LMFDB - Embedded newform 1323.2.f.h.883.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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			883.3
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.h.442.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.863305 + 1.49529i) q^{2} +(-0.490592 - 0.849731i) q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +O(q^{10})$	\(q+(-0.863305 + 1.49529i) q^{2} +(-0.490592 - 0.849731i) q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +6.06439 q^{10} +(-3.04532 + 5.27465i) q^{11} +(-0.560139 - 0.970190i) q^{13} +(2.49982 - 4.32982i) q^{16} +1.20396 q^{17} +2.20537 q^{19} +(-1.72311 + 2.98452i) q^{20} +(-5.25808 - 9.10727i) q^{22} +(-0.636695 - 1.10279i) q^{23} +(-3.66817 + 6.35345i) q^{25} +1.93429 q^{26} +(3.10262 - 5.37390i) q^{29} +(-0.0942019 - 0.163162i) q^{31} +(2.55712 + 4.42907i) q^{32} +(-1.03938 + 1.80026i) q^{34} +3.57670 q^{37} +(-1.90391 + 3.29767i) q^{38} +(3.08925 + 5.35074i) q^{40} +(1.68320 + 2.91538i) q^{41} +(-1.90276 + 3.29567i) q^{43} +5.97604 q^{44} +2.19865 q^{46} +(2.86035 - 4.95427i) q^{47} +(-6.33349 - 10.9699i) q^{50} +(-0.549600 + 0.951935i) q^{52} +8.33827 q^{53} +21.3922 q^{55} +(5.35702 + 9.27862i) q^{58} +(5.63427 + 9.75883i) q^{59} +(6.00109 - 10.3942i) q^{61} +0.325300 q^{62} +1.16898 q^{64} +(-1.96738 + 3.40761i) q^{65} +(3.95652 + 6.85289i) q^{67} +(-0.590651 - 1.02304i) q^{68} +12.2052 q^{71} +5.31473 q^{73} +(-3.08779 + 5.34820i) q^{74} +(-1.08194 - 1.87397i) q^{76} +(-4.60855 + 7.98225i) q^{79} -17.5603 q^{80} -5.81246 q^{82} +(0.624950 - 1.08245i) q^{83} +(-2.11433 - 3.66213i) q^{85} +(-3.28532 - 5.69034i) q^{86} +(5.35702 - 9.27862i) q^{88} +5.54131 q^{89} +(-0.624715 + 1.08204i) q^{92} +(4.93871 + 8.55409i) q^{94} +(-3.87298 - 6.70820i) q^{95} +(-8.24277 + 14.2769i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.863305	+	1.49529i	−0.610449	+	1.05733i	0.380716	+	0.924692i	$0.375678\pi$
$2$	−0.863305	+	1.49529i	−0.610449	+	1.05733i	−0.991165	+	0.132637i	$0.957656\pi$
$3$		0			0
$3$		0			0
$4$	−0.490592	−	0.849731i	−0.245296	−	0.424865i
$5$	−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
$10$	6.06439			1.91773
$11$	−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	0.777833	−	0.628471i	$-0.216319\pi$
$13$	−0.560139	−	0.970190i	−0.155355	−	0.269082i	−0.933188	+	0.359388i	$0.882985\pi$
$14$		0			0
$15$		0			0
$16$	2.49982	−	4.32982i	0.624956	−	1.08246i
$17$	1.20396			0.292002			0.146001	−	0.989284i	$-0.453360\pi$
$17$	1.20396			0.292002			0.146001	+	0.989284i	$0.453360\pi$
$18$		0			0
$19$	2.20537			0.505947			0.252974	−	0.967473i	$-0.418591\pi$
$19$	2.20537			0.505947			0.252974	+	0.967473i	$0.418591\pi$
$20$	−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
$26$	1.93429			0.379345
$27$		0			0
$28$		0			0
$29$	3.10262	−	5.37390i	0.576142	−	0.997907i	−0.419774	−	0.907628i	$-0.637891\pi$
$29$	3.10262	−	5.37390i	0.576142	−	0.997907i	0.995917	−	0.0902789i	$-0.0287758\pi$
$30$		0			0
$31$	−0.0942019	−	0.163162i	−0.0169192	−	0.0293048i	0.857442	−	0.514581i	$-0.172052\pi$
$31$	−0.0942019	−	0.163162i	−0.0169192	−	0.0293048i	−0.874361	+	0.485276i	$0.838719\pi$
$32$	2.55712	+	4.42907i	0.452040	+	0.782956i
$33$		0			0
$34$	−1.03938	+	1.80026i	−0.178252	+	0.308742i
$35$		0			0
$36$		0			0
$37$	3.57670			0.588006			0.294003	−	0.955804i	$-0.405012\pi$
$37$	3.57670			0.588006			0.294003	+	0.955804i	$0.405012\pi$
$38$	−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	0.967004	−	0.254762i	$-0.0819972\pi$
$41$	1.68320	+	2.91538i	0.262871	+	0.455307i	−0.704132	+	0.710069i	$0.748664\pi$
$42$		0			0
$43$	−1.90276	+	3.29567i	−0.290168	+	0.502585i	−0.973849	−	0.227195i	$-0.927044\pi$
$43$	−1.90276	+	3.29567i	−0.290168	+	0.502585i	0.683681	+	0.729781i	$0.260378\pi$
$44$	5.97604			0.900922
$45$		0			0
$46$	2.19865			0.324173
$47$	2.86035	−	4.95427i	0.417225	−	0.722654i	−0.578434	−	0.815729i	$-0.696336\pi$
$47$	2.86035	−	4.95427i	0.417225	−	0.722654i	0.995659	+	0.0930746i	$0.0296695\pi$
$48$		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
$53$	8.33827			1.14535			0.572675	−	0.819783i	$-0.305906\pi$
$53$	8.33827			1.14535			0.572675	+	0.819783i	$0.305906\pi$
$54$		0			0
$55$	21.3922			2.88453
$56$		0			0
$57$		0			0
$58$	5.35702	+	9.27862i	0.703411	+	1.21834i
$59$	5.63427	+	9.75883i	0.733519	+	1.27049i	0.955370	+	0.295411i	$0.0954567\pi$
$59$	5.63427	+	9.75883i	0.733519	+	1.27049i	−0.221851	+	0.975081i	$0.571210\pi$
$60$		0			0
$61$	6.00109	−	10.3942i	0.768361	−	1.33084i	−0.170091	−	0.985428i	$-0.554406\pi$
$61$	6.00109	−	10.3942i	0.768361	−	1.33084i	0.938451	−	0.345411i	$-0.112261\pi$
$62$	0.325300			0.0413131
$63$		0			0
$64$	1.16898			0.146123
$65$	−1.96738	+	3.40761i	−0.244024	+	0.422662i
$66$		0			0
$67$	3.95652	+	6.85289i	0.483366	+	0.837214i	0.999818	−	0.0191025i	$-0.00608088\pi$
$67$	3.95652	+	6.85289i	0.483366	+	0.837214i	−0.516452	+	0.856316i	$0.672748\pi$
