LMFDB - Embedded newform 5054.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.34730 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.34730 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.18479 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.34730 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.34730 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.18479 q^{9} -2.87939 q^{10} -0.652704 q^{11} -1.34730 q^{12} -1.53209 q^{13} +1.00000 q^{14} +3.87939 q^{15} +1.00000 q^{16} +5.63816 q^{17} -1.18479 q^{18} -2.87939 q^{20} -1.34730 q^{21} -0.652704 q^{22} +0.369585 q^{23} -1.34730 q^{24} +3.29086 q^{25} -1.53209 q^{26} +5.63816 q^{27} +1.00000 q^{28} -3.77332 q^{29} +3.87939 q^{30} +2.04189 q^{31} +1.00000 q^{32} +0.879385 q^{33} +5.63816 q^{34} -2.87939 q^{35} -1.18479 q^{36} +7.80066 q^{37} +2.06418 q^{39} -2.87939 q^{40} +12.7442 q^{41} -1.34730 q^{42} -9.45336 q^{43} -0.652704 q^{44} +3.41147 q^{45} +0.369585 q^{46} +4.18479 q^{47} -1.34730 q^{48} +1.00000 q^{49} +3.29086 q^{50} -7.59627 q^{51} -1.53209 q^{52} -10.4757 q^{53} +5.63816 q^{54} +1.87939 q^{55} +1.00000 q^{56} -3.77332 q^{58} -8.39693 q^{59} +3.87939 q^{60} -2.24123 q^{61} +2.04189 q^{62} -1.18479 q^{63} +1.00000 q^{64} +4.41147 q^{65} +0.879385 q^{66} -12.1557 q^{67} +5.63816 q^{68} -0.497941 q^{69} -2.87939 q^{70} -3.68004 q^{71} -1.18479 q^{72} -11.2490 q^{73} +7.80066 q^{74} -4.43376 q^{75} -0.652704 q^{77} +2.06418 q^{78} +5.66044 q^{79} -2.87939 q^{80} -4.04189 q^{81} +12.7442 q^{82} +0.403733 q^{83} -1.34730 q^{84} -16.2344 q^{85} -9.45336 q^{86} +5.08378 q^{87} -0.652704 q^{88} -12.8033 q^{89} +3.41147 q^{90} -1.53209 q^{91} +0.369585 q^{92} -2.75103 q^{93} +4.18479 q^{94} -1.34730 q^{96} -3.51754 q^{97} +1.00000 q^{98} +0.773318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{28} - 18 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{32} - 3 q^{33} - 3 q^{35} + 9 q^{37} - 3 q^{39} - 3 q^{40} + 9 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} - 6 q^{46} + 9 q^{47} - 3 q^{48} + 3 q^{49} - 6 q^{50} - 9 q^{51} - 12 q^{53} + 3 q^{56} - 18 q^{58} + 3 q^{59} + 6 q^{60} - 18 q^{61} + 3 q^{62} + 3 q^{64} + 3 q^{65} - 3 q^{66} + 3 q^{67} + 24 q^{69} - 3 q^{70} + 9 q^{71} - 21 q^{73} + 9 q^{74} + 3 q^{75} - 3 q^{77} - 3 q^{78} - 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 15 q^{83} - 3 q^{84} - 18 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} - 15 q^{89} - 6 q^{92} - 21 q^{93} + 9 q^{94} - 3 q^{96} + 12 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^28 - 18 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^32 - 3 * q^33 - 3 * q^35 + 9 * q^37 - 3 * q^39 - 3 * q^40 + 9 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 - 6 * q^46 + 9 * q^47 - 3 * q^48 + 3 * q^49 - 6 * q^50 - 9 * q^51 - 12 * q^53 + 3 * q^56 - 18 * q^58 + 3 * q^59 + 6 * q^60 - 18 * q^61 + 3 * q^62 + 3 * q^64 + 3 * q^65 - 3 * q^66 + 3 * q^67 + 24 * q^69 - 3 * q^70 + 9 * q^71 - 21 * q^73 + 9 * q^74 + 3 * q^75 - 3 * q^77 - 3 * q^78 - 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 15 * q^83 - 3 * q^84 - 18 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 - 15 * q^89 - 6 * q^92 - 21 * q^93 + 9 * q^94 - 3 * q^96 + 12 * q^97 + 3 * q^98 + 9 * 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
$3$	−1.34730	−0.777862	−0.388931	−	0.921267i	$-0.627156\pi$
$3$	−1.34730	−0.777862	−0.388931	+	0.921267i	$0.627156\pi$
$4$	1.00000	0.500000
$5$	−2.87939	−1.28770	−0.643850	−	0.765152i	$-0.722664\pi$
$5$	−2.87939	−1.28770	−0.643850	+	0.765152i	$0.722664\pi$
$6$	−1.34730	−0.550031
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.18479	−0.394931
$10$	−2.87939	−0.910542
$11$	−0.652704	−0.196798	−0.0983988	−	0.995147i	$-0.531372\pi$
$11$	−0.652704	−0.196798	−0.0983988	+	0.995147i	$0.531372\pi$
$12$	−1.34730	−0.388931
$13$	−1.53209	−0.424925	−0.212463	−	0.977169i	$-0.568148\pi$
$13$	−1.53209	−0.424925	−0.212463	+	0.977169i	$0.568148\pi$
$14$	1.00000	0.267261
$15$	3.87939	1.00165
$16$	1.00000	0.250000
$17$	5.63816	1.36745	0.683727	−	0.729738i	$-0.260358\pi$
$17$	5.63816	1.36745	0.683727	+	0.729738i	$0.260358\pi$
$18$	−1.18479	−0.279258
$19$	0	0
$19$	0	0
$20$	−2.87939	−0.643850
$21$	−1.34730	−0.294004
$22$	−0.652704	−0.139157
$23$	0.369585	0.0770638	0.0385319	−	0.999257i	$-0.487732\pi$
$23$	0.369585	0.0770638	0.0385319	+	0.999257i	$0.487732\pi$
$24$	−1.34730	−0.275016
$25$	3.29086	0.658172
$26$	−1.53209	−0.300467
$27$	5.63816	1.08506
$28$	1.00000	0.188982
$29$	−3.77332	−0.700688	−0.350344	−	0.936621i	$-0.613935\pi$
$29$	−3.77332	−0.700688	−0.350344	+	0.936621i	$0.613935\pi$
$30$	3.87939	0.708276
$31$	2.04189	0.366734	0.183367	−	0.983045i	$-0.441300\pi$
$31$	2.04189	0.366734	0.183367	+	0.983045i	$0.441300\pi$
$32$	1.00000	0.176777
$33$	0.879385	0.153081
$34$	5.63816	0.966936
$35$	−2.87939	−0.486705
$36$	−1.18479	−0.197465
$37$	7.80066	1.28242	0.641210	−	0.767365i	$-0.278433\pi$
$37$	7.80066	1.28242	0.641210	+	0.767365i	$0.278433\pi$
$38$	0	0
$39$	2.06418	0.330533
$40$	−2.87939	−0.455271
$41$	12.7442	1.99031	0.995157	−	0.0983024i	$-0.0313412\pi$
$41$	12.7442	1.99031	0.995157	+	0.0983024i	$0.0313412\pi$
$42$	−1.34730	−0.207892
$43$	−9.45336	−1.44162	−0.720812	−	0.693130i	$-0.756231\pi$
$43$	−9.45336	−1.44162	−0.720812	+	0.693130i	$0.756231\pi$
$44$	−0.652704	−0.0983988
$45$	3.41147	0.508553
$46$	0.369585	0.0544923
$47$	4.18479	0.610415	0.305207	−	0.952286i	$-0.401274\pi$
$47$	4.18479	0.610415	0.305207	+	0.952286i	$0.401274\pi$
$48$	−1.34730	−0.194465
$49$	1.00000	0.142857
$50$	3.29086	0.465398
$51$	−7.59627	−1.06369
$52$	−1.53209	−0.212463
$53$	−10.4757	−1.43894	−0.719471	−	0.694523i	$-0.755616\pi$
$53$	−10.4757	−1.43894	−0.719471	+	0.694523i	$0.755616\pi$
$54$	5.63816	0.767256
$55$	1.87939	0.253416
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.77332	−0.495461
