LMFDB - Embedded newform 4010.2.a.i.1.4

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:	$10$
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} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 $ x^10 - 3x^9 - 12x^8 + 34x^7 + 46x^6 - 104x^5 - 90x^4 + 89x^3 + 82x^2 + 12*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.0585304$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.47624 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.47624 q^{6} -2.32277 q^{7} -1.00000 q^{8} -0.820714 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.47624 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.47624 q^{6} -2.32277 q^{7} -1.00000 q^{8} -0.820714 q^{9} -1.00000 q^{10} +1.34500 q^{11} -1.47624 q^{12} +3.18375 q^{13} +2.32277 q^{14} -1.47624 q^{15} +1.00000 q^{16} +3.91915 q^{17} +0.820714 q^{18} -4.40549 q^{19} +1.00000 q^{20} +3.42897 q^{21} -1.34500 q^{22} -4.06300 q^{23} +1.47624 q^{24} +1.00000 q^{25} -3.18375 q^{26} +5.64029 q^{27} -2.32277 q^{28} -8.96640 q^{29} +1.47624 q^{30} +1.15541 q^{31} -1.00000 q^{32} -1.98554 q^{33} -3.91915 q^{34} -2.32277 q^{35} -0.820714 q^{36} +0.657687 q^{37} +4.40549 q^{38} -4.69998 q^{39} -1.00000 q^{40} +7.76836 q^{41} -3.42897 q^{42} +5.75543 q^{43} +1.34500 q^{44} -0.820714 q^{45} +4.06300 q^{46} -7.10781 q^{47} -1.47624 q^{48} -1.60474 q^{49} -1.00000 q^{50} -5.78561 q^{51} +3.18375 q^{52} +14.3417 q^{53} -5.64029 q^{54} +1.34500 q^{55} +2.32277 q^{56} +6.50357 q^{57} +8.96640 q^{58} -2.03120 q^{59} -1.47624 q^{60} +1.33841 q^{61} -1.15541 q^{62} +1.90633 q^{63} +1.00000 q^{64} +3.18375 q^{65} +1.98554 q^{66} -1.04497 q^{67} +3.91915 q^{68} +5.99796 q^{69} +2.32277 q^{70} +3.41086 q^{71} +0.820714 q^{72} -7.58356 q^{73} -0.657687 q^{74} -1.47624 q^{75} -4.40549 q^{76} -3.12412 q^{77} +4.69998 q^{78} -8.46523 q^{79} +1.00000 q^{80} -5.86429 q^{81} -7.76836 q^{82} -3.04080 q^{83} +3.42897 q^{84} +3.91915 q^{85} -5.75543 q^{86} +13.2366 q^{87} -1.34500 q^{88} -1.14409 q^{89} +0.820714 q^{90} -7.39512 q^{91} -4.06300 q^{92} -1.70567 q^{93} +7.10781 q^{94} -4.40549 q^{95} +1.47624 q^{96} +13.4841 q^{97} +1.60474 q^{98} -1.10386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * 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
$3$	−1.47624	−0.852308	−0.426154	−	0.904651i	$-0.640132\pi$
$3$	−1.47624	−0.852308	−0.426154	+	0.904651i	$0.640132\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.47624	0.602673
$7$	−2.32277	−0.877924	−0.438962	−	0.898506i	$-0.644654\pi$
$7$	−2.32277	−0.877924	−0.438962	+	0.898506i	$0.644654\pi$
$8$	−1.00000	−0.353553
$9$	−0.820714	−0.273571
$10$	−1.00000	−0.316228
$11$	1.34500	0.405532	0.202766	−	0.979227i	$-0.435007\pi$
$11$	1.34500	0.405532	0.202766	+	0.979227i	$0.435007\pi$
$12$	−1.47624	−0.426154
$13$	3.18375	0.883014	0.441507	−	0.897258i	$-0.354444\pi$
$13$	3.18375	0.883014	0.441507	+	0.897258i	$0.354444\pi$
$14$	2.32277	0.620786
$15$	−1.47624	−0.381164
$16$	1.00000	0.250000
$17$	3.91915	0.950534	0.475267	−	0.879842i	$-0.342351\pi$
$17$	3.91915	0.950534	0.475267	+	0.879842i	$0.342351\pi$
$18$	0.820714	0.193444
$19$	−4.40549	−1.01069	−0.505345	−	0.862917i	$-0.668635\pi$
$19$	−4.40549	−1.01069	−0.505345	+	0.862917i	$0.668635\pi$
$20$	1.00000	0.223607
$21$	3.42897	0.748262
$22$	−1.34500	−0.286755
$23$	−4.06300	−0.847193	−0.423597	−	0.905851i	$-0.639233\pi$
$23$	−4.06300	−0.847193	−0.423597	+	0.905851i	$0.639233\pi$
$24$	1.47624	0.301336
$25$	1.00000	0.200000
$26$	−3.18375	−0.624385
$27$	5.64029	1.08547
$28$	−2.32277	−0.438962
$29$	−8.96640	−1.66502	−0.832509	−	0.554011i	$-0.813097\pi$
$29$	−8.96640	−1.66502	−0.832509	+	0.554011i	$0.813097\pi$
$30$	1.47624	0.269523
$31$	1.15541	0.207518	0.103759	−	0.994602i	$-0.466913\pi$
$31$	1.15541	0.207518	0.103759	+	0.994602i	$0.466913\pi$
$32$	−1.00000	−0.176777
$33$	−1.98554	−0.345638
$34$	−3.91915	−0.672129
$35$	−2.32277	−0.392620
$36$	−0.820714	−0.136786
$37$	0.657687	0.108123	0.0540615	−	0.998538i	$-0.482783\pi$
$37$	0.657687	0.108123	0.0540615	+	0.998538i	$0.482783\pi$
$38$	4.40549	0.714666
$39$	−4.69998	−0.752599
$40$	−1.00000	−0.158114
$41$	7.76836	1.21321	0.606607	−	0.795002i	$-0.292530\pi$
$41$	7.76836	1.21321	0.606607	+	0.795002i	$0.292530\pi$
$42$	−3.42897	−0.529101
$43$	5.75543	0.877694	0.438847	−	0.898562i	$-0.355387\pi$
$43$	5.75543	0.877694	0.438847	+	0.898562i	$0.355387\pi$
$44$	1.34500	0.202766
$45$	−0.820714	−0.122345
$46$	4.06300	0.599056
$47$	−7.10781	−1.03678	−0.518391	−	0.855144i	$-0.673469\pi$
$47$	−7.10781	−1.03678	−0.518391	+	0.855144i	$0.673469\pi$
$48$	−1.47624	−0.213077
$49$	−1.60474	−0.229249
$50$	−1.00000	−0.141421
$51$	−5.78561	−0.810148
$52$	3.18375	0.441507
$53$	14.3417	1.96998	0.984991	−	0.172608i	$-0.0552193\pi$
$53$	14.3417	1.96998	0.984991	+	0.172608i	$0.0552193\pi$
$54$	−5.64029	−0.767547
$55$	1.34500	0.181360
$56$	2.32277	0.310393
$57$	6.50357	0.861419
$58$	8.96640	1.17735
$59$	−2.03120	−0.264440	−0.132220	−	0.991220i	$-0.542211\pi$
$59$	−2.03120	−0.264440	−0.132220	+	0.991220i	$0.542211\pi$
$60$	−1.47624	−0.190582
$61$	1.33841	0.171366	0.0856829	−	0.996322i	$-0.472693\pi$
$61$	1.33841	0.171366	0.0856829	+	0.996322i	$0.472693\pi$
$62$	−1.15541	−0.146738
$63$	1.90633	0.240175
$64$	1.00000	0.125000
$65$	3.18375	0.394896
$66$	1.98554	0.244403
$67$	−1.04497	−0.127663	−0.0638315	−	0.997961i	$-0.520332\pi$
$67$	−1.04497	−0.127663	−0.0638315	+	0.997961i	$0.520332\pi$
$68$	3.91915	0.475267
$69$	5.99796	0.722069
$70$	2.32277	0.277624
$71$	3.41086	0.404794	0.202397	−	0.979304i	$-0.435127\pi$
$71$	3.41086	0.404794	0.202397	+	0.979304i	$0.435127\pi$
