LMFDB - Embedded newform 1120.2.bi.a.463.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(463,1120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1120.463"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bi (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.14
Character	$\chi$	$=$	1120.463
Dual form			1120.2.bi.a.687.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.570077 - 0.570077i) q^{3} +(0.776798 - 2.09680i) q^{5} +(0.707107 + 0.707107i) q^{7} -2.35002i q^{9} +1.03673 q^{11} +(1.92581 - 1.92581i) q^{13} +(-1.63818 + 0.752505i) q^{15} +(0.113640 - 0.113640i) q^{17} +0.879182i q^{19} -0.806211i q^{21} +(0.250756 - 0.250756i) q^{23} +(-3.79317 - 3.25759i) q^{25} +(-3.04993 + 3.04993i) q^{27} +2.57802 q^{29} -5.78413i q^{31} +(-0.591015 - 0.591015i) q^{33} +(2.03194 - 0.933385i) q^{35} +(6.90394 + 6.90394i) q^{37} -2.19573 q^{39} -7.82998 q^{41} +(-7.89276 - 7.89276i) q^{43} +(-4.92754 - 1.82549i) q^{45} +(-0.137030 - 0.137030i) q^{47} +1.00000i q^{49} -0.129567 q^{51} +(6.52731 - 6.52731i) q^{53} +(0.805328 - 2.17381i) q^{55} +(0.501202 - 0.501202i) q^{57} -11.9683i q^{59} +1.41110i q^{61} +(1.66172 - 1.66172i) q^{63} +(-2.54209 - 5.53402i) q^{65} +(-6.46395 + 6.46395i) q^{67} -0.285901 q^{69} +3.26611i q^{71} +(3.50178 + 3.50178i) q^{73} +(0.305324 + 4.01948i) q^{75} +(0.733077 + 0.733077i) q^{77} -1.49268 q^{79} -3.57268 q^{81} +(-4.86134 - 4.86134i) q^{83} +(-0.150005 - 0.326555i) q^{85} +(-1.46967 - 1.46967i) q^{87} -12.9763i q^{89} +2.72351 q^{91} +(-3.29740 + 3.29740i) q^{93} +(1.84347 + 0.682947i) q^{95} +(-7.01973 + 7.01973i) q^{97} -2.43633i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{17} - 8 q^{25} + 64 q^{43} + 32 q^{51} - 8 q^{65} - 40 q^{73} - 112 q^{75} - 72 q^{81} - 80 q^{83} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^17 - 8 * q^25 + 64 * q^43 + 32 * q^51 - 8 * q^65 - 40 * q^73 - 112 * q^75 - 72 * q^81 - 80 * q^83 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.570077	−	0.570077i	−0.329134	−	0.329134i	0.523123	−	0.852257i	$-0.324767\pi$
$3$	−0.570077	−	0.570077i	−0.329134	−	0.329134i	−0.852257	+	0.523123i	$0.824767\pi$
$4$		0			0
$5$	0.776798	−	2.09680i	0.347395	−	0.937719i
$5$	0.776798	−	2.09680i	0.347395	−	0.937719i
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$		−	2.35002i		−	0.783341i
$10$		0			0
$11$	1.03673			0.312585			0.156292	−	0.987711i	$-0.450046\pi$
$11$	1.03673			0.312585			0.156292	+	0.987711i	$0.450046\pi$
$12$		0			0
$13$	1.92581	−	1.92581i	0.534125	−	0.534125i	−0.387672	−	0.921797i	$-0.626721\pi$
$13$	1.92581	−	1.92581i	0.534125	−	0.534125i	0.921797	+	0.387672i	$0.126721\pi$
$14$		0			0
$15$	−1.63818	+	0.752505i	−0.422975	+	0.194296i
$16$		0			0
$17$	0.113640	−	0.113640i	0.0275617	−	0.0275617i	−0.693192	−	0.720753i	$-0.743796\pi$
$17$	0.113640	−	0.113640i	0.0275617	−	0.0275617i	0.720753	+	0.693192i	$0.243796\pi$
$18$		0			0
$19$			0.879182i			0.201698i	0.994902	+	0.100849i	$0.0321559\pi$
$19$			0.879182i			0.201698i	−0.994902	+	0.100849i	$0.967844\pi$
$20$		0			0
$21$		−	0.806211i		−	0.175930i
$22$		0			0
$23$	0.250756	−	0.250756i	0.0522862	−	0.0522862i	−0.680480	−	0.732766i	$-0.738229\pi$
$23$	0.250756	−	0.250756i	0.0522862	−	0.0522862i	0.732766	+	0.680480i	$0.238229\pi$
$24$		0			0
$25$	−3.79317	−	3.25759i	−0.758634	−	0.651517i
$26$		0			0
$27$	−3.04993	+	3.04993i	−0.586959	+	0.586959i
$28$		0			0
$29$	2.57802			0.478726			0.239363	−	0.970930i	$-0.423061\pi$
$29$	2.57802			0.478726			0.239363	+	0.970930i	$0.423061\pi$
$30$		0			0
$31$		−	5.78413i		−	1.03886i	−0.854513	−	0.519430i	$-0.826144\pi$
$31$		−	5.78413i		−	1.03886i	0.854513	−	0.519430i	$-0.173856\pi$
$32$		0			0
$33$	−0.591015	−	0.591015i	−0.102882	−	0.102882i
$34$		0			0
$35$	2.03194	−	0.933385i	0.343461	−	0.157771i
$36$		0			0
$37$	6.90394	+	6.90394i	1.13500	+	1.13500i	0.989334	+	0.145668i	$0.0465331\pi$
$37$	6.90394	+	6.90394i	1.13500	+	1.13500i	0.145668	+	0.989334i	$0.453467\pi$
$38$		0			0
$39$	−2.19573			−0.351598
$40$		0			0
$41$	−7.82998			−1.22284			−0.611419	−	0.791307i	$-0.709401\pi$
$41$	−7.82998			−1.22284			−0.611419	+	0.791307i	$0.709401\pi$
$42$		0			0
$43$	−7.89276	−	7.89276i	−1.20363	−	1.20363i	−0.973053	−	0.230581i	$-0.925937\pi$
$43$	−7.89276	−	7.89276i	−1.20363	−	1.20363i	−0.230581	−	0.973053i	$-0.574063\pi$
$44$		0			0
$45$	−4.92754	−	1.82549i	−0.734554	−	0.272129i
$46$		0			0
$47$	−0.137030	−	0.137030i	−0.0199879	−	0.0199879i	0.697042	−	0.717030i	$-0.254499\pi$
$47$	−0.137030	−	0.137030i	−0.0199879	−	0.0199879i	−0.717030	+	0.697042i	$0.754499\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−0.129567			−0.0181430
$52$		0			0
$53$	6.52731	−	6.52731i	0.896595	−	0.896595i	−0.0985386	−	0.995133i	$-0.531417\pi$
$53$	6.52731	−	6.52731i	0.896595	−	0.896595i	0.995133	+	0.0985386i	$0.0314168\pi$
$54$		0			0
$55$	0.805328	−	2.17381i	0.108590	−	0.293117i
$56$		0			0
$57$	0.501202	−	0.501202i	0.0663858	−	0.0663858i
$58$		0			0
$59$		−	11.9683i		−	1.55814i	−0.626937	−	0.779070i	$-0.715692\pi$
$59$		−	11.9683i		−	1.55814i	0.626937	−	0.779070i	$-0.284308\pi$
$60$		0			0
$61$			1.41110i			0.180673i	0.995911	+	0.0903363i	$0.0287942\pi$
$61$			1.41110i			0.180673i	−0.995911	+	0.0903363i	$0.971206\pi$
$62$		0			0
$63$	1.66172	−	1.66172i	0.209357	−	0.209357i
$64$		0			0
$65$	−2.54209	−	5.53402i	−0.315307	−	0.686411i
$66$		0			0
$67$	−6.46395	+	6.46395i	−0.789697	+	0.789697i	−0.981444	−	0.191747i	$-0.938585\pi$
$67$	−6.46395	+	6.46395i	−0.789697	+	0.789697i	0.191747	+	0.981444i	$0.438585\pi$
$68$		0			0
$69$	−0.285901			−0.0344184
$70$		0			0
$71$			3.26611i			0.387616i	0.981039	+	0.193808i	$0.0620839\pi$
$71$			3.26611i			0.387616i	−0.981039	+	0.193808i	$0.937916\pi$
$72$		0			0
$73$	3.50178	+	3.50178i	0.409853	+	0.409853i	0.881687	−	0.471834i	$-0.156408\pi$
$73$	3.50178	+	3.50178i	0.409853	+	0.409853i	−0.471834	+	0.881687i	$0.656408\pi$
$74$		0			0
$75$	0.305324	+	4.01948i	0.0352558	+	0.464129i
$76$		0			0
$77$	0.733077	+	0.733077i	0.0835418	+	0.0835418i
$78$		0			0
$79$	−1.49268			−0.167939			−0.0839696	−	0.996468i	$-0.526760\pi$
$79$	−1.49268			−0.167939			−0.0839696	+	0.996468i	$0.526760\pi$
$80$		0			0
$81$	−3.57268			−0.396964
$82$		0			0
