LMFDB - Embedded newform 1690.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(1,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, 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("1690.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.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:	$13.4947179416$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.20439713.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 15x^{4} + 22x^{3} + 70x^{2} - 56x - 91 $ x^6 - 2x^5 - 15x^4 + 22x^3 + 70x^2 - 56*x - 91
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.79223$ of defining polynomial
Character	$\chi$	$=$	1690.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.79223 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79223 q^{6} +4.83875 q^{7} -1.00000 q^{8} +4.79655 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.79223 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79223 q^{6} +4.83875 q^{7} -1.00000 q^{8} +4.79655 q^{9} +1.00000 q^{10} -4.34911 q^{11} -2.79223 q^{12} -4.83875 q^{14} +2.79223 q^{15} +1.00000 q^{16} -5.73315 q^{17} -4.79655 q^{18} +0.986828 q^{19} -1.00000 q^{20} -13.5109 q^{21} +4.34911 q^{22} -0.818363 q^{23} +2.79223 q^{24} +1.00000 q^{25} -5.01638 q^{27} +4.83875 q^{28} +5.85325 q^{29} -2.79223 q^{30} +5.36463 q^{31} -1.00000 q^{32} +12.1437 q^{33} +5.73315 q^{34} -4.83875 q^{35} +4.79655 q^{36} -10.9443 q^{37} -0.986828 q^{38} +1.00000 q^{40} +2.23727 q^{41} +13.5109 q^{42} -1.98362 q^{43} -4.34911 q^{44} -4.79655 q^{45} +0.818363 q^{46} -0.820497 q^{47} -2.79223 q^{48} +16.4135 q^{49} -1.00000 q^{50} +16.0083 q^{51} +8.57238 q^{53} +5.01638 q^{54} +4.34911 q^{55} -4.83875 q^{56} -2.75545 q^{57} -5.85325 q^{58} -7.91612 q^{59} +2.79223 q^{60} +11.7202 q^{61} -5.36463 q^{62} +23.2093 q^{63} +1.00000 q^{64} -12.1437 q^{66} -3.10640 q^{67} -5.73315 q^{68} +2.28506 q^{69} +4.83875 q^{70} -4.17629 q^{71} -4.79655 q^{72} -2.56706 q^{73} +10.9443 q^{74} -2.79223 q^{75} +0.986828 q^{76} -21.0443 q^{77} -1.21853 q^{79} -1.00000 q^{80} -0.382754 q^{81} -2.23727 q^{82} -15.6103 q^{83} -13.5109 q^{84} +5.73315 q^{85} +1.98362 q^{86} -16.3436 q^{87} +4.34911 q^{88} +8.81888 q^{89} +4.79655 q^{90} -0.818363 q^{92} -14.9793 q^{93} +0.820497 q^{94} -0.986828 q^{95} +2.79223 q^{96} -10.1921 q^{97} -16.4135 q^{98} -20.8607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 16 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 16 * q^9	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 16 q^{9} + 6 q^{10} - 15 q^{11} - 2 q^{12} + 3 q^{14} + 2 q^{15} + 6 q^{16} - 3 q^{17} - 16 q^{18} - q^{19} - 6 q^{20} + 2 q^{21} + 15 q^{22} - 3 q^{23} + 2 q^{24} + 6 q^{25} - 20 q^{27} - 3 q^{28} + 7 q^{29} - 2 q^{30} - 6 q^{32} - 4 q^{33} + 3 q^{34} + 3 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 6 q^{40} - 2 q^{41} - 2 q^{42} - 22 q^{43} - 15 q^{44} - 16 q^{45} + 3 q^{46} - 7 q^{47} - 2 q^{48} + 31 q^{49} - 6 q^{50} - 22 q^{51} - 16 q^{53} + 20 q^{54} + 15 q^{55} + 3 q^{56} - 2 q^{57} - 7 q^{58} - 15 q^{59} + 2 q^{60} + 33 q^{61} - 25 q^{63} + 6 q^{64} + 4 q^{66} + 8 q^{67} - 3 q^{68} - 6 q^{69} - 3 q^{70} - 40 q^{71} - 16 q^{72} - 21 q^{73} + 6 q^{74} - 2 q^{75} - q^{76} - 34 q^{77} + 20 q^{79} - 6 q^{80} - 2 q^{81} + 2 q^{82} - 22 q^{83} + 2 q^{84} + 3 q^{85} + 22 q^{86} - 39 q^{87} + 15 q^{88} - 20 q^{89} + 16 q^{90} - 3 q^{92} - 48 q^{93} + 7 q^{94} + q^{95} + 2 q^{96} + 7 q^{97} - 31 q^{98} - 55 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 16 * q^9 + 6 * q^10 - 15 * q^11 - 2 * q^12 + 3 * q^14 + 2 * q^15 + 6 * q^16 - 3 * q^17 - 16 * q^18 - q^19 - 6 * q^20 + 2 * q^21 + 15 * q^22 - 3 * q^23 + 2 * q^24 + 6 * q^25 - 20 * q^27 - 3 * q^28 + 7 * q^29 - 2 * q^30 - 6 * q^32 - 4 * q^33 + 3 * q^34 + 3 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 6 * q^40 - 2 * q^41 - 2 * q^42 - 22 * q^43 - 15 * q^44 - 16 * q^45 + 3 * q^46 - 7 * q^47 - 2 * q^48 + 31 * q^49 - 6 * q^50 - 22 * q^51 - 16 * q^53 + 20 * q^54 + 15 * q^55 + 3 * q^56 - 2 * q^57 - 7 * q^58 - 15 * q^59 + 2 * q^60 + 33 * q^61 - 25 * q^63 + 6 * q^64 + 4 * q^66 + 8 * q^67 - 3 * q^68 - 6 * q^69 - 3 * q^70 - 40 * q^71 - 16 * q^72 - 21 * q^73 + 6 * q^74 - 2 * q^75 - q^76 - 34 * q^77 + 20 * q^79 - 6 * q^80 - 2 * q^81 + 2 * q^82 - 22 * q^83 + 2 * q^84 + 3 * q^85 + 22 * q^86 - 39 * q^87 + 15 * q^88 - 20 * q^89 + 16 * q^90 - 3 * q^92 - 48 * q^93 + 7 * q^94 + q^95 + 2 * q^96 + 7 * q^97 - 31 * q^98 - 55 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.79223	−1.61209	−0.806047	−	0.591851i	$-0.798397\pi$
$3$	−2.79223	−1.61209	−0.806047	+	0.591851i	$0.798397\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.79223	1.13992
$7$	4.83875	1.82888	0.914438	−	0.404726i	$-0.132633\pi$
$7$	4.83875	1.82888	0.914438	+	0.404726i	$0.132633\pi$
$8$	−1.00000	−0.353553
$9$	4.79655	1.59885
$10$	1.00000	0.316228
$11$	−4.34911	−1.31131	−0.655653	−	0.755062i	$-0.727607\pi$
$11$	−4.34911	−1.31131	−0.655653	+	0.755062i	$0.727607\pi$
$12$	−2.79223	−0.806047
$13$	0	0
$13$	0	0
$14$	−4.83875	−1.29321
$15$	2.79223	0.720951
$16$	1.00000	0.250000
$17$	−5.73315	−1.39049	−0.695247	−	0.718771i	$-0.744705\pi$
$17$	−5.73315	−1.39049	−0.695247	+	0.718771i	$0.744705\pi$
$18$	−4.79655	−1.13056
$19$	0.986828	0.226394	0.113197	−	0.993573i	$-0.463891\pi$
$19$	0.986828	0.226394	0.113197	+	0.993573i	$0.463891\pi$
$20$	−1.00000	−0.223607
$21$	−13.5109	−2.94832
$22$	4.34911	0.927234
$23$	−0.818363	−0.170640	−0.0853202	−	0.996354i	$-0.527191\pi$
$23$	−0.818363	−0.170640	−0.0853202	+	0.996354i	$0.527191\pi$
$24$	2.79223	0.569962
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.01638	−0.965403
$28$	4.83875	0.914438
$29$	5.85325	1.08692	0.543461	−	0.839435i	$-0.317114\pi$
$29$	5.85325	1.08692	0.543461	+	0.839435i	$0.317114\pi$
$30$	−2.79223	−0.509789
$31$	5.36463	0.963516	0.481758	−	0.876304i	$-0.339998\pi$
$31$	5.36463	0.963516	0.481758	+	0.876304i	$0.339998\pi$
$32$	−1.00000	−0.176777
$33$	12.1437	2.11395
$34$	5.73315	0.983228
$35$	−4.83875	−0.817898
$36$	4.79655	0.799425
$37$	−10.9443	−1.79923	−0.899615	−	0.436683i	$-0.856153\pi$
