LMFDB - Embedded newform 900.2.r.g.851.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,2,0,0,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			851.8
Character	$\chi$	$=$	900.851
Dual form			900.2.r.g.551.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.668359 + 1.24631i) q^{2} +(-0.461412 - 1.66946i) q^{3} +(-1.10659 - 1.66597i) q^{4} +(2.38906 + 0.540736i) q^{6} +(1.15604 - 0.667441i) q^{7} +(2.81592 - 0.265693i) q^{8} +(-2.57420 + 1.54062i) q^{9} +(2.18799 + 3.78971i) q^{11} +(-2.27068 + 2.61611i) q^{12} +(-2.05641 + 3.56180i) q^{13} +(0.0591892 + 1.88688i) q^{14} +(-1.55091 + 3.68710i) q^{16} -6.45392i q^{17} +(-0.199603 - 4.23794i) q^{18} +5.84202i q^{19} +(-1.64768 - 1.62200i) q^{21} +(-6.18554 + 0.194033i) q^{22} +(-0.0505284 + 0.0875178i) q^{23} +(-1.74286 - 4.57847i) q^{24} +(-3.06470 - 4.94349i) q^{26} +(3.75977 + 3.58666i) q^{27} +(-2.39120 - 1.18735i) q^{28} +(4.53226 - 2.61670i) q^{29} +(4.18262 + 2.41484i) q^{31} +(-3.55871 - 4.39722i) q^{32} +(5.31721 - 5.40139i) q^{33} +(8.04361 + 4.31354i) q^{34} +(5.41521 + 2.58370i) q^{36} +3.24337 q^{37} +(-7.28098 - 3.90457i) q^{38} +(6.89514 + 1.78964i) q^{39} +(3.50518 + 2.02372i) q^{41} +(3.12276 - 0.969443i) q^{42} +(3.33185 - 1.92364i) q^{43} +(3.89233 - 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(1.73649 + 3.00768i) q^{47} +(6.87107 + 0.887912i) q^{48} +(-2.60904 + 4.51900i) q^{49} +(-10.7746 + 2.97792i) q^{51} +(8.20946 - 0.515549i) q^{52} -2.77476i q^{53} +(-6.98298 + 2.28867i) q^{54} +(3.07799 - 2.18661i) q^{56} +(9.75302 - 2.69558i) q^{57} +(0.232051 + 7.39751i) q^{58} +(1.37318 - 2.37841i) q^{59} +(1.04419 + 1.80858i) q^{61} +(-5.80514 + 3.59888i) q^{62} +(-1.94761 + 3.49915i) q^{63} +(7.85881 - 1.49634i) q^{64} +(3.17801 + 10.2370i) q^{66} +(0.374638 + 0.216298i) q^{67} +(-10.7520 + 7.14186i) q^{68} +(0.169422 + 0.0439735i) q^{69} +8.41810 q^{71} +(-6.83941 + 5.02220i) q^{72} +7.28163 q^{73} +(-2.16773 + 4.04225i) q^{74} +(9.73262 - 6.46473i) q^{76} +(5.05882 + 2.92071i) q^{77} +(-6.83888 + 7.39739i) q^{78} +(-2.58753 + 1.49391i) q^{79} +(4.25299 - 7.93171i) q^{81} +(-4.86490 + 3.01598i) q^{82} +(6.70282 + 11.6096i) q^{83} +(-0.878898 + 4.53988i) q^{84} +(0.170590 + 5.43821i) q^{86} +(-6.45972 - 6.35905i) q^{87} +(7.16812 + 10.0902i) q^{88} -6.97377i q^{89} +5.49013i q^{91} +(0.201716 - 0.0126677i) q^{92} +(2.10157 - 8.09696i) q^{93} +(-4.90911 + 0.153993i) q^{94} +(-5.69896 + 7.97006i) q^{96} +(-1.20440 - 2.08608i) q^{97} +(-3.88831 - 6.27200i) q^{98} +(-11.4708 - 6.38462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−0.668359	+	1.24631i	−0.472601	+	0.881276i
$2$	−0.668359	+	1.24631i	−0.472601	+	0.881276i
$3$	−0.461412	−	1.66946i	−0.266396	−	0.963864i
$3$	−0.461412	−	1.66946i	−0.266396	−	0.963864i
$4$	−1.10659	−	1.66597i	−0.553296	−	0.832985i
$5$		0			0
$5$		0			0
$6$	2.38906	+	0.540736i	0.975329	+	0.220755i
$7$	1.15604	−	0.667441i	0.436943	−	0.252269i	−0.265357	−	0.964150i	$-0.585490\pi$
$7$	1.15604	−	0.667441i	0.436943	−	0.252269i	0.702300	+	0.711881i	$0.252157\pi$
$8$	2.81592	−	0.265693i	0.995578	−	0.0939368i
$9$	−2.57420	+	1.54062i	−0.858066	+	0.513539i
$10$		0			0
$11$	2.18799	+	3.78971i	0.659705	+	1.14264i	0.980692	+	0.195558i	$0.0626519\pi$
$11$	2.18799	+	3.78971i	0.659705	+	1.14264i	−0.320987	+	0.947083i	$0.604015\pi$
$12$	−2.27068	+	2.61611i	−0.655488	+	0.755206i
$13$	−2.05641	+	3.56180i	−0.570345	+	0.987867i	0.426185	+	0.904636i	$0.359857\pi$
$13$	−2.05641	+	3.56180i	−0.570345	+	0.987867i	−0.996530	+	0.0832309i	$0.973476\pi$
$14$	0.0591892	+	1.88688i	0.0158190	+	0.504290i
$15$		0			0
$16$	−1.55091	+	3.68710i	−0.387727	+	0.921774i
$17$		−	6.45392i		−	1.56531i	−0.622458	−	0.782653i	$-0.713866\pi$
$17$		−	6.45392i		−	1.56531i	0.622458	−	0.782653i	$-0.286134\pi$
$18$	−0.199603	−	4.23794i	−0.0470468	−	0.998893i
$19$			5.84202i			1.34025i	0.742248	+	0.670125i	$0.233760\pi$
$19$			5.84202i			1.34025i	−0.742248	+	0.670125i	$0.766240\pi$
$20$		0			0
$21$	−1.64768	−	1.62200i	−0.359553	−	0.353950i
$22$	−6.18554	+	0.194033i	−1.31876	+	0.0413679i
$23$	−0.0505284	+	0.0875178i	−0.0105359	+	0.0182487i	−0.871245	−	0.490848i	$-0.836687\pi$
$23$	−0.0505284	+	0.0875178i	−0.0105359	+	0.0182487i	0.860709	+	0.509097i	$0.170020\pi$
$24$	−1.74286	−	4.57847i	−0.355761	−	0.934577i
$25$		0			0
$26$	−3.06470	−	4.94349i	−0.601038	−	0.969499i
$27$	3.75977	+	3.58666i	0.723567	+	0.690254i
$28$	−2.39120	−	1.18735i	−0.451895	−	0.224387i
$29$	4.53226	−	2.61670i	0.841620	−	0.485909i	−0.0161948	−	0.999869i	$-0.505155\pi$
$29$	4.53226	−	2.61670i	0.841620	−	0.485909i	0.857814	+	0.513960i	$0.171822\pi$
$30$		0			0
$31$	4.18262	+	2.41484i	0.751222	+	0.433718i	0.826135	−	0.563472i	$-0.190535\pi$
$31$	4.18262	+	2.41484i	0.751222	+	0.433718i	−0.0749136	+	0.997190i	$0.523868\pi$
$32$	−3.55871	−	4.39722i	−0.629097	−	0.777327i
$33$	5.31721	−	5.40139i	0.925608	−	0.940261i
$34$	8.04361	+	4.31354i	1.37947	+	0.739766i
$35$		0			0
$36$	5.41521	+	2.58370i	0.902535	+	0.430617i
$37$	3.24337			0.533206			0.266603	−	0.963806i	$-0.414099\pi$
$37$	3.24337			0.533206			0.266603	+	0.963806i	$0.414099\pi$
$38$	−7.28098	−	3.90457i	−1.18113	−	0.633404i
$39$	6.89514	+	1.78964i	1.10411	+	0.286571i
$40$		0			0
$41$	3.50518	+	2.02372i	0.547417	+	0.316051i	0.748079	−	0.663609i	$-0.230976\pi$
$41$	3.50518	+	2.02372i	0.547417	+	0.316051i	−0.200663	+	0.979660i	$0.564310\pi$
$42$	3.12276	−	0.969443i	0.481853	−	0.149588i
$43$	3.33185	−	1.92364i	0.508102	−	0.293353i	−0.223951	−	0.974600i	$-0.571896\pi$
$43$	3.33185	−	1.92364i	0.508102	−	0.293353i	0.732053	+	0.681248i	$0.238562\pi$
$44$	3.89233	−	7.83880i	0.586792	−	1.18174i
$45$		0			0
$46$	−0.0753035	−	0.121468i	−0.0111029	−	0.0179094i
$47$	1.73649	+	3.00768i	0.253292	+	0.438715i	0.964430	−	0.264337i	$-0.0851532\pi$
$47$	1.73649	+	3.00768i	0.253292	+	0.438715i	−0.711138	+	0.703053i	$0.751820\pi$
$48$	6.87107	+	0.887912i	0.991754	+	0.128159i
$49$	−2.60904	+	4.51900i	−0.372721	+	0.645571i
$50$		0			0
$51$	−10.7746	+	2.97792i	−1.50874	+	0.416992i
$52$	8.20946	−	0.515549i	1.13845	−	0.0714938i
$53$		−	2.77476i		−	0.381143i	−0.981673	−	0.190571i	$-0.938966\pi$
$53$		−	2.77476i		−	0.381143i	0.981673	−	0.190571i	$-0.0610340\pi$
$54$	−6.98298	+	2.28867i	−0.950263	+	0.311448i
$55$		0			0
$56$	3.07799	−	2.18661i	0.411313	−	0.292199i
$57$	9.75302	−	2.69558i	1.29182	−	0.357038i
$58$	0.232051	+	7.39751i	0.0304698	+	0.971341i
$59$	1.37318	−	2.37841i	0.178772	−	0.309642i	−0.762688	−	0.646766i	$-0.776121\pi$
$59$	1.37318	−	2.37841i	0.178772	−	0.309642i	0.941460	+	0.337124i	$0.109454\pi$
$60$		0			0
$61$	1.04419	+	1.80858i	0.133694	+	0.231566i	0.925098	−	0.379729i	$-0.123983\pi$
$61$	1.04419	+	1.80858i	0.133694	+	0.231566i	−0.791404	+	0.611294i	$0.790649\pi$
$62$	−5.80514	+	3.59888i	−0.737254	+	0.457058i
$63$	−1.94761	+	3.49915i	−0.245376	+	0.440851i
$64$	7.85881	−	1.49634i	0.982352	−	0.187043i
$65$		0			0
$66$	3.17801	+	10.2370i	0.391186	+	1.26009i
$67$	0.374638	+	0.216298i	0.0457694	+	0.0264250i	0.522710	−	0.852511i	$-0.324921\pi$
$67$	0.374638	+	0.216298i	0.0457694	+	0.0264250i	−0.476941	+	0.878935i	$0.658254\pi$
$68$	−10.7520	+	7.14186i	−1.30388	+	0.866078i
$69$	0.169422	+	0.0439735i	0.0203960	+	0.00529379i
$70$		0			0
$71$	8.41810			0.999044			0.499522	−	0.866301i	$-0.333509\pi$
$71$	8.41810			0.999044			0.499522	+	0.866301i	$0.333509\pi$
$72$	−6.83941	+	5.02220i	−0.806032	+	0.591872i
$73$	7.28163			0.852250			0.426125	−	0.904664i	$-0.359878\pi$
$73$	7.28163			0.852250			0.426125	+	0.904664i	$0.359878\pi$
$74$	−2.16773	+	4.04225i	−0.251994	+	0.469902i
$75$		0			0
$76$	9.73262	−	6.46473i	1.11641	−	0.741555i
$77$	5.05882	+	2.92071i	0.576507	+	0.332846i
$78$	−6.83888	+	7.39739i	−0.774351	+	0.837589i
$79$	−2.58753	+	1.49391i	−0.291120	+	0.168078i	−0.638447	−	0.769666i	$-0.720423\pi$
$79$	−2.58753	+	1.49391i	−0.291120	+	0.168078i	0.347327	+	0.937744i	$0.387089\pi$
$80$		0			0
$81$	4.25299	−	7.93171i	0.472555	−	0.881301i
$82$	−4.86490	+	3.01598i	−0.537238	+	0.333059i
$83$	6.70282	+	11.6096i	0.735730	+	1.27432i	0.954402	+	0.298524i	$0.0964943\pi$
$83$	6.70282	+	11.6096i	0.735730	+	1.27432i	−0.218672	+	0.975798i	$0.570172\pi$
