LMFDB - Embedded newform 980.2.g.a.391.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.19
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0982654 + 1.41080i) q^{2} -0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} -1.00000i q^{5} +(-0.0650866 - 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +O(q^{10})$	\(q+(0.0982654 + 1.41080i) q^{2} -0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} -1.00000i q^{5} +(-0.0650866 - 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +(1.41080 - 0.0982654i) q^{10} -3.61296i q^{11} +(1.31192 - 0.183648i) q^{12} +5.83027i q^{13} +0.662355i q^{15} +(3.84625 - 1.09835i) q^{16} +1.36813i q^{17} +(-0.251686 - 3.61345i) q^{18} +4.09577 q^{19} +(0.277265 + 1.98069i) q^{20} +(5.09715 - 0.355029i) q^{22} -3.24519i q^{23} +(0.388005 + 1.83280i) q^{24} -1.00000 q^{25} +(-8.22532 + 0.572914i) q^{26} +3.68354 q^{27} +5.19327 q^{29} +(-0.934447 + 0.0650866i) q^{30} +8.86809 q^{31} +(1.92750 + 5.31834i) q^{32} +2.39306i q^{33} +(-1.93014 + 0.134439i) q^{34} +(5.07311 - 0.710155i) q^{36} +10.7958 q^{37} +(0.402472 + 5.77829i) q^{38} -3.86171i q^{39} +(-2.76710 + 0.585797i) q^{40} -0.832730i q^{41} +3.10642i q^{43} +(1.00175 + 7.15615i) q^{44} +2.56129i q^{45} +(4.57830 - 0.318890i) q^{46} +6.89601 q^{47} +(-2.54758 + 0.727497i) q^{48} +(-0.0982654 - 1.41080i) q^{50} -0.906184i q^{51} +(-1.61653 - 11.5479i) q^{52} -7.41752 q^{53} +(0.361965 + 5.19673i) q^{54} -3.61296 q^{55} -2.71285 q^{57} +(0.510319 + 7.32664i) q^{58} -7.47856 q^{59} +(-0.183648 - 1.31192i) q^{60} +1.48554i q^{61} +(0.871427 + 12.5111i) q^{62} +(-7.31368 + 3.24192i) q^{64} +5.83027 q^{65} +(-3.37612 + 0.235155i) q^{66} -2.53761i q^{67} +(-0.379333 - 2.70983i) q^{68} +2.14947i q^{69} -3.52502i q^{71} +(1.50039 + 7.08734i) q^{72} +5.16984i q^{73} +(1.06085 + 15.2306i) q^{74} +0.662355 q^{75} +(-8.11244 + 1.13561i) q^{76} +(5.44808 - 0.379472i) q^{78} -11.3401i q^{79} +(-1.09835 - 3.84625i) q^{80} +5.24405 q^{81} +(1.17481 - 0.0818286i) q^{82} +6.49145 q^{83} +1.36813 q^{85} +(-4.38252 + 0.305254i) q^{86} -3.43978 q^{87} +(-9.99743 + 2.11646i) q^{88} +9.39121i q^{89} +(-3.61345 + 0.251686i) q^{90} +(0.899777 + 6.42771i) q^{92} -5.87382 q^{93} +(0.677640 + 9.72886i) q^{94} -4.09577i q^{95} +(-1.27669 - 3.52263i) q^{96} -0.343189i q^{97} +9.25383i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.0982654	+	1.41080i	0.0694842	+	0.997583i
$2$	0.0982654	+	1.41080i	0.0694842	+	0.997583i
$3$	−0.662355			−0.382411			−0.191205	−	0.981550i	$-0.561240\pi$
$3$	−0.662355			−0.382411			−0.191205	+	0.981550i	$0.561240\pi$
$4$	−1.98069	+	0.277265i	−0.990344	+	0.138632i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.0650866	−	0.934447i	−0.0265715	−	0.381486i
$7$		0			0
$7$		0			0
$8$	−0.585797	−	2.76710i	−0.207111	−	0.978318i
$9$	−2.56129			−0.853762
$10$	1.41080	−	0.0982654i	0.446133	−	0.0310743i
$11$		−	3.61296i		−	1.08935i	−0.838648	−	0.544674i	$-0.816653\pi$
$11$		−	3.61296i		−	1.08935i	0.838648	−	0.544674i	$-0.183347\pi$
$12$	1.31192	−	0.183648i	0.378718	−	0.0530145i
$13$			5.83027i			1.61703i	0.588478	+	0.808513i	$0.299727\pi$
$13$			5.83027i			1.61703i	−0.588478	+	0.808513i	$0.700273\pi$
$14$		0			0
$15$			0.662355i			0.171019i
$16$	3.84625	−	1.09835i	0.961562	−	0.274588i
$17$			1.36813i			0.331819i	0.986141	+	0.165910i	$0.0530560\pi$
$17$			1.36813i			0.331819i	−0.986141	+	0.165910i	$0.946944\pi$
$18$	−0.251686	−	3.61345i	−0.0593229	−	0.851699i
$19$	4.09577			0.939634			0.469817	−	0.882764i	$-0.344320\pi$
$19$	4.09577			0.939634			0.469817	+	0.882764i	$0.344320\pi$
$20$	0.277265	+	1.98069i	0.0619983	+	0.442895i
$21$		0			0
$22$	5.09715	−	0.355029i	1.08672	−	0.0756925i
$23$		−	3.24519i		−	0.676669i	−0.941026	−	0.338334i	$-0.890136\pi$
$23$		−	3.24519i		−	0.676669i	0.941026	−	0.338334i	$-0.109864\pi$
$24$	0.388005	+	1.83280i	0.0792013	+	0.374119i
$25$	−1.00000			−0.200000
$26$	−8.22532	+	0.572914i	−1.61312	+	0.112358i
$27$	3.68354			0.708898
$28$		0			0
$29$	5.19327			0.964365			0.482183	−	0.876071i	$-0.339844\pi$
$29$	5.19327			0.964365			0.482183	+	0.876071i	$0.339844\pi$
$30$	−0.934447	+	0.0650866i	−0.170606	+	0.0118831i
$31$	8.86809			1.59276			0.796378	−	0.604799i	$-0.206746\pi$
$31$	8.86809			1.59276			0.796378	+	0.604799i	$0.206746\pi$
$32$	1.92750	+	5.31834i	0.340737	+	0.940159i
$33$			2.39306i			0.416579i
$34$	−1.93014	+	0.134439i	−0.331017	+	0.0230562i
$35$		0			0
$36$	5.07311	−	0.710155i	0.845518	−	0.118359i
$37$	10.7958			1.77482			0.887408	−	0.460985i	$-0.152504\pi$
$37$	10.7958			1.77482			0.887408	+	0.460985i	$0.152504\pi$
$38$	0.402472	+	5.77829i	0.0652897	+	0.937363i
$39$		−	3.86171i		−	0.618368i
$40$	−2.76710	+	0.585797i	−0.437517	+	0.0926227i
$41$		−	0.832730i		−	0.130051i	−0.997884	−	0.0650253i	$-0.979287\pi$
$41$		−	0.832730i		−	0.130051i	0.997884	−	0.0650253i	$-0.0207128\pi$
$42$		0			0
$43$			3.10642i			0.473725i	0.971543	+	0.236862i	$0.0761190\pi$
$43$			3.10642i			0.473725i	−0.971543	+	0.236862i	$0.923881\pi$
$44$	1.00175	+	7.15615i	0.151019	+	1.07883i
$45$			2.56129i			0.381814i
$46$	4.57830	−	0.318890i	0.675033	−	0.0470178i
$47$	6.89601			1.00589			0.502943	−	0.864319i	$-0.332250\pi$
$47$	6.89601			1.00589			0.502943	+	0.864319i	$0.332250\pi$
$48$	−2.54758	+	0.727497i	−0.367712	+	0.105005i
$49$		0			0
$50$	−0.0982654	−	1.41080i	−0.0138968	−	0.199517i
$51$		−	0.906184i		−	0.126891i
$52$	−1.61653	−	11.5479i	−0.224172	−	1.60141i
$53$	−7.41752			−1.01887			−0.509437	−	0.860508i	$-0.670146\pi$
$53$	−7.41752			−1.01887			−0.509437	+	0.860508i	$0.670146\pi$
$54$	0.361965	+	5.19673i	0.0492572	+	0.707185i
$55$	−3.61296			−0.487172
$56$		0			0
$57$	−2.71285			−0.359326
$58$	0.510319	+	7.32664i	0.0670081	+	0.962034i
