LMFDB - Embedded newform 401.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [401,2,Mod(1,401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(401, 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("401.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	401.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:	$3.20200112105$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 10 x^{10} + 34 x^{9} + 29 x^{8} - 129 x^{7} - 24 x^{6} + 203 x^{5} + x^{4} + \cdots + 4 $ x^12 - 3x^11 - 10x^10 + 34x^9 + 29x^8 - 129x^7 - 24x^6 + 203x^5 + x^4 - 130x^3 - 5x^2 + 22x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.960737$ of defining polynomial
Character	$\chi$	$=$	401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.960737 q^{2} +0.489694 q^{3} -1.07698 q^{4} -2.30095 q^{5} +0.470467 q^{6} -1.58751 q^{7} -2.95617 q^{8} -2.76020 q^{9} +O(q^{10})$	\(q+0.960737 q^{2} +0.489694 q^{3} -1.07698 q^{4} -2.30095 q^{5} +0.470467 q^{6} -1.58751 q^{7} -2.95617 q^{8} -2.76020 q^{9} -2.21061 q^{10} +2.94152 q^{11} -0.527393 q^{12} -5.02718 q^{13} -1.52518 q^{14} -1.12676 q^{15} -0.686134 q^{16} -3.58101 q^{17} -2.65183 q^{18} +5.75262 q^{19} +2.47809 q^{20} -0.777395 q^{21} +2.82603 q^{22} +3.36707 q^{23} -1.44762 q^{24} +0.294374 q^{25} -4.82979 q^{26} -2.82074 q^{27} +1.70973 q^{28} -7.15973 q^{29} -1.08252 q^{30} -1.42042 q^{31} +5.25315 q^{32} +1.44045 q^{33} -3.44041 q^{34} +3.65279 q^{35} +2.97269 q^{36} +6.40924 q^{37} +5.52675 q^{38} -2.46178 q^{39} +6.80201 q^{40} -1.19594 q^{41} -0.746872 q^{42} -1.94482 q^{43} -3.16797 q^{44} +6.35108 q^{45} +3.23487 q^{46} +5.94149 q^{47} -0.335996 q^{48} -4.47981 q^{49} +0.282816 q^{50} -1.75360 q^{51} +5.41419 q^{52} -1.07288 q^{53} -2.70999 q^{54} -6.76829 q^{55} +4.69296 q^{56} +2.81703 q^{57} -6.87861 q^{58} -6.19836 q^{59} +1.21351 q^{60} -13.9130 q^{61} -1.36465 q^{62} +4.38185 q^{63} +6.41916 q^{64} +11.5673 q^{65} +1.38389 q^{66} -1.56417 q^{67} +3.85669 q^{68} +1.64883 q^{69} +3.50937 q^{70} +9.66100 q^{71} +8.15963 q^{72} +9.05717 q^{73} +6.15760 q^{74} +0.144153 q^{75} -6.19549 q^{76} -4.66970 q^{77} -2.36512 q^{78} -13.6215 q^{79} +1.57876 q^{80} +6.89930 q^{81} -1.14898 q^{82} -3.65864 q^{83} +0.837243 q^{84} +8.23973 q^{85} -1.86846 q^{86} -3.50608 q^{87} -8.69564 q^{88} -8.53659 q^{89} +6.10172 q^{90} +7.98070 q^{91} -3.62628 q^{92} -0.695573 q^{93} +5.70821 q^{94} -13.2365 q^{95} +2.57244 q^{96} +12.2595 q^{97} -4.30392 q^{98} -8.11918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9} - 11 q^{10} - 11 q^{11} - 9 q^{12} - 11 q^{13} - 3 q^{14} - 11 q^{15} - 9 q^{16} + q^{17} - q^{18} - 34 q^{19} - 5 q^{20} - 3 q^{21} + 3 q^{22} - 7 q^{23} - 9 q^{24} + 7 q^{25} + 6 q^{26} - 2 q^{27} - 23 q^{28} - 6 q^{29} + 23 q^{30} - 52 q^{31} + 11 q^{32} + 4 q^{33} - 5 q^{34} + 12 q^{35} + 16 q^{36} + 3 q^{37} + 25 q^{38} - 24 q^{39} - 25 q^{40} - 16 q^{41} + 47 q^{42} - 2 q^{43} - 2 q^{44} - 23 q^{45} - 16 q^{46} - 3 q^{47} + 24 q^{48} + 6 q^{49} + 27 q^{50} - 16 q^{51} - 5 q^{52} + 19 q^{53} + 5 q^{54} - 43 q^{55} + 7 q^{56} + 11 q^{57} + 11 q^{58} - q^{59} + 30 q^{60} - 24 q^{61} + 39 q^{62} - 11 q^{63} - q^{64} + 13 q^{65} + 14 q^{66} + 6 q^{67} + 32 q^{68} + 29 q^{69} + 47 q^{70} - 15 q^{71} + 32 q^{72} - 20 q^{73} + 25 q^{74} + 31 q^{75} - 42 q^{76} + 38 q^{77} + 52 q^{78} - 53 q^{79} + 23 q^{80} - 8 q^{81} + 4 q^{82} + 17 q^{83} + 35 q^{84} + 7 q^{85} + 28 q^{86} - 5 q^{87} + 38 q^{88} - q^{89} + 58 q^{90} - 6 q^{91} + 46 q^{92} + 44 q^{93} - 4 q^{94} + 34 q^{95} + 28 q^{96} + 12 q^{97} + 27 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9 - 11 * q^10 - 11 * q^11 - 9 * q^12 - 11 * q^13 - 3 * q^14 - 11 * q^15 - 9 * q^16 + q^17 - q^18 - 34 * q^19 - 5 * q^20 - 3 * q^21 + 3 * q^22 - 7 * q^23 - 9 * q^24 + 7 * q^25 + 6 * q^26 - 2 * q^27 - 23 * q^28 - 6 * q^29 + 23 * q^30 - 52 * q^31 + 11 * q^32 + 4 * q^33 - 5 * q^34 + 12 * q^35 + 16 * q^36 + 3 * q^37 + 25 * q^38 - 24 * q^39 - 25 * q^40 - 16 * q^41 + 47 * q^42 - 2 * q^43 - 2 * q^44 - 23 * q^45 - 16 * q^46 - 3 * q^47 + 24 * q^48 + 6 * q^49 + 27 * q^50 - 16 * q^51 - 5 * q^52 + 19 * q^53 + 5 * q^54 - 43 * q^55 + 7 * q^56 + 11 * q^57 + 11 * q^58 - q^59 + 30 * q^60 - 24 * q^61 + 39 * q^62 - 11 * q^63 - q^64 + 13 * q^65 + 14 * q^66 + 6 * q^67 + 32 * q^68 + 29 * q^69 + 47 * q^70 - 15 * q^71 + 32 * q^72 - 20 * q^73 + 25 * q^74 + 31 * q^75 - 42 * q^76 + 38 * q^77 + 52 * q^78 - 53 * q^79 + 23 * q^80 - 8 * q^81 + 4 * q^82 + 17 * q^83 + 35 * q^84 + 7 * q^85 + 28 * q^86 - 5 * q^87 + 38 * q^88 - q^89 + 58 * q^90 - 6 * q^91 + 46 * q^92 + 44 * q^93 - 4 * q^94 + 34 * q^95 + 28 * q^96 + 12 * q^97 + 27 * q^98

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 $

$2$	0.960737	0.679343	0.339672	−	0.940544i	$-0.389684\pi$
$2$	0.960737	0.679343	0.339672	+	0.940544i	$0.389684\pi$
$3$	0.489694	0.282725	0.141363	−	0.989958i	$-0.454852\pi$
$3$	0.489694	0.282725	0.141363	+	0.989958i	$0.454852\pi$
$4$	−1.07698	−0.538492
$5$	−2.30095	−1.02902	−0.514508	−	0.857485i	$-0.672025\pi$
$5$	−2.30095	−1.02902	−0.514508	+	0.857485i	$0.672025\pi$
$6$	0.470467	0.192068
$7$	−1.58751	−0.600023	−0.300012	−	0.953936i	$-0.596991\pi$
$7$	−1.58751	−0.600023	−0.300012	+	0.953936i	$0.596991\pi$
$8$	−2.95617	−1.04516
$9$	−2.76020	−0.920066
$10$	−2.21061	−0.699056
$11$	2.94152	0.886902	0.443451	−	0.896299i	$-0.353754\pi$
$11$	2.94152	0.886902	0.443451	+	0.896299i	$0.353754\pi$
$12$	−0.527393	−0.152245
$13$	−5.02718	−1.39429	−0.697144	−	0.716931i	$-0.745546\pi$
$13$	−5.02718	−1.39429	−0.697144	+	0.716931i	$0.745546\pi$
$14$	−1.52518	−0.407622
$15$	−1.12676	−0.290929
$16$	−0.686134	−0.171534
$17$	−3.58101	−0.868523	−0.434261	−	0.900787i	$-0.642991\pi$
$17$	−3.58101	−0.868523	−0.434261	+	0.900787i	$0.642991\pi$
$18$	−2.65183	−0.625041
$19$	5.75262	1.31974	0.659871	−	0.751379i	$-0.270611\pi$
$19$	5.75262	1.31974	0.659871	+	0.751379i	$0.270611\pi$
$20$	2.47809	0.554118
$21$	−0.777395	−0.169642
$22$	2.82603	0.602511
$23$	3.36707	0.702082	0.351041	−	0.936360i	$-0.385828\pi$
$23$	3.36707	0.702082	0.351041	+	0.936360i	$0.385828\pi$
$24$	−1.44762	−0.295494
$25$	0.294374	0.0588748
$26$	−4.82979	−0.947200
$27$	−2.82074	−0.542851
$28$	1.70973	0.323108
