LMFDB - Embedded newform 675.2.u.b.124.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.3
Character	$\chi$	$=$	675.124
Dual form			675.2.u.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.267057 - 0.318266i) q^{2} +(1.72466 - 0.159815i) q^{3} +(0.317323 + 1.79963i) q^{4} +(0.409719 - 0.591580i) q^{6} +(-1.29958 - 0.229151i) q^{7} +(1.37711 + 0.795075i) q^{8} +(2.94892 - 0.551252i) q^{9} +O(q^{10})$	\(q+(0.267057 - 0.318266i) q^{2} +(1.72466 - 0.159815i) q^{3} +(0.317323 + 1.79963i) q^{4} +(0.409719 - 0.591580i) q^{6} +(-1.29958 - 0.229151i) q^{7} +(1.37711 + 0.795075i) q^{8} +(2.94892 - 0.551252i) q^{9} +(4.90067 - 1.78370i) q^{11} +(0.834881 + 3.05303i) q^{12} +(0.0116078 + 0.0138336i) q^{13} +(-0.419993 + 0.352416i) q^{14} +(-2.81355 + 1.02405i) q^{16} +(-2.71308 + 1.56640i) q^{17} +(0.612083 - 1.08575i) q^{18} +(0.208676 - 0.361438i) q^{19} +(-2.27796 - 0.187516i) q^{21} +(0.741067 - 2.03606i) q^{22} +(-1.01867 + 0.179619i) q^{23} +(2.50212 + 1.15115i) q^{24} +0.00750270 q^{26} +(4.99779 - 1.42200i) q^{27} -2.41147i q^{28} +(5.98068 + 5.01839i) q^{29} +(0.647649 + 3.67300i) q^{31} +(-1.51319 + 4.15744i) q^{32} +(8.16694 - 3.85948i) q^{33} +(-0.226015 + 1.28180i) q^{34} +(1.92781 + 5.13202i) q^{36} +(3.83195 - 2.21238i) q^{37} +(-0.0593049 - 0.162939i) q^{38} +(0.0222303 + 0.0220032i) q^{39} +(-2.81517 + 2.36221i) q^{41} +(-0.668024 + 0.674919i) q^{42} +(-2.84146 - 7.80685i) q^{43} +(4.76508 + 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(-6.99008 - 1.23254i) q^{47} +(-4.68877 + 2.21579i) q^{48} +(-4.94145 - 1.79854i) q^{49} +(-4.42881 + 3.13510i) q^{51} +(-0.0212119 + 0.0252794i) q^{52} +1.30057i q^{53} +(0.882118 - 1.97038i) q^{54} +(-1.60747 - 1.34883i) q^{56} +(0.302133 - 0.656707i) q^{57} +(3.19436 - 0.563252i) q^{58} +(-3.47856 - 1.26609i) q^{59} +(1.20064 - 6.80919i) q^{61} +(1.34195 + 0.774775i) q^{62} +(-3.95868 + 0.0406486i) q^{63} +(-2.07506 - 3.59410i) q^{64} +(0.952697 - 3.62996i) q^{66} +(-7.08789 - 8.44702i) q^{67} +(-3.67985 - 4.38548i) q^{68} +(-1.72816 + 0.472581i) q^{69} +(3.04214 + 5.26914i) q^{71} +(4.49927 + 1.58548i) q^{72} +(-0.473692 - 0.273486i) q^{73} +(0.319224 - 1.81041i) q^{74} +(0.716670 + 0.260847i) q^{76} +(-6.77756 + 1.19507i) q^{77} +(0.0129396 - 0.00119904i) q^{78} +(-0.374706 - 0.314416i) q^{79} +(8.39224 - 3.25120i) q^{81} +1.52681i q^{82} +(2.96561 - 3.53428i) q^{83} +(-0.385389 - 4.15898i) q^{84} +(-3.24348 - 1.18053i) q^{86} +(11.1167 + 7.69922i) q^{87} +(8.16694 + 1.44005i) q^{88} +(-1.68653 + 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(-0.646495 - 1.77623i) q^{92} +(1.70398 + 6.23118i) q^{93} +(-2.25902 + 1.89554i) q^{94} +(-1.94531 + 7.41201i) q^{96} +(-3.40014 - 9.34182i) q^{97} +(-1.89206 + 1.09238i) q^{98} +(13.4684 - 7.96149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4}+O(q^{10}) $ 24 * q + 12 * q^4	$ 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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 $

$2$	0.267057	−	0.318266i	0.188837	−	0.225048i	−0.663316	−	0.748339i	$-0.730852\pi$
$2$	0.267057	−	0.318266i	0.188837	−	0.225048i	0.852154	+	0.523291i	$0.175296\pi$
$3$	1.72466	−	0.159815i	0.995734	−	0.0922690i
$3$	1.72466	−	0.159815i	0.995734	−	0.0922690i
$4$	0.317323	+	1.79963i	0.158661	+	0.899813i
$5$		0			0
$5$		0			0
$6$	0.409719	−	0.591580i	0.167267	−	0.241512i
$7$	−1.29958	−	0.229151i	−0.491195	−	0.0866110i	−0.0774361	−	0.996997i	$-0.524673\pi$
$7$	−1.29958	−	0.229151i	−0.491195	−	0.0866110i	−0.413759	+	0.910386i	$0.635784\pi$
$8$	1.37711	+	0.795075i	0.486882	+	0.281102i
$9$	2.94892	−	0.551252i	0.982973	−	0.183751i
$10$		0			0
$11$	4.90067	−	1.78370i	1.47761	−	0.537805i	0.527454	−	0.849584i	$-0.323147\pi$
$11$	4.90067	−	1.78370i	1.47761	−	0.537805i	0.950155	+	0.311778i	$0.100925\pi$
$12$	0.834881	+	3.05303i	0.241009	+	0.881335i
$13$	0.0116078	+	0.0138336i	0.00321942	+	0.00383676i	0.767652	−	0.640867i	$-0.221425\pi$
$13$	0.0116078	+	0.0138336i	0.00321942	+	0.00383676i	−0.764432	+	0.644704i	$0.776981\pi$
$14$	−0.419993	+	0.352416i	−0.112248	+	0.0941870i
$15$		0			0
$16$	−2.81355	+	1.02405i	−0.703389	+	0.256012i
$17$	−2.71308	+	1.56640i	−0.658019	+	0.379907i	−0.791522	−	0.611141i	$-0.790711\pi$
$17$	−2.71308	+	1.56640i	−0.658019	+	0.379907i	0.133503	+	0.991048i	$0.457377\pi$
$18$	0.612083	−	1.08575i	0.144269	−	0.255915i
$19$	0.208676	−	0.361438i	0.0478736	−	0.0829195i	−0.841096	−	0.540886i	$-0.818089\pi$
$19$	0.208676	−	0.361438i	0.0478736	−	0.0829195i	0.888969	+	0.457967i	$0.151422\pi$
$20$		0			0
$21$	−2.27796	−	0.187516i	−0.497092	−	0.0409194i
$22$	0.741067	−	2.03606i	0.157996	−	0.434090i
$23$	−1.01867	+	0.179619i	−0.212408	+	0.0374532i	−0.278839	−	0.960338i	$-0.589950\pi$
$23$	−1.01867	+	0.179619i	−0.212408	+	0.0374532i	0.0664316	+	0.997791i	$0.478839\pi$
$24$	2.50212	+	1.15115i	0.510742	+	0.234978i
$25$		0			0
$26$	0.00750270			0.00147140
$27$	4.99779	−	1.42200i	0.961825	−	0.273665i
$28$		−	2.41147i		−	0.455726i
$29$	5.98068	+	5.01839i	1.11058	+	0.931891i	0.998091	−	0.0617615i	$-0.0196718\pi$
$29$	5.98068	+	5.01839i	1.11058	+	0.931891i	0.112493	+	0.993652i	$0.464116\pi$
$30$		0			0
$31$	0.647649	+	3.67300i	0.116321	+	0.659691i	0.986088	+	0.166227i	$0.0531584\pi$
$31$	0.647649	+	3.67300i	0.116321	+	0.659691i	−0.869766	+	0.493464i	$0.835730\pi$
$32$	−1.51319	+	4.15744i	−0.267496	+	0.734939i
$33$	8.16694	−	3.85948i	1.42168	−	0.671849i
$34$	−0.226015	+	1.28180i	−0.0387613	+	0.219826i
$35$		0			0
$36$	1.92781	+	5.13202i	0.321301	+	0.855337i
$37$	3.83195	−	2.21238i	0.629969	−	0.363713i	−0.150771	−	0.988569i	$-0.548176\pi$
$37$	3.83195	−	2.21238i	0.629969	−	0.363713i	0.780740	+	0.624856i	$0.214842\pi$
$38$	−0.0593049	−	0.162939i	−0.00962052	−	0.0264322i
$39$	0.0222303	+	0.0220032i	0.00355970	+	0.00352334i
$40$		0			0
$41$	−2.81517	+	2.36221i	−0.439655	+	0.368915i	−0.835580	−	0.549368i	$-0.814868\pi$
$41$	−2.81517	+	2.36221i	−0.439655	+	0.368915i	0.395925	+	0.918283i	$0.370424\pi$
$42$	−0.668024	+	0.674919i	−0.103078	+	0.104142i
$43$	−2.84146	−	7.80685i	−0.433319	−	1.19053i	−0.943763	−	0.330622i	$-0.892741\pi$
$43$	−2.84146	−	7.80685i	−0.433319	−	1.19053i	0.510445	−	0.859911i	$-0.329481\pi$
$44$	4.76508	+	8.25337i	0.718363	+	1.24424i
$45$		0			0
