LMFDB - Embedded newform 1859.2.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 8x^{6} + 18x^{5} + 7x^{4} - 22x^{3} - 3x^{2} + 6x + 1 $ x^8 - 2x^7 - 8x^6 + 18x^5 + 7x^4 - 22x^3 - 3x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.681121$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.681121 q^{2} -0.0549966 q^{3} -1.53607 q^{4} -3.68496 q^{5} +0.0374594 q^{6} +0.234733 q^{7} +2.40849 q^{8} -2.99698 q^{9} +O(q^{10})$	\(q-0.681121 q^{2} -0.0549966 q^{3} -1.53607 q^{4} -3.68496 q^{5} +0.0374594 q^{6} +0.234733 q^{7} +2.40849 q^{8} -2.99698 q^{9} +2.50991 q^{10} +1.00000 q^{11} +0.0844789 q^{12} -0.159881 q^{14} +0.202661 q^{15} +1.43167 q^{16} +4.66146 q^{17} +2.04130 q^{18} +3.14468 q^{19} +5.66038 q^{20} -0.0129095 q^{21} -0.681121 q^{22} +6.80837 q^{23} -0.132459 q^{24} +8.57896 q^{25} +0.329813 q^{27} -0.360567 q^{28} +3.72903 q^{29} -0.138036 q^{30} -4.79327 q^{31} -5.79213 q^{32} -0.0549966 q^{33} -3.17501 q^{34} -0.864981 q^{35} +4.60358 q^{36} -2.87587 q^{37} -2.14191 q^{38} -8.87521 q^{40} -9.28785 q^{41} +0.00879293 q^{42} +0.735404 q^{43} -1.53607 q^{44} +11.0437 q^{45} -4.63732 q^{46} -10.5401 q^{47} -0.0787372 q^{48} -6.94490 q^{49} -5.84331 q^{50} -0.256364 q^{51} -6.11295 q^{53} -0.224643 q^{54} -3.68496 q^{55} +0.565352 q^{56} -0.172947 q^{57} -2.53992 q^{58} +1.95945 q^{59} -0.311302 q^{60} +7.24883 q^{61} +3.26480 q^{62} -0.703488 q^{63} +1.08179 q^{64} +0.0374594 q^{66} +9.34656 q^{67} -7.16034 q^{68} -0.374437 q^{69} +0.589156 q^{70} +6.25027 q^{71} -7.21820 q^{72} -1.66649 q^{73} +1.95882 q^{74} -0.471814 q^{75} -4.83047 q^{76} +0.234733 q^{77} -6.85143 q^{79} -5.27566 q^{80} +8.97279 q^{81} +6.32614 q^{82} -15.1471 q^{83} +0.0198300 q^{84} -17.1773 q^{85} -0.500899 q^{86} -0.205084 q^{87} +2.40849 q^{88} +17.0601 q^{89} -7.52213 q^{90} -10.4582 q^{92} +0.263614 q^{93} +7.17906 q^{94} -11.5880 q^{95} +0.318548 q^{96} -7.75492 q^{97} +4.73032 q^{98} -2.99698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9} + 10 q^{10} + 8 q^{11} - 8 q^{12} - 6 q^{14} - 2 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{19} - 16 q^{20} - 2 q^{21} - 2 q^{22} - 14 q^{23} - 26 q^{24} + 12 q^{25} + 24 q^{27} - 20 q^{28} - 10 q^{29} + 14 q^{30} - 32 q^{31} + 40 q^{32} - 14 q^{34} + 10 q^{35} - 24 q^{37} + 12 q^{38} - 14 q^{40} - 2 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{46} - 18 q^{47} - 6 q^{48} + 2 q^{49} - 38 q^{50} + 12 q^{51} - 8 q^{53} - 2 q^{54} - 8 q^{55} - 28 q^{56} - 24 q^{57} + 14 q^{58} - 18 q^{59} + 14 q^{60} - 4 q^{61} - 8 q^{63} + 6 q^{64} - 4 q^{66} + 14 q^{67} - 34 q^{68} - 10 q^{69} - 18 q^{70} + 12 q^{71} - 8 q^{72} - 26 q^{73} + 2 q^{74} - 18 q^{75} - 54 q^{76} - 14 q^{77} + 26 q^{79} - 24 q^{80} - 16 q^{81} - 64 q^{82} - 16 q^{83} + 74 q^{84} - 56 q^{85} - 32 q^{86} - 18 q^{87} + 6 q^{88} + 8 q^{89} - 20 q^{90} - 30 q^{92} - 48 q^{93} - 4 q^{94} + 22 q^{95} - 16 q^{96} - 20 q^{97} + 46 q^{98} + 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9 + 10 * q^10 + 8 * q^11 - 8 * q^12 - 6 * q^14 - 2 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^18 - 4 * q^19 - 16 * q^20 - 2 * q^21 - 2 * q^22 - 14 * q^23 - 26 * q^24 + 12 * q^25 + 24 * q^27 - 20 * q^28 - 10 * q^29 + 14 * q^30 - 32 * q^31 + 40 * q^32 - 14 * q^34 + 10 * q^35 - 24 * q^37 + 12 * q^38 - 14 * q^40 - 2 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^46 - 18 * q^47 - 6 * q^48 + 2 * q^49 - 38 * q^50 + 12 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^55 - 28 * q^56 - 24 * q^57 + 14 * q^58 - 18 * q^59 + 14 * q^60 - 4 * q^61 - 8 * q^63 + 6 * q^64 - 4 * q^66 + 14 * q^67 - 34 * q^68 - 10 * q^69 - 18 * q^70 + 12 * q^71 - 8 * q^72 - 26 * q^73 + 2 * q^74 - 18 * q^75 - 54 * q^76 - 14 * q^77 + 26 * q^79 - 24 * q^80 - 16 * q^81 - 64 * q^82 - 16 * q^83 + 74 * q^84 - 56 * q^85 - 32 * q^86 - 18 * q^87 + 6 * q^88 + 8 * q^89 - 20 * q^90 - 30 * q^92 - 48 * q^93 - 4 * q^94 + 22 * q^95 - 16 * q^96 - 20 * q^97 + 46 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.681121	−0.481625	−0.240813	−	0.970572i	$-0.577414\pi$
$2$	−0.681121	−0.481625	−0.240813	+	0.970572i	$0.577414\pi$
$3$	−0.0549966	−0.0317523	−0.0158762	−	0.999874i	$-0.505054\pi$
$3$	−0.0549966	−0.0317523	−0.0158762	+	0.999874i	$0.505054\pi$
$4$	−1.53607	−0.768037
$5$	−3.68496	−1.64797	−0.823983	−	0.566615i	$-0.808253\pi$
$5$	−3.68496	−1.64797	−0.823983	+	0.566615i	$0.808253\pi$
$6$	0.0374594	0.0152927
$7$	0.234733	0.0887206	0.0443603	−	0.999016i	$-0.485875\pi$
$7$	0.234733	0.0887206	0.0443603	+	0.999016i	$0.485875\pi$
$8$	2.40849	0.851531
$9$	−2.99698	−0.998992
$10$	2.50991	0.793702
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.0844789	0.0243870
$13$	0	0
$13$	0	0
$14$	−0.159881	−0.0427301
$15$	0.202661	0.0523267
$16$	1.43167	0.357918
$17$	4.66146	1.13057	0.565285	−	0.824896i	$-0.308766\pi$
$17$	4.66146	1.13057	0.565285	+	0.824896i	$0.308766\pi$
$18$	2.04130	0.481140
$19$	3.14468	0.721440	0.360720	−	0.932674i	$-0.382531\pi$
$19$	3.14468	0.721440	0.360720	+	0.932674i	$0.382531\pi$
$20$	5.66038	1.26570
$21$	−0.0129095	−0.00281708
$22$	−0.681121	−0.145215
$23$	6.80837	1.41964	0.709822	−	0.704381i	$-0.248775\pi$
$23$	6.80837	1.41964	0.709822	+	0.704381i	$0.248775\pi$
$24$	−0.132459	−0.0270381
$25$	8.57896	1.71579
$26$	0	0
$27$	0.329813	0.0634726
$28$	−0.360567	−0.0681407
$29$	3.72903	0.692463	0.346231	−	0.938149i	$-0.387461\pi$
$29$	3.72903	0.692463	0.346231	+	0.938149i	$0.387461\pi$
$30$	−0.138036	−0.0252019
$31$	−4.79327	−0.860897	−0.430449	−	0.902615i	$-0.641645\pi$
$31$	−4.79327	−0.860897	−0.430449	+	0.902615i	$0.641645\pi$
$32$	−5.79213	−1.02391
$33$	−0.0549966	−0.00957369
$34$	−3.17501	−0.544511
$35$	−0.864981	−0.146208
$36$	4.60358	0.767263
$37$	−2.87587	−0.472790	−0.236395	−	0.971657i	$-0.575966\pi$
$37$	−2.87587	−0.472790	−0.236395	+	0.971657i	$0.575966\pi$
$38$	−2.14191	−0.347464
$39$	0	0
$40$	−8.87521	−1.40329
$41$	−9.28785	−1.45052	−0.725259	−	0.688476i	$-0.758280\pi$
$41$	−9.28785	−1.45052	−0.725259	+	0.688476i	$0.758280\pi$
