LMFDB - Embedded newform 2001.2.a.l.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.7
Root			$1.17662$ 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)

$f(q)$	$=$	$q+1.17662 q^{2} -1.00000 q^{3} -0.615555 q^{4} +2.85352 q^{5} -1.17662 q^{6} +3.62966 q^{7} -3.07753 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.17662 q^{2} -1.00000 q^{3} -0.615555 q^{4} +2.85352 q^{5} -1.17662 q^{6} +3.62966 q^{7} -3.07753 q^{8} +1.00000 q^{9} +3.35752 q^{10} +1.39936 q^{11} +0.615555 q^{12} +2.03682 q^{13} +4.27074 q^{14} -2.85352 q^{15} -2.38998 q^{16} -0.256641 q^{17} +1.17662 q^{18} +1.59337 q^{19} -1.75650 q^{20} -3.62966 q^{21} +1.64652 q^{22} +1.00000 q^{23} +3.07753 q^{24} +3.14260 q^{25} +2.39658 q^{26} -1.00000 q^{27} -2.23426 q^{28} -1.00000 q^{29} -3.35752 q^{30} +3.05203 q^{31} +3.34294 q^{32} -1.39936 q^{33} -0.301970 q^{34} +10.3573 q^{35} -0.615555 q^{36} -5.80359 q^{37} +1.87479 q^{38} -2.03682 q^{39} -8.78179 q^{40} +10.7828 q^{41} -4.27074 q^{42} -10.8584 q^{43} -0.861383 q^{44} +2.85352 q^{45} +1.17662 q^{46} +10.2706 q^{47} +2.38998 q^{48} +6.17441 q^{49} +3.69765 q^{50} +0.256641 q^{51} -1.25378 q^{52} -9.74574 q^{53} -1.17662 q^{54} +3.99311 q^{55} -11.1704 q^{56} -1.59337 q^{57} -1.17662 q^{58} -4.00720 q^{59} +1.75650 q^{60} +7.96095 q^{61} +3.59109 q^{62} +3.62966 q^{63} +8.71335 q^{64} +5.81213 q^{65} -1.64652 q^{66} +1.95063 q^{67} +0.157977 q^{68} -1.00000 q^{69} +12.1867 q^{70} -12.4876 q^{71} -3.07753 q^{72} -8.14520 q^{73} -6.82864 q^{74} -3.14260 q^{75} -0.980806 q^{76} +5.07920 q^{77} -2.39658 q^{78} +16.3016 q^{79} -6.81987 q^{80} +1.00000 q^{81} +12.6873 q^{82} +6.27397 q^{83} +2.23426 q^{84} -0.732331 q^{85} -12.7762 q^{86} +1.00000 q^{87} -4.30657 q^{88} +3.67645 q^{89} +3.35752 q^{90} +7.39297 q^{91} -0.615555 q^{92} -3.05203 q^{93} +12.0846 q^{94} +4.54671 q^{95} -3.34294 q^{96} +8.10595 q^{97} +7.26496 q^{98} +1.39936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.17662	0.831999	0.415999	−	0.909365i	$-0.363432\pi$
$2$	1.17662	0.831999	0.415999	+	0.909365i	$0.363432\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.615555	−0.307778
$5$	2.85352	1.27613	0.638067	−	0.769981i	$-0.279734\pi$
$5$	2.85352	1.27613	0.638067	+	0.769981i	$0.279734\pi$
$6$	−1.17662	−0.480355
$7$	3.62966	1.37188	0.685941	−	0.727657i	$-0.259391\pi$
$7$	3.62966	1.37188	0.685941	+	0.727657i	$0.259391\pi$
$8$	−3.07753	−1.08807
$9$	1.00000	0.333333
$10$	3.35752	1.06174
$11$	1.39936	0.421923	0.210961	−	0.977494i	$-0.432341\pi$
$11$	1.39936	0.421923	0.210961	+	0.977494i	$0.432341\pi$
$12$	0.615555	0.177696
$13$	2.03682	0.564913	0.282457	−	0.959280i	$-0.408851\pi$
$13$	2.03682	0.564913	0.282457	+	0.959280i	$0.408851\pi$
$14$	4.27074	1.14140
$15$	−2.85352	−0.736777
$16$	−2.38998	−0.597495
$17$	−0.256641	−0.0622445	−0.0311223	−	0.999516i	$-0.509908\pi$
$17$	−0.256641	−0.0622445	−0.0311223	+	0.999516i	$0.509908\pi$
$18$	1.17662	0.277333
$19$	1.59337	0.365543	0.182772	−	0.983155i	$-0.441493\pi$
$19$	1.59337	0.365543	0.182772	+	0.983155i	$0.441493\pi$
$20$	−1.75650	−0.392766
$21$	−3.62966	−0.792056
$22$	1.64652	0.351039
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.07753	0.628197
$25$	3.14260	0.628519
$26$	2.39658	0.470007
$27$	−1.00000	−0.192450
$28$	−2.23426	−0.422235
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−3.35752	−0.612997
$31$	3.05203	0.548160	0.274080	−	0.961707i	$-0.411627\pi$
$31$	3.05203	0.548160	0.274080	+	0.961707i	$0.411627\pi$
$32$	3.34294	0.590954
$33$	−1.39936	−0.243597
$34$	−0.301970	−0.0517874
$35$	10.3573	1.75071
$36$	−0.615555	−0.102593
$37$	−5.80359	−0.954104	−0.477052	−	0.878875i	$-0.658295\pi$
$37$	−5.80359	−0.954104	−0.477052	+	0.878875i	$0.658295\pi$
$38$	1.87479	0.304132
$39$	−2.03682	−0.326153
$40$	−8.78179	−1.38852
$41$	10.7828	1.68399	0.841993	−	0.539489i	$-0.181383\pi$
$41$	10.7828	1.68399	0.841993	+	0.539489i	$0.181383\pi$
$42$	−4.27074	−0.658990
$43$	−10.8584	−1.65589	−0.827944	−	0.560811i	$-0.810489\pi$
$43$	−10.8584	−1.65589	−0.827944	+	0.560811i	$0.810489\pi$
$44$	−0.861383	−0.129858
$45$	2.85352	0.425378
$46$	1.17662	0.173484
$47$	10.2706	1.49812	0.749060	−	0.662502i	$-0.230506\pi$
$47$	10.2706	1.49812	0.749060	+	0.662502i	$0.230506\pi$
$48$	2.38998	0.344964
$49$	6.17441	0.882059
$50$	3.69765	0.522927
$51$	0.256641	0.0359369
$52$	−1.25378	−0.173868
$53$	−9.74574	−1.33868	−0.669340	−	0.742956i	$-0.733423\pi$
$53$	−9.74574	−1.33868	−0.669340	+	0.742956i	$0.733423\pi$
$54$	−1.17662	−0.160118
$55$	3.99311	0.538430
$56$	−11.1704	−1.49270
$57$	−1.59337	−0.211047
$58$	−1.17662	−0.154498
$59$	−4.00720	−0.521693	−0.260846	−	0.965380i	$-0.584002\pi$
$59$	−4.00720	−0.521693	−0.260846	+	0.965380i	$0.584002\pi$
$60$	1.75650	0.226763
$61$	7.96095	1.01930	0.509648	−	0.860383i	$-0.329776\pi$
$61$	7.96095	1.01930	0.509648	+	0.860383i	$0.329776\pi$
$62$	3.59109	0.456068
$63$	3.62966	0.457294
$64$	8.71335	1.08917
$65$	5.81213	0.720905
$66$	−1.64652	−0.202673
$67$	1.95063	0.238307	0.119154	−	0.992876i	$-0.461982\pi$
$67$	1.95063	0.238307	0.119154	+	0.992876i	$0.461982\pi$
$68$	0.157977	0.0191575
$69$	−1.00000	−0.120386
$70$	12.1867	1.45658
$71$	−12.4876	−1.48200	−0.741000	−	0.671505i	$-0.765648\pi$
$71$	−12.4876	−1.48200	−0.741000	+	0.671505i	$0.765648\pi$
$72$	−3.07753	−0.362690
$73$	−8.14520	−0.953323	−0.476662	−	0.879087i	$-0.658153\pi$
$73$	−8.14520	−0.953323	−0.476662	+	0.879087i	$0.658153\pi$
$74$	−6.82864	−0.793813
$75$	−3.14260	−0.362876
$76$	−0.980806	−0.112506
$77$	5.07920	0.578828
$78$	−2.39658	−0.271359
