LMFDB - Embedded newform 4334.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} + \cdots + 16 $ x^17 - 5x^16 - 19x^15 + 121x^14 + 112x^13 - 1172x^12 - 25x^11 + 5845x^10 - 2233x^9 - 16035x^8 + 9174x^7 + 23882x^6 - 15232x^5 - 17609x^4 + 10764x^3 + 4764x^2 - 2368x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.50775$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.50775 q^{3} +1.00000 q^{4} +1.44362 q^{5} -2.50775 q^{6} -2.73850 q^{7} -1.00000 q^{8} +3.28879 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.50775 q^{3} +1.00000 q^{4} +1.44362 q^{5} -2.50775 q^{6} -2.73850 q^{7} -1.00000 q^{8} +3.28879 q^{9} -1.44362 q^{10} -1.00000 q^{11} +2.50775 q^{12} -0.891423 q^{13} +2.73850 q^{14} +3.62022 q^{15} +1.00000 q^{16} +2.79129 q^{17} -3.28879 q^{18} -6.47277 q^{19} +1.44362 q^{20} -6.86746 q^{21} +1.00000 q^{22} -1.36776 q^{23} -2.50775 q^{24} -2.91597 q^{25} +0.891423 q^{26} +0.724218 q^{27} -2.73850 q^{28} -6.52713 q^{29} -3.62022 q^{30} +5.89687 q^{31} -1.00000 q^{32} -2.50775 q^{33} -2.79129 q^{34} -3.95334 q^{35} +3.28879 q^{36} +0.874619 q^{37} +6.47277 q^{38} -2.23546 q^{39} -1.44362 q^{40} -8.89609 q^{41} +6.86746 q^{42} -8.70527 q^{43} -1.00000 q^{44} +4.74775 q^{45} +1.36776 q^{46} -6.67522 q^{47} +2.50775 q^{48} +0.499383 q^{49} +2.91597 q^{50} +6.99984 q^{51} -0.891423 q^{52} -5.03015 q^{53} -0.724218 q^{54} -1.44362 q^{55} +2.73850 q^{56} -16.2321 q^{57} +6.52713 q^{58} +6.23265 q^{59} +3.62022 q^{60} +0.914972 q^{61} -5.89687 q^{62} -9.00636 q^{63} +1.00000 q^{64} -1.28687 q^{65} +2.50775 q^{66} -3.25159 q^{67} +2.79129 q^{68} -3.43001 q^{69} +3.95334 q^{70} -1.30582 q^{71} -3.28879 q^{72} +9.60704 q^{73} -0.874619 q^{74} -7.31252 q^{75} -6.47277 q^{76} +2.73850 q^{77} +2.23546 q^{78} +9.86820 q^{79} +1.44362 q^{80} -8.05022 q^{81} +8.89609 q^{82} -3.53369 q^{83} -6.86746 q^{84} +4.02954 q^{85} +8.70527 q^{86} -16.3684 q^{87} +1.00000 q^{88} +7.02165 q^{89} -4.74775 q^{90} +2.44116 q^{91} -1.36776 q^{92} +14.7879 q^{93} +6.67522 q^{94} -9.34418 q^{95} -2.50775 q^{96} +14.1175 q^{97} -0.499383 q^{98} -3.28879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.50775	1.44785	0.723924	−	0.689880i	$-0.242337\pi$
$3$	2.50775	1.44785	0.723924	+	0.689880i	$0.242337\pi$
$4$	1.00000	0.500000
$5$	1.44362	0.645604	0.322802	−	0.946466i	$-0.395375\pi$
$5$	1.44362	0.645604	0.322802	+	0.946466i	$0.395375\pi$
$6$	−2.50775	−1.02378
$7$	−2.73850	−1.03506	−0.517528	−	0.855666i	$-0.673148\pi$
$7$	−2.73850	−1.03506	−0.517528	+	0.855666i	$0.673148\pi$
$8$	−1.00000	−0.353553
$9$	3.28879	1.09626
$10$	−1.44362	−0.456511
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.50775	0.723924
$13$	−0.891423	−0.247236	−0.123618	−	0.992330i	$-0.539450\pi$
$13$	−0.891423	−0.247236	−0.123618	+	0.992330i	$0.539450\pi$
$14$	2.73850	0.731895
$15$	3.62022	0.934737
$16$	1.00000	0.250000
$17$	2.79129	0.676986	0.338493	−	0.940969i	$-0.390083\pi$
$17$	2.79129	0.676986	0.338493	+	0.940969i	$0.390083\pi$
$18$	−3.28879	−0.775176
$19$	−6.47277	−1.48495	−0.742477	−	0.669871i	$-0.766349\pi$
$19$	−6.47277	−1.48495	−0.742477	+	0.669871i	$0.766349\pi$
$20$	1.44362	0.322802
$21$	−6.86746	−1.49860
$22$	1.00000	0.213201
$23$	−1.36776	−0.285199	−0.142599	−	0.989780i	$-0.545546\pi$
$23$	−1.36776	−0.285199	−0.142599	+	0.989780i	$0.545546\pi$
$24$	−2.50775	−0.511892
$25$	−2.91597	−0.583195
$26$	0.891423	0.174823
$27$	0.724218	0.139376
$28$	−2.73850	−0.517528
$29$	−6.52713	−1.21206	−0.606029	−	0.795442i	$-0.707239\pi$
$29$	−6.52713	−1.21206	−0.606029	+	0.795442i	$0.707239\pi$
$30$	−3.62022	−0.660959
$31$	5.89687	1.05911	0.529554	−	0.848276i	$-0.322359\pi$
$31$	5.89687	1.05911	0.529554	+	0.848276i	$0.322359\pi$
$32$	−1.00000	−0.176777
$33$	−2.50775	−0.436543
$34$	−2.79129	−0.478702
$35$	−3.95334	−0.668237
$36$	3.28879	0.548132
$37$	0.874619	0.143786	0.0718932	−	0.997412i	$-0.477096\pi$
$37$	0.874619	0.143786	0.0718932	+	0.997412i	$0.477096\pi$
$38$	6.47277	1.05002
$39$	−2.23546	−0.357961
$40$	−1.44362	−0.228256
$41$	−8.89609	−1.38934	−0.694668	−	0.719330i	$-0.744449\pi$
$41$	−8.89609	−1.38934	−0.694668	+	0.719330i	$0.744449\pi$
$42$	6.86746	1.05967
$43$	−8.70527	−1.32754	−0.663771	−	0.747936i	$-0.731045\pi$
$43$	−8.70527	−1.32754	−0.663771	+	0.747936i	$0.731045\pi$
$44$	−1.00000	−0.150756
$45$	4.74775	0.707753
$46$	1.36776	0.201666
$47$	−6.67522	−0.973680	−0.486840	−	0.873491i	$-0.661851\pi$
$47$	−6.67522	−0.973680	−0.486840	+	0.873491i	$0.661851\pi$
$48$	2.50775	0.361962
$49$	0.499383	0.0713404
$50$	2.91597	0.412381
$51$	6.99984	0.980173
$52$	−0.891423	−0.123618
$53$	−5.03015	−0.690944	−0.345472	−	0.938429i	$-0.612281\pi$
$53$	−5.03015	−0.690944	−0.345472	+	0.938429i	$0.612281\pi$
$54$	−0.724218	−0.0985536
$55$	−1.44362	−0.194657
$56$	2.73850	0.365947
$57$	−16.2321	−2.14999
$58$	6.52713	0.857055
$59$	6.23265	0.811422	0.405711	−	0.914001i	$-0.367024\pi$
$59$	6.23265	0.811422	0.405711	+	0.914001i	$0.367024\pi$
$60$	3.62022	0.467369
$61$	0.914972	0.117150	0.0585751	−	0.998283i	$-0.481344\pi$
$61$	0.914972	0.117150	0.0585751	+	0.998283i	$0.481344\pi$
$62$	−5.89687	−0.748903
$63$	−9.00636	−1.13469
$64$	1.00000	0.125000
$65$	−1.28687	−0.159617
$66$	2.50775	0.308682
$67$	−3.25159	−0.397245	−0.198623	−	0.980076i	$-0.563647\pi$
$67$	−3.25159	−0.397245	−0.198623	+	0.980076i	$0.563647\pi$
$68$	2.79129	0.338493
$69$	−3.43001	−0.412924
$70$	3.95334	0.472515
$71$	−1.30582	−0.154972	−0.0774859	−	0.996993i	$-0.524689\pi$
$71$	−1.30582	−0.154972	−0.0774859	+	0.996993i	$0.524689\pi$
$72$	−3.28879	−0.387588
