LMFDB - Embedded newform 349.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5x^{10} - x^{9} + 35x^{8} - 24x^{7} - 80x^{6} + 66x^{5} + 77x^{4} - 56x^{3} - 31x^{2} + 15x + 4 $ x^11 - 5x^10 - x^9 + 35x^8 - 24x^7 - 80x^6 + 66x^5 + 77x^4 - 56x^3 - 31x^2 + 15*x + 4
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			1.11
Root			$-1.91579$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.91579 q^{2} -2.24901 q^{3} +1.67025 q^{4} -1.23759 q^{5} -4.30862 q^{6} -3.37442 q^{7} -0.631741 q^{8} +2.05803 q^{9} +O(q^{10})$	\(q+1.91579 q^{2} -2.24901 q^{3} +1.67025 q^{4} -1.23759 q^{5} -4.30862 q^{6} -3.37442 q^{7} -0.631741 q^{8} +2.05803 q^{9} -2.37097 q^{10} -1.90742 q^{11} -3.75639 q^{12} -0.969429 q^{13} -6.46467 q^{14} +2.78336 q^{15} -4.55077 q^{16} +7.23100 q^{17} +3.94275 q^{18} -3.38741 q^{19} -2.06709 q^{20} +7.58908 q^{21} -3.65422 q^{22} +0.502070 q^{23} +1.42079 q^{24} -3.46836 q^{25} -1.85722 q^{26} +2.11849 q^{27} -5.63610 q^{28} -7.43021 q^{29} +5.33232 q^{30} +3.69567 q^{31} -7.45483 q^{32} +4.28981 q^{33} +13.8531 q^{34} +4.17616 q^{35} +3.43742 q^{36} +4.21994 q^{37} -6.48955 q^{38} +2.18025 q^{39} +0.781838 q^{40} +5.83941 q^{41} +14.5391 q^{42} -7.91618 q^{43} -3.18587 q^{44} -2.54701 q^{45} +0.961860 q^{46} -5.52226 q^{47} +10.2347 q^{48} +4.38668 q^{49} -6.64465 q^{50} -16.2626 q^{51} -1.61918 q^{52} +0.948585 q^{53} +4.05858 q^{54} +2.36062 q^{55} +2.13175 q^{56} +7.61830 q^{57} -14.2347 q^{58} -11.5514 q^{59} +4.64889 q^{60} +12.7978 q^{61} +7.08012 q^{62} -6.94465 q^{63} -5.18034 q^{64} +1.19976 q^{65} +8.21837 q^{66} -1.46912 q^{67} +12.0775 q^{68} -1.12916 q^{69} +8.00063 q^{70} -3.08176 q^{71} -1.30014 q^{72} -10.0694 q^{73} +8.08451 q^{74} +7.80037 q^{75} -5.65780 q^{76} +6.43644 q^{77} +4.17690 q^{78} +4.39393 q^{79} +5.63201 q^{80} -10.9386 q^{81} +11.1871 q^{82} +7.14069 q^{83} +12.6756 q^{84} -8.94904 q^{85} -15.1657 q^{86} +16.7106 q^{87} +1.20500 q^{88} +2.83001 q^{89} -4.87953 q^{90} +3.27126 q^{91} +0.838580 q^{92} -8.31159 q^{93} -10.5795 q^{94} +4.19223 q^{95} +16.7660 q^{96} +8.19520 q^{97} +8.40395 q^{98} -3.92554 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.91579	1.35467	0.677333	−	0.735676i	$-0.263135\pi$
$2$	1.91579	1.35467	0.677333	+	0.735676i	$0.263135\pi$
$3$	−2.24901	−1.29846	−0.649232	−	0.760590i	$-0.724910\pi$
$3$	−2.24901	−1.29846	−0.649232	+	0.760590i	$0.724910\pi$
$4$	1.67025	0.835123
$5$	−1.23759	−0.553469	−0.276734	−	0.960946i	$-0.589252\pi$
$5$	−1.23759	−0.553469	−0.276734	+	0.960946i	$0.589252\pi$
$6$	−4.30862	−1.75899
$7$	−3.37442	−1.27541	−0.637705	−	0.770281i	$-0.720116\pi$
$7$	−3.37442	−1.27541	−0.637705	+	0.770281i	$0.720116\pi$
$8$	−0.631741	−0.223354
$9$	2.05803	0.686011
$10$	−2.37097	−0.749766
$11$	−1.90742	−0.575110	−0.287555	−	0.957764i	$-0.592842\pi$
$11$	−1.90742	−0.575110	−0.287555	+	0.957764i	$0.592842\pi$
$12$	−3.75639	−1.08438
$13$	−0.969429	−0.268871	−0.134436	−	0.990922i	$-0.542922\pi$
$13$	−0.969429	−0.268871	−0.134436	+	0.990922i	$0.542922\pi$
$14$	−6.46467	−1.72775
$15$	2.78336	0.718660
$16$	−4.55077	−1.13769
$17$	7.23100	1.75378	0.876888	−	0.480695i	$-0.159616\pi$
$17$	7.23100	1.75378	0.876888	+	0.480695i	$0.159616\pi$
$18$	3.94275	0.929316
$19$	−3.38741	−0.777124	−0.388562	−	0.921423i	$-0.627028\pi$
$19$	−3.38741	−0.777124	−0.388562	+	0.921423i	$0.627028\pi$
$20$	−2.06709	−0.462214
$21$	7.58908	1.65607
$22$	−3.65422	−0.779082
$23$	0.502070	0.104689	0.0523444	−	0.998629i	$-0.483331\pi$
$23$	0.502070	0.104689	0.0523444	+	0.998629i	$0.483331\pi$
$24$	1.42079	0.290017
$25$	−3.46836	−0.693672
$26$	−1.85722	−0.364231
$27$	2.11849	0.407704
$28$	−5.63610	−1.06512
$29$	−7.43021	−1.37976	−0.689878	−	0.723926i	$-0.742336\pi$
$29$	−7.43021	−1.37976	−0.689878	+	0.723926i	$0.742336\pi$
$30$	5.33232	0.973545
$31$	3.69567	0.663762	0.331881	−	0.943321i	$-0.392317\pi$
$31$	3.69567	0.663762	0.331881	+	0.943321i	$0.392317\pi$
$32$	−7.45483	−1.31784
$33$	4.28981	0.746760
$34$	13.8531	2.37578
$35$	4.17616	0.705899
$36$	3.43742	0.572903
$37$	4.21994	0.693753	0.346877	−	0.937911i	$-0.387242\pi$
$37$	4.21994	0.693753	0.346877	+	0.937911i	$0.387242\pi$
$38$	−6.48955	−1.05274
$39$	2.18025	0.349120
$40$	0.781838	0.123619
$41$	5.83941	0.911963	0.455981	−	0.889989i	$-0.349288\pi$
$41$	5.83941	0.911963	0.455981	+	0.889989i	$0.349288\pi$
$42$	14.5391	2.24343
$43$	−7.91618	−1.20721	−0.603603	−	0.797285i	$-0.706269\pi$
$43$	−7.91618	−1.20721	−0.603603	+	0.797285i	$0.706269\pi$
$44$	−3.18587	−0.480287
$45$	−2.54701	−0.379686
$46$	0.961860	0.141818
$47$	−5.52226	−0.805504	−0.402752	−	0.915309i	$-0.631946\pi$
$47$	−5.52226	−0.805504	−0.402752	+	0.915309i	$0.631946\pi$
$48$	10.2347	1.47725
$49$	4.38668	0.626668
$50$	−6.64465	−0.939695
$51$	−16.2626	−2.27722
$52$	−1.61918	−0.224541
$53$	0.948585	0.130298	0.0651491	−	0.997876i	$-0.479248\pi$
$53$	0.948585	0.130298	0.0651491	+	0.997876i	$0.479248\pi$
$54$	4.05858	0.552303
$55$	2.36062	0.318305
$56$	2.13175	0.284868
$57$	7.61830	1.00907
$58$	−14.2347	−1.86911
$59$	−11.5514	−1.50387	−0.751935	−	0.659238i	$-0.770879\pi$
$59$	−11.5514	−1.50387	−0.751935	+	0.659238i	$0.770879\pi$
$60$	4.64889	0.600169
$61$	12.7978	1.63860	0.819298	−	0.573368i	$-0.194363\pi$
$61$	12.7978	1.63860	0.819298	+	0.573368i	$0.194363\pi$
$62$	7.08012	0.899176
$63$	−6.94465	−0.874944
$64$	−5.18034	−0.647543
$65$	1.19976	0.148812
$66$	8.21837	1.01161
$67$	−1.46912	−0.179482	−0.0897410	−	0.995965i	$-0.528604\pi$
$67$	−1.46912	−0.179482	−0.0897410	+	0.995965i	$0.528604\pi$
$68$	12.0775	1.46462
$69$	−1.12916	−0.135935
$70$	8.00063	0.956258
