LMFDB - Embedded newform 4334.2.a.b.1.14

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 8 x^{13} + 94 x^{12} - 13 x^{11} - 582 x^{10} + 295 x^{9} + 1814 x^{8} - 1056 x^{7} + \cdots - 45 $ x^15 - 6x^14 - 8x^13 + 94x^12 - 13x^11 - 582x^10 + 295x^9 + 1814x^8 - 1056x^7 - 2966x^6 + 1621x^5 + 2328x^4 - 1160x^3 - 589x^2 + 364x - 45
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.64609$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.64609 q^{3} +1.00000 q^{4} -2.29877 q^{5} +1.64609 q^{6} -1.96736 q^{7} +1.00000 q^{8} -0.290376 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.64609 q^{3} +1.00000 q^{4} -2.29877 q^{5} +1.64609 q^{6} -1.96736 q^{7} +1.00000 q^{8} -0.290376 q^{9} -2.29877 q^{10} +1.00000 q^{11} +1.64609 q^{12} +2.02976 q^{13} -1.96736 q^{14} -3.78400 q^{15} +1.00000 q^{16} -1.77340 q^{17} -0.290376 q^{18} +2.01714 q^{19} -2.29877 q^{20} -3.23846 q^{21} +1.00000 q^{22} -3.12623 q^{23} +1.64609 q^{24} +0.284360 q^{25} +2.02976 q^{26} -5.41627 q^{27} -1.96736 q^{28} -7.93513 q^{29} -3.78400 q^{30} +5.88752 q^{31} +1.00000 q^{32} +1.64609 q^{33} -1.77340 q^{34} +4.52251 q^{35} -0.290376 q^{36} -9.80360 q^{37} +2.01714 q^{38} +3.34118 q^{39} -2.29877 q^{40} +6.48643 q^{41} -3.23846 q^{42} -5.90601 q^{43} +1.00000 q^{44} +0.667508 q^{45} -3.12623 q^{46} +6.21274 q^{47} +1.64609 q^{48} -3.12950 q^{49} +0.284360 q^{50} -2.91919 q^{51} +2.02976 q^{52} -12.2468 q^{53} -5.41627 q^{54} -2.29877 q^{55} -1.96736 q^{56} +3.32040 q^{57} -7.93513 q^{58} -0.689995 q^{59} -3.78400 q^{60} -9.25198 q^{61} +5.88752 q^{62} +0.571274 q^{63} +1.00000 q^{64} -4.66596 q^{65} +1.64609 q^{66} -1.52557 q^{67} -1.77340 q^{68} -5.14606 q^{69} +4.52251 q^{70} +1.66958 q^{71} -0.290376 q^{72} -10.4475 q^{73} -9.80360 q^{74} +0.468084 q^{75} +2.01714 q^{76} -1.96736 q^{77} +3.34118 q^{78} +4.22304 q^{79} -2.29877 q^{80} -8.04455 q^{81} +6.48643 q^{82} +0.900493 q^{83} -3.23846 q^{84} +4.07665 q^{85} -5.90601 q^{86} -13.0620 q^{87} +1.00000 q^{88} +8.48861 q^{89} +0.667508 q^{90} -3.99327 q^{91} -3.12623 q^{92} +9.69141 q^{93} +6.21274 q^{94} -4.63695 q^{95} +1.64609 q^{96} +13.9789 q^{97} -3.12950 q^{98} -0.290376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * 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
$3$	1.64609	0.950373	0.475186	−	0.879885i	$-0.342381\pi$
$3$	1.64609	0.950373	0.475186	+	0.879885i	$0.342381\pi$
$4$	1.00000	0.500000
$5$	−2.29877	−1.02804	−0.514021	−	0.857777i	$-0.671845\pi$
$5$	−2.29877	−1.02804	−0.514021	+	0.857777i	$0.671845\pi$
$6$	1.64609	0.672015
$7$	−1.96736	−0.743592	−0.371796	−	0.928314i	$-0.621258\pi$
$7$	−1.96736	−0.743592	−0.371796	+	0.928314i	$0.621258\pi$
$8$	1.00000	0.353553
$9$	−0.290376	−0.0967919
$10$	−2.29877	−0.726936
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.64609	0.475186
$13$	2.02976	0.562955	0.281477	−	0.959568i	$-0.409176\pi$
$13$	2.02976	0.562955	0.281477	+	0.959568i	$0.409176\pi$
$14$	−1.96736	−0.525799
$15$	−3.78400	−0.977024
$16$	1.00000	0.250000
$17$	−1.77340	−0.430113	−0.215057	−	0.976602i	$-0.568994\pi$
$17$	−1.77340	−0.430113	−0.215057	+	0.976602i	$0.568994\pi$
$18$	−0.290376	−0.0684422
$19$	2.01714	0.462764	0.231382	−	0.972863i	$-0.425675\pi$
$19$	2.01714	0.462764	0.231382	+	0.972863i	$0.425675\pi$
$20$	−2.29877	−0.514021
$21$	−3.23846	−0.706689
$22$	1.00000	0.213201
$23$	−3.12623	−0.651864	−0.325932	−	0.945393i	$-0.605678\pi$
$23$	−3.12623	−0.651864	−0.325932	+	0.945393i	$0.605678\pi$
$24$	1.64609	0.336007
$25$	0.284360	0.0568720
$26$	2.02976	0.398069
$27$	−5.41627	−1.04236
$28$	−1.96736	−0.371796
$29$	−7.93513	−1.47352	−0.736758	−	0.676156i	$-0.763644\pi$
$29$	−7.93513	−1.47352	−0.736758	+	0.676156i	$0.763644\pi$
$30$	−3.78400	−0.690860
$31$	5.88752	1.05743	0.528715	−	0.848799i	$-0.322674\pi$
$31$	5.88752	1.05743	0.528715	+	0.848799i	$0.322674\pi$
$32$	1.00000	0.176777
$33$	1.64609	0.286548
$34$	−1.77340	−0.304136
$35$	4.52251	0.764444
$36$	−0.290376	−0.0483960
$37$	−9.80360	−1.61170	−0.805851	−	0.592119i	$-0.798292\pi$
$37$	−9.80360	−1.61170	−0.805851	+	0.592119i	$0.798292\pi$
$38$	2.01714	0.327224
$39$	3.34118	0.535017
$40$	−2.29877	−0.363468
$41$	6.48643	1.01301	0.506505	−	0.862237i	$-0.330937\pi$
$41$	6.48643	1.01301	0.506505	+	0.862237i	$0.330937\pi$
$42$	−3.23846	−0.499705
$43$	−5.90601	−0.900658	−0.450329	−	0.892863i	$-0.648693\pi$
$43$	−5.90601	−0.900658	−0.450329	+	0.892863i	$0.648693\pi$
$44$	1.00000	0.150756
$45$	0.667508	0.0995063
$46$	−3.12623	−0.460937
$47$	6.21274	0.906221	0.453110	−	0.891454i	$-0.350314\pi$
$47$	6.21274	0.906221	0.453110	+	0.891454i	$0.350314\pi$
$48$	1.64609	0.237593
$49$	−3.12950	−0.447071
$50$	0.284360	0.0402146
$51$	−2.91919	−0.408768
$52$	2.02976	0.281477
$53$	−12.2468	−1.68223	−0.841116	−	0.540855i	$-0.818101\pi$
$53$	−12.2468	−1.68223	−0.841116	+	0.540855i	$0.818101\pi$
$54$	−5.41627	−0.737061
$55$	−2.29877	−0.309967
$56$	−1.96736	−0.262899
$57$	3.32040	0.439798
$58$	−7.93513	−1.04193
$59$	−0.689995	−0.0898297	−0.0449149	−	0.998991i	$-0.514302\pi$
$59$	−0.689995	−0.0898297	−0.0449149	+	0.998991i	$0.514302\pi$
$60$	−3.78400	−0.488512
$61$	−9.25198	−1.18460	−0.592298	−	0.805719i	$-0.701779\pi$
$61$	−9.25198	−1.18460	−0.592298	+	0.805719i	$0.701779\pi$
$62$	5.88752	0.747716
$63$	0.571274	0.0719737
$64$	1.00000	0.125000
$65$	−4.66596	−0.578741
$66$	1.64609	0.202620
$67$	−1.52557	−0.186378	−0.0931889	−	0.995648i	$-0.529706\pi$
$67$	−1.52557	−0.186378	−0.0931889	+	0.995648i	$0.529706\pi$
$68$	−1.77340	−0.215057
$69$	−5.14606	−0.619513
$70$	4.52251	0.540544
$71$	1.66958	0.198143	0.0990716	−	0.995080i	$-0.468413\pi$