$72$	0.820714	0.0967221
$73$	−7.58356	−0.887589	−0.443794	−	0.896129i	$-0.646368\pi$
$73$	−7.58356	−0.887589	−0.443794	+	0.896129i	$0.646368\pi$
$74$	−0.657687	−0.0764545
$75$	−1.47624	−0.170462
$76$	−4.40549	−0.505345
$77$	−3.12412	−0.356027
$78$	4.69998	0.532168
$79$	−8.46523	−0.952412	−0.476206	−	0.879334i	$-0.657988\pi$
$79$	−8.46523	−0.952412	−0.476206	+	0.879334i	$0.657988\pi$
$80$	1.00000	0.111803
$81$	−5.86429	−0.651587
$82$	−7.76836	−0.857872
$83$	−3.04080	−0.333772	−0.166886	−	0.985976i	$-0.553371\pi$
$83$	−3.04080	−0.333772	−0.166886	+	0.985976i	$0.553371\pi$
$84$	3.42897	0.374131
$85$	3.91915	0.425092
$86$	−5.75543	−0.620624
$87$	13.2366	1.41911
$88$	−1.34500	−0.143377
$89$	−1.14409	−0.121273	−0.0606366	−	0.998160i	$-0.519313\pi$
$89$	−1.14409	−0.121273	−0.0606366	+	0.998160i	$0.519313\pi$
$90$	0.820714	0.0865109
$91$	−7.39512	−0.775219
$92$	−4.06300	−0.423597
$93$	−1.70567	−0.176870
$94$	7.10781	0.733115
$95$	−4.40549	−0.451994
$96$	1.47624	0.150668
$97$	13.4841	1.36910	0.684549	−	0.728966i	$-0.259999\pi$
$97$	13.4841	1.36910	0.684549	+	0.728966i	$0.259999\pi$
$98$	1.60474	0.162103
$99$	−1.10386	−0.110942
$100$	1.00000	0.100000
$101$	−14.2856	−1.42147	−0.710733	−	0.703462i	$-0.751637\pi$
$101$	−14.2856	−1.42147	−0.710733	+	0.703462i	$0.751637\pi$
$102$	5.78561	0.572861
$103$	−0.775780	−0.0764399	−0.0382200	−	0.999269i	$-0.512169\pi$
$103$	−0.775780	−0.0764399	−0.0382200	+	0.999269i	$0.512169\pi$
$104$	−3.18375	−0.312192
$105$	3.42897	0.334633
$106$	−14.3417	−1.39299
$107$	8.33906	0.806168	0.403084	−	0.915163i	$-0.367938\pi$
$107$	8.33906	0.806168	0.403084	+	0.915163i	$0.367938\pi$
$108$	5.64029	0.542737
$109$	9.07998	0.869704	0.434852	−	0.900502i	$-0.356801\pi$
$109$	9.07998	0.869704	0.434852	+	0.900502i	$0.356801\pi$
$110$	−1.34500	−0.128241
$111$	−0.970904	−0.0921541
$112$	−2.32277	−0.219481
$113$	−6.70185	−0.630457	−0.315229	−	0.949016i	$-0.602081\pi$
$113$	−6.70185	−0.630457	−0.315229	+	0.949016i	$0.602081\pi$
$114$	−6.50357	−0.609115
$115$	−4.06300	−0.378876
$116$	−8.96640	−0.832509
$117$	−2.61295	−0.241567
$118$	2.03120	0.186987
$119$	−9.10329	−0.834497
$120$	1.47624	0.134762
$121$	−9.19098	−0.835543
$122$	−1.33841	−0.121174
$123$	−11.4680	−1.03403
$124$	1.15541	0.103759
$125$	1.00000	0.0894427
$126$	−1.90633	−0.169829
$127$	−8.13046	−0.721462	−0.360731	−	0.932670i	$-0.617473\pi$
$127$	−8.13046	−0.721462	−0.360731	+	0.932670i	$0.617473\pi$
$128$	−1.00000	−0.0883883
$129$	−8.49639	−0.748066
$130$	−3.18375	−0.279233
$131$	−13.4752	−1.17733	−0.588667	−	0.808375i	$-0.700347\pi$
$131$	−13.4752	−1.17733	−0.588667	+	0.808375i	$0.700347\pi$
$132$	−1.98554	−0.172819
$133$	10.2330	0.887309
$134$	1.04497	0.0902713
$135$	5.64029	0.485439
$136$	−3.91915	−0.336065
$137$	9.92905	0.848296	0.424148	−	0.905593i	$-0.360574\pi$
$137$	9.92905	0.848296	0.424148	+	0.905593i	$0.360574\pi$
$138$	−5.99796	−0.510580
$139$	1.27837	0.108430	0.0542148	−	0.998529i	$-0.482734\pi$
$139$	1.27837	0.108430	0.0542148	+	0.998529i	$0.482734\pi$
$140$	−2.32277	−0.196310
$141$	10.4928	0.883657
$142$	−3.41086	−0.286233
$143$	4.28214	0.358091
$144$	−0.820714	−0.0683928
$145$	−8.96640	−0.744619
$146$	7.58356	0.627620
$147$	2.36898	0.195390
$148$	0.657687	0.0540615
$149$	−0.681369	−0.0558199	−0.0279100	−	0.999610i	$-0.508885\pi$
$149$	−0.681369	−0.0558199	−0.0279100	+	0.999610i	$0.508885\pi$
$150$	1.47624	0.120535
$151$	19.5237	1.58882	0.794408	−	0.607385i	$-0.207781\pi$
$151$	19.5237	1.58882	0.794408	+	0.607385i	$0.207781\pi$
$152$	4.40549	0.357333
$153$	−3.21650	−0.260039
$154$	3.12412	0.251749
$155$	1.15541	0.0928051
$156$	−4.69998	−0.376300
$157$	2.19525	0.175200	0.0875999	−	0.996156i	$-0.472080\pi$
$157$	2.19525	0.175200	0.0875999	+	0.996156i	$0.472080\pi$
$158$	8.46523	0.673457
$159$	−21.1718	−1.67903
$160$	−1.00000	−0.0790569
$161$	9.43740	0.743772
$162$	5.86429	0.460742
$163$	−11.2919	−0.884448	−0.442224	−	0.896905i	$-0.645810\pi$
$163$	−11.2919	−0.884448	−0.442224	+	0.896905i	$0.645810\pi$
$164$	7.76836	0.606607
$165$	−1.98554	−0.154574
$166$	3.04080	0.236012
$167$	4.27804	0.331045	0.165522	−	0.986206i	$-0.447069\pi$
$167$	4.27804	0.331045	0.165522	+	0.986206i	$0.447069\pi$
$168$	−3.42897	−0.264551
$169$	−2.86373	−0.220287
$170$	−3.91915	−0.300585
$171$	3.61565	0.276496
$172$	5.75543	0.438847
$173$	11.8805	0.903256	0.451628	−	0.892206i	$-0.350843\pi$
$173$	11.8805	0.903256	0.451628	+	0.892206i	$0.350843\pi$
$174$	−13.2366	−1.00346
$175$	−2.32277	−0.175585
$176$	1.34500	0.101383
$177$	2.99854	0.225384
$178$	1.14409	0.0857531
$179$	−7.09205	−0.530085	−0.265042	−	0.964237i	$-0.585386\pi$
$179$	−7.09205	−0.530085	−0.265042	+	0.964237i	$0.585386\pi$
$180$	−0.820714	−0.0611724
$181$	0.861521	0.0640364	0.0320182	−	0.999487i	$-0.489807\pi$
$181$	0.861521	0.0640364	0.0320182	+	0.999487i	$0.489807\pi$
$182$	7.39512	0.548163
$183$	−1.97581	−0.146056
$184$	4.06300	0.299528
$185$	0.657687	0.0483541
$186$	1.70567	0.125066
$187$	5.27126	0.385472
$188$	−7.10781	−0.518391
$189$	−13.1011	−0.952965
$190$	4.40549	0.319608
$191$	−16.2924	−1.17888	−0.589438	−	0.807814i	$-0.700651\pi$
$191$	−16.2924	−1.17888	−0.589438	+	0.807814i	$0.700651\pi$
$192$	−1.47624	−0.106538
$193$	−8.15952	−0.587335	−0.293668	−	0.955908i	$-0.594876\pi$
$193$	−8.15952	−0.587335	−0.293668	+	0.955908i	$0.594876\pi$
$194$	−13.4841	−0.968099
$195$	−4.69998	−0.336573
$196$	−1.60474	−0.114624
$197$	0.519778	0.0370326	0.0185163	−	0.999829i	$-0.494106\pi$
$197$	0.519778	0.0370326	0.0185163	+	0.999829i	$0.494106\pi$
$198$	1.10386	0.0784479
