LMFDB - Embedded newform 9251.2.a.t.1.14

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			1.14
Root			$-1.38880$ 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)

$f(q)$	$=$	$q+1.38880 q^{2} -3.17723 q^{3} -0.0712392 q^{4} -2.70517 q^{5} -4.41253 q^{6} -4.98785 q^{7} -2.87653 q^{8} +7.09477 q^{9} +O(q^{10})$	\(q+1.38880 q^{2} -3.17723 q^{3} -0.0712392 q^{4} -2.70517 q^{5} -4.41253 q^{6} -4.98785 q^{7} -2.87653 q^{8} +7.09477 q^{9} -3.75694 q^{10} -1.00000 q^{11} +0.226343 q^{12} -2.39272 q^{13} -6.92712 q^{14} +8.59495 q^{15} -3.85245 q^{16} -3.80406 q^{17} +9.85320 q^{18} -1.92540 q^{19} +0.192714 q^{20} +15.8475 q^{21} -1.38880 q^{22} -1.07964 q^{23} +9.13940 q^{24} +2.31797 q^{25} -3.32301 q^{26} -13.0100 q^{27} +0.355330 q^{28} +11.9367 q^{30} +1.59630 q^{31} +0.402796 q^{32} +3.17723 q^{33} -5.28307 q^{34} +13.4930 q^{35} -0.505425 q^{36} +0.558952 q^{37} -2.67399 q^{38} +7.60223 q^{39} +7.78152 q^{40} -10.5893 q^{41} +22.0090 q^{42} +7.74546 q^{43} +0.0712392 q^{44} -19.1926 q^{45} -1.49940 q^{46} +10.7277 q^{47} +12.2401 q^{48} +17.8786 q^{49} +3.21919 q^{50} +12.0864 q^{51} +0.170456 q^{52} +1.36455 q^{53} -18.0683 q^{54} +2.70517 q^{55} +14.3477 q^{56} +6.11743 q^{57} -11.5782 q^{59} -0.612297 q^{60} -12.4228 q^{61} +2.21693 q^{62} -35.3876 q^{63} +8.26430 q^{64} +6.47274 q^{65} +4.41253 q^{66} +15.6209 q^{67} +0.270998 q^{68} +3.43026 q^{69} +18.7391 q^{70} +4.55460 q^{71} -20.4083 q^{72} -4.77900 q^{73} +0.776271 q^{74} -7.36470 q^{75} +0.137164 q^{76} +4.98785 q^{77} +10.5580 q^{78} -3.02972 q^{79} +10.4215 q^{80} +20.0514 q^{81} -14.7064 q^{82} +7.00720 q^{83} -1.12896 q^{84} +10.2906 q^{85} +10.7569 q^{86} +2.87653 q^{88} +13.7390 q^{89} -26.6546 q^{90} +11.9345 q^{91} +0.0769126 q^{92} -5.07179 q^{93} +14.8987 q^{94} +5.20854 q^{95} -1.27977 q^{96} +2.83082 q^{97} +24.8298 q^{98} -7.09477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.38880	0.982029	0.491014	−	0.871151i	$-0.336626\pi$
$2$	1.38880	0.982029	0.491014	+	0.871151i	$0.336626\pi$
$3$	−3.17723	−1.83437	−0.917186	−	0.398459i	$-0.869545\pi$
$3$	−3.17723	−1.83437	−0.917186	+	0.398459i	$0.869545\pi$
$4$	−0.0712392	−0.0356196
$5$	−2.70517	−1.20979	−0.604895	−	0.796305i	$-0.706785\pi$
$5$	−2.70517	−1.20979	−0.604895	+	0.796305i	$0.706785\pi$
$6$	−4.41253	−1.80141
$7$	−4.98785	−1.88523	−0.942615	−	0.333882i	$-0.891641\pi$
$7$	−4.98785	−1.88523	−0.942615	+	0.333882i	$0.891641\pi$
$8$	−2.87653	−1.01701
$9$	7.09477	2.36492
$10$	−3.75694	−1.18805
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.226343	0.0653396
$13$	−2.39272	−0.663622	−0.331811	−	0.943346i	$-0.607660\pi$
$13$	−2.39272	−0.663622	−0.331811	+	0.943346i	$0.607660\pi$
$14$	−6.92712	−1.85135
$15$	8.59495	2.21921
$16$	−3.85245	−0.963112
$17$	−3.80406	−0.922619	−0.461310	−	0.887239i	$-0.652620\pi$
$17$	−3.80406	−0.922619	−0.461310	+	0.887239i	$0.652620\pi$
$18$	9.85320	2.32242
$19$	−1.92540	−0.441717	−0.220859	−	0.975306i	$-0.570886\pi$
$19$	−1.92540	−0.441717	−0.220859	+	0.975306i	$0.570886\pi$
$20$	0.192714	0.0430922
$21$	15.8475	3.45821
$22$	−1.38880	−0.296093
$23$	−1.07964	−0.225120	−0.112560	−	0.993645i	$-0.535905\pi$
$23$	−1.07964	−0.225120	−0.112560	+	0.993645i	$0.535905\pi$
$24$	9.13940	1.86557
$25$	2.31797	0.463593
$26$	−3.32301	−0.651696
$27$	−13.0100	−2.50378
$28$	0.355330	0.0671511
$29$	0	0
$29$	0	0
$30$	11.9367	2.17932
$31$	1.59630	0.286703	0.143352	−	0.989672i	$-0.454212\pi$
$31$	1.59630	0.286703	0.143352	+	0.989672i	$0.454212\pi$
$32$	0.402796	0.0712049
$33$	3.17723	0.553084
$34$	−5.28307	−0.906039
$35$	13.4930	2.28073
$36$	−0.505425	−0.0842376
$37$	0.558952	0.0918911	0.0459455	−	0.998944i	$-0.485370\pi$
$37$	0.558952	0.0918911	0.0459455	+	0.998944i	$0.485370\pi$
$38$	−2.67399	−0.433779
$39$	7.60223	1.21733
$40$	7.78152	1.23037
$41$	−10.5893	−1.65377	−0.826886	−	0.562370i	$-0.809890\pi$
$41$	−10.5893	−1.65377	−0.826886	+	0.562370i	$0.809890\pi$
$42$	22.0090	3.39606
$43$	7.74546	1.18117	0.590585	−	0.806975i	$-0.298897\pi$
$43$	7.74546	1.18117	0.590585	+	0.806975i	$0.298897\pi$
$44$	0.0712392	0.0107397
$45$	−19.1926	−2.86106
$46$	−1.49940	−0.221075
$47$	10.7277	1.56480	0.782401	−	0.622775i	$-0.213995\pi$
$47$	10.7277	1.56480	0.782401	+	0.622775i	$0.213995\pi$
$48$	12.2401	1.76671
$49$	17.8786	2.55409
$50$	3.21919	0.455262
$51$	12.0864	1.69243
$52$	0.170456	0.0236380
$53$	1.36455	0.187435	0.0937176	−	0.995599i	$-0.470125\pi$
$53$	1.36455	0.187435	0.0937176	+	0.995599i	$0.470125\pi$
$54$	−18.0683	−2.45878
$55$	2.70517	0.364766
$56$	14.3477	1.91729
$57$	6.11743	0.810274
$58$	0	0
$59$	−11.5782	−1.50735	−0.753675	−	0.657247i	$-0.771721\pi$
$59$	−11.5782	−1.50735	−0.753675	+	0.657247i	$0.771721\pi$
$60$	−0.612297	−0.0790472
$61$	−12.4228	−1.59057	−0.795286	−	0.606235i	$-0.792679\pi$
$61$	−12.4228	−1.59057	−0.795286	+	0.606235i	$0.792679\pi$
$62$	2.21693	0.281551
$63$	−35.3876	−4.45842
$64$	8.26430	1.03304
$65$	6.47274	0.802844
$66$	4.41253	0.543144
$67$	15.6209	1.90839	0.954197	−	0.299179i	$-0.0967126\pi$
$67$	15.6209	1.90839	0.954197	+	0.299179i	$0.0967126\pi$
$68$	0.270998	0.0328633
$69$	3.43026	0.412954
$70$	18.7391	2.23975
$71$	4.55460	0.540532	0.270266	−	0.962786i	$-0.412888\pi$
$71$	4.55460	0.540532	0.270266	+	0.962786i	$0.412888\pi$
$72$	−20.4083	−2.40515
$73$	−4.77900	−0.559339	−0.279670	−	0.960096i	$-0.590225\pi$
$73$	−4.77900	−0.559339	−0.279670	+	0.960096i	$0.590225\pi$
$74$	0.776271	0.0902397
$75$	−7.36470	−0.850402
$76$	0.137164	0.0157338
