LMFDB - Embedded newform 2738.2.a.t.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:	$6$
Coefficient field:	6.6.37902897.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} - x^{3} + 60x^{2} - 64 $ x^6 - 15x^4 - x^3 + 60x^2 - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.83388$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.83388 q^{3} +1.00000 q^{4} -1.87939 q^{5} -1.83388 q^{6} +3.44656 q^{7} +1.00000 q^{8} +0.363102 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.83388 q^{3} +1.00000 q^{4} -1.87939 q^{5} -1.83388 q^{6} +3.44656 q^{7} +1.00000 q^{8} +0.363102 q^{9} -1.87939 q^{10} -2.80966 q^{11} -1.83388 q^{12} -3.47077 q^{13} +3.44656 q^{14} +3.44656 q^{15} +1.00000 q^{16} -3.09926 q^{17} +0.363102 q^{18} +7.44656 q^{19} -1.87939 q^{20} -6.32056 q^{21} -2.80966 q^{22} -0.643537 q^{23} -1.83388 q^{24} -1.46791 q^{25} -3.47077 q^{26} +4.83575 q^{27} +3.44656 q^{28} +2.16899 q^{29} +3.44656 q^{30} +9.90716 q^{31} +1.00000 q^{32} +5.15257 q^{33} -3.09926 q^{34} -6.47741 q^{35} +0.363102 q^{36} +7.44656 q^{38} +6.36497 q^{39} -1.87939 q^{40} -10.6234 q^{41} -6.32056 q^{42} +8.30465 q^{43} -2.80966 q^{44} -0.682408 q^{45} -0.643537 q^{46} -7.85643 q^{47} -1.83388 q^{48} +4.87877 q^{49} -1.46791 q^{50} +5.68366 q^{51} -3.47077 q^{52} +4.83388 q^{53} +4.83575 q^{54} +5.28044 q^{55} +3.44656 q^{56} -13.6561 q^{57} +2.16899 q^{58} +0.553440 q^{59} +3.44656 q^{60} +7.01137 q^{61} +9.90716 q^{62} +1.25145 q^{63} +1.00000 q^{64} +6.52292 q^{65} +5.15257 q^{66} +0.211021 q^{67} -3.09926 q^{68} +1.18017 q^{69} -6.47741 q^{70} +5.05694 q^{71} +0.363102 q^{72} +10.2297 q^{73} +2.69197 q^{75} +7.44656 q^{76} -9.68366 q^{77} +6.36497 q^{78} -1.90486 q^{79} -1.87939 q^{80} -9.95746 q^{81} -10.6234 q^{82} +6.80966 q^{83} -6.32056 q^{84} +5.82471 q^{85} +8.30465 q^{86} -3.97765 q^{87} -2.80966 q^{88} -9.68773 q^{89} -0.682408 q^{90} -11.9622 q^{91} -0.643537 q^{92} -18.1685 q^{93} -7.85643 q^{94} -13.9950 q^{95} -1.83388 q^{96} +17.0598 q^{97} +4.87877 q^{98} -1.02019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9} - 3 q^{11} - 3 q^{14} - 3 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} + 21 q^{19} + 6 q^{21} - 3 q^{22} + 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28} - 6 q^{29} - 3 q^{30} + 21 q^{31} + 6 q^{32} - 3 q^{33} + 3 q^{34} - 3 q^{35} + 12 q^{36} + 21 q^{38} + 27 q^{39} + 18 q^{41} + 6 q^{42} + 18 q^{43} - 3 q^{44} + 6 q^{45} + 21 q^{46} - 9 q^{47} + 15 q^{49} - 18 q^{50} + 18 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} + 6 q^{57} - 6 q^{58} + 27 q^{59} - 3 q^{60} - 24 q^{61} + 21 q^{62} - 36 q^{63} + 6 q^{64} + 3 q^{65} - 3 q^{66} + 9 q^{67} + 3 q^{68} + 27 q^{69} - 3 q^{70} + 12 q^{72} + 27 q^{73} - 3 q^{75} + 21 q^{76} - 24 q^{77} + 27 q^{78} + 21 q^{79} - 6 q^{81} + 18 q^{82} + 27 q^{83} + 6 q^{84} - 3 q^{85} + 18 q^{86} - 3 q^{88} - 21 q^{89} + 6 q^{90} - 24 q^{91} + 21 q^{92} + 54 q^{93} - 9 q^{94} - 3 q^{95} + 42 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9 - 3 * q^11 - 3 * q^14 - 3 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 + 21 * q^19 + 6 * q^21 - 3 * q^22 + 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 - 6 * q^29 - 3 * q^30 + 21 * q^31 + 6 * q^32 - 3 * q^33 + 3 * q^34 - 3 * q^35 + 12 * q^36 + 21 * q^38 + 27 * q^39 + 18 * q^41 + 6 * q^42 + 18 * q^43 - 3 * q^44 + 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 - 18 * q^50 + 18 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 6 * q^57 - 6 * q^58 + 27 * q^59 - 3 * q^60 - 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 - 3 * q^66 + 9 * q^67 + 3 * q^68 + 27 * q^69 - 3 * q^70 + 12 * q^72 + 27 * q^73 - 3 * q^75 + 21 * q^76 - 24 * q^77 + 27 * q^78 + 21 * q^79 - 6 * q^81 + 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 - 3 * q^88 - 21 * q^89 + 6 * q^90 - 24 * q^91 + 21 * q^92 + 54 * q^93 - 9 * q^94 - 3 * q^95 + 42 * q^97 + 15 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.83388	−1.05879	−0.529394	−	0.848376i	$-0.677581\pi$
$3$	−1.83388	−1.05879	−0.529394	+	0.848376i	$0.677581\pi$
$4$	1.00000	0.500000
$5$	−1.87939	−0.840487	−0.420243	−	0.907411i	$-0.638055\pi$
$5$	−1.87939	−0.840487	−0.420243	+	0.907411i	$0.638055\pi$
$6$	−1.83388	−0.748677
$7$	3.44656	1.30268	0.651339	−	0.758787i	$-0.274208\pi$
$7$	3.44656	1.30268	0.651339	+	0.758787i	$0.274208\pi$
$8$	1.00000	0.353553
$9$	0.363102	0.121034
$10$	−1.87939	−0.594314
$11$	−2.80966	−0.847145	−0.423572	−	0.905862i	$-0.639224\pi$
$11$	−2.80966	−0.847145	−0.423572	+	0.905862i	$0.639224\pi$
$12$	−1.83388	−0.529394
$13$	−3.47077	−0.962620	−0.481310	−	0.876551i	$-0.659839\pi$
$13$	−3.47077	−0.962620	−0.481310	+	0.876551i	$0.659839\pi$
$14$	3.44656	0.921132
$15$	3.44656	0.889898
$16$	1.00000	0.250000
$17$	−3.09926	−0.751682	−0.375841	−	0.926684i	$-0.622646\pi$
$17$	−3.09926	−0.751682	−0.375841	+	0.926684i	$0.622646\pi$
$18$	0.363102	0.0855838
$19$	7.44656	1.70836	0.854179	−	0.519979i	$-0.174060\pi$
$19$	7.44656	1.70836	0.854179	+	0.519979i	$0.174060\pi$
$20$	−1.87939	−0.420243
$21$	−6.32056	−1.37926
$22$	−2.80966	−0.599022
$23$	−0.643537	−0.134187	−0.0670934	−	0.997747i	$-0.521373\pi$
$23$	−0.643537	−0.134187	−0.0670934	+	0.997747i	$0.521373\pi$
$24$	−1.83388	−0.374338
$25$	−1.46791	−0.293582
$26$	−3.47077	−0.680675
$27$	4.83575	0.930640
$28$	3.44656	0.651339
$29$	2.16899	0.402771	0.201385	−	0.979512i	$-0.435456\pi$
$29$	2.16899	0.402771	0.201385	+	0.979512i	$0.435456\pi$
$30$	3.44656	0.629253
$31$	9.90716	1.77938	0.889690	−	0.456566i	$-0.150921\pi$
$31$	9.90716	1.77938	0.889690	+	0.456566i	$0.150921\pi$
$32$	1.00000	0.176777
$33$	5.15257	0.896947
$34$	−3.09926	−0.531519
$35$	−6.47741	−1.09488
$36$	0.363102	0.0605169
$37$	0	0
$37$	0	0
$38$	7.44656	1.20799
$39$	6.36497	1.01921
$40$	−1.87939	−0.297157
$41$	−10.6234	−1.65910	−0.829552	−	0.558430i	$-0.811404\pi$
$41$	−10.6234	−1.65910	−0.829552	+	0.558430i	$0.811404\pi$
$42$	−6.32056	−0.975284
$43$	8.30465	1.26645	0.633224	−	0.773969i	$-0.281731\pi$
$43$	8.30465	1.26645	0.633224	+	0.773969i	$0.281731\pi$
