LMFDB - Embedded newform 2738.2.a.s.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:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{36})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} + 9x^{2} - 3 $ x^6 - 6x^4 + 9x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
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			$1.28558$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} -0.800038 q^{5} -1.87939 q^{6} +0.147334 q^{7} +1.00000 q^{8} +0.532089 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} -0.800038 q^{5} -1.87939 q^{6} +0.147334 q^{7} +1.00000 q^{8} +0.532089 q^{9} -0.800038 q^{10} -4.81140 q^{11} -1.87939 q^{12} +1.94818 q^{13} +0.147334 q^{14} +1.50358 q^{15} +1.00000 q^{16} +3.49082 q^{17} +0.532089 q^{18} +6.74601 q^{19} -0.800038 q^{20} -0.276898 q^{21} -4.81140 q^{22} +4.17551 q^{23} -1.87939 q^{24} -4.35994 q^{25} +1.94818 q^{26} +4.63816 q^{27} +0.147334 q^{28} -3.03841 q^{29} +1.50358 q^{30} -8.13740 q^{31} +1.00000 q^{32} +9.04247 q^{33} +3.49082 q^{34} -0.117873 q^{35} +0.532089 q^{36} +6.74601 q^{38} -3.66138 q^{39} -0.800038 q^{40} -3.89766 q^{41} -0.276898 q^{42} -8.10852 q^{43} -4.81140 q^{44} -0.425691 q^{45} +4.17551 q^{46} +8.33822 q^{47} -1.87939 q^{48} -6.97829 q^{49} -4.35994 q^{50} -6.56060 q^{51} +1.94818 q^{52} -10.8894 q^{53} +4.63816 q^{54} +3.84930 q^{55} +0.147334 q^{56} -12.6784 q^{57} -3.03841 q^{58} -8.67110 q^{59} +1.50358 q^{60} +0.351687 q^{61} -8.13740 q^{62} +0.0783950 q^{63} +1.00000 q^{64} -1.55862 q^{65} +9.04247 q^{66} -2.39941 q^{67} +3.49082 q^{68} -7.84740 q^{69} -0.117873 q^{70} +6.98332 q^{71} +0.532089 q^{72} -1.13399 q^{73} +8.19401 q^{75} +6.74601 q^{76} -0.708885 q^{77} -3.66138 q^{78} -1.89027 q^{79} -0.800038 q^{80} -10.3131 q^{81} -3.89766 q^{82} -9.90490 q^{83} -0.276898 q^{84} -2.79279 q^{85} -8.10852 q^{86} +5.71034 q^{87} -4.81140 q^{88} +10.1141 q^{89} -0.425691 q^{90} +0.287034 q^{91} +4.17551 q^{92} +15.2933 q^{93} +8.33822 q^{94} -5.39707 q^{95} -1.87939 q^{96} -5.87526 q^{97} -6.97829 q^{98} -2.56009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} - 12 q^{13} + 6 q^{15} + 6 q^{16} - 12 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 6 q^{22} + 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{29} + 6 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 12 q^{34} - 24 q^{35} - 6 q^{36} - 12 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} - 12 q^{42} - 6 q^{44} - 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} + 6 q^{50} - 24 q^{51} - 12 q^{52} - 24 q^{53} - 6 q^{54} - 36 q^{55} - 24 q^{57} + 6 q^{58} - 12 q^{59} + 6 q^{60} - 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} + 6 q^{66} + 18 q^{67} - 12 q^{68} - 24 q^{69} - 24 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{75} - 12 q^{76} + 30 q^{77} - 6 q^{78} - 12 q^{79} - 6 q^{80} - 18 q^{81} - 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} - 6 q^{87} - 6 q^{88} - 6 q^{90} - 12 q^{91} + 6 q^{92} + 36 q^{93} - 6 q^{94} + 18 q^{95} + 12 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 - 12 * q^13 + 6 * q^15 + 6 * q^16 - 12 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 6 * q^22 + 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^29 + 6 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 12 * q^34 - 24 * q^35 - 6 * q^36 - 12 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 - 12 * q^42 - 6 * q^44 - 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 + 6 * q^50 - 24 * q^51 - 12 * q^52 - 24 * q^53 - 6 * q^54 - 36 * q^55 - 24 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 + 6 * q^66 + 18 * q^67 - 12 * q^68 - 24 * q^69 - 24 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^75 - 12 * q^76 + 30 * q^77 - 6 * q^78 - 12 * q^79 - 6 * q^80 - 18 * q^81 - 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 - 6 * q^87 - 6 * q^88 - 6 * q^90 - 12 * q^91 + 6 * q^92 + 36 * q^93 - 6 * q^94 + 18 * q^95 + 12 * q^97 - 12 * q^98 + 12 * 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
$3$	−1.87939	−1.08506	−0.542532	−	0.840035i	$-0.682534\pi$
$3$	−1.87939	−1.08506	−0.542532	+	0.840035i	$0.682534\pi$
$4$	1.00000	0.500000
$5$	−0.800038	−0.357788	−0.178894	−	0.983868i	$-0.557252\pi$
$5$	−0.800038	−0.357788	−0.178894	+	0.983868i	$0.557252\pi$
$6$	−1.87939	−0.767256
$7$	0.147334	0.0556872	0.0278436	−	0.999612i	$-0.491136\pi$
$7$	0.147334	0.0556872	0.0278436	+	0.999612i	$0.491136\pi$
$8$	1.00000	0.353553
$9$	0.532089	0.177363
$10$	−0.800038	−0.252994
$11$	−4.81140	−1.45069	−0.725346	−	0.688385i	$-0.758320\pi$
$11$	−4.81140	−1.45069	−0.725346	+	0.688385i	$0.758320\pi$
$12$	−1.87939	−0.542532
$13$	1.94818	0.540328	0.270164	−	0.962814i	$-0.412922\pi$
$13$	1.94818	0.540328	0.270164	+	0.962814i	$0.412922\pi$
$14$	0.147334	0.0393768
$15$	1.50358	0.388223
$16$	1.00000	0.250000
$17$	3.49082	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$17$	3.49082	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$18$	0.532089	0.125415
$19$	6.74601	1.54764	0.773821	−	0.633405i	$-0.218343\pi$
$19$	6.74601	1.54764	0.773821	+	0.633405i	$0.218343\pi$
$20$	−0.800038	−0.178894
$21$	−0.276898	−0.0604241
$22$	−4.81140	−1.02579
$23$	4.17551	0.870655	0.435327	−	0.900272i	$-0.356633\pi$
$23$	4.17551	0.870655	0.435327	+	0.900272i	$0.356633\pi$
$24$	−1.87939	−0.383628
$25$	−4.35994	−0.871988
$26$	1.94818	0.382070
$27$	4.63816	0.892613
$28$	0.147334	0.0278436
$29$	−3.03841	−0.564219	−0.282109	−	0.959382i	$-0.591034\pi$
$29$	−3.03841	−0.564219	−0.282109	+	0.959382i	$0.591034\pi$
$30$	1.50358	0.274515
$31$	−8.13740	−1.46152	−0.730760	−	0.682634i	$-0.760834\pi$
$31$	−8.13740	−1.46152	−0.730760	+	0.682634i	$0.760834\pi$
$32$	1.00000	0.176777
$33$	9.04247	1.57409
$34$	3.49082	0.598671
$35$	−0.117873	−0.0199242
$36$	0.532089	0.0886815
$37$	0	0
$37$	0	0
$38$	6.74601	1.09435
$39$	−3.66138	−0.586290
$40$	−0.800038	−0.126497
$41$	−3.89766	−0.608713	−0.304356	−	0.952558i	$-0.598441\pi$
$41$	−3.89766	−0.608713	−0.304356	+	0.952558i	$0.598441\pi$
$42$	−0.276898	−0.0427263