$71$	−3.08176	−0.365738	−0.182869	−	0.983137i	$-0.558538\pi$
$71$	−3.08176	−0.365738	−0.182869	+	0.983137i	$0.558538\pi$
$72$	−1.30014	−0.153223
$73$	−10.0694	−1.17853	−0.589267	−	0.807938i	$-0.700584\pi$
$73$	−10.0694	−1.17853	−0.589267	+	0.807938i	$0.700584\pi$
$74$	8.08451	0.939805
$75$	7.80037	0.900709
$76$	−5.65780	−0.648994
$77$	6.43644	0.733500
$78$	4.17690	0.472941
$79$	4.39393	0.494356	0.247178	−	0.968970i	$-0.420497\pi$
$79$	4.39393	0.494356	0.247178	+	0.968970i	$0.420497\pi$
$80$	5.63201	0.629678
$81$	−10.9386	−1.21540
$82$	11.1871	1.23541
$83$	7.14069	0.783792	0.391896	−	0.920010i	$-0.371819\pi$
$83$	7.14069	0.783792	0.391896	+	0.920010i	$0.371819\pi$
$84$	12.6756	1.38302
$85$	−8.94904	−0.970660
$86$	−15.1657	−1.63536
$87$	16.7106	1.79156
$88$	1.20500	0.128453
$89$	2.83001	0.299981	0.149990	−	0.988687i	$-0.452076\pi$
$89$	2.83001	0.299981	0.149990	+	0.988687i	$0.452076\pi$
$90$	−4.87953	−0.514347
$91$	3.27126	0.342921
$92$	0.838580	0.0874280
$93$	−8.31159	−0.861871
$94$	−10.5795	−1.09119
$95$	4.19223	0.430114
$96$	16.7660	1.71117
$97$	8.19520	0.832096	0.416048	−	0.909343i	$-0.363415\pi$
$97$	8.19520	0.832096	0.416048	+	0.909343i	$0.363415\pi$
$98$	8.40395	0.848927
$99$	−3.92554	−0.394532
$100$	−5.79301	−0.579301
$101$	−16.7039	−1.66210	−0.831049	−	0.556199i	$-0.812259\pi$
$101$	−16.7039	−1.66210	−0.831049	+	0.556199i	$0.812259\pi$
$102$	−31.1557	−3.08487
$103$	−6.39410	−0.630029	−0.315015	−	0.949087i	$-0.602009\pi$
$103$	−6.39410	−0.630029	−0.315015	+	0.949087i	$0.602009\pi$
$104$	0.612428	0.0600535
$105$	−9.39220	−0.916585
$106$	1.81729	0.176511
$107$	−3.99044	−0.385770	−0.192885	−	0.981221i	$-0.561784\pi$
$107$	−3.99044	−0.385770	−0.192885	+	0.981221i	$0.561784\pi$
$108$	3.53840	0.340483
$109$	−12.0313	−1.15239	−0.576196	−	0.817311i	$-0.695464\pi$
$109$	−12.0313	−1.15239	−0.576196	+	0.817311i	$0.695464\pi$
$110$	4.52244	0.431198
$111$	−9.49067	−0.900814
$112$	15.3562	1.45102
$113$	−11.0305	−1.03766	−0.518830	−	0.854877i	$-0.673632\pi$
$113$	−11.0305	−1.03766	−0.518830	+	0.854877i	$0.673632\pi$
$114$	14.5951	1.36695
$115$	−0.621359	−0.0579420
$116$	−12.4103	−1.15227
$117$	−1.99512	−0.184449
$118$	−22.1301	−2.03724
$119$	−24.4004	−2.23678
$120$	−1.75836	−0.160516
$121$	−7.36173	−0.669249
$122$	24.5180	2.21975
$123$	−13.1329	−1.18415
$124$	6.17267	0.554322
$125$	10.4804	0.937395
$126$	−13.3045	−1.18526
$127$	16.4006	1.45532	0.727660	−	0.685938i	$-0.240608\pi$
$127$	16.4006	1.45532	0.727660	+	0.685938i	$0.240608\pi$
$128$	4.98523	0.440636
$129$	17.8035	1.56751
$130$	2.29849	0.201591
$131$	−18.7448	−1.63774	−0.818872	−	0.573977i	$-0.805400\pi$
$131$	−18.7448	−1.63774	−0.818872	+	0.573977i	$0.805400\pi$
$132$	7.16503	0.623636
$133$	11.4305	0.991151
$134$	−2.81453	−0.243138
$135$	−2.62183	−0.225651
$136$	−4.56812	−0.391713
$137$	−10.2975	−0.879775	−0.439887	−	0.898053i	$-0.644982\pi$
$137$	−10.2975	−0.879775	−0.439887	+	0.898053i	$0.644982\pi$
$138$	−2.16323	−0.184146
$139$	−16.6276	−1.41033	−0.705166	−	0.709043i	$-0.749127\pi$
$139$	−16.6276	−1.41033	−0.705166	+	0.709043i	$0.749127\pi$
$140$	6.97520	0.589512
$141$	12.4196	1.04592
$142$	−5.90401	−0.495453
$143$	1.84911	0.154631
$144$	−9.36563	−0.780469
$145$	9.19559	0.763652
$146$	−19.2909	−1.59652
$147$	−9.86567	−0.813707
$148$	7.04833	0.579369
$149$	1.00647	0.0824533	0.0412266	−	0.999150i	$-0.486873\pi$
$149$	1.00647	0.0824533	0.0412266	+	0.999150i	$0.486873\pi$
$150$	14.9439	1.22016
$151$	0.293856	0.0239136	0.0119568	−	0.999929i	$-0.496194\pi$
$151$	0.293856	0.0239136	0.0119568	+	0.999929i	$0.496194\pi$
$152$	2.13996	0.173574
$153$	14.8816	1.20311
$154$	12.3309	0.993649
$155$	−4.57374	−0.367371
$156$	3.64156	0.291558
$157$	13.9030	1.10958	0.554792	−	0.831989i	$-0.312798\pi$
$157$	13.9030	1.10958	0.554792	+	0.831989i	$0.312798\pi$
$158$	8.41784	0.669687
$159$	−2.13337	−0.169188
$160$	9.22606	0.729384
$161$	−1.69419	−0.133521
$162$	−20.9560	−1.64646
$163$	15.6685	1.22725	0.613626	−	0.789597i	$-0.289710\pi$
$163$	15.6685	1.22725	0.613626	+	0.789597i	$0.289710\pi$
$164$	9.75325	0.761601
$165$	−5.30904	−0.413308
$166$	13.6800	1.06178
$167$	5.53867	0.428595	0.214298	−	0.976768i	$-0.431254\pi$
$167$	5.53867	0.428595	0.214298	+	0.976768i	$0.431254\pi$
$168$	−4.79433	−0.369891
$169$	−12.0602	−0.927708
$170$	−17.1445	−1.31492
$171$	−6.97139	−0.533116
$172$	−13.2220	−1.00817
$173$	15.0097	1.14117	0.570584	−	0.821239i	$-0.306717\pi$
$173$	15.0097	1.14117	0.570584	+	0.821239i	$0.306717\pi$
$174$	32.0140	2.42697
$175$	11.7037	0.884716
$176$	8.68025	0.654299
$177$	25.9793	1.95272
$178$	5.42170	0.406374
$179$	17.9267	1.33990	0.669950	−	0.742406i	$-0.266315\pi$
$179$	17.9267	1.33990	0.669950	+	0.742406i	$0.266315\pi$
$180$	−4.25413	−0.317084
$181$	0.613991	0.0456376	0.0228188	−	0.999740i	$-0.492736\pi$
$181$	0.613991	0.0456376	0.0228188	+	0.999740i	$0.492736\pi$
$182$	6.26704	0.464544
$183$	−28.7824	−2.12766
$184$	−0.317178	−0.0233827
$185$	−5.22257	−0.383971
$186$	−15.9232	−1.16755
$187$	−13.7926	−1.00861
$188$	−9.22352	−0.672695
$189$	−7.14867	−0.519989
$190$	8.03143	0.582661
$191$	−12.6214	−0.913250	−0.456625	−	0.889659i	$-0.650942\pi$
$191$	−12.6214	−0.913250	−0.456625	+	0.889659i	$0.650942\pi$
$192$	11.6506	0.840811
$193$	7.14264	0.514138	0.257069	−	0.966393i	$-0.417243\pi$
$193$	7.14264	0.514138	0.257069	+	0.966393i	$0.417243\pi$
$194$	15.7003	1.12721
$195$	−2.69827	−0.193227
$196$	7.32683	0.523345
$197$	0.671588	0.0478487	0.0239243	−	0.999714i	$-0.492384\pi$
$197$	0.671588	0.0478487	0.0239243	+	0.999714i	$0.492384\pi$
$198$	−7.52050	−0.534459