$68$	−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
$73$	5.31473			0.622042			0.311021	−	0.950403i	$-0.399329\pi$
$73$	5.31473			0.622042			0.311021	+	0.950403i	$0.399329\pi$
$74$	−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
$79$	−4.60855	+	7.98225i	−0.518503	+	0.898073i	0.481266	+	0.876575i	$0.340177\pi$
$79$	−4.60855	+	7.98225i	−0.518503	+	0.898073i	−0.999769	+	0.0214988i	$0.993156\pi$
$80$	−17.5603			−1.96330
$81$		0			0
$82$	−5.81246			−0.641878
$83$	0.624950	−	1.08245i	0.0685972	−	0.118814i	−0.829687	−	0.558229i	$-0.811481\pi$
$83$	0.624950	−	1.08245i	0.0685972	−	0.118814i	0.898284	+	0.439415i	$0.144814\pi$
$84$		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
$89$	5.54131			0.587378			0.293689	−	0.955901i	$-0.405117\pi$
$89$	5.54131			0.587378			0.293689	+	0.955901i	$0.405117\pi$
$90$		0			0
$91$		0			0
$92$	−0.624715	+	1.08204i	−0.0651310	+	0.112810i
$93$		0			0
$94$	4.93871	+	8.55409i	0.509389	+	0.882287i
$95$	−3.87298	−	6.70820i	−0.397359	−	0.688246i
$96$		0			0
$97$	−8.24277	+	14.2769i	−0.836926	+	1.44960i	0.0555261	+	0.998457i	$0.482316\pi$
$97$	−8.24277	+	14.2769i	−0.836926	+	1.44960i	−0.892452	+	0.451142i	$0.851017\pi$
$98$		0			0
$99$		0			0
$100$	7.19829			0.719829
$101$	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
$107$	0.178480			0.0172544			0.00862718	−	0.999963i	$-0.497254\pi$
$107$	0.178480			0.0172544			0.00862718	+	0.999963i	$0.497254\pi$
$108$		0			0
$109$	9.35853			0.896385			0.448192	−	0.893937i	$-0.352068\pi$
$109$	9.35853			0.896385			0.448192	+	0.893937i	$0.352068\pi$
$110$	−18.4680	+	31.9876i	−1.76086	+	3.04989i
$111$		0			0
$112$		0			0
$113$	−4.21019	−	7.29226i	−0.396061	−	0.685998i	0.597175	−	0.802111i	$-0.296290\pi$
$113$	−4.21019	−	7.29226i	−0.396061	−	0.685998i	−0.993236	+	0.116113i	$0.962957\pi$
$114$		0			0
$115$	−2.23627	+	3.87333i	−0.208533	+	0.361190i
$116$	−6.08848			−0.565302
$117$		0			0
$118$	−19.4564			−1.79110
$119$		0			0
$120$		0			0
$121$	−13.0479	−	22.5997i	−1.18618	−	2.05452i
$122$	10.3615	+	17.9467i	0.938090	+	1.62482i
$123$		0			0
$124$	−0.0924294	+	0.160092i	−0.00830040	+	0.0143767i
$125$	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	$0.645136\pi$
$128$	−6.12343	+	10.6061i	−0.541240	+	0.937455i
$129$		0			0
$130$	−3.39691	−	5.88361i	−0.297928	−	0.516027i
$131$	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
$136$	−2.11788			−0.181606
$137$	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	0.846821	−	0.531878i	$-0.178513\pi$
$139$	−0.438687	−	0.759829i	−0.0372090	−	0.0644478i	−0.884030	+	0.467430i	$0.845180\pi$
$140$		0			0
$141$		0			0
$142$	−10.5368	+	18.2504i	−0.884233	+	1.53154i
$143$	6.82321			0.570586
$144$		0			0
$145$	−21.7947			−1.80995
$146$	−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	$0.140391\pi$
$152$	−3.87947			−0.314666
$153$		0			0
$154$		0			0
$155$	−0.330866	+	0.573077i	−0.0265758	+	0.0460307i
$156$		0			0
$157$	−1.52378	−	2.63927i	−0.121611	−	0.210636i	0.798792	−	0.601607i	$-0.205473\pi$
$157$	−1.52378	−	2.63927i	−0.121611	−	0.210636i	−0.920403	+	0.390971i	$0.872139\pi$
$158$	−7.95718	−	13.7822i	−0.633039	−	1.09646i
$159$		0			0
$160$	8.98141	−	15.5563i	0.710043	−	1.22983i
$161$		0			0
$162$		0			0
$163$	−5.38891			−0.422092			−0.211046	−	0.977476i	$-0.567687\pi$
$163$	−5.38891			−0.422092			−0.211046	+	0.977476i	$0.567687\pi$
$164$	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	−0.984840	−	0.173464i	$-0.944504\pi$
$167$	−8.30480	−	14.3843i	−0.642645	−	1.11309i	0.342196	−	0.939629i	$-0.388829\pi$
$168$		0			0
$169$	5.87249	−	10.1714i	0.451730	−	0.782419i
$170$	7.30126			0.559981
$171$		0			0
$172$	3.73391			0.284708
$173$	8.82516	−	15.2856i	0.670965	−	1.16214i	−0.306666	−	0.951817i	$-0.599214\pi$
$173$	8.82516	−	15.2856i	0.670965	−	1.16214i	0.977631	−	0.210328i	$-0.0674531\pi$
$174$		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
$179$	−2.62844			−0.196459			−0.0982294	−	0.995164i	$-0.531318\pi$
$179$	−2.62844			−0.196459			−0.0982294	+	0.995164i	$0.531318\pi$
$180$		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
$185$	−6.28125	−	10.8794i	−0.461806	−	0.799872i
$186$		0			0
$187$	−3.66643	+	6.35045i	−0.268116	+	0.464391i
$188$	−5.61306			−0.409374
$189$		0			0
$190$	13.3743			0.970270
$191$	−9.10295	+	15.7668i	−0.658666	+	1.14084i	0.322295	+	0.946639i	$0.395546\pi$
$191$	−9.10295	+	15.7668i	−0.658666	+	1.14084i	−0.980961	+	0.194204i	$0.937787\pi$
$192$		0			0
$193$	0.101193	+	0.175271i	0.00728401	+	0.0126163i	0.869644	−	0.493679i	$-0.164348\pi$
$193$	0.101193	+	0.175271i	0.00728401	+	0.0126163i	−0.862360	+	0.506295i	$0.831015\pi$
$194$	−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
$199$	−6.29211			−0.446036			−0.223018	−	0.974814i	$-0.571591\pi$
$199$	−6.29211			−0.446036			−0.223018	+	0.974814i	$0.571591\pi$
$200$	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
