LMFDB - Embedded newform 2166.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.90211$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0978870 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0978870 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.0978870 q^{10} +6.41164 q^{11} +1.00000 q^{12} +1.11507 q^{13} -2.61803 q^{14} +0.0978870 q^{15} +1.00000 q^{16} +4.91930 q^{17} -1.00000 q^{18} +0.0978870 q^{20} +2.61803 q^{21} -6.41164 q^{22} -1.58721 q^{23} -1.00000 q^{24} -4.99042 q^{25} -1.11507 q^{26} +1.00000 q^{27} +2.61803 q^{28} +4.65833 q^{29} -0.0978870 q^{30} +7.92522 q^{31} -1.00000 q^{32} +6.41164 q^{33} -4.91930 q^{34} +0.256271 q^{35} +1.00000 q^{36} -9.60845 q^{37} +1.11507 q^{39} -0.0978870 q^{40} -6.50651 q^{41} -2.61803 q^{42} -4.13412 q^{43} +6.41164 q^{44} +0.0978870 q^{45} +1.58721 q^{46} -1.90398 q^{47} +1.00000 q^{48} -0.145898 q^{49} +4.99042 q^{50} +4.91930 q^{51} +1.11507 q^{52} -4.65833 q^{53} -1.00000 q^{54} +0.627616 q^{55} -2.61803 q^{56} -4.65833 q^{58} +3.95605 q^{59} +0.0978870 q^{60} +4.02124 q^{61} -7.92522 q^{62} +2.61803 q^{63} +1.00000 q^{64} +0.109151 q^{65} -6.41164 q^{66} -14.9655 q^{67} +4.91930 q^{68} -1.58721 q^{69} -0.256271 q^{70} +10.3974 q^{71} -1.00000 q^{72} +1.75435 q^{73} +9.60845 q^{74} -4.99042 q^{75} +16.7859 q^{77} -1.11507 q^{78} -14.4329 q^{79} +0.0978870 q^{80} +1.00000 q^{81} +6.50651 q^{82} +15.1975 q^{83} +2.61803 q^{84} +0.481535 q^{85} +4.13412 q^{86} +4.65833 q^{87} -6.41164 q^{88} +6.35114 q^{89} -0.0978870 q^{90} +2.91930 q^{91} -1.58721 q^{92} +7.92522 q^{93} +1.90398 q^{94} -1.00000 q^{96} -15.8767 q^{97} +0.145898 q^{98} +6.41164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{21} - 12 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{27} + 6 q^{28} - 10 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{32} + 12 q^{33} - 4 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 4 q^{39} - 8 q^{40} + 8 q^{41} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 8 q^{45} - 12 q^{46} + 4 q^{47} + 4 q^{48} - 14 q^{49} - 6 q^{50} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 4 q^{54} + 24 q^{55} - 6 q^{56} + 10 q^{58} + 6 q^{59} + 8 q^{60} + 4 q^{61} - 8 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{65} - 12 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 12 q^{70} - 4 q^{72} - 10 q^{73} + 8 q^{74} + 6 q^{75} + 28 q^{77} - 4 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} + 8 q^{83} + 6 q^{84} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 12 q^{88} + 16 q^{89} - 8 q^{90} - 4 q^{91} + 12 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{96} - 8 q^{97} + 14 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^21 - 12 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^27 + 6 * q^28 - 10 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^32 + 12 * q^33 - 4 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 4 * q^39 - 8 * q^40 + 8 * q^41 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 8 * q^45 - 12 * q^46 + 4 * q^47 + 4 * q^48 - 14 * q^49 - 6 * q^50 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 4 * q^54 + 24 * q^55 - 6 * q^56 + 10 * q^58 + 6 * q^59 + 8 * q^60 + 4 * q^61 - 8 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^65 - 12 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 12 * q^70 - 4 * q^72 - 10 * q^73 + 8 * q^74 + 6 * q^75 + 28 * q^77 - 4 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 + 6 * q^84 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 12 * q^88 + 16 * q^89 - 8 * q^90 - 4 * q^91 + 12 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^96 - 8 * q^97 + 14 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.0978870	0.0437764	0.0218882	−	0.999760i	$-0.493032\pi$
$5$	0.0978870	0.0437764	0.0218882	+	0.999760i	$0.493032\pi$
$6$	−1.00000	−0.408248
$7$	2.61803	0.989524	0.494762	−	0.869029i	$-0.335255\pi$
$7$	2.61803	0.989524	0.494762	+	0.869029i	$0.335255\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.0978870	−0.0309546
$11$	6.41164	1.93318	0.966591	−	0.256324i	$-0.0825115\pi$
$11$	6.41164	1.93318	0.966591	+	0.256324i	$0.0825115\pi$
$12$	1.00000	0.288675
$13$	1.11507	0.309266	0.154633	−	0.987972i	$-0.450581\pi$
$13$	1.11507	0.309266	0.154633	+	0.987972i	$0.450581\pi$
$14$	−2.61803	−0.699699
$15$	0.0978870	0.0252743
$16$	1.00000	0.250000
$17$	4.91930	1.19311	0.596553	−	0.802574i	$-0.296537\pi$
$17$	4.91930	1.19311	0.596553	+	0.802574i	$0.296537\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	0.0978870	0.0218882
$21$	2.61803	0.571302
$22$	−6.41164	−1.36697
$23$	−1.58721	−0.330956	−0.165478	−	0.986213i	$-0.552917\pi$
$23$	−1.58721	−0.330956	−0.165478	+	0.986213i	$0.552917\pi$
$24$	−1.00000	−0.204124
$25$	−4.99042	−0.998084
$26$	−1.11507	−0.218684
$27$	1.00000	0.192450
$28$	2.61803	0.494762
$29$	4.65833	0.865030	0.432515	−	0.901627i	$-0.357626\pi$
$29$	4.65833	0.865030	0.432515	+	0.901627i	$0.357626\pi$
$30$	−0.0978870	−0.0178716
$31$	7.92522	1.42341	0.711706	−	0.702478i	$-0.247923\pi$
$31$	7.92522	1.42341	0.711706	+	0.702478i	$0.247923\pi$
$32$	−1.00000	−0.176777
$33$	6.41164	1.11612
$34$	−4.91930	−0.843653
$35$	0.256271	0.0433178
$36$	1.00000	0.166667
$37$	−9.60845	−1.57962	−0.789810	−	0.613352i	$-0.789821\pi$
$37$	−9.60845	−1.57962	−0.789810	+	0.613352i	$0.789821\pi$
$38$	0	0
$39$	1.11507	0.178555
$40$	−0.0978870	−0.0154773
$41$	−6.50651	−1.01615	−0.508073	−	0.861314i	$-0.669642\pi$
$41$	−6.50651	−1.01615	−0.508073	+	0.861314i	$0.669642\pi$
$42$	−2.61803	−0.403971
$43$	−4.13412	−0.630448	−0.315224	−	0.949017i	$-0.602080\pi$
$43$	−4.13412	−0.630448	−0.315224	+	0.949017i	$0.602080\pi$
$44$	6.41164	0.966591
$45$	0.0978870	0.0145921
$46$	1.58721	0.234021
$47$	−1.90398	−0.277724	−0.138862	−	0.990312i	$-0.544344\pi$
$47$	−1.90398	−0.277724	−0.138862	+	0.990312i	$0.544344\pi$
$48$	1.00000	0.144338
$49$	−0.145898	−0.0208426
$50$	4.99042	0.705752
$51$	4.91930	0.688840
