LMFDB - Embedded newform 2010.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2010,2,Mod(1,2010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2010, 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("2010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2010 = 2 \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2010.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:	$16.0499308063$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.70292.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} + 10x + 2 $ x^4 - x^3 - 8x^2 + 10x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.175890$ of defining polynomial
Character	$\chi$	$=$	2010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.96906 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.96906 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.04990 q^{11} -1.00000 q^{12} +0.919164 q^{13} +3.96906 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.351780 q^{17} -1.00000 q^{18} -0.351780 q^{19} -1.00000 q^{20} +3.96906 q^{21} -3.04990 q^{22} -3.43262 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.919164 q^{26} -1.00000 q^{27} -3.96906 q^{28} +9.37074 q^{29} -1.00000 q^{30} +2.91916 q^{31} -1.00000 q^{32} -3.04990 q^{33} -0.351780 q^{34} +3.96906 q^{35} +1.00000 q^{36} +5.40168 q^{37} +0.351780 q^{38} -0.919164 q^{39} +1.00000 q^{40} -8.45158 q^{41} -3.96906 q^{42} +6.09980 q^{43} +3.04990 q^{44} -1.00000 q^{45} +3.43262 q^{46} -13.2091 q^{47} -1.00000 q^{48} +8.75346 q^{49} -1.00000 q^{50} -0.351780 q^{51} +0.919164 q^{52} +5.93813 q^{53} +1.00000 q^{54} -3.04990 q^{55} +3.96906 q^{56} +0.351780 q^{57} -9.37074 q^{58} -8.45158 q^{59} +1.00000 q^{60} -1.96906 q^{61} -2.91916 q^{62} -3.96906 q^{63} +1.00000 q^{64} -0.919164 q^{65} +3.04990 q^{66} -1.00000 q^{67} +0.351780 q^{68} +3.43262 q^{69} -3.96906 q^{70} -5.61728 q^{71} -1.00000 q^{72} -12.8034 q^{73} -5.40168 q^{74} -1.00000 q^{75} -0.351780 q^{76} -12.1052 q^{77} +0.919164 q^{78} +11.8842 q^{79} -1.00000 q^{80} +1.00000 q^{81} +8.45158 q^{82} +0.105239 q^{83} +3.96906 q^{84} -0.351780 q^{85} -6.09980 q^{86} -9.37074 q^{87} -3.04990 q^{88} -16.2050 q^{89} +1.00000 q^{90} -3.64822 q^{91} -3.43262 q^{92} -2.91916 q^{93} +13.2091 q^{94} +0.351780 q^{95} +1.00000 q^{96} +3.04990 q^{97} -8.75346 q^{98} +3.04990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 3 q^{11} - 4 q^{12} + 2 q^{13} - q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{19} - 4 q^{20} - q^{21} + 3 q^{22} - 12 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 10 q^{31} - 4 q^{32} + 3 q^{33} + 2 q^{34} - q^{35} + 4 q^{36} + 3 q^{37} - 2 q^{38} - 2 q^{39} + 4 q^{40} + q^{42} - 6 q^{43} - 3 q^{44} - 4 q^{45} + 12 q^{46} - 14 q^{47} - 4 q^{48} + 13 q^{49} - 4 q^{50} + 2 q^{51} + 2 q^{52} - 10 q^{53} + 4 q^{54} + 3 q^{55} - q^{56} - 2 q^{57} - 2 q^{58} + 4 q^{60} + 9 q^{61} - 10 q^{62} + q^{63} + 4 q^{64} - 2 q^{65} - 3 q^{66} - 4 q^{67} - 2 q^{68} + 12 q^{69} + q^{70} - 9 q^{71} - 4 q^{72} - 14 q^{73} - 3 q^{74} - 4 q^{75} + 2 q^{76} - 23 q^{77} + 2 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 25 q^{83} - q^{84} + 2 q^{85} + 6 q^{86} - 2 q^{87} + 3 q^{88} - 9 q^{89} + 4 q^{90} - 18 q^{91} - 12 q^{92} - 10 q^{93} + 14 q^{94} - 2 q^{95} + 4 q^{96} - 3 q^{97} - 13 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 3 * q^11 - 4 * q^12 + 2 * q^13 - q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^19 - 4 * q^20 - q^21 + 3 * q^22 - 12 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 10 * q^31 - 4 * q^32 + 3 * q^33 + 2 * q^34 - q^35 + 4 * q^36 + 3 * q^37 - 2 * q^38 - 2 * q^39 + 4 * q^40 + q^42 - 6 * q^43 - 3 * q^44 - 4 * q^45 + 12 * q^46 - 14 * q^47 - 4 * q^48 + 13 * q^49 - 4 * q^50 + 2 * q^51 + 2 * q^52 - 10 * q^53 + 4 * q^54 + 3 * q^55 - q^56 - 2 * q^57 - 2 * q^58 + 4 * q^60 + 9 * q^61 - 10 * q^62 + q^63 + 4 * q^64 - 2 * q^65 - 3 * q^66 - 4 * q^67 - 2 * q^68 + 12 * q^69 + q^70 - 9 * q^71 - 4 * q^72 - 14 * q^73 - 3 * q^74 - 4 * q^75 + 2 * q^76 - 23 * q^77 + 2 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 25 * q^83 - q^84 + 2 * q^85 + 6 * q^86 - 2 * q^87 + 3 * q^88 - 9 * q^89 + 4 * q^90 - 18 * q^91 - 12 * q^92 - 10 * q^93 + 14 * q^94 - 2 * q^95 + 4 * q^96 - 3 * q^97 - 13 * q^98 - 3 * 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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	−3.96906	−1.50016	−0.750082	−	0.661344i	$-0.769986\pi$
$7$	−3.96906	−1.50016	−0.750082	+	0.661344i	$0.769986\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	3.04990	0.919579	0.459790	−	0.888028i	$-0.347925\pi$
$11$	3.04990	0.919579	0.459790	+	0.888028i	$0.347925\pi$
$12$	−1.00000	−0.288675
$13$	0.919164	0.254930	0.127465	−	0.991843i	$-0.459316\pi$
$13$	0.919164	0.254930	0.127465	+	0.991843i	$0.459316\pi$
$14$	3.96906	1.06078
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0.351780	0.0853192	0.0426596	−	0.999090i	$-0.486417\pi$
$17$	0.351780	0.0853192	0.0426596	+	0.999090i	$0.486417\pi$
$18$	−1.00000	−0.235702
$19$	−0.351780	−0.0807039	−0.0403519	−	0.999186i	$-0.512848\pi$
$19$	−0.351780	−0.0807039	−0.0403519	+	0.999186i	$0.512848\pi$
$20$	−1.00000	−0.223607
$21$	3.96906	0.866120
$22$	−3.04990	−0.650241
$23$	−3.43262	−0.715750	−0.357875	−	0.933770i	$-0.616499\pi$
$23$	−3.43262	−0.715750	−0.357875	+	0.933770i	$0.616499\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−0.919164	−0.180263
$27$	−1.00000	−0.192450
$28$	−3.96906	−0.750082
$29$	9.37074	1.74010	0.870051	−	0.492961i	$-0.164085\pi$
$29$	9.37074	1.74010	0.870051	+	0.492961i	$0.164085\pi$
$30$	−1.00000	−0.182574
$31$	2.91916	0.524297	0.262149	−	0.965027i	$-0.415569\pi$
$31$	2.91916	0.524297	0.262149	+	0.965027i	$0.415569\pi$
$32$	−1.00000	−0.176777
$33$	−3.04990	−0.530919
$34$	−0.351780	−0.0603298
$35$	3.96906	0.670894
$36$	1.00000	0.166667
$37$	5.40168	0.888030	0.444015	−	0.896019i	$-0.353554\pi$
$37$	5.40168	0.888030	0.444015	+	0.896019i	$0.353554\pi$
$38$	0.351780	0.0570663
$39$	−0.919164	−0.147184
$40$	1.00000	0.158114
$41$	−8.45158	−1.31991	−0.659957	−	0.751303i	$-0.729426\pi$
