LMFDB - Embedded newform 403.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(1,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("403.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.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:	$3.21797120146$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 19x^{5} + 21x^{4} - 31x^{3} - 29x^{2} - x + 1 $ x^8 - 3x^7 - 7x^6 + 19x^5 + 21x^4 - 31x^3 - 29x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.66697$ of defining polynomial
Character	$\chi$	$=$	403.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66697 q^{2} +1.08287 q^{3} +5.11275 q^{4} -1.31345 q^{5} -2.88800 q^{6} +1.98184 q^{7} -8.30164 q^{8} -1.82738 q^{9} +O(q^{10})$	\(q-2.66697 q^{2} +1.08287 q^{3} +5.11275 q^{4} -1.31345 q^{5} -2.88800 q^{6} +1.98184 q^{7} -8.30164 q^{8} -1.82738 q^{9} +3.50294 q^{10} -5.31799 q^{11} +5.53647 q^{12} -1.00000 q^{13} -5.28551 q^{14} -1.42230 q^{15} +11.9147 q^{16} -3.62621 q^{17} +4.87359 q^{18} -2.73707 q^{19} -6.71536 q^{20} +2.14608 q^{21} +14.1829 q^{22} +4.66054 q^{23} -8.98962 q^{24} -3.27484 q^{25} +2.66697 q^{26} -5.22745 q^{27} +10.1326 q^{28} +8.58248 q^{29} +3.79325 q^{30} -1.00000 q^{31} -15.1731 q^{32} -5.75871 q^{33} +9.67100 q^{34} -2.60305 q^{35} -9.34297 q^{36} -8.71453 q^{37} +7.29969 q^{38} -1.08287 q^{39} +10.9038 q^{40} +7.10060 q^{41} -5.72354 q^{42} -10.3208 q^{43} -27.1896 q^{44} +2.40018 q^{45} -12.4295 q^{46} -10.4975 q^{47} +12.9022 q^{48} -3.07233 q^{49} +8.73392 q^{50} -3.92672 q^{51} -5.11275 q^{52} +0.147212 q^{53} +13.9415 q^{54} +6.98492 q^{55} -16.4525 q^{56} -2.96390 q^{57} -22.8892 q^{58} +2.12773 q^{59} -7.27189 q^{60} -7.00860 q^{61} +2.66697 q^{62} -3.62158 q^{63} +16.6367 q^{64} +1.31345 q^{65} +15.3583 q^{66} +5.05576 q^{67} -18.5399 q^{68} +5.04678 q^{69} +6.94226 q^{70} -1.02614 q^{71} +15.1703 q^{72} +5.21181 q^{73} +23.2414 q^{74} -3.54624 q^{75} -13.9940 q^{76} -10.5394 q^{77} +2.88800 q^{78} +13.0030 q^{79} -15.6495 q^{80} -0.178509 q^{81} -18.9371 q^{82} -4.93490 q^{83} +10.9724 q^{84} +4.76285 q^{85} +27.5253 q^{86} +9.29374 q^{87} +44.1480 q^{88} +1.77443 q^{89} -6.40123 q^{90} -1.98184 q^{91} +23.8282 q^{92} -1.08287 q^{93} +27.9964 q^{94} +3.59501 q^{95} -16.4305 q^{96} -7.08058 q^{97} +8.19381 q^{98} +9.71801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9	\( 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9} + 9 q^{10} - 5 q^{11} - 9 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 3 q^{16} - 11 q^{17} - 30 q^{18} - 9 q^{19} - 31 q^{20} - 16 q^{21} - 2 q^{22} + 13 q^{24} + 19 q^{25} + 5 q^{26} - 9 q^{27} + 16 q^{28} - 12 q^{29} - 7 q^{30} - 8 q^{31} - 25 q^{32} - 14 q^{33} + 22 q^{34} + 7 q^{35} + 37 q^{36} - 9 q^{37} - 9 q^{38} + 3 q^{39} + 55 q^{40} - 25 q^{41} - 3 q^{42} + 7 q^{43} - 26 q^{44} - 45 q^{45} + 5 q^{46} - 17 q^{47} - 9 q^{48} - 11 q^{50} - 10 q^{51} - 9 q^{52} - 15 q^{53} + 54 q^{54} + 7 q^{55} - 14 q^{56} - 7 q^{57} - 5 q^{58} - 15 q^{59} + 61 q^{60} + 11 q^{61} + 5 q^{62} - 21 q^{63} + 47 q^{64} + 15 q^{65} + 83 q^{66} + 18 q^{67} - 16 q^{68} - 15 q^{69} - 24 q^{70} - 7 q^{71} - 21 q^{72} + 24 q^{73} + 48 q^{74} - 17 q^{75} - 3 q^{76} - 49 q^{77} + 33 q^{79} - 16 q^{80} + 20 q^{81} - q^{82} - 13 q^{83} - 6 q^{84} + q^{85} + 19 q^{86} + 18 q^{87} + 37 q^{88} - 23 q^{89} + 117 q^{90} + 4 q^{91} + 22 q^{92} + 3 q^{93} + 10 q^{94} + 43 q^{95} + 46 q^{96} - 17 q^{97} + 52 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9 + 9 * q^10 - 5 * q^11 - 9 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 3 * q^16 - 11 * q^17 - 30 * q^18 - 9 * q^19 - 31 * q^20 - 16 * q^21 - 2 * q^22 + 13 * q^24 + 19 * q^25 + 5 * q^26 - 9 * q^27 + 16 * q^28 - 12 * q^29 - 7 * q^30 - 8 * q^31 - 25 * q^32 - 14 * q^33 + 22 * q^34 + 7 * q^35 + 37 * q^36 - 9 * q^37 - 9 * q^38 + 3 * q^39 + 55 * q^40 - 25 * q^41 - 3 * q^42 + 7 * q^43 - 26 * q^44 - 45 * q^45 + 5 * q^46 - 17 * q^47 - 9 * q^48 - 11 * q^50 - 10 * q^51 - 9 * q^52 - 15 * q^53 + 54 * q^54 + 7 * q^55 - 14 * q^56 - 7 * q^57 - 5 * q^58 - 15 * q^59 + 61 * q^60 + 11 * q^61 + 5 * q^62 - 21 * q^63 + 47 * q^64 + 15 * q^65 + 83 * q^66 + 18 * q^67 - 16 * q^68 - 15 * q^69 - 24 * q^70 - 7 * q^71 - 21 * q^72 + 24 * q^73 + 48 * q^74 - 17 * q^75 - 3 * q^76 - 49 * q^77 + 33 * q^79 - 16 * q^80 + 20 * q^81 - q^82 - 13 * q^83 - 6 * q^84 + q^85 + 19 * q^86 + 18 * q^87 + 37 * q^88 - 23 * q^89 + 117 * q^90 + 4 * q^91 + 22 * q^92 + 3 * q^93 + 10 * q^94 + 43 * q^95 + 46 * q^96 - 17 * q^97 + 52 * q^98 + 51 * 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 $

$2$	−2.66697	−1.88584	−0.942918	−	0.333025i	$-0.891931\pi$
$2$	−2.66697	−1.88584	−0.942918	+	0.333025i	$0.891931\pi$
$3$	1.08287	0.625197	0.312599	−	0.949885i	$-0.398801\pi$
$3$	1.08287	0.625197	0.312599	+	0.949885i	$0.398801\pi$
$4$	5.11275	2.55638
$5$	−1.31345	−0.587394	−0.293697	−	0.955899i	$-0.594886\pi$
$5$	−1.31345	−0.587394	−0.293697	+	0.955899i	$0.594886\pi$
$6$	−2.88800	−1.17902
$7$	1.98184	0.749064	0.374532	−	0.927214i	$-0.377803\pi$
$7$	1.98184	0.749064	0.374532	+	0.927214i	$0.377803\pi$
$8$	−8.30164	−2.93507
$9$	−1.82738	−0.609128
$10$	3.50294	1.10773
$11$	−5.31799	−1.60343	−0.801717	−	0.597704i	$-0.796080\pi$
$11$	−5.31799	−1.60343	−0.801717	+	0.597704i	$0.796080\pi$
$12$	5.53647	1.59824
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.28551	−1.41261
$15$	−1.42230	−0.367237
$16$	11.9147	2.97869
$17$	−3.62621	−0.879484	−0.439742	−	0.898124i	$-0.644930\pi$
$17$	−3.62621	−0.879484	−0.439742	+	0.898124i	$0.644930\pi$
$18$	4.87359	1.14872
$19$	−2.73707	−0.627927	−0.313963	−	0.949435i	$-0.601657\pi$
$19$	−2.73707	−0.627927	−0.313963	+	0.949435i	$0.601657\pi$
$20$	−6.71536	−1.50160
$21$	2.14608	0.468313
$22$	14.1829	3.02381
$23$	4.66054	0.971790	0.485895	−	0.874017i	$-0.338494\pi$
$23$	4.66054	0.971790	0.485895	+	0.874017i	$0.338494\pi$
$24$	−8.98962	−1.83500
$25$	−3.27484	−0.654968
$26$	2.66697	0.523037
$27$	−5.22745	−1.00602
$28$	10.1326	1.91489
$29$	8.58248	1.59373	0.796863	−	0.604160i	$-0.206491\pi$
$29$	8.58248	1.59373	0.796863	+	0.604160i	$0.206491\pi$
$30$	3.79325	0.692549
