LMFDB - Embedded newform 980.2.c.e.979.18

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

$q$-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	$0.256832\pi$
$3$			2.50150i			1.44424i	−0.691767	+	0.722120i	$0.743168\pi$
$4$	−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	$-0.889830\pi$
$11$		−	2.25026i		−	0.678480i	0.940700	−	0.339240i	$-0.110170\pi$
$12$	−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	$-0.871296\pi$
$37$		−	4.78601i		−	0.786816i	0.919364	−	0.393408i	$-0.128704\pi$
$38$	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	$-0.757852\pi$
$41$		−	8.82927i		−	1.37890i	0.724333	−	0.689450i	$-0.242148\pi$
$42$		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	$0.245901\pi$
$47$			9.56972i			1.39589i	−0.716153	+	0.697943i	$0.754099\pi$
$48$	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	$-0.838796\pi$
$53$		−	7.06264i		−	0.970129i	0.874478	−	0.485064i	$-0.161204\pi$
$54$	−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	$0.0248833\pi$
$61$			1.21986i			0.156187i	−0.996946	+	0.0780935i	$0.975117\pi$
$62$	−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	$-0.833884\pi$
$71$		−	8.40090i		−	0.997003i	0.866889	−	0.498501i	$-0.166116\pi$
$72$	−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	$-0.760811\pi$
$79$		−	12.1357i		−	1.36537i	0.730711	−	0.682687i	$-0.239189\pi$
$80$	−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	$-0.790792\pi$
$83$		−	11.1319i		−	1.22188i	0.791677	−	0.610940i	$-0.209208\pi$
$84$		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	$-0.921974\pi$
$89$		−	4.57883i		−	0.485355i	0.970107	−	0.242677i	$-0.0780256\pi$
$90$	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	$0.00175986\pi$
$101$			0.111126i			0.0110574i	−0.999985	+	0.00552872i	$0.998240\pi$
$102$	6.48547	−	2.89381i	0.642157	−	0.286530i
$103$			12.9119i			1.27224i	0.771588	+	0.636122i	$0.219463\pi$
$103$			12.9119i			1.27224i	−0.771588	+	0.636122i	$0.780537\pi$
$104$	−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	$-0.965428\pi$
$113$		−	2.30454i		−	0.216793i	0.994108	−	0.108397i	$-0.0345717\pi$
$114$	−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	$0.0977597\pi$
$137$			7.07703i			0.604631i	−0.953208	+	0.302316i	$0.902240\pi$
$138$	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	$0.250689\pi$
$151$			17.4157i			1.41727i	−0.705574	+	0.708636i	$0.749311\pi$
$152$	−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	$0.211528\pi$
$167$			15.9389i			1.23339i	−0.787204	+	0.616693i	$0.788472\pi$
$168$		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	$-0.949857\pi$
$179$		−	4.19778i		−	0.313757i	0.987618	−	0.156878i	$-0.0501431\pi$
$180$	−7.60389	−	12.4260i	−0.566760	−	0.926182i
$181$			5.33135i			0.396276i	0.980174	+	0.198138i	$0.0634894\pi$
$181$			5.33135i			0.396276i	−0.980174	+	0.198138i	$0.936511\pi$
$182$		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	$0.207143\pi$
$191$			16.7444i			1.21158i	−0.795624	+	0.605791i	$0.792857\pi$
$192$	−11.6840	+	16.2470i	−0.843221	+	1.17252i
$193$		−	15.5425i		−	1.11877i	−0.828907	−	0.559386i	$-0.811037\pi$
$193$		−	15.5425i		−	1.11877i	0.828907	−	0.559386i	$-0.188963\pi$
$194$	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	$0.120893\pi$
$197$			10.4069i			0.741463i	−0.928740	+	0.370731i	$0.879107\pi$
$198$	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	$-0.883479\pi$
$211$		−	10.3988i		−	0.715879i	0.933745	−	0.357940i	$-0.116521\pi$
$212$	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	$0.124264\pi$
$223$			11.3655i			0.761093i	−0.924762	+	0.380547i	$0.875736\pi$
$224$		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	$0.0656510\pi$
$227$			6.17093i			0.409579i	−0.978806	+	0.204790i	$0.934349\pi$
