LMFDB - Embedded newform 9251.2.a.s.1.18

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			1.18
Root			$2.49854$ 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)

$f(q)$	$=$	$q+2.49854 q^{2} +1.52510 q^{3} +4.24268 q^{4} -2.15150 q^{5} +3.81052 q^{6} -0.0683885 q^{7} +5.60341 q^{8} -0.674063 q^{9} +O(q^{10})$	\(q+2.49854 q^{2} +1.52510 q^{3} +4.24268 q^{4} -2.15150 q^{5} +3.81052 q^{6} -0.0683885 q^{7} +5.60341 q^{8} -0.674063 q^{9} -5.37560 q^{10} +1.00000 q^{11} +6.47052 q^{12} -2.70467 q^{13} -0.170871 q^{14} -3.28126 q^{15} +5.51496 q^{16} -6.23112 q^{17} -1.68417 q^{18} -5.46409 q^{19} -9.12812 q^{20} -0.104299 q^{21} +2.49854 q^{22} +1.04004 q^{23} +8.54577 q^{24} -0.371043 q^{25} -6.75772 q^{26} -5.60332 q^{27} -0.290150 q^{28} -8.19834 q^{30} +4.61950 q^{31} +2.57250 q^{32} +1.52510 q^{33} -15.5687 q^{34} +0.147138 q^{35} -2.85983 q^{36} +8.46301 q^{37} -13.6522 q^{38} -4.12490 q^{39} -12.0557 q^{40} -0.313280 q^{41} -0.260596 q^{42} -3.59063 q^{43} +4.24268 q^{44} +1.45025 q^{45} +2.59858 q^{46} +7.29758 q^{47} +8.41087 q^{48} -6.99532 q^{49} -0.927064 q^{50} -9.50310 q^{51} -11.4750 q^{52} -0.512027 q^{53} -14.0001 q^{54} -2.15150 q^{55} -0.383208 q^{56} -8.33329 q^{57} -6.89069 q^{59} -13.9213 q^{60} -5.64988 q^{61} +11.5420 q^{62} +0.0460981 q^{63} -4.60244 q^{64} +5.81910 q^{65} +3.81052 q^{66} -11.7780 q^{67} -26.4366 q^{68} +1.58617 q^{69} +0.367629 q^{70} -1.35825 q^{71} -3.77705 q^{72} -8.79805 q^{73} +21.1451 q^{74} -0.565879 q^{75} -23.1824 q^{76} -0.0683885 q^{77} -10.3062 q^{78} -0.673775 q^{79} -11.8654 q^{80} -6.52345 q^{81} -0.782742 q^{82} +15.2943 q^{83} -0.442509 q^{84} +13.4063 q^{85} -8.97132 q^{86} +5.60341 q^{88} -16.5891 q^{89} +3.62349 q^{90} +0.184968 q^{91} +4.41256 q^{92} +7.04521 q^{93} +18.2333 q^{94} +11.7560 q^{95} +3.92332 q^{96} +13.3691 q^{97} -17.4781 q^{98} -0.674063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.49854	1.76673	0.883366	−	0.468685i	$-0.155272\pi$
$2$	2.49854	1.76673	0.883366	+	0.468685i	$0.155272\pi$
$3$	1.52510	0.880518	0.440259	−	0.897871i	$-0.354887\pi$
$3$	1.52510	0.880518	0.440259	+	0.897871i	$0.354887\pi$
$4$	4.24268	2.12134
$5$	−2.15150	−0.962181	−0.481090	−	0.876671i	$-0.659759\pi$
$5$	−2.15150	−0.962181	−0.481090	+	0.876671i	$0.659759\pi$
$6$	3.81052	1.55564
$7$	−0.0683885	−0.0258484	−0.0129242	−	0.999916i	$-0.504114\pi$
$7$	−0.0683885	−0.0258484	−0.0129242	+	0.999916i	$0.504114\pi$
$8$	5.60341	1.98110
$9$	−0.674063	−0.224688
$10$	−5.37560	−1.69991
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	6.47052	1.86788
$13$	−2.70467	−0.750141	−0.375070	−	0.926996i	$-0.622381\pi$
$13$	−2.70467	−0.750141	−0.375070	+	0.926996i	$0.622381\pi$
$14$	−0.170871	−0.0456672
$15$	−3.28126	−0.847217
$16$	5.51496	1.37874
$17$	−6.23112	−1.51127	−0.755635	−	0.654993i	$-0.772671\pi$
$17$	−6.23112	−1.51127	−0.755635	+	0.654993i	$0.772671\pi$
$18$	−1.68417	−0.396963
$19$	−5.46409	−1.25355	−0.626774	−	0.779201i	$-0.715625\pi$
$19$	−5.46409	−1.25355	−0.626774	+	0.779201i	$0.715625\pi$
$20$	−9.12812	−2.04111
$21$	−0.104299	−0.0227600
$22$	2.49854	0.532689
$23$	1.04004	0.216864	0.108432	−	0.994104i	$-0.465417\pi$
$23$	1.04004	0.216864	0.108432	+	0.994104i	$0.465417\pi$
$24$	8.54577	1.74440
$25$	−0.371043	−0.0742086
$26$	−6.75772	−1.32530
$27$	−5.60332	−1.07836
$28$	−0.290150	−0.0548332
$29$	0	0
$29$	0	0
$30$	−8.19834	−1.49681
$31$	4.61950	0.829687	0.414843	−	0.909893i	$-0.363836\pi$
$31$	4.61950	0.829687	0.414843	+	0.909893i	$0.363836\pi$
$32$	2.57250	0.454757
$33$	1.52510	0.265486
$34$	−15.5687	−2.67001
$35$	0.147138	0.0248708
$36$	−2.85983	−0.476639
$37$	8.46301	1.39131	0.695655	−	0.718376i	$-0.255114\pi$
$37$	8.46301	1.39131	0.695655	+	0.718376i	$0.255114\pi$
$38$	−13.6522	−2.21468
$39$	−4.12490	−0.660513
$40$	−12.0557	−1.90618
$41$	−0.313280	−0.0489262	−0.0244631	−	0.999701i	$-0.507788\pi$
$41$	−0.313280	−0.0489262	−0.0244631	+	0.999701i	$0.507788\pi$
$42$	−0.260596	−0.0402108
$43$	−3.59063	−0.547566	−0.273783	−	0.961791i	$-0.588275\pi$
$43$	−3.59063	−0.547566	−0.273783	+	0.961791i	$0.588275\pi$
$44$	4.24268	0.639608
$45$	1.45025	0.216190
$46$	2.59858	0.383140
$47$	7.29758	1.06446	0.532231	−	0.846599i	$-0.321354\pi$
$47$	7.29758	1.06446	0.532231	+	0.846599i	$0.321354\pi$
$48$	8.41087	1.21400
$49$	−6.99532	−0.999332
$50$	−0.927064	−0.131107
$51$	−9.50310	−1.33070
$52$	−11.4750	−1.59130
$53$	−0.512027	−0.0703323	−0.0351661	−	0.999381i	$-0.511196\pi$
$53$	−0.512027	−0.0703323	−0.0351661	+	0.999381i	$0.511196\pi$
$54$	−14.0001	−1.90517
$55$	−2.15150	−0.290108
$56$	−0.383208	−0.0512084
$57$	−8.33329	−1.10377
$58$	0	0
$59$	−6.89069	−0.897092	−0.448546	−	0.893760i	$-0.648058\pi$
$59$	−6.89069	−0.897092	−0.448546	+	0.893760i	$0.648058\pi$
$60$	−13.9213	−1.79724
$61$	−5.64988	−0.723393	−0.361696	−	0.932296i	$-0.617802\pi$
$61$	−5.64988	−0.723393	−0.361696	+	0.932296i	$0.617802\pi$
$62$	11.5420	1.46583
$63$	0.0460981	0.00580782
$64$	−4.60244	−0.575305
$65$	5.81910	0.721771
$66$	3.81052	0.469043
$67$	−11.7780	−1.43891	−0.719453	−	0.694541i	$-0.755608\pi$
$67$	−11.7780	−1.43891	−0.719453	+	0.694541i	$0.755608\pi$
$68$	−26.4366	−3.20591
$69$	1.58617	0.190952
$70$	0.367629	0.0439401
$71$	−1.35825	−0.161195	−0.0805974	−	0.996747i	$-0.525683\pi$
$71$	−1.35825	−0.161195	−0.0805974	+	0.996747i	$0.525683\pi$
$72$	−3.77705	−0.445130
$73$	−8.79805	−1.02973	−0.514867	−	0.857270i	$-0.672159\pi$
$73$	−8.79805	−1.02973	−0.514867	+	0.857270i	$0.672159\pi$
$74$	21.1451	2.45807
