LMFDB - Embedded newform 980.2.c.e.979.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(979,980)]

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, 1, 1]))

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

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

chi := DirichletCharacter("980.979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.c (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.19
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 - 1.48845i) q^{4} +(0.639901 + 2.14255i) q^{5} +(3.23064 + 1.44151i) q^{6} +(2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +O(q^{10})$	\(q+(-0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 - 1.48845i) q^{4} +(0.639901 + 2.14255i) q^{5} +(3.23064 + 1.44151i) q^{6} +(2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +(-3.13582 - 0.408241i) q^{10} +2.25026i q^{11} +(-3.72336 + 3.34164i) q^{12} -5.96620 q^{13} +(5.35959 - 1.60071i) q^{15} +(-0.430987 + 3.97671i) q^{16} +2.00749 q^{17} +(1.87716 - 4.20700i) q^{18} -7.81989 q^{19} +(2.33427 - 3.81460i) q^{20} +(-2.90618 - 1.29673i) q^{22} +2.99226 q^{23} +(-2.17005 - 6.73430i) q^{24} +(-4.18105 + 2.74204i) q^{25} +(3.43807 - 7.70524i) q^{26} +0.644123i q^{27} -4.87936 q^{29} +(-1.02122 + 7.84424i) q^{30} +1.49990 q^{31} +(-4.88750 - 2.84822i) q^{32} +5.62903 q^{33} +(-1.15683 + 2.59263i) q^{34} +(4.35154 + 4.84863i) q^{36} +4.78601i q^{37} +(4.50627 - 10.0992i) q^{38} +14.9244i q^{39} +(3.58134 + 5.21287i) q^{40} +8.82927i q^{41} -1.12695 q^{43} +(3.34941 - 3.00602i) q^{44} +(-2.08447 - 6.97935i) q^{45} +(-1.72431 + 3.86446i) q^{46} -9.56972i q^{47} +(9.94774 + 1.07811i) q^{48} +(-1.13193 - 6.97988i) q^{50} -5.02172i q^{51} +(7.96997 + 8.88040i) q^{52} +7.06264i q^{53} +(-0.831874 - 0.371181i) q^{54} +(-4.82131 + 1.43994i) q^{55} +19.5614i q^{57} +(2.81177 - 6.30161i) q^{58} -11.4057 q^{59} +(-9.54221 - 5.83918i) q^{60} -1.21986i q^{61} +(-0.864331 + 1.93710i) q^{62} +(6.49489 - 4.67081i) q^{64} +(-3.81777 - 12.7829i) q^{65} +(-3.24377 + 7.26979i) q^{66} -1.11485 q^{67} +(-2.68171 - 2.98805i) q^{68} -7.48514i q^{69} +8.40090i q^{71} +(-8.76953 + 2.82588i) q^{72} -5.88062 q^{73} +(-6.18105 - 2.75798i) q^{74} +(6.85921 + 10.4589i) q^{75} +(10.4462 + 11.6395i) q^{76} +(-19.2746 - 8.60032i) q^{78} +12.1357i q^{79} +(-8.79610 + 1.62129i) q^{80} -8.16121 q^{81} +(-11.4028 - 5.08793i) q^{82} +11.1319i q^{83} +(1.28459 + 4.30114i) q^{85} +(0.649414 - 1.45544i) q^{86} +12.2057i q^{87} +(1.95210 + 6.05795i) q^{88} +4.57883i q^{89} +(10.2149 + 1.32984i) q^{90} +(-3.99723 - 4.45385i) q^{92} -3.75201i q^{93} +(12.3591 + 5.51462i) q^{94} +(-5.00395 - 16.7545i) q^{95} +(-7.12483 + 12.2261i) q^{96} -4.62008 q^{97} -7.33022i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) $ 48 * q + 16 * q^4 - 64 * q^9	$ 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) $ 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

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 $

$2$	−0.576258	+	1.29148i	−0.407476	+	0.913216i
$2$	−0.576258	+	1.29148i	−0.407476	+	0.913216i
$3$		−	2.50150i		−	1.44424i	−0.691767	−	0.722120i	$-0.743168\pi$
$3$		−	2.50150i		−	1.44424i	0.691767	−	0.722120i	$-0.256832\pi$
$4$	−1.33585	−	1.48845i	−0.667927	−	0.744227i
$5$	0.639901	+	2.14255i	0.286172	+	0.958178i
$5$	0.639901	+	2.14255i	0.286172	+	0.958178i
$6$	3.23064	+	1.44151i	1.31890	+	0.588493i
$7$		0			0
$7$		0			0
$8$	2.69211	−	0.867500i	0.951804	−	0.306708i
$9$	−3.25749			−1.08583
$10$	−3.13582	−	0.408241i	−0.991632	−	0.129097i
$11$			2.25026i			0.678480i	0.940700	+	0.339240i	$0.110170\pi$
$11$			2.25026i			0.678480i	−0.940700	+	0.339240i	$0.889830\pi$
$12$	−3.72336	+	3.34164i	−1.07484	+	0.964648i
$13$	−5.96620			−1.65472			−0.827362	−	0.561668i	$-0.810160\pi$
$13$	−5.96620			−1.65472			−0.827362	+	0.561668i	$0.810160\pi$
$14$		0			0
$15$	5.35959	−	1.60071i	1.38384	−	0.413302i
$16$	−0.430987	+	3.97671i	−0.107747	+	0.994178i
$17$	2.00749			0.486887			0.243443	−	0.969915i	$-0.421723\pi$
$17$	2.00749			0.486887			0.243443	+	0.969915i	$0.421723\pi$
$18$	1.87716	−	4.20700i	0.442450	−	0.991599i
$19$	−7.81989			−1.79400			−0.897002	−	0.442026i	$-0.854260\pi$
$19$	−7.81989			−1.79400			−0.897002	+	0.442026i	$0.854260\pi$
$20$	2.33427	−	3.81460i	0.521960	−	0.852970i
$21$		0			0
$22$	−2.90618	−	1.29673i	−0.619599	−	0.276464i
$23$	2.99226			0.623930			0.311965	−	0.950094i	$-0.399013\pi$
$23$	2.99226			0.623930			0.311965	+	0.950094i	$0.399013\pi$
$24$	−2.17005	−	6.73430i	−0.442960	−	1.37463i
$25$	−4.18105	+	2.74204i	−0.836211	+	0.548408i
$26$	3.43807	−	7.70524i	0.674260	−	1.51112i
$27$			0.644123i			0.123962i
$28$		0			0
$29$	−4.87936			−0.906074			−0.453037	−	0.891492i	$-0.649659\pi$
$29$	−4.87936			−0.906074			−0.453037	+	0.891492i	$0.649659\pi$
$30$	−1.02122	+	7.84424i	−0.186448	+	1.43216i
$31$	1.49990			0.269391			0.134695	−	0.990887i	$-0.456994\pi$
$31$	1.49990			0.269391			0.134695	+	0.990887i	$0.456994\pi$
$32$	−4.88750	−	2.84822i	−0.863996	−	0.503500i
$33$	5.62903			0.979888
$34$	−1.15683	+	2.59263i	−0.198395	+	0.444633i
$35$		0			0
$36$	4.35154	+	4.84863i	0.725256	+	0.808105i
$37$			4.78601i			0.786816i	0.919364	+	0.393408i	$0.128704\pi$
$37$			4.78601i			0.786816i	−0.919364	+	0.393408i	$0.871296\pi$
$38$	4.50627	−	10.0992i	0.731013	−	1.63831i
$39$			14.9244i			2.38982i
$40$	3.58134	+	5.21287i	0.566260	+	0.824226i
$41$			8.82927i			1.37890i	0.724333	+	0.689450i	$0.242148\pi$
$41$			8.82927i			1.37890i	−0.724333	+	0.689450i	$0.757852\pi$
$42$		0			0
$43$	−1.12695			−0.171858			−0.0859292	−	0.996301i	$-0.527386\pi$
$43$	−1.12695			−0.171858			−0.0859292	+	0.996301i	$0.527386\pi$
$44$	3.34941	−	3.00602i	0.504943	−	0.453175i
$45$	−2.08447	−	6.97935i	−0.310735	−	1.04042i
$46$	−1.72431	+	3.86446i	−0.254236	+	0.569783i
$47$		−	9.56972i		−	1.39589i	−0.716153	−	0.697943i	$-0.754099\pi$
$47$		−	9.56972i		−	1.39589i	0.716153	−	0.697943i	$-0.245901\pi$
