LMFDB - Embedded newform 9251.2.a.t.1.9

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			1.9
Root			$0.259898$ 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)

$f(q)$	$=$	$q-0.259898 q^{2} +1.84448 q^{3} -1.93245 q^{4} -0.195055 q^{5} -0.479377 q^{6} -4.26156 q^{7} +1.02204 q^{8} +0.402120 q^{9} +O(q^{10})$	\(q-0.259898 q^{2} +1.84448 q^{3} -1.93245 q^{4} -0.195055 q^{5} -0.479377 q^{6} -4.26156 q^{7} +1.02204 q^{8} +0.402120 q^{9} +0.0506944 q^{10} -1.00000 q^{11} -3.56438 q^{12} +1.99248 q^{13} +1.10757 q^{14} -0.359777 q^{15} +3.59928 q^{16} +3.58683 q^{17} -0.104510 q^{18} +2.83007 q^{19} +0.376936 q^{20} -7.86039 q^{21} +0.259898 q^{22} -1.17385 q^{23} +1.88513 q^{24} -4.96195 q^{25} -0.517841 q^{26} -4.79175 q^{27} +8.23527 q^{28} +0.0935051 q^{30} +1.99753 q^{31} -2.97952 q^{32} -1.84448 q^{33} -0.932207 q^{34} +0.831241 q^{35} -0.777078 q^{36} +3.54413 q^{37} -0.735527 q^{38} +3.67510 q^{39} -0.199354 q^{40} +4.26050 q^{41} +2.04290 q^{42} +4.92705 q^{43} +1.93245 q^{44} -0.0784357 q^{45} +0.305081 q^{46} -5.68058 q^{47} +6.63882 q^{48} +11.1609 q^{49} +1.28960 q^{50} +6.61584 q^{51} -3.85037 q^{52} +10.2333 q^{53} +1.24536 q^{54} +0.195055 q^{55} -4.35547 q^{56} +5.22001 q^{57} -4.24123 q^{59} +0.695251 q^{60} -9.81044 q^{61} -0.519154 q^{62} -1.71366 q^{63} -6.42420 q^{64} -0.388644 q^{65} +0.479377 q^{66} +12.2393 q^{67} -6.93137 q^{68} -2.16515 q^{69} -0.216038 q^{70} +7.18740 q^{71} +0.410981 q^{72} +5.49438 q^{73} -0.921111 q^{74} -9.15224 q^{75} -5.46897 q^{76} +4.26156 q^{77} -0.955149 q^{78} -13.6258 q^{79} -0.702060 q^{80} -10.0447 q^{81} -1.10729 q^{82} -0.382230 q^{83} +15.1898 q^{84} -0.699630 q^{85} -1.28053 q^{86} -1.02204 q^{88} +12.8807 q^{89} +0.0203853 q^{90} -8.49108 q^{91} +2.26841 q^{92} +3.68442 q^{93} +1.47637 q^{94} -0.552020 q^{95} -5.49567 q^{96} -10.5075 q^{97} -2.90070 q^{98} -0.402120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.259898	−0.183775	−0.0918877	−	0.995769i	$-0.529290\pi$
$2$	−0.259898	−0.183775	−0.0918877	+	0.995769i	$0.529290\pi$
$3$	1.84448	1.06491	0.532457	−	0.846457i	$-0.321269\pi$
$3$	1.84448	1.06491	0.532457	+	0.846457i	$0.321269\pi$
$4$	−1.93245	−0.966227
$5$	−0.195055	−0.0872314	−0.0436157	−	0.999048i	$-0.513888\pi$
$5$	−0.195055	−0.0872314	−0.0436157	+	0.999048i	$0.513888\pi$
$6$	−0.479377	−0.195705
$7$	−4.26156	−1.61072	−0.805360	−	0.592786i	$-0.798028\pi$
$7$	−4.26156	−1.61072	−0.805360	+	0.592786i	$0.798028\pi$
$8$	1.02204	0.361344
$9$	0.402120	0.134040
$10$	0.0506944	0.0160310
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.56438	−1.02895
$13$	1.99248	0.552614	0.276307	−	0.961069i	$-0.410889\pi$
$13$	1.99248	0.552614	0.276307	+	0.961069i	$0.410889\pi$
$14$	1.10757	0.296011
$15$	−0.359777	−0.0928939
$16$	3.59928	0.899820
$17$	3.58683	0.869933	0.434967	−	0.900447i	$-0.356760\pi$
$17$	3.58683	0.869933	0.434967	+	0.900447i	$0.356760\pi$
$18$	−0.104510	−0.0246333
$19$	2.83007	0.649262	0.324631	−	0.945841i	$-0.394760\pi$
$19$	2.83007	0.649262	0.324631	+	0.945841i	$0.394760\pi$
$20$	0.376936	0.0842853
$21$	−7.86039	−1.71528
$22$	0.259898	0.0554104
$23$	−1.17385	−0.244765	−0.122383	−	0.992483i	$-0.539053\pi$
$23$	−1.17385	−0.244765	−0.122383	+	0.992483i	$0.539053\pi$
$24$	1.88513	0.384800
$25$	−4.96195	−0.992391
$26$	−0.517841	−0.101557
$27$	−4.79175	−0.922172
$28$	8.23527	1.55632
$29$	0	0
$29$	0	0
$30$	0.0935051	0.0170716
$31$	1.99753	0.358767	0.179384	−	0.983779i	$-0.442590\pi$
$31$	1.99753	0.358767	0.179384	+	0.983779i	$0.442590\pi$
$32$	−2.97952	−0.526709
$33$	−1.84448	−0.321083
$34$	−0.932207	−0.159872
$35$	0.831241	0.140505
$36$	−0.777078	−0.129513
$37$	3.54413	0.582651	0.291326	−	0.956624i	$-0.405904\pi$
$37$	3.54413	0.582651	0.291326	+	0.956624i	$0.405904\pi$
$38$	−0.735527	−0.119318
$39$	3.67510	0.588486
$40$	−0.199354	−0.0315206
$41$	4.26050	0.665379	0.332690	−	0.943036i	$-0.392044\pi$
$41$	4.26050	0.665379	0.332690	+	0.943036i	$0.392044\pi$
$42$	2.04290	0.315226
$43$	4.92705	0.751368	0.375684	−	0.926748i	$-0.377408\pi$
$43$	4.92705	0.751368	0.375684	+	0.926748i	$0.377408\pi$
$44$	1.93245	0.291328
$45$	−0.0784357	−0.0116925
$46$	0.305081	0.0449818
$47$	−5.68058	−0.828598	−0.414299	−	0.910141i	$-0.635973\pi$
$47$	−5.68058	−0.828598	−0.414299	+	0.910141i	$0.635973\pi$
$48$	6.63882	0.958231
$49$	11.1609	1.59442
$50$	1.28960	0.182377
$51$	6.61584	0.926403
$52$	−3.85037	−0.533951
$53$	10.2333	1.40565	0.702824	−	0.711364i	$-0.251922\pi$
$53$	10.2333	1.40565	0.702824	+	0.711364i	$0.251922\pi$
$54$	1.24536	0.169473
$55$	0.195055	0.0263013
$56$	−4.35547	−0.582024
$57$	5.22001	0.691407
$58$	0	0
$59$	−4.24123	−0.552161	−0.276080	−	0.961135i	$-0.589036\pi$
$59$	−4.24123	−0.552161	−0.276080	+	0.961135i	$0.589036\pi$
$60$	0.695251	0.0897566
$61$	−9.81044	−1.25610	−0.628049	−	0.778174i	$-0.716146\pi$
$61$	−9.81044	−1.25610	−0.628049	+	0.778174i	$0.716146\pi$
$62$	−0.519154	−0.0659326
$63$	−1.71366	−0.215901
$64$	−6.42420	−0.803024
$65$	−0.388644	−0.0482054
$66$	0.479377	0.0590072
$67$	12.2393	1.49526	0.747632	−	0.664114i	$-0.231191\pi$
$67$	12.2393	1.49526	0.747632	+	0.664114i	$0.231191\pi$
$68$	−6.93137	−0.840552
$69$	−2.16515	−0.260653
$70$	−0.216038	−0.0258214
$71$	7.18740	0.852987	0.426493	−	0.904491i	$-0.359749\pi$
$71$	7.18740	0.852987	0.426493	+	0.904491i	$0.359749\pi$
$72$	0.410981	0.0484346
$73$	5.49438	0.643068	0.321534	−	0.946898i	$-0.395801\pi$
$73$	5.49438	0.643068	0.321534	+	0.946898i	$0.395801\pi$
$74$	−0.921111	−0.107077
$75$	−9.15224	−1.05681
