LMFDB - Embedded newform 1920.2.bl.b.289.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (of order $4$, degree $2$, not 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.16
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.b.1249.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-0.607542 - 2.15195i) q^{5} +2.25286 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-0.607542 - 2.15195i) q^{5} +2.25286 q^{7} -1.00000i q^{9} +(-1.66088 + 1.66088i) q^{11} +(-4.76925 + 4.76925i) q^{13} +(-1.95126 - 1.09206i) q^{15} -6.99777i q^{17} +(-2.66634 - 2.66634i) q^{19} +(1.59301 - 1.59301i) q^{21} -4.41825 q^{23} +(-4.26178 + 2.61480i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-2.59286 - 2.59286i) q^{29} +3.93331 q^{31} +2.34884i q^{33} +(-1.36871 - 4.84805i) q^{35} +(-2.01181 - 2.01181i) q^{37} +6.74474i q^{39} +4.50104i q^{41} +(-7.14876 - 7.14876i) q^{43} +(-2.15195 + 0.607542i) q^{45} -10.1154i q^{47} -1.92461 q^{49} +(-4.94817 - 4.94817i) q^{51} +(0.649299 + 0.649299i) q^{53} +(4.58319 + 2.56508i) q^{55} -3.77078 q^{57} +(5.64696 - 5.64696i) q^{59} +(5.00520 + 5.00520i) q^{61} -2.25286i q^{63} +(13.1607 + 7.36567i) q^{65} +(-4.95274 + 4.95274i) q^{67} +(-3.12417 + 3.12417i) q^{69} -2.33178i q^{71} +2.18275 q^{73} +(-1.16459 + 4.86248i) q^{75} +(-3.74174 + 3.74174i) q^{77} -6.38450 q^{79} -1.00000 q^{81} +(5.25073 - 5.25073i) q^{83} +(-15.0589 + 4.25144i) q^{85} -3.66685 q^{87} +15.7100i q^{89} +(-10.7445 + 10.7445i) q^{91} +(2.78127 - 2.78127i) q^{93} +(-4.11792 + 7.35775i) q^{95} +4.61603i q^{97} +(1.66088 + 1.66088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 8 q^{19} + 48 q^{31} + 24 q^{35} + 48 q^{49} + 8 q^{51} - 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} - 16 q^{75} + 96 q^{79} - 48 q^{81} - 32 q^{91} + 48 q^{95}+O(q^{100}) $ 48 * q + 8 * q^19 + 48 * q^31 + 24 * q^35 + 48 * q^49 + 8 * q^51 - 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 - 16 * q^75 + 96 * q^79 - 48 * q^81 - 32 * q^91 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−0.607542	−	2.15195i	−0.271701	−	0.962382i
$5$	−0.607542	−	2.15195i	−0.271701	−	0.962382i
$6$		0			0
$7$	2.25286			0.851502			0.425751	−	0.904840i	$-0.360010\pi$
$7$	2.25286			0.851502			0.425751	+	0.904840i	$0.360010\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.66088	+	1.66088i	−0.500775	+	0.500775i	−0.911679	−	0.410904i	$-0.865213\pi$
$11$	−1.66088	+	1.66088i	−0.500775	+	0.500775i	0.410904	+	0.911679i	$0.365213\pi$
$12$		0			0
$13$	−4.76925	+	4.76925i	−1.32275	+	1.32275i	−0.411212	+	0.911540i	$0.634894\pi$
$13$	−4.76925	+	4.76925i	−1.32275	+	1.32275i	−0.911540	+	0.411212i	$0.865106\pi$
$14$		0			0
$15$	−1.95126	−	1.09206i	−0.503812	−	0.281969i
$16$		0			0
$17$		−	6.99777i		−	1.69721i	−0.529028	−	0.848604i	$-0.677443\pi$
$17$		−	6.99777i		−	1.69721i	0.529028	−	0.848604i	$-0.322557\pi$
$18$		0			0
$19$	−2.66634	−	2.66634i	−0.611701	−	0.611701i	0.331688	−	0.943389i	$-0.392382\pi$
$19$	−2.66634	−	2.66634i	−0.611701	−	0.611701i	−0.943389	+	0.331688i	$0.892382\pi$
$20$		0			0
$21$	1.59301	−	1.59301i	0.347624	−	0.347624i
$22$		0			0
$23$	−4.41825			−0.921269			−0.460634	−	0.887590i	$-0.652378\pi$
$23$	−4.41825			−0.921269			−0.460634	+	0.887590i	$0.652378\pi$
$24$		0			0
$25$	−4.26178	+	2.61480i	−0.852357	+	0.522960i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	−2.59286	−	2.59286i	−0.481481	−	0.481481i	0.424123	−	0.905604i	$-0.360582\pi$
$29$	−2.59286	−	2.59286i	−0.481481	−	0.481481i	−0.905604	+	0.424123i	$0.860582\pi$
$30$		0			0
$31$	3.93331			0.706443			0.353221	−	0.935540i	$-0.385086\pi$
$31$	3.93331			0.706443			0.353221	+	0.935540i	$0.385086\pi$
$32$		0			0
$33$			2.34884i			0.408881i
$34$		0			0
$35$	−1.36871	−	4.84805i	−0.231354	−	0.819470i
$36$		0			0
$37$	−2.01181	−	2.01181i	−0.330739	−	0.330739i	0.522128	−	0.852867i	$-0.325138\pi$
$37$	−2.01181	−	2.01181i	−0.330739	−	0.330739i	−0.852867	+	0.522128i	$0.825138\pi$
$38$		0			0
$39$			6.74474i			1.08002i
$40$		0			0
$41$			4.50104i			0.702945i	0.936198	+	0.351472i	$0.114319\pi$
$41$			4.50104i			0.702945i	−0.936198	+	0.351472i	$0.885681\pi$
$42$		0			0
$43$	−7.14876	−	7.14876i	−1.09017	−	1.09017i	−0.995509	−	0.0946658i	$-0.969822\pi$
$43$	−7.14876	−	7.14876i	−1.09017	−	1.09017i	−0.0946658	−	0.995509i	$-0.530178\pi$
$44$		0			0
$45$	−2.15195	+	0.607542i	−0.320794	+	0.0905671i
$46$		0			0
$47$		−	10.1154i		−	1.47548i	−0.675086	−	0.737739i	$-0.735893\pi$
$47$		−	10.1154i		−	1.47548i	0.675086	−	0.737739i	$-0.264107\pi$
$48$		0			0
$49$	−1.92461			−0.274945
$50$		0			0
$51$	−4.94817	−	4.94817i	−0.692883	−	0.692883i
$52$		0			0
$53$	0.649299	+	0.649299i	0.0891881	+	0.0891881i	0.750293	−	0.661105i	$-0.229912\pi$
$53$	0.649299	+	0.649299i	0.0891881	+	0.0891881i	−0.661105	+	0.750293i	$0.729912\pi$
$54$		0			0
$55$	4.58319	+	2.56508i	0.617997	+	0.345875i
$56$		0			0
$57$	−3.77078			−0.499452
$58$		0			0
$59$	5.64696	−	5.64696i	0.735172	−	0.735172i	−0.236468	−	0.971639i	$-0.575990\pi$
$59$	5.64696	−	5.64696i	0.735172	−	0.735172i	0.971639	+	0.236468i	$0.0759897\pi$
$60$		0			0
$61$	5.00520	+	5.00520i	0.640851	+	0.640851i	0.950765	−	0.309914i	$-0.100300\pi$
$61$	5.00520	+	5.00520i	0.640851	+	0.640851i	−0.309914	+	0.950765i	$0.600300\pi$
$62$		0			0
$63$		−	2.25286i		−	0.283834i
$64$		0			0
$65$	13.1607	+	7.36567i	1.63239	+	0.913599i
$66$		0			0
$67$	−4.95274	+	4.95274i	−0.605074	+	0.605074i	−0.941655	−	0.336581i	$-0.890729\pi$
$67$	−4.95274	+	4.95274i	−0.605074	+	0.605074i	0.336581	+	0.941655i	$0.390729\pi$
$68$		0			0
$69$	−3.12417	+	3.12417i	−0.376106	+	0.376106i
$70$		0			0
$71$		−	2.33178i		−	0.276732i	−0.990381	−	0.138366i	$-0.955815\pi$
$71$		−	2.33178i		−	0.276732i	0.990381	−	0.138366i	$-0.0441850\pi$
$72$		0			0
$73$	2.18275			0.255472			0.127736	−	0.991808i	$-0.459229\pi$
$73$	2.18275			0.255472			0.127736	+	0.991808i	$0.459229\pi$
$74$		0			0
$75$	−1.16459	+	4.86248i	−0.134476	+	0.561471i
$76$		0			0
$77$	−3.74174	+	3.74174i	−0.426410	+	0.426410i
$78$		0			0
$79$	−6.38450			−0.718312			−0.359156	−	0.933278i	$-0.616935\pi$
$79$	−6.38450			−0.718312			−0.359156	+	0.933278i	$0.616935\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	5.25073	−	5.25073i	0.576342	−	0.576342i	−0.357551	−	0.933894i	$-0.616388\pi$