$84$	−0.878898	+	4.53988i	−0.0958957	+	0.495341i
$85$		0			0
$86$	0.170590	+	5.43821i	0.0183952	+	0.586417i
$87$	−6.45972	−	6.35905i	−0.692555	−	0.681762i
$88$	7.16812	+	10.0902i	0.764124	+	1.07562i
$89$		−	6.97377i		−	0.739218i	−0.929187	−	0.369609i	$-0.879492\pi$
$89$		−	6.97377i		−	0.739218i	0.929187	−	0.369609i	$-0.120508\pi$
$90$		0			0
$91$			5.49013i			0.575522i
$92$	0.201716	−	0.0126677i	0.0210304	−	0.00132070i
$93$	2.10157	−	8.09696i	0.217922	−	0.839616i
$94$	−4.90911	+	0.153993i	−0.506336	+	0.0158831i
$95$		0			0
$96$	−5.69896	+	7.97006i	−0.581648	+	0.813441i
$97$	−1.20440	−	2.08608i	−0.122288	−	0.211809i	0.798382	−	0.602152i	$-0.205690\pi$
$97$	−1.20440	−	2.08608i	−0.122288	−	0.211809i	−0.920670	+	0.390343i	$0.872356\pi$
$98$	−3.88831	−	6.27200i	−0.392778	−	0.633568i
$99$	−11.4708	−	6.38462i	−1.15286	−	0.641678i
$100$		0			0
$101$	−3.92717	+	2.26735i	−0.390768	+	0.225610i	−0.682493	−	0.730892i	$-0.739104\pi$
$101$	−3.92717	+	2.26735i	−0.390768	+	0.225610i	0.291725	+	0.956502i	$0.405771\pi$
$102$	3.48987	−	15.4188i	0.345549	−	1.52669i
$103$	3.37992	+	1.95140i	0.333034	+	0.192277i	0.657187	−	0.753727i	$-0.271746\pi$
$103$	3.37992	+	1.95140i	0.333034	+	0.192277i	−0.324153	+	0.946005i	$0.605079\pi$
$104$	−4.84434	+	10.5761i	−0.475026	+	1.03708i
$105$		0			0
$106$	3.45822	+	1.85454i	0.335892	+	0.180129i
$107$	4.98830			0.482237			0.241118	−	0.970496i	$-0.422486\pi$
$107$	4.98830			0.482237			0.241118	+	0.970496i	$0.422486\pi$
$108$	1.81475	−	10.2326i	0.174624	−	0.984635i
$109$	4.98669			0.477638			0.238819	−	0.971064i	$-0.423240\pi$
$109$	4.98669			0.477638			0.238819	+	0.971064i	$0.423240\pi$
$110$		0			0
$111$	−1.49653	−	5.41467i	−0.142044	−	0.513938i
$112$	0.668004	+	5.29758i	0.0631204	+	0.500574i
$113$	−17.6768	−	10.2057i	−1.66290	−	0.960073i	−0.971322	−	0.237767i	$-0.923584\pi$
$113$	−17.6768	−	10.2057i	−1.66290	−	0.960073i	−0.691574	−	0.722306i	$-0.743082\pi$
$114$	−3.15899	+	13.9569i	−0.295866	+	1.30719i
$115$		0			0
$116$	−9.37471	−	4.65499i	−0.870420	−	0.432205i
$117$	−0.193775	−	12.3369i	−0.0179145	−	1.14055i
$118$	2.04647	+	3.30104i	0.188393	+	0.303885i
$119$	−4.30762	−	7.46101i	−0.394879	−	0.683950i
$120$		0			0
$121$	−4.07462	+	7.05746i	−0.370420	+	0.641587i
$122$	−2.95195	+	0.0925992i	−0.267257	+	0.00838354i
$123$	1.76118	−	6.78552i	0.158800	−	0.611830i
$124$	−0.605409	−	9.64037i	−0.0543673	−	0.865730i
$125$		0			0
$126$	−3.05933	−	4.76602i	−0.272547	−	0.424591i
$127$			19.1833i			1.70224i	0.524968	+	0.851122i	$0.324077\pi$
$127$			19.1833i			1.70224i	−0.524968	+	0.851122i	$0.675923\pi$
$128$	−3.38760	+	10.7946i	−0.299424	+	0.954120i
$129$	−4.74880	−	4.67479i	−0.418108	−	0.411593i
$130$		0			0
$131$	8.41433	−	14.5740i	0.735163	−	1.27334i	−0.219488	−	0.975615i	$-0.570439\pi$
$131$	8.41433	−	14.5740i	0.735163	−	1.27334i	0.954652	−	0.297725i	$-0.0962279\pi$
$132$	−14.8825	−	2.88119i	−1.29536	−	0.250775i
$133$	3.89920	+	6.75362i	0.338104	+	0.585613i
$134$	−0.519967	+	0.322352i	−0.0449183	+	0.0278470i
$135$		0			0
$136$	−1.71477	−	18.1737i	−0.147040	−	1.55839i
$137$	−5.19172	+	2.99744i	−0.443559	+	0.256089i	−0.705106	−	0.709102i	$-0.749101\pi$
$137$	−5.19172	+	2.99744i	−0.443559	+	0.256089i	0.261547	+	0.965191i	$0.415767\pi$
$138$	−0.168040	+	0.181763i	−0.0143045	+	0.0154727i
$139$	0.206175	+	0.119035i	0.0174875	+	0.0100964i	0.508718	−	0.860933i	$-0.330119\pi$
$139$	0.206175	+	0.119035i	0.0174875	+	0.0100964i	−0.491231	+	0.871029i	$0.663453\pi$
$140$		0			0
$141$	4.21997	−	4.28677i	0.355386	−	0.361012i
$142$	−5.62631	+	10.4916i	−0.472150	+	0.880434i
$143$	−17.9976			−1.50504
$144$	−1.68806	−	11.8807i	−0.140672	−	0.990056i
$145$		0			0
$146$	−4.86674	+	9.07519i	−0.402775	+	0.751068i
$147$	8.74813	+	2.27058i	0.721534	+	0.187274i
$148$	−3.58908	−	5.40335i	−0.295021	−	0.444153i
$149$	8.84885	+	5.10889i	0.724926	+	0.418536i	0.816563	−	0.577256i	$-0.195877\pi$
$149$	8.84885	+	5.10889i	0.724926	+	0.418536i	−0.0916368	+	0.995792i	$0.529210\pi$
$150$		0			0
$151$	−13.0489	+	7.53379i	−1.06190	+	0.613091i	−0.925958	−	0.377625i	$-0.876741\pi$
$151$	−13.0489	+	7.53379i	−1.06190	+	0.613091i	−0.135946	+	0.990716i	$0.543407\pi$
$152$	1.55219	+	16.4507i	0.125899	+	1.33432i
$153$	9.94303	+	16.6137i	0.803846	+	1.34314i
$154$	−7.02124	+	4.35279i	−0.565787	+	0.350758i
$155$		0			0
$156$	−4.64863	−	13.4675i	−0.372188	−	1.07826i
$157$	1.60184	−	2.77448i	0.127841	−	0.221427i	−0.794999	−	0.606611i	$-0.792529\pi$
$157$	1.60184	−	2.77448i	0.127841	−	0.221427i	0.922840	+	0.385184i	$0.125862\pi$
$158$	−0.132481	−	4.22334i	−0.0105396	−	0.335991i
$159$	−4.63235	+	1.28031i	−0.367370	+	0.101535i
$160$		0			0
$161$			0.134899i			0.0106315i
$162$	7.04287	+	10.6018i	0.553340	+	0.832956i
$163$			10.6182i			0.831684i	0.909437	+	0.415842i	$0.136513\pi$
$163$			10.6182i			0.831684i	−0.909437	+	0.415842i	$0.863487\pi$
$164$	−0.507353	−	8.07895i	−0.0396176	−	0.630860i
$165$		0			0
$166$	−18.9491	+	0.594411i	−1.47074	+	0.0461352i
$167$	−6.30046	+	10.9127i	−0.487544	+	0.844451i	−0.999897	−	0.0143236i	$-0.995440\pi$
$167$	−6.30046	+	10.9127i	−0.487544	+	0.844451i	0.512353	+	0.858775i	$0.328774\pi$
$168$	−5.07069	−	4.12965i	−0.391212	−	0.318609i
$169$	−1.95764	−	3.39073i	−0.150587	−	0.260825i
$170$		0			0
$171$	−9.00032	−	15.0385i	−0.688271	−	1.15002i
$172$	−6.89172	−	3.42207i	−0.525489	−	0.260930i
$173$	1.48639	−	0.858165i	0.113008	−	0.0652451i	−0.442431	−	0.896803i	$-0.645884\pi$
$173$	1.48639	−	0.858165i	0.113008	−	0.0652451i	0.555439	+	0.831558i	$0.312550\pi$
$174$	12.2428	−	3.80070i	0.928123	−	0.288130i
$175$		0			0
$176$	−17.3664	+	2.18984i	−1.30904	+	0.165065i
$177$	−4.60426	−	1.19504i	−0.346077	−	0.0898244i
$178$	8.69150	+	4.66099i	0.651456	+	0.349356i
$179$	18.6630			1.39494			0.697468	−	0.716616i	$-0.254310\pi$
$179$	18.6630			1.39494			0.697468	+	0.716616i	$0.254310\pi$
$180$		0			0
$181$	−19.9281			−1.48125			−0.740623	−	0.671920i	$-0.765470\pi$
$181$	−19.9281			−1.48125			−0.740623	+	0.671920i	$0.765470\pi$
$182$	−6.84242	−	3.66938i	−0.507194	−	0.271992i
$183$	2.53756	−	2.57773i	0.187582	−	0.190551i
$184$	−0.119031	+	0.259868i	−0.00877509	+	0.0191577i
$185$		0			0
$186$	8.68675	+	8.03089i	0.636943	+	0.588853i
$187$	24.4585	−	14.1211i	1.78859	−	1.03264i
$188$	3.08912	−	6.22121i	0.225298	−	0.453728i
$189$	6.74034	+	1.63691i	0.490287	+	0.119068i
$190$		0			0
$191$	−10.8229	−	18.7459i	−0.783121	−	1.35641i	−0.930115	−	0.367268i	$-0.880293\pi$
$191$	−10.8229	−	18.7459i	−0.783121	−	1.35641i	0.146994	−	0.989137i	$-0.453040\pi$
$192$	−6.12424	−	12.4296i	−0.441979	−	0.897026i
$193$	−5.19970	+	9.00614i	−0.374282	+	0.648276i	−0.990219	−	0.139519i	$-0.955444\pi$
$193$	−5.19970	+	9.00614i	−0.374282	+	0.648276i	0.615937	+	0.787795i	$0.288778\pi$
$194$	3.40487	−	0.106807i	0.244456	−	0.00766827i
$195$		0			0
$196$	10.4157	−	0.654097i	0.743976	−	0.0467212i
$197$		−	8.15715i		−	0.581173i	−0.956849	−	0.290586i	$-0.906150\pi$
$197$		−	8.15715i		−	0.581173i	0.956849	−	0.290586i	$-0.0938503\pi$
$198$	15.6239	−	10.0290i	1.11034	−	0.712732i
$199$		−	9.18172i		−	0.650875i	−0.945564	−	0.325438i	$-0.894488\pi$
$199$		−	9.18172i		−	0.650875i	0.945564	−	0.325438i	$-0.105512\pi$
$200$		0			0
$201$	0.188238	−	0.725246i	0.0132773	−	0.0511549i
$202$	−0.201070	−	6.40988i	−0.0141473	−	0.450998i
$203$	3.49299	−	6.05004i	0.245160	−	0.424629i
$204$	16.8842	+	14.6548i	1.18213	+	1.02604i
$205$		0			0
$206$	−4.69106	+	2.90821i	−0.326842	+	0.202624i
$207$	−0.00476130	−	0.303133i	−0.000330933	−	0.0210692i
$208$	−9.94341	−	13.1062i	−0.689452	−	0.908752i
$209$	−22.1396	+	12.7823i	−1.53143	+	0.884170i
$210$		0			0
$211$	8.87092	+	5.12163i	0.610699	+	0.352587i	0.773239	−	0.634115i	$-0.218635\pi$
$211$	8.87092	+	5.12163i	0.610699	+	0.352587i	−0.162540	+	0.986702i	$0.551969\pi$
$212$	−4.62267	+	3.07053i	−0.317486	+	0.210885i
$213$	−3.88421	−	14.0537i	−0.266142	−	0.962942i
$214$	−3.33397	+	6.21698i	−0.227906	+	0.424984i
$215$		0			0
$216$	11.5402	+	9.10081i	0.785208	+	0.619232i
$217$	6.44705			0.437655
$218$	−3.33290	+	6.21497i	−0.225732	+	0.420931i
$219$	−3.35983	−	12.1564i	−0.227036	−	0.821453i
$220$		0			0
