LMFDB - Embedded newform 1859.2.a.r.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 10x^{7} - x^{6} + 31x^{5} + 9x^{4} - 31x^{3} - 15x^{2} + 2x + 1 $ x^9 - 10x^7 - x^6 + 31x^5 + 9x^4 - 31x^3 - 15x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.17186$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.17186 q^{2} +1.56549 q^{3} -0.626755 q^{4} -0.982237 q^{5} +1.83452 q^{6} +0.0435046 q^{7} -3.07818 q^{8} -0.549249 q^{9} +O(q^{10})$	\(q+1.17186 q^{2} +1.56549 q^{3} -0.626755 q^{4} -0.982237 q^{5} +1.83452 q^{6} +0.0435046 q^{7} -3.07818 q^{8} -0.549249 q^{9} -1.15104 q^{10} -1.00000 q^{11} -0.981177 q^{12} +0.0509810 q^{14} -1.53768 q^{15} -2.35367 q^{16} -2.26011 q^{17} -0.643641 q^{18} +6.13600 q^{19} +0.615622 q^{20} +0.0681058 q^{21} -1.17186 q^{22} -8.18673 q^{23} -4.81885 q^{24} -4.03521 q^{25} -5.55631 q^{27} -0.0272667 q^{28} +1.10086 q^{29} -1.80194 q^{30} -3.74748 q^{31} +3.39820 q^{32} -1.56549 q^{33} -2.64852 q^{34} -0.0427318 q^{35} +0.344245 q^{36} -5.70673 q^{37} +7.19050 q^{38} +3.02350 q^{40} +1.45153 q^{41} +0.0798102 q^{42} +1.20690 q^{43} +0.626755 q^{44} +0.539493 q^{45} -9.59366 q^{46} -1.42862 q^{47} -3.68464 q^{48} -6.99811 q^{49} -4.72868 q^{50} -3.53817 q^{51} -3.44249 q^{53} -6.51119 q^{54} +0.982237 q^{55} -0.133915 q^{56} +9.60582 q^{57} +1.29005 q^{58} +0.0231303 q^{59} +0.963748 q^{60} -1.45213 q^{61} -4.39151 q^{62} -0.0238949 q^{63} +8.68953 q^{64} -1.83452 q^{66} -13.3099 q^{67} +1.41653 q^{68} -12.8162 q^{69} -0.0500755 q^{70} +5.68444 q^{71} +1.69069 q^{72} -0.514699 q^{73} -6.68746 q^{74} -6.31707 q^{75} -3.84577 q^{76} -0.0435046 q^{77} -7.51760 q^{79} +2.31186 q^{80} -7.05058 q^{81} +1.70098 q^{82} +5.62195 q^{83} -0.0426857 q^{84} +2.21996 q^{85} +1.41431 q^{86} +1.72339 q^{87} +3.07818 q^{88} +13.0459 q^{89} +0.632208 q^{90} +5.13107 q^{92} -5.86663 q^{93} -1.67413 q^{94} -6.02700 q^{95} +5.31983 q^{96} +9.03968 q^{97} -8.20077 q^{98} +0.549249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9	$ 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9} - 8 q^{10} - 9 q^{11} - 9 q^{12} - 3 q^{15} - 8 q^{16} - 8 q^{17} - 27 q^{18} + q^{19} - 12 q^{20} - 17 q^{21} + 6 q^{24} - 15 q^{25} - 23 q^{27} - 11 q^{28} - 22 q^{29} - 3 q^{30} + 6 q^{31} + 19 q^{32} + 5 q^{33} - 10 q^{34} - 15 q^{35} + 7 q^{36} + 15 q^{37} + q^{38} - 3 q^{40} - 10 q^{41} + 2 q^{42} - 19 q^{43} - 2 q^{44} + 2 q^{45} - 19 q^{46} + 2 q^{47} + 6 q^{48} - 20 q^{49} + 17 q^{50} - 2 q^{51} - 5 q^{53} + 27 q^{54} - 4 q^{55} - 16 q^{56} + 32 q^{57} + 11 q^{58} + 11 q^{59} + 6 q^{60} - 68 q^{61} - 21 q^{62} + 29 q^{63} - 23 q^{64} - 11 q^{66} - 5 q^{67} + 16 q^{68} - 34 q^{69} + 5 q^{70} + 34 q^{71} - 13 q^{72} - 26 q^{73} + q^{74} + 10 q^{75} + 11 q^{76} + q^{77} - 32 q^{79} - 8 q^{80} + 13 q^{81} - 42 q^{82} - 8 q^{83} + 13 q^{84} - 23 q^{85} - 30 q^{86} + 10 q^{87} + 3 q^{88} + 37 q^{89} + 21 q^{90} - 12 q^{92} - 20 q^{93} - 12 q^{94} - 4 q^{95} - 60 q^{96} - 3 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) $ 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9 - 8 * q^10 - 9 * q^11 - 9 * q^12 - 3 * q^15 - 8 * q^16 - 8 * q^17 - 27 * q^18 + q^19 - 12 * q^20 - 17 * q^21 + 6 * q^24 - 15 * q^25 - 23 * q^27 - 11 * q^28 - 22 * q^29 - 3 * q^30 + 6 * q^31 + 19 * q^32 + 5 * q^33 - 10 * q^34 - 15 * q^35 + 7 * q^36 + 15 * q^37 + q^38 - 3 * q^40 - 10 * q^41 + 2 * q^42 - 19 * q^43 - 2 * q^44 + 2 * q^45 - 19 * q^46 + 2 * q^47 + 6 * q^48 - 20 * q^49 + 17 * q^50 - 2 * q^51 - 5 * q^53 + 27 * q^54 - 4 * q^55 - 16 * q^56 + 32 * q^57 + 11 * q^58 + 11 * q^59 + 6 * q^60 - 68 * q^61 - 21 * q^62 + 29 * q^63 - 23 * q^64 - 11 * q^66 - 5 * q^67 + 16 * q^68 - 34 * q^69 + 5 * q^70 + 34 * q^71 - 13 * q^72 - 26 * q^73 + q^74 + 10 * q^75 + 11 * q^76 + q^77 - 32 * q^79 - 8 * q^80 + 13 * q^81 - 42 * q^82 - 8 * q^83 + 13 * q^84 - 23 * q^85 - 30 * q^86 + 10 * q^87 + 3 * q^88 + 37 * q^89 + 21 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^94 - 4 * q^95 - 60 * q^96 - 3 * q^97 + 9 * q^98 - 2 * 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 $

$2$	1.17186	0.828627	0.414313	−	0.910134i	$-0.364022\pi$
$2$	1.17186	0.828627	0.414313	+	0.910134i	$0.364022\pi$
$3$	1.56549	0.903835	0.451917	−	0.892060i	$-0.350740\pi$
$3$	1.56549	0.903835	0.451917	+	0.892060i	$0.350740\pi$
$4$	−0.626755	−0.313378
$5$	−0.982237	−0.439270	−0.219635	−	0.975582i	$-0.570487\pi$
$5$	−0.982237	−0.439270	−0.219635	+	0.975582i	$0.570487\pi$
$6$	1.83452	0.748942
$7$	0.0435046	0.0164432	0.00822159	−	0.999966i	$-0.497383\pi$
$7$	0.0435046	0.0164432	0.00822159	+	0.999966i	$0.497383\pi$
$8$	−3.07818	−1.08830
$9$	−0.549249	−0.183083
$10$	−1.15104	−0.363991
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.981177	−0.283241
$13$	0	0
$13$	0	0
$14$	0.0509810	0.0136253
$15$	−1.53768	−0.397027
$16$	−2.35367	−0.588417
$17$	−2.26011	−0.548156	−0.274078	−	0.961707i	$-0.588373\pi$
$17$	−2.26011	−0.548156	−0.274078	+	0.961707i	$0.588373\pi$
$18$	−0.643641	−0.151708
$19$	6.13600	1.40769	0.703847	−	0.710352i	$-0.251464\pi$
$19$	6.13600	1.40769	0.703847	+	0.710352i	$0.251464\pi$
$20$	0.615622	0.137657
$21$	0.0681058	0.0148619
$22$	−1.17186	−0.249840
$23$	−8.18673	−1.70705	−0.853525	−	0.521051i	$-0.825540\pi$
$23$	−8.18673	−1.70705	−0.853525	+	0.521051i	$0.825540\pi$
$24$	−4.81885	−0.983643
$25$	−4.03521	−0.807042
$26$	0	0
$27$	−5.55631	−1.06931
$28$	−0.0272667	−0.00515292
$29$	1.10086	0.204425	0.102212	−	0.994763i	$-0.467408\pi$
$29$	1.10086	0.204425	0.102212	+	0.994763i	$0.467408\pi$
$30$	−1.80194	−0.328987
$31$	−3.74748	−0.673067	−0.336534	−	0.941671i	$-0.609255\pi$
$31$	−3.74748	−0.673067	−0.336534	+	0.941671i	$0.609255\pi$
$32$	3.39820	0.600722
$33$	−1.56549	−0.272516
$34$	−2.64852	−0.454217
$35$	−0.0427318	−0.00722299
$36$	0.344245	0.0573741
$37$	−5.70673	−0.938181	−0.469090	−	0.883150i	$-0.655418\pi$
$37$	−5.70673	−0.938181	−0.469090	+	0.883150i	$0.655418\pi$
$38$	7.19050	1.16645
$39$	0	0
$40$	3.02350	0.478057