$199$	−26.9093	−1.90755	−0.953775	−	0.300522i	$-0.902839\pi$
$199$	−26.9093	−1.90755	−0.953775	+	0.300522i	$0.902839\pi$
$200$	−1.00000	−0.0707107
$201$	1.54262	0.108808
$202$	14.2856	1.00513
$203$	20.8269	1.46176
$204$	−5.78561	−0.405074
$205$	7.76836	0.542566
$206$	0.775780	0.0540512
$207$	3.33456	0.231768
$208$	3.18375	0.220753
$209$	−5.92539	−0.409868
$210$	−3.42897	−0.236621
$211$	−18.0183	−1.24043	−0.620217	−	0.784430i	$-0.712955\pi$
$211$	−18.0183	−1.24043	−0.620217	+	0.784430i	$0.712955\pi$
$212$	14.3417	0.984991
$213$	−5.03525	−0.345009
$214$	−8.33906	−0.570047
$215$	5.75543	0.392517
$216$	−5.64029	−0.383773
$217$	−2.68376	−0.182186
$218$	−9.07998	−0.614974
$219$	11.1952	0.756499
$220$	1.34500	0.0906798
$221$	12.4776	0.839335
$222$	0.970904	0.0651628
$223$	21.7185	1.45438	0.727188	−	0.686438i	$-0.240827\pi$
$223$	21.7185	1.45438	0.727188	+	0.686438i	$0.240827\pi$
$224$	2.32277	0.155197
$225$	−0.820714	−0.0547143
$226$	6.70185	0.445801
$227$	−9.53252	−0.632695	−0.316348	−	0.948643i	$-0.602457\pi$
$227$	−9.53252	−0.632695	−0.316348	+	0.948643i	$0.602457\pi$
$228$	6.50357	0.430709
$229$	−10.7735	−0.711935	−0.355967	−	0.934498i	$-0.615849\pi$
$229$	−10.7735	−0.711935	−0.355967	+	0.934498i	$0.615849\pi$
$230$	4.06300	0.267906
$231$	4.61196	0.303444
$232$	8.96640	0.588673
$233$	−9.78815	−0.641243	−0.320622	−	0.947207i	$-0.603892\pi$
$233$	−9.78815	−0.641243	−0.320622	+	0.947207i	$0.603892\pi$
$234$	2.61295	0.170814
$235$	−7.10781	−0.463663
$236$	−2.03120	−0.132220
$237$	12.4967	0.811748
$238$	9.10329	0.590079
$239$	11.1373	0.720412	0.360206	−	0.932873i	$-0.382706\pi$
$239$	11.1373	0.720412	0.360206	+	0.932873i	$0.382706\pi$
$240$	−1.47624	−0.0952909
$241$	8.44784	0.544173	0.272087	−	0.962273i	$-0.412286\pi$
$241$	8.44784	0.544173	0.272087	+	0.962273i	$0.412286\pi$
$242$	9.19098	0.590818
$243$	−8.26378	−0.530122
$244$	1.33841	0.0856829
$245$	−1.60474	−0.102523
$246$	11.4680	0.731171
$247$	−14.0260	−0.892453
$248$	−1.15541	−0.0733688
$249$	4.48896	0.284476
$250$	−1.00000	−0.0632456
$251$	−4.85336	−0.306342	−0.153171	−	0.988200i	$-0.548948\pi$
$251$	−4.85336	−0.306342	−0.153171	+	0.988200i	$0.548948\pi$
$252$	1.90633	0.120088
$253$	−5.46472	−0.343564
$254$	8.13046	0.510151
$255$	−5.78561	−0.362309
$256$	1.00000	0.0625000
$257$	−14.3234	−0.893471	−0.446736	−	0.894666i	$-0.647414\pi$
$257$	−14.3234	−0.893471	−0.446736	+	0.894666i	$0.647414\pi$
$258$	8.49639	0.528962
$259$	−1.52765	−0.0949238
$260$	3.18375	0.197448
$261$	7.35885	0.455501
$262$	13.4752	0.832501
$263$	−22.5762	−1.39211	−0.696055	−	0.717988i	$-0.745063\pi$
$263$	−22.5762	−1.39211	−0.696055	+	0.717988i	$0.745063\pi$
$264$	1.98554	0.122202
$265$	14.3417	0.881002
$266$	−10.2330	−0.627422
$267$	1.68895	0.103362
$268$	−1.04497	−0.0638315
$269$	−8.32706	−0.507710	−0.253855	−	0.967242i	$-0.581699\pi$
$269$	−8.32706	−0.507710	−0.253855	+	0.967242i	$0.581699\pi$
$270$	−5.64029	−0.343257
$271$	−7.35226	−0.446618	−0.223309	−	0.974748i	$-0.571686\pi$
$271$	−7.35226	−0.446618	−0.223309	+	0.974748i	$0.571686\pi$
$272$	3.91915	0.237633
$273$	10.9170	0.660726
$274$	−9.92905	−0.599836
$275$	1.34500	0.0811065
$276$	5.99796	0.361035
$277$	10.8848	0.654007	0.327003	−	0.945023i	$-0.393961\pi$
$277$	10.8848	0.654007	0.327003	+	0.945023i	$0.393961\pi$
$278$	−1.27837	−0.0766713
$279$	−0.948264	−0.0567711
$280$	2.32277	0.138812
$281$	−14.5030	−0.865177	−0.432589	−	0.901591i	$-0.642400\pi$
$281$	−14.5030	−0.865177	−0.432589	+	0.901591i	$0.642400\pi$
$282$	−10.4928	−0.624840
$283$	−6.97140	−0.414406	−0.207203	−	0.978298i	$-0.566436\pi$
$283$	−6.97140	−0.414406	−0.207203	+	0.978298i	$0.566436\pi$
$284$	3.41086	0.202397
$285$	6.50357	0.385238
$286$	−4.28214	−0.253208
$287$	−18.0441	−1.06511
$288$	0.820714	0.0483610
$289$	−1.64025	−0.0964851
$290$	8.96640	0.526525
$291$	−19.9057	−1.16689
$292$	−7.58356	−0.443794
$293$	20.4970	1.19745	0.598725	−	0.800955i	$-0.295674\pi$
$293$	20.4970	1.19745	0.598725	+	0.800955i	$0.295674\pi$
$294$	−2.36898	−0.138162
$295$	−2.03120	−0.118261
$296$	−0.657687	−0.0382273
$297$	7.58619	0.440195
$298$	0.681369	0.0394706
$299$	−12.9356	−0.748083
$300$	−1.47624	−0.0852308
$301$	−13.3685	−0.770549
$302$	−19.5237	−1.12346
$303$	21.0889	1.21153
$304$	−4.40549	−0.252672
$305$	1.33841	0.0766371
$306$	3.21650	0.183875
$307$	−16.0697	−0.917149	−0.458574	−	0.888656i	$-0.651640\pi$
$307$	−16.0697	−0.917149	−0.458574	+	0.888656i	$0.651640\pi$
$308$	−3.12412	−0.178013
$309$	1.14524	0.0651503
$310$	−1.15541	−0.0656231
$311$	1.53839	0.0872342	0.0436171	−	0.999048i	$-0.486112\pi$
$311$	1.53839	0.0872342	0.0436171	+	0.999048i	$0.486112\pi$
$312$	4.69998	0.266084
$313$	−22.2204	−1.25597	−0.627986	−	0.778224i	$-0.716121\pi$
$313$	−22.2204	−1.25597	−0.627986	+	0.778224i	$0.716121\pi$
$314$	−2.19525	−0.123885
$315$	1.90633	0.107410
$316$	−8.46523	−0.476206
$317$	−27.5374	−1.54665	−0.773327	−	0.634007i	$-0.781409\pi$
$317$	−27.5374	−1.54665	−0.773327	+	0.634007i	$0.781409\pi$
$318$	21.1718	1.18725
$319$	−12.0598	−0.675219
$320$	1.00000	0.0559017
$321$	−12.3105	−0.687103
$322$	−9.43740	−0.525926
$323$	−17.2658	−0.960695
$324$	−5.86429	−0.325794
$325$	3.18375	0.176603
$326$	11.2919	0.625399
$327$	−13.4042	−0.741256
$328$	−7.76836	−0.428936
$329$	16.5098	0.910216
$330$	1.98554	0.109300
$331$	−21.3607	−1.17409	−0.587045	−	0.809555i	$-0.699709\pi$
$331$	−21.3607	−1.17409	−0.587045	+	0.809555i	$0.699709\pi$
$332$	−3.04080	−0.166886
$333$	−0.539773	−0.0295794
$334$	−4.27804	−0.234084
$335$	−1.04497	−0.0570926
$336$	3.42897	0.187065
$337$	17.1788	0.935791	0.467895	−	0.883784i	$-0.345012\pi$
