LMFDB - Embedded newform 4010.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} + \cdots - 512 $ x^15 - 7x^14 - 7x^13 + 133x^12 - 99x^11 - 941x^10 + 1290x^9 + 3031x^8 - 5452x^7 - 4098x^6 + 9986x^5 + 850x^4 - 7216x^3 + 1688x^2 + 1441x - 512
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.07374$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.34293 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.34293 q^{6} +3.45446 q^{7} -1.00000 q^{8} +8.17517 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.34293 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.34293 q^{6} +3.45446 q^{7} -1.00000 q^{8} +8.17517 q^{9} +1.00000 q^{10} +3.65066 q^{11} -3.34293 q^{12} +3.49629 q^{13} -3.45446 q^{14} +3.34293 q^{15} +1.00000 q^{16} +4.44571 q^{17} -8.17517 q^{18} -6.26283 q^{19} -1.00000 q^{20} -11.5480 q^{21} -3.65066 q^{22} -7.57267 q^{23} +3.34293 q^{24} +1.00000 q^{25} -3.49629 q^{26} -17.3002 q^{27} +3.45446 q^{28} -2.62514 q^{29} -3.34293 q^{30} +3.28327 q^{31} -1.00000 q^{32} -12.2039 q^{33} -4.44571 q^{34} -3.45446 q^{35} +8.17517 q^{36} -7.45793 q^{37} +6.26283 q^{38} -11.6879 q^{39} +1.00000 q^{40} +4.62987 q^{41} +11.5480 q^{42} -9.40958 q^{43} +3.65066 q^{44} -8.17517 q^{45} +7.57267 q^{46} -4.02949 q^{47} -3.34293 q^{48} +4.93327 q^{49} -1.00000 q^{50} -14.8617 q^{51} +3.49629 q^{52} +4.07029 q^{53} +17.3002 q^{54} -3.65066 q^{55} -3.45446 q^{56} +20.9362 q^{57} +2.62514 q^{58} +4.53317 q^{59} +3.34293 q^{60} -11.7429 q^{61} -3.28327 q^{62} +28.2408 q^{63} +1.00000 q^{64} -3.49629 q^{65} +12.2039 q^{66} -2.55592 q^{67} +4.44571 q^{68} +25.3149 q^{69} +3.45446 q^{70} +13.5208 q^{71} -8.17517 q^{72} -12.2418 q^{73} +7.45793 q^{74} -3.34293 q^{75} -6.26283 q^{76} +12.6111 q^{77} +11.6879 q^{78} -11.7450 q^{79} -1.00000 q^{80} +33.3079 q^{81} -4.62987 q^{82} -9.38947 q^{83} -11.5480 q^{84} -4.44571 q^{85} +9.40958 q^{86} +8.77564 q^{87} -3.65066 q^{88} +1.01654 q^{89} +8.17517 q^{90} +12.0778 q^{91} -7.57267 q^{92} -10.9757 q^{93} +4.02949 q^{94} +6.26283 q^{95} +3.34293 q^{96} +3.76457 q^{97} -4.93327 q^{98} +29.8448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9} + 15 q^{10} - 2 q^{11} - 6 q^{12} - 13 q^{13} + 5 q^{14} + 6 q^{15} + 15 q^{16} + 11 q^{17} - 19 q^{18} - 15 q^{19} - 15 q^{20} - 2 q^{21} + 2 q^{22} - 3 q^{23} + 6 q^{24} + 15 q^{25} + 13 q^{26} - 12 q^{27} - 5 q^{28} + 28 q^{29} - 6 q^{30} - 12 q^{31} - 15 q^{32} - 22 q^{33} - 11 q^{34} + 5 q^{35} + 19 q^{36} - 23 q^{37} + 15 q^{38} - 2 q^{39} + 15 q^{40} + 24 q^{41} + 2 q^{42} - 24 q^{43} - 2 q^{44} - 19 q^{45} + 3 q^{46} - 3 q^{47} - 6 q^{48} + 20 q^{49} - 15 q^{50} - 5 q^{51} - 13 q^{52} + 10 q^{53} + 12 q^{54} + 2 q^{55} + 5 q^{56} - 11 q^{57} - 28 q^{58} + 2 q^{59} + 6 q^{60} + 15 q^{61} + 12 q^{62} - 2 q^{63} + 15 q^{64} + 13 q^{65} + 22 q^{66} - 48 q^{67} + 11 q^{68} + 21 q^{69} - 5 q^{70} + 15 q^{71} - 19 q^{72} - 47 q^{73} + 23 q^{74} - 6 q^{75} - 15 q^{76} + 7 q^{77} + 2 q^{78} - 34 q^{79} - 15 q^{80} + 43 q^{81} - 24 q^{82} - 32 q^{83} - 2 q^{84} - 11 q^{85} + 24 q^{86} + 14 q^{87} + 2 q^{88} + 25 q^{89} + 19 q^{90} - 32 q^{91} - 3 q^{92} - 42 q^{93} + 3 q^{94} + 15 q^{95} + 6 q^{96} - 34 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9 + 15 * q^10 - 2 * q^11 - 6 * q^12 - 13 * q^13 + 5 * q^14 + 6 * q^15 + 15 * q^16 + 11 * q^17 - 19 * q^18 - 15 * q^19 - 15 * q^20 - 2 * q^21 + 2 * q^22 - 3 * q^23 + 6 * q^24 + 15 * q^25 + 13 * q^26 - 12 * q^27 - 5 * q^28 + 28 * q^29 - 6 * q^30 - 12 * q^31 - 15 * q^32 - 22 * q^33 - 11 * q^34 + 5 * q^35 + 19 * q^36 - 23 * q^37 + 15 * q^38 - 2 * q^39 + 15 * q^40 + 24 * q^41 + 2 * q^42 - 24 * q^43 - 2 * q^44 - 19 * q^45 + 3 * q^46 - 3 * q^47 - 6 * q^48 + 20 * q^49 - 15 * q^50 - 5 * q^51 - 13 * q^52 + 10 * q^53 + 12 * q^54 + 2 * q^55 + 5 * q^56 - 11 * q^57 - 28 * q^58 + 2 * q^59 + 6 * q^60 + 15 * q^61 + 12 * q^62 - 2 * q^63 + 15 * q^64 + 13 * q^65 + 22 * q^66 - 48 * q^67 + 11 * q^68 + 21 * q^69 - 5 * q^70 + 15 * q^71 - 19 * q^72 - 47 * q^73 + 23 * q^74 - 6 * q^75 - 15 * q^76 + 7 * q^77 + 2 * q^78 - 34 * q^79 - 15 * q^80 + 43 * q^81 - 24 * q^82 - 32 * q^83 - 2 * q^84 - 11 * q^85 + 24 * q^86 + 14 * q^87 + 2 * q^88 + 25 * q^89 + 19 * q^90 - 32 * q^91 - 3 * q^92 - 42 * q^93 + 3 * q^94 + 15 * q^95 + 6 * q^96 - 34 * q^97 - 20 * q^98 + 4 * 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
$3$	−3.34293	−1.93004	−0.965020	−	0.262175i	$-0.915560\pi$
$3$	−3.34293	−1.93004	−0.965020	+	0.262175i	$0.915560\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.34293	1.36474
$7$	3.45446	1.30566	0.652831	−	0.757504i	$-0.273581\pi$
$7$	3.45446	1.30566	0.652831	+	0.757504i	$0.273581\pi$
$8$	−1.00000	−0.353553
$9$	8.17517	2.72506
$10$	1.00000	0.316228
$11$	3.65066	1.10072	0.550358	−	0.834929i	$-0.314491\pi$
$11$	3.65066	1.10072	0.550358	+	0.834929i	$0.314491\pi$
$12$	−3.34293	−0.965020
$13$	3.49629	0.969697	0.484849	−	0.874598i	$-0.338875\pi$
$13$	3.49629	0.969697	0.484849	+	0.874598i	$0.338875\pi$
$14$	−3.45446	−0.923242
$15$	3.34293	0.863140
$16$	1.00000	0.250000
$17$	4.44571	1.07824	0.539122	−	0.842228i	$-0.318756\pi$
$17$	4.44571	1.07824	0.539122	+	0.842228i	$0.318756\pi$
$18$	−8.17517	−1.92691
$19$	−6.26283	−1.43679	−0.718396	−	0.695635i	$-0.755123\pi$
$19$	−6.26283	−1.43679	−0.718396	+	0.695635i	$0.755123\pi$
$20$	−1.00000	−0.223607
$21$	−11.5480	−2.51998
$22$	−3.65066	−0.778324
$23$	−7.57267	−1.57901	−0.789506	−	0.613743i	$-0.789663\pi$
$23$	−7.57267	−1.57901	−0.789506	+	0.613743i	$0.789663\pi$
$24$	3.34293	0.682372
$25$	1.00000	0.200000
$26$	−3.49629	−0.685679
$27$	−17.3002	−3.32943
$28$	3.45446	0.652831
$29$	−2.62514	−0.487475	−0.243738	−	0.969841i	$-0.578374\pi$
$29$	−2.62514	−0.487475	−0.243738	+	0.969841i	$0.578374\pi$
$30$	−3.34293	−0.610332
$31$	3.28327	0.589692	0.294846	−	0.955545i	$-0.404732\pi$
$31$	3.28327	0.589692	0.294846	+	0.955545i	$0.404732\pi$
$32$	−1.00000	−0.176777
$33$	−12.2039	−2.12443
$34$	−4.44571	−0.762433
$35$	−3.45446	−0.583910
$36$	8.17517	1.36253
$37$	−7.45793	−1.22608	−0.613038	−	0.790053i	$-0.710053\pi$