$41$	1.45153	0.226691	0.113346	−	0.993556i	$-0.463843\pi$
$41$	1.45153	0.226691	0.113346	+	0.993556i	$0.463843\pi$
$42$	0.0798102	0.0123150
$43$	1.20690	0.184051	0.0920254	−	0.995757i	$-0.470666\pi$
$43$	1.20690	0.184051	0.0920254	+	0.995757i	$0.470666\pi$
$44$	0.626755	0.0944869
$45$	0.539493	0.0804229
$46$	−9.59366	−1.41451
$47$	−1.42862	−0.208385	−0.104193	−	0.994557i	$-0.533226\pi$
$47$	−1.42862	−0.208385	−0.104193	+	0.994557i	$0.533226\pi$
$48$	−3.68464	−0.531832
$49$	−6.99811	−0.999730
$50$	−4.72868	−0.668737
$51$	−3.53817	−0.495442
$52$	0	0
$53$	−3.44249	−0.472862	−0.236431	−	0.971648i	$-0.575978\pi$
$53$	−3.44249	−0.472862	−0.236431	+	0.971648i	$0.575978\pi$
$54$	−6.51119	−0.886060
$55$	0.982237	0.132445
$56$	−0.133915	−0.0178951
$57$	9.60582	1.27232
$58$	1.29005	0.169392
$59$	0.0231303	0.00301130	0.00150565	−	0.999999i	$-0.499521\pi$
$59$	0.0231303	0.00301130	0.00150565	+	0.999999i	$0.499521\pi$
$60$	0.963748	0.124419
$61$	−1.45213	−0.185926	−0.0929631	−	0.995670i	$-0.529634\pi$
$61$	−1.45213	−0.185926	−0.0929631	+	0.995670i	$0.529634\pi$
$62$	−4.39151	−0.557722
$63$	−0.0238949	−0.00301047
$64$	8.68953	1.08619
$65$	0	0
$66$	−1.83452	−0.225814
$67$	−13.3099	−1.62607	−0.813034	−	0.582216i	$-0.802186\pi$
$67$	−13.3099	−1.62607	−0.813034	+	0.582216i	$0.802186\pi$
$68$	1.41653	0.171780
$69$	−12.8162	−1.54289
$70$	−0.0500755	−0.00598516
$71$	5.68444	0.674619	0.337310	−	0.941394i	$-0.390483\pi$
$71$	5.68444	0.674619	0.337310	+	0.941394i	$0.390483\pi$
$72$	1.69069	0.199249
$73$	−0.514699	−0.0602410	−0.0301205	−	0.999546i	$-0.509589\pi$
$73$	−0.514699	−0.0602410	−0.0301205	+	0.999546i	$0.509589\pi$
$74$	−6.68746	−0.777402
$75$	−6.31707	−0.729433
$76$	−3.84577	−0.441140
$77$	−0.0435046	−0.00495780
$78$	0	0
$79$	−7.51760	−0.845796	−0.422898	−	0.906177i	$-0.638987\pi$
$79$	−7.51760	−0.845796	−0.422898	+	0.906177i	$0.638987\pi$
$80$	2.31186	0.258474
$81$	−7.05058	−0.783397
$82$	1.70098	0.187842
$83$	5.62195	0.617089	0.308544	−	0.951210i	$-0.400158\pi$
$83$	5.62195	0.617089	0.308544	+	0.951210i	$0.400158\pi$
$84$	−0.0426857	−0.00465739
$85$	2.21996	0.240788
$86$	1.41431	0.152509
$87$	1.72339	0.184766
$88$	3.07818	0.328135
$89$	13.0459	1.38286	0.691429	−	0.722445i	$-0.256982\pi$
$89$	13.0459	1.38286	0.691429	+	0.722445i	$0.256982\pi$
$90$	0.632208	0.0666406
$91$	0	0
$92$	5.13107	0.534951
$93$	−5.86663	−0.608342
$94$	−1.67413	−0.172674
$95$	−6.02700	−0.618357
$96$	5.31983	0.542953
$97$	9.03968	0.917840	0.458920	−	0.888478i	$-0.348236\pi$
$97$	9.03968	0.917840	0.458920	+	0.888478i	$0.348236\pi$
$98$	−8.20077	−0.828403
$99$	0.549249	0.0552016
$100$	2.52909	0.252909
$101$	1.35057	0.134386	0.0671932	−	0.997740i	$-0.478596\pi$
$101$	1.35057	0.134386	0.0671932	+	0.997740i	$0.478596\pi$
$102$	−4.14622	−0.410537
$103$	−2.26681	−0.223355	−0.111677	−	0.993745i	$-0.535622\pi$
$103$	−2.26681	−0.223355	−0.111677	+	0.993745i	$0.535622\pi$
$104$	0	0
$105$	−0.0668961	−0.00652839
$106$	−4.03410	−0.391826
$107$	19.1766	1.85387	0.926937	−	0.375218i	$-0.122432\pi$
$107$	19.1766	1.85387	0.926937	+	0.375218i	$0.122432\pi$
$108$	3.48244	0.335098
$109$	4.66571	0.446894	0.223447	−	0.974716i	$-0.428269\pi$
$109$	4.66571	0.446894	0.223447	+	0.974716i	$0.428269\pi$
$110$	1.15104	0.109747
$111$	−8.93381	−0.847960
$112$	−0.102395	−0.00967544
$113$	−6.18905	−0.582217	−0.291108	−	0.956690i	$-0.594024\pi$
$113$	−6.18905	−0.582217	−0.291108	+	0.956690i	$0.594024\pi$
$114$	11.2566	1.05428
$115$	8.04131	0.749856
$116$	−0.689971	−0.0640622
$117$	0	0
$118$	0.0271053	0.00249525
$119$	−0.0983249	−0.00901343
$120$	4.73325	0.432085
$121$	1.00000	0.0909091
$122$	−1.70169	−0.154063
$123$	2.27235	0.204891
$124$	2.34875	0.210924
$125$	8.87472	0.793779
$126$	−0.0280013	−0.00249456
$127$	−11.5013	−1.02057	−0.510285	−	0.860005i	$-0.670460\pi$
$127$	−11.5013	−1.02057	−0.510285	+	0.860005i	$0.670460\pi$
$128$	3.38648	0.299325
$129$	1.88939	0.166351
$130$	0	0
$131$	20.6370	1.80307	0.901534	−	0.432709i	$-0.142442\pi$
$131$	20.6370	1.80307	0.901534	+	0.432709i	$0.142442\pi$
$132$	0.981177	0.0854005
$133$	0.266944	0.0231470
$134$	−15.5973	−1.34740
$135$	5.45761	0.469716
$136$	6.95701	0.596558
$137$	14.8090	1.26522	0.632608	−	0.774472i	$-0.281984\pi$
$137$	14.8090	1.26522	0.632608	+	0.774472i	$0.281984\pi$
$138$	−15.0188	−1.27848
$139$	−17.3464	−1.47130	−0.735652	−	0.677359i	$-0.763124\pi$
$139$	−17.3464	−1.47130	−0.735652	+	0.677359i	$0.763124\pi$
$140$	0.0267824	0.00226352
$141$	−2.23648	−0.188346
$142$	6.66135	0.559008
$143$	0	0
$144$	1.29275	0.107729
$145$	−1.08131	−0.0897977
$146$	−0.603153	−0.0499173
$147$	−10.9554	−0.903590
$148$	3.57672	0.294005
$149$	−23.4858	−1.92403	−0.962015	−	0.272998i	$-0.911985\pi$
$149$	−23.4858	−1.92403	−0.962015	+	0.272998i	$0.911985\pi$
$150$	−7.40269	−0.604427
$151$	−14.9663	−1.21794	−0.608971	−	0.793193i	$-0.708417\pi$
$151$	−14.9663	−1.21794	−0.608971	+	0.793193i	$0.708417\pi$
$152$	−18.8877	−1.53199
$153$	1.24136	0.100358
$154$	−0.0509810	−0.00410817
$155$	3.68091	0.295658
$156$	0	0
$157$	−8.92644	−0.712408	−0.356204	−	0.934408i	$-0.615929\pi$
$157$	−8.92644	−0.712408	−0.356204	+	0.934408i	$0.615929\pi$
$158$	−8.80953	−0.700849
$159$	−5.38917	−0.427389
$160$	−3.33783	−0.263879
$161$	−0.356160	−0.0280693
$162$	−8.26226	−0.649144
$163$	20.6717	1.61913	0.809567	−	0.587027i	$-0.199702\pi$
$163$	20.6717	1.61913	0.809567	+	0.587027i	$0.199702\pi$
$164$	−0.909755	−0.0710399
$165$	1.53768	0.119708
$166$	6.58811	0.511336
$167$	18.1770	1.40658	0.703288	−	0.710905i	$-0.251715\pi$
$167$	18.1770	1.40658	0.703288	+	0.710905i	$0.251715\pi$
$168$	−0.209642	−0.0161742
$169$	0	0
$170$	2.60147	0.199524
$171$	−3.37019	−0.257725
$172$	−0.756432	−0.0576774
$173$	23.4324	1.78153	0.890767	−	0.454461i	$-0.150168\pi$
$173$	23.4324	1.78153	0.890767	+	0.454461i	$0.150168\pi$
$174$	2.01956	0.153102
$175$	−0.175550	−0.0132703
$176$	2.35367	0.177414
$177$	0.0362101	0.00272172
$178$	15.2879	1.14587
$179$	−12.8624	−0.961380	−0.480690	−	0.876891i	$-0.659614\pi$
