750$	1.90408	0.0695273
$751$	−34.1301	−1.24543	−0.622713	−	0.782450i	$-0.713970\pi$
$751$	−34.1301	−1.24543	−0.622713	+	0.782450i	$0.713970\pi$
$752$	−0.530787	−0.0193558
$753$	−14.0710	−0.512774
$754$	0.566593	0.0206341
$755$	−29.9029	−1.08828
$756$	7.24430	0.263473
$757$	−15.6198	−0.567710	−0.283855	−	0.958867i	$-0.591613\pi$
$757$	−15.6198	−0.567710	−0.283855	+	0.958867i	$0.591613\pi$
$758$	−4.19651	−0.152424
$759$	3.77836	0.137146
$760$	2.63646	0.0956346
$761$	−9.03111	−0.327377	−0.163689	−	0.986512i	$-0.552339\pi$
$761$	−9.03111	−0.327377	−0.163689	+	0.986512i	$0.552339\pi$
$762$	−1.39127	−0.0504006
$763$	62.1256	2.24910
$764$	1.23634	0.0447292
$765$	6.29498	0.227595
$766$	−3.21026	−0.115991
$767$	33.1128	1.19563
$768$	−13.9569	−0.503626
$769$	23.4779	0.846635	0.423318	−	0.905981i	$-0.360865\pi$
$769$	23.4779	0.846635	0.423318	+	0.905981i	$0.360865\pi$
$770$	4.65657	0.167811
$771$	−2.08470	−0.0750787
$772$	1.02049	0.0367282
$773$	−21.4602	−0.771871	−0.385935	−	0.922526i	$-0.626121\pi$
$773$	−21.4602	−0.771871	−0.385935	+	0.922526i	$0.626121\pi$
$774$	0.595024	0.0213877
$775$	2.39960	0.0861963
$776$	8.69039	0.311967
$777$	−19.6180	−0.703793
$778$	−1.11778	−0.0400743
$779$	23.7687	0.851601
$780$	14.4210	0.516353
$781$	−12.4016	−0.443765
$782$	−0.488212	−0.0174584
$783$	−1.00000	−0.0357371
$784$	24.8675	0.888125
$785$	−19.7357	−0.704398
$786$	0.738986	0.0263587
$787$	28.7283	1.02405	0.512026	−	0.858970i	$-0.328895\pi$
$787$	28.7283	1.02405	0.512026	+	0.858970i	$0.328895\pi$
$788$	0.118063	0.00420583
$789$	22.5597	0.803146
$790$	2.45799	0.0874513
$791$	23.8057	0.846434
$792$	−2.42318	−0.0861038
$793$	−38.1363	−1.35426
$794$	−3.74421	−0.132877
$795$	−6.28054	−0.222748
$796$	10.9521	0.388186
$797$	−21.6103	−0.765475	−0.382737	−	0.923857i	$-0.625019\pi$
$797$	−21.6103	−0.765475	−0.382737	+	0.923857i	$0.625019\pi$
$798$	1.17008	0.0414202
$799$	−0.417676	−0.0147763
$800$	−1.27505	−0.0450798
$801$	6.06380	0.214254
$802$	2.09666	0.0740355
$803$	5.78598	0.204183
$804$	9.02623	0.318330
$805$	−7.63666	−0.269157
$806$	−2.02928	−0.0714784
$807$	−21.7650	−0.766165
$808$	3.46110	0.121761
$809$	−38.6195	−1.35779	−0.678895	−	0.734235i	$-0.737541\pi$
$809$	−38.6195	−1.35779	−0.678895	+	0.734235i	$0.737541\pi$
$810$	0.335818	0.0117994
$811$	25.4982	0.895363	0.447681	−	0.894193i	$-0.352250\pi$
$811$	25.4982	0.895363	0.447681	+	0.894193i	$0.352250\pi$
$812$	−7.24430	−0.254225
$813$	19.0602	0.668469
$814$	3.25956	0.114247
$815$	42.8967	1.50261
$816$	−11.6300	−0.407131
$817$	−7.28402	−0.254836
$818$	−5.17897	−0.181079
$819$	12.8846	0.450225
$820$	49.4187	1.72578
$821$	27.1559	0.947747	0.473874	−	0.880593i	$-0.342855\pi$
$821$	27.1559	0.947747	0.473874	+	0.880593i	$0.342855\pi$
$822$	0.0590081	0.00205814
$823$	−15.3728	−0.535861	−0.267930	−	0.963438i	$-0.586340\pi$
$823$	−15.3728	−0.535861	−0.267930	+	0.963438i	$0.586340\pi$
$824$	−4.67484	−0.162856
$825$	2.53146	0.0881342
