LMFDB - Embedded newform 2738.2.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$21.8630400734$
Analytic rank:	$0$
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			1.2
Root			$3.18423$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.98762 q^{3} +1.00000 q^{4} -2.67223 q^{5} -2.98762 q^{6} +2.38780 q^{7} +1.00000 q^{8} +5.92589 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.98762 q^{3} +1.00000 q^{4} -2.67223 q^{5} -2.98762 q^{6} +2.38780 q^{7} +1.00000 q^{8} +5.92589 q^{9} -2.67223 q^{10} -1.89954 q^{11} -2.98762 q^{12} +6.39119 q^{13} +2.38780 q^{14} +7.98362 q^{15} +1.00000 q^{16} +0.000397822 q^{17} +5.92589 q^{18} +0.220201 q^{19} -2.67223 q^{20} -7.13384 q^{21} -1.89954 q^{22} -9.09601 q^{23} -2.98762 q^{24} +2.14083 q^{25} +6.39119 q^{26} -8.74145 q^{27} +2.38780 q^{28} +2.60973 q^{29} +7.98362 q^{30} -6.23122 q^{31} +1.00000 q^{32} +5.67510 q^{33} +0.000397822 q^{34} -6.38075 q^{35} +5.92589 q^{36} +0.220201 q^{38} -19.0945 q^{39} -2.67223 q^{40} -0.463700 q^{41} -7.13384 q^{42} -4.30279 q^{43} -1.89954 q^{44} -15.8354 q^{45} -9.09601 q^{46} +3.92144 q^{47} -2.98762 q^{48} -1.29842 q^{49} +2.14083 q^{50} -0.00118854 q^{51} +6.39119 q^{52} +6.25872 q^{53} -8.74145 q^{54} +5.07600 q^{55} +2.38780 q^{56} -0.657878 q^{57} +2.60973 q^{58} +13.1018 q^{59} +7.98362 q^{60} +8.68979 q^{61} -6.23122 q^{62} +14.1498 q^{63} +1.00000 q^{64} -17.0787 q^{65} +5.67510 q^{66} +4.36182 q^{67} +0.000397822 q^{68} +27.1754 q^{69} -6.38075 q^{70} +2.40414 q^{71} +5.92589 q^{72} +13.2216 q^{73} -6.39598 q^{75} +0.220201 q^{76} -4.53571 q^{77} -19.0945 q^{78} +7.71300 q^{79} -2.67223 q^{80} +8.33849 q^{81} -0.463700 q^{82} +5.13347 q^{83} -7.13384 q^{84} -0.00106307 q^{85} -4.30279 q^{86} -7.79689 q^{87} -1.89954 q^{88} -5.18018 q^{89} -15.8354 q^{90} +15.2609 q^{91} -9.09601 q^{92} +18.6165 q^{93} +3.92144 q^{94} -0.588429 q^{95} -2.98762 q^{96} -14.0131 q^{97} -1.29842 q^{98} -11.2564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.98762	−1.72490	−0.862452	−	0.506138i	$-0.831073\pi$
$3$	−2.98762	−1.72490	−0.862452	+	0.506138i	$0.831073\pi$
$4$	1.00000	0.500000
$5$	−2.67223	−1.19506	−0.597529	−	0.801847i	$-0.703851\pi$
$5$	−2.67223	−1.19506	−0.597529	+	0.801847i	$0.703851\pi$
$6$	−2.98762	−1.21969
$7$	2.38780	0.902503	0.451251	−	0.892397i	$-0.350978\pi$
$7$	2.38780	0.902503	0.451251	+	0.892397i	$0.350978\pi$
$8$	1.00000	0.353553
$9$	5.92589	1.97530
$10$	−2.67223	−0.845034
$11$	−1.89954	−0.572732	−0.286366	−	0.958120i	$-0.592447\pi$
$11$	−1.89954	−0.572732	−0.286366	+	0.958120i	$0.592447\pi$
$12$	−2.98762	−0.862452
$13$	6.39119	1.77260	0.886298	−	0.463115i	$-0.153268\pi$
$13$	6.39119	1.77260	0.886298	+	0.463115i	$0.153268\pi$
$14$	2.38780	0.638166
$15$	7.98362	2.06136
$16$	1.00000	0.250000
$17$	0.000397822 0	9.64861e−5 0	4.82430e−5	−	1.00000i	$-0.499985\pi$
$17$	0.000397822 0	9.64861e−5 0	4.82430e−5		1.00000i	$0.499985\pi$
$18$	5.92589	1.39675
$19$	0.220201	0.0505176	0.0252588	−	0.999681i	$-0.491959\pi$
$19$	0.220201	0.0505176	0.0252588	+	0.999681i	$0.491959\pi$
$20$	−2.67223	−0.597529
$21$	−7.13384	−1.55673
$22$	−1.89954	−0.404983
$23$	−9.09601	−1.89665	−0.948325	−	0.317302i	$-0.897223\pi$
$23$	−9.09601	−1.89665	−0.948325	+	0.317302i	$0.897223\pi$
$24$	−2.98762	−0.609846
$25$	2.14083	0.428165
$26$	6.39119	1.25342
$27$	−8.74145	−1.68229
$28$	2.38780	0.451251
$29$	2.60973	0.484615	0.242307	−	0.970200i	$-0.422096\pi$
$29$	2.60973	0.484615	0.242307	+	0.970200i	$0.422096\pi$
$30$	7.98362	1.45760
$31$	−6.23122	−1.11916	−0.559580	−	0.828776i	$-0.689038\pi$
$31$	−6.23122	−1.11916	−0.559580	+	0.828776i	$0.689038\pi$
$32$	1.00000	0.176777
$33$	5.67510	0.987908
$34$	0.000397822 0	6.82260e−5 0
$35$	−6.38075	−1.07854
$36$	5.92589	0.987648
$37$	0	0
$37$	0	0
$38$	0.220201	0.0357213
$39$	−19.0945	−3.05756
$40$	−2.67223	−0.422517
$41$	−0.463700	−0.0724177	−0.0362089	−	0.999344i	$-0.511528\pi$
$41$	−0.463700	−0.0724177	−0.0362089	+	0.999344i	$0.511528\pi$
$42$	−7.13384	−1.10077
$43$	−4.30279	−0.656170	−0.328085	−	0.944648i	$-0.606403\pi$
$43$	−4.30279	−0.656170	−0.328085	+	0.944648i	$0.606403\pi$
$44$	−1.89954	−0.286366
$45$	−15.8354	−2.36059
$46$	−9.09601	−1.34113
$47$	3.92144	0.572001	0.286000	−	0.958229i	$-0.407674\pi$
$47$	3.92144	0.572001	0.286000	+	0.958229i	$0.407674\pi$
$48$	−2.98762	−0.431226
$49$	−1.29842	−0.185489
$50$	2.14083	0.302759
$51$	−0.00118854	−0.000166429 0
$52$	6.39119	0.886298
$53$	6.25872	0.859702	0.429851	−	0.902900i	$-0.358566\pi$
$53$	6.25872	0.859702	0.429851	+	0.902900i	$0.358566\pi$
$54$	−8.74145	−1.18956
$55$	5.07600	0.684448
$56$	2.38780	0.319083
$57$	−0.657878	−0.0871381
$58$	2.60973	0.342674
$59$	13.1018	1.70571	0.852854	−	0.522149i	$-0.174869\pi$
$59$	13.1018	1.70571	0.852854	+	0.522149i	$0.174869\pi$
$60$	7.98362	1.03068
$61$	8.68979	1.11261	0.556307	−	0.830977i	$-0.312218\pi$
$61$	8.68979	1.11261	0.556307	+	0.830977i	$0.312218\pi$
$62$	−6.23122	−0.791366
$63$	14.1498	1.78271
$64$	1.00000	0.125000
$65$	−17.0787	−2.11836
$66$	5.67510	0.698556
$67$	4.36182	0.532881	0.266441	−	0.963851i	$-0.414152\pi$
$67$	4.36182	0.532881	0.266441	+	0.963851i	$0.414152\pi$
$68$	0.000397822 0	4.82430e−5 0
$69$	27.1754	3.27154
$70$	−6.38075	−0.762645
$71$	2.40414	0.285318	0.142659	−	0.989772i	$-0.454435\pi$
$71$	2.40414	0.285318	0.142659	+	0.989772i	$0.454435\pi$
$72$	5.92589	0.698373
$73$	13.2216	1.54747	0.773737	−	0.633507i	$-0.218385\pi$
$73$	13.2216	1.54747	0.773737	+	0.633507i	$0.218385\pi$
$74$	0	0
$75$	−6.39598	−0.738545
$76$	0.220201	0.0252588
