LMFDB - Embedded newform 2738.2.a.w.1.7

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:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 8 x^{16} + 209 x^{15} - 253 x^{14} - 1996 x^{13} + 4196 x^{12} + 8667 x^{11} + \cdots + 113 $ x^18 - 8x^17 - 8x^16 + 209x^15 - 253x^14 - 1996x^13 + 4196x^12 + 8667x^11 - 24522x^10 - 18284x^9 + 68697x^8 + 20865x^7 - 97011x^6 - 20844x^5 + 64568x^4 + 17499x^3 - 13387x^2 - 3713*x + 113
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.26200$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.771034 q^{3} +1.00000 q^{4} +0.437041 q^{5} +0.771034 q^{6} -4.61128 q^{7} -1.00000 q^{8} -2.40551 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.771034 q^{3} +1.00000 q^{4} +0.437041 q^{5} +0.771034 q^{6} -4.61128 q^{7} -1.00000 q^{8} -2.40551 q^{9} -0.437041 q^{10} -1.80283 q^{11} -0.771034 q^{12} -6.12279 q^{13} +4.61128 q^{14} -0.336973 q^{15} +1.00000 q^{16} +2.20519 q^{17} +2.40551 q^{18} -1.36293 q^{19} +0.437041 q^{20} +3.55545 q^{21} +1.80283 q^{22} +0.264734 q^{23} +0.771034 q^{24} -4.80900 q^{25} +6.12279 q^{26} +4.16783 q^{27} -4.61128 q^{28} -5.46031 q^{29} +0.336973 q^{30} -6.80007 q^{31} -1.00000 q^{32} +1.39004 q^{33} -2.20519 q^{34} -2.01532 q^{35} -2.40551 q^{36} +1.36293 q^{38} +4.72088 q^{39} -0.437041 q^{40} -9.16526 q^{41} -3.55545 q^{42} -4.47531 q^{43} -1.80283 q^{44} -1.05130 q^{45} -0.264734 q^{46} +6.57080 q^{47} -0.771034 q^{48} +14.2639 q^{49} +4.80900 q^{50} -1.70027 q^{51} -6.12279 q^{52} +8.81762 q^{53} -4.16783 q^{54} -0.787910 q^{55} +4.61128 q^{56} +1.05087 q^{57} +5.46031 q^{58} +14.1979 q^{59} -0.336973 q^{60} -3.60210 q^{61} +6.80007 q^{62} +11.0925 q^{63} +1.00000 q^{64} -2.67591 q^{65} -1.39004 q^{66} +2.02599 q^{67} +2.20519 q^{68} -0.204119 q^{69} +2.01532 q^{70} +10.9636 q^{71} +2.40551 q^{72} +7.17402 q^{73} +3.70790 q^{75} -1.36293 q^{76} +8.31336 q^{77} -4.72088 q^{78} -12.0992 q^{79} +0.437041 q^{80} +4.00299 q^{81} +9.16526 q^{82} -8.24969 q^{83} +3.55545 q^{84} +0.963757 q^{85} +4.47531 q^{86} +4.21009 q^{87} +1.80283 q^{88} -17.7715 q^{89} +1.05130 q^{90} +28.2339 q^{91} +0.264734 q^{92} +5.24309 q^{93} -6.57080 q^{94} -0.595658 q^{95} +0.771034 q^{96} -4.11851 q^{97} -14.2639 q^{98} +4.33672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} - 9 q^{13} - 18 q^{14} + 4 q^{15} + 18 q^{16} - 13 q^{17} - 26 q^{18} - 2 q^{19} - 9 q^{20} + 24 q^{21} - 10 q^{22} + 11 q^{23} - 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} - 30 q^{29} - 4 q^{30} + 8 q^{31} - 18 q^{32} + 42 q^{33} + 13 q^{34} - 25 q^{35} + 26 q^{36} + 2 q^{38} + 45 q^{39} + 9 q^{40} + 5 q^{41} - 24 q^{42} + 3 q^{43} + 10 q^{44} + 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} - 49 q^{50} - 10 q^{51} - 9 q^{52} + 25 q^{53} - 29 q^{54} + 44 q^{55} - 18 q^{56} - 22 q^{57} + 30 q^{58} - 26 q^{59} + 4 q^{60} - 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} - 42 q^{66} + 23 q^{67} - 13 q^{68} + 2 q^{69} + 25 q^{70} - 25 q^{71} - 26 q^{72} + 77 q^{73} - q^{75} - 2 q^{76} - 6 q^{77} - 45 q^{78} + 13 q^{79} - 9 q^{80} + 38 q^{81} - 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} + 55 q^{87} - 10 q^{88} - 55 q^{89} - 30 q^{90} - 12 q^{91} + 11 q^{92} + 58 q^{93} - 37 q^{94} - 18 q^{95} - 8 q^{96} + 59 q^{97} - 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 - 9 * q^13 - 18 * q^14 + 4 * q^15 + 18 * q^16 - 13 * q^17 - 26 * q^18 - 2 * q^19 - 9 * q^20 + 24 * q^21 - 10 * q^22 + 11 * q^23 - 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 - 30 * q^29 - 4 * q^30 + 8 * q^31 - 18 * q^32 + 42 * q^33 + 13 * q^34 - 25 * q^35 + 26 * q^36 + 2 * q^38 + 45 * q^39 + 9 * q^40 + 5 * q^41 - 24 * q^42 + 3 * q^43 + 10 * q^44 + 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 - 49 * q^50 - 10 * q^51 - 9 * q^52 + 25 * q^53 - 29 * q^54 + 44 * q^55 - 18 * q^56 - 22 * q^57 + 30 * q^58 - 26 * q^59 + 4 * q^60 - 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 - 42 * q^66 + 23 * q^67 - 13 * q^68 + 2 * q^69 + 25 * q^70 - 25 * q^71 - 26 * q^72 + 77 * q^73 - q^75 - 2 * q^76 - 6 * q^77 - 45 * q^78 + 13 * q^79 - 9 * q^80 + 38 * q^81 - 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 + 55 * q^87 - 10 * q^88 - 55 * q^89 - 30 * q^90 - 12 * q^91 + 11 * q^92 + 58 * q^93 - 37 * q^94 - 18 * q^95 - 8 * q^96 + 59 * q^97 - 50 * q^98 + 11 * 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
$3$	−0.771034	−0.445156	−0.222578	−	0.974915i	$-0.571447\pi$
$3$	−0.771034	−0.445156	−0.222578	+	0.974915i	$0.571447\pi$
$4$	1.00000	0.500000
$5$	0.437041	0.195451	0.0977253	−	0.995213i	$-0.468843\pi$
$5$	0.437041	0.195451	0.0977253	+	0.995213i	$0.468843\pi$
$6$	0.771034	0.314773
$7$	−4.61128	−1.74290	−0.871451	−	0.490483i	$-0.836820\pi$
$7$	−4.61128	−1.74290	−0.871451	+	0.490483i	$0.836820\pi$
$8$	−1.00000	−0.353553
$9$	−2.40551	−0.801836
$10$	−0.437041	−0.138204
$11$	−1.80283	−0.543574	−0.271787	−	0.962357i	$-0.587615\pi$
$11$	−1.80283	−0.543574	−0.271787	+	0.962357i	$0.587615\pi$
$12$	−0.771034	−0.222578
$13$	−6.12279	−1.69816	−0.849078	−	0.528268i	$-0.822842\pi$
$13$	−6.12279	−1.69816	−0.849078	+	0.528268i	$0.822842\pi$
$14$	4.61128	1.23242
$15$	−0.336973	−0.0870061
$16$	1.00000	0.250000
$17$	2.20519	0.534837	0.267418	−	0.963581i	$-0.413829\pi$
$17$	2.20519	0.534837	0.267418	+	0.963581i	$0.413829\pi$
$18$	2.40551	0.566983
$19$	−1.36293	−0.312678	−0.156339	−	0.987703i	$-0.549969\pi$
$19$	−1.36293	−0.312678	−0.156339	+	0.987703i	$0.549969\pi$
$20$	0.437041	0.0977253
$21$	3.55545	0.775864
$22$	1.80283	0.384365
$23$	0.264734	0.0552009	0.0276004	−	0.999619i	$-0.491213\pi$
$23$	0.264734	0.0552009	0.0276004	+	0.999619i	$0.491213\pi$
$24$	0.771034	0.157387
$25$	−4.80900	−0.961799
$26$	6.12279	1.20078
$27$	4.16783	0.802099
$28$	−4.61128	−0.871451
$29$	−5.46031	−1.01395	−0.506977	−	0.861959i	$-0.669237\pi$
$29$	−5.46031	−1.01395	−0.506977	+	0.861959i	$0.669237\pi$
$30$	0.336973	0.0615226
$31$	−6.80007	−1.22133	−0.610665	−	0.791889i	$-0.709098\pi$
$31$	−6.80007	−1.22133	−0.610665	+	0.791889i	$0.709098\pi$
$32$	−1.00000	−0.176777