$37$	−10.9443	−1.79923	−0.899615	+	0.436683i	$0.856153\pi$
$38$	−0.986828	−0.160085
$39$	0	0
$40$	1.00000	0.158114
$41$	2.23727	0.349403	0.174702	−	0.984621i	$-0.444104\pi$
$41$	2.23727	0.349403	0.174702	+	0.984621i	$0.444104\pi$
$42$	13.5109	2.08478
$43$	−1.98362	−0.302499	−0.151249	−	0.988496i	$-0.548330\pi$
$43$	−1.98362	−0.302499	−0.151249	+	0.988496i	$0.548330\pi$
$44$	−4.34911	−0.655653
$45$	−4.79655	−0.715028
$46$	0.818363	0.120661
$47$	−0.820497	−0.119682	−0.0598409	−	0.998208i	$-0.519059\pi$
$47$	−0.820497	−0.119682	−0.0598409	+	0.998208i	$0.519059\pi$
$48$	−2.79223	−0.403024
$49$	16.4135	2.34479
$50$	−1.00000	−0.141421
$51$	16.0083	2.24161
$52$	0	0
$53$	8.57238	1.17751	0.588753	−	0.808313i	$-0.299619\pi$
$53$	8.57238	1.17751	0.588753	+	0.808313i	$0.299619\pi$
$54$	5.01638	0.682643
$55$	4.34911	0.586434
$56$	−4.83875	−0.646605
$57$	−2.75545	−0.364968
$58$	−5.85325	−0.768570
$59$	−7.91612	−1.03059	−0.515296	−	0.857012i	$-0.672318\pi$
$59$	−7.91612	−1.03059	−0.515296	+	0.857012i	$0.672318\pi$
$60$	2.79223	0.360475
$61$	11.7202	1.50062	0.750309	−	0.661088i	$-0.229905\pi$
$61$	11.7202	1.50062	0.750309	+	0.661088i	$0.229905\pi$
$62$	−5.36463	−0.681308
$63$	23.2093	2.92410
$64$	1.00000	0.125000
$65$	0	0
$66$	−12.1437	−1.49479
$67$	−3.10640	−0.379507	−0.189754	−	0.981832i	$-0.560769\pi$
$67$	−3.10640	−0.379507	−0.189754	+	0.981832i	$0.560769\pi$
$68$	−5.73315	−0.695247
$69$	2.28506	0.275089
$70$	4.83875	0.578341
$71$	−4.17629	−0.495635	−0.247817	−	0.968807i	$-0.579713\pi$
$71$	−4.17629	−0.495635	−0.247817	+	0.968807i	$0.579713\pi$
$72$	−4.79655	−0.565279
$73$	−2.56706	−0.300452	−0.150226	−	0.988652i	$-0.548000\pi$
$73$	−2.56706	−0.300452	−0.150226	+	0.988652i	$0.548000\pi$
$74$	10.9443	1.27225
$75$	−2.79223	−0.322419
$76$	0.986828	0.113197
$77$	−21.0443	−2.39822
$78$	0	0
$79$	−1.21853	−0.137095	−0.0685474	−	0.997648i	$-0.521836\pi$
$79$	−1.21853	−0.137095	−0.0685474	+	0.997648i	$0.521836\pi$
$80$	−1.00000	−0.111803
$81$	−0.382754	−0.0425283
$82$	−2.23727	−0.247065
$83$	−15.6103	−1.71345	−0.856727	−	0.515771i	$-0.827506\pi$
$83$	−15.6103	−1.71345	−0.856727	+	0.515771i	$0.827506\pi$
$84$	−13.5109	−1.47416
$85$	5.73315	0.621848
$86$	1.98362	0.213899
$87$	−16.3436	−1.75222
$88$	4.34911	0.463617
$89$	8.81888	0.934800	0.467400	−	0.884046i	$-0.345191\pi$
$89$	8.81888	0.934800	0.467400	+	0.884046i	$0.345191\pi$
$90$	4.79655	0.505601
$91$	0	0
$92$	−0.818363	−0.0853202
$93$	−14.9793	−1.55328
$94$	0.820497	0.0846278
$95$	−0.986828	−0.101246
$96$	2.79223	0.284981
$97$	−10.1921	−1.03485	−0.517427	−	0.855727i	$-0.673110\pi$
$97$	−10.1921	−1.03485	−0.517427	+	0.855727i	$0.673110\pi$
$98$	−16.4135	−1.65801
$99$	−20.8607	−2.09658
$100$	1.00000	0.100000
$101$	−9.95828	−0.990886	−0.495443	−	0.868640i	$-0.664994\pi$
$101$	−9.95828	−0.990886	−0.495443	+	0.868640i	$0.664994\pi$
$102$	−16.0083	−1.58506
$103$	3.93789	0.388012	0.194006	−	0.981000i	$-0.437852\pi$
$103$	3.93789	0.388012	0.194006	+	0.981000i	$0.437852\pi$
$104$	0	0
$105$	13.5109	1.31853
$106$	−8.57238	−0.832623
$107$	−5.22223	−0.504852	−0.252426	−	0.967616i	$-0.581228\pi$
$107$	−5.22223	−0.504852	−0.252426	+	0.967616i	$0.581228\pi$
$108$	−5.01638	−0.482702
$109$	−17.8158	−1.70645	−0.853223	−	0.521547i	$-0.825355\pi$
$109$	−17.8158	−1.70645	−0.853223	+	0.521547i	$0.825355\pi$
$110$	−4.34911	−0.414671
$111$	30.5590	2.90053
$112$	4.83875	0.457219
$113$	7.67687	0.722180	0.361090	−	0.932531i	$-0.382405\pi$
$113$	7.67687	0.722180	0.361090	+	0.932531i	$0.382405\pi$
$114$	2.75545	0.258072
$115$	0.818363	0.0763127
$116$	5.85325	0.543461
$117$	0	0
$118$	7.91612	0.728738
$119$	−27.7413	−2.54304
$120$	−2.79223	−0.254895
$121$	7.91477	0.719524
$122$	−11.7202	−1.06110
$123$	−6.24698	−0.563271
$124$	5.36463	0.481758
$125$	−1.00000	−0.0894427
$126$	−23.2093	−2.06765
$127$	−14.1753	−1.25786	−0.628928	−	0.777463i	$-0.716506\pi$
$127$	−14.1753	−1.25786	−0.628928	+	0.777463i	$0.716506\pi$
$128$	−1.00000	−0.0883883
$129$	5.53872	0.487657
$130$	0	0
$131$	−0.495003	−0.0432486	−0.0216243	−	0.999766i	$-0.506884\pi$
$131$	−0.495003	−0.0432486	−0.0216243	+	0.999766i	$0.506884\pi$
$132$	12.1437	1.05698
$133$	4.77501	0.414046
$134$	3.10640	0.268352
$135$	5.01638	0.431742
$136$	5.73315	0.491614
$137$	−6.56322	−0.560734	−0.280367	−	0.959893i	$-0.590456\pi$
$137$	−6.56322	−0.560734	−0.280367	+	0.959893i	$0.590456\pi$
$138$	−2.28506	−0.194517
$139$	−1.34178	−0.113808	−0.0569041	−	0.998380i	$-0.518123\pi$
$139$	−1.34178	−0.113808	−0.0569041	+	0.998380i	$0.518123\pi$
$140$	−4.83875	−0.408949
$141$	2.29102	0.192938
$142$	4.17629	0.350467
$143$	0	0
$144$	4.79655	0.399713
$145$	−5.85325	−0.486086
$146$	2.56706	0.212452
$147$	−45.8303	−3.78002
$148$	−10.9443	−0.899615
$149$	17.5781	1.44006	0.720028	−	0.693945i	$-0.244129\pi$
$149$	17.5781	1.44006	0.720028	+	0.693945i	$0.244129\pi$
$150$	2.79223	0.227985
$151$	−7.27761	−0.592244	−0.296122	−	0.955150i	$-0.595693\pi$
$151$	−7.27761	−0.592244	−0.296122	+	0.955150i	$0.595693\pi$
$152$	−0.986828	−0.0800423
$153$	−27.4994	−2.22319
$154$	21.0443	1.69580
$155$	−5.36463	−0.430897
$156$	0	0
$157$	1.37061	0.109386	0.0546932	−	0.998503i	$-0.482582\pi$
$157$	1.37061	0.109386	0.0546932	+	0.998503i	$0.482582\pi$
$158$	1.21853	0.0969407
$159$	−23.9361	−1.89825
$160$	1.00000	0.0790569
$161$	−3.95985	−0.312080
$162$	0.382754	0.0300720
$163$	−25.2531	−1.97798	−0.988989	−	0.147989i	$-0.952720\pi$
$163$	−25.2531	−1.97798	−0.988989	+	0.147989i	$0.952720\pi$
$164$	2.23727	0.174702
$165$	−12.1437	−0.945387
$166$	15.6103	1.21159
$167$	5.49833	0.425474	0.212737	−	0.977110i	$-0.431762\pi$
$167$	5.49833	0.425474	0.212737	+	0.977110i	$0.431762\pi$
$168$	13.5109	1.04239
$169$	0	0
$170$	−5.73315	−0.439713
$171$	4.73337	0.361970
$172$	−1.98362	−0.151249
$173$	3.86243	0.293655	0.146828	−	0.989162i	$-0.453094\pi$
$173$	3.86243	0.293655	0.146828	+	0.989162i	$0.453094\pi$
$174$	16.3436	1.23901
$175$	4.83875	0.365775
$176$	−4.34911	−0.327827
$177$	22.1036	1.66141
$178$	−8.81888	−0.661003
$179$	−11.4902	−0.858815	−0.429408	−	0.903111i	$-0.641278\pi$