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−15.1731	−2.68224
$33$	−5.75871	−1.00246
$34$	9.67100	1.65856
$35$	−2.60305	−0.439995
$36$	−9.34297	−1.55716
$37$	−8.71453	−1.43266	−0.716330	−	0.697762i	$-0.754179\pi$
$37$	−8.71453	−1.43266	−0.716330	+	0.697762i	$0.754179\pi$
$38$	7.29969	1.18417
$39$	−1.08287	−0.173399
$40$	10.9038	1.72404
$41$	7.10060	1.10893	0.554463	−	0.832208i	$-0.312924\pi$
$41$	7.10060	1.10893	0.554463	+	0.832208i	$0.312924\pi$
$42$	−5.72354	−0.883161
$43$	−10.3208	−1.57391	−0.786953	−	0.617014i	$-0.788342\pi$
$43$	−10.3208	−1.57391	−0.786953	+	0.617014i	$0.788342\pi$
$44$	−27.1896	−4.09898
$45$	2.40018	0.357798
$46$	−12.4295	−1.83264
$47$	−10.4975	−1.53121	−0.765605	−	0.643310i	$-0.777560\pi$
$47$	−10.4975	−1.53121	−0.765605	+	0.643310i	$0.777560\pi$
$48$	12.9022	1.86227
$49$	−3.07233	−0.438904
$50$	8.73392	1.23516
$51$	−3.92672	−0.549851
$52$	−5.11275	−0.709011
$53$	0.147212	0.0202212	0.0101106	−	0.999949i	$-0.496782\pi$
$53$	0.147212	0.0202212	0.0101106	+	0.999949i	$0.496782\pi$
$54$	13.9415	1.89719
$55$	6.98492	0.941847
$56$	−16.4525	−2.19856
$57$	−2.96390	−0.392578
$58$	−22.8892	−3.00551
$59$	2.12773	0.277007	0.138504	−	0.990362i	$-0.455771\pi$
$59$	2.12773	0.277007	0.138504	+	0.990362i	$0.455771\pi$
$60$	−7.27189	−0.938796
$61$	−7.00860	−0.897359	−0.448680	−	0.893693i	$-0.648106\pi$
$61$	−7.00860	−0.897359	−0.448680	+	0.893693i	$0.648106\pi$
$62$	2.66697	0.338706
$63$	−3.62158	−0.456276
$64$	16.6367	2.07958
$65$	1.31345	0.162914
$66$	15.3583	1.89048
$67$	5.05576	0.617660	0.308830	−	0.951117i	$-0.400063\pi$
$67$	5.05576	0.617660	0.308830	+	0.951117i	$0.400063\pi$
$68$	−18.5399	−2.24829
$69$	5.04678	0.607561
$70$	6.94226	0.829759
$71$	−1.02614	−0.121781	−0.0608904	−	0.998144i	$-0.519394\pi$
$71$	−1.02614	−0.121781	−0.0608904	+	0.998144i	$0.519394\pi$
$72$	15.1703	1.78784
$73$	5.21181	0.609996	0.304998	−	0.952353i	$-0.401344\pi$
$73$	5.21181	0.609996	0.304998	+	0.952353i	$0.401344\pi$
$74$	23.2414	2.70176
$75$	−3.54624	−0.409484
$76$	−13.9940	−1.60522
$77$	−10.5394	−1.20107
$78$	2.88800	0.327001
$79$	13.0030	1.46295	0.731476	−	0.681867i	$-0.238832\pi$
$79$	13.0030	1.46295	0.731476	+	0.681867i	$0.238832\pi$
$80$	−15.6495	−1.74966
$81$	−0.178509	−0.0198344
$82$	−18.9371	−2.09125
$83$	−4.93490	−0.541675	−0.270838	−	0.962625i	$-0.587301\pi$
$83$	−4.93490	−0.541675	−0.270838	+	0.962625i	$0.587301\pi$
$84$	10.9724	1.19718
$85$	4.76285	0.516604
$86$	27.5253	2.96813
$87$	9.29374	0.996393
$88$	44.1480	4.70619
$89$	1.77443	0.188089	0.0940446	−	0.995568i	$-0.470020\pi$
$89$	1.77443	0.188089	0.0940446	+	0.995568i	$0.470020\pi$
$90$	−6.40123	−0.674749
$91$	−1.98184	−0.207753
$92$	23.8282	2.48426
$93$	−1.08287	−0.112289
$94$	27.9964	2.88761
$95$	3.59501	0.368840
$96$	−16.4305	−1.67693
$97$	−7.08058	−0.718924	−0.359462	−	0.933160i	$-0.617040\pi$
$97$	−7.08058	−0.718924	−0.359462	+	0.933160i	$0.617040\pi$
$98$	8.19381	0.827700
$99$	9.71801	0.976697
$100$	−16.7435	−1.67435
$101$	3.88536	0.386607	0.193304	−	0.981139i	$-0.438080\pi$
$101$	3.88536	0.386607	0.193304	+	0.981139i	$0.438080\pi$
$102$	10.4725	1.03693
$103$	−1.72738	−0.170204	−0.0851018	−	0.996372i	$-0.527122\pi$
$103$	−1.72738	−0.170204	−0.0851018	+	0.996372i	$0.527122\pi$
$104$	8.30164	0.814042
$105$	−2.81877	−0.275084
$106$	−0.392612	−0.0381338
$107$	−4.62656	−0.447267	−0.223633	−	0.974673i	$-0.571792\pi$
$107$	−4.62656	−0.447267	−0.223633	+	0.974673i	$0.571792\pi$
$108$	−26.7267	−2.57177
$109$	13.9901	1.34001	0.670006	−	0.742355i	$-0.266291\pi$
$109$	13.9901	1.34001	0.670006	+	0.742355i	$0.266291\pi$
$110$	−18.6286	−1.77617
$111$	−9.43673	−0.895695
$112$	23.6131	2.23123
$113$	−18.8128	−1.76976	−0.884881	−	0.465817i	$-0.845761\pi$
$113$	−18.8128	−1.76976	−0.884881	+	0.465817i	$0.845761\pi$
$114$	7.90465	0.740338
$115$	−6.12140	−0.570824
$116$	43.8801	4.07416
$117$	1.82738	0.168942
$118$	−5.67462	−0.522391
$119$	−7.18655	−0.658790
$120$	11.8074	1.07787
$121$	17.2810	1.57100
$122$	18.6918	1.69227
$123$	7.68905	0.693298
$124$	−5.11275	−0.459139
$125$	10.8686	0.972118
$126$	9.65866	0.860461
$127$	0.101029	0.00896486	0.00448243	−	0.999990i	$-0.498573\pi$
$127$	0.101029	0.00896486	0.00448243	+	0.999990i	$0.498573\pi$
$128$	−14.0234	−1.23951
$129$	−11.1761	−0.984001
$130$	−3.50294	−0.307229
$131$	−9.91028	−0.865865	−0.432933	−	0.901426i	$-0.642521\pi$
$131$	−9.91028	−0.865865	−0.432933	+	0.901426i	$0.642521\pi$
$132$	−29.4429	−2.56267
$133$	−5.42442	−0.470357
$134$	−13.4836	−1.16480
$135$	6.86600	0.590932
$136$	30.1035	2.58135
$137$	14.8425	1.26808	0.634039	−	0.773301i	$-0.281396\pi$
$137$	14.8425	1.26808	0.634039	+	0.773301i	$0.281396\pi$
$138$	−13.4596	−1.14576
$139$	12.4617	1.05699	0.528495	−	0.848937i	$-0.322757\pi$
$139$	12.4617	1.05699	0.528495	+	0.848937i	$0.322757\pi$
$140$	−13.3087	−1.12479
$141$	−11.3674	−0.957309
$142$	2.73670	0.229659
$143$	5.31799	0.444712
$144$	−21.7728	−1.81440
$145$	−11.2727	−0.936145
$146$	−13.8998	−1.15035
$147$	−3.32694	−0.274401
$148$	−44.5552	−3.66242
$149$	−12.7310	−1.04296	−0.521481	−	0.853263i	$-0.674620\pi$
$149$	−12.7310	−1.04296	−0.521481	+	0.853263i	$0.674620\pi$
$150$	9.45773	0.772221
$151$	−3.77773	−0.307427	−0.153714	−	0.988115i	$-0.549123\pi$
$151$	−3.77773	−0.307427	−0.153714	+	0.988115i	$0.549123\pi$
$152$	22.7222	1.84301
$153$	6.62648	0.535719
$154$	28.1083	2.26503
$155$	1.31345	0.105499
$156$	−5.53647	−0.443272
$157$	8.04832	0.642326	0.321163	−	0.947024i	$-0.395926\pi$
$157$	8.04832	0.642326	0.321163	+	0.947024i	$0.395926\pi$
$158$	−34.6787	−2.75889
$159$	0.159412	0.0126422
$160$	19.9291	1.57553
$161$	9.23643	0.727933
$162$	0.476080	0.0374044
$163$	−4.66805	−0.365630	−0.182815	−	0.983147i	$-0.558521\pi$
$163$	−4.66805	−0.365630	−0.182815	+	0.983147i	$0.558521\pi$
$164$	36.3036	2.83483
$165$	7.56379	0.588840
$166$	13.1612	1.02151
$167$	16.5449	1.28028	0.640142	−	0.768257i	$-0.278876\pi$
$167$	16.5449	1.28028	0.640142	+	0.768257i	$0.278876\pi$
$168$	−17.8160	−1.37453
$169$	1.00000	0.0769231
$170$	−12.7024	−0.974230
$171$	5.00168	0.382488
$172$	−52.7676	−4.02349
$173$	−24.6142	−1.87138	−0.935692	−	0.352818i	$-0.885223\pi$