$48$	9.94774	+	1.07811i	1.43583	+	0.155612i
$49$		0			0
$50$	−1.13193	−	6.97988i	−0.160079	−	0.987104i
$51$		−	5.02172i		−	0.703182i
$52$	7.96997	+	8.88040i	1.10524	+	1.23149i
$53$			7.06264i			0.970129i	0.874478	+	0.485064i	$0.161204\pi$
$53$			7.06264i			0.970129i	−0.874478	+	0.485064i	$0.838796\pi$
$54$	−0.831874	−	0.371181i	−0.113204	−	0.0505113i
$55$	−4.82131	+	1.43994i	−0.650105	+	0.194162i
$56$		0			0
$57$			19.5614i			2.59098i
$58$	2.81177	−	6.30161i	0.369203	−	0.827441i
$59$	−11.4057			−1.48490			−0.742450	−	0.669901i	$-0.766337\pi$
$59$	−11.4057			−1.48490			−0.742450	+	0.669901i	$0.766337\pi$
$60$	−9.54221	−	5.83918i	−1.23189	−	0.753835i
$61$		−	1.21986i		−	0.156187i	−0.996946	−	0.0780935i	$-0.975117\pi$
$61$		−	1.21986i		−	0.156187i	0.996946	−	0.0780935i	$-0.0248833\pi$
$62$	−0.864331	+	1.93710i	−0.109770	+	0.246012i
$63$		0			0
$64$	6.49489	−	4.67081i	0.811861	−	0.583851i
$65$	−3.81777	−	12.7829i	−0.473536	−	1.58552i
$66$	−3.24377	+	7.26979i	−0.399281	+	0.894850i
$67$	−1.11485			−0.136200			−0.0681000	−	0.997678i	$-0.521694\pi$
$67$	−1.11485			−0.136200			−0.0681000	+	0.997678i	$0.521694\pi$
$68$	−2.68171	−	2.98805i	−0.325205	−	0.362354i
$69$		−	7.48514i		−	0.901105i
$70$		0			0
$71$			8.40090i			0.997003i	0.866889	+	0.498501i	$0.166116\pi$
$71$			8.40090i			0.997003i	−0.866889	+	0.498501i	$0.833884\pi$
$72$	−8.76953	+	2.82588i	−1.03350	+	0.333033i
$73$	−5.88062			−0.688274			−0.344137	−	0.938919i	$-0.611828\pi$
$73$	−5.88062			−0.688274			−0.344137	+	0.938919i	$0.611828\pi$
$74$	−6.18105	−	2.75798i	−0.718533	−	0.320608i
$75$	6.85921	+	10.4589i	0.792033	+	1.20769i
$76$	10.4462	+	11.6395i	1.19826	+	1.33515i
$77$		0			0
$78$	−19.2746	−	8.60032i	−2.18242	−	0.973794i
$79$			12.1357i			1.36537i	0.730711	+	0.682687i	$0.239189\pi$
$79$			12.1357i			1.36537i	−0.730711	+	0.682687i	$0.760811\pi$
$80$	−8.79610	+	1.62129i	−0.983434	+	0.181266i
$81$	−8.16121			−0.906801
$82$	−11.4028	−	5.08793i	−1.25923	−	0.561868i
$83$			11.1319i			1.22188i	0.791677	+	0.610940i	$0.209208\pi$
$83$			11.1319i			1.22188i	−0.791677	+	0.610940i	$0.790792\pi$
$84$		0			0
$85$	1.28459	+	4.30114i	0.139334	+	0.466524i
$86$	0.649414	−	1.45544i	0.0700281	−	0.156944i
$87$			12.2057i			1.30859i
$88$	1.95210	+	6.05795i	0.208095	+	0.645780i
$89$			4.57883i			0.485355i	0.970107	+	0.242677i	$0.0780256\pi$
$89$			4.57883i			0.485355i	−0.970107	+	0.242677i	$0.921974\pi$
$90$	10.2149	+	1.32984i	1.07675	+	0.140178i
$91$		0			0
$92$	−3.99723	−	4.45385i	−0.416740	−	0.464345i
$93$		−	3.75201i		−	0.389065i
$94$	12.3591	+	5.51462i	1.27475	+	0.568790i
$95$	−5.00395	−	16.7545i	−0.513394	−	1.71898i
$96$	−7.12483	+	12.2261i	−0.727175	+	1.24782i
$97$	−4.62008			−0.469098			−0.234549	−	0.972104i	$-0.575361\pi$
$97$	−4.62008			−0.469098			−0.234549	+	0.972104i	$0.575361\pi$
$98$		0			0
$99$		−	7.33022i		−	0.736715i
$100$	9.66668	+	2.56034i	0.966668	+	0.256034i
$101$		−	0.111126i		−	0.0110574i	−0.999985	−	0.00552872i	$-0.998240\pi$
$101$		−	0.111126i		−	0.0110574i	0.999985	−	0.00552872i	$-0.00175986\pi$
$102$	6.48547	+	2.89381i	0.642157	+	0.286530i
$103$		−	12.9119i		−	1.27224i	−0.771588	−	0.636122i	$-0.780537\pi$
$103$		−	12.9119i		−	1.27224i	0.771588	−	0.636122i	$-0.219463\pi$
$104$	−16.0616	+	5.17567i	−1.57497	+	0.507517i
$105$		0			0
$106$	−9.12128	−	4.06990i	−0.885937	−	0.395304i
$107$	−14.6070			−1.41211			−0.706056	−	0.708156i	$-0.749527\pi$
$107$	−14.6070			−1.41211			−0.706056	+	0.708156i	$0.749527\pi$
$108$	0.958748	−	0.860455i	0.0922555	−	0.0827973i
$109$	4.45913			0.427107			0.213553	−	0.976931i	$-0.431496\pi$
$109$	4.45913			0.427107			0.213553	+	0.976931i	$0.431496\pi$
$110$	0.918650	−	7.05641i	0.0875899	−	0.672802i
$111$	11.9722			1.13635
$112$		0			0
$113$			2.30454i			0.216793i	0.994108	+	0.108397i	$0.0345717\pi$
$113$			2.30454i			0.216793i	−0.994108	+	0.108397i	$0.965428\pi$
$114$	−25.2632	−	11.2724i	−2.36612	−	1.05576i
$115$	1.91475	+	6.41108i	0.178551	+	0.597836i
$116$	6.51811	+	7.26270i	0.605191	+	0.674324i
$117$	19.4349			1.79675
$118$	6.57265	−	14.7303i	0.605061	−	1.35604i
$119$		0			0
$120$	13.0400	−	8.95873i	1.19038	−	0.817816i
$121$	5.93632			0.539665
$122$	1.57543	+	0.702953i	0.142632	+	0.0636424i
$123$	22.0864			1.99146
$124$	−2.00365	−	2.23254i	−0.179933	−	0.200488i
$125$	−8.55042	−	7.20349i	−0.764773	−	0.644300i
$126$		0			0
$127$	6.18242			0.548601			0.274300	−	0.961644i	$-0.411554\pi$
$127$	6.18242			0.548601			0.274300	+	0.961644i	$0.411554\pi$
$128$	2.28954	+	11.0796i	0.202368	+	0.979309i
$129$			2.81907i			0.248205i
$130$	18.7089	+	2.43565i	1.64088	+	0.213620i
$131$	8.16897			0.713726			0.356863	−	0.934157i	$-0.383846\pi$
$131$	8.16897			0.713726			0.356863	+	0.934157i	$0.383846\pi$
$132$	−7.51956	−	8.37855i	−0.654494	−	0.729259i
$133$		0			0
$134$	0.642438	−	1.43980i	0.0554982	−	0.124380i
$135$	−1.38007	+	0.412175i	−0.118777	+	0.0354744i
$136$	5.40437	−	1.74149i	0.463421	−	0.149332i
$137$		−	7.07703i		−	0.604631i	−0.953208	−	0.302316i	$-0.902240\pi$
$137$		−	7.07703i		−	0.604631i	0.953208	−	0.302316i	$-0.0977597\pi$
$138$	9.66693	+	4.31337i	0.822904	+	0.367179i
$139$	14.4633			1.22676			0.613382	−	0.789787i	$-0.289809\pi$
$139$	14.4633			1.22676			0.613382	+	0.789787i	$0.289809\pi$
$140$		0			0
$141$	−23.9386			−2.01600
$142$	−10.8496	−	4.84108i	−0.910479	−	0.406254i
$143$		−	13.4255i		−	1.12270i
$144$	1.40394	−	12.9541i	0.116995	−	1.07951i
$145$	−3.12230	−	10.4543i	−0.259293	−	0.868180i
$146$	3.38875	−	7.59471i	0.280455	−	0.628543i
$147$		0			0
$148$	7.12376	−	6.39342i	0.585569	−	0.525536i
$149$	19.6566			1.61033			0.805164	−	0.593053i	$-0.202077\pi$
$149$	19.6566			1.61033			0.805164	+	0.593053i	$0.202077\pi$
$150$	−17.4602	+	2.83153i	−1.42562	+	0.231193i
$151$		−	17.4157i		−	1.41727i	−0.705574	−	0.708636i	$-0.749311\pi$
$151$		−	17.4157i		−	1.41727i	0.705574	−	0.708636i	$-0.250689\pi$
$152$	−21.0520	+	6.78375i	−1.70754	+	0.550235i
$153$	−6.53938			−0.528677