$199$	22.1239	1.56832	0.784160	−	0.620558i	$-0.213094\pi$
$199$	22.1239	1.56832	0.784160	+	0.620558i	$0.213094\pi$
$200$	2.19110	0.154934
$201$	3.30407	0.233051
$202$	−32.0011	−2.25159
$203$	25.0726	1.75975
$204$	−27.1625	−1.90175
$205$	−7.22682	−0.504743
$206$	−12.2497	−0.853479
$207$	1.03328	0.0718176
$208$	4.41165	0.305893
$209$	6.46122	0.446932
$210$	−17.9935	−1.24167
$211$	−20.1544	−1.38749	−0.693743	−	0.720223i	$-0.744039\pi$
$211$	−20.1544	−1.38749	−0.693743	+	0.720223i	$0.744039\pi$
$212$	1.58437	0.108815
$213$	6.93091	0.474898
$214$	−7.64483	−0.522590
$215$	9.79702	0.668151
$216$	−1.33834	−0.0910623
$217$	−12.4707	−0.846568
$218$	−23.0495	−1.56111
$219$	22.6462	1.53029
$220$	3.94281	0.265824
$221$	−7.00995	−0.471540
$222$	−18.1821	−1.22030
$223$	−2.54819	−0.170639	−0.0853196	−	0.996354i	$-0.527191\pi$
$223$	−2.54819	−0.170639	−0.0853196	+	0.996354i	$0.527191\pi$
$224$	25.1557	1.68079
$225$	−7.13800	−0.475867
$226$	−21.1321	−1.40568
$227$	−23.8402	−1.58233	−0.791166	−	0.611601i	$-0.790526\pi$
$227$	−23.8402	−1.58233	−0.791166	+	0.611601i	$0.790526\pi$
$228$	12.7244	0.842696
$229$	−1.57966	−0.104387	−0.0521935	−	0.998637i	$-0.516621\pi$
$229$	−1.57966	−0.104387	−0.0521935	+	0.998637i	$0.516621\pi$
$230$	−1.19039	−0.0784921
$231$	−14.4756	−0.952424
$232$	4.69397	0.308174
$233$	20.9307	1.37122	0.685608	−	0.727971i	$-0.259536\pi$
$233$	20.9307	1.37122	0.685608	+	0.727971i	$0.259536\pi$
$234$	−3.82222	−0.249866
$235$	6.83431	0.445821
$236$	−19.2937	−1.25592
$237$	−9.88197	−0.641903
$238$	−46.7460	−3.03009
$239$	15.4647	1.00033	0.500163	−	0.865931i	$-0.333273\pi$
$239$	15.4647	1.00033	0.500163	+	0.865931i	$0.333273\pi$
$240$	−12.6664	−0.817614
$241$	18.9955	1.22361	0.611804	−	0.791009i	$-0.290444\pi$
$241$	18.9955	1.22361	0.611804	+	0.791009i	$0.290444\pi$
$242$	−14.1035	−0.906609
$243$	18.2455	1.17045
$244$	21.3755	1.36843
$245$	−5.42893	−0.346841
$246$	−25.1598	−1.60413
$247$	3.28385	0.208946
$248$	−2.33470	−0.148254
$249$	−16.0595	−1.01773
$250$	20.0782	1.26986
$251$	−22.5082	−1.42070	−0.710352	−	0.703847i	$-0.751464\pi$
$251$	−22.5082	−1.42070	−0.710352	+	0.703847i	$0.751464\pi$
$252$	−11.5993	−0.730686
$253$	−0.957660	−0.0602076
$254$	31.4201	1.97147
$255$	20.1265	1.26037
$256$	19.9113	1.24446
$257$	18.6200	1.16148	0.580741	−	0.814088i	$-0.302763\pi$
$257$	18.6200	1.16148	0.580741	+	0.814088i	$0.302763\pi$
$258$	34.1078	2.12346
$259$	−14.2398	−0.884819
$260$	2.00389	0.124276
$261$	−15.2916	−0.946527
$262$	−35.9111	−2.21860
$263$	−12.8774	−0.794054	−0.397027	−	0.917807i	$-0.629958\pi$
$263$	−12.8774	−0.794054	−0.397027	+	0.917807i	$0.629958\pi$
$264$	−2.71005	−0.166792
$265$	−1.17396	−0.0721159
$266$	21.8984	1.34268
$267$	−6.36472	−0.389514
$268$	−2.45380	−0.149890
$269$	−20.6124	−1.25676	−0.628380	−	0.777906i	$-0.716282\pi$
$269$	−20.6124	−1.25676	−0.628380	+	0.777906i	$0.716282\pi$
$270$	−5.02288	−0.305683
$271$	20.8159	1.26447	0.632237	−	0.774775i	$-0.282137\pi$
$271$	20.8159	1.26447	0.632237	+	0.774775i	$0.282137\pi$
$272$	−32.9066	−1.99526
$273$	−7.35708	−0.445271
$274$	−19.7278	−1.19180
$275$	6.61564	0.398938
$276$	−1.88597	−0.113522
$277$	15.5507	0.934353	0.467176	−	0.884164i	$-0.345271\pi$
$277$	15.5507	0.934353	0.467176	+	0.884164i	$0.345271\pi$
$278$	−31.8549	−1.91053
$279$	7.60581	0.455348
$280$	−2.63825	−0.157665
$281$	−19.6493	−1.17218	−0.586091	−	0.810246i	$-0.699334\pi$
$281$	−19.6493	−1.17218	−0.586091	+	0.810246i	$0.699334\pi$
$282$	23.7933	1.41687
$283$	10.4368	0.620405	0.310202	−	0.950671i	$-0.399603\pi$
$283$	10.4368	0.620405	0.310202	+	0.950671i	$0.399603\pi$
$284$	−5.14730	−0.305436
$285$	−9.42836	−0.558488
$286$	3.54251	0.209473
$287$	−19.7046	−1.16313
$288$	−15.3423	−0.904053
$289$	35.2874	2.07573
$290$	17.6168	1.03449
$291$	−18.4311	−1.08045
$292$	−16.8184	−0.984221
$293$	−3.12615	−0.182632	−0.0913159	−	0.995822i	$-0.529107\pi$
$293$	−3.12615	−0.182632	−0.0913159	+	0.995822i	$0.529107\pi$
$294$	−18.9005	−1.10230
$295$	14.2960	0.832345
$296$	−2.66591	−0.154953
$297$	−4.04086	−0.234475
$298$	1.92818	0.111697
$299$	−0.486721	−0.0281478
$300$	13.0285	0.752202
$301$	26.7125	1.53968
$302$	0.562965	0.0323950
$303$	37.5671	2.15818
$304$	15.4153	0.884129
$305$	−15.8385	−0.906912
$306$	28.5101	1.62981
$307$	−9.32045	−0.531946	−0.265973	−	0.963980i	$-0.585693\pi$
$307$	−9.32045	−0.531946	−0.265973	+	0.963980i	$0.585693\pi$
$308$	10.7504	0.612563
$309$	14.3804	0.818070
$310$	−8.76231	−0.497666
$311$	−26.7919	−1.51923	−0.759614	−	0.650374i	$-0.774612\pi$
$311$	−26.7919	−1.51923	−0.759614	+	0.650374i	$0.774612\pi$
$312$	−1.37735	−0.0779773
$313$	5.16206	0.291777	0.145888	−	0.989301i	$-0.453396\pi$
$313$	5.16206	0.291777	0.145888	+	0.989301i	$0.453396\pi$
$314$	26.6353	1.50312
$315$	8.59466	0.484254
$316$	7.33894	0.412847
$317$	14.0244	0.787688	0.393844	−	0.919177i	$-0.371145\pi$
$317$	14.0244	0.787688	0.393844	+	0.919177i	$0.371145\pi$
$318$	−4.08709	−0.229193
$319$	14.1726	0.793511
$320$	6.41116	0.358395
$321$	8.97452	0.500909
$322$	−3.24571	−0.180877
$323$	−24.4943	−1.36290
$324$	−18.2701	−1.01501
$325$	3.36233	0.186509
$326$	30.0176	1.66252
$327$	27.0585	1.49634
$328$	−3.68899	−0.203690
$329$	18.6344	1.02735
$330$	−10.1710	−0.559895
$331$	8.96001	0.492487	0.246243	−	0.969208i	$-0.420804\pi$
$331$	8.96001	0.492487	0.246243	+	0.969208i	$0.420804\pi$
$332$	11.9267	0.654562
$333$	8.68477	0.475922
$334$	10.6109	0.580604
$335$	1.81818	0.0993377
$336$	−34.5362	−1.88410
$337$	3.23650	0.176304	0.0881518	−	0.996107i	$-0.471904\pi$
$337$	3.23650	0.176304	0.0881518	+	0.996107i	$0.471904\pi$