$77$	4.98785	0.568418
$78$	10.5580	1.19545
$79$	−3.02972	−0.340870	−0.170435	−	0.985369i	$-0.554517\pi$
$79$	−3.02972	−0.340870	−0.170435	+	0.985369i	$0.554517\pi$
$80$	10.4215	1.16516
$81$	20.0514	2.22793
$82$	−14.7064	−1.62405
$83$	7.00720	0.769140	0.384570	−	0.923096i	$-0.374350\pi$
$83$	7.00720	0.769140	0.384570	+	0.923096i	$0.374350\pi$
$84$	−1.12896	−0.123180
$85$	10.2906	1.11618
$86$	10.7569	1.15994
$87$	0	0
$88$	2.87653	0.306640
$89$	13.7390	1.45633	0.728165	−	0.685402i	$-0.240374\pi$
$89$	13.7390	1.45633	0.728165	+	0.685402i	$0.240374\pi$
$90$	−26.6546	−2.80964
$91$	11.9345	1.25108
$92$	0.0769126	0.00801869
$93$	−5.07179	−0.525921
$94$	14.8987	1.53668
$95$	5.20854	0.534385
$96$	−1.27977	−0.130616
$97$	2.83082	0.287426	0.143713	−	0.989619i	$-0.454096\pi$
$97$	2.83082	0.287426	0.143713	+	0.989619i	$0.454096\pi$
$98$	24.8298	2.50819
$99$	−7.09477	−0.713051
$100$	−0.165130	−0.0165130
$101$	5.05718	0.503208	0.251604	−	0.967830i	$-0.419042\pi$
$101$	5.05718	0.503208	0.251604	+	0.967830i	$0.419042\pi$
$102$	16.7855	1.66201
$103$	−0.230613	−0.0227229	−0.0113615	−	0.999935i	$-0.503617\pi$
$103$	−0.230613	−0.0227229	−0.0113615	+	0.999935i	$0.503617\pi$
$104$	6.88275	0.674909
$105$	−42.8703	−4.18371
$106$	1.89508	0.184067
$107$	−6.82759	−0.660048	−0.330024	−	0.943973i	$-0.607057\pi$
$107$	−6.82759	−0.660048	−0.330024	+	0.943973i	$0.607057\pi$
$108$	0.926822	0.0891834
$109$	−2.38597	−0.228534	−0.114267	−	0.993450i	$-0.536452\pi$
$109$	−2.38597	−0.228534	−0.114267	+	0.993450i	$0.536452\pi$
$110$	3.75694	0.358210
$111$	−1.77592	−0.168562
$112$	19.2154	1.81569
$113$	0.704121	0.0662381	0.0331190	−	0.999451i	$-0.489456\pi$
$113$	0.704121	0.0662381	0.0331190	+	0.999451i	$0.489456\pi$
$114$	8.49588	0.795712
$115$	2.92061	0.272348
$116$	0	0
$117$	−16.9758	−1.56942
$118$	−16.0798	−1.48026
$119$	18.9741	1.73935
$120$	−24.7237	−2.25695
$121$	1.00000	0.0909091
$122$	−17.2527	−1.56199
$123$	33.6446	3.03363
$124$	−0.113719	−0.0102123
$125$	7.25537	0.648940
$126$	−49.1463	−4.37830
$127$	8.32549	0.738768	0.369384	−	0.929277i	$-0.379569\pi$
$127$	8.32549	0.738768	0.369384	+	0.929277i	$0.379569\pi$
$128$	10.6718	0.943267
$129$	−24.6091	−2.16671
$130$	8.98932	0.788416
$131$	−13.3512	−1.16650	−0.583249	−	0.812294i	$-0.698219\pi$
$131$	−13.3512	−1.16650	−0.583249	+	0.812294i	$0.698219\pi$
$132$	−0.226343	−0.0197006
$133$	9.60360	0.832738
$134$	21.6943	1.87410
$135$	35.1943	3.02904
$136$	10.9425	0.938312
$137$	14.4912	1.23807	0.619035	−	0.785363i	$-0.287524\pi$
$137$	14.4912	1.23807	0.619035	+	0.785363i	$0.287524\pi$
$138$	4.76393	0.405533
$139$	−16.7614	−1.42168	−0.710841	−	0.703352i	$-0.751686\pi$
$139$	−16.7614	−1.42168	−0.710841	+	0.703352i	$0.751686\pi$
$140$	−0.961230	−0.0812388
$141$	−34.0845	−2.87043
$142$	6.32542	0.530818
$143$	2.39272	0.200090
$144$	−27.3322	−2.27768
$145$	0	0
$146$	−6.63706	−0.549287
$147$	−56.8045	−4.68515
$148$	−0.0398192	−0.00327312
$149$	−22.4833	−1.84191	−0.920953	−	0.389673i	$-0.872588\pi$
$149$	−22.4833	−1.84191	−0.920953	+	0.389673i	$0.872588\pi$
$150$	−10.2281	−0.835119
$151$	0.380944	0.0310008	0.0155004	−	0.999880i	$-0.495066\pi$
$151$	0.380944	0.0310008	0.0155004	+	0.999880i	$0.495066\pi$
$152$	5.53848	0.449230
$153$	−26.9889	−2.18192
$154$	6.92712	0.558203
$155$	−4.31826	−0.346851
$156$	−0.541576	−0.0433608
$157$	−5.05587	−0.403503	−0.201751	−	0.979437i	$-0.564663\pi$
$157$	−5.05587	−0.403503	−0.201751	+	0.979437i	$0.564663\pi$
$158$	−4.20767	−0.334744
$159$	−4.33548	−0.343826
$160$	−1.08963	−0.0861430
$161$	5.38507	0.424403
$162$	27.8474	2.18790
$163$	−9.06330	−0.709892	−0.354946	−	0.934887i	$-0.615501\pi$
$163$	−9.06330	−0.709892	−0.354946	+	0.934887i	$0.615501\pi$
$164$	0.754374	0.0589067
$165$	−8.59495	−0.669116
$166$	9.73159	0.755318
$167$	−6.09077	−0.471318	−0.235659	−	0.971836i	$-0.575725\pi$
$167$	−6.09077	−0.471318	−0.235659	+	0.971836i	$0.575725\pi$
$168$	−45.5859	−3.51703
$169$	−7.27487	−0.559605
$170$	14.2916	1.09612
$171$	−13.6603	−1.04463
$172$	−0.551780	−0.0420728
$173$	18.9581	1.44136	0.720680	−	0.693268i	$-0.243830\pi$
$173$	18.9581	1.44136	0.720680	+	0.693268i	$0.243830\pi$
$174$	0	0
$175$	−11.5617	−0.873979
$176$	3.85245	0.290389
$177$	36.7865	2.76504
$178$	19.0807	1.43016
$179$	−12.3941	−0.926378	−0.463189	−	0.886260i	$-0.653295\pi$
$179$	−12.3941	−0.926378	−0.463189	+	0.886260i	$0.653295\pi$
$180$	1.36726	0.101910
$181$	−5.57875	−0.414665	−0.207333	−	0.978271i	$-0.566478\pi$
$181$	−5.57875	−0.414665	−0.207333	+	0.978271i	$0.566478\pi$
$182$	16.5747	1.22860
$183$	39.4699	2.91770
$184$	3.10562	0.228949
$185$	−1.51206	−0.111169
$186$	−7.04370	−0.516469
$187$	3.80406	0.278180
$188$	−0.764235	−0.0557376
$189$	64.8919	4.72019
$190$	7.23361	0.524781
$191$	24.8934	1.80122	0.900611	−	0.434626i	$-0.143119\pi$
$191$	24.8934	1.80122	0.900611	+	0.434626i	$0.143119\pi$
$192$	−26.2575	−1.89497
$193$	15.3483	1.10479	0.552397	−	0.833581i	$-0.313713\pi$
$193$	15.3483	1.10479	0.552397	+	0.833581i	$0.313713\pi$
$194$	3.93143	0.282260
$195$	−20.5653	−1.47271
$196$	−1.27366	−0.0909756
$197$	−2.65465	−0.189136	−0.0945680	−	0.995518i	$-0.530147\pi$
$197$	−2.65465	−0.189136	−0.0945680	+	0.995518i	$0.530147\pi$
$198$	−9.85320	−0.700236
$199$	−8.99168	−0.637403	−0.318702	−	0.947855i	$-0.603247\pi$
$199$	−8.99168	−0.637403	−0.318702	+	0.947855i	$0.603247\pi$
$200$	−6.66770	−0.471478
$201$	−49.6311	−3.50071
$202$	7.02340	0.494165
$203$	0	0
$204$	−0.861022	−0.0602836
$205$	28.6459	2.00072
$206$	−0.320274	−0.0223146