$76$	−5.46897	−0.627334
$77$	4.26156	0.485650
$78$	−0.955149	−0.108149
$79$	−13.6258	−1.53302	−0.766511	−	0.642231i	$-0.778009\pi$
$79$	−13.6258	−1.53302	−0.766511	+	0.642231i	$0.778009\pi$
$80$	−0.702060	−0.0784926
$81$	−10.0447	−1.11607
$82$	−1.10729	−0.122280
$83$	−0.382230	−0.0419552	−0.0209776	−	0.999780i	$-0.506678\pi$
$83$	−0.382230	−0.0419552	−0.0209776	+	0.999780i	$0.506678\pi$
$84$	15.1898	1.65735
$85$	−0.699630	−0.0758855
$86$	−1.28053	−0.138083
$87$	0	0
$88$	−1.02204	−0.108949
$89$	12.8807	1.36536	0.682678	−	0.730720i	$-0.260815\pi$
$89$	12.8807	1.36536	0.682678	+	0.730720i	$0.260815\pi$
$90$	0.0203853	0.00214879
$91$	−8.49108	−0.890107
$92$	2.26841	0.236498
$93$	3.68442	0.382056
$94$	1.47637	0.152276
$95$	−0.552020	−0.0566360
$96$	−5.49567	−0.560899
$97$	−10.5075	−1.06687	−0.533437	−	0.845840i	$-0.679100\pi$
$97$	−10.5075	−1.06687	−0.533437	+	0.845840i	$0.679100\pi$
$98$	−2.90070	−0.293015
$99$	−0.402120	−0.0404146
$100$	9.58874	0.958874
$101$	−19.2043	−1.91090	−0.955448	−	0.295160i	$-0.904627\pi$
$101$	−19.2043	−1.91090	−0.955448	+	0.295160i	$0.904627\pi$
$102$	−1.71944	−0.170250
$103$	−8.94229	−0.881110	−0.440555	−	0.897726i	$-0.645218\pi$
$103$	−8.94229	−0.881110	−0.440555	+	0.897726i	$0.645218\pi$
$104$	2.03638	0.199684
$105$	1.53321	0.149626
$106$	−2.65960	−0.258323
$107$	2.20964	0.213614	0.106807	−	0.994280i	$-0.465937\pi$
$107$	2.20964	0.213614	0.106807	+	0.994280i	$0.465937\pi$
$108$	9.25983	0.891027
$109$	0.0681470	0.00652730	0.00326365	−	0.999995i	$-0.498961\pi$
$109$	0.0681470	0.00652730	0.00326365	+	0.999995i	$0.498961\pi$
$110$	−0.0506944	−0.00483353
$111$	6.53709	0.620473
$112$	−15.3386	−1.44936
$113$	−9.95540	−0.936525	−0.468262	−	0.883589i	$-0.655120\pi$
$113$	−9.95540	−0.936525	−0.468262	+	0.883589i	$0.655120\pi$
$114$	−1.35667	−0.127064
$115$	0.228966	0.0213512
$116$	0	0
$117$	0.801216	0.0740724
$118$	1.10228	0.101474
$119$	−15.2855	−1.40122
$120$	−0.367704	−0.0335667
$121$	1.00000	0.0909091
$122$	2.54971	0.230840
$123$	7.85843	0.708571
$124$	−3.86014	−0.346651
$125$	1.94313	0.173799
$126$	0.445376	0.0396773
$127$	−10.2181	−0.906709	−0.453355	−	0.891330i	$-0.649773\pi$
$127$	−10.2181	−0.906709	−0.453355	+	0.891330i	$0.649773\pi$
$128$	7.62866	0.674285
$129$	9.08787	0.800142
$130$	0.101008	0.00885896
$131$	11.8795	1.03792	0.518958	−	0.854800i	$-0.326320\pi$
$131$	11.8795	1.03792	0.518958	+	0.854800i	$0.326320\pi$
$132$	3.56438	0.310239
$133$	−12.0605	−1.04578
$134$	−3.18095	−0.274793
$135$	0.934656	0.0804424
$136$	3.66586	0.314345
$137$	−10.9733	−0.937511	−0.468755	−	0.883328i	$-0.655297\pi$
$137$	−10.9733	−0.937511	−0.468755	+	0.883328i	$0.655297\pi$
$138$	0.562717	0.0479017
$139$	15.7613	1.33685	0.668427	−	0.743778i	$-0.266968\pi$
$139$	15.7613	1.33685	0.668427	+	0.743778i	$0.266968\pi$
$140$	−1.60633	−0.135760
$141$	−10.4777	−0.882385
$142$	−1.86799	−0.156758
$143$	−1.99248	−0.166620
$144$	1.44734	0.120612
$145$	0	0
$146$	−1.42798	−0.118180
$147$	20.5862	1.69792
$148$	−6.84886	−0.562973
$149$	−10.3147	−0.845012	−0.422506	−	0.906360i	$-0.638849\pi$
$149$	−10.3147	−0.845012	−0.422506	+	0.906360i	$0.638849\pi$
$150$	2.37865	0.194216
$151$	9.48014	0.771482	0.385741	−	0.922607i	$-0.373946\pi$
$151$	9.48014	0.771482	0.385741	+	0.922607i	$0.373946\pi$
$152$	2.89243	0.234607
$153$	1.44233	0.116606
$154$	−1.10757	−0.0892506
$155$	−0.389629	−0.0312958
$156$	−7.10195	−0.568611
$157$	13.2734	1.05933	0.529666	−	0.848207i	$-0.322317\pi$
$157$	13.2734	1.05933	0.529666	+	0.848207i	$0.322317\pi$
$158$	3.54131	0.281732
$159$	18.8751	1.49689
$160$	0.581171	0.0459456
$161$	5.00244	0.394248
$162$	2.61058	0.205107
$163$	−15.3122	−1.19935	−0.599674	−	0.800245i	$-0.704703\pi$
$163$	−15.3122	−1.19935	−0.599674	+	0.800245i	$0.704703\pi$
$164$	−8.23323	−0.642907
$165$	0.359777	0.0280086
$166$	0.0993408	0.00771034
$167$	6.70970	0.519212	0.259606	−	0.965715i	$-0.416407\pi$
$167$	6.70970	0.519212	0.259606	+	0.965715i	$0.416407\pi$
$168$	−8.03359	−0.619805
$169$	−9.03002	−0.694617
$170$	0.181832	0.0139459
$171$	1.13803	0.0870270
$172$	−9.52130	−0.725992
$173$	−2.41717	−0.183774	−0.0918870	−	0.995769i	$-0.529290\pi$
$173$	−2.41717	−0.183774	−0.0918870	+	0.995769i	$0.529290\pi$
$174$	0	0
$175$	21.1457	1.59846
$176$	−3.59928	−0.271306
$177$	−7.82287	−0.588003
$178$	−3.34767	−0.250919
$179$	20.0360	1.49756	0.748781	−	0.662817i	$-0.230639\pi$
$179$	20.0360	1.49756	0.748781	+	0.662817i	$0.230639\pi$
$180$	0.151573	0.0112976
$181$	−24.6466	−1.83197	−0.915983	−	0.401218i	$-0.868587\pi$
$181$	−24.6466	−1.83197	−0.915983	+	0.401218i	$0.868587\pi$
$182$	2.20681	0.163580
$183$	−18.0952	−1.33763
$184$	−1.19972	−0.0884444
$185$	−0.691302	−0.0508255
$186$	−0.957571	−0.0702125
$187$	−3.58683	−0.262295
$188$	10.9775	0.800613
$189$	20.4203	1.48536
$190$	0.143469	0.0104083
$191$	−2.65552	−0.192147	−0.0960734	−	0.995374i	$-0.530628\pi$
$191$	−2.65552	−0.192147	−0.0960734	+	0.995374i	$0.530628\pi$
$192$	−11.8493	−0.855151
$193$	−2.20052	−0.158397	−0.0791986	−	0.996859i	$-0.525236\pi$
$193$	−2.20052	−0.158397	−0.0791986	+	0.996859i	$0.525236\pi$
$194$	2.73087	0.196065
$195$	−0.716847	−0.0513345
$196$	−21.5680	−1.54057
$197$	16.3145	1.16236	0.581181	−	0.813774i	$-0.302591\pi$
$197$	16.3145	1.16236	0.581181	+	0.813774i	$0.302591\pi$
$198$	0.104510	0.00742720
$199$	−1.97591	−0.140068	−0.0700342	−	0.997545i	$-0.522311\pi$
$199$	−1.97591	−0.140068	−0.0700342	+	0.997545i	$0.522311\pi$
$200$	−5.07129	−0.358594
$201$	22.5751	1.59233
$202$	4.99114	0.351176
$203$	0	0
$204$	−12.7848	−0.895115
