LMFDB - Embedded newform 1920.2.bl.a.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.a.1249.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(2.15195 + 0.607542i) q^{5} +2.25286 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(2.15195 + 0.607542i) q^{5} +2.25286 q^{7} -1.00000i q^{9} +(1.66088 - 1.66088i) q^{11} +(4.76925 - 4.76925i) q^{13} +(1.95126 - 1.09206i) q^{15} +6.99777i q^{17} +(2.66634 + 2.66634i) q^{19} +(1.59301 - 1.59301i) q^{21} -4.41825 q^{23} +(4.26178 + 2.61480i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-2.59286 - 2.59286i) q^{29} -3.93331 q^{31} -2.34884i q^{33} +(4.84805 + 1.36871i) q^{35} +(2.01181 + 2.01181i) q^{37} -6.74474i q^{39} +4.50104i q^{41} +(-7.14876 - 7.14876i) q^{43} +(0.607542 - 2.15195i) q^{45} -10.1154i q^{47} -1.92461 q^{49} +(4.94817 + 4.94817i) q^{51} +(-0.649299 - 0.649299i) q^{53} +(4.58319 - 2.56508i) q^{55} +3.77078 q^{57} +(-5.64696 + 5.64696i) q^{59} +(5.00520 + 5.00520i) q^{61} -2.25286i q^{63} +(13.1607 - 7.36567i) q^{65} +(-4.95274 + 4.95274i) q^{67} +(-3.12417 + 3.12417i) q^{69} +2.33178i q^{71} -2.18275 q^{73} +(4.86248 - 1.16459i) q^{75} +(3.74174 - 3.74174i) q^{77} +6.38450 q^{79} -1.00000 q^{81} +(5.25073 - 5.25073i) q^{83} +(-4.25144 + 15.0589i) q^{85} -3.66685 q^{87} +15.7100i q^{89} +(10.7445 - 10.7445i) q^{91} +(-2.78127 + 2.78127i) q^{93} +(4.11792 + 7.35775i) q^{95} -4.61603i q^{97} +(-1.66088 - 1.66088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.15195	+	0.607542i	0.962382	+	0.271701i
$5$	2.15195	+	0.607542i	0.962382	+	0.271701i
$6$		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	−0.410904	−	0.911679i	$-0.634787\pi$
$11$	1.66088	−	1.66088i	0.500775	−	0.500775i	0.911679	+	0.410904i	$0.134787\pi$
$12$		0			0
$13$	4.76925	−	4.76925i	1.32275	−	1.32275i	0.411212	−	0.911540i	$-0.365106\pi$
$13$	4.76925	−	4.76925i	1.32275	−	1.32275i	0.911540	−	0.411212i	$-0.134894\pi$
$14$		0			0
$15$	1.95126	−	1.09206i	0.503812	−	0.281969i
$16$		0			0
$17$			6.99777i			1.69721i	0.529028	+	0.848604i	$0.322557\pi$
$17$			6.99777i			1.69721i	−0.529028	+	0.848604i	$0.677443\pi$
$18$		0			0
$19$	2.66634	+	2.66634i	0.611701	+	0.611701i	0.943389	−	0.331688i	$-0.107618\pi$
$19$	2.66634	+	2.66634i	0.611701	+	0.611701i	−0.331688	+	0.943389i	$0.607618\pi$
$20$		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	$-0.614914\pi$
$31$	−3.93331			−0.706443			−0.353221	+	0.935540i	$0.614914\pi$
$32$		0			0
$33$		−	2.34884i		−	0.408881i
$34$		0			0
$35$	4.84805	+	1.36871i	0.819470	+	0.231354i
$36$		0			0
$37$	2.01181	+	2.01181i	0.330739	+	0.330739i	0.852867	−	0.522128i	$-0.174862\pi$
$37$	2.01181	+	2.01181i	0.330739	+	0.330739i	−0.522128	+	0.852867i	$0.674862\pi$
$38$		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
$45$	0.607542	−	2.15195i	0.0905671	−	0.320794i
$46$		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	0.661105	−	0.750293i	$-0.270088\pi$
$53$	−0.649299	−	0.649299i	−0.0891881	−	0.0891881i	−0.750293	+	0.661105i	$0.770088\pi$
$54$		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	−0.971639	−	0.236468i	$-0.924010\pi$
$59$	−5.64696	+	5.64696i	−0.735172	+	0.735172i	0.236468	+	0.971639i	$0.424010\pi$
$60$		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	$0.0441850\pi$
