LMFDB - Embedded newform 4026.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.7537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 4x + 3 $ x^4 - x^3 - 5x^2 + 4x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.37933$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.09744 q^{5} -1.00000 q^{6} +1.89307 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.09744 q^{5} -1.00000 q^{6} +1.89307 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.09744 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.23184 q^{13} -1.89307 q^{14} +1.09744 q^{15} +1.00000 q^{16} -0.681143 q^{17} -1.00000 q^{18} -1.28190 q^{19} +1.09744 q^{20} +1.89307 q^{21} +1.00000 q^{22} -5.26291 q^{23} -1.00000 q^{24} -3.79563 q^{25} +2.23184 q^{26} +1.00000 q^{27} +1.89307 q^{28} -3.13440 q^{29} -1.09744 q^{30} -7.33288 q^{31} -1.00000 q^{32} -1.00000 q^{33} +0.681143 q^{34} +2.07752 q^{35} +1.00000 q^{36} -9.82670 q^{37} +1.28190 q^{38} -2.23184 q^{39} -1.09744 q^{40} +1.24493 q^{41} -1.89307 q^{42} -9.93363 q^{43} -1.00000 q^{44} +1.09744 q^{45} +5.26291 q^{46} +7.93003 q^{47} +1.00000 q^{48} -3.41630 q^{49} +3.79563 q^{50} -0.681143 q^{51} -2.23184 q^{52} +1.56472 q^{53} -1.00000 q^{54} -1.09744 q^{55} -1.89307 q^{56} -1.28190 q^{57} +3.13440 q^{58} -4.96396 q^{59} +1.09744 q^{60} +1.00000 q^{61} +7.33288 q^{62} +1.89307 q^{63} +1.00000 q^{64} -2.44930 q^{65} +1.00000 q^{66} +0.379334 q^{67} -0.681143 q^{68} -5.26291 q^{69} -2.07752 q^{70} -4.64813 q^{71} -1.00000 q^{72} -9.94800 q^{73} +9.82670 q^{74} -3.79563 q^{75} -1.28190 q^{76} -1.89307 q^{77} +2.23184 q^{78} -2.17690 q^{79} +1.09744 q^{80} +1.00000 q^{81} -1.24493 q^{82} -0.375732 q^{83} +1.89307 q^{84} -0.747512 q^{85} +9.93363 q^{86} -3.13440 q^{87} +1.00000 q^{88} +12.4009 q^{89} -1.09744 q^{90} -4.22502 q^{91} -5.26291 q^{92} -7.33288 q^{93} -7.93003 q^{94} -1.40680 q^{95} -1.00000 q^{96} +3.48793 q^{97} +3.41630 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} - q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + q^{15} + 4 q^{16} - 3 q^{17} - 4 q^{18} - 4 q^{19} + q^{20} - 4 q^{21} + 4 q^{22} + 10 q^{23} - 4 q^{24} - 7 q^{25} + 3 q^{26} + 4 q^{27} - 4 q^{28} - 10 q^{29} - q^{30} - 9 q^{31} - 4 q^{32} - 4 q^{33} + 3 q^{34} - q^{35} + 4 q^{36} - 6 q^{37} + 4 q^{38} - 3 q^{39} - q^{40} + 3 q^{41} + 4 q^{42} - 18 q^{43} - 4 q^{44} + q^{45} - 10 q^{46} + 21 q^{47} + 4 q^{48} - 10 q^{49} + 7 q^{50} - 3 q^{51} - 3 q^{52} - 20 q^{53} - 4 q^{54} - q^{55} + 4 q^{56} - 4 q^{57} + 10 q^{58} + 5 q^{59} + q^{60} + 4 q^{61} + 9 q^{62} - 4 q^{63} + 4 q^{64} - 16 q^{65} + 4 q^{66} - 3 q^{67} - 3 q^{68} + 10 q^{69} + q^{70} - 9 q^{71} - 4 q^{72} + 6 q^{74} - 7 q^{75} - 4 q^{76} + 4 q^{77} + 3 q^{78} - 31 q^{79} + q^{80} + 4 q^{81} - 3 q^{82} - 8 q^{83} - 4 q^{84} - 25 q^{85} + 18 q^{86} - 10 q^{87} + 4 q^{88} + 5 q^{89} - q^{90} - 9 q^{91} + 10 q^{92} - 9 q^{93} - 21 q^{94} + 13 q^{95} - 4 q^{96} - 25 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 - q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + q^15 + 4 * q^16 - 3 * q^17 - 4 * q^18 - 4 * q^19 + q^20 - 4 * q^21 + 4 * q^22 + 10 * q^23 - 4 * q^24 - 7 * q^25 + 3 * q^26 + 4 * q^27 - 4 * q^28 - 10 * q^29 - q^30 - 9 * q^31 - 4 * q^32 - 4 * q^33 + 3 * q^34 - q^35 + 4 * q^36 - 6 * q^37 + 4 * q^38 - 3 * q^39 - q^40 + 3 * q^41 + 4 * q^42 - 18 * q^43 - 4 * q^44 + q^45 - 10 * q^46 + 21 * q^47 + 4 * q^48 - 10 * q^49 + 7 * q^50 - 3 * q^51 - 3 * q^52 - 20 * q^53 - 4 * q^54 - q^55 + 4 * q^56 - 4 * q^57 + 10 * q^58 + 5 * q^59 + q^60 + 4 * q^61 + 9 * q^62 - 4 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 - 3 * q^67 - 3 * q^68 + 10 * q^69 + q^70 - 9 * q^71 - 4 * q^72 + 6 * q^74 - 7 * q^75 - 4 * q^76 + 4 * q^77 + 3 * q^78 - 31 * q^79 + q^80 + 4 * q^81 - 3 * q^82 - 8 * q^83 - 4 * q^84 - 25 * q^85 + 18 * q^86 - 10 * q^87 + 4 * q^88 + 5 * q^89 - q^90 - 9 * q^91 + 10 * q^92 - 9 * q^93 - 21 * q^94 + 13 * q^95 - 4 * q^96 - 25 * q^97 + 10 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.09744	0.490789	0.245395	−	0.969423i	$-0.421082\pi$
$5$	1.09744	0.490789	0.245395	+	0.969423i	$0.421082\pi$
$6$	−1.00000	−0.408248
$7$	1.89307	0.715512	0.357756	−	0.933815i	$-0.383542\pi$
$7$	1.89307	0.715512	0.357756	+	0.933815i	$0.383542\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.09744	−0.347040
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−2.23184	−0.619001	−0.309500	−	0.950899i	$-0.600162\pi$
$13$	−2.23184	−0.619001	−0.309500	+	0.950899i	$0.600162\pi$
$14$	−1.89307	−0.505944
$15$	1.09744	0.283357
$16$	1.00000	0.250000
$17$	−0.681143	−0.165201	−0.0826007	−	0.996583i	$-0.526323\pi$
$17$	−0.681143	−0.165201	−0.0826007	+	0.996583i	$0.526323\pi$
$18$	−1.00000	−0.235702
$19$	−1.28190	−0.294087	−0.147044	−	0.989130i	$-0.546976\pi$
$19$	−1.28190	−0.294087	−0.147044	+	0.989130i	$0.546976\pi$
$20$	1.09744	0.245395
$21$	1.89307	0.413101
$22$	1.00000	0.213201
$23$	−5.26291	−1.09739	−0.548696	−	0.836022i	$-0.684876\pi$
$23$	−5.26291	−1.09739	−0.548696	+	0.836022i	$0.684876\pi$
$24$	−1.00000	−0.204124
$25$	−3.79563	−0.759126
$26$	2.23184	0.437699
$27$	1.00000	0.192450
$28$	1.89307	0.357756
$29$	−3.13440	−0.582043	−0.291022	−	0.956716i	$-0.593995\pi$
$29$	−3.13440	−0.582043	−0.291022	+	0.956716i	$0.593995\pi$
$30$	−1.09744	−0.200364
$31$	−7.33288	−1.31702	−0.658512	−	0.752570i	$-0.728814\pi$
$31$	−7.33288	−1.31702	−0.658512	+	0.752570i	$0.728814\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	0.681143	0.116815
$35$	2.07752	0.351166
$36$	1.00000	0.166667
$37$	−9.82670	−1.61550	−0.807750	−	0.589526i	$-0.799315\pi$
$37$	−9.82670	−1.61550	−0.807750	+	0.589526i	$0.799315\pi$
$38$	1.28190	0.207951
$39$	−2.23184	−0.357380
$40$	−1.09744	−0.173520
$41$	1.24493	0.194426	0.0972130	−	0.995264i	$-0.469007\pi$
$41$	1.24493	0.194426	0.0972130	+	0.995264i	$0.469007\pi$
$42$	−1.89307	−0.292107
$43$	−9.93363	−1.51486	−0.757432	−	0.652914i	$-0.773546\pi$
$43$	−9.93363	−1.51486	−0.757432	+	0.652914i	$0.773546\pi$
$44$	−1.00000	−0.150756
$45$	1.09744	0.163596