$79$	16.3016	1.83407	0.917037	−	0.398803i	$-0.130574\pi$
$79$	16.3016	1.83407	0.917037	+	0.398803i	$0.130574\pi$
$80$	−6.81987	−0.762484
$81$	1.00000	0.111111
$82$	12.6873	1.40107
$83$	6.27397	0.688658	0.344329	−	0.938849i	$-0.388106\pi$
$83$	6.27397	0.688658	0.344329	+	0.938849i	$0.388106\pi$
$84$	2.23426	0.243777
$85$	−0.732331	−0.0794324
$86$	−12.7762	−1.37770
$87$	1.00000	0.107211
$88$	−4.30657	−0.459081
$89$	3.67645	0.389702	0.194851	−	0.980833i	$-0.437578\pi$
$89$	3.67645	0.389702	0.194851	+	0.980833i	$0.437578\pi$
$90$	3.35752	0.353914
$91$	7.39297	0.774994
$92$	−0.615555	−0.0641761
$93$	−3.05203	−0.316480
$94$	12.0846	1.24643
$95$	4.54671	0.466483
$96$	−3.34294	−0.341188
$97$	8.10595	0.823034	0.411517	−	0.911402i	$-0.364999\pi$
$97$	8.10595	0.823034	0.411517	+	0.911402i	$0.364999\pi$
$98$	7.26496	0.733872
$99$	1.39936	0.140641
$100$	−1.93444	−0.193444
$101$	10.7377	1.06844	0.534219	−	0.845346i	$-0.320606\pi$
$101$	10.7377	1.06844	0.534219	+	0.845346i	$0.320606\pi$
$102$	0.301970	0.0298995
$103$	8.05373	0.793557	0.396779	−	0.917914i	$-0.370128\pi$
$103$	8.05373	0.793557	0.396779	+	0.917914i	$0.370128\pi$
$104$	−6.26838	−0.614665
$105$	−10.3573	−1.01077
$106$	−11.4671	−1.11378
$107$	−5.29768	−0.512146	−0.256073	−	0.966657i	$-0.582429\pi$
$107$	−5.29768	−0.512146	−0.256073	+	0.966657i	$0.582429\pi$
$108$	0.615555	0.0592318
$109$	13.0862	1.25343	0.626715	−	0.779248i	$-0.284399\pi$
$109$	13.0862	1.25343	0.626715	+	0.779248i	$0.284399\pi$
$110$	4.69838	0.447973
$111$	5.80359	0.550852
$112$	−8.67481	−0.819693
$113$	15.5519	1.46300	0.731498	−	0.681843i	$-0.238821\pi$
$113$	15.5519	1.46300	0.731498	+	0.681843i	$0.238821\pi$
$114$	−1.87479	−0.175591
$115$	2.85352	0.266092
$116$	0.615555	0.0571529
$117$	2.03682	0.188304
$118$	−4.71496	−0.434048
$119$	−0.931518	−0.0853921
$120$	8.78179	0.801664
$121$	−9.04179	−0.821981
$122$	9.36705	0.848053
$123$	−10.7828	−0.972249
$124$	−1.87869	−0.168711
$125$	−5.30015	−0.474059
$126$	4.27074	0.380468
$127$	−3.62028	−0.321248	−0.160624	−	0.987016i	$-0.551351\pi$
$127$	−3.62028	−0.321248	−0.160624	+	0.987016i	$0.551351\pi$
$128$	3.56645	0.315233
$129$	10.8584	0.956027
$130$	6.83869	0.599793
$131$	18.8807	1.64962	0.824809	−	0.565412i	$-0.191283\pi$
$131$	18.8807	1.64962	0.824809	+	0.565412i	$0.191283\pi$
$132$	0.861383	0.0749738
$133$	5.78337	0.501482
$134$	2.29516	0.198271
$135$	−2.85352	−0.245592
$136$	0.789819	0.0677264
$137$	−2.83524	−0.242231	−0.121116	−	0.992638i	$-0.538647\pi$
$137$	−2.83524	−0.242231	−0.121116	+	0.992638i	$0.538647\pi$
$138$	−1.17662	−0.100161
$139$	−9.09684	−0.771584	−0.385792	−	0.922586i	$-0.626072\pi$
$139$	−9.09684	−0.771584	−0.385792	+	0.922586i	$0.626072\pi$
$140$	−6.37550	−0.538828
$141$	−10.2706	−0.864940
$142$	−14.6932	−1.23302
$143$	2.85025	0.238350
$144$	−2.38998	−0.199165
$145$	−2.85352	−0.236972
$146$	−9.58383	−0.793164
$147$	−6.17441	−0.509257
$148$	3.57243	0.293652
$149$	−10.6033	−0.868654	−0.434327	−	0.900755i	$-0.643014\pi$
$149$	−10.6033	−0.868654	−0.434327	+	0.900755i	$0.643014\pi$
$150$	−3.69765	−0.301912
$151$	4.73059	0.384970	0.192485	−	0.981300i	$-0.438345\pi$
$151$	4.73059	0.384970	0.192485	+	0.981300i	$0.438345\pi$
$152$	−4.90363	−0.397737
$153$	−0.256641	−0.0207482
$154$	5.97630	0.481584
$155$	8.70903	0.699526
$156$	1.25378	0.100383
$157$	−0.758791	−0.0605581	−0.0302791	−	0.999541i	$-0.509640\pi$
$157$	−0.758791	−0.0605581	−0.0302791	+	0.999541i	$0.509640\pi$
$158$	19.1809	1.52595
$159$	9.74574	0.772887
$160$	9.53917	0.754137
$161$	3.62966	0.286057
$162$	1.17662	0.0924443
$163$	−20.4320	−1.60035	−0.800177	−	0.599763i	$-0.795261\pi$
$163$	−20.4320	−1.60035	−0.800177	+	0.599763i	$0.795261\pi$
$164$	−6.63739	−0.518293
$165$	−3.99311	−0.310863
$166$	7.38211	0.572963
$167$	9.96742	0.771302	0.385651	−	0.922645i	$-0.373977\pi$
$167$	9.96742	0.771302	0.385651	+	0.922645i	$0.373977\pi$
$168$	11.1704	0.861812
$169$	−8.85135	−0.680873
$170$	−0.861678	−0.0660877
$171$	1.59337	0.121848
$172$	6.68394	0.509645
$173$	−25.3581	−1.92794	−0.963972	−	0.266004i	$-0.914297\pi$
$173$	−25.3581	−1.92794	−0.963972	+	0.266004i	$0.914297\pi$
$174$	1.17662	0.0891997
$175$	11.4065	0.862254
$176$	−3.34444	−0.252097
$177$	4.00720	0.301199
$178$	4.32580	0.324232
$179$	4.55470	0.340434	0.170217	−	0.985407i	$-0.445553\pi$
$179$	4.55470	0.340434	0.170217	+	0.985407i	$0.445553\pi$
$180$	−1.75650	−0.130922
$181$	−23.1724	−1.72239	−0.861195	−	0.508275i	$-0.830283\pi$
$181$	−23.1724	−1.72239	−0.861195	+	0.508275i	$0.830283\pi$
$182$	8.69875	0.644794
$183$	−7.96095	−0.588491
$184$	−3.07753	−0.226878
$185$	−16.5607	−1.21756
$186$	−3.59109	−0.263311
$187$	−0.359133	−0.0262624
$188$	−6.32212	−0.461088
$189$	−3.62966	−0.264019
$190$	5.34977	0.388113
$191$	4.19705	0.303688	0.151844	−	0.988404i	$-0.451479\pi$
$191$	4.19705	0.303688	0.151844	+	0.988404i	$0.451479\pi$
$192$	−8.71335	−0.628832
$193$	−1.76911	−0.127344	−0.0636718	−	0.997971i	$-0.520281\pi$
$193$	−1.76911	−0.127344	−0.0636718	+	0.997971i	$0.520281\pi$
$194$	9.53766	0.684764
$195$	−5.81213	−0.416215
$196$	−3.80069	−0.271478
$197$	−9.09621	−0.648078	−0.324039	−	0.946044i	$-0.605041\pi$
$197$	−9.09621	−0.648078	−0.324039	+	0.946044i	$0.605041\pi$
$198$	1.64652	0.117013
$199$	−5.30465	−0.376037	−0.188018	−	0.982166i	$-0.560206\pi$
$199$	−5.30465	−0.376037	−0.188018	+	0.982166i	$0.560206\pi$
$200$	−9.67142	−0.683873
$201$	−1.95063	−0.137587
$202$	12.6342	0.888939
$203$	−3.62966	−0.254752
$204$	−0.157977	−0.0110606
$205$	30.7689	2.14899
$206$	9.47621	0.660239
$207$	1.00000	0.0695048
