LMFDB - Embedded newform 2001.2.a.n.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 $ x^16 - x^15 - 28x^14 + 27x^13 + 316x^12 - 295x^11 - 1835x^10 + 1665x^9 + 5778x^8 - 5124x^7 - 9405x^6 + 8288x^5 + 6405x^4 - 6032x^3 - 400x^2 + 1088x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-2.39038$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.39038 q^{2} +1.00000 q^{3} +3.71391 q^{4} +3.15865 q^{5} +2.39038 q^{6} +2.42988 q^{7} +4.09689 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.39038 q^{2} +1.00000 q^{3} +3.71391 q^{4} +3.15865 q^{5} +2.39038 q^{6} +2.42988 q^{7} +4.09689 q^{8} +1.00000 q^{9} +7.55038 q^{10} -4.78063 q^{11} +3.71391 q^{12} -2.17768 q^{13} +5.80833 q^{14} +3.15865 q^{15} +2.36529 q^{16} -2.29507 q^{17} +2.39038 q^{18} +0.938360 q^{19} +11.7309 q^{20} +2.42988 q^{21} -11.4275 q^{22} -1.00000 q^{23} +4.09689 q^{24} +4.97709 q^{25} -5.20547 q^{26} +1.00000 q^{27} +9.02434 q^{28} -1.00000 q^{29} +7.55038 q^{30} +2.03157 q^{31} -2.53983 q^{32} -4.78063 q^{33} -5.48609 q^{34} +7.67514 q^{35} +3.71391 q^{36} +8.81831 q^{37} +2.24304 q^{38} -2.17768 q^{39} +12.9406 q^{40} -4.46994 q^{41} +5.80833 q^{42} -7.39000 q^{43} -17.7548 q^{44} +3.15865 q^{45} -2.39038 q^{46} +8.57229 q^{47} +2.36529 q^{48} -1.09569 q^{49} +11.8971 q^{50} -2.29507 q^{51} -8.08769 q^{52} -9.87266 q^{53} +2.39038 q^{54} -15.1003 q^{55} +9.95494 q^{56} +0.938360 q^{57} -2.39038 q^{58} -13.2918 q^{59} +11.7309 q^{60} -6.87382 q^{61} +4.85621 q^{62} +2.42988 q^{63} -10.8017 q^{64} -6.87853 q^{65} -11.4275 q^{66} +12.4288 q^{67} -8.52369 q^{68} -1.00000 q^{69} +18.3465 q^{70} -0.894099 q^{71} +4.09689 q^{72} +11.0287 q^{73} +21.0791 q^{74} +4.97709 q^{75} +3.48498 q^{76} -11.6163 q^{77} -5.20547 q^{78} -1.79625 q^{79} +7.47114 q^{80} +1.00000 q^{81} -10.6848 q^{82} -1.59927 q^{83} +9.02434 q^{84} -7.24934 q^{85} -17.6649 q^{86} -1.00000 q^{87} -19.5857 q^{88} -5.46304 q^{89} +7.55038 q^{90} -5.29149 q^{91} -3.71391 q^{92} +2.03157 q^{93} +20.4910 q^{94} +2.96395 q^{95} -2.53983 q^{96} +5.89728 q^{97} -2.61911 q^{98} -4.78063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * 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 $

$2$	2.39038	1.69025	0.845126	−	0.534567i	$-0.179525\pi$
$2$	2.39038	1.69025	0.845126	+	0.534567i	$0.179525\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.71391	1.85695
$5$	3.15865	1.41259	0.706296	−	0.707916i	$-0.250365\pi$
$5$	3.15865	1.41259	0.706296	+	0.707916i	$0.250365\pi$
$6$	2.39038	0.975868
$7$	2.42988	0.918408	0.459204	−	0.888331i	$-0.348135\pi$
$7$	2.42988	0.918408	0.459204	+	0.888331i	$0.348135\pi$
$8$	4.09689	1.44847
$9$	1.00000	0.333333
$10$	7.55038	2.38764
$11$	−4.78063	−1.44141	−0.720707	−	0.693240i	$-0.756183\pi$
$11$	−4.78063	−1.44141	−0.720707	+	0.693240i	$0.756183\pi$
$12$	3.71391	1.07211
$13$	−2.17768	−0.603979	−0.301989	−	0.953311i	$-0.597651\pi$
$13$	−2.17768	−0.603979	−0.301989	+	0.953311i	$0.597651\pi$
$14$	5.80833	1.55234
$15$	3.15865	0.815561
$16$	2.36529	0.591324
$17$	−2.29507	−0.556637	−0.278319	−	0.960489i	$-0.589777\pi$
$17$	−2.29507	−0.556637	−0.278319	+	0.960489i	$0.589777\pi$
$18$	2.39038	0.563418
$19$	0.938360	0.215275	0.107637	−	0.994190i	$-0.465671\pi$
$19$	0.938360	0.215275	0.107637	+	0.994190i	$0.465671\pi$
$20$	11.7309	2.62312
$21$	2.42988	0.530243
$22$	−11.4275	−2.43635
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	4.09689	0.836274
$25$	4.97709	0.995418
$26$	−5.20547	−1.02088
$27$	1.00000	0.192450
$28$	9.02434	1.70544
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	7.55038	1.37850
$31$	2.03157	0.364880	0.182440	−	0.983217i	$-0.441600\pi$
$31$	2.03157	0.364880	0.182440	+	0.983217i	$0.441600\pi$
$32$	−2.53983	−0.448982
$33$	−4.78063	−0.832201
$34$	−5.48609	−0.940858
$35$	7.67514	1.29734
$36$	3.71391	0.618985
$37$	8.81831	1.44972	0.724861	−	0.688896i	$-0.241904\pi$
$37$	8.81831	1.44972	0.724861	+	0.688896i	$0.241904\pi$
$38$	2.24304	0.363868
$39$	−2.17768	−0.348707
$40$	12.9406	2.04610
$41$	−4.46994	−0.698087	−0.349044	−	0.937107i	$-0.613493\pi$
$41$	−4.46994	−0.698087	−0.349044	+	0.937107i	$0.613493\pi$
$42$	5.80833	0.896245
$43$	−7.39000	−1.12696	−0.563482	−	0.826128i	$-0.690539\pi$
$43$	−7.39000	−1.12696	−0.563482	+	0.826128i	$0.690539\pi$
$44$	−17.7548	−2.67664
$45$	3.15865	0.470864
$46$	−2.39038	−0.352442
$47$	8.57229	1.25040	0.625199	−	0.780466i	$-0.285018\pi$
$47$	8.57229	1.25040	0.625199	+	0.780466i	$0.285018\pi$
$48$	2.36529	0.341401
$49$	−1.09569	−0.156527
$50$	11.8971	1.68251
$51$	−2.29507	−0.321375
$52$	−8.08769	−1.12156
$53$	−9.87266	−1.35611	−0.678057	−	0.735009i	$-0.737178\pi$
$53$	−9.87266	−1.35611	−0.678057	+	0.735009i	$0.737178\pi$
$54$	2.39038	0.325289
$55$	−15.1003	−2.03613
$56$	9.95494	1.33028
$57$	0.938360	0.124289
$58$	−2.39038	−0.313872
$59$	−13.2918	−1.73045	−0.865225	−	0.501384i	$-0.832824\pi$
$59$	−13.2918	−1.73045	−0.865225	+	0.501384i	$0.832824\pi$
$60$	11.7309	1.51446
$61$	−6.87382	−0.880102	−0.440051	−	0.897973i	$-0.645040\pi$
$61$	−6.87382	−0.880102	−0.440051	+	0.897973i	$0.645040\pi$
$62$	4.85621	0.616739
$63$	2.42988	0.306136
$64$	−10.8017	−1.35022
$65$	−6.87853	−0.853176
$66$	−11.4275	−1.40663
$67$	12.4288	1.51842	0.759212	−	0.650843i	$-0.225584\pi$
$67$	12.4288	1.51842	0.759212	+	0.650843i	$0.225584\pi$
$68$	−8.52369	−1.03365
$69$	−1.00000	−0.120386
$70$	18.3465	2.19283
$71$	−0.894099	−0.106110	−0.0530550	−	0.998592i	$-0.516896\pi$
$71$	−0.894099	−0.106110	−0.0530550	+	0.998592i	$0.516896\pi$
$72$	4.09689	0.482823
$73$	11.0287	1.29081	0.645403	−	0.763842i	$-0.276689\pi$
