LMFDB - Embedded newform 1323.2.h.h.226.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.10
Character	$\chi$	$=$	1323.226
Dual form			1323.2.h.h.802.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.72661 q^{2} +0.981184 q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +O(q^{10})$	\(q+1.72661 q^{2} +0.981184 q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +(-3.03220 - 5.25192i) q^{10} +(-3.04532 + 5.27465i) q^{11} +(-0.560139 + 0.970190i) q^{13} -4.99965 q^{16} +(-0.601978 - 1.04266i) q^{17} +(-1.10269 + 1.90991i) q^{19} +(-1.72311 - 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} +(-0.636695 - 1.10279i) q^{23} +(-3.66817 + 6.35345i) q^{25} +(-0.967143 + 1.67514i) q^{26} +(3.10262 + 5.37390i) q^{29} +0.188404 q^{31} -5.11425 q^{32} +(-1.03938 - 1.80026i) q^{34} +(-1.78835 + 3.09752i) q^{37} +(-1.90391 + 3.29767i) q^{38} +(3.08925 + 5.35074i) q^{40} +(1.68320 - 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} +(-2.98802 + 5.17540i) q^{44} +(-1.09932 - 1.90408i) q^{46} -5.72070 q^{47} +(-6.33349 + 10.9699i) q^{50} +(-0.549600 + 0.951935i) q^{52} +(-4.16913 - 7.22115i) q^{53} +21.3922 q^{55} +(5.35702 + 9.27862i) q^{58} -11.2685 q^{59} -12.0022 q^{61} +0.325300 q^{62} +1.16898 q^{64} +3.93477 q^{65} -7.91303 q^{67} +(-0.590651 - 1.02304i) q^{68} +12.2052 q^{71} +(-2.65737 - 4.60269i) q^{73} +(-3.08779 + 5.34820i) q^{74} +(-1.08194 + 1.87397i) q^{76} +9.21711 q^{79} +(8.78016 + 15.2077i) q^{80} +(2.90623 - 5.03373i) q^{82} +(0.624950 + 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} +(-3.28532 - 5.69034i) q^{86} +(5.35702 - 9.27862i) q^{88} +(-2.77066 + 4.79892i) q^{89} +(-0.624715 - 1.08204i) q^{92} -9.87741 q^{94} +7.74596 q^{95} +(-8.24277 - 14.2769i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.72661			1.22090			0.610449	−	0.792056i	$-0.290989\pi$
$2$	1.72661			1.22090			0.610449	+	0.792056i	$0.290989\pi$
$3$		0			0
$3$		0			0
$4$	0.981184			0.490592
$5$	−1.75616	−	3.04175i	−0.785377	−	1.36031i	−0.928774	−	0.370647i	$-0.879136\pi$
$5$	−1.75616	−	3.04175i	−0.785377	−	1.36031i	0.143397	−	0.989665i	$-0.454197\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.75910			−0.621935
$9$		0			0
$10$	−3.03220	−	5.25192i	−0.958865	−	1.66080i
$11$	−3.04532	+	5.27465i	−0.918199	+	1.59037i	−0.116049	+	0.993244i	$0.537023\pi$
$11$	−3.04532	+	5.27465i	−0.918199	+	1.59037i	−0.802150	+	0.597123i	$0.796310\pi$
$12$		0			0
$13$	−0.560139	+	0.970190i	−0.155355	+	0.269082i	−0.933188	−	0.359388i	$-0.882985\pi$
$13$	−0.560139	+	0.970190i	−0.155355	+	0.269082i	0.777833	+	0.628471i	$0.216319\pi$
$14$		0			0
$15$		0			0
$16$	−4.99965			−1.24991
$17$	−0.601978	−	1.04266i	−0.146001	−	0.252881i	0.783745	−	0.621083i	$-0.213307\pi$
$17$	−0.601978	−	1.04266i	−0.146001	−	0.252881i	−0.929746	+	0.368202i	$0.879974\pi$
$18$		0			0
$19$	−1.10269	+	1.90991i	−0.252974	+	0.438163i	−0.964343	−	0.264655i	$-0.914742\pi$
$19$	−1.10269	+	1.90991i	−0.252974	+	0.438163i	0.711370	+	0.702818i	$0.248075\pi$
$20$	−1.72311	−	2.98452i	−0.385300	−	0.667359i
$21$		0			0
$22$	−5.25808	+	9.10727i	−1.12103	+	1.94168i
$23$	−0.636695	−	1.10279i	−0.132760	−	0.229947i	0.791980	−	0.610548i	$-0.209051\pi$
$23$	−0.636695	−	1.10279i	−0.132760	−	0.229947i	−0.924740	+	0.380601i	$0.875717\pi$
$24$		0			0
$25$	−3.66817	+	6.35345i	−0.733633	+	1.27069i
$26$	−0.967143	+	1.67514i	−0.189672	+	0.328522i
$27$		0			0
$28$		0			0
$29$	3.10262	+	5.37390i	0.576142	+	0.997907i	0.995917	+	0.0902789i	$0.0287758\pi$
$29$	3.10262	+	5.37390i	0.576142	+	0.997907i	−0.419774	+	0.907628i	$0.637891\pi$
$30$		0			0
$31$	0.188404			0.0338383			0.0169192	−	0.999857i	$-0.494614\pi$
$31$	0.188404			0.0338383			0.0169192	+	0.999857i	$0.494614\pi$
$32$	−5.11425			−0.904079
$33$		0			0
$34$	−1.03938	−	1.80026i	−0.178252	−	0.308742i
$35$		0			0
$36$		0			0
$37$	−1.78835	+	3.09752i	−0.294003	+	0.509228i	−0.974753	−	0.223288i	$-0.928321\pi$
$37$	−1.78835	+	3.09752i	−0.294003	+	0.509228i	0.680749	+	0.732516i	$0.261654\pi$
$38$	−1.90391	+	3.29767i	−0.308855	+	0.534953i
$39$		0			0
$40$	3.08925	+	5.35074i	0.488453	+	0.846026i
$41$	1.68320	−	2.91538i	0.262871	−	0.455307i	−0.704132	−	0.710069i	$-0.748664\pi$
$41$	1.68320	−	2.91538i	0.262871	−	0.455307i	0.967004	+	0.254762i	$0.0819972\pi$
$42$		0			0
$43$	−1.90276	−	3.29567i	−0.290168	−	0.502585i	0.683681	−	0.729781i	$-0.260378\pi$
$43$	−1.90276	−	3.29567i	−0.290168	−	0.502585i	−0.973849	+	0.227195i	$0.927044\pi$
$44$	−2.98802	+	5.17540i	−0.450461	+	0.780221i
$45$		0			0
$46$	−1.09932	−	1.90408i	−0.162086	−	0.280742i
$47$	−5.72070			−0.834449			−0.417225	−	0.908803i	$-0.636997\pi$
$47$	−5.72070			−0.834449			−0.417225	+	0.908803i	$0.636997\pi$
$48$		0			0
$49$		0			0
$50$	−6.33349	+	10.9699i	−0.895691	+	1.55138i
$51$		0			0
$52$	−0.549600	+	0.951935i	−0.0762158	+	0.132010i
$53$	−4.16913	−	7.22115i	−0.572675	−	0.991901i	−0.996290	−	0.0860593i	$-0.972573\pi$
$53$	−4.16913	−	7.22115i	−0.572675	−	0.991901i	0.423615	−	0.905842i	$-0.360761\pi$
$54$		0			0
$55$	21.3922			2.88453
$56$		0			0
$57$		0			0
$58$	5.35702	+	9.27862i	0.703411	+	1.21834i
$59$	−11.2685			−1.46704			−0.733519	−	0.679669i	$-0.762123\pi$
$59$	−11.2685			−1.46704			−0.733519	+	0.679669i	$0.762123\pi$
$60$		0			0
$61$	−12.0022			−1.53672			−0.768361	−	0.640017i	$-0.778927\pi$
$61$	−12.0022			−1.53672			−0.768361	+	0.640017i	$0.778927\pi$
$62$	0.325300			0.0413131
$63$		0			0
$64$	1.16898			0.146123
$65$	3.93477			0.488048
$66$		0			0
$67$	−7.91303			−0.966731			−0.483366	−	0.875419i	$-0.660586\pi$
$67$	−7.91303			−0.966731			−0.483366	+	0.875419i	$0.660586\pi$
$68$	−0.590651	−	1.02304i	−0.0716270	−	0.124062i
$69$		0			0
$70$		0			0
$71$	12.2052			1.44850			0.724248	−	0.689540i	$-0.242187\pi$
$71$	12.2052			1.44850			0.724248	+	0.689540i	$0.242187\pi$
$72$		0			0
$73$	−2.65737	−	4.60269i	−0.311021	−	0.538704i	0.667563	−	0.744554i	$-0.267338\pi$
$73$	−2.65737	−	4.60269i	−0.311021	−	0.538704i	−0.978584	+	0.205849i	$0.934004\pi$
$74$	−3.08779	+	5.34820i	−0.358948	+	0.621716i
$75$		0			0
$76$	−1.08194	+	1.87397i	−0.124107	+	0.214959i
$77$		0			0
$78$		0			0
$79$	9.21711			1.03701			0.518503	−	0.855076i	$-0.326490\pi$
$79$	9.21711			1.03701			0.518503	+	0.855076i	$0.326490\pi$
$80$	8.78016	+	15.2077i	0.981651	+	1.70027i
$81$		0			0
$82$	2.90623	−	5.03373i	0.320939	−	0.555883i
$83$	0.624950	+	1.08245i	0.0685972	+	0.118814i	0.898284	−	0.439415i	$-0.144814\pi$
$83$	0.624950	+	1.08245i	0.0685972	+	0.118814i	−0.829687	+	0.558229i	$0.811481\pi$
$84$		0			0
$85$	−2.11433	+	3.66213i	−0.229332	+	0.397214i
$86$	−3.28532	−	5.69034i	−0.354265	−	0.613605i
$87$		0			0
$88$	5.35702	−	9.27862i	0.571060	−	0.989105i