$43$	−8.10852	−1.23654	−0.618269	−	0.785966i	$-0.712166\pi$
$43$	−8.10852	−1.23654	−0.618269	+	0.785966i	$0.712166\pi$
$44$	−4.81140	−0.725346
$45$	−0.425691	−0.0634583
$46$	4.17551	0.615646
$47$	8.33822	1.21625	0.608127	−	0.793840i	$-0.291921\pi$
$47$	8.33822	1.21625	0.608127	+	0.793840i	$0.291921\pi$
$48$	−1.87939	−0.271266
$49$	−6.97829	−0.996899
$50$	−4.35994	−0.616588
$51$	−6.56060	−0.918667
$52$	1.94818	0.270164
$53$	−10.8894	−1.49578	−0.747889	−	0.663824i	$-0.768932\pi$
$53$	−10.8894	−1.49578	−0.747889	+	0.663824i	$0.768932\pi$
$54$	4.63816	0.631173
$55$	3.84930	0.519040
$56$	0.147334	0.0196884
$57$	−12.6784	−1.67929
$58$	−3.03841	−0.398963
$59$	−8.67110	−1.12888	−0.564440	−	0.825474i	$-0.690908\pi$
$59$	−8.67110	−1.12888	−0.564440	+	0.825474i	$0.690908\pi$
$60$	1.50358	0.194111
$61$	0.351687	0.0450289	0.0225145	−	0.999747i	$-0.492833\pi$
$61$	0.351687	0.0450289	0.0225145	+	0.999747i	$0.492833\pi$
$62$	−8.13740	−1.03345
$63$	0.0783950	0.00987684
$64$	1.00000	0.125000
$65$	−1.55862	−0.193323
$66$	9.04247	1.11305
$67$	−2.39941	−0.293135	−0.146567	−	0.989201i	$-0.546823\pi$
$67$	−2.39941	−0.293135	−0.146567	+	0.989201i	$0.546823\pi$
$68$	3.49082	0.423324
$69$	−7.84740	−0.944716
$70$	−0.117873	−0.0140885
$71$	6.98332	0.828767	0.414384	−	0.910102i	$-0.363997\pi$
$71$	6.98332	0.828767	0.414384	+	0.910102i	$0.363997\pi$
$72$	0.532089	0.0627073
$73$	−1.13399	−0.132724	−0.0663618	−	0.997796i	$-0.521139\pi$
$73$	−1.13399	−0.132724	−0.0663618	+	0.997796i	$0.521139\pi$
$74$	0	0
$75$	8.19401	0.946162
$76$	6.74601	0.773821
$77$	−0.708885	−0.0807849
$78$	−3.66138	−0.414570
$79$	−1.89027	−0.212672	−0.106336	−	0.994330i	$-0.533912\pi$
$79$	−1.89027	−0.212672	−0.106336	+	0.994330i	$0.533912\pi$
$80$	−0.800038	−0.0894470
$81$	−10.3131	−1.14591
$82$	−3.89766	−0.430425
$83$	−9.90490	−1.08720	−0.543602	−	0.839343i	$-0.682940\pi$
$83$	−9.90490	−1.08720	−0.543602	+	0.839343i	$0.682940\pi$
$84$	−0.276898	−0.0302121
$85$	−2.79279	−0.302921
$86$	−8.10852	−0.874365
$87$	5.71034	0.612213
$88$	−4.81140	−0.512897
$89$	10.1141	1.07210	0.536048	−	0.844187i	$-0.319917\pi$
$89$	10.1141	1.07210	0.536048	+	0.844187i	$0.319917\pi$
$90$	−0.425691	−0.0448718
$91$	0.287034	0.0300893
$92$	4.17551	0.435327
$93$	15.2933	1.58584
$94$	8.33822	0.860022
$95$	−5.39707	−0.553727
$96$	−1.87939	−0.191814
$97$	−5.87526	−0.596542	−0.298271	−	0.954481i	$-0.596410\pi$
$97$	−5.87526	−0.596542	−0.298271	+	0.954481i	$0.596410\pi$
$98$	−6.97829	−0.704914
$99$	−2.56009	−0.257299
$100$	−4.35994	−0.435994
$101$	−17.0173	−1.69329	−0.846643	−	0.532161i	$-0.821380\pi$
$101$	−17.0173	−1.69329	−0.846643	+	0.532161i	$0.821380\pi$
$102$	−6.56060	−0.649596
$103$	−12.7468	−1.25598	−0.627992	−	0.778220i	$-0.716123\pi$
$103$	−12.7468	−1.25598	−0.627992	+	0.778220i	$0.716123\pi$
$104$	1.94818	0.191035
$105$	0.221529	0.0216190
$106$	−10.8894	−1.05767
$107$	14.2387	1.37650	0.688252	−	0.725472i	$-0.258378\pi$
$107$	14.2387	1.37650	0.688252	+	0.725472i	$0.258378\pi$
$108$	4.63816	0.446307
$109$	−19.7885	−1.89540	−0.947699	−	0.319166i	$-0.896597\pi$
$109$	−19.7885	−1.89540	−0.947699	+	0.319166i	$0.896597\pi$
$110$	3.84930	0.367017
$111$	0	0
$112$	0.147334	0.0139218
$113$	−8.50156	−0.799759	−0.399880	−	0.916568i	$-0.630948\pi$
$113$	−8.50156	−0.799759	−0.399880	+	0.916568i	$0.630948\pi$
$114$	−12.6784	−1.18744
$115$	−3.34057	−0.311510
$116$	−3.03841	−0.282109
$117$	1.03660	0.0958342
$118$	−8.67110	−0.798239
$119$	0.514318	0.0471475
$120$	1.50358	0.137257
$121$	12.1496	1.10450
$122$	0.351687	0.0318403
$123$	7.32521	0.660492
$124$	−8.13740	−0.730760
$125$	7.48831	0.669775
$126$	0.0783950	0.00698398
$127$	5.53267	0.490945	0.245473	−	0.969403i	$-0.421057\pi$
$127$	5.53267	0.490945	0.245473	+	0.969403i	$0.421057\pi$
$128$	1.00000	0.0883883
$129$	15.2390	1.34172
$130$	−1.55862	−0.136700
$131$	0.822948	0.0719013	0.0359507	−	0.999354i	$-0.488554\pi$
$131$	0.822948	0.0719013	0.0359507	+	0.999354i	$0.488554\pi$
$132$	9.04247	0.787046
$133$	0.993920	0.0861838
$134$	−2.39941	−0.207278
$135$	−3.71070	−0.319366
$136$	3.49082	0.299335
$137$	6.74232	0.576035	0.288018	−	0.957625i	$-0.407004\pi$
$137$	6.74232	0.576035	0.288018	+	0.957625i	$0.407004\pi$
$138$	−7.84740	−0.668015
$139$	12.0038	1.01815	0.509075	−	0.860722i	$-0.329988\pi$
$139$	12.0038	1.01815	0.509075	+	0.860722i	$0.329988\pi$
$140$	−0.117873	−0.00996210
$141$	−15.6707	−1.31971
$142$	6.98332	0.586027
$143$	−9.37347	−0.783849
$144$	0.532089	0.0443407
$145$	2.43084	0.201871
$146$	−1.13399	−0.0938497
$147$	13.1149	1.08170
$148$	0	0
$149$	−9.21354	−0.754803	−0.377401	−	0.926050i	$-0.623182\pi$
$149$	−9.21354	−0.754803	−0.377401	+	0.926050i	$0.623182\pi$
$150$	8.19401	0.669038
$151$	−11.7843	−0.958992	−0.479496	−	0.877544i	$-0.659181\pi$
$151$	−11.7843	−0.958992	−0.479496	+	0.877544i	$0.659181\pi$
$152$	6.74601	0.547174
$153$	1.85743	0.150164
$154$	−0.708885	−0.0571235
$155$	6.51023	0.522914
$156$	−3.66138	−0.293145
$157$	−17.3717	−1.38642	−0.693208	−	0.720738i	$-0.743803\pi$
$157$	−17.3717	−1.38642	−0.693208	+	0.720738i	$0.743803\pi$
$158$	−1.89027	−0.150382
$159$	20.4654	1.62301
$160$	−0.800038	−0.0632486
$161$	0.615197	0.0484843
$162$	−10.3131	−0.810277
$163$	−2.26115	−0.177107	−0.0885534	−	0.996071i	$-0.528224\pi$
$163$	−2.26115	−0.177107	−0.0885534	+	0.996071i	$0.528224\pi$
$164$	−3.89766	−0.304356
$165$	−7.23432	−0.563191
$166$	−9.90490	−0.768769
$167$	15.9560	1.23471	0.617357	−	0.786683i	$-0.288204\pi$
$167$	15.9560	1.23471	0.617357	+	0.786683i	$0.288204\pi$
$168$	−0.276898	−0.0213632
$169$	−9.20459	−0.708046
$170$	−2.79279	−0.214197
$171$	3.58948	0.274494
$172$	−8.10852	−0.618269
$173$	3.07517	0.233801	0.116900	−	0.993144i	$-0.462704\pi$
$173$	3.07517	0.233801	0.116900	+	0.993144i	$0.462704\pi$
$174$	5.71034	0.432900
$175$	−0.642369	−0.0485585
$176$	−4.81140	−0.362673
$177$	16.2963	1.22491
$178$	10.1141	0.758087
$179$	10.4466	0.780819	0.390410	−	0.920641i	$-0.372333\pi$
$179$	10.4466	0.780819	0.390410	+	0.920641i	$0.372333\pi$
$180$	−0.425691	−0.0317292
$181$	9.00625	0.669429	0.334715	−	0.942320i	$-0.391360\pi$
