LMFDB - Embedded newform 201.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("201.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21432 q^{2} -1.00000 q^{3} -0.525428 q^{4} +0.311108 q^{5} +1.21432 q^{6} -1.90321 q^{7} +3.06668 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.21432 q^{2} -1.00000 q^{3} -0.525428 q^{4} +0.311108 q^{5} +1.21432 q^{6} -1.90321 q^{7} +3.06668 q^{8} +1.00000 q^{9} -0.377784 q^{10} +5.52543 q^{11} +0.525428 q^{12} -0.474572 q^{13} +2.31111 q^{14} -0.311108 q^{15} -2.67307 q^{16} +2.28100 q^{17} -1.21432 q^{18} +5.95407 q^{19} -0.163465 q^{20} +1.90321 q^{21} -6.70964 q^{22} +5.49532 q^{23} -3.06668 q^{24} -4.90321 q^{25} +0.576283 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.24443 q^{29} +0.377784 q^{30} +8.18421 q^{31} -2.88739 q^{32} -5.52543 q^{33} -2.76986 q^{34} -0.592104 q^{35} -0.525428 q^{36} -5.14764 q^{37} -7.23014 q^{38} +0.474572 q^{39} +0.954067 q^{40} -6.26517 q^{41} -2.31111 q^{42} -1.00000 q^{43} -2.90321 q^{44} +0.311108 q^{45} -6.67307 q^{46} -0.709636 q^{47} +2.67307 q^{48} -3.37778 q^{49} +5.95407 q^{50} -2.28100 q^{51} +0.249353 q^{52} +13.4494 q^{53} +1.21432 q^{54} +1.71900 q^{55} -5.83654 q^{56} -5.95407 q^{57} -1.51114 q^{58} -6.07160 q^{59} +0.163465 q^{60} +1.65878 q^{61} -9.93825 q^{62} -1.90321 q^{63} +8.85236 q^{64} -0.147643 q^{65} +6.70964 q^{66} +1.00000 q^{67} -1.19850 q^{68} -5.49532 q^{69} +0.719004 q^{70} +8.14764 q^{71} +3.06668 q^{72} -1.94914 q^{73} +6.25088 q^{74} +4.90321 q^{75} -3.12843 q^{76} -10.5161 q^{77} -0.576283 q^{78} +9.37778 q^{79} -0.831613 q^{80} +1.00000 q^{81} +7.60793 q^{82} -9.02074 q^{83} -1.00000 q^{84} +0.709636 q^{85} +1.21432 q^{86} -1.24443 q^{87} +16.9447 q^{88} +9.00492 q^{89} -0.377784 q^{90} +0.903212 q^{91} -2.88739 q^{92} -8.18421 q^{93} +0.861725 q^{94} +1.85236 q^{95} +2.88739 q^{96} -18.3225 q^{97} +4.10171 q^{98} +5.52543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9} - q^{10} + 10 q^{11} - 5 q^{12} - 8 q^{13} + 7 q^{14} - q^{15} + 5 q^{16} + 3 q^{18} - 2 q^{19} - 7 q^{20} - q^{21} + 3 q^{23} - 9 q^{24} - 8 q^{25} - 18 q^{26} - 3 q^{27} + 3 q^{28} + 4 q^{29} + q^{30} + 11 q^{31} + 11 q^{32} - 10 q^{33} - 2 q^{34} + 5 q^{35} + 5 q^{36} - 9 q^{37} - 28 q^{38} + 8 q^{39} - 17 q^{40} + q^{41} - 7 q^{42} - 3 q^{43} - 2 q^{44} + q^{45} - 7 q^{46} + 18 q^{47} - 5 q^{48} - 10 q^{49} - 2 q^{50} - 32 q^{52} + 7 q^{53} - 3 q^{54} + 12 q^{55} - 11 q^{56} + 2 q^{57} - 4 q^{58} + 15 q^{59} + 7 q^{60} - 2 q^{61} + 3 q^{62} + q^{63} + 33 q^{64} + 6 q^{65} + 3 q^{67} + 16 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{71} + 9 q^{72} - 19 q^{73} + 5 q^{74} + 8 q^{75} - 42 q^{76} + 2 q^{77} + 18 q^{78} + 28 q^{79} - 29 q^{80} + 3 q^{81} + 29 q^{82} - 7 q^{83} - 3 q^{84} - 18 q^{85} - 3 q^{86} - 4 q^{87} + 4 q^{88} - 6 q^{89} - q^{90} - 4 q^{91} + 11 q^{92} - 11 q^{93} + 36 q^{94} + 12 q^{95} - 11 q^{96} - 8 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9 - q^10 + 10 * q^11 - 5 * q^12 - 8 * q^13 + 7 * q^14 - q^15 + 5 * q^16 + 3 * q^18 - 2 * q^19 - 7 * q^20 - q^21 + 3 * q^23 - 9 * q^24 - 8 * q^25 - 18 * q^26 - 3 * q^27 + 3 * q^28 + 4 * q^29 + q^30 + 11 * q^31 + 11 * q^32 - 10 * q^33 - 2 * q^34 + 5 * q^35 + 5 * q^36 - 9 * q^37 - 28 * q^38 + 8 * q^39 - 17 * q^40 + q^41 - 7 * q^42 - 3 * q^43 - 2 * q^44 + q^45 - 7 * q^46 + 18 * q^47 - 5 * q^48 - 10 * q^49 - 2 * q^50 - 32 * q^52 + 7 * q^53 - 3 * q^54 + 12 * q^55 - 11 * q^56 + 2 * q^57 - 4 * q^58 + 15 * q^59 + 7 * q^60 - 2 * q^61 + 3 * q^62 + q^63 + 33 * q^64 + 6 * q^65 + 3 * q^67 + 16 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^71 + 9 * q^72 - 19 * q^73 + 5 * q^74 + 8 * q^75 - 42 * q^76 + 2 * q^77 + 18 * q^78 + 28 * q^79 - 29 * q^80 + 3 * q^81 + 29 * q^82 - 7 * q^83 - 3 * q^84 - 18 * q^85 - 3 * q^86 - 4 * q^87 + 4 * q^88 - 6 * q^89 - q^90 - 4 * q^91 + 11 * q^92 - 11 * q^93 + 36 * q^94 + 12 * q^95 - 11 * q^96 - 8 * q^97 - 14 * q^98 + 10 * 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 $

$2$	−1.21432	−0.858654	−0.429327	−	0.903149i	$-0.641249\pi$
$2$	−1.21432	−0.858654	−0.429327	+	0.903149i	$0.641249\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.525428	−0.262714
$5$	0.311108	0.139132	0.0695658	−	0.997577i	$-0.477839\pi$
$5$	0.311108	0.139132	0.0695658	+	0.997577i	$0.477839\pi$
$6$	1.21432	0.495744
$7$	−1.90321	−0.719346	−0.359673	−	0.933078i	$-0.617112\pi$
$7$	−1.90321	−0.719346	−0.359673	+	0.933078i	$0.617112\pi$
$8$	3.06668	1.08423
$9$	1.00000	0.333333
$10$	−0.377784	−0.119466
$11$	5.52543	1.66598	0.832990	−	0.553289i	$-0.186627\pi$
$11$	5.52543	1.66598	0.832990	+	0.553289i	$0.186627\pi$
$12$	0.525428	0.151678
$13$	−0.474572	−0.131623	−0.0658114	−	0.997832i	$-0.520964\pi$
$13$	−0.474572	−0.131623	−0.0658114	+	0.997832i	$0.520964\pi$
$14$	2.31111	0.617670
$15$	−0.311108	−0.0803277
$16$	−2.67307	−0.668268
$17$	2.28100	0.553223	0.276611	−	0.960982i	$-0.410789\pi$
$17$	2.28100	0.553223	0.276611	+	0.960982i	$0.410789\pi$
$18$	−1.21432	−0.286218
$19$	5.95407	1.36596	0.682978	−	0.730439i	$-0.260684\pi$
$19$	5.95407	1.36596	0.682978	+	0.730439i	$0.260684\pi$
$20$	−0.163465	−0.0365518
$21$	1.90321	0.415315
$22$	−6.70964	−1.43050
$23$	5.49532	1.14585	0.572926	−	0.819607i	$-0.305808\pi$
$23$	5.49532	1.14585	0.572926	+	0.819607i	$0.305808\pi$
$24$	−3.06668	−0.625983
$25$	−4.90321	−0.980642
$26$	0.576283	0.113018
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	1.24443	0.231085	0.115543	−	0.993303i	$-0.463139\pi$
$29$	1.24443	0.231085	0.115543	+	0.993303i	$0.463139\pi$
$30$	0.377784	0.0689737
$31$	8.18421	1.46993	0.734964	−	0.678107i	$-0.237199\pi$
$31$	8.18421	1.46993	0.734964	+	0.678107i	$0.237199\pi$
$32$	−2.88739	−0.510423
$33$	−5.52543	−0.961853
$34$	−2.76986	−0.475027
$35$	−0.592104	−0.100084
$36$	−0.525428	−0.0875713
$37$	−5.14764	−0.846267	−0.423134	−	0.906067i	$-0.639070\pi$
$37$	−5.14764	−0.846267	−0.423134	+	0.906067i	$0.639070\pi$
$38$	−7.23014	−1.17288
$39$	0.474572	0.0759924
$40$	0.954067	0.150851
$41$	−6.26517	−0.978456	−0.489228	−	0.872156i	$-0.662721\pi$
$41$	−6.26517	−0.978456	−0.489228	+	0.872156i	$0.662721\pi$