$46$	5.26291	0.775973
$47$	7.93003	1.15671	0.578357	−	0.815784i	$-0.303694\pi$
$47$	7.93003	1.15671	0.578357	+	0.815784i	$0.303694\pi$
$48$	1.00000	0.144338
$49$	−3.41630	−0.488042
$50$	3.79563	0.536783
$51$	−0.681143	−0.0953791
$52$	−2.23184	−0.309500
$53$	1.56472	0.214930	0.107465	−	0.994209i	$-0.465727\pi$
$53$	1.56472	0.214930	0.107465	+	0.994209i	$0.465727\pi$
$54$	−1.00000	−0.136083
$55$	−1.09744	−0.147979
$56$	−1.89307	−0.252972
$57$	−1.28190	−0.169791
$58$	3.13440	0.411567
$59$	−4.96396	−0.646253	−0.323126	−	0.946356i	$-0.604734\pi$
$59$	−4.96396	−0.646253	−0.323126	+	0.946356i	$0.604734\pi$
$60$	1.09744	0.141679
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	7.33288	0.931276
$63$	1.89307	0.238504
$64$	1.00000	0.125000
$65$	−2.44930	−0.303799
$66$	1.00000	0.123091
$67$	0.379334	0.0463430	0.0231715	−	0.999732i	$-0.492624\pi$
$67$	0.379334	0.0463430	0.0231715	+	0.999732i	$0.492624\pi$
$68$	−0.681143	−0.0826007
$69$	−5.26291	−0.633580
$70$	−2.07752	−0.248312
$71$	−4.64813	−0.551632	−0.275816	−	0.961210i	$-0.588948\pi$
$71$	−4.64813	−0.551632	−0.275816	+	0.961210i	$0.588948\pi$
$72$	−1.00000	−0.117851
$73$	−9.94800	−1.16433	−0.582163	−	0.813072i	$-0.697793\pi$
$73$	−9.94800	−1.16433	−0.582163	+	0.813072i	$0.697793\pi$
$74$	9.82670	1.14233
$75$	−3.79563	−0.438282
$76$	−1.28190	−0.147044
$77$	−1.89307	−0.215735
$78$	2.23184	0.252706
$79$	−2.17690	−0.244921	−0.122460	−	0.992473i	$-0.539078\pi$
$79$	−2.17690	−0.244921	−0.122460	+	0.992473i	$0.539078\pi$
$80$	1.09744	0.122697
$81$	1.00000	0.111111
$82$	−1.24493	−0.137480
$83$	−0.375732	−0.0412420	−0.0206210	−	0.999787i	$-0.506564\pi$
$83$	−0.375732	−0.0412420	−0.0206210	+	0.999787i	$0.506564\pi$
$84$	1.89307	0.206551
$85$	−0.747512	−0.0810791
$86$	9.93363	1.07117
$87$	−3.13440	−0.336043
$88$	1.00000	0.106600
$89$	12.4009	1.31449	0.657247	−	0.753675i	$-0.271721\pi$
$89$	12.4009	1.31449	0.657247	+	0.753675i	$0.271721\pi$
$90$	−1.09744	−0.115680
$91$	−4.22502	−0.442902
$92$	−5.26291	−0.548696
$93$	−7.33288	−0.760384
$94$	−7.93003	−0.817920
$95$	−1.40680	−0.144335
$96$	−1.00000	−0.102062
$97$	3.48793	0.354145	0.177073	−	0.984198i	$-0.443337\pi$
$97$	3.48793	0.354145	0.177073	+	0.984198i	$0.443337\pi$
$98$	3.41630	0.345098
$99$	−1.00000	−0.100504
$100$	−3.79563	−0.379563
$101$	−11.0045	−1.09499	−0.547496	−	0.836809i	$-0.684419\pi$
$101$	−11.0045	−1.09499	−0.547496	+	0.836809i	$0.684419\pi$
$102$	0.681143	0.0674432
$103$	16.9457	1.66971	0.834855	−	0.550470i	$-0.185551\pi$
$103$	16.9457	1.66971	0.834855	+	0.550470i	$0.185551\pi$
$104$	2.23184	0.218850
$105$	2.07752	0.202746
$106$	−1.56472	−0.151979
$107$	−3.69424	−0.357136	−0.178568	−	0.983928i	$-0.557146\pi$
$107$	−3.69424	−0.357136	−0.178568	+	0.983928i	$0.557146\pi$
$108$	1.00000	0.0962250
$109$	−0.250827	−0.0240248	−0.0120124	−	0.999928i	$-0.503824\pi$
$109$	−0.250827	−0.0240248	−0.0120124	+	0.999928i	$0.503824\pi$
$110$	1.09744	0.104637
$111$	−9.82670	−0.932709
$112$	1.89307	0.178878
$113$	3.17496	0.298675	0.149338	−	0.988786i	$-0.452286\pi$
$113$	3.17496	0.298675	0.149338	+	0.988786i	$0.452286\pi$
$114$	1.28190	0.120061
$115$	−5.77572	−0.538588
$116$	−3.13440	−0.291022
$117$	−2.23184	−0.206334
$118$	4.96396	0.456970
$119$	−1.28945	−0.118204
$120$	−1.09744	−0.100182
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	1.24493	0.112252
$124$	−7.33288	−0.658512
$125$	−9.65266	−0.863360
$126$	−1.89307	−0.168648
$127$	−15.3189	−1.35933	−0.679664	−	0.733523i	$-0.737875\pi$
$127$	−15.3189	−1.35933	−0.679664	+	0.733523i	$0.737875\pi$
$128$	−1.00000	−0.0883883
$129$	−9.93363	−0.874607
$130$	2.44930	0.214818
$131$	3.97346	0.347163	0.173581	−	0.984820i	$-0.444466\pi$
$131$	3.97346	0.347163	0.173581	+	0.984820i	$0.444466\pi$
$132$	−1.00000	−0.0870388
$133$	−2.42671	−0.210423
$134$	−0.379334	−0.0327694
$135$	1.09744	0.0944524
$136$	0.681143	0.0584075
$137$	20.7171	1.76998	0.884990	−	0.465610i	$-0.154165\pi$
$137$	20.7171	1.76998	0.884990	+	0.465610i	$0.154165\pi$
$138$	5.26291	0.448008
$139$	−8.52683	−0.723236	−0.361618	−	0.932326i	$-0.617776\pi$
$139$	−8.52683	−0.723236	−0.361618	+	0.932326i	$0.617776\pi$
$140$	2.07752	0.175583
$141$	7.93003	0.667829
$142$	4.64813	0.390063
$143$	2.23184	0.186636
$144$	1.00000	0.0833333
$145$	−3.43981	−0.285661
$146$	9.94800	0.823303
$147$	−3.41630	−0.281771
$148$	−9.82670	−0.807750
$149$	−9.78974	−0.802006	−0.401003	−	0.916077i	$-0.631338\pi$
$149$	−9.78974	−0.802006	−0.401003	+	0.916077i	$0.631338\pi$
$150$	3.79563	0.309912
$151$	22.1720	1.80433	0.902166	−	0.431389i	$-0.141976\pi$
$151$	22.1720	1.80433	0.902166	+	0.431389i	$0.141976\pi$
$152$	1.28190	0.103975
$153$	−0.681143	−0.0550671
$154$	1.89307	0.152548
$155$	−8.04738	−0.646381
$156$	−2.23184	−0.178690
$157$	15.6053	1.24544	0.622718	−	0.782446i	$-0.286028\pi$
$157$	15.6053	1.24544	0.622718	+	0.782446i	$0.286028\pi$
$158$	2.17690	0.173185
$159$	1.56472	0.124090
$160$	−1.09744	−0.0867601
$161$	−9.96304	−0.785197
$162$	−1.00000	−0.0785674
$163$	11.8002	0.924260	0.462130	−	0.886812i	$-0.347085\pi$
$163$	11.8002	0.924260	0.462130	+	0.886812i	$0.347085\pi$
$164$	1.24493	0.0972130
$165$	−1.09744	−0.0854355
$166$	0.375732	0.0291625
$167$	4.59218	0.355354	0.177677	−	0.984089i	$-0.443142\pi$
$167$	4.59218	0.355354	0.177677	+	0.984089i	$0.443142\pi$
$168$	−1.89307	−0.146053
$169$	−8.01890	−0.616838
$170$	0.747512	0.0573316
$171$	−1.28190	−0.0980290
$172$	−9.93363	−0.757432
$173$	8.67257	0.659364	0.329682	−	0.944092i	$-0.393059\pi$
$173$	8.67257	0.659364	0.329682	+	0.944092i	$0.393059\pi$
$174$	3.13440	0.237618
$175$	−7.18538	−0.543164
$176$	−1.00000	−0.0753778
$177$	−4.96396	−0.373114
$178$	−12.4009	−0.929487
$179$	4.70954	0.352007	0.176004	−	0.984390i	$-0.443683\pi$
$179$	4.70954	0.352007	0.176004	+	0.984390i	$0.443683\pi$
$180$	1.09744	0.0817982
$181$	25.0480	1.86181	0.930903	−	0.365268i	$-0.119022\pi$
$181$	25.0480	1.86181	0.930903	+	0.365268i	$0.119022\pi$
$182$	4.22502	0.313179
$183$	1.00000	0.0739221
$184$	5.26291	0.387987
$185$	−10.7842	−0.792870