$75$	−0.565879	−0.0653420
$76$	−23.1824	−2.65920
$77$	−0.0683885	−0.00779359
$78$	−10.3062	−1.16695
$79$	−0.673775	−0.0758056	−0.0379028	−	0.999281i	$-0.512068\pi$
$79$	−0.673775	−0.0758056	−0.0379028	+	0.999281i	$0.512068\pi$
$80$	−11.8654	−1.32660
$81$	−6.52345	−0.724828
$82$	−0.782742	−0.0864394
$83$	15.2943	1.67877	0.839386	−	0.543536i	$-0.182915\pi$
$83$	15.2943	1.67877	0.839386	+	0.543536i	$0.182915\pi$
$84$	−0.442509	−0.0482817
$85$	13.4063	1.45411
$86$	−8.97132	−0.967402
$87$	0	0
$88$	5.60341	0.597325
$89$	−16.5891	−1.75844	−0.879219	−	0.476418i	$-0.841935\pi$
$89$	−16.5891	−1.75844	−0.879219	+	0.476418i	$0.841935\pi$
$90$	3.62349	0.381950
$91$	0.184968	0.0193899
$92$	4.41256	0.460041
$93$	7.04521	0.730554
$94$	18.2333	1.88062
$95$	11.7560	1.20614
$96$	3.92332	0.400422
$97$	13.3691	1.35743	0.678715	−	0.734402i	$-0.262537\pi$
$97$	13.3691	1.35743	0.678715	+	0.734402i	$0.262537\pi$
$98$	−17.4781	−1.76555
$99$	−0.674063	−0.0677459
$100$	−1.57422	−0.157422
$101$	12.2184	1.21578	0.607888	−	0.794022i	$-0.292017\pi$
$101$	12.2184	1.21578	0.607888	+	0.794022i	$0.292017\pi$
$102$	−23.7438	−2.35099
$103$	10.7486	1.05910	0.529548	−	0.848280i	$-0.322362\pi$
$103$	10.7486	1.05910	0.529548	+	0.848280i	$0.322362\pi$
$104$	−15.1554	−1.48611
$105$	0.224400	0.0218992
$106$	−1.27932	−0.124258
$107$	−2.91620	−0.281919	−0.140960	−	0.990015i	$-0.545019\pi$
$107$	−2.91620	−0.281919	−0.140960	+	0.990015i	$0.545019\pi$
$108$	−23.7731	−2.28757
$109$	−1.84384	−0.176608	−0.0883040	−	0.996094i	$-0.528145\pi$
$109$	−1.84384	−0.176608	−0.0883040	+	0.996094i	$0.528145\pi$
$110$	−5.37560	−0.512543
$111$	12.9069	1.22507
$112$	−0.377159	−0.0356382
$113$	0.573739	0.0539728	0.0269864	−	0.999636i	$-0.491409\pi$
$113$	0.573739	0.0539728	0.0269864	+	0.999636i	$0.491409\pi$
$114$	−20.8210	−1.95007
$115$	−2.23765	−0.208662
$116$	0	0
$117$	1.82312	0.168547
$118$	−17.2166	−1.58492
$119$	0.426137	0.0390639
$120$	−18.3862	−1.67843
$121$	1.00000	0.0909091
$122$	−14.1164	−1.27804
$123$	−0.477785	−0.0430804
$124$	19.5990	1.76005
$125$	11.5558	1.03358
$126$	0.115178	0.0102609
$127$	8.42444	0.747549	0.373774	−	0.927520i	$-0.378063\pi$
$127$	8.42444	0.747549	0.373774	+	0.927520i	$0.378063\pi$
$128$	−16.6444	−1.47117
$129$	−5.47608	−0.482142
$130$	14.5392	1.27518
$131$	−19.2095	−1.67834	−0.839170	−	0.543870i	$-0.816959\pi$
$131$	−19.2095	−1.67834	−0.839170	+	0.543870i	$0.816959\pi$
$132$	6.47052	0.563186
$133$	0.373681	0.0324022
$134$	−29.4276	−2.54216
$135$	12.0556	1.03758
$136$	−34.9155	−2.99398
$137$	−21.4218	−1.83019	−0.915096	−	0.403236i	$-0.867885\pi$
$137$	−21.4218	−1.83019	−0.915096	+	0.403236i	$0.867885\pi$
$138$	3.96310	0.337361
$139$	6.28160	0.532798	0.266399	−	0.963863i	$-0.414166\pi$
$139$	6.28160	0.532798	0.266399	+	0.963863i	$0.414166\pi$
$140$	0.624258	0.0527595
$141$	11.1296	0.937278
$142$	−3.39364	−0.284788
$143$	−2.70467	−0.226176
$144$	−3.71743	−0.309786
$145$	0	0
$146$	−21.9822	−1.81926
$147$	−10.6686	−0.879930
$148$	35.9058	2.95144
$149$	5.62539	0.460850	0.230425	−	0.973090i	$-0.425988\pi$
$149$	5.62539	0.460850	0.230425	+	0.973090i	$0.425988\pi$
$150$	−1.41387	−0.115442
$151$	−15.7905	−1.28501	−0.642506	−	0.766281i	$-0.722105\pi$
$151$	−15.7905	−1.28501	−0.642506	+	0.766281i	$0.722105\pi$
$152$	−30.6175	−2.48341
$153$	4.20017	0.339564
$154$	−0.170871	−0.0137692
$155$	−9.93886	−0.798308
$156$	−17.5006	−1.40117
$157$	−15.2046	−1.21346	−0.606729	−	0.794908i	$-0.707519\pi$
$157$	−15.2046	−1.21346	−0.606729	+	0.794908i	$0.707519\pi$
$158$	−1.68345	−0.133928
$159$	−0.780893	−0.0619289
$160$	−5.53473	−0.437559
$161$	−0.0711268	−0.00560558
$162$	−16.2991	−1.28058
$163$	6.65450	0.521221	0.260610	−	0.965444i	$-0.416076\pi$
$163$	6.65450	0.521221	0.260610	+	0.965444i	$0.416076\pi$
$164$	−1.32915	−0.103789
$165$	−3.28126	−0.255446
$166$	38.2134	2.96594
$167$	4.81232	0.372389	0.186194	−	0.982513i	$-0.440385\pi$
$167$	4.81232	0.372389	0.186194	+	0.982513i	$0.440385\pi$
$168$	−0.584432	−0.0450899
$169$	−5.68475	−0.437289
$170$	33.4960	2.56903
$171$	3.68314	0.281657
$172$	−15.2339	−1.16157
$173$	−22.6708	−1.72363	−0.861814	−	0.507225i	$-0.830671\pi$
$173$	−22.6708	−1.72363	−0.861814	+	0.507225i	$0.830671\pi$
$174$	0	0
$175$	0.0253751	0.00191817
$176$	5.51496	0.415705
$177$	−10.5090	−0.789906
$178$	−41.4484	−3.10669
$179$	−13.2253	−0.988502	−0.494251	−	0.869319i	$-0.664558\pi$
$179$	−13.2253	−0.988502	−0.494251	+	0.869319i	$0.664558\pi$
$180$	6.15293	0.458613
$181$	7.82774	0.581831	0.290916	−	0.956749i	$-0.406040\pi$
$181$	7.82774	0.581831	0.290916	+	0.956749i	$0.406040\pi$
$182$	0.462150	0.0342568
$183$	−8.61664	−0.636960
$184$	5.82777	0.429629
$185$	−18.2082	−1.33869
$186$	17.6027	1.29069
$187$	−6.23112	−0.455665
$188$	30.9613	2.25808
$189$	0.383203	0.0278739
$190$	29.3728	2.13092
$191$	17.4088	1.25966	0.629829	−	0.776734i	$-0.283125\pi$
$191$	17.4088	1.25966	0.629829	+	0.776734i	$0.283125\pi$
$192$	−7.01920	−0.506567
$193$	4.69448	0.337916	0.168958	−	0.985623i	$-0.445960\pi$
$193$	4.69448	0.337916	0.168958	+	0.985623i	$0.445960\pi$
$194$	33.4032	2.39821
$195$	8.87473	0.635532
$196$	−29.6789	−2.11992
$197$	21.2556	1.51440	0.757201	−	0.653182i	$-0.226566\pi$
$197$	21.2556	1.51440	0.757201	+	0.653182i	$0.226566\pi$
$198$	−1.68417	−0.119689
$199$	8.92558	0.632718	0.316359	−	0.948640i	$-0.397540\pi$
$199$	8.92558	0.632718	0.316359	+	0.948640i	$0.397540\pi$
$200$	−2.07911	−0.147015
$201$	−17.9626	−1.26698
$202$	30.5281	2.14795
$203$	0	0
$204$	−40.3186	−2.82287