$205$	−0.831035	−0.0580420
$206$	2.32408	0.161926
$207$	−0.472029	−0.0328083
$208$	7.17150	0.497254
$209$	−2.83007	−0.195760
$210$	−0.398478	−0.0274976
$211$	0.803677	0.0553274	0.0276637	−	0.999617i	$-0.491193\pi$
$211$	0.803677	0.0553274	0.0276637	+	0.999617i	$0.491193\pi$
$212$	−19.7753	−1.35817
$213$	13.2570	0.908357
$214$	−0.574280	−0.0392569
$215$	−0.961048	−0.0655430
$216$	−4.89733	−0.333221
$217$	−8.51261	−0.577874
$218$	−0.0177113	−0.00119956
$219$	10.1343	0.684812
$220$	−0.376936	−0.0254130
$221$	7.14668	0.480738
$222$	−1.69897	−0.114028
$223$	−15.3290	−1.02651	−0.513254	−	0.858237i	$-0.671560\pi$
$223$	−15.3290	−1.02651	−0.513254	+	0.858237i	$0.671560\pi$
$224$	12.6974	0.848380
$225$	−1.99530	−0.133020
$226$	2.58738	0.172110
$227$	−23.5071	−1.56022	−0.780112	−	0.625640i	$-0.784838\pi$
$227$	−23.5071	−1.56022	−0.780112	+	0.625640i	$0.784838\pi$
$228$	−10.0874	−0.668056
$229$	19.1758	1.26717	0.633585	−	0.773673i	$-0.281583\pi$
$229$	19.1758	1.26717	0.633585	+	0.773673i	$0.281583\pi$
$230$	−0.0595078	−0.00392383
$231$	7.86039	0.517175
$232$	0	0
$233$	−23.9456	−1.56873	−0.784365	−	0.620300i	$-0.787011\pi$
$233$	−23.9456	−1.56873	−0.784365	+	0.620300i	$0.787011\pi$
$234$	−0.208234	−0.0136127
$235$	1.10803	0.0722798
$236$	8.19597	0.533512
$237$	−25.1326	−1.63254
$238$	3.97266	0.257509
$239$	−19.1130	−1.23632	−0.618159	−	0.786053i	$-0.712121\pi$
$239$	−19.1130	−1.23632	−0.618159	+	0.786053i	$0.712121\pi$
$240$	−1.29494	−0.0835878
$241$	14.1371	0.910651	0.455326	−	0.890325i	$-0.349523\pi$
$241$	14.1371	0.910651	0.455326	+	0.890325i	$0.349523\pi$
$242$	−0.259898	−0.0167069
$243$	−4.15197	−0.266349
$244$	18.9582	1.21367
$245$	−2.17700	−0.139083
$246$	−2.04239	−0.130218
$247$	5.63885	0.358791
$248$	2.04155	0.129638
$249$	−0.705018	−0.0446787
$250$	−0.505016	−0.0319400
$251$	−26.3548	−1.66350	−0.831751	−	0.555150i	$-0.812661\pi$
$251$	−26.3548	−1.66350	−0.831751	+	0.555150i	$0.812661\pi$
$252$	3.31157	0.208609
$253$	1.17385	0.0737994
$254$	2.65566	0.166631
$255$	−1.29046	−0.0808115
$256$	10.8657	0.679107
$257$	−21.9904	−1.37173	−0.685863	−	0.727731i	$-0.740575\pi$
$257$	−21.9904	−1.37173	−0.685863	+	0.727731i	$0.740575\pi$
$258$	−2.36191	−0.147046
$259$	−15.1035	−0.938488
$260$	0.751036	0.0465773
$261$	0	0
$262$	−3.08745	−0.190743
$263$	30.6372	1.88917	0.944585	−	0.328268i	$-0.106465\pi$
$263$	30.6372	1.88917	0.944585	+	0.328268i	$0.106465\pi$
$264$	−1.88513	−0.116022
$265$	−1.99605	−0.122617
$266$	3.13450	0.192188
$267$	23.7583	1.45398
$268$	−23.6518	−1.44476
$269$	−7.17996	−0.437770	−0.218885	−	0.975751i	$-0.570242\pi$
$269$	−7.17996	−0.437770	−0.218885	+	0.975751i	$0.570242\pi$
$270$	−0.242915	−0.0147833
$271$	0.447840	0.0272043	0.0136022	−	0.999907i	$-0.495670\pi$
$271$	0.447840	0.0272043	0.0136022	+	0.999907i	$0.495670\pi$
$272$	12.9100	0.782784
$273$	−15.6617	−0.947887
$274$	2.85193	0.172291
$275$	4.96195	0.299217
$276$	4.18405	0.251850
$277$	−22.6763	−1.36248	−0.681242	−	0.732058i	$-0.738560\pi$
$277$	−22.6763	−1.36248	−0.681242	+	0.732058i	$0.738560\pi$
$278$	−4.09632	−0.245681
$279$	0.803248	0.0480892
$280$	0.849558	0.0507708
$281$	−26.2909	−1.56838	−0.784191	−	0.620520i	$-0.786922\pi$
$281$	−26.2909	−1.56838	−0.784191	+	0.620520i	$0.786922\pi$
$282$	2.72314	0.162161
$283$	−11.7461	−0.698231	−0.349116	−	0.937080i	$-0.613518\pi$
$283$	−11.7461	−0.698231	−0.349116	+	0.937080i	$0.613518\pi$
$284$	−13.8893	−0.824179
$285$	−1.01819	−0.0603124
$286$	0.517841	0.0306206
$287$	−18.1564	−1.07174
$288$	−1.19812	−0.0706001
$289$	−4.13468	−0.243216
$290$	0	0
$291$	−19.3809	−1.13613
$292$	−10.6176	−0.621350
$293$	−23.9514	−1.39926	−0.699628	−	0.714507i	$-0.746651\pi$
$293$	−23.9514	−1.39926	−0.699628	+	0.714507i	$0.746651\pi$
$294$	−5.35029	−0.312035
$295$	0.827274	0.0481658
$296$	3.62222	0.210538
$297$	4.79175	0.278045
$298$	2.68076	0.155292
$299$	−2.33888	−0.135261
$300$	17.6863	1.02112
$301$	−20.9969	−1.21024
$302$	−2.46386	−0.141779
$303$	−35.4219	−2.03494
$304$	10.1862	0.584219
$305$	1.91358	0.109571
$306$	−0.374859	−0.0214293
$307$	−29.3191	−1.67333	−0.836665	−	0.547715i	$-0.815498\pi$
$307$	−29.3191	−1.67333	−0.836665	+	0.547715i	$0.815498\pi$
$308$	−8.23527	−0.469248
$309$	−16.4939	−0.938305
$310$	0.101264	0.00575140
$311$	−20.3701	−1.15508	−0.577541	−	0.816361i	$-0.695988\pi$
$311$	−20.3701	−1.15508	−0.577541	+	0.816361i	$0.695988\pi$
$312$	3.75608	0.212646
$313$	0.498536	0.0281789	0.0140895	−	0.999901i	$-0.495515\pi$
$313$	0.498536	0.0281789	0.0140895	+	0.999901i	$0.495515\pi$
$314$	−3.44972	−0.194679
$315$	0.334259	0.0188333
$316$	26.3312	1.48125
$317$	−20.0446	−1.12582	−0.562910	−	0.826518i	$-0.690318\pi$
$317$	−20.0446	−1.12582	−0.562910	+	0.826518i	$0.690318\pi$
$318$	−4.90559	−0.275092
$319$	0	0
$320$	1.25307	0.0700490
$321$	4.07564	0.227480
$322$	−1.30012	−0.0724530
$323$	10.1510	0.564814
$324$	19.4108	1.07838
$325$	−9.88659	−0.548409
$326$	3.97962	0.220411
$327$	0.125696	0.00695101
$328$	4.35439	0.240431
$329$	24.2082	1.33464
$330$	−0.0935051	−0.00514728
$331$	3.37043	0.185255	0.0926277	−	0.995701i	$-0.470473\pi$
$331$	3.37043	0.185255	0.0926277	+	0.995701i	$0.470473\pi$
$332$	0.738642	0.0405383
$333$	1.42517	0.0780986
$334$	−1.74384	−0.0954184
$335$	−2.38733	−0.130434
$336$	−28.2917	−1.54344
$337$	−1.14232	−0.0622263	−0.0311131	−	0.999516i	$-0.509905\pi$
$337$	−1.14232	−0.0622263	−0.0311131	+	0.999516i	$0.509905\pi$
$338$	2.34688	0.127654
$339$	−18.3626	−0.997318
$340$	1.35200	0.0733226
$341$	−1.99753	−0.108172
$342$	−0.295770	−0.0159934
