LMFDB - Embedded newform 2738.2.a.x.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	$-0.531157\pi$
$5$	−0.437041	−0.195451	−0.0977253	+	0.995213i	$0.531157\pi$
$6$	−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	$-0.177158\pi$
$13$	6.12279	1.69816	0.849078	+	0.528268i	$0.177158\pi$
$14$	−4.61128	−1.23242
$15$	0.336973	0.0870061
$16$	1.00000	0.250000
$17$	−2.20519	−0.534837	−0.267418	−	0.963581i	$-0.586171\pi$
$17$	−2.20519	−0.534837	−0.267418	+	0.963581i	$0.586171\pi$
$18$	−2.40551	−0.566983
$19$	1.36293	0.312678	0.156339	−	0.987703i	$-0.450031\pi$
$19$	1.36293	0.312678	0.156339	+	0.987703i	$0.450031\pi$
$20$	−0.437041	−0.0977253
$21$	3.55545	0.775864
$22$	−1.80283	−0.384365
$23$	−0.264734	−0.0552009	−0.0276004	−	0.999619i	$-0.508787\pi$
$23$	−0.264734	−0.0552009	−0.0276004	+	0.999619i	$0.508787\pi$
$24$	−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	$-0.330763\pi$
$29$	5.46031	1.01395	0.506977	+	0.861959i	$0.330763\pi$
$30$	0.336973	0.0615226
$31$	6.80007	1.22133	0.610665	−	0.791889i	$-0.290902\pi$
$31$	6.80007	1.22133	0.610665	+	0.791889i	$0.290902\pi$
$32$	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	$-0.389153\pi$
$43$	4.47531	0.682478	0.341239	+	0.939977i	$0.389153\pi$
$44$	−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	$-0.875270\pi$
$59$	−14.1979	−1.84841	−0.924204	+	0.381898i	$0.875270\pi$
$60$	0.336973	0.0435030
$61$	3.60210	0.461201	0.230601	−	0.973049i	$-0.425931\pi$
$61$	3.60210	0.461201	0.230601	+	0.973049i	$0.425931\pi$
$62$	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	$-0.261705\pi$
$79$	12.0992	1.36127	0.680634	+	0.732624i	$0.261705\pi$
$80$	−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	$-0.109051\pi$
$89$	17.7715	1.88377	0.941887	+	0.335930i	$0.109051\pi$
$90$	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	$-0.432951\pi$
$97$	4.11851	0.418171	0.209086	+	0.977897i	$0.432951\pi$
$98$	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	$-0.603634\pi$
$103$	−6.49235	−0.639710	−0.319855	+	0.947466i	$0.603634\pi$
$104$	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	$-0.250473\pi$
$109$	14.7429	1.41211	0.706056	+	0.708156i	$0.250473\pi$
$110$	0.787910	0.0751243
$111$	0	0
$112$	−4.61128	−0.435725
$113$	4.86809	0.457951	0.228976	−	0.973432i	$-0.426462\pi$
$113$	4.86809	0.457951	0.228976	+	0.973432i	$0.426462\pi$
$114$	−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	$-0.533152\pi$
$131$	−2.37982	−0.207926	−0.103963	+	0.994581i	$0.533152\pi$
$132$	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	$-0.764332\pi$
$163$	−18.8499	−1.47644	−0.738218	+	0.674562i	$0.764332\pi$
$164$	−9.16526	−0.715687
$165$	−0.607505	−0.0472942
$166$	−8.24969	−0.640300
$167$	−8.01091	−0.619903	−0.309952	−	0.950752i	$-0.600313\pi$
$167$	−8.01091	−0.619903	−0.309952	+	0.950752i	$0.600313\pi$
$168$	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	$-0.458700\pi$
$179$	3.46205	0.258766	0.129383	+	0.991595i	$0.458700\pi$
$180$	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	$-0.745959\pi$
$191$	−19.2951	−1.39615	−0.698074	+	0.716026i	$0.745959\pi$
$192$	−0.771034	−0.0556446
$193$	2.85313	0.205373	0.102686	−	0.994714i	$-0.467256\pi$
$193$	2.85313	0.205373	0.102686	+	0.994714i	$0.467256\pi$
$194$	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	$-0.591639\pi$
$199$	−8.01075	−0.567867	−0.283933	+	0.958844i	$0.591639\pi$
$200$	−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	$-0.608768\pi$
$227$	−10.0974	−0.670187	−0.335093	+	0.942185i	$0.608768\pi$
$228$	−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	$-0.555565\pi$
$239$	−5.36999	−0.347356	−0.173678	+	0.984803i	$0.555565\pi$
$240$	0.336973	0.0217515
$241$	6.94226	0.447190	0.223595	−	0.974682i	$-0.428221\pi$
$241$	6.94226	0.447190	0.223595	+	0.974682i	$0.428221\pi$
$242$	−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	$-0.334304\pi$
$251$	15.7593	0.994715	0.497358	+	0.867546i	$0.334304\pi$
$252$	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	$-0.304433\pi$
$257$	18.4828	1.15292	0.576461	+	0.817124i	$0.304433\pi$
$258$	−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	$-0.364496\pi$
$277$	13.7460	0.825915	0.412958	+	0.910750i	$0.364496\pi$
$278$	−6.29845	−0.377756
$279$	−16.3576	−0.979305
$280$	2.01532	0.120438
$281$	18.0634	1.07757	0.538787	−	0.842442i	$-0.318883\pi$