$71$	1.66958	0.198143	0.0990716	+	0.995080i	$0.468413\pi$
$72$	−0.290376	−0.0342211
$73$	−10.4475	−1.22279	−0.611396	−	0.791324i	$-0.709392\pi$
$73$	−10.4475	−1.22279	−0.611396	+	0.791324i	$0.709392\pi$
$74$	−9.80360	−1.13965
$75$	0.468084	0.0540496
$76$	2.01714	0.231382
$77$	−1.96736	−0.224201
$78$	3.34118	0.378314
$79$	4.22304	0.475129	0.237564	−	0.971372i	$-0.423651\pi$
$79$	4.22304	0.475129	0.237564	+	0.971372i	$0.423651\pi$
$80$	−2.29877	−0.257011
$81$	−8.04455	−0.893839
$82$	6.48643	0.716306
$83$	0.900493	0.0988420	0.0494210	−	0.998778i	$-0.484262\pi$
$83$	0.900493	0.0988420	0.0494210	+	0.998778i	$0.484262\pi$
$84$	−3.23846	−0.353345
$85$	4.07665	0.442175
$86$	−5.90601	−0.636861
$87$	−13.0620	−1.40039
$88$	1.00000	0.106600
$89$	8.48861	0.899791	0.449896	−	0.893081i	$-0.351461\pi$
$89$	8.48861	0.899791	0.449896	+	0.893081i	$0.351461\pi$
$90$	0.667508	0.0703616
$91$	−3.99327	−0.418608
$92$	−3.12623	−0.325932
$93$	9.69141	1.00495
$94$	6.21274	0.640795
$95$	−4.63695	−0.475741
$96$	1.64609	0.168004
$97$	13.9789	1.41934	0.709672	−	0.704532i	$-0.248843\pi$
$97$	13.9789	1.41934	0.709672	+	0.704532i	$0.248843\pi$
$98$	−3.12950	−0.316127
$99$	−0.290376	−0.0291839
$100$	0.284360	0.0284360
$101$	−11.6436	−1.15858	−0.579290	−	0.815121i	$-0.696670\pi$
$101$	−11.6436	−1.15858	−0.579290	+	0.815121i	$0.696670\pi$
$102$	−2.91919	−0.289042
$103$	7.59047	0.747912	0.373956	−	0.927447i	$-0.378001\pi$
$103$	7.59047	0.747912	0.373956	+	0.927447i	$0.378001\pi$
$104$	2.02976	0.199034
$105$	7.44448	0.726507
$106$	−12.2468	−1.18952
$107$	4.03080	0.389672	0.194836	−	0.980836i	$-0.437583\pi$
$107$	4.03080	0.389672	0.194836	+	0.980836i	$0.437583\pi$
$108$	−5.41627	−0.521180
$109$	0.176538	0.0169092	0.00845462	−	0.999964i	$-0.497309\pi$
$109$	0.176538	0.0169092	0.00845462	+	0.999964i	$0.497309\pi$
$110$	−2.29877	−0.219179
$111$	−16.1376	−1.53172
$112$	−1.96736	−0.185898
$113$	−0.422748	−0.0397687	−0.0198844	−	0.999802i	$-0.506330\pi$
$113$	−0.422748	−0.0397687	−0.0198844	+	0.999802i	$0.506330\pi$
$114$	3.32040	0.310984
$115$	7.18649	0.670144
$116$	−7.93513	−0.736758
$117$	−0.589394	−0.0544895
$118$	−0.689995	−0.0635192
$119$	3.48892	0.319829
$120$	−3.78400	−0.345430
$121$	1.00000	0.0909091
$122$	−9.25198	−0.837635
$123$	10.6773	0.962737
$124$	5.88752	0.528715
$125$	10.8402	0.969576
$126$	0.571274	0.0508931
$127$	−18.4184	−1.63436	−0.817182	−	0.576379i	$-0.804465\pi$
$127$	−18.4184	−1.63436	−0.817182	+	0.576379i	$0.804465\pi$
$128$	1.00000	0.0883883
$129$	−9.72184	−0.855961
$130$	−4.66596	−0.409232
$131$	−8.95270	−0.782201	−0.391100	−	0.920348i	$-0.627906\pi$
$131$	−8.95270	−0.782201	−0.391100	+	0.920348i	$0.627906\pi$
$132$	1.64609	0.143274
$133$	−3.96844	−0.344108
$134$	−1.52557	−0.131789
$135$	12.4508	1.07159
$136$	−1.77340	−0.152068
$137$	1.50856	0.128885	0.0644424	−	0.997921i	$-0.479473\pi$
$137$	1.50856	0.128885	0.0644424	+	0.997921i	$0.479473\pi$
$138$	−5.14606	−0.438062
$139$	−13.1546	−1.11576	−0.557880	−	0.829922i	$-0.688385\pi$
$139$	−13.1546	−1.11576	−0.557880	+	0.829922i	$0.688385\pi$
$140$	4.52251	0.382222
$141$	10.2267	0.861248
$142$	1.66958	0.140108
$143$	2.02976	0.169737
$144$	−0.290376	−0.0241980
$145$	18.2411	1.51484
$146$	−10.4475	−0.864645
$147$	−5.15145	−0.424884
$148$	−9.80360	−0.805851
$149$	0.237742	0.0194766	0.00973831	−	0.999953i	$-0.496900\pi$
$149$	0.237742	0.0194766	0.00973831	+	0.999953i	$0.496900\pi$
$150$	0.468084	0.0382189
$151$	−12.1880	−0.991847	−0.495923	−	0.868366i	$-0.665170\pi$
$151$	−12.1880	−0.991847	−0.495923	+	0.868366i	$0.665170\pi$
$152$	2.01714	0.163612
$153$	0.514953	0.0416315
$154$	−1.96736	−0.158534
$155$	−13.5341	−1.08708
$156$	3.34118	0.267508
$157$	−15.9721	−1.27471	−0.637357	−	0.770569i	$-0.719972\pi$
$157$	−15.9721	−1.27471	−0.637357	+	0.770569i	$0.719972\pi$
$158$	4.22304	0.335967
$159$	−20.1594	−1.59875
$160$	−2.29877	−0.181734
$161$	6.15041	0.484720
$162$	−8.04455	−0.632040
$163$	−2.69898	−0.211401	−0.105700	−	0.994398i	$-0.533708\pi$
$163$	−2.69898	−0.211401	−0.105700	+	0.994398i	$0.533708\pi$
$164$	6.48643	0.506505
$165$	−3.78400	−0.294584
$166$	0.900493	0.0698918
$167$	2.40462	0.186075	0.0930376	−	0.995663i	$-0.470342\pi$
$167$	2.40462	0.186075	0.0930376	+	0.995663i	$0.470342\pi$
$168$	−3.23846	−0.249852
$169$	−8.88007	−0.683082
$170$	4.07665	0.312665
$171$	−0.585729	−0.0447918
$172$	−5.90601	−0.450329
$173$	9.84019	0.748136	0.374068	−	0.927401i	$-0.377963\pi$
$173$	9.84019	0.748136	0.374068	+	0.927401i	$0.377963\pi$
$174$	−13.0620	−0.990225
$175$	−0.559439	−0.0422896
$176$	1.00000	0.0753778
$177$	−1.13580	−0.0853717
$178$	8.48861	0.636248
$179$	1.57615	0.117807	0.0589035	−	0.998264i	$-0.481240\pi$
$179$	1.57615	0.117807	0.0589035	+	0.998264i	$0.481240\pi$
$180$	0.667508	0.0497531
$181$	−21.4187	−1.59204	−0.796018	−	0.605273i	$-0.793064\pi$
$181$	−21.4187	−1.59204	−0.796018	+	0.605273i	$0.793064\pi$
$182$	−3.99327	−0.296001
$183$	−15.2296	−1.12581
$184$	−3.12623	−0.230469
$185$	22.5363	1.65690
$186$	9.69141	0.710609
$187$	−1.77340	−0.129684
$188$	6.21274	0.453110
$189$	10.6557	0.775091
$190$	−4.63695	−0.336400
$191$	2.23013	0.161366	0.0806832	−	0.996740i	$-0.474290\pi$
$191$	2.23013	0.161366	0.0806832	+	0.996740i	$0.474290\pi$
$192$	1.64609	0.118797
$193$	−1.83684	−0.132219	−0.0661095	−	0.997812i	$-0.521059\pi$
$193$	−1.83684	−0.132219	−0.0661095	+	0.997812i	$0.521059\pi$
$194$	13.9789	1.00363
$195$	−7.68061	−0.550020
$196$	−3.12950	−0.223536
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−0.290376	−0.0206361
$199$	13.2387	0.938467	0.469234	−	0.883074i	$-0.344530\pi$
