LMFDB - Embedded newform 6014.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.42118 q^{3} +1.00000 q^{4} -1.30859 q^{5} -2.42118 q^{6} +3.90591 q^{7} +1.00000 q^{8} +2.86213 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.42118 q^{3} +1.00000 q^{4} -1.30859 q^{5} -2.42118 q^{6} +3.90591 q^{7} +1.00000 q^{8} +2.86213 q^{9} -1.30859 q^{10} +2.46570 q^{11} -2.42118 q^{12} -2.99157 q^{13} +3.90591 q^{14} +3.16833 q^{15} +1.00000 q^{16} -1.93680 q^{17} +2.86213 q^{18} -2.79542 q^{19} -1.30859 q^{20} -9.45694 q^{21} +2.46570 q^{22} +6.30951 q^{23} -2.42118 q^{24} -3.28760 q^{25} -2.99157 q^{26} +0.333798 q^{27} +3.90591 q^{28} -8.82965 q^{29} +3.16833 q^{30} +1.00000 q^{31} +1.00000 q^{32} -5.96990 q^{33} -1.93680 q^{34} -5.11122 q^{35} +2.86213 q^{36} -5.12812 q^{37} -2.79542 q^{38} +7.24313 q^{39} -1.30859 q^{40} -5.77424 q^{41} -9.45694 q^{42} +3.02521 q^{43} +2.46570 q^{44} -3.74535 q^{45} +6.30951 q^{46} -9.36679 q^{47} -2.42118 q^{48} +8.25616 q^{49} -3.28760 q^{50} +4.68934 q^{51} -2.99157 q^{52} -3.61127 q^{53} +0.333798 q^{54} -3.22657 q^{55} +3.90591 q^{56} +6.76822 q^{57} -8.82965 q^{58} +5.00305 q^{59} +3.16833 q^{60} +9.53671 q^{61} +1.00000 q^{62} +11.1792 q^{63} +1.00000 q^{64} +3.91472 q^{65} -5.96990 q^{66} -2.46098 q^{67} -1.93680 q^{68} -15.2765 q^{69} -5.11122 q^{70} -1.80300 q^{71} +2.86213 q^{72} -15.0984 q^{73} -5.12812 q^{74} +7.95990 q^{75} -2.79542 q^{76} +9.63079 q^{77} +7.24313 q^{78} +11.4783 q^{79} -1.30859 q^{80} -9.39459 q^{81} -5.77424 q^{82} +7.49348 q^{83} -9.45694 q^{84} +2.53446 q^{85} +3.02521 q^{86} +21.3782 q^{87} +2.46570 q^{88} +7.07301 q^{89} -3.74535 q^{90} -11.6848 q^{91} +6.30951 q^{92} -2.42118 q^{93} -9.36679 q^{94} +3.65804 q^{95} -2.42118 q^{96} -1.00000 q^{97} +8.25616 q^{98} +7.05715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.42118	−1.39787	−0.698936	−	0.715184i	$-0.746343\pi$
$3$	−2.42118	−1.39787	−0.698936	+	0.715184i	$0.746343\pi$
$4$	1.00000	0.500000
$5$	−1.30859	−0.585217	−0.292609	−	0.956232i	$-0.594523\pi$
$5$	−1.30859	−0.585217	−0.292609	+	0.956232i	$0.594523\pi$
$6$	−2.42118	−0.988444
$7$	3.90591	1.47630	0.738148	−	0.674639i	$-0.235700\pi$
$7$	3.90591	1.47630	0.738148	+	0.674639i	$0.235700\pi$
$8$	1.00000	0.353553
$9$	2.86213	0.954045
$10$	−1.30859	−0.413811
$11$	2.46570	0.743435	0.371718	−	0.928346i	$-0.378769\pi$
$11$	2.46570	0.743435	0.371718	+	0.928346i	$0.378769\pi$
$12$	−2.42118	−0.698936
$13$	−2.99157	−0.829711	−0.414855	−	0.909887i	$-0.636168\pi$
$13$	−2.99157	−0.829711	−0.414855	+	0.909887i	$0.636168\pi$
$14$	3.90591	1.04390
$15$	3.16833	0.818058
$16$	1.00000	0.250000
$17$	−1.93680	−0.469742	−0.234871	−	0.972027i	$-0.575467\pi$
$17$	−1.93680	−0.469742	−0.234871	+	0.972027i	$0.575467\pi$
$18$	2.86213	0.674612
$19$	−2.79542	−0.641312	−0.320656	−	0.947196i	$-0.603903\pi$
$19$	−2.79542	−0.641312	−0.320656	+	0.947196i	$0.603903\pi$
$20$	−1.30859	−0.292609
$21$	−9.45694	−2.06367
$22$	2.46570	0.525688
$23$	6.30951	1.31562	0.657812	−	0.753183i	$-0.271482\pi$
$23$	6.30951	1.31562	0.657812	+	0.753183i	$0.271482\pi$
$24$	−2.42118	−0.494222
$25$	−3.28760	−0.657521
$26$	−2.99157	−0.586694
$27$	0.333798	0.0642394
$28$	3.90591	0.738148
$29$	−8.82965	−1.63963	−0.819813	−	0.572632i	$-0.805922\pi$
$29$	−8.82965	−1.63963	−0.819813	+	0.572632i	$0.805922\pi$
$30$	3.16833	0.578455
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−5.96990	−1.03923
$34$	−1.93680	−0.332158
$35$	−5.11122	−0.863954
$36$	2.86213	0.477022
$37$	−5.12812	−0.843058	−0.421529	−	0.906815i	$-0.638507\pi$
$37$	−5.12812	−0.843058	−0.421529	+	0.906815i	$0.638507\pi$
$38$	−2.79542	−0.453476
$39$	7.24313	1.15983
$40$	−1.30859	−0.206906
$41$	−5.77424	−0.901785	−0.450893	−	0.892578i	$-0.648894\pi$
$41$	−5.77424	−0.901785	−0.450893	+	0.892578i	$0.648894\pi$
$42$	−9.45694	−1.45924
$43$	3.02521	0.461340	0.230670	−	0.973032i	$-0.425908\pi$
$43$	3.02521	0.461340	0.230670	+	0.973032i	$0.425908\pi$
$44$	2.46570	0.371718
$45$	−3.74535	−0.558323
$46$	6.30951	0.930286
$47$	−9.36679	−1.36629	−0.683143	−	0.730284i	$-0.739388\pi$
$47$	−9.36679	−1.36629	−0.683143	+	0.730284i	$0.739388\pi$
$48$	−2.42118	−0.349468
$49$	8.25616	1.17945
$50$	−3.28760	−0.464937
$51$	4.68934	0.656639
$52$	−2.99157	−0.414855
$53$	−3.61127	−0.496046	−0.248023	−	0.968754i	$-0.579781\pi$
$53$	−3.61127	−0.496046	−0.248023	+	0.968754i	$0.579781\pi$
$54$	0.333798	0.0454241
$55$	−3.22657	−0.435071
$56$	3.90591	0.521950
$57$	6.76822	0.896472
$58$	−8.82965	−1.15939
$59$	5.00305	0.651341	0.325671	−	0.945483i	$-0.394410\pi$
$59$	5.00305	0.651341	0.325671	+	0.945483i	$0.394410\pi$
$60$	3.16833	0.409029
$61$	9.53671	1.22105	0.610525	−	0.791997i	$-0.290958\pi$
$61$	9.53671	1.22105	0.610525	+	0.791997i	$0.290958\pi$
$62$	1.00000	0.127000
$63$	11.1792	1.40845
$64$	1.00000	0.125000
$65$	3.91472	0.485561
$66$	−5.96990	−0.734844
$67$	−2.46098	−0.300657	−0.150328	−	0.988636i	$-0.548033\pi$
$67$	−2.46098	−0.300657	−0.150328	+	0.988636i	$0.548033\pi$
$68$	−1.93680	−0.234871
$69$	−15.2765	−1.83907
$70$	−5.11122	−0.610908
$71$	−1.80300	−0.213976	−0.106988	−	0.994260i	$-0.534121\pi$
$71$	−1.80300	−0.213976	−0.106988	+	0.994260i	$0.534121\pi$
$72$	2.86213	0.337306
$73$	−15.0984	−1.76713	−0.883566	−	0.468307i	$-0.844864\pi$
$73$	−15.0984	−1.76713	−0.883566	+	0.468307i	$0.844864\pi$
$74$	−5.12812	−0.596132
$75$	7.95990	0.919130
$76$	−2.79542	−0.320656
$77$	9.63079	1.09753
$78$	7.24313	0.820123
$79$	11.4783	1.29141	0.645707	−	0.763585i	$-0.276563\pi$