$59$	−8.39693	−1.09319	−0.546593	−	0.837398i	$-0.684076\pi$
$59$	−8.39693	−1.09319	−0.546593	+	0.837398i	$0.684076\pi$
$60$	3.87939	0.500826
$61$	−2.24123	−0.286960	−0.143480	−	0.989653i	$-0.545829\pi$
$61$	−2.24123	−0.286960	−0.143480	+	0.989653i	$0.545829\pi$
$62$	2.04189	0.259320
$63$	−1.18479	−0.149270
$64$	1.00000	0.125000
$65$	4.41147	0.547176
$66$	0.879385	0.108245
$67$	−12.1557	−1.48505	−0.742527	−	0.669816i	$-0.766373\pi$
$67$	−12.1557	−1.48505	−0.742527	+	0.669816i	$0.766373\pi$
$68$	5.63816	0.683727
$69$	−0.497941	−0.0599450
$70$	−2.87939	−0.344152
$71$	−3.68004	−0.436741	−0.218370	−	0.975866i	$-0.570074\pi$
$71$	−3.68004	−0.436741	−0.218370	+	0.975866i	$0.570074\pi$
$72$	−1.18479	−0.139629
$73$	−11.2490	−1.31659	−0.658296	−	0.752759i	$-0.728723\pi$
$73$	−11.2490	−1.31659	−0.658296	+	0.752759i	$0.728723\pi$
$74$	7.80066	0.906808
$75$	−4.43376	−0.511967
$76$	0	0
$77$	−0.652704	−0.0743825
$78$	2.06418	0.233722
$79$	5.66044	0.636850	0.318425	−	0.947948i	$-0.396846\pi$
$79$	5.66044	0.636850	0.318425	+	0.947948i	$0.396846\pi$
$80$	−2.87939	−0.321925
$81$	−4.04189	−0.449099
$82$	12.7442	1.40736
$83$	0.403733	0.0443155	0.0221577	−	0.999754i	$-0.492946\pi$
$83$	0.403733	0.0443155	0.0221577	+	0.999754i	$0.492946\pi$
$84$	−1.34730	−0.147002
$85$	−16.2344	−1.76087
$86$	−9.45336	−1.01938
$87$	5.08378	0.545038
$88$	−0.652704	−0.0695784
$89$	−12.8033	−1.35715	−0.678576	−	0.734530i	$-0.737403\pi$
$89$	−12.8033	−1.35715	−0.678576	+	0.734530i	$0.737403\pi$
$90$	3.41147	0.359601
$91$	−1.53209	−0.160607
$92$	0.369585	0.0385319
$93$	−2.75103	−0.285268
$94$	4.18479	0.431628
$95$	0	0
$96$	−1.34730	−0.137508
$97$	−3.51754	−0.357152	−0.178576	−	0.983926i	$-0.557149\pi$
$97$	−3.51754	−0.357152	−0.178576	+	0.983926i	$0.557149\pi$
$98$	1.00000	0.101015
$99$	0.773318	0.0777214
$100$	3.29086	0.329086
$101$	−4.14796	−0.412737	−0.206369	−	0.978474i	$-0.566165\pi$
$101$	−4.14796	−0.412737	−0.206369	+	0.978474i	$0.566165\pi$
$102$	−7.59627	−0.752142
$103$	9.90941	0.976404	0.488202	−	0.872731i	$-0.337653\pi$
$103$	9.90941	0.976404	0.488202	+	0.872731i	$0.337653\pi$
$104$	−1.53209	−0.150234
$105$	3.87939	0.378589
$106$	−10.4757	−1.01749
$107$	−1.07873	−0.104284	−0.0521422	−	0.998640i	$-0.516605\pi$
$107$	−1.07873	−0.104284	−0.0521422	+	0.998640i	$0.516605\pi$
$108$	5.63816	0.542532
$109$	4.34998	0.416653	0.208326	−	0.978059i	$-0.433198\pi$
$109$	4.34998	0.416653	0.208326	+	0.978059i	$0.433198\pi$
$110$	1.87939	0.179192
$111$	−10.5098	−0.997546
$112$	1.00000	0.0944911
$113$	−5.82295	−0.547777	−0.273888	−	0.961761i	$-0.588310\pi$
$113$	−5.82295	−0.547777	−0.273888	+	0.961761i	$0.588310\pi$
$114$	0	0
$115$	−1.06418	−0.0992351
$116$	−3.77332	−0.350344
$117$	1.81521	0.167816
$118$	−8.39693	−0.773000
$119$	5.63816	0.516849
$120$	3.87939	0.354138
$121$	−10.5740	−0.961271
$122$	−2.24123	−0.202911
$123$	−17.1702	−1.54819
$124$	2.04189	0.183367
$125$	4.92127	0.440172
$126$	−1.18479	−0.105550
$127$	13.8726	1.23099	0.615496	−	0.788140i	$-0.288956\pi$
$127$	13.8726	1.23099	0.615496	+	0.788140i	$0.288956\pi$
$128$	1.00000	0.0883883
$129$	12.7365	1.12138
$130$	4.41147	0.386912
$131$	1.20439	0.105228	0.0526141	−	0.998615i	$-0.483245\pi$
$131$	1.20439	0.105228	0.0526141	+	0.998615i	$0.483245\pi$
$132$	0.879385	0.0765407
$133$	0	0
$134$	−12.1557	−1.05009
$135$	−16.2344	−1.39724
$136$	5.63816	0.483468
$137$	−0.965852	−0.0825183	−0.0412591	−	0.999148i	$-0.513137\pi$
$137$	−0.965852	−0.0825183	−0.0412591	+	0.999148i	$0.513137\pi$
$138$	−0.497941	−0.0423875
$139$	5.83069	0.494553	0.247276	−	0.968945i	$-0.420464\pi$
$139$	5.83069	0.494553	0.247276	+	0.968945i	$0.420464\pi$
$140$	−2.87939	−0.243352
$141$	−5.63816	−0.474818
$142$	−3.68004	−0.308822
$143$	1.00000	0.0836242
$144$	−1.18479	−0.0987327
$145$	10.8648	0.902276
$146$	−11.2490	−0.930971
$147$	−1.34730	−0.111123
$148$	7.80066	0.641210
$149$	−6.00774	−0.492173	−0.246087	−	0.969248i	$-0.579145\pi$
$149$	−6.00774	−0.492173	−0.246087	+	0.969248i	$0.579145\pi$
$150$	−4.43376	−0.362015
$151$	−13.0077	−1.05855	−0.529277	−	0.848449i	$-0.677537\pi$
$151$	−13.0077	−1.05855	−0.529277	+	0.848449i	$0.677537\pi$
$152$	0	0
$153$	−6.68004	−0.540050
$154$	−0.652704	−0.0525964
$155$	−5.87939	−0.472244
$156$	2.06418	0.165266
$157$	−14.6604	−1.17003	−0.585015	−	0.811022i	$-0.698912\pi$
$157$	−14.6604	−1.17003	−0.585015	+	0.811022i	$0.698912\pi$
$158$	5.66044	0.450321
$159$	14.1138	1.11930
$160$	−2.87939	−0.227635
$161$	0.369585	0.0291274
$162$	−4.04189	−0.317561
$163$	−16.4679	−1.28987	−0.644933	−	0.764239i	$-0.723115\pi$
$163$	−16.4679	−1.28987	−0.644933	+	0.764239i	$0.723115\pi$
$164$	12.7442	0.995157
$165$	−2.53209	−0.197123
$166$	0.403733	0.0313358
$167$	−0.170245	−0.0131739	−0.00658696	−	0.999978i	$-0.502097\pi$
$167$	−0.170245	−0.0131739	−0.00658696	+	0.999978i	$0.502097\pi$
$168$	−1.34730	−0.103946
$169$	−10.6527	−0.819439
$170$	−16.2344	−1.24512
$171$	0	0
$172$	−9.45336	−0.720812
$173$	16.2371	1.23448	0.617242	−	0.786773i	$-0.288250\pi$
$173$	16.2371	1.23448	0.617242	+	0.786773i	$0.288250\pi$
$174$	5.08378	0.385400
$175$	3.29086	0.248766
$176$	−0.652704	−0.0491994
$177$	11.3131	0.850348
$178$	−12.8033	−0.959651
$179$	21.6905	1.62122	0.810611	−	0.585585i	$-0.199135\pi$
$179$	21.6905	1.62122	0.810611	+	0.585585i	$0.199135\pi$
$180$	3.41147	0.254276
$181$	6.49020	0.482413	0.241206	−	0.970474i	$-0.422457\pi$
$181$	6.49020	0.482413	0.241206	+	0.970474i	$0.422457\pi$
$182$	−1.53209	−0.113566
$183$	3.01960	0.223215
$184$	0.369585	0.0272462
$185$	−22.4611	−1.65137
$186$	−2.75103	−0.201715
$187$	−3.68004	−0.269112
$188$	4.18479	0.305207
$189$	5.63816	0.410115
$190$	0	0
$191$	−8.81521	−0.637846	−0.318923	−	0.947781i	$-0.603321\pi$
$191$	−8.81521	−0.637846	−0.318923	+	0.947781i	$0.603321\pi$
$192$	−1.34730	−0.0972327
