LMFDB - Embedded newform 4010.2.a.i.1.8

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			1.8
Root			$-1.06458$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.696154 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.696154 q^{6} +2.65990 q^{7} -1.00000 q^{8} -2.51537 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.696154 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.696154 q^{6} +2.65990 q^{7} -1.00000 q^{8} -2.51537 q^{9} -1.00000 q^{10} -2.85414 q^{11} +0.696154 q^{12} +0.0375050 q^{13} -2.65990 q^{14} +0.696154 q^{15} +1.00000 q^{16} -1.02960 q^{17} +2.51537 q^{18} -7.38755 q^{19} +1.00000 q^{20} +1.85170 q^{21} +2.85414 q^{22} -1.48829 q^{23} -0.696154 q^{24} +1.00000 q^{25} -0.0375050 q^{26} -3.83955 q^{27} +2.65990 q^{28} +9.65453 q^{29} -0.696154 q^{30} +4.28085 q^{31} -1.00000 q^{32} -1.98692 q^{33} +1.02960 q^{34} +2.65990 q^{35} -2.51537 q^{36} -1.90641 q^{37} +7.38755 q^{38} +0.0261093 q^{39} -1.00000 q^{40} +8.37519 q^{41} -1.85170 q^{42} -6.07292 q^{43} -2.85414 q^{44} -2.51537 q^{45} +1.48829 q^{46} -3.89157 q^{47} +0.696154 q^{48} +0.0750867 q^{49} -1.00000 q^{50} -0.716757 q^{51} +0.0375050 q^{52} -9.19937 q^{53} +3.83955 q^{54} -2.85414 q^{55} -2.65990 q^{56} -5.14287 q^{57} -9.65453 q^{58} -10.3821 q^{59} +0.696154 q^{60} -14.5560 q^{61} -4.28085 q^{62} -6.69064 q^{63} +1.00000 q^{64} +0.0375050 q^{65} +1.98692 q^{66} -3.35202 q^{67} -1.02960 q^{68} -1.03608 q^{69} -2.65990 q^{70} +12.4861 q^{71} +2.51537 q^{72} +6.72519 q^{73} +1.90641 q^{74} +0.696154 q^{75} -7.38755 q^{76} -7.59174 q^{77} -0.0261093 q^{78} -6.67283 q^{79} +1.00000 q^{80} +4.87319 q^{81} -8.37519 q^{82} -7.88459 q^{83} +1.85170 q^{84} -1.02960 q^{85} +6.07292 q^{86} +6.72104 q^{87} +2.85414 q^{88} -5.63871 q^{89} +2.51537 q^{90} +0.0997598 q^{91} -1.48829 q^{92} +2.98013 q^{93} +3.89157 q^{94} -7.38755 q^{95} -0.696154 q^{96} +0.00211457 q^{97} -0.0750867 q^{98} +7.17922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.696154	0.401925	0.200962	−	0.979599i	$-0.435593\pi$
$3$	0.696154	0.401925	0.200962	+	0.979599i	$0.435593\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.696154	−0.284204
$7$	2.65990	1.00535	0.502675	−	0.864476i	$-0.332349\pi$
$7$	2.65990	1.00535	0.502675	+	0.864476i	$0.332349\pi$
$8$	−1.00000	−0.353553
$9$	−2.51537	−0.838456
$10$	−1.00000	−0.316228
$11$	−2.85414	−0.860556	−0.430278	−	0.902697i	$-0.641584\pi$
$11$	−2.85414	−0.860556	−0.430278	+	0.902697i	$0.641584\pi$
$12$	0.696154	0.200962
$13$	0.0375050	0.0104020	0.00520101	−	0.999986i	$-0.498344\pi$
$13$	0.0375050	0.0104020	0.00520101	+	0.999986i	$0.498344\pi$
$14$	−2.65990	−0.710889
$15$	0.696154	0.179746
$16$	1.00000	0.250000
$17$	−1.02960	−0.249713	−0.124857	−	0.992175i	$-0.539847\pi$
$17$	−1.02960	−0.249713	−0.124857	+	0.992175i	$0.539847\pi$
$18$	2.51537	0.592878
$19$	−7.38755	−1.69482	−0.847410	−	0.530939i	$-0.821839\pi$
$19$	−7.38755	−1.69482	−0.847410	+	0.530939i	$0.821839\pi$
$20$	1.00000	0.223607
$21$	1.85170	0.404075
$22$	2.85414	0.608505
$23$	−1.48829	−0.310331	−0.155165	−	0.987889i	$-0.549591\pi$
$23$	−1.48829	−0.310331	−0.155165	+	0.987889i	$0.549591\pi$
$24$	−0.696154	−0.142102
$25$	1.00000	0.200000
$26$	−0.0375050	−0.00735534
$27$	−3.83955	−0.738921
$28$	2.65990	0.502675
$29$	9.65453	1.79280	0.896401	−	0.443245i	$-0.146173\pi$
$29$	9.65453	1.79280	0.896401	+	0.443245i	$0.146173\pi$
$30$	−0.696154	−0.127100
$31$	4.28085	0.768863	0.384431	−	0.923154i	$-0.374398\pi$
$31$	4.28085	0.768863	0.384431	+	0.923154i	$0.374398\pi$
$32$	−1.00000	−0.176777
$33$	−1.98692	−0.345879
$34$	1.02960	0.176574
$35$	2.65990	0.449606
$36$	−2.51537	−0.419228
$37$	−1.90641	−0.313412	−0.156706	−	0.987645i	$-0.550087\pi$
$37$	−1.90641	−0.313412	−0.156706	+	0.987645i	$0.550087\pi$
$38$	7.38755	1.19842
$39$	0.0261093	0.00418083
$40$	−1.00000	−0.158114
$41$	8.37519	1.30798	0.653992	−	0.756501i	$-0.273093\pi$
$41$	8.37519	1.30798	0.653992	+	0.756501i	$0.273093\pi$
$42$	−1.85170	−0.285724
$43$	−6.07292	−0.926111	−0.463055	−	0.886329i	$-0.653247\pi$
$43$	−6.07292	−0.926111	−0.463055	+	0.886329i	$0.653247\pi$
$44$	−2.85414	−0.430278
$45$	−2.51537	−0.374969
$46$	1.48829	0.219437
$47$	−3.89157	−0.567644	−0.283822	−	0.958877i	$-0.591602\pi$
$47$	−3.89157	−0.567644	−0.283822	+	0.958877i	$0.591602\pi$
$48$	0.696154	0.100481
$49$	0.0750867	0.0107267
$50$	−1.00000	−0.141421
$51$	−0.716757	−0.100366
$52$	0.0375050	0.00520101
$53$	−9.19937	−1.26363	−0.631815	−	0.775119i	$-0.717690\pi$
$53$	−9.19937	−1.26363	−0.631815	+	0.775119i	$0.717690\pi$
$54$	3.83955	0.522496
$55$	−2.85414	−0.384852
$56$	−2.65990	−0.355445
$57$	−5.14287	−0.681190
$58$	−9.65453	−1.26770
$59$	−10.3821	−1.35164	−0.675820	−	0.737067i	$-0.736210\pi$
$59$	−10.3821	−1.35164	−0.675820	+	0.737067i	$0.736210\pi$
$60$	0.696154	0.0898731
$61$	−14.5560	−1.86371	−0.931854	−	0.362834i	$-0.881809\pi$
$61$	−14.5560	−1.86371	−0.931854	+	0.362834i	$0.881809\pi$
$62$	−4.28085	−0.543668
$63$	−6.69064	−0.842941
$64$	1.00000	0.125000
$65$	0.0375050	0.00465193
$66$	1.98692	0.244573
$67$	−3.35202	−0.409515	−0.204757	−	0.978813i	$-0.565641\pi$
$67$	−3.35202	−0.409515	−0.204757	+	0.978813i	$0.565641\pi$
$68$	−1.02960	−0.124857
$69$	−1.03608	−0.124730
$70$	−2.65990	−0.317919
$71$	12.4861	1.48182	0.740911	−	0.671603i	$-0.234394\pi$
$71$	12.4861	1.48182	0.740911	+	0.671603i	$0.234394\pi$
$72$	2.51537	0.296439
$73$	6.72519	0.787124	0.393562	−	0.919298i	$-0.371243\pi$
$73$	6.72519	0.787124	0.393562	+	0.919298i	$0.371243\pi$
$74$	1.90641	0.221616
$75$	0.696154	0.0803850
$76$	−7.38755	−0.847410