$73$	11.0287	1.29081	0.645403	+	0.763842i	$0.276689\pi$
$74$	21.0791	2.45040
$75$	4.97709	0.574705
$76$	3.48498	0.399755
$77$	−11.6163	−1.32381
$78$	−5.20547	−0.589404
$79$	−1.79625	−0.202093	−0.101047	−	0.994882i	$-0.532219\pi$
$79$	−1.79625	−0.202093	−0.101047	+	0.994882i	$0.532219\pi$
$80$	7.47114	0.835299
$81$	1.00000	0.111111
$82$	−10.6848	−1.17994
$83$	−1.59927	−0.175543	−0.0877715	−	0.996141i	$-0.527975\pi$
$83$	−1.59927	−0.175543	−0.0877715	+	0.996141i	$0.527975\pi$
$84$	9.02434	0.984637
$85$	−7.24934	−0.786302
$86$	−17.6649	−1.90485
$87$	−1.00000	−0.107211
$88$	−19.5857	−2.08784
$89$	−5.46304	−0.579081	−0.289540	−	0.957166i	$-0.593502\pi$
$89$	−5.46304	−0.579081	−0.289540	+	0.957166i	$0.593502\pi$
$90$	7.55038	0.795880
$91$	−5.29149	−0.554699
$92$	−3.71391	−0.387202
$93$	2.03157	0.210663
$94$	20.4910	2.11349
$95$	2.96395	0.304095
$96$	−2.53983	−0.259220
$97$	5.89728	0.598778	0.299389	−	0.954131i	$-0.403217\pi$
$97$	5.89728	0.598778	0.299389	+	0.954131i	$0.403217\pi$
$98$	−2.61911	−0.264571
$99$	−4.78063	−0.480471
$100$	18.4845	1.84845
$101$	12.0537	1.19938	0.599692	−	0.800231i	$-0.295290\pi$
$101$	12.0537	1.19938	0.599692	+	0.800231i	$0.295290\pi$
$102$	−5.48609	−0.543204
$103$	19.7379	1.94483	0.972417	−	0.233249i	$-0.0749356\pi$
$103$	19.7379	1.94483	0.972417	+	0.233249i	$0.0749356\pi$
$104$	−8.92170	−0.874844
$105$	7.67514	0.749017
$106$	−23.5994	−2.29217
$107$	12.5674	1.21494	0.607469	−	0.794343i	$-0.292185\pi$
$107$	12.5674	1.21494	0.607469	+	0.794343i	$0.292185\pi$
$108$	3.71391	0.357371
$109$	−15.8919	−1.52217	−0.761084	−	0.648654i	$-0.775332\pi$
$109$	−15.8919	−1.52217	−0.761084	+	0.648654i	$0.775332\pi$
$110$	−36.0955	−3.44157
$111$	8.81831	0.836997
$112$	5.74738	0.543076
$113$	5.60386	0.527167	0.263583	−	0.964637i	$-0.415096\pi$
$113$	5.60386	0.527167	0.263583	+	0.964637i	$0.415096\pi$
$114$	2.24304	0.210080
$115$	−3.15865	−0.294546
$116$	−3.71391	−0.344828
$117$	−2.17768	−0.201326
$118$	−31.7725	−2.92490
$119$	−5.57675	−0.511220
$120$	12.9406	1.18131
$121$	11.8544	1.07767
$122$	−16.4310	−1.48760
$123$	−4.46994	−0.403041
$124$	7.54505	0.677565
$125$	−0.0723603	−0.00647210
$126$	5.80833	0.517447
$127$	−7.87263	−0.698583	−0.349291	−	0.937014i	$-0.613578\pi$
$127$	−7.87263	−0.698583	−0.349291	+	0.937014i	$0.613578\pi$
$128$	−20.7406	−1.83323
$129$	−7.39000	−0.650653
$130$	−16.4423	−1.44208
$131$	15.8513	1.38493	0.692465	−	0.721451i	$-0.256525\pi$
$131$	15.8513	1.38493	0.692465	+	0.721451i	$0.256525\pi$
$132$	−17.7548	−1.54536
$133$	2.28010	0.197710
$134$	29.7096	2.56652
$135$	3.15865	0.271854
$136$	−9.40266	−0.806271
$137$	21.0030	1.79441	0.897203	−	0.441618i	$-0.145595\pi$
$137$	21.0030	1.79441	0.897203	+	0.441618i	$0.145595\pi$
$138$	−2.39038	−0.203482
$139$	−9.14257	−0.775463	−0.387731	−	0.921772i	$-0.626741\pi$
$139$	−9.14257	−0.775463	−0.387731	+	0.921772i	$0.626741\pi$
$140$	28.5048	2.40909
$141$	8.57229	0.721917
$142$	−2.13723	−0.179353
$143$	10.4107	0.870583
$144$	2.36529	0.197108
$145$	−3.15865	−0.262312
$146$	26.3627	2.18179
$147$	−1.09569	−0.0903710
$148$	32.7504	2.69207
$149$	−13.5588	−1.11078	−0.555389	−	0.831591i	$-0.687431\pi$
$149$	−13.5588	−1.11078	−0.555389	+	0.831591i	$0.687431\pi$
$150$	11.8971	0.971397
$151$	8.23773	0.670377	0.335189	−	0.942151i	$-0.391200\pi$
$151$	8.23773	0.670377	0.335189	+	0.942151i	$0.391200\pi$
$152$	3.84436	0.311818
$153$	−2.29507	−0.185546
$154$	−27.7675	−2.23757
$155$	6.41701	0.515427
$156$	−8.08769	−0.647534
$157$	11.8740	0.947651	0.473826	−	0.880619i	$-0.342873\pi$
$157$	11.8740	0.947651	0.473826	+	0.880619i	$0.342873\pi$
$158$	−4.29370	−0.341589
$159$	−9.87266	−0.782953
$160$	−8.02243	−0.634229
$161$	−2.42988	−0.191501
$162$	2.39038	0.187806
$163$	5.63979	0.441742	0.220871	−	0.975303i	$-0.429110\pi$
$163$	5.63979	0.441742	0.220871	+	0.975303i	$0.429110\pi$
$164$	−16.6009	−1.29632
$165$	−15.1003	−1.17556
$166$	−3.82287	−0.296712
$167$	−8.62963	−0.667781	−0.333891	−	0.942612i	$-0.608362\pi$
$167$	−8.62963	−0.667781	−0.333891	+	0.942612i	$0.608362\pi$
$168$	9.95494	0.768040
$169$	−8.25772	−0.635209
$170$	−17.3287	−1.32905
$171$	0.938360	0.0717582
$172$	−27.4458	−2.09272
$173$	2.10675	0.160173	0.0800867	−	0.996788i	$-0.474480\pi$
$173$	2.10675	0.160173	0.0800867	+	0.996788i	$0.474480\pi$
$174$	−2.39038	−0.181214
$175$	12.0937	0.914200
$176$	−11.3076	−0.852342
$177$	−13.2918	−0.999075
$178$	−13.0587	−0.978793
$179$	8.27923	0.618819	0.309409	−	0.950929i	$-0.399869\pi$
$179$	8.27923	0.618819	0.309409	+	0.950929i	$0.399869\pi$
$180$	11.7309	0.874373
$181$	17.9647	1.33530	0.667652	−	0.744474i	$-0.267299\pi$
$181$	17.9647	1.33530	0.667652	+	0.744474i	$0.267299\pi$
$182$	−12.6487	−0.937581
$183$	−6.87382	−0.508127
$184$	−4.09689	−0.302027
$185$	27.8540	2.04787
$186$	4.85621	0.356075
$187$	10.9719	0.802345
$188$	31.8367	2.32193
$189$	2.42988	0.176748
$190$	7.08497	0.513998
$191$	8.23898	0.596152	0.298076	−	0.954542i	$-0.403655\pi$
$191$	8.23898	0.596152	0.298076	+	0.954542i	$0.403655\pi$
$192$	−10.8017	−0.779548
$193$	−16.2131	−1.16704	−0.583522	−	0.812097i	$-0.698326\pi$
$193$	−16.2131	−1.16704	−0.583522	+	0.812097i	$0.698326\pi$
$194$	14.0967	1.01209
$195$	−6.87853	−0.492582
$196$	−4.06929	−0.290664
$197$	−7.32108	−0.521605	−0.260803	−	0.965392i	$-0.583987\pi$
$197$	−7.32108	−0.521605	−0.260803	+	0.965392i	$0.583987\pi$
$198$	−11.4275	−0.812118
$199$	0.0705871	0.00500379	0.00250189	−	0.999997i	$-0.499204\pi$
$199$	0.0705871	0.00500379	0.00250189	+	0.999997i	$0.499204\pi$
$200$	20.3906	1.44183