$42$	−2.31111	−0.356612
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−2.90321	−0.437676
$45$	0.311108	0.0463772
$46$	−6.67307	−0.983891
$47$	−0.709636	−0.103511	−0.0517555	−	0.998660i	$-0.516482\pi$
$47$	−0.709636	−0.103511	−0.0517555	+	0.998660i	$0.516482\pi$
$48$	2.67307	0.385825
$49$	−3.37778	−0.482541
$50$	5.95407	0.842032
$51$	−2.28100	−0.319403
$52$	0.249353	0.0345791
$53$	13.4494	1.84741	0.923707	−	0.383099i	$-0.125143\pi$
$53$	13.4494	1.84741	0.923707	+	0.383099i	$0.125143\pi$
$54$	1.21432	0.165248
$55$	1.71900	0.231790
$56$	−5.83654	−0.779940
$57$	−5.95407	−0.788635
$58$	−1.51114	−0.198422
$59$	−6.07160	−0.790455	−0.395227	−	0.918583i	$-0.629334\pi$
$59$	−6.07160	−0.790455	−0.395227	+	0.918583i	$0.629334\pi$
$60$	0.163465	0.0211032
$61$	1.65878	0.212385	0.106193	−	0.994346i	$-0.466134\pi$
$61$	1.65878	0.212385	0.106193	+	0.994346i	$0.466134\pi$
$62$	−9.93825	−1.26216
$63$	−1.90321	−0.239782
$64$	8.85236	1.10654
$65$	−0.147643	−0.0183129
$66$	6.70964	0.825899
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	−1.19850	−0.145339
$69$	−5.49532	−0.661558
$70$	0.719004	0.0859374
$71$	8.14764	0.966947	0.483474	−	0.875359i	$-0.339375\pi$
$71$	8.14764	0.966947	0.483474	+	0.875359i	$0.339375\pi$
$72$	3.06668	0.361411
$73$	−1.94914	−0.228130	−0.114065	−	0.993473i	$-0.536387\pi$
$73$	−1.94914	−0.228130	−0.114065	+	0.993473i	$0.536387\pi$
$74$	6.25088	0.726651
$75$	4.90321	0.566174
$76$	−3.12843	−0.358856
$77$	−10.5161	−1.19842
$78$	−0.576283	−0.0652512
$79$	9.37778	1.05508	0.527542	−	0.849529i	$-0.323114\pi$
$79$	9.37778	1.05508	0.527542	+	0.849529i	$0.323114\pi$
$80$	−0.831613	−0.0929772
$81$	1.00000	0.111111
$82$	7.60793	0.840155
$83$	−9.02074	−0.990155	−0.495078	−	0.868849i	$-0.664860\pi$
$83$	−9.02074	−0.990155	−0.495078	+	0.868849i	$0.664860\pi$
$84$	−1.00000	−0.109109
$85$	0.709636	0.0769708
$86$	1.21432	0.130943
$87$	−1.24443	−0.133417
$88$	16.9447	1.80631
$89$	9.00492	0.954520	0.477260	−	0.878762i	$-0.341630\pi$
$89$	9.00492	0.954520	0.477260	+	0.878762i	$0.341630\pi$
$90$	−0.377784	−0.0398220
$91$	0.903212	0.0946823
$92$	−2.88739	−0.301031
$93$	−8.18421	−0.848663
$94$	0.861725	0.0888801
$95$	1.85236	0.190048
$96$	2.88739	0.294693
$97$	−18.3225	−1.86037	−0.930183	−	0.367096i	$-0.880352\pi$
$97$	−18.3225	−1.86037	−0.930183	+	0.367096i	$0.880352\pi$
$98$	4.10171	0.414335
$99$	5.52543	0.555326
$100$	2.57628	0.257628
$101$	16.6494	1.65668	0.828339	−	0.560227i	$-0.189286\pi$
$101$	16.6494	1.65668	0.828339	+	0.560227i	$0.189286\pi$
$102$	2.76986	0.274257
$103$	12.5161	1.23324	0.616622	−	0.787259i	$-0.288501\pi$
$103$	12.5161	1.23324	0.616622	+	0.787259i	$0.288501\pi$
$104$	−1.45536	−0.142710
$105$	0.592104	0.0577834
$106$	−16.3319	−1.58629
$107$	1.52543	0.147469	0.0737343	−	0.997278i	$-0.476508\pi$
$107$	1.52543	0.147469	0.0737343	+	0.997278i	$0.476508\pi$
$108$	0.525428	0.0505593
$109$	11.7605	1.12645	0.563225	−	0.826303i	$-0.309560\pi$
$109$	11.7605	1.12645	0.563225	+	0.826303i	$0.309560\pi$
$110$	−2.08742	−0.199028
$111$	5.14764	0.488593
$112$	5.08742	0.480716
$113$	−12.5161	−1.17741	−0.588706	−	0.808347i	$-0.700362\pi$
$113$	−12.5161	−1.17741	−0.588706	+	0.808347i	$0.700362\pi$
$114$	7.23014	0.677165
$115$	1.70964	0.159424
$116$	−0.653858	−0.0607092
$117$	−0.474572	−0.0438742
$118$	7.37286	0.678727
$119$	−4.34122	−0.397959
$120$	−0.954067	−0.0870940
$121$	19.5303	1.77549
$122$	−2.01429	−0.182365
$123$	6.26517	0.564912
$124$	−4.30021	−0.386170
$125$	−3.08097	−0.275570
$126$	2.31111	0.205890
$127$	−1.46520	−0.130016	−0.0650079	−	0.997885i	$-0.520707\pi$
$127$	−1.46520	−0.130016	−0.0650079	+	0.997885i	$0.520707\pi$
$128$	−4.97481	−0.439715
$129$	1.00000	0.0880451
$130$	0.179286	0.0157244
$131$	−12.5462	−1.09616	−0.548082	−	0.836425i	$-0.684642\pi$
$131$	−12.5462	−1.09616	−0.548082	+	0.836425i	$0.684642\pi$
$132$	2.90321	0.252692
$133$	−11.3319	−0.982596
$134$	−1.21432	−0.104901
$135$	−0.311108	−0.0267759
$136$	6.99508	0.599823
$137$	5.50961	0.470717	0.235359	−	0.971909i	$-0.424374\pi$
$137$	5.50961	0.470717	0.235359	+	0.971909i	$0.424374\pi$
$138$	6.67307	0.568050
$139$	−14.4336	−1.22424	−0.612119	−	0.790765i	$-0.709683\pi$
$139$	−14.4336	−1.22424	−0.612119	+	0.790765i	$0.709683\pi$
$140$	0.311108	0.0262934
$141$	0.709636	0.0597621
$142$	−9.89384	−0.830273
$143$	−2.62222	−0.219281
$144$	−2.67307	−0.222756
$145$	0.387152	0.0321512
$146$	2.36689	0.195885
$147$	3.37778	0.278595
$148$	2.70471	0.222326
$149$	−6.66370	−0.545912	−0.272956	−	0.962027i	$-0.588001\pi$
$149$	−6.66370	−0.545912	−0.272956	+	0.962027i	$0.588001\pi$
$150$	−5.95407	−0.486148
$151$	−16.7511	−1.36319	−0.681594	−	0.731731i	$-0.738713\pi$
$151$	−16.7511	−1.36319	−0.681594	+	0.731731i	$0.738713\pi$
$152$	18.2592	1.48102
$153$	2.28100	0.184408
$154$	12.7699	1.02902
$155$	2.54617	0.204513
$156$	−0.249353	−0.0199643
$157$	−20.1842	−1.61088	−0.805438	−	0.592681i	$-0.798070\pi$
$157$	−20.1842	−1.61088	−0.805438	+	0.592681i	$0.798070\pi$
$158$	−11.3876	−0.905951
$159$	−13.4494	−1.06661
$160$	−0.898290	−0.0710160
$161$	−10.4588	−0.824265
$162$	−1.21432	−0.0954060
$163$	−14.6222	−1.14530	−0.572650	−	0.819800i	$-0.694085\pi$
$163$	−14.6222	−1.14530	−0.572650	+	0.819800i	$0.694085\pi$
$164$	3.29190	0.257054
$165$	−1.71900	−0.133824
$166$	10.9541	0.850200
$167$	4.35260	0.336814	0.168407	−	0.985718i	$-0.446138\pi$
$167$	4.35260	0.336814	0.168407	+	0.985718i	$0.446138\pi$
$168$	5.83654	0.450298
$169$	−12.7748	−0.982675
$170$	−0.861725	−0.0660913
$171$	5.95407	0.455319
$172$	0.525428	0.0400635
$173$	−10.5763	−0.804100	−0.402050	−	0.915618i	$-0.631702\pi$
$173$	−10.5763	−0.804100	−0.402050	+	0.915618i	$0.631702\pi$
$174$	1.51114	0.114559
$175$	9.33185	0.705422
$176$	−14.7699	−1.11332
$177$	6.07160	0.456369
$178$	−10.9349	−0.819602
$179$	7.95407	0.594515	0.297257	−	0.954797i	$-0.403928\pi$
$179$	7.95407	0.594515	0.297257	+	0.954797i	$0.403928\pi$
$180$	−0.163465	−0.0121839
$181$	−6.03657	−0.448694	−0.224347	−	0.974509i	$-0.572025\pi$
$181$	−6.03657	−0.448694	−0.224347	+	0.974509i	$0.572025\pi$
$182$	−1.09679	−0.0812993
$183$	−1.65878	−0.122621