$52$	1.11507	0.154633
$53$	−4.65833	−0.639871	−0.319935	−	0.947439i	$-0.603661\pi$
$53$	−4.65833	−0.639871	−0.319935	+	0.947439i	$0.603661\pi$
$54$	−1.00000	−0.136083
$55$	0.627616	0.0846277
$56$	−2.61803	−0.349850
$57$	0	0
$58$	−4.65833	−0.611668
$59$	3.95605	0.515033	0.257517	−	0.966274i	$-0.417096\pi$
$59$	3.95605	0.515033	0.257517	+	0.966274i	$0.417096\pi$
$60$	0.0978870	0.0126372
$61$	4.02124	0.514867	0.257434	−	0.966296i	$-0.417123\pi$
$61$	4.02124	0.514867	0.257434	+	0.966296i	$0.417123\pi$
$62$	−7.92522	−1.00650
$63$	2.61803	0.329841
$64$	1.00000	0.125000
$65$	0.109151	0.0135385
$66$	−6.41164	−0.789218
$67$	−14.9655	−1.82833	−0.914164	−	0.405344i	$-0.867152\pi$
$67$	−14.9655	−1.82833	−0.914164	+	0.405344i	$0.867152\pi$
$68$	4.91930	0.596553
$69$	−1.58721	−0.191078
$70$	−0.256271	−0.0306303
$71$	10.3974	1.23394	0.616970	−	0.786987i	$-0.288360\pi$
$71$	10.3974	1.23394	0.616970	+	0.786987i	$0.288360\pi$
$72$	−1.00000	−0.117851
$73$	1.75435	0.205331	0.102666	−	0.994716i	$-0.467263\pi$
$73$	1.75435	0.205331	0.102666	+	0.994716i	$0.467263\pi$
$74$	9.60845	1.11696
$75$	−4.99042	−0.576244
$76$	0	0
$77$	16.7859	1.91293
$78$	−1.11507	−0.126257
$79$	−14.4329	−1.62383	−0.811913	−	0.583778i	$-0.801574\pi$
$79$	−14.4329	−1.62383	−0.811913	+	0.583778i	$0.801574\pi$
$80$	0.0978870	0.0109441
$81$	1.00000	0.111111
$82$	6.50651	0.718524
$83$	15.1975	1.66815	0.834073	−	0.551655i	$-0.186003\pi$
$83$	15.1975	1.66815	0.834073	+	0.551655i	$0.186003\pi$
$84$	2.61803	0.285651
$85$	0.481535	0.0522298
$86$	4.13412	0.445794
$87$	4.65833	0.499425
$88$	−6.41164	−0.683483
$89$	6.35114	0.673220	0.336610	−	0.941644i	$-0.390720\pi$
$89$	6.35114	0.673220	0.336610	+	0.941644i	$0.390720\pi$
$90$	−0.0978870	−0.0103182
$91$	2.91930	0.306026
$92$	−1.58721	−0.165478
$93$	7.92522	0.821807
$94$	1.90398	0.196380
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−15.8767	−1.61203	−0.806017	−	0.591892i	$-0.798381\pi$
$97$	−15.8767	−1.61203	−0.806017	+	0.591892i	$0.798381\pi$
$98$	0.145898	0.0147379
$99$	6.41164	0.644394
$100$	−4.99042	−0.499042
$101$	−14.7829	−1.47095	−0.735475	−	0.677552i	$-0.763041\pi$
$101$	−14.7829	−1.47095	−0.735475	+	0.677552i	$0.763041\pi$
$102$	−4.91930	−0.487083
$103$	10.1198	0.997138	0.498569	−	0.866850i	$-0.333859\pi$
$103$	10.1198	0.997138	0.498569	+	0.866850i	$0.333859\pi$
$104$	−1.11507	−0.109342
$105$	0.256271	0.0250095
$106$	4.65833	0.452457
$107$	11.1458	1.07750	0.538752	−	0.842464i	$-0.318896\pi$
$107$	11.1458	1.07750	0.538752	+	0.842464i	$0.318896\pi$
$108$	1.00000	0.0962250
$109$	4.37238	0.418798	0.209399	−	0.977830i	$-0.432849\pi$
$109$	4.37238	0.418798	0.209399	+	0.977830i	$0.432849\pi$
$110$	−0.627616	−0.0598408
$111$	−9.60845	−0.911994
$112$	2.61803	0.247381
$113$	−0.120995	−0.0113822	−0.00569112	−	0.999984i	$-0.501812\pi$
$113$	−0.120995	−0.0113822	−0.00569112	+	0.999984i	$0.501812\pi$
$114$	0	0
$115$	−0.155367	−0.0144881
$116$	4.65833	0.432515
$117$	1.11507	0.103089
$118$	−3.95605	−0.364184
$119$	12.8789	1.18061
$120$	−0.0978870	−0.00893582
$121$	30.1091	2.73719
$122$	−4.02124	−0.364066
$123$	−6.50651	−0.586672
$124$	7.92522	0.711706
$125$	−0.977932	−0.0874689
$126$	−2.61803	−0.233233
$127$	−0.743841	−0.0660053	−0.0330026	−	0.999455i	$-0.510507\pi$
$127$	−0.743841	−0.0660053	−0.0330026	+	0.999455i	$0.510507\pi$
$128$	−1.00000	−0.0883883
$129$	−4.13412	−0.363989
$130$	−0.109151	−0.00957319
$131$	−17.0361	−1.48845	−0.744227	−	0.667927i	$-0.767182\pi$
$131$	−17.0361	−1.48845	−0.744227	+	0.667927i	$0.767182\pi$
$132$	6.41164	0.558061
$133$	0	0
$134$	14.9655	1.29282
$135$	0.0978870	0.00842477
$136$	−4.91930	−0.421826
$137$	−17.7675	−1.51798	−0.758992	−	0.651100i	$-0.774308\pi$
$137$	−17.7675	−1.51798	−0.758992	+	0.651100i	$0.774308\pi$
$138$	1.58721	0.135112
$139$	18.7829	1.59314	0.796571	−	0.604545i	$-0.206645\pi$
$139$	18.7829	1.59314	0.796571	+	0.604545i	$0.206645\pi$
$140$	0.256271	0.0216589
$141$	−1.90398	−0.160344
$142$	−10.3974	−0.872527
$143$	7.14945	0.597867
$144$	1.00000	0.0833333
$145$	0.455990	0.0378679
$146$	−1.75435	−0.145191
$147$	−0.145898	−0.0120335
$148$	−9.60845	−0.789810
$149$	4.99594	0.409284	0.204642	−	0.978837i	$-0.434397\pi$
$149$	4.99594	0.409284	0.204642	+	0.978837i	$0.434397\pi$
$150$	4.99042	0.407466
$151$	−18.2408	−1.48442	−0.742209	−	0.670168i	$-0.766222\pi$
$151$	−18.2408	−1.48442	−0.742209	+	0.670168i	$0.766222\pi$
$152$	0	0
$153$	4.91930	0.397702
$154$	−16.7859	−1.35265
$155$	0.775776	0.0623118
$156$	1.11507	0.0892773
$157$	−9.91711	−0.791471	−0.395736	−	0.918364i	$-0.629510\pi$
$157$	−9.91711	−0.791471	−0.395736	+	0.918364i	$0.629510\pi$
$158$	14.4329	1.14822
$159$	−4.65833	−0.369429
$160$	−0.0978870	−0.00773864
$161$	−4.15537	−0.327489
$162$	−1.00000	−0.0785674
$163$	−10.5065	−0.822933	−0.411467	−	0.911425i	$-0.634983\pi$
$163$	−10.5065	−0.822933	−0.411467	+	0.911425i	$0.634983\pi$
$164$	−6.50651	−0.508073
$165$	0.627616	0.0488598
$166$	−15.1975	−1.17956
$167$	5.56597	0.430707	0.215354	−	0.976536i	$-0.430910\pi$
$167$	5.56597	0.430707	0.215354	+	0.976536i	$0.430910\pi$
$168$	−2.61803	−0.201986
$169$	−11.7566	−0.904355
$170$	−0.481535	−0.0369321
$171$	0	0
$172$	−4.13412	−0.315224
$173$	17.5373	1.33334	0.666669	−	0.745354i	$-0.267719\pi$
$173$	17.5373	1.33334	0.666669	+	0.745354i	$0.267719\pi$
$174$	−4.65833	−0.353147
$175$	−13.0651	−0.987628
$176$	6.41164	0.483295
$177$	3.95605	0.297355
$178$	−6.35114	−0.476038
$179$	−17.7330	−1.32543	−0.662713	−	0.748873i	$-0.730595\pi$
$179$	−17.7330	−1.32543	−0.662713	+	0.748873i	$0.730595\pi$
$180$	0.0978870	0.00729606
$181$	14.8789	1.10594	0.552970	−	0.833201i	$-0.313495\pi$
$181$	14.8789	1.10594	0.552970	+	0.833201i	$0.313495\pi$
$182$	−2.91930	−0.216393
$183$	4.02124	0.297259
$184$	1.58721	0.117011
$185$	−0.940542	−0.0691500
$186$	−7.92522	−0.581105
$187$	31.5408	2.30649
$188$	−1.90398	−0.138862
$189$	2.61803	0.190434
$190$	0	0
$191$	14.5196	1.05060	0.525302	−	0.850916i	$-0.323952\pi$
