LMFDB - Embedded newform 349.2.a.a.1.3

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			1.3
Root			$2.17018$ 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)

$f(q)$	$=$	$q-2.17018 q^{2} -2.21125 q^{3} +2.70967 q^{4} -2.88560 q^{5} +4.79881 q^{6} +3.08193 q^{7} -1.54011 q^{8} +1.88963 q^{9} +O(q^{10})$	\(q-2.17018 q^{2} -2.21125 q^{3} +2.70967 q^{4} -2.88560 q^{5} +4.79881 q^{6} +3.08193 q^{7} -1.54011 q^{8} +1.88963 q^{9} +6.26228 q^{10} +0.107220 q^{11} -5.99176 q^{12} +4.63972 q^{13} -6.68833 q^{14} +6.38080 q^{15} -2.07703 q^{16} -0.436470 q^{17} -4.10083 q^{18} -2.33713 q^{19} -7.81904 q^{20} -6.81491 q^{21} -0.232686 q^{22} -1.19125 q^{23} +3.40557 q^{24} +3.32672 q^{25} -10.0690 q^{26} +2.45531 q^{27} +8.35100 q^{28} -4.02152 q^{29} -13.8475 q^{30} -2.66311 q^{31} +7.58774 q^{32} -0.237090 q^{33} +0.947217 q^{34} -8.89322 q^{35} +5.12027 q^{36} -11.6066 q^{37} +5.07198 q^{38} -10.2596 q^{39} +4.44415 q^{40} -2.06448 q^{41} +14.7896 q^{42} -4.51465 q^{43} +0.290530 q^{44} -5.45272 q^{45} +2.58522 q^{46} +0.377519 q^{47} +4.59283 q^{48} +2.49827 q^{49} -7.21956 q^{50} +0.965144 q^{51} +12.5721 q^{52} +12.9452 q^{53} -5.32845 q^{54} -0.309394 q^{55} -4.74651 q^{56} +5.16798 q^{57} +8.72741 q^{58} -8.88116 q^{59} +17.2899 q^{60} -3.73636 q^{61} +5.77943 q^{62} +5.82370 q^{63} -12.3127 q^{64} -13.3884 q^{65} +0.514527 q^{66} -7.94347 q^{67} -1.18269 q^{68} +2.63414 q^{69} +19.2999 q^{70} -10.0703 q^{71} -2.91024 q^{72} +11.7999 q^{73} +25.1884 q^{74} -7.35620 q^{75} -6.33285 q^{76} +0.330444 q^{77} +22.2651 q^{78} +11.2236 q^{79} +5.99348 q^{80} -11.0982 q^{81} +4.48030 q^{82} -7.81077 q^{83} -18.4662 q^{84} +1.25948 q^{85} +9.79760 q^{86} +8.89259 q^{87} -0.165130 q^{88} +10.6780 q^{89} +11.8334 q^{90} +14.2993 q^{91} -3.22789 q^{92} +5.88881 q^{93} -0.819283 q^{94} +6.74403 q^{95} -16.7784 q^{96} +13.3888 q^{97} -5.42168 q^{98} +0.202606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.17018	−1.53455	−0.767274	−	0.641320i	$-0.778387\pi$
$2$	−2.17018	−1.53455	−0.767274	+	0.641320i	$0.778387\pi$
$3$	−2.21125	−1.27667	−0.638333	−	0.769760i	$-0.720376\pi$
$3$	−2.21125	−1.27667	−0.638333	+	0.769760i	$0.720376\pi$
$4$	2.70967	1.35484
$5$	−2.88560	−1.29048	−0.645241	−	0.763979i	$-0.723243\pi$
$5$	−2.88560	−1.29048	−0.645241	+	0.763979i	$0.723243\pi$
$6$	4.79881	1.95910
$7$	3.08193	1.16486	0.582429	−	0.812881i	$-0.302102\pi$
$7$	3.08193	1.16486	0.582429	+	0.812881i	$0.302102\pi$
$8$	−1.54011	−0.544511
$9$	1.88963	0.629877
$10$	6.26228	1.98031
$11$	0.107220	0.0323280	0.0161640	−	0.999869i	$-0.494855\pi$
$11$	0.107220	0.0323280	0.0161640	+	0.999869i	$0.494855\pi$
$12$	−5.99176	−1.72967
$13$	4.63972	1.28683	0.643414	−	0.765518i	$-0.277517\pi$
$13$	4.63972	1.28683	0.643414	+	0.765518i	$0.277517\pi$
$14$	−6.68833	−1.78753
$15$	6.38080	1.64751
$16$	−2.07703	−0.519257
$17$	−0.436470	−0.105859	−0.0529297	−	0.998598i	$-0.516856\pi$
$17$	−0.436470	−0.105859	−0.0529297	+	0.998598i	$0.516856\pi$
$18$	−4.10083	−0.966575
$19$	−2.33713	−0.536174	−0.268087	−	0.963395i	$-0.586391\pi$
$19$	−2.33713	−0.536174	−0.268087	+	0.963395i	$0.586391\pi$
$20$	−7.81904	−1.74839
$21$	−6.81491	−1.48714
$22$	−0.232686	−0.0496088
$23$	−1.19125	−0.248392	−0.124196	−	0.992258i	$-0.539635\pi$
$23$	−1.19125	−0.248392	−0.124196	+	0.992258i	$0.539635\pi$
$24$	3.40557	0.695159
$25$	3.32672	0.665343
$26$	−10.0690	−1.97470
$27$	2.45531	0.472524
$28$	8.35100	1.57819
$29$	−4.02152	−0.746777	−0.373389	−	0.927675i	$-0.621804\pi$
$29$	−4.02152	−0.746777	−0.373389	+	0.927675i	$0.621804\pi$
$30$	−13.8475	−2.52819
$31$	−2.66311	−0.478310	−0.239155	−	0.970981i	$-0.576870\pi$
$31$	−2.66311	−0.478310	−0.239155	+	0.970981i	$0.576870\pi$
$32$	7.58774	1.34134
$33$	−0.237090	−0.0412721
$34$	0.947217	0.162446
$35$	−8.89322	−1.50323
$36$	5.12027	0.853379
$37$	−11.6066	−1.90812	−0.954058	−	0.299621i	$-0.903140\pi$
$37$	−11.6066	−1.90812	−0.954058	+	0.299621i	$0.903140\pi$
$38$	5.07198	0.822785
$39$	−10.2596	−1.64285
$40$	4.44415	0.702682
$41$	−2.06448	−0.322418	−0.161209	−	0.986920i	$-0.551539\pi$
$41$	−2.06448	−0.322418	−0.161209	+	0.986920i	$0.551539\pi$
$42$	14.7896	2.28208
$43$	−4.51465	−0.688478	−0.344239	−	0.938882i	$-0.611863\pi$
$43$	−4.51465	−0.688478	−0.344239	+	0.938882i	$0.611863\pi$
$44$	0.290530	0.0437991
$45$	−5.45272	−0.812844
$46$	2.58522	0.381169
$47$	0.377519	0.0550668	0.0275334	−	0.999621i	$-0.491235\pi$
$47$	0.377519	0.0550668	0.0275334	+	0.999621i	$0.491235\pi$
$48$	4.59283	0.662917
$49$	2.49827	0.356895
$50$	−7.21956	−1.02100
$51$	0.965144	0.135147
$52$	12.5721	1.74344
$53$	12.9452	1.77816	0.889081	−	0.457750i	$-0.151345\pi$
$53$	12.9452	1.77816	0.889081	+	0.457750i	$0.151345\pi$
$54$	−5.32845	−0.725111
$55$	−0.309394	−0.0417187
$56$	−4.74651	−0.634279
$57$	5.16798	0.684515
$58$	8.72741	1.14597
$59$	−8.88116	−1.15623	−0.578115	−	0.815956i	$-0.696211\pi$
$59$	−8.88116	−1.15623	−0.578115	+	0.815956i	$0.696211\pi$
$60$	17.2899	2.23211
$61$	−3.73636	−0.478391	−0.239196	−	0.970971i	$-0.576884\pi$
$61$	−3.73636	−0.478391	−0.239196	+	0.970971i	$0.576884\pi$
$62$	5.77943	0.733989
$63$	5.82370	0.733717
$64$	−12.3127	−1.53909
$65$	−13.3884	−1.66063
$66$	0.514527	0.0633339
$67$	−7.94347	−0.970450	−0.485225	−	0.874389i	$-0.661262\pi$
$67$	−7.94347	−0.970450	−0.485225	+	0.874389i	$0.661262\pi$
$68$	−1.18269	−0.143422
$69$	2.63414	0.317114
$70$	19.2999	2.30678
$71$	−10.0703	−1.19513	−0.597564	−	0.801821i	$-0.703865\pi$
$71$	−10.0703	−1.19513	−0.597564	+	0.801821i	$0.703865\pi$
$72$	−2.91024	−0.342975
