LMFDB - Embedded newform 9251.2.a.t.1.1

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			1.1
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	$-0.844728\pi$
$2$	−2.49854	−1.76673	−0.883366	+	0.468685i	$0.844728\pi$
$3$	−1.52510	−0.880518	−0.440259	−	0.897871i	$-0.645113\pi$
$3$	−1.52510	−0.880518	−0.440259	+	0.897871i	$0.645113\pi$
$4$	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	$-0.227329\pi$
$17$	6.23112	1.51127	0.755635	+	0.654993i	$0.227329\pi$
$18$	1.68417	0.396963
$19$	5.46409	1.25355	0.626774	−	0.779201i	$-0.284375\pi$
$19$	5.46409	1.25355	0.626774	+	0.779201i	$0.284375\pi$
$20$	−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	$-0.636164\pi$
$31$	−4.61950	−0.829687	−0.414843	+	0.909893i	$0.636164\pi$
$32$	−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	$-0.744886\pi$
$37$	−8.46301	−1.39131	−0.695655	+	0.718376i	$0.744886\pi$
$38$	−13.6522	−2.21468
$39$	4.12490	0.660513
$40$	12.0557	1.90618
$41$	0.313280	0.0489262	0.0244631	−	0.999701i	$-0.492212\pi$
$41$	0.313280	0.0489262	0.0244631	+	0.999701i	$0.492212\pi$
$42$	−0.260596	−0.0402108
$43$	3.59063	0.547566	0.273783	−	0.961791i	$-0.411725\pi$
$43$	3.59063	0.547566	0.273783	+	0.961791i	$0.411725\pi$
$44$	−4.24268	−0.639608
$45$	1.45025	0.216190
$46$	−2.59858	−0.383140
$47$	−7.29758	−1.06446	−0.532231	−	0.846599i	$-0.678646\pi$
$47$	−7.29758	−1.06446	−0.532231	+	0.846599i	$0.678646\pi$
$48$	−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	$-0.382198\pi$
$61$	5.64988	0.723393	0.361696	+	0.932296i	$0.382198\pi$
$62$	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	$-0.327841\pi$
$73$	8.79805	1.02973	0.514867	+	0.857270i	$0.327841\pi$
$74$	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	$-0.487932\pi$
$79$	0.673775	0.0758056	0.0379028	+	0.999281i	$0.487932\pi$
$80$	−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	$-0.158065\pi$
$89$	16.5891	1.75844	0.879219	+	0.476418i	$0.158065\pi$
$90$	−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	$-0.737463\pi$
$97$	−13.3691	−1.35743	−0.678715	+	0.734402i	$0.737463\pi$
$98$	17.4781	1.76555
$99$	0.674063	0.0677459
$100$	−1.57422	−0.157422
$101$	−12.2184	−1.21578	−0.607888	−	0.794022i	$-0.707983\pi$
$101$	−12.2184	−1.21578	−0.607888	+	0.794022i	$0.707983\pi$
$102$	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	$-0.508591\pi$
$113$	−0.573739	−0.0539728	−0.0269864	+	0.999636i	$0.508591\pi$
$114$	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	$-0.621937\pi$
$127$	−8.42444	−0.747549	−0.373774	+	0.927520i	$0.621937\pi$
$128$	16.6444	1.47117
$129$	−5.47608	−0.482142
$130$	−14.5392	−1.27518
$131$	19.2095	1.67834	0.839170	−	0.543870i	$-0.183041\pi$
$131$	19.2095	1.67834	0.839170	+	0.543870i	$0.183041\pi$
$132$	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	$-0.132115\pi$
$137$	21.4218	1.83019	0.915096	+	0.403236i	$0.132115\pi$
$138$	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	$-0.292481\pi$
$157$	15.2046	1.21346	0.606729	+	0.794908i	$0.292481\pi$
$158$	−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	$-0.583924\pi$
$163$	−6.65450	−0.521221	−0.260610	+	0.965444i	$0.583924\pi$
$164$	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	$-0.716875\pi$
$191$	−17.4088	−1.25966	−0.629829	+	0.776734i	$0.716875\pi$
$192$	7.01920	0.506567
$193$	−4.69448	−0.337916	−0.168958	−	0.985623i	$-0.554040\pi$
$193$	−4.69448	−0.337916	−0.168958	+	0.985623i	$0.554040\pi$
$194$	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	$-0.715673\pi$
$211$	−18.2122	−1.25378	−0.626891	+	0.779107i	$0.715673\pi$
$212$	−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	$-0.426773\pi$
$229$	6.90131	0.456052	0.228026	+	0.973655i	$0.426773\pi$
$230$	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	$-0.405778\pi$
$251$	9.24294	0.583409	0.291705	+	0.956508i	$0.405778\pi$
$252$	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	$-0.0535752\pi$
$263$	31.9762	1.97174	0.985869	+	0.167518i	$0.0535752\pi$
$264$	−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	$-0.344650\pi$
$269$	15.3811	0.937800	0.468900	+	0.883251i	$0.344650\pi$
$270$	30.1212	1.83312
$271$	−28.8222	−1.75082	−0.875412	−	0.483378i	$-0.839410\pi$
$271$	−28.8222	−1.75082	−0.875412	+	0.483378i	$0.839410\pi$
