LMFDB - Embedded newform 289.2.c.d.251.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,2,Mod(38,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.38"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.c (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.1
Root			$0.245576 - 0.245576i$ of defining polynomial
Character	$\chi$	$=$	289.251
Dual form			289.2.c.d.38.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.53209i q^{2} +(-0.952682 - 0.952682i) q^{3} -0.347296 q^{4} +(2.49756 + 2.49756i) q^{5} +(-1.45959 + 1.45959i) q^{6} +(-0.245576 + 0.245576i) q^{7} -2.53209i q^{8} -1.18479i q^{9} +(3.82649 - 3.82649i) q^{10} +(1.24364 - 1.24364i) q^{11} +(0.330863 + 0.330863i) q^{12} +3.29086 q^{13} +(0.376244 + 0.376244i) q^{14} -4.75877i q^{15} -4.57398 q^{16} -1.81521 q^{18} -1.53209i q^{19} +(-0.867395 - 0.867395i) q^{20} +0.467911 q^{21} +(-1.90536 - 1.90536i) q^{22} +(-1.99065 + 1.99065i) q^{23} +(-2.41228 + 2.41228i) q^{24} +7.47565i q^{25} -5.04189i q^{26} +(-3.98678 + 3.98678i) q^{27} +(0.0852875 - 0.0852875i) q^{28} +(-0.837775 - 0.837775i) q^{29} -7.29086 q^{30} +(-5.02475 - 5.02475i) q^{31} +1.94356i q^{32} -2.36959 q^{33} -1.22668 q^{35} +0.411474i q^{36} +(2.77276 + 2.77276i) q^{37} -2.34730 q^{38} +(-3.13514 - 3.13514i) q^{39} +(6.32405 - 6.32405i) q^{40} +(3.47987 - 3.47987i) q^{41} -0.716881i q^{42} +10.9855i q^{43} +(-0.431911 + 0.431911i) q^{44} +(2.95910 - 2.95910i) q^{45} +(3.04986 + 3.04986i) q^{46} +5.12061 q^{47} +(4.35755 + 4.35755i) q^{48} +6.87939i q^{49} +11.4534 q^{50} -1.14290 q^{52} +8.36959i q^{53} +(6.10810 + 6.10810i) q^{54} +6.21213 q^{55} +(0.621819 + 0.621819i) q^{56} +(-1.45959 + 1.45959i) q^{57} +(-1.28355 + 1.28355i) q^{58} -10.8648i q^{59} +1.65270i q^{60} +(-3.11938 + 3.11938i) q^{61} +(-7.69836 + 7.69836i) q^{62} +(0.290956 + 0.290956i) q^{63} -6.17024 q^{64} +(8.21913 + 8.21913i) q^{65} +3.63041i q^{66} +8.07192 q^{67} +3.79292 q^{69} +1.87939i q^{70} +(-7.95422 - 7.95422i) q^{71} -3.00000 q^{72} +(1.20373 + 1.20373i) q^{73} +(4.24811 - 4.24811i) q^{74} +(7.12192 - 7.12192i) q^{75} +0.532089i q^{76} +0.610815i q^{77} +(-4.80332 + 4.80332i) q^{78} +(-8.18951 + 8.18951i) q^{79} +(-11.4238 - 11.4238i) q^{80} +4.04189 q^{81} +(-5.33146 - 5.33146i) q^{82} +2.14796i q^{83} -0.162504 q^{84} +16.8307 q^{86} +1.59627i q^{87} +(-3.14900 - 3.14900i) q^{88} -6.41921 q^{89} +(-4.53360 - 4.53360i) q^{90} +(-0.808155 + 0.808155i) q^{91} +(0.691346 - 0.691346i) q^{92} +9.57398i q^{93} -7.84524i q^{94} +(3.82649 - 3.82649i) q^{95} +(1.85160 - 1.85160i) q^{96} +(2.88767 + 2.88767i) q^{97} +10.5398 q^{98} +(-1.47345 - 1.47345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{13} - 24 q^{16} - 36 q^{18} + 24 q^{21} - 24 q^{30} + 12 q^{35} - 24 q^{38} + 84 q^{47} + 84 q^{50} - 12 q^{52} - 24 q^{55} + 12 q^{64} - 36 q^{67} + 84 q^{69} - 36 q^{72} + 36 q^{81} - 12 q^{84}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q - 24 * q^13 - 24 * q^16 - 36 * q^18 + 24 * q^21 - 24 * q^30 + 12 * q^35 - 24 * q^38 + 84 * q^47 + 84 * q^50 - 12 * q^52 - 24 * q^55 + 12 * q^64 - 36 * q^67 + 84 * q^69 - 36 * q^72 + 36 * q^81 - 12 * q^84 + 24 * q^86 + 60 * q^89 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.53209i		−	1.08335i	−0.840588	−	0.541675i	$-0.817790\pi$
$2$		−	1.53209i		−	1.08335i	0.840588	−	0.541675i	$-0.182210\pi$
$3$	−0.952682	−	0.952682i	−0.550031	−	0.550031i	0.376418	−	0.926450i	$-0.377156\pi$
$3$	−0.952682	−	0.952682i	−0.550031	−	0.550031i	−0.926450	+	0.376418i	$0.877156\pi$
$4$	−0.347296			−0.173648
$5$	2.49756	+	2.49756i	1.11694	+	1.11694i	0.992187	+	0.124757i	$0.0398152\pi$
$5$	2.49756	+	2.49756i	1.11694	+	1.11694i	0.124757	+	0.992187i	$0.460185\pi$
$6$	−1.45959	+	1.45959i	−0.595877	+	0.595877i
$7$	−0.245576	+	0.245576i	−0.0928189	+	0.0928189i	−0.751992	−	0.659173i	$-0.770907\pi$
$7$	−0.245576	+	0.245576i	−0.0928189	+	0.0928189i	0.659173	+	0.751992i	$0.270907\pi$
$8$		−	2.53209i		−	0.895229i
$9$		−	1.18479i		−	0.394931i
$10$	3.82649	−	3.82649i	1.21004	−	1.21004i
$11$	1.24364	−	1.24364i	0.374971	−	0.374971i	−0.494313	−	0.869284i	$-0.664580\pi$
$11$	1.24364	−	1.24364i	0.374971	−	0.374971i	0.869284	+	0.494313i	$0.164580\pi$
$12$	0.330863	+	0.330863i	0.0955120	+	0.0955120i
$13$	3.29086			0.912720			0.456360	−	0.889795i	$-0.349153\pi$
$13$	3.29086			0.912720			0.456360	+	0.889795i	$0.349153\pi$
$14$	0.376244	+	0.376244i	0.100555	+	0.100555i
$15$		−	4.75877i		−	1.22871i
$16$	−4.57398			−1.14349
$17$		0			0
$17$		0			0
$18$	−1.81521			−0.427849
$19$		−	1.53209i		−	0.351485i	−0.984436	−	0.175743i	$-0.943767\pi$
$19$		−	1.53209i		−	0.351485i	0.984436	−	0.175743i	$-0.0562327\pi$
$20$	−0.867395	−	0.867395i	−0.193955	−	0.193955i
$21$	0.467911			0.102107
$22$	−1.90536	−	1.90536i	−0.406225	−	0.406225i
$23$	−1.99065	+	1.99065i	−0.415080	+	0.415080i	−0.883504	−	0.468424i	$-0.844822\pi$
$23$	−1.99065	+	1.99065i	−0.415080	+	0.415080i	0.468424	+	0.883504i	$0.344822\pi$
$24$	−2.41228	+	2.41228i	−0.492404	+	0.492404i
$25$			7.47565i			1.49513i
$26$		−	5.04189i		−	0.988796i
$27$	−3.98678	+	3.98678i	−0.767256	+	0.767256i
$28$	0.0852875	−	0.0852875i	0.0161178	−	0.0161178i
$29$	−0.837775	−	0.837775i	−0.155571	−	0.155571i	0.625030	−	0.780601i	$-0.285087\pi$
$29$	−0.837775	−	0.837775i	−0.155571	−	0.155571i	−0.780601	+	0.625030i	$0.785087\pi$
$30$	−7.29086			−1.33112
$31$	−5.02475	−	5.02475i	−0.902471	−	0.902471i	0.0931781	−	0.995649i	$-0.470297\pi$
$31$	−5.02475	−	5.02475i	−0.902471	−	0.902471i	−0.995649	+	0.0931781i	$0.970297\pi$
$32$			1.94356i			0.343577i
$33$	−2.36959			−0.412492
$34$		0			0
$35$	−1.22668			−0.207347
$36$			0.411474i			0.0685790i
$37$	2.77276	+	2.77276i	0.455839	+	0.455839i	0.897287	−	0.441448i	$-0.145535\pi$
$37$	2.77276	+	2.77276i	0.455839	+	0.455839i	−0.441448	+	0.897287i	$0.645535\pi$
$38$	−2.34730			−0.380782
$39$	−3.13514	−	3.13514i	−0.502025	−	0.502025i
$40$	6.32405	−	6.32405i	0.999921	−	0.999921i
$41$	3.47987	−	3.47987i	0.543464	−	0.543464i	−0.381079	−	0.924543i	$-0.624447\pi$
$41$	3.47987	−	3.47987i	0.543464	−	0.543464i	0.924543	+	0.381079i	$0.124447\pi$
$42$		−	0.716881i		−	0.110617i
$43$			10.9855i			1.67527i	0.546234	+	0.837633i	$0.316061\pi$
$43$			10.9855i			1.67527i	−0.546234	+	0.837633i	$0.683939\pi$
$44$	−0.431911	+	0.431911i	−0.0651131	+	0.0651131i
$45$	2.95910	−	2.95910i	0.441116	−	0.441116i
$46$	3.04986	+	3.04986i	0.449677	+	0.449677i
$47$	5.12061			0.746918			0.373459	−	0.927647i	$-0.378172\pi$
$47$	5.12061			0.746918			0.373459	+	0.927647i	$0.378172\pi$
$48$	4.35755	+	4.35755i	0.628958	+	0.628958i
$49$			6.87939i			0.982769i
$50$	11.4534			1.61975
$51$		0			0
$52$	−1.14290			−0.158492
$53$			8.36959i			1.14965i	0.818276	+	0.574825i	$0.194930\pi$
$53$			8.36959i			1.14965i	−0.818276	+	0.574825i	$0.805070\pi$
$54$	6.10810	+	6.10810i	0.831207	+	0.831207i
$55$	6.21213			0.837644
$56$	0.621819	+	0.621819i	0.0830941	+	0.0830941i
$57$	−1.45959	+	1.45959i	−0.193328	+	0.193328i
$58$	−1.28355	+	1.28355i	−0.168538	+	0.168538i
$59$		−	10.8648i		−	1.41448i	−0.706973	−	0.707241i	$-0.749940\pi$
$59$		−	10.8648i		−	1.41448i	0.706973	−	0.707241i	$-0.250060\pi$
$60$			1.65270i			0.213363i
$61$	−3.11938	+	3.11938i	−0.399396	+	0.399396i	−0.878020	−	0.478624i	$-0.841136\pi$
$61$	−3.11938	+	3.11938i	−0.399396	+	0.399396i	0.478624	+	0.878020i	$0.341136\pi$
$62$	−7.69836	+	7.69836i	−0.977693	+	0.977693i
$63$	0.290956	+	0.290956i	0.0366570	+	0.0366570i
$64$	−6.17024			−0.771281
$65$	8.21913	+	8.21913i	1.01946	+	1.01946i
$66$			3.63041i			0.446873i
$67$	8.07192			0.986142			0.493071	−	0.869989i	$-0.335874\pi$
$67$	8.07192			0.986142			0.493071	+	0.869989i	$0.335874\pi$
$68$		0			0
$69$	3.79292			0.456614
$70$			1.87939i			0.224630i
$71$	−7.95422	−	7.95422i	−0.943993	−	0.943993i	0.0545201	−	0.998513i	$-0.482637\pi$
$71$	−7.95422	−	7.95422i	−0.943993	−	0.943993i	−0.998513	+	0.0545201i	$0.982637\pi$