$59$	−7.47856			−0.973626			−0.486813	−	0.873506i	$-0.661841\pi$
$59$	−7.47856			−0.973626			−0.486813	+	0.873506i	$0.661841\pi$
$60$	−0.183648	−	1.31192i	−0.0237088	−	0.169368i
$61$			1.48554i			0.190204i	0.995468	+	0.0951022i	$0.0303178\pi$
$61$			1.48554i			0.190204i	−0.995468	+	0.0951022i	$0.969682\pi$
$62$	0.871427	+	12.5111i	0.110671	+	1.58891i
$63$		0			0
$64$	−7.31368	+	3.24192i	−0.914210	+	0.405240i
$65$	5.83027			0.723156
$66$	−3.37612	+	0.235155i	−0.415572	+	0.0289456i
$67$		−	2.53761i		−	0.310018i	−0.987913	−	0.155009i	$-0.950459\pi$
$67$		−	2.53761i		−	0.310018i	0.987913	−	0.155009i	$-0.0495407\pi$
$68$	−0.379333	−	2.70983i	−0.0460009	−	0.328615i
$69$			2.14947i			0.258765i
$70$		0			0
$71$		−	3.52502i		−	0.418342i	−0.977879	−	0.209171i	$-0.932923\pi$
$71$		−	3.52502i		−	0.418342i	0.977879	−	0.209171i	$-0.0670766\pi$
$72$	1.50039	+	7.08734i	0.176823	+	0.835250i
$73$			5.16984i			0.605084i	0.953136	+	0.302542i	$0.0978353\pi$
$73$			5.16984i			0.605084i	−0.953136	+	0.302542i	$0.902165\pi$
$74$	1.06085	+	15.2306i	0.123322	+	1.77053i
$75$	0.662355			0.0764821
$76$	−8.11244	+	1.13561i	−0.930561	+	0.130264i
$77$		0			0
$78$	5.44808	−	0.379472i	0.616873	−	0.0429668i
$79$		−	11.3401i		−	1.27586i	−0.770094	−	0.637931i	$-0.779791\pi$
$79$		−	11.3401i		−	1.27586i	0.770094	−	0.637931i	$-0.220209\pi$
$80$	−1.09835	−	3.84625i	−0.122799	−	0.430024i
$81$	5.24405			0.582672
$82$	1.17481	−	0.0818286i	0.129736	−	0.00903646i
$83$	6.49145			0.712529			0.356264	−	0.934385i	$-0.384050\pi$
$83$	6.49145			0.712529			0.356264	+	0.934385i	$0.384050\pi$
$84$		0			0
$85$	1.36813			0.148394
$86$	−4.38252	+	0.305254i	−0.472580	+	0.0329164i
$87$	−3.43978			−0.368783
$88$	−9.99743	+	2.11646i	−1.06573	+	0.225616i
$89$			9.39121i			0.995466i	0.867330	+	0.497733i	$0.165834\pi$
$89$			9.39121i			0.995466i	−0.867330	+	0.497733i	$0.834166\pi$
$90$	−3.61345	+	0.251686i	−0.380891	+	0.0265300i
$91$		0			0
$92$	0.899777	+	6.42771i	0.0938083	+	0.670135i
$93$	−5.87382			−0.609087
$94$	0.677640	+	9.72886i	0.0698932	+	1.00346i
$95$		−	4.09577i		−	0.420217i
$96$	−1.27669	−	3.52263i	−0.130302	−	0.359527i
$97$		−	0.343189i		−	0.0348455i	−0.999848	−	0.0174228i	$-0.994454\pi$
$97$		−	0.343189i		−	0.0348455i	0.999848	−	0.0174228i	$-0.00554612\pi$
$98$		0			0
$99$			9.25383i			0.930045i
$100$	1.98069	−	0.277265i	0.198069	−	0.0277265i
$101$		−	4.53635i		−	0.451384i	−0.974199	−	0.225692i	$-0.927536\pi$
$101$		−	4.53635i		−	0.451384i	0.974199	−	0.225692i	$-0.0724642\pi$
$102$	1.27844	−	0.0890466i	0.126584	−	0.00881693i
$103$	6.13812			0.604807			0.302404	−	0.953180i	$-0.402211\pi$
$103$	6.13812			0.604807			0.302404	+	0.953180i	$0.402211\pi$
$104$	16.1329	−	3.41536i	1.58196	−	0.334903i
$105$		0			0
$106$	−0.728886	−	10.4646i	−0.0707957	−	1.01641i
$107$		−	7.66797i		−	0.741291i	−0.928775	−	0.370645i	$-0.879137\pi$
$107$		−	7.66797i		−	0.741291i	0.928775	−	0.370645i	$-0.120863\pi$
$108$	−7.29595	+	1.02132i	−0.702053	+	0.0982763i
$109$	1.29523			0.124061			0.0620304	−	0.998074i	$-0.480242\pi$
$109$	1.29523			0.124061			0.0620304	+	0.998074i	$0.480242\pi$
$110$	−0.355029	−	5.09715i	−0.0338507	−	0.485994i
$111$	−7.15064			−0.678709
$112$		0			0
$113$	7.10591			0.668468			0.334234	−	0.942490i	$-0.391522\pi$
$113$	7.10591			0.668468			0.334234	+	0.942490i	$0.391522\pi$
$114$	−0.266580	−	3.82728i	−0.0249675	−	0.358457i
$115$	−3.24519			−0.302616
$116$	−10.2862	+	1.43991i	−0.955053	+	0.133692i
$117$		−	14.9330i		−	1.38056i
$118$	−0.734884	−	10.5507i	−0.0676516	−	0.971273i
$119$		0			0
$120$	1.83280	−	0.388005i	0.167311	−	0.0354199i
$121$	−2.05349			−0.186681
$122$	−2.09580	+	0.145978i	−0.189745	+	0.0132162i
$123$			0.551563i			0.0497327i
$124$	−17.5649	+	2.45881i	−1.57738	+	0.220808i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			17.0178i			1.51008i	0.655677	+	0.755041i	$0.272383\pi$
$127$			17.0178i			1.51008i	−0.655677	+	0.755041i	$0.727617\pi$
$128$	−5.29237	−	9.99954i	−0.467784	−	0.883843i
$129$		−	2.05755i		−	0.181157i
$130$	0.572914	+	8.22532i	0.0502479	+	0.721408i
$131$	1.20613			0.105380			0.0526901	−	0.998611i	$-0.483220\pi$
$131$	1.20613			0.105380			0.0526901	+	0.998611i	$0.483220\pi$
$132$	−0.663512	−	4.73991i	−0.0577513	−	0.412556i
$133$		0			0
$134$	3.58005	−	0.249359i	0.309269	−	0.0215414i
$135$		−	3.68354i		−	0.317029i
$136$	3.78574	−	0.801444i	0.324624	−	0.0687233i
$137$	2.14490			0.183252			0.0916258	−	0.995794i	$-0.470794\pi$
$137$	2.14490			0.183252			0.0916258	+	0.995794i	$0.470794\pi$
$138$	−3.03246	+	0.211218i	−0.258140	+	0.0179801i
$139$	−3.39555			−0.288007			−0.144004	−	0.989577i	$-0.545998\pi$
$139$	−3.39555			−0.288007			−0.144004	+	0.989577i	$0.545998\pi$
$140$		0			0
$141$	−4.56761			−0.384662
$142$	4.97308	−	0.346387i	0.417331	−	0.0290682i
$143$	21.0645			1.76151
$144$	−9.85134	+	2.81319i	−0.820945	+	0.234432i
$145$		−	5.19327i		−	0.431277i
$146$	−7.29359	+	0.508017i	−0.603622	+	0.0420438i
$147$		0			0
$148$	−21.3831	+	2.99329i	−1.75768	+	0.246047i
$149$	−19.0864			−1.56362			−0.781808	−	0.623519i	$-0.785703\pi$
$149$	−19.0864			−1.56362			−0.781808	+	0.623519i	$0.785703\pi$
$150$	0.0650866	+	0.934447i	0.00531430	+	0.0762973i
$151$			9.60595i			0.781721i	0.920450	+	0.390861i	$0.127823\pi$
$151$			9.60595i			0.781721i	−0.920450	+	0.390861i	$0.872177\pi$
$152$	−2.39929	−	11.3334i	−0.194608	−	0.919260i
$153$		−	3.50416i		−	0.283295i
$154$		0			0
$155$		−	8.86809i		−	0.712302i
$156$	1.07072	+	7.64883i	0.0857258	+	0.612397i
$157$		−	16.4624i		−	1.31384i	−0.753961	−	0.656919i	$-0.771859\pi$
$157$		−	16.4624i		−	1.31384i	0.753961	−	0.656919i	$-0.228141\pi$
$158$	15.9986	−	1.11434i	1.27278	−	0.0886522i
$159$	4.91303			0.389629
$160$	5.31834	−	1.92750i	0.420452	−	0.152382i