$79$	11.4783	1.29141	0.645707	+	0.763585i	$0.276563\pi$
$80$	−1.30859	−0.146304
$81$	−9.39459	−1.04384
$82$	−5.77424	−0.637659
$83$	7.49348	0.822517	0.411258	−	0.911519i	$-0.365089\pi$
$83$	7.49348	0.822517	0.411258	+	0.911519i	$0.365089\pi$
$84$	−9.45694	−1.03184
$85$	2.53446	0.274901
$86$	3.02521	0.326217
$87$	21.3782	2.29199
$88$	2.46570	0.262844
$89$	7.07301	0.749737	0.374869	−	0.927078i	$-0.377688\pi$
$89$	7.07301	0.749737	0.374869	+	0.927078i	$0.377688\pi$
$90$	−3.74535	−0.394794
$91$	−11.6848	−1.22490
$92$	6.30951	0.657812
$93$	−2.42118	−0.251065
$94$	−9.36679	−0.966111
$95$	3.65804	0.375307
$96$	−2.42118	−0.247111
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	8.25616	0.833998
$99$	7.05715	0.709270
$100$	−3.28760	−0.328760
$101$	−6.61680	−0.658397	−0.329198	−	0.944261i	$-0.606778\pi$
$101$	−6.61680	−0.658397	−0.329198	+	0.944261i	$0.606778\pi$
$102$	4.68934	0.464314
$103$	−6.60813	−0.651118	−0.325559	−	0.945522i	$-0.605553\pi$
$103$	−6.60813	−0.651118	−0.325559	+	0.945522i	$0.605553\pi$
$104$	−2.99157	−0.293347
$105$	12.3752	1.20770
$106$	−3.61127	−0.350757
$107$	12.2513	1.18437	0.592187	−	0.805801i	$-0.298265\pi$
$107$	12.2513	1.18437	0.592187	+	0.805801i	$0.298265\pi$
$108$	0.333798	0.0321197
$109$	−4.15513	−0.397989	−0.198994	−	0.980001i	$-0.563768\pi$
$109$	−4.15513	−0.397989	−0.198994	+	0.980001i	$0.563768\pi$
$110$	−3.22657	−0.307642
$111$	12.4161	1.17849
$112$	3.90591	0.369074
$113$	−0.295965	−0.0278420	−0.0139210	−	0.999903i	$-0.504431\pi$
$113$	−0.295965	−0.0278420	−0.0139210	+	0.999903i	$0.504431\pi$
$114$	6.76822	0.633902
$115$	−8.25653	−0.769925
$116$	−8.82965	−0.819813
$117$	−8.56226	−0.791581
$118$	5.00305	0.460568
$119$	−7.56495	−0.693478
$120$	3.16833	0.289227
$121$	−4.92035	−0.447304
$122$	9.53671	0.863413
$123$	13.9805	1.26058
$124$	1.00000	0.0898027
$125$	10.8450	0.970010
$126$	11.1792	0.995927
$127$	7.31369	0.648985	0.324492	−	0.945888i	$-0.394807\pi$
$127$	7.31369	0.648985	0.324492	+	0.945888i	$0.394807\pi$
$128$	1.00000	0.0883883
$129$	−7.32460	−0.644895
$130$	3.91472	0.343344
$131$	−9.11451	−0.796338	−0.398169	−	0.917312i	$-0.630354\pi$
$131$	−9.11451	−0.796338	−0.398169	+	0.917312i	$0.630354\pi$
$132$	−5.96990	−0.519613
$133$	−10.9187	−0.946767
$134$	−2.46098	−0.212596
$135$	−0.436803	−0.0375940
$136$	−1.93680	−0.166079
$137$	7.17793	0.613252	0.306626	−	0.951830i	$-0.400800\pi$
$137$	7.17793	0.613252	0.306626	+	0.951830i	$0.400800\pi$
$138$	−15.2765	−1.30042
$139$	−17.3845	−1.47453	−0.737265	−	0.675604i	$-0.763883\pi$
$139$	−17.3845	−1.47453	−0.737265	+	0.675604i	$0.763883\pi$
$140$	−5.11122	−0.431977
$141$	22.6787	1.90989
$142$	−1.80300	−0.151304
$143$	−7.37629	−0.616836
$144$	2.86213	0.238511
$145$	11.5544	0.959537
$146$	−15.0984	−1.24955
$147$	−19.9897	−1.64872
$148$	−5.12812	−0.421529
$149$	−6.91586	−0.566569	−0.283284	−	0.959036i	$-0.591424\pi$
$149$	−6.91586	−0.566569	−0.283284	+	0.959036i	$0.591424\pi$
$150$	7.95990	0.649923
$151$	4.80280	0.390846	0.195423	−	0.980719i	$-0.437392\pi$
$151$	4.80280	0.390846	0.195423	+	0.980719i	$0.437392\pi$
$152$	−2.79542	−0.226738
$153$	−5.54337	−0.448155
$154$	9.63079	0.776071
$155$	−1.30859	−0.105108
$156$	7.24313	0.579915
$157$	−13.3467	−1.06518	−0.532592	−	0.846372i	$-0.678782\pi$
$157$	−13.3467	−1.06518	−0.532592	+	0.846372i	$0.678782\pi$
$158$	11.4783	0.913167
$159$	8.74355	0.693408
$160$	−1.30859	−0.103453
$161$	24.6444	1.94225
$162$	−9.39459	−0.738109
$163$	−6.63411	−0.519623	−0.259812	−	0.965659i	$-0.583660\pi$
$163$	−6.63411	−0.519623	−0.259812	+	0.965659i	$0.583660\pi$
$164$	−5.77424	−0.450893
$165$	7.81213	0.608173
$166$	7.49348	0.581607
$167$	13.6897	1.05934	0.529671	−	0.848203i	$-0.322315\pi$
$167$	13.6897	1.05934	0.529671	+	0.848203i	$0.322315\pi$
$168$	−9.45694	−0.729619
$169$	−4.05054	−0.311580
$170$	2.53446	0.194384
$171$	−8.00086	−0.611841
$172$	3.02521	0.230670
$173$	−12.7861	−0.972107	−0.486054	−	0.873929i	$-0.661564\pi$
$173$	−12.7861	−0.972107	−0.486054	+	0.873929i	$0.661564\pi$
$174$	21.3782	1.62068
$175$	−12.8411	−0.970696
$176$	2.46570	0.185859
$177$	−12.1133	−0.910492
$178$	7.07301	0.530144
$179$	−6.04754	−0.452014	−0.226007	−	0.974126i	$-0.572567\pi$
$179$	−6.04754	−0.452014	−0.226007	+	0.974126i	$0.572567\pi$
$180$	−3.74535	−0.279162
$181$	−20.3742	−1.51440	−0.757200	−	0.653183i	$-0.773433\pi$
$181$	−20.3742	−1.51440	−0.757200	+	0.653183i	$0.773433\pi$
$182$	−11.6848	−0.866135
$183$	−23.0901	−1.70687
$184$	6.30951	0.465143
$185$	6.71059	0.493372
$186$	−2.42118	−0.177530
$187$	−4.77555	−0.349223
$188$	−9.36679	−0.683143
$189$	1.30378	0.0948364
$190$	3.65804	0.265382
$191$	9.82613	0.710994	0.355497	−	0.934677i	$-0.384312\pi$
$191$	9.82613	0.710994	0.355497	+	0.934677i	$0.384312\pi$
$192$	−2.42118	−0.174734
$193$	−1.08774	−0.0782974	−0.0391487	−	0.999233i	$-0.512465\pi$
$193$	−1.08774	−0.0782974	−0.0391487	+	0.999233i	$0.512465\pi$
$194$	−1.00000	−0.0717958
$195$	−9.47826	−0.678752
$196$	8.25616	0.589726
$197$	−11.6270	−0.828388	−0.414194	−	0.910189i	$-0.635936\pi$
$197$	−11.6270	−0.828388	−0.414194	+	0.910189i	$0.635936\pi$
$198$	7.05715	0.501530
$199$	−14.8610	−1.05347	−0.526734	−	0.850030i	$-0.676583\pi$
$199$	−14.8610	−1.05347	−0.526734	+	0.850030i	$0.676583\pi$
$200$	−3.28760	−0.232469
$201$	5.95849	0.420279
$202$	−6.61680	−0.465557
$203$	−34.4879	−2.42057
$204$	4.68934	0.328319
$205$	7.55609	0.527740
$206$	−6.60813	−0.460410
$207$	18.0587	1.25516
$208$	−2.99157	−0.207428
$209$	−6.89264	−0.476774
$210$	12.3752	0.853971