$73$	9.60704	1.12442	0.562209	−	0.826995i	$-0.309951\pi$
$73$	9.60704	1.12442	0.562209	+	0.826995i	$0.309951\pi$
$74$	−0.874619	−0.101672
$75$	−7.31252	−0.844378
$76$	−6.47277	−0.742477
$77$	2.73850	0.312081
$78$	2.23546	0.253116
$79$	9.86820	1.11026	0.555130	−	0.831764i	$-0.312669\pi$
$79$	9.86820	1.11026	0.555130	+	0.831764i	$0.312669\pi$
$80$	1.44362	0.161401
$81$	−8.05022	−0.894469
$82$	8.89609	0.982409
$83$	−3.53369	−0.387873	−0.193936	−	0.981014i	$-0.562126\pi$
$83$	−3.53369	−0.387873	−0.193936	+	0.981014i	$0.562126\pi$
$84$	−6.86746	−0.749302
$85$	4.02954	0.437065
$86$	8.70527	0.938713
$87$	−16.3684	−1.75488
$88$	1.00000	0.106600
$89$	7.02165	0.744293	0.372147	−	0.928174i	$-0.378622\pi$
$89$	7.02165	0.744293	0.372147	+	0.928174i	$0.378622\pi$
$90$	−4.74775	−0.500457
$91$	2.44116	0.255903
$92$	−1.36776	−0.142599
$93$	14.7879	1.53343
$94$	6.67522	0.688496
$95$	−9.34418	−0.958693
$96$	−2.50775	−0.255946
$97$	14.1175	1.43341	0.716707	−	0.697374i	$-0.245648\pi$
$97$	14.1175	1.43341	0.716707	+	0.697374i	$0.245648\pi$
$98$	−0.499383	−0.0504453
$99$	−3.28879	−0.330536
$100$	−2.91597	−0.291597
$101$	−10.7170	−1.06638	−0.533189	−	0.845996i	$-0.679006\pi$
$101$	−10.7170	−1.06638	−0.533189	+	0.845996i	$0.679006\pi$
$102$	−6.99984	−0.693087
$103$	2.19566	0.216345	0.108173	−	0.994132i	$-0.465500\pi$
$103$	2.19566	0.216345	0.108173	+	0.994132i	$0.465500\pi$
$104$	0.891423	0.0874113
$105$	−9.91398	−0.967505
$106$	5.03015	0.488571
$107$	14.0548	1.35873	0.679363	−	0.733802i	$-0.262256\pi$
$107$	14.0548	1.35873	0.679363	+	0.733802i	$0.262256\pi$
$108$	0.724218	0.0696879
$109$	−11.2134	−1.07405	−0.537026	−	0.843566i	$-0.680452\pi$
$109$	−11.2134	−1.07405	−0.537026	+	0.843566i	$0.680452\pi$
$110$	1.44362	0.137643
$111$	2.19332	0.208181
$112$	−2.73850	−0.258764
$113$	2.60801	0.245341	0.122671	−	0.992447i	$-0.460854\pi$
$113$	2.60801	0.245341	0.122671	+	0.992447i	$0.460854\pi$
$114$	16.2321	1.52027
$115$	−1.97453	−0.184126
$116$	−6.52713	−0.606029
$117$	−2.93171	−0.271036
$118$	−6.23265	−0.573762
$119$	−7.64394	−0.700719
$120$	−3.62022	−0.330479
$121$	1.00000	0.0909091
$122$	−0.914972	−0.0828377
$123$	−22.3091	−2.01155
$124$	5.89687	0.529554
$125$	−11.4276	−1.02212
$126$	9.00636	0.802350
$127$	10.0906	0.895398	0.447699	−	0.894184i	$-0.352244\pi$
$127$	10.0906	0.895398	0.447699	+	0.894184i	$0.352244\pi$
$128$	−1.00000	−0.0883883
$129$	−21.8306	−1.92208
$130$	1.28687	0.112866
$131$	11.7545	1.02699	0.513496	−	0.858092i	$-0.328350\pi$
$131$	11.7545	1.02699	0.513496	+	0.858092i	$0.328350\pi$
$132$	−2.50775	−0.218271
$133$	17.7257	1.53701
$134$	3.25159	0.280895
$135$	1.04549	0.0899817
$136$	−2.79129	−0.239351
$137$	−22.2287	−1.89913	−0.949564	−	0.313573i	$-0.898474\pi$
$137$	−22.2287	−1.89913	−0.949564	+	0.313573i	$0.898474\pi$
$138$	3.43001	0.291982
$139$	−11.5254	−0.977570	−0.488785	−	0.872404i	$-0.662560\pi$
$139$	−11.5254	−0.977570	−0.488785	+	0.872404i	$0.662560\pi$
$140$	−3.95334	−0.334118
$141$	−16.7397	−1.40974
$142$	1.30582	0.109582
$143$	0.891423	0.0745446
$144$	3.28879	0.274066
$145$	−9.42267	−0.782510
$146$	−9.60704	−0.795084
$147$	1.25232	0.103290
$148$	0.874619	0.0718932
$149$	−13.5516	−1.11019	−0.555097	−	0.831786i	$-0.687319\pi$
$149$	−13.5516	−1.11019	−0.555097	+	0.831786i	$0.687319\pi$
$150$	7.31252	0.597065
$151$	3.44538	0.280381	0.140190	−	0.990125i	$-0.455229\pi$
$151$	3.44538	0.280381	0.140190	+	0.990125i	$0.455229\pi$
$152$	6.47277	0.525011
$153$	9.17996	0.742156
$154$	−2.73850	−0.220675
$155$	8.51281	0.683765
$156$	−2.23546	−0.178980
$157$	−2.51133	−0.200426	−0.100213	−	0.994966i	$-0.531952\pi$
$157$	−2.51133	−0.200426	−0.100213	+	0.994966i	$0.531952\pi$
$158$	−9.86820	−0.785072
$159$	−12.6143	−1.00038
$160$	−1.44362	−0.114128
$161$	3.74562	0.295196
$162$	8.05022	0.632485
$163$	−13.0199	−1.01979	−0.509897	−	0.860236i	$-0.670316\pi$
$163$	−13.0199	−1.01979	−0.509897	+	0.860236i	$0.670316\pi$
$164$	−8.89609	−0.694668
$165$	−3.62022	−0.281834
$166$	3.53369	0.274268
$167$	−10.6075	−0.820830	−0.410415	−	0.911899i	$-0.634616\pi$
$167$	−10.6075	−0.820830	−0.410415	+	0.911899i	$0.634616\pi$
$168$	6.86746	0.529836
$169$	−12.2054	−0.938874
$170$	−4.02954	−0.309052
$171$	−21.2876	−1.62790
$172$	−8.70527	−0.663771
$173$	6.12887	0.465969	0.232985	−	0.972480i	$-0.425151\pi$
$173$	6.12887	0.465969	0.232985	+	0.972480i	$0.425151\pi$
$174$	16.3684	1.24089
$175$	7.98540	0.603639
$176$	−1.00000	−0.0753778
$177$	15.6299	1.17482
$178$	−7.02165	−0.526295
$179$	20.5519	1.53612	0.768060	−	0.640378i	$-0.221222\pi$
$179$	20.5519	1.53612	0.768060	+	0.640378i	$0.221222\pi$
$180$	4.74775	0.353877
$181$	−16.1585	−1.20105	−0.600524	−	0.799606i	$-0.705041\pi$
$181$	−16.1585	−1.20105	−0.600524	+	0.799606i	$0.705041\pi$
$182$	−2.44116	−0.180951
$183$	2.29452	0.169616
$184$	1.36776	0.100833
$185$	1.26261	0.0928292
$186$	−14.7879	−1.08430
$187$	−2.79129	−0.204119
$188$	−6.67522	−0.486840
$189$	−1.98327	−0.144262
$190$	9.34418	0.677898
$191$	7.06541	0.511235	0.255617	−	0.966778i	$-0.417721\pi$
$191$	7.06541	0.511235	0.255617	+	0.966778i	$0.417721\pi$
$192$	2.50775	0.180981
$193$	−15.7816	−1.13598	−0.567992	−	0.823034i	$-0.692279\pi$
$193$	−15.7816	−1.13598	−0.567992	+	0.823034i	$0.692279\pi$
$194$	−14.1175	−1.01358
$195$	−3.22715	−0.231101
$196$	0.499383	0.0356702
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	3.28879	0.233724
$199$	11.9777	0.849080	0.424540	−	0.905409i	$-0.360436\pi$
$199$	11.9777	0.849080	0.424540	+	0.905409i	$0.360436\pi$
$200$	2.91597	0.206191
$201$	−8.15416	−0.575150
$202$	10.7170	0.754043