$179$	−12.8624	−0.961380	−0.480690	+	0.876891i	$0.659614\pi$
$180$	−0.338130	−0.0252027
$181$	1.85268	0.137708	0.0688542	−	0.997627i	$-0.478066\pi$
$181$	1.85268	0.137708	0.0688542	+	0.997627i	$0.478066\pi$
$182$	0	0
$183$	−2.27329	−0.168046
$184$	25.2002	1.85778
$185$	5.60536	0.412114
$186$	−6.87485	−0.504088
$187$	2.26011	0.165275
$188$	0.895393	0.0653033
$189$	−0.241725	−0.0175829
$190$	−7.06277	−0.512387
$191$	−15.6974	−1.13582	−0.567912	−	0.823089i	$-0.692248\pi$
$191$	−15.6974	−1.13582	−0.567912	+	0.823089i	$0.692248\pi$
$192$	13.6033	0.981737
$193$	−0.105735	−0.00761095	−0.00380547	−	0.999993i	$-0.501211\pi$
$193$	−0.105735	−0.00761095	−0.00380547	+	0.999993i	$0.501211\pi$
$194$	10.5932	0.760547
$195$	0	0
$196$	4.38610	0.313293
$197$	2.72785	0.194351	0.0971756	−	0.995267i	$-0.469019\pi$
$197$	2.72785	0.194351	0.0971756	+	0.995267i	$0.469019\pi$
$198$	0.643641	0.0457416
$199$	26.0392	1.84587	0.922935	−	0.384957i	$-0.125784\pi$
$199$	26.0392	1.84587	0.922935	+	0.384957i	$0.125784\pi$
$200$	12.4211	0.878304
$201$	−20.8366	−1.46970
$202$	1.58267	0.111356
$203$	0.0478925	0.00336140
$204$	2.21756	0.155261
$205$	−1.42575	−0.0995785
$206$	−2.65637	−0.185078
$207$	4.49656	0.312532
$208$	0	0
$209$	−6.13600	−0.424436
$210$	−0.0783925	−0.00540960
$211$	−20.1916	−1.39005	−0.695025	−	0.718986i	$-0.744607\pi$
$211$	−20.1916	−1.39005	−0.695025	+	0.718986i	$0.744607\pi$
$212$	2.15760	0.148184
$213$	8.89893	0.609744
$214$	22.4722	1.53617
$215$	−1.18546	−0.0808479
$216$	17.1033	1.16373
$217$	−0.163032	−0.0110674
$218$	5.46754	0.370309
$219$	−0.805756	−0.0544479
$220$	−0.615622	−0.0415052
$221$	0	0
$222$	−10.4691	−0.702643
$223$	3.17003	0.212281	0.106141	−	0.994351i	$-0.466151\pi$
$223$	3.17003	0.212281	0.106141	+	0.994351i	$0.466151\pi$
$224$	0.147837	0.00987777
$225$	2.21634	0.147756
$226$	−7.25267	−0.482440
$227$	−16.5756	−1.10016	−0.550081	−	0.835111i	$-0.685403\pi$
$227$	−16.5756	−1.10016	−0.550081	+	0.835111i	$0.685403\pi$
$228$	−6.02050	−0.398717
$229$	17.6392	1.16563	0.582815	−	0.812605i	$-0.301951\pi$
$229$	17.6392	1.16563	0.582815	+	0.812605i	$0.301951\pi$
$230$	9.42325	0.621350
$231$	−0.0681058	−0.00448103
$232$	−3.38865	−0.222476
$233$	−7.39770	−0.484639	−0.242320	−	0.970196i	$-0.577908\pi$
$233$	−7.39770	−0.484639	−0.242320	+	0.970196i	$0.577908\pi$
$234$	0	0
$235$	1.40324	0.0915373
$236$	−0.0144970	−0.000943674 0
$237$	−11.7687	−0.764459
$238$	−0.115223	−0.00746877
$239$	−10.1803	−0.658510	−0.329255	−	0.944241i	$-0.606798\pi$
$239$	−10.1803	−0.658510	−0.329255	+	0.944241i	$0.606798\pi$
$240$	3.61919	0.233617
$241$	−27.6490	−1.78103	−0.890514	−	0.454956i	$-0.849655\pi$
$241$	−27.6490	−1.78103	−0.890514	+	0.454956i	$0.849655\pi$
$242$	1.17186	0.0753297
$243$	5.63133	0.361250
$244$	0.910129	0.0582651
$245$	6.87380	0.439151
$246$	2.66287	0.169778
$247$	0	0
$248$	11.5354	0.732499
$249$	8.80109	0.557746
$250$	10.3999	0.657746
$251$	−7.60061	−0.479747	−0.239873	−	0.970804i	$-0.577106\pi$
$251$	−7.60061	−0.479747	−0.239873	+	0.970804i	$0.577106\pi$
$252$	0.0149762	0.000943413 0
$253$	8.18673	0.514695
$254$	−13.4778	−0.845673
$255$	3.47532	0.217633
$256$	−13.4106	−0.838162
$257$	0.0964676	0.00601748	0.00300874	−	0.999995i	$-0.499042\pi$
$257$	0.0964676	0.00601748	0.00300874	+	0.999995i	$0.499042\pi$
$258$	2.21409	0.137843
$259$	−0.248269	−0.0154267
$260$	0	0
$261$	−0.604648	−0.0374268
$262$	24.1836	1.49407
$263$	−12.6952	−0.782818	−0.391409	−	0.920217i	$-0.628012\pi$
$263$	−12.6952	−0.782818	−0.391409	+	0.920217i	$0.628012\pi$
$264$	4.81885	0.296580
$265$	3.38134	0.207714
$266$	0.312819	0.0191802
$267$	20.4231	1.24987
$268$	8.34208	0.509573
$269$	18.3765	1.12043	0.560216	−	0.828347i	$-0.310718\pi$
$269$	18.3765	1.12043	0.560216	+	0.828347i	$0.310718\pi$
$270$	6.39553	0.389219
$271$	−10.2305	−0.621456	−0.310728	−	0.950499i	$-0.600573\pi$
$271$	−10.2305	−0.621456	−0.310728	+	0.950499i	$0.600573\pi$
$272$	5.31954	0.322544
$273$	0	0
$274$	17.3540	1.04839
$275$	4.03521	0.243332
$276$	8.03263	0.483507
$277$	21.7275	1.30548	0.652741	−	0.757581i	$-0.273619\pi$
$277$	21.7275	1.30548	0.652741	+	0.757581i	$0.273619\pi$
$278$	−20.3275	−1.21916
$279$	2.05830	0.123227
$280$	0.131536	0.00786078
$281$	−18.5429	−1.10618	−0.553088	−	0.833123i	$-0.686551\pi$
$281$	−18.5429	−1.10618	−0.553088	+	0.833123i	$0.686551\pi$
$282$	−2.62083	−0.156068
$283$	−9.54903	−0.567631	−0.283815	−	0.958879i	$-0.591600\pi$
$283$	−9.54903	−0.567631	−0.283815	+	0.958879i	$0.591600\pi$
$284$	−3.56275	−0.211411
$285$	−9.43519	−0.558893
$286$	0	0
$287$	0.0631482	0.00372752
$288$	−1.86646	−0.109982
$289$	−11.8919	−0.699525
$290$	−1.26714	−0.0744088
$291$	14.1515	0.829576
$292$	0.322590	0.0188782
$293$	26.6621	1.55762	0.778809	−	0.627261i	$-0.215824\pi$
$293$	26.6621	1.55762	0.778809	+	0.627261i	$0.215824\pi$
$294$	−12.8382	−0.748739
$295$	−0.0227194	−0.00132277
$296$	17.5663	1.02102
$297$	5.55631	0.322410
$298$	−27.5219	−1.59430
$299$	0	0
$300$	3.95926	0.228588
$301$	0.0525057	0.00302638
$302$	−17.5384	−1.00922
$303$	2.11430	0.121463
$304$	−14.4421	−0.828311
$305$	1.42634	0.0816717
$306$	1.45470	0.0831595
$307$	14.8797	0.849230	0.424615	−	0.905374i	$-0.360410\pi$
$307$	14.8797	0.849230	0.424615	+	0.905374i	$0.360410\pi$
$308$	0.0272667	0.00155366
$309$	−3.54865	−0.201876
$310$	4.31350	0.244990
$311$	−3.13315	−0.177665	−0.0888323	−	0.996047i	$-0.528314\pi$
$311$	−3.13315	−0.177665	−0.0888323	+	0.996047i	$0.528314\pi$
$312$	0	0
$313$	−29.8250	−1.68581	−0.842905	−	0.538063i	$-0.819156\pi$
$313$	−29.8250	−1.68581	−0.842905	+	0.538063i	$0.819156\pi$
$314$	−10.4605	−0.590320
$315$	0.0234704	0.00132241
$316$	4.71169	0.265053
$317$	−20.8234	−1.16956	−0.584778	−	0.811193i	$-0.698819\pi$
$317$	−20.8234	−1.16956	−0.584778	+	0.811193i	$0.698819\pi$
$318$	−6.31533	−0.354146
$319$	−1.10086	−0.0616364
$320$	−8.53518	−0.477131
$321$	30.0207	1.67559
$322$	−0.417368	−0.0232590
$323$	−13.8680	−0.771636
$324$	4.41898	0.245499
$325$	0	0