$154$		0			0
$155$	0.959789	+	3.21362i	0.0770921	+	0.258124i
$156$	22.2143	−	19.9369i	1.77857	−	1.59623i
$157$	−6.86058			−0.547534			−0.273767	−	0.961796i	$-0.588270\pi$
$157$	−6.86058			−0.547534			−0.273767	+	0.961796i	$0.588270\pi$
$158$	−15.6731	−	6.99330i	−1.24688	−	0.556357i
$159$	17.6672			1.40110
$160$	2.97495	−	12.2943i	0.235191	−	0.971949i
$161$		0			0
$162$	4.70296	−	10.5401i	0.369499	−	0.828105i
$163$	−2.86934			−0.224744			−0.112372	−	0.993666i	$-0.535845\pi$
$163$	−2.86934			−0.224744			−0.112372	+	0.993666i	$0.535845\pi$
$164$	13.1420	−	11.7946i	1.02621	−	0.921005i
$165$	3.60202	+	12.0605i	0.280417	+	0.938908i
$166$	−14.3766	−	6.41482i	−1.11584	−	0.497886i
$167$		−	15.9389i		−	1.23339i	−0.787204	−	0.616693i	$-0.788472\pi$
$167$		−	15.9389i		−	1.23339i	0.787204	−	0.616693i	$-0.211528\pi$
$168$		0			0
$169$	22.5955			1.73811
$170$	−6.29511	−	0.819539i	−0.482813	−	0.0628558i
$171$	25.4732			1.94799
$172$	1.50544	+	1.67741i	0.114789	+	0.127902i
$173$	−1.02406			−0.0778580			−0.0389290	−	0.999242i	$-0.512395\pi$
$173$	−1.02406			−0.0778580			−0.0389290	+	0.999242i	$0.512395\pi$
$174$	−15.7635	−	7.03363i	−1.19502	−	0.533218i
$175$		0			0
$176$	−8.94865	−	0.969834i	−0.674530	−	0.0731040i
$177$			28.5314i			2.14455i
$178$	−5.91348	−	2.63858i	−0.443234	−	0.197770i
$179$			4.19778i			0.313757i	0.987618	+	0.156878i	$0.0501431\pi$
$179$			4.19778i			0.313757i	−0.987618	+	0.156878i	$0.949857\pi$
$180$	−7.60389	+	12.4260i	−0.566760	+	0.926182i
$181$		−	5.33135i		−	0.396276i	−0.980174	−	0.198138i	$-0.936511\pi$
$181$		−	5.33135i		−	0.396276i	0.980174	−	0.198138i	$-0.0634894\pi$
$182$		0			0
$183$	−3.05148			−0.225572
$184$	8.05550	−	2.59579i	0.593859	−	0.191364i
$185$	−10.2543	+	3.06257i	−0.753910	+	0.225165i
$186$	4.84565	+	2.16212i	0.355300	+	0.158535i
$187$			4.51737i			0.330343i
$188$	−14.2441	+	12.7837i	−1.03886	+	0.932350i
$189$		0			0
$190$	24.5217	+	3.19240i	1.77899	+	0.231601i
$191$		−	16.7444i		−	1.21158i	−0.795624	−	0.605791i	$-0.792857\pi$
$191$		−	16.7444i		−	1.21158i	0.795624	−	0.605791i	$-0.207143\pi$
$192$	−11.6840	−	16.2470i	−0.843221	−	1.17252i
$193$			15.5425i			1.11877i	0.828907	+	0.559386i	$0.188963\pi$
$193$			15.5425i			1.11877i	−0.828907	+	0.559386i	$0.811037\pi$
$194$	2.66235	−	5.96675i	0.191146	−	0.428387i
$195$	−31.9764	+	9.55015i	−2.28987	+	0.683900i
$196$		0			0
$197$		−	10.4069i		−	0.741463i	−0.928740	−	0.370731i	$-0.879107\pi$
$197$		−	10.4069i		−	0.741463i	0.928740	−	0.370731i	$-0.120893\pi$
$198$	9.46685	+	4.22410i	0.672780	+	0.300193i
$199$	−15.4520			−1.09536			−0.547681	−	0.836687i	$-0.684489\pi$
$199$	−15.4520			−1.09536			−0.547681	+	0.836687i	$0.684489\pi$
$200$	−8.87713	+	11.0089i	−0.627708	+	0.778449i
$201$			2.78879i			0.196706i
$202$	0.143517	+	0.0640372i	0.0100978	+	0.00450564i
$203$		0			0
$204$	−7.47460	+	6.70829i	−0.523327	+	0.469674i
$205$	−18.9172	+	5.64985i	−1.32123	+	0.394603i
$206$	16.6755	+	7.44056i	1.16183	+	0.518409i
$207$	−9.74728			−0.677483
$208$	2.57135	−	23.7258i	0.178291	−	1.64509i
$209$		−	17.5968i		−	1.21720i
$210$		0			0
$211$			10.3988i			0.715879i	0.933745	+	0.357940i	$0.116521\pi$
$211$			10.3988i			0.715879i	−0.933745	+	0.357940i	$0.883479\pi$
$212$	10.5124	−	9.43466i	0.721996	−	0.647975i
$213$	21.0148			1.43991
$214$	8.41740	−	18.8647i	0.575402	−	1.28956i
$215$	−0.721137	−	2.41455i	−0.0491811	−	0.164671i
$216$	0.558777	+	1.73405i	0.0380200	+	0.117987i
$217$		0			0
$218$	−2.56960	+	5.75888i	−0.174036	+	0.390041i
$219$			14.7104i			0.994034i
$220$	8.58385	+	5.25273i	0.578723	+	0.354139i
$221$	−11.9771			−0.805664
$222$	−6.89908	+	15.4619i	−0.463036	+	1.03773i
$223$		−	11.3655i		−	0.761093i	−0.924762	−	0.380547i	$-0.875736\pi$
$223$		−	11.3655i		−	0.761093i	0.924762	−	0.380547i	$-0.124264\pi$
$224$		0			0
$225$	13.6198	−	8.93218i	0.907984	−	0.595479i
$226$	−2.97628	−	1.32801i	−0.197979	−	0.0883380i
$227$		−	6.17093i		−	0.409579i	−0.978806	−	0.204790i	$-0.934349\pi$
$227$		−	6.17093i		−	0.409579i	0.978806	−	0.204790i	$-0.0656510\pi$
$228$	29.1163	−	26.1312i	1.92827	−	1.73058i
$229$			8.28601i			0.547555i	0.961793	+	0.273778i	$0.0882732\pi$
$229$			8.28601i			0.547555i	−0.961793	+	0.273778i	$0.911727\pi$
$230$	−9.38319	−	1.22157i	−0.618709	−	0.0805477i
$231$		0			0
$232$	−13.1358	+	4.23284i	−0.862405	+	0.277900i
$233$		−	14.0909i		−	0.923124i	−0.887108	−	0.461562i	$-0.847289\pi$
$233$		−	14.0909i		−	0.923124i	0.887108	−	0.461562i	$-0.152711\pi$
$234$	−11.1995	+	25.0998i	−0.732133	+	1.64082i
$235$	20.5036	−	6.12367i	1.33751	−	0.399464i
$236$	15.2364	+	16.9769i	0.991806	+	1.10510i
$237$	30.3575			1.97193
$238$		0			0
$239$			8.30653i			0.537305i	0.963237	+	0.268652i	$0.0865783\pi$
$239$			8.30653i			0.537305i	−0.963237	+	0.268652i	$0.913422\pi$
$240$	4.05565	+	22.0034i	0.261791	+	1.42032i
$241$			25.7383i			1.65795i	0.559285	+	0.828975i	$0.311076\pi$
$241$			25.7383i			1.65795i	−0.559285	+	0.828975i	$0.688924\pi$
$242$	−3.42085	+	7.66665i	−0.219900	+	0.492831i
$243$			22.3476i			1.43360i
$244$	−1.81570	+	1.62955i	−0.116239	+	0.104322i
$245$		0			0
$246$	−12.7275	+	28.5242i	−0.811473	+	1.81864i
$247$	46.6550			2.96858
$248$	4.03790	−	1.30117i	0.256407	−	0.0826241i
$249$	27.8463			1.76469
$250$	14.2304	−	6.89165i	0.900011	−	0.435866i
$251$	−4.80612			−0.303360			−0.151680	−	0.988430i	$-0.548468\pi$
$251$	−4.80612			−0.303360			−0.151680	+	0.988430i	$0.548468\pi$
$252$		0			0
$253$			6.73338i			0.423324i
$254$	−3.56267	+	7.98448i	−0.223541	+	0.500991i
$255$	10.7593	−	3.21340i	0.673774	−	0.201231i
$256$	−15.6285	−	3.42782i	−0.976781	−	0.214239i
$257$	21.4125			1.33567			0.667837	−	0.744307i	$-0.267220\pi$
$257$	21.4125			1.33567			0.667837	+	0.744307i	$0.267220\pi$
$258$	−3.64078	−	1.62451i	−0.226665	−	0.101138i
$259$		0			0
$260$	−13.9267	+	22.7586i	−0.863699	+	1.41143i
$261$	15.8945			0.983844
$262$	−4.70743	+	10.5501i	−0.290826	+	0.651786i