$73$	11.7999	1.38108	0.690538	−	0.723296i	$-0.257374\pi$
$73$	11.7999	1.38108	0.690538	+	0.723296i	$0.257374\pi$
$74$	25.1884	2.92810
$75$	−7.35620	−0.849421
$76$	−6.33285	−0.726428
$77$	0.330444	0.0376575
$78$	22.2651	2.52103
$79$	11.2236	1.26275	0.631376	−	0.775477i	$-0.282490\pi$
$79$	11.2236	1.26275	0.631376	+	0.775477i	$0.282490\pi$
$80$	5.99348	0.670091
$81$	−11.0982	−1.23313
$82$	4.48030	0.494766
$83$	−7.81077	−0.857344	−0.428672	−	0.903460i	$-0.641018\pi$
$83$	−7.81077	−0.857344	−0.428672	+	0.903460i	$0.641018\pi$
$84$	−18.4662	−2.01482
$85$	1.25948	0.136610
$86$	9.79760	1.05650
$87$	8.89259	0.953385
$88$	−0.165130	−0.0176030
$89$	10.6780	1.13186	0.565931	−	0.824453i	$-0.308517\pi$
$89$	10.6780	1.13186	0.565931	+	0.824453i	$0.308517\pi$
$90$	11.8334	1.24735
$91$	14.2993	1.49897
$92$	−3.22789	−0.336530
$93$	5.88881	0.610642
$94$	−0.819283	−0.0845026
$95$	6.74403	0.691923
$96$	−16.7784	−1.71244
$97$	13.3888	1.35942	0.679712	−	0.733479i	$-0.262105\pi$
$97$	13.3888	1.35942	0.679712	+	0.733479i	$0.262105\pi$
$98$	−5.42168	−0.547673
$99$	0.202606	0.0203626
$100$	9.01430	0.901430
$101$	−9.51020	−0.946300	−0.473150	−	0.880982i	$-0.656883\pi$
$101$	−9.51020	−0.946300	−0.473150	+	0.880982i	$0.656883\pi$
$102$	−2.09453	−0.207390
$103$	−16.5786	−1.63354	−0.816771	−	0.576962i	$-0.804238\pi$
$103$	−16.5786	−1.63354	−0.816771	+	0.576962i	$0.804238\pi$
$104$	−7.14569	−0.700693
$105$	19.6651	1.91912
$106$	−28.0934	−2.72867
$107$	−13.9594	−1.34950	−0.674752	−	0.738044i	$-0.735750\pi$
$107$	−13.9594	−1.34950	−0.674752	+	0.738044i	$0.735750\pi$
$108$	6.65307	0.640192
$109$	−16.7917	−1.60836	−0.804178	−	0.594388i	$-0.797394\pi$
$109$	−16.7917	−1.60836	−0.804178	+	0.594388i	$0.797394\pi$
$110$	0.671440	0.0640193
$111$	25.6651	2.43603
$112$	−6.40124	−0.604861
$113$	8.15000	0.766688	0.383344	−	0.923606i	$-0.374772\pi$
$113$	8.15000	0.766688	0.383344	+	0.923606i	$0.374772\pi$
$114$	−11.2154	−1.05042
$115$	3.43747	0.320545
$116$	−10.8970	−1.01176
$117$	8.76736	0.810543
$118$	19.2737	1.77429
$119$	−1.34517	−0.123311
$120$	−9.82713	−0.897091
$121$	−10.9885	−0.998955
$122$	8.10856	0.734114
$123$	4.56509	0.411620
$124$	−7.21616	−0.648031
$125$	4.82844	0.431868
$126$	−12.6385	−1.12592
$127$	−19.2112	−1.70472	−0.852361	−	0.522954i	$-0.824830\pi$
$127$	−19.2112	−1.70472	−0.852361	+	0.522954i	$0.824830\pi$
$128$	11.5452	1.02046
$129$	9.98303	0.878957
$130$	29.0552	2.54831
$131$	−3.70657	−0.323845	−0.161922	−	0.986803i	$-0.551769\pi$
$131$	−3.70657	−0.323845	−0.161922	+	0.986803i	$0.551769\pi$
$132$	−0.642436	−0.0559168
$133$	−7.20286	−0.624567
$134$	17.2387	1.48920
$135$	−7.08505	−0.609784
$136$	0.672212	0.0576417
$137$	5.50581	0.470393	0.235197	−	0.971948i	$-0.424427\pi$
$137$	5.50581	0.470393	0.235197	+	0.971948i	$0.424427\pi$
$138$	−5.71656	−0.486626
$139$	−12.8261	−1.08790	−0.543949	−	0.839118i	$-0.683072\pi$
$139$	−12.8261	−1.08790	−0.543949	+	0.839118i	$0.683072\pi$
$140$	−24.0977	−2.03663
$141$	−0.834789	−0.0703019
$142$	21.8544	1.83398
$143$	0.497470	0.0416006
$144$	−3.92481	−0.327068
$145$	11.6045	0.963703
$146$	−25.6079	−2.11933
$147$	−5.52429	−0.455636
$148$	−31.4501	−2.58518
$149$	−12.4017	−1.01599	−0.507993	−	0.861361i	$-0.669612\pi$
$149$	−12.4017	−1.01599	−0.507993	+	0.861361i	$0.669612\pi$
$150$	15.9643	1.30348
$151$	−1.93965	−0.157846	−0.0789231	−	0.996881i	$-0.525148\pi$
$151$	−1.93965	−0.157846	−0.0789231	+	0.996881i	$0.525148\pi$
$152$	3.59944	0.291953
$153$	−0.824766	−0.0666784
$154$	−0.717121	−0.0577873
$155$	7.68470	0.617250
$156$	−27.8001	−2.22579
$157$	−12.6665	−1.01089	−0.505447	−	0.862858i	$-0.668672\pi$
$157$	−12.6665	−1.01089	−0.505447	+	0.862858i	$0.668672\pi$
$158$	−24.3572	−1.93775
$159$	−28.6251	−2.27012
$160$	−21.8952	−1.73097
$161$	−3.67133	−0.289342
$162$	24.0850	1.89230
$163$	18.8981	1.48021	0.740107	−	0.672489i	$-0.234775\pi$
$163$	18.8981	1.48021	0.740107	+	0.672489i	$0.234775\pi$
$164$	−5.59407	−0.436823
$165$	0.684148	0.0532608
$166$	16.9508	1.31563
$167$	−5.57472	−0.431385	−0.215692	−	0.976461i	$-0.569201\pi$
$167$	−5.57472	−0.431385	−0.215692	+	0.976461i	$0.569201\pi$
$168$	10.4957	0.809762
$169$	8.52704	0.655926
$170$	−2.73329	−0.209634
$171$	−4.41631	−0.337724
$172$	−12.2332	−0.932774
$173$	−4.48100	−0.340684	−0.170342	−	0.985385i	$-0.554487\pi$
$173$	−4.48100	−0.340684	−0.170342	+	0.985385i	$0.554487\pi$
$174$	−19.2985	−1.46301
$175$	10.2527	0.775031
$176$	−0.222698	−0.0167865
$177$	19.6385	1.47612
$178$	−23.1731	−1.73690
$179$	−24.9042	−1.86143	−0.930714	−	0.365748i	$-0.880813\pi$
$179$	−24.9042	−1.86143	−0.930714	+	0.365748i	$0.880813\pi$
$180$	−14.7751	−1.10127
$181$	17.0708	1.26887	0.634433	−	0.772978i	$-0.281234\pi$
$181$	17.0708	1.26887	0.634433	+	0.772978i	$0.281234\pi$
$182$	−31.0320	−2.30024
$183$	8.26202	0.610746
$184$	1.83465	0.135252
$185$	33.4921	2.46239
$186$	−12.7798	−0.937058
$187$	−0.0467982	−0.00342222
$188$	1.02295	0.0746065
$189$	7.56708	0.550424
$190$	−14.6357	−1.06179
$191$	7.10070	0.513789	0.256894	−	0.966439i	$-0.417301\pi$
$191$	7.10070	0.513789	0.256894	+	0.966439i	$0.417301\pi$
$192$	27.2264	1.96490
$193$	−22.1370	−1.59346	−0.796728	−	0.604338i	$-0.793438\pi$
$193$	−22.1370	−1.59346	−0.796728	+	0.604338i	$0.793438\pi$
$194$	−29.0560	−2.08610
$195$	29.6051	2.12007
$196$	6.76948	0.483534
$197$	5.28684	0.376671	0.188336	−	0.982105i	$-0.439691\pi$
$197$	5.28684	0.376671	0.188336	+	0.982105i	$0.439691\pi$
$198$	−0.439691	−0.0312474
$199$	8.21343	0.582235	0.291117	−	0.956687i	$-0.405973\pi$
$199$	8.21343	0.582235	0.291117	+	0.956687i	$0.405973\pi$
$200$	−5.12351	−0.362287