$77$	−4.53571	−0.516892
$78$	−19.0945	−2.16202
$79$	7.71300	0.867780	0.433890	−	0.900966i	$-0.357141\pi$
$79$	7.71300	0.867780	0.433890	+	0.900966i	$0.357141\pi$
$80$	−2.67223	−0.298765
$81$	8.33849	0.926498
$82$	−0.463700	−0.0512070
$83$	5.13347	0.563471	0.281736	−	0.959492i	$-0.409090\pi$
$83$	5.13347	0.563471	0.281736	+	0.959492i	$0.409090\pi$
$84$	−7.13384	−0.778365
$85$	−0.00106307	−0.000115307 0
$86$	−4.30279	−0.463982
$87$	−7.79689	−0.835914
$88$	−1.89954	−0.202491
$89$	−5.18018	−0.549098	−0.274549	−	0.961573i	$-0.588529\pi$
$89$	−5.18018	−0.549098	−0.274549	+	0.961573i	$0.588529\pi$
$90$	−15.8354	−1.66919
$91$	15.2609	1.59977
$92$	−9.09601	−0.948325
$93$	18.6165	1.93045
$94$	3.92144	0.404466
$95$	−0.588429	−0.0603715
$96$	−2.98762	−0.304923
$97$	−14.0131	−1.42282	−0.711409	−	0.702778i	$-0.751943\pi$
$97$	−14.0131	−1.42282	−0.711409	+	0.702778i	$0.751943\pi$
$98$	−1.29842	−0.131161
$99$	−11.2564	−1.13132
$100$	2.14083	0.214083
$101$	12.2300	1.21693	0.608463	−	0.793582i	$-0.291786\pi$
$101$	12.2300	1.21693	0.608463	+	0.793582i	$0.291786\pi$
$102$	−0.00118854	−0.000117683 0
$103$	−1.23770	−0.121954	−0.0609772	−	0.998139i	$-0.519422\pi$
$103$	−1.23770	−0.121954	−0.0609772	+	0.998139i	$0.519422\pi$
$104$	6.39119	0.626708
$105$	19.0633	1.86038
$106$	6.25872	0.607901
$107$	−4.60902	−0.445571	−0.222785	−	0.974868i	$-0.571515\pi$
$107$	−4.60902	−0.445571	−0.222785	+	0.974868i	$0.571515\pi$
$108$	−8.74145	−0.841146
$109$	8.13109	0.778817	0.389409	−	0.921065i	$-0.372679\pi$
$109$	8.13109	0.778817	0.389409	+	0.921065i	$0.372679\pi$
$110$	5.07600	0.483978
$111$	0	0
$112$	2.38780	0.225626
$113$	6.30361	0.592994	0.296497	−	0.955034i	$-0.404182\pi$
$113$	6.30361	0.592994	0.296497	+	0.955034i	$0.404182\pi$
$114$	−0.657878	−0.0616159
$115$	24.3067	2.26661
$116$	2.60973	0.242307
$117$	37.8735	3.50140
$118$	13.1018	1.20612
$119$	0.000949919 0	8.70789e−5 0
$120$	7.98362	0.728802
$121$	−7.39176	−0.671978
$122$	8.68979	0.786737
$123$	1.38536	0.124914
$124$	−6.23122	−0.559580
$125$	7.64038	0.683376
$126$	14.1498	1.26057
$127$	4.40231	0.390642	0.195321	−	0.980739i	$-0.437425\pi$
$127$	4.40231	0.390642	0.195321	+	0.980739i	$0.437425\pi$
$128$	1.00000	0.0883883
$129$	12.8551	1.13183
$130$	−17.0787	−1.49790
$131$	−9.24437	−0.807684	−0.403842	−	0.914829i	$-0.632326\pi$
$131$	−9.24437	−0.807684	−0.403842	+	0.914829i	$0.632326\pi$
$132$	5.67510	0.493954
$133$	0.525796	0.0455923
$134$	4.36182	0.376804
$135$	23.3592	2.01044
$136$	0.000397822 0	3.41130e−5 0
$137$	−2.76408	−0.236151	−0.118075	−	0.993005i	$-0.537672\pi$
$137$	−2.76408	−0.236151	−0.118075	+	0.993005i	$0.537672\pi$
$138$	27.1754	2.31333
$139$	21.2346	1.80110	0.900549	−	0.434755i	$-0.143165\pi$
$139$	21.2346	1.80110	0.900549	+	0.434755i	$0.143165\pi$
$140$	−6.38075	−0.539272
$141$	−11.7158	−0.986647
$142$	2.40414	0.201751
$143$	−12.1403	−1.01522
$144$	5.92589	0.493824
$145$	−6.97381	−0.579143
$146$	13.2216	1.09423
$147$	3.87920	0.319951
$148$	0	0
$149$	−20.3861	−1.67009	−0.835047	−	0.550178i	$-0.814560\pi$
$149$	−20.3861	−1.67009	−0.835047	+	0.550178i	$0.814560\pi$
$150$	−6.39598	−0.522230
$151$	11.6146	0.945182	0.472591	−	0.881282i	$-0.343319\pi$
$151$	11.6146	0.945182	0.472591	+	0.881282i	$0.343319\pi$
$152$	0.220201	0.0178607
$153$	0.00235745	0.000190589 0
$154$	−4.53571	−0.365498
$155$	16.6513	1.33746
$156$	−19.0945	−1.52878
$157$	17.2161	1.37400	0.686998	−	0.726660i	$-0.258928\pi$
$157$	17.2161	1.37400	0.686998	+	0.726660i	$0.258928\pi$
$158$	7.71300	0.613613
$159$	−18.6987	−1.48290
$160$	−2.67223	−0.211259
$161$	−21.7194	−1.71173
$162$	8.33849	0.655133
$163$	4.45838	0.349207	0.174603	−	0.984639i	$-0.444136\pi$
$163$	4.45838	0.349207	0.174603	+	0.984639i	$0.444136\pi$
$164$	−0.463700	−0.0362089
$165$	−15.1652	−1.18061
$166$	5.13347	0.398434
$167$	−14.1646	−1.09609	−0.548046	−	0.836448i	$-0.684628\pi$
$167$	−14.1646	−1.09609	−0.548046	+	0.836448i	$0.684628\pi$
$168$	−7.13384	−0.550387
$169$	27.8473	2.14210
$170$	−0.00106307	−8.15340e−5 0
$171$	1.30489	0.0997872
$172$	−4.30279	−0.328085
$173$	−2.21365	−0.168301	−0.0841504	−	0.996453i	$-0.526818\pi$
$173$	−2.21365	−0.168301	−0.0841504	+	0.996453i	$0.526818\pi$
$174$	−7.79689	−0.591081
$175$	5.11186	0.386420
$176$	−1.89954	−0.143183
$177$	−39.1432	−2.94219
$178$	−5.18018	−0.388271
$179$	2.72677	0.203809	0.101904	−	0.994794i	$-0.467506\pi$
$179$	2.72677	0.203809	0.101904	+	0.994794i	$0.467506\pi$
$180$	−15.8354	−1.18030
$181$	0.744051	0.0553049	0.0276524	−	0.999618i	$-0.491197\pi$
$181$	0.744051	0.0553049	0.0276524	+	0.999618i	$0.491197\pi$
$182$	15.2609	1.13121
$183$	−25.9618	−1.91915
$184$	−9.09601	−0.670567
$185$	0	0
$186$	18.6165	1.36503
$187$	−0.000755678 0	−5.52606e−5 0
$188$	3.92144	0.286000
$189$	−20.8728	−1.51827
$190$	−0.588429	−0.0426891
$191$	−3.65572	−0.264518	−0.132259	−	0.991215i	$-0.542223\pi$
$191$	−3.65572	−0.264518	−0.132259	+	0.991215i	$0.542223\pi$
$192$	−2.98762	−0.215613
$193$	11.0077	0.792350	0.396175	−	0.918175i	$-0.370337\pi$
$193$	11.0077	0.792350	0.396175	+	0.918175i	$0.370337\pi$
$194$	−14.0131	−1.00608
$195$	51.0248	3.65396
$196$	−1.29842	−0.0927446
$197$	−5.91904	−0.421714	−0.210857	−	0.977517i	$-0.567625\pi$
$197$	−5.91904	−0.421714	−0.210857	+	0.977517i	$0.567625\pi$
$198$	−11.2564	−0.799961
$199$	−10.0731	−0.714064	−0.357032	−	0.934092i	$-0.616211\pi$
$199$	−10.0731	−0.714064	−0.357032	+	0.934092i	$0.616211\pi$
$200$	2.14083	0.151379
$201$	−13.0315	−0.919169
$202$	12.2300	0.860497
$203$	6.23151	0.437366
$204$	−0.00118854	−8.32146e−5 0
$205$	1.23911	0.0865434