$72$	−3.00000			−0.353553
$73$	1.20373	+	1.20373i	0.140886	+	0.140886i	0.774032	−	0.633146i	$-0.218237\pi$
$73$	1.20373	+	1.20373i	0.140886	+	0.140886i	−0.633146	+	0.774032i	$0.718237\pi$
$74$	4.24811	−	4.24811i	0.493833	−	0.493833i
$75$	7.12192	−	7.12192i	0.822369	−	0.822369i
$76$			0.532089i			0.0610348i
$77$			0.610815i			0.0696088i
$78$	−4.80332	+	4.80332i	−0.543869	+	0.543869i
$79$	−8.18951	+	8.18951i	−0.921392	+	0.921392i	−0.997128	−	0.0757358i	$-0.975869\pi$
$79$	−8.18951	+	8.18951i	−0.921392	+	0.921392i	0.0757358	+	0.997128i	$0.475869\pi$
$80$	−11.4238	−	11.4238i	−1.27722	−	1.27722i
$81$	4.04189			0.449099
$82$	−5.33146	−	5.33146i	−0.588762	−	0.588762i
$83$			2.14796i			0.235769i	0.993027	+	0.117884i	$0.0376112\pi$
$83$			2.14796i			0.235769i	−0.993027	+	0.117884i	$0.962389\pi$
$84$	−0.162504			−0.0177306
$85$		0			0
$86$	16.8307			1.81490
$87$			1.59627i			0.171138i
$88$	−3.14900	−	3.14900i	−0.335685	−	0.335685i
$89$	−6.41921			−0.680435			−0.340218	−	0.940347i	$-0.610501\pi$
$89$	−6.41921			−0.680435			−0.340218	+	0.940347i	$0.610501\pi$
$90$	−4.53360	−	4.53360i	−0.477883	−	0.477883i
$91$	−0.808155	+	0.808155i	−0.0847176	+	0.0847176i
$92$	0.691346	−	0.691346i	0.0720778	−	0.0720778i
$93$			9.57398i			0.992775i
$94$		−	7.84524i		−	0.809174i
$95$	3.82649	−	3.82649i	0.392590	−	0.392590i
$96$	1.85160	−	1.85160i	0.188978	−	0.188978i
$97$	2.88767	+	2.88767i	0.293198	+	0.293198i	0.838342	−	0.545144i	$-0.183525\pi$
$97$	2.88767	+	2.88767i	0.293198	+	0.293198i	−0.545144	+	0.838342i	$0.683525\pi$
$98$	10.5398			1.06468
$99$	−1.47345	−	1.47345i	−0.148088	−	0.148088i
$100$		−	2.59627i		−	0.259627i
$101$	5.26857			0.524242			0.262121	−	0.965035i	$-0.415578\pi$
$101$	5.26857			0.524242			0.262121	+	0.965035i	$0.415578\pi$
$102$		0			0
$103$	−18.4388			−1.81683			−0.908415	−	0.418069i	$-0.862707\pi$
$103$	−18.4388			−1.81683			−0.908415	+	0.418069i	$0.862707\pi$
$104$		−	8.33275i		−	0.817093i
$105$	1.16864	+	1.16864i	0.114047	+	0.114047i
$106$	12.8229			1.24547
$107$	3.79140	+	3.79140i	0.366528	+	0.366528i	0.866209	−	0.499681i	$-0.166550\pi$
$107$	3.79140	+	3.79140i	0.366528	+	0.366528i	−0.499681	+	0.866209i	$0.666550\pi$
$108$	1.38459	−	1.38459i	0.133233	−	0.133233i
$109$	−10.9726	+	10.9726i	−1.05098	+	1.05098i	−0.0523518	+	0.998629i	$0.516672\pi$
$109$	−10.9726	+	10.9726i	−1.05098	+	1.05098i	−0.998629	+	0.0523518i	$0.983328\pi$
$110$		−	9.51754i		−	0.907462i
$111$		−	5.28312i		−	0.501451i
$112$	1.12326	−	1.12326i	0.106138	−	0.106138i
$113$	4.96908	−	4.96908i	0.467452	−	0.467452i	−0.433636	−	0.901088i	$-0.642770\pi$
$113$	4.96908	−	4.96908i	0.467452	−	0.467452i	0.901088	+	0.433636i	$0.142770\pi$
$114$	2.23623	+	2.23623i	0.209442	+	0.209442i
$115$	−9.94356			−0.927242
$116$	0.290956	+	0.290956i	0.0270146	+	0.0270146i
$117$		−	3.89899i		−	0.360461i
$118$	−16.6459			−1.53238
$119$		0			0
$120$	−12.0496			−1.09998
$121$			7.90673i			0.718793i
$122$	4.77917	+	4.77917i	0.432686	+	0.432686i
$123$	−6.63041			−0.597844
$124$	1.74508	+	1.74508i	0.156713	+	0.156713i
$125$	−6.18310	+	6.18310i	−0.553033	+	0.553033i
$126$	0.445771	−	0.445771i	0.0397124	−	0.0397124i
$127$			7.74422i			0.687189i	0.939118	+	0.343594i	$0.111645\pi$
$127$			7.74422i			0.687189i	−0.939118	+	0.343594i	$0.888355\pi$
$128$			13.3405i			1.17914i
$129$	10.4656	−	10.4656i	0.921449	−	0.921449i
$130$	12.5924	−	12.5924i	1.10443	−	1.10443i
$131$	13.1653	+	13.1653i	1.15026	+	1.15026i	0.986501	+	0.163758i	$0.0523615\pi$
$131$	13.1653	+	13.1653i	1.15026	+	1.15026i	0.163758	+	0.986501i	$0.447639\pi$
$132$	0.822948			0.0716285
$133$	0.376244	+	0.376244i	0.0326245	+	0.0326245i
$134$		−	12.3669i		−	1.06834i
$135$	−19.9145			−1.71396
$136$		0			0
$137$	10.0719			0.860502			0.430251	−	0.902709i	$-0.358425\pi$
$137$	10.0719			0.860502			0.430251	+	0.902709i	$0.358425\pi$
$138$		−	5.81109i		−	0.494673i
$139$	6.04886	+	6.04886i	0.513057	+	0.513057i	0.915462	−	0.402404i	$-0.131825\pi$
$139$	6.04886	+	6.04886i	0.513057	+	0.513057i	−0.402404	+	0.915462i	$0.631825\pi$
$140$	0.426022			0.0360054
$141$	−4.87832	−	4.87832i	−0.410829	−	0.410829i
$142$	−12.1866	+	12.1866i	−1.02267	+	1.02267i
$143$	4.09264	−	4.09264i	0.342244	−	0.342244i
$144$			5.41921i			0.451601i
$145$		−	4.18479i		−	0.347528i
$146$	1.84422	−	1.84422i	0.152629	−	0.152629i
$147$	6.55387	−	6.55387i	0.540554	−	0.540554i
$148$	−0.962969	−	0.962969i	−0.0791556	−	0.0791556i
$149$	−11.8794			−0.973197			−0.486599	−	0.873626i	$-0.661763\pi$
$149$	−11.8794			−0.973197			−0.486599	+	0.873626i	$0.661763\pi$
$150$	−10.9114	−	10.9114i	−0.890914	−	0.890914i
$151$		−	6.55943i		−	0.533799i	−0.963724	−	0.266899i	$-0.914001\pi$
$151$		−	6.55943i		−	0.533799i	0.963724	−	0.266899i	$-0.0859992\pi$
$152$	−3.87939			−0.314660
$153$		0			0
$154$	0.935822			0.0754107
$155$		−	25.0993i		−	2.01602i
$156$	1.08882	+	1.08882i	0.0871757	+	0.0871757i
$157$	−8.88444			−0.709055			−0.354528	−	0.935046i	$-0.615358\pi$
$157$	−8.88444			−0.709055			−0.354528	+	0.935046i	$0.615358\pi$
$158$	12.5471	+	12.5471i	0.998191	+	0.998191i
$159$	7.97356	−	7.97356i	0.632344	−	0.632344i
$160$	−4.85417	+	4.85417i	−0.383756	+	0.383756i
$161$		−	0.977711i		−	0.0770544i
$162$		−	6.19253i		−	0.486531i
$163$	−6.84483	+	6.84483i	−0.536128	+	0.536128i	−0.922389	−	0.386261i	$-0.873766\pi$
$163$	−6.84483	+	6.84483i	−0.536128	+	0.536128i	0.386261	+	0.922389i	$0.373766\pi$
$164$	−1.20854	+	1.20854i	−0.0943715	+	0.0943715i
$165$	−5.91819	−	5.91819i	−0.460730	−	0.460730i
$166$	3.29086			0.255420
$167$	−1.29931	−	1.29931i	−0.100543	−	0.100543i	0.655046	−	0.755589i	$-0.272649\pi$
$167$	−1.29931	−	1.29931i	−0.100543	−	0.100543i	−0.755589	+	0.655046i	$0.772649\pi$
$168$		−	1.18479i		−	0.0914087i
$169$	−2.17024			−0.166942
$170$		0			0
$171$	−1.81521			−0.138812
$172$		−	3.81521i		−	0.290907i
$173$	−16.0935	−	16.0935i	−1.22357	−	1.22357i	−0.966354	−	0.257215i	$-0.917195\pi$
$173$	−16.0935	−	16.0935i	−1.22357	−	1.22357i	−0.257215	−	0.966354i	$-0.582805\pi$
$174$	2.44562			0.185402
$175$	−1.83584	−	1.83584i	−0.138776	−	0.138776i
$176$	−5.68838	+	5.68838i	−0.428777	+	0.428777i
$177$	−10.3507	+	10.3507i	−0.778009	+	0.778009i
$178$			9.83481i			0.737150i
$179$		−	17.5253i		−	1.30990i	−0.755672	−	0.654951i	$-0.772689\pi$
$179$		−	17.5253i		−	1.30990i	0.755672	−	0.654951i	$-0.227311\pi$
$180$	−1.02768	+	1.02768i	−0.0765990	+	0.0765990i
$181$	3.22590	−	3.22590i	0.239780	−	0.239780i	−0.576979	−	0.816759i	$-0.695769\pi$
$181$	3.22590	−	3.22590i	0.239780	−	0.239780i	0.816759	+	0.576979i	$0.195769\pi$
$182$	1.23816	+	1.23816i	0.0917789	+	0.0917789i
$183$	5.94356			0.439361
$184$	5.04051	+	5.04051i	0.371591	+	0.371591i
$185$			13.8503i			1.01829i
$186$	14.6682			1.07552
$187$		0			0
$188$	−1.77837			−0.129701
$189$		−	1.95811i		−	0.142432i
$190$	−5.86252	−	5.86252i	−0.425312	−	0.425312i
$191$	9.72462			0.703649			0.351824	−	0.936066i	$-0.385561\pi$
$191$	9.72462			0.703649			0.351824	+	0.936066i	$0.385561\pi$
$192$	5.87828	+	5.87828i	0.424229	+	0.424229i
$193$	0.597013	−	0.597013i	0.0429739	−	0.0429739i	−0.685293	−	0.728267i	$-0.740326\pi$
$193$	0.597013	−	0.597013i	0.0429739	−	0.0429739i	0.728267	+	0.685293i	$0.240326\pi$
$194$	4.42416	−	4.42416i	0.317636	−	0.317636i
$195$		−	15.6604i		−	1.12147i
$196$		−	2.38919i		−	0.170656i
$197$	12.0215	−	12.0215i	0.856495	−	0.856495i	−0.134429	−	0.990923i	$-0.542920\pi$
$197$	12.0215	−	12.0215i	0.856495	−	0.856495i	0.990923	+	0.134429i	$0.0429199\pi$
$198$	−2.25746	+	2.25746i	−0.160431	+	0.160431i
$199$	−8.97709	−	8.97709i	−0.636369	−	0.636369i	0.313289	−	0.949658i	$-0.398569\pi$
$199$	−8.97709	−	8.97709i	−0.636369	−	0.636369i	−0.949658	+	0.313289i	$0.898569\pi$
$200$	18.9290			1.33848
$201$	−7.68997	−	7.68997i	−0.542409	−	0.542409i
$202$		−	8.07192i		−	0.567938i
$203$	0.411474			0.0288798
$204$		0			0
$205$	17.3824			1.21404
$206$			28.2499i			1.96826i
$207$	2.35851	+	2.35851i	0.163928	+	0.163928i
