LMFDB - Embedded newform 2738.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\Q(\zeta_{38})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 8x^{7} + 7x^{6} + 21x^{5} - 15x^{4} - 20x^{3} + 10x^{2} + 5x - 1 $ x^9 - x^8 - 8x^7 + 7x^6 + 21x^5 - 15x^4 - 20x^3 + 10x^2 + 5*x - 1
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			1.2
Root			$0.165159$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.72648 q^{3} +1.00000 q^{4} +0.0314505 q^{5} +2.72648 q^{6} +1.42593 q^{7} -1.00000 q^{8} +4.43367 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.72648 q^{3} +1.00000 q^{4} +0.0314505 q^{5} +2.72648 q^{6} +1.42593 q^{7} -1.00000 q^{8} +4.43367 q^{9} -0.0314505 q^{10} -2.88423 q^{11} -2.72648 q^{12} -4.12146 q^{13} -1.42593 q^{14} -0.0857489 q^{15} +1.00000 q^{16} +7.89557 q^{17} -4.43367 q^{18} +5.87288 q^{19} +0.0314505 q^{20} -3.88777 q^{21} +2.88423 q^{22} -9.03261 q^{23} +2.72648 q^{24} -4.99901 q^{25} +4.12146 q^{26} -3.90887 q^{27} +1.42593 q^{28} +3.11677 q^{29} +0.0857489 q^{30} -3.90941 q^{31} -1.00000 q^{32} +7.86378 q^{33} -7.89557 q^{34} +0.0448462 q^{35} +4.43367 q^{36} -5.87288 q^{38} +11.2371 q^{39} -0.0314505 q^{40} +1.47320 q^{41} +3.88777 q^{42} -1.61528 q^{43} -2.88423 q^{44} +0.139441 q^{45} +9.03261 q^{46} -0.804045 q^{47} -2.72648 q^{48} -4.96672 q^{49} +4.99901 q^{50} -21.5271 q^{51} -4.12146 q^{52} +7.26387 q^{53} +3.90887 q^{54} -0.0907103 q^{55} -1.42593 q^{56} -16.0123 q^{57} -3.11677 q^{58} +8.95583 q^{59} -0.0857489 q^{60} +11.4814 q^{61} +3.90941 q^{62} +6.32211 q^{63} +1.00000 q^{64} -0.129622 q^{65} -7.86378 q^{66} -2.69732 q^{67} +7.89557 q^{68} +24.6272 q^{69} -0.0448462 q^{70} +2.34472 q^{71} -4.43367 q^{72} -9.69533 q^{73} +13.6297 q^{75} +5.87288 q^{76} -4.11271 q^{77} -11.2371 q^{78} -4.63222 q^{79} +0.0314505 q^{80} -2.64358 q^{81} -1.47320 q^{82} +12.5742 q^{83} -3.88777 q^{84} +0.248319 q^{85} +1.61528 q^{86} -8.49781 q^{87} +2.88423 q^{88} +6.43862 q^{89} -0.139441 q^{90} -5.87691 q^{91} -9.03261 q^{92} +10.6589 q^{93} +0.804045 q^{94} +0.184705 q^{95} +2.72648 q^{96} +11.1627 q^{97} +4.96672 q^{98} -12.7877 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9	\( 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9} - 7 q^{10} - q^{11} - 7 q^{12} + 3 q^{13} + 14 q^{14} - 16 q^{15} + 9 q^{16} + 10 q^{17} - 8 q^{18} + 9 q^{19} + 7 q^{20} - 6 q^{21} + q^{22} - 3 q^{23} + 7 q^{24} - 10 q^{25} - 3 q^{26} - 19 q^{27} - 14 q^{28} + 12 q^{29} + 16 q^{30} + 2 q^{31} - 9 q^{32} - 14 q^{33} - 10 q^{34} - 13 q^{35} + 8 q^{36} - 9 q^{38} + 23 q^{39} - 7 q^{40} - 16 q^{41} + 6 q^{42} - 6 q^{43} - q^{44} + 40 q^{45} + 3 q^{46} - 15 q^{47} - 7 q^{48} + q^{49} + 10 q^{50} - 12 q^{51} + 3 q^{52} - 7 q^{53} + 19 q^{54} + 14 q^{55} + 14 q^{56} - 26 q^{57} - 12 q^{58} + q^{59} - 16 q^{60} + 7 q^{61} - 2 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 14 q^{66} - 66 q^{67} + 10 q^{68} + 34 q^{69} + 13 q^{70} - 15 q^{71} - 8 q^{72} - 50 q^{73} - 26 q^{75} + 9 q^{76} - 28 q^{77} - 23 q^{78} - 29 q^{79} + 7 q^{80} + 33 q^{81} + 16 q^{82} - 43 q^{83} - 6 q^{84} - 26 q^{85} + 6 q^{86} - 3 q^{87} + q^{88} + 6 q^{89} - 40 q^{90} - 30 q^{91} - 3 q^{92} + 28 q^{93} + 15 q^{94} - 12 q^{95} + 7 q^{96} + 50 q^{97} - q^{98} - 22 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9 - 7 * q^10 - q^11 - 7 * q^12 + 3 * q^13 + 14 * q^14 - 16 * q^15 + 9 * q^16 + 10 * q^17 - 8 * q^18 + 9 * q^19 + 7 * q^20 - 6 * q^21 + q^22 - 3 * q^23 + 7 * q^24 - 10 * q^25 - 3 * q^26 - 19 * q^27 - 14 * q^28 + 12 * q^29 + 16 * q^30 + 2 * q^31 - 9 * q^32 - 14 * q^33 - 10 * q^34 - 13 * q^35 + 8 * q^36 - 9 * q^38 + 23 * q^39 - 7 * q^40 - 16 * q^41 + 6 * q^42 - 6 * q^43 - q^44 + 40 * q^45 + 3 * q^46 - 15 * q^47 - 7 * q^48 + q^49 + 10 * q^50 - 12 * q^51 + 3 * q^52 - 7 * q^53 + 19 * q^54 + 14 * q^55 + 14 * q^56 - 26 * q^57 - 12 * q^58 + q^59 - 16 * q^60 + 7 * q^61 - 2 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 14 * q^66 - 66 * q^67 + 10 * q^68 + 34 * q^69 + 13 * q^70 - 15 * q^71 - 8 * q^72 - 50 * q^73 - 26 * q^75 + 9 * q^76 - 28 * q^77 - 23 * q^78 - 29 * q^79 + 7 * q^80 + 33 * q^81 + 16 * q^82 - 43 * q^83 - 6 * q^84 - 26 * q^85 + 6 * q^86 - 3 * q^87 + q^88 + 6 * q^89 - 40 * q^90 - 30 * q^91 - 3 * q^92 + 28 * q^93 + 15 * q^94 - 12 * q^95 + 7 * q^96 + 50 * q^97 - q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.72648	−1.57413	−0.787066	−	0.616869i	$-0.788401\pi$
$3$	−2.72648	−1.57413	−0.787066	+	0.616869i	$0.788401\pi$
$4$	1.00000	0.500000
$5$	0.0314505	0.0140651	0.00703254	−	0.999975i	$-0.497761\pi$
$5$	0.0314505	0.0140651	0.00703254	+	0.999975i	$0.497761\pi$
$6$	2.72648	1.11308
$7$	1.42593	0.538951	0.269476	−	0.963007i	$-0.413150\pi$
$7$	1.42593	0.538951	0.269476	+	0.963007i	$0.413150\pi$
$8$	−1.00000	−0.353553
$9$	4.43367	1.47789
$10$	−0.0314505	−0.00994551
$11$	−2.88423	−0.869627	−0.434814	−	0.900520i	$-0.643186\pi$
$11$	−2.88423	−0.869627	−0.434814	+	0.900520i	$0.643186\pi$
$12$	−2.72648	−0.787066
$13$	−4.12146	−1.14309	−0.571543	−	0.820572i	$-0.693655\pi$
$13$	−4.12146	−1.14309	−0.571543	+	0.820572i	$0.693655\pi$
$14$	−1.42593	−0.381096
$15$	−0.0857489	−0.0221403
$16$	1.00000	0.250000
$17$	7.89557	1.91496	0.957479	−	0.288504i	$-0.0931577\pi$
$17$	7.89557	1.91496	0.957479	+	0.288504i	$0.0931577\pi$
$18$	−4.43367	−1.04503
$19$	5.87288	1.34733	0.673665	−	0.739037i	$-0.264719\pi$
$19$	5.87288	1.34733	0.673665	+	0.739037i	$0.264719\pi$
$20$	0.0314505	0.00703254
$21$	−3.88777	−0.848380
$22$	2.88423	0.614919
$23$	−9.03261	−1.88343	−0.941715	−	0.336412i	$-0.890787\pi$
$23$	−9.03261	−1.88343	−0.941715	+	0.336412i	$0.890787\pi$
$24$	2.72648	0.556540
$25$	−4.99901	−0.999802
$26$	4.12146	0.808284
$27$	−3.90887	−0.752262
$28$	1.42593	0.269476
$29$	3.11677	0.578771	0.289385	−	0.957213i	$-0.406549\pi$
$29$	3.11677	0.578771	0.289385	+	0.957213i	$0.406549\pi$
$30$	0.0857489	0.0156555
$31$	−3.90941	−0.702150	−0.351075	−	0.936347i	$-0.614184\pi$
$31$	−3.90941	−0.702150	−0.351075	+	0.936347i	$0.614184\pi$
$32$	−1.00000	−0.176777
$33$	7.86378	1.36891
$34$	−7.89557	−1.35408
$35$	0.0448462	0.00758039
$36$	4.43367	0.738945