$77$	−7.59174	−0.865159
$78$	−0.0261093	−0.00295629
$79$	−6.67283	−0.750752	−0.375376	−	0.926873i	$-0.622486\pi$
$79$	−6.67283	−0.750752	−0.375376	+	0.926873i	$0.622486\pi$
$80$	1.00000	0.111803
$81$	4.87319	0.541466
$82$	−8.37519	−0.924885
$83$	−7.88459	−0.865447	−0.432723	−	0.901527i	$-0.642447\pi$
$83$	−7.88459	−0.865447	−0.432723	+	0.901527i	$0.642447\pi$
$84$	1.85170	0.202037
$85$	−1.02960	−0.111675
$86$	6.07292	0.654859
$87$	6.72104	0.720571
$88$	2.85414	0.304252
$89$	−5.63871	−0.597702	−0.298851	−	0.954300i	$-0.596603\pi$
$89$	−5.63871	−0.597702	−0.298851	+	0.954300i	$0.596603\pi$
$90$	2.51537	0.265143
$91$	0.0997598	0.0104577
$92$	−1.48829	−0.155165
$93$	2.98013	0.309025
$94$	3.89157	0.401385
$95$	−7.38755	−0.757947
$96$	−0.696154	−0.0710509
$97$	0.00211457	0.000214702 0	0.000107351	−	1.00000i	$-0.499966\pi$
$97$	0.00211457	0.000214702 0	0.000107351		1.00000i	$0.499966\pi$
$98$	−0.0750867	−0.00758490
$99$	7.17922	0.721538
$100$	1.00000	0.100000
$101$	−9.15058	−0.910517	−0.455258	−	0.890359i	$-0.650453\pi$
$101$	−9.15058	−0.910517	−0.455258	+	0.890359i	$0.650453\pi$
$102$	0.716757	0.0709695
$103$	−3.39406	−0.334427	−0.167213	−	0.985921i	$-0.553477\pi$
$103$	−3.39406	−0.334427	−0.167213	+	0.985921i	$0.553477\pi$
$104$	−0.0375050	−0.00367767
$105$	1.85170	0.180708
$106$	9.19937	0.893522
$107$	−17.1126	−1.65434	−0.827171	−	0.561950i	$-0.810051\pi$
$107$	−17.1126	−1.65434	−0.827171	+	0.561950i	$0.810051\pi$
$108$	−3.83955	−0.369461
$109$	6.07832	0.582198	0.291099	−	0.956693i	$-0.405979\pi$
$109$	6.07832	0.582198	0.291099	+	0.956693i	$0.405979\pi$
$110$	2.85414	0.272132
$111$	−1.32716	−0.125968
$112$	2.65990	0.251337
$113$	8.57048	0.806243	0.403122	−	0.915146i	$-0.367925\pi$
$113$	8.57048	0.806243	0.403122	+	0.915146i	$0.367925\pi$
$114$	5.14287	0.481674
$115$	−1.48829	−0.138784
$116$	9.65453	0.896401
$117$	−0.0943390	−0.00872165
$118$	10.3821	0.955753
$119$	−2.73862	−0.251049
$120$	−0.696154	−0.0635499
$121$	−2.85389	−0.259444
$122$	14.5560	1.31784
$123$	5.83042	0.525711
$124$	4.28085	0.384431
$125$	1.00000	0.0894427
$126$	6.69064	0.596050
$127$	−4.07183	−0.361317	−0.180658	−	0.983546i	$-0.557823\pi$
$127$	−4.07183	−0.361317	−0.180658	+	0.983546i	$0.557823\pi$
$128$	−1.00000	−0.0883883
$129$	−4.22769	−0.372227
$130$	−0.0375050	−0.00328941
$131$	1.30068	0.113641	0.0568206	−	0.998384i	$-0.481904\pi$
$131$	1.30068	0.113641	0.0568206	+	0.998384i	$0.481904\pi$
$132$	−1.98692	−0.172939
$133$	−19.6502	−1.70389
$134$	3.35202	0.289571
$135$	−3.83955	−0.330456
$136$	1.02960	0.0882871
$137$	17.9925	1.53720	0.768601	−	0.639728i	$-0.220953\pi$
$137$	17.9925	1.53720	0.768601	+	0.639728i	$0.220953\pi$
$138$	1.03608	0.0881971
$139$	4.30048	0.364762	0.182381	−	0.983228i	$-0.441620\pi$
$139$	4.30048	0.364762	0.182381	+	0.983228i	$0.441620\pi$
$140$	2.65990	0.224803
$141$	−2.70913	−0.228150
$142$	−12.4861	−1.04781
$143$	−0.107045	−0.00895152
$144$	−2.51537	−0.209614
$145$	9.65453	0.801765
$146$	−6.72519	−0.556581
$147$	0.0522719	0.00431131
$148$	−1.90641	−0.156706
$149$	−11.2429	−0.921058	−0.460529	−	0.887645i	$-0.652340\pi$
$149$	−11.2429	−0.921058	−0.460529	+	0.887645i	$0.652340\pi$
$150$	−0.696154	−0.0568407
$151$	−18.0929	−1.47238	−0.736189	−	0.676776i	$-0.763377\pi$
$151$	−18.0929	−1.47238	−0.736189	+	0.676776i	$0.763377\pi$
$152$	7.38755	0.599209
$153$	2.58981	0.209374
$154$	7.59174	0.611760
$155$	4.28085	0.343846
$156$	0.0261093	0.00209042
$157$	−22.1158	−1.76503	−0.882517	−	0.470281i	$-0.844153\pi$
$157$	−22.1158	−1.76503	−0.882517	+	0.470281i	$0.844153\pi$
$158$	6.67283	0.530862
$159$	−6.40418	−0.507884
$160$	−1.00000	−0.0790569
$161$	−3.95872	−0.311991
$162$	−4.87319	−0.382874
$163$	−18.2881	−1.43243	−0.716216	−	0.697879i	$-0.754127\pi$
$163$	−18.2881	−1.43243	−0.716216	+	0.697879i	$0.754127\pi$
$164$	8.37519	0.653992
$165$	−1.98692	−0.154682
$166$	7.88459	0.611963
$167$	17.8347	1.38009	0.690044	−	0.723768i	$-0.257591\pi$
$167$	17.8347	1.38009	0.690044	+	0.723768i	$0.257591\pi$
$168$	−1.85170	−0.142862
$169$	−12.9986	−0.999892
$170$	1.02960	0.0789663
$171$	18.5824	1.42103
$172$	−6.07292	−0.463055
$173$	13.3119	1.01208	0.506042	−	0.862509i	$-0.331108\pi$
$173$	13.3119	1.01208	0.506042	+	0.862509i	$0.331108\pi$
$174$	−6.72104	−0.509521
$175$	2.65990	0.201070
$176$	−2.85414	−0.215139
$177$	−7.22757	−0.543257
$178$	5.63871	0.422639
$179$	11.0871	0.828688	0.414344	−	0.910120i	$-0.364011\pi$
$179$	11.0871	0.828688	0.414344	+	0.910120i	$0.364011\pi$
$180$	−2.51537	−0.187485
$181$	−8.93318	−0.663998	−0.331999	−	0.943280i	$-0.607723\pi$
$181$	−8.93318	−0.663998	−0.331999	+	0.943280i	$0.607723\pi$
$182$	−0.0997598	−0.00739469
$183$	−10.1332	−0.749070
$184$	1.48829	0.109718
$185$	−1.90641	−0.140162
$186$	−2.98013	−0.218514
$187$	2.93861	0.214892
$188$	−3.89157	−0.283822
$189$	−10.2128	−0.742874
$190$	7.38755	0.535949
$191$	6.21680	0.449832	0.224916	−	0.974378i	$-0.427789\pi$
$191$	6.21680	0.449832	0.224916	+	0.974378i	$0.427789\pi$
$192$	0.696154	0.0502406
$193$	20.8831	1.50320	0.751598	−	0.659621i	$-0.229283\pi$
$193$	20.8831	1.50320	0.751598	+	0.659621i	$0.229283\pi$
$194$	−0.00211457	−0.000151817 0
$195$	0.0261093	0.00186972
$196$	0.0750867	0.00536333
$197$	6.64050	0.473116	0.236558	−	0.971617i	$-0.423981\pi$
$197$	6.64050	0.473116	0.236558	+	0.971617i	$0.423981\pi$
$198$	−7.17922	−0.510205
$199$	−13.3555	−0.946748	−0.473374	−	0.880861i	$-0.656964\pi$
$199$	−13.3555	−0.946748	−0.473374	+	0.880861i	$0.656964\pi$
$200$	−1.00000	−0.0707107
$201$	−2.33352	−0.164594
$202$	9.15058	0.643833
$203$	25.6801	1.80239
$204$	−0.716757	−0.0501830