$161$		0			0
$162$	0.515309	+	7.39828i	0.0404865	+	0.581264i
$163$			7.15612i			0.560510i	0.959926	+	0.280255i	$0.0904191\pi$
$163$			7.15612i			0.560510i	−0.959926	+	0.280255i	$0.909581\pi$
$164$	0.230887	+	1.64938i	0.0180292	+	0.128795i
$165$	2.39306			0.186300
$166$	0.637885	+	9.15810i	0.0495095	+	0.710807i
$167$	13.7127			1.06112			0.530562	−	0.847646i	$-0.321981\pi$
$167$	13.7127			1.06112			0.530562	+	0.847646i	$0.321981\pi$
$168$		0			0
$169$	−20.9920			−1.61477
$170$	0.134439	+	1.93014i	0.0103110	+	0.148035i
$171$	−10.4904			−0.802224
$172$	−0.861301	−	6.15285i	−0.0656736	−	0.469150i
$173$			3.92439i			0.298366i	0.988810	+	0.149183i	$0.0476643\pi$
$173$			3.92439i			0.298366i	−0.988810	+	0.149183i	$0.952336\pi$
$174$	−0.338012	−	4.85283i	−0.0256246	−	0.367892i
$175$		0			0
$176$	−3.96830	−	13.8963i	−0.299122	−	1.04748i
$177$	4.95346			0.372325
$178$	−13.2491	+	0.922831i	−0.993060	+	0.0691691i
$179$		−	20.5539i		−	1.53627i	−0.640289	−	0.768134i	$-0.721185\pi$
$179$		−	20.5539i		−	1.53627i	0.640289	−	0.768134i	$-0.278815\pi$
$180$	−0.710155	−	5.07311i	−0.0529318	−	0.378127i
$181$		−	13.0603i		−	0.970762i	−0.874303	−	0.485381i	$-0.838681\pi$
$181$		−	13.0603i		−	0.970762i	0.874303	−	0.485381i	$-0.161319\pi$
$182$		0			0
$183$		−	0.983957i		−	0.0727362i
$184$	−8.97976	+	1.90102i	−0.661997	+	0.140145i
$185$		−	10.7958i		−	0.793722i
$186$	−0.577194	−	8.28676i	−0.0423219	−	0.607615i
$187$	4.94298			0.361467
$188$	−13.6588	+	1.91202i	−0.996174	+	0.139449i
$189$		0			0
$190$	5.77829	−	0.402472i	0.419201	−	0.0291984i
$191$		−	12.4751i		−	0.902667i	−0.892355	−	0.451334i	$-0.850948\pi$
$191$		−	12.4751i		−	0.902667i	0.892355	−	0.451334i	$-0.149052\pi$
$192$	4.84425	−	2.14730i	0.349604	−	0.154968i
$193$	19.0645			1.37229			0.686147	−	0.727463i	$-0.259301\pi$
$193$	19.0645			1.37229			0.686147	+	0.727463i	$0.259301\pi$
$194$	0.484169	−	0.0337236i	0.0347613	−	0.00242121i
$195$	−3.86171			−0.276543
$196$		0			0
$197$	1.93188			0.137641			0.0688203	−	0.997629i	$-0.478076\pi$
$197$	1.93188			0.137641			0.0688203	+	0.997629i	$0.478076\pi$
$198$	−13.0553	+	0.909332i	−0.927797	+	0.0646234i
$199$	−20.5646			−1.45778			−0.728892	−	0.684629i	$-0.759964\pi$
$199$	−20.5646			−1.45778			−0.728892	+	0.684629i	$0.759964\pi$
$200$	0.585797	+	2.76710i	0.0414221	+	0.195664i
$201$			1.68080i			0.118554i
$202$	6.39986	−	0.445766i	0.450293	−	0.0313640i
$203$		0			0
$204$	0.251253	+	1.79487i	0.0175912	+	0.125666i
$205$	−0.832730			−0.0581604
$206$	0.603165	+	8.65963i	0.0420245	+	0.603345i
$207$			8.31186i			0.577714i
$208$	6.40368	+	22.4247i	0.444015	+	1.55487i
$209$		−	14.7979i		−	1.02359i
$210$		0			0
$211$		−	9.98398i		−	0.687326i	−0.939093	−	0.343663i	$-0.888332\pi$
$211$		−	9.98398i		−	0.687326i	0.939093	−	0.343663i	$-0.111668\pi$
$212$	14.6918	−	2.05662i	1.00904	−	0.141249i
$213$			2.33481i			0.159979i
$214$	10.8179	−	0.753496i	0.739499	−	0.0515079i
$215$	3.10642			0.211856
$216$	−2.15781	−	10.1927i	−0.146820	−	0.693528i
$217$		0			0
$218$	0.127277	+	1.82731i	0.00862026	+	0.123761i
$219$		−	3.42427i		−	0.231391i
$220$	7.15615	−	1.00175i	0.482467	−	0.0675378i
$221$	−7.97654			−0.536560
$222$	−0.702661	−	10.0881i	−0.0471595	−	0.677068i
$223$	16.8179			1.12621			0.563106	−	0.826384i	$-0.309606\pi$
$223$	16.8179			1.12621			0.563106	+	0.826384i	$0.309606\pi$
$224$		0			0
$225$	2.56129			0.170752
$226$	0.698266	+	10.0250i	0.0464479	+	0.666852i
$227$	19.8338			1.31642			0.658209	−	0.752835i	$-0.271314\pi$
$227$	19.8338			1.31642			0.658209	+	0.752835i	$0.271314\pi$
$228$	5.37331	−	0.752178i	0.355856	−	0.0498142i
$229$			13.9331i			0.920725i	0.887731	+	0.460363i	$0.152281\pi$
$229$			13.9331i			0.920725i	−0.887731	+	0.460363i	$0.847719\pi$
$230$	−0.318890	−	4.57830i	−0.0210270	−	0.301884i
$231$		0			0
$232$	−3.04220	−	14.3703i	−0.199730	−	0.943455i
$233$	10.2257			0.669905			0.334953	−	0.942235i	$-0.391280\pi$
$233$	10.2257			0.669905			0.334953	+	0.942235i	$0.391280\pi$
$234$	21.0674	−	1.46740i	1.37722	−	0.0959267i
$235$		−	6.89601i		−	0.449846i
$236$	14.8127	−	2.07354i	0.964225	−	0.134976i
$237$			7.51117i			0.487903i
$238$		0			0
$239$		−	17.0835i		−	1.10504i	−0.833501	−	0.552518i	$-0.813667\pi$
$239$		−	17.0835i		−	1.10504i	0.833501	−	0.552518i	$-0.186333\pi$
$240$	0.727497	+	2.54758i	0.0469598	+	0.164446i
$241$			18.4837i			1.19064i	0.803489	+	0.595320i	$0.202975\pi$
$241$			18.4837i			1.19064i	−0.803489	+	0.595320i	$0.797025\pi$
$242$	−0.201787	−	2.89705i	−0.0129714	−	0.186230i
$243$	−14.5241			−0.931718
$244$	−0.411889	−	2.94240i	−0.0263685	−	0.188368i
$245$		0			0
$246$	−0.778142	+	0.0541995i	−0.0496125	+	0.00345564i
$247$			23.8794i			1.51941i
$248$	−5.19490	−	24.5389i	−0.329877	−	1.55822i
$249$	−4.29964			−0.272479
$250$	−1.41080	+	0.0982654i	−0.0892265	+	0.00621485i
$251$	16.5313			1.04344			0.521722	−	0.853116i	$-0.325290\pi$
$251$	16.5313			1.04344			0.521722	+	0.853116i	$0.325290\pi$
$252$		0			0
$253$	−11.7247			−0.737128
$254$	−24.0086	+	1.67226i	−1.50643	+	0.104927i
$255$	−0.906184			−0.0567475
$256$	13.5873	−	8.44906i	0.849203	−	0.528066i
$257$		−	6.19499i		−	0.386433i	−0.981156	−	0.193216i	$-0.938108\pi$
$257$		−	6.19499i		−	0.386433i	0.981156	−	0.193216i	$-0.0618919\pi$
$258$	2.90279	−	0.202186i	0.180720	−	0.0125876i
$259$		0			0
$260$	−11.5479	+	1.61653i	−0.716173	+	0.100253i
$261$	−13.3014			−0.823338
$262$	0.118521	+	1.70161i	0.00732226	+	0.105126i
$263$			21.1536i			1.30439i	0.758053	+	0.652194i	$0.226151\pi$
$263$			21.1536i			1.30439i	−0.758053	+	0.652194i	$0.773849\pi$
$264$	6.62184	−	1.40185i	0.407546	−	0.0862778i
$265$			7.41752i			0.455655i
$266$		0			0
$267$		−	6.22031i		−	0.380677i
$268$	0.703590	+	5.02621i	0.0429786	+	0.307025i