$186$	7.33288	0.537673
$187$	0.681143	0.0498101
$188$	7.93003	0.578357
$189$	1.89307	0.137700
$190$	1.40680	0.102060
$191$	11.1194	0.804569	0.402284	−	0.915515i	$-0.368216\pi$
$191$	11.1194	0.804569	0.402284	+	0.915515i	$0.368216\pi$
$192$	1.00000	0.0721688
$193$	−22.9582	−1.65257	−0.826285	−	0.563252i	$-0.809550\pi$
$193$	−22.9582	−1.65257	−0.826285	+	0.563252i	$0.809550\pi$
$194$	−3.48793	−0.250419
$195$	−2.44930	−0.175398
$196$	−3.41630	−0.244021
$197$	22.7688	1.62221	0.811105	−	0.584900i	$-0.198866\pi$
$197$	22.7688	1.62221	0.811105	+	0.584900i	$0.198866\pi$
$198$	1.00000	0.0710669
$199$	23.2106	1.64535	0.822676	−	0.568510i	$-0.192480\pi$
$199$	23.2106	1.64535	0.822676	+	0.568510i	$0.192480\pi$
$200$	3.79563	0.268392
$201$	0.379334	0.0267561
$202$	11.0045	0.774276
$203$	−5.93363	−0.416459
$204$	−0.681143	−0.0476895
$205$	1.36624	0.0954222
$206$	−16.9457	−1.18066
$207$	−5.26291	−0.365797
$208$	−2.23184	−0.154750
$209$	1.28190	0.0886706
$210$	−2.07752	−0.143363
$211$	−20.7135	−1.42598	−0.712988	−	0.701177i	$-0.752658\pi$
$211$	−20.7135	−1.42598	−0.712988	+	0.701177i	$0.752658\pi$
$212$	1.56472	0.107465
$213$	−4.64813	−0.318485
$214$	3.69424	0.252533
$215$	−10.9015	−0.743479
$216$	−1.00000	−0.0680414
$217$	−13.8816	−0.942347
$218$	0.250827	0.0169881
$219$	−9.94800	−0.672224
$220$	−1.09744	−0.0739893
$221$	1.52020	0.102260
$222$	9.82670	0.659525
$223$	−18.7681	−1.25680	−0.628402	−	0.777889i	$-0.716290\pi$
$223$	−18.7681	−1.25680	−0.628402	+	0.777889i	$0.716290\pi$
$224$	−1.89307	−0.126486
$225$	−3.79563	−0.253042
$226$	−3.17496	−0.211195
$227$	−9.21553	−0.611656	−0.305828	−	0.952087i	$-0.598933\pi$
$227$	−9.21553	−0.611656	−0.305828	+	0.952087i	$0.598933\pi$
$228$	−1.28190	−0.0848956
$229$	−20.5664	−1.35906	−0.679532	−	0.733646i	$-0.737817\pi$
$229$	−20.5664	−1.35906	−0.679532	+	0.733646i	$0.737817\pi$
$230$	5.77572	0.380839
$231$	−1.89307	−0.124555
$232$	3.13440	0.205783
$233$	22.7946	1.49332	0.746662	−	0.665203i	$-0.231655\pi$
$233$	22.7946	1.49332	0.746662	+	0.665203i	$0.231655\pi$
$234$	2.23184	0.145900
$235$	8.70272	0.567703
$236$	−4.96396	−0.323126
$237$	−2.17690	−0.141405
$238$	1.28945	0.0835826
$239$	−16.3629	−1.05843	−0.529215	−	0.848488i	$-0.677514\pi$
$239$	−16.3629	−1.05843	−0.529215	+	0.848488i	$0.677514\pi$
$240$	1.09744	0.0708393
$241$	19.8816	1.28069	0.640344	−	0.768088i	$-0.278792\pi$
$241$	19.8816	1.28069	0.640344	+	0.768088i	$0.278792\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	−3.74917	−0.239526
$246$	−1.24493	−0.0793741
$247$	2.86098	0.182040
$248$	7.33288	0.465638
$249$	−0.375732	−0.0238111
$250$	9.65266	0.610488
$251$	27.2397	1.71935	0.859677	−	0.510838i	$-0.170665\pi$
$251$	27.2397	1.71935	0.859677	+	0.510838i	$0.170665\pi$
$252$	1.89307	0.119252
$253$	5.26291	0.330876
$254$	15.3189	0.961191
$255$	−0.747512	−0.0468110
$256$	1.00000	0.0625000
$257$	−11.4500	−0.714228	−0.357114	−	0.934061i	$-0.616239\pi$
$257$	−11.4500	−0.714228	−0.357114	+	0.934061i	$0.616239\pi$
$258$	9.93363	0.618441
$259$	−18.6026	−1.15591
$260$	−2.44930	−0.151899
$261$	−3.13440	−0.194014
$262$	−3.97346	−0.245481
$263$	−3.56545	−0.219855	−0.109928	−	0.993940i	$-0.535062\pi$
$263$	−3.56545	−0.219855	−0.109928	+	0.993940i	$0.535062\pi$
$264$	1.00000	0.0615457
$265$	1.71718	0.105485
$266$	2.42671	0.148791
$267$	12.4009	0.758923
$268$	0.379334	0.0231715
$269$	−1.21874	−0.0743080	−0.0371540	−	0.999310i	$-0.511829\pi$
$269$	−1.21874	−0.0743080	−0.0371540	+	0.999310i	$0.511829\pi$
$270$	−1.09744	−0.0667880
$271$	−12.5513	−0.762435	−0.381218	−	0.924485i	$-0.624495\pi$
$271$	−12.5513	−0.762435	−0.381218	+	0.924485i	$0.624495\pi$
$272$	−0.681143	−0.0413004
$273$	−4.22502	−0.255710
$274$	−20.7171	−1.25157
$275$	3.79563	0.228885
$276$	−5.26291	−0.316790
$277$	−15.9781	−0.960034	−0.480017	−	0.877259i	$-0.659369\pi$
$277$	−15.9781	−0.960034	−0.480017	+	0.877259i	$0.659369\pi$
$278$	8.52683	0.511405
$279$	−7.33288	−0.439008
$280$	−2.07752	−0.124156
$281$	−21.3516	−1.27373	−0.636864	−	0.770976i	$-0.719769\pi$
$281$	−21.3516	−1.27373	−0.636864	+	0.770976i	$0.719769\pi$
$282$	−7.93003	−0.472226
$283$	10.1285	0.602077	0.301039	−	0.953612i	$-0.402667\pi$
$283$	10.1285	0.602077	0.301039	+	0.953612i	$0.402667\pi$
$284$	−4.64813	−0.275816
$285$	−1.40680	−0.0833317
$286$	−2.23184	−0.131971
$287$	2.35674	0.139114
$288$	−1.00000	−0.0589256
$289$	−16.5360	−0.972708
$290$	3.43981	0.201993
$291$	3.48793	0.204466
$292$	−9.94800	−0.582163
$293$	14.3894	0.840638	0.420319	−	0.907376i	$-0.361918\pi$
$293$	14.3894	0.840638	0.420319	+	0.907376i	$0.361918\pi$
$294$	3.41630	0.199242
$295$	−5.44764	−0.317174
$296$	9.82670	0.571165
$297$	−1.00000	−0.0580259
$298$	9.78974	0.567104
$299$	11.7460	0.679286
$300$	−3.79563	−0.219141
$301$	−18.8050	−1.08390
$302$	−22.1720	−1.27586
$303$	−11.0045	−0.632194
$304$	−1.28190	−0.0735218
$305$	1.09744	0.0628391
$306$	0.681143	0.0389383
$307$	−6.97900	−0.398313	−0.199156	−	0.979968i	$-0.563820\pi$
$307$	−6.97900	−0.398313	−0.199156	+	0.979968i	$0.563820\pi$
$308$	−1.89307	−0.107868
$309$	16.9457	0.964008
$310$	8.04738	0.457061
$311$	32.4526	1.84022	0.920110	−	0.391660i	$-0.128099\pi$
$311$	32.4526	1.84022	0.920110	+	0.391660i	$0.128099\pi$
$312$	2.23184	0.126353
$313$	−1.57689	−0.0891309	−0.0445655	−	0.999006i	$-0.514190\pi$
$313$	−1.57689	−0.0891309	−0.0445655	+	0.999006i	$0.514190\pi$
$314$	−15.6053	−0.880657
$315$	2.07752	0.117055
$316$	−2.17690	−0.122460
$317$	−0.766221	−0.0430353	−0.0215176	−	0.999768i	$-0.506850\pi$
$317$	−0.766221	−0.0430353	−0.0215176	+	0.999768i	$0.506850\pi$
$318$	−1.56472	−0.0877449
$319$	3.13440	0.175493
$320$	1.09744	0.0613487
$321$	−3.69424	−0.206192
$322$	9.96304	0.555218
$323$	0.873154	0.0485836
$324$	1.00000	0.0555556
$325$	8.47123	0.469899
$326$	−11.8002	−0.653550
$327$	−0.250827	−0.0138707
$328$	−1.24493	−0.0687400
$329$	15.0121	0.827643
$330$	1.09744	0.0604120
$331$	−5.64686	−0.310379	−0.155190	−	0.987885i	$-0.549599\pi$
$331$	−5.64686	−0.310379	−0.155190	+	0.987885i	$0.549599\pi$