$71$			2.33178i			0.276732i	−0.990381	+	0.138366i	$0.955815\pi$
$72$		0			0
$73$	−2.18275			−0.255472			−0.127736	−	0.991808i	$-0.540771\pi$
$73$	−2.18275			−0.255472			−0.127736	+	0.991808i	$0.540771\pi$
$74$		0			0
$75$	4.86248	−	1.16459i	0.561471	−	0.134476i
$76$		0			0
$77$	3.74174	−	3.74174i	0.426410	−	0.426410i
$78$		0			0
$79$	6.38450			0.718312			0.359156	−	0.933278i	$-0.383065\pi$
$79$	6.38450			0.718312			0.359156	+	0.933278i	$0.383065\pi$
$80$		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
$85$	−4.25144	+	15.0589i	−0.461134	+	1.63336i
$86$		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	$-0.924706\pi$
$97$		−	4.61603i		−	0.468687i	0.972154	−	0.234343i	$-0.0752940\pi$
$98$		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	$0.00957199\pi$
$113$			0.639228i			0.0601335i	−0.999548	+	0.0300668i	$0.990428\pi$
$114$		0			0
$115$	−9.50786	−	2.68427i	−0.886612	−	0.250310i
$116$		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
$125$	7.58255	+	8.21614i	0.678204	+	0.734874i
$126$		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	0.670092	−	0.742278i	$-0.266255\pi$
$131$	−0.826200	−	0.826200i	−0.0721855	−	0.0721855i	−0.742278	+	0.670092i	$0.766255\pi$
$132$		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	$-0.375498\pi$
$137$	8.92457			0.762477			0.381239	+	0.924477i	$0.375498\pi$
$138$		0			0
$139$	−4.83668	+	4.83668i	−0.410242	+	0.410242i	−0.881823	−	0.471581i	$-0.843683\pi$
$139$	−4.83668	+	4.83668i	−0.410242	+	0.410242i	0.471581	+	0.881823i	$0.343683\pi$
$140$		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	$-0.872044\pi$
$151$		−	9.61540i		−	0.782490i	0.920287	−	0.391245i	$-0.127956\pi$
$152$		0			0
$153$	6.99777			0.565736
$154$		0			0
$155$	−8.46429	−	2.38965i	−0.679868	−	0.191941i
$156$		0			0
$157$	16.0158	−	16.0158i	1.27820	−	1.27820i	0.336521	−	0.941676i	$-0.390750\pi$
$157$	16.0158	−	16.0158i	1.27820	−	1.27820i	0.941676	−	0.336521i	$-0.109250\pi$
$158$		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
$165$	1.42702	−	5.05459i	0.111093	−	0.393499i
$166$		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	−0.999706	−	0.0242559i	$-0.992278\pi$
$173$	−12.8300	+	12.8300i	−0.975450	+	0.975450i	0.0242559	+	0.999706i	$0.492278\pi$
$174$		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	0.513396	−	0.858152i	$-0.328387\pi$
$179$	−4.61252	−	4.61252i	−0.344756	−	0.344756i	−0.858152	+	0.513396i	$0.828387\pi$
$180$		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	$-0.510982\pi$
$191$	−0.953399			−0.0689855			−0.0344928	+	0.999405i	$0.510982\pi$
$192$		0			0
$193$			4.82186i			0.347085i	0.984826	+	0.173543i	$0.0555214\pi$
$193$			4.82186i			0.347085i	−0.984826	+	0.173543i	$0.944479\pi$
$194$		0			0
$195$	4.09771	−	14.5143i	0.293443	−	1.03939i
$196$		0			0
$197$	2.47660	+	2.47660i	0.176451	+	0.176451i	0.789807	−	0.613356i	$-0.210181\pi$
$197$	2.47660	+	2.47660i	0.176451	+	0.176451i	−0.613356	+	0.789807i	$0.710181\pi$
$198$		0			0
$199$			17.4435i			1.23654i	0.785966	+	0.618270i	$0.212166\pi$
$199$			17.4435i			1.23654i	−0.785966	+	0.618270i	$0.787834\pi$
$200$		0			0
$201$			7.00424i			0.494041i
$202$		0			0
$203$	−5.84135	−	5.84135i	−0.409982	−	0.409982i
$204$		0			0
$205$	−2.73457	+	9.68602i	−0.190991	+	0.676501i