$42$	0.00879293	0.00135678
$43$	0.735404	0.112148	0.0560740	−	0.998427i	$-0.482142\pi$
$43$	0.735404	0.112148	0.0560740	+	0.998427i	$0.482142\pi$
$44$	−1.53607	−0.231572
$45$	11.0437	1.64630
$46$	−4.63732	−0.683736
$47$	−10.5401	−1.53743	−0.768713	−	0.639594i	$-0.779103\pi$
$47$	−10.5401	−1.53743	−0.768713	+	0.639594i	$0.779103\pi$
$48$	−0.0787372	−0.0113647
$49$	−6.94490	−0.992129
$50$	−5.84331	−0.826368
$51$	−0.256364	−0.0358982
$52$	0	0
$53$	−6.11295	−0.839678	−0.419839	−	0.907599i	$-0.637913\pi$
$53$	−6.11295	−0.839678	−0.419839	+	0.907599i	$0.637913\pi$
$54$	−0.224643	−0.0305700
$55$	−3.68496	−0.496880
$56$	0.565352	0.0755483
$57$	−0.172947	−0.0229074
$58$	−2.53992	−0.333507
$59$	1.95945	0.255098	0.127549	−	0.991832i	$-0.459289\pi$
$59$	1.95945	0.255098	0.127549	+	0.991832i	$0.459289\pi$
$60$	−0.311302	−0.0401889
$61$	7.24883	0.928118	0.464059	−	0.885804i	$-0.346393\pi$
$61$	7.24883	0.928118	0.464059	+	0.885804i	$0.346393\pi$
$62$	3.26480	0.414630
$63$	−0.703488	−0.0886311
$64$	1.08179	0.135224
$65$	0	0
$66$	0.0374594	0.00461093
$67$	9.34656	1.14186	0.570932	−	0.820997i	$-0.306582\pi$
$67$	9.34656	1.14186	0.570932	+	0.820997i	$0.306582\pi$
$68$	−7.16034	−0.868319
$69$	−0.374437	−0.0450770
$70$	0.589156	0.0704177
$71$	6.25027	0.741771	0.370886	−	0.928679i	$-0.379054\pi$
$71$	6.25027	0.741771	0.370886	+	0.928679i	$0.379054\pi$
$72$	−7.21820	−0.850673
$73$	−1.66649	−0.195048	−0.0975240	−	0.995233i	$-0.531092\pi$
$73$	−1.66649	−0.195048	−0.0975240	+	0.995233i	$0.531092\pi$
$74$	1.95882	0.227708
$75$	−0.471814	−0.0544804
$76$	−4.83047	−0.554093
$77$	0.234733	0.0267503
$78$	0	0
$79$	−6.85143	−0.770846	−0.385423	−	0.922740i	$-0.625944\pi$
$79$	−6.85143	−0.770846	−0.385423	+	0.922740i	$0.625944\pi$
$80$	−5.27566	−0.589837
$81$	8.97279	0.996976
$82$	6.32614	0.698606
$83$	−15.1471	−1.66261	−0.831305	−	0.555817i	$-0.812406\pi$
$83$	−15.1471	−1.66261	−0.831305	+	0.555817i	$0.812406\pi$
$84$	0.0198300	0.00216363
$85$	−17.1773	−1.86314
$86$	−0.500899	−0.0540133
$87$	−0.205084	−0.0219873
$88$	2.40849	0.256746
$89$	17.0601	1.80837	0.904185	−	0.427140i	$-0.140479\pi$
$89$	17.0601	1.80837	0.904185	+	0.427140i	$0.140479\pi$
$90$	−7.52213	−0.792902
$91$	0	0
$92$	−10.4582	−1.09034
$93$	0.263614	0.0273355
$94$	7.17906	0.740463
$95$	−11.5880	−1.18891
$96$	0.318548	0.0325116
$97$	−7.75492	−0.787393	−0.393696	−	0.919241i	$-0.628804\pi$
$97$	−7.75492	−0.787393	−0.393696	+	0.919241i	$0.628804\pi$
$98$	4.73032	0.477834
$99$	−2.99698	−0.301207
$100$	−13.1779	−1.31779
$101$	5.28275	0.525653	0.262826	−	0.964843i	$-0.415345\pi$
$101$	5.28275	0.525653	0.262826	+	0.964843i	$0.415345\pi$
$102$	0.174615	0.0172895
$103$	2.15665	0.212501	0.106251	−	0.994339i	$-0.466115\pi$
$103$	2.15665	0.212501	0.106251	+	0.994339i	$0.466115\pi$
$104$	0	0
$105$	0.0475710	0.00464246
$106$	4.16366	0.404410
$107$	5.15984	0.498821	0.249410	−	0.968398i	$-0.419763\pi$
$107$	5.15984	0.498821	0.249410	+	0.968398i	$0.419763\pi$
$108$	−0.506618	−0.0487493
$109$	−10.0882	−0.966276	−0.483138	−	0.875544i	$-0.660503\pi$
$109$	−10.0882	−0.966276	−0.483138	+	0.875544i	$0.660503\pi$
$110$	2.50991	0.239310
$111$	0.158163	0.0150122
$112$	0.336060	0.0317547
$113$	9.43178	0.887267	0.443634	−	0.896208i	$-0.353689\pi$
$113$	9.43178	0.887267	0.443634	+	0.896208i	$0.353689\pi$
$114$	0.117798	0.0110328
$115$	−25.0886	−2.33952
$116$	−5.72806	−0.531837
$117$	0	0
$118$	−1.33462	−0.122862
$119$	1.09420	0.100305
$120$	0.488107	0.0445579
$121$	1.00000	0.0909091
$122$	−4.93733	−0.447005
$123$	0.510800	0.0460573
$124$	7.36282	0.661201
$125$	−13.1883	−1.17960
$126$	0.479160	0.0426870
$127$	−21.0083	−1.86419	−0.932093	−	0.362218i	$-0.882020\pi$
$127$	−21.0083	−1.86419	−0.932093	+	0.362218i	$0.882020\pi$
$128$	10.8474	0.958786
$129$	−0.0404447	−0.00356096
$130$	0	0
$131$	0.199999	0.0174740	0.00873700	−	0.999962i	$-0.497219\pi$
$131$	0.199999	0.0174740	0.00873700	+	0.999962i	$0.497219\pi$
$132$	0.0844789	0.00735295
$133$	0.738159	0.0640065
$134$	−6.36614	−0.549951
$135$	−1.21535	−0.104601
$136$	11.2271	0.962715
$137$	0.131363	0.0112231	0.00561154	−	0.999984i	$-0.498214\pi$
$137$	0.131363	0.0112231	0.00561154	+	0.999984i	$0.498214\pi$
$138$	0.255037	0.0217102
$139$	−22.8925	−1.94172	−0.970858	−	0.239655i	$-0.922966\pi$
$139$	−22.8925	−1.94172	−0.970858	+	0.239655i	$0.922966\pi$
$140$	1.32867	0.112294
$141$	0.579668	0.0488169
$142$	−4.25719	−0.357256
$143$	0	0
$144$	−4.29069	−0.357557
$145$	−13.7413	−1.14116
$146$	1.13508	0.0939400
$147$	0.381946	0.0315024
$148$	4.41755	0.363121
$149$	−10.4908	−0.859444	−0.429722	−	0.902961i	$-0.641388\pi$
$149$	−10.4908	−0.859444	−0.429722	+	0.902961i	$0.641388\pi$
$150$	0.321362	0.0262391
$151$	15.4640	1.25844	0.629220	−	0.777227i	$-0.283374\pi$
$151$	15.4640	1.25844	0.629220	+	0.777227i	$0.283374\pi$
$152$	7.57395	0.614328
$153$	−13.9703	−1.12943
$154$	−0.159881	−0.0128836
$155$	17.6630	1.41873
$156$	0	0
$157$	−11.4008	−0.909887	−0.454943	−	0.890520i	$-0.650340\pi$
$157$	−11.4008	−0.909887	−0.454943	+	0.890520i	$0.650340\pi$
$158$	4.66665	0.371259
$159$	0.336192	0.0266617
$160$	21.3438	1.68737
$161$	1.59815	0.125952
$162$	−6.11155	−0.480169
$163$	−5.52069	−0.432414	−0.216207	−	0.976348i	$-0.569369\pi$
$163$	−5.52069	−0.432414	−0.216207	+	0.976348i	$0.569369\pi$
$164$	14.2668	1.11405
$165$	0.202661	0.0157771
$166$	10.3170	0.800755
$167$	−13.3331	−1.03175	−0.515873	−	0.856665i	$-0.672532\pi$
$167$	−13.3331	−1.03175	−0.515873	+	0.856665i	$0.672532\pi$
$168$	−0.0310925	−0.00239883
$169$	0	0
$170$	11.6998	0.897335
$171$	−9.42454	−0.720712
$172$	−1.12963	−0.0861339
$173$	19.4796	1.48101	0.740504	−	0.672052i	$-0.234587\pi$
$173$	19.4796	1.48101	0.740504	+	0.672052i	$0.234587\pi$
$174$	0.139687	0.0105896
$175$	2.01376	0.152226
$176$	1.43167	0.107916
$177$	−0.107763	−0.00809997
$178$	−11.6200	−0.870957
$179$	19.7046	1.47279	0.736397	−	0.676550i	$-0.236526\pi$
$179$	19.7046	1.47279	0.736397	+	0.676550i	$0.236526\pi$
$180$	−16.9640	−1.26442
