LMFDB - Embedded newform 3549.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 $ x^8 - 2x^7 - 9x^6 + 14x^5 + 25x^4 - 24x^3 - 16x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.45308$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45308 q^{2} +1.00000 q^{3} +4.01758 q^{4} -0.0682999 q^{5} -2.45308 q^{6} -1.00000 q^{7} -4.94928 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.45308 q^{2} +1.00000 q^{3} +4.01758 q^{4} -0.0682999 q^{5} -2.45308 q^{6} -1.00000 q^{7} -4.94928 q^{8} +1.00000 q^{9} +0.167545 q^{10} +0.678230 q^{11} +4.01758 q^{12} +2.45308 q^{14} -0.0682999 q^{15} +4.10580 q^{16} -0.934958 q^{17} -2.45308 q^{18} -2.06767 q^{19} -0.274400 q^{20} -1.00000 q^{21} -1.66375 q^{22} +4.29948 q^{23} -4.94928 q^{24} -4.99534 q^{25} +1.00000 q^{27} -4.01758 q^{28} +8.01446 q^{29} +0.167545 q^{30} -10.0622 q^{31} -0.173279 q^{32} +0.678230 q^{33} +2.29352 q^{34} +0.0682999 q^{35} +4.01758 q^{36} +0.527492 q^{37} +5.07216 q^{38} +0.338035 q^{40} -5.13776 q^{41} +2.45308 q^{42} -1.78857 q^{43} +2.72485 q^{44} -0.0682999 q^{45} -10.5470 q^{46} -4.22889 q^{47} +4.10580 q^{48} +1.00000 q^{49} +12.2539 q^{50} -0.934958 q^{51} -3.21495 q^{53} -2.45308 q^{54} -0.0463231 q^{55} +4.94928 q^{56} -2.06767 q^{57} -19.6601 q^{58} +8.32746 q^{59} -0.274400 q^{60} +1.01053 q^{61} +24.6833 q^{62} -1.00000 q^{63} -7.78654 q^{64} -1.66375 q^{66} +7.30030 q^{67} -3.75627 q^{68} +4.29948 q^{69} -0.167545 q^{70} -9.91104 q^{71} -4.94928 q^{72} +3.42254 q^{73} -1.29398 q^{74} -4.99534 q^{75} -8.30704 q^{76} -0.678230 q^{77} -14.0484 q^{79} -0.280426 q^{80} +1.00000 q^{81} +12.6033 q^{82} +7.03411 q^{83} -4.01758 q^{84} +0.0638575 q^{85} +4.38750 q^{86} +8.01446 q^{87} -3.35675 q^{88} +15.7543 q^{89} +0.167545 q^{90} +17.2735 q^{92} -10.0622 q^{93} +10.3738 q^{94} +0.141222 q^{95} -0.173279 q^{96} -16.6705 q^{97} -2.45308 q^{98} +0.678230 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * 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 $

$2$	−2.45308	−1.73459	−0.867293	−	0.497797i	$-0.834142\pi$
$2$	−2.45308	−1.73459	−0.867293	+	0.497797i	$0.834142\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.01758	2.00879
$5$	−0.0682999	−0.0305446	−0.0152723	−	0.999883i	$-0.504862\pi$
$5$	−0.0682999	−0.0305446	−0.0152723	+	0.999883i	$0.504862\pi$
$6$	−2.45308	−1.00146
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.94928	−1.74984
$9$	1.00000	0.333333
$10$	0.167545	0.0529823
$11$	0.678230	0.204494	0.102247	−	0.994759i	$-0.467397\pi$
$11$	0.678230	0.204494	0.102247	+	0.994759i	$0.467397\pi$
$12$	4.01758	1.15978
$13$	0	0
$13$	0	0
$14$	2.45308	0.655612
$15$	−0.0682999	−0.0176350
$16$	4.10580	1.02645
$17$	−0.934958	−0.226761	−0.113380	−	0.993552i	$-0.536168\pi$
$17$	−0.934958	−0.226761	−0.113380	+	0.993552i	$0.536168\pi$
$18$	−2.45308	−0.578196
$19$	−2.06767	−0.474356	−0.237178	−	0.971466i	$-0.576223\pi$
$19$	−2.06767	−0.474356	−0.237178	+	0.971466i	$0.576223\pi$
$20$	−0.274400	−0.0613578
$21$	−1.00000	−0.218218
$22$	−1.66375	−0.354713
$23$	4.29948	0.896503	0.448252	−	0.893907i	$-0.352047\pi$
$23$	4.29948	0.896503	0.448252	+	0.893907i	$0.352047\pi$
$24$	−4.94928	−1.01027
$25$	−4.99534	−0.999067
$26$	0	0
$27$	1.00000	0.192450
$28$	−4.01758	−0.759252
$29$	8.01446	1.48825	0.744124	−	0.668042i	$-0.232867\pi$
$29$	8.01446	1.48825	0.744124	+	0.668042i	$0.232867\pi$
$30$	0.167545	0.0305894
$31$	−10.0622	−1.80722	−0.903609	−	0.428358i	$-0.859092\pi$
$31$	−10.0622	−1.80722	−0.903609	+	0.428358i	$0.859092\pi$
$32$	−0.173279	−0.0306316
$33$	0.678230	0.118065
$34$	2.29352	0.393336
$35$	0.0682999	0.0115448
$36$	4.01758	0.669597
$37$	0.527492	0.0867191	0.0433596	−	0.999060i	$-0.486194\pi$
$37$	0.527492	0.0867191	0.0433596	+	0.999060i	$0.486194\pi$
$38$	5.07216	0.822812
$39$	0	0
$40$	0.338035	0.0534481
$41$	−5.13776	−0.802383	−0.401191	−	0.915994i	$-0.631404\pi$
$41$	−5.13776	−0.802383	−0.401191	+	0.915994i	$0.631404\pi$
$42$	2.45308	0.378518
$43$	−1.78857	−0.272755	−0.136377	−	0.990657i	$-0.543546\pi$
$43$	−1.78857	−0.272755	−0.136377	+	0.990657i	$0.543546\pi$
$44$	2.72485	0.410786
$45$	−0.0682999	−0.0101815
$46$	−10.5470	−1.55506
$47$	−4.22889	−0.616846	−0.308423	−	0.951249i	$-0.599801\pi$
$47$	−4.22889	−0.616846	−0.308423	+	0.951249i	$0.599801\pi$
$48$	4.10580	0.592621
$49$	1.00000	0.142857
$50$	12.2539	1.73297
$51$	−0.934958	−0.130920
$52$	0	0
$53$	−3.21495	−0.441608	−0.220804	−	0.975318i	$-0.570868\pi$
$53$	−3.21495	−0.441608	−0.220804	+	0.975318i	$0.570868\pi$
$54$	−2.45308	−0.333821
$55$	−0.0463231	−0.00624620
$56$	4.94928	0.661376
$57$	−2.06767	−0.273870
$58$	−19.6601	−2.58149
$59$	8.32746	1.08414	0.542071	−	0.840332i	$-0.317640\pi$
$59$	8.32746	1.08414	0.542071	+	0.840332i	$0.317640\pi$
$60$	−0.274400	−0.0354249
$61$	1.01053	0.129386	0.0646928	−	0.997905i	$-0.479393\pi$
$61$	1.01053	0.129386	0.0646928	+	0.997905i	$0.479393\pi$
$62$	24.6833	3.13478
$63$	−1.00000	−0.125988
$64$	−7.78654	−0.973317
$65$	0	0
$66$	−1.66375	−0.204794
$67$	7.30030	0.891874	0.445937	−	0.895064i	$-0.352871\pi$
$67$	7.30030	0.891874	0.445937	+	0.895064i	$0.352871\pi$
$68$	−3.75627	−0.455515
$69$	4.29948	0.517597
$70$	−0.167545	−0.0200254
$71$	−9.91104	−1.17622	−0.588112	−	0.808779i	$-0.700129\pi$
$71$	−9.91104	−1.17622	−0.588112	+	0.808779i	$0.700129\pi$
$72$	−4.94928	−0.583278
$73$	3.42254	0.400578	0.200289	−	0.979737i	$-0.435812\pi$
$73$	3.42254	0.400578	0.200289	+	0.979737i	$0.435812\pi$
$74$	−1.29398	−0.150422
$75$	−4.99534	−0.576812