$203$	17.8746	1.25455
$204$	6.99984	0.490087
$205$	−12.8425	−0.896962
$206$	−2.19566	−0.152979
$207$	−4.49829	−0.312653
$208$	−0.891423	−0.0618091
$209$	6.47277	0.447731
$210$	9.91398	0.684129
$211$	5.40901	0.372372	0.186186	−	0.982515i	$-0.440387\pi$
$211$	5.40901	0.372372	0.186186	+	0.982515i	$0.440387\pi$
$212$	−5.03015	−0.345472
$213$	−3.27466	−0.224376
$214$	−14.0548	−0.960764
$215$	−12.5671	−0.857066
$216$	−0.724218	−0.0492768
$217$	−16.1486	−1.09624
$218$	11.2134	0.759469
$219$	24.0920	1.62799
$220$	−1.44362	−0.0973285
$221$	−2.48822	−0.167376
$222$	−2.19332	−0.147206
$223$	−11.8315	−0.792299	−0.396149	−	0.918186i	$-0.629654\pi$
$223$	−11.8315	−0.792299	−0.396149	+	0.918186i	$0.629654\pi$
$224$	2.73850	0.182974
$225$	−9.59004	−0.639336
$226$	−2.60801	−0.173482
$227$	16.7053	1.10877	0.554384	−	0.832261i	$-0.312954\pi$
$227$	16.7053	1.10877	0.554384	+	0.832261i	$0.312954\pi$
$228$	−16.2321	−1.07499
$229$	16.3455	1.08014	0.540071	−	0.841619i	$-0.318397\pi$
$229$	16.3455	1.08014	0.540071	+	0.841619i	$0.318397\pi$
$230$	1.97453	0.130196
$231$	6.86746	0.451846
$232$	6.52713	0.428527
$233$	−2.73684	−0.179296	−0.0896482	−	0.995973i	$-0.528574\pi$
$233$	−2.73684	−0.179296	−0.0896482	+	0.995973i	$0.528574\pi$
$234$	2.93171	0.191652
$235$	−9.63644	−0.628612
$236$	6.23265	0.405711
$237$	24.7470	1.60749
$238$	7.64394	0.495483
$239$	15.4866	1.00175	0.500874	−	0.865520i	$-0.333012\pi$
$239$	15.4866	1.00175	0.500874	+	0.865520i	$0.333012\pi$
$240$	3.62022	0.233684
$241$	5.52753	0.356060	0.178030	−	0.984025i	$-0.443028\pi$
$241$	5.52753	0.356060	0.178030	+	0.984025i	$0.443028\pi$
$242$	−1.00000	−0.0642824
$243$	−22.3606	−1.43443
$244$	0.914972	0.0585751
$245$	0.720916	0.0460577
$246$	22.3091	1.42238
$247$	5.76997	0.367135
$248$	−5.89687	−0.374452
$249$	−8.86160	−0.561581
$250$	11.4276	0.722746
$251$	4.75431	0.300089	0.150045	−	0.988679i	$-0.452058\pi$
$251$	4.75431	0.300089	0.150045	+	0.988679i	$0.452058\pi$
$252$	−9.00636	−0.567347
$253$	1.36776	0.0859906
$254$	−10.0906	−0.633142
$255$	10.1051	0.632804
$256$	1.00000	0.0625000
$257$	−0.510379	−0.0318366	−0.0159183	−	0.999873i	$-0.505067\pi$
$257$	−0.510379	−0.0318366	−0.0159183	+	0.999873i	$0.505067\pi$
$258$	21.8306	1.35911
$259$	−2.39514	−0.148827
$260$	−1.28687	−0.0798084
$261$	−21.4664	−1.32874
$262$	−11.7545	−0.726193
$263$	−25.8394	−1.59333	−0.796664	−	0.604423i	$-0.793404\pi$
$263$	−25.8394	−1.59333	−0.796664	+	0.604423i	$0.793404\pi$
$264$	2.50775	0.154341
$265$	−7.26160	−0.446077
$266$	−17.7257	−1.08683
$267$	17.6085	1.07762
$268$	−3.25159	−0.198623
$269$	16.4972	1.00585	0.502926	−	0.864329i	$-0.332257\pi$
$269$	16.4972	1.00585	0.502926	+	0.864329i	$0.332257\pi$
$270$	−1.04549	−0.0636267
$271$	7.65127	0.464782	0.232391	−	0.972622i	$-0.425345\pi$
$271$	7.65127	0.464782	0.232391	+	0.972622i	$0.425345\pi$
$272$	2.79129	0.169247
$273$	6.12182	0.370509
$274$	22.2287	1.34289
$275$	2.91597	0.175840
$276$	−3.43001	−0.206462
$277$	9.78835	0.588125	0.294062	−	0.955786i	$-0.404993\pi$
$277$	9.78835	0.588125	0.294062	+	0.955786i	$0.404993\pi$
$278$	11.5254	0.691246
$279$	19.3936	1.16106
$280$	3.95334	0.236257
$281$	−22.3443	−1.33295	−0.666474	−	0.745528i	$-0.732197\pi$
$281$	−22.3443	−1.33295	−0.666474	+	0.745528i	$0.732197\pi$
$282$	16.7397	0.996838
$283$	1.93375	0.114949	0.0574747	−	0.998347i	$-0.481695\pi$
$283$	1.93375	0.114949	0.0574747	+	0.998347i	$0.481695\pi$
$284$	−1.30582	−0.0774859
$285$	−23.4328	−1.38804
$286$	−0.891423	−0.0527110
$287$	24.3620	1.43804
$288$	−3.28879	−0.193794
$289$	−9.20872	−0.541690
$290$	9.42267	0.553318
$291$	35.4031	2.07537
$292$	9.60704	0.562209
$293$	16.5921	0.969321	0.484661	−	0.874702i	$-0.338943\pi$
$293$	16.5921	0.969321	0.484661	+	0.874702i	$0.338943\pi$
$294$	−1.25232	−0.0730371
$295$	8.99755	0.523857
$296$	−0.874619	−0.0508362
$297$	−0.724218	−0.0420234
$298$	13.5516	0.785025
$299$	1.21926	0.0705115
$300$	−7.31252	−0.422189
$301$	23.8394	1.37408
$302$	−3.44538	−0.198259
$303$	−26.8754	−1.54395
$304$	−6.47277	−0.371239
$305$	1.32087	0.0756327
$306$	−9.17996	−0.524783
$307$	6.74572	0.384998	0.192499	−	0.981297i	$-0.438341\pi$
$307$	6.74572	0.384998	0.192499	+	0.981297i	$0.438341\pi$
$308$	2.73850	0.156041
$309$	5.50617	0.313235
$310$	−8.51281	−0.483495
$311$	5.06474	0.287195	0.143598	−	0.989636i	$-0.454133\pi$
$311$	5.06474	0.287195	0.143598	+	0.989636i	$0.454133\pi$
$312$	2.23546	0.126558
$313$	−12.2817	−0.694202	−0.347101	−	0.937828i	$-0.612834\pi$
$313$	−12.2817	−0.694202	−0.347101	+	0.937828i	$0.612834\pi$
$314$	2.51133	0.141722
$315$	−13.0017	−0.732564
$316$	9.86820	0.555130
$317$	−13.4075	−0.753042	−0.376521	−	0.926408i	$-0.622880\pi$
$317$	−13.4075	−0.753042	−0.376521	+	0.926408i	$0.622880\pi$
$318$	12.6143	0.707377
$319$	6.52713	0.365449
$320$	1.44362	0.0807006
$321$	35.2458	1.96723
$322$	−3.74562	−0.208735
$323$	−18.0673	−1.00529
$324$	−8.05022	−0.447235
$325$	2.59937	0.144187
$326$	13.0199	0.721103
$327$	−28.1204	−1.55506
$328$	8.89609	0.491205
$329$	18.2801	1.00781
$330$	3.62022	0.199287
$331$	−11.6417	−0.639883	−0.319942	−	0.947437i	$-0.603663\pi$
$331$	−11.6417	−0.639883	−0.319942	+	0.947437i	$0.603663\pi$
$332$	−3.53369	−0.193936
$333$	2.87644	0.157628
$334$	10.6075	0.580414
$335$	−4.69405	−0.256463
$336$	−6.86746	−0.374651
$337$	−6.82398	−0.371726	−0.185863	−	0.982576i	$-0.559508\pi$
$337$	−6.82398	−0.371726	−0.185863	+	0.982576i	$0.559508\pi$
$338$	12.2054	0.663884
$339$	6.54023	0.355217
$340$	4.02954	0.218533
$341$	−5.89687	−0.319333
$342$	21.2876	1.15110
$343$	17.8019	0.961214