$181$	9.00625	0.669429	0.334715	+	0.942320i	$0.391360\pi$
$182$	0.287034	0.0212764
$183$	−0.660956	−0.0488592
$184$	4.17551	0.307823
$185$	0	0
$186$	15.2933	1.12136
$187$	−16.7957	−1.22823
$188$	8.33822	0.608127
$189$	0.683360	0.0497071
$190$	−5.39707	−0.391544
$191$	−1.00551	−0.0727558	−0.0363779	−	0.999338i	$-0.511582\pi$
$191$	−1.00551	−0.0727558	−0.0363779	+	0.999338i	$0.511582\pi$
$192$	−1.87939	−0.135633
$193$	−10.9953	−0.791456	−0.395728	−	0.918368i	$-0.629508\pi$
$193$	−10.9953	−0.791456	−0.395728	+	0.918368i	$0.629508\pi$
$194$	−5.87526	−0.421819
$195$	2.92924	0.209768
$196$	−6.97829	−0.498449
$197$	25.9050	1.84566	0.922829	−	0.385211i	$-0.125871\pi$
$197$	25.9050	1.84566	0.922829	+	0.385211i	$0.125871\pi$
$198$	−2.56009	−0.181938
$199$	−15.5738	−1.10400	−0.552000	−	0.833844i	$-0.686135\pi$
$199$	−15.5738	−1.10400	−0.552000	+	0.833844i	$0.686135\pi$
$200$	−4.35994	−0.308294
$201$	4.50942	0.318070
$202$	−17.0173	−1.19733
$203$	−0.447662	−0.0314197
$204$	−6.56060	−0.459334
$205$	3.11828	0.217790
$206$	−12.7468	−0.888115
$207$	2.22174	0.154422
$208$	1.94818	0.135082
$209$	−32.4577	−2.24515
$210$	0.221529	0.0152870
$211$	−23.1742	−1.59538	−0.797688	−	0.603070i	$-0.793944\pi$
$211$	−23.1742	−1.59538	−0.797688	+	0.603070i	$0.793944\pi$
$212$	−10.8894	−0.747889
$213$	−13.1243	−0.899265
$214$	14.2387	0.973335
$215$	6.48713	0.442418
$216$	4.63816	0.315587
$217$	−1.19892	−0.0813880
$218$	−19.7885	−1.34025
$219$	2.13120	0.144013
$220$	3.84930	0.259520
$221$	6.80075	0.457468
$222$	0	0
$223$	9.91195	0.663754	0.331877	−	0.943323i	$-0.392318\pi$
$223$	9.91195	0.663754	0.331877	+	0.943323i	$0.392318\pi$
$224$	0.147334	0.00984420
$225$	−2.31988	−0.154658
$226$	−8.50156	−0.565515
$227$	2.00038	0.132770	0.0663850	−	0.997794i	$-0.478853\pi$
$227$	2.00038	0.132770	0.0663850	+	0.997794i	$0.478853\pi$
$228$	−12.6784	−0.839645
$229$	−8.94250	−0.590937	−0.295468	−	0.955353i	$-0.595476\pi$
$229$	−8.94250	−0.590937	−0.295468	+	0.955353i	$0.595476\pi$
$230$	−3.34057	−0.220271
$231$	1.33227	0.0876567
$232$	−3.03841	−0.199481
$233$	21.7350	1.42390	0.711952	−	0.702228i	$-0.247811\pi$
$233$	21.7350	1.42390	0.711952	+	0.702228i	$0.247811\pi$
$234$	1.03660	0.0677650
$235$	−6.67089	−0.435161
$236$	−8.67110	−0.564440
$237$	3.55254	0.230762
$238$	0.514318	0.0333383
$239$	7.91730	0.512127	0.256064	−	0.966660i	$-0.417574\pi$
$239$	7.91730	0.512127	0.256064	+	0.966660i	$0.417574\pi$
$240$	1.50358	0.0970557
$241$	−29.7786	−1.91821	−0.959103	−	0.283058i	$-0.908651\pi$
$241$	−29.7786	−1.91821	−0.959103	+	0.283058i	$0.908651\pi$
$242$	12.1496	0.781003
$243$	5.46791	0.350767
$244$	0.351687	0.0225145
$245$	5.58290	0.356678
$246$	7.32521	0.467038
$247$	13.1424	0.836234
$248$	−8.13740	−0.516726
$249$	18.6151	1.17969
$250$	7.48831	0.473602
$251$	−22.8359	−1.44139	−0.720695	−	0.693252i	$-0.756177\pi$
$251$	−22.8359	−1.44139	−0.720695	+	0.693252i	$0.756177\pi$
$252$	0.0783950	0.00493842
$253$	−20.0901	−1.26305
$254$	5.53267	0.347151
$255$	5.24873	0.328688
$256$	1.00000	0.0625000
$257$	−16.4123	−1.02377	−0.511886	−	0.859053i	$-0.671053\pi$
$257$	−16.4123	−1.02377	−0.511886	+	0.859053i	$0.671053\pi$
$258$	15.2390	0.948741
$259$	0	0
$260$	−1.55862	−0.0966614
$261$	−1.61670	−0.100071
$262$	0.822948	0.0508419
$263$	−1.55971	−0.0961756	−0.0480878	−	0.998843i	$-0.515313\pi$
$263$	−1.55971	−0.0961756	−0.0480878	+	0.998843i	$0.515313\pi$
$264$	9.04247	0.556526
$265$	8.71195	0.535171
$266$	0.993920	0.0609411
$267$	−19.0084	−1.16329
$268$	−2.39941	−0.146567
$269$	3.29854	0.201116	0.100558	−	0.994931i	$-0.467937\pi$
$269$	3.29854	0.201116	0.100558	+	0.994931i	$0.467937\pi$
$270$	−3.71070	−0.225826
$271$	3.60336	0.218889	0.109444	−	0.993993i	$-0.465093\pi$
$271$	3.60336	0.218889	0.109444	+	0.993993i	$0.465093\pi$
$272$	3.49082	0.211662
$273$	−0.539447	−0.0326488
$274$	6.74232	0.407318
$275$	20.9774	1.26498
$276$	−7.84740	−0.472358
$277$	−15.6880	−0.942603	−0.471302	−	0.881972i	$-0.656216\pi$
$277$	−15.6880	−0.942603	−0.471302	+	0.881972i	$0.656216\pi$
$278$	12.0038	0.719941
$279$	−4.32982	−0.259220
$280$	−0.117873	−0.00704427
$281$	−5.08861	−0.303561	−0.151780	−	0.988414i	$-0.548501\pi$
$281$	−5.08861	−0.303561	−0.151780	+	0.988414i	$0.548501\pi$
$282$	−15.6707	−0.933178
$283$	9.16443	0.544769	0.272385	−	0.962188i	$-0.412188\pi$
$283$	9.16443	0.544769	0.272385	+	0.962188i	$0.412188\pi$
$284$	6.98332	0.414384
$285$	10.1432	0.600829
$286$	−9.37347	−0.554265
$287$	−0.574260	−0.0338975
$288$	0.532089	0.0313536
$289$	−4.81417	−0.283186
$290$	2.43084	0.142744
$291$	11.0419	0.647286
$292$	−1.13399	−0.0663618
$293$	−25.3205	−1.47924	−0.739620	−	0.673024i	$-0.764995\pi$
$293$	−25.3205	−1.47924	−0.739620	+	0.673024i	$0.764995\pi$
$294$	13.1149	0.764877
$295$	6.93721	0.403900
$296$	0	0
$297$	−22.3160	−1.29491
$298$	−9.21354	−0.533726
$299$	8.13465	0.470439
$300$	8.19401	0.473081
$301$	−1.19466	−0.0688593
$302$	−11.7843	−0.678110
$303$	31.9821	1.83732
$304$	6.74601	0.386910
$305$	−0.281363	−0.0161108
$306$	1.85743	0.106182
$307$	8.70568	0.496860	0.248430	−	0.968650i	$-0.420085\pi$
$307$	8.70568	0.496860	0.248430	+	0.968650i	$0.420085\pi$
$308$	−0.708885	−0.0403924
$309$	23.9562	1.36282
$310$	6.51023	0.369756
$311$	−5.80918	−0.329409	−0.164704	−	0.986343i	$-0.552667\pi$
$311$	−5.80918	−0.329409	−0.164704	+	0.986343i	$0.552667\pi$
$312$	−3.66138	−0.207285
$313$	7.86544	0.444581	0.222291	−	0.974980i	$-0.428647\pi$
$313$	7.86544	0.444581	0.222291	+	0.974980i	$0.428647\pi$
$314$	−17.3717	−0.980344
$315$	−0.0627190	−0.00353382
$316$	−1.89027	−0.106336
$317$	5.59900	0.314471	0.157235	−	0.987561i	$-0.449742\pi$
$317$	5.59900	0.314471	0.157235	+	0.987561i	$0.449742\pi$
$318$	20.4654	1.14764
$319$	14.6190	0.818507
$320$	−0.800038	−0.0447235
$321$	−26.7599	−1.49359
$322$	0.615197	0.0342836
$323$	23.5491	1.31031
$324$	−10.3131	−0.572953
$325$	−8.49395	−0.471159
$326$	−2.26115	−0.125233
$327$	37.1903	2.05663
$328$	−3.89766	−0.215212
$329$	1.22851	0.0677298
$330$	−7.23432	−0.398236
$331$	−18.1905	−0.999842	−0.499921	−	0.866071i	$-0.666638\pi$