$83$	5.25073	−	5.25073i	0.576342	−	0.576342i	0.933894	+	0.357551i	$0.116388\pi$
$84$		0			0
$85$	−15.0589	+	4.25144i	−1.63336	+	0.461134i
$86$		0			0
$87$	−3.66685			−0.393128
$88$		0			0
$89$			15.7100i			1.66525i	0.553833	+	0.832627i	$0.313164\pi$
$89$			15.7100i			1.66525i	−0.553833	+	0.832627i	$0.686836\pi$
$90$		0			0
$91$	−10.7445	+	10.7445i	−1.12633	+	1.12633i
$92$		0			0
$93$	2.78127	−	2.78127i	0.288404	−	0.288404i
$94$		0			0
$95$	−4.11792	+	7.35775i	−0.422490	+	0.754889i
$96$		0			0
$97$			4.61603i			0.468687i	0.972154	+	0.234343i	$0.0752940\pi$
$97$			4.61603i			0.468687i	−0.972154	+	0.234343i	$0.924706\pi$
$98$		0			0
$99$	1.66088	+	1.66088i	0.166925	+	0.166925i
$100$		0			0
$101$	1.13980	−	1.13980i	0.113415	−	0.113415i	−0.648122	−	0.761537i	$-0.724445\pi$
$101$	1.13980	−	1.13980i	0.113415	−	0.113415i	0.761537	+	0.648122i	$0.224445\pi$
$102$		0			0
$103$	4.11257			0.405224			0.202612	−	0.979259i	$-0.435057\pi$
$103$	4.11257			0.405224			0.202612	+	0.979259i	$0.435057\pi$
$104$		0			0
$105$	−4.39591	−	2.46026i	−0.428997	−	0.240097i
$106$		0			0
$107$	−4.98634	−	4.98634i	−0.482048	−	0.482048i	0.423737	−	0.905785i	$-0.360718\pi$
$107$	−4.98634	−	4.98634i	−0.482048	−	0.482048i	−0.905785	+	0.423737i	$0.860718\pi$
$108$		0			0
$109$	−3.62560	−	3.62560i	−0.347269	−	0.347269i	0.511822	−	0.859091i	$-0.328971\pi$
$109$	−3.62560	−	3.62560i	−0.347269	−	0.347269i	−0.859091	+	0.511822i	$0.828971\pi$
$110$		0			0
$111$	−2.84512			−0.270047
$112$		0			0
$113$		−	0.639228i		−	0.0601335i	−0.999548	−	0.0300668i	$-0.990428\pi$
$113$		−	0.639228i		−	0.0601335i	0.999548	−	0.0300668i	$-0.00957199\pi$
$114$		0			0
$115$	2.68427	+	9.50786i	0.250310	+	0.886612i
$116$		0			0
$117$	4.76925	+	4.76925i	0.440917	+	0.440917i
$118$		0			0
$119$		−	15.7650i		−	1.44518i
$120$		0			0
$121$			5.48295i			0.498450i
$122$		0			0
$123$	3.18272	+	3.18272i	0.286976	+	0.286976i
$124$		0			0
$125$	8.21614	+	7.58255i	0.734874	+	0.678204i
$126$		0			0
$127$		−	17.5549i		−	1.55774i	−0.627184	−	0.778871i	$-0.715793\pi$
$127$		−	17.5549i		−	1.55774i	0.627184	−	0.778871i	$-0.284207\pi$
$128$		0			0
$129$	−10.1099			−0.890124
$130$		0			0
$131$	0.826200	+	0.826200i	0.0721855	+	0.0721855i	0.742278	−	0.670092i	$-0.233745\pi$
$131$	0.826200	+	0.826200i	0.0721855	+	0.0721855i	−0.670092	+	0.742278i	$0.733745\pi$
$132$		0			0
$133$	−6.00690	−	6.00690i	−0.520864	−	0.520864i
$134$		0			0
$135$	−1.09206	+	1.95126i	−0.0939897	+	0.167937i
$136$		0			0
$137$	−8.92457			−0.762477			−0.381239	−	0.924477i	$-0.624502\pi$
$137$	−8.92457			−0.762477			−0.381239	+	0.924477i	$0.624502\pi$
$138$		0			0
$139$	4.83668	−	4.83668i	0.410242	−	0.410242i	−0.471581	−	0.881823i	$-0.656317\pi$
$139$	4.83668	−	4.83668i	0.410242	−	0.410242i	0.881823	+	0.471581i	$0.156317\pi$
$140$		0			0
$141$	−7.15265	−	7.15265i	−0.602361	−	0.602361i
$142$		0			0
$143$		−	15.8423i		−	1.32480i
$144$		0			0
$145$	−4.00443	+	7.15497i	−0.332550	+	0.594188i
$146$		0			0
$147$	−1.36091	+	1.36091i	−0.112246	+	0.112246i
$148$		0			0
$149$	1.49085	−	1.49085i	0.122135	−	0.122135i	−0.643397	−	0.765533i	$-0.722476\pi$
$149$	1.49085	−	1.49085i	0.122135	−	0.122135i	0.765533	+	0.643397i	$0.222476\pi$
$150$		0			0
$151$			9.61540i			0.782490i	0.920287	+	0.391245i	$0.127956\pi$
$151$			9.61540i			0.782490i	−0.920287	+	0.391245i	$0.872044\pi$
$152$		0			0
$153$	−6.99777			−0.565736
$154$		0			0
$155$	−2.38965	−	8.46429i	−0.191941	−	0.679868i
$156$		0			0
$157$	−16.0158	+	16.0158i	−1.27820	+	1.27820i	−0.336521	+	0.941676i	$0.609250\pi$
$157$	−16.0158	+	16.0158i	−1.27820	+	1.27820i	−0.941676	+	0.336521i	$0.890750\pi$
$158$		0			0
$159$	0.918248			0.0728218
$160$		0			0
$161$	−9.95371			−0.784462
$162$		0			0
$163$	13.3477	−	13.3477i	1.04547	−	1.04547i	0.0465557	−	0.998916i	$-0.485176\pi$
$163$	13.3477	−	13.3477i	1.04547	−	1.04547i	0.998916	−	0.0465557i	$-0.0148245\pi$
$164$		0			0
$165$	5.05459	−	1.42702i	0.393499	−	0.111093i
$166$		0			0
$167$	−12.8029			−0.990720			−0.495360	−	0.868688i	$-0.664964\pi$
$167$	−12.8029			−0.990720			−0.495360	+	0.868688i	$0.664964\pi$
$168$		0			0
$169$		−	32.4915i		−	2.49934i
$170$		0			0
$171$	−2.66634	+	2.66634i	−0.203900	+	0.203900i
$172$		0			0
$173$	12.8300	−	12.8300i	0.975450	−	0.975450i	−0.0242559	−	0.999706i	$-0.507722\pi$
$173$	12.8300	−	12.8300i	0.975450	−	0.975450i	0.999706	+	0.0242559i	$0.00772166\pi$
$174$		0			0
$175$	−9.60121	+	5.89079i	−0.725784	+	0.445302i
$176$		0			0
$177$		−	7.98601i		−	0.600265i
$178$		0			0
$179$	4.61252	+	4.61252i	0.344756	+	0.344756i	0.858152	−	0.513396i	$-0.171613\pi$
$179$	4.61252	+	4.61252i	0.344756	+	0.344756i	−0.513396	+	0.858152i	$0.671613\pi$
$180$		0			0
$181$	4.12071	−	4.12071i	0.306290	−	0.306290i	−0.537179	−	0.843468i	$-0.680510\pi$
$181$	4.12071	−	4.12071i	0.306290	−	0.306290i	0.843468	+	0.537179i	$0.180510\pi$
$182$		0			0
$183$	7.07843			0.523252
$184$		0			0
$185$	−3.10705	+	5.55156i	−0.228435	+	0.408159i
$186$		0			0
$187$	11.6225	+	11.6225i	0.849919	+	0.849919i
$188$		0			0
$189$	−1.59301	−	1.59301i	−0.115875	−	0.115875i
$190$		0			0
$191$	0.953399			0.0689855			0.0344928	−	0.999405i	$-0.489018\pi$
$191$	0.953399			0.0689855			0.0344928	+	0.999405i	$0.489018\pi$
$192$		0			0
$193$		−	4.82186i		−	0.347085i	−0.984826	−	0.173543i	$-0.944479\pi$
$193$		−	4.82186i		−	0.347085i	0.984826	−	0.173543i	$-0.0555214\pi$
$194$		0			0
$195$	14.5143	−	4.09771i	1.03939	−	0.293443i
$196$		0			0
$197$	−2.47660	−	2.47660i	−0.176451	−	0.176451i	0.613356	−	0.789807i	$-0.289819\pi$
$197$	−2.47660	−	2.47660i	−0.176451	−	0.176451i	−0.789807	+	0.613356i	$0.789819\pi$
$198$		0			0
$199$		−	17.4435i		−	1.23654i	−0.785966	−	0.618270i	$-0.787834\pi$
$199$		−	17.4435i		−	1.23654i	0.785966	−	0.618270i	$-0.212166\pi$
$200$		0			0
$201$			7.00424i			0.494041i
$202$		0			0
$203$	−5.84135	−	5.84135i	−0.409982	−	0.409982i
$204$		0			0
$205$	9.68602	−	2.73457i	0.676501	−	0.190991i
$206$		0			0
$207$			4.41825i			0.307090i
$208$		0			0
$209$	8.85695			0.612648
$210$		0			0
$211$	5.41135	+	5.41135i	0.372533	+	0.372533i	0.868399	−	0.495866i	$-0.165149\pi$
$211$	5.41135	+	5.41135i	0.372533	+	0.372533i	−0.495866	+	0.868399i	$0.665149\pi$
$212$		0			0
$213$	−1.64882	−	1.64882i	−0.112975	−	0.112975i
$214$		0			0
$215$	−11.0406	+	19.7269i	−0.752963	+	1.34537i
$216$		0			0