$44$	−2.80966	−0.423572
$45$	−0.682408	−0.101727
$46$	−0.643537	−0.0948844
$47$	−7.85643	−1.14598	−0.572989	−	0.819563i	$-0.694216\pi$
$47$	−7.85643	−1.14598	−0.572989	+	0.819563i	$0.694216\pi$
$48$	−1.83388	−0.264697
$49$	4.87877	0.696968
$50$	−1.46791	−0.207594
$51$	5.68366	0.795872
$52$	−3.47077	−0.481310
$53$	4.83388	0.663984	0.331992	−	0.943282i	$-0.392279\pi$
$53$	4.83388	0.663984	0.331992	+	0.943282i	$0.392279\pi$
$54$	4.83575	0.658062
$55$	5.28044	0.712014
$56$	3.44656	0.460566
$57$	−13.6561	−1.80879
$58$	2.16899	0.284802
$59$	0.553440	0.0720518	0.0360259	−	0.999351i	$-0.488530\pi$
$59$	0.553440	0.0720518	0.0360259	+	0.999351i	$0.488530\pi$
$60$	3.44656	0.444949
$61$	7.01137	0.897714	0.448857	−	0.893604i	$-0.351831\pi$
$61$	7.01137	0.897714	0.448857	+	0.893604i	$0.351831\pi$
$62$	9.90716	1.25821
$63$	1.25145	0.157668
$64$	1.00000	0.125000
$65$	6.52292	0.809069
$66$	5.15257	0.634238
$67$	0.211021	0.0257804	0.0128902	−	0.999917i	$-0.495897\pi$
$67$	0.211021	0.0257804	0.0128902	+	0.999917i	$0.495897\pi$
$68$	−3.09926	−0.375841
$69$	1.18017	0.142075
$70$	−6.47741	−0.774199
$71$	5.05694	0.600148	0.300074	−	0.953916i	$-0.402989\pi$
$71$	5.05694	0.600148	0.300074	+	0.953916i	$0.402989\pi$
$72$	0.363102	0.0427919
$73$	10.2297	1.19730	0.598648	−	0.801012i	$-0.295705\pi$
$73$	10.2297	1.19730	0.598648	+	0.801012i	$0.295705\pi$
$74$	0	0
$75$	2.69197	0.310842
$76$	7.44656	0.854179
$77$	−9.68366	−1.10356
$78$	6.36497	0.720691
$79$	−1.90486	−0.214313	−0.107157	−	0.994242i	$-0.534175\pi$
$79$	−1.90486	−0.214313	−0.107157	+	0.994242i	$0.534175\pi$
$80$	−1.87939	−0.210122
$81$	−9.95746	−1.10638
$82$	−10.6234	−1.17316
$83$	6.80966	0.747457	0.373729	−	0.927538i	$-0.378079\pi$
$83$	6.80966	0.747457	0.373729	+	0.927538i	$0.378079\pi$
$84$	−6.32056	−0.689630
$85$	5.82471	0.631778
$86$	8.30465	0.895514
$87$	−3.97765	−0.426449
$88$	−2.80966	−0.299511
$89$	−9.68773	−1.02690	−0.513449	−	0.858120i	$-0.671632\pi$
$89$	−9.68773	−1.02690	−0.513449	+	0.858120i	$0.671632\pi$
$90$	−0.682408	−0.0719321
$91$	−11.9622	−1.25398
$92$	−0.643537	−0.0670934
$93$	−18.1685	−1.88399
$94$	−7.85643	−0.810329
$95$	−13.9950	−1.43585
$96$	−1.83388	−0.187169
$97$	17.0598	1.73216	0.866080	−	0.499905i	$-0.166632\pi$
$97$	17.0598	1.73216	0.866080	+	0.499905i	$0.166632\pi$
$98$	4.87877	0.492831
$99$	−1.02019	−0.102533
$100$	−1.46791	−0.146791
$101$	11.9782	1.19188	0.595938	−	0.803030i	$-0.296780\pi$
$101$	11.9782	1.19188	0.595938	+	0.803030i	$0.296780\pi$
$102$	5.68366	0.562767
$103$	12.9447	1.27547	0.637737	−	0.770254i	$-0.279871\pi$
$103$	12.9447	1.27547	0.637737	+	0.770254i	$0.279871\pi$
$104$	−3.47077	−0.340337
$105$	11.8788	1.15925
$106$	4.83388	0.469508
$107$	15.6265	1.51067	0.755333	−	0.655341i	$-0.227475\pi$
$107$	15.6265	1.51067	0.755333	+	0.655341i	$0.227475\pi$
$108$	4.83575	0.465320
$109$	1.55011	0.148474	0.0742369	−	0.997241i	$-0.476348\pi$
$109$	1.55011	0.148474	0.0742369	+	0.997241i	$0.476348\pi$
$110$	5.28044	0.503470
$111$	0	0
$112$	3.44656	0.325669
$113$	−5.11475	−0.481155	−0.240578	−	0.970630i	$-0.577337\pi$
$113$	−5.11475	−0.481155	−0.240578	+	0.970630i	$0.577337\pi$
$114$	−13.6561	−1.27901
$115$	1.20945	0.112782
$116$	2.16899	0.201385
$117$	−1.26024	−0.116510
$118$	0.553440	0.0509483
$119$	−10.6818	−0.979199
$120$	3.44656	0.314626
$121$	−3.10580	−0.282346
$122$	7.01137	0.634780
$123$	19.4821	1.75664
$124$	9.90716	0.889690
$125$	12.1557	1.08724
$126$	1.25145	0.111488
$127$	−7.09520	−0.629597	−0.314798	−	0.949159i	$-0.601937\pi$
$127$	−7.09520	−0.629597	−0.314798	+	0.949159i	$0.601937\pi$
$128$	1.00000	0.0883883
$129$	−15.2297	−1.34090
$130$	6.52292	0.572098
$131$	17.4639	1.52582	0.762912	−	0.646502i	$-0.223769\pi$
$131$	17.4639	1.52582	0.762912	+	0.646502i	$0.223769\pi$
$132$	5.15257	0.448474
$133$	25.6650	2.22544
$134$	0.211021	0.0182295
$135$	−9.08823	−0.782190
$136$	−3.09926	−0.265760
$137$	9.85704	0.842144	0.421072	−	0.907027i	$-0.361654\pi$
$137$	9.85704	0.842144	0.421072	+	0.907027i	$0.361654\pi$
$138$	1.18017	0.100463
$139$	−8.99490	−0.762938	−0.381469	−	0.924382i	$-0.624582\pi$
$139$	−8.99490	−0.762938	−0.381469	+	0.924382i	$0.624582\pi$
$140$	−6.47741	−0.547441
$141$	14.4077	1.21335
$142$	5.05694	0.424369
$143$	9.75170	0.815478
$144$	0.363102	0.0302585
$145$	−4.07636	−0.338524
$146$	10.2297	0.846616
$147$	−8.94707	−0.737942
$148$	0	0
$149$	−9.97301	−0.817021	−0.408511	−	0.912754i	$-0.633952\pi$
$149$	−9.97301	−0.817021	−0.408511	+	0.912754i	$0.633952\pi$
$150$	2.69197	0.219798
$151$	9.66271	0.786340	0.393170	−	0.919466i	$-0.371378\pi$
$151$	9.66271	0.786340	0.393170	+	0.919466i	$0.371378\pi$
$152$	7.44656	0.603996
$153$	−1.12535	−0.0909789
$154$	−9.68366	−0.780332
$155$	−18.6194	−1.49554
$156$	6.36497	0.509605
$157$	−8.78957	−0.701484	−0.350742	−	0.936472i	$-0.614071\pi$
$157$	−8.78957	−0.701484	−0.350742	+	0.936472i	$0.614071\pi$
$158$	−1.90486	−0.151542
$159$	−8.86473	−0.703019
$160$	−1.87939	−0.148578
$161$	−2.21799	−0.174802
$162$	−9.95746	−0.782332
$163$	−1.90716	−0.149381	−0.0746903	−	0.997207i	$-0.523797\pi$
$163$	−1.90716	−0.149381	−0.0746903	+	0.997207i	$0.523797\pi$
$164$	−10.6234	−0.829552
$165$	−9.68366	−0.753872
$166$	6.80966	0.528532
$167$	6.62762	0.512861	0.256430	−	0.966563i	$-0.417454\pi$
$167$	6.62762	0.512861	0.256430	+	0.966563i	$0.417454\pi$
$168$	−6.32056	−0.487642
$169$	−0.953724	−0.0733634
$170$	5.82471	0.446735
$171$	2.70386	0.206769
$172$	8.30465	0.633224
$173$	25.4093	1.93183	0.965916	−	0.258856i	$-0.0833454\pi$
$173$	25.4093	1.93183	0.965916	+	0.258856i	$0.0833454\pi$
$174$	−3.97765	−0.301545
$175$	−5.05924	−0.382443
$176$	−2.80966	−0.211786
$177$	−1.01494	−0.0762876
$178$	−9.68773	−0.726126
$179$	8.12492	0.607285	0.303643	−	0.952786i	$-0.401797\pi$
$179$	8.12492	0.607285	0.303643	+	0.952786i	$0.401797\pi$
$180$	−0.682408	−0.0508637
$181$	11.9069	0.885029	0.442515	−	0.896761i	$-0.354086\pi$
$181$	11.9069	0.885029	0.442515	+	0.896761i	$0.354086\pi$
$182$	−11.9622	−0.886700
$183$	−12.8580	−0.950490