$208$	−4.86797	−0.337533
$209$	2.22969	0.154231
$210$	−12.1867	−0.840960
$211$	6.16689	0.424546	0.212273	−	0.977210i	$-0.431913\pi$
$211$	6.16689	0.424546	0.212273	+	0.977210i	$0.431913\pi$
$212$	5.99904	0.412016
$213$	12.4876	0.855633
$214$	−6.23337	−0.426105
$215$	−30.9846	−2.11314
$216$	3.07753	0.209399
$217$	11.0778	0.752010
$218$	15.3975	1.04285
$219$	8.14520	0.550401
$220$	−2.45798	−0.165717
$221$	−0.522732	−0.0351628
$222$	6.82864	0.458308
$223$	−2.50370	−0.167660	−0.0838300	−	0.996480i	$-0.526715\pi$
$223$	−2.50370	−0.167660	−0.0838300	+	0.996480i	$0.526715\pi$
$224$	12.1337	0.810719
$225$	3.14260	0.209506
$226$	18.2987	1.21721
$227$	6.26477	0.415808	0.207904	−	0.978149i	$-0.433336\pi$
$227$	6.26477	0.415808	0.207904	+	0.978149i	$0.433336\pi$
$228$	0.980806	0.0649554
$229$	−21.4865	−1.41987	−0.709935	−	0.704267i	$-0.751276\pi$
$229$	−21.4865	−1.41987	−0.709935	+	0.704267i	$0.751276\pi$
$230$	3.35752	0.221389
$231$	−5.07920	−0.334187
$232$	3.07753	0.202049
$233$	−17.3695	−1.13791	−0.568955	−	0.822368i	$-0.692652\pi$
$233$	−17.3695	−1.13791	−0.568955	+	0.822368i	$0.692652\pi$
$234$	2.39658	0.156669
$235$	29.3074	1.91180
$236$	2.46665	0.160565
$237$	−16.3016	−1.05890
$238$	−1.09605	−0.0710462
$239$	−2.89711	−0.187399	−0.0936993	−	0.995601i	$-0.529869\pi$
$239$	−2.89711	−0.187399	−0.0936993	+	0.995601i	$0.529869\pi$
$240$	6.81987	0.440220
$241$	−3.98534	−0.256718	−0.128359	−	0.991728i	$-0.540971\pi$
$241$	−3.98534	−0.256718	−0.128359	+	0.991728i	$0.540971\pi$
$242$	−10.6388	−0.683887
$243$	−1.00000	−0.0641500
$244$	−4.90041	−0.313717
$245$	17.6188	1.12563
$246$	−12.6873	−0.808910
$247$	3.24541	0.206500
$248$	−9.39269	−0.596436
$249$	−6.27397	−0.397597
$250$	−6.23628	−0.394417
$251$	−16.9698	−1.07113	−0.535564	−	0.844495i	$-0.679901\pi$
$251$	−16.9698	−1.07113	−0.535564	+	0.844495i	$0.679901\pi$
$252$	−2.23426	−0.140745
$253$	1.39936	0.0879770
$254$	−4.25971	−0.267278
$255$	0.732331	0.0458603
$256$	−13.2303	−0.826895
$257$	7.22916	0.450943	0.225471	−	0.974250i	$-0.427608\pi$
$257$	7.22916	0.450943	0.225471	+	0.974250i	$0.427608\pi$
$258$	12.7762	0.795414
$259$	−21.0650	−1.30892
$260$	−3.57769	−0.221879
$261$	−1.00000	−0.0618984
$262$	22.2155	1.37248
$263$	−11.9092	−0.734355	−0.367177	−	0.930151i	$-0.619676\pi$
$263$	−11.9092	−0.734355	−0.367177	+	0.930151i	$0.619676\pi$
$264$	4.30657	0.265051
$265$	−27.8097	−1.70834
$266$	6.80486	0.417233
$267$	−3.67645	−0.224995
$268$	−1.20072	−0.0733456
$269$	17.5257	1.06856	0.534280	−	0.845307i	$-0.320583\pi$
$269$	17.5257	1.06856	0.534280	+	0.845307i	$0.320583\pi$
$270$	−3.35752	−0.204332
$271$	27.8599	1.69237	0.846185	−	0.532889i	$-0.178894\pi$
$271$	27.8599	1.69237	0.846185	+	0.532889i	$0.178894\pi$
$272$	0.613367	0.0371908
$273$	−7.39297	−0.447443
$274$	−3.33601	−0.201536
$275$	4.39762	0.265187
$276$	0.615555	0.0370521
$277$	7.82340	0.470062	0.235031	−	0.971988i	$-0.424481\pi$
$277$	7.82340	0.470062	0.235031	+	0.971988i	$0.424481\pi$
$278$	−10.7036	−0.641957
$279$	3.05203	0.182720
$280$	−31.8749	−1.90489
$281$	−23.0361	−1.37422	−0.687111	−	0.726553i	$-0.741121\pi$
$281$	−23.0361	−1.37422	−0.687111	+	0.726553i	$0.741121\pi$
$282$	−12.0846	−0.719629
$283$	10.5239	0.625581	0.312791	−	0.949822i	$-0.398736\pi$
$283$	10.5239	0.625581	0.312791	+	0.949822i	$0.398736\pi$
$284$	7.68678	0.456127
$285$	−4.54671	−0.269324
$286$	3.35367	0.198307
$287$	39.1377	2.31023
$288$	3.34294	0.196985
$289$	−16.9341	−0.996126
$290$	−3.35752	−0.197161
$291$	−8.10595	−0.475179
$292$	5.01382	0.293412
$293$	19.5780	1.14376	0.571878	−	0.820339i	$-0.306215\pi$
$293$	19.5780	1.14376	0.571878	+	0.820339i	$0.306215\pi$
$294$	−7.26496	−0.423701
$295$	−11.4346	−0.665750
$296$	17.8607	1.03813
$297$	−1.39936	−0.0811991
$298$	−12.4761	−0.722720
$299$	2.03682	0.117793
$300$	1.93444	0.111685
$301$	−39.4122	−2.27168
$302$	5.56613	0.320295
$303$	−10.7377	−0.616862
$304$	−3.80812	−0.218410
$305$	22.7168	1.30076
$306$	−0.301970	−0.0172625
$307$	−16.3395	−0.932543	−0.466272	−	0.884642i	$-0.654403\pi$
$307$	−16.3395	−0.932543	−0.466272	+	0.884642i	$0.654403\pi$
$308$	−3.12653	−0.178150
$309$	−8.05373	−0.458160
$310$	10.2472	0.582005
$311$	−14.4849	−0.821361	−0.410681	−	0.911779i	$-0.634709\pi$
$311$	−14.4849	−0.821361	−0.410681	+	0.911779i	$0.634709\pi$
$312$	6.26838	0.354877
$313$	−15.8990	−0.898663	−0.449331	−	0.893365i	$-0.648338\pi$
$313$	−15.8990	−0.898663	−0.449331	+	0.893365i	$0.648338\pi$
$314$	−0.892812	−0.0503843
$315$	10.3573	0.583568
$316$	−10.0345	−0.564487
$317$	−7.37522	−0.414234	−0.207117	−	0.978316i	$-0.566408\pi$
$317$	−7.37522	−0.414234	−0.207117	+	0.978316i	$0.566408\pi$
$318$	11.4671	0.643041
$319$	−1.39936	−0.0783491
$320$	24.8637	1.38993
$321$	5.29768	0.295687
$322$	4.27074	0.237999
$323$	−0.408923	−0.0227531
$324$	−0.615555	−0.0341975
$325$	6.40092	0.355059
$326$	−24.0407	−1.33149
$327$	−13.0862	−0.723668
$328$	−33.1842	−1.83229
$329$	37.2787	2.05524
$330$	−4.69838	−0.258638
$331$	−2.22314	−0.122195	−0.0610974	−	0.998132i	$-0.519460\pi$
$331$	−2.22314	−0.122195	−0.0610974	+	0.998132i	$0.519460\pi$
$332$	−3.86198	−0.211954
$333$	−5.80359	−0.318035
$334$	11.7279	0.641722
$335$	5.56616	0.304112
$336$	8.67481	0.473250
$337$	−21.8928	−1.19258	−0.596288	−	0.802771i	$-0.703358\pi$
$337$	−21.8928	−1.19258	−0.596288	+	0.802771i	$0.703358\pi$
$338$	−10.4147	−0.566485
$339$	−15.5519	−0.844661
$340$	0.450790	0.0244475
$341$	4.27088	0.231281
$342$	1.87479	0.101377
$343$	−2.99661	−0.161802
$344$	33.4170	1.80172
$345$	−2.85352	−0.153629
$346$	−29.8370	−1.60405