$331$	−18.1905	−0.999842	−0.499921	+	0.866071i	$0.666638\pi$
$332$	−9.90490	−0.543602
$333$	0	0
$334$	15.9560	0.873074
$335$	1.91962	0.104880
$336$	−0.276898	−0.0151060
$337$	33.0401	1.79981	0.899903	−	0.436090i	$-0.143637\pi$
$337$	33.0401	1.79981	0.899903	+	0.436090i	$0.143637\pi$
$338$	−9.20459	−0.500664
$339$	15.9777	0.867790
$340$	−2.79279	−0.151460
$341$	39.1523	2.12022
$342$	3.58948	0.194097
$343$	−2.05948	−0.111202
$344$	−8.10852	−0.437182
$345$	6.27822	0.338008
$346$	3.07517	0.165322
$347$	32.3019	1.73406	0.867029	−	0.498258i	$-0.166027\pi$
$347$	32.3019	1.73406	0.867029	+	0.498258i	$0.166027\pi$
$348$	5.71034	0.306107
$349$	2.28640	0.122388	0.0611940	−	0.998126i	$-0.480509\pi$
$349$	2.28640	0.122388	0.0611940	+	0.998126i	$0.480509\pi$
$350$	−0.642369	−0.0343361
$351$	9.03596	0.482304
$352$	−4.81140	−0.256448
$353$	6.42195	0.341806	0.170903	−	0.985288i	$-0.445332\pi$
$353$	6.42195	0.341806	0.170903	+	0.985288i	$0.445332\pi$
$354$	16.2963	0.866140
$355$	−5.58692	−0.296523
$356$	10.1141	0.536048
$357$	−0.966602	−0.0511580
$358$	10.4466	0.552123
$359$	−7.32244	−0.386463	−0.193232	−	0.981153i	$-0.561897\pi$
$359$	−7.32244	−0.386463	−0.193232	+	0.981153i	$0.561897\pi$
$360$	−0.425691	−0.0224359
$361$	26.5087	1.39519
$362$	9.00625	0.473358
$363$	−22.8337	−1.19846
$364$	0.287034	0.0150447
$365$	0.907235	0.0474869
$366$	−0.660956	−0.0345487
$367$	31.5546	1.64713	0.823567	−	0.567218i	$-0.191980\pi$
$367$	31.5546	1.64713	0.823567	+	0.567218i	$0.191980\pi$
$368$	4.17551	0.217664
$369$	−2.07390	−0.107963
$370$	0	0
$371$	−1.60439	−0.0832956
$372$	15.2933	0.792921
$373$	8.36944	0.433353	0.216677	−	0.976243i	$-0.430478\pi$
$373$	8.36944	0.433353	0.216677	+	0.976243i	$0.430478\pi$
$374$	−16.7957	−0.868487
$375$	−14.0734	−0.726748
$376$	8.33822	0.430011
$377$	−5.91937	−0.304863
$378$	0.683360	0.0351482
$379$	28.1864	1.44784	0.723919	−	0.689885i	$-0.242339\pi$
$379$	28.1864	1.44784	0.723919	+	0.689885i	$0.242339\pi$
$380$	−5.39707	−0.276864
$381$	−10.3980	−0.532707
$382$	−1.00551	−0.0514462
$383$	−9.09466	−0.464716	−0.232358	−	0.972630i	$-0.574644\pi$
$383$	−9.09466	−0.464716	−0.232358	+	0.972630i	$0.574644\pi$
$384$	−1.87939	−0.0959070
$385$	0.567135	0.0289039
$386$	−10.9953	−0.559644
$387$	−4.31446	−0.219316
$388$	−5.87526	−0.298271
$389$	2.00537	0.101676	0.0508381	−	0.998707i	$-0.483811\pi$
$389$	2.00537	0.101676	0.0508381	+	0.998707i	$0.483811\pi$
$390$	2.92924	0.148328
$391$	14.5760	0.737138
$392$	−6.97829	−0.352457
$393$	−1.54664	−0.0780175
$394$	25.9050	1.30508
$395$	1.51229	0.0760914
$396$	−2.56009	−0.128649
$397$	−19.0756	−0.957379	−0.478690	−	0.877984i	$-0.658888\pi$
$397$	−19.0756	−0.957379	−0.478690	+	0.877984i	$0.658888\pi$
$398$	−15.5738	−0.780646
$399$	−1.86796	−0.0935149
$400$	−4.35994	−0.217997
$401$	−24.7444	−1.23568	−0.617839	−	0.786305i	$-0.711992\pi$
$401$	−24.7444	−1.23568	−0.617839	+	0.786305i	$0.711992\pi$
$402$	4.50942	0.224909
$403$	−15.8531	−0.789700
$404$	−17.0173	−0.846643
$405$	8.25091	0.409991
$406$	−0.447662	−0.0222171
$407$	0	0
$408$	−6.56060	−0.324798
$409$	24.6462	1.21868	0.609338	−	0.792910i	$-0.291435\pi$
$409$	24.6462	1.21868	0.609338	+	0.792910i	$0.291435\pi$
$410$	3.11828	0.154001
$411$	−12.6714	−0.625035
$412$	−12.7468	−0.627992
$413$	−1.27755	−0.0628642
$414$	2.22174	0.109193
$415$	7.92430	0.388988
$416$	1.94818	0.0955174
$417$	−22.5598	−1.10476
$418$	−32.4577	−1.58756
$419$	−18.2771	−0.892894	−0.446447	−	0.894810i	$-0.647311\pi$
$419$	−18.2771	−0.892894	−0.446447	+	0.894810i	$0.647311\pi$
$420$	0.221529	0.0108095
$421$	37.5976	1.83240	0.916198	−	0.400726i	$-0.131242\pi$
$421$	37.5976	1.83240	0.916198	+	0.400726i	$0.131242\pi$
$422$	−23.1742	−1.12810
$423$	4.43667	0.215718
$424$	−10.8894	−0.528837
$425$	−15.2198	−0.738267
$426$	−13.1243	−0.635877
$427$	0.0518156	0.00250753
$428$	14.2387	0.688252
$429$	17.6164	0.850526
$430$	6.48713	0.312837
$431$	36.8773	1.77632	0.888158	−	0.459538i	$-0.151985\pi$
$431$	36.8773	1.77632	0.888158	+	0.459538i	$0.151985\pi$
$432$	4.63816	0.223153
$433$	10.8938	0.523522	0.261761	−	0.965133i	$-0.415697\pi$
$433$	10.8938	0.523522	0.261761	+	0.965133i	$0.415697\pi$
$434$	−1.19892	−0.0575500
$435$	−4.56849	−0.219042
$436$	−19.7885	−0.947699
$437$	28.1681	1.34746
$438$	2.13120	0.101833
$439$	18.6888	0.891968	0.445984	−	0.895041i	$-0.352854\pi$
$439$	18.6888	0.891968	0.445984	+	0.895041i	$0.352854\pi$
$440$	3.84930	0.183508
$441$	−3.71307	−0.176813
$442$	6.80075	0.323479
$443$	−18.1659	−0.863090	−0.431545	−	0.902092i	$-0.642031\pi$
$443$	−18.1659	−0.863090	−0.431545	+	0.902092i	$0.642031\pi$
$444$	0	0
$445$	−8.09170	−0.383583
$446$	9.91195	0.469345
$447$	17.3158	0.819009
$448$	0.147334	0.00696090
$449$	15.5694	0.734764	0.367382	−	0.930070i	$-0.380254\pi$
$449$	15.5694	0.734764	0.367382	+	0.930070i	$0.380254\pi$
$450$	−2.31988	−0.109360
$451$	18.7532	0.883054
$452$	−8.50156	−0.399880
$453$	22.1472	1.04057
$454$	2.00038	0.0938826
$455$	−0.229638	−0.0107656
$456$	−12.6784	−0.593718
$457$	−11.0242	−0.515693	−0.257846	−	0.966186i	$-0.583013\pi$
$457$	−11.0242	−0.515693	−0.257846	+	0.966186i	$0.583013\pi$
$458$	−8.94250	−0.417855
$459$	16.1910	0.755730
$460$	−3.34057	−0.155755
$461$	21.3475	0.994253	0.497126	−	0.867678i	$-0.334389\pi$
$461$	21.3475	0.994253	0.497126	+	0.867678i	$0.334389\pi$
$462$	1.33227	0.0619827
$463$	−33.1910	−1.54252	−0.771259	−	0.636521i	$-0.780373\pi$
$463$	−33.1910	−1.54252	−0.771259	+	0.636521i	$0.780373\pi$
$464$	−3.03841	−0.141055
$465$	−12.2352	−0.567395
$466$	21.7350	1.00685
$467$	−14.8124	−0.685437	−0.342719	−	0.939438i	$-0.611348\pi$
$467$	−14.8124	−0.685437	−0.342719	+	0.939438i	$0.611348\pi$
$468$	1.03660	0.0479171
$469$	−0.353516	−0.0163239
$470$	−6.67089	−0.307705
$471$	32.6482	1.50435
$472$	−8.67110	−0.399120
$473$	39.0133	1.79383
$474$	3.55254	0.163174
$475$	−29.4122	−1.34952
$476$	0.514318	0.0235737
$477$	−5.79414	−0.265295
$478$	7.91730	0.362129
$479$	9.00554	0.411474	0.205737	−	0.978607i	$-0.434041\pi$
$479$	9.00554	0.411474	0.205737	+	0.978607i	$0.434041\pi$
