LMFDB - Embedded newform 1334.2.a.k.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.61750$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.61750 q^{3} +1.00000 q^{4} +0.316103 q^{5} +2.61750 q^{6} -4.23734 q^{7} +1.00000 q^{8} +3.85129 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.61750 q^{3} +1.00000 q^{4} +0.316103 q^{5} +2.61750 q^{6} -4.23734 q^{7} +1.00000 q^{8} +3.85129 q^{9} +0.316103 q^{10} +2.97814 q^{11} +2.61750 q^{12} +3.99801 q^{13} -4.23734 q^{14} +0.827399 q^{15} +1.00000 q^{16} +4.57557 q^{17} +3.85129 q^{18} +1.78404 q^{19} +0.316103 q^{20} -11.0912 q^{21} +2.97814 q^{22} +1.00000 q^{23} +2.61750 q^{24} -4.90008 q^{25} +3.99801 q^{26} +2.22826 q^{27} -4.23734 q^{28} +1.00000 q^{29} +0.827399 q^{30} -0.0125038 q^{31} +1.00000 q^{32} +7.79529 q^{33} +4.57557 q^{34} -1.33944 q^{35} +3.85129 q^{36} -8.58267 q^{37} +1.78404 q^{38} +10.4648 q^{39} +0.316103 q^{40} +5.02992 q^{41} -11.0912 q^{42} -5.02894 q^{43} +2.97814 q^{44} +1.21741 q^{45} +1.00000 q^{46} -4.22367 q^{47} +2.61750 q^{48} +10.9550 q^{49} -4.90008 q^{50} +11.9766 q^{51} +3.99801 q^{52} -6.96969 q^{53} +2.22826 q^{54} +0.941400 q^{55} -4.23734 q^{56} +4.66972 q^{57} +1.00000 q^{58} +13.4570 q^{59} +0.827399 q^{60} -8.71786 q^{61} -0.0125038 q^{62} -16.3192 q^{63} +1.00000 q^{64} +1.26378 q^{65} +7.79529 q^{66} +9.45625 q^{67} +4.57557 q^{68} +2.61750 q^{69} -1.33944 q^{70} +14.8403 q^{71} +3.85129 q^{72} -13.5699 q^{73} -8.58267 q^{74} -12.8259 q^{75} +1.78404 q^{76} -12.6194 q^{77} +10.4648 q^{78} +3.99918 q^{79} +0.316103 q^{80} -5.72142 q^{81} +5.02992 q^{82} -15.2063 q^{83} -11.0912 q^{84} +1.44635 q^{85} -5.02894 q^{86} +2.61750 q^{87} +2.97814 q^{88} -8.37463 q^{89} +1.21741 q^{90} -16.9409 q^{91} +1.00000 q^{92} -0.0327288 q^{93} -4.22367 q^{94} +0.563940 q^{95} +2.61750 q^{96} +5.75162 q^{97} +10.9550 q^{98} +11.4697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.61750	1.51121	0.755606	−	0.655026i	$-0.227342\pi$
$3$	2.61750	1.51121	0.755606	+	0.655026i	$0.227342\pi$
$4$	1.00000	0.500000
$5$	0.316103	0.141366	0.0706828	−	0.997499i	$-0.477482\pi$
$5$	0.316103	0.141366	0.0706828	+	0.997499i	$0.477482\pi$
$6$	2.61750	1.06859
$7$	−4.23734	−1.60156	−0.800782	−	0.598956i	$-0.795582\pi$
$7$	−4.23734	−1.60156	−0.800782	+	0.598956i	$0.795582\pi$
$8$	1.00000	0.353553
$9$	3.85129	1.28376
$10$	0.316103	0.0999605
$11$	2.97814	0.897944	0.448972	−	0.893546i	$-0.351790\pi$
$11$	2.97814	0.897944	0.448972	+	0.893546i	$0.351790\pi$
$12$	2.61750	0.755606
$13$	3.99801	1.10885	0.554424	−	0.832235i	$-0.312939\pi$
$13$	3.99801	1.10885	0.554424	+	0.832235i	$0.312939\pi$
$14$	−4.23734	−1.13248
$15$	0.827399	0.213633
$16$	1.00000	0.250000
$17$	4.57557	1.10974	0.554870	−	0.831937i	$-0.312768\pi$
$17$	4.57557	1.10974	0.554870	+	0.831937i	$0.312768\pi$
$18$	3.85129	0.907759
$19$	1.78404	0.409287	0.204643	−	0.978837i	$-0.434397\pi$
$19$	1.78404	0.409287	0.204643	+	0.978837i	$0.434397\pi$
$20$	0.316103	0.0706828
$21$	−11.0912	−2.42030
$22$	2.97814	0.634943
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.61750	0.534294
$25$	−4.90008	−0.980016
$26$	3.99801	0.784074
$27$	2.22826	0.428829
$28$	−4.23734	−0.800782
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.827399	0.151062
$31$	−0.0125038	−0.00224575	−0.00112288	−	0.999999i	$-0.500357\pi$
$31$	−0.0125038	−0.00224575	−0.00112288	+	0.999999i	$0.500357\pi$
$32$	1.00000	0.176777
$33$	7.79529	1.35699
$34$	4.57557	0.784704
$35$	−1.33944	−0.226406
$36$	3.85129	0.641882
$37$	−8.58267	−1.41098	−0.705491	−	0.708719i	$-0.749273\pi$
$37$	−8.58267	−1.41098	−0.705491	+	0.708719i	$0.749273\pi$
$38$	1.78404	0.289410
$39$	10.4648	1.67570
$40$	0.316103	0.0499803
$41$	5.02992	0.785541	0.392771	−	0.919636i	$-0.371517\pi$
$41$	5.02992	0.785541	0.392771	+	0.919636i	$0.371517\pi$
$42$	−11.0912	−1.71141
$43$	−5.02894	−0.766907	−0.383453	−	0.923560i	$-0.625265\pi$
$43$	−5.02894	−0.766907	−0.383453	+	0.923560i	$0.625265\pi$
$44$	2.97814	0.448972
$45$	1.21741	0.181480
$46$	1.00000	0.147442
$47$	−4.22367	−0.616086	−0.308043	−	0.951372i	$-0.599674\pi$
$47$	−4.22367	−0.616086	−0.308043	+	0.951372i	$0.599674\pi$
$48$	2.61750	0.377803
$49$	10.9550	1.56501
$50$	−4.90008	−0.692976
$51$	11.9766	1.67705
$52$	3.99801	0.554424
$53$	−6.96969	−0.957361	−0.478680	−	0.877989i	$-0.658885\pi$
$53$	−6.96969	−0.957361	−0.478680	+	0.877989i	$0.658885\pi$
$54$	2.22826	0.303228
$55$	0.941400	0.126938
$56$	−4.23734	−0.566238
$57$	4.66972	0.618520
$58$	1.00000	0.131306
$59$	13.4570	1.75195	0.875975	−	0.482357i	$-0.160219\pi$
$59$	13.4570	1.75195	0.875975	+	0.482357i	$0.160219\pi$
$60$	0.827399	0.106817
$61$	−8.71786	−1.11621	−0.558104	−	0.829771i	$-0.688471\pi$
$61$	−8.71786	−1.11621	−0.558104	+	0.829771i	$0.688471\pi$
$62$	−0.0125038	−0.00158799
$63$	−16.3192	−2.05603
$64$	1.00000	0.125000
$65$	1.26378	0.156753
$66$	7.79529	0.959533
$67$	9.45625	1.15526	0.577632	−	0.816297i	$-0.303977\pi$
$67$	9.45625	1.15526	0.577632	+	0.816297i	$0.303977\pi$
$68$	4.57557	0.554870
$69$	2.61750	0.315110
$70$	−1.33944	−0.160093
$71$	14.8403	1.76122	0.880608	−	0.473845i	$-0.157134\pi$
$71$	14.8403	1.76122	0.880608	+	0.473845i	$0.157134\pi$
$72$	3.85129	0.453879
$73$	−13.5699	−1.58824	−0.794118	−	0.607764i	$-0.792067\pi$
$73$	−13.5699	−1.58824	−0.794118	+	0.607764i	$0.792067\pi$
$74$	−8.58267	−0.997715
$75$	−12.8259	−1.48101
$76$	1.78404	0.204643
$77$	−12.6194	−1.43812
$78$	10.4648	1.18490
$79$	3.99918	0.449943	0.224971	−	0.974365i	$-0.427771\pi$