$269$			30.9866i			1.88928i	0.328102	+	0.944642i	$0.393591\pi$
$269$			30.9866i			1.88928i	−0.328102	+	0.944642i	$0.606409\pi$
$270$	5.19673	−	0.361965i	0.316263	−	0.0220285i
$271$	−23.0381			−1.39946			−0.699732	−	0.714405i	$-0.746697\pi$
$271$	−23.0381			−1.39946			−0.699732	+	0.714405i	$0.746697\pi$
$272$	1.50268	+	5.26215i	0.0911134	+	0.319065i
$273$		0			0
$274$	0.210770	+	3.02602i	0.0127331	+	0.182809i
$275$			3.61296i			0.217870i
$276$	−0.595972	−	4.25742i	−0.0358733	−	0.256267i
$277$	6.94562			0.417322			0.208661	−	0.977988i	$-0.433089\pi$
$277$	6.94562			0.417322			0.208661	+	0.977988i	$0.433089\pi$
$278$	−0.333665	−	4.79043i	−0.0200119	−	0.287311i
$279$	−22.7137			−1.35984
$280$		0			0
$281$	−4.24391			−0.253170			−0.126585	−	0.991956i	$-0.540402\pi$
$281$	−4.24391			−0.253170			−0.126585	+	0.991956i	$0.540402\pi$
$282$	−0.448838	−	6.44396i	−0.0267279	−	0.383732i
$283$	8.53198			0.507174			0.253587	−	0.967313i	$-0.418390\pi$
$283$	8.53198			0.507174			0.253587	+	0.967313i	$0.418390\pi$
$284$	0.977363	+	6.98195i	0.0579958	+	0.414303i
$285$			2.71285i			0.160695i
$286$	2.06992	+	29.7178i	0.122397	+	1.75725i
$287$		0			0
$288$	−4.93688	−	13.6218i	−0.290909	−	0.802672i
$289$	15.1282			0.889896
$290$	7.32664	−	0.510319i	0.430235	−	0.0299669i
$291$			0.227313i			0.0133253i
$292$	−1.43342	−	10.2398i	−0.0838843	−	0.599241i
$293$		−	25.2319i		−	1.47406i	−0.675857	−	0.737032i	$-0.736227\pi$
$293$		−	25.2319i		−	1.47406i	0.675857	−	0.737032i	$-0.263773\pi$
$294$		0			0
$295$			7.47856i			0.435419i
$296$	−6.32414	−	29.8730i	−0.367583	−	1.73633i
$297$		−	13.3085i		−	0.772238i
$298$	−1.87553	−	26.9270i	−0.108647	−	1.55984i
$299$	18.9203			1.09419
$300$	−1.31192	+	0.183648i	−0.0757436	+	0.0106029i
$301$		0			0
$302$	−13.5520	+	0.943933i	−0.779832	+	0.0543172i
$303$			3.00467i			0.172614i
$304$	15.7533	−	4.49859i	0.903516	−	0.258012i
$305$	1.48554			0.0850620
$306$	4.94365	−	0.344338i	0.282610	−	0.0196845i
$307$	−29.2635			−1.67016			−0.835078	−	0.550132i	$-0.814577\pi$
$307$	−29.2635			−1.67016			−0.835078	+	0.550132i	$0.814577\pi$
$308$		0			0
$309$	−4.06561			−0.231285
$310$	12.5111	−	0.871427i	0.710581	−	0.0494937i
$311$	22.7461			1.28981			0.644906	−	0.764262i	$-0.276896\pi$
$311$	22.7461			1.28981			0.644906	+	0.764262i	$0.276896\pi$
$312$	−10.6857	+	2.26218i	−0.604960	+	0.128071i
$313$			6.58481i			0.372195i	0.982531	+	0.186098i	$0.0595841\pi$
$313$			6.58481i			0.372195i	−0.982531	+	0.186098i	$0.940416\pi$
$314$	23.2250	−	1.61768i	1.31066	−	0.0912910i
$315$		0			0
$316$	3.14421	+	22.4612i	0.176876	+	1.26354i
$317$	−14.1217			−0.793154			−0.396577	−	0.918001i	$-0.629802\pi$
$317$	−14.1217			−0.793154			−0.396577	+	0.918001i	$0.629802\pi$
$318$	0.482781	+	6.93128i	0.0270730	+	0.388687i
$319$		−	18.7631i		−	1.05053i
$320$	3.24192	+	7.31368i	0.181229	+	0.408847i
$321$			5.07891i			0.283477i
$322$		0			0
$323$			5.60352i			0.311788i
$324$	−10.3868	+	1.45399i	−0.577046	+	0.0807772i
$325$		−	5.83027i		−	0.323405i
$326$	−10.0958	+	0.703199i	−0.559155	+	0.0389466i
$327$	−0.857903			−0.0474422
$328$	−2.30425	+	0.487811i	−0.127231	+	0.0269349i
$329$		0			0
$330$	0.235155	+	3.37612i	0.0129449	+	0.185849i
$331$			20.3224i			1.11702i	0.829498	+	0.558510i	$0.188627\pi$
$331$			20.3224i			1.11702i	−0.829498	+	0.558510i	$0.811373\pi$
$332$	−12.8575	+	1.79985i	−0.705649	+	0.0987796i
$333$	−27.6511			−1.51527
$334$	1.34749	+	19.3459i	0.0737313	+	1.05856i
$335$	−2.53761			−0.138644
$336$		0			0
$337$	15.7704			0.859067			0.429533	−	0.903051i	$-0.358678\pi$
$337$	15.7704			0.859067			0.429533	+	0.903051i	$0.358678\pi$
$338$	−2.06279	−	29.6155i	−0.112201	−	1.61087i
$339$	−4.70663			−0.255629
$340$	−2.70983	+	0.379333i	−0.146961	+	0.0205722i
$341$		−	32.0401i		−	1.73507i
$342$	−1.03085	−	14.7999i	−0.0557418	−	0.800285i
$343$		0			0
$344$	8.59578	−	1.81973i	0.463453	−	0.0981134i
$345$	2.14947			0.115723
$346$	−5.53651	+	0.385632i	−0.297644	+	0.0207317i
$347$			3.04784i			0.163616i	0.996648	+	0.0818082i	$0.0260695\pi$
$347$			3.04784i			0.163616i	−0.996648	+	0.0818082i	$0.973930\pi$
$348$	6.81314	−	0.953731i	0.365222	−	0.0511254i
$349$		−	8.40462i		−	0.449889i	−0.974372	−	0.224944i	$-0.927780\pi$
$349$		−	8.40462i		−	0.449889i	0.974372	−	0.224944i	$-0.0722201\pi$
$350$		0			0
$351$			21.4761i			1.14631i
$352$	19.2150	−	6.96399i	1.02416	−	0.371182i
$353$		−	0.432821i		−	0.0230367i	−0.999934	−	0.0115184i	$-0.996334\pi$
$353$		−	0.432821i		−	0.0230367i	0.999934	−	0.0115184i	$-0.00366649\pi$
$354$	0.486754	+	6.98832i	0.0258707	+	0.371425i
$355$	−3.52502			−0.187088
$356$	−2.60385	−	18.6011i	−0.138004	−	0.985854i
$357$		0			0
$358$	28.9973	−	2.01973i	1.53255	−	0.106746i
$359$			26.9810i			1.42400i	0.702178	+	0.712002i	$0.252211\pi$
$359$			26.9810i			1.42400i	−0.702178	+	0.712002i	$0.747789\pi$
$360$	7.08734	−	1.50039i	0.373535	−	0.0790777i
$361$	−2.22468			−0.117088
$362$	18.4254	−	1.28337i	0.968415	−	0.0674526i
$363$	1.36014			0.0713888
$364$		0			0
$365$	5.16984			0.270602
$366$	1.38816	−	0.0966889i	0.0725604	−	0.00505401i
$367$	−20.8212			−1.08686			−0.543430	−	0.839455i	$-0.682875\pi$
$367$	−20.8212			−1.08686			−0.543430	+	0.839455i	$0.682875\pi$
$368$	−3.56436	−	12.4818i	−0.185805	−	0.650659i
$369$			2.13286i			0.111032i
$370$	15.2306	−	1.06085i	0.791804	−	0.0551511i
$371$		0			0
$372$	11.6342	−	1.62860i	0.603206	−	0.0844392i
$373$	−17.6614			−0.914475			−0.457237	−	0.889345i	$-0.651161\pi$
$373$	−17.6614			−0.914475			−0.457237	+	0.889345i	$0.651161\pi$
$374$	0.485724	+	6.97354i	0.0251162	+	0.360593i
$375$		−	0.662355i		−	0.0342038i
$376$	−4.03966	−	19.0820i	−0.208330	−	0.984077i
$377$			30.2781i			1.55940i
$378$		0			0
$379$		−	15.0551i		−	0.773331i	−0.922220	−	0.386665i	$-0.873627\pi$