$191$	14.5196	1.05060	0.525302	+	0.850916i	$0.323952\pi$
$192$	1.00000	0.0721688
$193$	5.71007	0.411020	0.205510	−	0.978655i	$-0.434115\pi$
$193$	5.71007	0.411020	0.205510	+	0.978655i	$0.434115\pi$
$194$	15.8767	1.13988
$195$	0.109151	0.00781647
$196$	−0.145898	−0.0104213
$197$	3.23492	0.230478	0.115239	−	0.993338i	$-0.463237\pi$
$197$	3.23492	0.230478	0.115239	+	0.993338i	$0.463237\pi$
$198$	−6.41164	−0.455655
$199$	19.9406	1.41355	0.706776	−	0.707437i	$-0.250149\pi$
$199$	19.9406	1.41355	0.706776	+	0.707437i	$0.250149\pi$
$200$	4.99042	0.352876
$201$	−14.9655	−1.05559
$202$	14.7829	1.04012
$203$	12.1957	0.855968
$204$	4.91930	0.344420
$205$	−0.636902	−0.0444832
$206$	−10.1198	−0.705083
$207$	−1.58721	−0.110319
$208$	1.11507	0.0773164
$209$	0	0
$210$	−0.256271	−0.0176844
$211$	5.56224	0.382920	0.191460	−	0.981500i	$-0.438678\pi$
$211$	5.56224	0.382920	0.191460	+	0.981500i	$0.438678\pi$
$212$	−4.65833	−0.319935
$213$	10.3974	0.712415
$214$	−11.1458	−0.761910
$215$	−0.404677	−0.0275987
$216$	−1.00000	−0.0680414
$217$	20.7485	1.40850
$218$	−4.37238	−0.296135
$219$	1.75435	0.118548
$220$	0.627616	0.0423139
$221$	5.48538	0.368986
$222$	9.60845	0.644877
$223$	14.2876	0.956770	0.478385	−	0.878150i	$-0.341222\pi$
$223$	14.2876	0.956770	0.478385	+	0.878150i	$0.341222\pi$
$224$	−2.61803	−0.174925
$225$	−4.99042	−0.332695
$226$	0.120995	0.00804846
$227$	2.73530	0.181548	0.0907741	−	0.995872i	$-0.471066\pi$
$227$	2.73530	0.181548	0.0907741	+	0.995872i	$0.471066\pi$
$228$	0	0
$229$	−23.1471	−1.52961	−0.764803	−	0.644264i	$-0.777164\pi$
$229$	−23.1471	−1.52961	−0.764803	+	0.644264i	$0.777164\pi$
$230$	0.155367	0.0102446
$231$	16.7859	1.10443
$232$	−4.65833	−0.305834
$233$	−0.798304	−0.0522986	−0.0261493	−	0.999658i	$-0.508325\pi$
$233$	−0.798304	−0.0522986	−0.0261493	+	0.999658i	$0.508325\pi$
$234$	−1.11507	−0.0728946
$235$	−0.186375	−0.0121577
$236$	3.95605	0.257517
$237$	−14.4329	−0.937516
$238$	−12.8789	−0.834815
$239$	13.0615	0.844881	0.422440	−	0.906391i	$-0.361174\pi$
$239$	13.0615	0.844881	0.422440	+	0.906391i	$0.361174\pi$
$240$	0.0978870	0.00631858
$241$	−7.69019	−0.495369	−0.247684	−	0.968841i	$-0.579670\pi$
$241$	−7.69019	−0.495369	−0.247684	+	0.968841i	$0.579670\pi$
$242$	−30.1091	−1.93549
$243$	1.00000	0.0641500
$244$	4.02124	0.257434
$245$	−0.0142815	−0.000912413 0
$246$	6.50651	0.414840
$247$	0	0
$248$	−7.92522	−0.503252
$249$	15.1975	0.963104
$250$	0.977932	0.0618498
$251$	5.77810	0.364710	0.182355	−	0.983233i	$-0.441628\pi$
$251$	5.77810	0.364710	0.182355	+	0.983233i	$0.441628\pi$
$252$	2.61803	0.164921
$253$	−10.1766	−0.639798
$254$	0.743841	0.0466728
$255$	0.481535	0.0301549
$256$	1.00000	0.0625000
$257$	−7.68093	−0.479123	−0.239562	−	0.970881i	$-0.577004\pi$
$257$	−7.68093	−0.479123	−0.239562	+	0.970881i	$0.577004\pi$
$258$	4.13412	0.257379
$259$	−25.1553	−1.56307
$260$	0.109151	0.00676926
$261$	4.65833	0.288343
$262$	17.0361	1.05250
$263$	4.26825	0.263191	0.131596	−	0.991303i	$-0.457990\pi$
$263$	4.26825	0.263191	0.131596	+	0.991303i	$0.457990\pi$
$264$	−6.41164	−0.394609
$265$	−0.455990	−0.0280112
$266$	0	0
$267$	6.35114	0.388684
$268$	−14.9655	−0.914164
$269$	14.9654	0.912459	0.456230	−	0.889862i	$-0.349200\pi$
$269$	14.9654	0.912459	0.456230	+	0.889862i	$0.349200\pi$
$270$	−0.0978870	−0.00595721
$271$	21.8349	1.32638	0.663189	−	0.748452i	$-0.269203\pi$
$271$	21.8349	1.32638	0.663189	+	0.748452i	$0.269203\pi$
$272$	4.91930	0.298276
$273$	2.91930	0.176684
$274$	17.7675	1.07338
$275$	−31.9968	−1.92948
$276$	−1.58721	−0.0955388
$277$	−20.9382	−1.25806	−0.629028	−	0.777382i	$-0.716547\pi$
$277$	−20.9382	−1.25806	−0.629028	+	0.777382i	$0.716547\pi$
$278$	−18.7829	−1.12652
$279$	7.92522	0.474471
$280$	−0.256271	−0.0153151
$281$	−13.1209	−0.782726	−0.391363	−	0.920236i	$-0.627996\pi$
$281$	−13.1209	−0.782726	−0.391363	+	0.920236i	$0.627996\pi$
$282$	1.90398	0.113380
$283$	−15.7257	−0.934797	−0.467398	−	0.884047i	$-0.654809\pi$
$283$	−15.7257	−0.934797	−0.467398	+	0.884047i	$0.654809\pi$
$284$	10.3974	0.616970
$285$	0	0
$286$	−7.14945	−0.422756
$287$	−17.0343	−1.00550
$288$	−1.00000	−0.0589256
$289$	7.19950	0.423500
$290$	−0.455990	−0.0267766
$291$	−15.8767	−0.930709
$292$	1.75435	0.102666
$293$	10.0711	0.588361	0.294181	−	0.955750i	$-0.404953\pi$
$293$	10.0711	0.588361	0.294181	+	0.955750i	$0.404953\pi$
$294$	0.145898	0.00850895
$295$	0.387245	0.0225463
$296$	9.60845	0.558480
$297$	6.41164	0.372041
$298$	−4.99594	−0.289407
$299$	−1.76985	−0.102353
$300$	−4.99042	−0.288122
$301$	−10.8233	−0.623843
$302$	18.2408	1.04964
$303$	−14.7829	−0.849254
$304$	0	0
$305$	0.393627	0.0225390
$306$	−4.91930	−0.281218
$307$	−1.00011	−0.0570795	−0.0285397	−	0.999593i	$-0.509086\pi$
$307$	−1.00011	−0.0570795	−0.0285397	+	0.999593i	$0.509086\pi$
$308$	16.7859	0.956465
$309$	10.1198	0.575698
$310$	−0.775776	−0.0440611
$311$	−33.6618	−1.90878	−0.954392	−	0.298557i	$-0.903495\pi$
$311$	−33.6618	−1.90878	−0.954392	+	0.298557i	$0.903495\pi$
$312$	−1.11507	−0.0631286
$313$	33.6500	1.90201	0.951005	−	0.309176i	$-0.100053\pi$
$313$	33.6500	1.90201	0.951005	+	0.309176i	$0.100053\pi$
$314$	9.91711	0.559655
$315$	0.256271	0.0144393
$316$	−14.4329	−0.811913
$317$	21.0924	1.18467	0.592333	−	0.805694i	$-0.298207\pi$
$317$	21.0924	1.18467	0.592333	+	0.805694i	$0.298207\pi$
$318$	4.65833	0.261226
$319$	29.8675	1.67226
$320$	0.0978870	0.00547205
$321$	11.1458	0.622097
$322$	4.15537	0.231570
$323$	0	0
$324$	1.00000	0.0555556
$325$	−5.56468	−0.308673
$326$	10.5065	0.581902
$327$	4.37238	0.241793
$328$	6.50651	0.359262
$329$	−4.98468	−0.274814
$330$	−0.627616	−0.0345491
$331$	−4.86368	−0.267332	−0.133666	−	0.991026i	$-0.542675\pi$
$331$	−4.86368	−0.267332	−0.133666	+	0.991026i	$0.542675\pi$
$332$	15.1975	0.834073
$333$	−9.60845	−0.526540
$334$	−5.56597	−0.304556
$335$	−1.46493	−0.0800376
$336$	2.61803	0.142825
$337$	−10.7829	−0.587380	−0.293690	−	0.955901i	$-0.594883\pi$