$184$	−0.643537	−0.0474422
$185$	0	0
$186$	−18.1685	−1.33218
$187$	8.70788	0.636783
$188$	−7.85643	−0.572989
$189$	16.6667	1.21232
$190$	−13.9950	−1.01530
$191$	0.266722	0.0192993	0.00964965	−	0.999953i	$-0.496928\pi$
$191$	0.266722	0.0192993	0.00964965	+	0.999953i	$0.496928\pi$
$192$	−1.83388	−0.132349
$193$	7.92835	0.570695	0.285348	−	0.958424i	$-0.407891\pi$
$193$	7.92835	0.570695	0.285348	+	0.958424i	$0.407891\pi$
$194$	17.0598	1.22482
$195$	−11.9622	−0.856633
$196$	4.87877	0.348484
$197$	−0.411629	−0.0293274	−0.0146637	−	0.999892i	$-0.504668\pi$
$197$	−0.411629	−0.0293274	−0.0146637	+	0.999892i	$0.504668\pi$
$198$	−1.02019	−0.0725019
$199$	−2.03503	−0.144259	−0.0721297	−	0.997395i	$-0.522980\pi$
$199$	−2.03503	−0.144259	−0.0721297	+	0.997395i	$0.522980\pi$
$200$	−1.46791	−0.103797
$201$	−0.386987	−0.0272960
$202$	11.9782	0.842784
$203$	7.47554	0.524680
$204$	5.68366	0.397936
$205$	19.9655	1.39445
$206$	12.9447	0.901897
$207$	−0.233669	−0.0162411
$208$	−3.47077	−0.240655
$209$	−20.9223	−1.44723
$210$	11.8788	0.819713
$211$	−15.7410	−1.08366	−0.541829	−	0.840489i	$-0.682268\pi$
$211$	−15.7410	−1.08366	−0.541829	+	0.840489i	$0.682268\pi$
$212$	4.83388	0.331992
$213$	−9.27380	−0.635430
$214$	15.6265	1.06820
$215$	−15.6076	−1.06443
$216$	4.83575	0.329031
$217$	34.1456	2.31796
$218$	1.55011	0.104987
$219$	−18.7600	−1.26768
$220$	5.28044	0.356007
$221$	10.7568	0.723584
$222$	0	0
$223$	−3.43531	−0.230045	−0.115023	−	0.993363i	$-0.536694\pi$
$223$	−3.43531	−0.230045	−0.115023	+	0.993363i	$0.536694\pi$
$224$	3.44656	0.230283
$225$	−0.533001	−0.0355334
$226$	−5.11475	−0.340228
$227$	−2.31280	−0.153506	−0.0767531	−	0.997050i	$-0.524455\pi$
$227$	−2.31280	−0.153506	−0.0767531	+	0.997050i	$0.524455\pi$
$228$	−13.6561	−0.904395
$229$	−5.91094	−0.390606	−0.195303	−	0.980743i	$-0.562569\pi$
$229$	−5.91094	−0.390606	−0.195303	+	0.980743i	$0.562569\pi$
$230$	1.20945	0.0797491
$231$	17.7586	1.16843
$232$	2.16899	0.142401
$233$	−28.3357	−1.85634	−0.928168	−	0.372162i	$-0.878617\pi$
$233$	−28.3357	−1.85634	−0.928168	+	0.372162i	$0.878617\pi$
$234$	−1.26024	−0.0823847
$235$	14.7653	0.963179
$236$	0.553440	0.0360259
$237$	3.49327	0.226912
$238$	−10.6818	−0.692398
$239$	24.2381	1.56783	0.783915	−	0.620868i	$-0.213220\pi$
$239$	24.2381	1.56783	0.783915	+	0.620868i	$0.213220\pi$
$240$	3.44656	0.222474
$241$	8.85069	0.570123	0.285061	−	0.958509i	$-0.407986\pi$
$241$	8.85069	0.570123	0.285061	+	0.958509i	$0.407986\pi$
$242$	−3.10580	−0.199649
$243$	3.75352	0.240788
$244$	7.01137	0.448857
$245$	−9.16909	−0.585792
$246$	19.4821	1.24213
$247$	−25.8453	−1.64450
$248$	9.90716	0.629105
$249$	−12.4881	−0.791400
$250$	12.1557	0.768794
$251$	6.59050	0.415988	0.207994	−	0.978130i	$-0.433306\pi$
$251$	6.59050	0.415988	0.207994	+	0.978130i	$0.433306\pi$
$252$	1.25145	0.0788340
$253$	1.80812	0.113676
$254$	−7.09520	−0.445192
$255$	−10.6818	−0.668920
$256$	1.00000	0.0625000
$257$	9.62572	0.600436	0.300218	−	0.953871i	$-0.402941\pi$
$257$	9.62572	0.600436	0.300218	+	0.953871i	$0.402941\pi$
$258$	−15.2297	−0.948160
$259$	0	0
$260$	6.52292	0.404534
$261$	0.787563	0.0487489
$262$	17.4639	1.07892
$263$	−1.59126	−0.0981214	−0.0490607	−	0.998796i	$-0.515623\pi$
$263$	−1.59126	−0.0981214	−0.0490607	+	0.998796i	$0.515623\pi$
$264$	5.15257	0.317119
$265$	−9.08472	−0.558070
$266$	25.6650	1.57362
$267$	17.7661	1.08727
$268$	0.211021	0.0128902
$269$	23.1198	1.40964	0.704819	−	0.709387i	$-0.251028\pi$
$269$	23.1198	1.40964	0.704819	+	0.709387i	$0.251028\pi$
$270$	−9.08823	−0.553092
$271$	0.183424	0.0111422	0.00557111	−	0.999984i	$-0.498227\pi$
$271$	0.183424	0.0111422	0.00557111	+	0.999984i	$0.498227\pi$
$272$	−3.09926	−0.187920
$273$	21.9373	1.32770
$274$	9.85704	0.595486
$275$	4.12433	0.248707
$276$	1.18017	0.0710377
$277$	−12.6914	−0.762549	−0.381275	−	0.924462i	$-0.624515\pi$
$277$	−12.6914	−0.762549	−0.381275	+	0.924462i	$0.624515\pi$
$278$	−8.99490	−0.539478
$279$	3.59731	0.215365
$280$	−6.47741	−0.387099
$281$	17.4361	1.04015	0.520075	−	0.854121i	$-0.325904\pi$
$281$	17.4361	1.04015	0.520075	+	0.854121i	$0.325904\pi$
$282$	14.4077	0.857967
$283$	−13.1339	−0.780730	−0.390365	−	0.920660i	$-0.627651\pi$
$283$	−13.1339	−0.780730	−0.390365	+	0.920660i	$0.627651\pi$
$284$	5.05694	0.300074
$285$	25.6650	1.52026
$286$	9.75170	0.576630
$287$	−36.6143	−2.16128
$288$	0.363102	0.0213960
$289$	−7.39457	−0.434975
$290$	−4.07636	−0.239372
$291$	−31.2856	−1.83399
$292$	10.2297	0.598648
$293$	6.78723	0.396514	0.198257	−	0.980150i	$-0.436472\pi$
$293$	6.78723	0.396514	0.198257	+	0.980150i	$0.436472\pi$
$294$	−8.94707	−0.521803
$295$	−1.04013	−0.0605586
$296$	0	0
$297$	−13.5868	−0.788386
$298$	−9.97301	−0.577721
$299$	2.23357	0.129171
$300$	2.69197	0.155421
$301$	28.6225	1.64977
$302$	9.66271	0.556026
$303$	−21.9666	−1.26195
$304$	7.44656	0.427089
$305$	−13.1771	−0.754517
$306$	−1.12535	−0.0643318
$307$	8.20485	0.468275	0.234138	−	0.972203i	$-0.424773\pi$
$307$	8.20485	0.468275	0.234138	+	0.972203i	$0.424773\pi$
$308$	−9.68366	−0.551778
$309$	−23.7389	−1.35046
$310$	−18.6194	−1.05751
$311$	−10.8530	−0.615420	−0.307710	−	0.951480i	$-0.599563\pi$
$311$	−10.8530	−0.615420	−0.307710	+	0.951480i	$0.599563\pi$
$312$	6.36497	0.360345
$313$	−8.65561	−0.489244	−0.244622	−	0.969619i	$-0.578664\pi$
$313$	−8.65561	−0.489244	−0.244622	+	0.969619i	$0.578664\pi$
$314$	−8.78957	−0.496024
$315$	−2.35196	−0.132518
$316$	−1.90486	−0.107157
$317$	−25.4252	−1.42802	−0.714012	−	0.700134i	$-0.753124\pi$
$317$	−25.4252	−1.42802	−0.714012	+	0.700134i	$0.753124\pi$
$318$	−8.86473	−0.497109
$319$	−6.09412	−0.341205
$320$	−1.87939	−0.105061
$321$	−28.6570	−1.59948
$322$	−2.21799	−0.123604
$323$	−23.0788	−1.28414
$324$	−9.95746	−0.553192
$325$	5.09479	0.282608
$326$	−1.90716	−0.105628
$327$	−2.84271	−0.157202
$328$	−10.6234	−0.586582
$329$	−27.0776	−1.49284
$330$	−9.68366	−0.533068
$331$	−20.8015	−1.14335	−0.571677	−	0.820479i	$-0.693707\pi$
$331$	−20.8015	−1.14335	−0.571677	+	0.820479i	$0.693707\pi$