$206$		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	0.495866	−	0.868399i	$-0.334851\pi$
$211$	−5.41135	−	5.41135i	−0.372533	−	0.372533i	−0.868399	+	0.495866i	$0.834851\pi$
$212$		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	$-0.472024\pi$
$233$	2.67972			0.175555			0.0877773	+	0.996140i	$0.472024\pi$
$234$		0			0
$235$	6.14551	−	21.7678i	0.400889	−	1.41997i
$236$		0			0
$237$	4.51452	−	4.51452i	0.293250	−	0.293250i
$238$		0			0
$239$	−26.0323			−1.68389			−0.841946	−	0.539562i	$-0.818590\pi$
$239$	−26.0323			−1.68389			−0.841946	+	0.539562i	$0.818590\pi$
$240$		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
$245$	−4.14167	−	1.16928i	−0.264602	−	0.0747028i
$246$		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	−0.921398	−	0.388620i	$-0.872952\pi$
$251$	−8.44080	+	8.44080i	−0.532779	+	0.532779i	0.388620	+	0.921398i	$0.372952\pi$
$252$		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	$0.243462\pi$
$257$			22.2011i			1.38487i	−0.721480	+	0.692435i	$0.756538\pi$
$258$		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	$-0.380816\pi$
$271$	12.0417			0.731482			0.365741	+	0.930717i	$0.380816\pi$
$272$		0			0
$273$		−	15.1950i		−	0.919641i
$274$		0			0
$275$	11.4212	−	2.73544i	0.688724	−	0.164953i
$276$		0			0
$277$	−17.9760	−	17.9760i	−1.08007	−	1.08007i	−0.996502	−	0.0835733i	$-0.973367\pi$
$277$	−17.9760	−	17.9760i	−1.08007	−	1.08007i	−0.0835733	−	0.996502i	$-0.526633\pi$
$278$		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
$285$	8.11453	+	2.29091i	0.480663	+	0.135702i
$286$		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	0.571955	−	0.820285i	$-0.306185\pi$
$293$	−4.25071	−	4.25071i	−0.248329	−	0.248329i	−0.820285	+	0.571955i	$0.806185\pi$
$294$		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	$0.449136\pi$
$311$			34.8210i			1.97452i	−0.159115	+	0.987260i	$0.550864\pi$
$312$		0			0
$313$	−17.3412			−0.980182			−0.490091	−	0.871671i	$-0.663036\pi$
$313$	−17.3412			−0.980182			−0.490091	+	0.871671i	$0.663036\pi$
$314$		0			0
$315$	1.36871	−	4.84805i	0.0771180	−	0.273157i
$316$		0			0
$317$	−10.1485	+	10.1485i	−0.569999	+	0.569999i	−0.932128	−	0.362129i	$-0.882050\pi$
$317$	−10.1485	+	10.1485i	−0.569999	+	0.569999i	0.362129	+	0.932128i	$0.382050\pi$
$318$		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
$325$	32.7962	−	7.85487i	1.81920	−	0.435710i
$326$		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	−0.410346	−	0.911930i	$-0.634592\pi$
$331$	9.12552	−	9.12552i	0.501584	−	0.501584i	0.911930	+	0.410346i	$0.134592\pi$
$332$		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	$-0.959785\pi$
$337$		−	4.62620i		−	0.252005i	0.992030	−	0.126002i	$-0.0402147\pi$
$338$		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	$-0.754489\pi$
$353$		−	26.1933i		−	1.39413i	0.717009	−	0.697064i	$-0.245511\pi$
$354$		0			0
$355$	−1.41666	+	5.01788i	−0.0751883	+	0.266322i
$356$		0			0
$357$	11.1475	+	11.1475i	0.589991	+	0.589991i
$358$		0			0
$359$			5.73157i			0.302501i	0.988495	+	0.151250i	$0.0483300\pi$
$359$			5.73157i			0.302501i	−0.988495	+	0.151250i	$0.951670\pi$
$360$		0			0
$361$		−	4.78125i		−	0.251645i
$362$		0			0
$363$	3.87703	+	3.87703i	0.203491	+	0.203491i
$364$		0			0