$211$	5.97308	0.411204	0.205602	−	0.978636i	$-0.434085\pi$
$211$	5.97308	0.411204	0.205602	+	0.978636i	$0.434085\pi$
$212$	−3.61127	−0.248023
$213$	4.36538	0.299111
$214$	12.2513	0.837479
$215$	−3.95875	−0.269984
$216$	0.333798	0.0227120
$217$	3.90591	0.265151
$218$	−4.15513	−0.281421
$219$	36.5560	2.47022
$220$	−3.22657	−0.217535
$221$	5.79405	0.389750
$222$	12.4161	0.833316
$223$	10.6240	0.711436	0.355718	−	0.934593i	$-0.384236\pi$
$223$	10.6240	0.711436	0.355718	+	0.934593i	$0.384236\pi$
$224$	3.90591	0.260975
$225$	−9.40957	−0.627304
$226$	−0.295965	−0.0196873
$227$	−9.11783	−0.605171	−0.302586	−	0.953122i	$-0.597850\pi$
$227$	−9.11783	−0.605171	−0.302586	+	0.953122i	$0.597850\pi$
$228$	6.76822	0.448236
$229$	−15.8905	−1.05007	−0.525037	−	0.851079i	$-0.675949\pi$
$229$	−15.8905	−1.05007	−0.525037	+	0.851079i	$0.675949\pi$
$230$	−8.25653	−0.544419
$231$	−23.3179	−1.53421
$232$	−8.82965	−0.579695
$233$	−17.3495	−1.13661	−0.568303	−	0.822819i	$-0.692400\pi$
$233$	−17.3495	−1.13661	−0.568303	+	0.822819i	$0.692400\pi$
$234$	−8.56226	−0.559733
$235$	12.2572	0.799574
$236$	5.00305	0.325671
$237$	−27.7912	−1.80523
$238$	−7.56495	−0.490363
$239$	13.9762	0.904047	0.452023	−	0.892006i	$-0.350702\pi$
$239$	13.9762	0.904047	0.452023	+	0.892006i	$0.350702\pi$
$240$	3.16833	0.204515
$241$	14.7515	0.950231	0.475115	−	0.879924i	$-0.342406\pi$
$241$	14.7515	0.950231	0.475115	+	0.879924i	$0.342406\pi$
$242$	−4.92035	−0.316292
$243$	21.7446	1.39492
$244$	9.53671	0.610525
$245$	−10.8039	−0.690235
$246$	13.9805	0.891365
$247$	8.36267	0.532104
$248$	1.00000	0.0635001
$249$	−18.1431	−1.14977
$250$	10.8450	0.685900
$251$	4.99482	0.315270	0.157635	−	0.987497i	$-0.449613\pi$
$251$	4.99482	0.315270	0.157635	+	0.987497i	$0.449613\pi$
$252$	11.1792	0.704227
$253$	15.5573	0.978080
$254$	7.31369	0.458902
$255$	−6.13640	−0.384276
$256$	1.00000	0.0625000
$257$	−1.24871	−0.0778925	−0.0389462	−	0.999241i	$-0.512400\pi$
$257$	−1.24871	−0.0778925	−0.0389462	+	0.999241i	$0.512400\pi$
$258$	−7.32460	−0.456009
$259$	−20.0300	−1.24460
$260$	3.91472	0.242781
$261$	−25.2717	−1.56428
$262$	−9.11451	−0.563096
$263$	−24.6061	−1.51728	−0.758638	−	0.651513i	$-0.774135\pi$
$263$	−24.6061	−1.51728	−0.758638	+	0.651513i	$0.774135\pi$
$264$	−5.96990	−0.367422
$265$	4.72565	0.290295
$266$	−10.9187	−0.669466
$267$	−17.1251	−1.04804
$268$	−2.46098	−0.150328
$269$	−25.4289	−1.55043	−0.775213	−	0.631699i	$-0.782358\pi$
$269$	−25.4289	−1.55043	−0.775213	+	0.631699i	$0.782358\pi$
$270$	−0.436803	−0.0265830
$271$	−9.50487	−0.577380	−0.288690	−	0.957423i	$-0.593220\pi$
$271$	−9.50487	−0.577380	−0.288690	+	0.957423i	$0.593220\pi$
$272$	−1.93680	−0.117435
$273$	28.2910	1.71225
$274$	7.17793	0.433635
$275$	−8.10623	−0.488824
$276$	−15.2765	−0.919536
$277$	3.88671	0.233530	0.116765	−	0.993160i	$-0.462748\pi$
$277$	3.88671	0.233530	0.116765	+	0.993160i	$0.462748\pi$
$278$	−17.3845	−1.04265
$279$	2.86213	0.171352
$280$	−5.11122	−0.305454
$281$	27.1825	1.62157	0.810787	−	0.585341i	$-0.199039\pi$
$281$	27.1825	1.62157	0.810787	+	0.585341i	$0.199039\pi$
$282$	22.6787	1.35050
$283$	−1.37527	−0.0817511	−0.0408756	−	0.999164i	$-0.513015\pi$
$283$	−1.37527	−0.0817511	−0.0408756	+	0.999164i	$0.513015\pi$
$284$	−1.80300	−0.106988
$285$	−8.85679	−0.524631
$286$	−7.37629	−0.436169
$287$	−22.5537	−1.33130
$288$	2.86213	0.168653
$289$	−13.2488	−0.779343
$290$	11.5544	0.678495
$291$	2.42118	0.141932
$292$	−15.0984	−0.883566
$293$	10.5469	0.616158	0.308079	−	0.951361i	$-0.400314\pi$
$293$	10.5469	0.616158	0.308079	+	0.951361i	$0.400314\pi$
$294$	−19.9897	−1.16582
$295$	−6.54692	−0.381176
$296$	−5.12812	−0.298066
$297$	0.823043	0.0477578
$298$	−6.91586	−0.400625
$299$	−18.8753	−1.09159
$300$	7.95990	0.459565
$301$	11.8162	0.681075
$302$	4.80280	0.276370
$303$	16.0205	0.920354
$304$	−2.79542	−0.160328
$305$	−12.4796	−0.714580
$306$	−5.54337	−0.316893
$307$	−25.6703	−1.46508	−0.732540	−	0.680724i	$-0.761665\pi$
$307$	−25.6703	−1.46508	−0.732540	+	0.680724i	$0.761665\pi$
$308$	9.63079	0.548765
$309$	15.9995	0.910180
$310$	−1.30859	−0.0743227
$311$	11.3075	0.641189	0.320594	−	0.947217i	$-0.396117\pi$
$311$	11.3075	0.641189	0.320594	+	0.947217i	$0.396117\pi$
$312$	7.24313	0.410062
$313$	−1.00342	−0.0567164	−0.0283582	−	0.999598i	$-0.509028\pi$
$313$	−1.00342	−0.0567164	−0.0283582	+	0.999598i	$0.509028\pi$
$314$	−13.3467	−0.753198
$315$	−14.6290	−0.824251
$316$	11.4783	0.645707
$317$	−14.4117	−0.809443	−0.404721	−	0.914440i	$-0.632632\pi$
$317$	−14.4117	−0.809443	−0.404721	+	0.914440i	$0.632632\pi$
$318$	8.74355	0.490314
$319$	−21.7712	−1.21896
$320$	−1.30859	−0.0731522
$321$	−29.6626	−1.65560
$322$	24.6444	1.37338
$323$	5.41415	0.301251
$324$	−9.39459	−0.521922
$325$	9.83508	0.545552
$326$	−6.63411	−0.367429
$327$	10.0603	0.556337
$328$	−5.77424	−0.318829
$329$	−36.5859	−2.01704
$330$	7.81213	0.430044
$331$	15.8013	0.868518	0.434259	−	0.900788i	$-0.357010\pi$
$331$	15.8013	0.868518	0.434259	+	0.900788i	$0.357010\pi$
$332$	7.49348	0.411258
$333$	−14.6774	−0.804316
$334$	13.6897	0.749068
$335$	3.22040	0.175949
$336$	−9.45694	−0.515918
$337$	−11.2432	−0.612456	−0.306228	−	0.951958i	$-0.599067\pi$
$337$	−11.2432	−0.612456	−0.306228	+	0.951958i	$0.599067\pi$
$338$	−4.05054	−0.220320
$339$	0.716585	0.0389196
$340$	2.53446	0.137451
$341$	2.46570	0.133525
$342$	−8.00086	−0.432637
$343$	4.90645	0.264923
$344$	3.02521	0.163108
$345$	19.9906	1.07626
$346$	−12.7861	−0.687383
$347$	0.654679	0.0351450	0.0175725	−	0.999846i	$-0.494406\pi$