$344$	8.70527	0.469357
$345$	−4.95161	−0.266586
$346$	−6.12887	−0.329490
$347$	28.8329	1.54783	0.773916	−	0.633288i	$-0.218295\pi$
$347$	28.8329	1.54783	0.773916	+	0.633288i	$0.218295\pi$
$348$	−16.3684	−0.877438
$349$	−5.44494	−0.291461	−0.145730	−	0.989324i	$-0.546553\pi$
$349$	−5.44494	−0.291461	−0.145730	+	0.989324i	$0.546553\pi$
$350$	−7.98540	−0.426837
$351$	−0.645585	−0.0344588
$352$	1.00000	0.0533002
$353$	9.07135	0.482819	0.241410	−	0.970423i	$-0.422390\pi$
$353$	9.07135	0.482819	0.241410	+	0.970423i	$0.422390\pi$
$354$	−15.6299	−0.830720
$355$	−1.88510	−0.100051
$356$	7.02165	0.372147
$357$	−19.1691	−1.01453
$358$	−20.5519	−1.08620
$359$	1.01295	0.0534615	0.0267308	−	0.999643i	$-0.491490\pi$
$359$	1.01295	0.0534615	0.0267308	+	0.999643i	$0.491490\pi$
$360$	−4.74775	−0.250228
$361$	22.8967	1.20509
$362$	16.1585	0.849270
$363$	2.50775	0.131623
$364$	2.44116	0.127952
$365$	13.8689	0.725930
$366$	−2.29452	−0.119936
$367$	0.647112	0.0337790	0.0168895	−	0.999857i	$-0.494624\pi$
$367$	0.647112	0.0337790	0.0168895	+	0.999857i	$0.494624\pi$
$368$	−1.36776	−0.0712997
$369$	−29.2574	−1.52308
$370$	−1.26261	−0.0656401
$371$	13.7751	0.715166
$372$	14.7879	0.766714
$373$	−9.33519	−0.483358	−0.241679	−	0.970356i	$-0.577698\pi$
$373$	−9.33519	−0.483358	−0.241679	+	0.970356i	$0.577698\pi$
$374$	2.79129	0.144334
$375$	−28.6576	−1.47987
$376$	6.67522	0.344248
$377$	5.81844	0.299665
$378$	1.98327	0.102009
$379$	−23.9566	−1.23057	−0.615285	−	0.788305i	$-0.710959\pi$
$379$	−23.9566	−1.23057	−0.615285	+	0.788305i	$0.710959\pi$
$380$	−9.34418	−0.479347
$381$	25.3047	1.29640
$382$	−7.06541	−0.361498
$383$	−12.5287	−0.640188	−0.320094	−	0.947386i	$-0.603714\pi$
$383$	−12.5287	−0.640188	−0.320094	+	0.947386i	$0.603714\pi$
$384$	−2.50775	−0.127973
$385$	3.95334	0.201481
$386$	15.7816	0.803262
$387$	−28.6298	−1.45534
$388$	14.1175	0.716707
$389$	4.34252	0.220175	0.110087	−	0.993922i	$-0.464887\pi$
$389$	4.34252	0.220175	0.110087	+	0.993922i	$0.464887\pi$
$390$	3.22715	0.163413
$391$	−3.81782	−0.193076
$392$	−0.499383	−0.0252226
$393$	29.4772	1.48693
$394$	1.00000	0.0503793
$395$	14.2459	0.716789
$396$	−3.28879	−0.165268
$397$	19.3179	0.969538	0.484769	−	0.874642i	$-0.338904\pi$
$397$	19.3179	0.969538	0.484769	+	0.874642i	$0.338904\pi$
$398$	−11.9777	−0.600390
$399$	44.4515	2.22536
$400$	−2.91597	−0.145799
$401$	−12.1723	−0.607856	−0.303928	−	0.952695i	$-0.598298\pi$
$401$	−12.1723	−0.607856	−0.303928	+	0.952695i	$0.598298\pi$
$402$	8.15416	0.406693
$403$	−5.25661	−0.261850
$404$	−10.7170	−0.533189
$405$	−11.6214	−0.577473
$406$	−17.8746	−0.887099
$407$	−0.874619	−0.0433532
$408$	−6.99984	−0.346544
$409$	−29.5873	−1.46300	−0.731499	−	0.681843i	$-0.761179\pi$
$409$	−29.5873	−1.46300	−0.731499	+	0.681843i	$0.761179\pi$
$410$	12.8425	0.634248
$411$	−55.7440	−2.74965
$412$	2.19566	0.108173
$413$	−17.0681	−0.839867
$414$	4.49829	0.221079
$415$	−5.10129	−0.250413
$416$	0.891423	0.0437056
$417$	−28.9027	−1.41537
$418$	−6.47277	−0.316593
$419$	13.4650	0.657806	0.328903	−	0.944364i	$-0.393321\pi$
$419$	13.4650	0.657806	0.328903	+	0.944364i	$0.393321\pi$
$420$	−9.91398	−0.483753
$421$	−9.32246	−0.454349	−0.227174	−	0.973854i	$-0.572949\pi$
$421$	−9.32246	−0.454349	−0.227174	+	0.973854i	$0.572949\pi$
$422$	−5.40901	−0.263307
$423$	−21.9534	−1.06741
$424$	5.03015	0.244286
$425$	−8.13932	−0.394815
$426$	3.27466	0.158658
$427$	−2.50565	−0.121257
$428$	14.0548	0.679363
$429$	2.23546	0.107929
$430$	12.5671	0.606038
$431$	6.01332	0.289651	0.144826	−	0.989457i	$-0.453738\pi$
$431$	6.01332	0.289651	0.144826	+	0.989457i	$0.453738\pi$
$432$	0.724218	0.0348440
$433$	−2.65774	−0.127723	−0.0638614	−	0.997959i	$-0.520342\pi$
$433$	−2.65774	−0.127723	−0.0638614	+	0.997959i	$0.520342\pi$
$434$	16.1486	0.775156
$435$	−23.6297	−1.13296
$436$	−11.2134	−0.537026
$437$	8.85322	0.423507
$438$	−24.0920	−1.15116
$439$	−4.13722	−0.197459	−0.0987294	−	0.995114i	$-0.531478\pi$
$439$	−4.13722	−0.197459	−0.0987294	+	0.995114i	$0.531478\pi$
$440$	1.44362	0.0688217
$441$	1.64237	0.0782079
$442$	2.48822	0.118352
$443$	31.0553	1.47548	0.737740	−	0.675085i	$-0.235893\pi$
$443$	31.0553	1.47548	0.737740	+	0.675085i	$0.235893\pi$
$444$	2.19332	0.104090
$445$	10.1366	0.480519
$446$	11.8315	0.560240
$447$	−33.9841	−1.60739
$448$	−2.73850	−0.129382
$449$	−10.1546	−0.479225	−0.239612	−	0.970869i	$-0.577020\pi$
$449$	−10.1546	−0.479225	−0.239612	+	0.970869i	$0.577020\pi$
$450$	9.59004	0.452079
$451$	8.89609	0.418901
$452$	2.60801	0.122671
$453$	8.64013	0.405949
$454$	−16.7053	−0.784018
$455$	3.52410	0.165212
$456$	16.2321	0.760136
$457$	−12.5538	−0.587243	−0.293621	−	0.955922i	$-0.594860\pi$
$457$	−12.5538	−0.587243	−0.293621	+	0.955922i	$0.594860\pi$
$458$	−16.3455	−0.763776
$459$	2.02150	0.0943556
$460$	−1.97453	−0.0920628
$461$	20.7552	0.966668	0.483334	−	0.875436i	$-0.339426\pi$
$461$	20.7552	0.966668	0.483334	+	0.875436i	$0.339426\pi$
$462$	−6.86746	−0.319503
$463$	−6.25560	−0.290722	−0.145361	−	0.989379i	$-0.546434\pi$
$463$	−6.25560	−0.290722	−0.145361	+	0.989379i	$0.546434\pi$
$464$	−6.52713	−0.303015
$465$	21.3480	0.989988
$466$	2.73684	0.126782
$467$	−1.63043	−0.0754475	−0.0377238	−	0.999288i	$-0.512011\pi$
$467$	−1.63043	−0.0754475	−0.0377238	+	0.999288i	$0.512011\pi$
$468$	−2.93171	−0.135518
$469$	8.90448	0.411171
$470$	9.63644	0.444496
$471$	−6.29777	−0.290186
$472$	−6.23265	−0.286881
$473$	8.70527	0.400269
$474$	−24.7470	−1.13667
$475$	18.8744	0.866018
$476$	−7.64394	−0.350359
$477$	−16.5431	−0.757457
$478$	−15.4866	−0.708343