$365$	−4.69717	−	1.32611i	−0.245861	−	0.0694119i
$366$		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	0.288740	−	0.957407i	$-0.406764\pi$
$373$	−12.9141	−	12.9141i	−0.668667	−	0.668667i	−0.957407	+	0.288740i	$0.906764\pi$
$374$		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	−0.883377	−	0.468663i	$-0.844736\pi$
$379$	−8.07361	+	8.07361i	−0.414713	+	0.414713i	0.468663	+	0.883377i	$0.344736\pi$
$380$		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
$395$	13.7391	+	3.87885i	0.691290	+	0.195166i
$396$		0			0
$397$	−1.07806	+	1.07806i	−0.0541061	+	0.0541061i	−0.733642	−	0.679536i	$-0.762181\pi$
$397$	−1.07806	+	1.07806i	−0.0541061	+	0.0541061i	0.679536	+	0.733642i	$0.262181\pi$
$398$		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
$405$	−2.15195	−	0.607542i	−0.106931	−	0.0301890i
$406$		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	$3.51942e-5\pi$
$419$	20.4718	+	20.4718i	1.00011	+	1.00011i	0.000110566		1.00000i	$0.499965\pi$
$420$		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	$-0.357488\pi$
$431$	17.9747			0.865812			0.432906	+	0.901439i	$0.357488\pi$
$432$		0			0
$433$			23.1120i			1.11069i	0.831619	+	0.555347i	$0.187414\pi$
$433$			23.1120i			1.11069i	−0.831619	+	0.555347i	$0.812586\pi$
$434$		0			0
$435$	−7.89089	−	2.22777i	−0.378339	−	0.106813i
$436$		0			0
$437$	−11.7806	−	11.7806i	−0.563541	−	0.563541i
$438$		0			0
$439$			2.65049i			0.126501i	0.997998	+	0.0632505i	$0.0201467\pi$
$439$			2.65049i			0.126501i	−0.997998	+	0.0632505i	$0.979853\pi$
$440$		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
$445$	−9.54448	+	33.8071i	−0.452452	+	1.60261i
$446$		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	$-0.292159\pi$
$457$	25.9752			1.21507			0.607535	+	0.794293i	$0.292159\pi$
$458$		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
$475$	4.39142	+	18.3353i	0.201492	+	0.841283i
$476$		0			0
$477$	−0.649299	+	0.649299i	−0.0297294	+	0.0297294i
$478$		0			0
$479$	−22.6500			−1.03490			−0.517452	−	0.855712i	$-0.673119\pi$
$479$	−22.6500			−1.03490			−0.517452	+	0.855712i	$0.673119\pi$
$480$		0			0
$481$	19.1896			0.874970
$482$		0			0
$483$	−7.03833	+	7.03833i	−0.320255	+	0.320255i
$484$		0			0
$485$	2.80443	−	9.93347i	0.127343	−	0.451056i
$486$		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	−0.997212	−	0.0746163i	$-0.976227\pi$
$491$	−20.4434	+	20.4434i	−0.922596	+	0.922596i	0.0746163	+	0.997212i	$0.476227\pi$
$492$		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	$-0.929051\pi$
$499$	−26.7236	−	26.7236i	−1.19631	−	1.19631i	−0.221052	−	0.975262i	$-0.570949\pi$
$500$		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
$515$	8.85005	+	2.49856i	0.389980	+	0.110100i
$516$		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
$525$	10.9545	−	2.62367i	0.478094	−	0.114506i
$526$		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
$555$	6.12256	+	1.72853i	0.259888	+	0.0733721i
$556$		0			0
$557$	0.616853	−	0.616853i	0.0261369	−	0.0261369i	−0.693918	−	0.720054i	$-0.744117\pi$
$557$	0.616853	−	0.616853i	0.0261369	−	0.0261369i	0.720054	+	0.693918i	$0.244117\pi$
$558$		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
$565$	−0.388358	+	1.37559i	−0.0163383	+	0.0578714i