$193$	−21.8229	−1.57085	−0.785425	−	0.618957i	$-0.787556\pi$
$193$	−21.8229	−1.57085	−0.785425	+	0.618957i	$0.787556\pi$
$194$	−3.51754	−0.252545
$195$	−5.94356	−0.425627
$196$	1.00000	0.0714286
$197$	−22.6236	−1.61187	−0.805933	−	0.592007i	$-0.798336\pi$
$197$	−22.6236	−1.61187	−0.805933	+	0.592007i	$0.798336\pi$
$198$	0.773318	0.0549573
$199$	−23.9709	−1.69925	−0.849626	−	0.527385i	$-0.823172\pi$
$199$	−23.9709	−1.69925	−0.849626	+	0.527385i	$0.823172\pi$
$200$	3.29086	0.232699
$201$	16.3773	1.15517
$202$	−4.14796	−0.291849
$203$	−3.77332	−0.264835
$204$	−7.59627	−0.531845
$205$	−36.6955	−2.56293
$206$	9.90941	0.690422
$207$	−0.437882	−0.0304349
$208$	−1.53209	−0.106231
$209$	0	0
$210$	3.87939	0.267703
$211$	−7.11381	−0.489735	−0.244867	−	0.969557i	$-0.578744\pi$
$211$	−7.11381	−0.489735	−0.244867	+	0.969557i	$0.578744\pi$
$212$	−10.4757	−0.719471
$213$	4.95811	0.339724
$214$	−1.07873	−0.0737402
$215$	27.2199	1.85638
$216$	5.63816	0.383628
$217$	2.04189	0.138612
$218$	4.34998	0.294618
$219$	15.1557	1.02413
$220$	1.87939	0.126708
$221$	−8.63816	−0.581065
$222$	−10.5098	−0.705372
$223$	15.8675	1.06257	0.531284	−	0.847194i	$-0.321710\pi$
$223$	15.8675	1.06257	0.531284	+	0.847194i	$0.321710\pi$
$224$	1.00000	0.0668153
$225$	−3.89899	−0.259932
$226$	−5.82295	−0.387337
$227$	15.9786	1.06054	0.530270	−	0.847829i	$-0.322091\pi$
$227$	15.9786	1.06054	0.530270	+	0.847829i	$0.322091\pi$
$228$	0	0
$229$	−27.9290	−1.84560	−0.922801	−	0.385278i	$-0.874106\pi$
$229$	−27.9290	−1.84560	−0.922801	+	0.385278i	$0.874106\pi$
$230$	−1.06418	−0.0701698
$231$	0.879385	0.0578593
$232$	−3.77332	−0.247730
$233$	−14.0428	−0.919976	−0.459988	−	0.887925i	$-0.652146\pi$
$233$	−14.0428	−0.919976	−0.459988	+	0.887925i	$0.652146\pi$
$234$	1.81521	0.118664
$235$	−12.0496	−0.786031
$236$	−8.39693	−0.546593
$237$	−7.62630	−0.495381
$238$	5.63816	0.365467
$239$	19.5844	1.26681	0.633405	−	0.773820i	$-0.281657\pi$
$239$	19.5844	1.26681	0.633405	+	0.773820i	$0.281657\pi$
$240$	3.87939	0.250413
$241$	5.37464	0.346211	0.173105	−	0.984903i	$-0.444620\pi$
$241$	5.37464	0.346211	0.173105	+	0.984903i	$0.444620\pi$
$242$	−10.5740	−0.679721
$243$	−11.4688	−0.735727
$244$	−2.24123	−0.143480
$245$	−2.87939	−0.183957
$246$	−17.1702	−1.09473
$247$	0	0
$248$	2.04189	0.129660
$249$	−0.543948	−0.0344713
$250$	4.92127	0.311249
$251$	−27.4807	−1.73457	−0.867283	−	0.497815i	$-0.834136\pi$
$251$	−27.4807	−1.73457	−0.867283	+	0.497815i	$0.834136\pi$
$252$	−1.18479	−0.0746349
$253$	−0.241230	−0.0151660
$254$	13.8726	0.870443
$255$	21.8726	1.36971
$256$	1.00000	0.0625000
$257$	16.7050	1.04203	0.521015	−	0.853547i	$-0.325553\pi$
$257$	16.7050	1.04203	0.521015	+	0.853547i	$0.325553\pi$
$258$	12.7365	0.792939
$259$	7.80066	0.484709
$260$	4.41147	0.273588
$261$	4.47060	0.276723
$262$	1.20439	0.0744076
$263$	−28.8188	−1.77705	−0.888523	−	0.458833i	$-0.848268\pi$
$263$	−28.8188	−1.77705	−0.888523	+	0.458833i	$0.848268\pi$
$264$	0.879385	0.0541224
$265$	30.1634	1.85293
$266$	0	0
$267$	17.2499	1.05568
$268$	−12.1557	−0.742527
$269$	−13.5175	−0.824179	−0.412090	−	0.911143i	$-0.635201\pi$
$269$	−13.5175	−0.824179	−0.412090	+	0.911143i	$0.635201\pi$
$270$	−16.2344	−0.987995
$271$	−5.17530	−0.314377	−0.157188	−	0.987569i	$-0.550243\pi$
$271$	−5.17530	−0.314377	−0.157188	+	0.987569i	$0.550243\pi$
$272$	5.63816	0.341863
$273$	2.06418	0.124930
$274$	−0.965852	−0.0583492
$275$	−2.14796	−0.129527
$276$	−0.497941	−0.0299725
$277$	−4.84430	−0.291066	−0.145533	−	0.989353i	$-0.546490\pi$
$277$	−4.84430	−0.291066	−0.145533	+	0.989353i	$0.546490\pi$
$278$	5.83069	0.349701
$279$	−2.41921	−0.144835
$280$	−2.87939	−0.172076
$281$	9.54664	0.569505	0.284752	−	0.958601i	$-0.408089\pi$
$281$	9.54664	0.569505	0.284752	+	0.958601i	$0.408089\pi$
$282$	−5.63816	−0.335747
$283$	−2.69190	−0.160017	−0.0800086	−	0.996794i	$-0.525495\pi$
$283$	−2.69190	−0.160017	−0.0800086	+	0.996794i	$0.525495\pi$
$284$	−3.68004	−0.218370
$285$	0	0
$286$	1.00000	0.0591312
$287$	12.7442	0.752268
$288$	−1.18479	−0.0698146
$289$	14.7888	0.869929
$290$	10.8648	0.638005
$291$	4.73917	0.277815
$292$	−11.2490	−0.658296
$293$	−6.27900	−0.366823	−0.183412	−	0.983036i	$-0.558714\pi$
$293$	−6.27900	−0.366823	−0.183412	+	0.983036i	$0.558714\pi$
$294$	−1.34730	−0.0785759
$295$	24.1780	1.40770
$296$	7.80066	0.453404
$297$	−3.68004	−0.213538
$298$	−6.00774	−0.348019
$299$	−0.566237	−0.0327463
$300$	−4.43376	−0.255983
$301$	−9.45336	−0.544883
$302$	−13.0077	−0.748511
$303$	5.58853	0.321052
$304$	0	0
$305$	6.45336	0.369519
$306$	−6.68004	−0.381873
$307$	14.1780	0.809180	0.404590	−	0.914498i	$-0.367414\pi$
$307$	14.1780	0.809180	0.404590	+	0.914498i	$0.367414\pi$
$308$	−0.652704	−0.0371912
$309$	−13.3509	−0.759507
$310$	−5.87939	−0.333927
$311$	−8.86753	−0.502831	−0.251416	−	0.967879i	$-0.580896\pi$
$311$	−8.86753	−0.502831	−0.251416	+	0.967879i	$0.580896\pi$
$312$	2.06418	0.116861
$313$	27.7374	1.56781	0.783906	−	0.620880i	$-0.213225\pi$
$313$	27.7374	1.56781	0.783906	+	0.620880i	$0.213225\pi$
$314$	−14.6604	−0.827337
$315$	3.41147	0.192215
$316$	5.66044	0.318425
$317$	−25.8871	−1.45397	−0.726983	−	0.686656i	$-0.759078\pi$
$317$	−25.8871	−1.45397	−0.726983	+	0.686656i	$0.759078\pi$
$318$	14.1138	0.791463
$319$	2.46286	0.137894
$320$	−2.87939	−0.160963
$321$	1.45336	0.0811188
$322$	0.369585	0.0205962
$323$	0	0
$324$	−4.04189	−0.224549
$325$	−5.04189	−0.279674
$326$	−16.4679	−0.912073
$327$	−5.86072	−0.324098
$328$	12.7442	0.703682
$329$	4.18479	0.230715
$330$	−2.53209	−0.139387
$331$	−12.0104	−0.660153	−0.330076	−	0.943954i	$-0.607075\pi$
$331$	−12.0104	−0.660153	−0.330076	+	0.943954i	$0.607075\pi$
$332$	0.403733	0.0221577
$333$	−9.24216	−0.506467
$334$	−0.170245	−0.00931537
$335$	35.0009	1.91231
$336$	−1.34730	−0.0735010
$337$	30.6509	1.66966	0.834832	−	0.550505i	$-0.185565\pi$