$89$	−2.77066	+	4.79892i	−0.293689	+	0.508684i	−0.974679	−	0.223608i	$-0.928216\pi$
$89$	−2.77066	+	4.79892i	−0.293689	+	0.508684i	0.680990	+	0.732293i	$0.261550\pi$
$90$		0			0
$91$		0			0
$92$	−0.624715	−	1.08204i	−0.0651310	−	0.112810i
$93$		0			0
$94$	−9.87741			−1.01878
$95$	7.74596			0.794718
$96$		0			0
$97$	−8.24277	−	14.2769i	−0.836926	−	1.44960i	−0.892452	−	0.451142i	$-0.851017\pi$
$97$	−8.24277	−	14.2769i	−0.836926	−	1.44960i	0.0555261	−	0.998457i	$-0.482316\pi$
$98$		0			0
$99$		0			0
$100$	−3.59915	+	6.23391i	−0.359915	+	0.623391i
$101$	6.48192	−	11.2270i	0.644975	−	1.11713i	−0.339332	−	0.940667i	$-0.610201\pi$
$101$	6.48192	−	11.2270i	0.644975	−	1.11713i	0.984307	−	0.176463i	$-0.0564657\pi$
$102$		0			0
$103$	1.35091	+	2.33984i	0.133109	+	0.230552i	0.924873	−	0.380275i	$-0.124171\pi$
$103$	1.35091	+	2.33984i	0.133109	+	0.230552i	−0.791765	+	0.610826i	$0.790837\pi$
$104$	0.985340	−	1.70666i	0.0966205	−	0.167352i
$105$		0			0
$106$	−7.19847	−	12.4681i	−0.699177	−	1.21101i
$107$	−0.0892402	+	0.154569i	−0.00862718	+	0.0149427i	−0.870307	−	0.492510i	$-0.836079\pi$
$107$	−0.0892402	+	0.154569i	−0.00862718	+	0.0149427i	0.861680	+	0.507453i	$0.169413\pi$
$108$		0			0
$109$	−4.67927	−	8.10473i	−0.448192	−	0.776292i	0.550076	−	0.835115i	$-0.314599\pi$
$109$	−4.67927	−	8.10473i	−0.448192	−	0.776292i	−0.998268	+	0.0588226i	$0.981265\pi$
$110$	36.9360			3.52171
$111$		0			0
$112$		0			0
$113$	−4.21019	+	7.29226i	−0.396061	+	0.685998i	−0.993236	−	0.116113i	$-0.962957\pi$
$113$	−4.21019	+	7.29226i	−0.396061	+	0.685998i	0.597175	+	0.802111i	$0.296290\pi$
$114$		0			0
$115$	−2.23627	+	3.87333i	−0.208533	+	0.361190i
$116$	3.04424	+	5.27278i	0.282651	+	0.489565i
$117$		0			0
$118$	−19.4564			−1.79110
$119$		0			0
$120$		0			0
$121$	−13.0479	−	22.5997i	−1.18618	−	2.05452i
$122$	−20.7231			−1.87618
$123$		0			0
$124$	0.184859			0.0166008
$125$	8.20593			0.733960
$126$		0			0
$127$	−9.92438			−0.880647			−0.440323	−	0.897839i	$-0.645136\pi$
$127$	−9.92438			−0.880647			−0.440323	+	0.897839i	$0.645136\pi$
$128$	12.2469			1.08248
$129$		0			0
$130$	6.79381			0.595857
$131$	7.62335	+	13.2040i	0.666055	+	1.15364i	0.978998	+	0.203870i	$0.0653519\pi$
$131$	7.62335	+	13.2040i	0.666055	+	1.15364i	−0.312943	+	0.949772i	$0.601315\pi$
$132$		0			0
$133$		0			0
$134$	−13.6627			−1.18028
$135$		0			0
$136$	1.05894	+	1.83413i	0.0908032	+	0.157276i
$137$	3.07350	−	5.32346i	0.262587	−	0.454814i	−0.704342	−	0.709861i	$-0.748758\pi$
$137$	3.07350	−	5.32346i	0.262587	−	0.454814i	0.966929	+	0.255047i	$0.0820910\pi$
$138$		0			0
$139$	−0.438687	+	0.759829i	−0.0372090	+	0.0644478i	−0.884030	−	0.467430i	$-0.845180\pi$
$139$	−0.438687	+	0.759829i	−0.0372090	+	0.0644478i	0.846821	+	0.531878i	$0.178513\pi$
$140$		0			0
$141$		0			0
$142$	21.0737			1.76847
$143$	−3.41161	−	5.90908i	−0.285293	−	0.494142i
$144$		0			0
$145$	10.8974	−	18.8748i	0.904977	−	1.56747i
$146$	−4.58824	−	7.94706i	−0.379725	−	0.657703i
$147$		0			0
$148$	−1.75470	+	3.03923i	−0.144236	+	0.249823i
$149$	2.88776	+	5.00175i	0.236575	+	0.409760i	0.959729	−	0.280927i	$-0.0906418\pi$
$149$	2.88776	+	5.00175i	0.236575	+	0.409760i	−0.723154	+	0.690686i	$0.757308\pi$
$150$		0			0
$151$	1.01321	−	1.75494i	0.0824541	−	0.142815i	−0.821849	−	0.569705i	$-0.807058\pi$
$151$	1.01321	−	1.75494i	0.0824541	−	0.142815i	0.904304	+	0.426890i	$0.140391\pi$
$152$	1.93973	−	3.35972i	0.157333	−	0.272509i
$153$		0			0
$154$		0			0
$155$	−0.330866	−	0.573077i	−0.0265758	−	0.0460307i
$156$		0			0
$157$	3.04756			0.243222			0.121611	−	0.992578i	$-0.461194\pi$
$157$	3.04756			0.243222			0.121611	+	0.992578i	$0.461194\pi$
$158$	15.9144			1.26608
$159$		0			0
$160$	8.98141	+	15.5563i	0.710043	+	1.22983i
$161$		0			0
$162$		0			0
$163$	2.69445	−	4.66693i	0.211046	−	0.365542i	−0.740996	−	0.671509i	$-0.765646\pi$
$163$	2.69445	−	4.66693i	0.211046	−	0.365542i	0.952042	+	0.305967i	$0.0989797\pi$
$164$	1.65153	−	2.86053i	0.128963	−	0.223370i
$165$		0			0
$166$	1.07905	+	1.86896i	0.0837502	+	0.145060i
$167$	−8.30480	+	14.3843i	−0.642645	+	1.11309i	0.342196	+	0.939629i	$0.388829\pi$
$167$	−8.30480	+	14.3843i	−0.642645	+	1.11309i	−0.984840	+	0.173464i	$0.944504\pi$
$168$		0			0
$169$	5.87249	+	10.1714i	0.451730	+	0.782419i
$170$	−3.65063	+	6.32308i	−0.279991	+	0.484958i
$171$		0			0
$172$	−1.86696	−	3.23366i	−0.142354	−	0.246564i
$173$	−17.6503			−1.34193			−0.670965	−	0.741489i	$-0.734120\pi$
$173$	−17.6503			−1.34193			−0.670965	+	0.741489i	$0.734120\pi$
$174$		0			0
$175$		0			0
$176$	15.2255	−	26.3714i	1.14767	−	1.98782i
$177$		0			0
$178$	−4.78384	+	8.28586i	−0.358564	+	0.621051i
$179$	1.31422	+	2.27630i	0.0982294	+	0.170138i	0.910952	−	0.412513i	$-0.135349\pi$
$179$	1.31422	+	2.27630i	0.0982294	+	0.170138i	−0.812722	+	0.582651i	$0.802015\pi$
$180$		0			0
$181$	−3.97391			−0.295378			−0.147689	−	0.989034i	$-0.547184\pi$
$181$	−3.97391			−0.295378			−0.147689	+	0.989034i	$0.547184\pi$
$182$		0			0
$183$		0			0
$184$	1.12001	+	1.93991i	0.0825681	+	0.143012i
$185$	12.5625			0.923613
$186$		0			0
$187$	7.33286			0.536232
$188$	−5.61306			−0.409374
$189$		0			0
$190$	13.3743			0.970270
$191$	18.2059			1.31733			0.658666	−	0.752435i	$-0.271121\pi$
$191$	18.2059			1.31733			0.658666	+	0.752435i	$0.271121\pi$
$192$		0			0
$193$	−0.202385			−0.0145680			−0.00728401	−	0.999973i	$-0.502319\pi$
$193$	−0.202385			−0.0145680			−0.00728401	+	0.999973i	$0.502319\pi$
$194$	−14.2321	−	24.6506i	−1.02180	−	1.76981i
$195$		0			0
$196$		0			0
$197$	1.63136			0.116229			0.0581147	−	0.998310i	$-0.481491\pi$
$197$	1.63136			0.116229			0.0581147	+	0.998310i	$0.481491\pi$
$198$		0			0
$199$	3.14605	+	5.44912i	0.223018	+	0.386278i	0.955723	−	0.294268i	$-0.0950759\pi$
$199$	3.14605	+	5.44912i	0.223018	+	0.386278i	−0.732705	+	0.680546i	$0.761743\pi$
$200$	6.45266	−	11.1763i	0.456272	−	0.790287i
$201$		0			0
$202$	11.1918	−	19.3847i	0.787449	−	1.36390i
$203$		0			0
$204$		0			0
$205$	−11.8238			−0.825812
$206$	2.33249	+	4.04000i	0.162512	+	0.281480i
$207$		0			0
$208$	2.80050	−	4.85061i	0.194180	−	0.336329i
$209$	−6.71607	−	11.6326i	−0.464560	−	0.804642i
$210$		0			0
$211$	8.14368	−	14.1053i	0.560634	−	0.971046i	−0.436807	−	0.899555i	$-0.643891\pi$
$211$	8.14368	−	14.1053i	0.560634	−	0.971046i	0.997441	−	0.0714912i	$-0.0227758\pi$
$212$	−4.09069	−	7.08528i	−0.280950	−	0.486619i
$213$		0			0
$214$	−0.154083	+	0.266880i	−0.0105329	+	0.0182435i
$215$	−6.68308	+	11.5754i	−0.455782	+	0.789438i
$216$		0			0
$217$		0			0
$218$	−8.07927	−	13.9937i	−0.547197	−	0.947773i
$219$		0			0
$220$	20.9897			1.41513
$221$	1.34877			0.0907278
$222$		0			0
$223$	9.98472	+	17.2940i	0.668626	+	1.15809i	0.978288	+	0.207248i	$0.0664507\pi$
