LMFDB - Embedded newform 639.2.z.a.269.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			269.7
Character	$\chi$	$=$	639.269
Dual form			639.2.z.a.620.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18077 - 0.504684i) q^{2} +(-0.242620 - 0.253761i) q^{4} +(-4.05679 - 1.31813i) q^{5} +(-3.29604 - 3.77262i) q^{7} +(1.06081 + 2.82652i) q^{8} +O(q^{10})$	\(q+(-1.18077 - 0.504684i) q^{2} +(-0.242620 - 0.253761i) q^{4} +(-4.05679 - 1.31813i) q^{5} +(-3.29604 - 3.77262i) q^{7} +(1.06081 + 2.82652i) q^{8} +(4.12488 + 3.60380i) q^{10} +(-2.61234 + 0.720959i) q^{11} +(0.293799 - 1.06456i) q^{13} +(1.98787 + 6.11804i) q^{14} +(0.142427 - 3.17138i) q^{16} +(-3.80603 + 2.76524i) q^{17} +(-0.949015 - 1.76357i) q^{19} +(0.649769 + 1.34926i) q^{20} +(3.44842 + 0.467120i) q^{22} +(1.97294 - 8.64400i) q^{23} +(10.6750 + 7.75583i) q^{25} +(-0.884173 + 1.10872i) q^{26} +(-0.157658 + 1.75172i) q^{28} +(5.91006 - 0.800571i) q^{29} +(3.07175 - 0.137953i) q^{31} +(0.851099 - 1.76732i) q^{32} +(5.88960 - 1.34426i) q^{34} +(8.39852 + 19.6493i) q^{35} +(0.232955 + 1.02064i) q^{37} +(0.230522 + 2.56131i) q^{38} +(-0.577763 - 12.8649i) q^{40} +(-3.91451 - 4.90864i) q^{41} +(-4.20303 - 0.378280i) q^{43} +(0.816758 + 0.487990i) q^{44} +(-6.69207 + 9.21084i) q^{46} +(-3.09526 + 0.561708i) q^{47} +(-2.42915 + 17.9327i) q^{49} +(-8.69042 - 14.5453i) q^{50} +(-0.341425 + 0.183728i) q^{52} +(-3.25474 + 3.40419i) q^{53} +(11.5480 + 0.518622i) q^{55} +(7.16691 - 13.3184i) q^{56} +(-7.38244 - 2.03742i) q^{58} +(2.45751 + 3.72296i) q^{59} +(1.22190 - 1.39858i) q^{61} +(-3.69665 - 1.38738i) q^{62} +(-6.67825 + 5.83461i) q^{64} +(-2.59511 + 3.93142i) q^{65} +(-0.237016 + 0.226611i) q^{67} +(1.62513 + 0.294917i) q^{68} -27.4399i q^{70} +(-8.26556 - 1.63725i) q^{71} +(-3.29820 + 7.71652i) q^{73} +(0.240037 - 1.32271i) q^{74} +(-0.217274 + 0.668700i) q^{76} +(11.3303 + 7.47904i) q^{77} +(2.65143 - 0.995100i) q^{79} +(-4.75809 + 12.6779i) q^{80} +(2.14481 + 7.77155i) q^{82} +(3.34828 - 2.21018i) q^{83} +(19.0852 - 6.20115i) q^{85} +(4.77189 + 2.56786i) q^{86} +(-4.80900 - 6.61903i) q^{88} +(0.930122 + 0.889287i) q^{89} +(-4.98454 + 2.40043i) q^{91} +(-2.67218 + 1.59656i) q^{92} +(3.93827 + 0.898885i) q^{94} +(1.52534 + 8.40534i) q^{95} +(-5.18423 - 4.13428i) q^{97} +(11.9186 - 19.9484i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{19}{70}\right)$	$-1$

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 $

$2$	−1.18077	−	0.504684i	−0.834928	−	0.356866i	−0.0672780	−	0.997734i	$-0.521431\pi$
$2$	−1.18077	−	0.504684i	−0.834928	−	0.356866i	−0.767650	+	0.640869i	$0.778574\pi$
$3$		0			0
$3$		0			0
$4$	−0.242620	−	0.253761i	−0.121310	−	0.126880i
$5$	−4.05679	−	1.31813i	−1.81425	−	0.589486i	−0.999959	−	0.00902996i	$-0.997126\pi$
$5$	−4.05679	−	1.31813i	−1.81425	−	0.589486i	−0.814292	−	0.580456i	$-0.802874\pi$
$6$		0			0
$7$	−3.29604	−	3.77262i	−1.24578	−	1.42592i	−0.865396	−	0.501089i	$-0.832933\pi$
$7$	−3.29604	−	3.77262i	−1.24578	−	1.42592i	−0.380389	−	0.924827i	$-0.624210\pi$
$8$	1.06081	+	2.82652i	0.375053	+	0.999326i
$9$		0			0
$10$	4.12488	+	3.60380i	1.30440	+	1.13962i
$11$	−2.61234	+	0.720959i	−0.787650	+	0.217377i	−0.636646	−	0.771156i	$-0.719679\pi$
$11$	−2.61234	+	0.720959i	−0.787650	+	0.217377i	−0.151003	+	0.988533i	$0.548250\pi$
$12$		0			0
$13$	0.293799	−	1.06456i	0.0814852	−	0.295255i	−0.911849	−	0.410526i	$-0.865345\pi$
$13$	0.293799	−	1.06456i	0.0814852	−	0.295255i	0.993334	+	0.115271i	$0.0367737\pi$
$14$	1.98787	+	6.11804i	0.531281	+	1.63512i
$15$		0			0
$16$	0.142427	−	3.17138i	0.0356067	−	0.792845i
$17$	−3.80603	+	2.76524i	−0.923097	+	0.670669i	−0.944293	−	0.329106i	$-0.893253\pi$
$17$	−3.80603	+	2.76524i	−0.923097	+	0.670669i	0.0211961	+	0.999775i	$0.493253\pi$
$18$		0			0
$19$	−0.949015	−	1.76357i	−0.217719	−	0.404590i	0.748185	−	0.663490i	$-0.230926\pi$
$19$	−0.949015	−	1.76357i	−0.217719	−	0.404590i	−0.965904	+	0.258900i	$0.916640\pi$
$20$	0.649769	+	1.34926i	0.145293	+	0.301704i
$21$		0			0
$22$	3.44842	+	0.467120i	0.735206	+	0.0995904i
$23$	1.97294	−	8.64400i	0.411386	−	1.80240i	−0.166226	−	0.986088i	$-0.553158\pi$
$23$	1.97294	−	8.64400i	0.411386	−	1.80240i	0.577612	−	0.816311i	$-0.303985\pi$
$24$		0			0
$25$	10.6750	+	7.75583i	2.13500	+	1.55117i
$26$	−0.884173	+	1.10872i	−0.173401	+	0.217437i
$27$		0			0
$28$	−0.157658	+	1.75172i	−0.0297945	+	0.331044i
$29$	5.91006	−	0.800571i	1.09747	−	0.148662i	0.436961	−	0.899481i	$-0.356055\pi$
$29$	5.91006	−	0.800571i	1.09747	−	0.148662i	0.660509	+	0.750818i	$0.270341\pi$
$30$		0			0
$31$	3.07175	−	0.137953i	0.551703	−	0.0247770i	0.232731	−	0.972541i	$-0.425234\pi$
$31$	3.07175	−	0.137953i	0.551703	−	0.0247770i	0.318972	+	0.947764i	$0.396662\pi$
$32$	0.851099	−	1.76732i	0.150454	−	0.312422i
$33$		0			0
$34$	5.88960	−	1.34426i	1.01006	−	0.230539i
$35$	8.39852	+	19.6493i	1.41961	+	3.32134i
$36$		0			0
$37$	0.232955	+	1.02064i	0.0382976	+	0.167793i	0.990460	−	0.137799i	$-0.0440028\pi$
$37$	0.232955	+	1.02064i	0.0382976	+	0.167793i	−0.952163	+	0.305592i	$0.901146\pi$
$38$	0.230522	+	2.56131i	0.0373957	+	0.415500i
$39$		0			0
$40$	−0.577763	−	12.8649i	−0.0913523	−	2.03412i
$41$	−3.91451	−	4.90864i	−0.611343	−	0.766600i	0.375754	−	0.926719i	$-0.377384\pi$
$41$	−3.91451	−	4.90864i	−0.611343	−	0.766600i	−0.987098	+	0.160119i	$0.948812\pi$
$42$		0			0
$43$	−4.20303	−	0.378280i	−0.640957	−	0.0576871i	−0.235606	−	0.971849i	$-0.575708\pi$
$43$	−4.20303	−	0.378280i	−0.640957	−	0.0576871i	−0.405350	+	0.914161i	$0.632850\pi$
$44$	0.816758	+	0.487990i	0.123131	+	0.0735673i
$45$		0			0
$46$	−6.69207	+	9.21084i	−0.986692	+	1.35806i
$47$	−3.09526	+	0.561708i	−0.451491	+	0.0819335i	−0.399539	−	0.916716i	$-0.630830\pi$
$47$	−3.09526	+	0.561708i	−0.451491	+	0.0819335i	−0.0519515	+	0.998650i	$0.516544\pi$
$48$		0			0
$49$	−2.42915	+	17.9327i	−0.347022	+	2.56182i
$50$	−8.69042	−	14.5453i	−1.22901	−	2.05702i
$51$		0			0
$52$	−0.341425	+	0.183728i	−0.0473471	+	0.0254785i
$53$	−3.25474	+	3.40419i	−0.447073	+	0.467602i	−0.907473	−	0.420109i	$-0.861992\pi$
$53$	−3.25474	+	3.40419i	−0.447073	+	0.467602i	0.460400	+	0.887712i	$0.347706\pi$
$54$		0			0
$55$	11.5480	+	0.518622i	1.55713	+	0.0699310i
$56$	7.16691	−	13.3184i	0.957719	−	1.77974i
$57$		0			0
$58$	−7.38244	−	2.03742i	−0.969361	−	0.267527i
$59$	2.45751	+	3.72296i	0.319940	+	0.484688i	0.958582	−	0.284815i	$-0.0919323\pi$
$59$	2.45751	+	3.72296i	0.319940	+	0.484688i	−0.638642	+	0.769504i	$0.720504\pi$
$60$		0			0
$61$	1.22190	−	1.39858i	0.156449	−	0.179070i	−0.669506	−	0.742807i	$-0.733494\pi$
$61$	1.22190	−	1.39858i	0.156449	−	0.179070i	0.825954	+	0.563737i	$0.190637\pi$
$62$	−3.69665	−	1.38738i	−0.469475	−	0.176197i
$63$		0			0
$64$	−6.67825	+	5.83461i	−0.834782	+	0.729327i
$65$	−2.59511	+	3.93142i	−0.321883	+	0.487632i
$66$		0			0
$67$	−0.237016	+	0.226611i	−0.0289561	+	0.0276849i	−0.705402	−	0.708807i	$-0.749234\pi$
$67$	−0.237016	+	0.226611i	−0.0289561	+	0.0276849i	0.676446	+	0.736492i	$0.263519\pi$
$68$	1.62513	+	0.294917i	0.197076	+	0.0357640i
$69$		0			0
$70$		−	27.4399i		−	3.27969i
$71$	−8.26556	−	1.63725i	−0.980941	−	0.194306i
$71$	−8.26556	−	1.63725i	−0.980941	−	0.194306i
$72$		0			0
$73$	−3.29820	+	7.71652i	−0.386025	+	0.903150i	0.607994	+	0.793942i	$0.291974\pi$
$73$	−3.29820	+	7.71652i	−0.386025	+	0.903150i	−0.994019	+	0.109209i	$0.965168\pi$
$74$	0.240037	−	1.32271i	0.0279037	−	0.153762i
$75$		0			0
$76$	−0.217274	+	0.668700i	−0.0249230	+	0.0767051i
$77$	11.3303	+	7.47904i	1.29120	+	0.852316i
$78$		0			0
$79$	2.65143	−	0.995100i	0.298310	−	0.111957i	−0.197732	−	0.980256i	$-0.563358\pi$