$79$	3.99918	0.449943	0.224971	+	0.974365i	$0.427771\pi$
$80$	0.316103	0.0353414
$81$	−5.72142	−0.635713
$82$	5.02992	0.555462
$83$	−15.2063	−1.66911	−0.834554	−	0.550927i	$-0.814274\pi$
$83$	−15.2063	−1.66911	−0.834554	+	0.550927i	$0.814274\pi$
$84$	−11.0912	−1.21015
$85$	1.44635	0.156879
$86$	−5.02894	−0.542285
$87$	2.61750	0.280625
$88$	2.97814	0.317471
$89$	−8.37463	−0.887709	−0.443854	−	0.896099i	$-0.646389\pi$
$89$	−8.37463	−0.887709	−0.443854	+	0.896099i	$0.646389\pi$
$90$	1.21741	0.128326
$91$	−16.9409	−1.77589
$92$	1.00000	0.104257
$93$	−0.0327288	−0.00339381
$94$	−4.22367	−0.435639
$95$	0.563940	0.0578591
$96$	2.61750	0.267147
$97$	5.75162	0.583988	0.291994	−	0.956420i	$-0.405681\pi$
$97$	5.75162	0.583988	0.291994	+	0.956420i	$0.405681\pi$
$98$	10.9550	1.10663
$99$	11.4697	1.15275
$100$	−4.90008	−0.490008
$101$	−14.6496	−1.45769	−0.728845	−	0.684679i	$-0.759942\pi$
$101$	−14.6496	−1.45769	−0.728845	+	0.684679i	$0.759942\pi$
$102$	11.9766	1.18586
$103$	−12.8626	−1.26739	−0.633693	−	0.773584i	$-0.718462\pi$
$103$	−12.8626	−1.26739	−0.633693	+	0.773584i	$0.718462\pi$
$104$	3.99801	0.392037
$105$	−3.50597	−0.342148
$106$	−6.96969	−0.676956
$107$	−0.317988	−0.0307410	−0.0153705	−	0.999882i	$-0.504893\pi$
$107$	−0.317988	−0.0307410	−0.0153705	+	0.999882i	$0.504893\pi$
$108$	2.22826	0.214414
$109$	−3.99729	−0.382871	−0.191435	−	0.981505i	$-0.561314\pi$
$109$	−3.99729	−0.382871	−0.191435	+	0.981505i	$0.561314\pi$
$110$	0.941400	0.0897590
$111$	−22.4651	−2.13229
$112$	−4.23734	−0.400391
$113$	4.75036	0.446877	0.223438	−	0.974718i	$-0.428272\pi$
$113$	4.75036	0.446877	0.223438	+	0.974718i	$0.428272\pi$
$114$	4.66972	0.437359
$115$	0.316103	0.0294767
$116$	1.00000	0.0928477
$117$	15.3975	1.42350
$118$	13.4570	1.23882
$119$	−19.3883	−1.77732
$120$	0.827399	0.0755308
$121$	−2.13065	−0.193696
$122$	−8.71786	−0.789278
$123$	13.1658	1.18712
$124$	−0.0125038	−0.00112288
$125$	−3.12944	−0.279906
$126$	−16.3192	−1.45383
$127$	7.45194	0.661253	0.330626	−	0.943762i	$-0.392740\pi$
$127$	7.45194	0.661253	0.330626	+	0.943762i	$0.392740\pi$
$128$	1.00000	0.0883883
$129$	−13.1632	−1.15896
$130$	1.26378	0.110841
$131$	9.99302	0.873094	0.436547	−	0.899681i	$-0.356201\pi$
$131$	9.99302	0.873094	0.436547	+	0.899681i	$0.356201\pi$
$132$	7.79529	0.678493
$133$	−7.55958	−0.655499
$134$	9.45625	0.816896
$135$	0.704359	0.0606216
$136$	4.57557	0.392352
$137$	−8.49233	−0.725549	−0.362775	−	0.931877i	$-0.618170\pi$
$137$	−8.49233	−0.725549	−0.362775	+	0.931877i	$0.618170\pi$
$138$	2.61750	0.222816
$139$	−4.17386	−0.354022	−0.177011	−	0.984209i	$-0.556643\pi$
$139$	−4.17386	−0.354022	−0.177011	+	0.984209i	$0.556643\pi$
$140$	−1.33944	−0.113203
$141$	−11.0555	−0.931037
$142$	14.8403	1.24537
$143$	11.9066	0.995683
$144$	3.85129	0.320941
$145$	0.316103	0.0262509
$146$	−13.5699	−1.12305
$147$	28.6748	2.36506
$148$	−8.58267	−0.705491
$149$	−3.12682	−0.256159	−0.128079	−	0.991764i	$-0.540881\pi$
$149$	−3.12682	−0.256159	−0.128079	+	0.991764i	$0.540881\pi$
$150$	−12.8259	−1.04723
$151$	−13.8272	−1.12524	−0.562620	−	0.826716i	$-0.690207\pi$
$151$	−13.8272	−1.12524	−0.562620	+	0.826716i	$0.690207\pi$
$152$	1.78404	0.144705
$153$	17.6219	1.42464
$154$	−12.6194	−1.01690
$155$	−0.00395250	−0.000317472 0
$156$	10.4648	0.837852
$157$	−10.4714	−0.835705	−0.417852	−	0.908515i	$-0.637217\pi$
$157$	−10.4714	−0.835705	−0.417852	+	0.908515i	$0.637217\pi$
$158$	3.99918	0.318157
$159$	−18.2431	−1.44678
$160$	0.316103	0.0249901
$161$	−4.23734	−0.333949
$162$	−5.72142	−0.449517
$163$	0.759602	0.0594966	0.0297483	−	0.999557i	$-0.490529\pi$
$163$	0.759602	0.0594966	0.0297483	+	0.999557i	$0.490529\pi$
$164$	5.02992	0.392771
$165$	2.46411	0.191831
$166$	−15.2063	−1.18024
$167$	−10.5946	−0.819833	−0.409917	−	0.912123i	$-0.634442\pi$
$167$	−10.5946	−0.819833	−0.409917	+	0.912123i	$0.634442\pi$
$168$	−11.0912	−0.855707
$169$	2.98406	0.229543
$170$	1.44635	0.110930
$171$	6.87086	0.525428
$172$	−5.02894	−0.383453
$173$	4.36295	0.331709	0.165854	−	0.986150i	$-0.446962\pi$
$173$	4.36295	0.331709	0.165854	+	0.986150i	$0.446962\pi$
$174$	2.61750	0.198432
$175$	20.7633	1.56956
$176$	2.97814	0.224486
$177$	35.2236	2.64757
$178$	−8.37463	−0.627705
$179$	15.6735	1.17149	0.585747	−	0.810494i	$-0.300801\pi$
$179$	15.6735	1.17149	0.585747	+	0.810494i	$0.300801\pi$
$180$	1.21741	0.0907400
$181$	1.95417	0.145252	0.0726262	−	0.997359i	$-0.476862\pi$
$181$	1.95417	0.145252	0.0726262	+	0.997359i	$0.476862\pi$
$182$	−16.9409	−1.25574
$183$	−22.8190	−1.68683
$184$	1.00000	0.0737210
$185$	−2.71301	−0.199464
$186$	−0.0327288	−0.00239979
$187$	13.6267	0.996484
$188$	−4.22367	−0.308043
$189$	−9.44189	−0.686796
$190$	0.563940	0.0409125
$191$	1.06020	0.0767131	0.0383566	−	0.999264i	$-0.487788\pi$
$191$	1.06020	0.0767131	0.0383566	+	0.999264i	$0.487788\pi$
$192$	2.61750	0.188902
$193$	−7.94999	−0.572253	−0.286127	−	0.958192i	$-0.592368\pi$
$193$	−7.94999	−0.572253	−0.286127	+	0.958192i	$0.592368\pi$
$194$	5.75162	0.412942
$195$	3.30795	0.236887
$196$	10.9550	0.782503
$197$	28.0218	1.99647	0.998236	−	0.0593641i	$-0.0189073\pi$
$197$	28.0218	1.99647	0.998236	+	0.0593641i	$0.0189073\pi$
$198$	11.4697	0.815117
$199$	0.0899332	0.00637519	0.00318760	−	0.999995i	$-0.498985\pi$
$199$	0.0899332	0.00637519	0.00318760	+	0.999995i	$0.498985\pi$
$200$	−4.90008	−0.346488
$201$	24.7517	1.74585
$202$	−14.6496	−1.03074
$203$	−4.23734	−0.297403
$204$	11.9766	0.838526
$205$	1.58997	0.111048
$206$	−12.8626	−0.896178
$207$	3.85129	0.267683
$208$	3.99801	0.277212