$173$	−24.6142	−1.87138	−0.935692	+	0.352818i	$0.885223\pi$
$174$	−24.7862	−1.87903
$175$	−6.49020	−0.490613
$176$	−63.3625	−4.77613
$177$	2.30407	0.173184
$178$	−4.73236	−0.354705
$179$	−15.2492	−1.13978	−0.569888	−	0.821723i	$-0.693013\pi$
$179$	−15.2492	−1.13978	−0.569888	+	0.821723i	$0.693013\pi$
$180$	12.2715	0.914667
$181$	−13.1914	−0.980507	−0.490254	−	0.871580i	$-0.663096\pi$
$181$	−13.1914	−0.980507	−0.490254	+	0.871580i	$0.663096\pi$
$182$	5.28551	0.391788
$183$	−7.58943	−0.561027
$184$	−38.6901	−2.85227
$185$	11.4461	0.841535
$186$	2.88800	0.211758
$187$	19.2841	1.41019
$188$	−53.6709	−3.91435
$189$	−10.3599	−0.753575
$190$	−9.58780	−0.695572
$191$	17.9703	1.30028	0.650142	−	0.759813i	$-0.274710\pi$
$191$	17.9703	1.30028	0.650142	+	0.759813i	$0.274710\pi$
$192$	18.0154	1.30015
$193$	−8.86248	−0.637936	−0.318968	−	0.947766i	$-0.603336\pi$
$193$	−8.86248	−0.637936	−0.318968	+	0.947766i	$0.603336\pi$
$194$	18.8837	1.35577
$195$	1.42230	0.101853
$196$	−15.7080	−1.12200
$197$	−4.59590	−0.327444	−0.163722	−	0.986506i	$-0.552350\pi$
$197$	−4.59590	−0.327444	−0.163722	+	0.986506i	$0.552350\pi$
$198$	−25.9177	−1.84189
$199$	−0.0502896	−0.00356494	−0.00178247	−	0.999998i	$-0.500567\pi$
$199$	−0.0502896	−0.00356494	−0.00178247	+	0.999998i	$0.500567\pi$
$200$	27.1865	1.92238
$201$	5.47475	0.386159
$202$	−10.3621	−0.729078
$203$	17.0091	1.19380
$204$	−20.0764	−1.40563
$205$	−9.32630	−0.651377
$206$	4.60687	0.320976
$207$	−8.51661	−0.591945
$208$	−11.9147	−0.826139
$209$	14.5557	1.00684
$210$	7.51759	0.518763
$211$	13.9175	0.958118	0.479059	−	0.877783i	$-0.340978\pi$
$211$	13.9175	0.958118	0.479059	+	0.877783i	$0.340978\pi$
$212$	0.752660	0.0516929
$213$	−1.11118	−0.0761370
$214$	12.3389	0.843472
$215$	13.5559	0.924502
$216$	43.3964	2.95275
$217$	−1.98184	−0.134536
$218$	−37.3114	−2.52704
$219$	5.64373	0.381368
$220$	35.7122	2.40772
$221$	3.62621	0.243925
$222$	25.1675	1.68913
$223$	14.9057	0.998159	0.499080	−	0.866556i	$-0.333672\pi$
$223$	14.9057	0.998159	0.499080	+	0.866556i	$0.333672\pi$
$224$	−30.0705	−2.00917
$225$	5.98440	0.398960
$226$	50.1734	3.33748
$227$	21.1896	1.40640	0.703200	−	0.710992i	$-0.251754\pi$
$227$	21.1896	1.40640	0.703200	+	0.710992i	$0.251754\pi$
$228$	−15.1537	−1.00358
$229$	−0.362533	−0.0239569	−0.0119784	−	0.999928i	$-0.503813\pi$
$229$	−0.362533	−0.0239569	−0.0119784	+	0.999928i	$0.503813\pi$
$230$	16.3256	1.07648
$231$	−11.4128	−0.750908
$232$	−71.2486	−4.67770
$233$	27.3613	1.79250	0.896249	−	0.443551i	$-0.146281\pi$
$233$	27.3613	1.79250	0.896249	+	0.443551i	$0.146281\pi$
$234$	−4.87359	−0.318597
$235$	13.7879	0.899424
$236$	10.8786	0.708136
$237$	14.0806	0.914634
$238$	19.1663	1.24237
$239$	16.2676	1.05227	0.526133	−	0.850402i	$-0.323641\pi$
$239$	16.2676	1.05227	0.526133	+	0.850402i	$0.323641\pi$
$240$	−16.9464	−1.09388
$241$	26.2945	1.69378	0.846890	−	0.531768i	$-0.178472\pi$
$241$	26.2945	1.69378	0.846890	+	0.531768i	$0.178472\pi$
$242$	−46.0880	−2.96265
$243$	15.4890	0.993622
$244$	−35.8333	−2.29399
$245$	4.03535	0.257809
$246$	−20.5065	−1.30745
$247$	2.73707	0.174156
$248$	8.30164	0.527154
$249$	−5.34387	−0.338654
$250$	−28.9863	−1.83326
$251$	2.43440	0.153658	0.0768289	−	0.997044i	$-0.475520\pi$
$251$	2.43440	0.153658	0.0768289	+	0.997044i	$0.475520\pi$
$252$	−18.5162	−1.16641
$253$	−24.7847	−1.55820
$254$	−0.269441	−0.0169063
$255$	5.15757	0.322979
$256$	4.12683	0.257927
$257$	−21.0220	−1.31132	−0.655658	−	0.755058i	$-0.727609\pi$
$257$	−21.0220	−1.31132	−0.655658	+	0.755058i	$0.727609\pi$
$258$	29.8064	1.85566
$259$	−17.2708	−1.07315
$260$	6.71536	0.416469
$261$	−15.6835	−0.970783
$262$	26.4305	1.63288
$263$	9.46294	0.583510	0.291755	−	0.956493i	$-0.405761\pi$
$263$	9.46294	0.583510	0.291755	+	0.956493i	$0.405761\pi$
$264$	47.8067	2.94230
$265$	−0.193356	−0.0118778
$266$	14.4668	0.887016
$267$	1.92148	0.117593
$268$	25.8489	1.57897
$269$	−28.9586	−1.76564	−0.882820	−	0.469712i	$-0.844358\pi$
$269$	−28.9586	−1.76564	−0.882820	+	0.469712i	$0.844358\pi$
$270$	−18.3115	−1.11440
$271$	−14.8372	−0.901297	−0.450648	−	0.892702i	$-0.648807\pi$
$271$	−14.8372	−0.901297	−0.450648	+	0.892702i	$0.648807\pi$
$272$	−43.2053	−2.61971
$273$	−2.14608	−0.129887
$274$	−39.5845	−2.39139
$275$	17.4156	1.05020
$276$	25.8029	1.55315
$277$	8.01794	0.481751	0.240876	−	0.970556i	$-0.422565\pi$
$277$	8.01794	0.481751	0.240876	+	0.970556i	$0.422565\pi$
$278$	−33.2351	−1.99331
$279$	1.82738	0.109403
$280$	21.6096	1.29142
$281$	−14.0913	−0.840618	−0.420309	−	0.907381i	$-0.638078\pi$
$281$	−14.0913	−0.840618	−0.420309	+	0.907381i	$0.638078\pi$
$282$	30.3166	1.80533
$283$	2.96473	0.176235	0.0881174	−	0.996110i	$-0.471915\pi$
$283$	2.96473	0.176235	0.0881174	+	0.996110i	$0.471915\pi$
$284$	−5.24642	−0.311318
$285$	3.89294	0.230598
$286$	−14.1829	−0.838655
$287$	14.0722	0.830657
$288$	27.7270	1.63383
$289$	−3.85062	−0.226507
$290$	30.0639	1.76542
$291$	−7.66737	−0.449469
$292$	26.6467	1.55938
$293$	−33.1320	−1.93559	−0.967795	−	0.251738i	$-0.918998\pi$
$293$	−33.1320	−1.93559	−0.967795	+	0.251738i	$0.918998\pi$
$294$	8.87287	0.517476
$295$	−2.79468	−0.162713
$296$	72.3448	4.20496
$297$	27.7995	1.61309
$298$	33.9532	1.96686
$299$	−4.66054	−0.269526
$300$	−18.1311	−1.04680
$301$	−20.4541	−1.17896
$302$	10.0751	0.579757
$303$	4.20735	0.241706
$304$	−32.6115	−1.87040
$305$	9.20547	0.527103
$306$	−17.6726	−1.01028
$307$	9.58875	0.547259	0.273630	−	0.961835i	$-0.411776\pi$
$307$	9.58875	0.547259	0.273630	+	0.961835i	$0.411776\pi$
$308$	−53.8853	−3.07040
$309$	−1.87053	−0.106411
$310$	−3.50294	−0.198954
$311$	−0.387955	−0.0219989	−0.0109994	−	0.999940i	$-0.503501\pi$
$311$	−0.387955	−0.0219989	−0.0109994	+	0.999940i	$0.503501\pi$
$312$	8.98962	0.508937
$313$	−0.286663	−0.0162032	−0.00810158	−	0.999967i	$-0.502579\pi$
$313$	−0.286663	−0.0162032	−0.00810158	+	0.999967i	$0.502579\pi$
$314$	−21.4647	−1.21132
$315$	4.75677	0.268014
$316$	66.4811	3.73986
$317$	−0.950284	−0.0533733	−0.0266866	−	0.999644i	$-0.508496\pi$
$317$	−0.950284	−0.0533733	−0.0266866	+	0.999644i	$0.508496\pi$
$318$	−0.425149	−0.0238411
$319$	−45.6415	−2.55543
$320$	−21.8515	−1.22153