$337$	17.1788	0.935791	0.467895	+	0.883784i	$0.345012\pi$
$338$	2.86373	0.155766
$339$	9.89355	0.537344
$340$	3.91915	0.212546
$341$	1.55403	0.0841555
$342$	−3.61565	−0.195512
$343$	19.9868	1.07919
$344$	−5.75543	−0.310312
$345$	5.99796	0.322919
$346$	−11.8805	−0.638698
$347$	4.60290	0.247097	0.123548	−	0.992339i	$-0.460573\pi$
$347$	4.60290	0.247097	0.123548	+	0.992339i	$0.460573\pi$
$348$	13.2366	0.709554
$349$	3.88184	0.207790	0.103895	−	0.994588i	$-0.466869\pi$
$349$	3.88184	0.207790	0.103895	+	0.994588i	$0.466869\pi$
$350$	2.32277	0.124157
$351$	17.9573	0.958489
$352$	−1.34500	−0.0716887
$353$	−25.3254	−1.34794	−0.673968	−	0.738761i	$-0.735411\pi$
$353$	−25.3254	−1.34794	−0.673968	+	0.738761i	$0.735411\pi$
$354$	−2.99854	−0.159371
$355$	3.41086	0.181030
$356$	−1.14409	−0.0606366
$357$	13.4386	0.711248
$358$	7.09205	0.374826
$359$	7.07677	0.373497	0.186749	−	0.982408i	$-0.440205\pi$
$359$	7.07677	0.373497	0.186749	+	0.982408i	$0.440205\pi$
$360$	0.820714	0.0432554
$361$	0.408385	0.0214940
$362$	−0.861521	−0.0452805
$363$	13.5681	0.712140
$364$	−7.39512	−0.387610
$365$	−7.58356	−0.396942
$366$	1.97581	0.103277
$367$	−26.2743	−1.37151	−0.685754	−	0.727833i	$-0.740527\pi$
$367$	−26.2743	−1.37151	−0.685754	+	0.727833i	$0.740527\pi$
$368$	−4.06300	−0.211798
$369$	−6.37561	−0.331901
$370$	−0.657687	−0.0341915
$371$	−33.3124	−1.72949
$372$	−1.70567	−0.0884348
$373$	5.63212	0.291620	0.145810	−	0.989313i	$-0.453421\pi$
$373$	5.63212	0.291620	0.145810	+	0.989313i	$0.453421\pi$
$374$	−5.27126	−0.272570
$375$	−1.47624	−0.0762327
$376$	7.10781	0.366558
$377$	−28.5468	−1.47023
$378$	13.1011	0.673848
$379$	−26.3918	−1.35566	−0.677829	−	0.735220i	$-0.737079\pi$
$379$	−26.3918	−1.35566	−0.677829	+	0.735220i	$0.737079\pi$
$380$	−4.40549	−0.225997
$381$	12.0025	0.614908
$382$	16.2924	0.833591
$383$	−14.4963	−0.740729	−0.370364	−	0.928887i	$-0.620767\pi$
$383$	−14.4963	−0.740729	−0.370364	+	0.928887i	$0.620767\pi$
$384$	1.47624	0.0753341
$385$	−3.12412	−0.159220
$386$	8.15952	0.415309
$387$	−4.72356	−0.240112
$388$	13.4841	0.684549
$389$	10.9095	0.553133	0.276566	−	0.960995i	$-0.410803\pi$
$389$	10.9095	0.553133	0.276566	+	0.960995i	$0.410803\pi$
$390$	4.69998	0.237993
$391$	−15.9235	−0.805286
$392$	1.60474	0.0810516
$393$	19.8926	1.00345
$394$	−0.519778	−0.0261860
$395$	−8.46523	−0.425932
$396$	−1.10386	−0.0554710
$397$	−10.1383	−0.508826	−0.254413	−	0.967096i	$-0.581882\pi$
$397$	−10.1383	−0.508826	−0.254413	+	0.967096i	$0.581882\pi$
$398$	26.9093	1.34884
$399$	−15.1063	−0.756261
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−1.54262	−0.0769390
$403$	3.67855	0.183242
$404$	−14.2856	−0.710733
$405$	−5.86429	−0.291399
$406$	−20.8269	−1.03362
$407$	0.884588	0.0438474
$408$	5.78561	0.286430
$409$	−35.2694	−1.74396	−0.871980	−	0.489541i	$-0.837164\pi$
$409$	−35.2694	−1.74396	−0.871980	+	0.489541i	$0.837164\pi$
$410$	−7.76836	−0.383652
$411$	−14.6577	−0.723009
$412$	−0.775780	−0.0382200
$413$	4.71801	0.232158
$414$	−3.33456	−0.163885
$415$	−3.04080	−0.149267
$416$	−3.18375	−0.156096
$417$	−1.88717	−0.0924153
$418$	5.92539	0.289820
$419$	14.0642	0.687081	0.343540	−	0.939138i	$-0.388374\pi$
$419$	14.0642	0.687081	0.343540	+	0.939138i	$0.388374\pi$
$420$	3.42897	0.167316
$421$	−5.76802	−0.281116	−0.140558	−	0.990072i	$-0.544890\pi$
$421$	−5.76802	−0.281116	−0.140558	+	0.990072i	$0.544890\pi$
$422$	18.0183	0.877119
$423$	5.83348	0.283634
$424$	−14.3417	−0.696494
$425$	3.91915	0.190107
$426$	5.03525	0.243958
$427$	−3.10882	−0.150446
$428$	8.33906	0.403084
$429$	−6.32147	−0.305203
$430$	−5.75543	−0.277551
$431$	−23.5594	−1.13482	−0.567408	−	0.823437i	$-0.692054\pi$
$431$	−23.5594	−1.13482	−0.567408	+	0.823437i	$0.692054\pi$
$432$	5.64029	0.271369
$433$	−22.2265	−1.06814	−0.534069	−	0.845441i	$-0.679338\pi$
$433$	−22.2265	−1.06814	−0.534069	+	0.845441i	$0.679338\pi$
$434$	2.68376	0.128825
$435$	13.2366	0.634645
$436$	9.07998	0.434852
$437$	17.8995	0.856250
$438$	−11.1952	−0.534926
$439$	−26.5932	−1.26922	−0.634611	−	0.772832i	$-0.718840\pi$
$439$	−26.5932	−1.26922	−0.634611	+	0.772832i	$0.718840\pi$
$440$	−1.34500	−0.0641203
$441$	1.31703	0.0627159
$442$	−12.4776	−0.593499
$443$	38.3551	1.82231	0.911153	−	0.412069i	$-0.135194\pi$
$443$	38.3551	1.82231	0.911153	+	0.412069i	$0.135194\pi$
$444$	−0.970904	−0.0460770
$445$	−1.14409	−0.0542350
$446$	−21.7185	−1.02840
$447$	1.00586	0.0475757
$448$	−2.32277	−0.109741
$449$	3.33232	0.157262	0.0786309	−	0.996904i	$-0.474945\pi$
$449$	3.33232	0.157262	0.0786309	+	0.996904i	$0.474945\pi$
$450$	0.820714	0.0386888
$451$	10.4484	0.491998
$452$	−6.70185	−0.315229
$453$	−28.8217	−1.35416
$454$	9.53252	0.447383
$455$	−7.39512	−0.346689
$456$	−6.50357	−0.304558
$457$	−24.6255	−1.15193	−0.575965	−	0.817474i	$-0.695374\pi$
$457$	−24.6255	−1.15193	−0.575965	+	0.817474i	$0.695374\pi$
$458$	10.7735	0.503414
$459$	22.1052	1.03178
$460$	−4.06300	−0.189438
$461$	−10.4502	−0.486713	−0.243356	−	0.969937i	$-0.578248\pi$
$461$	−10.4502	−0.486713	−0.243356	+	0.969937i	$0.578248\pi$
$462$	−4.61196	−0.214568
$463$	−13.0520	−0.606577	−0.303288	−	0.952899i	$-0.598085\pi$
$463$	−13.0520	−0.606577	−0.303288	+	0.952899i	$0.598085\pi$
$464$	−8.96640	−0.416255
$465$	−1.70567	−0.0790985
$466$	9.78815	0.453427
$467$	11.2065	0.518574	0.259287	−	0.965800i	$-0.416512\pi$
$467$	11.2065	0.518574	0.259287	+	0.965800i	$0.416512\pi$
$468$	−2.61295	−0.120784
$469$	2.42722	0.112078
$470$	7.10781	0.327859
$471$	−3.24071	−0.149324
$472$	2.03120	0.0934936
$473$	7.74104	0.355933