$208$	−15.0523			−1.04369
$209$	−1.90536	−	1.90536i	−0.131797	−	0.131797i
$210$	1.79046	−	1.79046i	0.123553	−	0.123553i
$211$	16.6385	−	16.6385i	1.14544	−	1.14544i	0.158000	−	0.987439i	$-0.449496\pi$
$211$	16.6385	−	16.6385i	1.14544	−	1.14544i	0.987439	−	0.158000i	$-0.0505045\pi$
$212$		−	2.90673i		−	0.199635i
$213$			15.1557i			1.03845i
$214$	5.80876	−	5.80876i	0.397078	−	0.397078i
$215$	−27.4369	+	27.4369i	−1.87118	+	1.87118i
$216$	10.0949	+	10.0949i	0.686869	+	0.686869i
$217$	2.46791			0.167533
$218$	16.8109	+	16.8109i	1.13858	+	1.13858i
$219$		−	2.29355i		−	0.154984i
$220$	−2.15745			−0.145455
$221$		0			0
$222$	−8.09421			−0.543248
$223$		−	4.97090i		−	0.332876i	−0.986052	−	0.166438i	$-0.946773\pi$
$223$		−	4.97090i		−	0.332876i	0.986052	−	0.166438i	$-0.0532266\pi$
$224$	−0.477292	−	0.477292i	−0.0318904	−	0.0318904i
$225$	8.85710			0.590473
$226$	−7.61307	−	7.61307i	−0.506414	−	0.506414i
$227$	3.71706	−	3.71706i	0.246710	−	0.246710i	−0.572909	−	0.819619i	$-0.694185\pi$
$227$	3.71706	−	3.71706i	0.246710	−	0.246710i	0.819619	+	0.572909i	$0.194185\pi$
$228$	0.506912	−	0.506912i	0.0335710	−	0.0335710i
$229$		−	24.2053i		−	1.59953i	−0.600311	−	0.799767i	$-0.704957\pi$
$229$		−	24.2053i		−	1.59953i	0.600311	−	0.799767i	$-0.295043\pi$
$230$			15.2344i			1.00453i
$231$	0.581912	−	0.581912i	0.0382870	−	0.0382870i
$232$	−2.12132	+	2.12132i	−0.139272	+	0.139272i
$233$	−20.3095	−	20.3095i	−1.33052	−	1.33052i	−0.904906	−	0.425612i	$-0.860059\pi$
$233$	−20.3095	−	20.3095i	−1.33052	−	1.33052i	−0.425612	−	0.904906i	$-0.639941\pi$
$234$	−5.97359			−0.390506
$235$	12.7891	+	12.7891i	0.834266	+	0.834266i
$236$			3.77332i			0.245622i
$237$	15.6040			1.01359
$238$		0			0
$239$	−2.63310			−0.170321			−0.0851606	−	0.996367i	$-0.527140\pi$
$239$	−2.63310			−0.170321			−0.0851606	+	0.996367i	$0.527140\pi$
$240$			21.7665i			1.40502i
$241$	17.9136	+	17.9136i	1.15392	+	1.15392i	0.985760	+	0.168157i	$0.0537817\pi$
$241$	17.9136	+	17.9136i	1.15392	+	1.15392i	0.168157	+	0.985760i	$0.446218\pi$
$242$	12.1138			0.778705
$243$	8.10970	+	8.10970i	0.520237	+	0.520237i
$244$	1.08335	−	1.08335i	0.0693544	−	0.0693544i
$245$	−17.1817	+	17.1817i	−1.09770	+	1.09770i
$246$			10.1584i			0.647675i
$247$		−	5.04189i		−	0.320808i
$248$	−12.7231	+	12.7231i	−0.807918	+	0.807918i
$249$	2.04632	−	2.04632i	0.129680	−	0.129680i
$250$	9.47306	+	9.47306i	0.599129	+	0.599129i
$251$	−10.6851			−0.674437			−0.337219	−	0.941426i	$-0.609486\pi$
$251$	−10.6851			−0.674437			−0.337219	+	0.941426i	$0.609486\pi$
$252$	−0.101048	−	0.101048i	−0.00636543	−	0.00636543i
$253$			4.95130i			0.311286i
$254$	11.8648			0.744466
$255$		0			0
$256$	8.09833			0.506145
$257$			3.73648i			0.233075i	0.993186	+	0.116538i	$0.0371796\pi$
$257$			3.73648i			0.233075i	−0.993186	+	0.116538i	$0.962820\pi$
$258$	−16.0343	−	16.0343i	−0.998252	−	0.998252i
$259$	−1.36184			−0.0846209
$260$	−2.85447	−	2.85447i	−0.177027	−	0.177027i
$261$	−0.992589	+	0.992589i	−0.0614397	+	0.0614397i
$262$	20.1704	−	20.1704i	1.24613	−	1.24613i
$263$			10.2094i			0.629541i	0.949168	+	0.314771i	$0.101928\pi$
$263$			10.2094i			0.629541i	−0.949168	+	0.314771i	$0.898072\pi$
$264$			6.00000i			0.369274i
$265$	−20.9036	+	20.9036i	−1.28410	+	1.28410i
$266$	0.576439	−	0.576439i	0.0353437	−	0.0353437i
$267$	6.11547	+	6.11547i	0.374261	+	0.374261i
$268$	−2.80335			−0.171242
$269$	−8.30085	−	8.30085i	−0.506112	−	0.506112i	0.407219	−	0.913331i	$-0.366499\pi$
$269$	−8.30085	−	8.30085i	−0.506112	−	0.506112i	−0.913331	+	0.407219i	$0.866499\pi$
$270$			30.5107i			1.85682i
$271$	17.0000			1.03268			0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000			1.03268			0.516338	+	0.856385i	$0.327295\pi$
$272$		0			0
$273$	1.53983			0.0931947
$274$		−	15.4311i		−	0.932225i
$275$	9.29701	+	9.29701i	0.560631	+	0.560631i
$276$	−1.31727			−0.0792901
$277$	−17.2132	−	17.2132i	−1.03424	−	1.03424i	−0.999393	−	0.0348500i	$-0.988905\pi$
$277$	−17.2132	−	17.2132i	−1.03424	−	1.03424i	−0.0348500	−	0.999393i	$-0.511095\pi$
$278$	9.26739	−	9.26739i	0.555821	−	0.555821i
$279$	−5.95328	+	5.95328i	−0.356414	+	0.356414i
$280$			3.10607i			0.185623i
$281$		−	5.79385i		−	0.345632i	−0.984954	−	0.172816i	$-0.944713\pi$
$281$		−	5.79385i		−	0.345632i	0.984954	−	0.172816i	$-0.0552866\pi$
$282$	−7.47402	+	7.47402i	−0.445071	+	0.445071i
$283$	10.8328	−	10.8328i	0.643946	−	0.643946i	−0.307577	−	0.951523i	$-0.599518\pi$
$283$	10.8328	−	10.8328i	0.643946	−	0.643946i	0.951523	+	0.307577i	$0.0995183\pi$
$284$	2.76247	+	2.76247i	0.163923	+	0.163923i
$285$	−7.29086			−0.431873
$286$	−6.27029	−	6.27029i	−0.370770	−	0.370770i
$287$			1.70914i			0.100887i
$288$	2.30272			0.135689
$289$		0			0
$290$	−6.41147			−0.376495
$291$		−	5.50206i		−	0.322536i
$292$	−0.418052	−	0.418052i	−0.0244646	−	0.0244646i
$293$	−2.98040			−0.174117			−0.0870584	−	0.996203i	$-0.527747\pi$
$293$	−2.98040			−0.174117			−0.0870584	+	0.996203i	$0.527747\pi$
$294$	−10.0411	−	10.0411i	−0.585609	−	0.585609i
$295$	27.1356	−	27.1356i	1.57990	−	1.57990i
$296$	7.02087	−	7.02087i	0.408080	−	0.408080i
$297$			9.91622i			0.575398i
$298$			18.2003i			1.05431i
$299$	−6.55096	+	6.55096i	−0.378852	+	0.378852i
$300$	−2.47342	+	2.47342i	−0.142803	+	0.142803i
$301$	−2.69776	−	2.69776i	−0.155496	−	0.155496i
$302$	−10.0496			−0.578291
$303$	−5.01927	−	5.01927i	−0.288350	−	0.288350i
$304$			7.00774i			0.401921i
$305$	−15.5817			−0.892207
$306$		0			0
$307$	−3.26857			−0.186547			−0.0932736	−	0.995641i	$-0.529733\pi$
$307$	−3.26857			−0.186547			−0.0932736	+	0.995641i	$0.529733\pi$
$308$		−	0.212134i		−	0.0120874i
$309$	17.5663	+	17.5663i	0.999314	+	0.999314i
$310$	−38.4543			−2.18406
$311$	2.49756	+	2.49756i	0.141624	+	0.141624i	0.774364	−	0.632740i	$-0.218070\pi$
$311$	2.49756	+	2.49756i	0.141624	+	0.141624i	−0.632740	+	0.774364i	$0.718070\pi$
$312$	−7.93846	+	7.93846i	−0.449427	+	0.449427i
$313$	1.04826	−	1.04826i	0.0592510	−	0.0592510i	−0.676860	−	0.736111i	$-0.736660\pi$
$313$	1.04826	−	1.04826i	0.0592510	−	0.0592510i	0.736111	+	0.676860i	$0.236660\pi$
$314$			13.6117i			0.768155i
$315$			1.45336i			0.0818877i
$316$	2.84419	−	2.84419i	0.159998	−	0.159998i
$317$	10.2274	−	10.2274i	0.574431	−	0.574431i	−0.358933	−	0.933363i	$-0.616859\pi$
$317$	10.2274	−	10.2274i	0.574431	−	0.574431i	0.933363	+	0.358933i	$0.116859\pi$
$318$	−12.2162	−	12.2162i	−0.685050	−	0.685050i
$319$	−2.08378			−0.116669
$320$	−15.4106	−	15.4106i	−0.861478	−	0.861478i
$321$		−	7.22399i		−	0.403204i
$322$	−1.49794			−0.0834770
$323$		0			0
$324$	−1.40373			−0.0779852
$325$			24.6013i			1.36464i
$326$	10.4869	+	10.4869i	0.580815	+	0.580815i
$327$	20.9067			1.15614
$328$	−8.81133	−	8.81133i	−0.486524	−	0.486524i
$329$	−1.25750	+	1.25750i	−0.0693281	+	0.0693281i
$330$	−9.06719	+	9.06719i	−0.499133	+	0.499133i
$331$		−	9.03508i		−	0.496613i	−0.968682	−	0.248307i	$-0.920126\pi$
$331$		−	9.03508i		−	0.496613i	0.968682	−	0.248307i	$-0.0798740\pi$
$332$		−	0.745977i		−	0.0409408i
$333$	3.28514	−	3.28514i	0.180025	−	0.180025i
$334$	−1.99065	+	1.99065i	−0.108924	+	0.108924i
$335$	20.1601	+	20.1601i	1.10147	+	1.10147i
$336$	−2.14022			−0.116758
$337$	12.7038	+	12.7038i	0.692019	+	0.692019i	0.962676	−	0.270657i	$-0.0872409\pi$
$337$	12.7038	+	12.7038i	0.692019	+	0.692019i	−0.270657	+	0.962676i	$0.587241\pi$
$338$			3.32501i			0.180857i
$339$	−9.46791			−0.514226
$340$		0			0
$341$	−12.4979			−0.676801
$342$			2.78106i			0.150382i
$343$	−3.40844	−	3.40844i	−0.184038	−	0.184038i
$344$	27.8161			1.49975
$345$	9.47306	+	9.47306i	0.510012	+	0.510012i
$346$	−24.6567	+	24.6567i	−1.32555	+	1.32555i
$347$	−5.50394	+	5.50394i	−0.295467	+	0.295467i	−0.839235	−	0.543768i	$-0.816997\pi$
$347$	−5.50394	+	5.50394i	−0.295467	+	0.295467i	0.543768	+	0.839235i	$0.316997\pi$
$348$		−	0.554378i		−	0.0297178i
$349$		−	6.65002i		−	0.355967i	−0.984033	−	0.177984i	$-0.943043\pi$