$205$	5.91192	−	10.2397i	0.412906	−	0.715174i
$206$	−4.66499			−0.325025
$207$		0			0
$208$	−5.60100			−0.388359
$209$	−6.71607	+	11.6326i	−0.464560	+	0.804642i
$210$		0			0
$211$	8.14368	+	14.1053i	0.560634	+	0.971046i	0.997441	+	0.0714912i	$0.0227758\pi$
$211$	8.14368	+	14.1053i	0.560634	+	0.971046i	−0.436807	+	0.899555i	$0.643891\pi$
$212$	−4.09069	−	7.08528i	−0.280950	−	0.486619i
$213$		0			0
$214$	−0.154083	+	0.266880i	−0.0105329	+	0.0182435i
$215$	13.3662			0.911564
$216$		0			0
$217$		0			0
$218$	−8.07927	+	13.9937i	−0.547197	+	0.947773i
$219$		0			0
$220$	−10.4949	−	18.1776i	−0.707563	−	1.22554i
$221$	−0.674383	−	1.16807i	−0.0453639	−	0.0785726i
$222$		0			0
$223$	9.98472	−	17.2940i	0.668626	−	1.15809i	−0.309662	−	0.950847i	$-0.600216\pi$
$223$	9.98472	−	17.2940i	0.668626	−	1.15809i	0.978288	−	0.207248i	$-0.0664507\pi$
$224$		0			0
$225$		0			0
$226$	14.5387			0.967101
$227$	−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
$233$	25.2542			1.65445			0.827227	−	0.561867i	$-0.189917\pi$
$233$	25.2542			1.65445			0.827227	+	0.561867i	$0.189917\pi$
$234$		0			0
$235$	−20.0929			−1.31071
$236$	5.52825	−	9.57521i	0.359859	−	0.623293i
$237$		0			0
$238$		0			0
$239$	4.49495	+	7.78549i	0.290754	+	0.503601i	0.973988	−	0.226598i	$-0.0727604\pi$
$239$	4.49495	+	7.78549i	0.290754	+	0.503601i	−0.683234	+	0.730200i	$0.739427\pi$
$240$		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	$0.0702952\pi$
$242$	45.0575			2.89640
$243$		0			0
$244$	−11.7763			−0.753903
$245$		0			0
$246$		0			0
$247$	−1.23532	−	2.13963i	−0.0786013	−	0.136141i
$248$	0.165710	+	0.287019i	0.0105226	+	0.0182257i
$249$		0			0
$250$	−7.08422	+	12.2702i	−0.448045	+	0.776037i
$251$	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
$254$	8.56777	−	14.8398i	0.537590	−	0.931133i
$255$		0			0
$256$	−9.40380	−	16.2879i	−0.587738	−	1.01799i
$257$	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
$262$	−26.3251			−1.62637
$263$	−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
$268$	3.88207	−	6.72395i	0.237135	−	0.410730i
$269$	−29.5703			−1.80293			−0.901466	−	0.432849i	$-0.857508\pi$
$269$	−29.5703			−1.80293			−0.901466	+	0.432849i	$0.857508\pi$
$270$		0			0
$271$	24.7915			1.50598			0.752989	−	0.658034i	$-0.228612\pi$
$271$	24.7915			1.50598			0.752989	+	0.658034i	$0.228612\pi$
$272$	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	$0.184640\pi$
$278$	1.51488			0.0908567
$279$		0			0
$280$		0			0
$281$	−6.03965	+	10.4610i	−0.360295	+	0.624049i	−0.988009	−	0.154395i	$-0.950657\pi$
$281$	−6.03965	+	10.4610i	−0.360295	+	0.624049i	0.627714	+	0.778444i	$0.283991\pi$
$282$		0			0
$283$	−13.9859	−	24.2244i	−0.831378	−	1.43999i	−0.896946	−	0.442140i	$-0.854219\pi$
$283$	−13.9859	−	24.2244i	−0.831378	−	1.43999i	0.0655680	−	0.997848i	$-0.479114\pi$
$284$	−5.98779	−	10.3712i	−0.355310	−	0.615415i
$285$		0			0
$286$	−5.89052	+	10.2027i	−0.348314	+	0.603297i
$287$		0			0
$288$		0			0
$289$	−15.5505			−0.914735
$290$	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	0.707903	−	0.706309i	$-0.249641\pi$
$293$	−4.41163	−	7.64117i	−0.257730	−	0.446402i	−0.965634	+	0.259908i	$0.916308\pi$
$294$		0			0
$295$	19.7893	−	34.2761i	1.15218	−	1.99563i
$296$	−6.29177			−0.365702
$297$		0			0
$298$	−9.97209			−0.577668
$299$	−0.713276	+	1.23543i	−0.0412498	+	0.0714467i
$300$		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
$305$	−42.1554			−2.41381
$306$		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
$311$	−1.53608	−	2.66056i	−0.0871029	−	0.150867i	0.819182	−	0.573533i	$-0.194428\pi$
$311$	−1.53608	−	2.66056i	−0.0871029	−	0.150867i	−0.906285	+	0.422666i	$0.861094\pi$
$312$		0			0
$313$	14.0810	−	24.3891i	0.795907	−	1.37855i	−0.126355	−	0.991985i	$-0.540328\pi$
$313$	14.0810	−	24.3891i	0.795907	−	1.37855i	0.922262	−	0.386566i	$-0.126339\pi$
$314$	5.26196			0.296949
$315$		0			0
$316$	9.04368			0.508747
$317$	6.42324	−	11.1254i	0.360765	−	0.624863i	−0.627322	−	0.778760i	$-0.715849\pi$
$317$	6.42324	−	11.1254i	0.360765	−	0.624863i	0.988087	+	0.153897i	$0.0491823\pi$
$318$		0			0
$319$	18.8969	+	32.7305i	1.05803	+	1.83255i
$320$	−2.05291	−	3.55575i	−0.114761	−	0.198772i
$321$		0			0
$322$		0			0
$323$	2.65517			0.147738
$324$		0			0
$325$	8.21874			0.455893
$326$	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
$331$	10.7780	−	18.6681i	0.592413	−	1.02609i	−0.401493	−	0.915862i	$-0.631509\pi$
$331$	10.7780	−	18.6681i	0.592413	−	1.02609i	0.993906	−	0.110228i	$-0.0351581\pi$
$332$	−1.22638			−0.0673065
$333$		0			0
$334$	28.6783			1.56921
$335$	13.8965	−	24.0695i	0.759248	−	1.31506i
$336$		0			0
$337$	6.30340	+	10.9178i	0.343368	+	0.594731i	0.985056	−	0.172235i	$-0.0550989\pi$
$337$	6.30340	+	10.9178i	0.343368	+	0.594731i	−0.641688	+	0.766966i	$0.721766\pi$
$338$	10.1395	+	17.5621i	0.551516	+	0.955254i
$339$		0			0
$340$	−2.07455	+	3.59323i	−0.112508	+	0.194870i