$83$	−4.86134	−	4.86134i	−0.533601	−	0.533601i	0.388041	−	0.921642i	$-0.373152\pi$
$83$	−4.86134	−	4.86134i	−0.533601	−	0.533601i	−0.921642	+	0.388041i	$0.873152\pi$
$84$		0			0
$85$	−0.150005	−	0.326555i	−0.0162703	−	0.0354199i
$86$		0			0
$87$	−1.46967	−	1.46967i	−0.157565	−	0.157565i
$88$		0			0
$89$		−	12.9763i		−	1.37549i	−0.725953	−	0.687745i	$-0.758601\pi$
$89$		−	12.9763i		−	1.37549i	0.725953	−	0.687745i	$-0.241399\pi$
$90$		0			0
$91$	2.72351			0.285502
$92$		0			0
$93$	−3.29740	+	3.29740i	−0.341925	+	0.341925i
$94$		0			0
$95$	1.84347	+	0.682947i	0.189136	+	0.0700688i
$96$		0			0
$97$	−7.01973	+	7.01973i	−0.712746	+	0.712746i	−0.967109	−	0.254363i	$-0.918134\pi$
$97$	−7.01973	+	7.01973i	−0.712746	+	0.712746i	0.254363	+	0.967109i	$0.418134\pi$
$98$		0			0
$99$		−	2.43633i		−	0.244861i
$100$		0			0
$101$		−	14.5485i		−	1.44763i	−0.689995	−	0.723815i	$-0.742387\pi$
$101$		−	14.5485i		−	1.44763i	0.689995	−	0.723815i	$-0.257613\pi$
$102$		0			0
$103$	11.0931	−	11.0931i	1.09304	−	1.09304i	0.0978327	−	0.995203i	$-0.468809\pi$
$103$	11.0931	−	11.0931i	1.09304	−	1.09304i	0.995203	−	0.0978327i	$-0.0311910\pi$
$104$		0			0
$105$	−1.69047	−	0.626263i	−0.164973	−	0.0611170i
$106$		0			0
$107$	−3.95864	+	3.95864i	−0.382696	+	0.382696i	−0.872073	−	0.489376i	$-0.837224\pi$
$107$	−3.95864	+	3.95864i	−0.382696	+	0.382696i	0.489376	+	0.872073i	$0.337224\pi$
$108$		0			0
$109$	−5.29817			−0.507472			−0.253736	−	0.967273i	$-0.581659\pi$
$109$	−5.29817			−0.507472			−0.253736	+	0.967273i	$0.581659\pi$
$110$		0			0
$111$		−	7.87157i		−	0.747136i
$112$		0			0
$113$	14.1628	+	14.1628i	1.33232	+	1.33232i	0.903288	+	0.429035i	$0.141146\pi$
$113$	14.1628	+	14.1628i	1.33232	+	1.33232i	0.429035	+	0.903288i	$0.358854\pi$
$114$		0			0
$115$	−0.330999	−	0.720573i	−0.0308658	−	0.0671938i
$116$		0			0
$117$	−4.52571	−	4.52571i	−0.418402	−	0.418402i
$118$		0			0
$119$	0.160711			0.0147323
$120$		0			0
$121$	−9.92520			−0.902291
$122$		0			0
$123$	4.46369	+	4.46369i	0.402478	+	0.402478i
$124$		0			0
$125$	−9.77704	+	5.42305i	−0.874485	+	0.485052i
$126$		0			0
$127$	11.4090	+	11.4090i	1.01238	+	1.01238i	0.999922	+	0.0124598i	$0.00396619\pi$
$127$	11.4090	+	11.4090i	1.01238	+	1.01238i	0.0124598	+	0.999922i	$0.496034\pi$
$128$		0			0
$129$			8.99897i			0.792315i
$130$		0			0
$131$	20.4978			1.79090			0.895452	−	0.445157i	$-0.146852\pi$
$131$	20.4978			1.79090			0.895452	+	0.445157i	$0.146852\pi$
$132$		0			0
$133$	−0.621675	+	0.621675i	−0.0539061	+	0.0539061i
$134$		0			0
$135$	4.02592	+	8.76428i	0.346496	+	0.754309i
$136$		0			0
$137$	9.02504	−	9.02504i	0.771061	−	0.771061i	−0.207231	−	0.978292i	$-0.566445\pi$
$137$	9.02504	−	9.02504i	0.771061	−	0.771061i	0.978292	+	0.207231i	$0.0664451\pi$
$138$		0			0
$139$			2.81121i			0.238444i	0.992868	+	0.119222i	$0.0380400\pi$
$139$			2.81121i			0.238444i	−0.992868	+	0.119222i	$0.961960\pi$
$140$		0			0
$141$			0.156235i			0.0131574i
$142$		0			0
$143$	1.99654	−	1.99654i	0.166959	−	0.166959i
$144$		0			0
$145$	2.00260	−	5.40560i	0.166307	−	0.448910i
$146$		0			0
$147$	0.570077	−	0.570077i	0.0470192	−	0.0470192i
$148$		0			0
$149$	−8.93623			−0.732084			−0.366042	−	0.930598i	$-0.619287\pi$
$149$	−8.93623			−0.732084			−0.366042	+	0.930598i	$0.619287\pi$
$150$		0			0
$151$		−	13.8418i		−	1.12643i	−0.826310	−	0.563216i	$-0.809564\pi$
$151$		−	13.8418i		−	1.12643i	0.826310	−	0.563216i	$-0.190436\pi$
$152$		0			0
$153$	−0.267056	−	0.267056i	−0.0215902	−	0.0215902i
$154$		0			0
$155$	−12.1282	−	4.49310i	−0.974160	−	0.360895i
$156$		0			0
$157$	−2.85341	−	2.85341i	−0.227727	−	0.227727i	0.584015	−	0.811743i	$-0.301481\pi$
$157$	−2.85341	−	2.85341i	−0.227727	−	0.227727i	−0.811743	+	0.584015i	$0.801481\pi$
$158$		0			0
$159$	−7.44214			−0.590200
$160$		0			0
$161$	0.354623			0.0279482
$162$		0			0
$163$	5.65449	+	5.65449i	0.442894	+	0.442894i	0.892983	−	0.450090i	$-0.148608\pi$
$163$	5.65449	+	5.65449i	0.442894	+	0.442894i	−0.450090	+	0.892983i	$0.648608\pi$
$164$		0			0
$165$	−1.69834	+	0.780143i	−0.132216	+	0.0607340i
$166$		0			0
$167$	16.7864	+	16.7864i	1.29897	+	1.29897i	0.929073	+	0.369897i	$0.120607\pi$
$167$	16.7864	+	16.7864i	1.29897	+	1.29897i	0.369897	+	0.929073i	$0.379393\pi$
$168$		0			0
$169$			5.58248i			0.429422i
$170$		0			0
$171$	2.06610			0.157998
$172$		0			0
$173$	2.55716	−	2.55716i	0.194417	−	0.194417i	−0.603184	−	0.797602i	$-0.706102\pi$
$173$	2.55716	−	2.55716i	0.194417	−	0.194417i	0.797602	+	0.603184i	$0.206102\pi$
$174$		0			0
$175$	−0.378715	−	4.98564i	−0.0286282	−	0.376879i
$176$		0			0
$177$	−6.82286	+	6.82286i	−0.512838	+	0.512838i
$178$		0			0
$179$		−	3.99312i		−	0.298460i	−0.988803	−	0.149230i	$-0.952321\pi$
$179$		−	3.99312i		−	0.298460i	0.988803	−	0.149230i	$-0.0476795\pi$
$180$		0			0
$181$			18.5560i			1.37926i	0.724163	+	0.689628i	$0.242226\pi$
$181$			18.5560i			1.37926i	−0.724163	+	0.689628i	$0.757774\pi$
$182$		0			0
$183$	0.804436	−	0.804436i	0.0594656	−	0.0594656i
$184$		0			0
$185$	19.8392	−	9.11324i	1.45861	−	0.670019i
$186$		0			0
$187$	0.117813	−	0.117813i	0.00861536	−	0.00861536i
$188$		0			0
$189$	−4.31325			−0.313743
$190$		0			0
$191$			24.3117i			1.75913i	0.475776	+	0.879566i	$0.342167\pi$
$191$			24.3117i			1.75913i	−0.475776	+	0.879566i	$0.657833\pi$
$192$		0			0
$193$	14.2660	+	14.2660i	1.02689	+	1.02689i	0.999628	+	0.0272630i	$0.00867916\pi$
$193$	14.2660	+	14.2660i	1.02689	+	1.02689i	0.0272630	+	0.999628i	$0.491321\pi$
$194$		0			0
$195$	−1.70564	+	4.60401i	−0.122143	+	0.329700i
$196$		0			0
$197$	11.0213	+	11.0213i	0.785235	+	0.785235i	0.980709	−	0.195474i	$-0.0626244\pi$
$197$	11.0213	+	11.0213i	0.785235	+	0.785235i	−0.195474	+	0.980709i	$0.562624\pi$
$198$		0			0
$199$	−14.2598			−1.01085			−0.505425	−	0.862870i	$-0.668664\pi$
$199$	−14.2598			−1.01085			−0.505425	+	0.862870i	$0.668664\pi$
$200$		0			0
$201$	7.36991			0.519833
$202$		0			0
$203$	1.82293	+	1.82293i	0.127945	+	0.127945i
$204$		0			0
$205$	−6.08231	+	16.4179i	−0.424807	+	1.14668i
$206$		0			0
$207$	−0.589282	−	0.589282i	−0.0409580	−	0.0409580i
$208$		0			0
$209$			0.911471i			0.0630478i
$210$		0			0
$211$	−1.36755			−0.0941461			−0.0470730	−	0.998891i	$-0.514989\pi$