$46$	−0.214876	+	0.372177i	−0.0316818	+	0.0548745i
$47$	−6.99008	−	1.23254i	−1.01961	−	0.179784i	−0.361234	−	0.932475i	$-0.617644\pi$
$47$	−6.99008	−	1.23254i	−1.01961	−	0.179784i	−0.658374	+	0.752691i	$0.728755\pi$
$48$	−4.68877	+	2.21579i	−0.676766	+	0.319821i
$49$	−4.94145	−	1.79854i	−0.705921	−	0.256934i
$50$		0			0
$51$	−4.42881	+	3.13510i	−0.620158	+	0.439001i
$52$	−0.0212119	+	0.0252794i	−0.00294157	+	0.00350562i
$53$			1.30057i			0.178648i	0.996003	+	0.0893238i	$0.0284706\pi$
$53$			1.30057i			0.178648i	−0.996003	+	0.0893238i	$0.971529\pi$
$54$	0.882118	−	1.97038i	0.120041	−	0.268135i
$55$		0			0
$56$	−1.60747	−	1.34883i	−0.214808	−	0.180245i
$57$	0.302133	−	0.656707i	0.0400185	−	0.0869830i
$58$	3.19436	−	0.563252i	0.419440	−	0.0739586i
$59$	−3.47856	−	1.26609i	−0.452871	−	0.164831i	0.105507	−	0.994419i	$-0.466354\pi$
$59$	−3.47856	−	1.26609i	−0.452871	−	0.164831i	−0.558377	+	0.829587i	$0.688576\pi$
$60$		0			0
$61$	1.20064	−	6.80919i	0.153727	−	0.871828i	−0.806214	−	0.591624i	$-0.798487\pi$
$61$	1.20064	−	6.80919i	0.153727	−	0.871828i	0.959941	−	0.280204i	$-0.0904020\pi$
$62$	1.34195	+	0.774775i	0.170428	+	0.0983965i
$63$	−3.95868	+	0.0406486i	−0.498747	+	0.00512125i
$64$	−2.07506	−	3.59410i	−0.259382	−	0.449263i
$65$		0			0
$66$	0.952697	−	3.62996i	0.117269	−	0.446817i
$67$	−7.08789	−	8.44702i	−0.865923	−	1.03197i	−0.999164	−	0.0408835i	$-0.986983\pi$
$67$	−7.08789	−	8.44702i	−0.865923	−	1.03197i	0.133241	−	0.991084i	$-0.457462\pi$
$68$	−3.67985	−	4.38548i	−0.446247	−	0.531817i
$69$	−1.72816	+	0.472581i	−0.208046	+	0.0568921i
$70$		0			0
$71$	3.04214	+	5.26914i	0.361035	+	0.625332i	0.988132	−	0.153610i	$-0.0490900\pi$
$71$	3.04214	+	5.26914i	0.361035	+	0.625332i	−0.627096	+	0.778942i	$0.715757\pi$
$72$	4.49927	+	1.58548i	0.530245	+	0.186850i
$73$	−0.473692	−	0.273486i	−0.0554415	−	0.0320092i	0.472023	−	0.881586i	$-0.343524\pi$
$73$	−0.473692	−	0.273486i	−0.0554415	−	0.0320092i	−0.527465	+	0.849577i	$0.676857\pi$
$74$	0.319224	−	1.81041i	0.0371090	−	0.210456i
$75$		0			0
$76$	0.716670	+	0.260847i	0.0822077	+	0.0299212i
$77$	−6.77756	+	1.19507i	−0.772374	+	0.136190i
$78$	0.0129396	−	0.00119904i	0.00146512	−	0.000135765i
$79$	−0.374706	−	0.314416i	−0.0421577	−	0.0353745i	0.621465	−	0.783442i	$-0.286538\pi$
$79$	−0.374706	−	0.314416i	−0.0421577	−	0.0353745i	−0.663623	+	0.748067i	$0.730982\pi$
$80$		0			0
$81$	8.39224	−	3.25120i	0.932471	−	0.361244i
$82$			1.52681i			0.168608i
$83$	2.96561	−	3.53428i	0.325518	−	0.387937i	−0.578321	−	0.815809i	$-0.696292\pi$
$83$	2.96561	−	3.53428i	0.325518	−	0.387937i	0.903839	+	0.427872i	$0.140737\pi$
$84$	−0.385389	−	4.15898i	−0.0420493	−	0.453782i
$85$		0			0
$86$	−3.24348	−	1.18053i	−0.349754	−	0.127300i
$87$	11.1167	+	7.69922i	1.19183	+	0.825443i
$88$	8.16694	+	1.44005i	0.870599	+	0.153510i
$89$	−1.68653	+	2.92116i	−0.178772	+	0.309642i	−0.941460	−	0.337124i	$-0.890546\pi$
$89$	−1.68653	+	2.92116i	−0.178772	+	0.309642i	0.762688	+	0.646766i	$0.223879\pi$
$90$		0			0
$91$	−0.0119153	−	0.0206379i	−0.00124906	−	0.00216344i
$92$	−0.646495	−	1.77623i	−0.0674018	−	0.185185i
$93$	1.70398	+	6.23118i	0.176694	+	0.646144i
$94$	−2.25902	+	1.89554i	−0.233000	+	0.195510i
$95$		0			0
$96$	−1.94531	+	7.41201i	−0.198543	+	0.756485i
$97$	−3.40014	−	9.34182i	−0.345232	−	0.948518i	−0.983850	−	0.178994i	$-0.942716\pi$
$97$	−3.40014	−	9.34182i	−0.345232	−	0.948518i	0.638618	−	0.769524i	$-0.279507\pi$
$98$	−1.89206	+	1.09238i	−0.191127	+	0.110347i
$99$	13.4684	−	7.96149i	1.35363	−	0.800160i
$100$		0			0
$101$	2.39626	−	13.5898i	0.238436	−	1.35224i	−0.596818	−	0.802377i	$-0.703569\pi$
$101$	2.39626	−	13.5898i	0.238436	−	1.35224i	0.835255	−	0.549863i	$-0.185320\pi$
$102$	−0.184950	+	2.24679i	−0.0183128	+	0.222465i
$103$	−1.56136	+	4.28981i	−0.153846	+	0.422687i	−0.992541	−	0.121914i	$-0.961097\pi$
$103$	−1.56136	+	4.28981i	−0.153846	+	0.422687i	0.838695	+	0.544601i	$0.183319\pi$
$104$	0.00498644	+	0.0282795i	0.000488961	+	0.00277303i
$105$		0			0
$106$	0.413928	+	0.347327i	0.0402042	+	0.0337354i
$107$		−	11.2965i		−	1.09207i	−0.837762	−	0.546035i	$-0.816136\pi$
$107$		−	11.2965i		−	1.09207i	0.837762	−	0.546035i	$-0.183864\pi$
$108$	4.14499	+	8.54292i	0.398851	+	0.822043i
$109$	−14.5032			−1.38915			−0.694577	−	0.719419i	$-0.744408\pi$
$109$	−14.5032			−1.38915			−0.694577	+	0.719419i	$0.744408\pi$
$110$		0			0
$111$	6.25525	−	4.42801i	0.593722	−	0.420288i
$112$	3.89110	−	0.686107i	0.367675	−	0.0648310i
$113$	−4.29523	+	11.8011i	−0.404062	+	1.11015i	0.556200	+	0.831049i	$0.312259\pi$
$113$	−4.29523	+	11.8011i	−0.404062	+	1.11015i	−0.960262	+	0.279102i	$0.909963\pi$
$114$	−0.128321	−	0.271536i	−0.0120183	−	0.0254317i
$115$		0			0
$116$	−7.13341	+	12.3554i	−0.662321	+	1.14717i
$117$	0.0418563	+	0.0343954i	0.00386961	+	0.00317986i
$118$	−1.33193	+	0.768989i	−0.122614	+	0.0707912i
$119$	3.88481	−	1.41395i	0.356120	−	0.129617i
$120$		0			0
$121$	12.4085	−	10.4120i	1.12805	−	0.946544i
$122$	−1.84649	−	2.20056i	−0.167174	−	0.199230i
$123$	−4.47770	+	4.52391i	−0.403740	+	0.407907i
$124$	−6.40452	+	2.33105i	−0.575143	+	0.209335i
$125$		0			0
$126$	−1.04425	+	1.27077i	−0.0930295	+	0.113209i
$127$	7.27027	+	4.19749i	0.645132	+	0.372467i	0.786589	−	0.617477i	$-0.211845\pi$
$127$	7.27027	+	4.19749i	0.645132	+	0.372467i	−0.141456	+	0.989944i	$0.545179\pi$
$128$	−10.4121	−	1.83594i	−0.920310	−	0.162276i
$129$	−6.14821	−	13.0101i	−0.541319	−	1.14547i
$130$		0			0
$131$	−2.69761	−	15.2989i	−0.235691	−	1.33667i	−0.841154	−	0.540796i	$-0.818123\pi$
$131$	−2.69761	−	15.2989i	−0.235691	−	1.33667i	0.605463	−	0.795874i	$-0.292988\pi$
$132$	9.53717	+	13.4727i	0.830104	+	1.17265i
$133$	−0.354015	+	0.421899i	−0.0306970	+	0.0365833i
$134$	−4.58126			−0.395761
$135$		0			0
$136$	−4.98162			−0.427170
$137$	−7.71820	+	9.19820i	−0.659411	+	0.785855i	−0.987301	−	0.158861i	$-0.949218\pi$
$137$	−7.71820	+	9.19820i	−0.659411	+	0.785855i	0.327890	+	0.944716i	$0.393662\pi$
$138$	−0.311110	+	0.676219i	−0.0264834	+	0.0575636i
$139$	−1.06709	−	6.05176i	−0.0905093	−	0.513304i	−0.996031	−	0.0890042i	$-0.971632\pi$
$139$	−1.06709	−	6.05176i	−0.0905093	−	0.513304i	0.905522	−	0.424299i	$-0.139480\pi$
$140$		0			0
$141$	−12.2525	−	1.00860i	−1.03185	−	0.0849392i