$206$	−1.23770	−0.0862347
$207$	−53.9019	−3.74644
$208$	6.39119	0.443149
$209$	−0.418280	−0.0289330
$210$	19.0633	1.31549
$211$	18.0856	1.24507	0.622533	−	0.782594i	$-0.286104\pi$
$211$	18.0856	1.24507	0.622533	+	0.782594i	$0.286104\pi$
$212$	6.25872	0.429851
$213$	−7.18265	−0.492147
$214$	−4.60902	−0.315066
$215$	11.4981	0.784161
$216$	−8.74145	−0.594780
$217$	−14.8789	−1.01005
$218$	8.13109	0.550707
$219$	−39.5012	−2.66924
$220$	5.07600	0.342224
$221$	0.00254256	0.000171031 0
$222$	0	0
$223$	9.64175	0.645659	0.322830	−	0.946457i	$-0.395366\pi$
$223$	9.64175	0.645659	0.322830	+	0.946457i	$0.395366\pi$
$224$	2.38780	0.159541
$225$	12.6863	0.845753
$226$	6.30361	0.419310
$227$	−6.85824	−0.455197	−0.227599	−	0.973755i	$-0.573087\pi$
$227$	−6.85824	−0.455197	−0.227599	+	0.973755i	$0.573087\pi$
$228$	−0.657878	−0.0435690
$229$	11.4979	0.759803	0.379902	−	0.925027i	$-0.375958\pi$
$229$	11.4979	0.759803	0.379902	+	0.925027i	$0.375958\pi$
$230$	24.3067	1.60273
$231$	13.5510	0.891589
$232$	2.60973	0.171337
$233$	3.76050	0.246358	0.123179	−	0.992384i	$-0.460691\pi$
$233$	3.76050	0.246358	0.123179	+	0.992384i	$0.460691\pi$
$234$	37.8735	2.47587
$235$	−10.4790	−0.683575
$236$	13.1018	0.852854
$237$	−23.0435	−1.49684
$238$	0.000949919 0	6.15741e−5 0
$239$	−4.61577	−0.298569	−0.149285	−	0.988794i	$-0.547697\pi$
$239$	−4.61577	−0.298569	−0.149285	+	0.988794i	$0.547697\pi$
$240$	7.98362	0.515341
$241$	19.6066	1.26297	0.631486	−	0.775387i	$-0.282445\pi$
$241$	19.6066	1.26297	0.631486	+	0.775387i	$0.282445\pi$
$242$	−7.39176	−0.475160
$243$	1.31210	0.0841712
$244$	8.68979	0.556307
$245$	3.46969	0.221670
$246$	1.38536	0.0883273
$247$	1.40735	0.0895474
$248$	−6.23122	−0.395683
$249$	−15.3369	−0.971934
$250$	7.64038	0.483220
$251$	13.8238	0.872553	0.436277	−	0.899813i	$-0.356297\pi$
$251$	13.8238	0.872553	0.436277	+	0.899813i	$0.356297\pi$
$252$	14.1498	0.891355
$253$	17.2782	1.08627
$254$	4.40231	0.276225
$255$	0.00317606	0.000198893 0
$256$	1.00000	0.0625000
$257$	17.2096	1.07350	0.536752	−	0.843740i	$-0.319651\pi$
$257$	17.2096	1.07350	0.536752	+	0.843740i	$0.319651\pi$
$258$	12.8551	0.800325
$259$	0	0
$260$	−17.0787	−1.05918
$261$	15.4650	0.957258
$262$	−9.24437	−0.571119
$263$	−10.5274	−0.649146	−0.324573	−	0.945861i	$-0.605221\pi$
$263$	−10.5274	−0.649146	−0.324573	+	0.945861i	$0.605221\pi$
$264$	5.67510	0.349278
$265$	−16.7248	−1.02739
$266$	0.525796	0.0322386
$267$	15.4764	0.947142
$268$	4.36182	0.266441
$269$	12.6651	0.772204	0.386102	−	0.922456i	$-0.373821\pi$
$269$	12.6651	0.772204	0.386102	+	0.922456i	$0.373821\pi$
$270$	23.3592	1.42159
$271$	24.9081	1.51306	0.756529	−	0.653961i	$-0.226894\pi$
$271$	24.9081	1.51306	0.756529	+	0.653961i	$0.226894\pi$
$272$	0.000397822 0	2.41215e−5 0
$273$	−45.5937	−2.75946
$274$	−2.76408	−0.166984
$275$	−4.06658	−0.245224
$276$	27.1754	1.63577
$277$	−10.3374	−0.621117	−0.310559	−	0.950554i	$-0.600516\pi$
$277$	−10.3374	−0.621117	−0.310559	+	0.950554i	$0.600516\pi$
$278$	21.2346	1.27357
$279$	−36.9255	−2.21067
$280$	−6.38075	−0.381323
$281$	20.9056	1.24712	0.623561	−	0.781774i	$-0.285685\pi$
$281$	20.9056	1.24712	0.623561	+	0.781774i	$0.285685\pi$
$282$	−11.7158	−0.697665
$283$	−14.7437	−0.876421	−0.438210	−	0.898872i	$-0.644388\pi$
$283$	−14.7437	−0.876421	−0.438210	+	0.898872i	$0.644388\pi$
$284$	2.40414	0.142659
$285$	1.75800	0.104135
$286$	−12.1403	−0.717871
$287$	−1.10722	−0.0653572
$288$	5.92589	0.349186
$289$	−17.0000	−1.00000
$290$	−6.97381	−0.409516
$291$	41.8660	2.45423
$292$	13.2216	0.773737
$293$	27.0174	1.57838	0.789188	−	0.614152i	$-0.210502\pi$
$293$	27.0174	1.57838	0.789188	+	0.614152i	$0.210502\pi$
$294$	3.87920	0.226240
$295$	−35.0111	−2.03842
$296$	0	0
$297$	16.6047	0.963503
$298$	−20.3861	−1.18094
$299$	−58.1343	−3.36199
$300$	−6.39598	−0.369272
$301$	−10.2742	−0.592195
$302$	11.6146	0.668345
$303$	−36.5385	−2.09908
$304$	0.220201	0.0126294
$305$	−23.2212	−1.32964
$306$	0.00235745	0.000134766 0
$307$	12.4627	0.711285	0.355643	−	0.934622i	$-0.384262\pi$
$307$	12.4627	0.711285	0.355643	+	0.934622i	$0.384262\pi$
$308$	−4.53571	−0.258446
$309$	3.69778	0.210360
$310$	16.6513	0.945729
$311$	−25.7845	−1.46210	−0.731051	−	0.682323i	$-0.760970\pi$
$311$	−25.7845	−1.46210	−0.731051	+	0.682323i	$0.760970\pi$
$312$	−19.0945	−1.08101
$313$	9.49854	0.536889	0.268445	−	0.963295i	$-0.413490\pi$
$313$	9.49854	0.536889	0.268445	+	0.963295i	$0.413490\pi$
$314$	17.2161	0.971562
$315$	−37.8116	−2.13044
$316$	7.71300	0.433890
$317$	27.1642	1.52570	0.762848	−	0.646578i	$-0.223800\pi$
$317$	27.1642	1.52570	0.762848	+	0.646578i	$0.223800\pi$
$318$	−18.6987	−1.04857
$319$	−4.95728	−0.277554
$320$	−2.67223	−0.149382
$321$	13.7700	0.768567
$322$	−21.7194	−1.21038
$323$	8.76009e−5 0	4.87425e−6 0
$324$	8.33849	0.463249
$325$	13.6824	0.758965
$326$	4.45838	0.246927
$327$	−24.2926	−1.34339
$328$	−0.463700	−0.0256035
$329$	9.36361	0.516232
$330$	−15.1652	−0.834816
$331$	−23.5255	−1.29308	−0.646539	−	0.762881i	$-0.723784\pi$
$331$	−23.5255	−1.29308	−0.646539	+	0.762881i	$0.723784\pi$
$332$	5.13347	0.281736
$333$	0	0
$334$	−14.1646	−0.775055
$335$	−11.6558	−0.636824
$336$	−7.13384	−0.389183
$337$	30.0729	1.63818	0.819088	−	0.573668i	$-0.194480\pi$
$337$	30.0729	1.63818	0.819088	+	0.573668i	$0.194480\pi$
$338$	27.8473	1.51469
$339$	−18.8328	−1.02286
$340$	−0.00106307	−5.76533e−5 0
$341$	11.8364	0.640979
$342$	1.30489	0.0705602
$343$	−19.8150	−1.06991
$344$	−4.30279	−0.231991
$345$	−72.6191	−3.90968
$346$	−2.21365	−0.119007
$347$	−5.99818	−0.321999	−0.161000	−	0.986954i	$-0.551472\pi$