$228$	29.1163	+	26.1312i	1.92827	+	1.73058i
$229$		−	8.28601i		−	0.547555i	−0.961793	−	0.273778i	$-0.911727\pi$
$229$		−	8.28601i		−	0.547555i	0.961793	−	0.273778i	$-0.0882732\pi$
$230$	−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	$0.152711\pi$
$233$			14.0909i			0.923124i	−0.887108	+	0.461562i	$0.847289\pi$
$234$	−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	$-0.913422\pi$
$239$		−	8.30653i		−	0.537305i	0.963237	−	0.268652i	$-0.0865783\pi$
$240$	4.05565	−	22.0034i	0.261791	−	1.42032i
$241$		−	25.7383i		−	1.65795i	−0.559285	−	0.828975i	$-0.688924\pi$
$241$		−	25.7383i		−	1.65795i	0.559285	−	0.828975i	$-0.311076\pi$
$242$	−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	$-0.986479\pi$
$269$		−	1.39293i		−	0.0849284i	0.999098	−	0.0424642i	$-0.0135208\pi$
$270$	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	$0.217467\pi$
$277$			21.0130i			1.26255i	−0.775560	+	0.631273i	$0.782533\pi$
$278$	−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	$-0.988607\pi$
$283$		−	1.20399i		−	0.0715696i	0.999360	−	0.0357848i	$-0.0113931\pi$
$284$	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	$-0.749761\pi$
$307$		−	24.7976i		−	1.41527i	0.706576	−	0.707637i	$-0.250239\pi$
$308$		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	$0.216079\pi$
$317$			22.3583i			1.25577i	−0.778307	+	0.627884i	$0.783921\pi$
$318$	−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	$0.231769\pi$
$331$			24.2144i			1.33094i	−0.746424	+	0.665471i	$0.768231\pi$
$332$	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	$0.0695354\pi$
$337$			7.95685i			0.433437i	−0.976234	+	0.216719i	$0.930465\pi$
$338$	−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	$-0.887927\pi$
$349$		−	12.8850i		−	0.689719i	0.938654	−	0.344859i	$-0.112073\pi$
$350$		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	$0.0152933\pi$
$359$			1.81996i			0.0960538i	−0.998846	+	0.0480269i	$0.984707\pi$
$360$	−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	$0.00888918\pi$
$367$			1.06984i			0.0558451i	−0.999610	+	0.0279226i	$0.991111\pi$
$368$	−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	$-0.889098\pi$
$373$		−	13.1871i		−	0.682803i	0.939918	−	0.341401i	$-0.110902\pi$
$374$	−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	$0.143691\pi$
$379$			16.9854i			0.872483i	−0.899830	+	0.436241i	$0.856309\pi$
$380$	−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	$0.0381160\pi$
$383$			4.67572i			0.238918i	−0.992839	+	0.119459i	$0.961884\pi$
$384$	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	$0.0269029\pi$
$409$			3.41447i			0.168834i	−0.996430	+	0.0844172i	$0.973097\pi$
$410$	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	$-0.769076\pi$
$431$		−	27.5487i		−	1.32697i	0.748188	−	0.663487i	$-0.230924\pi$
$432$	−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	$-0.844095\pi$
$457$		−	20.1137i		−	0.940879i	0.882432	−	0.470439i	$-0.155905\pi$
$458$	−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	$-0.988304\pi$
$461$		−	1.57753i		−	0.0734730i	0.999325	−	0.0367365i	$-0.0116962\pi$
$462$		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	$0.0685893\pi$
$467$			9.24121i			0.427632i	−0.976874	+	0.213816i	$0.931411\pi$
$468$	−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	$-0.994937\pi$
$491$		−	0.704833i		−	0.0318086i	0.999874	−	0.0159043i	$-0.00506272\pi$
$492$	−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	$0.0467153\pi$
$499$			6.53324i			0.292468i	−0.989250	+	0.146234i	$0.953285\pi$
$500$	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	$-0.772995\pi$
$503$		−	29.3454i		−	1.30845i	0.756301	−	0.654224i	$-0.227005\pi$
$504$		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	$-0.848886\pi$
