LMFDB - Embedded newform 9251.2.a.t.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 $ x^18 - 24x^16 - x^15 + 233x^14 + 24x^13 - 1184x^12 - 207x^11 + 3413x^10 + 820x^9 - 5661x^8 - 1595x^7 + 5262x^6 + 1498x^5 - 2567x^4 - 605x^3 + 583x^2 + 80*x - 41
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.411999$ of defining polynomial
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.411999 q^{2} +0.543925 q^{3} -1.83026 q^{4} +3.13700 q^{5} +0.224097 q^{6} +2.96282 q^{7} -1.57806 q^{8} -2.70415 q^{9} +O(q^{10})$	\(q+0.411999 q^{2} +0.543925 q^{3} -1.83026 q^{4} +3.13700 q^{5} +0.224097 q^{6} +2.96282 q^{7} -1.57806 q^{8} -2.70415 q^{9} +1.29244 q^{10} -1.00000 q^{11} -0.995522 q^{12} -1.21780 q^{13} +1.22068 q^{14} +1.70629 q^{15} +3.01035 q^{16} +4.03897 q^{17} -1.11411 q^{18} -2.02946 q^{19} -5.74151 q^{20} +1.61155 q^{21} -0.411999 q^{22} -7.09606 q^{23} -0.858347 q^{24} +4.84075 q^{25} -0.501731 q^{26} -3.10263 q^{27} -5.42273 q^{28} +0.702990 q^{30} -5.21402 q^{31} +4.39639 q^{32} -0.543925 q^{33} +1.66405 q^{34} +9.29437 q^{35} +4.94928 q^{36} -3.26678 q^{37} -0.836134 q^{38} -0.662390 q^{39} -4.95038 q^{40} -8.21600 q^{41} +0.663959 q^{42} +11.1376 q^{43} +1.83026 q^{44} -8.48290 q^{45} -2.92357 q^{46} -1.44777 q^{47} +1.63741 q^{48} +1.77833 q^{49} +1.99439 q^{50} +2.19690 q^{51} +2.22888 q^{52} -10.5310 q^{53} -1.27828 q^{54} -3.13700 q^{55} -4.67552 q^{56} -1.10387 q^{57} -13.5139 q^{59} -3.12295 q^{60} +3.52196 q^{61} -2.14817 q^{62} -8.01191 q^{63} -4.20940 q^{64} -3.82023 q^{65} -0.224097 q^{66} -8.52783 q^{67} -7.39236 q^{68} -3.85973 q^{69} +3.82927 q^{70} +6.78795 q^{71} +4.26731 q^{72} +3.97373 q^{73} -1.34591 q^{74} +2.63301 q^{75} +3.71443 q^{76} -2.96282 q^{77} -0.272904 q^{78} -10.6285 q^{79} +9.44347 q^{80} +6.42484 q^{81} -3.38498 q^{82} +15.7311 q^{83} -2.94956 q^{84} +12.6702 q^{85} +4.58868 q^{86} +1.57806 q^{88} +10.9220 q^{89} -3.49495 q^{90} -3.60812 q^{91} +12.9876 q^{92} -2.83604 q^{93} -0.596481 q^{94} -6.36640 q^{95} +2.39130 q^{96} -14.4039 q^{97} +0.732669 q^{98} +2.70415 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.411999	0.291327	0.145664	−	0.989334i	$-0.453468\pi$
$2$	0.411999	0.291327	0.145664	+	0.989334i	$0.453468\pi$
$3$	0.543925	0.314035	0.157018	−	0.987596i	$-0.449812\pi$
$3$	0.543925	0.314035	0.157018	+	0.987596i	$0.449812\pi$
$4$	−1.83026	−0.915128
$5$	3.13700	1.40291	0.701454	−	0.712715i	$-0.252535\pi$
$5$	3.13700	1.40291	0.701454	+	0.712715i	$0.252535\pi$
$6$	0.224097	0.0914870
$7$	2.96282	1.11984	0.559921	−	0.828546i	$-0.310831\pi$
$7$	2.96282	1.11984	0.559921	+	0.828546i	$0.310831\pi$
$8$	−1.57806	−0.557929
$9$	−2.70415	−0.901382
$10$	1.29244	0.408705
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.995522	−0.287383
$13$	−1.21780	−0.337756	−0.168878	−	0.985637i	$-0.554014\pi$
$13$	−1.21780	−0.337756	−0.168878	+	0.985637i	$0.554014\pi$
$14$	1.22068	0.326241
$15$	1.70629	0.440563
$16$	3.01035	0.752588
$17$	4.03897	0.979594	0.489797	−	0.871836i	$-0.337071\pi$
$17$	4.03897	0.979594	0.489797	+	0.871836i	$0.337071\pi$
$18$	−1.11411	−0.262597
$19$	−2.02946	−0.465589	−0.232795	−	0.972526i	$-0.574787\pi$
$19$	−2.02946	−0.465589	−0.232795	+	0.972526i	$0.574787\pi$
$20$	−5.74151	−1.28384
$21$	1.61155	0.351670
$22$	−0.411999	−0.0878385
$23$	−7.09606	−1.47963	−0.739816	−	0.672810i	$-0.765087\pi$
$23$	−7.09606	−1.47963	−0.739816	+	0.672810i	$0.765087\pi$
$24$	−0.858347	−0.175209
$25$	4.84075	0.968151
$26$	−0.501731	−0.0983976
$27$	−3.10263	−0.597101
$28$	−5.42273	−1.02480
$29$	0	0
$29$	0	0
$30$	0.702990	0.128348
$31$	−5.21402	−0.936466	−0.468233	−	0.883605i	$-0.655109\pi$
$31$	−5.21402	−0.936466	−0.468233	+	0.883605i	$0.655109\pi$
$32$	4.39639	0.777179
$33$	−0.543925	−0.0946852
$34$	1.66405	0.285383
$35$	9.29437	1.57104
$36$	4.94928	0.824880
$37$	−3.26678	−0.537055	−0.268527	−	0.963272i	$-0.586537\pi$
$37$	−3.26678	−0.537055	−0.268527	+	0.963272i	$0.586537\pi$
$38$	−0.836134	−0.135639
$39$	−0.662390	−0.106067
$40$	−4.95038	−0.782723
$41$	−8.21600	−1.28312	−0.641561	−	0.767072i	$-0.721713\pi$
$41$	−8.21600	−1.28312	−0.641561	+	0.767072i	$0.721713\pi$
$42$	0.663959	0.102451
$43$	11.1376	1.69847	0.849233	−	0.528018i	$-0.177065\pi$
$43$	11.1376	1.69847	0.849233	+	0.528018i	$0.177065\pi$
$44$	1.83026	0.275922
$45$	−8.48290	−1.26456
$46$	−2.92357	−0.431057
$47$	−1.44777	−0.211179	−0.105590	−	0.994410i	$-0.533673\pi$
$47$	−1.44777	−0.211179	−0.105590	+	0.994410i	$0.533673\pi$
$48$	1.63741	0.236339
$49$	1.77833	0.254047
$50$	1.99439	0.282049
$51$	2.19690	0.307627
$52$	2.22888	0.309090
$53$	−10.5310	−1.44655	−0.723273	−	0.690562i	$-0.757363\pi$
$53$	−10.5310	−1.44655	−0.723273	+	0.690562i	$0.757363\pi$
$54$	−1.27828	−0.173952
$55$	−3.13700	−0.422993
$56$	−4.67552	−0.624793
$57$	−1.10387	−0.146211
$58$	0	0
$59$	−13.5139	−1.75936	−0.879678	−	0.475570i	$-0.842242\pi$
$59$	−13.5139	−1.75936	−0.879678	+	0.475570i	$0.842242\pi$
$60$	−3.12295	−0.403171
$61$	3.52196	0.450941	0.225470	−	0.974250i	$-0.427608\pi$
$61$	3.52196	0.450941	0.225470	+	0.974250i	$0.427608\pi$
$62$	−2.14817	−0.272818
$63$	−8.01191	−1.00941
$64$	−4.20940	−0.526175
$65$	−3.82023	−0.473841
$66$	−0.224097	−0.0275844
$67$	−8.52783	−1.04184	−0.520920	−	0.853605i	$-0.674411\pi$
$67$	−8.52783	−1.04184	−0.520920	+	0.853605i	$0.674411\pi$
$68$	−7.39236	−0.896455
$69$	−3.85973	−0.464656
$70$	3.82927	0.457686
$71$	6.78795	0.805582	0.402791	−	0.915292i	$-0.368040\pi$
$71$	6.78795	0.805582	0.402791	+	0.915292i	$0.368040\pi$
$72$	4.26731	0.502907