$205$	8.37519	0.584948
$206$	3.39406	0.236475
$207$	3.74361	0.260199
$208$	0.0375050	0.00260051
$209$	21.0851	1.45849
$210$	−1.85170	−0.127780
$211$	−25.4796	−1.75409	−0.877045	−	0.480408i	$-0.840489\pi$
$211$	−25.4796	−1.75409	−0.877045	+	0.480408i	$0.840489\pi$
$212$	−9.19937	−0.631815
$213$	8.69222	0.595581
$214$	17.1126	1.16980
$215$	−6.07292	−0.414169
$216$	3.83955	0.261248
$217$	11.3866	0.772976
$218$	−6.07832	−0.411676
$219$	4.68177	0.316365
$220$	−2.85414	−0.192426
$221$	−0.0386150	−0.00259753
$222$	1.32716	0.0890728
$223$	17.6475	1.18177	0.590883	−	0.806757i	$-0.298780\pi$
$223$	17.6475	1.18177	0.590883	+	0.806757i	$0.298780\pi$
$224$	−2.65990	−0.177722
$225$	−2.51537	−0.167691
$226$	−8.57048	−0.570100
$227$	17.6554	1.17183	0.585916	−	0.810372i	$-0.300735\pi$
$227$	17.6554	1.17183	0.585916	+	0.810372i	$0.300735\pi$
$228$	−5.14287	−0.340595
$229$	−17.2580	−1.14044	−0.570219	−	0.821493i	$-0.693142\pi$
$229$	−17.2580	−1.14044	−0.570219	+	0.821493i	$0.693142\pi$
$230$	1.48829	0.0981352
$231$	−5.28502	−0.347729
$232$	−9.65453	−0.633851
$233$	−17.3621	−1.13743	−0.568715	−	0.822535i	$-0.692559\pi$
$233$	−17.3621	−1.13743	−0.568715	+	0.822535i	$0.692559\pi$
$234$	0.0943390	0.00616713
$235$	−3.89157	−0.253858
$236$	−10.3821	−0.675820
$237$	−4.64532	−0.301746
$238$	2.73862	0.177519
$239$	12.6335	0.817193	0.408596	−	0.912715i	$-0.366018\pi$
$239$	12.6335	0.817193	0.408596	+	0.912715i	$0.366018\pi$
$240$	0.696154	0.0449366
$241$	−5.73290	−0.369288	−0.184644	−	0.982805i	$-0.559113\pi$
$241$	−5.73290	−0.369288	−0.184644	+	0.982805i	$0.559113\pi$
$242$	2.85389	0.183455
$243$	14.9111	0.956550
$244$	−14.5560	−0.931854
$245$	0.0750867	0.00479711
$246$	−5.83042	−0.371734
$247$	−0.277070	−0.0176296
$248$	−4.28085	−0.271834
$249$	−5.48889	−0.347844
$250$	−1.00000	−0.0632456
$251$	21.4087	1.35130	0.675652	−	0.737220i	$-0.263862\pi$
$251$	21.4087	1.35130	0.675652	+	0.737220i	$0.263862\pi$
$252$	−6.69064	−0.421471
$253$	4.24780	0.267057
$254$	4.07183	0.255490
$255$	−0.716757	−0.0448851
$256$	1.00000	0.0625000
$257$	20.1176	1.25490	0.627449	−	0.778658i	$-0.284099\pi$
$257$	20.1176	1.25490	0.627449	+	0.778658i	$0.284099\pi$
$258$	4.22769	0.263204
$259$	−5.07087	−0.315088
$260$	0.0375050	0.00232596
$261$	−24.2847	−1.50319
$262$	−1.30068	−0.0803564
$263$	−27.0762	−1.66959	−0.834795	−	0.550561i	$-0.814414\pi$
$263$	−27.0762	−1.66959	−0.834795	+	0.550561i	$0.814414\pi$
$264$	1.98692	0.122287
$265$	−9.19937	−0.565113
$266$	19.6502	1.20483
$267$	−3.92541	−0.240231
$268$	−3.35202	−0.204757
$269$	−3.84789	−0.234610	−0.117305	−	0.993096i	$-0.537425\pi$
$269$	−3.84789	−0.234610	−0.117305	+	0.993096i	$0.537425\pi$
$270$	3.83955	0.233667
$271$	0.630614	0.0383071	0.0191535	−	0.999817i	$-0.493903\pi$
$271$	0.630614	0.0383071	0.0191535	+	0.999817i	$0.493903\pi$
$272$	−1.02960	−0.0624284
$273$	0.0694482	0.00420319
$274$	−17.9925	−1.08697
$275$	−2.85414	−0.172111
$276$	−1.03608	−0.0623648
$277$	18.0685	1.08563	0.542816	−	0.839852i	$-0.317358\pi$
$277$	18.0685	1.08563	0.542816	+	0.839852i	$0.317358\pi$
$278$	−4.30048	−0.257926
$279$	−10.7679	−0.644658
$280$	−2.65990	−0.158960
$281$	−16.3568	−0.975766	−0.487883	−	0.872909i	$-0.662231\pi$
$281$	−16.3568	−0.975766	−0.487883	+	0.872909i	$0.662231\pi$
$282$	2.70913	0.161326
$283$	−1.20167	−0.0714321	−0.0357160	−	0.999362i	$-0.511371\pi$
$283$	−1.20167	−0.0714321	−0.0357160	+	0.999362i	$0.511371\pi$
$284$	12.4861	0.740911
$285$	−5.14287	−0.304638
$286$	0.107045	0.00632968
$287$	22.2772	1.31498
$288$	2.51537	0.148220
$289$	−15.9399	−0.937643
$290$	−9.65453	−0.566934
$291$	0.00147207	8.62941e−5 0
$292$	6.72519	0.393562
$293$	−17.6326	−1.03011	−0.515054	−	0.857158i	$-0.672228\pi$
$293$	−17.6326	−1.03011	−0.515054	+	0.857158i	$0.672228\pi$
$294$	−0.0522719	−0.00304856
$295$	−10.3821	−0.604471
$296$	1.90641	0.110808
$297$	10.9586	0.635883
$298$	11.2429	0.651286
$299$	−0.0558185	−0.00322807
$300$	0.696154	0.0401925
$301$	−16.1534	−0.931065
$302$	18.0929	1.04113
$303$	−6.37021	−0.365959
$304$	−7.38755	−0.423705
$305$	−14.5560	−0.833475
$306$	−2.58981	−0.148050
$307$	29.5550	1.68679	0.843397	−	0.537291i	$-0.180552\pi$
$307$	29.5550	1.68679	0.843397	+	0.537291i	$0.180552\pi$
$308$	−7.59174	−0.432579
$309$	−2.36279	−0.134414
$310$	−4.28085	−0.243136
$311$	13.4662	0.763597	0.381799	−	0.924246i	$-0.375305\pi$
$311$	13.4662	0.763597	0.381799	+	0.924246i	$0.375305\pi$
$312$	−0.0261093	−0.00147815
$313$	18.4655	1.04373	0.521865	−	0.853028i	$-0.325236\pi$
$313$	18.4655	1.04373	0.521865	+	0.853028i	$0.325236\pi$
$314$	22.1158	1.24807
$315$	−6.69064	−0.376975
$316$	−6.67283	−0.375376
$317$	0.377432	0.0211987	0.0105993	−	0.999944i	$-0.496626\pi$
$317$	0.377432	0.0211987	0.0105993	+	0.999944i	$0.496626\pi$
$318$	6.40418	0.359129
$319$	−27.5554	−1.54281
$320$	1.00000	0.0559017
$321$	−11.9130	−0.664921
$322$	3.95872	0.220611
$323$	7.60619	0.423220
$324$	4.87319	0.270733
$325$	0.0375050	0.00208041
$326$	18.2881	1.01288
$327$	4.23145	0.234000
$328$	−8.37519	−0.462442
$329$	−10.3512	−0.570680
$330$	1.98692	0.109376
$331$	9.69431	0.532848	0.266424	−	0.963856i	$-0.414158\pi$
$331$	9.69431	0.532848	0.266424	+	0.963856i	$0.414158\pi$
$332$	−7.88459	−0.432723
$333$	4.79533	0.262782
$334$	−17.8347	−0.975869
$335$	−3.35202	−0.183141
$336$	1.85170	0.101019
$337$	9.62228	0.524159	0.262079	−	0.965046i	$-0.415592\pi$
$337$	9.62228	0.524159	0.262079	+	0.965046i	$0.415592\pi$
$338$	12.9986	0.707030
$339$	5.96638	0.324049
$340$	−1.02960	−0.0558376
$341$	−12.2181	−0.661649
$342$	−18.5824	−1.00482
$343$	−18.4196	−0.994565