$217$	8.86120			0.601538
$218$		0			0
$219$	1.54344	−	1.54344i	0.104296	−	0.104296i
$220$		0			0
$221$	33.3741	+	33.3741i	2.24499	+	2.24499i
$222$		0			0
$223$			18.2634i			1.22301i	0.791241	+	0.611505i	$0.209436\pi$
$223$			18.2634i			1.22301i	−0.791241	+	0.611505i	$0.790564\pi$
$224$		0			0
$225$	2.61480	+	4.26178i	0.174320	+	0.284119i
$226$		0			0
$227$	−2.23773	+	2.23773i	−0.148523	+	0.148523i	−0.777458	−	0.628935i	$-0.783491\pi$
$227$	−2.23773	+	2.23773i	−0.148523	+	0.148523i	0.628935	+	0.777458i	$0.283491\pi$
$228$		0			0
$229$	−6.40974	+	6.40974i	−0.423568	+	0.423568i	−0.886430	−	0.462862i	$-0.846822\pi$
$229$	−6.40974	+	6.40974i	−0.423568	+	0.423568i	0.462862	+	0.886430i	$0.346822\pi$
$230$		0			0
$231$			5.29162i			0.348163i
$232$		0			0
$233$	−2.67972			−0.175555			−0.0877773	−	0.996140i	$-0.527976\pi$
$233$	−2.67972			−0.175555			−0.0877773	+	0.996140i	$0.527976\pi$
$234$		0			0
$235$	−21.7678	+	6.14551i	−1.41997	+	0.400889i
$236$		0			0
$237$	−4.51452	+	4.51452i	−0.293250	+	0.293250i
$238$		0			0
$239$	26.0323			1.68389			0.841946	−	0.539562i	$-0.181410\pi$
$239$	26.0323			1.68389			0.841946	+	0.539562i	$0.181410\pi$
$240$		0			0
$241$	5.87408			0.378383			0.189191	−	0.981940i	$-0.439413\pi$
$241$	5.87408			0.378383			0.189191	+	0.981940i	$0.439413\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	1.16928	+	4.14167i	0.0747028	+	0.264602i
$246$		0			0
$247$	25.4329			1.61826
$248$		0			0
$249$		−	7.42565i		−	0.470582i
$250$		0			0
$251$	8.44080	−	8.44080i	0.532779	−	0.532779i	−0.388620	−	0.921398i	$-0.627048\pi$
$251$	8.44080	−	8.44080i	0.532779	−	0.532779i	0.921398	+	0.388620i	$0.127048\pi$
$252$		0			0
$253$	7.33819	−	7.33819i	0.461348	−	0.461348i
$254$		0			0
$255$	−7.64200	+	13.6544i	−0.478561	+	0.855075i
$256$		0			0
$257$		−	22.2011i		−	1.38487i	−0.721480	−	0.692435i	$-0.756538\pi$
$257$		−	22.2011i		−	1.38487i	0.721480	−	0.692435i	$-0.243462\pi$
$258$		0			0
$259$	−4.53232	−	4.53232i	−0.281625	−	0.281625i
$260$		0			0
$261$	−2.59286	+	2.59286i	−0.160494	+	0.160494i
$262$		0			0
$263$	−0.464456			−0.0286396			−0.0143198	−	0.999897i	$-0.504558\pi$
$263$	−0.464456			−0.0286396			−0.0143198	+	0.999897i	$0.504558\pi$
$264$		0			0
$265$	1.00278	−	1.79174i	0.0616005	−	0.110065i
$266$		0			0
$267$	11.1086	+	11.1086i	0.679837	+	0.679837i
$268$		0			0
$269$	−4.74205	−	4.74205i	−0.289128	−	0.289128i	0.547608	−	0.836735i	$-0.315539\pi$
$269$	−4.74205	−	4.74205i	−0.289128	−	0.289128i	−0.836735	+	0.547608i	$0.815539\pi$
$270$		0			0
$271$	−12.0417			−0.731482			−0.365741	−	0.930717i	$-0.619184\pi$
$271$	−12.0417			−0.731482			−0.365741	+	0.930717i	$0.619184\pi$
$272$		0			0
$273$			15.1950i			0.919641i
$274$		0			0
$275$	2.73544	−	11.4212i	0.164953	−	0.688724i
$276$		0			0
$277$	17.9760	+	17.9760i	1.08007	+	1.08007i	0.996502	+	0.0835733i	$0.0266333\pi$
$277$	17.9760	+	17.9760i	1.08007	+	1.08007i	0.0835733	+	0.996502i	$0.473367\pi$
$278$		0			0
$279$		−	3.93331i		−	0.235481i
$280$		0			0
$281$		−	9.58712i		−	0.571919i	−0.958242	−	0.285960i	$-0.907688\pi$
$281$		−	9.58712i		−	0.571919i	0.958242	−	0.285960i	$-0.0923123\pi$
$282$		0			0
$283$	−5.09022	−	5.09022i	−0.302582	−	0.302582i	0.539441	−	0.842023i	$-0.318636\pi$
$283$	−5.09022	−	5.09022i	−0.302582	−	0.302582i	−0.842023	+	0.539441i	$0.818636\pi$
$284$		0			0
$285$	2.29091	+	8.11453i	0.135702	+	0.480663i
$286$		0			0
$287$			10.1402i			0.598559i
$288$		0			0
$289$	−31.9688			−1.88052
$290$		0			0
$291$	3.26403	+	3.26403i	0.191341	+	0.191341i
$292$		0			0
$293$	4.25071	+	4.25071i	0.248329	+	0.248329i	0.820285	−	0.571955i	$-0.193815\pi$
$293$	4.25071	+	4.25071i	0.248329	+	0.248329i	−0.571955	+	0.820285i	$0.693815\pi$
$294$		0			0
$295$	−15.5827	−	8.72121i	−0.907263	−	0.507769i
$296$		0			0
$297$	2.34884			0.136294
$298$		0			0
$299$	21.0717	−	21.0717i	1.21861	−	1.21861i
$300$		0			0
$301$	−16.1052	−	16.1052i	−0.928286	−	0.928286i
$302$		0			0
$303$		−	1.61193i		−	0.0926028i
$304$		0			0
$305$	7.73008	−	13.8118i	0.442623	−	0.790863i
$306$		0			0
$307$	0.153856	−	0.153856i	0.00878103	−	0.00878103i	−0.702703	−	0.711484i	$-0.748024\pi$
$307$	0.153856	−	0.153856i	0.00878103	−	0.00878103i	0.711484	+	0.702703i	$0.248024\pi$
$308$		0			0
$309$	2.90803	−	2.90803i	0.165432	−	0.165432i
$310$		0			0
$311$		−	34.8210i		−	1.97452i	−0.159115	−	0.987260i	$-0.550864\pi$
$311$		−	34.8210i		−	1.97452i	0.159115	−	0.987260i	$-0.449136\pi$
$312$		0			0
$313$	17.3412			0.980182			0.490091	−	0.871671i	$-0.336964\pi$
$313$	17.3412			0.980182			0.490091	+	0.871671i	$0.336964\pi$
$314$		0			0
$315$	−4.84805	+	1.36871i	−0.273157	+	0.0771180i
$316$		0			0
$317$	10.1485	−	10.1485i	0.569999	−	0.569999i	−0.362129	−	0.932128i	$-0.617950\pi$
$317$	10.1485	−	10.1485i	0.569999	−	0.569999i	0.932128	+	0.362129i	$0.117950\pi$
$318$		0			0
$319$	8.61285			0.482227
$320$		0			0
$321$	−7.05175			−0.393591
$322$		0			0
$323$	−18.6584	+	18.6584i	−1.03818	+	1.03818i
$324$		0			0
$325$	7.85487	−	32.7962i	0.435710	−	1.81920i
$326$		0			0
$327$	−5.12737			−0.283544
$328$		0			0
$329$		−	22.7885i		−	1.25637i
$330$		0			0
$331$	−9.12552	+	9.12552i	−0.501584	+	0.501584i	−0.911930	−	0.410346i	$-0.865408\pi$
$331$	−9.12552	+	9.12552i	−0.501584	+	0.501584i	0.410346	+	0.911930i	$0.365408\pi$
$332$		0			0
$333$	−2.01181	+	2.01181i	−0.110246	+	0.110246i
$334$		0			0
$335$	13.6671	+	7.64906i	0.746711	+	0.417913i
$336$		0			0
$337$			4.62620i			0.252005i	0.992030	+	0.126002i	$0.0402147\pi$
$337$			4.62620i			0.252005i	−0.992030	+	0.126002i	$0.959785\pi$
$338$		0			0
$339$	−0.452002	−	0.452002i	−0.0245494	−	0.0245494i
$340$		0			0
$341$	−6.53276	+	6.53276i	−0.353769	+	0.353769i
$342$		0			0
$343$	−20.1059			−1.08562
$344$		0			0
$345$	8.62114	+	4.82500i	0.464146	+	0.259769i
$346$		0			0
$347$	16.1909	+	16.1909i	0.869173	+	0.869173i	0.992381	−	0.123208i	$-0.0393182\pi$
$347$	16.1909	+	16.1909i	0.869173	+	0.869173i	−0.123208	+	0.992381i	$0.539318\pi$
$348$		0			0
$349$	−21.6447	−	21.6447i	−1.15862	−	1.15862i	−0.984774	−	0.173842i	$-0.944382\pi$
$349$	−21.6447	−	21.6447i	−1.15862	−	1.15862i	−0.173842	−	0.984774i	$-0.555618\pi$
$350$		0			0
$351$	6.74474			0.360007
$352$		0			0
$353$			26.1933i			1.39413i	0.717009	+	0.697064i	$0.245511\pi$
$353$			26.1933i			1.39413i	−0.717009	+	0.697064i	$0.754489\pi$