$199$	13.2387	0.938467	0.469234	+	0.883074i	$0.344530\pi$
$200$	0.284360	0.0201073
$201$	−2.51123	−0.177128
$202$	−11.6436	−0.819240
$203$	15.6113	1.09570
$204$	−2.91919	−0.204384
$205$	−14.9108	−1.04142
$206$	7.59047	0.528853
$207$	0.907781	0.0630951
$208$	2.02976	0.140739
$209$	2.01714	0.139529
$210$	7.44448	0.513718
$211$	7.57376	0.521399	0.260699	−	0.965420i	$-0.416047\pi$
$211$	7.57376	0.521399	0.260699	+	0.965420i	$0.416047\pi$
$212$	−12.2468	−0.841116
$213$	2.74829	0.188310
$214$	4.03080	0.275540
$215$	13.5766	0.925915
$216$	−5.41627	−0.368530
$217$	−11.5829	−0.786297
$218$	0.176538	0.0119566
$219$	−17.1976	−1.16211
$220$	−2.29877	−0.154983
$221$	−3.59958	−0.242134
$222$	−16.1376	−1.08309
$223$	20.5525	1.37630	0.688149	−	0.725570i	$-0.258424\pi$
$223$	20.5525	1.37630	0.688149	+	0.725570i	$0.258424\pi$
$224$	−1.96736	−0.131450
$225$	−0.0825713	−0.00550476
$226$	−0.422748	−0.0281208
$227$	13.3632	0.886948	0.443474	−	0.896287i	$-0.353746\pi$
$227$	13.3632	0.886948	0.443474	+	0.896287i	$0.353746\pi$
$228$	3.32040	0.219899
$229$	−22.7015	−1.50016	−0.750079	−	0.661348i	$-0.769985\pi$
$229$	−22.7015	−1.50016	−0.750079	+	0.661348i	$0.769985\pi$
$230$	7.18649	0.473863
$231$	−3.23846	−0.213075
$232$	−7.93513	−0.520967
$233$	9.23374	0.604922	0.302461	−	0.953162i	$-0.402192\pi$
$233$	9.23374	0.604922	0.302461	+	0.953162i	$0.402192\pi$
$234$	−0.589394	−0.0385299
$235$	−14.2817	−0.931634
$236$	−0.689995	−0.0449149
$237$	6.95151	0.451549
$238$	3.48892	0.226153
$239$	10.1840	0.658747	0.329374	−	0.944200i	$-0.393162\pi$
$239$	10.1840	0.658747	0.329374	+	0.944200i	$0.393162\pi$
$240$	−3.78400	−0.244256
$241$	−4.13093	−0.266097	−0.133048	−	0.991110i	$-0.542477\pi$
$241$	−4.13093	−0.266097	−0.133048	+	0.991110i	$0.542477\pi$
$242$	1.00000	0.0642824
$243$	3.00671	0.192881
$244$	−9.25198	−0.592298
$245$	7.19401	0.459608
$246$	10.6773	0.680758
$247$	4.09432	0.260515
$248$	5.88752	0.373858
$249$	1.48230	0.0939367
$250$	10.8402	0.685594
$251$	−12.7643	−0.805677	−0.402838	−	0.915271i	$-0.631976\pi$
$251$	−12.7643	−0.805677	−0.402838	+	0.915271i	$0.631976\pi$
$252$	0.571274	0.0359869
$253$	−3.12623	−0.196544
$254$	−18.4184	−1.15567
$255$	6.71055	0.420231
$256$	1.00000	0.0625000
$257$	−1.72609	−0.107671	−0.0538354	−	0.998550i	$-0.517145\pi$
$257$	−1.72609	−0.107671	−0.0538354	+	0.998550i	$0.517145\pi$
$258$	−9.72184	−0.605256
$259$	19.2872	1.19845
$260$	−4.66596	−0.289371
$261$	2.30417	0.142625
$262$	−8.95270	−0.553100
$263$	12.9111	0.796131	0.398066	−	0.917357i	$-0.369682\pi$
$263$	12.9111	0.796131	0.398066	+	0.917357i	$0.369682\pi$
$264$	1.64609	0.101310
$265$	28.1527	1.72941
$266$	−3.96844	−0.243321
$267$	13.9731	0.855137
$268$	−1.52557	−0.0931889
$269$	−5.86336	−0.357495	−0.178748	−	0.983895i	$-0.557205\pi$
$269$	−5.86336	−0.357495	−0.178748	+	0.983895i	$0.557205\pi$
$270$	12.4508	0.757730
$271$	−4.90543	−0.297984	−0.148992	−	0.988838i	$-0.547603\pi$
$271$	−4.90543	−0.297984	−0.148992	+	0.988838i	$0.547603\pi$
$272$	−1.77340	−0.107528
$273$	−6.57330	−0.397834
$274$	1.50856	0.0911354
$275$	0.284360	0.0171476
$276$	−5.14606	−0.309757
$277$	0.624591	0.0375280	0.0187640	−	0.999824i	$-0.494027\pi$
$277$	0.624591	0.0375280	0.0187640	+	0.999824i	$0.494027\pi$
$278$	−13.1546	−0.788961
$279$	−1.70959	−0.102351
$280$	4.52251	0.270272
$281$	−1.71768	−0.102468	−0.0512342	−	0.998687i	$-0.516315\pi$
$281$	−1.71768	−0.102468	−0.0512342	+	0.998687i	$0.516315\pi$
$282$	10.2267	0.608994
$283$	18.3655	1.09172	0.545859	−	0.837877i	$-0.316203\pi$
$283$	18.3655	1.09172	0.545859	+	0.837877i	$0.316203\pi$
$284$	1.66958	0.0990716
$285$	−7.63286	−0.452131
$286$	2.02976	0.120022
$287$	−12.7611	−0.753266
$288$	−0.290376	−0.0171106
$289$	−13.8550	−0.815003
$290$	18.2411	1.07115
$291$	23.0106	1.34891
$292$	−10.4475	−0.611396
$293$	16.1805	0.945273	0.472637	−	0.881257i	$-0.343302\pi$
$293$	16.1805	0.945273	0.472637	+	0.881257i	$0.343302\pi$
$294$	−5.15145	−0.300438
$295$	1.58614	0.0923488
$296$	−9.80360	−0.569823
$297$	−5.41627	−0.314284
$298$	0.237742	0.0137720
$299$	−6.34550	−0.366970
$300$	0.468084	0.0270248
$301$	11.6192	0.669722
$302$	−12.1880	−0.701342
$303$	−19.1664	−1.10108
$304$	2.01714	0.115691
$305$	21.2682	1.21781
$306$	0.514953	0.0294379
$307$	28.4043	1.62112	0.810561	−	0.585655i	$-0.199163\pi$
$307$	28.4043	1.62112	0.810561	+	0.585655i	$0.199163\pi$
$308$	−1.96736	−0.112101
$309$	12.4946	0.710795
$310$	−13.5341	−0.768684
$311$	−5.80629	−0.329244	−0.164622	−	0.986357i	$-0.552640\pi$
$311$	−5.80629	−0.329244	−0.164622	+	0.986357i	$0.552640\pi$
$312$	3.34118	0.189157
$313$	29.3844	1.66091	0.830453	−	0.557088i	$-0.188081\pi$
$313$	29.3844	1.66091	0.830453	+	0.557088i	$0.188081\pi$
$314$	−15.9721	−0.901359
$315$	−1.31323	−0.0739920
$316$	4.22304	0.237564
$317$	−32.8156	−1.84311	−0.921554	−	0.388249i	$-0.873080\pi$
$317$	−32.8156	−1.84311	−0.921554	+	0.388249i	$0.873080\pi$
$318$	−20.1594	−1.13048
$319$	−7.93513	−0.444282
$320$	−2.29877	−0.128505
$321$	6.63507	0.370333
$322$	6.15041	0.342749
$323$	−3.57720	−0.199041
$324$	−8.04455	−0.446920
$325$	0.577183	0.0320164
$326$	−2.69898	−0.149483
$327$	0.290598	0.0160701
$328$	6.48643	0.358153
$329$	−12.2227	−0.673859
$330$	−3.78400	−0.208302
$331$	−10.6373	−0.584680	−0.292340	−	0.956314i	$-0.594434\pi$
$331$	−10.6373	−0.584680	−0.292340	+	0.956314i	$0.594434\pi$
$332$	0.900493	0.0494210
$333$	2.84673	0.156000
$334$	2.40462	0.131575
$335$	3.50694	0.191604
$336$	−3.23846	−0.176672
$337$	3.17671	0.173047	0.0865233	−	0.996250i	$-0.472424\pi$
$337$	3.17671	0.173047	0.0865233	+	0.996250i	$0.472424\pi$