$33$	1.39004	0.241975
$34$	−2.20519	−0.378187
$35$	−2.01532	−0.340651
$36$	−2.40551	−0.400918
$37$	0	0
$37$	0	0
$38$	1.36293	0.221097
$39$	4.72088	0.755945
$40$	−0.437041	−0.0691022
$41$	−9.16526	−1.43137	−0.715687	−	0.698421i	$-0.753886\pi$
$41$	−9.16526	−1.43137	−0.715687	+	0.698421i	$0.753886\pi$
$42$	−3.55545	−0.548618
$43$	−4.47531	−0.682478	−0.341239	−	0.939977i	$-0.610847\pi$
$43$	−4.47531	−0.682478	−0.341239	+	0.939977i	$0.610847\pi$
$44$	−1.80283	−0.271787
$45$	−1.05130	−0.156719
$46$	−0.264734	−0.0390329
$47$	6.57080	0.958449	0.479225	−	0.877692i	$-0.340918\pi$
$47$	6.57080	0.958449	0.479225	+	0.877692i	$0.340918\pi$
$48$	−0.771034	−0.111289
$49$	14.2639	2.03770
$50$	4.80900	0.680095
$51$	−1.70027	−0.238086
$52$	−6.12279	−0.849078
$53$	8.81762	1.21119	0.605597	−	0.795772i	$-0.292934\pi$
$53$	8.81762	1.21119	0.605597	+	0.795772i	$0.292934\pi$
$54$	−4.16783	−0.567170
$55$	−0.787910	−0.106242
$56$	4.61128	0.616209
$57$	1.05087	0.139191
$58$	5.46031	0.716974
$59$	14.1979	1.84841	0.924204	−	0.381898i	$-0.124730\pi$
$59$	14.1979	1.84841	0.924204	+	0.381898i	$0.124730\pi$
$60$	−0.336973	−0.0435030
$61$	−3.60210	−0.461201	−0.230601	−	0.973049i	$-0.574069\pi$
$61$	−3.60210	−0.461201	−0.230601	+	0.973049i	$0.574069\pi$
$62$	6.80007	0.863610
$63$	11.0925	1.39752
$64$	1.00000	0.125000
$65$	−2.67591	−0.331906
$66$	−1.39004	−0.171102
$67$	2.02599	0.247514	0.123757	−	0.992313i	$-0.460506\pi$
$67$	2.02599	0.247514	0.123757	+	0.992313i	$0.460506\pi$
$68$	2.20519	0.267418
$69$	−0.204119	−0.0245730
$70$	2.01532	0.240877
$71$	10.9636	1.30114	0.650568	−	0.759448i	$-0.274531\pi$
$71$	10.9636	1.30114	0.650568	+	0.759448i	$0.274531\pi$
$72$	2.40551	0.283492
$73$	7.17402	0.839656	0.419828	−	0.907604i	$-0.362090\pi$
$73$	7.17402	0.839656	0.419828	+	0.907604i	$0.362090\pi$
$74$	0	0
$75$	3.70790	0.428151
$76$	−1.36293	−0.156339
$77$	8.31336	0.947395
$78$	−4.72088	−0.534534
$79$	−12.0992	−1.36127	−0.680634	−	0.732624i	$-0.738295\pi$
$79$	−12.0992	−1.36127	−0.680634	+	0.732624i	$0.738295\pi$
$80$	0.437041	0.0488626
$81$	4.00299	0.444776
$82$	9.16526	1.01213
$83$	−8.24969	−0.905521	−0.452761	−	0.891632i	$-0.649561\pi$
$83$	−8.24969	−0.905521	−0.452761	+	0.891632i	$0.649561\pi$
$84$	3.55545	0.387932
$85$	0.963757	0.104534
$86$	4.47531	0.482585
$87$	4.21009	0.451369
$88$	1.80283	0.192182
$89$	−17.7715	−1.88377	−0.941887	−	0.335930i	$-0.890949\pi$
$89$	−17.7715	−1.88377	−0.941887	+	0.335930i	$0.890949\pi$
$90$	1.05130	0.110817
$91$	28.2339	2.95972
$92$	0.264734	0.0276004
$93$	5.24309	0.543683
$94$	−6.57080	−0.677726
$95$	−0.595658	−0.0611132
$96$	0.771034	0.0786933
$97$	−4.11851	−0.418171	−0.209086	−	0.977897i	$-0.567049\pi$
$97$	−4.11851	−0.418171	−0.209086	+	0.977897i	$0.567049\pi$
$98$	−14.2639	−1.44087
$99$	4.33672	0.435857
$100$	−4.80900	−0.480900
$101$	2.18445	0.217361	0.108680	−	0.994077i	$-0.465338\pi$
$101$	2.18445	0.217361	0.108680	+	0.994077i	$0.465338\pi$
$102$	1.70027	0.168352
$103$	6.49235	0.639710	0.319855	−	0.947466i	$-0.396366\pi$
$103$	6.49235	0.639710	0.319855	+	0.947466i	$0.396366\pi$
$104$	6.12279	0.600389
$105$	1.55388	0.151643
$106$	−8.81762	−0.856443
$107$	−13.5439	−1.30934	−0.654668	−	0.755917i	$-0.727191\pi$
$107$	−13.5439	−1.30934	−0.654668	+	0.755917i	$0.727191\pi$
$108$	4.16783	0.401049
$109$	−14.7429	−1.41211	−0.706056	−	0.708156i	$-0.749527\pi$
$109$	−14.7429	−1.41211	−0.706056	+	0.708156i	$0.749527\pi$
$110$	0.787910	0.0751243
$111$	0	0
$112$	−4.61128	−0.435725
$113$	−4.86809	−0.457951	−0.228976	−	0.973432i	$-0.573538\pi$
$113$	−4.86809	−0.457951	−0.228976	+	0.973432i	$0.573538\pi$
$114$	−1.05087	−0.0984228
$115$	0.115700	0.0107890
$116$	−5.46031	−0.506977
$117$	14.7284	1.36164
$118$	−14.1979	−1.30702
$119$	−10.1687	−0.932168
$120$	0.336973	0.0307613
$121$	−7.74980	−0.704528
$122$	3.60210	0.326118
$123$	7.06673	0.637185
$124$	−6.80007	−0.610665
$125$	−4.28693	−0.383435
$126$	−11.0925	−0.988196
$127$	15.2205	1.35060	0.675299	−	0.737544i	$-0.264014\pi$
$127$	15.2205	1.35060	0.675299	+	0.737544i	$0.264014\pi$
$128$	−1.00000	−0.0883883
$129$	3.45061	0.303810
$130$	2.67591	0.234693
$131$	2.37982	0.207926	0.103963	−	0.994581i	$-0.466848\pi$
$131$	2.37982	0.207926	0.103963	+	0.994581i	$0.466848\pi$
$132$	1.39004	0.120988
$133$	6.28487	0.544968
$134$	−2.02599	−0.175019
$135$	1.82151	0.156771
$136$	−2.20519	−0.189093
$137$	6.29894	0.538155	0.269077	−	0.963119i	$-0.413281\pi$
$137$	6.29894	0.538155	0.269077	+	0.963119i	$0.413281\pi$
$138$	0.204119	0.0173758
$139$	−6.29845	−0.534228	−0.267114	−	0.963665i	$-0.586070\pi$
$139$	−6.29845	−0.534228	−0.267114	+	0.963665i	$0.586070\pi$
$140$	−2.01532	−0.170326
$141$	−5.06630	−0.426660
$142$	−10.9636	−0.920042
$143$	11.0383	0.923073
$144$	−2.40551	−0.200459
$145$	−2.38638	−0.198178
$146$	−7.17402	−0.593726
$147$	−10.9980	−0.907097
$148$	0	0
$149$	21.4374	1.75622	0.878109	−	0.478461i	$-0.158805\pi$
$149$	21.4374	1.75622	0.878109	+	0.478461i	$0.158805\pi$
$150$	−3.70790	−0.302749
$151$	−14.8068	−1.20496	−0.602480	−	0.798134i	$-0.705821\pi$
$151$	−14.8068	−1.20496	−0.602480	+	0.798134i	$0.705821\pi$
$152$	1.36293	0.110549
$153$	−5.30460	−0.428851
$154$	−8.31336	−0.669910
$155$	−2.97191	−0.238710
$156$	4.72088	0.377973
$157$	13.8800	1.10774	0.553871	−	0.832602i	$-0.313150\pi$
$157$	13.8800	1.10774	0.553871	+	0.832602i	$0.313150\pi$
$158$	12.0992	0.962561
$159$	−6.79868	−0.539171
$160$	−0.437041	−0.0345511
$161$	−1.22076	−0.0962097
$162$	−4.00299	−0.314504
$163$	18.8499	1.47644	0.738218	−	0.674562i	$-0.235668\pi$
$163$	18.8499	1.47644	0.738218	+	0.674562i	$0.235668\pi$
$164$	−9.16526	−0.715687
$165$	0.607505	0.0472942
$166$	8.24969	0.640300
$167$	8.01091	0.619903	0.309952	−	0.950752i	$-0.399687\pi$
$167$	8.01091	0.619903	0.309952	+	0.950752i	$0.399687\pi$
$168$	−3.55545	−0.274309
$169$	24.4885	1.88373
$170$	−0.963757	−0.0739168
$171$	3.27855	0.250717
$172$	−4.47531	−0.341239
$173$	−23.7768	−1.80772	−0.903860	−	0.427829i	$-0.859279\pi$
$173$	−23.7768	−1.80772	−0.903860	+	0.427829i	$0.859279\pi$
$174$	−4.21009	−0.319166
$175$	22.1756	1.67632