$379$		−	15.0551i		−	0.773331i	0.922220	−	0.386665i	$-0.126373\pi$
$380$	1.13561	+	8.11244i	0.0582557	+	0.416159i
$381$		−	11.2718i		−	0.577472i
$382$	17.5998	−	1.22587i	0.900486	−	0.0627211i
$383$	−30.3505			−1.55084			−0.775420	−	0.631446i	$-0.782462\pi$
$383$	−30.3505			−1.55084			−0.775420	+	0.631446i	$0.782462\pi$
$384$	3.50542	+	6.62324i	0.178885	+	0.337991i
$385$		0			0
$386$	1.87338	+	26.8961i	0.0953527	+	1.36898i
$387$		−	7.95643i		−	0.404448i
$388$	0.0951542	+	0.679750i	0.00483072	+	0.0345091i
$389$	−6.27818			−0.318316			−0.159158	−	0.987253i	$-0.550878\pi$
$389$	−6.27818			−0.318316			−0.159158	+	0.987253i	$0.550878\pi$
$390$	−0.379472	−	5.44808i	−0.0192153	−	0.275874i
$391$	4.43983			0.224532
$392$		0			0
$393$	−0.798887			−0.0402985
$394$	0.189837	+	2.72549i	0.00956384	+	0.137308i
$395$	−11.3401			−0.570583
$396$	−2.56576	−	18.3289i	−0.128934	−	0.921064i
$397$		−	9.72207i		−	0.487937i	−0.969783	−	0.243968i	$-0.921551\pi$
$397$		−	9.72207i		−	0.487937i	0.969783	−	0.243968i	$-0.0784493\pi$
$398$	−2.02079	−	29.0124i	−0.101293	−	1.45426i
$399$		0			0
$400$	−3.84625	+	1.09835i	−0.192312	+	0.0549175i
$401$	6.98744			0.348936			0.174468	−	0.984663i	$-0.444179\pi$
$401$	6.98744			0.348936			0.174468	+	0.984663i	$0.444179\pi$
$402$	−2.37126	+	0.165164i	−0.118268	+	0.00823764i
$403$			51.7034i			2.57553i
$404$	1.25777	+	8.98509i	0.0625764	+	0.447025i
$405$		−	5.24405i		−	0.260579i
$406$		0			0
$407$		−	39.0048i		−	1.93339i
$408$	−2.50750	+	0.530840i	−0.124140	+	0.0262805i
$409$		−	2.24559i		−	0.111037i	−0.998458	−	0.0555186i	$-0.982319\pi$
$409$		−	2.24559i		−	0.111037i	0.998458	−	0.0555186i	$-0.0176812\pi$
$410$	−0.0818286	−	1.17481i	−0.00404123	−	0.0580198i
$411$	−1.42069			−0.0700773
$412$	−12.1577	+	1.70189i	−0.598967	+	0.0838459i
$413$		0			0
$414$	−11.7263	+	0.816769i	−0.576318	+	0.0401420i
$415$		−	6.49145i		−	0.318653i
$416$	−31.0074	+	11.2379i	−1.52026	+	0.550981i
$417$	2.24906			0.110137
$418$	20.8767	−	1.45412i	1.02111	−	0.0711232i
$419$	−18.3565			−0.896775			−0.448388	−	0.893839i	$-0.648002\pi$
$419$	−18.3565			−0.896775			−0.448388	+	0.893839i	$0.648002\pi$
$420$		0			0
$421$	2.27310			0.110784			0.0553921	−	0.998465i	$-0.482359\pi$
$421$	2.27310			0.110784			0.0553921	+	0.998465i	$0.482359\pi$
$422$	14.0854	−	0.981080i	0.685664	−	0.0477582i
$423$	−17.6627			−0.858788
$424$	4.34516	+	20.5250i	0.211020	+	0.996783i
$425$		−	1.36813i		−	0.0663638i
$426$	−3.29394	+	0.229431i	−0.159592	+	0.0111160i
$427$		0			0
$428$	2.12606	+	15.1879i	0.102767	+	0.734133i
$429$	−13.9522			−0.673618
$430$	0.305254	+	4.38252i	0.0147206	+	0.211344i
$431$			12.8610i			0.619490i	0.950820	+	0.309745i	$0.100244\pi$
$431$			12.8610i			0.619490i	−0.950820	+	0.309745i	$0.899756\pi$
$432$	14.1678	−	4.04582i	0.681650	−	0.194655i
$433$			33.6307i			1.61619i	0.589054	+	0.808094i	$0.299501\pi$
$433$			33.6307i			1.61619i	−0.589054	+	0.808094i	$0.700499\pi$
$434$		0			0
$435$			3.43978i			0.164925i
$436$	−2.56545	+	0.359122i	−0.122863	+	0.0171988i
$437$		−	13.2915i		−	0.635821i
$438$	4.83094	−	0.336487i	0.230831	−	0.0160780i
$439$	−24.8870			−1.18779			−0.593896	−	0.804542i	$-0.702411\pi$
$439$	−24.8870			−1.18779			−0.593896	+	0.804542i	$0.702411\pi$
$440$	2.11646	+	9.99743i	0.100898	+	0.476609i
$441$		0			0
$442$	−0.783818	−	11.2533i	−0.0372824	−	0.535263i
$443$			7.94772i			0.377608i	0.982015	+	0.188804i	$0.0604610\pi$
$443$			7.94772i			0.377608i	−0.982015	+	0.188804i	$0.939539\pi$
$444$	14.1632	−	1.98262i	0.672155	−	0.0940910i
$445$	9.39121			0.445186
$446$	1.65262	+	23.7267i	0.0782540	+	1.12349i
$447$	12.6420			0.597944
$448$		0			0
$449$	14.3027			0.674988			0.337494	−	0.941328i	$-0.390421\pi$
$449$	14.3027			0.674988			0.337494	+	0.941328i	$0.390421\pi$
$450$	0.251686	+	3.61345i	0.0118646	+	0.170340i
$451$	−3.00862			−0.141670
$452$	−14.0746	+	1.97022i	−0.662013	+	0.0926714i
$453$		−	6.36255i		−	0.298939i
$454$	1.94898	+	27.9815i	0.0914702	+	1.31324i
$455$		0			0
$456$	1.58918	+	7.50673i	0.0744202	+	0.351535i
$457$	22.1786			1.03747			0.518737	−	0.854934i	$-0.326403\pi$
$457$	22.1786			1.03747			0.518737	+	0.854934i	$0.326403\pi$
$458$	−19.6568	+	1.36914i	−0.918500	+	0.0639758i
$459$			5.03955i			0.235226i
$460$	6.42771	−	0.899777i	0.299693	−	0.0419523i
$461$			32.8587i			1.53038i	0.643803	+	0.765192i	$0.277356\pi$
$461$			32.8587i			1.53038i	−0.643803	+	0.765192i	$0.722644\pi$
$462$		0			0
$463$			3.31392i			0.154011i	0.997031	+	0.0770055i	$0.0245359\pi$
$463$			3.31392i			0.154011i	−0.997031	+	0.0770055i	$0.975464\pi$
$464$	19.9746	−	5.70402i	0.927297	−	0.264803i
$465$			5.87382i			0.272392i
$466$	1.00483	+	14.4263i	0.0465478	+	0.668286i
$467$	−35.1334			−1.62578			−0.812890	−	0.582417i	$-0.802107\pi$
$467$	−35.1334			−1.62578			−0.812890	+	0.582417i	$0.802107\pi$
$468$	4.14039	+	29.5776i	0.191390	+	1.36722i
$469$		0			0
$470$	9.72886	−	0.677640i	0.448759	−	0.0312572i
$471$			10.9039i			0.502426i
$472$	4.38092	+	20.6939i	0.201648	+	0.952516i
$473$	11.2234			0.516051
$474$	−10.5967	+	0.738088i	−0.486724	+	0.0339015i
$475$	−4.09577			−0.187927
$476$		0			0
$477$	18.9984			0.869877
$478$	24.1013	−	1.67871i	1.10237	−	0.0767825i
$479$	−22.3266			−1.02013			−0.510065	−	0.860136i	$-0.670379\pi$
$479$	−22.3266			−1.02013			−0.510065	+	0.860136i	$0.670379\pi$
$480$	−3.52263	+	1.27669i	−0.160785	+	0.0582726i
$481$			62.9423i			2.86992i
$482$	−26.0767	+	1.81631i	−1.18776	+	0.0827306i
$483$		0			0
$484$	4.06732	−	0.569361i	0.184878	−	0.0258800i
$485$	−0.343189			−0.0155834
$486$	−1.42721	−	20.4905i	−0.0647397	−	0.929466i
$487$			7.18519i			0.325592i	0.986660	+	0.162796i	$0.0520512\pi$
$487$			7.18519i			0.325592i	−0.986660	+	0.162796i	$0.947949\pi$