$179$	−11.4902	−0.858815	−0.429408	+	0.903111i	$0.641278\pi$
$180$	−4.79655	−0.357514
$181$	−6.63546	−0.493210	−0.246605	−	0.969116i	$-0.579315\pi$
$181$	−6.63546	−0.493210	−0.246605	+	0.969116i	$0.579315\pi$
$182$	0	0
$183$	−32.7255	−2.41914
$184$	0.818363	0.0603305
$185$	10.9443	0.804640
$186$	14.9793	1.09833
$187$	24.9341	1.82336
$188$	−0.820497	−0.0598409
$189$	−24.2730	−1.76560
$190$	0.986828	0.0715920
$191$	−13.8151	−0.999627	−0.499813	−	0.866133i	$-0.666598\pi$
$191$	−13.8151	−0.999627	−0.499813	+	0.866133i	$0.666598\pi$
$192$	−2.79223	−0.201512
$193$	−13.3454	−0.960620	−0.480310	−	0.877099i	$-0.659476\pi$
$193$	−13.3454	−0.960620	−0.480310	+	0.877099i	$0.659476\pi$
$194$	10.1921	0.731752
$195$	0	0
$196$	16.4135	1.17239
$197$	10.8185	0.770783	0.385391	−	0.922753i	$-0.374066\pi$
$197$	10.8185	0.770783	0.385391	+	0.922753i	$0.374066\pi$
$198$	20.8607	1.48251
$199$	0.0483356	0.00342642	0.00171321	−	0.999999i	$-0.499455\pi$
$199$	0.0483356	0.00342642	0.00171321	+	0.999999i	$0.499455\pi$
$200$	−1.00000	−0.0707107
$201$	8.67378	0.611801
$202$	9.95828	0.700662
$203$	28.3224	1.98784
$204$	16.0083	1.12080
$205$	−2.23727	−0.156258
$206$	−3.93789	−0.274366
$207$	−3.92532	−0.272828
$208$	0	0
$209$	−4.29183	−0.296872
$210$	−13.5109	−0.932341
$211$	−10.5000	−0.722850	−0.361425	−	0.932401i	$-0.617710\pi$
$211$	−10.5000	−0.722850	−0.361425	+	0.932401i	$0.617710\pi$
$212$	8.57238	0.588753
$213$	11.6612	0.799010
$214$	5.22223	0.356984
$215$	1.98362	0.135282
$216$	5.01638	0.341322
$217$	25.9581	1.76215
$218$	17.8158	1.20664
$219$	7.16783	0.484357
$220$	4.34911	0.293217
$221$	0	0
$222$	−30.5590	−2.05099
$223$	−12.4160	−0.831440	−0.415720	−	0.909493i	$-0.636470\pi$
$223$	−12.4160	−0.831440	−0.415720	+	0.909493i	$0.636470\pi$
$224$	−4.83875	−0.323303
$225$	4.79655	0.319770
$226$	−7.67687	−0.510658
$227$	−7.60172	−0.504544	−0.252272	−	0.967656i	$-0.581178\pi$
$227$	−7.60172	−0.504544	−0.252272	+	0.967656i	$0.581178\pi$
$228$	−2.75545	−0.182484
$229$	−20.9604	−1.38510	−0.692551	−	0.721369i	$-0.743513\pi$
$229$	−20.9604	−1.38510	−0.692551	+	0.721369i	$0.743513\pi$
$230$	−0.818363	−0.0539612
$231$	58.7604	3.86615
$232$	−5.85325	−0.384285
$233$	23.8446	1.56211	0.781056	−	0.624461i	$-0.214682\pi$
$233$	23.8446	1.56211	0.781056	+	0.624461i	$0.214682\pi$
$234$	0	0
$235$	0.820497	0.0535233
$236$	−7.91612	−0.515296
$237$	3.40240	0.221010
$238$	27.7413	1.79820
$239$	1.71728	0.111082	0.0555408	−	0.998456i	$-0.482312\pi$
$239$	1.71728	0.111082	0.0555408	+	0.998456i	$0.482312\pi$
$240$	2.79223	0.180238
$241$	15.7821	1.01661	0.508306	−	0.861176i	$-0.330272\pi$
$241$	15.7821	1.01661	0.508306	+	0.861176i	$0.330272\pi$
$242$	−7.91477	−0.508781
$243$	16.1179	1.03396
$244$	11.7202	0.750309
$245$	−16.4135	−1.04862
$246$	6.24698	0.398293
$247$	0	0
$248$	−5.36463	−0.340654
$249$	43.5876	2.76225
$250$	1.00000	0.0632456
$251$	3.51609	0.221933	0.110967	−	0.993824i	$-0.464605\pi$
$251$	3.51609	0.221933	0.110967	+	0.993824i	$0.464605\pi$
$252$	23.2093	1.46205
$253$	3.55915	0.223762
$254$	14.1753	0.889439
$255$	−16.0083	−1.00248
$256$	1.00000	0.0625000
$257$	0.123004	0.00767279	0.00383640	−	0.999993i	$-0.498779\pi$
$257$	0.123004	0.00767279	0.00383640	+	0.999993i	$0.498779\pi$
$258$	−5.53872	−0.344825
$259$	−52.9567	−3.29057
$260$	0	0
$261$	28.0754	1.73782
$262$	0.495003	0.0305814
$263$	−20.0185	−1.23439	−0.617197	−	0.786809i	$-0.711732\pi$
$263$	−20.0185	−1.23439	−0.617197	+	0.786809i	$0.711732\pi$
$264$	−12.1437	−0.747394
$265$	−8.57238	−0.526597
$266$	−4.77501	−0.292775
$267$	−24.6244	−1.50699
$268$	−3.10640	−0.189754
$269$	−4.02090	−0.245159	−0.122579	−	0.992459i	$-0.539117\pi$
$269$	−4.02090	−0.245159	−0.122579	+	0.992459i	$0.539117\pi$
$270$	−5.01638	−0.305287
$271$	−17.7684	−1.07935	−0.539677	−	0.841872i	$-0.681454\pi$
$271$	−17.7684	−1.07935	−0.539677	+	0.841872i	$0.681454\pi$
$272$	−5.73315	−0.347624
$273$	0	0
$274$	6.56322	0.396498
$275$	−4.34911	−0.262261
$276$	2.28506	0.137544
$277$	−24.5192	−1.47322	−0.736608	−	0.676320i	$-0.763574\pi$
$277$	−24.5192	−1.47322	−0.736608	+	0.676320i	$0.763574\pi$
$278$	1.34178	0.0804745
$279$	25.7317	1.54052
$280$	4.83875	0.289171
$281$	18.4233	1.09904	0.549520	−	0.835480i	$-0.314811\pi$
$281$	18.4233	1.09904	0.549520	+	0.835480i	$0.314811\pi$
$282$	−2.29102	−0.136428
$283$	4.07792	0.242407	0.121203	−	0.992628i	$-0.461325\pi$
$283$	4.07792	0.242407	0.121203	+	0.992628i	$0.461325\pi$
$284$	−4.17629	−0.247817
$285$	2.75545	0.163219
$286$	0	0
$287$	10.8256	0.639015
$288$	−4.79655	−0.282639
$289$	15.8691	0.933474
$290$	5.85325	0.343715
$291$	28.4588	1.66828
$292$	−2.56706	−0.150226
$293$	−1.65614	−0.0967527	−0.0483764	−	0.998829i	$-0.515405\pi$
$293$	−1.65614	−0.0967527	−0.0483764	+	0.998829i	$0.515405\pi$
$294$	45.8303	2.67288
$295$	7.91612	0.460894
$296$	10.9443	0.636124
$297$	21.8168	1.26594
$298$	−17.5781	−1.01827
$299$	0	0
$300$	−2.79223	−0.161209
$301$	−9.59823	−0.553233
$302$	7.27761	0.418780
$303$	27.8058	1.59740
$304$	0.986828	0.0565985
$305$	−11.7202	−0.671096
$306$	27.4994	1.57203
$307$	24.0562	1.37296	0.686479	−	0.727150i	$-0.259156\pi$
$307$	24.0562	1.37296	0.686479	+	0.727150i	$0.259156\pi$
$308$	−21.0443	−1.19911
$309$	−10.9955	−0.625512
$310$	5.36463	0.304690
$311$	−22.6981	−1.28709	−0.643545	−	0.765408i	$-0.722537\pi$
$311$	−22.6981	−1.28709	−0.643545	+	0.765408i	$0.722537\pi$
$312$	0	0
$313$	−10.3916	−0.587368	−0.293684	−	0.955903i	$-0.594881\pi$
$313$	−10.3916	−0.587368	−0.293684	+	0.955903i	$0.594881\pi$
$314$	−1.37061	−0.0773479
$315$	−23.2093	−1.30770
$316$	−1.21853	−0.0685474
$317$	−31.5378	−1.77134	−0.885671	−	0.464313i	$-0.846301\pi$
$317$	−31.5378	−1.77134	−0.885671	+	0.464313i	$0.846301\pi$
$318$	23.9361	1.34227
$319$	−25.4564	−1.42529
$320$	−1.00000	−0.0559017
$321$	14.5817	0.813869
$322$	3.95985	0.220674
$323$	−5.65764	−0.314799
$324$	−0.382754	−0.0212641
$325$	0	0
$326$	25.2531	1.39864
$327$	49.7458	2.75095
$328$	−2.23727	−0.123533
$329$	−3.97018	−0.218883
$330$	12.1437	0.668490