$347$	0.654679	0.0351450	0.0175725	+	0.999846i	$0.494406\pi$
$348$	21.3782	1.14599
$349$	−19.7947	−1.05959	−0.529793	−	0.848127i	$-0.677730\pi$
$349$	−19.7947	−1.05959	−0.529793	+	0.848127i	$0.677730\pi$
$350$	−12.8411	−0.686385
$351$	−0.998577	−0.0533001
$352$	2.46570	0.131422
$353$	−9.14649	−0.486819	−0.243409	−	0.969924i	$-0.578266\pi$
$353$	−9.14649	−0.486819	−0.243409	+	0.969924i	$0.578266\pi$
$354$	−12.1133	−0.643815
$355$	2.35937	0.125223
$356$	7.07301	0.374869
$357$	18.3162	0.969394
$358$	−6.04754	−0.319622
$359$	−18.9376	−0.999487	−0.499743	−	0.866173i	$-0.666572\pi$
$359$	−18.9376	−0.999487	−0.499743	+	0.866173i	$0.666572\pi$
$360$	−3.74535	−0.197397
$361$	−11.1856	−0.588718
$362$	−20.3742	−1.07084
$363$	11.9131	0.625274
$364$	−11.6848	−0.612450
$365$	19.7575	1.03416
$366$	−23.0901	−1.20694
$367$	24.7996	1.29453	0.647265	−	0.762265i	$-0.275913\pi$
$367$	24.7996	1.29453	0.647265	+	0.762265i	$0.275913\pi$
$368$	6.30951	0.328906
$369$	−16.5267	−0.860344
$370$	6.71059	0.348867
$371$	−14.1053	−0.732311
$372$	−2.42118	−0.125533
$373$	−2.48048	−0.128434	−0.0642171	−	0.997936i	$-0.520455\pi$
$373$	−2.48048	−0.128434	−0.0642171	+	0.997936i	$0.520455\pi$
$374$	−4.77555	−0.246938
$375$	−26.2578	−1.35595
$376$	−9.36679	−0.483055
$377$	26.4145	1.36042
$378$	1.30378	0.0670594
$379$	−8.12420	−0.417312	−0.208656	−	0.977989i	$-0.566909\pi$
$379$	−8.12420	−0.417312	−0.208656	+	0.977989i	$0.566909\pi$
$380$	3.65804	0.187654
$381$	−17.7078	−0.907198
$382$	9.82613	0.502749
$383$	−20.5193	−1.04849	−0.524243	−	0.851569i	$-0.675652\pi$
$383$	−20.5193	−1.04849	−0.524243	+	0.851569i	$0.675652\pi$
$384$	−2.42118	−0.123556
$385$	−12.6027	−0.642294
$386$	−1.08774	−0.0553646
$387$	8.65856	0.440139
$388$	−1.00000	−0.0507673
$389$	−1.71369	−0.0868876	−0.0434438	−	0.999056i	$-0.513833\pi$
$389$	−1.71369	−0.0868876	−0.0434438	+	0.999056i	$0.513833\pi$
$390$	−9.47826	−0.479950
$391$	−12.2202	−0.618003
$392$	8.25616	0.416999
$393$	22.0679	1.11318
$394$	−11.6270	−0.585759
$395$	−15.0204	−0.755758
$396$	7.05715	0.354635
$397$	5.21535	0.261751	0.130875	−	0.991399i	$-0.458221\pi$
$397$	5.21535	0.261751	0.130875	+	0.991399i	$0.458221\pi$
$398$	−14.8610	−0.744914
$399$	26.4361	1.32346
$400$	−3.28760	−0.164380
$401$	20.7575	1.03658	0.518290	−	0.855205i	$-0.326569\pi$
$401$	20.7575	1.03658	0.518290	+	0.855205i	$0.326569\pi$
$402$	5.95849	0.297182
$403$	−2.99157	−0.149020
$404$	−6.61680	−0.329198
$405$	12.2936	0.610875
$406$	−34.4879	−1.71160
$407$	−12.6444	−0.626759
$408$	4.68934	0.232157
$409$	15.9838	0.790347	0.395173	−	0.918607i	$-0.370685\pi$
$409$	15.9838	0.790347	0.395173	+	0.918607i	$0.370685\pi$
$410$	7.55609	0.373169
$411$	−17.3791	−0.857248
$412$	−6.60813	−0.325559
$413$	19.5415	0.961573
$414$	18.0587	0.887535
$415$	−9.80586	−0.481351
$416$	−2.99157	−0.146674
$417$	42.0910	2.06120
$418$	−6.89264	−0.337130
$419$	−36.9967	−1.80741	−0.903704	−	0.428158i	$-0.859163\pi$
$419$	−36.9967	−1.80741	−0.903704	+	0.428158i	$0.859163\pi$
$420$	12.3752	0.603848
$421$	6.23351	0.303803	0.151901	−	0.988396i	$-0.451460\pi$
$421$	6.23351	0.303803	0.151901	+	0.988396i	$0.451460\pi$
$422$	5.97308	0.290765
$423$	−26.8090	−1.30350
$424$	−3.61127	−0.175379
$425$	6.36742	0.308865
$426$	4.36538	0.211504
$427$	37.2496	1.80263
$428$	12.2513	0.592187
$429$	17.8594	0.862258
$430$	−3.95875	−0.190908
$431$	17.1319	0.825216	0.412608	−	0.910909i	$-0.364618\pi$
$431$	17.1319	0.825216	0.412608	+	0.910909i	$0.364618\pi$
$432$	0.333798	0.0160598
$433$	5.15670	0.247815	0.123908	−	0.992294i	$-0.460457\pi$
$433$	5.15670	0.247815	0.123908	+	0.992294i	$0.460457\pi$
$434$	3.90591	0.187490
$435$	−27.9752	−1.34131
$436$	−4.15513	−0.198994
$437$	−17.6377	−0.843725
$438$	36.5560	1.74671
$439$	−11.5932	−0.553312	−0.276656	−	0.960969i	$-0.589226\pi$
$439$	−11.5932	−0.553312	−0.276656	+	0.960969i	$0.589226\pi$
$440$	−3.22657	−0.153821
$441$	23.6302	1.12525
$442$	5.79405	0.275595
$443$	−1.80221	−0.0856255	−0.0428128	−	0.999083i	$-0.513632\pi$
$443$	−1.80221	−0.0856255	−0.0428128	+	0.999083i	$0.513632\pi$
$444$	12.4161	0.589244
$445$	−9.25563	−0.438759
$446$	10.6240	0.503061
$447$	16.7446	0.791991
$448$	3.90591	0.184537
$449$	18.1120	0.854759	0.427380	−	0.904072i	$-0.359437\pi$
$449$	18.1120	0.854759	0.427380	+	0.904072i	$0.359437\pi$
$450$	−9.40957	−0.443571
$451$	−14.2375	−0.670419
$452$	−0.295965	−0.0139210
$453$	−11.6285	−0.546353
$454$	−9.11783	−0.427921
$455$	15.2906	0.716832
$456$	6.76822	0.316951
$457$	25.9079	1.21192	0.605961	−	0.795494i	$-0.292789\pi$
$457$	25.9079	1.21192	0.605961	+	0.795494i	$0.292789\pi$
$458$	−15.8905	−0.742515
$459$	−0.646498	−0.0301759
$460$	−8.25653	−0.384963
$461$	6.72073	0.313015	0.156508	−	0.987677i	$-0.449976\pi$
$461$	6.72073	0.313015	0.156508	+	0.987677i	$0.449976\pi$
$462$	−23.3179	−1.08485
$463$	−11.3414	−0.527080	−0.263540	−	0.964648i	$-0.584890\pi$
$463$	−11.3414	−0.527080	−0.263540	+	0.964648i	$0.584890\pi$
$464$	−8.82965	−0.409906
$465$	3.16833	0.146928
$466$	−17.3495	−0.803702
$467$	−14.5881	−0.675056	−0.337528	−	0.941315i	$-0.609591\pi$
$467$	−14.5881	−0.675056	−0.337528	+	0.941315i	$0.609591\pi$
$468$	−8.56226	−0.395791
$469$	−9.61237	−0.443858
$470$	12.2572	0.565385
$471$	32.3148	1.48899
$472$	5.00305	0.230284
$473$	7.45925	0.342977
$474$	−27.7912	−1.27649
$475$	9.19022	0.421676
$476$	−7.56495	−0.346739
$477$	−10.3359	−0.473250
$478$	13.9762	0.639257
$479$	27.4533	1.25437	0.627186	−	0.778869i	$-0.284206\pi$
$479$	27.4533	1.25437	0.627186	+	0.778869i	$0.284206\pi$