$488$	4.11065	−	0.870227i	0.186080	−	0.0393933i
$489$		−	4.73989i		−	0.214345i
$490$		0			0
$491$			5.80059i			0.261777i	0.991397	+	0.130889i	$0.0417830\pi$
$491$			5.80059i			0.261777i	−0.991397	+	0.130889i	$0.958217\pi$
$492$	−0.152929	−	1.09247i	−0.00689457	−	0.0492525i
$493$			7.10504i			0.319995i
$494$	−33.6890	+	2.34652i	−1.51574	+	0.105575i
$495$	9.25383			0.415929
$496$	34.1089	−	9.74027i	1.53153	−	0.437351i
$497$		0			0
$498$	−0.422506	−	6.06591i	−0.0189329	−	0.271820i
$499$		−	39.6601i		−	1.77543i	−0.460394	−	0.887715i	$-0.652292\pi$
$499$		−	39.6601i		−	1.77543i	0.460394	−	0.887715i	$-0.347708\pi$
$500$	−0.277265	−	1.98069i	−0.0123997	−	0.0885791i
$501$	−9.08270			−0.405785
$502$	1.62445	+	23.3222i	0.0725028	+	1.04092i
$503$	8.22384			0.366683			0.183341	−	0.983049i	$-0.441309\pi$
$503$	8.22384			0.366683			0.183341	+	0.983049i	$0.441309\pi$
$504$		0			0
$505$	−4.53635			−0.201865
$506$	−1.15214	−	16.5412i	−0.0512187	−	0.735347i
$507$	13.9042			0.617506
$508$	−4.71843	−	33.7069i	−0.209346	−	1.49550i
$509$		−	32.5719i		−	1.44373i	−0.692036	−	0.721863i	$-0.743286\pi$
$509$		−	32.5719i		−	1.44373i	0.692036	−	0.721863i	$-0.256714\pi$
$510$	−0.0890466	−	1.27844i	−0.00394305	−	0.0566103i
$511$		0			0
$512$	13.2550	+	18.3386i	0.585796	+	0.810459i
$513$	15.0869			0.666105
$514$	8.73986	−	0.608753i	0.385499	−	0.0268509i
$515$		−	6.13812i		−	0.270478i
$516$	0.570487	+	4.07537i	0.0251143	+	0.179408i
$517$		−	24.9150i		−	1.09576i
$518$		0			0
$519$		−	2.59934i		−	0.114098i
$520$	−3.41536	−	16.1329i	−0.149773	−	0.707476i
$521$			5.64398i			0.247267i	0.992328	+	0.123634i	$0.0394547\pi$
$521$			5.64398i			0.247267i	−0.992328	+	0.123634i	$0.960545\pi$
$522$	−1.30707	−	18.7656i	−0.0572090	−	0.821348i
$523$	−2.73410			−0.119554			−0.0597770	−	0.998212i	$-0.519039\pi$
$523$	−2.73410			−0.119554			−0.0597770	+	0.998212i	$0.519039\pi$
$524$	−2.38897	+	0.334418i	−0.104363	+	0.0146091i
$525$		0			0
$526$	−29.8434	+	2.07867i	−1.30123	+	0.0906342i
$527$			12.1327i			0.528507i
$528$	2.62842	+	9.20431i	0.114387	+	0.400566i
$529$	12.4687			0.542119
$530$	−10.4646	+	0.728886i	−0.454553	+	0.0316608i
$531$	19.1547			0.831245
$532$		0			0
$533$	4.85504			0.210295
$534$	8.77559	−	0.611242i	0.379757	−	0.0264510i
$535$	−7.66797			−0.331515
$536$	−7.02182	+	1.48652i	−0.303296	+	0.0642081i
$537$			13.6139i			0.587485i
$538$	−43.7157	+	3.04491i	−1.88472	+	0.131275i
$539$		0			0
$540$	1.02132	+	7.29595i	0.0439505	+	0.313968i
$541$	28.2999			1.21671			0.608355	−	0.793665i	$-0.291830\pi$
$541$	28.2999			1.21671			0.608355	+	0.793665i	$0.291830\pi$
$542$	−2.26385	−	32.5020i	−0.0972406	−	1.39608i
$543$			8.65052i			0.371230i
$544$	−7.27616	+	2.63706i	−0.311963	+	0.113063i
$545$		−	1.29523i		−	0.0554817i
$546$		0			0
$547$			20.7596i			0.887616i	0.896122	+	0.443808i	$0.146373\pi$
$547$			20.7596i			0.887616i	−0.896122	+	0.443808i	$0.853627\pi$
$548$	−4.24839	+	0.594707i	−0.181482	+	0.0254046i
$549$		−	3.80490i		−	0.162389i
$550$	−5.09715	+	0.355029i	−0.217343	+	0.0151385i
$551$	21.2704			0.906150
$552$	5.94779	−	1.25915i	0.253155	−	0.0535930i
$553$		0			0
$554$	0.682514	+	9.79885i	0.0289973	+	0.416313i
$555$			7.15064i			0.303528i
$556$	6.72553	−	0.941468i	0.285226	−	0.0399271i
$557$	−18.7575			−0.794781			−0.397391	−	0.917650i	$-0.630084\pi$
$557$	−18.7575			−0.794781			−0.397391	+	0.917650i	$0.630084\pi$
$558$	−2.23197	−	32.0444i	−0.0944870	−	1.35655i
$559$	−18.1113			−0.766025
$560$		0			0
$561$	−3.27401			−0.138229
$562$	−0.417029	−	5.98728i	−0.0175913	−	0.252558i
$563$	33.3740			1.40655			0.703274	−	0.710919i	$-0.251721\pi$
$563$	33.3740			1.40655			0.703274	+	0.710919i	$0.251721\pi$
$564$	9.04700	−	1.26644i	0.380947	−	0.0533266i
$565$		−	7.10591i		−	0.298948i
$566$	0.838399	+	12.0369i	0.0352405	+	0.505948i
$567$		0			0
$568$	−9.75407	+	2.06494i	−0.409272	+	0.0866431i
$569$	13.0300			0.546247			0.273124	−	0.961979i	$-0.411943\pi$
$569$	13.0300			0.546247			0.273124	+	0.961979i	$0.411943\pi$
$570$	−3.82728	+	0.266580i	−0.160307	+	0.0111658i
$571$			32.9558i			1.37916i	0.724211	+	0.689579i	$0.242204\pi$
$571$			32.9558i			1.37916i	−0.724211	+	0.689579i	$0.757796\pi$
$572$	−41.7223	+	5.84046i	−1.74450	+	0.244202i
$573$			8.26295i			0.345190i
$574$		0			0
$575$			3.24519i			0.135334i
$576$	18.7324	−	8.30348i	0.780518	−	0.345978i
$577$			36.3874i			1.51483i	0.652935	+	0.757414i	$0.273538\pi$
$577$			36.3874i			1.51483i	−0.652935	+	0.757414i	$0.726462\pi$
$578$	1.48658	+	21.3428i	0.0618337	+	0.887745i
$579$	−12.6275			−0.524780
$580$	1.43991	+	10.2862i	0.0597890	+	0.427113i
$581$		0			0
$582$	−0.320692	+	0.0223370i	−0.0132931	+	0.000925898i
$583$			26.7992i			1.10991i
$584$	14.3055	−	3.02848i	0.591964	−	0.125319i
$585$	−14.9330			−0.617403
$586$	35.5971	−	2.47943i	1.47050	−	0.102424i
$587$	−28.4245			−1.17321			−0.586603	−	0.809875i	$-0.699535\pi$
$587$	−28.4245			−1.17321			−0.586603	+	0.809875i	$0.699535\pi$
$588$		0			0
$589$	36.3217			1.49661
$590$	−10.5507	+	0.734884i	−0.434366	+	0.0302547i
$591$	−1.27959			−0.0526352
$592$	41.5233	−	11.8576i	1.70660	−	0.487342i
$593$			7.57149i			0.310924i	0.987842	+	0.155462i	$0.0496866\pi$
$593$			7.57149i			0.310924i	−0.987842	+	0.155462i	$0.950313\pi$
$594$	18.7756	−	1.30777i	0.770371	−	0.0536583i
$595$		0			0
$596$	37.8042	−	5.29198i	1.54852	−	0.216768i
$597$	13.6210			0.557472
$598$	1.85921	+	26.6927i	0.0760289	+	1.09155i
$599$		−	47.4510i		−	1.93879i	−0.245499	−	0.969397i	$-0.578952\pi$
$599$		−	47.4510i		−	1.93879i	0.245499	−	0.969397i	$-0.421048\pi$
$600$	−0.388005	−	1.83280i	−0.0158403	−	0.0748238i
$601$		−	13.3242i		−	0.543506i	−0.962367	−	0.271753i	$-0.912397\pi$
$601$		−	13.3242i		−	0.543506i	0.962367	−	0.271753i	$-0.0876034\pi$
$602$		0			0