$41$	−8.45158	−1.31991	−0.659957	+	0.751303i	$0.729426\pi$
$42$	−3.96906	−0.612440
$43$	6.09980	0.930210	0.465105	−	0.885255i	$-0.346017\pi$
$43$	6.09980	0.930210	0.465105	+	0.885255i	$0.346017\pi$
$44$	3.04990	0.459790
$45$	−1.00000	−0.149071
$46$	3.43262	0.506112
$47$	−13.2091	−1.92674	−0.963370	−	0.268174i	$-0.913580\pi$
$47$	−13.2091	−1.92674	−0.963370	+	0.268174i	$0.913580\pi$
$48$	−1.00000	−0.144338
$49$	8.75346	1.25049
$50$	−1.00000	−0.141421
$51$	−0.351780	−0.0492591
$52$	0.919164	0.127465
$53$	5.93813	0.815664	0.407832	−	0.913057i	$-0.366285\pi$
$53$	5.93813	0.815664	0.407832	+	0.913057i	$0.366285\pi$
$54$	1.00000	0.136083
$55$	−3.04990	−0.411248
$56$	3.96906	0.530388
$57$	0.351780	0.0465944
$58$	−9.37074	−1.23044
$59$	−8.45158	−1.10030	−0.550151	−	0.835065i	$-0.685430\pi$
$59$	−8.45158	−1.10030	−0.550151	+	0.835065i	$0.685430\pi$
$60$	1.00000	0.129099
$61$	−1.96906	−0.252113	−0.126056	−	0.992023i	$-0.540232\pi$
$61$	−1.96906	−0.252113	−0.126056	+	0.992023i	$0.540232\pi$
$62$	−2.91916	−0.370734
$63$	−3.96906	−0.500055
$64$	1.00000	0.125000
$65$	−0.919164	−0.114008
$66$	3.04990	0.375417
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	0.351780	0.0426596
$69$	3.43262	0.413238
$70$	−3.96906	−0.474394
$71$	−5.61728	−0.666649	−0.333324	−	0.942812i	$-0.608170\pi$
$71$	−5.61728	−0.666649	−0.333324	+	0.942812i	$0.608170\pi$
$72$	−1.00000	−0.117851
$73$	−12.8034	−1.49852	−0.749260	−	0.662276i	$-0.769591\pi$
$73$	−12.8034	−1.49852	−0.749260	+	0.662276i	$0.769591\pi$
$74$	−5.40168	−0.627932
$75$	−1.00000	−0.115470
$76$	−0.351780	−0.0403519
$77$	−12.1052	−1.37952
$78$	0.919164	0.104075
$79$	11.8842	1.33708	0.668538	−	0.743678i	$-0.266920\pi$
$79$	11.8842	1.33708	0.668538	+	0.743678i	$0.266920\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	8.45158	0.933321
$83$	0.105239	0.0115515	0.00577573	−	0.999983i	$-0.498162\pi$
$83$	0.105239	0.0115515	0.00577573	+	0.999983i	$0.498162\pi$
$84$	3.96906	0.433060
$85$	−0.351780	−0.0381559
$86$	−6.09980	−0.657758
$87$	−9.37074	−1.00465
$88$	−3.04990	−0.325120
$89$	−16.2050	−1.71773	−0.858865	−	0.512202i	$-0.828830\pi$
$89$	−16.2050	−1.71773	−0.858865	+	0.512202i	$0.828830\pi$
$90$	1.00000	0.105409
$91$	−3.64822	−0.382437
$92$	−3.43262	−0.357875
$93$	−2.91916	−0.302703
$94$	13.2091	1.36241
$95$	0.351780	0.0360919
$96$	1.00000	0.102062
$97$	3.04990	0.309670	0.154835	−	0.987940i	$-0.450515\pi$
$97$	3.04990	0.309670	0.154835	+	0.987940i	$0.450515\pi$
$98$	−8.75346	−0.884233
$99$	3.04990	0.306526
$100$	1.00000	0.100000
$101$	−4.69812	−0.467480	−0.233740	−	0.972299i	$-0.575096\pi$
$101$	−4.69812	−0.467480	−0.233740	+	0.972299i	$0.575096\pi$
$102$	0.351780	0.0348314
$103$	2.09980	0.206899	0.103450	−	0.994635i	$-0.467012\pi$
$103$	2.09980	0.206899	0.103450	+	0.994635i	$0.467012\pi$
$104$	−0.919164	−0.0901315
$105$	−3.96906	−0.387341
$106$	−5.93813	−0.576762
$107$	−9.83833	−0.951107	−0.475554	−	0.879687i	$-0.657752\pi$
$107$	−9.83833	−0.951107	−0.475554	+	0.879687i	$0.657752\pi$
$108$	−1.00000	−0.0962250
$109$	1.26550	0.121213	0.0606066	−	0.998162i	$-0.480696\pi$
$109$	1.26550	0.121213	0.0606066	+	0.998162i	$0.480696\pi$
$110$	3.04990	0.290796
$111$	−5.40168	−0.512705
$112$	−3.96906	−0.375041
$113$	9.69158	0.911708	0.455854	−	0.890055i	$-0.349334\pi$
$113$	9.69158	0.911708	0.455854	+	0.890055i	$0.349334\pi$
$114$	−0.351780	−0.0329472
$115$	3.43262	0.320093
$116$	9.37074	0.870051
$117$	0.919164	0.0849768
$118$	8.45158	0.778031
$119$	−1.39624	−0.127993
$120$	−1.00000	−0.0912871
$121$	−1.69812	−0.154374
$122$	1.96906	0.178271
$123$	8.45158	0.762053
$124$	2.91916	0.262149
$125$	−1.00000	−0.0894427
$126$	3.96906	0.353592
$127$	−12.9650	−1.15046	−0.575230	−	0.817992i	$-0.695088\pi$
$127$	−12.9650	−1.15046	−0.575230	+	0.817992i	$0.695088\pi$
$128$	−1.00000	−0.0883883
$129$	−6.09980	−0.537057
$130$	0.919164	0.0806160
$131$	−12.5135	−1.09331	−0.546653	−	0.837359i	$-0.684098\pi$
$131$	−12.5135	−1.09331	−0.546653	+	0.837359i	$0.684098\pi$
$132$	−3.04990	−0.265460
$133$	1.39624	0.121069
$134$	1.00000	0.0863868
$135$	1.00000	0.0860663
$136$	−0.351780	−0.0301649
$137$	1.40168	0.119753	0.0598767	−	0.998206i	$-0.480929\pi$
$137$	1.40168	0.119753	0.0598767	+	0.998206i	$0.480929\pi$
$138$	−3.43262	−0.292204
$139$	6.02844	0.511325	0.255663	−	0.966766i	$-0.417706\pi$
$139$	6.02844	0.511325	0.255663	+	0.966766i	$0.417706\pi$
$140$	3.96906	0.335447
$141$	13.2091	1.11240
$142$	5.61728	0.471392
$143$	2.80336	0.234429
$144$	1.00000	0.0833333
$145$	−9.37074	−0.778198
$146$	12.8034	1.05961
$147$	−8.75346	−0.721973
$148$	5.40168	0.444015
$149$	9.37074	0.767681	0.383841	−	0.923399i	$-0.374601\pi$
$149$	9.37074	0.767681	0.383841	+	0.923399i	$0.374601\pi$
$150$	1.00000	0.0816497
$151$	−3.14021	−0.255547	−0.127773	−	0.991803i	$-0.540783\pi$
$151$	−3.14021	−0.255547	−0.127773	+	0.991803i	$0.540783\pi$
$152$	0.351780	0.0285331
$153$	0.351780	0.0284397
$154$	12.1052	0.975468
$155$	−2.91916	−0.234473
$156$	−0.919164	−0.0735920
$157$	14.5798	1.16360	0.581798	−	0.813333i	$-0.302350\pi$
$157$	14.5798	1.16360	0.581798	+	0.813333i	$0.302350\pi$
$158$	−11.8842	−0.945456
$159$	−5.93813	−0.470924
$160$	1.00000	0.0790569
$161$	13.6243	1.07374
$162$	−1.00000	−0.0785674
$163$	−4.59832	−0.360168	−0.180084	−	0.983651i	$-0.557637\pi$
$163$	−4.59832	−0.360168	−0.180084	+	0.983651i	$0.557637\pi$
$164$	−8.45158	−0.659957
$165$	3.04990	0.237434
$166$	−0.105239	−0.00816811
$167$	−6.40571	−0.495689	−0.247844	−	0.968800i	$-0.579722\pi$
$167$	−6.40571	−0.495689	−0.247844	+	0.968800i	$0.579722\pi$
$168$	−3.96906	−0.306220
$169$	−12.1551	−0.935011
$170$	0.351780	0.0269803
$171$	−0.351780	−0.0269013
$172$	6.09980	0.465105
$173$	−24.9625	−1.89787	−0.948933	−	0.315478i	$-0.897835\pi$
$173$	−24.9625	−1.89787	−0.948933	+	0.315478i	$0.897835\pi$
$174$	9.37074	0.710394
$175$	−3.96906	−0.300033
$176$	3.04990	0.229895
$177$	8.45158	0.635259
$178$	16.2050	1.21462
$179$	−14.1282	−1.05599	−0.527997	−	0.849246i	$-0.677057\pi$
$179$	−14.1282	−1.05599	−0.527997	+	0.849246i	$0.677057\pi$