$338$	−23.1048	−1.25674
$339$	24.8076	1.34736
$340$	−14.9471	−0.810620
$341$	−7.04921	−0.381736
$342$	−13.3557	−0.722194
$343$	8.81843	0.476151
$344$	5.00097	0.269634
$345$	1.39744	0.0752356
$346$	28.7555	1.54590
$347$	−0.305941	−0.0164238	−0.00821189	−	0.999966i	$-0.502614\pi$
$347$	−0.305941	−0.0164238	−0.00821189	+	0.999966i	$0.502614\pi$
$348$	27.9108	1.49618
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	22.4218	1.19850
$351$	−2.05373	−0.109620
$352$	14.2195	0.757903
$353$	−32.8124	−1.74643	−0.873213	−	0.487338i	$-0.837968\pi$
$353$	−32.8124	−1.74643	−0.873213	+	0.487338i	$0.837968\pi$
$354$	49.7708	2.64529
$355$	3.81397	0.202425
$356$	4.72681	0.250521
$357$	54.8767	2.90438
$358$	34.3437	1.81512
$359$	0.117758	0.00621506	0.00310753	−	0.999995i	$-0.499011\pi$
$359$	0.117758	0.00621506	0.00310753	+	0.999995i	$0.499011\pi$
$360$	1.60905	0.0848043
$361$	−7.52548	−0.396078
$362$	1.17628	0.0618237
$363$	16.5566	0.868996
$364$	5.46380	0.286381
$365$	12.4618	0.652282
$366$	−55.1411	−2.88227
$367$	27.5289	1.43700	0.718499	−	0.695528i	$-0.244829\pi$
$367$	27.5289	1.43700	0.718499	+	0.695528i	$0.244829\pi$
$368$	−2.28481	−0.119104
$369$	12.0177	0.625616
$370$	−10.0053	−0.520153
$371$	−3.20092	−0.166183
$372$	−13.8824	−0.719768
$373$	12.8733	0.666553	0.333276	−	0.942829i	$-0.391846\pi$
$373$	12.8733	0.666553	0.333276	+	0.942829i	$0.391846\pi$
$374$	−26.4237	−1.36634
$375$	−23.5705	−1.21717
$376$	3.48863	0.179913
$377$	7.20307	0.370977
$378$	−13.6953	−0.704413
$379$	−0.817420	−0.0419880	−0.0209940	−	0.999780i	$-0.506683\pi$
$379$	−0.817420	−0.0419880	−0.0209940	+	0.999780i	$0.506683\pi$
$380$	7.00206	0.359198
$381$	−36.8851	−1.88968
$382$	−24.1799	−1.23715
$383$	15.8953	0.812210	0.406105	−	0.913826i	$-0.366887\pi$
$383$	15.8953	0.812210	0.406105	+	0.913826i	$0.366887\pi$
$384$	−11.2118	−0.572151
$385$	−7.96570	−0.405970
$386$	13.6838	0.696486
$387$	−16.2918	−0.828156
$388$	13.6880	0.694902
$389$	−10.4594	−0.530311	−0.265156	−	0.964206i	$-0.585423\pi$
$389$	−10.4594	−0.530311	−0.265156	+	0.964206i	$0.585423\pi$
$390$	−5.16931	−0.261758
$391$	3.63047	0.183601
$392$	−2.77124	−0.139969
$393$	42.1573	2.12655
$394$	1.28662	0.0648190
$395$	−5.43790	−0.273610
$396$	−6.55661	−0.329482
$397$	−0.463291	−0.0232519	−0.0116260	−	0.999932i	$-0.503701\pi$
$397$	−0.463291	−0.0232519	−0.0116260	+	0.999932i	$0.503701\pi$
$398$	42.3847	2.12455
$399$	−25.7073	−1.28698
$400$	15.7837	0.789186
$401$	3.19254	0.159428	0.0797139	−	0.996818i	$-0.474599\pi$
$401$	3.19254	0.159428	0.0797139	+	0.996818i	$0.474599\pi$
$402$	6.32990	0.315707
$403$	−3.58269	−0.178467
$404$	−27.8996	−1.38806
$405$	13.5375	0.672686
$406$	48.0338	2.38388
$407$	−8.04921	−0.398984
$408$	10.2737	0.508625
$409$	15.1101	0.747144	0.373572	−	0.927601i	$-0.378133\pi$
$409$	15.1101	0.747144	0.373572	+	0.927601i	$0.378133\pi$
$410$	−13.8451	−0.683758
$411$	23.1591	1.14236
$412$	−10.6797	−0.526151
$413$	38.9794	1.91805
$414$	1.97954	0.0972890
$415$	−8.83727	−0.433804
$416$	7.22694	0.354330
$417$	37.3955	1.83127
$418$	12.3783	0.605444
$419$	−4.23054	−0.206675	−0.103338	−	0.994646i	$-0.532952\pi$
$419$	−4.23054	−0.206675	−0.103338	+	0.994646i	$0.532952\pi$
$420$	−15.6873	−0.765461
$421$	−24.9818	−1.21754	−0.608769	−	0.793347i	$-0.708337\pi$
$421$	−24.9818	−1.21754	−0.608769	+	0.793347i	$0.708337\pi$
$422$	−38.6115	−1.87958
$423$	−11.3650	−0.552584
$424$	−0.599259	−0.0291026
$425$	−25.0797	−1.21655
$426$	13.2782	0.643329
$427$	−43.1852	−2.08988
$428$	−6.66501	−0.322165
$429$	−4.15867	−0.200782
$430$	18.7690	0.905122
$431$	−30.6500	−1.47636	−0.738180	−	0.674604i	$-0.764315\pi$
$431$	−30.6500	−1.47636	−0.738180	+	0.674604i	$0.764315\pi$
$432$	−9.64078	−0.463842
$433$	−21.3442	−1.02574	−0.512869	−	0.858467i	$-0.671417\pi$
$433$	−21.3442	−1.02574	−0.512869	+	0.858467i	$0.671417\pi$
$434$	−23.8913	−1.14682
$435$	−20.6809	−0.991575
$436$	−20.0953	−0.962389
$437$	−1.70071	−0.0813562
$438$	43.3853	2.07303
$439$	−0.661311	−0.0315627	−0.0157813	−	0.999875i	$-0.505024\pi$
$439$	−0.661311	−0.0315627	−0.0157813	+	0.999875i	$0.505024\pi$
$440$	−1.49130	−0.0710948
$441$	9.02792	0.429901
$442$	−13.4296	−0.638780
$443$	−20.9845	−0.997004	−0.498502	−	0.866889i	$-0.666116\pi$
$443$	−20.9845	−0.997004	−0.498502	+	0.866889i	$0.666116\pi$
$444$	−15.8517	−0.752290
$445$	−3.50241	−0.166030
$446$	−4.88179	−0.231159
$447$	−2.26356	−0.107063
$448$	17.4806	0.825882
$449$	−24.2551	−1.14467	−0.572333	−	0.820021i	$-0.693962\pi$
$449$	−24.2551	−1.14467	−0.572333	+	0.820021i	$0.693962\pi$
$450$	−13.6749	−0.644641
$451$	−11.1382	−0.524479
$452$	−18.4236	−0.866573
$453$	−0.660884	−0.0310510
$454$	−45.6728	−2.14353
$455$	−4.04849	−0.189796
$456$	−4.81279	−0.225380
$457$	−8.04480	−0.376320	−0.188160	−	0.982138i	$-0.560252\pi$
$457$	−8.04480	−0.376320	−0.188160	+	0.982138i	$0.560252\pi$
$458$	−3.02630	−0.141409
$459$	15.3188	0.715021
$460$	−1.03782	−0.0483887
$461$	−5.17742	−0.241136	−0.120568	−	0.992705i	$-0.538472\pi$
$461$	−5.17742	−0.241136	−0.120568	+	0.992705i	$0.538472\pi$
$462$	−27.7322	−1.29022
$463$	23.1522	1.07598	0.537988	−	0.842953i	$-0.319185\pi$
$463$	23.1522	1.07598	0.537988	+	0.842953i	$0.319185\pi$
$464$	33.8132	1.56974
$465$	10.2864	0.477019
$466$	40.0988	1.85754
$467$	20.5022	0.948729	0.474364	−	0.880329i	$-0.342678\pi$
$467$	20.5022	0.948729	0.474364	+	0.880329i	$0.342678\pi$
$468$	−3.33233	−0.154037
$469$	4.95743	0.228913
$470$	13.0931	0.603939
$471$	−31.2680	−1.44075
$472$	7.29751	0.335895
$473$	15.0995	0.694276
$474$	−18.9318	−0.869565
$475$	11.7487	0.539070
$476$	−40.7547	−1.86799