$79$	2.65143	−	0.995100i	0.298310	−	0.111957i	0.496042	+	0.868299i	$0.334786\pi$
$80$	−4.75809	+	12.6779i	−0.531970	+	1.41743i
$81$		0			0
$82$	2.14481	+	7.77155i	0.236855	+	0.858224i
$83$	3.34828	−	2.21018i	0.367521	−	0.242599i	−0.353616	−	0.935391i	$-0.615048\pi$
$83$	3.34828	−	2.21018i	0.367521	−	0.242599i	0.721137	+	0.692792i	$0.243620\pi$
$84$		0			0
$85$	19.0852	−	6.20115i	2.07008	−	0.672609i
$86$	4.77189	+	2.56786i	0.514566	+	0.276900i
$87$		0			0
$88$	−4.80900	−	6.61903i	−0.512642	−	0.705591i
$89$	0.930122	+	0.889287i	0.0985927	+	0.0942643i	0.738750	−	0.673980i	$-0.235416\pi$
$89$	0.930122	+	0.889287i	0.0985927	+	0.0942643i	−0.640157	+	0.768244i	$0.721131\pi$
$90$		0			0
$91$	−4.98454	+	2.40043i	−0.522522	+	0.251633i
$92$	−2.67218	+	1.59656i	−0.278595	+	0.166452i
$93$		0			0
$94$	3.93827	+	0.898885i	0.406202	+	0.0927129i
$95$	1.52534	+	8.40534i	0.156497	+	0.862370i
$96$		0			0
$97$	−5.18423	−	4.13428i	−0.526378	−	0.419773i	0.323911	−	0.946087i	$-0.395002\pi$
$97$	−5.18423	−	4.13428i	−0.526378	−	0.419773i	−0.850290	+	0.526315i	$0.823573\pi$
$98$	11.9186	−	19.9484i	1.20396	−	2.01509i
$99$		0			0
$100$	−0.621841	−	4.59061i	−0.0621841	−	0.459061i
$101$	−1.48672	+	1.18562i	−0.147934	+	0.117974i	−0.694660	−	0.719338i	$-0.744445\pi$
$101$	−1.48672	+	1.18562i	−0.147934	+	0.117974i	0.546726	+	0.837312i	$0.315874\pi$
$102$		0			0
$103$	−13.1655	−	6.34018i	−1.29724	−	0.624717i	−0.347476	−	0.937689i	$-0.612961\pi$
$103$	−13.1655	−	6.34018i	−1.29724	−	0.624717i	−0.949762	+	0.312972i	$0.898675\pi$
$104$	3.32066	−	0.298865i	0.325617	−	0.0293061i
$105$		0			0
$106$	5.56114	−	2.37694i	0.540145	−	0.230869i
$107$	13.1265	−	5.61054i	1.26899	−	0.542391i	0.350026	−	0.936740i	$-0.386173\pi$
$107$	13.1265	−	5.61054i	1.26899	−	0.542391i	0.918961	+	0.394349i	$0.129030\pi$
$108$		0			0
$109$	13.0266	−	1.17241i	1.24772	−	0.112297i	0.553984	−	0.832527i	$-0.313107\pi$
$109$	13.0266	−	1.17241i	1.24772	−	0.112297i	0.693735	+	0.720231i	$0.255964\pi$
$110$	−13.3738	−	6.44047i	−1.27514	−	0.614075i
$111$		0			0
$112$	−12.4338	+	9.91566i	−1.17489	+	0.936942i
$113$	−1.00506	−	7.41964i	−0.0945480	−	0.697981i	−0.974737	−	0.223357i	$-0.928298\pi$
$113$	−1.00506	−	7.41964i	−0.0945480	−	0.697981i	0.880189	−	0.474624i	$-0.157416\pi$
$114$		0			0
$115$	−19.3977	+	32.4663i	−1.80885	+	3.02750i
$116$	−1.63705	−	1.30551i	−0.151997	−	0.121213i
$117$		0			0
$118$	−1.02282	−	5.63621i	−0.0941584	−	0.518856i
$119$	22.9770	+	5.24435i	2.10630	+	0.480749i
$120$		0			0
$121$	−3.13841	+	1.87511i	−0.285310	+	0.170465i
$122$	−2.14862	+	1.03472i	−0.194527	+	0.0936794i
$123$		0			0
$124$	−0.780277	−	0.746021i	−0.0700709	−	0.0669947i
$125$	−20.5468	−	28.2802i	−1.83776	−	2.52946i
$126$		0			0
$127$	6.81419	+	3.66687i	0.604661	+	0.325382i	0.747396	−	0.664379i	$-0.231304\pi$
$127$	6.81419	+	3.66687i	0.604661	+	0.325382i	−0.142735	+	0.989761i	$0.545590\pi$
$128$	7.09895	−	2.30659i	0.627464	−	0.203876i
$129$		0			0
$130$	5.04834	−	3.33238i	0.442769	−	0.292269i
$131$	3.67333	+	13.3100i	0.320940	+	1.16290i	0.929326	+	0.369259i	$0.120389\pi$
$131$	3.67333	+	13.3100i	0.320940	+	1.16290i	−0.608386	+	0.793641i	$0.708183\pi$
$132$		0			0
$133$	−3.52527	+	9.39305i	−0.305680	+	0.814481i
$134$	0.394228	−	0.147956i	0.0340561	−	0.0127815i
$135$		0			0
$136$	−11.8535	−	7.82441i	−1.01643	−	0.670938i
$137$	4.64049	−	14.2819i	0.396463	−	1.22019i	−0.531353	−	0.847151i	$-0.678316\pi$
$137$	4.64049	−	14.2819i	0.396463	−	1.22019i	0.927816	−	0.373038i	$-0.121684\pi$
$138$		0			0
$139$	−0.832730	+	4.58872i	−0.0706312	+	0.389210i	0.929177	+	0.369635i	$0.120517\pi$
$139$	−0.832730	+	4.58872i	−0.0706312	+	0.389210i	−0.999808	+	0.0195755i	$0.993769\pi$
$140$	2.94858	−	6.89854i	0.249200	−	0.583033i
$141$		0			0
$142$	8.93340	+	6.10471i	0.749674	+	0.512296i
$143$			2.99280i			0.250270i
$144$		0			0
$145$	−25.0311	−	4.54248i	−2.07872	−	0.377232i
$146$	7.78881	−	7.44686i	0.644606	−	0.616307i
$147$		0			0
$148$	0.202480	−	0.306744i	0.0166437	−	0.0252142i
$149$	−1.90996	+	1.66869i	−0.156470	+	0.136704i	−0.732614	−	0.680645i	$-0.761700\pi$
$149$	−1.90996	+	1.66869i	−0.156470	+	0.136704i	0.576143	+	0.817349i	$0.304557\pi$
$150$		0			0
$151$	−15.9723	−	5.99452i	−1.29981	−	0.487827i	−0.396982	−	0.917826i	$-0.629942\pi$
$151$	−15.9723	−	5.99452i	−1.29981	−	0.487827i	−0.902829	+	0.429999i	$0.858514\pi$
$152$	3.97803	−	4.55322i	0.322661	−	0.369315i
$153$		0			0
$154$	−9.60385	−	14.5492i	−0.773901	−	1.17241i
$155$	−12.6433	−	3.48933i	−1.01553	−	0.280270i
$156$		0			0
$157$	−7.37007	+	13.6959i	−0.588195	+	1.09305i	0.396380	+	0.918087i	$0.370266\pi$
$157$	−7.37007	+	13.6959i	−0.588195	+	1.09305i	−0.984575	+	0.174963i	$0.944019\pi$
$158$	−3.63294	−	0.163155i	−0.289021	−	0.0129799i
$159$		0			0
$160$	−5.78229	+	6.04780i	−0.457130	+	0.478121i
$161$	−39.1134	+	21.0478i	−3.08257	+	1.65880i
$162$		0			0
$163$	−0.768090	−	1.28557i	−0.0601614	−	0.100693i	0.826890	−	0.562363i	$-0.190108\pi$
$163$	−0.768090	−	1.28557i	−0.0601614	−	0.100693i	−0.887052	+	0.461670i	$0.847251\pi$
$164$	−0.295881	+	2.18428i	−0.0231044	+	0.170564i
$165$		0			0
$166$	−5.06898	+	0.919884i	−0.393429	+	0.0713968i
$167$	−4.64693	+	6.39595i	−0.359590	+	0.494934i	−0.950035	−	0.312145i	$-0.898953\pi$
$167$	−4.64693	+	6.39595i	−0.359590	+	0.494934i	0.590444	+	0.807079i	$0.298953\pi$
$168$		0			0
$169$	10.1129	+	6.04216i	0.777913	+	0.464781i
$170$	−25.6648	−	2.30987i	−1.96840	−	0.177159i
$171$		0			0
$172$	0.923749	+	1.15834i	0.0704352	+	0.0883229i
$173$	−0.284201	−	6.32822i	−0.0216074	−	0.481126i	−0.980400	−	0.197018i	$-0.936874\pi$
$173$	−0.284201	−	6.32822i	−0.0216074	−	0.481126i	0.958792	−	0.284107i	$-0.0916973\pi$
$174$		0			0
$175$	−5.92536	−	65.8361i	−0.447915	−	4.97674i
$176$	1.91437	+	8.38740i	0.144301	+	0.632224i
$177$		0			0
$178$	−0.649448	−	1.51946i	−0.0486782	−	0.113888i
$179$	9.79184	−	2.23492i	0.731877	−	0.167046i	0.159687	−	0.987168i	$-0.448951\pi$
$179$	9.79184	−	2.23492i	0.731877	−	0.167046i	0.572189	+	0.820122i	$0.306094\pi$
$180$		0			0
$181$	8.67597	−	18.0158i	0.644880	−	1.33911i	−0.280422	−	0.959877i	$-0.590474\pi$
$181$	8.67597	−	18.0158i	0.644880	−	1.33911i	0.925302	−	0.379230i	$-0.123811\pi$
$182$	7.09704	−	0.318728i	0.526067	−	0.0236257i
$183$		0			0
$184$	26.5254	−	3.59310i	1.95548	−	0.264887i
$185$	0.400291	−	4.44760i	0.0294300	−	0.326994i
$186$		0			0
$187$	7.94900	−	9.96773i	0.581288	−	0.728913i
$188$	0.893513	+	0.649175i	0.0651662	+	0.0473460i
$189$		0			0
$190$	2.44097	−	10.6946i	0.177086	−	0.775865i
$191$	−9.38187	−	1.27086i	−0.678848	−	0.0919563i	−0.213311	−	0.976984i	$-0.568425\pi$
$191$	−9.38187	−	1.27086i	−0.678848	−	0.0919563i	−0.465538	+	0.885028i	$0.654139\pi$
$192$		0			0
$193$	−8.73413	−	18.1366i	−0.628697	−	1.30550i	−0.935364	−	0.353685i	$-0.884928\pi$
$193$	−8.73413	−	18.1366i	−0.628697	−	1.30550i	0.306668	−	0.951817i	$-0.400786\pi$
$194$	4.03486	+	7.49802i	0.289686	+	0.538327i
$195$		0			0
$196$	5.13999	−	3.73442i	0.367142	−	0.266744i
$197$	−0.233192	+	5.19242i	−0.0166142	+	0.369944i	0.973412	+	0.229061i	$0.0735656\pi$
$197$	−0.233192	+	5.19242i	−0.0166142	+	0.369944i	−0.990026	+	0.140883i	$0.955006\pi$
$198$		0			0
$199$	5.93541	+	18.2673i	0.420750	+	1.29494i	0.907006	+	0.421118i	$0.138362\pi$
$199$	5.93541	+	18.2673i	0.420750	+	1.29494i	−0.486256	+	0.873817i	$0.661638\pi$
$200$	−10.5979	+	38.4005i	−0.749382	+	2.71533i
$201$		0			0
$202$	2.35384	−	0.649618i	0.165616	−	0.0457070i
$203$	−22.5000	−	19.6577i	−1.57919	−	1.37970i
$204$		0			0
$205$	9.41010	+	25.0731i	0.657230	+	1.75118i
$206$	12.3456	+	14.1307i	0.860161	+	0.984533i
$207$		0			0
$208$	−3.33427	−	1.08337i	−0.231190	−	0.0751181i