$343$	−17.7321	−0.957442
$344$	5.03562	0.271502
$345$	0.422324	0.0227372
$346$	0.628216	0.0337731
$347$	35.4824	1.90480	0.952398	−	0.304856i	$-0.0986084\pi$
$347$	35.4824	1.90480	0.952398	+	0.304856i	$0.0986084\pi$
$348$	0	0
$349$	1.95802	0.104810	0.0524051	−	0.998626i	$-0.483311\pi$
$349$	1.95802	0.104810	0.0524051	+	0.998626i	$0.483311\pi$
$350$	−5.49571	−0.293758
$351$	−9.54746	−0.509606
$352$	2.97952	0.158809
$353$	−33.8874	−1.80365	−0.901823	−	0.432105i	$-0.857771\pi$
$353$	−33.8874	−1.80365	−0.901823	+	0.432105i	$0.857771\pi$
$354$	2.03315	0.108060
$355$	−1.40194	−0.0744073
$356$	−24.8914	−1.31924
$357$	−28.1938	−1.49218
$358$	−5.20731	−0.275215
$359$	8.44769	0.445852	0.222926	−	0.974835i	$-0.428439\pi$
$359$	8.44769	0.445852	0.222926	+	0.974835i	$0.428439\pi$
$360$	−0.0801640	−0.00422502
$361$	−10.9907	−0.578459
$362$	6.40559	0.336670
$363$	1.84448	0.0968103
$364$	16.4086	0.860045
$365$	−1.07171	−0.0560958
$366$	4.70290	0.245824
$367$	−5.49740	−0.286962	−0.143481	−	0.989653i	$-0.545830\pi$
$367$	−5.49740	−0.286962	−0.143481	+	0.989653i	$0.545830\pi$
$368$	−4.22502	−0.220245
$369$	1.71323	0.0891874
$370$	0.179668	0.00934048
$371$	−43.6097	−2.26410
$372$	−7.11996	−0.369153
$373$	2.82671	0.146362	0.0731808	−	0.997319i	$-0.476685\pi$
$373$	2.82671	0.146362	0.0731808	+	0.997319i	$0.476685\pi$
$374$	0.932207	0.0482033
$375$	3.58408	0.185081
$376$	−5.80575	−0.299409
$377$	0	0
$378$	−5.30720	−0.272973
$379$	33.3619	1.71368	0.856842	−	0.515579i	$-0.172423\pi$
$379$	33.3619	1.71368	0.856842	+	0.515579i	$0.172423\pi$
$380$	1.06675	0.0547232
$381$	−18.8471	−0.965567
$382$	0.690164	0.0353119
$383$	−13.7257	−0.701351	−0.350675	−	0.936497i	$-0.614048\pi$
$383$	−13.7257	−0.701351	−0.350675	+	0.936497i	$0.614048\pi$
$384$	14.0709	0.718055
$385$	−0.831241	−0.0423640
$386$	0.571911	0.0291095
$387$	1.98127	0.100713
$388$	20.3052	1.03084
$389$	10.5380	0.534298	0.267149	−	0.963655i	$-0.413918\pi$
$389$	10.5380	0.534298	0.267149	+	0.963655i	$0.413918\pi$
$390$	0.186307	0.00943402
$391$	−4.21040	−0.212929
$392$	11.4069	0.576134
$393$	21.9115	1.10529
$394$	−4.24011	−0.213614
$395$	2.65779	0.133728
$396$	0.777078	0.0390496
$397$	23.9609	1.20257	0.601283	−	0.799036i	$-0.294657\pi$
$397$	23.9609	1.20257	0.601283	+	0.799036i	$0.294657\pi$
$398$	0.513533	0.0257411
$399$	−22.2454	−1.11366
$400$	−17.8595	−0.892973
$401$	1.06624	0.0532456	0.0266228	−	0.999646i	$-0.491525\pi$
$401$	1.06624	0.0532456	0.0266228	+	0.999646i	$0.491525\pi$
$402$	−5.86722	−0.292630
$403$	3.98004	0.198260
$404$	37.1113	1.84636
$405$	1.95927	0.0973567
$406$	0	0
$407$	−3.54413	−0.175676
$408$	6.76162	0.334750
$409$	−19.6537	−0.971811	−0.485905	−	0.874011i	$-0.661510\pi$
$409$	−19.6537	−0.971811	−0.485905	+	0.874011i	$0.661510\pi$
$410$	0.215984	0.0106667
$411$	−20.2400	−0.998367
$412$	17.2806	0.851352
$413$	18.0743	0.889376
$414$	0.122679	0.00602936
$415$	0.0745561	0.00365982
$416$	−5.93662	−0.291067
$417$	29.0714	1.42363
$418$	0.735527	0.0359758
$419$	−12.6909	−0.619990	−0.309995	−	0.950738i	$-0.600327\pi$
$419$	−12.6909	−0.619990	−0.309995	+	0.950738i	$0.600327\pi$
$420$	−2.96286	−0.144573
$421$	−28.1583	−1.37235	−0.686176	−	0.727436i	$-0.740712\pi$
$421$	−28.1583	−1.37235	−0.686176	+	0.727436i	$0.740712\pi$
$422$	−0.208874	−0.0101678
$423$	−2.28428	−0.111065
$424$	10.4588	0.507922
$425$	−17.7977	−0.863313
$426$	−3.44547	−0.166934
$427$	41.8078	2.02322
$428$	−4.27002	−0.206399
$429$	−3.67510	−0.177435
$430$	0.249774	0.0120452
$431$	−7.03812	−0.339014	−0.169507	−	0.985529i	$-0.554218\pi$
$431$	−7.03812	−0.339014	−0.169507	+	0.985529i	$0.554218\pi$
$432$	−17.2468	−0.829789
$433$	26.4731	1.27222	0.636109	−	0.771599i	$-0.280543\pi$
$433$	26.4731	1.27222	0.636109	+	0.771599i	$0.280543\pi$
$434$	2.21241	0.106199
$435$	0	0
$436$	−0.131691	−0.00630685
$437$	−3.32208	−0.158917
$438$	−2.63388	−0.125852
$439$	−7.81316	−0.372902	−0.186451	−	0.982464i	$-0.559699\pi$
$439$	−7.81316	−0.372902	−0.186451	+	0.982464i	$0.559699\pi$
$440$	0.199354	0.00950381
$441$	4.48803	0.213716
$442$	−1.85740	−0.0883477
$443$	8.84198	0.420095	0.210048	−	0.977691i	$-0.432638\pi$
$443$	8.84198	0.420095	0.210048	+	0.977691i	$0.432638\pi$
$444$	−12.6326	−0.599517
$445$	−2.51246	−0.119102
$446$	3.98398	0.188647
$447$	−19.0253	−0.899864
$448$	27.3771	1.29345
$449$	10.7794	0.508713	0.254357	−	0.967110i	$-0.418136\pi$
$449$	10.7794	0.508713	0.254357	+	0.967110i	$0.418136\pi$
$450$	0.518574	0.0244458
$451$	−4.26050	−0.200619
$452$	19.2383	0.904895
$453$	17.4860	0.821562
$454$	6.10945	0.286731
$455$	1.65623	0.0776453
$456$	5.33503	0.249836
$457$	38.0240	1.77869	0.889343	−	0.457241i	$-0.151162\pi$
$457$	38.0240	1.77869	0.889343	+	0.457241i	$0.151162\pi$
$458$	−4.98374	−0.232875
$459$	−17.1872	−0.802228
$460$	−0.442466	−0.0206301
$461$	−33.9980	−1.58345	−0.791723	−	0.610881i	$-0.790816\pi$
$461$	−33.9980	−1.58345	−0.791723	+	0.610881i	$0.790816\pi$
$462$	−2.04290	−0.0950441
$463$	12.5500	0.583247	0.291624	−	0.956533i	$-0.405805\pi$
$463$	12.5500	0.583247	0.291624	+	0.956533i	$0.405805\pi$
$464$	0	0
$465$	−0.718665	−0.0333273
$466$	6.22341	0.288294
$467$	14.5952	0.675383	0.337692	−	0.941257i	$-0.390354\pi$
$467$	14.5952	0.675383	0.337692	+	0.941257i	$0.390354\pi$
$468$	−1.54831	−0.0715708
$469$	−52.1584	−2.40845
$470$	−0.287974	−0.0132832
$471$	24.4825	1.12810
$472$	−4.33468	−0.199520
$473$	−4.92705	−0.226546
$474$	6.53189	0.300020
$475$	−14.0427	−0.644321
$476$	29.5385	1.35389
$477$	4.11500	0.188413
$478$	4.96743	0.227205
