LMFDB - Embedded newform 241.2.a.b.1.2

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			1.2
Root			$-2.02418$ 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)

$f(q)$	$=$	$q-2.02418 q^{2} +2.93498 q^{3} +2.09729 q^{4} +1.44091 q^{5} -5.94092 q^{6} +0.381245 q^{7} -0.196936 q^{8} +5.61411 q^{9} +O(q^{10})$	\(q-2.02418 q^{2} +2.93498 q^{3} +2.09729 q^{4} +1.44091 q^{5} -5.94092 q^{6} +0.381245 q^{7} -0.196936 q^{8} +5.61411 q^{9} -2.91665 q^{10} +0.280814 q^{11} +6.15551 q^{12} -4.00528 q^{13} -0.771706 q^{14} +4.22904 q^{15} -3.79595 q^{16} +2.60326 q^{17} -11.3640 q^{18} -3.86940 q^{19} +3.02200 q^{20} +1.11895 q^{21} -0.568418 q^{22} +0.698450 q^{23} -0.578002 q^{24} -2.92378 q^{25} +8.10740 q^{26} +7.67238 q^{27} +0.799581 q^{28} +1.62690 q^{29} -8.56032 q^{30} +9.73691 q^{31} +8.07755 q^{32} +0.824185 q^{33} -5.26945 q^{34} +0.549338 q^{35} +11.7744 q^{36} +4.41735 q^{37} +7.83234 q^{38} -11.7554 q^{39} -0.283766 q^{40} -0.0157665 q^{41} -2.26494 q^{42} -12.2173 q^{43} +0.588950 q^{44} +8.08942 q^{45} -1.41379 q^{46} +7.71890 q^{47} -11.1410 q^{48} -6.85465 q^{49} +5.91826 q^{50} +7.64051 q^{51} -8.40025 q^{52} -4.91852 q^{53} -15.5302 q^{54} +0.404628 q^{55} -0.0750807 q^{56} -11.3566 q^{57} -3.29313 q^{58} -14.1596 q^{59} +8.86953 q^{60} -6.97043 q^{61} -19.7092 q^{62} +2.14035 q^{63} -8.75848 q^{64} -5.77125 q^{65} -1.66830 q^{66} -2.97942 q^{67} +5.45979 q^{68} +2.04994 q^{69} -1.11196 q^{70} +7.28180 q^{71} -1.10562 q^{72} -0.165424 q^{73} -8.94150 q^{74} -8.58125 q^{75} -8.11525 q^{76} +0.107059 q^{77} +23.7951 q^{78} +11.1633 q^{79} -5.46962 q^{80} +5.67594 q^{81} +0.0319141 q^{82} -14.6259 q^{83} +2.34676 q^{84} +3.75106 q^{85} +24.7300 q^{86} +4.77491 q^{87} -0.0553024 q^{88} +14.3374 q^{89} -16.3744 q^{90} -1.52699 q^{91} +1.46485 q^{92} +28.5777 q^{93} -15.6244 q^{94} -5.57544 q^{95} +23.7074 q^{96} +8.75687 q^{97} +13.8750 q^{98} +1.57652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.02418	−1.43131	−0.715655	−	0.698454i	$-0.753871\pi$
$2$	−2.02418	−1.43131	−0.715655	+	0.698454i	$0.753871\pi$
$3$	2.93498	1.69451	0.847256	−	0.531185i	$-0.178253\pi$
$3$	2.93498	1.69451	0.847256	+	0.531185i	$0.178253\pi$
$4$	2.09729	1.04865
$5$	1.44091	0.644394	0.322197	−	0.946673i	$-0.395579\pi$
$5$	1.44091	0.644394	0.322197	+	0.946673i	$0.395579\pi$
$6$	−5.94092	−2.42537
$7$	0.381245	0.144097	0.0720485	−	0.997401i	$-0.477046\pi$
$7$	0.381245	0.144097	0.0720485	+	0.997401i	$0.477046\pi$
$8$	−0.196936	−0.0696273
$9$	5.61411	1.87137
$10$	−2.91665	−0.922327
$11$	0.280814	0.0846688	0.0423344	−	0.999103i	$-0.486521\pi$
$11$	0.280814	0.0846688	0.0423344	+	0.999103i	$0.486521\pi$
$12$	6.15551	1.77694
$13$	−4.00528	−1.11087	−0.555433	−	0.831561i	$-0.687447\pi$
$13$	−4.00528	−1.11087	−0.555433	+	0.831561i	$0.687447\pi$
$14$	−0.771706	−0.206247
$15$	4.22904	1.09193
$16$	−3.79595	−0.948988
$17$	2.60326	0.631383	0.315691	−	0.948862i	$-0.397764\pi$
$17$	2.60326	0.631383	0.315691	+	0.948862i	$0.397764\pi$
$18$	−11.3640	−2.67851
$19$	−3.86940	−0.887700	−0.443850	−	0.896101i	$-0.646388\pi$
$19$	−3.86940	−0.887700	−0.443850	+	0.896101i	$0.646388\pi$
$20$	3.02200	0.675741
$21$	1.11895	0.244174
$22$	−0.568418	−0.121187
$23$	0.698450	0.145637	0.0728185	−	0.997345i	$-0.476801\pi$
$23$	0.698450	0.145637	0.0728185	+	0.997345i	$0.476801\pi$
$24$	−0.578002	−0.117984
$25$	−2.92378	−0.584757
$26$	8.10740	1.58999
$27$	7.67238	1.47655
$28$	0.799581	0.151107
$29$	1.62690	0.302107	0.151054	−	0.988526i	$-0.451733\pi$
$29$	1.62690	0.302107	0.151054	+	0.988526i	$0.451733\pi$
$30$	−8.56032	−1.56289
$31$	9.73691	1.74880	0.874401	−	0.485205i	$-0.161255\pi$
$31$	9.73691	1.74880	0.874401	+	0.485205i	$0.161255\pi$
$32$	8.07755	1.42792
$33$	0.824185	0.143472
$34$	−5.26945	−0.903704
$35$	0.549338	0.0928551
$36$	11.7744	1.96241
$37$	4.41735	0.726208	0.363104	−	0.931749i	$-0.381717\pi$
$37$	4.41735	0.726208	0.363104	+	0.931749i	$0.381717\pi$
$38$	7.83234	1.27057
$39$	−11.7554	−1.88238
$40$	−0.283766	−0.0448674
$41$	−0.0157665	−0.00246231	−0.00123116	−	0.999999i	$-0.500392\pi$
$41$	−0.0157665	−0.00246231	−0.00123116	+	0.999999i	$0.500392\pi$
$42$	−2.26494	−0.349488
$43$	−12.2173	−1.86312	−0.931562	−	0.363583i	$-0.881553\pi$
$43$	−12.2173	−1.86312	−0.931562	+	0.363583i	$0.881553\pi$
$44$	0.588950	0.0887875
$45$	8.08942	1.20590
$46$	−1.41379	−0.208452
$47$	7.71890	1.12592	0.562958	−	0.826485i	$-0.309663\pi$
$47$	7.71890	1.12592	0.562958	+	0.826485i	$0.309663\pi$
$48$	−11.1410	−1.60807
$49$	−6.85465	−0.979236
$50$	5.91826	0.836968
$51$	7.64051	1.06989
$52$	−8.40025	−1.16491
$53$	−4.91852	−0.675611	−0.337806	−	0.941216i	$-0.609685\pi$
$53$	−4.91852	−0.675611	−0.337806	+	0.941216i	$0.609685\pi$
$54$	−15.5302	−2.11340
$55$	0.404628	0.0545600
$56$	−0.0750807	−0.0100331
$57$	−11.3566	−1.50422
$58$	−3.29313	−0.432409
$59$	−14.1596	−1.84342	−0.921709	−	0.387882i	$-0.873207\pi$
$59$	−14.1596	−1.84342	−0.921709	+	0.387882i	$0.873207\pi$
$60$	8.86953	1.14505
$61$	−6.97043	−0.892472	−0.446236	−	0.894915i	$-0.647236\pi$
$61$	−6.97043	−0.892472	−0.446236	+	0.894915i	$0.647236\pi$
$62$	−19.7092	−2.50308
$63$	2.14035	0.269659
$64$	−8.75848	−1.09481
$65$	−5.77125	−0.715835
$66$	−1.66830	−0.205353
$67$	−2.97942	−0.363994	−0.181997	−	0.983299i	$-0.558256\pi$
$67$	−2.97942	−0.363994	−0.181997	+	0.983299i	$0.558256\pi$
$68$	5.45979	0.662097
$69$	2.04994	0.246784
$70$	−1.11196	−0.132904
$71$	7.28180	0.864191	0.432095	−	0.901828i	$-0.357774\pi$
$71$	7.28180	0.864191	0.432095	+	0.901828i	$0.357774\pi$
$72$	−1.10562	−0.130298
$73$	−0.165424	−0.0193614	−0.00968072	−	0.999953i	$-0.503082\pi$