$209$	3.75061	+	3.92283i	0.259435	+	0.271348i
$210$		0			0
$211$	13.6575	+	5.83750i	0.940222	+	0.401870i	0.807889	−	0.589335i	$-0.200610\pi$
$211$	13.6575	+	5.83750i	0.940222	+	0.401870i	0.132333	+	0.991205i	$0.457753\pi$
$212$	1.65352			0.113564
$213$		0			0
$214$	−18.3309			−1.25307
$215$	16.5522	+	7.07475i	1.12885	+	0.482494i
$216$		0			0
$217$	−10.6451	−	11.1339i	−0.722634	−	0.755816i
$218$	−15.9730	−	5.18996i	−1.08183	−	0.351508i
$219$		0			0
$220$	−2.67018	−	3.05626i	−0.180023	−	0.206053i
$221$	1.82555	+	4.86416i	0.122800	+	0.327198i
$222$		0			0
$223$	−0.266076	−	0.232463i	−0.0178178	−	0.0155669i	0.648984	−	0.760802i	$-0.275194\pi$
$223$	−0.266076	−	0.232463i	−0.0178178	−	0.0155669i	−0.666802	+	0.745235i	$0.732337\pi$
$224$	−9.47269	+	2.61430i	−0.632921	+	0.174675i
$225$		0			0
$226$	−2.55783	+	9.26810i	−0.170145	+	0.616505i
$227$	−7.57550	−	23.3150i	−0.502803	−	1.54747i	−0.804432	−	0.594044i	$-0.797530\pi$
$227$	−7.57550	−	23.3150i	−0.502803	−	1.54747i	0.301629	−	0.953425i	$-0.402470\pi$
$228$		0			0
$229$	−0.241777	+	5.38357i	−0.0159770	+	0.355757i	0.975041	+	0.222026i	$0.0712670\pi$
$229$	−0.241777	+	5.38357i	−0.0159770	+	0.355757i	−0.991018	+	0.133730i	$0.957304\pi$
$230$	39.2894	−	28.5454i	2.59067	−	1.88223i
$231$		0			0
$232$	8.53228	+	15.8556i	0.560172	+	1.04097i
$233$	6.71444	+	13.9427i	0.439877	+	0.913415i	0.996575	+	0.0826994i	$0.0263541\pi$
$233$	6.71444	+	13.9427i	0.439877	+	0.913415i	−0.556697	+	0.830716i	$0.687932\pi$
$234$		0			0
$235$	13.2972	+	1.80123i	0.867416	+	0.117499i
$236$	0.348502	−	1.52688i	0.0226855	−	0.0993917i
$237$		0			0
$238$	−24.4837	−	17.7885i	−1.58705	−	1.15306i
$239$	−8.92682	+	11.1939i	−0.577428	+	0.724071i	−0.981672	−	0.190580i	$-0.938963\pi$
$239$	−8.92682	+	11.1939i	−0.577428	+	0.724071i	0.404244	+	0.914651i	$0.367535\pi$
$240$		0			0
$241$	−1.87611	+	20.8453i	−0.120851	+	1.34277i	0.675244	+	0.737594i	$0.264038\pi$
$241$	−1.87611	+	20.8453i	−0.120851	+	1.34277i	−0.796095	+	0.605171i	$0.793105\pi$
$242$	4.65207	−	0.630166i	0.299046	−	0.0405086i
$243$		0			0
$244$	−0.651363	+	0.0292528i	−0.0416993	+	0.00187272i
$245$	33.4922	−	69.5473i	2.13974	−	4.44322i
$246$		0			0
$247$	−2.15624	+	0.492147i	−0.137198	+	0.0313146i
$248$	3.64848	+	8.53604i	0.231679	+	0.542039i
$249$		0			0
$250$	9.98838	+	43.7620i	0.631721	+	2.76775i
$251$	−0.124831	−	1.38698i	−0.00787923	−	0.0875455i	0.991072	−	0.133325i	$-0.0425655\pi$
$251$	−0.124831	−	1.38698i	−0.00787923	−	0.0875455i	−0.998952	+	0.0457800i	$0.985423\pi$
$252$		0			0
$253$	1.07800	+	24.0035i	0.0677731	+	1.50908i
$254$	−6.19536	−	7.76873i	−0.388731	−	0.487454i
$255$		0			0
$256$	8.11834	+	0.730664i	0.507396	+	0.0456665i
$257$	3.97503	+	2.37497i	0.247955	+	0.148146i	0.631500	−	0.775376i	$-0.282440\pi$
$257$	3.97503	+	2.37497i	0.247955	+	0.148146i	−0.383545	+	0.923522i	$0.625297\pi$
$258$		0			0
$259$	3.08267	−	4.24293i	0.191548	−	0.263643i
$260$	1.62727	−	0.295305i	0.100919	−	0.0183140i
$261$		0			0
$262$	2.38000	−	17.5699i	0.147037	−	1.08547i
$263$	5.84599	+	9.78454i	0.360479	+	0.603340i	0.983937	−	0.178517i	$-0.0571298\pi$
$263$	5.84599	+	9.78454i	0.360479	+	0.603340i	−0.623458	+	0.781857i	$0.714273\pi$
$264$		0			0
$265$	17.6910	−	9.51992i	1.08675	−	0.584804i
$266$	8.90305	−	9.31186i	0.545881	−	0.570947i
$267$		0			0
$268$	0.115010	+	0.00516510i	0.00702535	+	0.000315509i
$269$	−14.3792	+	26.7211i	−0.876716	+	1.62921i	−0.103895	+	0.994588i	$0.533130\pi$
$269$	−14.3792	+	26.7211i	−0.876716	+	1.62921i	−0.772822	+	0.634623i	$0.781155\pi$
$270$		0			0
$271$	25.4444	+	7.02221i	1.54564	+	0.426569i	0.931832	−	0.362889i	$-0.118210\pi$
$271$	25.4444	+	7.02221i	1.54564	+	0.426569i	0.613805	+	0.789458i	$0.289638\pi$
$272$	8.22754	+	12.4642i	0.498868	+	0.755753i
$273$		0			0
$274$	−12.6872	+	14.5217i	−0.766462	+	0.877286i
$275$	−33.4783	−	12.5646i	−2.01882	−	0.757675i
$276$		0			0
$277$	−5.68516	+	4.96698i	−0.341588	+	0.298437i	−0.811588	−	0.584230i	$-0.801397\pi$
$277$	−5.68516	+	4.96698i	−0.341588	+	0.298437i	0.470000	+	0.882666i	$0.344254\pi$
$278$	3.29912	−	4.99795i	0.197868	−	0.299757i
$279$		0			0
$280$	−46.6300	+	44.5828i	−2.78667	+	2.66433i
$281$	−9.02141	−	1.63714i	−0.538172	−	0.0976639i	−0.0973363	−	0.995252i	$-0.531032\pi$
$281$	−9.02141	−	1.63714i	−0.538172	−	0.0976639i	−0.440836	+	0.897588i	$0.645318\pi$
$282$		0			0
$283$		−	28.7651i		−	1.70991i	−0.518705	−	0.854953i	$-0.673586\pi$
$283$		−	28.7651i		−	1.70991i	0.518705	−	0.854953i	$-0.326414\pi$
$284$	1.58992	+	2.49471i	0.0943444	+	0.148034i
$285$		0			0
$286$	1.51042	−	3.53380i	0.0893129	−	0.208958i
$287$	−5.61605	+	30.9470i	−0.331505	+	1.82674i
$288$		0			0
$289$	1.58599	−	4.88118i	0.0932937	−	0.287128i
$290$	27.2634	+	17.9964i	1.60096	+	1.05679i
$291$		0			0
$292$	2.75836	−	1.03523i	0.161421	−	0.0605823i
$293$	−6.93245	+	18.4714i	−0.404998	+	1.07911i	0.562625	+	0.826712i	$0.309792\pi$
$293$	−6.93245	+	18.4714i	−0.404998	+	1.07911i	−0.967623	+	0.252401i	$0.918780\pi$
$294$		0			0
$295$	−5.06223	−	18.3426i	−0.294734	−	1.06795i
$296$	−2.63775	+	1.74116i	−0.153316	+	0.101203i
$297$		0			0
$298$	3.09738	−	1.00640i	0.179427	−	0.0582992i
$299$	−8.62238	−	4.63990i	−0.498645	−	0.268333i
$300$		0			0
$301$	12.4262	+	17.1033i	0.716237	+	0.985816i
$302$	15.8343	+	15.1391i	0.911161	+	0.871159i
$303$		0			0
$304$	−5.72810	+	2.75851i	−0.328529	+	0.158211i
$305$	−6.80051	+	4.06312i	−0.389396	+	0.232653i
$306$		0			0
$307$	17.6755	+	4.03432i	1.00879	+	0.230251i	0.694822	−	0.719182i	$-0.255483\pi$
$307$	17.6755	+	4.03432i	1.00879	+	0.230251i	0.313972	+	0.949432i	$0.398340\pi$
$308$	−0.851064	−	4.68975i	−0.0484939	−	0.267223i
$309$		0			0
$310$	13.1678	+	10.5010i	0.747880	+	0.596414i
$311$	3.41505	−	5.71582i	0.193649	−	0.324115i	−0.746189	−	0.665734i	$-0.768118\pi$
$311$	3.41505	−	5.71582i	0.193649	−	0.324115i	0.939838	+	0.341620i	$0.110976\pi$
$312$		0			0
$313$	1.67218	+	12.3445i	0.0945172	+	0.697754i	0.974764	+	0.223238i	$0.0716627\pi$
$313$	1.67218	+	12.3445i	0.0945172	+	0.697754i	−0.880247	+	0.474516i	$0.842623\pi$
$314$	15.6144	−	12.4521i	0.881173	−	0.702712i
$315$		0			0
$316$	−0.895809	−	0.431399i	−0.0503932	−	0.0242681i
$317$	20.9781	−	1.88806i	1.17825	−	0.106044i	0.516848	−	0.856077i	$-0.327105\pi$
$317$	20.9781	−	1.88806i	1.17825	−	0.106044i	0.661400	+	0.750033i	$0.269963\pi$
$318$		0			0
$319$	−14.8619	+	6.35227i	−0.832106	+	0.355659i
$320$	34.7830	−	14.8670i	1.94443	−	0.831090i
$321$		0			0
$322$	56.8063	−	5.11266i	3.16569	−	0.284917i
$323$	8.48866	+	4.08792i	0.472322	+	0.227458i
$324$		0			0
$325$	11.3928	−	9.08547i	0.631960	−	0.503971i
$326$	0.258131	+	1.90560i	0.0142965	+	0.105541i
$327$		0			0
$328$	9.72181	−	16.2716i	0.536797	−	0.898447i
$329$	12.3212	+	9.82584i	0.679290	+	0.541716i
$330$		0			0
$331$	2.82568	+	15.5708i	0.155313	+	0.855848i	0.963658	+	0.267138i	$0.0860780\pi$
$331$	2.82568	+	15.5708i	0.155313	+	0.855848i	−0.808345	+	0.588709i	$0.799636\pi$
$332$	−1.37322	−	0.313428i	−0.0753651	−	0.0172016i
$333$		0			0
$334$	8.71488	−	5.20690i	0.476857	−	0.284909i
$335$	1.26023	−	0.606893i	0.0688536	−	0.0331581i
$336$		0			0
$337$	3.15877	+	3.02009i	0.172069	+	0.164515i	0.772184	−	0.635399i	$-0.219164\pi$
$337$	3.15877	+	3.02009i	0.172069	+	0.164515i	−0.600115	+	0.799914i	$0.704879\pi$
$338$	−8.89156	−	12.2382i	−0.483637	−	0.665670i
$339$		0			0
$340$	−6.20406	−	3.33855i	−0.336463	−	0.181058i
$341$	−7.92500	+	2.57499i	−0.429163	+	0.139444i
$342$		0			0
$343$	46.3935	−	30.6241i	2.50501	−	1.65355i
$344$	−3.38941	−	12.2812i	−0.182745	−	0.662160i
$345$		0			0
$346$	−2.85818	+	7.61559i	−0.153657	+	0.409416i
$347$	−19.6704	+	7.38242i	−1.05596	+	0.396309i	−0.818152	−	0.575002i	$-0.805001\pi$