$201$	12.4288	0.876663
$202$	28.8128	2.02726
$203$	−2.42988	−0.170544
$204$	−8.52369	−0.596778
$205$	−14.1190	−0.986113
$206$	47.1811	3.28726
$207$	−1.00000	−0.0695048
$208$	−5.15085	−0.357147
$209$	−4.48595	−0.310300
$210$	18.3465	1.26603
$211$	−13.5254	−0.931126	−0.465563	−	0.885015i	$-0.654148\pi$
$211$	−13.5254	−0.931126	−0.465563	+	0.885015i	$0.654148\pi$
$212$	−36.6661	−2.51824
$213$	−0.894099	−0.0612626
$214$	30.0409	2.05355
$215$	−23.3424	−1.59194
$216$	4.09689	0.278758
$217$	4.93646	0.335109
$218$	−37.9876	−2.57285
$219$	11.0287	0.745248
$220$	−56.0813	−3.78100
$221$	4.99793	0.336197
$222$	21.0791	1.41474
$223$	−4.16049	−0.278607	−0.139303	−	0.990250i	$-0.544486\pi$
$223$	−4.16049	−0.278607	−0.139303	+	0.990250i	$0.544486\pi$
$224$	−6.17147	−0.412349
$225$	4.97709	0.331806
$226$	13.3953	0.891045
$227$	3.67016	0.243597	0.121799	−	0.992555i	$-0.461134\pi$
$227$	3.67016	0.243597	0.121799	+	0.992555i	$0.461134\pi$
$228$	3.48498	0.230799
$229$	14.2122	0.939168	0.469584	−	0.882888i	$-0.344404\pi$
$229$	14.2122	0.939168	0.469584	+	0.882888i	$0.344404\pi$
$230$	−7.55038	−0.497857
$231$	−11.6163	−0.764299
$232$	−4.09689	−0.268974
$233$	−17.2860	−1.13244	−0.566221	−	0.824254i	$-0.691595\pi$
$233$	−17.2860	−1.13244	−0.566221	+	0.824254i	$0.691595\pi$
$234$	−5.20547	−0.340292
$235$	27.0769	1.76630
$236$	−49.3646	−3.21336
$237$	−1.79625	−0.116679
$238$	−13.3305	−0.864091
$239$	1.14677	0.0741787	0.0370893	−	0.999312i	$-0.488191\pi$
$239$	1.14677	0.0741787	0.0370893	+	0.999312i	$0.488191\pi$
$240$	7.47114	0.482260
$241$	−10.7407	−0.691869	−0.345934	−	0.938259i	$-0.612438\pi$
$241$	−10.7407	−0.691869	−0.345934	+	0.938259i	$0.612438\pi$
$242$	28.3365	1.82154
$243$	1.00000	0.0641500
$244$	−25.5287	−1.63431
$245$	−3.46091	−0.221109
$246$	−10.6848	−0.681241
$247$	−2.04345	−0.130021
$248$	8.32309	0.528517
$249$	−1.59927	−0.101350
$250$	−0.172968	−0.0109395
$251$	4.65534	0.293843	0.146921	−	0.989148i	$-0.453064\pi$
$251$	4.65534	0.293843	0.146921	+	0.989148i	$0.453064\pi$
$252$	9.02434	0.568480
$253$	4.78063	0.300556
$254$	−18.8186	−1.18078
$255$	−7.24934	−0.453972
$256$	−27.9744	−1.74840
$257$	14.4815	0.903329	0.451665	−	0.892188i	$-0.350830\pi$
$257$	14.4815	0.903329	0.451665	+	0.892188i	$0.350830\pi$
$258$	−17.6649	−1.09977
$259$	21.4274	1.33144
$260$	−25.5462	−1.58431
$261$	−1.00000	−0.0618984
$262$	37.8905	2.34088
$263$	−19.6332	−1.21063	−0.605317	−	0.795984i	$-0.706954\pi$
$263$	−19.6332	−1.21063	−0.605317	+	0.795984i	$0.706954\pi$
$264$	−19.5857	−1.20542
$265$	−31.1843	−1.91564
$266$	5.45030	0.334180
$267$	−5.46304	−0.334333
$268$	46.1596	2.81964
$269$	−24.7142	−1.50685	−0.753425	−	0.657534i	$-0.771600\pi$
$269$	−24.7142	−1.50685	−0.753425	+	0.657534i	$0.771600\pi$
$270$	7.55038	0.459501
$271$	13.6676	0.830251	0.415125	−	0.909764i	$-0.363738\pi$
$271$	13.6676	0.830251	0.415125	+	0.909764i	$0.363738\pi$
$272$	−5.42853	−0.329153
$273$	−5.29149	−0.320256
$274$	50.2051	3.03300
$275$	−23.7936	−1.43481
$276$	−3.71391	−0.223551
$277$	−12.1650	−0.730923	−0.365461	−	0.930826i	$-0.619089\pi$
$277$	−12.1650	−0.730923	−0.365461	+	0.930826i	$0.619089\pi$
$278$	−21.8542	−1.31073
$279$	2.03157	0.121627
$280$	31.4442	1.87915
$281$	13.6829	0.816256	0.408128	−	0.912925i	$-0.366182\pi$
$281$	13.6829	0.816256	0.408128	+	0.912925i	$0.366182\pi$
$282$	20.4910	1.22022
$283$	14.6941	0.873475	0.436738	−	0.899589i	$-0.356134\pi$
$283$	14.6941	0.873475	0.436738	+	0.899589i	$0.356134\pi$
$284$	−3.32060	−0.197041
$285$	2.96395	0.175569
$286$	24.8854	1.47151
$287$	−10.8614	−0.641129
$288$	−2.53983	−0.149661
$289$	−11.7326	−0.690155
$290$	−7.55038	−0.443373
$291$	5.89728	0.345704
$292$	40.9594	2.39697
$293$	−5.47872	−0.320070	−0.160035	−	0.987111i	$-0.551161\pi$
$293$	−5.47872	−0.320070	−0.160035	+	0.987111i	$0.551161\pi$
$294$	−2.61911	−0.152750
$295$	−41.9843	−2.44442
$296$	36.1276	2.09988
$297$	−4.78063	−0.277400
$298$	−32.4106	−1.87749
$299$	2.17768	0.125938
$300$	18.4845	1.06720
$301$	−17.9568	−1.03501
$302$	19.6913	1.13311
$303$	12.0537	0.692465
$304$	2.21950	0.127297
$305$	−21.7120	−1.24323
$306$	−5.48609	−0.313619
$307$	−17.7117	−1.01086	−0.505430	−	0.862868i	$-0.668666\pi$
$307$	−17.7117	−1.01086	−0.505430	+	0.862868i	$0.668666\pi$
$308$	−43.1420	−2.45825
$309$	19.7379	1.12285
$310$	15.3391	0.871201
$311$	10.0656	0.570767	0.285383	−	0.958413i	$-0.407879\pi$
$311$	10.0656	0.570767	0.285383	+	0.958413i	$0.407879\pi$
$312$	−8.92170	−0.505092
$313$	−16.9982	−0.960795	−0.480397	−	0.877051i	$-0.659508\pi$
$313$	−16.9982	−0.960795	−0.480397	+	0.877051i	$0.659508\pi$
$314$	28.3834	1.60177
$315$	7.67514	0.432445
$316$	−6.67109	−0.375278
$317$	1.56006	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$317$	1.56006	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$318$	−23.5994	−1.32339
$319$	4.78063	0.267664
$320$	−34.1189	−1.90731
$321$	12.5674	0.701445
$322$	−5.80833	−0.323685
$323$	−2.15361	−0.119830
$324$	3.71391	0.206328
$325$	−10.8385	−0.601212
$326$	13.4812	0.746656
$327$	−15.8919	−0.878824
$328$	−18.3128	−1.01116
$329$	20.8296	1.14837
$330$	−36.0955	−1.98699
$331$	11.8661	0.652220	0.326110	−	0.945332i	$-0.394262\pi$
$331$	11.8661	0.652220	0.326110	+	0.945332i	$0.394262\pi$
$332$	−5.93955	−0.325975
$333$	8.81831	0.483240
$334$	−20.6281	−1.12872
$335$	39.2584	2.14492
$336$	5.74738	0.313545
$337$	26.4173	1.43904	0.719521	−	0.694471i	$-0.244361\pi$
$337$	26.4173	1.43904	0.719521	+	0.694471i	$0.244361\pi$
$338$	−19.7391	−1.07366
$339$	5.60386	0.304360
$340$	−26.9234	−1.46013
$341$	−9.71216	−0.525943