$176$	−1.80283	−0.135893
$177$	−10.9471	−0.822831
$178$	17.7715	1.33203
$179$	−3.46205	−0.258766	−0.129383	−	0.991595i	$-0.541300\pi$
$179$	−3.46205	−0.258766	−0.129383	+	0.991595i	$0.541300\pi$
$180$	−1.05130	−0.0783596
$181$	−4.92424	−0.366016	−0.183008	−	0.983111i	$-0.558583\pi$
$181$	−4.92424	−0.366016	−0.183008	+	0.983111i	$0.558583\pi$
$182$	−28.2339	−2.09284
$183$	2.77734	0.205307
$184$	−0.264734	−0.0195165
$185$	0	0
$186$	−5.24309	−0.384442
$187$	−3.97558	−0.290723
$188$	6.57080	0.479225
$189$	−19.2190	−1.39798
$190$	0.595658	0.0432135
$191$	19.2951	1.39615	0.698074	−	0.716026i	$-0.254041\pi$
$191$	19.2951	1.39615	0.698074	+	0.716026i	$0.254041\pi$
$192$	−0.771034	−0.0556446
$193$	−2.85313	−0.205373	−0.102686	−	0.994714i	$-0.532744\pi$
$193$	−2.85313	−0.205373	−0.102686	+	0.994714i	$0.532744\pi$
$194$	4.11851	0.295692
$195$	2.06322	0.147750
$196$	14.2639	1.01885
$197$	−4.47251	−0.318653	−0.159326	−	0.987226i	$-0.550932\pi$
$197$	−4.47251	−0.318653	−0.159326	+	0.987226i	$0.550932\pi$
$198$	−4.33672	−0.308197
$199$	8.01075	0.567867	0.283933	−	0.958844i	$-0.408361\pi$
$199$	8.01075	0.567867	0.283933	+	0.958844i	$0.408361\pi$
$200$	4.80900	0.340047
$201$	−1.56210	−0.110182
$202$	−2.18445	−0.153697
$203$	25.1791	1.76722
$204$	−1.70027	−0.119043
$205$	−4.00559	−0.279763
$206$	−6.49235	−0.452343
$207$	−0.636820	−0.0442620
$208$	−6.12279	−0.424539
$209$	2.45714	0.169964
$210$	−1.55388	−0.107228
$211$	−8.39000	−0.577591	−0.288796	−	0.957391i	$-0.593255\pi$
$211$	−8.39000	−0.577591	−0.288796	+	0.957391i	$0.593255\pi$
$212$	8.81762	0.605597
$213$	−8.45328	−0.579209
$214$	13.5439	0.925840
$215$	−1.95589	−0.133391
$216$	−4.16783	−0.283585
$217$	31.3571	2.12866
$218$	14.7429	0.998514
$219$	−5.53141	−0.373778
$220$	−0.787910	−0.0531209
$221$	−13.5019	−0.908236
$222$	0	0
$223$	14.8715	0.995869	0.497935	−	0.867215i	$-0.334092\pi$
$223$	14.8715	0.995869	0.497935	+	0.867215i	$0.334092\pi$
$224$	4.61128	0.308104
$225$	11.5681	0.771205
$226$	4.86809	0.323821
$227$	10.0974	0.670187	0.335093	−	0.942185i	$-0.391232\pi$
$227$	10.0974	0.670187	0.335093	+	0.942185i	$0.391232\pi$
$228$	1.05087	0.0695954
$229$	1.50284	0.0993102	0.0496551	−	0.998766i	$-0.484188\pi$
$229$	1.50284	0.0993102	0.0496551	+	0.998766i	$0.484188\pi$
$230$	−0.115700	−0.00762901
$231$	−6.40988	−0.421739
$232$	5.46031	0.358487
$233$	−3.35874	−0.220038	−0.110019	−	0.993929i	$-0.535091\pi$
$233$	−3.35874	−0.220038	−0.110019	+	0.993929i	$0.535091\pi$
$234$	−14.7284	−0.962826
$235$	2.87171	0.187329
$236$	14.1979	0.924204
$237$	9.32890	0.605977
$238$	10.1687	0.659142
$239$	5.36999	0.347356	0.173678	−	0.984803i	$-0.444435\pi$
$239$	5.36999	0.347356	0.173678	+	0.984803i	$0.444435\pi$
$240$	−0.336973	−0.0217515
$241$	−6.94226	−0.447190	−0.223595	−	0.974682i	$-0.571779\pi$
$241$	−6.94226	−0.447190	−0.223595	+	0.974682i	$0.571779\pi$
$242$	7.74980	0.498176
$243$	−15.5899	−1.00009
$244$	−3.60210	−0.230601
$245$	6.23392	0.398270
$246$	−7.06673	−0.450558
$247$	8.34495	0.530977
$248$	6.80007	0.431805
$249$	6.36079	0.403099
$250$	4.28693	0.271129
$251$	−15.7593	−0.994715	−0.497358	−	0.867546i	$-0.665696\pi$
$251$	−15.7593	−0.994715	−0.497358	+	0.867546i	$0.665696\pi$
$252$	11.0925	0.698760
$253$	−0.477271	−0.0300057
$254$	−15.2205	−0.955018
$255$	−0.743089	−0.0465341
$256$	1.00000	0.0625000
$257$	−18.4828	−1.15292	−0.576461	−	0.817124i	$-0.695567\pi$
$257$	−18.4828	−1.15292	−0.576461	+	0.817124i	$0.695567\pi$
$258$	−3.45061	−0.214826
$259$	0	0
$260$	−2.67591	−0.165953
$261$	13.1348	0.813025
$262$	−2.37982	−0.147026
$263$	14.0173	0.864341	0.432171	−	0.901792i	$-0.357748\pi$
$263$	14.0173	0.864341	0.432171	+	0.901792i	$0.357748\pi$
$264$	−1.39004	−0.0855512
$265$	3.85366	0.236728
$266$	−6.28487	−0.385350
$267$	13.7024	0.838574
$268$	2.02599	0.123757
$269$	5.92245	0.361098	0.180549	−	0.983566i	$-0.442213\pi$
$269$	5.92245	0.361098	0.180549	+	0.983566i	$0.442213\pi$
$270$	−1.82151	−0.110854
$271$	0.657318	0.0399292	0.0199646	−	0.999801i	$-0.493645\pi$
$271$	0.657318	0.0399292	0.0199646	+	0.999801i	$0.493645\pi$
$272$	2.20519	0.133709
$273$	−21.7693	−1.31754
$274$	−6.29894	−0.380533
$275$	8.66980	0.522809
$276$	−0.204119	−0.0122865
$277$	−13.7460	−0.825915	−0.412958	−	0.910750i	$-0.635504\pi$
$277$	−13.7460	−0.825915	−0.412958	+	0.910750i	$0.635504\pi$
$278$	6.29845	0.377756
$279$	16.3576	0.979305
$280$	2.01532	0.120438
$281$	−18.0634	−1.07757	−0.538787	−	0.842442i	$-0.681117\pi$
$281$	−18.0634	−1.07757	−0.538787	+	0.842442i	$0.681117\pi$
$282$	5.06630	0.301694
$283$	−2.66354	−0.158331	−0.0791656	−	0.996861i	$-0.525226\pi$
$283$	−2.66354	−0.158331	−0.0791656	+	0.996861i	$0.525226\pi$
$284$	10.9636	0.650568
$285$	0.459272	0.0272049
$286$	−11.0383	−0.652711
$287$	42.2636	2.49474
$288$	2.40551	0.141746
$289$	−12.1371	−0.713950
$290$	2.38638	0.140133
$291$	3.17551	0.186152
$292$	7.17402	0.419828
$293$	18.2161	1.06420	0.532098	−	0.846683i	$-0.321404\pi$
$293$	18.2161	1.06420	0.532098	+	0.846683i	$0.321404\pi$
$294$	10.9980	0.641415
$295$	6.20506	0.361273
$296$	0	0
$297$	−7.51389	−0.436000
$298$	−21.4374	−1.24183
$299$	−1.62091	−0.0937397
$300$	3.70790	0.214076
$301$	20.6369	1.18949
$302$	14.8068	0.852036
$303$	−1.68428	−0.0967595
$304$	−1.36293	−0.0781696
$305$	−1.57426	−0.0901420
$306$	5.30460	0.303244
$307$	9.72722	0.555162	0.277581	−	0.960702i	$-0.410467\pi$
$307$	9.72722	0.555162	0.277581	+	0.960702i	$0.410467\pi$
$308$	8.31336	0.473698
$309$	−5.00582	−0.284771
$310$	2.97191	0.168793
$311$	−15.8511	−0.898832	−0.449416	−	0.893323i	$-0.648368\pi$
$311$	−15.8511	−0.898832	−0.449416	+	0.893323i	$0.648368\pi$
$312$	−4.72088	−0.267267
$313$	−0.512343	−0.0289594	−0.0144797	−	0.999895i	$-0.504609\pi$
$313$	−0.512343	−0.0289594	−0.0144797	+	0.999895i	$0.504609\pi$
$314$	−13.8800	−0.783293
$315$	4.84786	0.273146
$316$	−12.0992	−0.680634
$317$	−27.6762	−1.55445	−0.777225	−	0.629223i	$-0.783373\pi$
$317$	−27.6762	−1.55445	−0.777225	+	0.629223i	$0.783373\pi$
$318$	6.79868	0.381251
$319$	9.84402	0.551159
$320$	0.437041	0.0244313
$321$	10.4428	0.582859