$341$	1.14750			0.0621406
$342$		0			0
$343$		0			0
$344$	3.34714	−	5.79741i	0.180466	−	0.312575i
$345$		0			0
$346$	15.2376	+	26.3923i	0.819179	+	1.41886i
$347$	11.5683	+	20.0369i	0.621020	+	1.07564i	0.989296	+	0.145922i	$0.0466147\pi$
$347$	11.5683	+	20.0369i	0.621020	+	1.07564i	−0.368276	+	0.929716i	$0.620052\pi$
$348$		0			0
$349$	−8.24346	+	14.2781i	−0.441262	+	0.764289i	−0.997783	−	0.0665448i	$-0.978802\pi$
$349$	−8.24346	+	14.2781i	−0.441262	+	0.764289i	0.556521	+	0.830833i	$0.312136\pi$
$350$		0			0
$351$		0			0
$352$	−31.1490			−1.66025
$353$	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
$359$	−20.4777			−1.08077			−0.540386	−	0.841417i	$-0.681722\pi$
$359$	−20.4777			−1.08077			−0.540386	+	0.841417i	$0.681722\pi$
$360$		0			0
$361$	−14.1363			−0.744017
$362$	3.43070	−	5.94214i	0.180313	−	0.312312i
$363$		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	$-0.0306017\pi$
$368$	−6.36650			−0.331877
$369$		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	$0.514506\pi$
$374$	−6.33050	−	10.9647i	−0.327342	−	0.566974i
$375$		0			0
$376$	−5.03163	+	8.71504i	−0.259487	+	0.449444i
$377$	−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	$0.487371\pi$
$380$	−3.80011	+	6.58198i	−0.194941	+	0.337648i
$381$		0			0
$382$	−15.7173	−	27.2231i	−0.804165	−	1.39285i
$383$	−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
$388$	16.1753			0.821179
$389$	−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
$394$	−1.40836	+	2.43935i	−0.0709521	+	0.122893i
$395$	32.3734			1.62888
$396$		0			0
$397$	−0.0276349			−0.00138696			−0.000693478	−	1.00000i	$-0.500221\pi$
$397$	−0.0276349			−0.00138696			−0.000693478		1.00000i	$0.500221\pi$
$398$	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
$404$	−12.7199			−0.632840
$405$		0			0
$406$		0			0
$407$	−10.8922	+	18.8659i	−0.539907	+	0.935146i
$408$		0			0
$409$	15.6726	+	27.1458i	0.774963	+	1.34227i	0.934816	+	0.355134i	$0.115565\pi$
$409$	15.6726	+	27.1458i	0.774963	+	1.34227i	−0.159853	+	0.987141i	$0.551102\pi$
$410$	10.2076	+	17.6800i	0.504116	+	0.873155i
$411$		0			0
$412$	1.32549	−	2.29582i	0.0653022	−	0.113107i
$413$		0			0
$414$		0			0
$415$	−4.39004			−0.215499
$416$	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	0.988554	−	0.150866i	$-0.0482061\pi$
$419$	7.44319	+	12.8920i	0.363623	+	0.629814i	−0.624931	+	0.780680i	$0.714873\pi$
$420$		0			0
$421$	−4.54213	+	7.86721i	−0.221370	+	0.383424i	−0.955224	−	0.295883i	$-0.904386\pi$
$421$	−4.54213	+	7.86721i	−0.221370	+	0.383424i	0.733854	+	0.679307i	$0.237720\pi$
$422$	−28.1219			−1.36895
$423$		0			0
$424$	−14.6678			−0.712333
$425$	−4.41631	+	7.64927i	−0.214223	+	0.371044i
$426$		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
$431$	16.6355			0.801305			0.400652	−	0.916230i	$-0.368784\pi$
$431$	16.6355			0.801305			0.400652	+	0.916230i	$0.368784\pi$
$432$		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
$437$	−1.40415	−	2.43206i	−0.0671696	−	0.116341i
$438$		0			0
$439$	−3.36757	+	5.83280i	−0.160725	+	0.278384i	−0.935129	−	0.354307i	$-0.884717\pi$
$439$	−3.36757	+	5.83280i	−0.160725	+	0.278384i	0.774404	+	0.632692i	$0.218050\pi$
$440$	−37.6310			−1.79399
$441$		0			0
$442$	2.32879			0.110769
$443$	14.3202	−	24.8033i	0.680372	−	1.17844i	−0.294496	−	0.955653i	$-0.595152\pi$
$443$	14.3202	−	24.8033i	0.680372	−	1.17844i	0.974867	−	0.222786i	$-0.0715150\pi$
$444$		0			0
$445$	−9.73141	−	16.8553i	−0.461313	−	0.799017i
$446$	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
$451$	−20.5035			−0.965473
$452$	−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
$457$	14.3287	−	24.8180i	0.670266	−	1.16093i	−0.307563	−	0.951528i	$-0.599513\pi$
$457$	14.3287	−	24.8180i	0.670266	−	1.16093i	0.977829	−	0.209407i	$-0.0671533\pi$
$458$	−23.6799			−1.10649
$459$		0			0
$460$	4.38839			0.204610
$461$	−10.0087	+	17.3355i	−0.466150	+	0.807395i	−0.999253	−	0.0386554i	$-0.987693\pi$
$461$	−10.0087	+	17.3355i	−0.466150	+	0.807395i	0.533103	+	0.846050i	$0.321026\pi$
$462$		0			0
$463$	−4.95789	−	8.58731i	−0.230413	−	0.399086i	0.727517	−	0.686090i	$-0.240674\pi$
$463$	−4.95789	−	8.58731i	−0.230413	−	0.399086i	−0.957930	+	0.287003i	$0.907341\pi$
$464$	−15.5120	−	26.8676i	−0.720127	−	1.24730i
$465$		0			0
$466$	−21.8020	+	37.7623i	−1.00996	+	1.74930i
$467$	−16.0807			−0.744126			−0.372063	−	0.928207i	$-0.621349\pi$
$467$	−16.0807			−0.744126			−0.372063	+	0.928207i	$0.621349\pi$
$468$		0			0
$469$		0			0
$470$	17.3463	−	30.0446i	0.800124	−	1.38586i
$471$		0			0
$472$	−9.91123	−	17.1667i	−0.456201	−	0.790164i
$473$	−11.5890	−	20.0728i	−0.532863	−	0.922946i
$474$		0			0
$475$	−8.08967	+	14.0117i	−0.371180	+	0.642902i
$476$		0			0
$477$		0			0
$478$	−15.5221			−0.709963
$479$	−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
$485$	57.9023			2.62921
$486$		0			0
$487$	2.73680			0.124016			0.0620081	−	0.998076i	$-0.480250\pi$