$184$	16.8524	1.24237
$185$	−1.60147	−0.117743
$186$	9.93825	0.728708
$187$	12.6035	0.921658
$188$	0.372862	0.0271938
$189$	1.90321	0.138438
$190$	−2.24935	−0.163185
$191$	−4.56199	−0.330094	−0.165047	−	0.986286i	$-0.552778\pi$
$191$	−4.56199	−0.330094	−0.165047	+	0.986286i	$0.552778\pi$
$192$	−8.85236	−0.638864
$193$	10.6731	0.768264	0.384132	−	0.923278i	$-0.374501\pi$
$193$	10.6731	0.768264	0.384132	+	0.923278i	$0.374501\pi$
$194$	22.2494	1.59741
$195$	0.147643	0.0105729
$196$	1.77478	0.126770
$197$	−7.21432	−0.513999	−0.256999	−	0.966412i	$-0.582734\pi$
$197$	−7.21432	−0.513999	−0.256999	+	0.966412i	$0.582734\pi$
$198$	−6.70964	−0.476833
$199$	−3.57136	−0.253167	−0.126584	−	0.991956i	$-0.540401\pi$
$199$	−3.57136	−0.253167	−0.126584	+	0.991956i	$0.540401\pi$
$200$	−15.0366	−1.06325
$201$	−1.00000	−0.0705346
$202$	−20.2177	−1.42251
$203$	−2.36842	−0.166230
$204$	1.19850	0.0839117
$205$	−1.94914	−0.136134
$206$	−15.1985	−1.05893
$207$	5.49532	0.381951
$208$	1.26857	0.0879592
$209$	32.8988	2.27566
$210$	−0.719004	−0.0496160
$211$	−12.1432	−0.835972	−0.417986	−	0.908453i	$-0.637264\pi$
$211$	−12.1432	−0.835972	−0.417986	+	0.908453i	$0.637264\pi$
$212$	−7.06668	−0.485341
$213$	−8.14764	−0.558267
$214$	−1.85236	−0.126625
$215$	−0.311108	−0.0212174
$216$	−3.06668	−0.208661
$217$	−15.5763	−1.05739
$218$	−14.2810	−0.967231
$219$	1.94914	0.131711
$220$	−0.903212	−0.0608945
$221$	−1.08250	−0.0728167
$222$	−6.25088	−0.419532
$223$	0.368416	0.0246710	0.0123355	−	0.999924i	$-0.496073\pi$
$223$	0.368416	0.0246710	0.0123355	+	0.999924i	$0.496073\pi$
$224$	5.49532	0.367171
$225$	−4.90321	−0.326881
$226$	15.1985	1.01099
$227$	−4.22369	−0.280336	−0.140168	−	0.990128i	$-0.544764\pi$
$227$	−4.22369	−0.280336	−0.140168	+	0.990128i	$0.544764\pi$
$228$	3.12843	0.207185
$229$	−9.18421	−0.606910	−0.303455	−	0.952846i	$-0.598140\pi$
$229$	−9.18421	−0.606910	−0.303455	+	0.952846i	$0.598140\pi$
$230$	−2.07604	−0.136890
$231$	10.5161	0.691906
$232$	3.81627	0.250550
$233$	8.07604	0.529079	0.264540	−	0.964375i	$-0.414780\pi$
$233$	8.07604	0.529079	0.264540	+	0.964375i	$0.414780\pi$
$234$	0.576283	0.0376728
$235$	−0.220773	−0.0144017
$236$	3.19019	0.207663
$237$	−9.37778	−0.609153
$238$	5.27163	0.341709
$239$	26.0415	1.68448	0.842242	−	0.539100i	$-0.181235\pi$
$239$	26.0415	1.68448	0.842242	+	0.539100i	$0.181235\pi$
$240$	0.831613	0.0536804
$241$	22.0464	1.42013	0.710067	−	0.704134i	$-0.248665\pi$
$241$	22.0464	1.42013	0.710067	+	0.704134i	$0.248665\pi$
$242$	−23.7161	−1.52453
$243$	−1.00000	−0.0641500
$244$	−0.871569	−0.0557965
$245$	−1.05086	−0.0671367
$246$	−7.60793	−0.485064
$247$	−2.82564	−0.179791
$248$	25.0983	1.59374
$249$	9.02074	0.571666
$250$	3.74128	0.236619
$251$	7.61285	0.480519	0.240259	−	0.970709i	$-0.422768\pi$
$251$	7.61285	0.480519	0.240259	+	0.970709i	$0.422768\pi$
$252$	1.00000	0.0629941
$253$	30.3640	1.90897
$254$	1.77923	0.111639
$255$	−0.709636	−0.0444391
$256$	−11.6637	−0.728981
$257$	10.4889	0.654277	0.327139	−	0.944976i	$-0.393916\pi$
$257$	10.4889	0.654277	0.327139	+	0.944976i	$0.393916\pi$
$258$	−1.21432	−0.0756002
$259$	9.79706	0.608759
$260$	0.0775758	0.00481105
$261$	1.24443	0.0770284
$262$	15.2351	0.941225
$263$	17.3575	1.07031	0.535155	−	0.844754i	$-0.320253\pi$
$263$	17.3575	1.07031	0.535155	+	0.844754i	$0.320253\pi$
$264$	−16.9447	−1.04287
$265$	4.18421	0.257034
$266$	13.7605	0.843710
$267$	−9.00492	−0.551092
$268$	−0.525428	−0.0320956
$269$	−26.8845	−1.63918	−0.819588	−	0.572954i	$-0.805797\pi$
$269$	−26.8845	−1.63918	−0.819588	+	0.572954i	$0.805797\pi$
$270$	0.377784	0.0229912
$271$	23.4795	1.42628	0.713139	−	0.701023i	$-0.247273\pi$
$271$	23.4795	1.42628	0.713139	+	0.701023i	$0.247273\pi$
$272$	−6.09726	−0.369701
$273$	−0.903212	−0.0546649
$274$	−6.69042	−0.404183
$275$	−27.0923	−1.63373
$276$	2.88739	0.173800
$277$	−32.1941	−1.93435	−0.967177	−	0.254105i	$-0.918219\pi$
$277$	−32.1941	−1.93435	−0.967177	+	0.254105i	$0.918219\pi$
$278$	17.5270	1.05120
$279$	8.18421	0.489976
$280$	−1.81579	−0.108514
$281$	−7.52543	−0.448929	−0.224465	−	0.974482i	$-0.572063\pi$
$281$	−7.52543	−0.448929	−0.224465	+	0.974482i	$0.572063\pi$
$282$	−0.861725	−0.0513150
$283$	15.1985	0.903457	0.451728	−	0.892155i	$-0.350808\pi$
$283$	15.1985	0.903457	0.451728	+	0.892155i	$0.350808\pi$
$284$	−4.28100	−0.254030
$285$	−1.85236	−0.109724
$286$	3.18421	0.188286
$287$	11.9240	0.703849
$288$	−2.88739	−0.170141
$289$	−11.7971	−0.693944
$290$	−0.470127	−0.0276068
$291$	18.3225	1.07408
$292$	1.02413	0.0599329
$293$	0.152089	0.00888513	0.00444257	−	0.999990i	$-0.498586\pi$
$293$	0.152089	0.00888513	0.00444257	+	0.999990i	$0.498586\pi$
$294$	−4.10171	−0.239217
$295$	−1.88892	−0.109977
$296$	−15.7862	−0.917552
$297$	−5.52543	−0.320618
$298$	8.09187	0.468749
$299$	−2.60793	−0.150820
$300$	−2.57628	−0.148742
$301$	1.90321	0.109699
$302$	20.3412	1.17051
$303$	−16.6494	−0.956484
$304$	−15.9156	−0.912825
$305$	0.516060	0.0295495
$306$	−2.76986	−0.158342
$307$	−30.8385	−1.76005	−0.880024	−	0.474929i	$-0.842474\pi$
$307$	−30.8385	−1.76005	−0.880024	+	0.474929i	$0.842474\pi$
$308$	5.52543	0.314840
$309$	−12.5161	−0.712014
$310$	−3.09187	−0.175606
$311$	−13.3319	−0.755980	−0.377990	−	0.925810i	$-0.623385\pi$
$311$	−13.3319	−0.755980	−0.377990	+	0.925810i	$0.623385\pi$
$312$	1.45536	0.0823935
$313$	13.9541	0.788731	0.394365	−	0.918954i	$-0.370964\pi$
$313$	13.9541	0.788731	0.394365	+	0.918954i	$0.370964\pi$
$314$	24.5101	1.38318
$315$	−0.592104	−0.0333613
$316$	−4.92735	−0.277185
$317$	9.03657	0.507544	0.253772	−	0.967264i	$-0.418329\pi$
$317$	9.03657	0.507544	0.253772	+	0.967264i	$0.418329\pi$
$318$	16.3319	0.915845
$319$	6.87601	0.384983
$320$	2.75404	0.153955
$321$	−1.52543	−0.0851411
$322$	12.7003	0.707758
$323$	13.5812	0.755678
$324$	−0.525428	−0.0291904
$325$	2.32693	0.129075
$326$	17.7560	0.983416
$327$	−11.7605	−0.650357
$328$	−19.2133	−1.06088
$329$	1.35059	0.0744603
$330$	2.08742	0.114909
$331$	−13.2351	−0.727465	−0.363732	−	0.931503i	$-0.618498\pi$
$331$	−13.2351	−0.727465	−0.363732	+	0.931503i	$0.618498\pi$
$332$	4.73975	0.260127