$321$	−5.00998	−0.279630
$322$	−24.6333	−1.37276
$323$	9.92518	0.552252
$324$	−0.912674	−0.0507041
$325$	3.27484	0.181656
$326$	12.4496	0.689518
$327$	15.1496	0.837772
$328$	−58.9466	−3.25478
$329$	−20.8042	−1.14697
$330$	−20.1724	−1.11046
$331$	−14.7415	−0.810269	−0.405134	−	0.914257i	$-0.632775\pi$
$331$	−14.7415	−0.810269	−0.405134	+	0.914257i	$0.632775\pi$
$332$	−25.2309	−1.38473
$333$	15.9248	0.872673
$334$	−44.1248	−2.41440
$335$	−6.64050	−0.362809
$336$	25.5700	1.39496
$337$	−27.0379	−1.47285	−0.736423	−	0.676521i	$-0.763487\pi$
$337$	−27.0379	−1.47285	−0.736423	+	0.676521i	$0.763487\pi$
$338$	−2.66697	−0.145064
$339$	−20.3719	−1.10645
$340$	24.3513	1.32063
$341$	5.31799	0.287985
$342$	−13.3394	−0.721310
$343$	−19.9617	−1.07783
$344$	85.6794	4.61952
$345$	−6.62870	−0.356877
$346$	65.6455	3.52912
$347$	20.0064	1.07400	0.536999	−	0.843583i	$-0.319558\pi$
$347$	20.0064	1.07400	0.536999	+	0.843583i	$0.319558\pi$
$348$	47.5166	2.54716
$349$	31.9452	1.70999	0.854995	−	0.518636i	$-0.173560\pi$
$349$	31.9452	1.70999	0.854995	+	0.518636i	$0.173560\pi$
$350$	17.3092	0.925216
$351$	5.22745	0.279020
$352$	80.6901	4.30080
$353$	15.8462	0.843406	0.421703	−	0.906734i	$-0.361433\pi$
$353$	15.8462	0.843406	0.421703	+	0.906734i	$0.361433\pi$
$354$	−6.14489	−0.326597
$355$	1.34779	0.0715333
$356$	9.07222	0.480827
$357$	−7.78212	−0.411874
$358$	40.6691	2.14943
$359$	−36.6828	−1.93604	−0.968022	−	0.250864i	$-0.919285\pi$
$359$	−36.6828	−1.93604	−0.968022	+	0.250864i	$0.919285\pi$
$360$	−19.9255	−1.05016
$361$	−11.5085	−0.605708
$362$	35.1811	1.84908
$363$	18.7131	0.982184
$364$	−10.1326	−0.531095
$365$	−6.84547	−0.358308
$366$	20.2408	1.05800
$367$	21.6218	1.12865	0.564324	−	0.825553i	$-0.309137\pi$
$367$	21.6218	1.12865	0.564324	+	0.825553i	$0.309137\pi$
$368$	55.5292	2.89466
$369$	−12.9755	−0.675479
$370$	−30.5265	−1.58700
$371$	0.291751	0.0151469
$372$	−5.53647	−0.287052
$373$	−21.5990	−1.11836	−0.559178	−	0.829048i	$-0.688883\pi$
$373$	−21.5990	−1.11836	−0.559178	+	0.829048i	$0.688883\pi$
$374$	−51.4303	−2.65940
$375$	11.7693	0.607766
$376$	87.1460	4.49421
$377$	−8.58248	−0.442020
$378$	27.6297	1.42112
$379$	25.3432	1.30179	0.650896	−	0.759167i	$-0.274394\pi$
$379$	25.3432	1.30179	0.650896	+	0.759167i	$0.274394\pi$
$380$	18.3804	0.942895
$381$	0.109401	0.00560480
$382$	−47.9263	−2.45212
$383$	−35.3646	−1.80705	−0.903524	−	0.428538i	$-0.859029\pi$
$383$	−35.3646	−1.80705	−0.903524	+	0.428538i	$0.859029\pi$
$384$	−15.1856	−0.774937
$385$	13.8430	0.705503
$386$	23.6360	1.20304
$387$	18.8600	0.958710
$388$	−36.2012	−1.83784
$389$	−15.9911	−0.810782	−0.405391	−	0.914143i	$-0.632865\pi$
$389$	−15.9911	−0.810782	−0.405391	+	0.914143i	$0.632865\pi$
$390$	−3.79325	−0.192078
$391$	−16.9001	−0.854675
$392$	25.5053	1.28821
$393$	−10.7316	−0.541337
$394$	12.2571	0.617506
$395$	−17.0788	−0.859329
$396$	49.6858	2.49681
$397$	−26.7581	−1.34295	−0.671474	−	0.741028i	$-0.734339\pi$
$397$	−26.7581	−1.34295	−0.671474	+	0.741028i	$0.734339\pi$
$398$	0.134121	0.00672289
$399$	−5.87396	−0.294066
$400$	−39.0189	−1.95095
$401$	−17.6923	−0.883510	−0.441755	−	0.897136i	$-0.645644\pi$
$401$	−17.6923	−0.883510	−0.441755	+	0.897136i	$0.645644\pi$
$402$	−14.6010	−0.728233
$403$	1.00000	0.0498135
$404$	19.8649	0.988314
$405$	0.234463	0.0116506
$406$	−45.3627	−2.25131
$407$	46.3437	2.29717
$408$	32.5982	1.61385
$409$	1.63969	0.0810776	0.0405388	−	0.999178i	$-0.487093\pi$
$409$	1.63969	0.0810776	0.0405388	+	0.999178i	$0.487093\pi$
$410$	24.8730	1.22839
$411$	16.0725	0.792799
$412$	−8.83166	−0.435105
$413$	4.21682	0.207496
$414$	22.7136	1.11631
$415$	6.48175	0.318177
$416$	15.1731	0.743920
$417$	13.4945	0.660827
$418$	−38.8197	−1.89873
$419$	1.59184	0.0777666	0.0388833	−	0.999244i	$-0.487620\pi$
$419$	1.59184	0.0777666	0.0388833	+	0.999244i	$0.487620\pi$
$420$	−14.4117	−0.703218
$421$	−10.8647	−0.529511	−0.264756	−	0.964316i	$-0.585291\pi$
$421$	−10.8647	−0.529511	−0.264756	+	0.964316i	$0.585291\pi$
$422$	−37.1175	−1.80685
$423$	19.1829	0.932704
$424$	−1.22210	−0.0593506
$425$	11.8753	0.576035
$426$	2.96350	0.143582
$427$	−13.8899	−0.672179
$428$	−23.6545	−1.14338
$429$	5.75871	0.278033
$430$	−36.1531	−1.74346
$431$	8.91085	0.429221	0.214610	−	0.976700i	$-0.431152\pi$
$431$	8.91085	0.429221	0.214610	+	0.976700i	$0.431152\pi$
$432$	−62.2837	−2.99663
$433$	−35.9932	−1.72972	−0.864860	−	0.502013i	$-0.832593\pi$
$433$	−35.9932	−1.72972	−0.864860	+	0.502013i	$0.832593\pi$
$434$	5.28551	0.253712
$435$	−12.2069	−0.585275
$436$	71.5282	3.42558
$437$	−12.7562	−0.610213
$438$	−15.0517	−0.719198
$439$	34.1386	1.62935	0.814673	−	0.579921i	$-0.196917\pi$
$439$	34.1386	1.62935	0.814673	+	0.579921i	$0.196917\pi$
$440$	−57.9863	−2.76439
$441$	5.61432	0.267349
$442$	−9.67100	−0.460003
$443$	−24.3537	−1.15708	−0.578540	−	0.815654i	$-0.696377\pi$
$443$	−24.3537	−1.15708	−0.578540	+	0.815654i	$0.696377\pi$
$444$	−48.2477	−2.28973
$445$	−2.33063	−0.110482
$446$	−39.7531	−1.88236
$447$	−13.7860	−0.652058
$448$	32.9711	1.55774
$449$	27.9402	1.31858	0.659291	−	0.751888i	$-0.270857\pi$
$449$	27.9402	1.31858	0.659291	+	0.751888i	$0.270857\pi$
$450$	−15.9602	−0.752373
$451$	−37.7609	−1.77809
$452$	−96.1854	−4.52418
$453$	−4.09080	−0.192203
$454$	−56.5120	−2.65224
$455$	2.60305	0.122033
$456$	24.6052	1.15224
$457$	3.34266	0.156363	0.0781815	−	0.996939i	$-0.475089\pi$
$457$	3.34266	0.156363	0.0781815	+	0.996939i	$0.475089\pi$
$458$	0.966867	0.0451787
$459$	18.9558	0.884781
$460$	−31.2972	−1.45924
$461$	−1.00183	−0.0466600	−0.0233300	−	0.999728i	$-0.507427\pi$
$461$	−1.00183	−0.0466600	−0.0233300	+	0.999728i	$0.507427\pi$
$462$	30.4377	1.41609
$463$	3.40632	0.158305	0.0791525	−	0.996863i	$-0.474779\pi$
$463$	3.40632	0.158305	0.0791525	+	0.996863i	$0.474779\pi$
$464$	102.258	4.74721
$465$	1.42230	0.0659577
$466$	−72.9719	−3.38036
$467$	7.52974	0.348435	0.174217	−	0.984707i	$-0.444260\pi$
$467$	7.52974	0.348435	0.174217	+	0.984707i	$0.444260\pi$
$468$	9.34297	0.431879
$469$	10.0197	0.462666
$470$	−36.7720	−1.69617
$471$	8.71531	0.401580
$472$	−17.6637	−0.813037
$473$	54.8858	2.52365
$474$	−37.5526	−1.72485