$347$	−5.99818	−0.321999	−0.161000	+	0.986954i	$0.551472\pi$
$348$	−7.79689	−0.417957
$349$	−8.18585	−0.438178	−0.219089	−	0.975705i	$-0.570309\pi$
$349$	−8.18585	−0.438178	−0.219089	+	0.975705i	$0.570309\pi$
$350$	5.11186	0.273240
$351$	−55.8683	−2.98203
$352$	−1.89954	−0.101246
$353$	12.7006	0.675986	0.337993	−	0.941149i	$-0.390252\pi$
$353$	12.7006	0.675986	0.337993	+	0.941149i	$0.390252\pi$
$354$	−39.1432	−2.08044
$355$	−6.42441	−0.340972
$356$	−5.18018	−0.274549
$357$	−0.00283800	−0.000150203 0
$358$	2.72677	0.144114
$359$	−0.847562	−0.0447326	−0.0223663	−	0.999750i	$-0.507120\pi$
$359$	−0.847562	−0.0447326	−0.0223663	+	0.999750i	$0.507120\pi$
$360$	−15.8354	−0.834596
$361$	−18.9515	−0.997448
$362$	0.744051	0.0391064
$363$	22.0838	1.15910
$364$	15.2609	0.799887
$365$	−35.3312	−1.84932
$366$	−25.9618	−1.35705
$367$	22.1202	1.15466	0.577332	−	0.816509i	$-0.304094\pi$
$367$	22.1202	1.15466	0.577332	+	0.816509i	$0.304094\pi$
$368$	−9.09601	−0.474162
$369$	−2.74783	−0.143046
$370$	0	0
$371$	14.9446	0.775883
$372$	18.6165	0.965223
$373$	15.7676	0.816416	0.408208	−	0.912889i	$-0.366154\pi$
$373$	15.7676	0.816416	0.408208	+	0.912889i	$0.366154\pi$
$374$	−0.000755678 0	−3.90752e−5 0
$375$	−22.8266	−1.17876
$376$	3.92144	0.202233
$377$	16.6793	0.859027
$378$	−20.8728	−1.07358
$379$	−8.02033	−0.411977	−0.205988	−	0.978554i	$-0.566041\pi$
$379$	−8.02033	−0.411977	−0.205988	+	0.978554i	$0.566041\pi$
$380$	−0.588429	−0.0301858
$381$	−13.1524	−0.673820
$382$	−3.65572	−0.187043
$383$	26.6472	1.36161	0.680804	−	0.732466i	$-0.261631\pi$
$383$	26.6472	1.36161	0.680804	+	0.732466i	$0.261631\pi$
$384$	−2.98762	−0.152461
$385$	12.1205	0.617716
$386$	11.0077	0.560276
$387$	−25.4979	−1.29613
$388$	−14.0131	−0.711409
$389$	−8.10684	−0.411033	−0.205517	−	0.978654i	$-0.565887\pi$
$389$	−8.10684	−0.411033	−0.205517	+	0.978654i	$0.565887\pi$
$390$	51.0248	2.58374
$391$	−0.00361860	−0.000183000 0
$392$	−1.29842	−0.0655803
$393$	27.6187	1.39318
$394$	−5.91904	−0.298197
$395$	−20.6109	−1.03705
$396$	−11.2564	−0.565658
$397$	13.0537	0.655147	0.327573	−	0.944826i	$-0.393769\pi$
$397$	13.0537	0.655147	0.327573	+	0.944826i	$0.393769\pi$
$398$	−10.0731	−0.504919
$399$	−1.57088	−0.0786423
$400$	2.14083	0.107041
$401$	−14.3453	−0.716372	−0.358186	−	0.933650i	$-0.616605\pi$
$401$	−14.3453	−0.716372	−0.358186	+	0.933650i	$0.616605\pi$
$402$	−13.0315	−0.649951
$403$	−39.8249	−1.98382
$404$	12.2300	0.608463
$405$	−22.2824	−1.10722
$406$	6.23151	0.309265
$407$	0	0
$408$	−0.00118854	−5.88416e−5 0
$409$	−26.8235	−1.32634	−0.663168	−	0.748471i	$-0.730788\pi$
$409$	−26.8235	−1.32634	−0.663168	+	0.748471i	$0.730788\pi$
$410$	1.23911	0.0611954
$411$	8.25802	0.407338
$412$	−1.23770	−0.0609772
$413$	31.2844	1.53941
$414$	−53.9019	−2.64914
$415$	−13.7178	−0.673381
$416$	6.39119	0.313354
$417$	−63.4410	−3.10672
$418$	−0.418280	−0.0204588
$419$	−1.21506	−0.0593594	−0.0296797	−	0.999559i	$-0.509449\pi$
$419$	−1.21506	−0.0593594	−0.0296797	+	0.999559i	$0.509449\pi$
$420$	19.0633	0.930192
$421$	37.3400	1.81984	0.909920	−	0.414784i	$-0.136143\pi$
$421$	37.3400	1.81984	0.909920	+	0.414784i	$0.136143\pi$
$422$	18.0856	0.880394
$423$	23.2380	1.12987
$424$	6.25872	0.303950
$425$	0.000851669 0	4.13120e−5 0
$426$	−7.18265	−0.348001
$427$	20.7495	1.00414
$428$	−4.60902	−0.222785
$429$	36.2706	1.75116
$430$	11.4981	0.554486
$431$	−14.3390	−0.690687	−0.345343	−	0.938476i	$-0.612238\pi$
$431$	−14.3390	−0.690687	−0.345343	+	0.938476i	$0.612238\pi$
$432$	−8.74145	−0.420573
$433$	38.3811	1.84448	0.922239	−	0.386621i	$-0.126358\pi$
$433$	38.3811	1.84448	0.922239	+	0.386621i	$0.126358\pi$
$434$	−14.8789	−0.714210
$435$	20.8351	0.998967
$436$	8.13109	0.389409
$437$	−2.00295	−0.0958142
$438$	−39.5012	−1.88744
$439$	12.9002	0.615693	0.307846	−	0.951436i	$-0.400392\pi$
$439$	12.9002	0.615693	0.307846	+	0.951436i	$0.400392\pi$
$440$	5.07600	0.241989
$441$	−7.69431	−0.366396
$442$	0.00254256	0.000120937 0
$443$	−10.2696	−0.487924	−0.243962	−	0.969785i	$-0.578447\pi$
$443$	−10.2696	−0.487924	−0.243962	+	0.969785i	$0.578447\pi$
$444$	0	0
$445$	13.8427	0.656205
$446$	9.64175	0.456550
$447$	60.9060	2.88075
$448$	2.38780	0.112813
$449$	−25.6939	−1.21257	−0.606285	−	0.795248i	$-0.707341\pi$
$449$	−25.6939	−1.21257	−0.606285	+	0.795248i	$0.707341\pi$
$450$	12.6863	0.598038
$451$	0.880814	0.0414759
$452$	6.30361	0.296497
$453$	−34.7000	−1.63035
$454$	−6.85824	−0.321873
$455$	−40.7806	−1.91182
$456$	−0.657878	−0.0308080
$457$	−5.04458	−0.235976	−0.117988	−	0.993015i	$-0.537644\pi$
$457$	−5.04458	−0.235976	−0.117988	+	0.993015i	$0.537644\pi$
$458$	11.4979	0.537262
$459$	−0.00347754	−0.000162318 0
$460$	24.3067	1.13330
$461$	−37.2110	−1.73309	−0.866545	−	0.499099i	$-0.833664\pi$
$461$	−37.2110	−1.73309	−0.866545	+	0.499099i	$0.833664\pi$
$462$	13.5510	0.630449
$463$	28.2052	1.31081	0.655403	−	0.755280i	$-0.272499\pi$
$463$	28.2052	1.31081	0.655403	+	0.755280i	$0.272499\pi$
$464$	2.60973	0.121154
$465$	−49.7477	−2.30700
$466$	3.76050	0.174202
$467$	−34.2282	−1.58389	−0.791946	−	0.610592i	$-0.790932\pi$
$467$	−34.2282	−1.58389	−0.791946	+	0.610592i	$0.790932\pi$
$468$	37.8735	1.75070
$469$	10.4151	0.480927
$470$	−10.4790	−0.483360
$471$	−51.4353	−2.37001
$472$	13.1018	0.603059
$473$	8.17331	0.375809
$474$	−23.0435	−1.05842
$475$	0.471413	0.0216299
$476$	0.000949919 0	4.35395e−5 0
$477$	37.0885	1.69817
$478$	−4.61577	−0.211120
$479$	26.6202	1.21631	0.608155	−	0.793818i	$-0.291910\pi$
$479$	26.6202	1.21631	0.608155	+	0.793818i	$0.291910\pi$