$322$	1.22076	0.0680305
$323$	−3.00553	−0.167232
$324$	4.00299	0.222388
$325$	29.4445	1.63328
$326$	−18.8499	−1.04400
$327$	11.3673	0.628611
$328$	9.16526	0.506067
$329$	−30.2998	−1.67048
$330$	−0.607505	−0.0334421
$331$	14.1583	0.778212	0.389106	−	0.921193i	$-0.372784\pi$
$331$	14.1583	0.778212	0.389106	+	0.921193i	$0.372784\pi$
$332$	−8.24969	−0.452761
$333$	0	0
$334$	−8.01091	−0.438338
$335$	0.885439	0.0483767
$336$	3.55545	0.193966
$337$	16.6632	0.907700	0.453850	−	0.891078i	$-0.350050\pi$
$337$	16.6632	0.907700	0.453850	+	0.891078i	$0.350050\pi$
$338$	−24.4885	−1.33200
$339$	3.75346	0.203860
$340$	0.963757	0.0522671
$341$	12.2594	0.663883
$342$	−3.27855	−0.177283
$343$	−33.4960	−1.80862
$344$	4.47531	0.241292
$345$	−0.0892083	−0.00480281
$346$	23.7768	1.27825
$347$	−18.7895	−1.00867	−0.504336	−	0.863508i	$-0.668263\pi$
$347$	−18.7895	−1.00867	−0.504336	+	0.863508i	$0.668263\pi$
$348$	4.21009	0.225684
$349$	14.2446	0.762497	0.381248	−	0.924473i	$-0.375494\pi$
$349$	14.2446	0.762497	0.381248	+	0.924473i	$0.375494\pi$
$350$	−22.1756	−1.18534
$351$	−25.5187	−1.36209
$352$	1.80283	0.0960912
$353$	2.57698	0.137159	0.0685793	−	0.997646i	$-0.478153\pi$
$353$	2.57698	0.137159	0.0685793	+	0.997646i	$0.478153\pi$
$354$	10.9471	0.581829
$355$	4.79153	0.254308
$356$	−17.7715	−0.941887
$357$	7.84045	0.414960
$358$	3.46205	0.182975
$359$	−18.3888	−0.970525	−0.485263	−	0.874368i	$-0.661276\pi$
$359$	−18.3888	−0.970525	−0.485263	+	0.874368i	$0.661276\pi$
$360$	1.05130	0.0554086
$361$	−17.1424	−0.902232
$362$	4.92424	0.258812
$363$	5.97536	0.313625
$364$	28.2339	1.47986
$365$	3.13534	0.164111
$366$	−2.77734	−0.145174
$367$	22.0762	1.15237	0.576184	−	0.817320i	$-0.304541\pi$
$367$	22.0762	1.15237	0.576184	+	0.817320i	$0.304541\pi$
$368$	0.264734	0.0138002
$369$	22.0471	1.14773
$370$	0	0
$371$	−40.6605	−2.11099
$372$	5.24309	0.271841
$373$	28.7986	1.49114	0.745568	−	0.666429i	$-0.232178\pi$
$373$	28.7986	1.49114	0.745568	+	0.666429i	$0.232178\pi$
$374$	3.97558	0.205572
$375$	3.30537	0.170688
$376$	−6.57080	−0.338863
$377$	33.4324	1.72185
$378$	19.2190	0.988520
$379$	8.26297	0.424440	0.212220	−	0.977222i	$-0.431931\pi$
$379$	8.26297	0.424440	0.212220	+	0.977222i	$0.431931\pi$
$380$	−0.595658	−0.0305566
$381$	−11.7355	−0.601228
$382$	−19.2951	−0.987226
$383$	−1.97274	−0.100802	−0.0504012	−	0.998729i	$-0.516050\pi$
$383$	−1.97274	−0.100802	−0.0504012	+	0.998729i	$0.516050\pi$
$384$	0.771034	0.0393466
$385$	3.63328	0.185169
$386$	2.85313	0.145221
$387$	10.7654	0.547235
$388$	−4.11851	−0.209086
$389$	4.87551	0.247198	0.123599	−	0.992332i	$-0.460556\pi$
$389$	4.87551	0.247198	0.123599	+	0.992332i	$0.460556\pi$
$390$	−2.06322	−0.104475
$391$	0.583789	0.0295235
$392$	−14.2639	−0.720437
$393$	−1.83492	−0.0925595
$394$	4.47251	0.225322
$395$	−5.28785	−0.266060
$396$	4.33672	0.217928
$397$	−5.51844	−0.276963	−0.138481	−	0.990365i	$-0.544222\pi$
$397$	−5.51844	−0.276963	−0.138481	+	0.990365i	$0.544222\pi$
$398$	−8.01075	−0.401543
$399$	−4.84585	−0.242596
$400$	−4.80900	−0.240450
$401$	−37.9560	−1.89543	−0.947716	−	0.319115i	$-0.896614\pi$
$401$	−37.9560	−1.89543	−0.947716	+	0.319115i	$0.896614\pi$
$402$	1.56210	0.0779107
$403$	41.6354	2.07401
$404$	2.18445	0.108680
$405$	1.74947	0.0869318
$406$	−25.1791	−1.24962
$407$	0	0
$408$	1.70027	0.0841761
$409$	6.62852	0.327759	0.163880	−	0.986480i	$-0.447599\pi$
$409$	6.62852	0.327759	0.163880	+	0.986480i	$0.447599\pi$
$410$	4.00559	0.197822
$411$	−4.85669	−0.239563
$412$	6.49235	0.319855
$413$	−65.4705	−3.22159
$414$	0.636820	0.0312980
$415$	−3.60545	−0.176985
$416$	6.12279	0.300194
$417$	4.85632	0.237815
$418$	−2.45714	−0.120183
$419$	10.5288	0.514365	0.257183	−	0.966363i	$-0.417206\pi$
$419$	10.5288	0.514365	0.257183	+	0.966363i	$0.417206\pi$
$420$	1.55388	0.0758215
$421$	17.2148	0.838999	0.419499	−	0.907756i	$-0.362206\pi$
$421$	17.2148	0.838999	0.419499	+	0.907756i	$0.362206\pi$
$422$	8.39000	0.408419
$423$	−15.8061	−0.768519
$424$	−8.81762	−0.428222
$425$	−10.6047	−0.514406
$426$	8.45328	0.409563
$427$	16.6103	0.803828
$428$	−13.5439	−0.654668
$429$	−8.51094	−0.410912
$430$	1.95589	0.0943215
$431$	38.3116	1.84541	0.922703	−	0.385511i	$-0.125975\pi$
$431$	38.3116	1.84541	0.922703	+	0.385511i	$0.125975\pi$
$432$	4.16783	0.200525
$433$	−18.6148	−0.894571	−0.447285	−	0.894391i	$-0.647609\pi$
$433$	−18.6148	−0.894571	−0.447285	+	0.894391i	$0.647609\pi$
$434$	−31.3571	−1.50519
$435$	1.83998	0.0882203
$436$	−14.7429	−0.706056
$437$	−0.360815	−0.0172601
$438$	5.53141	0.264301
$439$	−10.0078	−0.477645	−0.238822	−	0.971063i	$-0.576761\pi$
$439$	−10.0078	−0.477645	−0.238822	+	0.971063i	$0.576761\pi$
$440$	0.787910	0.0375621
$441$	−34.3120	−1.63390
$442$	13.5019	0.642220
$443$	28.9727	1.37654	0.688268	−	0.725457i	$-0.258371\pi$
$443$	28.9727	1.37654	0.688268	+	0.725457i	$0.258371\pi$
$444$	0	0
$445$	−7.76687	−0.368185
$446$	−14.8715	−0.704186
$447$	−16.5289	−0.781792
$448$	−4.61128	−0.217863
$449$	9.39644	0.443445	0.221723	−	0.975110i	$-0.428832\pi$
$449$	9.39644	0.443445	0.221723	+	0.975110i	$0.428832\pi$
$450$	−11.5681	−0.545324
$451$	16.5234	0.778057
$452$	−4.86809	−0.228976
$453$	11.4165	0.536396
$454$	−10.0974	−0.473893
$455$	12.3394	0.578479
$456$	−1.05087	−0.0492114
$457$	27.0123	1.26358	0.631791	−	0.775139i	$-0.282320\pi$
$457$	27.0123	1.26358	0.631791	+	0.775139i	$0.282320\pi$
$458$	−1.50284	−0.0702229
$459$	9.19085	0.428992
$460$	0.115700	0.00539452
$461$	−27.6922	−1.28976	−0.644878	−	0.764286i	$-0.723092\pi$
$461$	−27.6922	−1.28976	−0.644878	+	0.764286i	$0.723092\pi$
$462$	6.40988	0.298215
$463$	−27.7284	−1.28865	−0.644323	−	0.764753i	$-0.722861\pi$
$463$	−27.7284	−1.28865	−0.644323	+	0.764753i	$0.722861\pi$
$464$	−5.46031	−0.253489
$465$	2.29144	0.106263
$466$	3.35874	0.155590
$467$	−5.72621	−0.264978	−0.132489	−	0.991185i	$-0.542297\pi$
$467$	−5.72621	−0.264978	−0.132489	+	0.991185i	$0.542297\pi$
$468$	14.7284	0.680821
$469$	−9.34240	−0.431392
$470$	−2.87171	−0.132462
$471$	−10.7019	−0.493119
$472$	−14.1979	−0.653511
$473$	8.06822	0.370977
$474$	−9.32890	−0.428490