$477$	1.95222	0.0893859
$478$	29.6270	1.35511
$479$	−12.0173	−0.549087	−0.274543	−	0.961575i	$-0.588527\pi$
$479$	−12.0173	−0.549087	−0.274543	+	0.961575i	$0.588527\pi$
$480$	−20.7495	−0.947079
$481$	−4.09093	−0.186530
$482$	36.3914	1.65758
$483$	3.81025	0.173372
$484$	−12.2959	−0.558905
$485$	−10.1423	−0.460539
$486$	34.9545	1.58557
$487$	−36.9932	−1.67632	−0.838162	−	0.545422i	$-0.816369\pi$
$487$	−36.9932	−1.67632	−0.838162	+	0.545422i	$0.816369\pi$
$488$	−8.08492	−0.365987
$489$	−35.2386	−1.59354
$490$	−10.4007	−0.469854
$491$	16.8815	0.761852	0.380926	−	0.924605i	$-0.375605\pi$
$491$	16.8815	0.761852	0.380926	+	0.924605i	$0.375605\pi$
$492$	−21.9351	−0.988911
$493$	−53.7279	−2.41978
$494$	6.29116	0.283053
$495$	4.85822	0.218361
$496$	−16.8181	−0.755157
$497$	10.3992	0.466466
$498$	−30.7665	−1.37868
$499$	17.7945	0.796591	0.398296	−	0.917257i	$-0.369602\pi$
$499$	17.7945	0.796591	0.398296	+	0.917257i	$0.369602\pi$
$500$	17.5048	0.782840
$501$	−12.4565	−0.556516
$502$	−43.1209	−1.92458
$503$	−40.6486	−1.81243	−0.906216	−	0.422816i	$-0.861042\pi$
$503$	−40.6486	−1.81243	−0.906216	+	0.422816i	$0.861042\pi$
$504$	4.38722	0.195422
$505$	20.6726	0.919919
$506$	−1.83467	−0.0815612
$507$	27.1235	1.20460
$508$	27.3931	1.21537
$509$	−23.7205	−1.05139	−0.525696	−	0.850673i	$-0.676195\pi$
$509$	−23.7205	−1.05139	−0.525696	+	0.850673i	$0.676195\pi$
$510$	38.5580	1.70738
$511$	33.9784	1.50311
$512$	28.1754	1.24519
$513$	−7.17620	−0.316837
$514$	35.6719	1.57342
$515$	7.91329	0.348701
$516$	29.7363	1.30907
$517$	10.5333	0.463253
$518$	−27.2805	−1.19864
$519$	−33.7570	−1.48177
$520$	−0.757937	−0.0332377
$521$	41.2684	1.80800	0.904000	−	0.427532i	$-0.140617\pi$
$521$	41.2684	1.80800	0.904000	+	0.427532i	$0.140617\pi$
$522$	−29.2955	−1.28223
$523$	−27.6570	−1.20935	−0.604677	−	0.796471i	$-0.706698\pi$
$523$	−27.6570	−1.20935	−0.604677	+	0.796471i	$0.706698\pi$
$524$	−31.3085	−1.36772
$525$	−26.3217	−1.14877
$526$	−24.6704	−1.07568
$527$	26.7234	1.16409
$528$	−19.5219	−0.849584
$529$	−22.7479	−0.989040
$530$	−2.24906	−0.0976931
$531$	−23.7732	−1.03167
$532$	19.0918	0.827733
$533$	−5.66090	−0.245201
$534$	−12.1935	−0.527662
$535$	4.93854	0.213512
$536$	0.928105	0.0400880
$537$	−40.3172	−1.73981
$538$	−39.4890	−1.70249
$539$	−8.36725	−0.360403
$540$	−4.37910	−0.188447
$541$	−26.0198	−1.11868	−0.559339	−	0.828939i	$-0.688945\pi$
$541$	−26.0198	−1.11868	−0.559339	+	0.828939i	$0.688945\pi$
$542$	39.8788	1.71294
$543$	−1.38087	−0.0592588
$544$	−53.9059	−2.31120
$545$	14.8899	0.637813
$546$	−14.0946	−0.603194
$547$	38.5410	1.64789	0.823947	−	0.566667i	$-0.191767\pi$
$547$	38.5410	1.64789	0.823947	+	0.566667i	$0.191767\pi$
$548$	−17.1993	−0.734720
$549$	26.3384	1.12409
$550$	12.6742	0.540428
$551$	25.1691	1.07224
$552$	0.713335	0.0303616
$553$	−14.8269	−0.630505
$554$	29.7919	1.26574
$555$	11.7456	0.498573
$556$	−27.7721	−1.17780
$557$	−12.9492	−0.548674	−0.274337	−	0.961634i	$-0.588458\pi$
$557$	−12.9492	−0.548674	−0.274337	+	0.961634i	$0.588458\pi$
$558$	14.5711	0.616844
$559$	7.67418	0.324583
$560$	−19.0047	−0.803096
$561$	31.0196	1.30965
$562$	−37.6440	−1.58791
$563$	29.9887	1.26387	0.631936	−	0.775021i	$-0.282261\pi$
$563$	29.9887	1.26387	0.631936	+	0.775021i	$0.282261\pi$
$564$	20.7438	0.873470
$565$	13.6513	0.574312
$566$	19.9947	0.840442
$567$	36.9114	1.55013
$568$	1.94688	0.0816891
$569$	3.95383	0.165753	0.0828766	−	0.996560i	$-0.473589\pi$
$569$	3.95383	0.165753	0.0828766	+	0.996560i	$0.473589\pi$
$570$	−18.0627	−0.756565
$571$	20.5522	0.860081	0.430041	−	0.902810i	$-0.358499\pi$
$571$	20.5522	0.860081	0.430041	+	0.902810i	$0.358499\pi$
$572$	3.08847	0.129135
$573$	28.3855	1.18582
$574$	−37.7498	−1.57565
$575$	−1.74136	−0.0726197
$576$	−10.6613	−0.444221
$577$	−38.3158	−1.59511	−0.797554	−	0.603247i	$-0.793873\pi$
$577$	−38.3158	−1.59511	−0.797554	+	0.603247i	$0.793873\pi$
$578$	67.6032	2.81192
$579$	−16.0638	−0.667590
$580$	15.3589	0.637743
$581$	−24.0956	−0.999656
$582$	−35.3100	−1.46365
$583$	−1.80935	−0.0749357
$584$	6.36125	0.263231
$585$	2.46914	0.102087
$586$	−5.98905	−0.247405
$587$	−3.35867	−0.138627	−0.0693135	−	0.997595i	$-0.522081\pi$
$587$	−3.35867	−0.138627	−0.0693135	+	0.997595i	$0.522081\pi$
$588$	−16.4781	−0.679545
$589$	−12.5187	−0.515825
$590$	27.3881	1.12755
$591$	−1.51041	−0.0621298
$592$	−19.2040	−0.789278
$593$	45.4184	1.86511	0.932555	−	0.361028i	$-0.117574\pi$
$593$	45.4184	1.86511	0.932555	+	0.361028i	$0.117574\pi$
$594$	−7.74144	−0.317635
$595$	30.1978	1.23799
$596$	1.68105	0.0688586
$597$	−49.7568	−2.03641
$598$	−0.932455	−0.0381309
$599$	20.0281	0.818326	0.409163	−	0.912461i	$-0.365821\pi$
$599$	20.0281	0.818326	0.409163	+	0.912461i	$0.365821\pi$
$600$	−4.92781	−0.201177
$601$	23.6159	0.963311	0.481656	−	0.876361i	$-0.340036\pi$
$601$	23.6159	0.963311	0.481656	+	0.876361i	$0.340036\pi$
$602$	51.1755	2.08576
$603$	−3.02350	−0.123127
$604$	0.490811	0.0199708
$605$	9.11084	0.370408
$606$	71.9707	2.92361
$607$	33.5345	1.36112	0.680562	−	0.732691i	$-0.261736\pi$
$607$	33.5345	1.36112	0.680562	+	0.732691i	$0.261736\pi$
$608$	25.2526	1.02413
$609$	−56.3885	−2.28498
$610$	−30.3433	−1.22856
$611$	5.35344	0.216577
$612$	24.8560	1.00474
$613$	−27.1181	−1.09529	−0.547645	−	0.836711i	$-0.684476\pi$
$613$	−27.1181	−1.09529	−0.547645	+	0.836711i	$0.684476\pi$
$614$	−17.8560	−0.720610
$615$	16.2532	0.655391
$616$	−4.06616	−0.163830
$617$	−27.7472	−1.11706	−0.558530	−	0.829484i	$-0.688635\pi$
$617$	−27.7472	−1.11706	−0.558530	+	0.829484i	$0.688635\pi$
$618$	27.5497	1.10821
