LMFDB - Embedded newform 2738.2.a.t.1.4

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			1.4
Root			$-1.27006$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.27006 q^{3} +1.00000 q^{4} +1.53209 q^{5} +1.27006 q^{6} +1.94585 q^{7} +1.00000 q^{8} -1.38694 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.27006 q^{3} +1.00000 q^{4} +1.53209 q^{5} +1.27006 q^{6} +1.94585 q^{7} +1.00000 q^{8} -1.38694 q^{9} +1.53209 q^{10} +0.441088 q^{11} +1.27006 q^{12} -2.11688 q^{13} +1.94585 q^{14} +1.94585 q^{15} +1.00000 q^{16} -3.82524 q^{17} -1.38694 q^{18} +5.94585 q^{19} +1.53209 q^{20} +2.47135 q^{21} +0.441088 q^{22} +5.71115 q^{23} +1.27006 q^{24} -2.65270 q^{25} -2.11688 q^{26} -5.57169 q^{27} +1.94585 q^{28} +2.73423 q^{29} +1.94585 q^{30} +9.87516 q^{31} +1.00000 q^{32} +0.560210 q^{33} -3.82524 q^{34} +2.98122 q^{35} -1.38694 q^{36} +5.94585 q^{38} -2.68857 q^{39} +1.53209 q^{40} +10.4012 q^{41} +2.47135 q^{42} +3.84681 q^{43} +0.441088 q^{44} -2.12491 q^{45} +5.71115 q^{46} +7.68632 q^{47} +1.27006 q^{48} -3.21367 q^{49} -2.65270 q^{50} -4.85829 q^{51} -2.11688 q^{52} +1.72994 q^{53} -5.57169 q^{54} +0.675787 q^{55} +1.94585 q^{56} +7.55161 q^{57} +2.73423 q^{58} +2.05415 q^{59} +1.94585 q^{60} -10.9355 q^{61} +9.87516 q^{62} -2.69877 q^{63} +1.00000 q^{64} -3.24324 q^{65} +0.560210 q^{66} -1.67354 q^{67} -3.82524 q^{68} +7.25353 q^{69} +2.98122 q^{70} -10.0577 q^{71} -1.38694 q^{72} -9.88570 q^{73} -3.36910 q^{75} +5.94585 q^{76} +0.858292 q^{77} -2.68857 q^{78} +13.3443 q^{79} +1.53209 q^{80} -2.91559 q^{81} +10.4012 q^{82} +3.55891 q^{83} +2.47135 q^{84} -5.86060 q^{85} +3.84681 q^{86} +3.47265 q^{87} +0.441088 q^{88} -11.8701 q^{89} -2.12491 q^{90} -4.11912 q^{91} +5.71115 q^{92} +12.5421 q^{93} +7.68632 q^{94} +9.10957 q^{95} +1.27006 q^{96} -0.593497 q^{97} -3.21367 q^{98} -0.611763 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.27006	0.733272	0.366636	−	0.930365i	$-0.380510\pi$
$3$	1.27006	0.733272	0.366636	+	0.930365i	$0.380510\pi$
$4$	1.00000	0.500000
$5$	1.53209	0.685171	0.342585	−	0.939487i	$-0.388697\pi$
$5$	1.53209	0.685171	0.342585	+	0.939487i	$0.388697\pi$
$6$	1.27006	0.518501
$7$	1.94585	0.735462	0.367731	−	0.929932i	$-0.380135\pi$
$7$	1.94585	0.735462	0.367731	+	0.929932i	$0.380135\pi$
$8$	1.00000	0.353553
$9$	−1.38694	−0.462313
$10$	1.53209	0.484489
$11$	0.441088	0.132993	0.0664966	−	0.997787i	$-0.478818\pi$
$11$	0.441088	0.132993	0.0664966	+	0.997787i	$0.478818\pi$
$12$	1.27006	0.366636
$13$	−2.11688	−0.587116	−0.293558	−	0.955941i	$-0.594839\pi$
$13$	−2.11688	−0.587116	−0.293558	+	0.955941i	$0.594839\pi$
$14$	1.94585	0.520050
$15$	1.94585	0.502416
$16$	1.00000	0.250000
$17$	−3.82524	−0.927756	−0.463878	−	0.885899i	$-0.653542\pi$
$17$	−3.82524	−0.927756	−0.463878	+	0.885899i	$0.653542\pi$
$18$	−1.38694	−0.326905
$19$	5.94585	1.36407	0.682036	−	0.731319i	$-0.261095\pi$
$19$	5.94585	1.36407	0.682036	+	0.731319i	$0.261095\pi$
$20$	1.53209	0.342585
$21$	2.47135	0.539294
$22$	0.441088	0.0940404
$23$	5.71115	1.19086	0.595429	−	0.803408i	$-0.296982\pi$
$23$	5.71115	1.19086	0.595429	+	0.803408i	$0.296982\pi$
$24$	1.27006	0.259251
$25$	−2.65270	−0.530541
$26$	−2.11688	−0.415153
$27$	−5.57169	−1.07227
$28$	1.94585	0.367731
$29$	2.73423	0.507735	0.253867	−	0.967239i	$-0.418297\pi$
$29$	2.73423	0.507735	0.253867	+	0.967239i	$0.418297\pi$
$30$	1.94585	0.355262
$31$	9.87516	1.77363	0.886816	−	0.462123i	$-0.152912\pi$
$31$	9.87516	1.77363	0.886816	+	0.462123i	$0.152912\pi$
$32$	1.00000	0.176777
$33$	0.560210	0.0975201
$34$	−3.82524	−0.656022
$35$	2.98122	0.503917
$36$	−1.38694	−0.231156
$37$	0	0
$37$	0	0
$38$	5.94585	0.964544
$39$	−2.68857	−0.430515
$40$	1.53209	0.242245
$41$	10.4012	1.62440	0.812198	−	0.583382i	$-0.198271\pi$
$41$	10.4012	1.62440	0.812198	+	0.583382i	$0.198271\pi$
$42$	2.47135	0.381338
$43$	3.84681	0.586633	0.293317	−	0.956015i	$-0.405241\pi$
$43$	3.84681	0.586633	0.293317	+	0.956015i	$0.405241\pi$
$44$	0.441088	0.0664966
$45$	−2.12491	−0.316763
$46$	5.71115	0.842063
$47$	7.68632	1.12116	0.560582	−	0.828099i	$-0.310577\pi$
$47$	7.68632	1.12116	0.560582	+	0.828099i	$0.310577\pi$
$48$	1.27006	0.183318
$49$	−3.21367	−0.459095
$50$	−2.65270	−0.375149
$51$	−4.85829	−0.680297
$52$	−2.11688	−0.293558
$53$	1.72994	0.237625	0.118813	−	0.992917i	$-0.462091\pi$
$53$	1.72994	0.237625	0.118813	+	0.992917i	$0.462091\pi$
$54$	−5.57169	−0.758211
$55$	0.675787	0.0911231
$56$	1.94585	0.260025
$57$	7.55161	1.00023
$58$	2.73423	0.359023
$59$	2.05415	0.267428	0.133714	−	0.991020i	$-0.457310\pi$
$59$	2.05415	0.267428	0.133714	+	0.991020i	$0.457310\pi$
$60$	1.94585	0.251208
$61$	−10.9355	−1.40015	−0.700077	−	0.714068i	$-0.746851\pi$
$61$	−10.9355	−1.40015	−0.700077	+	0.714068i	$0.746851\pi$
$62$	9.87516	1.25415
$63$	−2.69877	−0.340014
$64$	1.00000	0.125000
$65$	−3.24324	−0.402275
$66$	0.560210	0.0689571
$67$	−1.67354	−0.204455	−0.102228	−	0.994761i	$-0.532597\pi$
$67$	−1.67354	−0.204455	−0.102228	+	0.994761i	$0.532597\pi$
$68$	−3.82524	−0.463878
$69$	7.25353	0.873222
$70$	2.98122	0.356323
$71$	−10.0577	−1.19363	−0.596813	−	0.802381i	$-0.703567\pi$
$71$	−10.0577	−1.19363	−0.596813	+	0.802381i	$0.703567\pi$
$72$	−1.38694	−0.163452
$73$	−9.88570	−1.15703	−0.578517	−	0.815671i	$-0.696368\pi$
$73$	−9.88570	−1.15703	−0.578517	+	0.815671i	$0.696368\pi$
$74$	0	0
$75$	−3.36910	−0.389030
$76$	5.94585	0.682036
$77$	0.858292	0.0978115
$78$	−2.68857	−0.304420
$79$	13.3443	1.50135	0.750674	−	0.660673i	$-0.229729\pi$
$79$	13.3443	1.50135	0.750674	+	0.660673i	$0.229729\pi$