$73$	−0.165424	−0.0193614	−0.00968072	+	0.999953i	$0.503082\pi$
$74$	−8.94150	−1.03943
$75$	−8.58125	−0.990878
$76$	−8.11525	−0.930883
$77$	0.107059	0.0122005
$78$	23.7951	2.69426
$79$	11.1633	1.25597	0.627986	−	0.778225i	$-0.283880\pi$
$79$	11.1633	1.25597	0.627986	+	0.778225i	$0.283880\pi$
$80$	−5.46962	−0.611522
$81$	5.67594	0.630660
$82$	0.0319141	0.00352433
$83$	−14.6259	−1.60540	−0.802701	−	0.596382i	$-0.796604\pi$
$83$	−14.6259	−1.60540	−0.802701	+	0.596382i	$0.796604\pi$
$84$	2.34676	0.256052
$85$	3.75106	0.406859
$86$	24.7300	2.66671
$87$	4.77491	0.511924
$88$	−0.0553024	−0.00589525
$89$	14.3374	1.51976	0.759878	−	0.650066i	$-0.225259\pi$
$89$	14.3374	1.51976	0.759878	+	0.650066i	$0.225259\pi$
$90$	−16.3744	−1.72602
$91$	−1.52699	−0.160072
$92$	1.46485	0.152722
$93$	28.5777	2.96337
$94$	−15.6244	−1.61154
$95$	−5.57544	−0.572028
$96$	23.7074	2.41963
$97$	8.75687	0.889126	0.444563	−	0.895748i	$-0.353359\pi$
$97$	8.75687	0.889126	0.444563	+	0.895748i	$0.353359\pi$
$98$	13.8750	1.40159
$99$	1.57652	0.158447
$100$	−6.13203	−0.613203
$101$	−5.97227	−0.594263	−0.297132	−	0.954837i	$-0.596030\pi$
$101$	−5.97227	−0.594263	−0.297132	+	0.954837i	$0.596030\pi$
$102$	−15.4658	−1.53134
$103$	−17.0246	−1.67749	−0.838743	−	0.544527i	$-0.816709\pi$
$103$	−17.0246	−1.67749	−0.838743	+	0.544527i	$0.816709\pi$
$104$	0.788783	0.0773466
$105$	1.61230	0.157344
$106$	9.95596	0.967008
$107$	−6.06814	−0.586629	−0.293315	−	0.956016i	$-0.594758\pi$
$107$	−6.06814	−0.586629	−0.293315	+	0.956016i	$0.594758\pi$
$108$	16.0912	1.54838
$109$	−10.0495	−0.962568	−0.481284	−	0.876565i	$-0.659829\pi$
$109$	−10.0495	−0.962568	−0.481284	+	0.876565i	$0.659829\pi$
$110$	−0.819038	−0.0780922
$111$	12.9648	1.23057
$112$	−1.44719	−0.136746
$113$	3.24797	0.305543	0.152772	−	0.988262i	$-0.451180\pi$
$113$	3.24797	0.305543	0.152772	+	0.988262i	$0.451180\pi$
$114$	22.9878	2.15300
$115$	1.00640	0.0938476
$116$	3.41208	0.316803
$117$	−22.4861	−2.07884
$118$	28.6615	2.63850
$119$	0.992478	0.0909803
$120$	−0.832848	−0.0760283
$121$	−10.9211	−0.992831
$122$	14.1094	1.27740
$123$	−0.0462743	−0.00417241
$124$	20.4211	1.83387
$125$	−11.4174	−1.02121
$126$	−4.33245	−0.385965
$127$	0.309449	0.0274591	0.0137296	−	0.999906i	$-0.495630\pi$
$127$	0.309449	0.0274591	0.0137296	+	0.999906i	$0.495630\pi$
$128$	1.57362	0.139090
$129$	−35.8576	−3.15709
$130$	11.6820	1.02458
$131$	17.9939	1.57214	0.786068	−	0.618141i	$-0.212114\pi$
$131$	17.9939	1.57214	0.786068	+	0.618141i	$0.212114\pi$
$132$	1.72856	0.150452
$133$	−1.47519	−0.127915
$134$	6.03088	0.520989
$135$	11.0552	0.951479
$136$	−0.512674	−0.0439615
$137$	−8.91168	−0.761377	−0.380688	−	0.924703i	$-0.624313\pi$
$137$	−8.91168	−0.761377	−0.380688	+	0.924703i	$0.624313\pi$
$138$	−4.14944	−0.353224
$139$	7.82985	0.664119	0.332059	−	0.943258i	$-0.392257\pi$
$139$	7.82985	0.664119	0.332059	+	0.943258i	$0.392257\pi$
$140$	1.15212	0.0973721
$141$	22.6548	1.90788
$142$	−14.7396	−1.23692
$143$	−1.12474	−0.0940557
$144$	−21.3109	−1.77591
$145$	2.34421	0.194676
$146$	0.334848	0.0277122
$147$	−20.1183	−1.65933
$148$	9.26447	0.761535
$149$	20.5561	1.68402	0.842010	−	0.539462i	$-0.181372\pi$
$149$	20.5561	1.68402	0.842010	+	0.539462i	$0.181372\pi$
$150$	17.3700	1.41825
$151$	10.5866	0.861524	0.430762	−	0.902466i	$-0.358245\pi$
$151$	10.5866	0.861524	0.430762	+	0.902466i	$0.358245\pi$
$152$	0.762022	0.0618082
$153$	14.6150	1.18155
$154$	−0.216706	−0.0174627
$155$	14.0300	1.12692
$156$	−24.6546	−1.97395
$157$	7.79923	0.622447	0.311223	−	0.950337i	$-0.399261\pi$
$157$	7.79923	0.622447	0.311223	+	0.950337i	$0.399261\pi$
$158$	−22.5965	−1.79768
$159$	−14.4358	−1.14483
$160$	11.6390	0.920144
$161$	0.266280	0.0209858
$162$	−11.4891	−0.902669
$163$	17.1362	1.34221	0.671104	−	0.741363i	$-0.265820\pi$
$163$	17.1362	1.34221	0.671104	+	0.741363i	$0.265820\pi$
$164$	−0.0330669	−0.00258209
$165$	1.18758	0.0924526
$166$	29.6054	2.29783
$167$	−1.88493	−0.145860	−0.0729302	−	0.997337i	$-0.523235\pi$
$167$	−1.88493	−0.145860	−0.0729302	+	0.997337i	$0.523235\pi$
$168$	−0.220360	−0.0170012
$169$	3.04231	0.234024
$170$	−7.59280	−0.582341
$171$	−21.7232	−1.66122
$172$	−25.6233	−1.95376
$173$	−9.95946	−0.757203	−0.378602	−	0.925560i	$-0.623595\pi$
$173$	−9.95946	−0.757203	−0.378602	+	0.925560i	$0.623595\pi$
$174$	−9.66526	−0.732722
$175$	−1.11468	−0.0842616
$176$	−1.06596	−0.0803496
$177$	−41.5581	−3.12369
$178$	−29.0213	−2.17524
$179$	25.8971	1.93564	0.967820	−	0.251643i	$-0.0809708\pi$
$179$	25.8971	1.93564	0.967820	+	0.251643i	$0.0809708\pi$
$180$	16.9659	1.26456
$181$	−8.61696	−0.640494	−0.320247	−	0.947334i	$-0.603766\pi$
$181$	−8.61696	−0.640494	−0.320247	+	0.947334i	$0.603766\pi$
$182$	3.09090	0.229113
$183$	−20.4581	−1.51230
$184$	−0.137550	−0.0101403
$185$	6.36499	0.467964
$186$	−57.8462	−4.24149
$187$	0.731033	0.0534584
$188$	16.1888	1.18069
$189$	2.92505	0.212766
$190$	11.2857	0.818750
$191$	−7.40808	−0.536030	−0.268015	−	0.963415i	$-0.586368\pi$
$191$	−7.40808	−0.536030	−0.268015	+	0.963415i	$0.586368\pi$
$192$	−25.7060	−1.85517
$193$	−13.0485	−0.939252	−0.469626	−	0.882865i	$-0.655611\pi$
$193$	−13.0485	−0.939252	−0.469626	+	0.882865i	$0.655611\pi$
$194$	−17.7255	−1.27261
$195$	−16.9385	−1.21299
$196$	−14.3762	−1.02687
$197$	−2.32016	−0.165305	−0.0826524	−	0.996578i	$-0.526339\pi$
$197$	−2.32016	−0.165305	−0.0826524	+	0.996578i	$0.526339\pi$
$198$	−3.19116	−0.226786
$199$	21.5958	1.53089	0.765444	−	0.643502i	$-0.222519\pi$
$199$	21.5958	1.53089	0.765444	+	0.643502i	$0.222519\pi$
$200$	0.575797	0.0407150