$37$	0	0
$37$	0	0
$38$	−5.87288	−0.952706
$39$	11.2371	1.79937
$40$	−0.0314505	−0.00497275
$41$	1.47320	0.230075	0.115038	−	0.993361i	$-0.463301\pi$
$41$	1.47320	0.230075	0.115038	+	0.993361i	$0.463301\pi$
$42$	3.88777	0.599895
$43$	−1.61528	−0.246328	−0.123164	−	0.992386i	$-0.539304\pi$
$43$	−1.61528	−0.246328	−0.123164	+	0.992386i	$0.539304\pi$
$44$	−2.88423	−0.434814
$45$	0.139441	0.0207866
$46$	9.03261	1.33179
$47$	−0.804045	−0.117282	−0.0586410	−	0.998279i	$-0.518677\pi$
$47$	−0.804045	−0.117282	−0.0586410	+	0.998279i	$0.518677\pi$
$48$	−2.72648	−0.393533
$49$	−4.96672	−0.709532
$50$	4.99901	0.706967
$51$	−21.5271	−3.01440
$52$	−4.12146	−0.571543
$53$	7.26387	0.997769	0.498884	−	0.866669i	$-0.333743\pi$
$53$	7.26387	0.997769	0.498884	+	0.866669i	$0.333743\pi$
$54$	3.90887	0.531929
$55$	−0.0907103	−0.0122314
$56$	−1.42593	−0.190548
$57$	−16.0123	−2.12087
$58$	−3.11677	−0.409253
$59$	8.95583	1.16595	0.582975	−	0.812490i	$-0.301889\pi$
$59$	8.95583	1.16595	0.582975	+	0.812490i	$0.301889\pi$
$60$	−0.0857489	−0.0110701
$61$	11.4814	1.47004	0.735020	−	0.678045i	$-0.237173\pi$
$61$	11.4814	1.47004	0.735020	+	0.678045i	$0.237173\pi$
$62$	3.90941	0.496495
$63$	6.32211	0.796510
$64$	1.00000	0.125000
$65$	−0.129622	−0.0160776
$66$	−7.86378	−0.967964
$67$	−2.69732	−0.329530	−0.164765	−	0.986333i	$-0.552687\pi$
$67$	−2.69732	−0.329530	−0.164765	+	0.986333i	$0.552687\pi$
$68$	7.89557	0.957479
$69$	24.6272	2.96477
$70$	−0.0448462	−0.00536014
$71$	2.34472	0.278268	0.139134	−	0.990274i	$-0.455568\pi$
$71$	2.34472	0.278268	0.139134	+	0.990274i	$0.455568\pi$
$72$	−4.43367	−0.522513
$73$	−9.69533	−1.13475	−0.567376	−	0.823459i	$-0.692041\pi$
$73$	−9.69533	−1.13475	−0.567376	+	0.823459i	$0.692041\pi$
$74$	0	0
$75$	13.6297	1.57382
$76$	5.87288	0.673665
$77$	−4.11271	−0.468687
$78$	−11.2371	−1.27235
$79$	−4.63222	−0.521165	−0.260583	−	0.965452i	$-0.583915\pi$
$79$	−4.63222	−0.521165	−0.260583	+	0.965452i	$0.583915\pi$
$80$	0.0314505	0.00351627
$81$	−2.64358	−0.293731
$82$	−1.47320	−0.162688
$83$	12.5742	1.38020	0.690099	−	0.723715i	$-0.257567\pi$
$83$	12.5742	1.38020	0.690099	+	0.723715i	$0.257567\pi$
$84$	−3.88777	−0.424190
$85$	0.248319	0.0269340
$86$	1.61528	0.174181
$87$	−8.49781	−0.911061
$88$	2.88423	0.307460
$89$	6.43862	0.682493	0.341246	−	0.939974i	$-0.389151\pi$
$89$	6.43862	0.682493	0.341246	+	0.939974i	$0.389151\pi$
$90$	−0.139441	−0.0146984
$91$	−5.87691	−0.616068
$92$	−9.03261	−0.941715
$93$	10.6589	1.10528
$94$	0.804045	0.0829309
$95$	0.184705	0.0189503
$96$	2.72648	0.278270
$97$	11.1627	1.13340	0.566702	−	0.823923i	$-0.308219\pi$
$97$	11.1627	1.13340	0.566702	+	0.823923i	$0.308219\pi$
$98$	4.96672	0.501715
$99$	−12.7877	−1.28521
$100$	−4.99901	−0.499901
$101$	−0.528878	−0.0526253	−0.0263127	−	0.999654i	$-0.508377\pi$
$101$	−0.528878	−0.0526253	−0.0263127	+	0.999654i	$0.508377\pi$
$102$	21.5271	2.13150
$103$	−5.14980	−0.507425	−0.253712	−	0.967280i	$-0.581652\pi$
$103$	−5.14980	−0.507425	−0.253712	+	0.967280i	$0.581652\pi$
$104$	4.12146	0.404142
$105$	−0.122272	−0.0119325
$106$	−7.26387	−0.705529
$107$	−15.8462	−1.53191	−0.765957	−	0.642892i	$-0.777735\pi$
$107$	−15.8462	−1.53191	−0.765957	+	0.642892i	$0.777735\pi$
$108$	−3.90887	−0.376131
$109$	15.2435	1.46007	0.730033	−	0.683411i	$-0.239504\pi$
$109$	15.2435	1.46007	0.730033	+	0.683411i	$0.239504\pi$
$110$	0.0907103	0.00864889
$111$	0	0
$112$	1.42593	0.134738
$113$	−5.25063	−0.493937	−0.246969	−	0.969023i	$-0.579434\pi$
$113$	−5.25063	−0.493937	−0.246969	+	0.969023i	$0.579434\pi$
$114$	16.0123	1.49968
$115$	−0.284080	−0.0264906
$116$	3.11677	0.289385
$117$	−18.2732	−1.68936
$118$	−8.95583	−0.824451
$119$	11.2585	1.03207
$120$	0.0857489	0.00782777
$121$	−2.68123	−0.243748
$122$	−11.4814	−1.03948
$123$	−4.01665	−0.362169
$124$	−3.90941	−0.351075
$125$	−0.314473	−0.0281274
$126$	−6.32211	−0.563218
$127$	−14.3090	−1.26972	−0.634861	−	0.772626i	$-0.718943\pi$
$127$	−14.3090	−1.26972	−0.634861	+	0.772626i	$0.718943\pi$
$128$	−1.00000	−0.0883883
$129$	4.40403	0.387753
$130$	0.129622	0.0113686
$131$	4.77275	0.416998	0.208499	−	0.978023i	$-0.433142\pi$
$131$	4.77275	0.416998	0.208499	+	0.978023i	$0.433142\pi$
$132$	7.86378	0.684454
$133$	8.37431	0.726145
$134$	2.69732	0.233013
$135$	−0.122936	−0.0105806
$136$	−7.89557	−0.677040
$137$	1.37182	0.117203	0.0586013	−	0.998281i	$-0.481336\pi$
$137$	1.37182	0.117203	0.0586013	+	0.998281i	$0.481336\pi$
$138$	−24.6272	−2.09641
$139$	−10.3946	−0.881654	−0.440827	−	0.897592i	$-0.645315\pi$
$139$	−10.3946	−0.881654	−0.440827	+	0.897592i	$0.645315\pi$
$140$	0.0448462	0.00379019
$141$	2.19221	0.184617
$142$	−2.34472	−0.196765
$143$	11.8872	0.994059
$144$	4.43367	0.369473
$145$	0.0980240	0.00814045
$146$	9.69533	0.802391
$147$	13.5416	1.11690
$148$	0	0
$149$	6.47903	0.530783	0.265391	−	0.964141i	$-0.414499\pi$
$149$	6.47903	0.530783	0.265391	+	0.964141i	$0.414499\pi$
$150$	−13.6297	−1.11286
$151$	−3.66892	−0.298572	−0.149286	−	0.988794i	$-0.547698\pi$
$151$	−3.66892	−0.298572	−0.149286	+	0.988794i	$0.547698\pi$
$152$	−5.87288	−0.476353
$153$	35.0064	2.83010
$154$	4.11271	0.331411
$155$	−0.122953	−0.00987579
$156$	11.2371	0.899684
$157$	−21.3425	−1.70332	−0.851660	−	0.524095i	$-0.824404\pi$
$157$	−21.3425	−1.70332	−0.851660	+	0.524095i	$0.824404\pi$
$158$	4.63222	0.368519
$159$	−19.8048	−1.57062
$160$	−0.0314505	−0.00248638
$161$	−12.8799	−1.01508
$162$	2.64358	0.207699
$163$	15.3995	1.20618	0.603089	−	0.797674i	$-0.293936\pi$
$163$	15.3995	1.20618	0.603089	+	0.797674i	$0.293936\pi$
$164$	1.47320	0.115038
$165$	0.247319	0.0192538
$166$	−12.5742	−0.975947
$167$	5.32319	0.411921	0.205961	−	0.978560i	$-0.433968\pi$
$167$	5.32319	0.411921	0.205961	+	0.978560i	$0.433968\pi$
$168$	3.88777	0.299948
$169$	3.98641	0.306647
$170$	−0.248319	−0.0190452
$171$	26.0384	1.99121
$172$	−1.61528	−0.123164
$173$	−1.88977	−0.143677	−0.0718384	−	0.997416i	$-0.522887\pi$
$173$	−1.88977	−0.143677	−0.0718384	+	0.997416i	$0.522887\pi$
$174$	8.49781	0.644217
$175$	−7.12824	−0.538844
$176$	−2.88423	−0.217407
$177$	−24.4179	−1.83536
$178$	−6.43862	−0.482595