$479$	0.00550316	0.000251446 0	0.000125723	−	1.00000i	$-0.499960\pi$
$479$	0.00550316	0.000251446 0	0.000125723		1.00000i	$0.499960\pi$
$480$	−3.62022	−0.165240
$481$	−0.779656	−0.0355492
$482$	−5.52753	−0.251772
$483$	9.39307	0.427400
$484$	1.00000	0.0454545
$485$	20.3802	0.925419
$486$	22.3606	1.01430
$487$	−33.8716	−1.53487	−0.767434	−	0.641127i	$-0.778467\pi$
$487$	−33.8716	−1.53487	−0.767434	+	0.641127i	$0.778467\pi$
$488$	−0.914972	−0.0414189
$489$	−32.6505	−1.47651
$490$	−0.720916	−0.0325677
$491$	−15.9309	−0.718950	−0.359475	−	0.933155i	$-0.617044\pi$
$491$	−15.9309	−0.718950	−0.359475	+	0.933155i	$0.617044\pi$
$492$	−22.3091	−1.00577
$493$	−18.2191	−0.820547
$494$	−5.76997	−0.259603
$495$	−4.74775	−0.213396
$496$	5.89687	0.264777
$497$	3.57598	0.160404
$498$	8.86160	0.397098
$499$	10.5001	0.470049	0.235025	−	0.971989i	$-0.424483\pi$
$499$	10.5001	0.470049	0.235025	+	0.971989i	$0.424483\pi$
$500$	−11.4276	−0.511059
$501$	−26.6008	−1.18844
$502$	−4.75431	−0.212195
$503$	−0.577350	−0.0257428	−0.0128714	−	0.999917i	$-0.504097\pi$
$503$	−0.577350	−0.0257428	−0.0128714	+	0.999917i	$0.504097\pi$
$504$	9.00636	0.401175
$505$	−15.4712	−0.688458
$506$	−1.36776	−0.0608046
$507$	−30.6080	−1.35935
$508$	10.0906	0.447699
$509$	19.3876	0.859340	0.429670	−	0.902986i	$-0.358630\pi$
$509$	19.3876	0.859340	0.429670	+	0.902986i	$0.358630\pi$
$510$	−10.1051	−0.447460
$511$	−26.3089	−1.16384
$512$	−1.00000	−0.0441942
$513$	−4.68770	−0.206967
$514$	0.510379	0.0225119
$515$	3.16969	0.139673
$516$	−21.8306	−0.961039
$517$	6.67522	0.293576
$518$	2.39514	0.105237
$519$	15.3697	0.674653
$520$	1.28687	0.0564331
$521$	−34.6668	−1.51878	−0.759391	−	0.650635i	$-0.774503\pi$
$521$	−34.6668	−1.51878	−0.759391	+	0.650635i	$0.774503\pi$
$522$	21.4664	0.939558
$523$	−14.3486	−0.627421	−0.313710	−	0.949519i	$-0.601572\pi$
$523$	−14.3486	−0.627421	−0.313710	+	0.949519i	$0.601572\pi$
$524$	11.7545	0.513496
$525$	20.0253	0.873978
$526$	25.8394	1.12665
$527$	16.4598	0.717002
$528$	−2.50775	−0.109136
$529$	−21.1292	−0.918662
$530$	7.26160	0.315424
$531$	20.4979	0.889533
$532$	17.7257	0.768505
$533$	7.93019	0.343495
$534$	−17.6085	−0.761995
$535$	20.2897	0.877199
$536$	3.25159	0.140447
$537$	51.5389	2.22407
$538$	−16.4972	−0.711245
$539$	−0.499383	−0.0215099
$540$	1.04549	0.0449908
$541$	21.0359	0.904402	0.452201	−	0.891916i	$-0.350639\pi$
$541$	21.0359	0.904402	0.452201	+	0.891916i	$0.350639\pi$
$542$	−7.65127	−0.328650
$543$	−40.5213	−1.73894
$544$	−2.79129	−0.119675
$545$	−16.1879	−0.693412
$546$	−6.12182	−0.261990
$547$	−12.6509	−0.540913	−0.270457	−	0.962732i	$-0.587175\pi$
$547$	−12.6509	−0.540913	−0.270457	+	0.962732i	$0.587175\pi$
$548$	−22.2287	−0.949564
$549$	3.00915	0.128428
$550$	−2.91597	−0.124338
$551$	42.2486	1.79985
$552$	3.43001	0.145991
$553$	−27.0241	−1.14918
$554$	−9.78835	−0.415867
$555$	3.16631	0.134403
$556$	−11.5254	−0.488785
$557$	−5.91818	−0.250761	−0.125381	−	0.992109i	$-0.540015\pi$
$557$	−5.91818	−0.250761	−0.125381	+	0.992109i	$0.540015\pi$
$558$	−19.3936	−0.820996
$559$	7.76008	0.328216
$560$	−3.95334	−0.167059
$561$	−6.99984	−0.295533
$562$	22.3443	0.942537
$563$	18.1813	0.766249	0.383124	−	0.923697i	$-0.374848\pi$
$563$	18.1813	0.766249	0.383124	+	0.923697i	$0.374848\pi$
$564$	−16.7397	−0.704871
$565$	3.76497	0.158393
$566$	−1.93375	−0.0812815
$567$	22.0455	0.925825
$568$	1.30582	0.0547908
$569$	−16.9543	−0.710759	−0.355380	−	0.934722i	$-0.615648\pi$
$569$	−16.9543	−0.710759	−0.355380	+	0.934722i	$0.615648\pi$
$570$	23.4328	0.981494
$571$	19.2628	0.806125	0.403062	−	0.915173i	$-0.367946\pi$
$571$	19.2628	0.806125	0.403062	+	0.915173i	$0.367946\pi$
$572$	0.891423	0.0372723
$573$	17.7182	0.740190
$574$	−24.3620	−1.01685
$575$	3.98837	0.166326
$576$	3.28879	0.137033
$577$	−23.8837	−0.994292	−0.497146	−	0.867667i	$-0.665619\pi$
$577$	−23.8837	−0.994292	−0.497146	+	0.867667i	$0.665619\pi$
$578$	9.20872	0.383032
$579$	−39.5762	−1.64473
$580$	−9.42267	−0.391255
$581$	9.67701	0.401470
$582$	−35.4031	−1.46751
$583$	5.03015	0.208328
$584$	−9.60704	−0.397542
$585$	−4.23226	−0.174982
$586$	−16.5921	−0.685414
$587$	37.0242	1.52815	0.764076	−	0.645127i	$-0.223195\pi$
$587$	37.0242	1.52815	0.764076	+	0.645127i	$0.223195\pi$
$588$	1.25232	0.0516450
$589$	−38.1690	−1.57273
$590$	−8.99755	−0.370423
$591$	−2.50775	−0.103155
$592$	0.874619	0.0359466
$593$	−22.9193	−0.941184	−0.470592	−	0.882351i	$-0.655960\pi$
$593$	−22.9193	−0.941184	−0.470592	+	0.882351i	$0.655960\pi$
$594$	0.724218	0.0297150
$595$	−11.0349	−0.452387
$596$	−13.5516	−0.555097
$597$	30.0371	1.22934
$598$	−1.21926	−0.0498591
$599$	−16.7819	−0.685690	−0.342845	−	0.939392i	$-0.611391\pi$
$599$	−16.7819	−0.685690	−0.342845	+	0.939392i	$0.611391\pi$
$600$	7.31252	0.298533
$601$	−29.3844	−1.19862	−0.599308	−	0.800519i	$-0.704557\pi$
$601$	−29.3844	−1.19862	−0.599308	+	0.800519i	$0.704557\pi$
$602$	−23.8394	−0.971621
$603$	−10.6938	−0.435485
$604$	3.44538	0.140190
$605$	1.44362	0.0586913
$606$	26.8754	1.09174
$607$	16.4763	0.668754	0.334377	−	0.942439i	$-0.391474\pi$
$607$	16.4763	0.668754	0.334377	+	0.942439i	$0.391474\pi$
$608$	6.47277	0.262505
$609$	44.8249	1.81639
$610$	−1.32087	−0.0534804
$611$	5.95044	0.240729
$612$	9.17996	0.371078
$613$	20.9166	0.844813	0.422406	−	0.906407i	$-0.361186\pi$
$613$	20.9166	0.844813	0.422406	+	0.906407i	$0.361186\pi$
$614$	−6.74572	−0.272235
$615$	−32.2058	−1.29866
$616$	−2.73850	−0.110337
$617$	4.01771	0.161747	0.0808734	−	0.996724i	$-0.474229\pi$
$617$	4.01771	0.161747	0.0808734	+	0.996724i	$0.474229\pi$