$80$	1.53209	0.171293
$81$	−2.91559	−0.323954
$82$	10.4012	1.14862
$83$	3.55891	0.390641	0.195321	−	0.980739i	$-0.437425\pi$
$83$	3.55891	0.390641	0.195321	+	0.980739i	$0.437425\pi$
$84$	2.47135	0.269647
$85$	−5.86060	−0.635671
$86$	3.84681	0.414812
$87$	3.47265	0.372307
$88$	0.441088	0.0470202
$89$	−11.8701	−1.25823	−0.629115	−	0.777312i	$-0.716583\pi$
$89$	−11.8701	−1.25823	−0.629115	+	0.777312i	$0.716583\pi$
$90$	−2.12491	−0.223986
$91$	−4.11912	−0.431801
$92$	5.71115	0.595429
$93$	12.5421	1.30055
$94$	7.68632	0.792783
$95$	9.10957	0.934622
$96$	1.27006	0.129625
$97$	−0.593497	−0.0602604	−0.0301302	−	0.999546i	$-0.509592\pi$
$97$	−0.593497	−0.0602604	−0.0301302	+	0.999546i	$0.509592\pi$
$98$	−3.21367	−0.324629
$99$	−0.611763	−0.0614845
$100$	−2.65270	−0.265270
$101$	−13.2279	−1.31623	−0.658113	−	0.752919i	$-0.728645\pi$
$101$	−13.2279	−1.31623	−0.658113	+	0.752919i	$0.728645\pi$
$102$	−4.85829	−0.481043
$103$	−3.14999	−0.310378	−0.155189	−	0.987885i	$-0.549599\pi$
$103$	−3.14999	−0.310378	−0.155189	+	0.987885i	$0.549599\pi$
$104$	−2.11688	−0.207577
$105$	3.78633	0.369508
$106$	1.72994	0.168026
$107$	−3.70666	−0.358336	−0.179168	−	0.983818i	$-0.557341\pi$
$107$	−3.70666	−0.358336	−0.179168	+	0.983818i	$0.557341\pi$
$108$	−5.57169	−0.536136
$109$	14.9687	1.43374	0.716871	−	0.697206i	$-0.245574\pi$
$109$	14.9687	1.43374	0.716871	+	0.697206i	$0.245574\pi$
$110$	0.675787	0.0644337
$111$	0	0
$112$	1.94585	0.183866
$113$	−19.9268	−1.87455	−0.937277	−	0.348585i	$-0.886662\pi$
$113$	−19.9268	−1.87455	−0.937277	+	0.348585i	$0.886662\pi$
$114$	7.55161	0.707273
$115$	8.74999	0.815941
$116$	2.73423	0.253867
$117$	2.93598	0.271431
$118$	2.05415	0.189100
$119$	−7.44334	−0.682329
$120$	1.94585	0.177631
$121$	−10.8054	−0.982313
$122$	−10.9355	−0.990058
$123$	13.2102	1.19112
$124$	9.87516	0.886816
$125$	−11.7246	−1.04868
$126$	−2.69877	−0.240426
$127$	4.90318	0.435087	0.217543	−	0.976051i	$-0.430196\pi$
$127$	4.90318	0.435087	0.217543	+	0.976051i	$0.430196\pi$
$128$	1.00000	0.0883883
$129$	4.88570	0.430161
$130$	−3.24324	−0.284451
$131$	0.308931	0.0269915	0.0134957	−	0.999909i	$-0.495704\pi$
$131$	0.308931	0.0269915	0.0134957	+	0.999909i	$0.495704\pi$
$132$	0.560210	0.0487601
$133$	11.5697	1.00322
$134$	−1.67354	−0.144572
$135$	−8.53633	−0.734690
$136$	−3.82524	−0.328011
$137$	−20.3017	−1.73449	−0.867245	−	0.497882i	$-0.834111\pi$
$137$	−20.3017	−1.73449	−0.867245	+	0.497882i	$0.834111\pi$
$138$	7.25353	0.617461
$139$	−13.1379	−1.11434	−0.557170	−	0.830398i	$-0.688113\pi$
$139$	−13.1379	−1.11434	−0.557170	+	0.830398i	$0.688113\pi$
$140$	2.98122	0.251959
$141$	9.76211	0.822118
$142$	−10.0577	−0.844021
$143$	−0.933729	−0.0780824
$144$	−1.38694	−0.115578
$145$	4.18909	0.347885
$146$	−9.88570	−0.818146
$147$	−4.08156	−0.336641
$148$	0	0
$149$	−3.98826	−0.326731	−0.163366	−	0.986566i	$-0.552235\pi$
$149$	−3.98826	−0.326731	−0.163366	+	0.986566i	$0.552235\pi$
$150$	−3.36910	−0.275086
$151$	−19.6497	−1.59907	−0.799535	−	0.600620i	$-0.794921\pi$
$151$	−19.6497	−1.59907	−0.799535	+	0.600620i	$0.794921\pi$
$152$	5.94585	0.482272
$153$	5.30537	0.428913
$154$	0.858292	0.0691631
$155$	15.1296	1.21524
$156$	−2.68857	−0.215258
$157$	9.13115	0.728745	0.364372	−	0.931253i	$-0.381284\pi$
$157$	9.13115	0.728745	0.364372	+	0.931253i	$0.381284\pi$
$158$	13.3443	1.06161
$159$	2.19713	0.174244
$160$	1.53209	0.121122
$161$	11.1130	0.875831
$162$	−2.91559	−0.229070
$163$	−1.87516	−0.146874	−0.0734370	−	0.997300i	$-0.523397\pi$
$163$	−1.87516	−0.146874	−0.0734370	+	0.997300i	$0.523397\pi$
$164$	10.4012	0.812198
$165$	0.858292	0.0668179
$166$	3.55891	0.276225
$167$	4.60701	0.356501	0.178251	−	0.983985i	$-0.442956\pi$
$167$	4.60701	0.356501	0.178251	+	0.983985i	$0.442956\pi$
$168$	2.47135	0.190669
$169$	−8.51884	−0.655295
$170$	−5.86060	−0.449488
$171$	−8.24653	−0.630628
$172$	3.84681	0.293317
$173$	−15.0979	−1.14787	−0.573935	−	0.818901i	$-0.694584\pi$
$173$	−15.0979	−1.14787	−0.573935	+	0.818901i	$0.694584\pi$
$174$	3.47265	0.263261
$175$	−5.16176	−0.390193
$176$	0.441088	0.0332483
$177$	2.60890	0.196097
$178$	−11.8701	−0.889703
$179$	20.1143	1.50342	0.751708	−	0.659496i	$-0.229230\pi$
$179$	20.1143	1.50342	0.751708	+	0.659496i	$0.229230\pi$
$180$	−2.12491	−0.158382
$181$	9.31549	0.692415	0.346207	−	0.938158i	$-0.387469\pi$
$181$	9.31549	0.692415	0.346207	+	0.938158i	$0.387469\pi$
$182$	−4.11912	−0.305330
$183$	−13.8888	−1.02669
$184$	5.71115	0.421032
$185$	0	0
$186$	12.5421	0.919630
$187$	−1.68727	−0.123385
$188$	7.68632	0.560582
$189$	−10.8417	−0.788616
$190$	9.10957	0.660878
$191$	−10.6491	−0.770541	−0.385271	−	0.922804i	$-0.625892\pi$
$191$	−10.6491	−0.770541	−0.385271	+	0.922804i	$0.625892\pi$
$192$	1.27006	0.0916589
$193$	12.2527	0.881970	0.440985	−	0.897514i	$-0.354629\pi$
$193$	12.2527	0.881970	0.440985	+	0.897514i	$0.354629\pi$
$194$	−0.593497	−0.0426106
$195$	−4.11912	−0.294976
$196$	−3.21367	−0.229548
$197$	16.1232	1.14873	0.574365	−	0.818600i	$-0.305249\pi$
$197$	16.1232	1.14873	0.574365	+	0.818600i	$0.305249\pi$
$198$	−0.611763	−0.0434761
$199$	−1.99074	−0.141120	−0.0705599	−	0.997508i	$-0.522479\pi$
$199$	−1.99074	−0.141120	−0.0705599	+	0.997508i	$0.522479\pi$
$200$	−2.65270	−0.187574
$201$	−2.12550	−0.149921
$202$	−13.2279	−0.930713
$203$	5.32041	0.373420
$204$	−4.85829	−0.340148
$205$	15.9356	1.11299
$206$	−3.14999	−0.219470
$207$	−7.92102	−0.550549
$208$	−2.11688	−0.146779
$209$	2.62265	0.181412
$210$	3.78633	0.261282
$211$	−12.6051	−0.867771	−0.433885	−	0.900968i	$-0.642858\pi$