$180$	−1.00000	−0.0745356
$181$	−11.0729	−0.823042	−0.411521	−	0.911400i	$-0.635002\pi$
$181$	−11.0729	−0.823042	−0.411521	+	0.911400i	$0.635002\pi$
$182$	3.64822	0.270424
$183$	1.96906	0.145557
$184$	3.43262	0.253056
$185$	−5.40168	−0.397139
$186$	2.91916	0.214043
$187$	1.07289	0.0784577
$188$	−13.2091	−0.963370
$189$	3.96906	0.288707
$190$	−0.351780	−0.0255208
$191$	−18.0998	−1.30966	−0.654828	−	0.755778i	$-0.727259\pi$
$191$	−18.0998	−1.30966	−0.654828	+	0.755778i	$0.727259\pi$
$192$	−1.00000	−0.0721688
$193$	−11.6861	−0.841187	−0.420593	−	0.907249i	$-0.638178\pi$
$193$	−11.6861	−0.841187	−0.420593	+	0.907249i	$0.638178\pi$
$194$	−3.04990	−0.218970
$195$	0.919164	0.0658227
$196$	8.75346	0.625247
$197$	−0.161672	−0.0115186	−0.00575932	−	0.999983i	$-0.501833\pi$
$197$	−0.161672	−0.0115186	−0.00575932	+	0.999983i	$0.501833\pi$
$198$	−3.04990	−0.216747
$199$	−8.10524	−0.574565	−0.287283	−	0.957846i	$-0.592752\pi$
$199$	−8.10524	−0.574565	−0.287283	+	0.957846i	$0.592752\pi$
$200$	−1.00000	−0.0707107
$201$	1.00000	0.0705346
$202$	4.69812	0.330558
$203$	−37.1931	−2.61044
$204$	−0.351780	−0.0246295
$205$	8.45158	0.590284
$206$	−2.09980	−0.146300
$207$	−3.43262	−0.238583
$208$	0.919164	0.0637326
$209$	−1.07289	−0.0742136
$210$	3.96906	0.273891
$211$	18.3278	1.26174	0.630870	−	0.775889i	$-0.282698\pi$
$211$	18.3278	1.26174	0.630870	+	0.775889i	$0.282698\pi$
$212$	5.93813	0.407832
$213$	5.61728	0.384890
$214$	9.83833	0.672534
$215$	−6.09980	−0.416003
$216$	1.00000	0.0680414
$217$	−11.5863	−0.786532
$218$	−1.26550	−0.0857107
$219$	12.8034	0.865171
$220$	−3.04990	−0.205624
$221$	0.323344	0.0217504
$222$	5.40168	0.362537
$223$	−0.442091	−0.0296046	−0.0148023	−	0.999890i	$-0.504712\pi$
$223$	−0.442091	−0.0296046	−0.0148023	+	0.999890i	$0.504712\pi$
$224$	3.96906	0.265194
$225$	1.00000	0.0666667
$226$	−9.69158	−0.644675
$227$	−25.3344	−1.68150	−0.840750	−	0.541423i	$-0.817886\pi$
$227$	−25.3344	−1.68150	−0.840750	+	0.541423i	$0.817886\pi$
$228$	0.351780	0.0232972
$229$	8.06886	0.533205	0.266603	−	0.963807i	$-0.414099\pi$
$229$	8.06886	0.533205	0.266603	+	0.963807i	$0.414099\pi$
$230$	−3.43262	−0.226340
$231$	12.1052	0.796466
$232$	−9.37074	−0.615219
$233$	3.67121	0.240509	0.120255	−	0.992743i	$-0.461629\pi$
$233$	3.67121	0.240509	0.120255	+	0.992743i	$0.461629\pi$
$234$	−0.919164	−0.0600876
$235$	13.2091	0.861665
$236$	−8.45158	−0.550151
$237$	−11.8842	−0.771961
$238$	1.39624	0.0905046
$239$	12.9650	0.838638	0.419319	−	0.907839i	$-0.362269\pi$
$239$	12.9650	0.838638	0.419319	+	0.907839i	$0.362269\pi$
$240$	1.00000	0.0645497
$241$	−21.9531	−1.41412	−0.707060	−	0.707153i	$-0.749979\pi$
$241$	−21.9531	−1.41412	−0.707060	+	0.707153i	$0.749979\pi$
$242$	1.69812	0.109159
$243$	−1.00000	−0.0641500
$244$	−1.96906	−0.126056
$245$	−8.75346	−0.559238
$246$	−8.45158	−0.538853
$247$	−0.323344	−0.0205739
$248$	−2.91916	−0.185367
$249$	−0.105239	−0.00666924
$250$	1.00000	0.0632456
$251$	−4.59832	−0.290243	−0.145122	−	0.989414i	$-0.546357\pi$
$251$	−4.59832	−0.290243	−0.145122	+	0.989414i	$0.546357\pi$
$252$	−3.96906	−0.250027
$253$	−10.4691	−0.658189
$254$	12.9650	0.813498
$255$	0.351780	0.0220293
$256$	1.00000	0.0625000
$257$	19.7968	1.23489	0.617446	−	0.786613i	$-0.288167\pi$
$257$	19.7968	1.23489	0.617446	+	0.786613i	$0.288167\pi$
$258$	6.09980	0.379757
$259$	−21.4396	−1.33219
$260$	−0.919164	−0.0570041
$261$	9.37074	0.580034
$262$	12.5135	0.773084
$263$	−17.4705	−1.07728	−0.538640	−	0.842536i	$-0.681062\pi$
$263$	−17.4705	−1.07728	−0.538640	+	0.842536i	$0.681062\pi$
$264$	3.04990	0.187708
$265$	−5.93813	−0.364776
$266$	−1.39624	−0.0856088
$267$	16.2050	0.991732
$268$	−1.00000	−0.0610847
$269$	7.33282	0.447090	0.223545	−	0.974694i	$-0.428237\pi$
$269$	7.33282	0.447090	0.223545	+	0.974694i	$0.428237\pi$
$270$	−1.00000	−0.0608581
$271$	−14.1537	−0.859778	−0.429889	−	0.902882i	$-0.641447\pi$
$271$	−14.1537	−0.859778	−0.429889	+	0.902882i	$0.641447\pi$
$272$	0.351780	0.0213298
$273$	3.64822	0.220800
$274$	−1.40168	−0.0846785
$275$	3.04990	0.183916
$276$	3.43262	0.206619
$277$	13.6631	0.820939	0.410469	−	0.911874i	$-0.365365\pi$
$277$	13.6631	0.820939	0.410469	+	0.911874i	$0.365365\pi$
$278$	−6.02844	−0.361562
$279$	2.91916	0.174766
$280$	−3.96906	−0.237197
$281$	−1.67666	−0.100021	−0.0500105	−	0.998749i	$-0.515925\pi$
$281$	−1.67666	−0.100021	−0.0500105	+	0.998749i	$0.515925\pi$
$282$	−13.2091	−0.786589
$283$	0.978538	0.0581680	0.0290840	−	0.999577i	$-0.490741\pi$
$283$	0.978538	0.0581680	0.0290840	+	0.999577i	$0.490741\pi$
$284$	−5.61728	−0.333324
$285$	−0.351780	−0.0208377
$286$	−2.80336	−0.165766
$287$	33.5448	1.98009
$288$	−1.00000	−0.0589256
$289$	−16.8763	−0.992721
$290$	9.37074	0.550269
$291$	−3.04990	−0.178788
$292$	−12.8034	−0.749260
$293$	16.5823	0.968749	0.484374	−	0.874861i	$-0.339047\pi$
$293$	16.5823	0.968749	0.484374	+	0.874861i	$0.339047\pi$
$294$	8.75346	0.510512
$295$	8.45158	0.492070
$296$	−5.40168	−0.313966
$297$	−3.04990	−0.176973
$298$	−9.37074	−0.542832
$299$	−3.15514	−0.182466
$300$	−1.00000	−0.0577350
$301$	−24.2105	−1.39547
$302$	3.14021	0.180699
$303$	4.69812	0.269900
$304$	−0.351780	−0.0201760
$305$	1.96906	0.112748
$306$	−0.351780	−0.0201099
$307$	−24.3843	−1.39168	−0.695842	−	0.718195i	$-0.744968\pi$
$307$	−24.3843	−1.39168	−0.695842	+	0.718195i	$0.744968\pi$
$308$	−12.1052	−0.689760
$309$	−2.09980	−0.119453
$310$	2.91916	0.165797
$311$	6.03792	0.342379	0.171190	−	0.985238i	$-0.445239\pi$
$311$	6.03792	0.342379	0.171190	+	0.985238i	$0.445239\pi$
$312$	0.919164	0.0520374
$313$	11.4301	0.646068	0.323034	−	0.946387i	$-0.395297\pi$
$313$	11.4301	0.646068	0.323034	+	0.946387i	$0.395297\pi$
$314$	−14.5798	−0.822786
$315$	3.96906	0.223631
$316$	11.8842	0.668538
$317$	−29.3911	−1.65077	−0.825385	−	0.564571i	$-0.809042\pi$
$317$	−29.3911	−1.65077	−0.825385	+	0.564571i	$0.809042\pi$
$318$	5.93813	0.332994
$319$	28.5798	1.60016
$320$	−1.00000	−0.0559017
$321$	9.83833	0.549122
$322$	−13.6243	−0.759251
$323$	−0.123749	−0.00688559
$324$	1.00000	0.0555556
$325$	0.919164	0.0509861