$347$	−19.6704	+	7.38242i	−1.05596	+	0.396309i	−0.237811	+	0.971312i	$0.576430\pi$
$348$		0			0
$349$	−23.0803	−	15.2351i	−1.23546	−	0.815519i	−0.247297	−	0.968940i	$-0.579542\pi$
$349$	−23.0803	−	15.2351i	−1.23546	−	0.815519i	−0.988161	+	0.153421i	$0.950971\pi$
$350$	−26.2300	+	80.7275i	−1.40205	+	4.31507i
$351$		0			0
$352$	−0.949188	+	5.23046i	−0.0505919	+	0.278784i
$353$	−8.69423	+	20.3412i	−0.462747	+	1.08265i	0.511929	+	0.859028i	$0.328931\pi$
$353$	−8.69423	+	20.3412i	−0.462747	+	1.08265i	−0.974676	+	0.223623i	$0.928212\pi$
$354$		0			0
$355$	31.3735	+	17.5371i	1.66513	+	0.930771i
$356$		−	0.451788i		−	0.0239447i
$357$		0			0
$358$	−12.6898	−	2.30286i	−0.670678	−	0.121710i
$359$	25.2310	−	24.1233i	1.33164	−	1.27318i	0.396896	−	0.917864i	$-0.370087\pi$
$359$	25.2310	−	24.1233i	1.33164	−	1.27318i	0.934746	−	0.355316i	$-0.115627\pi$
$360$		0			0
$361$	8.25751	−	12.5096i	0.434606	−	0.658399i
$362$	−19.3366	+	16.8939i	−1.01631	+	0.887923i
$363$		0			0
$364$	1.81848	+	0.682489i	0.0953145	+	0.0357721i
$365$	23.5515	−	26.9568i	1.23274	−	1.41098i
$366$		0			0
$367$	−5.72767	−	8.67705i	−0.298982	−	0.452939i	0.653767	−	0.756696i	$-0.273187\pi$
$367$	−5.72767	−	8.67705i	−0.298982	−	0.452939i	−0.952750	+	0.303757i	$0.901759\pi$
$368$	−27.1324	−	7.48807i	−1.41437	−	0.390342i
$369$		0			0
$370$	−2.71728	+	5.04956i	−0.141265	+	0.262514i
$371$	23.5705	+	1.05855i	1.22372	+	0.0549573i
$372$		0			0
$373$	8.09244	−	8.46403i	0.419011	−	0.438251i	−0.479274	−	0.877666i	$-0.659100\pi$
$373$	8.09244	−	8.46403i	0.419011	−	0.438251i	0.898284	+	0.439415i	$0.144814\pi$
$374$	−14.4165	+	7.75783i	−0.745458	+	0.401148i
$375$		0			0
$376$	−4.87117	−	8.15296i	−0.251211	−	0.420457i
$377$	0.884115	−	6.52680i	0.0455342	−	0.336147i
$378$		0			0
$379$	−11.5539	+	2.09673i	−0.593485	+	0.107702i	−0.466985	−	0.884265i	$-0.654660\pi$
$379$	−11.5539	+	2.09673i	−0.593485	+	0.107702i	−0.126500	+	0.991967i	$0.540374\pi$
$380$	1.76287	−	2.42638i	0.0904332	−	0.124471i
$381$		0			0
$382$	10.4364	+	6.23547i	0.533974	+	0.319035i
$383$	17.5053	+	1.57551i	0.894479	+	0.0805046i	0.527333	−	0.849659i	$-0.323192\pi$
$383$	17.5053	+	1.57551i	0.894479	+	0.0805046i	0.367146	+	0.930163i	$0.380335\pi$
$384$		0			0
$385$	−36.1061	−	45.2757i	−1.84014	−	2.30746i
$386$	1.15972	+	25.8231i	0.0590280	+	1.31436i
$387$		0			0
$388$	0.208679	+	2.31861i	0.0105941	+	0.117710i
$389$	4.71597	+	20.6620i	0.239109	+	1.04761i	0.941817	+	0.336127i	$0.109117\pi$
$389$	4.71597	+	20.6620i	0.239109	+	1.04761i	−0.702708	+	0.711479i	$0.748026\pi$
$390$		0			0
$391$	16.3937	+	38.3549i	0.829064	+	1.93969i
$392$	−53.2641	+	12.1572i	−2.69024	+	0.614030i
$393$		0			0
$394$	2.89588	−	6.01335i	0.145892	−	0.302948i
$395$	−12.0680	+	0.541973i	−0.607206	+	0.0272696i
$396$		0			0
$397$	−23.3988	+	3.16958i	−1.17435	+	0.159077i	−0.695306	−	0.718714i	$-0.744731\pi$
$397$	−23.3988	+	3.16958i	−1.17435	+	0.159077i	−0.479045	+	0.877790i	$0.659017\pi$
$398$	2.21088	−	24.5649i	0.110822	−	1.23133i
$399$		0			0
$400$	26.1171	−	32.7498i	1.30585	−	1.63749i
$401$	−24.7847	−	18.0071i	−1.23769	−	0.899234i	−0.240247	−	0.970712i	$-0.577228\pi$
$401$	−24.7847	−	18.0071i	−1.23769	−	0.899234i	−0.997442	+	0.0714778i	$0.977228\pi$
$402$		0			0
$403$	0.755620	−	3.31059i	0.0376401	−	0.164912i
$404$	0.661574	+	0.0896163i	0.0329145	+	0.00445858i
$405$		0			0
$406$	16.6464	+	34.5665i	0.826145	+	1.71551i
$407$	−1.34440	−	2.49831i	−0.0666394	−	0.123837i
$408$		0			0
$409$	−23.5264	+	17.0929i	−1.16331	+	0.845192i	−0.990192	−	0.139710i	$-0.955383\pi$
$409$	−23.5264	+	17.0929i	−1.16331	+	0.845192i	−0.173114	+	0.984902i	$0.555383\pi$
$410$	1.54287	−	34.3547i	0.0761969	−	1.69666i
$411$		0			0
$412$	1.58533	+	4.87915i	0.0781038	+	0.240379i
$413$	5.94528	−	21.5422i	0.292548	−	1.06002i
$414$		0			0
$415$	−16.4966	+	4.55276i	−0.809784	+	0.223486i
$416$	−1.63137	−	1.42528i	−0.0799843	−	0.0698801i
$417$		0			0
$418$	−2.44881	−	6.52482i	−0.119775	−	0.319139i
$419$	5.42796	+	6.21280i	0.265173	+	0.303515i	0.870209	−	0.492684i	$-0.163984\pi$
$419$	5.42796	+	6.21280i	0.265173	+	0.303515i	−0.605036	+	0.796198i	$0.706841\pi$
$420$		0			0
$421$	15.8465	+	5.14884i	0.772310	+	0.250939i	0.668554	−	0.743664i	$-0.266914\pi$
$421$	15.8465	+	5.14884i	0.772310	+	0.250939i	0.103757	+	0.994603i	$0.466914\pi$
$422$	−13.1802	−	13.7855i	−0.641604	−	0.671066i
$423$		0			0
$424$	−13.0747	−	5.58839i	−0.634963	−	0.271396i
$425$	−62.0760			−3.01113
$426$		0			0
$427$	−9.30374			−0.450240
$428$	−4.60849	−	1.96976i	−0.222760	−	0.0952121i
$429$		0			0
$430$	−15.9738	−	16.7073i	−0.770324	−	0.805696i
$431$	9.39949	+	3.05408i	0.452757	+	0.147110i	0.526514	−	0.850167i	$-0.323499\pi$
$431$	9.39949	+	3.05408i	0.452757	+	0.147110i	−0.0737566	+	0.997276i	$0.523499\pi$
$432$		0			0
$433$	−11.7274	−	13.4230i	−0.563581	−	0.645070i	0.398715	−	0.917075i	$-0.369456\pi$
$433$	−11.7274	−	13.4230i	−0.563581	−	0.645070i	−0.962296	+	0.272005i	$0.912313\pi$
$434$	6.95026	+	18.5189i	0.333623	+	0.888935i
$435$		0			0
$436$	−3.45802	−	3.02118i	−0.165609	−	0.144688i
$437$	−17.1166	+	4.72389i	−0.818799	+	0.225974i
$438$		0			0
$439$	−0.417620	+	1.51321i	−0.0199319	+	0.0722216i	−0.973252	−	0.229739i	$-0.926213\pi$
$439$	−0.417620	+	1.51321i	−0.0199319	+	0.0722216i	0.953320	+	0.301961i	$0.0976412\pi$
$440$	10.7844	+	33.1909i	0.514125	+	1.58231i
$441$		0			0
$442$	0.299315	−	6.66476i	0.0142369	−	0.317010i
$443$	13.2899	−	9.65571i	0.631424	−	0.458757i	−0.225469	−	0.974250i	$-0.572391\pi$
$443$	13.2899	−	9.65571i	0.631424	−	0.458757i	0.856893	+	0.515494i	$0.172391\pi$
$444$		0			0
$445$	−2.60111	−	4.83367i	−0.123304	−	0.229138i
$446$	0.196853	+	0.408769i	0.00932126	+	0.0193558i
$447$		0			0
$448$	44.0235	+	5.96339i	2.07992	+	0.281744i
$449$	0.171018	−	0.749278i	0.00807083	−	0.0353606i	−0.970732	−	0.240165i	$-0.922799\pi$
$449$	0.171018	−	0.749278i	0.00807083	−	0.0353606i	0.978803	+	0.204804i	$0.0656557\pi$
$450$		0			0
$451$	13.7649	+	10.0008i	0.648166	+	0.470920i
$452$	−1.63897	+	2.05520i	−0.0770905	+	0.0966685i
$453$		0			0
$454$	−2.82180	+	31.3528i	−0.132434	+	1.47146i
$455$	23.3853	−	3.16775i	1.09632	−	0.148507i
$456$		0			0
$457$	−32.8410	+	1.47489i	−1.53624	+	0.0689925i	−0.796804	−	0.604238i	$-0.793478\pi$
$457$	−32.8410	+	1.47489i	−1.53624	+	0.0689925i	−0.739433	+	0.673230i	$0.764906\pi$
$458$	3.00249	−	6.23473i	0.140297	−	0.291330i
$459$		0			0
$460$	12.9450	−	2.95460i	0.603562	−	0.137759i
$461$	1.60963	+	3.76591i	0.0749678	+	0.175396i	0.952820	−	0.303535i	$-0.0981671\pi$
$461$	1.60963	+	3.76591i	0.0749678	+	0.175396i	−0.877852	+	0.478931i	$0.841024\pi$
$462$		0			0
$463$	−2.95772	−	12.9586i	−0.137457	−	0.602238i	−0.995989	−	0.0894778i	$-0.971480\pi$
$463$	−2.95772	−	12.9586i	−0.137457	−	0.602238i	0.858532	−	0.512760i	$-0.171377\pi$
$464$	−1.69716	−	18.8570i	−0.0787889	−	0.875416i
$465$		0			0
$466$	−0.891542	−	19.8517i	−0.0412999	−	0.919613i
$467$	2.12455	+	2.66410i	0.0983124	+	0.123280i	0.828554	−	0.559909i	$-0.189164\pi$
$467$	2.12455	+	2.66410i	0.0983124	+	0.123280i	−0.730242	+	0.683189i	$0.760593\pi$
$468$		0			0
$469$	1.63613	+	0.147254i	0.0755495	+	0.00679957i
$470$	−14.7919	−	8.83774i	−0.682299	−	0.407655i
$471$		0			0
$472$	−7.91608	+	10.8955i	−0.364367	+	0.501508i
$473$	11.2525	−	2.04202i	0.517389	−	0.0938923i
$474$		0			0
$475$	3.54719	−	26.1864i	0.162756	−	1.20152i
$476$	−4.24387	−	7.10305i	−0.194518	−	0.325568i
$477$		0			0
$478$	16.1899	−	8.71214i	0.740507	−	0.398484i
$479$	0.213758	−	0.223574i	0.00976686	−	0.0102153i	−0.717893	−	0.696153i	$-0.754893\pi$
$479$	0.213758	−	0.223574i	0.00976686	−	0.0102153i	0.727660	+	0.685938i	$0.240608\pi$