$201$	17.5650	1.23894
$202$	20.6388	1.45214
$203$	−12.3940	−0.869890
$204$	2.61522	0.183102
$205$	5.95728	0.416075
$206$	35.9786	2.50675
$207$	−2.25101	−0.156456
$208$	−9.63683	−0.668194
$209$	−0.250587	−0.0173334
$210$	−42.6768	−2.94498
$211$	23.3266	1.60587	0.802935	−	0.596067i	$-0.203271\pi$
$211$	23.3266	1.60587	0.802935	+	0.596067i	$0.203271\pi$
$212$	35.0773	2.40912
$213$	22.2680	1.52578
$214$	30.2943	2.07088
$215$	13.0275	0.888468
$216$	−3.78145	−0.257295
$217$	−8.20752	−0.557163
$218$	36.4411	2.46810
$219$	−26.0926	−1.76317
$220$	−0.838356	−0.0565220
$221$	−2.02510	−0.136223
$222$	−55.6979	−3.73820
$223$	−4.19990	−0.281246	−0.140623	−	0.990063i	$-0.544911\pi$
$223$	−4.19990	−0.281246	−0.140623	+	0.990063i	$0.544911\pi$
$224$	23.3848	1.56247
$225$	6.28626	0.419084
$226$	−17.6870	−1.17652
$227$	−12.4704	−0.827691	−0.413846	−	0.910347i	$-0.635815\pi$
$227$	−12.4704	−0.827691	−0.413846	+	0.910347i	$0.635815\pi$
$228$	14.0035	0.927406
$229$	21.8292	1.44251	0.721257	−	0.692668i	$-0.243565\pi$
$229$	21.8292	1.44251	0.721257	+	0.692668i	$0.243565\pi$
$230$	−7.45991	−0.491892
$231$	−0.730694	−0.0480761
$232$	6.19359	0.406629
$233$	22.1166	1.44891	0.724454	−	0.689323i	$-0.242092\pi$
$233$	22.1166	1.44891	0.724454	+	0.689323i	$0.242092\pi$
$234$	−19.0267	−1.24382
$235$	−1.08937	−0.0710627
$236$	−24.0650	−1.56650
$237$	−24.8182	−1.61211
$238$	2.91925	0.189227
$239$	−3.37916	−0.218580	−0.109290	−	0.994010i	$-0.534858\pi$
$239$	−3.37916	−0.218580	−0.109290	+	0.994010i	$0.534858\pi$
$240$	−13.2531	−0.855483
$241$	23.3721	1.50553	0.752765	−	0.658290i	$-0.228720\pi$
$241$	23.3721	1.50553	0.752765	+	0.658290i	$0.228720\pi$
$242$	23.8470	1.53294
$243$	17.1750	1.10177
$244$	−10.1243	−0.648142
$245$	−7.20901	−0.460567
$246$	−9.90706	−0.631651
$247$	−10.8436	−0.689964
$248$	4.10149	0.260445
$249$	17.2716	1.09454
$250$	−10.4786	−0.662723
$251$	−8.21474	−0.518510	−0.259255	−	0.965809i	$-0.583477\pi$
$251$	−8.21474	−0.518510	−0.259255	+	0.965809i	$0.583477\pi$
$252$	15.7803	0.994066
$253$	−0.127725	−0.00803002
$254$	41.6918	2.61598
$255$	−2.78502	−0.174405
$256$	−0.429845	−0.0268653
$257$	−21.7027	−1.35378	−0.676888	−	0.736086i	$-0.736672\pi$
$257$	−21.7027	−1.35378	−0.676888	+	0.736086i	$0.736672\pi$
$258$	−21.6649	−1.34880
$259$	−35.7707	−2.22269
$260$	−36.2782	−2.24988
$261$	−7.59918	−0.470377
$262$	8.04392	0.496955
$263$	−3.72886	−0.229931	−0.114966	−	0.993369i	$-0.536676\pi$
$263$	−3.72886	−0.229931	−0.114966	+	0.993369i	$0.536676\pi$
$264$	0.365145	0.0224731
$265$	−37.3548	−2.29469
$266$	15.6315	0.958428
$267$	−23.6116	−1.44501
$268$	−21.5242	−1.31480
$269$	27.7077	1.68937	0.844684	−	0.535266i	$-0.179788\pi$
$269$	27.7077	1.68937	0.844684	+	0.535266i	$0.179788\pi$
$270$	15.3758	0.935742
$271$	−6.64778	−0.403824	−0.201912	−	0.979404i	$-0.564716\pi$
$271$	−6.64778	−0.403824	−0.201912	+	0.979404i	$0.564716\pi$
$272$	0.906559	0.0549682
$273$	−31.6193	−1.91369
$274$	−11.9486	−0.721840
$275$	0.356690	0.0215092
$276$	7.13766	0.429637
$277$	6.41877	0.385667	0.192833	−	0.981232i	$-0.438232\pi$
$277$	6.41877	0.385667	0.192833	+	0.981232i	$0.438232\pi$
$278$	27.8350	1.66943
$279$	−5.03230	−0.301276
$280$	13.6965	0.818525
$281$	16.9386	1.01047	0.505237	−	0.862981i	$-0.331405\pi$
$281$	16.9386	1.01047	0.505237	+	0.862981i	$0.331405\pi$
$282$	1.81164	0.107882
$283$	17.3533	1.03155	0.515774	−	0.856725i	$-0.327504\pi$
$283$	17.3533	1.03155	0.515774	+	0.856725i	$0.327504\pi$
$284$	−27.2873	−1.61920
$285$	−14.9127	−0.883355
$286$	−1.07960	−0.0638380
$287$	−6.36258	−0.375572
$288$	14.3380	0.844876
$289$	−16.8095	−0.988794
$290$	−25.1839	−1.47885
$291$	−29.6059	−1.73553
$292$	31.9739	1.87113
$293$	6.65882	0.389013	0.194506	−	0.980901i	$-0.437690\pi$
$293$	6.65882	0.389013	0.194506	+	0.980901i	$0.437690\pi$
$294$	11.9887	0.699195
$295$	25.6275	1.49209
$296$	17.8755	1.03899
$297$	0.263258	0.0152758
$298$	26.9139	1.55908
$299$	−5.52705	−0.319638
$300$	−19.9329	−1.15083
$301$	−13.9138	−0.801979
$302$	4.20938	0.242222
$303$	21.0294	1.20811
$304$	4.85428	0.278412
$305$	10.7816	0.617355
$306$	1.78989	0.102321
$307$	−15.8179	−0.902774	−0.451387	−	0.892328i	$-0.649071\pi$
$307$	−15.8179	−0.902774	−0.451387	+	0.892328i	$0.649071\pi$
$308$	0.895393	0.0510198
$309$	36.6595	2.08549
$310$	−16.6772	−0.947199
$311$	15.7330	0.892138	0.446069	−	0.894998i	$-0.352824\pi$
$311$	15.7330	0.892138	0.446069	+	0.894998i	$0.352824\pi$
$312$	15.8009	0.894551
$313$	25.3497	1.43285	0.716424	−	0.697665i	$-0.245778\pi$
$313$	25.3497	1.43285	0.716424	+	0.697665i	$0.245778\pi$
$314$	27.4885	1.55126
$315$	−16.8049	−0.946848
$316$	30.4122	1.71082
$317$	−6.09907	−0.342558	−0.171279	−	0.985223i	$-0.554790\pi$
$317$	−6.09907	−0.342558	−0.171279	+	0.985223i	$0.554790\pi$
$318$	62.1216	3.48361
$319$	−0.431187	−0.0241418
$320$	35.5296	1.98616
$321$	30.8677	1.72287
$322$	7.96744	0.444008
$323$	1.02009	0.0567591
$324$	−30.0724	−1.67069
$325$	15.4350	0.856182
$326$	−41.0122	−2.27146
$327$	37.1307	2.05333
$328$	3.17953	0.175560
$329$	1.16349	0.0641450
$330$	−1.48472	−0.0817313
$331$	−11.6992	−0.643046	−0.321523	−	0.946902i	$-0.604195\pi$
$331$	−11.6992	−0.643046	−0.321523	+	0.946902i	$0.604195\pi$
$332$	−21.1646	−1.16156
$333$	−21.9322	−1.20188
$334$	12.0981	0.661981
$335$	22.9217	1.25235
$336$	14.1548	0.772205
$337$	−12.9064	−0.703057	−0.351529	−	0.936177i	$-0.614338\pi$
$337$	−12.9064	−0.703057	−0.351529	+	0.936177i	$0.614338\pi$
$338$	−18.5052	−1.00655
$339$	−18.0217	−0.978804
$340$	3.41277	0.185084
$341$	−0.285539	−0.0154628
$342$	9.58417	0.518253