$326$	24.2243	1.34166
$327$	7.30412	0.403919
$328$	−4.46807	−0.246708
$329$	−0.0621514	−0.00342652
$330$	1.80194	0.0991934
$331$	−4.89506	−0.269057	−0.134528	−	0.990910i	$-0.542952\pi$
$331$	−4.89506	−0.269057	−0.134528	+	0.990910i	$0.542952\pi$
$332$	−3.52358	−0.193382
$333$	3.13442	0.171765
$334$	21.3008	1.16553
$335$	13.0735	0.714283
$336$	−0.160299	−0.00874500
$337$	−23.2168	−1.26470	−0.632350	−	0.774683i	$-0.717910\pi$
$337$	−23.2168	−1.26470	−0.632350	+	0.774683i	$0.717910\pi$
$338$	0	0
$339$	−9.68888	−0.526228
$340$	−1.39137	−0.0754577
$341$	3.74748	0.202937
$342$	−3.94938	−0.213558
$343$	−0.608981	−0.0328819
$344$	−3.71506	−0.200302
$345$	12.5886	0.677745
$346$	27.4594	1.47623
$347$	10.1440	0.544558	0.272279	−	0.962218i	$-0.412223\pi$
$347$	10.1440	0.544558	0.272279	+	0.962218i	$0.412223\pi$
$348$	−1.08014	−0.0579016
$349$	20.5810	1.10168	0.550838	−	0.834612i	$-0.314308\pi$
$349$	20.5810	1.10168	0.550838	+	0.834612i	$0.314308\pi$
$350$	−0.205719	−0.0109962
$351$	0	0
$352$	−3.39820	−0.181124
$353$	3.92946	0.209144	0.104572	−	0.994517i	$-0.466653\pi$
$353$	3.92946	0.209144	0.104572	+	0.994517i	$0.466653\pi$
$354$	0.0424330	0.00225529
$355$	−5.58347	−0.296340
$356$	−8.17655	−0.433357
$357$	−0.153926	−0.00814665
$358$	−15.0729	−0.796625
$359$	−17.4462	−0.920773	−0.460387	−	0.887718i	$-0.652289\pi$
$359$	−17.4462	−0.920773	−0.460387	+	0.887718i	$0.652289\pi$
$360$	−1.66066	−0.0875242
$361$	18.6504	0.981603
$362$	2.17107	0.114109
$363$	1.56549	0.0821668
$364$	0	0
$365$	0.505557	0.0264621
$366$	−2.66397	−0.139248
$367$	−37.3415	−1.94921	−0.974604	−	0.223936i	$-0.928109\pi$
$367$	−37.3415	−1.94921	−0.974604	+	0.223936i	$0.928109\pi$
$368$	19.2688	1.00446
$369$	−0.797253	−0.0415033
$370$	6.56867	0.341489
$371$	−0.149764	−0.00777535
$372$	3.67694	0.190641
$373$	26.4630	1.37020	0.685100	−	0.728449i	$-0.259758\pi$
$373$	26.4630	1.37020	0.685100	+	0.728449i	$0.259758\pi$
$374$	2.64852	0.136952
$375$	13.8933	0.717445
$376$	4.39754	0.226786
$377$	0	0
$378$	−0.283266	−0.0145696
$379$	1.21419	0.0623687	0.0311843	−	0.999514i	$-0.490072\pi$
$379$	1.21419	0.0623687	0.0311843	+	0.999514i	$0.490072\pi$
$380$	3.77745	0.193779
$381$	−18.0051	−0.922427
$382$	−18.3951	−0.941174
$383$	5.92021	0.302508	0.151254	−	0.988495i	$-0.451669\pi$
$383$	5.92021	0.302508	0.151254	+	0.988495i	$0.451669\pi$
$384$	5.30149	0.270541
$385$	0.0427318	0.00217781
$386$	−0.123906	−0.00630664
$387$	−0.662890	−0.0336966
$388$	−5.66566	−0.287630
$389$	−6.52030	−0.330592	−0.165296	−	0.986244i	$-0.552858\pi$
$389$	−6.52030	−0.330592	−0.165296	+	0.986244i	$0.552858\pi$
$390$	0	0
$391$	18.5029	0.935730
$392$	21.5414	1.08801
$393$	32.3070	1.62967
$394$	3.19665	0.161045
$395$	7.38406	0.371532
$396$	−0.344245	−0.0172990
$397$	−12.5684	−0.630792	−0.315396	−	0.948960i	$-0.602137\pi$
$397$	−12.5684	−0.630792	−0.315396	+	0.948960i	$0.602137\pi$
$398$	30.5142	1.52954
$399$	0.417897	0.0209210
$400$	9.49755	0.474877
$401$	−23.0521	−1.15117	−0.575583	−	0.817744i	$-0.695225\pi$
$401$	−23.0521	−1.15117	−0.575583	+	0.817744i	$0.695225\pi$
$402$	−24.4174	−1.21783
$403$	0	0
$404$	−0.846475	−0.0421137
$405$	6.92534	0.344123
$406$	0.0561231	0.00278534
$407$	5.70673	0.282872
$408$	10.8911	0.539190
$409$	7.75744	0.383580	0.191790	−	0.981436i	$-0.438571\pi$
$409$	7.75744	0.383580	0.191790	+	0.981436i	$0.438571\pi$
$410$	−1.67077	−0.0825135
$411$	23.1833	1.14355
$412$	1.42073	0.0699944
$413$	0.00100627	4.95154e−5 0
$414$	5.26931	0.258973
$415$	−5.52208	−0.271068
$416$	0	0
$417$	−27.1556	−1.32982
$418$	−7.19050	−0.351699
$419$	29.4051	1.43654	0.718268	−	0.695767i	$-0.244935\pi$
$419$	29.4051	1.43654	0.718268	+	0.695767i	$0.244935\pi$
$420$	0.0419274	0.00204585
$421$	−35.6138	−1.73571	−0.867855	−	0.496817i	$-0.834502\pi$
$421$	−35.6138	−1.73571	−0.867855	+	0.496817i	$0.834502\pi$
$422$	−23.6617	−1.15183
$423$	0.784667	0.0381518
$424$	10.5966	0.514616
$425$	9.12000	0.442385
$426$	10.4283	0.505251
$427$	−0.0631742	−0.00305722
$428$	−12.0190	−0.580962
$429$	0	0
$430$	−1.38919	−0.0669928
$431$	−31.4361	−1.51422	−0.757112	−	0.653285i	$-0.773390\pi$
$431$	−31.4361	−1.51422	−0.757112	+	0.653285i	$0.773390\pi$
$432$	13.0777	0.629201
$433$	4.42569	0.212685	0.106343	−	0.994330i	$-0.466086\pi$
$433$	4.42569	0.212685	0.106343	+	0.994330i	$0.466086\pi$
$434$	−0.191050	−0.00917072
$435$	−1.69277	−0.0811622
$436$	−2.92426	−0.140047
$437$	−50.2337	−2.40301
$438$	−0.944229	−0.0451170
$439$	−34.8667	−1.66410	−0.832049	−	0.554702i	$-0.812832\pi$
$439$	−34.8667	−1.66410	−0.832049	+	0.554702i	$0.812832\pi$
$440$	−3.02350	−0.144140
$441$	3.84371	0.183034
$442$	0	0
$443$	35.9495	1.70801	0.854006	−	0.520262i	$-0.174166\pi$
$443$	35.9495	1.70801	0.854006	+	0.520262i	$0.174166\pi$
$444$	5.59931	0.265732
$445$	−12.8141	−0.607447
$446$	3.71482	0.175902
$447$	−36.7667	−1.73900
$448$	0.378034	0.0178604
$449$	25.8384	1.21939	0.609694	−	0.792637i	$-0.291292\pi$
$449$	25.8384	1.21939	0.609694	+	0.792637i	$0.291292\pi$
$450$	2.59723	0.122434
$451$	−1.45153	−0.0683499
$452$	3.87902	0.182454
$453$	−23.4296	−1.10082
$454$	−19.4242	−0.911625
$455$	0	0
$456$	−29.5684	−1.38467
$457$	4.07454	0.190599	0.0952995	−	0.995449i	$-0.469619\pi$
$457$	4.07454	0.190599	0.0952995	+	0.995449i	$0.469619\pi$
$458$	20.6706	0.965872
$459$	12.5578	0.586150
$460$	−5.03993	−0.234988
$461$	−28.3537	−1.32056	−0.660282	−	0.751018i	$-0.729563\pi$
$461$	−28.3537	−1.32056	−0.660282	+	0.751018i	$0.729563\pi$
$462$	−0.0798102	−0.00371311
$463$	−34.8455	−1.61941	−0.809704	−	0.586838i	$-0.800372\pi$
$463$	−34.8455	−1.61941	−0.809704	+	0.586838i	$0.800372\pi$
$464$	−2.59106	−0.120287
$465$	5.76242	0.267226
$466$	−8.66903	−0.401585
$467$	20.4055	0.944254	0.472127	−	0.881530i	$-0.343486\pi$
$467$	20.4055	0.944254	0.472127	+	0.881530i	$0.343486\pi$
$468$	0	0
$469$	−0.579043	−0.0267377
$470$	1.64440	0.0758503
$471$	−13.9742	−0.643899
$472$	−0.0711990	−0.00327720
$473$	−1.20690	−0.0554934
$474$	−13.7912	−0.633451
$475$	−24.7600	−1.13607