$142$	2.48941	+	0.438950i	0.208907	+	0.0368359i
$143$	0.0815610	+	0.0470893i	0.00682047	+	0.00393780i
$144$	−7.73243	+	4.57082i	−0.644369	+	0.380901i
$145$		0			0
$146$	−0.213544	+	0.0777237i	−0.0176730	+	0.00643246i
$147$	−8.80976	−	2.31216i	−0.726617	−	0.190704i
$148$	5.19742	+	6.19404i	0.427225	+	0.509147i
$149$	−0.676280	+	0.567466i	−0.0554030	+	0.0464886i	−0.670069	−	0.742299i	$-0.733735\pi$
$149$	−0.676280	+	0.567466i	−0.0554030	+	0.0464886i	0.614666	+	0.788788i	$0.289291\pi$
$150$		0			0
$151$	−7.72942	+	2.81328i	−0.629011	+	0.228941i	−0.636801	−	0.771028i	$-0.719743\pi$
$151$	−7.72942	+	2.81328i	−0.629011	+	0.228941i	0.00778980	+	0.999970i	$0.497520\pi$
$152$	0.574740	−	0.331826i	0.0466176	−	0.0269147i
$153$	−7.13717	+	6.11477i	−0.577006	+	0.494350i
$154$	−1.42964	+	2.47621i	−0.115204	+	0.199539i
$155$		0			0
$156$	−0.0325434	+	0.0469884i	−0.00260556	+	0.00376208i
$157$	4.29571	−	11.8024i	0.342835	−	0.941932i	−0.641733	−	0.766928i	$-0.721784\pi$
$157$	4.29571	−	11.8024i	0.342835	−	0.941932i	0.984568	−	0.175003i	$-0.0559937\pi$
$158$	−0.200135	+	0.0352893i	−0.0159219	+	0.00280746i
$159$	0.207851	+	2.24305i	0.0164836	+	0.177886i
$160$		0			0
$161$	1.36501			0.107578
$162$	1.20646	−	3.53922i	0.0947884	−	0.278067i
$163$		−	3.31466i		−	0.259624i	−0.991539	−	0.129812i	$-0.958563\pi$
$163$		−	3.31466i		−	0.259624i	0.991539	−	0.129812i	$-0.0414374\pi$
$164$	−5.14440	−	4.31667i	−0.401710	−	0.337075i
$165$		0			0
$166$	−0.332853	−	1.88770i	−0.0258344	−	0.146514i
$167$	−7.03295	+	19.3229i	−0.544226	+	1.49525i	0.297167	+	0.954826i	$0.403958\pi$
$167$	−7.03295	+	19.3229i	−0.544226	+	1.49525i	−0.841393	+	0.540424i	$0.818264\pi$
$168$	−2.98791	−	2.06938i	−0.230522	−	0.159656i
$169$	2.25737	−	12.8022i	0.173644	−	0.984783i
$170$		0			0
$171$	0.416126	−	1.18088i	0.0318219	−	0.0903044i
$172$	13.1477	−	7.59085i	1.00251	−	0.578797i
$173$	4.79966	+	13.1870i	0.364911	+	1.00259i	0.977269	+	0.212005i	$0.0679992\pi$
$173$	4.79966	+	13.1870i	0.364911	+	1.00259i	−0.612357	+	0.790581i	$0.709779\pi$
$174$	5.41917	−	1.48192i	0.410827	−	0.112344i
$175$		0			0
$176$	−11.9617	+	10.0371i	−0.901648	+	0.756572i
$177$	−6.20169	−	1.62766i	−0.466148	−	0.122342i
$178$	0.479305	+	1.31688i	0.0359254	+	0.0987043i
$179$	5.09500	+	8.82479i	0.380818	+	0.659596i	0.991179	−	0.132527i	$-0.0423091\pi$
$179$	5.09500	+	8.82479i	0.380818	+	0.659596i	−0.610361	+	0.792123i	$0.708976\pi$
$180$		0			0
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.0589331	+	0.998262i	$0.518770\pi$
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.835054	+	0.550169i	$0.814563\pi$
$182$	−0.00975037	−	0.00171925i	−0.000722746	−	0.000127440i
$183$	0.982498	−	11.9354i	0.0726283	−	0.882293i
$184$	−1.54563	−	0.562565i	−0.113946	−	0.0414728i
$185$		0			0
$186$	2.43823	+	1.12176i	0.178780	+	0.0822516i
$187$	−10.5019	+	12.5157i	−0.767978	+	0.915240i
$188$		−	12.9706i		−	0.945981i
$189$	−6.82089	+	0.702760i	−0.496146	+	0.0511182i
$190$		0			0
$191$	8.38541	+	7.03619i	0.606747	+	0.509121i	0.893606	−	0.448852i	$-0.148167\pi$
$191$	8.38541	+	7.03619i	0.606747	+	0.509121i	−0.286860	+	0.957973i	$0.592611\pi$
$192$	−4.15316	−	5.86699i	−0.299729	−	0.423414i
$193$	−10.6418	+	1.87644i	−0.766013	+	0.135069i	−0.542984	−	0.839743i	$-0.682706\pi$
$193$	−10.6418	+	1.87644i	−0.766013	+	0.135069i	−0.223029	+	0.974812i	$0.571595\pi$
$194$	−3.88121	−	1.41265i	−0.278655	−	0.101422i
$195$		0			0
$196$	1.66867	−	9.46347i	0.119190	−	0.675962i
$197$	19.1161	+	11.0367i	1.36196	+	0.786331i	0.989885	−	0.141870i	$-0.0453115\pi$
$197$	19.1161	+	11.0367i	1.36196	+	0.786331i	0.372080	+	0.928201i	$0.378645\pi$
$198$	1.06296	−	6.41270i	0.0755413	−	0.455731i
$199$	6.44338	+	11.1603i	0.456759	+	0.791130i	0.998787	−	0.0492301i	$-0.0156768\pi$
$199$	6.44338	+	11.1603i	0.456759	+	0.791130i	−0.542028	+	0.840360i	$0.682343\pi$
$200$		0			0
$201$	−13.5742	−	13.4355i	−0.957448	−	0.947667i
$202$	−3.68524	−	4.39190i	−0.259293	−	0.309013i
$203$	−6.62241	−	7.89228i	−0.464802	−	0.553929i
$204$	−7.04736	−	6.97537i	−0.493414	−	0.488374i
$205$		0			0
$206$	0.948326	+	1.64255i	0.0660730	+	0.114442i
$207$	−2.90496	+	1.09123i	−0.201909	+	0.0758456i
$208$	−0.0468255	−	0.0270347i	−0.00324676	−	0.00187452i
$209$	0.377957	−	2.14350i	0.0261439	−	0.148269i
$210$		0			0
$211$	22.5485	+	8.20699i	1.55230	+	0.564992i	0.968957	−	0.247230i	$-0.0795204\pi$
$211$	22.5485	+	8.20699i	1.55230	+	0.564992i	0.583347	+	0.812223i	$0.301743\pi$
$212$	−2.34055	+	0.412702i	−0.160749	+	0.0283445i
$213$	6.08875	+	8.60131i	0.417194	+	0.589352i
$214$	−3.59528	−	3.01680i	−0.245768	−	0.206224i
$215$		0			0
$216$	8.01311	+	2.01536i	0.545223	+	0.137128i
$217$		−	4.92177i		−	0.334112i
$218$	−3.87317	+	4.61587i	−0.262324	+	0.312626i
$219$	−0.860667	−	0.395969i	−0.0581585	−	0.0267571i
$220$		0			0
$221$	−0.0531618	−	0.0193493i	−0.00357605	−	0.00130158i
$222$	0.261224	−	3.17336i	0.0175322	−	0.212982i
$223$	−21.3331	−	3.76160i	−1.42857	−	0.251895i	−0.594740	−	0.803918i	$-0.702745\pi$
$223$	−21.3331	−	3.76160i	−1.42857	−	0.251895i	−0.833829	+	0.552023i	$0.813856\pi$
$224$	2.91919	−	5.05618i	0.195047	−	0.337831i
$225$		0			0
$226$	2.60880	+	4.51858i	0.173535	+	0.300571i
$227$	−7.40196	−	20.3367i	−0.491285	−	1.34979i	−0.899505	−	0.436911i	$-0.856072\pi$
$227$	−7.40196	−	20.3367i	−0.491285	−	1.34979i	0.408220	−	0.912884i	$-0.366150\pi$
$228$	1.27770	+	0.335338i	0.0846178	+	0.0222083i
$229$	8.27739	−	6.94555i	0.546985	−	0.458975i	−0.326934	−	0.945047i	$-0.606015\pi$
$229$	8.27739	−	6.94555i	0.546985	−	0.458975i	0.873919	+	0.486072i	$0.161571\pi$
$230$		0			0
$231$	−11.4980	+	3.14424i	−0.756513	+	0.206876i
$232$	4.24606	+	11.6660i	0.278768	+	0.765908i
$233$	−6.61557	+	3.81950i	−0.433400	+	0.250224i	−0.700794	−	0.713364i	$-0.747171\pi$
$233$	−6.61557	+	3.81950i	−0.433400	+	0.250224i	0.267394	+	0.963587i	$0.413838\pi$
$234$	0.0221249	−	0.00413588i	0.00144635	−	0.000270371i
$235$		0			0
$236$	1.17467	−	6.66187i	0.0764644	−	0.433651i
$237$	−0.696490	−	0.482377i	−0.0452419	−	0.0313338i
$238$	0.587451	−	1.61401i	0.0380788	−	0.104621i
$239$	0.561143	+	3.18240i	0.0362973	+	0.205852i	0.997563	−	0.0697711i	$-0.0222269\pi$
$239$	0.561143	+	3.18240i	0.0362973	+	0.205852i	−0.961266	+	0.275623i	$0.911116\pi$