$332$	−0.375732	−0.0206210
$333$	−9.82670	−0.538500
$334$	−4.59218	−0.251273
$335$	0.416295	0.0227446
$336$	1.89307	0.103275
$337$	17.9620	0.978454	0.489227	−	0.872157i	$-0.337279\pi$
$337$	17.9620	0.978454	0.489227	+	0.872157i	$0.337279\pi$
$338$	8.01890	0.436171
$339$	3.17496	0.172440
$340$	−0.747512	−0.0405395
$341$	7.33288	0.397098
$342$	1.28190	0.0693170
$343$	−19.7188	−1.06471
$344$	9.93363	0.535585
$345$	−5.77572	−0.310954
$346$	−8.67257	−0.466240
$347$	12.4217	0.666834	0.333417	−	0.942779i	$-0.391798\pi$
$347$	12.4217	0.666834	0.333417	+	0.942779i	$0.391798\pi$
$348$	−3.13440	−0.168021
$349$	−13.9412	−0.746254	−0.373127	−	0.927780i	$-0.621715\pi$
$349$	−13.9412	−0.746254	−0.373127	+	0.927780i	$0.621715\pi$
$350$	7.18538	0.384075
$351$	−2.23184	−0.119127
$352$	1.00000	0.0533002
$353$	22.6367	1.20483	0.602415	−	0.798183i	$-0.294205\pi$
$353$	22.6367	1.20483	0.602415	+	0.798183i	$0.294205\pi$
$354$	4.96396	0.263832
$355$	−5.10104	−0.270735
$356$	12.4009	0.657247
$357$	−1.28945	−0.0682449
$358$	−4.70954	−0.248907
$359$	−30.6791	−1.61918	−0.809591	−	0.586995i	$-0.800311\pi$
$359$	−30.6791	−1.61918	−0.809591	+	0.586995i	$0.800311\pi$
$360$	−1.09744	−0.0578401
$361$	−17.3567	−0.913513
$362$	−25.0480	−1.31650
$363$	1.00000	0.0524864
$364$	−4.22502	−0.221451
$365$	−10.9173	−0.571439
$366$	−1.00000	−0.0522708
$367$	3.41177	0.178093	0.0890464	−	0.996027i	$-0.471618\pi$
$367$	3.41177	0.178093	0.0890464	+	0.996027i	$0.471618\pi$
$368$	−5.26291	−0.274348
$369$	1.24493	0.0648087
$370$	10.7842	0.560644
$371$	2.96211	0.153785
$372$	−7.33288	−0.380192
$373$	−36.5324	−1.89157	−0.945787	−	0.324788i	$-0.894707\pi$
$373$	−36.5324	−1.89157	−0.945787	+	0.324788i	$0.894707\pi$
$374$	−0.681143	−0.0352211
$375$	−9.65266	−0.498461
$376$	−7.93003	−0.408960
$377$	6.99547	0.360285
$378$	−1.89307	−0.0973689
$379$	12.3952	0.636699	0.318349	−	0.947973i	$-0.396871\pi$
$379$	12.3952	0.636699	0.318349	+	0.947973i	$0.396871\pi$
$380$	−1.40680	−0.0721674
$381$	−15.3189	−0.784809
$382$	−11.1194	−0.568916
$383$	−26.4615	−1.35212	−0.676061	−	0.736846i	$-0.736314\pi$
$383$	−26.4615	−1.35212	−0.676061	+	0.736846i	$0.736314\pi$
$384$	−1.00000	−0.0510310
$385$	−2.07752	−0.105880
$386$	22.9582	1.16854
$387$	−9.93363	−0.504955
$388$	3.48793	0.177073
$389$	14.4379	0.732029	0.366015	−	0.930609i	$-0.380722\pi$
$389$	14.4379	0.732029	0.366015	+	0.930609i	$0.380722\pi$
$390$	2.44930	0.124025
$391$	3.58479	0.181291
$392$	3.41630	0.172549
$393$	3.97346	0.200434
$394$	−22.7688	−1.14708
$395$	−2.38902	−0.120204
$396$	−1.00000	−0.0502519
$397$	23.9308	1.20105	0.600525	−	0.799606i	$-0.294958\pi$
$397$	23.9308	1.20105	0.600525	+	0.799606i	$0.294958\pi$
$398$	−23.2106	−1.16344
$399$	−2.42671	−0.121488
$400$	−3.79563	−0.189781
$401$	16.3381	0.815888	0.407944	−	0.913007i	$-0.366246\pi$
$401$	16.3381	0.815888	0.407944	+	0.913007i	$0.366246\pi$
$402$	−0.379334	−0.0189195
$403$	16.3658	0.815238
$404$	−11.0045	−0.547496
$405$	1.09744	0.0545321
$406$	5.93363	0.294481
$407$	9.82670	0.487091
$408$	0.681143	0.0337216
$409$	7.87768	0.389526	0.194763	−	0.980850i	$-0.437606\pi$
$409$	7.87768	0.389526	0.194763	+	0.980850i	$0.437606\pi$
$410$	−1.36624	−0.0674737
$411$	20.7171	1.02190
$412$	16.9457	0.834855
$413$	−9.39712	−0.462402
$414$	5.26291	0.258658
$415$	−0.412343	−0.0202411
$416$	2.23184	0.109425
$417$	−8.52683	−0.417561
$418$	−1.28190	−0.0626996
$419$	−28.4228	−1.38855	−0.694273	−	0.719712i	$-0.744274\pi$
$419$	−28.4228	−1.38855	−0.694273	+	0.719712i	$0.744274\pi$
$420$	2.07752	0.101373
$421$	−11.7474	−0.572534	−0.286267	−	0.958150i	$-0.592414\pi$
$421$	−11.7474	−0.572534	−0.286267	+	0.958150i	$0.592414\pi$
$422$	20.7135	1.00832
$423$	7.93003	0.385571
$424$	−1.56472	−0.0759893
$425$	2.58537	0.125409
$426$	4.64813	0.225203
$427$	1.89307	0.0916120
$428$	−3.69424	−0.178568
$429$	2.23184	0.107754
$430$	10.9015	0.525719
$431$	−12.9291	−0.622773	−0.311387	−	0.950283i	$-0.600793\pi$
$431$	−12.9291	−0.622773	−0.311387	+	0.950283i	$0.600793\pi$
$432$	1.00000	0.0481125
$433$	3.25284	0.156321	0.0781607	−	0.996941i	$-0.475095\pi$
$433$	3.25284	0.156321	0.0781607	+	0.996941i	$0.475095\pi$
$434$	13.8816	0.666340
$435$	−3.43981	−0.164926
$436$	−0.250827	−0.0120124
$437$	6.74650	0.322729
$438$	9.94800	0.475334
$439$	−7.77001	−0.370842	−0.185421	−	0.982659i	$-0.559365\pi$
$439$	−7.77001	−0.370842	−0.185421	+	0.982659i	$0.559365\pi$
$440$	1.09744	0.0523183
$441$	−3.41630	−0.162681
$442$	−1.52020	−0.0723086
$443$	−39.2243	−1.86360	−0.931801	−	0.362969i	$-0.881763\pi$
$443$	−39.2243	−1.86360	−0.931801	+	0.362969i	$0.881763\pi$
$444$	−9.82670	−0.466354
$445$	13.6092	0.645139
$446$	18.7681	0.888694
$447$	−9.78974	−0.463039
$448$	1.89307	0.0894390
$449$	−40.2154	−1.89788	−0.948942	−	0.315451i	$-0.897844\pi$
$449$	−40.2154	−1.89788	−0.948942	+	0.315451i	$0.897844\pi$
$450$	3.79563	0.178928
$451$	−1.24493	−0.0586216
$452$	3.17496	0.149338
$453$	22.1720	1.04173
$454$	9.21553	0.432506
$455$	−4.63670	−0.217372
$456$	1.28190	0.0600303
$457$	10.3675	0.484973	0.242487	−	0.970155i	$-0.422037\pi$
$457$	10.3675	0.484973	0.242487	+	0.970155i	$0.422037\pi$
$458$	20.5664	0.961004
$459$	−0.681143	−0.0317930
$460$	−5.77572	−0.269294
$461$	−27.0570	−1.26017	−0.630085	−	0.776526i	$-0.716980\pi$
$461$	−27.0570	−1.26017	−0.630085	+	0.776526i	$0.716980\pi$
$462$	1.89307	0.0880735
$463$	9.07954	0.421962	0.210981	−	0.977490i	$-0.432334\pi$
$463$	9.07954	0.421962	0.210981	+	0.977490i	$0.432334\pi$
$464$	−3.13440	−0.145511
$465$	−8.04738	−0.373188
$466$	−22.7946	−1.05594
$467$	−36.2732	−1.67853	−0.839263	−	0.543726i	$-0.817013\pi$
$467$	−36.2732	−1.67853	−0.839263	+	0.543726i	$0.817013\pi$
$468$	−2.23184	−0.103167
$469$	0.718104	0.0331590
$470$	−8.70272	−0.401426
$471$	15.6053	0.719053
$472$	4.96396	0.228485
$473$	9.93363	0.456749
$474$	2.17690	0.0999885
$475$	4.86560	0.223249
$476$	−1.28945	−0.0591018
$477$	1.56472	0.0716434
$478$	16.3629	0.748423
$479$	31.2522	1.42795	0.713975	−	0.700171i	$-0.246893\pi$
$479$	31.2522	1.42795	0.713975	+	0.700171i	$0.246893\pi$