$326$	4.59832	0.254677
$327$	−1.26550	−0.0699825
$328$	8.45158	0.466660
$329$	52.4276	2.89043
$330$	−3.04990	−0.167891
$331$	−4.60781	−0.253268	−0.126634	−	0.991950i	$-0.540417\pi$
$331$	−4.60781	−0.253268	−0.126634	+	0.991950i	$0.540417\pi$
$332$	0.105239	0.00577573
$333$	5.40168	0.296010
$334$	6.40571	0.350505
$335$	1.00000	0.0546358
$336$	3.96906	0.216530
$337$	18.0095	0.981039	0.490520	−	0.871430i	$-0.336807\pi$
$337$	18.0095	0.981039	0.490520	+	0.871430i	$0.336807\pi$
$338$	12.1551	0.661152
$339$	−9.69158	−0.526375
$340$	−0.351780	−0.0190780
$341$	8.90315	0.482133
$342$	0.351780	0.0190221
$343$	−6.95959	−0.375782
$344$	−6.09980	−0.328879
$345$	−3.43262	−0.184806
$346$	24.9625	1.34199
$347$	−10.7239	−0.575691	−0.287845	−	0.957677i	$-0.592939\pi$
$347$	−10.7239	−0.575691	−0.287845	+	0.957677i	$0.592939\pi$
$348$	−9.37074	−0.502324
$349$	18.1996	0.974202	0.487101	−	0.873346i	$-0.338054\pi$
$349$	18.1996	0.974202	0.487101	+	0.873346i	$0.338054\pi$
$350$	3.96906	0.212155
$351$	−0.919164	−0.0490614
$352$	−3.04990	−0.162560
$353$	25.5863	1.36182	0.680912	−	0.732365i	$-0.261584\pi$
$353$	25.5863	1.36182	0.680912	+	0.732365i	$0.261584\pi$
$354$	−8.45158	−0.449196
$355$	5.61728	0.298134
$356$	−16.2050	−0.858865
$357$	1.39624	0.0738967
$358$	14.1282	0.746700
$359$	4.59038	0.242271	0.121135	−	0.992636i	$-0.461346\pi$
$359$	4.59038	0.242271	0.121135	+	0.992636i	$0.461346\pi$
$360$	1.00000	0.0527046
$361$	−18.8763	−0.993487
$362$	11.0729	0.581978
$363$	1.69812	0.0891281
$364$	−3.64822	−0.191219
$365$	12.8034	0.670158
$366$	−1.96906	−0.102925
$367$	26.9855	1.40863	0.704316	−	0.709886i	$-0.251254\pi$
$367$	26.9855	1.40863	0.704316	+	0.709886i	$0.251254\pi$
$368$	−3.43262	−0.178937
$369$	−8.45158	−0.439972
$370$	5.40168	0.280820
$371$	−23.5688	−1.22363
$372$	−2.91916	−0.151352
$373$	−16.7954	−0.869634	−0.434817	−	0.900519i	$-0.643187\pi$
$373$	−16.7954	−0.869634	−0.434817	+	0.900519i	$0.643187\pi$
$374$	−1.07289	−0.0554780
$375$	1.00000	0.0516398
$376$	13.2091	0.681206
$377$	8.61325	0.443605
$378$	−3.96906	−0.204147
$379$	−21.9047	−1.12517	−0.562584	−	0.826740i	$-0.690193\pi$
$379$	−21.9047	−1.12517	−0.562584	+	0.826740i	$0.690193\pi$
$380$	0.351780	0.0180459
$381$	12.9650	0.664219
$382$	18.0998	0.926066
$383$	−4.47457	−0.228640	−0.114320	−	0.993444i	$-0.536469\pi$
$383$	−4.47457	−0.228640	−0.114320	+	0.993444i	$0.536469\pi$
$384$	1.00000	0.0510310
$385$	12.1052	0.616940
$386$	11.6861	0.594809
$387$	6.09980	0.310070
$388$	3.04990	0.154835
$389$	30.4545	1.54411	0.772053	−	0.635559i	$-0.219230\pi$
$389$	30.4545	1.54411	0.772053	+	0.635559i	$0.219230\pi$
$390$	−0.919164	−0.0465437
$391$	−1.20753	−0.0610672
$392$	−8.75346	−0.442116
$393$	12.5135	0.631220
$394$	0.161672	0.00814491
$395$	−11.8842	−0.597959
$396$	3.04990	0.153263
$397$	27.3777	1.37405	0.687024	−	0.726634i	$-0.258917\pi$
$397$	27.3777	1.37405	0.687024	+	0.726634i	$0.258917\pi$
$398$	8.10524	0.406279
$399$	−1.39624	−0.0698993
$400$	1.00000	0.0500000
$401$	−34.0867	−1.70221	−0.851105	−	0.524996i	$-0.824067\pi$
$401$	−34.0867	−1.70221	−0.851105	+	0.524996i	$0.824067\pi$
$402$	−1.00000	−0.0498755
$403$	2.68319	0.133659
$404$	−4.69812	−0.233740
$405$	−1.00000	−0.0496904
$406$	37.1931	1.84586
$407$	16.4746	0.816614
$408$	0.351780	0.0174157
$409$	8.16167	0.403569	0.201784	−	0.979430i	$-0.435326\pi$
$409$	8.16167	0.403569	0.201784	+	0.979430i	$0.435326\pi$
$410$	−8.45158	−0.417394
$411$	−1.40168	−0.0691397
$412$	2.09980	0.103450
$413$	33.5448	1.65063
$414$	3.43262	0.168704
$415$	−0.105239	−0.00516597
$416$	−0.919164	−0.0450657
$417$	−6.02844	−0.295214
$418$	1.07289	0.0524769
$419$	27.3628	1.33676	0.668380	−	0.743820i	$-0.266988\pi$
$419$	27.3628	1.33676	0.668380	+	0.743820i	$0.266988\pi$
$420$	−3.96906	−0.193670
$421$	−15.9760	−0.778625	−0.389312	−	0.921106i	$-0.627287\pi$
$421$	−15.9760	−0.778625	−0.389312	+	0.921106i	$0.627287\pi$
$422$	−18.3278	−0.892185
$423$	−13.2091	−0.642247
$424$	−5.93813	−0.288381
$425$	0.351780	0.0170638
$426$	−5.61728	−0.272158
$427$	7.81533	0.378210
$428$	−9.83833	−0.475554
$429$	−2.80336	−0.135347
$430$	6.09980	0.294158
$431$	16.7900	0.808745	0.404372	−	0.914594i	$-0.367490\pi$
$431$	16.7900	0.808745	0.404372	+	0.914594i	$0.367490\pi$
$432$	−1.00000	−0.0481125
$433$	29.6352	1.42417	0.712087	−	0.702091i	$-0.247750\pi$
$433$	29.6352	1.42417	0.712087	+	0.702091i	$0.247750\pi$
$434$	11.5863	0.556162
$435$	9.37074	0.449293
$436$	1.26550	0.0606066
$437$	1.20753	0.0577638
$438$	−12.8034	−0.611768
$439$	1.99456	0.0951951	0.0475975	−	0.998867i	$-0.484844\pi$
$439$	1.99456	0.0951951	0.0475975	+	0.998867i	$0.484844\pi$
$440$	3.04990	0.145398
$441$	8.75346	0.416831
$442$	−0.323344	−0.0153799
$443$	−3.29644	−0.156619	−0.0783093	−	0.996929i	$-0.524952\pi$
$443$	−3.29644	−0.156619	−0.0783093	+	0.996929i	$0.524952\pi$
$444$	−5.40168	−0.256352
$445$	16.2050	0.768192
$446$	0.442091	0.0209336
$447$	−9.37074	−0.443221
$448$	−3.96906	−0.187521
$449$	−13.9196	−0.656907	−0.328454	−	0.944520i	$-0.606527\pi$
$449$	−13.9196	−0.656907	−0.328454	+	0.944520i	$0.606527\pi$
$450$	−1.00000	−0.0471405
$451$	−25.7765	−1.21377
$452$	9.69158	0.455854
$453$	3.14021	0.147540
$454$	25.3344	1.18900
$455$	3.64822	0.171031
$456$	−0.351780	−0.0164736
$457$	12.3897	0.579566	0.289783	−	0.957092i	$-0.406417\pi$
$457$	12.3897	0.579566	0.289783	+	0.957092i	$0.406417\pi$
$458$	−8.06886	−0.377033
$459$	−0.351780	−0.0164197
$460$	3.43262	0.160047
$461$	38.8537	1.80960	0.904799	−	0.425839i	$-0.140021\pi$
$461$	38.8537	1.80960	0.904799	+	0.425839i	$0.140021\pi$
$462$	−12.1052	−0.563187
$463$	−5.85076	−0.271908	−0.135954	−	0.990715i	$-0.543410\pi$
$463$	−5.85076	−0.271908	−0.135954	+	0.990715i	$0.543410\pi$
$464$	9.37074	0.435026
$465$	2.91916	0.135373
$466$	−3.67121	−0.170066
$467$	−6.37477	−0.294989	−0.147495	−	0.989063i	$-0.547121\pi$
$467$	−6.37477	−0.294989	−0.147495	+	0.989063i	$0.547121\pi$
$468$	0.919164	0.0424884
$469$	3.96906	0.183274
$470$	−13.2091	−0.609289
$471$	−14.5798	−0.671802
$472$	8.45158	0.389015
$473$	18.6038	0.855402
