LMFDB - Embedded newform 4011.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65342 q^{2} +1.00000 q^{3} +5.04066 q^{4} +4.09935 q^{5} -2.65342 q^{6} +1.00000 q^{7} -8.06816 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.65342 q^{2} +1.00000 q^{3} +5.04066 q^{4} +4.09935 q^{5} -2.65342 q^{6} +1.00000 q^{7} -8.06816 q^{8} +1.00000 q^{9} -10.8773 q^{10} +3.39961 q^{11} +5.04066 q^{12} +6.69857 q^{13} -2.65342 q^{14} +4.09935 q^{15} +11.3269 q^{16} -0.815918 q^{17} -2.65342 q^{18} -6.15932 q^{19} +20.6634 q^{20} +1.00000 q^{21} -9.02060 q^{22} +8.79425 q^{23} -8.06816 q^{24} +11.8047 q^{25} -17.7742 q^{26} +1.00000 q^{27} +5.04066 q^{28} +8.20916 q^{29} -10.8773 q^{30} +1.23046 q^{31} -13.9188 q^{32} +3.39961 q^{33} +2.16498 q^{34} +4.09935 q^{35} +5.04066 q^{36} -0.212244 q^{37} +16.3433 q^{38} +6.69857 q^{39} -33.0742 q^{40} -7.41377 q^{41} -2.65342 q^{42} -12.1454 q^{43} +17.1363 q^{44} +4.09935 q^{45} -23.3349 q^{46} +3.30218 q^{47} +11.3269 q^{48} +1.00000 q^{49} -31.3228 q^{50} -0.815918 q^{51} +33.7652 q^{52} -2.61038 q^{53} -2.65342 q^{54} +13.9362 q^{55} -8.06816 q^{56} -6.15932 q^{57} -21.7824 q^{58} -13.0320 q^{59} +20.6634 q^{60} -6.76704 q^{61} -3.26494 q^{62} +1.00000 q^{63} +14.2787 q^{64} +27.4598 q^{65} -9.02060 q^{66} +5.05668 q^{67} -4.11276 q^{68} +8.79425 q^{69} -10.8773 q^{70} +5.70040 q^{71} -8.06816 q^{72} +0.489698 q^{73} +0.563173 q^{74} +11.8047 q^{75} -31.0470 q^{76} +3.39961 q^{77} -17.7742 q^{78} -12.2887 q^{79} +46.4330 q^{80} +1.00000 q^{81} +19.6719 q^{82} -4.14677 q^{83} +5.04066 q^{84} -3.34473 q^{85} +32.2270 q^{86} +8.20916 q^{87} -27.4286 q^{88} +13.3874 q^{89} -10.8773 q^{90} +6.69857 q^{91} +44.3288 q^{92} +1.23046 q^{93} -8.76208 q^{94} -25.2492 q^{95} -13.9188 q^{96} -2.17442 q^{97} -2.65342 q^{98} +3.39961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * 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 $

$2$	−2.65342	−1.87625	−0.938127	−	0.346291i	$-0.887441\pi$
$2$	−2.65342	−1.87625	−0.938127	+	0.346291i	$0.887441\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.04066	2.52033
$5$	4.09935	1.83328	0.916642	−	0.399709i	$-0.130889\pi$
$5$	4.09935	1.83328	0.916642	+	0.399709i	$0.130889\pi$
$6$	−2.65342	−1.08326
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.06816	−2.85252
$9$	1.00000	0.333333
$10$	−10.8773	−3.43971
$11$	3.39961	1.02502	0.512510	−	0.858681i	$-0.328716\pi$
$11$	3.39961	1.02502	0.512510	+	0.858681i	$0.328716\pi$
$12$	5.04066	1.45511
$13$	6.69857	1.85785	0.928925	−	0.370268i	$-0.120734\pi$
$13$	6.69857	1.85785	0.928925	+	0.370268i	$0.120734\pi$
$14$	−2.65342	−0.709157
$15$	4.09935	1.05845
$16$	11.3269	2.83173
$17$	−0.815918	−0.197889	−0.0989446	−	0.995093i	$-0.531547\pi$
$17$	−0.815918	−0.197889	−0.0989446	+	0.995093i	$0.531547\pi$
$18$	−2.65342	−0.625418
$19$	−6.15932	−1.41304	−0.706522	−	0.707691i	$-0.749737\pi$
$19$	−6.15932	−1.41304	−0.706522	+	0.707691i	$0.749737\pi$
$20$	20.6634	4.62048
$21$	1.00000	0.218218
$22$	−9.02060	−1.92320
$23$	8.79425	1.83373	0.916864	−	0.399199i	$-0.130712\pi$
$23$	8.79425	1.83373	0.916864	+	0.399199i	$0.130712\pi$
$24$	−8.06816	−1.64691
$25$	11.8047	2.36093
$26$	−17.7742	−3.48580
$27$	1.00000	0.192450
$28$	5.04066	0.952595
$29$	8.20916	1.52440	0.762201	−	0.647340i	$-0.224119\pi$
$29$	8.20916	1.52440	0.762201	+	0.647340i	$0.224119\pi$
$30$	−10.8773	−1.98592
$31$	1.23046	0.220998	0.110499	−	0.993876i	$-0.464755\pi$
$31$	1.23046	0.220998	0.110499	+	0.993876i	$0.464755\pi$
$32$	−13.9188	−2.46052
$33$	3.39961	0.591796
$34$	2.16498	0.371290
$35$	4.09935	0.692916
$36$	5.04066	0.840110
$37$	−0.212244	−0.0348927	−0.0174463	−	0.999848i	$-0.505554\pi$
$37$	−0.212244	−0.0348927	−0.0174463	+	0.999848i	$0.505554\pi$
$38$	16.3433	2.65123
$39$	6.69857	1.07263
$40$	−33.0742	−5.22949
$41$	−7.41377	−1.15784	−0.578918	−	0.815385i	$-0.696525\pi$
$41$	−7.41377	−1.15784	−0.578918	+	0.815385i	$0.696525\pi$
$42$	−2.65342	−0.409432
$43$	−12.1454	−1.85216	−0.926081	−	0.377325i	$-0.876844\pi$
$43$	−12.1454	−1.85216	−0.926081	+	0.377325i	$0.876844\pi$
$44$	17.1363	2.58339
$45$	4.09935	0.611095
$46$	−23.3349	−3.44054
$47$	3.30218	0.481672	0.240836	−	0.970566i	$-0.422578\pi$
$47$	3.30218	0.481672	0.240836	+	0.970566i	$0.422578\pi$
$48$	11.3269	1.63490
$49$	1.00000	0.142857
$50$	−31.3228	−4.42971
$51$	−0.815918	−0.114251
$52$	33.7652	4.68239
$53$	−2.61038	−0.358563	−0.179281	−	0.983798i	$-0.557377\pi$
$53$	−2.61038	−0.358563	−0.179281	+	0.983798i	$0.557377\pi$
$54$	−2.65342	−0.361085
$55$	13.9362	1.87915
$56$	−8.06816	−1.07815
$57$	−6.15932	−0.815821
$58$	−21.7824	−2.86017
$59$	−13.0320	−1.69662	−0.848309	−	0.529501i	$-0.822379\pi$
$59$	−13.0320	−1.69662	−0.848309	+	0.529501i	$0.822379\pi$
$60$	20.6634	2.66764
$61$	−6.76704	−0.866431	−0.433215	−	0.901290i	$-0.642621\pi$
$61$	−6.76704	−0.866431	−0.433215	+	0.901290i	$0.642621\pi$
$62$	−3.26494	−0.414648
$63$	1.00000	0.125988
$64$	14.2787	1.78483
$65$	27.4598	3.40597
$66$	−9.02060	−1.11036
$67$	5.05668	0.617772	0.308886	−	0.951099i	$-0.400044\pi$
$67$	5.05668	0.617772	0.308886	+	0.951099i	$0.400044\pi$
$68$	−4.11276	−0.498746
$69$	8.79425	1.05870
$70$	−10.8773	−1.30009
$71$	5.70040	0.676513	0.338257	−	0.941054i	$-0.390163\pi$
$71$	5.70040	0.676513	0.338257	+	0.941054i	$0.390163\pi$
$72$	−8.06816	−0.950841
$73$	0.489698	0.0573148	0.0286574	−	0.999589i	$-0.490877\pi$
$73$	0.489698	0.0573148	0.0286574	+	0.999589i	$0.490877\pi$
$74$	0.563173	0.0654675
$75$	11.8047	1.36308