$201$	−8.74455	−0.616793
$202$	12.0889	0.850574
$203$	0.620245	0.0435327
$204$	16.0244	1.12193
$205$	−0.0227180	−0.00158670
$206$	34.4609	2.40100
$207$	3.92118	0.272541
$208$	15.2039	1.05420
$209$	−1.08658	−0.0751605
$210$	−3.26358	−0.225208
$211$	20.1477	1.38702	0.693512	−	0.720445i	$-0.256062\pi$
$211$	20.1477	1.38702	0.693512	+	0.720445i	$0.256062\pi$
$212$	−10.3156	−0.708477
$213$	21.3719	1.46438
$214$	12.2830	0.839648
$215$	−17.6040	−1.20059
$216$	−1.51096	−0.102808
$217$	3.71215	0.251997
$218$	20.3420	1.37773
$219$	−0.485517	−0.0328082
$220$	0.848623	0.0572141
$221$	−10.4268	−0.701382
$222$	−26.2431	−1.76132
$223$	−7.96809	−0.533583	−0.266792	−	0.963754i	$-0.585964\pi$
$223$	−7.96809	−0.533583	−0.266792	+	0.963754i	$0.585964\pi$
$224$	3.07952	0.205759
$225$	−16.4145	−1.09430
$226$	−6.57447	−0.437327
$227$	−19.2441	−1.27728	−0.638639	−	0.769506i	$-0.720502\pi$
$227$	−19.2441	−1.27728	−0.638639	+	0.769506i	$0.720502\pi$
$228$	−23.8181	−1.57739
$229$	12.7475	0.842380	0.421190	−	0.906972i	$-0.361612\pi$
$229$	12.7475	0.842380	0.421190	+	0.906972i	$0.361612\pi$
$230$	−2.03714	−0.134325
$231$	0.314216	0.0206739
$232$	−0.320394	−0.0210349
$233$	−10.2413	−0.670931	−0.335465	−	0.942053i	$-0.608894\pi$
$233$	−10.2413	−0.670931	−0.335465	+	0.942053i	$0.608894\pi$
$234$	45.5159	2.97547
$235$	11.1222	0.725534
$236$	−29.6967	−1.93309
$237$	32.7641	2.12826
$238$	−2.00895	−0.130221
$239$	22.4264	1.45064	0.725321	−	0.688411i	$-0.241691\pi$
$239$	22.4264	1.45064	0.725321	+	0.688411i	$0.241691\pi$
$240$	−16.0532	−1.03623
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	22.1063	1.42105
$243$	−6.35836	−0.407889
$244$	−14.6190	−0.935887
$245$	−9.87692	−0.631014
$246$	0.0936674	0.00597202
$247$	15.4980	0.986116
$248$	−1.91755	−0.121764
$249$	−42.9267	−2.72037
$250$	23.1109	1.46166
$251$	14.0729	0.888274	0.444137	−	0.895959i	$-0.353510\pi$
$251$	14.0729	0.888274	0.444137	+	0.895959i	$0.353510\pi$
$252$	4.48894	0.282777
$253$	0.196135	0.0123309
$254$	−0.626379	−0.0393025
$255$	11.0093	0.689428
$256$	14.3317	0.895730
$257$	1.46464	0.0913619	0.0456809	−	0.998956i	$-0.485454\pi$
$257$	1.46464	0.0913619	0.0456809	+	0.998956i	$0.485454\pi$
$258$	72.5821	4.51877
$259$	1.68409	0.104644
$260$	−12.1040	−0.750658
$261$	9.13358	0.565355
$262$	−36.4229	−2.25021
$263$	8.09273	0.499019	0.249509	−	0.968372i	$-0.419731\pi$
$263$	8.09273	0.499019	0.249509	+	0.968372i	$0.419731\pi$
$264$	−0.162311	−0.00998958
$265$	−7.08714	−0.435360
$266$	2.98604	0.183086
$267$	42.0799	2.57525
$268$	−6.24872	−0.381701
$269$	−25.2517	−1.53962	−0.769812	−	0.638271i	$-0.779650\pi$
$269$	−25.2517	−1.53962	−0.769812	+	0.638271i	$0.779650\pi$
$270$	−22.3777	−1.36186
$271$	6.04109	0.366970	0.183485	−	0.983023i	$-0.441262\pi$
$271$	6.04109	0.366970	0.183485	+	0.983023i	$0.441262\pi$
$272$	−9.88184	−0.599175
$273$	−4.48170	−0.271245
$274$	18.0388	1.08977
$275$	−0.821041	−0.0495106
$276$	4.29932	0.258789
$277$	−17.9271	−1.07714	−0.538568	−	0.842582i	$-0.681034\pi$
$277$	−17.9271	−1.07714	−0.538568	+	0.842582i	$0.681034\pi$
$278$	−15.8490	−0.950559
$279$	54.6641	3.27266
$280$	−0.108184	−0.00646525
$281$	4.13276	0.246540	0.123270	−	0.992373i	$-0.460662\pi$
$281$	4.13276	0.246540	0.123270	+	0.992373i	$0.460662\pi$
$282$	−45.8574	−2.73077
$283$	13.7771	0.818962	0.409481	−	0.912319i	$-0.365710\pi$
$283$	13.7771	0.818962	0.409481	+	0.912319i	$0.365710\pi$
$284$	15.2721	0.906230
$285$	−16.3638	−0.969309
$286$	2.27668	0.134623
$287$	−0.00601088	−0.000354811 0
$288$	45.3483	2.67217
$289$	−10.2230	−0.601356
$290$	−4.74509	−0.278641
$291$	25.7013	1.50663
$292$	−0.346943	−0.0203033
$293$	21.6053	1.26220	0.631098	−	0.775703i	$-0.282605\pi$
$293$	21.6053	1.26220	0.631098	+	0.775703i	$0.282605\pi$
$294$	40.7229	2.37501
$295$	−20.4026	−1.18789
$296$	−0.869934	−0.0505639
$297$	2.15451	0.125018
$298$	−41.6091	−2.41035
$299$	−2.79749	−0.161783
$300$	−17.9974	−1.03908
$301$	−4.65779	−0.268470
$302$	−21.4291	−1.23311
$303$	−17.5285	−1.00699
$304$	14.6880	0.842417
$305$	−10.0437	−0.575103
$306$	−29.5833	−1.69117
$307$	20.3178	1.15960	0.579800	−	0.814759i	$-0.303131\pi$
$307$	20.3178	1.15960	0.579800	+	0.814759i	$0.303131\pi$
$308$	0.224534	0.0127940
$309$	−49.9670	−2.84252
$310$	−28.3992	−1.61297
$311$	20.4778	1.16119	0.580595	−	0.814193i	$-0.302820\pi$
$311$	20.4778	1.16119	0.580595	+	0.814193i	$0.302820\pi$
$312$	2.31506	0.131065
$313$	1.98489	0.112192	0.0560962	−	0.998425i	$-0.482135\pi$
$313$	1.98489	0.112192	0.0560962	+	0.998425i	$0.482135\pi$
$314$	−15.7870	−0.890913
$315$	3.08405	0.173766
$316$	23.4127	1.31707
$317$	−28.5808	−1.60526	−0.802630	−	0.596477i	$-0.796567\pi$
$317$	−28.5808	−1.60526	−0.802630	+	0.596477i	$0.796567\pi$
$318$	29.2206	1.63861
$319$	0.456856	0.0255790
$320$	−12.6202	−0.705489
$321$	−17.8099	−0.994051
$322$	−0.538999	−0.0300372
$323$	−10.0730	−0.560479
$324$	11.9041	0.661339
$325$	11.7106	0.649587
$326$	−34.6867	−1.92112
$327$	−29.4951	−1.63108
$328$	0.00310498	0.000171444 0
$329$	2.94279	0.162241
$330$	−2.40386	−0.132328
$331$	−23.4089	−1.28667	−0.643334	−	0.765585i	$-0.722449\pi$
$331$	−23.4089	−1.28667	−0.643334	+	0.765585i	$0.722449\pi$
$332$	−30.6748	−1.68350
$333$	24.7995	1.35900
$334$	3.81544	0.208771
$335$	−4.29307	−0.234556
$336$	−4.24746	−0.231718
$337$	2.23389	0.121688	0.0608440	−	0.998147i	$-0.480621\pi$
$337$	2.23389	0.121688	0.0608440	+	0.998147i	$0.480621\pi$
$338$	−6.15817	−0.334960
$339$	9.53273	0.517747
$340$	7.86706	0.426651
$341$	2.73427	0.148069
$342$	43.9717	2.37772
$343$	−5.28201	−0.285202
$344$	2.40603	0.129724
$345$	2.95377	0.159026