$240$		0			0
$241$	−20.3346	−	17.0628i	−1.30987	−	1.09911i	−0.988349	−	0.152206i	$-0.951362\pi$
$241$	−20.3346	−	17.0628i	−1.30987	−	1.09911i	−0.321518	−	0.946903i	$-0.604193\pi$
$242$		−	6.72979i		−	0.432608i
$243$	13.9542	−	6.94842i	0.895162	−	0.445741i
$244$	12.6350			0.808873
$245$		0			0
$246$	0.244007	+	2.63324i	0.0155573	+	0.167889i
$247$	0.00742226	−	0.00130875i	0.000472267	−	8.32735e-5i
$248$	−2.02843	+	5.57306i	−0.128805	+	0.353890i
$249$	4.54985	−	6.56938i	0.288335	−	0.416318i
$250$		0			0
$251$	2.24965	−	3.89651i	0.141997	−	0.245945i	−0.786252	−	0.617906i	$-0.787981\pi$
$251$	2.24965	−	3.89651i	0.141997	−	0.245945i	0.928248	+	0.371961i	$0.121314\pi$
$252$	−1.32933	−	7.11124i	−0.0837399	−	0.447966i
$253$	−4.67179	+	2.69726i	−0.293713	+	0.169575i
$254$	3.27749	−	1.19291i	0.205648	−	0.0748498i
$255$		0			0
$256$	2.99340	−	2.51176i	0.187088	−	0.156985i
$257$	8.82895	+	10.5219i	0.550735	+	0.656340i	0.967559	−	0.252647i	$-0.0813011\pi$
$257$	8.82895	+	10.5219i	0.550735	+	0.656340i	−0.416824	+	0.908987i	$0.636857\pi$
$258$	−5.78258	−	1.51766i	−0.360007	−	0.0944854i
$259$	−5.48690	+	1.99707i	−0.340939	+	0.124092i
$260$		0			0
$261$	20.4029	+	11.5020i	1.26291	+	0.711953i
$262$	−5.58952	−	3.22711i	−0.345322	−	0.199372i
$263$	23.8349	+	4.20273i	1.46972	+	0.259151i	0.850462	−	0.526036i	$-0.176322\pi$
$263$	23.8349	+	4.20273i	1.46972	+	0.259151i	0.619258	+	0.785187i	$0.287433\pi$
$264$	14.3154	+	1.17841i	0.881049	+	0.0725260i
$265$		0			0
$266$	0.0397339	+	0.225342i	0.00243624	+	0.0138166i
$267$	−2.44185	+	5.30755i	−0.149439	+	0.324817i
$268$	12.9523	−	15.4360i	0.791189	−	0.942902i
$269$	−12.0062			−0.732032			−0.366016	−	0.930609i	$-0.619278\pi$
$269$	−12.0062			−0.732032			−0.366016	+	0.930609i	$0.619278\pi$
$270$		0			0
$271$	3.71777			0.225839			0.112919	−	0.993604i	$-0.463980\pi$
$271$	3.71777			0.225839			0.112919	+	0.993604i	$0.463980\pi$
$272$	6.02933	−	7.18547i	0.365582	−	0.435683i
$273$	−0.0238481	−	0.0336891i	−0.00144335	−	0.00203896i
$274$	0.866273	+	4.91288i	0.0523335	+	0.296798i
$275$		0			0
$276$	−1.39885	−	2.96008i	−0.0842011	−	0.178176i
$277$	−23.1264	−	4.07780i	−1.38953	−	0.245011i	−0.571695	−	0.820466i	$-0.693714\pi$
$277$	−23.1264	−	4.07780i	−1.38953	−	0.245011i	−0.817833	+	0.575455i	$0.804825\pi$
$278$	−2.21104	−	1.27654i	−0.132609	−	0.0765621i
$279$	3.93462	+	10.4744i	0.235559	+	0.627084i
$280$		0			0
$281$	19.1432	−	6.96754i	1.14199	−	0.415649i	0.299356	−	0.954142i	$-0.403228\pi$
$281$	19.1432	−	6.96754i	1.14199	−	0.415649i	0.842630	+	0.538493i	$0.181006\pi$
$282$	−3.59311	+	3.63020i	−0.213967	+	0.216175i
$283$	−7.45630	−	8.88607i	−0.443231	−	0.528222i	0.497460	−	0.867487i	$-0.334266\pi$
$283$	−7.45630	−	8.88607i	−0.443231	−	0.528222i	−0.940691	+	0.339265i	$0.889822\pi$
$284$	−8.51714	+	7.14673i	−0.505399	+	0.424080i
$285$		0			0
$286$	0.0367683	−	0.0133826i	0.00217416	−	0.000791328i
$287$	4.19984	−	2.42478i	0.247909	−	0.143130i
$288$	−2.17046	+	13.0941i	−0.127896	+	0.771578i
$289$	−3.59280	+	6.22291i	−0.211341	+	0.366053i
$290$		0			0
$291$	−7.35706	−	15.5681i	−0.431279	−	0.912618i
$292$	0.341860	−	0.939253i	0.0200058	−	0.0549656i
$293$	31.0945	−	5.48280i	1.81656	−	0.320308i	0.841165	−	0.540779i	$-0.181870\pi$
$293$	31.0945	−	5.48280i	1.81656	−	0.320308i	0.975394	+	0.220470i	$0.0707592\pi$
$294$	−3.08858	+	2.18637i	−0.180130	+	0.127511i
$295$		0			0
$296$	7.03603			0.408961
$297$	21.9561	−	15.8833i	1.27402	−	0.921644i
$298$			0.366782i			0.0212471i
$299$	−0.0143093	−	0.0120069i	−0.000827529	−	0.000694379i
$300$		0			0
$301$	1.90376	+	10.7968i	0.109731	+	0.622315i
$302$	−1.16882	+	3.21131i	−0.0672581	+	0.184790i
$303$	1.96088	−	23.8208i	0.112649	−	1.36847i
$304$	−0.216991	+	1.23062i	−0.0124453	+	0.0705809i
$305$		0			0
$306$	0.0400924	+	3.90451i	0.00229193	+	0.223206i
$307$	−7.03259	+	4.06027i	−0.401371	+	0.231732i	−0.687075	−	0.726586i	$-0.741106\pi$
$307$	−7.03259	+	4.06027i	−0.401371	+	0.231732i	0.285704	+	0.958318i	$0.407773\pi$
$308$	−4.30134	−	11.8178i	−0.245092	−	0.673384i
$309$	−2.00725	+	7.64800i	−0.114188	+	0.435079i
$310$		0			0
$311$	−18.2691	+	15.3296i	−1.03594	+	0.869259i	−0.991546	−	0.129754i	$-0.958581\pi$
$311$	−18.2691	+	15.3296i	−1.03594	+	0.869259i	−0.0443970	+	0.999014i	$0.514137\pi$
$312$	0.0131194	+	0.0479757i	0.000742740	+	0.00271609i
$313$	9.20392	+	25.2876i	0.520236	+	1.42934i	0.870258	+	0.492596i	$0.163952\pi$
$313$	9.20392	+	25.2876i	0.520236	+	1.42934i	−0.350022	+	0.936742i	$0.613826\pi$
$314$	−2.60909	−	4.51908i	−0.147240	−	0.255026i
$315$		0			0
$316$	0.446928	−	0.774102i	0.0251417	−	0.0435466i
$317$	−8.20574	−	1.44689i	−0.460881	−	0.0812657i	−0.0616130	−	0.998100i	$-0.519624\pi$
$317$	−8.20574	−	1.44689i	−0.460881	−	0.0812657i	−0.399268	+	0.916834i	$0.630736\pi$
$318$	0.769394	+	0.532870i	0.0431455	+	0.0298819i
$319$	38.2606	+	13.9257i	2.14218	+	0.779692i
$320$		0			0
$321$	−1.80534	−	19.4826i	−0.100764	−	1.08741i
$322$	0.364534	−	0.434435i	0.0203147	−	0.0242101i
$323$			1.30748i			0.0727501i
$324$	8.51398	+	14.0712i	0.472999	+	0.781734i
$325$		0			0
$326$	−1.05494	−	0.885201i	−0.0584278	−	0.0490268i
$327$	−25.0131	+	2.31782i	−1.38323	+	0.128176i
$328$	−5.75493	+	1.01475i	−0.317763	+	0.0560301i
$329$	8.80173	+	3.20357i	0.485255	+	0.176618i
$330$		0			0
$331$	−1.11487	+	6.32272i	−0.0612786	+	0.347528i	0.938717	+	0.344688i	$0.112015\pi$
$331$	−1.11487	+	6.32272i	−0.0612786	+	0.347528i	−0.999996	+	0.00284030i	$0.999096\pi$
$332$	7.30143	+	4.21548i	0.400718	+	0.231355i
$333$	10.0805	−	8.63650i	0.552410	−	0.473277i
$334$	4.27161	+	7.39865i	0.233732	+	0.404836i
$335$		0			0
$336$	6.60119	−	1.80516i	0.360124	−	0.0984794i
$337$	4.80477	+	5.72610i	0.261732	+	0.311921i	0.880867	−	0.473365i	$-0.156961\pi$
$337$	4.80477	+	5.72610i	0.261732	+	0.311921i	−0.619134	+	0.785285i	$0.712516\pi$
$338$	−3.47165	−	4.13735i	−0.188833	−	0.225042i
$339$	−5.52185	+	21.0393i	−0.299906	+	1.14270i
$340$		0			0
$341$	9.72545	+	16.8450i	0.526663	+	0.912206i
$342$	−0.264706	−	0.447801i	−0.0143136	−	0.0242143i
$343$	14.0095	+	8.08839i	0.756442	+	0.436732i
$344$	2.29403	−	13.0101i	0.123686	−	0.701456i
$345$		0			0
$346$	5.47874	+	1.99410i	0.294539	+	0.107203i
$347$	30.9766	−	5.46202i	1.66291	−	0.293216i	0.738399	−	0.674364i	$-0.235582\pi$