$207$	−7.65978	−0.532392
$208$	9.21784	0.639142
$209$	1.92540	0.133183
$210$	−59.5382	−4.10853
$211$	−14.1684	−0.975391	−0.487695	−	0.873014i	$-0.662162\pi$
$211$	−14.1684	−0.975391	−0.487695	+	0.873014i	$0.662162\pi$
$212$	−0.0972093	−0.00667636
$213$	−14.4710	−0.991536
$214$	−9.48215	−0.648186
$215$	−20.9528	−1.42897
$216$	37.4237	2.54636
$217$	−7.96208	−0.540501
$218$	−3.31362	−0.224427
$219$	15.1840	1.02604
$220$	−0.192714	−0.0129928
$221$	9.10206	0.612271
$222$	−2.46639	−0.165533
$223$	−2.47935	−0.166030	−0.0830149	−	0.996548i	$-0.526455\pi$
$223$	−2.47935	−0.166030	−0.0830149	+	0.996548i	$0.526455\pi$
$224$	−2.00908	−0.134238
$225$	16.4454	1.09636
$226$	0.977881	0.0650477
$227$	17.7898	1.18075	0.590376	−	0.807128i	$-0.298979\pi$
$227$	17.7898	1.18075	0.590376	+	0.807128i	$0.298979\pi$
$228$	−0.435801	−0.0288616
$229$	0.171650	0.0113429	0.00567146	−	0.999984i	$-0.498195\pi$
$229$	0.171650	0.0113429	0.00567146	+	0.999984i	$0.498195\pi$
$230$	4.05614	0.267454
$231$	−15.8475	−1.04269
$232$	0	0
$233$	−0.633689	−0.0415144	−0.0207572	−	0.999785i	$-0.506608\pi$
$233$	−0.633689	−0.0415144	−0.0207572	+	0.999785i	$0.506608\pi$
$234$	−23.5760	−1.54121
$235$	−29.0204	−1.89308
$236$	0.824820	0.0536912
$237$	9.62610	0.625282
$238$	26.3511	1.70809
$239$	11.4590	0.741221	0.370611	−	0.928788i	$-0.379148\pi$
$239$	11.4590	0.741221	0.370611	+	0.928788i	$0.379148\pi$
$240$	−33.1116	−2.13734
$241$	−14.9303	−0.961747	−0.480873	−	0.876790i	$-0.659680\pi$
$241$	−14.9303	−0.961747	−0.480873	+	0.876790i	$0.659680\pi$
$242$	1.38880	0.0892753
$243$	−24.6779	−1.58309
$244$	0.884987	0.0566555
$245$	−48.3648	−3.08991
$246$	46.7256	2.97912
$247$	4.60695	0.293133
$248$	−4.59180	−0.291580
$249$	−22.2635	−1.41089
$250$	10.0762	0.637278
$251$	−5.71899	−0.360980	−0.180490	−	0.983577i	$-0.557768\pi$
$251$	−5.71899	−0.360980	−0.180490	+	0.983577i	$0.557768\pi$
$252$	2.52098	0.158807
$253$	1.07964	0.0678763
$254$	11.5624	0.725491
$255$	−32.6957	−2.04748
$256$	−1.70755	−0.106722
$257$	3.07763	0.191977	0.0959886	−	0.995382i	$-0.469399\pi$
$257$	3.07763	0.191977	0.0959886	+	0.995382i	$0.469399\pi$
$258$	−34.1770	−2.12777
$259$	−2.78797	−0.173236
$260$	−0.461112	−0.0285970
$261$	0	0
$262$	−18.5421	−1.14553
$263$	−10.0860	−0.621931	−0.310965	−	0.950421i	$-0.600652\pi$
$263$	−10.0860	−0.621931	−0.310965	+	0.950421i	$0.600652\pi$
$264$	−9.13940	−0.562491
$265$	−3.69134	−0.226757
$266$	13.3375	0.817773
$267$	−43.6519	−2.67145
$268$	−1.11282	−0.0679762
$269$	12.0199	0.732863	0.366432	−	0.930445i	$-0.380579\pi$
$269$	12.0199	0.732863	0.366432	+	0.930445i	$0.380579\pi$
$270$	48.8778	2.97461
$271$	−5.60594	−0.340537	−0.170268	−	0.985398i	$-0.554463\pi$
$271$	−5.60594	−0.340537	−0.170268	+	0.985398i	$0.554463\pi$
$272$	14.6549	0.888586
$273$	−37.9188	−2.29495
$274$	20.1254	1.21582
$275$	−2.31797	−0.139779
$276$	−0.244369	−0.0147093
$277$	26.9959	1.62202	0.811012	−	0.585029i	$-0.198917\pi$
$277$	26.9959	1.62202	0.811012	+	0.585029i	$0.198917\pi$
$278$	−23.2782	−1.39613
$279$	11.3253	0.678031
$280$	−38.8131	−2.31952
$281$	−24.6503	−1.47051	−0.735256	−	0.677789i	$-0.762938\pi$
$281$	−24.6503	−1.47051	−0.735256	+	0.677789i	$0.762938\pi$
$282$	−47.3364	−2.81884
$283$	16.3316	0.970813	0.485406	−	0.874289i	$-0.338672\pi$
$283$	16.3316	0.970813	0.485406	+	0.874289i	$0.338672\pi$
$284$	−0.324466	−0.0192535
$285$	−16.5487	−0.980261
$286$	3.32301	0.196494
$287$	52.8179	3.11774
$288$	2.85774	0.168394
$289$	−2.52915	−0.148773
$290$	0	0
$291$	−8.99414	−0.527246
$292$	0.340452	0.0199234
$293$	−10.9350	−0.638832	−0.319416	−	0.947615i	$-0.603487\pi$
$293$	−10.9350	−0.638832	−0.319416	+	0.947615i	$0.603487\pi$
$294$	−78.8899	−4.60095
$295$	31.3210	1.82358
$296$	−1.60784	−0.0934540
$297$	13.0100	0.754917
$298$	−31.2248	−1.80881
$299$	2.58328	0.149395
$300$	0.524655	0.0302910
$301$	−38.6332	−2.22678
$302$	0.529055	0.0304437
$303$	−16.0678	−0.923070
$304$	7.41750	0.425423
$305$	33.6057	1.92426
$306$	−37.4821	−2.14271
$307$	4.75222	0.271224	0.135612	−	0.990762i	$-0.456700\pi$
$307$	4.75222	0.271224	0.135612	+	0.990762i	$0.456700\pi$
$308$	−0.355330	−0.0202468
$309$	0.732708	0.0416823
$310$	−5.99719	−0.340618
$311$	10.9579	0.621367	0.310683	−	0.950513i	$-0.399442\pi$
$311$	10.9579	0.621367	0.310683	+	0.950513i	$0.399442\pi$
$312$	−21.8681	−1.23804
$313$	−13.7181	−0.775392	−0.387696	−	0.921787i	$-0.626729\pi$
$313$	−13.7181	−0.775392	−0.387696	+	0.921787i	$0.626729\pi$
$314$	−7.02159	−0.396251
$315$	95.7297	5.39376
$316$	0.215835	0.0121416
$317$	19.1329	1.07461	0.537305	−	0.843388i	$-0.319442\pi$
$317$	19.1329	1.07461	0.537305	+	0.843388i	$0.319442\pi$
$318$	−6.02111	−0.337647
$319$	0	0
$320$	−22.3564	−1.24976
$321$	21.6928	1.21077
$322$	7.47878	0.416776
$323$	7.32433	0.407537
$324$	−1.42845	−0.0793581
$325$	−5.54625	−0.307651
$326$	−12.5871	−0.697135
$327$	7.58075	0.419217
$328$	30.4605	1.68190
$329$	−53.5083	−2.95001
$330$	−11.9367	−0.657091
$331$	26.5038	1.45678	0.728390	−	0.685163i	$-0.240269\pi$
$331$	26.5038	1.45678	0.728390	+	0.685163i	$0.240269\pi$
$332$	−0.499187	−0.0273965
$333$	3.96563	0.217315
$334$	−8.45885	−0.462848
$335$	−42.2572	−2.30876
$336$	−61.0517	−3.33065
$337$	−17.2119	−0.937593	−0.468796	−	0.883306i	$-0.655312\pi$
$337$	−17.2119	−0.937593	−0.468796	+	0.883306i	$0.655312\pi$
$338$	−10.1033	−0.549549
$339$	−2.23715	−0.121505
$340$	−0.733096	−0.0397577
$341$	−1.59630	−0.0864443
$342$	−18.9713	−1.02585
$343$	−54.2610	−2.92982
$344$	−22.2801	−1.20126