$343$	−13.8740	−0.749126
$344$	6.95307	0.374884
$345$	−7.60110	−0.409229
$346$	9.72457	0.522796
$347$	−7.86835	−0.422395	−0.211198	−	0.977443i	$-0.567736\pi$
$347$	−7.86835	−0.422395	−0.211198	+	0.977443i	$0.567736\pi$
$348$	24.0960	1.29168
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−22.2502	−1.18932
$351$	11.3919	0.608057
$352$	0.813556	0.0433627
$353$	23.0024	1.22429	0.612146	−	0.790744i	$-0.290306\pi$
$353$	23.0024	1.22429	0.612146	+	0.790744i	$0.290306\pi$
$354$	−42.6190	−2.26517
$355$	29.0590	1.54229
$356$	28.9338	1.53349
$357$	2.97450	0.157427
$358$	54.0465	2.85645
$359$	−7.39748	−0.390424	−0.195212	−	0.980761i	$-0.562539\pi$
$359$	−7.39748	−0.390424	−0.195212	+	0.980761i	$0.562539\pi$
$360$	8.39780	0.442603
$361$	−13.5378	−0.712517
$362$	−37.0468	−1.94714
$363$	24.2983	1.27533
$364$	38.7464	2.03086
$365$	−34.0499	−1.78225
$366$	−17.9301	−0.937219
$367$	19.5688	1.02148	0.510741	−	0.859734i	$-0.329371\pi$
$367$	19.5688	1.02148	0.510741	+	0.859734i	$0.329371\pi$
$368$	2.47425	0.128979
$369$	−3.90111	−0.203084
$370$	−72.6839	−3.77865
$371$	39.8962	2.07131
$372$	15.9567	0.827319
$373$	−8.05087	−0.416858	−0.208429	−	0.978037i	$-0.566835\pi$
$373$	−8.05087	−0.416858	−0.208429	+	0.978037i	$0.566835\pi$
$374$	0.101560	0.00525156
$375$	−10.6769	−0.551352
$376$	−0.581421	−0.0299845
$377$	−18.6587	−0.960974
$378$	−16.4219	−0.844651
$379$	−27.8909	−1.43266	−0.716330	−	0.697762i	$-0.754179\pi$
$379$	−27.8909	−1.43266	−0.716330	+	0.697762i	$0.754179\pi$
$380$	18.2741	0.937442
$381$	42.4809	2.17636
$382$	−15.4098	−0.788433
$383$	11.7008	0.597883	0.298942	−	0.954271i	$-0.403366\pi$
$383$	11.7008	0.597883	0.298942	+	0.954271i	$0.403366\pi$
$384$	−25.5294	−1.30279
$385$	−0.953530	−0.0485964
$386$	48.0412	2.44523
$387$	−8.53102	−0.433656
$388$	36.2792	1.84180
$389$	6.46474	0.327775	0.163888	−	0.986479i	$-0.447597\pi$
$389$	6.46474	0.327775	0.163888	+	0.986479i	$0.447597\pi$
$390$	−64.2484	−3.25334
$391$	0.519943	0.0262946
$392$	−3.84761	−0.194334
$393$	8.19616	0.413442
$394$	−11.4734	−0.578020
$395$	−32.3869	−1.62956
$396$	0.548995	0.0275880
$397$	−37.1741	−1.86572	−0.932858	−	0.360243i	$-0.882694\pi$
$397$	−37.1741	−1.86572	−0.932858	+	0.360243i	$0.882694\pi$
$398$	−17.8246	−0.893467
$399$	15.9273	0.797364
$400$	−6.90968	−0.345484
$401$	−26.9025	−1.34345	−0.671724	−	0.740801i	$-0.734446\pi$
$401$	−26.9025	−1.34345	−0.671724	+	0.740801i	$0.734446\pi$
$402$	−38.1192	−1.90121
$403$	−12.3561	−0.615502
$404$	−25.7695	−1.28208
$405$	32.0250	1.59133
$406$	26.8972	1.33489
$407$	−1.24446	−0.0616856
$408$	−1.48643	−0.0735892
$409$	−23.5278	−1.16338	−0.581689	−	0.813412i	$-0.697608\pi$
$409$	−23.5278	−1.16338	−0.581689	+	0.813412i	$0.697608\pi$
$410$	−12.9284	−0.638486
$411$	−12.1747	−0.600535
$412$	−44.9227	−2.21318
$413$	−27.3711	−1.34684
$414$	4.88510	0.240090
$415$	22.5388	1.10639
$416$	35.2050	1.72607
$417$	28.3618	1.38888
$418$	0.543817	0.0265990
$419$	12.0710	0.589708	0.294854	−	0.955542i	$-0.404729\pi$
$419$	12.0710	0.589708	0.294854	+	0.955542i	$0.404729\pi$
$420$	53.2860	2.60009
$421$	−2.64652	−0.128983	−0.0644917	−	0.997918i	$-0.520543\pi$
$421$	−2.64652	−0.128983	−0.0644917	+	0.997918i	$0.520543\pi$
$422$	−50.6229	−2.46428
$423$	0.713371	0.0346853
$424$	−19.9371	−0.968230
$425$	−1.45201	−0.0704329
$426$	−48.3256	−2.34138
$427$	−11.5152	−0.557258
$428$	−37.8253	−1.82836
$429$	−1.10003	−0.0531100
$430$	−28.2720	−1.36340
$431$	−7.85442	−0.378334	−0.189167	−	0.981945i	$-0.560579\pi$
$431$	−7.85442	−0.378334	−0.189167	+	0.981945i	$0.560579\pi$
$432$	−5.09974	−0.245361
$433$	−2.16901	−0.104236	−0.0521180	−	0.998641i	$-0.516597\pi$
$433$	−2.16901	−0.104236	−0.0521180	+	0.998641i	$0.516597\pi$
$434$	17.8118	0.854993
$435$	−25.6605	−1.23033
$436$	−45.5001	−2.17906
$437$	2.78410	0.133181
$438$	56.6255	2.70567
$439$	23.9080	1.14107	0.570533	−	0.821275i	$-0.306737\pi$
$439$	23.9080	1.14107	0.570533	+	0.821275i	$0.306737\pi$
$440$	0.476501	0.0227163
$441$	4.72080	0.224800
$442$	4.39482	0.209040
$443$	32.9092	1.56356	0.781782	−	0.623551i	$-0.214311\pi$
$443$	32.9092	1.56356	0.781782	+	0.623551i	$0.214311\pi$
$444$	69.5441	3.30042
$445$	−30.8124	−1.46065
$446$	9.11452	0.431585
$447$	27.4232	1.29707
$448$	−37.9468	−1.79282
$449$	−18.4302	−0.869773	−0.434886	−	0.900485i	$-0.643211\pi$
$449$	−18.4302	−0.869773	−0.434886	+	0.900485i	$0.643211\pi$
$450$	−13.6423	−0.643104
$451$	−0.221354	−0.0104231
$452$	22.0838	1.03874
$453$	4.28904	0.201517
$454$	27.0630	1.27013
$455$	−41.2621	−1.93440
$456$	−7.95926	−0.372726
$457$	15.1194	0.707254	0.353627	−	0.935387i	$-0.384948\pi$
$457$	15.1194	0.707254	0.353627	+	0.935387i	$0.384948\pi$
$458$	−47.3732	−2.21361
$459$	−1.07167	−0.0500211
$460$	9.31440	0.434286
$461$	17.8792	0.832719	0.416360	−	0.909200i	$-0.363306\pi$
$461$	17.8792	0.832719	0.416360	+	0.909200i	$0.363306\pi$
$462$	1.58573	0.0737751
$463$	−22.5342	−1.04725	−0.523627	−	0.851947i	$-0.675422\pi$
$463$	−22.5342	−1.04725	−0.523627	+	0.851947i	$0.675422\pi$
$464$	8.35280	0.387769
$465$	−16.9928	−0.788022
$466$	−47.9970	−2.22342
$467$	2.96082	0.137010	0.0685051	−	0.997651i	$-0.478177\pi$
$467$	2.96082	0.137010	0.0685051	+	0.997651i	$0.478177\pi$
$468$	23.7567	1.09815
$469$	−24.4812	−1.13044
$470$	2.36413	0.109049
$471$	28.0087	1.29057
$472$	13.6780	0.629580
$473$	−0.484060	−0.0222571
$474$	53.8598	2.47386
$475$	−7.77496	−0.356740
$476$	−3.64496	−0.167066
$477$	24.4617	1.12002
$478$	7.33338	0.335421
$479$	0.770845	0.0352208	0.0176104	−	0.999845i	$-0.494394\pi$
$479$	0.770845	0.0352208	0.0176104	+	0.999845i	$0.494394\pi$