$349$		−	6.65002i		−	0.355967i	0.984033	−	0.177984i	$-0.0569574\pi$
$350$	−2.81267	+	2.81267i	−0.150343	+	0.150343i
$351$	−13.1199	+	13.1199i	−0.700290	+	0.700290i
$352$	2.41709	+	2.41709i	0.128831	+	0.128831i
$353$	−4.14559			−0.220648			−0.110324	−	0.993896i	$-0.535189\pi$
$353$	−4.14559			−0.220648			−0.110324	+	0.993896i	$0.535189\pi$
$354$	15.8583	+	15.8583i	0.842857	+	0.842857i
$355$		−	39.7324i		−	2.10877i
$356$	2.22937			0.118156
$357$		0			0
$358$	−26.8503			−1.41908
$359$			17.0770i			0.901288i	0.892704	+	0.450644i	$0.148806\pi$
$359$			17.0770i			0.901288i	−0.892704	+	0.450644i	$0.851194\pi$
$360$	−7.49269	−	7.49269i	−0.394900	−	0.394900i
$361$	16.6527			0.876458
$362$	−4.94237	−	4.94237i	−0.259765	−	0.259765i
$363$	7.53260	−	7.53260i	0.395359	−	0.395359i
$364$	0.280669	−	0.280669i	0.0147111	−	0.0147111i
$365$			6.01279i			0.314724i
$366$		−	9.10607i		−	0.475982i
$367$	13.3153	−	13.3153i	0.695053	−	0.695053i	−0.268286	−	0.963339i	$-0.586457\pi$
$367$	13.3153	−	13.3153i	0.695053	−	0.695053i	0.963339	+	0.268286i	$0.0864572\pi$
$368$	9.10520	−	9.10520i	0.474641	−	0.474641i
$369$	−4.12292	−	4.12292i	−0.214631	−	0.214631i
$370$	21.2199			1.10317
$371$	−2.05537	−	2.05537i	−0.106709	−	0.106709i
$372$		−	3.32501i		−	0.172394i
$373$	−11.7314			−0.607430			−0.303715	−	0.952763i	$-0.598227\pi$
$373$	−11.7314			−0.607430			−0.303715	+	0.952763i	$0.598227\pi$
$374$		0			0
$375$	11.7811			0.608371
$376$		−	12.9659i		−	0.668663i
$377$	−2.75700	−	2.75700i	−0.141993	−	0.141993i
$378$	−3.00000			−0.154303
$379$	5.77366	+	5.77366i	0.296573	+	0.296573i	0.839670	−	0.543097i	$-0.182748\pi$
$379$	5.77366	+	5.77366i	0.296573	+	0.296573i	−0.543097	+	0.839670i	$0.682748\pi$
$380$	−1.32893	+	1.32893i	−0.0681725	+	0.0681725i
$381$	7.37778	−	7.37778i	0.377975	−	0.377975i
$382$		−	14.8990i		−	0.762298i
$383$			16.2540i			0.830542i	0.909698	+	0.415271i	$0.136313\pi$
$383$			16.2540i			0.830542i	−0.909698	+	0.415271i	$0.863687\pi$
$384$	12.7092	−	12.7092i	0.648566	−	0.648566i
$385$	−1.52555	+	1.52555i	−0.0777492	+	0.0777492i
$386$	−0.914676	−	0.914676i	−0.0465558	−	0.0465558i
$387$	13.0155			0.661614
$388$	−1.00288	−	1.00288i	−0.0509133	−	0.0509133i
$389$			5.80747i			0.294450i	0.989103	+	0.147225i	$0.0470342\pi$
$389$			5.80747i			0.294450i	−0.989103	+	0.147225i	$0.952966\pi$
$390$	−23.9932			−1.21494
$391$		0			0
$392$	17.4192			0.879803
$393$		−	25.0847i		−	1.26536i
$394$	−18.4180	−	18.4180i	−0.927884	−	0.927884i
$395$	−40.9077			−2.05829
$396$	0.511725	+	0.511725i	0.0257152	+	0.0257152i
$397$	−7.24902	+	7.24902i	−0.363818	+	0.363818i	−0.865216	−	0.501399i	$-0.832819\pi$
$397$	−7.24902	+	7.24902i	−0.363818	+	0.363818i	0.501399	+	0.865216i	$0.332819\pi$
$398$	−13.7537	+	13.7537i	−0.689411	+	0.689411i
$399$		−	0.716881i		−	0.0358890i
$400$		−	34.1935i		−	1.70967i
$401$	21.6107	−	21.6107i	1.07919	−	1.07919i	0.0826034	−	0.996582i	$-0.473677\pi$
$401$	21.6107	−	21.6107i	1.07919	−	1.07919i	0.996582	−	0.0826034i	$-0.0263235\pi$
$402$	−11.7817	+	11.7817i	−0.587619	+	0.587619i
$403$	−16.5357	−	16.5357i	−0.823704	−	0.823704i
$404$	−1.82976			−0.0910337
$405$	10.0949	+	10.0949i	0.501618	+	0.501618i
$406$		−	0.630415i		−	0.0312870i
$407$	6.89662			0.341853
$408$		0			0
$409$	19.9736			0.987631			0.493815	−	0.869567i	$-0.335602\pi$
$409$	19.9736			0.987631			0.493815	+	0.869567i	$0.335602\pi$
$410$		−	26.6313i		−	1.31523i
$411$	−9.59534	−	9.59534i	−0.473303	−	0.473303i
$412$	6.40373			0.315489
$413$	2.66814	+	2.66814i	0.131291	+	0.131291i
$414$	3.61345	−	3.61345i	0.177591	−	0.177591i
$415$	−5.36466	+	5.36466i	−0.263341	+	0.263341i
$416$			6.39599i			0.313589i
$417$		−	11.5253i		−	0.564395i
$418$	−2.91919	+	2.91919i	−0.142782	+	0.142782i
$419$	11.9706	−	11.9706i	0.584803	−	0.584803i	−0.351416	−	0.936219i	$-0.614300\pi$
$419$	11.9706	−	11.9706i	0.584803	−	0.584803i	0.936219	+	0.351416i	$0.114300\pi$
$420$	−0.405864	−	0.405864i	−0.0198041	−	0.0198041i
$421$	23.7297			1.15651			0.578257	−	0.815855i	$-0.303733\pi$
$421$	23.7297			1.15651			0.578257	+	0.815855i	$0.303733\pi$
$422$	−25.4916	−	25.4916i	−1.24091	−	1.24091i
$423$		−	6.06687i		−	0.294981i
$424$	21.1925			1.02920
$425$		0			0
$426$	23.2199			1.12501
$427$		−	1.53209i		−	0.0741430i
$428$	−1.31674	−	1.31674i	−0.0636469	−	0.0636469i
$429$	−7.79797			−0.376490
$430$	42.0357	+	42.0357i	2.02714	+	2.02714i
$431$	−16.6822	+	16.6822i	−0.803552	+	0.803552i	−0.983649	−	0.180097i	$-0.942359\pi$
$431$	−16.6822	+	16.6822i	−0.803552	+	0.803552i	0.180097	+	0.983649i	$0.442359\pi$
$432$	18.2354	−	18.2354i	0.877353	−	0.877353i
$433$		−	12.6946i		−	0.610063i	−0.952342	−	0.305032i	$-0.901333\pi$
$433$		−	12.6946i		−	0.610063i	0.952342	−	0.305032i	$-0.0986670\pi$
$434$		−	3.78106i		−	0.181497i
$435$	−3.98678	+	3.98678i	−0.191151	+	0.191151i
$436$	3.81073	−	3.81073i	0.182501	−	0.182501i
$437$	3.04986	+	3.04986i	0.145894	+	0.145894i
$438$	−3.51392			−0.167902
$439$	−16.5962	−	16.5962i	−0.792094	−	0.792094i	0.189740	−	0.981834i	$-0.439235\pi$
$439$	−16.5962	−	16.5962i	−0.792094	−	0.792094i	−0.981834	+	0.189740i	$0.939235\pi$
$440$		−	15.7297i		−	0.749883i
$441$	8.15064			0.388126
$442$		0			0
$443$	−19.4124			−0.922311			−0.461156	−	0.887319i	$-0.652565\pi$
$443$	−19.4124			−0.922311			−0.461156	+	0.887319i	$0.652565\pi$
$444$			1.83481i			0.0870761i
$445$	−16.0324	−	16.0324i	−0.760009	−	0.760009i
$446$	−7.61587			−0.360622
$447$	11.3173	+	11.3173i	0.535289	+	0.535289i
$448$	1.51526	−	1.51526i	0.0715894	−	0.0715894i
$449$	12.4637	−	12.4637i	0.588197	−	0.588197i	−0.348946	−	0.937143i	$-0.613460\pi$
$449$	12.4637	−	12.4637i	0.588197	−	0.588197i	0.937143	+	0.348946i	$0.113460\pi$
$450$		−	13.5699i		−	0.639689i
$451$		−	8.65539i		−	0.407566i
$452$	−1.72574	+	1.72574i	−0.0811721	+	0.0811721i
$453$	−6.24905	+	6.24905i	−0.293606	+	0.293606i
$454$	−5.69486	−	5.69486i	−0.267273	−	0.267273i
$455$	−4.03684			−0.189250
$456$	3.69582	+	3.69582i	0.173073	+	0.173073i
$457$			37.1215i			1.73647i	0.496151	+	0.868236i	$0.334746\pi$
$457$			37.1215i			1.73647i	−0.496151	+	0.868236i	$0.665254\pi$
$458$	−37.0847			−1.73285
$459$		0			0
$460$	3.45336			0.161014
$461$		−	29.4074i		−	1.36964i	−0.728714	−	0.684819i	$-0.759881\pi$
$461$		−	29.4074i		−	1.36964i	0.728714	−	0.684819i	$-0.240119\pi$
$462$	−0.891541	−	0.891541i	−0.0414783	−	0.0414783i
$463$	9.72462			0.451942			0.225971	−	0.974134i	$-0.427445\pi$
$463$	9.72462			0.451942			0.225971	+	0.974134i	$0.427445\pi$
$464$	3.83196	+	3.83196i	0.177894	+	0.177894i
$465$	−23.9116	+	23.9116i	−1.10887	+	1.10887i
$466$	−31.1159	+	31.1159i	−1.44142	+	1.44142i
$467$		−	4.62267i		−	0.213912i	−0.994264	−	0.106956i	$-0.965890\pi$
$467$		−	4.62267i		−	0.213912i	0.994264	−	0.106956i	$-0.0341104\pi$
$468$			1.35410i			0.0625935i
$469$	−1.98227	+	1.98227i	−0.0915326	+	0.0915326i
$470$	19.5940	−	19.5940i	0.903803	−	0.903803i
$471$	8.46405	+	8.46405i	0.390003	+	0.390003i
$472$	−27.5107			−1.26628
$473$	13.6619	+	13.6619i	0.628176	+	0.628176i
$474$		−	23.9067i		−	1.09807i
$475$	11.4534			0.525516
$476$		0			0
$477$	9.91622			0.454033
$478$			4.03415i			0.184518i
$479$	−4.83418	−	4.83418i	−0.220879	−	0.220879i	0.587989	−	0.808869i	$-0.299920\pi$
$479$	−4.83418	−	4.83418i	−0.220879	−	0.220879i	−0.808869	+	0.587989i	$0.799920\pi$
$480$	9.24897			0.422156
$481$	9.12476	+	9.12476i	0.416053	+	0.416053i
$482$	27.4453	−	27.4453i	1.25010	−	1.25010i
$483$	−0.931448	+	0.931448i	−0.0423824	+	0.0423824i
$484$		−	2.74598i		−	0.124817i
$485$			14.4243i			0.654972i
$486$	12.4248	−	12.4248i	0.563599	−	0.563599i
$487$	5.41842	−	5.41842i	0.245532	−	0.245532i	−0.573602	−	0.819134i	$-0.694454\pi$
$487$	5.41842	−	5.41842i	0.245532	−	0.245532i	0.819134	+	0.573602i	$0.194454\pi$
$488$	7.89856	+	7.89856i	0.357551	+	0.357551i
$489$	13.0419			0.589775
$490$	26.3239	+	26.3239i	1.18919	+	1.18919i
$491$		−	9.02465i		−	0.407277i	−0.979046	−	0.203638i	$-0.934723\pi$