$826$	5.58601	0.194362
$827$	−4.88039	−0.169708	−0.0848539	−	0.996393i	$-0.527042\pi$
$827$	−4.88039	−0.169708	−0.0848539	+	0.996393i	$0.527042\pi$
$828$	1.97396	0.0685997
$829$	27.6304	0.959645	0.479823	−	0.877366i	$-0.340701\pi$
$829$	27.6304	0.959645	0.479823	+	0.877366i	$0.340701\pi$
$830$	1.95679	0.0679210
$831$	5.11613	0.177477
$832$	−25.9160	−0.898476
$833$	19.5682	0.678000
$834$	1.97183	0.0682790
$835$	27.7642	0.960820
$836$	14.7345	0.509604
$837$	3.58155	0.123797
$838$	4.51985	0.156136
$839$	18.3181	0.632411	0.316206	−	0.948691i	$-0.397591\pi$
$839$	18.3181	0.632411	0.316206	+	0.948691i	$0.397591\pi$
$840$	4.89763	0.168984
$841$	1.00000	0.0344828
$842$	−3.83607	−0.132200
$843$	7.01306	0.241543
$844$	19.9232	0.685784
$845$	−1.40237	−0.0482429
$846$	−0.0222817	−0.000766062 0
$847$	12.0227	0.413104
$848$	11.6033	0.398460
$849$	18.5054	0.635102
$850$	−0.327098	−0.0112194
$851$	−5.34560	−0.183245
$852$	−6.47907	−0.221969
$853$	−38.3460	−1.31294	−0.656472	−	0.754351i	$-0.727952\pi$
$853$	−38.3460	−1.31294	−0.656472	+	0.754351i	$0.727952\pi$
$854$	−6.43346	−0.220148
$855$	−4.11093	−0.140591
$856$	3.80264	0.129972
$857$	6.81213	0.232698	0.116349	−	0.993208i	$-0.462881\pi$
$857$	6.81213	0.232698	0.116349	+	0.993208i	$0.462881\pi$
$858$	−2.14079	−0.0730854
$859$	−18.6302	−0.635656	−0.317828	−	0.948148i	$-0.602953\pi$
$859$	−18.6302	−0.635656	−0.317828	+	0.948148i	$0.602953\pi$
$860$	−15.1446	−0.516426
$861$	44.1539	1.50476
$862$	0.587076	0.0199959
$863$	−15.8372	−0.539105	−0.269552	−	0.962986i	$-0.586876\pi$
$863$	−15.8372	−0.539105	−0.269552	+	0.962986i	$0.586876\pi$
$864$	−1.90309	−0.0647443
$865$	19.9889	0.679643
$866$	6.33189	0.215166
$867$	7.84835	0.266544
$868$	25.9458	0.880659
$869$	27.6554	0.938144
$870$	−0.335818	−0.0113853
$871$	16.0539	0.543966
$872$	−10.8566	−0.367651
$873$	−13.5506	−0.458617
$874$	0.318827	0.0107845
$875$	−43.2998	−1.46380
$876$	3.02281	0.102131
$877$	−45.1404	−1.52428	−0.762141	−	0.647411i	$-0.775852\pi$
$877$	−45.1404	−1.52428	−0.762141	+	0.647411i	$0.775852\pi$
$878$	4.55162	0.153610
$879$	−7.86714	−0.265352
$880$	30.2258	1.01891
$881$	−54.7405	−1.84425	−0.922127	−	0.386887i	$-0.873550\pi$
$881$	−54.7405	−1.84425	−0.922127	+	0.386887i	$0.873550\pi$
$882$	1.04391	0.0351501
$883$	−47.5964	−1.60175	−0.800874	−	0.598833i	$-0.795631\pi$
$883$	−47.5964	−1.60175	−0.800874	+	0.598833i	$0.795631\pi$
$884$	−20.9652	−0.705137
$885$	−19.6258	−0.659715
$886$	−3.92504	−0.131864
$887$	3.05499	0.102577	0.0512883	−	0.998684i	$-0.483667\pi$
$887$	3.05499	0.102577	0.0512883	+	0.998684i	$0.483667\pi$
$888$	3.42830	0.115046
$889$	31.6383	1.06111
$890$	2.03633	0.0682580
$891$	3.77836	0.126580
$892$	5.23692	0.175345
$893$	0.272763	0.00912767
$894$	−0.439294	−0.0146922
$895$	21.4779	0.717927
$896$	−18.3404	−0.612709
$897$	3.51085	0.117224
$898$	6.61474	0.220737
$899$	−3.58155	−0.119451
$900$	1.32253	0.0440844
$901$	9.13066	0.304186
$902$	−7.33620	−0.244269