$205$	0.674023	0.0470758
$206$	26.8559	1.87114
$207$	−0.701053	−0.0487266
$208$	−14.9161	−1.03425
$209$	−5.46409	−0.377959
$210$	0.560672	0.0386900
$211$	18.2122	1.25378	0.626891	−	0.779107i	$-0.284327\pi$
$211$	18.2122	1.25378	0.626891	+	0.779107i	$0.284327\pi$
$212$	−2.17236	−0.149199
$213$	−2.07147	−0.141935
$214$	−7.28622	−0.498076
$215$	7.72525	0.526858
$216$	−31.3977	−2.13634
$217$	−0.315920	−0.0214461
$218$	−4.60690	−0.312019
$219$	−13.4179	−0.906699
$220$	−9.12812	−0.615418
$221$	16.8531	1.13366
$222$	32.2485	2.16438
$223$	22.5821	1.51221	0.756105	−	0.654450i	$-0.227100\pi$
$223$	22.5821	1.51221	0.756105	+	0.654450i	$0.227100\pi$
$224$	−0.175929	−0.0117547
$225$	0.250107	0.0166738
$226$	1.43351	0.0953555
$227$	0.562726	0.0373494	0.0186747	−	0.999826i	$-0.494055\pi$
$227$	0.562726	0.0373494	0.0186747	+	0.999826i	$0.494055\pi$
$228$	−35.3555	−2.34147
$229$	−6.90131	−0.456052	−0.228026	−	0.973655i	$-0.573227\pi$
$229$	−6.90131	−0.456052	−0.228026	+	0.973655i	$0.573227\pi$
$230$	−5.59085	−0.368649
$231$	−0.104299	−0.00686240
$232$	0	0
$233$	25.6260	1.67881	0.839407	−	0.543503i	$-0.182902\pi$
$233$	25.6260	1.67881	0.839407	+	0.543503i	$0.182902\pi$
$234$	4.55513	0.297778
$235$	−15.7008	−1.02420
$236$	−29.2350	−1.90304
$237$	−1.02758	−0.0667482
$238$	1.06472	0.0690154
$239$	−7.81169	−0.505296	−0.252648	−	0.967558i	$-0.581301\pi$
$239$	−7.81169	−0.505296	−0.252648	+	0.967558i	$0.581301\pi$
$240$	−18.0960	−1.16809
$241$	22.1520	1.42694	0.713469	−	0.700687i	$-0.247123\pi$
$241$	22.1520	1.42694	0.713469	+	0.700687i	$0.247123\pi$
$242$	2.49854	0.160612
$243$	6.86104	0.440136
$244$	−23.9706	−1.53456
$245$	15.0504	0.961538
$246$	−1.19376	−0.0761115
$247$	14.7786	0.940338
$248$	25.8849	1.64370
$249$	23.3254	1.47819
$250$	28.8726	1.82606
$251$	−9.24294	−0.583409	−0.291705	−	0.956508i	$-0.594222\pi$
$251$	−9.24294	−0.583409	−0.291705	+	0.956508i	$0.594222\pi$
$252$	0.195580	0.0123204
$253$	1.04004	0.0653868
$254$	21.0488	1.32072
$255$	20.4459	1.28037
$256$	−32.3816	−2.02385
$257$	−10.3497	−0.645596	−0.322798	−	0.946468i	$-0.604623\pi$
$257$	−10.3497	−0.645596	−0.322798	+	0.946468i	$0.604623\pi$
$258$	−13.6822	−0.851815
$259$	−0.578772	−0.0359631
$260$	24.6886	1.53112
$261$	0	0
$262$	−47.9955	−2.96517
$263$	−31.9762	−1.97174	−0.985869	−	0.167518i	$-0.946425\pi$
$263$	−31.9762	−1.97174	−0.985869	+	0.167518i	$0.946425\pi$
$264$	8.54577	0.525956
$265$	1.10163	0.0676724
$266$	0.933654	0.0572460
$267$	−25.3000	−1.54834
$268$	−49.9701	−3.05241
$269$	−15.3811	−0.937800	−0.468900	−	0.883251i	$-0.655350\pi$
$269$	−15.3811	−0.937800	−0.468900	+	0.883251i	$0.655350\pi$
$270$	30.1212	1.83312
$271$	28.8222	1.75082	0.875412	−	0.483378i	$-0.160590\pi$
$271$	28.8222	1.75082	0.875412	+	0.483378i	$0.160590\pi$
$272$	−34.3644	−2.08365
$273$	0.282096	0.0170732
$274$	−53.5232	−3.23346
$275$	−0.371043	−0.0223747
$276$	6.72960	0.405075
$277$	21.3933	1.28540	0.642700	−	0.766118i	$-0.277814\pi$
$277$	21.3933	1.28540	0.642700	+	0.766118i	$0.277814\pi$
$278$	15.6948	0.941311
$279$	−3.11383	−0.186420
$280$	0.824473	0.0492717
$281$	19.6777	1.17388	0.586938	−	0.809632i	$-0.300333\pi$
$281$	19.6777	1.17388	0.586938	+	0.809632i	$0.300333\pi$
$282$	27.8076	1.65592
$283$	−0.799104	−0.0475018	−0.0237509	−	0.999718i	$-0.507561\pi$
$283$	−0.799104	−0.0475018	−0.0237509	+	0.999718i	$0.507561\pi$
$284$	−5.76262	−0.341949
$285$	17.9291	1.06203
$286$	−6.75772	−0.399592
$287$	0.0214248	0.00126466
$288$	−1.73402	−0.102178
$289$	21.8269	1.28393
$290$	0	0
$291$	20.3893	1.19524
$292$	−37.3273	−2.18441
$293$	17.6408	1.03059	0.515294	−	0.857014i	$-0.327683\pi$
$293$	17.6408	1.03059	0.515294	+	0.857014i	$0.327683\pi$
$294$	−26.6558	−1.55460
$295$	14.8253	0.863164
$296$	47.4217	2.75633
$297$	−5.60332	−0.325138
$298$	14.0552	0.814198
$299$	−2.81297	−0.162678
$300$	−2.40084	−0.138613
$301$	0.245558	0.0141537
$302$	−39.4531	−2.27027
$303$	18.6343	1.07051
$304$	−30.1342	−1.72832
$305$	12.1557	0.696034
$306$	10.4943	0.599918
$307$	−9.82846	−0.560940	−0.280470	−	0.959863i	$-0.590490\pi$
$307$	−9.82846	−0.560940	−0.280470	+	0.959863i	$0.590490\pi$
$308$	−0.290150	−0.0165328
$309$	16.3928	0.932553
$310$	−24.8326	−1.41040
$311$	−5.57089	−0.315896	−0.157948	−	0.987447i	$-0.550488\pi$
$311$	−5.57089	−0.315896	−0.157948	+	0.987447i	$0.550488\pi$
$312$	−23.1135	−1.30854
$313$	−20.5056	−1.15905	−0.579524	−	0.814955i	$-0.696761\pi$
$313$	−20.5056	−1.15905	−0.579524	+	0.814955i	$0.696761\pi$
$314$	−37.9892	−2.14386
$315$	−0.0991802	−0.00558817
$316$	−2.85861	−0.160809
$317$	−12.7814	−0.717872	−0.358936	−	0.933362i	$-0.616860\pi$
$317$	−12.7814	−0.717872	−0.358936	+	0.933362i	$0.616860\pi$
$318$	−1.95109	−0.109412
$319$	0	0
$320$	9.90216	0.553548
$321$	−4.44750	−0.248235
$322$	−0.177713	−0.00990355
$323$	34.0474	1.89445
$324$	−27.6769	−1.53761
$325$	1.00355	0.0556669
$326$	16.6265	0.920857
$327$	−2.81205	−0.155507
$328$	−1.75544	−0.0969278
$329$	−0.499070	−0.0275146
$330$	−8.19834	−0.451304
$331$	−14.8109	−0.814081	−0.407041	−	0.913410i	$-0.633439\pi$
$331$	−14.8109	−0.814081	−0.407041	+	0.913410i	$0.633439\pi$
$332$	64.8889	3.56124
$333$	−5.70460	−0.312610
$334$	12.0238	0.657911
$335$	25.3403	1.38449
$336$	−0.575207	−0.0313801
$337$	2.11563	0.115246	0.0576229	−	0.998338i	$-0.481648\pi$
$337$	2.11563	0.115246	0.0576229	+	0.998338i	$0.481648\pi$
$338$	−14.2036	−0.772571
$339$	0.875011	0.0475241
$340$	56.8785	3.08467
$341$	4.61950	0.250160
$342$	9.20246	0.497612
$343$	0.957119	0.0516795