$344$	6.07292	0.327430
$345$	−1.03608	−0.0557808
$346$	−13.3119	−0.715651
$347$	−34.3809	−1.84566	−0.922831	−	0.385204i	$-0.874131\pi$
$347$	−34.3809	−1.84566	−0.922831	+	0.385204i	$0.874131\pi$
$348$	6.72104	0.360286
$349$	−26.4606	−1.41641	−0.708203	−	0.706009i	$-0.750494\pi$
$349$	−26.4606	−1.41641	−0.708203	+	0.706009i	$0.750494\pi$
$350$	−2.65990	−0.142178
$351$	−0.144002	−0.00768628
$352$	2.85414	0.152126
$353$	−22.8742	−1.21747	−0.608734	−	0.793374i	$-0.708323\pi$
$353$	−22.8742	−1.21747	−0.608734	+	0.793374i	$0.708323\pi$
$354$	7.22757	0.384141
$355$	12.4861	0.662691
$356$	−5.63871	−0.298851
$357$	−1.90650	−0.100903
$358$	−11.0871	−0.585971
$359$	−12.7326	−0.672000	−0.336000	−	0.941862i	$-0.609074\pi$
$359$	−12.7326	−0.672000	−0.336000	+	0.941862i	$0.609074\pi$
$360$	2.51537	0.132572
$361$	35.5759	1.87242
$362$	8.93318	0.469518
$363$	−1.98674	−0.104277
$364$	0.0997598	0.00522883
$365$	6.72519	0.352013
$366$	10.1332	0.529673
$367$	6.86945	0.358582	0.179291	−	0.983796i	$-0.442620\pi$
$367$	6.86945	0.358582	0.179291	+	0.983796i	$0.442620\pi$
$368$	−1.48829	−0.0775827
$369$	−21.0667	−1.09669
$370$	1.90641	0.0991095
$371$	−24.4694	−1.27039
$372$	2.98013	0.154513
$373$	29.5706	1.53111	0.765554	−	0.643372i	$-0.222465\pi$
$373$	29.5706	1.53111	0.765554	+	0.643372i	$0.222465\pi$
$374$	−2.93861	−0.151952
$375$	0.696154	0.0359492
$376$	3.89157	0.200692
$377$	0.362094	0.0186488
$378$	10.2128	0.525291
$379$	26.8611	1.37976	0.689881	−	0.723922i	$-0.257663\pi$
$379$	26.8611	1.37976	0.689881	+	0.723922i	$0.257663\pi$
$380$	−7.38755	−0.378973
$381$	−2.83462	−0.145222
$382$	−6.21680	−0.318079
$383$	−15.9093	−0.812925	−0.406463	−	0.913667i	$-0.633238\pi$
$383$	−15.9093	−0.812925	−0.406463	+	0.913667i	$0.633238\pi$
$384$	−0.696154	−0.0355255
$385$	−7.59174	−0.386911
$386$	−20.8831	−1.06292
$387$	15.2756	0.776504
$388$	0.00211457	0.000107351 0
$389$	−21.0610	−1.06783	−0.533916	−	0.845537i	$-0.679280\pi$
$389$	−21.0610	−1.06783	−0.533916	+	0.845537i	$0.679280\pi$
$390$	−0.0261093	−0.00132210
$391$	1.53234	0.0774938
$392$	−0.0750867	−0.00379245
$393$	0.905475	0.0456752
$394$	−6.64050	−0.334543
$395$	−6.67283	−0.335746
$396$	7.17922	0.360769
$397$	22.2540	1.11690	0.558448	−	0.829540i	$-0.311397\pi$
$397$	22.2540	1.11690	0.558448	+	0.829540i	$0.311397\pi$
$398$	13.3555	0.669452
$399$	−13.6795	−0.684834
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	2.33352	0.116386
$403$	0.160553	0.00799773
$404$	−9.15058	−0.455258
$405$	4.87319	0.242151
$406$	−25.6801	−1.27448
$407$	5.44116	0.269708
$408$	0.716757	0.0354848
$409$	−23.7118	−1.17247	−0.586235	−	0.810141i	$-0.699391\pi$
$409$	−23.7118	−1.17247	−0.586235	+	0.810141i	$0.699391\pi$
$410$	−8.37519	−0.413621
$411$	12.5256	0.617840
$412$	−3.39406	−0.167213
$413$	−27.6155	−1.35887
$414$	−3.74361	−0.183988
$415$	−7.88459	−0.387040
$416$	−0.0375050	−0.00183884
$417$	2.99380	0.146607
$418$	−21.0851	−1.03131
$419$	−33.8273	−1.65257	−0.826287	−	0.563250i	$-0.809551\pi$
$419$	−33.8273	−1.65257	−0.826287	+	0.563250i	$0.809551\pi$
$420$	1.85170	0.0903538
$421$	−9.07170	−0.442127	−0.221064	−	0.975259i	$-0.570953\pi$
$421$	−9.07170	−0.442127	−0.221064	+	0.975259i	$0.570953\pi$
$422$	25.4796	1.24033
$423$	9.78873	0.475944
$424$	9.19937	0.446761
$425$	−1.02960	−0.0499427
$426$	−8.69222	−0.421140
$427$	−38.7176	−1.87368
$428$	−17.1126	−0.827171
$429$	−0.0745196	−0.00359784
$430$	6.07292	0.292862
$431$	13.1477	0.633302	0.316651	−	0.948542i	$-0.397442\pi$
$431$	13.1477	0.633302	0.316651	+	0.948542i	$0.397442\pi$
$432$	−3.83955	−0.184730
$433$	12.6569	0.608250	0.304125	−	0.952632i	$-0.401636\pi$
$433$	12.6569	0.608250	0.304125	+	0.952632i	$0.401636\pi$
$434$	−11.3866	−0.546576
$435$	6.72104	0.322249
$436$	6.07832	0.291099
$437$	10.9948	0.525955
$438$	−4.68177	−0.223704
$439$	−22.3147	−1.06502	−0.532510	−	0.846424i	$-0.678751\pi$
$439$	−22.3147	−1.06502	−0.532510	+	0.846424i	$0.678751\pi$
$440$	2.85414	0.136066
$441$	−0.188871	−0.00899384
$442$	0.0386150	0.00183673
$443$	−0.221149	−0.0105071	−0.00525356	−	0.999986i	$-0.501672\pi$
$443$	−0.221149	−0.0105071	−0.00525356	+	0.999986i	$0.501672\pi$
$444$	−1.32716	−0.0629840
$445$	−5.63871	−0.267301
$446$	−17.6475	−0.835634
$447$	−7.82682	−0.370196
$448$	2.65990	0.125669
$449$	41.8242	1.97381	0.986904	−	0.161311i	$-0.0515721\pi$
$449$	41.8242	1.97381	0.986904	+	0.161311i	$0.0515721\pi$
$450$	2.51537	0.118576
$451$	−23.9040	−1.12559
$452$	8.57048	0.403122
$453$	−12.5954	−0.591785
$454$	−17.6554	−0.828611
$455$	0.0997598	0.00467681
$456$	5.14287	0.240837
$457$	−23.0398	−1.07776	−0.538879	−	0.842383i	$-0.681152\pi$
$457$	−23.0398	−1.07776	−0.538879	+	0.842383i	$0.681152\pi$
$458$	17.2580	0.806411
$459$	3.95318	0.184519
$460$	−1.48829	−0.0693921
$461$	10.3050	0.479950	0.239975	−	0.970779i	$-0.422861\pi$
$461$	10.3050	0.479950	0.239975	+	0.970779i	$0.422861\pi$
$462$	5.28502	0.245881
$463$	−7.58923	−0.352701	−0.176351	−	0.984327i	$-0.556429\pi$
$463$	−7.58923	−0.352701	−0.176351	+	0.984327i	$0.556429\pi$
$464$	9.65453	0.448200
$465$	2.98013	0.138200
$466$	17.3621	0.804284
$467$	−14.0631	−0.650764	−0.325382	−	0.945583i	$-0.605493\pi$
$467$	−14.0631	−0.650764	−0.325382	+	0.945583i	$0.605493\pi$
$468$	−0.0943390	−0.00436082
$469$	−8.91606	−0.411705
$470$	3.89157	0.179505
$471$	−15.3960	−0.709411
$472$	10.3821	0.477877
$473$	17.3330	0.796970
$474$	4.64532	0.213367
$475$	−7.38755	−0.338964
$476$	−2.73862	−0.125525
$477$	23.1398	1.05950
$478$	−12.6335	−0.577843
$479$	40.4539	1.84839	0.924193	−	0.381925i	$-0.124739\pi$
$479$	40.4539	1.84839	0.924193	+	0.381925i	$0.124739\pi$
