LMFDB - Embedded newform 4010.2.a.m.1.6

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:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + \cdots + 104 $ x^20 - 4x^19 - 35x^18 + 154x^17 + 460x^16 - 2392x^15 - 2591x^14 + 19157x^13 + 2776x^12 - 83577x^11 + 34362x^10 + 190617x^9 - 150697x^8 - 189098x^7 + 211360x^6 + 37365x^5 - 68876x^4 - 8984x^3 + 7920x^2 + 1972*x + 104
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.72088$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.72088 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.72088 q^{6} -0.251451 q^{7} -1.00000 q^{8} -0.0385865 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.72088 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.72088 q^{6} -0.251451 q^{7} -1.00000 q^{8} -0.0385865 q^{9} -1.00000 q^{10} +0.955927 q^{11} -1.72088 q^{12} -4.63659 q^{13} +0.251451 q^{14} -1.72088 q^{15} +1.00000 q^{16} +6.39077 q^{17} +0.0385865 q^{18} +4.45762 q^{19} +1.00000 q^{20} +0.432716 q^{21} -0.955927 q^{22} -4.09480 q^{23} +1.72088 q^{24} +1.00000 q^{25} +4.63659 q^{26} +5.22903 q^{27} -0.251451 q^{28} -3.79831 q^{29} +1.72088 q^{30} -3.73835 q^{31} -1.00000 q^{32} -1.64503 q^{33} -6.39077 q^{34} -0.251451 q^{35} -0.0385865 q^{36} +0.0328865 q^{37} -4.45762 q^{38} +7.97900 q^{39} -1.00000 q^{40} +2.38305 q^{41} -0.432716 q^{42} -9.98394 q^{43} +0.955927 q^{44} -0.0385865 q^{45} +4.09480 q^{46} +4.98851 q^{47} -1.72088 q^{48} -6.93677 q^{49} -1.00000 q^{50} -10.9977 q^{51} -4.63659 q^{52} -5.97521 q^{53} -5.22903 q^{54} +0.955927 q^{55} +0.251451 q^{56} -7.67102 q^{57} +3.79831 q^{58} +12.5470 q^{59} -1.72088 q^{60} +9.63334 q^{61} +3.73835 q^{62} +0.00970263 q^{63} +1.00000 q^{64} -4.63659 q^{65} +1.64503 q^{66} -0.0266179 q^{67} +6.39077 q^{68} +7.04664 q^{69} +0.251451 q^{70} +11.7655 q^{71} +0.0385865 q^{72} +10.5851 q^{73} -0.0328865 q^{74} -1.72088 q^{75} +4.45762 q^{76} -0.240369 q^{77} -7.97900 q^{78} -1.05241 q^{79} +1.00000 q^{80} -8.88275 q^{81} -2.38305 q^{82} -11.3928 q^{83} +0.432716 q^{84} +6.39077 q^{85} +9.98394 q^{86} +6.53641 q^{87} -0.955927 q^{88} -4.97937 q^{89} +0.0385865 q^{90} +1.16588 q^{91} -4.09480 q^{92} +6.43323 q^{93} -4.98851 q^{94} +4.45762 q^{95} +1.72088 q^{96} -3.23870 q^{97} +6.93677 q^{98} -0.0368859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * 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
$3$	−1.72088	−0.993548	−0.496774	−	0.867880i	$-0.665482\pi$
$3$	−1.72088	−0.993548	−0.496774	+	0.867880i	$0.665482\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.72088	0.702545
$7$	−0.251451	−0.0950396	−0.0475198	−	0.998870i	$-0.515132\pi$
$7$	−0.251451	−0.0950396	−0.0475198	+	0.998870i	$0.515132\pi$
$8$	−1.00000	−0.353553
$9$	−0.0385865	−0.0128622
$10$	−1.00000	−0.316228
$11$	0.955927	0.288223	0.144111	−	0.989561i	$-0.453968\pi$
$11$	0.955927	0.288223	0.144111	+	0.989561i	$0.453968\pi$
$12$	−1.72088	−0.496774
$13$	−4.63659	−1.28596	−0.642980	−	0.765883i	$-0.722302\pi$
$13$	−4.63659	−1.28596	−0.642980	+	0.765883i	$0.722302\pi$
$14$	0.251451	0.0672031
$15$	−1.72088	−0.444328
$16$	1.00000	0.250000
$17$	6.39077	1.54999	0.774994	−	0.631968i	$-0.217753\pi$
$17$	6.39077	1.54999	0.774994	+	0.631968i	$0.217753\pi$
$18$	0.0385865	0.00909493
$19$	4.45762	1.02265	0.511324	−	0.859388i	$-0.329155\pi$
$19$	4.45762	1.02265	0.511324	+	0.859388i	$0.329155\pi$
$20$	1.00000	0.223607
$21$	0.432716	0.0944264
$22$	−0.955927	−0.203804
$23$	−4.09480	−0.853825	−0.426912	−	0.904293i	$-0.640399\pi$
$23$	−4.09480	−0.853825	−0.426912	+	0.904293i	$0.640399\pi$
$24$	1.72088	0.351272
$25$	1.00000	0.200000
$26$	4.63659	0.909311
$27$	5.22903	1.00633
$28$	−0.251451	−0.0475198
$29$	−3.79831	−0.705328	−0.352664	−	0.935750i	$-0.614724\pi$
$29$	−3.79831	−0.705328	−0.352664	+	0.935750i	$0.614724\pi$
$30$	1.72088	0.314187
$31$	−3.73835	−0.671427	−0.335713	−	0.941964i	$-0.608977\pi$
$31$	−3.73835	−0.671427	−0.335713	+	0.941964i	$0.608977\pi$
$32$	−1.00000	−0.176777
$33$	−1.64503	−0.286363
$34$	−6.39077	−1.09601
$35$	−0.251451	−0.0425030
$36$	−0.0385865	−0.00643109
$37$	0.0328865	0.00540651	0.00270326	−	0.999996i	$-0.499140\pi$
$37$	0.0328865	0.00540651	0.00270326	+	0.999996i	$0.499140\pi$
$38$	−4.45762	−0.723122
$39$	7.97900	1.27766
$40$	−1.00000	−0.158114
$41$	2.38305	0.372170	0.186085	−	0.982534i	$-0.440420\pi$
$41$	2.38305	0.372170	0.186085	+	0.982534i	$0.440420\pi$
$42$	−0.432716	−0.0667695
$43$	−9.98394	−1.52254	−0.761269	−	0.648437i	$-0.775423\pi$
$43$	−9.98394	−1.52254	−0.761269	+	0.648437i	$0.775423\pi$
$44$	0.955927	0.144111
$45$	−0.0385865	−0.00575214
$46$	4.09480	0.603745
$47$	4.98851	0.727649	0.363824	−	0.931468i	$-0.381471\pi$
$47$	4.98851	0.727649	0.363824	+	0.931468i	$0.381471\pi$
$48$	−1.72088	−0.248387
$49$	−6.93677	−0.990967
$50$	−1.00000	−0.141421
$51$	−10.9977	−1.53999
$52$	−4.63659	−0.642980
$53$	−5.97521	−0.820759	−0.410379	−	0.911915i	$-0.634604\pi$
$53$	−5.97521	−0.820759	−0.410379	+	0.911915i	$0.634604\pi$
$54$	−5.22903	−0.711581
$55$	0.955927	0.128897
$56$	0.251451	0.0336016
$57$	−7.67102	−1.01605
$58$	3.79831	0.498742
$59$	12.5470	1.63348	0.816738	−	0.577009i	$-0.195780\pi$
$59$	12.5470	1.63348	0.816738	+	0.577009i	$0.195780\pi$
$60$	−1.72088	−0.222164
$61$	9.63334	1.23342	0.616711	−	0.787189i	$-0.288465\pi$
$61$	9.63334	1.23342	0.616711	+	0.787189i	$0.288465\pi$
$62$	3.73835	0.474770
$63$	0.00970263	0.00122242
$64$	1.00000	0.125000
$65$	−4.63659	−0.575099
$66$	1.64503	0.202489
$67$	−0.0266179	−0.00325190	−0.00162595	−	0.999999i	$-0.500518\pi$
$67$	−0.0266179	−0.00325190	−0.00162595	+	0.999999i	$0.500518\pi$
$68$	6.39077	0.774994
$69$	7.04664	0.848316