$209$	5.31313	0.367517
$210$	−3.50597	−0.241935
$211$	10.1808	0.700873	0.350436	−	0.936587i	$-0.386033\pi$
$211$	10.1808	0.700873	0.350436	+	0.936587i	$0.386033\pi$
$212$	−6.96969	−0.478680
$213$	38.8444	2.66157
$214$	−0.317988	−0.0217372
$215$	−1.58966	−0.108414
$216$	2.22826	0.151614
$217$	0.0529830	0.00359672
$218$	−3.99729	−0.270731
$219$	−35.5192	−2.40016
$220$	0.941400	0.0634692
$221$	18.2932	1.23053
$222$	−22.4651	−1.50776
$223$	−21.3726	−1.43121	−0.715607	−	0.698503i	$-0.753850\pi$
$223$	−21.3726	−1.43121	−0.715607	+	0.698503i	$0.753850\pi$
$224$	−4.23734	−0.283119
$225$	−18.8716	−1.25811
$226$	4.75036	0.315989
$227$	1.81073	0.120183	0.0600913	−	0.998193i	$-0.480861\pi$
$227$	1.81073	0.120183	0.0600913	+	0.998193i	$0.480861\pi$
$228$	4.66972	0.309260
$229$	1.77385	0.117219	0.0586097	−	0.998281i	$-0.481333\pi$
$229$	1.77385	0.117219	0.0586097	+	0.998281i	$0.481333\pi$
$230$	0.316103	0.0208432
$231$	−33.0313	−2.17330
$232$	1.00000	0.0656532
$233$	−8.76935	−0.574499	−0.287250	−	0.957856i	$-0.592741\pi$
$233$	−8.76935	−0.574499	−0.287250	+	0.957856i	$0.592741\pi$
$234$	15.3975	1.00657
$235$	−1.33512	−0.0870934
$236$	13.4570	0.875975
$237$	10.4678	0.679959
$238$	−19.3883	−1.25675
$239$	21.1378	1.36729	0.683644	−	0.729815i	$-0.260394\pi$
$239$	21.1378	1.36729	0.683644	+	0.729815i	$0.260394\pi$
$240$	0.827399	0.0534084
$241$	28.5825	1.84116	0.920580	−	0.390555i	$-0.127717\pi$
$241$	28.5825	1.84116	0.920580	+	0.390555i	$0.127717\pi$
$242$	−2.13065	−0.136964
$243$	−21.6606	−1.38953
$244$	−8.71786	−0.558104
$245$	3.46292	0.221238
$246$	13.1658	0.839421
$247$	7.13260	0.453837
$248$	−0.0125038	−0.000793994 0
$249$	−39.8024	−2.52238
$250$	−3.12944	−0.197923
$251$	−12.6724	−0.799875	−0.399938	−	0.916542i	$-0.630968\pi$
$251$	−12.6724	−0.799875	−0.399938	+	0.916542i	$0.630968\pi$
$252$	−16.3192	−1.02802
$253$	2.97814	0.187234
$254$	7.45194	0.467576
$255$	3.78582	0.237077
$256$	1.00000	0.0625000
$257$	23.0898	1.44030	0.720152	−	0.693817i	$-0.244072\pi$
$257$	23.0898	1.44030	0.720152	+	0.693817i	$0.244072\pi$
$258$	−13.1632	−0.819508
$259$	36.3677	2.25978
$260$	1.26378	0.0783764
$261$	3.85129	0.238389
$262$	9.99302	0.617371
$263$	5.27233	0.325106	0.162553	−	0.986700i	$-0.448027\pi$
$263$	5.27233	0.325106	0.162553	+	0.986700i	$0.448027\pi$
$264$	7.79529	0.479767
$265$	−2.20314	−0.135338
$266$	−7.55958	−0.463508
$267$	−21.9206	−1.34152
$268$	9.45625	0.577632
$269$	1.62421	0.0990296	0.0495148	−	0.998773i	$-0.484233\pi$
$269$	1.62421	0.0990296	0.0495148	+	0.998773i	$0.484233\pi$
$270$	0.704359	0.0428659
$271$	5.40691	0.328446	0.164223	−	0.986423i	$-0.447488\pi$
$271$	5.40691	0.328446	0.164223	+	0.986423i	$0.447488\pi$
$272$	4.57557	0.277435
$273$	−44.3428	−2.68375
$274$	−8.49233	−0.513041
$275$	−14.5931	−0.880000
$276$	2.61750	0.157555
$277$	−1.94957	−0.117138	−0.0585691	−	0.998283i	$-0.518654\pi$
$277$	−1.94957	−0.117138	−0.0585691	+	0.998283i	$0.518654\pi$
$278$	−4.17386	−0.250332
$279$	−0.0481559	−0.00288302
$280$	−1.33944	−0.0800466
$281$	−24.9138	−1.48623	−0.743117	−	0.669162i	$-0.766653\pi$
$281$	−24.9138	−1.48623	−0.743117	+	0.669162i	$0.766653\pi$
$282$	−11.0555	−0.658343
$283$	−29.9601	−1.78094	−0.890472	−	0.455037i	$-0.849626\pi$
$283$	−29.9601	−1.78094	−0.890472	+	0.455037i	$0.849626\pi$
$284$	14.8403	0.880608
$285$	1.47611	0.0874374
$286$	11.9066	0.704055
$287$	−21.3135	−1.25809
$288$	3.85129	0.226940
$289$	3.93587	0.231522
$290$	0.316103	0.0185622
$291$	15.0548	0.882531
$292$	−13.5699	−0.794118
$293$	19.5027	1.13936	0.569680	−	0.821867i	$-0.307067\pi$
$293$	19.5027	1.13936	0.569680	+	0.821867i	$0.307067\pi$
$294$	28.6748	1.67235
$295$	4.25379	0.247665
$296$	−8.58267	−0.498857
$297$	6.63608	0.385064
$298$	−3.12682	−0.181132
$299$	3.99801	0.231211
$300$	−12.8259	−0.740506
$301$	21.3093	1.22825
$302$	−13.8272	−0.795665
$303$	−38.3453	−2.20288
$304$	1.78404	0.102322
$305$	−2.75574	−0.157793
$306$	17.6219	1.00738
$307$	19.8693	1.13400	0.567000	−	0.823718i	$-0.308104\pi$
$307$	19.8693	1.13400	0.567000	+	0.823718i	$0.308104\pi$
$308$	−12.6194	−0.719058
$309$	−33.6677	−1.91529
$310$	−0.00395250	−0.000224487 0
$311$	−15.3912	−0.872755	−0.436378	−	0.899764i	$-0.643739\pi$
$311$	−15.3912	−0.872755	−0.436378	+	0.899764i	$0.643739\pi$
$312$	10.4648	0.592451
$313$	4.14323	0.234189	0.117095	−	0.993121i	$-0.462642\pi$
$313$	4.14323	0.234189	0.117095	+	0.993121i	$0.462642\pi$
$314$	−10.4714	−0.590933
$315$	−5.15856	−0.290652
$316$	3.99918	0.224971
$317$	−32.0671	−1.80107	−0.900533	−	0.434788i	$-0.856823\pi$
$317$	−32.0671	−1.80107	−0.900533	+	0.434788i	$0.856823\pi$
$318$	−18.2431	−1.02302
$319$	2.97814	0.166744
$320$	0.316103	0.0176707
$321$	−0.832332	−0.0464562
$322$	−4.23734	−0.236138
$323$	8.16301	0.454202
$324$	−5.72142	−0.317857
$325$	−19.5905	−1.08669
$326$	0.759602	0.0420705
$327$	−10.4629	−0.578600
$328$	5.02992	0.277731
$329$	17.8971	0.986701
$330$	2.46411	0.135645
$331$	16.3018	0.896027	0.448013	−	0.894027i	$-0.352132\pi$
$331$	16.3018	0.896027	0.448013	+	0.894027i	$0.352132\pi$
$332$	−15.2063	−0.834554
$333$	−33.0544	−1.81137
$334$	−10.5946	−0.579710
$335$	2.98915	0.163315
$336$	−11.0912	−0.605076
$337$	29.4922	1.60654	0.803271	−	0.595613i	$-0.203091\pi$
$337$	29.4922	1.60654	0.803271	+	0.595613i	$0.203091\pi$
$338$	2.98406	0.162311
$339$	12.4341	0.675326
$340$	1.44635	0.0784394
$341$	−0.0372382	−0.00201656
$342$	6.87086	0.371534
$343$	−16.7589	−0.904894
$344$	−5.02894	−0.271142
$345$	0.827399	0.0445456
$346$	4.36295	0.234554