$474$	11.8842	0.545859
$475$	−0.351780	−0.0161408
$476$	−1.39624	−0.0639964
$477$	5.93813	0.271888
$478$	−12.9650	−0.593007
$479$	13.5094	0.617261	0.308631	−	0.951182i	$-0.400129\pi$
$479$	13.5094	0.617261	0.308631	+	0.951182i	$0.400129\pi$
$480$	−1.00000	−0.0456435
$481$	4.96503	0.226386
$482$	21.9531	0.999934
$483$	−13.6243	−0.619926
$484$	−1.69812	−0.0771872
$485$	−3.04990	−0.138489
$486$	1.00000	0.0453609
$487$	24.4920	1.10984	0.554919	−	0.831904i	$-0.312749\pi$
$487$	24.4920	1.10984	0.554919	+	0.831904i	$0.312749\pi$
$488$	1.96906	0.0891353
$489$	4.59832	0.207943
$490$	8.75346	0.395441
$491$	1.59723	0.0720819	0.0360410	−	0.999350i	$-0.488525\pi$
$491$	1.59723	0.0720819	0.0360410	+	0.999350i	$0.488525\pi$
$492$	8.45158	0.381027
$493$	3.29644	0.148464
$494$	0.323344	0.0145479
$495$	−3.04990	−0.137083
$496$	2.91916	0.131074
$497$	22.2953	1.00008
$498$	0.105239	0.00471586
$499$	21.5837	0.966220	0.483110	−	0.875560i	$-0.339507\pi$
$499$	21.5837	0.966220	0.483110	+	0.875560i	$0.339507\pi$
$500$	−1.00000	−0.0447214
$501$	6.40571	0.286186
$502$	4.59832	0.205233
$503$	−34.3428	−1.53127	−0.765634	−	0.643277i	$-0.777575\pi$
$503$	−34.3428	−1.53127	−0.765634	+	0.643277i	$0.777575\pi$
$504$	3.96906	0.176796
$505$	4.69812	0.209064
$506$	10.4691	0.465410
$507$	12.1551	0.539829
$508$	−12.9650	−0.575230
$509$	25.3089	1.12180	0.560898	−	0.827885i	$-0.310456\pi$
$509$	25.3089	1.12180	0.560898	+	0.827885i	$0.310456\pi$
$510$	−0.351780	−0.0155771
$511$	50.8173	2.24803
$512$	−1.00000	−0.0441942
$513$	0.351780	0.0155315
$514$	−19.7968	−0.873200
$515$	−2.09980	−0.0925281
$516$	−6.09980	−0.268529
$517$	−40.2863	−1.77179
$518$	21.4396	0.942002
$519$	24.9625	1.09573
$520$	0.919164	0.0403080
$521$	−23.4545	−1.02756	−0.513781	−	0.857922i	$-0.671756\pi$
$521$	−23.4545	−1.02756	−0.513781	+	0.857922i	$0.671756\pi$
$522$	−9.37074	−0.410146
$523$	−19.4586	−0.850863	−0.425432	−	0.904991i	$-0.639878\pi$
$523$	−19.4586	−0.850863	−0.425432	+	0.904991i	$0.639878\pi$
$524$	−12.5135	−0.546653
$525$	3.96906	0.173224
$526$	17.4705	0.761752
$527$	1.02690	0.0447326
$528$	−3.04990	−0.132730
$529$	−11.2171	−0.487702
$530$	5.93813	0.257936
$531$	−8.45158	−0.366767
$532$	1.39624	0.0605346
$533$	−7.76839	−0.336486
$534$	−16.2050	−0.701260
$535$	9.83833	0.425348
$536$	1.00000	0.0431934
$537$	14.1282	0.609678
$538$	−7.33282	−0.316140
$539$	26.6972	1.14993
$540$	1.00000	0.0430331
$541$	−39.2389	−1.68701	−0.843507	−	0.537119i	$-0.819513\pi$
$541$	−39.2389	−1.68701	−0.843507	+	0.537119i	$0.819513\pi$
$542$	14.1537	0.607955
$543$	11.0729	0.475183
$544$	−0.351780	−0.0150824
$545$	−1.26550	−0.0542082
$546$	−3.64822	−0.156129
$547$	−26.1865	−1.11965	−0.559827	−	0.828609i	$-0.689133\pi$
$547$	−26.1865	−1.11965	−0.559827	+	0.828609i	$0.689133\pi$
$548$	1.40168	0.0598767
$549$	−1.96906	−0.0840375
$550$	−3.04990	−0.130048
$551$	−3.29644	−0.140433
$552$	−3.43262	−0.146102
$553$	−47.1691	−2.00583
$554$	−13.6631	−0.580492
$555$	5.40168	0.229288
$556$	6.02844	0.255663
$557$	−40.1326	−1.70047	−0.850236	−	0.526401i	$-0.823541\pi$
$557$	−40.1326	−1.70047	−0.850236	+	0.526401i	$0.823541\pi$
$558$	−2.91916	−0.123578
$559$	5.60671	0.237139
$560$	3.96906	0.167724
$561$	−1.07289	−0.0452976
$562$	1.67666	0.0707255
$563$	−18.0998	−0.762816	−0.381408	−	0.924407i	$-0.624561\pi$
$563$	−18.0998	−0.762816	−0.381408	+	0.924407i	$0.624561\pi$
$564$	13.2091	0.556202
$565$	−9.69158	−0.407728
$566$	−0.978538	−0.0411310
$567$	−3.96906	−0.166685
$568$	5.61728	0.235696
$569$	14.4905	0.607472	0.303736	−	0.952756i	$-0.401766\pi$
$569$	14.4905	0.607472	0.303736	+	0.952756i	$0.401766\pi$
$570$	0.351780	0.0147344
$571$	0.703560	0.0294431	0.0147215	−	0.999892i	$-0.495314\pi$
$571$	0.703560	0.0294431	0.0147215	+	0.999892i	$0.495314\pi$
$572$	2.80336	0.117214
$573$	18.0998	0.756130
$574$	−33.5448	−1.40013
$575$	−3.43262	−0.143150
$576$	1.00000	0.0416667
$577$	−32.8237	−1.36647	−0.683235	−	0.730199i	$-0.739427\pi$
$577$	−32.8237	−1.36647	−0.683235	+	0.730199i	$0.739427\pi$
$578$	16.8763	0.701959
$579$	11.6861	0.485660
$580$	−9.37074	−0.389099
$581$	−0.417699	−0.0173291
$582$	3.04990	0.126422
$583$	18.1107	0.750068
$584$	12.8034	0.529807
$585$	−0.919164	−0.0380028
$586$	−16.5823	−0.685009
$587$	−39.2929	−1.62179	−0.810895	−	0.585192i	$-0.801019\pi$
$587$	−39.2929	−1.62179	−0.810895	+	0.585192i	$0.801019\pi$
$588$	−8.75346	−0.360987
$589$	−1.02690	−0.0423128
$590$	−8.45158	−0.347946
$591$	0.161672	0.00665029
$592$	5.40168	0.222008
$593$	10.3048	0.423169	0.211584	−	0.977360i	$-0.432138\pi$
$593$	10.3048	0.423169	0.211584	+	0.977360i	$0.432138\pi$
$594$	3.04990	0.125139
$595$	1.39624	0.0572401
$596$	9.37074	0.383841
$597$	8.10524	0.331725
$598$	3.15514	0.129023
$599$	28.3183	1.15706	0.578528	−	0.815662i	$-0.303627\pi$
$599$	28.3183	1.15706	0.578528	+	0.815662i	$0.303627\pi$
$600$	1.00000	0.0408248
$601$	24.2335	0.988504	0.494252	−	0.869319i	$-0.335442\pi$
$601$	24.2335	0.988504	0.494252	+	0.869319i	$0.335442\pi$
$602$	24.2105	0.986745
$603$	−1.00000	−0.0407231
$604$	−3.14021	−0.127773
$605$	1.69812	0.0690383
$606$	−4.69812	−0.190848
$607$	27.6148	1.12085	0.560425	−	0.828205i	$-0.310638\pi$
$607$	27.6148	1.12085	0.560425	+	0.828205i	$0.310638\pi$
$608$	0.351780	0.0142666
$609$	37.1931	1.50714
$610$	−1.96906	−0.0797250
$611$	−12.1413	−0.491185
$612$	0.351780	0.0142199
$613$	37.7525	1.52481	0.762405	−	0.647101i	$-0.224019\pi$
$613$	37.7525	1.52481	0.762405	+	0.647101i	$0.224019\pi$
$614$	24.3843	0.984069
$615$	−8.45158	−0.340800
$616$	12.1052	0.487734
$617$	−25.5733	−1.02954	−0.514771	−	0.857328i	$-0.672123\pi$
$617$	−25.5733	−1.02954	−0.514771	+	0.857328i	$0.672123\pi$
$618$	2.09980	0.0844662
$619$	−20.3518	−0.818007	−0.409004	−	0.912533i	$-0.634124\pi$
$619$	−20.3518	−0.818007	−0.409004	+	0.912533i	$0.634124\pi$
$620$	−2.91916	−0.117236
$621$	3.43262	0.137746
$622$	−6.03792	−0.242099
$623$	64.3188	2.57688
$624$	−0.919164	−0.0367960
$625$	1.00000	0.0400000
$626$	−11.4301	−0.456839
$627$	1.07289	0.0428472
$628$	14.5798	0.581798
$629$	1.90020	0.0757660
$630$	−3.96906	−0.158131