$566$		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	$0.510834\pi$
$571$	−24.6949	+	24.6949i	−1.03345	+	1.03345i	−0.999421	+	0.0340299i	$0.989166\pi$
$572$		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	$-0.752829\pi$
$577$		−	33.6673i		−	1.40159i	0.713363	−	0.700795i	$-0.247171\pi$
$578$		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	$0.172708\pi$
$593$			25.1477i			1.03269i	−0.856380	+	0.516347i	$0.827292\pi$
$594$		0			0
$595$	−9.57791	+	33.9255i	−0.392656	+	1.39081i
$596$		0			0
$597$	12.3344	+	12.3344i	0.504815	+	0.504815i
$598$		0			0
$599$			18.0767i			0.738594i	0.929311	+	0.369297i	$0.120402\pi$
$599$			18.0767i			0.738594i	−0.929311	+	0.369297i	$0.879598\pi$
$600$		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
$605$	−3.33112	+	11.7990i	−0.135429	+	0.479699i
$606$		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	0.769677	−	0.638434i	$-0.220417\pi$
$613$	3.24941	+	3.24941i	0.131243	+	0.131243i	−0.638434	+	0.769677i	$0.720417\pi$
$614$		0			0
$615$	4.91542	+	8.78269i	0.198209	+	0.354152i
$616$		0			0
$617$	−18.4370			−0.742245			−0.371123	−	0.928584i	$-0.621027\pi$
$617$	−18.4370			−0.742245			−0.371123	+	0.928584i	$0.621027\pi$
$618$		0			0
$619$	−9.47769	+	9.47769i	−0.380941	+	0.380941i	−0.871441	−	0.490500i	$-0.836814\pi$
$619$	−9.47769	+	9.47769i	−0.380941	+	0.380941i	0.490500	+	0.871441i	$0.336814\pi$
$620$		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	$-0.932109\pi$
$631$		−	10.6343i		−	0.423346i	0.977341	−	0.211673i	$-0.0678912\pi$
$632$		0			0
$633$	−7.65281			−0.304172
$634$		0			0
$635$	10.6653	−	37.7772i	0.423240	−	1.49914i
$636$		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
$645$	−21.7559	−	6.14217i	−0.856639	−	0.241848i
$646$		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	$-0.470492\pi$
$653$	27.8096	−	27.8096i	1.08828	−	1.08828i	0.995706	−	0.0925688i	$-0.0295078\pi$
$654$		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	0.897207	−	0.441611i	$-0.145593\pi$
$659$	11.6956	+	11.6956i	0.455596	+	0.455596i	−0.441611	+	0.897207i	$0.645593\pi$
$660$		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	$0.122113\pi$
$673$			19.4197i			0.748575i	−0.927313	+	0.374287i	$0.877887\pi$
$674$		0			0
$675$	−1.16459	−	4.86248i	−0.0448252	−	0.187157i
$676$		0			0
$677$	22.0550	+	22.0550i	0.847643	+	0.847643i	0.989839	−	0.142196i	$-0.0454162\pi$
$677$	22.0550	+	22.0550i	0.847643	+	0.847643i	−0.142196	+	0.989839i	$0.545416\pi$
$678$		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
$685$	19.2052	+	5.42205i	0.733794	+	0.207166i
$686$		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	$0.0513288\pi$
$691$	30.1664	+	30.1664i	1.14758	+	1.14758i	0.160556	+	0.987027i	$0.448671\pi$
$692$		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
$715$	9.62488	−	34.0919i	0.359950	−	1.27496i
$716$		0			0
$717$	−18.4076	+	18.4076i	−0.687446	+	0.687446i
$718$		0			0
$719$	15.2528			0.568833			0.284417	−	0.958701i	$-0.408200\pi$
$719$	15.2528			0.568833			0.284417	+	0.958701i	$0.408200\pi$
$720$		0			0
$721$	9.26506			0.345049
$722$		0			0
$723$	4.15360	−	4.15360i	0.154474	−	0.154474i
$724$		0			0
$725$	−4.27039	−	17.8300i	−0.158598	−	0.662190i
$726$		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	−0.851874	−	0.523747i	$-0.824534\pi$