$211$	−1.36755			−0.0941461			−0.0470730	+	0.998891i	$0.514989\pi$
$212$		0			0
$213$	1.86194	−	1.86194i	0.127578	−	0.127578i
$214$		0			0
$215$	−22.6806	+	10.4185i	−1.54681	+	0.710535i
$216$		0			0
$217$	4.09000	−	4.09000i	0.277647	−	0.277647i
$218$		0			0
$219$		−	3.99258i		−	0.269793i
$220$		0			0
$221$		−	0.437698i		−	0.0294427i
$222$		0			0
$223$	−9.76435	+	9.76435i	−0.653869	+	0.653869i	−0.953922	−	0.300053i	$-0.902996\pi$
$223$	−9.76435	+	9.76435i	−0.653869	+	0.653869i	0.300053	+	0.953922i	$0.402996\pi$
$224$		0			0
$225$	−7.65540	+	8.91404i	−0.510360	+	0.594269i
$226$		0			0
$227$	−0.786454	+	0.786454i	−0.0521988	+	0.0521988i	−0.732724	−	0.680526i	$-0.761752\pi$
$227$	−0.786454	+	0.786454i	−0.0521988	+	0.0521988i	0.680526	+	0.732724i	$0.261752\pi$
$228$		0			0
$229$	−3.06651			−0.202640			−0.101320	−	0.994854i	$-0.532307\pi$
$229$	−3.06651			−0.202640			−0.101320	+	0.994854i	$0.532307\pi$
$230$		0			0
$231$		−	0.835821i		−	0.0549930i
$232$		0			0
$233$	−11.8889	−	11.8889i	−0.778865	−	0.778865i	0.200773	−	0.979638i	$-0.435655\pi$
$233$	−11.8889	−	11.8889i	−0.778865	−	0.778865i	−0.979638	+	0.200773i	$0.935655\pi$
$234$		0			0
$235$	−0.393769	+	0.180880i	−0.0256867	+	0.0117993i
$236$		0			0
$237$	0.850941	+	0.850941i	0.0552745	+	0.0552745i
$238$		0			0
$239$	−2.61651			−0.169248			−0.0846239	−	0.996413i	$-0.526969\pi$
$239$	−2.61651			−0.169248			−0.0846239	+	0.996413i	$0.526969\pi$
$240$		0			0
$241$	14.2806			0.919894			0.459947	−	0.887946i	$-0.347868\pi$
$241$	14.2806			0.919894			0.459947	+	0.887946i	$0.347868\pi$
$242$		0			0
$243$	11.1865	+	11.1865i	0.717614	+	0.717614i
$244$		0			0
$245$	2.09680	+	0.776798i	0.133960	+	0.0496278i
$246$		0			0
$247$	1.69314	+	1.69314i	0.107732	+	0.107732i
$248$		0			0
$249$			5.54268i			0.351253i
$250$		0			0
$251$	26.0535			1.64448			0.822241	−	0.569139i	$-0.192723\pi$
$251$	26.0535			1.64448			0.822241	+	0.569139i	$0.192723\pi$
$252$		0			0
$253$	0.259966	−	0.259966i	0.0163439	−	0.0163439i
$254$		0			0
$255$	−0.100647	+	0.271676i	−0.00630278	+	0.0170130i
$256$		0			0
$257$	−10.5553	+	10.5553i	−0.658420	+	0.658420i	−0.955006	−	0.296586i	$-0.904152\pi$
$257$	−10.5553	+	10.5553i	−0.658420	+	0.658420i	0.296586	+	0.955006i	$0.404152\pi$
$258$		0			0
$259$			9.76365i			0.606684i
$260$		0			0
$261$		−	6.05840i		−	0.375006i
$262$		0			0
$263$	−9.64346	+	9.64346i	−0.594641	+	0.594641i	−0.938882	−	0.344240i	$-0.888137\pi$
$263$	−9.64346	+	9.64346i	−0.594641	+	0.594641i	0.344240	+	0.938882i	$0.388137\pi$
$264$		0			0
$265$	−8.61608	−	18.7569i	−0.529282	−	1.15223i
$266$		0			0
$267$	−7.39752	+	7.39752i	−0.452721	+	0.452721i
$268$		0			0
$269$	17.5249			1.06851			0.534255	−	0.845323i	$-0.320592\pi$
$269$	17.5249			1.06851			0.534255	+	0.845323i	$0.320592\pi$
$270$		0			0
$271$		−	28.8960i		−	1.75530i	−0.479298	−	0.877652i	$-0.659109\pi$
$271$		−	28.8960i		−	1.75530i	0.479298	−	0.877652i	$-0.340891\pi$
$272$		0			0
$273$	−1.55261	−	1.55261i	−0.0939684	−	0.0939684i
$274$		0			0
$275$	−3.93248	−	3.37723i	−0.237138	−	0.203654i
$276$		0			0
$277$	10.6872	+	10.6872i	0.642131	+	0.642131i	0.951079	−	0.308948i	$-0.0999769\pi$
$277$	10.6872	+	10.6872i	0.642131	+	0.642131i	−0.308948	+	0.951079i	$0.599977\pi$
$278$		0			0
$279$	−13.5928			−0.813782
$280$		0			0
$281$	15.9862			0.953658			0.476829	−	0.878996i	$-0.341786\pi$
$281$	15.9862			0.953658			0.476829	+	0.878996i	$0.341786\pi$
$282$		0			0
$283$	18.8845	+	18.8845i	1.12257	+	1.12257i	0.991355	+	0.131211i	$0.0418864\pi$
$283$	18.8845	+	18.8845i	1.12257	+	1.12257i	0.131211	+	0.991355i	$0.458114\pi$
$284$		0			0
$285$	−0.661589	−	1.44025i	−0.0391891	−	0.0853133i
$286$		0			0
$287$	−5.53663	−	5.53663i	−0.326817	−	0.326817i
$288$		0			0
$289$			16.9742i			0.998481i
$290$		0			0
$291$	8.00358			0.469178
$292$		0			0
$293$	1.53899	−	1.53899i	0.0899087	−	0.0899087i	−0.660722	−	0.750631i	$-0.729750\pi$
$293$	1.53899	−	1.53899i	0.0899087	−	0.0899087i	0.750631	+	0.660722i	$0.229750\pi$
$294$		0			0
$295$	−25.0952	−	9.29695i	−1.46110	−	0.541290i
$296$		0			0
$297$	−3.16194	+	3.16194i	−0.183475	+	0.183475i
$298$		0			0
$299$		−	0.965819i		−	0.0558547i
$300$		0			0
$301$		−	11.1620i		−	0.643370i
$302$		0			0
$303$	−8.29377	+	8.29377i	−0.476465	+	0.476465i
$304$		0			0
$305$	2.95880	+	1.09614i	0.169420	+	0.0627647i
$306$		0			0
$307$	−5.13452	+	5.13452i	−0.293042	+	0.293042i	−0.838281	−	0.545238i	$-0.816439\pi$
$307$	−5.13452	+	5.13452i	−0.293042	+	0.293042i	0.545238	+	0.838281i	$0.316439\pi$
$308$		0			0
$309$	−12.6479			−0.719511
$310$		0			0
$311$		−	14.9705i		−	0.848901i	−0.905451	−	0.424450i	$-0.860467\pi$
$311$		−	14.9705i		−	0.848901i	0.905451	−	0.424450i	$-0.139533\pi$
$312$		0			0
$313$	−6.10822	−	6.10822i	−0.345257	−	0.345257i	0.513082	−	0.858339i	$-0.328504\pi$
$313$	−6.10822	−	6.10822i	−0.345257	−	0.345257i	−0.858339	+	0.513082i	$0.828504\pi$
$314$		0			0
$315$	−2.19348	−	4.77511i	−0.123588	−	0.269047i
$316$		0			0
$317$	20.7252	+	20.7252i	1.16404	+	1.16404i	0.983582	+	0.180461i	$0.0577590\pi$
$317$	20.7252	+	20.7252i	1.16404	+	1.16404i	0.180461	+	0.983582i	$0.442241\pi$
$318$		0			0
$319$	2.67270			0.149643
$320$		0			0
$321$	4.51346			0.251917
$322$		0			0
$323$	0.0999099	+	0.0999099i	0.00555914	+	0.00555914i
$324$		0			0
$325$	−13.5784	+	1.03144i	−0.753197	+	0.0572137i
$326$		0			0
$327$	3.02037	+	3.02037i	0.167027	+	0.167027i
$328$		0			0
$329$		−	0.193790i		−	0.0106840i
$330$		0			0
$331$	−27.4787			−1.51037			−0.755183	−	0.655514i	$-0.772452\pi$
$331$	−27.4787			−1.51037			−0.755183	+	0.655514i	$0.772452\pi$
$332$		0			0
$333$	16.2244	−	16.2244i	0.889093	−	0.889093i
$334$		0			0
$335$	8.53245	+	18.5748i	0.466178	+	1.01485i
$336$		0			0
$337$	−6.84115	+	6.84115i	−0.372661	+	0.372661i	−0.868446	−	0.495785i	$-0.834881\pi$
$337$	−6.84115	+	6.84115i	−0.372661	+	0.372661i	0.495785	+	0.868446i	$0.334881\pi$
$338$		0			0
$339$		−	16.1478i		−	0.877026i
$340$		0			0
$341$		−	5.99657i		−	0.324732i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	−0.222087	+	0.599478i	−0.0119568	+	0.0322748i
$346$		0			0
$347$	15.7089	−	15.7089i	0.843299	−	0.843299i	−0.145987	−	0.989286i	$-0.546636\pi$
$347$	15.7089	−	15.7089i	0.843299	−	0.843299i	0.989286	+	0.145987i	$0.0466359\pi$