$474$	−12.4967	−0.573993
$475$	−4.40549	−0.202138
$476$	−9.10329	−0.417249
$477$	−11.7704	−0.538931
$478$	−11.1373	−0.509408
$479$	−3.08020	−0.140738	−0.0703691	−	0.997521i	$-0.522418\pi$
$479$	−3.08020	−0.140738	−0.0703691	+	0.997521i	$0.522418\pi$
$480$	1.47624	0.0673808
$481$	2.09391	0.0954741
$482$	−8.44784	−0.384789
$483$	−13.9319	−0.633922
$484$	−9.19098	−0.417772
$485$	13.4841	0.612280
$486$	8.26378	0.374853
$487$	−6.57151	−0.297784	−0.148892	−	0.988853i	$-0.547571\pi$
$487$	−6.57151	−0.297784	−0.148892	+	0.988853i	$0.547571\pi$
$488$	−1.33841	−0.0605869
$489$	16.6695	0.753822
$490$	1.60474	0.0724948
$491$	21.6738	0.978126	0.489063	−	0.872248i	$-0.337339\pi$
$491$	21.6738	0.978126	0.489063	+	0.872248i	$0.337339\pi$
$492$	−11.4680	−0.517016
$493$	−35.1407	−1.58266
$494$	14.0260	0.631060
$495$	−1.10386	−0.0496148
$496$	1.15541	0.0518796
$497$	−7.92264	−0.355379
$498$	−4.48896	−0.201155
$499$	6.40991	0.286947	0.143473	−	0.989654i	$-0.454173\pi$
$499$	6.40991	0.286947	0.143473	+	0.989654i	$0.454173\pi$
$500$	1.00000	0.0447214
$501$	−6.31541	−0.282152
$502$	4.85336	0.216616
$503$	8.99634	0.401127	0.200564	−	0.979681i	$-0.435723\pi$
$503$	8.99634	0.401127	0.200564	+	0.979681i	$0.435723\pi$
$504$	−1.90633	−0.0849147
$505$	−14.2856	−0.635699
$506$	5.46472	0.242937
$507$	4.22755	0.187752
$508$	−8.13046	−0.360731
$509$	14.3619	0.636582	0.318291	−	0.947993i	$-0.396891\pi$
$509$	14.3619	0.636582	0.318291	+	0.947993i	$0.396891\pi$
$510$	5.78561	0.256191
$511$	17.6149	0.779236
$512$	−1.00000	−0.0441942
$513$	−24.8483	−1.09708
$514$	14.3234	0.631780
$515$	−0.775780	−0.0341850
$516$	−8.49639	−0.374033
$517$	−9.56000	−0.420448
$518$	1.52765	0.0671213
$519$	−17.5384	−0.769852
$520$	−3.18375	−0.139617
$521$	1.51348	0.0663069	0.0331534	−	0.999450i	$-0.489445\pi$
$521$	1.51348	0.0663069	0.0331534	+	0.999450i	$0.489445\pi$
$522$	−7.35885	−0.322088
$523$	−39.3370	−1.72009	−0.860043	−	0.510222i	$-0.829563\pi$
$523$	−39.3370	−1.72009	−0.860043	+	0.510222i	$0.829563\pi$
$524$	−13.4752	−0.588667
$525$	3.42897	0.149652
$526$	22.5762	0.984370
$527$	4.52824	0.197253
$528$	−1.98554	−0.0864096
$529$	−6.49207	−0.282264
$530$	−14.3417	−0.622963
$531$	1.66704	0.0723432
$532$	10.2330	0.443655
$533$	24.7325	1.07129
$534$	−1.68895	−0.0730881
$535$	8.33906	0.360529
$536$	1.04497	0.0451357
$537$	10.4696	0.451795
$538$	8.32706	0.359005
$539$	−2.15837	−0.0929677
$540$	5.64029	0.242720
$541$	−11.7550	−0.505386	−0.252693	−	0.967547i	$-0.581316\pi$
$541$	−11.7550	−0.505386	−0.252693	+	0.967547i	$0.581316\pi$
$542$	7.35226	0.315807
$543$	−1.27181	−0.0545787
$544$	−3.91915	−0.168032
$545$	9.07998	0.388944
$546$	−10.9170	−0.467203
$547$	−30.7898	−1.31648	−0.658239	−	0.752809i	$-0.728698\pi$
$547$	−30.7898	−1.31648	−0.658239	+	0.752809i	$0.728698\pi$
$548$	9.92905	0.424148
$549$	−1.09845	−0.0468808
$550$	−1.34500	−0.0573509
$551$	39.5014	1.68282
$552$	−5.99796	−0.255290
$553$	19.6628	0.836146
$554$	−10.8848	−0.462453
$555$	−0.970904	−0.0412126
$556$	1.27837	0.0542148
$557$	−8.73904	−0.370285	−0.185143	−	0.982712i	$-0.559275\pi$
$557$	−8.73904	−0.370285	−0.185143	+	0.982712i	$0.559275\pi$
$558$	0.948264	0.0401432
$559$	18.3238	0.775016
$560$	−2.32277	−0.0981549
$561$	−7.78164	−0.328541
$562$	14.5030	0.611773
$563$	25.5868	1.07836	0.539178	−	0.842192i	$-0.318735\pi$
$563$	25.5868	1.07836	0.539178	+	0.842192i	$0.318735\pi$
$564$	10.4928	0.441828
$565$	−6.70185	−0.281949
$566$	6.97140	0.293030
$567$	13.6214	0.572044
$568$	−3.41086	−0.143116
$569$	31.8055	1.33335	0.666677	−	0.745346i	$-0.267716\pi$
$569$	31.8055	1.33335	0.666677	+	0.745346i	$0.267716\pi$
$570$	−6.50357	−0.272405
$571$	5.58253	0.233622	0.116811	−	0.993154i	$-0.462733\pi$
$571$	5.58253	0.233622	0.116811	+	0.993154i	$0.462733\pi$
$572$	4.28214	0.179045
$573$	24.0515	1.00476
$574$	18.0441	0.753147
$575$	−4.06300	−0.169439
$576$	−0.820714	−0.0341964
$577$	−8.62270	−0.358968	−0.179484	−	0.983761i	$-0.557443\pi$
$577$	−8.62270	−0.358968	−0.179484	+	0.983761i	$0.557443\pi$
$578$	1.64025	0.0682253
$579$	12.0454	0.500590
$580$	−8.96640	−0.372309
$581$	7.06309	0.293026
$582$	19.9057	0.825118
$583$	19.2895	0.798891
$584$	7.58356	0.313810
$585$	−2.61295	−0.108032
$586$	−20.4970	−0.846725
$587$	−9.41965	−0.388790	−0.194395	−	0.980923i	$-0.562274\pi$
$587$	−9.41965	−0.388790	−0.194395	+	0.980923i	$0.562274\pi$
$588$	2.36898	0.0976952
$589$	−5.09017	−0.209737
$590$	2.03120	0.0836232
$591$	−0.767317	−0.0315632
$592$	0.657687	0.0270308
$593$	6.14848	0.252488	0.126244	−	0.991999i	$-0.459708\pi$
$593$	6.14848	0.252488	0.126244	+	0.991999i	$0.459708\pi$
$594$	−7.58619	−0.311265
$595$	−9.10329	−0.373198
$596$	−0.681369	−0.0279100
$597$	39.7246	1.62582
$598$	12.9356	0.528975
$599$	−13.8997	−0.567928	−0.283964	−	0.958835i	$-0.591650\pi$
$599$	−13.8997	−0.567928	−0.283964	+	0.958835i	$0.591650\pi$
$600$	1.47624	0.0602673
$601$	29.2093	1.19147	0.595735	−	0.803181i	$-0.296861\pi$
$601$	29.2093	1.19147	0.595735	+	0.803181i	$0.296861\pi$
$602$	13.3685	0.544861
$603$	0.857619	0.0349249
$604$	19.5237	0.794408
$605$	−9.19098	−0.373666
$606$	−21.0889	−0.856679
$607$	7.88674	0.320113	0.160056	−	0.987108i	$-0.448832\pi$
$607$	7.88674	0.320113	0.160056	+	0.987108i	$0.448832\pi$
$608$	4.40549	0.178666
$609$	−30.7455	−1.24587
$610$	−1.33841	−0.0541906
$611$	−22.6295	−0.915492
$612$	−3.21650	−0.130019
$613$	−21.1977	−0.856167	−0.428084	−	0.903739i	$-0.640811\pi$
$613$	−21.1977	−0.856167	−0.428084	+	0.903739i	$0.640811\pi$
$614$	16.0697	0.648522
$615$	−11.4680	−0.462433
$616$	3.12412	0.125874