$475$	6.55434	0.300734
$476$	−10.1687	−0.466084
$477$	−21.2109	−0.971178
$478$	−5.36999	−0.245618
$479$	−16.3598	−0.747497	−0.373748	−	0.927530i	$-0.621928\pi$
$479$	−16.3598	−0.747497	−0.373748	+	0.927530i	$0.621928\pi$
$480$	0.336973	0.0153806
$481$	0	0
$482$	6.94226	0.316211
$483$	0.941250	0.0428284
$484$	−7.74980	−0.352264
$485$	−1.79996	−0.0817318
$486$	15.5899	0.707173
$487$	17.8331	0.808096	0.404048	−	0.914738i	$-0.367603\pi$
$487$	17.8331	0.808096	0.404048	+	0.914738i	$0.367603\pi$
$488$	3.60210	0.163059
$489$	−14.5339	−0.657245
$490$	−6.23392	−0.281620
$491$	−6.51454	−0.293997	−0.146999	−	0.989137i	$-0.546961\pi$
$491$	−6.51454	−0.293997	−0.146999	+	0.989137i	$0.546961\pi$
$492$	7.06673	0.318593
$493$	−12.0410	−0.542300
$494$	−8.34495	−0.375457
$495$	1.89532	0.0851885
$496$	−6.80007	−0.305332
$497$	−50.5561	−2.26775
$498$	−6.36079	−0.285034
$499$	2.43802	0.109141	0.0545705	−	0.998510i	$-0.482621\pi$
$499$	2.43802	0.109141	0.0545705	+	0.998510i	$0.482621\pi$
$500$	−4.28693	−0.191717
$501$	−6.17668	−0.275954
$502$	15.7593	0.703370
$503$	2.80021	0.124855	0.0624275	−	0.998050i	$-0.480116\pi$
$503$	2.80021	0.124855	0.0624275	+	0.998050i	$0.480116\pi$
$504$	−11.0925	−0.494098
$505$	0.954692	0.0424833
$506$	0.477271	0.0212173
$507$	−18.8815	−0.838556
$508$	15.2205	0.675299
$509$	16.7670	0.743184	0.371592	−	0.928396i	$-0.378812\pi$
$509$	16.7670	0.743184	0.371592	+	0.928396i	$0.378812\pi$
$510$	0.743089	0.0329045
$511$	−33.0815	−1.46344
$512$	−1.00000	−0.0441942
$513$	−5.68047	−0.250799
$514$	18.4828	0.815239
$515$	2.83742	0.125032
$516$	3.45061	0.151905
$517$	−11.8460	−0.520988
$518$	0	0
$519$	18.3327	0.804718
$520$	2.67591	0.117346
$521$	−28.4899	−1.24816	−0.624082	−	0.781359i	$-0.714527\pi$
$521$	−28.4899	−1.24816	−0.624082	+	0.781359i	$0.714527\pi$
$522$	−13.1348	−0.574896
$523$	29.5378	1.29160	0.645798	−	0.763508i	$-0.276525\pi$
$523$	29.5378	1.29160	0.645798	+	0.763508i	$0.276525\pi$
$524$	2.37982	0.103963
$525$	−17.0982	−0.746225
$526$	−14.0173	−0.611181
$527$	−14.9954	−0.653212
$528$	1.39004	0.0604938
$529$	−22.9299	−0.996953
$530$	−3.85366	−0.167392
$531$	−34.1531	−1.48212
$532$	6.28487	0.272484
$533$	56.1170	2.43070
$534$	−13.7024	−0.592962
$535$	−5.91922	−0.255910
$536$	−2.02599	−0.0875093
$537$	2.66936	0.115191
$538$	−5.92245	−0.255335
$539$	−25.7154	−1.10764
$540$	1.82151	0.0783853
$541$	24.4083	1.04939	0.524697	−	0.851289i	$-0.324178\pi$
$541$	24.4083	1.04939	0.524697	+	0.851289i	$0.324178\pi$
$542$	−0.657318	−0.0282342
$543$	3.79675	0.162934
$544$	−2.20519	−0.0945467
$545$	−6.44324	−0.275998
$546$	21.7693	0.931640
$547$	−15.4314	−0.659798	−0.329899	−	0.944016i	$-0.607015\pi$
$547$	−15.4314	−0.659798	−0.329899	+	0.944016i	$0.607015\pi$
$548$	6.29894	0.269077
$549$	8.66487	0.369807
$550$	−8.66980	−0.369682
$551$	7.44205	0.317042
$552$	0.204119	0.00868788
$553$	55.7929	2.37255
$554$	13.7460	0.584010
$555$	0	0
$556$	−6.29845	−0.267114
$557$	7.37862	0.312642	0.156321	−	0.987706i	$-0.450037\pi$
$557$	7.37862	0.312642	0.156321	+	0.987706i	$0.450037\pi$
$558$	−16.3576	−0.692474
$559$	27.4014	1.15895
$560$	−2.01532	−0.0851628
$561$	3.06531	0.129417
$562$	18.0634	0.761959
$563$	12.6815	0.534462	0.267231	−	0.963632i	$-0.413891\pi$
$563$	12.6815	0.534462	0.267231	+	0.963632i	$0.413891\pi$
$564$	−5.06630	−0.213330
$565$	−2.12755	−0.0895069
$566$	2.66354	0.111957
$567$	−18.4589	−0.775201
$568$	−10.9636	−0.460021
$569$	10.2519	0.429782	0.214891	−	0.976638i	$-0.431060\pi$
$569$	10.2519	0.429782	0.214891	+	0.976638i	$0.431060\pi$
$570$	−0.459272	−0.0192368
$571$	−40.6996	−1.70322	−0.851612	−	0.524172i	$-0.824375\pi$
$571$	−40.6996	−1.70322	−0.851612	+	0.524172i	$0.824375\pi$
$572$	11.0383	0.461536
$573$	−14.8772	−0.621504
$574$	−42.2636	−1.76405
$575$	−1.27311	−0.0530922
$576$	−2.40551	−0.100229
$577$	−31.9538	−1.33026	−0.665128	−	0.746729i	$-0.731623\pi$
$577$	−31.9538	−1.33026	−0.665128	+	0.746729i	$0.731623\pi$
$578$	12.1371	0.504839
$579$	2.19986	0.0914231
$580$	−2.38638	−0.0990890
$581$	38.0416	1.57823
$582$	−3.17551	−0.131629
$583$	−15.8967	−0.658373
$584$	−7.17402	−0.296863
$585$	6.43692	0.266134
$586$	−18.2161	−0.752501
$587$	−25.5344	−1.05392	−0.526960	−	0.849890i	$-0.676668\pi$
$587$	−25.5344	−1.05392	−0.526960	+	0.849890i	$0.676668\pi$
$588$	−10.9980	−0.453549
$589$	9.26805	0.381883
$590$	−6.20506	−0.255458
$591$	3.44845	0.141850
$592$	0	0
$593$	8.36087	0.343340	0.171670	−	0.985155i	$-0.445084\pi$
$593$	8.36087	0.343340	0.171670	+	0.985155i	$0.445084\pi$
$594$	7.51389	0.308298
$595$	−4.44416	−0.182193
$596$	21.4374	0.878109
$597$	−6.17656	−0.252790
$598$	1.62091	0.0662840
$599$	−33.0454	−1.35020	−0.675098	−	0.737728i	$-0.735899\pi$
$599$	−33.0454	−1.35020	−0.675098	+	0.737728i	$0.735899\pi$
$600$	−3.70790	−0.151374
$601$	−24.7407	−1.00919	−0.504597	−	0.863355i	$-0.668359\pi$
$601$	−24.7407	−1.00919	−0.504597	+	0.863355i	$0.668359\pi$
$602$	−20.6369	−0.841098
$603$	−4.87353	−0.198465
$604$	−14.8068	−0.602480
$605$	−3.38698	−0.137700
$606$	1.68428	0.0684193
$607$	−4.91360	−0.199437	−0.0997184	−	0.995016i	$-0.531794\pi$
$607$	−4.91360	−0.199437	−0.0997184	+	0.995016i	$0.531794\pi$
$608$	1.36293	0.0552743
$609$	−19.4139	−0.786691
$610$	1.57426	0.0637400
$611$	−40.2316	−1.62760
$612$	−5.30460	−0.214426
$613$	7.85791	0.317378	0.158689	−	0.987329i	$-0.449273\pi$
$613$	7.85791	0.317378	0.158689	+	0.987329i	$0.449273\pi$
$614$	−9.72722	−0.392559
$615$	3.08845	0.124538
$616$	−8.31336	−0.334955
$617$	−15.2033	−0.612062	−0.306031	−	0.952022i	$-0.599001\pi$
$617$	−15.2033	−0.612062	−0.306031	+	0.952022i	$0.599001\pi$
$618$	5.00582	0.201364
$619$	−12.0193	−0.483097	−0.241548	−	0.970389i	$-0.577655\pi$
$619$	−12.0193	−0.483097	−0.241548	+	0.970389i	$0.577655\pi$
$620$	−2.97191	−0.119355
$621$	1.10337	0.0442766
$622$	15.8511	0.635570
$623$	81.9494	3.28323
$624$	4.72088	0.188986
$625$	22.1714	0.886857
$626$	0.512343	0.0204774
$627$	−1.89454	−0.0756605
$628$	13.8800	0.553871
$629$	0	0
$630$	−4.84786	−0.193143
$631$	−10.6060	−0.422220	−0.211110	−	0.977462i	$-0.567708\pi$