$631$	−17.7844	−0.707986	−0.353993	−	0.935248i	$-0.615176\pi$
$631$	−17.7844	−0.707986	−0.353993	+	0.935248i	$0.615176\pi$
$632$	−11.8842	−0.472728
$633$	−18.3278	−0.728466
$634$	29.3911	1.16727
$635$	12.9650	0.514501
$636$	−5.93813	−0.235462
$637$	8.04586	0.318789
$638$	−28.5798	−1.13149
$639$	−5.61728	−0.222216
$640$	1.00000	0.0395285
$641$	−37.4292	−1.47836	−0.739181	−	0.673506i	$-0.764787\pi$
$641$	−37.4292	−1.47836	−0.739181	+	0.673506i	$0.764787\pi$
$642$	−9.83833	−0.388288
$643$	25.7729	1.01638	0.508191	−	0.861244i	$-0.330314\pi$
$643$	25.7729	1.01638	0.508191	+	0.861244i	$0.330314\pi$
$644$	13.6243	0.536871
$645$	6.09980	0.240179
$646$	0.123749	0.00486885
$647$	−29.8658	−1.17415	−0.587073	−	0.809534i	$-0.699720\pi$
$647$	−29.8658	−1.17415	−0.587073	+	0.809534i	$0.699720\pi$
$648$	−1.00000	−0.0392837
$649$	−25.7765	−1.01181
$650$	−0.919164	−0.0360526
$651$	11.5863	0.454105
$652$	−4.59832	−0.180084
$653$	−48.8282	−1.91080	−0.955398	−	0.295322i	$-0.904573\pi$
$653$	−48.8282	−1.91080	−0.955398	+	0.295322i	$0.904573\pi$
$654$	1.26550	0.0494851
$655$	12.5135	0.488941
$656$	−8.45158	−0.329979
$657$	−12.8034	−0.499507
$658$	−52.4276	−2.04384
$659$	8.24110	0.321028	0.160514	−	0.987034i	$-0.448685\pi$
$659$	8.24110	0.321028	0.160514	+	0.987034i	$0.448685\pi$
$660$	3.04990	0.118717
$661$	−24.6053	−0.957036	−0.478518	−	0.878078i	$-0.658826\pi$
$661$	−24.6053	−0.957036	−0.478518	+	0.878078i	$0.658826\pi$
$662$	4.60781	0.179088
$663$	−0.323344	−0.0125576
$664$	−0.105239	−0.00408406
$665$	−1.39624	−0.0541438
$666$	−5.40168	−0.209311
$667$	−32.1662	−1.24548
$668$	−6.40571	−0.247844
$669$	0.442091	0.0170922
$670$	−1.00000	−0.0386334
$671$	−6.00544	−0.231838
$672$	−3.96906	−0.153110
$673$	−14.0822	−0.542831	−0.271415	−	0.962462i	$-0.587492\pi$
$673$	−14.0822	−0.542831	−0.271415	+	0.962462i	$0.587492\pi$
$674$	−18.0095	−0.693699
$675$	−1.00000	−0.0384900
$676$	−12.1551	−0.467505
$677$	5.67666	0.218172	0.109086	−	0.994032i	$-0.465208\pi$
$677$	5.67666	0.218172	0.109086	+	0.994032i	$0.465208\pi$
$678$	9.69158	0.372203
$679$	−12.1052	−0.464556
$680$	0.351780	0.0134901
$681$	25.3344	0.970815
$682$	−8.90315	−0.340919
$683$	3.63067	0.138924	0.0694618	−	0.997585i	$-0.477872\pi$
$683$	3.63067	0.138924	0.0694618	+	0.997585i	$0.477872\pi$
$684$	−0.351780	−0.0134506
$685$	−1.40168	−0.0535554
$686$	6.95959	0.265718
$687$	−8.06886	−0.307846
$688$	6.09980	0.232553
$689$	5.45811	0.207937
$690$	3.43262	0.130677
$691$	13.2374	0.503574	0.251787	−	0.967783i	$-0.418982\pi$
$691$	13.2374	0.503574	0.251787	+	0.967783i	$0.418982\pi$
$692$	−24.9625	−0.948933
$693$	−12.1052	−0.459840
$694$	10.7239	0.407075
$695$	−6.02844	−0.228672
$696$	9.37074	0.355197
$697$	−2.97310	−0.112614
$698$	−18.1996	−0.688865
$699$	−3.67121	−0.138858
$700$	−3.96906	−0.150016
$701$	−20.5125	−0.774746	−0.387373	−	0.921923i	$-0.626617\pi$
$701$	−20.5125	−0.774746	−0.387373	+	0.921923i	$0.626617\pi$
$702$	0.919164	0.0346916
$703$	−1.90020	−0.0716675
$704$	3.04990	0.114947
$705$	−13.2091	−0.497482
$706$	−25.5863	−0.962955
$707$	18.6471	0.701297
$708$	8.45158	0.317630
$709$	18.1946	0.683312	0.341656	−	0.939825i	$-0.389012\pi$
$709$	18.1946	0.683312	0.341656	+	0.939825i	$0.389012\pi$
$710$	−5.61728	−0.210813
$711$	11.8842	0.445692
$712$	16.2050	0.607309
$713$	−10.0204	−0.375266
$714$	−1.39624	−0.0522529
$715$	−2.80336	−0.104840
$716$	−14.1282	−0.527997
$717$	−12.9650	−0.484188
$718$	−4.59038	−0.171311
$719$	11.4990	0.428839	0.214420	−	0.976742i	$-0.431214\pi$
$719$	11.4990	0.428839	0.214420	+	0.976742i	$0.431214\pi$
$720$	−1.00000	−0.0372678
$721$	−8.33423	−0.310383
$722$	18.8763	0.702501
$723$	21.9531	0.816443
$724$	−11.0729	−0.411521
$725$	9.37074	0.348021
$726$	−1.69812	−0.0630231
$727$	25.8508	0.958751	0.479376	−	0.877610i	$-0.340863\pi$
$727$	25.8508	0.958751	0.479376	+	0.877610i	$0.340863\pi$
$728$	3.64822	0.135212
$729$	1.00000	0.0370370
$730$	−12.8034	−0.473874
$731$	2.14579	0.0793648
$732$	1.96906	0.0727787
$733$	32.1836	1.18873	0.594364	−	0.804196i	$-0.297404\pi$
$733$	32.1836	1.18873	0.594364	+	0.804196i	$0.297404\pi$
$734$	−26.9855	−0.996054
$735$	8.75346	0.322876
$736$	3.43262	0.126528
$737$	−3.04990	−0.112344
$738$	8.45158	0.311107
$739$	−9.32488	−0.343021	−0.171511	−	0.985182i	$-0.554865\pi$
$739$	−9.32488	−0.343021	−0.171511	+	0.985182i	$0.554865\pi$
$740$	−5.40168	−0.198570
$741$	0.323344	0.0118783
$742$	23.5688	0.865238
$743$	−12.5624	−0.460869	−0.230435	−	0.973088i	$-0.574015\pi$
$743$	−12.5624	−0.460869	−0.230435	+	0.973088i	$0.574015\pi$
$744$	2.91916	0.107022
$745$	−9.37074	−0.343317
$746$	16.7954	0.614924
$747$	0.105239	0.00385048
$748$	1.07289	0.0392289
$749$	39.0489	1.42682
$750$	−1.00000	−0.0365148
$751$	−16.1996	−0.591132	−0.295566	−	0.955322i	$-0.595508\pi$
$751$	−16.1996	−0.591132	−0.295566	+	0.955322i	$0.595508\pi$
$752$	−13.2091	−0.481685
$753$	4.59832	0.167572
$754$	−8.61325	−0.313676
$755$	3.14021	0.114284
$756$	3.96906	0.144353
$757$	16.8682	0.613084	0.306542	−	0.951857i	$-0.400828\pi$
$757$	16.8682	0.613084	0.306542	+	0.951857i	$0.400828\pi$
$758$	21.9047	0.795614
$759$	10.4691	0.380005
$760$	−0.351780	−0.0127604
$761$	21.1701	0.767414	0.383707	−	0.923455i	$-0.374647\pi$
$761$	21.1701	0.767414	0.383707	+	0.923455i	$0.374647\pi$
$762$	−12.9650	−0.469673
$763$	−5.02286	−0.181840
$764$	−18.0998	−0.654828
$765$	−0.351780	−0.0127186
$766$	4.47457	0.161673
$767$	−7.76839	−0.280500
$768$	−1.00000	−0.0360844
$769$	−11.2884	−0.407069	−0.203535	−	0.979068i	$-0.565243\pi$
$769$	−11.2884	−0.407069	−0.203535	+	0.979068i	$0.565243\pi$
$770$	−12.1052	−0.436243
$771$	−19.7968	−0.712965
$772$	−11.6861	−0.420593
$773$	48.8068	1.75546	0.877729	−	0.479158i	$-0.159058\pi$
$773$	48.8068	1.75546	0.877729	+	0.479158i	$0.159058\pi$
$774$	−6.09980	−0.219253
$775$	2.91916	0.104859
$776$	−3.04990	−0.109485
$777$	21.4396	0.769141
$778$	−30.4545	−1.09185
$779$	2.97310	0.106522
$780$	0.919164	0.0329114
$781$	−17.1321	−0.613036
$782$	1.20753	0.0431810
$783$	−9.37074	−0.334883
$784$	8.75346	0.312624
$785$	−14.5798	−0.520376