$337$	−10.7829	−0.587380	−0.293690	+	0.955901i	$0.594883\pi$
$338$	11.7566	0.639475
$339$	−0.120995	−0.00657154
$340$	0.481535	0.0261149
$341$	50.8137	2.75171
$342$	0	0
$343$	−18.7082	−1.01015
$344$	4.13412	0.222897
$345$	−0.155367	−0.00836468
$346$	−17.5373	−0.942813
$347$	0.492227	0.0264241	0.0132121	−	0.999913i	$-0.495794\pi$
$347$	0.492227	0.0264241	0.0132121	+	0.999913i	$0.495794\pi$
$348$	4.65833	0.249713
$349$	−4.48526	−0.240091	−0.120045	−	0.992768i	$-0.538304\pi$
$349$	−4.48526	−0.240091	−0.120045	+	0.992768i	$0.538304\pi$
$350$	13.0651	0.698358
$351$	1.11507	0.0595182
$352$	−6.41164	−0.341741
$353$	−18.7141	−0.996052	−0.498026	−	0.867162i	$-0.665942\pi$
$353$	−18.7141	−0.996052	−0.498026	+	0.867162i	$0.665942\pi$
$354$	−3.95605	−0.210261
$355$	1.01777	0.0540174
$356$	6.35114	0.336610
$357$	12.8789	0.681623
$358$	17.7330	0.937218
$359$	17.5680	0.927206	0.463603	−	0.886043i	$-0.346556\pi$
$359$	17.5680	0.927206	0.463603	+	0.886043i	$0.346556\pi$
$360$	−0.0978870	−0.00515910
$361$	0	0
$362$	−14.8789	−0.782017
$363$	30.1091	1.58032
$364$	2.91930	0.153013
$365$	0.171728	0.00898866
$366$	−4.02124	−0.210194
$367$	−5.42079	−0.282963	−0.141482	−	0.989941i	$-0.545187\pi$
$367$	−5.42079	−0.282963	−0.141482	+	0.989941i	$0.545187\pi$
$368$	−1.58721	−0.0827390
$369$	−6.50651	−0.338715
$370$	0.940542	0.0488965
$371$	−12.1957	−0.633167
$372$	7.92522	0.410904
$373$	33.7734	1.74872	0.874359	−	0.485279i	$-0.161282\pi$
$373$	33.7734	1.74872	0.874359	+	0.485279i	$0.161282\pi$
$374$	−31.5408	−1.63093
$375$	−0.977932	−0.0505002
$376$	1.90398	0.0981902
$377$	5.19438	0.267524
$378$	−2.61803	−0.134657
$379$	−18.7191	−0.961538	−0.480769	−	0.876847i	$-0.659642\pi$
$379$	−18.7191	−0.961538	−0.480769	+	0.876847i	$0.659642\pi$
$380$	0	0
$381$	−0.743841	−0.0381081
$382$	−14.5196	−0.742889
$383$	8.10685	0.414240	0.207120	−	0.978315i	$-0.433591\pi$
$383$	8.10685	0.414240	0.207120	+	0.978315i	$0.433591\pi$
$384$	−1.00000	−0.0510310
$385$	1.64312	0.0837411
$386$	−5.71007	−0.290635
$387$	−4.13412	−0.210149
$388$	−15.8767	−0.806017
$389$	25.9573	1.31609	0.658043	−	0.752980i	$-0.271384\pi$
$389$	25.9573	1.31609	0.658043	+	0.752980i	$0.271384\pi$
$390$	−0.109151	−0.00552708
$391$	−7.80796	−0.394865
$392$	0.145898	0.00736896
$393$	−17.0361	−0.859359
$394$	−3.23492	−0.162973
$395$	−1.41279	−0.0710852
$396$	6.41164	0.322197
$397$	−20.1979	−1.01370	−0.506851	−	0.862034i	$-0.669190\pi$
$397$	−20.1979	−1.01370	−0.506851	+	0.862034i	$0.669190\pi$
$398$	−19.9406	−0.999533
$399$	0	0
$400$	−4.99042	−0.249521
$401$	22.7866	1.13791	0.568954	−	0.822369i	$-0.307348\pi$
$401$	22.7866	1.13791	0.568954	+	0.822369i	$0.307348\pi$
$402$	14.9655	0.746412
$403$	8.83720	0.440212
$404$	−14.7829	−0.735475
$405$	0.0978870	0.00486404
$406$	−12.1957	−0.605260
$407$	−61.6059	−3.05369
$408$	−4.91930	−0.243542
$409$	4.59628	0.227271	0.113636	−	0.993522i	$-0.463750\pi$
$409$	4.59628	0.227271	0.113636	+	0.993522i	$0.463750\pi$
$410$	0.636902	0.0314544
$411$	−17.7675	−0.876409
$412$	10.1198	0.498569
$413$	10.3571	0.509638
$414$	1.58721	0.0780071
$415$	1.48764	0.0730254
$416$	−1.11507	−0.0546710
$417$	18.7829	0.919801
$418$	0	0
$419$	−30.1000	−1.47048	−0.735240	−	0.677807i	$-0.762930\pi$
$419$	−30.1000	−1.47048	−0.735240	+	0.677807i	$0.762930\pi$
$420$	0.256271	0.0125048
$421$	−15.5374	−0.757247	−0.378623	−	0.925551i	$-0.623602\pi$
$421$	−15.5374	−0.757247	−0.378623	+	0.925551i	$0.623602\pi$
$422$	−5.56224	−0.270765
$423$	−1.90398	−0.0925746
$424$	4.65833	0.226228
$425$	−24.5494	−1.19082
$426$	−10.3974	−0.503754
$427$	10.5278	0.509474
$428$	11.1458	0.538752
$429$	7.14945	0.345178
$430$	0.404677	0.0195153
$431$	−26.7806	−1.28997	−0.644987	−	0.764193i	$-0.723137\pi$
$431$	−26.7806	−1.28997	−0.644987	+	0.764193i	$0.723137\pi$
$432$	1.00000	0.0481125
$433$	4.85507	0.233320	0.116660	−	0.993172i	$-0.462781\pi$
$433$	4.85507	0.233320	0.116660	+	0.993172i	$0.462781\pi$
$434$	−20.7485	−0.995960
$435$	0.455990	0.0218630
$436$	4.37238	0.209399
$437$	0	0
$438$	−1.75435	−0.0838261
$439$	0.689286	0.0328978	0.0164489	−	0.999865i	$-0.494764\pi$
$439$	0.689286	0.0328978	0.0164489	+	0.999865i	$0.494764\pi$
$440$	−0.627616	−0.0299204
$441$	−0.145898	−0.00694753
$442$	−5.48538	−0.260913
$443$	−10.9518	−0.520336	−0.260168	−	0.965563i	$-0.583778\pi$
$443$	−10.9518	−0.520336	−0.260168	+	0.965563i	$0.583778\pi$
$444$	−9.60845	−0.455997
$445$	0.621694	0.0294711
$446$	−14.2876	−0.676539
$447$	4.99594	0.236300
$448$	2.61803	0.123690
$449$	−1.06384	−0.0502058	−0.0251029	−	0.999685i	$-0.507991\pi$
$449$	−1.06384	−0.0502058	−0.0251029	+	0.999685i	$0.507991\pi$
$450$	4.99042	0.235251
$451$	−41.7174	−1.96439
$452$	−0.120995	−0.00569112
$453$	−18.2408	−0.857029
$454$	−2.73530	−0.128374
$455$	0.285761	0.0133967
$456$	0	0
$457$	6.24199	0.291988	0.145994	−	0.989285i	$-0.453362\pi$
$457$	6.24199	0.291988	0.145994	+	0.989285i	$0.453362\pi$
$458$	23.1471	1.08159
$459$	4.91930	0.229613
$460$	−0.155367	−0.00724403
$461$	−3.85590	−0.179587	−0.0897935	−	0.995960i	$-0.528621\pi$
$461$	−3.85590	−0.179587	−0.0897935	+	0.995960i	$0.528621\pi$
$462$	−16.7859	−0.780950
$463$	−13.4260	−0.623959	−0.311979	−	0.950089i	$-0.600992\pi$
$463$	−13.4260	−0.623959	−0.311979	+	0.950089i	$0.600992\pi$
$464$	4.65833	0.216257
$465$	0.775776	0.0359757
$466$	0.798304	0.0369807
$467$	−9.35520	−0.432907	−0.216453	−	0.976293i	$-0.569449\pi$
$467$	−9.35520	−0.432907	−0.216453	+	0.976293i	$0.569449\pi$
$468$	1.11507	0.0515443
$469$	−39.1802	−1.80917
$470$	0.186375	0.00859682
$471$	−9.91711	−0.456956
$472$	−3.95605	−0.182092
$473$	−26.5065	−1.21877
$474$	14.4329	0.662924
$475$	0	0
$476$	12.8789	0.590303
$477$	−4.65833	−0.213290
$478$	−13.0615	−0.597421
$479$	−20.1031	−0.918535	−0.459267	−	0.888298i	$-0.651888\pi$
$479$	−20.1031	−0.918535	−0.459267	+	0.888298i	$0.651888\pi$
$480$	−0.0978870	−0.00446791
$481$	−10.7141	−0.488522
$482$	7.69019	0.350279
$483$	−4.15537	−0.189076
$484$	30.1091	1.36860