$618$	−5.50617	−0.221490
$619$	−1.88561	−0.0757889	−0.0378944	−	0.999282i	$-0.512065\pi$
$619$	−1.88561	−0.0757889	−0.0378944	+	0.999282i	$0.512065\pi$
$620$	8.51281	0.341883
$621$	−0.990560	−0.0397498
$622$	−5.06474	−0.203078
$623$	−19.2288	−0.770385
$624$	−2.23546	−0.0894902
$625$	−1.91722	−0.0766888
$626$	12.2817	0.490875
$627$	16.2321	0.648246
$628$	−2.51133	−0.100213
$629$	2.44131	0.0973414
$630$	13.0017	0.518001
$631$	25.6710	1.02195	0.510974	−	0.859596i	$-0.329285\pi$
$631$	25.6710	1.02195	0.510974	+	0.859596i	$0.329285\pi$
$632$	−9.86820	−0.392536
$633$	13.5644	0.539138
$634$	13.4075	0.532481
$635$	14.5670	0.578073
$636$	−12.6143	−0.500191
$637$	−0.445161	−0.0176379
$638$	−6.52713	−0.258412
$639$	−4.29456	−0.169890
$640$	−1.44362	−0.0570639
$641$	−0.0475913	−0.00187974	−0.000939872	−	1.00000i	$-0.500299\pi$
$641$	−0.0475913	−0.00187974	−0.000939872		1.00000i	$0.500299\pi$
$642$	−35.2458	−1.39104
$643$	1.75011	0.0690175	0.0345087	−	0.999404i	$-0.489013\pi$
$643$	1.75011	0.0690175	0.0345087	+	0.999404i	$0.489013\pi$
$644$	3.74562	0.147598
$645$	−31.5150	−1.24090
$646$	18.0673	0.710850
$647$	6.41621	0.252247	0.126124	−	0.992015i	$-0.459746\pi$
$647$	6.41621	0.252247	0.126124	+	0.992015i	$0.459746\pi$
$648$	8.05022	0.316243
$649$	−6.23265	−0.244653
$650$	−2.59937	−0.101956
$651$	−40.4965	−1.58718
$652$	−13.0199	−0.509897
$653$	41.0575	1.60670	0.803351	−	0.595506i	$-0.203048\pi$
$653$	41.0575	1.60670	0.803351	+	0.595506i	$0.203048\pi$
$654$	28.1204	1.09960
$655$	16.9689	0.663031
$656$	−8.89609	−0.347334
$657$	31.5956	1.23266
$658$	−18.2801	−0.712632
$659$	−45.1608	−1.75921	−0.879607	−	0.475701i	$-0.842194\pi$
$659$	−45.1608	−1.75921	−0.879607	+	0.475701i	$0.842194\pi$
$660$	−3.62022	−0.140917
$661$	−1.78785	−0.0695394	−0.0347697	−	0.999395i	$-0.511070\pi$
$661$	−1.78785	−0.0695394	−0.0347697	+	0.999395i	$0.511070\pi$
$662$	11.6417	0.452466
$663$	−6.23982	−0.242335
$664$	3.53369	0.137134
$665$	25.5890	0.992301
$666$	−2.87644	−0.111460
$667$	8.92758	0.345677
$668$	−10.6075	−0.410415
$669$	−29.6705	−1.14713
$670$	4.69405	0.181347
$671$	−0.914972	−0.0353221
$672$	6.86746	0.264918
$673$	−25.3761	−0.978177	−0.489088	−	0.872234i	$-0.662670\pi$
$673$	−25.3761	−0.978177	−0.489088	+	0.872234i	$0.662670\pi$
$674$	6.82398	0.262850
$675$	−2.11180	−0.0812833
$676$	−12.2054	−0.469437
$677$	26.0973	1.00300	0.501500	−	0.865157i	$-0.332782\pi$
$677$	26.0973	1.00300	0.501500	+	0.865157i	$0.332782\pi$
$678$	−6.54023	−0.251176
$679$	−38.6608	−1.48366
$680$	−4.02954	−0.154526
$681$	41.8926	1.60533
$682$	5.89687	0.225803
$683$	33.6704	1.28836	0.644182	−	0.764872i	$-0.277198\pi$
$683$	33.6704	1.28836	0.644182	+	0.764872i	$0.277198\pi$
$684$	−21.2876	−0.813951
$685$	−32.0897	−1.22609
$686$	−17.8019	−0.679681
$687$	40.9904	1.56388
$688$	−8.70527	−0.331885
$689$	4.48399	0.170827
$690$	4.95161	0.188505
$691$	−21.1909	−0.806141	−0.403071	−	0.915169i	$-0.632057\pi$
$691$	−21.1909	−0.806141	−0.403071	+	0.915169i	$0.632057\pi$
$692$	6.12887	0.232985
$693$	9.00636	0.342123
$694$	−28.8329	−1.09448
$695$	−16.6382	−0.631123
$696$	16.3684	0.620443
$697$	−24.8315	−0.940562
$698$	5.44494	0.206094
$699$	−6.86330	−0.259594
$700$	7.98540	0.301820
$701$	20.8739	0.788397	0.394198	−	0.919025i	$-0.371022\pi$
$701$	20.8739	0.788397	0.394198	+	0.919025i	$0.371022\pi$
$702$	0.645585	0.0243660
$703$	−5.66120	−0.213516
$704$	−1.00000	−0.0376889
$705$	−24.1658	−0.910135
$706$	−9.07135	−0.341405
$707$	29.3484	1.10376
$708$	15.6299	0.587408
$709$	−9.17338	−0.344513	−0.172257	−	0.985052i	$-0.555106\pi$
$709$	−9.17338	−0.344513	−0.172257	+	0.985052i	$0.555106\pi$
$710$	1.88510	0.0707464
$711$	32.4545	1.21714
$712$	−7.02165	−0.263147
$713$	−8.06553	−0.302056
$714$	19.1691	0.717384
$715$	1.28687	0.0481263
$716$	20.5519	0.768060
$717$	38.8366	1.45038
$718$	−1.01295	−0.0378030
$719$	6.98614	0.260539	0.130269	−	0.991479i	$-0.458416\pi$
$719$	6.98614	0.260539	0.130269	+	0.991479i	$0.458416\pi$
$720$	4.74775	0.176938
$721$	−6.01282	−0.223929
$722$	−22.8967	−0.852127
$723$	13.8616	0.515520
$724$	−16.1585	−0.600524
$725$	19.0330	0.706866
$726$	−2.50775	−0.0930712
$727$	38.6585	1.43376	0.716882	−	0.697195i	$-0.245569\pi$
$727$	38.6585	1.43376	0.716882	+	0.697195i	$0.245569\pi$
$728$	−2.44116	−0.0904755
$729$	−31.9240	−1.18237
$730$	−13.8689	−0.513310
$731$	−24.2989	−0.898727
$732$	2.29452	0.0848079
$733$	19.2369	0.710532	0.355266	−	0.934765i	$-0.384390\pi$
$733$	19.2369	0.710532	0.355266	+	0.934765i	$0.384390\pi$
$734$	−0.647112	−0.0238854
$735$	1.80788	0.0666845
$736$	1.36776	0.0504165
$737$	3.25159	0.119774
$738$	29.2574	1.07698
$739$	−49.4725	−1.81988	−0.909938	−	0.414745i	$-0.863871\pi$
$739$	−49.4725	−1.81988	−0.909938	+	0.414745i	$0.863871\pi$
$740$	1.26261	0.0464146
$741$	14.4696	0.531555
$742$	−13.7751	−0.505699
$743$	−35.5589	−1.30453	−0.652265	−	0.757991i	$-0.726181\pi$
$743$	−35.5589	−1.30453	−0.652265	+	0.757991i	$0.726181\pi$
$744$	−14.7879	−0.542149
$745$	−19.5633	−0.716746
$746$	9.33519	0.341786
$747$	−11.6216	−0.425211
$748$	−2.79129	−0.102060
$749$	−38.4890	−1.40636
$750$	28.6576	1.04643
$751$	51.4856	1.87873	0.939367	−	0.342913i	$-0.111414\pi$
$751$	51.4856	1.87873	0.939367	+	0.342913i	$0.111414\pi$
$752$	−6.67522	−0.243420
$753$	11.9226	0.434484
$754$	−5.81844	−0.211895
$755$	4.97380	0.181015
$756$	−1.98327	−0.0721309
$757$	27.4475	0.997597	0.498798	−	0.866718i	$-0.333775\pi$
$757$	27.4475	0.997597	0.498798	+	0.866718i	$0.333775\pi$
$758$	23.9566	0.870144
$759$	3.43001	0.124501
$760$	9.34418	0.338949