$480$	1.50358	0.0686287
$481$	0	0
$482$	−29.7786	−1.35638
$483$	−1.15619	−0.0526086
$484$	12.1496	0.552252
$485$	4.70043	0.213435
$486$	5.46791	0.248029
$487$	3.39198	0.153705	0.0768525	−	0.997042i	$-0.475513\pi$
$487$	3.39198	0.153705	0.0768525	+	0.997042i	$0.475513\pi$
$488$	0.351687	0.0159201
$489$	4.24957	0.192172
$490$	5.58290	0.252210
$491$	−20.7343	−0.935724	−0.467862	−	0.883801i	$-0.654976\pi$
$491$	−20.7343	−0.935724	−0.467862	+	0.883801i	$0.654976\pi$
$492$	7.32521	0.330246
$493$	−10.6065	−0.477695
$494$	13.1424	0.591307
$495$	2.04817	0.0920584
$496$	−8.13740	−0.365380
$497$	1.02888	0.0461517
$498$	18.6151	0.834164
$499$	24.6821	1.10492	0.552460	−	0.833539i	$-0.313689\pi$
$499$	24.6821	1.10492	0.552460	+	0.833539i	$0.313689\pi$
$500$	7.48831	0.334887
$501$	−29.9875	−1.33974
$502$	−22.8359	−1.01922
$503$	−16.6469	−0.742247	−0.371123	−	0.928584i	$-0.621027\pi$
$503$	−16.6469	−0.742247	−0.371123	+	0.928584i	$0.621027\pi$
$504$	0.0783950	0.00349199
$505$	13.6145	0.605837
$506$	−20.0901	−0.893112
$507$	17.2990	0.768275
$508$	5.53267	0.245473
$509$	−25.1337	−1.11403	−0.557016	−	0.830502i	$-0.688054\pi$
$509$	−25.1337	−1.11403	−0.557016	+	0.830502i	$0.688054\pi$
$510$	5.24873	0.232418
$511$	−0.167076	−0.00739100
$512$	1.00000	0.0441942
$513$	31.2891	1.38145
$514$	−16.4123	−0.723916
$515$	10.1980	0.449376
$516$	15.2390	0.670861
$517$	−40.1185	−1.76441
$518$	0	0
$519$	−5.77943	−0.253689
$520$	−1.55862	−0.0683499
$521$	28.8328	1.26319	0.631594	−	0.775299i	$-0.282401\pi$
$521$	28.8328	1.26319	0.631594	+	0.775299i	$0.282401\pi$
$522$	−1.61670	−0.0707612
$523$	−3.61438	−0.158046	−0.0790229	−	0.996873i	$-0.525180\pi$
$523$	−3.61438	−0.158046	−0.0790229	+	0.996873i	$0.525180\pi$
$524$	0.822948	0.0359507
$525$	1.20726	0.0526891
$526$	−1.55971	−0.0680064
$527$	−28.4062	−1.23739
$528$	9.04247	0.393523
$529$	−5.56509	−0.241961
$530$	8.71195	0.378423
$531$	−4.61379	−0.200222
$532$	0.993920	0.0430919
$533$	−7.59335	−0.328904
$534$	−19.0084	−0.822572
$535$	−11.3915	−0.492496
$536$	−2.39941	−0.103639
$537$	−19.6333	−0.847238
$538$	3.29854	0.142210
$539$	33.5753	1.44619
$540$	−3.71070	−0.159683
$541$	11.4221	0.491075	0.245538	−	0.969387i	$-0.421036\pi$
$541$	11.4221	0.491075	0.245538	+	0.969387i	$0.421036\pi$
$542$	3.60336	0.154778
$543$	−16.9262	−0.726373
$544$	3.49082	0.149668
$545$	15.8316	0.678150
$546$	−0.539447	−0.0230862
$547$	−33.4706	−1.43110	−0.715550	−	0.698561i	$-0.753824\pi$
$547$	−33.4706	−1.43110	−0.715550	+	0.698561i	$0.753824\pi$
$548$	6.74232	0.288018
$549$	0.187129	0.00798646
$550$	20.9774	0.894479
$551$	−20.4972	−0.873208
$552$	−7.84740	−0.334007
$553$	−0.278502	−0.0118431
$554$	−15.6880	−0.666521
$555$	0	0
$556$	12.0038	0.509075
$557$	−19.4504	−0.824141	−0.412070	−	0.911152i	$-0.635194\pi$
$557$	−19.4504	−0.824141	−0.412070	+	0.911152i	$0.635194\pi$
$558$	−4.32982	−0.183296
$559$	−15.7969	−0.668136
$560$	−0.117873	−0.00498105
$561$	31.5656	1.33270
$562$	−5.08861	−0.214650
$563$	18.9277	0.797710	0.398855	−	0.917014i	$-0.369408\pi$
$563$	18.9277	0.797710	0.398855	+	0.917014i	$0.369408\pi$
$564$	−15.6707	−0.659857
$565$	6.80157	0.286144
$566$	9.16443	0.385210
$567$	−1.51948	−0.0638122
$568$	6.98332	0.293013
$569$	7.75144	0.324957	0.162479	−	0.986712i	$-0.448051\pi$
$569$	7.75144	0.324957	0.162479	+	0.986712i	$0.448051\pi$
$570$	10.1432	0.424851
$571$	4.96115	0.207618	0.103809	−	0.994597i	$-0.466897\pi$
$571$	4.96115	0.207618	0.103809	+	0.994597i	$0.466897\pi$
$572$	−9.37347	−0.391924
$573$	1.88973	0.0789447
$574$	−0.574260	−0.0239691
$575$	−18.2050	−0.759200
$576$	0.532089	0.0221704
$577$	21.0978	0.878313	0.439156	−	0.898411i	$-0.355277\pi$
$577$	21.0978	0.878313	0.439156	+	0.898411i	$0.355277\pi$
$578$	−4.81417	−0.200243
$579$	20.6643	0.858780
$580$	2.43084	0.100935
$581$	−1.45933	−0.0605433
$582$	11.0419	0.457700
$583$	52.3933	2.16991
$584$	−1.13399	−0.0469248
$585$	−0.829323	−0.0342883
$586$	−25.3205	−1.04598
$587$	−0.000697336 0	−2.87821e−5 0	−1.43911e−5	−	1.00000i	$-0.500005\pi$
$587$	−0.000697336 0	−2.87821e−5 0	−1.43911e−5		1.00000i	$0.500005\pi$
$588$	13.1149	0.540849
$589$	−54.8950	−2.26191
$590$	6.93721	0.285600
$591$	−48.6855	−2.00266
$592$	0	0
$593$	−8.38840	−0.344470	−0.172235	−	0.985056i	$-0.555099\pi$
$593$	−8.38840	−0.344470	−0.172235	+	0.985056i	$0.555099\pi$
$594$	−22.3160	−0.915637
$595$	−0.411474	−0.0168688
$596$	−9.21354	−0.377401
$597$	29.2692	1.19791
$598$	8.13465	0.332651
$599$	26.2988	1.07454	0.537270	−	0.843411i	$-0.319456\pi$
$599$	26.2988	1.07454	0.537270	+	0.843411i	$0.319456\pi$
$600$	8.19401	0.334519
$601$	43.1751	1.76115	0.880574	−	0.473909i	$-0.157158\pi$
$601$	43.1751	1.76115	0.880574	+	0.473909i	$0.157158\pi$
$602$	−1.19466	−0.0486909
$603$	−1.27670	−0.0519913
$604$	−11.7843	−0.479496
$605$	−9.72010	−0.395178
$606$	31.9821	1.29918
$607$	−34.1693	−1.38689	−0.693446	−	0.720509i	$-0.743908\pi$
$607$	−34.1693	−1.38689	−0.693446	+	0.720509i	$0.743908\pi$
$608$	6.74601	0.273587
$609$	0.841330	0.0340924
$610$	−0.281363	−0.0113921
$611$	16.2444	0.657176
$612$	1.85743	0.0750820
$613$	−41.1907	−1.66368	−0.831838	−	0.555019i	$-0.812711\pi$
$613$	−41.1907	−1.66368	−0.831838	+	0.555019i	$0.812711\pi$
$614$	8.70568	0.351333
$615$	−5.86045	−0.236316
$616$	−0.708885	−0.0285618
$617$	31.9938	1.28802	0.644010	−	0.765017i	$-0.277269\pi$
$617$	31.9938	1.28802	0.644010	+	0.765017i	$0.277269\pi$
$618$	23.9562	0.963661
$619$	−6.20000	−0.249199	−0.124600	−	0.992207i	$-0.539765\pi$
$619$	−6.20000	−0.249199	−0.124600	+	0.992207i	$0.539765\pi$
$620$	6.51023	0.261457
$621$	19.3667	0.777158
$622$	−5.80918	−0.232927
$623$	1.49016	0.0597020
$624$	−3.66138	−0.146573
$625$	15.8088	0.632351
$626$	7.86544	0.314366
$627$	61.0006	2.43613
$628$	−17.3717	−0.693208
$629$	0	0
$630$	−0.0627190	−0.00249878
$631$	36.5166	1.45370	0.726851	−	0.686795i	$-0.240983\pi$
$631$	36.5166	1.45370	0.726851	+	0.686795i	$0.240983\pi$
$632$	−1.89027	−0.0751908
$633$	43.5532	1.73108
$634$	5.59900	0.222365
$635$	−4.42635	−0.175654
$636$	20.4654	0.811507
$637$	−13.5950	−0.538652
$638$	14.6190	0.578772
