LMFDB - Embedded newform 5054.2.a.bl.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 $ x^12 - 3x^11 - 24x^10 + 68x^9 + 213x^8 - 555x^7 - 814x^6 + 1911x^5 + 1005x^4 - 2326x^3 + 570x^2 + 105*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.95625$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.95625 q^{3} +1.00000 q^{4} -2.38328 q^{5} -1.95625 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.826915 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.95625 q^{3} +1.00000 q^{4} -2.38328 q^{5} -1.95625 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.826915 q^{9} +2.38328 q^{10} -4.91969 q^{11} +1.95625 q^{12} +5.88177 q^{13} -1.00000 q^{14} -4.66230 q^{15} +1.00000 q^{16} -5.04131 q^{17} -0.826915 q^{18} -2.38328 q^{20} +1.95625 q^{21} +4.91969 q^{22} +0.126989 q^{23} -1.95625 q^{24} +0.680041 q^{25} -5.88177 q^{26} -4.25110 q^{27} +1.00000 q^{28} +0.660836 q^{29} +4.66230 q^{30} +10.2942 q^{31} -1.00000 q^{32} -9.62414 q^{33} +5.04131 q^{34} -2.38328 q^{35} +0.826915 q^{36} -7.28732 q^{37} +11.5062 q^{39} +2.38328 q^{40} +5.02394 q^{41} -1.95625 q^{42} -1.39536 q^{43} -4.91969 q^{44} -1.97077 q^{45} -0.126989 q^{46} +6.36469 q^{47} +1.95625 q^{48} +1.00000 q^{49} -0.680041 q^{50} -9.86206 q^{51} +5.88177 q^{52} -3.15801 q^{53} +4.25110 q^{54} +11.7250 q^{55} -1.00000 q^{56} -0.660836 q^{58} +12.7742 q^{59} -4.66230 q^{60} +10.8372 q^{61} -10.2942 q^{62} +0.826915 q^{63} +1.00000 q^{64} -14.0179 q^{65} +9.62414 q^{66} -14.3038 q^{67} -5.04131 q^{68} +0.248422 q^{69} +2.38328 q^{70} +13.4030 q^{71} -0.826915 q^{72} +5.87714 q^{73} +7.28732 q^{74} +1.33033 q^{75} -4.91969 q^{77} -11.5062 q^{78} +8.08976 q^{79} -2.38328 q^{80} -10.7970 q^{81} -5.02394 q^{82} -2.32025 q^{83} +1.95625 q^{84} +12.0149 q^{85} +1.39536 q^{86} +1.29276 q^{87} +4.91969 q^{88} +6.84776 q^{89} +1.97077 q^{90} +5.88177 q^{91} +0.126989 q^{92} +20.1381 q^{93} -6.36469 q^{94} -1.95625 q^{96} +6.49650 q^{97} -1.00000 q^{98} -4.06816 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * 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
$3$	1.95625	1.12944	0.564721	−	0.825282i	$-0.308984\pi$
$3$	1.95625	1.12944	0.564721	+	0.825282i	$0.308984\pi$
$4$	1.00000	0.500000
$5$	−2.38328	−1.06584	−0.532918	−	0.846167i	$-0.678905\pi$
$5$	−2.38328	−1.06584	−0.532918	+	0.846167i	$0.678905\pi$
$6$	−1.95625	−0.798636
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0.826915	0.275638
$10$	2.38328	0.753660
$11$	−4.91969	−1.48334	−0.741671	−	0.670764i	$-0.765966\pi$
$11$	−4.91969	−1.48334	−0.741671	+	0.670764i	$0.765966\pi$
$12$	1.95625	0.564721
$13$	5.88177	1.63131	0.815655	−	0.578539i	$-0.196377\pi$
$13$	5.88177	1.63131	0.815655	+	0.578539i	$0.196377\pi$
$14$	−1.00000	−0.267261
$15$	−4.66230	−1.20380
$16$	1.00000	0.250000
$17$	−5.04131	−1.22270	−0.611348	−	0.791362i	$-0.709373\pi$
$17$	−5.04131	−1.22270	−0.611348	+	0.791362i	$0.709373\pi$
$18$	−0.826915	−0.194906
$19$	0	0
$19$	0	0
$20$	−2.38328	−0.532918
$21$	1.95625	0.426889
$22$	4.91969	1.04888
$23$	0.126989	0.0264790	0.0132395	−	0.999912i	$-0.495786\pi$
$23$	0.126989	0.0264790	0.0132395	+	0.999912i	$0.495786\pi$
$24$	−1.95625	−0.399318
$25$	0.680041	0.136008
$26$	−5.88177	−1.15351
$27$	−4.25110	−0.818124
$28$	1.00000	0.188982
$29$	0.660836	0.122714	0.0613570	−	0.998116i	$-0.480457\pi$
$29$	0.660836	0.122714	0.0613570	+	0.998116i	$0.480457\pi$
$30$	4.66230	0.851215
$31$	10.2942	1.84890	0.924451	−	0.381301i	$-0.124524\pi$
$31$	10.2942	1.84890	0.924451	+	0.381301i	$0.124524\pi$
$32$	−1.00000	−0.176777
$33$	−9.62414	−1.67535
$34$	5.04131	0.864577
$35$	−2.38328	−0.402848
$36$	0.826915	0.137819
$37$	−7.28732	−1.19803	−0.599014	−	0.800738i	$-0.704441\pi$
$37$	−7.28732	−1.19803	−0.599014	+	0.800738i	$0.704441\pi$
$38$	0	0
$39$	11.5062	1.84247
$40$	2.38328	0.376830
$41$	5.02394	0.784608	0.392304	−	0.919836i	$-0.371678\pi$
$41$	5.02394	0.784608	0.392304	+	0.919836i	$0.371678\pi$
$42$	−1.95625	−0.301856
$43$	−1.39536	−0.212790	−0.106395	−	0.994324i	$-0.533931\pi$
$43$	−1.39536	−0.212790	−0.106395	+	0.994324i	$0.533931\pi$
$44$	−4.91969	−0.741671
$45$	−1.97077	−0.293786
$46$	−0.126989	−0.0187235
$47$	6.36469	0.928386	0.464193	−	0.885734i	$-0.346344\pi$
$47$	6.36469	0.928386	0.464193	+	0.885734i	$0.346344\pi$
$48$	1.95625	0.282360
$49$	1.00000	0.142857
$50$	−0.680041	−0.0961723
$51$	−9.86206	−1.38096
$52$	5.88177	0.815655
$53$	−3.15801	−0.433786	−0.216893	−	0.976195i	$-0.569592\pi$
$53$	−3.15801	−0.433786	−0.216893	+	0.976195i	$0.569592\pi$
$54$	4.25110	0.578501
$55$	11.7250	1.58100
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−0.660836	−0.0867720
$59$	12.7742	1.66306	0.831532	−	0.555477i	$-0.187464\pi$
$59$	12.7742	1.66306	0.831532	+	0.555477i	$0.187464\pi$
$60$	−4.66230	−0.601900
$61$	10.8372	1.38756	0.693782	−	0.720185i	$-0.255943\pi$
$61$	10.8372	1.38756	0.693782	+	0.720185i	$0.255943\pi$
$62$	−10.2942	−1.30737
$63$	0.826915	0.104182
$64$	1.00000	0.125000
$65$	−14.0179	−1.73871
$66$	9.62414	1.18465
$67$	−14.3038	−1.74748	−0.873742	−	0.486390i	$-0.838314\pi$
$67$	−14.3038	−1.74748	−0.873742	+	0.486390i	$0.838314\pi$
$68$	−5.04131	−0.611348
$69$	0.248422	0.0299064
$70$	2.38328	0.284857
$71$	13.4030	1.59064	0.795320	−	0.606189i	$-0.207303\pi$
$71$	13.4030	1.59064	0.795320	+	0.606189i	$0.207303\pi$
$72$	−0.826915	−0.0974529
$73$	5.87714	0.687867	0.343933	−	0.938994i	$-0.388241\pi$
$73$	5.87714	0.687867	0.343933	+	0.938994i	$0.388241\pi$
$74$	7.28732	0.847134