$480$	7.98362	0.364401
$481$	0	0
$482$	19.6066	0.893056
$483$	64.8895	2.95257
$484$	−7.39176	−0.335989
$485$	37.4464	1.70035
$486$	1.31210	0.0595181
$487$	−33.1260	−1.50108	−0.750542	−	0.660822i	$-0.770208\pi$
$487$	−33.1260	−1.50108	−0.750542	+	0.660822i	$0.770208\pi$
$488$	8.68979	0.393368
$489$	−13.3199	−0.602349
$490$	3.46969	0.156745
$491$	−37.6345	−1.69842	−0.849210	−	0.528055i	$-0.822922\pi$
$491$	−37.6345	−1.69842	−0.849210	+	0.528055i	$0.822922\pi$
$492$	1.38536	0.0624568
$493$	0.00103821	4.67586e−5 0
$494$	1.40735	0.0633195
$495$	30.0798	1.35199
$496$	−6.23122	−0.279790
$497$	5.74059	0.257501
$498$	−15.3369	−0.687261
$499$	−35.5064	−1.58948	−0.794742	−	0.606947i	$-0.792394\pi$
$499$	−35.5064	−1.58948	−0.794742	+	0.606947i	$0.792394\pi$
$500$	7.64038	0.341688
$501$	42.3186	1.89066
$502$	13.8238	0.616988
$503$	9.05709	0.403836	0.201918	−	0.979402i	$-0.435283\pi$
$503$	9.05709	0.403836	0.201918	+	0.979402i	$0.435283\pi$
$504$	14.1498	0.630283
$505$	−32.6813	−1.45430
$506$	17.2782	0.768110
$507$	−83.1972	−3.69492
$508$	4.40231	0.195321
$509$	−29.2210	−1.29520	−0.647599	−	0.761982i	$-0.724227\pi$
$509$	−29.2210	−1.29520	−0.647599	+	0.761982i	$0.724227\pi$
$510$	0.00317606	0.000140638 0
$511$	31.5705	1.39660
$512$	1.00000	0.0441942
$513$	−1.92488	−0.0849854
$514$	17.2096	0.759082
$515$	3.30743	0.145743
$516$	12.8551	0.565915
$517$	−7.44892	−0.327603
$518$	0	0
$519$	6.61355	0.290303
$520$	−17.0787	−0.748952
$521$	38.6701	1.69417	0.847085	−	0.531458i	$-0.178356\pi$
$521$	38.6701	1.69417	0.847085	+	0.531458i	$0.178356\pi$
$522$	15.4650	0.676883
$523$	4.31142	0.188525	0.0942626	−	0.995547i	$-0.469951\pi$
$523$	4.31142	0.188525	0.0942626	+	0.995547i	$0.469951\pi$
$524$	−9.24437	−0.403842
$525$	−15.2723	−0.666538
$526$	−10.5274	−0.459015
$527$	−0.00247892	−0.000107983 0
$528$	5.67510	0.246977
$529$	59.7374	2.59728
$530$	−16.7248	−0.726477
$531$	77.6398	3.36928
$532$	0.525796	0.0227961
$533$	−2.96359	−0.128367
$534$	15.4764	0.669731
$535$	12.3164	0.532483
$536$	4.36182	0.188402
$537$	−8.14657	−0.351550
$538$	12.6651	0.546031
$539$	2.46640	0.106236
$540$	23.3592	1.00522
$541$	−14.2399	−0.612221	−0.306111	−	0.951996i	$-0.599028\pi$
$541$	−14.2399	−0.612221	−0.306111	+	0.951996i	$0.599028\pi$
$542$	24.9081	1.06989
$543$	−2.22294	−0.0953956
$544$	0.000397822 0	1.70565e−5 0
$545$	−21.7282	−0.930732
$546$	−45.5937	−1.95123
$547$	6.95340	0.297306	0.148653	−	0.988889i	$-0.452506\pi$
$547$	6.95340	0.297306	0.148653	+	0.988889i	$0.452506\pi$
$548$	−2.76408	−0.118075
$549$	51.4947	2.19774
$550$	−4.06658	−0.173400
$551$	0.574666	0.0244816
$552$	27.1754	1.15666
$553$	18.4171	0.783174
$554$	−10.3374	−0.439196
$555$	0	0
$556$	21.2346	0.900549
$557$	12.3706	0.524160	0.262080	−	0.965046i	$-0.415592\pi$
$557$	12.3706	0.524160	0.262080	+	0.965046i	$0.415592\pi$
$558$	−36.9255	−1.56318
$559$	−27.5000	−1.16312
$560$	−6.38075	−0.269636
$561$	0.00225768	9.53193e−5 0
$562$	20.9056	0.881849
$563$	19.9333	0.840089	0.420044	−	0.907504i	$-0.362015\pi$
$563$	19.9333	0.840089	0.420044	+	0.907504i	$0.362015\pi$
$564$	−11.7158	−0.493324
$565$	−16.8447	−0.708663
$566$	−14.7437	−0.619723
$567$	19.9106	0.836167
$568$	2.40414	0.100875
$569$	−38.7138	−1.62297	−0.811483	−	0.584375i	$-0.801340\pi$
$569$	−38.7138	−1.62297	−0.811483	+	0.584375i	$0.801340\pi$
$570$	1.75800	0.0736346
$571$	23.0412	0.964243	0.482122	−	0.876104i	$-0.339866\pi$
$571$	23.0412	0.964243	0.482122	+	0.876104i	$0.339866\pi$
$572$	−12.1403	−0.507611
$573$	10.9219	0.456269
$574$	−1.10722	−0.0462145
$575$	−19.4730	−0.812080
$576$	5.92589	0.246912
$577$	−6.84215	−0.284843	−0.142421	−	0.989806i	$-0.545489\pi$
$577$	−6.84215	−0.284843	−0.142421	+	0.989806i	$0.545489\pi$
$578$	−17.0000	−0.707107
$579$	−32.8868	−1.36673
$580$	−6.97381	−0.289572
$581$	12.2577	0.508534
$582$	41.8660	1.73540
$583$	−11.8887	−0.492379
$584$	13.2216	0.547114
$585$	−101.207	−4.18438
$586$	27.0174	1.11608
$587$	−4.13881	−0.170827	−0.0854135	−	0.996346i	$-0.527221\pi$
$587$	−4.13881	−0.170827	−0.0854135	+	0.996346i	$0.527221\pi$
$588$	3.87920	0.159976
$589$	−1.37212	−0.0565373
$590$	−35.0111	−1.44138
$591$	17.6839	0.727417
$592$	0	0
$593$	−23.3895	−0.960493	−0.480246	−	0.877134i	$-0.659453\pi$
$593$	−23.3895	−0.960493	−0.480246	+	0.877134i	$0.659453\pi$
$594$	16.6047	0.681299
$595$	−0.00253840	−0.000104064 0
$596$	−20.3861	−0.835047
$597$	30.0947	1.23169
$598$	−58.1343	−2.37729
$599$	−36.3352	−1.48461	−0.742307	−	0.670060i	$-0.766269\pi$
$599$	−36.3352	−1.48461	−0.742307	+	0.670060i	$0.766269\pi$
$600$	−6.39598	−0.261115
$601$	−2.71285	−0.110659	−0.0553297	−	0.998468i	$-0.517621\pi$
$601$	−2.71285	−0.110659	−0.0553297	+	0.998468i	$0.517621\pi$
$602$	−10.2742	−0.418745
$603$	25.8477	1.05260
$604$	11.6146	0.472591
$605$	19.7525	0.803053
$606$	−36.5385	−1.48428
$607$	9.70247	0.393811	0.196906	−	0.980422i	$-0.436911\pi$
$607$	9.70247	0.393811	0.196906	+	0.980422i	$0.436911\pi$
$608$	0.220201	0.00893034
$609$	−18.6174	−0.754415
$610$	−23.2212	−0.940197
$611$	25.0627	1.01393
$612$	0.00235745	9.52943e−5 0
$613$	−10.5942	−0.427896	−0.213948	−	0.976845i	$-0.568632\pi$
$613$	−10.5942	−0.427896	−0.213948	+	0.976845i	$0.568632\pi$
$614$	12.4627	0.502955
$615$	−3.70200	−0.149279
$616$	−4.53571	−0.182749
$617$	−1.54476	−0.0621895	−0.0310948	−	0.999516i	$-0.509899\pi$
$617$	−1.54476	−0.0621895	−0.0310948	+	0.999516i	$0.509899\pi$
$618$	3.69778	0.148747
$619$	−2.64172	−0.106180	−0.0530898	−	0.998590i	$-0.516907\pi$
$619$	−2.64172	−0.106180	−0.0530898	+	0.998590i	$0.516907\pi$
$620$	16.6513	0.668732