$331$	6.05592	0.332864	0.166432	−	0.986053i	$-0.446775\pi$
$331$	6.05592	0.332864	0.166432	+	0.986053i	$0.446775\pi$
$332$	−15.6103	−0.856727
$333$	−52.4949	−2.87670
$334$	−5.49833	−0.300855
$335$	3.10640	0.169721
$336$	−13.5109	−0.737080
$337$	−23.1282	−1.25988	−0.629938	−	0.776645i	$-0.716920\pi$
$337$	−23.1282	−1.25988	−0.629938	+	0.776645i	$0.716920\pi$
$338$	0	0
$339$	−21.4356	−1.16422
$340$	5.73315	0.310924
$341$	−23.3314	−1.26346
$342$	−4.73337	−0.255951
$343$	45.5496	2.45945
$344$	1.98362	0.106949
$345$	−2.28506	−0.123023
$346$	−3.86243	−0.207646
$347$	−23.3243	−1.25211	−0.626057	−	0.779777i	$-0.715332\pi$
$347$	−23.3243	−1.25211	−0.626057	+	0.779777i	$0.715332\pi$
$348$	−16.3436	−0.876111
$349$	−16.7136	−0.894661	−0.447331	−	0.894369i	$-0.647625\pi$
$349$	−16.7136	−0.894661	−0.447331	+	0.894369i	$0.647625\pi$
$350$	−4.83875	−0.258642
$351$	0	0
$352$	4.34911	0.231808
$353$	7.13055	0.379521	0.189760	−	0.981830i	$-0.439229\pi$
$353$	7.13055	0.379521	0.189760	+	0.981830i	$0.439229\pi$
$354$	−22.1036	−1.17480
$355$	4.17629	0.221655
$356$	8.81888	0.467400
$357$	77.4601	4.09962
$358$	11.4902	0.607274
$359$	−14.3154	−0.755541	−0.377770	−	0.925899i	$-0.623309\pi$
$359$	−14.3154	−0.755541	−0.377770	+	0.925899i	$0.623309\pi$
$360$	4.79655	0.252800
$361$	−18.0262	−0.948746
$362$	6.63546	0.348752
$363$	−22.0999	−1.15994
$364$	0	0
$365$	2.56706	0.134366
$366$	32.7255	1.71059
$367$	11.2749	0.588543	0.294271	−	0.955722i	$-0.404923\pi$
$367$	11.2749	0.588543	0.294271	+	0.955722i	$0.404923\pi$
$368$	−0.818363	−0.0426601
$369$	10.7312	0.558643
$370$	−10.9443	−0.568967
$371$	41.4796	2.15351
$372$	−14.9793	−0.776639
$373$	9.48572	0.491152	0.245576	−	0.969377i	$-0.421023\pi$
$373$	9.48572	0.491152	0.245576	+	0.969377i	$0.421023\pi$
$374$	−24.9341	−1.28931
$375$	2.79223	0.144190
$376$	0.820497	0.0423139
$377$	0	0
$378$	24.2730	1.24847
$379$	−0.0811125	−0.00416647	−0.00208323	−	0.999998i	$-0.500663\pi$
$379$	−0.0811125	−0.00416647	−0.00208323	+	0.999998i	$0.500663\pi$
$380$	−0.986828	−0.0506232
$381$	39.5808	2.02778
$382$	13.8151	0.706843
$383$	−28.8487	−1.47410	−0.737050	−	0.675838i	$-0.763782\pi$
$383$	−28.8487	−1.47410	−0.737050	+	0.675838i	$0.763782\pi$
$384$	2.79223	0.142490
$385$	21.0443	1.07251
$386$	13.3454	0.679261
$387$	−9.51452	−0.483650
$388$	−10.1921	−0.517427
$389$	22.1338	1.12223	0.561113	−	0.827739i	$-0.310373\pi$
$389$	22.1338	1.12223	0.561113	+	0.827739i	$0.310373\pi$
$390$	0	0
$391$	4.69180	0.237275
$392$	−16.4135	−0.829007
$393$	1.38216	0.0697209
$394$	−10.8185	−0.545026
$395$	1.21853	0.0613107
$396$	−20.8607	−1.04829
$397$	23.7326	1.19111	0.595553	−	0.803316i	$-0.296933\pi$
$397$	23.7326	1.19111	0.595553	+	0.803316i	$0.296933\pi$
$398$	−0.0483356	−0.00242284
$399$	−13.3329	−0.667482
$400$	1.00000	0.0500000
$401$	5.69046	0.284168	0.142084	−	0.989855i	$-0.454620\pi$
$401$	5.69046	0.284168	0.142084	+	0.989855i	$0.454620\pi$
$402$	−8.67378	−0.432609
$403$	0	0
$404$	−9.95828	−0.495443
$405$	0.382754	0.0190192
$406$	−28.3224	−1.40562
$407$	47.5980	2.35934
$408$	−16.0083	−0.792528
$409$	0.542111	0.0268056	0.0134028	−	0.999910i	$-0.495734\pi$
$409$	0.542111	0.0268056	0.0134028	+	0.999910i	$0.495734\pi$
$410$	2.23727	0.110491
$411$	18.3260	0.903956
$412$	3.93789	0.194006
$413$	−38.3041	−1.88482
$414$	3.92532	0.192919
$415$	15.6103	0.766280
$416$	0	0
$417$	3.74655	0.183470
$418$	4.29183	0.209920
$419$	28.8020	1.40707	0.703534	−	0.710661i	$-0.251604\pi$
$419$	28.8020	1.40707	0.703534	+	0.710661i	$0.251604\pi$
$420$	13.5109	0.659265
$421$	14.5843	0.710797	0.355398	−	0.934715i	$-0.384345\pi$
$421$	14.5843	0.710797	0.355398	+	0.934715i	$0.384345\pi$
$422$	10.5000	0.511132
$423$	−3.93555	−0.191353
$424$	−8.57238	−0.416312
$425$	−5.73315	−0.278099
$426$	−11.6612	−0.564986
$427$	56.7111	2.74444
$428$	−5.22223	−0.252426
$429$	0	0
$430$	−1.98362	−0.0956585
$431$	−25.3507	−1.22110	−0.610551	−	0.791977i	$-0.709052\pi$
$431$	−25.3507	−1.22110	−0.610551	+	0.791977i	$0.709052\pi$
$432$	−5.01638	−0.241351
$433$	−34.2558	−1.64623	−0.823115	−	0.567875i	$-0.807766\pi$
$433$	−34.2558	−1.64623	−0.823115	+	0.567875i	$0.807766\pi$
$434$	−25.9581	−1.24603
$435$	16.3436	0.783617
$436$	−17.8158	−0.853223
$437$	−0.807583	−0.0386320
$438$	−7.16783	−0.342492
$439$	3.83723	0.183141	0.0915704	−	0.995799i	$-0.470811\pi$
$439$	3.83723	0.183141	0.0915704	+	0.995799i	$0.470811\pi$
$440$	−4.34911	−0.207336
$441$	78.7282	3.74896
$442$	0	0
$443$	30.9113	1.46864	0.734321	−	0.678803i	$-0.237501\pi$
$443$	30.9113	1.46864	0.734321	+	0.678803i	$0.237501\pi$
$444$	30.5590	1.45027
$445$	−8.81888	−0.418055
$446$	12.4160	0.587917
$447$	−49.0822	−2.32151
$448$	4.83875	0.228609
$449$	−3.65278	−0.172385	−0.0861926	−	0.996278i	$-0.527470\pi$
$449$	−3.65278	−0.172385	−0.0861926	+	0.996278i	$0.527470\pi$
$450$	−4.79655	−0.226112
$451$	−9.73015	−0.458175
$452$	7.67687	0.361090
$453$	20.3208	0.954753
$454$	7.60172	0.356767
$455$	0	0
$456$	2.75545	0.129036
$457$	35.5304	1.66204	0.831021	−	0.556241i	$-0.187757\pi$
$457$	35.5304	1.66204	0.831021	+	0.556241i	$0.187757\pi$
$458$	20.9604	0.979415
$459$	28.7597	1.34239
$460$	0.818363	0.0381564
$461$	−3.69279	−0.171991	−0.0859953	−	0.996296i	$-0.527407\pi$
$461$	−3.69279	−0.171991	−0.0859953	+	0.996296i	$0.527407\pi$
$462$	−58.7604	−2.73378
$463$	33.4951	1.55665	0.778324	−	0.627862i	$-0.216070\pi$
$463$	33.4951	1.55665	0.778324	+	0.627862i	$0.216070\pi$
$464$	5.85325	0.271730
$465$	14.9793	0.694647
$466$	−23.8446	−1.10458
$467$	12.4322	0.575294	0.287647	−	0.957736i	$-0.407127\pi$
$467$	12.4322	0.575294	0.287647	+	0.957736i	$0.407127\pi$
$468$	0	0
$469$	−15.0311	−0.694071
$470$	−0.820497	−0.0378467
$471$	−3.82705	−0.176341
$472$	7.91612	0.364369
$473$	8.62697	0.396669
$474$	−3.40240	−0.156278
$475$	0.986828	0.0452788
$476$	−27.7413	−1.27152
$477$	41.1179	1.88266
$478$	−1.71728	−0.0785465
$479$	−23.4645	−1.07212	−0.536060	−	0.844180i	$-0.680088\pi$
$479$	−23.4645	−1.07212	−0.536060	+	0.844180i	$0.680088\pi$
$480$	−2.79223	−0.127447
$481$	0	0
$482$	−15.7821	−0.718854
$483$	11.0568	0.503103
$484$	7.91477	0.359762