$37$	−7.45793	−1.22608	−0.613038	+	0.790053i	$0.710053\pi$
$38$	6.26283	1.01597
$39$	−11.6879	−1.87156
$40$	1.00000	0.158114
$41$	4.62987	0.723064	0.361532	−	0.932360i	$-0.382254\pi$
$41$	4.62987	0.723064	0.361532	+	0.932360i	$0.382254\pi$
$42$	11.5480	1.78190
$43$	−9.40958	−1.43495	−0.717474	−	0.696585i	$-0.754702\pi$
$43$	−9.40958	−1.43495	−0.717474	+	0.696585i	$0.754702\pi$
$44$	3.65066	0.550358
$45$	−8.17517	−1.21868
$46$	7.57267	1.11653
$47$	−4.02949	−0.587762	−0.293881	−	0.955842i	$-0.594947\pi$
$47$	−4.02949	−0.587762	−0.293881	+	0.955842i	$0.594947\pi$
$48$	−3.34293	−0.482510
$49$	4.93327	0.704753
$50$	−1.00000	−0.141421
$51$	−14.8617	−2.08105
$52$	3.49629	0.484849
$53$	4.07029	0.559098	0.279549	−	0.960131i	$-0.409815\pi$
$53$	4.07029	0.559098	0.279549	+	0.960131i	$0.409815\pi$
$54$	17.3002	2.35426
$55$	−3.65066	−0.492255
$56$	−3.45446	−0.461621
$57$	20.9362	2.77307
$58$	2.62514	0.344697
$59$	4.53317	0.590169	0.295085	−	0.955471i	$-0.404652\pi$
$59$	4.53317	0.590169	0.295085	+	0.955471i	$0.404652\pi$
$60$	3.34293	0.431570
$61$	−11.7429	−1.50352	−0.751762	−	0.659435i	$-0.770796\pi$
$61$	−11.7429	−1.50352	−0.751762	+	0.659435i	$0.770796\pi$
$62$	−3.28327	−0.416975
$63$	28.2408	3.55800
$64$	1.00000	0.125000
$65$	−3.49629	−0.433662
$66$	12.2039	1.50220
$67$	−2.55592	−0.312255	−0.156128	−	0.987737i	$-0.549901\pi$
$67$	−2.55592	−0.312255	−0.156128	+	0.987737i	$0.549901\pi$
$68$	4.44571	0.539122
$69$	25.3149	3.04756
$70$	3.45446	0.412887
$71$	13.5208	1.60462	0.802311	−	0.596906i	$-0.203603\pi$
$71$	13.5208	1.60462	0.802311	+	0.596906i	$0.203603\pi$
$72$	−8.17517	−0.963453
$73$	−12.2418	−1.43279	−0.716395	−	0.697695i	$-0.754209\pi$
$73$	−12.2418	−1.43279	−0.716395	+	0.697695i	$0.754209\pi$
$74$	7.45793	0.866967
$75$	−3.34293	−0.386008
$76$	−6.26283	−0.718396
$77$	12.6111	1.43716
$78$	11.6879	1.32339
$79$	−11.7450	−1.32142	−0.660708	−	0.750643i	$-0.729744\pi$
$79$	−11.7450	−1.32142	−0.660708	+	0.750643i	$0.729744\pi$
$80$	−1.00000	−0.111803
$81$	33.3079	3.70088
$82$	−4.62987	−0.511284
$83$	−9.38947	−1.03063	−0.515314	−	0.857001i	$-0.672325\pi$
$83$	−9.38947	−1.03063	−0.515314	+	0.857001i	$0.672325\pi$
$84$	−11.5480	−1.25999
$85$	−4.44571	−0.482205
$86$	9.40958	1.01466
$87$	8.77564	0.940848
$88$	−3.65066	−0.389162
$89$	1.01654	0.107753	0.0538763	−	0.998548i	$-0.482842\pi$
$89$	1.01654	0.107753	0.0538763	+	0.998548i	$0.482842\pi$
$90$	8.17517	0.861739
$91$	12.0778	1.26610
$92$	−7.57267	−0.789506
$93$	−10.9757	−1.13813
$94$	4.02949	0.415610
$95$	6.26283	0.642553
$96$	3.34293	0.341186
$97$	3.76457	0.382234	0.191117	−	0.981567i	$-0.438789\pi$
$97$	3.76457	0.382234	0.191117	+	0.981567i	$0.438789\pi$
$98$	−4.93327	−0.498336
$99$	29.8448	2.99951
$100$	1.00000	0.100000
$101$	9.63337	0.958556	0.479278	−	0.877663i	$-0.340899\pi$
$101$	9.63337	0.958556	0.479278	+	0.877663i	$0.340899\pi$
$102$	14.8617	1.47153
$103$	−13.3052	−1.31100	−0.655498	−	0.755197i	$-0.727541\pi$
$103$	−13.3052	−1.31100	−0.655498	+	0.755197i	$0.727541\pi$
$104$	−3.49629	−0.342840
$105$	11.5480	1.12697
$106$	−4.07029	−0.395342
$107$	−8.65878	−0.837076	−0.418538	−	0.908199i	$-0.637457\pi$
$107$	−8.65878	−0.837076	−0.418538	+	0.908199i	$0.637457\pi$
$108$	−17.3002	−1.66472
$109$	−9.64624	−0.923942	−0.461971	−	0.886895i	$-0.652858\pi$
$109$	−9.64624	−0.923942	−0.461971	+	0.886895i	$0.652858\pi$
$110$	3.65066	0.348077
$111$	24.9313	2.36638
$112$	3.45446	0.326415
$113$	−9.31138	−0.875941	−0.437971	−	0.898989i	$-0.644303\pi$
$113$	−9.31138	−0.875941	−0.437971	+	0.898989i	$0.644303\pi$
$114$	−20.9362	−1.96085
$115$	7.57267	0.706155
$116$	−2.62514	−0.243738
$117$	28.5828	2.64248
$118$	−4.53317	−0.417313
$119$	15.3575	1.40782
$120$	−3.34293	−0.305166
$121$	2.32733	0.211575
$122$	11.7429	1.06315
$123$	−15.4773	−1.39554
$124$	3.28327	0.294846
$125$	−1.00000	−0.0894427
$126$	−28.2408	−2.51589
$127$	−7.95062	−0.705503	−0.352752	−	0.935717i	$-0.614754\pi$
$127$	−7.95062	−0.705503	−0.352752	+	0.935717i	$0.614754\pi$
$128$	−1.00000	−0.0883883
$129$	31.4556	2.76951
$130$	3.49629	0.306645
$131$	12.6694	1.10693	0.553467	−	0.832871i	$-0.313304\pi$
$131$	12.6694	1.10693	0.553467	+	0.832871i	$0.313304\pi$
$132$	−12.2039	−1.06221
$133$	−21.6347	−1.87596
$134$	2.55592	0.220798
$135$	17.3002	1.48897
$136$	−4.44571	−0.381217
$137$	0.305403	0.0260923	0.0130462	−	0.999915i	$-0.495847\pi$
$137$	0.305403	0.0260923	0.0130462	+	0.999915i	$0.495847\pi$
$138$	−25.3149	−2.15495
$139$	4.21702	0.357683	0.178841	−	0.983878i	$-0.442765\pi$
$139$	4.21702	0.357683	0.178841	+	0.983878i	$0.442765\pi$
$140$	−3.45446	−0.291955
$141$	13.4703	1.13440
$142$	−13.5208	−1.13464
$143$	12.7638	1.06736
$144$	8.17517	0.681264
$145$	2.62514	0.218006
$146$	12.2418	1.01314
$147$	−16.4916	−1.36020
$148$	−7.45793	−0.613038
$149$	−10.9607	−0.897937	−0.448968	−	0.893548i	$-0.648208\pi$
$149$	−10.9607	−0.897937	−0.448968	+	0.893548i	$0.648208\pi$
$150$	3.34293	0.272949
$151$	−5.55463	−0.452030	−0.226015	−	0.974124i	$-0.572570\pi$
$151$	−5.55463	−0.452030	−0.226015	+	0.974124i	$0.572570\pi$
$152$	6.26283	0.507983
$153$	36.3445	2.93828
$154$	−12.6111	−1.01623
$155$	−3.28327	−0.263718
$156$	−11.6879	−0.935778
$157$	−10.1392	−0.809193	−0.404597	−	0.914495i	$-0.632588\pi$
$157$	−10.1392	−0.809193	−0.404597	+	0.914495i	$0.632588\pi$
$158$	11.7450	0.934382
$159$	−13.6067	−1.07908
$160$	1.00000	0.0790569
$161$	−26.1595	−2.06166
$162$	−33.3079	−2.61692
$163$	11.3585	0.889668	0.444834	−	0.895613i	$-0.353263\pi$
$163$	11.3585	0.889668	0.444834	+	0.895613i	$0.353263\pi$
$164$	4.62987	0.361532
$165$	12.2039	0.950072
$166$	9.38947	0.728764
$167$	10.1324	0.784071	0.392036	−	0.919950i	$-0.371771\pi$
$167$	10.1324	0.784071	0.392036	+	0.919950i	$0.371771\pi$
$168$	11.5480	0.890948
$169$	−0.775935	−0.0596873
$170$	4.44571	0.340971
$171$	−51.1997	−3.91534
$172$	−9.40958	−0.717474
$173$	−17.6077	−1.33869	−0.669344	−	0.742953i	$-0.733425\pi$
$173$	−17.6077	−1.33869	−0.669344	+	0.742953i	$0.733425\pi$
$174$	−8.77564	−0.665280
$175$	3.45446	0.261132
$176$	3.65066	0.275179