$337$	30.6509	1.66966	0.834832	+	0.550505i	$0.185565\pi$
$338$	−10.6527	−0.579431
$339$	7.84524	0.426095
$340$	−16.2344	−0.880435
$341$	−1.33275	−0.0721724
$342$	0	0
$343$	1.00000	0.0539949
$344$	−9.45336	−0.509691
$345$	1.43376	0.0771912
$346$	16.2371	0.872912
$347$	−22.8821	−1.22837	−0.614187	−	0.789160i	$-0.710516\pi$
$347$	−22.8821	−1.22837	−0.614187	+	0.789160i	$0.710516\pi$
$348$	5.08378	0.272519
$349$	5.68510	0.304316	0.152158	−	0.988356i	$-0.451378\pi$
$349$	5.68510	0.304316	0.152158	+	0.988356i	$0.451378\pi$
$350$	3.29086	0.175904
$351$	−8.63816	−0.461071
$352$	−0.652704	−0.0347892
$353$	12.8057	0.681579	0.340790	−	0.940140i	$-0.389306\pi$
$353$	12.8057	0.681579	0.340790	+	0.940140i	$0.389306\pi$
$354$	11.3131	0.601287
$355$	10.5963	0.562391
$356$	−12.8033	−0.678576
$357$	−7.59627	−0.402037
$358$	21.6905	1.14638
$359$	20.4347	1.07850	0.539251	−	0.842145i	$-0.318707\pi$
$359$	20.4347	1.07850	0.539251	+	0.842145i	$0.318707\pi$
$360$	3.41147	0.179800
$361$	0	0
$362$	6.49020	0.341117
$363$	14.2463	0.747736
$364$	−1.53209	−0.0803033
$365$	32.3901	1.69538
$366$	3.01960	0.157837
$367$	−31.8316	−1.66160	−0.830799	−	0.556573i	$-0.812116\pi$
$367$	−31.8316	−1.66160	−0.830799	+	0.556573i	$0.812116\pi$
$368$	0.369585	0.0192660
$369$	−15.0993	−0.786036
$370$	−22.4611	−1.16770
$371$	−10.4757	−0.543869
$372$	−2.75103	−0.142634
$373$	11.2790	0.584004	0.292002	−	0.956418i	$-0.405679\pi$
$373$	11.2790	0.584004	0.292002	+	0.956418i	$0.405679\pi$
$374$	−3.68004	−0.190291
$375$	−6.63041	−0.342393
$376$	4.18479	0.215814
$377$	5.78106	0.297740
$378$	5.63816	0.289995
$379$	−3.31221	−0.170137	−0.0850685	−	0.996375i	$-0.527111\pi$
$379$	−3.31221	−0.170137	−0.0850685	+	0.996375i	$0.527111\pi$
$380$	0	0
$381$	−18.6905	−0.957542
$382$	−8.81521	−0.451025
$383$	−38.8871	−1.98704	−0.993520	−	0.113660i	$-0.963742\pi$
$383$	−38.8871	−1.98704	−0.993520	+	0.113660i	$0.963742\pi$
$384$	−1.34730	−0.0687539
$385$	1.87939	0.0957823
$386$	−21.8229	−1.11076
$387$	11.2003	0.569342
$388$	−3.51754	−0.178576
$389$	34.7888	1.76386	0.881931	−	0.471378i	$-0.156243\pi$
$389$	34.7888	1.76386	0.881931	+	0.471378i	$0.156243\pi$
$390$	−5.94356	−0.300964
$391$	2.08378	0.105381
$392$	1.00000	0.0505076
$393$	−1.62267	−0.0818531
$394$	−22.6236	−1.13976
$395$	−16.2986	−0.820072
$396$	0.773318	0.0388607
$397$	27.2814	1.36921	0.684606	−	0.728913i	$-0.259974\pi$
$397$	27.2814	1.36921	0.684606	+	0.728913i	$0.259974\pi$
$398$	−23.9709	−1.20155
$399$	0	0
$400$	3.29086	0.164543
$401$	24.4766	1.22230	0.611151	−	0.791514i	$-0.290707\pi$
$401$	24.4766	1.22230	0.611151	+	0.791514i	$0.290707\pi$
$402$	16.3773	0.816827
$403$	−3.12836	−0.155834
$404$	−4.14796	−0.206369
$405$	11.6382	0.578305
$406$	−3.77332	−0.187267
$407$	−5.09152	−0.252377
$408$	−7.59627	−0.376071
$409$	−5.12836	−0.253581	−0.126790	−	0.991930i	$-0.540468\pi$
$409$	−5.12836	−0.253581	−0.126790	+	0.991930i	$0.540468\pi$
$410$	−36.6955	−1.81226
$411$	1.30129	0.0641878
$412$	9.90941	0.488202
$413$	−8.39693	−0.413186
$414$	−0.437882	−0.0215207
$415$	−1.16250	−0.0570651
$416$	−1.53209	−0.0751168
$417$	−7.85567	−0.384694
$418$	0	0
$419$	−10.9222	−0.533585	−0.266792	−	0.963754i	$-0.585964\pi$
$419$	−10.9222	−0.533585	−0.266792	+	0.963754i	$0.585964\pi$
$420$	3.87939	0.189295
$421$	−37.4252	−1.82399	−0.911996	−	0.410198i	$-0.865459\pi$
$421$	−37.4252	−1.82399	−0.911996	+	0.410198i	$0.865459\pi$
$422$	−7.11381	−0.346295
$423$	−4.95811	−0.241072
$424$	−10.4757	−0.508743
$425$	18.5544	0.900020
$426$	4.95811	0.240221
$427$	−2.24123	−0.108461
$428$	−1.07873	−0.0521422
$429$	−1.34730	−0.0650481
$430$	27.2199	1.31266
$431$	9.91622	0.477648	0.238824	−	0.971063i	$-0.423238\pi$
$431$	9.91622	0.477648	0.238824	+	0.971063i	$0.423238\pi$
$432$	5.63816	0.271266
$433$	3.87845	0.186386	0.0931932	−	0.995648i	$-0.470293\pi$
$433$	3.87845	0.186386	0.0931932	+	0.995648i	$0.470293\pi$
$434$	2.04189	0.0980138
$435$	−14.6382	−0.701846
$436$	4.34998	0.208326
$437$	0	0
$438$	15.1557	0.724167
$439$	−17.9290	−0.855705	−0.427853	−	0.903849i	$-0.640730\pi$
$439$	−17.9290	−0.855705	−0.427853	+	0.903849i	$0.640730\pi$
$440$	1.87939	0.0895962
$441$	−1.18479	−0.0564187
$442$	−8.63816	−0.410875
$443$	−13.5868	−0.645527	−0.322763	−	0.946480i	$-0.604612\pi$
$443$	−13.5868	−0.645527	−0.322763	+	0.946480i	$0.604612\pi$
$444$	−10.5098	−0.498773
$445$	36.8658	1.74761
$446$	15.8675	0.751349
$447$	8.09421	0.382843
$448$	1.00000	0.0472456
$449$	8.75877	0.413352	0.206676	−	0.978409i	$-0.433735\pi$
$449$	8.75877	0.413352	0.206676	+	0.978409i	$0.433735\pi$
$450$	−3.89899	−0.183800
$451$	−8.31820	−0.391689
$452$	−5.82295	−0.273888
$453$	17.5253	0.823410
$454$	15.9786	0.749915
$455$	4.41147	0.206813
$456$	0	0
$457$	9.74928	0.456052	0.228026	−	0.973655i	$-0.426773\pi$
$457$	9.74928	0.456052	0.228026	+	0.973655i	$0.426773\pi$
$458$	−27.9290	−1.30504
$459$	31.7888	1.48377
$460$	−1.06418	−0.0496175
$461$	21.5895	1.00552	0.502761	−	0.864426i	$-0.332318\pi$
$461$	21.5895	1.00552	0.502761	+	0.864426i	$0.332318\pi$
$462$	0.879385	0.0409127
$463$	−37.8539	−1.75922	−0.879610	−	0.475695i	$-0.842197\pi$
$463$	−37.8539	−1.75922	−0.879610	+	0.475695i	$0.842197\pi$
$464$	−3.77332	−0.175172
$465$	7.92127	0.367340
$466$	−14.0428	−0.650521
$467$	−6.81252	−0.315246	−0.157623	−	0.987499i	$-0.550383\pi$
$467$	−6.81252	−0.315246	−0.157623	+	0.987499i	$0.550383\pi$
$468$	1.81521	0.0839080
$469$	−12.1557	−0.561298
$470$	−12.0496	−0.555808
$471$	19.7520	0.910122
$472$	−8.39693	−0.386500
$473$	6.17024	0.283708
$474$	−7.62630	−0.350287
$475$	0	0
$476$	5.63816	0.258424
$477$	12.4115	0.568282
$478$	19.5844	0.895770
$479$	14.0702	0.642882	0.321441	−	0.946930i	$-0.395833\pi$
$479$	14.0702	0.642882	0.321441	+	0.946930i	$0.395833\pi$
$480$	3.87939	0.177069
$481$	−11.9513	−0.544933