$354$		0			0
$355$	−5.01788	+	1.41666i	−0.266322	+	0.0751883i
$356$		0			0
$357$	−11.1475	−	11.1475i	−0.589991	−	0.589991i
$358$		0			0
$359$		−	5.73157i		−	0.302501i	−0.988495	−	0.151250i	$-0.951670\pi$
$359$		−	5.73157i		−	0.302501i	0.988495	−	0.151250i	$-0.0483300\pi$
$360$		0			0
$361$		−	4.78125i		−	0.251645i
$362$		0			0
$363$	3.87703	+	3.87703i	0.203491	+	0.203491i
$364$		0			0
$365$	−1.32611	−	4.69717i	−0.0694119	−	0.245861i
$366$		0			0
$367$			20.9879i			1.09556i	0.836623	+	0.547778i	$0.184526\pi$
$367$			20.9879i			1.09556i	−0.836623	+	0.547778i	$0.815474\pi$
$368$		0			0
$369$	4.50104			0.234315
$370$		0			0
$371$	1.46278	+	1.46278i	0.0759438	+	0.0759438i
$372$		0			0
$373$	12.9141	+	12.9141i	0.668667	+	0.668667i	0.957407	−	0.288740i	$-0.0932365\pi$
$373$	12.9141	+	12.9141i	0.668667	+	0.668667i	−0.288740	+	0.957407i	$0.593236\pi$
$374$		0			0
$375$	11.1714	−	0.448018i	0.576887	−	0.0231356i
$376$		0			0
$377$	24.7320			1.27376
$378$		0			0
$379$	8.07361	−	8.07361i	0.414713	−	0.414713i	−0.468663	−	0.883377i	$-0.655264\pi$
$379$	8.07361	−	8.07361i	0.414713	−	0.414713i	0.883377	+	0.468663i	$0.155264\pi$
$380$		0			0
$381$	−12.4132	−	12.4132i	−0.635945	−	0.635945i
$382$		0			0
$383$			9.23276i			0.471772i	0.971781	+	0.235886i	$0.0757992\pi$
$383$			9.23276i			0.471772i	−0.971781	+	0.235886i	$0.924201\pi$
$384$		0			0
$385$	10.3253	+	5.77877i	0.526226	+	0.294513i
$386$		0			0
$387$	−7.14876	+	7.14876i	−0.363392	+	0.363392i
$388$		0			0
$389$	6.32362	−	6.32362i	0.320620	−	0.320620i	−0.528385	−	0.849005i	$-0.677202\pi$
$389$	6.32362	−	6.32362i	0.320620	−	0.320620i	0.849005	+	0.528385i	$0.177202\pi$
$390$		0			0
$391$			30.9179i			1.56359i
$392$		0			0
$393$	1.16842			0.0589392
$394$		0			0
$395$	3.87885	+	13.7391i	0.195166	+	0.691290i
$396$		0			0
$397$	1.07806	−	1.07806i	0.0541061	−	0.0541061i	−0.679536	−	0.733642i	$-0.737819\pi$
$397$	1.07806	−	1.07806i	0.0541061	−	0.0541061i	0.733642	+	0.679536i	$0.237819\pi$
$398$		0			0
$399$	−8.49504			−0.425284
$400$		0			0
$401$	37.0966			1.85252			0.926258	−	0.376891i	$-0.123007\pi$
$401$	37.0966			1.85252			0.926258	+	0.376891i	$0.123007\pi$
$402$		0			0
$403$	−18.7589	+	18.7589i	−0.934449	+	0.934449i
$404$		0			0
$405$	0.607542	+	2.15195i	0.0301890	+	0.106931i
$406$		0			0
$407$	6.68274			0.331251
$408$		0			0
$409$			17.3422i			0.857518i	0.903419	+	0.428759i	$0.141049\pi$
$409$			17.3422i			0.857518i	−0.903419	+	0.428759i	$0.858951\pi$
$410$		0			0
$411$	−6.31062	+	6.31062i	−0.311280	+	0.311280i
$412$		0			0
$413$	12.7218	−	12.7218i	0.626000	−	0.626000i
$414$		0			0
$415$	−14.4894	−	8.10927i	−0.711254	−	0.398068i
$416$		0			0
$417$		−	6.84010i		−	0.334961i
$418$		0			0
$419$	−20.4718	−	20.4718i	−1.00011	−	1.00011i	−1.00000		0.000110566i	$-0.999965\pi$
$419$	−20.4718	−	20.4718i	−1.00011	−	1.00011i	−0.000110566	−	1.00000i	$-0.500035\pi$
$420$		0			0
$421$	10.6143	−	10.6143i	0.517308	−	0.517308i	−0.399448	−	0.916756i	$-0.630798\pi$
$421$	10.6143	−	10.6143i	0.517308	−	0.517308i	0.916756	+	0.399448i	$0.130798\pi$
$422$		0			0
$423$	−10.1154			−0.491826
$424$		0			0
$425$	18.2978	+	29.8230i	0.887573	+	1.44663i
$426$		0			0
$427$	11.2760	+	11.2760i	0.545685	+	0.545685i
$428$		0			0
$429$	−11.2022	−	11.2022i	−0.540848	−	0.540848i
$430$		0			0
$431$	−17.9747			−0.865812			−0.432906	−	0.901439i	$-0.642512\pi$
$431$	−17.9747			−0.865812			−0.432906	+	0.901439i	$0.642512\pi$
$432$		0			0
$433$		−	23.1120i		−	1.11069i	−0.831619	−	0.555347i	$-0.812586\pi$
$433$		−	23.1120i		−	1.11069i	0.831619	−	0.555347i	$-0.187414\pi$
$434$		0			0
$435$	2.22777	+	7.89089i	0.106813	+	0.378339i
$436$		0			0
$437$	11.7806	+	11.7806i	0.563541	+	0.563541i
$438$		0			0
$439$		−	2.65049i		−	0.126501i	−0.997998	−	0.0632505i	$-0.979853\pi$
$439$		−	2.65049i		−	0.126501i	0.997998	−	0.0632505i	$-0.0201467\pi$
$440$		0			0
$441$			1.92461i			0.0916482i
$442$		0			0
$443$	−0.977227	−	0.977227i	−0.0464294	−	0.0464294i	0.683511	−	0.729940i	$-0.260452\pi$
$443$	−0.977227	−	0.977227i	−0.0464294	−	0.0464294i	−0.729940	+	0.683511i	$0.760452\pi$
$444$		0			0
$445$	33.8071	−	9.54448i	1.60261	−	0.452452i
$446$		0			0
$447$		−	2.10838i		−	0.0997231i
$448$		0			0
$449$	−19.6612			−0.927867			−0.463934	−	0.885870i	$-0.653562\pi$
$449$	−19.6612			−0.927867			−0.463934	+	0.885870i	$0.653562\pi$
$450$		0			0
$451$	−7.47570	−	7.47570i	−0.352017	−	0.352017i
$452$		0			0
$453$	6.79911	+	6.79911i	0.319450	+	0.319450i
$454$		0			0
$455$	29.6493	+	16.5938i	1.38998	+	0.777931i
$456$		0			0
$457$	−25.9752			−1.21507			−0.607535	−	0.794293i	$-0.707841\pi$
$457$	−25.9752			−1.21507			−0.607535	+	0.794293i	$0.707841\pi$
$458$		0			0
$459$	−4.94817	+	4.94817i	−0.230961	+	0.230961i
$460$		0			0
$461$	1.94218	+	1.94218i	0.0904565	+	0.0904565i	0.750887	−	0.660431i	$-0.229626\pi$
$461$	1.94218	+	1.94218i	0.0904565	+	0.0904565i	−0.660431	+	0.750887i	$0.729626\pi$
$462$		0			0
$463$			12.7805i			0.593960i	0.954884	+	0.296980i	$0.0959795\pi$
$463$			12.7805i			0.593960i	−0.954884	+	0.296980i	$0.904021\pi$
$464$		0			0
$465$	−7.67489	−	4.29541i	−0.355915	−	0.199195i
$466$		0			0
$467$	−28.2154	+	28.2154i	−1.30565	+	1.30565i	−0.381129	+	0.924522i	$0.624465\pi$
$467$	−28.2154	+	28.2154i	−1.30565	+	1.30565i	−0.924522	+	0.381129i	$0.875535\pi$
$468$		0			0
$469$	−11.1578	+	11.1578i	−0.515222	+	0.515222i
$470$		0			0
$471$			22.6497i			1.04364i
$472$		0			0
$473$	23.7465			1.09186
$474$		0			0
$475$	18.3353	+	4.39142i	0.841283	+	0.201492i
$476$		0			0
$477$	0.649299	−	0.649299i	0.0297294	−	0.0297294i
$478$		0			0
$479$	22.6500			1.03490			0.517452	−	0.855712i	$-0.326881\pi$
$479$	22.6500			1.03490			0.517452	+	0.855712i	$0.326881\pi$
$480$		0			0
$481$	19.1896			0.874970
$482$		0			0
$483$	−7.03833	+	7.03833i	−0.320255	+	0.320255i
$484$		0			0
$485$	9.93347	−	2.80443i	0.451056	−	0.127343i
$486$		0			0
$487$	20.1202			0.911733			0.455866	−	0.890048i	$-0.349329\pi$
$487$	20.1202			0.911733			0.455866	+	0.890048i	$0.349329\pi$
$488$		0			0
$489$		−	18.8765i		−	0.853624i
$490$		0			0
$491$	20.4434	−	20.4434i	0.922596	−	0.922596i	−0.0746163	−	0.997212i	$-0.523773\pi$
$491$	20.4434	−	20.4434i	0.922596	−	0.922596i	0.997212	+	0.0746163i	$0.0237732\pi$
$492$		0			0
$493$	−18.1442	+	18.1442i	−0.817174	+	0.817174i
$494$		0			0
