LMFDB - Embedded newform 241.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(1,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("241.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.01020$ of defining polynomial
Character	$\chi$	$=$	241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.01020 q^{2} +0.500591 q^{3} +2.04092 q^{4} +1.92585 q^{5} +1.00629 q^{6} -0.852319 q^{7} +0.0822476 q^{8} -2.74941 q^{9} +O(q^{10})$	\(q+2.01020 q^{2} +0.500591 q^{3} +2.04092 q^{4} +1.92585 q^{5} +1.00629 q^{6} -0.852319 q^{7} +0.0822476 q^{8} -2.74941 q^{9} +3.87135 q^{10} +0.719546 q^{11} +1.02166 q^{12} -1.93309 q^{13} -1.71333 q^{14} +0.964064 q^{15} -3.91650 q^{16} +0.439843 q^{17} -5.52687 q^{18} +5.85432 q^{19} +3.93050 q^{20} -0.426663 q^{21} +1.44643 q^{22} -7.09215 q^{23} +0.0411724 q^{24} -1.29109 q^{25} -3.88589 q^{26} -2.87810 q^{27} -1.73951 q^{28} +10.0222 q^{29} +1.93796 q^{30} +5.69622 q^{31} -8.03745 q^{32} +0.360198 q^{33} +0.884173 q^{34} -1.64144 q^{35} -5.61131 q^{36} -3.17197 q^{37} +11.7684 q^{38} -0.967685 q^{39} +0.158397 q^{40} -6.39435 q^{41} -0.857679 q^{42} +4.29669 q^{43} +1.46853 q^{44} -5.29496 q^{45} -14.2567 q^{46} -0.642479 q^{47} -1.96056 q^{48} -6.27355 q^{49} -2.59536 q^{50} +0.220181 q^{51} -3.94526 q^{52} +0.729714 q^{53} -5.78557 q^{54} +1.38574 q^{55} -0.0701012 q^{56} +2.93062 q^{57} +20.1467 q^{58} +0.348904 q^{59} +1.96757 q^{60} +1.12656 q^{61} +11.4506 q^{62} +2.34337 q^{63} -8.32390 q^{64} -3.72284 q^{65} +0.724072 q^{66} +12.5549 q^{67} +0.897682 q^{68} -3.55026 q^{69} -3.29963 q^{70} +0.552289 q^{71} -0.226132 q^{72} -10.9882 q^{73} -6.37630 q^{74} -0.646309 q^{75} +11.9482 q^{76} -0.613283 q^{77} -1.94524 q^{78} +10.9569 q^{79} -7.54259 q^{80} +6.80748 q^{81} -12.8539 q^{82} +6.62478 q^{83} -0.870783 q^{84} +0.847072 q^{85} +8.63722 q^{86} +5.01703 q^{87} +0.0591810 q^{88} +12.5513 q^{89} -10.6439 q^{90} +1.64760 q^{91} -14.4745 q^{92} +2.85148 q^{93} -1.29151 q^{94} +11.2746 q^{95} -4.02347 q^{96} -5.00536 q^{97} -12.6111 q^{98} -1.97833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.01020	1.42143	0.710714	−	0.703481i	$-0.248372\pi$
$2$	2.01020	1.42143	0.710714	+	0.703481i	$0.248372\pi$
$3$	0.500591	0.289016	0.144508	−	0.989504i	$-0.453840\pi$
$3$	0.500591	0.289016	0.144508	+	0.989504i	$0.453840\pi$
$4$	2.04092	1.02046
$5$	1.92585	0.861267	0.430634	−	0.902527i	$-0.358290\pi$
$5$	1.92585	0.861267	0.430634	+	0.902527i	$0.358290\pi$
$6$	1.00629	0.410816
$7$	−0.852319	−0.322146	−0.161073	−	0.986942i	$-0.551495\pi$
$7$	−0.852319	−0.322146	−0.161073	+	0.986942i	$0.551495\pi$
$8$	0.0822476	0.0290789
$9$	−2.74941	−0.916470
$10$	3.87135	1.22423
$11$	0.719546	0.216951	0.108476	−	0.994099i	$-0.465403\pi$
$11$	0.719546	0.216951	0.108476	+	0.994099i	$0.465403\pi$
$12$	1.02166	0.294929
$13$	−1.93309	−0.536141	−0.268071	−	0.963399i	$-0.586386\pi$
$13$	−1.93309	−0.536141	−0.268071	+	0.963399i	$0.586386\pi$
$14$	−1.71333	−0.457908
$15$	0.964064	0.248920
$16$	−3.91650	−0.979124
$17$	0.439843	0.106678	0.0533388	−	0.998576i	$-0.483014\pi$
$17$	0.439843	0.106678	0.0533388	+	0.998576i	$0.483014\pi$
$18$	−5.52687	−1.30270
$19$	5.85432	1.34307	0.671537	−	0.740971i	$-0.265635\pi$
$19$	5.85432	1.34307	0.671537	+	0.740971i	$0.265635\pi$
$20$	3.93050	0.878887
$21$	−0.426663	−0.0931055
$22$	1.44643	0.308381
$23$	−7.09215	−1.47881	−0.739407	−	0.673258i	$-0.764894\pi$
$23$	−7.09215	−1.47881	−0.739407	+	0.673258i	$0.764894\pi$
$24$	0.0411724	0.00840428
$25$	−1.29109	−0.258219
$26$	−3.88589	−0.762086
$27$	−2.87810	−0.553891
$28$	−1.73951	−0.328737
$29$	10.0222	1.86108	0.930540	−	0.366190i	$-0.119338\pi$
$29$	10.0222	1.86108	0.930540	+	0.366190i	$0.119338\pi$
$30$	1.93796	0.353822
$31$	5.69622	1.02307	0.511536	−	0.859262i	$-0.329077\pi$
$31$	5.69622	1.02307	0.511536	+	0.859262i	$0.329077\pi$
$32$	−8.03745	−1.42083
$33$	0.360198	0.0627025
$34$	0.884173	0.151634
$35$	−1.64144	−0.277454
$36$	−5.61131	−0.935218
$37$	−3.17197	−0.521468	−0.260734	−	0.965411i	$-0.583965\pi$
$37$	−3.17197	−0.521468	−0.260734	+	0.965411i	$0.583965\pi$
$38$	11.7684	1.90908
$39$	−0.967685	−0.154954
$40$	0.158397	0.0250447
$41$	−6.39435	−0.998630	−0.499315	−	0.866421i	$-0.666415\pi$
$41$	−6.39435	−0.998630	−0.499315	+	0.866421i	$0.666415\pi$
$42$	−0.857679	−0.132343
$43$	4.29669	0.655239	0.327620	−	0.944810i	$-0.393754\pi$
$43$	4.29669	0.655239	0.327620	+	0.944810i	$0.393754\pi$
$44$	1.46853	0.221390
$45$	−5.29496	−0.789325
$46$	−14.2567	−2.10203
$47$	−0.642479	−0.0937152	−0.0468576	−	0.998902i	$-0.514921\pi$
$47$	−0.642479	−0.0937152	−0.0468576	+	0.998902i	$0.514921\pi$
$48$	−1.96056	−0.282983
$49$	−6.27355	−0.896222
$50$	−2.59536	−0.367039
$51$	0.220181	0.0308315
$52$	−3.94526	−0.547110
$53$	0.729714	0.100234	0.0501170	−	0.998743i	$-0.484041\pi$
$53$	0.729714	0.100234	0.0501170	+	0.998743i	$0.484041\pi$
$54$	−5.78557	−0.787316
$55$	1.38574	0.186853
$56$	−0.0701012	−0.00936766
$57$	2.93062	0.388170
$58$	20.1467	2.64539
$59$	0.348904	0.0454234	0.0227117	−	0.999742i	$-0.492770\pi$
$59$	0.348904	0.0454234	0.0227117	+	0.999742i	$0.492770\pi$
$60$	1.96757	0.254012
$61$	1.12656	0.144241	0.0721204	−	0.997396i	$-0.477023\pi$
$61$	1.12656	0.144241	0.0721204	+	0.997396i	$0.477023\pi$
$62$	11.4506	1.45422
$63$	2.34337	0.295237
$64$	−8.32390	−1.04049
$65$	−3.72284	−0.461761
$66$	0.724072	0.0891270
$67$	12.5549	1.53383	0.766915	−	0.641749i	$-0.221791\pi$
$67$	12.5549	1.53383	0.766915	+	0.641749i	$0.221791\pi$
$68$	0.897682	0.108860
$69$	−3.55026	−0.427401
$70$	−3.29963	−0.394381
$71$	0.552289	0.0655446	0.0327723	−	0.999463i	$-0.489566\pi$
