LMFDB - Embedded newform 1160.2.bl.d.713.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1160,2,Mod(713,1160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1160, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1160.713");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1160 = 2^{3} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1160.bl (of order $4$, degree $2$, 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:	$9.26264663447$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			713.17
Character	$\chi$	$=$	1160.713
Dual form			1160.2.bl.d.737.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.10106 q^{3} +(-2.18421 - 0.478777i) q^{5} +(1.94771 - 1.94771i) q^{7} +1.41447 q^{9} +(0.883443 - 0.883443i) q^{11} +(2.69535 - 2.69535i) q^{13} +(-4.58916 - 1.00594i) q^{15} -0.326749i q^{17} +(-5.28573 - 5.28573i) q^{19} +(4.09225 - 4.09225i) q^{21} +(-0.557485 - 0.557485i) q^{23} +(4.54155 + 2.09150i) q^{25} -3.33130 q^{27} +(-1.35994 + 5.21062i) q^{29} +(3.27551 - 3.27551i) q^{31} +(1.85617 - 1.85617i) q^{33} +(-5.18672 + 3.32168i) q^{35} +6.69183 q^{37} +(5.66311 - 5.66311i) q^{39} +(-6.35601 - 6.35601i) q^{41} -2.44518 q^{43} +(-3.08949 - 0.677214i) q^{45} +11.9618 q^{47} -0.587117i q^{49} -0.686521i q^{51} +(1.79572 + 1.79572i) q^{53} +(-2.35260 + 1.50665i) q^{55} +(-11.1057 - 11.1057i) q^{57} -6.73630i q^{59} +(5.50590 - 5.50590i) q^{61} +(2.75497 - 2.75497i) q^{63} +(-7.17769 + 4.59674i) q^{65} +(3.12885 + 3.12885i) q^{67} +(-1.17131 - 1.17131i) q^{69} -3.62645i q^{71} -11.1192i q^{73} +(9.54207 + 4.39437i) q^{75} -3.44137i q^{77} +(5.17391 + 5.17391i) q^{79} -11.2427 q^{81} +(3.60182 + 3.60182i) q^{83} +(-0.156440 + 0.713689i) q^{85} +(-2.85732 + 10.9478i) q^{87} +(10.8840 + 10.8840i) q^{89} -10.4995i q^{91} +(6.88206 - 6.88206i) q^{93} +(9.01446 + 14.0758i) q^{95} -3.89805 q^{97} +(1.24960 - 1.24960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 4 q^{3} - 2 q^{7} + 42 q^{9} - 4 q^{13} - 4 q^{15} - 6 q^{19} - 8 q^{21} + 10 q^{23} + 8 q^{25} + 32 q^{27} - 30 q^{29} - 4 q^{31} - 22 q^{33} + 2 q^{35} - 32 q^{37} - 38 q^{39} + 10 q^{41} + 30 q^{45}+ \cdots - 34 q^{99}+O(q^{100}) $ 42 * q - 4 * q^3 - 2 * q^7 + 42 * q^9 - 4 * q^13 - 4 * q^15 - 6 * q^19 - 8 * q^21 + 10 * q^23 + 8 * q^25 + 32 * q^27 - 30 * q^29 - 4 * q^31 - 22 * q^33 + 2 * q^35 - 32 * q^37 - 38 * q^39 + 10 * q^41 + 30 * q^45 + 16 * q^47 + 8 * q^53 - 4 * q^55 - 36 * q^57 + 18 * q^61 - 6 * q^63 + 8 * q^65 + 18 * q^67 - 8 * q^69 + 88 * q^75 + 32 * q^79 + 42 * q^81 - 18 * q^83 + 22 * q^85 - 36 * q^87 + 26 * q^89 - 38 * q^93 - 12 * q^95 - 34 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1160\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$697$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	2.10106			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$3$	2.10106			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$4$		0			0
$5$	−2.18421	−	0.478777i	−0.976808	−	0.214116i
$5$	−2.18421	−	0.478777i	−0.976808	−	0.214116i
$6$		0			0
$7$	1.94771	−	1.94771i	0.736164	−	0.736164i	−0.235670	−	0.971833i	$-0.575728\pi$
$7$	1.94771	−	1.94771i	0.736164	−	0.736164i	0.971833	+	0.235670i	$0.0757283\pi$
$8$		0			0
$9$	1.41447			0.471489
$10$		0			0
$11$	0.883443	−	0.883443i	0.266368	−	0.266368i	−0.561267	−	0.827635i	$-0.689686\pi$
$11$	0.883443	−	0.883443i	0.266368	−	0.266368i	0.827635	+	0.561267i	$0.189686\pi$
$12$		0			0
$13$	2.69535	−	2.69535i	0.747556	−	0.747556i	−0.226463	−	0.974020i	$-0.572716\pi$
$13$	2.69535	−	2.69535i	0.747556	−	0.747556i	0.974020	+	0.226463i	$0.0727164\pi$
$14$		0			0
$15$	−4.58916	−	1.00594i	−1.18492	−	0.259733i
$16$		0			0
$17$		−	0.326749i		−	0.0792484i	−0.999215	−	0.0396242i	$-0.987384\pi$
$17$		−	0.326749i		−	0.0792484i	0.999215	−	0.0396242i	$-0.0126161\pi$
$18$		0			0
$19$	−5.28573	−	5.28573i	−1.21263	−	1.21263i	−0.970158	−	0.242472i	$-0.922042\pi$
$19$	−5.28573	−	5.28573i	−1.21263	−	1.21263i	−0.242472	−	0.970158i	$-0.577958\pi$
$20$		0			0
$21$	4.09225	−	4.09225i	0.893003	−	0.893003i
$22$		0			0
$23$	−0.557485	−	0.557485i	−0.116244	−	0.116244i	0.646592	−	0.762836i	$-0.276194\pi$
$23$	−0.557485	−	0.557485i	−0.116244	−	0.116244i	−0.762836	+	0.646592i	$0.776194\pi$
$24$		0			0
$25$	4.54155	+	2.09150i	0.908309	+	0.418300i
$26$		0			0
$27$	−3.33130			−0.641110
$28$		0			0
$29$	−1.35994	+	5.21062i	−0.252535	+	0.967588i
$29$	−1.35994	+	5.21062i	−0.252535	+	0.967588i
$30$		0			0
$31$	3.27551	−	3.27551i	0.588300	−	0.588300i	−0.348871	−	0.937171i	$-0.613435\pi$
$31$	3.27551	−	3.27551i	0.588300	−	0.588300i	0.937171	+	0.348871i	$0.113435\pi$
$32$		0			0
$33$	1.85617	−	1.85617i	0.323118	−	0.323118i
$34$		0			0
$35$	−5.18672	+	3.32168i	−0.876715	+	0.561467i
$36$		0			0
$37$	6.69183			1.10013			0.550065	−	0.835122i	$-0.314603\pi$
$37$	6.69183			1.10013			0.550065	+	0.835122i	$0.314603\pi$
$38$		0			0
$39$	5.66311	−	5.66311i	0.906823	−	0.906823i
$40$		0			0
$41$	−6.35601	−	6.35601i	−0.992641	−	0.992641i	0.00733177	−	0.999973i	$-0.497666\pi$
$41$	−6.35601	−	6.35601i	−0.992641	−	0.992641i	−0.999973	+	0.00733177i	$0.997666\pi$
$42$		0			0
$43$	−2.44518			−0.372887			−0.186444	−	0.982466i	$-0.559696\pi$
$43$	−2.44518			−0.372887			−0.186444	+	0.982466i	$0.559696\pi$
$44$		0			0
$45$	−3.08949	−	0.677214i	−0.460554	−	0.100953i
$46$		0			0
$47$	11.9618			1.74480			0.872401	−	0.488791i	$-0.162562\pi$
$47$	11.9618			1.74480			0.872401	+	0.488791i	$0.162562\pi$
$48$		0			0
$49$		−	0.587117i		−	0.0838738i
$50$		0			0
$51$		−	0.686521i		−	0.0961322i
$52$		0			0
$53$	1.79572	+	1.79572i	0.246661	+	0.246661i	0.819599	−	0.572938i	$-0.194196\pi$
$53$	1.79572	+	1.79572i	0.246661	+	0.246661i	−0.572938	+	0.819599i	$0.694196\pi$
$54$		0			0
$55$	−2.35260	+	1.50665i	−0.317224	+	0.203157i
$56$		0			0
$57$	−11.1057	−	11.1057i	−1.47098	−	1.47098i
$58$		0			0
$59$		−	6.73630i		−	0.876991i	−0.898733	−	0.438495i	$-0.855512\pi$
$59$		−	6.73630i		−	0.876991i	0.898733	−	0.438495i	$-0.144488\pi$
$60$		0			0
$61$	5.50590	−	5.50590i	0.704958	−	0.704958i	−0.260512	−	0.965471i	$-0.583891\pi$
$61$	5.50590	−	5.50590i	0.704958	−	0.704958i	0.965471	+	0.260512i	$0.0838914\pi$
$62$		0			0
$63$	2.75497	−	2.75497i	0.347093	−	0.347093i
$64$		0			0
$65$	−7.17769	+	4.59674i	−0.890283	+	0.570156i
$66$		0			0
$67$	3.12885	+	3.12885i	0.382250	+	0.382250i	0.871912	−	0.489663i	$-0.162880\pi$