$480$	48.4158	2.20987
$481$	−53.8515	−2.45542
$482$	−50.7216	−2.31031
$483$	8.11824	0.369393
$484$	−29.7752	−1.35342
$485$	−38.6347	−1.75431
$486$	−37.2727	−1.69072
$487$	−10.4347	−0.472843	−0.236422	−	0.971651i	$-0.575975\pi$
$487$	−10.4347	−0.472843	−0.236422	+	0.971651i	$0.575975\pi$
$488$	5.75440	0.260490
$489$	−41.7884	−1.88974
$490$	15.6448	0.706761
$491$	38.1746	1.72280	0.861399	−	0.507930i	$-0.169589\pi$
$491$	38.1746	1.72280	0.861399	+	0.507930i	$0.169589\pi$
$492$	12.3699	0.557678
$493$	1.75527	0.0790534
$494$	23.5326	1.05878
$495$	−0.584640	−0.0262776
$496$	5.53136	0.248365
$497$	−31.0360	−1.39216
$498$	−37.4824	−1.67963
$499$	−22.4137	−1.00338	−0.501688	−	0.865048i	$-0.667288\pi$
$499$	−22.4137	−1.00338	−0.501688	+	0.865048i	$0.667288\pi$
$500$	13.0835	0.585111
$501$	12.3271	0.550735
$502$	17.8274	0.795678
$503$	−8.42129	−0.375487	−0.187743	−	0.982218i	$-0.560117\pi$
$503$	−8.42129	−0.375487	−0.187743	+	0.982218i	$0.560117\pi$
$504$	−8.96914	−0.399517
$505$	27.4427	1.22118
$506$	0.277186	0.0123224
$507$	−18.8554	−0.837399
$508$	−52.0561	−2.30962
$509$	−19.9513	−0.884325	−0.442162	−	0.896935i	$-0.645788\pi$
$509$	−19.9513	−0.884325	−0.442162	+	0.896935i	$0.645788\pi$
$510$	6.04400	0.267633
$511$	36.3665	1.60876
$512$	−22.1576	−0.979239
$513$	−5.73837	−0.253355
$514$	47.0986	2.07743
$515$	47.8394	2.10806
$516$	27.0507	1.19084
$517$	0.0404775	0.00178020
$518$	77.6289	3.41082
$519$	9.90862	0.434940
$520$	20.6196	0.904231
$521$	26.7326	1.17118	0.585589	−	0.810608i	$-0.300863\pi$
$521$	26.7326	1.17118	0.585589	+	0.810608i	$0.300863\pi$
$522$	16.4916	0.721816
$523$	30.9702	1.35423	0.677117	−	0.735876i	$-0.263229\pi$
$523$	30.9702	1.35423	0.677117	+	0.735876i	$0.263229\pi$
$524$	−10.0436	−0.438756
$525$	−22.6713	−0.989455
$526$	8.09229	0.352840
$527$	1.16237	0.0506336
$528$	0.492442	0.0214308
$529$	−21.5809	−0.938301
$530$	81.0665	3.52130
$531$	−16.7821	−0.728282
$532$	−19.5174	−0.846185
$533$	−9.57863	−0.414897
$534$	51.2415	2.21744
$535$	40.2813	1.74151
$536$	12.2338	0.528421
$537$	55.0694	2.37642
$538$	−60.1306	−2.59241
$539$	0.267864	0.0115377
$540$	−19.1981	−0.826157
$541$	10.1462	0.436219	0.218109	−	0.975924i	$-0.430011\pi$
$541$	10.1462	0.436219	0.218109	+	0.975924i	$0.430011\pi$
$542$	14.4269	0.619687
$543$	−37.7479	−1.61992
$544$	−3.31182	−0.141993
$545$	48.4543	2.07556
$546$	68.6195	2.93664
$547$	24.4349	1.04476	0.522380	−	0.852713i	$-0.325044\pi$
$547$	24.4349	1.04476	0.522380	+	0.852713i	$0.325044\pi$
$548$	14.9189	0.637305
$549$	−7.06033	−0.301328
$550$	−0.774081	−0.0330069
$551$	9.39881	0.400403
$552$	−4.05687	−0.172672
$553$	34.5903	1.47093
$554$	−13.9299	−0.591824
$555$	−74.0595	−3.14365
$556$	−34.7546	−1.47392
$557$	−1.02478	−0.0434213	−0.0217106	−	0.999764i	$-0.506911\pi$
$557$	−1.02478	−0.0434213	−0.0217106	+	0.999764i	$0.506911\pi$
$558$	10.9210	0.462322
$559$	−20.9467	−0.885953
$560$	18.4715	0.780561
$561$	0.103483	0.00436904
$562$	−36.7598	−1.55062
$563$	−24.9813	−1.05284	−0.526418	−	0.850226i	$-0.676465\pi$
$563$	−24.9813	−1.05284	−0.526418	+	0.850226i	$0.676465\pi$
$564$	−2.26200	−0.0952475
$565$	−23.5177	−0.989397
$566$	−37.6598	−1.58296
$567$	−34.2038	−1.43642
$568$	15.5094	0.650761
$569$	−1.37728	−0.0577387	−0.0288693	−	0.999583i	$-0.509191\pi$
$569$	−1.37728	−0.0577387	−0.0288693	+	0.999583i	$0.509191\pi$
$570$	32.3633	1.35555
$571$	11.4996	0.481241	0.240621	−	0.970619i	$-0.422649\pi$
$571$	11.4996	0.481241	0.240621	+	0.970619i	$0.422649\pi$
$572$	1.34798	0.0563619
$573$	−15.7014	−0.655937
$574$	13.8079	0.576332
$575$	−3.96294	−0.165266
$576$	−23.2664	−0.969434
$577$	−8.66346	−0.360665	−0.180332	−	0.983606i	$-0.557717\pi$
$577$	−8.66346	−0.360665	−0.180332	+	0.983606i	$0.557717\pi$
$578$	36.4796	1.51735
$579$	48.9504	2.03431
$580$	31.4444	1.30566
$581$	−24.0722	−0.998684
$582$	64.2501	2.66325
$583$	1.38798	0.0574844
$584$	−18.1732	−0.752012
$585$	−25.2991	−1.04599
$586$	−14.4508	−0.596958
$587$	−3.35529	−0.138488	−0.0692438	−	0.997600i	$-0.522059\pi$
$587$	−3.35529	−0.138488	−0.0692438	+	0.997600i	$0.522059\pi$
$588$	−14.9690	−0.617312
$589$	6.22404	0.256457
$590$	−55.6163	−2.28969
$591$	−11.6905	−0.480884
$592$	24.1073	0.990802
$593$	−2.78977	−0.114562	−0.0572811	−	0.998358i	$-0.518243\pi$
$593$	−2.78977	−0.114562	−0.0572811	+	0.998358i	$0.518243\pi$
$594$	−0.571316	−0.0234414
$595$	3.88162	0.159131
$596$	−33.6045	−1.37649
$597$	−18.1620	−0.743319
$598$	11.9947	0.490499
$599$	−25.7240	−1.05106	−0.525528	−	0.850776i	$-0.676132\pi$
$599$	−25.7240	−1.05106	−0.525528	+	0.850776i	$0.676132\pi$
$600$	11.3294	0.462520
$601$	4.00203	0.163246	0.0816232	−	0.996663i	$-0.473990\pi$
$601$	4.00203	0.163246	0.0816232	+	0.996663i	$0.473990\pi$
$602$	30.1955	1.23068
$603$	−15.0102	−0.611263
$604$	−5.25580	−0.213856
$605$	31.7085	1.28913
$606$	−45.6376	−1.85390
$607$	48.0929	1.95203	0.976015	−	0.217705i	$-0.0698571\pi$
$607$	48.0929	1.95203	0.976015	+	0.217705i	$0.0698571\pi$
$608$	−17.7335	−0.719189
$609$	27.4063	1.11056
$610$	−23.3981	−0.947361
$611$	1.75158	0.0708615
$612$	−2.23484	−0.0903382
$613$	27.6554	1.11699	0.558496	−	0.829507i	$-0.311379\pi$
$613$	27.6554	1.11699	0.558496	+	0.829507i	$0.311379\pi$
$614$	34.3276	1.38535
$615$	−13.1730	−0.531189
$616$	−0.508920	−0.0205050
$617$	−34.7698	−1.39978	−0.699890	−	0.714251i	$-0.746768\pi$
$617$	−34.7698	−1.39978	−0.699890	+	0.714251i	$0.746768\pi$
$618$	−79.5577	−3.20028
$619$	−4.09090	−0.164427	−0.0822135	−	0.996615i	$-0.526199\pi$
$619$	−4.09090	−0.164427	−0.0822135	+	0.996615i	$0.526199\pi$
$620$	20.8230	0.836272