$75$	1.33033	0.153613
$76$	0	0
$77$	−4.91969	−0.560650
$78$	−11.5062	−1.30282
$79$	8.08976	0.910169	0.455084	−	0.890448i	$-0.349609\pi$
$79$	8.08976	0.910169	0.455084	+	0.890448i	$0.349609\pi$
$80$	−2.38328	−0.266459
$81$	−10.7970	−1.19966
$82$	−5.02394	−0.554802
$83$	−2.32025	−0.254681	−0.127340	−	0.991859i	$-0.540644\pi$
$83$	−2.32025	−0.254681	−0.127340	+	0.991859i	$0.540644\pi$
$84$	1.95625	0.213444
$85$	12.0149	1.30320
$86$	1.39536	0.150466
$87$	1.29276	0.138598
$88$	4.91969	0.524440
$89$	6.84776	0.725861	0.362931	−	0.931816i	$-0.381776\pi$
$89$	6.84776	0.725861	0.362931	+	0.931816i	$0.381776\pi$
$90$	1.97077	0.207738
$91$	5.88177	0.616577
$92$	0.126989	0.0132395
$93$	20.1381	2.08823
$94$	−6.36469	−0.656468
$95$	0	0
$96$	−1.95625	−0.199659
$97$	6.49650	0.659620	0.329810	−	0.944047i	$-0.393015\pi$
$97$	6.49650	0.659620	0.329810	+	0.944047i	$0.393015\pi$
$98$	−1.00000	−0.101015
$99$	−4.06816	−0.408866
$100$	0.680041	0.0680041
$101$	2.80868	0.279474	0.139737	−	0.990189i	$-0.455374\pi$
$101$	2.80868	0.279474	0.139737	+	0.990189i	$0.455374\pi$
$102$	9.86206	0.976490
$103$	−1.05465	−0.103918	−0.0519589	−	0.998649i	$-0.516546\pi$
$103$	−1.05465	−0.103918	−0.0519589	+	0.998649i	$0.516546\pi$
$104$	−5.88177	−0.576755
$105$	−4.66230	−0.454994
$106$	3.15801	0.306733
$107$	−7.25726	−0.701586	−0.350793	−	0.936453i	$-0.614088\pi$
$107$	−7.25726	−0.701586	−0.350793	+	0.936453i	$0.614088\pi$
$108$	−4.25110	−0.409062
$109$	−6.02102	−0.576709	−0.288355	−	0.957524i	$-0.593108\pi$
$109$	−6.02102	−0.576709	−0.288355	+	0.957524i	$0.593108\pi$
$110$	−11.7250	−1.11794
$111$	−14.2558	−1.35310
$112$	1.00000	0.0944911
$113$	−5.71691	−0.537802	−0.268901	−	0.963168i	$-0.586660\pi$
$113$	−5.71691	−0.537802	−0.268901	+	0.963168i	$0.586660\pi$
$114$	0	0
$115$	−0.302650	−0.0282223
$116$	0.660836	0.0613570
$117$	4.86372	0.449651
$118$	−12.7742	−1.17596
$119$	−5.04131	−0.462136
$120$	4.66230	0.425608
$121$	13.2033	1.20030
$122$	−10.8372	−0.981156
$123$	9.82809	0.886169
$124$	10.2942	0.924451
$125$	10.2957	0.920874
$126$	−0.826915	−0.0736675
$127$	16.8122	1.49184	0.745919	−	0.666037i	$-0.232011\pi$
$127$	16.8122	1.49184	0.745919	+	0.666037i	$0.232011\pi$
$128$	−1.00000	−0.0883883
$129$	−2.72967	−0.240334
$130$	14.0179	1.22945
$131$	−8.67616	−0.758039	−0.379020	−	0.925389i	$-0.623739\pi$
$131$	−8.67616	−0.758039	−0.379020	+	0.925389i	$0.623739\pi$
$132$	−9.62414	−0.837674
$133$	0	0
$134$	14.3038	1.23566
$135$	10.1316	0.871987
$136$	5.04131	0.432289
$137$	−5.52071	−0.471666	−0.235833	−	0.971794i	$-0.575782\pi$
$137$	−5.52071	−0.471666	−0.235833	+	0.971794i	$0.575782\pi$
$138$	−0.248422	−0.0211470
$139$	8.36556	0.709558	0.354779	−	0.934950i	$-0.384556\pi$
$139$	8.36556	0.709558	0.354779	+	0.934950i	$0.384556\pi$
$140$	−2.38328	−0.201424
$141$	12.4509	1.04856
$142$	−13.4030	−1.12475
$143$	−28.9365	−2.41979
$144$	0.826915	0.0689096
$145$	−1.57496	−0.130793
$146$	−5.87714	−0.486395
$147$	1.95625	0.161349
$148$	−7.28732	−0.599014
$149$	5.68716	0.465911	0.232955	−	0.972487i	$-0.425160\pi$
$149$	5.68716	0.465911	0.232955	+	0.972487i	$0.425160\pi$
$150$	−1.33033	−0.108621
$151$	9.85582	0.802055	0.401028	−	0.916066i	$-0.368653\pi$
$151$	9.85582	0.802055	0.401028	+	0.916066i	$0.368653\pi$
$152$	0	0
$153$	−4.16873	−0.337022
$154$	4.91969	0.396440
$155$	−24.5341	−1.97063
$156$	11.5062	0.921234
$157$	8.92764	0.712503	0.356252	−	0.934390i	$-0.384055\pi$
$157$	8.92764	0.712503	0.356252	+	0.934390i	$0.384055\pi$
$158$	−8.08976	−0.643586
$159$	−6.17786	−0.489936
$160$	2.38328	0.188415
$161$	0.126989	0.0100081
$162$	10.7970	0.848289
$163$	2.42133	0.189653	0.0948267	−	0.995494i	$-0.469770\pi$
$163$	2.42133	0.189653	0.0948267	+	0.995494i	$0.469770\pi$
$164$	5.02394	0.392304
$165$	22.9371	1.78565
$166$	2.32025	0.180086
$167$	−16.1889	−1.25274	−0.626368	−	0.779528i	$-0.715459\pi$
$167$	−16.1889	−1.25274	−0.626368	+	0.779528i	$0.715459\pi$
$168$	−1.95625	−0.150928
$169$	21.5952	1.66117
$170$	−12.0149	−0.921498
$171$	0	0
$172$	−1.39536	−0.106395
$173$	12.5453	0.953804	0.476902	−	0.878957i	$-0.341760\pi$
$173$	12.5453	0.953804	0.476902	+	0.878957i	$0.341760\pi$
$174$	−1.29276	−0.0980039
$175$	0.680041	0.0514062
$176$	−4.91969	−0.370835
$177$	24.9896	1.87833
$178$	−6.84776	−0.513261
$179$	−8.98265	−0.671395	−0.335697	−	0.941970i	$-0.608972\pi$
$179$	−8.98265	−0.671395	−0.335697	+	0.941970i	$0.608972\pi$
$180$	−1.97077	−0.146893
$181$	18.0198	1.33940	0.669702	−	0.742630i	$-0.266422\pi$
$181$	18.0198	1.33940	0.669702	+	0.742630i	$0.266422\pi$
$182$	−5.88177	−0.435986
$183$	21.2003	1.56717
$184$	−0.126989	−0.00936173
$185$	17.3678	1.27690
$186$	−20.1381	−1.47660
$187$	24.8017	1.81368
$188$	6.36469	0.464193
$189$	−4.25110	−0.309222
$190$	0	0
$191$	5.06881	0.366766	0.183383	−	0.983042i	$-0.441295\pi$
$191$	5.06881	0.366766	0.183383	+	0.983042i	$0.441295\pi$
$192$	1.95625	0.141180
$193$	−0.193042	−0.0138955	−0.00694774	−	0.999976i	$-0.502212\pi$
$193$	−0.193042	−0.0138955	−0.00694774	+	0.999976i	$0.502212\pi$
$194$	−6.49650	−0.466422
$195$	−27.4226	−1.96377
$196$	1.00000	0.0714286
$197$	−14.7347	−1.04980	−0.524901	−	0.851163i	$-0.675898\pi$
$197$	−14.7347	−1.04980	−0.524901	+	0.851163i	$0.675898\pi$
$198$	4.06816	0.289112
$199$	19.8530	1.40734	0.703671	−	0.710526i	$-0.251543\pi$
$199$	19.8530	1.40734	0.703671	+	0.710526i	$0.251543\pi$
$200$	−0.680041	−0.0480861
$201$	−27.9818	−1.97368
$202$	−2.80868	−0.197618
$203$	0.660836	0.0463816
$204$	−9.86206	−0.690482