$345$	−9.27944	−0.499588
$346$	26.3290	1.41546
$347$	−16.8442	−0.904245	−0.452123	−	0.891956i	$-0.649333\pi$
$347$	−16.8442	−0.904245	−0.452123	+	0.891956i	$0.649333\pi$
$348$	0	0
$349$	1.51277	0.0809765	0.0404882	−	0.999180i	$-0.487109\pi$
$349$	1.51277	0.0809765	0.0404882	+	0.999180i	$0.487109\pi$
$350$	−16.0568	−0.858273
$351$	31.1293	1.66156
$352$	−0.402796	−0.0214691
$353$	−20.4550	−1.08871	−0.544356	−	0.838855i	$-0.683226\pi$
$353$	−20.4550	−1.08871	−0.544356	+	0.838855i	$0.683226\pi$
$354$	51.0890	2.71535
$355$	−12.3210	−0.653930
$356$	−0.978754	−0.0518739
$357$	−60.2849	−3.19061
$358$	−17.2129	−0.909730
$359$	−1.27692	−0.0673932	−0.0336966	−	0.999432i	$-0.510728\pi$
$359$	−1.27692	−0.0673932	−0.0336966	+	0.999432i	$0.510728\pi$
$360$	55.2081	2.90972
$361$	−15.2928	−0.804886
$362$	−7.74776	−0.407213
$363$	−3.17723	−0.166761
$364$	−0.850207	−0.0445630
$365$	12.9280	0.676683
$366$	54.8158	2.86527
$367$	21.3881	1.11645	0.558226	−	0.829689i	$-0.311482\pi$
$367$	21.3881	1.11645	0.558226	+	0.829689i	$0.311482\pi$
$368$	4.15925	0.216816
$369$	−75.1287	−3.91104
$370$	−2.09995	−0.109171
$371$	−6.80616	−0.353358
$372$	0.361310	0.0187331
$373$	−14.6085	−0.756399	−0.378199	−	0.925724i	$-0.623457\pi$
$373$	−14.6085	−0.756399	−0.378199	+	0.925724i	$0.623457\pi$
$374$	5.28307	0.273181
$375$	−23.0520	−1.19040
$376$	−30.8587	−1.59142
$377$	0	0
$378$	90.1218	4.63536
$379$	33.2605	1.70848	0.854238	−	0.519882i	$-0.174024\pi$
$379$	33.2605	1.70848	0.854238	+	0.519882i	$0.174024\pi$
$380$	−0.371052	−0.0190346
$381$	−26.4520	−1.35518
$382$	34.5719	1.76885
$383$	23.1968	1.18530	0.592651	−	0.805459i	$-0.298081\pi$
$383$	23.1968	1.18530	0.592651	+	0.805459i	$0.298081\pi$
$384$	−33.9069	−1.73030
$385$	−13.4930	−0.687667
$386$	21.3157	1.08494
$387$	54.9522	2.79338
$388$	−0.201665	−0.0102380
$389$	−18.7595	−0.951142	−0.475571	−	0.879677i	$-0.657759\pi$
$389$	−18.7595	−0.951142	−0.475571	+	0.879677i	$0.657759\pi$
$390$	−28.5611	−1.44625
$391$	4.10701	0.207700
$392$	−51.4285	−2.59753
$393$	42.4197	2.13979
$394$	−3.68677	−0.185737
$395$	8.19591	0.412381
$396$	0.505425	0.0253986
$397$	−29.4541	−1.47826	−0.739129	−	0.673564i	$-0.764763\pi$
$397$	−29.4541	−1.47826	−0.739129	+	0.673564i	$0.764763\pi$
$398$	−12.4876	−0.625948
$399$	−30.5128	−1.52755
$400$	−8.92984	−0.446492
$401$	−12.3197	−0.615218	−0.307609	−	0.951513i	$-0.599529\pi$
$401$	−12.3197	−0.615218	−0.307609	+	0.951513i	$0.599529\pi$
$402$	−68.9275	−3.43779
$403$	−3.81950	−0.190263
$404$	−0.360269	−0.0179241
$405$	−54.2425	−2.69533
$406$	0	0
$407$	−0.558952	−0.0277062
$408$	−34.7668	−1.72121
$409$	33.7569	1.66917	0.834585	−	0.550879i	$-0.185708\pi$
$409$	33.7569	1.66917	0.834585	+	0.550879i	$0.185708\pi$
$410$	39.7834	1.96476
$411$	−46.0420	−2.27108
$412$	0.0164286	0.000809381 0
$413$	57.7502	2.84170
$414$	−10.6379	−0.522824
$415$	−18.9557	−0.930499
$416$	−0.963779	−0.0472531
$417$	53.2547	2.60790
$418$	2.67399	0.130789
$419$	24.4167	1.19283	0.596417	−	0.802674i	$-0.296590\pi$
$419$	24.4167	1.19283	0.596417	+	0.802674i	$0.296590\pi$
$420$	3.05405	0.149022
$421$	3.52840	0.171964	0.0859818	−	0.996297i	$-0.472597\pi$
$421$	3.52840	0.171964	0.0859818	+	0.996297i	$0.472597\pi$
$422$	−19.6770	−0.957862
$423$	76.1108	3.70063
$424$	−3.92517	−0.190623
$425$	−8.81767	−0.427720
$426$	−20.0973	−0.973717
$427$	61.9628	2.99859
$428$	0.486392	0.0235106
$429$	−7.60223	−0.367039
$430$	−29.0992	−1.40329
$431$	−14.7594	−0.710936	−0.355468	−	0.934688i	$-0.615679\pi$
$431$	−14.7594	−0.710936	−0.355468	+	0.934688i	$0.615679\pi$
$432$	50.1203	2.41142
$433$	30.4600	1.46382	0.731908	−	0.681403i	$-0.238630\pi$
$433$	30.4600	1.46382	0.731908	+	0.681403i	$0.238630\pi$
$434$	−11.0577	−0.530788
$435$	0	0
$436$	0.169974	0.00814029
$437$	2.07874	0.0994394
$438$	21.0875	1.00760
$439$	12.3293	0.588447	0.294224	−	0.955737i	$-0.404939\pi$
$439$	12.3293	0.588447	0.294224	+	0.955737i	$0.404939\pi$
$440$	−7.78152	−0.370970
$441$	126.845	6.04022
$442$	12.6409	0.601268
$443$	11.0234	0.523738	0.261869	−	0.965103i	$-0.415661\pi$
$443$	11.0234	0.523738	0.261869	+	0.965103i	$0.415661\pi$
$444$	0.126515	0.00600412
$445$	−37.1663	−1.76185
$446$	−3.44332	−0.163046
$447$	71.4347	3.37874
$448$	−41.2211	−1.94751
$449$	−8.44924	−0.398744	−0.199372	−	0.979924i	$-0.563890\pi$
$449$	−8.44924	−0.398744	−0.199372	+	0.979924i	$0.563890\pi$
$450$	22.8394	1.07666
$451$	10.5893	0.498631
$452$	−0.0501610	−0.00235937
$453$	−1.21035	−0.0568671
$454$	24.7065	1.15953
$455$	−32.2850	−1.51355
$456$	−17.5970	−0.824055
$457$	−17.3188	−0.810139	−0.405070	−	0.914286i	$-0.632753\pi$
$457$	−17.3188	−0.810139	−0.405070	+	0.914286i	$0.632753\pi$
$458$	0.238387	0.0111391
$459$	49.4908	2.31003
$460$	−0.208062	−0.00970093
$461$	0.557108	0.0259471	0.0129736	−	0.999916i	$-0.495870\pi$
$461$	0.557108	0.0259471	0.0129736	+	0.999916i	$0.495870\pi$
$462$	−22.0090	−1.02395
$463$	10.3271	0.479940	0.239970	−	0.970780i	$-0.422862\pi$
$463$	10.3271	0.479940	0.239970	+	0.970780i	$0.422862\pi$
$464$	0	0
$465$	13.7201	0.636254
$466$	−0.880066	−0.0407683
$467$	−18.8273	−0.871225	−0.435613	−	0.900134i	$-0.643468\pi$
$467$	−18.8273	−0.871225	−0.435613	+	0.900134i	$0.643468\pi$
$468$	1.20934	0.0559019
$469$	−77.9146	−3.59776
$470$	−40.3035	−1.85906
$471$	16.0637	0.740174
$472$	33.3050	1.53299
$473$	−7.74546	−0.356136
$474$	13.3687	0.614045
$475$	−4.46301	−0.204777
$476$	−1.35170	−0.0619549
$477$	9.68115	0.443270
$478$	15.9142	0.727901
$479$	−3.22634	−0.147415	−0.0737077	−	0.997280i	$-0.523483\pi$