$621$	−2.92488	−0.117371
$622$	−34.1435	−1.36903
$623$	32.9087	1.31846
$624$	21.3094	0.853061
$625$	−30.5665	−1.22266
$626$	−55.0133	−2.19877
$627$	0.554110	0.0221290
$628$	−34.3219	−1.36959
$629$	5.06594	0.201992
$630$	36.4696	1.45298
$631$	−19.7477	−0.786143	−0.393072	−	0.919508i	$-0.628588\pi$
$631$	−19.7477	−0.786143	−0.393072	+	0.919508i	$0.628588\pi$
$632$	−17.2856	−0.687583
$633$	−51.5810	−2.05016
$634$	13.2361	0.525671
$635$	55.4360	2.19991
$636$	−77.5646	−3.07564
$637$	11.5913	0.459263
$638$	0.935752	0.0370468
$639$	−19.0292	−0.752783
$640$	−33.3150	−1.31689
$641$	−35.2099	−1.39071	−0.695354	−	0.718668i	$-0.744752\pi$
$641$	−35.2099	−1.39071	−0.695354	+	0.718668i	$0.744752\pi$
$642$	−66.9884	−2.64382
$643$	−18.1628	−0.716272	−0.358136	−	0.933669i	$-0.616588\pi$
$643$	−18.1628	−0.716272	−0.358136	+	0.933669i	$0.616588\pi$
$644$	−9.94810	−0.392010
$645$	−28.8071	−1.13428
$646$	−2.21377	−0.0870995
$647$	28.4432	1.11822	0.559108	−	0.829095i	$-0.311144\pi$
$647$	28.4432	1.11822	0.559108	+	0.829095i	$0.311144\pi$
$648$	17.0924	0.671455
$649$	−0.952237	−0.0373786
$650$	−33.4968	−1.31385
$651$	18.1489	0.711311
$652$	51.2076	2.00545
$653$	23.5047	0.919809	0.459905	−	0.887968i	$-0.347884\pi$
$653$	23.5047	0.919809	0.459905	+	0.887968i	$0.347884\pi$
$654$	−80.5803	−3.15094
$655$	10.6957	0.417916
$656$	4.28799	0.167418
$657$	22.2975	0.869908
$658$	−2.52497	−0.0984336
$659$	4.30564	0.167724	0.0838620	−	0.996477i	$-0.473275\pi$
$659$	4.30564	0.167724	0.0838620	+	0.996477i	$0.473275\pi$
$660$	1.85382	0.0721597
$661$	−20.6668	−0.803847	−0.401924	−	0.915673i	$-0.631658\pi$
$661$	−20.6668	−0.803847	−0.401924	+	0.915673i	$0.631658\pi$
$662$	25.3893	0.986784
$663$	4.47800	0.173911
$664$	12.0295	0.466834
$665$	20.7846	0.805992
$666$	47.5968	1.84434
$667$	4.79062	0.185494
$668$	−15.1057	−0.584455
$669$	9.28702	0.359057
$670$	−49.7442	−1.92179
$671$	−0.400612	−0.0154654
$672$	−51.7098	−1.99475
$673$	−0.931252	−0.0358971	−0.0179486	−	0.999839i	$-0.505714\pi$
$673$	−0.931252	−0.0358971	−0.0179486	+	0.999839i	$0.505714\pi$
$674$	28.0092	1.07887
$675$	8.16811	0.314391
$676$	23.1055	0.888672
$677$	−0.832006	−0.0319766	−0.0159883	−	0.999872i	$-0.505089\pi$
$677$	−0.832006	−0.0319766	−0.0159883	+	0.999872i	$0.505089\pi$
$678$	39.1103	1.50202
$679$	41.2632	1.58354
$680$	−1.93974	−0.0743855
$681$	27.5752	1.05669
$682$	0.619670	0.0237284
$683$	35.1602	1.34537	0.672684	−	0.739930i	$-0.265141\pi$
$683$	35.1602	1.34537	0.672684	+	0.739930i	$0.265141\pi$
$684$	−11.9667	−0.457560
$685$	−15.8876	−0.607034
$686$	30.1091	1.14957
$687$	−48.2698	−1.84161
$688$	9.37705	0.357497
$689$	60.0622	2.28819
$690$	16.4957	0.627982
$691$	−23.3223	−0.887223	−0.443612	−	0.896219i	$-0.646303\pi$
$691$	−23.3223	−0.887223	−0.443612	+	0.896219i	$0.646303\pi$
$692$	−12.1420	−0.461571
$693$	0.624416	0.0237196
$694$	17.0757	0.648185
$695$	37.0112	1.40391
$696$	−13.6956	−0.519129
$697$	0.901084	0.0341310
$698$	2.17018	0.0821424
$699$	−48.9054	−1.84977
$700$	27.7814	1.05004
$701$	27.8074	1.05027	0.525136	−	0.851018i	$-0.324014\pi$
$701$	27.8074	1.05027	0.525136	+	0.851018i	$0.324014\pi$
$702$	−24.7226	−0.933093
$703$	27.1262	1.02308
$704$	−1.32016	−0.0497556
$705$	2.40887	0.0907234
$706$	−49.9192	−1.87874
$707$	−29.3097	−1.10231
$708$	53.2138	1.99990
$709$	42.1509	1.58301	0.791506	−	0.611162i	$-0.209298\pi$
$709$	42.1509	1.58301	0.791506	+	0.611162i	$0.209298\pi$
$710$	−63.0632	−2.36672
$711$	21.2084	0.795378
$712$	−16.4452	−0.616312
$713$	3.17243	0.118808
$714$	−6.45520	−0.241580
$715$	−1.43550	−0.0536848
$716$	−67.4822	−2.52193
$717$	7.47217	0.279053
$718$	16.0538	0.599124
$719$	14.0958	0.525685	0.262842	−	0.964839i	$-0.415340\pi$
$719$	14.0958	0.525685	0.262842	+	0.964839i	$0.415340\pi$
$720$	11.3255	0.422075
$721$	−51.0942	−1.90285
$722$	29.3795	1.09339
$723$	−51.6816	−1.92206
$724$	46.2564	1.71910
$725$	−13.3785	−0.496863
$726$	−52.7317	−1.95706
$727$	23.6546	0.877301	0.438650	−	0.898658i	$-0.355457\pi$
$727$	23.6546	0.877301	0.438650	+	0.898658i	$0.355457\pi$
$728$	−22.0225	−0.816208
$729$	−4.68357	−0.173465
$730$	73.8944	2.73495
$731$	1.97051	0.0728819
$732$	22.3874	0.827460
$733$	13.7643	0.508394	0.254197	−	0.967152i	$-0.418189\pi$
$733$	13.7643	0.508394	0.254197	+	0.967152i	$0.418189\pi$
$734$	−42.4678	−1.56751
$735$	15.9409	0.587990
$736$	−9.03887	−0.333177
$737$	−0.851698	−0.0313727
$738$	8.46610	0.311641
$739$	−1.94226	−0.0714473	−0.0357237	−	0.999362i	$-0.511374\pi$
$739$	−1.94226	−0.0714473	−0.0357237	+	0.999362i	$0.511374\pi$
$740$	90.7526	3.33613
$741$	23.9780	0.880854
$742$	−86.5818	−3.17852
$743$	−35.4038	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$743$	−35.4038	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$744$	−9.06943	−0.332501
$745$	35.7864	1.31111
$746$	17.4718	0.639689
$747$	−14.7595	−0.540021
$748$	−0.126808	−0.00463655
$749$	−43.0218	−1.57198
$750$	23.1707	0.846075
$751$	−41.3484	−1.50882	−0.754412	−	0.656401i	$-0.772078\pi$
$751$	−41.3484	−1.50882	−0.754412	+	0.656401i	$0.772078\pi$
$752$	−0.784117	−0.0285938
$753$	18.1648	0.661964
$754$	40.4928	1.47466
$755$	5.59705	0.203698
$756$	20.5043	0.745733
$757$	4.83943	0.175892	0.0879460	−	0.996125i	$-0.471970\pi$
$757$	4.83943	0.175892	0.0879460	+	0.996125i	$0.471970\pi$
$758$	60.5282	2.19848
$759$	0.282433	0.0102517
$760$	−10.3866	−0.376760
$761$	−41.3460	−1.49879	−0.749395	−	0.662123i	$-0.769655\pi$
$761$	−41.3460	−1.49879	−0.749395	+	0.662123i	$0.769655\pi$
$762$	−92.1910	−3.33973
$763$	−51.7509	−1.87351
$764$	19.2406	0.696099
$765$	2.37995	0.0860472