$223$	9.98472	+	17.2940i	0.668626	+	1.15809i	−0.309662	+	0.950847i	$0.600216\pi$
$224$		0			0
$225$		0			0
$226$	−7.26936	+	12.5909i	−0.483551	+	0.837534i
$227$	−1.80642	+	3.12880i	−0.119896	+	0.207666i	−0.919726	−	0.392560i	$-0.871589\pi$
$227$	−1.80642	+	3.12880i	−0.119896	+	0.207666i	0.799830	+	0.600226i	$0.204923\pi$
$228$		0			0
$229$	6.85733	+	11.8772i	0.453145	+	0.784870i	0.998579	−	0.0532835i	$-0.0169687\pi$
$229$	6.85733	+	11.8772i	0.453145	+	0.784870i	−0.545435	+	0.838153i	$0.683635\pi$
$230$	−3.86117	+	6.68774i	−0.254598	+	0.440976i
$231$		0			0
$232$	−5.45781	−	9.45321i	−0.358323	−	0.620634i
$233$	−12.6271	+	21.8707i	−0.827227	+	1.43280i	0.0729776	+	0.997334i	$0.476750\pi$
$233$	−12.6271	+	21.8707i	−0.827227	+	1.43280i	−0.900205	+	0.435466i	$0.856583\pi$
$234$		0			0
$235$	10.0464	+	17.4009i	0.655357	+	1.13511i
$236$	−11.0565			−0.719717
$237$		0			0
$238$		0			0
$239$	4.49495	−	7.78549i	0.290754	−	0.503601i	−0.683234	−	0.730200i	$-0.739427\pi$
$239$	4.49495	−	7.78549i	0.290754	−	0.503601i	0.973988	+	0.226598i	$0.0727604\pi$
$240$		0			0
$241$	4.62862	−	8.01701i	0.298156	−	0.516421i	−0.677558	−	0.735469i	$-0.736962\pi$
$241$	4.62862	−	8.01701i	0.298156	−	0.516421i	0.975714	+	0.219048i	$0.0702952\pi$
$242$	−22.5287	−	39.0209i	−1.44820	−	2.50836i
$243$		0			0
$244$	−11.7763			−0.753903
$245$		0			0
$246$		0			0
$247$	−1.23532	−	2.13963i	−0.0786013	−	0.136141i
$248$	−0.331421			−0.0210452
$249$		0			0
$250$	14.1684			0.896091
$251$	20.6517			1.30353			0.651763	−	0.758422i	$-0.274030\pi$
$251$	20.6517			1.30353			0.651763	+	0.758422i	$0.274030\pi$
$252$		0			0
$253$	7.75576			0.487600
$254$	−17.1355			−1.07518
$255$		0			0
$256$	18.8076			1.17548
$257$	1.22289	+	2.11811i	0.0762819	+	0.132124i	0.901643	−	0.432481i	$-0.142362\pi$
$257$	1.22289	+	2.11811i	0.0762819	+	0.132124i	−0.825361	+	0.564605i	$0.809028\pi$
$258$		0			0
$259$		0			0
$260$	3.86073			0.239432
$261$		0			0
$262$	13.1626	+	22.7982i	0.813186	+	1.40848i
$263$	−12.2814	+	21.2720i	−0.757302	+	1.31169i	0.186919	+	0.982375i	$0.440150\pi$
$263$	−12.2814	+	21.2720i	−0.757302	+	1.31169i	−0.944222	+	0.329311i	$0.893184\pi$
$264$		0			0
$265$	−14.6433	+	25.3629i	−0.899531	+	1.55803i
$266$		0			0
$267$		0			0
$268$	−7.76415			−0.474271
$269$	14.7851	+	25.6086i	0.901466	+	1.56139i	0.825592	+	0.564268i	$0.190842\pi$
$269$	14.7851	+	25.6086i	0.901466	+	1.56139i	0.0758746	+	0.997117i	$0.475825\pi$
$270$		0			0
$271$	−12.3958	+	21.4701i	−0.752989	+	1.30421i	0.193380	+	0.981124i	$0.438055\pi$
$271$	−12.3958	+	21.4701i	−0.752989	+	1.30421i	−0.946368	+	0.323090i	$0.895278\pi$
$272$	3.00968	+	5.21291i	0.182488	+	0.316079i
$273$		0			0
$274$	5.30674	−	9.19154i	0.320592	−	0.555281i
$275$	−22.3415	−	38.6966i	−1.34724	−	2.33349i
$276$		0			0
$277$	−0.939249	+	1.62683i	−0.0564340	+	0.0977466i	−0.892862	−	0.450330i	$-0.851306\pi$
$277$	−0.939249	+	1.62683i	−0.0564340	+	0.0977466i	0.836428	+	0.548076i	$0.184640\pi$
$278$	−0.757442	+	1.31193i	−0.0454284	+	0.0786842i
$279$		0			0
$280$		0			0
$281$	−6.03965	−	10.4610i	−0.360295	−	0.624049i	0.627714	−	0.778444i	$-0.283991\pi$
$281$	−6.03965	−	10.4610i	−0.360295	−	0.624049i	−0.988009	+	0.154395i	$0.950657\pi$
$282$		0			0
$283$	27.9719			1.66276			0.831378	−	0.555708i	$-0.187553\pi$
$283$	27.9719			1.66276			0.831378	+	0.555708i	$0.187553\pi$
$284$	11.9756			0.710620
$285$		0			0
$286$	−5.89052	−	10.2027i	−0.348314	−	0.603297i
$287$		0			0
$288$		0			0
$289$	7.77524	−	13.4671i	0.457367	−	0.792183i
$290$	18.8155	−	32.5894i	1.10488	−	1.91372i
$291$		0			0
$292$	−2.60736	−	4.51609i	−0.152584	−	0.264284i
$293$	−4.41163	+	7.64117i	−0.257730	+	0.446402i	−0.965634	−	0.259908i	$-0.916308\pi$
$293$	−4.41163	+	7.64117i	−0.257730	+	0.446402i	0.707903	+	0.706309i	$0.249641\pi$
$294$		0			0
$295$	19.7893	+	34.2761i	1.15218	+	1.99563i
$296$	3.14589	−	5.44883i	0.182851	−	0.316707i
$297$		0			0
$298$	4.98604	+	8.63608i	0.288834	+	0.500275i
$299$	1.42655			0.0824996
$300$		0			0
$301$		0			0
$302$	1.74942	−	3.03009i	0.100668	−	0.174362i
$303$		0			0
$304$	5.51304	−	9.54887i	0.316195	−	0.547665i
$305$	21.0777	+	36.5076i	1.20691	+	2.09042i
$306$		0			0
$307$	−1.05532			−0.0602304			−0.0301152	−	0.999546i	$-0.509587\pi$
$307$	−1.05532			−0.0602304			−0.0301152	+	0.999546i	$0.509587\pi$
$308$		0			0
$309$		0			0
$310$	−0.571277	−	0.989481i	−0.0324464	−	0.0561988i
$311$	3.07215			0.174206			0.0871029	−	0.996199i	$-0.472239\pi$
$311$	3.07215			0.174206			0.0871029	+	0.996199i	$0.472239\pi$
$312$		0			0
$313$	−28.1621			−1.59181			−0.795907	−	0.605419i	$-0.793006\pi$
$313$	−28.1621			−1.59181			−0.795907	+	0.605419i	$0.793006\pi$
$314$	5.26196			0.296949
$315$		0			0
$316$	9.04368			0.508747
$317$	−12.8465			−0.721530			−0.360765	−	0.932657i	$-0.617484\pi$
$317$	−12.8465			−0.721530			−0.360765	+	0.932657i	$0.617484\pi$
$318$		0			0
$319$	−37.7939			−2.11605
$320$	−2.05291	−	3.55575i	−0.114761	−	0.198772i
$321$		0			0
$322$		0			0
$323$	2.65517			0.147738
$324$		0			0
$325$	−4.10937	−	7.11763i	−0.227947	−	0.394815i
$326$	4.65227	−	8.05797i	0.257665	−	0.446290i
$327$		0			0
$328$	−2.96091	+	5.12845i	−0.163489	+	0.283171i
$329$		0			0
$330$		0			0
$331$	−21.5560			−1.18483			−0.592413	−	0.805634i	$-0.701825\pi$
$331$	−21.5560			−1.18483			−0.592413	+	0.805634i	$0.701825\pi$
$332$	0.613191	+	1.06208i	0.0336532	+	0.0582891i
$333$		0			0
$334$	−14.3392	+	24.8361i	−0.784604	+	1.35897i
$335$	13.8965	+	24.0695i	0.759248	+	1.31506i
$336$		0			0
$337$	6.30340	−	10.9178i	0.343368	−	0.594731i	−0.641688	−	0.766966i	$-0.721766\pi$
$337$	6.30340	−	10.9178i	0.343368	−	0.594731i	0.985056	+	0.172235i	$0.0550989\pi$
$338$	10.1395	+	17.5621i	0.551516	+	0.955254i
$339$		0			0
$340$	−2.07455	+	3.59323i	−0.112508	+	0.194870i
$341$	−0.573750	+	0.993764i	−0.0310703	+	0.0538153i
$342$		0			0
$343$		0			0
$344$	3.34714	+	5.79741i	0.180466	+	0.312575i
$345$		0			0
$346$	−30.4752			−1.63836
$347$	−23.1366			−1.24204			−0.621020	−	0.783795i	$-0.713281\pi$
$347$	−23.1366			−1.24204			−0.621020	+	0.783795i	$0.713281\pi$
$348$		0			0
$349$	−8.24346	−	14.2781i	−0.441262	−	0.764289i	0.556521	−	0.830833i	$-0.312136\pi$
$349$	−8.24346	−	14.2781i	−0.441262	−	0.764289i	−0.997783	+	0.0665448i	$0.978802\pi$
$350$		0			0
$351$		0			0
$352$	15.5745	−	26.9759i	0.830124	−	1.43782i
$353$	12.2438	−	21.2068i	0.651669	−	1.12872i	−0.331049	−	0.943614i	$-0.607402\pi$
$353$	12.2438	−	21.2068i	0.651669	−	1.12872i	0.982718	−	0.185110i	$-0.0592642\pi$
$354$		0			0
$355$	−21.4343	−	37.1253i	−1.13761	−	1.97041i
$356$	−2.71852	+	4.70862i	−0.144081	+	0.249556i
$357$		0			0
$358$	2.26915	+	3.93028i	0.119928	+	0.207722i