$491$		−	9.02465i		−	0.407277i	0.979046	−	0.203638i	$-0.0652767\pi$
$492$	2.30272			0.103815
$493$		0			0
$494$	−7.72462			−0.347547
$495$		−	7.36009i		−	0.330811i
$496$	22.9831	+	22.9831i	1.03197	+	1.03197i
$497$	3.90673			0.175241
$498$	−3.13514	−	3.13514i	−0.140489	−	0.140489i
$499$	−18.8747	+	18.8747i	−0.844947	+	0.844947i	−0.989497	−	0.144550i	$-0.953826\pi$
$499$	−18.8747	+	18.8747i	−0.844947	+	0.844947i	0.144550	+	0.989497i	$0.453826\pi$
$500$	2.14737	−	2.14737i	0.0960332	−	0.0960332i
$501$			2.47565i			0.110604i
$502$			16.3705i			0.730652i
$503$	9.14052	−	9.14052i	0.407556	−	0.407556i	−0.473330	−	0.880885i	$-0.656948\pi$
$503$	9.14052	−	9.14052i	0.407556	−	0.407556i	0.880885	+	0.473330i	$0.156948\pi$
$504$	0.736727	−	0.736727i	0.0328164	−	0.0328164i
$505$	13.1586	+	13.1586i	0.585550	+	0.585550i
$506$	7.58584			0.337232
$507$	2.06755	+	2.06755i	0.0918233	+	0.0918233i
$508$		−	2.68954i		−	0.119329i
$509$	−27.8753			−1.23555			−0.617775	−	0.786355i	$-0.711966\pi$
$509$	−27.8753			−1.23555			−0.617775	+	0.786355i	$0.711966\pi$
$510$		0			0
$511$	−0.591214			−0.0261538
$512$			14.2736i			0.630811i
$513$	6.10810	+	6.10810i	0.269679	+	0.269679i
$514$	5.72462			0.252502
$515$	−46.0521	−	46.0521i	−2.02930	−	2.02930i
$516$	−3.63468	+	3.63468i	−0.160008	+	0.160008i
$517$	6.36819	−	6.36819i	0.280073	−	0.280073i
$518$			2.08647i			0.0916741i
$519$			30.6641i			1.34600i
$520$	20.8116	−	20.8116i	0.912648	−	0.912648i
$521$	−3.61958	+	3.61958i	−0.158577	+	0.158577i	−0.781936	−	0.623359i	$-0.785768\pi$
$521$	−3.61958	+	3.61958i	−0.158577	+	0.158577i	0.623359	+	0.781936i	$0.285768\pi$
$522$	1.52074	+	1.52074i	0.0665608	+	0.0665608i
$523$	−15.3182			−0.669818			−0.334909	−	0.942250i	$-0.608706\pi$
$523$	−15.3182			−0.669818			−0.334909	+	0.942250i	$0.608706\pi$
$524$	−4.57226	−	4.57226i	−0.199740	−	0.199740i
$525$			3.49794i			0.152663i
$526$	15.6418			0.682014
$527$		0			0
$528$	10.8384			0.471682
$529$			15.0746i			0.655418i
$530$	32.0261	+	32.0261i	1.39113	+	1.39113i
$531$	−12.8726			−0.558622
$532$	−0.130668	−	0.130668i	−0.00566518	−	0.00566518i
$533$	11.4518	−	11.4518i	0.496030	−	0.496030i
$534$	9.36945	−	9.36945i	0.405456	−	0.405456i
$535$			18.9385i			0.818783i
$536$		−	20.4388i		−	0.882822i
$537$	−16.6960	+	16.6960i	−0.720487	+	0.720487i
$538$	−12.7176	+	12.7176i	−0.548296	+	0.548296i
$539$	8.55547	+	8.55547i	0.368510	+	0.368510i
$540$	6.91622			0.297627
$541$	−26.4787	−	26.4787i	−1.13841	−	1.13841i	−0.988736	−	0.149673i	$-0.952178\pi$
$541$	−26.4787	−	26.4787i	−1.13841	−	1.13841i	−0.149673	−	0.988736i	$-0.547822\pi$
$542$		−	26.0455i		−	1.11875i
$543$	−6.14653			−0.263773
$544$		0			0
$545$	−54.8093			−2.34777
$546$		−	2.35916i		−	0.100963i
$547$	−19.3696	−	19.3696i	−0.828186	−	0.828186i	0.159080	−	0.987266i	$-0.449147\pi$
$547$	−19.3696	−	19.3696i	−0.828186	−	0.828186i	−0.987266	+	0.159080i	$0.949147\pi$
$548$	−3.49794			−0.149425
$549$	3.69582	+	3.69582i	0.157734	+	0.157734i
$550$	14.2438	−	14.2438i	0.607360	−	0.607360i
$551$	−1.28355	+	1.28355i	−0.0546809	+	0.0546809i
$552$		−	9.60401i		−	0.408774i
$553$		−	4.02229i		−	0.171045i
$554$	−26.3722	+	26.3722i	−1.12045	+	1.12045i
$555$	13.1949	−	13.1949i	0.560093	−	0.560093i
$556$	−2.10075	−	2.10075i	−0.0890915	−	0.0890915i
$557$	−9.07604			−0.384564			−0.192282	−	0.981340i	$-0.561589\pi$
$557$	−9.07604			−0.384564			−0.192282	+	0.981340i	$0.561589\pi$
$558$	9.12096	+	9.12096i	0.386121	+	0.386121i
$559$			36.1516i			1.52905i
$560$	5.61081			0.237100
$561$		0			0
$562$	−8.87670			−0.374441
$563$			38.4894i			1.62213i	0.584953	+	0.811067i	$0.301113\pi$
$563$			38.4894i			1.62213i	−0.584953	+	0.811067i	$0.698887\pi$
$564$	1.69422	+	1.69422i	0.0713396	+	0.0713396i
$565$	24.8212			1.04424
$566$	−16.5969	−	16.5969i	−0.697619	−	0.697619i
$567$	−0.992589	+	0.992589i	−0.0416848	+	0.0416848i
$568$	−20.1408	+	20.1408i	−0.845089	+	0.845089i
$569$			45.1830i			1.89417i	0.320981	+	0.947086i	$0.395988\pi$
$569$			45.1830i			1.89417i	−0.320981	+	0.947086i	$0.604012\pi$
$570$			11.1702i			0.467870i
$571$	−21.5363	+	21.5363i	−0.901268	+	0.901268i	−0.995546	−	0.0942781i	$-0.969946\pi$
$571$	−21.5363	+	21.5363i	−0.901268	+	0.901268i	0.0942781	+	0.995546i	$0.469946\pi$
$572$	−1.42136	+	1.42136i	−0.0594300	+	0.0594300i
$573$	−9.26448	−	9.26448i	−0.387029	−	0.387029i
$574$	2.61856			0.109296
$575$	−14.8814	−	14.8814i	−0.620598	−	0.620598i
$576$			7.31046i			0.304602i
$577$	−9.90167			−0.412212			−0.206106	−	0.978530i	$-0.566079\pi$
$577$	−9.90167			−0.412212			−0.206106	+	0.978530i	$0.566079\pi$
$578$		0			0
$579$	−1.13753			−0.0472740
$580$			1.45336i			0.0603476i
$581$	−0.527486	−	0.527486i	−0.0218838	−	0.0218838i
$582$	−8.42964			−0.349420
$583$	10.4087	+	10.4087i	0.431086	+	0.431086i
$584$	3.04796	−	3.04796i	0.126125	−	0.126125i
$585$	9.73797	−	9.73797i	0.402615	−	0.402615i
$586$			4.56624i			0.188630i
$587$		−	36.1343i		−	1.49142i	−0.666268	−	0.745712i	$-0.732110\pi$
$587$		−	36.1343i		−	1.49142i	0.666268	−	0.745712i	$-0.267890\pi$
$588$	−2.27613	+	2.27613i	−0.0938662	+	0.0938662i
$589$	−7.69836	+	7.69836i	−0.317205	+	0.317205i
$590$	−41.5742	−	41.5742i	−1.71158	−	1.71158i
$591$	−22.9053			−0.942198
$592$	−12.6825	−	12.6825i	−0.521249	−	0.521249i
$593$			7.41653i			0.304560i	0.988337	+	0.152280i	$0.0486616\pi$
$593$			7.41653i			0.304560i	−0.988337	+	0.152280i	$0.951338\pi$
$594$	15.1925			0.623357
$595$		0			0
$596$	4.12567			0.168994
$597$			17.1046i			0.700046i
$598$	10.0366	+	10.0366i	0.410429	+	0.410429i
$599$	−7.61350			−0.311079			−0.155540	−	0.987830i	$-0.549712\pi$
$599$	−7.61350			−0.311079			−0.155540	+	0.987830i	$0.549712\pi$
$600$	−18.0333	−	18.0333i	−0.736208	−	0.736208i
$601$	23.0327	−	23.0327i	0.939523	−	0.939523i	−0.0587493	−	0.998273i	$-0.518711\pi$
$601$	23.0327	−	23.0327i	0.939523	−	0.939523i	0.998273	+	0.0587493i	$0.0187113\pi$
$602$	−4.13321	+	4.13321i	−0.168457	+	0.168457i
$603$		−	9.56355i		−	0.389458i
$604$			2.27807i			0.0926932i
$605$	−19.7476	+	19.7476i	−0.802852	+	0.802852i
$606$	−7.68997	+	7.68997i	−0.312384	+	0.312384i
$607$	−2.13161	−	2.13161i	−0.0865193	−	0.0865193i	0.662523	−	0.749042i	$-0.269486\pi$
$607$	−2.13161	−	2.13161i	−0.0865193	−	0.0865193i	−0.749042	+	0.662523i	$0.769486\pi$
$608$	2.97771			0.120762
$609$	−0.392004	−	0.392004i	−0.0158848	−	0.0158848i
$610$			23.8726i			0.966572i
$611$	16.8512			0.681728
$612$		0			0
$613$	7.26857			0.293575			0.146787	−	0.989168i	$-0.453107\pi$
$613$	7.26857			0.293575			0.146787	+	0.989168i	$0.453107\pi$
$614$			5.00774i			0.202096i
$615$	−16.5599	−	16.5599i	−0.667759	−	0.667759i
$616$	1.54664			0.0623158
$617$	−24.2148	−	24.2148i	−0.974850	−	0.974850i	0.0248416	−	0.999691i	$-0.492092\pi$
$617$	−24.2148	−	24.2148i	−0.974850	−	0.974850i	−0.999691	+	0.0248416i	$0.992092\pi$
$618$	26.9132	−	26.9132i	1.08261	−	1.08261i
$619$	14.4459	−	14.4459i	0.580631	−	0.580631i	−0.354445	−	0.935077i	$-0.615330\pi$
$619$	14.4459	−	14.4459i	0.580631	−	0.580631i	0.935077	+	0.354445i	$0.115330\pi$
$620$			8.71688i			0.350078i
$621$		−	15.8726i		−	0.636945i
$622$	3.82649	−	3.82649i	0.153428	−	0.153428i
$623$	1.57640	−	1.57640i	0.0631572	−	0.0631572i
$624$	14.3401	+	14.3401i	0.574063	+	0.574063i
$625$	6.49289			0.259716
$626$	−1.60602	−	1.60602i	−0.0641896	−	0.0641896i
$627$			3.63041i			0.144985i
$628$	3.08553			0.123126
$629$		0			0
$630$	2.22668			0.0887131
$631$		−	15.5080i		−	0.617366i	−0.951165	−	0.308683i	$-0.900112\pi$
$631$		−	15.5080i		−	0.617366i	0.951165	−	0.308683i	$-0.0998881\pi$
$632$	20.7366	+	20.7366i	0.824857	+	0.824857i
$633$	−31.7023			−1.26005
$634$	−15.6694	−	15.6694i	−0.622310	−	0.622310i
$635$	−19.3417	+	19.3417i	−0.767552	+	0.767552i
$636$	−2.76919	+	2.76919i	−0.109805	+	0.109805i
$637$			22.6391i			0.896993i
$638$			3.19253i			0.126394i
$639$	−9.42410	+	9.42410i	−0.372812	+	0.372812i
$640$	−33.3187	+	33.3187i	−1.31704	+	1.31704i