$480$	3.16833	0.144614
$481$	15.3411	0.699495
$482$	14.7515	0.671915
$483$	−59.6686	−2.71502
$484$	−4.92035	−0.223652
$485$	1.30859	0.0594198
$486$	21.7446	0.986357
$487$	1.51400	0.0686058	0.0343029	−	0.999411i	$-0.489079\pi$
$487$	1.51400	0.0686058	0.0343029	+	0.999411i	$0.489079\pi$
$488$	9.53671	0.431707
$489$	16.0624	0.726367
$490$	−10.8039	−0.488070
$491$	−41.4835	−1.87212	−0.936062	−	0.351835i	$-0.885558\pi$
$491$	−41.4835	−1.87212	−0.936062	+	0.351835i	$0.885558\pi$
$492$	13.9805	0.630290
$493$	17.1012	0.770201
$494$	8.36267	0.376254
$495$	−9.23489	−0.415077
$496$	1.00000	0.0449013
$497$	−7.04234	−0.315892
$498$	−18.1431	−0.813012
$499$	−20.7259	−0.927818	−0.463909	−	0.885883i	$-0.653553\pi$
$499$	−20.7259	−0.927818	−0.463909	+	0.885883i	$0.653553\pi$
$500$	10.8450	0.485005
$501$	−33.1453	−1.48082
$502$	4.99482	0.222930
$503$	−39.9660	−1.78200	−0.890999	−	0.454006i	$-0.849994\pi$
$503$	−39.9660	−1.78200	−0.890999	+	0.454006i	$0.849994\pi$
$504$	11.1792	0.497963
$505$	8.65865	0.385305
$506$	15.5573	0.691607
$507$	9.80710	0.435549
$508$	7.31369	0.324492
$509$	−5.03872	−0.223337	−0.111669	−	0.993745i	$-0.535620\pi$
$509$	−5.03872	−0.223337	−0.111669	+	0.993745i	$0.535620\pi$
$510$	−6.13640	−0.271724
$511$	−58.9730	−2.60881
$512$	1.00000	0.0441942
$513$	−0.933103	−0.0411975
$514$	−1.24871	−0.0550783
$515$	8.64730	0.381046
$516$	−7.32460	−0.322447
$517$	−23.0956	−1.01575
$518$	−20.0300	−0.880068
$519$	30.9574	1.35888
$520$	3.91472	0.171672
$521$	−39.5422	−1.73238	−0.866188	−	0.499719i	$-0.833437\pi$
$521$	−39.5422	−1.73238	−0.866188	+	0.499719i	$0.833437\pi$
$522$	−25.2717	−1.10611
$523$	−28.4458	−1.24385	−0.621924	−	0.783078i	$-0.713649\pi$
$523$	−28.4458	−1.24385	−0.621924	+	0.783078i	$0.713649\pi$
$524$	−9.11451	−0.398169
$525$	31.0907	1.35691
$526$	−24.6061	−1.07288
$527$	−1.93680	−0.0843681
$528$	−5.96990	−0.259807
$529$	16.8099	0.730864
$530$	4.72565	0.205269
$531$	14.3194	0.621409
$532$	−10.9187	−0.473384
$533$	17.2740	0.748221
$534$	−17.1251	−0.741074
$535$	−16.0318	−0.693116
$536$	−2.46098	−0.106298
$537$	14.6422	0.631858
$538$	−25.4289	−1.09632
$539$	20.3572	0.876845
$540$	−0.436803	−0.0187970
$541$	−36.8762	−1.58543	−0.792716	−	0.609591i	$-0.791334\pi$
$541$	−36.8762	−1.58543	−0.792716	+	0.609591i	$0.791334\pi$
$542$	−9.50487	−0.408269
$543$	49.3296	2.11694
$544$	−1.93680	−0.0830394
$545$	5.43734	0.232910
$546$	28.2910	1.21074
$547$	−9.13445	−0.390561	−0.195280	−	0.980747i	$-0.562562\pi$
$547$	−9.13445	−0.390561	−0.195280	+	0.980747i	$0.562562\pi$
$548$	7.17793	0.306626
$549$	27.2954	1.16494
$550$	−8.10623	−0.345651
$551$	24.6826	1.05151
$552$	−15.2765	−0.650210
$553$	44.8334	1.90651
$554$	3.88671	0.165130
$555$	−16.2476	−0.689671
$556$	−17.3845	−0.737265
$557$	7.66022	0.324574	0.162287	−	0.986744i	$-0.448113\pi$
$557$	7.66022	0.324574	0.162287	+	0.986744i	$0.448113\pi$
$558$	2.86213	0.121164
$559$	−9.05012	−0.382779
$560$	−5.11122	−0.215989
$561$	11.5625	0.488168
$562$	27.1825	1.14663
$563$	−12.6592	−0.533521	−0.266760	−	0.963763i	$-0.585953\pi$
$563$	−12.6592	−0.533521	−0.266760	+	0.963763i	$0.585953\pi$
$564$	22.6787	0.954947
$565$	0.387295	0.0162936
$566$	−1.37527	−0.0578068
$567$	−36.6945	−1.54102
$568$	−1.80300	−0.0756520
$569$	36.7344	1.53999	0.769993	−	0.638052i	$-0.220259\pi$
$569$	36.7344	1.53999	0.769993	+	0.638052i	$0.220259\pi$
$570$	−8.85679	−0.370970
$571$	−3.14632	−0.131669	−0.0658346	−	0.997831i	$-0.520971\pi$
$571$	−3.14632	−0.131669	−0.0658346	+	0.997831i	$0.520971\pi$
$572$	−7.37629	−0.308418
$573$	−23.7909	−0.993878
$574$	−22.5537	−0.941373
$575$	−20.7432	−0.865050
$576$	2.86213	0.119256
$577$	2.37201	0.0987480	0.0493740	−	0.998780i	$-0.484277\pi$
$577$	2.37201	0.0987480	0.0493740	+	0.998780i	$0.484277\pi$
$578$	−13.2488	−0.551078
$579$	2.63362	0.109450
$580$	11.5544	0.479768
$581$	29.2689	1.21428
$582$	2.42118	0.100361
$583$	−8.90429	−0.368778
$584$	−15.0984	−0.624775
$585$	11.2045	0.463247
$586$	10.5469	0.435689
$587$	−1.82702	−0.0754092	−0.0377046	−	0.999289i	$-0.512005\pi$
$587$	−1.82702	−0.0754092	−0.0377046	+	0.999289i	$0.512005\pi$
$588$	−19.9897	−0.824361
$589$	−2.79542	−0.115183
$590$	−6.54692	−0.269532
$591$	28.1511	1.15798
$592$	−5.12812	−0.210765
$593$	31.5912	1.29729	0.648647	−	0.761089i	$-0.275335\pi$
$593$	31.5912	1.29729	0.648647	+	0.761089i	$0.275335\pi$
$594$	0.823043	0.0337699
$595$	9.89939	0.405835
$596$	−6.91586	−0.283284
$597$	35.9812	1.47261
$598$	−18.8753	−0.771869
$599$	23.2422	0.949650	0.474825	−	0.880080i	$-0.342511\pi$
$599$	23.2422	0.949650	0.474825	+	0.880080i	$0.342511\pi$
$600$	7.95990	0.324961
$601$	14.2700	0.582086	0.291043	−	0.956710i	$-0.405998\pi$
$601$	14.2700	0.582086	0.291043	+	0.956710i	$0.405998\pi$
$602$	11.8162	0.481593
$603$	−7.04366	−0.286840
$604$	4.80280	0.195423
$605$	6.43869	0.261770
$606$	16.0205	0.650789
$607$	3.33045	0.135179	0.0675894	−	0.997713i	$-0.478469\pi$
$607$	3.33045	0.135179	0.0675894	+	0.997713i	$0.478469\pi$
$608$	−2.79542	−0.113369
$609$	83.5015	3.38365
$610$	−12.4796	−0.505284
$611$	28.0214	1.13362
$612$	−5.54337	−0.224077
$613$	−26.0344	−1.05152	−0.525760	−	0.850633i	$-0.676219\pi$
$613$	−26.0344	−1.05152	−0.525760	+	0.850633i	$0.676219\pi$
$614$	−25.6703	−1.03597
$615$	−18.2947	−0.737713
$616$	9.63079	0.388036
$617$	34.7155	1.39759	0.698796	−	0.715321i	$-0.253720\pi$
$617$	34.7155	1.39759	0.698796	+	0.715321i	$0.253720\pi$
$618$	15.9995	0.643594
$619$	24.1581	0.970998	0.485499	−	0.874237i	$-0.338638\pi$