$179$	−5.00892	−0.374384	−0.187192	−	0.982323i	$-0.559939\pi$
$179$	−5.00892	−0.374384	−0.187192	+	0.982323i	$0.559939\pi$
$180$	0.139441	0.0103933
$181$	−18.4546	−1.37172	−0.685860	−	0.727734i	$-0.740574\pi$
$181$	−18.4546	−1.37172	−0.685860	+	0.727734i	$0.740574\pi$
$182$	5.87691	0.435626
$183$	−31.3037	−2.31404
$184$	9.03261	0.665893
$185$	0	0
$186$	−10.6589	−0.781549
$187$	−22.7726	−1.66530
$188$	−0.804045	−0.0586410
$189$	−5.57377	−0.405432
$190$	−0.184705	−0.0133999
$191$	−18.9527	−1.37137	−0.685685	−	0.727899i	$-0.740497\pi$
$191$	−18.9527	−1.37137	−0.685685	+	0.727899i	$0.740497\pi$
$192$	−2.72648	−0.196766
$193$	1.65313	0.118995	0.0594974	−	0.998228i	$-0.481050\pi$
$193$	1.65313	0.118995	0.0594974	+	0.998228i	$0.481050\pi$
$194$	−11.1627	−0.801437
$195$	0.353410	0.0253083
$196$	−4.96672	−0.354766
$197$	−16.7249	−1.19160	−0.595800	−	0.803133i	$-0.703165\pi$
$197$	−16.7249	−1.19160	−0.595800	+	0.803133i	$0.703165\pi$
$198$	12.7877	0.908783
$199$	−18.9464	−1.34308	−0.671538	−	0.740970i	$-0.734366\pi$
$199$	−18.9464	−1.34308	−0.671538	+	0.740970i	$0.734366\pi$
$200$	4.99901	0.353483
$201$	7.35418	0.518724
$202$	0.528878	0.0372117
$203$	4.44430	0.311929
$204$	−21.5271	−1.50720
$205$	0.0463329	0.00323603
$206$	5.14980	0.358803
$207$	−40.0476	−2.78350
$208$	−4.12146	−0.285772
$209$	−16.9387	−1.17168
$210$	0.122272	0.00843757
$211$	−9.95964	−0.685650	−0.342825	−	0.939399i	$-0.611384\pi$
$211$	−9.95964	−0.685650	−0.342825	+	0.939399i	$0.611384\pi$
$212$	7.26387	0.498884
$213$	−6.39283	−0.438030
$214$	15.8462	1.08323
$215$	−0.0508014	−0.00346463
$216$	3.90887	0.265965
$217$	−5.57454	−0.378425
$218$	−15.2435	−1.03242
$219$	26.4341	1.78625
$220$	−0.0907103	−0.00611569
$221$	−32.5413	−2.18896
$222$	0	0
$223$	−24.1653	−1.61823	−0.809114	−	0.587652i	$-0.800052\pi$
$223$	−24.1653	−1.61823	−0.809114	+	0.587652i	$0.800052\pi$
$224$	−1.42593	−0.0952740
$225$	−22.1640	−1.47760
$226$	5.25063	0.349267
$227$	−17.4538	−1.15845	−0.579224	−	0.815169i	$-0.696644\pi$
$227$	−17.4538	−1.15845	−0.579224	+	0.815169i	$0.696644\pi$
$228$	−16.0123	−1.06044
$229$	−5.23622	−0.346019	−0.173009	−	0.984920i	$-0.555349\pi$
$229$	−5.23622	−0.346019	−0.173009	+	0.984920i	$0.555349\pi$
$230$	0.284080	0.0187317
$231$	11.2132	0.737774
$232$	−3.11677	−0.204626
$233$	11.4296	0.748777	0.374388	−	0.927272i	$-0.377853\pi$
$233$	11.4296	0.748777	0.374388	+	0.927272i	$0.377853\pi$
$234$	18.2732	1.19456
$235$	−0.0252876	−0.00164958
$236$	8.95583	0.582975
$237$	12.6296	0.820383
$238$	−11.2585	−0.729783
$239$	−27.9375	−1.80713	−0.903564	−	0.428454i	$-0.859058\pi$
$239$	−27.9375	−1.80713	−0.903564	+	0.428454i	$0.859058\pi$
$240$	−0.0857489	−0.00553507
$241$	−8.35465	−0.538171	−0.269085	−	0.963116i	$-0.586721\pi$
$241$	−8.35465	−0.538171	−0.269085	+	0.963116i	$0.586721\pi$
$242$	2.68123	0.172356
$243$	18.9343	1.21463
$244$	11.4814	0.735020
$245$	−0.156206	−0.00997962
$246$	4.01665	0.256092
$247$	−24.2048	−1.54011
$248$	3.90941	0.248248
$249$	−34.2832	−2.17261
$250$	0.314473	0.0198890
$251$	−1.49117	−0.0941221	−0.0470610	−	0.998892i	$-0.514986\pi$
$251$	−1.49117	−0.0941221	−0.0470610	+	0.998892i	$0.514986\pi$
$252$	6.32211	0.398255
$253$	26.0521	1.63788
$254$	14.3090	0.897829
$255$	−0.677037	−0.0423977
$256$	1.00000	0.0625000
$257$	−1.32186	−0.0824554	−0.0412277	−	0.999150i	$-0.513127\pi$
$257$	−1.32186	−0.0824554	−0.0412277	+	0.999150i	$0.513127\pi$
$258$	−4.40403	−0.274183
$259$	0	0
$260$	−0.129622	−0.00803880
$261$	13.8188	0.855359
$262$	−4.77275	−0.294862
$263$	−11.6428	−0.717924	−0.358962	−	0.933352i	$-0.616869\pi$
$263$	−11.6428	−0.717924	−0.358962	+	0.933352i	$0.616869\pi$
$264$	−7.86378	−0.483982
$265$	0.228452	0.0140337
$266$	−8.37431	−0.513462
$267$	−17.5547	−1.07433
$268$	−2.69732	−0.164765
$269$	17.7240	1.08065	0.540325	−	0.841457i	$-0.318301\pi$
$269$	17.7240	1.08065	0.540325	+	0.841457i	$0.318301\pi$
$270$	0.122936	0.00748163
$271$	3.04339	0.184873	0.0924363	−	0.995719i	$-0.470535\pi$
$271$	3.04339	0.184873	0.0924363	+	0.995719i	$0.470535\pi$
$272$	7.89557	0.478739
$273$	16.0233	0.969772
$274$	−1.37182	−0.0828748
$275$	14.4183	0.869455
$276$	24.6272	1.48238
$277$	−11.7484	−0.705893	−0.352947	−	0.935643i	$-0.614820\pi$
$277$	−11.7484	−0.705893	−0.352947	+	0.935643i	$0.614820\pi$
$278$	10.3946	0.623424
$279$	−17.3330	−1.03770
$280$	−0.0448462	−0.00268007
$281$	−8.67926	−0.517761	−0.258881	−	0.965909i	$-0.583354\pi$
$281$	−8.67926	−0.517761	−0.258881	+	0.965909i	$0.583354\pi$
$282$	−2.19221	−0.130544
$283$	−3.66303	−0.217745	−0.108872	−	0.994056i	$-0.534724\pi$
$283$	−3.66303	−0.217745	−0.108872	+	0.994056i	$0.534724\pi$
$284$	2.34472	0.139134
$285$	−0.503593	−0.0298303
$286$	−11.8872	−0.702906
$287$	2.10068	0.123999
$288$	−4.43367	−0.261257
$289$	45.3401	2.66706
$290$	−0.0980240	−0.00575617
$291$	−30.4349	−1.78413
$292$	−9.69533	−0.567376
$293$	−20.1175	−1.17528	−0.587638	−	0.809124i	$-0.699942\pi$
$293$	−20.1175	−1.17528	−0.587638	+	0.809124i	$0.699942\pi$
$294$	−13.5416	−0.789765
$295$	0.281665	0.0163992
$296$	0	0
$297$	11.2741	0.654188
$298$	−6.47903	−0.375320
$299$	37.2275	2.15292
$300$	13.6297	0.786910
$301$	−2.30328	−0.132759
$302$	3.66892	0.211122
$303$	1.44197	0.0828392
$304$	5.87288	0.336832
$305$	0.361095	0.0206762
$306$	−35.0064	−2.00118
$307$	−12.3831	−0.706740	−0.353370	−	0.935484i	$-0.614964\pi$
$307$	−12.3831	−0.706740	−0.353370	+	0.935484i	$0.614964\pi$
$308$	−4.11271	−0.234343
$309$	14.0408	0.798753
$310$	0.122953	0.00698324
$311$	−9.44392	−0.535516	−0.267758	−	0.963486i	$-0.586283\pi$
$311$	−9.44392	−0.535516	−0.267758	+	0.963486i	$0.586283\pi$
$312$	−11.2371	−0.636173
$313$	−21.4723	−1.21369	−0.606844	−	0.794821i	$-0.707565\pi$
$313$	−21.4723	−1.21369	−0.606844	+	0.794821i	$0.707565\pi$
$314$	21.3425	1.20443
$315$	0.198833	0.0112030
$316$	−4.63222	−0.260583
$317$	3.28676	0.184603	0.0923015	−	0.995731i	$-0.470578\pi$
$317$	3.28676	0.184603	0.0923015	+	0.995731i	$0.470578\pi$
$318$	19.8048	1.11060
$319$	−8.98949	−0.503315
$320$	0.0314505	0.00175813
$321$	43.2044	2.41143
$322$	12.8799	0.717767
$323$	46.3697	2.58008
$324$	−2.64358	−0.146865