$487$	2.73680			0.124016			0.0620081	+	0.998076i	$0.480250\pi$
$488$	−10.5565	+	18.2844i	−0.477871	+	0.827696i
$489$		0			0
$490$		0			0
$491$	−9.85482	−	17.0690i	−0.444742	−	0.770315i	0.553293	−	0.832987i	$-0.313371\pi$
$491$	−9.85482	−	17.0690i	−0.444742	−	0.770315i	−0.998034	+	0.0626719i	$0.980038\pi$
$492$		0			0
$493$	3.73542	−	6.46993i	0.168235	−	0.291391i
$494$	4.26582			0.191928
$495$		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	$0.567785\pi$
$500$	−4.02576	−	6.97283i	−0.180038	−	0.311834i
$501$		0			0
$502$	−17.8288	+	30.8803i	−0.795737	+	1.37826i
$503$	−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
$506$	−6.69559	+	11.5971i	−0.297655	+	0.515554i
$507$		0			0
$508$	4.86882	+	8.43305i	0.216019	+	0.374156i
$509$	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
$514$	−4.22292			−0.186265
$515$	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
$520$	3.46082	−	5.99432i	0.151767	−	0.262868i
$521$	35.5490			1.55743			0.778714	−	0.627379i	$-0.215872\pi$
$521$	35.5490			1.55743			0.778714	+	0.627379i	$0.215872\pi$
$522$		0			0
$523$	26.7187			1.16833			0.584163	−	0.811636i	$-0.301423\pi$
$523$	26.7187			1.16833			0.584163	+	0.811636i	$0.301423\pi$
$524$	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
$530$	50.5665			2.19647
$531$		0			0
$532$		0			0
$533$	1.88565	−	3.26604i	0.0816766	−	0.141468i
$534$		0			0
$535$	−0.313440	−	0.542893i	−0.0135512	−	0.0234713i
$536$	−6.95990	−	12.0549i	−0.300622	−	0.520693i
$537$		0			0
$538$	25.5282	−	44.2161i	1.10060	−	1.90629i
$539$		0			0
$540$		0			0
$541$	37.5855			1.61593			0.807963	−	0.589233i	$-0.200570\pi$
$541$	37.5855			1.61593			0.807963	+	0.589233i	$0.200570\pi$
$542$	−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	−0.992520	−	0.122082i	$-0.961043\pi$
$547$	−9.13381	+	15.8202i	−0.390533	+	0.676424i	0.601986	+	0.798506i	$0.294376\pi$
$548$	−6.03134			−0.257646
$549$		0			0
$550$	77.1501			3.28969
$551$	6.84243	−	11.8514i	0.291498	−	0.504889i
$552$		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
$557$	3.89272			0.164940			0.0824698	−	0.996594i	$-0.473719\pi$
$557$	3.89272			0.164940			0.0824698	+	0.996594i	$0.473719\pi$
$558$		0			0
$559$	4.26324			0.180316
$560$		0			0
$561$		0			0
$562$	−10.4281	−	18.0620i	−0.439884	−	0.761901i
$563$	−1.66428	−	2.88261i	−0.0701409	−	0.121488i	0.828822	−	0.559512i	$-0.189012\pi$
$563$	−1.66428	−	2.88261i	−0.0701409	−	0.121488i	−0.898963	+	0.438025i	$0.855678\pi$
$564$		0			0
$565$	−14.7875	+	25.6127i	−0.622115	+	1.07753i
$566$	48.2965			2.03006
$567$		0			0
$568$	−21.4702			−0.900870
$569$	−18.3122	+	31.7177i	−0.767688	+	1.32967i	0.171126	+	0.985249i	$0.445259\pi$
$569$	−18.3122	+	31.7177i	−0.767688	+	1.32967i	−0.938814	+	0.344425i	$0.888074\pi$
$570$		0			0
$571$	11.2912	+	19.5569i	0.472522	+	0.818432i	0.999506	−	0.0314435i	$-0.0100104\pi$
$571$	11.2912	+	19.5569i	0.472522	+	0.818432i	−0.526984	+	0.849875i	$0.676677\pi$
$572$	−3.34742	−	5.79789i	−0.139962	−	0.242422i
$573$		0			0
$574$		0			0
$575$	9.34201			0.389589
$576$		0			0
$577$	−22.5449			−0.938557			−0.469279	−	0.883050i	$-0.655486\pi$
$577$	−22.5449			−0.938557			−0.469279	+	0.883050i	$0.655486\pi$
$578$	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
$583$	−25.3927	+	43.9814i	−1.05166	+	1.82152i
$584$	−9.34913			−0.386870
$585$		0			0
$586$	15.2343			0.629325
$587$	−12.1198	+	20.9921i	−0.500237	+	0.866436i	0.499763	+	0.866162i	$0.333421\pi$
$587$	−12.1198	+	20.9921i	−0.500237	+	0.866436i	−1.00000		0.000273884i	$0.999913\pi$
$588$		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
$593$	−45.7326			−1.87801			−0.939007	−	0.343898i	$-0.888253\pi$
$593$	−45.7326			−1.87801			−0.939007	+	0.343898i	$0.888253\pi$
$594$		0			0
$595$		0			0
$596$	2.83343	−	4.90764i	0.116062	−	0.201025i
$597$		0			0
$598$	−1.23155	−	2.13311i	−0.0503618	−	0.0872292i
$599$	−15.0834	−	26.1252i	−0.616290	−	1.06745i	−0.990157	−	0.139963i	$-0.955302\pi$
$599$	−15.0834	−	26.1252i	−0.616290	−	1.06745i	0.373866	−	0.927483i	$-0.378032\pi$
$600$		0			0
$601$	−7.36933	+	12.7641i	−0.300601	+	0.520657i	−0.976272	−	0.216547i	$-0.930521\pi$
$601$	−7.36933	+	12.7641i	−0.300601	+	0.520657i	0.675671	+	0.737203i	$0.263854\pi$
$602$		0			0
$603$		0			0
$604$	−1.98830			−0.0809027
$605$	−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
$611$	−6.40877			−0.259271
$612$		0			0
$613$	11.7734			0.475522			0.237761	−	0.971324i	$-0.423587\pi$
$613$	11.7734			0.475522			0.237761	+	0.971324i	$0.423587\pi$
$614$	0.911065	−	1.57801i	0.0367676	−	0.0636833i
$615$		0			0
$616$		0			0
$617$	16.0319	+	27.7680i	0.645418	+	1.11790i	0.984205	+	0.177034i	$0.0566503\pi$
$617$	16.0319	+	27.7680i	0.645418	+	1.11790i	−0.338786	+	0.940863i	$0.610016\pi$
$618$		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	$0.247837\pi$
$620$	0.649282			0.0260758
$621$		0			0
$622$	5.30441			0.212688
$623$		0			0
$624$		0			0