$485$	−1.55412	−0.0705690
$486$	−1.00000	−0.0453609
$487$	−9.36331	−0.424292	−0.212146	−	0.977238i	$-0.568045\pi$
$487$	−9.36331	−0.424292	−0.212146	+	0.977238i	$0.568045\pi$
$488$	−4.02124	−0.182033
$489$	−10.5065	−0.475121
$490$	0.0142815	0.000645173 0
$491$	−6.22700	−0.281020	−0.140510	−	0.990079i	$-0.544874\pi$
$491$	−6.22700	−0.281020	−0.140510	+	0.990079i	$0.544874\pi$
$492$	−6.50651	−0.293336
$493$	22.9157	1.03207
$494$	0	0
$495$	0.627616	0.0282092
$496$	7.92522	0.355853
$497$	27.2206	1.22101
$498$	−15.1975	−0.681017
$499$	−4.39736	−0.196853	−0.0984264	−	0.995144i	$-0.531381\pi$
$499$	−4.39736	−0.196853	−0.0984264	+	0.995144i	$0.531381\pi$
$500$	−0.977932	−0.0437344
$501$	5.56597	0.248669
$502$	−5.77810	−0.257889
$503$	−1.86380	−0.0831026	−0.0415513	−	0.999136i	$-0.513230\pi$
$503$	−1.86380	−0.0831026	−0.0415513	+	0.999136i	$0.513230\pi$
$504$	−2.61803	−0.116617
$505$	−1.44705	−0.0643929
$506$	10.1766	0.452406
$507$	−11.7566	−0.522129
$508$	−0.743841	−0.0330026
$509$	7.37593	0.326932	0.163466	−	0.986549i	$-0.447733\pi$
$509$	7.37593	0.326932	0.163466	+	0.986549i	$0.447733\pi$
$510$	−0.481535	−0.0213227
$511$	4.59295	0.203180
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	7.68093	0.338791
$515$	0.990601	0.0436511
$516$	−4.13412	−0.181995
$517$	−12.2076	−0.536890
$518$	25.1553	1.10526
$519$	17.5373	0.769803
$520$	−0.109151	−0.00478659
$521$	28.4590	1.24681	0.623406	−	0.781898i	$-0.285748\pi$
$521$	28.4590	1.24681	0.623406	+	0.781898i	$0.285748\pi$
$522$	−4.65833	−0.203889
$523$	−24.9039	−1.08897	−0.544485	−	0.838771i	$-0.683275\pi$
$523$	−24.9039	−1.08897	−0.544485	+	0.838771i	$0.683275\pi$
$524$	−17.0361	−0.744227
$525$	−13.0651	−0.570207
$526$	−4.26825	−0.186104
$527$	38.9865	1.69828
$528$	6.41164	0.279031
$529$	−20.4808	−0.890468
$530$	0.455990	0.0198069
$531$	3.95605	0.171678
$532$	0	0
$533$	−7.25523	−0.314259
$534$	−6.35114	−0.274841
$535$	1.09103	0.0471692
$536$	14.9655	0.646412
$537$	−17.7330	−0.765235
$538$	−14.9654	−0.645206
$539$	−0.935445	−0.0402925
$540$	0.0978870	0.00421238
$541$	15.2338	0.654951	0.327475	−	0.944860i	$-0.393802\pi$
$541$	15.2338	0.654951	0.327475	+	0.944860i	$0.393802\pi$
$542$	−21.8349	−0.937891
$543$	14.8789	0.638514
$544$	−4.91930	−0.210913
$545$	0.427999	0.0183335
$546$	−2.91930	−0.124934
$547$	10.8058	0.462021	0.231011	−	0.972951i	$-0.425797\pi$
$547$	10.8058	0.462021	0.231011	+	0.972951i	$0.425797\pi$
$548$	−17.7675	−0.758992
$549$	4.02124	0.171622
$550$	31.9968	1.36435
$551$	0	0
$552$	1.58721	0.0675561
$553$	−37.7858	−1.60681
$554$	20.9382	0.889580
$555$	−0.940542	−0.0399238
$556$	18.7829	0.796571
$557$	−40.2927	−1.70726	−0.853629	−	0.520882i	$-0.825603\pi$
$557$	−40.2927	−1.70726	−0.853629	+	0.520882i	$0.825603\pi$
$558$	−7.92522	−0.335501
$559$	−4.60985	−0.194976
$560$	0.256271	0.0108294
$561$	31.5408	1.33165
$562$	13.1209	0.553471
$563$	−30.7460	−1.29579	−0.647895	−	0.761730i	$-0.724350\pi$
$563$	−30.7460	−1.29579	−0.647895	+	0.761730i	$0.724350\pi$
$564$	−1.90398	−0.0801719
$565$	−0.0118438	−0.000498274 0
$566$	15.7257	0.661001
$567$	2.61803	0.109947
$568$	−10.3974	−0.436263
$569$	−13.2573	−0.555775	−0.277888	−	0.960614i	$-0.589634\pi$
$569$	−13.2573	−0.555775	−0.277888	+	0.960614i	$0.589634\pi$
$570$	0	0
$571$	0.172226	0.00720742	0.00360371	−	0.999994i	$-0.498853\pi$
$571$	0.172226	0.00720742	0.00360371	+	0.999994i	$0.498853\pi$
$572$	7.14945	0.298933
$573$	14.5196	0.606567
$574$	17.0343	0.710996
$575$	7.92084	0.330322
$576$	1.00000	0.0416667
$577$	−14.3270	−0.596439	−0.298220	−	0.954497i	$-0.596393\pi$
$577$	−14.3270	−0.596439	−0.298220	+	0.954497i	$0.596393\pi$
$578$	−7.19950	−0.299460
$579$	5.71007	0.237302
$580$	0.455990	0.0189339
$581$	39.7876	1.65067
$582$	15.8767	0.658110
$583$	−29.8675	−1.23699
$584$	−1.75435	−0.0725955
$585$	0.109151	0.00451284
$586$	−10.0711	−0.416034
$587$	−22.8813	−0.944414	−0.472207	−	0.881488i	$-0.656542\pi$
$587$	−22.8813	−0.944414	−0.472207	+	0.881488i	$0.656542\pi$
$588$	−0.145898	−0.00601673
$589$	0	0
$590$	−0.387245	−0.0159426
$591$	3.23492	0.133067
$592$	−9.60845	−0.394905
$593$	13.8248	0.567717	0.283859	−	0.958866i	$-0.408385\pi$
$593$	13.8248	0.567717	0.283859	+	0.958866i	$0.408385\pi$
$594$	−6.41164	−0.263073
$595$	1.26068	0.0516827
$596$	4.99594	0.204642
$597$	19.9406	0.816115
$598$	1.76985	0.0723747
$599$	−40.4661	−1.65340	−0.826700	−	0.562643i	$-0.809785\pi$
$599$	−40.4661	−1.65340	−0.826700	+	0.562643i	$0.809785\pi$
$600$	4.99042	0.203733
$601$	−19.1534	−0.781283	−0.390642	−	0.920543i	$-0.627747\pi$
$601$	−19.1534	−0.781283	−0.390642	+	0.920543i	$0.627747\pi$
$602$	10.8233	0.441124
$603$	−14.9655	−0.609443
$604$	−18.2408	−0.742209
$605$	2.94729	0.119824
$606$	14.7829	0.600513
$607$	−16.8868	−0.685414	−0.342707	−	0.939442i	$-0.611344\pi$
$607$	−16.8868	−0.685414	−0.342707	+	0.939442i	$0.611344\pi$
$608$	0	0
$609$	12.1957	0.494193
$610$	−0.393627	−0.0159375
$611$	−2.12307	−0.0858904
$612$	4.91930	0.198851
$613$	−35.7746	−1.44492	−0.722462	−	0.691411i	$-0.756990\pi$
$613$	−35.7746	−1.44492	−0.722462	+	0.691411i	$0.756990\pi$
$614$	1.00011	0.0403613
$615$	−0.636902	−0.0256824
$616$	−16.7859	−0.676323
$617$	6.10414	0.245743	0.122872	−	0.992423i	$-0.460790\pi$
$617$	6.10414	0.245743	0.122872	+	0.992423i	$0.460790\pi$
$618$	−10.1198	−0.407080
$619$	22.6794	0.911562	0.455781	−	0.890092i	$-0.349360\pi$
$619$	22.6794	0.911562	0.455781	+	0.890092i	$0.349360\pi$
$620$	0.775776	0.0311559
$621$	−1.58721	−0.0636925
$622$	33.6618	1.34971
$623$	16.6275	0.666167
$624$	1.11507	0.0446386
$625$	24.8564	0.994255
$626$	−33.6500	−1.34492
$627$	0	0
$628$	−9.91711	−0.395736
$629$	−47.2668	−1.88465
$630$	−0.256271	−0.0102101
$631$	−3.07101	−0.122255	−0.0611274	−	0.998130i	$-0.519470\pi$
$631$	−3.07101	−0.122255	−0.0611274	+	0.998130i	$0.519470\pi$
$632$	14.4329	0.574109
$633$	5.56224	0.221079
$634$	−21.0924	−0.837685
$635$	−0.0728124	−0.00288947
$636$	−4.65833	−0.184715