$76$	−8.30704	−0.952883
$77$	−0.678230	−0.0772915
$78$	0	0
$79$	−14.0484	−1.58057	−0.790283	−	0.612742i	$-0.790066\pi$
$79$	−14.0484	−1.58057	−0.790283	+	0.612742i	$0.790066\pi$
$80$	−0.280426	−0.0313526
$81$	1.00000	0.111111
$82$	12.6033	1.39180
$83$	7.03411	0.772094	0.386047	−	0.922479i	$-0.373840\pi$
$83$	7.03411	0.772094	0.386047	+	0.922479i	$0.373840\pi$
$84$	−4.01758	−0.438354
$85$	0.0638575	0.00692632
$86$	4.38750	0.473117
$87$	8.01446	0.859240
$88$	−3.35675	−0.357831
$89$	15.7543	1.66995	0.834975	−	0.550288i	$-0.185482\pi$
$89$	15.7543	1.66995	0.834975	+	0.550288i	$0.185482\pi$
$90$	0.167545	0.0176608
$91$	0	0
$92$	17.2735	1.80089
$93$	−10.0622	−1.04340
$94$	10.3738	1.06997
$95$	0.141222	0.0144890
$96$	−0.173279	−0.0176852
$97$	−16.6705	−1.69263	−0.846314	−	0.532684i	$-0.821183\pi$
$97$	−16.6705	−1.69263	−0.846314	+	0.532684i	$0.821183\pi$
$98$	−2.45308	−0.247798
$99$	0.678230	0.0681647
$100$	−20.0692	−2.00692
$101$	−1.50429	−0.149682	−0.0748412	−	0.997195i	$-0.523845\pi$
$101$	−1.50429	−0.149682	−0.0748412	+	0.997195i	$0.523845\pi$
$102$	2.29352	0.227093
$103$	−2.21721	−0.218468	−0.109234	−	0.994016i	$-0.534840\pi$
$103$	−2.21721	−0.218468	−0.109234	+	0.994016i	$0.534840\pi$
$104$	0	0
$105$	0.0682999	0.00666539
$106$	7.88652	0.766007
$107$	−19.7860	−1.91278	−0.956390	−	0.292092i	$-0.905649\pi$
$107$	−19.7860	−1.91278	−0.956390	+	0.292092i	$0.905649\pi$
$108$	4.01758	0.386592
$109$	−1.71086	−0.163870	−0.0819352	−	0.996638i	$-0.526110\pi$
$109$	−1.71086	−0.163870	−0.0819352	+	0.996638i	$0.526110\pi$
$110$	0.113634	0.0108346
$111$	0.527492	0.0500673
$112$	−4.10580	−0.387962
$113$	−13.6392	−1.28307	−0.641536	−	0.767093i	$-0.721702\pi$
$113$	−13.6392	−1.28307	−0.641536	+	0.767093i	$0.721702\pi$
$114$	5.07216	0.475051
$115$	−0.293654	−0.0273834
$116$	32.1987	2.98958
$117$	0	0
$118$	−20.4279	−1.88054
$119$	0.934958	0.0857075
$120$	0.338035	0.0308583
$121$	−10.5400	−0.958182
$122$	−2.47892	−0.224430
$123$	−5.13776	−0.463256
$124$	−40.4256	−3.63032
$125$	0.682680	0.0610608
$126$	2.45308	0.218537
$127$	−8.00439	−0.710275	−0.355138	−	0.934814i	$-0.615566\pi$
$127$	−8.00439	−0.710275	−0.355138	+	0.934814i	$0.615566\pi$
$128$	19.4475	1.71893
$129$	−1.78857	−0.157475
$130$	0	0
$131$	−10.2912	−0.899146	−0.449573	−	0.893244i	$-0.648424\pi$
$131$	−10.2912	−0.899146	−0.449573	+	0.893244i	$0.648424\pi$
$132$	2.72485	0.237167
$133$	2.06767	0.179290
$134$	−17.9082	−1.54703
$135$	−0.0682999	−0.00587832
$136$	4.62737	0.396794
$137$	3.61956	0.309239	0.154620	−	0.987974i	$-0.450585\pi$
$137$	3.61956	0.309239	0.154620	+	0.987974i	$0.450585\pi$
$138$	−10.5470	−0.897816
$139$	1.21815	0.103322	0.0516610	−	0.998665i	$-0.483548\pi$
$139$	1.21815	0.103322	0.0516610	+	0.998665i	$0.483548\pi$
$140$	0.274400	0.0231911
$141$	−4.22889	−0.356136
$142$	24.3125	2.04026
$143$	0	0
$144$	4.10580	0.342150
$145$	−0.547387	−0.0454580
$146$	−8.39574	−0.694836
$147$	1.00000	0.0824786
$148$	2.11924	0.174201
$149$	−16.5273	−1.35397	−0.676983	−	0.735999i	$-0.736713\pi$
$149$	−16.5273	−1.35397	−0.676983	+	0.735999i	$0.736713\pi$
$150$	12.2539	1.00053
$151$	20.3543	1.65641	0.828206	−	0.560424i	$-0.189362\pi$
$151$	20.3543	1.65641	0.828206	+	0.560424i	$0.189362\pi$
$152$	10.2335	0.830046
$153$	−0.934958	−0.0755869
$154$	1.66375	0.134069
$155$	0.687245	0.0552008
$156$	0	0
$157$	15.1583	1.20976	0.604881	−	0.796316i	$-0.293221\pi$
$157$	15.1583	1.20976	0.604881	+	0.796316i	$0.293221\pi$
$158$	34.4617	2.74163
$159$	−3.21495	−0.254962
$160$	0.0118349	0.000935632 0
$161$	−4.29948	−0.338846
$162$	−2.45308	−0.192732
$163$	−16.8412	−1.31910	−0.659551	−	0.751660i	$-0.729253\pi$
$163$	−16.8412	−1.31910	−0.659551	+	0.751660i	$0.729253\pi$
$164$	−20.6414	−1.61182
$165$	−0.0463231	−0.00360625
$166$	−17.2552	−1.33926
$167$	1.65129	0.127780	0.0638902	−	0.997957i	$-0.479649\pi$
$167$	1.65129	0.127780	0.0638902	+	0.997957i	$0.479649\pi$
$168$	4.94928	0.381845
$169$	0	0
$170$	−0.156647	−0.0120143
$171$	−2.06767	−0.158119
$172$	−7.18574	−0.547907
$173$	24.7787	1.88389	0.941943	−	0.335772i	$-0.108997\pi$
$173$	24.7787	1.88389	0.941943	+	0.335772i	$0.108997\pi$
$174$	−19.6601	−1.49043
$175$	4.99534	0.377612
$176$	2.78468	0.209903
$177$	8.32746	0.625930
$178$	−38.6465	−2.89667
$179$	−6.30284	−0.471097	−0.235548	−	0.971863i	$-0.575689\pi$
$179$	−6.30284	−0.471097	−0.235548	+	0.971863i	$0.575689\pi$
$180$	−0.274400	−0.0204526
$181$	−18.9468	−1.40830	−0.704152	−	0.710049i	$-0.748673\pi$
$181$	−18.9468	−1.40830	−0.704152	+	0.710049i	$0.748673\pi$
$182$	0	0
$183$	1.01053	0.0747008
$184$	−21.2793	−1.56873
$185$	−0.0360276	−0.00264880
$186$	24.6833	1.80986
$187$	−0.634117	−0.0463712
$188$	−16.9899	−1.23912
$189$	−1.00000	−0.0727393
$190$	−0.346428	−0.0251325
$191$	−8.79410	−0.636319	−0.318159	−	0.948037i	$-0.603065\pi$
$191$	−8.79410	−0.636319	−0.318159	+	0.948037i	$0.603065\pi$
$192$	−7.78654	−0.561945
$193$	6.19901	0.446215	0.223107	−	0.974794i	$-0.428380\pi$
$193$	6.19901	0.446215	0.223107	+	0.974794i	$0.428380\pi$
$194$	40.8939	2.93601
$195$	0	0
$196$	4.01758	0.286970
$197$	15.1434	1.07892	0.539460	−	0.842011i	$-0.318629\pi$
$197$	15.1434	1.07892	0.539460	+	0.842011i	$0.318629\pi$
$198$	−1.66375	−0.118238
$199$	15.0372	1.06596	0.532979	−	0.846128i	$-0.321072\pi$
$199$	15.0372	1.06596	0.532979	+	0.846128i	$0.321072\pi$
$200$	24.7233	1.74820
$201$	7.30030	0.514924
$202$	3.69014	0.259637
$203$	−8.01446	−0.562505
$204$	−3.75627	−0.262992
$205$	0.350908	0.0245085
$206$	5.43898	0.378952