$619$	−42.1303	−1.69336	−0.846679	−	0.532104i	$-0.821402\pi$
$619$	−42.1303	−1.69336	−0.846679	+	0.532104i	$0.821402\pi$
$620$	−7.63926	−0.306800
$621$	1.06363	0.0426821
$622$	−51.3276	−2.05805
$623$	−9.54964	−0.382598
$624$	−9.92183	−0.397191
$625$	4.37134	0.174853
$626$	9.88941	0.395260
$627$	−14.5313	−0.580325
$628$	23.2215	0.926638
$629$	30.5144	1.21669
$630$	16.4656	0.656003
$631$	33.9020	1.34962	0.674809	−	0.737993i	$-0.264226\pi$
$631$	33.9020	1.34962	0.674809	+	0.737993i	$0.264226\pi$
$632$	−2.77582	−0.110416
$633$	45.3274	1.80160
$634$	26.8678	1.06706
$635$	−20.2973	−0.805474
$636$	−3.56326	−0.141292
$637$	−4.25257	−0.168493
$638$	27.1516	1.07494
$639$	−6.34237	−0.250900
$640$	−6.16969	−0.243878
$641$	−40.7298	−1.60873	−0.804365	−	0.594135i	$-0.797494\pi$
$641$	−40.7298	−1.60873	−0.804365	+	0.594135i	$0.797494\pi$
$642$	17.1933	0.678565
$643$	−19.3339	−0.762457	−0.381228	−	0.924481i	$-0.624499\pi$
$643$	−19.3339	−0.762457	−0.381228	+	0.924481i	$0.624499\pi$
$644$	−2.82972	−0.111506
$645$	−22.0336	−0.867571
$646$	−46.9260	−1.84628
$647$	−4.12177	−0.162043	−0.0810217	−	0.996712i	$-0.525818\pi$
$647$	−4.12177	−0.162043	−0.0810217	+	0.996712i	$0.525818\pi$
$648$	6.91036	0.271464
$649$	22.0335	0.864890
$650$	6.44152	0.252657
$651$	28.0467	1.09924
$652$	26.1703	1.02491
$653$	−43.0070	−1.68299	−0.841496	−	0.540263i	$-0.818325\pi$
$653$	−43.0070	−1.68299	−0.841496	+	0.540263i	$0.818325\pi$
$654$	51.8384	2.02704
$655$	23.1985	0.906440
$656$	−26.5738	−1.03753
$657$	−20.7232	−0.808488
$658$	35.6995	1.39171
$659$	−32.3215	−1.25907	−0.629533	−	0.776974i	$-0.716754\pi$
$659$	−32.3215	−1.25907	−0.629533	+	0.776974i	$0.716754\pi$
$660$	−8.86740	−0.345163
$661$	−32.6184	−1.26871	−0.634354	−	0.773043i	$-0.718734\pi$
$661$	−32.6184	−1.26871	−0.634354	+	0.773043i	$0.718734\pi$
$662$	17.1655	0.667155
$663$	15.7654	0.612278
$664$	−4.51106	−0.175063
$665$	−14.1463	−0.548571
$666$	16.6382	0.644716
$667$	−3.73049	−0.144445
$668$	9.25094	0.357930
$669$	5.73089	0.221569
$670$	3.48325	0.134570
$671$	−24.4109	−0.942373
$672$	−56.5754	−2.18244
$673$	−48.9755	−1.88787	−0.943934	−	0.330133i	$-0.892906\pi$
$673$	−48.9755	−1.88787	−0.943934	+	0.330133i	$0.892906\pi$
$674$	6.20045	0.238833
$675$	−7.34770	−0.282813
$676$	−20.1435	−0.774750
$677$	13.1286	0.504574	0.252287	−	0.967653i	$-0.418817\pi$
$677$	13.1286	0.504574	0.252287	+	0.967653i	$0.418817\pi$
$678$	47.5261	1.82523
$679$	−27.6540	−1.06126
$680$	5.65347	0.216801
$681$	53.6169	2.05460
$682$	−13.5048	−0.517125
$683$	−37.4751	−1.43395	−0.716973	−	0.697101i	$-0.754473\pi$
$683$	−37.4751	−1.43395	−0.716973	+	0.697101i	$0.754473\pi$
$684$	−11.6439	−0.445217
$685$	12.7441	0.486928
$686$	16.8943	0.645026
$687$	3.55267	0.135543
$688$	36.0247	1.37343
$689$	−0.919586	−0.0350334
$690$	2.67720	0.101919
$691$	38.3737	1.45981	0.729903	−	0.683551i	$-0.239565\pi$
$691$	38.3737	1.45981	0.729903	+	0.683551i	$0.239565\pi$
$692$	25.0699	0.953016
$693$	13.2464	0.503189
$694$	−0.586119	−0.0222488
$695$	20.5782	0.780574
$696$	−10.5568	−0.400153
$697$	42.2248	1.59938
$698$	−1.91579	−0.0725137
$699$	−47.0733	−1.78048
$700$	19.5480	0.738846
$701$	−38.9236	−1.47012	−0.735062	−	0.678000i	$-0.762847\pi$
$701$	−38.9236	−1.47012	−0.735062	+	0.678000i	$0.762847\pi$
$702$	−3.93451	−0.148499
$703$	−14.2946	−0.539133
$704$	9.88111	0.372408
$705$	−15.3704	−0.578883
$706$	−62.8616	−2.36583
$707$	56.3658	2.11985
$708$	43.3917	1.63076
$709$	−44.3332	−1.66497	−0.832485	−	0.554048i	$-0.813082\pi$
$709$	−44.3332	−1.66497	−0.832485	+	0.554048i	$0.813082\pi$
$710$	7.30676	0.274218
$711$	9.04284	0.339133
$712$	−1.78783	−0.0670019
$713$	1.85548	0.0694884
$714$	105.132	3.93447
$715$	−2.28845	−0.0855832
$716$	29.9419	1.11898
$717$	−34.7802	−1.29889
$718$	0.225600	0.00841933
$719$	21.3284	0.795416	0.397708	−	0.917512i	$-0.369806\pi$
$719$	21.3284	0.795416	0.397708	+	0.917512i	$0.369806\pi$
$720$	11.5909	0.431966
$721$	21.5763	0.803545
$722$	−14.4172	−0.536553
$723$	−42.7210	−1.58881
$724$	1.02552	0.0381130
$725$	25.7707	0.957098
$726$	31.7189	1.17720
$727$	6.16426	0.228620	0.114310	−	0.993445i	$-0.463534\pi$
$727$	6.16426	0.228620	0.114310	+	0.993445i	$0.463534\pi$
$728$	−2.06659	−0.0765928
$729$	−8.21848	−0.304388
$730$	23.8742	0.883625
$731$	−57.2419	−2.11717
$732$	−48.0737	−1.77686
$733$	−43.7924	−1.61751	−0.808755	−	0.588146i	$-0.799858\pi$
$733$	−43.7924	−1.61751	−0.808755	+	0.588146i	$0.799858\pi$
$734$	52.7396	1.94665
$735$	12.2097	0.450361
$736$	−3.74285	−0.137963
$737$	2.80224	0.103222
$738$	23.0234	0.847501
$739$	28.3313	1.04218	0.521091	−	0.853501i	$-0.325525\pi$
$739$	28.3313	1.04218	0.521091	+	0.853501i	$0.325525\pi$
$740$	−8.72297	−0.320663
$741$	−7.38540	−0.271310
$742$	−6.13228	−0.225123
$743$	−20.7598	−0.761603	−0.380801	−	0.924657i	$-0.624352\pi$
$743$	−20.7598	−0.761603	−0.380801	+	0.924657i	$0.624352\pi$
$744$	5.25077	0.192502
$745$	−1.24560	−0.0456353
$746$	24.6625	0.902957
$747$	14.6958	0.537690
$748$	−23.0370	−0.842316
$749$	13.4654	0.492015
$750$	−45.1560	−1.64887
$751$	42.9054	1.56564	0.782819	−	0.622249i	$-0.213781\pi$
$751$	42.9054	1.56564	0.782819	+	0.622249i	$0.213781\pi$
$752$	25.1305	0.916416
$753$	50.6211	1.84473
$754$	13.7996	0.502550
$755$	−0.363674	−0.0132355
$756$	−11.9400	−0.434255
$757$	−12.9859	−0.471980	−0.235990	−	0.971756i	$-0.575833\pi$
$757$	−12.9859	−0.471980	−0.235990	+	0.971756i	$0.575833\pi$
$758$	−1.56600	−0.0568798
$759$	2.15378	0.0781774
$760$	−2.64840	−0.0960677
$761$	31.0968	1.12726	0.563629	−	0.826028i	$-0.309405\pi$
$761$	31.0968	1.12726	0.563629	+	0.826028i	$0.309405\pi$