$631$	−10.6060	−0.422220	−0.211110	+	0.977462i	$0.567708\pi$
$632$	12.0992	0.481281
$633$	6.46897	0.257119
$634$	27.6762	1.09916
$635$	6.65197	0.263975
$636$	−6.79868	−0.269585
$637$	−87.3350	−3.46034
$638$	−9.84402	−0.389728
$639$	−26.3729	−1.04330
$640$	−0.437041	−0.0172756
$641$	−15.3996	−0.608248	−0.304124	−	0.952632i	$-0.598364\pi$
$641$	−15.3996	−0.608248	−0.304124	+	0.952632i	$0.598364\pi$
$642$	−10.4428	−0.412144
$643$	−9.29202	−0.366441	−0.183221	−	0.983072i	$-0.558652\pi$
$643$	−9.29202	−0.366441	−0.183221	+	0.983072i	$0.558652\pi$
$644$	−1.22076	−0.0481048
$645$	1.50806	0.0593797
$646$	3.00553	0.118251
$647$	47.9199	1.88393	0.941964	−	0.335715i	$-0.108978\pi$
$647$	47.9199	1.88393	0.941964	+	0.335715i	$0.108978\pi$
$648$	−4.00299	−0.157252
$649$	−25.5964	−1.00475
$650$	−29.4445	−1.15491
$651$	−24.1773	−0.947585
$652$	18.8499	0.738218
$653$	−11.9266	−0.466723	−0.233361	−	0.972390i	$-0.574973\pi$
$653$	−11.9266	−0.466723	−0.233361	+	0.972390i	$0.574973\pi$
$654$	−11.3673	−0.444495
$655$	1.04008	0.0406392
$656$	−9.16526	−0.357843
$657$	−17.2572	−0.673266
$658$	30.2998	1.18121
$659$	−18.0042	−0.701343	−0.350672	−	0.936499i	$-0.614047\pi$
$659$	−18.0042	−0.701343	−0.350672	+	0.936499i	$0.614047\pi$
$660$	0.607505	0.0236471
$661$	−36.9012	−1.43529	−0.717646	−	0.696408i	$-0.754780\pi$
$661$	−36.9012	−1.43529	−0.717646	+	0.696408i	$0.754780\pi$
$662$	−14.1583	−0.550279
$663$	10.4104	0.404307
$664$	8.24969	0.320150
$665$	2.74675	0.106514
$666$	0	0
$667$	−1.44553	−0.0559712
$668$	8.01091	0.309952
$669$	−11.4664	−0.443318
$670$	−0.885439	−0.0342075
$671$	6.49397	0.250697
$672$	−3.55545	−0.137155
$673$	33.8175	1.30357	0.651784	−	0.758405i	$-0.274021\pi$
$673$	33.8175	1.30357	0.651784	+	0.758405i	$0.274021\pi$
$674$	−16.6632	−0.641841
$675$	−20.0431	−0.771458
$676$	24.4885	0.941867
$677$	−43.1009	−1.65650	−0.828252	−	0.560356i	$-0.810664\pi$
$677$	−43.1009	−1.65650	−0.828252	+	0.560356i	$0.810664\pi$
$678$	−3.75346	−0.144151
$679$	18.9916	0.728831
$680$	−0.963757	−0.0369584
$681$	−7.78542	−0.298338
$682$	−12.2594	−0.469436
$683$	−29.4821	−1.12810	−0.564050	−	0.825740i	$-0.690758\pi$
$683$	−29.4821	−1.12810	−0.564050	+	0.825740i	$0.690758\pi$
$684$	3.27855	0.125358
$685$	2.75289	0.105183
$686$	33.4960	1.27888
$687$	−1.15874	−0.0442086
$688$	−4.47531	−0.170620
$689$	−53.9884	−2.05680
$690$	0.0892083	0.00339610
$691$	21.3199	0.811048	0.405524	−	0.914084i	$-0.367089\pi$
$691$	21.3199	0.811048	0.405524	+	0.914084i	$0.367089\pi$
$692$	−23.7768	−0.903860
$693$	−19.9978	−0.759655
$694$	18.7895	0.713238
$695$	−2.75268	−0.104415
$696$	−4.21009	−0.159583
$697$	−20.2111	−0.765551
$698$	−14.2446	−0.539167
$699$	2.58970	0.0979514
$700$	22.1756	0.838160
$701$	23.2915	0.879709	0.439854	−	0.898069i	$-0.355030\pi$
$701$	23.2915	0.879709	0.439854	+	0.898069i	$0.355030\pi$
$702$	25.5187	0.963142
$703$	0	0
$704$	−1.80283	−0.0679467
$705$	−2.21418	−0.0833909
$706$	−2.57698	−0.0969857
$707$	−10.0731	−0.378838
$708$	−10.9471	−0.411416
$709$	−2.25990	−0.0848725	−0.0424362	−	0.999099i	$-0.513512\pi$
$709$	−2.25990	−0.0848725	−0.0424362	+	0.999099i	$0.513512\pi$
$710$	−4.79153	−0.179823
$711$	29.1047	1.09151
$712$	17.7715	0.666015
$713$	−1.80021	−0.0674184
$714$	−7.84045	−0.293421
$715$	4.82421	0.180415
$716$	−3.46205	−0.129383
$717$	−4.14044	−0.154628
$718$	18.3888	0.686265
$719$	−6.96984	−0.259931	−0.129966	−	0.991518i	$-0.541487\pi$
$719$	−6.96984	−0.259931	−0.129966	+	0.991518i	$0.541487\pi$
$720$	−1.05130	−0.0391798
$721$	−29.9381	−1.11495
$722$	17.1424	0.637975
$723$	5.35271	0.199070
$724$	−4.92424	−0.183008
$725$	26.2586	0.975221
$726$	−5.97536	−0.221766
$727$	−29.8920	−1.10863	−0.554316	−	0.832306i	$-0.687020\pi$
$727$	−29.8920	−1.10863	−0.554316	+	0.832306i	$0.687020\pi$
$728$	−28.2339	−1.04642
$729$	0.0113948	0.000422030 0
$730$	−3.13534	−0.116044
$731$	−9.86890	−0.365014
$732$	2.77734	0.102653
$733$	27.8795	1.02975	0.514876	−	0.857265i	$-0.327838\pi$
$733$	27.8795	1.02975	0.514876	+	0.857265i	$0.327838\pi$
$734$	−22.0762	−0.814847
$735$	−4.80656	−0.177293
$736$	−0.264734	−0.00975823
$737$	−3.65251	−0.134542
$738$	−22.0471	−0.811565
$739$	−13.3934	−0.492684	−0.246342	−	0.969183i	$-0.579229\pi$
$739$	−13.3934	−0.492684	−0.246342	+	0.969183i	$0.579229\pi$
$740$	0	0
$741$	−6.43424	−0.236368
$742$	40.6605	1.49270
$743$	0.0648738	0.00237999	0.00118999	−	0.999999i	$-0.499621\pi$
$743$	0.0648738	0.00237999	0.00118999	+	0.999999i	$0.499621\pi$
$744$	−5.24309	−0.192221
$745$	9.36900	0.343254
$746$	−28.7986	−1.05439
$747$	19.8447	0.726079
$748$	−3.97558	−0.145362
$749$	62.4546	2.28204
$750$	−3.30537	−0.120695
$751$	44.0394	1.60702	0.803510	−	0.595292i	$-0.202964\pi$
$751$	44.0394	1.60702	0.803510	+	0.595292i	$0.202964\pi$
$752$	6.57080	0.239612
$753$	12.1509	0.442804
$754$	−33.4324	−1.21753
$755$	−6.47118	−0.235510
$756$	−19.2190	−0.698989
$757$	−26.9804	−0.980619	−0.490309	−	0.871548i	$-0.663116\pi$
$757$	−26.9804	−0.980619	−0.490309	+	0.871548i	$0.663116\pi$
$758$	−8.26297	−0.300125
$759$	0.367992	0.0133573
$760$	0.595658	0.0216068
$761$	26.3086	0.953687	0.476844	−	0.878988i	$-0.341781\pi$
$761$	26.3086	0.953687	0.476844	+	0.878988i	$0.341781\pi$
$762$	11.7355	0.425132
$763$	67.9836	2.46117
$764$	19.2951	0.698074
$765$	−2.31833	−0.0838192
$766$	1.97274	0.0712781
$767$	−86.9307	−3.13889
$768$	−0.771034	−0.0278223
$769$	11.5497	0.416493	0.208247	−	0.978076i	$-0.433224\pi$
$769$	11.5497	0.416493	0.208247	+	0.978076i	$0.433224\pi$
$770$	−3.63328	−0.130934
$771$	14.2508	0.513231
$772$	−2.85313	−0.102686
$773$	−10.3121	−0.370899	−0.185449	−	0.982654i	$-0.559374\pi$
$773$	−10.3121	−0.370899	−0.185449	+	0.982654i	$0.559374\pi$
$774$	−10.7654	−0.386954
$775$	32.7015	1.17467
$776$	4.11851	0.147846
$777$	0	0
$778$	−4.87551	−0.174796
$779$	12.4916	0.447560
$780$	2.06322	0.0738750
$781$	−19.7655	−0.707263
$782$	−0.583789	−0.0208762
$783$	−22.7577	−0.813292
$784$	14.2639	0.509426
$785$	6.06612	0.216509
$786$	1.83492	0.0654495
$787$	42.1958	1.50412	0.752059	−	0.659095i	$-0.229061\pi$
$787$	42.1958	1.50412	0.752059	+	0.659095i	$0.229061\pi$