$181$	−1.95428	−0.145260	−0.0726301	−	0.997359i	$-0.523139\pi$
$181$	−1.95428	−0.145260	−0.0726301	+	0.997359i	$0.523139\pi$
$182$	0	0
$183$	−0.398661	−0.0294699
$184$	16.3979	1.20887
$185$	10.5975	0.779142
$186$	−0.179553	−0.0131655
$187$	4.66146	0.340879
$188$	16.1903	1.18080
$189$	0.0774179	0.00563133
$190$	7.89286	0.572608
$191$	−4.99448	−0.361388	−0.180694	−	0.983539i	$-0.557834\pi$
$191$	−4.99448	−0.361388	−0.180694	+	0.983539i	$0.557834\pi$
$192$	−0.0594950	−0.00429368
$193$	−2.19423	−0.157944	−0.0789722	−	0.996877i	$-0.525164\pi$
$193$	−2.19423	−0.157944	−0.0789722	+	0.996877i	$0.525164\pi$
$194$	5.28204	0.379228
$195$	0	0
$196$	10.6679	0.761992
$197$	−17.7231	−1.26272	−0.631359	−	0.775491i	$-0.717503\pi$
$197$	−17.7231	−1.26272	−0.631359	+	0.775491i	$0.717503\pi$
$198$	2.04130	0.145069
$199$	−15.0781	−1.06886	−0.534429	−	0.845214i	$-0.679473\pi$
$199$	−15.0781	−1.06886	−0.534429	+	0.845214i	$0.679473\pi$
$200$	20.6624	1.46105
$201$	−0.514030	−0.0362569
$202$	−3.59819	−0.253168
$203$	0.875324	0.0614357
$204$	0.393795	0.0275711
$205$	34.2254	2.39040
$206$	−1.46894	−0.102346
$207$	−20.4045	−1.41821
$208$	0	0
$209$	3.14468	0.217522
$210$	−0.0324016	−0.00223592
$211$	−21.4567	−1.47714	−0.738569	−	0.674178i	$-0.764498\pi$
$211$	−21.4567	−1.47714	−0.738569	+	0.674178i	$0.764498\pi$
$212$	9.38994	0.644904
$213$	−0.343744	−0.0235530
$214$	−3.51447	−0.240245
$215$	−2.70994	−0.184816
$216$	0.794354	0.0540489
$217$	−1.12514	−0.0763793
$218$	6.87130	0.465383
$219$	0.0916514	0.00619323
$220$	5.66038	0.381623
$221$	0	0
$222$	−0.107728	−0.00723025
$223$	−3.42825	−0.229573	−0.114786	−	0.993390i	$-0.536618\pi$
$223$	−3.42825	−0.229573	−0.114786	+	0.993390i	$0.536618\pi$
$224$	−1.35960	−0.0908422
$225$	−25.7109	−1.71406
$226$	−6.42418	−0.427330
$227$	−6.44246	−0.427601	−0.213801	−	0.976877i	$-0.568584\pi$
$227$	−6.44246	−0.427601	−0.213801	+	0.976877i	$0.568584\pi$
$228$	0.265659	0.0175937
$229$	4.59449	0.303613	0.151806	−	0.988410i	$-0.451491\pi$
$229$	4.59449	0.303613	0.151806	+	0.988410i	$0.451491\pi$
$230$	17.0884	1.12677
$231$	−0.0129095	−0.000849383 0
$232$	8.98134	0.589654
$233$	15.1245	0.990837	0.495419	−	0.868654i	$-0.335015\pi$
$233$	15.1245	0.990837	0.495419	+	0.868654i	$0.335015\pi$
$234$	0	0
$235$	38.8398	2.53363
$236$	−3.00986	−0.195925
$237$	0.376805	0.0244761
$238$	−0.745279	−0.0483093
$239$	−6.45923	−0.417813	−0.208906	−	0.977936i	$-0.566990\pi$
$239$	−6.45923	−0.417813	−0.208906	+	0.977936i	$0.566990\pi$
$240$	0.290144	0.0187287
$241$	−6.85805	−0.441766	−0.220883	−	0.975300i	$-0.570894\pi$
$241$	−6.85805	−0.441766	−0.220883	+	0.975300i	$0.570894\pi$
$242$	−0.681121	−0.0437841
$243$	−1.48291	−0.0951289
$244$	−11.1347	−0.712829
$245$	25.5917	1.63499
$246$	−0.347917	−0.0221824
$247$	0	0
$248$	−11.5446	−0.733081
$249$	0.833039	0.0527917
$250$	8.98285	0.568125
$251$	−18.5067	−1.16813	−0.584065	−	0.811707i	$-0.698539\pi$
$251$	−18.5067	−1.16813	−0.584065	+	0.811707i	$0.698539\pi$
$252$	1.08061	0.0680720
$253$	6.80837	0.428039
$254$	14.3092	0.897839
$255$	0.944694	0.0591590
$256$	−9.55200	−0.597000
$257$	−9.42769	−0.588083	−0.294042	−	0.955793i	$-0.595000\pi$
$257$	−9.42769	−0.588083	−0.294042	+	0.955793i	$0.595000\pi$
$258$	0.0275478	0.00171505
$259$	−0.675061	−0.0419462
$260$	0	0
$261$	−11.1758	−0.691765
$262$	−0.136224	−0.00841592
$263$	4.35864	0.268765	0.134383	−	0.990930i	$-0.457095\pi$
$263$	4.35864	0.268765	0.134383	+	0.990930i	$0.457095\pi$
$264$	−0.132459	−0.00815229
$265$	22.5260	1.38376
$266$	−0.502776	−0.0308272
$267$	−0.938250	−0.0574200
$268$	−14.3570	−0.876994
$269$	−2.73720	−0.166890	−0.0834451	−	0.996512i	$-0.526592\pi$
$269$	−2.73720	−0.166890	−0.0834451	+	0.996512i	$0.526592\pi$
$270$	0.827801	0.0503783
$271$	20.2440	1.22973	0.614867	−	0.788631i	$-0.289210\pi$
$271$	20.2440	1.22973	0.614867	+	0.788631i	$0.289210\pi$
$272$	6.67368	0.404651
$273$	0	0
$274$	−0.0894739	−0.00540532
$275$	8.57896	0.517331
$276$	0.575164	0.0346208
$277$	−12.4620	−0.748770	−0.374385	−	0.927273i	$-0.622146\pi$
$277$	−12.4620	−0.748770	−0.374385	+	0.927273i	$0.622146\pi$
$278$	15.5926	0.935179
$279$	14.3653	0.860029
$280$	−2.08330	−0.124501
$281$	17.3348	1.03411	0.517053	−	0.855954i	$-0.327029\pi$
$281$	17.3348	1.03411	0.517053	+	0.855954i	$0.327029\pi$
$282$	−0.394824	−0.0235114
$283$	−28.8399	−1.71436	−0.857178	−	0.515021i	$-0.827784\pi$
$283$	−28.8399	−1.71436	−0.857178	+	0.515021i	$0.827784\pi$
$284$	−9.60089	−0.569708
$285$	0.637303	0.0377506
$286$	0	0
$287$	−2.18016	−0.128691
$288$	17.3589	1.02288
$289$	4.72917	0.278187
$290$	9.35950	0.549609
$291$	0.426494	0.0250015
$292$	2.55985	0.149804
$293$	−3.73814	−0.218384	−0.109192	−	0.994021i	$-0.534826\pi$
$293$	−3.73814	−0.218384	−0.109192	+	0.994021i	$0.534826\pi$
$294$	−0.260151	−0.0151723
$295$	−7.22050	−0.420394
$296$	−6.92652	−0.402596
$297$	0.329813	0.0191377
$298$	7.14554	0.413930
$299$	0	0
$300$	0.724741	0.0418430
$301$	0.172623	0.00994984
$302$	−10.5328	−0.606097
$303$	−0.290533	−0.0166907
$304$	4.50216	0.258217
$305$	−26.7117	−1.52951
$306$	9.51544	0.543962
$307$	−18.2244	−1.04012	−0.520061	−	0.854129i	$-0.674091\pi$
$307$	−18.2244	−1.04012	−0.520061	+	0.854129i	$0.674091\pi$
$308$	−0.360567	−0.0205452
$309$	−0.118609	−0.00674741
$310$	−12.0307	−0.683296
$311$	−20.6916	−1.17331	−0.586657	−	0.809835i	$-0.699556\pi$
$311$	−20.6916	−1.17331	−0.586657	+	0.809835i	$0.699556\pi$
$312$	0	0
$313$	4.91431	0.277773	0.138887	−	0.990308i	$-0.455648\pi$
$313$	4.91431	0.277773	0.138887	+	0.990308i	$0.455648\pi$
$314$	7.76535	0.438224
$315$	2.59233	0.146061
$316$	10.5243	0.592038
$317$	−0.835533	−0.0469282	−0.0234641	−	0.999725i	$-0.507470\pi$
$317$	−0.835533	−0.0469282	−0.0234641	+	0.999725i	$0.507470\pi$
$318$	−0.228987	−0.0128410
$319$	3.72903	0.208785
$320$	−3.98637	−0.222845
$321$	−0.283774	−0.0158387
$322$	−1.08853	−0.0606614
$323$	14.6588	0.815637
$324$	−13.7829	−0.765715
$325$	0	0
$326$	3.76026	0.208261
$327$	0.554818	0.0306815
$328$	−22.3697	−1.23516
$329$	−2.47410	−0.136401