$344$	−20.1198	−1.08479
$345$	−3.41264	−0.183731
$346$	−56.6438	−3.04519
$347$	15.9475	0.856106	0.428053	−	0.903754i	$-0.359200\pi$
$347$	15.9475	0.856106	0.428053	+	0.903754i	$0.359200\pi$
$348$	0	0
$349$	−20.0528	−1.07340	−0.536700	−	0.843773i	$-0.680329\pi$
$349$	−20.0528	−1.07340	−0.536700	+	0.843773i	$0.680329\pi$
$350$	0.0634005	0.00338890
$351$	15.1551	0.808922
$352$	2.57250	0.137114
$353$	−33.1838	−1.76619	−0.883097	−	0.469191i	$-0.844546\pi$
$353$	−33.1838	−1.76619	−0.883097	+	0.469191i	$0.844546\pi$
$354$	−26.2571	−1.39555
$355$	2.92228	0.155098
$356$	−70.3821	−3.73024
$357$	0.649902	0.0343965
$358$	−33.0438	−1.74642
$359$	27.6730	1.46052	0.730261	−	0.683168i	$-0.239398\pi$
$359$	27.6730	1.46052	0.730261	+	0.683168i	$0.239398\pi$
$360$	8.12633	0.428295
$361$	10.8563	0.571382
$362$	19.5579	1.02794
$363$	1.52510	0.0800471
$364$	0.784761	0.0411326
$365$	18.9290	0.990790
$366$	−21.5290	−1.12534
$367$	−34.1209	−1.78110	−0.890549	−	0.454886i	$-0.849680\pi$
$367$	−34.1209	−1.78110	−0.890549	+	0.454886i	$0.849680\pi$
$368$	5.73578	0.298998
$369$	0.211171	0.0109931
$370$	−45.4937	−2.36511
$371$	0.0350167	0.00181798
$372$	29.8906	1.54975
$373$	8.89564	0.460599	0.230299	−	0.973120i	$-0.426029\pi$
$373$	8.89564	0.460599	0.230299	+	0.973120i	$0.426029\pi$
$374$	−15.5687	−0.805037
$375$	17.6238	0.910088
$376$	40.8913	2.10881
$377$	0	0
$378$	0.957445	0.0492457
$379$	19.6138	1.00749	0.503747	−	0.863851i	$-0.331954\pi$
$379$	19.6138	1.00749	0.503747	+	0.863851i	$0.331954\pi$
$380$	49.8769	2.55863
$381$	12.8481	0.658230
$382$	43.4966	2.22548
$383$	8.69608	0.444349	0.222174	−	0.975007i	$-0.428685\pi$
$383$	8.69608	0.444349	0.222174	+	0.975007i	$0.428685\pi$
$384$	−25.3843	−1.29539
$385$	0.147138	0.00749884
$386$	11.7293	0.597007
$387$	2.42031	0.123031
$388$	56.7209	2.87957
$389$	23.5335	1.19319	0.596597	−	0.802541i	$-0.296519\pi$
$389$	23.5335	1.19319	0.596597	+	0.802541i	$0.296519\pi$
$390$	22.1738	1.12281
$391$	−6.48062	−0.327739
$392$	−39.1976	−1.97978
$393$	−29.2964	−1.47781
$394$	53.1080	2.67554
$395$	1.44963	0.0729386
$396$	−2.85983	−0.143712
$397$	−34.2939	−1.72116	−0.860580	−	0.509316i	$-0.829898\pi$
$397$	−34.2939	−1.72116	−0.860580	+	0.509316i	$0.829898\pi$
$398$	22.3009	1.11784
$399$	0.569901	0.0285307
$400$	−2.04629	−0.102314
$401$	15.4710	0.772587	0.386293	−	0.922376i	$-0.373755\pi$
$401$	15.4710	0.772587	0.386293	+	0.922376i	$0.373755\pi$
$402$	−44.8802	−2.23842
$403$	−12.4942	−0.622382
$404$	51.8388	2.57907
$405$	14.0352	0.697415
$406$	0	0
$407$	8.46301	0.419496
$408$	−53.2497	−2.63625
$409$	−24.8196	−1.22725	−0.613624	−	0.789598i	$-0.710289\pi$
$409$	−24.8196	−1.22725	−0.613624	+	0.789598i	$0.710289\pi$
$410$	1.68407	0.0831703
$411$	−32.6705	−1.61152
$412$	45.6030	2.24670
$413$	0.471244	0.0231884
$414$	−1.75161	−0.0860868
$415$	−32.9058	−1.61528
$416$	−6.95775	−0.341132
$417$	9.58007	0.469138
$418$	−13.6522	−0.667752
$419$	3.27172	0.159834	0.0799169	−	0.996802i	$-0.474534\pi$
$419$	3.27172	0.159834	0.0799169	+	0.996802i	$0.474534\pi$
$420$	0.952058	0.0464557
$421$	17.6207	0.858781	0.429390	−	0.903119i	$-0.358728\pi$
$421$	17.6207	0.858781	0.429390	+	0.903119i	$0.358728\pi$
$422$	45.5039	2.21510
$423$	−4.91903	−0.239172
$424$	−2.86909	−0.139336
$425$	2.31202	0.112149
$426$	−5.17564	−0.250761
$427$	0.386386	0.0186986
$428$	−12.3725	−0.598047
$429$	−4.12490	−0.199152
$430$	19.3018	0.930816
$431$	3.09310	0.148989	0.0744947	−	0.997221i	$-0.476266\pi$
$431$	3.09310	0.148989	0.0744947	+	0.997221i	$0.476266\pi$
$432$	−30.9021	−1.48678
$433$	−32.0048	−1.53805	−0.769026	−	0.639218i	$-0.779258\pi$
$433$	−32.0048	−1.53805	−0.769026	+	0.639218i	$0.779258\pi$
$434$	−0.789338	−0.0378895
$435$	0	0
$436$	−7.82282	−0.374645
$437$	−5.68288	−0.271849
$438$	−33.5251	−1.60189
$439$	−3.26985	−0.156061	−0.0780306	−	0.996951i	$-0.524863\pi$
$439$	−3.26985	−0.156061	−0.0780306	+	0.996951i	$0.524863\pi$
$440$	−12.0557	−0.574735
$441$	4.71529	0.224538
$442$	42.1082	2.00288
$443$	6.11441	0.290505	0.145252	−	0.989395i	$-0.453601\pi$
$443$	6.11441	0.290505	0.145252	+	0.989395i	$0.453601\pi$
$444$	54.7600	2.59880
$445$	35.6914	1.69193
$446$	56.4222	2.67167
$447$	8.57930	0.405787
$448$	0.314754	0.0148707
$449$	17.7919	0.839652	0.419826	−	0.907605i	$-0.362091\pi$
$449$	17.7919	0.839652	0.419826	+	0.907605i	$0.362091\pi$
$450$	0.624900	0.0294581
$451$	−0.313280	−0.0147518
$452$	2.43419	0.114495
$453$	−24.0821	−1.13148
$454$	1.40599	0.0659864
$455$	−0.397960	−0.0186566
$456$	−46.6948	−2.18669
$457$	9.84033	0.460311	0.230156	−	0.973154i	$-0.426076\pi$
$457$	9.84033	0.460311	0.230156	+	0.973154i	$0.426076\pi$
$458$	−17.2432	−0.805721
$459$	34.9150	1.62969
$460$	−9.49363	−0.442643
$461$	−6.93067	−0.322793	−0.161397	−	0.986890i	$-0.551600\pi$
$461$	−6.93067	−0.322793	−0.161397	+	0.986890i	$0.551600\pi$
$462$	−0.260596	−0.0121240
$463$	−27.0948	−1.25920	−0.629600	−	0.776919i	$-0.716781\pi$
$463$	−27.0948	−1.25920	−0.629600	+	0.776919i	$0.716781\pi$
$464$	0	0
$465$	−15.1578	−0.702925
$466$	64.0274	2.96601
$467$	−42.1471	−1.95034	−0.975169	−	0.221464i	$-0.928916\pi$
$467$	−42.1471	−1.95034	−0.975169	+	0.221464i	$0.928916\pi$
$468$	7.73491	0.357546
$469$	0.805476	0.0371934
$470$	−39.2289	−1.80949
$471$	−23.1886	−1.06847
$472$	−38.6114	−1.77723
$473$	−3.59063	−0.165097
$474$	−2.56743	−0.117926
$475$	2.02741	0.0930241
$476$	1.80796	0.0828678
$477$	0.345138	0.0158028
$478$	−19.5178	−0.892722
$479$	−25.3458	−1.15808	−0.579040	−	0.815299i	$-0.696572\pi$