$346$	20.1597	1.08379
$347$	17.2084	0.923793	0.461897	−	0.886934i	$-0.347169\pi$
$347$	17.2084	0.923793	0.461897	+	0.886934i	$0.347169\pi$
$348$	10.0144	0.536827
$349$	21.1996	1.13479	0.567394	−	0.823447i	$-0.307952\pi$
$349$	21.1996	1.13479	0.567394	+	0.823447i	$0.307952\pi$
$350$	2.25630	0.120604
$351$	−30.7301	−1.64025
$352$	2.26829	0.120900
$353$	−9.42434	−0.501607	−0.250803	−	0.968038i	$-0.580695\pi$
$353$	−9.42434	−0.501607	−0.250803	+	0.968038i	$0.580695\pi$
$354$	84.1209	4.47097
$355$	10.4924	0.556879
$356$	30.0696	1.59369
$357$	2.91290	0.154167
$358$	−52.4203	−2.77050
$359$	8.50212	0.448725	0.224362	−	0.974506i	$-0.427970\pi$
$359$	8.50212	0.448725	0.224362	+	0.974506i	$0.427970\pi$
$360$	−1.59310	−0.0839635
$361$	−4.02777	−0.211988
$362$	17.4423	0.916744
$363$	−32.0533	−1.68236
$364$	−3.20255	−0.167859
$365$	−0.238361	−0.0124764
$366$	41.4108	2.16458
$367$	5.48335	0.286229	0.143114	−	0.989706i	$-0.454288\pi$
$367$	5.48335	0.286229	0.143114	+	0.989706i	$0.454288\pi$
$368$	−2.65128	−0.138208
$369$	−0.0885148	−0.00460790
$370$	−12.8839	−0.669801
$371$	−1.87516	−0.0973535
$372$	59.9357	3.10752
$373$	−23.6497	−1.22454	−0.612268	−	0.790650i	$-0.709743\pi$
$373$	−23.6497	−1.22454	−0.612268	+	0.790650i	$0.709743\pi$
$374$	−1.47974	−0.0765155
$375$	−33.5100	−1.73045
$376$	−1.52013	−0.0783945
$377$	−6.51618	−0.335601
$378$	−5.92082	−0.304534
$379$	4.37392	0.224673	0.112336	−	0.993670i	$-0.464167\pi$
$379$	4.37392	0.224673	0.112336	+	0.993670i	$0.464167\pi$
$380$	−11.6933	−0.599855
$381$	0.908227	0.0465299
$382$	14.9953	0.767224
$383$	22.2150	1.13514	0.567568	−	0.823327i	$-0.307885\pi$
$383$	22.2150	1.13514	0.567568	+	0.823327i	$0.307885\pi$
$384$	4.61855	0.235689
$385$	0.154262	0.00786193
$386$	26.4125	1.34436
$387$	−68.5894	−3.48660
$388$	18.3657	0.932378
$389$	−9.47112	−0.480205	−0.240102	−	0.970748i	$-0.577181\pi$
$389$	−9.47112	−0.480205	−0.240102	+	0.970748i	$0.577181\pi$
$390$	34.2865	1.73617
$391$	1.81825	0.0919527
$392$	1.34993	0.0681815
$393$	52.8118	2.66400
$394$	4.69642	0.236602
$395$	16.0853	0.809340
$396$	3.30643	0.166154
$397$	33.8693	1.69985	0.849925	−	0.526904i	$-0.176647\pi$
$397$	33.8693	1.69985	0.849925	+	0.526904i	$0.176647\pi$
$398$	−43.7138	−2.19118
$399$	−4.32964	−0.216753
$400$	11.0985	0.554927
$401$	26.1950	1.30812	0.654059	−	0.756444i	$-0.273065\pi$
$401$	26.1950	1.30812	0.654059	+	0.756444i	$0.273065\pi$
$402$	17.7005	0.882822
$403$	−38.9991	−1.94268
$404$	−12.5256	−0.623172
$405$	8.17850	0.406393
$406$	−1.25549	−0.0623087
$407$	1.24046	0.0614871
$408$	−1.50469	−0.0744932
$409$	−23.3301	−1.15360	−0.576800	−	0.816885i	$-0.695699\pi$
$409$	−23.3301	−1.15360	−0.576800	+	0.816885i	$0.695699\pi$
$410$	0.0459853	0.00227105
$411$	−26.1556	−1.29016
$412$	−35.7056	−1.75909
$413$	−5.39826	−0.265631
$414$	−7.93716	−0.390090
$415$	−21.0746	−1.03451
$416$	−32.3529	−1.58623
$417$	22.9805	1.12536
$418$	2.19944	0.107578
$419$	−17.9680	−0.877794	−0.438897	−	0.898537i	$-0.644631\pi$
$419$	−17.9680	−0.877794	−0.438897	+	0.898537i	$0.644631\pi$
$420$	3.38146	0.164998
$421$	20.6124	1.00459	0.502294	−	0.864697i	$-0.332489\pi$
$421$	20.6124	1.00459	0.502294	+	0.864697i	$0.332489\pi$
$422$	−40.7825	−1.98526
$423$	43.3348	2.10701
$424$	0.968633	0.0470410
$425$	−7.61136	−0.369205
$426$	−43.2606	−2.09598
$427$	−2.65744	−0.128602
$428$	−12.7267	−0.615166
$429$	−3.30110	−0.159378
$430$	35.6337	1.71841
$431$	−4.74707	−0.228659	−0.114329	−	0.993443i	$-0.536472\pi$
$431$	−4.74707	−0.228659	−0.114329	+	0.993443i	$0.536472\pi$
$432$	−29.1240	−1.40123
$433$	−40.8642	−1.96381	−0.981904	−	0.189378i	$-0.939353\pi$
$433$	−40.8642	−1.96381	−0.981904	+	0.189378i	$0.939353\pi$
$434$	−7.51404	−0.360685
$435$	6.88021	0.329881
$436$	−21.0767	−1.00939
$437$	−2.70258	−0.129282
$438$	0.982772	0.0469587
$439$	−23.5388	−1.12344	−0.561722	−	0.827326i	$-0.689861\pi$
$439$	−23.5388	−1.12344	−0.561722	+	0.827326i	$0.689861\pi$
$440$	−0.0796857	−0.00379886
$441$	−38.4828	−1.83251
$442$	21.1057	1.00389
$443$	27.9145	1.32626	0.663129	−	0.748505i	$-0.269228\pi$
$443$	27.9145	1.32626	0.663129	+	0.748505i	$0.269228\pi$
$444$	27.1910	1.29043
$445$	20.6588	0.979321
$446$	16.1288	0.763722
$447$	60.3317	2.85359
$448$	−3.33912	−0.157759
$449$	23.7869	1.12258	0.561288	−	0.827621i	$-0.310306\pi$
$449$	23.7869	1.12258	0.561288	+	0.827621i	$0.310306\pi$
$450$	33.2258	1.56628
$451$	−0.00442746	−0.000208481 0
$452$	6.81194	0.320407
$453$	31.0714	1.45986
$454$	38.9536	1.82818
$455$	−2.20026	−0.103150
$456$	2.23652	0.104735
$457$	33.9948	1.59021	0.795106	−	0.606471i	$-0.207415\pi$
$457$	33.9948	1.59021	0.795106	+	0.606471i	$0.207415\pi$
$458$	−25.8032	−1.20571
$459$	19.9732	0.932268
$460$	2.11072	0.0984128
$461$	18.0014	0.838410	0.419205	−	0.907892i	$-0.362309\pi$
$461$	18.0014	0.838410	0.419205	+	0.907892i	$0.362309\pi$
$462$	−0.636029	−0.0295908
$463$	11.9773	0.556634	0.278317	−	0.960489i	$-0.410223\pi$
$463$	11.9773	0.556634	0.278317	+	0.960489i	$0.410223\pi$
$464$	−6.17562	−0.286696
$465$	41.1778	1.90957
$466$	20.7302	0.960310
$467$	22.0474	1.02023	0.510117	−	0.860105i	$-0.329602\pi$
$467$	22.0474	1.02023	0.510117	+	0.860105i	$0.329602\pi$
$468$	−47.1600	−2.17997
$469$	−1.13589	−0.0524505
$470$	−22.5133	−1.03846
$471$	22.8906	1.05474
$472$	2.78852	0.128352
$473$	−3.43080	−0.157748
$474$	−66.3204	−3.04620
$475$	11.3133	0.519089
$476$	2.08152	0.0954061
$477$	−27.6132	−1.26432
$478$	−45.3950	−2.07632
$479$	14.1990	0.648769	0.324385	−	0.945925i	$-0.394843\pi$
$479$	14.1990	0.648769	0.324385	+	0.945925i	$0.394843\pi$
$480$	34.1603	1.55920
$481$	−17.6927	−0.806720