$73$	3.97373	0.465089	0.232545	−	0.972586i	$-0.425295\pi$
$73$	3.97373	0.465089	0.232545	+	0.972586i	$0.425295\pi$
$74$	−1.34591	−0.156459
$75$	2.63301	0.304033
$76$	3.71443	0.426074
$77$	−2.96282	−0.337645
$78$	−0.272904	−0.0309003
$79$	−10.6285	−1.19580	−0.597899	−	0.801572i	$-0.703997\pi$
$79$	−10.6285	−1.19580	−0.597899	+	0.801572i	$0.703997\pi$
$80$	9.44347	1.05581
$81$	6.42484	0.713871
$82$	−3.38498	−0.373809
$83$	15.7311	1.72671	0.863357	−	0.504593i	$-0.168358\pi$
$83$	15.7311	1.72671	0.863357	+	0.504593i	$0.168358\pi$
$84$	−2.94956	−0.321823
$85$	12.6702	1.37428
$86$	4.58868	0.494810
$87$	0	0
$88$	1.57806	0.168222
$89$	10.9220	1.15773	0.578866	−	0.815423i	$-0.303495\pi$
$89$	10.9220	1.15773	0.578866	+	0.815423i	$0.303495\pi$
$90$	−3.49495	−0.368400
$91$	−3.60812	−0.378234
$92$	12.9876	1.35405
$93$	−2.83604	−0.294083
$94$	−0.596481	−0.0615223
$95$	−6.36640	−0.653179
$96$	2.39130	0.244061
$97$	−14.4039	−1.46249	−0.731246	−	0.682113i	$-0.761061\pi$
$97$	−14.4039	−1.46249	−0.731246	+	0.682113i	$0.761061\pi$
$98$	0.732669	0.0740108
$99$	2.70415	0.271777
$100$	−8.85982	−0.885982
$101$	9.67986	0.963182	0.481591	−	0.876396i	$-0.340059\pi$
$101$	9.67986	0.963182	0.481591	+	0.876396i	$0.340059\pi$
$102$	0.905119	0.0896202
$103$	−5.33847	−0.526015	−0.263007	−	0.964794i	$-0.584714\pi$
$103$	−5.33847	−0.526015	−0.263007	+	0.964794i	$0.584714\pi$
$104$	1.92176	0.188444
$105$	5.05544	0.493361
$106$	−4.33877	−0.421418
$107$	−8.81966	−0.852629	−0.426314	−	0.904575i	$-0.640188\pi$
$107$	−8.81966	−0.852629	−0.426314	+	0.904575i	$0.640188\pi$
$108$	5.67860	0.546424
$109$	−18.2341	−1.74651	−0.873256	−	0.487263i	$-0.837995\pi$
$109$	−18.2341	−1.74651	−0.873256	+	0.487263i	$0.837995\pi$
$110$	−1.29244	−0.123229
$111$	−1.77688	−0.168654
$112$	8.91915	0.842780
$113$	−11.3824	−1.07076	−0.535381	−	0.844611i	$-0.679832\pi$
$113$	−11.3824	−1.07076	−0.535381	+	0.844611i	$0.679832\pi$
$114$	−0.454794	−0.0425954
$115$	−22.2603	−2.07579
$116$	0	0
$117$	3.29310	0.304447
$118$	−5.56770	−0.512548
$119$	11.9668	1.09699
$120$	−2.69263	−0.245803
$121$	1.00000	0.0909091
$122$	1.45104	0.131371
$123$	−4.46889	−0.402946
$124$	9.54300	0.856987
$125$	−0.499553	−0.0446814
$126$	−3.30090	−0.294067
$127$	14.8619	1.31878	0.659391	−	0.751800i	$-0.270814\pi$
$127$	14.8619	1.31878	0.659391	+	0.751800i	$0.270814\pi$
$128$	−10.5270	−0.930468
$129$	6.05801	0.533378
$130$	−1.57393	−0.138043
$131$	9.86379	0.861803	0.430901	−	0.902399i	$-0.358196\pi$
$131$	9.86379	0.861803	0.430901	+	0.902399i	$0.358196\pi$
$132$	0.995522	0.0866491
$133$	−6.01292	−0.521387
$134$	−3.51346	−0.303517
$135$	−9.73293	−0.837678
$136$	−6.37375	−0.546544
$137$	−7.84445	−0.670196	−0.335098	−	0.942183i	$-0.608769\pi$
$137$	−7.84445	−0.670196	−0.335098	+	0.942183i	$0.608769\pi$
$138$	−1.59020	−0.135367
$139$	−7.54064	−0.639589	−0.319794	−	0.947487i	$-0.603614\pi$
$139$	−7.54064	−0.639589	−0.319794	+	0.947487i	$0.603614\pi$
$140$	−17.0111	−1.43770
$141$	−0.787480	−0.0663177
$142$	2.79663	0.234688
$143$	1.21780	0.101837
$144$	−8.14044	−0.678370
$145$	0	0
$146$	1.63717	0.135493
$147$	0.967277	0.0797797
$148$	5.97904	0.491474
$149$	−2.12686	−0.174239	−0.0871196	−	0.996198i	$-0.527766\pi$
$149$	−2.12686	−0.174239	−0.0871196	+	0.996198i	$0.527766\pi$
$150$	1.08480	0.0885732
$151$	3.22018	0.262055	0.131027	−	0.991379i	$-0.458172\pi$
$151$	3.22018	0.262055	0.131027	+	0.991379i	$0.458172\pi$
$152$	3.20261	0.259766
$153$	−10.9220	−0.882989
$154$	−1.22068	−0.0983652
$155$	−16.3564	−1.31378
$156$	1.21234	0.0970652
$157$	4.34586	0.346837	0.173418	−	0.984848i	$-0.444519\pi$
$157$	4.34586	0.346837	0.173418	+	0.984848i	$0.444519\pi$
$158$	−4.37892	−0.348368
$159$	−5.72808	−0.454266
$160$	13.7915	1.09031
$161$	−21.0244	−1.65695
$162$	2.64703	0.207970
$163$	10.3023	0.806942	0.403471	−	0.914992i	$-0.367804\pi$
$163$	10.3023	0.806942	0.403471	+	0.914992i	$0.367804\pi$
$164$	15.0374	1.17422
$165$	−1.70629	−0.132835
$166$	6.48120	0.503039
$167$	−13.8192	−1.06936	−0.534682	−	0.845053i	$-0.679569\pi$
$167$	−13.8192	−1.06936	−0.534682	+	0.845053i	$0.679569\pi$
$168$	−2.54313	−0.196207
$169$	−11.5170	−0.885921
$170$	5.22013	0.400365
$171$	5.48795	0.419674
$172$	−20.3847	−1.55432
$173$	−10.5487	−0.802000	−0.401000	−	0.916078i	$-0.631337\pi$
$173$	−10.5487	−0.802000	−0.401000	+	0.916078i	$0.631337\pi$
$174$	0	0
$175$	14.3423	1.08418
$176$	−3.01035	−0.226914
$177$	−7.35053	−0.552500
$178$	4.49986	0.337279
$179$	−7.30873	−0.546280	−0.273140	−	0.961974i	$-0.588062\pi$
$179$	−7.30873	−0.546280	−0.273140	+	0.961974i	$0.588062\pi$
$180$	15.5259	1.15723
$181$	7.49726	0.557267	0.278633	−	0.960398i	$-0.410119\pi$
$181$	7.49726	0.557267	0.278633	+	0.960398i	$0.410119\pi$
$182$	−1.48654	−0.110190
$183$	1.91568	0.141611
$184$	11.1980	0.825529
$185$	−10.2479	−0.753438
$186$	−1.16844	−0.0856745
$187$	−4.03897	−0.295359
$188$	2.64980	0.193256
$189$	−9.19254	−0.668659
$190$	−2.62295	−0.190289
$191$	−12.2684	−0.887709	−0.443854	−	0.896099i	$-0.646389\pi$
$191$	−12.2684	−0.887709	−0.443854	+	0.896099i	$0.646389\pi$
$192$	−2.28960	−0.165238
$193$	20.5657	1.48035	0.740175	−	0.672415i	$-0.234743\pi$
$193$	20.5657	1.48035	0.740175	+	0.672415i	$0.234743\pi$
$194$	−5.93438	−0.426064
$195$	−2.07792	−0.148803
$196$	−3.25480	−0.232486
$197$	8.62241	0.614321	0.307161	−	0.951658i	$-0.400621\pi$
$197$	8.62241	0.614321	0.307161	+	0.951658i	$0.400621\pi$
$198$	1.11411	0.0791760
$199$	−19.5226	−1.38392	−0.691960	−	0.721936i	$-0.743252\pi$