$347$	32.5836	1.74918	0.874590	−	0.484863i	$-0.161131\pi$
$347$	32.5836	1.74918	0.874590	+	0.484863i	$0.161131\pi$
$348$	−0.615555	−0.0329972
$349$	−23.5157	−1.25877	−0.629384	−	0.777094i	$-0.716693\pi$
$349$	−23.5157	−1.25877	−0.629384	+	0.777094i	$0.716693\pi$
$350$	13.4212	0.717394
$351$	−2.03682	−0.108718
$352$	4.67798	0.249337
$353$	−27.3657	−1.45653	−0.728263	−	0.685297i	$-0.759672\pi$
$353$	−27.3657	−1.45653	−0.728263	+	0.685297i	$0.759672\pi$
$354$	4.71496	0.250598
$355$	−35.6335	−1.89123
$356$	−2.26306	−0.119942
$357$	0.931518	0.0493012
$358$	5.35917	0.283241
$359$	0.782857	0.0413176	0.0206588	−	0.999787i	$-0.493424\pi$
$359$	0.782857	0.0413176	0.0206588	+	0.999787i	$0.493424\pi$
$360$	−8.78179	−0.462841
$361$	−16.4612	−0.866378
$362$	−27.2652	−1.43303
$363$	9.04179	0.474571
$364$	−4.55079	−0.238526
$365$	−23.2425	−1.21657
$366$	−9.36705	−0.489624
$367$	0.508753	0.0265567	0.0132784	−	0.999912i	$-0.495773\pi$
$367$	0.508753	0.0265567	0.0132784	+	0.999912i	$0.495773\pi$
$368$	−2.38998	−0.124586
$369$	10.7828	0.561328
$370$	−19.4857	−1.01301
$371$	−35.3737	−1.83651
$372$	1.87869	0.0974056
$373$	−5.51685	−0.285651	−0.142826	−	0.989748i	$-0.545619\pi$
$373$	−5.51685	−0.285651	−0.142826	+	0.989748i	$0.545619\pi$
$374$	−0.422564	−0.0218503
$375$	5.30015	0.273698
$376$	−31.6080	−1.63006
$377$	−2.03682	−0.104902
$378$	−4.27074	−0.219663
$379$	−27.9568	−1.43605	−0.718023	−	0.696019i	$-0.754953\pi$
$379$	−27.9568	−1.43605	−0.718023	+	0.696019i	$0.754953\pi$
$380$	−2.79875	−0.143573
$381$	3.62028	0.185473
$382$	4.93835	0.252668
$383$	5.58188	0.285221	0.142610	−	0.989779i	$-0.454450\pi$
$383$	5.58188	0.285221	0.142610	+	0.989779i	$0.454450\pi$
$384$	−3.56645	−0.182000
$385$	14.4936	0.738662
$386$	−2.08158	−0.105950
$387$	−10.8584	−0.551963
$388$	−4.98966	−0.253312
$389$	−3.74821	−0.190042	−0.0950210	−	0.995475i	$-0.530292\pi$
$389$	−3.74821	−0.190042	−0.0950210	+	0.995475i	$0.530292\pi$
$390$	−6.83869	−0.346290
$391$	−0.256641	−0.0129789
$392$	−19.0019	−0.959741
$393$	−18.8807	−0.952407
$394$	−10.7028	−0.539201
$395$	46.5170	2.34052
$396$	−0.861383	−0.0432861
$397$	30.3805	1.52475	0.762377	−	0.647133i	$-0.224032\pi$
$397$	30.3805	1.52475	0.762377	+	0.647133i	$0.224032\pi$
$398$	−6.24158	−0.312862
$399$	−5.78337	−0.289531
$400$	−7.51074	−0.375537
$401$	3.30262	0.164925	0.0824626	−	0.996594i	$-0.473722\pi$
$401$	3.30262	0.164925	0.0824626	+	0.996594i	$0.473722\pi$
$402$	−2.29516	−0.114472
$403$	6.21644	0.309663
$404$	−6.60963	−0.328841
$405$	2.85352	0.141793
$406$	−4.27074	−0.211953
$407$	−8.12130	−0.402558
$408$	−0.789819	−0.0391019
$409$	−6.51701	−0.322246	−0.161123	−	0.986934i	$-0.551512\pi$
$409$	−6.51701	−0.322246	−0.161123	+	0.986934i	$0.551512\pi$
$410$	36.2034	1.78796
$411$	2.83524	0.139852
$412$	−4.95751	−0.244239
$413$	−14.5447	−0.715700
$414$	1.17662	0.0578279
$415$	17.9029	0.878820
$416$	6.80899	0.333838
$417$	9.09684	0.445474
$418$	2.62351	0.128320
$419$	38.1773	1.86508	0.932541	−	0.361063i	$-0.117586\pi$
$419$	38.1773	1.86508	0.932541	+	0.361063i	$0.117586\pi$
$420$	6.37550	0.311093
$421$	−35.6872	−1.73929	−0.869644	−	0.493679i	$-0.835652\pi$
$421$	−35.6872	−1.73929	−0.869644	+	0.493679i	$0.835652\pi$
$422$	7.25612	0.353222
$423$	10.2706	0.499373
$424$	29.9928	1.45658
$425$	−0.806518	−0.0391219
$426$	14.6932	0.711886
$427$	28.8955	1.39835
$428$	3.26101	0.157627
$429$	−2.85025	−0.137611
$430$	−36.4573	−1.75813
$431$	9.57775	0.461344	0.230672	−	0.973032i	$-0.425908\pi$
$431$	9.57775	0.461344	0.230672	+	0.973032i	$0.425908\pi$
$432$	2.38998	0.114988
$433$	11.4518	0.550336	0.275168	−	0.961396i	$-0.411266\pi$
$433$	11.4518	0.550336	0.275168	+	0.961396i	$0.411266\pi$
$434$	13.0344	0.625672
$435$	2.85352	0.136816
$436$	−8.05528	−0.385778
$437$	1.59337	0.0762211
$438$	9.58383	0.457933
$439$	18.4092	0.878624	0.439312	−	0.898335i	$-0.355222\pi$
$439$	18.4092	0.878624	0.439312	+	0.898335i	$0.355222\pi$
$440$	−12.2889	−0.585850
$441$	6.17441	0.294020
$442$	−0.615059	−0.0292554
$443$	12.4019	0.589232	0.294616	−	0.955616i	$-0.404808\pi$
$443$	12.4019	0.589232	0.294616	+	0.955616i	$0.404808\pi$
$444$	−3.57243	−0.169540
$445$	10.4908	0.497313
$446$	−2.94591	−0.139493
$447$	10.6033	0.501518
$448$	31.6265	1.49421
$449$	−23.9157	−1.12865	−0.564327	−	0.825551i	$-0.690864\pi$
$449$	−23.9157	−1.12865	−0.564327	+	0.825551i	$0.690864\pi$
$450$	3.69765	0.174309
$451$	15.0890	0.710512
$452$	−9.57304	−0.450278
$453$	−4.73059	−0.222263
$454$	7.37128	0.345952
$455$	21.0960	0.988997
$456$	4.90363	0.229633
$457$	3.61853	0.169268	0.0846339	−	0.996412i	$-0.473028\pi$
$457$	3.61853	0.169268	0.0846339	+	0.996412i	$0.473028\pi$
$458$	−25.2816	−1.18133
$459$	0.256641	0.0119790
$460$	−1.75650	−0.0818973
$461$	7.97110	0.371251	0.185626	−	0.982621i	$-0.440569\pi$
$461$	7.97110	0.371251	0.185626	+	0.982621i	$0.440569\pi$
$462$	−5.97630	−0.278043
$463$	−26.8314	−1.24696	−0.623480	−	0.781840i	$-0.714282\pi$
$463$	−26.8314	−1.24696	−0.623480	+	0.781840i	$0.714282\pi$
$464$	2.38998	0.110952
$465$	−8.70903	−0.403871
$466$	−20.4373	−0.946740
$467$	−12.0191	−0.556175	−0.278088	−	0.960556i	$-0.589701\pi$
$467$	−12.0191	−0.556175	−0.278088	+	0.960556i	$0.589701\pi$
$468$	−1.25378	−0.0579559
$469$	7.08011	0.326929
$470$	34.4838	1.59062
$471$	0.758791	0.0349633
$472$	12.3323	0.567638
$473$	−15.1948	−0.698657
$474$	−19.1809	−0.881006
$475$	5.00731	0.229751
$476$	0.573401	0.0262818
$477$	−9.74574	−0.446227
$478$	−3.40881	−0.155915
$479$	26.7408	1.22182	0.610909	−	0.791701i	$-0.290804\pi$