$338$	−8.88007	−0.483012
$339$	−0.695882	−0.0377951
$340$	4.07665	0.221087
$341$	5.88752	0.318827
$342$	−0.585729	−0.0316726
$343$	19.9284	1.07603
$344$	−5.90601	−0.318431
$345$	11.8296	0.636886
$346$	9.84019	0.529012
$347$	4.03804	0.216773	0.108387	−	0.994109i	$-0.465432\pi$
$347$	4.03804	0.216773	0.108387	+	0.994109i	$0.465432\pi$
$348$	−13.0620	−0.700195
$349$	4.05672	0.217151	0.108576	−	0.994088i	$-0.465371\pi$
$349$	4.05672	0.217151	0.108576	+	0.994088i	$0.465371\pi$
$350$	−0.559439	−0.0299033
$351$	−10.9937	−0.586802
$352$	1.00000	0.0533002
$353$	20.9778	1.11654	0.558269	−	0.829660i	$-0.311466\pi$
$353$	20.9778	1.11654	0.558269	+	0.829660i	$0.311466\pi$
$354$	−1.13580	−0.0603669
$355$	−3.83800	−0.203700
$356$	8.48861	0.449896
$357$	5.74309	0.303956
$358$	1.57615	0.0833021
$359$	7.21732	0.380916	0.190458	−	0.981695i	$-0.439003\pi$
$359$	7.21732	0.380916	0.190458	+	0.981695i	$0.439003\pi$
$360$	0.667508	0.0351808
$361$	−14.9311	−0.785849
$362$	−21.4187	−1.12574
$363$	1.64609	0.0863975
$364$	−3.99327	−0.209304
$365$	24.0165	1.25708
$366$	−15.2296	−0.796066
$367$	14.9122	0.778412	0.389206	−	0.921151i	$-0.372749\pi$
$367$	14.9122	0.778412	0.389206	+	0.921151i	$0.372749\pi$
$368$	−3.12623	−0.162966
$369$	−1.88350	−0.0980512
$370$	22.5363	1.17160
$371$	24.0939	1.25089
$372$	9.69141	0.502476
$373$	21.3714	1.10657	0.553283	−	0.832993i	$-0.313375\pi$
$373$	21.3714	1.10657	0.553283	+	0.832993i	$0.313375\pi$
$374$	−1.77340	−0.0917004
$375$	17.8440	0.921458
$376$	6.21274	0.320397
$377$	−16.1064	−0.829523
$378$	10.6557	0.548072
$379$	−7.80414	−0.400872	−0.200436	−	0.979707i	$-0.564236\pi$
$379$	−7.80414	−0.400872	−0.200436	+	0.979707i	$0.564236\pi$
$380$	−4.63695	−0.237871
$381$	−30.3183	−1.55326
$382$	2.23013	0.114103
$383$	12.0119	0.613778	0.306889	−	0.951745i	$-0.400712\pi$
$383$	12.0119	0.613778	0.306889	+	0.951745i	$0.400712\pi$
$384$	1.64609	0.0840019
$385$	4.52251	0.230489
$386$	−1.83684	−0.0934929
$387$	1.71496	0.0871764
$388$	13.9789	0.709672
$389$	3.11590	0.157983	0.0789913	−	0.996875i	$-0.474830\pi$
$389$	3.11590	0.157983	0.0789913	+	0.996875i	$0.474830\pi$
$390$	−7.68061	−0.388923
$391$	5.54406	0.280375
$392$	−3.12950	−0.158064
$393$	−14.7370	−0.743382
$394$	−1.00000	−0.0503793
$395$	−9.70781	−0.488453
$396$	−0.290376	−0.0145919
$397$	−23.9587	−1.20245	−0.601226	−	0.799079i	$-0.705321\pi$
$397$	−23.9587	−1.20245	−0.601226	+	0.799079i	$0.705321\pi$
$398$	13.2387	0.663597
$399$	−6.53243	−0.327030
$400$	0.284360	0.0142180
$401$	26.2315	1.30994	0.654970	−	0.755655i	$-0.272681\pi$
$401$	26.2315	1.30994	0.654970	+	0.755655i	$0.272681\pi$
$402$	−2.51123	−0.125249
$403$	11.9503	0.595285
$404$	−11.6436	−0.579290
$405$	18.4926	0.918905
$406$	15.6113	0.774773
$407$	−9.80360	−0.485946
$408$	−2.91919	−0.144521
$409$	4.45746	0.220407	0.110204	−	0.993909i	$-0.464850\pi$
$409$	4.45746	0.220407	0.110204	+	0.993909i	$0.464850\pi$
$410$	−14.9108	−0.736393
$411$	2.48323	0.122489
$412$	7.59047	0.373956
$413$	1.35747	0.0667967
$414$	0.907781	0.0446150
$415$	−2.07003	−0.101614
$416$	2.02976	0.0995172
$417$	−21.6537	−1.06039
$418$	2.01714	0.0986616
$419$	32.2361	1.57483	0.787417	−	0.616420i	$-0.211418\pi$
$419$	32.2361	1.57483	0.787417	+	0.616420i	$0.211418\pi$
$420$	7.44448	0.363253
$421$	8.47454	0.413024	0.206512	−	0.978444i	$-0.433789\pi$
$421$	8.47454	0.413024	0.206512	+	0.978444i	$0.433789\pi$
$422$	7.57376	0.368685
$423$	−1.80403	−0.0877149
$424$	−12.2468	−0.594759
$425$	−0.504285	−0.0244614
$426$	2.74829	0.133155
$427$	18.2020	0.880855
$428$	4.03080	0.194836
$429$	3.34118	0.161314
$430$	13.5766	0.654721
$431$	23.3038	1.12250	0.561251	−	0.827646i	$-0.310320\pi$
$431$	23.3038	1.12250	0.561251	+	0.827646i	$0.310320\pi$
$432$	−5.41627	−0.260590
$433$	26.0928	1.25394	0.626971	−	0.779043i	$-0.284295\pi$
$433$	26.0928	1.25394	0.626971	+	0.779043i	$0.284295\pi$
$434$	−11.5829	−0.555996
$435$	30.0265	1.43966
$436$	0.176538	0.00845462
$437$	−6.30604	−0.301659
$438$	−17.1976	−0.821735
$439$	−19.1428	−0.913634	−0.456817	−	0.889561i	$-0.651011\pi$
$439$	−19.1428	−0.913634	−0.456817	+	0.889561i	$0.651011\pi$
$440$	−2.29877	−0.109590
$441$	0.908730	0.0432729
$442$	−3.59958	−0.171215
$443$	−38.4620	−1.82738	−0.913692	−	0.406407i	$-0.866782\pi$
$443$	−38.4620	−1.82738	−0.913692	+	0.406407i	$0.866782\pi$
$444$	−16.1376	−0.765859
$445$	−19.5134	−0.925024
$446$	20.5525	0.973189
$447$	0.391346	0.0185100
$448$	−1.96736	−0.0929490
$449$	14.4444	0.681674	0.340837	−	0.940122i	$-0.389290\pi$
$449$	14.4444	0.681674	0.340837	+	0.940122i	$0.389290\pi$
$450$	−0.0825713	−0.00389245
$451$	6.48643	0.305434
$452$	−0.422748	−0.0198844
$453$	−20.0626	−0.942624
$454$	13.3632	0.627167
$455$	9.17962	0.430347
$456$	3.32040	0.155492
$457$	7.05524	0.330030	0.165015	−	0.986291i	$-0.447233\pi$
$457$	7.05524	0.330030	0.165015	+	0.986291i	$0.447233\pi$
$458$	−22.7015	−1.06077
$459$	9.60522	0.448333
$460$	7.18649	0.335072
$461$	32.3047	1.50458	0.752290	−	0.658833i	$-0.228949\pi$
$461$	32.3047	1.50458	0.752290	+	0.658833i	$0.228949\pi$
$462$	−3.23846	−0.150667
$463$	−6.06065	−0.281662	−0.140831	−	0.990034i	$-0.544977\pi$
$463$	−6.06065	−0.281662	−0.140831	+	0.990034i	$0.544977\pi$
$464$	−7.93513	−0.368379
$465$	−22.2784	−1.03313
$466$	9.23374	0.427745
$467$	21.3973	0.990151	0.495075	−	0.868850i	$-0.335140\pi$
$467$	21.3973	0.990151	0.495075	+	0.868850i	$0.335140\pi$
$468$	−0.589394	−0.0272447
$469$	3.00134	0.138589
$470$	−14.2817	−0.658765
$471$	−26.2916	−1.21145
$472$	−0.689995	−0.0317596
$473$	−5.90601	−0.271559
$474$	6.95151	0.319294
$475$	0.573595	0.0263183
$476$	3.48892	0.159914