$348$		0			0
$349$	18.3356			0.981482			0.490741	−	0.871305i	$-0.336726\pi$
$349$	18.3356			0.981482			0.490741	+	0.871305i	$0.336726\pi$
$350$		0			0
$351$			11.7472i			0.627018i
$352$		0			0
$353$	10.2442	+	10.2442i	0.545241	+	0.545241i	0.925061	−	0.379820i	$-0.124014\pi$
$353$	10.2442	+	10.2442i	0.545241	+	0.545241i	−0.379820	+	0.925061i	$0.624014\pi$
$354$		0			0
$355$	6.84839	+	2.53711i	0.363475	+	0.134656i
$356$		0			0
$357$	−0.0916176	−	0.0916176i	−0.00484892	−	0.00484892i
$358$		0			0
$359$	22.3306			1.17856			0.589281	−	0.807928i	$-0.299411\pi$
$359$	22.3306			1.17856			0.589281	+	0.807928i	$0.299411\pi$
$360$		0			0
$361$	18.2270			0.959318
$362$		0			0
$363$	5.65813	+	5.65813i	0.296975	+	0.296975i
$364$		0			0
$365$	10.0627	−	4.62237i	0.526707	−	0.241946i
$366$		0			0
$367$	−10.3200	−	10.3200i	−0.538698	−	0.538698i	0.384448	−	0.923147i	$-0.374392\pi$
$367$	−10.3200	−	10.3200i	−0.538698	−	0.538698i	−0.923147	+	0.384448i	$0.874392\pi$
$368$		0			0
$369$			18.4006i			0.957899i
$370$		0			0
$371$	9.23101			0.479250
$372$		0			0
$373$	−9.90602	+	9.90602i	−0.512914	+	0.512914i	−0.915418	−	0.402504i	$-0.868140\pi$
$373$	−9.90602	+	9.90602i	−0.512914	+	0.512914i	0.402504	+	0.915418i	$0.368140\pi$
$374$		0			0
$375$	8.66523	+	2.48212i	0.447470	+	0.128176i
$376$		0			0
$377$	4.96478	−	4.96478i	0.255699	−	0.255699i
$378$		0			0
$379$			1.88129i			0.0966353i	0.998832	+	0.0483177i	$0.0153860\pi$
$379$			1.88129i			0.0966353i	−0.998832	+	0.0483177i	$0.984614\pi$
$380$		0			0
$381$		−	13.0080i		−	0.666420i
$382$		0			0
$383$	17.7981	−	17.7981i	0.909441	−	0.909441i	−0.0867863	−	0.996227i	$-0.527660\pi$
$383$	17.7981	−	17.7981i	0.909441	−	0.909441i	0.996227	+	0.0867863i	$0.0276597\pi$
$384$		0			0
$385$	2.10657	−	0.967665i	0.107361	−	0.0493168i
$386$		0			0
$387$	−18.5482	+	18.5482i	−0.942856	+	0.942856i
$388$		0			0
$389$	−24.3093			−1.23253			−0.616266	−	0.787538i	$-0.711355\pi$
$389$	−24.3093			−1.23253			−0.616266	+	0.787538i	$0.711355\pi$
$390$		0			0
$391$		−	0.0569917i		−	0.00288219i
$392$		0			0
$393$	−11.6854	−	11.6854i	−0.589448	−	0.589448i
$394$		0			0
$395$	−1.15951	+	3.12985i	−0.0583412	+	0.157480i
$396$		0			0
$397$	−14.9323	−	14.9323i	−0.749433	−	0.749433i	0.224940	−	0.974373i	$-0.427781\pi$
$397$	−14.9323	−	14.9323i	−0.749433	−	0.749433i	−0.974373	+	0.224940i	$0.927781\pi$
$398$		0			0
$399$	0.708806			0.0354847
$400$		0			0
$401$	−9.18457			−0.458655			−0.229328	−	0.973349i	$-0.573653\pi$
$401$	−9.18457			−0.458655			−0.229328	+	0.973349i	$0.573653\pi$
$402$		0			0
$403$	−11.1392	−	11.1392i	−0.554881	−	0.554881i
$404$		0			0
$405$	−2.77525	+	7.49121i	−0.137903	+	0.372241i
$406$		0			0
$407$	7.15751	+	7.15751i	0.354784	+	0.354784i
$408$		0			0
$409$		−	37.3508i		−	1.84688i	−0.383747	−	0.923438i	$-0.625366\pi$
$409$		−	37.3508i		−	1.84688i	0.383747	−	0.923438i	$-0.374634\pi$
$410$		0			0
$411$	−10.2899			−0.507566
$412$		0			0
$413$	8.46287	−	8.46287i	0.416431	−	0.416431i
$414$		0			0
$415$	−13.9695	+	6.41699i	−0.685738	+	0.314998i
$416$		0			0
$417$	1.60261	−	1.60261i	0.0784800	−	0.0784800i
$418$		0			0
$419$			7.05353i			0.344588i	0.985046	+	0.172294i	$0.0551179\pi$
$419$			7.05353i			0.344588i	−0.985046	+	0.172294i	$0.944882\pi$
$420$		0			0
$421$		−	10.0803i		−	0.491284i	−0.969361	−	0.245642i	$-0.921001\pi$
$421$		−	10.0803i		−	0.491284i	0.969361	−	0.245642i	$-0.0789988\pi$
$422$		0			0
$423$	−0.322023	+	0.322023i	−0.0156573	+	0.0156573i
$424$		0			0
$425$	−0.801245	+	0.0608636i	−0.0388661	+	0.00295232i
$426$		0			0
$427$	−0.997797	+	0.997797i	−0.0482868	+	0.0482868i
$428$		0			0
$429$	−2.27637			−0.109904
$430$		0			0
$431$		−	1.32938i		−	0.0640342i	−0.999487	−	0.0320171i	$-0.989807\pi$
$431$		−	1.32938i		−	0.0640342i	0.999487	−	0.0320171i	$-0.0101931\pi$
$432$		0			0
$433$	−6.98227	−	6.98227i	−0.335546	−	0.335546i	0.519142	−	0.854688i	$-0.326252\pi$
$433$	−6.98227	−	6.98227i	−0.335546	−	0.335546i	−0.854688	+	0.519142i	$0.826252\pi$
$434$		0			0
$435$	−4.22325	+	1.93997i	−0.202489	+	0.0930145i
$436$		0			0
$437$	0.220460	+	0.220460i	0.0105460	+	0.0105460i
$438$		0			0
$439$	15.8594			0.756926			0.378463	−	0.925616i	$-0.376453\pi$
$439$	15.8594			0.756926			0.378463	+	0.925616i	$0.376453\pi$
$440$		0			0
$441$	2.35002			0.111906
$442$		0			0
$443$	−3.88362	−	3.88362i	−0.184517	−	0.184517i	0.608804	−	0.793321i	$-0.291650\pi$
$443$	−3.88362	−	3.88362i	−0.184517	−	0.184517i	−0.793321	+	0.608804i	$0.791650\pi$
$444$		0			0
$445$	−27.2088	−	10.0800i	−1.28982	−	0.477838i
$446$		0			0
$447$	5.09434	+	5.09434i	0.240954	+	0.240954i
$448$		0			0
$449$		−	14.8106i		−	0.698956i	−0.936945	−	0.349478i	$-0.886359\pi$
$449$		−	14.8106i		−	0.698956i	0.936945	−	0.349478i	$-0.113641\pi$
$450$		0			0
$451$	−8.11755			−0.382241
$452$		0			0
$453$	−7.89092	+	7.89092i	−0.370748	+	0.370748i
$454$		0			0
$455$	2.11562	−	5.71067i	0.0991817	−	0.267720i
$456$		0			0
$457$	−20.5237	+	20.5237i	−0.960059	+	0.960059i	−0.999232	−	0.0391734i	$-0.987528\pi$
$457$	−20.5237	+	20.5237i	−0.960059	+	0.960059i	0.0391734	+	0.999232i	$0.487528\pi$
$458$		0			0
$459$			0.693186i			0.0323551i
$460$		0			0
$461$			24.7037i			1.15057i	0.817954	+	0.575284i	$0.195108\pi$
$461$			24.7037i			1.15057i	−0.817954	+	0.575284i	$0.804892\pi$
$462$		0			0
$463$	−0.518667	+	0.518667i	−0.0241045	+	0.0241045i	−0.719056	−	0.694952i	$-0.755426\pi$
$463$	−0.518667	+	0.518667i	−0.0241045	+	0.0241045i	0.694952	+	0.719056i	$0.255426\pi$
$464$		0			0
$465$	4.35259	+	9.47542i	0.201847	+	0.439412i
$466$		0			0
$467$	9.62343	−	9.62343i	0.445319	−	0.445319i	−0.448476	−	0.893795i	$-0.648033\pi$
$467$	9.62343	−	9.62343i	0.445319	−	0.445319i	0.893795	+	0.448476i	$0.148033\pi$
$468$		0			0
$469$	−9.14141			−0.422111
$470$		0			0
$471$			3.25333i			0.149906i
$472$		0			0
$473$	−8.18264	−	8.18264i	−0.376238	−	0.376238i
$474$		0			0
$475$	2.86401	−	3.33489i	0.131410	−	0.153015i
$476$		0			0
$477$	−15.3393	−	15.3393i	−0.702339	−	0.702339i
$478$		0			0
$479$	38.0859			1.74019			0.870095	−	0.492884i	$-0.164057\pi$
$479$	38.0859			1.74019			0.870095	+	0.492884i	$0.164057\pi$
$480$		0			0
$481$	26.5914			1.21246
$482$		0			0
$483$	−0.202162	−	0.202162i	−0.00919870	−	0.00919870i