$29$	−7.15973	−1.32953	−0.664764	−	0.747053i	$-0.731468\pi$
$29$	−7.15973	−1.32953	−0.664764	+	0.747053i	$0.731468\pi$
$30$	−1.08252	−0.197641
$31$	−1.42042	−0.255116	−0.127558	−	0.991831i	$-0.540714\pi$
$31$	−1.42042	−0.255116	−0.127558	+	0.991831i	$0.540714\pi$
$32$	5.25315	0.928635
$33$	1.44045	0.250749
$34$	−3.44041	−0.590025
$35$	3.65279	0.617434
$36$	2.97269	0.495449
$37$	6.40924	1.05367	0.526837	−	0.849967i	$-0.323378\pi$
$37$	6.40924	1.05367	0.526837	+	0.849967i	$0.323378\pi$
$38$	5.52675	0.896558
$39$	−2.46178	−0.394200
$40$	6.80201	1.07549
$41$	−1.19594	−0.186774	−0.0933870	−	0.995630i	$-0.529769\pi$
$41$	−1.19594	−0.186774	−0.0933870	+	0.995630i	$0.529769\pi$
$42$	−0.746872	−0.115245
$43$	−1.94482	−0.296583	−0.148291	−	0.988944i	$-0.547377\pi$
$43$	−1.94482	−0.296583	−0.148291	+	0.988944i	$0.547377\pi$
$44$	−3.16797	−0.477590
$45$	6.35108	0.946764
$46$	3.23487	0.476955
$47$	5.94149	0.866656	0.433328	−	0.901236i	$-0.357339\pi$
$47$	5.94149	0.866656	0.433328	+	0.901236i	$0.357339\pi$
$48$	−0.335996	−0.0484968
$49$	−4.47981	−0.639972
$50$	0.282816	0.0399962
$51$	−1.75360	−0.245553
$52$	5.41419	0.750813
$53$	−1.07288	−0.147372	−0.0736858	−	0.997282i	$-0.523476\pi$
$53$	−1.07288	−0.147372	−0.0736858	+	0.997282i	$0.523476\pi$
$54$	−2.70999	−0.368782
$55$	−6.76829	−0.912636
$56$	4.69296	0.627123
$57$	2.81703	0.373124
$58$	−6.87861	−0.903206
$59$	−6.19836	−0.806958	−0.403479	−	0.914989i	$-0.632199\pi$
$59$	−6.19836	−0.806958	−0.403479	+	0.914989i	$0.632199\pi$
$60$	1.21351	0.156663
$61$	−13.9130	−1.78137	−0.890686	−	0.454620i	$-0.849775\pi$
$61$	−13.9130	−1.78137	−0.890686	+	0.454620i	$0.849775\pi$
$62$	−1.36465	−0.173311
$63$	4.38185	0.552061
$64$	6.41916	0.802395
$65$	11.5673	1.43475
$66$	1.38389	0.170345
$67$	−1.56417	−0.191093	−0.0955467	−	0.995425i	$-0.530460\pi$
$67$	−1.56417	−0.191093	−0.0955467	+	0.995425i	$0.530460\pi$
$68$	3.85669	0.467693
$69$	1.64883	0.198496
$70$	3.50937	0.419449
$71$	9.66100	1.14655	0.573275	−	0.819363i	$-0.305673\pi$
$71$	9.66100	1.14655	0.573275	+	0.819363i	$0.305673\pi$
$72$	8.15963	0.961621
$73$	9.05717	1.06006	0.530031	−	0.847978i	$-0.322180\pi$
$73$	9.05717	1.06006	0.530031	+	0.847978i	$0.322180\pi$
$74$	6.15760	0.715806
$75$	0.144153	0.0166454
$76$	−6.19549	−0.710671
$77$	−4.66970	−0.532161
$78$	−2.36512	−0.267797
$79$	−13.6215	−1.53254	−0.766270	−	0.642518i	$-0.777890\pi$
$79$	−13.6215	−1.53254	−0.766270	+	0.642518i	$0.777890\pi$
$80$	1.57876	0.176511
$81$	6.89930	0.766589
$82$	−1.14898	−0.126884
$83$	−3.65864	−0.401588	−0.200794	−	0.979633i	$-0.564352\pi$
$83$	−3.65864	−0.401588	−0.200794	+	0.979633i	$0.564352\pi$
$84$	0.837243	0.0913507
$85$	8.23973	0.893724
$86$	−1.86846	−0.201482
$87$	−3.50608	−0.375891
$88$	−8.69564	−0.926958
$89$	−8.53659	−0.904877	−0.452438	−	0.891796i	$-0.649446\pi$
$89$	−8.53659	−0.904877	−0.452438	+	0.891796i	$0.649446\pi$
$90$	6.10172	0.643178
$91$	7.98070	0.836605
$92$	−3.62628	−0.378066
$93$	−0.695573	−0.0721276
$94$	5.70821	0.588757
$95$	−13.2365	−1.35804
$96$	2.57244	0.262548
$97$	12.2595	1.24476	0.622380	−	0.782715i	$-0.286166\pi$
$97$	12.2595	1.24476	0.622380	+	0.782715i	$0.286166\pi$
$98$	−4.30392	−0.434761
$99$	−8.11918	−0.816008
$100$	−0.317037	−0.0317037
$101$	−3.86852	−0.384932	−0.192466	−	0.981304i	$-0.561649\pi$
$101$	−3.86852	−0.384932	−0.192466	+	0.981304i	$0.561649\pi$
$102$	−1.68475	−0.166815
$103$	−17.4846	−1.72281	−0.861406	−	0.507918i	$-0.830415\pi$
$103$	−17.4846	−1.72281	−0.861406	+	0.507918i	$0.830415\pi$
$104$	14.8612	1.45726
$105$	1.78875	0.174564
$106$	−1.03076	−0.100116
$107$	6.45778	0.624297	0.312148	−	0.950033i	$-0.398951\pi$
$107$	6.45778	0.624297	0.312148	+	0.950033i	$0.398951\pi$
$108$	3.03789	0.292321
$109$	−15.9048	−1.52341	−0.761703	−	0.647926i	$-0.775637\pi$
$109$	−15.9048	−1.52341	−0.761703	+	0.647926i	$0.775637\pi$
$110$	−6.50255	−0.619994
$111$	3.13857	0.297900
$112$	1.08925	0.102924
$113$	6.66267	0.626771	0.313386	−	0.949626i	$-0.398537\pi$
$113$	6.66267	0.626771	0.313386	+	0.949626i	$0.398537\pi$
$114$	2.70642	0.253480
$115$	−7.74746	−0.722454
$116$	7.71092	0.715941
$117$	13.8760	1.28284
$118$	−5.95499	−0.548202
$119$	5.68490	0.521133
$120$	3.33090	0.304069
$121$	−2.34746	−0.213406
$122$	−13.3667	−1.21016
$123$	−0.585644	−0.0528057
$124$	1.52977	0.137378
$125$	10.8274	0.968433
$126$	4.20980	0.375039
$127$	−1.80527	−0.160192	−0.0800959	−	0.996787i	$-0.525523\pi$
$127$	−1.80527	−0.160192	−0.0800959	+	0.996787i	$0.525523\pi$
$128$	−4.33918	−0.383533
$129$	−0.952369	−0.0838514
$130$	11.1131	0.974685
$131$	8.92883	0.780116	0.390058	−	0.920790i	$-0.372455\pi$
$131$	8.92883	0.780116	0.390058	+	0.920790i	$0.372455\pi$
$132$	−1.55134	−0.135027
$133$	−9.13235	−0.791875
$134$	−1.50275	−0.129818
$135$	6.49038	0.558603
$136$	10.5861	0.907749
$137$	−1.60563	−0.137178	−0.0685890	−	0.997645i	$-0.521850\pi$
$137$	−1.60563	−0.137178	−0.0685890	+	0.997645i	$0.521850\pi$
$138$	1.58410	0.134847
$139$	1.63217	0.138439	0.0692194	−	0.997601i	$-0.477949\pi$
$139$	1.63217	0.138439	0.0692194	+	0.997601i	$0.477949\pi$
$140$	−3.93400	−0.332483
$141$	2.90951	0.245025
$142$	9.28167	0.778901
$143$	−14.7875	−1.23660
$144$	1.89387	0.157822
$145$	16.4742	1.36811
$146$	8.70156	0.720146
$147$	−2.19374	−0.180936
$148$	−6.90266	−0.567395
$149$	−1.03527	−0.0848126	−0.0424063	−	0.999100i	$-0.513502\pi$
$149$	−1.03527	−0.0848126	−0.0424063	+	0.999100i	$0.513502\pi$
$150$	0.138493	0.0113079
$151$	11.7652	0.957442	0.478721	−	0.877967i	$-0.341101\pi$
$151$	11.7652	0.957442	0.478721	+	0.877967i	$0.341101\pi$
$152$	−17.0057	−1.37935
$153$	9.88430	0.799098
$154$	−4.48635	−0.361520
$155$	3.26833	0.262518
$156$	2.65130	0.212274
$157$	−4.45816	−0.355800	−0.177900	−	0.984049i	$-0.556930\pi$
$157$	−4.45816	−0.355800	−0.177900	+	0.984049i	$0.556930\pi$
$158$	−13.0867	−1.04112
$159$	−0.525384	−0.0416657
$160$	−12.0872	−0.955580
$161$	−5.34526	−0.421266
$162$	6.62841	0.520777
$163$	16.8560	1.32027	0.660133	−	0.751149i	$-0.270500\pi$
$163$	16.8560	1.32027	0.660133	+	0.751149i	$0.270500\pi$
$164$	1.28801	0.100576
$165$	−3.31439	−0.258025
$166$	−3.51499	−0.272816
$167$	−10.0760	−0.779704	−0.389852	−	0.920878i	$-0.627474\pi$