$479$	−3.22634	−0.147415	−0.0737077	+	0.997280i	$0.523483\pi$
$480$	3.46201	0.158018
$481$	−1.33742	−0.0609810
$482$	−20.7352	−0.944463
$483$	−17.1096	−0.778514
$484$	−0.0712392	−0.00323814
$485$	−7.65785	−0.347725
$486$	−34.2726	−1.55464
$487$	7.85487	0.355938	0.177969	−	0.984036i	$-0.443047\pi$
$487$	7.85487	0.355938	0.177969	+	0.984036i	$0.443047\pi$
$488$	35.7345	1.61762
$489$	28.7961	1.30221
$490$	−67.1690	−3.03438
$491$	−4.63557	−0.209200	−0.104600	−	0.994514i	$-0.533356\pi$
$491$	−4.63557	−0.209200	−0.104600	+	0.994514i	$0.533356\pi$
$492$	−2.39682	−0.108057
$493$	0	0
$494$	6.39813	0.287865
$495$	19.1926	0.862642
$496$	−6.14965	−0.276127
$497$	−22.7177	−1.01903
$498$	−30.9195	−1.38553
$499$	3.02671	0.135494	0.0677470	−	0.997703i	$-0.478419\pi$
$499$	3.02671	0.135494	0.0677470	+	0.997703i	$0.478419\pi$
$500$	−0.516867	−0.0231150
$501$	19.3518	0.864573
$502$	−7.94253	−0.354492
$503$	−16.2220	−0.723303	−0.361652	−	0.932313i	$-0.617787\pi$
$503$	−16.2220	−0.723303	−0.361652	+	0.932313i	$0.617787\pi$
$504$	101.794	4.53425
$505$	−13.6805	−0.608776
$506$	1.49940	0.0666565
$507$	23.1139	1.02652
$508$	−0.593101	−0.0263146
$509$	−13.0335	−0.577700	−0.288850	−	0.957374i	$-0.593273\pi$
$509$	−13.0335	−0.577700	−0.288850	+	0.957374i	$0.593273\pi$
$510$	−45.4077	−2.01069
$511$	23.8369	1.05448
$512$	−23.7151	−1.04807
$513$	25.0494	1.10596
$514$	4.27421	0.188527
$515$	0.623847	0.0274900
$516$	1.75313	0.0771772
$517$	−10.7277	−0.471805
$518$	−3.87192	−0.170122
$519$	−60.2343	−2.64399
$520$	−18.6190	−0.816499
$521$	12.8314	0.562154	0.281077	−	0.959685i	$-0.409308\pi$
$521$	12.8314	0.562154	0.281077	+	0.959685i	$0.409308\pi$
$522$	0	0
$523$	−7.46965	−0.326625	−0.163313	−	0.986574i	$-0.552218\pi$
$523$	−7.46965	−0.326625	−0.163313	+	0.986574i	$0.552218\pi$
$524$	0.951126	0.0415501
$525$	36.7340	1.60320
$526$	−14.0075	−0.610754
$527$	−6.07240	−0.264518
$528$	−12.2401	−0.532682
$529$	−21.8344	−0.949321
$530$	−5.12653	−0.222682
$531$	−82.1445	−3.56477
$532$	−0.684153	−0.0296618
$533$	25.3373	1.09748
$534$	−60.6236	−2.62344
$535$	18.4698	0.798520
$536$	−44.9340	−1.94085
$537$	39.3788	1.69932
$538$	16.6932	0.719693
$539$	−17.8786	−0.770087
$540$	−2.50721	−0.107893
$541$	23.5611	1.01297	0.506486	−	0.862248i	$-0.330944\pi$
$541$	23.5611	1.01297	0.506486	+	0.862248i	$0.330944\pi$
$542$	−7.78553	−0.334417
$543$	17.7249	0.760650
$544$	−1.53226	−0.0656950
$545$	6.45445	0.276478
$546$	−52.6615	−2.25370
$547$	30.3469	1.29754	0.648769	−	0.760985i	$-0.275284\pi$
$547$	30.3469	1.29754	0.648769	+	0.760985i	$0.275284\pi$
$548$	−1.03234	−0.0440996
$549$	−88.1366	−3.76158
$550$	−3.21919	−0.137267
$551$	0	0
$552$	−9.86725	−0.419978
$553$	15.1118	0.642618
$554$	37.4918	1.59287
$555$	4.80416	0.203925
$556$	1.19407	0.0506398
$557$	−17.6881	−0.749469	−0.374734	−	0.927132i	$-0.622266\pi$
$557$	−17.6881	−0.749469	−0.374734	+	0.927132i	$0.622266\pi$
$558$	15.7286	0.665846
$559$	−18.5327	−0.783851
$560$	−51.9811	−2.19660
$561$	−12.0864	−0.510286
$562$	−34.2343	−1.44409
$563$	24.8840	1.04873	0.524367	−	0.851492i	$-0.324302\pi$
$563$	24.8840	1.04873	0.524367	+	0.851492i	$0.324302\pi$
$564$	2.42815	0.102243
$565$	−1.90477	−0.0801342
$566$	22.6813	0.953366
$567$	−100.013	−4.20017
$568$	−13.1015	−0.549725
$569$	14.6334	0.613464	0.306732	−	0.951796i	$-0.400764\pi$
$569$	14.6334	0.613464	0.306732	+	0.951796i	$0.400764\pi$
$570$	−22.9828	−0.962645
$571$	−17.6835	−0.740030	−0.370015	−	0.929026i	$-0.620647\pi$
$571$	−17.6835	−0.740030	−0.370015	+	0.929026i	$0.620647\pi$
$572$	−0.170456	−0.00712711
$573$	−79.0919	−3.30411
$574$	73.3534	3.06171
$575$	−2.50257	−0.104364
$576$	58.6332	2.44305
$577$	−11.6689	−0.485784	−0.242892	−	0.970053i	$-0.578096\pi$
$577$	−11.6689	−0.485784	−0.242892	+	0.970053i	$0.578096\pi$
$578$	−3.51248	−0.146100
$579$	−48.7650	−2.02660
$580$	0	0
$581$	−34.9509	−1.45001
$582$	−12.4910	−0.517771
$583$	−1.36455	−0.0565138
$584$	13.7469	0.568853
$585$	45.9225	1.89866
$586$	−15.1866	−0.627351
$587$	−9.60087	−0.396270	−0.198135	−	0.980175i	$-0.563489\pi$
$587$	−9.60087	−0.396270	−0.198135	+	0.980175i	$0.563489\pi$
$588$	4.04670	0.166883
$589$	−3.07351	−0.126642
$590$	43.4985	1.79081
$591$	8.43443	0.346946
$592$	−2.15333	−0.0885014
$593$	−15.3449	−0.630140	−0.315070	−	0.949068i	$-0.602028\pi$
$593$	−15.3449	−0.630140	−0.315070	+	0.949068i	$0.602028\pi$
$594$	18.0683	0.741350
$595$	−51.3281	−2.10425
$596$	1.60169	0.0656080
$597$	28.5686	1.16923
$598$	3.58765	0.146710
$599$	33.3301	1.36183	0.680915	−	0.732362i	$-0.261582\pi$
$599$	33.3301	1.36183	0.680915	+	0.732362i	$0.261582\pi$
$600$	21.1848	0.864866
$601$	26.5513	1.08305	0.541525	−	0.840685i	$-0.317847\pi$
$601$	26.5513	1.08305	0.541525	+	0.840685i	$0.317847\pi$
$602$	−53.6537	−2.18676
$603$	110.826	4.51320
$604$	−0.0271382	−0.00110424
$605$	−2.70517	−0.109981
$606$	−22.3149	−0.906482
$607$	28.3531	1.15082	0.575408	−	0.817866i	$-0.304843\pi$
$607$	28.3531	1.15082	0.575408	+	0.817866i	$0.304843\pi$
$608$	−0.775543	−0.0314524
$609$	0	0
$610$	46.6716	1.88968
$611$	−25.6685	−1.03844
$612$	1.92267	0.0777192
$613$	29.1973	1.17927	0.589634	−	0.807671i	$-0.299272\pi$
$613$	29.1973	1.17927	0.589634	+	0.807671i	$0.299272\pi$
$614$	6.59988	0.266350
$615$	−91.0146	−3.67006
$616$	−14.3477	−0.578086
$617$	27.8871	1.12269	0.561347	−	0.827581i	$-0.310283\pi$
$617$	27.8871	1.12269	0.561347	+	0.827581i	$0.310283\pi$
$618$	1.01758	0.0409332
$619$	38.9857	1.56697	0.783484	−	0.621412i	$-0.213441\pi$