$70$	0.251451	0.0300541
$71$	11.7655	1.39631	0.698153	−	0.715949i	$-0.254006\pi$
$71$	11.7655	1.39631	0.698153	+	0.715949i	$0.254006\pi$
$72$	0.0385865	0.00454747
$73$	10.5851	1.23889	0.619446	−	0.785039i	$-0.287357\pi$
$73$	10.5851	1.23889	0.619446	+	0.785039i	$0.287357\pi$
$74$	−0.0328865	−0.00382298
$75$	−1.72088	−0.198710
$76$	4.45762	0.511324
$77$	−0.240369	−0.0273926
$78$	−7.97900	−0.903444
$79$	−1.05241	−0.118405	−0.0592027	−	0.998246i	$-0.518856\pi$
$79$	−1.05241	−0.118405	−0.0592027	+	0.998246i	$0.518856\pi$
$80$	1.00000	0.111803
$81$	−8.88275	−0.986972
$82$	−2.38305	−0.263164
$83$	−11.3928	−1.25052	−0.625262	−	0.780415i	$-0.715008\pi$
$83$	−11.3928	−1.25052	−0.625262	+	0.780415i	$0.715008\pi$
$84$	0.432716	0.0472132
$85$	6.39077	0.693176
$86$	9.98394	1.07660
$87$	6.53641	0.700777
$88$	−0.955927	−0.101902
$89$	−4.97937	−0.527812	−0.263906	−	0.964548i	$-0.585011\pi$
$89$	−4.97937	−0.527812	−0.263906	+	0.964548i	$0.585011\pi$
$90$	0.0385865	0.00406738
$91$	1.16588	0.122217
$92$	−4.09480	−0.426912
$93$	6.43323	0.667095
$94$	−4.98851	−0.514525
$95$	4.45762	0.457343
$96$	1.72088	0.175636
$97$	−3.23870	−0.328840	−0.164420	−	0.986390i	$-0.552575\pi$
$97$	−3.23870	−0.328840	−0.164420	+	0.986390i	$0.552575\pi$
$98$	6.93677	0.700720
$99$	−0.0368859	−0.00370717
$100$	1.00000	0.100000
$101$	6.28986	0.625865	0.312932	−	0.949775i	$-0.398689\pi$
$101$	6.28986	0.625865	0.312932	+	0.949775i	$0.398689\pi$
$102$	10.9977	1.08894
$103$	−7.04852	−0.694511	−0.347256	−	0.937771i	$-0.612886\pi$
$103$	−7.04852	−0.694511	−0.347256	+	0.937771i	$0.612886\pi$
$104$	4.63659	0.454656
$105$	0.432716	0.0422288
$106$	5.97521	0.580364
$107$	−0.343698	−0.0332265	−0.0166133	−	0.999862i	$-0.505288\pi$
$107$	−0.343698	−0.0332265	−0.0166133	+	0.999862i	$0.505288\pi$
$108$	5.22903	0.503164
$109$	19.3768	1.85596	0.927982	−	0.372626i	$-0.121543\pi$
$109$	19.3768	1.85596	0.927982	+	0.372626i	$0.121543\pi$
$110$	−0.955927	−0.0911440
$111$	−0.0565936	−0.00537163
$112$	−0.251451	−0.0237599
$113$	−12.7603	−1.20039	−0.600195	−	0.799854i	$-0.704910\pi$
$113$	−12.7603	−1.20039	−0.600195	+	0.799854i	$0.704910\pi$
$114$	7.67102	0.718456
$115$	−4.09480	−0.381842
$116$	−3.79831	−0.352664
$117$	0.178910	0.0165402
$118$	−12.5470	−1.15504
$119$	−1.60696	−0.147310
$120$	1.72088	0.157094
$121$	−10.0862	−0.916928
$122$	−9.63334	−0.872161
$123$	−4.10093	−0.369768
$124$	−3.73835	−0.335713
$125$	1.00000	0.0894427
$126$	−0.00970263	−0.000864379 0
$127$	4.60869	0.408955	0.204477	−	0.978871i	$-0.434451\pi$
$127$	4.60869	0.408955	0.204477	+	0.978871i	$0.434451\pi$
$128$	−1.00000	−0.0883883
$129$	17.1811	1.51271
$130$	4.63659	0.406656
$131$	0.728667	0.0636639	0.0318320	−	0.999493i	$-0.489866\pi$
$131$	0.728667	0.0636639	0.0318320	+	0.999493i	$0.489866\pi$
$132$	−1.64503	−0.143182
$133$	−1.12087	−0.0971921
$134$	0.0266179	0.00229944
$135$	5.22903	0.450043
$136$	−6.39077	−0.548004
$137$	−9.99220	−0.853691	−0.426846	−	0.904325i	$-0.640375\pi$
$137$	−9.99220	−0.853691	−0.426846	+	0.904325i	$0.640375\pi$
$138$	−7.04664	−0.599850
$139$	4.29748	0.364508	0.182254	−	0.983252i	$-0.441661\pi$
$139$	4.29748	0.364508	0.182254	+	0.983252i	$0.441661\pi$
$140$	−0.251451	−0.0212515
$141$	−8.58460	−0.722954
$142$	−11.7655	−0.987337
$143$	−4.43225	−0.370643
$144$	−0.0385865	−0.00321555
$145$	−3.79831	−0.315432
$146$	−10.5851	−0.876029
$147$	11.9373	0.984574
$148$	0.0328865	0.00270326
$149$	−15.0272	−1.23107	−0.615536	−	0.788109i	$-0.711061\pi$
$149$	−15.0272	−1.23107	−0.615536	+	0.788109i	$0.711061\pi$
$150$	1.72088	0.140509
$151$	0.105684	0.00860043	0.00430021	−	0.999991i	$-0.498631\pi$
$151$	0.105684	0.00860043	0.00430021	+	0.999991i	$0.498631\pi$
$152$	−4.45762	−0.361561
$153$	−0.246598	−0.0199362
$154$	0.240369	0.0193695
$155$	−3.73835	−0.300271
$156$	7.97900	0.638832
$157$	−21.5382	−1.71893	−0.859467	−	0.511192i	$-0.829204\pi$
$157$	−21.5382	−1.71893	−0.859467	+	0.511192i	$0.829204\pi$
$158$	1.05241	0.0837252
$159$	10.2826	0.815463
$160$	−1.00000	−0.0790569
$161$	1.02964	0.0811471
$162$	8.88275	0.697895
$163$	12.9269	1.01252	0.506258	−	0.862382i	$-0.331028\pi$
$163$	12.9269	1.01252	0.506258	+	0.862382i	$0.331028\pi$
$164$	2.38305	0.186085
$165$	−1.64503	−0.128066
$166$	11.3928	0.884254
$167$	3.89677	0.301541	0.150771	−	0.988569i	$-0.451825\pi$
$167$	3.89677	0.301541	0.150771	+	0.988569i	$0.451825\pi$
$168$	−0.432716	−0.0333848
$169$	8.49801	0.653693
$170$	−6.39077	−0.490149
$171$	−0.172004	−0.0131535
$172$	−9.98394	−0.761269
$173$	15.0673	1.14555	0.572773	−	0.819714i	$-0.305868\pi$
$173$	15.0673	1.14555	0.572773	+	0.819714i	$0.305868\pi$
$174$	−6.53641	−0.495524
$175$	−0.251451	−0.0190079
$176$	0.955927	0.0720557
$177$	−21.5918	−1.62294
$178$	4.97937	0.373220
$179$	20.7639	1.55197	0.775985	−	0.630752i	$-0.217253\pi$
$179$	20.7639	1.55197	0.775985	+	0.630752i	$0.217253\pi$
$180$	−0.0385865	−0.00287607
$181$	−6.06988	−0.451171	−0.225585	−	0.974223i	$-0.572429\pi$
$181$	−6.06988	−0.451171	−0.225585	+	0.974223i	$0.572429\pi$
$182$	−1.16588	−0.0864205
$183$	−16.5778	−1.22546
$184$	4.09480	0.301873
$185$	0.0328865	0.00241787
$186$	−6.43323	−0.471707
$187$	6.10910	0.446742
$188$	4.98851	0.363824
$189$	−1.31485	−0.0956409
$190$	−4.45762	−0.323390
$191$	6.81186	0.492889	0.246444	−	0.969157i	$-0.420738\pi$
$191$	6.81186	0.492889	0.246444	+	0.969157i	$0.420738\pi$
$192$	−1.72088	−0.124194
$193$	18.4716	1.32961	0.664807	−	0.747015i	$-0.268514\pi$
$193$	18.4716	1.32961	0.664807	+	0.747015i	$0.268514\pi$
$194$	3.23870	0.232525
$195$	7.97900	0.571388
$196$	−6.93677	−0.495484
$197$	−8.87189	−0.632096	−0.316048	−	0.948743i	$-0.602356\pi$