$484$		0			0
$485$	9.26608	+	20.1719i	0.420751	+	0.915959i
$486$		0			0
$487$	−1.61929	−	1.61929i	−0.0733772	−	0.0733772i	0.669466	−	0.742843i	$-0.266523\pi$
$487$	−1.61929	−	1.61929i	−0.0733772	−	0.0733772i	−0.742843	+	0.669466i	$0.766523\pi$
$488$		0			0
$489$		−	6.44699i		−	0.291543i
$490$		0			0
$491$	−16.3486			−0.737801			−0.368901	−	0.929469i	$-0.620266\pi$
$491$	−16.3486			−0.737801			−0.368901	+	0.929469i	$0.620266\pi$
$492$		0			0
$493$	0.292965	−	0.292965i	0.0131945	−	0.0131945i
$494$		0			0
$495$	−5.10851	−	1.89254i	−0.229611	−	0.0850633i
$496$		0			0
$497$	−2.30949	+	2.30949i	−0.103595	+	0.103595i
$498$		0			0
$499$			1.85067i			0.0828472i	0.999142	+	0.0414236i	$0.0131893\pi$
$499$			1.85067i			0.0828472i	−0.999142	+	0.0414236i	$0.986811\pi$
$500$		0			0
$501$		−	19.1391i		−	0.855071i
$502$		0			0
$503$	14.3079	−	14.3079i	0.637958	−	0.637958i	−0.312094	−	0.950051i	$-0.601030\pi$
$503$	14.3079	−	14.3079i	0.637958	−	0.637958i	0.950051	+	0.312094i	$0.101030\pi$
$504$		0			0
$505$	−30.5053	−	11.3012i	−1.35747	−	0.502899i
$506$		0			0
$507$	3.18245	−	3.18245i	0.141337	−	0.141337i
$508$		0			0
$509$	4.32114			0.191531			0.0957657	−	0.995404i	$-0.469470\pi$
$509$	4.32114			0.191531			0.0957657	+	0.995404i	$0.469470\pi$
$510$		0			0
$511$			4.95227i			0.219076i
$512$		0			0
$513$	−2.68144	−	2.68144i	−0.118388	−	0.118388i
$514$		0			0
$515$	−14.6430	−	31.8771i	−0.645246	−	1.40467i
$516$		0			0
$517$	−0.142063	−	0.142063i	−0.00624791	−	0.00624791i
$518$		0			0
$519$	−2.91556			−0.127979
$520$		0			0
$521$	−24.5474			−1.07544			−0.537721	−	0.843123i	$-0.680715\pi$
$521$	−24.5474			−1.07544			−0.537721	+	0.843123i	$0.680715\pi$
$522$		0			0
$523$	−18.1813	−	18.1813i	−0.795013	−	0.795013i	0.187292	−	0.982304i	$-0.440029\pi$
$523$	−18.1813	−	18.1813i	−0.795013	−	0.795013i	−0.982304	+	0.187292i	$0.940029\pi$
$524$		0			0
$525$	−2.62630	+	3.05810i	−0.114621	+	0.133466i
$526$		0			0
$527$	−0.657307	−	0.657307i	−0.0286327	−	0.0286327i
$528$		0			0
$529$			22.8742i			0.994532i
$530$		0			0
$531$	−28.1258			−1.22056
$532$		0			0
$533$	−15.0791	+	15.0791i	−0.653148	+	0.653148i
$534$		0			0
$535$	5.22543	+	11.3756i	0.225915	+	0.491808i
$536$		0			0
$537$	−2.27639	+	2.27639i	−0.0982334	+	0.0982334i
$538$		0			0
$539$			1.03673i			0.0446550i
$540$		0			0
$541$			7.97837i			0.343017i	0.985183	+	0.171508i	$0.0548641\pi$
$541$			7.97837i			0.343017i	−0.985183	+	0.171508i	$0.945136\pi$
$542$		0			0
$543$	10.5784	−	10.5784i	0.453961	−	0.453961i
$544$		0			0
$545$	−4.11560	+	11.1092i	−0.176293	+	0.475866i
$546$		0			0
$547$	23.2066	−	23.2066i	0.992243	−	0.992243i	−0.00772747	−	0.999970i	$-0.502460\pi$
$547$	23.2066	−	23.2066i	0.992243	−	0.992243i	0.999970	+	0.00772747i	$0.00245975\pi$
$548$		0			0
$549$	3.31611			0.141528
$550$		0			0
$551$			2.26655i			0.0965581i
$552$		0			0
$553$	−1.05548	−	1.05548i	−0.0448836	−	0.0448836i
$554$		0			0
$555$	−16.5051	−	6.11462i	−0.700604	−	0.259551i
$556$		0			0
$557$	5.74633	+	5.74633i	0.243480	+	0.243480i	0.818288	−	0.574808i	$-0.194923\pi$
$557$	5.74633	+	5.74633i	0.243480	+	0.243480i	−0.574808	+	0.818288i	$0.694923\pi$
$558$		0			0
$559$	−30.4000			−1.28578
$560$		0			0
$561$	−0.134325			−0.00567122
$562$		0			0
$563$	12.4446	+	12.4446i	0.524476	+	0.524476i	0.918920	−	0.394444i	$-0.129063\pi$
$563$	12.4446	+	12.4446i	0.524476	+	0.524476i	−0.394444	+	0.918920i	$0.629063\pi$
$564$		0			0
$565$	40.6982	−	18.6950i	1.71219	−	0.786503i
$566$		0			0
$567$	−2.52627	−	2.52627i	−0.106093	−	0.106093i
$568$		0			0
$569$		−	37.5046i		−	1.57228i	−0.618051	−	0.786138i	$-0.712078\pi$
$569$		−	37.5046i		−	1.57228i	0.618051	−	0.786138i	$-0.287922\pi$
$570$		0			0
$571$	25.2727			1.05763			0.528814	−	0.848738i	$-0.322637\pi$
$571$	25.2727			1.05763			0.528814	+	0.848738i	$0.322637\pi$
$572$		0			0
$573$	13.8595	−	13.8595i	0.578991	−	0.578991i
$574$		0			0
$575$	−1.76802	+	0.134301i	−0.0737315	+	0.00560074i
$576$		0			0
$577$	−9.17897	+	9.17897i	−0.382125	+	0.382125i	−0.871867	−	0.489742i	$-0.837091\pi$
$577$	−9.17897	+	9.17897i	−0.382125	+	0.382125i	0.489742	+	0.871867i	$0.337091\pi$
$578$		0			0
$579$		−	16.2655i		−	0.675970i
$580$		0			0
$581$		−	6.87497i		−	0.285222i
$582$		0			0
$583$	6.76704	−	6.76704i	0.280262	−	0.280262i
$584$		0			0
$585$	−13.0051	+	5.97396i	−0.537694	+	0.246993i
$586$		0			0
$587$	−2.45607	+	2.45607i	−0.101373	+	0.101373i	−0.755974	−	0.654601i	$-0.772837\pi$
$587$	−2.45607	+	2.45607i	−0.101373	+	0.101373i	0.654601	+	0.755974i	$0.272837\pi$
$588$		0			0
$589$	5.08530			0.209536
$590$		0			0
$591$		−	12.5660i		−	0.516896i
$592$		0			0
$593$	10.7822	+	10.7822i	0.442773	+	0.442773i	0.892943	−	0.450170i	$-0.148637\pi$
$593$	10.7822	+	10.7822i	0.442773	+	0.442773i	−0.450170	+	0.892943i	$0.648637\pi$
$594$		0			0
$595$	0.124840	−	0.336979i	0.00511793	−	0.0138148i
$596$		0			0
$597$	8.12919	+	8.12919i	0.332706	+	0.332706i
$598$		0			0
$599$	−1.35589			−0.0554002			−0.0277001	−	0.999616i	$-0.508818\pi$
$599$	−1.35589			−0.0554002			−0.0277001	+	0.999616i	$0.508818\pi$
$600$		0			0
$601$	3.40045			0.138707			0.0693536	−	0.997592i	$-0.477906\pi$
$601$	3.40045			0.138707			0.0693536	+	0.997592i	$0.477906\pi$
$602$		0			0
$603$	15.1904	+	15.1904i	0.618602	+	0.618602i
$604$		0			0
$605$	−7.70987	+	20.8112i	−0.313451	+	0.846095i
$606$		0			0
$607$	11.0503	+	11.0503i	0.448517	+	0.448517i	0.894861	−	0.446345i	$-0.147274\pi$
$607$	11.0503	+	11.0503i	0.448517	+	0.448517i	−0.446345	+	0.894861i	$0.647274\pi$
$608$		0			0
$609$		−	2.07843i		−	0.0842221i
$610$		0			0
$611$	−0.527788			−0.0213520
$612$		0			0
$613$	−3.68918	+	3.68918i	−0.149005	+	0.149005i	−0.777673	−	0.628669i	$-0.783600\pi$
$613$	−3.68918	+	3.68918i	−0.149005	+	0.149005i	0.628669	+	0.777673i	$0.283600\pi$
$614$		0			0
$615$	12.8269	−	5.89210i	0.517230	−	0.237592i
$616$		0			0
$617$	23.1225	−	23.1225i	0.930877	−	0.930877i	−0.0668841	−	0.997761i	$-0.521306\pi$
$617$	23.1225	−	23.1225i	0.930877	−	0.930877i	0.997761	+	0.0668841i	$0.0213058\pi$
$618$		0			0
$619$			4.21968i			0.169603i	0.996398	+	0.0848017i	$0.0270257\pi$
$619$			4.21968i			0.169603i	−0.996398	+	0.0848017i	$0.972974\pi$
$620$		0			0
$621$			1.52958i			0.0613797i