$479$	−25.3458	−1.15808	−0.579040	+	0.815299i	$0.696572\pi$
$480$	−8.44102	−0.385278
$481$	−22.8897	−1.04368
$482$	55.3477	2.52102
$483$	−0.108476	−0.00493581
$484$	4.24268	0.192849
$485$	−28.7637	−1.30609
$486$	17.1425	0.777602
$487$	9.69430	0.439291	0.219645	−	0.975580i	$-0.429510\pi$
$487$	9.69430	0.439291	0.219645	+	0.975580i	$0.429510\pi$
$488$	−31.6586	−1.43312
$489$	10.1488	0.458945
$490$	37.6041	1.69878
$491$	−15.8885	−0.717037	−0.358518	−	0.933523i	$-0.616718\pi$
$491$	−15.8885	−0.717037	−0.358518	+	0.933523i	$0.616718\pi$
$492$	−2.02709	−0.0913881
$493$	0	0
$494$	36.9248	1.66132
$495$	1.45025	0.0651838
$496$	25.4763	1.14392
$497$	0.0928887	0.00416663
$498$	58.2794	2.61156
$499$	21.5077	0.962818	0.481409	−	0.876496i	$-0.340125\pi$
$499$	21.5077	0.962818	0.481409	+	0.876496i	$0.340125\pi$
$500$	49.0276	2.19258
$501$	7.33929	0.327895
$502$	−23.0938	−1.03073
$503$	−32.6852	−1.45736	−0.728680	−	0.684854i	$-0.759866\pi$
$503$	−32.6852	−1.45736	−0.728680	+	0.684854i	$0.759866\pi$
$504$	0.258307	0.0115059
$505$	−26.2879	−1.16980
$506$	2.59858	0.115521
$507$	−8.66983	−0.385041
$508$	35.7422	1.58580
$509$	−40.9934	−1.81700	−0.908500	−	0.417885i	$-0.862772\pi$
$509$	−40.9934	−1.81700	−0.908500	+	0.417885i	$0.862772\pi$
$510$	51.0849	2.26208
$511$	0.601685	0.0266170
$512$	−47.6179	−2.10443
$513$	30.6170	1.35178
$514$	−25.8591	−1.14059
$515$	−23.1257	−1.01904
$516$	−23.2332	−1.02279
$517$	7.29758	0.320947
$518$	−1.44608	−0.0635372
$519$	−34.5753	−1.51769
$520$	32.6068	1.42990
$521$	17.0395	0.746515	0.373258	−	0.927728i	$-0.378241\pi$
$521$	17.0395	0.746515	0.373258	+	0.927728i	$0.378241\pi$
$522$	0	0
$523$	−9.29221	−0.406320	−0.203160	−	0.979146i	$-0.565121\pi$
$523$	−9.29221	−0.406320	−0.203160	+	0.979146i	$0.565121\pi$
$524$	−81.4996	−3.56033
$525$	0.0386996	0.00168899
$526$	−79.8937	−3.48353
$527$	−28.7847	−1.25388
$528$	8.41087	0.366036
$529$	−21.9183	−0.952970
$530$	2.75245	0.119559
$531$	4.64476	0.201566
$532$	1.58541	0.0687361
$533$	0.847321	0.0367015
$534$	−63.2130	−2.73549
$535$	6.27420	0.271257
$536$	−65.9967	−2.85062
$537$	−20.1699	−0.870394
$538$	−38.4301	−1.65684
$539$	−6.99532	−0.301310
$540$	51.1478	2.20105
$541$	18.4075	0.791402	0.395701	−	0.918379i	$-0.370502\pi$
$541$	18.4075	0.791402	0.395701	+	0.918379i	$0.370502\pi$
$542$	72.0133	3.09323
$543$	11.9381	0.512313
$544$	−16.0295	−0.687260
$545$	3.96703	0.169929
$546$	0.704826	0.0301638
$547$	−40.6487	−1.73801	−0.869007	−	0.494800i	$-0.835241\pi$
$547$	−40.6487	−1.73801	−0.869007	+	0.494800i	$0.835241\pi$
$548$	−90.8860	−3.88246
$549$	3.80837	0.162537
$550$	−0.927064	−0.0395302
$551$	0	0
$552$	8.88795	0.378296
$553$	0.0460784	0.00195945
$554$	53.4519	2.27096
$555$	−27.7693	−1.17874
$556$	26.6508	1.13024
$557$	25.2906	1.07160	0.535799	−	0.844345i	$-0.320010\pi$
$557$	25.2906	1.07160	0.535799	+	0.844345i	$0.320010\pi$
$558$	−7.78003	−0.329355
$559$	9.71148	0.410752
$560$	0.811459	0.0342904
$561$	−9.50310	−0.401221
$562$	49.1655	2.07392
$563$	−19.0431	−0.802570	−0.401285	−	0.915953i	$-0.631436\pi$
$563$	−19.0431	−0.802570	−0.401285	+	0.915953i	$0.631436\pi$
$564$	47.2191	1.98828
$565$	−1.23440	−0.0519316
$566$	−1.99659	−0.0839229
$567$	0.446129	0.0187356
$568$	−7.61083	−0.319343
$569$	30.6813	1.28623	0.643114	−	0.765770i	$-0.277642\pi$
$569$	30.6813	1.28623	0.643114	+	0.765770i	$0.277642\pi$
$570$	44.7965	1.87632
$571$	−20.4429	−0.855509	−0.427754	−	0.903895i	$-0.640695\pi$
$571$	−20.4429	−0.855509	−0.427754	+	0.903895i	$0.640695\pi$
$572$	−11.4750	−0.479796
$573$	26.5502	1.10915
$574$	0.0535305	0.00223432
$575$	−0.385900	−0.0160931
$576$	3.10234	0.129264
$577$	−30.9460	−1.28830	−0.644150	−	0.764899i	$-0.722789\pi$
$577$	−30.9460	−1.28830	−0.644150	+	0.764899i	$0.722789\pi$
$578$	54.5352	2.26837
$579$	7.15956	0.297541
$580$	0	0
$581$	−1.04596	−0.0433936
$582$	50.9433	2.11167
$583$	−0.512027	−0.0212060
$584$	−49.2990	−2.04001
$585$	−3.92244	−0.162173
$586$	44.0762	1.82077
$587$	0.596169	0.0246065	0.0123033	−	0.999924i	$-0.496084\pi$
$587$	0.596169	0.0246065	0.0123033	+	0.999924i	$0.496084\pi$
$588$	−45.2634	−1.86663
$589$	−25.2414	−1.04005
$590$	37.0416	1.52498
$591$	32.4170	1.33346
$592$	46.6731	1.91825
$593$	19.3920	0.796333	0.398166	−	0.917313i	$-0.369647\pi$
$593$	19.3920	0.796333	0.398166	+	0.917313i	$0.369647\pi$
$594$	−14.0001	−0.574431
$595$	−0.916834	−0.0375865
$596$	23.8667	0.977619
$597$	13.6124	0.557119
$598$	−7.02830	−0.287409
$599$	−26.0710	−1.06523	−0.532616	−	0.846357i	$-0.678791\pi$
$599$	−26.0710	−1.06523	−0.532616	+	0.846357i	$0.678791\pi$
$600$	−3.17085	−0.129449
$601$	30.9435	1.26221	0.631107	−	0.775696i	$-0.282601\pi$
$601$	30.9435	1.26221	0.631107	+	0.775696i	$0.282601\pi$
$602$	0.613535	0.0250058
$603$	7.93909	0.323305
$604$	−66.9939	−2.72594
$605$	−2.15150	−0.0874710
$606$	46.5585	1.89131
$607$	23.6405	0.959539	0.479770	−	0.877394i	$-0.340720\pi$
$607$	23.6405	0.959539	0.479770	+	0.877394i	$0.340720\pi$
$608$	−14.0563	−0.570060
$609$	0	0
$610$	30.3715	1.22971
$611$	−19.7376	−0.798496
$612$	17.8200	0.720329
$613$	38.3324	1.54823	0.774116	−	0.633044i	$-0.218195\pi$
$613$	38.3324	1.54823	0.774116	+	0.633044i	$0.218195\pi$
$614$	−24.5567	−0.991030
$615$	1.02795	0.0414511
$616$	−0.383208	−0.0154399
$617$	12.0206	0.483931	0.241965	−	0.970285i	$-0.422208\pi$
$617$	12.0206	0.483931	0.241965	+	0.970285i	$0.422208\pi$
$618$	40.9579	1.64757
$619$	31.9505	1.28420	0.642100	−	0.766621i	$-0.278063\pi$
$619$	31.9505	1.28420	0.642100	+	0.766621i	$0.278063\pi$