$621$	79.5123	3.19072
$622$	−25.7845	−1.03386
$623$	−12.3692	−0.495563
$624$	−19.0945	−0.764390
$625$	−31.1210	−1.24484
$626$	9.49854	0.379638
$627$	1.24966	0.0499067
$628$	17.2161	0.686998
$629$	0	0
$630$	−37.8116	−1.50645
$631$	−6.53624	−0.260204	−0.130102	−	0.991501i	$-0.541530\pi$
$631$	−6.53624	−0.260204	−0.130102	+	0.991501i	$0.541530\pi$
$632$	7.71300	0.306807
$633$	−54.0330	−2.14762
$634$	27.1642	1.07883
$635$	−11.7640	−0.466840
$636$	−18.6987	−0.741452
$637$	−8.29847	−0.328797
$638$	−4.95728	−0.196261
$639$	14.2466	0.563588
$640$	−2.67223	−0.105629
$641$	21.8886	0.864548	0.432274	−	0.901742i	$-0.357711\pi$
$641$	21.8886	0.864548	0.432274	+	0.901742i	$0.357711\pi$
$642$	13.7700	0.543459
$643$	−37.7553	−1.48892	−0.744462	−	0.667665i	$-0.767294\pi$
$643$	−37.7553	−1.48892	−0.744462	+	0.667665i	$0.767294\pi$
$644$	−21.7194	−0.855865
$645$	−34.3519	−1.35260
$646$	8.76009e−5 0	3.44661e−6 0
$647$	35.2414	1.38548	0.692741	−	0.721186i	$-0.256403\pi$
$647$	35.2414	1.38548	0.692741	+	0.721186i	$0.256403\pi$
$648$	8.33849	0.327567
$649$	−24.8873	−0.976914
$650$	13.6824	0.536669
$651$	44.4525	1.74223
$652$	4.45838	0.174603
$653$	−6.46268	−0.252904	−0.126452	−	0.991973i	$-0.540359\pi$
$653$	−6.46268	−0.252904	−0.126452	+	0.991973i	$0.540359\pi$
$654$	−24.2926	−0.949917
$655$	24.7031	0.965230
$656$	−0.463700	−0.0181044
$657$	78.3498	3.05672
$658$	9.36361	0.365031
$659$	6.42787	0.250394	0.125197	−	0.992132i	$-0.460044\pi$
$659$	6.42787	0.250394	0.125197	+	0.992132i	$0.460044\pi$
$660$	−15.1652	−0.590304
$661$	−40.8463	−1.58874	−0.794369	−	0.607435i	$-0.792198\pi$
$661$	−40.8463	−1.58874	−0.794369	+	0.607435i	$0.792198\pi$
$662$	−23.5255	−0.914345
$663$	−0.00759620	−0.000295012 0
$664$	5.13347	0.199217
$665$	−1.40505	−0.0544854
$666$	0	0
$667$	−23.7381	−0.919144
$668$	−14.1646	−0.548046
$669$	−28.8059	−1.11370
$670$	−11.6558	−0.450303
$671$	−16.5066	−0.637230
$672$	−7.13384	−0.275194
$673$	−43.4703	−1.67566	−0.837828	−	0.545935i	$-0.816175\pi$
$673$	−43.4703	−1.67566	−0.837828	+	0.545935i	$0.816175\pi$
$674$	30.0729	1.15837
$675$	−18.7139	−0.720300
$676$	27.8473	1.07105
$677$	−27.3476	−1.05105	−0.525527	−	0.850777i	$-0.676132\pi$
$677$	−27.3476	−1.05105	−0.525527	+	0.850777i	$0.676132\pi$
$678$	−18.8328	−0.723270
$679$	−33.4605	−1.28410
$680$	−0.00106307	−4.07670e−5 0
$681$	20.4898	0.785172
$682$	11.8364	0.453241
$683$	30.3517	1.16138	0.580689	−	0.814126i	$-0.302783\pi$
$683$	30.3517	1.16138	0.580689	+	0.814126i	$0.302783\pi$
$684$	1.30489	0.0498936
$685$	7.38625	0.282214
$686$	−19.8150	−0.756538
$687$	−34.3514	−1.31059
$688$	−4.30279	−0.164042
$689$	40.0007	1.52390
$690$	−72.6191	−2.76456
$691$	27.4177	1.04302	0.521509	−	0.853246i	$-0.325369\pi$
$691$	27.4177	1.04302	0.521509	+	0.853246i	$0.325369\pi$
$692$	−2.21365	−0.0841504
$693$	−26.8781	−1.02101
$694$	−5.99818	−0.227688
$695$	−56.7438	−2.15242
$696$	−7.79689	−0.295540
$697$	−0.000184470 0	−6.98730e−6 0
$698$	−8.18585	−0.309839
$699$	−11.2349	−0.424944
$700$	5.11186	0.193210
$701$	−5.62527	−0.212464	−0.106232	−	0.994341i	$-0.533879\pi$
$701$	−5.62527	−0.212464	−0.106232	+	0.994341i	$0.533879\pi$
$702$	−55.8683	−2.10861
$703$	0	0
$704$	−1.89954	−0.0715915
$705$	31.3073	1.17910
$706$	12.7006	0.477994
$707$	29.2027	1.09828
$708$	−39.1432	−1.47109
$709$	11.1614	0.419174	0.209587	−	0.977790i	$-0.432788\pi$
$709$	11.1614	0.419174	0.209587	+	0.977790i	$0.432788\pi$
$710$	−6.42441	−0.241104
$711$	45.7064	1.71412
$712$	−5.18018	−0.194136
$713$	56.6793	2.12266
$714$	−0.00283800	−0.000106209 0
$715$	32.4417	1.21325
$716$	2.72677	0.101904
$717$	13.7902	0.515003
$718$	−0.847562	−0.0316307
$719$	−2.10252	−0.0784109	−0.0392055	−	0.999231i	$-0.512483\pi$
$719$	−2.10252	−0.0784109	−0.0392055	+	0.999231i	$0.512483\pi$
$720$	−15.8354	−0.590149
$721$	−2.95538	−0.110064
$722$	−18.9515	−0.705302
$723$	−58.5771	−2.17851
$724$	0.744051	0.0276524
$725$	5.58698	0.207495
$726$	22.0838	0.819606
$727$	49.8782	1.84988	0.924941	−	0.380111i	$-0.124114\pi$
$727$	49.8782	1.84988	0.924941	+	0.380111i	$0.124114\pi$
$728$	15.2609	0.565605
$729$	−28.9355	−1.07169
$730$	−35.3312	−1.30767
$731$	−0.00171175	−6.33112e−5 0
$732$	−25.9618	−0.959577
$733$	−10.0966	−0.372928	−0.186464	−	0.982462i	$-0.559703\pi$
$733$	−10.0966	−0.372928	−0.186464	+	0.982462i	$0.559703\pi$
$734$	22.1202	0.816471
$735$	−10.3661	−0.382360
$736$	−9.09601	−0.335283
$737$	−8.28544	−0.305198
$738$	−2.74783	−0.101149
$739$	−11.2953	−0.415503	−0.207751	−	0.978182i	$-0.566614\pi$
$739$	−11.2953	−0.415503	−0.207751	+	0.978182i	$0.566614\pi$
$740$	0	0
$741$	−4.20462	−0.154461
$742$	14.9446	0.548632
$743$	−3.67252	−0.134732	−0.0673659	−	0.997728i	$-0.521459\pi$
$743$	−3.67252	−0.134732	−0.0673659	+	0.997728i	$0.521459\pi$
$744$	18.6165	0.682516
$745$	54.4764	1.99586
$746$	15.7676	0.577293
$747$	30.4204	1.11302
$748$	−0.000755678 0	−2.76303e−5 0
$749$	−11.0054	−0.402129
$750$	−22.8266	−0.833508
$751$	−27.5452	−1.00514	−0.502570	−	0.864537i	$-0.667612\pi$
$751$	−27.5452	−1.00514	−0.502570	+	0.864537i	$0.667612\pi$
$752$	3.92144	0.143000
$753$	−41.3004	−1.50507
$754$	16.6793	0.607424
$755$	−31.0369	−1.12955
$756$	−20.8728	−0.759137
$757$	7.37321	0.267984	0.133992	−	0.990982i	$-0.457220\pi$
$757$	7.37321	0.267984	0.133992	+	0.990982i	$0.457220\pi$
$758$	−8.02033	−0.291311
$759$	−51.6208	−1.87371
$760$	−0.588429	−0.0213446
$761$	−37.3941	−1.35553	−0.677767	−	0.735277i	$-0.737052\pi$
$761$	−37.3941	−1.35553	−0.677767	+	0.735277i	$0.737052\pi$
$762$	−13.1524	−0.476463
$763$	19.4154	0.702885
$764$	−3.65572	−0.132259