$167$	−10.0760	−0.779704	−0.389852	+	0.920878i	$0.627474\pi$
$168$	2.29812	0.177303
$169$	12.2725	0.944038
$170$	7.91621	0.607146
$171$	−15.8784	−1.21425
$172$	2.09454	0.159708
$173$	−11.4071	−0.867267	−0.433633	−	0.901089i	$-0.642769\pi$
$173$	−11.4071	−0.867267	−0.433633	+	0.901089i	$0.642769\pi$
$174$	−3.36842	−0.255359
$175$	−0.467322	−0.0353263
$176$	−2.01828	−0.152133
$177$	−3.03530	−0.228147
$178$	−8.20141	−0.614722
$179$	15.7058	1.17391	0.586953	−	0.809621i	$-0.300327\pi$
$179$	15.7058	1.17391	0.586953	+	0.809621i	$0.300327\pi$
$180$	−6.84002	−0.509825
$181$	−5.38840	−0.400517	−0.200258	−	0.979743i	$-0.564178\pi$
$181$	−5.38840	−0.400517	−0.200258	+	0.979743i	$0.564178\pi$
$182$	7.66735	0.568342
$183$	−6.81310	−0.503639
$184$	−9.95363	−0.733792
$185$	−14.7474	−1.08425
$186$	−0.668263	−0.0489994
$187$	−10.5336	−0.770294
$188$	−6.39890	−0.466687
$189$	4.47795	0.325723
$190$	−12.7168	−0.922573
$191$	−10.9067	−0.789180	−0.394590	−	0.918857i	$-0.629113\pi$
$191$	−10.9067	−0.789180	−0.394590	+	0.918857i	$0.629113\pi$
$192$	3.14343	0.226857
$193$	−11.5594	−0.832066	−0.416033	−	0.909349i	$-0.636580\pi$
$193$	−11.5594	−0.832066	−0.416033	+	0.909349i	$0.636580\pi$
$194$	11.7781	0.845620
$195$	5.66443	0.405639
$196$	4.82468	0.344620
$197$	−0.198237	−0.0141238	−0.00706191	−	0.999975i	$-0.502248\pi$
$197$	−0.198237	−0.0141238	−0.00706191	+	0.999975i	$0.502248\pi$
$198$	−7.80040	−0.554350
$199$	−10.6647	−0.755999	−0.377999	−	0.925806i	$-0.623388\pi$
$199$	−10.6647	−0.755999	−0.377999	+	0.925806i	$0.623388\pi$
$200$	−0.870221	−0.0615339
$201$	−0.765963	−0.0540269
$202$	−3.71663	−0.261501
$203$	11.3662	0.797747
$204$	1.88860	0.132229
$205$	2.75179	0.192194
$206$	−16.7981	−1.17038
$207$	−9.29378	−0.645962
$208$	3.44932	0.239167
$209$	16.9214	1.17048
$210$	1.71852	0.118589
$211$	−22.6485	−1.55919	−0.779595	−	0.626284i	$-0.784575\pi$
$211$	−22.6485	−1.55919	−0.779595	+	0.626284i	$0.784575\pi$
$212$	1.15548	0.0793585
$213$	4.73094	0.324158
$214$	6.20422	0.424112
$215$	4.47494	0.305188
$216$	8.33859	0.567369
$217$	2.25494	0.153075
$218$	−15.2804	−1.03492
$219$	4.43525	0.299706
$220$	7.28935	0.491448
$221$	18.0024	1.21097
$222$	3.01534	0.202376
$223$	−4.93227	−0.330289	−0.165144	−	0.986269i	$-0.552809\pi$
$223$	−4.93227	−0.330289	−0.165144	+	0.986269i	$0.552809\pi$
$224$	−8.33944	−0.557202
$225$	−0.812531	−0.0541688
$226$	6.40107	0.425793
$227$	9.62739	0.638992	0.319496	−	0.947588i	$-0.396486\pi$
$227$	9.62739	0.638992	0.319496	+	0.947588i	$0.396486\pi$
$228$	−3.03389	−0.200925
$229$	−21.1733	−1.39917	−0.699586	−	0.714548i	$-0.746632\pi$
$229$	−21.1733	−1.39917	−0.699586	+	0.714548i	$0.746632\pi$
$230$	−7.44327	−0.490795
$231$	−2.28672	−0.150455
$232$	21.1654	1.38958
$233$	9.78548	0.641068	0.320534	−	0.947237i	$-0.396138\pi$
$233$	9.78548	0.641068	0.320534	+	0.947237i	$0.396138\pi$
$234$	13.3312	0.871487
$235$	−13.6711	−0.891803
$236$	6.67554	0.434541
$237$	−6.67038	−0.433288
$238$	5.46169	0.354029
$239$	−15.8700	−1.02654	−0.513272	−	0.858226i	$-0.671567\pi$
$239$	−15.8700	−1.02654	−0.513272	+	0.858226i	$0.671567\pi$
$240$	0.773110	0.0499040
$241$	−18.0003	−1.15950	−0.579750	−	0.814795i	$-0.696850\pi$
$241$	−18.0003	−1.15950	−0.579750	+	0.814795i	$0.696850\pi$
$242$	−2.25529	−0.144976
$243$	11.8408	0.759585
$244$	14.9840	0.959255
$245$	10.3078	0.658542
$246$	−0.562649	−0.0358732
$247$	−28.9194	−1.84010
$248$	4.19902	0.266638
$249$	−1.79162	−0.113539
$250$	10.4023	0.657899
$251$	15.5169	0.979418	0.489709	−	0.871886i	$-0.337103\pi$
$251$	15.5169	0.979418	0.489709	+	0.871886i	$0.337103\pi$
$252$	−4.71918	−0.297281
$253$	9.90430	0.622678
$254$	−1.73439	−0.108825
$255$	4.03495	0.252678
$256$	−17.0071	−1.06295
$257$	−17.2639	−1.07689	−0.538445	−	0.842661i	$-0.680988\pi$
$257$	−17.2639	−1.07689	−0.538445	+	0.842661i	$0.680988\pi$
$258$	−0.914976	−0.0569639
$259$	−10.1747	−0.632228
$260$	−12.4578	−0.772599
$261$	19.7623	1.22325
$262$	8.57826	0.529967
$263$	24.2548	1.49561	0.747807	−	0.663917i	$-0.231107\pi$
$263$	24.2548	1.49561	0.747807	+	0.663917i	$0.231107\pi$
$264$	−4.25821	−0.262074
$265$	2.46865	0.151648
$266$	−8.77379	−0.537955
$267$	−4.18032	−0.255831
$268$	1.68458	0.102902
$269$	21.5023	1.31102	0.655511	−	0.755186i	$-0.272453\pi$
$269$	21.5023	1.31102	0.655511	+	0.755186i	$0.272453\pi$
$270$	6.23554	0.379483
$271$	−7.15015	−0.434341	−0.217170	−	0.976134i	$-0.569683\pi$
$271$	−7.15015	−0.434341	−0.217170	+	0.976134i	$0.569683\pi$
$272$	2.45705	0.148981
$273$	3.90810	0.236529
$274$	−1.54259	−0.0931910
$275$	0.865908	0.0522162
$276$	−1.77577	−0.106889
$277$	−31.1033	−1.86882	−0.934409	−	0.356202i	$-0.884072\pi$
$277$	−31.1033	−1.86882	−0.934409	+	0.356202i	$0.884072\pi$
$278$	1.56809	0.0940476
$279$	3.92065	0.234723
$280$	−10.7983	−0.645320
$281$	−13.6029	−0.811482	−0.405741	−	0.913988i	$-0.632987\pi$
$281$	−13.6029	−0.811482	−0.405741	+	0.913988i	$0.632987\pi$
$282$	2.79528	0.166456
$283$	−29.0294	−1.72562	−0.862808	−	0.505531i	$-0.831297\pi$
$283$	−29.0294	−1.72562	−0.862808	+	0.505531i	$0.831297\pi$
$284$	−10.4047	−0.617408
$285$	−6.48184	−0.383951
$286$	−14.2069	−0.840073
$287$	1.89856	0.112069
$288$	−14.4997	−0.854406
$289$	−4.17637	−0.245669
$290$	15.8274	0.929414
$291$	6.00339	0.351925
$292$	−9.75444	−0.570835
$293$	28.7732	1.68095	0.840475	−	0.541850i	$-0.182276\pi$
$293$	28.7732	1.68095	0.840475	+	0.541850i	$0.182276\pi$
$294$	−2.10760	−0.122918
$295$	14.2621	0.830373
$296$	−18.9468	−1.10126
$297$	−8.29725	−0.481456
$298$	−0.994621	−0.0576169
$299$	−16.9268	−0.978905
$300$	−0.155251	−0.00896342
$301$	3.08743	0.177956
$302$	11.3033	0.650432
$303$	−1.89439	−0.108830
$304$	−3.94707	−0.226380
$305$	32.0130	1.83306
$306$	9.49621	0.542862
$307$	28.8399	1.64598	0.822991	−	0.568054i	$-0.192304\pi$
$307$	28.8399	1.64598	0.822991	+	0.568054i	$0.192304\pi$
$308$	5.02919	0.286565
$309$	−8.56212	−0.487082
$310$	3.14000	0.178340
$311$	13.2946	0.753870	0.376935	−	0.926240i	$-0.376978\pi$
$311$	13.2946	0.753870	0.376935	+	0.926240i	$0.376978\pi$
$312$	7.27745	0.412004
$313$	21.4655	1.21330	0.606651	−	0.794968i	$-0.292512\pi$
$313$	21.4655	1.21330	0.606651	+	0.794968i	$0.292512\pi$
$314$	−4.28311	−0.241710
$315$	−10.0824	−0.568080
$316$	14.6702	0.825262