$347$	19.6170	1.05310	0.526548	−	0.850145i	$-0.323486\pi$
$347$	19.6170	1.05310	0.526548	+	0.850145i	$0.323486\pi$
$348$	2.61750	0.140313
$349$	35.7746	1.91497	0.957485	−	0.288482i	$-0.0931506\pi$
$349$	35.7746	1.91497	0.957485	+	0.288482i	$0.0931506\pi$
$350$	20.7633	1.10985
$351$	8.90859	0.475505
$352$	2.97814	0.158736
$353$	−14.6968	−0.782233	−0.391116	−	0.920341i	$-0.627911\pi$
$353$	−14.6968	−0.782233	−0.391116	+	0.920341i	$0.627911\pi$
$354$	35.2236	1.87211
$355$	4.69106	0.248975
$356$	−8.37463	−0.443854
$357$	−50.7487	−2.68591
$358$	15.6735	0.828372
$359$	11.3826	0.600752	0.300376	−	0.953821i	$-0.402888\pi$
$359$	11.3826	0.600752	0.300376	+	0.953821i	$0.402888\pi$
$360$	1.21741	0.0641629
$361$	−15.8172	−0.832484
$362$	1.95417	0.102709
$363$	−5.57698	−0.292716
$364$	−16.9409	−0.887945
$365$	−4.28948	−0.224522
$366$	−22.8190	−1.19277
$367$	9.19498	0.479974	0.239987	−	0.970776i	$-0.422857\pi$
$367$	9.19498	0.479974	0.239987	+	0.970776i	$0.422857\pi$
$368$	1.00000	0.0521286
$369$	19.3717	1.00845
$370$	−2.71301	−0.141042
$371$	29.5329	1.53327
$372$	−0.0327288	−0.00169691
$373$	35.0092	1.81271	0.906355	−	0.422517i	$-0.138853\pi$
$373$	35.0092	1.81271	0.906355	+	0.422517i	$0.138853\pi$
$374$	13.6267	0.704621
$375$	−8.19131	−0.422998
$376$	−4.22367	−0.217819
$377$	3.99801	0.205908
$378$	−9.44189	−0.485638
$379$	16.8272	0.864358	0.432179	−	0.901788i	$-0.357745\pi$
$379$	16.8272	0.864358	0.432179	+	0.901788i	$0.357745\pi$
$380$	0.563940	0.0289295
$381$	19.5054	0.999294
$382$	1.06020	0.0542444
$383$	3.66622	0.187335	0.0936677	−	0.995604i	$-0.470141\pi$
$383$	3.66622	0.187335	0.0936677	+	0.995604i	$0.470141\pi$
$384$	2.61750	0.133574
$385$	−3.98903	−0.203300
$386$	−7.94999	−0.404644
$387$	−19.3679	−0.984527
$388$	5.75162	0.291994
$389$	−22.5065	−1.14112	−0.570562	−	0.821255i	$-0.693274\pi$
$389$	−22.5065	−1.14112	−0.570562	+	0.821255i	$0.693274\pi$
$390$	3.30795	0.167504
$391$	4.57557	0.231397
$392$	10.9550	0.553313
$393$	26.1567	1.31943
$394$	28.0218	1.41172
$395$	1.26415	0.0636064
$396$	11.4697	0.576375
$397$	0.717657	0.0360182	0.0180091	−	0.999838i	$-0.494267\pi$
$397$	0.717657	0.0360182	0.0180091	+	0.999838i	$0.494267\pi$
$398$	0.0899332	0.00450794
$399$	−19.7872	−0.990599
$400$	−4.90008	−0.245004
$401$	−33.8919	−1.69248	−0.846239	−	0.532803i	$-0.821139\pi$
$401$	−33.8919	−1.69248	−0.846239	+	0.532803i	$0.821139\pi$
$402$	24.7517	1.23450
$403$	−0.0499904	−0.00249020
$404$	−14.6496	−0.728845
$405$	−1.80856	−0.0898679
$406$	−4.23734	−0.210296
$407$	−25.5604	−1.26698
$408$	11.9766	0.592928
$409$	18.5388	0.916686	0.458343	−	0.888775i	$-0.348443\pi$
$409$	18.5388	0.916686	0.458343	+	0.888775i	$0.348443\pi$
$410$	1.58997	0.0785231
$411$	−22.2287	−1.09646
$412$	−12.8626	−0.633693
$413$	−57.0218	−2.80586
$414$	3.85129	0.189281
$415$	−4.80675	−0.235954
$416$	3.99801	0.196018
$417$	−10.9251	−0.535003
$418$	5.31313	0.259874
$419$	32.5047	1.58796	0.793980	−	0.607944i	$-0.208005\pi$
$419$	32.5047	1.58796	0.793980	+	0.607944i	$0.208005\pi$
$420$	−3.50597	−0.171074
$421$	−9.25001	−0.450818	−0.225409	−	0.974264i	$-0.572372\pi$
$421$	−9.25001	−0.450818	−0.225409	+	0.974264i	$0.572372\pi$
$422$	10.1808	0.495592
$423$	−16.2666	−0.790910
$424$	−6.96969	−0.338478
$425$	−22.4207	−1.08756
$426$	38.8444	1.88202
$427$	36.9406	1.78768
$428$	−0.317988	−0.0153705
$429$	31.1656	1.50469
$430$	−1.58966	−0.0766604
$431$	−21.8295	−1.05149	−0.525745	−	0.850642i	$-0.676213\pi$
$431$	−21.8295	−1.05149	−0.525745	+	0.850642i	$0.676213\pi$
$432$	2.22826	0.107207
$433$	5.18372	0.249114	0.124557	−	0.992212i	$-0.460249\pi$
$433$	5.18372	0.249114	0.124557	+	0.992212i	$0.460249\pi$
$434$	0.0529830	0.00254327
$435$	0.827399	0.0396707
$436$	−3.99729	−0.191435
$437$	1.78404	0.0853422
$438$	−35.5192	−1.69717
$439$	17.7525	0.847280	0.423640	−	0.905831i	$-0.360752\pi$
$439$	17.7525	0.847280	0.423640	+	0.905831i	$0.360752\pi$
$440$	0.941400	0.0448795
$441$	42.1911	2.00910
$442$	18.2932	0.870117
$443$	23.7021	1.12612	0.563060	−	0.826416i	$-0.309624\pi$
$443$	23.7021	1.12612	0.563060	+	0.826416i	$0.309624\pi$
$444$	−22.4651	−1.06615
$445$	−2.64724	−0.125491
$446$	−21.3726	−1.01202
$447$	−8.18444	−0.387111
$448$	−4.23734	−0.200195
$449$	−15.7608	−0.743796	−0.371898	−	0.928274i	$-0.621293\pi$
$449$	−15.7608	−0.743796	−0.371898	+	0.928274i	$0.621293\pi$
$450$	−18.8716	−0.889618
$451$	14.9798	0.705372
$452$	4.75036	0.223438
$453$	−36.1926	−1.70048
$454$	1.81073	0.0849819
$455$	−5.35507	−0.251050
$456$	4.66972	0.218680
$457$	33.8352	1.58275	0.791373	−	0.611334i	$-0.209367\pi$
$457$	33.8352	1.58275	0.791373	+	0.611334i	$0.209367\pi$
$458$	1.77385	0.0828866
$459$	10.1956	0.475888
$460$	0.316103	0.0147384
$461$	−10.8270	−0.504261	−0.252131	−	0.967693i	$-0.581131\pi$
$461$	−10.8270	−0.504261	−0.252131	+	0.967693i	$0.581131\pi$
$462$	−33.0313	−1.53675
$463$	−23.3138	−1.08348	−0.541742	−	0.840545i	$-0.682235\pi$
$463$	−23.3138	−1.08348	−0.541742	+	0.840545i	$0.682235\pi$
$464$	1.00000	0.0464238
$465$	−0.0103457	−0.000479768 0
$466$	−8.76935	−0.406232
$467$	16.1762	0.748547	0.374274	−	0.927318i	$-0.377892\pi$
$467$	16.1762	0.748547	0.374274	+	0.927318i	$0.377892\pi$
$468$	15.3975	0.711750
$469$	−40.0693	−1.85023
$470$	−1.33512	−0.0615843
$471$	−27.4087	−1.26293
$472$	13.4570	0.619408
$473$	−14.9769	−0.688640
$474$	10.4678	0.480804
$475$	−8.74194	−0.401108
$476$	−19.3883	−0.888659
$477$	−26.8423	−1.22903
$478$	21.1378	0.966819
$479$	33.6438	1.53722	0.768612	−	0.639715i	$-0.220948\pi$
$479$	33.6438	1.53722	0.768612	+	0.639715i	$0.220948\pi$