$211$	−12.6051	−0.867771	−0.433885	+	0.900968i	$0.642858\pi$
$212$	1.72994	0.118813
$213$	−12.7739	−0.875252
$214$	−3.70666	−0.253382
$215$	5.89366	0.401944
$216$	−5.57169	−0.379106
$217$	19.2156	1.30444
$218$	14.9687	1.01381
$219$	−12.5555	−0.848419
$220$	0.675787	0.0455615
$221$	8.09755	0.544700
$222$	0	0
$223$	20.3949	1.36575	0.682873	−	0.730538i	$-0.260730\pi$
$223$	20.3949	1.36575	0.682873	+	0.730538i	$0.260730\pi$
$224$	1.94585	0.130013
$225$	3.67914	0.245276
$226$	−19.9268	−1.32551
$227$	−7.57264	−0.502614	−0.251307	−	0.967907i	$-0.580860\pi$
$227$	−7.57264	−0.502614	−0.251307	+	0.967907i	$0.580860\pi$
$228$	7.55161	0.500117
$229$	−0.312901	−0.0206771	−0.0103385	−	0.999947i	$-0.503291\pi$
$229$	−0.312901	−0.0206771	−0.0103385	+	0.999947i	$0.503291\pi$
$230$	8.74999	0.576957
$231$	1.09009	0.0717224
$232$	2.73423	0.179511
$233$	−0.683167	−0.0447557	−0.0223779	−	0.999750i	$-0.507124\pi$
$233$	−0.683167	−0.0447557	−0.0223779	+	0.999750i	$0.507124\pi$
$234$	2.93598	0.191931
$235$	11.7761	0.768190
$236$	2.05415	0.133714
$237$	16.9481	1.10090
$238$	−7.44334	−0.482480
$239$	11.2064	0.724882	0.362441	−	0.932007i	$-0.381944\pi$
$239$	11.2064	0.724882	0.362441	+	0.932007i	$0.381944\pi$
$240$	1.94585	0.125604
$241$	−5.18059	−0.333711	−0.166856	−	0.985981i	$-0.553361\pi$
$241$	−5.18059	−0.333711	−0.166856	+	0.985981i	$0.553361\pi$
$242$	−10.8054	−0.694600
$243$	13.0121	0.834726
$244$	−10.9355	−0.700077
$245$	−4.92362	−0.314559
$246$	13.2102	0.842251
$247$	−12.5866	−0.800868
$248$	9.87516	0.627073
$249$	4.52004	0.286446
$250$	−11.7246	−0.741530
$251$	−30.4921	−1.92464	−0.962321	−	0.271916i	$-0.912343\pi$
$251$	−30.4921	−1.92464	−0.962321	+	0.271916i	$0.912343\pi$
$252$	−2.69877	−0.170007
$253$	2.51912	0.158376
$254$	4.90318	0.307653
$255$	−7.44334	−0.466120
$256$	1.00000	0.0625000
$257$	5.86765	0.366014	0.183007	−	0.983112i	$-0.441417\pi$
$257$	5.86765	0.366014	0.183007	+	0.983112i	$0.441417\pi$
$258$	4.88570	0.304170
$259$	0	0
$260$	−3.24324	−0.201137
$261$	−3.79222	−0.234732
$262$	0.308931	0.0190858
$263$	16.3124	1.00587	0.502934	−	0.864325i	$-0.332254\pi$
$263$	16.3124	1.00587	0.502934	+	0.864325i	$0.332254\pi$
$264$	0.560210	0.0344786
$265$	2.65042	0.162814
$266$	11.5697	0.709386
$267$	−15.0758	−0.922625
$268$	−1.67354	−0.102228
$269$	−10.0060	−0.610079	−0.305039	−	0.952340i	$-0.598670\pi$
$269$	−10.0060	−0.610079	−0.305039	+	0.952340i	$0.598670\pi$
$270$	−8.53633	−0.519504
$271$	−12.3669	−0.751233	−0.375616	−	0.926775i	$-0.622569\pi$
$271$	−12.3669	−0.751233	−0.375616	+	0.926775i	$0.622569\pi$
$272$	−3.82524	−0.231939
$273$	−5.23155	−0.316628
$274$	−20.3017	−1.22647
$275$	−1.17008	−0.0705583
$276$	7.25353	0.436611
$277$	−21.2463	−1.27656	−0.638282	−	0.769803i	$-0.720355\pi$
$277$	−21.2463	−1.27656	−0.638282	+	0.769803i	$0.720355\pi$
$278$	−13.1379	−0.787958
$279$	−13.6962	−0.819973
$280$	2.98122	0.178162
$281$	16.1986	0.966328	0.483164	−	0.875530i	$-0.339487\pi$
$281$	16.1986	0.966328	0.483164	+	0.875530i	$0.339487\pi$
$282$	9.76211	0.581325
$283$	−4.98824	−0.296520	−0.148260	−	0.988948i	$-0.547367\pi$
$283$	−4.98824	−0.296520	−0.148260	+	0.988948i	$0.547367\pi$
$284$	−10.0577	−0.596813
$285$	11.5697	0.685332
$286$	−0.933729	−0.0552126
$287$	20.2392	1.19468
$288$	−1.38694	−0.0817261
$289$	−2.36757	−0.139269
$290$	4.18909	0.245992
$291$	−0.753778	−0.0441873
$292$	−9.88570	−0.578517
$293$	5.54920	0.324188	0.162094	−	0.986775i	$-0.448175\pi$
$293$	5.54920	0.324188	0.162094	+	0.986775i	$0.448175\pi$
$294$	−4.08156	−0.238041
$295$	3.14714	0.183234
$296$	0	0
$297$	−2.45761	−0.142605
$298$	−3.98826	−0.231034
$299$	−12.0898	−0.699171
$300$	−3.36910	−0.194515
$301$	7.48532	0.431447
$302$	−19.6497	−1.13071
$303$	−16.8003	−0.965151
$304$	5.94585	0.341018
$305$	−16.7542	−0.959344
$306$	5.30537	0.303288
$307$	15.1615	0.865311	0.432656	−	0.901559i	$-0.357577\pi$
$307$	15.1615	0.865311	0.432656	+	0.901559i	$0.357577\pi$
$308$	0.858292	0.0489057
$309$	−4.00069	−0.227591
$310$	15.1296	0.859305
$311$	15.2086	0.862401	0.431201	−	0.902256i	$-0.358090\pi$
$311$	15.2086	0.862401	0.431201	+	0.902256i	$0.358090\pi$
$312$	−2.68857	−0.152210
$313$	29.1716	1.64888	0.824438	−	0.565953i	$-0.191492\pi$
$313$	29.1716	1.64888	0.824438	+	0.565953i	$0.191492\pi$
$314$	9.13115	0.515300
$315$	−4.13476	−0.232968
$316$	13.3443	0.750674
$317$	−19.1896	−1.07779	−0.538897	−	0.842372i	$-0.681159\pi$
$317$	−19.1896	−1.07779	−0.538897	+	0.842372i	$0.681159\pi$
$318$	2.19713	0.123209
$319$	1.20604	0.0675252
$320$	1.53209	0.0856464
$321$	−4.70769	−0.262758
$322$	11.1130	0.619306
$323$	−22.7443	−1.26553
$324$	−2.91559	−0.161977
$325$	5.61544	0.311489
$326$	−1.87516	−0.103856
$327$	19.0112	1.05132
$328$	10.4012	0.574311
$329$	14.9564	0.824574
$330$	0.858292	0.0472474
$331$	−7.83308	−0.430545	−0.215273	−	0.976554i	$-0.569064\pi$
$331$	−7.83308	−0.430545	−0.215273	+	0.976554i	$0.569064\pi$
$332$	3.55891	0.195321
$333$	0	0
$334$	4.60701	0.252085
$335$	−2.56401	−0.140087
$336$	2.47135	0.134823
$337$	19.6648	1.07121	0.535605	−	0.844468i	$-0.320083\pi$
$337$	19.6648	1.07121	0.535605	+	0.844468i	$0.320083\pi$
$338$	−8.51884	−0.463364
$339$	−25.3083	−1.37456
$340$	−5.86060	−0.317836
$341$	4.35582	0.235881
$342$	−8.24653	−0.445921
$343$	−19.8743	−1.07311
$344$	3.84681	0.207406
$345$	11.1130	0.598306
$346$	−15.0979	−0.811667
$347$	21.5643	1.15763	0.578817	−	0.815457i	$-0.303515\pi$
$347$	21.5643	1.15763	0.578817	+	0.815457i	$0.303515\pi$
$348$	3.47265	0.186154
$349$	−26.8757	−1.43862	−0.719310	−	0.694689i	$-0.755542\pi$