$177$	−15.1541	−1.13905
$178$	−1.01654	−0.0761926
$179$	−24.2483	−1.81241	−0.906203	−	0.422843i	$-0.861032\pi$
$179$	−24.2483	−1.81241	−0.906203	+	0.422843i	$0.861032\pi$
$180$	−8.17517	−0.609341
$181$	−5.16159	−0.383658	−0.191829	−	0.981428i	$-0.561442\pi$
$181$	−5.16159	−0.383658	−0.191829	+	0.981428i	$0.561442\pi$
$182$	−12.0778	−0.895266
$183$	39.2557	2.90186
$184$	7.57267	0.558265
$185$	7.45793	0.548318
$186$	10.9757	0.804779
$187$	16.2298	1.18684
$188$	−4.02949	−0.293881
$189$	−59.7629	−4.34711
$190$	−6.26283	−0.454353
$191$	−14.8898	−1.07739	−0.538695	−	0.842501i	$-0.681083\pi$
$191$	−14.8898	−1.07739	−0.538695	+	0.842501i	$0.681083\pi$
$192$	−3.34293	−0.241255
$193$	10.3403	0.744312	0.372156	−	0.928170i	$-0.378619\pi$
$193$	10.3403	0.744312	0.372156	+	0.928170i	$0.378619\pi$
$194$	−3.76457	−0.270280
$195$	11.6879	0.836985
$196$	4.93327	0.352376
$197$	26.7271	1.90423	0.952114	−	0.305744i	$-0.0989052\pi$
$197$	26.7271	1.90423	0.952114	+	0.305744i	$0.0989052\pi$
$198$	−29.8448	−2.12098
$199$	−0.620373	−0.0439771	−0.0219885	−	0.999758i	$-0.507000\pi$
$199$	−0.620373	−0.0439771	−0.0219885	+	0.999758i	$0.507000\pi$
$200$	−1.00000	−0.0707107
$201$	8.54426	0.602665
$202$	−9.63337	−0.677802
$203$	−9.06842	−0.636478
$204$	−14.8617	−1.04053
$205$	−4.62987	−0.323364
$206$	13.3052	0.927014
$207$	−61.9079	−4.30290
$208$	3.49629	0.242424
$209$	−22.8635	−1.58150
$210$	−11.5480	−0.796888
$211$	−4.78650	−0.329516	−0.164758	−	0.986334i	$-0.552684\pi$
$211$	−4.78650	−0.329516	−0.164758	+	0.986334i	$0.552684\pi$
$212$	4.07029	0.279549
$213$	−45.1990	−3.09699
$214$	8.65878	0.591902
$215$	9.40958	0.641728
$216$	17.3002	1.17713
$217$	11.3419	0.769938
$218$	9.64624	0.653326
$219$	40.9233	2.76534
$220$	−3.65066	−0.246128
$221$	15.5435	1.04557
$222$	−24.9313	−1.67328
$223$	−27.9906	−1.87439	−0.937195	−	0.348806i	$-0.886587\pi$
$223$	−27.9906	−1.87439	−0.937195	+	0.348806i	$0.886587\pi$
$224$	−3.45446	−0.230811
$225$	8.17517	0.545012
$226$	9.31138	0.619384
$227$	−4.43698	−0.294493	−0.147246	−	0.989100i	$-0.547041\pi$
$227$	−4.43698	−0.294493	−0.147246	+	0.989100i	$0.547041\pi$
$228$	20.9362	1.38653
$229$	27.5641	1.82149	0.910744	−	0.412972i	$-0.135509\pi$
$229$	27.5641	1.82149	0.910744	+	0.412972i	$0.135509\pi$
$230$	−7.57267	−0.499327
$231$	−42.1578	−2.77378
$232$	2.62514	0.172349
$233$	−11.9986	−0.786057	−0.393029	−	0.919526i	$-0.628573\pi$
$233$	−11.9986	−0.786057	−0.393029	+	0.919526i	$0.628573\pi$
$234$	−28.5828	−1.86852
$235$	4.02949	0.262855
$236$	4.53317	0.295085
$237$	39.2627	2.55039
$238$	−15.3575	−0.995480
$239$	20.7284	1.34081	0.670406	−	0.741995i	$-0.266120\pi$
$239$	20.7284	1.34081	0.670406	+	0.741995i	$0.266120\pi$
$240$	3.34293	0.215785
$241$	21.3272	1.37381	0.686904	−	0.726748i	$-0.258969\pi$
$241$	21.3272	1.37381	0.686904	+	0.726748i	$0.258969\pi$
$242$	−2.32733	−0.149606
$243$	−59.4453	−3.81342
$244$	−11.7429	−0.751762
$245$	−4.93327	−0.315175
$246$	15.4773	0.986798
$247$	−21.8967	−1.39325
$248$	−3.28327	−0.208488
$249$	31.3883	1.98915
$250$	1.00000	0.0632456
$251$	13.0329	0.822630	0.411315	−	0.911493i	$-0.365070\pi$
$251$	13.0329	0.822630	0.411315	+	0.911493i	$0.365070\pi$
$252$	28.2408	1.77900
$253$	−27.6453	−1.73804
$254$	7.95062	0.498866
$255$	14.8617	0.930676
$256$	1.00000	0.0625000
$257$	9.04869	0.564442	0.282221	−	0.959349i	$-0.408929\pi$
$257$	9.04869	0.564442	0.282221	+	0.959349i	$0.408929\pi$
$258$	−31.4556	−1.95834
$259$	−25.7631	−1.60084
$260$	−3.49629	−0.216831
$261$	−21.4609	−1.32840
$262$	−12.6694	−0.782721
$263$	18.8162	1.16025	0.580127	−	0.814526i	$-0.303003\pi$
$263$	18.8162	1.16025	0.580127	+	0.814526i	$0.303003\pi$
$264$	12.2039	0.751098
$265$	−4.07029	−0.250036
$266$	21.6347	1.32651
$267$	−3.39821	−0.207967
$268$	−2.55592	−0.156128
$269$	−22.5925	−1.37749	−0.688744	−	0.725005i	$-0.741838\pi$
$269$	−22.5925	−1.37749	−0.688744	+	0.725005i	$0.741838\pi$
$270$	−17.3002	−1.05286
$271$	22.2738	1.35304	0.676518	−	0.736426i	$-0.263488\pi$
$271$	22.2738	1.35304	0.676518	+	0.736426i	$0.263488\pi$
$272$	4.44571	0.269561
$273$	−40.3752	−2.44362
$274$	−0.305403	−0.0184501
$275$	3.65066	0.220143
$276$	25.3149	1.52378
$277$	28.2150	1.69527	0.847637	−	0.530576i	$-0.178024\pi$
$277$	28.2150	1.69527	0.847637	+	0.530576i	$0.178024\pi$
$278$	−4.21702	−0.252920
$279$	26.8413	1.60694
$280$	3.45446	0.206443
$281$	−11.5833	−0.691000	−0.345500	−	0.938419i	$-0.612291\pi$
$281$	−11.5833	−0.691000	−0.345500	+	0.938419i	$0.612291\pi$
$282$	−13.4703	−0.802145
$283$	−11.3650	−0.675579	−0.337789	−	0.941222i	$-0.609679\pi$
$283$	−11.3650	−0.675579	−0.337789	+	0.941222i	$0.609679\pi$
$284$	13.5208	0.802311
$285$	−20.9362	−1.24015
$286$	−12.7638	−0.754738
$287$	15.9937	0.944078
$288$	−8.17517	−0.481727
$289$	2.76436	0.162610
$290$	−2.62514	−0.154153
$291$	−12.5847	−0.737727
$292$	−12.2418	−0.716395
$293$	2.36108	0.137936	0.0689678	−	0.997619i	$-0.478029\pi$
$293$	2.36108	0.137936	0.0689678	+	0.997619i	$0.478029\pi$
$294$	16.4916	0.961808
$295$	−4.53317	−0.263932
$296$	7.45793	0.433484
$297$	−63.1573	−3.66476
$298$	10.9607	0.634937
$299$	−26.4763	−1.53116
$300$	−3.34293	−0.193004
$301$	−32.5050	−1.87356
$302$	5.55463	0.319633
$303$	−32.2037	−1.85005
$304$	−6.26283	−0.359198
$305$	11.7429	0.672396
$306$	−36.3445	−2.07768
$307$	−6.48616	−0.370185	−0.185092	−	0.982721i	$-0.559258\pi$
$307$	−6.48616	−0.370185	−0.185092	+	0.982721i	$0.559258\pi$
$308$	12.6111	0.718581
$309$	44.4782	2.53028
$310$	3.28327	0.186477
$311$	−25.2762	−1.43328	−0.716640	−	0.697443i	$-0.754321\pi$
$311$	−25.2762	−1.43328	−0.716640	+	0.697443i	$0.754321\pi$
$312$	11.6879	0.661695
$313$	7.61926	0.430666	0.215333	−	0.976541i	$-0.430916\pi$
$313$	7.61926	0.430666	0.215333	+	0.976541i	$0.430916\pi$
$314$	10.1392	0.572186
$315$	−28.2408	−1.59119
$316$	−11.7450	−0.660708
$317$	16.5917	0.931884	0.465942	−	0.884815i	$-0.345716\pi$
$317$	16.5917	0.931884	0.465942	+	0.884815i	$0.345716\pi$
$318$	13.6067	0.763026
$319$	−9.58348	−0.536572
$320$	−1.00000	−0.0559017
$321$	28.9457	1.61559
$322$	26.1595	1.45781