$733$	−8.88368	+	8.88368i	−0.328126	+	0.328126i	0.523747	+	0.851874i	$0.324534\pi$
$734$		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	0.760223	−	0.649662i	$-0.225089\pi$
$739$	3.00557	+	3.00557i	0.110562	+	0.110562i	−0.649662	+	0.760223i	$0.725089\pi$
$740$		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	$-0.511192\pi$
$751$	−1.92675			−0.0703083			−0.0351541	+	0.999382i	$0.511192\pi$
$752$		0			0
$753$			11.9371i			0.435012i
$754$		0			0
$755$	5.84176	−	20.6919i	0.212603	−	0.753054i
$756$		0			0
$757$	−0.389306	−	0.389306i	−0.0141496	−	0.0141496i	0.699997	−	0.714146i	$-0.253185\pi$
$757$	−0.389306	−	0.389306i	−0.0141496	−	0.0141496i	−0.714146	+	0.699997i	$0.753185\pi$
$758$		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
$765$	15.0589	+	4.25144i	0.544454	+	0.153711i
$766$		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	0.507847	−	0.861447i	$-0.330442\pi$
$773$	−9.83112	−	9.83112i	−0.353601	−	0.353601i	−0.861447	+	0.507847i	$0.830442\pi$
$774$		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
$795$	−1.97602	−	0.557874i	−0.0700823	−	0.0197858i
$796$		0			0
$797$	−3.63103	+	3.63103i	−0.128618	+	0.128618i	−0.768485	−	0.639868i	$-0.778989\pi$
$797$	−3.63103	+	3.63103i	−0.128618	+	0.128618i	0.639868	+	0.768485i	$0.278989\pi$
$798$		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
$805$	−21.4199	−	6.04730i	−0.754952	−	0.213139i
$806$		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	−0.881357	−	0.472451i	$-0.843369\pi$
$811$	−11.6448	+	11.6448i	−0.408906	+	0.408906i	0.472451	+	0.881357i	$0.343369\pi$
$812$		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
$835$	−27.5513	−	7.77832i	−0.953451	−	0.269180i
$836$		0			0
$837$	2.78127	+	2.78127i	0.0961347	+	0.0961347i
$838$		0			0
$839$		−	9.50181i		−	0.328039i	−0.986457	−	0.164019i	$-0.947554\pi$
$839$		−	9.50181i		−	0.328039i	0.986457	−	0.164019i	$-0.0524460\pi$
$840$		0			0
$841$		−	15.5542i		−	0.536352i
$842$		0			0
$843$	−6.77911	−	6.77911i	−0.233485	−	0.233485i
$844$		0			0
$845$	19.7399	−	69.9200i	0.679075	−	2.40532i
$846$		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	0.908089	−	0.418778i	$-0.137542\pi$
$853$	14.2909	+	14.2909i	0.489310	+	0.489310i	−0.418778	+	0.908089i	$0.637542\pi$
$854$		0			0
$855$	7.35775	−	4.11792i	0.251630	−	0.140830i
$856$		0			0
$857$	24.4246			0.834327			0.417164	−	0.908831i	$-0.363024\pi$
$857$	24.4246			0.834327			0.417164	+	0.908831i	$0.363024\pi$
$858$		0			0
$859$	−21.3398	+	21.3398i	−0.728105	+	0.728105i	−0.970242	−	0.242137i	$-0.922152\pi$
$859$	−21.3398	+	21.3398i	−0.728105	+	0.728105i	0.242137	+	0.970242i	$0.422152\pi$
$860$		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
$875$	17.0824	+	18.5098i	0.577492	+	0.625747i
$876$		0			0
$877$	−8.43052	+	8.43052i	−0.284678	+	0.284678i	−0.834972	−	0.550293i	$-0.814516\pi$
$877$	−8.43052	+	8.43052i	−0.284678	+	0.284678i	0.550293	+	0.834972i	$0.314516\pi$
$878$		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
$885$	−4.85184	+	17.1855i	−0.163093	+	0.577684i
$886$		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	$-0.353980\pi$
$911$	26.7307			0.885627			0.442814	+	0.896614i	$0.353980\pi$
$912$		0			0
$913$		−	17.4417i		−	0.577235i