$495$	2.56508	−	4.58319i	0.115292	−	0.205999i
$496$		0			0
$497$		−	5.25319i		−	0.235638i
$498$		0			0
$499$	26.7236	+	26.7236i	1.19631	+	1.19631i	0.975262	+	0.221052i	$0.0709489\pi$
$499$	26.7236	+	26.7236i	1.19631	+	1.19631i	0.221052	+	0.975262i	$0.429051\pi$
$500$		0			0
$501$	−9.05304	+	9.05304i	−0.404460	+	0.404460i
$502$		0			0
$503$	17.4692			0.778911			0.389456	−	0.921045i	$-0.372663\pi$
$503$	17.4692			0.778911			0.389456	+	0.921045i	$0.372663\pi$
$504$		0			0
$505$	−3.14528	−	1.76032i	−0.139963	−	0.0783334i
$506$		0			0
$507$	−22.9749	−	22.9749i	−1.02035	−	1.02035i
$508$		0			0
$509$	−22.1370	−	22.1370i	−0.981205	−	0.981205i	0.0186215	−	0.999827i	$-0.494072\pi$
$509$	−22.1370	−	22.1370i	−0.981205	−	0.981205i	−0.999827	+	0.0186215i	$0.994072\pi$
$510$		0			0
$511$	4.91744			0.217535
$512$		0			0
$513$			3.77078i			0.166484i
$514$		0			0
$515$	−2.49856	−	8.85005i	−0.110100	−	0.389980i
$516$		0			0
$517$	16.8004	+	16.8004i	0.738882	+	0.738882i
$518$		0			0
$519$		−	18.1444i		−	0.796451i
$520$		0			0
$521$		−	20.7634i		−	0.909663i	−0.890577	−	0.454832i	$-0.849699\pi$
$521$		−	20.7634i		−	0.909663i	0.890577	−	0.454832i	$-0.150301\pi$
$522$		0			0
$523$	25.9884	+	25.9884i	1.13640	+	1.13640i	0.989091	+	0.147304i	$0.0470595\pi$
$523$	25.9884	+	25.9884i	1.13640	+	1.13640i	0.147304	+	0.989091i	$0.452941\pi$
$524$		0			0
$525$	−2.62367	+	10.9545i	−0.114506	+	0.478094i
$526$		0			0
$527$		−	27.5244i		−	1.19898i
$528$		0			0
$529$	−3.47907			−0.151264
$530$		0			0
$531$	−5.64696	−	5.64696i	−0.245057	−	0.245057i
$532$		0			0
$533$	−21.4666	−	21.4666i	−0.929821	−	0.929821i
$534$		0			0
$535$	−7.70095	+	13.7598i	−0.332941	+	0.594887i
$536$		0			0
$537$	6.52309			0.281492
$538$		0			0
$539$	3.19655	−	3.19655i	0.137685	−	0.137685i
$540$		0			0
$541$	−4.86704	−	4.86704i	−0.209250	−	0.209250i	0.594698	−	0.803949i	$-0.297271\pi$
$541$	−4.86704	−	4.86704i	−0.209250	−	0.209250i	−0.803949	+	0.594698i	$0.797271\pi$
$542$		0			0
$543$		−	5.82756i		−	0.250085i
$544$		0			0
$545$	−5.59940	+	10.0048i	−0.239852	+	0.428559i
$546$		0			0
$547$	16.2487	−	16.2487i	0.694742	−	0.694742i	−0.268529	−	0.963272i	$-0.586538\pi$
$547$	16.2487	−	16.2487i	0.694742	−	0.694742i	0.963272	+	0.268529i	$0.0865376\pi$
$548$		0			0
$549$	5.00520	−	5.00520i	0.213617	−	0.213617i
$550$		0			0
$551$			13.8269i			0.589045i
$552$		0			0
$553$	−14.3834			−0.611644
$554$		0			0
$555$	1.72853	+	6.12256i	0.0733721	+	0.259888i
$556$		0			0
$557$	−0.616853	+	0.616853i	−0.0261369	+	0.0261369i	−0.720054	−	0.693918i	$-0.755883\pi$
$557$	−0.616853	+	0.616853i	−0.0261369	+	0.0261369i	0.693918	+	0.720054i	$0.255883\pi$
$558$		0			0
$559$	68.1884			2.88406
$560$		0			0
$561$	16.4367			0.693956
$562$		0			0
$563$	17.4063	−	17.4063i	0.733587	−	0.733587i	−0.237742	−	0.971328i	$-0.576407\pi$
$563$	17.4063	−	17.4063i	0.733587	−	0.733587i	0.971328	+	0.237742i	$0.0764072\pi$
$564$		0			0
$565$	−1.37559	+	0.388358i	−0.0578714	+	0.0163383i
$566$		0			0
$567$	−2.25286			−0.0946113
$568$		0			0
$569$		−	1.57959i		−	0.0662197i	−0.999452	−	0.0331098i	$-0.989459\pi$
$569$		−	1.57959i		−	0.0662197i	0.999452	−	0.0331098i	$-0.0105411\pi$
$570$		0			0
$571$	24.6949	−	24.6949i	1.03345	−	1.03345i	0.0340299	−	0.999421i	$-0.489166\pi$
$571$	24.6949	−	24.6949i	1.03345	−	1.03345i	0.999421	−	0.0340299i	$-0.0108341\pi$
$572$		0			0
$573$	0.674155	−	0.674155i	0.0281632	−	0.0281632i
$574$		0			0
$575$	18.8296	−	11.5528i	0.785250	−	0.481787i
$576$		0			0
$577$			33.6673i			1.40159i	0.713363	+	0.700795i	$0.247171\pi$
$577$			33.6673i			1.40159i	−0.713363	+	0.700795i	$0.752829\pi$
$578$		0			0
$579$	−3.40957	−	3.40957i	−0.141697	−	0.141697i
$580$		0			0
$581$	11.8292	−	11.8292i	0.490757	−	0.490757i
$582$		0			0
$583$	−2.15682			−0.0893263
$584$		0			0
$585$	7.36567	−	13.1607i	0.304533	−	0.544128i
$586$		0			0
$587$	−30.6327	−	30.6327i	−1.26435	−	1.26435i	−0.948964	−	0.315385i	$-0.897866\pi$
$587$	−30.6327	−	30.6327i	−1.26435	−	1.26435i	−0.315385	−	0.948964i	$-0.602134\pi$
$588$		0			0
$589$	−10.4875	−	10.4875i	−0.432132	−	0.432132i
$590$		0			0
$591$	−3.50245			−0.144071
$592$		0			0
$593$		−	25.1477i		−	1.03269i	−0.856380	−	0.516347i	$-0.827292\pi$
$593$		−	25.1477i		−	1.03269i	0.856380	−	0.516347i	$-0.172708\pi$
$594$		0			0
$595$	−33.9255	+	9.57791i	−1.39081	+	0.392656i
$596$		0			0
$597$	−12.3344	−	12.3344i	−0.504815	−	0.504815i
$598$		0			0
$599$		−	18.0767i		−	0.738594i	−0.929311	−	0.369297i	$-0.879598\pi$
$599$		−	18.0767i		−	0.738594i	0.929311	−	0.369297i	$-0.120402\pi$
$600$		0			0
$601$			26.5291i			1.08214i	0.840977	+	0.541072i	$0.181981\pi$
$601$			26.5291i			1.08214i	−0.840977	+	0.541072i	$0.818019\pi$
$602$		0			0
$603$	4.95274	+	4.95274i	0.201691	+	0.201691i
$604$		0			0
$605$	11.7990	−	3.33112i	0.479699	−	0.135429i
$606$		0			0
$607$		−	28.3496i		−	1.15068i	−0.817916	−	0.575338i	$-0.804871\pi$
$607$		−	28.3496i		−	1.15068i	0.817916	−	0.575338i	$-0.195129\pi$
$608$		0			0
$609$	−8.26091			−0.334749
$610$		0			0
$611$	48.2427	+	48.2427i	1.95169	+	1.95169i
$612$		0			0
$613$	−3.24941	−	3.24941i	−0.131243	−	0.131243i	0.638434	−	0.769677i	$-0.279583\pi$
$613$	−3.24941	−	3.24941i	−0.131243	−	0.131243i	−0.769677	+	0.638434i	$0.779583\pi$
$614$		0			0
$615$	4.91542	−	8.78269i	0.198209	−	0.354152i
$616$		0			0
$617$	18.4370			0.742245			0.371123	−	0.928584i	$-0.378973\pi$
$617$	18.4370			0.742245			0.371123	+	0.928584i	$0.378973\pi$
$618$		0			0
$619$	9.47769	−	9.47769i	0.380941	−	0.380941i	−0.490500	−	0.871441i	$-0.663186\pi$
$619$	9.47769	−	9.47769i	0.380941	−	0.380941i	0.871441	+	0.490500i	$0.163186\pi$
$620$		0			0
$621$	3.12417	+	3.12417i	0.125369	+	0.125369i
$622$		0			0
$623$			35.3924i			1.41797i
$624$		0			0
$625$	11.3256	−	22.2874i	0.453025	−	0.891498i
$626$		0			0
$627$	6.26281	−	6.26281i	0.250113	−	0.250113i
$628$		0			0
$629$	−14.0782	+	14.0782i	−0.561333	+	0.561333i
$630$		0			0
$631$			10.6343i			0.423346i	0.977341	+	0.211673i	$0.0678912\pi$
$631$			10.6343i			0.423346i	−0.977341	+	0.211673i	$0.932109\pi$
$632$		0			0
$633$	7.65281			0.304172
$634$		0			0
$635$	−37.7772	+	10.6653i	−1.49914	+	0.423240i
$636$		0			0
$637$	9.17895	−	9.17895i	0.363683	−	0.363683i
$638$		0			0
$639$	−2.33178			−0.0922439
$640$		0			0
$641$	−21.4256			−0.846261			−0.423130	−	0.906069i	$-0.639069\pi$