$477$	3.55618	0.162826
$478$	10.1840	0.465805
$479$	−18.2227	−0.832616	−0.416308	−	0.909224i	$-0.636676\pi$
$479$	−18.2227	−0.832616	−0.416308	+	0.909224i	$0.636676\pi$
$480$	−3.78400	−0.172715
$481$	−19.8990	−0.907315
$482$	−4.13093	−0.188159
$483$	10.1242	0.460665
$484$	1.00000	0.0454545
$485$	−32.1344	−1.45915
$486$	3.00671	0.136387
$487$	36.3654	1.64788	0.823938	−	0.566680i	$-0.191773\pi$
$487$	36.3654	1.64788	0.823938	+	0.566680i	$0.191773\pi$
$488$	−9.25198	−0.418818
$489$	−4.44278	−0.200909
$490$	7.19401	0.324992
$491$	−2.15138	−0.0970906	−0.0485453	−	0.998821i	$-0.515459\pi$
$491$	−2.15138	−0.0970906	−0.0485453	+	0.998821i	$0.515459\pi$
$492$	10.6773	0.481368
$493$	14.0722	0.633779
$494$	4.09432	0.184212
$495$	0.667508	0.0300023
$496$	5.88752	0.264358
$497$	−3.28467	−0.147338
$498$	1.48230	0.0664233
$499$	10.0637	0.450512	0.225256	−	0.974300i	$-0.427678\pi$
$499$	10.0637	0.450512	0.225256	+	0.974300i	$0.427678\pi$
$500$	10.8402	0.484788
$501$	3.95823	0.176841
$502$	−12.7643	−0.569700
$503$	−19.4384	−0.866715	−0.433358	−	0.901222i	$-0.642671\pi$
$503$	−19.4384	−0.866715	−0.433358	+	0.901222i	$0.642671\pi$
$504$	0.571274	0.0254465
$505$	26.7660	1.19107
$506$	−3.12623	−0.138978
$507$	−14.6174	−0.649183
$508$	−18.4184	−0.817182
$509$	−34.2333	−1.51736	−0.758681	−	0.651462i	$-0.774156\pi$
$509$	−34.2333	−1.51736	−0.758681	+	0.651462i	$0.774156\pi$
$510$	6.71055	0.297148
$511$	20.5541	0.909259
$512$	1.00000	0.0441942
$513$	−10.9254	−0.482367
$514$	−1.72609	−0.0761347
$515$	−17.4488	−0.768885
$516$	−9.72184	−0.427980
$517$	6.21274	0.273236
$518$	19.2872	0.847431
$519$	16.1979	0.711008
$520$	−4.66596	−0.204616
$521$	27.4451	1.20239	0.601197	−	0.799101i	$-0.294691\pi$
$521$	27.4451	1.20239	0.601197	+	0.799101i	$0.294691\pi$
$522$	2.30417	0.100851
$523$	3.90863	0.170912	0.0854562	−	0.996342i	$-0.472765\pi$
$523$	3.90863	0.170912	0.0854562	+	0.996342i	$0.472765\pi$
$524$	−8.95270	−0.391100
$525$	−0.920888	−0.0401909
$526$	12.9111	0.562950
$527$	−10.4409	−0.454815
$528$	1.64609	0.0716370
$529$	−13.2267	−0.575074
$530$	28.1527	1.22287
$531$	0.200358	0.00869479
$532$	−3.96844	−0.172054
$533$	13.1659	0.570278
$534$	13.9731	0.604673
$535$	−9.26589	−0.400599
$536$	−1.52557	−0.0658945
$537$	2.59449	0.111961
$538$	−5.86336	−0.252787
$539$	−3.12950	−0.134797
$540$	12.4508	0.535796
$541$	7.21053	0.310005	0.155002	−	0.987914i	$-0.450461\pi$
$541$	7.21053	0.310005	0.155002	+	0.987914i	$0.450461\pi$
$542$	−4.90543	−0.210706
$543$	−35.2571	−1.51303
$544$	−1.77340	−0.0760340
$545$	−0.405820	−0.0173834
$546$	−6.57330	−0.281311
$547$	−28.4214	−1.21521	−0.607605	−	0.794239i	$-0.707870\pi$
$547$	−28.4214	−1.21521	−0.607605	+	0.794239i	$0.707870\pi$
$548$	1.50856	0.0644424
$549$	2.68655	0.114659
$550$	0.284360	0.0121252
$551$	−16.0063	−0.681891
$552$	−5.14606	−0.219031
$553$	−8.30823	−0.353302
$554$	0.624591	0.0265363
$555$	37.0968	1.57467
$556$	−13.1546	−0.557880
$557$	−11.4785	−0.486359	−0.243180	−	0.969981i	$-0.578190\pi$
$557$	−11.4785	−0.486359	−0.243180	+	0.969981i	$0.578190\pi$
$558$	−1.70959	−0.0723729
$559$	−11.9878	−0.507029
$560$	4.52251	0.191111
$561$	−2.91919	−0.123248
$562$	−1.71768	−0.0724560
$563$	11.2466	0.473988	0.236994	−	0.971511i	$-0.423838\pi$
$563$	11.2466	0.473988	0.236994	+	0.971511i	$0.423838\pi$
$564$	10.2267	0.430624
$565$	0.971801	0.0408840
$566$	18.3655	0.771961
$567$	15.8265	0.664652
$568$	1.66958	0.0700542
$569$	27.7715	1.16424	0.582121	−	0.813102i	$-0.302223\pi$
$569$	27.7715	1.16424	0.582121	+	0.813102i	$0.302223\pi$
$570$	−7.63286	−0.319705
$571$	29.5825	1.23799	0.618995	−	0.785395i	$-0.287540\pi$
$571$	29.5825	1.23799	0.618995	+	0.785395i	$0.287540\pi$
$572$	2.02976	0.0848686
$573$	3.67100	0.153358
$574$	−12.7611	−0.532639
$575$	−0.888975	−0.0370728
$576$	−0.290376	−0.0120990
$577$	−23.1260	−0.962747	−0.481373	−	0.876516i	$-0.659862\pi$
$577$	−23.1260	−0.962747	−0.481373	+	0.876516i	$0.659862\pi$
$578$	−13.8550	−0.576294
$579$	−3.02362	−0.125657
$580$	18.2411	0.757419
$581$	−1.77159	−0.0734981
$582$	23.0106	0.953820
$583$	−12.2468	−0.507212
$584$	−10.4475	−0.432323
$585$	1.35488	0.0560175
$586$	16.1805	0.668409
$587$	12.4976	0.515829	0.257915	−	0.966168i	$-0.416965\pi$
$587$	12.4976	0.515829	0.257915	+	0.966168i	$0.416965\pi$
$588$	−5.15145	−0.212442
$589$	11.8760	0.489341
$590$	1.58614	0.0653005
$591$	−1.64609	−0.0677112
$592$	−9.80360	−0.402925
$593$	−18.4519	−0.757731	−0.378865	−	0.925452i	$-0.623686\pi$
$593$	−18.4519	−0.757731	−0.378865	+	0.925452i	$0.623686\pi$
$594$	−5.41627	−0.222232
$595$	−8.02023	−0.328798
$596$	0.237742	0.00973831
$597$	21.7922	0.891894
$598$	−6.34550	−0.259487
$599$	−31.7019	−1.29531	−0.647653	−	0.761936i	$-0.724249\pi$
$599$	−31.7019	−1.29531	−0.647653	+	0.761936i	$0.724249\pi$
$600$	0.468084	0.0191094
$601$	−34.4748	−1.40626	−0.703128	−	0.711063i	$-0.748214\pi$
$601$	−34.4748	−1.40626	−0.703128	+	0.711063i	$0.748214\pi$
$602$	11.6192	0.473565
$603$	0.442988	0.0180399
$604$	−12.1880	−0.495923
$605$	−2.29877	−0.0934584
$606$	−19.1664	−0.778583
$607$	5.38011	0.218372	0.109186	−	0.994021i	$-0.465176\pi$
$607$	5.38011	0.218372	0.109186	+	0.994021i	$0.465176\pi$
$608$	2.01714	0.0818059
$609$	25.6976	1.04132
$610$	21.2682	0.861125
$611$	12.6104	0.510161
$612$	0.514953	0.0208157
$613$	−3.65936	−0.147800	−0.0739000	−	0.997266i	$-0.523545\pi$
$613$	−3.65936	−0.147800	−0.0739000	+	0.997266i	$0.523545\pi$
$614$	28.4043	1.14631
$615$	−24.5446	−0.989734
$616$	−1.96736	−0.0792672
$617$	−2.53107	−0.101897	−0.0509486	−	0.998701i	$-0.516224\pi$
$617$	−2.53107	−0.101897	−0.0509486	+	0.998701i	$0.516224\pi$