$71$	0.552289	0.0655446	0.0327723	+	0.999463i	$0.489566\pi$
$72$	−0.226132	−0.0266499
$73$	−10.9882	−1.28607	−0.643037	−	0.765835i	$-0.722326\pi$
$73$	−10.9882	−1.28607	−0.643037	+	0.765835i	$0.722326\pi$
$74$	−6.37630	−0.741229
$75$	−0.646309	−0.0746294
$76$	11.9482	1.37055
$77$	−0.613283	−0.0698901
$78$	−1.94524	−0.220255
$79$	10.9569	1.23275	0.616375	−	0.787453i	$-0.288600\pi$
$79$	10.9569	1.23275	0.616375	+	0.787453i	$0.288600\pi$
$80$	−7.54259	−0.843287
$81$	6.80748	0.756386
$82$	−12.8539	−1.41948
$83$	6.62478	0.727164	0.363582	−	0.931562i	$-0.381554\pi$
$83$	6.62478	0.727164	0.363582	+	0.931562i	$0.381554\pi$
$84$	−0.870783	−0.0950102
$85$	0.847072	0.0918779
$86$	8.63722	0.931375
$87$	5.01703	0.537882
$88$	0.0591810	0.00630871
$89$	12.5513	1.33044	0.665219	−	0.746648i	$-0.268338\pi$
$89$	12.5513	1.33044	0.665219	+	0.746648i	$0.268338\pi$
$90$	−10.6439	−1.12197
$91$	1.64760	0.172716
$92$	−14.4745	−1.50907
$93$	2.85148	0.295684
$94$	−1.29151	−0.133209
$95$	11.2746	1.15675
$96$	−4.02347	−0.410644
$97$	−5.00536	−0.508217	−0.254108	−	0.967176i	$-0.581782\pi$
$97$	−5.00536	−0.508217	−0.254108	+	0.967176i	$0.581782\pi$
$98$	−12.6111	−1.27391
$99$	−1.97833	−0.198829
$100$	−2.63501	−0.263501
$101$	0.191991	0.0191038	0.00955192	−	0.999954i	$-0.496959\pi$
$101$	0.191991	0.0191038	0.00955192	+	0.999954i	$0.496959\pi$
$102$	0.442609	0.0438248
$103$	−3.97237	−0.391409	−0.195705	−	0.980663i	$-0.562699\pi$
$103$	−3.97237	−0.391409	−0.195705	+	0.980663i	$0.562699\pi$
$104$	−0.158992	−0.0155904
$105$	−0.821690	−0.0801887
$106$	1.46687	0.142475
$107$	6.70922	0.648605	0.324303	−	0.945953i	$-0.394870\pi$
$107$	6.70922	0.648605	0.324303	+	0.945953i	$0.394870\pi$
$108$	−5.87396	−0.565222
$109$	4.03051	0.386053	0.193027	−	0.981194i	$-0.438170\pi$
$109$	4.03051	0.386053	0.193027	+	0.981194i	$0.438170\pi$
$110$	2.78562	0.265598
$111$	−1.58786	−0.150713
$112$	3.33810	0.315421
$113$	0.430322	0.0404813	0.0202407	−	0.999795i	$-0.493557\pi$
$113$	0.430322	0.0404813	0.0202407	+	0.999795i	$0.493557\pi$
$114$	5.89114	0.551756
$115$	−13.6584	−1.27365
$116$	20.4545	1.89915
$117$	5.31484	0.491357
$118$	0.701368	0.0645661
$119$	−0.374886	−0.0343658
$120$	0.0792919	0.00723833
$121$	−10.4823	−0.952932
$122$	2.26461	0.205028
$123$	−3.20095	−0.288620
$124$	11.6255	1.04400
$125$	−12.1157	−1.08366
$126$	4.71065	0.419658
$127$	−0.0290958	−0.00258183	−0.00129092	−	0.999999i	$-0.500411\pi$
$127$	−0.0290958	−0.00258183	−0.00129092	+	0.999999i	$0.500411\pi$
$128$	−0.657843	−0.0581457
$129$	2.15088	0.189375
$130$	−7.48366	−0.656360
$131$	−7.50804	−0.655980	−0.327990	−	0.944681i	$-0.606371\pi$
$131$	−7.50804	−0.655980	−0.327990	+	0.944681i	$0.606371\pi$
$132$	0.735134	0.0639852
$133$	−4.98975	−0.432666
$134$	25.2380	2.18023
$135$	−5.54280	−0.477048
$136$	0.0361760	0.00310207
$137$	−2.79071	−0.238427	−0.119213	−	0.992869i	$-0.538037\pi$
$137$	−2.79071	−0.238427	−0.119213	+	0.992869i	$0.538037\pi$
$138$	−7.13675	−0.607520
$139$	5.56312	0.471858	0.235929	−	0.971770i	$-0.424187\pi$
$139$	5.56312	0.471858	0.235929	+	0.971770i	$0.424187\pi$
$140$	−3.35004	−0.283130
$141$	−0.321619	−0.0270852
$142$	1.11021	0.0931669
$143$	−1.39094	−0.116317
$144$	10.7680	0.897337
$145$	19.3013	1.60289
$146$	−22.0886	−1.82806
$147$	−3.14048	−0.259023
$148$	−6.47372	−0.532136
$149$	14.8309	1.21500	0.607499	−	0.794321i	$-0.292173\pi$
$149$	14.8309	1.21500	0.607499	+	0.794321i	$0.292173\pi$
$150$	−1.29921	−0.106080
$151$	−19.6745	−1.60109	−0.800543	−	0.599276i	$-0.795455\pi$
$151$	−19.6745	−1.60109	−0.800543	+	0.599276i	$0.795455\pi$
$152$	0.481504	0.0390551
$153$	−1.20931	−0.0977667
$154$	−1.23282	−0.0993437
$155$	10.9701	0.881138
$156$	−1.97496	−0.158124
$157$	14.3437	1.14475	0.572377	−	0.819991i	$-0.306022\pi$
$157$	14.3437	1.14475	0.572377	+	0.819991i	$0.306022\pi$
$158$	22.0256	1.75227
$159$	0.365288	0.0289692
$160$	−15.4789	−1.22372
$161$	6.04477	0.476395
$162$	13.6844	1.07515
$163$	4.99007	0.390853	0.195426	−	0.980718i	$-0.437391\pi$
$163$	4.99007	0.390853	0.195426	+	0.980718i	$0.437391\pi$
$164$	−13.0503	−1.01906
$165$	0.693689	0.0540036
$166$	13.3172	1.03361
$167$	15.6290	1.20941	0.604703	−	0.796451i	$-0.293292\pi$
$167$	15.6290	1.20941	0.604703	+	0.796451i	$0.293292\pi$
$168$	−0.0350920	−0.00270741
$169$	−9.26318	−0.712552
$170$	1.70279	0.130598
$171$	−16.0959	−1.23089
$172$	8.76918	0.668644
$173$	0.833365	0.0633596	0.0316798	−	0.999498i	$-0.489914\pi$
$173$	0.833365	0.0633596	0.0316798	+	0.999498i	$0.489914\pi$
$174$	10.0853	0.764561
$175$	1.10042	0.0831842
$176$	−2.81810	−0.212422
$177$	0.174658	0.0131281
$178$	25.2307	1.89112
$179$	14.9985	1.12104	0.560520	−	0.828141i	$-0.310601\pi$
$179$	14.9985	1.12104	0.560520	+	0.828141i	$0.310601\pi$
$180$	−10.8066	−0.805473
$181$	−14.9752	−1.11310	−0.556550	−	0.830814i	$-0.687875\pi$
$181$	−14.9752	−1.11310	−0.556550	+	0.830814i	$0.687875\pi$
$182$	3.31202	0.245503
$183$	0.563944	0.0416879
$184$	−0.583312	−0.0430023
$185$	−6.10874	−0.449123
$186$	5.73204	0.420294
$187$	0.316487	0.0231438
$188$	−1.31125	−0.0956324
$189$	2.45306	0.178434
$190$	22.6641	1.64423
$191$	8.51858	0.616383	0.308191	−	0.951324i	$-0.400276\pi$
$191$	8.51858	0.616383	0.308191	+	0.951324i	$0.400276\pi$
$192$	−4.16687	−0.300718
$193$	−23.5303	−1.69375	−0.846874	−	0.531793i	$-0.821518\pi$
$193$	−23.5303	−1.69375	−0.846874	+	0.531793i	$0.821518\pi$
$194$	−10.0618	−0.722394
$195$	−1.86362	−0.133456
$196$	−12.8038	−0.914556
$197$	−26.7548	−1.90620	−0.953102	−	0.302649i	$-0.902129\pi$
$197$	−26.7548	−1.90620	−0.953102	+	0.302649i	$0.902129\pi$
$198$	−3.97684	−0.282622
$199$	−19.5915	−1.38880	−0.694401	−	0.719589i	$-0.744330\pi$