$199$	−19.5226	−1.38392	−0.691960	+	0.721936i	$0.743252\pi$
$200$	−7.63901	−0.540160
$201$	−4.63850	−0.327175
$202$	3.98809	0.280601
$203$	0	0
$204$	−4.02089	−0.281518
$205$	−25.7736	−1.80010
$206$	−2.19944	−0.153242
$207$	19.1888	1.33371
$208$	−3.66600	−0.254191
$209$	2.02946	0.140380
$210$	2.08284	0.143729
$211$	9.26059	0.637525	0.318763	−	0.947835i	$-0.396733\pi$
$211$	9.26059	0.637525	0.318763	+	0.947835i	$0.396733\pi$
$212$	19.2745	1.32378
$213$	3.69214	0.252981
$214$	−3.63369	−0.248394
$215$	34.9386	2.38279
$216$	4.89614	0.333140
$217$	−15.4482	−1.04869
$218$	−7.51243	−0.508806
$219$	2.16141	0.146054
$220$	5.74151	0.387093
$221$	−4.91865	−0.330864
$222$	−0.732073	−0.0491335
$223$	9.83278	0.658451	0.329226	−	0.944251i	$-0.393212\pi$
$223$	9.83278	0.658451	0.329226	+	0.944251i	$0.393212\pi$
$224$	13.0257	0.870318
$225$	−13.0901	−0.872674
$226$	−4.68952	−0.311942
$227$	25.9469	1.72216	0.861080	−	0.508470i	$-0.169789\pi$
$227$	25.9469	1.72216	0.861080	+	0.508470i	$0.169789\pi$
$228$	2.02037	0.133802
$229$	−18.6504	−1.23245	−0.616227	−	0.787569i	$-0.711340\pi$
$229$	−18.6504	−1.23245	−0.616227	+	0.787569i	$0.711340\pi$
$230$	−9.17123	−0.604733
$231$	−1.61155	−0.106032
$232$	0	0
$233$	24.3611	1.59595	0.797973	−	0.602693i	$-0.205906\pi$
$233$	24.3611	1.59595	0.797973	+	0.602693i	$0.205906\pi$
$234$	1.35675	0.0886938
$235$	−4.54166	−0.296265
$236$	24.7338	1.61004
$237$	−5.78109	−0.375522
$238$	4.93029	0.319583
$239$	−1.21152	−0.0783666	−0.0391833	−	0.999232i	$-0.512476\pi$
$239$	−1.21152	−0.0783666	−0.0391833	+	0.999232i	$0.512476\pi$
$240$	5.13654	0.331562
$241$	15.3850	0.991033	0.495516	−	0.868599i	$-0.334979\pi$
$241$	15.3850	0.991033	0.495516	+	0.868599i	$0.334979\pi$
$242$	0.411999	0.0264843
$243$	12.8025	0.821282
$244$	−6.44609	−0.412669
$245$	5.57861	0.356404
$246$	−1.84118	−0.117389
$247$	2.47147	0.157256
$248$	8.22805	0.522482
$249$	8.55655	0.542249
$250$	−0.205815	−0.0130169
$251$	6.87088	0.433686	0.216843	−	0.976206i	$-0.430424\pi$
$251$	6.87088	0.433686	0.216843	+	0.976206i	$0.430424\pi$
$252$	14.6639	0.923736
$253$	7.09606	0.446126
$254$	6.12310	0.384197
$255$	6.89166	0.431573
$256$	4.08167	0.255105
$257$	1.33356	0.0831855	0.0415927	−	0.999135i	$-0.486757\pi$
$257$	1.33356	0.0831855	0.0415927	+	0.999135i	$0.486757\pi$
$258$	2.49590	0.155388
$259$	−9.67888	−0.601416
$260$	6.99200	0.433625
$261$	0	0
$262$	4.06387	0.251067
$263$	−14.1043	−0.869710	−0.434855	−	0.900500i	$-0.643200\pi$
$263$	−14.1043	−0.869710	−0.434855	+	0.900500i	$0.643200\pi$
$264$	0.858347	0.0528276
$265$	−33.0358	−2.02937
$266$	−2.47732	−0.151894
$267$	5.94076	0.363569
$268$	15.6081	0.953418
$269$	−29.3546	−1.78978	−0.894891	−	0.446284i	$-0.852747\pi$
$269$	−29.3546	−1.78978	−0.894891	+	0.446284i	$0.852747\pi$
$270$	−4.00996	−0.244038
$271$	−19.5683	−1.18869	−0.594346	−	0.804209i	$-0.702589\pi$
$271$	−19.5683	−1.18869	−0.594346	+	0.804209i	$0.702589\pi$
$272$	12.1587	0.737232
$273$	−1.96255	−0.118779
$274$	−3.23190	−0.195246
$275$	−4.84075	−0.291908
$276$	7.06429	0.425220
$277$	−13.3065	−0.799511	−0.399755	−	0.916622i	$-0.630905\pi$
$277$	−13.3065	−0.799511	−0.399755	+	0.916622i	$0.630905\pi$
$278$	−3.10674	−0.186330
$279$	14.0995	0.844114
$280$	−14.6671	−0.876527
$281$	11.8226	0.705276	0.352638	−	0.935760i	$-0.385285\pi$
$281$	11.8226	0.705276	0.352638	+	0.935760i	$0.385285\pi$
$282$	−0.324441	−0.0193202
$283$	−3.52064	−0.209280	−0.104640	−	0.994510i	$-0.533369\pi$
$283$	−3.52064	−0.209280	−0.104640	+	0.994510i	$0.533369\pi$
$284$	−12.4237	−0.737211
$285$	−3.46284	−0.205121
$286$	0.501731	0.0296680
$287$	−24.3426	−1.43690
$288$	−11.8885	−0.700535
$289$	−0.686709	−0.0403947
$290$	0	0
$291$	−7.83463	−0.459274
$292$	−7.27294	−0.425617
$293$	−10.3558	−0.604990	−0.302495	−	0.953151i	$-0.597820\pi$
$293$	−10.3558	−0.604990	−0.302495	+	0.953151i	$0.597820\pi$
$294$	0.398517	0.0232420
$295$	−42.3930	−2.46821
$296$	5.15517	0.299638
$297$	3.10263	0.180033
$298$	−0.876264	−0.0507606
$299$	8.64157	0.499755
$300$	−4.81908	−0.278230
$301$	32.9987	1.90202
$302$	1.32671	0.0763437
$303$	5.26512	0.302473
$304$	−6.10938	−0.350397
$305$	11.0484	0.632628
$306$	−4.49984	−0.257239
$307$	−14.8970	−0.850217	−0.425108	−	0.905142i	$-0.639764\pi$
$307$	−14.8970	−0.850217	−0.425108	+	0.905142i	$0.639764\pi$
$308$	5.42273	0.308989
$309$	−2.90373	−0.165187
$310$	−6.73881	−0.382739
$311$	−7.94321	−0.450418	−0.225209	−	0.974310i	$-0.572307\pi$
$311$	−7.94321	−0.450418	−0.225209	+	0.974310i	$0.572307\pi$
$312$	1.04529	0.0591781
$313$	11.2280	0.634642	0.317321	−	0.948318i	$-0.397217\pi$
$313$	11.2280	0.634642	0.317321	+	0.948318i	$0.397217\pi$
$314$	1.79049	0.101043
$315$	−25.1333	−1.41610
$316$	19.4528	1.09431
$317$	12.8399	0.721158	0.360579	−	0.932729i	$-0.382579\pi$
$317$	12.8399	0.721158	0.360579	+	0.932729i	$0.382579\pi$
$318$	−2.35996	−0.132340
$319$	0	0
$320$	−13.2049	−0.738175
$321$	−4.79723	−0.267755
$322$	−8.66203	−0.482716
$323$	−8.19692	−0.456089
$324$	−11.7591	−0.653284
$325$	−5.89506	−0.326999
$326$	4.24456	0.235084
$327$	−9.91799	−0.548466
$328$	12.9653	0.715892
$329$	−4.28950	−0.236488
$330$	−0.702990	−0.0386983
$331$	27.4061	1.50638	0.753189	−	0.657804i	$-0.228515\pi$
$331$	27.4061	1.50638	0.753189	+	0.657804i	$0.228515\pi$
$332$	−28.7920	−1.58017
$333$	8.83384	0.484091
$334$	−5.69351	−0.311535
$335$	−26.7518	−1.46161
$336$	4.85135	0.264663
$337$	−6.15770	−0.335431	−0.167716	−	0.985835i	$-0.553639\pi$
$337$	−6.15770	−0.335431	−0.167716	+	0.985835i	$0.553639\pi$
$338$	−4.74498	−0.258093
$339$	−6.19115	−0.336257