$622$		0			0
$623$	9.17566	−	9.17566i	0.367615	−	0.367615i
$624$		0			0
$625$	3.77627	+	24.7131i	0.151051	+	0.988526i
$626$		0			0
$627$	0.519609	−	0.519609i	0.0207512	−	0.0207512i
$628$		0			0
$629$	1.56912			0.0625651
$630$		0			0
$631$		−	16.8115i		−	0.669254i	−0.942351	−	0.334627i	$-0.891390\pi$
$631$		−	16.8115i		−	0.669254i	0.942351	−	0.334627i	$-0.108610\pi$
$632$		0			0
$633$	0.779610	+	0.779610i	0.0309867	+	0.0309867i
$634$		0			0
$635$	32.7848	−	15.0599i	1.30103	−	0.597634i
$636$		0			0
$637$	1.92581	+	1.92581i	0.0763035	+	0.0763035i
$638$		0			0
$639$	7.67544			0.303636
$640$		0			0
$641$	−6.74104			−0.266255			−0.133128	−	0.991099i	$-0.542502\pi$
$641$	−6.74104			−0.266255			−0.133128	+	0.991099i	$0.542502\pi$
$642$		0			0
$643$	−31.6006	−	31.6006i	−1.24620	−	1.24620i	−0.957383	−	0.288821i	$-0.906737\pi$
$643$	−31.6006	−	31.6006i	−1.24620	−	1.24620i	−0.288821	−	0.957383i	$-0.593263\pi$
$644$		0			0
$645$	18.8691	+	6.99038i	0.742969	+	0.275246i
$646$		0			0
$647$	−9.23712	−	9.23712i	−0.363149	−	0.363149i	0.501822	−	0.864971i	$-0.332663\pi$
$647$	−9.23712	−	9.23712i	−0.363149	−	0.363149i	−0.864971	+	0.501822i	$0.832663\pi$
$648$		0			0
$649$		−	12.4079i		−	0.487051i
$650$		0			0
$651$	−4.66323			−0.182767
$652$		0			0
$653$	7.82082	−	7.82082i	0.306052	−	0.306052i	−0.537324	−	0.843376i	$-0.680565\pi$
$653$	7.82082	−	7.82082i	0.306052	−	0.306052i	0.843376	+	0.537324i	$0.180565\pi$
$654$		0			0
$655$	15.9227	−	42.9799i	0.622151	−	1.67937i
$656$		0			0
$657$	8.22927	−	8.22927i	0.321055	−	0.321055i
$658$		0			0
$659$			31.8697i			1.24147i	0.784022	+	0.620733i	$0.213165\pi$
$659$			31.8697i			1.24147i	−0.784022	+	0.620733i	$0.786835\pi$
$660$		0			0
$661$		−	42.1626i		−	1.63994i	−0.572409	−	0.819968i	$-0.693991\pi$
$661$		−	42.1626i		−	1.63994i	0.572409	−	0.819968i	$-0.306009\pi$
$662$		0			0
$663$	−0.249522	+	0.249522i	−0.00969062	+	0.00969062i
$664$		0			0
$665$	0.820615	+	1.78645i	0.0318221	+	0.0692754i
$666$		0			0
$667$	0.646453	−	0.646453i	0.0250308	−	0.0250308i
$668$		0			0
$669$	11.1329			0.430422
$670$		0			0
$671$			1.46292i			0.0564756i
$672$		0			0
$673$	−12.5299	−	12.5299i	−0.482992	−	0.482992i	0.423094	−	0.906086i	$-0.360944\pi$
$673$	−12.5299	−	12.5299i	−0.482992	−	0.482992i	−0.906086	+	0.423094i	$0.860944\pi$
$674$		0			0
$675$	21.5043	−	1.63349i	0.827701	−	0.0628732i
$676$		0			0
$677$	−21.6335	−	21.6335i	−0.831442	−	0.831442i	0.156272	−	0.987714i	$-0.450052\pi$
$677$	−21.6335	−	21.6335i	−0.831442	−	0.831442i	−0.987714	+	0.156272i	$0.950052\pi$
$678$		0			0
$679$	−9.92740			−0.380979
$680$		0			0
$681$	0.896679			0.0343608
$682$		0			0
$683$	5.87496	+	5.87496i	0.224799	+	0.224799i	0.810516	−	0.585717i	$-0.199187\pi$
$683$	5.87496	+	5.87496i	0.224799	+	0.224799i	−0.585717	+	0.810516i	$0.699187\pi$
$684$		0			0
$685$	−11.9131	−	25.9344i	−0.455176	−	0.990902i
$686$		0			0
$687$	1.74815	+	1.74815i	0.0666959	+	0.0666959i
$688$		0			0
$689$		−	25.1408i		−	0.957787i
$690$		0			0
$691$	−51.0090			−1.94047			−0.970237	−	0.242157i	$-0.922145\pi$
$691$	−51.0090			−1.94047			−0.970237	+	0.242157i	$0.922145\pi$
$692$		0			0
$693$	1.72275	−	1.72275i	0.0654418	−	0.0654418i
$694$		0			0
$695$	5.89455	+	2.18374i	0.223593	+	0.0828341i
$696$		0			0
$697$	−0.889796	+	0.889796i	−0.0337034	+	0.0337034i
$698$		0			0
$699$			13.5551i			0.512703i
$700$		0			0
$701$			23.8889i			0.902272i	0.892455	+	0.451136i	$0.148981\pi$
$701$			23.8889i			0.902272i	−0.892455	+	0.451136i	$0.851019\pi$
$702$		0			0
$703$	−6.06982	+	6.06982i	−0.228928	+	0.228928i
$704$		0			0
$705$	0.327595	+	0.121363i	0.0123379	+	0.00457081i
$706$		0			0
$707$	10.2873	−	10.2873i	0.386895	−	0.386895i
$708$		0			0
$709$	11.7004			0.439418			0.219709	−	0.975565i	$-0.429489\pi$
$709$	11.7004			0.439418			0.219709	+	0.975565i	$0.429489\pi$
$710$		0			0
$711$			3.50782i			0.131554i
$712$		0			0
$713$	−1.45041	−	1.45041i	−0.0543181	−	0.0543181i
$714$		0			0
$715$	−2.63545	−	5.73727i	−0.0985602	−	0.214562i
$716$		0			0
$717$	1.49161	+	1.49161i	0.0557052	+	0.0557052i
$718$		0			0
$719$	−16.3430			−0.609490			−0.304745	−	0.952434i	$-0.598571\pi$
$719$	−16.3430			−0.609490			−0.304745	+	0.952434i	$0.598571\pi$
$720$		0			0
$721$	15.6880			0.584252
$722$		0			0
$723$	−8.14105	−	8.14105i	−0.302769	−	0.302769i
$724$		0			0
$725$	−9.77886	−	8.39811i	−0.363178	−	0.311898i
$726$		0			0
$727$	1.84481	+	1.84481i	0.0684203	+	0.0684203i	0.740489	−	0.672069i	$-0.234594\pi$
$727$	1.84481	+	1.84481i	0.0684203	+	0.0684203i	−0.672069	+	0.740489i	$0.734594\pi$
$728$		0			0
$729$		−	2.03629i		−	0.0754182i
$730$		0			0
$731$	−1.79386			−0.0663483
$732$		0			0
$733$	−8.23868	+	8.23868i	−0.304303	+	0.304303i	−0.842695	−	0.538392i	$-0.819032\pi$
$733$	−8.23868	+	8.23868i	−0.304303	+	0.304303i	0.538392	+	0.842695i	$0.319032\pi$
$734$		0			0
$735$	−0.752505	−	1.63818i	−0.0277566	−	0.0604250i
$736$		0			0
$737$	−6.70135	+	6.70135i	−0.246848	+	0.246848i
$738$		0			0
$739$			28.2307i			1.03848i	0.854628	+	0.519241i	$0.173785\pi$
$739$			28.2307i			1.03848i	−0.854628	+	0.519241i	$0.826215\pi$
$740$		0			0
$741$		−	1.93044i		−	0.0709166i
$742$		0			0
$743$	28.1935	−	28.1935i	1.03432	−	1.03432i	0.0349291	−	0.999390i	$-0.488879\pi$
$743$	28.1935	−	28.1935i	1.03432	−	1.03432i	0.999390	−	0.0349291i	$-0.0111205\pi$
$744$		0			0
$745$	−6.94164	+	18.7375i	−0.254322	+	0.686489i
$746$		0			0
$747$	−11.4243	+	11.4243i	−0.417992	+	0.417992i
$748$		0			0
$749$	−5.59836			−0.204560
$750$		0			0
$751$			44.7778i			1.63396i	0.576663	+	0.816982i	$0.304355\pi$
$751$			44.7778i			1.63396i	−0.576663	+	0.816982i	$0.695645\pi$
$752$		0			0
$753$	−14.8525	−	14.8525i	−0.541256	−	0.541256i
$754$		0			0
$755$	−29.0236	−	10.7523i	−1.05628	−	0.391317i
$756$		0			0
$757$	13.5044	+	13.5044i	0.490828	+	0.490828i	0.908567	−	0.417739i	$-0.137177\pi$
$757$	13.5044	+	13.5044i	0.490828	+	0.490828i	−0.417739	+	0.908567i	$0.637177\pi$
$758$		0			0
$759$	−0.296401			−0.0107587
$760$		0			0
$761$	11.0243			0.399630			0.199815	−	0.979834i	$-0.435966\pi$
$761$	11.0243			0.399630			0.199815	+	0.979834i	$0.435966\pi$
$762$		0			0
$763$	−3.74637	−	3.74637i	−0.135628	−	0.135628i
$764$		0			0
$765$	−0.767412	+	0.352515i	−0.0277458	+	0.0127452i