$359$	10.2389	−	17.7342i	0.540386	−	0.935977i	−0.458495	−	0.888697i	$-0.651611\pi$
$359$	10.2389	−	17.7342i	0.540386	−	0.935977i	0.998882	−	0.0472797i	$-0.0150552\pi$
$360$		0			0
$361$	7.06816	+	12.2424i	0.372009	+	0.644338i
$362$	−6.86139			−0.360627
$363$		0			0
$364$		0			0
$365$	−9.33349	+	16.1661i	−0.488537	+	0.846172i
$366$		0			0
$367$	11.1269	−	19.2724i	0.580821	−	1.00601i	−0.414561	−	0.910021i	$-0.636065\pi$
$367$	11.1269	−	19.2724i	0.580821	−	1.00601i	0.995382	−	0.0959900i	$-0.0306017\pi$
$368$	3.18325	+	5.51355i	0.165938	+	0.287414i
$369$		0			0
$370$	21.6905			1.12764
$371$		0			0
$372$		0			0
$373$	16.2684	+	28.1777i	0.842347	+	1.45899i	0.887905	+	0.460027i	$0.152160\pi$
$373$	16.2684	+	28.1777i	0.842347	+	1.45899i	−0.0455576	+	0.998962i	$0.514506\pi$
$374$	12.6610			0.654685
$375$		0			0
$376$	10.0633			0.518973
$377$	−6.95160			−0.358026
$378$		0			0
$379$	1.54440			0.0793306			0.0396653	−	0.999213i	$-0.487371\pi$
$379$	1.54440			0.0793306			0.0396653	+	0.999213i	$0.487371\pi$
$380$	7.60021			0.389883
$381$		0			0
$382$	31.4345			1.60833
$383$	−15.8147	−	27.3919i	−0.808093	−	1.39966i	−0.914183	−	0.405302i	$-0.867166\pi$
$383$	−15.8147	−	27.3919i	−0.808093	−	1.39966i	0.106090	−	0.994357i	$-0.466167\pi$
$384$		0			0
$385$		0			0
$386$	−0.349441			−0.0177861
$387$		0			0
$388$	−8.08767	−	14.0083i	−0.410589	−	0.711162i
$389$	−2.62313	+	4.54340i	−0.132998	+	0.230359i	−0.924831	−	0.380378i	$-0.875794\pi$
$389$	−2.62313	+	4.54340i	−0.132998	+	0.230359i	0.791833	+	0.610738i	$0.209127\pi$
$390$		0			0
$391$	−0.766552	+	1.32771i	−0.0387662	+	0.0671451i
$392$		0			0
$393$		0			0
$394$	2.81672			0.141904
$395$	−16.1867	−	28.0362i	−0.814440	−	1.41065i
$396$		0			0
$397$	0.0138175	−	0.0239325i	0.000693478	−	0.00120114i	−0.865678	−	0.500600i	$-0.833113\pi$
$397$	0.0138175	−	0.0239325i	0.000693478	−	0.00120114i	0.866372	+	0.499399i	$0.166446\pi$
$398$	5.43201	+	9.40851i	0.272282	+	0.471606i
$399$		0			0
$400$	18.3395	−	31.7650i	0.916977	−	1.58825i
$401$	6.06885	+	10.5115i	0.303064	+	0.524922i	0.976828	−	0.214024i	$-0.0686572\pi$
$401$	6.06885	+	10.5115i	0.303064	+	0.524922i	−0.673765	+	0.738946i	$0.735324\pi$
$402$		0			0
$403$	−0.105532	+	0.182787i	−0.00525694	+	0.00910529i
$404$	6.35996	−	11.0158i	0.316420	−	0.548055i
$405$		0			0
$406$		0			0
$407$	−10.8922	−	18.8659i	−0.539907	−	0.935146i
$408$		0			0
$409$	−31.3453			−1.54993			−0.774963	−	0.632007i	$-0.782231\pi$
$409$	−31.3453			−1.54993			−0.774963	+	0.632007i	$0.782231\pi$
$410$	−20.4152			−1.00823
$411$		0			0
$412$	1.32549	+	2.29582i	0.0653022	+	0.113107i
$413$		0			0
$414$		0			0
$415$	2.19502	−	3.80189i	0.107749	−	0.186627i
$416$	2.86469	−	4.96179i	0.140453	−	0.243272i
$417$		0			0
$418$	−11.5960	−	20.0849i	−0.567181	−	0.982385i
$419$	7.44319	−	12.8920i	0.363623	−	0.629814i	−0.624931	−	0.780680i	$-0.714873\pi$
$419$	7.44319	−	12.8920i	0.363623	−	0.629814i	0.988554	+	0.150866i	$0.0482061\pi$
$420$		0			0
$421$	−4.54213	−	7.86721i	−0.221370	−	0.383424i	0.733854	−	0.679307i	$-0.237720\pi$
$421$	−4.54213	−	7.86721i	−0.221370	−	0.383424i	−0.955224	+	0.295883i	$0.904386\pi$
$422$	14.0610	−	24.3543i	0.684477	−	1.18555i
$423$		0			0
$424$	7.33392	+	12.7027i	0.356166	+	0.616898i
$425$	8.83262			0.428445
$426$		0			0
$427$		0			0
$428$	−0.0875611	+	0.151660i	−0.00423243	+	0.00733078i
$429$		0			0
$430$	−11.5391	+	19.9863i	−0.556463	+	0.963823i
$431$	−8.31776	−	14.4068i	−0.400652	−	0.693950i	0.593152	−	0.805090i	$-0.297883\pi$
$431$	−8.31776	−	14.4068i	−0.400652	−	0.693950i	−0.993805	+	0.111140i	$0.964550\pi$
$432$		0			0
$433$	−19.7423			−0.948756			−0.474378	−	0.880321i	$-0.657327\pi$
$433$	−19.7423			−0.948756			−0.474378	+	0.880321i	$0.657327\pi$
$434$		0			0
$435$		0			0
$436$	−4.59122	−	7.95223i	−0.219880	−	0.380843i
$437$	2.80830			0.134339
$438$		0			0
$439$	6.73514			0.321451			0.160725	−	0.986999i	$-0.448617\pi$
$439$	6.73514			0.321451			0.160725	+	0.986999i	$0.448617\pi$
$440$	−37.6310			−1.79399
$441$		0			0
$442$	2.32879			0.110769
$443$	−28.6403			−1.36074			−0.680372	−	0.732867i	$-0.738182\pi$
$443$	−28.6403			−1.36074			−0.680372	+	0.732867i	$0.738182\pi$
$444$		0			0
$445$	19.4628			0.922626
$446$	17.2397	+	29.8601i	0.816324	+	1.41392i
$447$		0			0
$448$		0			0
$449$	6.66872			0.314716			0.157358	−	0.987542i	$-0.449702\pi$
$449$	6.66872			0.314716			0.157358	+	0.987542i	$0.449702\pi$
$450$		0			0
$451$	10.2518	+	17.7566i	0.482736	+	0.836124i
$452$	−4.13097	+	7.15505i	−0.194305	+	0.336545i
$453$		0			0
$454$	−3.11898	+	5.40223i	−0.146381	+	0.253539i
$455$		0			0
$456$		0			0
$457$	−28.6573			−1.34053			−0.670266	−	0.742121i	$-0.733820\pi$
$457$	−28.6573			−1.34053			−0.670266	+	0.742121i	$0.733820\pi$
$458$	11.8399	+	20.5074i	0.553244	+	0.958246i
$459$		0			0
$460$	−2.19419	+	3.80045i	−0.102305	+	0.177197i
$461$	−10.0087	−	17.3355i	−0.466150	−	0.807395i	0.533103	−	0.846050i	$-0.321026\pi$
$461$	−10.0087	−	17.3355i	−0.466150	−	0.807395i	−0.999253	+	0.0386554i	$0.987693\pi$
$462$		0			0
$463$	−4.95789	+	8.58731i	−0.230413	+	0.399086i	−0.957930	−	0.287003i	$-0.907341\pi$
$463$	−4.95789	+	8.58731i	−0.230413	+	0.399086i	0.727517	+	0.686090i	$0.240674\pi$
$464$	−15.5120	−	26.8676i	−0.720127	−	1.24730i
$465$		0			0
$466$	−21.8020	+	37.7623i	−1.00996	+	1.74930i
$467$	8.04035	−	13.9263i	0.372063	−	0.644432i	−0.617820	−	0.786320i	$-0.711984\pi$
$467$	8.04035	−	13.9263i	0.372063	−	0.644432i	0.989883	+	0.141888i	$0.0453172\pi$
$468$		0			0
$469$		0			0
$470$	17.3463	+	30.0446i	0.800124	+	1.38586i
$471$		0			0
$472$	19.8225			0.912402
$473$	23.1780			1.06573
$474$		0			0
$475$	−8.08967	−	14.0117i	−0.371180	−	0.642902i
$476$		0			0
$477$		0			0
$478$	7.76103	−	13.4425i	0.354981	−	0.614846i
$479$	−4.10128	+	7.10362i	−0.187392	+	0.324573i	−0.944380	−	0.328856i	$-0.893337\pi$
$479$	−4.10128	+	7.10362i	−0.187392	+	0.324573i	0.756988	+	0.653429i	$0.226670\pi$
$480$		0			0
$481$	−2.00345	−	3.47008i	−0.0913496	−	0.158222i
$482$	7.99183	−	13.8423i	0.364018	−	0.630497i
$483$		0			0
$484$	−12.8024	−	22.1745i	−0.581929	−	1.00793i
$485$	−28.9512	+	50.1449i	−1.31460	+	2.27696i
$486$		0			0
$487$	−1.36840	−	2.37014i	−0.0620081	−	0.107401i	0.833355	−	0.552738i	$-0.186417\pi$
$487$	−1.36840	−	2.37014i	−0.0620081	−	0.107401i	−0.895363	+	0.445337i	$0.853084\pi$
$488$	21.1130			0.955741
$489$		0			0
$490$		0			0
$491$	−9.85482	+	17.0690i	−0.444742	+	0.770315i	−0.998034	−	0.0626719i	$-0.980038\pi$
$491$	−9.85482	+	17.0690i	−0.444742	+	0.770315i	0.553293	+	0.832987i	$0.313371\pi$
$492$		0			0
$493$	3.73542	−	6.46993i	0.168235	−	0.291391i
$494$	−2.13291	−	3.69431i	−0.0959642	−	0.166215i
$495$		0			0