$347$	30.9766	−	5.46202i	1.66291	−	0.293216i	0.924514	+	0.381148i	$0.124471\pi$
$348$	−10.3281	+	22.4490i	−0.553647	+	1.20339i
$349$	−9.07988	−	7.61893i	−0.486035	−	0.407832i	0.366568	−	0.930391i	$-0.380533\pi$
$349$	−9.07988	−	7.61893i	−0.486035	−	0.407832i	−0.852603	+	0.522560i	$0.824977\pi$
$350$		0			0
$351$	0.0776848	+	0.0526312i	0.00414651	+	0.00280925i
$352$			23.0733i			1.22981i
$353$	−5.27541	+	6.28699i	−0.280782	+	0.334623i	−0.887941	−	0.459958i	$-0.847865\pi$
$353$	−5.27541	+	6.28699i	−0.280782	+	0.334623i	0.607159	+	0.794580i	$0.292309\pi$
$354$	−2.17423	+	1.53911i	−0.115559	+	0.0818026i
$355$		0			0
$356$	−5.79217	−	2.10818i	−0.306984	−	0.111733i
$357$	6.47401	−	3.05944i	0.342641	−	0.161923i
$358$	4.16928	+	0.735157i	0.220353	+	0.0388542i
$359$	8.86365	−	15.3523i	0.467806	−	0.810263i	−0.531517	−	0.847047i	$-0.678378\pi$
$359$	8.86365	−	15.3523i	0.467806	−	0.810263i	0.999323	+	0.0367840i	$0.0117114\pi$
$360$		0			0
$361$	9.41291	+	16.3036i	0.495416	+	0.858086i
$362$	3.41812	+	9.39122i	0.179653	+	0.493591i
$363$	19.7365	−	19.9402i	1.03590	−	1.04659i
$364$	0.0333594	−	0.0279919i	0.00174851	−	0.00146717i
$365$		0			0
$366$	−3.53626	−	3.50013i	−0.184843	−	0.182955i
$367$	6.94969	+	19.0941i	0.362771	+	0.996704i	0.978045	+	0.208392i	$0.0668229\pi$
$367$	6.94969	+	19.0941i	0.362771	+	0.996704i	−0.615275	+	0.788313i	$0.710955\pi$
$368$	2.68215	−	1.54854i	0.139817	−	0.0807232i
$369$	−6.99953	+	8.51782i	−0.364381	+	0.443420i
$370$		0			0
$371$	0.298028	−	1.69020i	0.0154728	−	0.0877509i
$372$	−10.6731	+	5.04381i	−0.553374	+	0.261510i
$373$	3.31125	−	9.09758i	0.171450	−	0.471055i	−0.823972	−	0.566630i	$-0.808247\pi$
$373$	3.31125	−	9.09758i	0.171450	−	0.471055i	0.995422	+	0.0955754i	$0.0304691\pi$
$374$	1.17871	+	6.68481i	0.0609498	+	0.345663i
$375$		0			0
$376$	−8.64615	−	7.25498i	−0.445891	−	0.374147i
$377$			0.140987i			0.00726119i
$378$	−1.59790	+	2.35853i	−0.0821870	+	0.121310i
$379$	4.12905			0.212095			0.106048	−	0.994361i	$-0.466180\pi$
$379$	4.12905			0.212095			0.106048	+	0.994361i	$0.466180\pi$
$380$		0			0
$381$	13.2096	+	6.07736i	0.676748	+	0.311353i
$382$	4.47876	−	0.789725i	0.229153	−	0.0404059i
$383$	−1.62466	+	4.46371i	−0.0830162	+	0.228085i	−0.974255	−	0.225450i	$-0.927615\pi$
$383$	−1.62466	+	4.46371i	−0.0830162	+	0.228085i	0.891239	+	0.453535i	$0.149837\pi$
$384$	−18.2508	−	1.50236i	−0.931357	−	0.0766672i
$385$		0			0
$386$	−2.24476	+	3.88803i	−0.114255	+	0.197896i
$387$	−12.6828	−	21.4554i	−0.644702	−	1.09064i
$388$	15.7328	−	9.08336i	0.798714	−	0.461138i
$389$	−20.4978	+	7.46059i	−1.03928	+	0.378267i	−0.804607	−	0.593807i	$-0.797624\pi$
$389$	−20.4978	+	7.46059i	−1.03928	+	0.378267i	−0.234673	+	0.972074i	$0.575402\pi$
$390$		0			0
$391$	2.48238	−	2.08297i	0.125539	−	0.105340i
$392$	−5.37495	−	6.40561i	−0.271476	−	0.323532i
$393$	−7.09745	−	25.9543i	−0.358019	−	1.30922i
$394$	8.61767	−	3.13658i	0.434152	−	0.158018i
$395$		0			0
$396$	18.6015	+	21.7117i	0.934762	+	1.09106i
$397$	30.1802	+	17.4245i	1.51470	+	0.874512i	0.999852	+	0.0172294i	$0.00548457\pi$
$397$	30.1802	+	17.4245i	1.51470	+	0.874512i	0.514847	+	0.857282i	$0.327849\pi$
$398$	5.27268	+	0.929715i	0.264295	+	0.0466024i
$399$	−0.543131	+	0.784210i	−0.0271906	+	0.0392596i
$400$		0			0
$401$	−3.26911	−	18.5401i	−0.163252	−	0.925847i	−0.950849	−	0.309656i	$-0.899786\pi$
$401$	−3.26911	−	18.5401i	−0.163252	−	0.925847i	0.787597	−	0.616191i	$-0.211325\pi$
$402$	−7.90113	+	0.732152i	−0.394072	+	0.0365164i
$403$	−0.0432932	+	0.0515948i	−0.00215659	+	0.00257012i
$404$	25.2170			1.25459
$405$		0			0
$406$	−4.28040			−0.212433
$407$	14.8329	−	17.6772i	0.735241	−	0.876226i
$408$	−8.59160	+	0.796135i	−0.425348	+	0.0394145i
$409$	1.10439	+	6.26334i	0.0546088	+	0.309702i	0.999862	−	0.0166371i	$-0.00529599\pi$
$409$	1.10439	+	6.26334i	0.0546088	+	0.309702i	−0.945253	+	0.326339i	$0.894185\pi$
$410$		0			0
$411$	−11.8413	+	17.0973i	−0.584088	+	0.843346i
$412$	−8.21551	−	1.44862i	−0.404749	−	0.0713682i
$413$	4.23055	+	2.44251i	0.208172	+	0.120188i
$414$	−0.428490	+	1.21597i	−0.0210591	+	0.0597617i
$415$		0			0
$416$	−0.0750772	+	0.0273259i	−0.00368096	+	0.00133976i
$417$	−2.80753	−	10.2667i	−0.137485	−	0.502763i
$418$	−0.581267	−	0.692727i	−0.0284307	−	0.0338824i
$419$	18.6286	−	15.6313i	0.910069	−	0.763638i	−0.0620632	−	0.998072i	$-0.519768\pi$
$419$	18.6286	−	15.6313i	0.910069	−	0.763638i	0.972132	+	0.234434i	$0.0753236\pi$
$420$		0			0
$421$	7.50818	−	2.73275i	0.365926	−	0.133186i	−0.152511	−	0.988302i	$-0.548736\pi$
$421$	7.50818	−	2.73275i	0.365926	−	0.133186i	0.518438	+	0.855115i	$0.326514\pi$
$422$	8.63373	−	4.98469i	0.420283	−	0.242651i
$423$	−21.2926	+	0.218637i	−1.03528	+	0.0106305i
$424$	−1.03405	+	1.79103i	−0.0502181	+	0.0869803i
$425$		0			0
$426$	4.36354	+	0.359197i	0.211414	+	0.0174031i
$427$	−3.12067	+	8.57397i	−0.151020	+	0.414924i
$428$	20.3294	−	3.58462i	0.982659	−	0.173269i
$429$	0.148191	+	0.0681784i	0.00715472	+	0.00329169i
$430$		0			0
$431$	9.87124			0.475481			0.237740	−	0.971329i	$-0.423593\pi$
$431$	9.87124			0.475481			0.237740	+	0.971329i	$0.423593\pi$
$432$	−12.6053	+	9.11887i	−0.606475	+	0.438732i
$433$			6.10369i			0.293325i	0.989187	+	0.146662i	$0.0468531\pi$
$433$			6.10369i			0.293325i	−0.989187	+	0.146662i	$0.953147\pi$
$434$	−1.56643	−	1.31439i	−0.0751911	−	0.0630928i
$435$		0			0
$436$	−4.60219	−	26.1003i	−0.220405	−	1.24998i
$437$	−0.147651	+	0.405669i	−0.00706312	+	0.0194058i
$438$	−0.355870	+	0.168174i	−0.0170041	+	0.00803569i
$439$	2.62800	−	14.9041i	0.125427	−	0.711334i	−0.855626	−	0.517595i	$-0.826827\pi$
$439$	2.62800	−	14.9041i	0.125427	−	0.711334i	0.981053	−	0.193739i	$-0.0620615\pi$
$440$		0			0
$441$	−15.5634	−	2.57976i	−0.741113	−	0.122846i
$442$	−0.0203554	+	0.0117522i	−0.000968210	+	0.000558996i
$443$	−0.247210	−	0.679204i	−0.0117453	−	0.0322699i	0.933681	−	0.358105i	$-0.116577\pi$
$443$	−0.247210	−	0.679204i	−0.0117453	−	0.0322699i	−0.945427	+	0.325835i	$0.894355\pi$
$444$	9.95369	+	9.85201i	0.472381	+	0.467555i
$445$		0			0
$446$	−6.89432	+	5.78502i	−0.326456	+	0.273929i
$447$	−1.07566	+	1.08677i	−0.0508772	+	0.0514023i
$448$	1.87311	+	5.14633i	0.0884962	+	0.243141i