$619$	38.9857	1.56697	0.783484	+	0.621412i	$0.213441\pi$
$620$	0.307629	0.0123547
$621$	14.0461	0.563650
$622$	15.2183	0.610200
$623$	−68.5280	−2.74552
$624$	−29.2872	−1.17243
$625$	−31.2169	−1.24867
$626$	−19.0517	−0.761458
$627$	−6.11743	−0.244307
$628$	0.360176	0.0143726
$629$	−2.12628	−0.0847805
$630$	132.949	5.29682
$631$	13.4329	0.534754	0.267377	−	0.963592i	$-0.413843\pi$
$631$	13.4329	0.534754	0.267377	+	0.963592i	$0.413843\pi$
$632$	8.71508	0.346667
$633$	45.0161	1.78923
$634$	26.5717	1.05530
$635$	−22.5219	−0.893755
$636$	0.308856	0.0122469
$637$	−42.7786	−1.69495
$638$	0	0
$639$	32.3138	1.27832
$640$	−28.8692	−1.14116
$641$	31.8555	1.25822	0.629108	−	0.777318i	$-0.283420\pi$
$641$	31.8555	1.25822	0.629108	+	0.777318i	$0.283420\pi$
$642$	30.1269	1.18902
$643$	33.6685	1.32776	0.663879	−	0.747840i	$-0.268909\pi$
$643$	33.6685	1.32776	0.663879	+	0.747840i	$0.268909\pi$
$644$	−0.383628	−0.0151171
$645$	66.5718	2.62126
$646$	10.1720	0.400213
$647$	20.6905	0.813428	0.406714	−	0.913555i	$-0.366675\pi$
$647$	20.6905	0.813428	0.406714	+	0.913555i	$0.366675\pi$
$648$	−57.6786	−2.26583
$649$	11.5782	0.454483
$650$	−7.70263	−0.302122
$651$	25.2973	0.991481
$652$	0.645662	0.0252861
$653$	−18.3196	−0.716901	−0.358451	−	0.933549i	$-0.616695\pi$
$653$	−18.3196	−0.716901	−0.358451	+	0.933549i	$0.616695\pi$
$654$	10.5281	0.411683
$655$	36.1172	1.41122
$656$	40.7947	1.59277
$657$	−33.9059	−1.32279
$658$	−74.3123	−2.89699
$659$	−6.05272	−0.235781	−0.117890	−	0.993027i	$-0.537613\pi$
$659$	−6.05272	−0.235781	−0.117890	+	0.993027i	$0.537613\pi$
$660$	0.612297	0.0238336
$661$	−14.0581	−0.546798	−0.273399	−	0.961901i	$-0.588148\pi$
$661$	−14.0581	−0.546798	−0.273399	+	0.961901i	$0.588148\pi$
$662$	36.8084	1.43060
$663$	−28.9193	−1.12313
$664$	−20.1564	−0.782222
$665$	−25.9794	−1.00744
$666$	5.50746	0.213410
$667$	0	0
$668$	0.433901	0.0167882
$669$	7.87747	0.304560
$670$	−58.6867	−2.26727
$671$	12.4228	0.479575
$672$	6.38331	0.246242
$673$	−40.8659	−1.57527	−0.787633	−	0.616145i	$-0.788693\pi$
$673$	−40.8659	−1.57527	−0.787633	+	0.616145i	$0.788693\pi$
$674$	−23.9039	−0.920743
$675$	−30.1567	−1.16073
$676$	0.518256	0.0199329
$677$	3.03857	0.116782	0.0583908	−	0.998294i	$-0.481403\pi$
$677$	3.03857	0.116782	0.0583908	+	0.998294i	$0.481403\pi$
$678$	−3.10695	−0.119322
$679$	−14.1197	−0.541864
$680$	−29.6014	−1.13516
$681$	−56.5223	−2.16594
$682$	−2.21693	−0.0848908
$683$	39.0657	1.49481	0.747404	−	0.664370i	$-0.231300\pi$
$683$	39.0657	1.49481	0.747404	+	0.664370i	$0.231300\pi$
$684$	0.973146	0.0372092
$685$	−39.2013	−1.49781
$686$	−75.3575	−2.87716
$687$	−0.545370	−0.0208072
$688$	−29.8390	−1.13760
$689$	−3.26499	−0.124386
$690$	−12.8873	−0.490610
$691$	−46.0007	−1.74995	−0.874975	−	0.484168i	$-0.839122\pi$
$691$	−46.0007	−1.74995	−0.874975	+	0.484168i	$0.839122\pi$
$692$	−1.35056	−0.0513406
$693$	35.3876	1.34426
$694$	−23.3932	−0.887995
$695$	45.3425	1.71994
$696$	0	0
$697$	40.2823	1.52580
$698$	2.10093	0.0795212
$699$	2.01337	0.0761528
$700$	0.823643	0.0311308
$701$	7.16716	0.270700	0.135350	−	0.990798i	$-0.456784\pi$
$701$	7.16716	0.270700	0.135350	+	0.990798i	$0.456784\pi$
$702$	43.2324	1.63170
$703$	−1.07621	−0.0405898
$704$	−8.26430	−0.311472
$705$	92.2044	3.47262
$706$	−28.4079	−1.06915
$707$	−25.2244	−0.948662
$708$	−2.62064	−0.0984897
$709$	0.456524	0.0171451	0.00857256	−	0.999963i	$-0.497271\pi$
$709$	0.456524	0.0171451	0.00857256	+	0.999963i	$0.497271\pi$
$710$	−17.1114	−0.642178
$711$	−21.4951	−0.806131
$712$	−39.5207	−1.48110
$713$	−1.72342	−0.0645427
$714$	−83.7236	−3.13328
$715$	−6.47274	−0.242067
$716$	0.882945	0.0329972
$717$	−36.4078	−1.35968
$718$	−1.77338	−0.0661820
$719$	44.7849	1.67020	0.835098	−	0.550101i	$-0.185411\pi$
$719$	44.7849	1.67020	0.835098	+	0.550101i	$0.185411\pi$
$720$	73.9384	2.75552
$721$	1.15026	0.0428379
$722$	−21.2387	−0.790421
$723$	47.4370	1.76420
$724$	0.397425	0.0147702
$725$	0	0
$726$	−4.41253	−0.163764
$727$	−42.1281	−1.56245	−0.781223	−	0.624253i	$-0.785404\pi$
$727$	−42.1281	−1.56245	−0.781223	+	0.624253i	$0.785404\pi$
$728$	−34.3301	−1.27236
$729$	18.2529	0.676035
$730$	17.9544	0.664523
$731$	−29.4642	−1.08977
$732$	−2.81180	−0.103927
$733$	−15.8131	−0.584071	−0.292036	−	0.956407i	$-0.594333\pi$
$733$	−15.8131	−0.584071	−0.292036	+	0.956407i	$0.594333\pi$
$734$	29.7038	1.09639
$735$	153.666	5.66805
$736$	−0.434874	−0.0160297
$737$	−15.6209	−0.575403
$738$	−104.339	−3.84076
$739$	7.58981	0.279196	0.139598	−	0.990208i	$-0.455419\pi$
$739$	7.58981	0.279196	0.139598	+	0.990208i	$0.455419\pi$
$740$	0.107718	0.00395979
$741$	−14.6373	−0.537716
$742$	−9.45239	−0.347008
$743$	2.28474	0.0838191	0.0419096	−	0.999121i	$-0.486656\pi$
$743$	2.28474	0.0838191	0.0419096	+	0.999121i	$0.486656\pi$
$744$	14.5892	0.534865
$745$	60.8213	2.22832
$746$	−20.2882	−0.742805
$747$	49.7145	1.81896
$748$	−0.270998	−0.00990867
$749$	34.0550	1.24434
$750$	−32.0145	−1.16900
$751$	−33.2029	−1.21159	−0.605796	−	0.795620i	$-0.707145\pi$
$751$	−33.2029	−1.21159	−0.605796	+	0.795620i	$0.707145\pi$
$752$	−41.3280	−1.50708
$753$	18.1705	0.662171
$754$	0	0
$755$	−1.03052	−0.0375045
$756$	−4.62285	−0.168131
$757$	−16.4483	−0.597822	−0.298911	−	0.954281i	$-0.596623\pi$
$757$	−16.4483	−0.597822	−0.298911	+	0.954281i	$0.596623\pi$
$758$	46.1921	1.67777
$759$	−3.43026	−0.124510
$760$	−14.9825	−0.543474
$761$	−15.2520	−0.552883	−0.276442	−	0.961031i	$-0.589155\pi$
$761$	−15.2520	−0.552883	−0.276442	+	0.961031i	$0.589155\pi$