$340$	−23.1898	−1.25764
$341$	5.21402	0.282355
$342$	2.26103	0.122262
$343$	−15.4709	−0.835350
$344$	−17.5758	−0.947624
$345$	−12.1080	−0.651870
$346$	−4.34604	−0.233644
$347$	8.11735	0.435762	0.217881	−	0.975975i	$-0.430086\pi$
$347$	8.11735	0.435762	0.217881	+	0.975975i	$0.430086\pi$
$348$	0	0
$349$	−24.4165	−1.30699	−0.653493	−	0.756933i	$-0.726697\pi$
$349$	−24.4165	−1.30699	−0.653493	+	0.756933i	$0.726697\pi$
$350$	5.90901	0.315850
$351$	3.77837	0.201675
$352$	−4.39639	−0.234328
$353$	12.2427	0.651611	0.325806	−	0.945437i	$-0.394364\pi$
$353$	12.2427	0.651611	0.325806	+	0.945437i	$0.394364\pi$
$354$	−3.02841	−0.160958
$355$	21.2938	1.13016
$356$	−19.9901	−1.05947
$357$	6.50902	0.344494
$358$	−3.01119	−0.159146
$359$	15.4027	0.812923	0.406462	−	0.913668i	$-0.366763\pi$
$359$	15.4027	0.812923	0.406462	+	0.913668i	$0.366763\pi$
$360$	13.3865	0.705533
$361$	−14.8813	−0.783227
$362$	3.08886	0.162347
$363$	0.543925	0.0285487
$364$	6.60379	0.346132
$365$	12.4656	0.652478
$366$	0.789259	0.0412552
$367$	−9.76567	−0.509764	−0.254882	−	0.966972i	$-0.582037\pi$
$367$	−9.76567	−0.509764	−0.254882	+	0.966972i	$0.582037\pi$
$368$	−21.3617	−1.11355
$369$	22.2172	1.15658
$370$	−4.22211	−0.219497
$371$	−31.2015	−1.61990
$372$	5.19068	0.269124
$373$	8.14002	0.421474	0.210737	−	0.977543i	$-0.432414\pi$
$373$	8.14002	0.421474	0.210737	+	0.977543i	$0.432414\pi$
$374$	−1.66405	−0.0860461
$375$	−0.271719	−0.0140315
$376$	2.28467	0.117823
$377$	0	0
$378$	−3.78732	−0.194799
$379$	20.7520	1.06596	0.532980	−	0.846128i	$-0.321072\pi$
$379$	20.7520	1.06596	0.532980	+	0.846128i	$0.321072\pi$
$380$	11.6522	0.597743
$381$	8.08377	0.414144
$382$	−5.05456	−0.258614
$383$	−12.2760	−0.627273	−0.313636	−	0.949543i	$-0.601547\pi$
$383$	−12.2760	−0.627273	−0.313636	+	0.949543i	$0.601547\pi$
$384$	−5.72592	−0.292200
$385$	−9.29437	−0.473685
$386$	8.47303	0.431266
$387$	−30.1177	−1.53097
$388$	26.3628	1.33837
$389$	23.7102	1.20215	0.601076	−	0.799192i	$-0.294739\pi$
$389$	23.7102	1.20215	0.601076	+	0.799192i	$0.294739\pi$
$390$	−0.856100	−0.0433503
$391$	−28.6608	−1.44944
$392$	−2.80631	−0.141740
$393$	5.36516	0.270636
$394$	3.55242	0.178968
$395$	−33.3415	−1.67759
$396$	−4.94928	−0.248711
$397$	−30.7141	−1.54150	−0.770749	−	0.637139i	$-0.780118\pi$
$397$	−30.7141	−1.54150	−0.770749	+	0.637139i	$0.780118\pi$
$398$	−8.04328	−0.403173
$399$	−3.27058	−0.163734
$400$	14.5724	0.728619
$401$	0.570169	0.0284729	0.0142364	−	0.999899i	$-0.495468\pi$
$401$	0.570169	0.0284729	0.0142364	+	0.999899i	$0.495468\pi$
$402$	−1.91106	−0.0953149
$403$	6.34962	0.316297
$404$	−17.7166	−0.881435
$405$	20.1547	1.00150
$406$	0	0
$407$	3.26678	0.161928
$408$	−3.46684	−0.171634
$409$	20.2410	1.00085	0.500426	−	0.865779i	$-0.333177\pi$
$409$	20.2410	1.00085	0.500426	+	0.865779i	$0.333177\pi$
$410$	−10.6187	−0.524419
$411$	−4.26679	−0.210465
$412$	9.77077	0.481371
$413$	−40.0392	−1.97020
$414$	7.90576	0.388547
$415$	49.3485	2.42242
$416$	−5.35391	−0.262497
$417$	−4.10154	−0.200853
$418$	0.836134	0.0408967
$419$	0.578579	0.0282655	0.0141327	−	0.999900i	$-0.495501\pi$
$419$	0.578579	0.0282655	0.0141327	+	0.999900i	$0.495501\pi$
$420$	−9.25276	−0.451488
$421$	−14.3891	−0.701282	−0.350641	−	0.936510i	$-0.614036\pi$
$421$	−14.3891	−0.701282	−0.350641	+	0.936510i	$0.614036\pi$
$422$	3.81535	0.185728
$423$	3.91499	0.190353
$424$	16.6186	0.807070
$425$	19.5517	0.948395
$426$	1.52116	0.0737003
$427$	10.4349	0.504982
$428$	16.1422	0.780265
$429$	0.662390	0.0319805
$430$	14.3947	0.694172
$431$	−16.9557	−0.816729	−0.408364	−	0.912819i	$-0.633901\pi$
$431$	−16.9557	−0.816729	−0.408364	+	0.912819i	$0.633901\pi$
$432$	−9.34001	−0.449371
$433$	−34.5351	−1.65965	−0.829826	−	0.558022i	$-0.811561\pi$
$433$	−34.5351	−1.65965	−0.829826	+	0.558022i	$0.811561\pi$
$434$	−6.36466	−0.305513
$435$	0	0
$436$	33.3731	1.59828
$437$	14.4012	0.688901
$438$	0.890498	0.0425496
$439$	11.0535	0.527553	0.263776	−	0.964584i	$-0.415032\pi$
$439$	11.0535	0.527553	0.263776	+	0.964584i	$0.415032\pi$
$440$	4.95038	0.236000
$441$	−4.80886	−0.228993
$442$	−2.02648	−0.0963897
$443$	−3.85956	−0.183373	−0.0916866	−	0.995788i	$-0.529226\pi$
$443$	−3.85956	−0.183373	−0.0916866	+	0.995788i	$0.529226\pi$
$444$	3.25215	0.154340
$445$	34.2624	1.62419
$446$	4.05109	0.191825
$447$	−1.15685	−0.0547172
$448$	−12.4717	−0.589233
$449$	6.79692	0.320766	0.160383	−	0.987055i	$-0.448727\pi$
$449$	6.79692	0.320766	0.160383	+	0.987055i	$0.448727\pi$
$450$	−5.39311	−0.254234
$451$	8.21600	0.386876
$452$	20.8326	0.979885
$453$	1.75154	0.0822944
$454$	10.6901	0.501712
$455$	−11.3187	−0.530627
$456$	1.74198	0.0815756
$457$	5.50468	0.257498	0.128749	−	0.991677i	$-0.458904\pi$
$457$	5.50468	0.257498	0.128749	+	0.991677i	$0.458904\pi$
$458$	−7.68395	−0.359047
$459$	−12.5314	−0.584917
$460$	40.7421	1.89961
$461$	−1.14973	−0.0535482	−0.0267741	−	0.999642i	$-0.508523\pi$
$461$	−1.14973	−0.0535482	−0.0267741	+	0.999642i	$0.508523\pi$
$462$	−0.663959	−0.0308902
$463$	31.4648	1.46229	0.731146	−	0.682221i	$-0.238986\pi$
$463$	31.4648	1.46229	0.731146	+	0.682221i	$0.238986\pi$
$464$	0	0
$465$	−8.89664	−0.412572
$466$	10.0367	0.464942
$467$	28.2577	1.30761	0.653806	−	0.756662i	$-0.273171\pi$
$467$	28.2577	1.30761	0.653806	+	0.756662i	$0.273171\pi$
$468$	−6.02722	−0.278608
$469$	−25.2665	−1.16670
$470$	−1.87116	−0.0863101
$471$	2.36382	0.108919
$472$	21.3257	0.981596
$473$	−11.1376	−0.512107
$474$	−2.38180	−0.109400
$475$	−9.82410	−0.450761
$476$	−21.9023	−1.00389