$333$	−5.14764	−0.282089
$334$	−5.28544	−0.289207
$335$	0.311108	0.0169976
$336$	−5.08742	−0.277542
$337$	7.16992	0.390570	0.195285	−	0.980747i	$-0.437437\pi$
$337$	7.16992	0.390570	0.195285	+	0.980747i	$0.437437\pi$
$338$	15.5127	0.843778
$339$	12.5161	0.679779
$340$	−0.372862	−0.0202213
$341$	45.2212	2.44887
$342$	−7.23014	−0.390961
$343$	19.7511	1.06646
$344$	−3.06668	−0.165344
$345$	−1.70964	−0.0920437
$346$	12.8430	0.690443
$347$	33.8894	1.81928	0.909639	−	0.415399i	$-0.136358\pi$
$347$	33.8894	1.81928	0.909639	+	0.415399i	$0.136358\pi$
$348$	0.653858	0.0350505
$349$	−26.5353	−1.42040	−0.710200	−	0.704000i	$-0.751396\pi$
$349$	−26.5353	−1.42040	−0.710200	+	0.704000i	$0.751396\pi$
$350$	−11.3319	−0.605713
$351$	0.474572	0.0253308
$352$	−15.9541	−0.850355
$353$	−14.3111	−0.761703	−0.380852	−	0.924636i	$-0.624369\pi$
$353$	−14.3111	−0.761703	−0.380852	+	0.924636i	$0.624369\pi$
$354$	−7.37286	−0.391863
$355$	2.53480	0.134533
$356$	−4.73143	−0.250766
$357$	4.34122	0.229762
$358$	−9.65878	−0.510482
$359$	−26.8829	−1.41883	−0.709414	−	0.704792i	$-0.751040\pi$
$359$	−26.8829	−1.41883	−0.709414	+	0.704792i	$0.751040\pi$
$360$	0.954067	0.0502837
$361$	16.4509	0.865838
$362$	7.33032	0.385273
$363$	−19.5303	−1.02508
$364$	−0.474572	−0.0248744
$365$	−0.606394	−0.0317401
$366$	2.01429	0.105289
$367$	−14.4099	−0.752191	−0.376095	−	0.926581i	$-0.622734\pi$
$367$	−14.4099	−0.752191	−0.376095	+	0.926581i	$0.622734\pi$
$368$	−14.6894	−0.765736
$369$	−6.26517	−0.326152
$370$	1.94470	0.101100
$371$	−25.5970	−1.32893
$372$	4.30021	0.222955
$373$	9.56691	0.495356	0.247678	−	0.968842i	$-0.420332\pi$
$373$	9.56691	0.495356	0.247678	+	0.968842i	$0.420332\pi$
$374$	−15.3047	−0.791385
$375$	3.08097	0.159100
$376$	−2.17622	−0.112230
$377$	−0.590573	−0.0304160
$378$	−2.31111	−0.118871
$379$	37.9862	1.95122	0.975610	−	0.219513i	$-0.0704467\pi$
$379$	37.9862	1.95122	0.975610	+	0.219513i	$0.0704467\pi$
$380$	−0.973279	−0.0499282
$381$	1.46520	0.0750647
$382$	5.53972	0.283437
$383$	3.27607	0.167400	0.0836998	−	0.996491i	$-0.473326\pi$
$383$	3.27607	0.167400	0.0836998	+	0.996491i	$0.473326\pi$
$384$	4.97481	0.253870
$385$	−3.27163	−0.166738
$386$	−12.9605	−0.659673
$387$	−1.00000	−0.0508329
$388$	9.62714	0.488744
$389$	36.7797	1.86480	0.932402	−	0.361422i	$-0.117708\pi$
$389$	36.7797	1.86480	0.932402	+	0.361422i	$0.117708\pi$
$390$	−0.179286	−0.00907850
$391$	12.5348	0.633912
$392$	−10.3586	−0.523187
$393$	12.5462	0.632871
$394$	8.76049	0.441347
$395$	2.91750	0.146795
$396$	−2.90321	−0.145892
$397$	−23.1526	−1.16199	−0.580997	−	0.813906i	$-0.697337\pi$
$397$	−23.1526	−1.16199	−0.580997	+	0.813906i	$0.697337\pi$
$398$	4.33677	0.217383
$399$	11.3319	0.567302
$400$	13.1066	0.655332
$401$	9.11261	0.455062	0.227531	−	0.973771i	$-0.426935\pi$
$401$	9.11261	0.455062	0.227531	+	0.973771i	$0.426935\pi$
$402$	1.21432	0.0605648
$403$	−3.88400	−0.193476
$404$	−8.74806	−0.435232
$405$	0.311108	0.0154591
$406$	2.87601	0.142734
$407$	−28.4429	−1.40986
$408$	−6.99508	−0.346308
$409$	−27.2543	−1.34764	−0.673819	−	0.738897i	$-0.735347\pi$
$409$	−27.2543	−1.34764	−0.673819	+	0.738897i	$0.735347\pi$
$410$	2.36689	0.116892
$411$	−5.50961	−0.271769
$412$	−6.57628	−0.323990
$413$	11.5555	0.568611
$414$	−6.67307	−0.327964
$415$	−2.80642	−0.137762
$416$	1.37028	0.0671833
$417$	14.4336	0.706815
$418$	−39.9496	−1.95400
$419$	−37.8004	−1.84667	−0.923336	−	0.383992i	$-0.874549\pi$
$419$	−37.8004	−1.84667	−0.923336	+	0.383992i	$0.874549\pi$
$420$	−0.311108	−0.0151805
$421$	−16.7877	−0.818182	−0.409091	−	0.912494i	$-0.634154\pi$
$421$	−16.7877	−0.818182	−0.409091	+	0.912494i	$0.634154\pi$
$422$	14.7457	0.717811
$423$	−0.709636	−0.0345037
$424$	41.2449	2.00303
$425$	−11.1842	−0.542514
$426$	9.89384	0.479358
$427$	−3.15701	−0.152778
$428$	−0.801502	−0.0387420
$429$	2.62222	0.126602
$430$	0.377784	0.0182184
$431$	16.4588	0.792790	0.396395	−	0.918080i	$-0.370261\pi$
$431$	16.4588	0.792790	0.396395	+	0.918080i	$0.370261\pi$
$432$	2.67307	0.128608
$433$	−1.51114	−0.0726206	−0.0363103	−	0.999341i	$-0.511560\pi$
$433$	−1.51114	−0.0726206	−0.0363103	+	0.999341i	$0.511560\pi$
$434$	18.9146	0.907929
$435$	−0.387152	−0.0185625
$436$	−6.17929	−0.295934
$437$	32.7195	1.56518
$438$	−2.36689	−0.113094
$439$	−17.9684	−0.857583	−0.428791	−	0.903404i	$-0.641060\pi$
$439$	−17.9684	−0.857583	−0.428791	+	0.903404i	$0.641060\pi$
$440$	5.27163	0.251315
$441$	−3.37778	−0.160847
$442$	1.31450	0.0625243
$443$	−36.8113	−1.74896	−0.874480	−	0.485062i	$-0.838797\pi$
$443$	−36.8113	−1.74896	−0.874480	+	0.485062i	$0.838797\pi$
$444$	−2.70471	−0.128360
$445$	2.80150	0.132804
$446$	−0.447375	−0.0211838
$447$	6.66370	0.315182
$448$	−16.8479	−0.795989
$449$	−14.7699	−0.697033	−0.348516	−	0.937303i	$-0.613314\pi$
$449$	−14.7699	−0.697033	−0.348516	+	0.937303i	$0.613314\pi$
$450$	5.95407	0.280677
$451$	−34.6178	−1.63009
$452$	6.57628	0.309322
$453$	16.7511	0.787036
$454$	5.12891	0.240712
$455$	0.280996	0.0131733
$456$	−18.2592	−0.855065
$457$	41.6958	1.95045	0.975224	−	0.221219i	$-0.0710036\pi$
$457$	41.6958	1.95045	0.975224	+	0.221219i	$0.0710036\pi$
$458$	11.1526	0.521125
$459$	−2.28100	−0.106468
$460$	−0.898290	−0.0418830
$461$	−6.79706	−0.316570	−0.158285	−	0.987393i	$-0.550597\pi$
$461$	−6.79706	−0.316570	−0.158285	+	0.987393i	$0.550597\pi$
$462$	−12.7699	−0.594108
$463$	20.1383	0.935905	0.467953	−	0.883754i	$-0.344992\pi$
$463$	20.1383	0.935905	0.467953	+	0.883754i	$0.344992\pi$
$464$	−3.32645	−0.154427
$465$	−2.54617	−0.118076
$466$	−9.80690	−0.454296
$467$	−15.4652	−0.715644	−0.357822	−	0.933790i	$-0.616481\pi$
$467$	−15.4652	−0.715644	−0.357822	+	0.933790i	$0.616481\pi$
$468$	0.249353	0.0115264
$469$	−1.90321	−0.0878822
$470$	0.268089	0.0123660
$471$	20.1842	0.930039
$472$	−18.6196	−0.857038
$473$	−5.52543	−0.254059
$474$	11.3876	0.523051
$475$	−29.1941	−1.33951
$476$	2.28100	0.104549
$477$	13.4494	0.615805
$478$	−31.6227	−1.44639
$479$	1.73483	0.0792662	0.0396331	−	0.999214i	$-0.487381\pi$
$479$	1.73483	0.0792662	0.0396331	+	0.999214i	$0.487381\pi$
$480$	0.898290	0.0410011
$481$	2.44293	0.111388