$317$	30.0723	1.68903	0.844513	−	0.535535i	$-0.179890\pi$
$317$	30.0723	1.68903	0.844513	+	0.535535i	$0.179890\pi$
$318$	−0.504756	−0.0283053
$319$	−21.0605	−1.17916
$320$	−14.7702	−0.825678
$321$	3.16234	0.176504
$322$	−5.13539	−0.286184
$323$	−20.6002	−1.14623
$324$	−7.43044	−0.412802
$325$	−1.47987	−0.0820885
$326$	16.1942	0.896914
$327$	−7.78851	−0.430705
$328$	3.53540	0.195210
$329$	−9.43219	−0.520013
$330$	−3.18426	−0.175288
$331$	12.9472	0.711642	0.355821	−	0.934554i	$-0.384201\pi$
$331$	12.9472	0.711642	0.355821	+	0.934554i	$0.384201\pi$
$332$	3.94030	0.216252
$333$	−17.6908	−0.969449
$334$	−9.68038	−0.529687
$335$	3.59907	0.196638
$336$	0.533398	0.0290992
$337$	16.2579	0.885625	0.442813	−	0.896614i	$-0.353981\pi$
$337$	16.2579	0.885625	0.442813	+	0.896614i	$0.353981\pi$
$338$	11.7906	0.641326
$339$	3.26267	0.177204
$340$	−8.87406	−0.481264
$341$	−4.17820	−0.226262
$342$	−15.2549	−0.824893
$343$	18.2243	0.984021
$344$	5.74923	0.309978
$345$	−3.79389	−0.204256
$346$	−10.9592	−0.589172
$347$	35.1321	1.88599	0.942994	−	0.332809i	$-0.107996\pi$
$347$	35.1321	1.88599	0.942994	+	0.332809i	$0.107996\pi$
$348$	3.77599	0.202414
$349$	21.3041	1.14038	0.570191	−	0.821512i	$-0.306869\pi$
$349$	21.3041	1.14038	0.570191	+	0.821512i	$0.306869\pi$
$350$	−0.448974	−0.0239987
$351$	14.1803	0.756891
$352$	15.4522	0.823608
$353$	−20.2092	−1.07563	−0.537814	−	0.843063i	$-0.680750\pi$
$353$	−20.2092	−1.07563	−0.537814	+	0.843063i	$0.680750\pi$
$354$	−2.91613	−0.154990
$355$	−22.2295	−1.17982
$356$	9.19378	0.487269
$357$	2.78386	0.147338
$358$	15.0891	0.797486
$359$	−25.4008	−1.34060	−0.670302	−	0.742089i	$-0.733835\pi$
$359$	−25.4008	−1.34060	−0.670302	+	0.742089i	$0.733835\pi$
$360$	−18.7749	−0.989524
$361$	14.0926	0.741718
$362$	−5.17684	−0.272089
$363$	−1.14954	−0.0603351
$364$	−8.59509	−0.450505
$365$	−20.8401	−1.09082
$366$	−6.54559	−0.342144
$367$	3.35748	0.175259	0.0876296	−	0.996153i	$-0.472071\pi$
$367$	3.35748	0.175259	0.0876296	+	0.996153i	$0.472071\pi$
$368$	−2.31026	−0.120431
$369$	3.30102	0.171844
$370$	−14.1683	−0.736576
$371$	1.70321	0.0884264
$372$	0.749122	0.0388402
$373$	17.7504	0.919080	0.459540	−	0.888157i	$-0.348014\pi$
$373$	17.7504	0.919080	0.459540	+	0.888157i	$0.348014\pi$
$374$	−10.1200	−0.523294
$375$	5.30212	0.273800
$376$	−17.5641	−0.905798
$377$	35.9932	1.85374
$378$	4.30213	0.221278
$379$	−18.4867	−0.949596	−0.474798	−	0.880095i	$-0.657479\pi$
$379$	−18.4867	−0.949596	−0.474798	+	0.880095i	$0.657479\pi$
$380$	14.2555	0.731292
$381$	−0.884030	−0.0452902
$382$	−10.4785	−0.536124
$383$	6.32183	0.323031	0.161515	−	0.986870i	$-0.448362\pi$
$383$	6.32183	0.323031	0.161515	+	0.986870i	$0.448362\pi$
$384$	−2.12487	−0.108434
$385$	10.7447	0.547603
$386$	−11.1056	−0.565259
$387$	5.36810	0.272876
$388$	−13.2033	−0.670294
$389$	29.8625	1.51409	0.757044	−	0.653364i	$-0.226643\pi$
$389$	29.8625	1.51409	0.757044	+	0.653364i	$0.226643\pi$
$390$	5.44203	0.275568
$391$	−12.0575	−0.609774
$392$	13.2431	0.668877
$393$	4.37240	0.220558
$394$	−0.190454	−0.00959492
$395$	31.3424	1.57701
$396$	8.74423	0.439414
$397$	−18.7391	−0.940488	−0.470244	−	0.882537i	$-0.655834\pi$
$397$	−18.7391	−0.940488	−0.470244	+	0.882537i	$0.655834\pi$
$398$	−10.2459	−0.513583
$399$	−4.47206	−0.223883
$400$	−0.201980	−0.0100990
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−0.735889	−0.0367028
$403$	7.14072	0.355705
$404$	4.16634	0.207283
$405$	−15.8749	−0.788832
$406$	10.9199	0.541945
$407$	18.8529	0.934504
$408$	5.18395	0.256644
$409$	22.0999	1.09277	0.546384	−	0.837535i	$-0.316004\pi$
$409$	22.0999	1.09277	0.546384	+	0.837535i	$0.316004\pi$
$410$	2.64375	0.130565
$411$	−0.786267	−0.0387837
$412$	18.8307	0.927721
$413$	9.83997	0.484193
$414$	−8.92888	−0.438830
$415$	8.41835	0.413241
$416$	−26.4085	−1.29478
$417$	0.799265	0.0391402
$418$	16.2571	0.795159
$419$	6.77666	0.331061	0.165531	−	0.986205i	$-0.447066\pi$
$419$	6.77666	0.331061	0.165531	+	0.986205i	$0.447066\pi$
$420$	−1.92646	−0.0940014
$421$	29.1168	1.41906	0.709532	−	0.704673i	$-0.248906\pi$
$421$	29.1168	1.41906	0.709532	+	0.704673i	$0.248906\pi$
$422$	−21.7593	−1.05923
$423$	−16.3997	−0.797381
$424$	3.17162	0.154028
$425$	−1.05416	−0.0511341
$426$	4.54518	0.220215
$427$	22.0870	1.06886
$428$	−6.95493	−0.336179
$429$	−7.24137	−0.349617
$430$	4.29924	0.207328
$431$	40.0410	1.92871	0.964354	−	0.264616i	$-0.0852454\pi$
$431$	40.0410	1.92871	0.964354	+	0.264616i	$0.0852454\pi$
$432$	1.93540	0.0931172
$433$	−3.19065	−0.153333	−0.0766665	−	0.997057i	$-0.524428\pi$
$433$	−3.19065	−0.153333	−0.0766665	+	0.997057i	$0.524428\pi$
$434$	2.16640	0.103991
$435$	8.06731	0.386798
$436$	17.1293	0.820343
$437$	19.3695	0.926567
$438$	4.26110	0.203603
$439$	−34.0173	−1.62356	−0.811780	−	0.583964i	$-0.801501\pi$
$439$	−34.0173	−1.62356	−0.811780	+	0.583964i	$0.801501\pi$
$440$	20.0082	0.953855
$441$	12.3652	0.588817
$442$	17.2955	0.822665
$443$	−9.13742	−0.434132	−0.217066	−	0.976157i	$-0.569649\pi$
$443$	−9.13742	−0.434132	−0.217066	+	0.976157i	$0.569649\pi$
$444$	−3.38019	−0.160417
$445$	19.6423	0.931133
$446$	−4.73861	−0.224380
$447$	−0.506965	−0.0239786
$448$	−10.1905	−0.481456
$449$	23.1666	1.09330	0.546649	−	0.837362i	$-0.315903\pi$
$449$	23.1666	1.09330	0.546649	+	0.837362i	$0.315903\pi$
$450$	−0.780629	−0.0367992
$451$	−3.51787	−0.165650
$452$	−7.17559	−0.337511
$453$	5.76137	0.270693
$454$	9.24939	0.434095
$455$	−18.3632	−0.860880
$456$	−8.32762	−0.389976
$457$	−10.3059	−0.482091	−0.241045	−	0.970514i	$-0.577490\pi$
$457$	−10.3059	−0.482091	−0.241045	+	0.970514i	$0.577490\pi$
$458$	−20.3420	−0.950519
$459$	10.1011	0.471478
$460$	8.34389	0.389036
$461$	−13.7205	−0.639028	−0.319514	−	0.947582i	$-0.603520\pi$
$461$	−13.7205	−0.639028	−0.319514	+	0.947582i	$0.603520\pi$
$462$	−2.19694	−0.102211
$463$	−7.79313	−0.362177	−0.181089	−	0.983467i	$-0.557962\pi$
$463$	−7.79313	−0.362177	−0.181089	+	0.983467i	$0.557962\pi$
$464$	4.91253	0.228059
$465$	1.60048	0.0742205
$466$	9.40127	0.435505
$467$	−39.7549	−1.83964	−0.919819	−	0.392344i	$-0.871664\pi$
$467$	−39.7549	−1.83964	−0.919819	+	0.392344i	$0.871664\pi$
$468$	−14.9443	−0.690798
$469$	2.48313	0.114660
$470$	−13.1343	−0.605840