$205$	−11.9735	−0.836264
$206$	1.05465	0.0734809
$207$	0.105009	0.00729862
$208$	5.88177	0.407827
$209$	0	0
$210$	4.66230	0.321729
$211$	−21.9745	−1.51279	−0.756393	−	0.654118i	$-0.773040\pi$
$211$	−21.9745	−1.51279	−0.756393	+	0.654118i	$0.773040\pi$
$212$	−3.15801	−0.216893
$213$	26.2196	1.79654
$214$	7.25726	0.496096
$215$	3.32554	0.226800
$216$	4.25110	0.289251
$217$	10.2942	0.698819
$218$	6.02102	0.407795
$219$	11.4972	0.776905
$220$	11.7250	0.790500
$221$	−29.6518	−1.99460
$222$	14.2558	0.956789
$223$	17.9235	1.20025	0.600124	−	0.799907i	$-0.295118\pi$
$223$	17.9235	1.20025	0.600124	+	0.799907i	$0.295118\pi$
$224$	−1.00000	−0.0668153
$225$	0.562336	0.0374891
$226$	5.71691	0.380283
$227$	−1.21166	−0.0804208	−0.0402104	−	0.999191i	$-0.512803\pi$
$227$	−1.21166	−0.0804208	−0.0402104	+	0.999191i	$0.512803\pi$
$228$	0	0
$229$	−9.06882	−0.599284	−0.299642	−	0.954052i	$-0.596867\pi$
$229$	−9.06882	−0.599284	−0.299642	+	0.954052i	$0.596867\pi$
$230$	0.302650	0.0199561
$231$	−9.62414	−0.633222
$232$	−0.660836	−0.0433860
$233$	17.2961	1.13310	0.566552	−	0.824026i	$-0.308277\pi$
$233$	17.2961	1.13310	0.566552	+	0.824026i	$0.308277\pi$
$234$	−4.86372	−0.317952
$235$	−15.1689	−0.989508
$236$	12.7742	0.831532
$237$	15.8256	1.02798
$238$	5.04131	0.326779
$239$	12.3319	0.797684	0.398842	−	0.917020i	$-0.369412\pi$
$239$	12.3319	0.797684	0.398842	+	0.917020i	$0.369412\pi$
$240$	−4.66230	−0.300950
$241$	−19.4074	−1.25014	−0.625071	−	0.780568i	$-0.714930\pi$
$241$	−19.4074	−1.25014	−0.625071	+	0.780568i	$0.714930\pi$
$242$	−13.2033	−0.848741
$243$	−8.36826	−0.536824
$244$	10.8372	0.693782
$245$	−2.38328	−0.152262
$246$	−9.82809	−0.626616
$247$	0	0
$248$	−10.2942	−0.653686
$249$	−4.53899	−0.287647
$250$	−10.2957	−0.651156
$251$	7.12832	0.449935	0.224968	−	0.974366i	$-0.427772\pi$
$251$	7.12832	0.449935	0.224968	+	0.974366i	$0.427772\pi$
$252$	0.826915	0.0520908
$253$	−0.624744	−0.0392773
$254$	−16.8122	−1.05489
$255$	23.5041	1.47188
$256$	1.00000	0.0625000
$257$	9.70353	0.605290	0.302645	−	0.953103i	$-0.402130\pi$
$257$	9.70353	0.605290	0.302645	+	0.953103i	$0.402130\pi$
$258$	2.72967	0.169942
$259$	−7.28732	−0.452812
$260$	−14.0179	−0.869355
$261$	0.546455	0.0338247
$262$	8.67616	0.536015
$263$	28.7005	1.76975	0.884873	−	0.465832i	$-0.154245\pi$
$263$	28.7005	1.76975	0.884873	+	0.465832i	$0.154245\pi$
$264$	9.62414	0.592325
$265$	7.52643	0.462345
$266$	0	0
$267$	13.3959	0.819818
$268$	−14.3038	−0.873742
$269$	3.16919	0.193229	0.0966145	−	0.995322i	$-0.469199\pi$
$269$	3.16919	0.193229	0.0966145	+	0.995322i	$0.469199\pi$
$270$	−10.1316	−0.616588
$271$	−12.4179	−0.754332	−0.377166	−	0.926146i	$-0.623101\pi$
$271$	−12.4179	−0.754332	−0.377166	+	0.926146i	$0.623101\pi$
$272$	−5.04131	−0.305674
$273$	11.5062	0.696388
$274$	5.52071	0.333518
$275$	−3.34559	−0.201747
$276$	0.248422	0.0149532
$277$	−27.8899	−1.67574	−0.837870	−	0.545870i	$-0.816199\pi$
$277$	−27.8899	−1.67574	−0.837870	+	0.545870i	$0.816199\pi$
$278$	−8.36556	−0.501733
$279$	8.51247	0.509628
$280$	2.38328	0.142428
$281$	31.2282	1.86292	0.931458	−	0.363849i	$-0.118537\pi$
$281$	31.2282	1.86292	0.931458	+	0.363849i	$0.118537\pi$
$282$	−12.4509	−0.741442
$283$	21.7223	1.29126	0.645628	−	0.763652i	$-0.276596\pi$
$283$	21.7223	1.29126	0.645628	+	0.763652i	$0.276596\pi$
$284$	13.4030	0.795320
$285$	0	0
$286$	28.9365	1.71105
$287$	5.02394	0.296554
$288$	−0.826915	−0.0487264
$289$	8.41479	0.494988
$290$	1.57496	0.0924848
$291$	12.7088	0.745002
$292$	5.87714	0.343933
$293$	15.8945	0.928569	0.464285	−	0.885686i	$-0.346311\pi$
$293$	15.8945	0.928569	0.464285	+	0.885686i	$0.346311\pi$
$294$	−1.95625	−0.114091
$295$	−30.4446	−1.77255
$296$	7.28732	0.423567
$297$	20.9141	1.21356
$298$	−5.68716	−0.329449
$299$	0.746918	0.0431954
$300$	1.33033	0.0768066
$301$	−1.39536	−0.0804272
$302$	−9.85582	−0.567139
$303$	5.49449	0.315650
$304$	0	0
$305$	−25.8282	−1.47892
$306$	4.16873	0.238311
$307$	10.7312	0.612462	0.306231	−	0.951957i	$-0.400932\pi$
$307$	10.7312	0.612462	0.306231	+	0.951957i	$0.400932\pi$
$308$	−4.91969	−0.280325
$309$	−2.06316	−0.117369
$310$	24.5341	1.39344
$311$	10.1009	0.572770	0.286385	−	0.958115i	$-0.407546\pi$
$311$	10.1009	0.572770	0.286385	+	0.958115i	$0.407546\pi$
$312$	−11.5062	−0.651411
$313$	−0.108738	−0.00614623	−0.00307312	−	0.999995i	$-0.500978\pi$
$313$	−0.108738	−0.00614623	−0.00307312	+	0.999995i	$0.500978\pi$
$314$	−8.92764	−0.503816
$315$	−1.97077	−0.111041
$316$	8.08976	0.455084
$317$	8.96910	0.503755	0.251877	−	0.967759i	$-0.418952\pi$
$317$	8.96910	0.503755	0.251877	+	0.967759i	$0.418952\pi$
$318$	6.17786	0.346437
$319$	−3.25110	−0.182027
$320$	−2.38328	−0.133230
$321$	−14.1970	−0.792400
$322$	−0.126989	−0.00707680
$323$	0	0
$324$	−10.7970	−0.599831
$325$	3.99984	0.221871
$326$	−2.42133	−0.134105
$327$	−11.7786	−0.651359
$328$	−5.02394	−0.277401
$329$	6.36469	0.350897
$330$	−22.9371	−1.26264
$331$	−23.2345	−1.27708	−0.638541	−	0.769588i	$-0.720462\pi$
$331$	−23.2345	−1.27708	−0.638541	+	0.769588i	$0.720462\pi$
$332$	−2.32025	−0.127340
$333$	−6.02600	−0.330223
$334$	16.1889	0.885818
$335$	34.0899	1.86253
$336$	1.95625	0.106722
$337$	−11.5314	−0.628158	−0.314079	−	0.949397i	$-0.601696\pi$
$337$	−11.5314	−0.628158	−0.314079	+	0.949397i	$0.601696\pi$
$338$	−21.5952	−1.17462
$339$	−11.1837	−0.607416
$340$	12.0149	0.651598
$341$	−50.6445	−2.74255
$342$	0	0
$343$	1.00000	0.0539949
$344$	1.39536	0.0752328
$345$	−0.592059	−0.0318754
$346$	−12.5453	−0.674441