$349$	−26.8757	−1.43862	−0.719310	+	0.694689i	$0.755542\pi$
$350$	−5.16176	−0.275908
$351$	11.7946	0.629548
$352$	0.441088	0.0235101
$353$	−13.1785	−0.701419	−0.350710	−	0.936484i	$-0.614060\pi$
$353$	−13.1785	−0.701419	−0.350710	+	0.936484i	$0.614060\pi$
$354$	2.60890	0.138662
$355$	−15.4092	−0.817838
$356$	−11.8701	−0.629115
$357$	−9.45351	−0.500333
$358$	20.1143	1.06308
$359$	3.38568	0.178690	0.0893448	−	0.996001i	$-0.471523\pi$
$359$	3.38568	0.178690	0.0893448	+	0.996001i	$0.471523\pi$
$360$	−2.12491	−0.111993
$361$	16.3531	0.860691
$362$	9.31549	0.489611
$363$	−13.7236	−0.720302
$364$	−4.11912	−0.215901
$365$	−15.1458	−0.792765
$366$	−13.8888	−0.725981
$367$	6.59687	0.344354	0.172177	−	0.985066i	$-0.444920\pi$
$367$	6.59687	0.344354	0.172177	+	0.985066i	$0.444920\pi$
$368$	5.71115	0.297714
$369$	−14.4258	−0.750979
$370$	0	0
$371$	3.36620	0.174764
$372$	12.5421	0.650277
$373$	1.05692	0.0547254	0.0273627	−	0.999626i	$-0.491289\pi$
$373$	1.05692	0.0547254	0.0273627	+	0.999626i	$0.491289\pi$
$374$	−1.68727	−0.0872465
$375$	−14.8910	−0.768969
$376$	7.68632	0.396392
$377$	−5.78803	−0.298099
$378$	−10.8417	−0.557636
$379$	22.2144	1.14108	0.570538	−	0.821271i	$-0.306735\pi$
$379$	22.2144	1.14108	0.570538	+	0.821271i	$0.306735\pi$
$380$	9.10957	0.467311
$381$	6.22735	0.319037
$382$	−10.6491	−0.544855
$383$	9.34717	0.477618	0.238809	−	0.971067i	$-0.423243\pi$
$383$	9.34717	0.477618	0.238809	+	0.971067i	$0.423243\pi$
$384$	1.27006	0.0648127
$385$	1.31498	0.0670176
$386$	12.2527	0.623647
$387$	−5.33529	−0.271208
$388$	−0.593497	−0.0301302
$389$	2.41968	0.122683	0.0613413	−	0.998117i	$-0.480462\pi$
$389$	2.41968	0.122683	0.0613413	+	0.998117i	$0.480462\pi$
$390$	−4.11912	−0.208580
$391$	−21.8465	−1.10483
$392$	−3.21367	−0.162315
$393$	0.392362	0.0197921
$394$	16.1232	0.812274
$395$	20.4446	1.02868
$396$	−0.611763	−0.0307422
$397$	19.7041	0.988921	0.494460	−	0.869200i	$-0.335366\pi$
$397$	19.7041	0.988921	0.494460	+	0.869200i	$0.335366\pi$
$398$	−1.99074	−0.0997867
$399$	14.6943	0.735635
$400$	−2.65270	−0.132635
$401$	−29.2178	−1.45907	−0.729534	−	0.683944i	$-0.760263\pi$
$401$	−29.2178	−1.45907	−0.729534	+	0.683944i	$0.760263\pi$
$402$	−2.12550	−0.106010
$403$	−20.9045	−1.04133
$404$	−13.2279	−0.658113
$405$	−4.46694	−0.221964
$406$	5.32041	0.264048
$407$	0	0
$408$	−4.85829	−0.240521
$409$	−3.77390	−0.186608	−0.0933038	−	0.995638i	$-0.529743\pi$
$409$	−3.77390	−0.186608	−0.0933038	+	0.995638i	$0.529743\pi$
$410$	15.9356	0.787002
$411$	−25.7844	−1.27185
$412$	−3.14999	−0.155189
$413$	3.99707	0.196683
$414$	−7.92102	−0.389297
$415$	5.45257	0.267656
$416$	−2.11688	−0.103788
$417$	−16.6859	−0.817114
$418$	2.62265	0.128278
$419$	−36.2507	−1.77096	−0.885480	−	0.464677i	$-0.846171\pi$
$419$	−36.2507	−1.77096	−0.885480	+	0.464677i	$0.846171\pi$
$420$	3.78633	0.184754
$421$	16.1783	0.788480	0.394240	−	0.919008i	$-0.371008\pi$
$421$	16.1783	0.788480	0.394240	+	0.919008i	$0.371008\pi$
$422$	−12.6051	−0.613607
$423$	−10.6605	−0.518329
$424$	1.72994	0.0840131
$425$	10.1472	0.492212
$426$	−12.7739	−0.618896
$427$	−21.2789	−1.02976
$428$	−3.70666	−0.179168
$429$	−1.18590	−0.0572556
$430$	5.89366	0.284217
$431$	20.7296	0.998511	0.499256	−	0.866455i	$-0.333607\pi$
$431$	20.7296	0.998511	0.499256	+	0.866455i	$0.333607\pi$
$432$	−5.57169	−0.268068
$433$	26.7853	1.28722	0.643611	−	0.765353i	$-0.277436\pi$
$433$	26.7853	1.28722	0.643611	+	0.765353i	$0.277436\pi$
$434$	19.2156	0.922378
$435$	5.32041	0.255094
$436$	14.9687	0.716871
$437$	33.9577	1.62441
$438$	−12.5555	−0.599923
$439$	−8.39586	−0.400712	−0.200356	−	0.979723i	$-0.564210\pi$
$439$	−8.39586	−0.400712	−0.200356	+	0.979723i	$0.564210\pi$
$440$	0.675787	0.0322169
$441$	4.45716	0.212246
$442$	8.09755	0.385161
$443$	−19.6599	−0.934068	−0.467034	−	0.884239i	$-0.654677\pi$
$443$	−19.6599	−0.934068	−0.467034	+	0.884239i	$0.654677\pi$
$444$	0	0
$445$	−18.1861	−0.862103
$446$	20.3949	0.965728
$447$	−5.06535	−0.239583
$448$	1.94585	0.0919328
$449$	−27.1724	−1.28234	−0.641171	−	0.767398i	$-0.721551\pi$
$449$	−27.1724	−1.28234	−0.641171	+	0.767398i	$0.721551\pi$
$450$	3.67914	0.173436
$451$	4.58785	0.216034
$452$	−19.9268	−0.937277
$453$	−24.9564	−1.17255
$454$	−7.57264	−0.355402
$455$	−6.31086	−0.295858
$456$	7.55161	0.353636
$457$	−19.9670	−0.934018	−0.467009	−	0.884252i	$-0.654669\pi$
$457$	−19.9670	−0.934018	−0.467009	+	0.884252i	$0.654669\pi$
$458$	−0.312901	−0.0146209
$459$	21.3130	0.994807
$460$	8.74999	0.407971
$461$	7.86373	0.366251	0.183125	−	0.983090i	$-0.441379\pi$
$461$	7.86373	0.366251	0.183125	+	0.983090i	$0.441379\pi$
$462$	1.09009	0.0507154
$463$	−6.04210	−0.280800	−0.140400	−	0.990095i	$-0.544839\pi$
$463$	−6.04210	−0.280800	−0.140400	+	0.990095i	$0.544839\pi$
$464$	2.73423	0.126934
$465$	19.2156	0.891102
$466$	−0.683167	−0.0316471
$467$	29.3245	1.35698	0.678489	−	0.734611i	$-0.262635\pi$
$467$	29.3245	1.35698	0.678489	+	0.734611i	$0.262635\pi$
$468$	2.93598	0.135716
$469$	−3.25646	−0.150369
$470$	11.7761	0.543192
$471$	11.5971	0.534368
$472$	2.05415	0.0945499
$473$	1.69678	0.0780182
$474$	16.9481	0.778451
$475$	−15.7726	−0.723696
$476$	−7.44334	−0.341165
$477$	−2.39932	−0.109857
$478$	11.2064	0.512569
$479$	−4.13663	−0.189007	−0.0945036	−	0.995525i	$-0.530126\pi$
$479$	−4.13663	−0.189007	−0.0945036	+	0.995525i	$0.530126\pi$
$480$	1.94585	0.0888155
$481$	0	0
$482$	−5.18059	−0.235969
$483$	14.1143	0.642222
$484$	−10.8054	−0.491156
$485$	−0.909289	−0.0412887
$486$	13.0121	0.590241
$487$	28.9347	1.31116	0.655579	−	0.755126i	$-0.272425\pi$