$272$	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	$-0.672317\pi$
$293$	−17.6408	−1.03059	−0.515294	+	0.857014i	$0.672317\pi$
$294$	−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	$-0.409510\pi$
$307$	9.82846	0.560940	0.280470	+	0.959863i	$0.409510\pi$
$308$	0.290150	0.0165328
$309$	−16.3928	−0.932553
$310$	−24.8326	−1.41040
$311$	5.57089	0.315896	0.157948	−	0.987447i	$-0.449512\pi$
$311$	5.57089	0.315896	0.157948	+	0.987447i	$0.449512\pi$
$312$	−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	$-0.383140\pi$
$317$	12.7814	0.717872	0.358936	+	0.933362i	$0.383140\pi$
$318$	−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	$-0.366561\pi$
$331$	14.8109	0.814081	0.407041	+	0.913410i	$0.366561\pi$
$332$	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	$-0.518352\pi$
$337$	−2.11563	−0.115246	−0.0576229	+	0.998338i	$0.518352\pi$
$338$	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	$-0.760602\pi$
$359$	−27.6730	−1.46052	−0.730261	+	0.683168i	$0.760602\pi$
$360$	−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	$-0.150320\pi$
$367$	34.1209	1.78110	0.890549	+	0.454886i	$0.150320\pi$
$368$	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	$-0.668046\pi$
$379$	−19.6138	−1.00749	−0.503747	+	0.863851i	$0.668046\pi$
$380$	−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	$-0.703481\pi$
$389$	−23.5335	−1.19319	−0.596597	+	0.802541i	$0.703481\pi$
$390$	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	$-0.289711\pi$
$409$	24.8196	1.22725	0.613624	+	0.789598i	$0.289711\pi$
$410$	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	$-0.641272\pi$
$421$	−17.6207	−0.858781	−0.429390	+	0.903119i	$0.641272\pi$
$422$	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	$-0.220742\pi$
$433$	32.0048	1.53805	0.769026	+	0.639218i	$0.220742\pi$
$434$	−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	$-0.546399\pi$
$443$	−6.11441	−0.290505	−0.145252	+	0.989395i	$0.546399\pi$
$444$	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	$-0.637909\pi$
$449$	−17.7919	−0.839652	−0.419826	+	0.907605i	$0.637909\pi$
$450$	−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	$-0.448400\pi$
$461$	6.93067	0.322793	0.161397	+	0.986890i	$0.448400\pi$
$462$	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	$-0.0710836\pi$
$467$	42.1471	1.95034	0.975169	+	0.221464i	$0.0710836\pi$
$468$	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	$-0.303428\pi$
$479$	25.3458	1.15808	0.579040	+	0.815299i	$0.303428\pi$
$480$	−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	$-0.383282\pi$
$491$	15.8885	0.717037	0.358518	+	0.933523i	$0.383282\pi$
$492$	−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	$-0.240134\pi$
$503$	32.6852	1.45736	0.728680	+	0.684854i	$0.240134\pi$
$504$	−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	$-0.629498\pi$
$541$	−18.4075	−0.791402	−0.395701	+	0.918379i	$0.629498\pi$
$542$	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	$-0.368564\pi$
$563$	19.0431	0.802570	0.401285	+	0.915953i	$0.368564\pi$
$564$	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	$-0.722358\pi$
$569$	−30.6813	−1.28623	−0.643114	+	0.765770i	$0.722358\pi$
$570$	−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	$-0.277211\pi$
$577$	30.9460	1.28830	0.644150	+	0.764899i	$0.277211\pi$
$578$	−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	$-0.321209\pi$
$599$	26.0710	1.06523	0.532616	+	0.846357i	$0.321209\pi$
$600$	−3.17085	−0.129449
$601$	−30.9435	−1.26221	−0.631107	−	0.775696i	$-0.717399\pi$
$601$	−30.9435	−1.26221	−0.631107	+	0.775696i	$0.717399\pi$
$602$	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	$-0.659280\pi$
$607$	−23.6405	−0.959539	−0.479770	+	0.877394i	$0.659280\pi$
$608$	−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	$-0.577792\pi$
$617$	−12.0206	−0.483931	−0.241965	+	0.970285i	$0.577792\pi$
$618$	40.9579	1.64757
$619$	−31.9505	−1.28420	−0.642100	−	0.766621i	$-0.721937\pi$
$619$	−31.9505	−1.28420	−0.642100	+	0.766621i	$0.721937\pi$
$620$	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	$-0.269527\pi$
$641$	33.5426	1.32485	0.662426	+	0.749128i	$0.269527\pi$
$642$	−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	$-0.558230\pi$
$653$	−9.29735	−0.363833	−0.181917	+	0.983314i	$0.558230\pi$