$263$	−15.7285			−0.969863			−0.484931	−	0.874552i	$-0.661155\pi$
$263$	−15.7285			−0.969863			−0.484931	+	0.874552i	$0.661155\pi$
$264$	15.1540	−	4.88318i	0.932662	−	0.300539i
$265$	−15.1321	+	4.51939i	−0.929556	+	0.277624i
$266$		0			0
$267$	11.4539			0.700969
$268$	1.48927	+	1.65940i	0.0909717	+	0.101364i
$269$			1.39293i			0.0849284i	0.999098	+	0.0424642i	$0.0135208\pi$
$269$			1.39293i			0.0849284i	−0.999098	+	0.0424642i	$0.986479\pi$
$270$	0.262958	−	2.01985i	0.0160031	−	0.122924i
$271$	−14.2313			−0.864492			−0.432246	−	0.901756i	$-0.642279\pi$
$271$	−14.2313			−0.864492			−0.432246	+	0.901756i	$0.642279\pi$
$272$	−0.865200	+	7.98320i	−0.0524604	+	0.484052i
$273$		0			0
$274$	9.13986	+	4.07819i	0.552159	+	0.246373i
$275$	−6.17031	−	9.40847i	−0.372084	−	0.567352i
$276$	−11.1413	+	9.99906i	−0.670627	+	0.601873i
$277$		−	21.0130i		−	1.26255i	−0.775560	−	0.631273i	$-0.782533\pi$
$277$		−	21.0130i		−	1.26255i	0.775560	−	0.631273i	$-0.217467\pi$
$278$	−8.33460	+	18.6791i	−0.499876	+	1.12030i
$279$	−4.88593			−0.292513
$280$		0			0
$281$	3.92163			0.233945			0.116972	−	0.993135i	$-0.462681\pi$
$281$	3.92163			0.233945			0.116972	+	0.993135i	$0.462681\pi$
$282$	13.7948	−	30.9163i	0.821469	−	1.84104i
$283$			1.20399i			0.0715696i	0.999360	+	0.0357848i	$0.0113931\pi$
$283$			1.20399i			0.0715696i	−0.999360	+	0.0357848i	$0.988607\pi$
$284$	12.5043	−	11.2224i	0.741996	−	0.665925i
$285$	−41.9114	+	12.5174i	−2.48262	+	0.741465i
$286$	17.3388	+	7.73655i	1.02527	+	0.457472i
$287$		0			0
$288$	15.9210	+	9.27807i	0.938154	+	0.546716i
$289$	−12.9700			−0.762941
$290$	15.3008	+	1.99196i	0.898492	+	0.116972i
$291$			11.5571i			0.677490i
$292$	7.85565	+	8.75302i	0.459717	+	0.512232i
$293$	14.4715			0.845433			0.422716	−	0.906262i	$-0.361077\pi$
$293$	14.4715			0.845433			0.422716	+	0.906262i	$0.361077\pi$
$294$		0			0
$295$	−7.29854	−	24.4374i	−0.424937	−	1.42280i
$296$	4.15187	+	12.8845i	0.241322	+	0.748894i
$297$	−1.44945			−0.0841054
$298$	−11.3272	+	25.3861i	−0.656169	+	1.47058i
$299$	−17.8524			−1.03243
$300$	6.40468	−	24.1812i	0.369775	−	1.39610i
$301$		0			0
$302$	22.4921	+	10.0359i	1.29428	+	0.577504i
$303$	−0.277982			−0.0159696
$304$	3.37027	−	31.0974i	0.193298	−	1.78356i
$305$	2.61361	−	0.780589i	0.149655	−	0.0446964i
$306$	3.76837	−	8.44549i	0.215423	−	0.482797i
$307$			24.7976i			1.41527i	0.706576	+	0.707637i	$0.250239\pi$
$307$			24.7976i			1.41527i	−0.706576	+	0.707637i	$0.749761\pi$
$308$		0			0
$309$	−32.2990			−1.83743
$310$	−4.70342	−	0.612323i	−0.267136	−	0.0347776i
$311$	7.05694			0.400162			0.200081	−	0.979779i	$-0.435879\pi$
$311$	7.05694			0.400162			0.200081	+	0.979779i	$0.435879\pi$
$312$	12.9469	+	40.1782i	0.732976	+	2.27464i
$313$	−32.5746			−1.84123			−0.920613	−	0.390477i	$-0.872310\pi$
$313$	−32.5746			−1.84123			−0.920613	+	0.390477i	$0.872310\pi$
$314$	3.95346	−	8.86032i	0.223107	−	0.500017i
$315$		0			0
$316$	18.0634	−	16.2115i	1.01615	−	0.911971i
$317$		−	22.3583i		−	1.25577i	−0.778307	−	0.627884i	$-0.783921\pi$
$317$		−	22.3583i		−	1.25577i	0.778307	−	0.627884i	$-0.216079\pi$
$318$	−10.1809	+	22.8169i	−0.570914	+	1.27951i
$319$		−	10.9798i		−	0.614753i
$320$	14.1635	+	10.9268i	0.791765	+	0.610826i
$321$			36.5394i			2.03943i
$322$		0			0
$323$	−15.6983			−0.873478
$324$	10.9022	+	12.1476i	0.605677	+	0.674866i
$325$	24.9450	−	16.3595i	1.38370	−	0.907464i
$326$	1.65348	−	3.70570i	0.0915777	−	0.205240i
$327$		−	11.1545i		−	0.616845i
$328$	7.65939	+	23.7693i	0.422919	+	1.31244i
$329$		0			0
$330$	−17.6516	−	2.29800i	−0.971689	−	0.126501i
$331$		−	24.2144i		−	1.33094i	−0.746424	−	0.665471i	$-0.768231\pi$
$331$		−	24.2144i		−	1.33094i	0.746424	−	0.665471i	$-0.231769\pi$
$332$	16.5692	−	14.8705i	0.909356	−	0.816127i
$333$		−	15.5904i		−	0.854350i
$334$	20.5848	+	9.18489i	1.12635	+	0.502575i
$335$	−0.713390	−	2.38861i	−0.0389767	−	0.130504i
$336$		0			0
$337$		−	7.95685i		−	0.433437i	−0.976234	−	0.216719i	$-0.930465\pi$
$337$		−	7.95685i		−	0.433437i	0.976234	−	0.216719i	$-0.0695354\pi$
$338$	−13.0208	+	29.1817i	−0.708239	+	1.58727i
$339$	5.76482			0.313102
$340$	4.68602	−	7.65775i	0.254135	−	0.415300i
$341$			3.37518i			0.182776i
$342$	−14.6791	+	32.8982i	−0.793757	+	1.77893i
$343$		0			0
$344$	−3.03387	+	0.977630i	−0.163576	+	0.0527103i
$345$	16.0373	−	4.78975i	0.863420	−	0.257871i
$346$	0.590124	−	1.32256i	0.0317252	−	0.0711012i
$347$	−19.8756			−1.06698			−0.533489	−	0.845807i	$-0.679119\pi$
$347$	−19.8756			−1.06698			−0.533489	+	0.845807i	$0.679119\pi$
$348$	18.1676	−	16.3050i	0.973887	−	0.874042i
$349$			12.8850i			0.689719i	0.938654	+	0.344859i	$0.112073\pi$
$349$			12.8850i			0.689719i	−0.938654	+	0.344859i	$0.887927\pi$
$350$		0			0
$351$		−	3.84297i		−	0.205122i
$352$	6.40925	−	10.9982i	0.341614	−	0.586204i
$353$	−8.34671			−0.444250			−0.222125	−	0.975018i	$-0.571299\pi$
$353$	−8.34671			−0.444250			−0.222125	+	0.975018i	$0.571299\pi$
$354$	−36.8479	−	16.4415i	−1.95844	−	0.873854i
$355$	−17.9994	+	5.37574i	−0.955306	+	0.285315i
$356$	6.81537	−	6.11665i	0.361214	−	0.324182i
$357$		0			0
$358$	−5.42136	−	2.41900i	−0.286528	−	0.127848i
$359$		−	1.81996i		−	0.0960538i	−0.998846	−	0.0480269i	$-0.984707\pi$
$359$		−	1.81996i		−	0.0960538i	0.998846	−	0.0480269i	$-0.0152933\pi$
$360$	−11.6662	−	16.9809i	−0.614863	−	0.894971i
$361$	42.1506			2.21845
$362$	6.88534	+	3.07223i	0.361886	+	0.161473i
$363$		−	14.8497i		−	0.779406i
$364$		0			0
$365$	−3.76301	−	12.5995i	−0.196965	−	0.659489i
$366$	1.75844	−	3.94093i	0.0919149	−	0.205996i
$367$		−	1.06984i		−	0.0558451i	−0.999610	−	0.0279226i	$-0.991111\pi$
$367$		−	1.06984i		−	0.0558451i	0.999610	−	0.0279226i	$-0.00888918\pi$
$368$	−1.28963	+	11.8994i	−0.0672264	+	0.620298i
$369$		−	28.7613i		−	1.49725i
$370$	1.95385	−	15.0081i	0.101576	−	0.780232i
$371$		0			0
$372$	−5.58469	+	5.01213i	−0.289553	+	0.259867i
$373$			13.1871i			0.682803i	0.939918	+	0.341401i	$0.110902\pi$
$373$			13.1871i			0.682803i	−0.939918	+	0.341401i	$0.889098\pi$