$487$	28.9347	1.31116	0.655579	+	0.755126i	$0.272425\pi$
$488$	−10.9355	−0.495029
$489$	−2.38158	−0.107699
$490$	−4.92362	−0.222427
$491$	19.5423	0.881933	0.440967	−	0.897524i	$-0.354636\pi$
$491$	19.5423	0.881933	0.440967	+	0.897524i	$0.354636\pi$
$492$	13.2102	0.595562
$493$	−10.4591	−0.471054
$494$	−12.5866	−0.566299
$495$	−0.937275	−0.0421274
$496$	9.87516	0.443408
$497$	−19.5707	−0.877867
$498$	4.52004	0.202548
$499$	−42.2259	−1.89029	−0.945145	−	0.326651i	$-0.894080\pi$
$499$	−42.2259	−1.89029	−0.945145	+	0.326651i	$0.894080\pi$
$500$	−11.7246	−0.524341
$501$	5.85120	0.261412
$502$	−30.4921	−1.36093
$503$	−13.3293	−0.594325	−0.297163	−	0.954827i	$-0.596040\pi$
$503$	−13.3293	−0.594325	−0.297163	+	0.954827i	$0.596040\pi$
$504$	−2.69877	−0.120213
$505$	−20.2663	−0.901840
$506$	2.51912	0.111989
$507$	−10.8195	−0.480509
$508$	4.90318	0.217543
$509$	27.3349	1.21160	0.605799	−	0.795618i	$-0.292854\pi$
$509$	27.3349	1.21160	0.605799	+	0.795618i	$0.292854\pi$
$510$	−7.44334	−0.329596
$511$	−19.2361	−0.850954
$512$	1.00000	0.0441942
$513$	−33.1284	−1.46266
$514$	5.86765	0.258811
$515$	−4.82607	−0.212662
$516$	4.88570	0.215081
$517$	3.39035	0.149107
$518$	0	0
$519$	−19.1753	−0.841701
$520$	−3.24324	−0.142226
$521$	22.1857	0.971975	0.485987	−	0.873966i	$-0.338460\pi$
$521$	22.1857	0.971975	0.485987	+	0.873966i	$0.338460\pi$
$522$	−3.79222	−0.165981
$523$	−38.4029	−1.67924	−0.839621	−	0.543172i	$-0.817223\pi$
$523$	−38.4029	−1.67924	−0.839621	+	0.543172i	$0.817223\pi$
$524$	0.308931	0.0134957
$525$	−6.55577	−0.286117
$526$	16.3124	0.711255
$527$	−37.7748	−1.64550
$528$	0.560210	0.0243800
$529$	9.61726	0.418142
$530$	2.65042	0.115127
$531$	−2.84898	−0.123635
$532$	11.5697	0.501612
$533$	−22.0181	−0.953708
$534$	−15.0758	−0.652394
$535$	−5.67893	−0.245522
$536$	−1.67354	−0.0722859
$537$	25.5465	1.10241
$538$	−10.0060	−0.431391
$539$	−1.41751	−0.0610565
$540$	−8.53633	−0.367345
$541$	−35.5323	−1.52765	−0.763827	−	0.645421i	$-0.776682\pi$
$541$	−35.5323	−1.52765	−0.763827	+	0.645421i	$0.776682\pi$
$542$	−12.3669	−0.531202
$543$	11.8313	0.507728
$544$	−3.82524	−0.164006
$545$	22.9334	0.982358
$546$	−5.23155	−0.223890
$547$	39.8335	1.70316	0.851579	−	0.524227i	$-0.175646\pi$
$547$	39.8335	1.70316	0.851579	+	0.524227i	$0.175646\pi$
$548$	−20.3017	−0.867245
$549$	15.1669	0.647309
$550$	−1.17008	−0.0498922
$551$	16.2574	0.692586
$552$	7.25353	0.308731
$553$	25.9659	1.10418
$554$	−21.2463	−0.902667
$555$	0	0
$556$	−13.1379	−0.557170
$557$	−7.81215	−0.331011	−0.165506	−	0.986209i	$-0.552926\pi$
$557$	−7.81215	−0.331011	−0.165506	+	0.986209i	$0.552926\pi$
$558$	−13.6962	−0.579808
$559$	−8.14322	−0.344421
$560$	2.98122	0.125979
$561$	−2.14294	−0.0904748
$562$	16.1986	0.683297
$563$	−35.1396	−1.48096	−0.740479	−	0.672080i	$-0.765401\pi$
$563$	−35.1396	−1.48096	−0.740479	+	0.672080i	$0.765401\pi$
$564$	9.76211	0.411059
$565$	−30.5296	−1.28439
$566$	−4.98824	−0.209671
$567$	−5.67329	−0.238256
$568$	−10.0577	−0.422010
$569$	−26.8804	−1.12689	−0.563444	−	0.826155i	$-0.690524\pi$
$569$	−26.8804	−1.12689	−0.563444	+	0.826155i	$0.690524\pi$
$570$	11.5697	0.484603
$571$	39.9896	1.67351	0.836756	−	0.547576i	$-0.184449\pi$
$571$	39.9896	1.67351	0.836756	+	0.547576i	$0.184449\pi$
$572$	−0.933729	−0.0390412
$573$	−13.5250	−0.565016
$574$	20.2392	0.844768
$575$	−15.1500	−0.631798
$576$	−1.38694	−0.0577891
$577$	16.4991	0.686868	0.343434	−	0.939177i	$-0.388410\pi$
$577$	16.4991	0.686868	0.343434	+	0.939177i	$0.388410\pi$
$578$	−2.36757	−0.0984781
$579$	15.5617	0.646724
$580$	4.18909	0.173943
$581$	6.92511	0.287302
$582$	−0.753778	−0.0312451
$583$	0.763055	0.0316025
$584$	−9.88570	−0.409073
$585$	4.49818	0.185977
$586$	5.54920	0.229235
$587$	−27.7011	−1.14334	−0.571672	−	0.820482i	$-0.693705\pi$
$587$	−27.7011	−1.14334	−0.571672	+	0.820482i	$0.693705\pi$
$588$	−4.08156	−0.168321
$589$	58.7162	2.41936
$590$	3.14714	0.129566
$591$	20.4775	0.842331
$592$	0	0
$593$	−43.2875	−1.77760	−0.888802	−	0.458292i	$-0.848461\pi$
$593$	−43.2875	−1.77760	−0.888802	+	0.458292i	$0.848461\pi$
$594$	−2.45761	−0.100837
$595$	−11.4039	−0.467512
$596$	−3.98826	−0.163366
$597$	−2.52837	−0.103479
$598$	−12.0898	−0.494389
$599$	2.31595	0.0946272	0.0473136	−	0.998880i	$-0.484934\pi$
$599$	2.31595	0.0946272	0.0473136	+	0.998880i	$0.484934\pi$
$600$	−3.36910	−0.137543
$601$	13.3696	0.545358	0.272679	−	0.962105i	$-0.412090\pi$
$601$	13.3696	0.545358	0.272679	+	0.962105i	$0.412090\pi$
$602$	7.48532	0.305079
$603$	2.32110	0.0945224
$604$	−19.6497	−0.799535
$605$	−16.5549	−0.673052
$606$	−16.8003	−0.682465
$607$	35.7749	1.45206	0.726028	−	0.687665i	$-0.241364\pi$
$607$	35.7749	1.45206	0.726028	+	0.687665i	$0.241364\pi$
$608$	5.94585	0.241136
$609$	6.75726	0.273818
$610$	−16.7542	−0.678359
$611$	−16.2710	−0.658253
$612$	5.30537	0.214457
$613$	5.03777	0.203474	0.101737	−	0.994811i	$-0.467560\pi$
$613$	5.03777	0.203474	0.101737	+	0.994811i	$0.467560\pi$
$614$	15.1615	0.611868
$615$	20.2392	0.816123
$616$	0.858292	0.0345816
$617$	29.7870	1.19918	0.599590	−	0.800307i	$-0.295330\pi$
$617$	29.7870	1.19918	0.599590	+	0.800307i	$0.295330\pi$
$618$	−4.00069	−0.160931
$619$	11.6421	0.467935	0.233968	−	0.972244i	$-0.424829\pi$
$619$	11.6421	0.467935	0.233968	+	0.972244i	$0.424829\pi$
$620$	15.1296	0.607620
$621$	−31.8208	−1.27692
$622$	15.2086	0.609810
$623$	−23.0975	−0.925381
$624$	−2.68857	−0.107629
$625$	−4.69965	−0.187986
$626$	29.1716	1.16593
$627$	3.33093	0.133024
$628$	9.13115	0.364372
$629$	0	0
$630$	−4.13476	−0.164733