$482$	−2.02418	−0.0921987
$483$	0.781528	0.0355608
$484$	−22.9048	−1.04113
$485$	12.6178	0.572947
$486$	12.8704	0.583815
$487$	−40.8500	−1.85109	−0.925544	−	0.378639i	$-0.876392\pi$
$487$	−40.8500	−1.85109	−0.925544	+	0.378639i	$0.876392\pi$
$488$	1.37273	0.0621404
$489$	50.2944	2.27439
$490$	19.9926	0.903175
$491$	7.70287	0.347626	0.173813	−	0.984779i	$-0.444391\pi$
$491$	7.70287	0.347626	0.173813	+	0.984779i	$0.444391\pi$
$492$	−0.0970507	−0.00437539
$493$	4.23523	0.190745
$494$	−31.3708	−1.41144
$495$	2.27163	0.102102
$496$	−36.9608	−1.65959
$497$	2.77615	0.124527
$498$	86.8913	3.89369
$499$	−1.84960	−0.0827996	−0.0413998	−	0.999143i	$-0.513182\pi$
$499$	−1.84960	−0.0827996	−0.0413998	+	0.999143i	$0.513182\pi$
$500$	−23.9457	−1.07088
$501$	−5.53224	−0.247162
$502$	−28.4860	−1.27139
$503$	16.8921	0.753181	0.376590	−	0.926380i	$-0.377096\pi$
$503$	16.8921	0.753181	0.376590	+	0.926380i	$0.377096\pi$
$504$	−0.421511	−0.0187756
$505$	−8.60549	−0.382939
$506$	−0.397012	−0.0176493
$507$	8.92911	0.396556
$508$	0.649005	0.0287949
$509$	2.10162	0.0931524	0.0465762	−	0.998915i	$-0.485169\pi$
$509$	2.10162	0.0931524	0.0465762	+	0.998915i	$0.485169\pi$
$510$	−22.2847	−0.986784
$511$	−0.0630671	−0.00278992
$512$	−32.1571	−1.42116
$513$	−29.6875	−1.31073
$514$	−2.96470	−0.130767
$515$	−24.5309	−1.08096
$516$	−75.2039	−3.31067
$517$	2.16758	0.0953300
$518$	−3.40890	−0.149778
$519$	−29.2308	−1.28309
$520$	1.13656	0.0498416
$521$	−1.90175	−0.0833170	−0.0416585	−	0.999132i	$-0.513264\pi$
$521$	−1.90175	−0.0833170	−0.0416585	+	0.999132i	$0.513264\pi$
$522$	−18.4880	−0.809197
$523$	2.87743	0.125821	0.0629105	−	0.998019i	$-0.479962\pi$
$523$	2.87743	0.125821	0.0629105	+	0.998019i	$0.479962\pi$
$524$	37.7385	1.64861
$525$	−3.27156	−0.142782
$526$	−16.3811	−0.714250
$527$	25.3477	1.10416
$528$	−3.12857	−0.136153
$529$	−22.5122	−0.978790
$530$	14.3456	0.623134
$531$	−79.4934	−3.44972
$532$	−3.09390	−0.134137
$533$	0.0631492	0.00273530
$534$	−85.1771	−3.68597
$535$	−8.74363	−0.378020
$536$	0.586755	0.0253439
$537$	76.0075	3.27997
$538$	51.1139	2.20368
$539$	−1.92489	−0.0829107
$540$	23.1860	0.997765
$541$	3.56338	0.153202	0.0766009	−	0.997062i	$-0.475593\pi$
$541$	3.56338	0.153202	0.0766009	+	0.997062i	$0.475593\pi$
$542$	−12.2282	−0.525247
$543$	−25.2906	−1.08532
$544$	21.0279	0.901565
$545$	−14.4804	−0.620272
$546$	9.07175	0.388235
$547$	8.83030	0.377557	0.188778	−	0.982020i	$-0.439547\pi$
$547$	8.83030	0.377557	0.188778	+	0.982020i	$0.439547\pi$
$548$	−18.6904	−0.798414
$549$	−39.1328	−1.67015
$550$	1.66193	0.0708650
$551$	−6.29511	−0.268181
$552$	−0.403706	−0.0171829
$553$	4.25595	0.180982
$554$	36.2876	1.54171
$555$	18.6811	0.792970
$556$	16.4215	0.696425
$557$	−8.23306	−0.348846	−0.174423	−	0.984671i	$-0.555806\pi$
$557$	−8.23306	−0.348846	−0.174423	+	0.984671i	$0.555806\pi$
$558$	−110.650	−4.68418
$559$	48.9338	2.06968
$560$	−2.08526	−0.0881184
$561$	2.14557	0.0905859
$562$	−8.36544	−0.352875
$563$	−40.7923	−1.71919	−0.859596	−	0.510974i	$-0.829285\pi$
$563$	−40.7923	−1.71919	−0.859596	+	0.510974i	$0.829285\pi$
$564$	47.5138	2.00069
$565$	4.68003	0.196890
$566$	−27.8872	−1.17219
$567$	2.16392	0.0908761
$568$	−1.43405	−0.0601712
$569$	17.6055	0.738063	0.369031	−	0.929417i	$-0.379689\pi$
$569$	17.6055	0.738063	0.369031	+	0.929417i	$0.379689\pi$
$570$	33.1233	1.38738
$571$	16.2781	0.681216	0.340608	−	0.940205i	$-0.389367\pi$
$571$	16.2781	0.681216	0.340608	+	0.940205i	$0.389367\pi$
$572$	−2.35891	−0.0986311
$573$	−21.7426	−0.908309
$574$	0.0121671	0.000507845 0
$575$	−2.04212	−0.0851622
$576$	−49.1711	−2.04880
$577$	25.7002	1.06991	0.534956	−	0.844880i	$-0.320328\pi$
$577$	25.7002	1.06991	0.534956	+	0.844880i	$0.320328\pi$
$578$	20.6933	0.860726
$579$	−38.2971	−1.59157
$580$	4.91649	0.204146
$581$	−5.57604	−0.231333
$582$	−52.0239	−2.15646
$583$	−1.38119	−0.0572032
$584$	0.0325779	0.00134808
$585$	−32.4004	−1.33959
$586$	−43.7329	−1.80659
$587$	35.7831	1.47693	0.738464	−	0.674293i	$-0.235552\pi$
$587$	35.7831	1.47693	0.738464	+	0.674293i	$0.235552\pi$
$588$	−42.1939	−1.74005
$589$	−37.6760	−1.55241
$590$	41.2985	1.70023
$591$	−6.80964	−0.280111
$592$	−16.7680	−0.689162
$593$	−5.87794	−0.241378	−0.120689	−	0.992690i	$-0.538510\pi$
$593$	−5.87794	−0.241378	−0.120689	+	0.992690i	$0.538510\pi$
$594$	−4.36112	−0.178939
$595$	1.43007	0.0586271
$596$	43.1121	1.76594
$597$	63.3834	2.59411
$598$	5.66262	0.231562
$599$	21.9834	0.898218	0.449109	−	0.893477i	$-0.351741\pi$
$599$	21.9834	0.898218	0.449109	+	0.893477i	$0.351741\pi$
$600$	1.68995	0.0689921
$601$	21.9020	0.893400	0.446700	−	0.894684i	$-0.352599\pi$
$601$	21.9020	0.893400	0.446700	+	0.894684i	$0.352599\pi$
$602$	9.42818	0.384264
$603$	−16.7268	−0.681169
$604$	22.2031	0.903433
$605$	−15.7364	−0.639774
$606$	35.4808	1.44131
$607$	23.4846	0.953209	0.476604	−	0.879118i	$-0.341867\pi$
$607$	23.4846	0.953209	0.476604	+	0.879118i	$0.341867\pi$
$608$	−31.2552	−1.26757
$609$	1.82041	0.0737667
$610$	20.3303	0.823150
$611$	−30.9164	−1.25074
$612$	30.6519	1.23903
$613$	8.60887	0.347709	0.173854	−	0.984771i	$-0.444378\pi$
$613$	8.60887	0.347709	0.173854	+	0.984771i	$0.444378\pi$
$614$	−41.1269	−1.65975
$615$	−0.0666770	−0.00268868
$616$	−0.0210837	−0.000849488 0
$617$	−33.1258	−1.33360	−0.666798	−	0.745238i	$-0.732336\pi$
$617$	−33.1258	−1.33360	−0.666798	+	0.745238i	$0.732336\pi$
$618$	101.142	4.06853
$619$	−15.7965	−0.634915	−0.317457	−	0.948273i	$-0.602829\pi$
$619$	−15.7965	−0.634915	−0.317457	+	0.948273i	$0.602829\pi$
$620$	29.4250	1.18174
$621$	5.35878	0.215040
$622$	−41.4507	−1.66202