$482$	5.37464	0.244808
$483$	−0.497941	−0.0226571
$484$	−10.5740	−0.480635
$485$	10.1284	0.459905
$486$	−11.4688	−0.520237
$487$	−24.3327	−1.10262	−0.551311	−	0.834300i	$-0.685872\pi$
$487$	−24.3327	−1.10262	−0.551311	+	0.834300i	$0.685872\pi$
$488$	−2.24123	−0.101456
$489$	22.1872	1.00334
$490$	−2.87939	−0.130077
$491$	39.7452	1.79367	0.896837	−	0.442361i	$-0.145859\pi$
$491$	39.7452	1.79367	0.896837	+	0.442361i	$0.145859\pi$
$492$	−17.1702	−0.774094
$493$	−21.2746	−0.958158
$494$	0	0
$495$	−2.22668	−0.100082
$496$	2.04189	0.0916835
$497$	−3.68004	−0.165073
$498$	−0.543948	−0.0243749
$499$	−42.3550	−1.89607	−0.948036	−	0.318163i	$-0.896934\pi$
$499$	−42.3550	−1.89607	−0.948036	+	0.318163i	$0.896934\pi$
$500$	4.92127	0.220086
$501$	0.229370	0.0102475
$502$	−27.4807	−1.22652
$503$	−29.8298	−1.33004	−0.665022	−	0.746824i	$-0.731578\pi$
$503$	−29.8298	−1.33004	−0.665022	+	0.746824i	$0.731578\pi$
$504$	−1.18479	−0.0527749
$505$	11.9436	0.531482
$506$	−0.241230	−0.0107240
$507$	14.3523	0.637410
$508$	13.8726	0.615496
$509$	−14.3037	−0.633998	−0.316999	−	0.948426i	$-0.602675\pi$
$509$	−14.3037	−0.633998	−0.316999	+	0.948426i	$0.602675\pi$
$510$	21.8726	0.968534
$511$	−11.2490	−0.497625
$512$	1.00000	0.0441942
$513$	0	0
$514$	16.7050	0.736827
$515$	−28.5330	−1.25732
$516$	12.7365	0.560692
$517$	−2.73143	−0.120128
$518$	7.80066	0.342741
$519$	−21.8762	−0.960259
$520$	4.41147	0.193456
$521$	33.6810	1.47559	0.737795	−	0.675025i	$-0.235867\pi$
$521$	33.6810	1.47559	0.737795	+	0.675025i	$0.235867\pi$
$522$	4.47060	0.195673
$523$	−23.6527	−1.03426	−0.517130	−	0.855907i	$-0.673000\pi$
$523$	−23.6527	−1.03426	−0.517130	+	0.855907i	$0.673000\pi$
$524$	1.20439	0.0526141
$525$	−4.43376	−0.193505
$526$	−28.8188	−1.25656
$527$	11.5125	0.501492
$528$	0.879385	0.0382703
$529$	−22.8634	−0.994061
$530$	30.1634	1.31022
$531$	9.94862	0.431733
$532$	0	0
$533$	−19.5253	−0.845734
$534$	17.2499	0.746476
$535$	3.10607	0.134287
$536$	−12.1557	−0.525046
$537$	−29.2235	−1.26109
$538$	−13.5175	−0.582783
$539$	−0.652704	−0.0281139
$540$	−16.2344	−0.698618
$541$	22.1215	0.951080	0.475540	−	0.879694i	$-0.342253\pi$
$541$	22.1215	0.951080	0.475540	+	0.879694i	$0.342253\pi$
$542$	−5.17530	−0.222298
$543$	−8.74422	−0.375251
$544$	5.63816	0.241734
$545$	−12.5253	−0.536524
$546$	2.06418	0.0883387
$547$	11.6996	0.500241	0.250120	−	0.968215i	$-0.419530\pi$
$547$	11.6996	0.500241	0.250120	+	0.968215i	$0.419530\pi$
$548$	−0.965852	−0.0412591
$549$	2.65539	0.113329
$550$	−2.14796	−0.0915891
$551$	0	0
$552$	−0.497941	−0.0211938
$553$	5.66044	0.240707
$554$	−4.84430	−0.205815
$555$	30.2618	1.28454
$556$	5.83069	0.247276
$557$	−1.01455	−0.0429878	−0.0214939	−	0.999769i	$-0.506842\pi$
$557$	−1.01455	−0.0429878	−0.0214939	+	0.999769i	$0.506842\pi$
$558$	−2.41921	−0.102414
$559$	14.4834	0.612582
$560$	−2.87939	−0.121676
$561$	4.95811	0.209332
$562$	9.54664	0.402701
$563$	−0.716881	−0.0302129	−0.0151065	−	0.999886i	$-0.504809\pi$
$563$	−0.716881	−0.0302129	−0.0151065	+	0.999886i	$0.504809\pi$
$564$	−5.63816	−0.237409
$565$	16.7665	0.705372
$566$	−2.69190	−0.113149
$567$	−4.04189	−0.169743
$568$	−3.68004	−0.154411
$569$	21.8307	0.915190	0.457595	−	0.889161i	$-0.348711\pi$
$569$	21.8307	0.915190	0.457595	+	0.889161i	$0.348711\pi$
$570$	0	0
$571$	20.4056	0.853948	0.426974	−	0.904264i	$-0.359580\pi$
$571$	20.4056	0.853948	0.426974	+	0.904264i	$0.359580\pi$
$572$	1.00000	0.0418121
$573$	11.8767	0.496156
$574$	12.7442	0.531934
$575$	1.21625	0.0507212
$576$	−1.18479	−0.0493664
$577$	2.28817	0.0952578	0.0476289	−	0.998865i	$-0.484834\pi$
$577$	2.28817	0.0952578	0.0476289	+	0.998865i	$0.484834\pi$
$578$	14.7888	0.615133
$579$	29.4020	1.22190
$580$	10.8648	0.451138
$581$	0.403733	0.0167497
$582$	4.73917	0.196445
$583$	6.83750	0.283180
$584$	−11.2490	−0.465486
$585$	−5.22668	−0.216097
$586$	−6.27900	−0.259383
$587$	28.3841	1.17154	0.585769	−	0.810478i	$-0.300792\pi$
$587$	28.3841	1.17154	0.585769	+	0.810478i	$0.300792\pi$
$588$	−1.34730	−0.0555616
$589$	0	0
$590$	24.1780	0.995392
$591$	30.4807	1.25381
$592$	7.80066	0.320605
$593$	−31.2713	−1.28416	−0.642078	−	0.766639i	$-0.721928\pi$
$593$	−31.2713	−1.28416	−0.642078	+	0.766639i	$0.721928\pi$
$594$	−3.68004	−0.150994
$595$	−16.2344	−0.665546
$596$	−6.00774	−0.246087
$597$	32.2959	1.32178
$598$	−0.566237	−0.0231552
$599$	5.93582	0.242531	0.121266	−	0.992620i	$-0.461305\pi$
$599$	5.93582	0.242531	0.121266	+	0.992620i	$0.461305\pi$
$600$	−4.43376	−0.181008
$601$	−22.5458	−0.919663	−0.459832	−	0.888006i	$-0.652090\pi$
$601$	−22.5458	−0.919663	−0.459832	+	0.888006i	$0.652090\pi$
$602$	−9.45336	−0.385290
$603$	14.4020	0.586494
$604$	−13.0077	−0.529277
$605$	30.4466	1.23783
$606$	5.58853	0.227018
$607$	−38.6860	−1.57022	−0.785109	−	0.619358i	$-0.787393\pi$
$607$	−38.6860	−1.57022	−0.785109	+	0.619358i	$0.787393\pi$
$608$	0	0
$609$	5.08378	0.206005
$610$	6.45336	0.261289
$611$	−6.41147	−0.259380
$612$	−6.68004	−0.270025
$613$	4.66313	0.188342	0.0941711	−	0.995556i	$-0.469980\pi$
$613$	4.66313	0.188342	0.0941711	+	0.995556i	$0.469980\pi$
$614$	14.1780	0.572177
$615$	49.4397	1.99360
$616$	−0.652704	−0.0262982
$617$	32.8776	1.32360	0.661802	−	0.749679i	$-0.269792\pi$
$617$	32.8776	1.32360	0.661802	+	0.749679i	$0.269792\pi$
$618$	−13.3509	−0.537053
$619$	12.2003	0.490370	0.245185	−	0.969476i	$-0.421151\pi$
$619$	12.2003	0.490370	0.245185	+	0.969476i	$0.421151\pi$
$620$	−5.87939	−0.236122
$621$	2.08378	0.0836191
$622$	−8.86753	−0.355555
$623$	−12.8033	−0.512955
$624$	2.06418	0.0826332
$625$	−30.6245	−1.22498
$626$	27.7374	1.10861
$627$	0	0
$628$	−14.6604	−0.585015
$629$	43.9813	1.75365
$630$	3.41147	0.135916
$631$	−13.2003	−0.525495	−0.262747	−	0.964865i	$-0.584629\pi$
$631$	−13.2003	−0.525495	−0.262747	+	0.964865i	$0.584629\pi$
$632$	5.66044	0.225160