$76$	−31.0470	−3.56134
$77$	3.39961	0.387421
$78$	−17.7742	−2.01253
$79$	−12.2887	−1.38258	−0.691292	−	0.722575i	$-0.742958\pi$
$79$	−12.2887	−1.38258	−0.691292	+	0.722575i	$0.742958\pi$
$80$	46.4330	5.19137
$81$	1.00000	0.111111
$82$	19.6719	2.17240
$83$	−4.14677	−0.455167	−0.227584	−	0.973759i	$-0.573082\pi$
$83$	−4.14677	−0.455167	−0.227584	+	0.973759i	$0.573082\pi$
$84$	5.04066	0.549981
$85$	−3.34473	−0.362787
$86$	32.2270	3.47513
$87$	8.20916	0.880114
$88$	−27.4286	−2.92389
$89$	13.3874	1.41907	0.709533	−	0.704672i	$-0.248906\pi$
$89$	13.3874	1.41907	0.709533	+	0.704672i	$0.248906\pi$
$90$	−10.8773	−1.14657
$91$	6.69857	0.702201
$92$	44.3288	4.62160
$93$	1.23046	0.127593
$94$	−8.76208	−0.903740
$95$	−25.2492	−2.59051
$96$	−13.9188	−1.42058
$97$	−2.17442	−0.220779	−0.110389	−	0.993888i	$-0.535210\pi$
$97$	−2.17442	−0.220779	−0.110389	+	0.993888i	$0.535210\pi$
$98$	−2.65342	−0.268036
$99$	3.39961	0.341673
$100$	59.5033	5.95033
$101$	5.16180	0.513618	0.256809	−	0.966462i	$-0.417329\pi$
$101$	5.16180	0.513618	0.256809	+	0.966462i	$0.417329\pi$
$102$	2.16498	0.214365
$103$	−6.99800	−0.689534	−0.344767	−	0.938688i	$-0.612042\pi$
$103$	−6.99800	−0.689534	−0.344767	+	0.938688i	$0.612042\pi$
$104$	−54.0451	−5.29956
$105$	4.09935	0.400055
$106$	6.92644	0.672755
$107$	−7.67292	−0.741769	−0.370885	−	0.928679i	$-0.620945\pi$
$107$	−7.67292	−0.741769	−0.370885	+	0.928679i	$0.620945\pi$
$108$	5.04066	0.485038
$109$	−7.56723	−0.724809	−0.362405	−	0.932021i	$-0.618044\pi$
$109$	−7.56723	−0.724809	−0.362405	+	0.932021i	$0.618044\pi$
$110$	−36.9786	−3.52577
$111$	−0.212244	−0.0201453
$112$	11.3269	1.07029
$113$	−10.5971	−0.996892	−0.498446	−	0.866921i	$-0.666096\pi$
$113$	−10.5971	−0.996892	−0.498446	+	0.866921i	$0.666096\pi$
$114$	16.3433	1.53069
$115$	36.0507	3.36175
$116$	41.3796	3.84200
$117$	6.69857	0.619283
$118$	34.5794	3.18329
$119$	−0.815918	−0.0747950
$120$	−33.0742	−3.01925
$121$	0.557332	0.0506665
$122$	17.9558	1.62564
$123$	−7.41377	−0.668477
$124$	6.20235	0.556987
$125$	27.8947	2.49498
$126$	−2.65342	−0.236386
$127$	−1.53441	−0.136157	−0.0680783	−	0.997680i	$-0.521687\pi$
$127$	−1.53441	−0.136157	−0.0680783	+	0.997680i	$0.521687\pi$
$128$	−10.0497	−0.888278
$129$	−12.1454	−1.06935
$130$	−72.8625	−6.39046
$131$	16.0650	1.40360	0.701802	−	0.712372i	$-0.252379\pi$
$131$	16.0650	1.40360	0.701802	+	0.712372i	$0.252379\pi$
$132$	17.1363	1.49152
$133$	−6.15932	−0.534081
$134$	−13.4175	−1.15910
$135$	4.09935	0.352816
$136$	6.58295	0.564483
$137$	−10.8710	−0.928772	−0.464386	−	0.885633i	$-0.653725\pi$
$137$	−10.8710	−0.928772	−0.464386	+	0.885633i	$0.653725\pi$
$138$	−23.3349	−1.98640
$139$	1.69558	0.143817	0.0719085	−	0.997411i	$-0.477091\pi$
$139$	1.69558	0.143817	0.0719085	+	0.997411i	$0.477091\pi$
$140$	20.6634	1.74638
$141$	3.30218	0.278094
$142$	−15.1256	−1.26931
$143$	22.7725	1.90433
$144$	11.3269	0.943910
$145$	33.6522	2.79466
$146$	−1.29938	−0.107537
$147$	1.00000	0.0824786
$148$	−1.06985	−0.0879410
$149$	12.5752	1.03020	0.515100	−	0.857130i	$-0.327755\pi$
$149$	12.5752	1.03020	0.515100	+	0.857130i	$0.327755\pi$
$150$	−31.3228	−2.55749
$151$	−19.0519	−1.55042	−0.775212	−	0.631701i	$-0.782357\pi$
$151$	−19.0519	−1.55042	−0.775212	+	0.631701i	$0.782357\pi$
$152$	49.6943	4.03074
$153$	−0.815918	−0.0659630
$154$	−9.02060	−0.726901
$155$	5.04410	0.405152
$156$	33.7652	2.70338
$157$	−18.5493	−1.48039	−0.740196	−	0.672391i	$-0.765267\pi$
$157$	−18.5493	−1.48039	−0.740196	+	0.672391i	$0.765267\pi$
$158$	32.6071	2.59408
$159$	−2.61038	−0.207016
$160$	−57.0580	−4.51083
$161$	8.79425	0.693084
$162$	−2.65342	−0.208473
$163$	−12.4697	−0.976701	−0.488350	−	0.872648i	$-0.662401\pi$
$163$	−12.4697	−0.976701	−0.488350	+	0.872648i	$0.662401\pi$
$164$	−37.3703	−2.91813
$165$	13.9362	1.08493
$166$	11.0031	0.854009
$167$	12.9674	1.00345	0.501725	−	0.865027i	$-0.332699\pi$
$167$	12.9674	1.00345	0.501725	+	0.865027i	$0.332699\pi$
$168$	−8.06816	−0.622472
$169$	31.8709	2.45161
$170$	8.87499	0.680681
$171$	−6.15932	−0.471015
$172$	−61.2210	−4.66806
$173$	−24.0740	−1.83031	−0.915155	−	0.403102i	$-0.867932\pi$
$173$	−24.0740	−1.83031	−0.915155	+	0.403102i	$0.867932\pi$
$174$	−21.7824	−1.65132
$175$	11.8047	0.892348
$176$	38.5071	2.90258
$177$	−13.0320	−0.979543
$178$	−35.5226	−2.66253
$179$	−13.3166	−0.995333	−0.497666	−	0.867368i	$-0.665810\pi$
$179$	−13.3166	−0.995333	−0.497666	+	0.867368i	$0.665810\pi$
$180$	20.6634	1.54016
$181$	14.4274	1.07238	0.536190	−	0.844097i	$-0.319863\pi$
$181$	14.4274	1.07238	0.536190	+	0.844097i	$0.319863\pi$
$182$	−17.7742	−1.31751
$183$	−6.76704	−0.500234
$184$	−70.9534	−5.23075
$185$	−0.870061	−0.0639682
$186$	−3.26494	−0.239397
$187$	−2.77380	−0.202840
$188$	16.6452	1.21397
$189$	1.00000	0.0727393
$190$	66.9968	4.86046
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	14.2787	1.03047
$193$	−26.6197	−1.91613	−0.958064	−	0.286556i	$-0.907490\pi$
$193$	−26.6197	−1.91613	−0.958064	+	0.286556i	$0.907490\pi$
$194$	5.76965	0.414237
$195$	27.4598	1.96644
$196$	5.04066	0.360047
$197$	0.0212223	0.00151202	0.000756012	−	1.00000i	$-0.499759\pi$
$197$	0.0212223	0.00151202	0.000756012		1.00000i	$0.499759\pi$
$198$	−9.02060	−0.641066
$199$	−16.5987	−1.17665	−0.588324	−	0.808625i	$-0.700212\pi$
$199$	−16.5987	−1.17665	−0.588324	+	0.808625i	$0.700212\pi$
$200$	−95.2418	−6.73461
$201$	5.05668	0.356671
$202$	−13.6964	−0.963678
$203$	8.20916	0.576170
$204$	−4.11276	−0.287951
$205$	−30.3916	−2.12264
$206$	18.5687	1.29374