$479$	26.7408	1.22182	0.610909	+	0.791701i	$0.290804\pi$
$480$	−9.53917	−0.435401
$481$	−11.8209	−0.538986
$482$	−4.68925	−0.213589
$483$	−3.62966	−0.165155
$484$	5.56572	0.252987
$485$	23.1305	1.05030
$486$	−1.17662	−0.0533728
$487$	−27.3823	−1.24081	−0.620405	−	0.784281i	$-0.713032\pi$
$487$	−27.3823	−1.24081	−0.620405	+	0.784281i	$0.713032\pi$
$488$	−24.5000	−1.10906
$489$	20.4320	0.923965
$490$	20.7307	0.936519
$491$	−30.2527	−1.36529	−0.682644	−	0.730751i	$-0.739170\pi$
$491$	−30.2527	−1.36529	−0.682644	+	0.730751i	$0.739170\pi$
$492$	6.63739	0.299237
$493$	0.256641	0.0115585
$494$	3.81863	0.171808
$495$	3.99311	0.179477
$496$	−7.29428	−0.327523
$497$	−45.3255	−2.03313
$498$	−7.38211	−0.330800
$499$	−8.43684	−0.377685	−0.188842	−	0.982007i	$-0.560474\pi$
$499$	−8.43684	−0.377685	−0.188842	+	0.982007i	$0.560474\pi$
$500$	3.26253	0.145905
$501$	−9.96742	−0.445311
$502$	−19.9671	−0.891177
$503$	10.9875	0.489907	0.244953	−	0.969535i	$-0.421227\pi$
$503$	10.9875	0.489907	0.244953	+	0.969535i	$0.421227\pi$
$504$	−11.1704	−0.497568
$505$	30.6402	1.36347
$506$	1.64652	0.0731968
$507$	8.85135	0.393102
$508$	2.22849	0.0988730
$509$	13.4171	0.594704	0.297352	−	0.954768i	$-0.403897\pi$
$509$	13.4171	0.594704	0.297352	+	0.954768i	$0.403897\pi$
$510$	0.861678	0.0381557
$511$	−29.5643	−1.30785
$512$	−22.7000	−1.00321
$513$	−1.59337	−0.0703489
$514$	8.50601	0.375184
$515$	22.9815	1.01269
$516$	−6.68394	−0.294244
$517$	14.3723	0.632091
$518$	−24.7856	−1.08902
$519$	25.3581	1.11310
$520$	−17.8870	−0.784395
$521$	23.7404	1.04008	0.520042	−	0.854141i	$-0.325916\pi$
$521$	23.7404	1.04008	0.520042	+	0.854141i	$0.325916\pi$
$522$	−1.17662	−0.0514994
$523$	−22.9883	−1.00521	−0.502604	−	0.864517i	$-0.667625\pi$
$523$	−22.9883	−1.00521	−0.502604	+	0.864517i	$0.667625\pi$
$524$	−11.6221	−0.507716
$525$	−11.4065	−0.497822
$526$	−14.0127	−0.610982
$527$	−0.783274	−0.0341200
$528$	3.34444	0.145548
$529$	1.00000	0.0434783
$530$	−32.7215	−1.42133
$531$	−4.00720	−0.173898
$532$	−3.55999	−0.154345
$533$	21.9626	0.951306
$534$	−4.32580	−0.187195
$535$	−15.1170	−0.653567
$536$	−6.00311	−0.259295
$537$	−4.55470	−0.196550
$538$	20.6212	0.889042
$539$	8.64022	0.372161
$540$	1.75650	0.0755878
$541$	−11.3013	−0.485881	−0.242940	−	0.970041i	$-0.578112\pi$
$541$	−11.3013	−0.485881	−0.242940	+	0.970041i	$0.578112\pi$
$542$	32.7807	1.40805
$543$	23.1724	0.994422
$544$	−0.857935	−0.0367837
$545$	37.3418	1.59955
$546$	−8.69875	−0.372272
$547$	−18.2391	−0.779847	−0.389924	−	0.920847i	$-0.627499\pi$
$547$	−18.2391	−0.779847	−0.389924	+	0.920847i	$0.627499\pi$
$548$	1.74525	0.0745533
$549$	7.96095	0.339765
$550$	5.17435	0.220635
$551$	−1.59337	−0.0678797
$552$	3.07753	0.130988
$553$	59.1692	2.51613
$554$	9.20520	0.391091
$555$	16.5607	0.702961
$556$	5.59961	0.237476
$557$	−30.9415	−1.31103	−0.655516	−	0.755181i	$-0.727549\pi$
$557$	−30.9415	−1.31103	−0.655516	+	0.755181i	$0.727549\pi$
$558$	3.59109	0.152023
$559$	−22.1166	−0.935433
$560$	−24.7538	−1.04604
$561$	0.359133	0.0151626
$562$	−27.1049	−1.14335
$563$	41.8692	1.76458	0.882289	−	0.470709i	$-0.156002\pi$
$563$	41.8692	1.76458	0.882289	+	0.470709i	$0.156002\pi$
$564$	6.32212	0.266209
$565$	44.3776	1.86698
$566$	12.3827	0.520483
$567$	3.62966	0.152431
$568$	38.4308	1.61252
$569$	5.74370	0.240788	0.120394	−	0.992726i	$-0.461584\pi$
$569$	5.74370	0.240788	0.120394	+	0.992726i	$0.461584\pi$
$570$	−5.34977	−0.224077
$571$	6.60570	0.276440	0.138220	−	0.990402i	$-0.455862\pi$
$571$	6.60570	0.276440	0.138220	+	0.990402i	$0.455862\pi$
$572$	−1.75449	−0.0733588
$573$	−4.19705	−0.175334
$574$	46.0504	1.92211
$575$	3.14260	0.131055
$576$	8.71335	0.363056
$577$	42.1911	1.75644	0.878220	−	0.478258i	$-0.158731\pi$
$577$	42.1911	1.75644	0.878220	+	0.478258i	$0.158731\pi$
$578$	−19.9251	−0.828775
$579$	1.76911	0.0735219
$580$	1.75650	0.0729348
$581$	22.7724	0.944757
$582$	−9.53766	−0.395349
$583$	−13.6378	−0.564820
$584$	25.0671	1.03728
$585$	5.81213	0.240302
$586$	23.0359	0.951604
$587$	33.6266	1.38792	0.693959	−	0.720014i	$-0.255865\pi$
$587$	33.6266	1.38792	0.693959	+	0.720014i	$0.255865\pi$
$588$	3.80069	0.156738
$589$	4.86300	0.200376
$590$	−13.4543	−0.553903
$591$	9.09621	0.374168
$592$	13.8705	0.570072
$593$	38.6906	1.58883	0.794417	−	0.607372i	$-0.207776\pi$
$593$	38.6906	1.58883	0.794417	+	0.607372i	$0.207776\pi$
$594$	−1.64652	−0.0675576
$595$	−2.65811	−0.108972
$596$	6.52691	0.267352
$597$	5.30465	0.217105
$598$	2.39658	0.0980033
$599$	32.5145	1.32851	0.664254	−	0.747507i	$-0.268749\pi$
$599$	32.5145	1.32851	0.664254	+	0.747507i	$0.268749\pi$
$600$	9.67142	0.394834
$601$	−11.4682	−0.467800	−0.233900	−	0.972261i	$-0.575149\pi$
$601$	−11.4682	−0.467800	−0.233900	+	0.972261i	$0.575149\pi$
$602$	−46.3734	−1.89004
$603$	1.95063	0.0794357
$604$	−2.91194	−0.118485
$605$	−25.8010	−1.04896
$606$	−12.6342	−0.513229
$607$	−40.4823	−1.64313	−0.821564	−	0.570117i	$-0.806898\pi$
$607$	−40.4823	−1.64313	−0.821564	+	0.570117i	$0.806898\pi$
$608$	5.32653	0.216019
$609$	3.62966	0.147081
$610$	26.7291	1.08223
$611$	20.9194	0.846308
$612$	0.157977	0.00638583
$613$	−26.2959	−1.06208	−0.531041	−	0.847346i	$-0.678199\pi$
$613$	−26.2959	−1.06208	−0.531041	+	0.847346i	$0.678199\pi$
$614$	−19.2254	−0.775875
$615$	−30.7689	−1.24072
$616$	−15.6314	−0.629805
$617$	−2.31724	−0.0932886	−0.0466443	−	0.998912i	$-0.514853\pi$
$617$	−2.31724	−0.0932886	−0.0466443	+	0.998912i	$0.514853\pi$
$618$	−9.47621	−0.381189
$619$	17.3929	0.699079	0.349540	−	0.936922i	$-0.386338\pi$
$619$	17.3929	0.699079	0.349540	+	0.936922i	$0.386338\pi$