$496$	−0.941952			−0.0422949
$497$		0			0
$498$		0			0
$499$	16.5480	+	28.6619i	0.740789	+	1.28309i	0.952136	+	0.305674i	$0.0988817\pi$
$499$	16.5480	+	28.6619i	0.740789	+	1.28309i	−0.211347	+	0.977411i	$0.567785\pi$
$500$	8.05153			0.360075
$501$		0			0
$502$	35.6575			1.59147
$503$	−12.1860			−0.543346			−0.271673	−	0.962390i	$-0.587577\pi$
$503$	−12.1860			−0.543346			−0.271673	+	0.962390i	$0.587577\pi$
$504$		0			0
$505$	−45.5331			−2.02619
$506$	13.3912			0.595310
$507$		0			0
$508$	−9.73765			−0.432038
$509$	6.81965	+	11.8120i	0.302276	+	0.523557i	0.976651	−	0.214832i	$-0.0689204\pi$
$509$	6.81965	+	11.8120i	0.302276	+	0.523557i	−0.674375	+	0.738389i	$0.735587\pi$
$510$		0			0
$511$		0			0
$512$	7.97968			0.352656
$513$		0			0
$514$	2.11146	+	3.65715i	0.0931325	+	0.161310i
$515$	4.74481	−	8.21826i	0.209081	−	0.362140i
$516$		0			0
$517$	17.4214	−	30.1747i	0.766190	−	1.32708i
$518$		0			0
$519$		0			0
$520$	−6.92164			−0.303534
$521$	−17.7745	−	30.7863i	−0.778714	−	1.34877i	−0.932683	−	0.360697i	$-0.882539\pi$
$521$	−17.7745	−	30.7863i	−0.778714	−	1.34877i	0.153969	−	0.988076i	$-0.450794\pi$
$522$		0			0
$523$	−13.3593	+	23.1391i	−0.584163	+	1.01180i	0.410816	+	0.911718i	$0.365244\pi$
$523$	−13.3593	+	23.1391i	−0.584163	+	1.01180i	−0.994979	+	0.100082i	$0.968089\pi$
$524$	7.47991	+	12.9556i	0.326761	+	0.565967i
$525$		0			0
$526$	−21.2052	+	36.7284i	−0.924589	+	1.60143i
$527$	−0.113415	−	0.196440i	−0.00494043	−	0.00855708i
$528$		0			0
$529$	10.6892	−	18.5143i	0.464750	−	0.804970i
$530$	−25.2833	+	43.7919i	−1.09824	+	1.90220i
$531$		0			0
$532$		0			0
$533$	1.88565	+	3.26604i	0.0816766	+	0.141468i
$534$		0			0
$535$	0.626879			0.0271023
$536$	13.9198			0.601244
$537$		0			0
$538$	25.5282	+	44.2161i	1.10060	+	1.90629i
$539$		0			0
$540$		0			0
$541$	−18.7927	+	32.5500i	−0.807963	+	1.39943i	0.106309	+	0.994333i	$0.466097\pi$
$541$	−18.7927	+	32.5500i	−0.807963	+	1.39943i	−0.914272	+	0.405100i	$0.867237\pi$
$542$	−21.4026	+	37.0705i	−0.919322	+	1.59231i
$543$		0			0
$544$	3.07866	+	5.33240i	0.131997	+	0.228625i
$545$	−16.4350	+	28.4663i	−0.704000	+	1.21936i
$546$		0			0
$547$	−9.13381	−	15.8202i	−0.390533	−	0.676424i	0.601986	−	0.798506i	$-0.294376\pi$
$547$	−9.13381	−	15.8202i	−0.390533	−	0.676424i	−0.992520	+	0.122082i	$0.961043\pi$
$548$	3.01567	−	5.22329i	0.128823	−	0.223128i
$549$		0			0
$550$	−38.5750	−	66.8139i	−1.64485	−	2.84896i
$551$	−13.6849			−0.582995
$552$		0			0
$553$		0			0
$554$	−1.62172	+	2.80890i	−0.0689002	+	0.119339i
$555$		0			0
$556$	−0.430433	+	0.745532i	−0.0182544	+	0.0316176i
$557$	−1.94636	−	3.37119i	−0.0824698	−	0.142842i	0.821840	−	0.569718i	$-0.192947\pi$
$557$	−1.94636	−	3.37119i	−0.0824698	−	0.142842i	−0.904310	+	0.426876i	$0.859614\pi$
$558$		0			0
$559$	4.26324			0.180316
$560$		0			0
$561$		0			0
$562$	−10.4281	−	18.0620i	−0.439884	−	0.761901i
$563$	3.32855			0.140282			0.0701409	−	0.997537i	$-0.477655\pi$
$563$	3.32855			0.140282			0.0701409	+	0.997537i	$0.477655\pi$
$564$		0			0
$565$	29.5750			1.24423
$566$	48.2965			2.03006
$567$		0			0
$568$	−21.4702			−0.900870
$569$	36.6244			1.53538			0.767688	−	0.640824i	$-0.221407\pi$
$569$	36.6244			1.53538			0.767688	+	0.640824i	$0.221407\pi$
$570$		0			0
$571$	−22.5824			−0.945044			−0.472522	−	0.881319i	$-0.656656\pi$
$571$	−22.5824			−0.945044			−0.472522	+	0.881319i	$0.656656\pi$
$572$	−3.34742	−	5.79789i	−0.139962	−	0.242422i
$573$		0			0
$574$		0			0
$575$	9.34201			0.389589
$576$		0			0
$577$	11.2725	+	19.5245i	0.469279	+	0.812815i	0.999383	−	0.0351177i	$-0.0111806\pi$
$577$	11.2725	+	19.5245i	0.469279	+	0.812815i	−0.530104	+	0.847932i	$0.677847\pi$
$578$	13.4248	−	23.2525i	0.558399	−	0.967175i
$579$		0			0
$580$	10.6923	−	18.5197i	0.443975	−	0.768987i
$581$		0			0
$582$		0			0
$583$	50.7854			2.10332
$584$	4.67457	+	8.09659i	0.193435	+	0.335039i
$585$		0			0
$586$	−7.61717	+	13.1933i	−0.314662	+	0.545011i
$587$	−12.1198	−	20.9921i	−0.500237	−	0.866436i	−1.00000		0.000273884i	$-0.999913\pi$
$587$	−12.1198	−	20.9921i	−0.500237	−	0.866436i	0.499763	−	0.866162i	$-0.333421\pi$
$588$		0			0
$589$	−0.207750	+	0.359834i	−0.00856020	+	0.0148267i
$590$	34.1684	+	59.1814i	1.40669	+	2.43646i
$591$		0			0
$592$	8.94112	−	15.4865i	0.367478	−	0.636490i
$593$	22.8663	−	39.6056i	0.939007	−	1.62641i	0.171680	−	0.985153i	$-0.445081\pi$
$593$	22.8663	−	39.6056i	0.939007	−	1.62641i	0.767328	−	0.641255i	$-0.221586\pi$
$594$		0			0
$595$		0			0
$596$	2.83343	+	4.90764i	0.116062	+	0.201025i
$597$		0			0
$598$	2.46310			0.100724
$599$	30.1668			1.23258			0.616290	−	0.787519i	$-0.288635\pi$
$599$	30.1668			1.23258			0.616290	+	0.787519i	$0.288635\pi$
$600$		0			0
$601$	−7.36933	−	12.7641i	−0.300601	−	0.520657i	0.675671	−	0.737203i	$-0.263854\pi$
$601$	−7.36933	−	12.7641i	−0.300601	−	0.520657i	−0.976272	+	0.216547i	$0.930521\pi$
$602$		0			0
$603$		0			0
$604$	0.994149	−	1.72192i	0.0404513	−	0.0700638i
$605$	−45.8285	+	79.3772i	−1.86319	+	3.22714i
$606$		0			0
$607$	−3.03918	−	5.26401i	−0.123356	−	0.213660i	0.797733	−	0.603011i	$-0.206033\pi$
$607$	−3.03918	−	5.26401i	−0.123356	−	0.213660i	−0.921089	+	0.389351i	$0.872699\pi$
$608$	5.63941	−	9.76774i	0.228708	−	0.396134i
$609$		0			0
$610$	36.3930	+	63.0345i	1.47351	+	2.55219i
$611$	3.20439	−	5.55016i	0.129636	−	0.224535i
$612$		0			0
$613$	−5.88668	−	10.1960i	−0.237761	−	0.411814i	0.722311	−	0.691569i	$-0.243080\pi$
$613$	−5.88668	−	10.1960i	−0.237761	−	0.411814i	−0.960071	+	0.279755i	$0.909747\pi$
$614$	−1.82213			−0.0735352
$615$		0			0
$616$		0			0
$617$	16.0319	−	27.7680i	0.645418	−	1.11790i	−0.338786	−	0.940863i	$-0.610016\pi$
$617$	16.0319	−	27.7680i	0.645418	−	1.11790i	0.984205	−	0.177034i	$-0.0566503\pi$
$618$		0			0
$619$	−6.27588	+	10.8701i	−0.252249	+	0.436908i	−0.964145	−	0.265377i	$-0.914504\pi$
$619$	−6.27588	+	10.8701i	−0.252249	+	0.436908i	0.711896	+	0.702285i	$0.247837\pi$
$620$	−0.324641	−	0.562294i	−0.0130379	−	0.0225823i
$621$		0			0
$622$	5.30441			0.212688
$623$		0			0
$624$		0			0
$625$	3.92995	+	6.80687i	0.157198	+	0.272275i
$626$	−48.6249			−1.94344
$627$		0			0
$628$	2.99022			0.119323
$629$	4.30619			0.171699
$630$		0			0
$631$	33.4642			1.33219			0.666095	−	0.745867i	$-0.267964\pi$
$631$	33.4642			1.33219			0.666095	+	0.745867i	$0.267964\pi$
$632$	−16.2138			−0.644950
$633$		0			0
$634$	−22.1809			−0.880915
$635$	17.4288	+	30.1875i	0.691639	+	1.19795i
$636$		0			0
$637$		0			0
$638$	−65.2553			−2.58348
$639$		0			0
$640$	−21.5074	−	37.2519i	−0.850155	−	1.47251i
$641$	−9.49183	+	16.4403i	−0.374905	+	0.649354i	−0.990313	−	0.138855i	$-0.955658\pi$
$641$	−9.49183	+	16.4403i	−0.374905	+	0.649354i	0.615408	+	0.788209i	$0.288991\pi$