$197$	−8.87189	−0.632096	−0.316048	+	0.948743i	$0.602356\pi$
$198$	0.0368859	0.00262137
$199$	18.1568	1.28710	0.643552	−	0.765403i	$-0.277460\pi$
$199$	18.1568	1.28710	0.643552	+	0.765403i	$0.277460\pi$
$200$	−1.00000	−0.0707107
$201$	0.0458061	0.00323092
$202$	−6.28986	−0.442553
$203$	0.955088	0.0670340
$204$	−10.9977	−0.769994
$205$	2.38305	0.166439
$206$	7.04852	0.491093
$207$	0.158004	0.0109820
$208$	−4.63659	−0.321490
$209$	4.26116	0.294751
$210$	−0.432716	−0.0298602
$211$	23.6581	1.62869	0.814345	−	0.580381i	$-0.197096\pi$
$211$	23.6581	1.62869	0.814345	+	0.580381i	$0.197096\pi$
$212$	−5.97521	−0.410379
$213$	−20.2469	−1.38730
$214$	0.343698	0.0234947
$215$	−9.98394	−0.680899
$216$	−5.22903	−0.355790
$217$	0.940011	0.0638121
$218$	−19.3768	−1.31236
$219$	−18.2156	−1.23090
$220$	0.955927	0.0644486
$221$	−29.6314	−1.99322
$222$	0.0565936	0.00379832
$223$	−3.16838	−0.212171	−0.106085	−	0.994357i	$-0.533832\pi$
$223$	−3.16838	−0.212171	−0.106085	+	0.994357i	$0.533832\pi$
$224$	0.251451	0.0168008
$225$	−0.0385865	−0.00257244
$226$	12.7603	0.848804
$227$	5.62039	0.373038	0.186519	−	0.982451i	$-0.440279\pi$
$227$	5.62039	0.373038	0.186519	+	0.982451i	$0.440279\pi$
$228$	−7.67102	−0.508025
$229$	−1.10268	−0.0728673	−0.0364337	−	0.999336i	$-0.511600\pi$
$229$	−1.10268	−0.0728673	−0.0364337	+	0.999336i	$0.511600\pi$
$230$	4.09480	0.270003
$231$	0.413645	0.0272158
$232$	3.79831	0.249371
$233$	15.5484	1.01861	0.509304	−	0.860587i	$-0.329903\pi$
$233$	15.5484	1.01861	0.509304	+	0.860587i	$0.329903\pi$
$234$	−0.178910	−0.0116957
$235$	4.98851	0.325414
$236$	12.5470	0.816738
$237$	1.81107	0.117641
$238$	1.60696	0.104164
$239$	−14.2440	−0.921368	−0.460684	−	0.887564i	$-0.652396\pi$
$239$	−14.2440	−0.921368	−0.460684	+	0.887564i	$0.652396\pi$
$240$	−1.72088	−0.111082
$241$	3.69095	0.237755	0.118878	−	0.992909i	$-0.462070\pi$
$241$	3.69095	0.237755	0.118878	+	0.992909i	$0.462070\pi$
$242$	10.0862	0.648366
$243$	−0.400978	−0.0257228
$244$	9.63334	0.616711
$245$	−6.93677	−0.443174
$246$	4.10093	0.261466
$247$	−20.6682	−1.31509
$248$	3.73835	0.237385
$249$	19.6056	1.24246
$250$	−1.00000	−0.0632456
$251$	19.1189	1.20677	0.603387	−	0.797448i	$-0.293817\pi$
$251$	19.1189	1.20677	0.603387	+	0.797448i	$0.293817\pi$
$252$	0.00970263	0.000611208 0
$253$	−3.91433	−0.246092
$254$	−4.60869	−0.289175
$255$	−10.9977	−0.688704
$256$	1.00000	0.0625000
$257$	21.3354	1.33087	0.665433	−	0.746457i	$-0.268247\pi$
$257$	21.3354	1.33087	0.665433	+	0.746457i	$0.268247\pi$
$258$	−17.1811	−1.06965
$259$	−0.00826935	−0.000513833 0
$260$	−4.63659	−0.287549
$261$	0.146564	0.00907205
$262$	−0.728667	−0.0450172
$263$	−8.46474	−0.521958	−0.260979	−	0.965344i	$-0.584045\pi$
$263$	−8.46474	−0.521958	−0.260979	+	0.965344i	$0.584045\pi$
$264$	1.64503	0.101245
$265$	−5.97521	−0.367054
$266$	1.12087	0.0687252
$267$	8.56888	0.524407
$268$	−0.0266179	−0.00162595
$269$	14.4915	0.883559	0.441780	−	0.897124i	$-0.354347\pi$
$269$	14.4915	0.883559	0.441780	+	0.897124i	$0.354347\pi$
$270$	−5.22903	−0.318229
$271$	8.58845	0.521711	0.260856	−	0.965378i	$-0.415995\pi$
$271$	8.58845	0.521711	0.260856	+	0.965378i	$0.415995\pi$
$272$	6.39077	0.387497
$273$	−2.00633	−0.121429
$274$	9.99220	0.603651
$275$	0.955927	0.0576446
$276$	7.04664	0.424158
$277$	28.4689	1.71053	0.855264	−	0.518193i	$-0.173395\pi$
$277$	28.4689	1.71053	0.855264	+	0.518193i	$0.173395\pi$
$278$	−4.29748	−0.257746
$279$	0.144250	0.00863601
$280$	0.251451	0.0150271
$281$	−4.86117	−0.289993	−0.144997	−	0.989432i	$-0.546317\pi$
$281$	−4.86117	−0.289993	−0.144997	+	0.989432i	$0.546317\pi$
$282$	8.58460	0.511206
$283$	16.7437	0.995312	0.497656	−	0.867375i	$-0.334194\pi$
$283$	16.7437	0.995312	0.497656	+	0.867375i	$0.334194\pi$
$284$	11.7655	0.698153
$285$	−7.67102	−0.454392
$286$	4.43225	0.262084
$287$	−0.599220	−0.0353708
$288$	0.0385865	0.00227373
$289$	23.8419	1.40246
$290$	3.79831	0.223044
$291$	5.57340	0.326719
$292$	10.5851	0.619446
$293$	22.8627	1.33566	0.667828	−	0.744316i	$-0.267224\pi$
$293$	22.8627	1.33566	0.667828	+	0.744316i	$0.267224\pi$
$294$	−11.9373	−0.696199
$295$	12.5470	0.730513
$296$	−0.0328865	−0.00191149
$297$	4.99857	0.290046
$298$	15.0272	0.870500
$299$	18.9859	1.09798
$300$	−1.72088	−0.0993548
$301$	2.51047	0.144701
$302$	−0.105684	−0.00608142
$303$	−10.8241	−0.621827
$304$	4.45762	0.255662
$305$	9.63334	0.551603
$306$	0.246598	0.0140970
$307$	29.6774	1.69378	0.846889	−	0.531770i	$-0.178473\pi$
$307$	29.6774	1.69378	0.846889	+	0.531770i	$0.178473\pi$
$308$	−0.240369	−0.0136963
$309$	12.1296	0.690030
$310$	3.73835	0.212324
$311$	32.5439	1.84540	0.922698	−	0.385524i	$-0.125979\pi$
$311$	32.5439	1.84540	0.922698	+	0.385524i	$0.125979\pi$
$312$	−7.97900	−0.451722
$313$	24.7026	1.39628	0.698138	−	0.715963i	$-0.254012\pi$
$313$	24.7026	1.39628	0.698138	+	0.715963i	$0.254012\pi$
$314$	21.5382	1.21547
$315$	0.00970263	0.000546681 0
$316$	−1.05241	−0.0592027
$317$	−15.0511	−0.845352	−0.422676	−	0.906281i	$-0.638909\pi$
$317$	−15.0511	−0.845352	−0.422676	+	0.906281i	$0.638909\pi$
$318$	−10.2826	−0.576620
$319$	−3.63090	−0.203292
$320$	1.00000	0.0559017
$321$	0.591461	0.0330121
$322$	−1.02964	−0.0573797
$323$	28.4876	1.58509
$324$	−8.88275	−0.493486
$325$	−4.63659	−0.257192
$326$	−12.9269	−0.715957
$327$	−33.3451	−1.84399
$328$	−2.38305	−0.131582
$329$	−1.25437	−0.0691554
$330$	1.64503	0.0905560
$331$	5.27410	0.289891	0.144945	−	0.989440i	$-0.453699\pi$
$331$	5.27410	0.289891	0.144945	+	0.989440i	$0.453699\pi$
$332$	−11.3928	−0.625262
$333$	−0.00126898	−6.95396e−5 0
$334$	−3.89677	−0.213222
$335$	−0.0266179	−0.00145429
$336$	0.432716	0.0236066
$337$	−5.10995	−0.278357	−0.139178	−	0.990267i	$-0.544446\pi$