$480$		0			0
$481$	1.15497	+	0.0518700i	0.0526623	+	0.00236507i
$482$	12.7356	−	23.6666i	0.580089	−	1.07799i
$483$		0			0
$484$	1.23727	+	0.341465i	0.0562396	+	0.0155212i
$485$	15.5818	+	23.6054i	0.707532	+	1.07187i
$486$		0			0
$487$	1.77560	−	2.03234i	0.0804602	−	0.0920941i	−0.711432	−	0.702755i	$-0.751953\pi$
$487$	1.77560	−	2.03234i	0.0804602	−	0.0920941i	0.791892	+	0.610661i	$0.209096\pi$
$488$	5.24932	+	1.97010i	0.237626	+	0.0891824i
$489$		0			0
$490$	−74.6460	+	65.2162i	−3.37216	+	2.94617i
$491$	1.77855	−	2.69438i	0.0802647	−	0.121596i	−0.792223	−	0.610231i	$-0.791077\pi$
$491$	1.77855	−	2.69438i	0.0802647	−	0.121596i	0.872488	+	0.488635i	$0.162505\pi$
$492$		0			0
$493$	−20.2801	+	19.3897i	−0.913368	+	0.873269i
$494$	2.79439	+	0.507107i	0.125726	+	0.0228158i
$495$		0			0
$496$		−	9.76134i		−	0.438297i
$497$	21.0668	+	36.5792i	0.944977	+	1.64080i
$498$		0			0
$499$	−1.52148	+	3.55969i	−0.0681109	+	0.159353i	−0.950125	−	0.311870i	$-0.899045\pi$
$499$	−1.52148	+	3.55969i	−0.0681109	+	0.159353i	0.882014	+	0.471224i	$0.156187\pi$
$500$	−2.19135	+	12.0753i	−0.0980001	+	0.540025i
$501$		0			0
$502$	−0.552591	+	1.70070i	−0.0246634	+	0.0759060i
$503$	−23.6991	−	15.6436i	−1.05669	−	0.697514i	−0.101899	−	0.994795i	$-0.532492\pi$
$503$	−23.6991	−	15.6436i	−1.05669	−	0.697514i	−0.954790	+	0.297281i	$0.903920\pi$
$504$		0			0
$505$	7.59413	−	2.85012i	0.337934	−	0.126829i
$506$	10.8413	−	28.8865i	0.481955	−	1.28416i
$507$		0			0
$508$	−0.722752	−	2.61883i	−0.0320669	−	0.116192i
$509$	30.1138	−	19.8779i	1.33477	−	0.881074i	0.336607	−	0.941645i	$-0.390721\pi$
$509$	30.1138	−	19.8779i	1.33477	−	0.881074i	0.998164	+	0.0605708i	$0.0192921\pi$
$510$		0			0
$511$	39.9825	−	12.9911i	1.76872	−	0.574692i
$512$	−22.3631	−	12.0341i	−0.988320	−	0.531838i
$513$		0			0
$514$	−3.49497	−	4.81042i	−0.154157	−	0.212178i
$515$	45.0526	+	43.0747i	1.98525	+	1.89810i
$516$		0			0
$517$	7.68091	−	3.69893i	0.337806	−	0.162679i
$518$	−5.78125	+	3.45414i	−0.254014	+	0.151766i
$519$		0			0
$520$	−13.8651	−	3.16463i	−0.608027	−	0.138778i
$521$	5.49203	+	30.2636i	0.240610	+	1.32587i	0.847377	+	0.530991i	$0.178180\pi$
$521$	5.49203	+	30.2636i	0.240610	+	1.32587i	−0.606767	+	0.794880i	$0.707534\pi$
$522$		0			0
$523$	13.3030	+	10.6088i	0.581702	+	0.463892i	0.869591	−	0.493772i	$-0.164382\pi$
$523$	13.3030	+	10.6088i	0.581702	+	0.463892i	−0.287890	+	0.957664i	$0.592954\pi$
$524$	2.48634	−	4.16142i	0.108616	−	0.181793i
$525$		0			0
$526$	−1.96465	−	14.5036i	−0.0856629	−	0.632389i
$527$	−11.3097	+	9.01919i	−0.492658	+	0.392882i
$528$		0			0
$529$	−50.1040	−	24.1288i	−2.17844	−	1.04908i
$530$	−25.6935	+	2.31246i	−1.11605	+	0.100447i
$531$		0			0
$532$	3.23889	−	1.38437i	0.140424	−	0.0600200i
$533$	−6.37560	+	2.72506i	−0.276158	+	0.118036i
$534$		0			0
$535$	−60.6469	+	5.45832i	−2.62199	+	0.235984i
$536$	−0.891949	−	0.429540i	−0.0385263	−	0.0185533i
$537$		0			0
$538$	30.4642	−	24.2944i	1.31340	−	1.04741i
$539$	−6.58300	−	48.5977i	−0.283550	−	2.09325i
$540$		0			0
$541$	−3.19485	+	5.34728i	−0.137357	+	0.229897i	−0.919397	−	0.393332i	$-0.871322\pi$
$541$	−3.19485	+	5.34728i	−0.137357	+	0.229897i	0.782039	+	0.623229i	$0.214180\pi$
$542$	−26.4999	−	21.1330i	−1.13827	−	0.907739i
$543$		0			0
$544$	1.64777	+	9.07997i	0.0706476	+	0.389301i
$545$	−54.3914	−	12.4145i	−2.32987	−	0.531778i
$546$		0			0
$547$	13.2877	−	7.93906i	0.568143	−	0.339450i	−0.199932	−	0.979810i	$-0.564072\pi$
$547$	13.2877	−	7.93906i	0.568143	−	0.339450i	0.768075	+	0.640360i	$0.221215\pi$
$548$	−4.75008	+	2.28752i	−0.202913	+	0.0977178i
$549$		0			0
$550$	33.1889	+	31.7318i	1.41518	+	1.35305i
$551$	−7.02059	−	9.66302i	−0.299087	−	0.411658i
$552$		0			0
$553$	−12.4934	−	6.72296i	−0.531271	−	0.285889i
$554$	9.21961	−	2.99563i	0.391704	−	0.127272i
$555$		0			0
$556$	1.36648	−	0.902003i	0.0579515	−	0.0382534i
$557$	8.90130	+	32.2531i	0.377160	+	1.36661i	0.868521	+	0.495653i	$0.165071\pi$
$557$	8.90130	+	32.2531i	0.377160	+	1.36661i	−0.491361	+	0.870956i	$0.663500\pi$
$558$		0			0
$559$	−1.63755	+	4.36323i	−0.0692609	+	0.184545i
$560$	63.5116	−	23.8363i	2.68385	−	1.00727i
$561$		0			0
$562$	9.82595	+	6.48605i	0.414482	+	0.273598i
$563$	0.545056	−	1.67751i	0.0229714	−	0.0706986i	−0.938914	−	0.344153i	$-0.888166\pi$
$563$	0.545056	−	1.67751i	0.0229714	−	0.0706986i	0.961885	+	0.273454i	$0.0881662\pi$
$564$		0			0
$565$	−5.70274	+	31.4247i	−0.239916	+	1.32205i
$566$	−14.5173	+	33.9649i	−0.610207	+	1.42765i
$567$		0			0
$568$	−4.14046	−	25.0996i	−0.173730	−	1.05315i
$569$			33.7144i			1.41338i	0.707522	+	0.706692i	$0.249813\pi$
$569$			33.7144i			1.41338i	−0.707522	+	0.706692i	$0.750187\pi$
$570$		0			0
$571$	−14.0614	−	2.55177i	−0.588453	−	0.106788i	−0.123840	−	0.992302i	$-0.539521\pi$
$571$	−14.0614	−	2.55177i	−0.588453	−	0.106788i	−0.464613	+	0.885514i	$0.653807\pi$
$572$	0.759456	−	0.726114i	0.0317544	−	0.0303603i
$573$		0			0
$574$	22.2497	−	33.7068i	0.928684	−	1.40690i
$575$	88.1024	−	76.9728i	3.67413	−	3.20999i
$576$		0			0
$577$	−31.0837	−	11.6659i	−1.29403	−	0.485659i	−0.393052	−	0.919516i	$-0.628581\pi$
$577$	−31.0837	−	11.6659i	−1.29403	−	0.485659i	−0.900982	+	0.433857i	$0.857152\pi$
$578$	−4.33614	+	4.96311i	−0.180360	+	0.206438i
$579$		0			0
$580$	4.92035	+	7.45401i	0.204306	+	0.309511i
$581$	−19.3742	−	5.34694i	−0.803777	−	0.221828i
$582$		0			0
$583$	6.04820	−	11.2394i	0.250491	−	0.465490i
$584$	−25.3097	−	1.13666i	−1.04732	−	0.0470353i
$585$		0			0
$586$	17.5079	−	18.3118i	0.723243	−	0.756453i
$587$	−9.22467	+	4.96401i	−0.380743	+	0.204886i	−0.653034	−	0.757328i	$-0.726504\pi$
$587$	−9.22467	+	4.96401i	−0.380743	+	0.204886i	0.272291	+	0.962215i	$0.412219\pi$
$588$		0			0
$589$	−3.15843	−	5.28632i	−0.130141	−	0.217819i
$590$	−3.27989	+	24.2131i	−0.135031	+	0.996839i
$591$		0			0
$592$	3.27002	−	0.593422i	0.134397	−	0.0243895i
$593$	15.9178	−	21.9090i	0.653667	−	0.899695i	−0.345584	−	0.938388i	$-0.612319\pi$
$593$	15.9178	−	21.9090i	0.653667	−	0.899695i	0.999251	+	0.0386925i	$0.0123193\pi$
$594$		0			0
$595$	−86.3001	−	51.5619i	−3.53796	−	2.11383i
$596$	0.886843	+	0.0798174i	0.0363265	+	0.00326945i
$597$		0			0
$598$	7.83934	+	9.83023i	0.320575	+	0.401988i
$599$	0.139343	+	3.10272i	0.00569342	+	0.126774i	0.999827	+	0.0186125i	$0.00592488\pi$
$599$	0.139343	+	3.10272i	0.00569342	+	0.126774i	−0.994133	+	0.108161i	$0.965504\pi$
$600$		0			0
$601$	1.29749	+	14.4163i	0.0529258	+	0.588053i	0.978047	+	0.208383i	$0.0668199\pi$
$601$	1.29749	+	14.4163i	0.0529258	+	0.588053i	−0.925122	+	0.379671i	$0.876037\pi$
$602$	−6.04076	−	26.4663i	−0.246203	−	1.07869i
$603$		0			0
$604$	2.35404	+	5.50755i	0.0957845	+	0.224099i
$605$	15.2035	−	3.47010i	0.618110	−	0.141080i
$606$		0			0
$607$	11.7613	−	24.4225i	0.477375	−	0.991280i	−0.513699	−	0.857970i	$-0.671725\pi$
$607$	11.7613	−	24.4225i	0.477375	−	0.991280i	0.991074	−	0.133309i	$-0.0425604\pi$
$608$	−3.92450	+	0.176249i	−0.159159	+	0.00714786i
$609$		0			0
$610$	10.0804	−	1.36548i	0.408144	−	0.0552868i
$611$	−0.311416	+	3.46011i	−0.0125985	+	0.139981i
$612$		0			0
$613$	−0.263828	+	0.330830i	−0.0106559	+	0.0133621i	−0.787131	−	0.616786i	$-0.788434\pi$
$613$	−0.263828	+	0.330830i	−0.0106559	+	0.0133621i	0.776475	+	0.630148i	$0.217006\pi$
$614$	−18.8346	−	13.6841i	−0.760102	−	0.552247i
$615$		0			0
$616$	−9.12040	+	39.9591i	−0.367471	+	1.61000i
$617$	−9.03184	−	1.22345i	−0.363608	−	0.0492541i	−0.0498492	−	0.998757i	$-0.515874\pi$
$617$	−9.03184	−	1.22345i	−0.363608	−	0.0492541i	−0.313759	+	0.949503i	$0.601588\pi$
$618$		0			0
$619$	20.5842	+	42.7436i	0.827350	+	1.71801i	0.685438	+	0.728131i	$0.259611\pi$