$332$	6.80966	0.373729
$333$	0	0
$334$	6.62762	0.362647
$335$	−0.396590	−0.0216680
$336$	−6.32056	−0.344815
$337$	−2.47224	−0.134672	−0.0673359	−	0.997730i	$-0.521450\pi$
$337$	−2.47224	−0.134672	−0.0673359	+	0.997730i	$0.521450\pi$
$338$	−0.953724	−0.0518757
$339$	9.37981	0.509442
$340$	5.82471	0.315889
$341$	−27.8358	−1.50739
$342$	2.70386	0.146208
$343$	−7.31093	−0.394753
$344$	8.30465	0.447757
$345$	−2.21799	−0.119413
$346$	25.4093	1.36601
$347$	−5.85379	−0.314248	−0.157124	−	0.987579i	$-0.550222\pi$
$347$	−5.85379	−0.314248	−0.157124	+	0.987579i	$0.550222\pi$
$348$	−3.97765	−0.213225
$349$	3.14016	0.168089	0.0840445	−	0.996462i	$-0.473216\pi$
$349$	3.14016	0.168089	0.0840445	+	0.996462i	$0.473216\pi$
$350$	−5.05924	−0.270428
$351$	−16.7838	−0.895852
$352$	−2.80966	−0.149755
$353$	−11.2483	−0.598684	−0.299342	−	0.954146i	$-0.596767\pi$
$353$	−11.2483	−0.598684	−0.299342	+	0.954146i	$0.596767\pi$
$354$	−1.01494	−0.0539435
$355$	−9.50393	−0.504416
$356$	−9.68773	−0.513449
$357$	19.5891	1.03676
$358$	8.12492	0.429415
$359$	−23.0934	−1.21882	−0.609410	−	0.792855i	$-0.708594\pi$
$359$	−23.0934	−1.21882	−0.609410	+	0.792855i	$0.708594\pi$
$360$	−0.682408	−0.0359660
$361$	36.4513	1.91849
$362$	11.9069	0.625810
$363$	5.69566	0.298945
$364$	−11.9622	−0.626991
$365$	−19.2255	−1.00631
$366$	−12.8580	−0.672098
$367$	1.57151	0.0820320	0.0410160	−	0.999158i	$-0.486941\pi$
$367$	1.57151	0.0820320	0.0410160	+	0.999158i	$0.486941\pi$
$368$	−0.643537	−0.0335467
$369$	−3.85739	−0.200808
$370$	0	0
$371$	16.6602	0.864957
$372$	−18.1685	−0.941993
$373$	6.69192	0.346495	0.173247	−	0.984878i	$-0.444574\pi$
$373$	6.69192	0.346495	0.173247	+	0.984878i	$0.444574\pi$
$374$	8.70788	0.450274
$375$	−22.2920	−1.15116
$376$	−7.85643	−0.405164
$377$	−7.52807	−0.387715
$378$	16.6667	0.857242
$379$	−10.9720	−0.563592	−0.281796	−	0.959474i	$-0.590930\pi$
$379$	−10.9720	−0.563592	−0.281796	+	0.959474i	$0.590930\pi$
$380$	−13.9950	−0.717926
$381$	13.0117	0.666610
$382$	0.266722	0.0136467
$383$	−25.2571	−1.29058	−0.645288	−	0.763939i	$-0.723263\pi$
$383$	−25.2571	−1.29058	−0.645288	+	0.763939i	$0.723263\pi$
$384$	−1.83388	−0.0935846
$385$	18.1993	0.927524
$386$	7.92835	0.403542
$387$	3.01543	0.153283
$388$	17.0598	0.866080
$389$	−10.8120	−0.548190	−0.274095	−	0.961703i	$-0.588378\pi$
$389$	−10.8120	−0.548190	−0.274095	+	0.961703i	$0.588378\pi$
$390$	−11.9622	−0.605731
$391$	1.99449	0.100866
$392$	4.87877	0.246415
$393$	−32.0266	−1.61553
$394$	−0.411629	−0.0207376
$395$	3.57996	0.180127
$396$	−1.02019	−0.0512666
$397$	−10.8114	−0.542609	−0.271304	−	0.962494i	$-0.587455\pi$
$397$	−10.8114	−0.542609	−0.271304	+	0.962494i	$0.587455\pi$
$398$	−2.03503	−0.102007
$399$	−47.0665	−2.35627
$400$	−1.46791	−0.0733956
$401$	−34.6974	−1.73271	−0.866353	−	0.499432i	$-0.833542\pi$
$401$	−34.6974	−1.73271	−0.866353	+	0.499432i	$0.833542\pi$
$402$	−0.386987	−0.0193012
$403$	−34.3855	−1.71287
$404$	11.9782	0.595938
$405$	18.7139	0.929902
$406$	7.47554	0.371005
$407$	0	0
$408$	5.68366	0.281383
$409$	1.88711	0.0933114	0.0466557	−	0.998911i	$-0.485144\pi$
$409$	1.88711	0.0933114	0.0466557	+	0.998911i	$0.485144\pi$
$410$	19.9655	0.986028
$411$	−18.0766	−0.891653
$412$	12.9447	0.637737
$413$	1.90747	0.0938602
$414$	−0.233669	−0.0114842
$415$	−12.7980	−0.628228
$416$	−3.47077	−0.170169
$417$	16.4955	0.807790
$418$	−20.9223	−1.02334
$419$	−17.4276	−0.851394	−0.425697	−	0.904866i	$-0.639971\pi$
$419$	−17.4276	−0.851394	−0.425697	+	0.904866i	$0.639971\pi$
$420$	11.8788	0.579625
$421$	−18.1544	−0.884791	−0.442395	−	0.896820i	$-0.645871\pi$
$421$	−18.1544	−0.884791	−0.442395	+	0.896820i	$0.645871\pi$
$422$	−15.7410	−0.766262
$423$	−2.85268	−0.138702
$424$	4.83388	0.234754
$425$	4.54944	0.220680
$426$	−9.27380	−0.449317
$427$	24.1651	1.16943
$428$	15.6265	0.755333
$429$	−17.8834	−0.863419
$430$	−15.6076	−0.752667
$431$	28.3900	1.36750	0.683749	−	0.729717i	$-0.260348\pi$
$431$	28.3900	1.36750	0.683749	+	0.729717i	$0.260348\pi$
$432$	4.83575	0.232660
$433$	−7.46936	−0.358955	−0.179477	−	0.983762i	$-0.557441\pi$
$433$	−7.46936	−0.358955	−0.179477	+	0.983762i	$0.557441\pi$
$434$	34.1456	1.63904
$435$	7.47554	0.358425
$436$	1.55011	0.0742369
$437$	−4.79214	−0.229239
$438$	−18.7600	−0.896388
$439$	−34.5453	−1.64876	−0.824379	−	0.566038i	$-0.808476\pi$
$439$	−34.5453	−1.64876	−0.824379	+	0.566038i	$0.808476\pi$
$440$	5.28044	0.251735
$441$	1.77149	0.0843567
$442$	10.7568	0.511651
$443$	−2.89849	−0.137712	−0.0688558	−	0.997627i	$-0.521935\pi$
$443$	−2.89849	−0.137712	−0.0688558	+	0.997627i	$0.521935\pi$
$444$	0	0
$445$	18.2070	0.863094
$446$	−3.43531	−0.162667
$447$	18.2893	0.865053
$448$	3.44656	0.162835
$449$	27.8755	1.31552	0.657762	−	0.753225i	$-0.271503\pi$
$449$	27.8755	1.31552	0.657762	+	0.753225i	$0.271503\pi$
$450$	−0.533001	−0.0251259
$451$	29.8483	1.40550
$452$	−5.11475	−0.240578
$453$	−17.7202	−0.832568
$454$	−2.31280	−0.108545
$455$	22.4816	1.05396
$456$	−13.6561	−0.639504
$457$	9.76953	0.457000	0.228500	−	0.973544i	$-0.426618\pi$
$457$	9.76953	0.457000	0.228500	+	0.973544i	$0.426618\pi$
$458$	−5.91094	−0.276200
$459$	−14.9872	−0.699545
$460$	1.20945	0.0563911
$461$	15.4478	0.719476	0.359738	−	0.933053i	$-0.382866\pi$
$461$	15.4478	0.719476	0.359738	+	0.933053i	$0.382866\pi$
$462$	17.7586	0.826207
$463$	18.3049	0.850699	0.425349	−	0.905029i	$-0.360151\pi$
$463$	18.3049	0.850699	0.425349	+	0.905029i	$0.360151\pi$
$464$	2.16899	0.100693
$465$	34.1456	1.58347
$466$	−28.3357	−1.31263
$467$	23.6070	1.09240	0.546201	−	0.837654i	$-0.316074\pi$
$467$	23.6070	1.09240	0.546201	+	0.837654i	$0.316074\pi$
$468$	−1.26024	−0.0582548
$469$	0.727298	0.0335835
$470$	14.7653	0.681070
$471$	16.1190	0.742723
$472$	0.553440	0.0254742
$473$	−23.3333	−1.07286
$474$	3.49327	0.160451
$475$	−10.9309	−0.501544
$476$	−10.6818	−0.489599
$477$	1.75519	0.0803645
$478$	24.2381	1.10862
$479$	−8.68623	−0.396884	−0.198442	−	0.980113i	$-0.563588\pi$
$479$	−8.68623	−0.396884	−0.198442	+	0.980113i	$0.563588\pi$
$480$	3.44656	0.157313