$603$			6.49954i			0.264682i
$604$	−2.66339	−	19.0264i	−0.108372	−	0.774173i
$605$			2.05349i			0.0834862i
$606$	−4.23898	+	0.295255i	−0.172197	+	0.0119939i
$607$	−15.0816			−0.612143			−0.306072	−	0.952008i	$-0.599015\pi$
$607$	−15.0816			−0.612143			−0.306072	+	0.952008i	$0.599015\pi$
$608$	7.89460	+	21.7827i	0.320168	+	0.883405i
$609$		0			0
$610$	0.145978	+	2.09580i	0.00591046	+	0.0848564i
$611$			40.2056i			1.62654i
$612$	0.971581	+	6.94065i	0.0392738	+	0.280559i
$613$	−5.20469			−0.210215			−0.105108	−	0.994461i	$-0.533519\pi$
$613$	−5.20469			−0.210215			−0.105108	+	0.994461i	$0.533519\pi$
$614$	−2.87559	−	41.2848i	−0.116049	−	1.66612i
$615$	0.551563			0.0222412
$616$		0			0
$617$	−35.7404			−1.43885			−0.719426	−	0.694569i	$-0.755595\pi$
$617$	−35.7404			−1.43885			−0.719426	+	0.694569i	$0.755595\pi$
$618$	−0.399509	−	5.73575i	−0.0160706	−	0.230726i
$619$	−38.2437			−1.53715			−0.768573	−	0.639762i	$-0.779033\pi$
$619$	−38.2437			−1.53715			−0.768573	+	0.639762i	$0.779033\pi$
$620$	2.45881	+	17.5649i	0.0987482	+	0.705424i
$621$		−	11.9538i		−	0.479689i
$622$	2.23515	+	32.0901i	0.0896215	+	1.28670i
$623$		0			0
$624$	−4.24151	−	14.8531i	−0.169796	−	0.594599i
$625$	1.00000			0.0400000
$626$	−9.28981	+	0.647059i	−0.371296	+	0.0258617i
$627$			9.80143i			0.391431i
$628$	4.56443	+	32.6068i	0.182141	+	1.30115i
$629$			14.7700i			0.588918i
$630$		0			0
$631$			12.0334i			0.479042i	0.970891	+	0.239521i	$0.0769904\pi$
$631$			12.0334i			0.479042i	−0.970891	+	0.239521i	$0.923010\pi$
$632$	−31.3792	+	6.64300i	−1.24820	+	0.264244i
$633$			6.61294i			0.262841i
$634$	−1.38768	−	19.9229i	−0.0551117	−	0.791237i
$635$	17.0178			0.675329
$636$	−9.73118	+	1.36221i	−0.385866	+	0.0540152i
$637$		0			0
$638$	26.4709	−	1.84376i	1.04799	−	0.0729952i
$639$			9.02857i			0.357165i
$640$	−9.99954	+	5.29237i	−0.395267	+	0.209199i
$641$	22.9352			0.905888			0.452944	−	0.891539i	$-0.350374\pi$
$641$	22.9352			0.905888			0.452944	+	0.891539i	$0.350374\pi$
$642$	−7.16531	+	0.499082i	−0.282792	+	0.0196972i
$643$	−1.23955			−0.0488833			−0.0244416	−	0.999701i	$-0.507781\pi$
$643$	−1.23955			−0.0488833			−0.0244416	+	0.999701i	$0.507781\pi$
$644$		0			0
$645$	−2.05755			−0.0810160
$646$	−7.90543	+	0.550633i	−0.311035	+	0.0216644i
$647$	14.1415			0.555962			0.277981	−	0.960587i	$-0.410335\pi$
$647$	14.1415			0.555962			0.277981	+	0.960587i	$0.410335\pi$
$648$	−3.07195	−	14.5108i	−0.120678	−	0.570038i
$649$			27.0198i			1.06062i
$650$	8.22532	−	0.572914i	0.322624	−	0.0224715i
$651$		0			0
$652$	−1.98414	−	14.1740i	−0.0777049	−	0.555098i
$653$	−17.0916			−0.668845			−0.334423	−	0.942423i	$-0.608541\pi$
$653$	−17.0916			−0.668845			−0.334423	+	0.942423i	$0.608541\pi$
$654$	−0.0843022	−	1.21033i	−0.00329648	−	0.0473275i
$655$		−	1.20613i		−	0.0471275i
$656$	−0.914629	−	3.20289i	−0.0357103	−	0.125052i
$657$		−	13.2414i		−	0.516598i
$658$		0			0
$659$		−	3.45765i		−	0.134691i	−0.997730	−	0.0673455i	$-0.978547\pi$
$659$		−	3.45765i		−	0.134691i	0.997730	−	0.0673455i	$-0.0214530\pi$
$660$	−4.73991	+	0.663512i	−0.184501	+	0.0258272i
$661$		−	15.1632i		−	0.589780i	−0.955531	−	0.294890i	$-0.904717\pi$
$661$		−	15.1632i		−	0.589780i	0.955531	−	0.294890i	$-0.0952830\pi$
$662$	−28.6707	+	1.99699i	−1.11432	+	0.0776152i
$663$	5.28330			0.205186
$664$	−3.80267	−	17.9625i	−0.147572	−	0.697079i
$665$		0			0
$666$	−2.71715	−	39.0100i	−0.105287	−	1.51161i
$667$		−	16.8531i		−	0.652556i
$668$	−27.1607	+	3.80206i	−1.05088	+	0.147106i
$669$	−11.1394			−0.430676
$670$	−0.249359	−	3.58005i	−0.00963359	−	0.138309i
$671$	5.36721			0.207199
$672$		0			0
$673$	−11.2116			−0.432175			−0.216087	−	0.976374i	$-0.569330\pi$
$673$	−11.2116			−0.432175			−0.216087	+	0.976374i	$0.569330\pi$
$674$	1.54968	+	22.2488i	0.0596915	+	0.856991i
$675$	−3.68354			−0.141780
$676$	41.5787	−	5.82036i	1.59918	−	0.223860i
$677$			3.67637i			0.141294i	0.997501	+	0.0706471i	$0.0225064\pi$
$677$			3.67637i			0.141294i	−0.997501	+	0.0706471i	$0.977494\pi$
$678$	−0.462500	−	6.64010i	−0.0177622	−	0.255011i
$679$		0			0
$680$	−0.801444	−	3.78574i	−0.0307340	−	0.145176i
$681$	−13.1370			−0.503412
$682$	45.2020	−	3.14843i	1.73087	−	0.120560i
$683$		−	42.1877i		−	1.61427i	−0.590369	−	0.807133i	$-0.701018\pi$
$683$		−	42.1877i		−	1.61427i	0.590369	−	0.807133i	$-0.298982\pi$
$684$	20.7783	−	2.90863i	0.794477	−	0.111214i
$685$		−	2.14490i		−	0.0819526i
$686$		0			0
$687$		−	9.22865i		−	0.352095i
$688$	3.41194	+	11.9481i	0.130079	+	0.455516i
$689$		−	43.2461i		−	1.64755i
$690$	0.211218	+	3.03246i	0.00804094	+	0.115444i
$691$	23.1230			0.879640			0.439820	−	0.898086i	$-0.355042\pi$
$691$	23.1230			0.879640			0.439820	+	0.898086i	$0.355042\pi$
$692$	−1.08809	−	7.77298i	−0.0413631	−	0.295485i
$693$		0			0
$694$	−4.29987	+	0.299497i	−0.163221	+	0.0113688i
$695$			3.39555i			0.128801i
$696$	2.01502	+	9.51822i	0.0763790	+	0.360787i
$697$	1.13928			0.0431533
$698$	11.8572	−	0.825884i	0.448802	−	0.0312602i
$699$	−6.77301			−0.256179
$700$		0			0
$701$	29.3192			1.10737			0.553686	−	0.832725i	$-0.313221\pi$
$701$	29.3192			1.10737			0.553686	+	0.832725i	$0.313221\pi$
$702$	−30.2983	+	2.11035i	−1.14354	+	0.0796502i
$703$	44.2170			1.66768
$704$	11.7129	+	26.4241i	0.441448	+	0.995894i
$705$			4.56761i			0.172026i
$706$	0.610622	−	0.0425314i	0.0229811	−	0.00160069i
$707$		0			0
$708$	−9.81126	+	1.37342i	−0.368730	+	0.0516163i
$709$	3.35439			0.125977			0.0629884	−	0.998014i	$-0.479937\pi$
$709$	3.35439			0.125977			0.0629884	+	0.998014i	$0.479937\pi$
$710$	−0.346387	−	4.97308i	−0.0129997	−	0.186636i
$711$			29.0453i			1.08928i
$712$	25.9864	−	5.50134i	0.973882	−	0.206172i
$713$		−	28.7786i		−	1.07777i
$714$		0			0
$715$		−	21.0645i		−	0.787769i