$337$	−5.10995	−0.278357	−0.139178	+	0.990267i	$0.544446\pi$
$338$	−8.49801	−0.462231
$339$	21.9589	1.19264
$340$	6.39077	0.346588
$341$	−3.57358	−0.193520
$342$	0.172004	0.00930093
$343$	3.50442	0.189221
$344$	9.98394	0.538298
$345$	7.04664	0.379379
$346$	−15.0673	−0.810023
$347$	0.548757	0.0294588	0.0147294	−	0.999892i	$-0.495311\pi$
$347$	0.548757	0.0294588	0.0147294	+	0.999892i	$0.495311\pi$
$348$	6.53641	0.350389
$349$	−5.35023	−0.286391	−0.143196	−	0.989694i	$-0.545738\pi$
$349$	−5.35023	−0.286391	−0.143196	+	0.989694i	$0.545738\pi$
$350$	0.251451	0.0134406
$351$	−24.2449	−1.29410
$352$	−0.955927	−0.0509511
$353$	−18.2614	−0.971956	−0.485978	−	0.873971i	$-0.661537\pi$
$353$	−18.2614	−0.971956	−0.485978	+	0.873971i	$0.661537\pi$
$354$	21.5918	1.14759
$355$	11.7655	0.624447
$356$	−4.97937	−0.263906
$357$	2.76539	0.146360
$358$	−20.7639	−1.09741
$359$	−5.06667	−0.267409	−0.133704	−	0.991021i	$-0.542687\pi$
$359$	−5.06667	−0.267409	−0.133704	+	0.991021i	$0.542687\pi$
$360$	0.0385865	0.00203369
$361$	0.870406	0.0458108
$362$	6.06988	0.319026
$363$	17.3571	0.911012
$364$	1.16588	0.0611085
$365$	10.5851	0.554050
$366$	16.5778	0.866534
$367$	19.0794	0.995938	0.497969	−	0.867195i	$-0.334079\pi$
$367$	19.0794	0.995938	0.497969	+	0.867195i	$0.334079\pi$
$368$	−4.09480	−0.213456
$369$	−0.0919536	−0.00478691
$370$	−0.0328865	−0.00170969
$371$	1.50247	0.0780045
$372$	6.43323	0.333547
$373$	−11.9311	−0.617770	−0.308885	−	0.951099i	$-0.599956\pi$
$373$	−11.9311	−0.617770	−0.308885	+	0.951099i	$0.599956\pi$
$374$	−6.10910	−0.315894
$375$	−1.72088	−0.0888656
$376$	−4.98851	−0.257263
$377$	17.6112	0.907023
$378$	1.31485	0.0676283
$379$	−7.32510	−0.376265	−0.188133	−	0.982144i	$-0.560243\pi$
$379$	−7.32510	−0.376265	−0.188133	+	0.982144i	$0.560243\pi$
$380$	4.45762	0.228671
$381$	−7.93098	−0.406316
$382$	−6.81186	−0.348525
$383$	0.564290	0.0288339	0.0144169	−	0.999896i	$-0.495411\pi$
$383$	0.564290	0.0288339	0.0144169	+	0.999896i	$0.495411\pi$
$384$	1.72088	0.0878181
$385$	−0.240369	−0.0122503
$386$	−18.4716	−0.940179
$387$	0.385246	0.0195831
$388$	−3.23870	−0.164420
$389$	−27.4557	−1.39206	−0.696028	−	0.718014i	$-0.745051\pi$
$389$	−27.4557	−1.39206	−0.696028	+	0.718014i	$0.745051\pi$
$390$	−7.97900	−0.404033
$391$	−26.1689	−1.32342
$392$	6.93677	0.350360
$393$	−1.25395	−0.0632532
$394$	8.87189	0.446959
$395$	−1.05241	−0.0529525
$396$	−0.0368859	−0.00185359
$397$	16.7049	0.838395	0.419198	−	0.907895i	$-0.362311\pi$
$397$	16.7049	0.838395	0.419198	+	0.907895i	$0.362311\pi$
$398$	−18.1568	−0.910119
$399$	1.92888	0.0965650
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−0.0458061	−0.00228460
$403$	17.3332	0.863428
$404$	6.28986	0.312932
$405$	−8.88275	−0.441387
$406$	−0.955088	−0.0474002
$407$	0.0314371	0.00155828
$408$	10.9977	0.544468
$409$	13.1409	0.649775	0.324887	−	0.945753i	$-0.394674\pi$
$409$	13.1409	0.649775	0.324887	+	0.945753i	$0.394674\pi$
$410$	−2.38305	−0.117690
$411$	17.1953	0.848183
$412$	−7.04852	−0.347256
$413$	−3.15495	−0.155245
$414$	−0.158004	−0.00776548
$415$	−11.3928	−0.559251
$416$	4.63659	0.227328
$417$	−7.39543	−0.362156
$418$	−4.26116	−0.208420
$419$	27.8390	1.36002	0.680011	−	0.733201i	$-0.261975\pi$
$419$	27.8390	1.36002	0.680011	+	0.733201i	$0.261975\pi$
$420$	0.432716	0.0211144
$421$	−7.68508	−0.374548	−0.187274	−	0.982308i	$-0.559965\pi$
$421$	−7.68508	−0.374548	−0.187274	+	0.982308i	$0.559965\pi$
$422$	−23.6581	−1.15166
$423$	−0.192489	−0.00935915
$424$	5.97521	0.290182
$425$	6.39077	0.309998
$426$	20.2469	0.980967
$427$	−2.42231	−0.117224
$428$	−0.343698	−0.0166133
$429$	7.62734	0.368252
$430$	9.98394	0.481469
$431$	23.3351	1.12401	0.562006	−	0.827133i	$-0.310030\pi$
$431$	23.3351	1.12401	0.562006	+	0.827133i	$0.310030\pi$
$432$	5.22903	0.251582
$433$	27.7749	1.33478	0.667388	−	0.744710i	$-0.267412\pi$
$433$	27.7749	1.33478	0.667388	+	0.744710i	$0.267412\pi$
$434$	−0.940011	−0.0451220
$435$	6.53641	0.313397
$436$	19.3768	0.927982
$437$	−18.2531	−0.873163
$438$	18.2156	0.870377
$439$	16.0403	0.765563	0.382781	−	0.923839i	$-0.374966\pi$
$439$	16.0403	0.765563	0.382781	+	0.923839i	$0.374966\pi$
$440$	−0.955927	−0.0455720
$441$	0.267666	0.0127460
$442$	29.6314	1.40942
$443$	−19.1971	−0.912081	−0.456040	−	0.889959i	$-0.650733\pi$
$443$	−19.1971	−0.912081	−0.456040	+	0.889959i	$0.650733\pi$
$444$	−0.0565936	−0.00268582
$445$	−4.97937	−0.236045
$446$	3.16838	0.150027
$447$	25.8599	1.22313
$448$	−0.251451	−0.0118799
$449$	−16.1602	−0.762645	−0.381323	−	0.924442i	$-0.624531\pi$
$449$	−16.1602	−0.762645	−0.381323	+	0.924442i	$0.624531\pi$
$450$	0.0385865	0.00181899
$451$	2.27802	0.107268
$452$	−12.7603	−0.600195
$453$	−0.181869	−0.00854494
$454$	−5.62039	−0.263778
$455$	1.16588	0.0546571
$456$	7.67102	0.359228
$457$	−30.1267	−1.40927	−0.704633	−	0.709572i	$-0.748888\pi$
$457$	−30.1267	−1.40927	−0.704633	+	0.709572i	$0.748888\pi$
$458$	1.10268	0.0515250
$459$	33.4175	1.55980
$460$	−4.09480	−0.190921
$461$	−21.5248	−1.00251	−0.501256	−	0.865299i	$-0.667129\pi$
$461$	−21.5248	−1.00251	−0.501256	+	0.865299i	$0.667129\pi$
$462$	−0.413645	−0.0192445
$463$	8.21486	0.381777	0.190889	−	0.981612i	$-0.438863\pi$
$463$	8.21486	0.381777	0.190889	+	0.981612i	$0.438863\pi$
$464$	−3.79831	−0.176332
$465$	6.43323	0.298334
$466$	−15.5484	−0.720264
$467$	11.1701	0.516892	0.258446	−	0.966026i	$-0.416790\pi$
$467$	11.1701	0.516892	0.258446	+	0.966026i	$0.416790\pi$
$468$	0.178910	0.00827012
$469$	0.00669310	0.000309059 0
$470$	−4.98851	−0.230103
$471$	37.0645	1.70784
$472$	−12.5470	−0.577521
$473$	−9.54392	−0.438830
$474$	−1.81107	−0.0831850