$762$	−70.6641	−2.55989
$763$	40.5987	1.46977
$764$	−21.0808	−0.762675
$765$	−18.4174	−0.665883
$766$	30.4520	1.10027
$767$	11.1983	0.404347
$768$	−44.7807	−1.61588
$769$	−30.9611	−1.11649	−0.558244	−	0.829677i	$-0.688525\pi$
$769$	−30.9611	−1.11649	−0.558244	+	0.829677i	$0.688525\pi$
$770$	−15.2606	−0.549954
$771$	−41.8765	−1.50814
$772$	11.9300	0.429368
$773$	−13.1588	−0.473290	−0.236645	−	0.971596i	$-0.576048\pi$
$773$	−13.1588	−0.473290	−0.236645	+	0.971596i	$0.576048\pi$
$774$	−31.2116	−1.12188
$775$	−12.8179	−0.460433
$776$	−5.17724	−0.185852
$777$	32.0255	1.14891
$778$	−20.0379	−0.718395
$779$	−19.7805	−0.708708
$780$	−4.50677	−0.161368
$781$	5.87823	0.210340
$782$	6.95521	0.248718
$783$	−15.7408	−0.562532
$784$	−19.9628	−0.712956
$785$	−17.2063	−0.614120
$786$	80.7644	2.88077
$787$	−27.0020	−0.962518	−0.481259	−	0.876578i	$-0.659820\pi$
$787$	−27.0020	−0.962518	−0.481259	+	0.876578i	$0.659820\pi$
$788$	1.12172	0.0399595
$789$	28.9614	1.03105
$790$	−10.4179	−0.370651
$791$	37.2214	1.32344
$792$	2.47992	0.0881202
$793$	−12.4066	−0.440571
$794$	−0.887567	−0.0314986
$795$	2.64025	0.0936400
$796$	36.9523	1.30974
$797$	41.2844	1.46237	0.731184	−	0.682180i	$-0.238968\pi$
$797$	41.2844	1.46237	0.731184	+	0.682180i	$0.238968\pi$
$798$	−49.2498	−1.74342
$799$	−39.9315	−1.41267
$800$	25.8561	0.914150
$801$	5.82426	0.205790
$802$	6.11623	0.215972
$803$	19.2066	0.677787
$804$	5.51861	0.194626
$805$	2.09672	0.0738997
$806$	−6.86368	−0.241763
$807$	46.3574	1.63186
$808$	10.5525	0.371236
$809$	33.4283	1.17528	0.587639	−	0.809123i	$-0.300058\pi$
$809$	33.4283	1.17528	0.587639	+	0.809123i	$0.300058\pi$
$810$	25.9351	0.911266
$811$	−49.9822	−1.75511	−0.877556	−	0.479475i	$-0.840827\pi$
$811$	−49.9822	−1.75511	−0.877556	+	0.479475i	$0.840827\pi$
$812$	41.8774	1.46961
$813$	−46.8150	−1.64187
$814$	−15.4206	−0.540491
$815$	−19.3913	−0.679246
$816$	74.0073	2.59077
$817$	26.8153	0.938149
$818$	28.9477	1.01213
$819$	6.73235	0.235247
$820$	−12.0706	−0.421522
$821$	49.4941	1.72735	0.863677	−	0.504045i	$-0.168156\pi$
$821$	49.4941	1.72735	0.863677	+	0.504045i	$0.168156\pi$
$822$	44.3680	1.54751
$823$	−41.6146	−1.45059	−0.725297	−	0.688436i	$-0.758297\pi$
$823$	−41.6146	−1.45059	−0.725297	+	0.688436i	$0.758297\pi$
$824$	4.03941	0.140720
$825$	−14.8786	−0.518007
$826$	74.6762	2.59832
$827$	−5.59048	−0.194400	−0.0972001	−	0.995265i	$-0.530989\pi$
$827$	−5.59048	−0.194400	−0.0972001	+	0.995265i	$0.530989\pi$
$828$	1.72582	0.0599765
$829$	10.0998	0.350782	0.175391	−	0.984499i	$-0.443881\pi$
$829$	10.0998	0.350782	0.175391	+	0.984499i	$0.443881\pi$
$830$	−16.9303	−0.587661
$831$	−34.9737	−1.21322
$832$	5.02198	0.174106
$833$	31.7201	1.09904
$834$	71.6419	2.48075
$835$	−6.85463	−0.237214
$836$	10.7918	0.373243
$837$	7.82925	0.270618
$838$	−8.10482	−0.279976
$839$	8.76042	0.302443	0.151222	−	0.988500i	$-0.451679\pi$
$839$	8.76042	0.302443	0.151222	+	0.988500i	$0.451679\pi$
$840$	5.93344	0.204723
$841$	26.2081	0.903726
$842$	−47.8599	−1.64936
$843$	44.1915	1.52204
$844$	−33.6628	−1.15872
$845$	14.9256	0.513458
$846$	−21.7729	−0.748568
$847$	24.8415	0.853566
$848$	−4.31679	−0.148239
$849$	−23.4725	−0.805574
$850$	−48.0475	−1.64801
$851$	2.11870	0.0726282
$852$	11.5763	0.396598
$853$	−16.8188	−0.575863	−0.287932	−	0.957651i	$-0.592968\pi$
$853$	−16.8188	−0.575863	−0.287932	+	0.957651i	$0.592968\pi$
$854$	−82.7338	−2.83109
$855$	8.62775	0.295063
$856$	2.52092	0.0861633
$857$	−12.4136	−0.424039	−0.212020	−	0.977265i	$-0.568004\pi$
$857$	−12.4136	−0.424039	−0.212020	+	0.977265i	$0.568004\pi$
$858$	−7.96713	−0.271993
$859$	9.99961	0.341182	0.170591	−	0.985342i	$-0.445432\pi$
$859$	9.99961	0.341182	0.170591	+	0.985342i	$0.445432\pi$
$860$	16.3634	0.557988
$861$	44.3158	1.51028
$862$	−58.7190	−1.99998
$863$	18.7621	0.638669	0.319334	−	0.947642i	$-0.396541\pi$
$863$	18.7621	0.638669	0.319334	+	0.947642i	$0.396541\pi$
$864$	−15.7930	−0.537289
$865$	−18.5760	−0.631601
$866$	−40.8910	−1.38953
$867$	−79.3616	−2.69526
$868$	−20.8292	−0.706988
$869$	−8.38108	−0.284309
$870$	−39.6203	−1.34325
$871$	1.42421	0.0482576
$872$	7.60068	0.257391
$873$	16.8660	0.570827
$874$	−3.25821	−0.110211
$875$	−35.3652	−1.19556
$876$	37.8246	1.27798
$877$	−32.0420	−1.08198	−0.540991	−	0.841028i	$-0.681951\pi$
$877$	−32.0420	−1.08198	−0.540991	+	0.841028i	$0.681951\pi$
$878$	−1.26693	−0.0427569
$879$	7.03074	0.237141
$880$	−10.7426	−0.362134
$881$	19.6803	0.663045	0.331522	−	0.943447i	$-0.392438\pi$
$881$	19.6803	0.663045	0.331522	+	0.943447i	$0.392438\pi$
$882$	17.2956	0.582373
$883$	40.9231	1.37717	0.688586	−	0.725155i	$-0.258232\pi$
$883$	40.9231	1.37717	0.688586	+	0.725155i	$0.258232\pi$
$884$	−11.7083	−0.393794
$885$	−32.1518	−1.08077
$886$	−40.2019	−1.35061
$887$	−9.95383	−0.334217	−0.167108	−	0.985939i	$-0.553443\pi$
$887$	−9.95383	−0.334217	−0.167108	+	0.985939i	$0.553443\pi$
$888$	5.99564	0.201200
$889$	−55.3425	−1.85613
$890$	−6.70987	−0.224915
$891$	20.8645	0.698989
$892$	−4.25610	−0.142505
$893$	18.7061	0.625977
$894$	−4.33650	−0.145034
$895$	−22.1859	−0.741593
$896$	−16.8222	−0.561991
$897$	1.09464	0.0365490
$898$	−46.4676	−1.55064
$899$	−27.4596	−0.915829
$900$	−11.9222	−0.397407
$901$	6.85922	0.228514
$902$	−21.3385	−0.710494
$903$	−60.0766	−1.99922
$904$	6.96840	0.231765
$905$	−0.759871	−0.0252590
$906$	−1.26611	−0.0420638
$907$	39.1685	1.30057	0.650284	−	0.759691i	$-0.274650\pi$
$907$	39.1685	1.30057	0.650284	+	0.759691i	$0.274650\pi$
$908$	−39.8190	−1.32144
$909$	−34.3771	−1.14022
$910$	−7.75605	−0.257110
$911$	19.0561	0.631358	0.315679	−	0.948866i	$-0.397768\pi$