$619$	20.5842	+	42.7436i	0.827350	+	1.71801i	0.141912	+	0.989879i	$0.454675\pi$
$620$	2.18207	+	4.05496i	0.0876339	+	0.162851i
$621$		0			0
$622$	−6.91706	+	5.02554i	−0.277349	+	0.201506i
$623$	0.289226	−	6.44012i	0.0115876	−	0.258018i
$624$		0			0
$625$	25.6895	+	79.0642i	1.02758	+	3.16257i
$626$	4.25563	−	15.4199i	0.170089	−	0.616305i
$627$		0			0
$628$	5.26361	−	1.45266i	0.210041	−	0.0579676i
$629$	−3.70896	−	3.24042i	−0.147886	−	0.129204i
$630$		0			0
$631$	−16.7021	−	44.5026i	−0.664900	−	1.77162i	−0.635563	−	0.772049i	$-0.719232\pi$
$631$	−16.7021	−	44.5026i	−0.664900	−	1.77162i	−0.0293369	−	0.999570i	$-0.509340\pi$
$632$	5.62534	+	6.43872i	0.223764	+	0.256119i
$633$		0			0
$634$	−25.7231	−	8.35795i	−1.02160	−	0.331937i
$635$	−22.8103	−	23.8577i	−0.905199	−	0.946764i
$636$		0			0
$637$	18.3767	+	7.85459i	0.728112	+	0.311210i
$638$	20.7543			0.821671
$639$		0			0
$640$	−31.8393			−1.25856
$641$	−30.2679	−	12.9371i	−1.19551	−	0.510986i	−0.299105	−	0.954220i	$-0.596688\pi$
$641$	−30.2679	−	12.9371i	−1.19551	−	0.510986i	−0.896406	+	0.443235i	$0.853831\pi$
$642$		0			0
$643$	−23.3361	−	24.4077i	−0.920287	−	0.962544i	0.0791244	−	0.996865i	$-0.474788\pi$
$643$	−23.3361	−	24.4077i	−0.920287	−	0.962544i	−0.999411	+	0.0343205i	$0.989073\pi$
$644$	14.8308	+	4.81882i	0.584416	+	0.189888i
$645$		0			0
$646$	−7.96002	−	9.11098i	−0.313183	−	0.358467i
$647$	−8.70474	−	23.1937i	−0.342219	−	0.911838i	−0.988834	−	0.149022i	$-0.952387\pi$
$647$	−8.70474	−	23.1937i	−0.342219	−	0.911838i	0.646615	−	0.762816i	$-0.276184\pi$
$648$		0			0
$649$	−9.10394	−	7.95387i	−0.357361	−	0.312217i
$650$	−18.0376	+	4.97805i	−0.707491	+	0.195255i
$651$		0			0
$652$	−0.139872	+	0.506815i	−0.00547782	+	0.0198484i
$653$	14.1553	+	43.5656i	0.553941	+	1.70485i	0.698724	+	0.715391i	$0.253751\pi$
$653$	14.1553	+	43.5656i	0.553941	+	1.70485i	−0.144784	+	0.989463i	$0.546249\pi$
$654$		0			0
$655$	2.64241	−	58.8378i	0.103247	−	2.29898i
$656$	−16.1247	+	11.7153i	−0.629563	+	0.457404i
$657$		0			0
$658$	−9.58954	−	17.8203i	−0.373839	−	0.694709i
$659$	−3.89249	−	8.08285i	−0.151630	−	0.314863i	0.811293	−	0.584640i	$-0.198764\pi$
$659$	−3.89249	−	8.08285i	−0.151630	−	0.314863i	−0.962923	+	0.269777i	$0.913050\pi$
$660$		0			0
$661$	25.3096	+	3.42842i	0.984430	+	0.133350i	0.608718	−	0.793387i	$-0.291684\pi$
$661$	25.3096	+	3.42842i	0.984430	+	0.133350i	0.375712	+	0.926737i	$0.377398\pi$
$662$	4.52186	−	19.8115i	0.175747	−	0.769998i
$663$		0			0
$664$	9.79900	+	7.11939i	0.380275	+	0.276286i
$665$	26.6825	−	33.4589i	1.03470	−	1.29748i
$666$		0			0
$667$	4.74003	−	52.6660i	0.183535	−	2.03924i
$668$	2.75048	−	0.372578i	0.106419	−	0.0144155i
$669$		0			0
$670$	−1.79432	+	0.0805832i	−0.0693208	+	0.00311320i
$671$	−2.18370	+	4.53451i	−0.0843009	+	0.175053i
$672$		0			0
$673$	−21.2395	+	4.84779i	−0.818724	+	0.186868i	−0.611317	−	0.791386i	$-0.709360\pi$
$673$	−21.2395	+	4.84779i	−0.818724	+	0.186868i	−0.207408	+	0.978255i	$0.566503\pi$
$674$	−2.20558	−	5.16021i	−0.0849557	−	0.198764i
$675$		0			0
$676$	−0.920324	−	4.03220i	−0.0353971	−	0.155085i
$677$	−0.205439	−	2.28261i	−0.00789566	−	0.0877280i	0.991060	−	0.133416i	$-0.0425947\pi$
$677$	−0.205439	−	2.28261i	−0.00789566	−	0.0877280i	−0.998956	+	0.0456883i	$0.985452\pi$
$678$		0			0
$679$	1.49033	+	33.1849i	0.0571937	+	1.27352i
$680$	37.7735	+	47.3664i	1.44855	+	1.81642i
$681$		0			0
$682$	10.6571	+	0.959160i	0.408083	+	0.0367281i
$683$	−0.306936	−	0.183386i	−0.0117446	−	0.00701706i	0.507015	−	0.861937i	$-0.330749\pi$
$683$	−0.306936	−	0.183386i	−0.0117446	−	0.00701706i	−0.518760	+	0.854920i	$0.673606\pi$
$684$		0			0
$685$	−37.6509	+	51.8221i	−1.43857	+	1.98002i
$686$	−70.2354	+	12.7459i	−2.68160	+	0.486639i
$687$		0			0
$688$	−1.79829	+	13.2755i	−0.0685593	+	0.506125i
$689$	2.66772	+	4.46501i	0.101632	+	0.170103i
$690$		0			0
$691$	12.5939	−	6.77705i	0.479093	−	0.257811i	−0.216452	−	0.976293i	$-0.569449\pi$
$691$	12.5939	−	6.77705i	0.479093	−	0.257811i	0.695545	+	0.718482i	$0.255163\pi$
$692$	−1.53690	+	1.60747i	−0.0584243	+	0.0611070i
$693$		0			0
$694$	26.9520	+	1.21041i	1.02308	+	0.0459467i
$695$	9.42674	−	17.5178i	0.357577	−	0.664489i
$696$		0			0
$697$	28.4723	+	7.85785i	1.07846	+	0.297637i
$698$	19.5635	+	29.6374i	0.740489	+	1.12179i
$699$		0			0
$700$	−15.2690	+	17.4768i	−0.577115	+	0.660561i
$701$	12.1127	+	4.54596i	0.457489	+	0.171699i	0.569471	−	0.822012i	$-0.307148\pi$
$701$	12.1127	+	4.54596i	0.457489	+	0.171699i	−0.111981	+	0.993710i	$0.535720\pi$
$702$		0			0
$703$	1.57889	−	1.37944i	0.0595491	−	0.0520265i
$704$	13.2393	−	20.0567i	0.498976	−	0.755917i
$705$		0			0
$706$	20.5317	−	19.6303i	0.772721	−	0.738797i
$707$	9.37319	+	1.70098i	0.352515	+	0.0639721i
$708$		0			0
$709$			6.98478i			0.262319i	0.991361	+	0.131159i	$0.0418700\pi$
$709$			6.98478i			0.262319i	−0.991361	+	0.131159i	$0.958130\pi$
$710$	−28.1941	−	36.5409i	−1.05811	−	1.37136i
$711$		0			0
$712$	−1.52691	+	3.57237i	−0.0572232	+	0.133880i
$713$	4.86792	−	26.8244i	0.182305	−	1.00458i
$714$		0			0
$715$	3.94490	−	12.1412i	0.147531	−	0.454053i
$716$	−2.94284	−	1.94255i	−0.109979	−	0.0725965i
$717$		0			0
$718$	−41.9666	+	15.7503i	−1.56618	+	0.587797i
$719$	1.91025	−	5.08985i	0.0712405	−	0.189820i	−0.895792	−	0.444474i	$-0.853390\pi$
$719$	1.91025	−	5.08985i	0.0712405	−	0.189820i	0.967032	+	0.254655i	$0.0819619\pi$
$720$		0			0
$721$	19.4750	+	70.5660i	0.725286	+	2.62801i
$722$	−16.0636	+	10.6035i	−0.597825	+	0.394621i
$723$		0			0
$724$	−6.67669	+	2.16939i	−0.248137	+	0.0806246i
$725$	69.2988	+	37.2913i	2.57369	+	1.38496i
$726$		0			0
$727$	13.3591	+	18.3873i	0.495463	+	0.681946i	0.981384	−	0.192057i	$-0.0615158\pi$
$727$	13.3591	+	18.3873i	0.495463	+	0.681946i	−0.485921	+	0.874003i	$0.661516\pi$
$728$	−12.0725	−	11.5425i	−0.447437	−	0.427794i
$729$		0			0
$730$	−41.4135	+	19.9437i	−1.53278	+	0.738149i
$731$	17.0429	−	10.1827i	0.630354	−	0.376619i
$732$		0			0
$733$	−11.7478	−	2.68135i	−0.433914	−	0.0990379i	−1.56639e−5	−	1.00000i	$-0.500005\pi$
$733$	−11.7478	−	2.68135i	−0.433914	−	0.0990379i	−0.433898	+	0.900962i	$0.642862\pi$
$734$	2.38388	+	13.1362i	0.0879905	+	0.484868i
$735$		0			0
$736$	−13.5976	−	10.8437i	−0.501214	−	0.399705i
$737$	0.455789	−	0.762863i	0.0167892	−	0.0281004i
$738$		0			0
$739$	3.44233	+	25.4123i	0.126628	+	0.934806i	0.937108	+	0.349040i	$0.113492\pi$
$739$	3.44233	+	25.4123i	0.126628	+	0.934806i	−0.810480	+	0.585767i	$0.800794\pi$
$740$	−1.22575	+	0.977499i	−0.0450593	+	0.0359336i
$741$		0			0
$742$	−27.2970	−	13.1456i	−1.00211	−	0.482588i
$743$	41.2239	−	3.71022i	1.51236	−	0.136115i	0.697841	−	0.716252i	$-0.254144\pi$
$743$	41.2239	−	3.71022i	1.51236	−	0.136115i	0.814519	+	0.580138i	$0.197001\pi$
$744$		0			0
$745$	9.94787	−	4.25192i	0.364462	−	0.155778i
$746$	−13.8269	+	5.90992i	−0.506241	+	0.216378i
$747$		0			0
$748$	−4.45801	+	0.401228i	−0.163001	+	0.0146704i
$749$	−64.4318	−	31.0287i	−2.35429	−	1.13377i
$750$		0			0
$751$	−20.7707	+	16.5641i	−0.757934	+	0.604432i	−0.924316	−	0.381629i	$-0.875363\pi$
$751$	−20.7707	+	16.5641i	−0.757934	+	0.604432i	0.166381	+	0.986061i	$0.446792\pi$
$752$	1.34054	+	9.89625i	0.0488844	+	0.360879i
$753$		0			0
$754$	−4.33790	+	7.26043i	−0.157977	+	0.264409i
$755$	56.8949	+	45.3721i	2.07062	+	1.65126i
$756$		0			0
$757$	−5.93517	−	32.7055i	−0.215717	−	1.18870i	−0.891992	−	0.452051i	$-0.850692\pi$
$757$	−5.93517	−	32.7055i	−0.215717	−	1.18870i	0.676275	−	0.736650i	$-0.263593\pi$
$758$	14.7007	+	3.35533i	0.533952	+	0.121871i
$759$		0			0
$760$	−22.1398	+	13.2279i	−0.803094	+	0.479826i
$761$	−7.40940	+	3.56818i	−0.268590	+	0.129346i	−0.563332	−	0.826231i	$-0.690481\pi$