$482$	−26.7714	−1.21940
$483$	10.4588	0.475890
$484$	−10.2618	−0.466445
$485$	−5.70027	−0.258836
$486$	1.21432	0.0550827
$487$	40.5210	1.83618	0.918090	−	0.396371i	$-0.129731\pi$
$487$	40.5210	1.83618	0.918090	+	0.396371i	$0.129731\pi$
$488$	5.08694	0.230275
$489$	14.6222	0.661239
$490$	1.27607	0.0576472
$491$	−27.2143	−1.22817	−0.614083	−	0.789242i	$-0.710474\pi$
$491$	−27.2143	−1.22817	−0.614083	+	0.789242i	$0.710474\pi$
$492$	−3.29190	−0.148410
$493$	2.83854	0.127842
$494$	3.43123	0.154378
$495$	1.71900	0.0772635
$496$	−21.8770	−0.982305
$497$	−15.5067	−0.695570
$498$	−10.9541	−0.490863
$499$	−26.4099	−1.18227	−0.591135	−	0.806573i	$-0.701320\pi$
$499$	−26.4099	−1.18227	−0.591135	+	0.806573i	$0.701320\pi$
$500$	1.61882	0.0723960
$501$	−4.35260	−0.194460
$502$	−9.24443	−0.412599
$503$	−3.69042	−0.164548	−0.0822739	−	0.996610i	$-0.526218\pi$
$503$	−3.69042	−0.164548	−0.0822739	+	0.996610i	$0.526218\pi$
$504$	−5.83654	−0.259980
$505$	5.17976	0.230496
$506$	−36.8716	−1.63914
$507$	12.7748	0.567348
$508$	0.769859	0.0341570
$509$	10.0272	0.444448	0.222224	−	0.974996i	$-0.428668\pi$
$509$	10.0272	0.444448	0.222224	+	0.974996i	$0.428668\pi$
$510$	0.861725	0.0381578
$511$	3.70964	0.164105
$512$	24.1131	1.06566
$513$	−5.95407	−0.262878
$514$	−12.7368	−0.561798
$515$	3.89384	0.171583
$516$	−0.525428	−0.0231307
$517$	−3.92104	−0.172447
$518$	−11.8968	−0.522714
$519$	10.5763	0.464247
$520$	−0.452774	−0.0198555
$521$	−25.5067	−1.11747	−0.558734	−	0.829347i	$-0.688713\pi$
$521$	−25.5067	−1.11747	−0.558734	+	0.829347i	$0.688713\pi$
$522$	−1.51114	−0.0661407
$523$	−0.931792	−0.0407444	−0.0203722	−	0.999792i	$-0.506485\pi$
$523$	−0.931792	−0.0407444	−0.0203722	+	0.999792i	$0.506485\pi$
$524$	6.59210	0.287977
$525$	−9.33185	−0.407275
$526$	−21.0776	−0.919026
$527$	18.6681	0.813197
$528$	14.7699	0.642776
$529$	7.19850	0.312978
$530$	−5.08097	−0.220703
$531$	−6.07160	−0.263485
$532$	5.95407	0.258142
$533$	2.97328	0.128787
$534$	10.9349	0.473197
$535$	0.474572	0.0205176
$536$	3.06668	0.132460
$537$	−7.95407	−0.343243
$538$	32.6464	1.40748
$539$	−18.6637	−0.803903
$540$	0.163465	0.00703440
$541$	9.30465	0.400038	0.200019	−	0.979792i	$-0.435900\pi$
$541$	9.30465	0.400038	0.200019	+	0.979792i	$0.435900\pi$
$542$	−28.5116	−1.22468
$543$	6.03657	0.259054
$544$	−6.58613	−0.282378
$545$	3.65878	0.156725
$546$	1.09679	0.0469382
$547$	16.7190	0.714853	0.357426	−	0.933941i	$-0.383654\pi$
$547$	16.7190	0.714853	0.357426	+	0.933941i	$0.383654\pi$
$548$	−2.89490	−0.123664
$549$	1.65878	0.0707950
$550$	32.8988	1.40281
$551$	7.40943	0.315652
$552$	−16.8524	−0.717284
$553$	−17.8479	−0.758970
$554$	39.0939	1.66094
$555$	1.60147	0.0679787
$556$	7.58379	0.321624
$557$	2.11906	0.0897876	0.0448938	−	0.998992i	$-0.485705\pi$
$557$	2.11906	0.0897876	0.0448938	+	0.998992i	$0.485705\pi$
$558$	−9.93825	−0.420719
$559$	0.474572	0.0200723
$560$	1.58274	0.0668828
$561$	−12.6035	−0.532119
$562$	9.13828	0.385475
$563$	6.12891	0.258303	0.129151	−	0.991625i	$-0.458775\pi$
$563$	6.12891	0.258303	0.129151	+	0.991625i	$0.458775\pi$
$564$	−0.372862	−0.0157003
$565$	−3.89384	−0.163815
$566$	−18.4558	−0.775757
$567$	−1.90321	−0.0799274
$568$	24.9862	1.04840
$569$	43.3230	1.81619	0.908096	−	0.418761i	$-0.137535\pi$
$569$	43.3230	1.81619	0.908096	+	0.418761i	$0.137535\pi$
$570$	2.24935	0.0942150
$571$	31.4019	1.31413	0.657065	−	0.753834i	$-0.271798\pi$
$571$	31.4019	1.31413	0.657065	+	0.753834i	$0.271798\pi$
$572$	1.37778	0.0576081
$573$	4.56199	0.190580
$574$	−14.4795	−0.604362
$575$	−26.9447	−1.12367
$576$	8.85236	0.368848
$577$	21.5625	0.897657	0.448829	−	0.893618i	$-0.351841\pi$
$577$	21.5625	0.897657	0.448829	+	0.893618i	$0.351841\pi$
$578$	14.3254	0.595858
$579$	−10.6731	−0.443558
$580$	−0.203420	−0.00844658
$581$	17.1684	0.712265
$582$	−22.2494	−0.922265
$583$	74.3136	3.07775
$584$	−5.97740	−0.247346
$585$	−0.147643	−0.00610429
$586$	−0.184685	−0.00762925
$587$	32.2864	1.33260	0.666301	−	0.745683i	$-0.267877\pi$
$587$	32.2864	1.33260	0.666301	+	0.745683i	$0.267877\pi$
$588$	−1.77478	−0.0731907
$589$	48.7293	2.00786
$590$	2.29376	0.0944324
$591$	7.21432	0.296757
$592$	13.7600	0.565533
$593$	−24.5605	−1.00858	−0.504289	−	0.863535i	$-0.668245\pi$
$593$	−24.5605	−1.00858	−0.504289	+	0.863535i	$0.668245\pi$
$594$	6.70964	0.275300
$595$	−1.35059	−0.0553687
$596$	3.50129	0.143419
$597$	3.57136	0.146166
$598$	3.16686	0.129502
$599$	−34.4242	−1.40653	−0.703267	−	0.710926i	$-0.748276\pi$
$599$	−34.4242	−1.40653	−0.703267	+	0.710926i	$0.748276\pi$
$600$	15.0366	0.613865
$601$	8.06022	0.328783	0.164392	−	0.986395i	$-0.447434\pi$
$601$	8.06022	0.328783	0.164392	+	0.986395i	$0.447434\pi$
$602$	−2.31111	−0.0941937
$603$	1.00000	0.0407231
$604$	8.80150	0.358128
$605$	6.07604	0.247026
$606$	20.2177	0.821288
$607$	28.6178	1.16156	0.580780	−	0.814061i	$-0.302748\pi$
$607$	28.6178	1.16156	0.580780	+	0.814061i	$0.302748\pi$
$608$	−17.1917	−0.697216
$609$	2.36842	0.0959731
$610$	−0.626661	−0.0253728
$611$	0.336774	0.0136244
$612$	−1.19850	−0.0484464
$613$	−28.6731	−1.15809	−0.579047	−	0.815294i	$-0.696575\pi$
$613$	−28.6731	−1.15809	−0.579047	+	0.815294i	$0.696575\pi$
$614$	37.4479	1.51127
$615$	1.94914	0.0785971
$616$	−32.2494	−1.29936
$617$	9.28147	0.373658	0.186829	−	0.982392i	$-0.440179\pi$
$617$	9.28147	0.373658	0.186829	+	0.982392i	$0.440179\pi$
$618$	15.1985	0.611373
$619$	28.4657	1.14413	0.572066	−	0.820207i	$-0.306142\pi$
$619$	28.4657	1.14413	0.572066	+	0.820207i	$0.306142\pi$
$620$	−1.33783	−0.0537285
$621$	−5.49532	−0.220519
$622$	16.1891	0.649125
$623$	−17.1383	−0.686630
$624$	−1.26857	−0.0507833
$625$	23.5575	0.942302
$626$	−16.9447	−0.677246
$627$	−32.8988	−1.31385
$628$	10.6053	0.423199
$629$	−11.7418	−0.468174
$630$	0.719004	0.0286458
$631$	−25.8064	−1.02734	−0.513669	−	0.857989i	$-0.671714\pi$
$631$	−25.8064	−1.02734	−0.513669	+	0.857989i	$0.671714\pi$
$632$	28.7586	1.14396
$633$	12.1432	0.482649
$634$	−10.9733	−0.435805
$635$	−0.455837	−0.0180893
$636$	7.06668	0.280212
$637$	1.60300	0.0635133
$638$	−8.34968	−0.330567
$639$	8.14764	0.322316
$640$	−1.54770	−0.0611783