$631$	32.8294	1.30692	0.653458	−	0.756962i	$-0.273317\pi$
$631$	32.8294	1.30692	0.653458	+	0.756962i	$0.273317\pi$
$632$	13.3443	0.530807
$633$	−16.0093	−0.636312
$634$	−19.1896	−0.762115
$635$	7.51211	0.298109
$636$	2.19713	0.0871218
$637$	6.80293	0.269542
$638$	1.20604	0.0477476
$639$	13.9494	0.551828
$640$	1.53209	0.0605611
$641$	−10.1192	−0.399686	−0.199843	−	0.979828i	$-0.564043\pi$
$641$	−10.1192	−0.399686	−0.199843	+	0.979828i	$0.564043\pi$
$642$	−4.70769	−0.185798
$643$	19.8822	0.784077	0.392038	−	0.919949i	$-0.371770\pi$
$643$	19.8822	0.784077	0.392038	+	0.919949i	$0.371770\pi$
$644$	11.1130	0.437915
$645$	7.48532	0.294734
$646$	−22.7443	−0.894862
$647$	−8.91854	−0.350624	−0.175312	−	0.984513i	$-0.556093\pi$
$647$	−8.91854	−0.350624	−0.175312	+	0.984513i	$0.556093\pi$
$648$	−2.91559	−0.114535
$649$	0.906062	0.0355660
$650$	5.61544	0.220256
$651$	24.4050	0.956508
$652$	−1.87516	−0.0734370
$653$	37.9322	1.48440	0.742200	−	0.670178i	$-0.233782\pi$
$653$	37.9322	1.48440	0.742200	+	0.670178i	$0.233782\pi$
$654$	19.0112	0.743397
$655$	0.473310	0.0184938
$656$	10.4012	0.406099
$657$	13.7109	0.534911
$658$	14.9564	0.583062
$659$	6.56238	0.255634	0.127817	−	0.991798i	$-0.459203\pi$
$659$	6.56238	0.255634	0.127817	+	0.991798i	$0.459203\pi$
$660$	0.858292	0.0334090
$661$	16.8191	0.654186	0.327093	−	0.944992i	$-0.393931\pi$
$661$	16.8191	0.654186	0.327093	+	0.944992i	$0.393931\pi$
$662$	−7.83308	−0.304441
$663$	10.2844	0.399413
$664$	3.55891	0.138113
$665$	17.7259	0.687379
$666$	0	0
$667$	15.6156	0.604640
$668$	4.60701	0.178251
$669$	25.9028	1.00146
$670$	−2.56401	−0.0990564
$671$	−4.82354	−0.186211
$672$	2.47135	0.0953345
$673$	−8.17813	−0.315244	−0.157622	−	0.987500i	$-0.550383\pi$
$673$	−8.17813	−0.315244	−0.157622	+	0.987500i	$0.550383\pi$
$674$	19.6648	0.757461
$675$	14.7800	0.568884
$676$	−8.51884	−0.327648
$677$	26.4434	1.01630	0.508152	−	0.861268i	$-0.330329\pi$
$677$	26.4434	1.01630	0.508152	+	0.861268i	$0.330329\pi$
$678$	−25.3083	−0.971959
$679$	−1.15486	−0.0443193
$680$	−5.86060	−0.224744
$681$	−9.61773	−0.368552
$682$	4.35582	0.166793
$683$	12.4254	0.475447	0.237723	−	0.971333i	$-0.423599\pi$
$683$	12.4254	0.475447	0.237723	+	0.971333i	$0.423599\pi$
$684$	−8.24653	−0.315314
$685$	−31.1040	−1.18842
$686$	−19.8743	−0.758803
$687$	−0.397404	−0.0151619
$688$	3.84681	0.146658
$689$	−3.66206	−0.139513
$690$	11.1130	0.423066
$691$	−27.4790	−1.04535	−0.522675	−	0.852532i	$-0.675066\pi$
$691$	−27.4790	−1.04535	−0.522675	+	0.852532i	$0.675066\pi$
$692$	−15.0979	−0.573935
$693$	−1.19040	−0.0452195
$694$	21.5643	0.818571
$695$	−20.1284	−0.763514
$696$	3.47265	0.131631
$697$	−39.7871	−1.50704
$698$	−26.8757	−1.01726
$699$	−0.867665	−0.0328181
$700$	−5.16176	−0.195096
$701$	−19.5879	−0.739826	−0.369913	−	0.929066i	$-0.620612\pi$
$701$	−19.5879	−0.739826	−0.369913	+	0.929066i	$0.620612\pi$
$702$	11.7946	0.445157
$703$	0	0
$704$	0.441088	0.0166241
$705$	14.9564	0.563292
$706$	−13.1785	−0.495978
$707$	−25.7395	−0.968035
$708$	2.60890	0.0980485
$709$	18.8660	0.708528	0.354264	−	0.935145i	$-0.384731\pi$
$709$	18.8660	0.708528	0.354264	+	0.935145i	$0.384731\pi$
$710$	−15.4092	−0.578299
$711$	−18.5077	−0.694092
$712$	−11.8701	−0.444852
$713$	56.3986	2.11214
$714$	−9.45351	−0.353789
$715$	−1.43056	−0.0534998
$716$	20.1143	0.751708
$717$	14.2328	0.531535
$718$	3.38568	0.126353
$719$	16.2325	0.605372	0.302686	−	0.953090i	$-0.402117\pi$
$719$	16.2325	0.605372	0.302686	+	0.953090i	$0.402117\pi$
$720$	−2.12491	−0.0791908
$721$	−6.12942	−0.228271
$722$	16.3531	0.608601
$723$	−6.57968	−0.244701
$724$	9.31549	0.346207
$725$	−7.25312	−0.269374
$726$	−13.7236	−0.509330
$727$	−16.9653	−0.629209	−0.314604	−	0.949223i	$-0.601872\pi$
$727$	−16.9653	−0.629209	−0.314604	+	0.949223i	$0.601872\pi$
$728$	−4.11912	−0.152665
$729$	25.2729	0.936035
$730$	−15.1458	−0.560570
$731$	−14.7150	−0.544252
$732$	−13.8888	−0.513346
$733$	−33.7408	−1.24625	−0.623123	−	0.782124i	$-0.714136\pi$
$733$	−33.7408	−1.24625	−0.623123	+	0.782124i	$0.714136\pi$
$734$	6.59687	0.243495
$735$	−6.25331	−0.230657
$736$	5.71115	0.210516
$737$	−0.738179	−0.0271912
$738$	−14.4258	−0.531023
$739$	15.5694	0.572730	0.286365	−	0.958121i	$-0.407553\pi$
$739$	15.5694	0.572730	0.286365	+	0.958121i	$0.407553\pi$
$740$	0	0
$741$	−15.9858	−0.587253
$742$	3.36620	0.123577
$743$	−47.7823	−1.75296	−0.876480	−	0.481437i	$-0.840115\pi$
$743$	−47.7823	−1.75296	−0.876480	+	0.481437i	$0.840115\pi$
$744$	12.5421	0.459815
$745$	−6.11037	−0.223867
$746$	1.05692	0.0386967
$747$	−4.93599	−0.180599
$748$	−1.68727	−0.0616926
$749$	−7.21260	−0.263543
$750$	−14.8910	−0.543743
$751$	−27.2978	−0.996111	−0.498055	−	0.867145i	$-0.665952\pi$
$751$	−27.2978	−0.996111	−0.498055	+	0.867145i	$0.665952\pi$
$752$	7.68632	0.280291
$753$	−38.7269	−1.41129
$754$	−5.78803	−0.210788
$755$	−30.1051	−1.09564
$756$	−10.8417	−0.394308
$757$	−47.4356	−1.72408	−0.862038	−	0.506844i	$-0.830812\pi$
$757$	−47.4356	−1.72408	−0.862038	+	0.506844i	$0.830812\pi$
$758$	22.2144	0.806862
$759$	3.19945	0.116133
$760$	9.10957	0.330439
$761$	9.38178	0.340089	0.170045	−	0.985436i	$-0.445609\pi$
$761$	9.38178	0.340089	0.170045	+	0.985436i	$0.445609\pi$
$762$	6.22735	0.225593
$763$	29.1268	1.05446
$764$	−10.6491	−0.385271
$765$	8.12829	0.293879
$766$	9.34717	0.337727
$767$	−4.34838	−0.157011
$768$	1.27006	0.0458295
$769$	2.29724	0.0828405	0.0414203	−	0.999142i	$-0.486812\pi$
$769$	2.29724	0.0828405	0.0414203	+	0.999142i	$0.486812\pi$
$770$	1.31498	0.0473886
$771$	7.45229	0.268388
$772$	12.2527	0.440985