$330$	−0.138036	−0.00759865
$331$	−23.3209	−1.28183	−0.640917	−	0.767610i	$-0.721446\pi$
$331$	−23.3209	−1.28183	−0.640917	+	0.767610i	$0.721446\pi$
$332$	23.2671	1.27695
$333$	8.61892	0.472314
$334$	9.08144	0.496915
$335$	−34.4418	−1.88175
$336$	−0.0184822	−0.00100829
$337$	−2.91986	−0.159055	−0.0795275	−	0.996833i	$-0.525341\pi$
$337$	−2.91986	−0.159055	−0.0795275	+	0.996833i	$0.525341\pi$
$338$	0	0
$339$	−0.518716	−0.0281728
$340$	26.3856	1.43096
$341$	−4.79327	−0.259570
$342$	6.41925	0.347113
$343$	−3.27332	−0.176743
$344$	1.77122	0.0954975
$345$	1.37979	0.0742853
$346$	−13.2680	−0.713291
$347$	36.1733	1.94189	0.970943	−	0.239312i	$-0.0769220\pi$
$347$	36.1733	1.94189	0.970943	+	0.239312i	$0.0769220\pi$
$348$	0.315024	0.0168871
$349$	31.4456	1.68324	0.841621	−	0.540068i	$-0.181602\pi$
$349$	31.4456	1.68324	0.841621	+	0.540068i	$0.181602\pi$
$350$	−1.37161	−0.0733159
$351$	0	0
$352$	−5.79213	−0.308722
$353$	22.6447	1.20526	0.602629	−	0.798022i	$-0.294120\pi$
$353$	22.6447	1.20526	0.602629	+	0.798022i	$0.294120\pi$
$354$	0.0733997	0.00390115
$355$	−23.0320	−1.22241
$356$	−26.2056	−1.38890
$357$	−0.0601771	−0.00318491
$358$	−13.4212	−0.709334
$359$	−8.72791	−0.460641	−0.230321	−	0.973115i	$-0.573977\pi$
$359$	−8.72791	−0.460641	−0.230321	+	0.973115i	$0.573977\pi$
$360$	26.5988	1.40188
$361$	−9.11097	−0.479525
$362$	1.33110	0.0699609
$363$	−0.0549966	−0.00288657
$364$	0	0
$365$	6.14096	0.321432
$366$	0.271537	0.0141934
$367$	−18.7801	−0.980311	−0.490156	−	0.871635i	$-0.663060\pi$
$367$	−18.7801	−0.980311	−0.490156	+	0.871635i	$0.663060\pi$
$368$	9.74736	0.508116
$369$	27.8354	1.44906
$370$	−7.21817	−0.375255
$371$	−1.43491	−0.0744967
$372$	−0.404931	−0.0209947
$373$	−13.5002	−0.699016	−0.349508	−	0.936933i	$-0.613651\pi$
$373$	−13.5002	−0.699016	−0.349508	+	0.936933i	$0.613651\pi$
$374$	−3.17501	−0.164176
$375$	0.725314	0.0374550
$376$	−25.3857	−1.30917
$377$	0	0
$378$	−0.0527310	−0.00271219
$379$	11.3525	0.583137	0.291569	−	0.956550i	$-0.405823\pi$
$379$	11.3525	0.583137	0.291569	+	0.956550i	$0.405823\pi$
$380$	17.8001	0.913126
$381$	1.15539	0.0591923
$382$	3.40185	0.174054
$383$	2.26964	0.115973	0.0579866	−	0.998317i	$-0.481532\pi$
$383$	2.26964	0.115973	0.0579866	+	0.998317i	$0.481532\pi$
$384$	−0.596572	−0.0304437
$385$	−0.864981	−0.0440835
$386$	1.49454	0.0760700
$387$	−2.20399	−0.112035
$388$	11.9121	0.604747
$389$	−37.9291	−1.92308	−0.961542	−	0.274658i	$-0.911435\pi$
$389$	−37.9291	−1.92308	−0.961542	+	0.274658i	$0.911435\pi$
$390$	0	0
$391$	31.7369	1.60501
$392$	−16.7268	−0.844829
$393$	−0.0109993	−0.000554840 0
$394$	12.0716	0.608157
$395$	25.2473	1.27033
$396$	4.60358	0.231338
$397$	−15.3592	−0.770858	−0.385429	−	0.922737i	$-0.625947\pi$
$397$	−15.3592	−0.770858	−0.385429	+	0.922737i	$0.625947\pi$
$398$	10.2700	0.514789
$399$	−0.0405963	−0.00203236
$400$	12.2823	0.614113
$401$	−17.2400	−0.860927	−0.430463	−	0.902608i	$-0.641650\pi$
$401$	−17.2400	−0.860927	−0.430463	+	0.902608i	$0.641650\pi$
$402$	0.350116	0.0174622
$403$	0	0
$404$	−8.11469	−0.403721
$405$	−33.0644	−1.64298
$406$	−0.596201	−0.0295890
$407$	−2.87587	−0.142552
$408$	−0.617452	−0.0305684
$409$	−7.21409	−0.356714	−0.178357	−	0.983966i	$-0.557078\pi$
$409$	−7.21409	−0.356714	−0.178357	+	0.983966i	$0.557078\pi$
$410$	−23.3116	−1.15128
$411$	−0.00722451	−0.000356359 0
$412$	−3.31278	−0.163209
$413$	0.459946	0.0226325
$414$	13.8979	0.683047
$415$	55.8165	2.73992
$416$	0	0
$417$	1.25901	0.0616540
$418$	−2.14191	−0.104764
$419$	−7.47515	−0.365185	−0.182592	−	0.983189i	$-0.558449\pi$
$419$	−7.47515	−0.365185	−0.182592	+	0.983189i	$0.558449\pi$
$420$	−0.0730727	−0.00356558
$421$	−26.1988	−1.27685	−0.638425	−	0.769684i	$-0.720414\pi$
$421$	−26.1988	−1.27685	−0.638425	+	0.769684i	$0.720414\pi$
$422$	14.6146	0.711427
$423$	31.5883	1.53588
$424$	−14.7230	−0.715012
$425$	39.9904	1.93982
$426$	0.234131	0.0113437
$427$	1.70154	0.0823431
$428$	−7.92590	−0.383113
$429$	0	0
$430$	1.84579	0.0890121
$431$	19.4149	0.935183	0.467592	−	0.883945i	$-0.345122\pi$
$431$	19.4149	0.935183	0.467592	+	0.883945i	$0.345122\pi$
$432$	0.472185	0.0227180
$433$	−6.59158	−0.316771	−0.158386	−	0.987377i	$-0.550629\pi$
$433$	−6.59158	−0.316771	−0.158386	+	0.987377i	$0.550629\pi$
$434$	0.766354	0.0367862
$435$	0.755727	0.0362343
$436$	15.4963	0.742136
$437$	21.4102	1.02419
$438$	−0.0624257	−0.00298281
$439$	4.91174	0.234425	0.117212	−	0.993107i	$-0.462604\pi$
$439$	4.91174	0.234425	0.117212	+	0.993107i	$0.462604\pi$
$440$	−8.87521	−0.423109
$441$	20.8137	0.991128
$442$	0	0
$443$	15.8656	0.753799	0.376899	−	0.926254i	$-0.376990\pi$
$443$	15.8656	0.753799	0.376899	+	0.926254i	$0.376990\pi$
$444$	−0.242951	−0.0115299
$445$	−62.8660	−2.98013
$446$	2.33505	0.110568
$447$	0.576961	0.0272893
$448$	0.253932	0.0119972
$449$	−2.90549	−0.137118	−0.0685592	−	0.997647i	$-0.521840\pi$
$449$	−2.90549	−0.137118	−0.0685592	+	0.997647i	$0.521840\pi$
$450$	17.5122	0.825535
$451$	−9.28785	−0.437348
$452$	−14.4879	−0.681454
$453$	−0.850467	−0.0399584
$454$	4.38810	0.205944
$455$	0	0
$456$	−0.416542	−0.0195064
$457$	−6.51163	−0.304601	−0.152301	−	0.988334i	$-0.548668\pi$
$457$	−6.51163	−0.304601	−0.152301	+	0.988334i	$0.548668\pi$
$458$	−3.12941	−0.146228
$459$	1.53741	0.0717602
$460$	38.5380	1.79684
$461$	−16.8004	−0.782473	−0.391237	−	0.920290i	$-0.627953\pi$
$461$	−16.8004	−0.782473	−0.391237	+	0.920290i	$0.627953\pi$
$462$	0.00879293	0.000409084 0
$463$	19.5988	0.910832	0.455416	−	0.890279i	$-0.349491\pi$
$463$	19.5988	0.910832	0.455416	+	0.890279i	$0.349491\pi$
$464$	5.33875	0.247845
$465$	−0.971408	−0.0450479
$466$	−10.3016	−0.477212
$467$	−27.3872	−1.26733	−0.633665	−	0.773608i	$-0.718450\pi$
$467$	−27.3872	−1.26733	−0.633665	+	0.773608i	$0.718450\pi$
$468$	0	0
$469$	2.19394	0.101307
$470$	−26.4546	−1.22026
$471$	0.627008	0.0288910
$472$	4.71932	0.217224
$473$	0.735404	0.0338139
$474$	−0.256650	−0.0117883
$475$	26.9781	1.23784
$476$	−1.68077	−0.0770378
$477$	18.3204	0.838832
$478$	4.39952	0.201229