$642$		0			0
$643$	−4.81347	+	8.33718i	−0.189825	+	0.328786i	−0.945192	−	0.326516i	$-0.894125\pi$
$643$	−4.81347	+	8.33718i	−0.189825	+	0.328786i	0.755367	+	0.655302i	$0.227459\pi$
$644$		0			0
$645$		0			0
$646$	4.58445			0.180373
$647$	3.90607	+	6.76551i	0.153564	+	0.265980i	0.932535	−	0.361079i	$-0.117592\pi$
$647$	3.90607	+	6.76551i	0.153564	+	0.265980i	−0.778972	+	0.627059i	$0.784258\pi$
$648$		0			0
$649$	34.3163	−	59.4375i	1.34703	−	2.33313i
$650$	−7.09528	−	12.2894i	−0.278300	−	0.482029i
$651$		0			0
$652$	2.64376	−	4.57912i	0.103537	−	0.179332i
$653$	15.8714	+	27.4901i	0.621097	+	1.07577i	0.989282	+	0.146019i	$0.0466461\pi$
$653$	15.8714	+	27.4901i	0.621097	+	1.07577i	−0.368185	+	0.929753i	$0.620021\pi$
$654$		0			0
$655$	26.7756	−	46.3767i	1.04621	−	1.81209i
$656$	−8.41540	+	14.5759i	−0.328566	+	0.569093i
$657$		0			0
$658$		0			0
$659$	−3.10685	−	5.38122i	−0.121026	−	0.209623i	0.799147	−	0.601136i	$-0.205285\pi$
$659$	−3.10685	−	5.38122i	−0.121026	−	0.209623i	−0.920172	+	0.391513i	$0.871952\pi$
$660$		0			0
$661$	−27.5263			−1.07065			−0.535324	−	0.844647i	$-0.679810\pi$
$661$	−27.5263			−1.07065			−0.535324	+	0.844647i	$0.679810\pi$
$662$	−37.2189			−1.44655
$663$		0			0
$664$	−1.09935	−	1.90413i	−0.0426630	−	0.0738945i
$665$		0			0
$666$		0			0
$667$	3.95084	−	6.84306i	0.152977	−	0.264964i
$668$	−8.14854	+	14.1137i	−0.315276	+	0.546075i
$669$		0			0
$670$	23.9939	+	41.5586i	0.926965	+	1.60555i
$671$	36.5505	−	63.3073i	1.41102	−	2.44395i
$672$		0			0
$673$	−8.10894	−	14.0451i	−0.312577	−	0.541399i	0.666343	−	0.745646i	$-0.267859\pi$
$673$	−8.10894	−	14.0451i	−0.312577	−	0.541399i	−0.978919	+	0.204247i	$0.934526\pi$
$674$	10.8835	−	18.8508i	0.419217	−	0.726106i
$675$		0			0
$676$	5.76199	+	9.98006i	0.221615	+	0.383849i
$677$	−20.5090			−0.788225			−0.394112	−	0.919062i	$-0.628948\pi$
$677$	−20.5090			−0.788225			−0.394112	+	0.919062i	$0.628948\pi$
$678$		0			0
$679$		0			0
$680$	3.71932	−	6.44205i	0.142629	−	0.247041i
$681$		0			0
$682$	−0.990642	+	1.71584i	−0.0379337	+	0.0657030i
$683$	−0.0561542	−	0.0972618i	−0.00214868	−	0.00372162i	0.864949	−	0.501860i	$-0.167351\pi$
$683$	−0.0561542	−	0.0972618i	−0.00214868	−	0.00372162i	−0.867098	+	0.498138i	$0.834017\pi$
$684$		0			0
$685$	−21.5902			−0.824918
$686$		0			0
$687$		0			0
$688$	9.51311	+	16.4772i	0.362684	+	0.628187i
$689$	9.34118			0.355871
$690$		0			0
$691$	−18.8670			−0.717735			−0.358868	−	0.933388i	$-0.616837\pi$
$691$	−18.8670			−0.717735			−0.358868	+	0.933388i	$0.616837\pi$
$692$	−17.3182			−0.658340
$693$		0			0
$694$	−39.9480			−1.51640
$695$	3.08161			0.116892
$696$		0			0
$697$	−4.05299			−0.153518
$698$	−14.2332	−	24.6527i	−0.538736	−	0.933118i
$699$		0			0
$700$		0			0
$701$	3.16006			0.119354			0.0596770	−	0.998218i	$-0.480993\pi$
$701$	3.16006			0.119354			0.0596770	+	0.998218i	$0.480993\pi$
$702$		0			0
$703$	−3.94398	−	6.83118i	−0.148750	−	0.257643i
$704$	−3.55992	+	6.16596i	−0.134170	+	0.232388i
$705$		0			0
$706$	21.1402	−	36.6159i	0.795622	−	1.37806i
$707$		0			0
$708$		0			0
$709$	−21.5211			−0.808243			−0.404121	−	0.914705i	$-0.632423\pi$
$709$	−21.5211			−0.808243			−0.404121	+	0.914705i	$0.632423\pi$
$710$	−37.0087	−	64.1009i	−1.38891	−	2.40567i
$711$		0			0
$712$	4.87385	−	8.44176i	0.182655	−	0.316368i
$713$	−0.119956	−	0.207769i	−0.00449237	−	0.00778102i
$714$		0			0
$715$	−11.9826	+	20.7545i	−0.448125	+	0.776175i
$716$	1.28949	+	2.23347i	0.0481906	+	0.0834685i
$717$		0			0
$718$	17.6785	−	30.6201i	0.659757	−	1.14273i
$719$	9.41508	−	16.3074i	0.351123	−	0.608163i	−0.635323	−	0.772246i	$-0.719133\pi$
$719$	9.41508	−	16.3074i	0.351123	−	0.608163i	0.986447	+	0.164083i	$0.0524665\pi$
$720$		0			0
$721$		0			0
$722$	12.2040	+	21.1379i	0.454185	+	0.786671i
$723$		0			0
$724$	−3.89914			−0.144910
$725$	−45.5237			−1.69071
$726$		0			0
$727$	19.5426	+	33.8489i	0.724797	+	1.25538i	0.959058	+	0.283211i	$0.0913996\pi$
$727$	19.5426	+	33.8489i	0.724797	+	1.25538i	−0.234261	+	0.972174i	$0.575267\pi$
$728$		0			0
$729$		0			0
$730$	−16.1153	+	27.9125i	−0.596454	+	1.03309i
$731$	−2.29084	+	3.96784i	−0.0847296	+	0.146756i
$732$		0			0
$733$	9.29924	+	16.1068i	0.343475	+	0.594917i	0.985076	−	0.172123i	$-0.0550625\pi$
$733$	9.29924	+	16.1068i	0.343475	+	0.594917i	−0.641600	+	0.767039i	$0.721729\pi$
$734$	19.2119	−	33.2759i	0.709123	−	1.22824i
$735$		0			0
$736$	3.25621	+	5.63993i	0.120026	+	0.207890i
$737$	24.0977	−	41.7385i	0.887651	−	1.53746i
$738$		0			0
$739$	−2.75068	−	4.76432i	−0.101185	−	0.175258i	0.810988	−	0.585063i	$-0.198930\pi$
$739$	−2.75068	−	4.76432i	−0.101185	−	0.175258i	−0.912173	+	0.409805i	$0.865597\pi$
$740$	12.3261			0.453117
$741$		0			0
$742$		0			0
$743$	−10.2326	+	17.7234i	−0.375399	+	0.650210i	−0.990387	−	0.138327i	$-0.955828\pi$
$743$	−10.2326	+	17.7234i	−0.375399	+	0.650210i	0.614988	+	0.788537i	$0.289161\pi$
$744$		0			0
$745$	10.1427	−	17.5677i	0.371601	−	0.643631i
$746$	28.0892	+	48.6520i	1.02842	+	1.78128i
$747$		0			0
$748$	7.19489			0.263071
$749$		0			0
$750$		0			0
$751$	−19.0230	−	32.9488i	−0.694159	−	1.20232i	−0.970463	−	0.241248i	$-0.922443\pi$
$751$	−19.0230	−	32.9488i	−0.694159	−	1.20232i	0.276305	−	0.961070i	$-0.410890\pi$
$752$	28.6015			1.04299
$753$		0			0
$754$	−12.0027			−0.437113
$755$	−7.11744			−0.259030
$756$		0			0
$757$	−51.0780			−1.85646			−0.928230	−	0.372006i	$-0.878670\pi$
$757$	−51.0780			−1.85646			−0.928230	+	0.372006i	$0.878670\pi$
$758$	2.66658			0.0968546
$759$		0			0
$760$	−13.6259			−0.494263
$761$	20.0375	+	34.7059i	0.726357	+	1.25809i	0.958413	+	0.285385i	$0.0921216\pi$
$761$	20.0375	+	34.7059i	0.726357	+	1.25809i	−0.232055	+	0.972703i	$0.574545\pi$
$762$		0			0
$763$		0			0
$764$	17.8633			0.646273
$765$		0			0
$766$	−27.3058	−	47.2951i	−0.986599	−	1.70884i
$767$	6.31195	−	10.9326i	0.227911	−	0.394754i
$768$		0			0
$769$	−22.4828	+	38.9414i	−0.810751	+	1.40426i	0.101587	+	0.994827i	$0.467608\pi$
$769$	−22.4828	+	38.9414i	−0.810751	+	1.40426i	−0.912339	+	0.409436i	$0.865726\pi$
$770$		0			0
$771$		0			0
$772$	−0.198577			−0.00714695
$773$	12.1781	+	21.0930i	0.438014	+	0.758663i	0.997536	−	0.0701524i	$-0.0223485\pi$
$773$	12.1781	+	21.0930i	0.438014	+	0.758663i	−0.559522	+	0.828816i	$0.689015\pi$
$774$		0			0
$775$	−0.691096	+	1.19701i	−0.0248249	+	0.0429980i
$776$	14.4998	+	25.1145i	0.520514	+	0.901556i
$777$		0			0
$778$	−4.52913	+	7.84468i	−0.162377	+	0.281245i
$779$	3.71208	+	6.42951i	0.132999	+	0.230361i
$780$		0			0
$781$	−37.1689	+	64.3784i	−1.33001	+	2.30364i
$782$	−1.32354	+	2.29243i	−0.0473296	+	0.0819773i
$783$		0			0
$784$		0			0
$785$	−5.35200	−	9.26993i	−0.191021	−	0.330858i
$786$		0			0