$765$	−0.00629966	−0.000227765 0
$766$	26.6472	0.962802
$767$	83.7361	3.02353
$768$	−2.98762	−0.107807
$769$	33.2938	1.20061	0.600303	−	0.799773i	$-0.295047\pi$
$769$	33.2938	1.20061	0.600303	+	0.799773i	$0.295047\pi$
$770$	12.1205	0.436791
$771$	−51.4157	−1.85169
$772$	11.0077	0.396175
$773$	47.9494	1.72462	0.862311	−	0.506380i	$-0.169017\pi$
$773$	47.9494	1.72462	0.862311	+	0.506380i	$0.169017\pi$
$774$	−25.4979	−0.916502
$775$	−13.3400	−0.479186
$776$	−14.0131	−0.503042
$777$	0	0
$778$	−8.10684	−0.290644
$779$	−0.102107	−0.00365837
$780$	51.0248	1.82698
$781$	−4.56674	−0.163411
$782$	−0.00361860	−0.000129401 0
$783$	−22.8128	−0.815264
$784$	−1.29842	−0.0463723
$785$	−46.0055	−1.64201
$786$	27.6187	0.985126
$787$	3.57931	0.127589	0.0637943	−	0.997963i	$-0.479680\pi$
$787$	3.57931	0.127589	0.0637943	+	0.997963i	$0.479680\pi$
$788$	−5.91904	−0.210857
$789$	31.4518	1.11971
$790$	−20.6109	−0.733304
$791$	15.0517	0.535179
$792$	−11.2564	−0.399980
$793$	55.5381	1.97222
$794$	13.0537	0.463259
$795$	49.9673	1.77216
$796$	−10.0731	−0.357032
$797$	40.3127	1.42795	0.713974	−	0.700172i	$-0.246893\pi$
$797$	40.3127	1.42795	0.713974	+	0.700172i	$0.246893\pi$
$798$	−1.57088	−0.0556085
$799$	0.00156004	5.51901e−5 0
$800$	2.14083	0.0756897
$801$	−30.6972	−1.08463
$802$	−14.3453	−0.506552
$803$	−25.1149	−0.886287
$804$	−13.0315	−0.459585
$805$	58.0394	2.04562
$806$	−39.8249	−1.40277
$807$	−37.8385	−1.33198
$808$	12.2300	0.430249
$809$	14.0082	0.492503	0.246251	−	0.969206i	$-0.420801\pi$
$809$	14.0082	0.492503	0.246251	+	0.969206i	$0.420801\pi$
$810$	−22.2824	−0.782923
$811$	−7.19135	−0.252523	−0.126261	−	0.991997i	$-0.540298\pi$
$811$	−7.19135	−0.252523	−0.126261	+	0.991997i	$0.540298\pi$
$812$	6.23151	0.218683
$813$	−74.4159	−2.60988
$814$	0	0
$815$	−11.9138	−0.417323
$816$	−0.00118854	−4.16073e−5 0
$817$	−0.947480	−0.0331481
$818$	−26.8235	−0.937861
$819$	90.4342	3.16003
$820$	1.23911	0.0432717
$821$	38.1273	1.33065	0.665326	−	0.746553i	$-0.268293\pi$
$821$	38.1273	1.33065	0.665326	+	0.746553i	$0.268293\pi$
$822$	8.25802	0.288031
$823$	−13.8360	−0.482293	−0.241146	−	0.970489i	$-0.577523\pi$
$823$	−13.8360	−0.482293	−0.241146	+	0.970489i	$0.577523\pi$
$824$	−1.23770	−0.0431174
$825$	12.1494	0.422988
$826$	31.2844	1.08852
$827$	44.0582	1.53205	0.766026	−	0.642809i	$-0.222231\pi$
$827$	44.0582	1.53205	0.766026	+	0.642809i	$0.222231\pi$
$828$	−53.9019	−1.87322
$829$	−35.3772	−1.22870	−0.614350	−	0.789034i	$-0.710582\pi$
$829$	−35.3772	−1.22870	−0.614350	+	0.789034i	$0.710582\pi$
$830$	−13.7178	−0.476152
$831$	30.8844	1.07137
$832$	6.39119	0.221575
$833$	−0.000516542 0	−1.78971e−5 0
$834$	−63.4410	−2.19678
$835$	37.8512	1.30990
$836$	−0.418280	−0.0144665
$837$	54.4699	1.88276
$838$	−1.21506	−0.0419735
$839$	−6.28797	−0.217085	−0.108542	−	0.994092i	$-0.534618\pi$
$839$	−6.28797	−0.217085	−0.108542	+	0.994092i	$0.534618\pi$
$840$	19.0633	0.657745
$841$	−22.1893	−0.765149
$842$	37.3400	1.28682
$843$	−62.4580	−2.15117
$844$	18.0856	0.622533
$845$	−74.4145	−2.55994
$846$	23.2380	0.798940
$847$	−17.6500	−0.606462
$848$	6.25872	0.214925
$849$	44.0486	1.51174
$850$	0.000851669 0	2.92120e−5 0
$851$	0	0
$852$	−7.18265	−0.246074
$853$	−5.26735	−0.180350	−0.0901752	−	0.995926i	$-0.528743\pi$
$853$	−5.26735	−0.180350	−0.0901752	+	0.995926i	$0.528743\pi$
$854$	20.7495	0.710032
$855$	−3.48696	−0.119252
$856$	−4.60902	−0.157533
$857$	2.02428	0.0691480	0.0345740	−	0.999402i	$-0.488993\pi$
$857$	2.02428	0.0691480	0.0345740	+	0.999402i	$0.488993\pi$
$858$	36.2706	1.23826
$859$	−20.5137	−0.699917	−0.349958	−	0.936765i	$-0.613804\pi$
$859$	−20.5137	−0.699917	−0.349958	+	0.936765i	$0.613804\pi$
$860$	11.4981	0.392081
$861$	3.30796	0.112735
$862$	−14.3390	−0.488389
$863$	48.1223	1.63810	0.819051	−	0.573721i	$-0.194501\pi$
$863$	48.1223	1.63810	0.819051	+	0.573721i	$0.194501\pi$
$864$	−8.74145	−0.297390
$865$	5.91539	0.201129
$866$	38.3811	1.30424
$867$	50.7896	1.72490
$868$	−14.8789	−0.505023
$869$	−14.6511	−0.497005
$870$	20.8351	0.706376
$871$	27.8772	0.944584
$872$	8.13109	0.275354
$873$	−83.0403	−2.81049
$874$	−2.00295	−0.0677509
$875$	18.2437	0.616749
$876$	−39.5012	−1.33462
$877$	2.64193	0.0892115	0.0446058	−	0.999005i	$-0.485797\pi$
$877$	2.64193	0.0892115	0.0446058	+	0.999005i	$0.485797\pi$
$878$	12.9002	0.435361
$879$	−80.7179	−2.72255
$880$	5.07600	0.171112
$881$	28.2677	0.952362	0.476181	−	0.879347i	$-0.342021\pi$
$881$	28.2677	0.952362	0.476181	+	0.879347i	$0.342021\pi$
$882$	−7.69431	−0.259081
$883$	−45.1055	−1.51792	−0.758961	−	0.651137i	$-0.774293\pi$
$883$	−45.1055	−1.51792	−0.758961	+	0.651137i	$0.774293\pi$
$884$	0.00254256	8.55155e−5 0
$885$	104.600	3.51608
$886$	−10.2696	−0.345015
$887$	−29.6923	−0.996969	−0.498484	−	0.866899i	$-0.666110\pi$
$887$	−29.6923	−0.996969	−0.498484	+	0.866899i	$0.666110\pi$
$888$	0	0
$889$	10.5118	0.352555
$890$	13.8427	0.464007
$891$	−15.8393	−0.530635
$892$	9.64175	0.322830
$893$	0.863506	0.0288961
$894$	60.9060	2.03700
$895$	−7.28657	−0.243563
$896$	2.38780	0.0797707
$897$	173.683	5.79912
$898$	−25.6939	−0.857416
$899$	−16.2618	−0.542362
$900$	12.6863	0.422877
$901$	0.00248986	8.29492e−5 0
$902$	0.880814	0.0293279
$903$	30.6954	1.02148
$904$	6.30361	0.209655
$905$	−1.98828	−0.0660926
$906$	−34.7000	−1.15283
$907$	−51.5659	−1.71222	−0.856108	−	0.516796i	$-0.827124\pi$
$907$	−51.5659	−1.71222	−0.856108	+	0.516796i	$0.827124\pi$
$908$	−6.85824	−0.227599
$909$	72.4734	2.40379
$910$	−40.7806	−1.35186
$911$	22.5769	0.748006	0.374003	−	0.927427i	$-0.377985\pi$