$639$	3.71575	0.146993
$640$	−0.800038	−0.0316243
$641$	−19.9230	−0.786912	−0.393456	−	0.919343i	$-0.628721\pi$
$641$	−19.9230	−0.786912	−0.393456	+	0.919343i	$0.628721\pi$
$642$	−26.7599	−1.05613
$643$	−33.4800	−1.32032	−0.660161	−	0.751124i	$-0.729512\pi$
$643$	−33.4800	−1.32032	−0.660161	+	0.751124i	$0.729512\pi$
$644$	0.615197	0.0242422
$645$	−12.1918	−0.480052
$646$	23.5491	0.926528
$647$	−11.9401	−0.469414	−0.234707	−	0.972066i	$-0.575413\pi$
$647$	−11.9401	−0.469414	−0.234707	+	0.972066i	$0.575413\pi$
$648$	−10.3131	−0.405139
$649$	41.7201	1.63766
$650$	−8.49395	−0.333160
$651$	2.25323	0.0883111
$652$	−2.26115	−0.0885534
$653$	−13.6771	−0.535228	−0.267614	−	0.963526i	$-0.586235\pi$
$653$	−13.6771	−0.535228	−0.267614	+	0.963526i	$0.586235\pi$
$654$	37.1903	1.45425
$655$	−0.658390	−0.0257254
$656$	−3.89766	−0.152178
$657$	−0.603384	−0.0235402
$658$	1.22851	0.0478922
$659$	33.3017	1.29725	0.648625	−	0.761108i	$-0.275344\pi$
$659$	33.3017	1.29725	0.648625	+	0.761108i	$0.275344\pi$
$660$	−7.23432	−0.281596
$661$	−4.06152	−0.157975	−0.0789873	−	0.996876i	$-0.525169\pi$
$661$	−4.06152	−0.157975	−0.0789873	+	0.996876i	$0.525169\pi$
$662$	−18.1905	−0.706995
$663$	−12.7812	−0.496382
$664$	−9.90490	−0.384385
$665$	−0.795174	−0.0308355
$666$	0	0
$667$	−12.6869	−0.491240
$668$	15.9560	0.617357
$669$	−18.6284	−0.720215
$670$	1.91962	0.0741614
$671$	−1.69211	−0.0653231
$672$	−0.276898	−0.0106816
$673$	−18.1163	−0.698330	−0.349165	−	0.937061i	$-0.613535\pi$
$673$	−18.1163	−0.698330	−0.349165	+	0.937061i	$0.613535\pi$
$674$	33.0401	1.27266
$675$	−20.2221	−0.778348
$676$	−9.20459	−0.354023
$677$	−20.2945	−0.779982	−0.389991	−	0.920819i	$-0.627522\pi$
$677$	−20.2945	−0.779982	−0.389991	+	0.920819i	$0.627522\pi$
$678$	15.9777	0.613620
$679$	−0.865627	−0.0332197
$680$	−2.79279	−0.107099
$681$	−3.75949	−0.144064
$682$	39.1523	1.49922
$683$	23.7156	0.907451	0.453725	−	0.891142i	$-0.350095\pi$
$683$	23.7156	0.907451	0.453725	+	0.891142i	$0.350095\pi$
$684$	3.58948	0.137247
$685$	−5.39411	−0.206098
$686$	−2.05948	−0.0786315
$687$	16.8064	0.641204
$688$	−8.10852	−0.309135
$689$	−21.2146	−0.808210
$690$	6.27822	0.239008
$691$	3.51712	0.133797	0.0668987	−	0.997760i	$-0.478690\pi$
$691$	3.51712	0.133797	0.0668987	+	0.997760i	$0.478690\pi$
$692$	3.07517	0.116900
$693$	−0.377190	−0.0143282
$694$	32.3019	1.22616
$695$	−9.60350	−0.364282
$696$	5.71034	0.216450
$697$	−13.6060	−0.515366
$698$	2.28640	0.0865414
$699$	−40.8484	−1.54503
$700$	−0.642369	−0.0242793
$701$	18.9835	0.716996	0.358498	−	0.933530i	$-0.383289\pi$
$701$	18.9835	0.716996	0.358498	+	0.933530i	$0.383289\pi$
$702$	9.03596	0.341040
$703$	0	0
$704$	−4.81140	−0.181336
$705$	12.5372	0.472177
$706$	6.42195	0.241693
$707$	−2.50724	−0.0942943
$708$	16.2963	0.612454
$709$	13.0236	0.489113	0.244556	−	0.969635i	$-0.421358\pi$
$709$	13.0236	0.489113	0.244556	+	0.969635i	$0.421358\pi$
$710$	−5.58692	−0.209673
$711$	−1.00579	−0.0377201
$712$	10.1141	0.379043
$713$	−33.9778	−1.27248
$714$	−0.966602	−0.0361742
$715$	7.49913	0.280452
$716$	10.4466	0.390410
$717$	−14.8797	−0.555691
$718$	−7.32244	−0.273271
$719$	−25.1165	−0.936686	−0.468343	−	0.883547i	$-0.655149\pi$
$719$	−25.1165	−0.936686	−0.468343	+	0.883547i	$0.655149\pi$
$720$	−0.425691	−0.0158646
$721$	−1.87805	−0.0699422
$722$	26.5087	0.986551
$723$	55.9654	2.08138
$724$	9.00625	0.334715
$725$	13.2473	0.491992
$726$	−22.8337	−0.847438
$727$	19.3767	0.718641	0.359321	−	0.933214i	$-0.383008\pi$
$727$	19.3767	0.718641	0.359321	+	0.933214i	$0.383008\pi$
$728$	0.287034	0.0106382
$729$	20.6631	0.765301
$730$	0.907235	0.0335783
$731$	−28.3054	−1.04691
$732$	−0.660956	−0.0244296
$733$	10.7969	0.398791	0.199396	−	0.979919i	$-0.436102\pi$
$733$	10.7969	0.398791	0.199396	+	0.979919i	$0.436102\pi$
$734$	31.5546	1.16470
$735$	−10.4924	−0.387019
$736$	4.17551	0.153911
$737$	11.5445	0.425248
$738$	−2.07390	−0.0763414
$739$	28.0429	1.03157	0.515787	−	0.856717i	$-0.327500\pi$
$739$	28.0429	1.03157	0.515787	+	0.856717i	$0.327500\pi$
$740$	0	0
$741$	−24.6997	−0.907367
$742$	−1.60439	−0.0588989
$743$	−17.8858	−0.656165	−0.328082	−	0.944649i	$-0.606402\pi$
$743$	−17.8858	−0.656165	−0.328082	+	0.944649i	$0.606402\pi$
$744$	15.2933	0.560680
$745$	7.37119	0.270059
$746$	8.36944	0.306427
$747$	−5.27029	−0.192830
$748$	−16.7957	−0.614113
$749$	2.09785	0.0766536
$750$	−14.0734	−0.513888
$751$	2.64277	0.0964359	0.0482179	−	0.998837i	$-0.484646\pi$
$751$	2.64277	0.0964359	0.0482179	+	0.998837i	$0.484646\pi$
$752$	8.33822	0.304064
$753$	42.9175	1.56400
$754$	−5.91937	−0.215571
$755$	9.42788	0.343116
$756$	0.683360	0.0248536
$757$	−48.0087	−1.74491	−0.872453	−	0.488697i	$-0.837472\pi$
$757$	−48.0087	−1.74491	−0.872453	+	0.488697i	$0.837472\pi$
$758$	28.1864	1.02378
$759$	37.7570	1.37049
$760$	−5.39707	−0.195772
$761$	3.21805	0.116654	0.0583271	−	0.998298i	$-0.481423\pi$
$761$	3.21805	0.116654	0.0583271	+	0.998298i	$0.481423\pi$
$762$	−10.3980	−0.376681
$763$	−2.91553	−0.105549
$764$	−1.00551	−0.0363779
$765$	−1.48601	−0.0537269
$766$	−9.09466	−0.328604
$767$	−16.8929	−0.609966
$768$	−1.87939	−0.0678165
$769$	−20.1626	−0.727081	−0.363541	−	0.931578i	$-0.618432\pi$
$769$	−20.1626	−0.727081	−0.363541	+	0.931578i	$0.618432\pi$
$770$	0.567135	0.0204381
$771$	30.8451	1.11086
$772$	−10.9953	−0.395728
$773$	−20.8176	−0.748755	−0.374378	−	0.927276i	$-0.622144\pi$
$773$	−20.8176	−0.748755	−0.374378	+	0.927276i	$0.622144\pi$
$774$	−4.31446	−0.155080
$775$	35.4786	1.27443
$776$	−5.87526	−0.210909
$777$	0	0
$778$	2.00537	0.0718960
$779$	−26.2937	−0.942069
$780$	2.92924	0.104884
$781$	−33.5995	−1.20229
$782$	14.5760	0.521236
$783$	−14.0926	−0.503629
$784$	−6.97829	−0.249225
$785$	13.8981	0.496043
$786$	−1.54664	−0.0551667
$787$	−9.43590	−0.336353	−0.168177	−	0.985757i	$-0.553788\pi$
$787$	−9.43590	−0.336353	−0.168177	+	0.985757i	$0.553788\pi$
$788$	25.9050	0.922829
$789$	2.93129	0.104357
$790$	1.51229	0.0538047
$791$	−1.25257	−0.0445364
$792$	−2.56009	−0.0909689
$793$	0.685150	0.0243304
$794$	−19.0756	−0.676969