$637$	−0.162687	−0.00644589
$638$	−29.8675	−1.18247
$639$	10.3974	0.411313
$640$	−0.0978870	−0.00386932
$641$	27.6655	1.09272	0.546361	−	0.837550i	$-0.316013\pi$
$641$	27.6655	1.09272	0.546361	+	0.837550i	$0.316013\pi$
$642$	−11.1458	−0.439889
$643$	−16.3724	−0.645664	−0.322832	−	0.946456i	$-0.604635\pi$
$643$	−16.3724	−0.645664	−0.322832	+	0.946456i	$0.604635\pi$
$644$	−4.15537	−0.163744
$645$	−0.404677	−0.0159341
$646$	0	0
$647$	−31.1340	−1.22400	−0.612002	−	0.790856i	$-0.709636\pi$
$647$	−31.1340	−1.22400	−0.612002	+	0.790856i	$0.709636\pi$
$648$	−1.00000	−0.0392837
$649$	25.3647	0.995653
$650$	5.56468	0.218265
$651$	20.7485	0.813198
$652$	−10.5065	−0.411467
$653$	−25.9056	−1.01377	−0.506883	−	0.862015i	$-0.669202\pi$
$653$	−25.9056	−1.01377	−0.506883	+	0.862015i	$0.669202\pi$
$654$	−4.37238	−0.170974
$655$	−1.66761	−0.0651591
$656$	−6.50651	−0.254036
$657$	1.75435	0.0684437
$658$	4.98468	0.194323
$659$	17.0190	0.662966	0.331483	−	0.943461i	$-0.392451\pi$
$659$	17.0190	0.662966	0.331483	+	0.943461i	$0.392451\pi$
$660$	0.627616	0.0244299
$661$	14.8004	0.575668	0.287834	−	0.957680i	$-0.407065\pi$
$661$	14.8004	0.575668	0.287834	+	0.957680i	$0.407065\pi$
$662$	4.86368	0.189032
$663$	5.48538	0.213034
$664$	−15.1975	−0.589778
$665$	0	0
$666$	9.60845	0.372320
$667$	−7.39374	−0.286287
$668$	5.56597	0.215354
$669$	14.2876	0.552392
$670$	1.46493	0.0565951
$671$	25.7828	0.995332
$672$	−2.61803	−0.100993
$673$	16.2420	0.626083	0.313041	−	0.949739i	$-0.398652\pi$
$673$	16.2420	0.626083	0.313041	+	0.949739i	$0.398652\pi$
$674$	10.7829	0.415341
$675$	−4.99042	−0.192081
$676$	−11.7566	−0.452177
$677$	−6.00585	−0.230824	−0.115412	−	0.993318i	$-0.536819\pi$
$677$	−6.00585	−0.230824	−0.115412	+	0.993318i	$0.536819\pi$
$678$	0.120995	0.00464678
$679$	−41.5657	−1.59515
$680$	−0.481535	−0.0184660
$681$	2.73530	0.104817
$682$	−50.8137	−1.94576
$683$	11.2718	0.431303	0.215652	−	0.976470i	$-0.430812\pi$
$683$	11.2718	0.431303	0.215652	+	0.976470i	$0.430812\pi$
$684$	0	0
$685$	−1.73921	−0.0664519
$686$	18.7082	0.714283
$687$	−23.1471	−0.883118
$688$	−4.13412	−0.157612
$689$	−5.19438	−0.197890
$690$	0.155367	0.00591472
$691$	5.55722	0.211407	0.105703	−	0.994398i	$-0.466291\pi$
$691$	5.55722	0.211407	0.105703	+	0.994398i	$0.466291\pi$
$692$	17.5373	0.666669
$693$	16.7859	0.637643
$694$	−0.492227	−0.0186847
$695$	1.83860	0.0697420
$696$	−4.65833	−0.176573
$697$	−32.0075	−1.21237
$698$	4.48526	0.169770
$699$	−0.798304	−0.0301946
$700$	−13.0651	−0.493814
$701$	33.5477	1.26708	0.633540	−	0.773710i	$-0.281601\pi$
$701$	33.5477	1.26708	0.633540	+	0.773710i	$0.281601\pi$
$702$	−1.11507	−0.0420857
$703$	0	0
$704$	6.41164	0.241648
$705$	−0.186375	−0.00701927
$706$	18.7141	0.704315
$707$	−38.7021	−1.45554
$708$	3.95605	0.148677
$709$	36.9230	1.38667	0.693337	−	0.720614i	$-0.256140\pi$
$709$	36.9230	1.38667	0.693337	+	0.720614i	$0.256140\pi$
$710$	−1.01777	−0.0381961
$711$	−14.4329	−0.541275
$712$	−6.35114	−0.238019
$713$	−12.5790	−0.471087
$714$	−12.8789	−0.481980
$715$	0.699838	0.0261724
$716$	−17.7330	−0.662713
$717$	13.0615	0.487792
$718$	−17.5680	−0.655634
$719$	−34.2872	−1.27870	−0.639348	−	0.768917i	$-0.720796\pi$
$719$	−34.2872	−1.27870	−0.639348	+	0.768917i	$0.720796\pi$
$720$	0.0978870	0.00364803
$721$	26.4941	0.986692
$722$	0	0
$723$	−7.69019	−0.286001
$724$	14.8789	0.552970
$725$	−23.2470	−0.863372
$726$	−30.1091	−1.11745
$727$	33.2148	1.23187	0.615934	−	0.787798i	$-0.288779\pi$
$727$	33.2148	1.23187	0.615934	+	0.787798i	$0.288779\pi$
$728$	−2.91930	−0.108196
$729$	1.00000	0.0370370
$730$	−0.171728	−0.00635594
$731$	−20.3370	−0.752191
$732$	4.02124	0.148629
$733$	−48.2703	−1.78291	−0.891453	−	0.453114i	$-0.850313\pi$
$733$	−48.2703	−1.78291	−0.891453	+	0.453114i	$0.850313\pi$
$734$	5.42079	0.200085
$735$	−0.0142815	−0.000526782 0
$736$	1.58721	0.0585053
$737$	−95.9535	−3.53449
$738$	6.50651	0.239508
$739$	1.83731	0.0675867	0.0337933	−	0.999429i	$-0.489241\pi$
$739$	1.83731	0.0675867	0.0337933	+	0.999429i	$0.489241\pi$
$740$	−0.940542	−0.0345750
$741$	0	0
$742$	12.1957	0.447717
$743$	−7.37959	−0.270731	−0.135365	−	0.990796i	$-0.543221\pi$
$743$	−7.37959	−0.270731	−0.135365	+	0.990796i	$0.543221\pi$
$744$	−7.92522	−0.290553
$745$	0.489038	0.0179170
$746$	−33.7734	−1.23653
$747$	15.1975	0.556048
$748$	31.5408	1.15324
$749$	29.1800	1.06622
$750$	0.977932	0.0357090
$751$	−2.85242	−0.104086	−0.0520431	−	0.998645i	$-0.516573\pi$
$751$	−2.85242	−0.104086	−0.0520431	+	0.998645i	$0.516573\pi$
$752$	−1.90398	−0.0694309
$753$	5.77810	0.210566
$754$	−5.19438	−0.189168
$755$	−1.78554	−0.0649825
$756$	2.61803	0.0952170
$757$	50.0652	1.81965	0.909824	−	0.414993i	$-0.136216\pi$
$757$	50.0652	1.81965	0.909824	+	0.414993i	$0.136216\pi$
$758$	18.7191	0.679910
$759$	−10.1766	−0.369388
$760$	0	0
$761$	13.1707	0.477437	0.238719	−	0.971089i	$-0.423273\pi$
$761$	13.1707	0.477437	0.238719	+	0.971089i	$0.423273\pi$
$762$	0.743841	0.0269465
$763$	11.4471	0.414411
$764$	14.5196	0.525302
$765$	0.481535	0.0174099
$766$	−8.10685	−0.292912
$767$	4.41128	0.159282
$768$	1.00000	0.0360844
$769$	−41.0415	−1.48000	−0.739998	−	0.672609i	$-0.765174\pi$
$769$	−41.0415	−1.48000	−0.739998	+	0.672609i	$0.765174\pi$
$770$	−1.64312	−0.0592139
$771$	−7.68093	−0.276622
$772$	5.71007	0.205510
$773$	12.8351	0.461645	0.230822	−	0.972996i	$-0.425858\pi$
$773$	12.8351	0.461645	0.230822	+	0.972996i	$0.425858\pi$
$774$	4.13412	0.148598
$775$	−39.5502	−1.42068
$776$	15.8767	0.569940
$777$	−25.1553	−0.902440
$778$	−25.9573	−0.930614
$779$	0	0
$780$	0.109151	0.00390824
$781$	66.6641	2.38543
$782$	7.80796	0.279212
$783$	4.65833	0.166475
$784$	−0.145898	−0.00521064
$785$	−0.970756	−0.0346478
$786$	17.0361	0.607658
$787$	−11.3058	−0.403009	−0.201505	−	0.979488i	$-0.564583\pi$
$787$	−11.3058	−0.403009	−0.201505	+	0.979488i	$0.564583\pi$
$788$	3.23492	0.115239
$789$	4.26825	0.151954
$790$	1.41279	0.0502648
$791$	−0.316769	−0.0112630