$786$	−12.5135	−0.446340
$787$	17.4880	0.623379	0.311689	−	0.950184i	$-0.399105\pi$
$787$	17.4880	0.623379	0.311689	+	0.950184i	$0.399105\pi$
$788$	−0.161672	−0.00575932
$789$	17.4705	0.621968
$790$	11.8842	0.422821
$791$	−38.4665	−1.36771
$792$	−3.04990	−0.108373
$793$	−1.80989	−0.0642711
$794$	−27.3777	−0.971599
$795$	5.93813	0.210604
$796$	−8.10524	−0.287283
$797$	40.7200	1.44238	0.721189	−	0.692739i	$-0.243596\pi$
$797$	40.7200	1.44238	0.721189	+	0.692739i	$0.243596\pi$
$798$	1.39624	0.0494263
$799$	−4.64669	−0.164388
$800$	−1.00000	−0.0353553
$801$	−16.2050	−0.572577
$802$	34.0867	1.20364
$803$	−39.0489	−1.37801
$804$	1.00000	0.0352673
$805$	−13.6243	−0.480192
$806$	−2.68319	−0.0945114
$807$	−7.33282	−0.258127
$808$	4.69812	0.165279
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	1.00000	0.0351364
$811$	−1.32725	−0.0466061	−0.0233031	−	0.999728i	$-0.507418\pi$
$811$	−1.32725	−0.0466061	−0.0233031	+	0.999728i	$0.507418\pi$
$812$	−37.1931	−1.30522
$813$	14.1537	0.496393
$814$	−16.4746	−0.577433
$815$	4.59832	0.161072
$816$	−0.351780	−0.0123148
$817$	−2.14579	−0.0750716
$818$	−8.16167	−0.285366
$819$	−3.64822	−0.127479
$820$	8.45158	0.295142
$821$	−0.775046	−0.0270493	−0.0135246	−	0.999909i	$-0.504305\pi$
$821$	−0.775046	−0.0270493	−0.0135246	+	0.999909i	$0.504305\pi$
$822$	1.40168	0.0488892
$823$	−7.00295	−0.244108	−0.122054	−	0.992523i	$-0.538948\pi$
$823$	−7.00295	−0.244108	−0.122054	+	0.992523i	$0.538948\pi$
$824$	−2.09980	−0.0731499
$825$	−3.04990	−0.106184
$826$	−33.5448	−1.16717
$827$	8.24296	0.286636	0.143318	−	0.989677i	$-0.454223\pi$
$827$	8.24296	0.286636	0.143318	+	0.989677i	$0.454223\pi$
$828$	−3.43262	−0.119292
$829$	−17.2346	−0.598581	−0.299291	−	0.954162i	$-0.596750\pi$
$829$	−17.2346	−0.598581	−0.299291	+	0.954162i	$0.596750\pi$
$830$	0.105239	0.00365289
$831$	−13.6631	−0.473969
$832$	0.919164	0.0318663
$833$	3.07929	0.106691
$834$	6.02844	0.208748
$835$	6.40571	0.221679
$836$	−1.07289	−0.0371068
$837$	−2.91916	−0.100901
$838$	−27.3628	−0.945232
$839$	−11.8951	−0.410664	−0.205332	−	0.978692i	$-0.565827\pi$
$839$	−11.8951	−0.410664	−0.205332	+	0.978692i	$0.565827\pi$
$840$	3.96906	0.136946
$841$	58.8108	2.02796
$842$	15.9760	0.550571
$843$	1.67666	0.0577471
$844$	18.3278	0.630870
$845$	12.1551	0.418149
$846$	13.2091	0.454137
$847$	6.73994	0.231587
$848$	5.93813	0.203916
$849$	−0.978538	−0.0335833
$850$	−0.351780	−0.0120660
$851$	−18.5419	−0.635608
$852$	5.61728	0.192445
$853$	−25.9841	−0.889679	−0.444840	−	0.895610i	$-0.646739\pi$
$853$	−25.9841	−0.889679	−0.444840	+	0.895610i	$0.646739\pi$
$854$	−7.81533	−0.267435
$855$	0.351780	0.0120306
$856$	9.83833	0.336267
$857$	43.6785	1.49203	0.746015	−	0.665929i	$-0.231965\pi$
$857$	43.6785	1.49203	0.746015	+	0.665929i	$0.231965\pi$
$858$	2.80336	0.0957050
$859$	−13.1682	−0.449293	−0.224647	−	0.974440i	$-0.572123\pi$
$859$	−13.1682	−0.449293	−0.224647	+	0.974440i	$0.572123\pi$
$860$	−6.09980	−0.208001
$861$	−33.5448	−1.14321
$862$	−16.7900	−0.571869
$863$	−12.3059	−0.418898	−0.209449	−	0.977820i	$-0.567167\pi$
$863$	−12.3059	−0.418898	−0.209449	+	0.977820i	$0.567167\pi$
$864$	1.00000	0.0340207
$865$	24.9625	0.848751
$866$	−29.6352	−1.00704
$867$	16.8763	0.573148
$868$	−11.5863	−0.393266
$869$	36.2456	1.22955
$870$	−9.37074	−0.317698
$871$	−0.919164	−0.0311447
$872$	−1.26550	−0.0428553
$873$	3.04990	0.103223
$874$	−1.20753	−0.0408452
$875$	3.96906	0.134179
$876$	12.8034	0.432585
$877$	41.1407	1.38922	0.694611	−	0.719386i	$-0.255577\pi$
$877$	41.1407	1.38922	0.694611	+	0.719386i	$0.255577\pi$
$878$	−1.99456	−0.0673131
$879$	−16.5823	−0.559307
$880$	−3.04990	−0.102812
$881$	−25.6122	−0.862895	−0.431448	−	0.902138i	$-0.641997\pi$
$881$	−25.6122	−0.862895	−0.431448	+	0.902138i	$0.641997\pi$
$882$	−8.75346	−0.294744
$883$	−5.96208	−0.200640	−0.100320	−	0.994955i	$-0.531987\pi$
$883$	−5.96208	−0.200640	−0.100320	+	0.994955i	$0.531987\pi$
$884$	0.323344	0.0108752
$885$	−8.45158	−0.284097
$886$	3.29644	0.110746
$887$	−1.79388	−0.0602327	−0.0301163	−	0.999546i	$-0.509588\pi$
$887$	−1.79388	−0.0602327	−0.0301163	+	0.999546i	$0.509588\pi$
$888$	5.40168	0.181268
$889$	51.4590	1.72588
$890$	−16.2050	−0.543194
$891$	3.04990	0.102175
$892$	−0.442091	−0.0148023
$893$	4.64669	0.155495
$894$	9.37074	0.313404
$895$	14.1282	0.472255
$896$	3.96906	0.132597
$897$	3.15514	0.105347
$898$	13.9196	0.464504
$899$	27.3547	0.912331
$900$	1.00000	0.0333333
$901$	2.08891	0.0695918
$902$	25.7765	0.858262
$903$	24.2105	0.805674
$904$	−9.69158	−0.322337
$905$	11.0729	0.368075
$906$	−3.14021	−0.104326
$907$	−54.3603	−1.80500	−0.902502	−	0.430685i	$-0.858272\pi$
$907$	−54.3603	−1.80500	−0.902502	+	0.430685i	$0.858272\pi$
$908$	−25.3344	−0.840750
$909$	−4.69812	−0.155827
$910$	−3.64822	−0.120937
$911$	20.1890	0.668892	0.334446	−	0.942415i	$-0.391451\pi$
$911$	20.1890	0.668892	0.334446	+	0.942415i	$0.391451\pi$
$912$	0.351780	0.0116486
$913$	0.320968	0.0106225
$914$	−12.3897	−0.409815
$915$	−1.96906	−0.0650952
$916$	8.06886	0.266603
$917$	49.6667	1.64014
$918$	0.351780	0.0116105
$919$	−37.9221	−1.25094	−0.625468	−	0.780250i	$-0.715092\pi$
$919$	−37.9221	−1.25094	−0.625468	+	0.780250i	$0.715092\pi$
$920$	−3.43262	−0.113170
$921$	24.3843	0.803489
$922$	−38.8537	−1.27958
$923$	−5.16320	−0.169949
$924$	12.1052	0.398233
$925$	5.40168	0.177606
$926$	5.85076	0.192268
$927$	2.09980	0.0689664
$928$	−9.37074	−0.307610
$929$	−51.0074	−1.67350	−0.836750	−	0.547585i	$-0.815547\pi$
$929$	−51.0074	−1.67350	−0.836750	+	0.547585i	$0.815547\pi$
$930$	−2.91916	−0.0957232
$931$	−3.07929	−0.100920
$932$	3.67121	0.120255
$933$	−6.03792	−0.197673
$934$	6.37477	0.208589
$935$	−1.07289	−0.0350874
$936$	−0.919164	−0.0300438
$937$	−36.9290	−1.20642	−0.603208	−	0.797584i	$-0.706111\pi$
$937$	−36.9290	−1.20642	−0.603208	+	0.797584i	$0.706111\pi$
$938$	−3.96906	−0.129594
$939$	−11.4301	−0.373008
$940$	13.2091	0.430832
$941$	−45.0489	−1.46855	−0.734277	−	0.678850i	$-0.762479\pi$
$941$	−45.0489	−1.46855	−0.734277	+	0.678850i	$0.762479\pi$
$942$	14.5798	0.475036