$480$	−1.09744	−0.0500910
$481$	21.9316	0.999995
$482$	−19.8816	−0.905584
$483$	−9.96304	−0.453334
$484$	1.00000	0.0454545
$485$	3.82779	0.173811
$486$	−1.00000	−0.0453609
$487$	−39.5203	−1.79083	−0.895417	−	0.445228i	$-0.853123\pi$
$487$	−39.5203	−1.79083	−0.895417	+	0.445228i	$0.853123\pi$
$488$	−1.00000	−0.0452679
$489$	11.8002	0.533621
$490$	3.74917	0.169370
$491$	16.6941	0.753396	0.376698	−	0.926336i	$-0.377059\pi$
$491$	16.6941	0.753396	0.376698	+	0.926336i	$0.377059\pi$
$492$	1.24493	0.0561260
$493$	2.13497	0.0961544
$494$	−2.86098	−0.128722
$495$	−1.09744	−0.0493262
$496$	−7.33288	−0.329256
$497$	−8.79923	−0.394699
$498$	0.375732	0.0168370
$499$	27.9042	1.24916	0.624582	−	0.780959i	$-0.285269\pi$
$499$	27.9042	1.24916	0.624582	+	0.780959i	$0.285269\pi$
$500$	−9.65266	−0.431680
$501$	4.59218	0.205164
$502$	−27.2397	−1.21577
$503$	5.58269	0.248920	0.124460	−	0.992225i	$-0.460280\pi$
$503$	5.58269	0.248920	0.124460	+	0.992225i	$0.460280\pi$
$504$	−1.89307	−0.0843239
$505$	−12.0768	−0.537410
$506$	−5.26291	−0.233965
$507$	−8.01890	−0.356132
$508$	−15.3189	−0.679664
$509$	37.1870	1.64828	0.824141	−	0.566384i	$-0.191658\pi$
$509$	37.1870	1.64828	0.824141	+	0.566384i	$0.191658\pi$
$510$	0.747512	0.0331004
$511$	−18.8322	−0.833089
$512$	−1.00000	−0.0441942
$513$	−1.28190	−0.0565971
$514$	11.4500	0.505036
$515$	18.5969	0.819476
$516$	−9.93363	−0.437304
$517$	−7.93003	−0.348762
$518$	18.6026	0.817351
$519$	8.67257	0.380684
$520$	2.44930	0.107409
$521$	−42.4810	−1.86113	−0.930564	−	0.366130i	$-0.880682\pi$
$521$	−42.4810	−1.86113	−0.930564	+	0.366130i	$0.880682\pi$
$522$	3.13440	0.137189
$523$	4.96900	0.217279	0.108640	−	0.994081i	$-0.465351\pi$
$523$	4.96900	0.217279	0.108640	+	0.994081i	$0.465351\pi$
$524$	3.97346	0.173581
$525$	−7.18538	−0.313596
$526$	3.56545	0.155461
$527$	4.99474	0.217574
$528$	−1.00000	−0.0435194
$529$	4.69819	0.204269
$530$	−1.71718	−0.0745895
$531$	−4.96396	−0.215418
$532$	−2.42671	−0.105211
$533$	−2.77849	−0.120350
$534$	−12.4009	−0.536640
$535$	−4.05420	−0.175278
$536$	−0.379334	−0.0163847
$537$	4.70954	0.203231
$538$	1.21874	0.0525437
$539$	3.41630	0.147150
$540$	1.09744	0.0472262
$541$	−24.3973	−1.04892	−0.524461	−	0.851434i	$-0.675733\pi$
$541$	−24.3973	−1.04892	−0.524461	+	0.851434i	$0.675733\pi$
$542$	12.5513	0.539123
$543$	25.0480	1.07491
$544$	0.681143	0.0292038
$545$	−0.275267	−0.0117911
$546$	4.22502	0.180814
$547$	−42.1161	−1.80075	−0.900376	−	0.435112i	$-0.856709\pi$
$547$	−42.1161	−1.80075	−0.900376	+	0.435112i	$0.856709\pi$
$548$	20.7171	0.884990
$549$	1.00000	0.0426790
$550$	−3.79563	−0.161846
$551$	4.01797	0.171171
$552$	5.26291	0.224004
$553$	−4.12103	−0.175244
$554$	15.9781	0.678846
$555$	−10.7842	−0.457764
$556$	−8.52683	−0.361618
$557$	−5.40292	−0.228929	−0.114465	−	0.993427i	$-0.536515\pi$
$557$	−5.40292	−0.228929	−0.114465	+	0.993427i	$0.536515\pi$
$558$	7.33288	0.310425
$559$	22.1703	0.937702
$560$	2.07752	0.0877914
$561$	0.681143	0.0287579
$562$	21.3516	0.900662
$563$	−9.19975	−0.387723	−0.193862	−	0.981029i	$-0.562101\pi$
$563$	−9.19975	−0.387723	−0.193862	+	0.981029i	$0.562101\pi$
$564$	7.93003	0.333914
$565$	3.48433	0.146587
$566$	−10.1285	−0.425733
$567$	1.89307	0.0795014
$568$	4.64813	0.195031
$569$	38.5036	1.61416	0.807078	−	0.590445i	$-0.201048\pi$
$569$	38.5036	1.61416	0.807078	+	0.590445i	$0.201048\pi$
$570$	1.40680	0.0589244
$571$	−15.8679	−0.664051	−0.332025	−	0.943270i	$-0.607732\pi$
$571$	−15.8679	−0.664051	−0.332025	+	0.943270i	$0.607732\pi$
$572$	2.23184	0.0933178
$573$	11.1194	0.464518
$574$	−2.35674	−0.0983686
$575$	19.9760	0.833059
$576$	1.00000	0.0416667
$577$	3.64546	0.151762	0.0758812	−	0.997117i	$-0.475823\pi$
$577$	3.64546	0.151762	0.0758812	+	0.997117i	$0.475823\pi$
$578$	16.5360	0.687809
$579$	−22.9582	−0.954112
$580$	−3.43981	−0.142830
$581$	−0.711287	−0.0295091
$582$	−3.48793	−0.144579
$583$	−1.56472	−0.0648039
$584$	9.94800	0.411651
$585$	−2.44930	−0.101266
$586$	−14.3894	−0.594421
$587$	10.5624	0.435958	0.217979	−	0.975953i	$-0.430054\pi$
$587$	10.5624	0.435958	0.217979	+	0.975953i	$0.430054\pi$
$588$	−3.41630	−0.140886
$589$	9.39998	0.387320
$590$	5.44764	0.224276
$591$	22.7688	0.936584
$592$	−9.82670	−0.403875
$593$	−24.8969	−1.02239	−0.511197	−	0.859463i	$-0.670798\pi$
$593$	−24.8969	−1.02239	−0.511197	+	0.859463i	$0.670798\pi$
$594$	1.00000	0.0410305
$595$	−1.41509	−0.0580131
$596$	−9.78974	−0.401003
$597$	23.2106	0.949945
$598$	−11.7460	−0.480328
$599$	−11.6412	−0.475645	−0.237822	−	0.971309i	$-0.576434\pi$
$599$	−11.6412	−0.475645	−0.237822	+	0.971309i	$0.576434\pi$
$600$	3.79563	0.154956
$601$	−25.3150	−1.03262	−0.516310	−	0.856402i	$-0.672695\pi$
$601$	−25.3150	−1.03262	−0.516310	+	0.856402i	$0.672695\pi$
$602$	18.8050	0.766436
$603$	0.379334	0.0154477
$604$	22.1720	0.902166
$605$	1.09744	0.0446172
$606$	11.0045	0.447028
$607$	21.8181	0.885571	0.442785	−	0.896628i	$-0.353990\pi$
$607$	21.8181	0.885571	0.442785	+	0.896628i	$0.353990\pi$
$608$	1.28190	0.0519877
$609$	−5.93363	−0.240443
$610$	−1.09744	−0.0444340
$611$	−17.6985	−0.716006
$612$	−0.681143	−0.0275336
$613$	−44.2177	−1.78594	−0.892969	−	0.450118i	$-0.851382\pi$
$613$	−44.2177	−1.78594	−0.892969	+	0.450118i	$0.851382\pi$
$614$	6.97900	0.281649
$615$	1.36624	0.0550920
$616$	1.89307	0.0762739
$617$	11.2273	0.451995	0.225997	−	0.974128i	$-0.427436\pi$
$617$	11.2273	0.451995	0.225997	+	0.974128i	$0.427436\pi$
$618$	−16.9457	−0.681656
$619$	5.37344	0.215977	0.107988	−	0.994152i	$-0.465559\pi$
$619$	5.37344	0.215977	0.107988	+	0.994152i	$0.465559\pi$
$620$	−8.04738	−0.323191
$621$	−5.26291	−0.211193
$622$	−32.4526	−1.30123
$623$	23.4758	0.940536
$624$	−2.23184	−0.0893450
$625$	8.38495	0.335398
$626$	1.57689	0.0630251
$627$	1.28190	0.0511940
$628$	15.6053	0.622718
$629$	6.69339	0.266883
$630$	−2.07752	−0.0827706
$631$	12.9902	0.517130	0.258565	−	0.965994i	$-0.416750\pi$
$631$	12.9902	0.517130	0.258565	+	0.965994i	$0.416750\pi$
$632$	2.17690	0.0865926
$633$	−20.7135	−0.823287