$207$	8.79425	0.611243
$208$	75.8742	5.26093
$209$	−20.9393	−1.44840
$210$	−10.8773	−0.750606
$211$	−7.93847	−0.546507	−0.273254	−	0.961942i	$-0.588100\pi$
$211$	−7.93847	−0.546507	−0.273254	+	0.961942i	$0.588100\pi$
$212$	−13.1580	−0.903696
$213$	5.70040	0.390585
$214$	20.3595	1.39175
$215$	−49.7884	−3.39554
$216$	−8.06816	−0.548968
$217$	1.23046	0.0835293
$218$	20.0791	1.35993
$219$	0.489698	0.0330907
$220$	70.2475	4.73609
$221$	−5.46549	−0.367648
$222$	0.563173	0.0377977
$223$	−23.3855	−1.56601	−0.783003	−	0.622018i	$-0.786313\pi$
$223$	−23.3855	−1.56601	−0.783003	+	0.622018i	$0.786313\pi$
$224$	−13.9188	−0.929990
$225$	11.8047	0.786977
$226$	28.1186	1.87042
$227$	1.82093	0.120859	0.0604297	−	0.998172i	$-0.480753\pi$
$227$	1.82093	0.120859	0.0604297	+	0.998172i	$0.480753\pi$
$228$	−31.0470	−2.05614
$229$	12.0638	0.797199	0.398599	−	0.917125i	$-0.369496\pi$
$229$	12.0638	0.797199	0.398599	+	0.917125i	$0.369496\pi$
$230$	−95.6578	−6.30749
$231$	3.39961	0.223678
$232$	−66.2328	−4.34840
$233$	2.93455	0.192249	0.0961245	−	0.995369i	$-0.469355\pi$
$233$	2.93455	0.192249	0.0961245	+	0.995369i	$0.469355\pi$
$234$	−17.7742	−1.16193
$235$	13.5368	0.883043
$236$	−65.6897	−4.27604
$237$	−12.2887	−0.798235
$238$	2.16498	0.140335
$239$	−15.4436	−0.998961	−0.499481	−	0.866325i	$-0.666476\pi$
$239$	−15.4436	−0.998961	−0.499481	+	0.866325i	$0.666476\pi$
$240$	46.4330	2.99724
$241$	12.5379	0.807640	0.403820	−	0.914838i	$-0.367682\pi$
$241$	12.5379	0.807640	0.403820	+	0.914838i	$0.367682\pi$
$242$	−1.47884	−0.0950632
$243$	1.00000	0.0641500
$244$	−34.1103	−2.18369
$245$	4.09935	0.261898
$246$	19.6719	1.25423
$247$	−41.2586	−2.62522
$248$	−9.92757	−0.630402
$249$	−4.14677	−0.262791
$250$	−74.0164	−4.68121
$251$	−19.4459	−1.22741	−0.613706	−	0.789535i	$-0.710322\pi$
$251$	−19.4459	−1.22741	−0.613706	+	0.789535i	$0.710322\pi$
$252$	5.04066	0.317532
$253$	29.8970	1.87961
$254$	4.07143	0.255464
$255$	−3.34473	−0.209455
$256$	−1.89115	−0.118197
$257$	−14.5752	−0.909176	−0.454588	−	0.890702i	$-0.650214\pi$
$257$	−14.5752	−0.909176	−0.454588	+	0.890702i	$0.650214\pi$
$258$	32.2270	2.00636
$259$	−0.212244	−0.0131882
$260$	138.415	8.58416
$261$	8.20916	0.508134
$262$	−42.6272	−2.63352
$263$	−8.26262	−0.509495	−0.254748	−	0.967008i	$-0.581992\pi$
$263$	−8.26262	−0.509495	−0.254748	+	0.967008i	$0.581992\pi$
$264$	−27.4286	−1.68811
$265$	−10.7008	−0.657348
$266$	16.3433	1.00207
$267$	13.3874	0.819298
$268$	25.4890	1.55699
$269$	−7.90073	−0.481716	−0.240858	−	0.970560i	$-0.577429\pi$
$269$	−7.90073	−0.481716	−0.240858	+	0.970560i	$0.577429\pi$
$270$	−10.8773	−0.661972
$271$	−25.6471	−1.55795	−0.778974	−	0.627056i	$-0.784260\pi$
$271$	−25.6471	−1.55795	−0.778974	+	0.627056i	$0.784260\pi$
$272$	−9.24183	−0.560368
$273$	6.69857	0.405416
$274$	28.8454	1.74261
$275$	40.1312	2.42000
$276$	44.3288	2.66828
$277$	−5.92940	−0.356263	−0.178132	−	0.984007i	$-0.557005\pi$
$277$	−5.92940	−0.356263	−0.178132	+	0.984007i	$0.557005\pi$
$278$	−4.49908	−0.269837
$279$	1.23046	0.0736659
$280$	−33.0742	−1.97656
$281$	22.7092	1.35472	0.677358	−	0.735654i	$-0.263125\pi$
$281$	22.7092	1.35472	0.677358	+	0.735654i	$0.263125\pi$
$282$	−8.76208	−0.521774
$283$	14.9243	0.887159	0.443580	−	0.896235i	$-0.353708\pi$
$283$	14.9243	0.887159	0.443580	+	0.896235i	$0.353708\pi$
$284$	28.7338	1.70504
$285$	−25.2492	−1.49563
$286$	−60.4252	−3.57301
$287$	−7.41377	−0.437621
$288$	−13.9188	−0.820174
$289$	−16.3343	−0.960840
$290$	−89.2936	−5.24350
$291$	−2.17442	−0.127467
$292$	2.46840	0.144452
$293$	−21.7278	−1.26935	−0.634675	−	0.772779i	$-0.718866\pi$
$293$	−21.7278	−1.26935	−0.634675	+	0.772779i	$0.718866\pi$
$294$	−2.65342	−0.154751
$295$	−53.4226	−3.11039
$296$	1.71242	0.0995322
$297$	3.39961	0.197265
$298$	−33.3673	−1.93292
$299$	58.9090	3.40679
$300$	59.5033	3.43542
$301$	−12.1454	−0.700051
$302$	50.5528	2.90899
$303$	5.16180	0.296537
$304$	−69.7661	−4.00136
$305$	−27.7405	−1.58841
$306$	2.16498	0.123763
$307$	29.9705	1.71051	0.855253	−	0.518211i	$-0.173402\pi$
$307$	29.9705	1.71051	0.855253	+	0.518211i	$0.173402\pi$
$308$	17.1363	0.976429
$309$	−6.99800	−0.398102
$310$	−13.3841	−0.760168
$311$	6.10846	0.346379	0.173190	−	0.984889i	$-0.444593\pi$
$311$	6.10846	0.346379	0.173190	+	0.984889i	$0.444593\pi$
$312$	−54.0451	−3.05970
$313$	11.4608	0.647800	0.323900	−	0.946091i	$-0.395006\pi$
$313$	11.4608	0.647800	0.323900	+	0.946091i	$0.395006\pi$
$314$	49.2190	2.77759
$315$	4.09935	0.230972
$316$	−61.9430	−3.48457
$317$	15.3932	0.864568	0.432284	−	0.901738i	$-0.357708\pi$
$317$	15.3932	0.864568	0.432284	+	0.901738i	$0.357708\pi$
$318$	6.92644	0.388415
$319$	27.9079	1.56254
$320$	58.5332	3.27211
$321$	−7.67292	−0.428261
$322$	−23.3349	−1.30040
$323$	5.02550	0.279626
$324$	5.04066	0.280037
$325$	79.0744	4.38626
$326$	33.0874	1.83254
$327$	−7.56723	−0.418469
$328$	59.8155	3.30276
$329$	3.30218	0.182055
$330$	−36.9786	−2.03560
$331$	5.43609	0.298794	0.149397	−	0.988777i	$-0.452267\pi$
$331$	5.43609	0.298794	0.149397	+	0.988777i	$0.452267\pi$
$332$	−20.9024	−1.14717
$333$	−0.212244	−0.0116309
$334$	−34.4081	−1.88273
$335$	20.7291	1.13255
$336$	11.3269	0.617934
$337$	2.29233	0.124871	0.0624356	−	0.998049i	$-0.480113\pi$
$337$	2.29233	0.124871	0.0624356	+	0.998049i	$0.480113\pi$
$338$	−84.5670	−4.59984
$339$	−10.5971	−0.575556
$340$	−16.8596	−0.914343
$341$	4.18309	0.226527
$342$	16.3433	0.883743
$343$	1.00000	0.0539949
$344$	97.9913	5.28334
$345$	36.0507	1.94091