$325$	20.6032	1.14286
$326$	−15.3995	−0.852897
$327$	−41.5612	−2.29834
$328$	−1.47320	−0.0813439
$329$	−1.14651	−0.0632093
$330$	−0.247319	−0.0136145
$331$	12.5840	0.691681	0.345841	−	0.938293i	$-0.387594\pi$
$331$	12.5840	0.691681	0.345841	+	0.938293i	$0.387594\pi$
$332$	12.5742	0.690099
$333$	0	0
$334$	−5.32319	−0.291272
$335$	−0.0848320	−0.00463487
$336$	−3.88777	−0.212095
$337$	10.8167	0.589225	0.294613	−	0.955617i	$-0.404809\pi$
$337$	10.8167	0.589225	0.294613	+	0.955617i	$0.404809\pi$
$338$	−3.98641	−0.216832
$339$	14.3157	0.777523
$340$	0.248319	0.0134670
$341$	11.2756	0.610609
$342$	−26.0384	−1.40799
$343$	−17.0637	−0.921354
$344$	1.61528	0.0870903
$345$	0.774537	0.0416997
$346$	1.88977	0.101595
$347$	14.8812	0.798866	0.399433	−	0.916762i	$-0.369207\pi$
$347$	14.8812	0.798866	0.399433	+	0.916762i	$0.369207\pi$
$348$	−8.49781	−0.455530
$349$	21.8440	1.16928	0.584641	−	0.811292i	$-0.301235\pi$
$349$	21.8440	1.16928	0.584641	+	0.811292i	$0.301235\pi$
$350$	7.12824	0.381021
$351$	16.1102	0.859900
$352$	2.88423	0.153730
$353$	4.94603	0.263251	0.131625	−	0.991300i	$-0.457980\pi$
$353$	4.94603	0.263251	0.131625	+	0.991300i	$0.457980\pi$
$354$	24.4179	1.29779
$355$	0.0737427	0.00391385
$356$	6.43862	0.341246
$357$	−30.6961	−1.62461
$358$	5.00892	0.264730
$359$	18.7808	0.991211	0.495605	−	0.868548i	$-0.334946\pi$
$359$	18.7808	0.991211	0.495605	+	0.868548i	$0.334946\pi$
$360$	−0.139441	−0.00734918
$361$	15.4907	0.815298
$362$	18.4546	0.969952
$363$	7.31031	0.383692
$364$	−5.87691	−0.308034
$365$	−0.304922	−0.0159604
$366$	31.3037	1.63627
$367$	−18.7585	−0.979185	−0.489592	−	0.871951i	$-0.662854\pi$
$367$	−18.7585	−0.979185	−0.489592	+	0.871951i	$0.662854\pi$
$368$	−9.03261	−0.470857
$369$	6.53169	0.340026
$370$	0	0
$371$	10.3578	0.537749
$372$	10.6589	0.552638
$373$	−28.6240	−1.48210	−0.741048	−	0.671452i	$-0.765671\pi$
$373$	−28.6240	−1.48210	−0.741048	+	0.671452i	$0.765671\pi$
$374$	22.7726	1.17754
$375$	0.857404	0.0442762
$376$	0.804045	0.0414655
$377$	−12.8457	−0.661585
$378$	5.57377	0.286684
$379$	18.2281	0.936313	0.468157	−	0.883646i	$-0.344918\pi$
$379$	18.2281	0.936313	0.468157	+	0.883646i	$0.344918\pi$
$380$	0.184705	0.00947515
$381$	39.0132	1.99871
$382$	18.9527	0.969705
$383$	−0.714686	−0.0365188	−0.0182594	−	0.999833i	$-0.505812\pi$
$383$	−0.714686	−0.0365188	−0.0182594	+	0.999833i	$0.505812\pi$
$384$	2.72648	0.139135
$385$	−0.129347	−0.00659211
$386$	−1.65313	−0.0841420
$387$	−7.16164	−0.364046
$388$	11.1627	0.566702
$389$	19.7347	1.00059	0.500296	−	0.865855i	$-0.333225\pi$
$389$	19.7347	1.00059	0.500296	+	0.865855i	$0.333225\pi$
$390$	−0.353410	−0.0178956
$391$	−71.3176	−3.60669
$392$	4.96672	0.250857
$393$	−13.0128	−0.656409
$394$	16.7249	0.842588
$395$	−0.145685	−0.00733023
$396$	−12.7877	−0.642607
$397$	33.7582	1.69428	0.847138	−	0.531373i	$-0.178324\pi$
$397$	33.7582	1.69428	0.847138	+	0.531373i	$0.178324\pi$
$398$	18.9464	0.949698
$399$	−22.8324	−1.14305
$400$	−4.99901	−0.249951
$401$	9.18432	0.458643	0.229322	−	0.973351i	$-0.426349\pi$
$401$	9.18432	0.458643	0.229322	+	0.973351i	$0.426349\pi$
$402$	−7.35418	−0.366793
$403$	16.1125	0.802619
$404$	−0.528878	−0.0263127
$405$	−0.0831418	−0.00413135
$406$	−4.44430	−0.220567
$407$	0	0
$408$	21.5271	1.06575
$409$	1.53594	0.0759473	0.0379736	−	0.999279i	$-0.487910\pi$
$409$	1.53594	0.0759473	0.0379736	+	0.999279i	$0.487910\pi$
$410$	−0.0463329	−0.00228822
$411$	−3.74024	−0.184492
$412$	−5.14980	−0.253712
$413$	12.7704	0.628390
$414$	40.0476	1.96823
$415$	0.395464	0.0194126
$416$	4.12146	0.202071
$417$	28.3405	1.38784
$418$	16.9387	0.828499
$419$	−26.5921	−1.29911	−0.649555	−	0.760314i	$-0.725045\pi$
$419$	−26.5921	−1.29911	−0.649555	+	0.760314i	$0.725045\pi$
$420$	−0.122272	−0.00596626
$421$	1.41403	0.0689157	0.0344578	−	0.999406i	$-0.489030\pi$
$421$	1.41403	0.0689157	0.0344578	+	0.999406i	$0.489030\pi$
$422$	9.95964	0.484828
$423$	−3.56487	−0.173330
$424$	−7.26387	−0.352765
$425$	−39.4701	−1.91458
$426$	6.39283	0.309734
$427$	16.3716	0.792280
$428$	−15.8462	−0.765957
$429$	−32.4102	−1.56478
$430$	0.0508014	0.00244986
$431$	24.7122	1.19035	0.595173	−	0.803598i	$-0.297083\pi$
$431$	24.7122	1.19035	0.595173	+	0.803598i	$0.297083\pi$
$432$	−3.90887	−0.188065
$433$	−30.0120	−1.44229	−0.721143	−	0.692787i	$-0.756383\pi$
$433$	−30.0120	−1.44229	−0.721143	+	0.692787i	$0.756383\pi$
$434$	5.57454	0.267587
$435$	−0.267260	−0.0128141
$436$	15.2435	0.730033
$437$	−53.0474	−2.53760
$438$	−26.4341	−1.26307
$439$	−23.5029	−1.12173	−0.560867	−	0.827906i	$-0.689532\pi$
$439$	−23.5029	−1.12173	−0.560867	+	0.827906i	$0.689532\pi$
$440$	0.0907103	0.00432444
$441$	−22.0208	−1.04861
$442$	32.5413	1.54783
$443$	−0.273380	−0.0129887	−0.00649434	−	0.999979i	$-0.502067\pi$
$443$	−0.273380	−0.0129887	−0.00649434	+	0.999979i	$0.502067\pi$
$444$	0	0
$445$	0.202498	0.00959931
$446$	24.1653	1.14426
$447$	−17.6649	−0.835522
$448$	1.42593	0.0673689
$449$	−16.1467	−0.762008	−0.381004	−	0.924573i	$-0.624422\pi$
$449$	−16.1467	−0.762008	−0.381004	+	0.924573i	$0.624422\pi$
$450$	22.1640	1.04482
$451$	−4.24905	−0.200080
$452$	−5.25063	−0.246969
$453$	10.0032	0.469992
$454$	17.4538	0.819146
$455$	−0.184832	−0.00866504
$456$	16.0123	0.749842
$457$	−35.4187	−1.65682	−0.828409	−	0.560124i	$-0.810753\pi$
$457$	−35.4187	−1.65682	−0.828409	+	0.560124i	$0.810753\pi$
$458$	5.23622	0.244672
$459$	−30.8627	−1.44055
$460$	−0.284080	−0.0132453
$461$	34.7608	1.61897	0.809487	−	0.587138i	$-0.199745\pi$
$461$	34.7608	1.61897	0.809487	+	0.587138i	$0.199745\pi$
$462$	−11.2132	−0.521685
$463$	−33.3017	−1.54766	−0.773830	−	0.633393i	$-0.781662\pi$
$463$	−33.3017	−1.54766	−0.773830	+	0.633393i	$0.781662\pi$
$464$	3.11677	0.144693
$465$	0.335227	0.0155458
$466$	−11.4296	−0.529465
$467$	1.43661	0.0664785	0.0332393	−	0.999447i	$-0.489418\pi$
$467$	1.43661	0.0664785	0.0332393	+	0.999447i	$0.489418\pi$
$468$	−18.2732	−0.844678
$469$	−3.84619	−0.177601
$470$	0.0252876	0.00116643
$471$	58.1899	2.68125
$472$	−8.95583	−0.412226
$473$	4.65885	0.214214
$474$	−12.6296	−0.580098
$475$	−29.3586	−1.34706