$480$	0.827399	0.0377654
$481$	−34.3136	−1.56456
$482$	28.5825	1.30190
$483$	−11.0912	−0.504668
$484$	−2.13065	−0.0968479
$485$	1.81810	0.0825558
$486$	−21.6606	−0.982544
$487$	−29.4639	−1.33514	−0.667568	−	0.744549i	$-0.732665\pi$
$487$	−29.4639	−1.33514	−0.667568	+	0.744549i	$0.732665\pi$
$488$	−8.71786	−0.394639
$489$	1.98826	0.0899121
$490$	3.46292	0.156439
$491$	−21.5740	−0.973622	−0.486811	−	0.873507i	$-0.661840\pi$
$491$	−21.5740	−0.973622	−0.486811	+	0.873507i	$0.661840\pi$
$492$	13.1658	0.593560
$493$	4.57557	0.206073
$494$	7.13260	0.320911
$495$	3.62561	0.162959
$496$	−0.0125038	−0.000561439 0
$497$	−62.8833	−2.82070
$498$	−39.8024	−1.78359
$499$	33.9292	1.51888	0.759439	−	0.650578i	$-0.225474\pi$
$499$	33.9292	1.51888	0.759439	+	0.650578i	$0.225474\pi$
$500$	−3.12944	−0.139953
$501$	−27.7313	−1.23894
$502$	−12.6724	−0.565597
$503$	22.2387	0.991576	0.495788	−	0.868444i	$-0.334879\pi$
$503$	22.2387	0.991576	0.495788	+	0.868444i	$0.334879\pi$
$504$	−16.3192	−0.726917
$505$	−4.63078	−0.206067
$506$	2.97814	0.132395
$507$	7.81076	0.346888
$508$	7.45194	0.330626
$509$	−8.66278	−0.383971	−0.191985	−	0.981398i	$-0.561493\pi$
$509$	−8.66278	−0.383971	−0.191985	+	0.981398i	$0.561493\pi$
$510$	3.78582	0.167639
$511$	57.5002	2.54366
$512$	1.00000	0.0441942
$513$	3.97530	0.175514
$514$	23.0898	1.01845
$515$	−4.06590	−0.179165
$516$	−13.1632	−0.579480
$517$	−12.5787	−0.553211
$518$	36.3677	1.59790
$519$	11.4200	0.501283
$520$	1.26378	0.0554205
$521$	−27.2795	−1.19514	−0.597568	−	0.801818i	$-0.703866\pi$
$521$	−27.2795	−1.19514	−0.597568	+	0.801818i	$0.703866\pi$
$522$	3.85129	0.168567
$523$	−9.08165	−0.397113	−0.198556	−	0.980089i	$-0.563625\pi$
$523$	−9.08165	−0.397113	−0.198556	+	0.980089i	$0.563625\pi$
$524$	9.99302	0.436547
$525$	54.3479	2.37194
$526$	5.27233	0.229885
$527$	−0.0572122	−0.00249220
$528$	7.79529	0.339246
$529$	1.00000	0.0434783
$530$	−2.20314	−0.0956983
$531$	51.8268	2.24909
$532$	−7.55958	−0.327750
$533$	20.1096	0.871045
$534$	−21.9206	−0.948596
$535$	−0.100517	−0.00434572
$536$	9.45625	0.408448
$537$	41.0254	1.77038
$538$	1.62421	0.0700245
$539$	32.6257	1.40529
$540$	0.704359	0.0303108
$541$	9.30074	0.399870	0.199935	−	0.979809i	$-0.435927\pi$
$541$	9.30074	0.399870	0.199935	+	0.979809i	$0.435927\pi$
$542$	5.40691	0.232246
$543$	5.11504	0.219507
$544$	4.57557	0.196176
$545$	−1.26356	−0.0541248
$546$	−44.3428	−1.89770
$547$	−44.0137	−1.88189	−0.940944	−	0.338561i	$-0.890060\pi$
$547$	−44.0137	−1.88189	−0.940944	+	0.338561i	$0.890060\pi$
$548$	−8.49233	−0.362775
$549$	−33.5751	−1.43295
$550$	−14.5931	−0.622254
$551$	1.78404	0.0760027
$552$	2.61750	0.111408
$553$	−16.9459	−0.720612
$554$	−1.94957	−0.0828292
$555$	−7.10129	−0.301433
$556$	−4.17386	−0.177011
$557$	34.4560	1.45995	0.729974	−	0.683475i	$-0.239532\pi$
$557$	34.4560	1.45995	0.729974	+	0.683475i	$0.239532\pi$
$558$	−0.0481559	−0.00203860
$559$	−20.1057	−0.850382
$560$	−1.33944	−0.0566015
$561$	35.6679	1.50590
$562$	−24.9138	−1.05093
$563$	2.29128	0.0965661	0.0482830	−	0.998834i	$-0.484625\pi$
$563$	2.29128	0.0965661	0.0482830	+	0.998834i	$0.484625\pi$
$564$	−11.0555	−0.465519
$565$	1.50160	0.0631729
$566$	−29.9601	−1.25932
$567$	24.2436	1.01814
$568$	14.8403	0.622684
$569$	23.9278	1.00311	0.501553	−	0.865127i	$-0.332762\pi$
$569$	23.9278	1.00311	0.501553	+	0.865127i	$0.332762\pi$
$570$	1.47611	0.0618275
$571$	18.7754	0.785728	0.392864	−	0.919597i	$-0.371484\pi$
$571$	18.7754	0.785728	0.392864	+	0.919597i	$0.371484\pi$
$572$	11.9066	0.497842
$573$	2.77506	0.115930
$574$	−21.3135	−0.889607
$575$	−4.90008	−0.204347
$576$	3.85129	0.160471
$577$	−5.73781	−0.238868	−0.119434	−	0.992842i	$-0.538108\pi$
$577$	−5.73781	−0.238868	−0.119434	+	0.992842i	$0.538108\pi$
$578$	3.93587	0.163710
$579$	−20.8091	−0.864796
$580$	0.316103	0.0131255
$581$	64.4342	2.67318
$582$	15.0548	0.624043
$583$	−20.7567	−0.859657
$584$	−13.5699	−0.561526
$585$	4.86719	0.201234
$586$	19.5027	0.805649
$587$	20.5484	0.848123	0.424062	−	0.905633i	$-0.360604\pi$
$587$	20.5484	0.848123	0.424062	+	0.905633i	$0.360604\pi$
$588$	28.6748	1.18253
$589$	−0.0223073	−0.000919158 0
$590$	4.25379	0.175126
$591$	73.3471	3.01710
$592$	−8.58267	−0.352745
$593$	−23.3939	−0.960671	−0.480336	−	0.877085i	$-0.659485\pi$
$593$	−23.3939	−0.960671	−0.480336	+	0.877085i	$0.659485\pi$
$594$	6.63608	0.272282
$595$	−6.12868	−0.251252
$596$	−3.12682	−0.128079
$597$	0.235400	0.00963428
$598$	3.99801	0.163491
$599$	−36.8749	−1.50667	−0.753334	−	0.657639i	$-0.771555\pi$
$599$	−36.8749	−1.50667	−0.753334	+	0.657639i	$0.771555\pi$
$600$	−12.8259	−0.523617
$601$	−6.08467	−0.248199	−0.124099	−	0.992270i	$-0.539604\pi$
$601$	−6.08467	−0.248199	−0.124099	+	0.992270i	$0.539604\pi$
$602$	21.3093	0.868504
$603$	36.4188	1.48309
$604$	−13.8272	−0.562620
$605$	−0.673506	−0.0273819
$606$	−38.3453	−1.55767
$607$	−21.8801	−0.888085	−0.444043	−	0.896006i	$-0.646456\pi$
$607$	−21.8801	−0.888085	−0.444043	+	0.896006i	$0.646456\pi$
$608$	1.78404	0.0723524
$609$	−11.0912	−0.449439
$610$	−2.75574	−0.111577
$611$	−16.8863	−0.683146
$612$	17.6219	0.712322
$613$	−11.2378	−0.453891	−0.226946	−	0.973907i	$-0.572874\pi$
$613$	−11.2378	−0.453891	−0.226946	+	0.973907i	$0.572874\pi$
$614$	19.8693	0.801859
$615$	4.16175	0.167818
$616$	−12.6194	−0.508451
$617$	19.3676	0.779709	0.389855	−	0.920876i	$-0.372525\pi$
$617$	19.3676	0.779709	0.389855	+	0.920876i	$0.372525\pi$
$618$	−33.6677	−1.35432
$619$	44.0210	1.76935	0.884676	−	0.466206i	$-0.154379\pi$