$207$	4.29948	0.298834
$208$	0	0
$209$	−1.40236	−0.0970031
$210$	−0.167545	−0.0115617
$211$	25.4741	1.75371	0.876856	−	0.480752i	$-0.159636\pi$
$211$	25.4741	1.75371	0.876856	+	0.480752i	$0.159636\pi$
$212$	−12.9163	−0.887097
$213$	−9.91104	−0.679093
$214$	48.5365	3.31788
$215$	0.122159	0.00833119
$216$	−4.94928	−0.336756
$217$	10.0622	0.683064
$218$	4.19686	0.284248
$219$	3.42254	0.231274
$220$	−0.186107	−0.0125473
$221$	0	0
$222$	−1.29398	−0.0868461
$223$	7.00654	0.469192	0.234596	−	0.972093i	$-0.424623\pi$
$223$	7.00654	0.469192	0.234596	+	0.972093i	$0.424623\pi$
$224$	0.173279	0.0115777
$225$	−4.99534	−0.333022
$226$	33.4581	2.22560
$227$	27.7571	1.84230	0.921151	−	0.389206i	$-0.127251\pi$
$227$	27.7571	1.84230	0.921151	+	0.389206i	$0.127251\pi$
$228$	−8.30704	−0.550147
$229$	−3.61011	−0.238563	−0.119281	−	0.992860i	$-0.538059\pi$
$229$	−3.61011	−0.238563	−0.119281	+	0.992860i	$0.538059\pi$
$230$	0.720355	0.0474988
$231$	−0.678230	−0.0446243
$232$	−39.6658	−2.60419
$233$	−15.6176	−1.02315	−0.511573	−	0.859240i	$-0.670937\pi$
$233$	−15.6176	−1.02315	−0.511573	+	0.859240i	$0.670937\pi$
$234$	0	0
$235$	0.288832	0.0188413
$236$	33.4562	2.17782
$237$	−14.0484	−0.912540
$238$	−2.29352	−0.148667
$239$	−27.9831	−1.81008	−0.905038	−	0.425332i	$-0.860157\pi$
$239$	−27.9831	−1.81008	−0.905038	+	0.425332i	$0.860157\pi$
$240$	−0.280426	−0.0181014
$241$	−25.9732	−1.67308	−0.836541	−	0.547904i	$-0.815426\pi$
$241$	−25.9732	−1.67308	−0.836541	+	0.547904i	$0.815426\pi$
$242$	25.8554	1.66205
$243$	1.00000	0.0641500
$244$	4.05990	0.259909
$245$	−0.0682999	−0.00436352
$246$	12.6033	0.803558
$247$	0	0
$248$	49.8005	3.16233
$249$	7.03411	0.445769
$250$	−1.67467	−0.105915
$251$	−6.38525	−0.403033	−0.201517	−	0.979485i	$-0.564587\pi$
$251$	−6.38525	−0.403033	−0.201517	+	0.979485i	$0.564587\pi$
$252$	−4.01758	−0.253084
$253$	2.91604	0.183330
$254$	19.6354	1.23203
$255$	0.0638575	0.00399891
$256$	−32.1332	−2.00832
$257$	−13.8179	−0.861934	−0.430967	−	0.902368i	$-0.641827\pi$
$257$	−13.8179	−0.861934	−0.430967	+	0.902368i	$0.641827\pi$
$258$	4.38750	0.273154
$259$	−0.527492	−0.0327767
$260$	0	0
$261$	8.01446	0.496083
$262$	25.2451	1.55965
$263$	−11.3364	−0.699033	−0.349517	−	0.936930i	$-0.613654\pi$
$263$	−11.3364	−0.699033	−0.349517	+	0.936930i	$0.613654\pi$
$264$	−3.35675	−0.206594
$265$	0.219581	0.0134887
$266$	−5.07216	−0.310994
$267$	15.7543	0.964146
$268$	29.3296	1.79159
$269$	21.0002	1.28040	0.640202	−	0.768206i	$-0.278851\pi$
$269$	21.0002	1.28040	0.640202	+	0.768206i	$0.278851\pi$
$270$	0.167545	0.0101965
$271$	−29.2450	−1.77651	−0.888253	−	0.459354i	$-0.848081\pi$
$271$	−29.2450	−1.77651	−0.888253	+	0.459354i	$0.848081\pi$
$272$	−3.83875	−0.232759
$273$	0	0
$274$	−8.87904	−0.536403
$275$	−3.38799	−0.204303
$276$	17.2735	1.03974
$277$	16.5036	0.991603	0.495801	−	0.868436i	$-0.334874\pi$
$277$	16.5036	0.991603	0.495801	+	0.868436i	$0.334874\pi$
$278$	−2.98821	−0.179221
$279$	−10.0622	−0.602406
$280$	−0.338035	−0.0202015
$281$	−1.12161	−0.0669094	−0.0334547	−	0.999440i	$-0.510651\pi$
$281$	−1.12161	−0.0669094	−0.0334547	+	0.999440i	$0.510651\pi$
$282$	10.3738	0.617749
$283$	10.9412	0.650387	0.325194	−	0.945647i	$-0.394571\pi$
$283$	10.9412	0.650387	0.325194	+	0.945647i	$0.394571\pi$
$284$	−39.8184	−2.36279
$285$	0.141222	0.00836525
$286$	0	0
$287$	5.13776	0.303272
$288$	−0.173279	−0.0102105
$289$	−16.1259	−0.948580
$290$	1.34278	0.0788508
$291$	−16.6705	−0.977239
$292$	13.7503	0.804677
$293$	15.5503	0.908457	0.454229	−	0.890885i	$-0.349915\pi$
$293$	15.5503	0.908457	0.454229	+	0.890885i	$0.349915\pi$
$294$	−2.45308	−0.143066
$295$	−0.568764	−0.0331147
$296$	−2.61071	−0.151744
$297$	0.678230	0.0393549
$298$	40.5426	2.34857
$299$	0	0
$300$	−20.0692	−1.15869
$301$	1.78857	0.103092
$302$	−49.9307	−2.87319
$303$	−1.50429	−0.0864192
$304$	−8.48945	−0.486903
$305$	−0.0690193	−0.00395203
$306$	2.29352	0.131112
$307$	−0.119003	−0.00679184	−0.00339592	−	0.999994i	$-0.501081\pi$
$307$	−0.119003	−0.00679184	−0.00339592	+	0.999994i	$0.501081\pi$
$308$	−2.72485	−0.155263
$309$	−2.21721	−0.126133
$310$	−1.68586	−0.0957506
$311$	−31.4738	−1.78472	−0.892358	−	0.451327i	$-0.850951\pi$
$311$	−31.4738	−1.78472	−0.892358	+	0.451327i	$0.850951\pi$
$312$	0	0
$313$	14.1243	0.798355	0.399178	−	0.916874i	$-0.369296\pi$
$313$	14.1243	0.798355	0.399178	+	0.916874i	$0.369296\pi$
$314$	−37.1844	−2.09844
$315$	0.0682999	0.00384826
$316$	−56.4405	−3.17503
$317$	−18.6470	−1.04732	−0.523661	−	0.851927i	$-0.675434\pi$
$317$	−18.6470	−1.04732	−0.523661	+	0.851927i	$0.675434\pi$
$318$	7.88652	0.442254
$319$	5.43565	0.304338
$320$	0.531820	0.0297296
$321$	−19.7860	−1.10434
$322$	10.5470	0.587759
$323$	1.93319	0.107565
$324$	4.01758	0.223199
$325$	0	0
$326$	41.3126	2.28810
$327$	−1.71086	−0.0946107
$328$	25.4282	1.40404
$329$	4.22889	0.233146
$330$	0.113634	0.00625535
$331$	−22.0843	−1.21386	−0.606930	−	0.794755i	$-0.707599\pi$
$331$	−22.0843	−1.21386	−0.606930	+	0.794755i	$0.707599\pi$
$332$	28.2601	1.55098
$333$	0.527492	0.0289064
$334$	−4.05073	−0.221646
$335$	−0.498610	−0.0272420
$336$	−4.10580	−0.223990
$337$	−32.5355	−1.77232	−0.886161	−	0.463377i	$-0.846638\pi$
$337$	−32.5355	−1.77232	−0.886161	+	0.463377i	$0.846638\pi$
$338$	0	0
$339$	−13.6392	−0.740782
$340$	0.256553	0.0139135
$341$	−6.82447	−0.369566
$342$	5.07216	0.274271
$343$	−1.00000	−0.0539949
$344$	8.85215	0.477276
$345$	−0.293654	−0.0158098
$346$	−60.7839	−3.26776