$633$	9.58441	0.380946
$634$	−25.8871	−1.02811
$635$	−39.9445	−1.58515
$636$	14.1138	0.559649
$637$	−1.53209	−0.0607036
$638$	2.46286	0.0975055
$639$	4.36009	0.172482
$640$	−2.87939	−0.113818
$641$	25.0351	0.988826	0.494413	−	0.869227i	$-0.335383\pi$
$641$	25.0351	0.988826	0.494413	+	0.869227i	$0.335383\pi$
$642$	1.45336	0.0573597
$643$	20.2175	0.797301	0.398650	−	0.917103i	$-0.369479\pi$
$643$	20.2175	0.797301	0.398650	+	0.917103i	$0.369479\pi$
$644$	0.369585	0.0145637
$645$	−36.6732	−1.44401
$646$	0	0
$647$	33.1061	1.30153	0.650767	−	0.759278i	$-0.274448\pi$
$647$	33.1061	1.30153	0.650767	+	0.759278i	$0.274448\pi$
$648$	−4.04189	−0.158780
$649$	5.48070	0.215136
$650$	−5.04189	−0.197759
$651$	−2.75103	−0.107821
$652$	−16.4679	−0.644933
$653$	−33.1421	−1.29695	−0.648475	−	0.761236i	$-0.724593\pi$
$653$	−33.1421	−1.29695	−0.648475	+	0.761236i	$0.724593\pi$
$654$	−5.86072	−0.229172
$655$	−3.46791	−0.135502
$656$	12.7442	0.497578
$657$	13.3277	0.519963
$658$	4.18479	0.163140
$659$	12.7956	0.498446	0.249223	−	0.968446i	$-0.419825\pi$
$659$	12.7956	0.498446	0.249223	+	0.968446i	$0.419825\pi$
$660$	−2.53209	−0.0985614
$661$	7.74422	0.301215	0.150608	−	0.988594i	$-0.451877\pi$
$661$	7.74422	0.301215	0.150608	+	0.988594i	$0.451877\pi$
$662$	−12.0104	−0.466799
$663$	11.6382	0.451989
$664$	0.403733	0.0156679
$665$	0	0
$666$	−9.24216	−0.358127
$667$	−1.39456	−0.0539977
$668$	−0.170245	−0.00658696
$669$	−21.3783	−0.826531
$670$	35.0009	1.35220
$671$	1.46286	0.0564730
$672$	−1.34730	−0.0519731
$673$	−35.5202	−1.36920	−0.684602	−	0.728917i	$-0.740024\pi$
$673$	−35.5202	−1.36920	−0.684602	+	0.728917i	$0.740024\pi$
$674$	30.6509	1.18063
$675$	18.5544	0.714158
$676$	−10.6527	−0.409719
$677$	−9.96048	−0.382812	−0.191406	−	0.981511i	$-0.561305\pi$
$677$	−9.96048	−0.382812	−0.191406	+	0.981511i	$0.561305\pi$
$678$	7.84524	0.301295
$679$	−3.51754	−0.134991
$680$	−16.2344	−0.622562
$681$	−21.5280	−0.824954
$682$	−1.33275	−0.0510336
$683$	26.0838	0.998068	0.499034	−	0.866582i	$-0.333688\pi$
$683$	26.0838	0.998068	0.499034	+	0.866582i	$0.333688\pi$
$684$	0	0
$685$	2.78106	0.106259
$686$	1.00000	0.0381802
$687$	37.6287	1.43562
$688$	−9.45336	−0.360406
$689$	16.0496	0.611442
$690$	1.43376	0.0545824
$691$	50.7520	1.93070	0.965348	−	0.260967i	$-0.0840412\pi$
$691$	50.7520	1.93070	0.965348	+	0.260967i	$0.0840412\pi$
$692$	16.2371	0.617242
$693$	0.773318	0.0293759
$694$	−22.8821	−0.868592
$695$	−16.7888	−0.636835
$696$	5.08378	0.192700
$697$	71.8539	2.72166
$698$	5.68510	0.215184
$699$	18.9198	0.715614
$700$	3.29086	0.124383
$701$	51.9178	1.96091	0.980453	−	0.196751i	$-0.0630391\pi$
$701$	51.9178	1.96091	0.980453	+	0.196751i	$0.0630391\pi$
$702$	−8.63816	−0.326026
$703$	0	0
$704$	−0.652704	−0.0245997
$705$	16.2344	0.611424
$706$	12.8057	0.481949
$707$	−4.14796	−0.156000
$708$	11.3131	0.425174
$709$	−0.270325	−0.0101523	−0.00507614	−	0.999987i	$-0.501616\pi$
$709$	−0.270325	−0.0101523	−0.00507614	+	0.999987i	$0.501616\pi$
$710$	10.5963	0.397671
$711$	−6.70645	−0.251512
$712$	−12.8033	−0.479826
$713$	0.754652	0.0282619
$714$	−7.59627	−0.284283
$715$	−2.87939	−0.107683
$716$	21.6905	0.810611
$717$	−26.3860	−0.985403
$718$	20.4347	0.762616
$719$	23.2398	0.866698	0.433349	−	0.901226i	$-0.357332\pi$
$719$	23.2398	0.866698	0.433349	+	0.901226i	$0.357332\pi$
$720$	3.41147	0.127138
$721$	9.90941	0.369046
$722$	0	0
$723$	−7.24123	−0.269304
$724$	6.49020	0.241206
$725$	−12.4175	−0.461173
$726$	14.2463	0.528729
$727$	8.56986	0.317838	0.158919	−	0.987292i	$-0.449199\pi$
$727$	8.56986	0.317838	0.158919	+	0.987292i	$0.449199\pi$
$728$	−1.53209	−0.0567830
$729$	27.5776	1.02139
$730$	32.3901	1.19881
$731$	−53.2995	−1.97135
$732$	3.01960	0.111608
$733$	41.0627	1.51669	0.758344	−	0.651855i	$-0.226009\pi$
$733$	41.0627	1.51669	0.758344	+	0.651855i	$0.226009\pi$
$734$	−31.8316	−1.17493
$735$	3.87939	0.143093
$736$	0.369585	0.0136231
$737$	7.93407	0.292255
$738$	−15.0993	−0.555811
$739$	−38.8357	−1.42860	−0.714298	−	0.699842i	$-0.753254\pi$
$739$	−38.8357	−1.42860	−0.714298	+	0.699842i	$0.753254\pi$
$740$	−22.4611	−0.825687
$741$	0	0
$742$	−10.4757	−0.384573
$743$	23.2882	0.854360	0.427180	−	0.904167i	$-0.359507\pi$
$743$	23.2882	0.854360	0.427180	+	0.904167i	$0.359507\pi$
$744$	−2.75103	−0.100858
$745$	17.2986	0.633772
$746$	11.2790	0.412954
$747$	−0.478340	−0.0175016
$748$	−3.68004	−0.134556
$749$	−1.07873	−0.0394158
$750$	−6.63041	−0.242109
$751$	−14.1566	−0.516583	−0.258291	−	0.966067i	$-0.583159\pi$
$751$	−14.1566	−0.516583	−0.258291	+	0.966067i	$0.583159\pi$
$752$	4.18479	0.152604
$753$	37.0247	1.34925
$754$	5.78106	0.210534
$755$	37.4543	1.36310
$756$	5.63816	0.205058
$757$	−43.3560	−1.57580	−0.787900	−	0.615803i	$-0.788832\pi$
$757$	−43.3560	−1.57580	−0.787900	+	0.615803i	$0.788832\pi$
$758$	−3.31221	−0.120305
$759$	0.325008	0.0117970
$760$	0	0
$761$	−1.40972	−0.0511023	−0.0255511	−	0.999674i	$-0.508134\pi$
$761$	−1.40972	−0.0511023	−0.0255511	+	0.999674i	$0.508134\pi$
$762$	−18.6905	−0.677084
$763$	4.34998	0.157480
$764$	−8.81521	−0.318923
$765$	19.2344	0.695422
$766$	−38.8871	−1.40505
$767$	12.8648	0.464522
$768$	−1.34730	−0.0486164
$769$	−5.86989	−0.211674	−0.105837	−	0.994384i	$-0.533752\pi$
$769$	−5.86989	−0.211674	−0.105837	+	0.994384i	$0.533752\pi$
$770$	1.87939	0.0677283
$771$	−22.5066	−0.810556
$772$	−21.8229	−0.785425
$773$	−14.3105	−0.514711	−0.257356	−	0.966317i	$-0.582851\pi$
$773$	−14.3105	−0.514711	−0.257356	+	0.966317i	$0.582851\pi$
$774$	11.2003	0.402586
$775$	6.71957	0.241374
$776$	−3.51754	−0.126272
$777$	−10.5098	−0.377037
$778$	34.7888	1.24724
$779$	0	0
$780$	−5.94356	−0.212814
$781$	2.40198	0.0859496
$782$	2.08378	0.0745158
$783$	−21.2746	−0.760291
$784$	1.00000	0.0357143
$785$	42.2131	1.50665
$786$	−1.62267	−0.0578789
$787$	1.50030	0.0534801	0.0267400	−	0.999642i	$-0.491487\pi$