$346$	63.8784	3.43413
$347$	9.81431	0.526860	0.263430	−	0.964679i	$-0.415146\pi$
$347$	9.81431	0.526860	0.263430	+	0.964679i	$0.415146\pi$
$348$	41.3796	2.21818
$349$	18.8276	1.00782	0.503910	−	0.863756i	$-0.331894\pi$
$349$	18.8276	1.00782	0.503910	+	0.863756i	$0.331894\pi$
$350$	−31.3228	−1.67427
$351$	6.69857	0.357543
$352$	−47.3185	−2.52208
$353$	4.97101	0.264580	0.132290	−	0.991211i	$-0.457767\pi$
$353$	4.97101	0.264580	0.132290	+	0.991211i	$0.457767\pi$
$354$	34.5794	1.83787
$355$	23.3679	1.24024
$356$	67.4815	3.57651
$357$	−0.815918	−0.0431829
$358$	35.3347	1.86750
$359$	16.4199	0.866610	0.433305	−	0.901247i	$-0.357347\pi$
$359$	16.4199	0.866610	0.433305	+	0.901247i	$0.357347\pi$
$360$	−33.0742	−1.74316
$361$	18.9372	0.996694
$362$	−38.2820	−2.01206
$363$	0.557332	0.0292523
$364$	33.7652	1.76978
$365$	2.00744	0.105074
$366$	17.9558	0.938566
$367$	−11.6264	−0.606892	−0.303446	−	0.952849i	$-0.598137\pi$
$367$	−11.6264	−0.606892	−0.303446	+	0.952849i	$0.598137\pi$
$368$	99.6118	5.19262
$369$	−7.41377	−0.385946
$370$	2.30864	0.120021
$371$	−2.61038	−0.135524
$372$	6.20235	0.321577
$373$	−20.3271	−1.05250	−0.526250	−	0.850330i	$-0.676402\pi$
$373$	−20.3271	−1.05250	−0.526250	+	0.850330i	$0.676402\pi$
$374$	7.36007	0.380580
$375$	27.8947	1.44047
$376$	−26.6425	−1.37398
$377$	54.9897	2.83211
$378$	−2.65342	−0.136477
$379$	11.6505	0.598445	0.299222	−	0.954183i	$-0.403273\pi$
$379$	11.6505	0.598445	0.299222	+	0.954183i	$0.403273\pi$
$380$	−127.273	−6.52894
$381$	−1.53441	−0.0786100
$382$	−2.65342	−0.135761
$383$	−34.9384	−1.78527	−0.892635	−	0.450779i	$-0.851146\pi$
$383$	−34.9384	−1.78527	−0.892635	+	0.450779i	$0.851146\pi$
$384$	−10.0497	−0.512848
$385$	13.9362	0.710253
$386$	70.6333	3.59514
$387$	−12.1454	−0.617387
$388$	−10.9605	−0.556435
$389$	−13.8385	−0.701642	−0.350821	−	0.936443i	$-0.614097\pi$
$389$	−13.8385	−0.701642	−0.350821	+	0.936443i	$0.614097\pi$
$390$	−72.8625	−3.68953
$391$	−7.17539	−0.362875
$392$	−8.06816	−0.407503
$393$	16.0650	0.810371
$394$	−0.0563116	−0.00283694
$395$	−50.3756	−2.53467
$396$	17.1363	0.861129
$397$	7.38639	0.370712	0.185356	−	0.982671i	$-0.440656\pi$
$397$	7.38639	0.370712	0.185356	+	0.982671i	$0.440656\pi$
$398$	44.0433	2.20769
$399$	−6.15932	−0.308352
$400$	133.710	6.68552
$401$	9.09996	0.454430	0.227215	−	0.973845i	$-0.427038\pi$
$401$	9.09996	0.454430	0.227215	+	0.973845i	$0.427038\pi$
$402$	−13.4175	−0.669205
$403$	8.24235	0.410581
$404$	26.0189	1.29449
$405$	4.09935	0.203698
$406$	−21.7824	−1.08104
$407$	−0.721546	−0.0357657
$408$	6.58295	0.325905
$409$	7.27789	0.359868	0.179934	−	0.983679i	$-0.442412\pi$
$409$	7.27789	0.359868	0.179934	+	0.983679i	$0.442412\pi$
$410$	80.6419	3.98262
$411$	−10.8710	−0.536227
$412$	−35.2745	−1.73785
$413$	−13.0320	−0.641262
$414$	−23.3349	−1.14685
$415$	−16.9991	−0.834451
$416$	−93.2362	−4.57128
$417$	1.69558	0.0830328
$418$	55.5607	2.71756
$419$	1.31284	0.0641365	0.0320682	−	0.999486i	$-0.489791\pi$
$419$	1.31284	0.0641365	0.0320682	+	0.999486i	$0.489791\pi$
$420$	20.6634	1.00827
$421$	7.59994	0.370399	0.185199	−	0.982701i	$-0.440707\pi$
$421$	7.59994	0.370399	0.185199	+	0.982701i	$0.440707\pi$
$422$	21.0641	1.02539
$423$	3.30218	0.160557
$424$	21.0609	1.02281
$425$	−9.63163	−0.467203
$426$	−15.1256	−0.732837
$427$	−6.76704	−0.327480
$428$	−38.6766	−1.86950
$429$	22.7725	1.09947
$430$	132.110	6.37089
$431$	7.97585	0.384183	0.192092	−	0.981377i	$-0.438473\pi$
$431$	7.97585	0.384183	0.192092	+	0.981377i	$0.438473\pi$
$432$	11.3269	0.544967
$433$	−1.73303	−0.0832841	−0.0416420	−	0.999133i	$-0.513259\pi$
$433$	−1.73303	−0.0832841	−0.0416420	+	0.999133i	$0.513259\pi$
$434$	−3.26494	−0.156722
$435$	33.6522	1.61350
$436$	−38.1438	−1.82676
$437$	−54.1666	−2.59114
$438$	−1.29938	−0.0620865
$439$	10.6705	0.509275	0.254637	−	0.967037i	$-0.418044\pi$
$439$	10.6705	0.509275	0.254637	+	0.967037i	$0.418044\pi$
$440$	−112.439	−5.36033
$441$	1.00000	0.0476190
$442$	14.5022	0.689802
$443$	−25.1907	−1.19685	−0.598423	−	0.801180i	$-0.704206\pi$
$443$	−25.1907	−1.19685	−0.598423	+	0.801180i	$0.704206\pi$
$444$	−1.06985	−0.0507728
$445$	54.8798	2.60155
$446$	62.0515	2.93822
$447$	12.5752	0.594786
$448$	14.2787	0.674603
$449$	−3.53961	−0.167045	−0.0835223	−	0.996506i	$-0.526617\pi$
$449$	−3.53961	−0.167045	−0.0835223	+	0.996506i	$0.526617\pi$
$450$	−31.3228	−1.47657
$451$	−25.2039	−1.18681
$452$	−53.4164	−2.51250
$453$	−19.0519	−0.895138
$454$	−4.83170	−0.226763
$455$	27.4598	1.28733
$456$	49.6943	2.32715
$457$	−4.41900	−0.206712	−0.103356	−	0.994644i	$-0.532958\pi$
$457$	−4.41900	−0.206712	−0.103356	+	0.994644i	$0.532958\pi$
$458$	−32.0104	−1.49575
$459$	−0.815918	−0.0380838
$460$	181.719	8.47271
$461$	33.2497	1.54859	0.774297	−	0.632823i	$-0.218104\pi$
$461$	33.2497	1.54859	0.774297	+	0.632823i	$0.218104\pi$
$462$	−9.02060	−0.419676
$463$	−29.4006	−1.36636	−0.683181	−	0.730249i	$-0.739404\pi$
$463$	−29.4006	−1.36636	−0.683181	+	0.730249i	$0.739404\pi$
$464$	92.9845	4.31670
$465$	5.04410	0.233915
$466$	−7.78661	−0.360708
$467$	10.3772	0.480198	0.240099	−	0.970748i	$-0.422820\pi$
$467$	10.3772	0.480198	0.240099	+	0.970748i	$0.422820\pi$
$468$	33.7652	1.56080
$469$	5.05668	0.233496
$470$	−35.9188	−1.65681
$471$	−18.5493	−0.854705
$472$	105.144	4.83965
$473$	−41.2897	−1.89850
$474$	32.6071	1.49769
$475$	−72.7086	−3.33610
$476$	−4.11276	−0.188508
$477$	−2.61038	−0.119521
$478$	40.9783	1.87431
$479$	35.9012	1.64037	0.820184	−	0.572100i	$-0.193871\pi$