$199$	−19.5915	−1.38880	−0.694401	+	0.719589i	$0.744330\pi$
$200$	−0.106189	−0.00750872
$201$	6.28488	0.443301
$202$	0.385941	0.0271547
$203$	−8.54213	−0.599540
$204$	0.449371	0.0314623
$205$	−12.3146	−0.860087
$206$	−7.98527	−0.556360
$207$	19.4992	1.35529
$208$	7.57092	0.524949
$209$	4.21246	0.291382
$210$	−1.65176	−0.113982
$211$	4.58617	0.315725	0.157862	−	0.987461i	$-0.449540\pi$
$211$	4.58617	0.315725	0.157862	+	0.987461i	$0.449540\pi$
$212$	1.48928	0.102284
$213$	0.276471	0.0189435
$214$	13.4869	0.921946
$215$	8.27479	0.564336
$216$	−0.236717	−0.0161065
$217$	−4.85500	−0.329579
$218$	8.10215	0.548747
$219$	−5.50060	−0.371696
$220$	2.82818	0.190676
$221$	−0.850254	−0.0571943
$222$	−3.19191	−0.214227
$223$	−11.8124	−0.791018	−0.395509	−	0.918462i	$-0.629432\pi$
$223$	−11.8124	−0.791018	−0.395509	+	0.918462i	$0.629432\pi$
$224$	6.85047	0.457716
$225$	3.54974	0.236650
$226$	0.865035	0.0575413
$227$	−10.4668	−0.694703	−0.347352	−	0.937735i	$-0.612919\pi$
$227$	−10.4668	−0.694703	−0.347352	+	0.937735i	$0.612919\pi$
$228$	5.98114	0.396111
$229$	−28.8373	−1.90562	−0.952811	−	0.303563i	$-0.901824\pi$
$229$	−28.8373	−1.90562	−0.952811	+	0.303563i	$0.901824\pi$
$230$	−27.4562	−1.81041
$231$	−0.307004	−0.0201994
$232$	0.824304	0.0541182
$233$	0.483058	0.0316462	0.0158231	−	0.999875i	$-0.494963\pi$
$233$	0.483058	0.0316462	0.0158231	+	0.999875i	$0.494963\pi$
$234$	10.6839	0.698429
$235$	−1.23732	−0.0807138
$236$	0.712084	0.0463527
$237$	5.48494	0.356285
$238$	−0.753597	−0.0488485
$239$	−2.08293	−0.134734	−0.0673668	−	0.997728i	$-0.521460\pi$
$239$	−2.08293	−0.134734	−0.0673668	+	0.997728i	$0.521460\pi$
$240$	−3.77575	−0.243724
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−21.0715	−1.35452
$243$	12.0421	0.772499
$244$	2.29921	0.147192
$245$	−12.0819	−0.771887
$246$	−6.43456	−0.410253
$247$	−11.3169	−0.720077
$248$	0.468501	0.0297498
$249$	3.31631	0.210162
$250$	−24.3550	−1.54035
$251$	−9.67130	−0.610447	−0.305223	−	0.952281i	$-0.598731\pi$
$251$	−9.67130	−0.610447	−0.305223	+	0.952281i	$0.598731\pi$
$252$	4.78262	0.301277
$253$	−5.10313	−0.320831
$254$	−0.0584884	−0.00366989
$255$	0.424037	0.0265542
$256$	15.3254	0.957838
$257$	−16.0352	−1.00025	−0.500123	−	0.865954i	$-0.666712\pi$
$257$	−16.0352	−1.00025	−0.500123	+	0.865954i	$0.666712\pi$
$258$	4.32371	0.269183
$259$	2.70353	0.167989
$260$	−7.59799	−0.471208
$261$	−27.5552	−1.70562
$262$	−15.0927	−0.932429
$263$	26.9402	1.66120	0.830602	−	0.556867i	$-0.187997\pi$
$263$	26.9402	1.66120	0.830602	+	0.556867i	$0.187997\pi$
$264$	0.0296254	0.00182332
$265$	1.40532	0.0863282
$266$	−10.0304	−0.615004
$267$	6.28308	0.384518
$268$	25.6236	1.56521
$269$	30.7223	1.87317	0.936585	−	0.350441i	$-0.113968\pi$
$269$	30.7223	1.87317	0.936585	+	0.350441i	$0.113968\pi$
$270$	−11.1421	−0.678089
$271$	−32.2539	−1.95928	−0.979641	−	0.200757i	$-0.935660\pi$
$271$	−32.2539	−1.95928	−0.979641	+	0.200757i	$0.935660\pi$
$272$	−1.72264	−0.104451
$273$	0.824776	0.0499177
$274$	−5.60990	−0.338906
$275$	−0.929002	−0.0560209
$276$	−7.24579	−0.436145
$277$	9.84003	0.591230	0.295615	−	0.955307i	$-0.404475\pi$
$277$	9.84003	0.591230	0.295615	+	0.955307i	$0.404475\pi$
$278$	11.1830	0.670712
$279$	−15.6612	−0.937614
$280$	−0.135004	−0.00806806
$281$	0.0623558	0.00371983	0.00185992	−	0.999998i	$-0.499408\pi$
$281$	0.0623558	0.00371983	0.00185992	+	0.999998i	$0.499408\pi$
$282$	−0.646519	−0.0384997
$283$	−23.1136	−1.37396	−0.686979	−	0.726677i	$-0.741064\pi$
$283$	−23.1136	−1.37396	−0.686979	+	0.726677i	$0.741064\pi$
$284$	1.12717	0.0668855
$285$	5.64394	0.334318
$286$	−2.79608	−0.165336
$287$	5.45002	0.321705
$288$	22.0982	1.30215
$289$	−16.8065	−0.988620
$290$	38.7996	2.27839
$291$	−2.50564	−0.146883
$292$	−22.4260	−1.31238
$293$	−7.59717	−0.443831	−0.221916	−	0.975066i	$-0.571231\pi$
$293$	−7.59717	−0.443831	−0.221916	+	0.975066i	$0.571231\pi$
$294$	−6.31301	−0.368182
$295$	0.671938	0.0391217
$296$	−0.260887	−0.0151637
$297$	−2.07093	−0.120167
$298$	29.8132	1.72703
$299$	13.7097	0.792854
$300$	−1.31906	−0.0761561
$301$	−3.66215	−0.211083
$302$	−39.5497	−2.27583
$303$	0.0961090	0.00552132
$304$	−22.9284	−1.31504
$305$	2.16958	0.124230
$306$	−2.43095	−0.138968
$307$	−15.3566	−0.876447	−0.438224	−	0.898866i	$-0.644392\pi$
$307$	−15.3566	−0.876447	−0.438224	+	0.898866i	$0.644392\pi$
$308$	−1.25166	−0.0713198
$309$	−1.98853	−0.113124
$310$	22.0521	1.25247
$311$	25.0513	1.42053	0.710263	−	0.703936i	$-0.248576\pi$
$311$	25.0513	1.42053	0.710263	+	0.703936i	$0.248576\pi$
$312$	−0.0795897	−0.00450588
$313$	−8.95197	−0.505995	−0.252997	−	0.967467i	$-0.581416\pi$
$313$	−8.95197	−0.505995	−0.252997	+	0.967467i	$0.581416\pi$
$314$	28.8338	1.62718
$315$	4.51299	0.254278
$316$	22.3622	1.25797
$317$	20.7326	1.16446	0.582228	−	0.813025i	$-0.302181\pi$
$317$	20.7326	1.16446	0.582228	+	0.813025i	$0.302181\pi$
$318$	0.734303	0.0411777
$319$	7.21146	0.403764
$320$	−16.0306	−0.896138
$321$	3.35858	0.187457
$322$	12.1512	0.677161
$323$	2.57498	0.143276
$324$	13.8935	0.771860
$325$	2.49579	0.138442
$326$	10.0311	0.555569
$327$	2.01764	0.111576
$328$	−0.525920	−0.0290391
$329$	0.547597	0.0301900
$330$	1.39445	0.0767622
$331$	6.99950	0.384727	0.192364	−	0.981324i	$-0.438385\pi$
$331$	6.99950	0.384727	0.192364	+	0.981324i	$0.438385\pi$
$332$	13.5206	0.742040
$333$	8.72103	0.477910
$334$	31.4174	1.71908
$335$	24.1789	1.32104
$336$	1.67102	0.0911618
$337$	1.75653	0.0956843	0.0478421	−	0.998855i	$-0.484766\pi$
$337$	1.75653	0.0956843	0.0478421	+	0.998855i	$0.484766\pi$
$338$	−18.6209	−1.01284
$339$	0.215415	0.0116998
$340$	1.72880	0.0937575
$341$	4.09870	0.221957