$619$	44.0210	1.76935	0.884676	+	0.466206i	$0.154379\pi$
$620$	−0.00395250	−0.000158736 0
$621$	2.22826	0.0894169
$622$	−15.3912	−0.617131
$623$	35.4861	1.42172
$624$	10.4648	0.418926
$625$	23.5112	0.940447
$626$	4.14323	0.165597
$627$	13.9071	0.555396
$628$	−10.4714	−0.417852
$629$	−39.2706	−1.56582
$630$	−5.15856	−0.205522
$631$	27.6682	1.10145	0.550726	−	0.834686i	$-0.314351\pi$
$631$	27.6682	1.10145	0.550726	+	0.834686i	$0.314351\pi$
$632$	3.99918	0.159079
$633$	26.6481	1.05917
$634$	−32.0671	−1.27355
$635$	2.35558	0.0934784
$636$	−18.2431	−0.723388
$637$	43.7984	1.73535
$638$	2.97814	0.117906
$639$	57.1543	2.26099
$640$	0.316103	0.0124951
$641$	−14.5553	−0.574898	−0.287449	−	0.957796i	$-0.592807\pi$
$641$	−14.5553	−0.574898	−0.287449	+	0.957796i	$0.592807\pi$
$642$	−0.832332	−0.0328495
$643$	−3.07930	−0.121436	−0.0607178	−	0.998155i	$-0.519339\pi$
$643$	−3.07930	−0.121436	−0.0607178	+	0.998155i	$0.519339\pi$
$644$	−4.23734	−0.166975
$645$	−4.16094	−0.163837
$646$	8.16301	0.321169
$647$	8.09304	0.318170	0.159085	−	0.987265i	$-0.449146\pi$
$647$	8.09304	0.318170	0.159085	+	0.987265i	$0.449146\pi$
$648$	−5.72142	−0.224759
$649$	40.0768	1.57315
$650$	−19.5905	−0.768404
$651$	0.138683	0.00543541
$652$	0.759602	0.0297483
$653$	−42.9439	−1.68053	−0.840263	−	0.542179i	$-0.817599\pi$
$653$	−42.9439	−1.68053	−0.840263	+	0.542179i	$0.817599\pi$
$654$	−10.4629	−0.409132
$655$	3.15882	0.123425
$656$	5.02992	0.196385
$657$	−52.2616	−2.03892
$658$	17.8971	0.697703
$659$	1.51989	0.0592065	0.0296032	−	0.999562i	$-0.490576\pi$
$659$	1.51989	0.0592065	0.0296032	+	0.999562i	$0.490576\pi$
$660$	2.46411	0.0959155
$661$	−1.05977	−0.0412203	−0.0206102	−	0.999788i	$-0.506561\pi$
$661$	−1.05977	−0.0412203	−0.0206102	+	0.999788i	$0.506561\pi$
$662$	16.3018	0.633586
$663$	47.8823	1.85960
$664$	−15.2063	−0.590119
$665$	−2.38961	−0.0926650
$666$	−33.0544	−1.28083
$667$	1.00000	0.0387202
$668$	−10.5946	−0.409917
$669$	−55.9427	−2.16287
$670$	2.98915	0.115481
$671$	−25.9631	−1.00229
$672$	−11.0912	−0.427853
$673$	27.0573	1.04298	0.521490	−	0.853257i	$-0.325376\pi$
$673$	27.0573	1.04298	0.521490	+	0.853257i	$0.325376\pi$
$674$	29.4922	1.13600
$675$	−10.9186	−0.420259
$676$	2.98406	0.114771
$677$	−43.9973	−1.69095	−0.845476	−	0.534013i	$-0.820683\pi$
$677$	−43.9973	−1.69095	−0.845476	+	0.534013i	$0.820683\pi$
$678$	12.4341	0.477527
$679$	−24.3716	−0.935294
$680$	1.44635	0.0554651
$681$	4.73959	0.181622
$682$	−0.0372382	−0.00142593
$683$	−1.36860	−0.0523680	−0.0261840	−	0.999657i	$-0.508336\pi$
$683$	−1.36860	−0.0523680	−0.0261840	+	0.999657i	$0.508336\pi$
$684$	6.87086	0.262714
$685$	−2.68445	−0.102568
$686$	−16.7589	−0.639857
$687$	4.64305	0.177143
$688$	−5.02894	−0.191727
$689$	−27.8649	−1.06157
$690$	0.827399	0.0314985
$691$	−31.0271	−1.18033	−0.590164	−	0.807284i	$-0.700937\pi$
$691$	−31.0271	−1.18033	−0.590164	+	0.807284i	$0.700937\pi$
$692$	4.36295	0.165854
$693$	−48.6011	−1.84620
$694$	19.6170	0.744652
$695$	−1.31937	−0.0500465
$696$	2.61750	0.0992160
$697$	23.0148	0.871746
$698$	35.7746	1.35409
$699$	−22.9538	−0.868191
$700$	20.7633	0.784779
$701$	−3.70651	−0.139993	−0.0699965	−	0.997547i	$-0.522299\pi$
$701$	−3.70651	−0.139993	−0.0699965	+	0.997547i	$0.522299\pi$
$702$	8.90859	0.336233
$703$	−15.3118	−0.577496
$704$	2.97814	0.112243
$705$	−3.49466	−0.131617
$706$	−14.6968	−0.553122
$707$	62.0753	2.33458
$708$	35.2236	1.32378
$709$	1.38943	0.0521812	0.0260906	−	0.999660i	$-0.491694\pi$
$709$	1.38943	0.0521812	0.0260906	+	0.999660i	$0.491694\pi$
$710$	4.69106	0.176052
$711$	15.4020	0.577620
$712$	−8.37463	−0.313852
$713$	−0.0125038	−0.000468272 0
$714$	−50.7487	−1.89922
$715$	3.76372	0.140755
$716$	15.6735	0.585747
$717$	55.3281	2.06626
$718$	11.3826	0.424796
$719$	−0.457232	−0.0170519	−0.00852594	−	0.999964i	$-0.502714\pi$
$719$	−0.457232	−0.0170519	−0.00852594	+	0.999964i	$0.502714\pi$
$720$	1.21741	0.0453700
$721$	54.5031	2.02980
$722$	−15.8172	−0.588655
$723$	74.8146	2.78238
$724$	1.95417	0.0726262
$725$	−4.90008	−0.181984
$726$	−5.57698	−0.206981
$727$	47.4523	1.75991	0.879954	−	0.475059i	$-0.157573\pi$
$727$	47.4523	1.75991	0.879954	+	0.475059i	$0.157573\pi$
$728$	−16.9409	−0.627872
$729$	−39.5322	−1.46416
$730$	−4.28948	−0.158761
$731$	−23.0103	−0.851066
$732$	−22.8190	−0.843414
$733$	43.6772	1.61325	0.806626	−	0.591062i	$-0.201291\pi$
$733$	43.6772	1.61325	0.806626	+	0.591062i	$0.201291\pi$
$734$	9.19498	0.339393
$735$	9.06419	0.334338
$736$	1.00000	0.0368605
$737$	28.1621	1.03736
$738$	19.3717	0.713082
$739$	−11.0625	−0.406942	−0.203471	−	0.979081i	$-0.565222\pi$
$739$	−11.0625	−0.406942	−0.203471	+	0.979081i	$0.565222\pi$
$740$	−2.71301	−0.0997321
$741$	18.6696	0.685844
$742$	29.5329	1.08419
$743$	19.1245	0.701608	0.350804	−	0.936449i	$-0.385908\pi$
$743$	19.1245	0.701608	0.350804	+	0.936449i	$0.385908\pi$
$744$	−0.0327288	−0.00119989
$745$	−0.988396	−0.0362120
$746$	35.0092	1.28178
$747$	−58.5639	−2.14274
$748$	13.6267	0.498242
$749$	1.34742	0.0492337
$750$	−8.19131	−0.299104
$751$	44.7058	1.63134	0.815669	−	0.578519i	$-0.196369\pi$
$751$	44.7058	1.63134	0.815669	+	0.578519i	$0.196369\pi$
$752$	−4.22367	−0.154022
$753$	−33.1700	−1.20878
$754$	3.99801	0.145599
$755$	−4.37081	−0.159070
$756$	−9.44189	−0.343398
$757$	−18.2112	−0.661899	−0.330949	−	0.943649i	$-0.607369\pi$
$757$	−18.2112	−0.661899	−0.330949	+	0.943649i	$0.607369\pi$
$758$	16.8272	0.611193
$759$	7.79529	0.282951
$760$	0.563940	0.0204563
$761$	4.91212	0.178064	0.0890322	−	0.996029i	$-0.471623\pi$