$485$	10.1921	0.462801
$486$	−16.1179	−0.731122
$487$	−19.3287	−0.875865	−0.437932	−	0.899008i	$-0.644289\pi$
$487$	−19.3287	−0.875865	−0.437932	+	0.899008i	$0.644289\pi$
$488$	−11.7202	−0.530548
$489$	70.5126	3.18869
$490$	16.4135	0.741487
$491$	−25.6544	−1.15777	−0.578884	−	0.815410i	$-0.696512\pi$
$491$	−25.6544	−1.15777	−0.578884	+	0.815410i	$0.696512\pi$
$492$	−6.24698	−0.281636
$493$	−33.5576	−1.51136
$494$	0	0
$495$	20.8607	0.937620
$496$	5.36463	0.240879
$497$	−20.2080	−0.906454
$498$	−43.5876	−1.95321
$499$	−23.7013	−1.06101	−0.530507	−	0.847681i	$-0.677998\pi$
$499$	−23.7013	−1.06101	−0.530507	+	0.847681i	$0.677998\pi$
$500$	−1.00000	−0.0447214
$501$	−15.3526	−0.685904
$502$	−3.51609	−0.156931
$503$	−3.31591	−0.147849	−0.0739245	−	0.997264i	$-0.523552\pi$
$503$	−3.31591	−0.147849	−0.0739245	+	0.997264i	$0.523552\pi$
$504$	−23.2093	−1.03382
$505$	9.95828	0.443138
$506$	−3.55915	−0.158224
$507$	0	0
$508$	−14.1753	−0.628928
$509$	0.593388	0.0263015	0.0131507	−	0.999914i	$-0.495814\pi$
$509$	0.593388	0.0263015	0.0131507	+	0.999914i	$0.495814\pi$
$510$	16.0083	0.708859
$511$	−12.4214	−0.549489
$512$	−1.00000	−0.0441942
$513$	−4.95031	−0.218561
$514$	−0.123004	−0.00542548
$515$	−3.93789	−0.173524
$516$	5.53872	0.243828
$517$	3.56843	0.156939
$518$	52.9567	2.32678
$519$	−10.7848	−0.473400
$520$	0	0
$521$	32.9877	1.44522	0.722608	−	0.691258i	$-0.242943\pi$
$521$	32.9877	1.44522	0.722608	+	0.691258i	$0.242943\pi$
$522$	−28.0754	−1.22883
$523$	26.9186	1.17707	0.588533	−	0.808473i	$-0.299706\pi$
$523$	26.9186	1.17707	0.588533	+	0.808473i	$0.299706\pi$
$524$	−0.495003	−0.0216243
$525$	−13.5109	−0.589664
$526$	20.0185	0.872848
$527$	−30.7562	−1.33976
$528$	12.1437	0.528488
$529$	−22.3303	−0.970882
$530$	8.57238	0.372360
$531$	−37.9701	−1.64776
$532$	4.77501	0.207023
$533$	0	0
$534$	24.6244	1.06560
$535$	5.22223	0.225777
$536$	3.10640	0.134176
$537$	32.0832	1.38449
$538$	4.02090	0.173353
$539$	−71.3842	−3.07473
$540$	5.01638	0.215871
$541$	−22.7819	−0.979469	−0.489735	−	0.871872i	$-0.662906\pi$
$541$	−22.7819	−0.979469	−0.489735	+	0.871872i	$0.662906\pi$
$542$	17.7684	0.763218
$543$	18.5277	0.795101
$544$	5.73315	0.245807
$545$	17.8158	0.763145
$546$	0	0
$547$	−27.3537	−1.16956	−0.584780	−	0.811192i	$-0.698819\pi$
$547$	−27.3537	−1.16956	−0.584780	+	0.811192i	$0.698819\pi$
$548$	−6.56322	−0.280367
$549$	56.2165	2.39926
$550$	4.34911	0.185447
$551$	5.77615	0.246072
$552$	−2.28506	−0.0972585
$553$	−5.89614	−0.250729
$554$	24.5192	1.04172
$555$	−30.5590	−1.29716
$556$	−1.34178	−0.0569041
$557$	−16.0919	−0.681834	−0.340917	−	0.940093i	$-0.610737\pi$
$557$	−16.0919	−0.681834	−0.340917	+	0.940093i	$0.610737\pi$
$558$	−25.7317	−1.08931
$559$	0	0
$560$	−4.83875	−0.204475
$561$	−69.6218	−2.93944
$562$	−18.4233	−0.777139
$563$	37.1827	1.56706	0.783531	−	0.621352i	$-0.213416\pi$
$563$	37.1827	1.56706	0.783531	+	0.621352i	$0.213416\pi$
$564$	2.29102	0.0964692
$565$	−7.67687	−0.322969
$566$	−4.07792	−0.171408
$567$	−1.85205	−0.0777789
$568$	4.17629	0.175233
$569$	−16.4861	−0.691133	−0.345566	−	0.938394i	$-0.612313\pi$
$569$	−16.4861	−0.691133	−0.345566	+	0.938394i	$0.612313\pi$
$570$	−2.75545	−0.115413
$571$	−25.4000	−1.06296	−0.531479	−	0.847071i	$-0.678364\pi$
$571$	−25.4000	−1.06296	−0.531479	+	0.847071i	$0.678364\pi$
$572$	0	0
$573$	38.5750	1.61149
$574$	−10.8256	−0.451852
$575$	−0.818363	−0.0341281
$576$	4.79655	0.199856
$577$	22.7846	0.948537	0.474269	−	0.880380i	$-0.342713\pi$
$577$	22.7846	0.948537	0.474269	+	0.880380i	$0.342713\pi$
$578$	−15.8691	−0.660066
$579$	37.2633	1.54861
$580$	−5.85325	−0.243043
$581$	−75.5343	−3.13369
$582$	−28.4588	−1.17965
$583$	−37.2822	−1.54407
$584$	2.56706	0.106226
$585$	0	0
$586$	1.65614	0.0684145
$587$	−44.4349	−1.83402	−0.917012	−	0.398860i	$-0.869406\pi$
$587$	−44.4349	−1.83402	−0.917012	+	0.398860i	$0.869406\pi$
$588$	−45.8303	−1.89001
$589$	5.29397	0.218134
$590$	−7.91612	−0.325902
$591$	−30.2076	−1.24257
$592$	−10.9443	−0.449808
$593$	35.2691	1.44833	0.724164	−	0.689628i	$-0.242226\pi$
$593$	35.2691	1.44833	0.724164	+	0.689628i	$0.242226\pi$
$594$	−21.8168	−0.895154
$595$	27.7413	1.13728
$596$	17.5781	0.720028
$597$	−0.134964	−0.00552371
$598$	0	0
$599$	6.27821	0.256521	0.128260	−	0.991741i	$-0.459061\pi$
$599$	6.27821	0.256521	0.128260	+	0.991741i	$0.459061\pi$
$600$	2.79223	0.113992
$601$	46.4173	1.89340	0.946701	−	0.322114i	$-0.104393\pi$
$601$	46.4173	1.89340	0.946701	+	0.322114i	$0.104393\pi$
$602$	9.59823	0.391195
$603$	−14.9000	−0.606775
$604$	−7.27761	−0.296122
$605$	−7.91477	−0.321781
$606$	−27.8058	−1.12953
$607$	43.6232	1.77061	0.885305	−	0.465012i	$-0.153950\pi$
$607$	43.6232	1.77061	0.885305	+	0.465012i	$0.153950\pi$
$608$	−0.986828	−0.0400212
$609$	−79.0827	−3.20459
$610$	11.7202	0.474537
$611$	0	0
$612$	−27.4994	−1.11160
$613$	16.0047	0.646424	0.323212	−	0.946327i	$-0.395237\pi$
$613$	16.0047	0.646424	0.323212	+	0.946327i	$0.395237\pi$
$614$	−24.0562	−0.970827
$615$	6.24698	0.251903
$616$	21.0443	0.847898
$617$	−19.7549	−0.795303	−0.397652	−	0.917537i	$-0.630175\pi$
$617$	−19.7549	−0.795303	−0.397652	+	0.917537i	$0.630175\pi$
$618$	10.9955	0.442304
$619$	−17.2823	−0.694633	−0.347317	−	0.937748i	$-0.612907\pi$
$619$	−17.2823	−0.694633	−0.347317	+	0.937748i	$0.612907\pi$
$620$	−5.36463	−0.215449
$621$	4.10522	0.164737
$622$	22.6981	0.910110
$623$	42.6724	1.70963
$624$	0	0
$625$	1.00000	0.0400000
$626$	10.3916	0.415332
$627$	11.9838	0.478585
$628$	1.37061	0.0546932
$629$	62.7453	2.50182
$630$	23.2093	0.924681
$631$	−9.43536	−0.375616	−0.187808	−	0.982206i	$-0.560138\pi$
$631$	−9.43536	−0.375616	−0.187808	+	0.982206i	$0.560138\pi$
$632$	1.21853	0.0484703
$633$	29.3184	1.16530
$634$	31.5378	1.25253
$635$	14.1753	0.562531
$636$	−23.9361	−0.949126
$637$	0	0
$638$	25.4564	1.00783
$639$	−20.0318	−0.792446
$640$	1.00000	0.0395285
$641$	31.4461	1.24205	0.621024	−	0.783791i	$-0.286717\pi$
$641$	31.4461	1.24205	0.621024	+	0.783791i	$0.286717\pi$
$642$	−14.5817	−0.575493
$643$	10.7627	0.424438	0.212219	−	0.977222i	$-0.431931\pi$