$911$	19.0561	0.631358	0.315679	+	0.948866i	$0.397768\pi$
$912$	−34.6691	−1.14801
$913$	−13.6203	−0.450767
$914$	−15.4121	−0.509788
$915$	35.6210	1.17759
$916$	−2.63842	−0.0871759
$917$	63.2528	2.08879
$918$	29.3476	0.968616
$919$	−5.91927	−0.195259	−0.0976294	−	0.995223i	$-0.531126\pi$
$919$	−5.91927	−0.195259	−0.0976294	+	0.995223i	$0.531126\pi$
$920$	0.392537	0.0129416
$921$	20.9618	0.690714
$922$	−9.91883	−0.326659
$923$	2.98755	0.0983365
$924$	−24.1778	−0.795391
$925$	−14.6363	−0.481237
$926$	44.3548	1.45759
$927$	−13.1593	−0.432207
$928$	55.3910	1.81830
$929$	−44.7742	−1.46900	−0.734498	−	0.678611i	$-0.762582\pi$
$929$	−44.7742	−1.46900	−0.734498	+	0.678611i	$0.762582\pi$
$930$	19.7065	0.646202
$931$	−14.8595	−0.486999
$932$	34.9594	1.14513
$933$	60.2551	1.97266
$934$	39.2779	1.28521
$935$	17.0696	0.558236
$936$	1.26040	0.0411973
$937$	−17.6144	−0.575438	−0.287719	−	0.957715i	$-0.592897\pi$
$937$	−17.6144	−0.575438	−0.287719	+	0.957715i	$0.592897\pi$
$938$	9.49740	0.310101
$939$	−11.6095	−0.378862
$940$	11.4150	0.372315
$941$	8.62072	0.281027	0.140514	−	0.990079i	$-0.455125\pi$
$941$	8.62072	0.281027	0.140514	+	0.990079i	$0.455125\pi$
$942$	−59.9029	−1.95174
$943$	2.93179	0.0954723
$944$	52.5680	1.71094
$945$	8.84715	0.287798
$946$	28.9275	0.940513
$947$	−60.8849	−1.97849	−0.989247	−	0.146255i	$-0.953278\pi$
$947$	−60.8849	−1.97849	−0.989247	+	0.146255i	$0.953278\pi$
$948$	−16.5053	−0.536068
$949$	9.76158	0.316874
$950$	22.5081	0.730260
$951$	−31.5410	−1.02279
$952$	15.4147	0.499594
$953$	−17.0126	−0.551091	−0.275546	−	0.961288i	$-0.588859\pi$
$953$	−17.0126	−0.551091	−0.275546	+	0.961288i	$0.588859\pi$
$954$	3.74004	0.121088
$955$	15.6201	0.505455
$956$	25.8298	0.835396
$957$	−31.8742	−1.03035
$958$	−23.0227	−0.743830
$959$	34.7480	1.12207
$960$	−14.4187	−0.465363
$961$	−17.3420	−0.559420
$962$	−7.83736	−0.252687
$963$	−8.21245	−0.264642
$964$	31.7272	1.02186
$965$	−8.83968	−0.284560
$966$	7.29963	0.234862
$967$	−3.15774	−0.101546	−0.0507730	−	0.998710i	$-0.516168\pi$
$967$	−3.15774	−0.101546	−0.0507730	+	0.998710i	$0.516168\pi$
$968$	4.65071	0.149479
$969$	55.0880	1.76968
$970$	−19.4306	−0.623878
$971$	59.4710	1.90851	0.954257	−	0.298987i	$-0.0966488\pi$
$971$	59.4710	1.90851	0.954257	+	0.298987i	$0.0966488\pi$
$972$	30.4745	0.977469
$973$	56.1083	1.79875
$974$	−70.8712	−2.27086
$975$	−7.56191	−0.242175
$976$	−58.2401	−1.86422
$977$	−13.4967	−0.431797	−0.215898	−	0.976416i	$-0.569268\pi$
$977$	−13.4967	−0.431797	−0.215898	+	0.976416i	$0.569268\pi$
$978$	−67.5097	−2.15872
$979$	−5.39803	−0.172522
$980$	−9.06764	−0.289655
$981$	−24.7609	−0.790554
$982$	32.3414	1.03206
$983$	40.7654	1.30022	0.650108	−	0.759842i	$-0.274724\pi$
$983$	40.7654	1.30022	0.650108	+	0.759842i	$0.274724\pi$
$984$	8.29657	0.264485
$985$	−0.831153	−0.0264827
$986$	−102.931	−3.27800
$987$	−41.9089	−1.33397
$988$	5.48484	0.174496
$989$	−3.97448	−0.126381
$990$	9.30733	0.295806
$991$	49.9738	1.58747	0.793736	−	0.608263i	$-0.208133\pi$
$991$	49.9738	1.58747	0.793736	+	0.608263i	$0.208133\pi$
$992$	−27.5506	−0.874732
$993$	−20.1511	−0.639477
$994$	19.9226	0.631906
$995$	−27.3804	−0.868017
$996$	−26.8232	−0.849926
$997$	34.9877	1.10807	0.554036	−	0.832492i	$-0.313087\pi$
$997$	34.9877	1.10807	0.554036	+	0.832492i	$0.313087\pi$
$998$	34.0905	1.07912
$999$	8.93990	0.282846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.a.1.11	✓	11
3.2	odd	2		3141.2.a.b.1.1		11
4.3	odd	2		5584.2.a.j.1.10		11
5.4	even	2		8725.2.a.l.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.a.1.11	✓	11	1.1	even	1	trivial
3141.2.a.b.1.1		11	3.2	odd	2
5584.2.a.j.1.10		11	4.3	odd	2
8725.2.a.l.1.1		11	5.4	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q+1.91579 q^{2} -2.24901 q^{3} +1.67025 q^{4} -1.23759 q^{5} -4.30862 q^{6} -3.37442 q^{7} -0.631741 q^{8} +2.05803 q^{9} +O(q^{10})\)	\(q+1.91579 q^{2} -2.24901 q^{3} +1.67025 q^{4} -1.23759 q^{5} -4.30862 q^{6} -3.37442 q^{7} -0.631741 q^{8} +2.05803 q^{9} -2.37097 q^{10} -1.90742 q^{11} -3.75639 q^{12} -0.969429 q^{13} -6.46467 q^{14} +2.78336 q^{15} -4.55077 q^{16} +7.23100 q^{17} +3.94275 q^{18} -3.38741 q^{19} -2.06709 q^{20} +7.58908 q^{21} -3.65422 q^{22} +0.502070 q^{23} +1.42079 q^{24} -3.46836 q^{25} -1.85722 q^{26} +2.11849 q^{27} -5.63610 q^{28} -7.43021 q^{29} +5.33232 q^{30} +3.69567 q^{31} -7.45483 q^{32} +4.28981 q^{33} +13.8531 q^{34} +4.17616 q^{35} +3.43742 q^{36} +4.21994 q^{37} -6.48955 q^{38} +2.18025 q^{39} +0.781838 q^{40} +5.83941 q^{41} +14.5391 q^{42} -7.91618 q^{43} -3.18587 q^{44} -2.54701 q^{45} +0.961860 q^{46} -5.52226 q^{47} +10.2347 q^{48} +4.38668 q^{49} -6.64465 q^{50} -16.2626 q^{51} -1.61918 q^{52} +0.948585 q^{53} +4.05858 q^{54} +2.36062 q^{55} +2.13175 q^{56} +7.61830 q^{57} -14.2347 q^{58} -11.5514 q^{59} +4.64889 q^{60} +12.7978 q^{61} +7.08012 q^{62} -6.94465 q^{63} -5.18034 q^{64} +1.19976 q^{65} +8.21837 q^{66} -1.46912 q^{67} +12.0775 q^{68} -1.12916 q^{69} +8.00063 q^{70} -3.08176 q^{71} -1.30014 q^{72} -10.0694 q^{73} +8.08451 q^{74} +7.80037 q^{75} -5.65780 q^{76} +6.43644 q^{77} +4.17690 q^{78} +4.39393 q^{79} +5.63201 q^{80} -10.9386 q^{81} +11.1871 q^{82} +7.14069 q^{83} +12.6756 q^{84} -8.94904 q^{85} -15.1657 q^{86} +16.7106 q^{87} +1.20500 q^{88} +2.83001 q^{89} -4.87953 q^{90} +3.27126 q^{91} +0.838580 q^{92} -8.31159 q^{93} -10.5795 q^{94} +4.19223 q^{95} +16.7660 q^{96} +8.19520 q^{97} +8.40395 q^{98} -3.92554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * q^99

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