$476$	11.2585	0.516034
$477$	32.2056	1.47459
$478$	27.9375	1.27783
$479$	−3.51476	−0.160594	−0.0802968	−	0.996771i	$-0.525587\pi$
$479$	−3.51476	−0.160594	−0.0802968	+	0.996771i	$0.525587\pi$
$480$	0.0857489	0.00391388
$481$	0	0
$482$	8.35465	0.380544
$483$	35.1167	1.59786
$484$	−2.68123	−0.121874
$485$	0.351073	0.0159414
$486$	−18.9343	−0.858875
$487$	26.8670	1.21746	0.608731	−	0.793377i	$-0.291679\pi$
$487$	26.8670	1.21746	0.608731	+	0.793377i	$0.291679\pi$
$488$	−11.4814	−0.519738
$489$	−41.9862	−1.89868
$490$	0.156206	0.00705665
$491$	−17.0718	−0.770439	−0.385219	−	0.922825i	$-0.625874\pi$
$491$	−17.0718	−0.770439	−0.385219	+	0.922825i	$0.625874\pi$
$492$	−4.01665	−0.181084
$493$	24.6087	1.10832
$494$	24.2048	1.08903
$495$	−0.402180	−0.0180766
$496$	−3.90941	−0.175538
$497$	3.34341	0.149973
$498$	34.2832	1.53627
$499$	7.65115	0.342513	0.171256	−	0.985227i	$-0.445217\pi$
$499$	7.65115	0.342513	0.171256	+	0.985227i	$0.445217\pi$
$500$	−0.314473	−0.0140637
$501$	−14.5136	−0.648418
$502$	1.49117	0.0665544
$503$	−2.19488	−0.0978648	−0.0489324	−	0.998802i	$-0.515582\pi$
$503$	−2.19488	−0.0978648	−0.0489324	+	0.998802i	$0.515582\pi$
$504$	−6.32211	−0.281609
$505$	−0.0166335	−0.000740179 0
$506$	−26.0521	−1.15816
$507$	−10.8689	−0.482703
$508$	−14.3090	−0.634861
$509$	−3.32994	−0.147597	−0.0737986	−	0.997273i	$-0.523512\pi$
$509$	−3.32994	−0.147597	−0.0737986	+	0.997273i	$0.523512\pi$
$510$	0.677037	0.0299797
$511$	−13.8249	−0.611576
$512$	−1.00000	−0.0441942
$513$	−22.9563	−1.01354
$514$	1.32186	0.0583048
$515$	−0.161964	−0.00713697
$516$	4.40403	0.193877
$517$	2.31905	0.101992
$518$	0	0
$519$	5.15242	0.226166
$520$	0.129622	0.00568429
$521$	−2.07309	−0.0908237	−0.0454118	−	0.998968i	$-0.514460\pi$
$521$	−2.07309	−0.0908237	−0.0454118	+	0.998968i	$0.514460\pi$
$522$	−13.8188	−0.604830
$523$	−19.5625	−0.855407	−0.427704	−	0.903919i	$-0.640677\pi$
$523$	−19.5625	−0.855407	−0.427704	+	0.903919i	$0.640677\pi$
$524$	4.77275	0.208499
$525$	19.4350	0.848212
$526$	11.6428	0.507649
$527$	−30.8670	−1.34459
$528$	7.86378	0.342227
$529$	58.5881	2.54731
$530$	−0.228452	−0.00992332
$531$	39.7072	1.72315
$532$	8.37431	0.363072
$533$	−6.07174	−0.262996
$534$	17.5547	0.759668
$535$	−0.498372	−0.0215465
$536$	2.69732	0.116506
$537$	13.6567	0.589330
$538$	−17.7240	−0.764134
$539$	14.3252	0.617028
$540$	−0.122936	−0.00529031
$541$	−19.2806	−0.828937	−0.414469	−	0.910064i	$-0.636033\pi$
$541$	−19.2806	−0.828937	−0.414469	+	0.910064i	$0.636033\pi$
$542$	−3.04339	−0.130725
$543$	50.3160	2.15927
$544$	−7.89557	−0.338520
$545$	0.479417	0.0205359
$546$	−16.0233	−0.685732
$547$	−0.188089	−0.00804210	−0.00402105	−	0.999992i	$-0.501280\pi$
$547$	−0.188089	−0.00804210	−0.00402105	+	0.999992i	$0.501280\pi$
$548$	1.37182	0.0586013
$549$	50.9047	2.17256
$550$	−14.4183	−0.614798
$551$	18.3044	0.779795
$552$	−24.6272	−1.04820
$553$	−6.60522	−0.280883
$554$	11.7484	0.499142
$555$	0	0
$556$	−10.3946	−0.440827
$557$	−32.7674	−1.38840	−0.694200	−	0.719782i	$-0.744242\pi$
$557$	−32.7674	−1.38840	−0.694200	+	0.719782i	$0.744242\pi$
$558$	17.3330	0.733765
$559$	6.65732	0.281575
$560$	0.0448462	0.00189510
$561$	62.0890	2.62140
$562$	8.67926	0.366112
$563$	−29.2089	−1.23101	−0.615505	−	0.788133i	$-0.711048\pi$
$563$	−29.2089	−1.23101	−0.615505	+	0.788133i	$0.711048\pi$
$564$	2.19221	0.0923087
$565$	−0.165135	−0.00694727
$566$	3.66303	0.153969
$567$	−3.76956	−0.158307
$568$	−2.34472	−0.0983824
$569$	10.4367	0.437531	0.218766	−	0.975777i	$-0.429797\pi$
$569$	10.4367	0.437531	0.218766	+	0.975777i	$0.429797\pi$
$570$	0.503593	0.0210932
$571$	−5.94417	−0.248756	−0.124378	−	0.992235i	$-0.539694\pi$
$571$	−5.94417	−0.248756	−0.124378	+	0.992235i	$0.539694\pi$
$572$	11.8872	0.497030
$573$	51.6741	2.15872
$574$	−2.10068	−0.0876808
$575$	45.1541	1.88306
$576$	4.43367	0.184736
$577$	46.3002	1.92750	0.963752	−	0.266800i	$-0.0859664\pi$
$577$	46.3002	1.92750	0.963752	+	0.266800i	$0.0859664\pi$
$578$	−45.3401	−1.88590
$579$	−4.50721	−0.187313
$580$	0.0980240	0.00407022
$581$	17.9299	0.743859
$582$	30.4349	1.26157
$583$	−20.9506	−0.867687
$584$	9.69533	0.401195
$585$	−0.574700	−0.0237609
$586$	20.1175	0.831046
$587$	−1.87602	−0.0774318	−0.0387159	−	0.999250i	$-0.512327\pi$
$587$	−1.87602	−0.0774318	−0.0387159	+	0.999250i	$0.512327\pi$
$588$	13.5416	0.558448
$589$	−22.9595	−0.946028
$590$	−0.281665	−0.0115960
$591$	45.6000	1.87573
$592$	0	0
$593$	−41.1273	−1.68889	−0.844447	−	0.535639i	$-0.820071\pi$
$593$	−41.1273	−1.68889	−0.844447	+	0.535639i	$0.820071\pi$
$594$	−11.2741	−0.462580
$595$	0.354086	0.0145161
$596$	6.47903	0.265391
$597$	51.6569	2.11418
$598$	−37.2275	−1.52235
$599$	16.5318	0.675473	0.337737	−	0.941241i	$-0.390339\pi$
$599$	16.5318	0.675473	0.337737	+	0.941241i	$0.390339\pi$
$600$	−13.6297	−0.556429
$601$	21.9552	0.895569	0.447785	−	0.894141i	$-0.352213\pi$
$601$	21.9552	0.895569	0.447785	+	0.894141i	$0.352213\pi$
$602$	2.30328	0.0938748
$603$	−11.9590	−0.487009
$604$	−3.66892	−0.149286
$605$	−0.0843259	−0.00342834
$606$	−1.44197	−0.0585761
$607$	−30.6151	−1.24263	−0.621315	−	0.783561i	$-0.713401\pi$
$607$	−30.6151	−1.24263	−0.621315	+	0.783561i	$0.713401\pi$
$608$	−5.87288	−0.238177
$609$	−12.1173	−0.491017
$610$	−0.361095	−0.0146203
$611$	3.31384	0.134064
$612$	35.0064	1.41505
$613$	−2.87381	−0.116072	−0.0580359	−	0.998314i	$-0.518484\pi$
$613$	−2.87381	−0.116072	−0.0580359	+	0.998314i	$0.518484\pi$
$614$	12.3831	0.499741
$615$	−0.126325	−0.00509393
$616$	4.11271	0.165706
$617$	16.2965	0.656074	0.328037	−	0.944665i	$-0.393613\pi$
$617$	16.2965	0.656074	0.328037	+	0.944665i	$0.393613\pi$
$618$	−14.0408	−0.564804
$619$	−7.98772	−0.321054	−0.160527	−	0.987031i	$-0.551319\pi$
$619$	−7.98772	−0.321054	−0.160527	+	0.987031i	$0.551319\pi$
$620$	−0.122953	−0.00493790
$621$	35.3073	1.41683
$622$	9.44392	0.378667
$623$	9.18103	0.367830
$624$	11.2371	0.449842
$625$	24.9852	0.999407
$626$	21.4723	0.858208
$627$	46.1830	1.84437
$628$	−21.3425	−0.851660
$629$	0	0
$630$	−0.198833	−0.00792170
$631$	1.37450	0.0547182	0.0273591	−	0.999626i	$-0.491290\pi$