$617$	7.45682	0.300200	0.150100	−	0.988671i	$-0.452040\pi$
$617$	7.45682	0.300200	0.150100	+	0.988671i	$0.452040\pi$
$618$	−1.14524	−0.0460682
$619$	−26.1113	−1.04950	−0.524751	−	0.851256i	$-0.675842\pi$
$619$	−26.1113	−1.04950	−0.524751	+	0.851256i	$0.675842\pi$
$620$	1.15541	0.0464025
$621$	−22.9165	−0.919607
$622$	−1.53839	−0.0616839
$623$	2.65746	0.106469
$624$	−4.69998	−0.188150
$625$	1.00000	0.0400000
$626$	22.2204	0.888107
$627$	8.74729	0.349333
$628$	2.19525	0.0875999
$629$	2.57757	0.102775
$630$	−1.90633	−0.0759500
$631$	48.9494	1.94865	0.974323	−	0.225156i	$-0.0722891\pi$
$631$	48.9494	1.94865	0.974323	+	0.225156i	$0.0722891\pi$
$632$	8.46523	0.336729
$633$	26.5994	1.05723
$634$	27.5374	1.09365
$635$	−8.13046	−0.322648
$636$	−21.1718	−0.839515
$637$	−5.10909	−0.202430
$638$	12.0598	0.477452
$639$	−2.79934	−0.110740
$640$	−1.00000	−0.0395285
$641$	40.1041	1.58402	0.792009	−	0.610509i	$-0.209035\pi$
$641$	40.1041	1.58402	0.792009	+	0.610509i	$0.209035\pi$
$642$	12.3105	0.485855
$643$	5.29357	0.208758	0.104379	−	0.994538i	$-0.466715\pi$
$643$	5.29357	0.208758	0.104379	+	0.994538i	$0.466715\pi$
$644$	9.43740	0.371886
$645$	−8.49639	−0.334545
$646$	17.2658	0.679314
$647$	7.86240	0.309103	0.154551	−	0.987985i	$-0.450607\pi$
$647$	7.86240	0.309103	0.154551	+	0.987985i	$0.450607\pi$
$648$	5.86429	0.230371
$649$	−2.73196	−0.107239
$650$	−3.18375	−0.124877
$651$	3.96188	0.155278
$652$	−11.2919	−0.442224
$653$	−0.370814	−0.0145111	−0.00725554	−	0.999974i	$-0.502310\pi$
$653$	−0.370814	−0.0145111	−0.00725554	+	0.999974i	$0.502310\pi$
$654$	13.4042	0.524147
$655$	−13.4752	−0.526520
$656$	7.76836	0.303304
$657$	6.22394	0.242819
$658$	−16.5098	−0.643620
$659$	10.7571	0.419038	0.209519	−	0.977805i	$-0.432810\pi$
$659$	10.7571	0.419038	0.209519	+	0.977805i	$0.432810\pi$
$660$	−1.98554	−0.0772871
$661$	17.7361	0.689855	0.344927	−	0.938629i	$-0.387904\pi$
$661$	17.7361	0.689855	0.344927	+	0.938629i	$0.387904\pi$
$662$	21.3607	0.830206
$663$	−18.4199	−0.715371
$664$	3.04080	0.118006
$665$	10.2330	0.396817
$666$	0.539773	0.0209158
$667$	36.4304	1.41059
$668$	4.27804	0.165522
$669$	−32.0617	−1.23958
$670$	1.04497	0.0403706
$671$	1.80016	0.0694944
$672$	−3.42897	−0.132275
$673$	−11.0896	−0.427472	−0.213736	−	0.976891i	$-0.568563\pi$
$673$	−11.0896	−0.427472	−0.213736	+	0.976891i	$0.568563\pi$
$674$	−17.1788	−0.661704
$675$	5.64029	0.217095
$676$	−2.86373	−0.110143
$677$	−11.1620	−0.428990	−0.214495	−	0.976725i	$-0.568811\pi$
$677$	−11.1620	−0.428990	−0.214495	+	0.976725i	$0.568811\pi$
$678$	−9.89355	−0.379959
$679$	−31.3204	−1.20197
$680$	−3.91915	−0.150293
$681$	14.0723	0.539251
$682$	−1.55403	−0.0595069
$683$	42.1623	1.61330	0.806648	−	0.591032i	$-0.201279\pi$
$683$	42.1623	1.61330	0.806648	+	0.591032i	$0.201279\pi$
$684$	3.61565	0.138248
$685$	9.92905	0.379369
$686$	−19.9868	−0.763101
$687$	15.9043	0.606787
$688$	5.75543	0.219424
$689$	45.6603	1.73952
$690$	−5.99796	−0.228338
$691$	21.7076	0.825796	0.412898	−	0.910777i	$-0.364517\pi$
$691$	21.7076	0.825796	0.412898	+	0.910777i	$0.364517\pi$
$692$	11.8805	0.451628
$693$	2.56401	0.0973988
$694$	−4.60290	−0.174724
$695$	1.27837	0.0484912
$696$	−13.2366	−0.501731
$697$	30.4454	1.15320
$698$	−3.88184	−0.146930
$699$	14.4497	0.546537
$700$	−2.32277	−0.0877924
$701$	20.7094	0.782184	0.391092	−	0.920352i	$-0.372097\pi$
$701$	20.7094	0.782184	0.391092	+	0.920352i	$0.372097\pi$
$702$	−17.9573	−0.677754
$703$	−2.89743	−0.109279
$704$	1.34500	0.0506916
$705$	10.4928	0.395183
$706$	25.3254	0.953135
$707$	33.1821	1.24794
$708$	2.99854	0.112692
$709$	−36.9626	−1.38816	−0.694081	−	0.719897i	$-0.744189\pi$
$709$	−36.9626	−1.38816	−0.694081	+	0.719897i	$0.744189\pi$
$710$	−3.41086	−0.128007
$711$	6.94753	0.260553
$712$	1.14409	0.0428766
$713$	−4.69444	−0.175808
$714$	−13.4386	−0.502929
$715$	4.28214	0.160143
$716$	−7.09205	−0.265042
$717$	−16.4413	−0.614013
$718$	−7.07677	−0.264103
$719$	−9.63101	−0.359176	−0.179588	−	0.983742i	$-0.557476\pi$
$719$	−9.63101	−0.359176	−0.179588	+	0.983742i	$0.557476\pi$
$720$	−0.820714	−0.0305862
$721$	1.80196	0.0671085
$722$	−0.408385	−0.0151985
$723$	−12.4710	−0.463803
$724$	0.861521	0.0320182
$725$	−8.96640	−0.333004
$726$	−13.5681	−0.503559
$727$	−5.92699	−0.219820	−0.109910	−	0.993942i	$-0.535056\pi$
$727$	−5.92699	−0.219820	−0.109910	+	0.993942i	$0.535056\pi$
$728$	7.39512	0.274081
$729$	29.7922	1.10341
$730$	7.58356	0.280680
$731$	22.5564	0.834278
$732$	−1.97581	−0.0730282
$733$	0.775978	0.0286614	0.0143307	−	0.999897i	$-0.495438\pi$
$733$	0.775978	0.0286614	0.0143307	+	0.999897i	$0.495438\pi$
$734$	26.2743	0.969803
$735$	2.36898	0.0873812
$736$	4.06300	0.149764
$737$	−1.40548	−0.0517715
$738$	6.37561	0.234689
$739$	−48.5768	−1.78693	−0.893463	−	0.449137i	$-0.851732\pi$
$739$	−48.5768	−1.78693	−0.893463	+	0.449137i	$0.851732\pi$
$740$	0.657687	0.0241770
$741$	20.7057	0.760645
$742$	33.3124	1.22294
$743$	6.88535	0.252599	0.126299	−	0.991992i	$-0.459690\pi$
$743$	6.88535	0.252599	0.126299	+	0.991992i	$0.459690\pi$
$744$	1.70567	0.0625328
$745$	−0.681369	−0.0249634
$746$	−5.63212	−0.206207
$747$	2.49563	0.0913104
$748$	5.27126	0.192736
$749$	−19.3697	−0.707754
$750$	1.47624	0.0539047
$751$	7.52640	0.274642	0.137321	−	0.990527i	$-0.456151\pi$
$751$	7.52640	0.274642	0.137321	+	0.990527i	$0.456151\pi$
$752$	−7.10781	−0.259195
$753$	7.16473	0.261097
$754$	28.5468	1.03961
$755$	19.5237	0.710540
$756$	−13.1011	−0.476482
$757$	32.9357	1.19707	0.598535	−	0.801097i	$-0.295750\pi$
$757$	32.9357	1.19707	0.598535	+	0.801097i	$0.295750\pi$
$758$	26.3918	0.958594