$641$	−21.4256			−0.846261			−0.423130	+	0.906069i	$0.639069\pi$
$642$		0			0
$643$	28.7046	−	28.7046i	1.13200	−	1.13200i	0.142152	−	0.989845i	$-0.454598\pi$
$643$	28.7046	−	28.7046i	1.13200	−	1.13200i	0.989845	−	0.142152i	$-0.0454022\pi$
$644$		0			0
$645$	6.14217	+	21.7559i	0.241848	+	0.856639i
$646$		0			0
$647$	−36.8695			−1.44949			−0.724746	−	0.689017i	$-0.758043\pi$
$647$	−36.8695			−1.44949			−0.724746	+	0.689017i	$0.758043\pi$
$648$		0			0
$649$			18.7579i			0.736311i
$650$		0			0
$651$	6.26582	−	6.26582i	0.245577	−	0.245577i
$652$		0			0
$653$	−27.8096	+	27.8096i	−1.08828	+	1.08828i	−0.0925688	+	0.995706i	$0.529508\pi$
$653$	−27.8096	+	27.8096i	−1.08828	+	1.08828i	−0.995706	+	0.0925688i	$0.970492\pi$
$654$		0			0
$655$	1.27599	−	2.27989i	0.0498571	−	0.0890829i
$656$		0			0
$657$		−	2.18275i		−	0.0851572i
$658$		0			0
$659$	−11.6956	−	11.6956i	−0.455596	−	0.455596i	0.441611	−	0.897207i	$-0.354407\pi$
$659$	−11.6956	−	11.6956i	−0.455596	−	0.455596i	−0.897207	+	0.441611i	$0.854407\pi$
$660$		0			0
$661$	−29.7275	+	29.7275i	−1.15627	+	1.15627i	−0.170994	+	0.985272i	$0.554698\pi$
$661$	−29.7275	+	29.7275i	−1.15627	+	1.15627i	−0.985272	+	0.170994i	$0.945302\pi$
$662$		0			0
$663$	47.1981			1.83302
$664$		0			0
$665$	−9.27711	+	16.5760i	−0.359751	+	0.642790i
$666$		0			0
$667$	11.4559	+	11.4559i	0.443574	+	0.443574i
$668$		0			0
$669$	12.9142	+	12.9142i	0.499292	+	0.499292i
$670$		0			0
$671$	−16.6261			−0.641843
$672$		0			0
$673$		−	19.4197i		−	0.748575i	−0.927313	−	0.374287i	$-0.877887\pi$
$673$		−	19.4197i		−	0.748575i	0.927313	−	0.374287i	$-0.122113\pi$
$674$		0			0
$675$	4.86248	+	1.16459i	0.187157	+	0.0448252i
$676$		0			0
$677$	−22.0550	−	22.0550i	−0.847643	−	0.847643i	0.142196	−	0.989839i	$-0.454584\pi$
$677$	−22.0550	−	22.0550i	−0.847643	−	0.847643i	−0.989839	+	0.142196i	$0.954584\pi$
$678$		0			0
$679$			10.3993i			0.399088i
$680$		0			0
$681$			3.16462i			0.121269i
$682$		0			0
$683$	9.95729	+	9.95729i	0.381005	+	0.381005i	0.871464	−	0.490459i	$-0.163171\pi$
$683$	9.95729	+	9.95729i	0.381005	+	0.381005i	−0.490459	+	0.871464i	$0.663171\pi$
$684$		0			0
$685$	5.42205	+	19.2052i	0.207166	+	0.733794i
$686$		0			0
$687$			9.06474i			0.345842i
$688$		0			0
$689$	−6.19334			−0.235947
$690$		0			0
$691$	−30.1664	−	30.1664i	−1.14758	−	1.14758i	−0.987027	−	0.160556i	$-0.948671\pi$
$691$	−30.1664	−	30.1664i	−1.14758	−	1.14758i	−0.160556	−	0.987027i	$-0.551329\pi$
$692$		0			0
$693$	3.74174	+	3.74174i	0.142137	+	0.142137i
$694$		0			0
$695$	−13.3468	−	7.46981i	−0.506272	−	0.283346i
$696$		0			0
$697$	31.4973			1.19304
$698$		0			0
$699$	−1.89485	+	1.89485i	−0.0716698	+	0.0716698i
$700$		0			0
$701$	2.10793	+	2.10793i	0.0796155	+	0.0796155i	0.745793	−	0.666178i	$-0.232071\pi$
$701$	2.10793	+	2.10793i	0.0796155	+	0.0796155i	−0.666178	+	0.745793i	$0.732071\pi$
$702$		0			0
$703$			10.7283i			0.404626i
$704$		0			0
$705$	−11.0466	+	19.7377i	−0.416039	+	0.743364i
$706$		0			0
$707$	2.56782	−	2.56782i	0.0965729	−	0.0965729i
$708$		0			0
$709$	29.5759	−	29.5759i	1.11075	−	1.11075i	0.117697	−	0.993050i	$-0.462449\pi$
$709$	29.5759	−	29.5759i	1.11075	−	1.11075i	0.993050	−	0.117697i	$-0.0375512\pi$
$710$		0			0
$711$			6.38450i			0.239437i
$712$		0			0
$713$	−17.3783			−0.650824
$714$		0			0
$715$	−34.0919	+	9.62488i	−1.27496	+	0.359950i
$716$		0			0
$717$	18.4076	−	18.4076i	0.687446	−	0.687446i
$718$		0			0
$719$	−15.2528			−0.568833			−0.284417	−	0.958701i	$-0.591800\pi$
$719$	−15.2528			−0.568833			−0.284417	+	0.958701i	$0.591800\pi$
$720$		0			0
$721$	9.26506			0.345049
$722$		0			0
$723$	4.15360	−	4.15360i	0.154474	−	0.154474i
$724$		0			0
$725$	17.8300	+	4.27039i	0.662190	+	0.158598i
$726$		0			0
$727$	−22.5396			−0.835947			−0.417973	−	0.908459i	$-0.637260\pi$
$727$	−22.5396			−0.835947			−0.417973	+	0.908459i	$0.637260\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−50.0254	+	50.0254i	−1.85025	+	1.85025i
$732$		0			0
$733$	8.88368	−	8.88368i	0.328126	−	0.328126i	−0.523747	−	0.851874i	$-0.675466\pi$
$733$	8.88368	−	8.88368i	0.328126	−	0.328126i	0.851874	+	0.523747i	$0.175466\pi$
$734$		0			0
$735$	3.75541	+	2.10180i	0.138520	+	0.0775259i
$736$		0			0
$737$		−	16.4518i		−	0.606011i
$738$		0			0
$739$	−3.00557	−	3.00557i	−0.110562	−	0.110562i	0.649662	−	0.760223i	$-0.274911\pi$
$739$	−3.00557	−	3.00557i	−0.110562	−	0.110562i	−0.760223	+	0.649662i	$0.774911\pi$
$740$		0			0
$741$	17.9838	−	17.9838i	0.660650	−	0.660650i
$742$		0			0
$743$	14.5808			0.534919			0.267459	−	0.963569i	$-0.413816\pi$
$743$	14.5808			0.534919			0.267459	+	0.963569i	$0.413816\pi$
$744$		0			0
$745$	−4.11399	−	2.30248i	−0.150725	−	0.0843565i
$746$		0			0
$747$	−5.25073	−	5.25073i	−0.192114	−	0.192114i
$748$		0			0
$749$	−11.2335	−	11.2335i	−0.410465	−	0.410465i
$750$		0			0
$751$	1.92675			0.0703083			0.0351541	−	0.999382i	$-0.488808\pi$
$751$	1.92675			0.0703083			0.0351541	+	0.999382i	$0.488808\pi$
$752$		0			0
$753$		−	11.9371i		−	0.435012i
$754$		0			0
$755$	20.6919	−	5.84176i	0.753054	−	0.212603i
$756$		0			0
$757$	0.389306	+	0.389306i	0.0141496	+	0.0141496i	0.714146	−	0.699997i	$-0.246815\pi$
$757$	0.389306	+	0.389306i	0.0141496	+	0.0141496i	−0.699997	+	0.714146i	$0.746815\pi$
$758$		0			0
$759$		−	10.3778i		−	0.376689i
$760$		0			0
$761$			18.0200i			0.653223i	0.945159	+	0.326612i	$0.105907\pi$
$761$			18.0200i			0.653223i	−0.945159	+	0.326612i	$0.894093\pi$
$762$		0			0
$763$	−8.16797	−	8.16797i	−0.295700	−	0.295700i
$764$		0			0
$765$	4.25144	+	15.0589i	0.153711	+	0.544454i
$766$		0			0
$767$			53.8635i			1.94490i
$768$		0			0
$769$	−34.9422			−1.26005			−0.630024	−	0.776576i	$-0.716955\pi$
$769$	−34.9422			−1.26005			−0.630024	+	0.776576i	$0.716955\pi$
$770$		0			0
$771$	−15.6986	−	15.6986i	−0.565371	−	0.565371i
$772$		0			0
$773$	9.83112	+	9.83112i	0.353601	+	0.353601i	0.861447	−	0.507847i	$-0.169558\pi$
$773$	9.83112	+	9.83112i	0.353601	+	0.353601i	−0.507847	+	0.861447i	$0.669558\pi$
$774$		0			0
$775$	−16.7629	+	10.2848i	−0.602142	+	0.369442i
$776$		0			0
$777$	−6.40967			−0.229946
$778$		0			0
$779$	12.0013	−	12.0013i	0.429992	−	0.429992i
$780$		0			0
$781$	3.87282	+	3.87282i	0.138580	+	0.138580i
$782$		0			0
$783$			3.66685i			0.131043i
$784$		0			0
$785$	44.1954	+	24.7349i	1.57740	+	0.882826i