$631$	1.37450	0.0547182	0.0273591	+	0.999626i	$0.491290\pi$
$632$	4.63222	0.184260
$633$	27.1547	1.07930
$634$	−3.28676	−0.130534
$635$	−0.450026	−0.0178587
$636$	−19.8048	−0.785310
$637$	20.4701	0.811056
$638$	8.98949	0.355897
$639$	10.3957	0.411249
$640$	−0.0314505	−0.00124319
$641$	21.8776	0.864113	0.432056	−	0.901847i	$-0.357788\pi$
$641$	21.8776	0.864113	0.432056	+	0.901847i	$0.357788\pi$
$642$	−43.2044	−1.70514
$643$	−36.3614	−1.43395	−0.716976	−	0.697098i	$-0.754474\pi$
$643$	−36.3614	−1.43395	−0.716976	+	0.697098i	$0.754474\pi$
$644$	−12.8799	−0.507538
$645$	0.138509	0.00545378
$646$	−46.3697	−1.82439
$647$	21.5748	0.848192	0.424096	−	0.905617i	$-0.360592\pi$
$647$	21.5748	0.848192	0.424096	+	0.905617i	$0.360592\pi$
$648$	2.64358	0.103850
$649$	−25.8307	−1.01394
$650$	−20.6032	−0.808124
$651$	15.1989	0.595690
$652$	15.3995	0.603089
$653$	−15.0266	−0.588035	−0.294017	−	0.955800i	$-0.594992\pi$
$653$	−15.0266	−0.588035	−0.294017	+	0.955800i	$0.594992\pi$
$654$	41.5612	1.62517
$655$	0.150105	0.00586510
$656$	1.47320	0.0575189
$657$	−42.9859	−1.67704
$658$	1.14651	0.0446957
$659$	29.9183	1.16545	0.582725	−	0.812669i	$-0.301986\pi$
$659$	29.9183	1.16545	0.582725	+	0.812669i	$0.301986\pi$
$660$	0.247319	0.00962689
$661$	6.64726	0.258548	0.129274	−	0.991609i	$-0.458735\pi$
$661$	6.64726	0.258548	0.129274	+	0.991609i	$0.458735\pi$
$662$	−12.5840	−0.489092
$663$	88.7230	3.44571
$664$	−12.5742	−0.487973
$665$	0.263376	0.0102133
$666$	0	0
$667$	−28.1526	−1.09007
$668$	5.32319	0.205961
$669$	65.8861	2.54730
$670$	0.0848320	0.00327734
$671$	−33.1149	−1.27839
$672$	3.88777	0.149974
$673$	25.2502	0.973323	0.486662	−	0.873590i	$-0.338214\pi$
$673$	25.2502	0.973323	0.486662	+	0.873590i	$0.338214\pi$
$674$	−10.8167	−0.416645
$675$	19.5405	0.752113
$676$	3.98641	0.153323
$677$	−18.0493	−0.693692	−0.346846	−	0.937922i	$-0.612747\pi$
$677$	−18.0493	−0.693692	−0.346846	+	0.937922i	$0.612747\pi$
$678$	−14.3157	−0.549791
$679$	15.9173	0.610849
$680$	−0.248319	−0.00952261
$681$	47.5873	1.82355
$682$	−11.2756	−0.431766
$683$	7.62049	0.291590	0.145795	−	0.989315i	$-0.453426\pi$
$683$	7.62049	0.291590	0.145795	+	0.989315i	$0.453426\pi$
$684$	26.0384	0.995603
$685$	0.0431444	0.00164846
$686$	17.0637	0.651496
$687$	14.2764	0.544679
$688$	−1.61528	−0.0615821
$689$	−29.9377	−1.14054
$690$	−0.774537	−0.0294861
$691$	−14.7559	−0.561342	−0.280671	−	0.959804i	$-0.590557\pi$
$691$	−14.7559	−0.561342	−0.280671	+	0.959804i	$0.590557\pi$
$692$	−1.88977	−0.0718384
$693$	−18.2344	−0.692667
$694$	−14.8812	−0.564883
$695$	−0.326913	−0.0124005
$696$	8.49781	0.322109
$697$	11.6318	0.440585
$698$	−21.8440	−0.826807
$699$	−31.1625	−1.17867
$700$	−7.12824	−0.269422
$701$	−46.8162	−1.76822	−0.884111	−	0.467277i	$-0.845235\pi$
$701$	−46.8162	−1.76822	−0.884111	+	0.467277i	$0.845235\pi$
$702$	−16.1102	−0.608041
$703$	0	0
$704$	−2.88423	−0.108703
$705$	0.0689460	0.00259666
$706$	−4.94603	−0.186146
$707$	−0.754143	−0.0283625
$708$	−24.4179	−0.917679
$709$	−18.0655	−0.678465	−0.339233	−	0.940703i	$-0.610167\pi$
$709$	−18.0655	−0.678465	−0.339233	+	0.940703i	$0.610167\pi$
$710$	−0.0737427	−0.00276751
$711$	−20.5377	−0.770225
$712$	−6.43862	−0.241298
$713$	35.3122	1.32245
$714$	30.6961	1.14877
$715$	0.373859	0.0139815
$716$	−5.00892	−0.187192
$717$	76.1709	2.84466
$718$	−18.7808	−0.700892
$719$	19.5343	0.728508	0.364254	−	0.931300i	$-0.381324\pi$
$719$	19.5343	0.728508	0.364254	+	0.931300i	$0.381324\pi$
$720$	0.139441	0.00519666
$721$	−7.34326	−0.273477
$722$	−15.4907	−0.576503
$723$	22.7788	0.847151
$724$	−18.4546	−0.685860
$725$	−15.5808	−0.578656
$726$	−7.31031	−0.271311
$727$	−8.22944	−0.305213	−0.152606	−	0.988287i	$-0.548767\pi$
$727$	−8.22944	−0.305213	−0.152606	+	0.988287i	$0.548767\pi$
$728$	5.87691	0.217813
$729$	−43.6931	−1.61826
$730$	0.304922	0.0112857
$731$	−12.7536	−0.471709
$732$	−31.3037	−1.15702
$733$	16.6217	0.613936	0.306968	−	0.951720i	$-0.400686\pi$
$733$	16.6217	0.613936	0.306968	+	0.951720i	$0.400686\pi$
$734$	18.7585	0.692388
$735$	0.425891	0.0157092
$736$	9.03261	0.332946
$737$	7.77969	0.286568
$738$	−6.53169	−0.240435
$739$	−35.8385	−1.31834	−0.659171	−	0.751993i	$-0.729093\pi$
$739$	−35.8385	−1.31834	−0.659171	+	0.751993i	$0.729093\pi$
$740$	0	0
$741$	65.9938	2.42434
$742$	−10.3578	−0.380246
$743$	25.8053	0.946705	0.473352	−	0.880873i	$-0.343044\pi$
$743$	25.8053	0.946705	0.473352	+	0.880873i	$0.343044\pi$
$744$	−10.6589	−0.390774
$745$	0.203769	0.00746550
$746$	28.6240	1.04800
$747$	55.7498	2.03978
$748$	−22.7726	−0.832650
$749$	−22.5956	−0.825627
$750$	−0.857404	−0.0313080
$751$	34.2105	1.24836	0.624180	−	0.781281i	$-0.285433\pi$
$751$	34.2105	1.24836	0.624180	+	0.781281i	$0.285433\pi$
$752$	−0.804045	−0.0293205
$753$	4.06565	0.148161
$754$	12.8457	0.467811
$755$	−0.115389	−0.00419944
$756$	−5.57377	−0.202716
$757$	−16.6402	−0.604798	−0.302399	−	0.953182i	$-0.597787\pi$
$757$	−16.6402	−0.604798	−0.302399	+	0.953182i	$0.597787\pi$
$758$	−18.2281	−0.662073
$759$	−71.0304	−2.57824
$760$	−0.184705	−0.00669994
$761$	11.1801	0.405280	0.202640	−	0.979253i	$-0.435048\pi$
$761$	11.1801	0.405280	0.202640	+	0.979253i	$0.435048\pi$
$762$	−39.0132	−1.41330
$763$	21.7362	0.786905
$764$	−18.9527	−0.685685
$765$	1.10097	0.0398055
$766$	0.714686	0.0258227
$767$	−36.9111	−1.33278
$768$	−2.72648	−0.0983832
$769$	−14.2475	−0.513777	−0.256888	−	0.966441i	$-0.582697\pi$
$769$	−14.2475	−0.513777	−0.256888	+	0.966441i	$0.582697\pi$
$770$	0.129347	0.00466133
$771$	3.60402	0.129796
$772$	1.65313	0.0594974
$773$	−36.1105	−1.29880	−0.649402	−	0.760446i	$-0.724981\pi$
$773$	−36.1105	−1.29880	−0.649402	+	0.760446i	$0.724981\pi$
$774$	7.16164	0.257420
$775$	19.5432	0.702011
$776$	−11.1627	−0.400719
$777$	0	0
$778$	−19.7347	−0.707525
$779$	8.65193	0.309988
$780$	0.353410	0.0126541
$781$	−6.76272	−0.241989
$782$	71.3176	2.55031
$783$	−12.1831	−0.435387
$784$	−4.96672	−0.177383
$785$	−0.671233	−0.0239573
$786$	13.0128	0.464151
$787$	11.7830	0.420019	0.210009	−	0.977699i	$-0.432651\pi$
$787$	11.7830	0.420019	0.210009	+	0.977699i	$0.432651\pi$
$788$	−16.7249	−0.595800
$789$	31.7437	1.13011