$347$	4.67386	0.250906	0.125453	−	0.992100i	$-0.459962\pi$
$347$	4.67386	0.250906	0.125453	+	0.992100i	$0.459962\pi$
$348$	1.29276	0.0692992
$349$	34.0342	1.82181	0.910904	−	0.412619i	$-0.135386\pi$
$349$	34.0342	1.82181	0.910904	+	0.412619i	$0.135386\pi$
$350$	−0.680041	−0.0363497
$351$	−25.0040	−1.33461
$352$	4.91969	0.262220
$353$	−17.7867	−0.946693	−0.473346	−	0.880876i	$-0.656954\pi$
$353$	−17.7867	−0.946693	−0.473346	+	0.880876i	$0.656954\pi$
$354$	−24.9896	−1.32818
$355$	−31.9431	−1.69536
$356$	6.84776	0.362931
$357$	−9.86206	−0.521956
$358$	8.98265	0.474748
$359$	−18.5130	−0.977077	−0.488538	−	0.872542i	$-0.662470\pi$
$359$	−18.5130	−0.977077	−0.488538	+	0.872542i	$0.662470\pi$
$360$	1.97077	0.103869
$361$	0	0
$362$	−18.0198	−0.947102
$363$	25.8290	1.35567
$364$	5.88177	0.308288
$365$	−14.0069	−0.733154
$366$	−21.2003	−1.10816
$367$	3.07233	0.160375	0.0801873	−	0.996780i	$-0.474448\pi$
$367$	3.07233	0.160375	0.0801873	+	0.996780i	$0.474448\pi$
$368$	0.126989	0.00661974
$369$	4.15438	0.216268
$370$	−17.3678	−0.902907
$371$	−3.15801	−0.163956
$372$	20.1381	1.04411
$373$	−27.3387	−1.41555	−0.707773	−	0.706440i	$-0.750300\pi$
$373$	−27.3387	−1.41555	−0.707773	+	0.706440i	$0.750300\pi$
$374$	−24.8017	−1.28246
$375$	20.1409	1.04007
$376$	−6.36469	−0.328234
$377$	3.88688	0.200185
$378$	4.25110	0.218653
$379$	0.500637	0.0257160	0.0128580	−	0.999917i	$-0.495907\pi$
$379$	0.500637	0.0257160	0.0128580	+	0.999917i	$0.495907\pi$
$380$	0	0
$381$	32.8888	1.68494
$382$	−5.06881	−0.259343
$383$	−9.19105	−0.469641	−0.234820	−	0.972039i	$-0.575450\pi$
$383$	−9.19105	−0.469641	−0.234820	+	0.972039i	$0.575450\pi$
$384$	−1.95625	−0.0998295
$385$	11.7250	0.597562
$386$	0.193042	0.00982559
$387$	−1.15384	−0.0586532
$388$	6.49650	0.329810
$389$	18.3835	0.932082	0.466041	−	0.884763i	$-0.345680\pi$
$389$	18.3835	0.932082	0.466041	+	0.884763i	$0.345680\pi$
$390$	27.4226	1.38860
$391$	−0.640189	−0.0323757
$392$	−1.00000	−0.0505076
$393$	−16.9727	−0.856161
$394$	14.7347	0.742322
$395$	−19.2802	−0.970091
$396$	−4.06816	−0.204433
$397$	−25.2632	−1.26792	−0.633962	−	0.773364i	$-0.718572\pi$
$397$	−25.2632	−1.26792	−0.633962	+	0.773364i	$0.718572\pi$
$398$	−19.8530	−0.995142
$399$	0	0
$400$	0.680041	0.0340020
$401$	5.87405	0.293336	0.146668	−	0.989186i	$-0.453145\pi$
$401$	5.87405	0.293336	0.146668	+	0.989186i	$0.453145\pi$
$402$	27.9818	1.39560
$403$	60.5484	3.01613
$404$	2.80868	0.139737
$405$	25.7322	1.27864
$406$	−0.660836	−0.0327967
$407$	35.8513	1.77709
$408$	9.86206	0.488245
$409$	−8.97638	−0.443854	−0.221927	−	0.975063i	$-0.571235\pi$
$409$	−8.97638	−0.443854	−0.221927	+	0.975063i	$0.571235\pi$
$410$	11.9735	0.591328
$411$	−10.7999	−0.532719
$412$	−1.05465	−0.0519589
$413$	12.7742	0.628579
$414$	−0.105009	−0.00516090
$415$	5.52982	0.271448
$416$	−5.88177	−0.288377
$417$	16.3651	0.801404
$418$	0	0
$419$	6.36984	0.311187	0.155594	−	0.987821i	$-0.450271\pi$
$419$	6.36984	0.311187	0.155594	+	0.987821i	$0.450271\pi$
$420$	−4.66230	−0.227497
$421$	9.94408	0.484645	0.242322	−	0.970196i	$-0.422091\pi$
$421$	9.94408	0.484645	0.242322	+	0.970196i	$0.422091\pi$
$422$	21.9745	1.06970
$423$	5.26306	0.255899
$424$	3.15801	0.153366
$425$	−3.42830	−0.166297
$426$	−26.2196	−1.27034
$427$	10.8372	0.524450
$428$	−7.25726	−0.350793
$429$	−56.6070	−2.73301
$430$	−3.32554	−0.160372
$431$	5.56887	0.268243	0.134121	−	0.990965i	$-0.457179\pi$
$431$	5.56887	0.268243	0.134121	+	0.990965i	$0.457179\pi$
$432$	−4.25110	−0.204531
$433$	20.9285	1.00576	0.502880	−	0.864356i	$-0.332274\pi$
$433$	20.9285	1.00576	0.502880	+	0.864356i	$0.332274\pi$
$434$	−10.2942	−0.494140
$435$	−3.08101	−0.147723
$436$	−6.02102	−0.288355
$437$	0	0
$438$	−11.4972	−0.549355
$439$	−9.00669	−0.429866	−0.214933	−	0.976629i	$-0.568953\pi$
$439$	−9.00669	−0.429866	−0.214933	+	0.976629i	$0.568953\pi$
$440$	−11.7250	−0.558968
$441$	0.826915	0.0393769
$442$	29.6518	1.41039
$443$	−14.3382	−0.681229	−0.340614	−	0.940203i	$-0.610635\pi$
$443$	−14.3382	−0.681229	−0.340614	+	0.940203i	$0.610635\pi$
$444$	−14.2558	−0.676552
$445$	−16.3202	−0.773649
$446$	−17.9235	−0.848703
$447$	11.1255	0.526219
$448$	1.00000	0.0472456
$449$	−38.7203	−1.82732	−0.913662	−	0.406476i	$-0.866758\pi$
$449$	−38.7203	−1.82732	−0.913662	+	0.406476i	$0.866758\pi$
$450$	−0.562336	−0.0265088
$451$	−24.7162	−1.16384
$452$	−5.71691	−0.268901
$453$	19.2804	0.905875
$454$	1.21166	0.0568661
$455$	−14.0179	−0.657170
$456$	0	0
$457$	−15.9692	−0.747008	−0.373504	−	0.927629i	$-0.621844\pi$
$457$	−15.9692	−0.747008	−0.373504	+	0.927629i	$0.621844\pi$
$458$	9.06882	0.423758
$459$	21.4311	1.00032
$460$	−0.302650	−0.0141111
$461$	16.3729	0.762563	0.381282	−	0.924459i	$-0.375483\pi$
$461$	16.3729	0.762563	0.381282	+	0.924459i	$0.375483\pi$
$462$	9.62414	0.447755
$463$	2.33207	0.108380	0.0541902	−	0.998531i	$-0.482742\pi$
$463$	2.33207	0.108380	0.0541902	+	0.998531i	$0.482742\pi$
$464$	0.660836	0.0306785
$465$	−47.9949	−2.22571
$466$	−17.2961	−0.801225
$467$	−24.8314	−1.14906	−0.574531	−	0.818483i	$-0.694815\pi$
$467$	−24.8314	−1.14906	−0.574531	+	0.818483i	$0.694815\pi$
$468$	4.86372	0.224826
$469$	−14.3038	−0.660487
$470$	15.1689	0.699688
$471$	17.4647	0.804731
$472$	−12.7742	−0.587982
$473$	6.86473	0.315641
$474$	−15.8256	−0.726893
$475$	0	0
$476$	−5.04131	−0.231068
$477$	−2.61141	−0.119568
$478$	−12.3319	−0.564048
$479$	−29.3406	−1.34061	−0.670303	−	0.742087i	$-0.733836\pi$
$479$	−29.3406	−1.34061	−0.670303	+	0.742087i	$0.733836\pi$