$509$		−	20.6256i		−	0.914213i	0.889412	−	0.457107i	$-0.151114\pi$
$510$	−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	$0.0411093\pi$
$521$			5.87937i			0.257580i	−0.991672	+	0.128790i	$0.958891\pi$
$522$	−9.15932	−	20.5274i	−0.400892	−	0.898462i
$523$		−	23.1425i		−	1.01195i	−0.862548	−	0.505975i	$-0.831133\pi$
$523$		−	23.1425i		−	1.01195i	0.862548	−	0.505975i	$-0.168867\pi$
$524$	−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	$0.200113\pi$
$557$			27.7580i			1.17614i	−0.808808	+	0.588072i	$0.799887\pi$
$558$	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	$-0.730182\pi$
$563$		−	35.5787i		−	1.49947i	0.661741	−	0.749733i	$-0.269818\pi$
$564$	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	$-0.995553\pi$
$571$		−	0.667681i		−	0.0279416i	0.999902	−	0.0139708i	$-0.00444718\pi$
$572$	−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	$0.0391434\pi$
$587$			5.94377i			0.245326i	−0.992448	+	0.122663i	$0.960857\pi$
$588$		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	$0.108783\pi$
$599$			16.4047i			0.670277i	−0.942169	+	0.335139i	$0.891217\pi$
$600$	27.5388	−	22.2061i	1.12427	−	0.906561i
$601$		−	17.5151i		−	0.714458i	−0.934017	−	0.357229i	$-0.883722\pi$
$601$		−	17.5151i		−	0.714458i	0.934017	−	0.357229i	$-0.116278\pi$
$602$		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	$0.0179140\pi$
$607$			2.77165i			0.112498i	−0.998417	+	0.0562489i	$0.982086\pi$
$608$	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	$0.144484\pi$
$613$			21.7127i			0.876966i	−0.898739	+	0.438483i	$0.855516\pi$
$614$	−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	$-0.969512\pi$
$617$		−	4.75106i		−	0.191271i	0.995416	−	0.0956353i	$-0.0304883\pi$
$618$	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	$-0.915290\pi$
$631$		−	13.2126i		−	0.525986i	0.964798	−	0.262993i	$-0.0847096\pi$
$632$	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	$-0.946160\pi$
$643$		−	8.53718i		−	0.336673i	0.985730	−	0.168337i	$-0.0538396\pi$
$644$		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	$-0.844565\pi$
$647$		−	23.8661i		−	0.938275i	0.883125	−	0.469137i	$-0.155435\pi$
$648$	−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	$0.115048\pi$
$653$			18.0725i			0.707230i	−0.935391	+	0.353615i	$0.884952\pi$
$654$	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	$-0.916334\pi$
$659$		−	13.3401i		−	0.519657i	0.965655	−	0.259828i	$-0.0836660\pi$
$660$	13.1397	+	21.4725i	0.511462	+	0.835816i
$661$		−	18.4115i		−	0.716123i	−0.933698	−	0.358062i	$-0.883438\pi$
$661$		−	18.4115i		−	0.716123i	0.933698	−	0.358062i	$-0.116562\pi$
$662$	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	$-0.682720\pi$
$673$		−	43.5683i		−	1.67944i	0.543023	−	0.839718i	$-0.317280\pi$
$674$	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	$-0.911175\pi$
$727$		−	14.8535i		−	0.550886i	0.961317	−	0.275443i	$-0.0888245\pi$
$728$		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	$0.304170\pi$
$739$			44.4004i			1.63329i	−0.577137	+	0.816647i	$0.695830\pi$
$740$	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	$-0.888400\pi$
$751$		−	18.8248i		−	0.686927i	0.939166	−	0.343463i	$-0.111600\pi$
$752$	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	$-0.546415\pi$
$757$		−	54.4433i		−	1.97878i	0.145301	−	0.989388i	$-0.453585\pi$
$758$	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	$-0.845017\pi$
$761$		−	25.8142i		−	0.935765i	0.883791	−	0.467883i	$-0.154983\pi$
$762$	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	$-0.742513\pi$
$769$		−	40.1288i		−	1.44708i	0.690281	−	0.723542i	$-0.257487\pi$
$770$		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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more