$623$	5.46604	0.218992
$624$	44.6231	1.78635
$625$	−1.83257	−0.0733027
$626$	−4.01776	−0.160582
$627$	−3.18910	−0.127360
$628$	16.3573	0.652726
$629$	11.4995	0.458515
$630$	−6.24266	−0.248714
$631$	−41.7674	−1.66273	−0.831367	−	0.555724i	$-0.812441\pi$
$631$	−41.7674	−1.66273	−0.831367	+	0.555724i	$0.812441\pi$
$632$	−2.19846	−0.0874499
$633$	59.1331	2.35033
$634$	57.8527	2.29762
$635$	0.445887	0.0176945
$636$	−30.2760	−1.20052
$637$	27.4548	1.08780
$638$	−0.924758	−0.0366115
$639$	40.8809	1.61722
$640$	2.26744	0.0896286
$641$	12.5409	0.495337	0.247669	−	0.968845i	$-0.420336\pi$
$641$	12.5409	0.495337	0.247669	+	0.968845i	$0.420336\pi$
$642$	36.0503	1.42279
$643$	−15.0272	−0.592616	−0.296308	−	0.955092i	$-0.595756\pi$
$643$	−15.0272	−0.592616	−0.296308	+	0.955092i	$0.595756\pi$
$644$	0.558468	0.0220067
$645$	−51.6675	−2.03441
$646$	20.3896	0.802218
$647$	0.131198	0.00515792	0.00257896	−	0.999997i	$-0.499179\pi$
$647$	0.131198	0.00515792	0.00257896	+	0.999997i	$0.499179\pi$
$648$	−1.11779	−0.0439111
$649$	−3.97621	−0.156080
$650$	−23.7043	−0.929759
$651$	10.8951	0.427012
$652$	35.9396	1.40750
$653$	29.9259	1.17109	0.585546	−	0.810639i	$-0.300880\pi$
$653$	29.9259	1.17109	0.585546	+	0.810639i	$0.300880\pi$
$654$	59.7033	2.33458
$655$	25.9276	1.01307
$656$	0.0598488	0.00233670
$657$	−0.928710	−0.0362324
$658$	−5.95672	−0.232217
$659$	−38.8457	−1.51321	−0.756606	−	0.653871i	$-0.773144\pi$
$659$	−38.8457	−1.51321	−0.756606	+	0.653871i	$0.773144\pi$
$660$	2.49069	0.0969500
$661$	−41.0165	−1.59536	−0.797678	−	0.603084i	$-0.793938\pi$
$661$	−41.0165	−1.59536	−0.797678	+	0.603084i	$0.793938\pi$
$662$	47.3837	1.84162
$663$	−30.6024	−1.18850
$664$	2.88036	0.111780
$665$	−2.12561	−0.0824275
$666$	−50.1986	−1.94516
$667$	1.13631	0.0439980
$668$	−3.95325	−0.152956
$669$	−23.3862	−0.904163
$670$	8.68994	0.335722
$671$	−1.95740	−0.0755645
$672$	9.03834	0.348661
$673$	8.97729	0.346049	0.173024	−	0.984918i	$-0.444646\pi$
$673$	8.97729	0.346049	0.173024	+	0.984918i	$0.444646\pi$
$674$	−4.52180	−0.174173
$675$	−22.4324	−0.863422
$676$	6.38060	0.245408
$677$	4.52843	0.174042	0.0870209	−	0.996206i	$-0.472265\pi$
$677$	4.52843	0.174042	0.0870209	+	0.996206i	$0.472265\pi$
$678$	−19.2959	−0.741056
$679$	3.33851	0.128120
$680$	−0.738717	−0.0283285
$681$	−56.4812	−2.16436
$682$	−5.53464	−0.211932
$683$	3.48350	0.133292	0.0666462	−	0.997777i	$-0.478770\pi$
$683$	3.48350	0.133292	0.0666462	+	0.997777i	$0.478770\pi$
$684$	−45.5600	−1.74203
$685$	−12.8409	−0.490626
$686$	10.6917	0.408212
$687$	37.4138	1.42742
$688$	46.3763	1.76808
$689$	19.7001	0.750514
$690$	−5.97896	−0.227615
$691$	−44.5762	−1.69576	−0.847879	−	0.530190i	$-0.822121\pi$
$691$	−44.5762	−1.69576	−0.847879	+	0.530190i	$0.822121\pi$
$692$	−20.8879	−0.794038
$693$	0.601042	0.0228317
$694$	−34.8328	−1.32223
$695$	11.2821	0.427954
$696$	−0.940350	−0.0356439
$697$	−0.0410442	−0.00155466
$698$	−42.9117	−1.62423
$699$	−30.0581	−1.13690
$700$	−2.33780	−0.0883606
$701$	8.90961	0.336511	0.168256	−	0.985743i	$-0.446187\pi$
$701$	8.90961	0.336511	0.168256	+	0.985743i	$0.446187\pi$
$702$	62.2031	2.34770
$703$	−17.0925	−0.644655
$704$	−2.45951	−0.0926962
$705$	32.6435	1.22943
$706$	19.0765	0.717955
$707$	−2.27690	−0.0856315
$708$	−87.1594	−3.27565
$709$	−13.4817	−0.506315	−0.253158	−	0.967425i	$-0.581469\pi$
$709$	−13.4817	−0.506315	−0.253158	+	0.967425i	$0.581469\pi$
$710$	−21.2385	−0.797066
$711$	62.6721	2.35039
$712$	−2.82354	−0.105816
$713$	6.80075	0.254690
$714$	−5.89623	−0.220661
$715$	−1.62065	−0.0606089
$716$	54.3138	2.02980
$717$	65.8210	2.45813
$718$	−17.2098	−0.642264
$719$	25.1548	0.938118	0.469059	−	0.883167i	$-0.344593\pi$
$719$	25.1548	0.938118	0.469059	+	0.883167i	$0.344593\pi$
$720$	−30.7071	−1.14438
$721$	−6.49055	−0.241721
$722$	8.15293	0.303421
$723$	2.93498	0.109153
$724$	−18.0723	−0.671651
$725$	−4.75669	−0.176659
$726$	64.8816	2.40798
$727$	−1.31218	−0.0486659	−0.0243330	−	0.999704i	$-0.507746\pi$
$727$	−1.31218	−0.0486659	−0.0243330	+	0.999704i	$0.507746\pi$
$728$	0.300719	0.0111454
$729$	−35.6895	−1.32183
$730$	0.482485	0.0178576
$731$	−31.8048	−1.17634
$732$	−42.9066	−1.58587
$733$	22.8551	0.844173	0.422087	−	0.906556i	$-0.361298\pi$
$733$	22.8551	0.844173	0.422087	+	0.906556i	$0.361298\pi$
$734$	−11.0993	−0.409682
$735$	−28.9886	−1.06926
$736$	5.64177	0.207958
$737$	−0.836665	−0.0308190
$738$	0.179170	0.00659533
$739$	10.2085	0.375525	0.187762	−	0.982214i	$-0.439877\pi$
$739$	10.2085	0.375525	0.187762	+	0.982214i	$0.439877\pi$
$740$	13.3492	0.490728
$741$	45.4864	1.67099
$742$	3.79566	0.139343
$743$	26.3806	0.967810	0.483905	−	0.875120i	$-0.339218\pi$
$743$	26.3806	0.967810	0.483905	+	0.875120i	$0.339218\pi$
$744$	−5.62796	−0.206331
$745$	29.6194	1.08517
$746$	47.8712	1.75269
$747$	−82.1115	−3.00430
$748$	1.53319	0.0560589
$749$	−2.31345	−0.0845315
$750$	67.8301	2.47681
$751$	−31.8074	−1.16067	−0.580335	−	0.814378i	$-0.697078\pi$
$751$	−31.8074	−1.16067	−0.580335	+	0.814378i	$0.697078\pi$
$752$	−29.3006	−1.06848
$753$	41.3037	1.50519
$754$	13.1899	0.480348
$755$	15.2543	0.555160
$756$	6.13469	0.223116
$757$	−33.6767	−1.22400	−0.612000	−	0.790858i	$-0.709635\pi$
$757$	−33.6767	−1.22400	−0.612000	+	0.790858i	$0.709635\pi$
$758$	−8.85358	−0.321576
$759$	0.575653	0.0208949
$760$	1.09800	0.0398288
$761$	−14.9020	−0.540197	−0.270098	−	0.962833i	$-0.587056\pi$
$761$	−14.9020	−0.540197	−0.270098	+	0.962833i	$0.587056\pi$
$762$	−1.83841	−0.0665986
$763$	−3.83132	−0.138703
$764$	−15.5369	−0.562105
$765$	21.0589	0.761385
$766$	−44.9672	−1.62473
$767$	56.7131	2.04779