$374$	−5.83411	−	2.60317i	−0.301675	−	0.134607i
$375$	−18.0195	+	21.3889i	−0.930524	+	1.10452i
$376$	−8.30173	−	25.7627i	−0.428129	−	1.32861i
$377$	29.1112			1.49930
$378$		0			0
$379$		−	16.9854i		−	0.872483i	−0.899830	−	0.436241i	$-0.856309\pi$
$379$		−	16.9854i		−	0.872483i	0.899830	−	0.436241i	$-0.143691\pi$
$380$	−18.2538	+	29.8297i	−0.936398	+	1.53023i
$381$		−	15.4653i		−	0.792312i
$382$	21.6251	+	9.64908i	1.10644	+	0.493690i
$383$		−	4.67572i		−	0.238918i	−0.992839	−	0.119459i	$-0.961884\pi$
$383$		−	4.67572i		−	0.238918i	0.992839	−	0.119459i	$-0.0381160\pi$
$384$	27.7157	−	5.72727i	1.41436	−	0.292269i
$385$		0			0
$386$	−20.0728	−	8.95648i	−1.02168	−	0.455873i
$387$	3.67104			0.186609
$388$	6.17175	+	6.87677i	0.313323	+	0.349115i
$389$	−25.7985			−1.30803			−0.654017	−	0.756480i	$-0.726918\pi$
$389$	−25.7985			−1.30803			−0.654017	+	0.756480i	$0.726918\pi$
$390$	6.09277	−	46.8003i	0.308519	−	2.36982i
$391$	6.00693			0.303783
$392$		0			0
$393$		−	20.4347i		−	1.03079i
$394$	13.4404	+	5.99707i	0.677116	+	0.302128i
$395$	−26.0014	+	7.76565i	−1.30827	+	0.390732i
$396$	−10.9107	+	9.79211i	−0.548283	+	0.492072i
$397$	26.6167			1.33586			0.667928	−	0.744226i	$-0.267182\pi$
$397$	26.6167			1.33586			0.667928	+	0.744226i	$0.267182\pi$
$398$	8.90433	−	19.9560i	0.446334	−	1.00030i
$399$		0			0
$400$	−9.10233	−	17.8086i	−0.455116	−	0.890432i
$401$	−9.02978			−0.450926			−0.225463	−	0.974252i	$-0.572389\pi$
$401$	−9.02978			−0.450926			−0.225463	+	0.974252i	$0.572389\pi$
$402$	−3.60167	−	1.60706i	−0.179635	−	0.0801528i
$403$	−8.94872			−0.445767
$404$	−0.165406	+	0.148448i	−0.00822925	+	0.00738557i
$405$	−5.22236	−	17.4858i	−0.259501	−	0.868877i
$406$		0			0
$407$	−10.7698			−0.533839
$408$	−4.35634	−	13.5190i	−0.215671	−	0.669291i
$409$		−	3.41447i		−	0.168834i	−0.996430	−	0.0844172i	$-0.973097\pi$
$409$		−	3.41447i		−	0.168834i	0.996430	−	0.0844172i	$-0.0269029\pi$
$410$	3.60447	−	27.6870i	0.178012	−	1.36736i
$411$	−17.7032			−0.873233
$412$	−19.2187	+	17.2484i	−0.946838	+	0.849766i
$413$		0			0
$414$	5.61695	−	12.5884i	0.276058	−	0.618688i
$415$	−23.8506	+	7.12328i	−1.17078	+	0.349668i
$416$	29.1598	+	16.9931i	1.42967	+	0.833153i
$417$		−	36.1800i		−	1.77174i
$418$	22.7260	+	10.1403i	1.11156	+	0.495978i
$419$	−15.7994			−0.771850			−0.385925	−	0.922530i	$-0.626118\pi$
$419$	−15.7994			−0.771850			−0.385925	+	0.922530i	$0.626118\pi$
$420$		0			0
$421$	20.8340			1.01538			0.507692	−	0.861538i	$-0.330499\pi$
$421$	20.8340			1.01538			0.507692	+	0.861538i	$0.330499\pi$
$422$	−13.4298	−	5.99236i	−0.653753	−	0.291703i
$423$			31.1733i			1.51570i
$424$	6.12684	+	19.0134i	0.297546	+	0.923372i
$425$	−8.39341	+	5.50461i	−0.407140	+	0.267013i
$426$	−12.1100	+	27.1403i	−0.586729	+	1.31495i
$427$		0			0
$428$	19.5128	+	21.7418i	0.943188	+	1.05093i
$429$	−33.5839			−1.62145
$430$	3.53391	+	0.460068i	0.170420	+	0.0221865i
$431$			27.5487i			1.32697i	0.748188	+	0.663487i	$0.230924\pi$
$431$			27.5487i			1.32697i	−0.748188	+	0.663487i	$0.769076\pi$
$432$	−2.56149	−	0.277609i	−0.123240	−	0.0133565i
$433$	2.28113			0.109624			0.0548121	−	0.998497i	$-0.482544\pi$
$433$	2.28113			0.109624			0.0548121	+	0.998497i	$0.482544\pi$
$434$		0			0
$435$	−26.1514	+	7.81044i	−1.25386	+	0.374482i
$436$	−5.95674	−	6.63720i	−0.285276	−	0.317864i
$437$	−23.3992			−1.11933
$438$	−18.9982	−	8.47695i	−0.907768	−	0.405045i
$439$	−9.26625			−0.442254			−0.221127	−	0.975245i	$-0.570973\pi$
$439$	−9.26625			−0.442254			−0.221127	+	0.975245i	$0.570973\pi$
$440$	−11.7303	+	8.05897i	−0.559221	+	0.384196i
$441$		0			0
$442$	6.90187	−	15.4682i	0.328288	−	0.735745i
$443$	−27.3290			−1.29844			−0.649221	−	0.760600i	$-0.724905\pi$
$443$	−27.3290			−1.29844			−0.649221	+	0.760600i	$0.724905\pi$
$444$	−15.9931	−	17.8201i	−0.759000	−	0.845703i
$445$	−9.81037	+	2.92999i	−0.465056	+	0.138895i
$446$	14.6784	+	6.54948i	0.695042	+	0.310127i
$447$		−	49.1708i		−	2.32570i
$448$		0			0
$449$	31.5958			1.49110			0.745549	−	0.666451i	$-0.232187\pi$
$449$	31.5958			1.49110			0.745549	+	0.666451i	$0.232187\pi$
$450$	3.68726	+	22.7369i	0.173819	+	1.07183i
$451$	−19.8682			−0.935556
$452$	3.43021	−	3.07854i	0.161343	−	0.144802i
$453$	−43.5654			−2.04688
$454$	7.96965	+	3.55605i	0.374034	+	0.166893i
$455$		0			0
$456$	16.9695	+	52.6615i	0.794672	+	2.46610i
$457$			20.1137i			0.940879i	0.882432	+	0.470439i	$0.155905\pi$
$457$			20.1137i			0.940879i	−0.882432	+	0.470439i	$0.844095\pi$
$458$	−10.7012	−	4.77488i	−0.500036	−	0.223115i
$459$			1.29307i			0.0603553i
$460$	6.98476	−	11.4143i	0.325666	−	0.532194i
$461$			1.57753i			0.0734730i	0.999325	+	0.0367365i	$0.0116962\pi$
$461$			1.57753i			0.0734730i	−0.999325	+	0.0367365i	$0.988304\pi$
$462$		0			0
$463$	27.7330			1.28886			0.644431	−	0.764663i	$-0.277094\pi$
$463$	27.7330			1.28886			0.644431	+	0.764663i	$0.277094\pi$
$464$	2.10294	−	19.4038i	0.0976265	−	0.900799i
$465$	8.03887	−	2.40091i	0.372794	−	0.111340i
$466$	18.1981	+	8.11998i	0.843012	+	0.376151i
$467$		−	9.24121i		−	0.427632i	−0.976874	−	0.213816i	$-0.931411\pi$
$467$		−	9.24121i		−	0.427632i	0.976874	−	0.213816i	$-0.0685893\pi$
$468$	−25.9621	−	28.9279i	−1.20010	−	1.33719i
$469$		0			0
$470$	−3.90675	+	30.0089i	−0.180205	+	1.38421i
$471$			17.1617i			0.790771i
$472$	−30.7055	+	9.89448i	−1.41333	+	0.455430i
$473$		−	2.53594i		−	0.116603i
$474$	−17.4937	+	39.2061i	−0.803513	+	1.80080i
$475$	32.6954	−	21.4424i	1.50017	−	0.983847i
$476$		0			0
$477$		−	23.0065i		−	1.05340i
$478$	−10.7277	−	4.78670i	−0.490675	−	0.218939i
$479$	10.5454			0.481833			0.240916	−	0.970546i	$-0.422552\pi$
$479$	10.5454			0.481833			0.240916	+	0.970546i	$0.422552\pi$
$480$	−30.7542	−	7.44184i	−1.40373	−	0.339672i
$481$		−	28.5543i		−	1.30196i
$482$	−33.2406	−	14.8319i	−1.51407	−	0.675575i
$483$		0			0
$484$	−7.93005	−	8.83593i	−0.360457	−	0.401633i
$485$	−2.95639	−	9.89875i	−0.134243	−	0.449479i