$476$	0.0616256	0.00282461
$477$	1.89078	0.0865731
$478$	−11.9299	−0.545659
$479$	5.56607	0.254320	0.127160	−	0.991882i	$-0.459414\pi$
$479$	5.56607	0.254320	0.127160	+	0.991882i	$0.459414\pi$
$480$	−5.22533	−0.238503
$481$	0	0
$482$	−32.4006	−1.47581
$483$	−0.557564	−0.0253700
$484$	−0.626755	−0.0284889
$485$	−8.87910	−0.403179
$486$	6.59910	0.299341
$487$	−10.8191	−0.490261	−0.245130	−	0.969490i	$-0.578831\pi$
$487$	−10.8191	−0.490261	−0.245130	+	0.969490i	$0.578831\pi$
$488$	4.46991	0.202343
$489$	32.3613	1.46343
$490$	8.05510	0.363892
$491$	11.4063	0.514761	0.257381	−	0.966310i	$-0.417141\pi$
$491$	11.4063	0.514761	0.257381	+	0.966310i	$0.417141\pi$
$492$	−1.42421	−0.0642083
$493$	−2.48806	−0.112057
$494$	0	0
$495$	−0.539493	−0.0242484
$496$	8.82033	0.396044
$497$	0.247299	0.0110929
$498$	10.3136	0.462164
$499$	−33.1006	−1.48179	−0.740893	−	0.671624i	$-0.765597\pi$
$499$	−33.1006	−1.48179	−0.740893	+	0.671624i	$0.765597\pi$
$500$	−5.56227	−0.248752
$501$	28.4558	1.27131
$502$	−8.90682	−0.397531
$503$	3.48894	0.155564	0.0777821	−	0.996970i	$-0.475216\pi$
$503$	3.48894	0.155564	0.0777821	+	0.996970i	$0.475216\pi$
$504$	0.0735526	0.00327629
$505$	−1.32658	−0.0590319
$506$	9.59366	0.426490
$507$	0	0
$508$	7.20847	0.319824
$509$	18.8866	0.837132	0.418566	−	0.908186i	$-0.362533\pi$
$509$	18.8866	0.837132	0.418566	+	0.908186i	$0.362533\pi$
$510$	4.07257	0.180336
$511$	−0.0223918	−0.000990554 0
$512$	−22.4882	−0.993849
$513$	−34.0935	−1.50526
$514$	0.113046	0.00498625
$515$	2.22654	0.0981131
$516$	−1.18418	−0.0521308
$517$	1.42862	0.0628305
$518$	−0.290935	−0.0127830
$519$	36.6831	1.61021
$520$	0	0
$521$	−16.7614	−0.734328	−0.367164	−	0.930156i	$-0.619671\pi$
$521$	−16.7614	−0.734328	−0.367164	+	0.930156i	$0.619671\pi$
$522$	−0.708560	−0.0310128
$523$	33.9123	1.48288	0.741441	−	0.671019i	$-0.234143\pi$
$523$	33.9123	1.48288	0.741441	+	0.671019i	$0.234143\pi$
$524$	−12.9344	−0.565041
$525$	−0.274821	−0.0119942
$526$	−14.8769	−0.648664
$527$	8.46970	0.368946
$528$	3.68464	0.160353
$529$	44.0225	1.91402
$530$	3.96244	0.172117
$531$	−0.0127043	−0.000551319 0
$532$	−0.167308	−0.00725374
$533$	0	0
$534$	23.9329	1.03568
$535$	−18.8360	−0.814350
$536$	40.9704	1.76965
$537$	−20.1359	−0.868928
$538$	21.5345	0.928420
$539$	6.99811	0.301430
$540$	−3.42058	−0.147198
$541$	28.9463	1.24450	0.622249	−	0.782819i	$-0.286219\pi$
$541$	28.9463	1.24450	0.622249	+	0.782819i	$0.286219\pi$
$542$	−11.9886	−0.514956
$543$	2.90034	0.124466
$544$	−7.68028	−0.329289
$545$	−4.58284	−0.196307
$546$	0	0
$547$	0.742291	0.0317381	0.0158690	−	0.999874i	$-0.494949\pi$
$547$	0.742291	0.0317381	0.0158690	+	0.999874i	$0.494949\pi$
$548$	−9.28160	−0.396490
$549$	0.797581	0.0340399
$550$	4.72868	0.201632
$551$	6.75489	0.287768
$552$	39.4506	1.67913
$553$	−0.327050	−0.0139076
$554$	25.4615	1.08176
$555$	8.77512	0.372483
$556$	10.8720	0.461074
$557$	−5.78382	−0.245068	−0.122534	−	0.992464i	$-0.539102\pi$
$557$	−5.78382	−0.245068	−0.122534	+	0.992464i	$0.539102\pi$
$558$	2.41203	0.102109
$559$	0	0
$560$	0.100576	0.00425013
$561$	3.53817	0.149382
$562$	−21.7296	−0.916607
$563$	42.7115	1.80008	0.900038	−	0.435812i	$-0.143539\pi$
$563$	42.7115	1.80008	0.900038	+	0.435812i	$0.143539\pi$
$564$	1.40173	0.0590233
$565$	6.07911	0.255750
$566$	−11.1901	−0.470354
$567$	−0.306732	−0.0128815
$568$	−17.4977	−0.734188
$569$	−12.2145	−0.512057	−0.256028	−	0.966669i	$-0.582414\pi$
$569$	−12.2145	−0.512057	−0.256028	+	0.966669i	$0.582414\pi$
$570$	−11.0567	−0.463113
$571$	−5.31802	−0.222552	−0.111276	−	0.993790i	$-0.535494\pi$
$571$	−5.31802	−0.222552	−0.111276	+	0.993790i	$0.535494\pi$
$572$	0	0
$573$	−24.5741	−1.02660
$574$	0.0740006	0.00308872
$575$	33.0352	1.37766
$576$	−4.77272	−0.198863
$577$	25.9884	1.08191	0.540956	−	0.841051i	$-0.318063\pi$
$577$	25.9884	1.08191	0.540956	+	0.841051i	$0.318063\pi$
$578$	−13.9356	−0.579645
$579$	−0.165526	−0.00687904
$580$	0.677715	0.0281406
$581$	0.244580	0.0101469
$582$	16.5835	0.687409
$583$	3.44249	0.142573
$584$	1.58434	0.0655603
$585$	0	0
$586$	31.2441	1.29068
$587$	−38.3242	−1.58181	−0.790904	−	0.611941i	$-0.790389\pi$
$587$	−38.3242	−1.58181	−0.790904	+	0.611941i	$0.790389\pi$
$588$	6.86638	0.283165
$589$	−22.9945	−0.947473
$590$	−0.0266238	−0.00109609
$591$	4.27041	0.175661
$592$	13.4317	0.552041
$593$	−37.4861	−1.53937	−0.769686	−	0.638423i	$-0.779587\pi$
$593$	−37.4861	−1.53937	−0.769686	+	0.638423i	$0.779587\pi$
$594$	6.51119	0.267157
$595$	0.0965783	0.00395933
$596$	14.7198	0.602948
$597$	40.7640	1.66836
$598$	0	0
$599$	−21.6410	−0.884226	−0.442113	−	0.896959i	$-0.645771\pi$
$599$	−21.6410	−0.884226	−0.442113	+	0.896959i	$0.645771\pi$
$600$	19.4451	0.793841
$601$	−26.9910	−1.10099	−0.550493	−	0.834840i	$-0.685560\pi$
$601$	−26.9910	−1.10099	−0.550493	+	0.834840i	$0.685560\pi$
$602$	0.0615291	0.00250774
$603$	7.31048	0.297706
$604$	9.38021	0.381675
$605$	−0.982237	−0.0399336
$606$	2.47765	0.100648
$607$	18.1455	0.736505	0.368252	−	0.929726i	$-0.379956\pi$
$607$	18.1455	0.736505	0.368252	+	0.929726i	$0.379956\pi$
$608$	20.8513	0.845632
$609$	0.0749751	0.00303815
$610$	1.67146	0.0676754
$611$	0	0
$612$	−0.778030	−0.0314500
$613$	24.2627	0.979962	0.489981	−	0.871733i	$-0.337004\pi$
$613$	24.2627	0.979962	0.489981	+	0.871733i	$0.337004\pi$
$614$	17.4369	0.703695
$615$	−2.23199	−0.0900025
$616$	0.133915	0.00539558
$617$	−10.2109	−0.411074	−0.205537	−	0.978649i	$-0.565894\pi$
$617$	−10.2109	−0.411074	−0.205537	+	0.978649i	$0.565894\pi$
$618$	−4.15851	−0.167280
$619$	11.0078	0.442441	0.221221	−	0.975224i	$-0.428996\pi$
$619$	11.0078	0.442441	0.221221	+	0.975224i	$0.428996\pi$
$620$	−2.30703	−0.0926526
$621$	45.4880	1.82537
$622$	−3.67160	−0.147218
$623$	0.567554	0.0227386
$624$	0	0
$625$	11.4590	0.458359
$626$	−34.9506	−1.39691
$627$	−9.60582	−0.383620
$628$	5.59469	0.223253
$629$	12.8978	0.514270
$630$	0.0275039	0.00109578
$631$	28.7415	1.14418	0.572091	−	0.820190i	$-0.306132\pi$