$479$	21.9742	1.00403	0.502014	−	0.864859i	$-0.332593\pi$
$479$	21.9742	1.00403	0.502014	+	0.864859i	$0.332593\pi$
$480$	−1.17384	−0.0535781
$481$	0	0
$482$	4.67116	0.212766
$483$	−0.0878927	−0.00399925
$484$	−1.53607	−0.0698216
$485$	28.5766	1.29760
$486$	1.01004	0.0458165
$487$	−29.8966	−1.35474	−0.677372	−	0.735640i	$-0.736881\pi$
$487$	−29.8966	−1.35474	−0.677372	+	0.735640i	$0.736881\pi$
$488$	17.4588	0.790321
$489$	0.303619	0.0137301
$490$	−17.4310	−0.787454
$491$	−10.1737	−0.459131	−0.229565	−	0.973293i	$-0.573730\pi$
$491$	−10.1737	−0.459131	−0.229565	+	0.973293i	$0.573730\pi$
$492$	−0.784627	−0.0353737
$493$	17.3827	0.782877
$494$	0	0
$495$	11.0437	0.496379
$496$	−6.86240	−0.308131
$497$	1.46714	0.0658103
$498$	−0.567400	−0.0254258
$499$	7.68790	0.344158	0.172079	−	0.985083i	$-0.444952\pi$
$499$	7.68790	0.344158	0.172079	+	0.985083i	$0.444952\pi$
$500$	20.2583	0.905977
$501$	0.733275	0.0327603
$502$	12.6053	0.562601
$503$	2.15684	0.0961687	0.0480843	−	0.998843i	$-0.484688\pi$
$503$	2.15684	0.0961687	0.0480843	+	0.998843i	$0.484688\pi$
$504$	−1.69435	−0.0754722
$505$	−19.4667	−0.866258
$506$	−4.63732	−0.206154
$507$	0	0
$508$	32.2703	1.43176
$509$	6.07978	0.269482	0.134741	−	0.990881i	$-0.456980\pi$
$509$	6.07978	0.269482	0.134741	+	0.990881i	$0.456980\pi$
$510$	−0.643450	−0.0284925
$511$	−0.391180	−0.0173048
$512$	−15.1888	−0.671256
$513$	1.03716	0.0457917
$514$	6.42140	0.283236
$515$	−7.94718	−0.350195
$516$	0.0621261	0.00273495
$517$	−10.5401	−0.463552
$518$	0.459798	0.0202024
$519$	−1.07131	−0.0470254
$520$	0	0
$521$	18.1673	0.795924	0.397962	−	0.917402i	$-0.369718\pi$
$521$	18.1673	0.795924	0.397962	+	0.917402i	$0.369718\pi$
$522$	7.61207	0.333171
$523$	30.9797	1.35465	0.677324	−	0.735685i	$-0.263139\pi$
$523$	30.9797	1.35465	0.677324	+	0.735685i	$0.263139\pi$
$524$	−0.307214	−0.0134207
$525$	−0.110750	−0.00483353
$526$	−2.96876	−0.129444
$527$	−22.3436	−0.973304
$528$	−0.0787372	−0.00342660
$529$	23.3539	1.01539
$530$	−15.3429	−0.666454
$531$	−5.87242	−0.254841
$532$	−1.13387	−0.0491594
$533$	0	0
$534$	0.639062	0.0276549
$535$	−19.0138	−0.822039
$536$	22.5111	0.972333
$537$	−1.08369	−0.0467646
$538$	1.86437	0.0803785
$539$	−6.94490	−0.299138
$540$	1.86687	0.0803373
$541$	−32.8609	−1.41280	−0.706401	−	0.707812i	$-0.749683\pi$
$541$	−32.8609	−1.41280	−0.706401	+	0.707812i	$0.749683\pi$
$542$	−13.7886	−0.592271
$543$	0.107479	0.00461235
$544$	−26.9998	−1.15761
$545$	37.1747	1.59239
$546$	0	0
$547$	−1.99012	−0.0850916	−0.0425458	−	0.999095i	$-0.513547\pi$
$547$	−1.99012	−0.0850916	−0.0425458	+	0.999095i	$0.513547\pi$
$548$	−0.201783	−0.00861974
$549$	−21.7246	−0.927182
$550$	−5.84331	−0.249159
$551$	11.7266	0.499570
$552$	−0.901830	−0.0383845
$553$	−1.60825	−0.0683899
$554$	8.48813	0.360626
$555$	−0.582826	−0.0247396
$556$	35.1646	1.49131
$557$	−10.0296	−0.424968	−0.212484	−	0.977165i	$-0.568155\pi$
$557$	−10.0296	−0.424968	−0.212484	+	0.977165i	$0.568155\pi$
$558$	−9.78452	−0.414212
$559$	0	0
$560$	−1.23837	−0.0523307
$561$	−0.256364	−0.0108237
$562$	−11.8071	−0.498051
$563$	−23.1729	−0.976620	−0.488310	−	0.872670i	$-0.662386\pi$
$563$	−23.1729	−0.976620	−0.488310	+	0.872670i	$0.662386\pi$
$564$	−0.890413	−0.0374932
$565$	−34.7558	−1.46219
$566$	19.6435	0.825677
$567$	2.10621	0.0884523
$568$	15.0537	0.631641
$569$	24.9904	1.04765	0.523825	−	0.851826i	$-0.324505\pi$
$569$	24.9904	1.04765	0.523825	+	0.851826i	$0.324505\pi$
$570$	−0.434081	−0.0181816
$571$	−1.42615	−0.0596826	−0.0298413	−	0.999555i	$-0.509500\pi$
$571$	−1.42615	−0.0596826	−0.0298413	+	0.999555i	$0.509500\pi$
$572$	0	0
$573$	0.274680	0.0114749
$574$	1.48495	0.0619807
$575$	58.4087	2.43581
$576$	−3.24211	−0.135088
$577$	−7.70467	−0.320750	−0.160375	−	0.987056i	$-0.551270\pi$
$577$	−7.70467	−0.320750	−0.160375	+	0.987056i	$0.551270\pi$
$578$	−3.22114	−0.133982
$579$	0.120676	0.00501510
$580$	21.1077	0.876450
$581$	−3.55552	−0.147508
$582$	−0.290494	−0.0120414
$583$	−6.11295	−0.253172
$584$	−4.01373	−0.166089
$585$	0	0
$586$	2.54612	0.105179
$587$	−7.62975	−0.314913	−0.157457	−	0.987526i	$-0.550329\pi$
$587$	−7.62975	−0.314913	−0.157457	+	0.987526i	$0.550329\pi$
$588$	−0.586698	−0.0241950
$589$	−15.0733	−0.621085
$590$	4.91803	0.202472
$591$	0.974710	0.0400942
$592$	−4.11731	−0.169220
$593$	20.6540	0.848156	0.424078	−	0.905626i	$-0.360598\pi$
$593$	20.6540	0.848156	0.424078	+	0.905626i	$0.360598\pi$
$594$	−0.224643	−0.00921721
$595$	−4.03207	−0.165299
$596$	16.1147	0.660085
$597$	0.829244	0.0339387
$598$	0	0
$599$	26.6287	1.08802	0.544009	−	0.839079i	$-0.316906\pi$
$599$	26.6287	1.08802	0.544009	+	0.839079i	$0.316906\pi$
$600$	−1.13636	−0.0463917
$601$	36.3794	1.48394	0.741972	−	0.670430i	$-0.233890\pi$
$601$	36.3794	1.48394	0.741972	+	0.670430i	$0.233890\pi$
$602$	−0.117577	−0.00479209
$603$	−28.0114	−1.14071
$604$	−23.7538	−0.966529
$605$	−3.68496	−0.149815
$606$	0.197888	0.00803866
$607$	−13.8140	−0.560693	−0.280346	−	0.959899i	$-0.590449\pi$
$607$	−13.8140	−0.560693	−0.280346	+	0.959899i	$0.590449\pi$
$608$	−18.2144	−0.738692
$609$	−0.0481399	−0.00195073
$610$	18.1939	0.736649
$611$	0	0
$612$	21.4594	0.867444
$613$	34.5619	1.39594	0.697971	−	0.716126i	$-0.254087\pi$
$613$	34.5619	1.39594	0.697971	+	0.716126i	$0.254087\pi$
$614$	12.4130	0.500949
$615$	−1.88228	−0.0759009
$616$	0.565352	0.0227787
$617$	17.3221	0.697363	0.348681	−	0.937241i	$-0.386630\pi$
$617$	17.3221	0.697363	0.348681	+	0.937241i	$0.386630\pi$
$618$	0.0807868	0.00324972
$619$	17.2108	0.691760	0.345880	−	0.938279i	$-0.387580\pi$
$619$	17.2108	0.691760	0.345880	+	0.938279i	$0.387580\pi$
$620$	−27.1317	−1.08964
$621$	2.24549	0.0901085
$622$	14.0935	0.565098
$623$	4.00457	0.160440
$624$	0	0
$625$	5.70374	0.228149
$626$	−3.34724	−0.133782
$627$	−0.172947	−0.00690684
$628$	17.5125	0.698827
$629$	−13.4057	−0.534522
$630$	−1.76569	−0.0703467
$631$	35.8705	1.42798	0.713991	−	0.700155i	$-0.246886\pi$
$631$	35.8705	1.42798	0.713991	+	0.700155i	$0.246886\pi$
$632$	−16.5016	−0.656399