$795$	−16.3731	−0.580695
$796$	−15.5738	−0.552000
$797$	−44.7532	−1.58524	−0.792619	−	0.609717i	$-0.791283\pi$
$797$	−44.7532	−1.58524	−0.792619	+	0.609717i	$0.791283\pi$
$798$	−1.86796	−0.0661250
$799$	29.1072	1.02974
$800$	−4.35994	−0.154147
$801$	5.38162	0.190150
$802$	−24.7444	−0.873756
$803$	5.45608	0.192541
$804$	4.50942	0.159035
$805$	−0.492181	−0.0173471
$806$	−15.8531	−0.558403
$807$	−6.19924	−0.218223
$808$	−17.0173	−0.598667
$809$	−21.1368	−0.743129	−0.371565	−	0.928407i	$-0.621179\pi$
$809$	−21.1368	−0.743129	−0.371565	+	0.928407i	$0.621179\pi$
$810$	8.25091	0.289907
$811$	7.61142	0.267273	0.133637	−	0.991030i	$-0.457335\pi$
$811$	7.61142	0.267273	0.133637	+	0.991030i	$0.457335\pi$
$812$	−0.447662	−0.0157099
$813$	−6.77210	−0.237508
$814$	0	0
$815$	1.80900	0.0633666
$816$	−6.56060	−0.229667
$817$	−54.7002	−1.91372
$818$	24.6462	0.861735
$819$	0.152728	0.00533673
$820$	3.11828	0.108895
$821$	6.14650	0.214514	0.107257	−	0.994231i	$-0.465793\pi$
$821$	6.14650	0.214514	0.107257	+	0.994231i	$0.465793\pi$
$822$	−12.6714	−0.441966
$823$	27.8950	0.972360	0.486180	−	0.873859i	$-0.338390\pi$
$823$	27.8950	0.972360	0.486180	+	0.873859i	$0.338390\pi$
$824$	−12.7468	−0.444058
$825$	−39.4246	−1.37259
$826$	−1.27755	−0.0444517
$827$	−24.4353	−0.849700	−0.424850	−	0.905264i	$-0.639673\pi$
$827$	−24.4353	−0.849700	−0.424850	+	0.905264i	$0.639673\pi$
$828$	2.22174	0.0772109
$829$	−47.2497	−1.64105	−0.820524	−	0.571611i	$-0.806318\pi$
$829$	−47.2497	−1.64105	−0.820524	+	0.571611i	$0.806318\pi$
$830$	7.92430	0.275056
$831$	29.4839	1.02278
$832$	1.94818	0.0675410
$833$	−24.3600	−0.844023
$834$	−22.5598	−0.781181
$835$	−12.7654	−0.441765
$836$	−32.4577	−1.12257
$837$	−37.7425	−1.30457
$838$	−18.2771	−0.631372
$839$	47.0602	1.62470	0.812349	−	0.583171i	$-0.198188\pi$
$839$	47.0602	1.62470	0.812349	+	0.583171i	$0.198188\pi$
$840$	0.221529	0.00764348
$841$	−19.7681	−0.681657
$842$	37.5976	1.29570
$843$	9.56345	0.329383
$844$	−23.1742	−0.797688
$845$	7.36403	0.253330
$846$	4.43667	0.152536
$847$	1.79005	0.0615067
$848$	−10.8894	−0.373944
$849$	−17.2235	−0.591109
$850$	−15.2198	−0.522034
$851$	0	0
$852$	−13.1243	−0.449633
$853$	−27.7605	−0.950502	−0.475251	−	0.879850i	$-0.657643\pi$
$853$	−27.7605	−0.950502	−0.475251	+	0.879850i	$0.657643\pi$
$854$	0.0518156	0.00177309
$855$	−2.87172	−0.0982107
$856$	14.2387	0.486667
$857$	23.8545	0.814853	0.407426	−	0.913238i	$-0.366426\pi$
$857$	23.8545	0.814853	0.407426	+	0.913238i	$0.366426\pi$
$858$	17.6164	0.601413
$859$	−44.2977	−1.51142	−0.755708	−	0.654908i	$-0.772707\pi$
$859$	−44.2977	−1.51142	−0.755708	+	0.654908i	$0.772707\pi$
$860$	6.48713	0.221209
$861$	1.07926	0.0367809
$862$	36.8773	1.25605
$863$	43.2099	1.47088	0.735441	−	0.677589i	$-0.236975\pi$
$863$	43.2099	1.47088	0.735441	+	0.677589i	$0.236975\pi$
$864$	4.63816	0.157793
$865$	−2.46025	−0.0836512
$866$	10.8938	0.370186
$867$	9.04767	0.307275
$868$	−1.19892	−0.0406940
$869$	9.09483	0.308521
$870$	−4.56849	−0.154886
$871$	−4.67449	−0.158389
$872$	−19.7885	−0.670124
$873$	−3.12616	−0.105804
$874$	28.1681	0.952799
$875$	1.10329	0.0372979
$876$	2.13120	0.0720067
$877$	−40.5106	−1.36794	−0.683972	−	0.729508i	$-0.739749\pi$
$877$	−40.5106	−1.36794	−0.683972	+	0.729508i	$0.739749\pi$
$878$	18.6888	0.630717
$879$	47.5870	1.60507
$880$	3.84930	0.129760
$881$	−24.4214	−0.822776	−0.411388	−	0.911460i	$-0.634956\pi$
$881$	−24.4214	−0.822776	−0.411388	+	0.911460i	$0.634956\pi$
$882$	−3.71307	−0.125026
$883$	24.1246	0.811857	0.405929	−	0.913905i	$-0.366948\pi$
$883$	24.1246	0.811857	0.405929	+	0.913905i	$0.366948\pi$
$884$	6.80075	0.228734
$885$	−13.0377	−0.438257
$886$	−18.1659	−0.610296
$887$	4.81523	0.161679	0.0808397	−	0.996727i	$-0.474240\pi$
$887$	4.81523	0.161679	0.0808397	+	0.996727i	$0.474240\pi$
$888$	0	0
$889$	0.815153	0.0273394
$890$	−8.09170	−0.271234
$891$	49.6207	1.66235
$892$	9.91195	0.331877
$893$	56.2497	1.88233
$894$	17.3158	0.579127
$895$	−8.35772	−0.279368
$896$	0.147334	0.00492210
$897$	−15.2881	−0.510456
$898$	15.5694	0.519557
$899$	24.7248	0.824617
$900$	−2.31988	−0.0773292
$901$	−38.0130	−1.26640
$902$	18.7532	0.624413
$903$	2.24524	0.0747168
$904$	−8.50156	−0.282758
$905$	−7.20534	−0.239514
$906$	22.1472	0.735792
$907$	4.68041	0.155410	0.0777052	−	0.996976i	$-0.475241\pi$
$907$	4.68041	0.155410	0.0777052	+	0.996976i	$0.475241\pi$
$908$	2.00038	0.0663850
$909$	−9.05472	−0.300326
$910$	−0.229638	−0.00761243
$911$	8.81799	0.292153	0.146077	−	0.989273i	$-0.453335\pi$
$911$	8.81799	0.292153	0.146077	+	0.989273i	$0.453335\pi$
$912$	−12.6784	−0.419822
$913$	47.6564	1.57720
$914$	−11.0242	−0.364650
$915$	0.528790	0.0174812
$916$	−8.94250	−0.295468
$917$	0.121249	0.00400398
$918$	16.1910	0.534382
$919$	−8.95913	−0.295535	−0.147767	−	0.989022i	$-0.547209\pi$
$919$	−8.95913	−0.295535	−0.147767	+	0.989022i	$0.547209\pi$
$920$	−3.34057	−0.110135
$921$	−16.3613	−0.539124
$922$	21.3475	0.703043
$923$	13.6048	0.447806
$924$	1.33227	0.0438284
$925$	0	0
$926$	−33.1910	−1.09073
$927$	−6.78246	−0.222765
$928$	−3.03841	−0.0997407
$929$	−36.0961	−1.18428	−0.592138	−	0.805837i	$-0.701716\pi$
$929$	−36.0961	−1.18428	−0.592138	+	0.805837i	$0.701716\pi$
$930$	−12.2352	−0.401209
$931$	−47.0756	−1.54284
$932$	21.7350	0.711952
$933$	10.9177	0.357429
$934$	−14.8124	−0.484677
$935$	13.4372	0.439444
$936$	1.03660	0.0338825
$937$	−7.63521	−0.249431	−0.124716	−	0.992193i	$-0.539802\pi$
$937$	−7.63521	−0.249431	−0.124716	+	0.992193i	$0.539802\pi$
$938$	−0.353516	−0.0115427
$939$	−14.7822	−0.482399
$940$	−6.67089	−0.217581
$941$	−44.9151	−1.46419	−0.732095	−	0.681203i	$-0.761457\pi$
$941$	−44.9151	−1.46419	−0.732095	+	0.681203i	$0.761457\pi$
$942$	32.6482	1.06374
$943$	−16.2747	−0.529978
$944$	−8.67110	−0.282220
$945$	−0.546714	−0.0177846
$946$	39.0133	1.26843
$947$	7.12727	0.231605	0.115803	−	0.993272i	$-0.463056\pi$
$947$	7.12727	0.231605	0.115803	+	0.993272i	$0.463056\pi$
$948$	3.55254	0.115381
$949$	−2.20922	−0.0717142
$950$	−29.4122	−0.954258
$951$	−10.5227	−0.341221
$952$	0.514318	0.0166691