$449$	0.834224	+	1.44492i	0.0393695	+	0.0681899i	0.885039	−	0.465517i	$-0.154132\pi$
$449$	0.834224	+	1.44492i	0.0393695	+	0.0681899i	−0.845669	+	0.533707i	$0.820798\pi$
$450$		0			0
$451$	−9.58275	+	16.5978i	−0.451234	+	0.781560i
$452$	−22.6005	−	3.98507i	−1.06304	−	0.187442i
$453$	−12.8810	+	6.08723i	−0.605204	+	0.286003i
$454$	−8.44922	−	3.07526i	−0.396541	−	0.144329i
$455$		0			0
$456$	0.938202	−	0.664140i	0.0439353	−	0.0311012i
$457$	−7.12430	+	8.49041i	−0.333261	+	0.397165i	−0.906488	−	0.422232i	$-0.861247\pi$
$457$	−7.12430	+	8.49041i	−0.333261	+	0.397165i	0.573227	+	0.819397i	$0.305691\pi$
$458$		−	4.48926i		−	0.209769i
$459$	−11.3320	+	11.6865i	−0.528932	+	0.545481i
$460$		0			0
$461$	−16.7644	−	14.0670i	−0.780797	−	0.655166i	0.162653	−	0.986683i	$-0.447995\pi$
$461$	−16.7644	−	14.0670i	−0.780797	−	0.655166i	−0.943449	+	0.331517i	$0.892439\pi$
$462$	−2.06992	+	4.49911i	−0.0963012	+	0.209318i
$463$	24.4742	−	4.31546i	1.13741	−	0.200556i	0.426938	−	0.904281i	$-0.359592\pi$
$463$	24.4742	−	4.31546i	1.13741	−	0.200556i	0.710473	+	0.703724i	$0.248481\pi$
$464$	−21.9660	−	7.99499i	−1.01975	−	0.371158i
$465$		0			0
$466$	−0.551115	+	3.12553i	−0.0255299	+	0.144787i
$467$	10.2499	+	5.91777i	0.474308	+	0.273842i	0.718041	−	0.696001i	$-0.245039\pi$
$467$	10.2499	+	5.91777i	0.474308	+	0.273842i	−0.243734	+	0.969842i	$0.578372\pi$
$468$	−0.0486170	+	0.0862400i	−0.00224732	+	0.00398645i
$469$	7.27564	+	12.6018i	0.335958	+	0.581896i
$470$		0			0
$471$	5.52246	−	21.0416i	0.254462	−	0.969547i
$472$	−3.78373	−	4.50927i	−0.174160	−	0.207556i
$473$	−27.8501	−	33.1905i	−1.28055	−	1.52610i
$474$	−0.339526	+	0.0928466i	−0.0155950	+	0.00426459i
$475$		0			0
$476$	3.77733	+	6.54252i	0.173134	+	0.299876i
$477$	0.716944	+	3.83529i	0.0328266	+	0.175606i
$478$	1.16270	+	0.671288i	0.0531809	+	0.0307040i
$479$	−0.501383	+	2.84349i	−0.0229088	+	0.129922i	−0.994117	−	0.108309i	$-0.965456\pi$
$479$	−0.501383	+	2.84349i	−0.0229088	+	0.129922i	0.971209	+	0.238231i	$0.0765676\pi$
$480$		0			0
$481$	0.0750857	+	0.0273290i	0.00342361	+	0.00124609i
$482$	−10.8610	+	1.91508i	−0.494704	+	0.0872297i
$483$	2.35417	−	0.218148i	0.107119	−	0.00992607i
$484$	22.6752	+	19.0267i	1.03069	+	0.864852i
$485$		0			0
$486$	1.51512	−	6.29676i	0.0687271	−	0.285627i
$487$			8.75903i			0.396910i	0.980110	+	0.198455i	$0.0635923\pi$
$487$			8.75903i			0.396910i	−0.980110	+	0.198455i	$0.936408\pi$
$488$	7.06724	−	8.42241i	0.319919	−	0.381265i
$489$	−0.529731	−	5.71667i	−0.0239553	−	0.258517i
$490$		0			0
$491$	21.2117	+	7.72044i	0.957272	+	0.348418i	0.772964	−	0.634450i	$-0.218773\pi$
$491$	21.2117	+	7.72044i	0.957272	+	0.348418i	0.184308	+	0.982869i	$0.440996\pi$
$492$	−9.56222	−	6.62264i	−0.431098	−	0.298572i
$493$	−24.0869	−	4.24716i	−1.08482	−	0.191283i
$494$	0.00156564	−	0.00271176i	7.04413e−5	−	0.000122008i
$495$		0			0
$496$	−5.58354	−	9.67097i	−0.250708	−	0.434239i
$497$	−2.74608	−	7.54478i	−0.123178	−	0.338430i
$498$	−0.875741	−	3.20246i	−0.0392429	−	0.143505i
$499$	19.4061	−	16.2836i	0.868734	−	0.728955i	−0.0950968	−	0.995468i	$-0.530316\pi$
$499$	19.4061	−	16.2836i	0.868734	−	0.728955i	0.963831	+	0.266513i	$0.0858716\pi$
$500$		0			0
$501$	−9.04139	+	34.4494i	−0.403940	+	1.53909i
$502$	−0.639340	−	1.75657i	−0.0285352	−	0.0783997i
$503$	−3.24252	+	1.87207i	−0.144577	+	0.0834714i	−0.570543	−	0.821267i	$-0.693267\pi$
$503$	−3.24252	+	1.87207i	−0.144577	+	0.0834714i	0.425967	+	0.904739i	$0.359934\pi$
$504$	−5.48386	−	3.09147i	−0.244270	−	0.137705i
$505$		0			0
$506$	−0.389187	+	2.20719i	−0.0173015	+	0.0981216i
$507$	1.84723	−	22.4402i	0.0820382	−	0.996604i
$508$	−5.24690	+	14.4157i	−0.232793	+	0.639595i
$509$	−4.22831	−	23.9800i	−0.187417	−	1.06289i	−0.922811	−	0.385253i	$-0.874114\pi$
$509$	−4.22831	−	23.9800i	−0.187417	−	1.06289i	0.735394	−	0.677640i	$-0.236997\pi$
$510$		0			0
$511$	0.552932	+	0.463965i	0.0244603	+	0.0205246i
$512$		−	22.7690i		−	1.00626i
$513$	0.528954	−	2.10313i	0.0233539	−	0.0928554i
$514$	5.70660			0.251707
$515$		0			0
$516$	21.4623	−	15.1929i	0.944824	−	0.668828i
$517$	−36.4546	+	6.42792i	−1.60327	+	0.282700i
$518$	−0.829715	+	2.27962i	−0.0364556	+	0.100161i
$519$	10.3853	+	21.9760i	0.455862	+	0.964639i
$520$		0			0
$521$	−9.81046	+	16.9922i	−0.429804	+	0.744443i	−0.996856	−	0.0792397i	$-0.974751\pi$
$521$	−9.81046	+	16.9922i	−0.429804	+	0.744443i	0.567051	+	0.823682i	$0.308084\pi$
$522$	9.10941	−	3.42188i	0.398708	−	0.149772i
$523$	−18.0267	+	10.4077i	−0.788251	+	0.455097i	−0.839346	−	0.543597i	$-0.817062\pi$
$523$	−18.0267	+	10.4077i	−0.788251	+	0.455097i	0.0510956	+	0.998694i	$0.483729\pi$
$524$	26.6763	−	9.70937i	1.16536	−	0.424156i
$525$		0			0
$526$	7.70284	−	6.46345i	0.335860	−	0.281820i
$527$	−7.51051	−	8.95067i	−0.327163	−	0.389897i
$528$	−19.0258	+	19.2222i	−0.827993	+	0.836539i
$529$	−20.6075	+	7.50052i	−0.895978	+	0.326109i
$530$		0			0
$531$	−10.9559	−	1.81604i	−0.475447	−	0.0788095i
$532$	−0.871598	−	0.503217i	−0.0377886	−	0.0218172i
$533$	−0.0653558	−	0.0115240i	−0.00283087	−	0.000499159i
$534$	1.03710	+	2.19457i	0.0448795	+	0.0949685i
$535$		0			0
$536$	−3.04479	−	17.2679i	−0.131515	−	0.745859i
$537$	10.1975	+	14.4055i	0.440054	+	0.621645i
$538$	−3.20634	+	3.82117i	−0.138235	+	0.164742i
$539$	−27.4245			−1.18126
$540$		0			0
$541$	−30.6272			−1.31676			−0.658382	−	0.752684i	$-0.728759\pi$
$541$	−30.6272			−1.31676			−0.658382	+	0.752684i	$0.728759\pi$
$542$	0.992856	−	1.18324i	0.0426468	−	0.0508245i
$543$	−17.4139	+	37.8503i	−0.747301	+	1.62431i
$544$	−2.40681	−	13.6497i	−0.103191	−	0.585227i
$545$		0			0
$546$	−0.0170909	−	0.00140688i	−0.000731421	−	6.02089e-5i
$547$	22.3036	+	3.93273i	0.953633	+	0.168151i	0.628754	−	0.777604i	$-0.283565\pi$
$547$	22.3036	+	3.93273i	0.953633	+	0.168151i	0.324879	+	0.945756i	$0.394676\pi$
$548$	−19.0025	−	10.9711i	−0.811745	−	0.468661i
$549$	−0.212980	−	20.7416i	−0.00908976	−	0.885231i
$550$		0			0
$551$	3.06186	−	1.11443i	0.130440	−	0.0474761i
$552$	−2.75560	−	0.723220i	−0.117286	−	0.0307823i
$553$	0.414912	+	0.494473i	0.0176439	+	0.0210271i
$554$	−7.47387	+	6.27132i	−0.317534	+	0.266443i
$555$		0			0
$556$	10.5523	−	3.84072i	0.447517	−	0.162883i
$557$	31.5682	−	18.2259i	1.33759	−	0.772256i	0.351138	−	0.936324i	$-0.385795\pi$