$911$	22.5769	0.748006	0.374003	+	0.927427i	$0.377985\pi$
$912$	−0.657878	−0.0217845
$913$	−9.75121	−0.322718
$914$	−5.04458	−0.166860
$915$	69.3760	2.29350
$916$	11.4979	0.379902
$917$	−22.0737	−0.728937
$918$	−0.00347754	−0.000114776 0
$919$	−10.5430	−0.347780	−0.173890	−	0.984765i	$-0.555634\pi$
$919$	−10.5430	−0.347780	−0.173890	+	0.984765i	$0.555634\pi$
$920$	24.3067	0.801367
$921$	−37.2339	−1.22690
$922$	−37.2110	−1.22548
$923$	15.3653	0.505755
$924$	13.5510	0.445795
$925$	0	0
$926$	28.2052	0.926879
$927$	−7.33448	−0.240896
$928$	2.60973	0.0856686
$929$	−5.00452	−0.164193	−0.0820965	−	0.996624i	$-0.526162\pi$
$929$	−5.00452	−0.164193	−0.0820965	+	0.996624i	$0.526162\pi$
$930$	−49.7477	−1.63129
$931$	−0.285914	−0.00937047
$932$	3.76050	0.123179
$933$	77.0342	2.52199
$934$	−34.2282	−1.11998
$935$	0.00201935	6.60397e−5 0
$936$	37.8735	1.23793
$937$	12.2061	0.398757	0.199378	−	0.979923i	$-0.436108\pi$
$937$	12.2061	0.398757	0.199378	+	0.979923i	$0.436108\pi$
$938$	10.4151	0.340067
$939$	−28.3781	−0.926083
$940$	−10.4790	−0.341787
$941$	−43.5003	−1.41807	−0.709034	−	0.705174i	$-0.750869\pi$
$941$	−43.5003	−1.41807	−0.709034	+	0.705174i	$0.750869\pi$
$942$	−51.4353	−1.67585
$943$	4.21782	0.137351
$944$	13.1018	0.426427
$945$	55.7770	1.81443
$946$	8.17331	0.265737
$947$	−22.0361	−0.716079	−0.358039	−	0.933707i	$-0.616555\pi$
$947$	−22.0361	−0.716079	−0.358039	+	0.933707i	$0.616555\pi$
$948$	−23.0435	−0.748419
$949$	84.5018	2.74305
$950$	0.471413	0.0152946
$951$	−81.1565	−2.63168
$952$	0.000949919 0	3.07870e−5 0
$953$	−16.0799	−0.520880	−0.260440	−	0.965490i	$-0.583868\pi$
$953$	−16.0799	−0.520880	−0.260440	+	0.965490i	$0.583868\pi$
$954$	37.0885	1.20078
$955$	9.76893	0.316115
$956$	−4.61577	−0.149285
$957$	14.8105	0.478755
$958$	26.6202	0.860061
$959$	−6.60005	−0.213127
$960$	7.98362	0.257670
$961$	7.82816	0.252521
$962$	0	0
$963$	−27.3125	−0.880134
$964$	19.6066	0.631486
$965$	−29.4151	−0.946905
$966$	64.8895	2.08778
$967$	−15.6511	−0.503305	−0.251653	−	0.967818i	$-0.580974\pi$
$967$	−15.6511	−0.503305	−0.251653	+	0.967818i	$0.580974\pi$
$968$	−7.39176	−0.237580
$969$	−0.000261718 0	−8.40761e−6 0
$970$	37.4464	1.20233
$971$	−31.8250	−1.02131	−0.510657	−	0.859785i	$-0.670598\pi$
$971$	−31.8250	−1.02131	−0.510657	+	0.859785i	$0.670598\pi$
$972$	1.31210	0.0420856
$973$	50.7040	1.62549
$974$	−33.1260	−1.06143
$975$	−40.8779	−1.30914
$976$	8.68979	0.278154
$977$	13.1421	0.420454	0.210227	−	0.977653i	$-0.432580\pi$
$977$	13.1421	0.420454	0.210227	+	0.977653i	$0.432580\pi$
$978$	−13.3199	−0.425925
$979$	9.83995	0.314486
$980$	3.46969	0.110835
$981$	48.1839	1.53839
$982$	−37.6345	−1.20096
$983$	9.38725	0.299407	0.149703	−	0.988731i	$-0.452168\pi$
$983$	9.38725	0.299407	0.149703	+	0.988731i	$0.452168\pi$
$984$	1.38536	0.0441636
$985$	15.8170	0.503973
$986$	0.00103821	3.30633e−5 0
$987$	−27.9749	−0.890452
$988$	1.40735	0.0447737
$989$	39.1383	1.24452
$990$	30.0798	0.956000
$991$	−1.52680	−0.0485005	−0.0242503	−	0.999706i	$-0.507720\pi$
$991$	−1.52680	−0.0485005	−0.0242503	+	0.999706i	$0.507720\pi$
$992$	−6.23122	−0.197842
$993$	70.2853	2.23044
$994$	5.74059	0.182080
$995$	26.9177	0.853348
$996$	−15.3369	−0.485967
$997$	−7.22896	−0.228943	−0.114472	−	0.993427i	$-0.536518\pi$
$997$	−7.22896	−0.228943	−0.114472	+	0.993427i	$0.536518\pi$
$998$	−35.5064	−1.12393
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.x.1.2	yes	18
37.36	even	2		2738.2.a.w.1.2	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.w.1.2	✓	18	37.36	even	2
2738.2.a.x.1.2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.98762 q^{3} +1.00000 q^{4} -2.67223 q^{5} -2.98762 q^{6} +2.38780 q^{7} +1.00000 q^{8} +5.92589 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.98762 q^{3} +1.00000 q^{4} -2.67223 q^{5} -2.98762 q^{6} +2.38780 q^{7} +1.00000 q^{8} +5.92589 q^{9} -2.67223 q^{10} -1.89954 q^{11} -2.98762 q^{12} +6.39119 q^{13} +2.38780 q^{14} +7.98362 q^{15} +1.00000 q^{16} +0.000397822 q^{17} +5.92589 q^{18} +0.220201 q^{19} -2.67223 q^{20} -7.13384 q^{21} -1.89954 q^{22} -9.09601 q^{23} -2.98762 q^{24} +2.14083 q^{25} +6.39119 q^{26} -8.74145 q^{27} +2.38780 q^{28} +2.60973 q^{29} +7.98362 q^{30} -6.23122 q^{31} +1.00000 q^{32} +5.67510 q^{33} +0.000397822 q^{34} -6.38075 q^{35} +5.92589 q^{36} +0.220201 q^{38} -19.0945 q^{39} -2.67223 q^{40} -0.463700 q^{41} -7.13384 q^{42} -4.30279 q^{43} -1.89954 q^{44} -15.8354 q^{45} -9.09601 q^{46} +3.92144 q^{47} -2.98762 q^{48} -1.29842 q^{49} +2.14083 q^{50} -0.00118854 q^{51} +6.39119 q^{52} +6.25872 q^{53} -8.74145 q^{54} +5.07600 q^{55} +2.38780 q^{56} -0.657878 q^{57} +2.60973 q^{58} +13.1018 q^{59} +7.98362 q^{60} +8.68979 q^{61} -6.23122 q^{62} +14.1498 q^{63} +1.00000 q^{64} -17.0787 q^{65} +5.67510 q^{66} +4.36182 q^{67} +0.000397822 q^{68} +27.1754 q^{69} -6.38075 q^{70} +2.40414 q^{71} +5.92589 q^{72} +13.2216 q^{73} -6.39598 q^{75} +0.220201 q^{76} -4.53571 q^{77} -19.0945 q^{78} +7.71300 q^{79} -2.67223 q^{80} +8.33849 q^{81} -0.463700 q^{82} +5.13347 q^{83} -7.13384 q^{84} -0.00106307 q^{85} -4.30279 q^{86} -7.79689 q^{87} -1.89954 q^{88} -5.18018 q^{89} -15.8354 q^{90} +15.2609 q^{91} -9.09601 q^{92} +18.6165 q^{93} +3.92144 q^{94} -0.588429 q^{95} -2.98762 q^{96} -14.0131 q^{97} -1.29842 q^{98} -11.2564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} + 8 q^{3} + 18 q^{4} + 9 q^{5} + 8 q^{6} + 18 q^{7} + 18 q^{8} + 26 q^{9}+O(q^{10}) \) 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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