$347$	4.41223	0.236861	0.118431	−	0.992962i	$-0.462214\pi$
$347$	4.41223	0.236861	0.118431	+	0.992962i	$0.462214\pi$
$348$	32.1987	1.72603
$349$	−7.12421	−0.381350	−0.190675	−	0.981653i	$-0.561068\pi$
$349$	−7.12421	−0.381350	−0.190675	+	0.981653i	$0.561068\pi$
$350$	−12.2539	−0.655000
$351$	0	0
$352$	−0.117523	−0.00626399
$353$	−3.33664	−0.177591	−0.0887957	−	0.996050i	$-0.528302\pi$
$353$	−3.33664	−0.177591	−0.0887957	+	0.996050i	$0.528302\pi$
$354$	−20.4279	−1.08573
$355$	0.676923	0.0359273
$356$	63.2941	3.35458
$357$	0.934958	0.0494832
$358$	15.4614	0.817158
$359$	24.5869	1.29765	0.648823	−	0.760940i	$-0.275262\pi$
$359$	24.5869	1.29765	0.648823	+	0.760940i	$0.275262\pi$
$360$	0.338035	0.0178160
$361$	−14.7247	−0.774986
$362$	46.4779	2.44282
$363$	−10.5400	−0.553207
$364$	0	0
$365$	−0.233759	−0.0122355
$366$	−2.47892	−0.129575
$367$	−15.0766	−0.786991	−0.393495	−	0.919327i	$-0.628734\pi$
$367$	−15.0766	−0.786991	−0.393495	+	0.919327i	$0.628734\pi$
$368$	17.6528	0.920216
$369$	−5.13776	−0.267461
$370$	0.0883785	0.00459458
$371$	3.21495	0.166912
$372$	−40.4256	−2.09597
$373$	−25.2471	−1.30725	−0.653623	−	0.756820i	$-0.726752\pi$
$373$	−25.2471	−1.30725	−0.653623	+	0.756820i	$0.726752\pi$
$374$	1.55554	0.0804349
$375$	0.682680	0.0352535
$376$	20.9299	1.07938
$377$	0	0
$378$	2.45308	0.126173
$379$	−24.0432	−1.23502	−0.617508	−	0.786565i	$-0.711858\pi$
$379$	−24.0432	−1.23502	−0.617508	+	0.786565i	$0.711858\pi$
$380$	0.567370	0.0291055
$381$	−8.00439	−0.410077
$382$	21.5726	1.10375
$383$	4.53923	0.231944	0.115972	−	0.993252i	$-0.463002\pi$
$383$	4.53923	0.231944	0.115972	+	0.993252i	$0.463002\pi$
$384$	19.4475	0.992427
$385$	0.0463231	0.00236084
$386$	−15.2067	−0.773998
$387$	−1.78857	−0.0909182
$388$	−66.9749	−3.40014
$389$	19.7847	1.00313	0.501563	−	0.865121i	$-0.332758\pi$
$389$	19.7847	1.00313	0.501563	+	0.865121i	$0.332758\pi$
$390$	0	0
$391$	−4.01983	−0.203292
$392$	−4.94928	−0.249976
$393$	−10.2912	−0.519122
$394$	−37.1478	−1.87148
$395$	0.959502	0.0482778
$396$	2.72485	0.136929
$397$	−10.4584	−0.524892	−0.262446	−	0.964947i	$-0.584529\pi$
$397$	−10.4584	−0.524892	−0.262446	+	0.964947i	$0.584529\pi$
$398$	−36.8874	−1.84900
$399$	2.06767	0.103513
$400$	−20.5099	−1.02549
$401$	−22.4236	−1.11978	−0.559891	−	0.828566i	$-0.689157\pi$
$401$	−22.4236	−1.11978	−0.559891	+	0.828566i	$0.689157\pi$
$402$	−17.9082	−0.893180
$403$	0	0
$404$	−6.04361	−0.300681
$405$	−0.0682999	−0.00339385
$406$	19.6601	0.975713
$407$	0.357761	0.0177336
$408$	4.62737	0.229089
$409$	−24.4405	−1.20851	−0.604253	−	0.796793i	$-0.706528\pi$
$409$	−24.4405	−1.20851	−0.604253	+	0.796793i	$0.706528\pi$
$410$	−0.860805	−0.0425121
$411$	3.61956	0.178539
$412$	−8.90782	−0.438857
$413$	−8.32746	−0.409767
$414$	−10.5470	−0.518354
$415$	−0.480429	−0.0235833
$416$	0	0
$417$	1.21815	0.0596529
$418$	3.44009	0.168260
$419$	27.7961	1.35793	0.678965	−	0.734170i	$-0.262429\pi$
$419$	27.7961	1.35793	0.678965	+	0.734170i	$0.262429\pi$
$420$	0.274400	0.0133894
$421$	15.8324	0.771626	0.385813	−	0.922577i	$-0.373921\pi$
$421$	15.8324	0.771626	0.385813	+	0.922577i	$0.373921\pi$
$422$	−62.4900	−3.04197
$423$	−4.22889	−0.205615
$424$	15.9117	0.772741
$425$	4.67043	0.226549
$426$	24.3125	1.17795
$427$	−1.01053	−0.0489031
$428$	−79.4917	−3.84238
$429$	0	0
$430$	−0.299666	−0.0144512
$431$	−18.2098	−0.877135	−0.438567	−	0.898698i	$-0.644514\pi$
$431$	−18.2098	−0.877135	−0.438567	+	0.898698i	$0.644514\pi$
$432$	4.10580	0.197540
$433$	−9.40449	−0.451951	−0.225975	−	0.974133i	$-0.572557\pi$
$433$	−9.40449	−0.451951	−0.225975	+	0.974133i	$0.572557\pi$
$434$	−24.6833	−1.18483
$435$	−0.547387	−0.0262452
$436$	−6.87351	−0.329182
$437$	−8.88991	−0.425262
$438$	−8.39574	−0.401164
$439$	−19.2339	−0.917984	−0.458992	−	0.888440i	$-0.651789\pi$
$439$	−19.2339	−0.917984	−0.458992	+	0.888440i	$0.651789\pi$
$440$	0.229266	0.0109298
$441$	1.00000	0.0476190
$442$	0	0
$443$	−5.40445	−0.256773	−0.128387	−	0.991724i	$-0.540980\pi$
$443$	−5.40445	−0.256773	−0.128387	+	0.991724i	$0.540980\pi$
$444$	2.11924	0.100575
$445$	−1.07602	−0.0510080
$446$	−17.1876	−0.813855
$447$	−16.5273	−0.781713
$448$	7.78654	0.367879
$449$	13.5534	0.639623	0.319812	−	0.947481i	$-0.396380\pi$
$449$	13.5534	0.639623	0.319812	+	0.947481i	$0.396380\pi$
$450$	12.2539	0.577656
$451$	−3.48458	−0.164083
$452$	−54.7968	−2.57742
$453$	20.3543	0.956329
$454$	−68.0902	−3.19563
$455$	0	0
$456$	10.2335	0.479227
$457$	29.8229	1.39506	0.697528	−	0.716558i	$-0.254283\pi$
$457$	29.8229	1.39506	0.697528	+	0.716558i	$0.254283\pi$
$458$	8.85588	0.413808
$459$	−0.934958	−0.0436401
$460$	−1.17978	−0.0550075
$461$	−2.22803	−0.103770	−0.0518849	−	0.998653i	$-0.516523\pi$
$461$	−2.22803	−0.103770	−0.0518849	+	0.998653i	$0.516523\pi$
$462$	1.66375	0.0774047
$463$	−21.6086	−1.00424	−0.502118	−	0.864799i	$-0.667446\pi$
$463$	−21.6086	−1.00424	−0.502118	+	0.864799i	$0.667446\pi$
$464$	32.9058	1.52761
$465$	0.687245	0.0318702
$466$	38.3112	1.77473
$467$	−24.0068	−1.11090	−0.555452	−	0.831549i	$-0.687455\pi$
$467$	−24.0068	−1.11090	−0.555452	+	0.831549i	$0.687455\pi$
$468$	0	0
$469$	−7.30030	−0.337097
$470$	−0.708528	−0.0326819
$471$	15.1583	0.698456
$472$	−41.2149	−1.89707
$473$	−1.21306	−0.0557767
$474$	34.4617	1.58288
$475$	10.3287	0.473914
$476$	3.75627	0.172168
$477$	−3.21495	−0.147203
$478$	68.6446	3.13973
$479$	−30.6921	−1.40236	−0.701179	−	0.712985i	$-0.747343\pi$
$479$	−30.6921	−1.40236	−0.701179	+	0.712985i	$0.747343\pi$
$480$	0.0118349	0.000540187 0