$914$		0			0
$915$	15.2324	+	4.30044i	0.503568	+	0.142168i
$916$		0			0
$917$	−1.86132	−	1.86132i	−0.0614661	−	0.0614661i
$918$		0			0
$919$			24.5598i			0.810154i	0.914282	+	0.405077i	$0.132755\pi$
$919$			24.5598i			0.810154i	−0.914282	+	0.405077i	$0.867245\pi$
$920$		0			0
$921$		−	0.217585i		−	0.00716968i
$922$		0			0
$923$	11.1209	+	11.1209i	0.366047	+	0.366047i
$924$		0			0
$925$	3.31341	+	13.8344i	0.108944	+	0.454871i
$926$		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	$-0.318585\pi$
$937$	33.0332			1.07915			0.539574	+	0.841938i	$0.318585\pi$
$938$		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	$-0.411255\pi$
$953$	16.9913			0.550403			0.275201	+	0.961387i	$0.411255\pi$
$954$		0			0
$955$	−2.05167	−	0.579230i	−0.0663904	−	0.0187434i
$956$		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
$965$	−2.92948	+	10.3764i	−0.0943034	+	0.334028i
$966$		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	$-0.388427\pi$
$971$	39.9663	−	39.9663i	1.28258	−	1.28258i	0.939196	−	0.343383i	$-0.111573\pi$
$972$		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	$-0.653558\pi$
$977$		−	55.3797i		−	1.77175i	0.463921	−	0.885877i	$-0.346442\pi$
$978$		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	$-0.446209\pi$
$991$	10.5891			0.336373			0.168186	+	0.985755i	$0.446209\pi$
$992$		0			0
$993$		−	12.9054i		−	0.409541i
$994$		0			0
$995$	−10.5977	+	37.5376i	−0.335969	+	1.19002i
$996$		0			0
$997$	18.1735	+	18.1735i	0.575559	+	0.575559i	0.933677	−	0.358117i	$-0.116581\pi$
$997$	18.1735	+	18.1735i	0.575559	+	0.575559i	−0.358117	+	0.933677i	$0.616581\pi$
$998$		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.a.289.16		48
4.3	odd	2		1920.2.bl.b.289.9		48
5.4	even	2	inner	1920.2.bl.a.289.9		48
8.3	odd	2		960.2.bl.a.529.14		48
8.5	even	2		240.2.bl.a.109.4	✓	48
16.3	odd	4		960.2.bl.a.49.8		48
16.5	even	4	inner	1920.2.bl.a.1249.9		48
16.11	odd	4		1920.2.bl.b.1249.16		48
16.13	even	4		240.2.bl.a.229.21	yes	48
20.19	odd	2		1920.2.bl.b.289.16		48
24.5	odd	2		720.2.bm.h.109.21		48
40.19	odd	2		960.2.bl.a.529.8		48
40.29	even	2		240.2.bl.a.109.21	yes	48
48.29	odd	4		720.2.bm.h.469.4		48
80.19	odd	4		960.2.bl.a.49.14		48
80.29	even	4		240.2.bl.a.229.4	yes	48
80.59	odd	4		1920.2.bl.b.1249.9		48
80.69	even	4	inner	1920.2.bl.a.1249.16		48
120.29	odd	2		720.2.bm.h.109.4		48
240.29	odd	4		720.2.bm.h.469.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.4	✓	48	8.5	even	2
240.2.bl.a.109.21	yes	48	40.29	even	2
240.2.bl.a.229.4	yes	48	80.29	even	4
240.2.bl.a.229.21	yes	48	16.13	even	4
720.2.bm.h.109.4		48	120.29	odd	2
720.2.bm.h.109.21		48	24.5	odd	2
720.2.bm.h.469.4		48	48.29	odd	4
720.2.bm.h.469.21		48	240.29	odd	4
960.2.bl.a.49.8		48	16.3	odd	4
960.2.bl.a.49.14		48	80.19	odd	4
960.2.bl.a.529.8		48	40.19	odd	2
960.2.bl.a.529.14		48	8.3	odd	2
1920.2.bl.a.289.9		48	5.4	even	2	inner
1920.2.bl.a.289.16		48	1.1	even	1	trivial
1920.2.bl.a.1249.9		48	16.5	even	4	inner
1920.2.bl.a.1249.16		48	80.69	even	4	inner
1920.2.bl.b.289.9		48	4.3	odd	2
1920.2.bl.b.289.16		48	20.19	odd	2
1920.2.bl.b.1249.9		48	80.59	odd	4
1920.2.bl.b.1249.16		48	16.11	odd	4

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)

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more