$716$	5.69886	+	40.7108i	0.212977	+	1.52143i
$717$			11.3153i			0.422578i
$718$	−38.0647	+	2.65130i	−1.42056	+	0.0989457i
$719$	31.0284			1.15717			0.578583	−	0.815624i	$-0.303606\pi$
$719$	31.0284			1.15717			0.578583	+	0.815624i	$0.303606\pi$
$720$	2.81319	+	9.85134i	0.104841	+	0.367138i
$721$		0			0
$722$	−0.218609	−	3.13857i	−0.00813579	−	0.116805i
$723$		−	12.2428i		−	0.455313i
$724$	3.62115	+	25.8683i	0.134579	+	0.961388i
$725$	−5.19327			−0.192873
$726$	0.133655	+	1.91888i	0.00496039	+	0.0712162i
$727$	37.9906			1.40899			0.704497	−	0.709707i	$-0.251173\pi$
$727$	37.9906			1.40899			0.704497	+	0.709707i	$0.251173\pi$
$728$		0			0
$729$	−6.11207			−0.226373
$730$	0.508017	+	7.29359i	0.0188025	+	0.269948i
$731$	−4.24997			−0.157191
$732$	0.272817	+	1.94891i	0.0100836	+	0.0720338i
$733$		−	30.9751i		−	1.14409i	−0.820222	−	0.572046i	$-0.806150\pi$
$733$		−	30.9751i		−	1.14409i	0.820222	−	0.572046i	$-0.193850\pi$
$734$	−2.04601	−	29.3745i	−0.0755195	−	1.08423i
$735$		0			0
$736$	17.2590	−	6.25511i	0.636176	−	0.230566i
$737$	−9.16828			−0.337718
$738$	−3.00903	+	0.209586i	−0.110764	+	0.00771498i
$739$		−	2.92228i		−	0.107498i	−0.998554	−	0.0537488i	$-0.982883\pi$
$739$		−	2.92228i		−	0.107498i	0.998554	−	0.0537488i	$-0.0171170\pi$
$740$	2.99329	+	21.3831i	0.110036	+	0.786058i
$741$		−	15.8167i		−	0.581039i
$742$		0			0
$743$		−	36.6505i		−	1.34457i	−0.740290	−	0.672287i	$-0.765312\pi$
$743$		−	36.6505i		−	1.34457i	0.740290	−	0.672287i	$-0.234688\pi$
$744$	3.44087	+	16.2535i	0.126148	+	0.595881i
$745$			19.0864i			0.699271i
$746$	−1.73551	−	24.9167i	−0.0635415	−	0.912265i
$747$	−16.6265			−0.608330
$748$	−9.79051	+	1.37052i	−0.357976	+	0.0501110i
$749$		0			0
$750$	0.934447	−	0.0650866i	0.0341212	−	0.00237663i
$751$		−	36.1831i		−	1.32034i	−0.751116	−	0.660170i	$-0.770484\pi$
$751$		−	36.1831i		−	1.32034i	0.751116	−	0.660170i	$-0.229516\pi$
$752$	26.5238	−	7.57424i	0.967223	−	0.276204i
$753$	−10.9496			−0.399024
$754$	−42.7163	+	2.97529i	−1.55563	+	0.108354i
$755$	9.60595			0.349596
$756$		0			0
$757$	−1.44394			−0.0524807			−0.0262404	−	0.999656i	$-0.508354\pi$
$757$	−1.44394			−0.0524807			−0.0262404	+	0.999656i	$0.508354\pi$
$758$	21.2397	−	1.47940i	0.771462	−	0.0537342i
$759$	7.76594			0.281886
$760$	−11.3334	+	2.39929i	−0.411106	+	0.0870314i
$761$		−	28.2334i		−	1.02346i	−0.859146	−	0.511730i	$-0.829005\pi$
$761$		−	28.2334i		−	1.02346i	0.859146	−	0.511730i	$-0.170995\pi$
$762$	15.9022	−	1.10763i	0.576076	−	0.0401251i
$763$		0			0
$764$	3.45891	+	24.7093i	0.125139	+	0.893951i
$765$	−3.50416			−0.126693
$766$	−2.98241	−	42.8184i	−0.107759	−	1.54709i
$767$		−	43.6020i		−	1.57438i
$768$	−8.99958	+	5.59627i	−0.324744	+	0.201938i
$769$			38.3866i			1.38426i	0.721774	+	0.692129i	$0.243327\pi$
$769$			38.3866i			1.38426i	−0.721774	+	0.692129i	$0.756673\pi$
$770$		0			0
$771$			4.10328i			0.147776i
$772$	−37.7608	+	5.28592i	−1.35904	+	0.190244i
$773$		−	19.0817i		−	0.686322i	−0.939277	−	0.343161i	$-0.888502\pi$
$773$		−	19.0817i		−	0.686322i	0.939277	−	0.343161i	$-0.111498\pi$
$774$	11.2249	−	0.781842i	0.403471	−	0.0281027i
$775$	−8.86809			−0.318551
$776$	−0.949638	+	0.201039i	−0.0340900	+	0.00721688i
$777$		0			0
$778$	−0.616928	−	8.85722i	−0.0221179	−	0.317547i
$779$		−	3.41067i		−	0.122200i
$780$	7.64883	−	1.07072i	0.273872	−	0.0383378i
$781$	−12.7357			−0.455721
$782$	0.436281	+	6.26369i	0.0156014	+

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0982654 + 1.41080i) q^{2} -0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} -1.00000i q^{5} +(-0.0650866 - 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +O(q^{10})\)	\(q+(0.0982654 + 1.41080i) q^{2} -0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} -1.00000i q^{5} +(-0.0650866 - 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +(1.41080 - 0.0982654i) q^{10} -3.61296i q^{11} +(1.31192 - 0.183648i) q^{12} +5.83027i q^{13} +0.662355i q^{15} +(3.84625 - 1.09835i) q^{16} +1.36813i q^{17} +(-0.251686 - 3.61345i) q^{18} +4.09577 q^{19} +(0.277265 + 1.98069i) q^{20} +(5.09715 - 0.355029i) q^{22} -3.24519i q^{23} +(0.388005 + 1.83280i) q^{24} -1.00000 q^{25} +(-8.22532 + 0.572914i) q^{26} +3.68354 q^{27} +5.19327 q^{29} +(-0.934447 + 0.0650866i) q^{30} +8.86809 q^{31} +(1.92750 + 5.31834i) q^{32} +2.39306i q^{33} +(-1.93014 + 0.134439i) q^{34} +(5.07311 - 0.710155i) q^{36} +10.7958 q^{37} +(0.402472 + 5.77829i) q^{38} -3.86171i q^{39} +(-2.76710 + 0.585797i) q^{40} -0.832730i q^{41} +3.10642i q^{43} +(1.00175 + 7.15615i) q^{44} +2.56129i q^{45} +(4.57830 - 0.318890i) q^{46} +6.89601 q^{47} +(-2.54758 + 0.727497i) q^{48} +(-0.0982654 - 1.41080i) q^{50} -0.906184i q^{51} +(-1.61653 - 11.5479i) q^{52} -7.41752 q^{53} +(0.361965 + 5.19673i) q^{54} -3.61296 q^{55} -2.71285 q^{57} +(0.510319 + 7.32664i) q^{58} -7.47856 q^{59} +(-0.183648 - 1.31192i) q^{60} +1.48554i q^{61} +(0.871427 + 12.5111i) q^{62} +(-7.31368 + 3.24192i) q^{64} +5.83027 q^{65} +(-3.37612 + 0.235155i) q^{66} -2.53761i q^{67} +(-0.379333 - 2.70983i) q^{68} +2.14947i q^{69} -3.52502i q^{71} +(1.50039 + 7.08734i) q^{72} +5.16984i q^{73} +(1.06085 + 15.2306i) q^{74} +0.662355 q^{75} +(-8.11244 + 1.13561i) q^{76} +(5.44808 - 0.379472i) q^{78} -11.3401i q^{79} +(-1.09835 - 3.84625i) q^{80} +5.24405 q^{81} +(1.17481 - 0.0818286i) q^{82} +6.49145 q^{83} +1.36813 q^{85} +(-4.38252 + 0.305254i) q^{86} -3.43978 q^{87} +(-9.99743 + 2.11646i) q^{88} +9.39121i q^{89} +(-3.61345 + 0.251686i) q^{90} +(0.899777 + 6.42771i) q^{92} -5.87382 q^{93} +(0.677640 + 9.72886i) q^{94} -4.09577i q^{95} +(-1.27669 - 3.52263i) q^{96} -0.343189i q^{97} +9.25383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

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