$620$	−5.36089	−0.215298
$621$	−1.00000	−0.0401286
$622$	−17.0432	−0.683372
$623$	13.3442	0.534626
$624$	4.86797	0.194875
$625$	−30.8371	−1.23348
$626$	−18.7071	−0.747687
$627$	−2.22969	−0.0890454
$628$	0.467078	0.0186384
$629$	1.48944	0.0593877
$630$	12.1867	0.485528
$631$	−2.58190	−0.102784	−0.0513920	−	0.998679i	$-0.516366\pi$
$631$	−2.58190	−0.102784	−0.0513920	+	0.998679i	$0.516366\pi$
$632$	−50.1686	−1.99560
$633$	−6.16689	−0.245112
$634$	−8.67787	−0.344642
$635$	−10.3306	−0.409956
$636$	−5.99904	−0.237877
$637$	12.5762	0.498287
$638$	−1.64652	−0.0651864
$639$	−12.4876	−0.494000
$640$	10.1770	0.402279
$641$	−41.7793	−1.65018	−0.825092	−	0.564998i	$-0.808877\pi$
$641$	−41.7793	−1.65018	−0.825092	+	0.564998i	$0.808877\pi$
$642$	6.23337	0.246012
$643$	−14.2474	−0.561864	−0.280932	−	0.959728i	$-0.590644\pi$
$643$	−14.2474	−0.561864	−0.280932	+	0.959728i	$0.590644\pi$
$644$	−2.23426	−0.0880420
$645$	30.9846	1.22002
$646$	−0.481149	−0.0189305
$647$	−39.6911	−1.56042	−0.780209	−	0.625519i	$-0.784887\pi$
$647$	−39.6911	−1.56042	−0.780209	+	0.625519i	$0.784887\pi$
$648$	−3.07753	−0.120897
$649$	−5.60751	−0.220114
$650$	7.53147	0.295409
$651$	−11.0778	−0.434173
$652$	12.5770	0.492554
$653$	−11.1782	−0.437438	−0.218719	−	0.975788i	$-0.570188\pi$
$653$	−11.1782	−0.437438	−0.218719	+	0.975788i	$0.570188\pi$
$654$	−15.3975	−0.602091
$655$	53.8766	2.10513
$656$	−25.7706	−1.00617
$657$	−8.14520	−0.317774
$658$	43.8631	1.70996
$659$	40.4792	1.57684	0.788422	−	0.615134i	$-0.210898\pi$
$659$	40.4792	1.57684	0.788422	+	0.615134i	$0.210898\pi$
$660$	2.45798	0.0956767
$661$	11.3921	0.443101	0.221551	−	0.975149i	$-0.428888\pi$
$661$	11.3921	0.443101	0.221551	+	0.975149i	$0.428888\pi$
$662$	−2.61580	−0.101666
$663$	0.522732	0.0203012
$664$	−19.3083	−0.749308
$665$	16.5030	0.639959
$666$	−6.82864	−0.264604
$667$	−1.00000	−0.0387202
$668$	−6.13550	−0.237390
$669$	2.50370	0.0967985
$670$	6.54928	0.253021
$671$	11.1402	0.430064
$672$	−12.1337	−0.468069
$673$	36.8502	1.42047	0.710235	−	0.703964i	$-0.248589\pi$
$673$	36.8502	1.42047	0.710235	+	0.703964i	$0.248589\pi$
$674$	−25.7596	−0.992222
$675$	−3.14260	−0.120959
$676$	5.44849	0.209557
$677$	−18.5311	−0.712209	−0.356104	−	0.934446i	$-0.615895\pi$
$677$	−18.5311	−0.712209	−0.356104	+	0.934446i	$0.615895\pi$
$678$	−18.2987	−0.702757
$679$	29.4218	1.12911
$680$	2.25377	0.0864280
$681$	−6.26477	−0.240067
$682$	5.02522	0.192426
$683$	20.8679	0.798489	0.399244	−	0.916845i	$-0.369273\pi$
$683$	20.8679	0.798489	0.399244	+	0.916845i	$0.369273\pi$
$684$	−0.980806	−0.0375020
$685$	−8.09043	−0.309119
$686$	−3.52588	−0.134619
$687$	21.4865	0.819763
$688$	25.9513	0.989385
$689$	−19.8504	−0.756238
$690$	−3.35752	−0.127819
$691$	12.5961	0.479178	0.239589	−	0.970874i	$-0.422987\pi$
$691$	12.5961	0.479178	0.239589	+	0.970874i	$0.422987\pi$
$692$	15.6093	0.593378
$693$	5.07920	0.192943
$694$	38.3387	1.45532
$695$	−25.9580	−0.984645
$696$	−3.07753	−0.116653
$697$	−2.76730	−0.104819
$698$	−27.6692	−1.04729
$699$	17.3695	0.656973
$700$	−7.02136	−0.265383
$701$	37.2561	1.40714	0.703572	−	0.710624i	$-0.251587\pi$
$701$	37.2561	1.40714	0.703572	+	0.710624i	$0.251587\pi$
$702$	−2.39658	−0.0904530
$703$	−9.24724	−0.348766
$704$	12.1931	0.459545
$705$	−29.3074	−1.10378
$706$	−32.1991	−1.21183
$707$	38.9740	1.46577
$708$	−2.46665	−0.0927024
$709$	−4.74456	−0.178186	−0.0890928	−	0.996023i	$-0.528397\pi$
$709$	−4.74456	−0.178186	−0.0890928	+	0.996023i	$0.528397\pi$
$710$	−41.9273	−1.57350
$711$	16.3016	0.611358
$712$	−11.3144	−0.424023
$713$	3.05203	0.114299
$714$	1.09605	0.0410185
$715$	8.13325	0.304166
$716$	−2.80367	−0.104778
$717$	2.89711	0.108195
$718$	0.921128	0.0343762
$719$	−22.5184	−0.839793	−0.419897	−	0.907572i	$-0.637934\pi$
$719$	−22.5184	−0.839793	−0.419897	+	0.907572i	$0.637934\pi$
$720$	−6.81987	−0.254161
$721$	29.2323	1.08867
$722$	−19.3686	−0.720826
$723$	3.98534	0.148216
$724$	14.2639	0.530113
$725$	−3.14260	−0.116713
$726$	10.6388	0.394843
$727$	−16.0168	−0.594031	−0.297016	−	0.954873i	$-0.595991\pi$
$727$	−16.0168	−0.594031	−0.297016	+	0.954873i	$0.595991\pi$
$728$	−22.7521	−0.843248
$729$	1.00000	0.0370370
$730$	−27.3477	−1.01218
$731$	2.78670	0.103070
$732$	4.90041	0.181124
$733$	−48.9162	−1.80676	−0.903380	−	0.428840i	$-0.858922\pi$
$733$	−48.9162	−1.80676	−0.903380	+	0.428840i	$0.858922\pi$
$734$	0.598612	0.0220952
$735$	−17.6188	−0.649880
$736$	3.34294	0.123223
$737$	2.72963	0.100547
$738$	12.6873	0.467025
$739$	20.3156	0.747322	0.373661	−	0.927565i	$-0.378102\pi$
$739$	20.3156	0.747322	0.373661	+	0.927565i	$0.378102\pi$
$740$	10.1940	0.374739
$741$	−3.24541	−0.119223
$742$	−41.6215	−1.52797
$743$	−10.8760	−0.399003	−0.199502	−	0.979898i	$-0.563932\pi$
$743$	−10.8760	−0.399003	−0.199502	+	0.979898i	$0.563932\pi$
$744$	9.39269	0.344353
$745$	−30.2567	−1.10852
$746$	−6.49125	−0.237662
$747$	6.27397	0.229553
$748$	0.221066	0.00808298
$749$	−19.2287	−0.702603
$750$	6.23628	0.227717
$751$	15.1517	0.552895	0.276447	−	0.961029i	$-0.410843\pi$
$751$	15.1517	0.552895	0.276447	+	0.961029i	$0.410843\pi$
$752$	−24.5465	−0.895119
$753$	16.9698	0.618416
$754$	−2.39658	−0.0872782
$755$	13.4989	0.491274
$756$	2.23426	0.0812591
$757$	4.21203	0.153089	0.0765444	−	0.997066i	$-0.475611\pi$
$757$	4.21203	0.153089	0.0765444	+	0.997066i	$0.475611\pi$
$758$	−32.8947	−1.19479
$759$	−1.39936	−0.0507935
$760$	−13.9926	−0.507566
$761$	−54.5237	−1.97648	−0.988242	−	0.152901i	$-0.951139\pi$
$761$	−54.5237	−1.97648	−0.988242	+	0.152901i	$0.951139\pi$