$759$	8.06725	0.292823
$760$	4.40549	0.159804
$761$	16.1450	0.585258	0.292629	−	0.956226i	$-0.405470\pi$
$761$	16.1450	0.585258	0.292629	+	0.956226i	$0.405470\pi$
$762$	−12.0025	−0.434805
$763$	−21.0907	−0.763535
$764$	−16.2924	−0.589438
$765$	−3.21650	−0.116293
$766$	14.4963	0.523774
$767$	−6.46684	−0.233504
$768$	−1.47624	−0.0532692
$769$	−32.9580	−1.18850	−0.594249	−	0.804281i	$-0.702551\pi$
$769$	−32.9580	−1.18850	−0.594249	+	0.804281i	$0.702551\pi$
$770$	3.12412	0.112586
$771$	21.1448	0.761513
$772$	−8.15952	−0.293668
$773$	−2.86137	−0.102916	−0.0514582	−	0.998675i	$-0.516387\pi$
$773$	−2.86137	−0.102916	−0.0514582	+	0.998675i	$0.516387\pi$
$774$	4.72356	0.169785
$775$	1.15541	0.0415037
$776$	−13.4841	−0.484050
$777$	2.25519	0.0809043
$778$	−10.9095	−0.391124
$779$	−34.2235	−1.22618
$780$	−4.69998	−0.168286
$781$	4.58760	0.164157
$782$	15.9235	0.569423
$783$	−50.5731	−1.80734
$784$	−1.60474	−0.0573121
$785$	2.19525	0.0783518
$786$	−19.8926	−0.709547
$787$	9.82801	0.350331	0.175165	−	0.984539i	$-0.443954\pi$
$787$	9.82801	0.350331	0.175165	+	0.984539i	$0.443954\pi$
$788$	0.519778	0.0185163
$789$	33.3279	1.18651
$790$	8.46523	0.301179
$791$	15.5669	0.553494
$792$	1.10386	0.0392239
$793$	4.26116	0.151318
$794$	10.1383	0.359794
$795$	−21.1718	−0.750885
$796$	−26.9093	−0.953775
$797$	−7.07485	−0.250604	−0.125302	−	0.992119i	$-0.539990\pi$
$797$	−7.07485	−0.250604	−0.125302	+	0.992119i	$0.539990\pi$
$798$	15.1063	0.534757
$799$	−27.8566	−0.985496
$800$	−1.00000	−0.0353553
$801$	0.938970	0.0331769
$802$	−1.00000	−0.0353112
$803$	−10.1999	−0.359946
$804$	1.54262	0.0544041
$805$	9.43740	0.332625
$806$	−3.67855	−0.129571
$807$	12.2927	0.432725
$808$	14.2856	0.502564
$809$	38.0755	1.33866	0.669331	−	0.742965i	$-0.266581\pi$
$809$	38.0755	1.33866	0.669331	+	0.742965i	$0.266581\pi$
$810$	5.86429	0.206050
$811$	−8.49597	−0.298334	−0.149167	−	0.988812i	$-0.547659\pi$
$811$	−8.49597	−0.298334	−0.149167	+	0.988812i	$0.547659\pi$
$812$	20.8269	0.730880
$813$	10.8537	0.380656
$814$	−0.884588	−0.0310048
$815$	−11.2919	−0.395537
$816$	−5.78561	−0.202537
$817$	−25.3555	−0.887077
$818$	35.2694	1.23317
$819$	6.06928	0.212078
$820$	7.76836	0.271283
$821$	38.7707	1.35311	0.676553	−	0.736394i	$-0.263473\pi$
$821$	38.7707	1.35311	0.676553	+	0.736394i	$0.263473\pi$
$822$	14.6577	0.511245
$823$	36.3890	1.26844	0.634220	−	0.773153i	$-0.281321\pi$
$823$	36.3890	1.26844	0.634220	+	0.773153i	$0.281321\pi$
$824$	0.775780	0.0270256
$825$	−1.98554	−0.0691277
$826$	−4.71801	−0.164161
$827$	10.3868	0.361184	0.180592	−	0.983558i	$-0.442199\pi$
$827$	10.3868	0.361184	0.180592	+	0.983558i	$0.442199\pi$
$828$	3.33456	0.115884
$829$	55.8712	1.94049	0.970244	−	0.242129i	$-0.0778458\pi$
$829$	55.8712	1.94049	0.970244	+	0.242129i	$0.0778458\pi$
$830$	3.04080	0.105548
$831$	−16.0686	−0.557415
$832$	3.18375	0.110377
$833$	−6.28922	−0.217909
$834$	1.88717	0.0653475
$835$	4.27804	0.148048
$836$	−5.92539	−0.204934
$837$	6.51687	0.225256
$838$	−14.0642	−0.485840
$839$	−31.2402	−1.07853	−0.539266	−	0.842136i	$-0.681298\pi$
$839$	−31.2402	−1.07853	−0.539266	+	0.842136i	$0.681298\pi$
$840$	−3.42897	−0.118311
$841$	51.3963	1.77229
$842$	5.76802	0.198779
$843$	21.4099	0.737397
$844$	−18.0183	−0.620217
$845$	−2.86373	−0.0985152
$846$	−5.83348	−0.200559
$847$	21.3485	0.733544
$848$	14.3417	0.492495
$849$	10.2915	0.353202
$850$	−3.91915	−0.134426
$851$	−2.67218	−0.0916011
$852$	−5.03525	−0.172505
$853$	23.4882	0.804222	0.402111	−	0.915591i	$-0.368277\pi$
$853$	23.4882	0.804222	0.402111	+	0.915591i	$0.368277\pi$
$854$	3.10882	0.106381
$855$	3.61565	0.123653
$856$	−8.33906	−0.285023
$857$	−48.2529	−1.64829	−0.824143	−	0.566382i	$-0.808343\pi$
$857$	−48.2529	−1.64829	−0.824143	+	0.566382i	$0.808343\pi$
$858$	6.32147	0.215811
$859$	−39.4759	−1.34690	−0.673450	−	0.739232i	$-0.735188\pi$
$859$	−39.4759	−1.34690	−0.673450	+	0.739232i	$0.735188\pi$
$860$	5.75543	0.196258
$861$	26.6375	0.907802
$862$	23.5594	0.802436
$863$	9.61873	0.327425	0.163713	−	0.986508i	$-0.447653\pi$
$863$	9.61873	0.327425	0.163713	+	0.986508i	$0.447653\pi$
$864$	−5.64029	−0.191887
$865$	11.8805	0.403948
$866$	22.2265	0.755287
$867$	2.42140	0.0822350
$868$	−2.68376	−0.0910928
$869$	−11.3857	−0.386234
$870$	−13.2366	−0.448761
$871$	−3.32691	−0.112728
$872$	−9.07998	−0.307487
$873$	−11.0666	−0.374546
$874$	−17.8995	−0.605460
$875$	−2.32277	−0.0785240
$876$	11.1952	0.378249
$877$	41.0508	1.38619	0.693093	−	0.720848i	$-0.256247\pi$
$877$	41.0508	1.38619	0.693093	+	0.720848i	$0.256247\pi$
$878$	26.5932	0.897476
$879$	−30.2586	−1.02060
$880$	1.34500	0.0453399
$881$	21.6318	0.728792	0.364396	−	0.931244i	$-0.381275\pi$
$881$	21.6318	0.728792	0.364396	+	0.931244i	$0.381275\pi$
$882$	−1.31703	−0.0443468
$883$	−35.7699	−1.20375	−0.601876	−	0.798589i	$-0.705580\pi$
$883$	−35.7699	−1.20375	−0.601876	+	0.798589i	$0.705580\pi$
$884$	12.4776	0.419667
$885$	2.99854	0.100795
$886$	−38.3551	−1.28856
$887$	−13.2697	−0.445554	−0.222777	−	0.974869i	$-0.571512\pi$
$887$	−13.2697	−0.445554	−0.222777	+	0.974869i	$0.571512\pi$
$888$	0.970904	0.0325814
$889$	18.8852	0.633389
$890$	1.14409	0.0383500
$891$	−7.88746	−0.264240
$892$	21.7185	0.727188
$893$	31.3134	1.04786
$894$	−1.00586	−0.0336411
$895$	−7.09205	−0.237061
$896$	2.32277	0.0775983
$897$	19.0960	0.637597
$898$	−3.33232	−0.111201
$899$	−10.3599	−0.345522
$900$	−0.820714	−0.0273571
$901$	56.2072	1.87253
$902$	−10.4484	−0.347895
$903$	19.7352	0.656745
$904$	6.70185	0.222900
$905$	0.861521	0.0286379
$906$	28.8217	0.957535
$907$	−16.5813	−0.550574	−0.275287	−	0.961362i	$-0.588773\pi$