$342$	−32.3561	−1.74962
$343$	11.3133	0.610861
$344$	0.353393	0.0190536
$345$	−6.83728	−0.368107
$346$	1.67523	0.0900611
$347$	−11.0359	−0.592440	−0.296220	−	0.955120i	$-0.595726\pi$
$347$	−11.0359	−0.592440	−0.296220	+	0.955120i	$0.595726\pi$
$348$	10.2393	0.548886
$349$	−22.8659	−1.22398	−0.611992	−	0.790864i	$-0.709631\pi$
$349$	−22.8659	−1.22398	−0.611992	+	0.790864i	$0.709631\pi$
$350$	2.21207	0.118240
$351$	5.56361	0.296964
$352$	−5.78332	−0.308252
$353$	−19.2684	−1.02556	−0.512778	−	0.858522i	$-0.671383\pi$
$353$	−19.2684	−1.02556	−0.512778	+	0.858522i	$0.671383\pi$
$354$	0.351098	0.0186607
$355$	1.06363	0.0564514
$356$	25.6162	1.35766
$357$	−0.187665	−0.00993226
$358$	30.1500	1.59348
$359$	20.1999	1.06611	0.533056	−	0.846080i	$-0.321043\pi$
$359$	20.1999	1.06611	0.533056	+	0.846080i	$0.321043\pi$
$360$	−0.435497	−0.0229527
$361$	15.2731	0.803847
$362$	−30.1033	−1.58219
$363$	−5.24732	−0.275413
$364$	3.36262	0.176249
$365$	−21.1617	−1.10765
$366$	1.13364	0.0592564
$367$	3.91082	0.204143	0.102072	−	0.994777i	$-0.467453\pi$
$367$	3.91082	0.204143	0.102072	+	0.994777i	$0.467453\pi$
$368$	27.7764	1.44794
$369$	17.5807	0.915214
$370$	−12.2798	−0.638397
$371$	−0.621949	−0.0322900
$372$	5.81962	0.301733
$373$	9.05376	0.468786	0.234393	−	0.972142i	$-0.424690\pi$
$373$	9.05376	0.468786	0.234393	+	0.972142i	$0.424690\pi$
$374$	0.636204	0.0328973
$375$	−6.06502	−0.313196
$376$	−0.0528424	−0.00272514
$377$	−19.3738	−0.997802
$378$	4.93115	0.253631
$379$	28.2491	1.45106	0.725530	−	0.688191i	$-0.241595\pi$
$379$	28.2491	1.45106	0.725530	+	0.688191i	$0.241595\pi$
$380$	23.0104	1.18041
$381$	−0.0145651	−0.000746192 0
$382$	17.1241	0.876144
$383$	31.6901	1.61929	0.809645	−	0.586920i	$-0.199660\pi$
$383$	31.6901	1.61929	0.809645	+	0.586920i	$0.199660\pi$
$384$	−0.329310	−0.0168050
$385$	−1.18109	−0.0601940
$386$	−47.3007	−2.40754
$387$	−11.8134	−0.600507
$388$	−10.2155	−0.518614
$389$	23.1689	1.17471	0.587355	−	0.809330i	$-0.300169\pi$
$389$	23.1689	1.17471	0.587355	+	0.809330i	$0.300169\pi$
$390$	−3.74625	−0.189699
$391$	−3.11943	−0.157756
$392$	−0.515985	−0.0260612
$393$	−3.75845	−0.189589
$394$	−53.7827	−2.70953
$395$	21.1014	1.06173
$396$	−4.03760	−0.202897
$397$	30.6366	1.53761	0.768804	−	0.639484i	$-0.220852\pi$
$397$	30.6366	1.53761	0.768804	+	0.639484i	$0.220852\pi$
$398$	−39.3828	−1.97408
$399$	−2.49782	−0.125047
$400$	5.05656	0.252828
$401$	−8.47109	−0.423026	−0.211513	−	0.977375i	$-0.567839\pi$
$401$	−8.47109	−0.423026	−0.211513	+	0.977375i	$0.567839\pi$
$402$	12.6339	0.630121
$403$	−11.0113	−0.548511
$404$	0.391838	0.0194947
$405$	13.1102	0.651451
$406$	−17.1714	−0.852203
$407$	−2.28238	−0.113133
$408$	0.0181094	0.000896548 0
$409$	23.2857	1.15140	0.575702	−	0.817660i	$-0.304729\pi$
$409$	23.2857	1.15140	0.575702	+	0.817660i	$0.304729\pi$
$410$	−24.7548	−1.22255
$411$	−1.39701	−0.0689092
$412$	−8.10727	−0.399416
$413$	−0.297377	−0.0146330
$414$	39.1974	1.92645
$415$	12.7584	0.626283
$416$	15.5371	0.761767
$417$	2.78485	0.136375
$418$	8.46789	0.414178
$419$	−9.29059	−0.453875	−0.226937	−	0.973909i	$-0.572871\pi$
$419$	−9.29059	−0.453875	−0.226937	+	0.973909i	$0.572871\pi$
$420$	−1.67700	−0.0818292
$421$	15.4991	0.755380	0.377690	−	0.925932i	$-0.376719\pi$
$421$	15.4991	0.755380	0.377690	+	0.925932i	$0.376719\pi$
$422$	9.21913	0.448780
$423$	1.76644	0.0858871
$424$	0.0600172	0.00291469
$425$	−0.567878	−0.0275461
$426$	0.555762	0.0269268
$427$	−0.960185	−0.0464666
$428$	13.6930	0.661874
$429$	−0.696294	−0.0336174
$430$	16.6340	0.802163
$431$	−19.5308	−0.940765	−0.470382	−	0.882463i	$-0.655884\pi$
$431$	−19.5308	−0.940765	−0.470382	+	0.882463i	$0.655884\pi$
$432$	11.2721	0.542328
$433$	−5.89329	−0.283213	−0.141607	−	0.989923i	$-0.545227\pi$
$433$	−5.89329	−0.283213	−0.141607	+	0.989923i	$0.545227\pi$
$434$	−9.75953	−0.468472
$435$	9.66206	0.463261
$436$	8.22594	0.393951
$437$	−41.5197	−1.98616
$438$	−11.0573	−0.528340
$439$	22.1839	1.05878	0.529390	−	0.848379i	$-0.322421\pi$
$439$	22.1839	1.05878	0.529390	+	0.848379i	$0.322421\pi$
$440$	0.113974	0.00543349
$441$	17.2486	0.821360
$442$	−1.70918	−0.0812975
$443$	−14.6268	−0.694940	−0.347470	−	0.937691i	$-0.612959\pi$
$443$	−14.6268	−0.694940	−0.347470	+	0.937691i	$0.612959\pi$
$444$	−3.24068	−0.153796
$445$	24.1720	1.14586
$446$	−23.7454	−1.12438
$447$	7.42423	0.351154
$448$	7.09462	0.335189
$449$	−34.2308	−1.61545	−0.807726	−	0.589558i	$-0.799302\pi$
$449$	−34.2308	−1.61545	−0.807726	+	0.589558i	$0.799302\pi$
$450$	7.13570	0.336380
$451$	−4.60103	−0.216654
$452$	0.878251	0.0413095
$453$	−9.84886	−0.462740
$454$	−21.0403	−0.987470
$455$	3.17304	0.148755
$456$	0.241036	0.0112876
$457$	−24.3534	−1.13921	−0.569603	−	0.821920i	$-0.692903\pi$
$457$	−24.3534	−1.13921	−0.569603	+	0.821920i	$0.692903\pi$
$458$	−57.9688	−2.70871
$459$	−1.26591	−0.0590877
$460$	−27.8757	−1.29971
$461$	10.3474	0.481924	0.240962	−	0.970535i	$-0.422537\pi$
$461$	10.3474	0.481924	0.240962	+	0.970535i	$0.422537\pi$
$462$	−0.617140	−0.0287119
$463$	30.7015	1.42682	0.713409	−	0.700748i	$-0.247150\pi$
$463$	30.7015	1.42682	0.713409	+	0.700748i	$0.247150\pi$
$464$	−39.2520	−1.82223
$465$	5.49152	0.254663
$466$	0.971044	0.0449828
$467$	−20.5093	−0.949056	−0.474528	−	0.880240i	$-0.657381\pi$
$467$	−20.5093	−0.949056	−0.474528	+	0.880240i	$0.657381\pi$
$468$	10.8471	0.501409
$469$	−10.7008	−0.494117
$470$	−2.48726	−0.114729
$471$	7.18033	0.330852
$472$	0.0286965	0.00132086
$473$	3.09167	0.142155
$474$	11.0258	0.506433
$475$	−7.55848	−0.346807
$476$	−0.765111	−0.0350688
$477$	−2.00628	−0.0918614
$478$	−4.18711	−0.191514