$471$	−2.18313	−0.100594
$472$	18.3234	0.843404
$473$	−5.72073	−0.263040
$474$	−6.40848	−0.294351
$475$	1.69342	0.0776996
$476$	−6.12255	−0.280626
$477$	2.96137	0.135592
$478$	−15.2469	−0.697376
$479$	−42.9634	−1.96305	−0.981523	−	0.191342i	$-0.938716\pi$
$479$	−42.9634	−1.96305	−0.981523	+	0.191342i	$0.938716\pi$
$480$	−5.91905	−0.270167
$481$	−32.2204	−1.46912
$482$	−17.2935	−0.787699
$483$	−2.61754	−0.119102
$484$	2.52818	0.114917
$485$	−28.2084	−1.28088
$486$	11.3759	0.516019
$487$	−7.35737	−0.333394	−0.166697	−	0.986008i	$-0.553310\pi$
$487$	−7.35737	−0.333394	−0.166697	+	0.986008i	$0.553310\pi$
$488$	41.1291	1.86183
$489$	8.25430	0.373272
$490$	9.90310	0.447376
$491$	22.6605	1.02266	0.511328	−	0.859386i	$-0.329154\pi$
$491$	22.6605	1.02266	0.511328	+	0.859386i	$0.329154\pi$
$492$	0.630729	0.0284355
$493$	25.6391	1.15473
$494$	−27.7840	−1.25006
$495$	18.6818	0.839686
$496$	0.974601	0.0437609
$497$	−15.3369	−0.687956
$498$	−1.72127	−0.0771320
$499$	27.0155	1.20938	0.604691	−	0.796460i	$-0.293297\pi$
$499$	27.0155	1.20938	0.604691	+	0.796460i	$0.293297\pi$
$500$	−11.6610	−0.521494
$501$	−4.93416	−0.220442
$502$	14.9077	0.665361
$503$	−11.1826	−0.498607	−0.249303	−	0.968425i	$-0.580202\pi$
$503$	−11.1826	−0.498607	−0.249303	+	0.968425i	$0.580202\pi$
$504$	−12.9535	−0.576995
$505$	8.90128	0.396102
$506$	9.51542	0.423012
$507$	6.00977	0.266903
$508$	1.94425	0.0862620
$509$	−22.3083	−0.988797	−0.494398	−	0.869235i	$-0.664612\pi$
$509$	−22.3083	−0.988797	−0.494398	+	0.869235i	$0.664612\pi$
$510$	3.87652	0.171655
$511$	−14.3784	−0.636062
$512$	−7.66103	−0.338573
$513$	−16.2266	−0.716423
$514$	−16.5860	−0.731578
$515$	40.2313	1.77280
$516$	1.02569	0.0451533
$517$	17.4770	0.768638
$518$	−9.77525	−0.429500
$519$	−5.58600	−0.245198
$520$	−34.1949	−1.49955
$521$	4.24388	0.185928	0.0929639	−	0.995669i	$-0.470366\pi$
$521$	4.24388	0.185928	0.0929639	+	0.995669i	$0.470366\pi$
$522$	18.9863	0.831010
$523$	−35.1097	−1.53524	−0.767621	−	0.640904i	$-0.778560\pi$
$523$	−35.1097	−1.53524	−0.767621	+	0.640904i	$0.778560\pi$
$524$	−9.61622	−0.420086
$525$	−0.228845	−0.00998762
$526$	23.3024	1.01603
$527$	5.08655	0.221574
$528$	−0.988339	−0.0430119
$529$	−11.6629	−0.507080
$530$	2.37172	0.103021
$531$	17.1087	0.742455
$532$	9.83541	0.426419
$533$	6.01219	0.260417
$534$	−4.01619	−0.173797
$535$	−14.8590	−0.642412
$536$	4.62395	0.199724
$537$	7.69104	0.331893
$538$	20.6581	0.890634
$539$	−13.1774	−0.567593
$540$	−6.99004	−0.300803
$541$	−13.2469	−0.569528	−0.284764	−	0.958598i	$-0.591915\pi$
$541$	−13.2469	−0.569528	−0.284764	+	0.958598i	$0.591915\pi$
$542$	−6.86942	−0.295067
$543$	−2.63867	−0.113236
$544$	−18.8116	−0.806540
$545$	36.5962	1.56761
$546$	3.75466	0.160685
$547$	25.6671	1.09745	0.548723	−	0.836004i	$-0.315114\pi$
$547$	25.6671	1.09745	0.548723	+	0.836004i	$0.315114\pi$
$548$	1.72924	0.0738693
$549$	38.4025	1.63898
$550$	0.831909	0.0354727
$551$	−41.1872	−1.75463
$552$	−4.87424	−0.207461
$553$	21.6243	0.919560
$554$	−29.8821	−1.26957
$555$	−7.22169	−0.306544
$556$	−1.75782	−0.0745483
$557$	21.6864	0.918882	0.459441	−	0.888208i	$-0.348050\pi$
$557$	21.6864	0.918882	0.459441	+	0.888208i	$0.348050\pi$
$558$	3.76672	0.159458
$559$	9.77697	0.413522
$560$	−2.50630	−0.105911
$561$	−5.15825	−0.217781
$562$	−13.0688	−0.551275
$563$	−21.5947	−0.910108	−0.455054	−	0.890464i	$-0.650380\pi$
$563$	−21.5947	−0.910108	−0.455054	+	0.890464i	$0.650380\pi$
$564$	−3.13350	−0.131944
$565$	−15.3305	−0.644958
$566$	−27.8896	−1.17229
$567$	−10.9527	−0.459971
$568$	−28.5596	−1.19833
$569$	10.3238	0.432797	0.216399	−	0.976305i	$-0.430569\pi$
$569$	10.3238	0.432797	0.216399	+	0.976305i	$0.430569\pi$
$570$	−6.22734	−0.260835
$571$	42.6777	1.78601	0.893003	−	0.450052i	$-0.148594\pi$
$571$	42.6777	1.78601	0.893003	+	0.450052i	$0.148594\pi$
$572$	15.9260	0.665898
$573$	−5.34094	−0.223121
$574$	1.82402	0.0761331
$575$	0.991178	0.0413350
$576$	−17.7182	−0.738257
$577$	−24.2641	−1.01013	−0.505064	−	0.863082i	$-0.668531\pi$
$577$	−24.2641	−1.01013	−0.505064	+	0.863082i	$0.668531\pi$
$578$	−4.01239	−0.166893
$579$	−5.66059	−0.235246
$580$	−17.7424	−0.736715
$581$	5.80814	0.240962
$582$	5.76768	0.239078
$583$	−3.15590	−0.130704
$584$	−26.7746	−1.10794
$585$	−31.9280	−1.32006
$586$	27.6435	1.14194
$587$	22.8982	0.945110	0.472555	−	0.881301i	$-0.343332\pi$
$587$	22.8982	0.945110	0.472555	+	0.881301i	$0.343332\pi$
$588$	2.36262	0.0974328
$589$	−8.17116	−0.336687
$590$	13.7021	0.564109
$591$	−0.0970756	−0.00399316
$592$	−4.39760	−0.180740
$593$	−36.8294	−1.51240	−0.756202	−	0.654338i	$-0.772947\pi$
$593$	−36.8294	−1.51240	−0.756202	+	0.654338i	$0.772947\pi$
$594$	−7.97148	−0.327074
$595$	−13.0807	−0.536255
$596$	1.11497	0.0456709
$597$	−5.22243	−0.213740
$598$	−16.2622	−0.665013
$599$	−3.06440	−0.125208	−0.0626040	−	0.998038i	$-0.519941\pi$
$599$	−3.06440	−0.125208	−0.0626040	+	0.998038i	$0.519941\pi$
$600$	−0.426142	−0.0173972
$601$	9.91876	0.404595	0.202297	−	0.979324i	$-0.435159\pi$
$601$	9.91876	0.404595	0.202297	+	0.979324i	$0.435159\pi$
$602$	2.96621	0.120894
$603$	4.31741	0.175819
$604$	−12.6710	−0.515575
$605$	5.40139	0.219598
$606$	−1.82001	−0.0739330
$607$	−24.9149	−1.01126	−0.505632	−	0.862749i	$-0.668741\pi$
$607$	−24.9149	−1.01126	−0.505632	+	0.862749i	$0.668741\pi$
$608$	30.2194	1.22556
$609$	5.56594	0.225543
$610$	30.7561	1.24528
$611$	−29.8689	−1.20837
$612$	−10.6452	−0.430308
$613$	30.3430	1.22554	0.612772	−	0.790260i	$-0.290055\pi$
$613$	30.3430	1.22554	0.612772	+	0.790260i	$0.290055\pi$
$614$	27.7076	1.11819
$615$	1.34754	0.0543379
$616$	13.8044	0.556196
$617$	−23.1147	−0.930563	−0.465282	−	0.885163i	$-0.654047\pi$
$617$	−23.1147	−0.930563	−0.465282	+	0.885163i	$0.654047\pi$
$618$	−8.22595	−0.330896
$619$	0.931269	0.0374308	0.0187154	−	0.999825i	$-0.494042\pi$
$619$	0.931269	0.0374308	0.0187154	+	0.999825i	$0.494042\pi$
$620$	−3.51994	−0.141364
$621$	−9.49761	−0.381126
$622$	12.7726	0.512136
$623$	13.5519	0.542947
$624$	1.68911	0.0676186
$625$	−26.3852	−1.05541
$626$	20.6227	0.824249
$627$	8.28634	0.330924
$628$	4.80137	0.191595
$629$	−22.9516	−0.915139
$630$	−9.68655	−0.385921
$631$	−5.14182	−0.204693	−0.102346	−	0.994749i	$-0.532635\pi$