$766$		0			0
$767$	−23.0487	−	23.0487i	−0.832241	−	0.832241i
$768$		0			0
$769$			37.9234i			1.36755i	0.729691	+	0.683777i	$0.239664\pi$
$769$			37.9234i			1.36755i	−0.729691	+	0.683777i	$0.760336\pi$
$770$		0			0
$771$	12.0347			0.433418
$772$		0			0
$773$	14.8575	−	14.8575i	0.534388	−	0.534388i	−0.387487	−	0.921875i	$-0.626657\pi$
$773$	14.8575	−	14.8575i	0.534388	−	0.534388i	0.921875	+	0.387487i	$0.126657\pi$
$774$		0			0
$775$	−18.8423	+	21.9402i	−0.676836	+	0.788115i
$776$		0			0
$777$	5.56604	−	5.56604i	0.199680	−	0.199680i
$778$		0			0
$779$		−	6.88397i		−	0.246644i
$780$		0			0
$781$			3.38607i			0.121163i
$782$		0			0
$783$	−7.86277	+	7.86277i	−0.280992	+	0.280992i
$784$		0			0
$785$	−8.19958	+	3.76652i	−0.292655	+	0.134433i
$786$		0			0
$787$	−29.8385	+	29.8385i	−1.06363	+	1.06363i	−0.0657956	+	0.997833i	$0.520959\pi$
$787$	−29.8385	+	29.8385i	−1.06363	+	1.06363i	−0.997833	+	0.0657956i	$0.979041\pi$
$788$		0			0
$789$	10.9950			0.391434
$790$		0			0
$791$			20.0292i			0.712156i
$792$		0			0
$793$	2.71751	+	2.71751i	0.0965017	+	0.0965017i
$794$		0			0
$795$	−5.78104	+	15.6047i	−0.205032	+	0.553442i
$796$		0			0
$797$	−12.9205	−	12.9205i	−0.457666	−	0.457666i	0.440222	−	0.897889i	$-0.354900\pi$
$797$	−12.9205	−	12.9205i	−0.457666	−	0.457666i	−0.897889	+	0.440222i	$0.854900\pi$
$798$		0			0
$799$	−0.0311441			−0.00110180
$800$		0			0
$801$	−30.4947			−1.07748
$802$		0			0
$803$	3.63039	+	3.63039i	0.128114	+	0.128114i
$804$		0			0
$805$	0.275470	−	0.743574i	0.00970904	−	0.0262075i
$806$		0			0
$807$	−9.99054	−	9.99054i	−0.351684	−	0.351684i
$808$		0			0
$809$		−	28.1463i		−	0.989570i	−0.869015	−	0.494785i	$-0.835247\pi$
$809$		−	28.1463i		−	0.989570i	0.869015	−	0.494785i	$-0.164753\pi$
$810$		0			0
$811$	−5.31804			−0.186742			−0.0933708	−	0.995631i	$-0.529764\pi$
$811$	−5.31804			−0.186742			−0.0933708	+	0.995631i	$0.529764\pi$
$812$		0			0
$813$	−16.4729	+	16.4729i	−0.577731	+	0.577731i
$814$		0			0
$815$	16.2487	−	7.46395i	0.569169	−	0.261451i
$816$		0			0
$817$	6.93917	−	6.93917i	0.242771	−	0.242771i
$818$		0			0
$819$		−	6.40032i		−	0.223645i
$820$		0			0
$821$		−	26.7232i		−	0.932645i	−0.884615	−	0.466322i	$-0.845579\pi$
$821$		−	26.7232i		−	0.932645i	0.884615	−	0.466322i	$-0.154421\pi$
$822$		0			0
$823$	−23.0489	+	23.0489i	−0.803434	+	0.803434i	−0.983631	−	0.180196i	$-0.942327\pi$
$823$	−23.0489	+	23.0489i	−0.803434	+	0.803434i	0.180196	+	0.983631i	$0.442327\pi$
$824$		0			0
$825$	0.316538	+	4.16710i	0.0110204	+	0.145080i
$826$		0			0
$827$	18.1319	−	18.1319i	0.630509	−	0.630509i	−0.317687	−	0.948196i	$-0.602906\pi$
$827$	18.1319	−	18.1319i	0.630509	−	0.630509i	0.948196	+	0.317687i	$0.102906\pi$
$828$		0			0
$829$	14.5544			0.505495			0.252748	−	0.967532i	$-0.418666\pi$
$829$	14.5544			0.505495			0.252748	+	0.967532i	$0.418666\pi$
$830$		0			0
$831$		−	12.1851i		−	0.422695i
$832$		0			0
$833$	0.113640	+	0.113640i	0.00393738	+	0.00393738i
$834$		0			0
$835$	48.2374	−	22.1581i	1.66932	−	0.766814i
$836$		0			0
$837$	17.6412	+	17.6412i	0.609769	+	0.609769i
$838$		0			0
$839$	−17.4147			−0.601223			−0.300611	−	0.953747i	$-0.597191\pi$
$839$	−17.4147			−0.601223			−0.300611	+	0.953747i	$0.597191\pi$
$840$		0			0
$841$	−22.3538			−0.770822
$842$		0			0
$843$	−9.11339	−	9.11339i	−0.313882	−	0.313882i
$844$		0			0
$845$	11.7054	+	4.33646i	0.402677	+	0.149179i
$846$		0			0
$847$	−7.01817	−	7.01817i	−0.241147	−	0.241147i
$848$		0			0
$849$		−	21.5312i		−	0.738950i
$850$		0			0
$851$	3.46241			0.118690
$852$		0			0
$853$	−11.3951	+	11.3951i	−0.390162	+	0.390162i	−0.874745	−	0.484583i	$-0.838971\pi$
$853$	−11.3951	+	11.3951i	−0.390162	+	0.390162i	0.484583	+	0.874745i	$0.338971\pi$
$854$		0			0
$855$	1.60494	−	4.33220i	0.0548878	−	0.148158i
$856$		0			0
$857$	1.78066	−	1.78066i	0.0608263	−	0.0608263i	−0.676039	−	0.736866i	$-0.736305\pi$
$857$	1.78066	−	1.78066i	0.0608263	−	0.0608263i	0.736866	+	0.676039i	$0.236305\pi$
$858$		0			0
$859$			27.6536i			0.943528i	0.881725	+	0.471764i	$0.156382\pi$
$859$			27.6536i			0.943528i	−0.881725	+	0.471764i	$0.843618\pi$
$860$		0			0
$861$			6.31262i			0.215133i
$862$		0			0
$863$	−31.5082	+	31.5082i	−1.07255	+	1.07255i	−0.0753980	+	0.997154i	$0.524023\pi$
$863$	−31.5082	+	31.5082i	−1.07255	+	1.07255i	−0.997154	+	0.0753980i	$0.975977\pi$
$864$		0			0
$865$	−3.37546	−	7.34826i	−0.114769	−	0.249848i
$866$		0			0
$867$	9.67659	−	9.67659i	0.328634	−	0.328634i
$868$		0			0
$869$	−1.54750			−0.0524953
$870$		0			0
$871$			24.8967i			0.843594i
$872$		0			0
$873$	16.4965	+	16.4965i	0.558323	+	0.558323i
$874$		0			0
$875$	−10.7481	−	3.07874i	−0.363352	−	0.104080i
$876$		0			0
$877$	−11.2425	−	11.2425i	−0.379632	−	0.379632i	0.491337	−	0.870969i	$-0.336508\pi$
$877$	−11.2425	−	11.2425i	−0.379632	−	0.379632i	−0.870969	+	0.491337i	$0.836508\pi$
$878$		0			0
$879$	−1.75469			−0.0591841
$880$		0			0
$881$	−8.61502			−0.290247			−0.145124	−	0.989414i	$-0.546358\pi$
$881$	−8.61502			−0.290247			−0.145124	+	0.989414i	$0.546358\pi$
$882$		0			0
$883$	26.5622	+	26.5622i	0.893889	+	0.893889i	0.994887	−	0.100998i	$-0.0322035\pi$
$883$	26.5622	+	26.5622i	0.893889	+	0.893889i	−0.100998	+	0.994887i	$0.532203\pi$
$884$		0			0
$885$	9.00621	+	19.6062i	0.302741	+	0.659055i
$886$		0			0
$887$	7.73084	+	7.73084i	0.259576	+	0.259576i	0.824882	−	0.565306i	$-0.191242\pi$
$887$	7.73084	+	7.73084i	0.259576	+	0.259576i	−0.565306	+	0.824882i	$0.691242\pi$
$888$		0			0
$889$			16.1347i			0.541141i
$890$		0			0
$891$	−3.70389			−0.124085
$892$		0			0
$893$	0.120474	−	0.120474i	0.00403151	−	0.00403151i
$894$		0			0
$895$	−8.37279	−	3.10185i	−0.279872	−	0.103683i
$896$		0			0
$897$	−0.550592	+	0.550592i	−0.0183837	+	0.0183837i
$898$		0			0
$899$		−	14.9116i		−	0.497330i
$900$		0			0
$901$		−	1.48352i		−	0.0494233i
$902$		0			0
$903$	−6.36323	+	6.36323i	−0.211755	+	0.211755i
$904$		0			0
$905$	38.9083	+	14.4143i	1.29336	+	0.479146i
$906$		0			0
$907$	−16.6156	+	16.6156i	−0.551713	+	0.551713i	−0.926935	−	0.375222i	$-0.877567\pi$
$907$	−16.6156	+	16.6156i	−0.551713	+	0.551713i	0.375222	+	0.926935i	$0.377567\pi$
$908$		0			0
$909$	−34.1893			−1.13399
$910$		0			0
$911$			6.01637i			0.199331i	0.995021	+	0.0996656i	$0.0317773\pi$