$641$	−23.2286	−0.917475	−0.458737	−	0.888572i	$-0.651698\pi$
$641$	−23.2286	−0.917475	−0.458737	+	0.888572i	$0.651698\pi$
$642$	1.85236	0.0731067
$643$	29.7101	1.17165	0.585826	−	0.810437i	$-0.300770\pi$
$643$	29.7101	1.17165	0.585826	+	0.810437i	$0.300770\pi$
$644$	5.49532	0.216546
$645$	0.311108	0.0122499
$646$	−16.4919	−0.648866
$647$	−22.8287	−0.897489	−0.448744	−	0.893660i	$-0.648129\pi$
$647$	−22.8287	−0.897489	−0.448744	+	0.893660i	$0.648129\pi$
$648$	3.06668	0.120470
$649$	−33.5482	−1.31688
$650$	−2.82564	−0.110831
$651$	15.5763	0.610483
$652$	7.68292	0.300886
$653$	−10.7081	−0.419041	−0.209520	−	0.977804i	$-0.567190\pi$
$653$	−10.7081	−0.419041	−0.209520	+	0.977804i	$0.567190\pi$
$654$	14.2810	0.558431
$655$	−3.90321	−0.152511
$656$	16.7473	0.653870
$657$	−1.94914	−0.0760434
$658$	−1.64004	−0.0639356
$659$	−12.9619	−0.504924	−0.252462	−	0.967607i	$-0.581240\pi$
$659$	−12.9619	−0.504924	−0.252462	+	0.967607i	$0.581240\pi$
$660$	0.903212	0.0351575
$661$	−12.3555	−0.480574	−0.240287	−	0.970702i	$-0.577241\pi$
$661$	−12.3555	−0.480574	−0.240287	+	0.970702i	$0.577241\pi$
$662$	16.0716	0.624640
$663$	1.08250	0.0420407
$664$	−27.6637	−1.07356
$665$	−3.52543	−0.136710
$666$	6.25088	0.242217
$667$	6.83854	0.264789
$668$	−2.28697	−0.0884857
$669$	−0.368416	−0.0142438
$670$	−0.377784	−0.0145951
$671$	9.16547	0.353829
$672$	−5.49532	−0.211986
$673$	−9.21141	−0.355074	−0.177537	−	0.984114i	$-0.556813\pi$
$673$	−9.21141	−0.355074	−0.177537	+	0.984114i	$0.556813\pi$
$674$	−8.70657	−0.335365
$675$	4.90321	0.188725
$676$	6.71222	0.258162
$677$	15.9427	0.612727	0.306364	−	0.951915i	$-0.400888\pi$
$677$	15.9427	0.612727	0.306364	+	0.951915i	$0.400888\pi$
$678$	−15.1985	−0.583695
$679$	34.8716	1.33825
$680$	2.17622	0.0834544
$681$	4.22369	0.161852
$682$	−54.9131	−2.10273
$683$	−40.9733	−1.56780	−0.783899	−	0.620888i	$-0.786772\pi$
$683$	−40.9733	−1.56780	−0.783899	+	0.620888i	$0.786772\pi$
$684$	−3.12843	−0.119619
$685$	1.71408	0.0654917
$686$	−23.9842	−0.915720
$687$	9.18421	0.350399
$688$	2.67307	0.101910
$689$	−6.38271	−0.243162
$690$	2.07604	0.0790337
$691$	27.4193	1.04308	0.521539	−	0.853227i	$-0.325358\pi$
$691$	27.4193	1.04308	0.521539	+	0.853227i	$0.325358\pi$
$692$	5.55707	0.211248
$693$	−10.5161	−0.399472
$694$	−41.1526	−1.56213
$695$	−4.49039	−0.170330
$696$	−3.81627	−0.144655
$697$	−14.2908	−0.541304
$698$	32.2223	1.21963
$699$	−8.07604	−0.305464
$700$	−4.90321	−0.185324
$701$	−10.4543	−0.394854	−0.197427	−	0.980318i	$-0.563258\pi$
$701$	−10.4543	−0.394854	−0.197427	+	0.980318i	$0.563258\pi$
$702$	−0.576283	−0.0217504
$703$	−30.6494	−1.15596
$704$	48.9131	1.84348
$705$	0.220773	0.00831480
$706$	17.3783	0.654039
$707$	−31.6874	−1.19173
$708$	−3.19019	−0.119895
$709$	40.1338	1.50726	0.753629	−	0.657300i	$-0.228302\pi$
$709$	40.1338	1.50726	0.753629	+	0.657300i	$0.228302\pi$
$710$	−3.07805	−0.115517
$711$	9.37778	0.351694
$712$	27.6152	1.03492
$713$	44.9748	1.68432
$714$	−5.27163	−0.197286
$715$	−0.815792	−0.0305089
$716$	−4.17929	−0.156187
$717$	−26.0415	−0.972537
$718$	32.6445	1.21828
$719$	−19.4909	−0.726887	−0.363443	−	0.931616i	$-0.618399\pi$
$719$	−19.4909	−0.726887	−0.363443	+	0.931616i	$0.618399\pi$
$720$	−0.831613	−0.0309924
$721$	−23.8207	−0.887130
$722$	−19.9767	−0.743455
$723$	−22.0464	−0.819915
$724$	3.17178	0.117878
$725$	−6.10171	−0.226612
$726$	23.7161	0.880187
$727$	−42.8578	−1.58951	−0.794753	−	0.606933i	$-0.792400\pi$
$727$	−42.8578	−1.58951	−0.794753	+	0.606933i	$0.792400\pi$
$728$	2.76986	0.102658
$729$	1.00000	0.0370370
$730$	0.736356	0.0272538
$731$	−2.28100	−0.0843657
$732$	0.871569	0.0322141
$733$	−9.52987	−0.351994	−0.175997	−	0.984391i	$-0.556315\pi$
$733$	−9.52987	−0.351994	−0.175997	+	0.984391i	$0.556315\pi$
$734$	17.4982	0.645871
$735$	1.05086	0.0387614
$736$	−15.8671	−0.584870
$737$	5.52543	0.203532
$738$	7.60793	0.280052
$739$	−19.3082	−0.710263	−0.355132	−	0.934816i	$-0.615564\pi$
$739$	−19.3082	−0.710263	−0.355132	+	0.934816i	$0.615564\pi$
$740$	0.841458	0.0309326
$741$	2.82564	0.103802
$742$	31.0830	1.14109
$743$	38.2893	1.40470	0.702349	−	0.711833i	$-0.252134\pi$
$743$	38.2893	1.40470	0.702349	+	0.711833i	$0.252134\pi$
$744$	−25.0983	−0.920149
$745$	−2.07313	−0.0759536
$746$	−11.6173	−0.425339
$747$	−9.02074	−0.330052
$748$	−6.62222	−0.242132
$749$	−2.90321	−0.106081
$750$	−3.74128	−0.136612
$751$	−34.6035	−1.26270	−0.631349	−	0.775498i	$-0.717499\pi$
$751$	−34.6035	−1.26270	−0.631349	+	0.775498i	$0.717499\pi$
$752$	1.89691	0.0691731
$753$	−7.61285	−0.277428
$754$	0.717144	0.0261169
$755$	−5.21141	−0.189662
$756$	−1.00000	−0.0363696
$757$	16.6637	0.605653	0.302826	−	0.953046i	$-0.402070\pi$
$757$	16.6637	0.605653	0.302826	+	0.953046i	$0.402070\pi$
$758$	−46.1274	−1.67542
$759$	−30.3640	−1.10214
$760$	5.68058	0.206056
$761$	−31.4893	−1.14149	−0.570744	−	0.821128i	$-0.693345\pi$
$761$	−31.4893	−1.14149	−0.570744	+	0.821128i	$0.693345\pi$
$762$	−1.77923	−0.0644546
$763$	−22.3827	−0.810308
$764$	2.39700	0.0867203
$765$	0.709636	0.0256569
$766$	−3.97820	−0.143738
$767$	2.88141	0.104042
$768$	11.6637	0.420878
$769$	44.1704	1.59283	0.796413	−	0.604754i	$-0.206728\pi$
$769$	44.1704	1.59283	0.796413	+	0.604754i	$0.206728\pi$
$770$	3.97280	0.143170
$771$	−10.4889	−0.377747
$772$	−5.60793	−0.201834
$773$	−40.1116	−1.44271	−0.721356	−	0.692564i	$-0.756481\pi$
$773$	−40.1116	−1.44271	−0.721356	+	0.692564i	$0.756481\pi$
$774$	1.21432	0.0436478
$775$	−40.1289	−1.44147
$776$	−56.1891	−2.01707
$777$	−9.79706	−0.351467
$778$	−44.6623	−1.60122
$779$	−37.3033	−1.33653
$780$	−0.0775758	−0.00277766
$781$	45.0192	1.61091
$782$	−15.2212	−0.544311
$783$	−1.24443	−0.0444723
$784$	9.02906	0.322466
$785$	−6.27946	−0.224124
$786$	−15.2351	−0.543417
$787$	−4.54278	−0.161933	−0.0809663	−	0.996717i	$-0.525801\pi$
$787$	−4.54278	−0.161933	−0.0809663	+	0.996717i	$0.525801\pi$
$788$	3.79060	0.135035
$789$	−17.3575	−0.617944
$790$	−3.54278	−0.126046
$791$	23.8207	0.846967
$792$	16.9447	0.602104
$793$	−0.787212	−0.0279547
$794$	28.1146	0.997750
$795$	−4.18421	−0.148399
$796$	1.87649	0.0665105