$620$	−42.1674	−1.69348
$621$	−5.82769	−0.233857
$622$	−13.9191	−0.558104
$623$	1.13450	0.0454528
$624$	−22.7486	−0.910675
$625$	−23.0071	−0.920284
$626$	−51.2341	−2.04773
$627$	−8.33329	−0.332800
$628$	−64.5082	−2.57416
$629$	−52.7340	−2.10264
$630$	−0.247805	−0.00987280
$631$	−26.4540	−1.05312	−0.526558	−	0.850139i	$-0.676518\pi$
$631$	−26.4540	−1.05312	−0.526558	+	0.850139i	$0.676518\pi$
$632$	−3.77543	−0.150179
$633$	27.7755	1.10398
$634$	−31.9347	−1.26829
$635$	−18.1252	−0.719277
$636$	−3.31308	−0.131372
$637$	18.9201	0.749640
$638$	0	0
$639$	0.915547	0.0362185
$640$	35.8103	1.41553
$641$	−33.5426	−1.32485	−0.662426	−	0.749128i	$-0.730473\pi$
$641$	−33.5426	−1.32485	−0.662426	+	0.749128i	$0.730473\pi$
$642$	−11.1122	−0.438565
$643$	−30.4505	−1.20085	−0.600425	−	0.799681i	$-0.705002\pi$
$643$	−30.4505	−1.20085	−0.600425	+	0.799681i	$0.705002\pi$
$644$	−0.301768	−0.0118913
$645$	11.7818	0.463908
$646$	85.0686	3.34698
$647$	−34.1857	−1.34398	−0.671990	−	0.740561i	$-0.734560\pi$
$647$	−34.1857	−1.34398	−0.671990	+	0.740561i	$0.734560\pi$
$648$	−36.5535	−1.43596
$649$	−6.89069	−0.270483
$650$	2.50740	0.0983485
$651$	−0.481811	−0.0188837
$652$	28.2329	1.10569
$653$	9.29735	0.363833	0.181917	−	0.983314i	$-0.441770\pi$
$653$	9.29735	0.363833	0.181917	+	0.983314i	$0.441770\pi$
$654$	−7.02600	−0.274738
$655$	41.3292	1.61487
$656$	−1.72773	−0.0674564
$657$	5.93044	0.231368
$658$	−1.24695	−0.0486110
$659$	24.8986	0.969913	0.484956	−	0.874538i	$-0.338836\pi$
$659$	24.8986	0.969913	0.484956	+	0.874538i	$0.338836\pi$
$660$	−13.9213	−0.541887
$661$	3.50774	0.136435	0.0682177	−	0.997670i	$-0.478269\pi$
$661$	3.50774	0.136435	0.0682177	+	0.997670i	$0.478269\pi$
$662$	−37.0056	−1.43826
$663$	25.7028	0.998212
$664$	85.7004	3.32582
$665$	−0.803974	−0.0311768
$666$	−14.2531	−0.552298
$667$	0	0
$668$	20.4171	0.789963
$669$	34.4400	1.33153
$670$	63.3136	2.44602
$671$	−5.64988	−0.218111
$672$	−0.268310	−0.0103503
$673$	32.7070	1.26076	0.630382	−	0.776285i	$-0.282898\pi$
$673$	32.7070	1.26076	0.630382	+	0.776285i	$0.282898\pi$
$674$	5.28598	0.203608
$675$	2.07907	0.0800236
$676$	−24.1186	−0.927637
$677$	48.5181	1.86470	0.932351	−	0.361555i	$-0.117754\pi$
$677$	48.5181	1.86470	0.932351	+	0.361555i	$0.117754\pi$
$678$	2.18624	0.0839622
$679$	−0.914294	−0.0350874
$680$	75.1208	2.88075
$681$	0.858214	0.0328868
$682$	11.5420	0.441965
$683$	−40.5842	−1.55291	−0.776456	−	0.630172i	$-0.782984\pi$
$683$	−40.5842	−1.55291	−0.776456	+	0.630172i	$0.782984\pi$
$684$	15.6264	0.597490
$685$	46.0891	1.76097
$686$	2.39139	0.0913039
$687$	−10.5252	−0.401562
$688$	−19.8022	−0.754951
$689$	1.38486	0.0527591
$690$	−8.52661	−0.324603
$691$	−4.70288	−0.178906	−0.0894531	−	0.995991i	$-0.528512\pi$
$691$	−4.70288	−0.178906	−0.0894531	+	0.995991i	$0.528512\pi$
$692$	−96.1848	−3.65640
$693$	0.0460981	0.00175112
$694$	39.8453	1.51251
$695$	−13.5149	−0.512648
$696$	0	0
$697$	1.95209	0.0739406
$698$	−50.1025	−1.89641
$699$	39.0822	1.47823
$700$	0.107658	0.00406910
$701$	−4.35124	−0.164344	−0.0821719	−	0.996618i	$-0.526186\pi$
$701$	−4.35124	−0.164344	−0.0821719	+	0.996618i	$0.526186\pi$
$702$	37.8657	1.42915
$703$	−46.2426	−1.74407
$704$	−4.60244	−0.173461
$705$	−23.9453	−0.901831
$706$	−82.9108	−3.12039
$707$	−0.835598	−0.0314259
$708$	−44.5863	−1.67566
$709$	−49.1642	−1.84640	−0.923200	−	0.384319i	$-0.874436\pi$
$709$	−49.1642	−1.84640	−0.923200	+	0.384319i	$0.874436\pi$
$710$	7.30141	0.274017
$711$	0.454167	0.0170326
$712$	−92.9553	−3.48365
$713$	4.80447	0.179929
$714$	1.62380	0.0607693
$715$	5.81910	0.217622
$716$	−56.1105	−2.09695
$717$	−11.9136	−0.444922
$718$	69.1418	2.58035
$719$	43.5731	1.62500	0.812501	−	0.582960i	$-0.198105\pi$
$719$	43.5731	1.62500	0.812501	+	0.582960i	$0.198105\pi$
$720$	7.99805	0.298070
$721$	−0.735083	−0.0273759
$722$	27.1248	1.00948
$723$	33.7841	1.25645
$724$	33.2106	1.23426
$725$	0	0
$726$	3.81052	0.141422
$727$	−17.4880	−0.648594	−0.324297	−	0.945955i	$-0.605128\pi$
$727$	−17.4880	−0.648594	−0.324297	+	0.945955i	$0.605128\pi$
$728$	1.03645	0.0384135
$729$	30.0341	1.11238
$730$	47.2948	1.75046
$731$	22.3737	0.827520
$732$	−36.5576	−1.35121
$733$	−25.6674	−0.948045	−0.474023	−	0.880513i	$-0.657199\pi$
$733$	−25.6674	−0.948045	−0.474023	+	0.880513i	$0.657199\pi$
$734$	−85.2524	−3.14672
$735$	22.9535	0.846651
$736$	2.67550	0.0986203
$737$	−11.7780	−0.433847
$738$	0.527618	0.0194219
$739$	−10.1219	−0.372340	−0.186170	−	0.982518i	$-0.559608\pi$
$739$	−10.1219	−0.372340	−0.186170	+	0.982518i	$0.559608\pi$
$740$	−77.2514	−2.83982
$741$	22.5388	0.827984
$742$	0.0874905	0.00321188
$743$	15.6808	0.575272	0.287636	−	0.957740i	$-0.407131\pi$
$743$	15.6808	0.575272	0.287636	+	0.957740i	$0.407131\pi$
$744$	39.4772	1.44730
$745$	−12.1030	−0.443421
$746$	22.2261	0.813754
$747$	−10.3094	−0.377199
$748$	−26.4366	−0.966619
$749$	0.199434	0.00728717
$750$	44.0336	1.60788
$751$	24.5680	0.896500	0.448250	−	0.893908i	$-0.352047\pi$
$751$	24.5680	0.896500	0.448250	+	0.893908i	$0.352047\pi$
$752$	40.2459	1.46762
$753$	−14.0964	−0.513702
$754$	0	0
$755$	33.9732	1.23641
$756$	1.62580	0.0591299
$757$	−17.0198	−0.618593	−0.309297	−	0.950966i	$-0.600094\pi$
$757$	−17.0198	−0.618593	−0.309297	+	0.950966i	$0.600094\pi$
$758$	49.0058	1.77997
$759$	1.58617	0.0575743
$760$	65.8736	2.38949
$761$	−11.4959	−0.416726	−0.208363	−	0.978052i	$-0.566814\pi$
$761$	−11.4959	−0.416726	−0.208363	+	0.978052i	$0.566814\pi$
$762$	32.1015	1.16292
$763$	0.126097	0.00456503