$631$	28.7415	1.14418	0.572091	+	0.820190i	$0.306132\pi$
$632$	23.1405	0.920479
$633$	−31.6098	−1.25637
$634$	−24.4020	−0.969126
$635$	11.2970	0.448306
$636$	3.37769	0.133934
$637$	0	0
$638$	−1.29005	−0.0510736
$639$	−3.12218	−0.123511
$640$	−3.32633	−0.131485
$641$	−26.7191	−1.05534	−0.527670	−	0.849449i	$-0.676934\pi$
$641$	−26.7191	−1.05534	−0.527670	+	0.849449i	$0.676934\pi$
$642$	35.1800	1.38844
$643$	41.1167	1.62148	0.810742	−	0.585404i	$-0.199064\pi$
$643$	41.1167	1.62148	0.810742	+	0.585404i	$0.199064\pi$
$644$	0.223225	0.00879630
$645$	−1.85583	−0.0730731
$646$	−16.2513	−0.639398
$647$	−11.7907	−0.463542	−0.231771	−	0.972770i	$-0.574452\pi$
$647$	−11.7907	−0.463542	−0.231771	+	0.972770i	$0.574452\pi$
$648$	21.7029	0.852571
$649$	−0.0231303	−0.000907942 0
$650$	0	0
$651$	−0.255225	−0.0100031
$652$	−12.9561	−0.507400
$653$	−25.2104	−0.986558	−0.493279	−	0.869871i	$-0.664202\pi$
$653$	−25.2104	−0.986558	−0.493279	+	0.869871i	$0.664202\pi$
$654$	8.55937	0.334698
$655$	−20.2705	−0.792033
$656$	−3.41642	−0.133389
$657$	0.282698	0.0110291
$658$	−0.0728324	−0.00283930
$659$	2.14366	0.0835053	0.0417526	−	0.999128i	$-0.486706\pi$
$659$	2.14366	0.0835053	0.0417526	+	0.999128i	$0.486706\pi$
$660$	−0.963748	−0.0375138
$661$	−22.4714	−0.874035	−0.437018	−	0.899453i	$-0.643965\pi$
$661$	−22.4714	−0.874035	−0.437018	+	0.899453i	$0.643965\pi$
$662$	−5.73630	−0.222948
$663$	0	0
$664$	−17.3053	−0.671578
$665$	−0.262202	−0.0101678
$666$	3.67309	0.142329
$667$	−9.01246	−0.348964
$668$	−11.3925	−0.440789
$669$	4.96265	0.191867
$670$	15.3203	0.591874
$671$	1.45213	0.0560588
$672$	0.231437	0.00892787
$673$	30.7644	1.18588	0.592941	−	0.805246i	$-0.297967\pi$
$673$	30.7644	1.18588	0.592941	+	0.805246i	$0.297967\pi$
$674$	−27.2067	−1.04796
$675$	22.4209	0.862979
$676$	0	0
$677$	16.7206	0.642626	0.321313	−	0.946973i	$-0.395876\pi$
$677$	16.7206	0.642626	0.321313	+	0.946973i	$0.395876\pi$
$678$	−11.3540	−0.436046
$679$	0.393267	0.0150922
$680$	−6.83343	−0.262050
$681$	−25.9489	−0.994365
$682$	4.39151	0.168159
$683$	−15.3907	−0.588910	−0.294455	−	0.955665i	$-0.595138\pi$
$683$	−15.3907	−0.588910	−0.294455	+	0.955665i	$0.595138\pi$
$684$	2.11229	0.0807652
$685$	−14.5459	−0.555771
$686$	−0.713638	−0.0272468
$687$	27.6139	1.05354
$688$	−2.84065	−0.108299
$689$	0	0
$690$	14.7520	0.561598
$691$	19.7068	0.749680	0.374840	−	0.927089i	$-0.377698\pi$
$691$	19.7068	0.749680	0.374840	+	0.927089i	$0.377698\pi$
$692$	−14.6864	−0.558292
$693$	0.0238949	0.000907690 0
$694$	11.8873	0.451235
$695$	17.0383	0.646299
$696$	−5.30489	−0.201081
$697$	−3.28061	−0.124262
$698$	24.1179	0.912878
$699$	−11.5810	−0.438034
$700$	0.110027	0.00415862
$701$	−42.4624	−1.60378	−0.801891	−	0.597471i	$-0.796172\pi$
$701$	−42.4624	−1.60378	−0.801891	+	0.597471i	$0.796172\pi$
$702$	0	0
$703$	−35.0165	−1.32067
$704$	−8.68953	−0.327499
$705$	2.19676	0.0827346
$706$	4.60476	0.173302
$707$	0.0587558	0.00220974
$708$	−0.0226949	−0.000852926 0
$709$	−1.93037	−0.0724967	−0.0362484	−	0.999343i	$-0.511541\pi$
$709$	−1.93037	−0.0724967	−0.0362484	+	0.999343i	$0.511541\pi$
$710$	−6.54302	−0.245555
$711$	4.12904	0.154851
$712$	−40.1574	−1.50496
$713$	30.6796	1.14896
$714$	−0.180379	−0.00675053
$715$	0	0
$716$	8.06157	0.301275
$717$	−15.9372	−0.595184
$718$	−20.4444	−0.762978
$719$	−27.4786	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$719$	−27.4786	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$720$	−1.26979	−0.0473222
$721$	−0.0986164	−0.00367266
$722$	21.8556	0.813382
$723$	−43.2841	−1.60975
$724$	−1.16118	−0.0431547
$725$	−4.44221	−0.164980
$726$	1.83452	0.0680856
$727$	0.663445	0.0246058	0.0123029	−	0.999924i	$-0.496084\pi$
$727$	0.663445	0.0246058	0.0123029	+	0.999924i	$0.496084\pi$
$728$	0	0
$729$	29.9675	1.10991
$730$	0.592439	0.0219272
$731$	−2.72773	−0.100889
$732$	1.42480	0.0526620
$733$	37.9064	1.40010	0.700052	−	0.714092i	$-0.253160\pi$
$733$	37.9064	1.40010	0.700052	+	0.714092i	$0.253160\pi$
$734$	−43.7588	−1.61517
$735$	10.7608	0.396920
$736$	−27.8201	−1.02546
$737$	13.3099	0.490278
$738$	−0.934265	−0.0343908
$739$	24.1584	0.888681	0.444340	−	0.895858i	$-0.353438\pi$
$739$	24.1584	0.888681	0.444340	+	0.895858i	$0.353438\pi$
$740$	−3.51319	−0.129147
$741$	0	0
$742$	−0.175502	−0.00644287
$743$	−17.9716	−0.659313	−0.329656	−	0.944101i	$-0.606933\pi$
$743$	−17.9716	−0.659313	−0.329656	+	0.944101i	$0.606933\pi$
$744$	18.0585	0.662058
$745$	23.0686	0.845168
$746$	31.0108	1.13539
$747$	−3.08785	−0.112979
$748$	−1.41653	−0.0517936
$749$	0.834270	0.0304836
$750$	16.2809	0.594494
$751$	−30.4523	−1.11122	−0.555611	−	0.831442i	$-0.687516\pi$
$751$	−30.4523	−1.11122	−0.555611	+	0.831442i	$0.687516\pi$
$752$	3.36249	0.122617
$753$	−11.8987	−0.433611
$754$	0	0
$755$	14.7005	0.535005
$756$	0.151502	0.00551008
$757$	−27.4402	−0.997332	−0.498666	−	0.866794i	$-0.666177\pi$
$757$	−27.4402	−0.997332	−0.498666	+	0.866794i	$0.666177\pi$
$758$	1.42285	0.0516804
$759$	12.8162	0.465199
$760$	18.5522	0.672958
$761$	−7.71679	−0.279733	−0.139867	−	0.990170i	$-0.544667\pi$
$761$	−7.71679	−0.279733	−0.139867	+	0.990170i	$0.544667\pi$
$762$	−21.0993	−0.764348
$763$	0.202980	0.00734836
$764$	9.83842	0.355942
$765$	−1.21931	−0.0440843
$766$	6.93763	0.250667
$767$	0	0
$768$	−20.9941	−0.757560
$769$	40.6121	1.46451	0.732256	−	0.681030i	$-0.238468\pi$
$769$	40.6121	1.46451	0.732256	+	0.681030i	$0.238468\pi$
$770$	0.0500755	0.00180459
$771$	0.151019	0.00543881
$772$	0.0662697	0.00238510
$773$	−7.61322	−0.273828	−0.136914	−	0.990583i	$-0.543718\pi$
$773$	−7.61322	−0.273828	−0.136914	+	0.990583i	$0.543718\pi$
$774$	−0.776811	−0.0279219
$775$	15.1219	0.543194
$776$	−27.8257	−0.998885
$777$	−0.388662	−0.0139432
$778$	−7.64084	−0.273937
$779$	8.90659	0.319112
$780$	0	0
$781$	−5.68444	−0.203405
$782$	21.6827	0.775371
$783$	−6.11673	−0.218594
$784$	16.4712	0.588258
$785$	8.76788	0.312939
$786$	37.8592	1.35039
$787$	−48.8427	−1.74106	−0.870528	−	0.492119i	$-0.836222\pi$