$221$	22.9876	+	13.2719i	1.54631	+	0.892765i
$222$	7.74859	+	1.75381i	0.520052	+	0.117708i
$223$	20.1343	−	11.6245i	1.34829	−	0.778436i	0.360283	−	0.932843i	$-0.382680\pi$
$223$	20.1343	−	11.6245i	1.34829	−	0.778436i	0.988007	+	0.154407i	$0.0493467\pi$
$224$	−7.04891	−	2.70815i	−0.470975	−	0.180946i
$225$		0			0
$226$	24.5340	−	15.2098i	1.63198	−	1.01174i
$227$	−8.50750	−	14.7354i	−0.564663	−	0.978024i	−0.997081	−	0.0763513i	$-0.975673\pi$
$227$	−8.50750	−	14.7354i	−0.564663	−	0.978024i	0.432418	−	0.901673i	$-0.357660\pi$
$228$	−15.2834	−	13.2653i	−1.01217	−	0.878518i
$229$	0.750685	−	1.30022i	0.0496066	−	0.0859212i	−0.840156	−	0.542345i	$-0.817537\pi$
$229$	0.750685	−	1.30022i	0.0496066	−	0.0859212i	0.889762	+	0.456424i	$0.150870\pi$
$230$		0			0
$231$	2.54182	−	9.79316i	0.167239	−	0.644343i
$232$	12.0672	−	8.57262i	0.792253	−	0.562820i
$233$			13.5483i			0.887579i	0.896131	+	0.443789i	$0.146366\pi$
$233$			13.5483i			0.887579i	−0.896131	+	0.443789i	$0.853634\pi$
$234$	15.5052	+	8.00400i	1.01361	+	0.523238i
$235$		0			0
$236$	−5.48190	+	0.344260i	−0.356841	+	0.0224094i
$237$	3.68794	+	3.63047i	0.239557	+	0.235824i
$238$	12.1778	−	0.382002i	0.789369	−	0.0247615i
$239$	−7.32324	+	12.6842i	−0.473701	+	0.820474i	−0.999547	−	0.0301057i	$-0.990416\pi$
$239$	−7.32324	+	12.6842i	−0.473701	+	0.820474i	0.525846	+	0.850580i	$0.323749\pi$
$240$		0			0
$241$	−12.2259	−	21.1758i	−0.787537	−	1.36405i	−0.927472	−	0.373894i	$-0.878022\pi$
$241$	−12.2259	−	21.1758i	−0.787537	−	1.36405i	0.139934	−	0.990161i	$-0.455311\pi$
$242$	−6.07249	−	9.79517i	−0.390354	−	0.629658i
$243$	−15.2041	−	3.44042i	−0.975341	−	0.220703i
$244$	1.85756	−	3.74095i	0.118918	−	0.239490i
$245$		0			0
$246$	7.27978	+	6.73015i	0.464142	+	0.429099i
$247$	−20.8081	−	12.0136i	−1.32399	−	0.764406i
$248$	12.4195	+	5.68870i	0.788642	+	0.361233i
$249$	16.2891	−	16.5469i	1.03228	−	1.04862i
$250$		0			0
$251$	13.1808			0.831965			0.415982	−	0.909373i	$-0.363438\pi$
$251$	13.1808			0.831965			0.415982	+	0.909373i	$0.363438\pi$
$252$	7.98468	−	0.627467i	0.502988	−	0.0395267i
$253$	−0.442223			−0.0278024
$254$	−23.9084	−	12.8214i	−1.50015	−	0.804483i
$255$		0			0
$256$	−11.1894	−	11.4367i	−0.699335	−	0.714794i
$257$	−6.03633	−	3.48508i	−0.376536	−	0.217393i	0.299774	−	0.954010i	$-0.403089\pi$
$257$	−6.03633	−	3.48508i	−0.376536	−	0.217393i	−0.676310	+	0.736617i	$0.736422\pi$
$258$	9.00016	−	2.79405i	0.560325	−	0.173950i
$259$	3.74947	−	2.16476i	0.232981	−	0.134511i
$260$		0			0
$261$	−7.63560	+	13.7184i	−0.472632	+	0.849147i
$262$	12.5400	+	20.2276i	0.774725	+	1.24966i
$263$	−8.07190	−	13.9809i	−0.497735	−	0.862102i	0.502262	−	0.864716i	$-0.332501\pi$
$263$	−8.07190	−	13.9809i	−0.497735	−	0.862102i	−0.999997	+	0.00261352i	$0.999168\pi$
$264$	13.5377	−	16.6226i	0.833190	−	1.02305i
$265$		0			0
$266$	−11.0232	+	0.345784i	−0.675875	+	0.0212014i
$267$	−11.6424	+	3.21778i	−0.712506	+	0.196925i
$268$	−0.0542266	−	0.863489i	−0.00331242	−	0.0527460i
$269$			21.7634i			1.32694i	0.748204	+	0.663468i	$0.230916\pi$
$269$			21.7634i			1.32694i	−0.748204	+	0.663468i	$0.769084\pi$
$270$		0			0
$271$			30.1548i			1.83177i	0.401436	+	0.915887i	$0.368511\pi$
$271$			30.1548i			1.83177i	−0.401436	+	0.915887i	$0.631489\pi$
$272$	23.7962	+	10.0095i	1.44286	+	0.606912i
$273$	9.16556	−	2.53321i	0.554725	−	0.153317i
$274$	−0.265815	−	8.47388i	−0.0160585	−	0.511926i
$275$		0			0
$276$	−0.114223	−	0.330913i	−0.00687539	−	0.0199186i
$277$	6.50177	+	11.2614i	0.390654	+	0.676632i	0.992536	−	0.121953i	$-0.0389157\pi$
$277$	6.50177	+	11.2614i	0.390654	+	0.676632i	−0.601882	+	0.798585i	$0.705582\pi$
$278$	−0.286153	+	0.177400i	−0.0171623	+	0.0106397i
$279$	−14.4872	+	0.227550i	−0.867329	+	0.0136231i
$280$		0			0
$281$	−0.936692	+	0.540799i	−0.0558784	+	0.0322614i	−0.527679	−	0.849444i	$-0.676938\pi$
$281$	−0.936692	+	0.540799i	−0.0558784	+	0.0322614i	0.471801	+	0.881705i	$0.343604\pi$
$282$	2.52221	+	8.12451i	0.150195	+	0.483808i
$283$	−25.3154	−	14.6158i	−1.50484	−	0.868821i	−0.999984	−	0.00561859i	$-0.998212\pi$
$283$	−25.3154	−	14.6158i	−1.50484	−	0.868821i	−0.504858	−	0.863202i	$-0.668455\pi$
$284$	−9.31540	−	14.0243i	−0.552767	−	0.832189i
$285$		0			0
$286$	12.0289	−	22.4307i	0.711283	−	1.32635i
$287$	5.40284			0.318920
$288$	15.9353	+	5.83671i	0.938995	+	0.343931i
$289$	−24.6531			−1.45019
$290$		0			0
$291$	−2.92690	+	2.97323i	−0.171578	+	0.174294i
$292$	−8.05779	−	12.1310i	−0.471547	−	0.709911i
$293$	4.87662	+	2.81552i	0.284895	+	0.164484i	0.635637	−	0.771988i	$-0.280737\pi$
$293$	4.87662	+	2.81552i	0.284895	+	0.164484i	−0.350742	+	0.936472i	$0.614071\pi$
$294$	−8.67675	+	9.38535i	−0.506038	+	0.547365i
$295$		0			0
$296$	9.13306	−	0.861741i	0.530848	−	0.0500877i
$297$	−5.36609	+	22.0960i	−0.311372	+	1.28214i
$298$	−12.2815	+	7.61387i	−0.711447	+	0.441060i
$299$	−0.207814	−	0.359945i	−0.0120182	−	0.0208162i
$300$		0			0
$301$	2.56784	−	4.44762i	0.148008	−	0.256357i
$302$	−0.668101	−	21.2983i	−0.0384449	−	1.22558i
$303$	5.59729	+	5.51007i	0.321556	+	0.316545i
$304$	−21.5401	−	9.06044i	−1.23541	−	0.519652i
$305$		0			0
$306$	−27.3514	+	1.28822i	−1.56357	+	0.0736426i
$307$		−	15.2931i		−	0.872826i	−0.899747	−	0.436413i	$-0.856249\pi$
$307$		−	15.2931i		−	0.872826i	0.899747	−	0.436413i	$-0.143751\pi$
$308$	−0.732233	−	11.6599i	−0.0417229	−	0.664384i
$309$	1.69825	−	6.54305i	0.0966100	−	0.372221i
$310$		0			0
$311$	1.83417	−	3.17688i	0.104006	−	0.180144i	−0.809326	−	0.587360i	$-0.800167\pi$
$311$	1.83417	−	3.17688i	0.104006	−	0.180144i	0.913332	+	0.407216i	$0.133500\pi$
$312$	19.8917	+	3.20748i	1.12614	+	0.181588i
$313$	−12.3149	−	21.3301i	−0.696081	−	1.20565i	−0.969815	−	0.243842i	$-0.921592\pi$
$313$	−12.3149	−	21.3301i	−0.696081	−	1.20565i	0.273734	−	0.961805i	$-0.411741\pi$
$314$	2.38726	+	3.85075i	0.134721	+	0.217310i
$315$		0			0
$316$	5.35215	+	2.65759i	0.301082	+	0.149501i
$317$	−9.22258	+	5.32466i	−0.517992	+	0.299063i	−0.736113	−	0.676859i	$-0.763341\pi$
$317$	−9.22258	+	5.32466i	−0.517992	+	0.299063i	0.218121	+	0.975922i	$0.430007\pi$
$318$	1.50041	−	6.62907i	0.0841390	−	0.371740i
$319$	19.8331	+	11.4506i	1.11044	+	0.641113i
$320$		0			0
$321$	−2.30166	−	8.32777i	−0.128466	−	0.464811i
$322$	−0.168126	−	0.0901611i	−0.00936932	−	0.00502448i
$323$	37.7039			2.09790
$324$	−17.9203	+	1.69181i	−0.995573	+	0.0939894i
$325$		0			0
$326$	−13.2336	−	7.09679i	−0.732943	−	0.393055i
$327$	−2.30092	−	8.32508i	−0.127241	−	0.460378i
$328$	10.4080	+	4.76732i	0.574685	+	0.263231i
$329$	4.01490	+	2.31800i	0.221349	+	0.127796i
$330$		0			0
$331$	3.04582	−	1.75851i	0.167414	−	0.0966563i	−0.413952	−	0.910299i	$-0.635852\pi$
$331$	3.04582	−	1.75851i	0.167414	−	0.0966563i	0.581366	+	0.813642i	$0.302519\pi$
$332$	11.9240	−	24.0138i	0.654415	−	1.31793i
$333$	−8.34907	+	4.99679i	−0.457526	+	0.273822i
$334$	−9.38969	−	15.1460i	−0.513781	−	0.828750i
$335$		0			0
$336$	8.53588	−	3.55957i	0.465670	−	0.194191i
$337$	−11.7643	+	20.3763i	−0.640841	+	1.10997i	0.344405	+	0.938821i	$0.388081\pi$
$337$	−11.7643	+	20.3763i	−0.640841	+	1.10997i	−0.985245	+	0.171147i	$0.945253\pi$
$338$	5.53431	−	0.173605i	0.301027	−	0.00944284i
$339$	−8.88175	+	34.2198i	−0.482391	+	1.85856i
$340$		0			0
$341$			21.1346i			1.14450i
$342$	24.7581	−	1.16608i	1.33877	−	0.0630545i
$343$			16.3097i			0.880642i
$344$	8.87111	−	6.30207i	0.478298	−	0.339785i
$345$		0			0
$346$	0.0761027	+	2.42607i	0.00409131	+	0.130426i
$347$	2.09663	−	3.63147i	0.112553	−	0.194947i	−0.804246	−	0.594297i	$-0.797431\pi$
$347$	2.09663	−	3.63147i	0.112553	−	0.194947i	0.916799	+	0.399349i	$0.130764\pi$
$348$	−3.44572	+	17.7986i	−0.184710	+	0.954104i
$349$	−2.78198	−	4.81854i	−0.148916	−	0.257930i	0.781911	−	0.623390i	$-0.214245\pi$
$349$	−2.78198	−	4.81854i	−0.148916	−	0.257930i	−0.930827	+	0.365460i	$0.880912\pi$
$350$		0			0
$351$	−20.5066	+	6.01591i	−1.09456	+	0.321105i
$352$	8.87779	−	23.1076i	0.473188	−	1.23164i
$353$	9.54549	−	5.51109i	0.508055	−	0.293326i	−0.223979	−	0.974594i	$-0.571905\pi$
$353$	9.54549	−	5.51109i	0.508055	−	0.293326i	0.732034	+	0.681268i	$0.238571\pi$
$354$	4.56669	−	4.93964i	0.242717	−	0.262539i
$355$		0			0