$633$	1.18004	0.0469025
$634$	0.569099	0.0226018
$635$	77.4149	3.07212
$636$	−0.516415	−0.0204772
$637$	0	0
$638$	−2.53992	−0.100556
$639$	−18.7319	−0.741023
$640$	−39.9724	−1.58005
$641$	45.2190	1.78604	0.893022	−	0.450012i	$-0.148580\pi$
$641$	45.2190	1.78604	0.893022	+	0.450012i	$0.148580\pi$
$642$	0.193284	0.00762832
$643$	35.7262	1.40890	0.704451	−	0.709752i	$-0.251193\pi$
$643$	35.7262	1.40890	0.704451	+	0.709752i	$0.251193\pi$
$644$	−2.45487	−0.0967355
$645$	0.149037	0.00586834
$646$	−9.98441	−0.392832
$647$	30.1045	1.18353	0.591766	−	0.806110i	$-0.298431\pi$
$647$	30.1045	1.18353	0.591766	+	0.806110i	$0.298431\pi$
$648$	21.6109	0.848957
$649$	1.95945	0.0769151
$650$	0	0
$651$	0.0618787	0.00242522
$652$	8.48019	0.332110
$653$	−21.1744	−0.828619	−0.414309	−	0.910136i	$-0.635977\pi$
$653$	−21.1744	−0.828619	−0.414309	+	0.910136i	$0.635977\pi$
$654$	−0.377898	−0.0147770
$655$	−0.736990	−0.0287966
$656$	−13.2972	−0.519167
$657$	4.99443	0.194851
$658$	1.68516	0.0656943
$659$	−34.4982	−1.34386	−0.671930	−	0.740614i	$-0.734535\pi$
$659$	−34.4982	−1.34386	−0.671930	+	0.740614i	$0.734535\pi$
$660$	−0.311302	−0.0121174
$661$	−31.3070	−1.21770	−0.608850	−	0.793286i	$-0.708369\pi$
$661$	−31.3070	−1.21770	−0.608850	+	0.793286i	$0.708369\pi$
$662$	15.8844	0.617364
$663$	0	0
$664$	−36.4817	−1.41576
$665$	−2.72009	−0.105481
$666$	−5.87052	−0.227478
$667$	25.3886	0.983050
$668$	20.4806	0.792419
$669$	0.188542	0.00728947
$670$	23.4590	0.906300
$671$	7.24883	0.279838
$672$	0.0747735	0.00288445
$673$	−13.4109	−0.516951	−0.258475	−	0.966018i	$-0.583220\pi$
$673$	−13.4109	−0.516951	−0.258475	+	0.966018i	$0.583220\pi$
$674$	1.98878	0.0766049
$675$	2.82946	0.108906
$676$	0	0
$677$	−16.4334	−0.631588	−0.315794	−	0.948828i	$-0.602271\pi$
$677$	−16.4334	−0.631588	−0.315794	+	0.948828i	$0.602271\pi$
$678$	0.353308	0.0135687
$679$	−1.82033	−0.0698579
$680$	−41.3714	−1.58652
$681$	0.354314	0.0135773
$682$	3.26480	0.125016
$683$	−44.1078	−1.68774	−0.843868	−	0.536550i	$-0.819727\pi$
$683$	−44.1078	−1.68774	−0.843868	+	0.536550i	$0.819727\pi$
$684$	14.4768	0.553534
$685$	−0.484067	−0.0184953
$686$	2.22953	0.0851238
$687$	−0.252682	−0.00964041
$688$	1.05286	0.0401398
$689$	0	0
$690$	−0.939803	−0.0357777
$691$	47.3335	1.80065	0.900326	−	0.435216i	$-0.143328\pi$
$691$	47.3335	1.80065	0.900326	+	0.435216i	$0.143328\pi$
$692$	−29.9221	−1.13747
$693$	−0.703488	−0.0267233
$694$	−24.6384	−0.935261
$695$	84.3580	3.19988
$696$	−0.493943	−0.0187229
$697$	−43.2949	−1.63991
$698$	−21.4182	−0.810692
$699$	−0.831795	−0.0314614
$700$	−3.09329	−0.116915
$701$	−18.7852	−0.709507	−0.354753	−	0.934960i	$-0.615435\pi$
$701$	−18.7852	−0.709507	−0.354753	+	0.934960i	$0.615435\pi$
$702$	0	0
$703$	−9.04370	−0.341090
$704$	1.08179	0.0407716
$705$	−2.13606	−0.0804485
$706$	−15.4238	−0.580483
$707$	1.24003	0.0466362
$708$	0.165532	0.00622108
$709$	−14.6334	−0.549571	−0.274785	−	0.961506i	$-0.588607\pi$
$709$	−14.6334	−0.549571	−0.274785	+	0.961506i	$0.588607\pi$
$710$	15.6876	0.588745
$711$	20.5336	0.770069
$712$	41.0892	1.53988
$713$	−32.6344	−1.22217
$714$	0.0409879	0.00153393
$715$	0	0
$716$	−30.2678	−1.13116
$717$	0.355236	0.0132665
$718$	5.94476	0.221856
$719$	−42.0001	−1.56634	−0.783170	−	0.621808i	$-0.786399\pi$
$719$	−42.0001	−1.56634	−0.783170	+	0.621808i	$0.786399\pi$
$720$	15.8110	0.589243
$721$	0.506236	0.0188532
$722$	6.20567	0.230951
$723$	0.377170	0.0140271
$724$	3.00191	0.111565
$725$	31.9912	1.18812
$726$	0.0374594	0.00139025
$727$	−41.4214	−1.53624	−0.768118	−	0.640308i	$-0.778807\pi$
$727$	−41.4214	−1.53624	−0.768118	+	0.640308i	$0.778807\pi$
$728$	0	0
$729$	−26.8368	−0.993956
$730$	−4.18273	−0.154810
$731$	3.42805	0.126791
$732$	0.612374	0.0226340
$733$	−46.9101	−1.73266	−0.866332	−	0.499469i	$-0.833529\pi$
$733$	−46.9101	−1.73266	−0.866332	+	0.499469i	$0.833529\pi$
$734$	12.7915	0.472143
$735$	−1.40746	−0.0519149
$736$	−39.4350	−1.45359
$737$	9.34656	0.344285
$738$	−18.9593	−0.697901
$739$	−47.1375	−1.73398	−0.866990	−	0.498325i	$-0.833949\pi$
$739$	−47.1375	−1.73398	−0.866990	+	0.498325i	$0.833949\pi$
$740$	−16.2785	−0.598410
$741$	0	0
$742$	0.977346	0.0358795
$743$	15.5912	0.571987	0.285994	−	0.958232i	$-0.407676\pi$
$743$	15.5912	0.571987	0.285994	+	0.958232i	$0.407676\pi$
$744$	0.634912	0.0232770
$745$	38.6584	1.41633
$746$	9.19529	0.336664
$747$	45.3955	1.66093
$748$	−7.16034	−0.261808
$749$	1.21118	0.0442556
$750$	−0.494026	−0.0180393
$751$	−9.97667	−0.364054	−0.182027	−	0.983294i	$-0.558266\pi$
$751$	−9.97667	−0.364054	−0.182027	+	0.983294i	$0.558266\pi$
$752$	−15.0899	−0.550273
$753$	1.01780	0.0370908
$754$	0	0
$755$	−56.9842	−2.07387
$756$	−0.118920	−0.00432507
$757$	−26.0756	−0.947732	−0.473866	−	0.880597i	$-0.657142\pi$
$757$	−26.0756	−0.947732	−0.473866	+	0.880597i	$0.657142\pi$
$758$	−7.73240	−0.280854
$759$	−0.374437	−0.0135912
$760$	−27.9097	−1.01239
$761$	−28.3109	−1.02627	−0.513135	−	0.858308i	$-0.671516\pi$
$761$	−28.3109	−1.02627	−0.513135	+	0.858308i	$0.671516\pi$
$762$	−0.786958	−0.0285085
$763$	−2.36803	−0.0857286
$764$	7.67189	0.277559
$765$	51.4799	1.86126
$766$	−1.54590	−0.0558556
$767$	0	0
$768$	0.525328	0.0189561
$769$	−36.4413	−1.31411	−0.657054	−	0.753844i	$-0.728198\pi$
$769$	−36.4413	−1.31411	−0.657054	+	0.753844i	$0.728198\pi$
$770$	0.589156	0.0212317
$771$	0.518491	0.0186730
$772$	3.37051	0.121307
$773$	−8.36629	−0.300915	−0.150457	−	0.988617i	$-0.548075\pi$
$773$	−8.36629	−0.300915	−0.150457	+	0.988617i	$0.548075\pi$
$774$	1.50118	0.0539589
$775$	−41.1213	−1.47712
$776$	−18.6777	−0.670489
$777$	0.0371261	0.00133189
$778$	25.8343	0.926206
$779$	−29.2073	−1.04646
$780$	0	0
$781$	6.25027	0.223652
$782$	−21.6167	−0.773011
$783$	1.22988	0.0439524
$784$	−9.94283	−0.355101
$785$	42.0117	1.49946
$786$	0.00749184	0.000267225 0
$787$	23.0873	0.822975	0.411487	−	0.911415i	$-0.365009\pi$
$787$	23.0873	0.822975	0.411487	+	0.911415i	$0.365009\pi$
$788$	27.2240	0.969814
$789$	−0.239711	−0.00853393
$790$	−17.1964	−0.611822