$480$	−0.696154	−0.0317749
$481$	−0.0715000	−0.00326012
$482$	5.73290	0.261126
$483$	−2.75588	−0.125397
$484$	−2.85389	−0.129722
$485$	0.00211457	9.60177e−5 0
$486$	−14.9111	−0.676383
$487$	−23.5057	−1.06514	−0.532571	−	0.846385i	$-0.678774\pi$
$487$	−23.5057	−1.06514	−0.532571	+	0.846385i	$0.678774\pi$
$488$	14.5560	0.658920
$489$	−12.7313	−0.575730
$490$	−0.0750867	−0.00339207
$491$	29.0932	1.31296	0.656478	−	0.754345i	$-0.272045\pi$
$491$	29.0932	1.31296	0.656478	+	0.754345i	$0.272045\pi$
$492$	5.83042	0.262856
$493$	−9.94026	−0.447687
$494$	0.277070	0.0124660
$495$	7.17922	0.322682
$496$	4.28085	0.192216
$497$	33.2117	1.48975
$498$	5.48889	0.245963
$499$	1.02863	0.0460480	0.0230240	−	0.999735i	$-0.492671\pi$
$499$	1.02863	0.0460480	0.0230240	+	0.999735i	$0.492671\pi$
$500$	1.00000	0.0447214
$501$	12.4157	0.554691
$502$	−21.4087	−0.955517
$503$	−17.3276	−0.772600	−0.386300	−	0.922373i	$-0.626247\pi$
$503$	−17.3276	−0.772600	−0.386300	+	0.922373i	$0.626247\pi$
$504$	6.69064	0.298025
$505$	−9.15058	−0.407195
$506$	−4.24780	−0.188838
$507$	−9.04902	−0.401881
$508$	−4.07183	−0.180658
$509$	−36.9550	−1.63800	−0.819000	−	0.573793i	$-0.805471\pi$
$509$	−36.9550	−1.63800	−0.819000	+	0.573793i	$0.805471\pi$
$510$	0.716757	0.0317385
$511$	17.8884	0.791335
$512$	−1.00000	−0.0441942
$513$	28.3648	1.25234
$514$	−20.1176	−0.887347
$515$	−3.39406	−0.149560
$516$	−4.22769	−0.186113
$517$	11.1071	0.488489
$518$	5.07087	0.222801
$519$	9.26712	0.406782
$520$	−0.0375050	−0.00164470
$521$	22.6421	0.991966	0.495983	−	0.868332i	$-0.334808\pi$
$521$	22.6421	0.991966	0.495983	+	0.868332i	$0.334808\pi$
$522$	24.2847	1.06291
$523$	24.0765	1.05279	0.526397	−	0.850239i	$-0.323543\pi$
$523$	24.0765	1.05279	0.526397	+	0.850239i	$0.323543\pi$
$524$	1.30068	0.0568206
$525$	1.85170	0.0808149
$526$	27.0762	1.18058
$527$	−4.40754	−0.191995
$528$	−1.98692	−0.0864697
$529$	−20.7850	−0.903695
$530$	9.19937	0.399595
$531$	26.1149	1.13329
$532$	−19.6502	−0.851943
$533$	0.314112	0.0136057
$534$	3.92541	0.169869
$535$	−17.1126	−0.739844
$536$	3.35202	0.144785
$537$	7.71832	0.333070
$538$	3.84789	0.165894
$539$	−0.214308	−0.00923089
$540$	−3.83955	−0.165228
$541$	13.0610	0.561537	0.280768	−	0.959776i	$-0.409411\pi$
$541$	13.0610	0.561537	0.280768	+	0.959776i	$0.409411\pi$
$542$	−0.630614	−0.0270872
$543$	−6.21887	−0.266877
$544$	1.02960	0.0441435
$545$	6.07832	0.260367
$546$	−0.0694482	−0.00297211
$547$	−14.7095	−0.628933	−0.314466	−	0.949269i	$-0.601826\pi$
$547$	−14.7095	−0.628933	−0.314466	+	0.949269i	$0.601826\pi$
$548$	17.9925	0.768601
$549$	36.6138	1.56264
$550$	2.85414	0.121701
$551$	−71.3233	−3.03848
$552$	1.03608	0.0440986
$553$	−17.7491	−0.754768
$554$	−18.0685	−0.767658
$555$	−1.32716	−0.0563346
$556$	4.30048	0.182381
$557$	−0.463082	−0.0196214	−0.00981071	−	0.999952i	$-0.503123\pi$
$557$	−0.463082	−0.0196214	−0.00981071	+	0.999952i	$0.503123\pi$
$558$	10.7679	0.455842
$559$	−0.227765	−0.00963343
$560$	2.65990	0.112401
$561$	2.04572	0.0863706
$562$	16.3568	0.689971
$563$	23.6664	0.997422	0.498711	−	0.866768i	$-0.333807\pi$
$563$	23.6664	0.997422	0.498711	+	0.866768i	$0.333807\pi$
$564$	−2.70913	−0.114075
$565$	8.57048	0.360563
$566$	1.20167	0.0505101
$567$	12.9622	0.544362
$568$	−12.4861	−0.523903
$569$	−15.1693	−0.635931	−0.317966	−	0.948102i	$-0.603000\pi$
$569$	−15.1693	−0.635931	−0.317966	+	0.948102i	$0.603000\pi$
$570$	5.14287	0.215411
$571$	27.6020	1.15511	0.577553	−	0.816353i	$-0.304008\pi$
$571$	27.6020	1.15511	0.577553	+	0.816353i	$0.304008\pi$
$572$	−0.107045	−0.00447576
$573$	4.32785	0.180799
$574$	−22.2772	−0.929832
$575$	−1.48829	−0.0620661
$576$	−2.51537	−0.104807
$577$	1.39037	0.0578820	0.0289410	−	0.999581i	$-0.490787\pi$
$577$	1.39037	0.0578820	0.0289410	+	0.999581i	$0.490787\pi$
$578$	15.9399	0.663014
$579$	14.5378	0.604172
$580$	9.65453	0.400883
$581$	−20.9723	−0.870076
$582$	−0.00147207	−6.10191e−5 0
$583$	26.2563	1.08742
$584$	−6.72519	−0.278291
$585$	−0.0943390	−0.00390044
$586$	17.6326	0.728396
$587$	−28.6625	−1.18303	−0.591514	−	0.806294i	$-0.701470\pi$
$587$	−28.6625	−1.18303	−0.591514	+	0.806294i	$0.701470\pi$
$588$	0.0522719	0.00215566
$589$	−31.6250	−1.30308
$590$	10.3821	0.427426
$591$	4.62281	0.190157
$592$	−1.90641	−0.0783530
$593$	−29.1603	−1.19747	−0.598735	−	0.800947i	$-0.704330\pi$
$593$	−29.1603	−1.19747	−0.598735	+	0.800947i	$0.704330\pi$
$594$	−10.9586	−0.449637
$595$	−2.73862	−0.112273
$596$	−11.2429	−0.460529
$597$	−9.29751	−0.380522
$598$	0.0558185	0.00228259
$599$	−31.1199	−1.27152	−0.635762	−	0.771885i	$-0.719314\pi$
$599$	−31.1199	−1.27152	−0.635762	+	0.771885i	$0.719314\pi$
$600$	−0.696154	−0.0284204
$601$	29.9444	1.22146	0.610729	−	0.791840i	$-0.290876\pi$
$601$	29.9444	1.22146	0.610729	+	0.791840i	$0.290876\pi$
$602$	16.1534	0.658362
$603$	8.43157	0.343360
$604$	−18.0929	−0.736189
$605$	−2.85389	−0.116027
$606$	6.37021	0.258772
$607$	1.87477	0.0760944	0.0380472	−	0.999276i	$-0.487886\pi$
$607$	1.87477	0.0760944	0.0380472	+	0.999276i	$0.487886\pi$
$608$	7.38755	0.299605
$609$	17.8773	0.724426
$610$	14.5560	0.589356
$611$	−0.145953	−0.00590464
$612$	2.58981	0.104687
$613$	−25.8197	−1.04285	−0.521425	−	0.853297i	$-0.674599\pi$
$613$	−25.8197	−1.04285	−0.521425	+	0.853297i	$0.674599\pi$
$614$	−29.5550	−1.19274
$615$	5.83042	0.235105
$616$	7.59174	0.305880
$617$	35.2336	1.41845	0.709226	−	0.704982i	$-0.249045\pi$
$617$	35.2336	1.41845	0.709226	+	0.704982i	$0.249045\pi$
$618$	2.36279	0.0950453
$619$	−16.0444	−0.644880	−0.322440	−	0.946590i	$-0.604503\pi$