$481$	0	0
$482$	8.85069	0.403138
$483$	4.06752	0.185078
$484$	−3.10580	−0.141173
$485$	−32.0619	−1.45586
$486$	3.75352	0.170263
$487$	20.9350	0.948654	0.474327	−	0.880349i	$-0.342691\pi$
$487$	20.9350	0.948654	0.474327	+	0.880349i	$0.342691\pi$
$488$	7.01137	0.317390
$489$	3.49750	0.158162
$490$	−9.16909	−0.414217
$491$	43.2110	1.95009	0.975044	−	0.222013i	$-0.0712628\pi$
$491$	43.2110	1.95009	0.975044	+	0.222013i	$0.0712628\pi$
$492$	19.4821	0.878320
$493$	−6.72226	−0.302755
$494$	−25.8453	−1.16284
$495$	1.91733	0.0861778
$496$	9.90716	0.444845
$497$	17.4290	0.781799
$498$	−12.4881	−0.559604
$499$	−6.76702	−0.302934	−0.151467	−	0.988462i	$-0.548400\pi$
$499$	−6.76702	−0.302934	−0.151467	+	0.988462i	$0.548400\pi$
$500$	12.1557	0.543619
$501$	−12.1542	−0.543011
$502$	6.59050	0.294148
$503$	−27.4443	−1.22368	−0.611841	−	0.790981i	$-0.709571\pi$
$503$	−27.4443	−1.22368	−0.611841	+	0.790981i	$0.709571\pi$
$504$	1.25145	0.0557441
$505$	−22.5117	−1.00176
$506$	1.80812	0.0803808
$507$	1.74901	0.0776763
$508$	−7.09520	−0.314798
$509$	20.9883	0.930289	0.465145	−	0.885235i	$-0.346002\pi$
$509$	20.9883	0.930289	0.465145	+	0.885235i	$0.346002\pi$
$510$	−10.6818	−0.472998
$511$	35.2573	1.55969
$512$	1.00000	0.0441942
$513$	36.0097	1.58987
$514$	9.62572	0.424572
$515$	−24.3280	−1.07202
$516$	−15.2297	−0.670450
$517$	22.0739	0.970809
$518$	0	0
$519$	−46.5975	−2.04540
$520$	6.52292	0.286049
$521$	−37.5667	−1.64583	−0.822913	−	0.568167i	$-0.807653\pi$
$521$	−37.5667	−1.64583	−0.822913	+	0.568167i	$0.807653\pi$
$522$	0.787563	0.0344707
$523$	18.9180	0.827228	0.413614	−	0.910452i	$-0.364266\pi$
$523$	18.9180	0.827228	0.413614	+	0.910452i	$0.364266\pi$
$524$	17.4639	0.762912
$525$	9.27803	0.404926
$526$	−1.59126	−0.0693823
$527$	−30.7049	−1.33753
$528$	5.15257	0.224237
$529$	−22.5859	−0.981994
$530$	−9.08472	−0.394615
$531$	0.200955	0.00872071
$532$	25.6650	1.11272
$533$	36.8716	1.59709
$534$	17.7661	0.768814
$535$	−29.3681	−1.26969
$536$	0.211021	0.00911473
$537$	−14.9001	−0.642987
$538$	23.1198	0.996764
$539$	−13.7077	−0.590432
$540$	−9.08823	−0.391095
$541$	16.4748	0.708306	0.354153	−	0.935187i	$-0.384769\pi$
$541$	16.4748	0.708306	0.354153	+	0.935187i	$0.384769\pi$
$542$	0.183424	0.00787874
$543$	−21.8357	−0.937059
$544$	−3.09926	−0.132880
$545$	−2.91326	−0.124790
$546$	21.9373	0.938828
$547$	−12.0013	−0.513140	−0.256570	−	0.966526i	$-0.582592\pi$
$547$	−12.0013	−0.513140	−0.256570	+	0.966526i	$0.582592\pi$
$548$	9.85704	0.421072
$549$	2.54584	0.108654
$550$	4.12433	0.175862
$551$	16.1515	0.688077
$552$	1.18017	0.0502313
$553$	−6.56520	−0.279181
$554$	−12.6914	−0.539204
$555$	0	0
$556$	−8.99490	−0.381469
$557$	−42.7827	−1.81276	−0.906381	−	0.422462i	$-0.861166\pi$
$557$	−42.7827	−1.81276	−0.906381	+	0.422462i	$0.861166\pi$
$558$	3.59731	0.152286
$559$	−28.8236	−1.21911
$560$	−6.47741	−0.273721
$561$	−15.9692	−0.674219
$562$	17.4361	0.735497
$563$	23.7476	1.00084	0.500421	−	0.865782i	$-0.333179\pi$
$563$	23.7476	1.00084	0.500421	+	0.865782i	$0.333179\pi$
$564$	14.4077	0.606674
$565$	9.61258	0.404404
$566$	−13.1339	−0.552060
$567$	−34.3190	−1.44126
$568$	5.05694	0.212184
$569$	−5.28664	−0.221628	−0.110814	−	0.993841i	$-0.535346\pi$
$569$	−5.28664	−0.221628	−0.110814	+	0.993841i	$0.535346\pi$
$570$	25.6650	1.07499
$571$	−24.2477	−1.01473	−0.507367	−	0.861730i	$-0.669381\pi$
$571$	−24.2477	−1.01473	−0.507367	+	0.861730i	$0.669381\pi$
$572$	9.75170	0.407739
$573$	−0.489134	−0.0204339
$574$	−36.6143	−1.52825
$575$	0.944656	0.0393949
$576$	0.363102	0.0151292
$577$	−1.70941	−0.0711636	−0.0355818	−	0.999367i	$-0.511328\pi$
$577$	−1.70941	−0.0711636	−0.0355818	+	0.999367i	$0.511328\pi$
$578$	−7.39457	−0.307573
$579$	−14.5396	−0.604246
$580$	−4.07636	−0.169262
$581$	23.4699	0.973696
$582$	−31.2856	−1.29683
$583$	−13.5816	−0.562490
$584$	10.2297	0.423308
$585$	2.36848	0.0979247
$586$	6.78723	0.280378
$587$	26.0026	1.07324	0.536621	−	0.843823i	$-0.319701\pi$
$587$	26.0026	1.07324	0.536621	+	0.843823i	$0.319701\pi$
$588$	−8.94707	−0.368971
$589$	73.7743	3.03982
$590$	−1.04013	−0.0428214
$591$	0.754877	0.0310515
$592$	0	0
$593$	19.5933	0.804601	0.402300	−	0.915508i	$-0.368211\pi$
$593$	19.5933	0.804601	0.402300	+	0.915508i	$0.368211\pi$
$594$	−13.5868	−0.557473
$595$	20.0752	0.823003
$596$	−9.97301	−0.408511
$597$	3.73199	0.152740
$598$	2.23357	0.0913376
$599$	37.0752	1.51485	0.757426	−	0.652921i	$-0.226457\pi$
$599$	37.0752	1.51485	0.757426	+	0.652921i	$0.226457\pi$
$600$	2.69197	0.109899
$601$	−18.4933	−0.754358	−0.377179	−	0.926140i	$-0.623106\pi$
$601$	−18.4933	−0.754358	−0.377179	+	0.926140i	$0.623106\pi$
$602$	28.6225	1.16656
$603$	0.0766222	0.00312030
$604$	9.66271	0.393170
$605$	5.83700	0.237308
$606$	−21.9666	−0.892330
$607$	5.31756	0.215833	0.107917	−	0.994160i	$-0.465582\pi$
$607$	5.31756	0.215833	0.107917	+	0.994160i	$0.465582\pi$
$608$	7.44656	0.301998
$609$	−13.7092	−0.555526
$610$	−13.1771	−0.533524
$611$	27.2679	1.10314
$612$	−1.12535	−0.0454895
$613$	40.4178	1.63246	0.816230	−	0.577727i	$-0.196060\pi$
$613$	40.4178	1.63246	0.816230	+	0.577727i	$0.196060\pi$
$614$	8.20485	0.331121
$615$	−36.6143	−1.47643
$616$	−9.68366	−0.390166
$617$	−32.7970	−1.32036	−0.660178	−	0.751109i	$-0.729519\pi$
$617$	−32.7970	−1.32036	−0.660178	+	0.751109i	$0.729519\pi$
$618$	−23.7389	−0.954918
$619$	−4.15075	−0.166833	−0.0834163	−	0.996515i	$-0.526583\pi$
$619$	−4.15075	−0.166833	−0.0834163	+	0.996515i	$0.526583\pi$
$620$	−18.6194	−0.747772
$621$	−3.11198	−0.124880
$622$	−10.8530	−0.435167
$623$	−33.3893	−1.33772
$624$	6.36497	0.254803
$625$	−15.5057	−0.620227
$626$	−8.65561	−0.345948
$627$	38.3689	1.53231
$628$	−8.78957	−0.350742
$629$	0	0
$630$	−2.35196	−0.0937043
$631$	29.9206	1.19112	0.595561	−	0.803310i	$-0.296930\pi$
$631$	29.9206	1.19112	0.595561	+	0.803310i	$0.296930\pi$
$632$	−1.90486	−0.0757712
$633$	28.8671	1.14736
$634$	−25.4252	−1.00977
$635$	13.3346	0.529168
$636$	−8.86473	−0.351509
$637$	−16.9331	−0.670915
$638$	−6.09412	−0.241269
$639$	1.83618	0.0726382