$475$	8.96347	0.411272
$476$	−36.7431	−1.68412
$477$	−0.269014	−0.0123173
$478$	−43.3854	−1.98440
$479$	23.9570	1.09462	0.547312	−	0.836929i	$-0.315651\pi$
$479$	23.9570	1.09462	0.547312	+	0.836929i	$0.315651\pi$
$480$	21.5807	0.985019
$481$	8.71453	0.397348
$482$	−70.1269	−3.19419
$483$	10.0019	0.455102
$484$	88.3535	4.01607
$485$	9.30000	0.422291
$486$	−41.3089	−1.87381
$487$	−16.6249	−0.753348	−0.376674	−	0.926346i	$-0.622932\pi$
$487$	−16.6249	−0.753348	−0.376674	+	0.926346i	$0.622932\pi$
$488$	58.1829	2.63381
$489$	−5.05491	−0.228591
$490$	−10.7622	−0.486186
$491$	−7.77589	−0.350921	−0.175461	−	0.984486i	$-0.556141\pi$
$491$	−7.77589	−0.350921	−0.175461	+	0.984486i	$0.556141\pi$
$492$	39.3122	1.77233
$493$	−31.1218	−1.40166
$494$	−7.29969	−0.328429
$495$	−12.7641	−0.573706
$496$	−11.9147	−0.534988
$497$	−2.03365	−0.0912216
$498$	14.2520	0.638646
$499$	1.57451	0.0704848	0.0352424	−	0.999379i	$-0.488780\pi$
$499$	1.57451	0.0704848	0.0352424	+	0.999379i	$0.488780\pi$
$500$	55.5685	2.48510
$501$	17.9160	0.800429
$502$	−6.49248	−0.289773
$503$	−41.7455	−1.86134	−0.930671	−	0.365858i	$-0.880776\pi$
$503$	−41.7455	−1.86134	−0.930671	+	0.365858i	$0.880776\pi$
$504$	30.0650	1.33920
$505$	−5.10323	−0.227091
$506$	66.1002	2.93851
$507$	1.08287	0.0480921
$508$	0.516535	0.0229176
$509$	−15.8120	−0.700854	−0.350427	−	0.936590i	$-0.613964\pi$
$509$	−15.8120	−0.700854	−0.350427	+	0.936590i	$0.613964\pi$
$510$	−13.7551	−0.609086
$511$	10.3290	0.456926
$512$	17.0407	0.753100
$513$	14.3079	0.631709
$514$	56.0651	2.47293
$515$	2.26883	0.0999765
$516$	−57.1407	−2.51548
$517$	55.8253	2.45520
$518$	46.0607	2.02379
$519$	−26.6541	−1.16998
$520$	−10.9038	−0.478164
$521$	14.9677	0.655745	0.327873	−	0.944722i	$-0.393668\pi$
$521$	14.9677	0.655745	0.327873	+	0.944722i	$0.393668\pi$
$522$	41.8275	1.83074
$523$	−11.5858	−0.506613	−0.253306	−	0.967386i	$-0.581518\pi$
$523$	−11.5858	−0.506613	−0.253306	+	0.967386i	$0.581518\pi$
$524$	−50.6688	−2.21348
$525$	−7.02807	−0.306730
$526$	−25.2374	−1.10040
$527$	3.62621	0.157960
$528$	−68.6135	−2.98602
$529$	−1.27934	−0.0556235
$530$	0.515677	0.0223996
$531$	−3.88819	−0.168733
$532$	−27.7337	−1.20241
$533$	−7.10060	−0.307561
$534$	−5.12454	−0.221761
$535$	6.07677	0.262722
$536$	−41.9711	−1.81288
$537$	−16.5129	−0.712584
$538$	77.2320	3.32971
$539$	16.3386	0.703753
$540$	35.1042	1.51064
$541$	−5.00197	−0.215052	−0.107526	−	0.994202i	$-0.534293\pi$
$541$	−5.00197	−0.215052	−0.107526	+	0.994202i	$0.534293\pi$
$542$	39.5705	1.69970
$543$	−14.2846	−0.613011
$544$	55.0206	2.35899
$545$	−18.3754	−0.787115
$546$	5.72354	0.244945
$547$	16.4897	0.705051	0.352525	−	0.935802i	$-0.385323\pi$
$547$	16.4897	0.705051	0.352525	+	0.935802i	$0.385323\pi$
$548$	75.8859	3.24169
$549$	12.8074	0.546607
$550$	−46.4469	−1.98050
$551$	−23.4908	−1.00074
$552$	−41.8965	−1.78323
$553$	25.7698	1.09584
$554$	−21.3836	−0.908503
$555$	12.3947	0.526126
$556$	63.7137	2.70206
$557$	−6.33270	−0.268325	−0.134162	−	0.990959i	$-0.542834\pi$
$557$	−6.33270	−0.268325	−0.134162	+	0.990959i	$0.542834\pi$
$558$	−4.87359	−0.206315
$559$	10.3208	0.436523
$560$	−31.0147	−1.31061
$561$	20.8823	0.881650
$562$	37.5812	1.58527
$563$	−6.49276	−0.273637	−0.136819	−	0.990596i	$-0.543688\pi$
$563$	−6.49276	−0.273637	−0.136819	+	0.990596i	$0.543688\pi$
$564$	−58.1188	−2.44724
$565$	24.7098	1.03955
$566$	−7.90686	−0.332350
$567$	−0.353776	−0.0148572
$568$	8.51867	0.357435
$569$	−5.76727	−0.241777	−0.120888	−	0.992666i	$-0.538574\pi$
$569$	−5.76727	−0.241777	−0.120888	+	0.992666i	$0.538574\pi$
$570$	−10.3824	−0.434870
$571$	−24.7021	−1.03375	−0.516875	−	0.856061i	$-0.672905\pi$
$571$	−24.7021	−1.03375	−0.516875	+	0.856061i	$0.672905\pi$
$572$	27.1896	1.13685
$573$	19.4595	0.812934
$574$	−37.5302	−1.56648
$575$	−15.2625	−0.636492
$576$	−30.4016	−1.26673
$577$	4.26377	0.177503	0.0887515	−	0.996054i	$-0.471712\pi$
$577$	4.26377	0.177503	0.0887515	+	0.996054i	$0.471712\pi$
$578$	10.2695	0.427155
$579$	−9.59695	−0.398836
$580$	−57.6344	−2.39314
$581$	−9.78016	−0.405749
$582$	20.4487	0.847625
$583$	−0.782873	−0.0324233
$584$	−43.2666	−1.79038
$585$	−2.40018	−0.0992354
$586$	88.3621	3.65021
$587$	12.2550	0.505819	0.252910	−	0.967490i	$-0.418612\pi$
$587$	12.2550	0.505819	0.252910	+	0.967490i	$0.418612\pi$
$588$	−17.0098	−0.701473
$589$	2.73707	0.112779
$590$	7.45334	0.306849
$591$	−4.97678	−0.204717
$592$	−103.831	−4.26744
$593$	−36.2164	−1.48723	−0.743616	−	0.668607i	$-0.766891\pi$
$593$	−36.2164	−1.48723	−0.743616	+	0.668607i	$0.766891\pi$
$594$	−74.1406	−3.04202
$595$	9.43919	0.386969
$596$	−65.0904	−2.66621
$597$	−0.0544573	−0.00222879
$598$	12.4295	0.508282
$599$	−21.6376	−0.884087	−0.442044	−	0.896994i	$-0.645746\pi$
$599$	−21.6376	−0.884087	−0.442044	+	0.896994i	$0.645746\pi$
$600$	29.4396	1.20187
$601$	26.9186	1.09803	0.549017	−	0.835811i	$-0.315002\pi$
$601$	26.9186	1.09803	0.549017	+	0.835811i	$0.315002\pi$
$602$	54.5506	2.22332
$603$	−9.23882	−0.376234
$604$	−19.3146	−0.785900
$605$	−22.6978	−0.922795
$606$	−11.2209	−0.455818
$607$	48.6745	1.97564	0.987819	−	0.155610i	$-0.0497343\pi$
$607$	48.6745	1.97564	0.987819	+	0.155610i	$0.0497343\pi$
$608$	41.5297	1.68425
$609$	18.4187	0.746362
$610$	−24.5507	−0.994031
$611$	10.4975	0.424682
$612$	33.8795	1.36950
$613$	−21.7213	−0.877314	−0.438657	−	0.898655i	$-0.644546\pi$
$613$	−21.7213	−0.877314	−0.438657	+	0.898655i	$0.644546\pi$
$614$	−25.5730	−1.03204
$615$	−10.0992	−0.407239
$616$	87.4941	3.52524
$617$	−23.4893	−0.945643	−0.472821	−	0.881158i	$-0.656764\pi$
$617$	−23.4893	−0.945643	−0.472821	+	0.881158i	$0.656764\pi$
$618$	4.98866	0.200673
$619$	−18.0246	−0.724469	−0.362235	−	0.932087i	$-0.617986\pi$
$619$	−18.0246	−0.724469	−0.362235	+	0.932087i	$0.617986\pi$
$620$	6.71536	0.269695
$621$	−24.3627	−0.977643
$622$	1.03467	0.0414863
$623$	3.51663	0.140891
$624$	−12.9022	−0.516500
$625$	2.09880	0.0839521
$626$	0.764523	0.0305565
$627$	15.7620	0.629473
$628$	41.1491	1.64203
$629$	31.6007	1.26000
$630$	−12.6862	−0.505430
$631$	−34.4992	−1.37339	−0.686696	−	0.726944i	$-0.740940\pi$
$631$	−34.4992	−1.37339	−0.686696	+	0.726944i	$0.740940\pi$