$479$	35.9012	1.64037	0.820184	+	0.572100i	$0.193871\pi$
$480$	−57.0580	−2.60433
$481$	−1.42173	−0.0648254
$482$	−33.2685	−1.51534
$483$	8.79425	0.400152
$484$	2.80932	0.127696
$485$	−8.91369	−0.404750
$486$	−2.65342	−0.120362
$487$	30.7588	1.39381	0.696906	−	0.717162i	$-0.254559\pi$
$487$	30.7588	1.39381	0.696906	+	0.717162i	$0.254559\pi$
$488$	54.5975	2.47151
$489$	−12.4697	−0.563899
$490$	−10.8773	−0.491387
$491$	1.66974	0.0753545	0.0376773	−	0.999290i	$-0.488004\pi$
$491$	1.66974	0.0753545	0.0376773	+	0.999290i	$0.488004\pi$
$492$	−37.3703	−1.68478
$493$	−6.69800	−0.301663
$494$	109.477	4.92559
$495$	13.9362	0.626385
$496$	13.9374	0.625806
$497$	5.70040	0.255698
$498$	11.0031	0.493062
$499$	20.6065	0.922474	0.461237	−	0.887277i	$-0.347406\pi$
$499$	20.6065	0.922474	0.461237	+	0.887277i	$0.347406\pi$
$500$	140.608	6.28816
$501$	12.9674	0.579342
$502$	51.5981	2.30294
$503$	33.1766	1.47927	0.739636	−	0.673007i	$-0.234998\pi$
$503$	33.1766	1.47927	0.739636	+	0.673007i	$0.234998\pi$
$504$	−8.06816	−0.359384
$505$	21.1600	0.941608
$506$	−79.3294	−3.52662
$507$	31.8709	1.41544
$508$	−7.73442	−0.343159
$509$	−19.6228	−0.869766	−0.434883	−	0.900487i	$-0.643210\pi$
$509$	−19.6228	−0.869766	−0.434883	+	0.900487i	$0.643210\pi$
$510$	8.87499	0.392991
$511$	0.489698	0.0216629
$512$	25.1175	1.11005
$513$	−6.15932	−0.271940
$514$	38.6742	1.70585
$515$	−28.6872	−1.26411
$516$	−61.2210	−2.69510
$517$	11.2261	0.493724
$518$	0.563173	0.0247444
$519$	−24.0740	−1.05673
$520$	−221.550	−9.71560
$521$	12.3571	0.541377	0.270688	−	0.962667i	$-0.412749\pi$
$521$	12.3571	0.541377	0.270688	+	0.962667i	$0.412749\pi$
$522$	−21.7824	−0.953389
$523$	−3.56165	−0.155740	−0.0778700	−	0.996964i	$-0.524812\pi$
$523$	−3.56165	−0.155740	−0.0778700	+	0.996964i	$0.524812\pi$
$524$	80.9781	3.53754
$525$	11.8047	0.515198
$526$	21.9242	0.955943
$527$	−1.00396	−0.0437331
$528$	38.5071	1.67581
$529$	54.3389	2.36256
$530$	28.3939	1.23335
$531$	−13.0320	−0.565540
$532$	−31.0470	−1.34606
$533$	−49.6617	−2.15109
$534$	−35.5226	−1.53721
$535$	−31.4540	−1.35987
$536$	−40.7981	−1.76221
$537$	−13.3166	−0.574656
$538$	20.9640	0.903821
$539$	3.39961	0.146431
$540$	20.6634	0.889212
$541$	32.0583	1.37829	0.689147	−	0.724621i	$-0.257985\pi$
$541$	32.0583	1.37829	0.689147	+	0.724621i	$0.257985\pi$
$542$	68.0525	2.92311
$543$	14.4274	0.619139
$544$	11.3566	0.486910
$545$	−31.0207	−1.32878
$546$	−17.7742	−0.760664
$547$	−22.6863	−0.969998	−0.484999	−	0.874515i	$-0.661180\pi$
$547$	−22.6863	−0.969998	−0.484999	+	0.874515i	$0.661180\pi$
$548$	−54.7970	−2.34081
$549$	−6.76704	−0.288810
$550$	−106.485	−4.54054
$551$	−50.5628	−2.15405
$552$	−70.9534	−3.01998
$553$	−12.2887	−0.522568
$554$	15.7332	0.668441
$555$	−0.870061	−0.0369321
$556$	8.54682	0.362466
$557$	−5.40309	−0.228936	−0.114468	−	0.993427i	$-0.536516\pi$
$557$	−5.40309	−0.228936	−0.114468	+	0.993427i	$0.536516\pi$
$558$	−3.26494	−0.138216
$559$	−81.3571	−3.44104
$560$	46.4330	1.96215
$561$	−2.77380	−0.117110
$562$	−60.2571	−2.54179
$563$	18.9096	0.796945	0.398473	−	0.917180i	$-0.369540\pi$
$563$	18.9096	0.796945	0.398473	+	0.917180i	$0.369540\pi$
$564$	16.6452	0.700888
$565$	−43.4412	−1.82759
$566$	−39.6006	−1.66454
$567$	1.00000	0.0419961
$568$	−45.9917	−1.92977
$569$	−2.81773	−0.118126	−0.0590628	−	0.998254i	$-0.518811\pi$
$569$	−2.81773	−0.118126	−0.0590628	+	0.998254i	$0.518811\pi$
$570$	66.9968	2.80619
$571$	−14.2811	−0.597646	−0.298823	−	0.954309i	$-0.596594\pi$
$571$	−14.2811	−0.597646	−0.298823	+	0.954309i	$0.596594\pi$
$572$	114.789	4.79955
$573$	1.00000	0.0417756
$574$	19.6719	0.821088
$575$	103.813	4.32931
$576$	14.2787	0.594944
$577$	14.6502	0.609897	0.304949	−	0.952369i	$-0.401361\pi$
$577$	14.6502	0.609897	0.304949	+	0.952369i	$0.401361\pi$
$578$	43.3418	1.80278
$579$	−26.6197	−1.10628
$580$	169.629	7.04347
$581$	−4.14677	−0.172037
$582$	5.76965	0.239160
$583$	−8.87426	−0.367534
$584$	−3.95096	−0.163492
$585$	27.4598	1.13532
$586$	57.6530	2.38162
$587$	28.2954	1.16787	0.583937	−	0.811799i	$-0.301511\pi$
$587$	28.2954	1.16787	0.583937	+	0.811799i	$0.301511\pi$
$588$	5.04066	0.207873
$589$	−7.57882	−0.312280
$590$	141.753	5.83587
$591$	0.0212223	0.000872967 0
$592$	−2.40407	−0.0988066
$593$	−12.6419	−0.519141	−0.259570	−	0.965724i	$-0.583581\pi$
$593$	−12.6419	−0.519141	−0.259570	+	0.965724i	$0.583581\pi$
$594$	−9.02060	−0.370120
$595$	−3.34473	−0.137121
$596$	63.3873	2.59644
$597$	−16.5987	−0.679338
$598$	−156.310	−6.39201
$599$	28.0660	1.14674	0.573372	−	0.819295i	$-0.305635\pi$
$599$	28.0660	1.14674	0.573372	+	0.819295i	$0.305635\pi$
$600$	−95.2418	−3.88823
$601$	24.1712	0.985962	0.492981	−	0.870040i	$-0.335907\pi$
$601$	24.1712	0.985962	0.492981	+	0.870040i	$0.335907\pi$
$602$	32.2270	1.31347
$603$	5.05668	0.205924
$604$	−96.0343	−3.90758
$605$	2.28470	0.0928861
$606$	−13.6964	−0.556380
$607$	−43.5841	−1.76903	−0.884513	−	0.466516i	$-0.845509\pi$
$607$	−43.5841	−1.76903	−0.884513	+	0.466516i	$0.845509\pi$
$608$	85.7304	3.47682
$609$	8.20916	0.332652
$610$	73.6072	2.98027
$611$	22.1199	0.894875
$612$	−4.11276	−0.166249
$613$	12.3574	0.499110	0.249555	−	0.968361i	$-0.419716\pi$
$613$	12.3574	0.499110	0.249555	+	0.968361i	$0.419716\pi$
$614$	−79.5244	−3.20934
$615$	−30.3916	−1.22551
$616$	−27.4286	−1.10513
$617$	15.2585	0.614284	0.307142	−	0.951664i	$-0.400627\pi$
$617$	15.2585	0.614284	0.307142	+	0.951664i	$0.400627\pi$
$618$	18.5687	0.746941
$619$	26.3269	1.05817	0.529084	−	0.848569i	$-0.322536\pi$