$911$			6.01637i			0.199331i	−0.995021	+	0.0996656i	$0.968223\pi$
$912$		0			0
$913$	−5.03988	−	5.03988i	−0.166796	−	0.166796i
$914$		0			0
$915$	−1.06186	−	2.31163i	−0.0351040	−	0.0764200i
$916$		0			0
$917$	14.4942	+	14.4942i	0.478639	+	0.478639i
$918$		0			0
$919$	28.9735			0.955748			0.477874	−	0.878428i	$-0.341407\pi$
$919$	28.9735			0.955748			0.477874	+	0.878428i	$0.341407\pi$
$920$		0			0
$921$	5.85415			0.192901
$922$		0			0
$923$	6.28992	+	6.28992i	0.207035	+	0.207035i
$924$		0			0
$925$	−3.69764	−	48.6780i	−0.121578	−	1.60052i
$926$		0			0
$927$	−26.0690	−	26.0690i	−0.856220	−	0.856220i
$928$		0			0
$929$		−	10.6090i		−	0.348071i	−0.984739	−	0.174036i	$-0.944319\pi$
$929$		−	10.6090i		−	0.348071i	0.984739	−	0.174036i	$-0.0556808\pi$
$930$		0			0
$931$	−0.879182			−0.0288140
$932$		0			0
$933$	−8.53436	+	8.53436i	−0.279402	+	0.279402i
$934$		0			0
$935$	−0.155514	−	0.338549i	−0.00508586	−	0.0110717i
$936$		0			0
$937$	−13.4910	+	13.4910i	−0.440733	+	0.440733i	−0.892258	−	0.451525i	$-0.850880\pi$
$937$	−13.4910	+	13.4910i	−0.440733	+	0.440733i	0.451525	+	0.892258i	$0.350880\pi$
$938$		0			0
$939$			6.96432i			0.227272i
$940$		0			0
$941$			57.2435i			1.86608i	0.359766	+	0.933042i	$0.382856\pi$
$941$			57.2435i			1.86608i	−0.359766	+	0.933042i	$0.617144\pi$
$942$		0			0
$943$	−1.96341	+	1.96341i	−0.0639376	+	0.0639376i
$944$		0			0
$945$	−3.35052	+	9.04404i	−0.108993	+	0.294203i
$946$		0			0
$947$	−2.00024	+	2.00024i	−0.0649991	+	0.0649991i	−0.738859	−	0.673860i	$-0.764635\pi$
$947$	−2.00024	+	2.00024i	−0.0649991	+	0.0649991i	0.673860	+	0.738859i	$0.264635\pi$
$948$		0			0
$949$	13.4876			0.437825
$950$		0			0
$951$		−	23.6299i		−	0.766253i
$952$		0			0
$953$	5.44413	+	5.44413i	0.176353	+	0.176353i	0.789764	−	0.613411i	$-0.210203\pi$
$953$	5.44413	+	5.44413i	0.176353	+	0.176353i	−0.613411	+	0.789764i	$0.710203\pi$
$954$		0			0
$955$	50.9768	+	18.8853i	1.64957	+	0.611113i
$956$		0			0
$957$	−1.52365	−	1.52365i	−0.0492525	−	0.0492525i
$958$		0			0
$959$	12.7633			0.412150
$960$		0			0
$961$	−2.45619			−0.0792321
$962$		0			0
$963$	9.30290	+	9.30290i	0.299782	+	0.299782i
$964$		0			0
$965$	40.9949	−	18.8312i	1.31967	−	0.606199i
$966$		0			0
$967$	28.1955	+	28.1955i	0.906706	+	0.906706i	0.996005	−	0.0892989i	$-0.0284626\pi$
$967$	28.1955	+	28.1955i	0.906706	+	0.906706i	−0.0892989	+	0.996005i	$0.528463\pi$
$968$		0			0
$969$		−	0.113913i		−	0.00365941i
$970$		0			0
$971$	−0.503002			−0.0161421			−0.00807106	−	0.999967i	$-0.502569\pi$
$971$	−0.503002			−0.0161421			−0.00807106	+	0.999967i	$0.502569\pi$
$972$		0			0
$973$	−1.98783	+	1.98783i	−0.0637268	+	0.0637268i
$974$		0			0
$975$	8.32876	+	7.15277i	0.266734	+	0.229072i
$976$		0			0
$977$	21.8461	−	21.8461i	0.698918	−	0.698918i	−0.265259	−	0.964177i	$-0.585457\pi$
$977$	21.8461	−	21.8461i	0.698918	−	0.698918i	0.964177	+	0.265259i	$0.0854575\pi$
$978$		0			0
$979$		−	13.4529i		−	0.429957i
$980$		0			0
$981$			12.4508i			0.397524i
$982$		0			0
$983$	−31.4383	+	31.4383i	−1.00273	+	1.00273i	−0.00272895	+	0.999996i	$0.500869\pi$
$983$	−31.4383	+	31.4383i	−1.00273	+	1.00273i	−0.999996	+	0.00272895i	$0.999131\pi$
$984$		0			0
$985$	31.6708	−	14.5482i	1.00912	−	0.463544i
$986$		0			0
$987$	−0.110475	+	0.110475i	−0.00351646	+	0.00351646i
$988$		0			0
$989$	−3.95831			−0.125867
$990$		0			0
$991$			51.0233i			1.62081i	0.585872	+	0.810404i	$0.300752\pi$
$991$			51.0233i			1.62081i	−0.585872	+	0.810404i	$0.699248\pi$
$992$		0			0
$993$	15.6650	+	15.6650i	0.497113	+	0.497113i
$994$		0			0
$995$	−11.0770	+	29.9000i	−0.351164	+	0.947894i
$996$		0			0
$997$	−17.3574	−	17.3574i	−0.549716	−	0.549716i	0.376643	−	0.926359i	$-0.377078\pi$
$997$	−17.3574	−	17.3574i	−0.549716	−	0.549716i	−0.926359	+	0.376643i	$0.877078\pi$
$998$		0			0
$999$	−42.1131			−1.33240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bi.a.463.14		72
4.3	odd	2		280.2.w.a.43.19	✓	72
5.2	odd	4	inner	1120.2.bi.a.687.13		72
8.3	odd	2	inner	1120.2.bi.a.463.13		72
8.5	even	2		280.2.w.a.43.35	yes	72
20.7	even	4		280.2.w.a.267.35	yes	72
40.27	even	4	inner	1120.2.bi.a.687.14		72
40.37	odd	4		280.2.w.a.267.19	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.19	✓	72	4.3	odd	2
280.2.w.a.43.35	yes	72	8.5	even	2
280.2.w.a.267.19	yes	72	40.37	odd	4
280.2.w.a.267.35	yes	72	20.7	even	4
1120.2.bi.a.463.13		72	8.3	odd	2	inner
1120.2.bi.a.463.14		72	1.1	even	1	trivial
1120.2.bi.a.687.13		72	5.2	odd	4	inner
1120.2.bi.a.687.14		72	40.27	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bi (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.570077 - 0.570077i) q^{3} +(0.776798 - 2.09680i) q^{5} +(0.707107 + 0.707107i) q^{7} -2.35002i q^{9} +1.03673 q^{11} +(1.92581 - 1.92581i) q^{13} +(-1.63818 + 0.752505i) q^{15} +(0.113640 - 0.113640i) q^{17} +0.879182i q^{19} -0.806211i q^{21} +(0.250756 - 0.250756i) q^{23} +(-3.79317 - 3.25759i) q^{25} +(-3.04993 + 3.04993i) q^{27} +2.57802 q^{29} -5.78413i q^{31} +(-0.591015 - 0.591015i) q^{33} +(2.03194 - 0.933385i) q^{35} +(6.90394 + 6.90394i) q^{37} -2.19573 q^{39} -7.82998 q^{41} +(-7.89276 - 7.89276i) q^{43} +(-4.92754 - 1.82549i) q^{45} +(-0.137030 - 0.137030i) q^{47} +1.00000i q^{49} -0.129567 q^{51} +(6.52731 - 6.52731i) q^{53} +(0.805328 - 2.17381i) q^{55} +(0.501202 - 0.501202i) q^{57} -11.9683i q^{59} +1.41110i q^{61} +(1.66172 - 1.66172i) q^{63} +(-2.54209 - 5.53402i) q^{65} +(-6.46395 + 6.46395i) q^{67} -0.285901 q^{69} +3.26611i q^{71} +(3.50178 + 3.50178i) q^{73} +(0.305324 + 4.01948i) q^{75} +(0.733077 + 0.733077i) q^{77} -1.49268 q^{79} -3.57268 q^{81} +(-4.86134 - 4.86134i) q^{83} +(-0.150005 - 0.326555i) q^{85} +(-1.46967 - 1.46967i) q^{87} -12.9763i q^{89} +2.72351 q^{91} +(-3.29740 + 3.29740i) q^{93} +(1.84347 + 0.682947i) q^{95} +(-7.01973 + 7.01973i) q^{97} -2.43633i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{17} - 8 q^{25} + 64 q^{43} + 32 q^{51} - 8 q^{65} - 40 q^{73} - 112 q^{75} - 72 q^{81} - 80 q^{83} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^17 - 8 * q^25 + 64 * q^43 + 32 * q^51 - 8 * q^65 - 40 * q^73 - 112 * q^75 - 72 * q^81 - 80 * q^83 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more