$643$	10.7627	0.424438	0.212219	+	0.977222i	$0.431931\pi$
$644$	−3.95985	−0.156040
$645$	−5.53872	−0.218087
$646$	5.65764	0.222597
$647$	3.33835	0.131244	0.0656221	−	0.997845i	$-0.479097\pi$
$647$	3.33835	0.131244	0.0656221	+	0.997845i	$0.479097\pi$
$648$	0.382754	0.0150360
$649$	34.4281	1.35142
$650$	0	0
$651$	−72.4810	−2.84075
$652$	−25.2531	−0.988989
$653$	−9.59726	−0.375570	−0.187785	−	0.982210i	$-0.560131\pi$
$653$	−9.59726	−0.375570	−0.187785	+	0.982210i	$0.560131\pi$
$654$	−49.7458	−1.94522
$655$	0.495003	0.0193414
$656$	2.23727	0.0873508
$657$	−12.3130	−0.480378
$658$	3.97018	0.154774
$659$	7.37469	0.287277	0.143639	−	0.989630i	$-0.454120\pi$
$659$	7.37469	0.287277	0.143639	+	0.989630i	$0.454120\pi$
$660$	−12.1437	−0.472694
$661$	23.1832	0.901720	0.450860	−	0.892595i	$-0.351117\pi$
$661$	23.1832	0.901720	0.450860	+	0.892595i	$0.351117\pi$
$662$	−6.05592	−0.235370
$663$	0	0
$664$	15.6103	0.605797
$665$	−4.77501	−0.185167
$666$	52.4949	2.03413
$667$	−4.79008	−0.185473
$668$	5.49833	0.212737
$669$	34.6684	1.34036
$670$	−3.10640	−0.120011
$671$	−50.9724	−1.96777
$672$	13.5109	0.521194
$673$	38.9953	1.50316	0.751580	−	0.659642i	$-0.229292\pi$
$673$	38.9953	1.50316	0.751580	+	0.659642i	$0.229292\pi$
$674$	23.1282	0.890867
$675$	−5.01638	−0.193081
$676$	0	0
$677$	35.0798	1.34823	0.674113	−	0.738629i	$-0.264526\pi$
$677$	35.0798	1.34823	0.674113	+	0.738629i	$0.264526\pi$
$678$	21.4356	0.823229
$679$	−49.3172	−1.89262
$680$	−5.73315	−0.219856
$681$	21.2258	0.813373
$682$	23.3314	0.893404
$683$	23.3434	0.893211	0.446605	−	0.894731i	$-0.352633\pi$
$683$	23.3434	0.893211	0.446605	+	0.894731i	$0.352633\pi$
$684$	4.73337	0.180985
$685$	6.56322	0.250768
$686$	−45.5496	−1.73909
$687$	58.5263	2.23292
$688$	−1.98362	−0.0756247
$689$	0	0
$690$	2.28506	0.0869906
$691$	29.1504	1.10893	0.554467	−	0.832206i	$-0.312922\pi$
$691$	29.1504	1.10893	0.554467	+	0.832206i	$0.312922\pi$
$692$	3.86243	0.146828
$693$	−100.940	−3.83439
$694$	23.3243	0.885379
$695$	1.34178	0.0508965
$696$	16.3436	0.619504
$697$	−12.8266	−0.485843
$698$	16.7136	0.632621
$699$	−66.5796	−2.51827
$700$	4.83875	0.182888
$701$	26.3331	0.994588	0.497294	−	0.867582i	$-0.334327\pi$
$701$	26.3331	0.994588	0.497294	+	0.867582i	$0.334327\pi$
$702$	0	0
$703$	−10.8001	−0.407335
$704$	−4.34911	−0.163913
$705$	−2.29102	−0.0862847
$706$	−7.13055	−0.268362
$707$	−48.1856	−1.81221
$708$	22.1036	0.830706
$709$	−13.4979	−0.506922	−0.253461	−	0.967346i	$-0.581569\pi$
$709$	−13.4979	−0.506922	−0.253461	+	0.967346i	$0.581569\pi$
$710$	−4.17629	−0.156733
$711$	−5.84472	−0.219194
$712$	−8.81888	−0.330502
$713$	−4.39021	−0.164415
$714$	−77.4601	−2.89887
$715$	0	0
$716$	−11.4902	−0.429408
$717$	−4.79504	−0.179074
$718$	14.3154	0.534248
$719$	−49.8584	−1.85940	−0.929702	−	0.368314i	$-0.879935\pi$
$719$	−49.8584	−1.85940	−0.929702	+	0.368314i	$0.879935\pi$
$720$	−4.79655	−0.178757
$721$	19.0545	0.709626
$722$	18.0262	0.670865
$723$	−44.0672	−1.63888
$724$	−6.63546	−0.246605
$725$	5.85325	0.217384
$726$	22.0999	0.820203
$727$	−10.2925	−0.381729	−0.190864	−	0.981616i	$-0.561129\pi$
$727$	−10.2925	−0.381729	−0.190864	+	0.981616i	$0.561129\pi$
$728$	0	0
$729$	−43.8566	−1.62432
$730$	−2.56706	−0.0950113
$731$	11.3724	0.420623
$732$	−32.7255	−1.20957
$733$	−39.0094	−1.44085	−0.720423	−	0.693535i	$-0.756052\pi$
$733$	−39.0094	−1.44085	−0.720423	+	0.693535i	$0.756052\pi$
$734$	−11.2749	−0.416163
$735$	45.8303	1.69048
$736$	0.818363	0.0301653
$737$	13.5101	0.497650
$738$	−10.7312	−0.395021
$739$	−20.4147	−0.750967	−0.375484	−	0.926829i	$-0.622523\pi$
$739$	−20.4147	−0.750967	−0.375484	+	0.926829i	$0.622523\pi$
$740$	10.9443	0.402320
$741$	0	0
$742$	−41.4796	−1.52276
$743$	21.9947	0.806907	0.403453	−	0.915000i	$-0.367810\pi$
$743$	21.9947	0.806907	0.403453	+	0.915000i	$0.367810\pi$
$744$	14.9793	0.549167
$745$	−17.5781	−0.644012
$746$	−9.48572	−0.347297
$747$	−74.8756	−2.73955
$748$	24.9341	0.911682
$749$	−25.2691	−0.923312
$750$	−2.79223	−0.101958
$751$	40.6916	1.48486	0.742430	−	0.669924i	$-0.233673\pi$
$751$	40.6916	1.48486	0.742430	+	0.669924i	$0.233673\pi$
$752$	−0.820497	−0.0299204
$753$	−9.81773	−0.357778
$754$	0	0
$755$	7.27761	0.264860
$756$	−24.2730	−0.882801
$757$	−48.6022	−1.76648	−0.883238	−	0.468924i	$-0.844642\pi$
$757$	−48.6022	−1.76648	−0.883238	+	0.468924i	$0.844642\pi$
$758$	0.0811125	0.00294614
$759$	−9.93797	−0.360725
$760$	0.986828	0.0357960
$761$	−11.8820	−0.430722	−0.215361	−	0.976534i	$-0.569093\pi$
$761$	−11.8820	−0.430722	−0.215361	+	0.976534i	$0.569093\pi$
$762$	−39.5808	−1.43386
$763$	−86.2063	−3.12088
$764$	−13.8151	−0.499813
$765$	27.4994	0.994242
$766$	28.8487	1.04235
$767$	0	0
$768$	−2.79223	−0.100756
$769$	−6.83278	−0.246396	−0.123198	−	0.992382i	$-0.539315\pi$
$769$	−6.83278	−0.246396	−0.123198	+	0.992382i	$0.539315\pi$
$770$	−21.0443	−0.758383
$771$	−0.343456	−0.0123693
$772$	−13.3454	−0.480310
$773$	23.8354	0.857300	0.428650	−	0.903471i	$-0.358989\pi$
$773$	23.8354	0.857300	0.428650	+	0.903471i	$0.358989\pi$
$774$	9.51452	0.341992
$775$	5.36463	0.192703
$776$	10.1921	0.365876
$777$	147.867	5.30471
$778$	−22.1338	−0.793534
$779$	2.20780	0.0791028
$780$	0	0
$781$	18.1632	0.649929
$782$	−4.69180	−0.167778
$783$	−29.3622	−1.04932
$784$	16.4135	0.586197
$785$	−1.37061	−0.0489191
$786$	−1.38216	−0.0493001
$787$	−29.0766	−1.03647	−0.518234	−	0.855239i	$-0.673410\pi$
$787$	−29.0766	−1.03647	−0.518234	+	0.855239i	$0.673410\pi$
$788$	10.8185	0.385391
$789$	55.8962	1.98996
$790$	−1.21853	−0.0433532
$791$	37.1465	1.32078
$792$	20.8607	0.741254
$793$	0	0
$794$	−23.7326	−0.842239
$795$	23.9361	0.848924
$796$	0.0483356	0.00171321
$797$	−29.2183	−1.03497	−0.517483	−	0.855693i	$-0.673131\pi$
$797$	−29.2183	−1.03497	−0.517483	+	0.855693i	$0.673131\pi$
$798$	13.3329	0.471981
$799$	4.70403	0.166417
$800$	−1.00000	−0.0353553
$801$	42.3002	1.49460
$802$	−5.69046	−0.200937
$803$	11.1644	0.393985
$804$	8.67378	0.305901
$805$	3.95985	0.139566
$806$	0	0
$807$	11.2273	0.395219
$808$	9.95828	0.350331
$809$	−7.01224	−0.246537	−0.123269	−	0.992373i	$-0.539338\pi$