$486$	−28.8616	−	12.8780i	−1.30919	−	0.584158i
$487$	18.0001			0.815661			0.407830	−	0.913058i	$-0.366285\pi$
$487$	18.0001			0.815661			0.407830	+	0.913058i	$0.366285\pi$
$488$	−1.05823	−	3.28399i	−0.0479037	−	0.148659i
$489$			7.17765i			0.324584i
$490$		0			0
$491$			0.704833i			0.0318086i	0.999874	+	0.0159043i	$0.00506272\pi$
$491$			0.704833i			0.0318086i	−0.999874	+	0.0159043i	$0.994937\pi$
$492$	−29.5042	−	32.8746i	−1.33015	−	1.48210i
$493$	−9.79524			−0.441156
$494$	−26.8853	+	60.2541i	−1.20963	+	2.71096i
$495$	15.7054	−	4.69061i	0.705904	−	0.210827i
$496$	−0.646439	+	5.96469i	−0.0290259	+	0.267822i
$497$		0			0
$498$	−16.0467	+	35.9630i	−0.719068	+	1.61154i
$499$		−	6.53324i		−	0.292468i	−0.989250	−	0.146234i	$-0.953285\pi$
$499$		−	6.53324i		−	0.292468i	0.989250	−	0.146234i	$-0.0467153\pi$
$500$	0.700054	+	22.3497i	0.0313074	+	0.999510i
$501$	−39.8710			−1.78131
$502$	2.76956	−	6.20702i	0.123612	−	0.277033i
$503$			29.3454i			1.30845i	0.756301	+	0.654224i	$0.227005\pi$
$503$			29.3454i			1.30845i	−0.756301	+	0.654224i	$0.772995\pi$
$504$		0			0
$505$	0.238093	−	0.0711096i	0.0105950	−	0.00316433i
$506$	−8.69604	−	3.88016i	−0.386586	−	0.172494i
$507$		−	56.5226i		−	2.51026i
$508$	−8.25881	−	9.20224i	−0.366425	−	0.408283i
$509$			20.6256i			0.914213i	0.889412	+	0.457107i	$0.151114\pi$
$509$			20.6256i			0.914213i	−0.889412	+	0.457107i	$0.848886\pi$
$510$	−2.05008	+	15.7472i	−0.0907789	+	0.697298i
$511$		0			0
$512$	13.4330	−	18.2086i	0.593661	−	0.804715i
$513$		−	5.03697i		−	0.222388i
$514$	−12.3391	+	27.6539i	−0.544255	+	1.21976i
$515$	27.6643	−	8.26231i	1.21904	−	0.364081i
$516$	4.19605	−	3.76586i	0.184721	−	0.165783i
$517$	21.5344			0.947081
$518$		0			0
$519$			2.56169i			0.112446i
$520$	−21.3670	−	31.1010i	−0.937005	−	1.36387i
$521$		−	5.87937i		−	0.257580i	−0.991672	−	0.128790i	$-0.958891\pi$
$521$		−	5.87937i		−	0.257580i	0.991672	−	0.128790i	$-0.0411093\pi$
$522$	−9.15932	+	20.5274i	−0.400892	+	0.898462i
$523$			23.1425i			1.01195i	0.862548	+	0.505975i	$0.168867\pi$
$523$			23.1425i			1.01195i	−0.862548	+	0.505975i	$0.831133\pi$
$524$	−10.9125	−	12.1591i	−0.476717	−	0.531174i
$525$		0			0
$526$	9.06369	−	20.3131i	0.395196	−	0.885694i
$527$	3.01104			0.131163
$528$	−2.42604	+	22.3850i	−0.105580	+	0.974184i
$529$	−14.0464			−0.610711
$530$	2.88326	−	22.1471i	0.125241	−	0.962011i
$531$	37.1541			1.61235
$532$		0			0
$533$		−	52.6771i		−	2.28170i
$534$	−6.60042	+	14.7926i	−0.285628	+	0.640136i
$535$	−9.34703	−	31.2963i	−0.404107	−	1.35306i
$536$	−3.00129	+	0.967129i	−0.129636	+	0.0417736i
$537$	10.5007			0.453141
$538$	−1.79894	−	0.802686i	−0.0775580	−	0.0346062i
$539$		0			0
$540$	2.45707	+	1.50356i	0.105736	+	0.0647029i
$541$	1.76517			0.0758907			0.0379453	−	0.999280i	$-0.487919\pi$
$541$	1.76517			0.0758907			0.0379453	+	0.999280i	$0.487919\pi$
$542$	8.20092	−	18.3795i	0.352260	−	0.789468i
$543$	−13.3364			−0.572318
$544$	−9.81158	−	5.71777i	−0.420668	−	0.245147i
$545$	2.85340	+	9.55391i	0.122226	+	0.409244i
$546$		0			0
$547$	−28.3140			−1.21062			−0.605310	−	0.795990i	$-0.706951\pi$
$547$	−28.3140			−1.21062			−0.605310	+	0.795990i	$0.706951\pi$
$548$	−10.5338	+	9.45388i	−0.449983	+	0.403850i
$549$			3.97369i			0.169593i
$550$	15.7066	−	2.54715i	0.669730	−	0.108611i
$551$	38.1560			1.62550
$552$	−6.49336	−	20.1508i	−0.276376	−	0.857676i
$553$		0			0
$554$	27.1379	+	12.1089i	1.15298	+	0.514457i
$555$	7.66102	+	25.6511i	0.325192	+	1.08883i
$556$	−19.3209	−	21.5280i	−0.819388	−	0.912990i
$557$		−	27.7580i		−	1.17614i	−0.808808	−	0.588072i	$-0.799887\pi$
$557$		−	27.7580i		−	1.17614i	0.808808	−	0.588072i	$-0.200113\pi$
$558$	2.81555	−	6.31009i	0.119192	−	0.267127i
$559$	6.72361			0.284378
$560$		0			0
$561$	11.3002			0.477095
$562$	−2.25987	+	5.06472i	−0.0953269	+	0.213642i
$563$			35.5787i			1.49947i	0.661741	+	0.749733i	$0.269818\pi$
$563$			35.5787i			1.49947i	−0.661741	+	0.749733i	$0.730182\pi$
$564$	31.9785	+	35.6315i	1.34654	+	1.50036i
$565$	−4.93761	+	1.47468i	−0.207727	+	0.0620402i
$566$	−1.55493	−	0.693807i	−0.0653585	−	0.0291629i
$567$		0			0
$568$	7.28778	+	22.6161i	0.305788	+	0.948951i
$569$	11.2535			0.471770			0.235885	−	0.971781i	$-0.424201\pi$
$569$	11.2535			0.471770			0.235885	+	0.971781i	$0.424201\pi$
$570$	7.98579	−	61.3410i	0.334488	−	2.56929i
$571$			0.667681i			0.0279416i	0.999902	+	0.0139708i	$0.00444718\pi$
$571$			0.667681i			0.0279416i	−0.999902	+	0.0139708i	$0.995553\pi$
$572$	−19.9832	+	17.9345i	−0.835541	+	0.749880i
$573$	−41.8861			−1.74982
$574$		0			0
$575$	−12.5108	+	8.20491i	−0.521737	+	0.342168i
$576$	−21.1571	+	15.2151i	−0.881544	+	0.633964i
$577$	32.2214			1.34139			0.670696	−	0.741732i	$-0.265995\pi$
$577$	32.2214			1.34139			0.670696	+	0.741732i	$0.265995\pi$
$578$	7.47406	−	16.7505i	0.310880	−	0.696730i
$579$	38.8795			1.61578
$580$	−11.3898	+	18.6128i	−0.472934	+	0.772854i
$581$		0			0
$582$	−14.9258	−	6.65987i	−0.618695	−	0.276061i
$583$	−15.8928			−0.658213
$584$	−15.8313	+	5.10143i	−0.655102	+	0.211099i
$585$	12.4364	+	41.6402i	0.514181	+	1.72161i
$586$	−8.33930	+	18.6897i	−0.344493	+	0.772063i
$587$		−	5.94377i		−	0.245326i	−0.992448	−	0.122663i	$-0.960857\pi$
$587$		−	5.94377i		−	0.245326i	0.992448	−	0.122663i	$-0.0391434\pi$
$588$		0			0
$589$	−11.7291			−0.483288
$590$	35.7663	+	4.65629i	1.47248	+	0.191697i
$591$	−26.0329			−1.07085
$592$	−19.0326	−	2.06271i	−0.782235	−	0.0847768i
$593$	32.3521			1.32854			0.664270	−	0.747493i	$-0.268743\pi$
$593$	32.3521			1.32854			0.664270	+	0.747493i	$0.268743\pi$
$594$	0.835255	−	1.87194i	0.0342709	−	0.0768064i
$595$		0			0
$596$	−26.2583	−	29.2579i	−1.07558	−	1.19845i
$597$			38.6531i			1.58197i
$598$	10.2876	−	23.0561i	0.420691	−	0.942834i
$599$		−	16.4047i		−	0.670277i	−0.942169	−	0.335139i	$-0.891217\pi$
$599$		−	16.4047i		−	0.670277i	0.942169	−	0.335139i	$-0.108783\pi$
$600$	27.5388	+	22.2061i	1.12427	+	0.906561i