$475$	4.45762	0.204530
$476$	−1.60696	−0.0736551
$477$	0.230563	0.0105567
$478$	14.2440	0.651506
$479$	0.336640	0.0153815	0.00769074	−	0.999970i	$-0.497552\pi$
$479$	0.336640	0.0153815	0.00769074	+	0.999970i	$0.497552\pi$
$480$	1.72088	0.0785469
$481$	−0.152482	−0.00695256
$482$	−3.69095	−0.168118
$483$	−1.77189	−0.0806236
$484$	−10.0862	−0.458464
$485$	−3.23870	−0.147062
$486$	0.400978	0.0181887
$487$	−8.07204	−0.365779	−0.182890	−	0.983133i	$-0.558545\pi$
$487$	−8.07204	−0.365779	−0.182890	+	0.983133i	$0.558545\pi$
$488$	−9.63334	−0.436081
$489$	−22.2457	−1.00598
$490$	6.93677	0.313371
$491$	−26.9316	−1.21541	−0.607703	−	0.794165i	$-0.707909\pi$
$491$	−26.9316	−1.21541	−0.607703	+	0.794165i	$0.707909\pi$
$492$	−4.10093	−0.184884
$493$	−24.2741	−1.09325
$494$	20.6682	0.929906
$495$	−0.0368859	−0.00165790
$496$	−3.73835	−0.167857
$497$	−2.95844	−0.132704
$498$	−19.6056	−0.878548
$499$	−16.5565	−0.741169	−0.370585	−	0.928799i	$-0.620843\pi$
$499$	−16.5565	−0.741169	−0.370585	+	0.928799i	$0.620843\pi$
$500$	1.00000	0.0447214
$501$	−6.70586	−0.299596
$502$	−19.1189	−0.853319
$503$	−27.6971	−1.23495	−0.617477	−	0.786589i	$-0.711845\pi$
$503$	−27.6971	−1.23495	−0.617477	+	0.786589i	$0.711845\pi$
$504$	−0.00970263	−0.000432189 0
$505$	6.28986	0.279895
$506$	3.91433	0.174013
$507$	−14.6240	−0.649476
$508$	4.60869	0.204477
$509$	31.8200	1.41040	0.705199	−	0.709009i	$-0.250857\pi$
$509$	31.8200	1.41040	0.705199	+	0.709009i	$0.250857\pi$
$510$	10.9977	0.486987
$511$	−2.66164	−0.117744
$512$	−1.00000	−0.0441942
$513$	23.3090	1.02912
$514$	−21.3354	−0.941065
$515$	−7.04852	−0.310595
$516$	17.1811	0.756357
$517$	4.76865	0.209725
$518$	0.00826935	0.000363335 0
$519$	−25.9289	−1.13815
$520$	4.63659	0.203328
$521$	19.2981	0.845465	0.422733	−	0.906254i	$-0.361071\pi$
$521$	19.2981	0.845465	0.422733	+	0.906254i	$0.361071\pi$
$522$	−0.146564	−0.00641491
$523$	16.3535	0.715088	0.357544	−	0.933896i	$-0.383614\pi$
$523$	16.3535	0.715088	0.357544	+	0.933896i	$0.383614\pi$
$524$	0.728667	0.0318320
$525$	0.432716	0.0188853
$526$	8.46474	0.369080
$527$	−23.8909	−1.04070
$528$	−1.64503	−0.0715908
$529$	−6.23261	−0.270983
$530$	5.97521	0.259547
$531$	−0.484144	−0.0210101
$532$	−1.12087	−0.0485961
$533$	−11.0492	−0.478595
$534$	−8.56888	−0.370812
$535$	−0.343698	−0.0148593
$536$	0.0266179	0.00114972
$537$	−35.7321	−1.54196
$538$	−14.4915	−0.624771
$539$	−6.63105	−0.285619
$540$	5.22903	0.225022
$541$	11.7502	0.505182	0.252591	−	0.967573i	$-0.418717\pi$
$541$	11.7502	0.505182	0.252591	+	0.967573i	$0.418717\pi$
$542$	−8.58845	−0.368905
$543$	10.4455	0.448260
$544$	−6.39077	−0.274002
$545$	19.3768	0.830012
$546$	2.00633	0.0858629
$547$	38.3720	1.64067	0.820335	−	0.571884i	$-0.193787\pi$
$547$	38.3720	1.64067	0.820335	+	0.571884i	$0.193787\pi$
$548$	−9.99220	−0.426846
$549$	−0.371717	−0.0158645
$550$	−0.955927	−0.0407609
$551$	−16.9314	−0.721303
$552$	−7.04664	−0.299925
$553$	0.264630	0.0112532
$554$	−28.4689	−1.20953
$555$	−0.0565936	−0.00240227
$556$	4.29748	0.182254
$557$	16.5047	0.699326	0.349663	−	0.936876i	$-0.386296\pi$
$557$	16.5047	0.699326	0.349663	+	0.936876i	$0.386296\pi$
$558$	−0.144250	−0.00610658
$559$	46.2915	1.95792
$560$	−0.251451	−0.0106257
$561$	−10.5130	−0.443860
$562$	4.86117	0.205056
$563$	5.38324	0.226876	0.113438	−	0.993545i	$-0.463814\pi$
$563$	5.38324	0.226876	0.113438	+	0.993545i	$0.463814\pi$
$564$	−8.58460	−0.361477
$565$	−12.7603	−0.536831
$566$	−16.7437	−0.703792
$567$	2.23358	0.0938014
$568$	−11.7655	−0.493668
$569$	18.6489	0.781803	0.390902	−	0.920432i	$-0.372163\pi$
$569$	18.6489	0.781803	0.390902	+	0.920432i	$0.372163\pi$
$570$	7.67102	0.321304
$571$	28.8429	1.20704	0.603519	−	0.797349i	$-0.293765\pi$
$571$	28.8429	1.20704	0.603519	+	0.797349i	$0.293765\pi$
$572$	−4.43225	−0.185321
$573$	−11.7224	−0.489709
$574$	0.599220	0.0250110
$575$	−4.09480	−0.170765
$576$	−0.0385865	−0.00160777
$577$	0.548493	0.0228341	0.0114170	−	0.999935i	$-0.496366\pi$
$577$	0.548493	0.0228341	0.0114170	+	0.999935i	$0.496366\pi$
$578$	−23.8419	−0.991692
$579$	−31.7873	−1.32104
$580$	−3.79831	−0.157716
$581$	2.86473	0.118849
$582$	−5.57340	−0.231025
$583$	−5.71187	−0.236561
$584$	−10.5851	−0.438015
$585$	0.178910	0.00739702
$586$	−22.8627	−0.944451
$587$	−1.39565	−0.0576045	−0.0288023	−	0.999585i	$-0.509169\pi$
$587$	−1.39565	−0.0576045	−0.0288023	+	0.999585i	$0.509169\pi$
$588$	11.9373	0.492287
$589$	−16.6641	−0.686634
$590$	−12.5470	−0.516551
$591$	15.2674	0.628017
$592$	0.0328865	0.00135163
$593$	−30.3338	−1.24566	−0.622829	−	0.782358i	$-0.714017\pi$
$593$	−30.3338	−1.24566	−0.622829	+	0.782358i	$0.714017\pi$
$594$	−4.99857	−0.205094
$595$	−1.60696	−0.0658791
$596$	−15.0272	−0.615536
$597$	−31.2456	−1.27880
$598$	−18.9859	−0.776392
$599$	31.6484	1.29312	0.646560	−	0.762863i	$-0.276207\pi$
$599$	31.6484	1.29312	0.646560	+	0.762863i	$0.276207\pi$
$600$	1.72088	0.0702545
$601$	−16.3669	−0.667622	−0.333811	−	0.942640i	$-0.608335\pi$
$601$	−16.3669	−0.667622	−0.333811	+	0.942640i	$0.608335\pi$
$602$	−2.51047	−0.102319
$603$	0.00102709	4.18265e−5 0
$604$	0.105684	0.00430021
$605$	−10.0862	−0.410063
$606$	10.8241	0.439698
$607$	17.1918	0.697794	0.348897	−	0.937161i	$-0.386556\pi$
$607$	17.1918	0.697794	0.348897	+	0.937161i	$0.386556\pi$
$608$	−4.45762	−0.180780
$609$	−1.64359	−0.0666016
$610$	−9.63334	−0.390042
$611$	−23.1297	−0.935727
$612$	−0.246598	−0.00996812
$613$	18.9974	0.767299	0.383650	−	0.923479i	$-0.374667\pi$
$613$	18.9974	0.767299	0.383650	+	0.923479i	$0.374667\pi$
$614$	−29.6774	−1.19768
$615$	−4.10093	−0.165365
$616$	0.240369	0.00968473
$617$	−8.47109	−0.341033	−0.170517	−	0.985355i	$-0.554544\pi$