$903$	−13.5312	−0.450289
$904$	−4.16011	−0.138363
$905$	19.4434	0.646321
$906$	2.31915	0.0770485
$907$	−24.3521	−0.808599	−0.404300	−	0.914627i	$-0.632485\pi$
$907$	−24.3521	−0.808599	−0.404300	+	0.914627i	$0.632485\pi$
$908$	3.99749	0.132661
$909$	−5.39674	−0.178999
$910$	4.32688	0.143435
$911$	8.64600	0.286455	0.143227	−	0.989690i	$-0.454252\pi$
$911$	8.64600	0.286455	0.143227	+	0.989690i	$0.454252\pi$
$912$	7.59496	0.251494
$913$	22.0162	0.728630
$914$	1.58308	0.0523637
$915$	22.6032	0.747240
$916$	3.43999	0.113660
$917$	−16.8049	−0.554947
$918$	−0.488212	−0.0161134
$919$	38.3295	1.26437	0.632187	−	0.774816i	$-0.282157\pi$
$919$	38.3295	1.26437	0.632187	+	0.774816i	$0.282157\pi$
$920$	1.33452	0.0439980
$921$	1.52335	0.0501962
$922$	−3.97351	−0.130860
$923$	−11.5236	−0.379304
$924$	27.3716	0.900458
$925$	−3.58150	−0.117759
$926$	1.63201	0.0536311
$927$	7.28928	0.239411
$928$	1.90309	0.0624719
$929$	34.5501	1.13355	0.566776	−	0.823872i	$-0.308191\pi$
$929$	34.5501	1.13355	0.566776	+	0.823872i	$0.308191\pi$
$930$	1.20275	0.0394397
$931$	−12.7790	−0.418816
$932$	−21.3570	−0.699572
$933$	−15.6060	−0.510918
$934$	0.0354916	0.00116132
$935$	23.7847	0.777842
$936$	−2.25162	−0.0735964
$937$	31.5802	1.03168	0.515839	−	0.856685i	$-0.327480\pi$
$937$	31.5802	1.03168	0.515839	+	0.856685i	$0.327480\pi$
$938$	2.70824	0.0884272
$939$	8.42755	0.275023
$940$	0.567116	0.0184973
$941$	−17.7672	−0.579195	−0.289597	−	0.957149i	$-0.593521\pi$
$941$	−17.7672	−0.579195	−0.289597	+	0.957149i	$0.593521\pi$
$942$	1.53062	0.0498703
$943$	12.0312	0.391790
$944$	36.2588	1.18012
$945$	−7.63666	−0.248421
$946$	2.24821	0.0730958
$947$	−0.409000	−0.0132907	−0.00664535	−	0.999978i	$-0.502115\pi$
$947$	−0.409000	−0.0132907	−0.00664535	+	0.999978i	$0.502115\pi$
$948$	14.4482	0.469255
$949$	5.37633	0.174523
$950$	0.213611	0.00693045
$951$	8.28338	0.268607
$952$	−7.12018	−0.230766
$953$	−15.6870	−0.508151	−0.254076	−	0.967184i	$-0.581771\pi$
$953$	−15.6870	−0.508151	−0.254076	+	0.967184i	$0.581771\pi$
$954$	0.487093	0.0157702
$955$	−1.30330	−0.0421738
$956$	−26.7500	−0.865157
$957$	−3.77836	−0.122137
$958$	−2.73728	−0.0884376
$959$	−1.34187	−0.0433314
$960$	15.3603	0.495752
$961$	−18.1725	−0.586209
$962$	3.02878	0.0976518
$963$	−5.92929	−0.191069
$964$	33.7254	1.08622
$965$	−1.07576	−0.0346299
$966$	0.592268	0.0190559
$967$	48.0986	1.54675	0.773373	−	0.633951i	$-0.218568\pi$
$967$	48.0986	1.54675	0.773373	+	0.633951i	$0.218568\pi$
$968$	−2.10099	−0.0675283
$969$	5.97648	0.191992
$970$	−4.55052	−0.146108
$971$	−24.7927	−0.795636	−0.397818	−	0.917464i	$-0.630232\pi$
$971$	−24.7927	−0.795636	−0.397818	+	0.917464i	$0.630232\pi$
$972$	1.97396	0.0633146
$973$	−44.8405	−1.43752
$974$	4.52730	0.145064
$975$	2.35224	0.0753318
$976$	−41.7595	−1.33669
$977$	−26.6260	−0.851841	−0.425921	−	0.904761i	$-0.640050\pi$
$977$	−26.6260	−0.851841	−0.425921	+	0.904761i	$0.640050\pi$
$978$	−3.32689	−0.106382