$786$		0			0
$787$	34.3615	−	34.3615i	1.22486	−	1.22486i	0.258970	−	0.965885i	$-0.416617\pi$
$787$	34.3615	−	34.3615i	1.22486	−	1.22486i	0.965885	−	0.258970i	$-0.0833831\pi$
$788$		0			0
$789$	−0.328420	+	0.328420i	−0.0116921	+	0.0116921i
$790$		0			0
$791$		−	1.44009i		−	0.0512038i
$792$		0			0
$793$	−47.7421			−1.69537
$794$		0			0
$795$	−0.557874	−	1.97602i	−0.0197858	−	0.0700823i
$796$		0			0
$797$	3.63103	−	3.63103i	0.128618	−	0.128618i	−0.639868	−	0.768485i	$-0.721011\pi$
$797$	3.63103	−	3.63103i	0.128618	−	0.128618i	0.768485	+	0.639868i	$0.221011\pi$
$798$		0			0
$799$	−70.7850			−2.50419
$800$		0			0
$801$	15.7100			0.555085
$802$		0			0
$803$	−3.62529	+	3.62529i	−0.127934	+	0.127934i
$804$		0			0
$805$	6.04730	+	21.4199i	0.213139	+	0.754952i
$806$		0			0
$807$	−6.70626			−0.236072
$808$		0			0
$809$		−	15.9241i		−	0.559860i	−0.960020	−	0.279930i	$-0.909689\pi$
$809$		−	15.9241i		−	0.559860i	0.960020	−	0.279930i	$-0.0903113\pi$
$810$		0			0
$811$	11.6448	−	11.6448i	0.408906	−	0.408906i	−0.472451	−	0.881357i	$-0.656631\pi$
$811$	11.6448	−	11.6448i	0.408906	−	0.408906i	0.881357	+	0.472451i	$0.156631\pi$
$812$		0			0
$813$	−8.51477	+	8.51477i	−0.298626	+	0.298626i
$814$		0			0
$815$	−36.8328	−	20.6143i	−1.29020	−	0.722087i
$816$		0			0
$817$			38.1220i			1.33372i
$818$		0			0
$819$	10.7445	+	10.7445i	0.375442	+	0.375442i
$820$		0			0
$821$	−24.3703	+	24.3703i	−0.850530	+	0.850530i	−0.990198	−	0.139669i	$-0.955396\pi$
$821$	−24.3703	+	24.3703i	−0.850530	+	0.850530i	0.139669	+	0.990198i	$0.455396\pi$
$822$		0			0
$823$	−51.2425			−1.78620			−0.893101	−	0.449856i	$-0.851475\pi$
$823$	−51.2425			−1.78620			−0.893101	+	0.449856i	$0.851475\pi$
$824$		0			0
$825$	−6.14176	−	10.0103i	−0.213828	−	0.348512i
$826$		0			0
$827$	−9.55201	−	9.55201i	−0.332156	−	0.332156i	0.521249	−	0.853405i	$-0.325466\pi$
$827$	−9.55201	−	9.55201i	−0.332156	−	0.332156i	−0.853405	+	0.521249i	$0.825466\pi$
$828$		0			0
$829$	33.3127	+	33.3127i	1.15700	+	1.15700i	0.985118	+	0.171879i	$0.0549837\pi$
$829$	33.3127	+	33.3127i	1.15700	+	1.15700i	0.171879	+	0.985118i	$0.445016\pi$
$830$		0			0
$831$	25.4219			0.881877
$832$		0			0
$833$			13.4680i			0.466638i
$834$		0			0
$835$	7.77832	+	27.5513i	0.269180	+	0.953451i
$836$		0			0
$837$	−2.78127	−	2.78127i	−0.0961347	−	0.0961347i
$838$		0			0
$839$			9.50181i			0.328039i	0.986457	+	0.164019i	$0.0524460\pi$
$839$			9.50181i			0.328039i	−0.986457	+	0.164019i	$0.947554\pi$
$840$		0			0
$841$		−	15.5542i		−	0.536352i
$842$		0			0
$843$	−6.77911	−	6.77911i	−0.233485	−	0.233485i
$844$		0			0
$845$	−69.9200	+	19.7399i	−2.40532	+	0.679075i
$846$		0			0
$847$			12.3523i			0.424431i
$848$		0			0
$849$	−7.19866			−0.247057
$850$		0			0
$851$	8.88866	+	8.88866i	0.304699	+	0.304699i
$852$		0			0
$853$	−14.2909	−	14.2909i	−0.489310	−	0.489310i	0.418778	−	0.908089i	$-0.362458\pi$
$853$	−14.2909	−	14.2909i	−0.489310	−	0.489310i	−0.908089	+	0.418778i	$0.862458\pi$
$854$		0			0
$855$	7.35775	+	4.11792i	0.251630	+	0.140830i
$856$		0			0
$857$	−24.4246			−0.834327			−0.417164	−	0.908831i	$-0.636976\pi$
$857$	−24.4246			−0.834327			−0.417164	+	0.908831i	$0.636976\pi$
$858$		0			0
$859$	21.3398	−	21.3398i	0.728105	−	0.728105i	−0.242137	−	0.970242i	$-0.577848\pi$
$859$	21.3398	−	21.3398i	0.728105	−	0.728105i	0.970242	+	0.242137i	$0.0778485\pi$
$860$		0			0
$861$	7.17022	+	7.17022i	0.244361	+	0.244361i
$862$		0			0
$863$		−	54.8339i		−	1.86657i	−0.359138	−	0.933284i	$-0.616929\pi$
$863$		−	54.8339i		−	1.86657i	0.359138	−	0.933284i	$-0.383071\pi$
$864$		0			0
$865$	−35.4044	−	19.8148i	−1.20379	−	0.673724i
$866$		0			0
$867$	−22.6054	+	22.6054i	−0.767718	+	0.767718i
$868$		0			0
$869$	10.6039	−	10.6039i	0.359712	−	0.359712i
$870$		0			0
$871$		−	47.2417i		−	1.60072i
$872$		0			0
$873$	4.61603			0.156229
$874$		0			0
$875$	18.5098	+	17.0824i	0.625747	+	0.577492i
$876$		0			0
$877$	8.43052	−	8.43052i	0.284678	−	0.284678i	−0.550293	−	0.834972i	$-0.685484\pi$
$877$	8.43052	−	8.43052i	0.284678	−	0.284678i	0.834972	+	0.550293i	$0.185484\pi$
$878$		0			0
$879$	6.01142			0.202760
$880$		0			0
$881$	−33.7215			−1.13611			−0.568053	−	0.822992i	$-0.692303\pi$
$881$	−33.7215			−1.13611			−0.568053	+	0.822992i	$0.692303\pi$
$882$		0			0
$883$	−33.5737	+	33.5737i	−1.12984	+	1.12984i	−0.139642	+	0.990202i	$0.544595\pi$
$883$	−33.5737	+	33.5737i	−1.12984	+	1.12984i	−0.990202	+	0.139642i	$0.955405\pi$
$884$		0			0
$885$	−17.1855	+	4.85184i	−0.577684	+	0.163093i
$886$		0			0
$887$	−7.09705			−0.238295			−0.119148	−	0.992877i	$-0.538016\pi$
$887$	−7.09705			−0.238295			−0.119148	+	0.992877i	$0.538016\pi$
$888$		0			0
$889$		−	39.5487i		−	1.32642i
$890$		0			0
$891$	1.66088	−	1.66088i	0.0556416	−	0.0556416i
$892$		0			0
$893$	−26.9710	+	26.9710i	−0.902551	+	0.902551i
$894$		0			0
$895$	7.12362	−	12.7282i	0.238116	−	0.425457i
$896$		0			0
$897$		−	29.7999i		−	0.994991i
$898$		0			0
$899$	−10.1985	−	10.1985i	−0.340139	−	0.340139i
$900$		0			0
$901$	4.54365	−	4.54365i	0.151371	−	0.151371i
$902$		0			0
$903$	−22.7761			−0.757942
$904$		0			0
$905$	−11.3711	−	6.36405i	−0.377987	−	0.211548i
$906$		0			0
$907$	−4.37877	−	4.37877i	−0.145395	−	0.145395i	0.630662	−	0.776057i	$-0.282783\pi$
$907$	−4.37877	−	4.37877i	−0.145395	−	0.145395i	−0.776057	+	0.630662i	$0.782783\pi$
$908$		0			0
$909$	−1.13980	−	1.13980i	−0.0378049	−	0.0378049i
$910$		0			0
$911$	−26.7307			−0.885627			−0.442814	−	0.896614i	$-0.646020\pi$
$911$	−26.7307			−0.885627			−0.442814	+	0.896614i	$0.646020\pi$
$912$		0			0
$913$			17.4417i			0.577235i
$914$		0			0
$915$	−4.30044	−	15.2324i	−0.142168	−	0.503568i
$916$		0			0
$917$	1.86132	+	1.86132i	0.0614661	+	0.0614661i
$918$		0			0
$919$		−	24.5598i		−	0.810154i	−0.914282	−	0.405077i	$-0.867245\pi$
$919$		−	24.5598i		−	0.810154i	0.914282	−	0.405077i	$-0.132755\pi$
$920$		0			0
$921$		−	0.217585i		−	0.00716968i
$922$		0			0
$923$	11.1209	+	11.1209i	0.366047	+	0.366047i
$924$		0			0
$925$	13.8344	+	3.31341i	0.454871	+	0.108944i
$926$		0			0
$927$		−	4.11257i		−	0.135075i
$928$		0			0
$929$	6.25552			0.205237			0.102619	−	0.994721i	$-0.467278\pi$
$929$	6.25552			0.205237			0.102619	+	0.994721i	$0.467278\pi$
$930$		0			0
$931$	5.13167	+	5.13167i	0.168184	+	0.168184i
$932$		0			0
$933$	−24.6222	−	24.6222i	−0.806095	−	0.806095i