$601$			17.5151i			0.714458i	0.934017	+	0.357229i	$0.116278\pi$
$601$			17.5151i			0.714458i	−0.934017	+	0.357229i	$0.883722\pi$
$602$		0			0
$603$	3.63160			0.147890
$604$	−25.9225	+	23.2649i	−1.05477	+	0.946634i
$605$	3.79865	+	12.7189i	0.154437	+	0.517095i
$606$	0.160189	−	0.359008i	0.00650723	−	0.0145837i
$607$		−	2.77165i		−	0.112498i	−0.998417	−	0.0562489i	$-0.982086\pi$
$607$		−	2.77165i		−	0.112498i	0.998417	−	0.0562489i	$-0.0179140\pi$
$608$	38.2197	+	22.2728i	1.55001	+	0.903281i
$609$		0			0
$610$	−0.497997	+	3.82525i	−0.0201633	+	0.154880i
$611$			57.0948i			2.30981i
$612$	8.73565	+	9.73356i	0.353118	+	0.393456i
$613$		−	21.7127i		−	0.876966i	−0.898739	−	0.438483i	$-0.855516\pi$
$613$		−	21.7127i		−	0.876966i	0.898739	−	0.438483i	$-0.144484\pi$
$614$	−32.0257	−	14.2898i	−1.29245	−	0.576690i
$615$	14.1331	+	47.3213i	0.569902	+	1.90818i
$616$		0			0
$617$			4.75106i			0.191271i	0.995416	+	0.0956353i	$0.0304883\pi$
$617$			4.75106i			0.191271i	−0.995416	+	0.0956353i	$0.969512\pi$
$618$	18.6126	−	41.7136i	0.748707	−	1.67797i
$619$	31.5652			1.26871			0.634357	−	0.773040i	$-0.281265\pi$
$619$	31.5652			1.26871			0.634357	+	0.773040i	$0.281265\pi$
$620$	3.50119	−	5.72153i	0.140611	−	0.229782i
$621$			1.92739i			0.0773434i
$622$	−4.06662	+	9.11391i	−0.163056	+	0.365435i
$623$		0			0
$624$	−59.3502	−	6.43223i	−2.37591	−	0.257495i
$625$	9.96243	−	22.9292i	0.398497	−	0.917169i
$626$	18.7714	−	42.0695i	0.750255	−	1.68144i
$627$	−44.0184			−1.75792
$628$	9.16474	+	10.2117i	0.365713	+	0.407490i
$629$			9.60786i			0.383090i
$630$		0			0
$631$			13.2126i			0.525986i	0.964798	+	0.262993i	$0.0847096\pi$
$631$			13.2126i			0.525986i	−0.964798	+	0.262993i	$0.915290\pi$
$632$	10.5277	+	32.6706i	0.418771	+	1.29957i
$633$	26.0125			1.03390
$634$	28.8754	+	12.8841i	1.14679	+	0.511695i
$635$	3.95613	+	13.2461i	0.156994	+	0.525657i
$636$	−23.6008	−	26.2968i	−0.935832	−	1.04274i
$637$		0			0
$638$	14.1803	+	6.32722i	0.561402	+	0.250497i
$639$		−	27.3659i		−	1.08258i
$640$	−22.2736	+	11.9953i	−0.880441	+	0.474156i
$641$	14.2989			0.564773			0.282386	−	0.959301i	$-0.408874\pi$
$641$	14.2989			0.564773			0.282386	+	0.959301i	$0.408874\pi$
$642$	−47.1900	−	21.0561i	−1.86244	−	0.831018i
$643$			8.53718i			0.336673i	0.985730	+	0.168337i	$0.0538396\pi$
$643$			8.53718i			0.336673i	−0.985730	+	0.168337i	$0.946160\pi$
$644$		0			0
$645$	−6.04000	+	1.80392i	−0.237825	+	0.0710294i
$646$	9.04627	−	20.2741i	0.355921	−	0.797674i
$647$			23.8661i			0.938275i	0.883125	+	0.469137i	$0.155435\pi$
$647$			23.8661i			0.938275i	−0.883125	+	0.469137i	$0.844565\pi$
$648$	−21.9709	+	7.07985i	−0.863097	+	0.278123i
$649$		−	25.6659i		−	1.00748i
$650$	6.75333	+	41.6433i	0.264887	+	1.63339i
$651$		0			0
$652$	3.83302	+	4.27088i	0.150113	+	0.167260i
$653$		−	18.0725i		−	0.707230i	−0.935391	−	0.353615i	$-0.884952\pi$
$653$		−	18.0725i		−	0.707230i	0.935391	−	0.353615i	$-0.115048\pi$
$654$	14.4058	+	6.42786i	0.563313	+	0.251349i
$655$	5.22733	+	17.5024i	0.204249	+	0.683877i
$656$	−35.1115	−	3.80530i	−1.37087	−	0.148572i
$657$	19.1561			0.747350
$658$		0			0
$659$			13.3401i			0.519657i	0.965655	+	0.259828i	$0.0836660\pi$
$659$			13.3401i			0.519657i	−0.965655	+	0.259828i	$0.916334\pi$
$660$	13.1397	−	21.4725i	0.511462	−	0.835816i
$661$			18.4115i			0.716123i	0.933698	+	0.358062i	$0.116562\pi$
$661$			18.4115i			0.716123i	−0.933698	+	0.358062i	$0.883438\pi$
$662$	31.2724	+	13.9537i	1.21544	+	0.542327i
$663$			29.9606i			1.16357i
$664$	9.65688	+	29.9682i	0.374760	+	1.16299i
$665$		0			0
$666$	20.1348	+	8.98410i	0.780206	+	0.348127i
$667$	−14.6003			−0.565327
$668$	−23.7243	+	21.2920i	−0.917919	+	0.823812i
$669$	−28.4309			−1.09920
$670$	3.49595	+	0.455126i	0.135060	+	0.0175831i
$671$	2.74500			0.105970
$672$		0			0
$673$			43.5683i			1.67944i	0.543023	+	0.839718i	$0.317280\pi$
$673$			43.5683i			1.67944i	−0.543023	+	0.839718i	$0.682720\pi$
$674$	10.2761	+	4.58520i	0.395822	+	0.176615i
$675$	−1.76621	−	2.69311i	−0.0679815	−	0.103658i
$676$	−30.1843	−	33.6323i	−1.16093	−	1.29355i
$677$	12.8331			0.493218			0.246609	−	0.969115i	$-0.420684\pi$
$677$	12.8331			0.493218			0.246609	+	0.969115i	$0.420684\pi$
$678$	−3.32202	+	7.44516i	−0.127581	+	0.285930i
$679$		0			0
$680$	7.18950	+	10.4648i	0.275705	+	0.401305i
$681$	−15.4366			−0.591531
$682$	−4.35898	−	1.94497i	−0.166914	−	0.0744768i
$683$	0.937655			0.0358784			0.0179392	−	0.999839i	$-0.494289\pi$
$683$	0.937655			0.0358784			0.0179392	+	0.999839i	$0.494289\pi$
$684$	−34.0285	−	37.9157i	−1.30111	−	1.44974i
$685$	15.1629	−	4.52860i	0.579345	−	0.173029i
$686$		0			0
$687$	20.7274			0.790801
$688$	0.485701	−	4.48156i	0.0185172	−	0.170858i
$689$		−	42.1371i		−	1.60530i
$690$	−3.05574	+	23.4720i	−0.116330	+	0.893565i
$691$	8.12642			0.309144			0.154572	−	0.987982i	$-0.450600\pi$
$691$	8.12642			0.309144			0.154572	+	0.987982i	$0.450600\pi$
$692$	1.36800	+	1.52427i	0.0520035	+	0.0579440i
$693$		0			0
$694$	11.4535	−	25.6690i	0.434767	−	0.974381i
$695$	9.25509	+	30.9884i	0.351066	+	1.17546i
$696$	10.5884	+	32.8591i	0.401354	+	1.24552i
$697$			17.7246i			0.671369i
$698$	−16.6408	−	7.42508i	−0.629862	−	0.281044i
$699$	−35.2483			−1.33321
$700$		0			0
$701$	−27.4244			−1.03580			−0.517902	−	0.855440i	$-0.673287\pi$
$701$	−27.4244			−1.03580			−0.517902	+	0.855440i	$0.673287\pi$
$702$	4.96312	+	2.21454i	0.187321	+	0.0835824i
$703$		−	37.4261i		−	1.41155i
$704$	10.5105	+	14.6152i	0.396131	+	0.550831i
$705$	−15.3183	−	51.2898i	−0.576922	−	1.93168i
$706$	4.80985	−	10.7796i	0.181021	−	0.405697i
$707$		0			0
$708$	42.4677	−	38.1139i	1.59603	−	1.43241i
$709$	21.4972			0.807346			0.403673	−	0.914903i	$-0.367733\pi$
$709$	21.4972			0.807346			0.403673	+	0.914903i	$0.367733\pi$
$710$	3.42959	−	26.3437i	0.128710	−	0.988660i
$711$		−	39.5320i		−	1.48257i
$712$	3.97213	+	12.3267i	0.148862	+	0.461963i
$713$	4.48811			0.168081
$714$		0			0
$715$	28.7648	−	8.59099i	1.07574	−	0.321285i