$479$	28.0475	1.28152	0.640761	−	0.767740i	$-0.278619\pi$
$479$	28.0475	1.28152	0.640761	+	0.767740i	$0.278619\pi$
$480$	−7.74861	−0.353674
$481$	6.13168	0.279581
$482$	2.01020	0.0915622
$483$	3.02596	0.137686
$484$	−21.3934	−0.972427
$485$	−9.63958	−0.437711
$486$	24.2070	1.09805
$487$	10.9035	0.494085	0.247043	−	0.969005i	$-0.420541\pi$
$487$	10.9035	0.494085	0.247043	+	0.969005i	$0.420541\pi$
$488$	0.0926566	0.00419437
$489$	2.49798	0.112963
$490$	−24.2871	−1.09718
$491$	−27.6672	−1.24860	−0.624301	−	0.781184i	$-0.714616\pi$
$491$	−27.6672	−1.24860	−0.624301	+	0.781184i	$0.714616\pi$
$492$	−6.53287	−0.294525
$493$	4.40820	0.198536
$494$	−22.7493	−1.02354
$495$	−3.80997	−0.171245
$496$	−22.3092	−1.00171
$497$	−0.470726	−0.0211149
$498$	6.66645	0.298731
$499$	−17.3522	−0.776792	−0.388396	−	0.921493i	$-0.626971\pi$
$499$	−17.3522	−0.776792	−0.388396	+	0.921493i	$0.626971\pi$
$500$	−24.7271	−1.10583
$501$	7.82371	0.349538
$502$	−19.4413	−0.867706
$503$	−26.4875	−1.18102	−0.590510	−	0.807030i	$-0.701074\pi$
$503$	−26.4875	−1.18102	−0.590510	+	0.807030i	$0.701074\pi$
$504$	0.192737	0.00858518
$505$	0.369747	0.0164535
$506$	−10.2583	−0.456038
$507$	−4.63706	−0.205939
$508$	−0.0593820	−0.00263465
$509$	3.50048	0.155156	0.0775780	−	0.996986i	$-0.475281\pi$
$509$	3.50048	0.155156	0.0775780	+	0.996986i	$0.475281\pi$
$510$	0.852399	0.0377449
$511$	9.36547	0.414304
$512$	32.1229	1.41964
$513$	−16.8493	−0.743916
$514$	−32.2339	−1.42178
$515$	−7.65019	−0.337108
$516$	4.38977	0.193249
$517$	−0.462293	−0.0203316
$518$	5.43464	0.238784
$519$	0.417175	0.0183119
$520$	−0.306194	−0.0134275
$521$	8.93651	0.391516	0.195758	−	0.980652i	$-0.437283\pi$
$521$	8.93651	0.391516	0.195758	+	0.980652i	$0.437283\pi$
$522$	−55.3915	−2.42442
$523$	6.13438	0.268238	0.134119	−	0.990965i	$-0.457180\pi$
$523$	6.13438	0.268238	0.134119	+	0.990965i	$0.457180\pi$
$524$	−15.3233	−0.669400
$525$	0.550862	0.0240416
$526$	54.1552	2.36128
$527$	2.50544	0.109139
$528$	−1.41071	−0.0613935
$529$	27.2986	1.18689
$530$	2.82498	0.122709
$531$	−0.959280	−0.0416292
$532$	−10.1837	−0.441517
$533$	12.3608	0.535407
$534$	12.6303	0.546565
$535$	12.9210	0.558622
$536$	1.03261	0.0446021
$537$	7.50810	0.323999
$538$	61.7580	2.66258
$539$	−4.51411	−0.194437
$540$	−11.3124	−0.486807
$541$	32.8484	1.41226	0.706132	−	0.708081i	$-0.250439\pi$
$541$	32.8484	1.41226	0.706132	+	0.708081i	$0.250439\pi$
$542$	−64.8368	−2.78498
$543$	−7.49647	−0.321704
$544$	−3.53521	−0.151571
$545$	7.76217	0.332495
$546$	1.65797	0.0709544
$547$	−27.5818	−1.17931	−0.589656	−	0.807655i	$-0.700737\pi$
$547$	−27.5818	−1.17931	−0.589656	+	0.807655i	$0.700737\pi$
$548$	−5.69561	−0.243304
$549$	−3.09736	−0.132192
$550$	−1.86748	−0.0796297
$551$	58.6733	2.49957
$552$	−0.292001	−0.0124284
$553$	−9.33879	−0.397126
$554$	19.7805	0.840391
$555$	−3.05798	−0.129804
$556$	11.3539	0.481511
$557$	12.3393	0.522834	0.261417	−	0.965226i	$-0.415810\pi$
$557$	12.3393	0.522834	0.261417	+	0.965226i	$0.415810\pi$
$558$	−31.4823	−1.33275
$559$	−8.30587	−0.351301
$560$	6.42869	0.271662
$561$	0.158431	0.00668895
$562$	0.125348	0.00528748
$563$	−35.3473	−1.48971	−0.744855	−	0.667227i	$-0.767481\pi$
$563$	−35.3473	−1.48971	−0.744855	+	0.667227i	$0.767481\pi$
$564$	−0.656397	−0.0276393
$565$	0.828737	0.0348652
$566$	−46.4629	−1.95298
$567$	−5.80214	−0.243667
$568$	0.0454244	0.00190597
$569$	19.0099	0.796938	0.398469	−	0.917182i	$-0.369542\pi$
$569$	19.0099	0.796938	0.398469	+	0.917182i	$0.369542\pi$
$570$	11.3455	0.475209
$571$	23.9059	1.00043	0.500215	−	0.865901i	$-0.333254\pi$
$571$	23.9059	1.00043	0.500215	+	0.865901i	$0.333254\pi$
$572$	−2.83880	−0.118696
$573$	4.26432	0.178145
$574$	10.9557	0.457280
$575$	9.15662	0.381858
$576$	22.8858	0.953576
$577$	24.7986	1.03238	0.516190	−	0.856474i	$-0.327350\pi$
$577$	24.7986	1.03238	0.516190	+	0.856474i	$0.327350\pi$
$578$	−33.7845	−1.40525
$579$	−11.7791	−0.489521
$580$	39.3924	1.63568
$581$	−5.64643	−0.234253
$582$	−5.03683	−0.208784
$583$	0.525063	0.0217459
$584$	−0.903755	−0.0373977
$585$	10.2356	0.423190
$586$	−15.2718	−0.630874
$587$	−45.8195	−1.89117	−0.945586	−	0.325373i	$-0.894510\pi$
$587$	−45.8195	−1.89117	−0.945586	+	0.325373i	$0.894510\pi$
$588$	−6.40946	−0.264322
$589$	33.3475	1.37406
$590$	1.35073	0.0556087
$591$	−13.3932	−0.550924
$592$	12.4230	0.510582
$593$	12.9205	0.530581	0.265290	−	0.964169i	$-0.414532\pi$
$593$	12.9205	0.530581	0.265290	+	0.964169i	$0.414532\pi$
$594$	−4.16298	−0.170809
$595$	−0.721976	−0.0295981
$596$	30.2687	1.23985
$597$	−9.80730	−0.401386
$598$	27.5593	1.12698
$599$	26.4741	1.08170	0.540851	−	0.841118i	$-0.318102\pi$
$599$	26.4741	1.08170	0.540851	+	0.841118i	$0.318102\pi$
$600$	−0.0531574	−0.00217014
$601$	12.3729	0.504702	0.252351	−	0.967636i	$-0.418796\pi$
$601$	12.3729	0.504702	0.252351	+	0.967636i	$0.418796\pi$
$602$	−7.36166	−0.300039
$603$	−34.5186	−1.40571
$604$	−40.1539	−1.63384
$605$	−20.1873	−0.820729
$606$	0.193199	0.00784816
$607$	−6.58880	−0.267431	−0.133716	−	0.991020i	$-0.542691\pi$
$607$	−6.58880	−0.267431	−0.133716	+	0.991020i	$0.542691\pi$
$608$	−47.0538	−1.90828
$609$	−4.27611	−0.173277
$610$	4.36130	0.176584
$611$	1.24197	0.0502446
$612$	−2.46809	−0.0997668
$613$	−32.6185	−1.31745	−0.658724	−	0.752384i	$-0.728904\pi$
$613$	−32.6185	−1.31745	−0.658724	+	0.752384i	$0.728904\pi$
$614$	−30.8699	−1.24581
$615$	−6.16456	−0.248579
$616$	−0.0504410	−0.00203233
$617$	44.7802	1.80278	0.901391	−	0.433006i	$-0.142547\pi$
$617$	44.7802	1.80278	0.901391	+	0.433006i	$0.142547\pi$
$618$	−3.99735	−0.160797
$619$	36.4386	1.46459	0.732296	−	0.680986i	$-0.238449\pi$