$480$	4.66230	0.212804
$481$	−42.8624	−1.95436
$482$	19.4074	0.883983
$483$	0.248422	0.0113036
$484$	13.2033	0.600151
$485$	−15.4830	−0.703047
$486$	8.36826	0.379592
$487$	−20.1678	−0.913892	−0.456946	−	0.889495i	$-0.651057\pi$
$487$	−20.1678	−0.913892	−0.456946	+	0.889495i	$0.651057\pi$
$488$	−10.8372	−0.490578
$489$	4.73673	0.214203
$490$	2.38328	0.107666
$491$	24.3346	1.09820	0.549102	−	0.835755i	$-0.314970\pi$
$491$	24.3346	1.09820	0.549102	+	0.835755i	$0.314970\pi$
$492$	9.82809	0.443085
$493$	−3.33148	−0.150042
$494$	0	0
$495$	9.69559	0.435784
$496$	10.2942	0.462225
$497$	13.4030	0.601206
$498$	4.53899	0.203397
$499$	23.4055	1.04777	0.523886	−	0.851788i	$-0.324482\pi$
$499$	23.4055	1.04777	0.523886	+	0.851788i	$0.324482\pi$
$500$	10.2957	0.460437
$501$	−31.6696	−1.41489
$502$	−7.12832	−0.318152
$503$	0.243054	0.0108372	0.00541862	−	0.999985i	$-0.498275\pi$
$503$	0.243054	0.0108372	0.00541862	+	0.999985i	$0.498275\pi$
$504$	−0.826915	−0.0368337
$505$	−6.69389	−0.297874
$506$	0.624744	0.0277733
$507$	42.2456	1.87619
$508$	16.8122	0.745919
$509$	−22.3781	−0.991892	−0.495946	−	0.868353i	$-0.665179\pi$
$509$	−22.3781	−0.991892	−0.495946	+	0.868353i	$0.665179\pi$
$510$	−23.5041	−1.04078
$511$	5.87714	0.259989
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−9.70353	−0.428004
$515$	2.51353	0.110759
$516$	−2.72967	−0.120167
$517$	−31.3123	−1.37711
$518$	7.28732	0.320187
$519$	24.5418	1.07727
$520$	14.0179	0.614727
$521$	37.6667	1.65021	0.825105	−	0.564979i	$-0.191116\pi$
$521$	37.6667	1.65021	0.825105	+	0.564979i	$0.191116\pi$
$522$	−0.546455	−0.0239177
$523$	2.71077	0.118534	0.0592669	−	0.998242i	$-0.481124\pi$
$523$	2.71077	0.118534	0.0592669	+	0.998242i	$0.481124\pi$
$524$	−8.67616	−0.379020
$525$	1.33033	0.0580604
$526$	−28.7005	−1.25140
$527$	−51.8965	−2.26065
$528$	−9.62414	−0.418837
$529$	−22.9839	−0.999299
$530$	−7.52643	−0.326927
$531$	10.5632	0.458404
$532$	0	0
$533$	29.5497	1.27994
$534$	−13.3959	−0.579699
$535$	17.2961	0.747776
$536$	14.3038	0.617829
$537$	−17.5723	−0.758301
$538$	−3.16919	−0.136634
$539$	−4.91969	−0.211906
$540$	10.1316	0.435993
$541$	−5.78366	−0.248659	−0.124329	−	0.992241i	$-0.539678\pi$
$541$	−5.78366	−0.248659	−0.124329	+	0.992241i	$0.539678\pi$
$542$	12.4179	0.533393
$543$	35.2513	1.51278
$544$	5.04131	0.216144
$545$	14.3498	0.614678
$546$	−11.5062	−0.492420
$547$	33.0142	1.41159	0.705794	−	0.708417i	$-0.250591\pi$
$547$	33.0142	1.41159	0.705794	+	0.708417i	$0.250591\pi$
$548$	−5.52071	−0.235833
$549$	8.96146	0.382466
$550$	3.34559	0.142656
$551$	0	0
$552$	−0.248422	−0.0105735
$553$	8.08976	0.344011
$554$	27.8899	1.18493
$555$	33.9757	1.44219
$556$	8.36556	0.354779
$557$	−19.6594	−0.832994	−0.416497	−	0.909137i	$-0.636742\pi$
$557$	−19.6594	−0.832994	−0.416497	+	0.909137i	$0.636742\pi$
$558$	−8.51247	−0.360362
$559$	−8.20718	−0.347127
$560$	−2.38328	−0.100712
$561$	48.5183	2.04844
$562$	−31.2282	−1.31728
$563$	−10.6031	−0.446869	−0.223435	−	0.974719i	$-0.571727\pi$
$563$	−10.6031	−0.446869	−0.223435	+	0.974719i	$0.571727\pi$
$564$	12.4509	0.524279
$565$	13.6250	0.573209
$566$	−21.7223	−0.913055
$567$	−10.7970	−0.453430
$568$	−13.4030	−0.562376
$569$	−1.05853	−0.0443759	−0.0221879	−	0.999754i	$-0.507063\pi$
$569$	−1.05853	−0.0443759	−0.0221879	+	0.999754i	$0.507063\pi$
$570$	0	0
$571$	19.8412	0.830330	0.415165	−	0.909746i	$-0.363724\pi$
$571$	19.8412	0.830330	0.415165	+	0.909746i	$0.363724\pi$
$572$	−28.9365	−1.20989
$573$	9.91586	0.414241
$574$	−5.02394	−0.209695
$575$	0.0863575	0.00360135
$576$	0.826915	0.0344548
$577$	−19.4839	−0.811124	−0.405562	−	0.914067i	$-0.632924\pi$
$577$	−19.4839	−0.811124	−0.405562	+	0.914067i	$0.632924\pi$
$578$	−8.41479	−0.350009
$579$	−0.377639	−0.0156941
$580$	−1.57496	−0.0653966
$581$	−2.32025	−0.0962603
$582$	−12.7088	−0.526796
$583$	15.5364	0.643452
$584$	−5.87714	−0.243198
$585$	−11.5916	−0.479255
$586$	−15.8945	−0.656598
$587$	−7.01515	−0.289546	−0.144773	−	0.989465i	$-0.546245\pi$
$587$	−7.01515	−0.289546	−0.144773	+	0.989465i	$0.546245\pi$
$588$	1.95625	0.0806744
$589$	0	0
$590$	30.4446	1.25339
$591$	−28.8247	−1.18569
$592$	−7.28732	−0.299507
$593$	−6.09049	−0.250106	−0.125053	−	0.992150i	$-0.539910\pi$
$593$	−6.09049	−0.250106	−0.125053	+	0.992150i	$0.539910\pi$
$594$	−20.9141	−0.858115
$595$	12.0149	0.492562
$596$	5.68716	0.232955
$597$	38.8375	1.58951
$598$	−0.746918	−0.0305437
$599$	27.3318	1.11675	0.558374	−	0.829589i	$-0.311425\pi$
$599$	27.3318	1.11675	0.558374	+	0.829589i	$0.311425\pi$
$600$	−1.33033	−0.0543105
$601$	33.5081	1.36683	0.683413	−	0.730032i	$-0.260495\pi$
$601$	33.5081	1.36683	0.683413	+	0.730032i	$0.260495\pi$
$602$	1.39536	0.0568706
$603$	−11.8280	−0.481674
$604$	9.85582	0.401028
$605$	−31.4673	−1.27933
$606$	−5.49449	−0.223198
$607$	21.9303	0.890124	0.445062	−	0.895500i	$-0.353182\pi$
$607$	21.9303	0.890124	0.445062	+	0.895500i	$0.353182\pi$
$608$	0	0
$609$	1.29276	0.0523853
$610$	25.8282	1.04575
$611$	37.4357	1.51448
$612$	−4.16873	−0.168511
$613$	−38.3260	−1.54797	−0.773986	−	0.633203i	$-0.781740\pi$
$613$	−38.3260	−1.54797	−0.773986	+	0.633203i	$0.781740\pi$
$614$	−10.7312	−0.433076
$615$	−23.4231	−0.944512
$616$	4.91969	0.198220
$617$	15.8503	0.638110	0.319055	−	0.947736i	$-0.396635\pi$
$617$	15.8503	0.638110	0.319055	+	0.947736i	$0.396635\pi$
$618$	2.06316	0.0829924
$619$	40.2691	1.61855	0.809276	−	0.587428i	$-0.199860\pi$
$619$	40.2691	1.61855	0.809276	+	0.587428i	$0.199860\pi$