$654$	−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	$-0.661164\pi$
$659$	−24.8986	−0.969913	−0.484956	+	0.874538i	$0.661164\pi$
$660$	−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	$-0.882246\pi$
$677$	−48.5181	−1.86470	−0.932351	+	0.361555i	$0.882246\pi$
$678$	−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	$-0.394872\pi$
$727$	17.4880	0.648594	0.324297	+	0.945955i	$0.394872\pi$
$728$	−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	$-0.342801\pi$
$733$	25.6674	0.948045	0.474023	+	0.880513i	$0.342801\pi$
$734$	−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	$-0.440392\pi$
$739$	10.1219	0.372340	0.186170	+	0.982518i	$0.440392\pi$
$740$	77.2514	2.83982
$741$	22.5388	0.827984
$742$	−0.0874905	−0.00321188
$743$	−15.6808	−0.575272	−0.287636	−	0.957740i	$-0.592869\pi$
$743$	−15.6808	−0.575272	−0.287636	+	0.957740i	$0.592869\pi$
$744$	−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	$-0.647953\pi$
$751$	−24.5680	−0.896500	−0.448250	+	0.893908i	$0.647953\pi$
$752$	−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	$-0.399906\pi$
$757$	17.0198	0.618593	0.309297	+	0.950966i	$0.399906\pi$
$758$	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	$-0.457738\pi$
$769$	7.34201	0.264760	0.132380	+	0.991199i	$0.457738\pi$
$770$	0.367629	0.0132484
$771$	15.7843	0.568459
$772$	−19.9172	−0.716834
$773$	0.353156	0.0127021	0.00635107	−	0.999980i	$-0.497978\pi$
$773$	0.353156	0.0127021	0.00635107	+	0.999980i	$0.497978\pi$
$774$	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	$-0.479247\pi$
$797$	3.67866	0.130305	0.0651524	+	0.997875i	$0.479247\pi$
$798$	−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	$-0.606871\pi$
$809$	−18.7424	−0.658947	−0.329473	+	0.944165i	$0.606871\pi$
$810$	−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	$-0.195771\pi$
$823$	46.8621	1.63351	0.816754	+	0.576986i	$0.195771\pi$
$824$	−60.2291	−2.09818
$825$	−0.565879	−0.0197014
$826$	−1.17742	−0.0409677
$827$	−46.5609	−1.61908	−0.809540	−	0.587065i	$-0.800283\pi$
$827$	−46.5609	−1.61908	−0.809540	+	0.587065i	$0.800283\pi$
$828$	−2.97434	−0.103366
$829$	−2.26242	−0.0785773	−0.0392886	−	0.999228i	$-0.512509\pi$
$829$	−2.26242	−0.0785773	−0.0392886	+	0.999228i	$0.512509\pi$
$830$	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	$-0.561594\pi$
$839$	−11.1400	−0.384595	−0.192297	+	0.981337i	$0.561594\pi$
$840$	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	$-0.449360\pi$
$853$	9.25361	0.316838	0.158419	+	0.987372i	$0.449360\pi$
$854$	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	$-0.426366\pi$
$859$	13.4391	0.458538	0.229269	+	0.973363i	$0.426366\pi$
$860$	−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	$-0.486436\pi$
$881$	2.52894	0.0852021	0.0426011	+	0.999092i	$0.486436\pi$
$882$	−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	$-0.314740\pi$
$887$	32.7433	1.09941	0.549706	+	0.835358i	$0.314740\pi$
$888$	−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	$-0.508841\pi$
$907$	−1.67274	−0.0555426	−0.0277713	+	0.999614i	$0.508841\pi$
$908$	2.38746	0.0792308
$909$	8.23598	0.273170
$910$	0.994316	0.0329612
$911$	−39.6902	−1.31499	−0.657497	−	0.753457i	$-0.728385\pi$
$911$	−39.6902	−1.31499	−0.657497	+	0.753457i	$0.728385\pi$
$912$	−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	$-0.526064\pi$
$947$	−5.03395	−0.163582	−0.0817908	+	0.996650i	$0.526064\pi$
$948$	−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	$-0.378785\pi$
$967$	23.1155	0.743345	0.371672	+	0.928364i	$0.378785\pi$
$968$	−5.60341	−0.180100
$969$	−51.9258	−1.66810
$970$	−71.8671	−2.30751
$971$	57.8474	1.85641	0.928206	−	0.372067i	$-0.121351\pi$
$971$	57.8474	1.85641	0.928206	+	0.372067i	$0.121351\pi$
$972$	−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	$-0.605868\pi$
$983$	−20.4732	−0.652995	−0.326498	+	0.945198i	$0.605868\pi$
$984$	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	$-0.588043\pi$
$997$	−17.2453	−0.546165	−0.273083	+	0.961991i	$0.588043\pi$
$998$	−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.t.1.1	yes	18
29.28	even	2		9251.2.a.s.1.18	✓	18

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

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