$479$	7.91073	0.361451	0.180725	−	0.983534i	$-0.442155\pi$
$479$	7.91073	0.361451	0.180725	+	0.983534i	$0.442155\pi$
$480$	1.07196	0.0489280
$481$	7.06160	0.321981
$482$	−3.67420	−0.167355
$483$	9.22693	0.419840
$484$	−1.93245	−0.0878388
$485$	2.04954	0.0930650
$486$	1.07909	0.0489484
$487$	−17.9803	−0.814766	−0.407383	−	0.913257i	$-0.633559\pi$
$487$	−17.9803	−0.814766	−0.407383	+	0.913257i	$0.633559\pi$
$488$	−10.0266	−0.453883
$489$	−28.2432	−1.27720
$490$	0.565797	0.0255601
$491$	12.6747	0.572000	0.286000	−	0.958230i	$-0.407674\pi$
$491$	12.6747	0.572000	0.286000	+	0.958230i	$0.407674\pi$
$492$	−15.1861	−0.684640
$493$	0	0
$494$	−1.46552	−0.0659370
$495$	0.0784357	0.00352542
$496$	7.18968	0.322826
$497$	−30.6295	−1.37392
$498$	0.183232	0.00821084
$499$	1.70641	0.0763892	0.0381946	−	0.999270i	$-0.487839\pi$
$499$	1.70641	0.0763892	0.0381946	+	0.999270i	$0.487839\pi$
$500$	−3.75501	−0.167929
$501$	12.3759	0.552916
$502$	6.84955	0.305711
$503$	−11.3682	−0.506883	−0.253442	−	0.967351i	$-0.581563\pi$
$503$	−11.3682	−0.506883	−0.253442	+	0.967351i	$0.581563\pi$
$504$	−1.75142	−0.0780145
$505$	3.74590	0.166690
$506$	−0.305081	−0.0135625
$507$	−16.6557	−0.739707
$508$	19.7460	0.876087
$509$	33.4515	1.48271	0.741356	−	0.671112i	$-0.234183\pi$
$509$	33.4515	1.48271	0.741356	+	0.671112i	$0.234183\pi$
$510$	0.335386	0.0148512
$511$	−23.4146	−1.03580
$512$	−18.0813	−0.799088
$513$	−13.5610	−0.598731
$514$	5.71526	0.252089
$515$	1.74424	0.0768605
$516$	−17.5619	−0.773119
$517$	5.68058	0.249832
$518$	3.92537	0.172471
$519$	−4.45843	−0.195703
$520$	−0.397208	−0.0174187
$521$	−43.5318	−1.90716	−0.953581	−	0.301138i	$-0.902634\pi$
$521$	−43.5318	−1.90716	−0.953581	+	0.301138i	$0.902634\pi$
$522$	0	0
$523$	29.9235	1.30846	0.654231	−	0.756295i	$-0.272992\pi$
$523$	29.9235	1.30846	0.654231	+	0.756295i	$0.272992\pi$
$524$	−22.9566	−1.00286
$525$	39.0029	1.70222
$526$	−7.96253	−0.347183
$527$	7.16480	0.312104
$528$	−6.63882	−0.288917
$529$	−21.6221	−0.940090
$530$	0.518770	0.0225339
$531$	−1.70548	−0.0740116
$532$	23.3064	1.01046
$533$	8.48897	0.367698
$534$	−6.17473	−0.267207
$535$	−0.431002	−0.0186338
$536$	12.5090	0.540304
$537$	36.9561	1.59477
$538$	1.86605	0.0804513
$539$	−11.1609	−0.480735
$540$	−1.80618	−0.0777256
$541$	−17.8129	−0.765834	−0.382917	−	0.923783i	$-0.625081\pi$
$541$	−17.8129	−0.765834	−0.382917	+	0.923783i	$0.625081\pi$
$542$	−0.116392	−0.00499949
$543$	−45.4602	−1.95088
$544$	−10.6870	−0.458201
$545$	−0.0132924	−0.000569386 0
$546$	4.07043	0.174198
$547$	33.2404	1.42126	0.710629	−	0.703567i	$-0.248410\pi$
$547$	33.2404	1.42126	0.710629	+	0.703567i	$0.248410\pi$
$548$	21.2054	0.905848
$549$	−3.94497	−0.168367
$550$	−1.28960	−0.0549887
$551$	0	0
$552$	−2.21286	−0.0941856
$553$	58.0672	2.46927
$554$	5.89351	0.250391
$555$	−1.27509	−0.0541247
$556$	−30.4579	−1.29170
$557$	20.2050	0.856114	0.428057	−	0.903752i	$-0.359198\pi$
$557$	20.2050	0.856114	0.428057	+	0.903752i	$0.359198\pi$
$558$	−0.208762	−0.00883761
$559$	9.81705	0.415217
$560$	2.99187	0.126430
$561$	−6.61584	−0.279321
$562$	6.83293	0.288230
$563$	−34.0913	−1.43678	−0.718389	−	0.695641i	$-0.755120\pi$
$563$	−34.0913	−1.43678	−0.718389	+	0.695641i	$0.755120\pi$
$564$	20.2477	0.852583
$565$	1.94185	0.0816944
$566$	3.05277	0.128318
$567$	42.8060	1.79768
$568$	7.34577	0.308222
$569$	−5.25293	−0.220214	−0.110107	−	0.993920i	$-0.535119\pi$
$569$	−5.25293	−0.220214	−0.110107	+	0.993920i	$0.535119\pi$
$570$	0.264625	0.0110839
$571$	−15.3821	−0.643722	−0.321861	−	0.946787i	$-0.604308\pi$
$571$	−15.3821	−0.643722	−0.321861	+	0.946787i	$0.604308\pi$
$572$	3.85037	0.160992
$573$	−4.89807	−0.204620
$574$	4.71881	0.196959
$575$	5.82460	0.242903
$576$	−2.58330	−0.107637
$577$	3.25324	0.135434	0.0677172	−	0.997705i	$-0.478428\pi$
$577$	3.25324	0.135434	0.0677172	+	0.997705i	$0.478428\pi$
$578$	1.07459	0.0446972
$579$	−4.05883	−0.168679
$580$	0	0
$581$	1.62890	0.0675781
$582$	5.03705	0.208793
$583$	−10.2333	−0.423819
$584$	5.61545	0.232369
$585$	−0.156282	−0.00646145
$586$	6.22491	0.257149
$587$	−1.92070	−0.0792759	−0.0396380	−	0.999214i	$-0.512620\pi$
$587$	−1.92070	−0.0792759	−0.0396380	+	0.999214i	$0.512620\pi$
$588$	−39.7818	−1.64057
$589$	5.65315	0.232934
$590$	−0.215007	−0.00885168
$591$	30.0919	1.23782
$592$	12.7563	0.524281
$593$	−16.7228	−0.686721	−0.343361	−	0.939204i	$-0.611565\pi$
$593$	−16.7228	−0.686721	−0.343361	+	0.939204i	$0.611565\pi$
$594$	−1.24536	−0.0510979
$595$	2.98152	0.122230
$596$	19.9326	0.816473
$597$	−3.64453	−0.149161
$598$	0.607868	0.0248576
$599$	9.22913	0.377092	0.188546	−	0.982064i	$-0.439623\pi$
$599$	9.22913	0.377092	0.188546	+	0.982064i	$0.439623\pi$
$600$	−9.35391	−0.381872
$601$	27.4119	1.11815	0.559076	−	0.829116i	$-0.311156\pi$
$601$	27.4119	1.11815	0.559076	+	0.829116i	$0.311156\pi$
$602$	5.45706	0.222413
$603$	4.92165	0.200425
$604$	−18.3199	−0.745427
$605$	−0.195055	−0.00793013
$606$	9.20608	0.373971
$607$	−32.3064	−1.31127	−0.655637	−	0.755076i	$-0.727600\pi$
$607$	−32.3064	−1.31127	−0.655637	+	0.755076i	$0.727600\pi$
$608$	−8.43222	−0.341972
$609$	0	0
$610$	−0.497335	−0.0201365
$611$	−11.3184	−0.457895
$612$	−2.78724	−0.112668
$613$	−34.9634	−1.41216	−0.706080	−	0.708132i	$-0.749538\pi$
$613$	−34.9634	−1.41216	−0.706080	+	0.708132i	$0.749538\pi$
$614$	7.61997	0.307517
$615$	−1.53283	−0.0618097
$616$	4.35547	0.175487
$617$	25.5178	1.02731	0.513654	−	0.857997i	$-0.328291\pi$
$617$	25.5178	1.02731	0.513654	+	0.857997i	$0.328291\pi$
$618$	4.28673	0.172437