$477$	28.4774	1.30389
$478$	−0.499144	−0.0228303
$479$	26.7730	1.22329	0.611645	−	0.791133i	$-0.290508\pi$
$479$	26.7730	1.22329	0.611645	+	0.791133i	$0.290508\pi$
$480$	7.50152	0.342396
$481$	3.97827	0.181393
$482$	6.33859	0.288715
$483$	−11.4357	−0.520342
$484$	−1.83026	−0.0831935
$485$	−45.1849	−2.05174
$486$	5.27462	0.239262
$487$	1.41318	0.0640372	0.0320186	−	0.999487i	$-0.489806\pi$
$487$	1.41318	0.0640372	0.0320186	+	0.999487i	$0.489806\pi$
$488$	−5.55787	−0.251593
$489$	5.60370	0.253408
$490$	2.29838	0.103830
$491$	35.0007	1.57956	0.789780	−	0.613390i	$-0.210194\pi$
$491$	35.0007	1.57956	0.789780	+	0.613390i	$0.210194\pi$
$492$	8.17921	0.368747
$493$	0	0
$494$	1.01824	0.0458129
$495$	8.48290	0.381278
$496$	−15.6961	−0.704774
$497$	20.1115	0.902125
$498$	3.52529	0.157972
$499$	−16.2033	−0.725361	−0.362680	−	0.931914i	$-0.618138\pi$
$499$	−16.2033	−0.725361	−0.362680	+	0.931914i	$0.618138\pi$
$500$	0.914310	0.0408892
$501$	−7.51662	−0.335818
$502$	2.83080	0.126345
$503$	−14.4794	−0.645603	−0.322801	−	0.946467i	$-0.604625\pi$
$503$	−14.4794	−0.645603	−0.322801	+	0.946467i	$0.604625\pi$
$504$	12.6433	0.563177
$505$	30.3657	1.35126
$506$	2.92357	0.129969
$507$	−6.26437	−0.278210
$508$	−27.2011	−1.20686
$509$	−38.3636	−1.70044	−0.850219	−	0.526429i	$-0.823530\pi$
$509$	−38.3636	−1.70044	−0.850219	+	0.526429i	$0.823530\pi$
$510$	2.83936	0.125729
$511$	11.7735	0.520827
$512$	22.7357	1.00479
$513$	6.29665	0.278004
$514$	0.549427	0.0242342
$515$	−16.7468	−0.737951
$516$	−11.0877	−0.488110
$517$	1.44777	0.0636730
$518$	−3.98769	−0.175209
$519$	−5.73768	−0.251856
$520$	6.02855	0.264370
$521$	−25.9474	−1.13678	−0.568388	−	0.822761i	$-0.692433\pi$
$521$	−25.9474	−1.13678	−0.568388	+	0.822761i	$0.692433\pi$
$522$	0	0
$523$	−27.1237	−1.18604	−0.593019	−	0.805189i	$-0.702064\pi$
$523$	−27.1237	−1.18604	−0.593019	+	0.805189i	$0.702064\pi$
$524$	−18.0533	−0.788660
$525$	7.80114	0.340470
$526$	−5.81097	−0.253370
$527$	−21.0593	−0.917357
$528$	−1.63741	−0.0712590
$529$	27.3541	1.18931
$530$	−13.6107	−0.591211
$531$	36.5435	1.58585
$532$	11.0052	0.477136
$533$	10.0054	0.433383
$534$	2.44759	0.105917
$535$	−27.6673	−1.19616
$536$	13.4574	0.581273
$537$	−3.97540	−0.171551
$538$	−12.0941	−0.521412
$539$	−1.77833	−0.0765980
$540$	17.8138	0.766583
$541$	45.7285	1.96602	0.983011	−	0.183549i	$-0.0587585\pi$
$541$	45.7285	1.96602	0.983011	+	0.183549i	$0.0587585\pi$
$542$	−8.06214	−0.346298
$543$	4.07795	0.175001
$544$	17.7569	0.761320
$545$	−57.2004	−2.45019
$546$	−0.808567	−0.0346035
$547$	−0.709298	−0.0303274	−0.0151637	−	0.999885i	$-0.504827\pi$
$547$	−0.709298	−0.0303274	−0.0151637	+	0.999885i	$0.504827\pi$
$548$	14.3574	0.613316
$549$	−9.52389	−0.406470
$550$	−1.99439	−0.0850409
$551$	0	0
$552$	6.09089	0.259245
$553$	−31.4903	−1.33910
$554$	−5.48227	−0.232919
$555$	−5.57407	−0.236606
$556$	13.8013	0.585306
$557$	−45.4719	−1.92671	−0.963353	−	0.268236i	$-0.913559\pi$
$557$	−45.4719	−1.92671	−0.963353	+	0.268236i	$0.913559\pi$
$558$	5.80897	0.245913
$559$	−13.5633	−0.573668
$560$	27.9794	1.18234
$561$	−2.19690	−0.0927531
$562$	4.87089	0.205466
$563$	−25.6767	−1.08214	−0.541071	−	0.840977i	$-0.681981\pi$
$563$	−25.6767	−1.08214	−0.541071	+	0.840977i	$0.681981\pi$
$564$	1.44129	0.0606893
$565$	−35.7064	−1.50218
$566$	−1.45050	−0.0609690
$567$	19.0357	0.799423
$568$	−10.7118	−0.449458
$569$	−6.92037	−0.290117	−0.145058	−	0.989423i	$-0.546337\pi$
$569$	−6.92037	−0.290117	−0.145058	+	0.989423i	$0.546337\pi$
$570$	−1.42669	−0.0597574
$571$	−20.7002	−0.866277	−0.433139	−	0.901327i	$-0.642594\pi$
$571$	−20.7002	−0.866277	−0.433139	+	0.901327i	$0.642594\pi$
$572$	−2.22888	−0.0931942
$573$	−6.67308	−0.278772
$574$	−10.0291	−0.418607
$575$	−34.3503	−1.43251
$576$	11.3828	0.474285
$577$	−25.2578	−1.05150	−0.525749	−	0.850640i	$-0.676215\pi$
$577$	−25.2578	−1.05150	−0.525749	+	0.850640i	$0.676215\pi$
$578$	−0.282924	−0.0117681
$579$	11.1862	0.464882
$580$	0	0
$581$	46.6085	1.93365
$582$	−3.22786	−0.133799
$583$	10.5310	0.436150
$584$	−6.27079	−0.259487
$585$	10.3305	0.427112
$586$	−4.26656	−0.176250
$587$	−15.6975	−0.647905	−0.323952	−	0.946073i	$-0.605012\pi$
$587$	−15.6975	−0.647905	−0.323952	+	0.946073i	$0.605012\pi$
$588$	−1.77037	−0.0730086
$589$	10.5816	0.436009
$590$	−17.4659	−0.719058
$591$	4.68994	0.192918
$592$	−9.83415	−0.404181
$593$	22.0988	0.907491	0.453745	−	0.891131i	$-0.350088\pi$
$593$	22.0988	0.907491	0.453745	+	0.891131i	$0.350088\pi$
$594$	1.27828	0.0524484
$595$	37.5397	1.53898
$596$	3.89270	0.159451
$597$	−10.6188	−0.434599
$598$	3.56032	0.145592
$599$	4.85330	0.198301	0.0991503	−	0.995072i	$-0.468388\pi$
$599$	4.85330	0.198301	0.0991503	+	0.995072i	$0.468388\pi$
$600$	−4.15505	−0.169629
$601$	17.7139	0.722567	0.361283	−	0.932456i	$-0.382339\pi$
$601$	17.7139	0.722567	0.361283	+	0.932456i	$0.382339\pi$
$602$	13.5954	0.554109
$603$	23.0605	0.939096
$604$	−5.89376	−0.239814
$605$	3.13700	0.127537
$606$	2.16922	0.0881187
$607$	−25.1617	−1.02128	−0.510641	−	0.859794i	$-0.670592\pi$
$607$	−25.1617	−1.02128	−0.510641	+	0.859794i	$0.670592\pi$
$608$	−8.92228	−0.361846
$609$	0	0
$610$	4.55192	0.184302
$611$	1.76309	0.0713271
$612$	19.9900	0.808048
$613$	−29.5965	−1.19539	−0.597696	−	0.801723i	$-0.703917\pi$
$613$	−29.5965	−1.19539	−0.597696	+	0.801723i	$0.703917\pi$
$614$	−6.13755	−0.247691
$615$	−14.0189	−0.565296
$616$	4.67552	0.188382
$617$	1.59846	0.0643517	0.0321759	−	0.999482i	$-0.489756\pi$
$617$	1.59846	0.0643517	0.0321759	+	0.999482i	$0.489756\pi$