$761$	−7.40940	+	3.56818i	−0.268590	+	0.129346i	0.294741	+	0.955577i	$0.404766\pi$
$762$		0			0
$763$	−47.3591	−	45.2799i	−1.71451	−	1.63924i
$764$	1.95374	+	2.68909i	0.0706837	+	0.0972878i
$765$		0			0
$766$	−19.8746	−	10.6950i	−0.718097	−	0.386424i
$767$	4.68532	−	1.52235i	0.169177	−	0.0549689i
$768$		0			0
$769$	−27.7079	+	18.2898i	−0.999174	+	0.659549i	−0.940876	−	0.338750i	$-0.889996\pi$
$769$	−27.7079	+	18.2898i	−0.999174	+	0.659549i	−0.0582975	+	0.998299i	$0.518567\pi$
$770$	19.7830	+	71.6822i	0.712931	+	2.58325i
$771$		0			0
$772$	−2.48329	+	6.61669i	−0.0893754	+	0.238140i
$773$	−32.8785	+	12.3395i	−1.18256	+	0.443821i	−0.863712	−	0.503986i	$-0.831866\pi$
$773$	−32.8785	+	12.3395i	−1.18256	+	0.443821i	−0.318844	+	0.947807i	$0.603295\pi$
$774$		0			0
$775$	33.8609	+	22.3514i	1.21632	+	0.802884i
$776$	6.18615	−	19.0390i	0.222070	−	0.683461i
$777$		0			0
$778$	4.85933	−	26.7771i	0.174215	−	0.960005i
$779$	−4.94178	+	11.5619i	−0.177058	+	0.414247i
$780$		0			0
$781$	22.7728	−	1.68207i	0.814875	−	0.0601893i
$782$		−	53.5619i		−	1.91537i
$783$		0			0
$784$	56.5255	+	10.2579i	2.01877	+	0.366352i
$785$	47.9517	−	45.8466i	1.71147	−	1.63633i
$786$		0			0
$787$	−24.8934	+	37.7119i	−0.887354	+	1.34428i	0.0510332	+	0.998697i	$0.483749\pi$
$787$	−24.8934	+	37.7119i	−0.887354	+	1.34428i	−0.938387	+	0.345586i	$0.887680\pi$
$788$	1.37421	−	1.20061i	0.0489542	−	0.0427700i
$789$		0			0
$790$	14.5230	+	5.45057i	0.516705	+	0.193923i
$791$	−24.6788	+	28.2471i	−0.877476	+	1.00435i
$792$		0			0
$793$	−1.12987	−	1.71169i	−0.0401230	−	0.0607837i
$794$	29.2281	+	8.06645i	1.03727	+	0.286268i
$795$		0			0
$796$	3.19548	−	5.93819i	0.113261	−	0.210474i
$797$	−41.7774	−	1.87623i	−1.47983	−	0.0664594i	−0.709773	−	0.704431i	$-0.751202\pi$
$797$	−41.7774	−	1.87623i	−1.47983	−	0.0664594i	−0.770060	+	0.637971i	$0.779774\pi$
$798$		0			0
$799$	10.2274	−	10.6970i	0.361819	−	0.378433i
$800$	22.7925	−	12.2652i	0.805837	−	0.433640i
$801$		0			0
$802$	20.1771	+	33.7707i	0.712476	+	1.19248i
$803$	3.05271	−	22.5360i	0.107728	−	0.795279i
$804$		0			0
$805$	186.419	−	33.8300i	6.57039	−	1.19235i
$806$	−2.56301	+	3.52768i	−0.0902783	+	0.124257i
$807$		0			0
$808$	−4.92832	−	2.94453i	−0.173378	−	0.103588i
$809$	26.6082	+	2.39478i	0.935494	+	0.0841960i	0.546886	−	0.837207i	$-0.315813\pi$
$809$	26.6082	+	2.39478i	0.935494	+	0.0841960i	0.388608	+	0.921403i	$0.372956\pi$
$810$		0			0
$811$	−12.6623	−	15.8781i	−0.444635	−	0.557555i	0.508123	−	0.861284i	$-0.330339\pi$
$811$	−12.6623	−	15.8781i	−0.444635	−	0.557555i	−0.952758	+	0.303730i	$0.901768\pi$
$812$	0.470611	+	10.4790i	0.0165152	+	0.367740i
$813$		0			0
$814$	0.326564	+	3.62842i	0.0114461	+	0.127176i
$815$	1.42143	+	6.22771i	0.0497907	+	0.218147i
$816$		0			0
$817$	3.32162	+	7.77132i	0.116209	+	0.271884i
$818$	36.4058	−	8.30938i	1.27290	−	0.290531i
$819$		0			0
$820$	4.07950	−	8.47117i	0.142462	−	0.295826i
$821$	27.2630	−	1.22438i	0.951484	−	0.0427312i	0.436291	−	0.899805i	$-0.356292\pi$
$821$	27.2630	−	1.22438i	0.951484	−	0.0427312i	0.515193	+	0.857074i	$0.327720\pi$
$822$		0			0
$823$	7.88928	−	1.06868i	0.275003	−	0.0372517i	0.00456668	−	0.999990i	$-0.498546\pi$
$823$	7.88928	−	1.06868i	0.275003	−	0.0372517i	0.270436	+	0.962738i	$0.412832\pi$
$824$	3.95452	−	43.9384i	0.137762	−	1.53067i
$825$		0			0
$826$	−17.8920	+	22.4359i	−0.622543	+	0.780644i
$827$	10.7915	+	7.84047i	0.375256	+	0.272640i	0.759387	−	0.650639i	$-0.225499\pi$
$827$	10.7915	+	7.84047i	0.375256	+	0.272640i	−0.384131	+	0.923279i	$0.625499\pi$
$828$		0			0
$829$	10.2808	−	45.0429i	0.357065	−	1.56441i	−0.403398	−	0.915025i	$-0.632171\pi$
$829$	10.2808	−	45.0429i	0.357065	−	1.56441i	0.760463	−	0.649381i	$-0.224972\pi$
$830$	21.7763	+	2.94980i	0.755866	+	0.102389i
$831$		0			0
$832$	4.24921	+	8.82358i	0.147315	+	0.305903i
$833$	−40.3429	−	74.9696i	−1.39780	−	2.59754i
$834$		0			0
$835$	27.2823	−	19.8218i	0.944144	−	0.685961i
$836$	0.0854870	−	1.90352i	0.00295663	−	0.0658345i
$837$		0			0
$838$	−3.27365	−	10.0753i	−0.113086	−	0.348044i
$839$	−9.83400	+	35.6327i	−0.339507	+	1.23018i	0.572466	+	0.819928i	$0.305987\pi$
$839$	−9.83400	+	35.6327i	−0.339507	+	1.23018i	−0.911974	+	0.410249i	$0.865442\pi$
$840$		0			0
$841$	6.33292	−	1.74777i	0.218377	−	0.0602681i
$842$	−16.1125	−	14.0770i	−0.555273	−	0.485127i
$843$		0			0
$844$	−1.83226	−	4.88204i	−0.0630690	−	0.168047i
$845$	−33.0614	−	37.8418i	−1.13735	−	1.30180i
$846$		0			0
$847$	17.4184	+	5.65958i	0.598503	+	0.194465i
$848$	10.3324	+	10.8069i	0.354817	+	0.371110i
$849$		0			0
$850$	73.2973	+	31.3287i	2.51407	+	1.07457i
$851$	9.28205			0.318185
$852$		0			0
$853$	10.4293			0.357091			0.178546	−	0.983932i	$-0.442861\pi$
$853$	10.4293			0.357091			0.178546	+	0.983932i	$0.442861\pi$
$854$	10.9856	+	4.69545i	0.375918	+	0.160675i
$855$		0			0
$856$	29.7830	+	31.1506i	1.01796	+	1.06471i
$857$	6.87856	+	2.23498i	0.234967	+	0.0763455i	0.424134	−	0.905600i	$-0.360579\pi$
$857$	6.87856	+	2.23498i	0.234967	+	0.0763455i	−0.189167	+	0.981945i	$0.560579\pi$
$858$		0			0
$859$	−4.72248	−	5.40531i	−0.161129	−	0.184427i	0.666840	−	0.745201i	$-0.267646\pi$
$859$	−4.72248	−	5.40531i	−0.161129	−	0.184427i	−0.827969	+	0.560774i	$0.810504\pi$
$860$	−2.22060	−	5.91678i	−0.0757220	−	0.201760i
$861$		0			0
$862$	−9.55726	−	8.34993i	−0.325522	−	0.284400i
$863$	−36.5094	+	10.0760i	−1.24280	+	0.342990i	−0.824782	−	0.565451i	$-0.808702\pi$
$863$	−36.5094	+	10.0760i	−1.24280	+	0.342990i	−0.418014	+	0.908441i	$0.637274\pi$
$864$		0			0
$865$	−7.18848	+	26.0469i	−0.244416	+	0.885620i
$866$	7.07288	+	21.7681i	0.240346	+	0.739710i
$867$		0			0
$868$	−0.242631	+	5.40260i	−0.00823544	+	0.183376i
$869$	−6.20901	+	4.51111i	−0.210626	+	0.153029i
$870$		0			0
$871$	0.171605	+	0.318895i	0.00581461	+	0.0108054i
$872$	17.1326	+	35.5762i	0.580182	+	1.20476i
$873$		0			0
$874$	22.5948	+	3.06067i	0.764281	+	0.103529i
$875$	−38.9675	+	170.728i	−1.31734	+	5.77165i
$876$		0			0
$877$	−38.6097	−	28.0516i	−1.30376	−	0.947234i	−0.303772	−	0.952745i	$-0.598246\pi$
$877$	−38.6097	−	28.0516i	−1.30376	−	0.947234i	−0.999985	+	0.00551050i	$0.998246\pi$
$878$	1.25681	−	1.57598i	0.0424151	−	0.0531869i
$879$		0			0
$880$	3.28949	−	36.5493i	0.110889	−	1.23208i
$881$	−23.2199	+	3.14535i	−0.782298	+	0.105969i	−0.514482	−	0.857501i	$-0.672016\pi$
$881$	−23.2199	+	3.14535i	−0.782298	+	0.105969i	−0.267815	+	0.963470i	$0.586302\pi$
$882$		0			0
$883$	−22.6672	+	1.01798i	−0.762812	+	0.0342579i	−0.422872	−	0.906189i	$-0.638978\pi$
$883$	−22.6672	+	1.01798i	−0.762812	+	0.0342579i	−0.339940	+	0.940447i	$0.610407\pi$
$884$	0.791418	−	1.64340i	0.0266183	−	0.0552734i
$885$		0			0
$886$	−20.5654	+	4.69392i	−0.690909	+	0.157695i
$887$	6.99768	+	16.3719i	0.234959	+	0.549714i	0.994967	−	0.100199i	$-0.0319480\pi$
$887$	6.99768	+	16.3719i	0.234959	+	0.549714i	−0.760008	+	0.649913i	$0.774805\pi$
$888$		0			0
$889$	−8.62611	−	37.7935i	−0.289310	−	1.26755i
$890$	0.631828	+	7.02018i	0.0211789	+	0.235317i
$891$		0			0
$892$	0.00556525	+	0.123920i	0.000186338	+	0.00414915i
$893$	3.92806	+	4.92563i	0.131448	+	0.164830i
$894$		0			0
$895$	−42.6694	−	3.84031i	−1.42628	−	0.128367i
$896$	−32.1003	−	19.1790i	−1.07239	−	0.640726i
$897$		0			0
$898$	−0.580081	+	0.798412i	−0.0193575	+	0.0266434i
$899$	18.0438	−	3.27447i	0.601794	−	0.109210i
$900$		0			0
$901$	2.97422	−	21.9566i	0.0990857	−	0.731480i
$902$	−11.2059	−	18.7556i	−0.373117	−	0.624493i
$903$		0			0
$904$	19.9056	−	10.7117i	0.662050	−	0.356264i
$905$	−58.9438	+	61.6504i	−1.95936	+	2.04933i
$906$		0			0
$907$	−20.0661	−	0.901170i	−0.666284	−	0.0299229i	−0.290846	−	0.956770i	$-0.593937\pi$