$768$	42.0632	1.51782
$769$	−23.5992	−0.851010	−0.425505	−	0.904956i	$-0.639904\pi$
$769$	−23.5992	−0.851010	−0.425505	+	0.904956i	$0.639904\pi$
$770$	−0.312254	−0.0112529
$771$	4.29870	0.154814
$772$	−27.3665	−0.984943
$773$	30.4365	1.09472	0.547362	−	0.836896i	$-0.315632\pi$
$773$	30.4365	1.09472	0.547362	+	0.836896i	$0.315632\pi$
$774$	138.837	4.99040
$775$	−28.4686	−1.02262
$776$	−1.72454	−0.0619074
$777$	4.94277	0.177321
$778$	19.1712	0.687321
$779$	0.0610068	0.00218579
$780$	−35.5250	−1.27200
$781$	2.04483	0.0731699
$782$	−3.68045	−0.131613
$783$	12.4822	0.446076
$784$	26.0199	0.929283
$785$	11.2380	0.401101
$786$	−106.900	−3.81301
$787$	0.281399	0.0100308	0.00501539	−	0.999987i	$-0.498404\pi$
$787$	0.281399	0.0100308	0.00501539	+	0.999987i	$0.498404\pi$
$788$	−4.86606	−0.173346
$789$	23.7520	0.845593
$790$	−32.5595	−1.15842
$791$	1.23827	0.0440279
$792$	−0.310474	−0.0110322
$793$	27.9185	0.991417
$794$	−68.5574	−2.43301
$795$	−20.8006	−0.737722
$796$	45.2928	1.60536
$797$	26.6128	0.942673	0.471336	−	0.881954i	$-0.343772\pi$
$797$	26.6128	0.942673	0.471336	+	0.881954i	$0.343772\pi$
$798$	8.76396	0.310241
$799$	20.0943	0.710885
$800$	−23.6170	−0.834987
$801$	80.4915	2.84403
$802$	−53.0234	−1.87232
$803$	−0.0464535	−0.00163931
$804$	−18.3399	−0.646798
$805$	0.383686	0.0135231
$806$	78.9411	2.78058
$807$	−74.1133	−2.60891
$808$	1.17615	0.0413769
$809$	13.2472	0.465748	0.232874	−	0.972507i	$-0.425187\pi$
$809$	13.2472	0.465748	0.232874	+	0.972507i	$0.425187\pi$
$810$	−16.5547	−0.581674
$811$	35.8348	1.25833	0.629165	−	0.777272i	$-0.283397\pi$
$811$	35.8348	1.25833	0.629165	+	0.777272i	$0.283397\pi$
$812$	1.30084	0.0456504
$813$	17.7305	0.621835
$814$	−2.51090	−0.0880071
$815$	24.6917	0.864911
$816$	−29.0030	−1.01531
$817$	47.2737	1.65390
$818$	47.2243	1.65116
$819$	−8.57271	−0.299555
$820$	−0.0476464	−0.00166388
$821$	−1.76973	−0.0617640	−0.0308820	−	0.999523i	$-0.509832\pi$
$821$	−1.76973	−0.0617640	−0.0308820	+	0.999523i	$0.509832\pi$
$822$	52.9436	1.84662
$823$	−29.0119	−1.01129	−0.505645	−	0.862742i	$-0.668745\pi$
$823$	−29.0119	−1.01129	−0.505645	+	0.862742i	$0.668745\pi$
$824$	3.35276	0.116799
$825$	−2.40974	−0.0838964
$826$	10.9270	0.380200
$827$	−15.9224	−0.553675	−0.276838	−	0.960917i	$-0.589286\pi$
$827$	−15.9224	−0.553675	−0.276838	+	0.960917i	$0.589286\pi$
$828$	8.22386	0.285799
$829$	−31.0294	−1.07770	−0.538849	−	0.842403i	$-0.681141\pi$
$829$	−31.0294	−1.07770	−0.538849	+	0.842403i	$0.681141\pi$
$830$	42.6587	1.48070
$831$	−52.6157	−1.82522
$832$	35.0802	1.21619
$833$	−17.8444	−0.618273
$834$	−46.5165	−1.61073
$835$	−2.71601	−0.0939916
$836$	−2.27888	−0.0788167
$837$	74.7053	2.58219
$838$	36.3704	1.25639
$839$	−54.4602	−1.88017	−0.940087	−	0.340935i	$-0.889256\pi$
$839$	−54.4602	−1.88017	−0.940087	+	0.340935i	$0.889256\pi$
$840$	−0.317519	−0.0109554
$841$	−26.3532	−0.908731
$842$	−41.7232	−1.43788
$843$	12.1296	0.417765
$844$	42.2556	1.45450
$845$	4.38368	0.150803
$846$	−87.7172	−3.01578
$847$	−4.16363	−0.143064
$848$	18.6705	0.641147
$849$	40.4355	1.38774
$850$	15.4067	0.528447
$851$	3.08530	0.105763
$852$	44.8232	1.53562
$853$	−5.82777	−0.199539	−0.0997694	−	0.995011i	$-0.531811\pi$
$853$	−5.82777	−0.199539	−0.0997694	+	0.995011i	$0.531811\pi$
$854$	5.37912	0.184070
$855$	−31.3012	−1.07048
$856$	1.19503	0.0408454
$857$	−48.9503	−1.67211	−0.836056	−	0.548644i	$-0.815144\pi$
$857$	−48.9503	−1.67211	−0.836056	+	0.548644i	$0.815144\pi$
$858$	6.68200	0.228120
$859$	−23.1193	−0.788819	−0.394409	−	0.918935i	$-0.629051\pi$
$859$	−23.1193	−0.788819	−0.394409	+	0.918935i	$0.629051\pi$
$860$	−36.9208	−1.25899
$861$	−0.0176418	−0.000601232 0
$862$	9.60892	0.327281
$863$	−24.5041	−0.834129	−0.417065	−	0.908877i	$-0.636941\pi$
$863$	−24.5041	−0.834129	−0.417065	+	0.908877i	$0.636941\pi$
$864$	61.9740	2.10840
$865$	−14.3507	−0.487937
$866$	82.7164	2.81082
$867$	−30.0045	−1.01900
$868$	7.78545	0.264255
$869$	3.13482	0.106342
$870$	−13.9268	−0.472161
$871$	11.9334	0.404349
$872$	1.97911	0.0670210
$873$	49.1621	1.66388
$874$	5.47050	0.185043
$875$	−4.35284	−0.147153
$876$	−1.01827	−0.0344042
$877$	−11.9231	−0.402614	−0.201307	−	0.979528i	$-0.564519\pi$
$877$	−11.9231	−0.402614	−0.201307	+	0.979528i	$0.564519\pi$
$878$	47.6466	1.60800
$879$	63.4112	2.13881
$880$	−1.53595	−0.0517768
$881$	−12.2901	−0.414063	−0.207032	−	0.978334i	$-0.566380\pi$
$881$	−12.2901	−0.414063	−0.207032	+	0.978334i	$0.566380\pi$
$882$	77.8960	2.62289
$883$	−48.1400	−1.62004	−0.810020	−	0.586403i	$-0.800544\pi$
$883$	−48.1400	−1.62004	−0.810020	+	0.586403i	$0.800544\pi$
$884$	−21.8680	−0.735501
$885$	−59.8813	−2.01289
$886$	−56.5039	−1.89829
$887$	20.7341	0.696184	0.348092	−	0.937460i	$-0.386830\pi$
$887$	20.7341	0.696184	0.348092	+	0.937460i	$0.386830\pi$
$888$	−2.55324	−0.0856811
$889$	0.117976	0.00395678
$890$	−41.8171	−1.40171
$891$	1.59389	0.0533972
$892$	−16.7114	−0.559540
$893$	−29.8675	−0.999477
$894$	−122.122	−4.08437
$895$	37.3153	1.24731
$896$	0.599935	0.0200424
$897$	−8.21059	−0.274144
$898$	−48.1490	−1.60675
$899$	15.8410	0.528325
$900$	−34.4259	−1.14753
$901$	−12.8042	−0.426569
$902$	0.00896195	0.000298400 0
$903$	−13.6705	−0.454926
$904$	−0.639641	−0.0212742
$905$	−12.4162	−0.412730
$906$	−62.8940	−2.08951
$907$	−7.02598	−0.233294	−0.116647	−	0.993173i	$-0.537215\pi$
$907$	−7.02598	−0.233294	−0.116647	+	0.993173i	$0.537215\pi$
$908$	−40.3606	−1.33941
$909$	−33.5290	−1.11209
$910$	4.45371	0.147639
$911$	58.0477	1.92320	0.961602	−	0.274446i	$-0.0884946\pi$
$911$	58.0477	1.92320	0.961602	+	0.274446i	$0.0884946\pi$
$912$	43.1091	1.42749