$787$	−48.8427	−1.74106	−0.870528	+	0.492119i	$0.836222\pi$
$788$	−1.70969	−0.0609053
$789$	−19.8741	−0.707538
$790$	8.65305	0.307862
$791$	−0.269252	−0.00957349
$792$	−1.69069	−0.0600759
$793$	0	0
$794$	−14.7284	−0.522691
$795$	5.29344	0.187739
$796$	−16.3202	−0.578454
$797$	−44.1124	−1.56254	−0.781272	−	0.624191i	$-0.785429\pi$
$797$	−44.1124	−1.56254	−0.781272	+	0.624191i	$0.785429\pi$
$798$	0.489715	0.0173357
$799$	3.22883	0.114228
$800$	−13.7124	−0.484808
$801$	−7.16543	−0.253178
$802$	−27.0137	−0.953886
$803$	0.514699	0.0181634
$804$	13.0594	0.460570
$805$	0.349833	0.0123300
$806$	0	0
$807$	28.7681	1.01269
$808$	−4.15728	−0.146253
$809$	19.8850	0.699119	0.349560	−	0.936914i	$-0.386331\pi$
$809$	19.8850	0.699119	0.349560	+	0.936914i	$0.386331\pi$
$810$	8.11549	0.285149
$811$	−16.7300	−0.587469	−0.293734	−	0.955887i	$-0.594898\pi$
$811$	−16.7300	−0.587469	−0.293734	+	0.955887i	$0.594898\pi$
$812$	−0.0300169	−0.00105339
$813$	−16.0157	−0.561694
$814$	6.68746	0.234395
$815$	−20.3045	−0.711237
$816$	8.32767	0.291527
$817$	7.40554	0.259087
$818$	9.09059	0.317845
$819$	0	0
$820$	0.893595	0.0312057
$821$	17.0899	0.596442	0.298221	−	0.954497i	$-0.403607\pi$
$821$	17.0899	0.596442	0.298221	+	0.954497i	$0.403607\pi$
$822$	27.1674	0.947573
$823$	15.2843	0.532778	0.266389	−	0.963866i	$-0.414169\pi$
$823$	15.2843	0.532778	0.266389	+	0.963866i	$0.414169\pi$
$824$	6.97763	0.243077
$825$	6.31707	0.219932
$826$	0.00117920	4.10298e−5 0
$827$	1.45085	0.0504511	0.0252255	−	0.999682i	$-0.491970\pi$
$827$	1.45085	0.0504511	0.0252255	+	0.999682i	$0.491970\pi$
$828$	−2.81824	−0.0979406
$829$	−29.1376	−1.01199	−0.505996	−	0.862536i	$-0.668875\pi$
$829$	−29.1376	−1.01199	−0.505996	+	0.862536i	$0.668875\pi$
$830$	−6.47108	−0.224615
$831$	34.0142	1.17994
$832$	0	0
$833$	15.8165	0.548008
$834$	−31.8224	−1.10192
$835$	−17.8541	−0.617866
$836$	3.84577	0.133009
$837$	20.8221	0.719719
$838$	34.4586	1.19035
$839$	0.243333	0.00840078	0.00420039	−	0.999991i	$-0.498663\pi$
$839$	0.243333	0.00840078	0.00420039	+	0.999991i	$0.498663\pi$
$840$	0.205918	0.00710484
$841$	−27.7881	−0.958210
$842$	−41.7342	−1.43826
$843$	−29.0287	−0.999800
$844$	12.6552	0.435610
$845$	0	0
$846$	0.919517	0.0316136
$847$	0.0435046	0.00149483
$848$	8.10247	0.278240
$849$	−14.9489	−0.513044
$850$	10.6873	0.366572
$851$	46.7194	1.60152
$852$	−5.57745	−0.191080
$853$	−18.0297	−0.617325	−0.308663	−	0.951172i	$-0.599881\pi$
$853$	−18.0297	−0.617325	−0.308663	+	0.951172i	$0.599881\pi$
$854$	−0.0740311	−0.00253329
$855$	3.31033	0.113211
$856$	−59.0290	−2.01757
$857$	21.5932	0.737608	0.368804	−	0.929507i	$-0.379767\pi$
$857$	21.5932	0.737608	0.368804	+	0.929507i	$0.379767\pi$
$858$	0	0
$859$	26.1602	0.892576	0.446288	−	0.894889i	$-0.352746\pi$
$859$	26.1602	0.892576	0.446288	+	0.894889i	$0.352746\pi$
$860$	0.742995	0.0253359
$861$	0.0988578	0.00336906
$862$	−36.8386	−1.25473
$863$	47.8823	1.62993	0.814966	−	0.579509i	$-0.196756\pi$
$863$	47.8823	1.62993	0.814966	+	0.579509i	$0.196756\pi$
$864$	−18.8814	−0.642359
$865$	−23.0162	−0.782573
$866$	5.18627	0.176237
$867$	−18.6167	−0.632255
$868$	0.102181	0.00346826
$869$	7.51760	0.255017
$870$	−1.98368	−0.0672532
$871$	0	0
$872$	−14.3619	−0.486355
$873$	−4.96504	−0.168041
$874$	−58.8667	−1.99119
$875$	0.386091	0.0130522
$876$	0.505011	0.0170628
$877$	−47.3277	−1.59814	−0.799072	−	0.601235i	$-0.794676\pi$
$877$	−47.3277	−1.59814	−0.799072	+	0.601235i	$0.794676\pi$
$878$	−40.8588	−1.37892
$879$	41.7392	1.40783
$880$	−2.31186	−0.0779328
$881$	13.3279	0.449030	0.224515	−	0.974471i	$-0.427920\pi$
$881$	13.3279	0.449030	0.224515	+	0.974471i	$0.427920\pi$
$882$	4.50427	0.151667
$883$	−13.8030	−0.464508	−0.232254	−	0.972655i	$-0.574610\pi$
$883$	−13.8030	−0.464508	−0.232254	+	0.972655i	$0.574610\pi$
$884$	0	0
$885$	−0.0355669	−0.00119557
$886$	42.1276	1.41531
$887$	−9.25137	−0.310631	−0.155315	−	0.987865i	$-0.549639\pi$
$887$	−9.25137	−0.310631	−0.155315	+	0.987865i	$0.549639\pi$
$888$	27.4999	0.922835
$889$	−0.500357	−0.0167814
$890$	−15.0163	−0.503347
$891$	7.05058	0.236203
$892$	−1.98684	−0.0665242
$893$	−8.76599	−0.293343
$894$	−43.0852	−1.44099
$895$	12.6339	0.422305
$896$	0.147327	0.00492186
$897$	0	0
$898$	30.2788	1.01042
$899$	−4.12546	−0.137592
$900$	−1.38910	−0.0463034
$901$	7.78039	0.259202
$902$	−1.70098	−0.0566366
$903$	0.0821970	0.00273535
$904$	19.0510	0.633626
$905$	−1.81977	−0.0604911
$906$	−27.4561	−0.912167
$907$	20.0496	0.665736	0.332868	−	0.942974i	$-0.391984\pi$
$907$	20.0496	0.665736	0.332868	+	0.942974i	$0.391984\pi$
$908$	10.3889	0.344766
$909$	−0.741798	−0.0246039
$910$	0	0
$911$	45.6738	1.51324	0.756620	−	0.653855i	$-0.226850\pi$
$911$	45.6738	1.51324	0.756620	+	0.653855i	$0.226850\pi$
$912$	−22.6089	−0.748656
$913$	−5.62195	−0.186059
$914$	4.77477	0.157935
$915$	2.23291	0.0738177
$916$	−11.0554	−0.365282
$917$	0.897806	0.0296481
$918$	14.7160	0.485699
$919$	−48.3469	−1.59482	−0.797409	−	0.603440i	$-0.793796\pi$
$919$	−48.3469	−1.59482	−0.797409	+	0.603440i	$0.793796\pi$
$920$	−24.7526	−0.816068
$921$	23.2940	0.767563
$922$	−33.2264	−1.09425
$923$	0	0
$924$	0.0426857	0.00140426
$925$	23.0279	0.757151
$926$	−40.8339	−1.34189
$927$	1.24504	0.0408925
$928$	3.74094	0.122803
$929$	28.7878	0.944498	0.472249	−	0.881465i	$-0.343442\pi$
$929$	28.7878	0.944498	0.472249	+	0.881465i	$0.343442\pi$
$930$	6.75273	0.221431
$931$	−42.9404	−1.40731
$932$	4.63654	0.151875
$933$	−4.90490	−0.160579
$934$	23.9123	0.782434
$935$	−2.21996	−0.0726004
$936$	0	0
$937$	−53.3172	−1.74180	−0.870898	−	0.491463i	$-0.836462\pi$
$937$	−53.3172	−1.74180	−0.870898	+	0.491463i	$0.836462\pi$
$938$	−0.678555	−0.0221556
$939$	−46.6907	−1.52369
$940$	−0.879488	−0.0286857
$941$	0.483980	0.0157773	0.00788864	−	0.999969i	$-0.497489\pi$
$941$	0.483980	0.0157773	0.00788864	+	0.999969i	$0.497489\pi$
$942$	−16.3758	−0.533552
$943$	−11.8833	−0.386973
$944$	−0.0544409	−0.00177190
$945$	0.237431	0.00772362
$946$	−1.41431	−0.0459833