$632$	−107.946	−4.29387
$633$	15.0709	0.599013
$634$	2.53438	0.100653
$635$	−0.132697	−0.00526590
$636$	0.815036	0.0323183
$637$	3.07233	0.121730
$638$	121.725	4.81913
$639$	1.87516	0.0741802
$640$	18.4191	0.728079
$641$	15.2238	0.601306	0.300653	−	0.953734i	$-0.402795\pi$
$641$	15.2238	0.601306	0.300653	+	0.953734i	$0.402795\pi$
$642$	13.3615	0.527336
$643$	21.1491	0.834038	0.417019	−	0.908898i	$-0.363075\pi$
$643$	21.1491	0.834038	0.417019	+	0.908898i	$0.363075\pi$
$644$	47.2236	1.86087
$645$	14.6793	0.577996
$646$	−26.4702	−1.04146
$647$	−25.7186	−1.01110	−0.505552	−	0.862796i	$-0.668711\pi$
$647$	−25.7186	−1.01110	−0.505552	+	0.862796i	$0.668711\pi$
$648$	1.48192	0.0582153
$649$	−11.3153	−0.444163
$650$	−8.73392	−0.342573
$651$	−2.14608	−0.0841114
$652$	−23.8666	−0.934688
$653$	30.9296	1.21037	0.605184	−	0.796085i	$-0.293099\pi$
$653$	30.9296	1.21037	0.605184	+	0.796085i	$0.293099\pi$
$654$	−40.4035	−1.57990
$655$	13.0167	0.508604
$656$	84.6018	3.30314
$657$	−9.52399	−0.371566
$658$	55.4844	2.16301
$659$	26.0186	1.01354	0.506771	−	0.862081i	$-0.330839\pi$
$659$	26.0186	1.01354	0.506771	+	0.862081i	$0.330839\pi$
$660$	38.6718	1.50530
$661$	−14.1025	−0.548523	−0.274261	−	0.961655i	$-0.588433\pi$
$661$	−14.1025	−0.548523	−0.274261	+	0.961655i	$0.588433\pi$
$662$	39.3153	1.52803
$663$	3.92672	0.152501
$664$	40.9677	1.58986
$665$	7.12472	0.276285
$666$	−42.4710	−1.64572
$667$	39.9990	1.54877
$668$	84.5900	3.27289
$669$	16.1410	0.624046
$670$	17.7101	0.684199
$671$	37.2717	1.43886
$672$	−32.5625	−1.25613
$673$	−36.1410	−1.39313	−0.696567	−	0.717491i	$-0.745290\pi$
$673$	−36.1410	−1.39313	−0.696567	+	0.717491i	$0.745290\pi$
$674$	72.1093	2.77755
$675$	17.1191	0.658913
$676$	5.11275	0.196644
$677$	−29.5908	−1.13727	−0.568634	−	0.822591i	$-0.692528\pi$
$677$	−29.5908	−1.13727	−0.568634	+	0.822591i	$0.692528\pi$
$678$	54.3314	2.08658
$679$	−14.0325	−0.538520
$680$	−39.5395	−1.51627
$681$	22.9456	0.879278
$682$	−14.1829	−0.543093
$683$	−15.6128	−0.597407	−0.298703	−	0.954346i	$-0.596554\pi$
$683$	−15.6128	−0.597407	−0.298703	+	0.954346i	$0.596554\pi$
$684$	25.5724	0.977783
$685$	−19.4949	−0.744861
$686$	53.2373	2.03261
$687$	−0.392577	−0.0149778
$688$	−122.970	−4.68817
$689$	−0.147212	−0.00560834
$690$	17.6786	0.673012
$691$	−19.1914	−0.730074	−0.365037	−	0.930993i	$-0.618944\pi$
$691$	−19.1914	−0.730074	−0.365037	+	0.930993i	$0.618944\pi$
$692$	−125.846	−4.78396
$693$	19.2595	0.731608
$694$	−53.3565	−2.02538
$695$	−16.3679	−0.620869
$696$	−77.1532	−2.92448
$697$	−25.7482	−0.975284
$698$	−85.1972	−3.22476
$699$	29.6288	1.12067
$700$	−33.1828	−1.25419
$701$	−4.11061	−0.155256	−0.0776279	−	0.996982i	$-0.524735\pi$
$701$	−4.11061	−0.155256	−0.0776279	+	0.996982i	$0.524735\pi$
$702$	−13.9415	−0.526187
$703$	23.8523	0.899605
$704$	−88.4735	−3.33447
$705$	14.9306	0.562317
$706$	−42.2613	−1.59052
$707$	7.70014	0.289594
$708$	11.7801	0.442724
$709$	−17.9506	−0.674151	−0.337075	−	0.941478i	$-0.609438\pi$
$709$	−17.9506	−0.674151	−0.337075	+	0.941478i	$0.609438\pi$
$710$	−3.59452	−0.134900
$711$	−23.7615	−0.891126
$712$	−14.7307	−0.552055
$713$	−4.66054	−0.174539
$714$	20.7547	0.776726
$715$	−6.98492	−0.261221
$716$	−77.9652	−2.91370
$717$	17.6158	0.657874
$718$	97.8321	3.65106
$719$	−14.7874	−0.551477	−0.275738	−	0.961233i	$-0.588922\pi$
$719$	−14.7874	−0.551477	−0.275738	+	0.961233i	$0.588922\pi$
$720$	28.5976	1.06577
$721$	−3.42338	−0.127493
$722$	30.6927	1.14227
$723$	28.4737	1.05895
$724$	−67.4443	−2.50655
$725$	−28.1063	−1.04384
$726$	−49.9074	−1.85224
$727$	8.34854	0.309630	0.154815	−	0.987943i	$-0.450522\pi$
$727$	8.34854	0.309630	0.154815	+	0.987943i	$0.450522\pi$
$728$	16.4525	0.609770
$729$	17.3082	0.641044
$730$	18.2567	0.675710
$731$	37.4253	1.38423
$732$	−38.8029	−1.43420
$733$	−54.0183	−1.99521	−0.997606	−	0.0691500i	$-0.977971\pi$
$733$	−54.0183	−1.99521	−0.997606	+	0.0691500i	$0.977971\pi$
$734$	−57.6648	−2.12845
$735$	4.36978	0.161182
$736$	−70.7147	−2.60658
$737$	−26.8865	−0.990376
$738$	34.6054	1.27384
$739$	−24.6725	−0.907594	−0.453797	−	0.891105i	$-0.649931\pi$
$739$	−24.6725	−0.907594	−0.453797	+	0.891105i	$0.649931\pi$
$740$	58.5212	2.15128
$741$	2.96390	0.108882
$742$	−0.778092	−0.0285646
$743$	42.4437	1.55711	0.778555	−	0.627576i	$-0.215953\pi$
$743$	42.4437	1.55711	0.778555	+	0.627576i	$0.215953\pi$
$744$	8.98962	0.329576
$745$	16.7215	0.612630
$746$	57.6040	2.10903
$747$	9.01796	0.329950
$748$	98.5950	3.60499
$749$	−9.16909	−0.335031
$750$	−31.3885	−1.14615
$751$	3.74940	0.136817	0.0684087	−	0.997657i	$-0.478208\pi$
$751$	3.74940	0.136817	0.0684087	+	0.997657i	$0.478208\pi$
$752$	−125.074	−4.56100
$753$	2.63614	0.0960664
$754$	22.8892	0.833577
$755$	4.96187	0.180581
$756$	−52.9678	−1.92642
$757$	40.8022	1.48298	0.741490	−	0.670964i	$-0.234119\pi$
$757$	40.8022	1.48298	0.741490	+	0.670964i	$0.234119\pi$
$758$	−67.5896	−2.45496
$759$	−26.8387	−0.974183
$760$	−29.8445	−1.08257
$761$	−43.8190	−1.58844	−0.794218	−	0.607633i	$-0.792119\pi$
$761$	−43.8190	−1.58844	−0.794218	+	0.607633i	$0.792119\pi$
$762$	−0.291771	−0.0105697
$763$	27.7262	1.00375
$764$	91.8776	3.32401
$765$	−8.70356	−0.314678
$766$	94.3165	3.40779
$767$	−2.12773	−0.0768281
$768$	4.46883	0.161255
$769$	−31.2204	−1.12584	−0.562919	−	0.826512i	$-0.690322\pi$
$769$	−31.2204	−1.12584	−0.562919	+	0.826512i	$0.690322\pi$
$770$	−36.9189	−1.33046
$771$	−22.7642	−0.819831
$772$	−45.3117	−1.63080
$773$	−5.71285	−0.205477	−0.102739	−	0.994708i	$-0.532761\pi$
$773$	−5.71285	−0.205477	−0.102739	+	0.994708i	$0.532761\pi$
$774$	−50.2993	−1.80797
$775$	3.27484	0.117636
$776$	58.7804	2.11009
$777$	−18.7021	−0.670932
$778$	42.6479	1.52900
$779$	−19.4348	−0.696325
$780$	7.27189	0.260375
$781$	5.45702	0.195267
$782$	45.0721	1.61178
$783$	−44.8644	−1.60332
$784$	−36.6060	−1.30736
$785$	−10.5711	−0.377298
$786$	28.6209	1.02087
$787$	−26.0795	−0.929633	−0.464816	−	0.885407i	$-0.653880\pi$
$787$	−26.0795	−0.929633	−0.464816	+	0.885407i	$0.653880\pi$
$788$	−23.4977	−0.837071
$789$	10.2472	0.364809
$790$	45.5488	1.62055
$791$	−37.2840	−1.32566
$792$	−80.6754	−2.86667