$766$	−25.3928	−0.917480
$767$	−41.2061	−1.48787
$768$	0.950494	0.0342980
$769$	31.9937	1.15372	0.576860	−	0.816843i	$-0.304278\pi$
$769$	31.9937	1.15372	0.576860	+	0.816843i	$0.304278\pi$
$770$	2.06933	0.0745734
$771$	47.9900	1.72832
$772$	−59.9840	−2.15887
$773$	12.3119	0.442828	0.221414	−	0.975180i	$-0.428933\pi$
$773$	12.3119	0.442828	0.221414	+	0.975180i	$0.428933\pi$
$774$	18.5138	0.665466
$775$	−8.85943	−0.318240
$776$	−20.6202	−0.740222
$777$	79.0981	2.83763
$778$	−14.0296	−0.502987
$779$	4.82496	0.172872
$780$	80.2202	2.87234
$781$	−1.07974	−0.0386361
$782$	−1.12837	−0.0403504
$783$	−9.87406	−0.352870
$784$	−5.18897	−0.185320
$785$	36.5504	1.30454
$786$	−17.7871	−0.634446
$787$	1.51247	0.0539138	0.0269569	−	0.999637i	$-0.491418\pi$
$787$	1.51247	0.0539138	0.0269569	+	0.999637i	$0.491418\pi$
$788$	14.3256	0.510328
$789$	8.24544	0.293546
$790$	70.2852	2.50064
$791$	25.1177	0.893083
$792$	−0.312035	−0.0110877
$793$	−17.3357	−0.615607
$794$	80.6745	2.86303
$795$	82.6008	2.92955
$796$	22.2557	0.788832
$797$	16.9110	0.599017	0.299508	−	0.954094i	$-0.403177\pi$
$797$	16.9110	0.599017	0.299508	+	0.954094i	$0.403177\pi$
$798$	−34.5651	−1.22359
$799$	−0.164776	−0.00582934
$800$	25.2423	0.892448
$801$	20.1774	0.712933
$802$	58.3833	2.06159
$803$	1.26519	0.0446474
$804$	47.5954	1.67856
$805$	10.5940	0.373390
$806$	26.8150	0.944517
$807$	−61.2686	−2.15676
$808$	14.6468	0.515271
$809$	−36.9044	−1.29749	−0.648745	−	0.761006i	$-0.724706\pi$
$809$	−36.9044	−1.29749	−0.648745	+	0.761006i	$0.724706\pi$
$810$	−69.4999	−2.44198
$811$	15.7775	0.554023	0.277012	−	0.960867i	$-0.410656\pi$
$811$	15.7775	0.554023	0.277012	+	0.960867i	$0.410656\pi$
$812$	−33.5837	−1.17856
$813$	14.6999	0.515549
$814$	2.70070	0.0946595
$815$	−54.5325	−1.91019
$816$	−2.00463	−0.0701761
$817$	10.5513	0.369144
$818$	51.0596	1.78526
$819$	27.0204	0.944167
$820$	16.1423	0.563713
$821$	12.0473	0.420455	0.210228	−	0.977652i	$-0.432579\pi$
$821$	12.0473	0.420455	0.210228	+	0.977652i	$0.432579\pi$
$822$	26.4213	0.921549
$823$	8.50987	0.296635	0.148318	−	0.988940i	$-0.452614\pi$
$823$	8.50987	0.296635	0.148318	+	0.988940i	$0.452614\pi$
$824$	25.5330	0.889483
$825$	−0.788731	−0.0274601
$826$	59.4001	2.06679
$827$	−19.8541	−0.690393	−0.345197	−	0.938530i	$-0.612188\pi$
$827$	−19.8541	−0.690393	−0.345197	+	0.938530i	$0.612188\pi$
$828$	−6.09951	−0.211973
$829$	13.0828	0.454386	0.227193	−	0.973850i	$-0.427045\pi$
$829$	13.0828	0.454386	0.227193	+	0.973850i	$0.427045\pi$
$830$	−48.9132	−1.69780
$831$	−14.1935	−0.492368
$832$	−57.1275	−1.98054
$833$	−1.09042	−0.0377807
$834$	−61.5502	−2.13131
$835$	16.0864	0.556694
$836$	−0.679007	−0.0234840
$837$	−6.53877	−0.226013
$838$	−26.1963	−0.904935
$839$	−27.4067	−0.946184	−0.473092	−	0.881013i	$-0.656862\pi$
$839$	−27.4067	−0.946184	−0.473092	+	0.881013i	$0.656862\pi$
$840$	−30.2865	−1.04498
$841$	−12.8274	−0.442324
$842$	5.74342	0.197931
$843$	−37.4555	−1.29004
$844$	63.2074	2.17569
$845$	−24.6057	−0.846461
$846$	−1.54814	−0.0532262
$847$	−33.8658	−1.16364
$848$	−26.8876	−0.923322
$849$	−38.3726	−1.31694
$850$	3.15112	0.108083
$851$	13.8263	0.473961
$852$	60.3390	2.06718
$853$	−3.58637	−0.122795	−0.0613975	−	0.998113i	$-0.519556\pi$
$853$	−3.58637	−0.122795	−0.0613975	+	0.998113i	$0.519556\pi$
$854$	24.9900	0.855139
$855$	12.7437	0.435826
$856$	21.4990	0.734821
$857$	−28.1673	−0.962177	−0.481089	−	0.876672i	$-0.659758\pi$
$857$	−28.1673	−0.962177	−0.481089	+	0.876672i	$0.659758\pi$
$858$	2.38726	0.0814999
$859$	−25.1507	−0.858132	−0.429066	−	0.903273i	$-0.641157\pi$
$859$	−25.1507	−0.858132	−0.429066	+	0.903273i	$0.641157\pi$
$860$	35.3002	1.20373
$861$	14.0693	0.479479
$862$	17.0455	0.580572
$863$	−7.48428	−0.254768	−0.127384	−	0.991853i	$-0.540658\pi$
$863$	−7.48428	−0.254768	−0.127384	+	0.991853i	$0.540658\pi$
$864$	18.6302	0.633813
$865$	12.9304	0.439647
$866$	4.70714	0.159955
$867$	37.1700	1.26236
$868$	−22.2397	−0.754864
$869$	1.20339	0.0408223
$870$	55.6878	1.88799
$871$	−36.8555	−1.24880
$872$	25.8611	0.875769
$873$	25.2998	0.856269
$874$	−6.04198	−0.204373
$875$	14.8809	0.503066
$876$	−70.7023	−2.38881
$877$	51.9252	1.75339	0.876694	−	0.481048i	$-0.159744\pi$
$877$	51.9252	1.75339	0.876694	+	0.481048i	$0.159744\pi$
$878$	−51.8846	−1.75102
$879$	−14.7243	−0.496639
$880$	0.642620	0.0216627
$881$	18.6452	0.628174	0.314087	−	0.949394i	$-0.398302\pi$
$881$	18.6452	0.628174	0.314087	+	0.949394i	$0.398302\pi$
$882$	−10.2450	−0.344966
$883$	58.3166	1.96251	0.981255	−	0.192714i	$-0.0617291\pi$
$883$	58.3166	1.96251	0.981255	+	0.192714i	$0.0617291\pi$
$884$	−5.48735	−0.184560
$885$	−56.6689	−1.90490
$886$	−71.4189	−2.39936
$887$	−24.0268	−0.806740	−0.403370	−	0.915037i	$-0.632161\pi$
$887$	−24.0268	−0.806740	−0.403370	+	0.915037i	$0.632161\pi$
$888$	−39.5272	−1.32645
$889$	−59.2076	−1.98576
$890$	66.8683	2.24143
$891$	−1.18995	−0.0398647
$892$	−11.3803	−0.381042
$893$	−0.882311	−0.0295254
$894$	−59.5133	−1.99042
$895$	71.8637	2.40214
$896$	35.5816	1.18870
$897$	12.2217	0.408071
$898$	39.9967	1.33471
$899$	10.7098	0.357191
$900$	17.0337	0.567790
$901$	−5.65019	−0.188235
$902$	0.480377	0.0159948
$903$	30.7670	1.02386
$904$	−12.5519	−0.417470
$905$	−49.2597	−1.63745
$906$	−9.30799	−0.309237
$907$	−12.1090	−0.402072	−0.201036	−	0.979584i	$-0.564431\pi$
$907$	−12.1090	−0.402072	−0.201036	+	0.979584i	$0.564431\pi$
$908$	−33.7907	−1.12139
$909$	−17.9707	−0.596052
$910$	89.5461	2.96842
$911$	37.7819	1.25177	0.625885	−	0.779916i	$-0.284738\pi$
$911$	37.7819	1.25177	0.625885	+	0.779916i	$0.284738\pi$