$67$	3.12885	+	3.12885i	0.382250	+	0.382250i	−0.489663	+	0.871912i	$0.662880\pi$
$68$		0			0
$69$	−1.17131	−	1.17131i	−0.141009	−	0.141009i
$70$		0			0
$71$		−	3.62645i		−	0.430380i	−0.976572	−	0.215190i	$-0.930963\pi$
$71$		−	3.62645i		−	0.430380i	0.976572	−	0.215190i	$-0.0690371\pi$
$72$		0			0
$73$		−	11.1192i		−	1.30141i	−0.759332	−	0.650704i	$-0.774474\pi$
$73$		−	11.1192i		−	1.30141i	0.759332	−	0.650704i	$-0.225526\pi$
$74$		0			0
$75$	9.54207	+	4.39437i	1.10182	+	0.507418i
$76$		0			0
$77$		−	3.44137i		−	0.392181i
$78$		0			0
$79$	5.17391	+	5.17391i	0.582110	+	0.582110i	0.935483	−	0.353372i	$-0.114965\pi$
$79$	5.17391	+	5.17391i	0.582110	+	0.582110i	−0.353372	+	0.935483i	$0.614965\pi$
$80$		0			0
$81$	−11.2427			−1.24919
$82$		0			0
$83$	3.60182	+	3.60182i	0.395351	+	0.395351i	0.876590	−	0.481238i	$-0.159813\pi$
$83$	3.60182	+	3.60182i	0.395351	+	0.395351i	−0.481238	+	0.876590i	$0.659813\pi$
$84$		0			0
$85$	−0.156440	+	0.713689i	−0.0169683	+	0.0774105i
$86$		0			0
$87$	−2.85732	+	10.9478i	−0.306337	+	1.17373i
$88$		0			0
$89$	10.8840	+	10.8840i	1.15370	+	1.15370i	0.985804	+	0.167898i	$0.0536979\pi$
$89$	10.8840	+	10.8840i	1.15370	+	1.15370i	0.167898	+	0.985804i	$0.446302\pi$
$90$		0			0
$91$		−	10.4995i		−	1.10065i
$92$		0			0
$93$	6.88206	−	6.88206i	0.713636	−	0.713636i
$94$		0			0
$95$	9.01446	+	14.0758i	0.924865	+	1.44415i
$96$		0			0
$97$	−3.89805			−0.395787			−0.197894	−	0.980224i	$-0.563410\pi$
$97$	−3.89805			−0.395787			−0.197894	+	0.980224i	$0.563410\pi$
$98$		0			0
$99$	1.24960	−	1.24960i	0.125590	−	0.125590i
$100$		0			0
$101$	−7.74849	+	7.74849i	−0.771003	+	0.771003i	−0.978282	−	0.207279i	$-0.933539\pi$
$101$	−7.74849	+	7.74849i	−0.771003	+	0.771003i	0.207279	+	0.978282i	$0.433539\pi$
$102$		0			0
$103$	4.79779	+	4.79779i	0.472740	+	0.472740i	0.902800	−	0.430060i	$-0.141508\pi$
$103$	4.79779	+	4.79779i	0.472740	+	0.472740i	−0.430060	+	0.902800i	$0.641508\pi$
$104$		0			0
$105$	−10.8976	+	6.97906i	−1.06350	+	0.681087i
$106$		0			0
$107$	−10.7751	+	10.7751i	−1.04167	+	1.04167i	−0.0425795	+	0.999093i	$0.513558\pi$
$107$	−10.7751	+	10.7751i	−1.04167	+	1.04167i	−0.999093	+	0.0425795i	$0.986442\pi$
$108$		0			0
$109$	−14.3723			−1.37662			−0.688311	−	0.725416i	$-0.741647\pi$
$109$	−14.3723			−1.37662			−0.688311	+	0.725416i	$0.741647\pi$
$110$		0			0
$111$	14.0600			1.33451
$112$		0			0
$113$		−	0.237524i		−	0.0223444i	−0.999938	−	0.0111722i	$-0.996444\pi$
$113$		−	0.237524i		−	0.0223444i	0.999938	−	0.0111722i	$-0.00355629\pi$
$114$		0			0
$115$	0.950753	+	1.48457i	0.0886582	+	0.138437i
$116$		0			0
$117$	3.81249	−	3.81249i	0.352465	−	0.352465i
$118$		0			0
$119$	−0.636412	−	0.636412i	−0.0583398	−	0.0583398i
$120$		0			0
$121$			9.43906i			0.858096i
$122$		0			0
$123$	−13.3544	−	13.3544i	−1.20412	−	1.20412i
$124$		0			0
$125$	−8.91833	−	6.74266i	−0.797679	−	0.603082i
$126$		0			0
$127$			5.00723i			0.444320i	0.975010	+	0.222160i	$0.0713107\pi$
$127$			5.00723i			0.444320i	−0.975010	+	0.222160i	$0.928689\pi$
$128$		0			0
$129$	−5.13749			−0.452330
$130$		0			0
$131$	12.8392	+	12.8392i	1.12177	+	1.12177i	0.991476	+	0.130292i	$0.0415913\pi$
$131$	12.8392	+	12.8392i	1.12177	+	1.12177i	0.130292	+	0.991476i	$0.458409\pi$
$132$		0			0
$133$	−20.5901			−1.78539
$134$		0			0
$135$	7.27627	+	1.59495i	0.626242	+	0.137272i
$136$		0			0
$137$			13.4656i			1.15045i	0.817996	+	0.575224i	$0.195085\pi$
$137$			13.4656i			1.15045i	−0.817996	+	0.575224i	$0.804915\pi$
$138$		0			0
$139$		−	10.2882i		−	0.872637i	−0.899792	−	0.436319i	$-0.856282\pi$
$139$		−	10.2882i		−	0.872637i	0.899792	−	0.436319i	$-0.143718\pi$
$140$		0			0
$141$	25.1324			2.11653
$142$		0			0
$143$		−	4.76238i		−	0.398250i
$144$		0			0
$145$	5.46512	−	10.7300i	0.453854	−	0.891076i
$146$		0			0
$147$		−	1.23357i		−	0.101743i
$148$		0			0
$149$	−15.6963			−1.28589			−0.642944	−	0.765913i	$-0.722287\pi$
$149$	−15.6963			−1.28589			−0.642944	+	0.765913i	$0.722287\pi$
$150$		0			0
$151$			8.21302i			0.668366i	0.942508	+	0.334183i	$0.108460\pi$
$151$			8.21302i			0.668366i	−0.942508	+	0.334183i	$0.891540\pi$
$152$		0			0
$153$		−	0.462176i		−	0.0373647i
$154$		0			0
$155$	−8.72265	+	5.58617i	−0.700620	+	0.448692i
$156$		0			0
$157$	11.3146			0.903006			0.451503	−	0.892270i	$-0.350888\pi$
$157$	11.3146			0.903006			0.451503	+	0.892270i	$0.350888\pi$
$158$		0			0
$159$	3.77292	+	3.77292i	0.299212	+	0.299212i
$160$		0			0
$161$	−2.17163			−0.171149
$162$		0			0
$163$		−	18.0379i		−	1.41284i	−0.707793	−	0.706420i	$-0.750309\pi$
$163$		−	18.0379i		−	1.41284i	0.707793	−	0.706420i	$-0.249691\pi$
$164$		0			0
$165$	−4.94296	+	3.16557i	−0.384809	+	0.246440i
$166$		0			0
$167$	8.11754	+	8.11754i	0.628154	+	0.628154i	0.947603	−	0.319449i	$-0.103498\pi$
$167$	8.11754	+	8.11754i	0.628154	+	0.628154i	−0.319449	+	0.947603i	$0.603498\pi$
$168$		0			0
$169$		−	1.52985i		−	0.117681i
$170$		0			0
$171$	−7.47650	−	7.47650i	−0.571742	−	0.571742i
$172$		0			0
$173$	−0.288382	+	0.288382i	−0.0219253	+	0.0219253i	−0.717984	−	0.696059i	$-0.754935\pi$
$173$	−0.288382	+	0.288382i	−0.0219253	+	0.0219253i	0.696059	+	0.717984i	$0.254935\pi$
$174$		0			0
$175$	12.9192	−	4.77197i	0.976601	−	0.360727i
$176$		0			0
$177$		−	14.1534i		−	1.06383i
$178$		0			0
$179$	4.24083			0.316974			0.158487	−	0.987361i	$-0.449338\pi$
$179$	4.24083			0.316974			0.158487	+	0.987361i	$0.449338\pi$
$180$		0			0
$181$	7.99022			0.593908			0.296954	−	0.954892i	$-0.404029\pi$
$181$	7.99022			0.593908			0.296954	+	0.954892i	$0.404029\pi$
$182$		0			0
$183$	11.5682	−	11.5682i	0.855150	−	0.855150i
$184$		0			0
$185$	−14.6164	−	3.20389i	−1.07462	−	0.235555i
$186$		0			0
$187$	−0.288664	−	0.288664i	−0.0211092	−	0.0211092i
$188$		0			0
$189$	−6.48840	+	6.48840i	−0.471962	+	0.471962i
$190$		0			0
$191$	−9.91272	+	9.91272i	−0.717260	+	0.717260i	−0.968043	−	0.250784i	$-0.919312\pi$
$191$	−9.91272	+	9.91272i	−0.717260	+	0.717260i	0.250784	+	0.968043i	$0.419312\pi$
$192$		0			0
$193$	−23.3002			−1.67719			−0.838593	−	0.544758i	$-0.816621\pi$
$193$	−23.3002			−1.67719			−0.838593	+	0.544758i	$0.816621\pi$
$194$		0			0
$195$	−15.0808	+	9.65805i	−1.07996	+	0.691627i
$196$		0			0
$197$	−0.108668	+	0.108668i	−0.00774225	+	0.00774225i	−0.710967	−	0.703225i	$-0.751743\pi$
$197$	−0.108668	+	0.108668i	−0.00774225	+	0.00774225i	0.703225	+	0.710967i	$0.251743\pi$