$342$	2.24304	0.121289
$343$	−19.6715	−1.06216
$344$	−30.2760	−1.63237
$345$	−3.15865	−0.170056
$346$	5.03593	0.270734
$347$	−0.659727	−0.0354160	−0.0177080	−	0.999843i	$-0.505637\pi$
$347$	−0.659727	−0.0354160	−0.0177080	+	0.999843i	$0.505637\pi$
$348$	−3.71391	−0.199086
$349$	−11.7501	−0.628968	−0.314484	−	0.949263i	$-0.601831\pi$
$349$	−11.7501	−0.628968	−0.314484	+	0.949263i	$0.601831\pi$
$350$	28.9086	1.54523
$351$	−2.17768	−0.116236
$352$	12.1420	0.647169
$353$	16.8656	0.897668	0.448834	−	0.893615i	$-0.351839\pi$
$353$	16.8656	0.897668	0.448834	+	0.893615i	$0.351839\pi$
$354$	−31.7725	−1.68869
$355$	−2.82415	−0.149890
$356$	−20.2892	−1.07533
$357$	−5.57675	−0.295153
$358$	19.7905	1.04596
$359$	14.7760	0.779850	0.389925	−	0.920847i	$-0.372501\pi$
$359$	14.7760	0.779850	0.389925	+	0.920847i	$0.372501\pi$
$360$	12.9406	0.682032
$361$	−18.1195	−0.953657
$362$	42.9424	2.25700
$363$	11.8544	0.622195
$364$	−19.6521	−1.03005
$365$	34.8357	1.82338
$366$	−16.4310	−0.858864
$367$	18.7271	0.977548	0.488774	−	0.872411i	$-0.337444\pi$
$367$	18.7271	0.977548	0.488774	+	0.872411i	$0.337444\pi$
$368$	−2.36529	−0.123299
$369$	−4.46994	−0.232696
$370$	66.5816	3.46141
$371$	−23.9894	−1.24547
$372$	7.54505	0.391192
$373$	27.3333	1.41526	0.707632	−	0.706581i	$-0.249763\pi$
$373$	27.3333	1.41526	0.707632	+	0.706581i	$0.249763\pi$
$374$	26.2270	1.35616
$375$	−0.0723603	−0.00373667
$376$	35.1197	1.81116
$377$	2.17768	0.112156
$378$	5.80833	0.298748
$379$	29.7499	1.52815	0.764074	−	0.645128i	$-0.223196\pi$
$379$	29.7499	1.52815	0.764074	+	0.645128i	$0.223196\pi$
$380$	11.0079	0.564691
$381$	−7.87263	−0.403327
$382$	19.6943	1.00765
$383$	−19.3342	−0.987934	−0.493967	−	0.869481i	$-0.664454\pi$
$383$	−19.3342	−0.987934	−0.493967	+	0.869481i	$0.664454\pi$
$384$	−20.7406	−1.05841
$385$	−36.6920	−1.87000
$386$	−38.7554	−1.97260
$387$	−7.39000	−0.375655
$388$	21.9019	1.11190
$389$	−32.2003	−1.63262	−0.816309	−	0.577615i	$-0.803984\pi$
$389$	−32.2003	−1.63262	−0.816309	+	0.577615i	$0.803984\pi$
$390$	−16.4423	−0.832587
$391$	2.29507	0.116067
$392$	−4.48892	−0.226725
$393$	15.8513	0.799590
$394$	−17.5002	−0.881645
$395$	−5.67372	−0.285476
$396$	−17.7548	−0.892213
$397$	−23.9354	−1.20129	−0.600643	−	0.799518i	$-0.705089\pi$
$397$	−23.9354	−1.20129	−0.600643	+	0.799518i	$0.705089\pi$
$398$	0.168730	0.00845766
$399$	2.28010	0.114148
$400$	11.7723	0.588614
$401$	3.39086	0.169332	0.0846658	−	0.996409i	$-0.473018\pi$
$401$	3.39086	0.169332	0.0846658	+	0.996409i	$0.473018\pi$
$402$	29.7096	1.48178
$403$	−4.42409	−0.220380
$404$	44.7662	2.22720
$405$	3.15865	0.156955
$406$	−5.80833	−0.288263
$407$	−42.1571	−2.08965
$408$	−9.40266	−0.465501
$409$	−17.0266	−0.841909	−0.420955	−	0.907082i	$-0.638305\pi$
$409$	−17.0266	−0.841909	−0.420955	+	0.907082i	$0.638305\pi$
$410$	−33.7497	−1.66678
$411$	21.0030	1.03600
$412$	73.3048	3.61147
$413$	−32.2975	−1.58926
$414$	−2.39038	−0.117481
$415$	−5.05155	−0.247971
$416$	5.53092	0.271176
$417$	−9.14257	−0.447714
$418$	−10.7231	−0.524485
$419$	−2.81255	−0.137402	−0.0687009	−	0.997637i	$-0.521885\pi$
$419$	−2.81255	−0.137402	−0.0687009	+	0.997637i	$0.521885\pi$
$420$	28.5048	1.39089
$421$	−31.0768	−1.51459	−0.757294	−	0.653074i	$-0.773479\pi$
$421$	−31.0768	−1.51459	−0.757294	+	0.653074i	$0.773479\pi$
$422$	−32.3308	−1.57384
$423$	8.57229	0.416799
$424$	−40.4472	−1.96429
$425$	−11.4228	−0.554087
$426$	−2.13723	−0.103549
$427$	−16.7025	−0.808293
$428$	46.6743	2.25609
$429$	10.4107	0.502632
$430$	−55.7973	−2.69078
$431$	14.6439	0.705374	0.352687	−	0.935741i	$-0.385268\pi$
$431$	14.6439	0.705374	0.352687	+	0.935741i	$0.385268\pi$
$432$	2.36529	0.113800
$433$	−0.248219	−0.0119286	−0.00596431	−	0.999982i	$-0.501899\pi$
$433$	−0.248219	−0.0119286	−0.00596431	+	0.999982i	$0.501899\pi$
$434$	11.8000	0.566418
$435$	−3.15865	−0.151446
$436$	−59.0210	−2.82659
$437$	−0.938360	−0.0448878
$438$	26.3627	1.25966
$439$	13.7025	0.653985	0.326993	−	0.945027i	$-0.393965\pi$
$439$	13.7025	0.653985	0.326993	+	0.945027i	$0.393965\pi$
$440$	−61.8644	−2.94927
$441$	−1.09569	−0.0521757
$442$	11.9469	0.568258
$443$	0.365423	0.0173618	0.00868088	−	0.999962i	$-0.497237\pi$
$443$	0.365423	0.0173618	0.00868088	+	0.999962i	$0.497237\pi$
$444$	32.7504	1.55426
$445$	−17.2558	−0.818006
$446$	−9.94514	−0.470916
$447$	−13.5588	−0.641308
$448$	−26.2469	−1.24005
$449$	11.4622	0.540936	0.270468	−	0.962729i	$-0.412822\pi$
$449$	11.4622	0.540936	0.270468	+	0.962729i	$0.412822\pi$
$450$	11.8971	0.560836
$451$	21.3691	1.00623
$452$	20.8122	0.978924
$453$	8.23773	0.387042
$454$	8.77307	0.411741
$455$	−16.7140	−0.783564
$456$	3.84436	0.180028
$457$	26.1310	1.22236	0.611178	−	0.791493i	$-0.290696\pi$
$457$	26.1310	1.22236	0.611178	+	0.791493i	$0.290696\pi$
$458$	33.9725	1.58743
$459$	−2.29507	−0.107125
$460$	−11.7309	−0.546958
$461$	−33.7314	−1.57103	−0.785515	−	0.618843i	$-0.787602\pi$
$461$	−33.7314	−1.57103	−0.785515	+	0.618843i	$0.787602\pi$
$462$	−27.7675	−1.29186
$463$	31.5775	1.46753	0.733765	−	0.679404i	$-0.237761\pi$
$463$	31.5775	1.46753	0.733765	+	0.679404i	$0.237761\pi$
$464$	−2.36529	−0.109806
$465$	6.41701	0.297582
$466$	−41.3200	−1.91411
$467$	−24.1995	−1.11982	−0.559909	−	0.828554i	$-0.689164\pi$
$467$	−24.1995	−1.11982	−0.559909	+	0.828554i	$0.689164\pi$
$468$	−8.08769	−0.373854
$469$	30.2006	1.39453
$470$	64.7240	2.98550
$471$	11.8740	0.547127
$472$	−54.4551	−2.50650
$473$	35.3288	1.62442
$474$	−4.29370	−0.197216
$475$	4.67030	0.214288
$476$	−20.7115	−0.949312
$477$	−9.87266	−0.452038