$790$	0.145685	0.00518325
$791$	−7.48703	−0.266208
$792$	12.7877	0.454392
$793$	−47.3200	−1.68038
$794$	−33.7582	−1.19803
$795$	−0.622869	−0.0220909
$796$	−18.9464	−0.671538
$797$	53.5999	1.89861	0.949303	−	0.314364i	$-0.101791\pi$
$797$	53.5999	1.89861	0.949303	+	0.314364i	$0.101791\pi$
$798$	22.8324	0.808257
$799$	−6.34840	−0.224590
$800$	4.99901	0.176742
$801$	28.5467	1.00865
$802$	−9.18432	−0.324310
$803$	27.9635	0.986811
$804$	7.35418	0.259362
$805$	−0.405078	−0.0142771
$806$	−16.1125	−0.567537
$807$	−48.3240	−1.70108
$808$	0.528878	0.0186059
$809$	25.6901	0.903215	0.451608	−	0.892217i	$-0.350851\pi$
$809$	25.6901	0.903215	0.451608	+	0.892217i	$0.350851\pi$
$810$	0.0831418	0.00292130
$811$	−6.64298	−0.233267	−0.116633	−	0.993175i	$-0.537210\pi$
$811$	−6.64298	−0.233267	−0.116633	+	0.993175i	$0.537210\pi$
$812$	4.44430	0.155964
$813$	−8.29772	−0.291014
$814$	0	0
$815$	0.484320	0.0169650
$816$	−21.5271	−0.753599
$817$	−9.48636	−0.331886
$818$	−1.53594	−0.0537028
$819$	−26.0563	−0.910480
$820$	0.0463329	0.00161801
$821$	25.9650	0.906185	0.453093	−	0.891463i	$-0.350321\pi$
$821$	25.9650	0.906185	0.453093	+	0.891463i	$0.350321\pi$
$822$	3.74024	0.130456
$823$	−42.0489	−1.46573	−0.732867	−	0.680372i	$-0.761818\pi$
$823$	−42.0489	−1.46573	−0.732867	+	0.680372i	$0.761818\pi$
$824$	5.14980	0.179402
$825$	−39.3111	−1.36864
$826$	−12.7704	−0.444339
$827$	−39.8410	−1.38541	−0.692704	−	0.721222i	$-0.743581\pi$
$827$	−39.8410	−1.38541	−0.692704	+	0.721222i	$0.743581\pi$
$828$	−40.0476	−1.39175
$829$	−30.8697	−1.07215	−0.536075	−	0.844170i	$-0.680094\pi$
$829$	−30.8697	−1.07215	−0.536075	+	0.844170i	$0.680094\pi$
$830$	−0.395464	−0.0137268
$831$	32.0317	1.11117
$832$	−4.12146	−0.142886
$833$	−39.2151	−1.35872
$834$	−28.3405	−0.981351
$835$	0.167417	0.00579370
$836$	−16.9387	−0.585838
$837$	15.2814	0.528201
$838$	26.5921	0.918610
$839$	11.7653	0.406184	0.203092	−	0.979160i	$-0.434901\pi$
$839$	11.7653	0.406184	0.203092	+	0.979160i	$0.434901\pi$
$840$	0.122272	0.00421878
$841$	−19.2857	−0.665025
$842$	−1.41403	−0.0487307
$843$	23.6638	0.815024
$844$	−9.95964	−0.342825
$845$	0.125374	0.00431301
$846$	3.56487	0.122563
$847$	−3.82325	−0.131368
$848$	7.26387	0.249442
$849$	9.98717	0.342759
$850$	39.4701	1.35381
$851$	0	0
$852$	−6.39283	−0.219015
$853$	−8.28250	−0.283587	−0.141794	−	0.989896i	$-0.545287\pi$
$853$	−8.28250	−0.283587	−0.141794	+	0.989896i	$0.545287\pi$
$854$	−16.3716	−0.560226
$855$	0.818919	0.0280065
$856$	15.8462	0.541614
$857$	−26.0562	−0.890064	−0.445032	−	0.895515i	$-0.646808\pi$
$857$	−26.0562	−0.890064	−0.445032	+	0.895515i	$0.646808\pi$
$858$	32.4102	1.10647
$859$	42.0397	1.43437	0.717187	−	0.696880i	$-0.245429\pi$
$859$	42.0397	1.43437	0.717187	+	0.696880i	$0.245429\pi$
$860$	−0.0508014	−0.00173231
$861$	−5.72746	−0.195191
$862$	−24.7122	−0.841702
$863$	−10.7465	−0.365816	−0.182908	−	0.983130i	$-0.558551\pi$
$863$	−10.7465	−0.365816	−0.182908	+	0.983130i	$0.558551\pi$
$864$	3.90887	0.132982
$865$	−0.0594342	−0.00202082
$866$	30.0120	1.01985
$867$	−123.619	−4.19831
$868$	−5.57454	−0.189212
$869$	13.3604	0.453220
$870$	0.267260	0.00906096
$871$	11.1169	0.376681
$872$	−15.2435	−0.516212
$873$	49.4919	1.67505
$874$	53.0474	1.79436
$875$	−0.448417	−0.0151593
$876$	26.4341	0.893124
$877$	−40.8712	−1.38012	−0.690061	−	0.723751i	$-0.742416\pi$
$877$	−40.8712	−1.38012	−0.690061	+	0.723751i	$0.742416\pi$
$878$	23.5029	0.793185
$879$	54.8499	1.85004
$880$	−0.0907103	−0.00305784
$881$	−38.7909	−1.30690	−0.653449	−	0.756971i	$-0.726679\pi$
$881$	−38.7909	−1.30690	−0.653449	+	0.756971i	$0.726679\pi$
$882$	22.0208	0.741479
$883$	4.31100	0.145077	0.0725383	−	0.997366i	$-0.476890\pi$
$883$	4.31100	0.145077	0.0725383	+	0.997366i	$0.476890\pi$
$884$	−32.5413	−1.09448
$885$	−0.767953	−0.0258145
$886$	0.273380	0.00918438
$887$	22.5623	0.757567	0.378783	−	0.925485i	$-0.376343\pi$
$887$	22.5623	0.757567	0.378783	+	0.925485i	$0.376343\pi$
$888$	0	0
$889$	−20.4037	−0.684318
$890$	−0.202498	−0.00678774
$891$	7.62468	0.255437
$892$	−24.1653	−0.809114
$893$	−4.72206	−0.158018
$894$	17.6649	0.590803
$895$	−0.157533	−0.00526574
$896$	−1.42593	−0.0476370
$897$	−101.500	−3.38898
$898$	16.1467	0.538821
$899$	−12.1847	−0.406384
$900$	−22.1640	−0.738799
$901$	57.3524	1.91068
$902$	4.24905	0.141478
$903$	6.27984	0.208980
$904$	5.25063	0.174633
$905$	−0.580406	−0.0192933
$906$	−10.0032	−0.332334
$907$	23.4928	0.780066	0.390033	−	0.920801i	$-0.372464\pi$
$907$	23.4928	0.780066	0.390033	+	0.920801i	$0.372464\pi$
$908$	−17.4538	−0.579224
$909$	−2.34487	−0.0777744
$910$	0.184832	0.00612711
$911$	−6.25854	−0.207355	−0.103677	−	0.994611i	$-0.533061\pi$
$911$	−6.25854	−0.207355	−0.103677	+	0.994611i	$0.533061\pi$
$912$	−16.0123	−0.530219
$913$	−36.2668	−1.20026
$914$	35.4187	1.17155
$915$	−0.984516	−0.0325471
$916$	−5.23622	−0.173009
$917$	6.80562	0.224741
$918$	30.8627	1.01862
$919$	13.5389	0.446608	0.223304	−	0.974749i	$-0.428316\pi$
$919$	13.5389	0.446608	0.223304	+	0.974749i	$0.428316\pi$
$920$	0.284080	0.00936583
$921$	33.7622	1.11250
$922$	−34.7608	−1.14479
$923$	−9.66368	−0.318084
$924$	11.2132	0.368887
$925$	0	0
$926$	33.3017	1.09436
$927$	−22.8325	−0.749918
$928$	−3.11677	−0.102313
$929$	−58.4078	−1.91630	−0.958149	−	0.286270i	$-0.907585\pi$
$929$	−58.4078	−1.91630	−0.958149	+	0.286270i	$0.907585\pi$
$930$	−0.335227	−0.0109925
$931$	−29.1689	−0.955973
$932$	11.4296	0.374388
$933$	25.7486	0.842972
$934$	−1.43661	−0.0470074
$935$	−0.716210	−0.0234226
$936$	18.2732	0.597278
$937$	33.6423	1.09905	0.549523	−	0.835478i	$-0.314809\pi$
$937$	33.6423	1.09905	0.549523	+	0.835478i	$0.314809\pi$
$938$	3.84619	0.125583
$939$	58.5438	1.91051
$940$	−0.0252876	−0.000824790 0
$941$	8.60072	0.280375	0.140188	−	0.990125i	$-0.455229\pi$
$941$	8.60072	0.280375	0.140188	+	0.990125i	$0.455229\pi$
$942$	−58.1899	−1.89593
$943$	−13.3069	−0.433331
$944$	8.95583	0.291487
$945$	−0.175298	−0.00570244
$946$	−4.65885	−0.151472
$947$	−33.2184	−1.07945	−0.539726	−	0.841841i	$-0.681472\pi$
$947$	−33.2184	−1.07945	−0.539726	+	0.841841i	$0.681472\pi$
$948$	12.6296	0.410191