$198$		0			0
$199$		−	6.43805i		−	0.456382i	−0.973616	−	0.228191i	$-0.926719\pi$
$199$		−	6.43805i		−	0.456382i	0.973616	−	0.228191i	$-0.0732810\pi$
$200$		0			0
$201$	6.57391	+	6.57391i	0.463688	+	0.463688i
$202$		0			0
$203$	7.49999	+	12.7975i	0.526396	+	0.898210i
$204$		0			0
$205$	10.8397	+	16.9260i	0.757080	+	1.18216i
$206$		0			0
$207$	−0.788544	−	0.788544i	−0.0548076	−	0.0548076i
$208$		0			0
$209$	−9.33929			−0.646012
$210$		0			0
$211$	15.3334	+	15.3334i	1.05559	+	1.05559i	0.998361	+	0.0572336i	$0.0182280\pi$
$211$	15.3334	+	15.3334i	1.05559	+	1.05559i	0.0572336	+	0.998361i	$0.481772\pi$
$212$		0			0
$213$		−	7.61940i		−	0.522072i
$214$		0			0
$215$	5.34080	+	1.17070i	0.364239	+	0.0798409i
$216$		0			0
$217$		−	12.7595i		−	0.866169i
$218$		0			0
$219$		−	23.3622i		−	1.57867i
$220$		0			0
$221$	−0.880705	−	0.880705i	−0.0592426	−	0.0592426i
$222$		0			0
$223$	−0.698377	−	0.698377i	−0.0467668	−	0.0467668i	0.683337	−	0.730103i	$-0.260528\pi$
$223$	−0.698377	−	0.698377i	−0.0467668	−	0.0467668i	−0.730103	+	0.683337i	$0.760528\pi$
$224$		0			0
$225$	6.42387	+	2.95836i	0.428258	+	0.197224i
$226$		0			0
$227$	−4.90838	+	4.90838i	−0.325780	+	0.325780i	−0.850979	−	0.525199i	$-0.823991\pi$
$227$	−4.90838	+	4.90838i	−0.325780	+	0.325780i	0.525199	+	0.850979i	$0.323991\pi$
$228$		0			0
$229$	10.6218	−	10.6218i	0.701906	−	0.701906i	−0.262913	−	0.964819i	$-0.584683\pi$
$229$	10.6218	−	10.6218i	0.701906	−	0.701906i	0.964819	+	0.262913i	$0.0846834\pi$
$230$		0			0
$231$		−	7.23055i		−	0.475735i
$232$		0			0
$233$	−2.89799	−	2.89799i	−0.189854	−	0.189854i	0.605779	−	0.795633i	$-0.292862\pi$
$233$	−2.89799	−	2.89799i	−0.189854	−	0.189854i	−0.795633	+	0.605779i	$0.792862\pi$
$234$		0			0
$235$	−26.1270	−	5.72701i	−1.70434	−	0.373589i
$236$		0			0
$237$	10.8707	+	10.8707i	0.706129	+	0.706129i
$238$		0			0
$239$		−	7.30996i		−	0.472842i	−0.971651	−	0.236421i	$-0.924026\pi$
$239$		−	7.30996i		−	0.472842i	0.971651	−	0.236421i	$-0.0759745\pi$
$240$		0			0
$241$		−	3.62739i		−	0.233661i	−0.993152	−	0.116830i	$-0.962727\pi$
$241$		−	3.62739i		−	0.233661i	0.993152	−	0.116830i	$-0.0372734\pi$
$242$		0			0
$243$	−13.6277			−0.874216
$244$		0			0
$245$	−0.281098	+	1.28239i	−0.0179587	+	0.0819287i
$246$		0			0
$247$	−28.4938			−1.81302
$248$		0			0
$249$	7.56765	+	7.56765i	0.479581	+	0.479581i
$250$		0			0
$251$	4.11985	−	4.11985i	0.260043	−	0.260043i	−0.565028	−	0.825071i	$-0.691135\pi$
$251$	4.11985	−	4.11985i	0.260043	−	0.260043i	0.825071	+	0.565028i	$0.191135\pi$
$252$		0			0
$253$	−0.985012			−0.0619272
$254$		0			0
$255$	−0.328690	+	1.49951i	−0.0205834	+	0.0939027i
$256$		0			0
$257$	7.92255	−	7.92255i	0.494195	−	0.494195i	−0.415430	−	0.909625i	$-0.636369\pi$
$257$	7.92255	−	7.92255i	0.494195	−	0.494195i	0.909625	+	0.415430i	$0.136369\pi$
$258$		0			0
$259$	13.0337	−	13.0337i	0.809876	−	0.809876i
$260$		0			0
$261$	−1.92359	+	7.37025i	−0.119067	+	0.456207i
$262$		0			0
$263$	23.6548			1.45862			0.729308	−	0.684185i	$-0.239842\pi$
$263$	23.6548			1.45862			0.729308	+	0.684185i	$0.239842\pi$
$264$		0			0
$265$	−3.06248	−	4.78198i	−0.188127	−	0.293755i
$266$		0			0
$267$	22.8680	+	22.8680i	1.39950	+	1.39950i
$268$		0			0
$269$	−9.81352	+	9.81352i	−0.598341	+	0.598341i	−0.939871	−	0.341530i	$-0.889055\pi$
$269$	−9.81352	+	9.81352i	−0.598341	+	0.598341i	0.341530	+	0.939871i	$0.389055\pi$
$270$		0			0
$271$	13.5466	+	13.5466i	0.822899	+	0.822899i	0.986523	−	0.163624i	$-0.0523184\pi$
$271$	13.5466	+	13.5466i	0.822899	+	0.822899i	−0.163624	+	0.986523i	$0.552318\pi$
$272$		0			0
$273$		−	22.0601i		−	1.33514i
$274$		0			0
$275$	5.85992	−	2.16448i	0.353366	−	0.130523i
$276$		0			0
$277$	−3.77310	+	3.77310i	−0.226703	+	0.226703i	−0.811314	−	0.584611i	$-0.801247\pi$
$277$	−3.77310	+	3.77310i	−0.226703	+	0.226703i	0.584611	+	0.811314i	$0.301247\pi$
$278$		0			0
$279$	4.63311	−	4.63311i	0.277377	−	0.277377i
$280$		0			0
$281$	33.1089			1.97511			0.987554	−	0.157278i	$-0.0502718\pi$
$281$	33.1089			1.97511			0.987554	+	0.157278i	$0.0502718\pi$
$282$		0			0
$283$	−18.9994	+	18.9994i	−1.12940	+	1.12940i	−0.139121	+	0.990275i	$0.544428\pi$
$283$	−18.9994	+	18.9994i	−1.12940	+	1.12940i	−0.990275	+	0.139121i	$0.955572\pi$
$284$		0			0
$285$	18.9400	+	29.5742i	1.12191	+	1.75183i
$286$		0			0
$287$	−24.7593			−1.46149
$288$		0			0
$289$	16.8932			0.993720
$290$		0			0
$291$	−8.19005			−0.480109
$292$		0			0
$293$	−12.7648			−0.745728			−0.372864	−	0.927886i	$-0.621624\pi$
$293$	−12.7648			−0.745728			−0.372864	+	0.927886i	$0.621624\pi$
$294$		0			0
$295$	−3.22518	+	14.7135i	−0.187777	+	0.856652i
$296$		0			0
$297$	−2.94302	+	2.94302i	−0.170771	+	0.170771i
$298$		0			0
$299$	−3.00524			−0.173797
$300$		0			0
$301$	−4.76250	+	4.76250i	−0.274506	+	0.274506i
$302$		0			0
$303$	−16.2801	+	16.2801i	−0.935265	+	0.935265i
$304$		0			0
$305$	−14.6621	+	9.38995i	−0.839552	+	0.537667i
$306$		0			0
$307$			31.0310i			1.77103i	0.464607	+	0.885517i	$0.346196\pi$
$307$			31.0310i			1.77103i	−0.464607	+	0.885517i	$0.653804\pi$
$308$		0			0
$309$	10.0805	+	10.0805i	0.573458	+	0.573458i
$310$		0			0
$311$	9.20844	−	9.20844i	0.522162	−	0.522162i	−0.396062	−	0.918224i	$-0.629623\pi$
$311$	9.20844	−	9.20844i	0.522162	−	0.522162i	0.918224	+	0.396062i	$0.129623\pi$
$312$		0			0
$313$	−15.1195	−	15.1195i	−0.854604	−	0.854604i	0.136092	−	0.990696i	$-0.456546\pi$
$313$	−15.1195	−	15.1195i	−0.854604	−	0.854604i	−0.990696	+	0.136092i	$0.956546\pi$
$314$		0			0
$315$	−7.33644	+	4.69841i	−0.413361	+	0.264725i
$316$		0			0
$317$	−9.15875			−0.514406			−0.257203	−	0.966357i	$-0.582801\pi$
$317$	−9.15875			−0.514406			−0.257203	+	0.966357i	$0.582801\pi$
$318$		0			0
$319$	3.40185	+	5.80472i	0.190467	+	0.325002i
$320$		0			0
$321$	−22.6393	+	22.6393i	−1.26360	+	1.26360i
$322$		0			0
$323$	−1.72711	+	1.72711i	−0.0960990	+	0.0960990i
$324$		0			0
$325$	17.8784	−	6.60374i	0.991715	−	0.366310i
$326$		0			0
$327$	−30.1972			−1.66991
$328$		0			0
$329$	23.2980	−	23.2980i	1.28446	−	1.28446i
$330$		0			0
$331$	−5.48552	−	5.48552i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$331$	−5.48552	−	5.48552i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$332$		0			0
$333$	9.46537			0.518699
$334$		0			0
$335$	−5.33604	−	8.33208i	−0.291539	−	0.455230i
$336$		0			0
$337$	−21.9596			−1.19622			−0.598108	−	0.801416i	$-0.704081\pi$