$617$	−8.47109	−0.341033	−0.170517	+	0.985355i	$0.554544\pi$
$618$	−12.1296	−0.487925
$619$	−3.00103	−0.120622	−0.0603108	−	0.998180i	$-0.519209\pi$
$619$	−3.00103	−0.120622	−0.0603108	+	0.998180i	$0.519209\pi$
$620$	−3.73835	−0.150136
$621$	−21.4118	−0.859227
$622$	−32.5439	−1.30489
$623$	1.25207	0.0501630
$624$	7.97900	0.319416
$625$	1.00000	0.0400000
$626$	−24.7026	−0.987316
$627$	−7.33293	−0.292849
$628$	−21.5382	−0.859467
$629$	0.210170	0.00838003
$630$	−0.00970263	−0.000386562 0
$631$	4.38170	0.174433	0.0872164	−	0.996189i	$-0.472203\pi$
$631$	4.38170	0.174433	0.0872164	+	0.996189i	$0.472203\pi$
$632$	1.05241	0.0418626
$633$	−40.7126	−1.61818
$634$	15.0511	0.597754
$635$	4.60869	0.182890
$636$	10.2826	0.407732
$637$	32.1630	1.27434
$638$	3.63090	0.143749
$639$	−0.453989	−0.0179595
$640$	−1.00000	−0.0395285
$641$	35.7017	1.41013	0.705066	−	0.709141i	$-0.250917\pi$
$641$	35.7017	1.41013	0.705066	+	0.709141i	$0.250917\pi$
$642$	−0.591461	−0.0233431
$643$	37.2179	1.46773	0.733866	−	0.679294i	$-0.237714\pi$
$643$	37.2179	1.46773	0.733866	+	0.679294i	$0.237714\pi$
$644$	1.02964	0.0405736
$645$	17.1811	0.676506
$646$	−28.4876	−1.12083
$647$	−6.19465	−0.243537	−0.121768	−	0.992559i	$-0.538857\pi$
$647$	−6.19465	−0.243537	−0.121768	+	0.992559i	$0.538857\pi$
$648$	8.88275	0.348947
$649$	11.9940	0.470805
$650$	4.63659	0.181862
$651$	−1.61764	−0.0634004
$652$	12.9269	0.506258
$653$	−10.9984	−0.430399	−0.215199	−	0.976570i	$-0.569040\pi$
$653$	−10.9984	−0.430399	−0.215199	+	0.976570i	$0.569040\pi$
$654$	33.3451	1.30390
$655$	0.728667	0.0284714
$656$	2.38305	0.0930424
$657$	−0.408442	−0.0159349
$658$	1.25437	0.0489003
$659$	33.2493	1.29521	0.647605	−	0.761976i	$-0.275771\pi$
$659$	33.2493	1.29521	0.647605	+	0.761976i	$0.275771\pi$
$660$	−1.64503	−0.0640328
$661$	−18.0177	−0.700807	−0.350403	−	0.936599i	$-0.613955\pi$
$661$	−18.0177	−0.700807	−0.350403	+	0.936599i	$0.613955\pi$
$662$	−5.27410	−0.204984
$663$	50.9920	1.98036
$664$	11.3928	0.442127
$665$	−1.12087	−0.0434656
$666$	0.00126898	4.91719e−5 0
$667$	15.5533	0.602227
$668$	3.89677	0.150771
$669$	5.45239	0.210802
$670$	0.0266179	0.00102834
$671$	9.20877	0.355500
$672$	−0.432716	−0.0166924
$673$	25.9985	1.00217	0.501085	−	0.865398i	$-0.332934\pi$
$673$	25.9985	1.00217	0.501085	+	0.865398i	$0.332934\pi$
$674$	5.10995	0.196828
$675$	5.22903	0.201265
$676$	8.49801	0.326847
$677$	−2.99870	−0.115249	−0.0576247	−	0.998338i	$-0.518353\pi$
$677$	−2.99870	−0.115249	−0.0576247	+	0.998338i	$0.518353\pi$
$678$	−21.9589	−0.843327
$679$	0.814375	0.0312528
$680$	−6.39077	−0.245075
$681$	−9.67199	−0.370632
$682$	3.57358	0.136840
$683$	−51.4746	−1.96962	−0.984810	−	0.173633i	$-0.944449\pi$
$683$	−51.4746	−1.96962	−0.984810	+	0.173633i	$0.944449\pi$
$684$	−0.172004	−0.00657675
$685$	−9.99220	−0.381782
$686$	−3.50442	−0.133799
$687$	1.89758	0.0723972
$688$	−9.98394	−0.380634
$689$	27.7046	1.05546
$690$	−7.04664	−0.268261
$691$	44.1496	1.67953	0.839765	−	0.542950i	$-0.182693\pi$
$691$	44.1496	1.67953	0.839765	+	0.542950i	$0.182693\pi$
$692$	15.0673	0.572773
$693$	0.00927500	0.000352328 0
$694$	−0.548757	−0.0208305
$695$	4.29748	0.163013
$696$	−6.53641	−0.247762
$697$	15.2295	0.576859
$698$	5.35023	0.202509
$699$	−26.7568	−1.01204
$700$	−0.251451	−0.00950396
$701$	−38.3872	−1.44986	−0.724932	−	0.688821i	$-0.758129\pi$
$701$	−38.3872	−1.44986	−0.724932	+	0.688821i	$0.758129\pi$
$702$	24.2449	0.915065
$703$	0.146596	0.00552897
$704$	0.955927	0.0360278
$705$	−8.58460	−0.323315
$706$	18.2614	0.687277
$707$	−1.58159	−0.0594819
$708$	−21.5918	−0.811469
$709$	−20.1179	−0.755542	−0.377771	−	0.925899i	$-0.623309\pi$
$709$	−20.1179	−0.755542	−0.377771	+	0.925899i	$0.623309\pi$
$710$	−11.7655	−0.441550
$711$	0.0406089	0.00152295
$712$	4.97937	0.186610
$713$	15.3078	0.573281
$714$	−2.76539	−0.103492
$715$	−4.43225	−0.165757
$716$	20.7639	0.775985
$717$	24.5122	0.915424
$718$	5.06667	0.189087
$719$	−22.2299	−0.829034	−0.414517	−	0.910041i	$-0.636050\pi$
$719$	−22.2299	−0.829034	−0.414517	+	0.910041i	$0.636050\pi$
$720$	−0.0385865	−0.00143804
$721$	1.77236	0.0660060
$722$	−0.870406	−0.0323931
$723$	−6.35167	−0.236221
$724$	−6.06988	−0.225585
$725$	−3.79831	−0.141066
$726$	−17.3571	−0.644183
$727$	−16.6536	−0.617648	−0.308824	−	0.951119i	$-0.599935\pi$
$727$	−16.6536	−0.617648	−0.308824	+	0.951119i	$0.599935\pi$
$728$	−1.16588	−0.0432103
$729$	27.3383	1.01253
$730$	−10.5851	−0.391772
$731$	−63.8051	−2.35992
$732$	−16.5778	−0.612732
$733$	−30.6252	−1.13117	−0.565583	−	0.824691i	$-0.691349\pi$
$733$	−30.6252	−1.13117	−0.565583	+	0.824691i	$0.691349\pi$
$734$	−19.0794	−0.704234
$735$	11.9373	0.440315
$736$	4.09480	0.150936
$737$	−0.0254448	−0.000937271 0
$738$	0.0919536	0.00338486
$739$	−30.6571	−1.12774	−0.563870	−	0.825863i	$-0.690688\pi$
$739$	−30.6571	−1.12774	−0.563870	+	0.825863i	$0.690688\pi$
$740$	0.0328865	0.00120893
$741$	35.5674	1.30660
$742$	−1.50247	−0.0551575
$743$	−7.58193	−0.278154	−0.139077	−	0.990282i	$-0.544414\pi$
$743$	−7.58193	−0.278154	−0.139077	+	0.990282i	$0.544414\pi$
$744$	−6.43323	−0.235854
$745$	−15.0272	−0.550552
$746$	11.9311	0.436829
$747$	0.439609	0.0160845
$748$	6.10910	0.223371
$749$	0.0864231	0.00315783
$750$	1.72088	0.0628375
$751$	53.9473	1.96857	0.984283	−	0.176600i	$-0.0565100\pi$
$751$	53.9473	1.96857	0.984283	+	0.176600i	$0.0565100\pi$
$752$	4.98851	0.181912
$753$	−32.9013	−1.19899
$754$	−17.6112	−0.641362
$755$	0.105684	0.00384623
$756$	−1.31485	−0.0478205
$757$	27.5401	1.00096	0.500481	−	0.865748i	$-0.333157\pi$
$757$	27.5401	1.00096	0.500481	+	0.865748i	$0.333157\pi$
$758$	7.32510	0.266060
$759$	6.73607	0.244504