$913$	−4.10716	−0.135927
$914$	−68.8116	−2.27608
$915$	−29.4782	−0.974519
$916$	26.7353	0.883359
$917$	6.86008	0.226540
$918$	−40.4292	−1.33436
$919$	17.9524	0.592194	0.296097	−	0.955158i	$-0.404315\pi$
$919$	17.9524	0.592194	0.296097	+	0.955158i	$0.404315\pi$
$920$	−0.198197	−0.00653435
$921$	59.6324	1.96496
$922$	−36.4381	−1.20002
$923$	−29.1657	−0.960000
$924$	0.659003	0.0216796
$925$	−12.9154	−0.424655
$926$	−24.2442	−0.796715
$927$	−95.5782	−3.13920
$928$	13.1413	0.431385
$929$	−20.8907	−0.685403	−0.342701	−	0.939444i	$-0.611342\pi$
$929$	−20.8907	−0.685403	−0.342701	+	0.939444i	$0.611342\pi$
$930$	−83.3511	−2.73319
$931$	26.5234	0.869268
$932$	−21.4790	−0.703569
$933$	60.1019	1.96765
$934$	−44.6279	−1.46027
$935$	1.05335	0.0344483
$936$	4.42832	0.144744
$937$	−39.5712	−1.29273	−0.646367	−	0.763027i	$-0.723712\pi$
$937$	−39.5712	−1.29273	−0.646367	+	0.763027i	$0.723712\pi$
$938$	2.29924	0.0750728
$939$	5.82561	0.190112
$940$	23.3265	0.760828
$941$	−2.21402	−0.0721750	−0.0360875	−	0.999349i	$-0.511490\pi$
$941$	−2.21402	−0.0721750	−0.0360875	+	0.999349i	$0.511490\pi$
$942$	−46.3346	−1.50966
$943$	−0.0110121	−0.000358603 0
$944$	53.7490	1.74938
$945$	4.21473	0.137105
$946$	6.94455	0.225787
$947$	−27.2239	−0.884659	−0.442330	−	0.896853i	$-0.645848\pi$
$947$	−27.2239	−0.884659	−0.442330	+	0.896853i	$0.645848\pi$
$948$	68.7159	2.23179
$949$	0.662571	0.0215080
$950$	−22.9001	−0.742977
$951$	−83.8842	−2.72013
$952$	−0.195454	−0.00633471
$953$	−49.1033	−1.59061	−0.795305	−	0.606209i	$-0.792689\pi$
$953$	−49.1033	−1.59061	−0.795305	+	0.606209i	$0.792689\pi$
$954$	55.8939	1.80963
$955$	−10.6744	−0.345414
$956$	47.0347	1.52121
$957$	1.34086	0.0433440
$958$	−28.7413	−0.928590
$959$	−3.39753	−0.109712
$960$	−37.0400	−1.19546
$961$	63.8075	2.05831
$962$	35.8132	1.15467
$963$	−34.0672	−1.09780
$964$	2.09729	0.0675492
$965$	−18.8017	−0.605248
$966$	−1.58195	−0.0508984
$967$	−2.12457	−0.0683214	−0.0341607	−	0.999416i	$-0.510876\pi$
$967$	−2.12457	−0.0683214	−0.0341607	+	0.999416i	$0.510876\pi$
$968$	2.15076	0.0691281
$969$	−29.5642	−0.949738
$970$	−25.5407	−0.820064
$971$	32.0749	1.02933	0.514666	−	0.857391i	$-0.327916\pi$
$971$	32.0749	1.02933	0.514666	+	0.857391i	$0.327916\pi$
$972$	−13.3353	−0.427731
$973$	2.98509	0.0956975
$974$	82.6876	2.64948
$975$	34.3704	1.10073
$976$	26.4594	0.846945
$977$	−1.85481	−0.0593406	−0.0296703	−	0.999560i	$-0.509446\pi$
$977$	−1.85481	−0.0593406	−0.0296703	+	0.999560i	$0.509446\pi$
$978$	−101.805	−3.25535
$979$	4.02614	0.128676
$980$	−20.7148	−0.661710
$981$	−56.4190	−1.80132
$982$	−15.5920	−0.497560
$983$	−48.0786	−1.53347	−0.766734	−	0.641965i	$-0.778119\pi$
$983$	−48.0786	−1.53347	−0.766734	+	0.641965i	$0.778119\pi$
$984$	0.00911306	0.000290514 0
$985$	−3.34314	−0.106521
$986$	−8.57286	−0.273015
$987$	8.63703	0.274920
$988$	32.5039	1.03409
$989$	−8.53319	−0.271340
$990$	−4.59817	−0.146140
$991$	45.7585	1.45357	0.726783	−	0.686867i	$-0.241015\pi$
$991$	45.7585	1.45357	0.726783	+	0.686867i	$0.241015\pi$
$992$	78.6504	2.49715
$993$	−68.7046	−2.18028
$994$	−5.61941	−0.178237
$995$	31.1176	0.986495
$996$	−90.0299	−2.85271
$997$	−17.8475	−0.565235	−0.282618	−	0.959233i	$-0.591203\pi$
$997$	−17.8475	−0.565235	−0.282618	+	0.959233i	$0.591203\pi$
$998$	3.74393	0.118512
$999$	33.8916	1.07228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.2	✓	12
3.2	odd	2		2169.2.a.h.1.11		12
4.3	odd	2		3856.2.a.n.1.1		12
5.4	even	2		6025.2.a.h.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.2	✓	12	1.1	even	1	trivial
2169.2.a.h.1.11		12	3.2	odd	2
3856.2.a.n.1.1		12	4.3	odd	2
6025.2.a.h.1.11		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)

\(f(q)\)	\(=\)	\(q-2.02418 q^{2} +2.93498 q^{3} +2.09729 q^{4} +1.44091 q^{5} -5.94092 q^{6} +0.381245 q^{7} -0.196936 q^{8} +5.61411 q^{9} +O(q^{10})\)	\(q-2.02418 q^{2} +2.93498 q^{3} +2.09729 q^{4} +1.44091 q^{5} -5.94092 q^{6} +0.381245 q^{7} -0.196936 q^{8} +5.61411 q^{9} -2.91665 q^{10} +0.280814 q^{11} +6.15551 q^{12} -4.00528 q^{13} -0.771706 q^{14} +4.22904 q^{15} -3.79595 q^{16} +2.60326 q^{17} -11.3640 q^{18} -3.86940 q^{19} +3.02200 q^{20} +1.11895 q^{21} -0.568418 q^{22} +0.698450 q^{23} -0.578002 q^{24} -2.92378 q^{25} +8.10740 q^{26} +7.67238 q^{27} +0.799581 q^{28} +1.62690 q^{29} -8.56032 q^{30} +9.73691 q^{31} +8.07755 q^{32} +0.824185 q^{33} -5.26945 q^{34} +0.549338 q^{35} +11.7744 q^{36} +4.41735 q^{37} +7.83234 q^{38} -11.7554 q^{39} -0.283766 q^{40} -0.0157665 q^{41} -2.26494 q^{42} -12.2173 q^{43} +0.588950 q^{44} +8.08942 q^{45} -1.41379 q^{46} +7.71890 q^{47} -11.1410 q^{48} -6.85465 q^{49} +5.91826 q^{50} +7.64051 q^{51} -8.40025 q^{52} -4.91852 q^{53} -15.5302 q^{54} +0.404628 q^{55} -0.0750807 q^{56} -11.3566 q^{57} -3.29313 q^{58} -14.1596 q^{59} +8.86953 q^{60} -6.97043 q^{61} -19.7092 q^{62} +2.14035 q^{63} -8.75848 q^{64} -5.77125 q^{65} -1.66830 q^{66} -2.97942 q^{67} +5.45979 q^{68} +2.04994 q^{69} -1.11196 q^{70} +7.28180 q^{71} -1.10562 q^{72} -0.165424 q^{73} -8.94150 q^{74} -8.58125 q^{75} -8.11525 q^{76} +0.107059 q^{77} +23.7951 q^{78} +11.1633 q^{79} -5.46962 q^{80} +5.67594 q^{81} +0.0319141 q^{82} -14.6259 q^{83} +2.34676 q^{84} +3.75106 q^{85} +24.7300 q^{86} +4.77491 q^{87} -0.0553024 q^{88} +14.3374 q^{89} -16.3744 q^{90} -1.52699 q^{91} +1.46485 q^{92} +28.5777 q^{93} -15.6244 q^{94} -5.57544 q^{95} +23.7074 q^{96} +8.75687 q^{97} +13.8750 q^{98} +1.57652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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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