$947$	−16.3227	−0.530416	−0.265208	−	0.964191i	$-0.585441\pi$
$947$	−16.3227	−0.530416	−0.265208	+	0.964191i	$0.585441\pi$
$948$	7.37609	0.239564
$949$	0	0
$950$	−29.0152	−0.941377
$951$	−32.5987	−1.05709
$952$	0.302661	0.00980931
$953$	32.8570	1.06434	0.532171	−	0.846637i	$-0.321376\pi$
$953$	32.8570	1.06434	0.532171	+	0.846637i	$0.321376\pi$
$954$	2.21573	0.0717368
$955$	15.4186	0.498933
$956$	6.38056	0.206362
$957$	−1.72339	−0.0557091
$958$	6.52262	0.210736
$959$	0.644258	0.0208042
$960$	−13.3617	−0.431247
$961$	−16.9564	−0.546980
$962$	0	0
$963$	−10.5327	−0.339413
$964$	17.3291	0.558134
$965$	0.103856	0.00334326
$966$	−0.653384	−0.0210223
$967$	−10.9452	−0.351973	−0.175987	−	0.984393i	$-0.556312\pi$
$967$	−10.9452	−0.351973	−0.175987	+	0.984393i	$0.556312\pi$
$968$	−3.07818	−0.0989364
$969$	−21.7102	−0.697431
$970$	−10.4050	−0.334085
$971$	−36.9233	−1.18492	−0.592462	−	0.805598i	$-0.701844\pi$
$971$	−36.9233	−1.18492	−0.592462	+	0.805598i	$0.701844\pi$
$972$	−3.52946	−0.113208
$973$	−0.754648	−0.0241929
$974$	−12.6784	−0.406243
$975$	0	0
$976$	3.41783	0.109402
$977$	−17.6966	−0.566164	−0.283082	−	0.959096i	$-0.591357\pi$
$977$	−17.6966	−0.566164	−0.283082	+	0.959096i	$0.591357\pi$
$978$	37.9228	1.21264
$979$	−13.0459	−0.416947
$980$	−4.30819	−0.137620
$981$	−2.56264	−0.0818188
$982$	13.3666	0.426545
$983$	−12.5327	−0.399729	−0.199865	−	0.979823i	$-0.564050\pi$
$983$	−12.5327	−0.399729	−0.199865	+	0.979823i	$0.564050\pi$
$984$	−6.99471	−0.222983
$985$	−2.67939	−0.0853726
$986$	−2.91565	−0.0928533
$987$	−0.0972972	−0.00309700
$988$	0	0
$989$	−9.88057	−0.314184
$990$	−0.632208	−0.0200929
$991$	37.6299	1.19535	0.597677	−	0.801737i	$-0.296090\pi$
$991$	37.6299	1.19535	0.597677	+	0.801737i	$0.296090\pi$
$992$	−12.7347	−0.404326
$993$	−7.66315	−0.243183
$994$	0.289799	0.00919186
$995$	−25.5767	−0.810834
$996$	−5.51613	−0.174785
$997$	−54.1250	−1.71416	−0.857078	−	0.515187i	$-0.827723\pi$
$997$	−54.1250	−1.71416	−0.857078	+	0.515187i	$0.827723\pi$
$998$	−38.7891	−1.22785
$999$	31.7083	1.00321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.r.1.7	yes	9
13.12	even	2		1859.2.a.q.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.q.1.3	✓	9	13.12	even	2
1859.2.a.r.1.7	yes	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+1.17186 q^{2} +1.56549 q^{3} -0.626755 q^{4} -0.982237 q^{5} +1.83452 q^{6} +0.0435046 q^{7} -3.07818 q^{8} -0.549249 q^{9} +O(q^{10})\)	\(q+1.17186 q^{2} +1.56549 q^{3} -0.626755 q^{4} -0.982237 q^{5} +1.83452 q^{6} +0.0435046 q^{7} -3.07818 q^{8} -0.549249 q^{9} -1.15104 q^{10} -1.00000 q^{11} -0.981177 q^{12} +0.0509810 q^{14} -1.53768 q^{15} -2.35367 q^{16} -2.26011 q^{17} -0.643641 q^{18} +6.13600 q^{19} +0.615622 q^{20} +0.0681058 q^{21} -1.17186 q^{22} -8.18673 q^{23} -4.81885 q^{24} -4.03521 q^{25} -5.55631 q^{27} -0.0272667 q^{28} +1.10086 q^{29} -1.80194 q^{30} -3.74748 q^{31} +3.39820 q^{32} -1.56549 q^{33} -2.64852 q^{34} -0.0427318 q^{35} +0.344245 q^{36} -5.70673 q^{37} +7.19050 q^{38} +3.02350 q^{40} +1.45153 q^{41} +0.0798102 q^{42} +1.20690 q^{43} +0.626755 q^{44} +0.539493 q^{45} -9.59366 q^{46} -1.42862 q^{47} -3.68464 q^{48} -6.99811 q^{49} -4.72868 q^{50} -3.53817 q^{51} -3.44249 q^{53} -6.51119 q^{54} +0.982237 q^{55} -0.133915 q^{56} +9.60582 q^{57} +1.29005 q^{58} +0.0231303 q^{59} +0.963748 q^{60} -1.45213 q^{61} -4.39151 q^{62} -0.0238949 q^{63} +8.68953 q^{64} -1.83452 q^{66} -13.3099 q^{67} +1.41653 q^{68} -12.8162 q^{69} -0.0500755 q^{70} +5.68444 q^{71} +1.69069 q^{72} -0.514699 q^{73} -6.68746 q^{74} -6.31707 q^{75} -3.84577 q^{76} -0.0435046 q^{77} -7.51760 q^{79} +2.31186 q^{80} -7.05058 q^{81} +1.70098 q^{82} +5.62195 q^{83} -0.0426857 q^{84} +2.21996 q^{85} +1.41431 q^{86} +1.72339 q^{87} +3.07818 q^{88} +13.0459 q^{89} +0.632208 q^{90} +5.13107 q^{92} -5.86663 q^{93} -1.67413 q^{94} -6.02700 q^{95} +5.31983 q^{96} +9.03968 q^{97} -8.20077 q^{98} +0.549249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9	\( 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9} - 8 q^{10} - 9 q^{11} - 9 q^{12} - 3 q^{15} - 8 q^{16} - 8 q^{17} - 27 q^{18} + q^{19} - 12 q^{20} - 17 q^{21} + 6 q^{24} - 15 q^{25} - 23 q^{27} - 11 q^{28} - 22 q^{29} - 3 q^{30} + 6 q^{31} + 19 q^{32} + 5 q^{33} - 10 q^{34} - 15 q^{35} + 7 q^{36} + 15 q^{37} + q^{38} - 3 q^{40} - 10 q^{41} + 2 q^{42} - 19 q^{43} - 2 q^{44} + 2 q^{45} - 19 q^{46} + 2 q^{47} + 6 q^{48} - 20 q^{49} + 17 q^{50} - 2 q^{51} - 5 q^{53} + 27 q^{54} - 4 q^{55} - 16 q^{56} + 32 q^{57} + 11 q^{58} + 11 q^{59} + 6 q^{60} - 68 q^{61} - 21 q^{62} + 29 q^{63} - 23 q^{64} - 11 q^{66} - 5 q^{67} + 16 q^{68} - 34 q^{69} + 5 q^{70} + 34 q^{71} - 13 q^{72} - 26 q^{73} + q^{74} + 10 q^{75} + 11 q^{76} + q^{77} - 32 q^{79} - 8 q^{80} + 13 q^{81} - 42 q^{82} - 8 q^{83} + 13 q^{84} - 23 q^{85} - 30 q^{86} + 10 q^{87} + 3 q^{88} + 37 q^{89} + 21 q^{90} - 12 q^{92} - 20 q^{93} - 12 q^{94} - 4 q^{95} - 60 q^{96} - 3 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9 - 8 * q^10 - 9 * q^11 - 9 * q^12 - 3 * q^15 - 8 * q^16 - 8 * q^17 - 27 * q^18 + q^19 - 12 * q^20 - 17 * q^21 + 6 * q^24 - 15 * q^25 - 23 * q^27 - 11 * q^28 - 22 * q^29 - 3 * q^30 + 6 * q^31 + 19 * q^32 + 5 * q^33 - 10 * q^34 - 15 * q^35 + 7 * q^36 + 15 * q^37 + q^38 - 3 * q^40 - 10 * q^41 + 2 * q^42 - 19 * q^43 - 2 * q^44 + 2 * q^45 - 19 * q^46 + 2 * q^47 + 6 * q^48 - 20 * q^49 + 17 * q^50 - 2 * q^51 - 5 * q^53 + 27 * q^54 - 4 * q^55 - 16 * q^56 + 32 * q^57 + 11 * q^58 + 11 * q^59 + 6 * q^60 - 68 * q^61 - 21 * q^62 + 29 * q^63 - 23 * q^64 - 11 * q^66 - 5 * q^67 + 16 * q^68 - 34 * q^69 + 5 * q^70 + 34 * q^71 - 13 * q^72 - 26 * q^73 + q^74 + 10 * q^75 + 11 * q^76 + q^77 - 32 * q^79 - 8 * q^80 + 13 * q^81 - 42 * q^82 - 8 * q^83 + 13 * q^84 - 23 * q^85 - 30 * q^86 + 10 * q^87 + 3 * q^88 + 37 * q^89 + 21 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^94 - 4 * q^95 - 60 * q^96 - 3 * q^97 + 9 * q^98 - 2 * q^99

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