$979$	22.9112	0.732245
$980$	−26.5695	−0.848733
$981$	16.9282	0.540477
$982$	6.12644	0.195503
$983$	6.74470	0.215123	0.107561	−	0.994198i	$-0.465696\pi$
$983$	6.74470	0.215123	0.107561	+	0.994198i	$0.465696\pi$
$984$	−7.71599	−0.245977
$985$	−0.124458	−0.00396555
$986$	0.488212	0.0155479
$987$	0.506698	0.0161284
$988$	13.6913	0.435579
$989$	−3.68702	−0.117240
$990$	1.26884	0.0403263
$991$	40.4589	1.28522	0.642610	−	0.766193i	$-0.277851\pi$
$991$	40.4589	1.28522	0.642610	+	0.766193i	$0.277851\pi$
$992$	−6.81600	−0.216408
$993$	21.2067	0.672976
$994$	−1.94399	−0.0616596
$995$	−11.5453	−0.366010
$996$	11.5021	0.364458
$997$	−29.3174	−0.928491	−0.464246	−	0.885706i	$-0.653675\pi$
$997$	−29.3174	−0.928491	−0.464246	+	0.885706i	$0.653675\pi$
$998$	0.812889	0.0257316
$999$	−5.34560	−0.169127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.k.1.4	✓	10
3.2	odd	2		6003.2.a.k.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.k.1.4	✓	10	1.1	even	1	trivial
6003.2.a.k.1.7		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)

\(f(q)\)	\(=\)	\(q+0.161383 q^{2} -1.00000 q^{3} -1.97396 q^{4} +2.08087 q^{5} -0.161383 q^{6} +3.66994 q^{7} -0.641331 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.161383 q^{2} -1.00000 q^{3} -1.97396 q^{4} +2.08087 q^{5} -0.161383 q^{6} +3.66994 q^{7} -0.641331 q^{8} +1.00000 q^{9} +0.335818 q^{10} +3.77836 q^{11} +1.97396 q^{12} +3.51085 q^{13} +0.592268 q^{14} -2.08087 q^{15} +3.84441 q^{16} +3.02517 q^{17} +0.161383 q^{18} -1.97558 q^{19} -4.10754 q^{20} -3.66994 q^{21} +0.609764 q^{22} -1.00000 q^{23} +0.641331 q^{24} -0.669990 q^{25} +0.566593 q^{26} -1.00000 q^{27} -7.24430 q^{28} +1.00000 q^{29} -0.335818 q^{30} -3.58155 q^{31} +1.90309 q^{32} -3.77836 q^{33} +0.488212 q^{34} +7.63666 q^{35} -1.97396 q^{36} +5.34560 q^{37} -0.318827 q^{38} -3.51085 q^{39} -1.33452 q^{40} -12.0312 q^{41} -0.592268 q^{42} +3.68702 q^{43} -7.45831 q^{44} +2.08087 q^{45} -0.161383 q^{46} -0.138067 q^{47} -3.84441 q^{48} +6.46848 q^{49} -0.108125 q^{50} -3.02517 q^{51} -6.93026 q^{52} +3.01823 q^{53} -0.161383 q^{54} +7.86226 q^{55} -2.35365 q^{56} +1.97558 q^{57} +0.161383 q^{58} +9.43156 q^{59} +4.10754 q^{60} -10.8624 q^{61} -0.578003 q^{62} +3.66994 q^{63} -7.38169 q^{64} +7.30561 q^{65} -0.609764 q^{66} +4.57266 q^{67} -5.97155 q^{68} +1.00000 q^{69} +1.23243 q^{70} -3.28228 q^{71} -0.641331 q^{72} +1.53135 q^{73} +0.862691 q^{74} +0.669990 q^{75} +3.89971 q^{76} +13.8664 q^{77} -0.566593 q^{78} +7.31941 q^{79} +7.99971 q^{80} +1.00000 q^{81} -1.94164 q^{82} +5.82693 q^{83} +7.24430 q^{84} +6.29498 q^{85} +0.595024 q^{86} -1.00000 q^{87} -2.42318 q^{88} +6.06380 q^{89} +0.335818 q^{90} +12.8846 q^{91} +1.97396 q^{92} +3.58155 q^{93} -0.0222817 q^{94} -4.11093 q^{95} -1.90309 q^{96} -13.5506 q^{97} +1.04391 q^{98} +3.77836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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