$809$	−7.01224	−0.246537	−0.123269	+	0.992373i	$0.539338\pi$
$810$	−0.382754	−0.0134486
$811$	20.5209	0.720586	0.360293	−	0.932839i	$-0.382677\pi$
$811$	20.5209	0.720586	0.360293	+	0.932839i	$0.382677\pi$
$812$	28.3224	0.993922
$813$	49.6135	1.74002
$814$	−47.5980	−1.66831
$815$	25.2531	0.884579
$816$	16.0083	0.560402
$817$	−1.95749	−0.0684839
$818$	−0.542111	−0.0189544
$819$	0	0
$820$	−2.23727	−0.0781289
$821$	−34.8425	−1.21601	−0.608005	−	0.793933i	$-0.708030\pi$
$821$	−34.8425	−1.21601	−0.608005	+	0.793933i	$0.708030\pi$
$822$	−18.3260	−0.639193
$823$	27.6747	0.964679	0.482340	−	0.875984i	$-0.339787\pi$
$823$	27.6747	0.964679	0.482340	+	0.875984i	$0.339787\pi$
$824$	−3.93789	−0.137183
$825$	12.1437	0.422790
$826$	38.3041	1.33277
$827$	−13.1378	−0.456846	−0.228423	−	0.973562i	$-0.573357\pi$
$827$	−13.1378	−0.456846	−0.228423	+	0.973562i	$0.573357\pi$
$828$	−3.92532	−0.136414
$829$	39.1573	1.35999	0.679994	−	0.733218i	$-0.261982\pi$
$829$	39.1573	1.35999	0.679994	+	0.733218i	$0.261982\pi$
$830$	−15.6103	−0.541841
$831$	68.4633	2.37497
$832$	0	0
$833$	−94.1011	−3.26041
$834$	−3.74655	−0.129733
$835$	−5.49833	−0.190278
$836$	−4.29183	−0.148436
$837$	−26.9110	−0.930181
$838$	−28.8020	−0.994948
$839$	−9.20133	−0.317665	−0.158833	−	0.987306i	$-0.550773\pi$
$839$	−9.20133	−0.317665	−0.158833	+	0.987306i	$0.550773\pi$
$840$	−13.5109	−0.466171
$841$	5.26057	0.181399
$842$	−14.5843	−0.502609
$843$	−51.4420	−1.77176
$844$	−10.5000	−0.361425
$845$	0	0
$846$	3.93555	0.135307
$847$	38.2976	1.31592
$848$	8.57238	0.294377
$849$	−11.3865	−0.390783
$850$	5.73315	0.196646
$851$	8.95640	0.307022
$852$	11.6612	0.399505
$853$	52.4019	1.79421	0.897104	−	0.441820i	$-0.145667\pi$
$853$	52.4019	1.79421	0.897104	+	0.441820i	$0.145667\pi$
$854$	−56.7111	−1.94061
$855$	−4.73337	−0.161878
$856$	5.22223	0.178492
$857$	−5.03744	−0.172076	−0.0860379	−	0.996292i	$-0.527421\pi$
$857$	−5.03744	−0.172076	−0.0860379	+	0.996292i	$0.527421\pi$
$858$	0	0
$859$	6.20406	0.211680	0.105840	−	0.994383i	$-0.466247\pi$
$859$	6.20406	0.211680	0.105840	+	0.994383i	$0.466247\pi$
$860$	1.98362	0.0676408
$861$	−30.2276	−1.03015
$862$	25.3507	0.863449
$863$	6.55198	0.223032	0.111516	−	0.993763i	$-0.464429\pi$
$863$	6.55198	0.223032	0.111516	+	0.993763i	$0.464429\pi$
$864$	5.01638	0.170661
$865$	−3.86243	−0.131327
$866$	34.2558	1.16406
$867$	−44.3101	−1.50485
$868$	25.9581	0.881075
$869$	5.29950	0.179773
$870$	−16.3436	−0.554101
$871$	0	0
$872$	17.8158	0.603319
$873$	−48.8871	−1.65458
$874$	0.807583	0.0273169
$875$	−4.83875	−0.163580
$876$	7.16783	0.242179
$877$	11.7187	0.395713	0.197856	−	0.980231i	$-0.436602\pi$
$877$	11.7187	0.395713	0.197856	+	0.980231i	$0.436602\pi$
$878$	−3.83723	−0.129500
$879$	4.62433	0.155975
$880$	4.34911	0.146609
$881$	−29.9366	−1.00859	−0.504295	−	0.863532i	$-0.668248\pi$
$881$	−29.9366	−1.00859	−0.504295	+	0.863532i	$0.668248\pi$
$882$	−78.7282	−2.65092
$883$	−0.556177	−0.0187169	−0.00935843	−	0.999956i	$-0.502979\pi$
$883$	−0.556177	−0.0187169	−0.00935843	+	0.999956i	$0.502979\pi$
$884$	0	0
$885$	−22.1036	−0.743006
$886$	−30.9113	−1.03849
$887$	15.0693	0.505977	0.252989	−	0.967469i	$-0.418586\pi$
$887$	15.0693	0.505977	0.252989	+	0.967469i	$0.418586\pi$
$888$	−30.5590	−1.02549
$889$	−68.5908	−2.30046
$890$	8.81888	0.295610
$891$	1.66464	0.0557676
$892$	−12.4160	−0.415720
$893$	−0.809689	−0.0270952
$894$	49.0822	1.64155
$895$	11.4902	0.384074
$896$	−4.83875	−0.161651
$897$	0	0
$898$	3.65278	0.121895
$899$	31.4005	1.04727
$900$	4.79655	0.159885
$901$	−49.1468	−1.63732
$902$	9.73015	0.323978
$903$	26.8005	0.891863
$904$	−7.67687	−0.255329
$905$	6.63546	0.220570
$906$	−20.3208	−0.675113
$907$	−19.4686	−0.646443	−0.323221	−	0.946323i	$-0.604766\pi$
$907$	−19.4686	−0.646443	−0.323221	+	0.946323i	$0.604766\pi$
$908$	−7.60172	−0.252272
$909$	−47.7654	−1.58428
$910$	0	0
$911$	−45.2378	−1.49880	−0.749398	−	0.662120i	$-0.769657\pi$
$911$	−45.2378	−1.49880	−0.749398	+	0.662120i	$0.769657\pi$
$912$	−2.75545	−0.0912421
$913$	67.8909	2.24686
$914$	−35.5304	−1.17524
$915$	32.7255	1.08187
$916$	−20.9604	−0.692551
$917$	−2.39520	−0.0790963
$918$	−28.7597	−0.949211
$919$	11.4706	0.378379	0.189190	−	0.981941i	$-0.439414\pi$
$919$	11.4706	0.378379	0.189190	+	0.981941i	$0.439414\pi$
$920$	−0.818363	−0.0269806
$921$	−67.1703	−2.21334
$922$	3.69279	0.121616
$923$	0	0
$924$	58.7604	1.93308
$925$	−10.9443	−0.359846
$926$	−33.4951	−1.10072
$927$	18.8883	0.620373
$928$	−5.85325	−0.192142
$929$	−21.2097	−0.695869	−0.347935	−	0.937519i	$-0.613117\pi$
$929$	−21.2097	−0.695869	−0.347935	+	0.937519i	$0.613117\pi$
$930$	−14.9793	−0.491190
$931$	16.1973	0.530845
$932$	23.8446	0.781056
$933$	63.3783	2.07491
$934$	−12.4322	−0.406795
$935$	−24.9341	−0.815433
$936$	0	0
$937$	−30.1976	−0.986513	−0.493256	−	0.869884i	$-0.664194\pi$
$937$	−30.1976	−0.986513	−0.493256	+	0.869884i	$0.664194\pi$
$938$	15.0311	0.490783
$939$	29.0157	0.946893
$940$	0.820497	0.0267617
$941$	−21.7676	−0.709602	−0.354801	−	0.934942i	$-0.615451\pi$
$941$	−21.7676	−0.709602	−0.354801	+	0.934942i	$0.615451\pi$
$942$	3.82705	0.124692
$943$	−1.83090	−0.0596223
$944$	−7.91612	−0.257648
$945$	24.2730	0.789602
$946$	−8.62697	−0.280487
$947$	−6.41073	−0.208321	−0.104160	−	0.994561i	$-0.533216\pi$
$947$	−6.41073	−0.208321	−0.104160	+	0.994561i	$0.533216\pi$
$948$	3.40240	0.110505
$949$	0	0
$950$	−0.986828	−0.0320169
$951$	88.0609	2.85557
$952$	27.7413	0.899101
$953$	13.3204	0.431490	0.215745	−	0.976450i	$-0.430782\pi$
$953$	13.3204	0.431490	0.215745	+	0.976450i	$0.430782\pi$
$954$	−41.1179	−1.33124
$955$	13.8151	0.447047
$956$	1.71728	0.0555408
$957$	71.0803	2.29770
$958$	23.4645	0.758104
$959$	−31.7578	−1.02551
$960$	2.79223	0.0901188
$961$	−2.22076	−0.0716375
$962$	0	0
$963$	−25.0487	−0.807183
$964$	15.7821	0.508306
$965$	13.3454	0.429602
$966$	−11.0568	−0.355747
$967$	−3.15620	−0.101497	−0.0507483	−	0.998711i	$-0.516161\pi$
$967$	−3.15620	−0.101497	−0.0507483	+	0.998711i	$0.516161\pi$
$968$	−7.91477	−0.254390
$969$	15.7974	0.507487