$618$	12.4946	0.502608
$619$	8.75050	0.351712	0.175856	−	0.984416i	$-0.443731\pi$
$619$	8.75050	0.351712	0.175856	+	0.984416i	$0.443731\pi$
$620$	−13.5341	−0.543542
$621$	16.9325	0.679477
$622$	−5.80629	−0.232811
$623$	−16.7002	−0.669077
$624$	3.34118	0.133754
$625$	−26.3409	−1.05364
$626$	29.3844	1.17444
$627$	3.32040	0.132604
$628$	−15.9721	−0.637357
$629$	17.3857	0.693214
$630$	−1.31323	−0.0523203
$631$	−20.4518	−0.814172	−0.407086	−	0.913390i	$-0.633455\pi$
$631$	−20.4518	−0.814172	−0.407086	+	0.913390i	$0.633455\pi$
$632$	4.22304	0.167983
$633$	12.4671	0.495523
$634$	−32.8156	−1.30327
$635$	42.3396	1.68020
$636$	−20.1594	−0.799373
$637$	−6.35213	−0.251681
$638$	−7.93513	−0.314155
$639$	−0.484807	−0.0191787
$640$	−2.29877	−0.0908670
$641$	−35.1054	−1.38658	−0.693290	−	0.720658i	$-0.743840\pi$
$641$	−35.1054	−1.38658	−0.693290	+	0.720658i	$0.743840\pi$
$642$	6.63507	0.261865
$643$	4.48609	0.176914	0.0884570	−	0.996080i	$-0.471806\pi$
$643$	4.48609	0.176914	0.0884570	+	0.996080i	$0.471806\pi$
$644$	6.15041	0.242360
$645$	22.3483	0.879964
$646$	−3.57720	−0.140743
$647$	−24.4296	−0.960427	−0.480213	−	0.877152i	$-0.659441\pi$
$647$	−24.4296	−0.960427	−0.480213	+	0.877152i	$0.659441\pi$
$648$	−8.04455	−0.316020
$649$	−0.689995	−0.0270847
$650$	0.577183	0.0226390
$651$	−19.0665	−0.747275
$652$	−2.69898	−0.105700
$653$	−13.5160	−0.528922	−0.264461	−	0.964396i	$-0.585194\pi$
$653$	−13.5160	−0.528922	−0.264461	+	0.964396i	$0.585194\pi$
$654$	0.290598	0.0113633
$655$	20.5802	0.804136
$656$	6.48643	0.253252
$657$	3.03371	0.118356
$658$	−12.2227	−0.476490
$659$	2.77587	0.108133	0.0540663	−	0.998537i	$-0.482782\pi$
$659$	2.77587	0.108133	0.0540663	+	0.998537i	$0.482782\pi$
$660$	−3.78400	−0.147292
$661$	−25.5439	−0.993543	−0.496772	−	0.867881i	$-0.665481\pi$
$661$	−25.5439	−0.993543	−0.496772	+	0.867881i	$0.665481\pi$
$662$	−10.6373	−0.413431
$663$	−5.92525	−0.230118
$664$	0.900493	0.0349459
$665$	9.12255	0.353757
$666$	2.84673	0.110308
$667$	24.8070	0.960532
$668$	2.40462	0.0930376
$669$	33.8314	1.30800
$670$	3.50694	0.135485
$671$	−9.25198	−0.357169
$672$	−3.23846	−0.124926
$673$	0.0702236	0.00270692	0.00135346	−	0.999999i	$-0.499569\pi$
$673$	0.0702236	0.00270692	0.00135346	+	0.999999i	$0.499569\pi$
$674$	3.17671	0.122362
$675$	−1.54017	−0.0592812
$676$	−8.88007	−0.341541
$677$	−24.6288	−0.946561	−0.473280	−	0.880912i	$-0.656930\pi$
$677$	−24.6288	−0.946561	−0.473280	+	0.880912i	$0.656930\pi$
$678$	−0.695882	−0.0267252
$679$	−27.5015	−1.05541
$680$	4.07665	0.156332
$681$	21.9971	0.842931
$682$	5.88752	0.225445
$683$	6.21012	0.237624	0.118812	−	0.992917i	$-0.462091\pi$
$683$	6.21012	0.237624	0.118812	+	0.992917i	$0.462091\pi$
$684$	−0.585729	−0.0223959
$685$	−3.46783	−0.132499
$686$	19.9284	0.760868
$687$	−37.3688	−1.42571
$688$	−5.90601	−0.225164
$689$	−24.8581	−0.947020
$690$	11.8296	0.450347
$691$	15.2338	0.579521	0.289760	−	0.957099i	$-0.406424\pi$
$691$	15.2338	0.579521	0.289760	+	0.957099i	$0.406424\pi$
$692$	9.84019	0.374068
$693$	0.571274	0.0217009
$694$	4.03804	0.153282
$695$	30.2395	1.14705
$696$	−13.0620	−0.495113
$697$	−11.5030	−0.435709
$698$	4.05672	0.153549
$699$	15.1996	0.574902
$700$	−0.559439	−0.0211448
$701$	12.0212	0.454033	0.227017	−	0.973891i	$-0.427103\pi$
$701$	12.0212	0.454033	0.227017	+	0.973891i	$0.427103\pi$
$702$	−10.9937	−0.414932
$703$	−19.7752	−0.745838
$704$	1.00000	0.0376889
$705$	−23.5090	−0.885399
$706$	20.9778	0.789511
$707$	22.9071	0.861511
$708$	−1.13580	−0.0426859
$709$	−4.64193	−0.174331	−0.0871656	−	0.996194i	$-0.527781\pi$
$709$	−4.64193	−0.174331	−0.0871656	+	0.996194i	$0.527781\pi$
$710$	−3.83800	−0.144037
$711$	−1.22627	−0.0459886
$712$	8.48861	0.318124
$713$	−18.4057	−0.689300
$714$	5.74309	0.214930
$715$	−4.66596	−0.174497
$716$	1.57615	0.0589035
$717$	16.7638	0.626055
$718$	7.21732	0.269348
$719$	−35.6804	−1.33065	−0.665327	−	0.746552i	$-0.731708\pi$
$719$	−35.6804	−1.33065	−0.665327	+	0.746552i	$0.731708\pi$
$720$	0.667508	0.0248766
$721$	−14.9332	−0.556141
$722$	−14.9311	−0.555679
$723$	−6.79990	−0.252891
$724$	−21.4187	−0.796018
$725$	−2.25644	−0.0838019
$726$	1.64609	0.0610923
$727$	−25.2091	−0.934955	−0.467477	−	0.884005i	$-0.654837\pi$
$727$	−25.2091	−0.934955	−0.467477	+	0.884005i	$0.654837\pi$
$728$	−3.99327	−0.148000
$729$	29.0830	1.07715
$730$	24.0165	0.888892
$731$	10.4737	0.387385
$732$	−15.2296	−0.562903
$733$	35.9002	1.32600	0.663001	−	0.748618i	$-0.269282\pi$
$733$	35.9002	1.32600	0.663001	+	0.748618i	$0.269282\pi$
$734$	14.9122	0.550421
$735$	11.8420	0.436799
$736$	−3.12623	−0.115234
$737$	−1.52557	−0.0561950
$738$	−1.88350	−0.0693326
$739$	21.8106	0.802315	0.401158	−	0.916009i	$-0.368608\pi$
$739$	21.8106	0.802315	0.401158	+	0.916009i	$0.368608\pi$
$740$	22.5363	0.828449
$741$	6.73963	0.247586
$742$	24.0939	0.884515
$743$	42.2205	1.54892	0.774459	−	0.632624i	$-0.218022\pi$
$743$	42.2205	1.54892	0.774459	+	0.632624i	$0.218022\pi$
$744$	9.69141	0.355304
$745$	−0.546516	−0.0200228
$746$	21.3714	0.782461
$747$	−0.261482	−0.00956711
$748$	−1.77340	−0.0648420
$749$	−7.93003	−0.289757
$750$	17.8440	0.651569
$751$	−16.9829	−0.619715	−0.309858	−	0.950783i	$-0.600281\pi$
$751$	−16.9829	−0.619715	−0.309858	+	0.950783i	$0.600281\pi$
$752$	6.21274	0.226555
$753$	−21.0113	−0.765693
$754$	−16.1064	−0.586561
$755$	28.0175	1.01966
$756$	10.6557	0.387546
$757$	−17.5154	−0.636609	−0.318305	−	0.947988i	$-0.603113\pi$
$757$	−17.5154	−0.636609	−0.318305	+	0.947988i	$0.603113\pi$
$758$	−7.80414	−0.283459
$759$	−5.14606	−0.186790
$760$	−4.63695	−0.168200