$912$	−10.7340	−0.355439
$913$	−0.837470	−0.0277162
$914$	−32.8117	−1.08531
$915$	−23.8409	−0.788157
$916$	59.1499	1.95437
$917$	−11.4234	−0.377233
$918$	2.32571	0.0767598
$919$	43.4137	1.43209	0.716043	−	0.698056i	$-0.245951\pi$
$919$	43.4137	1.43209	0.716043	+	0.698056i	$0.245951\pi$
$920$	−5.29408	−0.174541
$921$	34.9773	1.15254
$922$	−38.8011	−1.27785
$923$	−46.7235	−1.53792
$924$	−1.97994	−0.0651352
$925$	−38.6119	−1.26955
$926$	48.9033	1.60706
$927$	−31.3275	−1.02893
$928$	−30.5142	−1.00168
$929$	−0.655946	−0.0215209	−0.0107604	−	0.999942i	$-0.503425\pi$
$929$	−0.655946	−0.0215209	−0.0107604	+	0.999942i	$0.503425\pi$
$930$	36.8774	1.20926
$931$	−5.83877	−0.191358
$932$	59.9288	1.96303
$933$	−34.7897	−1.13896
$934$	−6.42550	−0.210249
$935$	0.135041	0.00441632
$936$	−13.5027	−0.441350
$937$	43.6011	1.42438	0.712192	−	0.701984i	$-0.247702\pi$
$937$	43.6011	1.42438	0.712192	+	0.701984i	$0.247702\pi$
$938$	53.1285	1.73471
$939$	−56.0545	−1.82927
$940$	−2.95184	−0.0962783
$941$	−37.2013	−1.21273	−0.606364	−	0.795188i	$-0.707372\pi$
$941$	−37.2013	−1.21273	−0.606364	+	0.795188i	$0.707372\pi$
$942$	−60.7839	−1.98045
$943$	2.45931	0.0800861
$944$	18.4464	0.600380
$945$	−21.8356	−0.710312
$946$	1.05050	0.0341546
$947$	43.6893	1.41971	0.709855	−	0.704348i	$-0.248760\pi$
$947$	43.6893	1.41971	0.709855	+	0.704348i	$0.248760\pi$
$948$	−67.2491	−2.18415
$949$	54.7484	1.77721
$950$	16.8731	0.547434
$951$	13.4866	0.437332
$952$	2.07171	0.0671444
$953$	9.03201	0.292576	0.146288	−	0.989242i	$-0.453267\pi$
$953$	9.03201	0.292576	0.146288	+	0.989242i	$0.453267\pi$
$954$	−53.0861	−1.71873
$955$	−20.4898	−0.663035
$956$	−9.15641	−0.296139
$957$	0.953462	0.0308210
$958$	−1.67287	−0.0540480
$959$	16.9685	0.547941
$960$	−78.5647	−2.53567
$961$	−23.9078	−0.771220
$962$	116.867	3.76795
$963$	−26.3781	−0.850021
$964$	63.3307	2.03974
$965$	63.8786	2.05633
$966$	−17.6180	−0.566850
$967$	−14.1131	−0.453848	−0.226924	−	0.973912i	$-0.572867\pi$
$967$	−14.1131	−0.453848	−0.226924	+	0.973912i	$0.572867\pi$
$968$	16.9235	0.543942
$969$	−2.25567	−0.0724624
$970$	83.8442	2.69207
$971$	−14.8843	−0.477661	−0.238830	−	0.971061i	$-0.576764\pi$
$971$	−14.8843	−0.477661	−0.238830	+	0.971061i	$0.576764\pi$
$972$	46.5385	1.49272
$973$	−39.5292	−1.26725
$974$	22.6452	0.725600
$975$	−34.1308	−1.09306
$976$	7.76051	0.248408
$977$	−31.4183	−1.00516	−0.502581	−	0.864530i	$-0.667616\pi$
$977$	−31.4183	−1.00516	−0.502581	+	0.864530i	$0.667616\pi$
$978$	90.6883	2.89989
$979$	1.14489	0.0365908
$980$	−19.5340	−0.623992
$981$	−31.7302	−1.01307
$982$	−82.8457	−2.64371
$983$	−21.7270	−0.692984	−0.346492	−	0.938053i	$-0.612627\pi$
$983$	−21.7270	−0.692984	−0.346492	+	0.938053i	$0.612627\pi$
$984$	−7.03075	−0.224132
$985$	−15.2557	−0.486088
$986$	−3.80925	−0.121311
$987$	−2.57276	−0.0818918
$988$	−29.3827	−0.934787
$989$	5.37806	0.171012
$990$	1.26877	0.0403243
$991$	28.9190	0.918643	0.459321	−	0.888270i	$-0.348093\pi$
$991$	28.9190	0.918643	0.459321	+	0.888270i	$0.348093\pi$
$992$	−20.2070	−0.641574
$993$	25.8698	0.820955
$994$	67.3536	2.13633
$995$	−23.7007	−0.751363
$996$	46.8003	1.48292
$997$	−24.5200	−0.776556	−0.388278	−	0.921542i	$-0.626930\pi$
$997$	−24.5200	−0.776556	−0.388278	+	0.921542i	$0.626930\pi$
$998$	48.6418	1.53973
$999$	−28.4978	−0.901631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.a.1.3	✓	11
3.2	odd	2		3141.2.a.b.1.9		11
4.3	odd	2		5584.2.a.j.1.9		11
5.4	even	2		8725.2.a.l.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.a.1.3	✓	11	1.1	even	1	trivial
3141.2.a.b.1.9		11	3.2	odd	2
5584.2.a.j.1.9		11	4.3	odd	2
8725.2.a.l.1.9		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)

\(f(q)\)	\(=\)	\(q-2.17018 q^{2} -2.21125 q^{3} +2.70967 q^{4} -2.88560 q^{5} +4.79881 q^{6} +3.08193 q^{7} -1.54011 q^{8} +1.88963 q^{9} +O(q^{10})\)	\(q-2.17018 q^{2} -2.21125 q^{3} +2.70967 q^{4} -2.88560 q^{5} +4.79881 q^{6} +3.08193 q^{7} -1.54011 q^{8} +1.88963 q^{9} +6.26228 q^{10} +0.107220 q^{11} -5.99176 q^{12} +4.63972 q^{13} -6.68833 q^{14} +6.38080 q^{15} -2.07703 q^{16} -0.436470 q^{17} -4.10083 q^{18} -2.33713 q^{19} -7.81904 q^{20} -6.81491 q^{21} -0.232686 q^{22} -1.19125 q^{23} +3.40557 q^{24} +3.32672 q^{25} -10.0690 q^{26} +2.45531 q^{27} +8.35100 q^{28} -4.02152 q^{29} -13.8475 q^{30} -2.66311 q^{31} +7.58774 q^{32} -0.237090 q^{33} +0.947217 q^{34} -8.89322 q^{35} +5.12027 q^{36} -11.6066 q^{37} +5.07198 q^{38} -10.2596 q^{39} +4.44415 q^{40} -2.06448 q^{41} +14.7896 q^{42} -4.51465 q^{43} +0.290530 q^{44} -5.45272 q^{45} +2.58522 q^{46} +0.377519 q^{47} +4.59283 q^{48} +2.49827 q^{49} -7.21956 q^{50} +0.965144 q^{51} +12.5721 q^{52} +12.9452 q^{53} -5.32845 q^{54} -0.309394 q^{55} -4.74651 q^{56} +5.16798 q^{57} +8.72741 q^{58} -8.88116 q^{59} +17.2899 q^{60} -3.73636 q^{61} +5.77943 q^{62} +5.82370 q^{63} -12.3127 q^{64} -13.3884 q^{65} +0.514527 q^{66} -7.94347 q^{67} -1.18269 q^{68} +2.63414 q^{69} +19.2999 q^{70} -10.0703 q^{71} -2.91024 q^{72} +11.7999 q^{73} +25.1884 q^{74} -7.35620 q^{75} -6.33285 q^{76} +0.330444 q^{77} +22.2651 q^{78} +11.2236 q^{79} +5.99348 q^{80} -11.0982 q^{81} +4.48030 q^{82} -7.81077 q^{83} -18.4662 q^{84} +1.25948 q^{85} +9.79760 q^{86} +8.89259 q^{87} -0.165130 q^{88} +10.6780 q^{89} +11.8334 q^{90} +14.2993 q^{91} -3.22789 q^{92} +5.88881 q^{93} -0.819283 q^{94} +6.74403 q^{95} -16.7784 q^{96} +13.3888 q^{97} -5.42168 q^{98} +0.202606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 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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