$761$	4.91212	0.178064	0.0890322	+	0.996029i	$0.471623\pi$
$762$	19.5054	0.706608
$763$	16.9379	0.613192
$764$	1.06020	0.0383566
$765$	5.57033	0.201396
$766$	3.66622	0.132466
$767$	53.8011	1.94265
$768$	2.61750	0.0944508
$769$	25.9596	0.936127	0.468064	−	0.883695i	$-0.344952\pi$
$769$	25.9596	0.936127	0.468064	+	0.883695i	$0.344952\pi$
$770$	−3.98903	−0.143755
$771$	60.4375	2.17660
$772$	−7.94999	−0.286127
$773$	25.7547	0.926330	0.463165	−	0.886272i	$-0.346714\pi$
$773$	25.7547	0.926330	0.463165	+	0.886272i	$0.346714\pi$
$774$	−19.3679	−0.696166
$775$	0.0612698	0.00220088
$776$	5.75162	0.206471
$777$	95.1923	3.41500
$778$	−22.5065	−0.806896
$779$	8.97358	0.321512
$780$	3.30795	0.118443
$781$	44.1965	1.58148
$782$	4.57557	0.163622
$783$	2.22826	0.0796315
$784$	10.9550	0.391252
$785$	−3.31003	−0.118140
$786$	26.1567	0.932979
$787$	−36.0086	−1.28357	−0.641783	−	0.766886i	$-0.721805\pi$
$787$	−36.0086	−1.28357	−0.641783	+	0.766886i	$0.721805\pi$
$788$	28.0218	0.998236
$789$	13.8003	0.491304
$790$	1.26415	0.0449765
$791$	−20.1289	−0.715701
$792$	11.4697	0.407558
$793$	−34.8541	−1.23770
$794$	0.717657	0.0254687
$795$	−5.76671	−0.204524
$796$	0.0899332	0.00318760
$797$	−2.65831	−0.0941620	−0.0470810	−	0.998891i	$-0.514992\pi$
$797$	−2.65831	−0.0941620	−0.0470810	+	0.998891i	$0.514992\pi$
$798$	−19.7872	−0.700459
$799$	−19.3257	−0.683695
$800$	−4.90008	−0.173244
$801$	−32.2532	−1.13961
$802$	−33.8919	−1.19676
$803$	−40.4131	−1.42615
$804$	24.7517	0.872926
$805$	−1.33944	−0.0472089
$806$	−0.0499904	−0.00176084
$807$	4.25136	0.149655
$808$	−14.6496	−0.515371
$809$	−38.3759	−1.34923	−0.674613	−	0.738172i	$-0.735689\pi$
$809$	−38.3759	−1.34923	−0.674613	+	0.738172i	$0.735689\pi$
$810$	−1.80856	−0.0635462
$811$	41.8260	1.46871	0.734355	−	0.678765i	$-0.237485\pi$
$811$	41.8260	1.46871	0.734355	+	0.678765i	$0.237485\pi$
$812$	−4.23734	−0.148701
$813$	14.1526	0.496352
$814$	−25.5604	−0.895892
$815$	0.240112	0.00841077
$816$	11.9766	0.419263
$817$	−8.97184	−0.313885
$818$	18.5388	0.648195
$819$	−65.2444	−2.27982
$820$	1.58997	0.0555242
$821$	5.32273	0.185765	0.0928823	−	0.995677i	$-0.470392\pi$
$821$	5.32273	0.185765	0.0928823	+	0.995677i	$0.470392\pi$
$822$	−22.2287	−0.775314
$823$	−4.26314	−0.148604	−0.0743019	−	0.997236i	$-0.523673\pi$
$823$	−4.26314	−0.148604	−0.0743019	+	0.997236i	$0.523673\pi$
$824$	−12.8626	−0.448089
$825$	−38.1975	−1.32987
$826$	−57.0218	−1.98404
$827$	36.1665	1.25763	0.628816	−	0.777554i	$-0.283540\pi$
$827$	36.1665	1.25763	0.628816	+	0.777554i	$0.283540\pi$
$828$	3.85129	0.133842
$829$	−20.5540	−0.713870	−0.356935	−	0.934129i	$-0.616178\pi$
$829$	−20.5540	−0.713870	−0.356935	+	0.934129i	$0.616178\pi$
$830$	−4.80675	−0.166845
$831$	−5.10299	−0.177021
$832$	3.99801	0.138606
$833$	50.1256	1.73675
$834$	−10.9251	−0.378304
$835$	−3.34898	−0.115896
$836$	5.31313	0.183758
$837$	−0.0278618	−0.000963044 0
$838$	32.5047	1.12286
$839$	−2.97655	−0.102762	−0.0513810	−	0.998679i	$-0.516362\pi$
$839$	−2.97655	−0.102762	−0.0513810	+	0.998679i	$0.516362\pi$
$840$	−3.50597	−0.120967
$841$	1.00000	0.0344828
$842$	−9.25001	−0.318776
$843$	−65.2118	−2.24602
$844$	10.1808	0.350436
$845$	0.943269	0.0324494
$846$	−16.2666	−0.559258
$847$	9.02830	0.310216
$848$	−6.96969	−0.239340
$849$	−78.4206	−2.69139
$850$	−22.4207	−0.769023
$851$	−8.58267	−0.294210
$852$	38.8444	1.33079
$853$	26.6847	0.913666	0.456833	−	0.889553i	$-0.348984\pi$
$853$	26.6847	0.913666	0.456833	+	0.889553i	$0.348984\pi$
$854$	36.9406	1.26408
$855$	2.17190	0.0742774
$856$	−0.317988	−0.0108686
$857$	2.67175	0.0912654	0.0456327	−	0.998958i	$-0.485470\pi$
$857$	2.67175	0.0912654	0.0456327	+	0.998958i	$0.485470\pi$
$858$	31.1656	1.06398
$859$	−40.3328	−1.37614	−0.688069	−	0.725645i	$-0.741541\pi$
$859$	−40.3328	−1.37614	−0.688069	+	0.725645i	$0.741541\pi$
$860$	−1.58966	−0.0542071
$861$	−55.7880	−1.90125
$862$	−21.8295	−0.743516
$863$	49.1657	1.67362	0.836810	−	0.547494i	$-0.184418\pi$
$863$	49.1657	1.67362	0.836810	+	0.547494i	$0.184418\pi$
$864$	2.22826	0.0758069
$865$	1.37914	0.0468922
$866$	5.18372	0.176150
$867$	10.3021	0.349878
$868$	0.0529830	0.00179836
$869$	11.9101	0.404023
$870$	0.827399	0.0280514
$871$	37.8061	1.28101
$872$	−3.99729	−0.135365
$873$	22.1512	0.749703
$874$	1.78404	0.0603461
$875$	13.2605	0.448287
$876$	−35.5192	−1.20008
$877$	−41.5439	−1.40284	−0.701418	−	0.712750i	$-0.747450\pi$
$877$	−41.5439	−1.40284	−0.701418	+	0.712750i	$0.747450\pi$
$878$	17.7525	0.599117
$879$	51.0483	1.72182
$880$	0.941400	0.0317346
$881$	28.6672	0.965821	0.482911	−	0.875670i	$-0.339580\pi$
$881$	28.6672	0.965821	0.482911	+	0.875670i	$0.339580\pi$
$882$	42.1911	1.42065
$883$	14.8304	0.499083	0.249541	−	0.968364i	$-0.419720\pi$
$883$	14.8304	0.499083	0.249541	+	0.968364i	$0.419720\pi$
$884$	18.2932	0.615266
$885$	11.1343	0.374275
$886$	23.7021	0.796287
$887$	−10.0344	−0.336922	−0.168461	−	0.985708i	$-0.553880\pi$
$887$	−10.0344	−0.336922	−0.168461	+	0.985708i	$0.553880\pi$
$888$	−22.4651	−0.753880
$889$	−31.5764	−1.05904
$890$	−2.64724	−0.0887358
$891$	−17.0392	−0.570835
$892$	−21.3726	−0.715607
$893$	−7.53521	−0.252156
$894$	−8.18444	−0.273729
$895$	4.95445	0.165609
$896$	−4.23734	−0.141560
$897$	10.4648	0.349409
$898$	−15.7608	−0.525943
$899$	−0.0125038	−0.000417026 0
$900$	−18.8716	−0.629055
$901$	−31.8903	−1.06242
$902$	14.9798	0.498774
$903$	55.7771	1.85615
$904$	4.75036	0.157995
$905$	0.617719	0.0205337
$906$	−36.1926	−1.20242
$907$	−57.0069	−1.89288	−0.946441	−	0.322878i	$-0.895350\pi$