$970$	−10.1921	−0.327250
$971$	61.0020	1.95765	0.978823	−	0.204708i	$-0.0656245\pi$
$971$	61.0020	1.95765	0.978823	+	0.204708i	$0.0656245\pi$
$972$	16.1179	0.516981
$973$	−6.49253	−0.208141
$974$	19.3287	0.619330
$975$	0	0
$976$	11.7202	0.375154
$977$	−10.4517	−0.334378	−0.167189	−	0.985925i	$-0.553469\pi$
$977$	−10.4517	−0.334378	−0.167189	+	0.985925i	$0.553469\pi$
$978$	−70.5126	−2.25474
$979$	−38.3543	−1.22581
$980$	−16.4135	−0.524310
$981$	−85.4544	−2.72835
$982$	25.6544	0.818666
$983$	−1.62043	−0.0516836	−0.0258418	−	0.999666i	$-0.508227\pi$
$983$	−1.62043	−0.0516836	−0.0258418	+	0.999666i	$0.508227\pi$
$984$	6.24698	0.199146
$985$	−10.8185	−0.344705
$986$	33.5576	1.06869
$987$	11.0857	0.352860
$988$	0	0
$989$	1.62332	0.0516185
$990$	−20.8607	−0.662998
$991$	43.9729	1.39685	0.698423	−	0.715685i	$-0.253885\pi$
$991$	43.9729	1.39685	0.698423	+	0.715685i	$0.253885\pi$
$992$	−5.36463	−0.170327
$993$	−16.9095	−0.536608
$994$	20.2080	0.640960
$995$	−0.0483356	−0.00153234
$996$	43.5876	1.38112
$997$	−45.3877	−1.43744	−0.718722	−	0.695297i	$-0.755273\pi$
$997$	−45.3877	−1.43744	−0.718722	+	0.695297i	$0.755273\pi$
$998$	23.7013	0.750250
$999$	54.9008	1.73698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.a.v.1.2	✓	6
5.4	even	2		8450.2.a.cq.1.5		6
13.2	odd	12		1690.2.l.n.1161.1		24
13.3	even	3		1690.2.e.v.191.5		12
13.4	even	6		1690.2.e.u.991.5		12
13.5	odd	4		1690.2.d.l.1351.8		12
13.6	odd	12		1690.2.l.n.361.9		24
13.7	odd	12		1690.2.l.n.361.1		24
13.8	odd	4		1690.2.d.l.1351.2		12
13.9	even	3		1690.2.e.v.991.5		12
13.10	even	6		1690.2.e.u.191.5		12
13.11	odd	12		1690.2.l.n.1161.9		24
13.12	even	2		1690.2.a.w.1.2	yes	6
65.64	even	2		8450.2.a.cp.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.v.1.2	✓	6	1.1	even	1	trivial
1690.2.a.w.1.2	yes	6	13.12	even	2
1690.2.d.l.1351.2		12	13.8	odd	4
1690.2.d.l.1351.8		12	13.5	odd	4
1690.2.e.u.191.5		12	13.10	even	6
1690.2.e.u.991.5		12	13.4	even	6
1690.2.e.v.191.5		12	13.3	even	3
1690.2.e.v.991.5		12	13.9	even	3
1690.2.l.n.361.1		24	13.7	odd	12
1690.2.l.n.361.9		24	13.6	odd	12
1690.2.l.n.1161.1		24	13.2	odd	12
1690.2.l.n.1161.9		24	13.11	odd	12
8450.2.a.cp.1.5		6	65.64	even	2
8450.2.a.cq.1.5		6	5.4	even	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.79223 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79223 q^{6} +4.83875 q^{7} -1.00000 q^{8} +4.79655 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.79223 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79223 q^{6} +4.83875 q^{7} -1.00000 q^{8} +4.79655 q^{9} +1.00000 q^{10} -4.34911 q^{11} -2.79223 q^{12} -4.83875 q^{14} +2.79223 q^{15} +1.00000 q^{16} -5.73315 q^{17} -4.79655 q^{18} +0.986828 q^{19} -1.00000 q^{20} -13.5109 q^{21} +4.34911 q^{22} -0.818363 q^{23} +2.79223 q^{24} +1.00000 q^{25} -5.01638 q^{27} +4.83875 q^{28} +5.85325 q^{29} -2.79223 q^{30} +5.36463 q^{31} -1.00000 q^{32} +12.1437 q^{33} +5.73315 q^{34} -4.83875 q^{35} +4.79655 q^{36} -10.9443 q^{37} -0.986828 q^{38} +1.00000 q^{40} +2.23727 q^{41} +13.5109 q^{42} -1.98362 q^{43} -4.34911 q^{44} -4.79655 q^{45} +0.818363 q^{46} -0.820497 q^{47} -2.79223 q^{48} +16.4135 q^{49} -1.00000 q^{50} +16.0083 q^{51} +8.57238 q^{53} +5.01638 q^{54} +4.34911 q^{55} -4.83875 q^{56} -2.75545 q^{57} -5.85325 q^{58} -7.91612 q^{59} +2.79223 q^{60} +11.7202 q^{61} -5.36463 q^{62} +23.2093 q^{63} +1.00000 q^{64} -12.1437 q^{66} -3.10640 q^{67} -5.73315 q^{68} +2.28506 q^{69} +4.83875 q^{70} -4.17629 q^{71} -4.79655 q^{72} -2.56706 q^{73} +10.9443 q^{74} -2.79223 q^{75} +0.986828 q^{76} -21.0443 q^{77} -1.21853 q^{79} -1.00000 q^{80} -0.382754 q^{81} -2.23727 q^{82} -15.6103 q^{83} -13.5109 q^{84} +5.73315 q^{85} +1.98362 q^{86} -16.3436 q^{87} +4.34911 q^{88} +8.81888 q^{89} +4.79655 q^{90} -0.818363 q^{92} -14.9793 q^{93} +0.820497 q^{94} -0.986828 q^{95} +2.79223 q^{96} -10.1921 q^{97} -16.4135 q^{98} -20.8607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 16 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 16 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 16 q^{9} + 6 q^{10} - 15 q^{11} - 2 q^{12} + 3 q^{14} + 2 q^{15} + 6 q^{16} - 3 q^{17} - 16 q^{18} - q^{19} - 6 q^{20} + 2 q^{21} + 15 q^{22} - 3 q^{23} + 2 q^{24} + 6 q^{25} - 20 q^{27} - 3 q^{28} + 7 q^{29} - 2 q^{30} - 6 q^{32} - 4 q^{33} + 3 q^{34} + 3 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 6 q^{40} - 2 q^{41} - 2 q^{42} - 22 q^{43} - 15 q^{44} - 16 q^{45} + 3 q^{46} - 7 q^{47} - 2 q^{48} + 31 q^{49} - 6 q^{50} - 22 q^{51} - 16 q^{53} + 20 q^{54} + 15 q^{55} + 3 q^{56} - 2 q^{57} - 7 q^{58} - 15 q^{59} + 2 q^{60} + 33 q^{61} - 25 q^{63} + 6 q^{64} + 4 q^{66} + 8 q^{67} - 3 q^{68} - 6 q^{69} - 3 q^{70} - 40 q^{71} - 16 q^{72} - 21 q^{73} + 6 q^{74} - 2 q^{75} - q^{76} - 34 q^{77} + 20 q^{79} - 6 q^{80} - 2 q^{81} + 2 q^{82} - 22 q^{83} + 2 q^{84} + 3 q^{85} + 22 q^{86} - 39 q^{87} + 15 q^{88} - 20 q^{89} + 16 q^{90} - 3 q^{92} - 48 q^{93} + 7 q^{94} + q^{95} + 2 q^{96} + 7 q^{97} - 31 q^{98} - 55 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 16 * q^9 + 6 * q^10 - 15 * q^11 - 2 * q^12 + 3 * q^14 + 2 * q^15 + 6 * q^16 - 3 * q^17 - 16 * q^18 - q^19 - 6 * q^20 + 2 * q^21 + 15 * q^22 - 3 * q^23 + 2 * q^24 + 6 * q^25 - 20 * q^27 - 3 * q^28 + 7 * q^29 - 2 * q^30 - 6 * q^32 - 4 * q^33 + 3 * q^34 + 3 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 6 * q^40 - 2 * q^41 - 2 * q^42 - 22 * q^43 - 15 * q^44 - 16 * q^45 + 3 * q^46 - 7 * q^47 - 2 * q^48 + 31 * q^49 - 6 * q^50 - 22 * q^51 - 16 * q^53 + 20 * q^54 + 15 * q^55 + 3 * q^56 - 2 * q^57 - 7 * q^58 - 15 * q^59 + 2 * q^60 + 33 * q^61 - 25 * q^63 + 6 * q^64 + 4 * q^66 + 8 * q^67 - 3 * q^68 - 6 * q^69 - 3 * q^70 - 40 * q^71 - 16 * q^72 - 21 * q^73 + 6 * q^74 - 2 * q^75 - q^76 - 34 * q^77 + 20 * q^79 - 6 * q^80 - 2 * q^81 + 2 * q^82 - 22 * q^83 + 2 * q^84 + 3 * q^85 + 22 * q^86 - 39 * q^87 + 15 * q^88 - 20 * q^89 + 16 * q^90 - 3 * q^92 - 48 * q^93 + 7 * q^94 + q^95 + 2 * q^96 + 7 * q^97 - 31 * q^98 - 55 * q^99

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