$356$	−11.6181	+	7.71712i	−0.615758	+	0.409006i
$357$	−10.4683	+	10.6340i	−0.554040	+	0.562811i
$358$	−12.4736	+	23.2599i	−0.659248	+	1.22932i
$359$	27.2920			1.44042			0.720209	−	0.693757i	$-0.244046\pi$
$359$	27.2920			1.44042			0.720209	+	0.693757i	$0.244046\pi$
$360$		0			0
$361$	−15.1292			−0.796272
$362$	13.3192	−	24.8367i	0.700039	−	1.30539i
$363$	13.6622	+	3.54603i	0.717081	+	0.186118i
$364$	9.14639	−	6.07533i	0.479401	−	0.318434i
$365$		0			0
$366$	1.51666	+	4.88545i	0.0792770	+	0.255366i
$367$	−27.2699	+	15.7443i	−1.42348	+	0.821846i	−0.996594	−	0.0824597i	$-0.973722\pi$
$367$	−27.2699	+	15.7443i	−1.42348	+	0.821846i	−0.426885	+	0.904306i	$0.640389\pi$
$368$	−0.244322	−	0.322035i	−0.0127361	−	0.0167873i
$369$	−12.1408	+	0.190695i	−0.632024	+	0.00992717i
$370$		0			0
$371$	−1.85199	−	3.20774i	−0.0961505	−	0.166538i
$372$	−15.8149	+	5.45889i	−0.819963	+	0.283030i
$373$	−11.7195	+	20.2988i	−0.606812	+	1.05103i	0.384950	+	0.922937i	$0.374219\pi$
$373$	−11.7195	+	20.2988i	−0.606812	+	1.05103i	−0.991762	+	0.128092i	$0.959115\pi$
$374$	1.25227	+	39.9210i	0.0647535	+	2.06426i
$375$		0			0
$376$	5.68893	+	8.00802i	0.293384	+	0.412982i
$377$			21.5240i			1.10854i
$378$	−6.54507	+	7.30652i	−0.336642	+	0.375807i
$379$			11.5529i			0.593434i	0.954965	+	0.296717i	$0.0958918\pi$
$379$			11.5529i			0.593434i	−0.954965	+	0.296717i	$0.904108\pi$
$380$		0			0
$381$	32.0258	−	8.85141i	1.64073	−	0.453472i
$382$	30.5969	−	0.959787i	1.56547	−	0.0491070i
$383$	−13.1068	+	22.7016i	−0.669725	+	1.16000i	0.308256	+	0.951304i	$0.400255\pi$
$383$	−13.1068	+	22.7016i	−0.669725	+	1.16000i	−0.977981	+	0.208695i	$0.933079\pi$
$384$	19.5843	+	0.674692i	0.999407	+	0.0344302i
$385$		0			0
$386$	−7.74920	−	12.4998i	−0.394424	−	0.636222i
$387$	−5.61323	+	10.0849i	−0.285337	+	0.512646i
$388$	−2.14256	+	4.31492i	−0.108772	+	0.219057i
$389$	1.38545	−	0.799888i	0.0702449	−	0.0405559i	−0.464466	−	0.885591i	$-0.653754\pi$
$389$	1.38545	−	0.799888i	0.0702449	−	0.0405559i	0.534711	+	0.845035i	$0.320420\pi$
$390$		0			0
$391$	0.564834	+	0.326107i	0.0285649	+	0.0164919i
$392$	−6.14619	+	13.4183i	−0.310430	+	0.677729i
$393$	−28.2133	−	7.32275i	−1.42317	−	0.369384i
$394$	10.1664	+	5.45190i	0.512174	+	0.274663i
$395$		0			0
$396$	2.05695	+	26.1752i	0.103366	+	1.31535i
$397$	−25.9373			−1.30176			−0.650879	−	0.759182i	$-0.725599\pi$
$397$	−25.9373			−1.30176			−0.650879	+	0.759182i	$0.725599\pi$
$398$	11.4433	+	6.13669i	0.573601	+	0.307605i
$399$	9.47576	−	9.62577i	0.474382	−	0.481891i
$400$		0			0
$401$	−21.5383	−	12.4351i	−1.07557	−	0.620980i	−0.145872	−	0.989304i	$-0.546599\pi$
$401$	−21.5383	−	12.4351i	−1.07557	−	0.620980i	−0.929698	+	0.368323i	$0.879932\pi$
$402$	0.778073	+	0.719328i	0.0388068	+	0.0358768i
$403$	−17.2024	+	9.93179i	−0.856911	+	0.494738i
$404$	8.12311	+	4.03351i	0.404140	+	0.200675i
$405$		0			0
$406$	5.20567	+	8.39696i	0.258353	+	0.416734i
$407$	7.09646	+	12.2914i	0.351759	+	0.609264i
$408$	−29.5491	+	11.2483i	−1.46290	+	0.556874i
$409$	10.6869	−	18.5102i	0.528433	−	0.915272i	−0.471018	−	0.882124i	$-0.656113\pi$
$409$	10.6869	−	18.5102i	0.528433	−	0.915272i	0.999450	−	0.0331484i	$-0.0105534\pi$
$410$		0			0
$411$	7.39963	+	7.28432i	0.364997	+	0.359309i
$412$	−0.489223	−	7.79025i	−0.0241023	−	0.383798i
$413$		−	3.66606i		−	0.180395i
$414$	0.380981	+	0.196668i	0.0187242	+	0.00966570i
$415$		0			0
$416$	22.9802	−	3.63295i	1.12670	−	0.178120i
$417$	0.103593	−	0.399124i	0.00507296	−	0.0195452i
$418$	−1.13354	−	36.1360i	−0.0554434	−	1.76747i
$419$	−3.12824	+	5.41826i	−0.152824	+	0.264700i	−0.932265	−	0.361777i	$-0.882170\pi$
$419$	−3.12824	+	5.41826i	−0.152824	+	0.264700i	0.779440	+	0.626476i	$0.215504\pi$
$420$		0			0
$421$	15.3599	+	26.6041i	0.748596	+	1.29661i	0.948496	+	0.316790i	$0.102605\pi$
$421$	15.3599	+	26.6041i	0.748596	+	1.29661i	−0.199900	+	0.979816i	$0.564062\pi$
$422$	−12.3121	+	7.63286i	−0.599344	+	0.371562i
$423$	−9.10375	−	5.06711i	−0.442639	−	0.246371i
$424$	−0.737236	−	7.81350i	−0.0358033	−	0.379457i
$425$		0			0
$426$	20.1113	+	4.55197i	0.974397	+	0.220544i
$427$	2.41425	+	1.39387i	0.116834	+	0.0674540i
$428$	−5.52001	−	8.31035i	−0.266820	−	0.401696i
$429$	8.30432	+	30.0463i	0.400936	+	1.45065i
$430$		0			0
$431$	35.1049			1.69094			0.845472	−	0.534020i	$-0.179319\pi$
$431$	35.1049			1.69094			0.845472	+	0.534020i	$0.179319\pi$
$432$	−19.0554	+	8.30003i	−0.916805	+	0.399335i
$433$	24.5043			1.17760			0.588800	−	0.808279i	$-0.299601\pi$
$433$	24.5043			1.17760			0.588800	+	0.808279i	$0.299601\pi$
$434$	−4.30895	+	8.03505i	−0.206836	+	0.385695i
$435$		0			0
$436$	−5.51823	−	8.30767i	−0.264275	−	0.397865i
$437$	−0.511281	−	0.295188i	−0.0244579	−	0.0141208i
$438$	17.3962	+	3.93744i	0.831225	+	0.188138i
$439$	−15.3741	+	8.87623i	−0.733765	+	0.423639i	−0.819798	−	0.572653i	$-0.805914\pi$
$439$	−15.3741	+	8.87623i	−0.733765	+	0.423639i	0.0860332	+	0.996292i	$0.472581\pi$
$440$		0			0
$441$	−0.245850	−	15.6523i	−0.0117072	−	0.745349i
$442$	−31.9049	+	19.7794i	−1.51756	+	0.940808i
$443$	−3.51442	−	6.08715i	−0.166975	−	0.289209i	0.770380	−	0.637585i	$-0.220067\pi$
$443$	−3.51442	−	6.08715i	−0.166975	−	0.289209i	−0.937355	+	0.348376i	$0.886733\pi$
$444$	−7.36463	+	8.48500i	−0.349510	+	0.402680i
$445$		0			0
$446$	1.03087	+	32.8630i	0.0488132	+	1.55611i
$447$	4.44612	−	17.1301i	0.210294	−	0.810227i
$448$	8.08640	−	6.97513i	0.382047	−	0.329544i
$449$		−	16.6756i		−	0.786971i	−0.919331	−	0.393485i	$-0.871269\pi$
$449$		−	16.6756i		−	0.786971i	0.919331	−	0.393485i	$-0.128731\pi$
$450$		0			0
$451$			17.7115i			0.834002i
$452$	2.55861	+	40.7426i	0.120347	+	1.91637i
$453$	18.5983	+	18.3085i	0.873823	+	0.860206i
$454$	24.0510	−	0.754451i	1.12877	−	0.0354081i
$455$		0			0
$456$	26.7475	−	10.1818i	1.25257	−	0.476808i
$457$	−14.8490	−	25.7193i	−0.694608	−	1.20310i	−0.970313	−	0.241854i	$-0.922244\pi$
$457$	−14.8490	−	25.7193i	−0.694608	−	1.20310i	0.275704	−	0.961242i	$-0.411089\pi$
$458$	1.11876	+	1.80460i	0.0522762	+	0.0843236i
$459$	23.1481	−	24.2652i	1.08046	−	1.13260i
$460$		0			0
$461$	12.2647	−	7.08100i	0.571222	−	0.329795i	−0.186415	−	0.982471i	$-0.559687\pi$
$461$	12.2647	−	7.08100i	0.571222	−	0.329795i	0.757637	+	0.652676i	$0.226354\pi$
$462$	10.5065	+	9.71325i	0.488806	+	0.451901i
$463$	4.94535	+	2.85520i	0.229830	+	0.132692i	0.610494	−	0.792021i	$-0.290971\pi$
$463$	4.94535	+	2.85520i	0.229830	+	0.132692i	−0.380664	+	0.924714i	$0.624304\pi$
$464$	2.61891	+	20.7691i	0.121580	+	0.964184i
$465$		0			0
$466$	−16.8854	−	9.05513i	−0.782202	−	0.419471i
$467$	−18.7968			−0.869813			−0.434907	−	0.900476i	$-0.643219\pi$
$467$	−18.7968			−0.869813			−0.434907	+	0.900476i	$0.643219\pi$
$468$	−20.3385	+	13.9748i	−0.940149	+	0.645984i
$469$	0.577464			0.0266648
$470$		0			0
$471$	−5.37099	−	1.39404i	−0.247482	−	0.0642340i
$472$	3.23482	−	7.06225i	0.148895	−	0.325067i
$473$	14.5801	+	8.41783i	0.670394	+	0.387052i
$474$	−6.98957	+	2.16987i	−0.321042	+	0.0996654i
$475$		0			0
$476$	−7.66304	+	15.4327i	−0.351235	+	0.707354i
$477$	4.27485	+	7.14278i	0.195732	+	0.327046i
$478$	−10.9140	−	17.6047i	−0.499193	−	0.805219i
$479$	−15.2061	−	26.3377i	−0.694783	−	1.20340i	−0.970254	−	0.242090i	$-0.922167\pi$
$479$	−15.2061	−	26.3377i	−0.694783	−	1.20340i	0.275471	−	0.961309i	$-0.411166\pi$
$480$		0			0
$481$	−6.66969	+	11.5522i	−0.304112	+	0.526737i
$482$	34.5630	−	1.08420i	1.57430	−	0.0493839i
$483$	0.225209	−	0.0622440i	0.0102474	−	0.00283220i
$484$	16.2665	−	1.02152i	0.739384	−	0.0464329i
$485$		0			0
$486$	14.4496	−	16.6496i	0.655448	−	0.755240i
$487$			3.67889i			0.166706i	0.996520	+	0.0833532i	$0.0265630\pi$
$487$			3.67889i			0.166706i	−0.996520	+	0.0833532i	$0.973437\pi$
$488$	3.42088	+	4.81540i	0.154856	+	0.217983i
$489$	17.7267	−	4.89938i	0.801630	−	0.221557i
$490$		0			0
$491$	−9.05671	+	15.6867i	−0.408724	+	0.707930i	−0.994747	−	0.102364i	$-0.967359\pi$
$491$	−9.05671	+	15.6867i	−0.408724	+	0.707930i	0.586023	+	0.810294i	$0.300693\pi$
$492$	−13.2534	+	4.57473i	−0.597509	+	0.206245i
$493$	−16.8880	−	29.2509i	−0.760597	−	1.31739i
$494$	28.8800	−	17.9040i	1.29937	−	0.805541i
$495$		0			0
$496$	−15.3906	+	11.6765i	−0.691059	+	0.524292i