$793$	7.00860	0.248883
$794$	71.3631	2.53258
$795$	−0.209381	−0.00742596
$796$	−0.257119	−0.00911332
$797$	3.42789	0.121422	0.0607111	−	0.998155i	$-0.480663\pi$
$797$	3.42789	0.121422	0.0607111	+	0.998155i	$0.480663\pi$
$798$	15.6657	0.554560
$799$	38.0659	1.34668
$800$	49.6893	1.75678
$801$	−3.24257	−0.114570
$802$	47.1848	1.66615
$803$	−27.7163	−0.978089
$804$	27.9911	0.987168
$805$	−12.1316	−0.427583
$806$	−2.66697	−0.0939402
$807$	−31.3585	−1.10387
$808$	−32.2548	−1.13472
$809$	32.3478	1.13729	0.568645	−	0.822583i	$-0.307468\pi$
$809$	32.3478	1.13729	0.568645	+	0.822583i	$0.307468\pi$
$810$	−0.625308	−0.0219711
$811$	−53.0802	−1.86390	−0.931950	−	0.362588i	$-0.881893\pi$
$811$	−53.0802	−1.86390	−0.931950	+	0.362588i	$0.881893\pi$
$812$	86.9631	3.05181
$813$	−16.0668	−0.563488
$814$	−123.598	−4.33209
$815$	6.13127	0.214769
$816$	−46.7859	−1.63783
$817$	28.2487	0.988297
$818$	−4.37302	−0.152899
$819$	3.62158	0.126548
$820$	−47.6831	−1.66516
$821$	29.3065	1.02280	0.511402	−	0.859342i	$-0.329126\pi$
$821$	29.3065	1.02280	0.511402	+	0.859342i	$0.329126\pi$
$822$	−42.8650	−1.49509
$823$	2.39223	0.0833880	0.0416940	−	0.999130i	$-0.486725\pi$
$823$	2.39223	0.0833880	0.0416940	+	0.999130i	$0.486725\pi$
$824$	14.3401	0.499560
$825$	18.8589	0.656581
$826$	−11.2462	−0.391304
$827$	7.02273	0.244204	0.122102	−	0.992518i	$-0.461036\pi$
$827$	7.02273	0.244204	0.122102	+	0.992518i	$0.461036\pi$
$828$	−43.5433	−1.51323
$829$	−7.00771	−0.243388	−0.121694	−	0.992568i	$-0.538833\pi$
$829$	−7.00771	−0.243388	−0.121694	+	0.992568i	$0.538833\pi$
$830$	−17.2867	−0.600029
$831$	8.68241	0.301189
$832$	−16.6367	−0.576772
$833$	11.1409	0.386009
$834$	−35.9894	−1.24621
$835$	−21.7309	−0.752030
$836$	74.4197	2.57386
$837$	5.22745	0.180687
$838$	−4.24541	−0.146655
$839$	10.1436	0.350194	0.175097	−	0.984551i	$-0.443976\pi$
$839$	10.1436	0.350194	0.175097	+	0.984551i	$0.443976\pi$
$840$	23.4004	0.807391
$841$	44.6589	1.53996
$842$	28.9758	0.998571
$843$	−15.2591	−0.525552
$844$	71.1566	2.44931
$845$	−1.31345	−0.0451841
$846$	−51.1603	−1.75893
$847$	34.2481	1.17678
$848$	1.75400	0.0602325
$849$	3.21043	0.110182
$850$	−31.6710	−1.08631
$851$	−40.6144	−1.39224
$852$	−5.68121	−0.194635
$853$	−12.7419	−0.436273	−0.218137	−	0.975918i	$-0.569998\pi$
$853$	−12.7419	−0.436273	−0.218137	+	0.975918i	$0.569998\pi$
$854$	37.0440	1.26762
$855$	−6.56947	−0.224671
$856$	38.4081	1.31276
$857$	−32.8928	−1.12360	−0.561799	−	0.827274i	$-0.689891\pi$
$857$	−32.8928	−1.12360	−0.561799	+	0.827274i	$0.689891\pi$
$858$	−15.3583	−0.524325
$859$	58.0786	1.98162	0.990809	−	0.135270i	$-0.0431903\pi$
$859$	58.0786	1.98162	0.990809	+	0.135270i	$0.0431903\pi$
$860$	69.3078	2.36338
$861$	15.2384	0.519324
$862$	−23.7650	−0.809439
$863$	9.91575	0.337536	0.168768	−	0.985656i	$-0.446021\pi$
$863$	9.91575	0.337536	0.168768	+	0.985656i	$0.446021\pi$
$864$	79.3163	2.69840
$865$	32.3296	1.09924
$866$	95.9928	3.26197
$867$	−4.16974	−0.141612
$868$	−10.1326	−0.343924
$869$	−69.1498	−2.34575
$870$	32.5554	1.10373
$871$	−5.05576	−0.171308
$872$	−116.141	−3.93303
$873$	12.9389	0.437917
$874$	34.0205	1.15076
$875$	21.5398	0.728178
$876$	28.8550	0.974921
$877$	4.14822	0.140076	0.0700378	−	0.997544i	$-0.477688\pi$
$877$	4.14822	0.140076	0.0700378	+	0.997544i	$0.477688\pi$
$878$	−91.0467	−3.07268
$879$	−35.8777	−1.21013
$880$	83.2236	2.80547
$881$	36.3291	1.22396	0.611979	−	0.790874i	$-0.290374\pi$
$881$	36.3291	1.22396	0.611979	+	0.790874i	$0.290374\pi$
$882$	−14.9733	−0.504176
$883$	−8.31898	−0.279956	−0.139978	−	0.990155i	$-0.544703\pi$
$883$	−8.31898	−0.279956	−0.139978	+	0.990155i	$0.544703\pi$
$884$	18.5399	0.623565
$885$	−3.02628	−0.101727
$886$	64.9507	2.18206
$887$	−23.0621	−0.774349	−0.387175	−	0.922006i	$-0.626549\pi$
$887$	−23.0621	−0.774349	−0.387175	+	0.922006i	$0.626549\pi$
$888$	78.3403	2.62893
$889$	0.200223	0.00671525
$890$	6.21573	0.208352
$891$	0.949310	0.0318031
$892$	76.2091	2.55167
$893$	28.7323	0.961488
$894$	36.7670	1.22967
$895$	20.0290	0.669497
$896$	−27.7921	−0.928470
$897$	−5.04678	−0.168507
$898$	−74.5159	−2.48663
$899$	−8.58248	−0.286242
$900$	30.5968	1.01989
$901$	−0.533822	−0.0177842
$902$	100.707	3.35319
$903$	−22.1492	−0.737080
$904$	156.177	5.19438
$905$	17.3263	0.575944
$906$	10.9101	0.362463
$907$	−42.3932	−1.40764	−0.703821	−	0.710377i	$-0.748524\pi$
$907$	−42.3932	−1.40764	−0.703821	+	0.710377i	$0.748524\pi$
$908$	108.337	3.59529
$909$	−7.10004	−0.235494
$910$	−6.94226	−0.230134
$911$	−21.7979	−0.722196	−0.361098	−	0.932528i	$-0.617598\pi$
$911$	−21.7979	−0.722196	−0.361098	+	0.932528i	$0.617598\pi$
$912$	−35.3141	−1.16937
$913$	26.2437	0.868540
$914$	−8.91478	−0.294875
$915$	9.96835	0.329544
$916$	−1.85354	−0.0612428
$917$	−19.6406	−0.648588
$918$	−50.5547	−1.66855
$919$	−8.76900	−0.289263	−0.144631	−	0.989486i	$-0.546200\pi$
$919$	−8.76900	−0.289263	−0.144631	+	0.989486i	$0.546200\pi$
$920$	50.8177	1.67541
$921$	10.3834	0.342145
$922$	2.67186	0.0879930
$923$	1.02614	0.0337759
$924$	−58.3509	−1.91960
$925$	28.5387	0.938347
$926$	−9.08456	−0.298537
$927$	3.15658	0.103676
$928$	−130.222	−4.27476
$929$	6.04954	0.198479	0.0992395	−	0.995064i	$-0.468359\pi$
$929$	6.04954	0.198479	0.0992395	+	0.995064i	$0.468359\pi$
$930$	−3.79325	−0.124385
$931$	8.40917	0.275599
$932$	139.892	4.58230
$933$	−0.420106	−0.0137536
$934$	−20.0816	−0.657091
$935$	−25.3288	−0.828340
$936$	−15.1703	−0.495856
$937$	−21.5172	−0.702937	−0.351469	−	0.936200i	$-0.614318\pi$
$937$	−21.5172	−0.702937	−0.351469	+	0.936200i	$0.614318\pi$
$938$	−26.7223	−0.872513
$939$	−0.310420	−0.0101302
$940$	70.4942	2.29927
$941$	−46.2548	−1.50786	−0.753932	−	0.656953i	$-0.771845\pi$
$941$	−46.2548	−1.50786	−0.753932	+	0.656953i	$0.771845\pi$
$942$	−23.2435	−0.757315
$943$	33.0926	1.07764
$944$	25.3514	0.825118
$945$	13.6073	0.442645
$946$	−146.379	−4.75919
$947$	41.7901	1.35800	0.678998	−	0.734140i	$-0.262414\pi$
$947$	41.7901	1.35800	0.678998	+	0.734140i	$0.262414\pi$
$948$	71.9907	2.33815
$949$	−5.21181	−0.169183
$950$	−23.9053	−0.775592
$951$	−1.02904	−0.0333688
$952$	59.6601	1.93360
$953$	40.0591	1.29764	0.648821	−	0.760941i	$-0.275262\pi$