$716$	6.24820	−	5.60762i	0.233506	−	0.209567i
$717$	20.7788			0.775998
$718$	2.35045	+	1.04877i	0.0877178	+	0.0391396i
$719$	−26.9012			−1.00325			−0.501623	−	0.865087i	$-0.667263\pi$
$719$	−26.9012			−1.00325			−0.501623	+	0.865087i	$0.667263\pi$
$720$	28.6533	−	5.28134i	1.06784	−	0.196824i
$721$		0			0
$722$	−24.2896	+	54.4368i	−0.903966	+	2.02593i
$723$	64.3844			2.39448
$724$	−7.93547	+	7.12191i	−0.294919	+	0.264684i
$725$	20.4009	−	13.3794i	0.757669	−	0.496898i
$726$	19.1781	+	8.55724i	0.711766	+	0.317589i
$727$			14.8535i			0.550886i	0.961317	+	0.275443i	$0.0888245\pi$
$727$			14.8535i			0.550886i	−0.961317	+	0.275443i	$0.911175\pi$
$728$		0			0
$729$	31.4189			1.16366
$730$	18.4405	+	2.40071i	0.682515	+	0.0888543i
$731$	−2.26234			−0.0836756
$732$	4.07633	+	4.54198i	0.150665	+	0.167876i
$733$	−16.4626			−0.608059			−0.304030	−	0.952663i	$-0.598332\pi$
$733$	−16.4626			−0.608059			−0.304030	+	0.952663i	$0.598332\pi$
$734$	1.38168	+	0.616503i	0.0509987	+	0.0227555i
$735$		0			0
$736$	−14.6247	−	8.52264i	−0.539073	−	0.314149i
$737$		−	2.50870i		−	0.0924090i
$738$	37.1447	+	16.5739i	1.36732	+	0.610094i
$739$		−	44.4004i		−	1.63329i	−0.577137	−	0.816647i	$-0.695830\pi$
$739$		−	44.4004i		−	1.63329i	0.577137	−	0.816647i	$-0.304170\pi$
$740$	18.2567	+	11.1719i	0.671131	+	0.410686i
$741$		−	116.707i		−	4.28735i
$742$		0			0
$743$	−34.9014			−1.28041			−0.640204	−	0.768205i	$-0.721150\pi$
$743$	−34.9014			−1.28041			−0.640204	+	0.768205i	$0.721150\pi$
$744$	−3.25487	−	10.1008i	−0.119329	−	0.370314i
$745$	12.5782	+	42.1152i	0.460831	+	1.54298i
$746$	−17.0309	−	7.59917i	−0.623546	−	0.278226i
$747$		−	36.2620i		−	1.32676i
$748$	6.72390	−	6.03455i	0.245850	−	0.220645i
$749$		0			0
$750$	−17.2395	−	35.5974i	−0.629496	−	1.29983i
$751$			18.8248i			0.686927i	0.939166	+	0.343463i	$0.111600\pi$
$751$			18.8248i			0.686927i	−0.939166	+	0.343463i	$0.888400\pi$
$752$	38.0560	+	4.12442i	1.38776	+	0.150402i
$753$			12.0225i			0.438124i
$754$	−16.7756	+	37.5966i	−0.610930	+	1.36919i
$755$	37.3141	−	11.1443i	1.35800	−	0.405584i
$756$		0			0
$757$			54.4433i			1.97878i	0.145301	+	0.989388i	$0.453585\pi$
$757$			54.4433i			1.97878i	−0.145301	+	0.989388i	$0.546415\pi$
$758$	21.9364	+	9.78798i	0.796765	+	0.355516i
$759$	16.8435			0.611382
$760$	−28.0057	−	40.7640i	−1.01587	−	1.47867i
$761$			25.8142i			0.935765i	0.883791	+	0.467883i	$0.154983\pi$
$761$			25.8142i			0.935765i	−0.883791	+	0.467883i	$0.845017\pi$
$762$	19.9732	+	8.91200i	0.723552	+	0.322848i
$763$		0			0
$764$	−24.9232	+	22.3681i	−0.901691	+	0.809248i
$765$	−4.18455	−	14.0110i	−0.151293	−	0.506567i
$766$	6.03861	+	2.69442i	0.218184	+	0.0973533i
$767$	68.0489			2.45710
$768$	−8.57469	+	39.0947i	−0.309412	+	1.41071i
$769$			40.1288i			1.44708i	0.690281	+	0.723542i	$0.257487\pi$
$769$			40.1288i			1.44708i	−0.690281	+	0.723542i	$0.742513\pi$
$770$		0			0
$771$		−	53.5633i		−	1.92904i
$772$	23.1343	−	20.7625i	0.832620	−	0.747259i
$773$	−49.0224			−1.76321			−0.881607	−	0.471983i	$-0.843538\pi$
$773$	−49.0224			−1.76321			−0.881607	+	0.471983i	$0.843538\pi$
$774$	−2.11546	+	4.74108i	−0.0760388	+	0.170415i
$775$	−6.27118	+	4.11280i	−0.225267	+	0.147736i
$776$	−12.4377	+	4.00792i	−0.446489	+	0.143876i
$777$		0			0
$778$	14.8666	−	33.3183i	0.532992	−	1.19452i
$779$		−	69.0439i		−	2.47375i
$780$	56.9307	+	34.8377i	2.03845	+	1.24739i
$781$

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 - 1.48845i) q^{4} +(0.639901 + 2.14255i) q^{5} +(3.23064 + 1.44151i) q^{6} +(2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +O(q^{10})\)	\(q+(-0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 - 1.48845i) q^{4} +(0.639901 + 2.14255i) q^{5} +(3.23064 + 1.44151i) q^{6} +(2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +(-3.13582 - 0.408241i) q^{10} +2.25026i q^{11} +(-3.72336 + 3.34164i) q^{12} -5.96620 q^{13} +(5.35959 - 1.60071i) q^{15} +(-0.430987 + 3.97671i) q^{16} +2.00749 q^{17} +(1.87716 - 4.20700i) q^{18} -7.81989 q^{19} +(2.33427 - 3.81460i) q^{20} +(-2.90618 - 1.29673i) q^{22} +2.99226 q^{23} +(-2.17005 - 6.73430i) q^{24} +(-4.18105 + 2.74204i) q^{25} +(3.43807 - 7.70524i) q^{26} +0.644123i q^{27} -4.87936 q^{29} +(-1.02122 + 7.84424i) q^{30} +1.49990 q^{31} +(-4.88750 - 2.84822i) q^{32} +5.62903 q^{33} +(-1.15683 + 2.59263i) q^{34} +(4.35154 + 4.84863i) q^{36} +4.78601i q^{37} +(4.50627 - 10.0992i) q^{38} +14.9244i q^{39} +(3.58134 + 5.21287i) q^{40} +8.82927i q^{41} -1.12695 q^{43} +(3.34941 - 3.00602i) q^{44} +(-2.08447 - 6.97935i) q^{45} +(-1.72431 + 3.86446i) q^{46} -9.56972i q^{47} +(9.94774 + 1.07811i) q^{48} +(-1.13193 - 6.97988i) q^{50} -5.02172i q^{51} +(7.96997 + 8.88040i) q^{52} +7.06264i q^{53} +(-0.831874 - 0.371181i) q^{54} +(-4.82131 + 1.43994i) q^{55} +19.5614i q^{57} +(2.81177 - 6.30161i) q^{58} -11.4057 q^{59} +(-9.54221 - 5.83918i) q^{60} -1.21986i q^{61} +(-0.864331 + 1.93710i) q^{62} +(6.49489 - 4.67081i) q^{64} +(-3.81777 - 12.7829i) q^{65} +(-3.24377 + 7.26979i) q^{66} -1.11485 q^{67} +(-2.68171 - 2.98805i) q^{68} -7.48514i q^{69} +8.40090i q^{71} +(-8.76953 + 2.82588i) q^{72} -5.88062 q^{73} +(-6.18105 - 2.75798i) q^{74} +(6.85921 + 10.4589i) q^{75} +(10.4462 + 11.6395i) q^{76} +(-19.2746 - 8.60032i) q^{78} +12.1357i q^{79} +(-8.79610 + 1.62129i) q^{80} -8.16121 q^{81} +(-11.4028 - 5.08793i) q^{82} +11.1319i q^{83} +(1.28459 + 4.30114i) q^{85} +(0.649414 - 1.45544i) q^{86} +12.2057i q^{87} +(1.95210 + 6.05795i) q^{88} +4.57883i q^{89} +(10.2149 + 1.32984i) q^{90} +(-3.99723 - 4.45385i) q^{92} -3.75201i q^{93} +(12.3591 + 5.51462i) q^{94} +(-5.00395 - 16.7545i) q^{95} +(-7.12483 + 12.2261i) q^{96} -4.62008 q^{97} -7.33022i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) \) 48 * q + 16 * q^4 - 64 * q^9	\( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) \) 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

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