$634$	0.766221	0.0304305
$635$	−16.8115	−0.667144
$636$	1.56472	0.0620450
$637$	7.62462	0.302098
$638$	−3.13440	−0.124092
$639$	−4.64813	−0.183877
$640$	−1.09744	−0.0433801
$641$	11.2773	0.445426	0.222713	−	0.974884i	$-0.428509\pi$
$641$	11.2773	0.445426	0.222713	+	0.974884i	$0.428509\pi$
$642$	3.69424	0.145800
$643$	−34.5108	−1.36097	−0.680486	−	0.732761i	$-0.738231\pi$
$643$	−34.5108	−1.36097	−0.680486	+	0.732761i	$0.738231\pi$
$644$	−9.96304	−0.392599
$645$	−10.9015	−0.429248
$646$	−0.873154	−0.0343538
$647$	−33.8046	−1.32900	−0.664498	−	0.747290i	$-0.731355\pi$
$647$	−33.8046	−1.32900	−0.664498	+	0.747290i	$0.731355\pi$
$648$	−1.00000	−0.0392837
$649$	4.96396	0.194853
$650$	−8.47123	−0.332269
$651$	−13.8816	−0.544064
$652$	11.8002	0.462130
$653$	21.5888	0.844835	0.422418	−	0.906401i	$-0.361182\pi$
$653$	21.5888	0.844835	0.422418	+	0.906401i	$0.361182\pi$
$654$	0.250827	0.00980810
$655$	4.36062	0.170384
$656$	1.24493	0.0486065
$657$	−9.94800	−0.388109
$658$	−15.0121	−0.585232
$659$	−17.0164	−0.662864	−0.331432	−	0.943479i	$-0.607532\pi$
$659$	−17.0164	−0.662864	−0.331432	+	0.943479i	$0.607532\pi$
$660$	−1.09744	−0.0427177
$661$	2.27527	0.0884976	0.0442488	−	0.999021i	$-0.485911\pi$
$661$	2.27527	0.0884976	0.0442488	+	0.999021i	$0.485911\pi$
$662$	5.64686	0.219471
$663$	1.52020	0.0590397
$664$	0.375732	0.0145812
$665$	−2.66317	−0.103273
$666$	9.82670	0.380777
$667$	16.4961	0.638730
$668$	4.59218	0.177677
$669$	−18.7681	−0.725616
$670$	−0.416295	−0.0160829
$671$	−1.00000	−0.0386046
$672$	−1.89307	−0.0730267
$673$	32.1321	1.23860	0.619301	−	0.785154i	$-0.287416\pi$
$673$	32.1321	1.23860	0.619301	+	0.785154i	$0.287416\pi$
$674$	−17.9620	−0.691871
$675$	−3.79563	−0.146094
$676$	−8.01890	−0.308419
$677$	14.6716	0.563874	0.281937	−	0.959433i	$-0.409023\pi$
$677$	14.6716	0.563874	0.281937	+	0.959433i	$0.409023\pi$
$678$	−3.17496	−0.121934
$679$	6.60288	0.253395
$680$	0.747512	0.0286658
$681$	−9.21553	−0.353140
$682$	−7.33288	−0.280790
$683$	−16.8678	−0.645430	−0.322715	−	0.946496i	$-0.604595\pi$
$683$	−16.8678	−0.645430	−0.322715	+	0.946496i	$0.604595\pi$
$684$	−1.28190	−0.0490145
$685$	22.7357	0.868687
$686$	19.7188	0.752865
$687$	−20.5664	−0.784656
$688$	−9.93363	−0.378716
$689$	−3.49219	−0.133042
$690$	5.77572	0.219878
$691$	−30.4512	−1.15842	−0.579210	−	0.815179i	$-0.696639\pi$
$691$	−30.4512	−1.15842	−0.579210	+	0.815179i	$0.696639\pi$
$692$	8.67257	0.329682
$693$	−1.89307	−0.0719117
$694$	−12.4217	−0.471523
$695$	−9.35767	−0.354957
$696$	3.13440	0.118809
$697$	−0.847978	−0.0321195
$698$	13.9412	0.527682
$699$	22.7946	0.862171
$700$	−7.18538	−0.271582
$701$	21.2720	0.803431	0.401715	−	0.915765i	$-0.368414\pi$
$701$	21.2720	0.803431	0.401715	+	0.915765i	$0.368414\pi$
$702$	2.23184	0.0842353
$703$	12.5968	0.475097
$704$	−1.00000	−0.0376889
$705$	8.70272	0.327763
$706$	−22.6367	−0.851943
$707$	−20.8323	−0.783480
$708$	−4.96396	−0.186557
$709$	−27.9123	−1.04827	−0.524133	−	0.851636i	$-0.675611\pi$
$709$	−27.9123	−1.04827	−0.524133	+	0.851636i	$0.675611\pi$
$710$	5.10104	0.191439
$711$	−2.17690	−0.0816403
$712$	−12.4009	−0.464744
$713$	38.5923	1.44529
$714$	1.28945	0.0482564
$715$	2.44930	0.0915988
$716$	4.70954	0.176004
$717$	−16.3629	−0.611085
$718$	30.6791	1.14493
$719$	−43.7145	−1.63028	−0.815138	−	0.579266i	$-0.803339\pi$
$719$	−43.7145	−1.63028	−0.815138	+	0.579266i	$0.803339\pi$
$720$	1.09744	0.0408991
$721$	32.0794	1.19470
$722$	17.3567	0.645951
$723$	19.8816	0.739406
$724$	25.0480	0.930903
$725$	11.8970	0.441844
$726$	−1.00000	−0.0371135
$727$	51.3419	1.90417	0.952083	−	0.305838i	$-0.0989368\pi$
$727$	51.3419	1.90417	0.952083	+	0.305838i	$0.0989368\pi$
$728$	4.22502	0.156590
$729$	1.00000	0.0370370
$730$	10.9173	0.404068
$731$	6.76622	0.250258
$732$	1.00000	0.0369611
$733$	33.2479	1.22804	0.614019	−	0.789291i	$-0.289552\pi$
$733$	33.2479	1.22804	0.614019	+	0.789291i	$0.289552\pi$
$734$	−3.41177	−0.125931
$735$	−3.74917	−0.138290
$736$	5.26291	0.193993
$737$	−0.379334	−0.0139729
$738$	−1.24493	−0.0458266
$739$	2.02185	0.0743751	0.0371875	−	0.999308i	$-0.488160\pi$
$739$	2.02185	0.0743751	0.0371875	+	0.999308i	$0.488160\pi$
$740$	−10.7842	−0.396435
$741$	2.86098	0.105101
$742$	−2.96211	−0.108743
$743$	−32.6676	−1.19846	−0.599229	−	0.800578i	$-0.704526\pi$
$743$	−32.6676	−1.19846	−0.599229	+	0.800578i	$0.704526\pi$
$744$	7.33288	0.268836
$745$	−10.7436	−0.393616
$746$	36.5324	1.33754
$747$	−0.375732	−0.0137473
$748$	0.681143	0.0249050
$749$	−6.99344	−0.255535
$750$	9.65266	0.352465
$751$	−0.527916	−0.0192639	−0.00963197	−	0.999954i	$-0.503066\pi$
$751$	−0.527916	−0.0192639	−0.00963197	+	0.999954i	$0.503066\pi$
$752$	7.93003	0.289178
$753$	27.2397	0.992669
$754$	−6.99547	−0.254760
$755$	24.3324	0.885547
$756$	1.89307	0.0688502
$757$	−43.3383	−1.57516	−0.787579	−	0.616213i	$-0.788666\pi$
$757$	−43.3383	−1.57516	−0.787579	+	0.616213i	$0.788666\pi$
$758$	−12.3952	−0.450214
$759$	5.26291	0.191031
$760$	1.40680	0.0510300
$761$	−28.2789	−1.02511	−0.512554	−	0.858655i	$-0.671301\pi$
$761$	−28.2789	−1.02511	−0.512554	+	0.858655i	$0.671301\pi$
$762$	15.3189	0.554944
$763$	−0.474832	−0.0171901
$764$	11.1194	0.402284
$765$	−0.747512	−0.0270264
$766$	26.4615	0.956095
$767$	11.0788	0.400031
$768$	1.00000	0.0360844
$769$	40.2542	1.45161	0.725803	−	0.687903i	$-0.241469\pi$
$769$	40.2542	1.45161	0.725803	+	0.687903i	$0.241469\pi$
$770$	2.07752	0.0748688
$771$	−11.4500	−0.412360
$772$	−22.9582	−0.826285
$773$	45.5694	1.63902	0.819509	−	0.573067i	$-0.194246\pi$
$773$	45.5694	1.63902	0.819509	+	0.573067i	$0.194246\pi$
$774$	9.93363	0.357057
$775$	27.8329	0.999787
$776$	−3.48793	−0.125209
$777$	−18.6026	−0.667365
$778$	−14.4379	−0.517623
$779$	−1.59588	−0.0571782
$780$	−2.44930	−0.0876992
$781$	4.64813	0.166323
$782$	−3.58479	−0.128192
$783$	−3.13440	−0.112014
$784$	−3.41630	−0.122011
$785$	17.1258	0.611247
$786$	−3.97346	−0.141729
$787$	−34.3460	−1.22430	−0.612151	−	0.790741i	$-0.709695\pi$
$787$	−34.3460	−1.22430	−0.612151	+	0.790741i	$0.709695\pi$