$625$	3.92995	+	6.80687i	0.157198	+	0.272275i
$626$	24.3125	+	42.1104i	0.971721	+	1.68307i
$627$		0			0
$628$	−1.49511	+	2.58961i	−0.0596614	+	0.103337i
$629$	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	$0.267964\pi$
$632$	8.10690	−	14.0416i	0.322475	−	0.558543i
$633$		0			0
$634$	11.0904	+	19.2092i	0.440457	+	0.762894i
$635$	17.4288	+	30.1875i	0.691639	+	1.19795i
$636$		0			0
$637$		0			0
$638$	−65.2553			−2.58348
$639$		0			0
$640$	43.0148			1.70031
$641$	−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	0.755367	−	0.655302i	$-0.227459\pi$
$643$	−4.81347	−	8.33718i	−0.189825	−	0.328786i	−0.945192	+	0.326516i	$0.894125\pi$
$644$		0			0
$645$		0			0
$646$	−2.29222	+	3.97025i	−0.0901864	+	0.156207i
$647$	−7.81214			−0.307127			−0.153564	−	0.988139i	$-0.549075\pi$
$647$	−7.81214			−0.307127			−0.153564	+	0.988139i	$0.549075\pi$
$648$		0			0
$649$	−68.6326			−2.69406
$650$	−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
$656$	16.8308			0.657132
$657$		0			0
$658$		0			0
$659$	−3.10685	+	5.38122i	−0.121026	+	0.209623i	−0.920172	−	0.391513i	$-0.871952\pi$
$659$	−3.10685	+	5.38122i	−0.121026	+	0.209623i	0.799147	+	0.601136i	$0.205285\pi$
$660$		0			0
$661$	13.7631	+	23.8384i	0.535324	+	0.927208i	0.999148	+	0.0412802i	$0.0131436\pi$
$661$	13.7631	+	23.8384i	0.535324	+	0.927208i	−0.463824	+	0.885927i	$0.653523\pi$
$662$	18.6094	+	32.2325i	0.723276	+	1.25275i
$663$		0			0
$664$	−1.09935	+	1.90413i	−0.0426630	+	0.0738945i
$665$		0			0
$666$		0			0
$667$	−7.90169			−0.305955
$668$	−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	−0.978919	−	0.204247i	$-0.934526\pi$
$673$	−8.10894	+	14.0451i	−0.312577	+	0.541399i	0.666343	+	0.745646i	$0.267859\pi$
$674$	−21.7670			−0.838434
$675$		0			0
$676$	−11.5240			−0.443230
$677$	10.2545	−	17.7613i	0.394112	−	0.682623i	−0.598875	−	0.800842i	$-0.704385\pi$
$677$	10.2545	−	17.7613i	0.394112	−	0.682623i	0.992987	+	0.118220i	$0.0377188\pi$
$678$		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
$683$	0.112308			0.00429736			0.00214868	−	0.999998i	$-0.499316\pi$
$683$	0.112308			0.00429736			0.00214868	+	0.999998i	$0.499316\pi$
$684$		0			0
$685$	−21.5902			−0.824918
$686$		0			0
$687$		0			0
$688$	9.51311	+	16.4772i	0.362684	+	0.628187i
$689$	−4.67059	−	8.08970i	−0.177935	−	0.308193i
$690$		0			0
$691$	9.43351	−	16.3393i	0.358868	−	0.621577i	−0.628904	−	0.777483i	$-0.716496\pi$
$691$	9.43351	−	16.3393i	0.358868	−	0.621577i	0.987772	+	0.155906i	$0.0498296\pi$
$692$	−17.3182			−0.658340
$693$		0			0
$694$	−39.9480			−1.51640
$695$	−1.54081	+	2.66876i	−0.0584461	+	0.101232i
$696$		0			0
$697$	2.02650	+	3.51000i	0.0767590	+	0.132951i
$698$	−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
$703$	7.88796			0.297500
$704$	−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
$709$	10.7606	−	18.6378i	0.404121	−	0.699959i	−0.590097	−	0.807332i	$-0.700911\pi$
$709$	10.7606	−	18.6378i	0.404121	−	0.699959i	0.994219	+	0.107373i	$0.0342440\pi$
$710$	74.0174			2.77782
$711$		0			0
$712$	−9.74771			−0.365311
$713$	−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
$719$	−18.8302			−0.702246			−0.351123	−	0.936329i	$-0.614200\pi$
$719$	−18.8302			−0.702246			−0.351123	+	0.936329i	$0.614200\pi$
$720$		0			0
$721$		0			0
$722$	12.2040	−	21.1379i	0.454185	−	0.786671i
$723$		0			0
$724$	1.94957	+	3.37675i	0.0724551	+	0.125496i
$725$	22.7618	+	39.4247i	0.845354	+	1.46420i
$726$		0			0
$727$	19.5426	−	33.8489i	0.724797	−	1.25538i	−0.234261	−	0.972174i	$-0.575267\pi$
$727$	19.5426	−	33.8489i	0.724797	−	1.25538i	0.959058	−	0.283211i	$-0.0913996\pi$
$728$		0			0
$729$		0			0
$730$	32.2306			1.19291
$731$	−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
$737$	−48.1954			−1.77530
$738$		0			0
$739$	5.50136			0.202371			0.101185	−	0.994868i	$-0.467736\pi$
$739$	5.50136			0.202371			0.101185	+	0.994868i	$0.467736\pi$
$740$	−6.16306	+	10.6747i	−0.226559	+	0.392411i
$741$		0			0
$742$		0			0
$743$	−10.2326	−	17.7234i	−0.375399	−	0.650210i	0.614988	−	0.788537i	$-0.289161\pi$
$743$	−10.2326	−	17.7234i	−0.375399	−	0.650210i	−0.990387	+	0.138327i	$0.955828\pi$
$744$		0			0
$745$	10.1427	−	17.5677i	0.371601	−	0.643631i
$746$	−56.1785			−2.05684
$747$		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	$-0.410890\pi$
$752$	−14.3007	−	24.7696i	−0.521494	−	0.903254i
$753$		0			0
$754$	6.00135	−	10.3946i	0.218556	−	0.378551i
$755$	−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	$0.878670\pi$
$758$	−1.33329	+	2.30933i	−0.0484273	+	0.0838786i
$759$		0			0
$760$	6.81295	+	11.8004i	0.247132	+	0.428045i
$761$	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
$766$	54.6116			1.97320
$767$	6.31195	−	10.9326i	0.227911	−	0.394754i
$768$		0			0
$769$	−22.4828	−	38.9414i	−0.810751	−	1.40426i	−0.912339	−	0.409436i	$-0.865726\pi$
$769$	−22.4828	−	38.9414i	−0.810751	−	1.40426i	0.101587	−	0.994827i	$-0.467608\pi$
$770$		0			0
$771$		0			0