$641$	23.0478	+	23.0478i	0.910333	+	0.910333i	0.996298	−	0.0859648i	$-0.0273973\pi$
$641$	23.0478	+	23.0478i	0.910333	+	0.910333i	−0.0859648	+	0.996298i	$0.527397\pi$
$642$	−11.0678			−0.436811
$643$	29.1385	+	29.1385i	1.14911	+	1.14911i	0.986728	+	0.162381i	$0.0519173\pi$
$643$	29.1385	+	29.1385i	1.14911	+	1.14911i	0.162381	+	0.986728i	$0.448083\pi$
$644$			0.339556i			0.0133804i
$645$	52.2772			2.05841
$646$		0			0
$647$	26.5131			1.04234			0.521169	−	0.853454i	$-0.325496\pi$
$647$	26.5131			1.04234			0.521169	+	0.853454i	$0.325496\pi$
$648$		−	10.2344i		−	0.402046i
$649$	−13.5119	−	13.5119i	−0.530390	−	0.530390i
$650$	37.6914			1.47838
$651$	−2.35114	−	2.35114i	−0.0921483	−	0.0921483i
$652$	2.37718	−	2.37718i	0.0930977	−	0.0930977i
$653$	10.0321	−	10.0321i	0.392585	−	0.392585i	−0.483023	−	0.875608i	$-0.660461\pi$
$653$	10.0321	−	10.0321i	0.392585	−	0.392585i	0.875608	+	0.483023i	$0.160461\pi$
$654$		−	32.0310i		−	1.25251i
$655$			65.7624i			2.56955i
$656$	−15.9168	+	15.9168i	−0.621448	+	0.621448i
$657$	1.42617	−	1.42617i	0.0556403	−	0.0556403i
$658$	1.92660	+	1.92660i	0.0751066	+	0.0751066i
$659$	28.3628			1.10486			0.552428	−	0.833560i	$-0.313701\pi$
$659$	28.3628			1.10486			0.552428	+	0.833560i	$0.313701\pi$
$660$	2.05537	+	2.05537i	0.0800050	+	0.0800050i
$661$		−	29.1661i		−	1.13443i	−0.823569	−	0.567215i	$-0.808021\pi$
$661$		−	29.1661i		−	1.13443i	0.823569	−	0.567215i	$-0.191979\pi$
$662$	−13.8425			−0.538006
$663$		0			0
$664$	5.43882			0.211067
$665$			1.87939i			0.0728794i
$666$	−5.03313	−	5.03313i	−0.195030	−	0.195030i
$667$	3.33544			0.129149
$668$	0.451244	+	0.451244i	0.0174592	+	0.0174592i
$669$	−4.73569	+	4.73569i	−0.183092	+	0.183092i
$670$	30.8871	−	30.8871i	1.19327	−	1.19327i
$671$			7.75877i			0.299524i
$672$			0.909415i			0.0350814i
$673$	20.7662	−	20.7662i	0.800478	−	0.800478i	−0.182692	−	0.983170i	$-0.558481\pi$
$673$	20.7662	−	20.7662i	0.800478	−	0.800478i	0.983170	+	0.182692i	$0.0584812\pi$
$674$	19.4633	−	19.4633i	0.749699	−	0.749699i
$675$	−29.8038	−	29.8038i	−1.14715	−	1.14715i
$676$	0.753718			0.0289892
$677$	27.8446	+	27.8446i	1.07016	+	1.07016i	0.997346	+	0.0728104i	$0.0231968\pi$
$677$	27.8446	+	27.8446i	1.07016	+	1.07016i	0.0728104	+	0.997346i	$0.476803\pi$
$678$			14.5057i			0.557087i
$679$	−1.41828			−0.0544286
$680$		0			0
$681$	−7.08235			−0.271396
$682$			19.1480i			0.733213i
$683$	19.2075	+	19.2075i	0.734953	+	0.734953i	0.971596	−	0.236644i	$-0.0760474\pi$
$683$	19.2075	+	19.2075i	0.734953	+	0.734953i	−0.236644	+	0.971596i	$0.576047\pi$
$684$	0.630415			0.0241045
$685$	25.1553	+	25.1553i	0.961133	+	0.961133i
$686$	−5.22203	+	5.22203i	−0.199378	+	0.199378i
$687$	−23.0600	+	23.0600i	−0.879793	+	0.879793i
$688$		−	50.2472i		−	1.91566i
$689$			27.5431i			1.04931i
$690$	14.5136	−	14.5136i	0.552522	−	0.552522i
$691$	−23.9358	+	23.9358i	−0.910560	+	0.910560i	−0.996316	−	0.0857565i	$-0.972669\pi$
$691$	−23.9358	+	23.9358i	−0.910560	+	0.910560i	0.0857565	+	0.996316i	$0.472669\pi$
$692$	5.58923	+	5.58923i	0.212471	+	0.212471i
$693$	0.723689			0.0274907
$694$	8.43253	+	8.43253i	0.320094	+	0.320094i
$695$			30.2148i			1.14611i
$696$	4.04189			0.153207
$697$		0			0
$698$	−10.1884			−0.385637
$699$			38.6970i			1.46365i
$700$	0.637580	+	0.637580i	0.0240982	+	0.0240982i
$701$	−20.9540			−0.791421			−0.395711	−	0.918375i	$-0.629502\pi$
$701$	−20.9540			−0.791421			−0.395711	+	0.918375i	$0.629502\pi$
$702$	20.1009	+	20.1009i	0.758659	+	0.758659i
$703$	4.24811	−	4.24811i	0.160221	−	0.160221i
$704$	−7.67355	+	7.67355i	−0.289208	+	0.289208i
$705$		−	24.3678i		−	0.917746i
$706$			6.35142i			0.239039i
$707$	−1.29383	+	1.29383i	−0.0486596	+	0.0486596i
$708$	3.59477	−	3.59477i	0.135100	−	0.135100i
$709$	22.1491	+	22.1491i	0.831827	+	0.831827i	0.987767	−	0.155939i	$-0.0498404\pi$
$709$	22.1491	+	22.1491i	0.831827	+	0.831827i	−0.155939	+	0.987767i	$0.549840\pi$
$710$	−60.8735			−2.28454
$711$	9.70287	+	9.70287i	0.363886	+	0.363886i
$712$			16.2540i			0.609145i
$713$	20.0051			0.749195
$714$		0			0
$715$	20.4433			0.764535
$716$			6.08647i			0.227462i
$717$	2.50851	+	2.50851i	0.0936821	+	0.0936821i
$718$	26.1634			0.976411
$719$	31.4024	+	31.4024i	1.17111	+	1.17111i	0.981945	+	0.189168i	$0.0605789\pi$
$719$	31.4024	+	31.4024i	1.17111	+	1.17111i	0.189168	+	0.981945i	$0.439421\pi$
$720$	−13.5348	+	13.5348i	−0.504414	+	0.504414i
$721$	4.52812	−	4.52812i	0.168636	−	0.168636i
$722$		−	25.5134i		−	0.949511i
$723$		−	34.1320i		−	1.26938i
$724$	−1.12034	+	1.12034i	−0.0416373	+	0.0416373i
$725$	6.26291	−	6.26291i	0.232599	−	0.232599i
$726$	−11.5406	−	11.5406i	−0.428312	−	0.428312i
$727$	39.5354			1.46629			0.733143	−	0.680074i	$-0.238053\pi$
$727$	39.5354			1.46629			0.733143	+	0.680074i	$0.238053\pi$
$728$	2.04632	+	2.04632i	0.0758417	+	0.0758417i
$729$		−	27.5776i		−	1.02139i
$730$	9.21213			0.340956
$731$		0			0
$732$	−2.06418			−0.0762942
$733$		−	13.8990i		−	0.513371i	−0.966495	−	0.256685i	$-0.917370\pi$
$733$		−	13.8990i		−	0.513371i	0.966495	−	0.256685i	$-0.0826304\pi$
$734$	−20.4002	−	20.4002i	−0.752986	−	0.752986i
$735$	32.7374			1.20754
$736$	−3.86896	−	3.86896i	−0.142612	−	0.142612i
$737$	10.0385	−	10.0385i	0.369775	−	0.369775i
$738$	−6.31668	+	6.31668i	−0.232520	+	0.232520i
$739$			11.4037i			0.419493i	0.977756	+	0.209747i	$0.0672639\pi$
$739$			11.4037i			0.419493i	−0.977756	+	0.209747i	$0.932736\pi$
$740$		−	4.81016i		−	0.176825i
$741$	−4.80332	+	4.80332i	−0.176454	+	0.176454i
$742$	−3.14900	+	3.14900i	−0.115604	+	0.115604i
$743$	10.3386	+	10.3386i	0.379285	+	0.379285i	0.870844	−	0.491559i	$-0.163573\pi$
$743$	10.3386	+	10.3386i	0.379285	+	0.379285i	−0.491559	+	0.870844i	$0.663573\pi$
$744$	24.2422			0.888761
$745$	−29.6695	−	29.6695i	−1.08701	−	1.08701i
$746$			17.9736i			0.658060i
$747$	2.54488			0.0931124
$748$		0			0
$749$	−1.86215			−0.0680414
$750$		−	18.0496i		−	0.659079i
$751$	19.8128	+	19.8128i	0.722981	+	0.722981i	0.969211	−	0.246230i	$-0.0791919\pi$
$751$	19.8128	+	19.8128i	0.722981	+	0.722981i	−0.246230	+	0.969211i	$0.579192\pi$
$752$	−23.4216			−0.854097
$753$	10.1795	+	10.1795i	0.370962	+	0.370962i
$754$	−4.22397	+	4.22397i	−0.153828	+	0.153828i
$755$	16.3826	−	16.3826i	0.596224	−	0.596224i
$756$			0.680045i			0.0247330i
$757$			15.6186i			0.567666i	0.958874	+	0.283833i	$0.0916061\pi$
$757$			15.6186i			0.567666i	−0.958874	+	0.283833i	$0.908394\pi$
$758$	8.84576	−	8.84576i	0.321293	−	0.321293i
$759$	4.71702	−	4.71702i	0.171217	−	0.171217i
$760$	−9.68901	−	9.68901i	−0.351457	−	0.351457i
$761$	−20.5868			−0.746270			−0.373135	−	0.927777i	$-0.621717\pi$
$761$	−20.5868			−0.746270			−0.373135	+	0.927777i	$0.621717\pi$
$762$	−11.3034	−	11.3034i	−0.409480	−	0.409480i
$763$		−	5.38919i		−	0.195102i
$764$	−3.37733			−0.122187
$765$		0			0
$766$	24.9026			0.899768
$767$		−	35.7547i		−	1.29103i
$768$	−7.71513	−	7.71513i	−0.278396	−	0.278396i
$769$	−22.2249			−0.801451			−0.400726	−	0.916198i	$-0.631242\pi$
$769$	−22.2249			−0.801451			−0.400726	+	0.916198i	$0.631242\pi$
$770$	2.33728	+	2.33728i	0.0842296	+	0.0842296i
$771$	3.55968	−	3.55968i	0.128199	−	0.128199i
$772$	−0.207340	+	0.207340i	−0.00746234	+	0.00746234i
$773$		−	27.0087i		−	0.971434i	−0.874116	−	0.485717i	$-0.838558\pi$
$773$		−	27.0087i		−	0.971434i	0.874116	−	0.485717i	$-0.161442\pi$
$774$		−	19.9409i		−	0.716760i
$775$	37.5633	−	37.5633i	1.34931	−	1.34931i
$776$	7.31183	−	7.31183i	0.262479	−	0.262479i
$777$	1.29741	+	1.29741i	0.0465441	+	0.0465441i
$778$	8.89756			0.318993
$779$	−5.33146	−	5.33146i	−0.191020	−	0.191020i
$780$			5.43882i			0.194741i
$781$	−19.7844			−0.707940
$782$		0			0
$783$	6.68004			0.238725
$784$		−	31.4662i		−	1.12379i
$785$	−22.1895	−	22.1895i	−0.791975	−	0.791975i
$786$	−38.4320			−1.37082
$787$	−14.8358	−	14.8358i	−0.528840	−	0.528840i	0.391387	−	0.920226i	$-0.371996\pi$
$787$	−14.8358	−	14.8358i	−0.528840	−	0.528840i	−0.920226	+	0.391387i	$0.871996\pi$