$323$	−27.8427	−1.54921
$324$	33.3079	1.85044
$325$	3.49629	0.193939
$326$	−11.3585	−0.629090
$327$	32.2467	1.78325
$328$	−4.62987	−0.255642
$329$	−13.9197	−0.767418
$330$	−12.2039	−0.671803
$331$	−16.0676	−0.883157	−0.441578	−	0.897223i	$-0.645581\pi$
$331$	−16.0676	−0.883157	−0.441578	+	0.897223i	$0.645581\pi$
$332$	−9.38947	−0.515314
$333$	−60.9699	−3.34113
$334$	−10.1324	−0.554422
$335$	2.55592	0.139645
$336$	−11.5480	−0.629995
$337$	−32.4640	−1.76843	−0.884213	−	0.467084i	$-0.845305\pi$
$337$	−32.4640	−1.76843	−0.884213	+	0.467084i	$0.845305\pi$
$338$	0.775935	0.0422053
$339$	31.1273	1.69060
$340$	−4.44571	−0.241103
$341$	11.9861	0.649083
$342$	51.1997	2.76856
$343$	−7.13943	−0.385493
$344$	9.40958	0.507331
$345$	−25.3149	−1.36291
$346$	17.6077	0.946595
$347$	−25.8709	−1.38882	−0.694410	−	0.719579i	$-0.744335\pi$
$347$	−25.8709	−1.38882	−0.694410	+	0.719579i	$0.744335\pi$
$348$	8.77564	0.470424
$349$	16.1470	0.864330	0.432165	−	0.901794i	$-0.357750\pi$
$349$	16.1470	0.864330	0.432165	+	0.901794i	$0.357750\pi$
$350$	−3.45446	−0.184648
$351$	−60.4867	−3.22854
$352$	−3.65066	−0.194581
$353$	26.9240	1.43302	0.716511	−	0.697576i	$-0.245738\pi$
$353$	26.9240	1.43302	0.716511	+	0.697576i	$0.245738\pi$
$354$	15.1541	0.805430
$355$	−13.5208	−0.717609
$356$	1.01654	0.0538763
$357$	−51.3391	−2.71715
$358$	24.2483	1.28156
$359$	9.66274	0.509980	0.254990	−	0.966944i	$-0.417928\pi$
$359$	9.66274	0.509980	0.254990	+	0.966944i	$0.417928\pi$
$360$	8.17517	0.430869
$361$	20.2230	1.06437
$362$	5.16159	0.271287
$363$	−7.78009	−0.408349
$364$	12.0778	0.633048
$365$	12.2418	0.640763
$366$	−39.2557	−2.05193
$367$	23.3113	1.21684	0.608419	−	0.793616i	$-0.291804\pi$
$367$	23.3113	1.21684	0.608419	+	0.793616i	$0.291804\pi$
$368$	−7.57267	−0.394753
$369$	37.8500	1.97039
$370$	−7.45793	−0.387719
$371$	14.0606	0.729992
$372$	−10.9757	−0.569065
$373$	18.7188	0.969223	0.484612	−	0.874729i	$-0.338961\pi$
$373$	18.7188	0.969223	0.484612	+	0.874729i	$0.338961\pi$
$374$	−16.2298	−0.839223
$375$	3.34293	0.172628
$376$	4.02949	0.207805
$377$	−9.17824	−0.472704
$378$	59.7629	3.07387
$379$	−28.5930	−1.46872	−0.734362	−	0.678758i	$-0.762519\pi$
$379$	−28.5930	−1.46872	−0.734362	+	0.678758i	$0.762519\pi$
$380$	6.26283	0.321276
$381$	26.5784	1.36165
$382$	14.8898	0.761830
$383$	−4.40398	−0.225033	−0.112516	−	0.993650i	$-0.535891\pi$
$383$	−4.40398	−0.225033	−0.112516	+	0.993650i	$0.535891\pi$
$384$	3.34293	0.170593
$385$	−12.6111	−0.642719
$386$	−10.3403	−0.526308
$387$	−76.9250	−3.91032
$388$	3.76457	0.191117
$389$	−24.5618	−1.24533	−0.622667	−	0.782487i	$-0.713951\pi$
$389$	−24.5618	−1.24533	−0.622667	+	0.782487i	$0.713951\pi$
$390$	−11.6879	−0.591838
$391$	−33.6659	−1.70256
$392$	−4.93327	−0.249168
$393$	−42.3530	−2.13643
$394$	−26.7271	−1.34649
$395$	11.7450	0.590955
$396$	29.8448	1.49976
$397$	15.5751	0.781691	0.390845	−	0.920456i	$-0.372183\pi$
$397$	15.5751	0.781691	0.390845	+	0.920456i	$0.372183\pi$
$398$	0.620373	0.0310965
$399$	72.3232	3.62069
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−8.54426	−0.426149
$403$	11.4793	0.571823
$404$	9.63337	0.479278
$405$	−33.3079	−1.65508
$406$	9.06842	0.450058
$407$	−27.2264	−1.34956
$408$	14.8617	0.735764
$409$	−22.2350	−1.09945	−0.549724	−	0.835346i	$-0.685267\pi$
$409$	−22.2350	−1.09945	−0.549724	+	0.835346i	$0.685267\pi$
$410$	4.62987	0.228653
$411$	−1.02094	−0.0503593
$412$	−13.3052	−0.655498
$413$	15.6597	0.770561
$414$	61.9079	3.04261
$415$	9.38947	0.460911
$416$	−3.49629	−0.171420
$417$	−14.0972	−0.690343
$418$	22.8635	1.11829
$419$	21.5003	1.05036	0.525179	−	0.850992i	$-0.323998\pi$
$419$	21.5003	1.05036	0.525179	+	0.850992i	$0.323998\pi$
$420$	11.5480	0.563485
$421$	−35.3921	−1.72490	−0.862452	−	0.506139i	$-0.831072\pi$
$421$	−35.3921	−1.72490	−0.862452	+	0.506139i	$0.831072\pi$
$422$	4.78650	0.233003
$423$	−32.9418	−1.60168
$424$	−4.07029	−0.197671
$425$	4.44571	0.215649
$426$	45.1990	2.18990
$427$	−40.5653	−1.96309
$428$	−8.65878	−0.418538
$429$	−42.6684	−2.06005
$430$	−9.40958	−0.453770
$431$	17.4615	0.841089	0.420544	−	0.907272i	$-0.361839\pi$
$431$	17.4615	0.841089	0.420544	+	0.907272i	$0.361839\pi$
$432$	−17.3002	−0.832358
$433$	25.5592	1.22830	0.614149	−	0.789190i	$-0.289499\pi$
$433$	25.5592	1.22830	0.614149	+	0.789190i	$0.289499\pi$
$434$	−11.3419	−0.544429
$435$	−8.77564	−0.420760
$436$	−9.64624	−0.461971
$437$	47.4264	2.26871
$438$	−40.9233	−1.95539
$439$	0.954774	0.0455689	0.0227844	−	0.999740i	$-0.492747\pi$
$439$	0.954774	0.0455689	0.0227844	+	0.999740i	$0.492747\pi$
$440$	3.65066	0.174038
$441$	40.3303	1.92049
$442$	−15.5435	−0.739330
$443$	−22.2117	−1.05531	−0.527654	−	0.849459i	$-0.676928\pi$
$443$	−22.2117	−1.05531	−0.527654	+	0.849459i	$0.676928\pi$
$444$	24.9313	1.18319
$445$	−1.01654	−0.0481884
$446$	27.9906	1.32539
$447$	36.6409	1.73305
$448$	3.45446	0.163208
$449$	−10.9315	−0.515891	−0.257945	−	0.966159i	$-0.583045\pi$
$449$	−10.9315	−0.515891	−0.257945	+	0.966159i	$0.583045\pi$
$450$	−8.17517	−0.385381
$451$	16.9021	0.795888
$452$	−9.31138	−0.437971
$453$	18.5687	0.872436
$454$	4.43698	0.208238
$455$	−12.0778	−0.566216
$456$	−20.9362	−0.980427
$457$	18.8479	0.881667	0.440833	−	0.897589i	$-0.354683\pi$
$457$	18.8479	0.881667	0.440833	+	0.897589i	$0.354683\pi$
$458$	−27.5641	−1.28799
$459$	−76.9119	−3.58994
$460$	7.57267	0.353078
$461$	−13.9256	−0.648580	−0.324290	−	0.945958i	$-0.605125\pi$
$461$	−13.9256	−0.648580	−0.324290	+	0.945958i	$0.605125\pi$
$462$	42.1578	1.96136
$463$	−7.79458	−0.362245	−0.181123	−	0.983461i	$-0.557973\pi$
$463$	−7.79458	−0.362245	−0.181123	+	0.983461i	$0.557973\pi$
$464$	−2.62514	−0.121869
$465$	10.9757	0.508987
$466$	11.9986	0.555826
$467$	−30.0377	−1.38998	−0.694990	−	0.719019i	$-0.744591\pi$
$467$	−30.0377	−1.38998	−0.694990	+	0.719019i	$0.744591\pi$
$468$	28.5828	1.32124
$469$	−8.82931	−0.407700
$470$	−4.02949	−0.185867
$471$	33.8945	1.56178
$472$	−4.53317	−0.208656
$473$	−34.3512	−1.57947
$474$	−39.2627	−1.80340
$475$	−6.26283	−0.287358
$476$	15.3575	0.703911
$477$	33.2753	1.52357