$949$	39.9589	1.29712
$950$	29.3586	0.952518
$951$	−8.96128	−0.290590
$952$	−11.2585	−0.364891
$953$	−38.3954	−1.24375	−0.621875	−	0.783117i	$-0.713629\pi$
$953$	−38.3954	−1.24375	−0.621875	+	0.783117i	$0.713629\pi$
$954$	−32.2056	−1.04269
$955$	−0.596071	−0.0192884
$956$	−27.9375	−0.903564
$957$	24.5096	0.792284
$958$	3.51476	0.113557
$959$	1.95612	0.0631665
$960$	−0.0857489	−0.00276753
$961$	−15.7165	−0.506985
$962$	0	0
$963$	−70.2570	−2.26400
$964$	−8.35465	−0.269085
$965$	0.0519916	0.00167367
$966$	−35.1167	−1.12986
$967$	34.0127	1.09377	0.546887	−	0.837206i	$-0.315813\pi$
$967$	34.0127	1.09377	0.546887	+	0.837206i	$0.315813\pi$
$968$	2.68123	0.0861780
$969$	−126.426	−4.06138
$970$	−0.351073	−0.0112723
$971$	−6.27197	−0.201277	−0.100638	−	0.994923i	$-0.532089\pi$
$971$	−6.27197	−0.201277	−0.100638	+	0.994923i	$0.532089\pi$
$972$	18.9343	0.607317
$973$	−14.8219	−0.475169
$974$	−26.8670	−0.860875
$975$	−56.1742	−1.79901
$976$	11.4814	0.367510
$977$	58.5353	1.87271	0.936356	−	0.351053i	$-0.114176\pi$
$977$	58.5353	1.87271	0.936356	+	0.351053i	$0.114176\pi$
$978$	41.9862	1.34257
$979$	−18.5705	−0.593514
$980$	−0.156206	−0.00498981
$981$	67.5849	2.15782
$982$	17.0718	0.544782
$983$	36.9272	1.17779	0.588897	−	0.808208i	$-0.299562\pi$
$983$	36.9272	1.17779	0.588897	+	0.808208i	$0.299562\pi$
$984$	4.01665	0.128046
$985$	−0.526006	−0.0167599
$986$	−24.6087	−0.783701
$987$	3.12594	0.0994997
$988$	−24.2048	−0.770057
$989$	14.5902	0.463942
$990$	0.402180	0.0127821
$991$	33.8939	1.07667	0.538337	−	0.842729i	$-0.319053\pi$
$991$	33.8939	1.07667	0.538337	+	0.842729i	$0.319053\pi$
$992$	3.90941	0.124124
$993$	−34.3101	−1.08880
$994$	−3.34341	−0.106047
$995$	−0.595873	−0.0188905
$996$	−34.2832	−1.08631
$997$	18.2898	0.579244	0.289622	−	0.957141i	$-0.406470\pi$
$997$	18.2898	0.579244	0.289622	+	0.957141i	$0.406470\pi$
$998$	−7.65115	−0.242193
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.u.1.2	✓	9
37.36	even	2		2738.2.a.v.1.2	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.u.1.2	✓	9	1.1	even	1	trivial
2738.2.a.v.1.2	yes	9	37.36	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.72648 q^{3} +1.00000 q^{4} +0.0314505 q^{5} +2.72648 q^{6} +1.42593 q^{7} -1.00000 q^{8} +4.43367 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.72648 q^{3} +1.00000 q^{4} +0.0314505 q^{5} +2.72648 q^{6} +1.42593 q^{7} -1.00000 q^{8} +4.43367 q^{9} -0.0314505 q^{10} -2.88423 q^{11} -2.72648 q^{12} -4.12146 q^{13} -1.42593 q^{14} -0.0857489 q^{15} +1.00000 q^{16} +7.89557 q^{17} -4.43367 q^{18} +5.87288 q^{19} +0.0314505 q^{20} -3.88777 q^{21} +2.88423 q^{22} -9.03261 q^{23} +2.72648 q^{24} -4.99901 q^{25} +4.12146 q^{26} -3.90887 q^{27} +1.42593 q^{28} +3.11677 q^{29} +0.0857489 q^{30} -3.90941 q^{31} -1.00000 q^{32} +7.86378 q^{33} -7.89557 q^{34} +0.0448462 q^{35} +4.43367 q^{36} -5.87288 q^{38} +11.2371 q^{39} -0.0314505 q^{40} +1.47320 q^{41} +3.88777 q^{42} -1.61528 q^{43} -2.88423 q^{44} +0.139441 q^{45} +9.03261 q^{46} -0.804045 q^{47} -2.72648 q^{48} -4.96672 q^{49} +4.99901 q^{50} -21.5271 q^{51} -4.12146 q^{52} +7.26387 q^{53} +3.90887 q^{54} -0.0907103 q^{55} -1.42593 q^{56} -16.0123 q^{57} -3.11677 q^{58} +8.95583 q^{59} -0.0857489 q^{60} +11.4814 q^{61} +3.90941 q^{62} +6.32211 q^{63} +1.00000 q^{64} -0.129622 q^{65} -7.86378 q^{66} -2.69732 q^{67} +7.89557 q^{68} +24.6272 q^{69} -0.0448462 q^{70} +2.34472 q^{71} -4.43367 q^{72} -9.69533 q^{73} +13.6297 q^{75} +5.87288 q^{76} -4.11271 q^{77} -11.2371 q^{78} -4.63222 q^{79} +0.0314505 q^{80} -2.64358 q^{81} -1.47320 q^{82} +12.5742 q^{83} -3.88777 q^{84} +0.248319 q^{85} +1.61528 q^{86} -8.49781 q^{87} +2.88423 q^{88} +6.43862 q^{89} -0.139441 q^{90} -5.87691 q^{91} -9.03261 q^{92} +10.6589 q^{93} +0.804045 q^{94} +0.184705 q^{95} +2.72648 q^{96} +11.1627 q^{97} +4.96672 q^{98} -12.7877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9	\( 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9} - 7 q^{10} - q^{11} - 7 q^{12} + 3 q^{13} + 14 q^{14} - 16 q^{15} + 9 q^{16} + 10 q^{17} - 8 q^{18} + 9 q^{19} + 7 q^{20} - 6 q^{21} + q^{22} - 3 q^{23} + 7 q^{24} - 10 q^{25} - 3 q^{26} - 19 q^{27} - 14 q^{28} + 12 q^{29} + 16 q^{30} + 2 q^{31} - 9 q^{32} - 14 q^{33} - 10 q^{34} - 13 q^{35} + 8 q^{36} - 9 q^{38} + 23 q^{39} - 7 q^{40} - 16 q^{41} + 6 q^{42} - 6 q^{43} - q^{44} + 40 q^{45} + 3 q^{46} - 15 q^{47} - 7 q^{48} + q^{49} + 10 q^{50} - 12 q^{51} + 3 q^{52} - 7 q^{53} + 19 q^{54} + 14 q^{55} + 14 q^{56} - 26 q^{57} - 12 q^{58} + q^{59} - 16 q^{60} + 7 q^{61} - 2 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 14 q^{66} - 66 q^{67} + 10 q^{68} + 34 q^{69} + 13 q^{70} - 15 q^{71} - 8 q^{72} - 50 q^{73} - 26 q^{75} + 9 q^{76} - 28 q^{77} - 23 q^{78} - 29 q^{79} + 7 q^{80} + 33 q^{81} + 16 q^{82} - 43 q^{83} - 6 q^{84} - 26 q^{85} + 6 q^{86} - 3 q^{87} + q^{88} + 6 q^{89} - 40 q^{90} - 30 q^{91} - 3 q^{92} + 28 q^{93} + 15 q^{94} - 12 q^{95} + 7 q^{96} + 50 q^{97} - q^{98} - 22 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9 - 7 * q^10 - q^11 - 7 * q^12 + 3 * q^13 + 14 * q^14 - 16 * q^15 + 9 * q^16 + 10 * q^17 - 8 * q^18 + 9 * q^19 + 7 * q^20 - 6 * q^21 + q^22 - 3 * q^23 + 7 * q^24 - 10 * q^25 - 3 * q^26 - 19 * q^27 - 14 * q^28 + 12 * q^29 + 16 * q^30 + 2 * q^31 - 9 * q^32 - 14 * q^33 - 10 * q^34 - 13 * q^35 + 8 * q^36 - 9 * q^38 + 23 * q^39 - 7 * q^40 - 16 * q^41 + 6 * q^42 - 6 * q^43 - q^44 + 40 * q^45 + 3 * q^46 - 15 * q^47 - 7 * q^48 + q^49 + 10 * q^50 - 12 * q^51 + 3 * q^52 - 7 * q^53 + 19 * q^54 + 14 * q^55 + 14 * q^56 - 26 * q^57 - 12 * q^58 + q^59 - 16 * q^60 + 7 * q^61 - 2 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 14 * q^66 - 66 * q^67 + 10 * q^68 + 34 * q^69 + 13 * q^70 - 15 * q^71 - 8 * q^72 - 50 * q^73 - 26 * q^75 + 9 * q^76 - 28 * q^77 - 23 * q^78 - 29 * q^79 + 7 * q^80 + 33 * q^81 + 16 * q^82 - 43 * q^83 - 6 * q^84 - 26 * q^85 + 6 * q^86 - 3 * q^87 + q^88 + 6 * q^89 - 40 * q^90 - 30 * q^91 - 3 * q^92 + 28 * q^93 + 15 * q^94 - 12 * q^95 + 7 * q^96 + 50 * q^97 - q^98 - 22 * q^99

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