$497$	9.73168	−	5.61859i	0.436525	−	0.252028i
$498$	9.73570	+	31.3606i	0.436267	+	1.40530i
$499$	−19.9488	−	11.5175i	−0.893032	−	0.515592i	−0.0180991	−	0.999836i	$-0.505761\pi$
$499$	−19.9488	−	11.5175i	−0.893032	−	0.515592i	−0.874933	+	0.484244i	$0.839095\pi$
$500$		0			0
$501$	21.1255	+	5.48311i	0.943816	+	0.244967i
$502$	−8.80951	+	16.4274i	−0.393188	+	0.733191i
$503$	−31.1266			−1.38787			−0.693934	−	0.720039i	$-0.744124\pi$
$503$	−31.1266			−1.38787			−0.693934	+	0.720039i	$0.744124\pi$
$504$	−4.55462	+	10.3708i	−0.202879	+	0.461951i
$505$		0			0
$506$	0.295564	−	0.551149i	0.0131394	−	0.0245016i
$507$	−4.75741	+	4.83272i	−0.211284	+	0.214629i
$508$	31.9588	−	21.2281i	1.41794	−	0.941845i
$509$	0.489681	+	0.282717i	0.0217047	+	0.0125312i	0.510813	−	0.859692i	$-0.329344\pi$
$509$	0.489681	+	0.282717i	0.0217047	+	0.0125312i	−0.489108	+	0.872223i	$0.662678\pi$
$510$		0			0
$511$	8.41787	−	4.86006i	0.372385	−	0.214996i
$512$	21.7322	−	6.30162i	0.960438	−	0.278495i
$513$	−20.9534	+	21.9646i	−0.925113	+	0.969762i
$514$	8.37793	−	5.19387i	0.369535	−	0.229092i
$515$		0			0
$516$	−2.53308	+	13.0844i	−0.111513	+	0.576010i
$517$	−7.59884	+	13.1616i	−0.334196	+	0.578845i
$518$	0.191972	+	6.11985i	0.00843477	+	0.268891i
$519$	−2.11851	−	2.08550i	−0.0929923	−	0.0915431i
$520$		0			0
$521$		−	4.80678i		−	0.210589i	−0.994441	−	0.105294i	$-0.966422\pi$
$521$		−	4.80678i		−	0.210589i	0.994441	−	0.105294i	$-0.0335785\pi$
$522$	−11.9941	−	18.6852i	−0.524967	−	0.817827i
$523$		−	19.6207i		−	0.857954i	−0.903315	−	0.428977i	$-0.858874\pi$
$523$		−	19.6207i		−	0.857954i	0.903315	−	0.428977i	$-0.141126\pi$
$524$	−33.5911	+	2.10950i	−1.46744	+	0.0921540i
$525$		0			0
$526$	22.8196	−	0.715822i	0.994980	−	0.0312113i
$527$	15.5852	−	26.9943i	0.678902	−	1.17589i
$528$	11.6689	+	27.9821i	0.507824	+	1.21777i
$529$	11.4949	+	19.9097i	0.499778	+	0.865641i
$530$		0			0
$531$	0.129394	+	8.23803i	0.00561523	+	0.357500i
$532$	6.93650	−	13.9695i	0.300735	−	0.605653i
$533$	−14.4162	+	8.32317i	−0.624433	+	0.360517i
$534$	3.77097	−	16.6608i	0.163186	−	0.720981i
$535$		0			0
$536$	1.11242	+	0.509538i	0.0480493	+	0.0220087i
$537$	−8.61131	−	31.1571i	−0.371606	−	1.34453i
$538$	−27.1240	−	14.5458i	−1.16940	−	0.627112i
$539$	−22.8343			−0.983542
$540$		0			0
$541$	40.3065			1.73291			0.866457	−	0.499252i	$-0.166392\pi$
$541$	40.3065			1.73291			0.866457	+	0.499252i	$0.166392\pi$
$542$	−37.5823	−	20.1542i	−1.61430	−	0.865699i
$543$	9.19508	+	33.2692i	0.394599	+	1.42772i
$544$	−28.3793	+	22.9677i	−1.21675	+	0.984730i
$545$		0			0
$546$	−2.96871	+	13.1162i	−0.127049	+	0.561324i
$547$	2.49763	−	1.44201i	0.106791	−	0.0616557i	−0.445653	−	0.895206i	$-0.647029\pi$
$547$	2.49763	−	1.44201i	0.106791	−	0.0616557i	0.552444	+	0.833550i	$0.313695\pi$
$548$	10.7388	+	5.33231i	0.458737	+	0.227785i
$549$	−5.47428	−	3.04696i	−0.233637	−	0.130041i
$550$		0			0
$551$	15.2868	+	26.4775i	0.651240	+	1.12798i
$552$	0.488762	+	0.0788115i	0.0208031	+	0.00335444i
$553$	−1.99419	+	3.45405i	−0.0848018	+	0.146881i
$554$	−18.3807	+	0.576582i	−0.780923	+	0.0244966i
$555$		0			0
$556$	−0.0298425	−	0.475204i	−0.00126560	−	0.0201531i
$557$			17.0510i			0.722475i	0.932474	+	0.361237i	$0.117646\pi$
$557$			17.0510i			0.722475i	−0.932474	+	0.361237i	$0.882354\pi$
$558$	9.39909	−	18.2077i	0.397895	−	0.770795i
$559$			15.8232i			0.669249i
$560$		0			0
$561$	−34.8601	−	34.3169i	−1.47180	−	1.44886i
$562$	−0.0479585	−	1.52886i	−0.00202301	−	0.0644910i
$563$	11.0182	−	19.0842i	0.464364	−	0.804302i	−0.534809	−	0.844973i	$-0.679616\pi$
$563$	11.0182	−	19.0842i	0.464364	−	0.804302i	0.999173	+	0.0406715i	$0.0129497\pi$
$564$	−11.8114	−	2.28663i	−0.497351	−	0.0962847i
$565$		0			0
$566$	35.1357	−	21.7822i	1.47686	−	0.915576i
$567$	−0.377311	−	12.0080i	−0.0158456	−	0.504289i
$568$	23.7047	−	2.23663i	0.994627	−	0.0938470i
$569$	24.1641	−	13.9512i	1.01301	−	0.584864i	0.100941	−	0.994892i	$-0.467815\pi$
$569$	24.1641	−	13.9512i	1.01301	−	0.584864i	0.912073	+	0.410029i	$0.134481\pi$
$570$		0			0
$571$	−11.2510	−	6.49576i	−0.470839	−	0.271839i	0.245752	−	0.969333i	$-0.420965\pi$
$571$	−11.2510	−	6.49576i	−0.470839	−	0.271839i	−0.716591	+	0.697494i	$0.754298\pi$
$572$	19.9160	+	29.9835i	0.832731	+	1.25367i
$573$	−26.3017	+	26.7181i	−1.09877	+	1.11616i
$574$	−3.61104	+	6.73364i	−0.150722	+	0.281057i
$575$		0			0
$576$	−17.9249	+	15.9593i	−0.746869	+	0.664971i
$577$	34.6251			1.44146			0.720730	−	0.693216i	$-0.243807\pi$
$577$	34.6251			1.44146			0.720730	+	0.693216i	$0.243807\pi$
$578$	16.4772	−	30.7255i	0.685359	−	1.27801i
$579$	17.4346	+	4.52515i	0.724557	+	0.188059i
$580$		0			0
$581$	15.4975	+	8.94748i	0.642944	+	0.371204i
$582$	−1.74936	−	5.63502i	−0.0725132	−	0.233579i
$583$	10.5156	−	6.07116i	0.435510	−	0.251442i
$584$	20.5045	−	1.93468i	0.848482	−	0.0800577i
$585$		0			0
$586$	−6.76835	+	4.19601i	−0.279598	+	0.173336i
$587$	−5.43407	−	9.41209i	−0.224288	−	0.388479i	0.731817	−	0.681501i	$-0.238672\pi$
$587$	−5.43407	−	9.41209i	−0.224288	−	0.388479i	−0.956106	+	0.293022i	$0.905339\pi$
$588$	−5.89790	−	17.0867i	−0.243225	−	0.704645i
$589$	−14.1075	+	24.4350i	−0.581291	+	1.00683i
$590$		0			0
$591$	−13.6180	+	3.76380i	−0.560171	+	0.154822i
$592$	−5.03017	+	11.9586i	−0.206739	+	0.491496i
$593$			4.49540i			0.184604i	0.995731	+	0.0923019i	$0.0294225\pi$
$593$			4.49540i			0.184604i	−0.995731	+	0.0923019i	$0.970578\pi$
$594$	−23.9521	−	21.4559i	−0.982767	−	0.880347i
$595$		0			0
$596$	−1.28082	−	20.3954i	−0.0524643	−	0.835427i
$597$	−15.3285	+	4.23656i	−0.627355	+	0.173391i
$598$	0.587499	−	0.0184291i	0.0240246	−	0.000753623i
$599$	3.45192	−	5.97890i	0.141042	−	0.244291i	−0.786847	−	0.617148i	$-0.788288\pi$
$599$	3.45192	−	5.97890i	0.141042	−	0.244291i	0.927889	+	0.372856i	$0.121621\pi$
$600$		0			0
$601$	−15.7058	−	27.2032i	−0.640653	−	1.10964i	−0.985287	−	0.170906i	$-0.945331\pi$
$601$	−15.7058	−	27.2032i	−0.640653	−	1.10964i	0.344635	−	0.938737i	$-0.388003\pi$
$602$	3.82689	+	6.17294i	0.155973	+	0.251590i
$603$	−1.29763	+	0.0203817i	−0.0528434	+	0.000830008i
$604$	26.9909	+	13.4022i	1.09824	+	0.545330i
$605$		0			0
$606$	−10.6083	+	3.29327i	−0.430932	+	0.133780i
$607$	16.9977	+	9.81362i	0.689915	+	0.398322i	0.803580	−	0.595197i	$-0.202926\pi$
$607$	16.9977	+	9.81362i	0.689915	+	0.398322i	−0.113665	+	0.993519i	$0.536259\pi$
$608$	25.6887	−	20.7901i	1.04181	−	0.843148i
$609$	−11.7120	−	3.03985i	−0.474594	−	0.123181i
$610$		0			0
$611$	−14.2837			−0.577857
$612$	16.6750	−	34.9494i	0.674047	−	1.41274i
$613$	28.8088			1.16358			0.581788	−	0.813340i	$-0.302353\pi$
$613$	28.8088			1.16358			0.581788	+	0.813340i	$0.302353\pi$
$614$	19.0600	+	10.2213i	0.769200	+	0.412499i
$615$		0			0
$616$	15.0213	+	6.88040i	0.605224	+	0.277219i
$617$	13.8957	+	8.02269i	0.559420	+	0.322981i	0.752913	−	0.658120i	$-0.228648\pi$
$617$	13.8957	+	8.02269i	0.559420	+	0.322981i	−0.193493	+	0.981102i	$0.561982\pi$
$618$	7.01965	+	6.48966i	0.282372	+	0.261052i
$619$	2.13387	−	1.23199i	0.0857674	−	0.0495178i	−0.456503	−	0.889722i	$-0.650898\pi$
$619$	2.13387	−	1.23199i	0.0857674	−	0.0495178i	0.542270	+	0.840204i	$0.317565\pi$
$620$		0			0
$621$	−0.503872	+	0.147818i	−0.0202197	+	0.00593173i
$622$	2.73350	+	4.40924i	0.109603	+	0.176795i
$623$	−4.65458	−	8.06198i	−0.186482	−	0.322996i
$624$	−17.2923	+	22.6475i	−0.692246	+	0.906626i
$625$		0			0
$626$	34.8148	−	1.09210i	1.39148	−	0.0436490i
$627$	31.5550	+	31.0633i	1.26019	+	1.24055i
$628$	−6.39478	+	0.401588i	−0.255179	+	0.0160251i
$629$		−	20.9324i		−	0.834631i
$630$		0			0
$631$		−	44.4737i		−	1.77047i	−0.465144	−	0.885235i	$-0.653997\pi$
$631$		−	44.4737i		−	1.77047i	0.465144	−	0.885235i	$-0.346003\pi$
$632$	−6.88935	+	4.89422i	−0.274044	+	0.194682i
$633$	4.45721	−	17.1728i	0.177158	−	0.682559i
$634$	−0.472194	−	15.0530i	−0.0187532	−	0.597831i
$635$		0			0
$636$	7.25908	+	6.30058i	0.287841	+	0.249834i
$637$	−10.7305	−	18.5858i	−0.425159	−	0.736397i
$638$	−27.5267	+	17.0651i	−1.08979	+	0.675614i
$639$	−21.6698	+	12.9691i	−0.857246	+	0.513048i
$640$		0			0
$641$	−14.1935	+	8.19465i	−0.560611	+	0.323669i	−0.753391	−	0.657573i	$-0.771583\pi$