$337$	−21.9596			−1.19622			−0.598108	+	0.801416i	$0.704081\pi$
$338$		0			0
$339$		−	0.499053i		−	0.0271048i
$340$		0			0
$341$		−	5.78746i		−	0.313408i
$342$		0			0
$343$	12.4904	+	12.4904i	0.674419	+	0.674419i
$344$		0			0
$345$	1.99759	+	3.11918i	0.107547	+	0.167931i
$346$		0			0
$347$	−14.1927	−	14.1927i	−0.761904	−	0.761904i	0.214763	−	0.976666i	$-0.431102\pi$
$347$	−14.1927	−	14.1927i	−0.761904	−	0.761904i	−0.976666	+	0.214763i	$0.931102\pi$
$348$		0			0
$349$			11.5541i			0.618476i	0.950985	+	0.309238i	$0.100074\pi$
$349$			11.5541i			0.618476i	−0.950985	+	0.309238i	$0.899926\pi$
$350$		0			0
$351$	−8.97904	+	8.97904i	−0.479266	+	0.479266i
$352$		0			0
$353$	−22.9709	+	22.9709i	−1.22262	+	1.22262i	−0.255917	+	0.966699i	$0.582377\pi$
$353$	−22.9709	+	22.9709i	−1.22262	+	1.22262i	−0.966699	+	0.255917i	$0.917623\pi$
$354$		0			0
$355$	−1.73626	+	7.92092i	−0.0921511	+	0.420399i
$356$		0			0
$357$	−1.33714	−	1.33714i	−0.0707690	−	0.0707690i
$358$		0			0
$359$	14.3952	+	14.3952i	0.759748	+	0.759748i	0.976276	−	0.216528i	$-0.0694734\pi$
$359$	14.3952	+	14.3952i	0.759748	+	0.759748i	−0.216528	+	0.976276i	$0.569473\pi$
$360$		0			0
$361$			36.8780i			1.94095i
$362$		0			0
$363$			19.8321i			1.04091i
$364$		0			0
$365$	−5.32363	+	24.2867i	−0.278651	+	1.27123i
$366$		0			0
$367$		−	9.65343i		−	0.503905i	−0.967740	−	0.251953i	$-0.918927\pi$
$367$		−	9.65343i		−	0.503905i	0.967740	−	0.251953i	$-0.0810727\pi$
$368$		0			0
$369$	−8.99036	−	8.99036i	−0.468020	−	0.468020i
$370$		0			0
$371$	6.99507			0.363166
$372$		0			0
$373$	−5.81049	−	5.81049i	−0.300856	−	0.300856i	0.540493	−	0.841349i	$-0.318238\pi$
$373$	−5.81049	−	5.81049i	−0.300856	−	0.300856i	−0.841349	+	0.540493i	$0.818238\pi$
$374$		0			0
$375$	−18.7380	−	14.1668i	−0.967625	−	0.731568i
$376$		0			0
$377$	10.3789	+	17.7100i	0.534542	+	0.912110i
$378$		0			0
$379$	−21.5192	−	21.5192i	−1.10537	−	1.10537i	−0.993751	−	0.111618i	$-0.964397\pi$
$379$	−21.5192	−	21.5192i	−1.10537	−	1.10537i	−0.111618	−	0.993751i	$-0.535603\pi$
$380$		0			0
$381$			10.5205i			0.538982i
$382$		0			0
$383$	−7.15942	+	7.15942i	−0.365829	+	0.365829i	−0.865954	−	0.500124i	$-0.833288\pi$
$383$	−7.15942	+	7.15942i	−0.365829	+	0.365829i	0.500124	+	0.865954i	$0.333288\pi$
$384$		0			0
$385$	−1.64765	+	7.51668i	−0.0839720	+	0.383086i
$386$		0			0
$387$	−3.45863			−0.175812
$388$		0			0
$389$	12.3444	−	12.3444i	0.625887	−	0.625887i	−0.321144	−	0.947030i	$-0.604067\pi$
$389$	12.3444	−	12.3444i	0.625887	−	0.625887i	0.947030	+	0.321144i	$0.104067\pi$
$390$		0			0
$391$	−0.182158	+	0.182158i	−0.00921211	+	0.00921211i
$392$		0			0
$393$	26.9760	+	26.9760i	1.36076	+	1.36076i
$394$		0			0
$395$	−8.82376	−	13.7781i	−0.443971	−	0.693249i
$396$		0			0
$397$	9.88573	−	9.88573i	0.496151	−	0.496151i	−0.414087	−	0.910237i	$-0.635899\pi$
$397$	9.88573	−	9.88573i	0.496151	−	0.496151i	0.910237	+	0.414087i	$0.135899\pi$
$398$		0			0
$399$	−43.2611			−2.16577
$400$		0			0
$401$	−4.42061			−0.220755			−0.110377	−	0.993890i	$-0.535206\pi$
$401$	−4.42061			−0.220755			−0.110377	+	0.993890i	$0.535206\pi$
$402$		0			0
$403$		−	17.6573i		−	0.879574i
$404$		0			0
$405$	24.5564	+	5.38274i	1.22022	+	0.267470i
$406$		0			0
$407$	5.91185	−	5.91185i	0.293040	−	0.293040i
$408$		0			0
$409$	18.3976	+	18.3976i	0.909702	+	0.909702i	0.996248	−	0.0865462i	$-0.0275830\pi$
$409$	18.3976	+	18.3976i	0.909702	+	0.909702i	−0.0865462	+	0.996248i	$0.527583\pi$
$410$		0			0
$411$			28.2922i			1.39555i
$412$		0			0
$413$	−13.1203	−	13.1203i	−0.645609	−	0.645609i
$414$		0			0
$415$	−6.14266	−	9.59160i	−0.301532	−	0.470833i
$416$		0			0
$417$		−	21.6162i		−	1.05855i
$418$		0			0
$419$	11.9789			0.585208			0.292604	−	0.956234i	$-0.405478\pi$
$419$	11.9789			0.585208			0.292604	+	0.956234i	$0.405478\pi$
$420$		0			0
$421$	13.1646	+	13.1646i	0.641605	+	0.641605i	0.950950	−	0.309345i	$-0.100110\pi$
$421$	13.1646	+	13.1646i	0.641605	+	0.641605i	−0.309345	+	0.950950i	$0.600110\pi$
$422$		0			0
$423$	16.9195			0.822655
$424$		0			0
$425$	0.683396	−	1.48395i	0.0331496	−	0.0719820i
$426$		0			0
$427$		−	21.4478i		−	1.03793i
$428$		0			0
$429$		−	10.0061i		−	0.483097i
$430$		0			0
$431$	33.9147			1.63361			0.816807	−	0.576911i	$-0.195742\pi$
$431$	33.9147			1.63361			0.816807	+	0.576911i	$0.195742\pi$
$432$		0			0
$433$		−	24.8729i		−	1.19531i	−0.801752	−	0.597657i	$-0.796098\pi$
$433$		−	24.8729i		−	1.19531i	0.801752	−	0.597657i	$-0.203902\pi$
$434$		0			0
$435$	11.4826	−	22.5444i	0.550547	−	1.08092i
$436$		0			0
$437$			5.89343i			0.281921i
$438$		0			0
$439$	21.5991			1.03087			0.515433	−	0.856930i	$-0.327631\pi$
$439$	21.5991			1.03087			0.515433	+	0.856930i	$0.327631\pi$
$440$		0			0
$441$		−	0.830457i		−	0.0395456i
$442$		0			0
$443$			5.25883i			0.249855i	0.992166	+	0.124927i	$0.0398698\pi$
$443$			5.25883i			0.249855i	−0.992166	+	0.124927i	$0.960130\pi$
$444$		0			0
$445$	−18.5619	−	28.9840i	−0.879920	−	1.37397i
$446$		0			0
$447$	−32.9788			−1.55985
$448$		0			0
$449$	20.2305	+	20.2305i	0.954738	+	0.954738i	0.999019	−	0.0442813i	$-0.0140998\pi$
$449$	20.2305	+	20.2305i	0.954738	+	0.954738i	−0.0442813	+	0.999019i	$0.514100\pi$
$450$		0			0
$451$	−11.2303			−0.528816
$452$		0			0
$453$			17.2561i			0.810762i
$454$		0			0
$455$	−5.02692	+	22.9331i	−0.235666	+	1.07512i
$456$		0			0
$457$	2.36773	+	2.36773i	0.110758	+	0.110758i	0.760314	−	0.649556i	$-0.225045\pi$
$457$	2.36773	+	2.36773i	0.110758	+	0.110758i	−0.649556	+	0.760314i	$0.725045\pi$
$458$		0			0
$459$			1.08850i			0.0508069i
$460$		0			0
$461$	−18.0665	−	18.0665i	−0.841441	−	0.841441i	0.147605	−	0.989046i	$-0.452843\pi$
$461$	−18.0665	−	18.0665i	−0.841441	−	0.841441i	−0.989046	+	0.147605i	$0.952843\pi$
$462$		0			0
$463$	23.6401	−	23.6401i	1.09865	−	1.09865i	0.104080	−	0.994569i	$-0.466810\pi$
$463$	23.6401	−	23.6401i	1.09865	−	1.09865i	0.994569	−	0.104080i	$-0.0331899\pi$
$464$		0			0
$465$	−18.3268	+	11.7369i	−0.849887	+	0.544285i
$466$		0			0
$467$		−	0.686553i		−	0.0317699i	−0.999874	−	0.0158849i	$-0.994943\pi$
$467$		−	0.686553i		−	0.0317699i	0.999874	−	0.0158849i	$-0.00505655\pi$
$468$		0			0
$469$	12.1881			0.562796
$470$		0			0
$471$	23.7727			1.09539
$472$		0			0
$473$	−2.16018	+	2.16018i	−0.0993252	+	0.0993252i
$474$		0			0
$475$	−12.9503	−	35.0605i	−0.594200	−	1.60869i
$476$		0			0