$619$	−6.67688	−0.268366	−0.134183	−	0.990957i	$-0.542841\pi$
$619$	−6.67688	−0.268366	−0.134183	+	0.990957i	$0.542841\pi$
$620$	0.752941	0.0302388
$621$	5.62480	0.225715
$622$	5.29414	0.212276
$623$	−54.8921	−2.19921
$624$	13.2277	0.529532
$625$	24.4307	0.977230
$626$	−0.129568	−0.00517859
$627$	−5.22001	−0.208467
$628$	−25.6502	−1.02355
$629$	12.7122	0.506868
$630$	−0.0868731	−0.00346111
$631$	13.7658	0.548009	0.274005	−	0.961728i	$-0.411652\pi$
$631$	13.7658	0.548009	0.274005	+	0.961728i	$0.411652\pi$
$632$	−13.9260	−0.553948
$633$	1.48237	0.0589189
$634$	5.20956	0.206898
$635$	1.99309	0.0790936
$636$	−36.4752	−1.44634
$637$	22.2379	0.881099
$638$	0	0
$639$	2.89020	0.114334
$640$	−1.48801	−0.0588188
$641$	38.7892	1.53208	0.766041	−	0.642792i	$-0.222224\pi$
$641$	38.7892	1.53208	0.766041	+	0.642792i	$0.222224\pi$
$642$	−1.05925	−0.0418052
$643$	1.26779	0.0499966	0.0249983	−	0.999687i	$-0.492042\pi$
$643$	1.26779	0.0499966	0.0249983	+	0.999687i	$0.492042\pi$
$644$	−9.66699	−0.380933
$645$	−1.77264	−0.0697976
$646$	−2.63821	−0.103799
$647$	−47.4642	−1.86601	−0.933005	−	0.359864i	$-0.882823\pi$
$647$	−47.4642	−1.86601	−0.933005	+	0.359864i	$0.882823\pi$
$648$	−10.2660	−0.403286
$649$	4.24123	0.166483
$650$	2.56950	0.100784
$651$	−15.7014	−0.615385
$652$	29.5902	1.15884
$653$	23.8207	0.932175	0.466087	−	0.884739i	$-0.345663\pi$
$653$	23.8207	0.932175	0.466087	+	0.884739i	$0.345663\pi$
$654$	−0.0326681	−0.00127742
$655$	−2.31716	−0.0905389
$656$	15.3348	0.598722
$657$	2.20940	0.0861969
$658$	−6.29164	−0.245274
$659$	−47.6738	−1.85711	−0.928553	−	0.371199i	$-0.878947\pi$
$659$	−47.6738	−1.85711	−0.928553	+	0.371199i	$0.878947\pi$
$660$	−0.695251	−0.0270626
$661$	−9.25214	−0.359866	−0.179933	−	0.983679i	$-0.557588\pi$
$661$	−9.25214	−0.359866	−0.179933	+	0.983679i	$0.557588\pi$
$662$	−0.875966	−0.0340454
$663$	13.1819	0.511944
$664$	−0.390653	−0.0151603
$665$	2.35247	0.0912248
$666$	−0.370397	−0.0143526
$667$	0	0
$668$	−12.9662	−0.501677
$669$	−28.2742	−1.09314
$670$	0.620462	0.0239705
$671$	9.81044	0.378728
$672$	23.4201	0.903451
$673$	−12.6974	−0.489450	−0.244725	−	0.969593i	$-0.578698\pi$
$673$	−12.6974	−0.489450	−0.244725	+	0.969593i	$0.578698\pi$
$674$	0.296887	0.0114357
$675$	23.7764	0.915155
$676$	17.4501	0.671158
$677$	−26.7447	−1.02788	−0.513941	−	0.857825i	$-0.671815\pi$
$677$	−26.7447	−1.02788	−0.513941	+	0.857825i	$0.671815\pi$
$678$	4.77239	0.183282
$679$	44.7784	1.71844
$680$	−0.715046	−0.0274208
$681$	−43.3585	−1.66150
$682$	0.519154	0.0198794
$683$	27.1676	1.03954	0.519770	−	0.854306i	$-0.326018\pi$
$683$	27.1676	1.03954	0.519770	+	0.854306i	$0.326018\pi$
$684$	−2.19918	−0.0840878
$685$	2.14040	0.0817804
$686$	4.60852	0.175954
$687$	35.3694	1.34943
$688$	17.7339	0.676097
$689$	20.3896	0.776781
$690$	−0.109761	−0.00417853
$691$	39.6649	1.50892	0.754462	−	0.656344i	$-0.227898\pi$
$691$	39.6649	1.50892	0.754462	+	0.656344i	$0.227898\pi$
$692$	4.67106	0.177567
$693$	1.71366	0.0650966
$694$	−9.22180	−0.350055
$695$	−3.07432	−0.116616
$696$	0	0
$697$	15.2817	0.578835
$698$	−0.508884	−0.0192615
$699$	−44.1673	−1.67056
$700$	−40.8630	−1.54448
$701$	−39.4666	−1.49063	−0.745317	−	0.666710i	$-0.767702\pi$
$701$	−39.4666	−1.49063	−0.745317	+	0.666710i	$0.767702\pi$
$702$	2.48136	0.0936530
$703$	10.0301	0.378293
$704$	6.42420	0.242121
$705$	2.04374	0.0769717
$706$	8.80726	0.331466
$707$	81.8402	3.07792
$708$	15.1173	0.568144
$709$	21.7796	0.817949	0.408974	−	0.912546i	$-0.365887\pi$
$709$	21.7796	0.817949	0.408974	+	0.912546i	$0.365887\pi$
$710$	0.364361	0.0136742
$711$	−5.47921	−0.205486
$712$	13.1646	0.493363
$713$	−2.34481	−0.0878137
$714$	7.32751	0.274225
$715$	0.388644	0.0145345
$716$	−38.7187	−1.44698
$717$	−35.2536	−1.31657
$718$	−2.19553	−0.0819366
$719$	5.52553	0.206068	0.103034	−	0.994678i	$-0.467145\pi$
$719$	5.52553	0.206068	0.103034	+	0.994678i	$0.467145\pi$
$720$	−0.282312	−0.0105212
$721$	38.1081	1.41922
$722$	2.85646	0.106307
$723$	26.0757	0.969764
$724$	47.6284	1.77009
$725$	0	0
$726$	−0.479377	−0.0177913
$727$	−11.7656	−0.436363	−0.218181	−	0.975908i	$-0.570012\pi$
$727$	−11.7656	−0.436363	−0.218181	+	0.975908i	$0.570012\pi$
$728$	−8.67818	−0.321635
$729$	22.4757	0.832435
$730$	0.278534	0.0103090
$731$	17.6725	0.653640
$732$	34.9681	1.29246
$733$	−7.58953	−0.280326	−0.140163	−	0.990128i	$-0.544763\pi$
$733$	−7.58953	−0.280326	−0.140163	+	0.990128i	$0.544763\pi$
$734$	1.42876	0.0527365
$735$	−4.01544	−0.148112
$736$	3.49751	0.128920
$737$	−12.2393	−0.450839
$738$	−0.445265	−0.0163904
$739$	29.1709	1.07307	0.536534	−	0.843878i	$-0.319733\pi$
$739$	29.1709	1.07307	0.536534	+	0.843878i	$0.319733\pi$
$740$	1.33591	0.0491090
$741$	10.4008	0.382082
$742$	11.3341	0.416087
$743$	6.89224	0.252852	0.126426	−	0.991976i	$-0.459649\pi$
$743$	6.89224	0.252852	0.126426	+	0.991976i	$0.459649\pi$
$744$	3.76560	0.138054
$745$	2.01193	0.0737116
$746$	−0.734656	−0.0268977
$747$	−0.153703	−0.00562368
$748$	6.93137	0.253436
$749$	−9.41651	−0.344072
$750$	−0.931493	−0.0340133
$751$	−28.0837	−1.02479	−0.512395	−	0.858750i	$-0.671242\pi$
$751$	−28.0837	−1.02479	−0.512395	+	0.858750i	$0.671242\pi$
$752$	−20.4460	−0.745589
$753$	−48.6110	−1.77148
$754$	0	0
$755$	−1.84915	−0.0672975
$756$	−39.4613	−1.43520
$757$	−21.6668	−0.787495	−0.393747	−	0.919219i	$-0.628822\pi$
$757$	−21.6668	−0.787495	−0.393747	+	0.919219i	$0.628822\pi$
$758$	−8.67067	−0.314933
$759$	2.16515	0.0785900
$760$	−0.564184	−0.0204651
$761$	−37.5773	−1.36218	−0.681089	−	0.732201i	$-0.738493\pi$