$788$	−4.47251	−0.159326
$789$	−10.8078	−0.384767
$790$	5.28785	0.188133
$791$	22.4481	0.798164
$792$	−4.33672	−0.154099
$793$	22.0549	0.783191
$794$	5.51844	0.195842
$795$	−2.97130	−0.105381
$796$	8.01075	0.283933
$797$	−12.5500	−0.444543	−0.222272	−	0.974985i	$-0.571347\pi$
$797$	−12.5500	−0.444543	−0.222272	+	0.974985i	$0.571347\pi$
$798$	4.84585	0.171541
$799$	14.4898	0.512614
$800$	4.80900	0.170024
$801$	42.7494	1.51048
$802$	37.9560	1.34027
$803$	−12.9335	−0.456415
$804$	−1.56210	−0.0550912
$805$	−0.533524	−0.0188042
$806$	−41.6354	−1.46654
$807$	−4.56641	−0.160745
$808$	−2.18445	−0.0768486
$809$	30.4565	1.07079	0.535397	−	0.844601i	$-0.320162\pi$
$809$	30.4565	1.07079	0.535397	+	0.844601i	$0.320162\pi$
$810$	−1.74947	−0.0614700
$811$	24.9265	0.875286	0.437643	−	0.899149i	$-0.355813\pi$
$811$	24.9265	0.875286	0.437643	+	0.899149i	$0.355813\pi$
$812$	25.1791	0.883612
$813$	−0.506814	−0.0177748
$814$	0	0
$815$	8.23816	0.288570
$816$	−1.70027	−0.0595215
$817$	6.09955	0.213396
$818$	−6.62852	−0.231761
$819$	−67.9169	−2.37321
$820$	−4.00559	−0.139881
$821$	35.9315	1.25402	0.627008	−	0.779013i	$-0.284279\pi$
$821$	35.9315	1.25402	0.627008	+	0.779013i	$0.284279\pi$
$822$	4.85669	0.169397
$823$	8.77287	0.305803	0.152902	−	0.988241i	$-0.451138\pi$
$823$	8.77287	0.305803	0.152902	+	0.988241i	$0.451138\pi$
$824$	−6.49235	−0.226172
$825$	−6.68471	−0.232732
$826$	65.4705	2.27801
$827$	−2.05039	−0.0712992	−0.0356496	−	0.999364i	$-0.511350\pi$
$827$	−2.05039	−0.0712992	−0.0356496	+	0.999364i	$0.511350\pi$
$828$	−0.636820	−0.0221310
$829$	4.74434	0.164778	0.0823888	−	0.996600i	$-0.473745\pi$
$829$	4.74434	0.164778	0.0823888	+	0.996600i	$0.473745\pi$
$830$	3.60545	0.125147
$831$	10.5986	0.367662
$832$	−6.12279	−0.212269
$833$	31.4547	1.08984
$834$	−4.85632	−0.168161
$835$	3.50110	0.121160
$836$	2.45714	0.0849819
$837$	−28.3415	−0.979627
$838$	−10.5288	−0.363711
$839$	38.6738	1.33517	0.667584	−	0.744535i	$-0.267329\pi$
$839$	38.6738	1.33517	0.667584	+	0.744535i	$0.267329\pi$
$840$	−1.55388	−0.0536139
$841$	0.815037	0.0281047
$842$	−17.2148	−0.593262
$843$	13.9275	0.479689
$844$	−8.39000	−0.288796
$845$	10.7025	0.368177
$846$	15.8061	0.543425
$847$	35.7365	1.22792
$848$	8.81762	0.302798
$849$	2.05368	0.0704821
$850$	10.6047	0.363740
$851$	0	0
$852$	−8.45328	−0.289605
$853$	21.4284	0.733693	0.366846	−	0.930282i	$-0.380437\pi$
$853$	21.4284	0.733693	0.366846	+	0.930282i	$0.380437\pi$
$854$	−16.6103	−0.568392
$855$	1.43286	0.0490027
$856$	13.5439	0.462920
$857$	−31.0899	−1.06201	−0.531006	−	0.847368i	$-0.678186\pi$
$857$	−31.0899	−1.06201	−0.531006	+	0.847368i	$0.678186\pi$
$858$	8.51094	0.290559
$859$	12.3979	0.423010	0.211505	−	0.977377i	$-0.432164\pi$
$859$	12.3979	0.423010	0.211505	+	0.977377i	$0.432164\pi$
$860$	−1.95589	−0.0666954
$861$	−32.5867	−1.11055
$862$	−38.3116	−1.30490
$863$	−37.7541	−1.28516	−0.642582	−	0.766217i	$-0.722137\pi$
$863$	−37.7541	−1.28516	−0.642582	+	0.766217i	$0.722137\pi$
$864$	−4.16783	−0.141792
$865$	−10.3914	−0.353320
$866$	18.6148	0.632557
$867$	9.35815	0.317819
$868$	31.3571	1.06433
$869$	21.8128	0.739949
$870$	−1.83998	−0.0623811
$871$	−12.4047	−0.420317
$872$	14.7429	0.499257
$873$	9.90710	0.335305
$874$	0.360815	0.0122047
$875$	19.7683	0.668289
$876$	−5.53141	−0.186889
$877$	−6.49746	−0.219404	−0.109702	−	0.993965i	$-0.534990\pi$
$877$	−6.49746	−0.219404	−0.109702	+	0.993965i	$0.534990\pi$
$878$	10.0078	0.337746
$879$	−14.0452	−0.473734
$880$	−0.787910	−0.0265604
$881$	7.92161	0.266886	0.133443	−	0.991057i	$-0.457397\pi$
$881$	7.92161	0.266886	0.133443	+	0.991057i	$0.457397\pi$
$882$	34.3120	1.15534
$883$	−32.1806	−1.08296	−0.541481	−	0.840713i	$-0.682136\pi$
$883$	−32.1806	−1.08296	−0.541481	+	0.840713i	$0.682136\pi$
$884$	−13.5019	−0.454118
$885$	−4.78431	−0.160823
$886$	−28.9727	−0.973358
$887$	−0.113136	−0.00379873	−0.00189937	−	0.999998i	$-0.500605\pi$
$887$	−0.113136	−0.00379873	−0.00189937	+	0.999998i	$0.500605\pi$
$888$	0	0
$889$	−70.1859	−2.35396
$890$	7.76687	0.260346
$891$	−7.21670	−0.241769
$892$	14.8715	0.497935
$893$	−8.95556	−0.299686
$894$	16.5289	0.552810
$895$	−1.51306	−0.0505760
$896$	4.61128	0.154052
$897$	1.24978	0.0417288
$898$	−9.39644	−0.313563
$899$	37.1305	1.23837
$900$	11.5681	0.385602
$901$	19.4445	0.647791
$902$	−16.5234	−0.550170
$903$	−15.9118	−0.529510
$904$	4.86809	0.161910
$905$	−2.15209	−0.0715380
$906$	−11.4165	−0.379289
$907$	−50.2529	−1.66862	−0.834310	−	0.551295i	$-0.814134\pi$
$907$	−50.2529	−1.66862	−0.834310	+	0.551295i	$0.814134\pi$
$908$	10.0974	0.335093
$909$	−5.25470	−0.174287
$910$	−12.3394	−0.409046
$911$	−35.7354	−1.18397	−0.591983	−	0.805951i	$-0.701655\pi$
$911$	−35.7354	−1.18397	−0.591983	+	0.805951i	$0.701655\pi$
$912$	1.05087	0.0347977
$913$	14.8728	0.492217
$914$	−27.0123	−0.893488
$915$	1.21381	0.0401273
$916$	1.50284	0.0496551
$917$	−10.9740	−0.362394
$918$	−9.19085	−0.303343
$919$	−12.5483	−0.413932	−0.206966	−	0.978348i	$-0.566359\pi$
$919$	−12.5483	−0.413932	−0.206966	+	0.978348i	$0.566359\pi$
$920$	−0.115700	−0.00381450
$921$	−7.50002	−0.247134
$922$	27.6922	0.911995
$923$	−67.1276	−2.20953
$924$	−6.40988	−0.210870
$925$	0	0
$926$	27.7284	0.911211
$927$	−15.6174	−0.512942
$928$	5.46031	0.179244
$929$	26.0839	0.855783	0.427892	−	0.903830i	$-0.359256\pi$
$929$	26.0839	0.855783	0.427892	+	0.903830i	$0.359256\pi$
$930$	−2.29144	−0.0751393
$931$	−19.4408	−0.637146
$932$	−3.35874	−0.110019
$933$	12.2217	0.400121
$934$	5.72621	0.187367
$935$	−1.73749	−0.0568220
$936$	−14.7284	−0.481413
$937$	22.2574	0.727119	0.363560	−	0.931571i	$-0.381561\pi$
$937$	22.2574	0.727119	0.363560	+	0.931571i	$0.381561\pi$
$938$	9.34240	0.305040
$939$	0.395034	0.0128914
$940$	2.87171	0.0936647
$941$	1.07662	0.0350967	0.0175484	−	0.999846i	$-0.494414\pi$
$941$	1.07662	0.0350967	0.0175484	+	0.999846i	$0.494414\pi$
$942$	10.7019	0.348688
$943$	−2.42636	−0.0790131
$944$	14.1979	0.462102
$945$	−8.39950	−0.273236
$946$	−8.06822	−0.262320
$947$	27.9357	0.907787	0.453894	−	0.891056i	$-0.350035\pi$