$557$	31.5682	−	18.2259i	1.33759	−	0.772256i	0.986449	+	0.164067i	$0.0524615\pi$
$558$	4.38440	+	1.54500i	0.185606	+	0.0654049i
$559$	0.0750139	−	0.129928i	0.00317275	−	0.00549537i
$560$		0			0
$561$	−16.1121	+	23.2637i	−0.680253	+	0.982196i
$562$	2.89478	−	7.95334i	0.122109	−	0.335491i
$563$	26.1134	−	4.60450i	1.10055	−	0.194056i	0.406263	−	0.913756i	$-0.366832\pi$
$563$	26.1134	−	4.60450i	1.10055	−	0.194056i	0.694285	+	0.719700i	$0.255721\pi$
$564$	−2.07290	−	22.3700i	−0.0872847	−	0.941945i
$565$		0			0
$566$	−4.81938			−0.202574
$567$	−11.6514	+	2.30210i	−0.489313	+	0.0966791i
$568$			9.67492i			0.405950i
$569$	−17.5941	−	14.7632i	−0.737581	−	0.618904i	0.194606	−	0.980882i	$-0.437657\pi$
$569$	−17.5941	−	14.7632i	−0.737581	−	0.618904i	−0.932187	+	0.361978i	$0.882102\pi$
$570$		0			0
$571$	−0.833165	−	4.72511i	−0.0348669	−	0.197740i	0.962399	−	0.271641i	$-0.0875662\pi$
$571$	−0.833165	−	4.72511i	−0.0348669	−	0.197740i	−0.997266	+	0.0739009i	$0.976455\pi$
$572$	−0.0588619	+	0.161722i	−0.00246114	+	0.00676193i
$573$	15.5865	+	10.7949i	0.651134	+	0.450965i
$574$	0.349871	−	1.98422i	0.0146033	−	0.0828197i
$575$		0			0
$576$	−8.10043	−	9.45484i	−0.337518	−	0.393952i
$577$	−3.73545	+	2.15666i	−0.155509	+	0.0897831i	−0.575735	−	0.817636i	$-0.695284\pi$
$577$	−3.73545	+	2.15666i	−0.155509	+	0.0897831i	0.420226	+	0.907419i	$0.361951\pi$
$578$	1.02106	+	2.80533i	0.0424704	+	0.116686i
$579$	−18.0536	+	4.93693i	−0.750283	+	0.205172i
$580$		0			0
$581$	−4.66393	+	3.91351i	−0.193493	+	0.162360i
$582$	−6.91954	−	1.81606i	−0.286824	−	0.0752782i
$583$	2.31983	+	6.37369i	0.0960777	+	0.263971i
$584$	−0.434885	−	0.753242i	−0.0179957	−	0.0311694i
$585$		0			0
$586$	6.55900	−	11.3605i	0.270950	−	0.469299i
$587$	41.1868	+	7.26235i	1.69996	+	0.299749i	0.937681	−	0.347497i	$-0.112968\pi$
$587$	41.1868	+	7.26235i	1.69996	+	0.299749i	0.762281	+	0.647246i	$0.224079\pi$
$588$	1.36548	−	16.5880i	0.0563116	−	0.684076i
$589$	1.46271	+	0.532383i	0.0602699	+	0.0219365i
$590$		0			0
$591$	34.7326	+	15.9795i	1.42871	+	0.657309i
$592$	−8.51582	+	10.1488i	−0.349998	+	0.417111i
$593$			31.5370i			1.29507i	0.762035	+	0.647536i	$0.224200\pi$
$593$			31.5370i			1.29507i	−0.762035	+	0.647536i	$0.775800\pi$
$594$	0.808405	−	11.2296i	0.0331693	−	0.460757i
$595$		0			0
$596$	−1.23583	−	1.03698i	−0.0506214	−	0.0424764i
$597$	12.8962	+	18.2179i	0.527807	+	0.745611i
$598$	−0.00764279	+	0.00134763i	−0.000312537	+	5.51087e-5i
$599$	−11.8686	−	4.31982i	−0.484938	−	0.176503i	0.0879695	−	0.996123i	$-0.471962\pi$
$599$	−11.8686	−	4.31982i	−0.484938	−	0.176503i	−0.572907	+	0.819620i	$0.694184\pi$
$600$		0			0
$601$	3.56725	−	20.2309i	0.145511	−	0.825235i	−0.821444	−	0.570289i	$-0.806831\pi$
$601$	3.56725	−	20.2309i	0.145511	−	0.825235i	0.966955	−	0.254946i	$-0.0820577\pi$
$602$	3.94465	+	2.27744i	0.160772	+	0.0928216i
$603$	−25.5580	−	21.0023i	−1.04080	−	0.855282i
$604$	−7.51556	−	13.0173i	−0.305804	−	0.529668i
$605$		0			0
$606$	−7.05769	−	6.98559i	−0.286699	−	0.283770i
$607$	8.30003	+	9.89160i	0.336888	+	0.401487i	0.907718	−	0.419581i	$-0.137823\pi$
$607$	8.30003	+	9.89160i	0.336888	+	0.401487i	−0.570830	+	0.821068i	$0.693378\pi$
$608$	1.18689	+	1.41448i	0.0481348	+	0.0573648i
$609$	−12.6827	−	12.5532i	−0.513930	−	0.508680i
$610$		0			0
$611$	−0.0640889	−	0.111005i	−0.00259276	−	0.00449079i
$612$	−13.2691	−	10.9039i	−0.536371	−	0.440763i
$613$	−26.9851	−	15.5799i	−1.08992	−	0.629265i	−0.156364	−	0.987699i	$-0.549977\pi$
$613$	−26.9851	−	15.5799i	−1.08992	−	0.629265i	−0.933555	+	0.358434i	$0.883311\pi$
$614$	−0.585856	+	3.32255i	−0.0236432	+	0.134087i
$615$		0			0
$616$	−10.2836	−	3.74293i	−0.414339	−	0.150807i
$617$	7.03230	−	1.23998i	0.283110	−	0.0499199i	−0.0302901	−	0.999541i	$-0.509643\pi$
$617$	7.03230	−	1.23998i	0.283110	−	0.0499199i	0.313400	+	0.949621i	$0.398532\pi$
$618$	1.89805	+	2.68129i	0.0763506	+	0.107857i
$619$	7.68412	+	6.44774i	0.308851	+	0.259157i	0.784017	−	0.620740i	$-0.213168\pi$
$619$	7.68412	+	6.44774i	0.308851	+	0.259157i	−0.475166	+	0.879896i	$0.657612\pi$
$620$		0			0
$621$	−4.83569	+	2.34625i	−0.194049	+	0.0941520i
$622$			9.90827i			0.397285i
$623$	2.86117	−	3.40981i	0.114630	−	0.136611i
$624$	−0.0850787	−	0.0391423i	−0.00340587	−	0.00156695i
$625$		0			0
$626$	10.5061	+	3.82392i	0.419909	+	0.152835i
$627$	0.309286	−	3.75722i	0.0123517	−	0.150049i
$628$	22.6030	+	3.98552i	0.901957	+	0.159039i
$629$	−6.93093	+	12.0047i	−0.276354	+	0.478660i
$630$		0			0
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	0.927812	−	0.373047i	$-0.121687\pi$
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	−0.786975	+	0.616985i	$0.788354\pi$
$632$	−0.266028	−	0.730905i	−0.0105820	−	0.0290738i
$633$	40.2002	+	10.5507i	1.59781	+	0.419353i
$634$	−2.65189	+	2.22520i	−0.105320	+	0.0883741i
$635$		0			0
$636$	−3.97070	+	1.08582i	−0.157448	+	0.0430557i
$637$	−0.0324790	−	0.0892352i	−0.00128686	−	0.00353563i
$638$	14.6498	−	8.45809i	0.579993	−	0.334859i
$639$	11.8756	+	13.8613i	0.469793	+	0.548344i
$640$		0			0
$641$	−0.870188	+	4.93508i	−0.0343704	+	0.194924i	−0.997158	−	0.0753337i	$-0.975998\pi$
$641$	−0.870188	+	4.93508i	−0.0343704	+	0.194924i	0.962788	+	0.270258i	$0.0871089\pi$
$642$	−6.68277	−	4.62838i	−0.263748	−	0.182667i
$643$	−0.560367	+	1.53960i	−0.0220987	+	0.0607157i	−0.950251	−	0.311484i	$-0.899174\pi$
$643$	−0.560367	+	1.53960i	−0.0220987	+	0.0607157i	0.928153	+	0.372199i	$0.121396\pi$
$644$	0.433147	+	2.45650i	0.0170684	+	0.0967997i
$645$		0			0
$646$	0.416126	+	0.349171i	0.0163722	+	0.0137379i
$647$			34.4927i			1.35605i	0.735040	+	0.678024i	$0.237164\pi$
$647$			34.4927i			1.35605i	−0.735040	+	0.678024i	$0.762836\pi$
$648$	14.1420	+	2.19521i	0.555550	+	0.0862359i
$649$	−19.3056			−0.757813
$650$		0			0
$651$	−0.786571	−	8.48840i	−0.0308282	−	0.332687i
$652$	5.96515	−	1.05182i	0.233613	−	0.0411923i
$653$	−13.2569	+	36.4230i	−0.518783	+	1.42534i	0.353080	+	0.935593i	$0.385134\pi$
$653$	−13.2569	+	36.4230i	−0.518783	+	1.42534i	−0.871862	+	0.489751i	$0.837088\pi$
$654$	−5.94223	+	8.57980i	−0.232360	+	0.335497i
$655$		0			0
$656$	5.50161	−	9.52907i	0.214802	−	0.372048i
$657$	−1.54764	−	0.545365i	−0.0603792	−	0.0212767i
$658$	3.37015	−	1.94575i	0.131382	−	0.0758534i