$792$	−6.41164	−0.227828
$793$	4.48398	0.159231
$794$	20.1979	0.716795
$795$	−0.455990	−0.0161723
$796$	19.9406	0.706776
$797$	2.77103	0.0981548	0.0490774	−	0.998795i	$-0.484372\pi$
$797$	2.77103	0.0981548	0.0490774	+	0.998795i	$0.484372\pi$
$798$	0	0
$799$	−9.36624	−0.331354
$800$	4.99042	0.176438
$801$	6.35114	0.224407
$802$	−22.7866	−0.804623
$803$	11.2483	0.396942
$804$	−14.9655	−0.527793
$805$	−0.406756	−0.0143363
$806$	−8.83720	−0.311277
$807$	14.9654	0.526809
$808$	14.7829	0.520060
$809$	−32.0695	−1.12750	−0.563752	−	0.825944i	$-0.690643\pi$
$809$	−32.0695	−1.12750	−0.563752	+	0.825944i	$0.690643\pi$
$810$	−0.0978870	−0.00343940
$811$	39.1721	1.37552	0.687759	−	0.725939i	$-0.258594\pi$
$811$	39.1721	1.37552	0.687759	+	0.725939i	$0.258594\pi$
$812$	12.1957	0.427984
$813$	21.8349	0.765785
$814$	61.6059	2.15929
$815$	−1.02845	−0.0360250
$816$	4.91930	0.172210
$817$	0	0
$818$	−4.59628	−0.160705
$819$	2.91930	0.102009
$820$	−0.636902	−0.0222416
$821$	31.4671	1.09821	0.549105	−	0.835753i	$-0.314969\pi$
$821$	31.4671	1.09821	0.549105	+	0.835753i	$0.314969\pi$
$822$	17.7675	0.619714
$823$	−8.43308	−0.293959	−0.146979	−	0.989140i	$-0.546955\pi$
$823$	−8.43308	−0.293959	−0.146979	+	0.989140i	$0.546955\pi$
$824$	−10.1198	−0.352541
$825$	−31.9968	−1.11398
$826$	−10.3571	−0.360368
$827$	36.6891	1.27581	0.637903	−	0.770117i	$-0.279802\pi$
$827$	36.6891	1.27581	0.637903	+	0.770117i	$0.279802\pi$
$828$	−1.58721	−0.0551593
$829$	3.44204	0.119547	0.0597734	−	0.998212i	$-0.480962\pi$
$829$	3.44204	0.119547	0.0597734	+	0.998212i	$0.480962\pi$
$830$	−1.48764	−0.0516367
$831$	−20.9382	−0.726339
$832$	1.11507	0.0386582
$833$	−0.717716	−0.0248674
$834$	−18.7829	−0.650398
$835$	0.544836	0.0188548
$836$	0	0
$837$	7.92522	0.273936
$838$	30.1000	1.03979
$839$	−42.7280	−1.47514	−0.737568	−	0.675273i	$-0.764026\pi$
$839$	−42.7280	−1.47514	−0.737568	+	0.675273i	$0.764026\pi$
$840$	−0.256271	−0.00884220
$841$	−7.29998	−0.251723
$842$	15.5374	0.535454
$843$	−13.1209	−0.451907
$844$	5.56224	0.191460
$845$	−1.15082	−0.0395894
$846$	1.90398	0.0654601
$847$	78.8267	2.70852
$848$	−4.65833	−0.159968
$849$	−15.7257	−0.539705
$850$	24.5494	0.842036
$851$	15.2506	0.522785
$852$	10.3974	0.356208
$853$	40.1018	1.37306	0.686530	−	0.727101i	$-0.259133\pi$
$853$	40.1018	1.37306	0.686530	+	0.727101i	$0.259133\pi$
$854$	−10.5278	−0.360252
$855$	0	0
$856$	−11.1458	−0.380955
$857$	−53.7902	−1.83744	−0.918719	−	0.394911i	$-0.870775\pi$
$857$	−53.7902	−1.83744	−0.918719	+	0.394911i	$0.870775\pi$
$858$	−7.14945	−0.244078
$859$	1.02486	0.0349678	0.0174839	−	0.999847i	$-0.494434\pi$
$859$	1.02486	0.0349678	0.0174839	+	0.999847i	$0.494434\pi$
$860$	−0.404677	−0.0137994
$861$	−17.0343	−0.580526
$862$	26.7806	0.912150
$863$	29.0474	0.988785	0.494392	−	0.869239i	$-0.335391\pi$
$863$	29.0474	0.988785	0.494392	+	0.869239i	$0.335391\pi$
$864$	−1.00000	−0.0340207
$865$	1.71668	0.0583687
$866$	−4.85507	−0.164982
$867$	7.19950	0.244508
$868$	20.7485	0.704250
$869$	−92.5384	−3.13915
$870$	−0.455990	−0.0154595
$871$	−16.6876	−0.565439
$872$	−4.37238	−0.148068
$873$	−15.8767	−0.537345
$874$	0	0
$875$	−2.56026	−0.0865525
$876$	1.75435	0.0592740
$877$	−20.4507	−0.690570	−0.345285	−	0.938498i	$-0.612218\pi$
$877$	−20.4507	−0.690570	−0.345285	+	0.938498i	$0.612218\pi$
$878$	−0.689286	−0.0232623
$879$	10.0711	0.339690
$880$	0.627616	0.0211569
$881$	−25.4266	−0.856644	−0.428322	−	0.903626i	$-0.640895\pi$
$881$	−25.4266	−0.856644	−0.428322	+	0.903626i	$0.640895\pi$
$882$	0.145898	0.00491264
$883$	−20.5123	−0.690294	−0.345147	−	0.938549i	$-0.612171\pi$
$883$	−20.5123	−0.690294	−0.345147	+	0.938549i	$0.612171\pi$
$884$	5.48538	0.184493
$885$	0.387245	0.0130171
$886$	10.9518	0.367933
$887$	32.2051	1.08134	0.540670	−	0.841234i	$-0.318171\pi$
$887$	32.2051	1.08134	0.540670	+	0.841234i	$0.318171\pi$
$888$	9.60845	0.322439
$889$	−1.94740	−0.0653138
$890$	−0.621694	−0.0208392
$891$	6.41164	0.214798
$892$	14.2876	0.478385
$893$	0	0
$894$	−4.99594	−0.167089
$895$	−1.73583	−0.0580224
$896$	−2.61803	−0.0874624
$897$	−1.76985	−0.0590937
$898$	1.06384	0.0355009
$899$	36.9183	1.23129
$900$	−4.99042	−0.166347
$901$	−22.9157	−0.763433
$902$	41.7174	1.38904
$903$	−10.8233	−0.360176
$904$	0.120995	0.00402423
$905$	1.45645	0.0484140
$906$	18.2408	0.606011
$907$	6.56004	0.217823	0.108911	−	0.994051i	$-0.465264\pi$
$907$	6.56004	0.217823	0.108911	+	0.994051i	$0.465264\pi$
$908$	2.73530	0.0907741
$909$	−14.7829	−0.490317
$910$	−0.285761	−0.00947290
$911$	19.0959	0.632676	0.316338	−	0.948647i	$-0.397547\pi$
$911$	19.0959	0.632676	0.316338	+	0.948647i	$0.397547\pi$
$912$	0	0
$913$	97.4410	3.22483
$914$	−6.24199	−0.206467
$915$	0.393627	0.0130129
$916$	−23.1471	−0.764803
$917$	−44.6012	−1.47286
$918$	−4.91930	−0.162361
$919$	38.4744	1.26915	0.634577	−	0.772860i	$-0.281174\pi$
$919$	38.4744	1.26915	0.634577	+	0.772860i	$0.281174\pi$
$920$	0.155367	0.00512230
$921$	−1.00011	−0.0329548
$922$	3.85590	0.126987
$923$	11.5938	0.381615
$924$	16.7859	0.552215
$925$	47.9502	1.57659
$926$	13.4260	0.441205
$927$	10.1198	0.332379
$928$	−4.65833	−0.152917
$929$	27.3416	0.897050	0.448525	−	0.893770i	$-0.351950\pi$
$929$	27.3416	0.897050	0.448525	+	0.893770i	$0.351950\pi$
$930$	−0.775776	−0.0254387
$931$	0	0
$932$	−0.798304	−0.0261493
$933$	−33.6618	−1.10204
$934$	9.35520	0.306111
$935$	3.08743	0.100970
$936$	−1.11507	−0.0364473
$937$	10.5856	0.345817	0.172909	−	0.984938i	$-0.444683\pi$
$937$	10.5856	0.345817	0.172909	+	0.984938i	$0.444683\pi$
$938$	39.1802	1.27928
$939$	33.6500	1.09813
$940$	−0.186375	−0.00607887
$941$	26.6964	0.870279	0.435139	−	0.900363i	$-0.356699\pi$
$941$	26.6964	0.870279	0.435139	+	0.900363i	$0.356699\pi$
$942$	9.91711	0.323117
$943$	10.3272	0.336300
$944$	3.95605	0.128758
$945$	0.256271	0.00833651
$946$	26.5065	0.861801
$947$	1.62345	0.0527549	0.0263775	−	0.999652i	$-0.491603\pi$
$947$	1.62345	0.0527549	0.0263775	+	0.999652i	$0.491603\pi$