$797$	42.8113	1.51646	0.758228	−	0.651990i	$-0.226065\pi$
$797$	42.8113	1.51646	0.758228	+	0.651990i	$0.226065\pi$
$798$	−13.7605	−0.487116
$799$	−1.61868	−0.0572647
$800$	14.1575	0.500543
$801$	9.00492	0.318173
$802$	−11.0656	−0.390741
$803$	−10.7699	−0.380060
$804$	0.525428	0.0185304
$805$	−3.25380	−0.114681
$806$	4.71642	0.166129
$807$	26.8845	0.946378
$808$	51.0584	1.79623
$809$	−20.0400	−0.704567	−0.352284	−	0.935893i	$-0.614595\pi$
$809$	−20.0400	−0.704567	−0.352284	+	0.935893i	$0.614595\pi$
$810$	−0.377784	−0.0132740
$811$	−31.7338	−1.11432	−0.557162	−	0.830404i	$-0.688110\pi$
$811$	−31.7338	−1.11432	−0.557162	+	0.830404i	$0.688110\pi$
$812$	1.24443	0.0436710
$813$	−23.4795	−0.823462
$814$	34.5388	1.21058
$815$	−4.54909	−0.159348
$816$	6.09726	0.213447
$817$	−5.95407	−0.208306
$818$	33.0954	1.15715
$819$	0.903212	0.0315608
$820$	1.02413	0.0357643
$821$	48.2578	1.68421	0.842105	−	0.539314i	$-0.181316\pi$
$821$	48.2578	1.68421	0.842105	+	0.539314i	$0.181316\pi$
$822$	6.69042	0.233355
$823$	−26.4113	−0.920640	−0.460320	−	0.887753i	$-0.652265\pi$
$823$	−26.4113	−0.920640	−0.460320	+	0.887753i	$0.652265\pi$
$824$	38.3827	1.33712
$825$	27.0923	0.943234
$826$	−14.0321	−0.488240
$827$	55.8149	1.94087	0.970437	−	0.241355i	$-0.0775919\pi$
$827$	55.8149	1.94087	0.970437	+	0.241355i	$0.0775919\pi$
$828$	−2.88739	−0.100344
$829$	−16.9175	−0.587569	−0.293785	−	0.955872i	$-0.594915\pi$
$829$	−16.9175	−0.587569	−0.293785	+	0.955872i	$0.594915\pi$
$830$	3.40790	0.118290
$831$	32.1941	1.11680
$832$	−4.20108	−0.145646
$833$	−7.70471	−0.266953
$834$	−17.5270	−0.606909
$835$	1.35413	0.0468615
$836$	−17.2859	−0.597846
$837$	−8.18421	−0.282888
$838$	45.9018	1.58565
$839$	−8.91306	−0.307713	−0.153856	−	0.988093i	$-0.549169\pi$
$839$	−8.91306	−0.307713	−0.153856	+	0.988093i	$0.549169\pi$
$840$	1.81579	0.0626508
$841$	−27.4514	−0.946600
$842$	20.3856	0.702535
$843$	7.52543	0.259189
$844$	6.38037	0.219621
$845$	−3.97433	−0.136721
$846$	0.861725	0.0296267
$847$	−37.1704	−1.27719
$848$	−35.9512	−1.23457
$849$	−15.1985	−0.521611
$850$	13.5812	0.465831
$851$	−28.2879	−0.969698
$852$	4.28100	0.146665
$853$	−34.2034	−1.17110	−0.585551	−	0.810635i	$-0.699122\pi$
$853$	−34.2034	−1.17110	−0.585551	+	0.810635i	$0.699122\pi$
$854$	3.83362	0.131184
$855$	1.85236	0.0633493
$856$	4.67799	0.159891
$857$	44.0859	1.50595	0.752973	−	0.658052i	$-0.228619\pi$
$857$	44.0859	1.50595	0.752973	+	0.658052i	$0.228619\pi$
$858$	−3.18421	−0.108707
$859$	−38.1704	−1.30236	−0.651179	−	0.758925i	$-0.725725\pi$
$859$	−38.1704	−1.30236	−0.651179	+	0.758925i	$0.725725\pi$
$860$	0.163465	0.00557410
$861$	−11.9240	−0.406367
$862$	−19.9862	−0.680732
$863$	−26.8370	−0.913543	−0.456771	−	0.889584i	$-0.650994\pi$
$863$	−26.8370	−0.913543	−0.456771	+	0.889584i	$0.650994\pi$
$864$	2.88739	0.0982310
$865$	−3.29036	−0.111876
$866$	1.83500	0.0623560
$867$	11.7971	0.400649
$868$	8.18421	0.277790
$869$	51.8163	1.75775
$870$	0.470127	0.0159388
$871$	−0.474572	−0.0160803
$872$	36.0656	1.22134
$873$	−18.3225	−0.620122
$874$	−39.7319	−1.34395
$875$	5.86373	0.198230
$876$	−1.02413	−0.0346023
$877$	−6.73683	−0.227487	−0.113743	−	0.993510i	$-0.536284\pi$
$877$	−6.73683	−0.227487	−0.113743	+	0.993510i	$0.536284\pi$
$878$	21.8193	0.736367
$879$	−0.152089	−0.00512983
$880$	−4.59502	−0.154898
$881$	−15.9585	−0.537656	−0.268828	−	0.963188i	$-0.586636\pi$
$881$	−15.9585	−0.537656	−0.268828	+	0.963188i	$0.586636\pi$
$882$	4.10171	0.138112
$883$	−31.7654	−1.06899	−0.534496	−	0.845171i	$-0.679498\pi$
$883$	−31.7654	−1.06899	−0.534496	+	0.845171i	$0.679498\pi$
$884$	0.568774	0.0191299
$885$	1.88892	0.0634954
$886$	44.7007	1.50175
$887$	46.5703	1.56368	0.781839	−	0.623480i	$-0.214282\pi$
$887$	46.5703	1.56368	0.781839	+	0.623480i	$0.214282\pi$
$888$	15.7862	0.529749
$889$	2.78859	0.0935265
$890$	−3.40192	−0.114033
$891$	5.52543	0.185109
$892$	−0.193576	−0.00648141
$893$	−4.22522	−0.141392
$894$	−8.09187	−0.270632
$895$	2.47457	0.0827158
$896$	9.46812	0.316308
$897$	2.60793	0.0870761
$898$	17.9353	0.598510
$899$	10.1847	0.339678
$900$	2.57628	0.0858761
$901$	30.6780	1.02203
$902$	42.0370	1.39968
$903$	−1.90321	−0.0633349
$904$	−38.3827	−1.27659
$905$	−1.87802	−0.0624276
$906$	−20.3412	−0.675792
$907$	0.336774	0.0111824	0.00559119	−	0.999984i	$-0.498220\pi$
$907$	0.336774	0.0111824	0.00559119	+	0.999984i	$0.498220\pi$
$908$	2.21924	0.0736481
$909$	16.6494	0.552226
$910$	−0.341219	−0.0113113
$911$	23.8809	0.791211	0.395605	−	0.918421i	$-0.370535\pi$
$911$	23.8809	0.791211	0.395605	+	0.918421i	$0.370535\pi$
$912$	15.9156	0.527020
$913$	−49.8435	−1.64958
$914$	−50.6321	−1.67476
$915$	−0.516060	−0.0170604
$916$	4.82564	0.159444
$917$	23.8780	0.788522
$918$	2.76986	0.0914190
$919$	−36.5339	−1.20514	−0.602571	−	0.798065i	$-0.705857\pi$
$919$	−36.5339	−1.20514	−0.602571	+	0.798065i	$0.705857\pi$
$920$	5.24290	0.172853
$921$	30.8385	1.01616
$922$	8.25380	0.271824
$923$	−3.86665	−0.127272
$924$	−5.52543	−0.181773
$925$	25.2400	0.829886
$926$	−24.4543	−0.803618
$927$	12.5161	0.411081
$928$	−3.59316	−0.117951
$929$	−38.6307	−1.26743	−0.633716	−	0.773566i	$-0.718471\pi$
$929$	−38.6307	−1.26743	−0.633716	+	0.773566i	$0.718471\pi$
$930$	3.09187	0.101386
$931$	−20.1116	−0.659130
$932$	−4.24338	−0.138996
$933$	13.3319	0.436465
$934$	18.7797	0.614491
$935$	3.92104	0.128232
$936$	−1.45536	−0.0475699
$937$	41.2301	1.34693	0.673465	−	0.739219i	$-0.264805\pi$
$937$	41.2301	1.34693	0.673465	+	0.739219i	$0.264805\pi$
$938$	2.31111	0.0754603
$939$	−13.9541	−0.455374
$940$	0.116000	0.00378351
$941$	12.9447	0.421985	0.210993	−	0.977488i	$-0.432330\pi$
$941$	12.9447	0.421985	0.210993	+	0.977488i	$0.432330\pi$
$942$	−24.5101	−0.798582
$943$	−34.4291	−1.12117
$944$	16.2298	0.528235
$945$	0.592104	0.0192611
$946$	6.70964	0.218149
$947$	−25.4766	−0.827878	−0.413939	−	0.910305i	$-0.635847\pi$
$947$	−25.4766	−0.827878	−0.413939	+	0.910305i	$0.635847\pi$
$948$	4.92735	0.160033
$949$	0.925010	0.0300271
$950$	35.4509	1.15018
$951$	−9.03657	−0.293031
$952$	−13.3131	−0.431481
$953$	10.6508	0.345013	0.172507	−	0.985008i	$-0.444813\pi$