$788$	−4.17501	+	4.17501i	−0.148729	+	0.148729i
$789$	9.72636	−	9.72636i	0.346268	−	0.346268i
$790$			62.6742i			2.22985i
$791$			2.44057i			0.0867767i
$792$	−3.73092	+	3.73092i	−0.132572	+	0.132572i
$793$	−10.2655	+	10.2655i	−0.364537	+	0.364537i
$794$	11.1061	+	11.1061i	0.394142	+	0.394142i
$795$	39.8289			1.41259
$796$	3.11771	+	3.11771i	0.110504	+	0.110504i
$797$		−	34.4347i		−	1.21974i	−0.792502	−	0.609870i	$-0.791222\pi$
$797$		−	34.4347i		−	1.21974i	0.792502	−	0.609870i	$-0.208778\pi$
$798$	−1.09833			−0.0388803
$799$		0			0
$800$	−14.5294			−0.513692
$801$			7.60544i			0.268725i
$802$	−33.1095	−	33.1095i	−1.16914	−	1.16914i
$803$	2.99401			0.105656
$804$	2.67070	+	2.67070i	0.0941883	+	0.0941883i
$805$	2.44190	−	2.44190i	0.0860655	−	0.0860655i
$806$	−25.3342	+	25.3342i	−0.892360	+	0.892360i
$807$			15.8161i			0.556755i
$808$		−	13.3405i		−	0.469317i
$809$	−20.4528	+	20.4528i	−0.719081	+	0.719081i	−0.968417	−	0.249336i	$-0.919788\pi$
$809$	−20.4528	+	20.4528i	−0.719081	+	0.719081i	0.249336	+	0.968417i	$0.419788\pi$
$810$	15.4662	−	15.4662i	0.543429	−	0.543429i
$811$	−27.3110	−	27.3110i	−0.959019	−	0.959019i	0.0401733	−	0.999193i	$-0.487209\pi$
$811$	−27.3110	−	27.3110i	−0.959019	−	0.959019i	−0.999193	+	0.0401733i	$0.987209\pi$
$812$	−0.142903			−0.00501493
$813$	−16.1956	−	16.1956i	−0.568005	−	0.568005i
$814$		−	10.5662i		−	0.370346i
$815$	−34.1908			−1.19765
$816$		0			0
$817$	16.8307			0.588831
$818$		−	30.6013i		−	1.06995i
$819$	0.957496	+	0.957496i	0.0334576	+	0.0334576i
$820$	−6.03684			−0.210815
$821$	−3.81554	−	3.81554i	−0.133163	−	0.133163i	0.637383	−	0.770547i	$-0.280017\pi$
$821$	−3.81554	−	3.81554i	−0.133163	−	0.133163i	−0.770547	+	0.637383i	$0.780017\pi$
$822$	−14.7009	+	14.7009i	−0.512753	+	0.512753i
$823$	−21.6995	+	21.6995i	−0.756398	+	0.756398i	−0.975665	−	0.219267i	$-0.929634\pi$
$823$	−21.6995	+	21.6995i	−0.756398	+	0.756398i	0.219267	+	0.975665i	$0.429634\pi$
$824$			46.6887i			1.62648i
$825$		−	17.7142i		−	0.616729i
$826$	4.08783	−	4.08783i	0.142234	−	0.142234i
$827$	25.1292	−	25.1292i	0.873828	−	0.873828i	−0.119059	−	0.992887i	$-0.537988\pi$
$827$	25.1292	−	25.1292i	0.873828	−	0.873828i	0.992887	+	0.119059i	$0.0379877\pi$
$828$	−0.819102	−	0.819102i	−0.0284658	−	0.0284658i
$829$	−3.17200			−0.110168			−0.0550840	−	0.998482i	$-0.517543\pi$
$829$	−3.17200			−0.110168			−0.0550840	+	0.998482i	$0.517543\pi$
$830$	8.21913	+	8.21913i	0.285290	+	0.285290i
$831$			32.7975i			1.13773i
$832$	−20.3054			−0.703963
$833$		0			0
$834$	−17.6578			−0.611438
$835$		−	6.49020i		−	0.224603i
$836$	0.661726	+	0.661726i	0.0228863	+	0.0228863i
$837$	40.0651			1.38485
$838$	−18.3401	−	18.3401i	−0.633547	−	0.633547i
$839$	−26.0323	+	26.0323i	−0.898734	+	0.898734i	−0.995324	−	0.0965900i	$-0.969206\pi$
$839$	−26.0323	+	26.0323i	−0.898734	+	0.898734i	0.0965900	+	0.995324i	$0.469206\pi$
$840$	2.95910	−	2.95910i	0.102098	−	0.102098i
$841$		−	27.5963i		−	0.951595i
$842$		−	36.3560i		−	1.25291i
$843$	−5.51970	+	5.51970i	−0.190109	+	0.190109i
$844$	−5.77848	+	5.77848i	−0.198903	+	0.198903i
$845$	−5.42032	−	5.42032i	−0.186465	−	0.186465i
$846$	−9.29498			−0.319568
$847$	−1.94170	−	1.94170i	−0.0667176	−	0.0667176i
$848$		−	38.2823i		−	1.31462i
$849$	−20.6405			−0.708381
$850$		0			0
$851$	−11.0392			−0.378419
$852$		−	5.26352i		−	0.180325i
$853$	14.1882	+	14.1882i	0.485794	+	0.485794i	0.906976	−	0.421182i	$-0.138385\pi$
$853$	14.1882	+	14.1882i	0.485794	+	0.485794i	−0.421182	+	0.906976i	$0.638385\pi$
$854$	−2.34730			−0.0803228
$855$	−4.53360	−	4.53360i	−0.155046	−	0.155046i
$856$	9.60015	−	9.60015i	0.328126	−	0.328126i
$857$	−14.0926	+	14.0926i	−0.481394	+	0.481394i	−0.905577	−	0.424183i	$-0.860561\pi$
$857$	−14.0926	+	14.0926i	−0.481394	+	0.481394i	0.424183	+	0.905577i	$0.360561\pi$
$858$			11.9472i			0.407870i
$859$		−	23.3527i		−	0.796783i	−0.917215	−	0.398391i	$-0.869569\pi$
$859$		−	23.3527i		−	0.796783i	0.917215	−	0.398391i	$-0.130431\pi$
$860$	9.52872	−	9.52872i	0.324927	−	0.324927i
$861$	1.62827	−	1.62827i	0.0554912	−	0.0554912i
$862$	25.5586	+	25.5586i	0.870528	+	0.870528i
$863$	−44.3878			−1.51098			−0.755488	−	0.655162i	$-0.772600\pi$
$863$	−44.3878			−1.51098			−0.755488	+	0.655162i	$0.772600\pi$
$864$	−7.74855	−	7.74855i	−0.263611	−	0.263611i
$865$		−	80.3893i		−	2.73332i
$866$	−19.4492			−0.660912
$867$		0			0
$868$	−0.857097			−0.0290918
$869$			20.3696i			0.690991i
$870$	6.10810	+	6.10810i	0.207084	+	0.207084i
$871$	26.5635			0.900072
$872$	27.7835	+	27.7835i	0.940868	+	0.940868i
$873$	3.42129	−	3.42129i	0.115793	−	0.115793i
$874$	4.67265	−	4.67265i	0.158055	−	0.158055i
$875$		−	3.03684i		−	0.102664i
$876$			0.796541i			0.0269126i
$877$	6.46982	−	6.46982i	0.218470	−	0.218470i	−0.589383	−	0.807854i	$-0.700629\pi$
$877$	6.46982	−	6.46982i	0.218470	−	0.218470i	0.807854	+	0.589383i	$0.200629\pi$
$878$	−25.4269	+	25.4269i	−0.858116	+	0.858116i
$879$	2.83937	+	2.83937i	0.0957697	+	0.0957697i
$880$	−28.4142			−0.957841
$881$	−4.78566	−	4.78566i	−0.161233	−	0.161233i	0.621880	−	0.783113i	$-0.286369\pi$
$881$	−4.78566	−	4.78566i	−0.161233	−	0.161233i	−0.783113	+	0.621880i	$0.786369\pi$
$882$		−	12.4875i		−	0.420476i
$883$	−47.9760			−1.61452			−0.807260	−	0.590196i	$-0.799050\pi$
$883$	−47.9760			−1.61452			−0.807260	+	0.590196i	$0.799050\pi$
$884$		0			0
$885$	−51.7033			−1.73799
$886$			29.7415i			0.999186i
$887$	29.4851	+	29.4851i	0.990012	+	0.990012i	0.999951	−	0.00993817i	$-0.00316347\pi$
$887$	29.4851	+	29.4851i	0.990012	+	0.990012i	−0.00993817	+	0.999951i	$0.503163\pi$
$888$	−13.3773			−0.448914
$889$	−1.90179	−	1.90179i	−0.0637841	−	0.0637841i
$890$	−24.5631	+	24.5631i	−0.823356	+	0.823356i
$891$	5.02665	−	5.02665i	0.168399	−	0.168399i
$892$			1.72638i			0.0578034i
$893$		−	7.84524i		−	0.262531i
$894$	17.3391	−	17.3391i	0.579906	−	0.579906i
$895$	43.7705	−	43.7705i	1.46309	−	1.46309i
$896$	−3.27610	−	3.27610i	−0.109447	−	0.109447i
$897$	12.4820			0.416761
$898$	−19.0955	−	19.0955i	−0.637224	−	0.637224i
$899$			8.41921i			0.280797i
$900$	−3.07604			−0.102535
$901$		0			0
$902$	−13.2608			−0.441537
$903$			5.14022i			0.171056i
$904$	−12.5822	−	12.5822i	−0.418476	−	0.418476i
$905$	16.1138			0.535641
$906$	9.57411	+	9.57411i	0.318078	+	0.318078i
$907$	−23.2886	+	23.2886i	−0.773284	+	0.773284i	−0.978679	−	0.205395i	$-0.934152\pi$
$907$	−23.2886	+	23.2886i	−0.773284	+	0.773284i	0.205395	+	0.978679i	$0.434152\pi$
$908$	−1.29092	+	1.29092i	−0.0428407	+	0.0428407i
$909$		−	6.24216i		−	0.207039i
$910$			6.18479i			0.205024i
$911$	13.0762	−	13.0762i	0.433234	−	0.433234i	−0.456493	−	0.889727i	$-0.650895\pi$
$911$	13.0762	−	13.0762i	0.433234	−	0.433234i	0.889727	+	0.456493i	$0.150895\pi$
$912$	6.67615	−	6.67615i	0.221069	−	0.221069i
$913$	2.67128	+	2.67128i	0.0884065	+	0.0884065i
$914$	56.8735			1.88121
$915$	14.8444	+	14.8444i	0.490742	+	0.490742i
$916$			8.40642i			0.277756i
$917$	−6.46616			−0.213531
$918$		0			0
$919$	−13.3909			−0.441726			−0.220863	−	0.975305i	$-0.570887\pi$
$919$	−13.3909			−0.441726			−0.220863	+	0.975305i	$0.570887\pi$
$920$			25.1780i			0.830094i
$921$	3.11391	+	3.11391i	0.102607	+	0.102607i
$922$	−45.0547			−1.48380
$923$	−26.1762	−	26.1762i	−0.861601	−	0.861601i
$924$	−0.202096	+	0.202096i	−0.00664847	+	0.00664847i
$925$	−20.7282	+	20.7282i	−0.681539	+	0.681539i
$926$		−	14.8990i		−	0.489611i
$927$			21.8462i			0.717522i
$928$	1.62827	−	1.62827i	0.0534505	−	0.0534505i
$929$	−3.77564	+	3.77564i	−0.123875	+	0.123875i	−0.766326	−	0.642452i	$-0.777917\pi$
$929$	−3.77564	+	3.77564i	−0.123875	+	0.123875i	0.642452	+	0.766326i	$0.277917\pi$
$930$	36.6347	+	36.6347i	1.20130	+	1.20130i
$931$	10.5398			0.345429
$932$	7.05341	+	7.05341i	0.231042	+	0.231042i
$933$		−	4.75877i		−	0.155795i
$934$	−7.08235			−0.231741
$935$		0			0
$936$	−9.87258			−0.322695
$937$		−	41.4361i		−	1.35366i	−0.736140	−	0.676830i	$-0.763353\pi$