$947$	27.9357	0.907787	0.453894	+	0.891056i	$0.350035\pi$
$948$	9.32890	0.302988
$949$	−43.9250	−1.42587
$950$	−6.55434	−0.212651
$951$	21.3393	0.691973
$952$	10.1687	0.329571
$953$	34.7908	1.12698	0.563492	−	0.826122i	$-0.309458\pi$
$953$	34.7908	1.12698	0.563492	+	0.826122i	$0.309458\pi$
$954$	21.2109	0.686727
$955$	8.43277	0.272878
$956$	5.36999	0.173678
$957$	−7.59007	−0.245352
$958$	16.3598	0.528560
$959$	−29.0462	−0.937950
$960$	−0.336973	−0.0108758
$961$	15.2410	0.491645
$962$	0	0
$963$	32.5799	1.04987
$964$	−6.94226	−0.223595
$965$	−1.24694	−0.0401403
$966$	−0.941250	−0.0302842
$967$	−20.3517	−0.654467	−0.327233	−	0.944944i	$-0.606116\pi$
$967$	−20.3517	−0.654467	−0.327233	+	0.944944i	$0.606116\pi$
$968$	7.74980	0.249088
$969$	2.31736	0.0744444
$970$	1.79996	0.0577931
$971$	−26.5861	−0.853189	−0.426594	−	0.904443i	$-0.640287\pi$
$971$	−26.5861	−0.853189	−0.426594	+	0.904443i	$0.640287\pi$
$972$	−15.5899	−0.500047
$973$	29.0439	0.931106
$974$	−17.8331	−0.571410
$975$	−22.7027	−0.727067
$976$	−3.60210	−0.115300
$977$	−24.9760	−0.799054	−0.399527	−	0.916721i	$-0.630826\pi$
$977$	−24.9760	−0.799054	−0.399527	+	0.916721i	$0.630826\pi$
$978$	14.5339	0.464742
$979$	32.0390	1.02397
$980$	6.23392	0.199135
$981$	35.4641	1.13228
$982$	6.51454	0.207887
$983$	−26.3797	−0.841383	−0.420692	−	0.907204i	$-0.638213\pi$
$983$	−26.3797	−0.841383	−0.420692	+	0.907204i	$0.638213\pi$
$984$	−7.06673	−0.225279
$985$	−1.95467	−0.0622809
$986$	12.0410	0.383464
$987$	23.3622	0.743626
$988$	8.34495	0.265488
$989$	−1.18477	−0.0376734
$990$	−1.89532	−0.0602373
$991$	−3.41775	−0.108568	−0.0542842	−	0.998526i	$-0.517288\pi$
$991$	−3.41775	−0.108568	−0.0542842	+	0.998526i	$0.517288\pi$
$992$	6.80007	0.215903
$993$	−10.9165	−0.346426
$994$	50.5561	1.60354
$995$	3.50102	0.110990
$996$	6.36079	0.201549
$997$	−14.4208	−0.456712	−0.228356	−	0.973578i	$-0.573335\pi$
$997$	−14.4208	−0.456712	−0.228356	+	0.973578i	$0.573335\pi$
$998$	−2.43802	−0.0771743
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.w.1.7	✓	18
37.36	even	2		2738.2.a.x.1.7	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.w.1.7	✓	18	1.1	even	1	trivial
2738.2.a.x.1.7	yes	18	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.771034 q^{3} +1.00000 q^{4} +0.437041 q^{5} +0.771034 q^{6} -4.61128 q^{7} -1.00000 q^{8} -2.40551 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.771034 q^{3} +1.00000 q^{4} +0.437041 q^{5} +0.771034 q^{6} -4.61128 q^{7} -1.00000 q^{8} -2.40551 q^{9} -0.437041 q^{10} -1.80283 q^{11} -0.771034 q^{12} -6.12279 q^{13} +4.61128 q^{14} -0.336973 q^{15} +1.00000 q^{16} +2.20519 q^{17} +2.40551 q^{18} -1.36293 q^{19} +0.437041 q^{20} +3.55545 q^{21} +1.80283 q^{22} +0.264734 q^{23} +0.771034 q^{24} -4.80900 q^{25} +6.12279 q^{26} +4.16783 q^{27} -4.61128 q^{28} -5.46031 q^{29} +0.336973 q^{30} -6.80007 q^{31} -1.00000 q^{32} +1.39004 q^{33} -2.20519 q^{34} -2.01532 q^{35} -2.40551 q^{36} +1.36293 q^{38} +4.72088 q^{39} -0.437041 q^{40} -9.16526 q^{41} -3.55545 q^{42} -4.47531 q^{43} -1.80283 q^{44} -1.05130 q^{45} -0.264734 q^{46} +6.57080 q^{47} -0.771034 q^{48} +14.2639 q^{49} +4.80900 q^{50} -1.70027 q^{51} -6.12279 q^{52} +8.81762 q^{53} -4.16783 q^{54} -0.787910 q^{55} +4.61128 q^{56} +1.05087 q^{57} +5.46031 q^{58} +14.1979 q^{59} -0.336973 q^{60} -3.60210 q^{61} +6.80007 q^{62} +11.0925 q^{63} +1.00000 q^{64} -2.67591 q^{65} -1.39004 q^{66} +2.02599 q^{67} +2.20519 q^{68} -0.204119 q^{69} +2.01532 q^{70} +10.9636 q^{71} +2.40551 q^{72} +7.17402 q^{73} +3.70790 q^{75} -1.36293 q^{76} +8.31336 q^{77} -4.72088 q^{78} -12.0992 q^{79} +0.437041 q^{80} +4.00299 q^{81} +9.16526 q^{82} -8.24969 q^{83} +3.55545 q^{84} +0.963757 q^{85} +4.47531 q^{86} +4.21009 q^{87} +1.80283 q^{88} -17.7715 q^{89} +1.05130 q^{90} +28.2339 q^{91} +0.264734 q^{92} +5.24309 q^{93} -6.57080 q^{94} -0.595658 q^{95} +0.771034 q^{96} -4.11851 q^{97} -14.2639 q^{98} +4.33672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} - 9 q^{13} - 18 q^{14} + 4 q^{15} + 18 q^{16} - 13 q^{17} - 26 q^{18} - 2 q^{19} - 9 q^{20} + 24 q^{21} - 10 q^{22} + 11 q^{23} - 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} - 30 q^{29} - 4 q^{30} + 8 q^{31} - 18 q^{32} + 42 q^{33} + 13 q^{34} - 25 q^{35} + 26 q^{36} + 2 q^{38} + 45 q^{39} + 9 q^{40} + 5 q^{41} - 24 q^{42} + 3 q^{43} + 10 q^{44} + 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} - 49 q^{50} - 10 q^{51} - 9 q^{52} + 25 q^{53} - 29 q^{54} + 44 q^{55} - 18 q^{56} - 22 q^{57} + 30 q^{58} - 26 q^{59} + 4 q^{60} - 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} - 42 q^{66} + 23 q^{67} - 13 q^{68} + 2 q^{69} + 25 q^{70} - 25 q^{71} - 26 q^{72} + 77 q^{73} - q^{75} - 2 q^{76} - 6 q^{77} - 45 q^{78} + 13 q^{79} - 9 q^{80} + 38 q^{81} - 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} + 55 q^{87} - 10 q^{88} - 55 q^{89} - 30 q^{90} - 12 q^{91} + 11 q^{92} + 58 q^{93} - 37 q^{94} - 18 q^{95} - 8 q^{96} + 59 q^{97} - 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 - 9 * q^13 - 18 * q^14 + 4 * q^15 + 18 * q^16 - 13 * q^17 - 26 * q^18 - 2 * q^19 - 9 * q^20 + 24 * q^21 - 10 * q^22 + 11 * q^23 - 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 - 30 * q^29 - 4 * q^30 + 8 * q^31 - 18 * q^32 + 42 * q^33 + 13 * q^34 - 25 * q^35 + 26 * q^36 + 2 * q^38 + 45 * q^39 + 9 * q^40 + 5 * q^41 - 24 * q^42 + 3 * q^43 + 10 * q^44 + 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 - 49 * q^50 - 10 * q^51 - 9 * q^52 + 25 * q^53 - 29 * q^54 + 44 * q^55 - 18 * q^56 - 22 * q^57 + 30 * q^58 - 26 * q^59 + 4 * q^60 - 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 - 42 * q^66 + 23 * q^67 - 13 * q^68 + 2 * q^69 + 25 * q^70 - 25 * q^71 - 26 * q^72 + 77 * q^73 - q^75 - 2 * q^76 - 6 * q^77 - 45 * q^78 + 13 * q^79 - 9 * q^80 + 38 * q^81 - 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 + 55 * q^87 - 10 * q^88 - 55 * q^89 - 30 * q^90 - 12 * q^91 + 11 * q^92 + 58 * q^93 - 37 * q^94 - 18 * q^95 - 8 * q^96 + 59 * q^97 - 50 * q^98 + 11 * q^99

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