$619$	24.1581	0.970998	0.485499	+	0.874237i	$0.338638\pi$
$620$	−1.30859	−0.0525541
$621$	2.10610	0.0845148
$622$	11.3075	0.453389
$623$	27.6265	1.10683
$624$	7.24313	0.289957
$625$	2.24636	0.0898545
$626$	−1.00342	−0.0401046
$627$	16.6884	0.666469
$628$	−13.3467	−0.532592
$629$	9.93213	0.396020
$630$	−14.6290	−0.582833
$631$	22.8790	0.910797	0.455398	−	0.890288i	$-0.349497\pi$
$631$	22.8790	0.910797	0.455398	+	0.890288i	$0.349497\pi$
$632$	11.4783	0.456584
$633$	−14.4619	−0.574811
$634$	−14.4117	−0.572363
$635$	−9.57059	−0.379797
$636$	8.74355	0.346704
$637$	−24.6988	−0.978604
$638$	−21.7712	−0.861931
$639$	−5.16042	−0.204143
$640$	−1.30859	−0.0517264
$641$	−31.8002	−1.25603	−0.628016	−	0.778200i	$-0.716133\pi$
$641$	−31.8002	−1.25603	−0.628016	+	0.778200i	$0.716133\pi$
$642$	−29.6626	−1.17069
$643$	−5.16614	−0.203732	−0.101866	−	0.994798i	$-0.532481\pi$
$643$	−5.16614	−0.203732	−0.101866	+	0.994798i	$0.532481\pi$
$644$	24.6444	0.971125
$645$	9.58486	0.377403
$646$	5.41415	0.213017
$647$	5.45638	0.214513	0.107256	−	0.994231i	$-0.465793\pi$
$647$	5.45638	0.214513	0.107256	+	0.994231i	$0.465793\pi$
$648$	−9.39459	−0.369054
$649$	12.3360	0.484230
$650$	9.83508	0.385764
$651$	−9.45694	−0.370647
$652$	−6.63411	−0.259812
$653$	14.9758	0.586047	0.293024	−	0.956105i	$-0.405339\pi$
$653$	14.9758	0.586047	0.293024	+	0.956105i	$0.405339\pi$
$654$	10.0603	0.393390
$655$	11.9271	0.466031
$656$	−5.77424	−0.225446
$657$	−43.2136	−1.68592
$658$	−36.5859	−1.42627
$659$	24.7677	0.964814	0.482407	−	0.875947i	$-0.339763\pi$
$659$	24.7677	0.964814	0.482407	+	0.875947i	$0.339763\pi$
$660$	7.81213	0.304087
$661$	−40.7970	−1.58682	−0.793410	−	0.608688i	$-0.791696\pi$
$661$	−40.7970	−1.58682	−0.793410	+	0.608688i	$0.791696\pi$
$662$	15.8013	0.614135
$663$	−14.0285	−0.544820
$664$	7.49348	0.290804
$665$	14.2880	0.554064
$666$	−14.6774	−0.568737
$667$	−55.7108	−2.15713
$668$	13.6897	0.529671
$669$	−25.7227	−0.994496
$670$	3.22040	0.124415
$671$	23.5146	0.907772
$672$	−9.45694	−0.364809
$673$	6.79188	0.261808	0.130904	−	0.991395i	$-0.458212\pi$
$673$	6.79188	0.261808	0.130904	+	0.991395i	$0.458212\pi$
$674$	−11.2432	−0.433071
$675$	−1.09739	−0.0422387
$676$	−4.05054	−0.155790
$677$	−2.74209	−0.105387	−0.0526935	−	0.998611i	$-0.516781\pi$
$677$	−2.74209	−0.105387	−0.0526935	+	0.998611i	$0.516781\pi$
$678$	0.716585	0.0275203
$679$	−3.90591	−0.149895
$680$	2.53446	0.0971922
$681$	22.0759	0.845952
$682$	2.46570	0.0944163
$683$	5.08902	0.194726	0.0973630	−	0.995249i	$-0.468959\pi$
$683$	5.08902	0.194726	0.0973630	+	0.995249i	$0.468959\pi$
$684$	−8.00086	−0.305920
$685$	−9.39294	−0.358886
$686$	4.90645	0.187329
$687$	38.4739	1.46787
$688$	3.02521	0.115335
$689$	10.8033	0.411575
$690$	19.9906	0.761028
$691$	27.3216	1.03936	0.519681	−	0.854360i	$-0.326051\pi$
$691$	27.3216	1.03936	0.519681	+	0.854360i	$0.326051\pi$
$692$	−12.7861	−0.486054
$693$	27.5646	1.04709
$694$	0.654679	0.0248513
$695$	22.7490	0.862920
$696$	21.3782	0.810339
$697$	11.1835	0.423606
$698$	−19.7947	−0.749240
$699$	42.0064	1.58883
$700$	−12.8411	−0.485348
$701$	24.7718	0.935619	0.467809	−	0.883829i	$-0.345043\pi$
$701$	24.7718	0.935619	0.467809	+	0.883829i	$0.345043\pi$
$702$	−0.998577	−0.0376889
$703$	14.3352	0.540664
$704$	2.46570	0.0929294
$705$	−29.6771	−1.11770
$706$	−9.14649	−0.344233
$707$	−25.8447	−0.971989
$708$	−12.1133	−0.455246
$709$	−19.4200	−0.729334	−0.364667	−	0.931138i	$-0.618817\pi$
$709$	−19.4200	−0.729334	−0.364667	+	0.931138i	$0.618817\pi$
$710$	2.35937	0.0885457
$711$	32.8525	1.23207
$712$	7.07301	0.265072
$713$	6.30951	0.236293
$714$	18.3162	0.685465
$715$	9.65250	0.360983
$716$	−6.04754	−0.226007
$717$	−33.8390	−1.26374
$718$	−18.9376	−0.706744
$719$	47.3538	1.76600	0.883000	−	0.469373i	$-0.155520\pi$
$719$	47.3538	1.76600	0.883000	+	0.469373i	$0.155520\pi$
$720$	−3.74535	−0.139581
$721$	−25.8108	−0.961244
$722$	−11.1856	−0.416287
$723$	−35.7162	−1.32830
$724$	−20.3742	−0.757200
$725$	29.0284	1.07809
$726$	11.9131	0.442135
$727$	36.5670	1.35619	0.678097	−	0.734972i	$-0.262805\pi$
$727$	36.5670	1.35619	0.678097	+	0.734972i	$0.262805\pi$
$728$	−11.6848	−0.433067
$729$	−24.4640	−0.906075
$730$	19.7575	0.731258
$731$	−5.85922	−0.216711
$732$	−23.0901	−0.853436
$733$	34.3356	1.26821	0.634107	−	0.773245i	$-0.281368\pi$
$733$	34.3356	1.26821	0.634107	+	0.773245i	$0.281368\pi$
$734$	24.7996	0.915370
$735$	26.1582	0.964860
$736$	6.30951	0.232572
$737$	−6.06803	−0.223519
$738$	−16.5267	−0.608355
$739$	−7.40297	−0.272323	−0.136161	−	0.990687i	$-0.543477\pi$
$739$	−7.40297	−0.272323	−0.136161	+	0.990687i	$0.543477\pi$
$740$	6.71059	0.246686
$741$	−20.2476	−0.743813
$742$	−14.1053	−0.517822
$743$	42.6062	1.56307	0.781536	−	0.623861i	$-0.214437\pi$
$743$	42.6062	1.56307	0.781536	+	0.623861i	$0.214437\pi$
$744$	−2.42118	−0.0887649
$745$	9.04999	0.331566
$746$	−2.48048	−0.0908166
$747$	21.4474	0.784718
$748$	−4.77555	−0.174611
$749$	47.8523	1.74849
$750$	−26.2578	−0.958801
$751$	2.35087	0.0857846	0.0428923	−	0.999080i	$-0.486343\pi$
$751$	2.35087	0.0857846	0.0428923	+	0.999080i	$0.486343\pi$
$752$	−9.36679	−0.341572
$753$	−12.0934	−0.440707
$754$	26.4145	0.961959
$755$	−6.28488	−0.228730
$756$	1.30378	0.0474182
$757$	31.4536	1.14320	0.571601	−	0.820532i	$-0.306323\pi$
$757$	31.4536	1.14320	0.571601	+	0.820532i	$0.306323\pi$
$758$	−8.12420	−0.295084
$759$	−37.6671	−1.36723
$760$	3.65804	0.132691
$761$	19.5214	0.707649	0.353825	−	0.935312i	$-0.384881\pi$