$481$	0	0
$482$	63.7143	2.90211
$483$	−4.29948	−0.195633
$484$	−42.3453	−1.92479
$485$	1.13859	0.0517007
$486$	−2.45308	−0.111274
$487$	17.8707	0.809798	0.404899	−	0.914361i	$-0.367307\pi$
$487$	17.8707	0.809798	0.404899	+	0.914361i	$0.367307\pi$
$488$	−5.00142	−0.226403
$489$	−16.8412	−0.761583
$490$	0.167545	0.00756890
$491$	−13.5696	−0.612388	−0.306194	−	0.951969i	$-0.599056\pi$
$491$	−13.5696	−0.612388	−0.306194	+	0.951969i	$0.599056\pi$
$492$	−20.6414	−0.930585
$493$	−7.49318	−0.337476
$494$	0	0
$495$	−0.0463231	−0.00208207
$496$	−41.3132	−1.85502
$497$	9.91104	0.444571
$498$	−17.2552	−0.773225
$499$	−10.4240	−0.466644	−0.233322	−	0.972399i	$-0.574960\pi$
$499$	−10.4240	−0.466644	−0.233322	+	0.972399i	$0.574960\pi$
$500$	2.74272	0.122658
$501$	1.65129	0.0737740
$502$	15.6635	0.699096
$503$	5.04813	0.225085	0.112543	−	0.993647i	$-0.464101\pi$
$503$	5.04813	0.225085	0.112543	+	0.993647i	$0.464101\pi$
$504$	4.94928	0.220459
$505$	0.102743	0.00457199
$506$	−7.15326	−0.318001
$507$	0	0
$508$	−32.1583	−1.42679
$509$	8.99245	0.398583	0.199292	−	0.979940i	$-0.436136\pi$
$509$	8.99245	0.398583	0.199292	+	0.979940i	$0.436136\pi$
$510$	−0.156647	−0.00693646
$511$	−3.42254	−0.151404
$512$	39.9301	1.76468
$513$	−2.06767	−0.0912899
$514$	33.8962	1.49510
$515$	0.151435	0.00667303
$516$	−7.18574	−0.316334
$517$	−2.86816	−0.126141
$518$	1.29398	0.0568541
$519$	24.7787	1.08766
$520$	0	0
$521$	−9.21666	−0.403789	−0.201895	−	0.979407i	$-0.564710\pi$
$521$	−9.21666	−0.403789	−0.201895	+	0.979407i	$0.564710\pi$
$522$	−19.6601	−0.860498
$523$	18.6656	0.816191	0.408096	−	0.912939i	$-0.366193\pi$
$523$	18.6656	0.816191	0.408096	+	0.912939i	$0.366193\pi$
$524$	−41.3457	−1.80620
$525$	4.99534	0.218014
$526$	27.8091	1.21253
$527$	9.40770	0.409806
$528$	2.78468	0.121188
$529$	−4.51447	−0.196281
$530$	−0.538648	−0.0233974
$531$	8.32746	0.361381
$532$	8.30704	0.360156
$533$	0	0
$534$	−38.6465	−1.67240
$535$	1.35138	0.0584252
$536$	−36.1313	−1.56063
$537$	−6.30284	−0.271988
$538$	−51.5151	−2.22097
$539$	0.678230	0.0292135
$540$	−0.274400	−0.0118083
$541$	−16.3383	−0.702437	−0.351219	−	0.936293i	$-0.614233\pi$
$541$	−16.3383	−0.702437	−0.351219	+	0.936293i	$0.614233\pi$
$542$	71.7402	3.08150
$543$	−18.9468	−0.813085
$544$	0.162008	0.00694605
$545$	0.116851	0.00500536
$546$	0	0
$547$	5.07719	0.217085	0.108542	−	0.994092i	$-0.465382\pi$
$547$	5.07719	0.217085	0.108542	+	0.994092i	$0.465382\pi$
$548$	14.5419	0.621197
$549$	1.01053	0.0431285
$550$	8.31099	0.354382
$551$	−16.5713	−0.705960
$552$	−21.2793	−0.905709
$553$	14.0484	0.597398
$554$	−40.4845	−1.72002
$555$	−0.0360276	−0.00152929
$556$	4.89401	0.207552
$557$	−1.28369	−0.0543917	−0.0271959	−	0.999630i	$-0.508658\pi$
$557$	−1.28369	−0.0543917	−0.0271959	+	0.999630i	$0.508658\pi$
$558$	24.6833	1.04493
$559$	0	0
$560$	0.280426	0.0118502
$561$	−0.634117	−0.0267725
$562$	2.75138	0.116060
$563$	16.9798	0.715613	0.357807	−	0.933796i	$-0.383525\pi$
$563$	16.9798	0.715613	0.357807	+	0.933796i	$0.383525\pi$
$564$	−16.9899	−0.715404
$565$	0.931558	0.0391909
$566$	−26.8396	−1.12815
$567$	−1.00000	−0.0419961
$568$	49.0525	2.05820
$569$	−35.9628	−1.50764	−0.753820	−	0.657080i	$-0.771791\pi$
$569$	−35.9628	−1.50764	−0.753820	+	0.657080i	$0.771791\pi$
$570$	−0.346428	−0.0145103
$571$	−20.6811	−0.865475	−0.432738	−	0.901520i	$-0.642452\pi$
$571$	−20.6811	−0.865475	−0.432738	+	0.901520i	$0.642452\pi$
$572$	0	0
$573$	−8.79410	−0.367379
$574$	−12.6033	−0.526052
$575$	−21.4773	−0.895667
$576$	−7.78654	−0.324439
$577$	3.67781	0.153109	0.0765546	−	0.997065i	$-0.475608\pi$
$577$	3.67781	0.153109	0.0765546	+	0.997065i	$0.475608\pi$
$578$	39.5579	1.64539
$579$	6.19901	0.257622
$580$	−2.19917	−0.0913156
$581$	−7.03411	−0.291824
$582$	40.8939	1.69511
$583$	−2.18048	−0.0903062
$584$	−16.9391	−0.700945
$585$	0	0
$586$	−38.1460	−1.57580
$587$	−12.0433	−0.497078	−0.248539	−	0.968622i	$-0.579950\pi$
$587$	−12.0433	−0.497078	−0.248539	+	0.968622i	$0.579950\pi$
$588$	4.01758	0.165682
$589$	20.8052	0.857265
$590$	1.39522	0.0574404
$591$	15.1434	0.622914
$592$	2.16578	0.0890129
$593$	24.4737	1.00501	0.502507	−	0.864573i	$-0.332411\pi$
$593$	24.4737	1.00501	0.502507	+	0.864573i	$0.332411\pi$
$594$	−1.66375	−0.0682645
$595$	−0.0638575	−0.00261790
$596$	−66.3996	−2.71984
$597$	15.0372	0.615431
$598$	0	0
$599$	−21.8012	−0.890773	−0.445387	−	0.895338i	$-0.646934\pi$
$599$	−21.8012	−0.890773	−0.445387	+	0.895338i	$0.646934\pi$
$600$	24.7233	1.00933
$601$	6.58213	0.268491	0.134245	−	0.990948i	$-0.457139\pi$
$601$	6.58213	0.268491	0.134245	+	0.990948i	$0.457139\pi$
$602$	−4.38750	−0.178821
$603$	7.30030	0.297291
$604$	81.7752	3.32738
$605$	0.719881	0.0292673
$606$	3.69014	0.149902
$607$	45.6933	1.85463	0.927317	−	0.374278i	$-0.122109\pi$
$607$	45.6933	1.85463	0.927317	+	0.374278i	$0.122109\pi$
$608$	0.358283	0.0145303
$609$	−8.01446	−0.324762
$610$	0.169310	0.00685515
$611$	0	0
$612$	−3.75627	−0.151838
$613$	41.9953	1.69618	0.848088	−	0.529855i	$-0.177754\pi$
$613$	41.9953	1.69618	0.848088	+	0.529855i	$0.177754\pi$
$614$	0.291923	0.0117810
$615$	0.350908	0.0141500
$616$	3.35675	0.135247
$617$	−24.4374	−0.983811	−0.491906	−	0.870648i	$-0.663700\pi$
$617$	−24.4374	−0.983811	−0.491906	+	0.870648i	$0.663700\pi$
$618$	5.43898	0.218788
$619$	−24.1245	−0.969644	−0.484822	−	0.874613i	$-0.661116\pi$
$619$	−24.1245	−0.969644	−0.484822	+	0.874613i	$0.661116\pi$
$620$	2.76106	0.110887
$621$	4.29948	0.172532
$622$	77.2077	3.09575