$477$	2.53999	+	2.53999i	0.116298	+	0.116298i
$478$		0			0
$479$	−27.6104	+	27.6104i	−1.26155	+	1.26155i	−0.311212	+	0.950340i	$0.600735\pi$
$479$	−27.6104	+	27.6104i	−1.26155	+	1.26155i	−0.950340	+	0.311212i	$0.899265\pi$
$480$		0			0
$481$	18.0368	−	18.0368i	0.822409	−	0.822409i
$482$		0			0
$483$	−4.56274			−0.207612
$484$		0			0
$485$	8.51416	+	1.86630i	0.386608	+	0.0847442i
$486$		0			0
$487$	24.4884	−	24.4884i	1.10968	−	1.10968i	0.116483	−	0.993193i	$-0.462838\pi$
$487$	24.4884	−	24.4884i	1.10968	−	1.10968i	0.993193	−	0.116483i	$-0.0371620\pi$
$488$		0			0
$489$		−	37.8988i		−	1.71384i
$490$		0			0
$491$	−3.63405	−	3.63405i	−0.164002	−	0.164002i	0.620335	−	0.784337i	$-0.286997\pi$
$491$	−3.63405	−	3.63405i	−0.164002	−	0.164002i	−0.784337	+	0.620335i	$0.786997\pi$
$492$		0			0
$493$	1.70257	+	0.444360i	0.0766797	+	0.0200130i
$494$		0			0
$495$	−3.32767	+	2.13111i	−0.149568	+	0.0957863i
$496$		0			0
$497$	−7.06325	−	7.06325i	−0.316830	−	0.316830i
$498$		0			0
$499$	12.7461			0.570592			0.285296	−	0.958439i	$-0.407908\pi$
$499$	12.7461			0.570592			0.285296	+	0.958439i	$0.407908\pi$
$500$		0			0
$501$	17.0555	+	17.0555i	0.761982	+	0.761982i
$502$		0			0
$503$		−	12.2048i		−	0.544185i	−0.962271	−	0.272092i	$-0.912284\pi$
$503$		−	12.2048i		−	0.544185i	0.962271	−	0.272092i	$-0.0877156\pi$
$504$		0			0
$505$	20.6341	−	13.2145i	0.918206	−	0.588039i
$506$		0			0
$507$		−	3.21431i		−	0.142753i
$508$		0			0
$509$		−	28.3545i		−	1.25679i	−0.777894	−	0.628396i	$-0.783712\pi$
$509$		−	28.3545i		−	1.25679i	0.777894	−	0.628396i	$-0.216288\pi$
$510$		0			0
$511$	−21.6570	−	21.6570i	−0.958049	−	0.958049i
$512$		0			0
$513$	17.6084	+	17.6084i	0.777429	+	0.777429i
$514$		0			0
$515$	−8.18231	−	12.7765i	−0.360556	−	0.562998i
$516$		0			0
$517$	10.5675	−	10.5675i	0.464759	−	0.464759i
$518$		0			0
$519$	−0.605909	+	0.605909i	−0.0265964	+	0.0265964i
$520$		0			0
$521$		−	21.8728i		−	0.958267i	−0.877742	−	0.479133i	$-0.840951\pi$
$521$		−	21.8728i		−	0.958267i	0.877742	−	0.479133i	$-0.159049\pi$
$522$		0			0
$523$	−4.55629	−	4.55629i	−0.199232	−	0.199232i	0.600438	−	0.799671i	$-0.294993\pi$
$523$	−4.55629	−	4.55629i	−0.199232	−	0.199232i	−0.799671	+	0.600438i	$0.794993\pi$
$524$		0			0
$525$	27.1441	−	10.0262i	1.18467	−	0.437580i
$526$		0			0
$527$	−1.07027	−	1.07027i	−0.0466218	−	0.0466218i
$528$		0			0
$529$		−	22.3784i		−	0.972975i
$530$		0			0
$531$		−	9.52827i		−	0.413492i
$532$		0			0
$533$	−34.2634			−1.48411
$534$		0			0
$535$	28.6941	−	18.3763i	1.24055	−	0.794476i
$536$		0			0
$537$	8.91024			0.384505
$538$		0			0
$539$	−0.518684	−	0.518684i	−0.0223413	−	0.0223413i
$540$		0			0
$541$	1.47906	−	1.47906i	0.0635899	−	0.0635899i	−0.674597	−	0.738187i	$-0.735682\pi$
$541$	1.47906	−	1.47906i	0.0635899	−	0.0635899i	0.738187	+	0.674597i	$0.235682\pi$
$542$		0			0
$543$	16.7880			0.720440
$544$		0			0
$545$	31.3922	+	6.88115i	1.34470	+	0.294756i
$546$		0			0
$547$	−3.08962	+	3.08962i	−0.132103	+	0.132103i	−0.770066	−	0.637964i	$-0.779777\pi$
$547$	−3.08962	+	3.08962i	−0.132103	+	0.132103i	0.637964	+	0.770066i	$0.279777\pi$
$548$		0			0
$549$	7.78792	−	7.78792i	0.332380	−	0.332380i
$550$		0			0
$551$	34.7302	−	20.3537i	1.47956	−	0.867095i
$552$		0			0
$553$	20.1545			0.857057
$554$		0			0
$555$	−30.7099	−	6.73158i	−1.30356	−	0.285740i
$556$		0			0
$557$	−21.6536	−	21.6536i	−0.917492	−	0.917492i	0.0793546	−	0.996846i	$-0.474714\pi$
$557$	−21.6536	−	21.6536i	−0.917492	−	0.917492i	−0.996846	+	0.0793546i	$0.974714\pi$
$558$		0			0
$559$	−6.59063	+	6.59063i	−0.278754	+	0.278754i
$560$		0			0
$561$	−0.606502	−	0.606502i	−0.0256065	−	0.0256065i
$562$		0			0
$563$		−	21.2513i		−	0.895635i	−0.894125	−	0.447818i	$-0.852201\pi$
$563$		−	21.2513i		−	0.895635i	0.894125	−	0.447818i	$-0.147799\pi$
$564$		0			0
$565$	−0.113721	+	0.518802i	−0.00478428	+	0.0218262i
$566$		0			0
$567$	−21.8974	+	21.8974i	−0.919606	+	0.919606i
$568$		0			0
$569$	6.11396	−	6.11396i	0.256311	−	0.256311i	−0.567241	−	0.823552i	$-0.691989\pi$
$569$	6.11396	−	6.11396i	0.256311	−	0.256311i	0.823552	+	0.567241i	$0.191989\pi$
$570$		0			0
$571$	−34.2533			−1.43345			−0.716727	−	0.697354i	$-0.754361\pi$
$571$	−34.2533			−1.43345			−0.716727	+	0.697354i	$0.754361\pi$
$572$		0			0
$573$	−20.8273	+	20.8273i	−0.870071	+	0.870071i
$574$		0			0
$575$	−1.36586	−	3.69782i	−0.0569605	−	0.154210i
$576$		0			0
$577$	33.2376			1.38370			0.691850	−	0.722041i	$-0.256796\pi$
$577$	33.2376			1.38370			0.691850	+	0.722041i	$0.256796\pi$
$578$		0			0
$579$	−48.9552			−2.03451
$580$		0			0
$581$	14.0306			0.582086
$582$		0			0
$583$	3.17283			0.131405
$584$		0			0
$585$	−10.1526	+	6.50194i	−0.419758	+	0.268822i
$586$		0			0
$587$	−1.03039	+	1.03039i	−0.0425287	+	0.0425287i	−0.728051	−	0.685523i	$-0.759574\pi$
$587$	−1.03039	+	1.03039i	−0.0425287	+	0.0425287i	0.685523	+	0.728051i	$0.259574\pi$
$588$		0			0
$589$	−34.6270			−1.42678
$590$		0			0
$591$	−0.228318	+	0.228318i	−0.00939173	+	0.00939173i
$592$		0			0
$593$	0.937969	−	0.937969i	0.0385178	−	0.0385178i	−0.687586	−	0.726103i	$-0.741329\pi$
$593$	0.937969	−	0.937969i	0.0385178	−	0.0385178i	0.726103	+	0.687586i	$0.241329\pi$
$594$		0			0
$595$	1.08536	+	1.69476i	0.0444953	+	0.0694782i
$596$		0			0
$597$		−	13.5268i		−	0.553613i
$598$		0			0
$599$	−27.8033	−	27.8033i	−1.13601	−	1.13601i	−0.989158	−	0.146855i	$-0.953085\pi$
$599$	−27.8033	−	27.8033i	−1.13601	−	1.13601i	−0.146855	−	0.989158i	$-0.546915\pi$
$600$		0			0
$601$	1.33565	−	1.33565i	0.0544824	−	0.0544824i	−0.679341	−	0.733823i	$-0.737734\pi$
$601$	1.33565	−	1.33565i	0.0544824	−	0.0544824i	0.733823	+	0.679341i	$0.237734\pi$
$602$		0			0
$603$	4.42565	+	4.42565i	0.180226	+	0.180226i
$604$		0			0
$605$	4.51920	−	20.6169i	0.183732	−	0.838195i
$606$		0			0
$607$	4.08518			0.165812			0.0829061	−	0.996557i	$-0.473580\pi$
$607$	4.08518			0.165812			0.0829061	+	0.996557i	$0.473580\pi$
$608$		0			0
$609$	15.7580	+	26.8884i	0.638544	+	1.08957i
$610$		0			0
$611$	32.2412	−	32.2412i	1.30434	−	1.30434i
$612$		0			0
$613$	−4.25352	+	4.25352i	−0.171798	+	0.171798i	−0.787769	−	0.615971i	$-0.788764\pi$
$613$	−4.25352	+	4.25352i	−0.171798	+	0.171798i	0.615971	+	0.787769i	$0.288764\pi$
$614$		0			0
$615$	22.7750	+	35.5625i	0.918376	+	1.43402i
$616$		0			0
$617$	−27.4779			−1.10622			−0.553110	−	0.833108i	$-0.686559\pi$