$281$	18.0634	1.07757	0.538787	+	0.842442i	$0.318883\pi$
$282$	−5.06630	−0.301694
$283$	2.66354	0.158331	0.0791656	−	0.996861i	$-0.474774\pi$
$283$	2.66354	0.158331	0.0791656	+	0.996861i	$0.474774\pi$
$284$	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	$-0.351632\pi$
$311$	15.8511	0.898832	0.449416	+	0.893323i	$0.351632\pi$
$312$	−4.72088	−0.267267
$313$	0.512343	0.0289594	0.0144797	−	0.999895i	$-0.495391\pi$
$313$	0.512343	0.0289594	0.0144797	+	0.999895i	$0.495391\pi$
$314$	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	$-0.627216\pi$
$331$	−14.1583	−0.778212	−0.389106	+	0.921193i	$0.627216\pi$
$332$	−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	$-0.331737\pi$
$347$	18.7895	1.00867	0.504336	+	0.863508i	$0.331737\pi$
$348$	−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	$-0.521847\pi$
$353$	−2.57698	−0.137159	−0.0685793	+	0.997646i	$0.521847\pi$
$354$	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	$-0.483950\pi$
$383$	1.97274	0.100802	0.0504012	+	0.998729i	$0.483950\pi$
$384$	−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	$-0.539444\pi$
$389$	−4.87551	−0.247198	−0.123599	+	0.992332i	$0.539444\pi$
$390$	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	$-0.103386\pi$
$401$	37.9560	1.89543	0.947716	+	0.319115i	$0.103386\pi$
$402$	−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	$-0.552401\pi$
$409$	−6.62852	−0.327759	−0.163880	+	0.986480i	$0.552401\pi$
$410$	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	$-0.637794\pi$
$421$	−17.2148	−0.838999	−0.419499	+	0.907756i	$0.637794\pi$
$422$	−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	$-0.874025\pi$
$431$	−38.3116	−1.84541	−0.922703	+	0.385511i	$0.874025\pi$
$432$	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	$-0.423239\pi$
$439$	10.0078	0.477645	0.238822	+	0.971063i	$0.423239\pi$
$440$	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	$-0.571168\pi$
$449$	−9.39644	−0.443445	−0.221723	+	0.975110i	$0.571168\pi$
$450$	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	$-0.717680\pi$
$457$	−27.0123	−1.26358	−0.631791	+	0.775139i	$0.717680\pi$
$458$	1.50284	0.0702229
$459$	−9.19085	−0.428992
$460$	0.115700	0.00539452
$461$	27.6922	1.28976	0.644878	−	0.764286i	$-0.276908\pi$
$461$	27.6922	1.28976	0.644878	+	0.764286i	$0.276908\pi$
$462$	−6.40988	−0.298215
$463$	27.7284	1.28865	0.644323	−	0.764753i	$-0.277139\pi$
$463$	27.7284	1.28865	0.644323	+	0.764753i	$0.277139\pi$
$464$	5.46031	0.253489
$465$	2.29144	0.106263
$466$	−3.35874	−0.155590
$467$	5.72621	0.264978	0.132489	−	0.991185i	$-0.457703\pi$
$467$	5.72621	0.264978	0.132489	+	0.991185i	$0.457703\pi$
$468$	−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	$-0.378072\pi$
$479$	16.3598	0.747497	0.373748	+	0.927530i	$0.378072\pi$
$480$	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	$-0.632397\pi$
$487$	−17.8331	−0.808096	−0.404048	+	0.914738i	$0.632397\pi$
$488$	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	$-0.517379\pi$
$499$	−2.43802	−0.109141	−0.0545705	+	0.998510i	$0.517379\pi$
$500$	4.28693	0.191717
$501$	6.17668	0.275954
$502$	15.7593	0.703370
$503$	−2.80021	−0.124855	−0.0624275	−	0.998050i	$-0.519884\pi$
$503$	−2.80021	−0.124855	−0.0624275	+	0.998050i	$0.519884\pi$
$504$	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	$-0.723475\pi$
$523$	−29.5378	−1.29160	−0.645798	+	0.763508i	$0.723475\pi$
$524$	−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	$-0.675822\pi$
$541$	−24.4083	−1.04939	−0.524697	+	0.851289i	$0.675822\pi$
$542$	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	$-0.392985\pi$
$547$	15.4314	0.659798	0.329899	+	0.944016i	$0.392985\pi$
$548$	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	$-0.549963\pi$
$557$	−7.37862	−0.312642	−0.156321	+	0.987706i	$0.549963\pi$
$558$	−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	$-0.586109\pi$
$563$	−12.6815	−0.534462	−0.267231	+	0.963632i	$0.586109\pi$
$564$	−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	$-0.568940\pi$
$569$	−10.2519	−0.429782	−0.214891	+	0.976638i	$0.568940\pi$
$570$	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	$-0.268377\pi$
$577$	31.9538	1.33026	0.665128	+	0.746729i	$0.268377\pi$
$578$	−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	$-0.323332\pi$