$791$	2.21395	0.0787188
$792$	−7.21820	−0.256487
$793$	0	0
$794$	10.4615	0.371265
$795$	−1.23885	−0.0439376
$796$	23.1611	0.820922
$797$	−34.2092	−1.21175	−0.605876	−	0.795559i	$-0.707177\pi$
$797$	−34.2092	−1.21175	−0.605876	+	0.795559i	$0.707177\pi$
$798$	0.0276510	0.000978834 0
$799$	−49.1321	−1.73817
$800$	−49.6904	−1.75682
$801$	−51.1288	−1.80655
$802$	11.7426	0.414644
$803$	−1.66649	−0.0588092
$804$	0.789588	0.0278466
$805$	−5.88911	−0.207564
$806$	0	0
$807$	0.150537	0.00529915
$808$	12.7235	0.447610
$809$	−2.06524	−0.0726099	−0.0363049	−	0.999341i	$-0.511559\pi$
$809$	−2.06524	−0.0726099	−0.0363049	+	0.999341i	$0.511559\pi$
$810$	22.5208	0.791302
$811$	−34.0483	−1.19560	−0.597799	−	0.801646i	$-0.703958\pi$
$811$	−34.0483	−1.19560	−0.597799	+	0.801646i	$0.703958\pi$
$812$	−1.34456	−0.0471849
$813$	−1.11335	−0.0390469
$814$	1.95882	0.0686565
$815$	20.3435	0.712603
$816$	−0.367030	−0.0128486
$817$	2.31261	0.0809080
$818$	4.91367	0.171802
$819$	0	0
$820$	−52.5727	−1.83592
$821$	1.65849	0.0578816	0.0289408	−	0.999581i	$-0.490787\pi$
$821$	1.65849	0.0578816	0.0289408	+	0.999581i	$0.490787\pi$
$822$	0.00492077	0.000171631 0
$823$	50.9419	1.77572	0.887861	−	0.460111i	$-0.152190\pi$
$823$	50.9419	1.77572	0.887861	+	0.460111i	$0.152190\pi$
$824$	5.19428	0.180951
$825$	−0.471814	−0.0164264
$826$	−0.313279	−0.0109004
$827$	−17.4702	−0.607497	−0.303748	−	0.952752i	$-0.598238\pi$
$827$	−17.4702	−0.607497	−0.303748	+	0.952752i	$0.598238\pi$
$828$	31.3429	1.08924
$829$	−28.7681	−0.999156	−0.499578	−	0.866269i	$-0.666512\pi$
$829$	−28.7681	−0.999156	−0.499578	+	0.866269i	$0.666512\pi$
$830$	−38.0178	−1.31962
$831$	0.685369	0.0237752
$832$	0	0
$833$	−32.3733	−1.12167
$834$	−0.857538	−0.0296941
$835$	49.1320	1.70028
$836$	−4.83047	−0.167065
$837$	−1.58089	−0.0546434
$838$	5.09148	0.175882
$839$	−24.7828	−0.855597	−0.427798	−	0.903874i	$-0.640711\pi$
$839$	−24.7828	−0.855597	−0.427798	+	0.903874i	$0.640711\pi$
$840$	0.114575	0.00395320
$841$	−15.0944	−0.520495
$842$	17.8445	0.614963
$843$	−0.953353	−0.0328352
$844$	32.9590	1.13450
$845$	0	0
$846$	−21.5155	−0.739717
$847$	0.234733	0.00806551
$848$	−8.75175	−0.300536
$849$	1.58610	0.0544348
$850$	−27.2383	−0.934267
$851$	−19.5800	−0.671194
$852$	0.528016	0.0180895
$853$	−11.8821	−0.406836	−0.203418	−	0.979092i	$-0.565205\pi$
$853$	−11.8821	−0.406836	−0.203418	+	0.979092i	$0.565205\pi$
$854$	−1.15895	−0.0396585
$855$	34.7291	1.18771
$856$	12.4274	0.424761
$857$	44.3608	1.51534	0.757668	−	0.652640i	$-0.226338\pi$
$857$	44.3608	1.51534	0.757668	+	0.652640i	$0.226338\pi$
$858$	0	0
$859$	38.0740	1.29907	0.649534	−	0.760333i	$-0.274964\pi$
$859$	38.0740	1.29907	0.649534	+	0.760333i	$0.274964\pi$
$860$	4.16266	0.141946
$861$	0.119901	0.00408623
$862$	−13.2239	−0.450408
$863$	42.5151	1.44723	0.723616	−	0.690203i	$-0.242479\pi$
$863$	42.5151	1.44723	0.723616	+	0.690203i	$0.242479\pi$
$864$	−1.91032	−0.0649905
$865$	−71.7817	−2.44065
$866$	4.48966	0.152565
$867$	−0.260089	−0.00883307
$868$	1.72829	0.0586621
$869$	−6.85143	−0.232419
$870$	−0.514741	−0.0174514
$871$	0	0
$872$	−24.2974	−0.822814
$873$	23.2413	0.786599
$874$	−14.5829	−0.493274
$875$	−3.09573	−0.104655
$876$	−0.140783	−0.00475663
$877$	−20.0714	−0.677763	−0.338881	−	0.940829i	$-0.610049\pi$
$877$	−20.0714	−0.677763	−0.338881	+	0.940829i	$0.610049\pi$
$878$	−3.34549	−0.112905
$879$	0.205585	0.00693421
$880$	−5.27566	−0.177843
$881$	−53.7606	−1.81124	−0.905620	−	0.424091i	$-0.860594\pi$
$881$	−53.7606	−1.81124	−0.905620	+	0.424091i	$0.860594\pi$
$882$	−14.1766	−0.477352
$883$	32.7988	1.10377	0.551884	−	0.833921i	$-0.313909\pi$
$883$	32.7988	1.10377	0.551884	+	0.833921i	$0.313909\pi$
$884$	0	0
$885$	0.397103	0.0133485
$886$	−10.8064	−0.363049
$887$	43.2852	1.45337	0.726687	−	0.686969i	$-0.241059\pi$
$887$	43.2852	1.45337	0.726687	+	0.686969i	$0.241059\pi$
$888$	0.380935	0.0127834
$889$	−4.93134	−0.165392
$890$	42.8193	1.43531
$891$	8.97279	0.300600
$892$	5.26605	0.176320
$893$	−33.1452	−1.10916
$894$	−0.392980	−0.0131432
$895$	−72.6109	−2.42711
$896$	2.54624	0.0850641
$897$	0	0
$898$	1.97899	0.0660397
$899$	−17.8742	−0.596139
$900$	39.4939	1.31646
$901$	−28.4952	−0.949314
$902$	6.32614	0.210638
$903$	−0.00949369	−0.000315930 0
$904$	22.7164	0.755536
$905$	7.20143	0.239384
$906$	0.579271	0.0192450
$907$	29.7483	0.987776	0.493888	−	0.869525i	$-0.335575\pi$
$907$	29.7483	0.987776	0.493888	+	0.869525i	$0.335575\pi$
$908$	9.89610	0.328414
$909$	−15.8323	−0.525123
$910$	0	0
$911$	−38.9120	−1.28921	−0.644606	−	0.764515i	$-0.722978\pi$
$911$	−38.9120	−1.28921	−0.644606	+	0.764515i	$0.722978\pi$
$912$	−0.247604	−0.00819897
$913$	−15.1471	−0.501296
$914$	4.43521	0.146704
$915$	1.46905	0.0485654
$916$	−7.05749	−0.233186
$917$	0.0469463	0.00155030
$918$	−1.04716	−0.0345615
$919$	−48.3074	−1.59351	−0.796757	−	0.604300i	$-0.793453\pi$
$919$	−48.3074	−1.59351	−0.796757	+	0.604300i	$0.793453\pi$
$920$	−60.4257	−1.99218
$921$	1.00228	0.0330263
$922$	11.4431	0.376859
$923$	0	0
$924$	0.0198300	0.000652357 0
$925$	−24.6720	−0.811210
$926$	−13.3491	−0.438680
$927$	−6.46343	−0.212287
$928$	−21.5990	−0.709022
$929$	40.4852	1.32828	0.664138	−	0.747610i	$-0.268799\pi$
$929$	40.4852	1.32828	0.664138	+	0.747610i	$0.268799\pi$
$930$	0.661646	0.0216962
$931$	−21.8395	−0.715761
$932$	−23.2323	−0.761000
$933$	1.13797	0.0372555
$934$	18.6540	0.610378
$935$	−17.1773	−0.561758
$936$	0	0
$937$	21.0707	0.688350	0.344175	−	0.938905i	$-0.388159\pi$
$937$	21.0707	0.688350	0.344175	+	0.938905i	$0.388159\pi$
$938$	−1.49434	−0.0487919
$939$	−0.270270	−0.00881994
$940$	−59.6608	−1.94592
$941$	25.9551	0.846113	0.423057	−	0.906103i	$-0.360957\pi$
$941$	25.9551	0.846113	0.423057	+	0.906103i	$0.360957\pi$
$942$	−0.427068	−0.0139146
$943$	−63.2351	−2.05922
$944$	2.80529	0.0913044
$945$	−0.285282	−0.00928024
$946$	−0.500899	−0.0162856
$947$	−1.74719	−0.0567760	−0.0283880	−	0.999597i	$-0.509037\pi$
$947$	−1.74719	−0.0567760	−0.0283880	+	0.999597i	$0.509037\pi$
$948$	−0.578801	−0.0187986