$761$	19.5214	0.707649	0.353825	+	0.935312i	$0.384881\pi$
$762$	−17.7078	−0.641486
$763$	−16.2296	−0.587550
$764$	9.82613	0.355497
$765$	7.25397	0.262268
$766$	−20.5193	−0.741392
$767$	−14.9669	−0.540425
$768$	−2.42118	−0.0873670
$769$	−32.3829	−1.16776	−0.583879	−	0.811841i	$-0.698466\pi$
$769$	−32.3829	−1.16776	−0.583879	+	0.811841i	$0.698466\pi$
$770$	−12.6027	−0.454170
$771$	3.02336	0.108884
$772$	−1.08774	−0.0391487
$773$	10.8313	0.389573	0.194787	−	0.980846i	$-0.437599\pi$
$773$	10.8313	0.389573	0.194787	+	0.980846i	$0.437599\pi$
$774$	8.65856	0.311226
$775$	−3.28760	−0.118094
$776$	−1.00000	−0.0358979
$777$	48.4963	1.73980
$778$	−1.71369	−0.0614388
$779$	16.1414	0.578326
$780$	−9.47826	−0.339376
$781$	−4.44564	−0.159077
$782$	−12.2202	−0.436994
$783$	−2.94732	−0.105329
$784$	8.25616	0.294863
$785$	17.4653	0.623364
$786$	22.0679	0.787136
$787$	−4.55717	−0.162445	−0.0812227	−	0.996696i	$-0.525883\pi$
$787$	−4.55717	−0.162445	−0.0812227	+	0.996696i	$0.525883\pi$
$788$	−11.6270	−0.414194
$789$	59.5758	2.12096
$790$	−15.0204	−0.534401
$791$	−1.15601	−0.0411031
$792$	7.05715	0.250765
$793$	−28.5297	−1.01312
$794$	5.21535	0.185086
$795$	−11.4417	−0.405794
$796$	−14.8610	−0.526734
$797$	26.4120	0.935560	0.467780	−	0.883845i	$-0.345054\pi$
$797$	26.4120	0.935560	0.467780	+	0.883845i	$0.345054\pi$
$798$	26.4361	0.935827
$799$	18.1416	0.641802
$800$	−3.28760	−0.116234
$801$	20.2439	0.715283
$802$	20.7575	0.732973
$803$	−37.2280	−1.31375
$804$	5.95849	0.210140
$805$	−32.2493	−1.13664
$806$	−2.99157	−0.105373
$807$	61.5680	2.16730
$808$	−6.61680	−0.232778
$809$	−13.1062	−0.460789	−0.230395	−	0.973097i	$-0.574002\pi$
$809$	−13.1062	−0.460789	−0.230395	+	0.973097i	$0.574002\pi$
$810$	12.2936	0.431954
$811$	−12.2622	−0.430583	−0.215292	−	0.976550i	$-0.569070\pi$
$811$	−12.2622	−0.430583	−0.215292	+	0.976550i	$0.569070\pi$
$812$	−34.4879	−1.21029
$813$	23.0130	0.807103
$814$	−12.6444	−0.443186
$815$	8.68129	0.304092
$816$	4.68934	0.164160
$817$	−8.45672	−0.295863
$818$	15.9838	0.558860
$819$	−33.4435	−1.16861
$820$	7.55609	0.263870
$821$	9.61138	0.335439	0.167720	−	0.985835i	$-0.446360\pi$
$821$	9.61138	0.335439	0.167720	+	0.985835i	$0.446360\pi$
$822$	−17.3791	−0.606166
$823$	9.72187	0.338883	0.169441	−	0.985540i	$-0.445804\pi$
$823$	9.72187	0.338883	0.169441	+	0.985540i	$0.445804\pi$
$824$	−6.60813	−0.230205
$825$	19.6267	0.683313
$826$	19.5415	0.679935
$827$	16.5365	0.575032	0.287516	−	0.957776i	$-0.407171\pi$
$827$	16.5365	0.575032	0.287516	+	0.957776i	$0.407171\pi$
$828$	18.0587	0.627582
$829$	−24.1284	−0.838015	−0.419007	−	0.907983i	$-0.637622\pi$
$829$	−24.1284	−0.838015	−0.419007	+	0.907983i	$0.637622\pi$
$830$	−9.80586	−0.340367
$831$	−9.41044	−0.326445
$832$	−2.99157	−0.103714
$833$	−15.9905	−0.554038
$834$	42.0910	1.45749
$835$	−17.9142	−0.619946
$836$	−6.89264	−0.238387
$837$	0.333798	0.0115377
$838$	−36.9967	−1.27803
$839$	50.6255	1.74779	0.873894	−	0.486117i	$-0.161587\pi$
$839$	50.6255	1.74779	0.873894	+	0.486117i	$0.161587\pi$
$840$	12.3752	0.426985
$841$	48.9628	1.68837
$842$	6.23351	0.214821
$843$	−65.8140	−2.26675
$844$	5.97308	0.205602
$845$	5.30047	0.182342
$846$	−26.8090	−0.921713
$847$	−19.2184	−0.660354
$848$	−3.61127	−0.124011
$849$	3.32977	0.114278
$850$	6.36742	0.218401
$851$	−32.3559	−1.10915
$852$	4.36538	0.149556
$853$	−9.19212	−0.314732	−0.157366	−	0.987540i	$-0.550300\pi$
$853$	−9.19212	−0.314732	−0.157366	+	0.987540i	$0.550300\pi$
$854$	37.2496	1.27465
$855$	10.4698	0.358060
$856$	12.2513	0.418739
$857$	7.50427	0.256341	0.128171	−	0.991752i	$-0.459090\pi$
$857$	7.50427	0.256341	0.128171	+	0.991752i	$0.459090\pi$
$858$	17.8594	0.609708
$859$	21.1767	0.722540	0.361270	−	0.932461i	$-0.382343\pi$
$859$	21.1767	0.722540	0.361270	+	0.932461i	$0.382343\pi$
$860$	−3.95875	−0.134992
$861$	54.6067	1.86099
$862$	17.1319	0.583516
$863$	25.8130	0.878685	0.439343	−	0.898320i	$-0.355211\pi$
$863$	25.8130	0.878685	0.439343	+	0.898320i	$0.355211\pi$
$864$	0.333798	0.0113560
$865$	16.7317	0.568894
$866$	5.15670	0.175232
$867$	32.0778	1.08942
$868$	3.90591	0.132575
$869$	28.3021	0.960082
$870$	−27.9752	−0.948449
$871$	7.36218	0.249458
$872$	−4.15513	−0.140710
$873$	−2.86213	−0.0968686
$874$	−17.6377	−0.596604
$875$	42.3598	1.43202
$876$	36.5560	1.23511
$877$	−0.259937	−0.00877745	−0.00438873	−	0.999990i	$-0.501397\pi$
$877$	−0.259937	−0.00877745	−0.00438873	+	0.999990i	$0.501397\pi$
$878$	−11.5932	−0.391251
$879$	−25.5360	−0.861309
$880$	−3.22657	−0.108768
$881$	−25.5311	−0.860164	−0.430082	−	0.902790i	$-0.641515\pi$
$881$	−25.5311	−0.860164	−0.430082	+	0.902790i	$0.641515\pi$
$882$	23.6302	0.795671
$883$	53.2145	1.79081	0.895406	−	0.445251i	$-0.146885\pi$
$883$	53.2145	1.79081	0.895406	+	0.445251i	$0.146885\pi$
$884$	5.79405	0.194875
$885$	15.8513	0.532835
$886$	−1.80221	−0.0605464
$887$	9.22254	0.309663	0.154831	−	0.987941i	$-0.450517\pi$
$887$	9.22254	0.309663	0.154831	+	0.987941i	$0.450517\pi$
$888$	12.4161	0.416658
$889$	28.5666	0.958094
$890$	−9.25563	−0.310250
$891$	−23.1642	−0.776030
$892$	10.6240	0.355718
$893$	26.1841	0.876217
$894$	16.7446	0.560022
$895$	7.91372	0.264527
$896$	3.90591	0.130487
$897$	45.7006	1.52590
$898$	18.1120	0.604406
$899$	−8.82965	−0.294485
$900$	−9.40957	−0.313652
$901$	6.99429	0.233013
$902$	−14.2375	−0.474058
$903$	−28.6092	−0.952056
$904$	−0.295965	−0.00984364
$905$	26.6614	0.886253
$906$	−11.6285	−0.386330
$907$	44.3062	1.47116	0.735581	−	0.677437i	$-0.236909\pi$
$907$	44.3062	1.47116	0.735581	+	0.677437i	$0.236909\pi$