$641$	−14.1935	+	8.19465i	−0.560611	+	0.323669i	0.192779	+	0.981242i	$0.438250\pi$
$642$	11.9173	+	2.69735i	0.470340	+	0.106456i
$643$	−30.3987	−	17.5507i	−1.19881	−	0.692133i	−0.238520	−	0.971138i	$-0.576662\pi$
$643$	−30.3987	−	17.5507i	−1.19881	−	0.692133i	−0.960290	+	0.279005i	$0.909995\pi$
$644$	0.224738	−	0.149278i	0.00885591	−	0.00588239i
$645$		0			0
$646$	−25.1998	+	46.9909i	−0.991472	+	1.84883i
$647$	−19.0579			−0.749243			−0.374621	−	0.927178i	$-0.622227\pi$
$647$	−19.0579			−0.749243			−0.374621	+	0.927178i	$0.622227\pi$
$648$	9.86869	−	23.4651i	0.387679	−	0.921795i
$649$	12.0180			0.471747
$650$		0			0
$651$	−2.97475	−	10.7631i	−0.116590	−	0.421839i
$652$	17.6896	−	11.7500i	0.692780	−	0.460167i
$653$	36.4956	+	21.0708i	1.42818	+	0.824563i	0.996978	−	0.0776903i	$-0.0247545\pi$
$653$	36.4956	+	21.0708i	1.42818	+	0.824563i	0.431207	+	0.902253i	$0.358088\pi$
$654$	11.9135	+	2.69648i	0.465854	+	0.105441i
$655$		0			0
$656$	−12.8978	+	9.78533i	−0.503576	+	0.382053i
$657$	−18.7444	+	11.2182i	−0.731287	+	0.437664i
$658$	−5.57236	+	3.45456i	−0.217233	+	0.134673i
$659$	−10.0696	−	17.4410i	−0.392256	−	0.679407i	0.600491	−	0.799631i	$-0.294972\pi$
$659$	−10.0696	−	17.4410i	−0.392256	−	0.679407i	−0.992747	+	0.120225i	$0.961638\pi$
$660$		0			0
$661$	3.54725	−	6.14402i	0.137972	−	0.238975i	−0.788757	−	0.614705i	$-0.789275\pi$
$661$	3.54725	−	6.14402i	0.137972	−	0.238975i	0.926729	+	0.375731i	$0.122608\pi$
$662$	0.155946	+	4.97136i	0.00606100	+	0.193218i
$663$	11.5502	−	44.5007i	0.448571	−	1.72827i
$664$	21.9592	+	30.9109i	0.852183	+	1.19958i
$665$		0			0
$666$	−0.647384	−	13.7452i	−0.0250856	−	0.532616i
$667$			0.528872i			0.0204780i
$668$	25.1523	−	1.57955i	0.973171	−	0.0611145i
$669$	−28.6969	−	28.2497i	−1.10949	−	1.09220i
$670$		0			0
$671$	−4.56935	+	7.91434i	−0.176398	+	0.305530i
$672$	−1.26869	+	13.0174i	−0.0489409	+	0.502159i
$673$	−11.4551	−	19.8408i	−0.441561	−	0.764806i	0.556245	−	0.831018i	$-0.312242\pi$
$673$	−11.4551	−	19.8408i	−0.441561	−	0.764806i	−0.997806	+	0.0662129i	$0.978908\pi$
$674$	−17.5325	−	28.2807i	−0.675327	−	1.08933i
$675$		0			0
$676$	−3.48254	+	7.01351i	−0.133944	+	0.269750i
$677$	20.1311	−	11.6227i	0.773699	−	0.446696i	−0.0604934	−	0.998169i	$-0.519267\pi$
$677$	20.1311	−	11.6227i	0.773699	−	0.446696i	0.834193	+	0.551473i	$0.185934\pi$
$678$	−36.7124	−	33.9406i	−1.40993	−	1.30348i
$679$	−2.78467	−	1.60773i	−0.106866	−	0.0616989i
$680$		0			0
$681$	−20.6748	+	21.0020i	−0.792258	+	0.804800i
$682$	−26.3403	−	14.1255i	−1.00862	−	0.540894i
$683$	30.3578			1.16161			0.580804	−	0.814043i	$-0.302738\pi$
$683$	30.3578			1.16161			0.580804	+	0.814043i	$0.302738\pi$
$684$	−15.0940	+	31.6357i	−0.577134	+	1.20962i
$685$		0			0
$686$	−20.3270	−	10.9007i	−0.776089	−	0.416193i
$687$	−2.51705	−	0.653300i	−0.0960313	−	0.0249249i
$688$	1.92526	+	15.2682i	0.0734000	+	0.582096i
$689$	9.88316	+	5.70604i	0.376518	+	0.217383i
$690$		0			0
$691$	10.6015	−	6.12077i	0.403299	−	0.232845i	−0.284607	−	0.958644i	$-0.591863\pi$
$691$	10.6015	−	6.12077i	0.403299	−	0.232845i	0.687907	+	0.725799i	$0.258530\pi$
$692$	−3.07450	−	1.52664i	−0.116875	−	0.0580340i
$693$	−17.5221	+	0.275219i	−0.665610	+	0.0104547i
$694$	3.12464	+	5.04018i	0.118610	+	0.191323i
$695$		0			0
$696$	−19.8796	−	16.1903i	−0.753535	−	0.613691i
$697$	13.0609	−	22.6222i	0.494717	−	0.856875i
$698$	7.86477	−	0.246708i	0.297686	−	0.00933804i
$699$	22.6184	−	6.25134i	0.855505	−	0.236448i
$700$		0			0
$701$			0.0365464i			0.00138034i	1.00000		0.000690169i	$0.000219688\pi$
$701$			0.0365464i			0.00138034i	−1.00000		0.000690169i	$0.999780\pi$
$702$	6.20808	−	29.5784i	0.234309	−	1.11637i
$703$			18.9478i			0.714630i
$704$	22.8657	+	26.5087i	0.861785	+	0.999083i
$705$		0			0
$706$	0.488727	+	15.5801i	0.0183935	+	0.586363i
$707$	−3.02665	+	5.24231i	−0.113829	+	0.197157i
$708$	3.10414	+	8.99297i	0.116661	+	0.337977i
$709$	−13.6359	−	23.6181i	−0.512109	−	0.886998i	−0.999901	−	0.0140387i	$-0.995531\pi$
$709$	−13.6359	−	23.6181i	−0.512109	−	0.886998i	0.487793	−	0.872959i	$-0.337802\pi$
$710$		0			0
$711$	4.35927	−	7.83201i	0.163485	−	0.293723i
$712$	−1.85289	−	19.6376i	−0.0694398	−	0.735950i
$713$	−0.422683	+	0.244036i	−0.0158296	+	0.00913923i
$714$	−6.25671	−	20.1541i	−0.234152	−	0.754248i
$715$		0			0
$716$	−20.6523	−	31.0919i	−0.771812	−	1.16196i
$717$	24.5548	+	6.37321i	0.917017	+	0.238012i
$718$	−18.2409	+	34.0144i	−0.680743	+	1.26941i
$719$	7.73269			0.288381			0.144190	−	0.989550i	$-0.453942\pi$
$719$	7.73269			0.288381			0.144190	+	0.989550i	$0.453942\pi$
$720$		0			0
$721$	5.20978			0.194022
$722$	10.1117	−	18.8557i	0.376319	−	0.701735i
$723$	−29.7110	+	30.1814i	−1.10497	+	1.12246i
$724$	22.0523	+	33.1997i	0.819568	+	1.23386i
$725$		0			0
$726$	−13.5507	+	14.6574i	−0.502915	+	0.543987i
$727$	14.2887	−	8.24957i	0.529938	−	0.305960i	−0.211053	−	0.977475i	$-0.567689\pi$
$727$	14.2887	−	8.24957i	0.529938	−	0.305960i	0.740991	+	0.671515i	$0.234356\pi$
$728$	1.45869	+	15.4598i	0.0540627	+	0.572977i
$729$	1.27169	+	26.9700i	0.0470995	+	0.998890i
$730$		0			0
$731$	−12.4150	−	21.5035i	−0.459187	−	0.795335i
$732$	−7.10247	−	1.37500i	−0.262515	−	0.0508216i
$733$	21.4427	−	37.1399i	0.792006	−	1.37179i	−0.132717	−	0.991154i	$-0.542370\pi$
$733$	21.4427	−	37.1399i	0.792006	−	1.37179i	0.924723	−	0.380641i	$-0.124297\pi$
$734$	−1.39622	−	44.5097i	−0.0515353	−	1.64288i
$735$		0			0
$736$	0.564652	−	0.0892658i	0.0208133	−	0.00329038i
$737$			1.89303i			0.0697307i
$738$	7.87675	−	15.2587i	0.289947	−	0.561680i
$739$			3.04457i			0.111996i	0.998431	+	0.0559981i	$0.0178341\pi$
$739$			3.04457i			0.111996i	−0.998431	+	0.0559981i	$0.982166\pi$
$740$		0			0
$741$	−10.4551	+	40.2816i	−0.384077	+	1.47978i
$742$	5.23564	−	0.164236i	0.192207	−	0.00602928i
$743$	20.2194	−	35.0211i	0.741779	−	1.28480i	−0.209905	−	0.977722i	$-0.567316\pi$
$743$	20.2194	−	35.0211i	0.741779	−	1.28480i	0.951684	−	0.307078i	$-0.0993511\pi$
$744$	3.76654	−	23.3588i	0.138088	−	0.856374i
$745$		0			0
$746$	−17.4658	−	28.1730i	−0.639467	−	1.03149i
$747$	−35.1404	−	19.5590i	−1.28572	−	0.715626i
$748$	−50.5910	−	25.1208i	−1.84979	−	0.918509i
$749$	5.76668	−	3.32940i	0.210710	−	0.121653i
$750$		0			0
$751$	12.0862	+	6.97795i	0.441030	+	0.254629i	0.704034	−	0.710166i	$-0.251380\pi$
$751$	12.0862	+	6.97795i	0.441030	+	0.254629i	−0.263004	+	0.964795i	$0.584713\pi$
$752$	−13.7827	+	1.73795i	−0.502605	+	0.0633765i
$753$	−6.08178	−	22.0048i	−0.221632	−	0.801901i
$754$	−26.8257	−	14.3858i	−0.976934	−	0.523900i
$755$		0			0
$756$	−4.73176	−	13.0406i	−0.172092	−	0.474282i
$757$	31.7859			1.15528			0.577639	−	0.816293i	$-0.303974\pi$
$757$	31.7859			1.15528			0.577639	+	0.816293i	$0.303974\pi$
$758$	−14.3986	−	7.72151i	−0.522979	−	0.280458i
$759$	0.204047	+	0.738275i	0.00740644	+	0.0267977i
$760$		0			0
$761$	−21.6921	−	12.5240i	−0.786339	−	0.453993i	0.0523332	−	0.998630i	$-0.483334\pi$
$761$	−21.6921	−	12.5240i	−0.786339	−	0.453993i	−0.838672	+	0.544637i	$0.816668\pi$
$762$	−10.3731	+	45.8301i	−0.375778	+	1.66025i
$763$	5.76482	−	3.32832i	0.208700	−	0.120493i
$764$	−19.2535	+	38.7748i	−0.696568	+	1.40282i
$765$		0			0
$766$	−19.5333	−	31.5080i	−0.705766	−	1.13843i
$767$	5.64762	+	9.78196i	0.203924	+	0.353206i
$768$	−13.9302	+	23.9572i	−0.502664	+	0.864482i
$769$	1.59810	−	2.76799i	0.0576290	−	0.0998164i	−0.835772	−	0.549077i	$-0.814979\pi$
$769$	1.59810	−	2.76799i	0.0576290	−	0.0998164i	0.893401	+	0.449261i	$0.148313\pi$
$770$		0			0
$771$	−3.03296	+	11.6855i	−0.109230	+	0.420842i
$772$	20.7579	−	1.30358i	0.747093	−	0.0469170i
$773$		−	26.8609i		−	0.966121i	−0.875587	−	0.483060i	$-0.839525\pi$
$773$		−	26.8609i		−	0.966121i	0.875587	−	0.483060i	$-0.160475\pi$
$774$	−8.81733	−	13.7362i	−0.316932	−	0.493738i
$775$		0			0
$776$	−3.94574	−	5.55422i	−0.141644	−	0.199385i
$777$	−5.34403	−	5.26075i	−0.191716	−	0.188728i
$778$	0.0709346	+	2.26131i	0.00254313	+	0.0810720i
$779$	−11.8226	+	20.4773i	−0.423588	+	0.733676i
$780$		0			0
$781$	18.4187	+	31.9022i	0.659074	+	1.14155i
$782$	−0.783943	+	0.486003i	−0.0280337	+	0.0173794i
$783$	26.4255	+	6.41751i	0.944369	+	0.229343i
$784$	−12.6156	−	16.6284i	−0.450557	−	0.593870i