$478$	2.74122	0.125381
$479$	−11.9413	−0.545614	−0.272807	−	0.962069i	$-0.587952\pi$
$479$	−11.9413	−0.545614	−0.272807	+	0.962069i	$0.587952\pi$
$480$	−8.02243	−0.366172
$481$	−19.2034	−0.875601
$482$	−25.6743	−1.16943
$483$	−2.42988	−0.110563
$484$	44.0262	2.00119
$485$	18.6275	0.845829
$486$	2.39038	0.108430
$487$	30.8043	1.39588	0.697938	−	0.716158i	$-0.254101\pi$
$487$	30.8043	1.39588	0.697938	+	0.716158i	$0.254101\pi$
$488$	−28.1613	−1.27480
$489$	5.63979	0.255040
$490$	−8.27287	−0.373730
$491$	−8.46946	−0.382221	−0.191111	−	0.981568i	$-0.561209\pi$
$491$	−8.46946	−0.382221	−0.191111	+	0.981568i	$0.561209\pi$
$492$	−16.6009	−0.748428
$493$	2.29507	0.103365
$494$	−4.88461	−0.219769
$495$	−15.1003	−0.678710
$496$	4.80525	0.215762
$497$	−2.17255	−0.0974522
$498$	−3.82287	−0.171307
$499$	−20.0685	−0.898388	−0.449194	−	0.893434i	$-0.648289\pi$
$499$	−20.0685	−0.898388	−0.449194	+	0.893434i	$0.648289\pi$
$500$	−0.268739	−0.0120184
$501$	−8.62963	−0.385544
$502$	11.1280	0.496668
$503$	−28.3993	−1.26626	−0.633131	−	0.774045i	$-0.718231\pi$
$503$	−28.3993	−1.26626	−0.633131	+	0.774045i	$0.718231\pi$
$504$	9.95494	0.443428
$505$	38.0733	1.69424
$506$	11.4275	0.508015
$507$	−8.25772	−0.366738
$508$	−29.2382	−1.29724
$509$	−27.3417	−1.21190	−0.605951	−	0.795502i	$-0.707207\pi$
$509$	−27.3417	−1.21190	−0.605951	+	0.795502i	$0.707207\pi$
$510$	−17.3287	−0.767327
$511$	26.7983	1.18549
$512$	−25.3881	−1.12201
$513$	0.938360	0.0414296
$514$	34.6162	1.52685
$515$	62.3452	2.74726
$516$	−27.4458	−1.20823
$517$	−40.9809	−1.80234
$518$	51.2196	2.25046
$519$	2.10675	0.0924762
$520$	−28.1805	−1.23580
$521$	22.4253	0.982472	0.491236	−	0.871026i	$-0.336545\pi$
$521$	22.4253	0.982472	0.491236	+	0.871026i	$0.336545\pi$
$522$	−2.39038	−0.104624
$523$	19.1790	0.838638	0.419319	−	0.907839i	$-0.362269\pi$
$523$	19.1790	0.838638	0.419319	+	0.907839i	$0.362269\pi$
$524$	58.8701	2.57175
$525$	12.0937	0.527814
$526$	−46.9307	−2.04628
$527$	−4.66259	−0.203106
$528$	−11.3076	−0.492100
$529$	1.00000	0.0434783
$530$	−74.5423	−3.23791
$531$	−13.2918	−0.576816
$532$	8.46808	0.367138
$533$	9.73408	0.421630
$534$	−13.0587	−0.565106
$535$	39.6961	1.71621
$536$	50.9195	2.19939
$537$	8.27923	0.357275
$538$	−59.0762	−2.54696
$539$	5.23809	0.225620
$540$	11.7309	0.504820
$541$	12.1208	0.521113	0.260557	−	0.965459i	$-0.416094\pi$
$541$	12.1208	0.521113	0.260557	+	0.965459i	$0.416094\pi$
$542$	32.6708	1.40333
$543$	17.9647	0.770938
$544$	5.82909	0.249920
$545$	−50.1970	−2.15020
$546$	−12.6487	−0.541313
$547$	6.56447	0.280677	0.140338	−	0.990104i	$-0.455181\pi$
$547$	6.56447	0.280677	0.140338	+	0.990104i	$0.455181\pi$
$548$	78.0031	3.33213
$549$	−6.87382	−0.293367
$550$	−56.8758	−2.42519
$551$	−0.938360	−0.0399755
$552$	−4.09689	−0.174375
$553$	−4.36466	−0.185604
$554$	−29.0789	−1.23544
$555$	27.8540	1.18234
$556$	−33.9547	−1.44000
$557$	28.2143	1.19548	0.597740	−	0.801690i	$-0.296066\pi$
$557$	28.2143	1.19548	0.597740	+	0.801690i	$0.296066\pi$
$558$	4.85621	0.205580
$559$	16.0930	0.680663
$560$	18.1540	0.767145
$561$	10.9719	0.463234
$562$	32.7074	1.37968
$563$	−3.65291	−0.153952	−0.0769758	−	0.997033i	$-0.524526\pi$
$563$	−3.65291	−0.153952	−0.0769758	+	0.997033i	$0.524526\pi$
$564$	31.8367	1.34057
$565$	17.7006	0.744672
$566$	35.1245	1.47639
$567$	2.42988	0.102045
$568$	−3.66302	−0.153697
$569$	28.6879	1.20266	0.601331	−	0.799000i	$-0.294637\pi$
$569$	28.6879	1.20266	0.601331	+	0.799000i	$0.294637\pi$
$570$	7.08497	0.296757
$571$	−22.5670	−0.944401	−0.472200	−	0.881491i	$-0.656540\pi$
$571$	−22.5670	−0.944401	−0.472200	+	0.881491i	$0.656540\pi$
$572$	38.6642	1.61663
$573$	8.23898	0.344188
$574$	−25.9629	−1.08367
$575$	−4.97709	−0.207559
$576$	−10.8017	−0.450072
$577$	27.8932	1.16121	0.580604	−	0.814186i	$-0.302816\pi$
$577$	27.8932	1.16121	0.580604	+	0.814186i	$0.302816\pi$
$578$	−28.0454	−1.16654
$579$	−16.2131	−0.673793
$580$	−11.7309	−0.487101
$581$	−3.88604	−0.161220
$582$	14.0967	0.584328
$583$	47.1975	1.95472
$584$	45.1832	1.86969
$585$	−6.87853	−0.284392
$586$	−13.0962	−0.541000
$587$	−14.2541	−0.588329	−0.294164	−	0.955755i	$-0.595041\pi$
$587$	−14.2541	−0.588329	−0.294164	+	0.955755i	$0.595041\pi$
$588$	−4.06929	−0.167815
$589$	1.90634	0.0785494
$590$	−100.358	−4.13169
$591$	−7.32108	−0.301149
$592$	20.8579	0.857254
$593$	34.0157	1.39686	0.698429	−	0.715679i	$-0.253883\pi$
$593$	34.0157	1.39686	0.698429	+	0.715679i	$0.253883\pi$
$594$	−11.4275	−0.468876
$595$	−17.6150	−0.722146
$596$	−50.3560	−2.06266
$597$	0.0705871	0.00288894
$598$	5.20547	0.212868
$599$	−47.8118	−1.95354	−0.976769	−	0.214294i	$-0.931255\pi$
$599$	−47.8118	−1.95354	−0.976769	+	0.214294i	$0.931255\pi$
$600$	20.3906	0.832442
$601$	−7.29685	−0.297645	−0.148822	−	0.988864i	$-0.547548\pi$
$601$	−7.29685	−0.297645	−0.148822	+	0.988864i	$0.547548\pi$
$602$	−42.9235	−1.74943
$603$	12.4288	0.506141
$604$	30.5942	1.24486
$605$	37.4440	1.52231
$606$	28.8128	1.17044
$607$	31.5054	1.27876	0.639382	−	0.768889i	$-0.279190\pi$
$607$	31.5054	1.27876	0.639382	+	0.768889i	$0.279190\pi$
$608$	−2.38327	−0.0966544
$609$	−2.42988	−0.0984636
$610$	−51.8999	−2.10137
$611$	−18.6677	−0.755214
$612$	−8.52369	−0.344550
$613$	48.1582	1.94509	0.972546	−	0.232712i	$-0.0747599\pi$
$613$	48.1582	1.94509	0.972546	+	0.232712i	$0.0747599\pi$
$614$	−42.3376	−1.70861
$615$	−14.1190	−0.569332
$616$	−47.5909	−1.91749
$617$	41.4816	1.66999	0.834993	−	0.550260i	$-0.185472\pi$
$617$	41.4816	1.66999	0.834993	+	0.550260i	$0.185472\pi$
$618$	47.1811	1.89790