$760$	−4.45762	−0.161695
$761$	−29.4997	−1.06936	−0.534682	−	0.845054i	$-0.679568\pi$
$761$	−29.4997	−1.06936	−0.534682	+	0.845054i	$0.679568\pi$
$762$	7.93098	0.287309
$763$	−4.87232	−0.176390
$764$	6.81186	0.246444
$765$	−0.246598	−0.00891575
$766$	−0.564290	−0.0203886
$767$	−58.1752	−2.10059
$768$	−1.72088	−0.0620968
$769$	−22.0129	−0.793804	−0.396902	−	0.917861i	$-0.629915\pi$
$769$	−22.0129	−0.793804	−0.396902	+	0.917861i	$0.629915\pi$
$770$	0.240369	0.00866229
$771$	−36.7156	−1.32228
$772$	18.4716	0.664807
$773$	−2.21833	−0.0797877	−0.0398938	−	0.999204i	$-0.512702\pi$
$773$	−2.21833	−0.0797877	−0.0398938	+	0.999204i	$0.512702\pi$
$774$	−0.385246	−0.0138474
$775$	−3.73835	−0.134285
$776$	3.23870	0.116263
$777$	0.0142305	0.000510517 0
$778$	27.4557	0.984333
$779$	10.6227	0.380599
$780$	7.97900	0.285694
$781$	11.2469	0.402447
$782$	26.1689	0.935798
$783$	−19.8615	−0.709791
$784$	−6.93677	−0.247742
$785$	−21.5382	−0.768730
$786$	1.25395	0.0447268
$787$	−5.11039	−0.182166	−0.0910828	−	0.995843i	$-0.529033\pi$
$787$	−5.11039	−0.182166	−0.0910828	+	0.995843i	$0.529033\pi$
$788$	−8.87189	−0.316048
$789$	14.5668	0.518591
$790$	1.05241	0.0374431
$791$	3.20859	0.114084
$792$	0.0368859	0.00131068
$793$	−44.6659	−1.58613
$794$	−16.7049	−0.592835
$795$	10.2826	0.364686
$796$	18.1568	0.643552
$797$	−26.6950	−0.945585	−0.472793	−	0.881174i	$-0.656754\pi$
$797$	−26.6950	−0.945585	−0.472793	+	0.881174i	$0.656754\pi$
$798$	−1.92888	−0.0682818
$799$	31.8804	1.12785
$800$	−1.00000	−0.0353553
$801$	0.192137	0.00678881
$802$	1.00000	0.0353112
$803$	10.1186	0.357077
$804$	0.0458061	0.00161546
$805$	1.02964	0.0362901
$806$	−17.3332	−0.610536
$807$	−24.9380	−0.877859
$808$	−6.28986	−0.221277
$809$	−22.1574	−0.779011	−0.389505	−	0.921024i	$-0.627354\pi$
$809$	−22.1574	−0.779011	−0.389505	+	0.921024i	$0.627354\pi$
$810$	8.88275	0.312108
$811$	3.66523	0.128704	0.0643519	−	0.997927i	$-0.479502\pi$
$811$	3.66523	0.128704	0.0643519	+	0.997927i	$0.479502\pi$
$812$	0.955088	0.0335170
$813$	−14.7797	−0.518345
$814$	−0.0314371	−0.00110187
$815$	12.9269	0.452811
$816$	−10.9977	−0.384997
$817$	−44.5047	−1.55702
$818$	−13.1409	−0.459460
$819$	−0.0449871	−0.00157198
$820$	2.38305	0.0832196
$821$	22.8918	0.798931	0.399465	−	0.916748i	$-0.369196\pi$
$821$	22.8918	0.798931	0.399465	+	0.916748i	$0.369196\pi$
$822$	−17.1953	−0.599756
$823$	42.9417	1.49685	0.748427	−	0.663217i	$-0.230810\pi$
$823$	42.9417	1.49685	0.748427	+	0.663217i	$0.230810\pi$
$824$	7.04852	0.245547
$825$	−1.64503	−0.0572726
$826$	3.15495	0.109775
$827$	−28.3807	−0.986893	−0.493446	−	0.869776i	$-0.664263\pi$
$827$	−28.3807	−0.986893	−0.493446	+	0.869776i	$0.664263\pi$
$828$	0.158004	0.00549102
$829$	−2.81073	−0.0976207	−0.0488104	−	0.998808i	$-0.515543\pi$
$829$	−2.81073	−0.0976207	−0.0488104	+	0.998808i	$0.515543\pi$
$830$	11.3928	0.395450
$831$	−48.9914	−1.69949
$832$	−4.63659	−0.160745
$833$	−44.3313	−1.53599
$834$	7.39543	0.256083
$835$	3.89677	0.134853
$836$	4.26116	0.147375
$837$	−19.5479	−0.675675
$838$	−27.8390	−0.961681
$839$	6.37781	0.220186	0.110093	−	0.993921i	$-0.464885\pi$
$839$	6.37781	0.220186	0.110093	+	0.993921i	$0.464885\pi$
$840$	−0.432716	−0.0149301
$841$	−14.5729	−0.502513
$842$	7.68508	0.264845
$843$	8.36547	0.288122
$844$	23.6581	0.814345
$845$	8.49801	0.292341
$846$	0.192489	0.00661792
$847$	2.53619	0.0871444
$848$	−5.97521	−0.205190
$849$	−28.8139	−0.988890
$850$	−6.39077	−0.219201
$851$	−0.134664	−0.00461622
$852$	−20.2469	−0.693648
$853$	−28.7790	−0.985375	−0.492688	−	0.870206i	$-0.663985\pi$
$853$	−28.7790	−0.985375	−0.492688	+	0.870206i	$0.663985\pi$
$854$	2.42231	0.0828898
$855$	−0.172004	−0.00588242
$856$	0.343698	0.0117473
$857$	−26.7038	−0.912185	−0.456093	−	0.889932i	$-0.650751\pi$
$857$	−26.7038	−0.912185	−0.456093	+	0.889932i	$0.650751\pi$
$858$	−7.62734	−0.260393
$859$	39.0910	1.33377	0.666884	−	0.745161i	$-0.267628\pi$
$859$	39.0910	1.33377	0.666884	+	0.745161i	$0.267628\pi$
$860$	−9.98394	−0.340450
$861$	1.03118	0.0351426
$862$	−23.3351	−0.794797
$863$	31.3556	1.06736	0.533679	−	0.845687i	$-0.320809\pi$
$863$	31.3556	1.06736	0.533679	+	0.845687i	$0.320809\pi$
$864$	−5.22903	−0.177895
$865$	15.0673	0.512304
$866$	−27.7749	−0.943829
$867$	−41.0289	−1.39342
$868$	0.940011	0.0319060
$869$	−1.00603	−0.0341271
$870$	−6.53641	−0.221605
$871$	0.123417	0.00418181
$872$	−19.3768	−0.656182
$873$	0.124970	0.00422960
$874$	18.2531	0.617420
$875$	−0.251451	−0.00850060
$876$	−18.2156	−0.615450
$877$	41.1469	1.38943	0.694717	−	0.719284i	$-0.255530\pi$
$877$	41.1469	1.38943	0.694717	+	0.719284i	$0.255530\pi$
$878$	−16.0403	−0.541335
$879$	−39.3439	−1.32704
$880$	0.955927	0.0322243
$881$	−38.6147	−1.30096	−0.650480	−	0.759523i	$-0.725432\pi$
$881$	−38.6147	−1.30096	−0.650480	+	0.759523i	$0.725432\pi$
$882$	−0.267666	−0.00901278
$883$	42.5148	1.43074	0.715369	−	0.698747i	$-0.246259\pi$
$883$	42.5148	1.43074	0.715369	+	0.698747i	$0.246259\pi$
$884$	−29.6314	−0.996612
$885$	−21.5918	−0.725800
$886$	19.1971	0.644938
$887$	−54.4876	−1.82951	−0.914757	−	0.404004i	$-0.867618\pi$
$887$	−54.4876	−1.82951	−0.914757	+	0.404004i	$0.867618\pi$
$888$	0.0565936	0.00189916
$889$	−1.15886	−0.0388669
$890$	4.97937	0.166909
$891$	−8.49126	−0.284468
$892$	−3.16838	−0.106085
$893$	22.2369	0.744129
$894$	−25.8599	−0.864883
$895$	20.7639	0.694062
$896$	0.251451	0.00840039
$897$	−32.6724	−1.09090
$898$	16.1602	0.539272
$899$	14.1994	0.473576
$900$	−0.0385865	−0.00128622
$901$	−38.1862	−1.27217
$902$	−2.27802	−0.0758497
$903$	−4.32021	−0.143768
$904$	12.7603	0.424402
$905$	−6.06988	−0.201770
$906$	0.181869	0.00604218