$640$	−1.87939	−0.0742892
$641$	6.83554	0.269988	0.134994	−	0.990846i	$-0.456899\pi$
$641$	6.83554	0.269988	0.134994	+	0.990846i	$0.456899\pi$
$642$	−28.6570	−1.13100
$643$	37.5185	1.47958	0.739792	−	0.672835i	$-0.234924\pi$
$643$	37.5185	1.47958	0.739792	+	0.672835i	$0.234924\pi$
$644$	−2.21799	−0.0874010
$645$	28.6225	1.12701
$646$	−23.0788	−0.908025
$647$	2.64427	0.103957	0.0519786	−	0.998648i	$-0.483447\pi$
$647$	2.64427	0.103957	0.0519786	+	0.998648i	$0.483447\pi$
$648$	−9.95746	−0.391166
$649$	−1.55498	−0.0610383
$650$	5.09479	0.199834
$651$	−62.6189	−2.45423
$652$	−1.90716	−0.0746903
$653$	−44.7483	−1.75114	−0.875568	−	0.483095i	$-0.839513\pi$
$653$	−44.7483	−1.75114	−0.875568	+	0.483095i	$0.839513\pi$
$654$	−2.84271	−0.111159
$655$	−32.8213	−1.28244
$656$	−10.6234	−0.414776
$657$	3.71442	0.144913
$658$	−27.0776	−1.05560
$659$	−4.55119	−0.177289	−0.0886446	−	0.996063i	$-0.528254\pi$
$659$	−4.55119	−0.177289	−0.0886446	+	0.996063i	$0.528254\pi$
$660$	−9.68366	−0.376936
$661$	−43.5632	−1.69441	−0.847206	−	0.531265i	$-0.821717\pi$
$661$	−43.5632	−1.69441	−0.847206	+	0.531265i	$0.821717\pi$
$662$	−20.8015	−0.808474
$663$	−19.7267	−0.766122
$664$	6.80966	0.264266
$665$	−48.2344	−1.87045
$666$	0	0
$667$	−1.39582	−0.0540465
$668$	6.62762	0.256430
$669$	6.29993	0.243569
$670$	−0.396590	−0.0153216
$671$	−19.6996	−0.760494
$672$	−6.32056	−0.243821
$673$	38.0547	1.46690	0.733451	−	0.679742i	$-0.237908\pi$
$673$	38.0547	1.46690	0.733451	+	0.679742i	$0.237908\pi$
$674$	−2.47224	−0.0952273
$675$	−7.09844	−0.273219
$676$	−0.953724	−0.0366817
$677$	44.0262	1.69206	0.846032	−	0.533132i	$-0.178985\pi$
$677$	44.0262	1.69206	0.846032	+	0.533132i	$0.178985\pi$
$678$	9.37981	0.360230
$679$	58.7976	2.25645
$680$	5.82471	0.223367
$681$	4.24139	0.162531
$682$	−27.8358	−1.06589
$683$	18.8006	0.719385	0.359693	−	0.933071i	$-0.382882\pi$
$683$	18.8006	0.719385	0.359693	+	0.933071i	$0.382882\pi$
$684$	2.70386	0.103385
$685$	−18.5252	−0.707811
$686$	−7.31093	−0.279133
$687$	10.8399	0.413569
$688$	8.30465	0.316612
$689$	−16.7773	−0.639164
$690$	−2.21799	−0.0844374
$691$	26.9373	1.02474	0.512372	−	0.858764i	$-0.328767\pi$
$691$	26.9373	1.02474	0.512372	+	0.858764i	$0.328767\pi$
$692$	25.4093	0.965916
$693$	−3.51615	−0.133568
$694$	−5.85379	−0.222207
$695$	16.9049	0.641239
$696$	−3.97765	−0.150773
$697$	32.9248	1.24712
$698$	3.14016	0.118857
$699$	51.9642	1.96547
$700$	−5.05924	−0.191221
$701$	7.43149	0.280684	0.140342	−	0.990103i	$-0.455180\pi$
$701$	7.43149	0.280684	0.140342	+	0.990103i	$0.455180\pi$
$702$	−16.7838	−0.633463
$703$	0	0
$704$	−2.80966	−0.105893
$705$	−27.0776	−1.01980
$706$	−11.2483	−0.423334
$707$	41.2836	1.55263
$708$	−1.01494	−0.0381438
$709$	0.834473	0.0313393	0.0156697	−	0.999877i	$-0.495012\pi$
$709$	0.834473	0.0313393	0.0156697	+	0.999877i	$0.495012\pi$
$710$	−9.50393	−0.356676
$711$	−0.691657	−0.0259391
$712$	−9.68773	−0.363063
$713$	−6.37563	−0.238769
$714$	19.5891	0.733103
$715$	−18.3272	−0.685398
$716$	8.12492	0.303643
$717$	−44.4496	−1.66000
$718$	−23.0934	−0.861836
$719$	−5.03823	−0.187894	−0.0939471	−	0.995577i	$-0.529948\pi$
$719$	−5.03823	−0.187894	−0.0939471	+	0.995577i	$0.529948\pi$
$720$	−0.682408	−0.0254318
$721$	44.6145	1.66153
$722$	36.4513	1.35658
$723$	−16.2311	−0.603640
$724$	11.9069	0.442515
$725$	−3.18388	−0.118246
$726$	5.69566	0.211386
$727$	18.6140	0.690354	0.345177	−	0.938538i	$-0.387819\pi$
$727$	18.6140	0.690354	0.345177	+	0.938538i	$0.387819\pi$
$728$	−11.9622	−0.443350
$729$	22.9889	0.851441
$730$	−19.2255	−0.711569
$731$	−25.7383	−0.951965
$732$	−12.8580	−0.475245
$733$	4.59054	0.169556	0.0847778	−	0.996400i	$-0.472982\pi$
$733$	4.59054	0.169556	0.0847778	+	0.996400i	$0.472982\pi$
$734$	1.57151	0.0580054
$735$	16.8150	0.620230
$736$	−0.643537	−0.0237211
$737$	−0.592898	−0.0218397
$738$	−3.85739	−0.141992
$739$	−46.9098	−1.72560	−0.862802	−	0.505542i	$-0.831292\pi$
$739$	−46.9098	−1.72560	−0.862802	+	0.505542i	$0.831292\pi$
$740$	0	0
$741$	47.3971	1.74118
$742$	16.6602	0.611617
$743$	4.99139	0.183116	0.0915582	−	0.995800i	$-0.470815\pi$
$743$	4.99139	0.183116	0.0915582	+	0.995800i	$0.470815\pi$
$744$	−18.1685	−0.666090
$745$	18.7431	0.686695
$746$	6.69192	0.245009
$747$	2.47260	0.0904676
$748$	8.70788	0.318392
$749$	53.8575	1.96791
$750$	−22.2920	−0.813990
$751$	18.8284	0.687060	0.343530	−	0.939142i	$-0.388377\pi$
$751$	18.8284	0.687060	0.343530	+	0.939142i	$0.388377\pi$
$752$	−7.85643	−0.286494
$753$	−12.0862	−0.440444
$754$	−7.52807	−0.274156
$755$	−18.1599	−0.660908
$756$	16.6667	0.606161
$757$	0.781650	0.0284095	0.0142048	−	0.999899i	$-0.495478\pi$
$757$	0.781650	0.0284095	0.0142048	+	0.999899i	$0.495478\pi$
$758$	−10.9720	−0.398520
$759$	−3.31587	−0.120358
$760$	−13.9950	−0.507650
$761$	−30.3717	−1.10097	−0.550486	−	0.834844i	$-0.685558\pi$
$761$	−30.3717	−1.10097	−0.550486	+	0.834844i	$0.685558\pi$
$762$	13.0117	0.471365
$763$	5.34255	0.193413
$764$	0.266722	0.00964965
$765$	2.11496	0.0764666
$766$	−25.2571	−0.912575
$767$	−1.92087	−0.0693585
$768$	−1.83388	−0.0661743
$769$	−15.9646	−0.575697	−0.287848	−	0.957676i	$-0.592940\pi$
$769$	−15.9646	−0.575697	−0.287848	+	0.957676i	$0.592940\pi$
$770$	18.1993	0.655859
$771$	−17.6524	−0.635735
$772$	7.92835	0.285348
$773$	26.4978	0.953059	0.476529	−	0.879158i	$-0.341895\pi$
$773$	26.4978	0.953059	0.476529	+	0.879158i	$0.341895\pi$
$774$	3.01543	0.108387
$775$	−14.5428	−0.522394
$776$	17.0598	0.612411
$777$	0	0
$778$	−10.8120	−0.387629
$779$	−79.1081	−2.83434
$780$	−11.9622	−0.428317
$781$	−14.2083	−0.508412
$782$	1.99449	0.0713229
$783$	10.4887	0.374834
$784$	4.87877	0.174242
$785$	16.5190	0.589588
$786$	−32.0266	−1.14235
$787$	−48.3738	−1.72434	−0.862171	−	0.506618i	$-0.830895\pi$
$787$	−48.3738	−1.72434	−0.862171	+	0.506618i	$0.830895\pi$
$788$	−0.411629	−0.0146637
$789$	2.91818	0.103890
$790$	3.57996	0.127369
$791$	−17.6283	−0.626790
$792$	−1.02019	−0.0362510
$793$	−24.3349	−0.864157
$794$	−10.8114	−0.383682
$795$	16.6602	0.590878
$796$	−2.03503	−0.0721297