$788$	22.7688	0.811105
$789$	−3.56545	−0.126933
$790$	2.38902	0.0849974
$791$	6.01042	0.213706
$792$	1.00000	0.0355335
$793$	−2.23184	−0.0792549
$794$	−23.9308	−0.849271
$795$	1.71718	0.0609021
$796$	23.2106	0.822676
$797$	42.2162	1.49537	0.747687	−	0.664052i	$-0.231164\pi$
$797$	42.2162	1.49537	0.747687	+	0.664052i	$0.231164\pi$
$798$	2.42671	0.0859048
$799$	−5.40148	−0.191091
$800$	3.79563	0.134196
$801$	12.4009	0.438165
$802$	−16.3381	−0.576920
$803$	9.94800	0.351057
$804$	0.379334	0.0133781
$805$	−10.9338	−0.385367
$806$	−16.3658	−0.576461
$807$	−1.21874	−0.0429018
$808$	11.0045	0.387138
$809$	−48.6770	−1.71139	−0.855696	−	0.517479i	$-0.826870\pi$
$809$	−48.6770	−1.71139	−0.855696	+	0.517479i	$0.826870\pi$
$810$	−1.09744	−0.0385601
$811$	36.5079	1.28197	0.640983	−	0.767555i	$-0.278527\pi$
$811$	36.5079	1.28197	0.640983	+	0.767555i	$0.278527\pi$
$812$	−5.93363	−0.208230
$813$	−12.5513	−0.440192
$814$	−9.82670	−0.344426
$815$	12.9499	0.453617
$816$	−0.681143	−0.0238448
$817$	12.7339	0.445502
$818$	−7.87768	−0.275437
$819$	−4.22502	−0.147634
$820$	1.36624	0.0477111
$821$	29.7837	1.03946	0.519729	−	0.854331i	$-0.326033\pi$
$821$	29.7837	1.03946	0.519729	+	0.854331i	$0.326033\pi$
$822$	−20.7171	−0.722591
$823$	−25.2877	−0.881475	−0.440737	−	0.897636i	$-0.645283\pi$
$823$	−25.2877	−0.881475	−0.440737	+	0.897636i	$0.645283\pi$
$824$	−16.9457	−0.590332
$825$	3.79563	0.132147
$826$	9.39712	0.326968
$827$	25.4033	0.883358	0.441679	−	0.897173i	$-0.354383\pi$
$827$	25.4033	0.883358	0.441679	+	0.897173i	$0.354383\pi$
$828$	−5.26291	−0.182899
$829$	−12.9522	−0.449848	−0.224924	−	0.974376i	$-0.572213\pi$
$829$	−12.9522	−0.449848	−0.224924	+	0.974376i	$0.572213\pi$
$830$	0.412343	0.0143126
$831$	−15.9781	−0.554276
$832$	−2.23184	−0.0773751
$833$	2.32699	0.0806253
$834$	8.52683	0.295260
$835$	5.03964	0.174404
$836$	1.28190	0.0443353
$837$	−7.33288	−0.253461
$838$	28.4228	0.981851
$839$	21.0013	0.725045	0.362522	−	0.931975i	$-0.381916\pi$
$839$	21.0013	0.725045	0.362522	+	0.931975i	$0.381916\pi$
$840$	−2.07752	−0.0716814
$841$	−19.1755	−0.661225
$842$	11.7474	0.404843
$843$	−21.3516	−0.735388
$844$	−20.7135	−0.712988
$845$	−8.80025	−0.302738
$846$	−7.93003	−0.272640
$847$	1.89307	0.0650466
$848$	1.56472	0.0537326
$849$	10.1285	0.347609
$850$	−2.58537	−0.0886773
$851$	51.7170	1.77284
$852$	−4.64813	−0.159242
$853$	28.6195	0.979912	0.489956	−	0.871747i	$-0.337013\pi$
$853$	28.6195	0.979912	0.489956	+	0.871747i	$0.337013\pi$
$854$	−1.89307	−0.0647794
$855$	−1.40680	−0.0481116
$856$	3.69424	0.126266
$857$	31.4924	1.07576	0.537879	−	0.843022i	$-0.319226\pi$
$857$	31.4924	1.07576	0.537879	+	0.843022i	$0.319226\pi$
$858$	−2.23184	−0.0761937
$859$	−50.7420	−1.73129	−0.865647	−	0.500655i	$-0.833093\pi$
$859$	−50.7420	−1.73129	−0.865647	+	0.500655i	$0.833093\pi$
$860$	−10.9015	−0.371740
$861$	2.35674	0.0803176
$862$	12.9291	0.440367
$863$	33.5565	1.14228	0.571139	−	0.820853i	$-0.306502\pi$
$863$	33.5565	1.14228	0.571139	+	0.820853i	$0.306502\pi$
$864$	−1.00000	−0.0340207
$865$	9.51761	0.323609
$866$	−3.25284	−0.110536
$867$	−16.5360	−0.561594
$868$	−13.8816	−0.471173
$869$	2.17690	0.0738464
$870$	3.43981	0.116620
$871$	−0.846612	−0.0286863
$872$	0.250827	0.00849406
$873$	3.48793	0.118048
$874$	−6.74650	−0.228204
$875$	−18.2731	−0.617745
$876$	−9.94800	−0.336112
$877$	−22.3493	−0.754682	−0.377341	−	0.926074i	$-0.623162\pi$
$877$	−22.3493	−0.754682	−0.377341	+	0.926074i	$0.623162\pi$
$878$	7.77001	0.262225
$879$	14.3894	0.485342
$880$	−1.09744	−0.0369946
$881$	1.50433	0.0506822	0.0253411	−	0.999679i	$-0.491933\pi$
$881$	1.50433	0.0506822	0.0253411	+	0.999679i	$0.491933\pi$
$882$	3.41630	0.115033
$883$	13.6853	0.460546	0.230273	−	0.973126i	$-0.426038\pi$
$883$	13.6853	0.460546	0.230273	+	0.973126i	$0.426038\pi$
$884$	1.52020	0.0511299
$885$	−5.44764	−0.183121
$886$	39.2243	1.31777
$887$	2.02403	0.0679602	0.0339801	−	0.999423i	$-0.489182\pi$
$887$	2.02403	0.0679602	0.0339801	+	0.999423i	$0.489182\pi$
$888$	9.82670	0.329762
$889$	−28.9996	−0.972616
$890$	−13.6092	−0.456182
$891$	−1.00000	−0.0335013
$892$	−18.7681	−0.628402
$893$	−10.1655	−0.340174
$894$	9.78974	0.327418
$895$	5.16842	0.172761
$896$	−1.89307	−0.0632429
$897$	11.7460	0.392186
$898$	40.2154	1.34201
$899$	22.9842	0.766565
$900$	−3.79563	−0.126521
$901$	−1.06580	−0.0355068
$902$	1.24493	0.0414518
$903$	−18.8050	−0.625792
$904$	−3.17496	−0.105598
$905$	27.4887	0.913754
$906$	−22.1720	−0.736616
$907$	8.19201	0.272011	0.136006	−	0.990708i	$-0.456573\pi$
$907$	8.19201	0.272011	0.136006	+	0.990708i	$0.456573\pi$
$908$	−9.21553	−0.305828
$909$	−11.0045	−0.364997
$910$	4.63670	0.153705
$911$	−20.9303	−0.693453	−0.346726	−	0.937966i	$-0.612707\pi$
$911$	−20.9303	−0.693453	−0.346726	+	0.937966i	$0.612707\pi$
$912$	−1.28190	−0.0424478
$913$	0.375732	0.0124349
$914$	−10.3675	−0.342928
$915$	1.09744	0.0362802
$916$	−20.5664	−0.679532
$917$	7.52202	0.248399
$918$	0.681143	0.0224811
$919$	16.6805	0.550238	0.275119	−	0.961410i	$-0.411283\pi$
$919$	16.6805	0.550238	0.275119	+	0.961410i	$0.411283\pi$
$920$	5.77572	0.190420
$921$	−6.97900	−0.229966
$922$	27.0570	0.891074
$923$	10.3739	0.341460
$924$	−1.89307	−0.0622773
$925$	37.2985	1.22637
$926$	−9.07954	−0.298372
$927$	16.9457	0.556570
$928$	3.13440	0.102892
$929$	−43.0814	−1.41346	−0.706728	−	0.707486i	$-0.749829\pi$
$929$	−43.0814	−1.41346	−0.706728	+	0.707486i	$0.749829\pi$
$930$	8.04738	0.263884
$931$	4.37933	0.143527
$932$	22.7946	0.746662
$933$	32.4526	1.06245
$934$	36.2732	1.18690
$935$	0.747512	0.0244463
$936$	2.23184	0.0729499
$937$	46.8708	1.53120	0.765602	−	0.643315i	$-0.222441\pi$
$937$	46.8708	1.53120	0.765602	+	0.643315i	$0.222441\pi$
$938$	−0.718104	−0.0234469
$939$	−1.57689	−0.0514598
$940$	8.70272	0.283851
$941$	−54.6845	−1.78266	−0.891331	−	0.453353i	$-0.850228\pi$
$941$	−54.6845	−1.78266	−0.891331	+	0.453353i	$0.850228\pi$
$942$	−15.6053	−0.508447
$943$	−6.55197	−0.213362
$944$	−4.96396	−0.161563
$945$	2.07752	0.0675819