$785$		0			0
$786$	27.9830	−	30.2683i	0.998122	−	1.07964i
$787$	−29.1883	−	16.8518i	−1.04045	−	0.600703i	−0.120488	−	0.992715i	$-0.538446\pi$
$787$	−29.1883	−	16.8518i	−1.04045	−	0.600703i	−0.919960	+	0.392011i	$0.871779\pi$
$788$	−13.5896	+	9.02663i	−0.484108	+	0.321560i
$789$	−19.6162	+	19.9267i	−0.698354	+	0.709409i
$790$		0			0
$791$	−27.2469			−0.968787
$792$	−33.9973	−	14.9308i	−1.20804	−	0.530545i
$793$	−8.58910			−0.305008
$794$	17.3355	−	32.3260i	0.615212	−	1.14721i
$795$		0			0
$796$	−15.2965	+	10.1604i	−0.542169	+	0.360127i
$797$	−25.0624	−	14.4698i	−0.887755	−	0.512546i	−0.0145477	−	0.999894i	$-0.504631\pi$
$797$	−25.0624	−	14.4698i	−0.887755	−	0.512546i	−0.873208	+	0.487348i	$0.837964\pi$
$798$	5.66350	+	18.2432i	0.200486	+	0.645804i
$799$	19.4113	−	11.2071i	0.686724	−	0.396480i
$800$		0			0
$801$	10.7439	+	17.9519i	0.379618	+	0.634298i
$802$	29.8934	−	18.5323i	1.05557	−	0.654398i
$803$	15.9322	+	27.5953i	0.562233	+	0.973817i
$804$	−1.41654	+	0.488953i	−0.0499575	+	0.0172441i
$805$		0			0
$806$	−0.880759	−	28.0775i	−0.0310234	−	0.988989i
$807$	36.3331	−	10.0419i	1.27899	−	0.353491i
$808$	−10.4562	+	7.42810i	−0.367847	+	0.261320i
$809$		−	14.9996i		−	0.527358i	−0.964610	−	0.263679i	$-0.915064\pi$
$809$		−	14.9996i		−	0.527358i	0.964610	−	0.263679i	$-0.0849360\pi$
$810$		0			0
$811$		−	17.4677i		−	0.613376i	−0.951810	−	0.306688i	$-0.900779\pi$
$811$		−	17.4677i		−	0.613376i	0.951810	−	0.306688i	$-0.0992207\pi$
$812$	−13.9445	+	0.875705i	−0.489356	+	0.0307312i
$813$	50.3423	−	13.9138i	1.76558	−	0.487978i
$814$	−20.0620	+	0.629319i	−0.703171	+	0.0220576i
$815$		0			0
$816$	5.73052	−	44.3454i	0.200608	−	1.55240i
$817$	11.2379	+	19.4647i	0.393166	+	0.680984i
$818$	15.9269	+	25.6907i	0.556870	+	0.898254i
$819$	−8.45819	−	14.1327i	−0.295553	−	0.493836i
$820$		0			0
$821$	15.8290	−	9.13886i	0.552435	−	0.318948i	−0.197669	−	0.980269i	$-0.563337\pi$
$821$	15.8290	−	9.13886i	0.552435	−	0.318948i	0.750103	+	0.661320i	$0.230004\pi$
$822$	−14.0242	+	4.35372i	−0.489149	+	0.151853i
$823$	25.3518	+	14.6369i	0.883710	+	0.510210i	0.871880	−	0.489720i	$-0.162901\pi$
$823$	25.3518	+	14.6369i	0.883710	+	0.510210i	0.0118300	+	0.999930i	$0.496234\pi$
$824$	10.0361	+	4.59696i	0.349623	+	0.160143i
$825$		0			0
$826$	4.56905	+	2.45024i	0.158978	+	0.0852548i
$827$	24.5270			0.852886			0.426443	−	0.904514i	$-0.359767\pi$
$827$	24.5270			0.852886			0.426443	+	0.904514i	$0.359767\pi$
$828$	−0.499742	+	0.343377i	−0.0173672	+	0.0119332i
$829$	42.2094			1.46599			0.732996	−	0.680233i	$-0.238121\pi$
$829$	42.2094			1.46599			0.732996	+	0.680233i	$0.238121\pi$
$830$		0			0
$831$	15.8005	−	16.0506i	0.548112	−	0.556789i
$832$	−10.8313	+	31.0687i	−0.375506	+	1.07711i
$833$	29.1653	+	16.8386i	1.01052	+	0.583422i
$834$	0.428197	+	0.395868i	0.0148272	+	0.0137078i
$835$		0			0
$836$	45.7944	+	22.7391i	1.58383	+	0.786448i
$837$	7.06447	+	24.0809i	0.244184	+	0.832358i
$838$	−4.66207	−	7.52011i	−0.161048	−	0.259778i
$839$	18.2179	+	31.5544i	0.628953	+	1.08938i	0.987762	+	0.155967i	$0.0498494\pi$
$839$	18.2179	+	31.5544i	0.628953	+	1.08938i	−0.358810	+	0.933411i	$0.616817\pi$
$840$		0			0
$841$	−0.805742	+	1.39559i	−0.0277842	+	0.0481237i
$842$	−43.4230	+	1.36213i	−1.49646	+	0.0469420i
$843$	1.33504	+	1.31424i	0.0459814	+	0.0452648i
$844$	−1.28401	−	20.4462i	−0.0441975	−	0.703788i
$845$		0			0
$846$	12.3998	−	7.95947i	0.426313	−	0.273652i
$847$			10.8783i			0.373783i
$848$	10.2308	+	4.30340i	0.351327	+	0.147779i
$849$	−12.7197	+	49.0069i	−0.436541	+	1.68191i
$850$		0			0
$851$	−0.163882	+	0.283852i	−0.00561781	+	0.00973033i
$852$	−19.1148	+	22.0227i	−0.654861	+	0.754484i
$853$	−15.6536	−	27.1128i	−0.535968	−	0.928324i	−0.999116	−	0.0420430i	$-0.986613\pi$
$853$	−15.6536	−	27.1128i	−0.535968	−	0.928324i	0.463148	−	0.886281i	$-0.346720\pi$
$854$	−3.35078	+	2.07731i	−0.114661	+	0.0710839i
$855$		0			0
$856$	14.0466	−	1.32536i	0.480104	−	0.0452998i
$857$	7.97029	−	4.60165i	0.272260	−	0.157189i	−0.357654	−	0.933854i	$-0.616423\pi$
$857$	7.97029	−	4.60165i	0.272260	−	0.157189i	0.629914	+	0.776665i	$0.283090\pi$
$858$	−42.9974	−	9.73197i	−1.46791	−	0.332244i
$859$	−4.62482	−	2.67014i	−0.157797	−	0.0911040i	0.419022	−	0.907976i	$-0.362373\pi$
$859$	−4.62482	−	2.67014i	−0.157797	−	0.0911040i	−0.576819	+	0.816872i	$0.695706\pi$
$860$		0			0
$861$	−2.49294	−	9.01984i	−0.0849590	−	0.307395i
$862$	−23.4627	+	43.7517i	−0.799142	+	1.49019i
$863$	−19.0360			−0.647992			−0.323996	−	0.946058i	$-0.605026\pi$
$863$	−19.0360			−0.647992			−0.323996	+	0.946058i	$0.605026\pi$
$864$	2.39144	−	29.2964i	0.0813584	−	0.996685i
$865$		0			0
$866$	−16.3776	+	30.5400i	−0.556535	+	1.03779i
$867$	11.3753	+	41.1575i	0.386324	+	1.39778i
$868$	−7.13426	−	10.7406i	−0.242152	−	0.364560i
$869$	−11.3230	−	6.53733i	−0.384106	−	0.221764i
$870$		0			0
$871$	−1.54082	+	0.889593i	−0.0522087	+	0.0301427i
$872$	14.0421	−	1.32493i	0.475526	−	0.0448678i
$873$	6.31420	+	3.51446i	0.213703	+	0.118946i
$874$	0.709616	−	0.439924i	0.0240031	−	0.0148807i
$875$		0			0
$876$	−16.5342	+	19.0495i	−0.558640	+	0.643624i
$877$	12.1891	−	21.1121i	0.411595	−	0.712904i	−0.583469	−	0.812135i	$-0.698305\pi$
$877$	12.1891	−	21.1121i	0.411595	−	0.712904i	0.995064	+	0.0992316i	$0.0316385\pi$
$878$	−0.787150	−	25.0934i	−0.0265650	−	0.846862i
$879$	2.45026	−	9.44043i	0.0826454	−	0.318418i
$880$		0			0
$881$		−	42.8577i		−	1.44391i	−0.691939	−	0.721956i	$-0.743243\pi$
$881$		−	42.8577i		−	1.44391i	0.691939	−	0.721956i	$-0.256757\pi$
$882$	19.6720	+	10.1550i	0.662391	+	0.341936i
$883$			28.8663i			0.971427i	0.874118	+	0.485713i	$0.161440\pi$
$883$			28.8663i			0.971427i	−0.874118	+	0.485713i	$0.838560\pi$
$884$	−3.32732	−	52.9833i	−0.111910	−	1.78202i
$885$		0			0
$886$	9.93539	−	0.311661i	0.333786	−	0.0104705i
$887$	−7.59206	+	13.1498i	−0.254917	+	0.441528i	−0.964873	−	0.262717i	$-0.915381\pi$
$887$	−7.59206	+	13.1498i	−0.254917	+	0.441528i	0.709956	+	0.704246i	$0.248715\pi$
$888$	−5.65274	−	14.8497i	−0.189694	−	0.498322i
$889$	12.8037	+	22.1767i	0.429424	+	0.743784i
$890$		0			0
$891$	39.3644	−	1.23689i	1.31876	−	0.0414375i
$892$	−41.6465	−	20.6795i	−1.39443	−	0.692400i
$893$	−17.5709	+	10.1446i	−0.587989	+	0.339475i
$894$	18.3779	+	16.9903i	0.614648	+	0.568242i
$895$		0			0
$896$	3.28858	+	14.7401i	0.109864	+	0.492432i
$897$	−0.505026	+	0.513021i	−0.0168623	+	0.0171293i
$898$	20.7830	+	11.1453i	0.693539	+	0.371923i
$899$	25.2757			0.842990
$900$		0			0
$901$	−17.9081			−0.596605
$902$	−22.0741	−	11.8376i	−0.734986	−	0.394150i
$903$	−8.60996	−	2.23472i	−0.286522	−	0.0743667i
$904$	−52.4881	−	24.0419i	−1.74573	−	0.799621i
$905$		0			0
$906$	−35.2484	+	10.9427i	−1.17105	+	0.363545i
$907$	−23.4865	+	13.5599i	−0.779856	+	0.450250i	−0.836379	−	0.548151i	$-0.815332\pi$
$907$	−23.4865	+	13.5599i	−0.779856	+	0.450250i	0.0565230	+	0.998401i	$0.481999\pi$
$908$	−15.1344	+	30.4793i	−0.502254	+	1.01149i
$909$	6.61619	−	11.8869i	0.219445	−	0.394263i
$910$		0			0
$911$	−3.77888	−	6.54521i	−0.125200	−	0.216852i	0.796611	−	0.604492i	$-0.206624\pi$
$911$	−3.77888	−	6.54521i	−0.125200	−	0.216852i	−0.921811	+	0.387640i	$0.873291\pi$
$912$	−5.18720	+	40.1409i	−0.171765	+	1.32920i
$913$	−29.3315	+	50.8036i	−0.970729	+	1.68135i
$914$	41.9787	−	1.31682i	1.38853	−	0.0435566i
$915$		0			0
$916$	−2.99683	+	0.188199i	−0.0990182	+	0.00621828i
$917$		−	22.4643i		−	0.741836i
$918$	14.7709	+	45.0676i	0.487512	+	1.48745i
$919$		−	33.7674i		−	1.11388i	−0.830552	−	0.556942i	$-0.811975\pi$
$919$		−	33.7674i		−	1.11388i	0.830552	−	0.556942i	$-0.188025\pi$
$920$		0			0
$921$	−25.5313	+	7.05643i	−0.841285	+	0.232517i
$922$	0.627948	+	20.0183i	0.0206804	+	0.659266i
$923$	−17.3110	+	29.9836i	−0.569800	+	0.986923i
$924$	−19.1279	+	6.60244i	−0.629260	+	0.217204i
$925$		0			0
$926$	−6.86375	+	4.25516i	−0.225557	+	0.139833i
$927$	−11.7070	+	0.183880i	−0.384507	+	0.00603943i
$928$	−27.6352	−	10.6173i	−0.907171	−	0.348529i
$929$	−43.7091	+	25.2355i	−1.43405	+	0.827949i	−0.997427	−	0.0716964i	$-0.977159\pi$
$929$	−43.7091	+	25.2355i	−1.43405	+	0.827949i	−0.436622	+	0.899645i	$0.643825\pi$
$930$		0			0