$619$	36.4386	1.46459	0.732296	+	0.680986i	$0.238449\pi$
$620$	22.3890	0.899164
$621$	20.4119	0.819102
$622$	50.3581	2.01918
$623$	−10.6977	−0.428596
$624$	3.78993	0.151719
$625$	−16.8776	−0.675104
$626$	−17.9953	−0.719235
$627$	2.10872	0.0842140
$628$	29.2743	1.16817
$629$	−1.39517	−0.0556290
$630$	9.07202	0.361438
$631$	19.4629	0.774804	0.387402	−	0.921911i	$-0.373373\pi$
$631$	19.4629	0.774804	0.387402	+	0.921911i	$0.373373\pi$
$632$	0.901181	0.0358470
$633$	2.29579	0.0912496
$634$	41.6767	1.65519
$635$	−0.0560342	−0.00222365
$636$	0.745522	0.0295619
$637$	12.1273	0.480502
$638$	14.4965	0.573921
$639$	−1.51847	−0.0600696
$640$	−1.26691	−0.0500790
$641$	27.8560	1.10025	0.550123	−	0.835084i	$-0.314581\pi$
$641$	27.8560	1.10025	0.550123	+	0.835084i	$0.314581\pi$
$642$	6.75142	0.266457
$643$	−5.63664	−0.222288	−0.111144	−	0.993804i	$-0.535451\pi$
$643$	−5.63664	−0.222288	−0.111144	+	0.993804i	$0.535451\pi$
$644$	12.3369	0.486140
$645$	4.14228	0.163102
$646$	5.17624	0.203656
$647$	−17.7323	−0.697127	−0.348563	−	0.937285i	$-0.613330\pi$
$647$	−17.7323	−0.697127	−0.348563	+	0.937285i	$0.613330\pi$
$648$	0.559899	0.0219949
$649$	0.251053	0.00985468
$650$	5.01705	0.196785
$651$	−2.43037	−0.0952536
$652$	10.1843	0.398849
$653$	14.1435	0.553477	0.276739	−	0.960945i	$-0.410746\pi$
$653$	14.1435	0.553477	0.276739	+	0.960945i	$0.410746\pi$
$654$	4.05586	0.158597
$655$	−14.4594	−0.564974
$656$	25.0434	0.977782
$657$	30.2111	1.17865
$658$	1.10078	0.0429129
$659$	20.0695	0.781798	0.390899	−	0.920434i	$-0.372164\pi$
$659$	20.0695	0.781798	0.390899	+	0.920434i	$0.372164\pi$
$660$	1.41576	0.0551084
$661$	−6.85193	−0.266509	−0.133255	−	0.991082i	$-0.542543\pi$
$661$	−6.85193	−0.266509	−0.133255	+	0.991082i	$0.542543\pi$
$662$	14.0704	0.546862
$663$	−0.425629	−0.0165301
$664$	0.544873	0.0211452
$665$	−9.60952	−0.372641
$666$	17.5310	0.679314
$667$	−71.0791	−2.75219
$668$	31.8974	1.23415
$669$	−5.91319	−0.228617
$670$	48.6046	1.87776
$671$	0.810610	0.0312932
$672$	3.42928	0.132287
$673$	17.5575	0.676791	0.338396	−	0.941004i	$-0.390116\pi$
$673$	17.5575	0.676791	0.338396	+	0.941004i	$0.390116\pi$
$674$	3.53098	0.136008
$675$	3.71590	0.143025
$676$	−18.9054	−0.727129
$677$	22.0052	0.845728	0.422864	−	0.906193i	$-0.361025\pi$
$677$	22.0052	0.845728	0.422864	+	0.906193i	$0.361025\pi$
$678$	0.433028	0.0166304
$679$	4.26616	0.163720
$680$	0.0696697	0.00267171
$681$	−5.23956	−0.200780
$682$	8.23921	0.315496
$683$	32.7325	1.25248	0.626238	−	0.779632i	$-0.284594\pi$
$683$	32.7325	1.25248	0.626238	+	0.779632i	$0.284594\pi$
$684$	−32.8504	−1.25607
$685$	−5.37450	−0.205349
$686$	22.7420	0.868294
$687$	−14.4357	−0.550756
$688$	−16.8280	−0.641560
$689$	−1.41060	−0.0537396
$690$	−13.7443	−0.523237
$691$	−42.8793	−1.63121	−0.815604	−	0.578611i	$-0.803595\pi$
$691$	−42.8793	−1.63121	−0.815604	+	0.578611i	$0.803595\pi$
$692$	1.70083	0.0646558
$693$	1.68617	0.0640521
$694$	−22.1844	−0.842110
$695$	10.7138	0.406396
$696$	0.412639	0.0156410
$697$	−2.81251	−0.106531
$698$	−45.9651	−1.73980
$699$	0.241814	0.00914626
$700$	2.24587	0.0848859
$701$	−9.59945	−0.362566	−0.181283	−	0.983431i	$-0.558025\pi$
$701$	−9.59945	−0.362566	−0.181283	+	0.983431i	$0.558025\pi$
$702$	11.1840	0.422113
$703$	−18.5697	−0.700370
$704$	−5.98944	−0.225735
$705$	−0.619391	−0.0233276
$706$	−38.7335	−1.45775
$707$	−0.163638	−0.00615423
$708$	0.356462	0.0133967
$709$	−20.6550	−0.775717	−0.387858	−	0.921719i	$-0.626785\pi$
$709$	−20.6550	−0.775717	−0.387858	+	0.921719i	$0.626785\pi$
$710$	2.13810	0.0802416
$711$	−30.1251	−1.12978
$712$	1.03232	0.0386877
$713$	−40.3984	−1.51293
$714$	−0.377244	−0.0141180
$715$	−2.67875	−0.100180
$716$	30.6106	1.14397
$717$	−1.04270	−0.0389402
$718$	40.6060	1.51540
$719$	−36.5196	−1.36195	−0.680975	−	0.732307i	$-0.738444\pi$
$719$	−36.5196	−1.36195	−0.680975	+	0.732307i	$0.738444\pi$
$720$	20.7377	0.772847
$721$	3.38572	0.126091
$722$	30.7020	1.14261
$723$	0.500591	0.0186172
$724$	−30.5632	−1.13587
$725$	−12.9396	−0.480566
$726$	−10.5482	−0.391479
$727$	53.4718	1.98316	0.991579	−	0.129503i	$-0.0413381\pi$
$727$	53.4718	1.98316	0.991579	+	0.129503i	$0.0413381\pi$
$728$	0.135512	0.00502239
$729$	−14.3943	−0.533122
$730$	−42.5393	−1.57445
$731$	1.88987	0.0698993
$732$	1.15096	0.0425408
$733$	−47.4390	−1.75220	−0.876100	−	0.482129i	$-0.839864\pi$
$733$	−47.4390	−1.75220	−0.876100	+	0.482129i	$0.839864\pi$
$734$	7.86154	0.290175
$735$	−6.04810	−0.223088
$736$	57.0027	2.10115
$737$	9.03386	0.332766
$738$	35.3407	1.30091
$739$	24.6810	0.907904	0.453952	−	0.891026i	$-0.350014\pi$
$739$	24.6810	0.907904	0.453952	+	0.891026i	$0.350014\pi$
$740$	−12.4674	−0.458311
$741$	−5.66514	−0.208114
$742$	−1.25024	−0.0458979
$743$	−41.1925	−1.51121	−0.755603	−	0.655030i	$-0.772656\pi$
$743$	−41.1925	−1.51121	−0.755603	+	0.655030i	$0.772656\pi$
$744$	0.234527	0.00859818
$745$	28.5622	1.04644
$746$	18.1999	0.666345
$747$	−18.2142	−0.666424
$748$	0.645924	0.0236173
$749$	−5.71840	−0.208946
$750$	−12.1919	−0.445186
$751$	−16.0787	−0.586719	−0.293360	−	0.956002i	$-0.594773\pi$
$751$	−16.0787	−0.586719	−0.293360	+	0.956002i	$0.594773\pi$
$752$	2.51627	0.0917588
$753$	−4.84136	−0.176429
$754$	−38.9453	−1.41830
$755$	−37.8901	−1.37896
$756$	5.00649	0.182084
$757$	−38.0614	−1.38336	−0.691682	−	0.722202i	$-0.743130\pi$
$757$	−38.0614	−1.38336	−0.691682	+	0.722202i	$0.743130\pi$
$758$	56.7865	2.06258
$759$	−2.55458	−0.0927253
$760$	0.927305	0.0336369
$761$	29.7253	1.07754	0.538770	−	0.842453i	$-0.318889\pi$
$761$	29.7253	1.07754	0.538770	+	0.842453i	$0.318889\pi$
$762$	−0.0292788	−0.00106066
$763$	−3.43528	−0.124366
$764$	17.3857	0.628992