$623$	−15.7543	−0.631182
$624$	0	0
$625$	24.9300	0.997202
$626$	−34.6481	−1.38482
$627$	−1.40236	−0.0560048
$628$	60.8996	2.43016
$629$	−0.493183	−0.0196645
$630$	−0.167545	−0.00667514
$631$	−23.5737	−0.938456	−0.469228	−	0.883077i	$-0.655468\pi$
$631$	−23.5737	−0.938456	−0.469228	+	0.883077i	$0.655468\pi$
$632$	69.5294	2.76573
$633$	25.4741	1.01251
$634$	45.7426	1.81667
$635$	0.546699	0.0216951
$636$	−12.9163	−0.512166
$637$	0	0
$638$	−13.3341	−0.527901
$639$	−9.91104	−0.392075
$640$	−1.32826	−0.0525042
$641$	36.8958	1.45730	0.728648	−	0.684889i	$-0.240149\pi$
$641$	36.8958	1.45730	0.728648	+	0.684889i	$0.240149\pi$
$642$	48.5365	1.91558
$643$	−25.1777	−0.992911	−0.496455	−	0.868062i	$-0.665365\pi$
$643$	−25.1777	−0.992911	−0.496455	+	0.868062i	$0.665365\pi$
$644$	−17.2735	−0.680672
$645$	0.122159	0.00481002
$646$	−4.74225	−0.186581
$647$	5.00172	0.196638	0.0983189	−	0.995155i	$-0.468653\pi$
$647$	5.00172	0.196638	0.0983189	+	0.995155i	$0.468653\pi$
$648$	−4.94928	−0.194426
$649$	5.64794	0.221701
$650$	0	0
$651$	10.0622	0.394367
$652$	−67.6607	−2.64980
$653$	−27.8545	−1.09003	−0.545015	−	0.838426i	$-0.683476\pi$
$653$	−27.8545	−1.09003	−0.545015	+	0.838426i	$0.683476\pi$
$654$	4.19686	0.164110
$655$	0.702887	0.0274641
$656$	−21.0946	−0.823606
$657$	3.42254	0.133526
$658$	−10.3738	−0.404412
$659$	4.79936	0.186957	0.0934783	−	0.995621i	$-0.470201\pi$
$659$	4.79936	0.186957	0.0934783	+	0.995621i	$0.470201\pi$
$660$	−0.186107	−0.00724419
$661$	3.05390	0.118783	0.0593914	−	0.998235i	$-0.481084\pi$
$661$	3.05390	0.118783	0.0593914	+	0.998235i	$0.481084\pi$
$662$	54.1744	2.10555
$663$	0	0
$664$	−34.8138	−1.35104
$665$	−0.141222	−0.00547634
$666$	−1.29398	−0.0501406
$667$	34.4580	1.33422
$668$	6.63418	0.256684
$669$	7.00654	0.270888
$670$	1.22313	0.0472535
$671$	0.685375	0.0264586
$672$	0.173279	0.00668437
$673$	12.7900	0.493016	0.246508	−	0.969141i	$-0.420717\pi$
$673$	12.7900	0.493016	0.246508	+	0.969141i	$0.420717\pi$
$674$	79.8121	3.07425
$675$	−4.99534	−0.192271
$676$	0	0
$677$	21.6803	0.833240	0.416620	−	0.909081i	$-0.363215\pi$
$677$	21.6803	0.833240	0.416620	+	0.909081i	$0.363215\pi$
$678$	33.4581	1.28495
$679$	16.6705	0.639753
$680$	−0.316049	−0.0121199
$681$	27.7571	1.06365
$682$	16.7409	0.641043
$683$	−33.9669	−1.29971	−0.649854	−	0.760059i	$-0.725170\pi$
$683$	−33.9669	−1.29971	−0.649854	+	0.760059i	$0.725170\pi$
$684$	−8.30704	−0.317628
$685$	−0.247215	−0.00944561
$686$	2.45308	0.0936589
$687$	−3.61011	−0.137734
$688$	−7.34352	−0.279969
$689$	0	0
$690$	0.720355	0.0274235
$691$	43.2170	1.64405	0.822026	−	0.569450i	$-0.192844\pi$
$691$	43.2170	1.64405	0.822026	+	0.569450i	$0.192844\pi$
$692$	99.5503	3.78433
$693$	−0.678230	−0.0257638
$694$	−10.8235	−0.410856
$695$	−0.0831993	−0.00315593
$696$	−39.6658	−1.50353
$697$	4.80359	0.181949
$698$	17.4762	0.661485
$699$	−15.6176	−0.590713
$700$	20.0692	0.758543
$701$	−0.456718	−0.0172500	−0.00862500	−	0.999963i	$-0.502745\pi$
$701$	−0.456718	−0.0172500	−0.00862500	+	0.999963i	$0.502745\pi$
$702$	0	0
$703$	−1.09068	−0.0411358
$704$	−5.28107	−0.199038
$705$	0.288832	0.0108781
$706$	8.18503	0.308048
$707$	1.50429	0.0565746
$708$	33.4562	1.25736
$709$	−14.8844	−0.558994	−0.279497	−	0.960147i	$-0.590168\pi$
$709$	−14.8844	−0.558994	−0.279497	+	0.960147i	$0.590168\pi$
$710$	−1.66054	−0.0623191
$711$	−14.0484	−0.526855
$712$	−77.9724	−2.92214
$713$	−43.2621	−1.62018
$714$	−2.29352	−0.0858330
$715$	0	0
$716$	−25.3222	−0.946335
$717$	−27.9831	−1.04505
$718$	−60.3135	−2.25088
$719$	9.97486	0.372000	0.186000	−	0.982550i	$-0.440448\pi$
$719$	9.97486	0.372000	0.186000	+	0.982550i	$0.440448\pi$
$720$	−0.280426	−0.0104509
$721$	2.21721	0.0825732
$722$	36.1209	1.34428
$723$	−25.9732	−0.965955
$724$	−76.1203	−2.82899
$725$	−40.0349	−1.48686
$726$	25.8554	0.959585
$727$	10.4392	0.387169	0.193585	−	0.981084i	$-0.437989\pi$
$727$	10.4392	0.387169	0.193585	+	0.981084i	$0.437989\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.573428	0.0212235
$731$	1.67224	0.0618500
$732$	4.05990	0.150058
$733$	−22.7887	−0.841718	−0.420859	−	0.907126i	$-0.638271\pi$
$733$	−22.7887	−0.841718	−0.420859	+	0.907126i	$0.638271\pi$
$734$	36.9840	1.36510
$735$	−0.0682999	−0.00251928
$736$	−0.745008	−0.0274614
$737$	4.95129	0.182383
$738$	12.6033	0.463934
$739$	42.2796	1.55528	0.777640	−	0.628710i	$-0.216417\pi$
$739$	42.2796	1.55528	0.777640	+	0.628710i	$0.216417\pi$
$740$	−0.144744	−0.00532089
$741$	0	0
$742$	−7.88652	−0.289523
$743$	6.98202	0.256145	0.128073	−	0.991765i	$-0.459121\pi$
$743$	6.98202	0.256145	0.128073	+	0.991765i	$0.459121\pi$
$744$	49.8005	1.82577
$745$	1.12881	0.0413564
$746$	61.9331	2.26753
$747$	7.03411	0.257365
$748$	−2.54762	−0.0931501
$749$	19.7860	0.722963
$750$	−1.67467	−0.0611502
$751$	35.5530	1.29735	0.648673	−	0.761067i	$-0.275324\pi$
$751$	35.5530	1.29735	0.648673	+	0.761067i	$0.275324\pi$
$752$	−17.3630	−0.633162
$753$	−6.38525	−0.232691
$754$	0	0
$755$	−1.39020	−0.0505945
$756$	−4.01758	−0.146118
$757$	−13.1171	−0.476749	−0.238374	−	0.971173i	$-0.576615\pi$
$757$	−13.1171	−0.476749	−0.238374	+	0.971173i	$0.576615\pi$
$758$	58.9798	2.14224
$759$	2.91604	0.105845
$760$	−0.698946	−0.0253534
$761$	3.28595	0.119116	0.0595578	−	0.998225i	$-0.481031\pi$
$761$	3.28595	0.119116	0.0595578	+	0.998225i	$0.481031\pi$
$762$	19.6354	0.711315
$763$	1.71086	0.0619372
$764$	−35.3310	−1.27823
$765$	0.0638575	0.00230877
$766$	−11.1351	−0.402327
$767$	0	0
$768$	−32.1332	−1.15951