$478$	−20.7284	−0.948097
$479$	−12.4327	−0.568063	−0.284032	−	0.958815i	$-0.591672\pi$
$479$	−12.4327	−0.568063	−0.284032	+	0.958815i	$0.591672\pi$
$480$	−3.34293	−0.152583
$481$	−26.0751	−1.18892
$482$	−21.3272	−0.971429
$483$	87.4493	3.97908
$484$	2.32733	0.105788
$485$	−3.76457	−0.170940
$486$	59.4453	2.69650
$487$	−15.1280	−0.685515	−0.342758	−	0.939424i	$-0.611361\pi$
$487$	−15.1280	−0.685515	−0.342758	+	0.939424i	$0.611361\pi$
$488$	11.7429	0.531576
$489$	−37.9707	−1.71710
$490$	4.93327	0.222862
$491$	−28.3599	−1.27986	−0.639932	−	0.768431i	$-0.721038\pi$
$491$	−28.3599	−1.27986	−0.639932	+	0.768431i	$0.721038\pi$
$492$	−15.4773	−0.697772
$493$	−11.6706	−0.525617
$494$	21.8967	0.985178
$495$	−29.8448	−1.34142
$496$	3.28327	0.147423
$497$	46.7070	2.09509
$498$	−31.3883	−1.40654
$499$	12.2680	0.549190	0.274595	−	0.961560i	$-0.411456\pi$
$499$	12.2680	0.549190	0.274595	+	0.961560i	$0.411456\pi$
$500$	−1.00000	−0.0447214
$501$	−33.8720	−1.51329
$502$	−13.0329	−0.581687
$503$	−0.349538	−0.0155851	−0.00779257	−	0.999970i	$-0.502480\pi$
$503$	−0.349538	−0.0155851	−0.00779257	+	0.999970i	$0.502480\pi$
$504$	−28.2408	−1.25794
$505$	−9.63337	−0.428679
$506$	27.6453	1.22898
$507$	2.59390	0.115199
$508$	−7.95062	−0.352752
$509$	14.2824	0.633058	0.316529	−	0.948583i	$-0.397483\pi$
$509$	14.2824	0.633058	0.316529	+	0.948583i	$0.397483\pi$
$510$	−14.8617	−0.658087
$511$	−42.2886	−1.87074
$512$	−1.00000	−0.0441942
$513$	108.348	4.78370
$514$	−9.04869	−0.399121
$515$	13.3052	0.586295
$516$	31.4556	1.38475
$517$	−14.7103	−0.646958
$518$	25.7631	1.13197
$519$	58.8612	2.58372
$520$	3.49629	0.153323
$521$	−2.68168	−0.117486	−0.0587432	−	0.998273i	$-0.518709\pi$
$521$	−2.68168	−0.117486	−0.0587432	+	0.998273i	$0.518709\pi$
$522$	21.4609	0.939320
$523$	0.564206	0.0246710	0.0123355	−	0.999924i	$-0.496073\pi$
$523$	0.564206	0.0246710	0.0123355	+	0.999924i	$0.496073\pi$
$524$	12.6694	0.553467
$525$	−11.5480	−0.503996
$526$	−18.8162	−0.820424
$527$	14.5965	0.635832
$528$	−12.2039	−0.531107
$529$	34.3454	1.49328
$530$	4.07029	0.176802
$531$	37.0595	1.60824
$532$	−21.6347	−0.937982
$533$	16.1874	0.701154
$534$	3.39821	0.147055
$535$	8.65878	0.374352
$536$	2.55592	0.110399
$537$	81.0605	3.49802
$538$	22.5925	0.974031
$539$	18.0097	0.775733
$540$	17.3002	0.744484
$541$	−0.472310	−0.0203062	−0.0101531	−	0.999948i	$-0.503232\pi$
$541$	−0.472310	−0.0203062	−0.0101531	+	0.999948i	$0.503232\pi$
$542$	−22.2738	−0.956740
$543$	17.2548	0.740475
$544$	−4.44571	−0.190608
$545$	9.64624	0.413200
$546$	40.3752	1.72790
$547$	−10.3468	−0.442399	−0.221199	−	0.975229i	$-0.570997\pi$
$547$	−10.3468	−0.442399	−0.221199	+	0.975229i	$0.570997\pi$
$548$	0.305403	0.0130462
$549$	−96.0002	−4.09719
$550$	−3.65066	−0.155665
$551$	16.4408	0.700401
$552$	−25.3149	−1.07747
$553$	−40.5726	−1.72532
$554$	−28.2150	−1.19874
$555$	−24.9313	−1.05828
$556$	4.21702	0.178841
$557$	19.3194	0.818591	0.409296	−	0.912402i	$-0.365774\pi$
$557$	19.3194	0.818591	0.409296	+	0.912402i	$0.365774\pi$
$558$	−26.8413	−1.13628
$559$	−32.8987	−1.39146
$560$	−3.45446	−0.145977
$561$	−54.2550	−2.29065
$562$	11.5833	0.488610
$563$	31.5587	1.33004	0.665020	−	0.746825i	$-0.268423\pi$
$563$	31.5587	1.33004	0.665020	+	0.746825i	$0.268423\pi$
$564$	13.4703	0.567202
$565$	9.31138	0.391733
$566$	11.3650	0.477706
$567$	115.061	4.83210
$568$	−13.5208	−0.567320
$569$	5.72419	0.239970	0.119985	−	0.992776i	$-0.461715\pi$
$569$	5.72419	0.239970	0.119985	+	0.992776i	$0.461715\pi$
$570$	20.9362	0.876921
$571$	33.3106	1.39400	0.697002	−	0.717069i	$-0.254517\pi$
$571$	33.3106	1.39400	0.697002	+	0.717069i	$0.254517\pi$
$572$	12.7638	0.533681
$573$	49.7756	2.07941
$574$	−15.9937	−0.667564
$575$	−7.57267	−0.315802
$576$	8.17517	0.340632
$577$	−28.0651	−1.16836	−0.584182	−	0.811623i	$-0.698584\pi$
$577$	−28.0651	−1.16836	−0.584182	+	0.811623i	$0.698584\pi$
$578$	−2.76436	−0.114982
$579$	−34.5669	−1.43655
$580$	2.62514	0.109003
$581$	−32.4355	−1.34565
$582$	12.5847	0.521652
$583$	14.8593	0.615408
$584$	12.2418	0.506568
$585$	−28.5828	−1.18175
$586$	−2.36108	−0.0975352
$587$	7.95389	0.328292	0.164146	−	0.986436i	$-0.447513\pi$
$587$	7.95389	0.328292	0.164146	+	0.986436i	$0.447513\pi$
$588$	−16.4916	−0.680101
$589$	−20.5625	−0.847265
$590$	4.53317	0.186628
$591$	−89.3468	−3.67524
$592$	−7.45793	−0.306519
$593$	19.8773	0.816264	0.408132	−	0.912923i	$-0.366180\pi$
$593$	19.8773	0.816264	0.408132	+	0.912923i	$0.366180\pi$
$594$	63.1573	2.59138
$595$	−15.3575	−0.629597
$596$	−10.9607	−0.448968
$597$	2.07386	0.0848775
$598$	26.4763	1.08270
$599$	−0.352831	−0.0144163	−0.00720814	−	0.999974i	$-0.502294\pi$
$599$	−0.352831	−0.0144163	−0.00720814	+	0.999974i	$0.502294\pi$
$600$	3.34293	0.136474
$601$	−6.66728	−0.271964	−0.135982	−	0.990711i	$-0.543419\pi$
$601$	−6.66728	−0.271964	−0.135982	+	0.990711i	$0.543419\pi$
$602$	32.5050	1.32480
$603$	−20.8951	−0.850914
$604$	−5.55463	−0.226015
$605$	−2.32733	−0.0946194
$606$	32.2037	1.30818
$607$	−32.8036	−1.33146	−0.665729	−	0.746194i	$-0.731879\pi$
$607$	−32.8036	−1.33146	−0.665729	+	0.746194i	$0.731879\pi$
$608$	6.26283	0.253991
$609$	30.3151	1.22843
$610$	−11.7429	−0.475456
$611$	−14.0883	−0.569951
$612$	36.3445	1.46914
$613$	16.3431	0.660090	0.330045	−	0.943965i	$-0.392936\pi$
$613$	16.3431	0.660090	0.330045	+	0.943965i	$0.392936\pi$
$614$	6.48616	0.261760
$615$	15.4773	0.624106
$616$	−12.6111	−0.508114
$617$	28.0275	1.12834	0.564172	−	0.825657i	$-0.309195\pi$
$617$	28.0275	1.12834	0.564172	+	0.825657i	$0.309195\pi$
$618$	−44.4782	−1.78917
$619$	20.9690	0.842815	0.421407	−	0.906871i	$-0.361536\pi$
$619$	20.9690	0.842815	0.421407	+	0.906871i	$0.361536\pi$
$620$	−3.28327	−0.131859
$621$	131.009	5.25721
$622$	25.2762	1.01348
$623$	3.51158	0.140688
$624$	−11.6879	−0.467889
$625$	1.00000	0.0400000
$626$	−7.61926	−0.304527
$627$	76.4309	3.05236
$628$	−10.1392	−0.404597
$629$	−33.1558	−1.32201
$630$	28.2408	1.12514
$631$	−34.5444	−1.37519	−0.687594	−	0.726095i	$-0.741333\pi$
$631$	−34.5444	−1.37519	−0.687594	+	0.726095i	$0.741333\pi$