$797$	23.6916	0.839198	0.419599	−	0.907709i	$-0.362171\pi$
$797$	23.6916	0.839198	0.419599	+	0.907709i	$0.362171\pi$
$798$	−47.0665	−1.66613
$799$	24.3491	0.861411
$800$	−1.46791	−0.0518985
$801$	−3.51763	−0.124289
$802$	−34.6974	−1.22521
$803$	−28.7420	−1.01428
$804$	−0.386987	−0.0136480
$805$	4.16846	0.146919
$806$	−34.3855	−1.21118
$807$	−42.3988	−1.49251
$808$	11.9782	0.421392
$809$	0.796534	0.0280046	0.0140023	−	0.999902i	$-0.495543\pi$
$809$	0.796534	0.0280046	0.0140023	+	0.999902i	$0.495543\pi$
$810$	18.7139	0.657540
$811$	13.8546	0.486501	0.243250	−	0.969964i	$-0.421786\pi$
$811$	13.8546	0.486501	0.243250	+	0.969964i	$0.421786\pi$
$812$	7.47554	0.262340
$813$	−0.336377	−0.0117973
$814$	0	0
$815$	3.58429	0.125552
$816$	5.68366	0.198968
$817$	61.8411	2.16355
$818$	1.88711	0.0659811
$819$	−4.34350	−0.151774
$820$	19.9655	0.697227
$821$	−21.8621	−0.762992	−0.381496	−	0.924370i	$-0.624591\pi$
$821$	−21.8621	−0.762992	−0.381496	+	0.924370i	$0.624591\pi$
$822$	−18.0766	−0.630494
$823$	34.5237	1.20342	0.601710	−	0.798715i	$-0.294486\pi$
$823$	34.5237	1.20342	0.601710	+	0.798715i	$0.294486\pi$
$824$	12.9447	0.450948
$825$	−7.56352	−0.263328
$826$	1.90747	0.0663692
$827$	3.97283	0.138149	0.0690744	−	0.997612i	$-0.477995\pi$
$827$	3.97283	0.138149	0.0690744	+	0.997612i	$0.477995\pi$
$828$	−0.233669	−0.00812057
$829$	−16.8012	−0.583529	−0.291765	−	0.956490i	$-0.594242\pi$
$829$	−16.8012	−0.583529	−0.291765	+	0.956490i	$0.594242\pi$
$830$	−12.7980	−0.444224
$831$	23.2744	0.807379
$832$	−3.47077	−0.120327
$833$	−15.1206	−0.523898
$834$	16.4955	0.571194
$835$	−12.4559	−0.431053
$836$	−20.9223	−0.723613
$837$	47.9085	1.65596
$838$	−17.4276	−0.602026
$839$	6.73686	0.232582	0.116291	−	0.993215i	$-0.462899\pi$
$839$	6.73686	0.232582	0.116291	+	0.993215i	$0.462899\pi$
$840$	11.8788	0.409857
$841$	−24.2955	−0.837776
$842$	−18.1544	−0.625641
$843$	−31.9756	−1.10130
$844$	−15.7410	−0.541829
$845$	1.79241	0.0616609
$846$	−2.85268	−0.0980772
$847$	−10.7043	−0.367805
$848$	4.83388	0.165996
$849$	24.0860	0.826629
$850$	4.54944	0.156045
$851$	0	0
$852$	−9.27380	−0.317715
$853$	42.9154	1.46940	0.734698	−	0.678395i	$-0.237324\pi$
$853$	42.9154	1.46940	0.734698	+	0.678395i	$0.237324\pi$
$854$	24.1651	0.826913
$855$	−5.08159	−0.173787
$856$	15.6265	0.534101
$857$	−27.6910	−0.945906	−0.472953	−	0.881088i	$-0.656812\pi$
$857$	−27.6910	−0.945906	−0.472953	+	0.881088i	$0.656812\pi$
$858$	−17.8834	−0.610530
$859$	18.8542	0.643298	0.321649	−	0.946859i	$-0.395763\pi$
$859$	18.8542	0.643298	0.321649	+	0.946859i	$0.395763\pi$
$860$	−15.6076	−0.532216
$861$	67.1461	2.28833
$862$	28.3900	0.966967
$863$	29.8158	1.01494	0.507471	−	0.861669i	$-0.330580\pi$
$863$	29.8158	1.01494	0.507471	+	0.861669i	$0.330580\pi$
$864$	4.83575	0.164515
$865$	−47.7538	−1.62368
$866$	−7.46936	−0.253819
$867$	13.5607	0.460546
$868$	34.1456	1.15898
$869$	5.35200	0.181554
$870$	7.47554	0.253445
$871$	−0.732407	−0.0248167
$872$	1.55011	0.0524934
$873$	6.19444	0.209650
$874$	−4.79214	−0.162097
$875$	41.8953	1.41632
$876$	−18.7600	−0.633842
$877$	4.23584	0.143034	0.0715170	−	0.997439i	$-0.477216\pi$
$877$	4.23584	0.143034	0.0715170	+	0.997439i	$0.477216\pi$
$878$	−34.5453	−1.16585
$879$	−12.4469	−0.419825
$880$	5.28044	0.178003
$881$	6.59141	0.222070	0.111035	−	0.993816i	$-0.464583\pi$
$881$	6.59141	0.222070	0.111035	+	0.993816i	$0.464583\pi$
$882$	1.77149	0.0596492
$883$	−12.3790	−0.416588	−0.208294	−	0.978066i	$-0.566791\pi$
$883$	−12.3790	−0.416588	−0.208294	+	0.978066i	$0.566791\pi$
$884$	10.7568	0.361792
$885$	1.90747	0.0641187
$886$	−2.89849	−0.0973768
$887$	−25.0422	−0.840833	−0.420417	−	0.907331i	$-0.638116\pi$
$887$	−25.0422	−0.840833	−0.420417	+	0.907331i	$0.638116\pi$
$888$	0	0
$889$	−24.4540	−0.820161
$890$	18.2070	0.610299
$891$	27.9771	0.937268
$892$	−3.43531	−0.115023
$893$	−58.5034	−1.95774
$894$	18.2893	0.611685
$895$	−15.2699	−0.510415
$896$	3.44656	0.115141
$897$	−4.09610	−0.136765
$898$	27.8755	0.930217
$899$	21.4885	0.716682
$900$	−0.533001	−0.0177667
$901$	−14.9815	−0.499105
$902$	29.8483	0.993839
$903$	−52.4901	−1.74676
$904$	−5.11475	−0.170114
$905$	−22.3776	−0.743855
$906$	−17.7202	−0.588714
$907$	−57.8878	−1.92213	−0.961067	−	0.276315i	$-0.910887\pi$
$907$	−57.8878	−1.92213	−0.961067	+	0.276315i	$0.910887\pi$
$908$	−2.31280	−0.0767531
$909$	4.34931	0.144257
$910$	22.4816	0.745259
$911$	−8.36746	−0.277226	−0.138613	−	0.990347i	$-0.544264\pi$
$911$	−8.36746	−0.277226	−0.138613	+	0.990347i	$0.544264\pi$
$912$	−13.6561	−0.452198
$913$	−19.1328	−0.633205
$914$	9.76953	0.323147
$915$	24.1651	0.798874
$916$	−5.91094	−0.195303
$917$	60.1902	1.98766
$918$	−14.9872	−0.494653
$919$	3.64798	0.120336	0.0601678	−	0.998188i	$-0.480836\pi$
$919$	3.64798	0.120336	0.0601678	+	0.998188i	$0.480836\pi$
$920$	1.20945	0.0398745
$921$	−15.0467	−0.495805
$922$	15.4478	0.508746
$923$	−17.5515	−0.577714
$924$	17.7586	0.584216
$925$	0	0
$926$	18.3049	0.601535
$927$	4.70022	0.154376
$928$	2.16899	0.0712005
$929$	53.1559	1.74399	0.871994	−	0.489516i	$-0.162827\pi$
$929$	53.1559	1.74399	0.871994	+	0.489516i	$0.162827\pi$
$930$	34.1456	1.11968
$931$	36.3301	1.19067
$932$	−28.3357	−0.928168
$933$	19.9031	0.651600
$934$	23.6070	0.772445
$935$	−16.3655	−0.535208
$936$	−1.26024	−0.0411923
$937$	0.461589	0.0150795	0.00753973	−	0.999972i	$-0.497600\pi$
$937$	0.461589	0.0150795	0.00753973	+	0.999972i	$0.497600\pi$
$938$	0.727298	0.0237471
$939$	15.8733	0.518006
$940$	14.7653	0.481589
$941$	45.1298	1.47119	0.735594	−	0.677422i	$-0.236903\pi$
$941$	45.1298	1.47119	0.735594	+	0.677422i	$0.236903\pi$
$942$	16.1190	0.525185
$943$	6.83658	0.222630
$944$	0.553440	0.0180129
$945$	−31.3231	−1.01894
$946$	−23.3333	−0.758630
$947$	−1.10720	−0.0359792	−0.0179896	−	0.999838i	$-0.505727\pi$
$947$	−1.10720	−0.0359792	−0.0179896	+	0.999838i	$0.505727\pi$
$948$	3.49327	0.113456
$949$	−35.5050	−1.15254
$950$	−10.9309	−0.354645
$951$	46.6267	1.51198
$952$	−10.6818	−0.346199
$953$	−4.51823	−0.146360	−0.0731799	−	0.997319i	$-0.523315\pi$