$619$	26.3269	1.05817	0.529084	+	0.848569i	$0.322536\pi$
$620$	25.4256	1.02112
$621$	8.79425	0.352901
$622$	−16.2083	−0.649895
$623$	13.3874	0.536357
$624$	75.8742	3.03740
$625$	55.3267	2.21307
$626$	−30.4102	−1.21544
$627$	−20.9393	−0.836234
$628$	−93.5005	−3.73108
$629$	0.173173	0.00690488
$630$	−10.8773	−0.433362
$631$	−14.7281	−0.586316	−0.293158	−	0.956064i	$-0.594706\pi$
$631$	−14.7281	−0.586316	−0.293158	+	0.956064i	$0.594706\pi$
$632$	99.1470	3.94385
$633$	−7.93847	−0.315526
$634$	−40.8447	−1.62215
$635$	−6.29007	−0.249614
$636$	−13.1580	−0.521749
$637$	6.69857	0.265407
$638$	−74.0516	−2.93173
$639$	5.70040	0.225504
$640$	−41.1973	−1.62847
$641$	−21.9381	−0.866504	−0.433252	−	0.901273i	$-0.642634\pi$
$641$	−21.9381	−0.866504	−0.433252	+	0.901273i	$0.642634\pi$
$642$	20.3595	0.803526
$643$	33.1417	1.30698	0.653491	−	0.756934i	$-0.273304\pi$
$643$	33.1417	1.30698	0.653491	+	0.756934i	$0.273304\pi$
$644$	44.3288	1.74680
$645$	−49.7884	−1.96042
$646$	−13.3348	−0.524650
$647$	2.30156	0.0904838	0.0452419	−	0.998976i	$-0.485594\pi$
$647$	2.30156	0.0904838	0.0452419	+	0.998976i	$0.485594\pi$
$648$	−8.06816	−0.316947
$649$	−44.3036	−1.73907
$650$	−209.818	−8.22973
$651$	1.23046	0.0482257
$652$	−62.8554	−2.46161
$653$	−20.3999	−0.798311	−0.399155	−	0.916883i	$-0.630697\pi$
$653$	−20.3999	−0.798311	−0.399155	+	0.916883i	$0.630697\pi$
$654$	20.0791	0.785154
$655$	65.8559	2.57320
$656$	−83.9752	−3.27868
$657$	0.489698	0.0191049
$658$	−8.76208	−0.341582
$659$	10.8245	0.421661	0.210830	−	0.977523i	$-0.432383\pi$
$659$	10.8245	0.421661	0.210830	+	0.977523i	$0.432383\pi$
$660$	70.2475	2.73438
$661$	5.29989	0.206142	0.103071	−	0.994674i	$-0.467133\pi$
$661$	5.29989	0.206142	0.103071	+	0.994674i	$0.467133\pi$
$662$	−14.4242	−0.560614
$663$	−5.46549	−0.212262
$664$	33.4568	1.29837
$665$	−25.2492	−0.979122
$666$	0.563173	0.0218225
$667$	72.1934	2.79534
$668$	65.3644	2.52903
$669$	−23.3855	−0.904134
$670$	−55.0031	−2.12495
$671$	−23.0053	−0.888109
$672$	−13.9188	−0.536930
$673$	−1.45089	−0.0559275	−0.0279638	−	0.999609i	$-0.508902\pi$
$673$	−1.45089	−0.0559275	−0.0279638	+	0.999609i	$0.508902\pi$
$674$	−6.08253	−0.234290
$675$	11.8047	0.454362
$676$	160.650	6.17886
$677$	16.6715	0.640737	0.320368	−	0.947293i	$-0.396193\pi$
$677$	16.6715	0.640737	0.320368	+	0.947293i	$0.396193\pi$
$678$	28.1186	1.07989
$679$	−2.17442	−0.0834465
$680$	26.9858	1.03486
$681$	1.82093	0.0697782
$682$	−11.0995	−0.425023
$683$	−50.0569	−1.91537	−0.957686	−	0.287814i	$-0.907072\pi$
$683$	−50.0569	−1.91537	−0.957686	+	0.287814i	$0.907072\pi$
$684$	−31.0470	−1.18711
$685$	−44.5640	−1.70270
$686$	−2.65342	−0.101308
$687$	12.0638	0.460263
$688$	−137.570	−5.24482
$689$	−17.4858	−0.666156
$690$	−95.6578	−3.64163
$691$	−11.0586	−0.420688	−0.210344	−	0.977627i	$-0.567458\pi$
$691$	−11.0586	−0.420688	−0.210344	+	0.977627i	$0.567458\pi$
$692$	−121.349	−4.61298
$693$	3.39961	0.129140
$694$	−26.0415	−0.988522
$695$	6.95076	0.263657
$696$	−66.2328	−2.51055
$697$	6.04903	0.229123
$698$	−49.9576	−1.89092
$699$	2.93455	0.110995
$700$	59.5033	2.24901
$701$	−12.5891	−0.475482	−0.237741	−	0.971329i	$-0.576407\pi$
$701$	−12.5891	−0.475482	−0.237741	+	0.971329i	$0.576407\pi$
$702$	−17.7742	−0.670842
$703$	1.30728	0.0493049
$704$	48.5418	1.82949
$705$	13.5368	0.509825
$706$	−13.1902	−0.496419
$707$	5.16180	0.194129
$708$	−65.6897	−2.46877
$709$	−4.24055	−0.159257	−0.0796286	−	0.996825i	$-0.525373\pi$
$709$	−4.24055	−0.159257	−0.0796286	+	0.996825i	$0.525373\pi$
$710$	−62.0050	−2.32701
$711$	−12.2887	−0.460861
$712$	−108.012	−4.04792
$713$	10.8210	0.405250
$714$	2.16498	0.0810222
$715$	93.3525	3.49119
$716$	−67.1247	−2.50857
$717$	−15.4436	−0.576751
$718$	−43.5690	−1.62598
$719$	−8.25460	−0.307845	−0.153922	−	0.988083i	$-0.549191\pi$
$719$	−8.25460	−0.307845	−0.153922	+	0.988083i	$0.549191\pi$
$720$	46.4330	1.73046
$721$	−6.99800	−0.260619
$722$	−50.2484	−1.87005
$723$	12.5379	0.466291
$724$	72.7236	2.70275
$725$	96.9063	3.59901
$726$	−1.47884	−0.0548848
$727$	35.9229	1.33231	0.666154	−	0.745814i	$-0.267939\pi$
$727$	35.9229	1.33231	0.666154	+	0.745814i	$0.267939\pi$
$728$	−54.0451	−2.00305
$729$	1.00000	0.0370370
$730$	−5.32659	−0.197146
$731$	9.90968	0.366523
$732$	−34.1103	−1.26075
$733$	15.6017	0.576263	0.288131	−	0.957591i	$-0.406966\pi$
$733$	15.6017	0.576263	0.288131	+	0.957591i	$0.406966\pi$
$734$	30.8497	1.13868
$735$	4.09935	0.151207
$736$	−122.406	−4.51193
$737$	17.1907	0.633229
$738$	19.6719	0.724132
$739$	−39.4921	−1.45274	−0.726370	−	0.687304i	$-0.758794\pi$
$739$	−39.4921	−1.45274	−0.726370	+	0.687304i	$0.758794\pi$
$740$	−4.38568	−0.161221
$741$	−41.2586	−1.51567
$742$	6.92644	0.254277
$743$	−22.0369	−0.808457	−0.404228	−	0.914658i	$-0.632460\pi$
$743$	−22.0369	−0.808457	−0.404228	+	0.914658i	$0.632460\pi$
$744$	−9.92757	−0.363963
$745$	51.5501	1.88865
$746$	53.9365	1.97476
$747$	−4.14677	−0.151722
$748$	−13.9818	−0.511224
$749$	−7.67292	−0.280362
$750$	−74.0164	−2.70270
$751$	16.2927	0.594530	0.297265	−	0.954795i	$-0.403926\pi$
$751$	16.2927	0.594530	0.297265	+	0.954795i	$0.403926\pi$
$752$	37.4035	1.36397
$753$	−19.4459	−0.708647
$754$	−145.911	−5.31376
$755$	−78.1005	−2.84237
$756$	5.04066	0.183327
$757$	28.1660	1.02371	0.511855	−	0.859072i	$-0.328959\pi$
$757$	28.1660	1.02371	0.511855	+	0.859072i	$0.328959\pi$
$758$	−30.9137	−1.12283
$759$	29.8970	1.08519
$760$	203.714	7.38950
$761$	−16.8063	−0.609229	−0.304615	−	0.952476i	$-0.598528\pi$