$762$	4.25971	0.154313
$763$	47.4984	1.71956
$764$	−2.58352	−0.0934684
$765$	−0.732331	−0.0264775
$766$	6.56778	0.237304
$767$	−8.16195	−0.294711
$768$	13.2303	0.477408
$769$	31.5349	1.13718	0.568590	−	0.822621i	$-0.307489\pi$
$769$	31.5349	1.13718	0.568590	+	0.822621i	$0.307489\pi$
$770$	17.0535	0.614566
$771$	−7.22916	−0.260352
$772$	1.08899	0.0391935
$773$	−10.3929	−0.373806	−0.186903	−	0.982378i	$-0.559845\pi$
$773$	−10.3929	−0.373806	−0.186903	+	0.982378i	$0.559845\pi$
$774$	−12.7762	−0.459232
$775$	9.59128	0.344529
$776$	−24.9463	−0.895519
$777$	21.0650	0.755704
$778$	−4.41024	−0.158115
$779$	17.1809	0.615570
$780$	3.57769	0.128102
$781$	−17.4746	−0.625290
$782$	−0.301970	−0.0107984
$783$	1.00000	0.0357371
$784$	−14.7567	−0.527026
$785$	−2.16523	−0.0772803
$786$	−22.2155	−0.792402
$787$	−1.22731	−0.0437487	−0.0218744	−	0.999761i	$-0.506963\pi$
$787$	−1.22731	−0.0437487	−0.0218744	+	0.999761i	$0.506963\pi$
$788$	5.59922	0.199464
$789$	11.9092	0.423980
$790$	54.7330	1.94731
$791$	56.4479	2.00706
$792$	−4.30657	−0.153027
$793$	16.2151	0.575814
$794$	35.7464	1.26859
$795$	27.8097	0.986308
$796$	3.26530	0.115736
$797$	48.7301	1.72611	0.863054	−	0.505112i	$-0.168549\pi$
$797$	48.7301	1.72611	0.863054	+	0.505112i	$0.168549\pi$
$798$	−6.80486	−0.240889
$799$	−2.63585	−0.0932498
$800$	10.5055	0.371426
$801$	3.67645	0.129901
$802$	3.88595	0.137218
$803$	−11.3981	−0.402229
$804$	1.20072	0.0423461
$805$	10.3573	0.365047
$806$	7.31441	0.257639
$807$	−17.5257	−0.616934
$808$	−33.0454	−1.16253
$809$	40.2800	1.41617	0.708084	−	0.706128i	$-0.249560\pi$
$809$	40.2800	1.41617	0.708084	+	0.706128i	$0.249560\pi$
$810$	3.35752	0.117971
$811$	−29.8631	−1.04863	−0.524317	−	0.851523i	$-0.675679\pi$
$811$	−29.8631	−1.04863	−0.524317	+	0.851523i	$0.675679\pi$
$812$	2.23426	0.0784070
$813$	−27.8599	−0.977090
$814$	−9.55572	−0.334928
$815$	−58.3031	−2.04227
$816$	−0.613367	−0.0214721
$817$	−17.3014	−0.605299
$818$	−7.66808	−0.268108
$819$	7.39297	0.258331
$820$	−18.9399	−0.661412
$821$	−16.0595	−0.560480	−0.280240	−	0.959930i	$-0.590414\pi$
$821$	−16.0595	−0.560480	−0.280240	+	0.959930i	$0.590414\pi$
$822$	3.33601	0.116357
$823$	13.8721	0.483552	0.241776	−	0.970332i	$-0.422270\pi$
$823$	13.8721	0.483552	0.241776	+	0.970332i	$0.422270\pi$
$824$	−24.7855	−0.863445
$825$	−4.39762	−0.153106
$826$	−17.1137	−0.595462
$827$	41.4361	1.44087	0.720436	−	0.693521i	$-0.243942\pi$
$827$	41.4361	1.44087	0.720436	+	0.693521i	$0.243942\pi$
$828$	−0.615555	−0.0213920
$829$	−17.5188	−0.608455	−0.304227	−	0.952599i	$-0.598398\pi$
$829$	−17.5188	−0.608455	−0.304227	+	0.952599i	$0.598398\pi$
$830$	21.0650	0.731178
$831$	−7.82340	−0.271391
$832$	17.7476	0.615286
$833$	−1.58461	−0.0549033
$834$	10.7036	0.370634
$835$	28.4423	0.984285
$836$	−1.37250	−0.0474689
$837$	−3.05203	−0.105493
$838$	44.9203	1.55175
$839$	2.33207	0.0805121	0.0402561	−	0.999189i	$-0.487183\pi$
$839$	2.33207	0.0805121	0.0402561	+	0.999189i	$0.487183\pi$
$840$	31.8749	1.09979
$841$	1.00000	0.0344828
$842$	−41.9904	−1.44709
$843$	23.0361	0.793407
$844$	−3.79606	−0.130666
$845$	−25.2575	−0.868885
$846$	12.0846	0.415478
$847$	−32.8186	−1.12766
$848$	23.2921	0.799855
$849$	−10.5239	−0.361179
$850$	−0.948969	−0.0325494
$851$	−5.80359	−0.198944
$852$	−7.68678	−0.263345
$853$	−34.2974	−1.17432	−0.587160	−	0.809471i	$-0.699754\pi$
$853$	−34.2974	−1.17432	−0.587160	+	0.809471i	$0.699754\pi$
$854$	33.9992	1.16343
$855$	4.54671	0.155494
$856$	16.3037	0.557250
$857$	4.44845	0.151956	0.0759780	−	0.997109i	$-0.475792\pi$
$857$	4.44845	0.151956	0.0759780	+	0.997109i	$0.475792\pi$
$858$	−3.35367	−0.114493
$859$	22.6653	0.773329	0.386664	−	0.922220i	$-0.373627\pi$
$859$	22.6653	0.773329	0.386664	+	0.922220i	$0.373627\pi$
$860$	19.0728	0.650376
$861$	−39.1377	−1.33381
$862$	11.2694	0.383838
$863$	−16.6196	−0.565739	−0.282870	−	0.959158i	$-0.591286\pi$
$863$	−16.6196	−0.565739	−0.282870	+	0.959158i	$0.591286\pi$
$864$	−3.34294	−0.113729
$865$	−72.3601	−2.46032
$866$	13.4744	0.457879
$867$	16.9341	0.575113
$868$	−6.81900	−0.231452
$869$	22.8118	0.773838
$870$	3.35752	0.113831
$871$	3.97309	0.134623
$872$	−40.2731	−1.36382
$873$	8.10595	0.274345
$874$	1.87479	0.0634158
$875$	−19.2377	−0.650353
$876$	−5.01382	−0.169401
$877$	37.0821	1.25217	0.626087	−	0.779753i	$-0.284656\pi$
$877$	37.0821	1.25217	0.626087	+	0.779753i	$0.284656\pi$
$878$	21.6607	0.731014
$879$	−19.5780	−0.660348
$880$	−9.54345	−0.321709
$881$	−25.6008	−0.862511	−0.431256	−	0.902230i	$-0.641929\pi$
$881$	−25.6008	−0.862511	−0.431256	+	0.902230i	$0.641929\pi$
$882$	7.26496	0.244624
$883$	14.6206	0.492022	0.246011	−	0.969267i	$-0.420880\pi$
$883$	14.6206	0.492022	0.246011	+	0.969267i	$0.420880\pi$
$884$	0.321771	0.0108223
$885$	11.4346	0.384371
$886$	14.5924	0.490240
$887$	−40.2276	−1.35071	−0.675356	−	0.737492i	$-0.736010\pi$
$887$	−40.2276	−1.35071	−0.675356	+	0.737492i	$0.736010\pi$
$888$	−17.8607	−0.599365
$889$	−13.1404	−0.440714
$890$	12.3438	0.413764
$891$	1.39936	0.0468803
$892$	1.54116	0.0516020
$893$	16.3648	0.547628
$894$	12.4761	0.417262
$895$	12.9969	0.434440
$896$	12.9450	0.432462
$897$	−2.03682	−0.0680076
$898$	−28.1398	−0.939039
$899$	−3.05203	−0.101791
$900$	−1.93444	−0.0644814
$901$	2.50115	0.0833255
$902$	17.7540	0.591145
$903$	39.4122	1.31156
$904$	−47.8613	−1.59184
$905$	−66.1229	−2.19800
$906$	−5.56613	−0.184922
$907$	−48.0277	−1.59474	−0.797368	−	0.603494i	$-0.793775\pi$
$907$	−48.0277	−1.59474	−0.797368	+	0.603494i	$0.793775\pi$
$908$	−3.85632	−0.127976