$761$	−37.5773	−1.36218	−0.681089	+	0.732201i	$0.738493\pi$
$762$	4.89832	0.177447
$763$	−0.290413	−0.0105137
$764$	5.13167	0.185657
$765$	−0.281335	−0.0101717
$766$	3.56728	0.128891
$767$	−8.45056	−0.305132
$768$	20.0416	0.723190
$769$	−35.1347	−1.26699	−0.633494	−	0.773747i	$-0.718380\pi$
$769$	−35.1347	−1.26699	−0.633494	+	0.773747i	$0.718380\pi$
$770$	0.216038	0.00778546
$771$	−40.5610	−1.46077
$772$	4.25241	0.153048
$773$	−23.0619	−0.829480	−0.414740	−	0.909940i	$-0.636127\pi$
$773$	−23.0619	−0.829480	−0.414740	+	0.909940i	$0.636127\pi$
$774$	−0.514926	−0.0185086
$775$	−9.91166	−0.356037
$776$	−10.7390	−0.385509
$777$	−27.8582	−0.999408
$778$	−2.73880	−0.0981907
$779$	12.0575	0.432005
$780$	1.38527	0.0496008
$781$	−7.18740	−0.257185
$782$	1.09427	0.0391311
$783$	0	0
$784$	40.1713	1.43469
$785$	−2.58905	−0.0924070
$786$	−5.69476	−0.203125
$787$	−21.0349	−0.749814	−0.374907	−	0.927062i	$-0.622325\pi$
$787$	−21.0349	−0.749814	−0.374907	+	0.927062i	$0.622325\pi$
$788$	−31.5271	−1.12311
$789$	56.5098	2.01180
$790$	−0.690752	−0.0245759
$791$	42.4256	1.50848
$792$	−0.410981	−0.0146036
$793$	−19.5471	−0.694138
$794$	−6.22739	−0.221002
$795$	−3.68169	−0.130576
$796$	3.81835	0.135338
$797$	−20.5578	−0.728194	−0.364097	−	0.931361i	$-0.618622\pi$
$797$	−20.5578	−0.728194	−0.364097	+	0.931361i	$0.618622\pi$
$798$	5.78153	0.204664
$799$	−20.3753	−0.720825
$800$	14.7842	0.522701
$801$	5.17960	0.183012
$802$	−0.277114	−0.00978524
$803$	−5.49438	−0.193892
$804$	−43.6253	−1.53855
$805$	−0.975754	−0.0343908
$806$	−1.03440	−0.0364353
$807$	−13.2433	−0.466187
$808$	−19.6274	−0.690491
$809$	45.2781	1.59189	0.795946	−	0.605368i	$-0.206974\pi$
$809$	45.2781	1.59189	0.795946	+	0.605368i	$0.206974\pi$
$810$	−0.509208	−0.0178918
$811$	−16.4042	−0.576031	−0.288015	−	0.957626i	$-0.592995\pi$
$811$	−16.4042	−0.576031	−0.288015	+	0.957626i	$0.592995\pi$
$812$	0	0
$813$	0.826033	0.0289702
$814$	0.921111	0.0322849
$815$	2.98674	0.104621
$816$	23.8123	0.833597
$817$	13.9439	0.487835
$818$	5.10794	0.178595
$819$	−3.41443	−0.119310
$820$	1.60594	0.0560817
$821$	52.6577	1.83777	0.918883	−	0.394531i	$-0.129093\pi$
$821$	52.6577	1.83777	0.918883	+	0.394531i	$0.129093\pi$
$822$	5.26034	0.183475
$823$	19.4167	0.676824	0.338412	−	0.940998i	$-0.390110\pi$
$823$	19.4167	0.676824	0.338412	+	0.940998i	$0.390110\pi$
$824$	−9.13933	−0.318384
$825$	9.15224	0.318640
$826$	−4.69746	−0.163445
$827$	−14.0299	−0.487868	−0.243934	−	0.969792i	$-0.578438\pi$
$827$	−14.0299	−0.487868	−0.243934	+	0.969792i	$0.578438\pi$
$828$	0.912175	0.0317003
$829$	45.5547	1.58218	0.791090	−	0.611700i	$-0.209514\pi$
$829$	45.5547	1.58218	0.791090	+	0.611700i	$0.209514\pi$
$830$	−0.0193770	−0.000672584 0
$831$	−41.8260	−1.45093
$832$	−12.8001	−0.443763
$833$	40.0323	1.38704
$834$	−7.55559	−0.261629
$835$	−1.30876	−0.0452916
$836$	5.46897	0.189148
$837$	−9.57167	−0.330845
$838$	3.29833	0.113939
$839$	19.7372	0.681404	0.340702	−	0.940171i	$-0.389335\pi$
$839$	19.7372	0.681404	0.340702	+	0.940171i	$0.389335\pi$
$840$	1.56700	0.0540665
$841$	0	0
$842$	7.31828	0.252204
$843$	−48.4931	−1.67019
$844$	−1.55307	−0.0534588
$845$	1.76136	0.0605925
$846$	0.593678	0.0204111
$847$	−4.26156	−0.146429
$848$	36.8324	1.26483
$849$	−21.6654	−0.743556
$850$	4.62557	0.158656
$851$	−4.16028	−0.142613
$852$	−25.6186	−0.877679
$853$	−37.5714	−1.28642	−0.643210	−	0.765690i	$-0.722398\pi$
$853$	−37.5714	−1.28642	−0.643210	+	0.765690i	$0.722398\pi$
$854$	−10.8657	−0.371818
$855$	−0.221978	−0.00759149
$856$	2.25833	0.0771881
$857$	4.70273	0.160642	0.0803211	−	0.996769i	$-0.474405\pi$
$857$	4.70273	0.160642	0.0803211	+	0.996769i	$0.474405\pi$
$858$	0.955149	0.0326082
$859$	27.1642	0.926829	0.463415	−	0.886142i	$-0.346624\pi$
$859$	27.1642	0.926829	0.463415	+	0.886142i	$0.346624\pi$
$860$	1.85718	0.0633293
$861$	−33.4892	−1.14131
$862$	1.82919	0.0623025
$863$	31.5547	1.07413	0.537067	−	0.843539i	$-0.319532\pi$
$863$	31.5547	1.07413	0.537067	+	0.843539i	$0.319532\pi$
$864$	14.2771	0.485716
$865$	0.471482	0.0160309
$866$	−6.88030	−0.233802
$867$	−7.62635	−0.259004
$868$	16.4502	0.558357
$869$	13.6258	0.462224
$870$	0	0
$871$	24.3865	0.826304
$872$	0.0696487	0.00235860
$873$	−4.22528	−0.143004
$874$	0.863400	0.0292049
$875$	−8.28079	−0.279942
$876$	−19.5840	−0.661684
$877$	−47.2772	−1.59644	−0.798219	−	0.602368i	$-0.794224\pi$
$877$	−47.2772	−1.59644	−0.798219	+	0.602368i	$0.794224\pi$
$878$	2.03062	0.0685301
$879$	−44.1780	−1.49009
$880$	0.702060	0.0236664
$881$	6.41911	0.216265	0.108133	−	0.994136i	$-0.465513\pi$
$881$	6.41911	0.216265	0.108133	+	0.994136i	$0.465513\pi$
$882$	−1.16643	−0.0392757
$883$	49.2880	1.65867	0.829337	−	0.558749i	$-0.188718\pi$
$883$	49.2880	1.65867	0.829337	+	0.558749i	$0.188718\pi$
$884$	−13.8106	−0.464501
$885$	1.52589	0.0512924
$886$	−2.29801	−0.0772032
$887$	−4.53205	−0.152171	−0.0760857	−	0.997101i	$-0.524242\pi$
$887$	−4.53205	−0.152171	−0.0760857	+	0.997101i	$0.524242\pi$
$888$	6.68113	0.224204
$889$	43.5451	1.46045
$890$	0.652982	0.0218880
$891$	10.0447	0.336509
$892$	29.6226	0.991839
$893$	−16.0764	−0.537977
$894$	4.94462	0.165373
$895$	−3.90813	−0.130635
$896$	−32.5100	−1.08608
$897$	−4.31402	−0.144041
$898$	−2.80155	−0.0934890
$899$	0	0
$900$	3.85583	0.128528
$901$	36.7050	1.22282
$902$	1.10729	0.0368689
$903$	−38.7285	−1.28880
$904$	−10.1748	−0.338408
$905$	4.80745	0.159805
$906$	−4.54456	−0.150983
$907$	−2.95705	−0.0981873	−0.0490937	−	0.998794i	$-0.515633\pi$
$907$	−2.95705	−0.0981873	−0.0490937	+	0.998794i	$0.515633\pi$