$949$	0	0
$950$	−18.3753	−0.596175
$951$	0.0459515	0.00149008
$952$	2.63536	0.0854126
$953$	33.4574	1.08379	0.541896	−	0.840446i	$-0.317707\pi$
$953$	33.4574	1.08379	0.541896	+	0.840446i	$0.317707\pi$
$954$	−12.4784	−0.404002
$955$	18.4045	0.595555
$956$	9.92186	0.320896
$957$	−0.205084	−0.00662942
$958$	−14.9671	−0.483565
$959$	0.0308351	0.000995718 0
$960$	0.219237	0.00707584
$961$	−8.02454	−0.258856
$962$	0	0
$963$	−15.4639	−0.498318
$964$	10.5345	0.339293
$965$	8.08567	0.260287
$966$	0.0598655	0.00192614
$967$	−27.9684	−0.899402	−0.449701	−	0.893179i	$-0.648469\pi$
$967$	−27.9684	−0.899402	−0.449701	+	0.893179i	$0.648469\pi$
$968$	2.40849	0.0774119
$969$	−0.806185	−0.0258984
$970$	−19.4641	−0.624955
$971$	49.0556	1.57427	0.787134	−	0.616782i	$-0.211564\pi$
$971$	49.0556	1.57427	0.787134	+	0.616782i	$0.211564\pi$
$972$	2.27787	0.0730626
$973$	−5.37361	−0.172270
$974$	20.3632	0.652479
$975$	0	0
$976$	10.3780	0.332190
$977$	−18.9542	−0.606398	−0.303199	−	0.952927i	$-0.598055\pi$
$977$	−18.9542	−0.606398	−0.303199	+	0.952927i	$0.598055\pi$
$978$	−0.206801	−0.00661278
$979$	17.0601	0.545244
$980$	−39.3108	−1.25574
$981$	30.2341	0.965302
$982$	6.92949	0.221129
$983$	29.3987	0.937674	0.468837	−	0.883285i	$-0.344673\pi$
$983$	29.3987	0.937674	0.468837	+	0.883285i	$0.344673\pi$
$984$	1.23026	0.0392192
$985$	65.3090	2.08092
$986$	−11.8397	−0.377053
$987$	0.136067	0.00433106
$988$	0	0
$989$	5.00690	0.159210
$990$	−7.52213	−0.239069
$991$	42.0912	1.33707	0.668535	−	0.743681i	$-0.266922\pi$
$991$	42.0912	1.33707	0.668535	+	0.743681i	$0.266922\pi$
$992$	27.7633	0.881484
$993$	1.28257	0.0407012
$994$	−0.999301	−0.0316959
$995$	55.5622	1.76144
$996$	−1.27961	−0.0405460
$997$	−20.7942	−0.658559	−0.329280	−	0.944232i	$-0.606806\pi$
$997$	−20.7942	−0.658559	−0.329280	+	0.944232i	$0.606806\pi$
$998$	−5.23639	−0.165755
$999$	−0.948501	−0.0300093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.o.1.4		8
13.6	odd	12		143.2.j.b.23.7	✓	16
13.11	odd	12		143.2.j.b.56.7	yes	16
13.12	even	2		1859.2.a.p.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.j.b.23.7	✓	16	13.6	odd	12
143.2.j.b.56.7	yes	16	13.11	odd	12
1859.2.a.o.1.4		8	1.1	even	1	trivial
1859.2.a.p.1.5		8	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.681121 q^{2} -0.0549966 q^{3} -1.53607 q^{4} -3.68496 q^{5} +0.0374594 q^{6} +0.234733 q^{7} +2.40849 q^{8} -2.99698 q^{9} +O(q^{10})\)	\(q-0.681121 q^{2} -0.0549966 q^{3} -1.53607 q^{4} -3.68496 q^{5} +0.0374594 q^{6} +0.234733 q^{7} +2.40849 q^{8} -2.99698 q^{9} +2.50991 q^{10} +1.00000 q^{11} +0.0844789 q^{12} -0.159881 q^{14} +0.202661 q^{15} +1.43167 q^{16} +4.66146 q^{17} +2.04130 q^{18} +3.14468 q^{19} +5.66038 q^{20} -0.0129095 q^{21} -0.681121 q^{22} +6.80837 q^{23} -0.132459 q^{24} +8.57896 q^{25} +0.329813 q^{27} -0.360567 q^{28} +3.72903 q^{29} -0.138036 q^{30} -4.79327 q^{31} -5.79213 q^{32} -0.0549966 q^{33} -3.17501 q^{34} -0.864981 q^{35} +4.60358 q^{36} -2.87587 q^{37} -2.14191 q^{38} -8.87521 q^{40} -9.28785 q^{41} +0.00879293 q^{42} +0.735404 q^{43} -1.53607 q^{44} +11.0437 q^{45} -4.63732 q^{46} -10.5401 q^{47} -0.0787372 q^{48} -6.94490 q^{49} -5.84331 q^{50} -0.256364 q^{51} -6.11295 q^{53} -0.224643 q^{54} -3.68496 q^{55} +0.565352 q^{56} -0.172947 q^{57} -2.53992 q^{58} +1.95945 q^{59} -0.311302 q^{60} +7.24883 q^{61} +3.26480 q^{62} -0.703488 q^{63} +1.08179 q^{64} +0.0374594 q^{66} +9.34656 q^{67} -7.16034 q^{68} -0.374437 q^{69} +0.589156 q^{70} +6.25027 q^{71} -7.21820 q^{72} -1.66649 q^{73} +1.95882 q^{74} -0.471814 q^{75} -4.83047 q^{76} +0.234733 q^{77} -6.85143 q^{79} -5.27566 q^{80} +8.97279 q^{81} +6.32614 q^{82} -15.1471 q^{83} +0.0198300 q^{84} -17.1773 q^{85} -0.500899 q^{86} -0.205084 q^{87} +2.40849 q^{88} +17.0601 q^{89} -7.52213 q^{90} -10.4582 q^{92} +0.263614 q^{93} +7.17906 q^{94} -11.5880 q^{95} +0.318548 q^{96} -7.75492 q^{97} +4.73032 q^{98} -2.99698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9} + 10 q^{10} + 8 q^{11} - 8 q^{12} - 6 q^{14} - 2 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{19} - 16 q^{20} - 2 q^{21} - 2 q^{22} - 14 q^{23} - 26 q^{24} + 12 q^{25} + 24 q^{27} - 20 q^{28} - 10 q^{29} + 14 q^{30} - 32 q^{31} + 40 q^{32} - 14 q^{34} + 10 q^{35} - 24 q^{37} + 12 q^{38} - 14 q^{40} - 2 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{46} - 18 q^{47} - 6 q^{48} + 2 q^{49} - 38 q^{50} + 12 q^{51} - 8 q^{53} - 2 q^{54} - 8 q^{55} - 28 q^{56} - 24 q^{57} + 14 q^{58} - 18 q^{59} + 14 q^{60} - 4 q^{61} - 8 q^{63} + 6 q^{64} - 4 q^{66} + 14 q^{67} - 34 q^{68} - 10 q^{69} - 18 q^{70} + 12 q^{71} - 8 q^{72} - 26 q^{73} + 2 q^{74} - 18 q^{75} - 54 q^{76} - 14 q^{77} + 26 q^{79} - 24 q^{80} - 16 q^{81} - 64 q^{82} - 16 q^{83} + 74 q^{84} - 56 q^{85} - 32 q^{86} - 18 q^{87} + 6 q^{88} + 8 q^{89} - 20 q^{90} - 30 q^{92} - 48 q^{93} - 4 q^{94} + 22 q^{95} - 16 q^{96} - 20 q^{97} + 46 q^{98} + 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9 + 10 * q^10 + 8 * q^11 - 8 * q^12 - 6 * q^14 - 2 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^18 - 4 * q^19 - 16 * q^20 - 2 * q^21 - 2 * q^22 - 14 * q^23 - 26 * q^24 + 12 * q^25 + 24 * q^27 - 20 * q^28 - 10 * q^29 + 14 * q^30 - 32 * q^31 + 40 * q^32 - 14 * q^34 + 10 * q^35 - 24 * q^37 + 12 * q^38 - 14 * q^40 - 2 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^46 - 18 * q^47 - 6 * q^48 + 2 * q^49 - 38 * q^50 + 12 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^55 - 28 * q^56 - 24 * q^57 + 14 * q^58 - 18 * q^59 + 14 * q^60 - 4 * q^61 - 8 * q^63 + 6 * q^64 - 4 * q^66 + 14 * q^67 - 34 * q^68 - 10 * q^69 - 18 * q^70 + 12 * q^71 - 8 * q^72 - 26 * q^73 + 2 * q^74 - 18 * q^75 - 54 * q^76 - 14 * q^77 + 26 * q^79 - 24 * q^80 - 16 * q^81 - 64 * q^82 - 16 * q^83 + 74 * q^84 - 56 * q^85 - 32 * q^86 - 18 * q^87 + 6 * q^88 + 8 * q^89 - 20 * q^90 - 30 * q^92 - 48 * q^93 - 4 * q^94 + 22 * q^95 - 16 * q^96 - 20 * q^97 + 46 * q^98 + 2 * q^99

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