$953$	10.6508	0.345013	0.172507	+	0.985008i	$0.444813\pi$
$954$	−16.3319	−0.528763
$955$	−1.41927	−0.0459265
$956$	−13.6829	−0.442537
$957$	−6.87601	−0.222270
$958$	−2.10663	−0.0680622
$959$	−10.4859	−0.338609
$960$	−2.75404	−0.0888862
$961$	35.9813	1.16069
$962$	−2.96650	−0.0956437
$963$	1.52543	0.0491562
$964$	−11.5838	−0.373089
$965$	3.32048	0.106890
$966$	−12.7003	−0.408624
$967$	−10.5446	−0.339093	−0.169546	−	0.985522i	$-0.554230\pi$
$967$	−10.5446	−0.339093	−0.169546	+	0.985522i	$0.554230\pi$
$968$	59.8933	1.92504
$969$	−13.5812	−0.436291
$970$	6.92195	0.222250
$971$	37.0049	1.18754	0.593772	−	0.804633i	$-0.297638\pi$
$971$	37.0049	1.18754	0.593772	+	0.804633i	$0.297638\pi$
$972$	0.525428	0.0168531
$973$	27.4701	0.880652
$974$	−49.2054	−1.57664
$975$	−2.32693	−0.0745214
$976$	−4.43404	−0.141930
$977$	15.1526	0.484774	0.242387	−	0.970180i	$-0.422070\pi$
$977$	15.1526	0.484774	0.242387	+	0.970180i	$0.422070\pi$
$978$	−17.7560	−0.567776
$979$	49.7560	1.59021
$980$	0.552148	0.0176377
$981$	11.7605	0.375484
$982$	33.0469	1.05457
$983$	29.8894	0.953324	0.476662	−	0.879087i	$-0.341847\pi$
$983$	29.8894	0.953324	0.476662	+	0.879087i	$0.341847\pi$
$984$	19.2133	0.612497
$985$	−2.24443	−0.0715135
$986$	−3.44690	−0.109772
$987$	−1.35059	−0.0429897
$988$	1.48467	0.0472336
$989$	−5.49532	−0.174741
$990$	−2.08742	−0.0663426
$991$	16.4148	0.521434	0.260717	−	0.965415i	$-0.416041\pi$
$991$	16.4148	0.521434	0.260717	+	0.965415i	$0.416041\pi$
$992$	−23.6310	−0.750285
$993$	13.2351	0.420002
$994$	18.8301	0.597254
$995$	−1.11108	−0.0352235
$996$	−4.73975	−0.150185
$997$	33.3225	1.05533	0.527667	−	0.849451i	$-0.323067\pi$
$997$	33.3225	1.05533	0.527667	+	0.849451i	$0.323067\pi$
$998$	32.0701	1.01516
$999$	5.14764	0.162864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.a.d.1.1	✓	3
3.2	odd	2		603.2.a.i.1.3		3
4.3	odd	2		3216.2.a.u.1.2		3
5.4	even	2		5025.2.a.m.1.3		3
7.6	odd	2		9849.2.a.ba.1.1		3
12.11	even	2		9648.2.a.bn.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.a.d.1.1	✓	3	1.1	even	1	trivial
603.2.a.i.1.3		3	3.2	odd	2
3216.2.a.u.1.2		3	4.3	odd	2
5025.2.a.m.1.3		3	5.4	even	2
9648.2.a.bn.1.2		3	12.11	even	2
9849.2.a.ba.1.1		3	7.6	odd	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21432 q^{2} -1.00000 q^{3} -0.525428 q^{4} +0.311108 q^{5} +1.21432 q^{6} -1.90321 q^{7} +3.06668 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.21432 q^{2} -1.00000 q^{3} -0.525428 q^{4} +0.311108 q^{5} +1.21432 q^{6} -1.90321 q^{7} +3.06668 q^{8} +1.00000 q^{9} -0.377784 q^{10} +5.52543 q^{11} +0.525428 q^{12} -0.474572 q^{13} +2.31111 q^{14} -0.311108 q^{15} -2.67307 q^{16} +2.28100 q^{17} -1.21432 q^{18} +5.95407 q^{19} -0.163465 q^{20} +1.90321 q^{21} -6.70964 q^{22} +5.49532 q^{23} -3.06668 q^{24} -4.90321 q^{25} +0.576283 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.24443 q^{29} +0.377784 q^{30} +8.18421 q^{31} -2.88739 q^{32} -5.52543 q^{33} -2.76986 q^{34} -0.592104 q^{35} -0.525428 q^{36} -5.14764 q^{37} -7.23014 q^{38} +0.474572 q^{39} +0.954067 q^{40} -6.26517 q^{41} -2.31111 q^{42} -1.00000 q^{43} -2.90321 q^{44} +0.311108 q^{45} -6.67307 q^{46} -0.709636 q^{47} +2.67307 q^{48} -3.37778 q^{49} +5.95407 q^{50} -2.28100 q^{51} +0.249353 q^{52} +13.4494 q^{53} +1.21432 q^{54} +1.71900 q^{55} -5.83654 q^{56} -5.95407 q^{57} -1.51114 q^{58} -6.07160 q^{59} +0.163465 q^{60} +1.65878 q^{61} -9.93825 q^{62} -1.90321 q^{63} +8.85236 q^{64} -0.147643 q^{65} +6.70964 q^{66} +1.00000 q^{67} -1.19850 q^{68} -5.49532 q^{69} +0.719004 q^{70} +8.14764 q^{71} +3.06668 q^{72} -1.94914 q^{73} +6.25088 q^{74} +4.90321 q^{75} -3.12843 q^{76} -10.5161 q^{77} -0.576283 q^{78} +9.37778 q^{79} -0.831613 q^{80} +1.00000 q^{81} +7.60793 q^{82} -9.02074 q^{83} -1.00000 q^{84} +0.709636 q^{85} +1.21432 q^{86} -1.24443 q^{87} +16.9447 q^{88} +9.00492 q^{89} -0.377784 q^{90} +0.903212 q^{91} -2.88739 q^{92} -8.18421 q^{93} +0.861725 q^{94} +1.85236 q^{95} +2.88739 q^{96} -18.3225 q^{97} +4.10171 q^{98} +5.52543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9} - q^{10} + 10 q^{11} - 5 q^{12} - 8 q^{13} + 7 q^{14} - q^{15} + 5 q^{16} + 3 q^{18} - 2 q^{19} - 7 q^{20} - q^{21} + 3 q^{23} - 9 q^{24} - 8 q^{25} - 18 q^{26} - 3 q^{27} + 3 q^{28} + 4 q^{29} + q^{30} + 11 q^{31} + 11 q^{32} - 10 q^{33} - 2 q^{34} + 5 q^{35} + 5 q^{36} - 9 q^{37} - 28 q^{38} + 8 q^{39} - 17 q^{40} + q^{41} - 7 q^{42} - 3 q^{43} - 2 q^{44} + q^{45} - 7 q^{46} + 18 q^{47} - 5 q^{48} - 10 q^{49} - 2 q^{50} - 32 q^{52} + 7 q^{53} - 3 q^{54} + 12 q^{55} - 11 q^{56} + 2 q^{57} - 4 q^{58} + 15 q^{59} + 7 q^{60} - 2 q^{61} + 3 q^{62} + q^{63} + 33 q^{64} + 6 q^{65} + 3 q^{67} + 16 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{71} + 9 q^{72} - 19 q^{73} + 5 q^{74} + 8 q^{75} - 42 q^{76} + 2 q^{77} + 18 q^{78} + 28 q^{79} - 29 q^{80} + 3 q^{81} + 29 q^{82} - 7 q^{83} - 3 q^{84} - 18 q^{85} - 3 q^{86} - 4 q^{87} + 4 q^{88} - 6 q^{89} - q^{90} - 4 q^{91} + 11 q^{92} - 11 q^{93} + 36 q^{94} + 12 q^{95} - 11 q^{96} - 8 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9 - q^10 + 10 * q^11 - 5 * q^12 - 8 * q^13 + 7 * q^14 - q^15 + 5 * q^16 + 3 * q^18 - 2 * q^19 - 7 * q^20 - q^21 + 3 * q^23 - 9 * q^24 - 8 * q^25 - 18 * q^26 - 3 * q^27 + 3 * q^28 + 4 * q^29 + q^30 + 11 * q^31 + 11 * q^32 - 10 * q^33 - 2 * q^34 + 5 * q^35 + 5 * q^36 - 9 * q^37 - 28 * q^38 + 8 * q^39 - 17 * q^40 + q^41 - 7 * q^42 - 3 * q^43 - 2 * q^44 + q^45 - 7 * q^46 + 18 * q^47 - 5 * q^48 - 10 * q^49 - 2 * q^50 - 32 * q^52 + 7 * q^53 - 3 * q^54 + 12 * q^55 - 11 * q^56 + 2 * q^57 - 4 * q^58 + 15 * q^59 + 7 * q^60 - 2 * q^61 + 3 * q^62 + q^63 + 33 * q^64 + 6 * q^65 + 3 * q^67 + 16 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^71 + 9 * q^72 - 19 * q^73 + 5 * q^74 + 8 * q^75 - 42 * q^76 + 2 * q^77 + 18 * q^78 + 28 * q^79 - 29 * q^80 + 3 * q^81 + 29 * q^82 - 7 * q^83 - 3 * q^84 - 18 * q^85 - 3 * q^86 - 4 * q^87 + 4 * q^88 - 6 * q^89 - q^90 - 4 * q^91 + 11 * q^92 - 11 * q^93 + 36 * q^94 + 12 * q^95 - 11 * q^96 - 8 * q^97 - 14 * q^98 + 10 * q^99

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