$772$	0.0992886	−	0.171973i	0.00357348	−	0.00618944i
$773$	−24.3561			−0.876029			−0.438014	−	0.898968i	$-0.644318\pi$
$773$	−24.3561			−0.876029			−0.438014	+	0.898968i	$0.644318\pi$
$774$		0			0
$775$	1.38219			0.0496498
$776$	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
$782$	2.64707			0.0946592
$783$		0			0
$784$		0			0
$785$	−5.35200	+	9.26993i	−0.191021	+	0.330858i
$786$		0			0
$787$	20.7617	+	35.9603i	0.740073	+	1.28184i	0.952461	+	0.304659i	$0.0985426\pi$
$787$	20.7617	+	35.9603i	0.740073	+	1.28184i	−0.212388	+	0.977185i	$0.568124\pi$
$788$	−0.800331	−	1.38621i	−0.0285106	−	0.0493818i
$789$		0			0
$790$	−27.9481	+	48.4075i	−0.994349	+	1.72226i
$791$		0			0
$792$		0			0
$793$	−13.4458			−0.477474
$794$	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	−0.990756	−	0.135657i	$-0.956685\pi$
$797$	−17.3018	−	29.9676i	−0.612861	−	1.06151i	0.377895	−	0.925848i	$-0.376648\pi$
$798$		0			0
$799$	3.44373	−	5.96472i	0.121831	−	0.211017i
$800$	−37.5198			−1.32653
$801$		0			0
$802$	−20.9571			−0.740020
$803$	−16.1851	+	28.0333i	−0.571158	+	0.989275i
$804$		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
$809$	11.2519			0.395597			0.197799	−	0.980243i	$-0.436621\pi$
$809$	11.2519			0.395597			0.197799	+	0.980243i	$0.436621\pi$
$810$		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
$815$	9.46376	+	16.3917i	0.331501	+	0.574177i
$816$		0			0
$817$	−4.19629	+	7.26819i	−0.146810	+	0.254282i
$818$	−54.1211			−1.89230
$819$		0			0
$820$	−11.6014			−0.405137
$821$	17.3215	−	30.0018i	0.604526	−	1.04707i	−0.387600	−	0.921828i	$-0.626696\pi$
$821$	17.3215	−	30.0018i	0.604526	−	1.04707i	0.992126	−	0.125242i	$-0.0399709\pi$
$822$		0			0
$823$	−18.1935	−	31.5121i	−0.634186	−	1.09844i	−0.986687	−	0.162631i	$-0.948002\pi$
$823$	−18.1935	−	31.5121i	−0.634186	−	1.09844i	0.352501	−	0.935811i	$-0.385331\pi$
$824$	−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
$829$	−39.1702			−1.36044			−0.680219	−	0.733009i	$-0.738115\pi$
$829$	−39.1702			−1.36044			−0.680219	+	0.733009i	$0.738115\pi$
$830$	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
$835$	−29.1690	+	50.5223i	−1.00944	+	1.74839i
$836$	13.1794			0.455819
$837$		0			0
$838$	−25.7030			−0.887894
$839$	−17.1739	+	29.7460i	−0.592907	+	1.02695i	0.400931	+	0.916108i	$0.368687\pi$
$839$	−17.1739	+	29.7460i	−0.592907	+	1.02695i	−0.993839	+	0.110838i	$0.964647\pi$
$840$		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
$845$	−41.2520			−1.41911
$846$		0			0
$847$		0			0
$848$	20.8442	−	36.1032i	0.715793	−	1.23979i
$849$		0			0
$850$	−7.62525	−	13.2073i	−0.261544	−	0.453007i
$851$	−2.27727	−	3.94434i	−0.0780637	−	0.135210i
$852$		0			0
$853$	16.3371	−	28.2967i	0.559373	−	0.968862i	−0.438176	−	0.898889i	$-0.644375\pi$
$853$	16.3371	−	28.2967i	0.559373	−	0.968862i	0.997549	−	0.0699730i	$-0.0222913\pi$
$854$		0			0
$855$		0			0
$856$	−0.313965			−0.0107311
$857$	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
$863$	23.1776			0.788974			0.394487	−	0.918901i	$-0.370922\pi$
$863$	23.1776			0.788974			0.394487	+	0.918901i	$0.370922\pi$
$864$		0			0
$865$	−61.9934			−2.10784
$866$	17.0437	−	29.5205i	0.579167	−	1.00315i
$867$		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
$872$	−16.4626			−0.557493
$873$		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	$0.829357\pi$
$878$	−5.81448	−	10.0710i	−0.196229	−	0.339879i
$879$		0			0
$880$	53.4768	−	92.6245i	1.80270	−	3.12237i
$881$	−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	$0.241796\pi$
$884$	−0.661694	+	1.14609i	−0.0222552	+	0.0385471i
$885$		0			0
$886$	24.7254	+	42.8256i	0.830664	+	1.43875i
$887$	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
$892$	−19.5937			−0.656046
$893$	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
$898$	−5.75714	+	9.97165i	−0.192118	+	0.332758i
$899$	−1.16909			−0.0389913
$900$		0			0
$901$	10.0389			0.334444
$902$	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	$-0.0849611\pi$
$908$	3.54485			0.117640
$909$		0			0
$910$		0			0
$911$	−3.04869	+	5.28049i	−0.101008	+	0.174950i	−0.912100	−	0.409968i	$-0.865540\pi$
$911$	−3.04869	+	5.28049i	−0.101008	+	0.174950i	0.811092	+	0.584918i	$0.198873\pi$
$912$		0			0
$913$	3.80635	+	6.59278i	0.125972	+	0.218189i
$914$	24.7400	+	42.8509i	0.818327	+	1.41738i
$915$		0			0
$916$	6.72830	−	11.6538i	0.222309	−	0.385051i
$917$		0			0
$918$		0			0
$919$	24.8613			0.820100			0.410050	−	0.912063i	$-0.365511\pi$
$919$	24.8613			0.820100			0.410050	+	0.912063i	$0.365511\pi$
$920$	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
$926$	17.1207			0.562621
$927$		0			0
$928$	31.7351			1.04176
$929$	20.9201	−	36.2347i	0.686366	−	1.18882i	−0.286639	−	0.958039i	$-0.592538\pi$
$929$	20.9201	−	36.2347i	0.686366	−	1.18882i	0.973005	−	0.230783i	$-0.0741287\pi$
$930$		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
$935$	25.7553			0.842288