$761$	54.6517	1.98112	0.990561	−	0.137075i	$-0.0437701\pi$
$761$	54.6517	1.98112	0.990561	+	0.137075i	$0.0437701\pi$
$762$	−25.3047	−0.916693
$763$	30.7080	1.11170
$764$	7.06541	0.255617
$765$	13.2523	0.479139
$766$	12.5287	0.452681
$767$	−5.55593	−0.200613
$768$	2.50775	0.0904905
$769$	16.8356	0.607109	0.303554	−	0.952814i	$-0.401827\pi$
$769$	16.8356	0.607109	0.303554	+	0.952814i	$0.401827\pi$
$770$	−3.95334	−0.142469
$771$	−1.27990	−0.0460945
$772$	−15.7816	−0.567992
$773$	−28.4382	−1.02285	−0.511425	−	0.859328i	$-0.670882\pi$
$773$	−28.4382	−1.02285	−0.511425	+	0.859328i	$0.670882\pi$
$774$	28.6298	1.02908
$775$	−17.1951	−0.617667
$776$	−14.1175	−0.506789
$777$	−6.00641	−0.215479
$778$	−4.34252	−0.155687
$779$	57.5823	2.06310
$780$	−3.22715	−0.115551
$781$	1.30582	0.0467258
$782$	3.81782	0.136525
$783$	−4.72707	−0.168932
$784$	0.499383	0.0178351
$785$	−3.62539	−0.129396
$786$	−29.4772	−1.05142
$787$	−54.5600	−1.94485	−0.972427	−	0.233208i	$-0.925078\pi$
$787$	−54.5600	−1.94485	−0.972427	+	0.233208i	$0.925078\pi$
$788$	−1.00000	−0.0356235
$789$	−64.7988	−2.30690
$790$	−14.2459	−0.506846
$791$	−7.14204	−0.253942
$792$	3.28879	0.116862
$793$	−0.815628	−0.0289638
$794$	−19.3179	−0.685567
$795$	−18.2103	−0.645851
$796$	11.9777	0.424540
$797$	49.9596	1.76966	0.884830	−	0.465914i	$-0.154274\pi$
$797$	49.9596	1.76966	0.884830	+	0.465914i	$0.154274\pi$
$798$	−44.4515	−1.57357
$799$	−18.6324	−0.659168
$800$	2.91597	0.103095
$801$	23.0928	0.815942
$802$	12.1723	0.429819
$803$	−9.60704	−0.339025
$804$	−8.15416	−0.287575
$805$	5.40724	0.190580
$806$	5.25661	0.185156
$807$	41.3708	1.45632
$808$	10.7170	0.377021
$809$	−34.2514	−1.20421	−0.602107	−	0.798415i	$-0.705672\pi$
$809$	−34.2514	−1.20421	−0.602107	+	0.798415i	$0.705672\pi$
$810$	11.6214	0.408335
$811$	−34.5489	−1.21318	−0.606588	−	0.795017i	$-0.707462\pi$
$811$	−34.5489	−1.21318	−0.606588	+	0.795017i	$0.707462\pi$
$812$	17.8746	0.627274
$813$	19.1874	0.672933
$814$	0.874619	0.0306554
$815$	−18.7957	−0.658383
$816$	6.99984	0.245043
$817$	56.3472	1.97134
$818$	29.5873	1.03450
$819$	8.02848	0.280538
$820$	−12.8425	−0.448481
$821$	9.14785	0.319262	0.159631	−	0.987177i	$-0.448970\pi$
$821$	9.14785	0.319262	0.159631	+	0.987177i	$0.448970\pi$
$822$	55.7440	1.94430
$823$	−43.6520	−1.52161	−0.760806	−	0.648979i	$-0.775196\pi$
$823$	−43.6520	−1.52161	−0.760806	+	0.648979i	$0.775196\pi$
$824$	−2.19566	−0.0764895
$825$	7.31252	0.254589
$826$	17.0681	0.593875
$827$	−37.4013	−1.30057	−0.650286	−	0.759690i	$-0.725351\pi$
$827$	−37.4013	−1.30057	−0.650286	+	0.759690i	$0.725351\pi$
$828$	−4.49829	−0.156327
$829$	−22.3501	−0.776250	−0.388125	−	0.921607i	$-0.626877\pi$
$829$	−22.3501	−0.776250	−0.388125	+	0.921607i	$0.626877\pi$
$830$	5.10129	0.177068
$831$	24.5467	0.851516
$832$	−0.891423	−0.0309045
$833$	1.39392	0.0482964
$834$	28.9027	1.00082
$835$	−15.3131	−0.529931
$836$	6.47277	0.223865
$837$	4.27062	0.147614
$838$	−13.4650	−0.465139
$839$	−50.7682	−1.75271	−0.876356	−	0.481663i	$-0.840033\pi$
$839$	−50.7682	−1.75271	−0.876356	+	0.481663i	$0.840033\pi$
$840$	9.91398	0.342065
$841$	13.6035	0.469085
$842$	9.32246	0.321273
$843$	−56.0338	−1.92991
$844$	5.40901	0.186186
$845$	−17.6199	−0.606141
$846$	21.9534	0.754773
$847$	−2.73850	−0.0940960
$848$	−5.03015	−0.172736
$849$	4.84935	0.166429
$850$	8.13932	0.279176
$851$	−1.19627	−0.0410077
$852$	−3.27466	−0.112188
$853$	−4.34276	−0.148693	−0.0743466	−	0.997232i	$-0.523687\pi$
$853$	−4.34276	−0.148693	−0.0743466	+	0.997232i	$0.523687\pi$
$854$	2.50565	0.0857416
$855$	−30.7311	−1.05098
$856$	−14.0548	−0.480382
$857$	−9.99417	−0.341395	−0.170697	−	0.985324i	$-0.554602\pi$
$857$	−9.99417	−0.341395	−0.170697	+	0.985324i	$0.554602\pi$
$858$	−2.23546	−0.0763175
$859$	−49.0103	−1.67221	−0.836105	−	0.548569i	$-0.815173\pi$
$859$	−49.0103	−1.67221	−0.836105	+	0.548569i	$0.815173\pi$
$860$	−12.5671	−0.428533
$861$	61.0936	2.08206
$862$	−6.01332	−0.204814
$863$	−34.4968	−1.17429	−0.587143	−	0.809483i	$-0.699747\pi$
$863$	−34.4968	−1.17429	−0.587143	+	0.809483i	$0.699747\pi$
$864$	−0.724218	−0.0246384
$865$	8.84773	0.300832
$866$	2.65774	0.0903137
$867$	−23.0931	−0.784284
$868$	−16.1486	−0.548118
$869$	−9.86820	−0.334756
$870$	23.6297	0.801121
$871$	2.89854	0.0982134
$872$	11.2134	0.379735
$873$	46.4295	1.57140
$874$	−8.85322	−0.299465
$875$	31.2945	1.05795
$876$	24.0920	0.813994
$877$	−9.17560	−0.309838	−0.154919	−	0.987927i	$-0.549512\pi$
$877$	−9.17560	−0.309838	−0.154919	+	0.987927i	$0.549512\pi$
$878$	4.13722	0.139624
$879$	41.6088	1.40343
$880$	−1.44362	−0.0486643
$881$	39.6678	1.33644	0.668221	−	0.743963i	$-0.267056\pi$
$881$	39.6678	1.33644	0.668221	+	0.743963i	$0.267056\pi$
$882$	−1.64237	−0.0553013
$883$	15.5434	0.523077	0.261538	−	0.965193i	$-0.415770\pi$
$883$	15.5434	0.523077	0.261538	+	0.965193i	$0.415770\pi$
$884$	−2.48822	−0.0836878
$885$	22.5636	0.758466
$886$	−31.0553	−1.04332
$887$	26.4801	0.889114	0.444557	−	0.895750i	$-0.353361\pi$
$887$	26.4801	0.889114	0.444557	+	0.895750i	$0.353361\pi$
$888$	−2.19332	−0.0736031
$889$	−27.6332	−0.926786
$890$	−10.1366	−0.339778
$891$	8.05022	0.269693
$892$	−11.8315	−0.396149
$893$	43.2071	1.44587
$894$	33.9841	1.13660
$895$	29.6690	0.991726
$896$	2.73850	0.0914869
$897$	3.05759	0.102090
$898$	10.1546	0.338863
$899$	−38.4897	−1.28370
$900$	−9.59004	−0.319668
$901$	−14.0406	−0.467760
$902$	−8.89609	−0.296208
$903$	59.7831	1.98946
$904$	−2.60801	−0.0867412
$905$	−23.3266	−0.775402
$906$	−8.64013	−0.287049
$907$	−44.3614	−1.47300	−0.736498	−	0.676440i	$-0.763522\pi$