$617$	−27.4779			−1.10622			−0.553110	+	0.833108i	$0.686559\pi$
$618$		0			0
$619$	29.7608	−	29.7608i	1.19619	−	1.19619i	0.220886	−	0.975300i	$-0.429105\pi$
$619$	29.7608	−	29.7608i	1.19619	−	1.19619i	0.975300	−	0.220886i	$-0.0708949\pi$
$620$		0			0
$621$	1.85715	+	1.85715i	0.0745249	+	0.0745249i
$622$		0			0
$623$	42.3977			1.69863
$624$		0			0
$625$	16.2513	+	18.9973i	0.650051	+	0.759891i
$626$		0			0
$627$	−19.6224			−0.783645
$628$		0			0
$629$		−	2.18655i		−	0.0871835i
$630$		0			0
$631$		−	6.63723i		−	0.264224i	−0.991235	−	0.132112i	$-0.957824\pi$
$631$		−	6.63723i		−	0.264224i	0.991235	−	0.132112i	$-0.0421758\pi$
$632$		0			0
$633$	32.2164	+	32.2164i	1.28049	+	1.28049i
$634$		0			0
$635$	2.39735	−	10.9368i	0.0951358	−	0.434015i
$636$		0			0
$637$	−1.58249	−	1.58249i	−0.0627004	−	0.0627004i
$638$		0			0
$639$		−	5.12949i		−	0.202920i
$640$		0			0
$641$	−23.3527	+	23.3527i	−0.922376	+	0.922376i	−0.997197	−	0.0748212i	$-0.976161\pi$
$641$	−23.3527	+	23.3527i	−0.922376	+	0.922376i	0.0748212	+	0.997197i	$0.476161\pi$
$642$		0			0
$643$	−28.2503	+	28.2503i	−1.11408	+	1.11408i	−0.121491	+	0.992592i	$0.538768\pi$
$643$	−28.2503	+	28.2503i	−1.11408	+	1.11408i	−0.992592	+	0.121491i	$0.961232\pi$
$644$		0			0
$645$	11.2213	+	2.45971i	0.441840	+	0.0968510i
$646$		0			0
$647$	12.0944	+	12.0944i	0.475480	+	0.475480i	0.903683	−	0.428203i	$-0.140853\pi$
$647$	12.0944	+	12.0944i	0.475480	+	0.475480i	−0.428203	+	0.903683i	$0.640853\pi$
$648$		0			0
$649$	−5.95113	−	5.95113i	−0.233602	−	0.233602i
$650$		0			0
$651$		−	26.8085i		−	1.05071i
$652$		0			0
$653$		−	32.2827i		−	1.26332i	−0.775246	−	0.631659i	$-0.782374\pi$
$653$		−	32.2827i		−	1.26332i	0.775246	−	0.631659i	$-0.217626\pi$
$654$		0			0
$655$	−21.8964	−	34.1907i	−0.855564	−	1.33594i
$656$		0			0
$657$		−	15.7278i		−	0.613599i
$658$		0			0
$659$	32.9138	+	32.9138i	1.28214	+	1.28214i	0.939448	+	0.342692i	$0.111339\pi$
$659$	32.9138	+	32.9138i	1.28214	+	1.28214i	0.342692	+	0.939448i	$0.388661\pi$
$660$		0			0
$661$	−12.4860			−0.485649			−0.242825	−	0.970070i	$-0.578074\pi$
$661$	−12.4860			−0.485649			−0.242825	+	0.970070i	$0.578074\pi$
$662$		0			0
$663$	−1.85042	−	1.85042i	−0.0718642	−	0.0718642i
$664$		0			0
$665$	44.9731	+	9.85807i	1.74398	+	0.382279i
$666$		0			0
$667$	3.66299	−	2.14669i	0.141831	−	0.0831203i
$668$		0			0
$669$	−1.46734	−	1.46734i	−0.0567305	−	0.0567305i
$670$		0			0
$671$		−	9.72830i		−	0.375557i
$672$		0			0
$673$	30.5512	−	30.5512i	1.17766	−	1.17766i	0.197324	−	0.980338i	$-0.436775\pi$
$673$	30.5512	−	30.5512i	1.17766	−	1.17766i	0.980338	−	0.197324i	$-0.0632250\pi$
$674$		0			0
$675$	−15.1293	−	6.96742i	−0.582326	−	0.268176i
$676$		0			0
$677$	−35.2511			−1.35481			−0.677405	−	0.735610i	$-0.736895\pi$
$677$	−35.2511			−1.35481			−0.677405	+	0.735610i	$0.736895\pi$
$678$		0			0
$679$	−7.59226	+	7.59226i	−0.291364	+	0.291364i
$680$		0			0
$681$	−10.3128	+	10.3128i	−0.395188	+	0.395188i
$682$		0			0
$683$	7.41154	+	7.41154i	0.283595	+	0.283595i	0.834541	−	0.550946i	$-0.185733\pi$
$683$	7.41154	+	7.41154i	0.283595	+	0.283595i	−0.550946	+	0.834541i	$0.685733\pi$
$684$		0			0
$685$	6.44704	−	29.4118i	0.246329	−	1.12377i
$686$		0			0
$687$	22.3170	−	22.3170i	0.851447	−	0.851447i
$688$		0			0
$689$	9.68020			0.368786
$690$		0			0
$691$	3.46515			0.131820			0.0659102	−	0.997826i	$-0.479005\pi$
$691$	3.46515			0.131820			0.0659102	+	0.997826i	$0.479005\pi$
$692$		0			0
$693$		−	4.86771i		−	0.184909i
$694$		0			0
$695$	−4.92577	+	22.4717i	−0.186845	+	0.852399i
$696$		0			0
$697$	−2.07682	+	2.07682i	−0.0786652	+	0.0786652i
$698$		0			0
$699$	−6.08887	−	6.08887i	−0.230302	−	0.230302i
$700$		0			0
$701$		−	48.3739i		−	1.82706i	−0.406773	−	0.913529i	$-0.633346\pi$
$701$		−	48.3739i		−	1.82706i	0.406773	−	0.913529i	$-0.366654\pi$
$702$		0			0
$703$	−35.3712	−	35.3712i	−1.33405	−	1.33405i
$704$		0			0
$705$	−54.8945	−	12.0328i	−2.06744	−	0.453182i
$706$		0			0
$707$			30.1835i			1.13517i
$708$		0			0
$709$	−17.5666			−0.659728			−0.329864	−	0.944028i	$-0.607003\pi$
$709$	−17.5666			−0.659728			−0.329864	+	0.944028i	$0.607003\pi$
$710$		0			0
$711$	7.31832	+	7.31832i	0.274459	+	0.274459i
$712$		0			0
$713$	−3.65210			−0.136772
$714$		0			0
$715$	−2.28012	+	10.4020i	−0.0852716	+	0.389014i
$716$		0			0
$717$		−	15.3587i		−	0.573581i
$718$		0			0
$719$			42.7327i			1.59366i	0.604202	+	0.796831i	$0.293492\pi$
$719$			42.7327i			1.59366i	−0.604202	+	0.796831i	$0.706508\pi$
$720$		0			0
$721$	18.6894			0.696029
$722$		0			0
$723$		−	7.62137i		−	0.283442i
$724$		0			0
$725$	−17.0742	+	20.8200i	−0.634121	+	0.773234i
$726$		0			0
$727$			12.8458i			0.476423i	0.971213	+	0.238211i	$0.0765611\pi$
$727$			12.8458i			0.476423i	−0.971213	+	0.238211i	$0.923439\pi$
$728$		0			0
$729$	5.09544			0.188720
$730$		0			0
$731$			0.798962i			0.0295507i
$732$		0			0
$733$			16.6173i			0.613773i	0.951746	+	0.306887i	$0.0992873\pi$
$733$			16.6173i			0.613773i	−0.951746	+	0.306887i	$0.900713\pi$
$734$		0			0
$735$	−0.590605	+	2.69438i	−0.0217848	+	0.0993835i
$736$		0			0
$737$	5.52832			0.203638
$738$		0			0
$739$	4.90421	+	4.90421i	0.180404	+	0.180404i	0.791532	−	0.611128i	$-0.209284\pi$
$739$	4.90421	+	4.90421i	0.180404	+	0.180404i	−0.611128	+	0.791532i	$0.709284\pi$
$740$		0			0
$741$	−59.8673			−2.19928
$742$		0			0
$743$			5.82549i			0.213716i	0.994274	+	0.106858i	$0.0340791\pi$
$743$			5.82549i			0.213716i	−0.994274	+	0.106858i	$0.965921\pi$
$744$		0			0
$745$	34.2839	+	7.51500i	1.25607	+	0.275328i
$746$		0			0
$747$	5.09466	+	5.09466i	0.186404	+	0.186404i
$748$		0			0
$749$			41.9736i			1.53368i
$750$		0			0
$751$	24.8635	+	24.8635i	0.907281	+	0.907281i	0.996052	−	0.0887708i	$-0.0282939\pi$
$751$	24.8635	+	24.8635i	0.907281	+	0.907281i	−0.0887708	+	0.996052i	$0.528294\pi$
$752$		0			0
$753$	8.65607	−	8.65607i	0.315445	−	0.315445i
$754$		0			0
$755$	3.93221	−	17.9390i	0.143108	−	0.652866i
$756$		0			0
$757$			13.0727i			0.475134i	0.971371	+	0.237567i	$0.0763500\pi$
$757$			13.0727i			0.475134i	−0.971371	+	0.237567i	$0.923650\pi$
$758$		0			0
$759$	−2.06957			−0.0751207
$760$		0			0
$761$	0.295680			0.0107184			0.00535920	−	0.999986i	$-0.498294\pi$
$761$	0.295680			0.0107184			0.00535920	+	0.999986i	$0.498294\pi$
$762$		0			0
$763$	−27.9931	+	27.9931i	−1.01342	+	1.01342i
$764$		0			0
$765$	−0.221279	+	1.00949i	−0.00800037	+	0.0364982i