$762$	−36.7365	−1.33082
$763$	11.9008	0.430839
$764$	−1.77338	−0.0641588
$765$	73.0097	2.63967
$766$	32.2157	1.16400
$767$	27.7034	1.00031
$768$	5.42526	0.195767
$769$	32.5085	1.17229	0.586143	−	0.810207i	$-0.300646\pi$
$769$	32.5085	1.17229	0.586143	+	0.810207i	$0.300646\pi$
$770$	−18.7391	−0.675309
$771$	−9.77832	−0.352158
$772$	−1.09340	−0.0393523
$773$	25.0858	0.902275	0.451137	−	0.892455i	$-0.351018\pi$
$773$	25.0858	0.902275	0.451137	+	0.892455i	$0.351018\pi$
$774$	76.3175	2.74318
$775$	3.70016	0.132914
$776$	−8.14294	−0.292314
$777$	8.85800	0.317779
$778$	−26.0531	−0.934049
$779$	20.3887	0.730499
$780$	1.46506	0.0524575
$781$	−4.55460	−0.162976
$782$	5.70381	0.203968
$783$	0	0
$784$	−68.8765	−2.45987
$785$	13.6770	0.488154
$786$	58.9124	2.10134
$787$	29.6488	1.05686	0.528432	−	0.848976i	$-0.322780\pi$
$787$	29.6488	1.05686	0.528432	+	0.848976i	$0.322780\pi$
$788$	0.189115	0.00673695
$789$	32.0456	1.14085
$790$	11.3825	0.404970
$791$	−3.51205	−0.124874
$792$	20.4083	0.725179
$793$	29.7242	1.05554
$794$	−40.9058	−1.45169
$795$	11.7282	0.415957
$796$	0.640560	0.0227040
$797$	−47.5404	−1.68397	−0.841984	−	0.539503i	$-0.818612\pi$
$797$	−47.5404	−1.68397	−0.841984	+	0.539503i	$0.818612\pi$
$798$	−42.3762	−1.50010
$799$	−40.8089	−1.44372
$800$	0.933666	0.0330101
$801$	97.4749	3.44411
$802$	−17.1096	−0.604162
$803$	4.77900	0.168647
$804$	3.53568	0.124694
$805$	−14.5676	−0.513439
$806$	−5.30451	−0.186843
$807$	−38.1898	−1.34434
$808$	−14.5471	−0.511766
$809$	3.68317	0.129493	0.0647466	−	0.997902i	$-0.479376\pi$
$809$	3.68317	0.129493	0.0647466	+	0.997902i	$0.479376\pi$
$810$	−75.3320	−2.64690
$811$	53.8111	1.88956	0.944782	−	0.327698i	$-0.106273\pi$
$811$	53.8111	1.88956	0.944782	+	0.327698i	$0.106273\pi$
$812$	0	0
$813$	17.8114	0.624671
$814$	−0.776271	−0.0272083
$815$	24.5178	0.858821
$816$	−46.5620	−1.63000
$817$	−14.9131	−0.521743
$818$	46.8815	1.63917
$819$	84.6728	2.95871
$820$	−2.04071	−0.0712647
$821$	−22.4842	−0.784705	−0.392352	−	0.919815i	$-0.628339\pi$
$821$	−22.4842	−0.784705	−0.392352	+	0.919815i	$0.628339\pi$
$822$	−63.9430	−2.23027
$823$	−49.3368	−1.71977	−0.859886	−	0.510486i	$-0.829466\pi$
$823$	−49.3368	−1.71977	−0.859886	+	0.510486i	$0.829466\pi$
$824$	0.663365	0.0231094
$825$	7.36470	0.256406
$826$	80.2034	2.79063
$827$	−7.05035	−0.245165	−0.122582	−	0.992458i	$-0.539118\pi$
$827$	−7.05035	−0.245165	−0.122582	+	0.992458i	$0.539118\pi$
$828$	0.545677	0.0189636
$829$	34.8556	1.21059	0.605293	−	0.796003i	$-0.293056\pi$
$829$	34.8556	1.21059	0.605293	+	0.796003i	$0.293056\pi$
$830$	−26.3256	−0.913776
$831$	−85.7720	−2.97540
$832$	−19.7742	−0.685546
$833$	−68.0113	−2.35645
$834$	73.9601	2.56103
$835$	16.4766	0.570196
$836$	−0.137164	−0.00474391
$837$	−20.7678	−0.717841
$838$	33.9099	1.17140
$839$	39.4235	1.36105	0.680525	−	0.732725i	$-0.261752\pi$
$839$	39.4235	1.36105	0.680525	+	0.732725i	$0.261752\pi$
$840$	123.318	4.25487
$841$	0	0
$842$	4.90023	0.168873
$843$	78.3195	2.69747
$844$	1.00934	0.0347430
$845$	19.6798	0.677005
$846$	105.703	3.63413
$847$	−4.98785	−0.171385
$848$	−5.25685	−0.180521
$849$	−51.8892	−1.78083
$850$	−12.2460	−0.420033
$851$	−0.603466	−0.0206865
$852$	1.03090	0.0353181
$853$	2.76472	0.0946623	0.0473311	−	0.998879i	$-0.484928\pi$
$853$	2.76472	0.0946623	0.0473311	+	0.998879i	$0.484928\pi$
$854$	86.0539	2.94470
$855$	36.9534	1.26378
$856$	19.6398	0.671274
$857$	−4.72611	−0.161441	−0.0807204	−	0.996737i	$-0.525722\pi$
$857$	−4.72611	−0.161441	−0.0807204	+	0.996737i	$0.525722\pi$
$858$	−10.5580	−0.360443
$859$	40.4162	1.37898	0.689491	−	0.724294i	$-0.257834\pi$
$859$	40.4162	1.37898	0.689491	+	0.724294i	$0.257834\pi$
$860$	1.49266	0.0508993
$861$	−167.814	−5.71910
$862$	−20.4979	−0.698160
$863$	4.07125	0.138587	0.0692935	−	0.997596i	$-0.477926\pi$
$863$	4.07125	0.138587	0.0692935	+	0.997596i	$0.477926\pi$
$864$	−5.24037	−0.178281
$865$	−51.2850	−1.74374
$866$	42.3029	1.43751
$867$	8.03567	0.272906
$868$	0.567212	0.0192524
$869$	3.02972	0.102776
$870$	0	0
$871$	−37.3765	−1.26645
$872$	6.86331	0.232421
$873$	20.0840	0.679740
$874$	2.88695	0.0976524
$875$	−36.1887	−1.22340
$876$	−1.08169	−0.0365470
$877$	−1.38106	−0.0466350	−0.0233175	−	0.999728i	$-0.507423\pi$
$877$	−1.38106	−0.0466350	−0.0233175	+	0.999728i	$0.507423\pi$
$878$	17.1230	0.577872
$879$	34.7431	1.17186
$880$	−10.4215	−0.351310
$881$	2.14925	0.0724101	0.0362051	−	0.999344i	$-0.488473\pi$
$881$	2.14925	0.0724101	0.0362051	+	0.999344i	$0.488473\pi$
$882$	176.162	5.93167
$883$	51.7083	1.74012	0.870062	−	0.492943i	$-0.164079\pi$
$883$	51.7083	1.74012	0.870062	+	0.492943i	$0.164079\pi$
$884$	−0.648423	−0.0218088
$885$	−99.5139	−3.34512
$886$	15.3093	0.514325
$887$	−3.05626	−0.102619	−0.0513096	−	0.998683i	$-0.516340\pi$
$887$	−3.05626	−0.102619	−0.0513096	+	0.998683i	$0.516340\pi$
$888$	5.10848	0.171429
$889$	−41.5263	−1.39275
$890$	−51.6166	−1.73019
$891$	−20.0514	−0.671747
$892$	0.176627	0.00591391
$893$	−20.6552	−0.691199
$894$	99.2083	3.31802
$895$	33.5282	1.12072
$896$	−53.2296	−1.77827
$897$	−8.20766	−0.274046
$898$	−11.7343	−0.391578
$899$	0	0
$900$	−1.17156	−0.0390519
$901$	−5.19082	−0.172931
$902$	14.7064	0.489670
$903$	122.746	4.08474
$904$	−2.02543	−0.0673647
$905$	15.0915	0.501658
$906$	−1.68093	−0.0558451
$907$	52.1478	1.73154	0.865769	−	0.500443i	$-0.166830\pi$
$907$	52.1478	1.73154	0.865769	+	0.500443i	$0.166830\pi$
$908$	−1.26733	−0.0420579
$909$	35.8795	1.19005
$910$	−44.8374	−1.48634