$948$	−14.4329	−0.468758
$949$	1.95623	0.0635019
$950$	0	0
$951$	21.0924	0.683967
$952$	−12.8789	−0.417407
$953$	16.1908	0.524470	0.262235	−	0.965004i	$-0.415540\pi$
$953$	16.1908	0.524470	0.262235	+	0.965004i	$0.415540\pi$
$954$	4.65833	0.150819
$955$	1.42128	0.0459916
$956$	13.0615	0.422440
$957$	29.8675	0.965480
$958$	20.1031	0.649502
$959$	−46.5160	−1.50208
$960$	0.0978870	0.00315929
$961$	31.8091	1.02610
$962$	10.7141	0.345437
$963$	11.1458	0.359168
$964$	−7.69019	−0.247684
$965$	0.558941	0.0179930
$966$	4.15537	0.133697
$967$	−3.62988	−0.116729	−0.0583645	−	0.998295i	$-0.518589\pi$
$967$	−3.62988	−0.116729	−0.0583645	+	0.998295i	$0.518589\pi$
$968$	−30.1091	−0.967743
$969$	0	0
$970$	1.55412	0.0498999
$971$	−12.6076	−0.404598	−0.202299	−	0.979324i	$-0.564841\pi$
$971$	−12.6076	−0.404598	−0.202299	+	0.979324i	$0.564841\pi$
$972$	1.00000	0.0320750
$973$	49.1742	1.57645
$974$	9.36331	0.300020
$975$	−5.56468	−0.178212
$976$	4.02124	0.128717
$977$	−11.4992	−0.367891	−0.183945	−	0.982936i	$-0.558887\pi$
$977$	−11.4992	−0.367891	−0.183945	+	0.982936i	$0.558887\pi$
$978$	10.5065	0.335961
$979$	40.7212	1.30146
$980$	−0.0142815	−0.000456206 0
$981$	4.37238	0.139599
$982$	6.22700	0.198711
$983$	−7.58490	−0.241921	−0.120960	−	0.992657i	$-0.538597\pi$
$983$	−7.58490	−0.241921	−0.120960	+	0.992657i	$0.538597\pi$
$984$	6.50651	0.207420
$985$	0.316656	0.0100895
$986$	−22.9157	−0.729785
$987$	−4.98468	−0.158664
$988$	0	0
$989$	6.56172	0.208651
$990$	−0.627616	−0.0199469
$991$	16.8605	0.535593	0.267796	−	0.963476i	$-0.413705\pi$
$991$	16.8605	0.535593	0.267796	+	0.963476i	$0.413705\pi$
$992$	−7.92522	−0.251626
$993$	−4.86368	−0.154344
$994$	−27.2206	−0.863386
$995$	1.95193	0.0618802
$996$	15.1975	0.481552
$997$	20.8152	0.659223	0.329611	−	0.944117i	$-0.393082\pi$
$997$	20.8152	0.659223	0.329611	+	0.944117i	$0.393082\pi$
$998$	4.39736	0.139196
$999$	−9.60845	−0.303998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.w.1.1	✓	4
3.2	odd	2		6498.2.a.by.1.4		4
19.18	odd	2		2166.2.a.x.1.1	yes	4
57.56	even	2		6498.2.a.bv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.2.a.w.1.1	✓	4	1.1	even	1	trivial
2166.2.a.x.1.1	yes	4	19.18	odd	2
6498.2.a.bv.1.4		4	57.56	even	2
6498.2.a.by.1.4		4	3.2	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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0978870 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0978870 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.0978870 q^{10} +6.41164 q^{11} +1.00000 q^{12} +1.11507 q^{13} -2.61803 q^{14} +0.0978870 q^{15} +1.00000 q^{16} +4.91930 q^{17} -1.00000 q^{18} +0.0978870 q^{20} +2.61803 q^{21} -6.41164 q^{22} -1.58721 q^{23} -1.00000 q^{24} -4.99042 q^{25} -1.11507 q^{26} +1.00000 q^{27} +2.61803 q^{28} +4.65833 q^{29} -0.0978870 q^{30} +7.92522 q^{31} -1.00000 q^{32} +6.41164 q^{33} -4.91930 q^{34} +0.256271 q^{35} +1.00000 q^{36} -9.60845 q^{37} +1.11507 q^{39} -0.0978870 q^{40} -6.50651 q^{41} -2.61803 q^{42} -4.13412 q^{43} +6.41164 q^{44} +0.0978870 q^{45} +1.58721 q^{46} -1.90398 q^{47} +1.00000 q^{48} -0.145898 q^{49} +4.99042 q^{50} +4.91930 q^{51} +1.11507 q^{52} -4.65833 q^{53} -1.00000 q^{54} +0.627616 q^{55} -2.61803 q^{56} -4.65833 q^{58} +3.95605 q^{59} +0.0978870 q^{60} +4.02124 q^{61} -7.92522 q^{62} +2.61803 q^{63} +1.00000 q^{64} +0.109151 q^{65} -6.41164 q^{66} -14.9655 q^{67} +4.91930 q^{68} -1.58721 q^{69} -0.256271 q^{70} +10.3974 q^{71} -1.00000 q^{72} +1.75435 q^{73} +9.60845 q^{74} -4.99042 q^{75} +16.7859 q^{77} -1.11507 q^{78} -14.4329 q^{79} +0.0978870 q^{80} +1.00000 q^{81} +6.50651 q^{82} +15.1975 q^{83} +2.61803 q^{84} +0.481535 q^{85} +4.13412 q^{86} +4.65833 q^{87} -6.41164 q^{88} +6.35114 q^{89} -0.0978870 q^{90} +2.91930 q^{91} -1.58721 q^{92} +7.92522 q^{93} +1.90398 q^{94} -1.00000 q^{96} -15.8767 q^{97} +0.145898 q^{98} +6.41164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{21} - 12 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{27} + 6 q^{28} - 10 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{32} + 12 q^{33} - 4 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 4 q^{39} - 8 q^{40} + 8 q^{41} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 8 q^{45} - 12 q^{46} + 4 q^{47} + 4 q^{48} - 14 q^{49} - 6 q^{50} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 4 q^{54} + 24 q^{55} - 6 q^{56} + 10 q^{58} + 6 q^{59} + 8 q^{60} + 4 q^{61} - 8 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{65} - 12 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 12 q^{70} - 4 q^{72} - 10 q^{73} + 8 q^{74} + 6 q^{75} + 28 q^{77} - 4 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} + 8 q^{83} + 6 q^{84} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 12 q^{88} + 16 q^{89} - 8 q^{90} - 4 q^{91} + 12 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{96} - 8 q^{97} + 14 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^21 - 12 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^27 + 6 * q^28 - 10 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^32 + 12 * q^33 - 4 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 4 * q^39 - 8 * q^40 + 8 * q^41 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 8 * q^45 - 12 * q^46 + 4 * q^47 + 4 * q^48 - 14 * q^49 - 6 * q^50 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 4 * q^54 + 24 * q^55 - 6 * q^56 + 10 * q^58 + 6 * q^59 + 8 * q^60 + 4 * q^61 - 8 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^65 - 12 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 12 * q^70 - 4 * q^72 - 10 * q^73 + 8 * q^74 + 6 * q^75 + 28 * q^77 - 4 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 + 6 * q^84 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 12 * q^88 + 16 * q^89 - 8 * q^90 - 4 * q^91 + 12 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^96 - 8 * q^97 + 14 * q^98 + 12 * q^99

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