$619$	−16.0444	−0.644880	−0.322440	+	0.946590i	$0.604503\pi$
$620$	4.28085	0.171923
$621$	5.71437	0.229310
$622$	−13.4662	−0.539945
$623$	−14.9984	−0.600899
$624$	0.0261093	0.00104521
$625$	1.00000	0.0400000
$626$	−18.4655	−0.738029
$627$	14.6785	0.586202
$628$	−22.1158	−0.882517
$629$	1.96283	0.0782632
$630$	6.69064	0.266561
$631$	−4.67025	−0.185920	−0.0929599	−	0.995670i	$-0.529633\pi$
$631$	−4.67025	−0.185920	−0.0929599	+	0.995670i	$0.529633\pi$
$632$	6.67283	0.265431
$633$	−17.7378	−0.705012
$634$	−0.377432	−0.0149897
$635$	−4.07183	−0.161586
$636$	−6.40418	−0.253942
$637$	0.00281613	0.000111579 0
$638$	27.5554	1.09093
$639$	−31.4071	−1.24244
$640$	−1.00000	−0.0395285
$641$	−13.1204	−0.518226	−0.259113	−	0.965847i	$-0.583430\pi$
$641$	−13.1204	−0.518226	−0.259113	+	0.965847i	$0.583430\pi$
$642$	11.9130	0.470170
$643$	−4.64694	−0.183257	−0.0916286	−	0.995793i	$-0.529207\pi$
$643$	−4.64694	−0.183257	−0.0916286	+	0.995793i	$0.529207\pi$
$644$	−3.95872	−0.155995
$645$	−4.22769	−0.166465
$646$	−7.60619	−0.299261
$647$	42.6147	1.67536	0.837679	−	0.546163i	$-0.183912\pi$
$647$	42.6147	1.67536	0.837679	+	0.546163i	$0.183912\pi$
$648$	−4.87319	−0.191437
$649$	29.6321	1.16316
$650$	−0.0375050	−0.00147107
$651$	7.92686	0.310678
$652$	−18.2881	−0.716216
$653$	0.246098	0.00963054	0.00481527	−	0.999988i	$-0.498467\pi$
$653$	0.246098	0.00963054	0.00481527	+	0.999988i	$0.498467\pi$
$654$	−4.23145	−0.165463
$655$	1.30068	0.0508219
$656$	8.37519	0.326996
$657$	−16.9163	−0.659970
$658$	10.3512	0.403532
$659$	16.4663	0.641438	0.320719	−	0.947174i	$-0.396076\pi$
$659$	16.4663	0.641438	0.320719	+	0.947174i	$0.396076\pi$
$660$	−1.98692	−0.0773408
$661$	46.2706	1.79972	0.899859	−	0.436182i	$-0.143670\pi$
$661$	46.2706	1.79972	0.899859	+	0.436182i	$0.143670\pi$
$662$	−9.69431	−0.376780
$663$	−0.0268820	−0.00104401
$664$	7.88459	0.305982
$665$	−19.6502	−0.762001
$666$	−4.79533	−0.185815
$667$	−14.3688	−0.556361
$668$	17.8347	0.690044
$669$	12.2854	0.474981
$670$	3.35202	0.129500
$671$	41.5449	1.60382
$672$	−1.85170	−0.0714310
$673$	28.1747	1.08606	0.543028	−	0.839715i	$-0.317278\pi$
$673$	28.1747	1.08606	0.543028	+	0.839715i	$0.317278\pi$
$674$	−9.62228	−0.370636
$675$	−3.83955	−0.147784
$676$	−12.9986	−0.499946
$677$	29.6039	1.13777	0.568885	−	0.822417i	$-0.307375\pi$
$677$	29.6039	1.13777	0.568885	+	0.822417i	$0.307375\pi$
$678$	−5.96638	−0.229137
$679$	0.00562455	0.000215851 0
$680$	1.02960	0.0394832
$681$	12.2909	0.470988
$682$	12.2181	0.467857
$683$	10.3329	0.395378	0.197689	−	0.980265i	$-0.436656\pi$
$683$	10.3329	0.395378	0.197689	+	0.980265i	$0.436656\pi$
$684$	18.5824	0.710517
$685$	17.9925	0.687458
$686$	18.4196	0.703264
$687$	−12.0142	−0.458370
$688$	−6.07292	−0.231528
$689$	−0.345023	−0.0131443
$690$	1.03608	0.0394430
$691$	−5.72697	−0.217864	−0.108932	−	0.994049i	$-0.534743\pi$
$691$	−5.72697	−0.217864	−0.108932	+	0.994049i	$0.534743\pi$
$692$	13.3119	0.506042
$693$	19.0960	0.725398
$694$	34.3809	1.30508
$695$	4.30048	0.163127
$696$	−6.72104	−0.254760
$697$	−8.62305	−0.326621
$698$	26.4606	1.00155
$699$	−12.0867	−0.457161
$700$	2.65990	0.100535
$701$	44.3202	1.67395	0.836976	−	0.547239i	$-0.184321\pi$
$701$	44.3202	1.67395	0.836976	+	0.547239i	$0.184321\pi$
$702$	0.144002	0.00543502
$703$	14.0837	0.531177
$704$	−2.85414	−0.107569
$705$	−2.70913	−0.102032
$706$	22.8742	0.860881
$707$	−24.3397	−0.915387
$708$	−7.22757	−0.271629
$709$	10.1220	0.380139	0.190069	−	0.981771i	$-0.439129\pi$
$709$	10.1220	0.380139	0.190069	+	0.981771i	$0.439129\pi$
$710$	−12.4861	−0.468593
$711$	16.7846	0.629473
$712$	5.63871	0.211320
$713$	−6.37116	−0.238602
$714$	1.90650	0.0713491
$715$	−0.107045	−0.00400324
$716$	11.0871	0.414344
$717$	8.79486	0.328450
$718$	12.7326	0.475176
$719$	24.9058	0.928828	0.464414	−	0.885618i	$-0.346265\pi$
$719$	24.9058	0.928828	0.464414	+	0.885618i	$0.346265\pi$
$720$	−2.51537	−0.0937423
$721$	−9.02788	−0.336216
$722$	−35.5759	−1.32400
$723$	−3.99098	−0.148426
$724$	−8.93318	−0.331999
$725$	9.65453	0.358560
$726$	1.98674	0.0737350
$727$	−35.9493	−1.33329	−0.666643	−	0.745377i	$-0.732270\pi$
$727$	−35.9493	−1.33329	−0.666643	+	0.745377i	$0.732270\pi$
$728$	−0.0997598	−0.00369734
$729$	−4.23913	−0.157005
$730$	−6.72519	−0.248911
$731$	6.25264	0.231262
$732$	−10.1332	−0.374535
$733$	−6.50206	−0.240159	−0.120080	−	0.992764i	$-0.538315\pi$
$733$	−6.50206	−0.240159	−0.120080	+	0.992764i	$0.538315\pi$
$734$	−6.86945	−0.253556
$735$	0.0522719	0.00192808
$736$	1.48829	0.0548592
$737$	9.56714	0.352410
$738$	21.0667	0.775476
$739$	−3.62083	−0.133194	−0.0665971	−	0.997780i	$-0.521214\pi$
$739$	−3.62083	−0.133194	−0.0665971	+	0.997780i	$0.521214\pi$
$740$	−1.90641	−0.0700810
$741$	−0.192884	−0.00708576
$742$	24.4694	0.898301
$743$	−50.0811	−1.83730	−0.918649	−	0.395076i	$-0.870718\pi$
$743$	−50.0811	−1.83730	−0.918649	+	0.395076i	$0.870718\pi$
$744$	−2.98013	−0.109257
$745$	−11.2429	−0.411910
$746$	−29.5706	−1.08266
$747$	19.8327	0.725639
$748$	2.93861	0.107446
$749$	−45.5180	−1.66319
$750$	−0.696154	−0.0254200
$751$	1.63536	0.0596753	0.0298376	−	0.999555i	$-0.490501\pi$
$751$	1.63536	0.0596753	0.0298376	+	0.999555i	$0.490501\pi$
$752$	−3.89157	−0.141911
$753$	14.9037	0.543123
$754$	−0.362094	−0.0131867
$755$	−18.0929	−0.658468
$756$	−10.2128	−0.371437
$757$	8.12371	0.295261	0.147631	−	0.989043i	$-0.452835\pi$
$757$	8.12371	0.295261	0.147631	+	0.989043i	$0.452835\pi$
$758$	−26.8611	−0.975640
$759$	2.95712	0.107337
$760$	7.38755	0.267975
$761$	44.7571	1.62244	0.811222	−	0.584739i	$-0.198803\pi$
$761$	44.7571	1.62244	0.811222	+	0.584739i	$0.198803\pi$