$761$	−16.8063	−0.609229	−0.304615	+	0.952476i	$0.598528\pi$
$762$	4.07143	0.147492
$763$	−7.56723	−0.273952
$764$	5.04066	0.182365
$765$	−3.34473	−0.120929
$766$	92.7065	3.34962
$767$	−87.2957	−3.15206
$768$	−1.89115	−0.0682411
$769$	0.603876	0.0217763	0.0108882	−	0.999941i	$-0.496534\pi$
$769$	0.603876	0.0217763	0.0108882	+	0.999941i	$0.496534\pi$
$770$	−36.9786	−1.33262
$771$	−14.5752	−0.524913
$772$	−134.181	−4.82927
$773$	−11.7460	−0.422474	−0.211237	−	0.977435i	$-0.567749\pi$
$773$	−11.7460	−0.422474	−0.211237	+	0.977435i	$0.567749\pi$
$774$	32.2270	1.15838
$775$	14.5252	0.521761
$776$	17.5435	0.629776
$777$	−0.212244	−0.00761420
$778$	36.7195	1.31646
$779$	45.6638	1.63607
$780$	138.415	4.95607
$781$	19.3791	0.693440
$782$	19.0393	0.680846
$783$	8.20916	0.293371
$784$	11.3269	0.404533
$785$	−76.0399	−2.71398
$786$	−42.6272	−1.52046
$787$	−29.6086	−1.05543	−0.527717	−	0.849420i	$-0.676952\pi$
$787$	−29.6086	−1.05543	−0.527717	+	0.849420i	$0.676952\pi$
$788$	0.106974	0.00381080
$789$	−8.26262	−0.294157
$790$	133.668	4.75569
$791$	−10.5971	−0.376790
$792$	−27.4286	−0.974632
$793$	−45.3295	−1.60970
$794$	−19.5992	−0.695551
$795$	−10.7008	−0.379520
$796$	−83.6682	−2.96554
$797$	10.2910	0.364526	0.182263	−	0.983250i	$-0.441658\pi$
$797$	10.2910	0.364526	0.182263	+	0.983250i	$0.441658\pi$
$798$	16.3433	0.578546
$799$	−2.69431	−0.0953177
$800$	−164.307	−5.80912
$801$	13.3874	0.473022
$802$	−24.1460	−0.852626
$803$	1.66478	0.0587488
$804$	25.4890	0.898928
$805$	36.0507	1.27062
$806$	−21.8705	−0.770354
$807$	−7.90073	−0.278119
$808$	−41.6462	−1.46511
$809$	53.0686	1.86579	0.932896	−	0.360147i	$-0.117273\pi$
$809$	53.0686	1.86579	0.932896	+	0.360147i	$0.117273\pi$
$810$	−10.8773	−0.382190
$811$	8.36148	0.293611	0.146806	−	0.989165i	$-0.453101\pi$
$811$	8.36148	0.293611	0.146806	+	0.989165i	$0.453101\pi$
$812$	41.3796	1.45214
$813$	−25.6471	−0.899482
$814$	1.91457	0.0671055
$815$	−51.1176	−1.79057
$816$	−9.24183	−0.323529
$817$	74.8076	2.61719
$818$	−19.3113	−0.675204
$819$	6.69857	0.234067
$820$	−153.194	−5.34976
$821$	−16.7169	−0.583425	−0.291712	−	0.956506i	$-0.594225\pi$
$821$	−16.7169	−0.583425	−0.291712	+	0.956506i	$0.594225\pi$
$822$	28.8454	1.00610
$823$	6.29676	0.219491	0.109746	−	0.993960i	$-0.464996\pi$
$823$	6.29676	0.219491	0.109746	+	0.993960i	$0.464996\pi$
$824$	56.4610	1.96691
$825$	40.1312	1.39719
$826$	34.5794	1.20317
$827$	−4.07922	−0.141848	−0.0709241	−	0.997482i	$-0.522595\pi$
$827$	−4.07922	−0.141848	−0.0709241	+	0.997482i	$0.522595\pi$
$828$	44.3288	1.54053
$829$	−10.3403	−0.359133	−0.179567	−	0.983746i	$-0.557470\pi$
$829$	−10.3403	−0.359133	−0.179567	+	0.983746i	$0.557470\pi$
$830$	45.1057	1.56564
$831$	−5.92940	−0.205689
$832$	95.6467	3.31595
$833$	−0.815918	−0.0282699
$834$	−4.49908	−0.155791
$835$	53.1580	1.83961
$836$	−105.548	−3.65044
$837$	1.23046	0.0425311
$838$	−3.48352	−0.120336
$839$	−20.2443	−0.698912	−0.349456	−	0.936953i	$-0.613634\pi$
$839$	−20.2443	−0.698912	−0.349456	+	0.936953i	$0.613634\pi$
$840$	−33.0742	−1.14117
$841$	38.3903	1.32380
$842$	−20.1659	−0.694962
$843$	22.7092	0.782145
$844$	−40.0151	−1.37738
$845$	130.650	4.49449
$846$	−8.76208	−0.301247
$847$	0.557332	0.0191501
$848$	−29.5675	−1.01535
$849$	14.9243	0.512202
$850$	25.5568	0.876591
$851$	−1.86653	−0.0639837
$852$	28.7338	0.984403
$853$	6.49379	0.222343	0.111172	−	0.993801i	$-0.464540\pi$
$853$	6.49379	0.222343	0.111172	+	0.993801i	$0.464540\pi$
$854$	17.9558	0.614436
$855$	−25.2492	−0.863504
$856$	61.9063	2.11591
$857$	33.5404	1.14572	0.572859	−	0.819654i	$-0.305834\pi$
$857$	33.5404	1.14572	0.572859	+	0.819654i	$0.305834\pi$
$858$	−60.4252	−2.06288
$859$	30.3515	1.03558	0.517790	−	0.855508i	$-0.326755\pi$
$859$	30.3515	1.03558	0.517790	+	0.855508i	$0.326755\pi$
$860$	−250.966	−8.55788
$861$	−7.41377	−0.252661
$862$	−21.1633	−0.720825
$863$	55.9658	1.90510	0.952549	−	0.304384i	$-0.0984506\pi$
$863$	55.9658	1.90510	0.952549	+	0.304384i	$0.0984506\pi$
$864$	−13.9188	−0.473527
$865$	−98.6876	−3.35548
$866$	4.59846	0.156262
$867$	−16.3343	−0.554741
$868$	6.20235	0.210521
$869$	−41.7767	−1.41718
$870$	−89.2936	−3.02734
$871$	33.8726	1.14773
$872$	61.0536	2.06754
$873$	−2.17442	−0.0735929
$874$	143.727	4.86164
$875$	27.8947	0.943012
$876$	2.46840	0.0833994
$877$	45.0989	1.52288	0.761441	−	0.648234i	$-0.224492\pi$
$877$	45.0989	1.52288	0.761441	+	0.648234i	$0.224492\pi$
$878$	−28.3133	−0.955529
$879$	−21.7278	−0.732860
$880$	157.854	5.32126
$881$	5.21904	0.175834	0.0879169	−	0.996128i	$-0.471979\pi$
$881$	5.21904	0.175834	0.0879169	+	0.996128i	$0.471979\pi$
$882$	−2.65342	−0.0893454
$883$	13.4055	0.451131	0.225566	−	0.974228i	$-0.427577\pi$
$883$	13.4055	0.451131	0.225566	+	0.974228i	$0.427577\pi$
$884$	−27.5496	−0.926595
$885$	−53.4226	−1.79578
$886$	66.8416	2.24559
$887$	−30.7765	−1.03338	−0.516688	−	0.856174i	$-0.672835\pi$
$887$	−30.7765	−1.03338	−0.516688	+	0.856174i	$0.672835\pi$
$888$	1.71242	0.0574649
$889$	−1.53441	−0.0514623
$890$	−145.619	−4.88117
$891$	3.39961	0.113891
$892$	−117.878	−3.94685
$893$	−20.3392	−0.680624
$894$	−33.3673	−1.11597
$895$	−54.5896	−1.82473
$896$	−10.0497	−0.335738
$897$	58.9090	1.96691
$898$	9.39209	0.313418
$899$	10.1011	0.336890
$900$	59.5033	1.98344
$901$	2.12985	0.0709557
$902$	66.8767	2.22675
$903$	−12.1454	−0.404175
$904$	85.4991	2.84366
$905$	59.1430	1.96598
$906$	50.5528	1.67951
$907$	33.2147	1.10287	0.551437	−	0.834216i	$-0.314080\pi$
$907$	33.2147	1.10287	0.551437	+	0.834216i	$0.314080\pi$