$764$	73.8600	2.67216
$765$	−9.03667	−0.326721
$766$	21.7275	0.785045
$767$	18.6371	0.672945
$768$	−49.3853	−1.78204
$769$	−7.34201	−0.264760	−0.132380	−	0.991199i	$-0.542262\pi$
$769$	−7.34201	−0.264760	−0.132380	+	0.991199i	$0.542262\pi$
$770$	0.367629	0.0132484
$771$	−15.7843	−0.568459
$772$	19.9172	0.716834
$773$	−0.353156	−0.0127021	−0.00635107	−	0.999980i	$-0.502022\pi$
$773$	−0.353156	−0.0127021	−0.00635107	+	0.999980i	$0.502022\pi$
$774$	6.04724	0.217363
$775$	−1.71403	−0.0615699
$776$	74.9127	2.68921
$777$	−0.882686	−0.0316662
$778$	58.7992	2.10805
$779$	1.71179	0.0613313
$780$	37.6526	1.34818
$781$	−1.35825	−0.0486020
$782$	−16.1921	−0.579027
$783$	0	0
$784$	−38.5789	−1.37782
$785$	32.7127	1.16757
$786$	−73.1981	−2.61089
$787$	7.66653	0.273282	0.136641	−	0.990621i	$-0.456369\pi$
$787$	7.66653	0.273282	0.136641	+	0.990621i	$0.456369\pi$
$788$	90.1808	3.21256
$789$	−48.7670	−1.73615
$790$	3.62194	0.128863
$791$	−0.0392371	−0.00139511
$792$	−3.77705	−0.134212
$793$	15.2811	0.542647
$794$	−85.6844	−3.04083
$795$	1.68009	0.0595867
$796$	37.8684	1.34221
$797$	−3.67866	−0.130305	−0.0651524	−	0.997875i	$-0.520753\pi$
$797$	−3.67866	−0.130305	−0.0651524	+	0.997875i	$0.520753\pi$
$798$	1.42392	0.0504061
$799$	−45.4721	−1.60869
$800$	−0.954507	−0.0337469
$801$	11.1821	0.395099
$802$	38.6549	1.36495
$803$	−8.79805	−0.310476
$804$	−76.2095	−2.68770
$805$	0.153029	0.00539358
$806$	−31.2173	−1.09958
$807$	−23.4577	−0.825750
$808$	68.4647	2.40858
$809$	18.7424	0.658947	0.329473	−	0.944165i	$-0.393129\pi$
$809$	18.7424	0.658947	0.329473	+	0.944165i	$0.393129\pi$
$810$	35.0675	1.23214
$811$	23.7777	0.834948	0.417474	−	0.908689i	$-0.362915\pi$
$811$	23.7777	0.834948	0.417474	+	0.908689i	$0.362915\pi$
$812$	0	0
$813$	43.9568	1.54163
$814$	21.1451	0.741136
$815$	−14.3172	−0.501509
$816$	−52.4092	−1.83469
$817$	19.6195	0.686400
$818$	−62.0125	−2.16822
$819$	−0.124680	−0.00435668
$820$	2.85966	0.0998638
$821$	0.690381	0.0240945	0.0120472	−	0.999927i	$-0.496165\pi$
$821$	0.690381	0.0240945	0.0120472	+	0.999927i	$0.496165\pi$
$822$	−81.6284	−2.84712
$823$	−46.8621	−1.63351	−0.816754	−	0.576986i	$-0.804229\pi$
$823$	−46.8621	−1.63351	−0.816754	+	0.576986i	$0.804229\pi$
$824$	60.2291	2.09818
$825$	−0.565879	−0.0197014
$826$	1.17742	0.0409677
$827$	46.5609	1.61908	0.809540	−	0.587065i	$-0.199717\pi$
$827$	46.5609	1.61908	0.809540	+	0.587065i	$0.199717\pi$
$828$	−2.97434	−0.103366
$829$	2.26242	0.0785773	0.0392886	−	0.999228i	$-0.487491\pi$
$829$	2.26242	0.0785773	0.0392886	+	0.999228i	$0.487491\pi$
$830$	−82.2163	−2.85377
$831$	32.6270	1.13182
$832$	12.4481	0.431560
$833$	43.5887	1.51026
$834$	23.9362	0.828841
$835$	−10.3537	−0.358305
$836$	−23.1824	−0.801779
$837$	−25.8845	−0.894701
$838$	8.17450	0.282383
$839$	11.1400	0.384595	0.192297	−	0.981337i	$-0.438406\pi$
$839$	11.1400	0.384595	0.192297	+	0.981337i	$0.438406\pi$
$840$	1.25741	0.0433846
$841$	0	0
$842$	44.0259	1.51723
$843$	30.0106	1.03362
$844$	77.2687	2.65970
$845$	12.2307	0.420751
$846$	−12.2904	−0.422552
$847$	−0.0683885	−0.00234986
$848$	−2.82381	−0.0969699
$849$	−1.21872	−0.0418262
$850$	5.77665	0.198137
$851$	8.80187	0.301724
$852$	−8.78858	−0.301092
$853$	−9.25361	−0.316838	−0.158419	−	0.987372i	$-0.550640\pi$
$853$	−9.25361	−0.316838	−0.158419	+	0.987372i	$0.550640\pi$
$854$	0.965400	0.0330353
$855$	−7.92428	−0.271005
$856$	−16.3406	−0.558512
$857$	9.75047	0.333070	0.166535	−	0.986036i	$-0.446742\pi$
$857$	9.75047	0.333070	0.166535	+	0.986036i	$0.446742\pi$
$858$	−10.3062	−0.351848
$859$	−13.4391	−0.458538	−0.229269	−	0.973363i	$-0.573634\pi$
$859$	−13.4391	−0.458538	−0.229269	+	0.973363i	$0.573634\pi$
$860$	32.7757	1.11764
$861$	0.0326750	0.00111356
$862$	7.72822	0.263224
$863$	−6.94756	−0.236498	−0.118249	−	0.992984i	$-0.537728\pi$
$863$	−6.94756	−0.236498	−0.118249	+	0.992984i	$0.537728\pi$
$864$	−14.4145	−0.490392
$865$	48.7762	1.65844
$866$	−79.9651	−2.71732
$867$	33.2882	1.13053
$868$	−1.34035	−0.0454944
$869$	−0.673775	−0.0228562
$870$	0	0
$871$	31.8555	1.07938
$872$	−10.3318	−0.349879
$873$	−9.01164	−0.304998
$874$	−14.1989	−0.480284
$875$	−0.790284	−0.0267165
$876$	−56.9279	−1.92342
$877$	1.74635	0.0589701	0.0294850	−	0.999565i	$-0.490613\pi$
$877$	1.74635	0.0589701	0.0294850	+	0.999565i	$0.490613\pi$
$878$	−8.16982	−0.275718
$879$	26.9041	0.907451
$880$	−11.8654	−0.399984
$881$	−2.52894	−0.0852021	−0.0426011	−	0.999092i	$-0.513564\pi$
$881$	−2.52894	−0.0852021	−0.0426011	+	0.999092i	$0.513564\pi$
$882$	11.7813	0.396698
$883$	−44.1664	−1.48632	−0.743159	−	0.669115i	$-0.766673\pi$
$883$	−44.1664	−1.48632	−0.743159	+	0.669115i	$0.766673\pi$
$884$	71.5024	2.40489
$885$	22.6101	0.760032
$886$	15.2771	0.513243
$887$	−32.7433	−1.09941	−0.549706	−	0.835358i	$-0.685260\pi$
$887$	−32.7433	−1.09941	−0.549706	+	0.835358i	$0.685260\pi$
$888$	72.3229	2.42700
$889$	−0.576135	−0.0193229
$890$	89.1762	2.98919
$891$	−6.52345	−0.218544
$892$	95.8087	3.20791
$893$	−39.8746	−1.33435
$894$	21.4357	0.716916
$895$	28.4541	0.951117
$896$	1.13828	0.0380273
$897$	−4.29007	−0.143241
$898$	44.4537	1.48344
$899$	0	0
$900$	1.06112	0.0353707
$901$	3.19050	0.106291
$902$	−0.782742	−0.0260625
$903$	0.374501	0.0124626
$904$	3.21489	0.106926
$905$	−16.8414	−0.559827
$906$	−60.1700	−1.99901
$907$	1.67274	0.0555426	0.0277713	−	0.999614i	$-0.491159\pi$
$907$	1.67274	0.0555426	0.0277713	+	0.999614i	$0.491159\pi$
$908$	2.38746	0.0792308
$909$	−8.23598	−0.273170
$910$	−0.994316	−0.0329612