$619$	40.8839	1.64326	0.821631	−	0.570019i	$-0.193064\pi$
$619$	40.8839	1.64326	0.821631	+	0.570019i	$0.193064\pi$
$620$	23.8322	0.957123
$621$	−1.00000	−0.0401286
$622$	24.0605	0.964740
$623$	−13.2745	−0.531832
$624$	−5.15085	−0.206199
$625$	−25.1140	−1.00456
$626$	−40.6321	−1.62399
$627$	−4.48595	−0.179152
$628$	44.0991	1.75974
$629$	−20.2387	−0.806969
$630$	18.3465	0.730942
$631$	−11.8414	−0.471397	−0.235699	−	0.971826i	$-0.575738\pi$
$631$	−11.8414	−0.471397	−0.235699	+	0.971826i	$0.575738\pi$
$632$	−7.35901	−0.292726
$633$	−13.5254	−0.537586
$634$	3.72913	0.148103
$635$	−24.8669	−0.986813
$636$	−36.6661	−1.45391
$637$	2.38606	0.0945391
$638$	11.4275	0.452419
$639$	−0.894099	−0.0353700
$640$	−65.5123	−2.58960
$641$	−22.4092	−0.885108	−0.442554	−	0.896742i	$-0.645928\pi$
$641$	−22.4092	−0.885108	−0.442554	+	0.896742i	$0.645928\pi$
$642$	30.0409	1.18562
$643$	−14.1825	−0.559304	−0.279652	−	0.960101i	$-0.590219\pi$
$643$	−14.1825	−0.559304	−0.279652	+	0.960101i	$0.590219\pi$
$644$	−9.02434	−0.355609
$645$	−23.3424	−0.919108
$646$	−5.14793	−0.202543
$647$	−8.37854	−0.329394	−0.164697	−	0.986344i	$-0.552665\pi$
$647$	−8.37854	−0.329394	−0.164697	+	0.986344i	$0.552665\pi$
$648$	4.09689	0.160941
$649$	63.5433	2.49429
$650$	−25.9081	−1.01620
$651$	4.93646	0.193475
$652$	20.9457	0.820295
$653$	−3.06753	−0.120042	−0.0600208	−	0.998197i	$-0.519117\pi$
$653$	−3.06753	−0.120042	−0.0600208	+	0.998197i	$0.519117\pi$
$654$	−37.9876	−1.48543
$655$	50.0686	1.95634
$656$	−10.5727	−0.412795
$657$	11.0287	0.430269
$658$	49.7907	1.94104
$659$	13.2636	0.516677	0.258338	−	0.966055i	$-0.416825\pi$
$659$	13.2636	0.516677	0.258338	+	0.966055i	$0.416825\pi$
$660$	−56.0813	−2.18296
$661$	−33.8991	−1.31852	−0.659261	−	0.751914i	$-0.729131\pi$
$661$	−33.8991	−1.31852	−0.659261	+	0.751914i	$0.729131\pi$
$662$	28.3645	1.10242
$663$	4.99793	0.194104
$664$	−6.55204	−0.254268
$665$	7.20205	0.279283
$666$	21.0791	0.816798
$667$	1.00000	0.0387202
$668$	−32.0497	−1.24004
$669$	−4.16049	−0.160854
$670$	93.8424	3.62545
$671$	32.8612	1.26859
$672$	−6.17147	−0.238070
$673$	−47.4292	−1.82826	−0.914131	−	0.405419i	$-0.867126\pi$
$673$	−47.4292	−1.82826	−0.914131	+	0.405419i	$0.867126\pi$
$674$	63.1473	2.43234
$675$	4.97709	0.191568
$676$	−30.6684	−1.17955
$677$	−42.6889	−1.64067	−0.820335	−	0.571884i	$-0.806213\pi$
$677$	−42.6889	−1.64067	−0.820335	+	0.571884i	$0.806213\pi$
$678$	13.3953	0.514445
$679$	14.3297	0.549922
$680$	−29.6997	−1.13893
$681$	3.67016	0.140641
$682$	−23.2157	−0.888976
$683$	−28.3839	−1.08608	−0.543039	−	0.839707i	$-0.682727\pi$
$683$	−28.3839	−1.08608	−0.543039	+	0.839707i	$0.682727\pi$
$684$	3.48498	0.133252
$685$	66.3411	2.53476
$686$	−47.0224	−1.79532
$687$	14.2122	0.542229
$688$	−17.4795	−0.666400
$689$	21.4995	0.819064
$690$	−7.55038	−0.287438
$691$	33.1507	1.26111	0.630555	−	0.776144i	$-0.282827\pi$
$691$	33.1507	1.26111	0.630555	+	0.776144i	$0.282827\pi$
$692$	7.82428	0.297435
$693$	−11.6163	−0.441268
$694$	−1.57700	−0.0598619
$695$	−28.8782	−1.09541
$696$	−4.09689	−0.155292
$697$	10.2588	0.388581
$698$	−28.0872	−1.06311
$699$	−17.2860	−0.653815
$700$	44.9150	1.69763
$701$	−27.3546	−1.03317	−0.516585	−	0.856236i	$-0.672797\pi$
$701$	−27.3546	−1.03317	−0.516585	+	0.856236i	$0.672797\pi$
$702$	−5.20547	−0.196468
$703$	8.27475	0.312088
$704$	51.6391	1.94622
$705$	27.0769	1.01978
$706$	40.3153	1.51729
$707$	29.2889	1.10152
$708$	−49.3646	−1.85524
$709$	−43.4221	−1.63075	−0.815375	−	0.578933i	$-0.803469\pi$
$709$	−43.4221	−1.63075	−0.815375	+	0.578933i	$0.803469\pi$
$710$	−6.75078	−0.253352
$711$	−1.79625	−0.0673645
$712$	−22.3815	−0.838780
$713$	−2.03157	−0.0760827
$714$	−13.3305	−0.498883
$715$	32.8837	1.22978
$716$	30.7483	1.14912
$717$	1.14677	0.0428271
$718$	35.3203	1.31814
$719$	−30.4399	−1.13522	−0.567609	−	0.823299i	$-0.692131\pi$
$719$	−30.4399	−1.13522	−0.567609	+	0.823299i	$0.692131\pi$
$720$	7.47114	0.278433
$721$	47.9607	1.78615
$722$	−43.3124	−1.61192
$723$	−10.7407	−0.399450
$724$	66.7191	2.47960
$725$	−4.97709	−0.184845
$726$	28.3365	1.05167
$727$	10.0827	0.373946	0.186973	−	0.982365i	$-0.440132\pi$
$727$	10.0827	0.373946	0.186973	+	0.982365i	$0.440132\pi$
$728$	−21.6786	−0.803464
$729$	1.00000	0.0370370
$730$	83.2705	3.08198
$731$	16.9606	0.627310
$732$	−25.5287	−0.943569
$733$	20.4391	0.754935	0.377468	−	0.926023i	$-0.376795\pi$
$733$	20.4391	0.754935	0.377468	+	0.926023i	$0.376795\pi$
$734$	44.7649	1.65230
$735$	−3.46091	−0.127657
$736$	2.53983	0.0936193
$737$	−59.4177	−2.18868
$738$	−10.6848	−0.393314
$739$	40.4826	1.48918	0.744589	−	0.667524i	$-0.232646\pi$
$739$	40.4826	1.48918	0.744589	+	0.667524i	$0.232646\pi$
$740$	103.447	3.80279
$741$	−2.04345	−0.0750678
$742$	−57.3436	−2.10515
$743$	25.5835	0.938567	0.469283	−	0.883048i	$-0.344512\pi$
$743$	25.5835	0.938567	0.469283	+	0.883048i	$0.344512\pi$
$744$	8.32309	0.305139
$745$	−42.8275	−1.56908
$746$	65.3369	2.39215
$747$	−1.59927	−0.0585143
$748$	40.7486	1.48992
$749$	30.5373	1.11581
$750$	−0.172968	−0.00631591
$751$	43.2730	1.57906	0.789528	−	0.613715i	$-0.210325\pi$
$751$	43.2730	1.57906	0.789528	+	0.613715i	$0.210325\pi$
$752$	20.2760	0.739390
$753$	4.65534	0.169650
$754$	5.20547	0.189572
$755$	26.0201	0.946970
$756$	9.02434	0.328212
$757$	6.79084	0.246817	0.123409	−	0.992356i	$-0.460617\pi$
$757$	6.79084	0.246817	0.123409	+	0.992356i	$0.460617\pi$
$758$	71.1135	2.58296
$759$	4.78063	0.173526
$760$	12.1430	0.440472
$761$	−14.6792	−0.532120	−0.266060	−	0.963956i	$-0.585722\pi$
$761$	−14.6792	−0.532120	−0.266060	+	0.963956i	$0.585722\pi$