$907$	−57.0069	−1.89288	−0.946441	+	0.322878i	$0.895350\pi$
$908$	1.81073	0.0600913
$909$	−56.4199	−1.87133
$910$	−5.35507	−0.177519
$911$	−55.8527	−1.85048	−0.925242	−	0.379378i	$-0.876138\pi$
$911$	−55.8527	−1.85048	−0.925242	+	0.379378i	$0.876138\pi$
$912$	4.66972	0.154630
$913$	−45.2865	−1.49877
$914$	33.8352	1.11917
$915$	−7.21315	−0.238459
$916$	1.77385	0.0586097
$917$	−42.3438	−1.39832
$918$	10.1956	0.336504
$919$	12.3128	0.406161	0.203080	−	0.979162i	$-0.434905\pi$
$919$	12.3128	0.406161	0.203080	+	0.979162i	$0.434905\pi$
$920$	0.316103	0.0104216
$921$	52.0078	1.71372
$922$	−10.8270	−0.356567
$923$	59.3315	1.95292
$924$	−33.0313	−1.08665
$925$	42.0557	1.38278
$926$	−23.3138	−0.766139
$927$	−49.5375	−1.62703
$928$	1.00000	0.0328266
$929$	−26.4918	−0.869169	−0.434584	−	0.900631i	$-0.643105\pi$
$929$	−26.4918	−0.869169	−0.434584	+	0.900631i	$0.643105\pi$
$930$	−0.0103457	−0.000339247 0
$931$	19.5442	0.640537
$932$	−8.76935	−0.287250
$933$	−40.2864	−1.31892
$934$	16.1762	0.529303
$935$	4.30745	0.140869
$936$	15.3975	0.503283
$937$	−55.5288	−1.81405	−0.907024	−	0.421080i	$-0.861651\pi$
$937$	−55.5288	−1.81405	−0.907024	+	0.421080i	$0.861651\pi$
$938$	−40.0693	−1.30831
$939$	10.8449	0.353910
$940$	−1.33512	−0.0435467
$941$	25.6450	0.836004	0.418002	−	0.908446i	$-0.362730\pi$
$941$	25.6450	0.836004	0.418002	+	0.908446i	$0.362730\pi$
$942$	−27.4087	−0.893025
$943$	5.02992	0.163797
$944$	13.4570	0.437987
$945$	−2.98461	−0.0970893
$946$	−14.9769	−0.486942
$947$	29.6823	0.964546	0.482273	−	0.876021i	$-0.339811\pi$
$947$	29.6823	0.964546	0.482273	+	0.876021i	$0.339811\pi$
$948$	10.4678	0.339979
$949$	−54.2525	−1.76111
$950$	−8.74194	−0.283626
$951$	−83.9355	−2.72179
$952$	−19.3883	−0.628377
$953$	−26.0577	−0.844091	−0.422045	−	0.906575i	$-0.638688\pi$
$953$	−26.0577	−0.844091	−0.422045	+	0.906575i	$0.638688\pi$
$954$	−26.8423	−0.869052
$955$	0.335131	0.0108446
$956$	21.1378	0.683644
$957$	7.79529	0.251986
$958$	33.6438	1.08698
$959$	35.9849	1.16201
$960$	0.827399	0.0267042
$961$	−30.9998	−0.999995
$962$	−34.3136	−1.10631
$963$	−1.22466	−0.0394642
$964$	28.5825	0.920580
$965$	−2.51302	−0.0808969
$966$	−11.0912	−0.356854
$967$	25.6836	0.825928	0.412964	−	0.910747i	$-0.364494\pi$
$967$	25.6836	0.825928	0.412964	+	0.910747i	$0.364494\pi$
$968$	−2.13065	−0.0684818
$969$	21.3666	0.686396
$970$	1.81810	0.0583758
$971$	22.7824	0.731123	0.365562	−	0.930787i	$-0.380877\pi$
$971$	22.7824	0.731123	0.365562	+	0.930787i	$0.380877\pi$
$972$	−21.6606	−0.694763
$973$	17.6861	0.566989
$974$	−29.4639	−0.944084
$975$	−51.2782	−1.64222
$976$	−8.71786	−0.279052
$977$	−48.8163	−1.56177	−0.780885	−	0.624674i	$-0.785232\pi$
$977$	−48.8163	−1.56177	−0.780885	+	0.624674i	$0.785232\pi$
$978$	1.98826	0.0635774
$979$	−24.9409	−0.797113
$980$	3.46292	0.110619
$981$	−15.3947	−0.491516
$982$	−21.5740	−0.688454
$983$	−10.3851	−0.331233	−0.165616	−	0.986190i	$-0.552961\pi$
$983$	−10.3851	−0.331233	−0.165616	+	0.986190i	$0.552961\pi$
$984$	13.1658	0.419710
$985$	8.85778	0.282232
$986$	4.57557	0.145716
$987$	46.8457	1.49112
$988$	7.13260	0.226918
$989$	−5.02894	−0.159911
$990$	3.62561	0.115229
$991$	−46.1635	−1.46643	−0.733216	−	0.679996i	$-0.761981\pi$
$991$	−46.1635	−1.46643	−0.733216	+	0.679996i	$0.761981\pi$
$992$	−0.0125038	−0.000396997 0
$993$	42.6699	1.35409
$994$	−62.8833	−1.99454
$995$	0.0284281	0.000901233 0
$996$	−39.8024	−1.26119
$997$	21.9164	0.694099	0.347049	−	0.937847i	$-0.387184\pi$
$997$	21.9164	0.694099	0.347049	+	0.937847i	$0.387184\pi$
$998$	33.9292	1.07401
$999$	−19.1244	−0.605069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.8	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.61750 q^{3} +1.00000 q^{4} +0.316103 q^{5} +2.61750 q^{6} -4.23734 q^{7} +1.00000 q^{8} +3.85129 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.61750 q^{3} +1.00000 q^{4} +0.316103 q^{5} +2.61750 q^{6} -4.23734 q^{7} +1.00000 q^{8} +3.85129 q^{9} +0.316103 q^{10} +2.97814 q^{11} +2.61750 q^{12} +3.99801 q^{13} -4.23734 q^{14} +0.827399 q^{15} +1.00000 q^{16} +4.57557 q^{17} +3.85129 q^{18} +1.78404 q^{19} +0.316103 q^{20} -11.0912 q^{21} +2.97814 q^{22} +1.00000 q^{23} +2.61750 q^{24} -4.90008 q^{25} +3.99801 q^{26} +2.22826 q^{27} -4.23734 q^{28} +1.00000 q^{29} +0.827399 q^{30} -0.0125038 q^{31} +1.00000 q^{32} +7.79529 q^{33} +4.57557 q^{34} -1.33944 q^{35} +3.85129 q^{36} -8.58267 q^{37} +1.78404 q^{38} +10.4648 q^{39} +0.316103 q^{40} +5.02992 q^{41} -11.0912 q^{42} -5.02894 q^{43} +2.97814 q^{44} +1.21741 q^{45} +1.00000 q^{46} -4.22367 q^{47} +2.61750 q^{48} +10.9550 q^{49} -4.90008 q^{50} +11.9766 q^{51} +3.99801 q^{52} -6.96969 q^{53} +2.22826 q^{54} +0.941400 q^{55} -4.23734 q^{56} +4.66972 q^{57} +1.00000 q^{58} +13.4570 q^{59} +0.827399 q^{60} -8.71786 q^{61} -0.0125038 q^{62} -16.3192 q^{63} +1.00000 q^{64} +1.26378 q^{65} +7.79529 q^{66} +9.45625 q^{67} +4.57557 q^{68} +2.61750 q^{69} -1.33944 q^{70} +14.8403 q^{71} +3.85129 q^{72} -13.5699 q^{73} -8.58267 q^{74} -12.8259 q^{75} +1.78404 q^{76} -12.6194 q^{77} +10.4648 q^{78} +3.99918 q^{79} +0.316103 q^{80} -5.72142 q^{81} +5.02992 q^{82} -15.2063 q^{83} -11.0912 q^{84} +1.44635 q^{85} -5.02894 q^{86} +2.61750 q^{87} +2.97814 q^{88} -8.37463 q^{89} +1.21741 q^{90} -16.9409 q^{91} +1.00000 q^{92} -0.0327288 q^{93} -4.22367 q^{94} +0.563940 q^{95} +2.61750 q^{96} +5.75162 q^{97} +10.9550 q^{98} +11.4697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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