$618$	−1.19633	−0.0481235
$619$	36.1797	1.45419	0.727093	−	0.686539i	$-0.240871\pi$
$619$	36.1797	1.45419	0.727093	+	0.686539i	$0.240871\pi$
$620$	29.9364	1.20227
$621$	22.0164	0.883489
$622$	−3.27259	−0.131219
$623$	32.3600	1.29648
$624$	−1.99403	−0.0798251
$625$	−25.7709	−1.03083
$626$	4.62591	0.184889
$627$	1.10387	0.0440844
$628$	−7.95403	−0.317400
$629$	−13.1944	−0.526096
$630$	−10.3549	−0.412549
$631$	45.1114	1.79586	0.897928	−	0.440141i	$-0.145072\pi$
$631$	45.1114	1.79586	0.897928	+	0.440141i	$0.145072\pi$
$632$	16.7724	0.667170
$633$	5.03707	0.200205
$634$	5.29001	0.210093
$635$	46.6218	1.85013
$636$	10.4839	0.415712
$637$	−2.16564	−0.0858059
$638$	0	0
$639$	−18.3556	−0.726137
$640$	−33.0233	−1.30536
$641$	−20.8623	−0.824013	−0.412007	−	0.911181i	$-0.635172\pi$
$641$	−20.8623	−0.824013	−0.412007	+	0.911181i	$0.635172\pi$
$642$	−1.97645	−0.0780045
$643$	12.1199	0.477964	0.238982	−	0.971024i	$-0.423186\pi$
$643$	12.1199	0.477964	0.238982	+	0.971024i	$0.423186\pi$
$644$	38.4800	1.51633
$645$	19.0040	0.748281
$646$	−3.37712	−0.132871
$647$	−30.1427	−1.18503	−0.592516	−	0.805559i	$-0.701865\pi$
$647$	−30.1427	−1.18503	−0.592516	+	0.805559i	$0.701865\pi$
$648$	−10.1388	−0.398289
$649$	13.5139	0.530466
$650$	−2.42876	−0.0952637
$651$	−8.40268	−0.329327
$652$	−18.8559	−0.738456
$653$	42.5982	1.66700	0.833499	−	0.552521i	$-0.186334\pi$
$653$	42.5982	1.66700	0.833499	+	0.552521i	$0.186334\pi$
$654$	−4.08620	−0.159783
$655$	30.9427	1.20903
$656$	−24.7331	−0.965664
$657$	−10.7455	−0.419223
$658$	−1.76727	−0.0688953
$659$	−37.5224	−1.46166	−0.730832	−	0.682558i	$-0.760868\pi$
$659$	−37.5224	−1.46166	−0.730832	+	0.682558i	$0.760868\pi$
$660$	3.12295	0.121561
$661$	−15.1235	−0.588238	−0.294119	−	0.955769i	$-0.595026\pi$
$661$	−15.1235	−0.588238	−0.294119	+	0.955769i	$0.595026\pi$
$662$	11.2913	0.438849
$663$	−2.67538	−0.103903
$664$	−24.8247	−0.963384
$665$	−18.8625	−0.731458
$666$	3.63953	0.141029
$667$	0	0
$668$	25.2927	0.978605
$669$	5.34829	0.206777
$670$	−11.0217	−0.425806
$671$	−3.52196	−0.135964
$672$	7.08501	0.273310
$673$	−24.7116	−0.952560	−0.476280	−	0.879294i	$-0.658015\pi$
$673$	−24.7116	−0.952560	−0.476280	+	0.879294i	$0.658015\pi$
$674$	−2.53696	−0.0977202
$675$	−15.0191	−0.578084
$676$	21.0790	0.810731
$677$	17.6507	0.678370	0.339185	−	0.940720i	$-0.389849\pi$
$677$	17.6507	0.678370	0.339185	+	0.940720i	$0.389849\pi$
$678$	−2.55075	−0.0979608
$679$	−42.6762	−1.63776
$680$	−19.9944	−0.766751
$681$	14.1132	0.540819
$682$	2.14817	0.0822578
$683$	33.5404	1.28339	0.641694	−	0.766960i	$-0.278232\pi$
$683$	33.5404	1.28339	0.641694	+	0.766960i	$0.278232\pi$
$684$	−10.0444	−0.384055
$685$	−24.6080	−0.940224
$686$	−6.37399	−0.243360
$687$	−10.1444	−0.387034
$688$	33.5281	1.27825
$689$	12.8246	0.488580
$690$	−4.98846	−0.189908
$691$	39.5754	1.50552	0.752760	−	0.658295i	$-0.228722\pi$
$691$	39.5754	1.50552	0.752760	+	0.658295i	$0.228722\pi$
$692$	19.3068	0.733933
$693$	8.01191	0.304347
$694$	3.34434	0.126949
$695$	−23.6550	−0.897284
$696$	0	0
$697$	−33.1842	−1.25694
$698$	−10.0596	−0.380761
$699$	13.2506	0.501183
$700$	−26.2501	−0.992161
$701$	−42.4991	−1.60517	−0.802585	−	0.596538i	$-0.796542\pi$
$701$	−42.4991	−1.60517	−0.802585	+	0.596538i	$0.796542\pi$
$702$	1.55668	0.0587533
$703$	6.62978	0.250047
$704$	4.20940	0.158648
$705$	−2.47032	−0.0930377
$706$	5.04397	0.189832
$707$	28.6797	1.07861
$708$	13.4534	0.505608
$709$	−43.7238	−1.64208	−0.821040	−	0.570871i	$-0.806606\pi$
$709$	−43.7238	−1.64208	−0.821040	+	0.570871i	$0.806606\pi$
$710$	8.77302	0.329246
$711$	28.7409	1.07787
$712$	−17.2356	−0.645932
$713$	36.9990	1.38563
$714$	2.68171	0.100360
$715$	3.82023	0.142868
$716$	13.3768	0.499916
$717$	−0.658975	−0.0246099
$718$	6.34589	0.236827
$719$	−15.1276	−0.564163	−0.282082	−	0.959390i	$-0.591025\pi$
$719$	−15.1276	−0.564163	−0.282082	+	0.959390i	$0.591025\pi$
$720$	−25.5365	−0.951690
$721$	−15.8169	−0.589054
$722$	−6.13108	−0.228175
$723$	8.36827	0.311219
$724$	−13.7219	−0.509971
$725$	0	0
$726$	0.224097	0.00831700
$727$	−28.0066	−1.03871	−0.519355	−	0.854559i	$-0.673828\pi$
$727$	−28.0066	−1.03871	−0.519355	+	0.854559i	$0.673828\pi$
$728$	5.69384	0.211028
$729$	−12.3109	−0.455960
$730$	5.13580	0.190085
$731$	44.9844	1.66381
$732$	−3.50619	−0.129592
$733$	19.0501	0.703630	0.351815	−	0.936069i	$-0.385565\pi$
$733$	19.0501	0.703630	0.351815	+	0.936069i	$0.385565\pi$
$734$	−4.02345	−0.148508
$735$	3.03435	0.111924
$736$	−31.1970	−1.14994
$737$	8.52783	0.314127
$738$	9.15348	0.336944
$739$	41.8225	1.53846	0.769232	−	0.638970i	$-0.220639\pi$
$739$	41.8225	1.53846	0.769232	+	0.638970i	$0.220639\pi$
$740$	18.7562	0.689493
$741$	1.34429	0.0493838
$742$	−12.8550	−0.471922
$743$	34.7839	1.27610	0.638049	−	0.769995i	$-0.279742\pi$
$743$	34.7839	1.27610	0.638049	+	0.769995i	$0.279742\pi$
$744$	4.47544	0.164078
$745$	−6.67195	−0.244441
$746$	3.35368	0.122787
$747$	−42.5392	−1.55643
$748$	7.39236	0.270291
$749$	−26.1311	−0.954810
$750$	−0.111948	−0.00408777
$751$	40.1240	1.46414	0.732072	−	0.681227i	$-0.238553\pi$
$751$	40.1240	1.46414	0.732072	+	0.681227i	$0.238553\pi$
$752$	−4.35831	−0.158931
$753$	3.73724	0.136193
$754$	0	0
$755$	10.1017	0.367639
$756$	16.8247	0.611909
$757$	−25.5278	−0.927822	−0.463911	−	0.885882i	$-0.653554\pi$
$757$	−25.5278	−0.927822	−0.463911	+	0.885882i	$0.653554\pi$
$758$	8.54981	0.310543
$759$	3.85973	0.140099
$760$	10.0466	0.364428
$761$	−32.7259	−1.18631	−0.593156	−	0.805088i	$-0.702118\pi$
$761$	−32.7259	−1.18631	−0.593156	+	0.805088i	$0.702118\pi$