$773$	−21.0429	−0.756859	−0.378430	−	0.925630i	$-0.623536\pi$
$773$	−21.0429	−0.756859	−0.378430	+	0.925630i	$0.623536\pi$
$774$	−5.33529	−0.191773
$775$	−26.1959	−0.940984
$776$	−0.593497	−0.0213053
$777$	0	0
$778$	2.41968	0.0867497
$779$	61.8440	2.21579
$780$	−4.11912	−0.147488
$781$	−4.43632	−0.158744
$782$	−21.8465	−0.781229
$783$	−15.2343	−0.544430
$784$	−3.21367	−0.114774
$785$	13.9897	0.499315
$786$	0.392362	0.0139951
$787$	−19.8930	−0.709109	−0.354555	−	0.935035i	$-0.615367\pi$
$787$	−19.8930	−0.709109	−0.354555	+	0.935035i	$0.615367\pi$
$788$	16.1232	0.574365
$789$	20.7178	0.737574
$790$	20.4446	0.727386
$791$	−38.7745	−1.37866
$792$	−0.611763	−0.0217380
$793$	23.1492	0.822052
$794$	19.7041	0.699272
$795$	3.36620	0.119387
$796$	−1.99074	−0.0705599
$797$	−22.8226	−0.808419	−0.404209	−	0.914666i	$-0.632453\pi$
$797$	−22.8226	−0.808419	−0.404209	+	0.914666i	$0.632453\pi$
$798$	14.6943	0.520172
$799$	−29.4020	−1.04017
$800$	−2.65270	−0.0937872
$801$	16.4631	0.581696
$802$	−29.2178	−1.03172
$803$	−4.36047	−0.153877
$804$	−2.12550	−0.0749607
$805$	17.0262	0.600094
$806$	−20.9045	−0.736329
$807$	−12.7083	−0.447354
$808$	−13.2279	−0.465356
$809$	8.51846	0.299493	0.149746	−	0.988724i	$-0.452154\pi$
$809$	8.51846	0.299493	0.149746	+	0.988724i	$0.452154\pi$
$810$	−4.46694	−0.156952
$811$	54.8736	1.92687	0.963436	−	0.267939i	$-0.0863426\pi$
$811$	54.8736	1.92687	0.963436	+	0.267939i	$0.0863426\pi$
$812$	5.32041	0.186710
$813$	−15.7067	−0.550858
$814$	0	0
$815$	−2.87292	−0.100634
$816$	−4.85829	−0.170074
$817$	22.8726	0.800210
$818$	−3.77390	−0.131951
$819$	5.71297	0.199627
$820$	15.9356	0.556495
$821$	−24.9235	−0.869838	−0.434919	−	0.900470i	$-0.643223\pi$
$821$	−24.9235	−0.869838	−0.434919	+	0.900470i	$0.643223\pi$
$822$	−25.7844	−0.899335
$823$	34.7551	1.21149	0.605744	−	0.795660i	$-0.292876\pi$
$823$	34.7551	1.21149	0.605744	+	0.795660i	$0.292876\pi$
$824$	−3.14999	−0.109735
$825$	−1.48607	−0.0517384
$826$	3.99707	0.139076
$827$	11.9761	0.416449	0.208225	−	0.978081i	$-0.433232\pi$
$827$	11.9761	0.416449	0.208225	+	0.978081i	$0.433232\pi$
$828$	−7.92102	−0.275274
$829$	−7.17450	−0.249181	−0.124590	−	0.992208i	$-0.539762\pi$
$829$	−7.17450	−0.249181	−0.124590	+	0.992208i	$0.539762\pi$
$830$	5.45257	0.189261
$831$	−26.9841	−0.936068
$832$	−2.11688	−0.0733894
$833$	12.2930	0.425928
$834$	−16.6859	−0.577787
$835$	7.05835	0.244264
$836$	2.62265	0.0907061
$837$	−55.0214	−1.90182
$838$	−36.2507	−1.25226
$839$	21.6860	0.748683	0.374342	−	0.927291i	$-0.377869\pi$
$839$	21.6860	0.748683	0.374342	+	0.927291i	$0.377869\pi$
$840$	3.78633	0.130641
$841$	−21.5240	−0.742205
$842$	16.1783	0.557540
$843$	20.5733	0.708581
$844$	−12.6051	−0.433885
$845$	−13.0516	−0.448989
$846$	−10.6605	−0.366514
$847$	−21.0258	−0.722454
$848$	1.72994	0.0594063
$849$	−6.33538	−0.217430
$850$	10.1472	0.348047
$851$	0	0
$852$	−12.7739	−0.437626
$853$	−35.8472	−1.22738	−0.613692	−	0.789545i	$-0.710316\pi$
$853$	−35.8472	−1.22738	−0.613692	+	0.789545i	$0.710316\pi$
$854$	−21.2789	−0.728150
$855$	−12.6344	−0.432088
$856$	−3.70666	−0.126691
$857$	−16.3281	−0.557757	−0.278879	−	0.960326i	$-0.589963\pi$
$857$	−16.3281	−0.557757	−0.278879	+	0.960326i	$0.589963\pi$
$858$	−1.18590	−0.0404858
$859$	13.9567	0.476197	0.238099	−	0.971241i	$-0.423476\pi$
$859$	13.9567	0.476197	0.238099	+	0.971241i	$0.423476\pi$
$860$	5.89366	0.200972
$861$	25.7051	0.876026
$862$	20.7296	0.706054
$863$	−49.1039	−1.67152	−0.835759	−	0.549097i	$-0.814972\pi$
$863$	−49.1039	−1.67152	−0.835759	+	0.549097i	$0.814972\pi$
$864$	−5.57169	−0.189553
$865$	−23.1313	−0.786487
$866$	26.7853	0.910203
$867$	−3.00697	−0.102122
$868$	19.2156	0.652220
$869$	5.88600	0.199669
$870$	5.32041	0.180379
$871$	3.54267	0.120039
$872$	14.9687	0.506904
$873$	0.823143	0.0278592
$874$	33.9577	1.14863
$875$	−22.8144	−0.771266
$876$	−12.5555	−0.424210
$877$	34.0005	1.14811	0.574057	−	0.818815i	$-0.305369\pi$
$877$	34.0005	1.14811	0.574057	+	0.818815i	$0.305369\pi$
$878$	−8.39586	−0.283346
$879$	7.04784	0.237718
$880$	0.675787	0.0227808
$881$	53.1557	1.79086	0.895430	−	0.445202i	$-0.146868\pi$
$881$	53.1557	1.79086	0.895430	+	0.445202i	$0.146868\pi$
$882$	4.45716	0.150080
$883$	15.4892	0.521254	0.260627	−	0.965440i	$-0.416071\pi$
$883$	15.4892	0.521254	0.260627	+	0.965440i	$0.416071\pi$
$884$	8.09755	0.272350
$885$	3.99707	0.134360
$886$	−19.6599	−0.660486
$887$	17.6841	0.593774	0.296887	−	0.954913i	$-0.404052\pi$
$887$	17.6841	0.593774	0.296887	+	0.954913i	$0.404052\pi$
$888$	0	0
$889$	9.54086	0.319990
$890$	−18.1861	−0.609599
$891$	−1.28603	−0.0430837
$892$	20.3949	0.682873
$893$	45.7017	1.52935
$894$	−5.06535	−0.169411
$895$	30.8170	1.03010
$896$	1.94585	0.0650063
$897$	−15.3548	−0.512682
$898$	−27.1724	−0.906753
$899$	27.0010	0.900534
$900$	3.67914	0.122638
$901$	−6.61741	−0.220458
$902$	4.58785	0.152759
$903$	9.50683	0.316368
$904$	−19.9268	−0.662755
$905$	14.2722	0.474423
$906$	−24.9564	−0.829120
$907$	−36.4777	−1.21122	−0.605611	−	0.795761i	$-0.707071\pi$
$907$	−36.4777	−1.21122	−0.605611	+	0.795761i	$0.707071\pi$
$908$	−7.57264	−0.251307
$909$	18.3463	0.608508
$910$	−6.31086	−0.209203
$911$	−7.68257	−0.254535	−0.127267	−	0.991868i	$-0.540621\pi$
$911$	−7.68257	−0.254535	−0.127267	+	0.991868i	$0.540621\pi$
$912$	7.55161	0.250059
$913$	1.56979	0.0519526
$914$	−19.9670	−0.660451
$915$	−21.2789	−0.703460
$916$	−0.312901	−0.0103385
$917$	0.601134	0.0198512
$918$	21.3130	0.703435
$919$	−0.166200	−0.00548242	−0.00274121	−	0.999996i	$-0.500873\pi$