$911$	16.9210	0.560617	0.280308	−	0.959910i	$-0.409563\pi$
$911$	16.9210	0.560617	0.280308	+	0.959910i	$0.409563\pi$
$912$	−23.5671	−0.780384
$913$	−7.00720	−0.231905
$914$	−24.0523	−0.795580
$915$	−106.773	−3.52981
$916$	−0.0122282	−0.000404030 0
$917$	66.5936	2.19911
$918$	68.7327	2.26852
$919$	5.48168	0.180824	0.0904119	−	0.995904i	$-0.471182\pi$
$919$	5.48168	0.180824	0.0904119	+	0.995904i	$0.471182\pi$
$920$	−8.40123	−0.276980
$921$	−15.0989	−0.497525
$922$	0.773711	0.0254808
$923$	−10.8979	−0.358709
$924$	1.12896	0.0371402
$925$	1.29563	0.0426001
$926$	14.3422	0.471315
$927$	−1.63614	−0.0537380
$928$	0	0
$929$	−7.82584	−0.256757	−0.128379	−	0.991725i	$-0.540977\pi$
$929$	−7.82584	−0.256757	−0.128379	+	0.991725i	$0.540977\pi$
$930$	19.0544	0.624819
$931$	−34.4235	−1.12819
$932$	0.0451435	0.00147872
$933$	−34.8158	−1.13982
$934$	−26.1474	−0.855568
$935$	−10.2906	−0.336540
$936$	48.8315	1.59611
$937$	12.4087	0.405375	0.202687	−	0.979243i	$-0.435032\pi$
$937$	12.4087	0.405375	0.202687	+	0.979243i	$0.435032\pi$
$938$	−108.208	−3.53310
$939$	43.5855	1.42236
$940$	2.06739	0.0674308
$941$	−18.3170	−0.597116	−0.298558	−	0.954391i	$-0.596506\pi$
$941$	−18.3170	−0.597116	−0.298558	+	0.954391i	$0.596506\pi$
$942$	22.3092	0.726872
$943$	11.4326	0.372298
$944$	44.6043	1.45175
$945$	−175.544	−5.71044
$946$	−10.7569	−0.349736
$947$	36.9910	1.20205	0.601024	−	0.799231i	$-0.294760\pi$
$947$	36.9910	1.20205	0.601024	+	0.799231i	$0.294760\pi$
$948$	−0.685755	−0.0222723
$949$	11.4348	0.371190
$950$	−6.19822	−0.201097
$951$	−60.7896	−1.97124
$952$	−54.5795	−1.76893
$953$	43.5992	1.41232	0.706159	−	0.708054i	$-0.250426\pi$
$953$	43.5992	1.41232	0.706159	+	0.708054i	$0.250426\pi$
$954$	13.4452	0.435303
$955$	−67.3409	−2.17910
$956$	−0.816330	−0.0264020
$957$	0	0
$958$	−4.48074	−0.144766
$959$	−72.2801	−2.33405
$960$	71.0312	2.29252
$961$	−28.4518	−0.917801
$962$	−1.85740	−0.0598851
$963$	−48.4402	−1.56096
$964$	1.06362	0.0342570
$965$	−41.5198	−1.33657
$966$	−23.7618	−0.764523
$967$	−5.45091	−0.175289	−0.0876447	−	0.996152i	$-0.527934\pi$
$967$	−5.45091	−0.175289	−0.0876447	+	0.996152i	$0.527934\pi$
$968$	−2.87653	−0.0924553
$969$	−23.2711	−0.747574
$970$	−10.6352	−0.341476
$971$	−5.49388	−0.176307	−0.0881535	−	0.996107i	$-0.528097\pi$
$971$	−5.49388	−0.176307	−0.0881535	+	0.996107i	$0.528097\pi$
$972$	1.75803	0.0563889
$973$	83.6033	2.68020
$974$	10.9088	0.349541
$975$	17.6217	0.564346
$976$	47.8580	1.53190
$977$	2.67067	0.0854423	0.0427212	−	0.999087i	$-0.486397\pi$
$977$	2.67067	0.0854423	0.0427212	+	0.999087i	$0.486397\pi$
$978$	39.9920	1.27880
$979$	−13.7390	−0.439100
$980$	3.44547	0.110061
$981$	−16.9279	−0.540465
$982$	−6.43787	−0.205441
$983$	−19.7658	−0.630433	−0.315216	−	0.949020i	$-0.602077\pi$
$983$	−19.7658	−0.630433	−0.315216	+	0.949020i	$0.602077\pi$
$984$	−96.7799	−3.08523
$985$	7.18129	0.228815
$986$	0	0
$987$	170.008	5.41142
$988$	−0.328195	−0.0104413
$989$	−8.36229	−0.265905
$990$	26.6546	0.847139
$991$	33.8240	1.07446	0.537228	−	0.843437i	$-0.319472\pi$
$991$	33.8240	1.07446	0.537228	+	0.843437i	$0.319472\pi$
$992$	0.642981	0.0204147
$993$	−84.2085	−2.67228
$994$	−31.5502	−1.00071
$995$	24.3241	0.771124
$996$	1.58603	0.0502553
$997$	−35.1316	−1.11263	−0.556314	−	0.830972i	$-0.687785\pi$
$997$	−35.1316	−1.11263	−0.556314	+	0.830972i	$0.687785\pi$
$998$	4.20349	0.133059
$999$	−7.27196	−0.230075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.14	yes	18
29.28	even	2		9251.2.a.s.1.5	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.5	✓	18	29.28	even	2
9251.2.a.t.1.14	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)

\(f(q)\)	\(=\)	\(q+1.38880 q^{2} -3.17723 q^{3} -0.0712392 q^{4} -2.70517 q^{5} -4.41253 q^{6} -4.98785 q^{7} -2.87653 q^{8} +7.09477 q^{9} +O(q^{10})\)	\(q+1.38880 q^{2} -3.17723 q^{3} -0.0712392 q^{4} -2.70517 q^{5} -4.41253 q^{6} -4.98785 q^{7} -2.87653 q^{8} +7.09477 q^{9} -3.75694 q^{10} -1.00000 q^{11} +0.226343 q^{12} -2.39272 q^{13} -6.92712 q^{14} +8.59495 q^{15} -3.85245 q^{16} -3.80406 q^{17} +9.85320 q^{18} -1.92540 q^{19} +0.192714 q^{20} +15.8475 q^{21} -1.38880 q^{22} -1.07964 q^{23} +9.13940 q^{24} +2.31797 q^{25} -3.32301 q^{26} -13.0100 q^{27} +0.355330 q^{28} +11.9367 q^{30} +1.59630 q^{31} +0.402796 q^{32} +3.17723 q^{33} -5.28307 q^{34} +13.4930 q^{35} -0.505425 q^{36} +0.558952 q^{37} -2.67399 q^{38} +7.60223 q^{39} +7.78152 q^{40} -10.5893 q^{41} +22.0090 q^{42} +7.74546 q^{43} +0.0712392 q^{44} -19.1926 q^{45} -1.49940 q^{46} +10.7277 q^{47} +12.2401 q^{48} +17.8786 q^{49} +3.21919 q^{50} +12.0864 q^{51} +0.170456 q^{52} +1.36455 q^{53} -18.0683 q^{54} +2.70517 q^{55} +14.3477 q^{56} +6.11743 q^{57} -11.5782 q^{59} -0.612297 q^{60} -12.4228 q^{61} +2.21693 q^{62} -35.3876 q^{63} +8.26430 q^{64} +6.47274 q^{65} +4.41253 q^{66} +15.6209 q^{67} +0.270998 q^{68} +3.43026 q^{69} +18.7391 q^{70} +4.55460 q^{71} -20.4083 q^{72} -4.77900 q^{73} +0.776271 q^{74} -7.36470 q^{75} +0.137164 q^{76} +4.98785 q^{77} +10.5580 q^{78} -3.02972 q^{79} +10.4215 q^{80} +20.0514 q^{81} -14.7064 q^{82} +7.00720 q^{83} -1.12896 q^{84} +10.2906 q^{85} +10.7569 q^{86} +2.87653 q^{88} +13.7390 q^{89} -26.6546 q^{90} +11.9345 q^{91} +0.0769126 q^{92} -5.07179 q^{93} +14.8987 q^{94} +5.20854 q^{95} -1.27977 q^{96} +2.83082 q^{97} +24.8298 q^{98} -7.09477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 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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