$762$	3.33051	0.120651
$763$	−54.0245	−1.95582
$764$	22.4543	0.812368
$765$	−34.2622	−1.23875
$766$	−5.05769	−0.182742
$767$	16.4571	0.594233
$768$	2.22012	0.0801118
$769$	−48.2825	−1.74111	−0.870556	−	0.492069i	$-0.836241\pi$
$769$	−48.2825	−1.74111	−0.870556	+	0.492069i	$0.836241\pi$
$770$	−3.82927	−0.137997
$771$	0.725359	0.0261232
$772$	−37.6405	−1.35471
$773$	−42.5485	−1.53036	−0.765182	−	0.643815i	$-0.777351\pi$
$773$	−42.5485	−1.53036	−0.765182	+	0.643815i	$0.777351\pi$
$774$	−12.4084	−0.446012
$775$	−25.2398	−0.906641
$776$	22.7302	0.815967
$777$	−5.26458	−0.188866
$778$	9.76856	0.350220
$779$	16.6740	0.597408
$780$	3.80312	0.136174
$781$	−6.78795	−0.242892
$782$	−11.8082	−0.422261
$783$	0	0
$784$	5.35340	0.191193
$785$	13.6329	0.486580
$786$	2.21044	0.0788438
$787$	3.53403	0.125974	0.0629872	−	0.998014i	$-0.479937\pi$
$787$	3.53403	0.125974	0.0629872	+	0.998014i	$0.479937\pi$
$788$	−15.7812	−0.562183
$789$	−7.67170	−0.273120
$790$	−13.7367	−0.488729
$791$	−33.7239	−1.19908
$792$	−4.26731	−0.151632
$793$	−4.28903	−0.152308
$794$	−12.6542	−0.449080
$795$	−17.9690	−0.637294
$796$	35.7313	1.26646
$797$	41.1135	1.45632	0.728158	−	0.685409i	$-0.240377\pi$
$797$	41.1135	1.45632	0.728158	+	0.685409i	$0.240377\pi$
$798$	−1.34748	−0.0477001
$799$	−5.84751	−0.206870
$800$	21.2818	0.752426
$801$	−29.5347	−1.04356
$802$	0.234909	0.00829492
$803$	−3.97373	−0.140230
$804$	8.48965	0.299407
$805$	−65.9535	−2.32455
$806$	2.61604	0.0921460
$807$	−15.9667	−0.562055
$808$	−15.2754	−0.537387
$809$	−16.0619	−0.564705	−0.282353	−	0.959311i	$-0.591115\pi$
$809$	−16.0619	−0.564705	−0.282353	+	0.959311i	$0.591115\pi$
$810$	8.30372	0.291763
$811$	−25.4303	−0.892979	−0.446490	−	0.894789i	$-0.647326\pi$
$811$	−25.4303	−0.892979	−0.446490	+	0.894789i	$0.647326\pi$
$812$	0	0
$813$	−10.6437	−0.373291
$814$	1.34591	0.0471740
$815$	32.3184	1.13207
$816$	6.61344	0.231517
$817$	−22.6033	−0.790788
$818$	8.33927	0.291576
$819$	9.75688	0.340933
$820$	47.1722	1.64733
$821$	−8.32320	−0.290482	−0.145241	−	0.989396i	$-0.546396\pi$
$821$	−8.32320	−0.290482	−0.145241	+	0.989396i	$0.546396\pi$
$822$	−1.75791	−0.0613143
$823$	−36.3317	−1.26644	−0.633221	−	0.773971i	$-0.718268\pi$
$823$	−36.3317	−1.26644	−0.633221	+	0.773971i	$0.718268\pi$
$824$	8.42443	0.293479
$825$	−2.63301	−0.0916695
$826$	−16.4961	−0.573973
$827$	−37.9666	−1.32023	−0.660114	−	0.751166i	$-0.729492\pi$
$827$	−37.9666	−1.32023	−0.660114	+	0.751166i	$0.729492\pi$
$828$	−35.1204	−1.22052
$829$	−43.5691	−1.51322	−0.756608	−	0.653868i	$-0.773145\pi$
$829$	−43.5691	−1.51322	−0.756608	+	0.653868i	$0.773145\pi$
$830$	20.3315	0.705717
$831$	−7.23775	−0.251075
$832$	5.12620	0.177719
$833$	7.18262	0.248863
$834$	−1.68983	−0.0585141
$835$	−43.3509	−1.50022
$836$	−3.71443	−0.128466
$837$	16.1772	0.559165
$838$	0.238374	0.00823450
$839$	12.3487	0.426325	0.213163	−	0.977017i	$-0.431624\pi$
$839$	12.3487	0.426325	0.213163	+	0.977017i	$0.431624\pi$
$840$	−7.97780	−0.275260
$841$	0	0
$842$	−5.92829	−0.204302
$843$	6.43060	0.221482
$844$	−16.9493	−0.583417
$845$	−36.1287	−1.24287
$846$	1.61297	0.0554551
$847$	2.96282	0.101804
$848$	−31.7021	−1.08865
$849$	−1.91496	−0.0657213
$850$	8.05527	0.276293
$851$	23.1812	0.794643
$852$	−6.75756	−0.231510
$853$	48.8095	1.67120	0.835602	−	0.549335i	$-0.185119\pi$
$853$	48.8095	1.67120	0.835602	+	0.549335i	$0.185119\pi$
$854$	4.29919	0.147115
$855$	17.2157	0.588764
$856$	13.9180	0.475706
$857$	10.1182	0.345630	0.172815	−	0.984954i	$-0.444714\pi$
$857$	10.1182	0.345630	0.172815	+	0.984954i	$0.444714\pi$
$858$	0.272904	0.00931679
$859$	−35.3513	−1.20617	−0.603085	−	0.797677i	$-0.706062\pi$
$859$	−35.3513	−1.20617	−0.603085	+	0.797677i	$0.706062\pi$
$860$	−63.9466	−2.18056
$861$	−13.2405	−0.451236
$862$	−6.98574	−0.237935
$863$	−27.2397	−0.927251	−0.463625	−	0.886031i	$-0.653452\pi$
$863$	−27.2397	−0.927251	−0.463625	+	0.886031i	$0.653452\pi$
$864$	−13.6403	−0.464054
$865$	−33.0911	−1.12513
$866$	−14.2284	−0.483502
$867$	−0.373518	−0.0126853
$868$	28.2742	0.959690
$869$	10.6285	0.360546
$870$	0	0
$871$	10.3852	0.351888
$872$	28.7746	0.974429
$873$	38.9502	1.31826
$874$	5.93326	0.200696
$875$	−1.48009	−0.0500361
$876$	−3.95593	−0.133659
$877$	28.3836	0.958445	0.479222	−	0.877694i	$-0.340919\pi$
$877$	28.3836	0.958445	0.479222	+	0.877694i	$0.340919\pi$
$878$	4.55401	0.153690
$879$	−5.63276	−0.189988
$880$	−9.44347	−0.318339
$881$	17.0237	0.573543	0.286772	−	0.957999i	$-0.407418\pi$
$881$	17.0237	0.573543	0.286772	+	0.957999i	$0.407418\pi$
$882$	−1.98124	−0.0667120
$883$	17.7905	0.598698	0.299349	−	0.954144i	$-0.403231\pi$
$883$	17.7905	0.598698	0.299349	+	0.954144i	$0.403231\pi$
$884$	9.00239	0.302783
$885$	−23.0586	−0.775106
$886$	−1.59013	−0.0534216
$887$	−6.70117	−0.225003	−0.112502	−	0.993652i	$-0.535886\pi$
$887$	−6.70117	−0.225003	−0.112502	+	0.993652i	$0.535886\pi$
$888$	2.80403	0.0940970
$889$	44.0333	1.47683
$890$	14.1161	0.473171
$891$	−6.42484	−0.215240
$892$	−17.9965	−0.602568
$893$	2.93819	0.0983228
$894$	−0.476622	−0.0159406
$895$	−22.9275	−0.766380
$896$	−31.1898	−1.04198
$897$	4.70036	0.156941
$898$	2.80032	0.0934480
$899$	0	0
$900$	23.9583	0.798608
$901$	−42.5345	−1.41703
$902$	3.38498	0.112708
$903$	17.9488	0.597300
$904$	17.9621	0.597409
$905$	23.5189	0.781794
$906$	0.721631	0.0239746
$907$	19.7558	0.655981	0.327991	−	0.944681i	$-0.393629\pi$
$907$	19.7558	0.655981	0.327991	+	0.944681i	$0.393629\pi$
$908$	−47.4896	−1.57600
$909$	−26.1757	−0.868195