$907$	−44.3614	−1.47300	−0.736498	+	0.676440i	$0.763522\pi$
$908$	16.7053	0.554384
$909$	−35.2459	−1.16903
$910$	−3.52410	−0.116823
$911$	−9.93023	−0.329003	−0.164502	−	0.986377i	$-0.552602\pi$
$911$	−9.93023	−0.329003	−0.164502	+	0.986377i	$0.552602\pi$
$912$	−16.2321	−0.537497
$913$	3.53369	0.116948
$914$	12.5538	0.415243
$915$	3.31240	0.109505
$916$	16.3455	0.540071
$917$	−32.1896	−1.06299
$918$	−2.02150	−0.0667195
$919$	−0.414601	−0.0136764	−0.00683821	−	0.999977i	$-0.502177\pi$
$919$	−0.414601	−0.0136764	−0.00683821	+	0.999977i	$0.502177\pi$
$920$	1.97453	0.0650982
$921$	16.9165	0.557419
$922$	−20.7552	−0.683537
$923$	1.16403	0.0383147
$924$	6.86746	0.225923
$925$	−2.55037	−0.0838555
$926$	6.25560	0.205572
$927$	7.22108	0.237171
$928$	6.52713	0.214264
$929$	−42.7155	−1.40145	−0.700726	−	0.713431i	$-0.747140\pi$
$929$	−42.7155	−1.40145	−0.700726	+	0.713431i	$0.747140\pi$
$930$	−21.3480	−0.700028
$931$	−3.23239	−0.105937
$932$	−2.73684	−0.0896482
$933$	12.7011	0.415815
$934$	1.63043	0.0533495
$935$	−4.02954	−0.131780
$936$	2.93171	0.0958258
$937$	51.5466	1.68395	0.841977	−	0.539513i	$-0.181392\pi$
$937$	51.5466	1.68395	0.841977	+	0.539513i	$0.181392\pi$
$938$	−8.90448	−0.290742
$939$	−30.7994	−1.00510
$940$	−9.63644	−0.314306
$941$	10.8972	0.355240	0.177620	−	0.984099i	$-0.443160\pi$
$941$	10.8972	0.355240	0.177620	+	0.984099i	$0.443160\pi$
$942$	6.29777	0.205192
$943$	12.1678	0.396237
$944$	6.23265	0.202855
$945$	−2.86308	−0.0931361
$946$	−8.70527	−0.283033
$947$	−38.7697	−1.25985	−0.629923	−	0.776658i	$-0.716913\pi$
$947$	−38.7697	−1.25985	−0.629923	+	0.776658i	$0.716913\pi$
$948$	24.7470	0.803744
$949$	−8.56394	−0.277997
$950$	−18.8744	−0.612367
$951$	−33.6227	−1.09029
$952$	7.64394	0.247741
$953$	43.2786	1.40193	0.700966	−	0.713195i	$-0.252752\pi$
$953$	43.2786	1.40193	0.700966	+	0.713195i	$0.252752\pi$
$954$	16.5431	0.535603
$955$	10.1997	0.330055
$956$	15.4866	0.500874
$957$	16.3684	0.529115
$958$	−0.00550316	−0.000177799 0
$959$	60.8734	1.96570
$960$	3.62022	0.116842
$961$	3.77306	0.121712
$962$	0.779656	0.0251371
$963$	46.2232	1.48952
$964$	5.52753	0.178030
$965$	−22.7825	−0.733396
$966$	−9.39307	−0.302217
$967$	26.1033	0.839424	0.419712	−	0.907657i	$-0.362131\pi$
$967$	26.1033	0.839424	0.419712	+	0.907657i	$0.362131\pi$
$968$	−1.00000	−0.0321412
$969$	−45.3083	−1.45551
$970$	−20.3802	−0.654370
$971$	−25.5961	−0.821417	−0.410708	−	0.911767i	$-0.634719\pi$
$971$	−25.5961	−0.821417	−0.410708	+	0.911767i	$0.634719\pi$
$972$	−22.3606	−0.717216
$973$	31.5622	1.01184
$974$	33.8716	1.08532
$975$	6.51856	0.208761
$976$	0.914972	0.0292876
$977$	1.46514	0.0468740	0.0234370	−	0.999725i	$-0.492539\pi$
$977$	1.46514	0.0468740	0.0234370	+	0.999725i	$0.492539\pi$
$978$	32.6505	1.04405
$979$	−7.02165	−0.224413
$980$	0.720916	0.0230288
$981$	−36.8786	−1.17744
$982$	15.9309	0.508374
$983$	38.1377	1.21640	0.608201	−	0.793783i	$-0.291891\pi$
$983$	38.1377	1.21640	0.608201	+	0.793783i	$0.291891\pi$
$984$	22.3091	0.711190
$985$	−1.44362	−0.0459974
$986$	18.2191	0.580214
$987$	45.8418	1.45916
$988$	5.76997	0.183567
$989$	11.9068	0.378613
$990$	4.74775	0.150893
$991$	55.9268	1.77657	0.888287	−	0.459289i	$-0.151896\pi$
$991$	55.9268	1.77657	0.888287	+	0.459289i	$0.151896\pi$
$992$	−5.89687	−0.187226
$993$	−29.1943	−0.926454
$994$	−3.57598	−0.113423
$995$	17.2913	0.548170
$996$	−8.86160	−0.280791
$997$	25.1466	0.796401	0.398200	−	0.917298i	$-0.369635\pi$
$997$	25.1466	0.796401	0.398200	+	0.917298i	$0.369635\pi$
$998$	−10.5001	−0.332375
$999$	0.633415	0.0200404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.15	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.15	✓	17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.50775 q^{3} +1.00000 q^{4} +1.44362 q^{5} -2.50775 q^{6} -2.73850 q^{7} -1.00000 q^{8} +3.28879 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.50775 q^{3} +1.00000 q^{4} +1.44362 q^{5} -2.50775 q^{6} -2.73850 q^{7} -1.00000 q^{8} +3.28879 q^{9} -1.44362 q^{10} -1.00000 q^{11} +2.50775 q^{12} -0.891423 q^{13} +2.73850 q^{14} +3.62022 q^{15} +1.00000 q^{16} +2.79129 q^{17} -3.28879 q^{18} -6.47277 q^{19} +1.44362 q^{20} -6.86746 q^{21} +1.00000 q^{22} -1.36776 q^{23} -2.50775 q^{24} -2.91597 q^{25} +0.891423 q^{26} +0.724218 q^{27} -2.73850 q^{28} -6.52713 q^{29} -3.62022 q^{30} +5.89687 q^{31} -1.00000 q^{32} -2.50775 q^{33} -2.79129 q^{34} -3.95334 q^{35} +3.28879 q^{36} +0.874619 q^{37} +6.47277 q^{38} -2.23546 q^{39} -1.44362 q^{40} -8.89609 q^{41} +6.86746 q^{42} -8.70527 q^{43} -1.00000 q^{44} +4.74775 q^{45} +1.36776 q^{46} -6.67522 q^{47} +2.50775 q^{48} +0.499383 q^{49} +2.91597 q^{50} +6.99984 q^{51} -0.891423 q^{52} -5.03015 q^{53} -0.724218 q^{54} -1.44362 q^{55} +2.73850 q^{56} -16.2321 q^{57} +6.52713 q^{58} +6.23265 q^{59} +3.62022 q^{60} +0.914972 q^{61} -5.89687 q^{62} -9.00636 q^{63} +1.00000 q^{64} -1.28687 q^{65} +2.50775 q^{66} -3.25159 q^{67} +2.79129 q^{68} -3.43001 q^{69} +3.95334 q^{70} -1.30582 q^{71} -3.28879 q^{72} +9.60704 q^{73} -0.874619 q^{74} -7.31252 q^{75} -6.47277 q^{76} +2.73850 q^{77} +2.23546 q^{78} +9.86820 q^{79} +1.44362 q^{80} -8.05022 q^{81} +8.89609 q^{82} -3.53369 q^{83} -6.86746 q^{84} +4.02954 q^{85} +8.70527 q^{86} -16.3684 q^{87} +1.00000 q^{88} +7.02165 q^{89} -4.74775 q^{90} +2.44116 q^{91} -1.36776 q^{92} +14.7879 q^{93} +6.67522 q^{94} -9.34418 q^{95} -2.50775 q^{96} +14.1175 q^{97} -0.499383 q^{98} -3.28879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

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