$908$	45.4265	1.50753
$909$	−7.72242	−0.256136
$910$	−0.430451	−0.0142693
$911$	35.7486	1.18440	0.592202	−	0.805789i	$-0.298259\pi$
$911$	35.7486	1.18440	0.592202	+	0.805789i	$0.298259\pi$
$912$	18.7883	0.622142
$913$	0.382230	0.0126500
$914$	−9.88234	−0.326879
$915$	3.52956	0.116684
$916$	−37.0563	−1.22437
$917$	−50.6252	−1.67179
$918$	4.46690	0.147430
$919$	−9.01630	−0.297420	−0.148710	−	0.988881i	$-0.547512\pi$
$919$	−9.01630	−0.297420	−0.148710	+	0.988881i	$0.547512\pi$
$920$	0.234011	0.00771513
$921$	−54.0786	−1.78195
$922$	8.83600	0.290998
$923$	14.3207	0.471373
$924$	−15.1898	−0.499709
$925$	−17.5858	−0.578218
$926$	−3.26171	−0.107186
$927$	−3.59587	−0.118104
$928$	0	0
$929$	−47.5045	−1.55857	−0.779285	−	0.626669i	$-0.784418\pi$
$929$	−47.5045	−1.55857	−0.779285	+	0.626669i	$0.784418\pi$
$930$	0.186779	0.00612474
$931$	31.5862	1.03519
$932$	46.2738	1.51575
$933$	−37.5723	−1.23006
$934$	−3.79325	−0.124119
$935$	0.699630	0.0228803
$936$	0.818871	0.0267656
$937$	14.0537	0.459114	0.229557	−	0.973295i	$-0.426272\pi$
$937$	14.0537	0.459114	0.229557	+	0.973295i	$0.426272\pi$
$938$	13.5558	0.442614
$939$	0.919541	0.0300081
$940$	−2.14121	−0.0698386
$941$	−16.9869	−0.553758	−0.276879	−	0.960905i	$-0.589300\pi$
$941$	−16.9869	−0.553758	−0.276879	+	0.960905i	$0.589300\pi$
$942$	−6.36295	−0.207316
$943$	−5.00120	−0.162862
$944$	−15.2654	−0.496846
$945$	−3.98310	−0.129570
$946$	1.28053	0.0416336
$947$	56.9044	1.84915	0.924573	−	0.381005i	$-0.124422\pi$
$947$	56.9044	1.84915	0.924573	+	0.381005i	$0.124422\pi$
$948$	48.5675	1.57740
$949$	10.9474	0.355369
$950$	3.64965	0.118410
$951$	−36.9720	−1.19890
$952$	−15.6223	−0.506322
$953$	−37.5074	−1.21498	−0.607492	−	0.794325i	$-0.707825\pi$
$953$	−37.5074	−1.21498	−0.607492	+	0.794325i	$0.707825\pi$
$954$	−1.06948	−0.0346257
$955$	0.517974	0.0167612
$956$	36.9350	1.19456
$957$	0	0
$958$	−2.05598	−0.0664257
$959$	46.7633	1.51007
$960$	2.31127	0.0745961
$961$	−27.0099	−0.871286
$962$	−1.83529	−0.0591723
$963$	0.888540	0.0286328
$964$	−27.3193	−0.879895
$965$	0.429224	0.0138172
$966$	−2.39806	−0.0771562
$967$	−2.57577	−0.0828312	−0.0414156	−	0.999142i	$-0.513187\pi$
$967$	−2.57577	−0.0828312	−0.0414156	+	0.999142i	$0.513187\pi$
$968$	1.02204	0.0328495
$969$	18.7233	0.601478
$970$	−0.532672	−0.0171031
$971$	37.1688	1.19280	0.596401	−	0.802686i	$-0.296597\pi$
$971$	37.1688	1.19280	0.596401	+	0.802686i	$0.296597\pi$
$972$	8.02349	0.257353
$973$	−67.1677	−2.15330
$974$	4.67304	0.149734
$975$	−18.2357	−0.584008
$976$	−35.3105	−1.13026
$977$	−40.3850	−1.29203	−0.646015	−	0.763325i	$-0.723565\pi$
$977$	−40.3850	−1.29203	−0.646015	+	0.763325i	$0.723565\pi$
$978$	7.34034	0.234718
$979$	−12.8807	−0.411670
$980$	4.20695	0.134386
$981$	0.0274033	0.000874920 0
$982$	−3.29411	−0.105119
$983$	0.852007	0.0271748	0.0135874	−	0.999908i	$-0.495675\pi$
$983$	0.852007	0.0271748	0.0135874	+	0.999908i	$0.495675\pi$
$984$	8.03159	0.256038
$985$	−3.18224	−0.101395
$986$	0	0
$987$	44.6515	1.42127
$988$	−10.8968	−0.346674
$989$	−5.78363	−0.183909
$990$	−0.0203853	−0.000647886 0
$991$	40.9052	1.29940	0.649699	−	0.760192i	$-0.274895\pi$
$991$	40.9052	1.29940	0.649699	+	0.760192i	$0.274895\pi$
$992$	−5.95168	−0.188966
$993$	6.21670	0.197281
$994$	7.96055	0.252493
$995$	0.385411	0.0122184
$996$	1.36241	0.0431697
$997$	−28.2323	−0.894127	−0.447064	−	0.894502i	$-0.647530\pi$
$997$	−28.2323	−0.894127	−0.447064	+	0.894502i	$0.647530\pi$
$998$	−0.443491	−0.0140385
$999$	−16.9826	−0.537305

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.10	✓	18	29.28	even	2
9251.2.a.t.1.9	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)

\(f(q)\)	\(=\)	\(q-0.259898 q^{2} +1.84448 q^{3} -1.93245 q^{4} -0.195055 q^{5} -0.479377 q^{6} -4.26156 q^{7} +1.02204 q^{8} +0.402120 q^{9} +O(q^{10})\)	\(q-0.259898 q^{2} +1.84448 q^{3} -1.93245 q^{4} -0.195055 q^{5} -0.479377 q^{6} -4.26156 q^{7} +1.02204 q^{8} +0.402120 q^{9} +0.0506944 q^{10} -1.00000 q^{11} -3.56438 q^{12} +1.99248 q^{13} +1.10757 q^{14} -0.359777 q^{15} +3.59928 q^{16} +3.58683 q^{17} -0.104510 q^{18} +2.83007 q^{19} +0.376936 q^{20} -7.86039 q^{21} +0.259898 q^{22} -1.17385 q^{23} +1.88513 q^{24} -4.96195 q^{25} -0.517841 q^{26} -4.79175 q^{27} +8.23527 q^{28} +0.0935051 q^{30} +1.99753 q^{31} -2.97952 q^{32} -1.84448 q^{33} -0.932207 q^{34} +0.831241 q^{35} -0.777078 q^{36} +3.54413 q^{37} -0.735527 q^{38} +3.67510 q^{39} -0.199354 q^{40} +4.26050 q^{41} +2.04290 q^{42} +4.92705 q^{43} +1.93245 q^{44} -0.0784357 q^{45} +0.305081 q^{46} -5.68058 q^{47} +6.63882 q^{48} +11.1609 q^{49} +1.28960 q^{50} +6.61584 q^{51} -3.85037 q^{52} +10.2333 q^{53} +1.24536 q^{54} +0.195055 q^{55} -4.35547 q^{56} +5.22001 q^{57} -4.24123 q^{59} +0.695251 q^{60} -9.81044 q^{61} -0.519154 q^{62} -1.71366 q^{63} -6.42420 q^{64} -0.388644 q^{65} +0.479377 q^{66} +12.2393 q^{67} -6.93137 q^{68} -2.16515 q^{69} -0.216038 q^{70} +7.18740 q^{71} +0.410981 q^{72} +5.49438 q^{73} -0.921111 q^{74} -9.15224 q^{75} -5.46897 q^{76} +4.26156 q^{77} -0.955149 q^{78} -13.6258 q^{79} -0.702060 q^{80} -10.0447 q^{81} -1.10729 q^{82} -0.382230 q^{83} +15.1898 q^{84} -0.699630 q^{85} -1.28053 q^{86} -1.02204 q^{88} +12.8807 q^{89} +0.0203853 q^{90} -8.49108 q^{91} +2.26841 q^{92} +3.68442 q^{93} +1.47637 q^{94} -0.552020 q^{95} -5.49567 q^{96} -10.5075 q^{97} -2.90070 q^{98} -0.402120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 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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