$587$	25.5344	1.05392	0.526960	+	0.849890i	$0.323332\pi$
$588$	−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	$-0.468206\pi$
$607$	4.91360	0.199437	0.0997184	+	0.995016i	$0.468206\pi$
$608$	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	$-0.432292\pi$
$631$	10.6060	0.422220	0.211110	+	0.977462i	$0.432292\pi$
$632$	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	$-0.441348\pi$
$643$	9.29202	0.366441	0.183221	+	0.983072i	$0.441348\pi$
$644$	1.22076	0.0481048
$645$	1.50806	0.0593797
$646$	−3.00553	−0.118251
$647$	−47.9199	−1.88393	−0.941964	−	0.335715i	$-0.891022\pi$
$647$	−47.9199	−1.88393	−0.941964	+	0.335715i	$0.891022\pi$
$648$	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	$-0.425027\pi$
$653$	11.9266	0.466723	0.233361	+	0.972390i	$0.425027\pi$
$654$	−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	$-0.245220\pi$
$661$	36.9012	1.43529	0.717646	+	0.696408i	$0.245220\pi$
$662$	−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	$-0.309242\pi$
$683$	29.4821	1.12810	0.564050	+	0.825740i	$0.309242\pi$
$684$	−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	$-0.644970\pi$
$701$	−23.2915	−0.879709	−0.439854	+	0.898069i	$0.644970\pi$
$702$	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	$-0.486488\pi$
$709$	2.25990	0.0848725	0.0424362	+	0.999099i	$0.486488\pi$
$710$	−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	$-0.312980\pi$
$727$	29.8920	1.10863	0.554316	+	0.832306i	$0.312980\pi$
$728$	−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	$-0.336884\pi$
$757$	26.9804	0.980619	0.490309	+	0.871548i	$0.336884\pi$
$758$	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	$-0.566776\pi$
$769$	−11.5497	−0.416493	−0.208247	+	0.978076i	$0.566776\pi$
$770$	−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	$-0.428653\pi$
$797$	12.5500	0.444543	0.222272	+	0.974985i	$0.428653\pi$
$798$	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	$-0.679838\pi$
$809$	−30.4565	−1.07079	−0.535397	+	0.844601i	$0.679838\pi$
$810$	−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	$-0.488650\pi$
$827$	2.05039	0.0712992	0.0356496	+	0.999364i	$0.488650\pi$
$828$	0.636820	0.0221310
$829$	−4.74434	−0.164778	−0.0823888	−	0.996600i	$-0.526255\pi$
$829$	−4.74434	−0.164778	−0.0823888	+	0.996600i	$0.526255\pi$
$830$	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	$-0.619563\pi$
$853$	−21.4284	−0.733693	−0.366846	+	0.930282i	$0.619563\pi$
$854$	−16.6103	−0.568392
$855$	1.43286	0.0490027
$856$	−13.5439	−0.462920
$857$	31.0899	1.06201	0.531006	−	0.847368i	$-0.321814\pi$
$857$	31.0899	1.06201	0.531006	+	0.847368i	$0.321814\pi$
$858$	8.51094	0.290559
$859$	−12.3979	−0.423010	−0.211505	−	0.977377i	$-0.567836\pi$
$859$	−12.3979	−0.423010	−0.211505	+	0.977377i	$0.567836\pi$
$860$	−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	$-0.317864\pi$
$883$	32.1806	1.08296	0.541481	+	0.840713i	$0.317864\pi$
$884$	−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	$-0.185866\pi$
$907$	50.2529	1.66862	0.834310	+	0.551295i	$0.185866\pi$
$908$	−10.0974	−0.335093
$909$	−5.25470	−0.174287
$910$	12.3394	0.409046
$911$	35.7354	1.18397	0.591983	−	0.805951i	$-0.298345\pi$
$911$	35.7354	1.18397	0.591983	+	0.805951i	$0.298345\pi$
$912$	−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	$-0.433641\pi$
$919$	12.5483	0.413932	0.206966	+	0.978348i	$0.433641\pi$
$920$	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	$-0.649965\pi$
$947$	−27.9357	−0.907787	−0.453894	+	0.891056i	$0.649965\pi$
$948$	−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	$-0.393884\pi$
$967$	20.3517	0.654467	0.327233	+	0.944944i	$0.393884\pi$
$968$	−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	$-0.369174\pi$
$977$	24.9760	0.799054	0.399527	+	0.916721i	$0.369174\pi$
$978$	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	$-0.482712\pi$
$991$	3.41775	0.108568	0.0542842	+	0.998526i	$0.482712\pi$
$992$	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	$-0.426665\pi$
$997$	14.4208	0.456712	0.228356	+	0.973578i	$0.426665\pi$
$998$	−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.x.1.7	yes	18
37.36	even	2		2738.2.a.w.1.7	✓	18

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
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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