$769$	−1.28809	−0.0464498	−0.0232249	−	0.999730i	$-0.507393\pi$
$769$	−1.28809	−0.0464498	−0.0232249	+	0.999730i	$0.507393\pi$
$770$	−0.113634	−0.00409508
$771$	−13.8179	−0.497638
$772$	24.9051	0.896352
$773$	−22.0147	−0.791813	−0.395907	−	0.918291i	$-0.629570\pi$
$773$	−22.0147	−0.791813	−0.395907	+	0.918291i	$0.629570\pi$
$774$	4.38750	0.157706
$775$	50.2639	1.80553
$776$	82.5068	2.96182
$777$	−0.527492	−0.0189237
$778$	−48.5335	−1.74001
$779$	10.6232	0.380615
$780$	0	0
$781$	−6.72197	−0.240531
$782$	9.86096	0.352627
$783$	8.01446	0.286413
$784$	4.10580	0.146636
$785$	−1.03531	−0.0369517
$786$	25.2451	0.900462
$787$	5.09721	0.181696	0.0908479	−	0.995865i	$-0.471042\pi$
$787$	5.09721	0.181696	0.0908479	+	0.995865i	$0.471042\pi$
$788$	60.8397	2.16732
$789$	−11.3364	−0.403587
$790$	−2.35373	−0.0837420
$791$	13.6392	0.484955
$792$	−3.35675	−0.119277
$793$	0	0
$794$	25.6553	0.910471
$795$	0.219581	0.00778773
$796$	60.4132	2.14129
$797$	−41.5555	−1.47197	−0.735986	−	0.676997i	$-0.763281\pi$
$797$	−41.5555	−1.47197	−0.735986	+	0.676997i	$0.763281\pi$
$798$	−5.07216	−0.179552
$799$	3.95383	0.139877
$800$	0.865585	0.0306031
$801$	15.7543	0.556650
$802$	55.0068	1.94236
$803$	2.32127	0.0819158
$804$	29.3296	1.03437
$805$	0.293654	0.0103499
$806$	0	0
$807$	21.0002	0.739242
$808$	7.44515	0.261920
$809$	22.0300	0.774532	0.387266	−	0.921968i	$-0.373419\pi$
$809$	22.0300	0.774532	0.387266	+	0.921968i	$0.373419\pi$
$810$	0.167545	0.00588692
$811$	−20.0797	−0.705094	−0.352547	−	0.935794i	$-0.614684\pi$
$811$	−20.0797	−0.705094	−0.352547	+	0.935794i	$0.614684\pi$
$812$	−32.1987	−1.12995
$813$	−29.2450	−1.02567
$814$	−0.877615	−0.0307604
$815$	1.15025	0.0402915
$816$	−3.83875	−0.134383
$817$	3.69818	0.129383
$818$	59.9544	2.09626
$819$	0	0
$820$	1.40980	0.0492324
$821$	13.8647	0.483882	0.241941	−	0.970291i	$-0.422216\pi$
$821$	13.8647	0.483882	0.241941	+	0.970291i	$0.422216\pi$
$822$	−8.87904	−0.309692
$823$	−14.7804	−0.515213	−0.257606	−	0.966250i	$-0.582934\pi$
$823$	−14.7804	−0.515213	−0.257606	+	0.966250i	$0.582934\pi$
$824$	10.9736	0.382283
$825$	−3.38799	−0.117955
$826$	20.4279	0.710777
$827$	26.2554	0.912988	0.456494	−	0.889726i	$-0.349105\pi$
$827$	26.2554	0.912988	0.456494	+	0.889726i	$0.349105\pi$
$828$	17.2735	0.600296
$829$	14.3216	0.497408	0.248704	−	0.968579i	$-0.419995\pi$
$829$	14.3216	0.497408	0.248704	+	0.968579i	$0.419995\pi$
$830$	1.17853	0.0409073
$831$	16.5036	0.572502
$832$	0	0
$833$	−0.934958	−0.0323944
$834$	−2.98821	−0.103473
$835$	−0.112783	−0.00390301
$836$	−5.63409	−0.194859
$837$	−10.0622	−0.347799
$838$	−68.1861	−2.35545
$839$	−34.5482	−1.19274	−0.596368	−	0.802711i	$-0.703390\pi$
$839$	−34.5482	−1.19274	−0.596368	+	0.802711i	$0.703390\pi$
$840$	−0.338035	−0.0116633
$841$	35.2315	1.21488
$842$	−38.8382	−1.33845
$843$	−1.12161	−0.0386302
$844$	102.344	3.52284
$845$	0	0
$846$	10.3738	0.356658
$847$	10.5400	0.362159
$848$	−13.2000	−0.453288
$849$	10.9412	0.375501
$850$	−11.4569	−0.392969
$851$	2.26794	0.0777440
$852$	−39.8184	−1.36416
$853$	40.2048	1.37659	0.688294	−	0.725432i	$-0.258360\pi$
$853$	40.2048	1.37659	0.688294	+	0.725432i	$0.258360\pi$
$854$	2.47892	0.0848267
$855$	0.141222	0.00482968
$856$	97.9263	3.34705
$857$	24.2988	0.830031	0.415015	−	0.909814i	$-0.363776\pi$
$857$	24.2988	0.830031	0.415015	+	0.909814i	$0.363776\pi$
$858$	0	0
$859$	−38.8589	−1.32585	−0.662924	−	0.748687i	$-0.730685\pi$
$859$	−38.8589	−1.32585	−0.662924	+	0.748687i	$0.730685\pi$
$860$	0.490785	0.0167356
$861$	5.13776	0.175094
$862$	44.6700	1.52147
$863$	−30.0838	−1.02406	−0.512032	−	0.858966i	$-0.671107\pi$
$863$	−30.0838	−1.02406	−0.512032	+	0.858966i	$0.671107\pi$
$864$	−0.173279	−0.00589506
$865$	−1.69238	−0.0575426
$866$	23.0699	0.783948
$867$	−16.1259	−0.547663
$868$	40.4256	1.37213
$869$	−9.52804	−0.323216
$870$	1.34278	0.0455245
$871$	0	0
$872$	8.46752	0.286746
$873$	−16.6705	−0.564209
$874$	21.8076	0.737654
$875$	−0.682680	−0.0230788
$876$	13.7503	0.464580
$877$	−14.7532	−0.498179	−0.249090	−	0.968480i	$-0.580131\pi$
$877$	−14.7532	−0.498179	−0.249090	+	0.968480i	$0.580131\pi$
$878$	47.1822	1.59232
$879$	15.5503	0.524498
$880$	−0.190193	−0.00641141
$881$	34.5537	1.16414	0.582072	−	0.813137i	$-0.302242\pi$
$881$	34.5537	1.16414	0.582072	+	0.813137i	$0.302242\pi$
$882$	−2.45308	−0.0825994
$883$	7.47582	0.251581	0.125791	−	0.992057i	$-0.459853\pi$
$883$	7.47582	0.251581	0.125791	+	0.992057i	$0.459853\pi$
$884$	0	0
$885$	−0.568764	−0.0191188
$886$	13.2575	0.445396
$887$	−20.3565	−0.683503	−0.341752	−	0.939790i	$-0.611020\pi$
$887$	−20.3565	−0.683503	−0.341752	+	0.939790i	$0.611020\pi$
$888$	−2.61071	−0.0876095
$889$	8.00439	0.268459
$890$	2.63955	0.0884778
$891$	0.678230	0.0227216
$892$	28.1493	0.942509
$893$	8.74395	0.292605
$894$	40.5426	1.35595
$895$	0.430484	0.0143895
$896$	−19.4475	−0.649696
$897$	0	0
$898$	−33.2475	−1.10948
$899$	−80.6428	−2.68959
$900$	−20.0692	−0.668972
$901$	3.00585	0.100139
$902$	8.54795	0.284616
$903$	1.78857	0.0595200
$904$	67.5044	2.24516
$905$	1.29406	0.0430161
$906$	−49.9307	−1.65884
$907$	−9.91111	−0.329093	−0.164546	−	0.986369i	$-0.552616\pi$
$907$	−9.91111	−0.329093	−0.164546	+	0.986369i	$0.552616\pi$
$908$	111.516	3.70080
$909$	−1.50429	−0.0498941
$910$	0	0
$911$	−11.7109	−0.387998	−0.193999	−	0.981002i	$-0.562146\pi$
$911$	−11.7109	−0.387998	−0.193999	+	0.981002i	$0.562146\pi$
$912$	−8.48945	−0.281114
$913$	4.77075	0.157889
$914$	−73.1578	−2.41984
$915$	−0.0690193	−0.00228171