$632$	11.7450	0.467191
$633$	16.0009	0.635979
$634$	−16.5917	−0.658941
$635$	7.95062	0.315511
$636$	−13.6067	−0.539541
$637$	17.2482	0.683397
$638$	9.58348	0.379414
$639$	110.535	4.37269
$640$	1.00000	0.0395285
$641$	37.2692	1.47205	0.736023	−	0.676956i	$-0.236701\pi$
$641$	37.2692	1.47205	0.736023	+	0.676956i	$0.236701\pi$
$642$	−28.9457	−1.14240
$643$	16.9416	0.668112	0.334056	−	0.942553i	$-0.391583\pi$
$643$	16.9416	0.668112	0.334056	+	0.942553i	$0.391583\pi$
$644$	−26.1595	−1.03083
$645$	−31.4556	−1.23856
$646$	27.8427	1.09546
$647$	−26.5263	−1.04286	−0.521428	−	0.853296i	$-0.674600\pi$
$647$	−26.5263	−1.04286	−0.521428	+	0.853296i	$0.674600\pi$
$648$	−33.3079	−1.30846
$649$	16.5491	0.649608
$650$	−3.49629	−0.137136
$651$	−37.9152	−1.48601
$652$	11.3585	0.444834
$653$	−29.6548	−1.16048	−0.580242	−	0.814444i	$-0.697042\pi$
$653$	−29.6548	−1.16048	−0.580242	+	0.814444i	$0.697042\pi$
$654$	−32.2467	−1.26095
$655$	−12.6694	−0.495036
$656$	4.62987	0.180766
$657$	−100.079	−3.90444
$658$	13.9197	0.542646
$659$	−43.3932	−1.69036	−0.845180	−	0.534481i	$-0.820507\pi$
$659$	−43.3932	−1.69036	−0.845180	+	0.534481i	$0.820507\pi$
$660$	12.2039	0.475036
$661$	−8.56314	−0.333068	−0.166534	−	0.986036i	$-0.553257\pi$
$661$	−8.56314	−0.333068	−0.166534	+	0.986036i	$0.553257\pi$
$662$	16.0676	0.624486
$663$	−51.9609	−2.01799
$664$	9.38947	0.364382
$665$	21.6347	0.838957
$666$	60.9699	2.36254
$667$	19.8793	0.769729
$668$	10.1324	0.392036
$669$	93.5706	3.61765
$670$	−2.55592	−0.0987438
$671$	−42.8693	−1.65495
$672$	11.5480	0.445474
$673$	27.5521	1.06205	0.531027	−	0.847355i	$-0.321806\pi$
$673$	27.5521	1.06205	0.531027	+	0.847355i	$0.321806\pi$
$674$	32.4640	1.25047
$675$	−17.3002	−0.665886
$676$	−0.775935	−0.0298437
$677$	11.9822	0.460515	0.230258	−	0.973130i	$-0.426043\pi$
$677$	11.9822	0.460515	0.230258	+	0.973130i	$0.426043\pi$
$678$	−31.1273	−1.19544
$679$	13.0045	0.499068
$680$	4.44571	0.170485
$681$	14.8325	0.568383
$682$	−11.9861	−0.458971
$683$	−36.5333	−1.39791	−0.698954	−	0.715166i	$-0.746351\pi$
$683$	−36.5333	−1.39791	−0.698954	+	0.715166i	$0.746351\pi$
$684$	−51.1997	−1.95767
$685$	−0.305403	−0.0116688
$686$	7.13943	0.272585
$687$	−92.1449	−3.51555
$688$	−9.40958	−0.358737
$689$	14.2309	0.542155
$690$	25.3149	0.963722
$691$	29.2002	1.11083	0.555413	−	0.831575i	$-0.312560\pi$
$691$	29.2002	1.11083	0.555413	+	0.831575i	$0.312560\pi$
$692$	−17.6077	−0.669344
$693$	103.098	3.91635
$694$	25.8709	0.982044
$695$	−4.21702	−0.159961
$696$	−8.77564	−0.332640
$697$	20.5831	0.779640
$698$	−16.1470	−0.611174
$699$	40.1106	1.51712
$700$	3.45446	0.130566
$701$	12.8440	0.485112	0.242556	−	0.970137i	$-0.422014\pi$
$701$	12.8440	0.485112	0.242556	+	0.970137i	$0.422014\pi$
$702$	60.4867	2.28292
$703$	46.7078	1.76162
$704$	3.65066	0.137589
$705$	−13.4703	−0.507321
$706$	−26.9240	−1.01330
$707$	33.2781	1.25155
$708$	−15.1541	−0.569525
$709$	−36.5289	−1.37187	−0.685936	−	0.727662i	$-0.740607\pi$
$709$	−36.5289	−1.37187	−0.685936	+	0.727662i	$0.740607\pi$
$710$	13.5208	0.507426
$711$	−96.0174	−3.60093
$712$	−1.01654	−0.0380963
$713$	−24.8631	−0.931131
$714$	51.3391	1.92132
$715$	−12.7638	−0.477338
$716$	−24.2483	−0.906203
$717$	−69.2937	−2.58782
$718$	−9.66274	−0.360610
$719$	29.5026	1.10026	0.550130	−	0.835079i	$-0.314578\pi$
$719$	29.5026	1.10026	0.550130	+	0.835079i	$0.314578\pi$
$720$	−8.17517	−0.304671
$721$	−45.9621	−1.71172
$722$	−20.2230	−0.752623
$723$	−71.2955	−2.65151
$724$	−5.16159	−0.191829
$725$	−2.62514	−0.0974951
$726$	7.78009	0.288746
$727$	35.2323	1.30670	0.653348	−	0.757058i	$-0.273364\pi$
$727$	35.2323	1.30670	0.653348	+	0.757058i	$0.273364\pi$
$728$	−12.0778	−0.447633
$729$	98.7977	3.65918
$730$	−12.2418	−0.453088
$731$	−41.8323	−1.54722
$732$	39.2557	1.45093
$733$	−43.3304	−1.60045	−0.800223	−	0.599703i	$-0.795285\pi$
$733$	−43.3304	−1.60045	−0.800223	+	0.599703i	$0.795285\pi$
$734$	−23.3113	−0.860434
$735$	16.4916	0.608301
$736$	7.57267	0.279132
$737$	−9.33080	−0.343704
$738$	−37.8500	−1.39328
$739$	21.8997	0.805592	0.402796	−	0.915290i	$-0.368038\pi$
$739$	21.8997	0.805592	0.402796	+	0.915290i	$0.368038\pi$
$740$	7.45793	0.274159
$741$	73.1991	2.68903
$742$	−14.0606	−0.516183
$743$	29.8275	1.09426	0.547132	−	0.837047i	$-0.315720\pi$
$743$	29.8275	1.09426	0.547132	+	0.837047i	$0.315720\pi$
$744$	10.9757	0.402390
$745$	10.9607	0.401569
$746$	−18.7188	−0.685344
$747$	−76.7605	−2.80852
$748$	16.2298	0.593420
$749$	−29.9114	−1.09294
$750$	−3.34293	−0.122066
$751$	−41.1292	−1.50083	−0.750413	−	0.660970i	$-0.770145\pi$
$751$	−41.1292	−1.50083	−0.750413	+	0.660970i	$0.770145\pi$
$752$	−4.02949	−0.146940
$753$	−43.5681	−1.58771
$754$	9.17824	0.334252
$755$	5.55463	0.202154
$756$	−59.7629	−2.17356
$757$	6.82806	0.248170	0.124085	−	0.992272i	$-0.460400\pi$
$757$	6.82806	0.248170	0.124085	+	0.992272i	$0.460400\pi$
$758$	28.5930	1.03854
$759$	92.4162	3.35449
$760$	−6.26283	−0.227177
$761$	−54.4981	−1.97555	−0.987777	−	0.155872i	$-0.950181\pi$
$761$	−54.4981	−1.97555	−0.987777	+	0.155872i	$0.950181\pi$
$762$	−26.5784	−0.962832
$763$	−33.3225	−1.20636
$764$	−14.8898	−0.538695
$765$	−36.3445	−1.31404
$766$	4.40398	0.159122
$767$	15.8493	0.572285
$768$	−3.34293	−0.120628
$769$	11.2232	0.404719	0.202359	−	0.979311i	$-0.435139\pi$
$769$	11.2232	0.404719	0.202359	+	0.979311i	$0.435139\pi$
$770$	12.6111	0.454471
$771$	−30.2491	−1.08940
$772$	10.3403	0.372156
$773$	50.1349	1.80323	0.901613	−	0.432544i	$-0.142384\pi$
$773$	50.1349	1.80323	0.901613	+	0.432544i	$0.142384\pi$
$774$	76.9250	2.76501
$775$	3.28327	0.117938
$776$	−3.76457	−0.135140
$777$	86.1242	3.08969
$778$	24.5618	0.880584
$779$	−28.9961	−1.03889
$780$	11.6879	0.418492
$781$	49.3598	1.76623
$782$	33.6659	1.20389
$783$	45.4155	1.62302
$784$	4.93327	0.176188
$785$	10.1392	0.361882
$786$	42.3530	1.51068
$787$	−26.6032	−0.948303	−0.474152	−	0.880443i	$-0.657245\pi$
$787$	−26.6032	−0.948303	−0.474152	+	0.880443i	$0.657245\pi$
$788$	26.7271	0.952114
$789$	−62.9011	−2.23934
$790$	−11.7450	−0.417868