$909$	10.7377	0.356146
$910$	24.8221	0.822844
$911$	33.9316	1.12420	0.562102	−	0.827068i	$-0.309993\pi$
$911$	33.9316	1.12420	0.562102	+	0.827068i	$0.309993\pi$
$912$	3.80812	0.126099
$913$	8.77955	0.290561
$914$	4.25765	0.140831
$915$	−22.7168	−0.750993
$916$	13.2262	0.437005
$917$	68.5306	2.26308
$918$	0.301970	0.00996649
$919$	−0.863726	−0.0284917	−0.0142458	−	0.999899i	$-0.504535\pi$
$919$	−0.863726	−0.0284917	−0.0142458	+	0.999899i	$0.504535\pi$
$920$	−8.78179	−0.289527
$921$	16.3395	0.538404
$922$	9.37899	0.308881
$923$	−25.4350	−0.837202
$924$	3.12653	0.102855
$925$	−18.2383	−0.599672
$926$	−31.5704	−1.03747
$927$	8.05373	0.264519
$928$	−3.34294	−0.109737
$929$	4.15824	0.136427	0.0682137	−	0.997671i	$-0.478270\pi$
$929$	4.15824	0.136427	0.0682137	+	0.997671i	$0.478270\pi$
$930$	−10.2472	−0.336021
$931$	9.83810	0.322431
$932$	10.6919	0.350224
$933$	14.4849	0.474213
$934$	−14.1419	−0.462737
$935$	−1.02479	−0.0335143
$936$	−6.26838	−0.204888
$937$	33.0339	1.07917	0.539584	−	0.841931i	$-0.318581\pi$
$937$	33.0339	1.07917	0.539584	+	0.841931i	$0.318581\pi$
$938$	8.33063	0.272005
$939$	15.8990	0.518843
$940$	−18.0403	−0.588410
$941$	−40.0659	−1.30611	−0.653056	−	0.757309i	$-0.726513\pi$
$941$	−40.0659	−1.30611	−0.653056	+	0.757309i	$0.726513\pi$
$942$	0.892812	0.0290894
$943$	10.7828	0.351135
$944$	9.57712	0.311709
$945$	−10.3573	−0.336923
$946$	−17.8785	−0.581282
$947$	5.68021	0.184582	0.0922911	−	0.995732i	$-0.470581\pi$
$947$	5.68021	0.184582	0.0922911	+	0.995732i	$0.470581\pi$
$948$	10.0345	0.325907
$949$	−16.5903	−0.538545
$950$	5.89172	0.191153
$951$	7.37522	0.239158
$952$	2.86677	0.0929126
$953$	31.6297	1.02459	0.512293	−	0.858811i	$-0.328796\pi$
$953$	31.6297	1.02459	0.512293	+	0.858811i	$0.328796\pi$
$954$	−11.4671	−0.371260
$955$	11.9764	0.387547
$956$	1.78333	0.0576771
$957$	1.39936	0.0452349
$958$	31.4639	1.01655
$959$	−10.2910	−0.332312
$960$	−24.8637	−0.802474
$961$	−21.6851	−0.699521
$962$	−13.9087	−0.448436
$963$	−5.29768	−0.170715
$964$	2.45320	0.0790122
$965$	−5.04821	−0.162508
$966$	−4.27074	−0.137409
$967$	18.3461	0.589972	0.294986	−	0.955502i	$-0.404685\pi$
$967$	18.3461	0.589972	0.294986	+	0.955502i	$0.404685\pi$
$968$	27.8264	0.894373
$969$	0.408923	0.0131365
$970$	27.2159	0.873851
$971$	−16.7230	−0.536668	−0.268334	−	0.963326i	$-0.586473\pi$
$971$	−16.7230	−0.536668	−0.268334	+	0.963326i	$0.586473\pi$
$972$	0.615555	0.0197439
$973$	−33.0184	−1.05852
$974$	−32.2187	−1.03235
$975$	−6.40092	−0.204993
$976$	−19.0265	−0.609024
$977$	23.7818	0.760849	0.380424	−	0.924812i	$-0.375778\pi$
$977$	23.7818	0.760849	0.380424	+	0.924812i	$0.375778\pi$
$978$	24.0407	0.768738
$979$	5.14467	0.164424
$980$	−10.8454	−0.346442
$981$	13.0862	0.417810
$982$	−35.5961	−1.13592
$983$	12.9711	0.413714	0.206857	−	0.978371i	$-0.433676\pi$
$983$	12.9711	0.413714	0.206857	+	0.978371i	$0.433676\pi$
$984$	33.1842	1.05787
$985$	−25.9563	−0.827035
$986$	0.301970	0.00961668
$987$	−37.2787	−1.18659
$988$	−1.99773	−0.0635562
$989$	−10.8584	−0.345276
$990$	4.69838	0.149324
$991$	−42.1423	−1.33870	−0.669348	−	0.742949i	$-0.733426\pi$
$991$	−42.1423	−1.33870	−0.669348	+	0.742949i	$0.733426\pi$
$992$	10.2027	0.323937
$993$	2.22314	0.0705492
$994$	−53.3311	−1.69156
$995$	−15.1369	−0.479873
$996$	3.86198	0.122371
$997$	−53.5460	−1.69582	−0.847909	−	0.530142i	$-0.822139\pi$
$997$	−53.5460	−1.69582	−0.847909	+	0.530142i	$0.822139\pi$
$998$	−9.92699	−0.314233
$999$	5.80359	0.183617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.7	✓	11
3.2	odd	2		6003.2.a.m.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.7	✓	11	1.1	even	1	trivial
6003.2.a.m.1.5		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.17662 q^{2} -1.00000 q^{3} -0.615555 q^{4} +2.85352 q^{5} -1.17662 q^{6} +3.62966 q^{7} -3.07753 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.17662 q^{2} -1.00000 q^{3} -0.615555 q^{4} +2.85352 q^{5} -1.17662 q^{6} +3.62966 q^{7} -3.07753 q^{8} +1.00000 q^{9} +3.35752 q^{10} +1.39936 q^{11} +0.615555 q^{12} +2.03682 q^{13} +4.27074 q^{14} -2.85352 q^{15} -2.38998 q^{16} -0.256641 q^{17} +1.17662 q^{18} +1.59337 q^{19} -1.75650 q^{20} -3.62966 q^{21} +1.64652 q^{22} +1.00000 q^{23} +3.07753 q^{24} +3.14260 q^{25} +2.39658 q^{26} -1.00000 q^{27} -2.23426 q^{28} -1.00000 q^{29} -3.35752 q^{30} +3.05203 q^{31} +3.34294 q^{32} -1.39936 q^{33} -0.301970 q^{34} +10.3573 q^{35} -0.615555 q^{36} -5.80359 q^{37} +1.87479 q^{38} -2.03682 q^{39} -8.78179 q^{40} +10.7828 q^{41} -4.27074 q^{42} -10.8584 q^{43} -0.861383 q^{44} +2.85352 q^{45} +1.17662 q^{46} +10.2706 q^{47} +2.38998 q^{48} +6.17441 q^{49} +3.69765 q^{50} +0.256641 q^{51} -1.25378 q^{52} -9.74574 q^{53} -1.17662 q^{54} +3.99311 q^{55} -11.1704 q^{56} -1.59337 q^{57} -1.17662 q^{58} -4.00720 q^{59} +1.75650 q^{60} +7.96095 q^{61} +3.59109 q^{62} +3.62966 q^{63} +8.71335 q^{64} +5.81213 q^{65} -1.64652 q^{66} +1.95063 q^{67} +0.157977 q^{68} -1.00000 q^{69} +12.1867 q^{70} -12.4876 q^{71} -3.07753 q^{72} -8.14520 q^{73} -6.82864 q^{74} -3.14260 q^{75} -0.980806 q^{76} +5.07920 q^{77} -2.39658 q^{78} +16.3016 q^{79} -6.81987 q^{80} +1.00000 q^{81} +12.6873 q^{82} +6.27397 q^{83} +2.23426 q^{84} -0.732331 q^{85} -12.7762 q^{86} +1.00000 q^{87} -4.30657 q^{88} +3.67645 q^{89} +3.35752 q^{90} +7.39297 q^{91} -0.615555 q^{92} -3.05203 q^{93} +12.0846 q^{94} +4.54671 q^{95} -3.34294 q^{96} +8.10595 q^{97} +7.26496 q^{98} +1.39936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

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