$916$	−14.5039	−0.479223
$917$	10.2912	0.339845
$918$	2.29352	0.0756976
$919$	−20.7949	−0.685962	−0.342981	−	0.939342i	$-0.611437\pi$
$919$	−20.7949	−0.685962	−0.342981	+	0.939342i	$0.611437\pi$
$920$	1.45338	0.0479164
$921$	−0.119003	−0.00392127
$922$	5.46553	0.179998
$923$	0	0
$924$	−2.72485	−0.0896409
$925$	−2.63500	−0.0866382
$926$	53.0075	1.74194
$927$	−2.21721	−0.0728227
$928$	−1.38873	−0.0455875
$929$	51.1824	1.67924	0.839620	−	0.543174i	$-0.182778\pi$
$929$	51.1824	1.67924	0.839620	+	0.543174i	$0.182778\pi$
$930$	−1.68586	−0.0552816
$931$	−2.06767	−0.0677652
$932$	−62.7451	−2.05528
$933$	−31.4738	−1.03041
$934$	58.8906	1.92696
$935$	0.0433101	0.00141639
$936$	0	0
$937$	46.1728	1.50840	0.754200	−	0.656645i	$-0.228025\pi$
$937$	46.1728	1.50840	0.754200	+	0.656645i	$0.228025\pi$
$938$	17.9082	0.584723
$939$	14.1243	0.460931
$940$	1.16041	0.0378483
$941$	31.6254	1.03096	0.515480	−	0.856902i	$-0.327614\pi$
$941$	31.6254	1.03096	0.515480	+	0.856902i	$0.327614\pi$
$942$	−37.1844	−1.21153
$943$	−22.0897	−0.719339
$944$	34.1909	1.11282
$945$	0.0682999	0.00222180
$946$	2.97574	0.0967496
$947$	19.2256	0.624747	0.312373	−	0.949959i	$-0.398876\pi$
$947$	19.2256	0.624747	0.312373	+	0.949959i	$0.398876\pi$
$948$	−56.4405	−1.83310
$949$	0	0
$950$	−25.3371	−0.822045
$951$	−18.6470	−0.604671
$952$	−4.62737	−0.149974
$953$	14.4415	0.467806	0.233903	−	0.972260i	$-0.424850\pi$
$953$	14.4415	0.467806	0.233903	+	0.972260i	$0.424850\pi$
$954$	7.88652	0.255336
$955$	0.600636	0.0194361
$956$	−112.424	−3.63606
$957$	5.43565	0.175710
$958$	75.2901	2.43251
$959$	−3.61956	−0.116882
$960$	0.531820	0.0171644
$961$	70.2471	2.26604
$962$	0	0
$963$	−19.7860	−0.637593
$964$	−104.350	−3.36087
$965$	−0.423392	−0.0136295
$966$	10.5470	0.339343
$967$	−3.28457	−0.105625	−0.0528123	−	0.998604i	$-0.516819\pi$
$967$	−3.28457	−0.105625	−0.0528123	+	0.998604i	$0.516819\pi$
$968$	52.1655	1.67666
$969$	1.93319	0.0621029
$970$	−2.79305	−0.0896794
$971$	−15.9721	−0.512568	−0.256284	−	0.966601i	$-0.582498\pi$
$971$	−15.9721	−0.512568	−0.256284	+	0.966601i	$0.582498\pi$
$972$	4.01758	0.128864
$973$	−1.21815	−0.0390520
$974$	−43.8382	−1.40467
$975$	0	0
$976$	4.14905	0.132808
$977$	21.9335	0.701714	0.350857	−	0.936429i	$-0.385890\pi$
$977$	21.9335	0.701714	0.350857	+	0.936429i	$0.385890\pi$
$978$	41.3126	1.32103
$979$	10.6850	0.341495
$980$	−0.274400	−0.00876540
$981$	−1.71086	−0.0546235
$982$	33.2873	1.06224
$983$	22.0867	0.704456	0.352228	−	0.935914i	$-0.385424\pi$
$983$	22.0867	0.704456	0.352228	+	0.935914i	$0.385424\pi$
$984$	25.4282	0.810622
$985$	−1.03429	−0.0329552
$986$	18.3814	0.585382
$987$	4.22889	0.134607
$988$	0	0
$989$	−7.68993	−0.244526
$990$	0.113634	0.00361153
$991$	4.36458	0.138645	0.0693227	−	0.997594i	$-0.477916\pi$
$991$	4.36458	0.138645	0.0693227	+	0.997594i	$0.477916\pi$
$992$	1.74356	0.0553580
$993$	−22.0843	−0.700823
$994$	−24.3125	−0.771147
$995$	−1.02704	−0.0325593
$996$	28.2601	0.895456
$997$	55.3319	1.75238	0.876189	−	0.481967i	$-0.160078\pi$
$997$	55.3319	1.75238	0.876189	+	0.481967i	$0.160078\pi$
$998$	25.5710	0.809435
$999$	0.527492	0.0166891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bb.1.2		8
13.6	odd	12		273.2.bd.a.127.8	yes	16
13.11	odd	12		273.2.bd.a.43.8	✓	16
13.12	even	2		3549.2.a.bd.1.7		8
39.11	even	12		819.2.ct.b.316.1		16
39.32	even	12		819.2.ct.b.127.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.8	✓	16	13.11	odd	12
273.2.bd.a.127.8	yes	16	13.6	odd	12
819.2.ct.b.127.1		16	39.32	even	12
819.2.ct.b.316.1		16	39.11	even	12
3549.2.a.bb.1.2		8	1.1	even	1	trivial
3549.2.a.bd.1.7		8	13.12	even	2

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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45308 q^{2} +1.00000 q^{3} +4.01758 q^{4} -0.0682999 q^{5} -2.45308 q^{6} -1.00000 q^{7} -4.94928 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.45308 q^{2} +1.00000 q^{3} +4.01758 q^{4} -0.0682999 q^{5} -2.45308 q^{6} -1.00000 q^{7} -4.94928 q^{8} +1.00000 q^{9} +0.167545 q^{10} +0.678230 q^{11} +4.01758 q^{12} +2.45308 q^{14} -0.0682999 q^{15} +4.10580 q^{16} -0.934958 q^{17} -2.45308 q^{18} -2.06767 q^{19} -0.274400 q^{20} -1.00000 q^{21} -1.66375 q^{22} +4.29948 q^{23} -4.94928 q^{24} -4.99534 q^{25} +1.00000 q^{27} -4.01758 q^{28} +8.01446 q^{29} +0.167545 q^{30} -10.0622 q^{31} -0.173279 q^{32} +0.678230 q^{33} +2.29352 q^{34} +0.0682999 q^{35} +4.01758 q^{36} +0.527492 q^{37} +5.07216 q^{38} +0.338035 q^{40} -5.13776 q^{41} +2.45308 q^{42} -1.78857 q^{43} +2.72485 q^{44} -0.0682999 q^{45} -10.5470 q^{46} -4.22889 q^{47} +4.10580 q^{48} +1.00000 q^{49} +12.2539 q^{50} -0.934958 q^{51} -3.21495 q^{53} -2.45308 q^{54} -0.0463231 q^{55} +4.94928 q^{56} -2.06767 q^{57} -19.6601 q^{58} +8.32746 q^{59} -0.274400 q^{60} +1.01053 q^{61} +24.6833 q^{62} -1.00000 q^{63} -7.78654 q^{64} -1.66375 q^{66} +7.30030 q^{67} -3.75627 q^{68} +4.29948 q^{69} -0.167545 q^{70} -9.91104 q^{71} -4.94928 q^{72} +3.42254 q^{73} -1.29398 q^{74} -4.99534 q^{75} -8.30704 q^{76} -0.678230 q^{77} -14.0484 q^{79} -0.280426 q^{80} +1.00000 q^{81} +12.6033 q^{82} +7.03411 q^{83} -4.01758 q^{84} +0.0638575 q^{85} +4.38750 q^{86} +8.01446 q^{87} -3.35675 q^{88} +15.7543 q^{89} +0.167545 q^{90} +17.2735 q^{92} -10.0622 q^{93} +10.3738 q^{94} +0.141222 q^{95} -0.173279 q^{96} -16.6705 q^{97} -2.45308 q^{98} +0.678230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * q^99

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