$631$	−5.14182	−0.204693	−0.102346	+	0.994749i	$0.532635\pi$
$632$	40.2676	1.60176
$633$	−11.0909	−0.440822
$634$	28.8915	1.14743
$635$	4.15384	0.164840
$636$	0.565831	0.0224367
$637$	22.5208	0.892306
$638$	−20.2336	−0.801055
$639$	−26.6663	−1.05490
$640$	9.98423	0.394661
$641$	−29.9574	−1.18325	−0.591623	−	0.806215i	$-0.701513\pi$
$641$	−29.9574	−1.18325	−0.591623	+	0.806215i	$0.701513\pi$
$642$	3.03817	0.119907
$643$	−15.6777	−0.618268	−0.309134	−	0.951019i	$-0.600039\pi$
$643$	−15.6777	−0.618268	−0.309134	+	0.951019i	$0.600039\pi$
$644$	5.75676	0.226848
$645$	2.19135	0.0862845
$646$	−19.7914	−0.778681
$647$	−13.1758	−0.517992	−0.258996	−	0.965878i	$-0.583392\pi$
$647$	−13.1758	−0.517992	−0.258996	+	0.965878i	$0.583392\pi$
$648$	−20.3955	−0.801212
$649$	−18.2326	−0.715692
$650$	−1.42177	−0.0557663
$651$	1.10423	0.0432782
$652$	−18.1537	−0.710953
$653$	−25.3347	−0.991424	−0.495712	−	0.868487i	$-0.665093\pi$
$653$	−25.3347	−0.991424	−0.495712	+	0.868487i	$0.665093\pi$
$654$	−7.48270	−0.292597
$655$	−20.5448	−0.802752
$656$	0.820573	0.0320380
$657$	−24.9996	−0.975328
$658$	−9.06185	−0.353268
$659$	1.79688	0.0699966	0.0349983	−	0.999387i	$-0.488857\pi$
$659$	1.79688	0.0699966	0.0349983	+	0.999387i	$0.488857\pi$
$660$	3.56955	0.138945
$661$	−27.4860	−1.06908	−0.534541	−	0.845143i	$-0.679515\pi$
$661$	−27.4860	−1.06908	−0.534541	+	0.845143i	$0.679515\pi$
$662$	12.4389	0.483450
$663$	8.81566	0.342372
$664$	10.8156	0.419726
$665$	21.0131	0.814853
$666$	−16.9962	−0.658589
$667$	−24.1073	−0.933438
$668$	10.8517	0.419865
$669$	−2.41530	−0.0933810
$670$	3.45776	0.133585
$671$	−40.9252	−1.57990
$672$	−4.08378	−0.157535
$673$	−10.7850	−0.415731	−0.207866	−	0.978157i	$-0.566652\pi$
$673$	−10.7850	−0.415731	−0.207866	+	0.978157i	$0.566652\pi$
$674$	15.6196	0.601644
$675$	−0.830352	−0.0319603
$676$	−13.2173	−0.508358
$677$	21.4421	0.824089	0.412044	−	0.911164i	$-0.364815\pi$
$677$	21.4421	0.824089	0.412044	+	0.911164i	$0.364815\pi$
$678$	3.13457	0.120382
$679$	−19.4620	−0.746885
$680$	−24.3581	−0.934089
$681$	4.71448	0.180659
$682$	−4.01415	−0.153710
$683$	21.7887	0.833721	0.416861	−	0.908970i	$-0.363130\pi$
$683$	21.7887	0.833721	0.416861	+	0.908970i	$0.363130\pi$
$684$	17.1008	0.653865
$685$	3.69447	0.141158
$686$	17.5088	0.668488
$687$	−10.3685	−0.395581
$688$	1.33441	0.0508739
$689$	5.39357	0.205479
$690$	−3.64493	−0.138760
$691$	−7.62650	−0.290126	−0.145063	−	0.989422i	$-0.546338\pi$
$691$	−7.62650	−0.290126	−0.145063	+	0.989422i	$0.546338\pi$
$692$	12.2853	0.467017
$693$	12.8893	0.489624
$694$	33.7527	1.28123
$695$	−3.75554	−0.142456
$696$	10.3646	0.392868
$697$	4.28266	0.162217
$698$	20.4676	0.774711
$699$	4.79189	0.181246
$700$	0.503299	0.0190229
$701$	−47.7656	−1.80408	−0.902041	−	0.431651i	$-0.857931\pi$
$701$	−47.7656	−1.80408	−0.902041	+	0.431651i	$0.857931\pi$
$702$	13.6236	0.514189
$703$	36.8699	1.39058
$704$	18.8821	0.711646
$705$	−6.69465	−0.252135
$706$	−19.4157	−0.730721
$707$	6.14132	0.230968
$708$	3.26898	0.122856
$709$	−40.8157	−1.53286	−0.766432	−	0.642325i	$-0.777970\pi$
$709$	−40.8157	−1.53286	−0.766432	+	0.642325i	$0.777970\pi$
$710$	−21.3567	−0.801502
$711$	37.5981	1.41004
$712$	25.2356	0.945745
$713$	−4.78266	−0.179112
$714$	2.67456	0.100093
$715$	34.0254	1.27248
$716$	−16.9149	−0.632140
$717$	−7.77145	−0.290230
$718$	−24.4035	−0.910730
$719$	18.8292	0.702212	0.351106	−	0.936336i	$-0.385806\pi$
$719$	18.8292	0.702212	0.351106	+	0.936336i	$0.385806\pi$
$720$	−4.35769	−0.162402
$721$	27.7570	1.03373
$722$	13.5393	0.503882
$723$	−8.81463	−0.327820
$724$	5.80323	0.215675
$725$	−2.10764	−0.0782757
$726$	−1.10440	−0.0409883
$727$	−32.9852	−1.22335	−0.611676	−	0.791108i	$-0.709504\pi$
$727$	−32.9852	−1.22335	−0.611676	+	0.791108i	$0.709504\pi$
$728$	−23.5923	−0.874390
$729$	−14.8995	−0.551835
$730$	−20.0219	−0.741042
$731$	6.96443	0.257589
$732$	7.33760	0.271206
$733$	53.6983	1.98339	0.991696	−	0.128604i	$-0.0410497\pi$
$733$	53.6983	1.98339	0.991696	+	0.128604i	$0.0410497\pi$
$734$	3.22566	0.119061
$735$	5.04768	0.186186
$736$	17.6877	0.651978
$737$	−4.60103	−0.169481
$738$	3.17142	0.116741
$739$	−33.3007	−1.22499	−0.612494	−	0.790475i	$-0.709834\pi$
$739$	−33.3007	−1.22499	−0.612494	+	0.790475i	$0.709834\pi$
$740$	15.8827	0.583859
$741$	−14.1617	−0.520243
$742$	1.63634	0.0600719
$743$	4.82603	0.177050	0.0885249	−	0.996074i	$-0.471785\pi$
$743$	4.82603	0.177050	0.0885249	+	0.996074i	$0.471785\pi$
$744$	2.05624	0.0753852
$745$	2.38210	0.0872735
$746$	17.0534	0.624371
$747$	10.0986	0.369488
$748$	11.3445	0.414797
$749$	−10.2518	−0.374592
$750$	5.09394	0.186005
$751$	25.5783	0.933364	0.466682	−	0.884425i	$-0.345449\pi$
$751$	25.5783	0.933364	0.466682	+	0.884425i	$0.345449\pi$
$752$	−4.07666	−0.148660
$753$	7.59854	0.276906
$754$	34.5800	1.25933
$755$	−27.0712	−0.985223
$756$	−4.82269	−0.175399
$757$	24.1223	0.876739	0.438369	−	0.898795i	$-0.355556\pi$
$757$	24.1223	0.876739	0.438369	+	0.898795i	$0.355556\pi$
$758$	−17.7608	−0.645102
$759$	4.85008	0.176047
$760$	39.1294	1.41937
$761$	−32.6205	−1.18249	−0.591245	−	0.806492i	$-0.701363\pi$
$761$	−32.6205	−1.18249	−0.591245	+	0.806492i	$0.701363\pi$
$762$	−0.849320	−0.0307676
$763$	25.2491	0.914079
$764$	11.7463	0.424967
$765$	−22.7433	−0.822285
$766$	6.07362	0.219449
$767$	31.1603	1.12513
$768$	−8.32830	−0.300522
$769$	−22.7490	−0.820350	−0.410175	−	0.912007i	$-0.634532\pi$
$769$	−22.7490	−0.820350	−0.410175	+	0.912007i	$0.634532\pi$
$770$	10.3229	0.372010
$771$	−8.45401	−0.304464
$772$	12.4493	0.448061
$773$	−19.3524	−0.696057	−0.348029	−	0.937484i	$-0.613149\pi$
$773$	−19.3524	−0.696057	−0.348029	+	0.937484i	$0.613149\pi$
$774$	5.15733	0.185376
$775$	−0.418136	−0.0150199
$776$	−36.2411	−1.30098
$777$	−4.98252	−0.178747
$778$	28.6900	1.02859
$779$	−6.87977	−0.246493
$780$	−6.10051	−0.218433
$781$	28.4180	1.01688
$782$	−11.5841	−0.414246
$783$	20.1957	0.721736
$784$	3.07375	0.109777
$785$	10.2580	0.366124
$786$	4.20072	0.149835
$787$	5.23133	0.186477	0.0932384	−	0.995644i	$-0.470278\pi$
$787$	5.23133	0.186477	0.0932384	+	0.995644i	$0.470278\pi$
$788$	0.213498	0.00760556
$789$	11.8774	0.422847
$790$	30.1118	1.07133
$791$	−10.5771	−0.376077