$953$	−11.0286	−0.357250	−0.178625	−	0.983917i	$-0.557165\pi$
$953$	−11.0286	−0.357250	−0.178625	+	0.983917i	$0.557165\pi$
$954$	−5.79414	−0.187592
$955$	0.804443	0.0260312
$956$	7.91730	0.256064
$957$	−27.4747	−0.888132
$958$	9.00554	0.290956
$959$	0.993376	0.0320778
$960$	1.50358	0.0485278
$961$	35.2173	1.13604
$962$	0	0
$963$	7.57623	0.244141
$964$	−29.7786	−0.959103
$965$	8.79663	0.283173
$966$	−1.15619	−0.0371999
$967$	−27.0127	−0.868669	−0.434335	−	0.900752i	$-0.643016\pi$
$967$	−27.0127	−0.868669	−0.434335	+	0.900752i	$0.643016\pi$
$968$	12.1496	0.390501
$969$	−44.2579	−1.42177
$970$	4.70043	0.150922
$971$	−50.4137	−1.61785	−0.808927	−	0.587909i	$-0.799951\pi$
$971$	−50.4137	−1.61785	−0.808927	+	0.587909i	$0.799951\pi$
$972$	5.46791	0.175383
$973$	1.76857	0.0566979
$974$	3.39198	0.108686
$975$	15.9634	0.511238
$976$	0.351687	0.0112572
$977$	−19.9596	−0.638564	−0.319282	−	0.947660i	$-0.603442\pi$
$977$	−19.9596	−0.638564	−0.319282	+	0.947660i	$0.603442\pi$
$978$	4.24957	0.135886
$979$	−48.6631	−1.55528
$980$	5.58290	0.178339
$981$	−10.5293	−0.336173
$982$	−20.7343	−0.661657
$983$	10.6447	0.339514	0.169757	−	0.985486i	$-0.445702\pi$
$983$	10.6447	0.339514	0.169757	+	0.985486i	$0.445702\pi$
$984$	7.32521	0.233519
$985$	−20.7250	−0.660354
$986$	−10.6065	−0.337781
$987$	−2.30884	−0.0734911
$988$	13.1424	0.418117
$989$	−33.8572	−1.07660
$990$	2.04817	0.0650951
$991$	33.2740	1.05698	0.528492	−	0.848938i	$-0.322758\pi$
$991$	33.2740	1.05698	0.528492	+	0.848938i	$0.322758\pi$
$992$	−8.13740	−0.258363
$993$	34.1870	1.08489
$994$	1.02888	0.0326342
$995$	12.4597	0.394998
$996$	18.6151	0.589843
$997$	13.7018	0.433941	0.216971	−	0.976178i	$-0.430382\pi$
$997$	13.7018	0.433941	0.216971	+	0.976178i	$0.430382\pi$
$998$	24.6821	0.781297
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.s.1.2		6
37.5	odd	36		74.2.h.a.25.1	yes	12
37.15	odd	36		74.2.h.a.3.1	✓	12
37.36	even	2		2738.2.a.r.1.1		6
111.5	even	36		666.2.bj.c.469.2		12
111.89	even	36		666.2.bj.c.595.2		12
148.15	even	36		592.2.bq.b.225.2		12
148.79	even	36		592.2.bq.b.321.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.3.1	✓	12	37.15	odd	36
74.2.h.a.25.1	yes	12	37.5	odd	36
592.2.bq.b.225.2		12	148.15	even	36
592.2.bq.b.321.2		12	148.79	even	36
666.2.bj.c.469.2		12	111.5	even	36
666.2.bj.c.595.2		12	111.89	even	36
2738.2.a.r.1.1		6	37.36	even	2
2738.2.a.s.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} -0.800038 q^{5} -1.87939 q^{6} +0.147334 q^{7} +1.00000 q^{8} +0.532089 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} -0.800038 q^{5} -1.87939 q^{6} +0.147334 q^{7} +1.00000 q^{8} +0.532089 q^{9} -0.800038 q^{10} -4.81140 q^{11} -1.87939 q^{12} +1.94818 q^{13} +0.147334 q^{14} +1.50358 q^{15} +1.00000 q^{16} +3.49082 q^{17} +0.532089 q^{18} +6.74601 q^{19} -0.800038 q^{20} -0.276898 q^{21} -4.81140 q^{22} +4.17551 q^{23} -1.87939 q^{24} -4.35994 q^{25} +1.94818 q^{26} +4.63816 q^{27} +0.147334 q^{28} -3.03841 q^{29} +1.50358 q^{30} -8.13740 q^{31} +1.00000 q^{32} +9.04247 q^{33} +3.49082 q^{34} -0.117873 q^{35} +0.532089 q^{36} +6.74601 q^{38} -3.66138 q^{39} -0.800038 q^{40} -3.89766 q^{41} -0.276898 q^{42} -8.10852 q^{43} -4.81140 q^{44} -0.425691 q^{45} +4.17551 q^{46} +8.33822 q^{47} -1.87939 q^{48} -6.97829 q^{49} -4.35994 q^{50} -6.56060 q^{51} +1.94818 q^{52} -10.8894 q^{53} +4.63816 q^{54} +3.84930 q^{55} +0.147334 q^{56} -12.6784 q^{57} -3.03841 q^{58} -8.67110 q^{59} +1.50358 q^{60} +0.351687 q^{61} -8.13740 q^{62} +0.0783950 q^{63} +1.00000 q^{64} -1.55862 q^{65} +9.04247 q^{66} -2.39941 q^{67} +3.49082 q^{68} -7.84740 q^{69} -0.117873 q^{70} +6.98332 q^{71} +0.532089 q^{72} -1.13399 q^{73} +8.19401 q^{75} +6.74601 q^{76} -0.708885 q^{77} -3.66138 q^{78} -1.89027 q^{79} -0.800038 q^{80} -10.3131 q^{81} -3.89766 q^{82} -9.90490 q^{83} -0.276898 q^{84} -2.79279 q^{85} -8.10852 q^{86} +5.71034 q^{87} -4.81140 q^{88} +10.1141 q^{89} -0.425691 q^{90} +0.287034 q^{91} +4.17551 q^{92} +15.2933 q^{93} +8.33822 q^{94} -5.39707 q^{95} -1.87939 q^{96} -5.87526 q^{97} -6.97829 q^{98} -2.56009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} - 12 q^{13} + 6 q^{15} + 6 q^{16} - 12 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 6 q^{22} + 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{29} + 6 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 12 q^{34} - 24 q^{35} - 6 q^{36} - 12 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} - 12 q^{42} - 6 q^{44} - 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} + 6 q^{50} - 24 q^{51} - 12 q^{52} - 24 q^{53} - 6 q^{54} - 36 q^{55} - 24 q^{57} + 6 q^{58} - 12 q^{59} + 6 q^{60} - 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} + 6 q^{66} + 18 q^{67} - 12 q^{68} - 24 q^{69} - 24 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{75} - 12 q^{76} + 30 q^{77} - 6 q^{78} - 12 q^{79} - 6 q^{80} - 18 q^{81} - 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} - 6 q^{87} - 6 q^{88} - 6 q^{90} - 12 q^{91} + 6 q^{92} + 36 q^{93} - 6 q^{94} + 18 q^{95} + 12 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 - 12 * q^13 + 6 * q^15 + 6 * q^16 - 12 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 6 * q^22 + 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^29 + 6 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 12 * q^34 - 24 * q^35 - 6 * q^36 - 12 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 - 12 * q^42 - 6 * q^44 - 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 + 6 * q^50 - 24 * q^51 - 12 * q^52 - 24 * q^53 - 6 * q^54 - 36 * q^55 - 24 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 + 6 * q^66 + 18 * q^67 - 12 * q^68 - 24 * q^69 - 24 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^75 - 12 * q^76 + 30 * q^77 - 6 * q^78 - 12 * q^79 - 6 * q^80 - 18 * q^81 - 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 - 6 * q^87 - 6 * q^88 - 6 * q^90 - 12 * q^91 + 6 * q^92 + 36 * q^93 - 6 * q^94 + 18 * q^95 + 12 * q^97 - 12 * q^98 + 12 * q^99

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