$762$	2.83462	0.102688
$763$	16.1678	0.585312
$764$	6.21680	0.224916
$765$	2.58981	0.0936349
$766$	15.9093	0.574825
$767$	−0.389382	−0.0140598
$768$	0.696154	0.0251203
$769$	−12.7234	−0.458816	−0.229408	−	0.973330i	$-0.573679\pi$
$769$	−12.7234	−0.458816	−0.229408	+	0.973330i	$0.573679\pi$
$770$	7.59174	0.273587
$771$	14.0049	0.504375
$772$	20.8831	0.751598
$773$	14.5070	0.521781	0.260891	−	0.965368i	$-0.415984\pi$
$773$	14.5070	0.521781	0.260891	+	0.965368i	$0.415984\pi$
$774$	−15.2756	−0.549071
$775$	4.28085	0.153773
$776$	−0.00211457	−7.59087e−5 0
$777$	−3.53010	−0.126642
$778$	21.0610	0.755072
$779$	−61.8721	−2.21680
$780$	0.0261093	0.000934862 0
$781$	−35.6370	−1.27519
$782$	−1.53234	−0.0547964
$783$	−37.0690	−1.32474
$784$	0.0750867	0.00268167
$785$	−22.1158	−0.789347
$786$	−0.905475	−0.0322972
$787$	−15.4745	−0.551605	−0.275803	−	0.961214i	$-0.588944\pi$
$787$	−15.4745	−0.551605	−0.275803	+	0.961214i	$0.588944\pi$
$788$	6.64050	0.236558
$789$	−18.8492	−0.671049
$790$	6.67283	0.237409
$791$	22.7967	0.810556
$792$	−7.17922	−0.255102
$793$	−0.545924	−0.0193863
$794$	−22.2540	−0.789764
$795$	−6.40418	−0.227133
$796$	−13.3555	−0.473374
$797$	15.8753	0.562331	0.281166	−	0.959659i	$-0.409279\pi$
$797$	15.8753	0.562331	0.281166	+	0.959659i	$0.409279\pi$
$798$	13.6795	0.484251
$799$	4.00674	0.141748
$800$	−1.00000	−0.0353553
$801$	14.1834	0.501147
$802$	−1.00000	−0.0353112
$803$	−19.1946	−0.677364
$804$	−2.33352	−0.0822971
$805$	−3.95872	−0.139526
$806$	−0.160553	−0.00565525
$807$	−2.67872	−0.0942954
$808$	9.15058	0.321916
$809$	20.3904	0.716888	0.358444	−	0.933551i	$-0.383307\pi$
$809$	20.3904	0.716888	0.358444	+	0.933551i	$0.383307\pi$
$810$	−4.87319	−0.171227
$811$	−41.4037	−1.45388	−0.726941	−	0.686700i	$-0.759059\pi$
$811$	−41.4037	−1.45388	−0.726941	+	0.686700i	$0.759059\pi$
$812$	25.6801	0.901196
$813$	0.439004	0.0153966
$814$	−5.44116	−0.190713
$815$	−18.2881	−0.640603
$816$	−0.716757	−0.0250915
$817$	44.8640	1.56959
$818$	23.7118	0.829062
$819$	−0.250933	−0.00876830
$820$	8.37519	0.292474
$821$	−22.2301	−0.775836	−0.387918	−	0.921694i	$-0.626806\pi$
$821$	−22.2301	−0.775836	−0.387918	+	0.921694i	$0.626806\pi$
$822$	−12.5256	−0.436879
$823$	−30.5016	−1.06322	−0.531610	−	0.846989i	$-0.678413\pi$
$823$	−30.5016	−1.06322	−0.531610	+	0.846989i	$0.678413\pi$
$824$	3.39406	0.118238
$825$	−1.98692	−0.0691757
$826$	27.6155	0.960866
$827$	16.2473	0.564973	0.282487	−	0.959271i	$-0.408841\pi$
$827$	16.2473	0.564973	0.282487	+	0.959271i	$0.408841\pi$
$828$	3.74361	0.130099
$829$	−13.2892	−0.461552	−0.230776	−	0.973007i	$-0.574127\pi$
$829$	−13.2892	−0.461552	−0.230776	+	0.973007i	$0.574127\pi$
$830$	7.88459	0.273678
$831$	12.5785	0.436342
$832$	0.0375050	0.00130025
$833$	−0.0773089	−0.00267859
$834$	−2.99380	−0.103667
$835$	17.8347	0.617194
$836$	21.0851	0.729244
$837$	−16.4365	−0.568129
$838$	33.8273	1.16855
$839$	−36.4776	−1.25935	−0.629673	−	0.776860i	$-0.716811\pi$
$839$	−36.4776	−1.25935	−0.629673	+	0.776860i	$0.716811\pi$
$840$	−1.85170	−0.0638898
$841$	64.2100	2.21414
$842$	9.07170	0.312631
$843$	−11.3869	−0.392185
$844$	−25.4796	−0.877045
$845$	−12.9986	−0.447165
$846$	−9.78873	−0.336544
$847$	−7.59106	−0.260832
$848$	−9.19937	−0.315908
$849$	−0.836550	−0.0287103
$850$	1.02960	0.0353148
$851$	2.83730	0.0972613
$852$	8.69222	0.297791
$853$	−52.3016	−1.79077	−0.895386	−	0.445290i	$-0.853101\pi$
$853$	−52.3016	−1.79077	−0.895386	+	0.445290i	$0.853101\pi$
$854$	38.7176	1.32489
$855$	18.5824	0.635505
$856$	17.1126	0.584898
$857$	−3.70388	−0.126522	−0.0632611	−	0.997997i	$-0.520150\pi$
$857$	−3.70388	−0.126522	−0.0632611	+	0.997997i	$0.520150\pi$
$858$	0.0745196	0.00254406
$859$	−16.4440	−0.561063	−0.280532	−	0.959845i	$-0.590511\pi$
$859$	−16.4440	−0.561063	−0.280532	+	0.959845i	$0.590511\pi$
$860$	−6.07292	−0.207085
$861$	15.5084	0.528523
$862$	−13.1477	−0.447812
$863$	46.7402	1.59105	0.795527	−	0.605918i	$-0.207194\pi$
$863$	46.7402	1.59105	0.795527	+	0.605918i	$0.207194\pi$
$864$	3.83955	0.130624
$865$	13.3119	0.452618
$866$	−12.6569	−0.430098
$867$	−11.0967	−0.376862
$868$	11.3866	0.386488
$869$	19.0452	0.646064
$870$	−6.72104	−0.227865
$871$	−0.125718	−0.00425978
$872$	−6.07832	−0.205838
$873$	−0.00531893	−0.000180018 0
$874$	−10.9948	−0.371906
$875$	2.65990	0.0899212
$876$	4.68177	0.158182
$877$	46.8547	1.58217	0.791085	−	0.611706i	$-0.209516\pi$
$877$	46.8547	1.58217	0.791085	+	0.611706i	$0.209516\pi$
$878$	22.3147	0.753083
$879$	−12.2750	−0.414026
$880$	−2.85414	−0.0962130
$881$	11.3007	0.380731	0.190366	−	0.981713i	$-0.439033\pi$
$881$	11.3007	0.380731	0.190366	+	0.981713i	$0.439033\pi$
$882$	0.188871	0.00635961
$883$	37.3318	1.25632	0.628158	−	0.778086i	$-0.283809\pi$
$883$	37.3318	1.25632	0.628158	+	0.778086i	$0.283809\pi$
$884$	−0.0386150	−0.00129876
$885$	−7.22757	−0.242952
$886$	0.221149	0.00742966
$887$	37.1233	1.24648	0.623239	−	0.782031i	$-0.285816\pi$
$887$	37.1233	1.24648	0.623239	+	0.782031i	$0.285816\pi$
$888$	1.32716	0.0445364
$889$	−10.8307	−0.363250
$890$	5.63871	0.189010
$891$	−13.9088	−0.465961
$892$	17.6475	0.590883
$893$	28.7492	0.962054
$894$	7.82682	0.261768
$895$	11.0871	0.370601
$896$	−2.65990	−0.0888611
$897$	−0.0388583	−0.00129744
$898$	−41.8242	−1.39569
$899$	41.3296	1.37842
$900$	−2.51537	−0.0838456
$901$	9.47163	0.315546
$902$	23.9040	0.795915
$903$	−11.2452	−0.374218
$904$	−8.57048	−0.285050
$905$	−8.93318	−0.296949
$906$	12.5954	0.418455
$907$	−37.0817	−1.23128	−0.615639	−	0.788029i	$-0.711102\pi$
$907$	−37.0817	−1.23128	−0.615639	+	0.788029i	$0.711102\pi$