$787$	−41.5233			−1.48015			−0.740073	−	0.672526i	$-0.765209\pi$
$787$	−41.5233			−1.48015			−0.740073	+	0.672526i	$0.765209\pi$
$788$	1.60066			0.0570212
$789$		0			0
$790$	−27.9481	−	48.4075i	−0.994349	−	1.72226i
$791$		0			0
$792$		0			0
$793$	6.72289	−	11.6444i	0.238737	−	0.413504i
$794$	0.0238574	−	0.0413222i	0.000846666	−	0.00146647i
$795$		0			0
$796$	3.08686	+	5.34659i	0.109411	+	0.189505i
$797$	−17.3018	+	29.9676i	−0.612861	+	1.06151i	0.377895	+	0.925848i	$0.376648\pi$
$797$	−17.3018	+	29.9676i	−0.612861	+	1.06151i	−0.990756	+	0.135657i	$0.956685\pi$
$798$		0			0
$799$	3.44373	+	5.96472i	0.121831	+	0.211017i
$800$	18.7599	−	32.4931i	0.663263	−	1.14880i
$801$		0			0
$802$	10.4785	+	18.1494i	0.370010	+	0.640876i
$803$	32.3701			1.14232
$804$		0			0
$805$		0			0
$806$	−0.182213	+	0.315603i	−0.00641819	+	0.0111166i
$807$		0			0
$808$	−11.4023	+	19.7494i	−0.401133	+	0.694782i
$809$	−5.62597	−	9.74446i	−0.197799	−	0.342597i	0.750016	−	0.661420i	$-0.230046\pi$
$809$	−5.62597	−	9.74446i	−0.197799	−	0.342597i	−0.947814	+	0.318823i	$0.896713\pi$
$810$		0			0
$811$	29.6803			1.04222			0.521108	−	0.853491i	$-0.325519\pi$
$811$	29.6803			1.04222			0.521108	+	0.853491i	$0.325519\pi$
$812$		0			0
$813$		0			0
$814$	−18.8066	−	32.5740i	−0.659171	−	1.14172i
$815$	−18.9275			−0.663002
$816$		0			0
$817$	8.39258			0.293619
$818$	−54.1211			−1.89230
$819$		0			0
$820$	−11.6014			−0.405137
$821$	−34.6431			−1.20905			−0.604526	−	0.796585i	$-0.706638\pi$
$821$	−34.6431			−1.20905			−0.604526	+	0.796585i	$0.706638\pi$
$822$		0			0
$823$	36.3870			1.26837			0.634186	−	0.773180i	$-0.281335\pi$
$823$	36.3870			1.26837			0.634186	+	0.773180i	$0.281335\pi$
$824$	−2.37638	−	4.11601i	−0.0827851	−	0.143388i
$825$		0			0
$826$		0			0
$827$	24.3576			0.846997			0.423498	−	0.905897i	$-0.360802\pi$
$827$	24.3576			0.846997			0.423498	+	0.905897i	$0.360802\pi$
$828$		0			0
$829$	19.5851	+	33.9224i	0.680219	+	1.17817i	0.974914	+	0.222583i	$0.0714488\pi$
$829$	19.5851	+	33.9224i	0.680219	+	1.17817i	−0.294694	+	0.955592i	$0.595218\pi$
$830$	3.78994	−	6.56438i	0.131551	−	0.227853i
$831$		0			0
$832$	−0.654792	+	1.13413i	−0.0227008	+	0.0393190i
$833$		0			0
$834$		0			0
$835$	58.3381			2.01887
$836$	−6.58970	−	11.4137i	−0.227910	−	0.394751i
$837$		0			0
$838$	12.8515	−	22.2594i	0.443947	−	0.768939i
$839$	−17.1739	−	29.7460i	−0.592907	−	1.02695i	−0.993839	−	0.110838i	$-0.964647\pi$
$839$	−17.1739	−	29.7460i	−0.592907	−	1.02695i	0.400931	−	0.916108i	$-0.368687\pi$
$840$		0			0
$841$	−4.75250	+	8.23157i	−0.163879	+	0.283847i
$842$	−7.84250	−	13.5836i	−0.270270	−	0.468122i
$843$		0			0
$844$	7.99045	−	13.8399i	0.275043	−	0.476388i
$845$	20.6260	−	35.7253i	0.709556	−	1.22899i
$846$		0			0
$847$		0			0
$848$	20.8442	+	36.1032i	0.715793	+	1.23979i
$849$		0			0
$850$	15.2505			0.523088
$851$	4.55454			0.156127
$852$		0			0
$853$	16.3371	+	28.2967i	0.559373	+	0.968862i	0.997549	+	0.0699730i	$0.0222913\pi$
$853$	16.3371	+	28.2967i	0.559373	+	0.968862i	−0.438176	+	0.898889i	$0.644375\pi$
$854$		0			0
$855$		0			0
$856$	0.156982	−	0.271901i	0.00536555	−	0.00929340i
$857$	28.8340	−	49.9419i	0.984950	−	1.70598i	0.342791	−	0.939412i	$-0.388628\pi$
$857$	28.8340	−	49.9419i	0.984950	−	1.70598i	0.642159	−	0.766571i	$-0.278039\pi$
$858$		0			0
$859$	14.9884	+	25.9607i	0.511397	+	0.885766i	0.999913	+	0.0132108i	$0.00420525\pi$
$859$	14.9884	+	25.9607i	0.511397	+	0.885766i	−0.488515	+	0.872555i	$0.662461\pi$
$860$	−6.55733	+	11.3576i	−0.223603	+	0.387292i
$861$		0			0
$862$	−14.3615	−	24.8749i	−0.489156	−	0.847243i
$863$	−11.5888	+	20.0724i	−0.394487	+	0.683272i	−0.993036	−	0.117815i	$-0.962411\pi$
$863$	−11.5888	+	20.0724i	−0.394487	+	0.683272i	0.598548	+	0.801087i	$0.295744\pi$
$864$		0			0
$865$	30.9967	+	53.6879i	1.05392	+	1.82544i
$866$	−34.0873			−1.15833
$867$		0			0
$868$		0			0
$869$	−28.0690	+	48.6170i	−0.952177	+	1.64922i
$870$		0			0
$871$	4.43240	−	7.67715i	0.150186	−	0.260130i
$872$	8.23129	+	14.2570i	0.278747	+	0.482803i
$873$		0			0
$874$	4.84884			0.164014
$875$		0			0
$876$		0			0
$877$	0.369978	+	0.640820i	0.0124933	+	0.0216390i	0.872204	−	0.489141i	$-0.162690\pi$
$877$	0.369978	+	0.640820i	0.0124933	+	0.0216390i	−0.859711	+	0.510780i	$0.829357\pi$
$878$	11.6290			0.392458
$879$		0			0
$880$	−106.954			−3.60540
$881$	−18.0285			−0.607395			−0.303697	−	0.952769i	$-0.598221\pi$
$881$	−18.0285			−0.607395			−0.303697	+	0.952769i	$0.598221\pi$
$882$		0			0
$883$	43.0928			1.45019			0.725095	−	0.688649i	$-0.241796\pi$
$883$	43.0928			1.45019			0.725095	+	0.688649i	$0.241796\pi$
$884$	1.32339			0.0445104
$885$		0			0
$886$	−49.4507			−1.66133
$887$	15.4763	+	26.8058i	0.519645	+	0.900051i	0.999739	+	0.0228344i	$0.00726904\pi$
$887$	15.4763	+	26.8058i	0.519645	+	0.900051i	−0.480094	+	0.877217i	$0.659398\pi$
$888$		0			0
$889$		0			0
$890$	33.6047			1.12643
$891$		0			0
$892$	9.79685	+	16.9686i	0.328023	+	0.568152i
$893$	6.30813	−	10.9260i	0.211094	−	0.365625i
$894$		0			0
$895$	4.61595	−	7.99506i	0.154294	−	0.267245i
$896$		0			0
$897$		0			0
$898$	11.5143			0.384236
$899$	0.584545	+	1.01246i	0.0194957	+	0.0337675i
$900$		0			0
$901$	−5.01945	+	8.69395i	−0.167222	+	0.289637i
$902$	17.7008	+	30.6587i	0.589372	+	1.02082i
$903$		0			0
$904$	7.40614	−	12.8278i	0.246324	−	0.426646i
$905$	6.97880	+	12.0876i	0.231983	+	0.401807i
$906$		0			0
$907$	21.4042	−	37.0731i	0.710714	−	1.23099i	−0.253876	−	0.967237i	$-0.581706\pi$
$907$	21.4042	−	37.0731i	0.710714	−	1.23099i	0.964590	−	0.263755i	$-0.0849611\pi$
$908$	−1.77243	+	3.06993i	−0.0588200	+	0.101879i
$909$		0			0
$910$		0			0
$911$	−3.04869	−	5.28049i	−0.101008	−	0.174950i	0.811092	−	0.584918i	$-0.198873\pi$
$911$	−3.04869	−	5.28049i	−0.101008	−	0.174950i	−0.912100	+	0.409968i	$0.865540\pi$
$912$		0			0
$913$	−7.61269			−0.251943
$914$	−49.4800			−1.63665
$915$		0			0
$916$	6.72830	+	11.6538i	0.222309	+	0.385051i
$917$		0			0
$918$		0			0
$919$	−12.4307	+	21.5305i	−0.410050	+	0.710227i	−0.994895	−	0.100918i	$-0.967822\pi$
$919$	−12.4307	+	21.5305i	−0.410050	+	0.710227i	0.584845	+	0.811145i	$0.301155\pi$
$920$	3.93382	−	6.81357i	0.129694	−	0.224637i
$921$		0			0
$922$	−17.2811	−	29.9317i	−0.569121	−	0.985747i
$923$	−6.83664	+	11.8414i	−0.225031	+	0.389764i
$924$		0			0
$925$	−13.1199	−	22.7244i	−0.431381	−	0.747174i
$926$	−8.56034	+	14.8269i	−0.281310	+	0.487244i
$927$		0			0
$928$	−15.8676	−	27.4834i	−0.520878	−	0.902188i
$929$	−41.8402			−1.37273			−0.686366	−	0.727256i	$-0.740795\pi$
$929$	−41.8402			−1.37273			−0.686366	+	0.727256i	$0.740795\pi$
$930$		0			0
$931$		0			0
$932$	−12.3895	+	21.4592i	−0.405831	+	0.702920i
$933$		0			0