$791$	−32.1658	−1.14368
$792$	−29.8448	−1.06049
$793$	−41.0566	−1.45796
$794$	−15.5751	−0.552739
$795$	13.6067	0.482580
$796$	−0.620373	−0.0219885
$797$	36.3267	1.28676	0.643379	−	0.765548i	$-0.277532\pi$
$797$	36.3267	1.28676	0.643379	+	0.765548i	$0.277532\pi$
$798$	−72.3232	−2.56021
$799$	−17.9140	−0.633750
$800$	−1.00000	−0.0353553
$801$	8.31036	0.293632
$802$	1.00000	0.0353112
$803$	−44.6905	−1.57709
$804$	8.54426	0.301333
$805$	26.1595	0.922000
$806$	−11.4793	−0.404340
$807$	75.5251	2.65861
$808$	−9.63337	−0.338901
$809$	−44.2243	−1.55484	−0.777421	−	0.628980i	$-0.783473\pi$
$809$	−44.2243	−1.55484	−0.777421	+	0.628980i	$0.783473\pi$
$810$	33.3079	1.17032
$811$	3.63339	0.127585	0.0637927	−	0.997963i	$-0.479680\pi$
$811$	3.63339	0.127585	0.0637927	+	0.997963i	$0.479680\pi$
$812$	−9.06842	−0.318239
$813$	−74.4596	−2.61141
$814$	27.2264	0.954284
$815$	−11.3585	−0.397872
$816$	−14.8617	−0.520264
$817$	58.9306	2.06172
$818$	22.2350	0.777427
$819$	98.7380	3.45019
$820$	−4.62987	−0.161682
$821$	20.5307	0.716528	0.358264	−	0.933620i	$-0.383369\pi$
$821$	20.5307	0.716528	0.358264	+	0.933620i	$0.383369\pi$
$822$	1.02094	0.0356094
$823$	18.6824	0.651227	0.325614	−	0.945503i	$-0.394429\pi$
$823$	18.6824	0.651227	0.325614	+	0.945503i	$0.394429\pi$
$824$	13.3052	0.463507
$825$	−12.2039	−0.424885
$826$	−15.6597	−0.544869
$827$	43.2438	1.50373	0.751867	−	0.659315i	$-0.229153\pi$
$827$	43.2438	1.50373	0.751867	+	0.659315i	$0.229153\pi$
$828$	−61.9079	−2.15145
$829$	7.38348	0.256439	0.128219	−	0.991746i	$-0.459074\pi$
$829$	7.38348	0.256439	0.128219	+	0.991746i	$0.459074\pi$
$830$	−9.38947	−0.325913
$831$	−94.3207	−3.27195
$832$	3.49629	0.121212
$833$	21.9319	0.759895
$834$	14.0972	0.488146
$835$	−10.1324	−0.350647
$836$	−22.8635	−0.790750
$837$	−56.8013	−1.96334
$838$	−21.5003	−0.742716
$839$	33.9771	1.17302	0.586509	−	0.809942i	$-0.300502\pi$
$839$	33.9771	1.17302	0.586509	+	0.809942i	$0.300502\pi$
$840$	−11.5480	−0.398444
$841$	−22.1087	−0.762368
$842$	35.3921	1.21969
$843$	38.7220	1.33366
$844$	−4.78650	−0.164758
$845$	0.775935	0.0266930
$846$	32.9418	1.13256
$847$	8.03966	0.276246
$848$	4.07029	0.139774
$849$	37.9924	1.30389
$850$	−4.44571	−0.152487
$851$	56.4765	1.93599
$852$	−45.1990	−1.54849
$853$	39.3182	1.34623	0.673114	−	0.739539i	$-0.264956\pi$
$853$	39.3182	1.34623	0.673114	+	0.739539i	$0.264956\pi$
$854$	40.5653	1.38812
$855$	51.1997	1.75099
$856$	8.65878	0.295951
$857$	−55.1736	−1.88469	−0.942347	−	0.334636i	$-0.891387\pi$
$857$	−55.1736	−1.88469	−0.942347	+	0.334636i	$0.891387\pi$
$858$	42.6684	1.45668
$859$	23.4800	0.801129	0.400564	−	0.916269i	$-0.368814\pi$
$859$	23.4800	0.801129	0.400564	+	0.916269i	$0.368814\pi$
$860$	9.40958	0.320864
$861$	−53.4658	−1.82211
$862$	−17.4615	−0.594740
$863$	35.4240	1.20585	0.602923	−	0.797799i	$-0.294003\pi$
$863$	35.4240	1.20585	0.602923	+	0.797799i	$0.294003\pi$
$864$	17.3002	0.588566
$865$	17.6077	0.598679
$866$	−25.5592	−0.868538
$867$	−9.24107	−0.313843
$868$	11.3419	0.384969
$869$	−42.8770	−1.45450
$870$	8.77564	0.297522
$871$	−8.93624	−0.302793
$872$	9.64624	0.326663
$873$	30.7760	1.04161
$874$	−47.4264	−1.60422
$875$	−3.45446	−0.116782
$876$	40.9233	1.38267
$877$	−20.9567	−0.707656	−0.353828	−	0.935310i	$-0.615120\pi$
$877$	−20.9567	−0.707656	−0.353828	+	0.935310i	$0.615120\pi$
$878$	−0.954774	−0.0322221
$879$	−7.89291	−0.266221
$880$	−3.65066	−0.123064
$881$	−16.7761	−0.565200	−0.282600	−	0.959238i	$-0.591197\pi$
$881$	−16.7761	−0.565200	−0.282600	+	0.959238i	$0.591197\pi$
$882$	−40.3303	−1.35799
$883$	20.5408	0.691253	0.345626	−	0.938372i	$-0.387666\pi$
$883$	20.5408	0.691253	0.345626	+	0.938372i	$0.387666\pi$
$884$	15.5435	0.522785
$885$	15.1541	0.509399
$886$	22.2117	0.746216
$887$	−24.4967	−0.822517	−0.411259	−	0.911519i	$-0.634911\pi$
$887$	−24.4967	−0.822517	−0.411259	+	0.911519i	$0.634911\pi$
$888$	−24.9313	−0.836641
$889$	−27.4651	−0.921149
$890$	1.01654	0.0340744
$891$	121.596	4.07362
$892$	−27.9906	−0.937195
$893$	25.2360	0.844491
$894$	−36.6409	−1.22545
$895$	24.2483	0.810533
$896$	−3.45446	−0.115405
$897$	88.5083	2.95521
$898$	10.9315	0.364790
$899$	−8.61902	−0.287460
$900$	8.17517	0.272506
$901$	18.0953	0.602843
$902$	−16.9021	−0.562778
$903$	108.662	3.61604
$904$	9.31138	0.309692
$905$	5.16159	0.171577
$906$	−18.5687	−0.616905
$907$	−44.9621	−1.49294	−0.746471	−	0.665418i	$-0.768254\pi$
$907$	−44.9621	−1.49294	−0.746471	+	0.665418i	$0.768254\pi$
$908$	−4.43698	−0.147246
$909$	78.7545	2.61212
$910$	12.0778	0.400375
$911$	−37.0311	−1.22689	−0.613447	−	0.789736i	$-0.710218\pi$
$911$	−37.0311	−1.22689	−0.613447	+	0.789736i	$0.710218\pi$
$912$	20.9362	0.693267
$913$	−34.2778	−1.13443
$914$	−18.8479	−0.623433
$915$	−39.2557	−1.29775
$916$	27.5641	0.910744
$917$	43.7660	1.44528
$918$	76.9119	2.53847
$919$	−0.942269	−0.0310826	−0.0155413	−	0.999879i	$-0.504947\pi$
$919$	−0.942269	−0.0310826	−0.0155413	+	0.999879i	$0.504947\pi$
$920$	−7.57267	−0.249664
$921$	21.6828	0.714472
$922$	13.9256	0.458615
$923$	47.2726	1.55600
$924$	−42.1578	−1.38689
$925$	−7.45793	−0.245215
$926$	7.79458	0.256146
$927$	−108.772	−3.57254
$928$	2.62514	0.0861743
$929$	28.8335	0.945996	0.472998	−	0.881063i	$-0.343172\pi$
$929$	28.8335	0.945996	0.472998	+	0.881063i	$0.343172\pi$
$930$	−10.9757	−0.359908
$931$	−30.8962	−1.01258
$932$	−11.9986	−0.393029
$933$	84.4965	2.76629
$934$	30.0377	0.982864
$935$	−16.2298	−0.530771
$936$	−28.5828	−0.934258
$937$	−37.0807	−1.21137	−0.605686	−	0.795704i	$-0.707101\pi$
$937$	−37.0807	−1.21137	−0.605686	+	0.795704i	$0.707101\pi$
$938$	8.82931	0.288287
$939$	−25.4707	−0.831204
$940$	4.02949	0.131427
$941$	19.3937	0.632217	0.316108	−	0.948723i	$-0.397624\pi$
$941$	19.3937	0.632217	0.316108	+	0.948723i	$0.397624\pi$
$942$	−33.8945	−1.10434
$943$	−35.0605	−1.14173
$944$	4.53317	0.147542
$945$	59.7629	1.94409
$946$	34.3512	1.11685
$947$	−59.4392	−1.93151	−0.965757	−	0.259449i	$-0.916459\pi$
$947$	−59.4392	−1.93151	−0.965757	+	0.259449i	$0.916459\pi$
$948$	39.2627	1.27519
$949$	−42.8008	−1.38937
$950$	6.26283	0.203193