$907$	22.9719	0.762770	0.381385	−	0.924416i	$-0.375447\pi$
$907$	22.9719	0.762770	0.381385	+	0.924416i	$0.375447\pi$
$908$	5.62039	0.186519
$909$	−0.242704	−0.00804998
$910$	−1.16588	−0.0386484
$911$	−42.9479	−1.42293	−0.711464	−	0.702723i	$-0.751967\pi$
$911$	−42.9479	−1.42293	−0.711464	+	0.702723i	$0.751967\pi$
$912$	−7.67102	−0.254013
$913$	−10.8907	−0.360429
$914$	30.1267	0.996502
$915$	−16.5778	−0.548044
$916$	−1.10268	−0.0364337
$917$	−0.183224	−0.00605059
$918$	−33.4175	−1.10294
$919$	31.5988	1.04235	0.521174	−	0.853451i	$-0.325494\pi$
$919$	31.5988	1.04235	0.521174	+	0.853451i	$0.325494\pi$
$920$	4.09480	0.135002
$921$	−51.0711	−1.68285
$922$	21.5248	0.708883
$923$	−54.5518	−1.79559
$924$	0.413645	0.0136079
$925$	0.0328865	0.00108130
$926$	−8.21486	−0.269957
$927$	0.271978	0.00893293
$928$	3.79831	0.124686
$929$	37.0832	1.21666	0.608330	−	0.793685i	$-0.291840\pi$
$929$	37.0832	1.21666	0.608330	+	0.793685i	$0.291840\pi$
$930$	−6.43323	−0.210954
$931$	−30.9215	−1.01341
$932$	15.5484	0.509304
$933$	−56.0040	−1.83349
$934$	−11.1701	−0.365498
$935$	6.10910	0.199789
$936$	−0.178910	−0.00584786
$937$	24.4347	0.798245	0.399123	−	0.916898i	$-0.369315\pi$
$937$	24.4347	0.798245	0.399123	+	0.916898i	$0.369315\pi$
$938$	−0.00669310	−0.000218538 0
$939$	−42.5102	−1.38727
$940$	4.98851	0.162707
$941$	−32.7166	−1.06653	−0.533266	−	0.845948i	$-0.679036\pi$
$941$	−32.7166	−1.06653	−0.533266	+	0.845948i	$0.679036\pi$
$942$	−37.0645	−1.20763
$943$	−9.75811	−0.317768
$944$	12.5470	0.408369
$945$	−1.31485	−0.0427719
$946$	9.54392	0.310300
$947$	6.77219	0.220067	0.110033	−	0.993928i	$-0.464904\pi$
$947$	6.77219	0.220067	0.110033	+	0.993928i	$0.464904\pi$
$948$	1.81107	0.0588207
$949$	−49.0788	−1.59317
$950$	−4.45762	−0.144624
$951$	25.9010	0.839898
$952$	1.60696	0.0520820
$953$	30.3218	0.982218	0.491109	−	0.871098i	$-0.336592\pi$
$953$	30.3218	0.982218	0.491109	+	0.871098i	$0.336592\pi$
$954$	−0.230563	−0.00746475
$955$	6.81186	0.220427
$956$	−14.2440	−0.460684
$957$	6.24833	0.201980
$958$	−0.336640	−0.0108763
$959$	2.51255	0.0811344
$960$	−1.72088	−0.0555410
$961$	−17.0248	−0.549186
$962$	0.152482	0.00491620
$963$	0.0132621	0.000427365 0
$964$	3.69095	0.118878
$965$	18.4716	0.594622
$966$	1.77189	0.0570095
$967$	3.95483	0.127179	0.0635894	−	0.997976i	$-0.479745\pi$
$967$	3.95483	0.127179	0.0635894	+	0.997976i	$0.479745\pi$
$968$	10.0862	0.324183
$969$	−49.0237	−1.57487
$970$	3.23870	0.103988
$971$	8.49978	0.272771	0.136386	−	0.990656i	$-0.456451\pi$
$971$	8.49978	0.272771	0.136386	+	0.990656i	$0.456451\pi$
$972$	−0.400978	−0.0128614
$973$	−1.08061	−0.0346426
$974$	8.07204	0.258645
$975$	7.97900	0.255533
$976$	9.63334	0.308356
$977$	57.2939	1.83299	0.916497	−	0.400041i	$-0.131004\pi$
$977$	57.2939	1.83299	0.916497	+	0.400041i	$0.131004\pi$
$978$	22.2457	0.711338
$979$	−4.75991	−0.152127
$980$	−6.93677	−0.221587
$981$	−0.747685	−0.0238717
$982$	26.9316	0.859421
$983$	−17.1444	−0.546821	−0.273411	−	0.961897i	$-0.588152\pi$
$983$	−17.1444	−0.546821	−0.273411	+	0.961897i	$0.588152\pi$
$984$	4.10093	0.130733
$985$	−8.87189	−0.282682
$986$	24.2741	0.773045
$987$	2.15861	0.0687092
$988$	−20.6682	−0.657543
$989$	40.8823	1.29998
$990$	0.0368859	0.00117231
$991$	−55.1667	−1.75243	−0.876214	−	0.481922i	$-0.839939\pi$
$991$	−55.1667	−1.75243	−0.876214	+	0.481922i	$0.839939\pi$
$992$	3.73835	0.118693
$993$	−9.07607	−0.288020
$994$	2.95844	0.0938361
$995$	18.1568	0.575610
$996$	19.6056	0.621228
$997$	−37.0910	−1.17468	−0.587342	−	0.809339i	$-0.699826\pi$
$997$	−37.0910	−1.17468	−0.587342	+	0.809339i	$0.699826\pi$
$998$	16.5565	0.524086
$999$	0.171965	0.00544072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.6	✓	20	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.72088 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.72088 q^{6} -0.251451 q^{7} -1.00000 q^{8} -0.0385865 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.72088 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.72088 q^{6} -0.251451 q^{7} -1.00000 q^{8} -0.0385865 q^{9} -1.00000 q^{10} +0.955927 q^{11} -1.72088 q^{12} -4.63659 q^{13} +0.251451 q^{14} -1.72088 q^{15} +1.00000 q^{16} +6.39077 q^{17} +0.0385865 q^{18} +4.45762 q^{19} +1.00000 q^{20} +0.432716 q^{21} -0.955927 q^{22} -4.09480 q^{23} +1.72088 q^{24} +1.00000 q^{25} +4.63659 q^{26} +5.22903 q^{27} -0.251451 q^{28} -3.79831 q^{29} +1.72088 q^{30} -3.73835 q^{31} -1.00000 q^{32} -1.64503 q^{33} -6.39077 q^{34} -0.251451 q^{35} -0.0385865 q^{36} +0.0328865 q^{37} -4.45762 q^{38} +7.97900 q^{39} -1.00000 q^{40} +2.38305 q^{41} -0.432716 q^{42} -9.98394 q^{43} +0.955927 q^{44} -0.0385865 q^{45} +4.09480 q^{46} +4.98851 q^{47} -1.72088 q^{48} -6.93677 q^{49} -1.00000 q^{50} -10.9977 q^{51} -4.63659 q^{52} -5.97521 q^{53} -5.22903 q^{54} +0.955927 q^{55} +0.251451 q^{56} -7.67102 q^{57} +3.79831 q^{58} +12.5470 q^{59} -1.72088 q^{60} +9.63334 q^{61} +3.73835 q^{62} +0.00970263 q^{63} +1.00000 q^{64} -4.63659 q^{65} +1.64503 q^{66} -0.0266179 q^{67} +6.39077 q^{68} +7.04664 q^{69} +0.251451 q^{70} +11.7655 q^{71} +0.0385865 q^{72} +10.5851 q^{73} -0.0328865 q^{74} -1.72088 q^{75} +4.45762 q^{76} -0.240369 q^{77} -7.97900 q^{78} -1.05241 q^{79} +1.00000 q^{80} -8.88275 q^{81} -2.38305 q^{82} -11.3928 q^{83} +0.432716 q^{84} +6.39077 q^{85} +9.98394 q^{86} +6.53641 q^{87} -0.955927 q^{88} -4.97937 q^{89} +0.0385865 q^{90} +1.16588 q^{91} -4.09480 q^{92} +6.43323 q^{93} -4.98851 q^{94} +4.45762 q^{95} +1.72088 q^{96} -3.23870 q^{97} +6.93677 q^{98} -0.0368859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * q^99

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