$787$	1.50030	0.0534801	0.0267400	+	0.999642i	$0.491487\pi$
$788$	−22.6236	−0.805933
$789$	38.8275	1.38230
$790$	−16.2986	−0.579878
$791$	−5.82295	−0.207040
$792$	0.773318	0.0274787
$793$	3.43376	0.121936
$794$	27.2814	0.968179
$795$	−40.6391	−1.44132
$796$	−23.9709	−0.849626
$797$	25.6500	0.908570	0.454285	−	0.890856i	$-0.349895\pi$
$797$	25.6500	0.908570	0.454285	+	0.890856i	$0.349895\pi$
$798$	0	0
$799$	23.5945	0.834714
$800$	3.29086	0.116349
$801$	15.1693	0.535981
$802$	24.4766	0.864298
$803$	7.34224	0.259102
$804$	16.3773	0.577584
$805$	−1.06418	−0.0375073
$806$	−3.12836	−0.110192
$807$	18.2121	0.641097
$808$	−4.14796	−0.145925
$809$	4.90766	0.172544	0.0862721	−	0.996272i	$-0.472505\pi$
$809$	4.90766	0.172544	0.0862721	+	0.996272i	$0.472505\pi$
$810$	11.6382	0.408923
$811$	36.9454	1.29733	0.648665	−	0.761074i	$-0.275328\pi$
$811$	36.9454	1.29733	0.648665	+	0.761074i	$0.275328\pi$
$812$	−3.77332	−0.132418
$813$	6.97266	0.244542
$814$	−5.09152	−0.178458
$815$	47.4175	1.66096
$816$	−7.59627	−0.265923
$817$	0	0
$818$	−5.12836	−0.179309
$819$	1.81521	0.0634285
$820$	−36.6955	−1.28146
$821$	20.7502	0.724187	0.362094	−	0.932142i	$-0.382062\pi$
$821$	20.7502	0.724187	0.362094	+	0.932142i	$0.382062\pi$
$822$	1.30129	0.0453876
$823$	−19.8553	−0.692114	−0.346057	−	0.938214i	$-0.612480\pi$
$823$	−19.8553	−0.692114	−0.346057	+	0.938214i	$0.612480\pi$
$824$	9.90941	0.345211
$825$	2.89393	0.100754
$826$	−8.39693	−0.292166
$827$	50.4680	1.75495	0.877473	−	0.479627i	$-0.159228\pi$
$827$	50.4680	1.75495	0.877473	+	0.479627i	$0.159228\pi$
$828$	−0.437882	−0.0152174
$829$	−37.7897	−1.31249	−0.656246	−	0.754547i	$-0.727857\pi$
$829$	−37.7897	−1.31249	−0.656246	+	0.754547i	$0.727857\pi$
$830$	−1.16250	−0.0403511
$831$	6.52671	0.226409
$832$	−1.53209	−0.0531156
$833$	5.63816	0.195351
$834$	−7.85567	−0.272019
$835$	0.490200	0.0169641
$836$	0	0
$837$	11.5125	0.397930
$838$	−10.9222	−0.377301
$839$	−31.2704	−1.07958	−0.539788	−	0.841801i	$-0.681495\pi$
$839$	−31.2704	−1.07958	−0.539788	+	0.841801i	$0.681495\pi$
$840$	3.87939	0.133852
$841$	−14.7621	−0.509037
$842$	−37.4252	−1.28976
$843$	−12.8621	−0.442996
$844$	−7.11381	−0.244867
$845$	30.6732	1.05519
$846$	−4.95811	−0.170463
$847$	−10.5740	−0.363326
$848$	−10.4757	−0.359735
$849$	3.62679	0.124471
$850$	18.5544	0.636410
$851$	2.88301	0.0988282
$852$	4.95811	0.169862
$853$	4.71864	0.161563	0.0807815	−	0.996732i	$-0.474258\pi$
$853$	4.71864	0.161563	0.0807815	+	0.996732i	$0.474258\pi$
$854$	−2.24123	−0.0766933
$855$	0	0
$856$	−1.07873	−0.0368701
$857$	10.8226	0.369694	0.184847	−	0.982767i	$-0.440821\pi$
$857$	10.8226	0.369694	0.184847	+	0.982767i	$0.440821\pi$
$858$	−1.34730	−0.0459959
$859$	−12.8949	−0.439967	−0.219984	−	0.975504i	$-0.570600\pi$
$859$	−12.8949	−0.439967	−0.219984	+	0.975504i	$0.570600\pi$
$860$	27.2199	0.928190
$861$	−17.1702	−0.585160
$862$	9.91622	0.337748
$863$	−23.0196	−0.783596	−0.391798	−	0.920051i	$-0.628147\pi$
$863$	−23.0196	−0.783596	−0.391798	+	0.920051i	$0.628147\pi$
$864$	5.63816	0.191814
$865$	−46.7529	−1.58965
$866$	3.87845	0.131795
$867$	−19.9249	−0.676685
$868$	2.04189	0.0693062
$869$	−3.69459	−0.125330
$870$	−14.6382	−0.496280
$871$	18.6236	0.631037
$872$	4.34998	0.147309
$873$	4.16756	0.141050
$874$	0	0
$875$	4.92127	0.166369
$876$	15.1557	0.512064
$877$	−47.5090	−1.60426	−0.802132	−	0.597147i	$-0.796301\pi$
$877$	−47.5090	−1.60426	−0.802132	+	0.597147i	$0.796301\pi$
$878$	−17.9290	−0.605075
$879$	8.45967	0.285338
$880$	1.87939	0.0633541
$881$	−17.9932	−0.606206	−0.303103	−	0.952958i	$-0.598023\pi$
$881$	−17.9932	−0.606206	−0.303103	+	0.952958i	$0.598023\pi$
$882$	−1.18479	−0.0398940
$883$	−14.6212	−0.492044	−0.246022	−	0.969264i	$-0.579124\pi$
$883$	−14.6212	−0.492044	−0.246022	+	0.969264i	$0.579124\pi$
$884$	−8.63816	−0.290533
$885$	−32.5749	−1.09499
$886$	−13.5868	−0.456457
$887$	−17.0678	−0.573081	−0.286540	−	0.958068i	$-0.592505\pi$
$887$	−17.0678	−0.573081	−0.286540	+	0.958068i	$0.592505\pi$
$888$	−10.5098	−0.352686
$889$	13.8726	0.465271
$890$	36.8658	1.23574
$891$	2.63816	0.0883815
$892$	15.8675	0.531284
$893$	0	0
$894$	8.09421	0.270711
$895$	−62.4552	−2.08765
$896$	1.00000	0.0334077
$897$	0.762889	0.0254721
$898$	8.75877	0.292284
$899$	−7.70470	−0.256966
$900$	−3.89899	−0.129966
$901$	−59.0634	−1.96769
$902$	−8.31820	−0.276966
$903$	12.7365	0.423844
$904$	−5.82295	−0.193668
$905$	−18.6878	−0.621203
$906$	17.5253	0.582238
$907$	−0.289105	−0.00959956	−0.00479978	−	0.999988i	$-0.501528\pi$
$907$	−0.289105	−0.00959956	−0.00479978	+	0.999988i	$0.501528\pi$
$908$	15.9786	0.530270
$909$	4.91447	0.163003
$910$	4.41147	0.146239
$911$	−16.6895	−0.552949	−0.276475	−	0.961021i	$-0.589166\pi$
$911$	−16.6895	−0.552949	−0.276475	+	0.961021i	$0.589166\pi$
$912$	0	0
$913$	−0.263518	−0.00872118
$914$	9.74928	0.322477
$915$	−8.69459	−0.287434
$916$	−27.9290	−0.922801
$917$	1.20439	0.0397726
$918$	31.7888	1.04919
$919$	−42.4303	−1.39964	−0.699822	−	0.714317i	$-0.746738\pi$
$919$	−42.4303	−1.39964	−0.699822	+	0.714317i	$0.746738\pi$
$920$	−1.06418	−0.0350849
$921$	−19.1019	−0.629431
$922$	21.5895	0.711011
$923$	5.63816	0.185582
$924$	0.879385	0.0289297
$925$	25.6709	0.844053
$926$	−37.8539	−1.24396
$927$	−11.7406	−0.385612
$928$	−3.77332	−0.123865
$929$	−47.4853	−1.55794	−0.778970	−	0.627061i	$-0.784258\pi$
$929$	−47.4853	−1.55794	−0.778970	+	0.627061i	$0.784258\pi$
$930$	7.92127	0.259749
$931$	0	0
$932$	−14.0428	−0.459988
$933$	11.9472	0.391133
$934$	−6.81252	−0.222912
$935$	10.5963	0.346535
$936$	1.81521	0.0593319
$937$	−9.63310	−0.314700	−0.157350	−	0.987543i	$-0.550295\pi$
$937$	−9.63310	−0.314700	−0.157350	+	0.987543i	$0.550295\pi$
$938$	−12.1557	−0.396898
$939$	−37.3705	−1.21954
$940$	−12.0496	−0.393016
$941$	16.9796	0.553518	0.276759	−	0.960939i	$-0.410740\pi$