$931$	−26.4001	−	15.2421i	−0.865227	−	0.499539i
$932$	22.5711	−	14.9924i	0.739339	−	0.491094i
$933$	−6.14998	−	1.59623i	−0.201341	−	0.0522581i
$934$	12.5630	−	23.4267i	0.411075	−	0.766546i
$935$		0			0
$936$	−3.82350	−	34.6883i	−0.124975	−	1.13382i
$937$	−43.7549			−1.42941			−0.714706	−	0.699425i	$-0.753439\pi$
$937$	−43.7549			−1.42941			−0.714706	+	0.699425i	$0.753439\pi$
$938$	−0.385953	+	0.719701i	−0.0126018	+	0.0234991i
$939$	−29.9275	+	30.4012i	−0.976646	+	0.992107i
$940$		0			0
$941$	−12.5420	−	7.24115i	−0.408859	−	0.236055i	0.281441	−	0.959579i	$-0.409188\pi$
$941$	−12.5420	−	7.24115i	−0.408859	−	0.236055i	−0.690299	+	0.723524i	$0.742521\pi$
$942$	5.32716	−	5.76221i	0.173568	−	0.187743i
$943$	−0.354222	+	0.204510i	−0.0115351	+	0.00665977i
$944$	6.63975	+	8.75173i	0.216106	+	0.284844i
$945$		0			0
$946$	−20.2360	+	12.5452i	−0.657929	+	0.407881i
$947$	18.6995	+	32.3885i	0.607653	+	1.05249i	0.991626	+	0.129141i	$0.0412221\pi$
$947$	18.6995	+	32.3885i	0.607653	+	1.05249i	−0.383973	+	0.923344i	$0.625445\pi$
$948$	1.96721	−	10.1614i	0.0638919	−	0.330028i
$949$	−14.9740	+	25.9357i	−0.486077	+	0.841910i
$950$		0			0
$951$	13.1447	+	12.9399i	0.426247	+	0.419604i
$952$	−14.1122	−	19.8651i	−0.457381	−	0.643832i
$953$		−	22.8733i		−	0.740937i	−0.928845	−	0.370469i	$-0.879197\pi$
$953$		−	22.8733i		−	0.740937i	0.928845	−	0.370469i	$-0.120803\pi$
$954$	−11.7593	+	0.553849i	−0.380721	+	0.0179315i
$955$		0			0
$956$	29.2354	−	1.83596i	0.945539	−	0.0593793i
$957$	9.96518	−	38.3941i	0.322129	−	1.24110i
$958$	42.9881	−	1.34848i	1.38888	−	0.0435676i
$959$	−4.00123	+	6.93034i	−0.129207	+	0.223792i
$960$		0			0
$961$	−3.83710	−	6.64606i	−0.123777	−	0.214389i
$962$	−9.93996	−	16.0336i	−0.320477	−	0.516943i
$963$	−12.8409	+	7.68506i	−0.413791	+	0.247648i
$964$	−21.7492	+	43.8009i	−0.700496	+	1.41073i
$965$		0			0
$966$	−0.0729448	+	0.322282i	−0.00234696	+	0.0103693i
$967$	50.5672	+	29.1950i	1.62613	+	0.938848i	0.985232	+	0.171223i	$0.0547717\pi$
$967$	50.5672	+	29.1950i	1.62613	+	0.938848i	0.640899	+	0.767625i	$0.278562\pi$
$968$	−9.59870	+	20.9558i	−0.308514	+	0.673546i
$969$	−17.3970	−	62.9452i	−0.558874	−	2.02209i
$970$		0			0
$971$	−35.2792			−1.13216			−0.566082	−	0.824349i	$-0.691541\pi$
$971$	−35.2792			−1.13216			−0.566082	+	0.824349i	$0.691541\pi$
$972$	11.0931	+	29.1366i	0.355810	+	0.934558i
$973$	0.317795			0.0101881
$974$	−4.58505	−	2.45882i	−0.146914	−	0.0787856i
$975$		0			0
$976$	−8.28787	+	1.04507i	−0.265288	+	0.0334518i
$977$	−8.29548	−	4.78940i	−0.265396	−	0.153226i	0.361398	−	0.932412i	$-0.382300\pi$
$977$	−8.29548	−	4.78940i	−0.265396	−	0.153226i	−0.626794	+	0.779185i	$0.715633\pi$
$978$	−5.74166	+	25.3676i	−0.183598	+	0.811166i
$979$	26.4286	−	15.2586i	0.844662	−	0.487666i
$980$		0			0
$981$	−12.8367	+	7.68258i	−0.409845	+	0.245286i
$982$	−13.4974	−	21.7718i	−0.430719	−	0.694767i
$983$	−15.7419	−	27.2657i	−0.502088	−	0.869641i	−0.999997	−	0.00241215i	$-0.999232\pi$
$983$	−15.7419	−	27.2657i	−0.502088	−	0.869641i	0.497910	−	0.867229i	$-0.334101\pi$
$984$	3.15648	−	19.5754i	0.100625	−	0.624042i
$985$		0			0
$986$	47.7430	−	1.49764i	1.52045	−	0.0476946i
$987$	2.01729	−	7.77228i	0.0642112	−	0.247394i
$988$	3.01185	+	47.9598i	0.0958196	+	1.52581i
$989$			0.388795i			0.0123629i
$990$		0			0
$991$		−	30.7819i		−	0.977818i	−0.872335	−	0.488909i	$-0.837395\pi$
$991$		−	30.7819i		−	0.977818i	0.872335	−	0.488909i	$-0.162605\pi$
$992$	−4.26616	−	26.9857i	−0.135451	−	0.856795i
$993$	−4.34114	−	4.27349i	−0.137762	−	0.135615i
$994$	0.498260	+	15.8839i	0.0158039	+	0.503808i
$995$		0			0
$996$	−45.5920	−	8.82639i	−1.44464	−	0.279675i
$997$	−16.8539	−	29.1919i	−0.533770	−	0.924516i	−0.999222	−	0.0394432i	$-0.987442\pi$
$997$	−16.8539	−	29.1919i	−0.533770	−	0.924516i	0.465452	−	0.885073i	$-0.345892\pi$
$998$	27.6873	−	17.1647i	0.876428	−	0.543338i
$999$	12.1943	+	11.6329i	0.385811	+	0.368048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.g.851.8		48
4.3	odd	2	inner	900.2.r.g.851.1		48
5.2	odd	4		180.2.n.d.59.5	✓	48
5.3	odd	4		180.2.n.d.59.20	yes	48
5.4	even	2	inner	900.2.r.g.851.17		48
9.2	odd	6	inner	900.2.r.g.551.1		48
15.2	even	4		540.2.n.d.179.20		48
15.8	even	4		540.2.n.d.179.5		48
20.3	even	4		180.2.n.d.59.12	yes	48
20.7	even	4		180.2.n.d.59.13	yes	48
20.19	odd	2	inner	900.2.r.g.851.24		48
36.11	even	6	inner	900.2.r.g.551.8		48
45.2	even	12		180.2.n.d.119.12	yes	48
45.7	odd	12		540.2.n.d.359.13		48
45.29	odd	6	inner	900.2.r.g.551.24		48
45.38	even	12		180.2.n.d.119.13	yes	48
45.43	odd	12		540.2.n.d.359.12		48
60.23	odd	4		540.2.n.d.179.13		48
60.47	odd	4		540.2.n.d.179.12		48
180.7	even	12		540.2.n.d.359.5		48
180.43	even	12		540.2.n.d.359.20		48
180.47	odd	12		180.2.n.d.119.20	yes	48
180.83	odd	12		180.2.n.d.119.5	yes	48
180.119	even	6	inner	900.2.r.g.551.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.5	✓	48	5.2	odd	4
180.2.n.d.59.12	yes	48	20.3	even	4
180.2.n.d.59.13	yes	48	20.7	even	4
180.2.n.d.59.20	yes	48	5.3	odd	4
180.2.n.d.119.5	yes	48	180.83	odd	12
180.2.n.d.119.12	yes	48	45.2	even	12
180.2.n.d.119.13	yes	48	45.38	even	12
180.2.n.d.119.20	yes	48	180.47	odd	12
540.2.n.d.179.5		48	15.8	even	4
540.2.n.d.179.12		48	60.47	odd	4
540.2.n.d.179.13		48	60.23	odd	4
540.2.n.d.179.20		48	15.2	even	4
540.2.n.d.359.5		48	180.7	even	12
540.2.n.d.359.12		48	45.43	odd	12
540.2.n.d.359.13		48	45.7	odd	12
540.2.n.d.359.20		48	180.43	even	12
900.2.r.g.551.1		48	9.2	odd	6	inner
900.2.r.g.551.8		48	36.11	even	6	inner
900.2.r.g.551.17		48	180.119	even	6	inner
900.2.r.g.551.24		48	45.29	odd	6	inner
900.2.r.g.851.1		48	4.3	odd	2	inner
900.2.r.g.851.8		48	1.1	even	1	trivial
900.2.r.g.851.17		48	5.4	even	2	inner
900.2.r.g.851.24		48	20.19	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.668359 + 1.24631i) q^{2} +(-0.461412 - 1.66946i) q^{3} +(-1.10659 - 1.66597i) q^{4} +(2.38906 + 0.540736i) q^{6} +(1.15604 - 0.667441i) q^{7} +(2.81592 - 0.265693i) q^{8} +(-2.57420 + 1.54062i) q^{9} +(2.18799 + 3.78971i) q^{11} +(-2.27068 + 2.61611i) q^{12} +(-2.05641 + 3.56180i) q^{13} +(0.0591892 + 1.88688i) q^{14} +(-1.55091 + 3.68710i) q^{16} -6.45392i q^{17} +(-0.199603 - 4.23794i) q^{18} +5.84202i q^{19} +(-1.64768 - 1.62200i) q^{21} +(-6.18554 + 0.194033i) q^{22} +(-0.0505284 + 0.0875178i) q^{23} +(-1.74286 - 4.57847i) q^{24} +(-3.06470 - 4.94349i) q^{26} +(3.75977 + 3.58666i) q^{27} +(-2.39120 - 1.18735i) q^{28} +(4.53226 - 2.61670i) q^{29} +(4.18262 + 2.41484i) q^{31} +(-3.55871 - 4.39722i) q^{32} +(5.31721 - 5.40139i) q^{33} +(8.04361 + 4.31354i) q^{34} +(5.41521 + 2.58370i) q^{36} +3.24337 q^{37} +(-7.28098 - 3.90457i) q^{38} +(6.89514 + 1.78964i) q^{39} +(3.50518 + 2.02372i) q^{41} +(3.12276 - 0.969443i) q^{42} +(3.33185 - 1.92364i) q^{43} +(3.89233 - 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(1.73649 + 3.00768i) q^{47} +(6.87107 + 0.887912i) q^{48} +(-2.60904 + 4.51900i) q^{49} +(-10.7746 + 2.97792i) q^{51} +(8.20946 - 0.515549i) q^{52} -2.77476i q^{53} +(-6.98298 + 2.28867i) q^{54} +(3.07799 - 2.18661i) q^{56} +(9.75302 - 2.69558i) q^{57} +(0.232051 + 7.39751i) q^{58} +(1.37318 - 2.37841i) q^{59} +(1.04419 + 1.80858i) q^{61} +(-5.80514 + 3.59888i) q^{62} +(-1.94761 + 3.49915i) q^{63} +(7.85881 - 1.49634i) q^{64} +(3.17801 + 10.2370i) q^{66} +(0.374638 + 0.216298i) q^{67} +(-10.7520 + 7.14186i) q^{68} +(0.169422 + 0.0439735i) q^{69} +8.41810 q^{71} +(-6.83941 + 5.02220i) q^{72} +7.28163 q^{73} +(-2.16773 + 4.04225i) q^{74} +(9.73262 - 6.46473i) q^{76} +(5.05882 + 2.92071i) q^{77} +(-6.83888 + 7.39739i) q^{78} +(-2.58753 + 1.49391i) q^{79} +(4.25299 - 7.93171i) q^{81} +(-4.86490 + 3.01598i) q^{82} +(6.70282 + 11.6096i) q^{83} +(-0.878898 + 4.53988i) q^{84} +(0.170590 + 5.43821i) q^{86} +(-6.45972 - 6.35905i) q^{87} +(7.16812 + 10.0902i) q^{88} -6.97377i q^{89} +5.49013i q^{91} +(0.201716 - 0.0126677i) q^{92} +(2.10157 - 8.09696i) q^{93} +(-4.90911 + 0.153993i) q^{94} +(-5.69896 + 7.97006i) q^{96} +(-1.20440 - 2.08608i) q^{97} +(-3.88831 - 6.27200i) q^{98} +(-11.4708 - 6.38462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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