$765$	−2.32895	−0.0842033
$766$	63.7036	2.30170
$767$	−0.674461	−0.0243534
$768$	7.67176	0.276831
$769$	−50.1093	−1.80699	−0.903494	−	0.428602i	$-0.859006\pi$
$769$	−50.1093	−1.80699	−0.903494	+	0.428602i	$0.859006\pi$
$770$	−2.37423	−0.0855615
$771$	−8.02705	−0.289087
$772$	−48.0234	−1.72840
$773$	1.44897	0.0521159	0.0260579	−	0.999660i	$-0.491705\pi$
$773$	1.44897	0.0521159	0.0260579	+	0.999660i	$0.491705\pi$
$774$	−23.7473	−0.853577
$775$	−7.35435	−0.264176
$776$	−0.411679	−0.0147784
$777$	1.35336	0.0485515
$778$	46.5742	1.66976
$779$	−37.4346	−1.34123
$780$	−3.80349	−0.136187
$781$	0.397397	0.0142200
$782$	−6.27069	−0.224239
$783$	−28.8450	−1.03084
$784$	24.5703	0.877512
$785$	27.6239	0.985938
$786$	−7.55525	−0.269487
$787$	10.5396	0.375695	0.187848	−	0.982198i	$-0.439849\pi$
$787$	10.5396	0.375695	0.187848	+	0.982198i	$0.439849\pi$
$788$	−54.6044	−1.94520
$789$	13.4860	0.480115
$790$	42.4181	1.50917
$791$	−0.366772	−0.0130409
$792$	−0.162713	−0.00578174
$793$	−2.17773	−0.0773335
$794$	61.5858	2.18560
$795$	0.703491	0.0249503
$796$	−39.9845	−1.41721
$797$	31.2275	1.10614	0.553068	−	0.833136i	$-0.313457\pi$
$797$	31.2275	1.10614	0.553068	+	0.833136i	$0.313457\pi$
$798$	−5.02113	−0.177746
$799$	−0.282590	−0.00999731
$800$	10.3771	0.366886
$801$	−34.5087	−1.21931
$802$	−17.0286	−0.601301
$803$	−7.90654	−0.279016
$804$	12.8269	0.452370
$805$	11.6413	0.410303
$806$	−22.1349	−0.779669
$807$	15.3793	0.541376
$808$	0.0157908	0.000555519 0
$809$	−38.9547	−1.36957	−0.684787	−	0.728743i	$-0.740105\pi$
$809$	−38.9547	−1.36957	−0.684787	+	0.728743i	$0.740105\pi$
$810$	26.3541	0.925990
$811$	3.89413	0.136741	0.0683707	−	0.997660i	$-0.478220\pi$
$811$	3.89413	0.136741	0.0683707	+	0.997660i	$0.478220\pi$
$812$	−17.4338	−0.611805
$813$	−16.1460	−0.566264
$814$	−4.58804	−0.160811
$815$	9.61014	0.336629
$816$	−0.862339	−0.0301879
$817$	25.1542	0.880035
$818$	46.8090	1.63664
$819$	−4.52994	−0.158289
$820$	−25.1330	−0.877682
$821$	−14.5536	−0.507923	−0.253962	−	0.967214i	$-0.581734\pi$
$821$	−14.5536	−0.507923	−0.253962	+	0.967214i	$0.581734\pi$
$822$	−2.80826	−0.0979495
$823$	37.0978	1.29315	0.646575	−	0.762851i	$-0.276201\pi$
$823$	37.0978	1.29315	0.646575	+	0.762851i	$0.276201\pi$
$824$	−0.326718	−0.0113818
$825$	−0.465050	−0.0161909
$826$	−0.597789	−0.0207997
$827$	−46.8558	−1.62934	−0.814668	−	0.579928i	$-0.803081\pi$
$827$	−46.8558	−1.62934	−0.814668	+	0.579928i	$0.803081\pi$
$828$	39.7962	1.38301
$829$	43.4487	1.50904	0.754518	−	0.656280i	$-0.227871\pi$
$829$	43.4487	1.50904	0.754518	+	0.656280i	$0.227871\pi$
$830$	25.6469	0.890216
$831$	4.92583	0.170875
$832$	16.0908	0.557849
$833$	−2.75938	−0.0956068
$834$	5.59811	0.193847
$835$	30.0991	1.04162
$836$	8.59727	0.297343
$837$	−16.3943	−0.566670
$838$	−18.6760	−0.645150
$839$	45.0114	1.55397	0.776983	−	0.629521i	$-0.216749\pi$
$839$	45.0114	1.55397	0.776983	+	0.629521i	$0.216749\pi$
$840$	−0.0675820	−0.00233180
$841$	71.4450	2.46362
$842$	31.1563	1.07372
$843$	0.0312147	0.00107509
$844$	9.35998	0.322184
$845$	−17.8395	−0.613698
$846$	3.55090	0.122082
$847$	8.93422	0.306983
$848$	−2.85792	−0.0981415
$849$	−11.5704	−0.397096
$850$	−1.14155	−0.0391549
$851$	22.4961	0.771155
$852$	0.564253	0.0193310
$853$	5.62487	0.192592	0.0962959	−	0.995353i	$-0.469300\pi$
$853$	5.62487	0.192592	0.0962959	+	0.995353i	$0.469300\pi$
$854$	−1.93017	−0.0660490
$855$	−30.9984	−1.06012
$856$	0.551818	0.0188607
$857$	−1.42125	−0.0485491	−0.0242746	−	0.999705i	$-0.507728\pi$
$857$	−1.42125	−0.0485491	−0.0242746	+	0.999705i	$0.507728\pi$
$858$	−1.39969	−0.0477847
$859$	−2.58506	−0.0882010	−0.0441005	−	0.999027i	$-0.514042\pi$
$859$	−2.58506	−0.0882010	−0.0441005	+	0.999027i	$0.514042\pi$
$860$	16.8881	0.575881
$861$	2.72823	0.0929779
$862$	−39.2608	−1.33723
$863$	−46.3980	−1.57941	−0.789703	−	0.613490i	$-0.789765\pi$
$863$	−46.3980	−1.57941	−0.789703	+	0.613490i	$0.789765\pi$
$864$	23.1326	0.786986
$865$	1.60494	0.0545695
$866$	−11.8467	−0.402567
$867$	−8.41320	−0.285727
$868$	−9.90864	−0.336321
$869$	7.88402	0.267447
$870$	19.4227	0.658491
$871$	−24.2698	−0.822349
$872$	0.331500	0.0112260
$873$	13.7618	0.465765
$874$	−83.4630	−2.82318
$875$	10.3265	0.349098
$876$	−11.2263	−0.379300
$877$	−9.47791	−0.320046	−0.160023	−	0.987113i	$-0.551157\pi$
$877$	−9.47791	−0.320046	−0.160023	+	0.987113i	$0.551157\pi$
$878$	44.5941	1.50498
$879$	−3.80307	−0.128274
$880$	−5.42724	−0.182952
$881$	50.5681	1.70368	0.851841	−	0.523800i	$-0.175486\pi$
$881$	50.5681	1.70368	0.851841	+	0.523800i	$0.175486\pi$
$882$	34.6731	1.16750
$883$	−18.3321	−0.616925	−0.308462	−	0.951237i	$-0.599814\pi$
$883$	−18.3321	−0.616925	−0.308462	+	0.951237i	$0.599814\pi$
$884$	−1.73530	−0.0583643
$885$	0.336366	0.0113068
$886$	−29.4028	−0.987807
$887$	22.4382	0.753401	0.376701	−	0.926335i	$-0.377059\pi$
$887$	22.4382	0.753401	0.376701	+	0.926335i	$0.377059\pi$
$888$	−0.130597	−0.00438256
$889$	0.0247989	0.000831728 0
$890$	48.5906	1.62876
$891$	4.89829	0.164099
$892$	−24.1082	−0.807201
$893$	−3.76128	−0.125866
$894$	14.9242	0.499140
$895$	28.8849	0.965515
$896$	0.560692	0.0187314
$897$	6.86296	0.229148
$898$	−68.8109	−2.29625
$899$	57.0888	1.90402
$900$	7.24472	0.241491
$901$	0.320960	0.0106927
$902$	−9.24900	−0.307958
$903$	−1.83324	−0.0610064
$904$	0.0353930	0.00117715
$905$	−28.8401	−0.958677
$906$	−19.7982	−0.657751
$907$	−44.1063	−1.46452	−0.732262	−	0.681023i	$-0.761535\pi$
$907$	−44.1063	−1.46452	−0.732262	+	0.681023i	$0.761535\pi$
$908$	−21.3618	−0.708915
$909$	−0.527862	−0.0175081
$910$	6.37846	0.211444
$911$	36.5594	1.21127	0.605633	−	0.795744i	$-0.292920\pi$