$941$	16.9796	0.553518	0.276759	+	0.960939i	$0.410740\pi$
$942$	19.7520	0.643554
$943$	4.71007	0.153381
$944$	−8.39693	−0.273297
$945$	−16.2344	−0.528106
$946$	6.17024	0.200612
$947$	−58.5562	−1.90282	−0.951411	−	0.307923i	$-0.900366\pi$
$947$	−58.5562	−1.90282	−0.951411	+	0.307923i	$0.900366\pi$
$948$	−7.62630	−0.247691
$949$	17.2344	0.559453
$950$	0	0
$951$	34.8776	1.13098
$952$	5.63816	0.182734
$953$	45.9709	1.48914	0.744572	−	0.667542i	$-0.232654\pi$
$953$	45.9709	1.48914	0.744572	+	0.667542i	$0.232654\pi$
$954$	12.4115	0.401836
$955$	25.3824	0.821354
$956$	19.5844	0.633405
$957$	−3.31820	−0.107262
$958$	14.0702	0.454586
$959$	−0.965852	−0.0311890
$960$	3.87939	0.125207
$961$	−26.8307	−0.865506
$962$	−11.9513	−0.385325
$963$	1.27807	0.0411851
$964$	5.37464	0.173105
$965$	62.8367	2.02278
$966$	−0.497941	−0.0160210
$967$	5.79830	0.186461	0.0932303	−	0.995645i	$-0.470281\pi$
$967$	5.79830	0.186461	0.0932303	+	0.995645i	$0.470281\pi$
$968$	−10.5740	−0.339861
$969$	0	0
$970$	10.1284	0.325202
$971$	−22.5749	−0.724463	−0.362232	−	0.932088i	$-0.617985\pi$
$971$	−22.5749	−0.724463	−0.362232	+	0.932088i	$0.617985\pi$
$972$	−11.4688	−0.367863
$973$	5.83069	0.186923
$974$	−24.3327	−0.779672
$975$	6.79292	0.217548
$976$	−2.24123	−0.0717400
$977$	22.4561	0.718433	0.359216	−	0.933254i	$-0.383044\pi$
$977$	22.4561	0.718433	0.359216	+	0.933254i	$0.383044\pi$
$978$	22.1872	0.709467
$979$	8.35679	0.267084
$980$	−2.87939	−0.0919786
$981$	−5.15383	−0.164549
$982$	39.7452	1.26832
$983$	−24.7801	−0.790363	−0.395182	−	0.918603i	$-0.629318\pi$
$983$	−24.7801	−0.790363	−0.395182	+	0.918603i	$0.629318\pi$
$984$	−17.1702	−0.547367
$985$	65.1421	2.07560
$986$	−21.2746	−0.677520
$987$	−5.63816	−0.179464
$988$	0	0
$989$	−3.49382	−0.111097
$990$	−2.22668	−0.0707686
$991$	6.12836	0.194674	0.0973368	−	0.995251i	$-0.468968\pi$
$991$	6.12836	0.194674	0.0973368	+	0.995251i	$0.468968\pi$
$992$	2.04189	0.0648300
$993$	16.1816	0.513508
$994$	−3.68004	−0.116724
$995$	69.0215	2.18813
$996$	−0.543948	−0.0172357
$997$	−31.1985	−0.988067	−0.494034	−	0.869443i	$-0.664478\pi$
$997$	−31.1985	−0.988067	−0.494034	+	0.869443i	$0.664478\pi$
$998$	−42.3550	−1.34073
$999$	43.9813	1.39151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.t.1.2		3
19.6	even	9		266.2.u.a.169.1	yes	6
19.16	even	9		266.2.u.a.85.1	✓	6
19.18	odd	2		5054.2.a.s.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.a.85.1	✓	6	19.16	even	9
266.2.u.a.169.1	yes	6	19.6	even	9
5054.2.a.s.1.2		3	19.18	odd	2
5054.2.a.t.1.2		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.34730 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.34730 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.18479 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.34730 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.34730 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.18479 q^{9} -2.87939 q^{10} -0.652704 q^{11} -1.34730 q^{12} -1.53209 q^{13} +1.00000 q^{14} +3.87939 q^{15} +1.00000 q^{16} +5.63816 q^{17} -1.18479 q^{18} -2.87939 q^{20} -1.34730 q^{21} -0.652704 q^{22} +0.369585 q^{23} -1.34730 q^{24} +3.29086 q^{25} -1.53209 q^{26} +5.63816 q^{27} +1.00000 q^{28} -3.77332 q^{29} +3.87939 q^{30} +2.04189 q^{31} +1.00000 q^{32} +0.879385 q^{33} +5.63816 q^{34} -2.87939 q^{35} -1.18479 q^{36} +7.80066 q^{37} +2.06418 q^{39} -2.87939 q^{40} +12.7442 q^{41} -1.34730 q^{42} -9.45336 q^{43} -0.652704 q^{44} +3.41147 q^{45} +0.369585 q^{46} +4.18479 q^{47} -1.34730 q^{48} +1.00000 q^{49} +3.29086 q^{50} -7.59627 q^{51} -1.53209 q^{52} -10.4757 q^{53} +5.63816 q^{54} +1.87939 q^{55} +1.00000 q^{56} -3.77332 q^{58} -8.39693 q^{59} +3.87939 q^{60} -2.24123 q^{61} +2.04189 q^{62} -1.18479 q^{63} +1.00000 q^{64} +4.41147 q^{65} +0.879385 q^{66} -12.1557 q^{67} +5.63816 q^{68} -0.497941 q^{69} -2.87939 q^{70} -3.68004 q^{71} -1.18479 q^{72} -11.2490 q^{73} +7.80066 q^{74} -4.43376 q^{75} -0.652704 q^{77} +2.06418 q^{78} +5.66044 q^{79} -2.87939 q^{80} -4.04189 q^{81} +12.7442 q^{82} +0.403733 q^{83} -1.34730 q^{84} -16.2344 q^{85} -9.45336 q^{86} +5.08378 q^{87} -0.652704 q^{88} -12.8033 q^{89} +3.41147 q^{90} -1.53209 q^{91} +0.369585 q^{92} -2.75103 q^{93} +4.18479 q^{94} -1.34730 q^{96} -3.51754 q^{97} +1.00000 q^{98} +0.773318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{28} - 18 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{32} - 3 q^{33} - 3 q^{35} + 9 q^{37} - 3 q^{39} - 3 q^{40} + 9 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} - 6 q^{46} + 9 q^{47} - 3 q^{48} + 3 q^{49} - 6 q^{50} - 9 q^{51} - 12 q^{53} + 3 q^{56} - 18 q^{58} + 3 q^{59} + 6 q^{60} - 18 q^{61} + 3 q^{62} + 3 q^{64} + 3 q^{65} - 3 q^{66} + 3 q^{67} + 24 q^{69} - 3 q^{70} + 9 q^{71} - 21 q^{73} + 9 q^{74} + 3 q^{75} - 3 q^{77} - 3 q^{78} - 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 15 q^{83} - 3 q^{84} - 18 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} - 15 q^{89} - 6 q^{92} - 21 q^{93} + 9 q^{94} - 3 q^{96} + 12 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^28 - 18 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^32 - 3 * q^33 - 3 * q^35 + 9 * q^37 - 3 * q^39 - 3 * q^40 + 9 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 - 6 * q^46 + 9 * q^47 - 3 * q^48 + 3 * q^49 - 6 * q^50 - 9 * q^51 - 12 * q^53 + 3 * q^56 - 18 * q^58 + 3 * q^59 + 6 * q^60 - 18 * q^61 + 3 * q^62 + 3 * q^64 + 3 * q^65 - 3 * q^66 + 3 * q^67 + 24 * q^69 - 3 * q^70 + 9 * q^71 - 21 * q^73 + 9 * q^74 + 3 * q^75 - 3 * q^77 - 3 * q^78 - 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 15 * q^83 - 3 * q^84 - 18 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 - 15 * q^89 - 6 * q^92 - 21 * q^93 + 9 * q^94 - 3 * q^96 + 12 * q^97 + 3 * q^98 + 9 * q^99

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