$934$		0			0
$935$	17.9498	−	32.0721i	0.587023	−	1.04887i
$936$		0			0
$937$	−33.0332			−1.07915			−0.539574	−	0.841938i	$-0.681415\pi$
$937$	−33.0332			−1.07915			−0.539574	+	0.841938i	$0.681415\pi$
$938$		0			0
$939$	12.2621	−	12.2621i	0.400158	−	0.400158i
$940$		0			0
$941$	24.4774	+	24.4774i	0.797941	+	0.797941i	0.982771	−	0.184830i	$-0.0591733\pi$
$941$	24.4774	+	24.4774i	0.797941	+	0.797941i	−0.184830	+	0.982771i	$0.559173\pi$
$942$		0			0
$943$		−	19.8867i		−	0.647601i
$944$		0			0
$945$	−2.46026	+	4.39591i	−0.0800324	+	0.142999i
$946$		0			0
$947$	34.7666	−	34.7666i	1.12976	−	1.12976i	0.139546	−	0.990216i	$-0.455436\pi$
$947$	34.7666	−	34.7666i	1.12976	−	1.12976i	0.990216	−	0.139546i	$-0.0445643\pi$
$948$		0			0
$949$	−10.4101	+	10.4101i	−0.337925	+	0.337925i
$950$		0			0
$951$		−	14.3522i		−	0.465402i
$952$		0			0
$953$	−16.9913			−0.550403			−0.275201	−	0.961387i	$-0.588745\pi$
$953$	−16.9913			−0.550403			−0.275201	+	0.961387i	$0.588745\pi$
$954$		0			0
$955$	−0.579230	−	2.05167i	−0.0187434	−	0.0663904i
$956$		0			0
$957$	6.09021	−	6.09021i	0.196868	−	0.196868i
$958$		0			0
$959$	−20.1058			−0.649251
$960$		0			0
$961$	−15.5291			−0.500938
$962$		0			0
$963$	−4.98634	+	4.98634i	−0.160683	+	0.160683i
$964$		0			0
$965$	−10.3764	+	2.92948i	−0.334028	+	0.0943034i
$966$		0			0
$967$	57.8174			1.85928			0.929641	−	0.368467i	$-0.120117\pi$
$967$	57.8174			1.85928			0.929641	+	0.368467i	$0.120117\pi$
$968$		0			0
$969$			26.3870i			0.847674i
$970$		0			0
$971$	−39.9663	+	39.9663i	−1.28258	+	1.28258i	−0.343383	+	0.939196i	$0.611573\pi$
$971$	−39.9663	+	39.9663i	−1.28258	+	1.28258i	−0.939196	+	0.343383i	$0.888427\pi$
$972$		0			0
$973$	10.8964	−	10.8964i	0.349322	−	0.349322i
$974$		0			0
$975$	−17.6362	−	28.7446i	−0.564809	−	0.920564i
$976$		0			0
$977$			55.3797i			1.77175i	0.463921	+	0.885877i	$0.346442\pi$
$977$			55.3797i			1.77175i	−0.463921	+	0.885877i	$0.653558\pi$
$978$		0			0
$979$	−26.0924	−	26.0924i	−0.833917	−	0.833917i
$980$		0			0
$981$	−3.62560	+	3.62560i	−0.115756	+	0.115756i
$982$		0			0
$983$	−3.19883			−0.102027			−0.0510134	−	0.998698i	$-0.516245\pi$
$983$	−3.19883			−0.102027			−0.0510134	+	0.998698i	$0.516245\pi$
$984$		0			0
$985$	−3.82489	+	6.83417i	−0.121871	+	0.217755i
$986$		0			0
$987$	−16.1139	−	16.1139i	−0.512912	−	0.512912i
$988$		0			0
$989$	31.5850	+	31.5850i	1.00434	+	1.00434i
$990$		0			0
$991$	−10.5891			−0.336373			−0.168186	−	0.985755i	$-0.553791\pi$
$991$	−10.5891			−0.336373			−0.168186	+	0.985755i	$0.553791\pi$
$992$		0			0
$993$			12.9054i			0.409541i
$994$		0			0
$995$	−37.5376	+	10.5977i	−1.19002	+	0.335969i
$996$		0			0
$997$	−18.1735	−	18.1735i	−0.575559	−	0.575559i	0.358117	−	0.933677i	$-0.383419\pi$
$997$	−18.1735	−	18.1735i	−0.575559	−	0.575559i	−0.933677	+	0.358117i	$0.883419\pi$
$998$		0			0
$999$			2.84512i			0.0900157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.b.289.16		48
4.3	odd	2		1920.2.bl.a.289.9		48
5.4	even	2	inner	1920.2.bl.b.289.9		48
8.3	odd	2		240.2.bl.a.109.21	yes	48
8.5	even	2		960.2.bl.a.529.8		48
16.3	odd	4		240.2.bl.a.229.4	yes	48
16.5	even	4	inner	1920.2.bl.b.1249.9		48
16.11	odd	4		1920.2.bl.a.1249.16		48
16.13	even	4		960.2.bl.a.49.14		48
20.19	odd	2		1920.2.bl.a.289.16		48
24.11	even	2		720.2.bm.h.109.4		48
40.19	odd	2		240.2.bl.a.109.4	✓	48
40.29	even	2		960.2.bl.a.529.14		48
48.35	even	4		720.2.bm.h.469.21		48
80.19	odd	4		240.2.bl.a.229.21	yes	48
80.29	even	4		960.2.bl.a.49.8		48
80.59	odd	4		1920.2.bl.a.1249.9		48
80.69	even	4	inner	1920.2.bl.b.1249.16		48
120.59	even	2		720.2.bm.h.109.21		48
240.179	even	4		720.2.bm.h.469.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.4	✓	48	40.19	odd	2
240.2.bl.a.109.21	yes	48	8.3	odd	2
240.2.bl.a.229.4	yes	48	16.3	odd	4
240.2.bl.a.229.21	yes	48	80.19	odd	4
720.2.bm.h.109.4		48	24.11	even	2
720.2.bm.h.109.21		48	120.59	even	2
720.2.bm.h.469.4		48	240.179	even	4
720.2.bm.h.469.21		48	48.35	even	4
960.2.bl.a.49.8		48	80.29	even	4
960.2.bl.a.49.14		48	16.13	even	4
960.2.bl.a.529.8		48	8.5	even	2
960.2.bl.a.529.14		48	40.29	even	2
1920.2.bl.a.289.9		48	4.3	odd	2
1920.2.bl.a.289.16		48	20.19	odd	2
1920.2.bl.a.1249.9		48	80.59	odd	4
1920.2.bl.a.1249.16		48	16.11	odd	4
1920.2.bl.b.289.9		48	5.4	even	2	inner
1920.2.bl.b.289.16		48	1.1	even	1	trivial
1920.2.bl.b.1249.9		48	16.5	even	4	inner
1920.2.bl.b.1249.16		48	80.69	even	4	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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.607542 - 2.15195i) q^{5} +2.25286 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.607542 - 2.15195i) q^{5} +2.25286 q^{7} -1.00000i q^{9} +(-1.66088 + 1.66088i) q^{11} +(-4.76925 + 4.76925i) q^{13} +(-1.95126 - 1.09206i) q^{15} -6.99777i q^{17} +(-2.66634 - 2.66634i) q^{19} +(1.59301 - 1.59301i) q^{21} -4.41825 q^{23} +(-4.26178 + 2.61480i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-2.59286 - 2.59286i) q^{29} +3.93331 q^{31} +2.34884i q^{33} +(-1.36871 - 4.84805i) q^{35} +(-2.01181 - 2.01181i) q^{37} +6.74474i q^{39} +4.50104i q^{41} +(-7.14876 - 7.14876i) q^{43} +(-2.15195 + 0.607542i) q^{45} -10.1154i q^{47} -1.92461 q^{49} +(-4.94817 - 4.94817i) q^{51} +(0.649299 + 0.649299i) q^{53} +(4.58319 + 2.56508i) q^{55} -3.77078 q^{57} +(5.64696 - 5.64696i) q^{59} +(5.00520 + 5.00520i) q^{61} -2.25286i q^{63} +(13.1607 + 7.36567i) q^{65} +(-4.95274 + 4.95274i) q^{67} +(-3.12417 + 3.12417i) q^{69} -2.33178i q^{71} +2.18275 q^{73} +(-1.16459 + 4.86248i) q^{75} +(-3.74174 + 3.74174i) q^{77} -6.38450 q^{79} -1.00000 q^{81} +(5.25073 - 5.25073i) q^{83} +(-15.0589 + 4.25144i) q^{85} -3.66685 q^{87} +15.7100i q^{89} +(-10.7445 + 10.7445i) q^{91} +(2.78127 - 2.78127i) q^{93} +(-4.11792 + 7.35775i) q^{95} +4.61603i q^{97} +(1.66088 + 1.66088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 8 q^{19} + 48 q^{31} + 24 q^{35} + 48 q^{49} + 8 q^{51} - 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} - 16 q^{75} + 96 q^{79} - 48 q^{81} - 32 q^{91} + 48 q^{95}+O(q^{100}) \) 48 * q + 8 * q^19 + 48 * q^31 + 24 * q^35 + 48 * q^49 + 8 * q^51 - 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 - 16 * q^75 + 96 * q^79 - 48 * q^81 - 32 * q^91 + 48 * q^95

Introduction

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