$911$	36.5594	1.21127	0.605633	+	0.795744i	$0.292920\pi$
$912$	−11.4778	−0.380067
$913$	4.76684	0.157759
$914$	−48.9554	−1.61930
$915$	1.08607	0.0359044
$916$	−58.8545	−1.94461
$917$	6.39924	0.211322
$918$	−2.54474	−0.0839889
$919$	−47.3887	−1.56321	−0.781605	−	0.623774i	$-0.785599\pi$
$919$	−47.3887	−1.56321	−0.781605	+	0.623774i	$0.785599\pi$
$920$	−1.12337	−0.0370365
$921$	−7.68737	−0.253307
$922$	20.8003	0.685021
$923$	−1.06762	−0.0351412
$924$	−0.626568	−0.0206126
$925$	4.09531	0.134653
$926$	61.7162	2.02812
$927$	10.9217	0.358715
$928$	−80.5531	−2.64428
$929$	23.8472	0.782400	0.391200	−	0.920306i	$-0.372060\pi$
$929$	23.8472	0.782400	0.391200	+	0.920306i	$0.372060\pi$
$930$	11.0391	0.361985
$931$	−36.7274	−1.20369
$932$	0.985880	0.0322936
$933$	12.5404	0.410555
$934$	−41.2278	−1.34901
$935$	0.609508	0.0199330
$936$	0.437133	0.0142881
$937$	31.9624	1.04417	0.522083	−	0.852895i	$-0.325155\pi$
$937$	31.9624	1.04417	0.522083	+	0.852895i	$0.325155\pi$
$938$	−21.5108	−0.702352
$939$	−4.48127	−0.146241
$940$	−2.52526	−0.0823650
$941$	23.8740	0.778271	0.389136	−	0.921180i	$-0.372774\pi$
$941$	23.8740	0.778271	0.389136	+	0.921180i	$0.372774\pi$
$942$	14.4339	0.470283
$943$	45.3497	1.47679
$944$	−1.36648	−0.0444752
$945$	4.72423	0.153679
$946$	6.21488	0.202063
$947$	44.4722	1.44515	0.722575	−	0.691292i	$-0.242958\pi$
$947$	44.4722	1.44515	0.722575	+	0.691292i	$0.242958\pi$
$948$	11.1943	0.363574
$949$	21.2412	0.689518
$950$	−15.1941	−0.492961
$951$	10.3785	0.336547
$952$	−0.0308335	−0.000999319 0
$953$	−54.1645	−1.75456	−0.877280	−	0.479980i	$-0.840644\pi$
$953$	−54.1645	−1.75456	−0.877280	+	0.479980i	$0.840644\pi$
$954$	−4.03303	−0.130574
$955$	16.4055	0.530870
$956$	−4.25109	−0.137490
$957$	3.60999	0.116694
$958$	56.3811	1.82159
$959$	2.37858	0.0768083
$960$	−8.02477	−0.258998
$961$	1.44694	0.0466756
$962$	12.3259	0.397404
$963$	−18.4464	−0.594427
$964$	2.04092	0.0657334
$965$	−45.3159	−1.45877
$966$	6.08278	0.195710
$967$	−35.3826	−1.13783	−0.568914	−	0.822397i	$-0.692636\pi$
$967$	−35.3826	−1.13783	−0.568914	+	0.822397i	$0.692636\pi$
$968$	−0.862140	−0.0277102
$969$	1.28901	0.0414090
$970$	−19.3775	−0.622174
$971$	−8.91001	−0.285936	−0.142968	−	0.989727i	$-0.545665\pi$
$971$	−8.91001	−0.285936	−0.142968	+	0.989727i	$0.545665\pi$
$972$	24.5768	0.788302
$973$	−4.74155	−0.152007
$974$	21.9183	0.702307
$975$	1.24937	0.0400119
$976$	−4.41215	−0.141230
$977$	21.0250	0.672650	0.336325	−	0.941746i	$-0.390816\pi$
$977$	21.0250	0.672650	0.336325	+	0.941746i	$0.390816\pi$
$978$	5.02146	0.160568
$979$	9.03126	0.288640
$980$	−24.6582	−0.787677
$981$	−11.0815	−0.353806
$982$	−55.6166	−1.77480
$983$	−33.5818	−1.07109	−0.535546	−	0.844506i	$-0.679894\pi$
$983$	−33.5818	−1.07109	−0.535546	+	0.844506i	$0.679894\pi$
$984$	−0.263271	−0.00839276
$985$	−51.5259	−1.64175
$986$	8.86138	0.282204
$987$	0.274122	0.00872540
$988$	−23.0968	−0.734808
$989$	−30.4728	−0.968978
$990$	−7.65880	−0.243413
$991$	−32.0529	−1.01819	−0.509097	−	0.860709i	$-0.670021\pi$
$991$	−32.0529	−1.01819	−0.509097	+	0.860709i	$0.670021\pi$
$992$	−45.7831	−1.45361
$993$	3.50389	0.111192
$994$	−0.946255	−0.0300134
$995$	−37.7302	−1.19613
$996$	6.76830	0.214462
$997$	37.4198	1.18510	0.592548	−	0.805535i	$-0.298122\pi$
$997$	37.4198	1.18510	0.592548	+	0.805535i	$0.298122\pi$
$998$	−34.8815	−1.10415
$999$	9.12924	0.288836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.10	✓	12
3.2	odd	2		2169.2.a.h.1.3		12
4.3	odd	2		3856.2.a.n.1.6		12
5.4	even	2		6025.2.a.h.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.10	✓	12	1.1	even	1	trivial
2169.2.a.h.1.3		12	3.2	odd	2
3856.2.a.n.1.6		12	4.3	odd	2
6025.2.a.h.1.3		12	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.a (trivial)

\(f(q)\)	\(=\)	\(q+2.01020 q^{2} +0.500591 q^{3} +2.04092 q^{4} +1.92585 q^{5} +1.00629 q^{6} -0.852319 q^{7} +0.0822476 q^{8} -2.74941 q^{9} +O(q^{10})\)	\(q+2.01020 q^{2} +0.500591 q^{3} +2.04092 q^{4} +1.92585 q^{5} +1.00629 q^{6} -0.852319 q^{7} +0.0822476 q^{8} -2.74941 q^{9} +3.87135 q^{10} +0.719546 q^{11} +1.02166 q^{12} -1.93309 q^{13} -1.71333 q^{14} +0.964064 q^{15} -3.91650 q^{16} +0.439843 q^{17} -5.52687 q^{18} +5.85432 q^{19} +3.93050 q^{20} -0.426663 q^{21} +1.44643 q^{22} -7.09215 q^{23} +0.0411724 q^{24} -1.29109 q^{25} -3.88589 q^{26} -2.87810 q^{27} -1.73951 q^{28} +10.0222 q^{29} +1.93796 q^{30} +5.69622 q^{31} -8.03745 q^{32} +0.360198 q^{33} +0.884173 q^{34} -1.64144 q^{35} -5.61131 q^{36} -3.17197 q^{37} +11.7684 q^{38} -0.967685 q^{39} +0.158397 q^{40} -6.39435 q^{41} -0.857679 q^{42} +4.29669 q^{43} +1.46853 q^{44} -5.29496 q^{45} -14.2567 q^{46} -0.642479 q^{47} -1.96056 q^{48} -6.27355 q^{49} -2.59536 q^{50} +0.220181 q^{51} -3.94526 q^{52} +0.729714 q^{53} -5.78557 q^{54} +1.38574 q^{55} -0.0701012 q^{56} +2.93062 q^{57} +20.1467 q^{58} +0.348904 q^{59} +1.96757 q^{60} +1.12656 q^{61} +11.4506 q^{62} +2.34337 q^{63} -8.32390 q^{64} -3.72284 q^{65} +0.724072 q^{66} +12.5549 q^{67} +0.897682 q^{68} -3.55026 q^{69} -3.29963 q^{70} +0.552289 q^{71} -0.226132 q^{72} -10.9882 q^{73} -6.37630 q^{74} -0.646309 q^{75} +11.9482 q^{76} -0.613283 q^{77} -1.94524 q^{78} +10.9569 q^{79} -7.54259 q^{80} +6.80748 q^{81} -12.8539 q^{82} +6.62478 q^{83} -0.870783 q^{84} +0.847072 q^{85} +8.63722 q^{86} +5.01703 q^{87} +0.0591810 q^{88} +12.5513 q^{89} -10.6439 q^{90} +1.64760 q^{91} -14.4745 q^{92} +2.85148 q^{93} -1.29151 q^{94} +11.2746 q^{95} -4.02347 q^{96} -5.00536 q^{97} -12.6111 q^{98} -1.97833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * q^99

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