$936$		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
$941$	1.67869	+	2.90757i	0.0547236	+	0.0947841i	0.892090	−	0.451859i	$-0.149239\pi$
$941$	1.67869	+	2.90757i	0.0547236	+	0.0947841i	−0.837366	+	0.546643i	$0.815906\pi$
$942$		0			0
$943$	2.14337	−	3.71242i	0.0697976	−	0.120893i
$944$	56.3387			1.83367
$945$		0			0
$946$	40.0194			1.30114
$947$	2.63300	−	4.56050i	0.0855612	−	0.148196i	−0.820069	−	0.572265i	$-0.806065\pi$
$947$	2.63300	−	4.56050i	0.0855612	−	0.148196i	0.905630	+	0.424068i	$0.139398\pi$
$948$		0			0
$949$	−2.97699	−	5.15630i	−0.0966372	−	0.167381i
$950$	−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
$955$	63.9448			2.06921
$956$	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
$961$	15.4823	−	26.8160i	0.499427	−	0.865034i
$962$	6.91836			0.223057
$963$		0			0
$964$	−9.08306			−0.292546
$965$	0.355420	−	0.615606i	0.0114414	−	0.0198171i
$966$		0			0
$967$	−6.88641	−	11.9276i	−0.221452	−	0.383566i	0.733797	−	0.679369i	$-0.237746\pi$
$967$	−6.88641	−	11.9276i	−0.221452	−	0.383566i	−0.955249	+	0.295803i	$0.904413\pi$
$968$	22.9526	+	39.7551i	0.737725	+	1.27778i
$969$		0			0
$970$	−49.9874	+	86.5807i	−1.60500	+	2.77994i
$971$	51.3254			1.64711			0.823555	−	0.567236i	$-0.191987\pi$
$971$	51.3254			1.64711			0.823555	+	0.567236i	$0.191987\pi$
$972$		0			0
$973$		0			0
$974$	−2.36269	+	4.09230i	−0.0757055	+	0.131126i
$975$		0			0
$976$	−30.0033	−	51.9673i	−0.960383	−	1.66343i
$977$	8.84252	+	15.3157i	0.282897	+	0.489992i	0.972097	−	0.234579i	$-0.0753711\pi$
$977$	8.84252	+	15.3157i	0.282897	+	0.489992i	−0.689200	+	0.724571i	$0.742038\pi$
$978$		0			0
$979$	−16.8751	+	29.2285i	−0.539329	+	0.934146i
$980$		0			0
$981$		0			0
$982$	34.0309			1.08597
$983$	−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
$989$	4.84590			0.154091
$990$		0			0
$991$	−10.8664			−0.345182			−0.172591	−	0.984994i	$-0.555214\pi$
$991$	−10.8664			−0.345182			−0.172591	+	0.984994i	$0.555214\pi$
$992$	0.481771	−	0.834453i	0.0152963	−	0.0264939i
$993$		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	$0.941505\pi$
$998$	−57.1438			−1.80886
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.9	✓	24	9.5	odd	6
441.2.f.h.148.10	yes	24	63.41	even	6
441.2.f.h.295.9	yes	24	3.2	odd	2
441.2.f.h.295.10	yes	24	21.20	even	2
441.2.g.h.67.9		24	63.23	odd	6
441.2.g.h.67.10		24	63.5	even	6
441.2.g.h.79.9		24	21.11	odd	6
441.2.g.h.79.10		24	21.17	even	6
441.2.h.h.214.3		24	21.5	even	6
441.2.h.h.214.4		24	21.2	odd	6
441.2.h.h.373.3		24	63.59	even	6
441.2.h.h.373.4		24	63.32	odd	6
1323.2.f.h.442.3		24	9.4	even	3	inner
1323.2.f.h.442.4		24	63.13	odd	6	inner
1323.2.f.h.883.3		24	1.1	even	1	trivial
1323.2.f.h.883.4		24	7.6	odd	2	inner
1323.2.g.h.361.3		24	63.40	odd	6
1323.2.g.h.361.4		24	63.58	even	3
1323.2.g.h.667.3		24	7.3	odd	6
1323.2.g.h.667.4		24	7.4	even	3
1323.2.h.h.226.9		24	63.31	odd	6
1323.2.h.h.226.10		24	63.4	even	3
1323.2.h.h.802.9		24	7.5	odd	6
1323.2.h.h.802.10		24	7.2	even	3
3969.2.a.bh.1.3		12	9.2	odd	6
3969.2.a.bh.1.4		12	63.20	even	6
3969.2.a.bi.1.9		12	63.34	odd	6
3969.2.a.bi.1.10		12	9.7	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.863305 + 1.49529i) q^{2} +(-0.490592 - 0.849731i) q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +O(q^{10})\)	\(q+(-0.863305 + 1.49529i) q^{2} +(-0.490592 - 0.849731i) q^{4} +(-1.75616 - 3.04175i) q^{5} -1.75910 q^{8} +6.06439 q^{10} +(-3.04532 + 5.27465i) q^{11} +(-0.560139 - 0.970190i) q^{13} +(2.49982 - 4.32982i) q^{16} +1.20396 q^{17} +2.20537 q^{19} +(-1.72311 + 2.98452i) q^{20} +(-5.25808 - 9.10727i) q^{22} +(-0.636695 - 1.10279i) q^{23} +(-3.66817 + 6.35345i) q^{25} +1.93429 q^{26} +(3.10262 - 5.37390i) q^{29} +(-0.0942019 - 0.163162i) q^{31} +(2.55712 + 4.42907i) q^{32} +(-1.03938 + 1.80026i) q^{34} +3.57670 q^{37} +(-1.90391 + 3.29767i) q^{38} +(3.08925 + 5.35074i) q^{40} +(1.68320 + 2.91538i) q^{41} +(-1.90276 + 3.29567i) q^{43} +5.97604 q^{44} +2.19865 q^{46} +(2.86035 - 4.95427i) q^{47} +(-6.33349 - 10.9699i) q^{50} +(-0.549600 + 0.951935i) q^{52} +8.33827 q^{53} +21.3922 q^{55} +(5.35702 + 9.27862i) q^{58} +(5.63427 + 9.75883i) q^{59} +(6.00109 - 10.3942i) q^{61} +0.325300 q^{62} +1.16898 q^{64} +(-1.96738 + 3.40761i) q^{65} +(3.95652 + 6.85289i) q^{67} +(-0.590651 - 1.02304i) q^{68} +12.2052 q^{71} +5.31473 q^{73} +(-3.08779 + 5.34820i) q^{74} +(-1.08194 - 1.87397i) q^{76} +(-4.60855 + 7.98225i) q^{79} -17.5603 q^{80} -5.81246 q^{82} +(0.624950 - 1.08245i) q^{83} +(-2.11433 - 3.66213i) q^{85} +(-3.28532 - 5.69034i) q^{86} +(5.35702 - 9.27862i) q^{88} +5.54131 q^{89} +(-0.624715 + 1.08204i) q^{92} +(4.93871 + 8.55409i) q^{94} +(-3.87298 - 6.70820i) q^{95} +(-8.24277 + 14.2769i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Introduction

L-functions

Modular forms

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Database

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