$620$	−24.5341	−0.985314
$621$	−0.539841	−0.0216631
$622$	−10.1009	−0.405010
$623$	6.84776	0.274350
$624$	11.5062	0.460617
$625$	−27.9377	−1.11751
$626$	0.108738	0.00434604
$627$	0	0
$628$	8.92764	0.356252
$629$	36.7376	1.46483
$630$	1.97077	0.0785175
$631$	−29.2641	−1.16499	−0.582494	−	0.812835i	$-0.697923\pi$
$631$	−29.2641	−1.16499	−0.582494	+	0.812835i	$0.697923\pi$
$632$	−8.08976	−0.321793
$633$	−42.9876	−1.70860
$634$	−8.96910	−0.356208
$635$	−40.0681	−1.59006
$636$	−6.17786	−0.244968
$637$	5.88177	0.233044
$638$	3.25110	0.128712
$639$	11.0831	0.438442
$640$	2.38328	0.0942076
$641$	20.1288	0.795041	0.397520	−	0.917593i	$-0.369871\pi$
$641$	20.1288	0.795041	0.397520	+	0.917593i	$0.369871\pi$
$642$	14.1970	0.560312
$643$	17.7479	0.699908	0.349954	−	0.936767i	$-0.386197\pi$
$643$	17.7479	0.699908	0.349954	+	0.936767i	$0.386197\pi$
$644$	0.126989	0.00500405
$645$	6.50558	0.256157
$646$	0	0
$647$	33.2343	1.30658	0.653288	−	0.757110i	$-0.273389\pi$
$647$	33.2343	1.30658	0.653288	+	0.757110i	$0.273389\pi$
$648$	10.7970	0.424145
$649$	−62.8452	−2.46689
$650$	−3.99984	−0.156887
$651$	20.1381	0.789276
$652$	2.42133	0.0948267
$653$	−1.76408	−0.0690339	−0.0345169	−	0.999404i	$-0.510989\pi$
$653$	−1.76408	−0.0690339	−0.0345169	+	0.999404i	$0.510989\pi$
$654$	11.7786	0.460581
$655$	20.6777	0.807946
$656$	5.02394	0.196152
$657$	4.85989	0.189603
$658$	−6.36469	−0.248122
$659$	27.8033	1.08306	0.541532	−	0.840680i	$-0.317845\pi$
$659$	27.8033	1.08306	0.541532	+	0.840680i	$0.317845\pi$
$660$	22.9371	0.892824
$661$	−7.62756	−0.296678	−0.148339	−	0.988937i	$-0.547393\pi$
$661$	−7.62756	−0.296678	−0.148339	+	0.988937i	$0.547393\pi$
$662$	23.2345	0.903033
$663$	−58.0064	−2.25278
$664$	2.32025	0.0900432
$665$	0	0
$666$	6.02600	0.233503
$667$	0.0839186	0.00324934
$668$	−16.1889	−0.626368
$669$	35.0629	1.35561
$670$	−34.0899	−1.31701
$671$	−53.3157	−2.05823
$672$	−1.95625	−0.0754640
$673$	2.06068	0.0794334	0.0397167	−	0.999211i	$-0.487354\pi$
$673$	2.06068	0.0794334	0.0397167	+	0.999211i	$0.487354\pi$
$674$	11.5314	0.444175
$675$	−2.89092	−0.111272
$676$	21.5952	0.830585
$677$	33.2994	1.27980	0.639899	−	0.768459i	$-0.278976\pi$
$677$	33.2994	1.27980	0.639899	+	0.768459i	$0.278976\pi$
$678$	11.1837	0.429508
$679$	6.49650	0.249313
$680$	−12.0149	−0.460749
$681$	−2.37031	−0.0908306
$682$	50.6445	1.93928
$683$	44.6468	1.70836	0.854181	−	0.519976i	$-0.174059\pi$
$683$	44.6468	1.70836	0.854181	+	0.519976i	$0.174059\pi$
$684$	0	0
$685$	13.1574	0.502719
$686$	−1.00000	−0.0381802
$687$	−17.7409	−0.676857
$688$	−1.39536	−0.0531976
$689$	−18.5747	−0.707639
$690$	0.592059	0.0225393
$691$	−27.1949	−1.03454	−0.517271	−	0.855821i	$-0.673052\pi$
$691$	−27.1949	−1.03454	−0.517271	+	0.855821i	$0.673052\pi$
$692$	12.5453	0.476902
$693$	−4.06816	−0.154537
$694$	−4.67386	−0.177417
$695$	−19.9375	−0.756273
$696$	−1.29276	−0.0490019
$697$	−25.3272	−0.959338
$698$	−34.0342	−1.28821
$699$	33.8354	1.27977
$700$	0.680041	0.0257031
$701$	−35.9135	−1.35643	−0.678216	−	0.734862i	$-0.737247\pi$
$701$	−35.9135	−1.35643	−0.678216	+	0.734862i	$0.737247\pi$
$702$	25.0040	0.943714
$703$	0	0
$704$	−4.91969	−0.185418
$705$	−29.6741	−1.11759
$706$	17.7867	0.669413
$707$	2.80868	0.105631
$708$	24.9896	0.939167
$709$	32.6844	1.22749	0.613744	−	0.789505i	$-0.289663\pi$
$709$	32.6844	1.22749	0.613744	+	0.789505i	$0.289663\pi$
$710$	31.9431	1.19880
$711$	6.68954	0.250877
$712$	−6.84776	−0.256631
$713$	1.30725	0.0489570
$714$	9.86206	0.369078
$715$	68.9638	2.57910
$716$	−8.98265	−0.335697
$717$	24.1243	0.900937
$718$	18.5130	0.690898
$719$	28.9009	1.07782	0.538911	−	0.842363i	$-0.318836\pi$
$719$	28.9009	1.07782	0.538911	+	0.842363i	$0.318836\pi$
$720$	−1.97077	−0.0734464
$721$	−1.05465	−0.0392772
$722$	0	0
$723$	−37.9658	−1.41196
$724$	18.0198	0.669702
$725$	0.449395	0.0166901
$726$	−25.8290	−0.958604
$727$	−13.1177	−0.486510	−0.243255	−	0.969962i	$-0.578215\pi$
$727$	−13.1177	−0.486510	−0.243255	+	0.969962i	$0.578215\pi$
$728$	−5.88177	−0.217993
$729$	16.0205	0.593351
$730$	14.0069	0.518418
$731$	7.03444	0.260178
$732$	21.2003	0.783586
$733$	38.8574	1.43523	0.717615	−	0.696440i	$-0.245234\pi$
$733$	38.8574	1.43523	0.717615	+	0.696440i	$0.245234\pi$
$734$	−3.07233	−0.113402
$735$	−4.66230	−0.171971
$736$	−0.126989	−0.00468086
$737$	70.3701	2.59212
$738$	−4.15438	−0.152925
$739$	−23.5792	−0.867374	−0.433687	−	0.901064i	$-0.642788\pi$
$739$	−23.5792	−0.867374	−0.433687	+	0.901064i	$0.642788\pi$
$740$	17.3678	0.638452
$741$	0	0
$742$	3.15801	0.115934
$743$	12.6625	0.464544	0.232272	−	0.972651i	$-0.425384\pi$
$743$	12.6625	0.464544	0.232272	+	0.972651i	$0.425384\pi$
$744$	−20.1381	−0.738300
$745$	−13.5541	−0.496585
$746$	27.3387	1.00094
$747$	−1.91865	−0.0701998
$748$	24.8017	0.906838
$749$	−7.25726	−0.265175
$750$	−20.1409	−0.735443
$751$	−48.0904	−1.75484	−0.877421	−	0.479721i	$-0.840738\pi$
$751$	−48.0904	−1.75484	−0.877421	+	0.479721i	$0.840738\pi$
$752$	6.36469	0.232097
$753$	13.9448	0.508176
$754$	−3.88688	−0.141552
$755$	−23.4892	−0.854860
$756$	−4.25110	−0.154611
$757$	27.1694	0.987489	0.493745	−	0.869607i	$-0.335628\pi$
$757$	27.1694	0.987489	0.493745	+	0.869607i	$0.335628\pi$
$758$	−0.500637	−0.0181840
$759$	−1.22216	−0.0443615
$760$	0	0
$761$	−38.2421	−1.38628	−0.693138	−	0.720805i	$-0.743772\pi$
$761$	−38.2421	−1.38628	−0.693138	+	0.720805i	$0.743772\pi$
$762$	−32.8888	−1.19144
$763$	−6.02102	−0.217976
$764$	5.06881	0.183383
$765$	9.93528	0.359211