$762$	−18.8186	−0.681725
$763$	−38.6154	−1.39797
$764$	30.5988	1.10703
$765$	−7.24934	−0.262101
$766$	−46.2161	−1.66986
$767$	28.9453	1.04516
$768$	−27.9744	−1.00944
$769$	17.8923	0.645213	0.322607	−	0.946533i	$-0.395441\pi$
$769$	17.8923	0.645213	0.322607	+	0.946533i	$0.395441\pi$
$770$	−87.7078	−3.16077
$771$	14.4815	0.521537
$772$	−60.2139	−2.16715
$773$	9.53626	0.342996	0.171498	−	0.985185i	$-0.445139\pi$
$773$	9.53626	0.342996	0.171498	+	0.985185i	$0.445139\pi$
$774$	−17.6649	−0.634951
$775$	10.1113	0.363208
$776$	24.1605	0.867310
$777$	21.4274	0.768704
$778$	−76.9708	−2.75954
$779$	−4.19441	−0.150280
$780$	−25.5462	−0.914701
$781$	4.27435	0.152948
$782$	5.48609	0.196182
$783$	−1.00000	−0.0357371
$784$	−2.59163	−0.0925582
$785$	37.5060	1.33865
$786$	37.8905	1.35151
$787$	23.8968	0.851830	0.425915	−	0.904763i	$-0.359952\pi$
$787$	23.8968	0.851830	0.425915	+	0.904763i	$0.359952\pi$
$788$	−27.1898	−0.968597
$789$	−19.6332	−0.698960
$790$	−13.5623	−0.482526
$791$	13.6167	0.484154
$792$	−19.5857	−0.695947
$793$	14.9690	0.531563
$794$	−57.2147	−2.03048
$795$	−31.1843	−1.10599
$796$	0.262154	0.00929180
$797$	42.1568	1.49327	0.746635	−	0.665234i	$-0.231668\pi$
$797$	42.1568	1.49327	0.746635	+	0.665234i	$0.231668\pi$
$798$	5.45030	0.192939
$799$	−19.6740	−0.696018
$800$	−12.6409	−0.446925
$801$	−5.46304	−0.193027
$802$	8.10545	0.286213
$803$	−52.7239	−1.86059
$804$	46.1596	1.62792
$805$	−7.67514	−0.270513
$806$	−10.5753	−0.372497
$807$	−24.7142	−0.869980
$808$	49.3825	1.73727
$809$	−39.1673	−1.37705	−0.688524	−	0.725214i	$-0.741741\pi$
$809$	−39.1673	−1.37705	−0.688524	+	0.725214i	$0.741741\pi$
$810$	7.55038	0.265293
$811$	−3.04999	−0.107100	−0.0535498	−	0.998565i	$-0.517054\pi$
$811$	−3.04999	−0.107100	−0.0535498	+	0.998565i	$0.517054\pi$
$812$	−9.02434	−0.316692
$813$	13.6676	0.479345
$814$	−100.771	−3.53203
$815$	17.8141	0.624002
$816$	−5.42853	−0.190036
$817$	−6.93448	−0.242607
$818$	−40.6999	−1.42304
$819$	−5.29149	−0.184900
$820$	−52.4366	−1.83117
$821$	11.0845	0.386853	0.193426	−	0.981115i	$-0.438040\pi$
$821$	11.0845	0.386853	0.193426	+	0.981115i	$0.438040\pi$
$822$	50.2051	1.75110
$823$	9.62712	0.335580	0.167790	−	0.985823i	$-0.446337\pi$
$823$	9.62712	0.335580	0.167790	+	0.985823i	$0.446337\pi$
$824$	80.8640	2.81703
$825$	−23.7936	−0.828388
$826$	−77.2033	−2.68625
$827$	10.5464	0.366735	0.183368	−	0.983044i	$-0.441300\pi$
$827$	10.5464	0.366735	0.183368	+	0.983044i	$0.441300\pi$
$828$	−3.71391	−0.129067
$829$	−5.96252	−0.207087	−0.103544	−	0.994625i	$-0.533018\pi$
$829$	−5.96252	−0.207087	−0.103544	+	0.994625i	$0.533018\pi$
$830$	−12.0751	−0.419133
$831$	−12.1650	−0.421999
$832$	23.5227	0.815503
$833$	2.51469	0.0871289
$834$	−21.8542	−0.756749
$835$	−27.2580	−0.943303
$836$	−16.6604	−0.576212
$837$	2.03157	0.0702212
$838$	−6.72305	−0.232244
$839$	−17.6819	−0.610449	−0.305224	−	0.952280i	$-0.598731\pi$
$839$	−17.6819	−0.610449	−0.305224	+	0.952280i	$0.598731\pi$
$840$	31.4442	1.08493
$841$	1.00000	0.0344828
$842$	−74.2852	−2.56004
$843$	13.6829	0.471266
$844$	−50.2320	−1.72906
$845$	−26.0833	−0.897292
$846$	20.4910	0.704496
$847$	28.8048	0.989744
$848$	−23.3517	−0.801902
$849$	14.6941	0.504301
$850$	−27.3048	−0.936547
$851$	−8.81831	−0.302288
$852$	−3.32060	−0.113762
$853$	−11.8538	−0.405868	−0.202934	−	0.979192i	$-0.565048\pi$
$853$	−11.8538	−0.405868	−0.202934	+	0.979192i	$0.565048\pi$
$854$	−39.9254	−1.36622
$855$	2.96395	0.101365
$856$	51.4873	1.75980
$857$	−38.7345	−1.32314	−0.661572	−	0.749881i	$-0.730111\pi$
$857$	−38.7345	−1.32314	−0.661572	+	0.749881i	$0.730111\pi$
$858$	24.8854	0.849574
$859$	−17.4284	−0.594649	−0.297325	−	0.954776i	$-0.596094\pi$
$859$	−17.4284	−0.594649	−0.297325	+	0.954776i	$0.596094\pi$
$860$	−86.6917	−2.95616
$861$	−10.8614	−0.370156
$862$	35.0046	1.19226
$863$	−14.8652	−0.506017	−0.253009	−	0.967464i	$-0.581420\pi$
$863$	−14.8652	−0.506017	−0.253009	+	0.967464i	$0.581420\pi$
$864$	−2.53983	−0.0864067
$865$	6.65450	0.226260
$866$	−0.593336	−0.0201624
$867$	−11.7326	−0.398461
$868$	18.3335	0.622281
$869$	8.58718	0.291300
$870$	−7.55038	−0.255982
$871$	−27.0660	−0.917096
$872$	−65.1073	−2.20481
$873$	5.89728	0.199593
$874$	−2.24304	−0.0758718
$875$	−0.175827	−0.00594403
$876$	40.9594	1.38389
$877$	7.07319	0.238845	0.119422	−	0.992844i	$-0.461896\pi$
$877$	7.07319	0.238845	0.119422	+	0.992844i	$0.461896\pi$
$878$	32.7542	1.10540
$879$	−5.47872	−0.184793
$880$	−35.7168	−1.20401
$881$	−27.5511	−0.928221	−0.464111	−	0.885777i	$-0.653626\pi$
$881$	−27.5511	−0.928221	−0.464111	+	0.885777i	$0.653626\pi$
$882$	−2.61911	−0.0881902
$883$	−13.7429	−0.462485	−0.231243	−	0.972896i	$-0.574279\pi$
$883$	−13.7429	−0.462485	−0.231243	+	0.972896i	$0.574279\pi$
$884$	18.5619	0.624303
$885$	−41.9843	−1.41129
$886$	0.873499	0.0293458
$887$	27.3298	0.917644	0.458822	−	0.888528i	$-0.348272\pi$
$887$	27.3298	0.917644	0.458822	+	0.888528i	$0.348272\pi$
$888$	36.1276	1.21236
$889$	−19.1295	−0.641584
$890$	−41.2480	−1.38264
$891$	−4.78063	−0.160157
$892$	−15.4517	−0.517360
$893$	8.04390	0.269179
$894$	−32.4106	−1.08397
$895$	26.1512	0.874139
$896$	−50.3971	−1.68365
$897$	2.17768	0.0727105
$898$	27.3990	0.914318
$899$	−2.03157	−0.0677565
$900$	18.4845	0.616149
$901$	22.6585	0.754863
$902$	51.0803	1.70079
$903$	−17.9568	−0.597565
$904$	22.9584	0.763584
$905$	56.7442	1.88624
$906$	19.6913	0.654199
$907$	0.183241	0.00608442	0.00304221	−	0.999995i	$-0.499032\pi$
$907$	0.183241	0.00608442	0.00304221	+	0.999995i	$0.499032\pi$
$908$	13.6306	0.452349