$761$	−31.2645	−1.13334	−0.566669	−	0.823945i	$-0.691768\pi$
$761$	−31.2645	−1.13334	−0.566669	+	0.823945i	$0.691768\pi$
$762$	−30.3183	−1.09832
$763$	−0.347313	−0.0125736
$764$	2.23013	0.0806832
$765$	−1.18376	−0.0427989
$766$	12.0119	0.434006
$767$	−1.40053	−0.0505701
$768$	1.64609	0.0593983
$769$	−20.0942	−0.724616	−0.362308	−	0.932058i	$-0.618011\pi$
$769$	−20.0942	−0.724616	−0.362308	+	0.932058i	$0.618011\pi$
$770$	4.52251	0.162980
$771$	−2.84131	−0.102327
$772$	−1.83684	−0.0661095
$773$	−4.49934	−0.161830	−0.0809150	−	0.996721i	$-0.525784\pi$
$773$	−4.49934	−0.161830	−0.0809150	+	0.996721i	$0.525784\pi$
$774$	1.71496	0.0616430
$775$	1.67418	0.0601382
$776$	13.9789	0.501814
$777$	31.7485	1.13897
$778$	3.11590	0.111711
$779$	13.0840	0.468784
$780$	−7.68061	−0.275010
$781$	1.66958	0.0597424
$782$	5.54406	0.198255
$783$	42.9788	1.53594
$784$	−3.12950	−0.111768
$785$	36.7163	1.31046
$786$	−14.7370	−0.525651
$787$	−39.0850	−1.39323	−0.696616	−	0.717445i	$-0.745312\pi$
$787$	−39.0850	−1.39323	−0.696616	+	0.717445i	$0.745312\pi$
$788$	−1.00000	−0.0356235
$789$	21.2528	0.756621
$790$	−9.70781	−0.345388
$791$	0.831696	0.0295717
$792$	−0.290376	−0.0103181
$793$	−18.7793	−0.666873
$794$	−23.9587	−0.850262
$795$	46.3420	1.64358
$796$	13.2387	0.469234
$797$	13.7768	0.488000	0.244000	−	0.969775i	$-0.421540\pi$
$797$	13.7768	0.488000	0.244000	+	0.969775i	$0.421540\pi$
$798$	−6.53243	−0.231245
$799$	−11.0177	−0.389777
$800$	0.284360	0.0100537
$801$	−2.46489	−0.0870925
$802$	26.2315	0.926267
$803$	−10.4475	−0.368686
$804$	−2.51123	−0.0885642
$805$	−14.1384	−0.498313
$806$	11.9503	0.420930
$807$	−9.65164	−0.339754
$808$	−11.6436	−0.409620
$809$	24.9291	0.876460	0.438230	−	0.898863i	$-0.355606\pi$
$809$	24.9291	0.876460	0.438230	+	0.898863i	$0.355606\pi$
$810$	18.4926	0.649764
$811$	−44.5331	−1.56377	−0.781884	−	0.623424i	$-0.785741\pi$
$811$	−44.5331	−1.56377	−0.781884	+	0.623424i	$0.785741\pi$
$812$	15.6113	0.547848
$813$	−8.07480	−0.283196
$814$	−9.80360	−0.343616
$815$	6.20435	0.217329
$816$	−2.91919	−0.102192
$817$	−11.9133	−0.416792
$818$	4.45746	0.155851
$819$	1.15955	0.0405179
$820$	−14.9108	−0.520709
$821$	−23.4452	−0.818244	−0.409122	−	0.912480i	$-0.634165\pi$
$821$	−23.4452	−0.818244	−0.409122	+	0.912480i	$0.634165\pi$
$822$	2.48323	0.0866126
$823$	18.3230	0.638701	0.319351	−	0.947637i	$-0.396535\pi$
$823$	18.3230	0.638701	0.319351	+	0.947637i	$0.396535\pi$
$824$	7.59047	0.264427
$825$	0.468084	0.0162966
$826$	1.35747	0.0472324
$827$	31.1647	1.08370	0.541851	−	0.840474i	$-0.317724\pi$
$827$	31.1647	1.08370	0.541851	+	0.840474i	$0.317724\pi$
$828$	0.907781	0.0315476
$829$	−16.0894	−0.558809	−0.279404	−	0.960174i	$-0.590137\pi$
$829$	−16.0894	−0.558809	−0.279404	+	0.960174i	$0.590137\pi$
$830$	−2.07003	−0.0718518
$831$	1.02814	0.0356656
$832$	2.02976	0.0703693
$833$	5.54986	0.192291
$834$	−21.6537	−0.749807
$835$	−5.52768	−0.191293
$836$	2.01714	0.0697643
$837$	−31.8884	−1.10222
$838$	32.2361	1.11358
$839$	−45.1372	−1.55831	−0.779154	−	0.626833i	$-0.784351\pi$
$839$	−45.1372	−1.55831	−0.779154	+	0.626833i	$0.784351\pi$
$840$	7.44448	0.256859
$841$	33.9663	1.17125
$842$	8.47454	0.292052
$843$	−2.82747	−0.0973831
$844$	7.57376	0.260699
$845$	20.4133	0.702238
$846$	−1.80403	−0.0620238
$847$	−1.96736	−0.0675993
$848$	−12.2468	−0.420558
$849$	30.2314	1.03754
$850$	−0.504285	−0.0172968
$851$	30.6483	1.05061
$852$	2.74829	0.0941550
$853$	−25.6351	−0.877730	−0.438865	−	0.898553i	$-0.644619\pi$
$853$	−25.6351	−0.877730	−0.438865	+	0.898553i	$0.644619\pi$
$854$	18.2020	0.622859
$855$	1.34646	0.0460479
$856$	4.03080	0.137770
$857$	−0.799728	−0.0273182	−0.0136591	−	0.999907i	$-0.504348\pi$
$857$	−0.799728	−0.0273182	−0.0136591	+	0.999907i	$0.504348\pi$
$858$	3.34118	0.114066
$859$	8.70423	0.296984	0.148492	−	0.988914i	$-0.452558\pi$
$859$	8.70423	0.296984	0.148492	+	0.988914i	$0.452558\pi$
$860$	13.5766	0.462957
$861$	−21.0060	−0.715883
$862$	23.3038	0.793729
$863$	−2.05762	−0.0700423	−0.0350211	−	0.999387i	$-0.511150\pi$
$863$	−2.05762	−0.0700423	−0.0350211	+	0.999387i	$0.511150\pi$
$864$	−5.41627	−0.184265
$865$	−22.6204	−0.769116
$866$	26.0928	0.886670
$867$	−22.8067	−0.774556
$868$	−11.5829	−0.393148
$869$	4.22304	0.143257
$870$	30.0265	1.01799
$871$	−3.09654	−0.104922
$872$	0.176538	0.00597832
$873$	−4.05914	−0.137381
$874$	−6.30604	−0.213305
$875$	−21.3265	−0.720969
$876$	−17.1976	−0.581054
$877$	−44.7871	−1.51235	−0.756177	−	0.654367i	$-0.772935\pi$
$877$	−44.7871	−1.51235	−0.756177	+	0.654367i	$0.772935\pi$
$878$	−19.1428	−0.646037
$879$	26.6346	0.898362
$880$	−2.29877	−0.0774916
$881$	−35.7968	−1.20603	−0.603013	−	0.797731i	$-0.706033\pi$
$881$	−35.7968	−1.20603	−0.603013	+	0.797731i	$0.706033\pi$
$882$	0.908730	0.0305985
$883$	6.82953	0.229832	0.114916	−	0.993375i	$-0.463340\pi$
$883$	6.82953	0.229832	0.114916	+	0.993375i	$0.463340\pi$
$884$	−3.59958	−0.121067
$885$	2.61094	0.0877658
$886$	−38.4620	−1.29216
$887$	11.3575	0.381346	0.190673	−	0.981654i	$-0.438933\pi$
$887$	11.3575	0.381346	0.190673	+	0.981654i	$0.438933\pi$
$888$	−16.1376	−0.541544
$889$	36.2355	1.21530
$890$	−19.5134	−0.654091
$891$	−8.04455	−0.269503
$892$	20.5525	0.688149
$893$	12.5320	0.419366
$894$	0.391346	0.0130886
$895$	−3.62321	−0.121111
$896$	−1.96736	−0.0657249
$897$	−10.4453	−0.348758
$898$	14.4444	0.482016
$899$	−46.7183	−1.55814
$900$	−0.0825713	−0.00275238
$901$	21.7186	0.723550
$902$	6.48643	0.215974
$903$	19.1264	0.636485
$904$	−0.422748	−0.0140604
$905$	49.2366	1.63668
$906$	−20.0626	−0.666536
$907$	17.7826	0.590460	0.295230	−	0.955426i	$-0.404604\pi$