$910$	−4.66328	−0.154586
$911$	−29.4539	−0.975852	−0.487926	−	0.872885i	$-0.662246\pi$
$911$	−29.4539	−0.975852	−0.487926	+	0.872885i	$0.662246\pi$
$912$	−3.32305	−0.110037
$913$	−15.7311	−0.520624
$914$	2.26792	0.0750161
$915$	6.00949	0.198668
$916$	34.1350	1.12785
$917$	29.2247	0.965083
$918$	−5.16293	−0.170402
$919$	−43.8891	−1.44777	−0.723883	−	0.689922i	$-0.757645\pi$
$919$	−43.8891	−1.44777	−0.723883	+	0.689922i	$0.757645\pi$
$920$	35.1282	1.15814
$921$	−8.10285	−0.266998
$922$	−0.473687	−0.0156001
$923$	−8.26635	−0.272090
$924$	2.94956	0.0970333
$925$	−15.8137	−0.519950
$926$	12.9634	0.426005
$927$	14.4360	0.474140
$928$	0	0
$929$	−7.18387	−0.235695	−0.117848	−	0.993032i	$-0.537599\pi$
$929$	−7.18387	−0.235695	−0.117848	+	0.993032i	$0.537599\pi$
$930$	−3.66541	−0.120193
$931$	−3.60904	−0.118282
$932$	−44.5870	−1.46050
$933$	−4.32051	−0.141447
$934$	11.6422	0.380943
$935$	−12.6702	−0.414361
$936$	−5.19672	−0.169860
$937$	35.2285	1.15086	0.575432	−	0.817849i	$-0.304834\pi$
$937$	35.2285	1.15086	0.575432	+	0.817849i	$0.304834\pi$
$938$	−10.4098	−0.339891
$939$	6.10717	0.199300
$940$	8.31240	0.271121
$941$	56.0567	1.82740	0.913699	−	0.406393i	$-0.133213\pi$
$941$	56.0567	1.82740	0.913699	+	0.406393i	$0.133213\pi$
$942$	0.973891	0.0317311
$943$	58.3012	1.89855
$944$	−40.6815	−1.32407
$945$	−28.8370	−0.938067
$946$	−4.58868	−0.149191
$947$	−11.5566	−0.375539	−0.187769	−	0.982213i	$-0.560126\pi$
$947$	−11.5566	−0.375539	−0.187769	+	0.982213i	$0.560126\pi$
$948$	10.5809	0.343651
$949$	−4.83919	−0.157087
$950$	−4.04752	−0.131319
$951$	6.98392	0.226469
$952$	−18.8843	−0.612043
$953$	39.1378	1.26780	0.633899	−	0.773416i	$-0.281453\pi$
$953$	39.1378	1.26780	0.633899	+	0.773416i	$0.281453\pi$
$954$	11.7327	0.379859
$955$	−38.4859	−1.24537
$956$	2.21739	0.0717155
$957$	0	0
$958$	11.0304	0.356377
$959$	−23.2417	−0.750514
$960$	−7.18247	−0.231813
$961$	−3.81395	−0.123031
$962$	1.63904	0.0528449
$963$	23.8496	0.768544
$964$	−28.1584	−0.906922
$965$	64.5145	2.07679
$966$	−4.71149	−0.151590
$967$	−34.2020	−1.09986	−0.549931	−	0.835210i	$-0.685346\pi$
$967$	−34.2020	−1.09986	−0.549931	+	0.835210i	$0.685346\pi$
$968$	−1.57806	−0.0507208
$969$	−4.45851	−0.143228
$970$	−18.6162	−0.597729
$971$	23.2462	0.746007	0.373004	−	0.927830i	$-0.378328\pi$
$971$	23.2462	0.746007	0.373004	+	0.927830i	$0.378328\pi$
$972$	−23.4319	−0.751578
$973$	−22.3416	−0.716239
$974$	0.582228	0.0186558
$975$	−3.20647	−0.102689
$976$	10.6023	0.339373
$977$	−11.8500	−0.379115	−0.189558	−	0.981870i	$-0.560705\pi$
$977$	−11.8500	−0.379115	−0.189558	+	0.981870i	$0.560705\pi$
$978$	2.30872	0.0738247
$979$	−10.9220	−0.349069
$980$	−10.2103	−0.326156
$981$	49.3077	1.57427
$982$	14.4203	0.460169
$983$	−9.31575	−0.297126	−0.148563	−	0.988903i	$-0.547465\pi$
$983$	−9.31575	−0.297126	−0.148563	+	0.988903i	$0.547465\pi$
$984$	7.05218	0.224815
$985$	27.0485	0.861836
$986$	0	0
$987$	−2.33316	−0.0742654
$988$	−4.52342	−0.143909
$989$	−79.0330	−2.51310
$990$	3.49495	0.111077
$991$	30.2814	0.961919	0.480960	−	0.876743i	$-0.340288\pi$
$991$	30.2814	0.961919	0.480960	+	0.876743i	$0.340288\pi$
$992$	−22.9229	−0.727802
$993$	14.9069	0.473056
$994$	8.28592	0.262813
$995$	−61.2423	−1.94151
$996$	−15.6607	−0.496228
$997$	15.4607	0.489644	0.244822	−	0.969568i	$-0.421270\pi$
$997$	15.4607	0.489644	0.244822	+	0.969568i	$0.421270\pi$
$998$	−6.67576	−0.211317
$999$	10.1356	0.320676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.10	yes	18
29.28	even	2		9251.2.a.s.1.9	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.9	✓	18	29.28	even	2
9251.2.a.t.1.10	yes	18	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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q+0.411999 q^{2} +0.543925 q^{3} -1.83026 q^{4} +3.13700 q^{5} +0.224097 q^{6} +2.96282 q^{7} -1.57806 q^{8} -2.70415 q^{9} +O(q^{10})\)	\(q+0.411999 q^{2} +0.543925 q^{3} -1.83026 q^{4} +3.13700 q^{5} +0.224097 q^{6} +2.96282 q^{7} -1.57806 q^{8} -2.70415 q^{9} +1.29244 q^{10} -1.00000 q^{11} -0.995522 q^{12} -1.21780 q^{13} +1.22068 q^{14} +1.70629 q^{15} +3.01035 q^{16} +4.03897 q^{17} -1.11411 q^{18} -2.02946 q^{19} -5.74151 q^{20} +1.61155 q^{21} -0.411999 q^{22} -7.09606 q^{23} -0.858347 q^{24} +4.84075 q^{25} -0.501731 q^{26} -3.10263 q^{27} -5.42273 q^{28} +0.702990 q^{30} -5.21402 q^{31} +4.39639 q^{32} -0.543925 q^{33} +1.66405 q^{34} +9.29437 q^{35} +4.94928 q^{36} -3.26678 q^{37} -0.836134 q^{38} -0.662390 q^{39} -4.95038 q^{40} -8.21600 q^{41} +0.663959 q^{42} +11.1376 q^{43} +1.83026 q^{44} -8.48290 q^{45} -2.92357 q^{46} -1.44777 q^{47} +1.63741 q^{48} +1.77833 q^{49} +1.99439 q^{50} +2.19690 q^{51} +2.22888 q^{52} -10.5310 q^{53} -1.27828 q^{54} -3.13700 q^{55} -4.67552 q^{56} -1.10387 q^{57} -13.5139 q^{59} -3.12295 q^{60} +3.52196 q^{61} -2.14817 q^{62} -8.01191 q^{63} -4.20940 q^{64} -3.82023 q^{65} -0.224097 q^{66} -8.52783 q^{67} -7.39236 q^{68} -3.85973 q^{69} +3.82927 q^{70} +6.78795 q^{71} +4.26731 q^{72} +3.97373 q^{73} -1.34591 q^{74} +2.63301 q^{75} +3.71443 q^{76} -2.96282 q^{77} -0.272904 q^{78} -10.6285 q^{79} +9.44347 q^{80} +6.42484 q^{81} -3.38498 q^{82} +15.7311 q^{83} -2.94956 q^{84} +12.6702 q^{85} +4.58868 q^{86} +1.57806 q^{88} +10.9220 q^{89} -3.49495 q^{90} -3.60812 q^{91} +12.9876 q^{92} -2.83604 q^{93} -0.596481 q^{94} -6.36640 q^{95} +2.39130 q^{96} -14.4039 q^{97} +0.732669 q^{98} +2.70415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

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