$919$	−0.166200	−0.00548242	−0.00274121	+	0.999996i	$0.500873\pi$
$920$	8.74999	0.288479
$921$	19.2560	0.634508
$922$	7.86373	0.258978
$923$	21.2908	0.700796
$924$	1.09009	0.0358612
$925$	0	0
$926$	−6.04210	−0.198556
$927$	4.36885	0.143492
$928$	2.73423	0.0897557
$929$	35.3852	1.16095	0.580475	−	0.814278i	$-0.302867\pi$
$929$	35.3852	1.16095	0.580475	+	0.814278i	$0.302867\pi$
$930$	19.2156	0.630104
$931$	−19.1080	−0.626239
$932$	−0.683167	−0.0223779
$933$	19.3159	0.632374
$934$	29.3245	0.959528
$935$	−2.58504	−0.0845400
$936$	2.93598	0.0959654
$937$	15.4386	0.504358	0.252179	−	0.967681i	$-0.418853\pi$
$937$	15.4386	0.504358	0.252179	+	0.967681i	$0.418853\pi$
$938$	−3.25646	−0.106327
$939$	37.0498	1.20907
$940$	11.7761	0.384095
$941$	−23.3868	−0.762387	−0.381194	−	0.924495i	$-0.624487\pi$
$941$	−23.3868	−0.762387	−0.381194	+	0.924495i	$0.624487\pi$
$942$	11.5971	0.377855
$943$	59.4029	1.93442
$944$	2.05415	0.0668569
$945$	−16.6104	−0.540337
$946$	1.69678	0.0551672
$947$	−26.7656	−0.869764	−0.434882	−	0.900487i	$-0.643210\pi$
$947$	−26.7656	−0.869764	−0.434882	+	0.900487i	$0.643210\pi$
$948$	16.9481	0.550448
$949$	20.9268	0.679312
$950$	−15.7726	−0.511730
$951$	−24.3720	−0.790315
$952$	−7.44334	−0.241240
$953$	−42.7621	−1.38520	−0.692599	−	0.721322i	$-0.743535\pi$
$953$	−42.7621	−1.38520	−0.692599	+	0.721322i	$0.743535\pi$
$954$	−2.39932	−0.0776807
$955$	−16.3154	−0.527952
$956$	11.2064	0.362441
$957$	1.53175	0.0495143
$958$	−4.13663	−0.133648
$959$	−39.5040	−1.27565
$960$	1.94585	0.0628020
$961$	66.5188	2.14577
$962$	0	0
$963$	5.14091	0.165663
$964$	−5.18059	−0.166856
$965$	18.7723	0.604301
$966$	14.1143	0.454119
$967$	−3.49180	−0.112289	−0.0561443	−	0.998423i	$-0.517881\pi$
$967$	−3.49180	−0.112289	−0.0561443	+	0.998423i	$0.517881\pi$
$968$	−10.8054	−0.347300
$969$	−28.8867	−0.927974
$970$	−0.909289	−0.0291955
$971$	6.21530	0.199458	0.0997292	−	0.995015i	$-0.468202\pi$
$971$	6.21530	0.199458	0.0997292	+	0.995015i	$0.468202\pi$
$972$	13.0121	0.417363
$973$	−25.5643	−0.819555
$974$	28.9347	0.927129
$975$	7.13197	0.228406
$976$	−10.9355	−0.350038
$977$	−0.135446	−0.00433331	−0.00216665	−	0.999998i	$-0.500690\pi$
$977$	−0.135446	−0.00433331	−0.00216665	+	0.999998i	$0.500690\pi$
$978$	−2.38158	−0.0761544
$979$	−5.23577	−0.167336
$980$	−4.92362	−0.157279
$981$	−20.7607	−0.662837
$982$	19.5423	0.623621
$983$	−2.05164	−0.0654372	−0.0327186	−	0.999465i	$-0.510417\pi$
$983$	−2.05164	−0.0654372	−0.0327186	+	0.999465i	$0.510417\pi$
$984$	13.2102	0.421126
$985$	24.7022	0.787076
$986$	−10.4591	−0.333085
$987$	18.9956	0.604637
$988$	−12.5866	−0.400434
$989$	21.9697	0.698597
$990$	−0.937275	−0.0297885
$991$	17.3981	0.552669	0.276335	−	0.961061i	$-0.410880\pi$
$991$	17.3981	0.552669	0.276335	+	0.961061i	$0.410880\pi$
$992$	9.87516	0.313537
$993$	−9.94851	−0.315707
$994$	−19.5707	−0.620745
$995$	−3.04999	−0.0966912
$996$	4.52004	0.143223
$997$	7.10509	0.225020	0.112510	−	0.993651i	$-0.464111\pi$
$997$	7.10509	0.225020	0.112510	+	0.993651i	$0.464111\pi$
$998$	−42.2259	−1.33664
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.t.1.4		6
37.7	even	9		74.2.f.b.49.2	✓	12
37.16	even	9		74.2.f.b.71.2	yes	12
37.36	even	2		2738.2.a.q.1.4		6
111.44	odd	18		666.2.x.g.271.1		12
111.53	odd	18		666.2.x.g.145.1		12
148.7	odd	18		592.2.bc.d.49.1		12
148.127	odd	18		592.2.bc.d.145.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.49.2	✓	12	37.7	even	9
74.2.f.b.71.2	yes	12	37.16	even	9
592.2.bc.d.49.1		12	148.7	odd	18
592.2.bc.d.145.1		12	148.127	odd	18
666.2.x.g.145.1		12	111.53	odd	18
666.2.x.g.271.1		12	111.44	odd	18
2738.2.a.q.1.4		6	37.36	even	2
2738.2.a.t.1.4		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.27006 q^{3} +1.00000 q^{4} +1.53209 q^{5} +1.27006 q^{6} +1.94585 q^{7} +1.00000 q^{8} -1.38694 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.27006 q^{3} +1.00000 q^{4} +1.53209 q^{5} +1.27006 q^{6} +1.94585 q^{7} +1.00000 q^{8} -1.38694 q^{9} +1.53209 q^{10} +0.441088 q^{11} +1.27006 q^{12} -2.11688 q^{13} +1.94585 q^{14} +1.94585 q^{15} +1.00000 q^{16} -3.82524 q^{17} -1.38694 q^{18} +5.94585 q^{19} +1.53209 q^{20} +2.47135 q^{21} +0.441088 q^{22} +5.71115 q^{23} +1.27006 q^{24} -2.65270 q^{25} -2.11688 q^{26} -5.57169 q^{27} +1.94585 q^{28} +2.73423 q^{29} +1.94585 q^{30} +9.87516 q^{31} +1.00000 q^{32} +0.560210 q^{33} -3.82524 q^{34} +2.98122 q^{35} -1.38694 q^{36} +5.94585 q^{38} -2.68857 q^{39} +1.53209 q^{40} +10.4012 q^{41} +2.47135 q^{42} +3.84681 q^{43} +0.441088 q^{44} -2.12491 q^{45} +5.71115 q^{46} +7.68632 q^{47} +1.27006 q^{48} -3.21367 q^{49} -2.65270 q^{50} -4.85829 q^{51} -2.11688 q^{52} +1.72994 q^{53} -5.57169 q^{54} +0.675787 q^{55} +1.94585 q^{56} +7.55161 q^{57} +2.73423 q^{58} +2.05415 q^{59} +1.94585 q^{60} -10.9355 q^{61} +9.87516 q^{62} -2.69877 q^{63} +1.00000 q^{64} -3.24324 q^{65} +0.560210 q^{66} -1.67354 q^{67} -3.82524 q^{68} +7.25353 q^{69} +2.98122 q^{70} -10.0577 q^{71} -1.38694 q^{72} -9.88570 q^{73} -3.36910 q^{75} +5.94585 q^{76} +0.858292 q^{77} -2.68857 q^{78} +13.3443 q^{79} +1.53209 q^{80} -2.91559 q^{81} +10.4012 q^{82} +3.55891 q^{83} +2.47135 q^{84} -5.86060 q^{85} +3.84681 q^{86} +3.47265 q^{87} +0.441088 q^{88} -11.8701 q^{89} -2.12491 q^{90} -4.11912 q^{91} +5.71115 q^{92} +12.5421 q^{93} +7.68632 q^{94} +9.10957 q^{95} +1.27006 q^{96} -0.593497 q^{97} -3.21367 q^{98} -0.611763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 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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