$907$	−16.5813	−0.550574	−0.275287	+	0.961362i	$0.588773\pi$
$908$	−9.53252	−0.316348
$909$	11.7244	0.388873
$910$	7.39512	0.245146
$911$	−19.4322	−0.643819	−0.321909	−	0.946770i	$-0.604325\pi$
$911$	−19.4322	−0.643819	−0.321909	+	0.946770i	$0.604325\pi$
$912$	6.50357	0.215355
$913$	−4.08988	−0.135355
$914$	24.6255	0.814538
$915$	−1.97581	−0.0653184
$916$	−10.7735	−0.355967
$917$	31.2998	1.03361
$918$	−22.1052	−0.729579
$919$	24.2476	0.799853	0.399927	−	0.916547i	$-0.369036\pi$
$919$	24.2476	0.799853	0.399927	+	0.916547i	$0.369036\pi$
$920$	4.06300	0.133953
$921$	23.7228	0.781693
$922$	10.4502	0.344158
$923$	10.8593	0.357439
$924$	4.61196	0.151722
$925$	0.657687	0.0216246
$926$	13.0520	0.428914
$927$	0.636694	0.0209118
$928$	8.96640	0.294336
$929$	1.52858	0.0501511	0.0250756	−	0.999686i	$-0.492017\pi$
$929$	1.52858	0.0501511	0.0250756	+	0.999686i	$0.492017\pi$
$930$	1.70567	0.0559311
$931$	7.06967	0.231699
$932$	−9.78815	−0.320622
$933$	−2.27104	−0.0743504
$934$	−11.2065	−0.366687
$935$	5.27126	0.172388
$936$	2.61295	0.0854069
$937$	−30.9500	−1.01109	−0.505546	−	0.862800i	$-0.668709\pi$
$937$	−30.9500	−1.01109	−0.505546	+	0.862800i	$0.668709\pi$
$938$	−2.42722	−0.0792514
$939$	32.8027	1.07048
$940$	−7.10781	−0.231831
$941$	−14.9037	−0.485848	−0.242924	−	0.970045i	$-0.578107\pi$
$941$	−14.9037	−0.485848	−0.242924	+	0.970045i	$0.578107\pi$
$942$	3.24071	0.105588
$943$	−31.5628	−1.02783
$944$	−2.03120	−0.0661100
$945$	−13.1011	−0.426179
$946$	−7.74104	−0.251683
$947$	28.5094	0.926431	0.463215	−	0.886246i	$-0.346696\pi$
$947$	28.5094	0.926431	0.463215	+	0.886246i	$0.346696\pi$
$948$	12.4967	0.405874
$949$	−24.1442	−0.783753
$950$	4.40549	0.142933
$951$	40.6518	1.31823
$952$	9.10329	0.295039
$953$	23.1394	0.749559	0.374780	−	0.927114i	$-0.377718\pi$
$953$	23.1394	0.749559	0.374780	+	0.927114i	$0.377718\pi$
$954$	11.7704	0.381081
$955$	−16.2924	−0.527209
$956$	11.1373	0.360206
$957$	17.8032	0.575494
$958$	3.08020	0.0995169
$959$	−23.0629	−0.744740
$960$	−1.47624	−0.0476455
$961$	−29.6650	−0.956936
$962$	−2.09391	−0.0675104
$963$	−6.84399	−0.220544
$964$	8.44784	0.272087
$965$	−8.15952	−0.262664
$966$	13.9319	0.448251
$967$	−2.69699	−0.0867294	−0.0433647	−	0.999059i	$-0.513808\pi$
$967$	−2.69699	−0.0867294	−0.0433647	+	0.999059i	$0.513808\pi$
$968$	9.19098	0.295409
$969$	25.4885	0.818808
$970$	−13.4841	−0.432947
$971$	16.8068	0.539356	0.269678	−	0.962951i	$-0.413083\pi$
$971$	16.8068	0.539356	0.269678	+	0.962951i	$0.413083\pi$
$972$	−8.26378	−0.265061
$973$	−2.96935	−0.0951929
$974$	6.57151	0.210565
$975$	−4.69998	−0.150520
$976$	1.33841	0.0428414
$977$	33.4094	1.06886	0.534431	−	0.845212i	$-0.320526\pi$
$977$	33.4094	1.06886	0.534431	+	0.845212i	$0.320526\pi$
$978$	−16.6695	−0.533032
$979$	−1.53880	−0.0491802
$980$	−1.60474	−0.0512615
$981$	−7.45207	−0.237926
$982$	−21.6738	−0.691640
$983$	−46.7735	−1.49184	−0.745921	−	0.666034i	$-0.767990\pi$
$983$	−46.7735	−1.49184	−0.745921	+	0.666034i	$0.767990\pi$
$984$	11.4680	0.365586
$985$	0.519778	0.0165615
$986$	35.1407	1.11911
$987$	−24.3725	−0.775784
$988$	−14.0260	−0.446226
$989$	−23.3843	−0.743577
$990$	1.10386	0.0350830
$991$	−10.3315	−0.328191	−0.164095	−	0.986444i	$-0.552470\pi$
$991$	−10.3315	−0.328191	−0.164095	+	0.986444i	$0.552470\pi$
$992$	−1.15541	−0.0366844
$993$	31.5335	1.00069
$994$	7.92264	0.251291
$995$	−26.9093	−0.853082
$996$	4.48896	0.142238
$997$	−28.6650	−0.907829	−0.453915	−	0.891045i	$-0.649973\pi$
$997$	−28.6650	−0.907829	−0.453915	+	0.891045i	$0.649973\pi$
$998$	−6.40991	−0.202902
$999$	3.70954	0.117365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.4	✓	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.47624 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.47624 q^{6} -2.32277 q^{7} -1.00000 q^{8} -0.820714 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.47624 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.47624 q^{6} -2.32277 q^{7} -1.00000 q^{8} -0.820714 q^{9} -1.00000 q^{10} +1.34500 q^{11} -1.47624 q^{12} +3.18375 q^{13} +2.32277 q^{14} -1.47624 q^{15} +1.00000 q^{16} +3.91915 q^{17} +0.820714 q^{18} -4.40549 q^{19} +1.00000 q^{20} +3.42897 q^{21} -1.34500 q^{22} -4.06300 q^{23} +1.47624 q^{24} +1.00000 q^{25} -3.18375 q^{26} +5.64029 q^{27} -2.32277 q^{28} -8.96640 q^{29} +1.47624 q^{30} +1.15541 q^{31} -1.00000 q^{32} -1.98554 q^{33} -3.91915 q^{34} -2.32277 q^{35} -0.820714 q^{36} +0.657687 q^{37} +4.40549 q^{38} -4.69998 q^{39} -1.00000 q^{40} +7.76836 q^{41} -3.42897 q^{42} +5.75543 q^{43} +1.34500 q^{44} -0.820714 q^{45} +4.06300 q^{46} -7.10781 q^{47} -1.47624 q^{48} -1.60474 q^{49} -1.00000 q^{50} -5.78561 q^{51} +3.18375 q^{52} +14.3417 q^{53} -5.64029 q^{54} +1.34500 q^{55} +2.32277 q^{56} +6.50357 q^{57} +8.96640 q^{58} -2.03120 q^{59} -1.47624 q^{60} +1.33841 q^{61} -1.15541 q^{62} +1.90633 q^{63} +1.00000 q^{64} +3.18375 q^{65} +1.98554 q^{66} -1.04497 q^{67} +3.91915 q^{68} +5.99796 q^{69} +2.32277 q^{70} +3.41086 q^{71} +0.820714 q^{72} -7.58356 q^{73} -0.657687 q^{74} -1.47624 q^{75} -4.40549 q^{76} -3.12412 q^{77} +4.69998 q^{78} -8.46523 q^{79} +1.00000 q^{80} -5.86429 q^{81} -7.76836 q^{82} -3.04080 q^{83} +3.42897 q^{84} +3.91915 q^{85} -5.75543 q^{86} +13.2366 q^{87} -1.34500 q^{88} -1.14409 q^{89} +0.820714 q^{90} -7.39512 q^{91} -4.06300 q^{92} -1.70567 q^{93} +7.10781 q^{94} -4.40549 q^{95} +1.47624 q^{96} +13.4841 q^{97} +1.60474 q^{98} -1.10386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

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