$934$	13.8826	−	24.0453i	0.454251	−	0.786786i
$935$	−12.8776	−	22.3047i	−0.421144	−	0.729443i
$936$		0			0
$937$	29.2537			0.955676			0.477838	−	0.878448i	$-0.341421\pi$
$937$	29.2537			0.955676			0.477838	+	0.878448i	$0.341421\pi$
$938$		0			0
$939$		0			0
$940$	9.85740	+	17.0735i	0.321513	+	0.556877i
$941$	−3.35737			−0.109447			−0.0547236	−	0.998502i	$-0.517428\pi$
$941$	−3.35737			−0.109447			−0.0547236	+	0.998502i	$0.517428\pi$
$942$		0			0
$943$	−4.28673			−0.139595
$944$	56.3387			1.83367
$945$		0			0
$946$	40.0194			1.30114
$947$	−5.26601			−0.171122			−0.0855612	−	0.996333i	$-0.527268\pi$
$947$	−5.26601			−0.171122			−0.0855612	+	0.996333i	$0.527268\pi$
$948$		0			0
$949$	5.95398			0.193274
$950$	−13.9677	−	24.1928i	−0.453173	−	0.784918i
$951$		0			0
$952$		0			0
$953$	−56.2520			−1.82218			−0.911090	−	0.412208i	$-0.864758\pi$
$953$	−56.2520			−1.82218			−0.911090	+	0.412208i	$0.864758\pi$
$954$		0			0
$955$	−31.9724	−	55.3778i	−1.03460	−	1.79198i
$956$	4.41038	−	7.63900i	0.142642	−	0.247063i
$957$		0			0
$958$	−7.08131	+	12.2652i	−0.228787	+	0.396270i
$959$		0			0
$960$		0			0
$961$	−30.9645			−0.998855
$962$	−3.45918	−	5.99148i	−0.111528	−	0.193173i
$963$		0			0
$964$	4.54153	−	7.86616i	0.146273	−	0.253352i
$965$	0.355420	+	0.615606i	0.0114414	+	0.0198171i
$966$		0			0
$967$	−6.88641	+	11.9276i	−0.221452	+	0.383566i	−0.955249	−	0.295803i	$-0.904413\pi$
$967$	−6.88641	+	11.9276i	−0.221452	+	0.383566i	0.733797	+	0.679369i	$0.237746\pi$
$968$	22.9526	+	39.7551i	0.737725	+	1.27778i
$969$		0			0
$970$	−49.9874	+	86.5807i	−1.60500	+	2.77994i
$971$	−25.6627	+	44.4491i	−0.823555	+	1.42644i	0.0794635	+	0.996838i	$0.474679\pi$
$971$	−25.6627	+	44.4491i	−0.823555	+	1.42644i	−0.903019	+	0.429602i	$0.858654\pi$
$972$		0			0
$973$		0			0
$974$	−2.36269	−	4.09230i	−0.0757055	−	0.131126i
$975$		0			0
$976$	60.0066			1.92077
$977$	−17.6850			−0.565794			−0.282897	−	0.959150i	$-0.591296\pi$
$977$	−17.6850			−0.565794			−0.282897	+	0.959150i	$0.591296\pi$
$978$		0			0
$979$	−16.8751	−	29.2285i	−0.539329	−	0.934146i
$980$		0			0
$981$		0			0
$982$	−17.0154	+	29.4716i	−0.542984	+	0.940476i
$983$	−8.00207	+	13.8600i	−0.255226	+	0.442065i	−0.964957	−	0.262408i	$-0.915483\pi$
$983$	−8.00207	+	13.8600i	−0.255226	+	0.442065i	0.709731	+	0.704473i	$0.248817\pi$
$984$		0			0
$985$	−2.86492	−	4.96218i	−0.0912839	−	0.158108i
$986$	6.44961	−	11.1711i	0.205397	−	0.355759i
$987$		0			0
$988$	−1.21207	−	2.09937i	−0.0385612	−	0.0667899i
$989$	−2.42295	+	4.19667i	−0.0770454	+	0.133446i
$990$		0			0
$991$	5.43319	+	9.41055i	0.172591	+	0.298936i	0.939325	−	0.343029i	$-0.111453\pi$
$991$	5.43319	+	9.41055i	0.172591	+	0.298936i	−0.766734	+	0.641965i	$0.778120\pi$
$992$	−0.963543			−0.0305925
$993$		0			0
$994$		0			0
$995$	11.0499	−	19.1390i	0.350306	−	0.606748i
$996$		0			0
$997$	−20.5187	+	35.5395i	−0.649835	+	1.12555i	0.333327	+	0.942811i	$0.391829\pi$
$997$	−20.5187	+	35.5395i	−0.649835	+	1.12555i	−0.983162	+	0.182736i	$0.941505\pi$
$998$	28.5719	+	49.4880i	0.904428	+	1.56652i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.h.226.10		24
3.2	odd	2		441.2.h.h.373.4		24
7.2	even	3		1323.2.f.h.442.3		24
7.3	odd	6		1323.2.g.h.361.3		24
7.4	even	3		1323.2.g.h.361.4		24
7.5	odd	6		1323.2.f.h.442.4		24
7.6	odd	2	inner	1323.2.h.h.226.9		24
9.2	odd	6		441.2.g.h.79.9		24
9.7	even	3		1323.2.g.h.667.4		24
21.2	odd	6		441.2.f.h.148.9	✓	24
21.5	even	6		441.2.f.h.148.10	yes	24
21.11	odd	6		441.2.g.h.67.9		24
21.17	even	6		441.2.g.h.67.10		24
21.20	even	2		441.2.h.h.373.3		24
63.2	odd	6		441.2.f.h.295.9	yes	24
63.5	even	6		3969.2.a.bh.1.4		12
63.11	odd	6		441.2.h.h.214.4		24
63.16	even	3		1323.2.f.h.883.3		24
63.20	even	6		441.2.g.h.79.10		24
63.23	odd	6		3969.2.a.bh.1.3		12
63.25	even	3	inner	1323.2.h.h.802.10		24
63.34	odd	6		1323.2.g.h.667.3		24
63.38	even	6		441.2.h.h.214.3		24
63.40	odd	6		3969.2.a.bi.1.9		12
63.47	even	6		441.2.f.h.295.10	yes	24
63.52	odd	6	inner	1323.2.h.h.802.9		24
63.58	even	3		3969.2.a.bi.1.10		12
63.61	odd	6		1323.2.f.h.883.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.9	✓	24	21.2	odd	6
441.2.f.h.148.10	yes	24	21.5	even	6
441.2.f.h.295.9	yes	24	63.2	odd	6
441.2.f.h.295.10	yes	24	63.47	even	6
441.2.g.h.67.9		24	21.11	odd	6
441.2.g.h.67.10		24	21.17	even	6
441.2.g.h.79.9		24	9.2	odd	6
441.2.g.h.79.10		24	63.20	even	6
441.2.h.h.214.3		24	63.38	even	6
441.2.h.h.214.4		24	63.11	odd	6
441.2.h.h.373.3		24	21.20	even	2
441.2.h.h.373.4		24	3.2	odd	2
1323.2.f.h.442.3		24	7.2	even	3
1323.2.f.h.442.4		24	7.5	odd	6
1323.2.f.h.883.3		24	63.16	even	3
1323.2.f.h.883.4		24	63.61	odd	6
1323.2.g.h.361.3		24	7.3	odd	6
1323.2.g.h.361.4		24	7.4	even	3
1323.2.g.h.667.3		24	63.34	odd	6
1323.2.g.h.667.4		24	9.7	even	3
1323.2.h.h.226.9		24	7.6	odd	2	inner
1323.2.h.h.226.10		24	1.1	even	1	trivial
1323.2.h.h.802.9		24	63.52	odd	6	inner
1323.2.h.h.802.10		24	63.25	even	3	inner
3969.2.a.bh.1.3		12	63.23	odd	6
3969.2.a.bh.1.4		12	63.5	even	6
3969.2.a.bi.1.9		12	63.40	odd	6
3969.2.a.bi.1.10		12	63.58	even	3

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.72661 q^{2} +0.981184 q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +O(q^{10})\)	\(q+1.72661 q^{2} +0.981184 q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +(-3.03220 - 5.25192i) q^{10} +(-3.04532 + 5.27465i) q^{11} +(-0.560139 + 0.970190i) q^{13} -4.99965 q^{16} +(-0.601978 - 1.04266i) q^{17} +(-1.10269 + 1.90991i) q^{19} +(-1.72311 - 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} +(-0.636695 - 1.10279i) q^{23} +(-3.66817 + 6.35345i) q^{25} +(-0.967143 + 1.67514i) q^{26} +(3.10262 + 5.37390i) q^{29} +0.188404 q^{31} -5.11425 q^{32} +(-1.03938 - 1.80026i) q^{34} +(-1.78835 + 3.09752i) q^{37} +(-1.90391 + 3.29767i) q^{38} +(3.08925 + 5.35074i) q^{40} +(1.68320 - 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} +(-2.98802 + 5.17540i) q^{44} +(-1.09932 - 1.90408i) q^{46} -5.72070 q^{47} +(-6.33349 + 10.9699i) q^{50} +(-0.549600 + 0.951935i) q^{52} +(-4.16913 - 7.22115i) q^{53} +21.3922 q^{55} +(5.35702 + 9.27862i) q^{58} -11.2685 q^{59} -12.0022 q^{61} +0.325300 q^{62} +1.16898 q^{64} +3.93477 q^{65} -7.91303 q^{67} +(-0.590651 - 1.02304i) q^{68} +12.2052 q^{71} +(-2.65737 - 4.60269i) q^{73} +(-3.08779 + 5.34820i) q^{74} +(-1.08194 + 1.87397i) q^{76} +9.21711 q^{79} +(8.78016 + 15.2077i) q^{80} +(2.90623 - 5.03373i) q^{82} +(0.624950 + 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} +(-3.28532 - 5.69034i) q^{86} +(5.35702 - 9.27862i) q^{88} +(-2.77066 + 4.79892i) q^{89} +(-0.624715 - 1.08204i) q^{92} -9.87741 q^{94} +7.74596 q^{95} +(-8.24277 - 14.2769i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more