$766$	9.19105	0.332086
$767$	75.1351	2.71297
$768$	1.95625	0.0705901
$769$	9.16033	0.330330	0.165165	−	0.986266i	$-0.447184\pi$
$769$	9.16033	0.330330	0.165165	+	0.986266i	$0.447184\pi$
$770$	−11.7250	−0.422540
$771$	18.9825	0.683639
$772$	−0.193042	−0.00694774
$773$	39.3297	1.41459	0.707296	−	0.706917i	$-0.249915\pi$
$773$	39.3297	1.41459	0.707296	+	0.706917i	$0.249915\pi$
$774$	1.15384	0.0414741
$775$	7.00051	0.251466
$776$	−6.49650	−0.233211
$777$	−14.2558	−0.511425
$778$	−18.3835	−0.659082
$779$	0	0
$780$	−27.4226	−0.981885
$781$	−65.9385	−2.35946
$782$	0.640189	0.0228931
$783$	−2.80928	−0.100395
$784$	1.00000	0.0357143
$785$	−21.2771	−0.759412
$786$	16.9727	0.605397
$787$	−29.9038	−1.06596	−0.532978	−	0.846129i	$-0.678927\pi$
$787$	−29.9038	−1.06596	−0.532978	+	0.846129i	$0.678927\pi$
$788$	−14.7347	−0.524901
$789$	56.1453	1.99883
$790$	19.2802	0.685958
$791$	−5.71691	−0.203270
$792$	4.06816	0.144556
$793$	63.7420	2.26355
$794$	25.2632	0.896557
$795$	14.7236	0.522192
$796$	19.8530	0.703671
$797$	4.84712	0.171694	0.0858469	−	0.996308i	$-0.472640\pi$
$797$	4.84712	0.171694	0.0858469	+	0.996308i	$0.472640\pi$
$798$	0	0
$799$	−32.0864	−1.13513
$800$	−0.680041	−0.0240431
$801$	5.66252	0.200075
$802$	−5.87405	−0.207420
$803$	−28.9137	−1.02034
$804$	−27.9818	−0.986841
$805$	−0.302650	−0.0106670
$806$	−60.5484	−2.13273
$807$	6.19973	0.218241
$808$	−2.80868	−0.0988091
$809$	−37.0728	−1.30341	−0.651705	−	0.758473i	$-0.725946\pi$
$809$	−37.0728	−1.30341	−0.651705	+	0.758473i	$0.725946\pi$
$810$	−25.7322	−0.904138
$811$	5.42548	0.190514	0.0952572	−	0.995453i	$-0.469633\pi$
$811$	5.42548	0.190514	0.0952572	+	0.995453i	$0.469633\pi$
$812$	0.660836	0.0231908
$813$	−24.2925	−0.851974
$814$	−35.8513	−1.25659
$815$	−5.77073	−0.202140
$816$	−9.86206	−0.345241
$817$	0	0
$818$	8.97638	0.313852
$819$	4.86372	0.169952
$820$	−11.9735	−0.418132
$821$	−21.5806	−0.753167	−0.376584	−	0.926383i	$-0.622901\pi$
$821$	−21.5806	−0.753167	−0.376584	+	0.926383i	$0.622901\pi$
$822$	10.7999	0.376689
$823$	14.6938	0.512192	0.256096	−	0.966651i	$-0.417564\pi$
$823$	14.6938	0.512192	0.256096	+	0.966651i	$0.417564\pi$
$824$	1.05465	0.0367405
$825$	−6.54481	−0.227861
$826$	−12.7742	−0.444473
$827$	17.7505	0.617247	0.308624	−	0.951184i	$-0.400132\pi$
$827$	17.7505	0.617247	0.308624	+	0.951184i	$0.400132\pi$
$828$	0.105009	0.00364931
$829$	−14.4044	−0.500286	−0.250143	−	0.968209i	$-0.580478\pi$
$829$	−14.4044	−0.500286	−0.250143	+	0.968209i	$0.580478\pi$
$830$	−5.52982	−0.191943
$831$	−54.5596	−1.89265
$832$	5.88177	0.203914
$833$	−5.04131	−0.174671
$834$	−16.3651	−0.566678
$835$	38.5828	1.33521
$836$	0	0
$837$	−43.7619	−1.51263
$838$	−6.36984	−0.220043
$839$	−7.76677	−0.268139	−0.134069	−	0.990972i	$-0.542805\pi$
$839$	−7.76677	−0.268139	−0.134069	+	0.990972i	$0.542805\pi$
$840$	4.66230	0.160865
$841$	−28.5633	−0.984941
$842$	−9.94408	−0.342696
$843$	61.0901	2.10405
$844$	−21.9745	−0.756393
$845$	−51.4675	−1.77054
$846$	−5.26306	−0.180948
$847$	13.2033	0.453671
$848$	−3.15801	−0.108446
$849$	42.4942	1.45840
$850$	3.42830	0.117590
$851$	−0.925407	−0.0317226
$852$	26.2196	0.898268
$853$	−40.3064	−1.38006	−0.690032	−	0.723779i	$-0.742404\pi$
$853$	−40.3064	−1.38006	−0.690032	+	0.723779i	$0.742404\pi$
$854$	−10.8372	−0.370842
$855$	0	0
$856$	7.25726	0.248048
$857$	40.3686	1.37897	0.689483	−	0.724302i	$-0.257838\pi$
$857$	40.3686	1.37897	0.689483	+	0.724302i	$0.257838\pi$
$858$	56.6070	1.93253
$859$	39.7559	1.35646	0.678228	−	0.734852i	$-0.262748\pi$
$859$	39.7559	1.35646	0.678228	+	0.734852i	$0.262748\pi$
$860$	3.32554	0.113400
$861$	9.82809	0.334940
$862$	−5.56887	−0.189676
$863$	20.0186	0.681440	0.340720	−	0.940165i	$-0.389329\pi$
$863$	20.0186	0.681440	0.340720	+	0.940165i	$0.389329\pi$
$864$	4.25110	0.144625
$865$	−29.8991	−1.01660
$866$	−20.9285	−0.711180
$867$	16.4614	0.559060
$868$	10.2942	0.349410
$869$	−39.7991	−1.35009
$870$	3.08101	0.104456
$871$	−84.1315	−2.85069
$872$	6.02102	0.203898
$873$	5.37206	0.181817
$874$	0	0
$875$	10.2957	0.348058
$876$	11.4972	0.388453
$877$	−15.7639	−0.532310	−0.266155	−	0.963930i	$-0.585753\pi$
$877$	−15.7639	−0.532310	−0.266155	+	0.963930i	$0.585753\pi$
$878$	9.00669	0.303961
$879$	31.0937	1.04876
$880$	11.7250	0.395250
$881$	54.0766	1.82189	0.910944	−	0.412530i	$-0.135355\pi$
$881$	54.0766	1.82189	0.910944	+	0.412530i	$0.135355\pi$
$882$	−0.826915	−0.0278437
$883$	18.4916	0.622293	0.311147	−	0.950362i	$-0.399287\pi$
$883$	18.4916	0.622293	0.311147	+	0.950362i	$0.399287\pi$
$884$	−29.6518	−0.997298
$885$	−59.5573	−2.00200
$886$	14.3382	0.481701
$887$	−26.2102	−0.880051	−0.440026	−	0.897985i	$-0.645031\pi$
$887$	−26.2102	−0.880051	−0.440026	+	0.897985i	$0.645031\pi$
$888$	14.2558	0.478394
$889$	16.8122	0.563862
$890$	16.3202	0.547053
$891$	53.1176	1.77951
$892$	17.9235	0.600124
$893$	0	0
$894$	−11.1255	−0.372093
$895$	21.4082	0.715597
$896$	−1.00000	−0.0334077
$897$	1.46116	0.0487867
$898$	38.7203	1.29211
$899$	6.80281	0.226886
$900$	0.562336	0.0187445
$901$	15.9205	0.530389
$902$	24.7162	0.822960
$903$	−2.72967	−0.0908378
$904$	5.71691	0.190142
$905$	−42.9464	−1.42759
$906$	−19.2804	−0.640550
$907$	−28.6205	−0.950328	−0.475164	−	0.879897i	$-0.657611\pi$
$907$	−28.6205	−0.950328	−0.475164	+	0.879897i	$0.657611\pi$
$908$	−1.21166	−0.0402104
$909$	2.32254	0.0770339
$910$	14.0179	0.464690
$911$	−14.4946	−0.480229	−0.240114	−	0.970745i	$-0.577185\pi$
$911$	−14.4946	−0.480229	−0.240114	+	0.970745i	$0.577185\pi$