$911$	39.6902	1.31499	0.657497	−	0.753457i	$-0.271615\pi$
$911$	39.6902	1.31499	0.657497	+	0.753457i	$0.271615\pi$
$912$	−45.9578	−1.52181
$913$	15.2943	0.506169
$914$	24.5864	0.813246
$915$	18.5387	0.612871
$916$	−29.2801	−0.967440
$917$	1.31371	0.0433824
$918$	87.2363	2.87923
$919$	16.0633	0.529881	0.264940	−	0.964265i	$-0.414648\pi$
$919$	16.0633	0.529881	0.264940	+	0.964265i	$0.414648\pi$
$920$	−12.5385	−0.413381
$921$	−14.9894	−0.493918
$922$	−17.3165	−0.570289
$923$	3.67362	0.120919
$924$	−0.442509	−0.0145575
$925$	−3.14014	−0.103247
$926$	−67.6972	−2.22467
$927$	−7.24527	−0.237966
$928$	0	0
$929$	36.5549	1.19933	0.599664	−	0.800252i	$-0.295301\pi$
$929$	36.5549	1.19933	0.599664	+	0.800252i	$0.295301\pi$
$930$	−37.8722	−1.24188
$931$	38.2231	1.25271
$932$	108.723	3.56133
$933$	−8.49618	−0.278153
$934$	−105.306	−3.44572
$935$	13.4063	0.438432
$936$	10.2157	0.333910
$937$	−30.8682	−1.00842	−0.504210	−	0.863581i	$-0.668216\pi$
$937$	−30.8682	−1.00842	−0.504210	+	0.863581i	$0.668216\pi$
$938$	2.01251	0.0657108
$939$	−31.2732	−1.02056
$940$	−66.6133	−2.17268
$941$	8.24620	0.268818	0.134409	−	0.990926i	$-0.457086\pi$
$941$	8.24620	0.268818	0.134409	+	0.990926i	$0.457086\pi$
$942$	−57.9374	−1.88770
$943$	−0.325825	−0.0106103
$944$	−38.0019	−1.23686
$945$	−0.824461	−0.0268197
$946$	−8.97132	−0.291683
$947$	5.03395	0.163582	0.0817908	−	0.996650i	$-0.473936\pi$
$947$	5.03395	0.163582	0.0817908	+	0.996650i	$0.473936\pi$
$948$	−4.35967	−0.141596
$949$	23.7958	0.772445
$950$	5.06556	0.164349
$951$	−19.4929	−0.632100
$952$	2.38782	0.0773896
$953$	0.153766	0.00498096	0.00249048	−	0.999997i	$-0.499207\pi$
$953$	0.153766	0.00498096	0.00249048	+	0.999997i	$0.499207\pi$
$954$	0.862340	0.0279193
$955$	−37.4551	−1.21202
$956$	−33.1425	−1.07190
$957$	0	0
$958$	−63.3274	−2.04602
$959$	1.46501	0.0473075
$960$	15.1018	0.487409
$961$	−9.66022	−0.311620
$962$	−57.1906	−1.84390
$963$	1.96570	0.0633438
$964$	93.9840	3.02702
$965$	−10.1002	−0.325136
$966$	−0.271030	−0.00872025
$967$	−23.1155	−0.743345	−0.371672	−	0.928364i	$-0.621215\pi$
$967$	−23.1155	−0.743345	−0.371672	+	0.928364i	$0.621215\pi$
$968$	5.60341	0.180100
$969$	51.9258	1.66810
$970$	−71.8671	−2.30751
$971$	−57.8474	−1.85641	−0.928206	−	0.372067i	$-0.878649\pi$
$971$	−57.8474	−1.85641	−0.928206	+	0.372067i	$0.878649\pi$
$972$	29.1092	0.933677
$973$	−0.429589	−0.0137720
$974$	24.2215	0.776108
$975$	1.53052	0.0490157
$976$	−31.1588	−0.997370
$977$	16.3138	0.521926	0.260963	−	0.965349i	$-0.415960\pi$
$977$	16.3138	0.521926	0.260963	+	0.965349i	$0.415960\pi$
$978$	25.3571	0.810832
$979$	−16.5891	−0.530189
$980$	63.8542	2.03975
$981$	1.24287	0.0396816
$982$	−39.6979	−1.26681
$983$	20.4732	0.652995	0.326498	−	0.945198i	$-0.394132\pi$
$983$	20.4732	0.652995	0.326498	+	0.945198i	$0.394132\pi$
$984$	−2.67722	−0.0853467
$985$	−45.7315	−1.45713
$986$	0	0
$987$	−0.761133	−0.0242271
$988$	62.7007	1.99477
$989$	−3.73440	−0.118747
$990$	3.62349	0.115162
$991$	42.5983	1.35318	0.676591	−	0.736359i	$-0.263457\pi$
$991$	42.5983	1.35318	0.676591	+	0.736359i	$0.263457\pi$
$992$	11.8836	0.377306
$993$	−22.5881	−0.716813
$994$	0.232086	0.00736131
$995$	−19.2034	−0.608789
$996$	98.9623	3.13574
$997$	17.2453	0.546165	0.273083	−	0.961991i	$-0.411957\pi$
$997$	17.2453	0.546165	0.273083	+	0.961991i	$0.411957\pi$
$998$	53.7378	1.70104
$999$	−47.4209	−1.50033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.s.1.18	✓	18
29.28	even	2		9251.2.a.t.1.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.18	✓	18	1.1	even	1	trivial
9251.2.a.t.1.1	yes	18	29.28	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q+2.49854 q^{2} +1.52510 q^{3} +4.24268 q^{4} -2.15150 q^{5} +3.81052 q^{6} -0.0683885 q^{7} +5.60341 q^{8} -0.674063 q^{9} +O(q^{10})\)	\(q+2.49854 q^{2} +1.52510 q^{3} +4.24268 q^{4} -2.15150 q^{5} +3.81052 q^{6} -0.0683885 q^{7} +5.60341 q^{8} -0.674063 q^{9} -5.37560 q^{10} +1.00000 q^{11} +6.47052 q^{12} -2.70467 q^{13} -0.170871 q^{14} -3.28126 q^{15} +5.51496 q^{16} -6.23112 q^{17} -1.68417 q^{18} -5.46409 q^{19} -9.12812 q^{20} -0.104299 q^{21} +2.49854 q^{22} +1.04004 q^{23} +8.54577 q^{24} -0.371043 q^{25} -6.75772 q^{26} -5.60332 q^{27} -0.290150 q^{28} -8.19834 q^{30} +4.61950 q^{31} +2.57250 q^{32} +1.52510 q^{33} -15.5687 q^{34} +0.147138 q^{35} -2.85983 q^{36} +8.46301 q^{37} -13.6522 q^{38} -4.12490 q^{39} -12.0557 q^{40} -0.313280 q^{41} -0.260596 q^{42} -3.59063 q^{43} +4.24268 q^{44} +1.45025 q^{45} +2.59858 q^{46} +7.29758 q^{47} +8.41087 q^{48} -6.99532 q^{49} -0.927064 q^{50} -9.50310 q^{51} -11.4750 q^{52} -0.512027 q^{53} -14.0001 q^{54} -2.15150 q^{55} -0.383208 q^{56} -8.33329 q^{57} -6.89069 q^{59} -13.9213 q^{60} -5.64988 q^{61} +11.5420 q^{62} +0.0460981 q^{63} -4.60244 q^{64} +5.81910 q^{65} +3.81052 q^{66} -11.7780 q^{67} -26.4366 q^{68} +1.58617 q^{69} +0.367629 q^{70} -1.35825 q^{71} -3.77705 q^{72} -8.79805 q^{73} +21.1451 q^{74} -0.565879 q^{75} -23.1824 q^{76} -0.0683885 q^{77} -10.3062 q^{78} -0.673775 q^{79} -11.8654 q^{80} -6.52345 q^{81} -0.782742 q^{82} +15.2943 q^{83} -0.442509 q^{84} +13.4063 q^{85} -8.97132 q^{86} +5.60341 q^{88} -16.5891 q^{89} +3.62349 q^{90} +0.184968 q^{91} +4.41256 q^{92} +7.04521 q^{93} +18.2333 q^{94} +11.7560 q^{95} +3.92332 q^{96} +13.3691 q^{97} -17.4781 q^{98} -0.674063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 9 q^{9}+O(q^{10}) \) 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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