$946$	−9.93363	−0.322970
$947$	18.9356	0.615323	0.307662	−	0.951496i	$-0.400454\pi$
$947$	18.9356	0.615323	0.307662	+	0.951496i	$0.400454\pi$
$948$	−2.17690	−0.0707025
$949$	22.2023	0.720718
$950$	−4.86560	−0.157861
$951$	−0.766221	−0.0248464
$952$	1.28945	0.0417913
$953$	24.6894	0.799769	0.399885	−	0.916566i	$-0.369050\pi$
$953$	24.6894	0.799769	0.399885	+	0.916566i	$0.369050\pi$
$954$	−1.56472	−0.0506596
$955$	12.2028	0.394874
$956$	−16.3629	−0.529215
$957$	3.13440	0.101321
$958$	−31.2522	−1.00971
$959$	39.2188	1.26644
$960$	1.09744	0.0354197
$961$	22.7711	0.734552
$962$	−21.9316	−0.707103
$963$	−3.69424	−0.119045
$964$	19.8816	0.640344
$965$	−25.1952	−0.811064
$966$	9.96304	0.320556
$967$	−5.76421	−0.185364	−0.0926822	−	0.995696i	$-0.529544\pi$
$967$	−5.76421	−0.185364	−0.0926822	+	0.995696i	$0.529544\pi$
$968$	−1.00000	−0.0321412
$969$	0.873154	0.0280497
$970$	−3.82779	−0.122903
$971$	7.17968	0.230407	0.115203	−	0.993342i	$-0.463248\pi$
$971$	7.17968	0.230407	0.115203	+	0.993342i	$0.463248\pi$
$972$	1.00000	0.0320750
$973$	−16.1419	−0.517484
$974$	39.5203	1.26631
$975$	8.47123	0.271296
$976$	1.00000	0.0320092
$977$	6.46043	0.206687	0.103344	−	0.994646i	$-0.467046\pi$
$977$	6.46043	0.206687	0.103344	+	0.994646i	$0.467046\pi$
$978$	−11.8002	−0.377327
$979$	−12.4009	−0.396335
$980$	−3.74917	−0.119763
$981$	−0.250827	−0.00800828
$982$	−16.6941	−0.532732
$983$	−4.86350	−0.155121	−0.0775607	−	0.996988i	$-0.524713\pi$
$983$	−4.86350	−0.155121	−0.0775607	+	0.996988i	$0.524713\pi$
$984$	−1.24493	−0.0396870
$985$	24.9874	0.796164
$986$	−2.13497	−0.0679914
$987$	15.0121	0.477840
$988$	2.86098	0.0910200
$989$	52.2798	1.66240
$990$	1.09744	0.0348789
$991$	−7.85572	−0.249545	−0.124773	−	0.992185i	$-0.539820\pi$
$991$	−7.85572	−0.249545	−0.124773	+	0.992185i	$0.539820\pi$
$992$	7.33288	0.232819
$993$	−5.64686	−0.179198
$994$	8.79923	0.279095
$995$	25.4722	0.807522
$996$	−0.375732	−0.0119055
$997$	19.6343	0.621825	0.310912	−	0.950439i	$-0.399365\pi$
$997$	19.6343	0.621825	0.310912	+	0.950439i	$0.399365\pi$
$998$	−27.9042	−0.883293
$999$	−9.82670	−0.310903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.r.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.r.1.3	✓	4	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.09744 q^{5} -1.00000 q^{6} +1.89307 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.09744 q^{5} -1.00000 q^{6} +1.89307 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.09744 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.23184 q^{13} -1.89307 q^{14} +1.09744 q^{15} +1.00000 q^{16} -0.681143 q^{17} -1.00000 q^{18} -1.28190 q^{19} +1.09744 q^{20} +1.89307 q^{21} +1.00000 q^{22} -5.26291 q^{23} -1.00000 q^{24} -3.79563 q^{25} +2.23184 q^{26} +1.00000 q^{27} +1.89307 q^{28} -3.13440 q^{29} -1.09744 q^{30} -7.33288 q^{31} -1.00000 q^{32} -1.00000 q^{33} +0.681143 q^{34} +2.07752 q^{35} +1.00000 q^{36} -9.82670 q^{37} +1.28190 q^{38} -2.23184 q^{39} -1.09744 q^{40} +1.24493 q^{41} -1.89307 q^{42} -9.93363 q^{43} -1.00000 q^{44} +1.09744 q^{45} +5.26291 q^{46} +7.93003 q^{47} +1.00000 q^{48} -3.41630 q^{49} +3.79563 q^{50} -0.681143 q^{51} -2.23184 q^{52} +1.56472 q^{53} -1.00000 q^{54} -1.09744 q^{55} -1.89307 q^{56} -1.28190 q^{57} +3.13440 q^{58} -4.96396 q^{59} +1.09744 q^{60} +1.00000 q^{61} +7.33288 q^{62} +1.89307 q^{63} +1.00000 q^{64} -2.44930 q^{65} +1.00000 q^{66} +0.379334 q^{67} -0.681143 q^{68} -5.26291 q^{69} -2.07752 q^{70} -4.64813 q^{71} -1.00000 q^{72} -9.94800 q^{73} +9.82670 q^{74} -3.79563 q^{75} -1.28190 q^{76} -1.89307 q^{77} +2.23184 q^{78} -2.17690 q^{79} +1.09744 q^{80} +1.00000 q^{81} -1.24493 q^{82} -0.375732 q^{83} +1.89307 q^{84} -0.747512 q^{85} +9.93363 q^{86} -3.13440 q^{87} +1.00000 q^{88} +12.4009 q^{89} -1.09744 q^{90} -4.22502 q^{91} -5.26291 q^{92} -7.33288 q^{93} -7.93003 q^{94} -1.40680 q^{95} -1.00000 q^{96} +3.48793 q^{97} +3.41630 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} - q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + q^{15} + 4 q^{16} - 3 q^{17} - 4 q^{18} - 4 q^{19} + q^{20} - 4 q^{21} + 4 q^{22} + 10 q^{23} - 4 q^{24} - 7 q^{25} + 3 q^{26} + 4 q^{27} - 4 q^{28} - 10 q^{29} - q^{30} - 9 q^{31} - 4 q^{32} - 4 q^{33} + 3 q^{34} - q^{35} + 4 q^{36} - 6 q^{37} + 4 q^{38} - 3 q^{39} - q^{40} + 3 q^{41} + 4 q^{42} - 18 q^{43} - 4 q^{44} + q^{45} - 10 q^{46} + 21 q^{47} + 4 q^{48} - 10 q^{49} + 7 q^{50} - 3 q^{51} - 3 q^{52} - 20 q^{53} - 4 q^{54} - q^{55} + 4 q^{56} - 4 q^{57} + 10 q^{58} + 5 q^{59} + q^{60} + 4 q^{61} + 9 q^{62} - 4 q^{63} + 4 q^{64} - 16 q^{65} + 4 q^{66} - 3 q^{67} - 3 q^{68} + 10 q^{69} + q^{70} - 9 q^{71} - 4 q^{72} + 6 q^{74} - 7 q^{75} - 4 q^{76} + 4 q^{77} + 3 q^{78} - 31 q^{79} + q^{80} + 4 q^{81} - 3 q^{82} - 8 q^{83} - 4 q^{84} - 25 q^{85} + 18 q^{86} - 10 q^{87} + 4 q^{88} + 5 q^{89} - q^{90} - 9 q^{91} + 10 q^{92} - 9 q^{93} - 21 q^{94} + 13 q^{95} - 4 q^{96} - 25 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 - q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + q^15 + 4 * q^16 - 3 * q^17 - 4 * q^18 - 4 * q^19 + q^20 - 4 * q^21 + 4 * q^22 + 10 * q^23 - 4 * q^24 - 7 * q^25 + 3 * q^26 + 4 * q^27 - 4 * q^28 - 10 * q^29 - q^30 - 9 * q^31 - 4 * q^32 - 4 * q^33 + 3 * q^34 - q^35 + 4 * q^36 - 6 * q^37 + 4 * q^38 - 3 * q^39 - q^40 + 3 * q^41 + 4 * q^42 - 18 * q^43 - 4 * q^44 + q^45 - 10 * q^46 + 21 * q^47 + 4 * q^48 - 10 * q^49 + 7 * q^50 - 3 * q^51 - 3 * q^52 - 20 * q^53 - 4 * q^54 - q^55 + 4 * q^56 - 4 * q^57 + 10 * q^58 + 5 * q^59 + q^60 + 4 * q^61 + 9 * q^62 - 4 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 - 3 * q^67 - 3 * q^68 + 10 * q^69 + q^70 - 9 * q^71 - 4 * q^72 + 6 * q^74 - 7 * q^75 - 4 * q^76 + 4 * q^77 + 3 * q^78 - 31 * q^79 + q^80 + 4 * q^81 - 3 * q^82 - 8 * q^83 - 4 * q^84 - 25 * q^85 + 18 * q^86 - 10 * q^87 + 4 * q^88 + 5 * q^89 - q^90 - 9 * q^91 + 10 * q^92 - 9 * q^93 - 21 * q^94 + 13 * q^95 - 4 * q^96 - 25 * q^97 + 10 * q^98 - 4 * q^99

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