$792$	24.0017	0.852863
$793$	69.9429	2.48374
$794$	−18.0033	−0.638914
$795$	1.20888	0.0428747
$796$	11.4857	0.407100
$797$	−31.1816	−1.10451	−0.552254	−	0.833676i	$-0.686232\pi$
$797$	−31.1816	−1.10451	−0.552254	+	0.833676i	$0.686232\pi$
$798$	−4.29647	−0.152094
$799$	−21.2765	−0.752710
$800$	1.54639	0.0546732
$801$	23.5627	0.832547
$802$	−0.960737	−0.0339248
$803$	26.6419	0.940171
$804$	0.824931	0.0290931
$805$	12.2992	0.433489
$806$	6.86035	0.241646
$807$	10.5296	0.370659
$808$	11.4360	0.402318
$809$	11.3827	0.400195	0.200098	−	0.979776i	$-0.435874\pi$
$809$	11.3827	0.400195	0.200098	+	0.979776i	$0.435874\pi$
$810$	−15.2516	−0.535888
$811$	−23.8039	−0.835870	−0.417935	−	0.908477i	$-0.637246\pi$
$811$	−23.8039	−0.835870	−0.417935	+	0.908477i	$0.637246\pi$
$812$	−12.2412	−0.429581
$813$	−3.50139	−0.122799
$814$	18.1127	0.634849
$815$	−38.7849	−1.35857
$816$	1.20320	0.0421206
$817$	−11.1878	−0.391413
$818$	21.2321	0.742365
$819$	−22.0283	−0.769732
$820$	−2.96364	−0.103495
$821$	−46.1871	−1.61194	−0.805971	−	0.591955i	$-0.798356\pi$
$821$	−46.1871	−1.61194	−0.805971	+	0.591955i	$0.798356\pi$
$822$	−0.755395	−0.0263474
$823$	−1.37173	−0.0478153	−0.0239077	−	0.999714i	$-0.507611\pi$
$823$	−1.37173	−0.0478153	−0.0239077	+	0.999714i	$0.507611\pi$
$824$	51.6876	1.80062
$825$	0.424030	0.0147628
$826$	9.45362	0.328934
$827$	20.4262	0.710288	0.355144	−	0.934812i	$-0.384432\pi$
$827$	20.4262	0.710288	0.355144	+	0.934812i	$0.384432\pi$
$828$	10.0093	0.347846
$829$	−25.2861	−0.878221	−0.439111	−	0.898433i	$-0.644706\pi$
$829$	−25.2861	−0.878221	−0.439111	+	0.898433i	$0.644706\pi$
$830$	8.08782	0.280732
$831$	−15.2311	−0.528362
$832$	−32.2703	−1.11877
$833$	16.0422	0.555830
$834$	0.767883	0.0265896
$835$	23.1844	0.802328
$836$	−18.2241	−0.630295
$837$	4.00664	0.138490
$838$	6.51058	0.224904
$839$	28.0449	0.968216	0.484108	−	0.875008i	$-0.339144\pi$
$839$	28.0449	0.968216	0.484108	+	0.875008i	$0.339144\pi$
$840$	−5.28785	−0.182448
$841$	22.2617	0.767645
$842$	27.9735	0.964032
$843$	−6.66127	−0.229426
$844$	24.3921	0.839612
$845$	−28.2384	−0.971431
$846$	−15.7558	−0.541695
$847$	3.72662	0.128048
$848$	0.736141	0.0252792
$849$	−14.2155	−0.487875
$850$	−1.01277	−0.0347376
$851$	21.5804	0.739765
$852$	−5.09515	−0.174557
$853$	9.45290	0.323661	0.161831	−	0.986819i	$-0.448260\pi$
$853$	9.45290	0.323661	0.161831	+	0.986819i	$0.448260\pi$
$854$	21.2198	0.726126
$855$	36.5354	1.24948
$856$	−19.0903	−0.652493
$857$	2.67378	0.0913344	0.0456672	−	0.998957i	$-0.485459\pi$
$857$	2.67378	0.0913344	0.0456672	+	0.998957i	$0.485459\pi$
$858$	−6.95705	−0.237510
$859$	48.8637	1.66721	0.833604	−	0.552362i	$-0.186273\pi$
$859$	48.8637	1.66721	0.833604	+	0.552362i	$0.186273\pi$
$860$	−4.81944	−0.164342
$861$	0.929716	0.0316846
$862$	38.4689	1.31025
$863$	−1.07085	−0.0364523	−0.0182262	−	0.999834i	$-0.505802\pi$
$863$	−1.07085	−0.0364523	−0.0182262	+	0.999834i	$0.505802\pi$
$864$	−14.8178	−0.504110
$865$	26.2472	0.892432
$866$	−3.06538	−0.104166
$867$	−2.04514	−0.0694567
$868$	−2.42854	−0.0824299
$869$	−40.0680	−1.35921
$870$	7.75056	0.262769
$871$	7.86334	0.266439
$872$	47.0174	1.59221
$873$	−33.8386	−1.14526
$874$	18.6090	0.629457
$875$	−17.1886	−0.581082
$876$	−4.77669	−0.161390
$877$	26.8047	0.905132	0.452566	−	0.891731i	$-0.350509\pi$
$877$	26.8047	0.905132	0.452566	+	0.891731i	$0.350509\pi$
$878$	−32.6817	−1.10295
$879$	14.0901	0.475247
$880$	4.64396	0.156548
$881$	0.704807	0.0237456	0.0118728	−	0.999930i	$-0.496221\pi$
$881$	0.704807	0.0237456	0.0118728	+	0.999930i	$0.496221\pi$
$882$	11.8797	0.400009
$883$	0.797866	0.0268503	0.0134252	−	0.999910i	$-0.495727\pi$
$883$	0.797866	0.0268503	0.0134252	+	0.999910i	$0.495727\pi$
$884$	−19.3883	−0.652098
$885$	6.98408	0.234767
$886$	−8.77866	−0.294925
$887$	−10.4276	−0.350126	−0.175063	−	0.984557i	$-0.556013\pi$
$887$	−10.4276	−0.350126	−0.175063	+	0.984557i	$0.556013\pi$
$888$	−9.27815	−0.311354
$889$	2.86589	0.0961187
$890$	18.8711	0.632559
$891$	20.2944	0.679889
$892$	5.31198	0.177858
$893$	34.1791	1.14376
$894$	−0.487060	−0.0162897
$895$	−36.1383	−1.20797
$896$	6.88849	0.230128
$897$	−8.28898	−0.276761
$898$	22.2570	0.742725
$899$	10.1698	0.339183
$900$	0.875084	0.0291695
$901$	3.84200	0.127996
$902$	−3.37975	−0.112533
$903$	1.51190	0.0503128
$904$	−19.6960	−0.655079
$905$	12.3985	0.412138
$906$	5.53516	0.183893
$907$	−41.0609	−1.36340	−0.681702	−	0.731630i	$-0.738760\pi$
$907$	−41.0609	−1.36340	−0.681702	+	0.731630i	$0.738760\pi$
$908$	−10.3686	−0.344092
$909$	10.6779	0.354163
$910$	−17.6422	−0.584833
$911$	15.5164	0.514083	0.257041	−	0.966400i	$-0.417252\pi$
$911$	15.5164	0.514083	0.257041	+	0.966400i	$0.417252\pi$
$912$	−1.93286	−0.0640033
$913$	−10.7620	−0.356169
$914$	−9.90128	−0.327505
$915$	15.6766	0.518252
$916$	22.8034	0.753444
$917$	−14.1746	−0.468087
$918$	9.70449	0.320296
$919$	41.8153	1.37936	0.689679	−	0.724115i	$-0.257752\pi$
$919$	41.8153	1.37936	0.689679	+	0.724115i	$0.257752\pi$
$920$	22.9028	0.755084
$921$	14.1228	0.465361
$922$	−13.1818	−0.434119
$923$	−48.5675	−1.59862
$924$	2.46277	0.0810191
$925$	1.88672	0.0620348
$926$	−7.48715	−0.246043
$927$	48.2611	1.58510
$928$	−37.6111	−1.23465
$929$	−50.2050	−1.64717	−0.823587	−	0.567191i	$-0.808030\pi$
$929$	−50.2050	−1.64717	−0.823587	+	0.567191i	$0.808030\pi$
$930$	1.53764	0.0504212
$931$	−25.7706	−0.844598
$932$	−10.5388	−0.345210
$933$	6.51031	0.213138
$934$	−38.1940	−1.24975
$935$	24.2373	0.792645
$936$	−41.0199	−1.34078
$937$	28.4792	0.930374	0.465187	−	0.885212i	$-0.345987\pi$
$937$	28.4792	0.930374	0.465187	+	0.885212i	$0.345987\pi$
$938$	2.38564	0.0778938
$939$	10.5115	0.343031
$940$	14.7235	0.480229
$941$	−58.9009	−1.92012	−0.960058	−	0.279802i	$-0.909731\pi$
$941$	−58.9009	−1.92012	−0.960058	+	0.279802i	$0.909731\pi$
$942$	−2.09742	−0.0683375
$943$	−4.02680	−0.131131
$944$	4.25291	0.138420
$945$	−10.3035	−0.335174
$946$	−5.49612	−0.178694
$947$	9.61407	0.312415	0.156208	−	0.987724i	$-0.450073\pi$
$947$	9.61407	0.312415	0.156208	+	0.987724i	$0.450073\pi$
$948$	7.18390	0.233322
$949$	−45.5320	−1.47803
$950$	1.62693	0.0527847
$951$	14.7262	0.477530
$952$	−16.8055	−0.544670
$953$	−29.6613	−0.960825	−0.480413	−	0.877043i	$-0.659513\pi$