$943$	29.0110	0.944729
$944$	−8.45158	−0.275075
$945$	−3.96906	−0.129114
$946$	−18.6038	−0.604861
$947$	−5.68210	−0.184643	−0.0923217	−	0.995729i	$-0.529429\pi$
$947$	−5.68210	−0.184643	−0.0923217	+	0.995729i	$0.529429\pi$
$948$	−11.8842	−0.385981
$949$	−11.7684	−0.382018
$950$	0.351780	0.0114133
$951$	29.3911	0.953072
$952$	1.39624	0.0452523
$953$	34.3738	1.11348	0.556739	−	0.830688i	$-0.312053\pi$
$953$	34.3738	1.11348	0.556739	+	0.830688i	$0.312053\pi$
$954$	−5.93813	−0.192254
$955$	18.0998	0.585696
$956$	12.9650	0.419319
$957$	−28.5798	−0.923854
$958$	−13.5094	−0.436469
$959$	−5.56335	−0.179650
$960$	1.00000	0.0322749
$961$	−22.4785	−0.725112
$962$	−4.96503	−0.160079
$963$	−9.83833	−0.317036
$964$	−21.9531	−0.707060
$965$	11.6861	0.376190
$966$	13.6243	0.438354
$967$	−55.7314	−1.79220	−0.896100	−	0.443852i	$-0.853611\pi$
$967$	−55.7314	−1.79220	−0.896100	+	0.443852i	$0.853611\pi$
$968$	1.69812	0.0545796
$969$	0.123749	0.00397540
$970$	3.04990	0.0979263
$971$	−41.3438	−1.32679	−0.663394	−	0.748271i	$-0.730884\pi$
$971$	−41.3438	−1.32679	−0.663394	+	0.748271i	$0.730884\pi$
$972$	−1.00000	−0.0320750
$973$	−23.9272	−0.767072
$974$	−24.4920	−0.784774
$975$	−0.919164	−0.0294368
$976$	−1.96906	−0.0630282
$977$	−61.0643	−1.95362	−0.976810	−	0.214107i	$-0.931316\pi$
$977$	−61.0643	−1.95362	−0.976810	+	0.214107i	$0.931316\pi$
$978$	−4.59832	−0.147038
$979$	−49.4237	−1.57959
$980$	−8.75346	−0.279619
$981$	1.26550	0.0404044
$982$	−1.59723	−0.0509696
$983$	5.76557	0.183893	0.0919466	−	0.995764i	$-0.470691\pi$
$983$	5.76557	0.183893	0.0919466	+	0.995764i	$0.470691\pi$
$984$	−8.45158	−0.269426
$985$	0.161672	0.00515129
$986$	−3.29644	−0.104980
$987$	−52.4276	−1.66879
$988$	−0.323344	−0.0102869
$989$	−20.9383	−0.665798
$990$	3.04990	0.0969321
$991$	22.5339	0.715814	0.357907	−	0.933757i	$-0.383490\pi$
$991$	22.5339	0.715814	0.357907	+	0.933757i	$0.383490\pi$
$992$	−2.91916	−0.0926836
$993$	4.60781	0.146224
$994$	−22.2953	−0.707165
$995$	8.10524	0.256953
$996$	−0.105239	−0.00333462
$997$	6.21310	0.196771	0.0983855	−	0.995148i	$-0.468632\pi$
$997$	6.21310	0.196771	0.0983855	+	0.995148i	$0.468632\pi$
$998$	−21.5837	−0.683221
$999$	−5.40168	−0.170902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2010.2.a.r.1.1	✓	4
3.2	odd	2		6030.2.a.bu.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2010.2.a.r.1.1	✓	4	1.1	even	1	trivial
6030.2.a.bu.1.1		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.96906 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.96906 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.04990 q^{11} -1.00000 q^{12} +0.919164 q^{13} +3.96906 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.351780 q^{17} -1.00000 q^{18} -0.351780 q^{19} -1.00000 q^{20} +3.96906 q^{21} -3.04990 q^{22} -3.43262 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.919164 q^{26} -1.00000 q^{27} -3.96906 q^{28} +9.37074 q^{29} -1.00000 q^{30} +2.91916 q^{31} -1.00000 q^{32} -3.04990 q^{33} -0.351780 q^{34} +3.96906 q^{35} +1.00000 q^{36} +5.40168 q^{37} +0.351780 q^{38} -0.919164 q^{39} +1.00000 q^{40} -8.45158 q^{41} -3.96906 q^{42} +6.09980 q^{43} +3.04990 q^{44} -1.00000 q^{45} +3.43262 q^{46} -13.2091 q^{47} -1.00000 q^{48} +8.75346 q^{49} -1.00000 q^{50} -0.351780 q^{51} +0.919164 q^{52} +5.93813 q^{53} +1.00000 q^{54} -3.04990 q^{55} +3.96906 q^{56} +0.351780 q^{57} -9.37074 q^{58} -8.45158 q^{59} +1.00000 q^{60} -1.96906 q^{61} -2.91916 q^{62} -3.96906 q^{63} +1.00000 q^{64} -0.919164 q^{65} +3.04990 q^{66} -1.00000 q^{67} +0.351780 q^{68} +3.43262 q^{69} -3.96906 q^{70} -5.61728 q^{71} -1.00000 q^{72} -12.8034 q^{73} -5.40168 q^{74} -1.00000 q^{75} -0.351780 q^{76} -12.1052 q^{77} +0.919164 q^{78} +11.8842 q^{79} -1.00000 q^{80} +1.00000 q^{81} +8.45158 q^{82} +0.105239 q^{83} +3.96906 q^{84} -0.351780 q^{85} -6.09980 q^{86} -9.37074 q^{87} -3.04990 q^{88} -16.2050 q^{89} +1.00000 q^{90} -3.64822 q^{91} -3.43262 q^{92} -2.91916 q^{93} +13.2091 q^{94} +0.351780 q^{95} +1.00000 q^{96} +3.04990 q^{97} -8.75346 q^{98} +3.04990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 3 q^{11} - 4 q^{12} + 2 q^{13} - q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{19} - 4 q^{20} - q^{21} + 3 q^{22} - 12 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 10 q^{31} - 4 q^{32} + 3 q^{33} + 2 q^{34} - q^{35} + 4 q^{36} + 3 q^{37} - 2 q^{38} - 2 q^{39} + 4 q^{40} + q^{42} - 6 q^{43} - 3 q^{44} - 4 q^{45} + 12 q^{46} - 14 q^{47} - 4 q^{48} + 13 q^{49} - 4 q^{50} + 2 q^{51} + 2 q^{52} - 10 q^{53} + 4 q^{54} + 3 q^{55} - q^{56} - 2 q^{57} - 2 q^{58} + 4 q^{60} + 9 q^{61} - 10 q^{62} + q^{63} + 4 q^{64} - 2 q^{65} - 3 q^{66} - 4 q^{67} - 2 q^{68} + 12 q^{69} + q^{70} - 9 q^{71} - 4 q^{72} - 14 q^{73} - 3 q^{74} - 4 q^{75} + 2 q^{76} - 23 q^{77} + 2 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 25 q^{83} - q^{84} + 2 q^{85} + 6 q^{86} - 2 q^{87} + 3 q^{88} - 9 q^{89} + 4 q^{90} - 18 q^{91} - 12 q^{92} - 10 q^{93} + 14 q^{94} - 2 q^{95} + 4 q^{96} - 3 q^{97} - 13 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 3 * q^11 - 4 * q^12 + 2 * q^13 - q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^19 - 4 * q^20 - q^21 + 3 * q^22 - 12 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 10 * q^31 - 4 * q^32 + 3 * q^33 + 2 * q^34 - q^35 + 4 * q^36 + 3 * q^37 - 2 * q^38 - 2 * q^39 + 4 * q^40 + q^42 - 6 * q^43 - 3 * q^44 - 4 * q^45 + 12 * q^46 - 14 * q^47 - 4 * q^48 + 13 * q^49 - 4 * q^50 + 2 * q^51 + 2 * q^52 - 10 * q^53 + 4 * q^54 + 3 * q^55 - q^56 - 2 * q^57 - 2 * q^58 + 4 * q^60 + 9 * q^61 - 10 * q^62 + q^63 + 4 * q^64 - 2 * q^65 - 3 * q^66 - 4 * q^67 - 2 * q^68 + 12 * q^69 + q^70 - 9 * q^71 - 4 * q^72 - 14 * q^73 - 3 * q^74 - 4 * q^75 + 2 * q^76 - 23 * q^77 + 2 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 25 * q^83 - q^84 + 2 * q^85 + 6 * q^86 - 2 * q^87 + 3 * q^88 - 9 * q^89 + 4 * q^90 - 18 * q^91 - 12 * q^92 - 10 * q^93 + 14 * q^94 - 2 * q^95 + 4 * q^96 - 3 * q^97 - 13 * q^98 - 3 * q^99

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