$951$	−55.4649	−1.79857
$952$	−15.3575	−0.497740
$953$	−32.8523	−1.06419	−0.532095	−	0.846685i	$-0.678595\pi$
$953$	−32.8523	−1.06419	−0.532095	+	0.846685i	$0.678595\pi$
$954$	−33.2753	−1.07733
$955$	14.8898	0.481824
$956$	20.7284	0.670406
$957$	32.0369	1.03561
$958$	12.4327	0.401681
$959$	1.05500	0.0340678
$960$	3.34293	0.107893
$961$	−20.2202	−0.652263
$962$	26.0751	0.840696
$963$	−70.7870	−2.28108
$964$	21.3272	0.686904
$965$	−10.3403	−0.332866
$966$	−87.4493	−2.81363
$967$	−3.24879	−0.104474	−0.0522370	−	0.998635i	$-0.516635\pi$
$967$	−3.24879	−0.104474	−0.0522370	+	0.998635i	$0.516635\pi$
$968$	−2.32733	−0.0748032
$969$	93.0763	2.99004
$970$	3.76457	0.120873
$971$	−13.5736	−0.435598	−0.217799	−	0.975994i	$-0.569888\pi$
$971$	−13.5736	−0.435598	−0.217799	+	0.975994i	$0.569888\pi$
$972$	−59.4453	−1.90671
$973$	14.5675	0.467013
$974$	15.1280	0.484733
$975$	−11.6879	−0.374311
$976$	−11.7429	−0.375881
$977$	−21.3061	−0.681644	−0.340822	−	0.940128i	$-0.610705\pi$
$977$	−21.3061	−0.681644	−0.340822	+	0.940128i	$0.610705\pi$
$978$	37.9707	1.21417
$979$	3.71103	0.118605
$980$	−4.93327	−0.157588
$981$	−78.8597	−2.51780
$982$	28.3599	0.905001
$983$	60.6251	1.93364	0.966821	−	0.255456i	$-0.0822257\pi$
$983$	60.6251	1.93364	0.966821	+	0.255456i	$0.0822257\pi$
$984$	15.4773	0.493399
$985$	−26.7271	−0.851596
$986$	11.6706	0.371668
$987$	46.5326	1.48115
$988$	−21.8967	−0.696626
$989$	71.2557	2.26580
$990$	29.8448	0.948530
$991$	17.5578	0.557741	0.278870	−	0.960329i	$-0.410040\pi$
$991$	17.5578	0.557741	0.278870	+	0.960329i	$0.410040\pi$
$992$	−3.28327	−0.104244
$993$	53.7130	1.70453
$994$	−46.7070	−1.48146
$995$	0.620373	0.0196671
$996$	31.3883	0.994577
$997$	26.6488	0.843976	0.421988	−	0.906602i	$-0.361333\pi$
$997$	26.6488	0.843976	0.421988	+	0.906602i	$0.361333\pi$
$998$	−12.2680	−0.388336
$999$	129.024	4.08214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.k.1.1	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.k.1.1	✓	15	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.34293 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.34293 q^{6} +3.45446 q^{7} -1.00000 q^{8} +8.17517 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.34293 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.34293 q^{6} +3.45446 q^{7} -1.00000 q^{8} +8.17517 q^{9} +1.00000 q^{10} +3.65066 q^{11} -3.34293 q^{12} +3.49629 q^{13} -3.45446 q^{14} +3.34293 q^{15} +1.00000 q^{16} +4.44571 q^{17} -8.17517 q^{18} -6.26283 q^{19} -1.00000 q^{20} -11.5480 q^{21} -3.65066 q^{22} -7.57267 q^{23} +3.34293 q^{24} +1.00000 q^{25} -3.49629 q^{26} -17.3002 q^{27} +3.45446 q^{28} -2.62514 q^{29} -3.34293 q^{30} +3.28327 q^{31} -1.00000 q^{32} -12.2039 q^{33} -4.44571 q^{34} -3.45446 q^{35} +8.17517 q^{36} -7.45793 q^{37} +6.26283 q^{38} -11.6879 q^{39} +1.00000 q^{40} +4.62987 q^{41} +11.5480 q^{42} -9.40958 q^{43} +3.65066 q^{44} -8.17517 q^{45} +7.57267 q^{46} -4.02949 q^{47} -3.34293 q^{48} +4.93327 q^{49} -1.00000 q^{50} -14.8617 q^{51} +3.49629 q^{52} +4.07029 q^{53} +17.3002 q^{54} -3.65066 q^{55} -3.45446 q^{56} +20.9362 q^{57} +2.62514 q^{58} +4.53317 q^{59} +3.34293 q^{60} -11.7429 q^{61} -3.28327 q^{62} +28.2408 q^{63} +1.00000 q^{64} -3.49629 q^{65} +12.2039 q^{66} -2.55592 q^{67} +4.44571 q^{68} +25.3149 q^{69} +3.45446 q^{70} +13.5208 q^{71} -8.17517 q^{72} -12.2418 q^{73} +7.45793 q^{74} -3.34293 q^{75} -6.26283 q^{76} +12.6111 q^{77} +11.6879 q^{78} -11.7450 q^{79} -1.00000 q^{80} +33.3079 q^{81} -4.62987 q^{82} -9.38947 q^{83} -11.5480 q^{84} -4.44571 q^{85} +9.40958 q^{86} +8.77564 q^{87} -3.65066 q^{88} +1.01654 q^{89} +8.17517 q^{90} +12.0778 q^{91} -7.57267 q^{92} -10.9757 q^{93} +4.02949 q^{94} +6.26283 q^{95} +3.34293 q^{96} +3.76457 q^{97} -4.93327 q^{98} +29.8448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9} + 15 q^{10} - 2 q^{11} - 6 q^{12} - 13 q^{13} + 5 q^{14} + 6 q^{15} + 15 q^{16} + 11 q^{17} - 19 q^{18} - 15 q^{19} - 15 q^{20} - 2 q^{21} + 2 q^{22} - 3 q^{23} + 6 q^{24} + 15 q^{25} + 13 q^{26} - 12 q^{27} - 5 q^{28} + 28 q^{29} - 6 q^{30} - 12 q^{31} - 15 q^{32} - 22 q^{33} - 11 q^{34} + 5 q^{35} + 19 q^{36} - 23 q^{37} + 15 q^{38} - 2 q^{39} + 15 q^{40} + 24 q^{41} + 2 q^{42} - 24 q^{43} - 2 q^{44} - 19 q^{45} + 3 q^{46} - 3 q^{47} - 6 q^{48} + 20 q^{49} - 15 q^{50} - 5 q^{51} - 13 q^{52} + 10 q^{53} + 12 q^{54} + 2 q^{55} + 5 q^{56} - 11 q^{57} - 28 q^{58} + 2 q^{59} + 6 q^{60} + 15 q^{61} + 12 q^{62} - 2 q^{63} + 15 q^{64} + 13 q^{65} + 22 q^{66} - 48 q^{67} + 11 q^{68} + 21 q^{69} - 5 q^{70} + 15 q^{71} - 19 q^{72} - 47 q^{73} + 23 q^{74} - 6 q^{75} - 15 q^{76} + 7 q^{77} + 2 q^{78} - 34 q^{79} - 15 q^{80} + 43 q^{81} - 24 q^{82} - 32 q^{83} - 2 q^{84} - 11 q^{85} + 24 q^{86} + 14 q^{87} + 2 q^{88} + 25 q^{89} + 19 q^{90} - 32 q^{91} - 3 q^{92} - 42 q^{93} + 3 q^{94} + 15 q^{95} + 6 q^{96} - 34 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9 + 15 * q^10 - 2 * q^11 - 6 * q^12 - 13 * q^13 + 5 * q^14 + 6 * q^15 + 15 * q^16 + 11 * q^17 - 19 * q^18 - 15 * q^19 - 15 * q^20 - 2 * q^21 + 2 * q^22 - 3 * q^23 + 6 * q^24 + 15 * q^25 + 13 * q^26 - 12 * q^27 - 5 * q^28 + 28 * q^29 - 6 * q^30 - 12 * q^31 - 15 * q^32 - 22 * q^33 - 11 * q^34 + 5 * q^35 + 19 * q^36 - 23 * q^37 + 15 * q^38 - 2 * q^39 + 15 * q^40 + 24 * q^41 + 2 * q^42 - 24 * q^43 - 2 * q^44 - 19 * q^45 + 3 * q^46 - 3 * q^47 - 6 * q^48 + 20 * q^49 - 15 * q^50 - 5 * q^51 - 13 * q^52 + 10 * q^53 + 12 * q^54 + 2 * q^55 + 5 * q^56 - 11 * q^57 - 28 * q^58 + 2 * q^59 + 6 * q^60 + 15 * q^61 + 12 * q^62 - 2 * q^63 + 15 * q^64 + 13 * q^65 + 22 * q^66 - 48 * q^67 + 11 * q^68 + 21 * q^69 - 5 * q^70 + 15 * q^71 - 19 * q^72 - 47 * q^73 + 23 * q^74 - 6 * q^75 - 15 * q^76 + 7 * q^77 + 2 * q^78 - 34 * q^79 - 15 * q^80 + 43 * q^81 - 24 * q^82 - 32 * q^83 - 2 * q^84 - 11 * q^85 + 24 * q^86 + 14 * q^87 + 2 * q^88 + 25 * q^89 + 19 * q^90 - 32 * q^91 - 3 * q^92 - 42 * q^93 + 3 * q^94 + 15 * q^95 + 6 * q^96 - 34 * q^97 - 20 * q^98 + 4 * q^99

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