$912$	0	0
$913$	11.4149	0.377779
$914$	15.9692	0.528214
$915$	−50.5264	−1.67035
$916$	−9.06882	−0.299642
$917$	−8.67616	−0.286512
$918$	−21.4311	−0.707332
$919$	−18.9087	−0.623741	−0.311870	−	0.950125i	$-0.600955\pi$
$919$	−18.9087	−0.623741	−0.311870	+	0.950125i	$0.600955\pi$
$920$	0.302650	0.00997807
$921$	20.9929	0.691740
$922$	−16.3729	−0.539214
$923$	78.8332	2.59483
$924$	−9.62414	−0.316611
$925$	−4.95568	−0.162942
$926$	−2.33207	−0.0766365
$927$	−0.872106	−0.0286437
$928$	−0.660836	−0.0216930
$929$	−13.1941	−0.432883	−0.216441	−	0.976296i	$-0.569445\pi$
$929$	−13.1941	−0.432883	−0.216441	+	0.976296i	$0.569445\pi$
$930$	47.9949	1.57381
$931$	0	0
$932$	17.2961	0.566552
$933$	19.7599	0.646911
$934$	24.8314	0.812509
$935$	−59.1094	−1.93308
$936$	−4.86372	−0.158976
$937$	−29.1815	−0.953317	−0.476659	−	0.879089i	$-0.658152\pi$
$937$	−29.1815	−0.953317	−0.476659	+	0.879089i	$0.658152\pi$
$938$	14.3038	0.467035
$939$	−0.212719	−0.00694181
$940$	−15.1689	−0.494754
$941$	−44.4796	−1.44999	−0.724997	−	0.688752i	$-0.758159\pi$
$941$	−44.4796	−1.44999	−0.724997	+	0.688752i	$0.758159\pi$
$942$	−17.4647	−0.569031
$943$	0.637984	0.0207756
$944$	12.7742	0.415766
$945$	10.1316	0.329580
$946$	−6.86473	−0.223192
$947$	−34.9972	−1.13726	−0.568628	−	0.822595i	$-0.692525\pi$
$947$	−34.9972	−1.13726	−0.568628	+	0.822595i	$0.692525\pi$
$948$	15.8256	0.513991
$949$	34.5680	1.12212
$950$	0	0
$951$	17.5458	0.568962
$952$	5.04131	0.163390
$953$	−26.7973	−0.868048	−0.434024	−	0.900901i	$-0.642907\pi$
$953$	−26.7973	−0.868048	−0.434024	+	0.900901i	$0.642907\pi$
$954$	2.61141	0.0845474
$955$	−12.0804	−0.390913
$956$	12.3319	0.398842
$957$	−6.35997	−0.205589
$958$	29.3406	0.947952
$959$	−5.52071	−0.178273
$960$	−4.66230	−0.150475
$961$	74.9716	2.41844
$962$	42.8624	1.38194
$963$	−6.00114	−0.193384
$964$	−19.4074	−0.625071
$965$	0.460074	0.0148103
$966$	−0.248422	−0.00799283
$967$	−9.48781	−0.305107	−0.152554	−	0.988295i	$-0.548750\pi$
$967$	−9.48781	−0.305107	−0.152554	+	0.988295i	$0.548750\pi$
$968$	−13.2033	−0.424371
$969$	0	0
$970$	15.4830	0.497129
$971$	−14.9777	−0.480656	−0.240328	−	0.970692i	$-0.577255\pi$
$971$	−14.9777	−0.480656	−0.240328	+	0.970692i	$0.577255\pi$
$972$	−8.36826	−0.268412
$973$	8.36556	0.268188
$974$	20.1678	0.646219
$975$	7.82469	0.250591
$976$	10.8372	0.346891
$977$	−41.3302	−1.32227	−0.661135	−	0.750267i	$-0.729925\pi$
$977$	−41.3302	−1.32227	−0.661135	+	0.750267i	$0.729925\pi$
$978$	−4.73673	−0.151464
$979$	−33.6888	−1.07670
$980$	−2.38328	−0.0761312
$981$	−4.97887	−0.158963
$982$	−24.3346	−0.776547
$983$	20.0999	0.641088	0.320544	−	0.947234i	$-0.396134\pi$
$983$	20.0999	0.641088	0.320544	+	0.947234i	$0.396134\pi$
$984$	−9.82809	−0.313308
$985$	35.1169	1.11892
$986$	3.33148	0.106096
$987$	12.4509	0.396318
$988$	0	0
$989$	−0.177195	−0.00563447
$990$	−9.69559	−0.308146
$991$	−41.5083	−1.31855	−0.659277	−	0.751901i	$-0.729137\pi$
$991$	−41.5083	−1.31855	−0.659277	+	0.751901i	$0.729137\pi$
$992$	−10.2942	−0.326843
$993$	−45.4524	−1.44239
$994$	−13.4030	−0.425117
$995$	−47.3154	−1.50000
$996$	−4.53899	−0.143824
$997$	−26.5180	−0.839834	−0.419917	−	0.907563i	$-0.637941\pi$
$997$	−26.5180	−0.839834	−0.419917	+	0.907563i	$0.637941\pi$
$998$	−23.4055	−0.740887
$999$	30.9791	0.980136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bl.1.9		12
19.4	even	9		266.2.u.d.225.2	✓	24
19.5	even	9		266.2.u.d.253.2	yes	24
19.18	odd	2		5054.2.a.bm.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.d.225.2	✓	24	19.4	even	9
266.2.u.d.253.2	yes	24	19.5	even	9
5054.2.a.bl.1.9		12	1.1	even	1	trivial
5054.2.a.bm.1.4		12	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.95625 q^{3} +1.00000 q^{4} -2.38328 q^{5} -1.95625 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.826915 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.95625 q^{3} +1.00000 q^{4} -2.38328 q^{5} -1.95625 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.826915 q^{9} +2.38328 q^{10} -4.91969 q^{11} +1.95625 q^{12} +5.88177 q^{13} -1.00000 q^{14} -4.66230 q^{15} +1.00000 q^{16} -5.04131 q^{17} -0.826915 q^{18} -2.38328 q^{20} +1.95625 q^{21} +4.91969 q^{22} +0.126989 q^{23} -1.95625 q^{24} +0.680041 q^{25} -5.88177 q^{26} -4.25110 q^{27} +1.00000 q^{28} +0.660836 q^{29} +4.66230 q^{30} +10.2942 q^{31} -1.00000 q^{32} -9.62414 q^{33} +5.04131 q^{34} -2.38328 q^{35} +0.826915 q^{36} -7.28732 q^{37} +11.5062 q^{39} +2.38328 q^{40} +5.02394 q^{41} -1.95625 q^{42} -1.39536 q^{43} -4.91969 q^{44} -1.97077 q^{45} -0.126989 q^{46} +6.36469 q^{47} +1.95625 q^{48} +1.00000 q^{49} -0.680041 q^{50} -9.86206 q^{51} +5.88177 q^{52} -3.15801 q^{53} +4.25110 q^{54} +11.7250 q^{55} -1.00000 q^{56} -0.660836 q^{58} +12.7742 q^{59} -4.66230 q^{60} +10.8372 q^{61} -10.2942 q^{62} +0.826915 q^{63} +1.00000 q^{64} -14.0179 q^{65} +9.62414 q^{66} -14.3038 q^{67} -5.04131 q^{68} +0.248422 q^{69} +2.38328 q^{70} +13.4030 q^{71} -0.826915 q^{72} +5.87714 q^{73} +7.28732 q^{74} +1.33033 q^{75} -4.91969 q^{77} -11.5062 q^{78} +8.08976 q^{79} -2.38328 q^{80} -10.7970 q^{81} -5.02394 q^{82} -2.32025 q^{83} +1.95625 q^{84} +12.0149 q^{85} +1.39536 q^{86} +1.29276 q^{87} +4.91969 q^{88} +6.84776 q^{89} +1.97077 q^{90} +5.88177 q^{91} +0.126989 q^{92} +20.1381 q^{93} -6.36469 q^{94} -1.95625 q^{96} +6.49650 q^{97} -1.00000 q^{98} -4.06816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * q^99

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