$953$	−29.6613	−0.960825	−0.480413	+	0.877043i	$0.659513\pi$
$954$	2.84510	0.0921134
$955$	25.0957	0.812079
$956$	17.0917	0.552786
$957$	−10.3132	−0.333378
$958$	−41.2765	−1.33358
$959$	2.54895	0.0823100
$960$	−7.23287	−0.233440
$961$	−28.9824	−0.934916
$962$	−30.9553	−0.998039
$963$	−17.8248	−0.574395
$964$	19.3860	0.624382
$965$	26.5977	0.856210
$966$	−2.51477	−0.0809114
$967$	−7.10072	−0.228344	−0.114172	−	0.993461i	$-0.536421\pi$
$967$	−7.10072	−0.228344	−0.114172	+	0.993461i	$0.536421\pi$
$968$	6.93950	0.223044
$969$	−10.0878	−0.324067
$970$	−27.1009	−0.870157
$971$	−16.4814	−0.528913	−0.264456	−	0.964398i	$-0.585192\pi$
$971$	−16.4814	−0.528913	−0.264456	+	0.964398i	$0.585192\pi$
$972$	−12.7523	−0.409031
$973$	−2.59109	−0.0830665
$974$	−7.06849	−0.226489
$975$	−0.724684	−0.0232085
$976$	9.54615	0.305565
$977$	−30.2809	−0.968772	−0.484386	−	0.874854i	$-0.660957\pi$
$977$	−30.2809	−0.968772	−0.484386	+	0.874854i	$0.660957\pi$
$978$	7.93021	0.253580
$979$	−25.1105	−0.802536
$980$	−11.1014	−0.354620
$981$	43.9005	1.40164
$982$	21.7708	0.694734
$983$	44.8916	1.43182	0.715909	−	0.698193i	$-0.246012\pi$
$983$	44.8916	1.43182	0.715909	+	0.698193i	$0.246012\pi$
$984$	1.73126	0.0551907
$985$	0.456134	0.0145336
$986$	24.6324	0.784455
$987$	−4.61889	−0.147021
$988$	31.1458	0.990880
$989$	−6.54835	−0.208225
$990$	17.9483	0.570435
$991$	−29.8425	−0.947978	−0.473989	−	0.880531i	$-0.657186\pi$
$991$	−29.8425	−0.947978	−0.473989	+	0.880531i	$0.657186\pi$
$992$	−7.46170	−0.236909
$993$	6.34017	0.201199
$994$	−14.7348	−0.467358
$995$	24.5389	0.777935
$996$	1.92954	0.0611399
$997$	−0.831349	−0.0263291	−0.0131645	−	0.999913i	$-0.504191\pi$
$997$	−0.831349	−0.0263291	−0.0131645	+	0.999913i	$0.504191\pi$
$998$	25.9548	0.821585
$999$	−18.0788	−0.571988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	401.2.a.a.1.9	✓	12
3.2	odd	2		3609.2.a.b.1.4		12
4.3	odd	2		6416.2.a.k.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
401.2.a.a.1.9	✓	12	1.1	even	1	trivial
3609.2.a.b.1.4		12	3.2	odd	2
6416.2.a.k.1.4		12	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:	\( N \)	\(=\)	\( 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	401.a (trivial)

\(f(q)\)	\(=\)	\(q+0.960737 q^{2} +0.489694 q^{3} -1.07698 q^{4} -2.30095 q^{5} +0.470467 q^{6} -1.58751 q^{7} -2.95617 q^{8} -2.76020 q^{9} +O(q^{10})\)	\(q+0.960737 q^{2} +0.489694 q^{3} -1.07698 q^{4} -2.30095 q^{5} +0.470467 q^{6} -1.58751 q^{7} -2.95617 q^{8} -2.76020 q^{9} -2.21061 q^{10} +2.94152 q^{11} -0.527393 q^{12} -5.02718 q^{13} -1.52518 q^{14} -1.12676 q^{15} -0.686134 q^{16} -3.58101 q^{17} -2.65183 q^{18} +5.75262 q^{19} +2.47809 q^{20} -0.777395 q^{21} +2.82603 q^{22} +3.36707 q^{23} -1.44762 q^{24} +0.294374 q^{25} -4.82979 q^{26} -2.82074 q^{27} +1.70973 q^{28} -7.15973 q^{29} -1.08252 q^{30} -1.42042 q^{31} +5.25315 q^{32} +1.44045 q^{33} -3.44041 q^{34} +3.65279 q^{35} +2.97269 q^{36} +6.40924 q^{37} +5.52675 q^{38} -2.46178 q^{39} +6.80201 q^{40} -1.19594 q^{41} -0.746872 q^{42} -1.94482 q^{43} -3.16797 q^{44} +6.35108 q^{45} +3.23487 q^{46} +5.94149 q^{47} -0.335996 q^{48} -4.47981 q^{49} +0.282816 q^{50} -1.75360 q^{51} +5.41419 q^{52} -1.07288 q^{53} -2.70999 q^{54} -6.76829 q^{55} +4.69296 q^{56} +2.81703 q^{57} -6.87861 q^{58} -6.19836 q^{59} +1.21351 q^{60} -13.9130 q^{61} -1.36465 q^{62} +4.38185 q^{63} +6.41916 q^{64} +11.5673 q^{65} +1.38389 q^{66} -1.56417 q^{67} +3.85669 q^{68} +1.64883 q^{69} +3.50937 q^{70} +9.66100 q^{71} +8.15963 q^{72} +9.05717 q^{73} +6.15760 q^{74} +0.144153 q^{75} -6.19549 q^{76} -4.66970 q^{77} -2.36512 q^{78} -13.6215 q^{79} +1.57876 q^{80} +6.89930 q^{81} -1.14898 q^{82} -3.65864 q^{83} +0.837243 q^{84} +8.23973 q^{85} -1.86846 q^{86} -3.50608 q^{87} -8.69564 q^{88} -8.53659 q^{89} +6.10172 q^{90} +7.98070 q^{91} -3.62628 q^{92} -0.695573 q^{93} +5.70821 q^{94} -13.2365 q^{95} +2.57244 q^{96} +12.2595 q^{97} -4.30392 q^{98} -8.11918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9} - 11 q^{10} - 11 q^{11} - 9 q^{12} - 11 q^{13} - 3 q^{14} - 11 q^{15} - 9 q^{16} + q^{17} - q^{18} - 34 q^{19} - 5 q^{20} - 3 q^{21} + 3 q^{22} - 7 q^{23} - 9 q^{24} + 7 q^{25} + 6 q^{26} - 2 q^{27} - 23 q^{28} - 6 q^{29} + 23 q^{30} - 52 q^{31} + 11 q^{32} + 4 q^{33} - 5 q^{34} + 12 q^{35} + 16 q^{36} + 3 q^{37} + 25 q^{38} - 24 q^{39} - 25 q^{40} - 16 q^{41} + 47 q^{42} - 2 q^{43} - 2 q^{44} - 23 q^{45} - 16 q^{46} - 3 q^{47} + 24 q^{48} + 6 q^{49} + 27 q^{50} - 16 q^{51} - 5 q^{52} + 19 q^{53} + 5 q^{54} - 43 q^{55} + 7 q^{56} + 11 q^{57} + 11 q^{58} - q^{59} + 30 q^{60} - 24 q^{61} + 39 q^{62} - 11 q^{63} - q^{64} + 13 q^{65} + 14 q^{66} + 6 q^{67} + 32 q^{68} + 29 q^{69} + 47 q^{70} - 15 q^{71} + 32 q^{72} - 20 q^{73} + 25 q^{74} + 31 q^{75} - 42 q^{76} + 38 q^{77} + 52 q^{78} - 53 q^{79} + 23 q^{80} - 8 q^{81} + 4 q^{82} + 17 q^{83} + 35 q^{84} + 7 q^{85} + 28 q^{86} - 5 q^{87} + 38 q^{88} - q^{89} + 58 q^{90} - 6 q^{91} + 46 q^{92} + 44 q^{93} - 4 q^{94} + 34 q^{95} + 28 q^{96} + 12 q^{97} + 27 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9 - 11 * q^10 - 11 * q^11 - 9 * q^12 - 11 * q^13 - 3 * q^14 - 11 * q^15 - 9 * q^16 + q^17 - q^18 - 34 * q^19 - 5 * q^20 - 3 * q^21 + 3 * q^22 - 7 * q^23 - 9 * q^24 + 7 * q^25 + 6 * q^26 - 2 * q^27 - 23 * q^28 - 6 * q^29 + 23 * q^30 - 52 * q^31 + 11 * q^32 + 4 * q^33 - 5 * q^34 + 12 * q^35 + 16 * q^36 + 3 * q^37 + 25 * q^38 - 24 * q^39 - 25 * q^40 - 16 * q^41 + 47 * q^42 - 2 * q^43 - 2 * q^44 - 23 * q^45 - 16 * q^46 - 3 * q^47 + 24 * q^48 + 6 * q^49 + 27 * q^50 - 16 * q^51 - 5 * q^52 + 19 * q^53 + 5 * q^54 - 43 * q^55 + 7 * q^56 + 11 * q^57 + 11 * q^58 - q^59 + 30 * q^60 - 24 * q^61 + 39 * q^62 - 11 * q^63 - q^64 + 13 * q^65 + 14 * q^66 + 6 * q^67 + 32 * q^68 + 29 * q^69 + 47 * q^70 - 15 * q^71 + 32 * q^72 - 20 * q^73 + 25 * q^74 + 31 * q^75 - 42 * q^76 + 38 * q^77 + 52 * q^78 - 53 * q^79 + 23 * q^80 - 8 * q^81 + 4 * q^82 + 17 * q^83 + 35 * q^84 + 7 * q^85 + 28 * q^86 - 5 * q^87 + 38 * q^88 - q^89 + 58 * q^90 - 6 * q^91 + 46 * q^92 + 44 * q^93 - 4 * q^94 + 34 * q^95 + 28 * q^96 + 12 * q^97 + 27 * q^98

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