$766$		0			0
$767$	−18.1567	−	18.1567i	−0.655600	−	0.655600i
$768$		0			0
$769$	−20.4410	+	20.4410i	−0.737120	+	0.737120i	−0.972020	−	0.234899i	$-0.924524\pi$
$769$	−20.4410	+	20.4410i	−0.737120	+	0.737120i	0.234899	+	0.972020i	$0.424524\pi$
$770$		0			0
$771$	16.6458	−	16.6458i	0.599483	−	0.599483i
$772$		0			0
$773$	−11.2143			−0.403351			−0.201676	−	0.979452i	$-0.564639\pi$
$773$	−11.2143			−0.403351			−0.201676	+	0.979452i	$0.564639\pi$
$774$		0			0
$775$	21.7266	−	8.02516i	0.780443	−	0.288272i
$776$		0			0
$777$	27.3847	−	27.3847i	0.982419	−	0.982419i
$778$		0			0
$779$			67.1923i			2.40741i
$780$		0			0
$781$	−3.20376	−	3.20376i	−0.114640	−	0.114640i
$782$		0			0
$783$	4.53038	−	17.3582i	0.161903	−	0.620330i
$784$		0			0
$785$	−24.7135	−	5.41718i	−0.882063	−	0.193347i
$786$		0			0
$787$	22.9932	+	22.9932i	0.819620	+	0.819620i	0.986053	−	0.166432i	$-0.0532248\pi$
$787$	22.9932	+	22.9932i	0.819620	+	0.819620i	−0.166432	+	0.986053i	$0.553225\pi$
$788$		0			0
$789$	49.7002			1.76937
$790$		0			0
$791$	−0.462627	−	0.462627i	−0.0164491	−	0.0164491i
$792$		0			0
$793$		−	29.6807i		−	1.05399i
$794$		0			0
$795$	−6.43447	−	10.0472i	−0.228207	−	0.356339i
$796$		0			0
$797$			17.6986i			0.626916i	0.949602	+	0.313458i	$0.101487\pi$
$797$			17.6986i			0.626916i	−0.949602	+	0.313458i	$0.898513\pi$
$798$		0			0
$799$		−	3.90850i		−	0.138273i
$800$		0			0
$801$	15.3951	+	15.3951i	0.543958	+	0.543958i
$802$		0			0
$803$	−9.82320	−	9.82320i	−0.346653	−	0.346653i
$804$		0			0
$805$	4.74330	+	1.03973i	0.167179	+	0.0366456i
$806$		0			0
$807$	−20.6188	+	20.6188i	−0.725817	+	0.725817i
$808$		0			0
$809$	−19.4828	+	19.4828i	−0.684979	+	0.684979i	−0.961118	−	0.276139i	$-0.910945\pi$
$809$	−19.4828	+	19.4828i	−0.684979	+	0.684979i	0.276139	+	0.961118i	$0.410945\pi$
$810$		0			0
$811$			11.9464i			0.419494i	0.977756	+	0.209747i	$0.0672640\pi$
$811$			11.9464i			0.419494i	−0.977756	+	0.209747i	$0.932736\pi$
$812$		0			0
$813$	28.4623	+	28.4623i	0.998217	+	0.998217i
$814$		0			0
$815$	−8.63614	+	39.3986i	−0.302511	+	1.38007i
$816$		0			0
$817$	12.9246	+	12.9246i	0.452174	+	0.452174i
$818$		0			0
$819$		−	14.8512i		−	0.518943i
$820$		0			0
$821$		−	44.5244i		−	1.55391i	−0.629555	−	0.776956i	$-0.716763\pi$
$821$		−	44.5244i		−	1.55391i	0.629555	−	0.776956i	$-0.283237\pi$
$822$		0			0
$823$	14.9390			0.520741			0.260370	−	0.965509i	$-0.416155\pi$
$823$	14.9390			0.520741			0.260370	+	0.965509i	$0.416155\pi$
$824$		0			0
$825$	12.3121	−	4.54770i	0.428651	−	0.158331i
$826$		0			0
$827$	−19.2376			−0.668957			−0.334478	−	0.942403i	$-0.608560\pi$
$827$	−19.2376			−0.668957			−0.334478	+	0.942403i	$0.608560\pi$
$828$		0			0
$829$	−29.2184	−	29.2184i	−1.01480	−	1.01480i	−0.999889	−	0.0149076i	$-0.995255\pi$
$829$	−29.2184	−	29.2184i	−1.01480	−	1.01480i	−0.0149076	−	0.999889i	$-0.504745\pi$
$830$		0			0
$831$	−7.92751	+	7.92751i	−0.275002	+	0.275002i
$832$		0			0
$833$	−0.191840			−0.00664686
$834$		0			0
$835$	−13.8439	−	21.6169i	−0.479089	−	0.748084i
$836$		0			0
$837$	−10.9117	+	10.9117i	−0.377165	+	0.377165i
$838$		0			0
$839$	29.2430	−	29.2430i	1.00958	−	1.00958i	0.00962721	−	0.999954i	$-0.496936\pi$
$839$	29.2430	−	29.2430i	1.00958	−	1.00958i	0.999954	−	0.00962721i	$-0.00306448\pi$
$840$		0			0
$841$	−25.3011	−	14.1723i	−0.872452	−	0.488699i
$842$		0			0
$843$	69.5638			2.39590
$844$		0			0
$845$	−0.732457	+	3.34151i	−0.0251973	+	0.114952i
$846$		0			0
$847$	18.3845	+	18.3845i	0.631699	+	0.631699i
$848$		0			0
$849$	−39.9189	+	39.9189i	−1.37001	+	1.37001i
$850$		0			0
$851$	−3.73059	−	3.73059i	−0.127883	−	0.127883i
$852$		0			0
$853$			0.451413i			0.0154561i	0.999970	+	0.00772804i	$0.00245994\pi$
$853$			0.451413i			0.0154561i	−0.999970	+	0.00772804i	$0.997540\pi$
$854$		0			0
$855$	12.7507	+	19.9098i	0.436064	+	0.680901i
$856$		0			0
$857$	15.4044	−	15.4044i	0.526203	−	0.526203i	−0.393235	−	0.919438i	$-0.628644\pi$
$857$	15.4044	−	15.4044i	0.526203	−	0.526203i	0.919438	+	0.393235i	$0.128644\pi$
$858$		0			0
$859$	25.5734	−	25.5734i	0.872555	−	0.872555i	−0.120196	−	0.992750i	$-0.538352\pi$
$859$	25.5734	−	25.5734i	0.872555	−	0.872555i	0.992750	+	0.120196i	$0.0383522\pi$
$860$		0			0
$861$	−52.0208			−1.77286
$862$		0			0
$863$	16.9266	−	16.9266i	0.576188	−	0.576188i	−0.357663	−	0.933851i	$-0.616426\pi$
$863$	16.9266	−	16.9266i	0.576188	−	0.576188i	0.933851	+	0.357663i	$0.116426\pi$
$864$		0			0
$865$	0.767957	−	0.491816i	0.0261113	−	0.0167222i
$866$		0			0
$867$	35.4938			1.20543
$868$		0			0
$869$	9.14171			0.310111
$870$		0			0
$871$	16.8667			0.571506
$872$		0			0
$873$	−5.51366			−0.186609
$874$		0			0
$875$	−30.5030	+	4.23757i	−1.03119	+	0.143256i
$876$		0			0
$877$	5.79759	−	5.79759i	0.195771	−	0.195771i	−0.602413	−	0.798184i	$-0.705794\pi$
$877$	5.79759	−	5.79759i	0.195771	−	0.195771i	0.798184	+	0.602413i	$0.205794\pi$
$878$		0			0
$879$	−26.8197			−0.904604
$880$		0			0
$881$	−33.4393	+	33.4393i	−1.12660	+	1.12660i	−0.135874	+	0.990726i	$0.543384\pi$
$881$	−33.4393	+	33.4393i	−1.12660	+	1.12660i	−0.990726	+	0.135874i	$0.956616\pi$
$882$		0			0
$883$	8.69563	−	8.69563i	0.292631	−	0.292631i	−0.545488	−	0.838119i	$-0.683656\pi$
$883$	8.69563	−	8.69563i	0.292631	−	0.292631i	0.838119	+	0.545488i	$0.183656\pi$
$884$		0			0
$885$	−6.77631	+	30.9140i	−0.227783	+	1.03916i
$886$		0			0
$887$			55.5610i			1.86555i	0.360453	+	0.932777i	$0.382622\pi$
$887$			55.5610i			1.86555i	−0.360453	+	0.932777i	$0.617378\pi$
$888$		0			0
$889$	9.75261	+	9.75261i	0.327092	+	0.327092i
$890$		0			0
$891$	−9.93227	+	9.93227i	−0.332744	+	0.332744i
$892$		0			0
$893$	−63.2267	−	63.2267i	−2.11580	−	2.11580i
$894$		0			0
$895$	−9.26285	−	2.03041i	−0.309623	−	0.0678691i
$896$		0			0
$897$	−6.31419			−0.210825
$898$		0			0
$899$	12.6129	+	21.5220i	0.420665	+	0.717798i
$900$		0			0
$901$	0.586750	−	0.586750i	0.0195475	−	0.0195475i
$902$		0			0
$903$	−10.0063	+	10.0063i	−0.332989	+	0.332989i
$904$		0			0
$905$	−17.4523	−	3.82553i	−0.580134	−	0.127165i
$906$		0			0
$907$	−33.1251			−1.09990			−0.549951	−	0.835197i	$-0.685353\pi$
$907$	−33.1251			−1.09990			−0.549951	+	0.835197i	$0.685353\pi$
$908$		0			0
$909$	−10.9600	+	10.9600i	−0.363520	+	0.363520i
$910$		0			0
$911$	10.3153	+	10.3153i	0.341762	+	0.341762i	0.857029	−	0.515267i	$-0.172307\pi$
$911$	10.3153	+	10.3153i	0.341762	+	0.341762i	−0.515267	+	0.857029i	$0.672307\pi$