$908$	9.17868	0.304605
$909$	5.16180	0.171206
$910$	−72.8625	−2.41537
$911$	18.2468	0.604545	0.302272	−	0.953222i	$-0.402255\pi$
$911$	18.2468	0.604545	0.302272	+	0.953222i	$0.402255\pi$
$912$	−69.7661	−2.31019
$913$	−14.0974	−0.466555
$914$	11.7255	0.387844
$915$	−27.7405	−0.917071
$916$	60.8095	2.00920
$917$	16.0650	0.530512
$918$	2.16498	0.0714548
$919$	16.5273	0.545186	0.272593	−	0.962129i	$-0.412119\pi$
$919$	16.5273	0.545186	0.272593	+	0.962129i	$0.412119\pi$
$920$	−290.863	−9.58946
$921$	29.9705	0.987561
$922$	−88.2256	−2.90555
$923$	38.1846	1.25686
$924$	17.1363	0.563742
$925$	−2.50547	−0.0823792
$926$	78.0123	2.56364
$927$	−6.99800	−0.229845
$928$	−114.262	−3.75083
$929$	1.94014	0.0636540	0.0318270	−	0.999493i	$-0.489867\pi$
$929$	1.94014	0.0636540	0.0318270	+	0.999493i	$0.489867\pi$
$930$	−13.3841	−0.438883
$931$	−6.15932	−0.201863
$932$	14.7921	0.484531
$933$	6.10846	0.199982
$934$	−27.5350	−0.900974
$935$	−11.3708	−0.371864
$936$	−54.0451	−1.76652
$937$	44.5619	1.45577	0.727886	−	0.685698i	$-0.240503\pi$
$937$	44.5619	1.45577	0.727886	+	0.685698i	$0.240503\pi$
$938$	−13.4175	−0.438098
$939$	11.4608	0.374008
$940$	68.2343	2.22556
$941$	17.1726	0.559811	0.279906	−	0.960028i	$-0.409697\pi$
$941$	17.1726	0.559811	0.279906	+	0.960028i	$0.409697\pi$
$942$	49.2190	1.60364
$943$	−65.1986	−2.12316
$944$	−147.612	−4.80437
$945$	4.09935	0.133352
$946$	109.559	3.56207
$947$	12.9886	0.422072	0.211036	−	0.977478i	$-0.432316\pi$
$947$	12.9886	0.422072	0.211036	+	0.977478i	$0.432316\pi$
$948$	−61.9430	−2.01182
$949$	3.28028	0.106482
$950$	192.927	6.25937
$951$	15.3932	0.499159
$952$	6.58295	0.213355
$953$	23.4797	0.760582	0.380291	−	0.924867i	$-0.375824\pi$
$953$	23.4797	0.760582	0.380291	+	0.924867i	$0.375824\pi$
$954$	6.92644	0.224252
$955$	4.09935	0.132652
$956$	−77.8458	−2.51771
$957$	27.9079	0.902135
$958$	−95.2611	−3.07775
$959$	−10.8710	−0.351043
$960$	58.5332	1.88915
$961$	−29.4860	−0.951160
$962$	3.77246	0.121629
$963$	−7.67292	−0.247256
$964$	63.1995	2.03552
$965$	−109.123	−3.51281
$966$	−23.3349	−0.750788
$967$	52.1925	1.67840	0.839199	−	0.543825i	$-0.183024\pi$
$967$	52.1925	1.67840	0.839199	+	0.543825i	$0.183024\pi$
$968$	−4.49664	−0.144527
$969$	5.02550	0.161442
$970$	23.6518	0.759414
$971$	50.9635	1.63550	0.817749	−	0.575576i	$-0.195222\pi$
$971$	50.9635	1.63550	0.817749	+	0.575576i	$0.195222\pi$
$972$	5.04066	0.161679
$973$	1.69558	0.0543577
$974$	−81.6161	−2.61515
$975$	79.0744	2.53241
$976$	−76.6497	−2.45350
$977$	−36.6300	−1.17190	−0.585949	−	0.810348i	$-0.699278\pi$
$977$	−36.6300	−1.17190	−0.585949	+	0.810348i	$0.699278\pi$
$978$	33.0874	1.05802
$979$	45.5121	1.45457
$980$	20.6634	0.660069
$981$	−7.56723	−0.241603
$982$	−4.43054	−0.141384
$983$	−12.5130	−0.399102	−0.199551	−	0.979887i	$-0.563948\pi$
$983$	−12.5130	−0.399102	−0.199551	+	0.979887i	$0.563948\pi$
$984$	59.8155	1.90685
$985$	0.0869974	0.00277197
$986$	17.7726	0.565996
$987$	3.30218	0.105110
$988$	−207.971	−6.61643
$989$	−106.810	−3.39636
$990$	−36.9786	−1.17526
$991$	22.5944	0.717733	0.358867	−	0.933389i	$-0.383163\pi$
$991$	22.5944	0.717733	0.358867	+	0.933389i	$0.383163\pi$
$992$	−17.1266	−0.543770
$993$	5.43609	0.172509
$994$	−15.1256	−0.479754
$995$	−68.0437	−2.15713
$996$	−20.9024	−0.662319
$997$	18.9671	0.600694	0.300347	−	0.953830i	$-0.402898\pi$
$997$	18.9671	0.600694	0.300347	+	0.953830i	$0.402898\pi$
$998$	−54.6778	−1.73080
$999$	−0.212244	−0.00671510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.1	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.1	✓	27	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65342 q^{2} +1.00000 q^{3} +5.04066 q^{4} +4.09935 q^{5} -2.65342 q^{6} +1.00000 q^{7} -8.06816 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.65342 q^{2} +1.00000 q^{3} +5.04066 q^{4} +4.09935 q^{5} -2.65342 q^{6} +1.00000 q^{7} -8.06816 q^{8} +1.00000 q^{9} -10.8773 q^{10} +3.39961 q^{11} +5.04066 q^{12} +6.69857 q^{13} -2.65342 q^{14} +4.09935 q^{15} +11.3269 q^{16} -0.815918 q^{17} -2.65342 q^{18} -6.15932 q^{19} +20.6634 q^{20} +1.00000 q^{21} -9.02060 q^{22} +8.79425 q^{23} -8.06816 q^{24} +11.8047 q^{25} -17.7742 q^{26} +1.00000 q^{27} +5.04066 q^{28} +8.20916 q^{29} -10.8773 q^{30} +1.23046 q^{31} -13.9188 q^{32} +3.39961 q^{33} +2.16498 q^{34} +4.09935 q^{35} +5.04066 q^{36} -0.212244 q^{37} +16.3433 q^{38} +6.69857 q^{39} -33.0742 q^{40} -7.41377 q^{41} -2.65342 q^{42} -12.1454 q^{43} +17.1363 q^{44} +4.09935 q^{45} -23.3349 q^{46} +3.30218 q^{47} +11.3269 q^{48} +1.00000 q^{49} -31.3228 q^{50} -0.815918 q^{51} +33.7652 q^{52} -2.61038 q^{53} -2.65342 q^{54} +13.9362 q^{55} -8.06816 q^{56} -6.15932 q^{57} -21.7824 q^{58} -13.0320 q^{59} +20.6634 q^{60} -6.76704 q^{61} -3.26494 q^{62} +1.00000 q^{63} +14.2787 q^{64} +27.4598 q^{65} -9.02060 q^{66} +5.05668 q^{67} -4.11276 q^{68} +8.79425 q^{69} -10.8773 q^{70} +5.70040 q^{71} -8.06816 q^{72} +0.489698 q^{73} +0.563173 q^{74} +11.8047 q^{75} -31.0470 q^{76} +3.39961 q^{77} -17.7742 q^{78} -12.2887 q^{79} +46.4330 q^{80} +1.00000 q^{81} +19.6719 q^{82} -4.14677 q^{83} +5.04066 q^{84} -3.34473 q^{85} +32.2270 q^{86} +8.20916 q^{87} -27.4286 q^{88} +13.3874 q^{89} -10.8773 q^{90} +6.69857 q^{91} +44.3288 q^{92} +1.23046 q^{93} -8.76208 q^{94} -25.2492 q^{95} -13.9188 q^{96} -2.17442 q^{97} -2.65342 q^{98} +3.39961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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