$937$		−	41.4361i		−	1.35366i	0.736140	−	0.676830i	$-0.236647\pi$
$938$	3.03701	+	3.03701i	0.0991618	+	0.0991618i
$939$	−1.99731			−0.0651798
$940$	−4.44160	−	4.44160i	−0.144869	−	0.144869i
$941$	29.7410	−	29.7410i	0.969527	−	0.969527i	−0.0300219	−	0.999549i	$-0.509558\pi$
$941$	29.7410	−	29.7410i	0.969527	−	0.969527i	0.999549	+	0.0300219i	$0.00955770\pi$
$942$	12.9677	−	12.9677i	0.422510	−	0.422510i
$943$			13.8544i			0.451162i
$944$			49.6955i			1.61745i
$945$	4.89051	−	4.89051i	0.159088	−	0.159088i
$946$	20.9313	−	20.9313i	0.680535	−	0.680535i
$947$	−29.2933	−	29.2933i	−0.951904	−	0.951904i	0.0469915	−	0.998895i	$-0.485037\pi$
$947$	−29.2933	−	29.2933i	−0.951904	−	0.951904i	−0.998895	+	0.0469915i	$0.985037\pi$
$948$	−5.41921			−0.176008
$949$	3.96131	+	3.96131i	0.128590	+	0.128590i
$950$		−	17.5476i		−	0.569318i
$951$	−19.4870			−0.631910
$952$		0			0
$953$	27.0719			0.876945			0.438473	−	0.898744i	$-0.355520\pi$
$953$	27.0719			0.876945			0.438473	+	0.898744i	$0.355520\pi$
$954$		−	15.1925i		−	0.491876i
$955$	24.2879	+	24.2879i	0.785937	+	0.785937i
$956$	0.914467			0.0295760
$957$	1.98518	+	1.98518i	0.0641717	+	0.0641717i
$958$	−7.40639	+	7.40639i	−0.239290	+	0.239290i
$959$	−2.47342	+	2.47342i	−0.0798708	+	0.0798708i
$960$			29.3628i			0.947680i
$961$			19.4962i			0.628909i
$962$	13.9799	−	13.9799i	0.450732	−	0.450732i
$963$	4.49202	−	4.49202i	0.144753	−	0.144753i
$964$	−6.22133	−	6.22133i	−0.200376	−	0.200376i
$965$	2.98215			0.0959989
$966$	1.42706	+	1.42706i	0.0459150	+	0.0459150i
$967$			43.3637i			1.39448i	0.716836	+	0.697241i	$0.245589\pi$
$967$			43.3637i			1.39448i	−0.716836	+	0.697241i	$0.754411\pi$
$968$	20.0205			0.643484
$969$		0			0
$970$	22.0993			0.709564
$971$			1.27126i			0.0407966i	0.999792	+	0.0203983i	$0.00649344\pi$
$971$			1.27126i			0.0407966i	−0.999792	+	0.0203983i	$0.993507\pi$
$972$	−2.81647	−	2.81647i	−0.0903383	−	0.0903383i
$973$	−2.97090			−0.0952428
$974$	−8.30151	−	8.30151i	−0.265997	−	0.265997i
$975$	23.4372	−	23.4372i	0.750593	−	0.750593i
$976$	14.2680	−	14.2680i	0.456707	−	0.456707i
$977$		−	24.7641i		−	0.792275i	−0.918191	−	0.396138i	$-0.870350\pi$
$977$		−	24.7641i		−	0.792275i	0.918191	−	0.396138i	$-0.129650\pi$
$978$		−	19.9813i		−	0.638933i
$979$	−7.98318	+	7.98318i	−0.255144	+	0.255144i
$980$	5.96714	−	5.96714i	0.190613	−	0.190613i
$981$	13.0002	+	13.0002i	0.415065	+	0.415065i
$982$	−13.8266			−0.441224
$983$	−28.0116	−	28.0116i	−0.893432	−	0.893432i	0.101412	−	0.994845i	$-0.467664\pi$
$983$	−28.0116	−	28.0116i	−0.893432	−	0.893432i	−0.994845	+	0.101412i	$0.967664\pi$
$984$			16.7888i			0.535207i
$985$	60.0488			1.91331
$986$		0			0
$987$	2.39599			0.0762653
$988$			1.75103i			0.0557077i
$989$	−21.8682	−	21.8682i	−0.695369	−	0.695369i
$990$	−11.2763			−0.358385
$991$	23.5564	+	23.5564i	0.748293	+	0.748293i	0.974159	−	0.225865i	$-0.0725209\pi$
$991$	23.5564	+	23.5564i	0.748293	+	0.748293i	−0.225865	+	0.974159i	$0.572521\pi$
$992$	9.76591	−	9.76591i	0.310068	−	0.310068i
$993$	−8.60756	+	8.60756i	−0.273153	+	0.273153i
$994$		−	5.98545i		−	0.189847i
$995$		−	44.8417i		−	1.42158i
$996$	−0.710679	+	0.710679i	−0.0225187	+	0.0225187i
$997$	−18.3111	+	18.3111i	−0.579918	+	0.579918i	−0.934881	−	0.354962i	$-0.884494\pi$
$997$	−18.3111	+	18.3111i	−0.579918	+	0.579918i	0.354962	+	0.934881i	$0.384494\pi$
$998$	28.9177	+	28.9177i	0.915374	+	0.915374i
$999$	−22.1088			−0.699490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.c.d.251.1		12
17.2	even	8		289.2.a.d.1.3	✓	3
17.3	odd	16		289.2.d.f.134.1		24
17.4	even	4	inner	289.2.c.d.38.5		12
17.5	odd	16		289.2.d.f.155.6		24
17.6	odd	16		289.2.d.f.179.5		24
17.7	odd	16		289.2.d.f.110.1		24
17.8	even	8		289.2.b.d.288.2		6
17.9	even	8		289.2.b.d.288.1		6
17.10	odd	16		289.2.d.f.110.2		24
17.11	odd	16		289.2.d.f.179.6		24
17.12	odd	16		289.2.d.f.155.5		24
17.13	even	4	inner	289.2.c.d.38.6		12
17.14	odd	16		289.2.d.f.134.2		24
17.15	even	8		289.2.a.e.1.3	yes	3
17.16	even	2	inner	289.2.c.d.251.2		12
51.2	odd	8		2601.2.a.x.1.1		3
51.32	odd	8		2601.2.a.w.1.1		3
68.15	odd	8		4624.2.a.bd.1.2		3
68.19	odd	8		4624.2.a.bg.1.2		3
85.19	even	8		7225.2.a.t.1.1		3
85.49	even	8		7225.2.a.s.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.3	✓	3	17.2	even	8
289.2.a.e.1.3	yes	3	17.15	even	8
289.2.b.d.288.1		6	17.9	even	8
289.2.b.d.288.2		6	17.8	even	8
289.2.c.d.38.5		12	17.4	even	4	inner
289.2.c.d.38.6		12	17.13	even	4	inner
289.2.c.d.251.1		12	1.1	even	1	trivial
289.2.c.d.251.2		12	17.16	even	2	inner
289.2.d.f.110.1		24	17.7	odd	16
289.2.d.f.110.2		24	17.10	odd	16
289.2.d.f.134.1		24	17.3	odd	16
289.2.d.f.134.2		24	17.14	odd	16
289.2.d.f.155.5		24	17.12	odd	16
289.2.d.f.155.6		24	17.5	odd	16
289.2.d.f.179.5		24	17.6	odd	16
289.2.d.f.179.6		24	17.11	odd	16
2601.2.a.w.1.1		3	51.32	odd	8
2601.2.a.x.1.1		3	51.2	odd	8
4624.2.a.bd.1.2		3	68.15	odd	8
4624.2.a.bg.1.2		3	68.19	odd	8
7225.2.a.s.1.1		3	85.49	even	8
7225.2.a.t.1.1		3	85.19	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.c (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.53209i q^{2} +(-0.952682 - 0.952682i) q^{3} -0.347296 q^{4} +(2.49756 + 2.49756i) q^{5} +(-1.45959 + 1.45959i) q^{6} +(-0.245576 + 0.245576i) q^{7} -2.53209i q^{8} -1.18479i q^{9} +(3.82649 - 3.82649i) q^{10} +(1.24364 - 1.24364i) q^{11} +(0.330863 + 0.330863i) q^{12} +3.29086 q^{13} +(0.376244 + 0.376244i) q^{14} -4.75877i q^{15} -4.57398 q^{16} -1.81521 q^{18} -1.53209i q^{19} +(-0.867395 - 0.867395i) q^{20} +0.467911 q^{21} +(-1.90536 - 1.90536i) q^{22} +(-1.99065 + 1.99065i) q^{23} +(-2.41228 + 2.41228i) q^{24} +7.47565i q^{25} -5.04189i q^{26} +(-3.98678 + 3.98678i) q^{27} +(0.0852875 - 0.0852875i) q^{28} +(-0.837775 - 0.837775i) q^{29} -7.29086 q^{30} +(-5.02475 - 5.02475i) q^{31} +1.94356i q^{32} -2.36959 q^{33} -1.22668 q^{35} +0.411474i q^{36} +(2.77276 + 2.77276i) q^{37} -2.34730 q^{38} +(-3.13514 - 3.13514i) q^{39} +(6.32405 - 6.32405i) q^{40} +(3.47987 - 3.47987i) q^{41} -0.716881i q^{42} +10.9855i q^{43} +(-0.431911 + 0.431911i) q^{44} +(2.95910 - 2.95910i) q^{45} +(3.04986 + 3.04986i) q^{46} +5.12061 q^{47} +(4.35755 + 4.35755i) q^{48} +6.87939i q^{49} +11.4534 q^{50} -1.14290 q^{52} +8.36959i q^{53} +(6.10810 + 6.10810i) q^{54} +6.21213 q^{55} +(0.621819 + 0.621819i) q^{56} +(-1.45959 + 1.45959i) q^{57} +(-1.28355 + 1.28355i) q^{58} -10.8648i q^{59} +1.65270i q^{60} +(-3.11938 + 3.11938i) q^{61} +(-7.69836 + 7.69836i) q^{62} +(0.290956 + 0.290956i) q^{63} -6.17024 q^{64} +(8.21913 + 8.21913i) q^{65} +3.63041i q^{66} +8.07192 q^{67} +3.79292 q^{69} +1.87939i q^{70} +(-7.95422 - 7.95422i) q^{71} -3.00000 q^{72} +(1.20373 + 1.20373i) q^{73} +(4.24811 - 4.24811i) q^{74} +(7.12192 - 7.12192i) q^{75} +0.532089i q^{76} +0.610815i q^{77} +(-4.80332 + 4.80332i) q^{78} +(-8.18951 + 8.18951i) q^{79} +(-11.4238 - 11.4238i) q^{80} +4.04189 q^{81} +(-5.33146 - 5.33146i) q^{82} +2.14796i q^{83} -0.162504 q^{84} +16.8307 q^{86} +1.59627i q^{87} +(-3.14900 - 3.14900i) q^{88} -6.41921 q^{89} +(-4.53360 - 4.53360i) q^{90} +(-0.808155 + 0.808155i) q^{91} +(0.691346 - 0.691346i) q^{92} +9.57398i q^{93} -7.84524i q^{94} +(3.82649 - 3.82649i) q^{95} +(1.85160 - 1.85160i) q^{96} +(2.88767 + 2.88767i) q^{97} +10.5398 q^{98} +(-1.47345 - 1.47345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{13} - 24 q^{16} - 36 q^{18} + 24 q^{21} - 24 q^{30} + 12 q^{35} - 24 q^{38} + 84 q^{47} + 84 q^{50} - 12 q^{52} - 24 q^{55} + 12 q^{64} - 36 q^{67} + 84 q^{69} - 36 q^{72} + 36 q^{81} - 12 q^{84}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q - 24 * q^13 - 24 * q^16 - 36 * q^18 + 24 * q^21 - 24 * q^30 + 12 * q^35 - 24 * q^38 + 84 * q^47 + 84 * q^50 - 12 * q^52 - 24 * q^55 + 12 * q^64 - 36 * q^67 + 84 * q^69 - 36 * q^72 + 36 * q^81 - 12 * q^84 + 24 * q^86 + 60 * q^89 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more