$907$	−20.0661	−	0.901170i	−0.666284	−	0.0299229i	−0.375439	+	0.926847i	$0.622508\pi$
$908$	−4.07846	+	7.57905i	−0.135349	+	0.251520i
$909$		0			0
$910$	−29.2113	−	8.06181i	−0.968345	−	0.267246i
$911$	1.91752	+	2.90491i	0.0635302	+	0.0962441i	0.864950	−	0.501858i	$-0.167350\pi$
$911$	1.91752	+	2.90491i	0.0635302	+	0.0962441i	−0.801420	+	0.598102i	$0.795922\pi$
$912$		0			0
$913$	−7.15338	+	8.18770i	−0.236742	+	0.270973i
$914$	39.5219	+	14.8328i	1.30727	+	0.490626i
$915$		0			0
$916$	1.42480	−	1.24481i	0.0470767	−	0.0411297i
$917$	38.1061	−	57.7283i	1.25838	−	1.90636i
$918$		0			0
$919$	−3.83137	+	3.66316i	−0.126385	+	0.120837i	−0.751609	−	0.659609i	$-0.770722\pi$
$919$	−3.83137	+	3.66316i	−0.126385	+	0.120837i	0.625224	+	0.780445i	$0.285008\pi$
$920$	−112.344	−	20.3874i	−3.70387	−	0.672154i
$921$		0			0
$922$		−	5.25902i		−	0.173197i
$923$	−4.17136	+	8.31813i	−0.137302	+	0.273795i
$924$		0			0
$925$	−5.42914	+	12.7021i	−0.178509	+	0.417643i
$926$	−3.04763	+	16.7938i	−0.100151	+	0.551879i
$927$		0			0
$928$	3.61517	−	11.1264i	0.118674	−	0.365240i
$929$	−30.3327	−	20.0225i	−0.995185	−	0.656916i	−0.0553225	−	0.998469i	$-0.517619\pi$
$929$	−30.3327	−	20.0225i	−0.995185	−	0.656916i	−0.939863	+	0.341553i	$0.889047\pi$
$930$		0			0
$931$	33.9309	−	12.7345i	1.11204	−	0.417355i
$932$	1.90905	−	5.08664i	0.0625329	−	0.166618i
$933$		0			0
$934$	−1.16407	−	4.21791i	−0.0380895	−	0.138014i
$935$	−45.3862	+	29.9592i	−1.48429	+	0.979769i
$936$		0			0
$937$	−2.84036	+	0.922890i	−0.0927906	+	0.0301495i	−0.355044	−	0.934849i	$-0.615534\pi$
$937$	−2.84036	+	0.922890i	−0.0927906	+	0.0301495i	0.262254	+	0.964999i	$0.415534\pi$
$938$	−1.85757	−	0.999602i	−0.0606519	−	0.0326382i
$939$		0			0
$940$	−2.76910	−	3.81133i	−0.0903180	−	0.124312i
$941$	−24.1199	−	23.0610i	−0.786286	−	0.751766i	0.186753	−	0.982407i	$-0.440203\pi$
$941$	−24.1199	−	23.0610i	−0.786286	−	0.751766i	−0.973039	+	0.230641i	$0.925918\pi$
$942$		0			0
$943$	−50.1533	+	24.1526i	−1.63322	+	0.786516i
$944$	12.1569	−	7.26343i	0.395674	−	0.236405i
$945$		0			0
$946$	−14.3171	−	3.26779i	−0.465490	−	0.106245i
$947$	−5.41062	−	29.8150i	−0.175821	−	0.968856i	−0.944326	−	0.329012i	$-0.893284\pi$
$947$	−5.41062	−	29.8150i	−0.175821	−	0.968856i	0.768504	−	0.639845i	$-0.221001\pi$
$948$		0			0
$949$	7.24567	+	5.77823i	0.235204	+	0.187569i
$950$	−17.4043	+	29.1299i	−0.564670	+	0.945098i
$951$		0			0
$952$	9.55099	+	70.5082i	0.309549	+	2.28518i
$953$	−14.2924	+	11.3978i	−0.462975	+	0.369210i	−0.827021	−	0.562171i	$-0.809966\pi$
$953$	−14.2924	+	11.3978i	−0.462975	+	0.369210i	0.364046	+	0.931381i	$0.381395\pi$
$954$		0			0
$955$	36.3851	+	17.5221i	1.17739	+	0.567003i
$956$	5.00639	−	0.450584i	0.161918	−	0.0145729i
$957$		0			0
$958$	−0.365233	+	0.156108i	−0.0118001	+	0.00504362i
$959$	−69.1755	+	29.5670i	−2.23379	+	0.954770i
$960$		0			0
$961$	−21.4586	+	1.93131i	−0.692211	+	0.0623002i
$962$	−1.33758	−	0.644144i	−0.0431253	−	0.0207680i
$963$		0			0
$964$	5.74491	−	4.58142i	0.185031	−	0.147557i
$965$	11.5261	+	85.0891i	0.371038	+	2.73912i
$966$		0			0
$967$	−1.39365	+	2.33258i	−0.0448169	+	0.0750108i	−0.880038	−	0.474904i	$-0.842483\pi$
$967$	−1.39365	+	2.33258i	−0.0448169	+	0.0750108i	0.835221	+	0.549915i	$0.185340\pi$
$968$	−8.62930	−	6.88164i	−0.277356	−	0.221184i
$969$		0			0
$970$	−6.48519	−	35.7364i	−0.208227	−	1.14743i
$971$	22.6475	+	5.16915i	0.726794	+	0.165886i	0.569882	−	0.821727i	$-0.306989\pi$
$971$	22.6475	+	5.16915i	0.726794	+	0.165886i	0.156912	+	0.987613i	$0.449846\pi$
$972$		0			0
$973$	20.0562	−	11.9830i	0.642972	−	0.384158i
$974$	−3.12226	+	1.50360i	−0.100044	+	0.0481785i
$975$		0			0
$976$	−4.26139	−	4.07431i	−0.136404	−	0.130415i
$977$	18.1404	+	24.9681i	0.580361	+	0.798799i	0.993735	−	0.111763i	$-0.0356497\pi$
$977$	18.1404	+	24.9681i	0.580361	+	0.798799i	−0.413374	+	0.910561i	$0.635650\pi$
$978$		0			0
$979$	−3.07093	−	1.65254i	−0.0981474	−	0.0528154i
$980$	−25.7743	+	8.37458i	−0.823330	+	0.267516i
$981$		0			0
$982$	−3.45986	+	2.28383i	−0.110409	+	0.0728801i
$983$	−6.75281	−	24.4683i	−0.215381	−	0.780416i	−0.989145	−	0.146942i	$-0.953057\pi$
$983$	−6.75281	−	24.4683i	−0.215381	−	0.780416i	0.773764	−	0.633474i	$-0.218372\pi$
$984$		0			0
$985$	7.79029	−	20.7572i	0.248219	−	0.661378i
$986$	33.7317	−	12.6597i	1.07424	−	0.403168i
$987$		0			0
$988$	0.648034	+	0.427764i	0.0206167	+	0.0136090i
$989$	−11.5622	+	35.5847i	−0.367656	+	1.13153i
$990$		0			0
$991$	6.56187	−	36.1589i	0.208445	−	1.14862i	−0.694704	−	0.719296i	$-0.744465\pi$
$991$	6.56187	−	36.1589i	0.208445	−	1.14862i	0.903148	−	0.429329i	$-0.141250\pi$
$992$	2.37056	−	5.54620i	0.0752653	−	0.176092i
$993$		0			0
$994$	−6.41409	−	53.8237i	−0.203443	−	1.70718i
$995$		−	81.9302i		−	2.59736i
$996$		0			0
$997$	51.4568	+	9.33803i	1.62965	+	0.295738i	0.914913	−	0.403652i	$-0.132259\pi$
$997$	51.4568	+	9.33803i	1.62965	+	0.295738i	0.714740	+	0.699390i	$0.246545\pi$
$998$	3.59303	−	3.43529i	0.113735	−	0.108742i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.269.7	✓	576
3.2	odd	2	inner	639.2.z.a.269.18	yes	576
71.52	odd	70	inner	639.2.z.a.620.18	yes	576
213.194	even	70	inner	639.2.z.a.620.7	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.269.7	✓	576	1.1	even	1	trivial
639.2.z.a.269.18	yes	576	3.2	odd	2	inner
639.2.z.a.620.7	yes	576	213.194	even	70	inner
639.2.z.a.620.18	yes	576	71.52	odd	70	inner

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18077 - 0.504684i) q^{2} +(-0.242620 - 0.253761i) q^{4} +(-4.05679 - 1.31813i) q^{5} +(-3.29604 - 3.77262i) q^{7} +(1.06081 + 2.82652i) q^{8} +O(q^{10})\)	\(q+(-1.18077 - 0.504684i) q^{2} +(-0.242620 - 0.253761i) q^{4} +(-4.05679 - 1.31813i) q^{5} +(-3.29604 - 3.77262i) q^{7} +(1.06081 + 2.82652i) q^{8} +(4.12488 + 3.60380i) q^{10} +(-2.61234 + 0.720959i) q^{11} +(0.293799 - 1.06456i) q^{13} +(1.98787 + 6.11804i) q^{14} +(0.142427 - 3.17138i) q^{16} +(-3.80603 + 2.76524i) q^{17} +(-0.949015 - 1.76357i) q^{19} +(0.649769 + 1.34926i) q^{20} +(3.44842 + 0.467120i) q^{22} +(1.97294 - 8.64400i) q^{23} +(10.6750 + 7.75583i) q^{25} +(-0.884173 + 1.10872i) q^{26} +(-0.157658 + 1.75172i) q^{28} +(5.91006 - 0.800571i) q^{29} +(3.07175 - 0.137953i) q^{31} +(0.851099 - 1.76732i) q^{32} +(5.88960 - 1.34426i) q^{34} +(8.39852 + 19.6493i) q^{35} +(0.232955 + 1.02064i) q^{37} +(0.230522 + 2.56131i) q^{38} +(-0.577763 - 12.8649i) q^{40} +(-3.91451 - 4.90864i) q^{41} +(-4.20303 - 0.378280i) q^{43} +(0.816758 + 0.487990i) q^{44} +(-6.69207 + 9.21084i) q^{46} +(-3.09526 + 0.561708i) q^{47} +(-2.42915 + 17.9327i) q^{49} +(-8.69042 - 14.5453i) q^{50} +(-0.341425 + 0.183728i) q^{52} +(-3.25474 + 3.40419i) q^{53} +(11.5480 + 0.518622i) q^{55} +(7.16691 - 13.3184i) q^{56} +(-7.38244 - 2.03742i) q^{58} +(2.45751 + 3.72296i) q^{59} +(1.22190 - 1.39858i) q^{61} +(-3.69665 - 1.38738i) q^{62} +(-6.67825 + 5.83461i) q^{64} +(-2.59511 + 3.93142i) q^{65} +(-0.237016 + 0.226611i) q^{67} +(1.62513 + 0.294917i) q^{68} -27.4399i q^{70} +(-8.26556 - 1.63725i) q^{71} +(-3.29820 + 7.71652i) q^{73} +(0.240037 - 1.32271i) q^{74} +(-0.217274 + 0.668700i) q^{76} +(11.3303 + 7.47904i) q^{77} +(2.65143 - 0.995100i) q^{79} +(-4.75809 + 12.6779i) q^{80} +(2.14481 + 7.77155i) q^{82} +(3.34828 - 2.21018i) q^{83} +(19.0852 - 6.20115i) q^{85} +(4.77189 + 2.56786i) q^{86} +(-4.80900 - 6.61903i) q^{88} +(0.930122 + 0.889287i) q^{89} +(-4.98454 + 2.40043i) q^{91} +(-2.67218 + 1.59656i) q^{92} +(3.93827 + 0.898885i) q^{94} +(1.52534 + 8.40534i) q^{95} +(-5.18423 - 4.13428i) q^{97} +(11.9186 - 19.9484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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