$908$	−9.11783	−0.302586
$909$	−18.9382	−0.628140
$910$	15.2906	0.506877
$911$	−32.2447	−1.06832	−0.534158	−	0.845385i	$-0.679371\pi$
$911$	−32.2447	−1.06832	−0.534158	+	0.845385i	$0.679371\pi$
$912$	6.76822	0.224118
$913$	18.4766	0.611488
$914$	25.9079	0.856959
$915$	30.2154	0.998891
$916$	−15.8905	−0.525037
$917$	−35.6005	−1.17563
$918$	−0.646498	−0.0213376
$919$	−38.7093	−1.27690	−0.638451	−	0.769662i	$-0.720425\pi$
$919$	−38.7093	−1.27690	−0.638451	+	0.769662i	$0.720425\pi$
$920$	−8.25653	−0.272210
$921$	62.1525	2.04799
$922$	6.72073	0.221335
$923$	5.39378	0.177538
$924$	−23.3179	−0.767103
$925$	16.8592	0.554328
$926$	−11.3414	−0.372702
$927$	−18.9134	−0.621196
$928$	−8.82965	−0.289848
$929$	−22.6870	−0.744336	−0.372168	−	0.928165i	$-0.621385\pi$
$929$	−22.6870	−0.744336	−0.372168	+	0.928165i	$0.621385\pi$
$930$	3.16833	0.103894
$931$	−23.0794	−0.756397
$932$	−17.3495	−0.568303
$933$	−27.3775	−0.896300
$934$	−14.5881	−0.477337
$935$	6.24921	0.204371
$936$	−8.56226	−0.279866
$937$	−39.1636	−1.27942	−0.639710	−	0.768617i	$-0.720945\pi$
$937$	−39.1636	−1.27942	−0.639710	+	0.768617i	$0.720945\pi$
$938$	−9.61237	−0.313855
$939$	2.42946	0.0792823
$940$	12.2572	0.399787
$941$	−35.5805	−1.15989	−0.579946	−	0.814655i	$-0.696926\pi$
$941$	−35.5805	−1.15989	−0.579946	+	0.814655i	$0.696926\pi$
$942$	32.3148	1.05287
$943$	−36.4326	−1.18641
$944$	5.00305	0.162835
$945$	−1.70611	−0.0554999
$946$	7.45925	0.242521
$947$	−18.9499	−0.615790	−0.307895	−	0.951420i	$-0.599625\pi$
$947$	−18.9499	−0.615790	−0.307895	+	0.951420i	$0.599625\pi$
$948$	−27.7912	−0.902615
$949$	45.1678	1.46621
$950$	9.19022	0.298170
$951$	34.8934	1.13150
$952$	−7.56495	−0.245182
$953$	−34.9345	−1.13164	−0.565820	−	0.824529i	$-0.691440\pi$
$953$	−34.9345	−1.13164	−0.565820	+	0.824529i	$0.691440\pi$
$954$	−10.3359	−0.334638
$955$	−12.8583	−0.416086
$956$	13.9762	0.452023
$957$	52.7122	1.70394
$958$	27.4533	0.886976
$959$	28.0364	0.905342
$960$	3.16833	0.102257
$961$	1.00000	0.0322581
$962$	15.3411	0.494618
$963$	35.0647	1.12995
$964$	14.7515	0.475115
$965$	1.42340	0.0458210
$966$	−59.6686	−1.91981
$967$	22.9237	0.737177	0.368589	−	0.929593i	$-0.379841\pi$
$967$	22.9237	0.737177	0.368589	+	0.929593i	$0.379841\pi$
$968$	−4.92035	−0.158146
$969$	−13.1087	−0.421111
$970$	1.30859	0.0420161
$971$	25.0752	0.804703	0.402351	−	0.915485i	$-0.368193\pi$
$971$	25.0752	0.804703	0.402351	+	0.915485i	$0.368193\pi$
$972$	21.7446	0.697460
$973$	−67.9022	−2.17684
$974$	1.51400	0.0485117
$975$	−23.8125	−0.762612
$976$	9.53671	0.305263
$977$	23.4560	0.750423	0.375211	−	0.926939i	$-0.377570\pi$
$977$	23.4560	0.750423	0.375211	+	0.926939i	$0.377570\pi$
$978$	16.0624	0.513619
$979$	17.4399	0.557381
$980$	−10.8039	−0.345118
$981$	−11.8925	−0.379699
$982$	−41.4835	−1.32379
$983$	−23.8828	−0.761744	−0.380872	−	0.924628i	$-0.624376\pi$
$983$	−23.8828	−0.761744	−0.380872	+	0.924628i	$0.624376\pi$
$984$	13.9805	0.445682
$985$	15.2149	0.484787
$986$	17.1012	0.544614
$987$	88.5811	2.81957
$988$	8.36267	0.266052
$989$	19.0876	0.606950
$990$	−9.23489	−0.293504
$991$	22.0116	0.699221	0.349610	−	0.936895i	$-0.386314\pi$
$991$	22.0116	0.699221	0.349610	+	0.936895i	$0.386314\pi$
$992$	1.00000	0.0317500
$993$	−38.2579	−1.21408
$994$	−7.04234	−0.223370
$995$	19.4469	0.616507
$996$	−18.1431	−0.574886
$997$	−4.32534	−0.136985	−0.0684925	−	0.997652i	$-0.521819\pi$
$997$	−4.32534	−0.136985	−0.0684925	+	0.997652i	$0.521819\pi$
$998$	−20.7259	−0.656066
$999$	−1.71176	−0.0541575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.4	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.4	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.42118 q^{3} +1.00000 q^{4} -1.30859 q^{5} -2.42118 q^{6} +3.90591 q^{7} +1.00000 q^{8} +2.86213 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.42118 q^{3} +1.00000 q^{4} -1.30859 q^{5} -2.42118 q^{6} +3.90591 q^{7} +1.00000 q^{8} +2.86213 q^{9} -1.30859 q^{10} +2.46570 q^{11} -2.42118 q^{12} -2.99157 q^{13} +3.90591 q^{14} +3.16833 q^{15} +1.00000 q^{16} -1.93680 q^{17} +2.86213 q^{18} -2.79542 q^{19} -1.30859 q^{20} -9.45694 q^{21} +2.46570 q^{22} +6.30951 q^{23} -2.42118 q^{24} -3.28760 q^{25} -2.99157 q^{26} +0.333798 q^{27} +3.90591 q^{28} -8.82965 q^{29} +3.16833 q^{30} +1.00000 q^{31} +1.00000 q^{32} -5.96990 q^{33} -1.93680 q^{34} -5.11122 q^{35} +2.86213 q^{36} -5.12812 q^{37} -2.79542 q^{38} +7.24313 q^{39} -1.30859 q^{40} -5.77424 q^{41} -9.45694 q^{42} +3.02521 q^{43} +2.46570 q^{44} -3.74535 q^{45} +6.30951 q^{46} -9.36679 q^{47} -2.42118 q^{48} +8.25616 q^{49} -3.28760 q^{50} +4.68934 q^{51} -2.99157 q^{52} -3.61127 q^{53} +0.333798 q^{54} -3.22657 q^{55} +3.90591 q^{56} +6.76822 q^{57} -8.82965 q^{58} +5.00305 q^{59} +3.16833 q^{60} +9.53671 q^{61} +1.00000 q^{62} +11.1792 q^{63} +1.00000 q^{64} +3.91472 q^{65} -5.96990 q^{66} -2.46098 q^{67} -1.93680 q^{68} -15.2765 q^{69} -5.11122 q^{70} -1.80300 q^{71} +2.86213 q^{72} -15.0984 q^{73} -5.12812 q^{74} +7.95990 q^{75} -2.79542 q^{76} +9.63079 q^{77} +7.24313 q^{78} +11.4783 q^{79} -1.30859 q^{80} -9.39459 q^{81} -5.77424 q^{82} +7.49348 q^{83} -9.45694 q^{84} +2.53446 q^{85} +3.02521 q^{86} +21.3782 q^{87} +2.46570 q^{88} +7.07301 q^{89} -3.74535 q^{90} -11.6848 q^{91} +6.30951 q^{92} -2.42118 q^{93} -9.36679 q^{94} +3.65804 q^{95} -2.42118 q^{96} -1.00000 q^{97} +8.25616 q^{98} +7.05715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

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