$912$		0			0
$913$	6.36401			0.210618
$914$		0			0
$915$	−30.8061	+	19.7289i	−1.01842	+	0.652216i
$916$		0			0
$917$	50.0140			1.65161
$918$		0			0
$919$			1.08806i			0.0358917i	0.999839	+	0.0179458i	$0.00571265\pi$
$919$			1.08806i			0.0358917i	−0.999839	+	0.0179458i	$0.994287\pi$
$920$		0			0
$921$			65.1982i			2.14835i
$922$		0			0
$923$	−9.77455	−	9.77455i	−0.321733	−	0.321733i
$924$		0			0
$925$	30.3912	+	13.9959i	0.999258	+	0.460184i
$926$		0			0
$927$	6.78632	+	6.78632i	0.222892	+	0.222892i
$928$		0			0
$929$		−	35.2436i		−	1.15630i	−0.815929	−	0.578152i	$-0.803774\pi$
$929$		−	35.2436i		−	1.15630i	0.815929	−	0.578152i	$-0.196226\pi$
$930$		0			0
$931$	−3.10334	+	3.10334i	−0.101708	+	0.101708i
$932$		0			0
$933$	19.3475	−	19.3475i	0.633409	−	0.633409i
$934$		0			0
$935$	0.492298	+	0.768710i	0.0160999	+	0.0251395i
$936$		0			0
$937$	−19.4962	−	19.4962i	−0.636913	−	0.636913i	0.312880	−	0.949793i	$-0.398706\pi$
$937$	−19.4962	−	19.4962i	−0.636913	−	0.636913i	−0.949793	+	0.312880i	$0.898706\pi$
$938$		0			0
$939$	−31.7670	−	31.7670i	−1.03668	−	1.03668i
$940$		0			0
$941$			12.3219i			0.401681i	0.979624	+	0.200841i	$0.0643674\pi$
$941$			12.3219i			0.401681i	−0.979624	+	0.200841i	$0.935633\pi$
$942$		0			0
$943$			7.08675i			0.230776i
$944$		0			0
$945$	17.2785	−	11.0655i	0.562071	−	0.359962i
$946$		0			0
$947$		−	43.7634i		−	1.42212i	−0.703131	−	0.711060i	$-0.748215\pi$
$947$		−	43.7634i		−	1.42212i	0.703131	−	0.711060i	$-0.251785\pi$
$948$		0			0
$949$	−29.9702	−	29.9702i	−0.972875	−	0.972875i
$950$		0			0
$951$	−19.2431			−0.624000
$952$		0			0
$953$	−8.66865	−	8.66865i	−0.280805	−	0.280805i	0.552625	−	0.833430i	$-0.313626\pi$
$953$	−8.66865	−	8.66865i	−0.280805	−	0.280805i	−0.833430	+	0.552625i	$0.813626\pi$
$954$		0			0
$955$	26.3975	−	16.9055i	0.854202	−	0.547049i
$956$		0			0
$957$	7.14751	+	12.1961i	0.231046	+	0.394243i
$958$		0			0
$959$	26.2271	+	26.2271i	0.846917	+	0.846917i
$960$		0			0
$961$			9.54203i			0.307807i
$962$		0			0
$963$	−15.2411	+	15.2411i	−0.491137	+	0.491137i
$964$		0			0
$965$	50.8926	+	11.1556i	1.63829	+	0.359112i
$966$		0			0
$967$	48.4687			1.55865			0.779324	−	0.626621i	$-0.215563\pi$
$967$	48.4687			1.55865			0.779324	+	0.626621i	$0.215563\pi$
$968$		0			0
$969$	−3.62877	+	3.62877i	−0.116573	+	0.116573i
$970$		0			0
$971$	−21.4570	+	21.4570i	−0.688587	+	0.688587i	−0.961920	−	0.273333i	$-0.911874\pi$
$971$	−21.4570	+	21.4570i	−0.688587	+	0.688587i	0.273333	+	0.961920i	$0.411874\pi$
$972$		0			0
$973$	−20.0385	−	20.0385i	−0.642404	−	0.642404i
$974$		0			0
$975$	37.5636	−	13.8749i	1.20300	−	0.444352i
$976$		0			0
$977$	−8.07528	+	8.07528i	−0.258351	+	0.258351i	−0.824383	−	0.566032i	$-0.808478\pi$
$977$	−8.07528	+	8.07528i	−0.258351	+	0.258351i	0.566032	+	0.824383i	$0.308478\pi$
$978$		0			0
$979$	19.2308			0.614619
$980$		0			0
$981$	−20.3292			−0.649062
$982$		0			0
$983$			18.0478i			0.575635i	0.957685	+	0.287817i	$0.0929296\pi$
$983$			18.0478i			0.575635i	−0.957685	+	0.287817i	$0.907070\pi$
$984$		0			0
$985$	0.289381	−	0.185325i	0.00922043	−	0.00590496i
$986$		0			0
$987$	48.9505	−	48.9505i	1.55811	−	1.55811i
$988$		0			0
$989$	1.36315	+	1.36315i	0.0433457	+	0.0433457i
$990$		0			0
$991$		−	55.6527i		−	1.76787i	−0.467613	−	0.883933i	$-0.654886\pi$
$991$		−	55.6527i		−	1.76787i	0.467613	−	0.883933i	$-0.345114\pi$
$992$		0			0
$993$	−11.5254	−	11.5254i	−0.365748	−	0.365748i
$994$		0			0
$995$	−3.08239	+	14.0621i	−0.0977184	+	0.445797i
$996$		0			0
$997$			32.6196i			1.03307i	0.856265	+	0.516537i	$0.172779\pi$
$997$			32.6196i			1.03307i	−0.856265	+	0.516537i	$0.827221\pi$
$998$		0			0
$999$	−22.2925			−0.705304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1160.2.bl.d.713.17	yes	42
5.2	odd	4		1160.2.s.c.17.5	✓	42
29.12	odd	4		1160.2.s.c.273.17	yes	42
145.12	even	4	inner	1160.2.bl.d.737.17	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.s.c.17.5	✓	42	5.2	odd	4
1160.2.s.c.273.17	yes	42	29.12	odd	4
1160.2.bl.d.713.17	yes	42	1.1	even	1	trivial
1160.2.bl.d.737.17	yes	42	145.12	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:	\( N \)	\(=\)	\( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1160.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.10106 q^{3} +(-2.18421 - 0.478777i) q^{5} +(1.94771 - 1.94771i) q^{7} +1.41447 q^{9} +(0.883443 - 0.883443i) q^{11} +(2.69535 - 2.69535i) q^{13} +(-4.58916 - 1.00594i) q^{15} -0.326749i q^{17} +(-5.28573 - 5.28573i) q^{19} +(4.09225 - 4.09225i) q^{21} +(-0.557485 - 0.557485i) q^{23} +(4.54155 + 2.09150i) q^{25} -3.33130 q^{27} +(-1.35994 + 5.21062i) q^{29} +(3.27551 - 3.27551i) q^{31} +(1.85617 - 1.85617i) q^{33} +(-5.18672 + 3.32168i) q^{35} +6.69183 q^{37} +(5.66311 - 5.66311i) q^{39} +(-6.35601 - 6.35601i) q^{41} -2.44518 q^{43} +(-3.08949 - 0.677214i) q^{45} +11.9618 q^{47} -0.587117i q^{49} -0.686521i q^{51} +(1.79572 + 1.79572i) q^{53} +(-2.35260 + 1.50665i) q^{55} +(-11.1057 - 11.1057i) q^{57} -6.73630i q^{59} +(5.50590 - 5.50590i) q^{61} +(2.75497 - 2.75497i) q^{63} +(-7.17769 + 4.59674i) q^{65} +(3.12885 + 3.12885i) q^{67} +(-1.17131 - 1.17131i) q^{69} -3.62645i q^{71} -11.1192i q^{73} +(9.54207 + 4.39437i) q^{75} -3.44137i q^{77} +(5.17391 + 5.17391i) q^{79} -11.2427 q^{81} +(3.60182 + 3.60182i) q^{83} +(-0.156440 + 0.713689i) q^{85} +(-2.85732 + 10.9478i) q^{87} +(10.8840 + 10.8840i) q^{89} -10.4995i q^{91} +(6.88206 - 6.88206i) q^{93} +(9.01446 + 14.0758i) q^{95} -3.89805 q^{97} +(1.24960 - 1.24960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 4 q^{3} - 2 q^{7} + 42 q^{9} - 4 q^{13} - 4 q^{15} - 6 q^{19} - 8 q^{21} + 10 q^{23} + 8 q^{25} + 32 q^{27} - 30 q^{29} - 4 q^{31} - 22 q^{33} + 2 q^{35} - 32 q^{37} - 38 q^{39} + 10 q^{41} + 30 q^{45}+ \cdots - 34 q^{99}+O(q^{100}) \) 42 * q - 4 * q^3 - 2 * q^7 + 42 * q^9 - 4 * q^13 - 4 * q^15 - 6 * q^19 - 8 * q^21 + 10 * q^23 + 8 * q^25 + 32 * q^27 - 30 * q^29 - 4 * q^31 - 22 * q^33 + 2 * q^35 - 32 * q^37 - 38 * q^39 + 10 * q^41 + 30 * q^45 + 16 * q^47 + 8 * q^53 - 4 * q^55 - 36 * q^57 + 18 * q^61 - 6 * q^63 + 8 * q^65 + 18 * q^67 - 8 * q^69 + 88 * q^75 + 32 * q^79 + 42 * q^81 - 18 * q^83 + 22 * q^85 - 36 * q^87 + 26 * q^89 - 38 * q^93 - 12 * q^95 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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