$953$	−4.51823	−0.146360	−0.0731799	+	0.997319i	$0.523315\pi$
$954$	1.75519	0.0568263
$955$	−0.501273	−0.0162208
$956$	24.2381	0.783915
$957$	11.1759	0.361264
$958$	−8.68623	−0.280639
$959$	33.9729	1.09704
$960$	3.44656	0.111237
$961$	67.1519	2.16619
$962$	0	0
$963$	5.67399	0.182842
$964$	8.85069	0.285061
$965$	−14.9004	−0.479662
$966$	4.06752	0.130870
$967$	−34.5494	−1.11103	−0.555517	−	0.831506i	$-0.687479\pi$
$967$	−34.5494	−1.11103	−0.555517	+	0.831506i	$0.687479\pi$
$968$	−3.10580	−0.0998243
$969$	42.3237	1.35963
$970$	−32.0619	−1.02945
$971$	−9.84659	−0.315992	−0.157996	−	0.987440i	$-0.550503\pi$
$971$	−9.84659	−0.315992	−0.157996	+	0.987440i	$0.550503\pi$
$972$	3.75352	0.120394
$973$	−31.0015	−0.993861
$974$	20.9350	0.670800
$975$	−9.34321	−0.299222
$976$	7.01137	0.224429
$977$	39.4685	1.26271	0.631355	−	0.775494i	$-0.282499\pi$
$977$	39.4685	1.26271	0.631355	+	0.775494i	$0.282499\pi$
$978$	3.49750	0.111838
$979$	27.2192	0.869931
$980$	−9.16909	−0.292896
$981$	0.562848	0.0179704
$982$	43.2110	1.37892
$983$	15.4855	0.493910	0.246955	−	0.969027i	$-0.420570\pi$
$983$	15.4855	0.493910	0.246955	+	0.969027i	$0.420570\pi$
$984$	19.4821	0.621066
$985$	0.773610	0.0246493
$986$	−6.72226	−0.214080
$987$	49.6570	1.58060
$988$	−25.8453	−0.822249
$989$	−5.34435	−0.169941
$990$	1.91733	0.0609369
$991$	5.20470	0.165333	0.0826663	−	0.996577i	$-0.473656\pi$
$991$	5.20470	0.165333	0.0826663	+	0.996577i	$0.473656\pi$
$992$	9.90716	0.314553
$993$	38.1474	1.21057
$994$	17.4290	0.552815
$995$	3.82460	0.121248
$996$	−12.4881	−0.395700
$997$	37.2990	1.18127	0.590635	−	0.806939i	$-0.298877\pi$
$997$	37.2990	1.18127	0.590635	+	0.806939i	$0.298877\pi$
$998$	−6.76702	−0.214206
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.t.1.2		6
37.9	even	9		74.2.f.b.7.2	✓	12
37.33	even	9		74.2.f.b.53.2	yes	12
37.36	even	2		2738.2.a.q.1.2		6
111.83	odd	18		666.2.x.g.451.2		12
111.107	odd	18		666.2.x.g.127.2		12
148.83	odd	18		592.2.bc.d.81.1		12
148.107	odd	18		592.2.bc.d.497.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.7.2	✓	12	37.9	even	9
74.2.f.b.53.2	yes	12	37.33	even	9
592.2.bc.d.81.1		12	148.83	odd	18
592.2.bc.d.497.1		12	148.107	odd	18
666.2.x.g.127.2		12	111.107	odd	18
666.2.x.g.451.2		12	111.83	odd	18
2738.2.a.q.1.2		6	37.36	even	2
2738.2.a.t.1.2		6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.83388 q^{3} +1.00000 q^{4} -1.87939 q^{5} -1.83388 q^{6} +3.44656 q^{7} +1.00000 q^{8} +0.363102 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.83388 q^{3} +1.00000 q^{4} -1.87939 q^{5} -1.83388 q^{6} +3.44656 q^{7} +1.00000 q^{8} +0.363102 q^{9} -1.87939 q^{10} -2.80966 q^{11} -1.83388 q^{12} -3.47077 q^{13} +3.44656 q^{14} +3.44656 q^{15} +1.00000 q^{16} -3.09926 q^{17} +0.363102 q^{18} +7.44656 q^{19} -1.87939 q^{20} -6.32056 q^{21} -2.80966 q^{22} -0.643537 q^{23} -1.83388 q^{24} -1.46791 q^{25} -3.47077 q^{26} +4.83575 q^{27} +3.44656 q^{28} +2.16899 q^{29} +3.44656 q^{30} +9.90716 q^{31} +1.00000 q^{32} +5.15257 q^{33} -3.09926 q^{34} -6.47741 q^{35} +0.363102 q^{36} +7.44656 q^{38} +6.36497 q^{39} -1.87939 q^{40} -10.6234 q^{41} -6.32056 q^{42} +8.30465 q^{43} -2.80966 q^{44} -0.682408 q^{45} -0.643537 q^{46} -7.85643 q^{47} -1.83388 q^{48} +4.87877 q^{49} -1.46791 q^{50} +5.68366 q^{51} -3.47077 q^{52} +4.83388 q^{53} +4.83575 q^{54} +5.28044 q^{55} +3.44656 q^{56} -13.6561 q^{57} +2.16899 q^{58} +0.553440 q^{59} +3.44656 q^{60} +7.01137 q^{61} +9.90716 q^{62} +1.25145 q^{63} +1.00000 q^{64} +6.52292 q^{65} +5.15257 q^{66} +0.211021 q^{67} -3.09926 q^{68} +1.18017 q^{69} -6.47741 q^{70} +5.05694 q^{71} +0.363102 q^{72} +10.2297 q^{73} +2.69197 q^{75} +7.44656 q^{76} -9.68366 q^{77} +6.36497 q^{78} -1.90486 q^{79} -1.87939 q^{80} -9.95746 q^{81} -10.6234 q^{82} +6.80966 q^{83} -6.32056 q^{84} +5.82471 q^{85} +8.30465 q^{86} -3.97765 q^{87} -2.80966 q^{88} -9.68773 q^{89} -0.682408 q^{90} -11.9622 q^{91} -0.643537 q^{92} -18.1685 q^{93} -7.85643 q^{94} -13.9950 q^{95} -1.83388 q^{96} +17.0598 q^{97} +4.87877 q^{98} -1.02019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9} - 3 q^{11} - 3 q^{14} - 3 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} + 21 q^{19} + 6 q^{21} - 3 q^{22} + 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28} - 6 q^{29} - 3 q^{30} + 21 q^{31} + 6 q^{32} - 3 q^{33} + 3 q^{34} - 3 q^{35} + 12 q^{36} + 21 q^{38} + 27 q^{39} + 18 q^{41} + 6 q^{42} + 18 q^{43} - 3 q^{44} + 6 q^{45} + 21 q^{46} - 9 q^{47} + 15 q^{49} - 18 q^{50} + 18 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} + 6 q^{57} - 6 q^{58} + 27 q^{59} - 3 q^{60} - 24 q^{61} + 21 q^{62} - 36 q^{63} + 6 q^{64} + 3 q^{65} - 3 q^{66} + 9 q^{67} + 3 q^{68} + 27 q^{69} - 3 q^{70} + 12 q^{72} + 27 q^{73} - 3 q^{75} + 21 q^{76} - 24 q^{77} + 27 q^{78} + 21 q^{79} - 6 q^{81} + 18 q^{82} + 27 q^{83} + 6 q^{84} - 3 q^{85} + 18 q^{86} - 3 q^{88} - 21 q^{89} + 6 q^{90} - 24 q^{91} + 21 q^{92} + 54 q^{93} - 9 q^{94} - 3 q^{95} + 42 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9 - 3 * q^11 - 3 * q^14 - 3 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 + 21 * q^19 + 6 * q^21 - 3 * q^22 + 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 - 6 * q^29 - 3 * q^30 + 21 * q^31 + 6 * q^32 - 3 * q^33 + 3 * q^34 - 3 * q^35 + 12 * q^36 + 21 * q^38 + 27 * q^39 + 18 * q^41 + 6 * q^42 + 18 * q^43 - 3 * q^44 + 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 - 18 * q^50 + 18 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 6 * q^57 - 6 * q^58 + 27 * q^59 - 3 * q^60 - 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 - 3 * q^66 + 9 * q^67 + 3 * q^68 + 27 * q^69 - 3 * q^70 + 12 * q^72 + 27 * q^73 - 3 * q^75 + 21 * q^76 - 24 * q^77 + 27 * q^78 + 21 * q^79 - 6 * q^81 + 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 - 3 * q^88 - 21 * q^89 + 6 * q^90 - 24 * q^91 + 21 * q^92 + 54 * q^93 - 9 * q^94 - 3 * q^95 + 42 * q^97 + 15 * q^98 - 36 * q^99

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