$907$	17.7826	0.590460	0.295230	+	0.955426i	$0.404604\pi$
$908$	13.3632	0.443474
$909$	3.38102	0.112141
$910$	9.17962	0.304302
$911$	32.2821	1.06955	0.534777	−	0.844993i	$-0.320395\pi$
$911$	32.2821	1.06955	0.534777	+	0.844993i	$0.320395\pi$
$912$	3.32040	0.109950
$913$	0.900493	0.0298020
$914$	7.05524	0.233366
$915$	35.0095	1.15738
$916$	−22.7015	−0.750079
$917$	17.6132	0.581638
$918$	9.60522	0.317019
$919$	−20.4705	−0.675258	−0.337629	−	0.941279i	$-0.609625\pi$
$919$	−20.4705	−0.675258	−0.337629	+	0.941279i	$0.609625\pi$
$920$	7.18649	0.236932
$921$	46.7562	1.54067
$922$	32.3047	1.06390
$923$	3.38886	0.111546
$924$	−3.23846	−0.106537
$925$	−2.78775	−0.0916608
$926$	−6.06065	−0.199165
$927$	−2.20409	−0.0723918
$928$	−7.93513	−0.260483
$929$	−35.1457	−1.15309	−0.576547	−	0.817064i	$-0.695600\pi$
$929$	−35.1457	−1.15309	−0.576547	+	0.817064i	$0.695600\pi$
$930$	−22.2784	−0.730536
$931$	−6.31264	−0.206888
$932$	9.23374	0.302461
$933$	−9.55769	−0.312905
$934$	21.3973	0.700142
$935$	4.07665	0.133321
$936$	−0.589394	−0.0192649
$937$	−13.5201	−0.441681	−0.220841	−	0.975310i	$-0.570880\pi$
$937$	−13.5201	−0.441681	−0.220841	+	0.975310i	$0.570880\pi$
$938$	3.00134	0.0979973
$939$	48.3695	1.57848
$940$	−14.2817	−0.465817
$941$	37.0857	1.20896	0.604479	−	0.796621i	$-0.293381\pi$
$941$	37.0857	1.20896	0.604479	+	0.796621i	$0.293381\pi$
$942$	−26.2916	−0.856627
$943$	−20.2780	−0.660344
$944$	−0.689995	−0.0224574
$945$	−24.4951	−0.796827
$946$	−5.90601	−0.192021
$947$	−47.4451	−1.54176	−0.770879	−	0.636981i	$-0.780183\pi$
$947$	−47.4451	−1.54176	−0.770879	+	0.636981i	$0.780183\pi$
$948$	6.95151	0.225775
$949$	−21.2060	−0.688377
$950$	0.573595	0.0186099
$951$	−54.0176	−1.75164
$952$	3.48892	0.113076
$953$	−48.2129	−1.56177	−0.780884	−	0.624676i	$-0.785231\pi$
$953$	−48.2129	−1.56177	−0.780884	+	0.624676i	$0.785231\pi$
$954$	3.55618	0.115136
$955$	−5.12656	−0.165892
$956$	10.1840	0.329374
$957$	−13.0620	−0.422233
$958$	−18.2227	−0.588748
$959$	−2.96788	−0.0958377
$960$	−3.78400	−0.122128
$961$	3.66292	0.118159
$962$	−19.8990	−0.641568
$963$	−1.17045	−0.0377171
$964$	−4.13093	−0.133048
$965$	4.22249	0.135927
$966$	10.1242	0.325739
$967$	−56.3245	−1.81127	−0.905637	−	0.424054i	$-0.860607\pi$
$967$	−56.3245	−1.81127	−0.905637	+	0.424054i	$0.860607\pi$
$968$	1.00000	0.0321412
$969$	−5.88841	−0.189163
$970$	−32.1344	−1.03177
$971$	−47.8433	−1.53536	−0.767682	−	0.640831i	$-0.778590\pi$
$971$	−47.8433	−1.53536	−0.767682	+	0.640831i	$0.778590\pi$
$972$	3.00671	0.0964403
$973$	25.8798	0.829670
$974$	36.3654	1.16522
$975$	0.950098	0.0304275
$976$	−9.25198	−0.296149
$977$	−20.2391	−0.647506	−0.323753	−	0.946142i	$-0.604945\pi$
$977$	−20.2391	−0.647506	−0.323753	+	0.946142i	$0.604945\pi$
$978$	−4.44278	−0.142064
$979$	8.48861	0.271297
$980$	7.19401	0.229804
$981$	−0.0512623	−0.00163668
$982$	−2.15138	−0.0686534
$983$	41.0931	1.31067	0.655333	−	0.755340i	$-0.272528\pi$
$983$	41.0931	1.31067	0.655333	+	0.755340i	$0.272528\pi$
$984$	10.6773	0.340379
$985$	2.29877	0.0732450
$986$	14.0722	0.448149
$987$	−20.1197	−0.640417
$988$	4.09432	0.130258
$989$	18.4635	0.587106
$990$	0.667508	0.0212148
$991$	−43.8219	−1.39205	−0.696024	−	0.718018i	$-0.745049\pi$
$991$	−43.8219	−1.39205	−0.696024	+	0.718018i	$0.745049\pi$
$992$	5.88752	0.186929
$993$	−17.5100	−0.555664
$994$	−3.28467	−0.104184
$995$	−30.4328	−0.964785
$996$	1.48230	0.0469684
$997$	−5.90825	−0.187116	−0.0935582	−	0.995614i	$-0.529824\pi$
$997$	−5.90825	−0.187116	−0.0935582	+	0.995614i	$0.529824\pi$
$998$	10.0637	0.318560
$999$	53.0989	1.67998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.b.1.14	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.b.1.14	✓	15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.64609 q^{3} +1.00000 q^{4} -2.29877 q^{5} +1.64609 q^{6} -1.96736 q^{7} +1.00000 q^{8} -0.290376 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.64609 q^{3} +1.00000 q^{4} -2.29877 q^{5} +1.64609 q^{6} -1.96736 q^{7} +1.00000 q^{8} -0.290376 q^{9} -2.29877 q^{10} +1.00000 q^{11} +1.64609 q^{12} +2.02976 q^{13} -1.96736 q^{14} -3.78400 q^{15} +1.00000 q^{16} -1.77340 q^{17} -0.290376 q^{18} +2.01714 q^{19} -2.29877 q^{20} -3.23846 q^{21} +1.00000 q^{22} -3.12623 q^{23} +1.64609 q^{24} +0.284360 q^{25} +2.02976 q^{26} -5.41627 q^{27} -1.96736 q^{28} -7.93513 q^{29} -3.78400 q^{30} +5.88752 q^{31} +1.00000 q^{32} +1.64609 q^{33} -1.77340 q^{34} +4.52251 q^{35} -0.290376 q^{36} -9.80360 q^{37} +2.01714 q^{38} +3.34118 q^{39} -2.29877 q^{40} +6.48643 q^{41} -3.23846 q^{42} -5.90601 q^{43} +1.00000 q^{44} +0.667508 q^{45} -3.12623 q^{46} +6.21274 q^{47} +1.64609 q^{48} -3.12950 q^{49} +0.284360 q^{50} -2.91919 q^{51} +2.02976 q^{52} -12.2468 q^{53} -5.41627 q^{54} -2.29877 q^{55} -1.96736 q^{56} +3.32040 q^{57} -7.93513 q^{58} -0.689995 q^{59} -3.78400 q^{60} -9.25198 q^{61} +5.88752 q^{62} +0.571274 q^{63} +1.00000 q^{64} -4.66596 q^{65} +1.64609 q^{66} -1.52557 q^{67} -1.77340 q^{68} -5.14606 q^{69} +4.52251 q^{70} +1.66958 q^{71} -0.290376 q^{72} -10.4475 q^{73} -9.80360 q^{74} +0.468084 q^{75} +2.01714 q^{76} -1.96736 q^{77} +3.34118 q^{78} +4.22304 q^{79} -2.29877 q^{80} -8.04455 q^{81} +6.48643 q^{82} +0.900493 q^{83} -3.23846 q^{84} +4.07665 q^{85} -5.90601 q^{86} -13.0620 q^{87} +1.00000 q^{88} +8.48861 q^{89} +0.667508 q^{90} -3.99327 q^{91} -3.12623 q^{92} +9.69141 q^{93} +6.21274 q^{94} -4.63695 q^{95} +1.64609 q^{96} +13.9789 q^{97} -3.12950 q^{98} -0.290376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

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