$908$	17.6554	0.585916
$909$	23.0171	0.763429
$910$	−0.0997598	−0.00330700
$911$	−28.3851	−0.940440	−0.470220	−	0.882549i	$-0.655825\pi$
$911$	−28.3851	−0.940440	−0.470220	+	0.882549i	$0.655825\pi$
$912$	−5.14287	−0.170298
$913$	22.5037	0.744765
$914$	23.0398	0.762090
$915$	−10.1332	−0.334994
$916$	−17.2580	−0.570219
$917$	3.45969	0.114249
$918$	−3.95318	−0.130474
$919$	1.81903	0.0600043	0.0300022	−	0.999550i	$-0.490449\pi$
$919$	1.81903	0.0600043	0.0300022	+	0.999550i	$0.490449\pi$
$920$	1.48829	0.0490676
$921$	20.5748	0.677964
$922$	−10.3050	−0.339376
$923$	0.468290	0.0154140
$924$	−5.28502	−0.173864
$925$	−1.90641	−0.0626824
$926$	7.58923	0.249397
$927$	8.53732	0.280402
$928$	−9.65453	−0.316925
$929$	29.2371	0.959238	0.479619	−	0.877477i	$-0.340775\pi$
$929$	29.2371	0.959238	0.479619	+	0.877477i	$0.340775\pi$
$930$	−2.98013	−0.0977223
$931$	−0.554707	−0.0181798
$932$	−17.3621	−0.568715
$933$	9.37454	0.306909
$934$	14.0631	0.460159
$935$	2.93861	0.0961028
$936$	0.0943390	0.00308357
$937$	10.5322	0.344073	0.172036	−	0.985091i	$-0.444965\pi$
$937$	10.5322	0.344073	0.172036	+	0.985091i	$0.444965\pi$
$938$	8.91606	0.291120
$939$	12.8548	0.419501
$940$	−3.89157	−0.126929
$941$	−31.2021	−1.01716	−0.508580	−	0.861015i	$-0.669829\pi$
$941$	−31.2021	−1.01716	−0.508580	+	0.861015i	$0.669829\pi$
$942$	15.3960	0.501629
$943$	−12.4647	−0.405908
$944$	−10.3821	−0.337910
$945$	−10.2128	−0.332223
$946$	−17.3330	−0.563543
$947$	24.7127	0.803053	0.401527	−	0.915847i	$-0.368480\pi$
$947$	24.7127	0.803053	0.401527	+	0.915847i	$0.368480\pi$
$948$	−4.64532	−0.150873
$949$	0.252229	0.00818769
$950$	7.38755	0.239684
$951$	0.262751	0.00852027
$952$	2.73862	0.0887593
$953$	−41.9226	−1.35801	−0.679003	−	0.734136i	$-0.737588\pi$
$953$	−41.9226	−1.35801	−0.679003	+	0.734136i	$0.737588\pi$
$954$	−23.1398	−0.749179
$955$	6.21680	0.201171
$956$	12.6335	0.408596
$957$	−19.1828	−0.620092
$958$	−40.4539	−1.30701
$959$	47.8583	1.54543
$960$	0.696154	0.0224683
$961$	−12.6743	−0.408850
$962$	0.0715000	0.00230525
$963$	43.0446	1.38709
$964$	−5.73290	−0.184644
$965$	20.8831	0.672250
$966$	2.75588	0.0886689
$967$	5.93617	0.190894	0.0954472	−	0.995434i	$-0.469572\pi$
$967$	5.93617	0.190894	0.0954472	+	0.995434i	$0.469572\pi$
$968$	2.85389	0.0917273
$969$	5.29508	0.170102
$970$	−0.00211457	−6.78948e−5 0
$971$	−41.4457	−1.33006	−0.665029	−	0.746818i	$-0.731581\pi$
$971$	−41.4457	−1.33006	−0.665029	+	0.746818i	$0.731581\pi$
$972$	14.9111	0.478275
$973$	11.4389	0.366713
$974$	23.5057	0.753170
$975$	0.0261093	0.000836166 0
$976$	−14.5560	−0.465927
$977$	49.8864	1.59601	0.798004	−	0.602652i	$-0.205889\pi$
$977$	49.8864	1.59601	0.798004	+	0.602652i	$0.205889\pi$
$978$	12.7313	0.407102
$979$	16.0937	0.514356
$980$	0.0750867	0.00239856
$981$	−15.2892	−0.488147
$982$	−29.0932	−0.928400
$983$	−44.4265	−1.41698	−0.708492	−	0.705719i	$-0.750624\pi$
$983$	−44.4265	−1.41698	−0.708492	+	0.705719i	$0.750624\pi$
$984$	−5.83042	−0.185867
$985$	6.64050	0.211584
$986$	9.94026	0.316562
$987$	−7.20603	−0.229370
$988$	−0.277070	−0.00881478
$989$	9.03828	0.287401
$990$	−7.17922	−0.228170
$991$	−58.1947	−1.84862	−0.924308	−	0.381647i	$-0.875357\pi$
$991$	−58.1947	−1.84862	−0.924308	+	0.381647i	$0.875357\pi$
$992$	−4.28085	−0.135917
$993$	6.74873	0.214165
$994$	−33.2117	−1.05341
$995$	−13.3555	−0.423399
$996$	−5.48889	−0.173922
$997$	30.3412	0.960914	0.480457	−	0.877018i	$-0.340471\pi$
$997$	30.3412	0.960914	0.480457	+	0.877018i	$0.340471\pi$
$998$	−1.02863	−0.0325608
$999$	7.31975	0.231587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.8	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.696154 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.696154 q^{6} +2.65990 q^{7} -1.00000 q^{8} -2.51537 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.696154 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.696154 q^{6} +2.65990 q^{7} -1.00000 q^{8} -2.51537 q^{9} -1.00000 q^{10} -2.85414 q^{11} +0.696154 q^{12} +0.0375050 q^{13} -2.65990 q^{14} +0.696154 q^{15} +1.00000 q^{16} -1.02960 q^{17} +2.51537 q^{18} -7.38755 q^{19} +1.00000 q^{20} +1.85170 q^{21} +2.85414 q^{22} -1.48829 q^{23} -0.696154 q^{24} +1.00000 q^{25} -0.0375050 q^{26} -3.83955 q^{27} +2.65990 q^{28} +9.65453 q^{29} -0.696154 q^{30} +4.28085 q^{31} -1.00000 q^{32} -1.98692 q^{33} +1.02960 q^{34} +2.65990 q^{35} -2.51537 q^{36} -1.90641 q^{37} +7.38755 q^{38} +0.0261093 q^{39} -1.00000 q^{40} +8.37519 q^{41} -1.85170 q^{42} -6.07292 q^{43} -2.85414 q^{44} -2.51537 q^{45} +1.48829 q^{46} -3.89157 q^{47} +0.696154 q^{48} +0.0750867 q^{49} -1.00000 q^{50} -0.716757 q^{51} +0.0375050 q^{52} -9.19937 q^{53} +3.83955 q^{54} -2.85414 q^{55} -2.65990 q^{56} -5.14287 q^{57} -9.65453 q^{58} -10.3821 q^{59} +0.696154 q^{60} -14.5560 q^{61} -4.28085 q^{62} -6.69064 q^{63} +1.00000 q^{64} +0.0375050 q^{65} +1.98692 q^{66} -3.35202 q^{67} -1.02960 q^{68} -1.03608 q^{69} -2.65990 q^{70} +12.4861 q^{71} +2.51537 q^{72} +6.72519 q^{73} +1.90641 q^{74} +0.696154 q^{75} -7.38755 q^{76} -7.59174 q^{77} -0.0261093 q^{78} -6.67283 q^{79} +1.00000 q^{80} +4.87319 q^{81} -8.37519 q^{82} -7.88459 q^{83} +1.85170 q^{84} -1.02960 q^{85} +6.07292 q^{86} +6.72104 q^{87} +2.85414 q^{88} -5.63871 q^{89} +2.51537 q^{90} +0.0997598 q^{91} -1.48829 q^{92} +2.98013 q^{93} +3.89157 q^{94} -7.38755 q^{95} -0.696154 q^{96} +0.00211457 q^{97} -0.0750867 q^{98} +7.17922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 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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