$909$	12.0537	0.399795
$910$	−39.9527	−1.32442
$911$	7.12816	0.236167	0.118083	−	0.993004i	$-0.462325\pi$
$911$	7.12816	0.236167	0.118083	+	0.993004i	$0.462325\pi$
$912$	2.21950	0.0734949
$913$	7.64553	0.253030
$914$	62.4629	2.06609
$915$	−21.7120	−0.717777
$916$	52.7827	1.74399
$917$	38.5166	1.27193
$918$	−5.48609	−0.181068
$919$	9.27976	0.306111	0.153055	−	0.988218i	$-0.451089\pi$
$919$	9.27976	0.306111	0.153055	+	0.988218i	$0.451089\pi$
$920$	−12.9406	−0.426640
$921$	−17.7117	−0.583620
$922$	−80.6309	−2.65544
$923$	1.94706	0.0640882
$924$	−43.1420	−1.41927
$925$	43.8895	1.44308
$926$	75.4821	2.48050
$927$	19.7379	0.648278
$928$	2.53983	0.0833739
$929$	−3.42936	−0.112514	−0.0562568	−	0.998416i	$-0.517917\pi$
$929$	−3.42936	−0.112514	−0.0562568	+	0.998416i	$0.517917\pi$
$930$	15.3391	0.502988
$931$	−1.02815	−0.0336963
$932$	−64.1985	−2.10289
$933$	10.0656	0.329532
$934$	−57.8459	−1.89278
$935$	34.6564	1.13339
$936$	−8.92170	−0.291615
$937$	44.4249	1.45130	0.725649	−	0.688065i	$-0.241540\pi$
$937$	44.4249	1.45130	0.725649	+	0.688065i	$0.241540\pi$
$938$	72.1908	2.35711
$939$	−16.9982	−0.554715
$940$	100.561	3.27994
$941$	−50.8611	−1.65802	−0.829012	−	0.559231i	$-0.811096\pi$
$941$	−50.8611	−1.65802	−0.829012	+	0.559231i	$0.811096\pi$
$942$	28.3834	0.924782
$943$	4.46994	0.145561
$944$	−31.4391	−1.02326
$945$	7.67514	0.249672
$946$	84.4493	2.74568
$947$	28.1631	0.915179	0.457589	−	0.889164i	$-0.348713\pi$
$947$	28.1631	0.915179	0.457589	+	0.889164i	$0.348713\pi$
$948$	−6.67109	−0.216667
$949$	−24.0169	−0.779620
$950$	11.1638	0.362201
$951$	1.56006	0.0505883
$952$	−22.8473	−0.740486
$953$	−43.2630	−1.40143	−0.700713	−	0.713444i	$-0.747134\pi$
$953$	−43.2630	−1.40143	−0.700713	+	0.713444i	$0.747134\pi$
$954$	−23.5994	−0.764058
$955$	26.0241	0.842119
$956$	4.25901	0.137746
$957$	4.78063	0.154536
$958$	−28.5443	−0.922225
$959$	51.0347	1.64800
$960$	−34.1189	−1.10118
$961$	−26.8727	−0.866863
$962$	−45.9035	−1.47999
$963$	12.5674	0.404980
$964$	−39.8899	−1.28477
$965$	−51.2116	−1.64856
$966$	−5.80833	−0.186880
$967$	−52.7067	−1.69493	−0.847466	−	0.530850i	$-0.821873\pi$
$967$	−52.7067	−1.69493	−0.847466	+	0.530850i	$0.821873\pi$
$968$	48.5662	1.56098
$969$	−2.15361	−0.0691838
$970$	44.5267	1.42966
$971$	−36.3426	−1.16629	−0.583145	−	0.812368i	$-0.698178\pi$
$971$	−36.3426	−1.16629	−0.583145	+	0.812368i	$0.698178\pi$
$972$	3.71391	0.119124
$973$	−22.2153	−0.712191
$974$	73.6339	2.35938
$975$	−10.8385	−0.347110
$976$	−16.2586	−0.520425
$977$	−36.6007	−1.17096	−0.585480	−	0.810687i	$-0.699094\pi$
$977$	−36.6007	−1.17096	−0.585480	+	0.810687i	$0.699094\pi$
$978$	13.4812	0.431082
$979$	26.1168	0.834695
$980$	−12.8535	−0.410590
$981$	−15.8919	−0.507389
$982$	−20.2452	−0.646051
$983$	−27.5375	−0.878310	−0.439155	−	0.898411i	$-0.644722\pi$
$983$	−27.5375	−0.878310	−0.439155	+	0.898411i	$0.644722\pi$
$984$	−18.3128	−0.583792
$985$	−23.1248	−0.736816
$986$	5.48609	0.174713
$987$	20.8296	0.663014
$988$	−7.58917	−0.241444
$989$	7.39000	0.234988
$990$	−36.0955	−1.14719
$991$	−8.95507	−0.284467	−0.142234	−	0.989833i	$-0.545428\pi$
$991$	−8.95507	−0.284467	−0.142234	+	0.989833i	$0.545428\pi$
$992$	−5.15982	−0.163825
$993$	11.8661	0.376560
$994$	−5.19322	−0.164719
$995$	0.222960	0.00706831
$996$	−5.93955	−0.188202
$997$	60.8600	1.92745	0.963727	−	0.266889i	$-0.0859958\pi$
$997$	60.8600	1.92745	0.963727	+	0.266889i	$0.0859958\pi$
$998$	−47.9712	−1.51850
$999$	8.81831	0.278999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.n.1.14	✓	16
3.2	odd	2		6003.2.a.r.1.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.n.1.14	✓	16	1.1	even	1	trivial
6003.2.a.r.1.3		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.39038 q^{2} +1.00000 q^{3} +3.71391 q^{4} +3.15865 q^{5} +2.39038 q^{6} +2.42988 q^{7} +4.09689 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.39038 q^{2} +1.00000 q^{3} +3.71391 q^{4} +3.15865 q^{5} +2.39038 q^{6} +2.42988 q^{7} +4.09689 q^{8} +1.00000 q^{9} +7.55038 q^{10} -4.78063 q^{11} +3.71391 q^{12} -2.17768 q^{13} +5.80833 q^{14} +3.15865 q^{15} +2.36529 q^{16} -2.29507 q^{17} +2.39038 q^{18} +0.938360 q^{19} +11.7309 q^{20} +2.42988 q^{21} -11.4275 q^{22} -1.00000 q^{23} +4.09689 q^{24} +4.97709 q^{25} -5.20547 q^{26} +1.00000 q^{27} +9.02434 q^{28} -1.00000 q^{29} +7.55038 q^{30} +2.03157 q^{31} -2.53983 q^{32} -4.78063 q^{33} -5.48609 q^{34} +7.67514 q^{35} +3.71391 q^{36} +8.81831 q^{37} +2.24304 q^{38} -2.17768 q^{39} +12.9406 q^{40} -4.46994 q^{41} +5.80833 q^{42} -7.39000 q^{43} -17.7548 q^{44} +3.15865 q^{45} -2.39038 q^{46} +8.57229 q^{47} +2.36529 q^{48} -1.09569 q^{49} +11.8971 q^{50} -2.29507 q^{51} -8.08769 q^{52} -9.87266 q^{53} +2.39038 q^{54} -15.1003 q^{55} +9.95494 q^{56} +0.938360 q^{57} -2.39038 q^{58} -13.2918 q^{59} +11.7309 q^{60} -6.87382 q^{61} +4.85621 q^{62} +2.42988 q^{63} -10.8017 q^{64} -6.87853 q^{65} -11.4275 q^{66} +12.4288 q^{67} -8.52369 q^{68} -1.00000 q^{69} +18.3465 q^{70} -0.894099 q^{71} +4.09689 q^{72} +11.0287 q^{73} +21.0791 q^{74} +4.97709 q^{75} +3.48498 q^{76} -11.6163 q^{77} -5.20547 q^{78} -1.79625 q^{79} +7.47114 q^{80} +1.00000 q^{81} -10.6848 q^{82} -1.59927 q^{83} +9.02434 q^{84} -7.24934 q^{85} -17.6649 q^{86} -1.00000 q^{87} -19.5857 q^{88} -5.46304 q^{89} +7.55038 q^{90} -5.29149 q^{91} -3.71391 q^{92} +2.03157 q^{93} +20.4910 q^{94} +2.96395 q^{95} -2.53983 q^{96} +5.89728 q^{97} -2.61911 q^{98} -4.78063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * q^99

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