$953$	40.0591	1.29764	0.648821	+	0.760941i	$0.275262\pi$
$954$	0.717452	0.0232284
$955$	−23.6031	−0.763778
$956$	83.1724	2.68999
$957$	−49.4240	−1.59765
$958$	−63.8928	−2.06428
$959$	29.4153	0.949871
$960$	−23.6624	−0.763699
$961$	1.00000	0.0322581
$962$	−23.2414	−0.749333
$963$	8.45452	0.272443
$964$	134.438	4.32994
$965$	11.6405	0.374719
$966$	−26.6748	−0.858247
$967$	4.35689	0.140108	0.0700540	−	0.997543i	$-0.477683\pi$
$967$	4.35689	0.140108	0.0700540	+	0.997543i	$0.477683\pi$
$968$	−143.460	−4.61099
$969$	10.7477	0.345266
$970$	−24.8029	−0.796372
$971$	40.2587	1.29196	0.645981	−	0.763353i	$-0.276448\pi$
$971$	40.2587	1.29196	0.645981	+	0.763353i	$0.276448\pi$
$972$	79.1916	2.54007
$973$	24.6971	0.791752
$974$	44.3383	1.42069
$975$	3.54624	0.113571
$976$	−83.5057	−2.67295
$977$	11.1746	0.357507	0.178754	−	0.983894i	$-0.442793\pi$
$977$	11.1746	0.357507	0.178754	+	0.983894i	$0.442793\pi$
$978$	13.4813	0.431085
$979$	−9.43639	−0.301588
$980$	20.6318	0.659058
$981$	−25.5654	−0.816240
$982$	20.7381	0.661779
$983$	1.59560	0.0508917	0.0254459	−	0.999676i	$-0.491899\pi$
$983$	1.59560	0.0508917	0.0254459	+	0.999676i	$0.491899\pi$
$984$	−63.8317	−2.03488
$985$	6.03650	0.192339
$986$	83.0011	2.64329
$987$	−22.5284	−0.717085
$988$	13.9940	0.445207
$989$	−48.1005	−1.52951
$990$	34.0417	1.08191
$991$	−58.8280	−1.86873	−0.934366	−	0.356314i	$-0.884033\pi$
$991$	−58.8280	−1.86873	−0.934366	+	0.356314i	$0.884033\pi$
$992$	15.1731	0.481745
$993$	−15.9632	−0.506578
$994$	5.42369	0.172029
$995$	0.0660531	0.00209402
$996$	−27.3219	−0.865727
$997$	−17.9414	−0.568209	−0.284105	−	0.958793i	$-0.591696\pi$
$997$	−17.9414	−0.568209	−0.284105	+	0.958793i	$0.591696\pi$
$998$	−4.19918	−0.132923
$999$	45.5547	1.44129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.d.1.1	✓	8
3.2	odd	2		3627.2.a.q.1.8		8
4.3	odd	2		6448.2.a.bf.1.3		8
13.12	even	2		5239.2.a.j.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.d.1.1	✓	8	1.1	even	1	trivial
3627.2.a.q.1.8		8	3.2	odd	2
5239.2.a.j.1.8		8	13.12	even	2
6448.2.a.bf.1.3		8	4.3	odd	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66697 q^{2} +1.08287 q^{3} +5.11275 q^{4} -1.31345 q^{5} -2.88800 q^{6} +1.98184 q^{7} -8.30164 q^{8} -1.82738 q^{9} +O(q^{10})\)	\(q-2.66697 q^{2} +1.08287 q^{3} +5.11275 q^{4} -1.31345 q^{5} -2.88800 q^{6} +1.98184 q^{7} -8.30164 q^{8} -1.82738 q^{9} +3.50294 q^{10} -5.31799 q^{11} +5.53647 q^{12} -1.00000 q^{13} -5.28551 q^{14} -1.42230 q^{15} +11.9147 q^{16} -3.62621 q^{17} +4.87359 q^{18} -2.73707 q^{19} -6.71536 q^{20} +2.14608 q^{21} +14.1829 q^{22} +4.66054 q^{23} -8.98962 q^{24} -3.27484 q^{25} +2.66697 q^{26} -5.22745 q^{27} +10.1326 q^{28} +8.58248 q^{29} +3.79325 q^{30} -1.00000 q^{31} -15.1731 q^{32} -5.75871 q^{33} +9.67100 q^{34} -2.60305 q^{35} -9.34297 q^{36} -8.71453 q^{37} +7.29969 q^{38} -1.08287 q^{39} +10.9038 q^{40} +7.10060 q^{41} -5.72354 q^{42} -10.3208 q^{43} -27.1896 q^{44} +2.40018 q^{45} -12.4295 q^{46} -10.4975 q^{47} +12.9022 q^{48} -3.07233 q^{49} +8.73392 q^{50} -3.92672 q^{51} -5.11275 q^{52} +0.147212 q^{53} +13.9415 q^{54} +6.98492 q^{55} -16.4525 q^{56} -2.96390 q^{57} -22.8892 q^{58} +2.12773 q^{59} -7.27189 q^{60} -7.00860 q^{61} +2.66697 q^{62} -3.62158 q^{63} +16.6367 q^{64} +1.31345 q^{65} +15.3583 q^{66} +5.05576 q^{67} -18.5399 q^{68} +5.04678 q^{69} +6.94226 q^{70} -1.02614 q^{71} +15.1703 q^{72} +5.21181 q^{73} +23.2414 q^{74} -3.54624 q^{75} -13.9940 q^{76} -10.5394 q^{77} +2.88800 q^{78} +13.0030 q^{79} -15.6495 q^{80} -0.178509 q^{81} -18.9371 q^{82} -4.93490 q^{83} +10.9724 q^{84} +4.76285 q^{85} +27.5253 q^{86} +9.29374 q^{87} +44.1480 q^{88} +1.77443 q^{89} -6.40123 q^{90} -1.98184 q^{91} +23.8282 q^{92} -1.08287 q^{93} +27.9964 q^{94} +3.59501 q^{95} -16.4305 q^{96} -7.08058 q^{97} +8.19381 q^{98} +9.71801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9	\( 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9} + 9 q^{10} - 5 q^{11} - 9 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 3 q^{16} - 11 q^{17} - 30 q^{18} - 9 q^{19} - 31 q^{20} - 16 q^{21} - 2 q^{22} + 13 q^{24} + 19 q^{25} + 5 q^{26} - 9 q^{27} + 16 q^{28} - 12 q^{29} - 7 q^{30} - 8 q^{31} - 25 q^{32} - 14 q^{33} + 22 q^{34} + 7 q^{35} + 37 q^{36} - 9 q^{37} - 9 q^{38} + 3 q^{39} + 55 q^{40} - 25 q^{41} - 3 q^{42} + 7 q^{43} - 26 q^{44} - 45 q^{45} + 5 q^{46} - 17 q^{47} - 9 q^{48} - 11 q^{50} - 10 q^{51} - 9 q^{52} - 15 q^{53} + 54 q^{54} + 7 q^{55} - 14 q^{56} - 7 q^{57} - 5 q^{58} - 15 q^{59} + 61 q^{60} + 11 q^{61} + 5 q^{62} - 21 q^{63} + 47 q^{64} + 15 q^{65} + 83 q^{66} + 18 q^{67} - 16 q^{68} - 15 q^{69} - 24 q^{70} - 7 q^{71} - 21 q^{72} + 24 q^{73} + 48 q^{74} - 17 q^{75} - 3 q^{76} - 49 q^{77} + 33 q^{79} - 16 q^{80} + 20 q^{81} - q^{82} - 13 q^{83} - 6 q^{84} + q^{85} + 19 q^{86} + 18 q^{87} + 37 q^{88} - 23 q^{89} + 117 q^{90} + 4 q^{91} + 22 q^{92} + 3 q^{93} + 10 q^{94} + 43 q^{95} + 46 q^{96} - 17 q^{97} + 52 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9 + 9 * q^10 - 5 * q^11 - 9 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 3 * q^16 - 11 * q^17 - 30 * q^18 - 9 * q^19 - 31 * q^20 - 16 * q^21 - 2 * q^22 + 13 * q^24 + 19 * q^25 + 5 * q^26 - 9 * q^27 + 16 * q^28 - 12 * q^29 - 7 * q^30 - 8 * q^31 - 25 * q^32 - 14 * q^33 + 22 * q^34 + 7 * q^35 + 37 * q^36 - 9 * q^37 - 9 * q^38 + 3 * q^39 + 55 * q^40 - 25 * q^41 - 3 * q^42 + 7 * q^43 - 26 * q^44 - 45 * q^45 + 5 * q^46 - 17 * q^47 - 9 * q^48 - 11 * q^50 - 10 * q^51 - 9 * q^52 - 15 * q^53 + 54 * q^54 + 7 * q^55 - 14 * q^56 - 7 * q^57 - 5 * q^58 - 15 * q^59 + 61 * q^60 + 11 * q^61 + 5 * q^62 - 21 * q^63 + 47 * q^64 + 15 * q^65 + 83 * q^66 + 18 * q^67 - 16 * q^68 - 15 * q^69 - 24 * q^70 - 7 * q^71 - 21 * q^72 + 24 * q^73 + 48 * q^74 - 17 * q^75 - 3 * q^76 - 49 * q^77 + 33 * q^79 - 16 * q^80 + 20 * q^81 - q^82 - 13 * q^83 - 6 * q^84 + q^85 + 19 * q^86 + 18 * q^87 + 37 * q^88 - 23 * q^89 + 117 * q^90 + 4 * q^91 + 22 * q^92 + 3 * q^93 + 10 * q^94 + 43 * q^95 + 46 * q^96 - 17 * q^97 + 52 * q^98 + 51 * q^99

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