$659$	8.82552	−	3.21223i	0.343794	−	0.125131i	−0.164352	−	0.986402i	$-0.552553\pi$
$659$	8.82552	−	3.21223i	0.343794	−	0.125131i	0.508146	+	0.861271i	$0.330331\pi$
$660$		0			0
$661$	−18.4980	+	15.5217i	−0.719489	+	0.603723i	−0.927244	−	0.374458i	$-0.877829\pi$
$661$	−18.4980	+	15.5217i	−0.719489	+	0.603723i	0.207755	+	0.978181i	$0.433384\pi$
$662$	1.71457	+	2.04335i	0.0666387	+	0.0794169i
$663$	−0.0947785	−	0.0248750i	−0.00368089	−	0.000966065i
$664$	6.89399	−	2.50921i	0.267539	−	0.0973761i
$665$		0			0
$666$	−0.0566265	−	5.51472i	−0.00219423	−	0.213691i
$667$	−6.99375	−	4.03784i	−0.270799	−	0.156346i
$668$	−37.0057	−	6.52510i	−1.43179	−	0.252464i
$669$	−37.3935	−	3.07815i	−1.44572	−	0.119008i
$670$		0			0
$671$	−6.26159	−	35.5112i	−0.241726	−	1.37090i
$672$	4.22656	−	9.18674i	0.163043	−	0.354386i
$673$	−17.0121	+	20.2742i	−0.655768	+	0.781514i	−0.986772	−	0.162115i	$-0.948168\pi$
$673$	−17.0121	+	20.2742i	−0.655768	+	0.781514i	0.331003	+	0.943630i	$0.392613\pi$
$674$	3.10557			0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	−19.9694	+	23.7986i	−0.767486	+	0.914654i	−0.998296	−	0.0583448i	$-0.981418\pi$
$677$	−19.9694	+	23.7986i	−0.767486	+	0.914654i	0.230811	+	0.972999i	$0.425862\pi$
$678$	5.22143	+	7.37609i	0.200528	+	0.283277i
$679$	2.27807	+	12.9196i	0.0874245	+	0.495809i
$680$		0			0
$681$	−16.0160	−	33.8910i	−0.613734	−	1.29871i
$682$	7.95842	+	1.40328i	0.304744	+	0.0537345i
$683$	33.0268	+	19.0681i	1.26374	+	0.729619i	0.973796	−	0.227425i	$-0.0730308\pi$
$683$	33.0268	+	19.0681i	1.26374	+	0.729619i	0.289942	+	0.957044i	$0.406364\pi$
$684$	2.25719	+	0.374149i	0.0863060	+	0.0143060i
$685$		0			0
$686$	6.31558	−	2.29868i	0.241130	−	0.0877642i
$687$	13.1657	−	13.3016i	0.502303	−	0.507487i
$688$	15.9892	+	19.0552i	0.609583	+	0.726472i
$689$	−0.0179917	+	0.0150968i	−0.000685428	+	0.000575142i
$690$		0			0
$691$	−30.9436	+	11.2626i	−1.17715	+	0.428448i	−0.855195	−	0.518306i	$-0.826563\pi$
$691$	−30.9436	+	11.2626i	−1.17715	+	0.428448i	−0.321957	+	0.946754i	$0.604341\pi$
$692$	−22.2085	+	12.8221i	−0.844242	+	0.487424i
$693$	−19.3277	+	7.26030i	−0.734198	+	0.275796i
$694$	6.53414	−	11.3175i	0.248033	−	0.429605i
$695$		0			0
$696$	9.18742	+	19.4413i	0.348248	+	0.736919i
$697$	3.93762	−	10.8185i	0.149148	−	0.409781i
$698$	−4.84968	+	0.855130i	−0.183563	+	0.0323672i
$699$	−10.7992	+	7.64461i	−0.408463	+	0.289146i
$700$		0			0
$701$	−2.30710			−0.0871381			−0.0435690	−	0.999050i	$-0.513873\pi$
$701$	−2.30710			−0.0871381			−0.0435690	+	0.999050i	$0.513873\pi$
$702$	0.0374969	−	0.0106689i	0.00141523	−	0.000402671i
$703$		−	1.84668i		−	0.0696490i
$704$	−16.5800	−	13.9123i	−0.624881	−	0.524338i
$705$		0			0
$706$	0.592100	+	3.35796i	0.0222840	+	0.126379i
$707$	−6.22826	+	17.1120i	−0.234238	+	0.643563i
$708$	0.961241	−	11.6772i	0.0361257	−	0.438857i
$709$	1.93654	−	10.9826i	0.0727281	−	0.412462i	−0.926608	−	0.376029i	$-0.877289\pi$
$709$	1.93654	−	10.9826i	0.0727281	−	0.412462i	0.999336	−	0.0364329i	$-0.0115995\pi$
$710$		0			0
$711$	−1.27830	−	0.720629i	−0.0479400	−	0.0270257i
$712$	−4.64508	+	2.68184i	−0.174082	+	0.100506i
$713$	−1.31948	−	3.62525i	−0.0494151	−	0.135767i
$714$	0.755212	−	2.87750i	0.0282631	−	0.107688i
$715$		0			0
$716$	−14.2646	+	11.9694i	−0.533092	+	0.447317i
$717$	1.47637	+	5.39888i	0.0551362	+	0.201625i
$718$	−2.51901	−	6.92093i	−0.0940087	−	0.258287i
$719$	−16.0850	−	27.8600i	−0.599869	−	1.03900i	−0.992840	−	0.119453i	$-0.961886\pi$
$719$	−16.0850	−	27.8600i	−0.599869	−	1.03900i	0.392971	−	0.919551i	$-0.371447\pi$
$720$		0			0
$721$	3.01213	−	5.21717i	0.112178	−	0.194297i
$722$	7.70267	+	1.35819i	0.286664	+	0.0505465i
$723$	−37.7972	−	26.1777i	−1.40569	−	0.973560i
$724$	−41.3064	−	15.0343i	−1.53514	−	0.558745i
$725$		0			0
$726$	−1.07552	−	11.6066i	−0.0399163	−	0.430762i
$727$	3.44888	−	4.11022i	0.127912	−	0.152440i	−0.698287	−	0.715818i	$-0.746054\pi$
$727$	3.44888	−	4.11022i	0.127912	−	0.152440i	0.826199	+	0.563378i	$0.190499\pi$
$728$		−	0.0378942i		−	0.00140445i
$729$	22.9558	−	14.2138i	0.850215	−	0.526435i
$730$		0			0
$731$	19.9377	+	16.7297i	0.737424	+	0.618772i
$732$	21.7911	−	2.01926i	0.805422	−	0.0746338i
$733$	−14.3746	+	2.53463i	−0.530938	+	0.0936187i	−0.432689	−	0.901543i	$-0.642435\pi$
$733$	−14.3746	+	2.53463i	−0.530938	+	0.0936187i	−0.0982489	+	0.995162i	$0.531324\pi$
$734$	7.93296	+	2.88736i	0.292811	+	0.106574i
$735$		0			0
$736$	0.794682	−	4.50687i	0.0292924	−	0.166125i
$737$	−49.8023	−	28.7534i	−1.83449	−	1.05915i
$738$	0.841659	+	4.50245i	0.0309819	+	0.165737i
$739$	−21.6083	−	37.4266i	−0.794873	−	1.37676i	−0.922920	−	0.384992i	$-0.874204\pi$
$739$	−21.6083	−	37.4266i	−0.794873	−	1.37676i	0.128047	−	0.991768i	$-0.459129\pi$
$740$		0			0
$741$	0.0125917	−	0.00344333i	0.000462569	−	0.000126494i
$742$	−0.458343	−	0.546231i	−0.0168263	−	0.0200528i
$743$	−5.21443	−	6.21431i	−0.191299	−	0.227981i	0.661866	−	0.749622i	$-0.269765\pi$
$743$	−5.21443	−	6.21431i	−0.191299	−	0.227981i	−0.853165	+	0.521641i	$0.825320\pi$
$744$	−2.60770	+	9.93582i	−0.0956028	+	0.364265i
$745$		0			0
$746$	−2.01116	−	3.48342i	−0.0736336	−	0.127537i
$747$	6.79706	−	12.0571i	0.248692	−	0.441146i
$748$	−25.8561	−	14.9280i	−0.945393	−	0.545823i
$749$	−2.58860	+	14.6807i	−0.0945854	+	0.536420i
$750$		0			0
$751$	−8.22744	−	2.99454i	−0.300223	−	0.109272i	0.187516	−	0.982261i	$-0.439956\pi$
$751$	−8.22744	−	2.99454i	−0.300223	−	0.109272i	−0.487740	+	0.872989i	$0.662178\pi$
$752$	20.9291	−	3.69037i	0.763207	−	0.134574i
$753$	3.25717	−	7.07968i	0.118698	−	0.257998i
$754$	0.0448713	+	0.0376515i	0.00163412	+	0.00137119i
$755$		0			0
$756$	−3.42913	−	12.0520i	−0.124716	−	0.438329i
$757$		−	32.1511i		−	1.16855i	−0.811555	−	0.584276i	$-0.801378\pi$
$757$		−	32.1511i		−	1.16855i	0.811555	−	0.584276i	$-0.198622\pi$
$758$	1.10269	−	1.31414i	0.0400515	−	0.0477316i
$759$	−7.62620	+	5.39848i	−0.276813	+	0.195952i
$760$		0			0
$761$	23.0656	+	8.39520i	0.836128	+	0.304326i	0.724371	−	0.689410i	$-0.242130\pi$
$761$	23.0656	+	8.39520i	0.836128	+	0.304326i	0.111756	+	0.993736i	$0.464352\pi$
$762$	5.46192	−	2.58116i	0.197865	−	0.0935054i
$763$	18.8481	+	3.32342i	0.682346	+	0.120316i
$764$	−10.0016	+	17.3233i	−0.361846	+	0.626736i
$765$		0			0
$766$	0.986770	+	1.70914i	0.0356535	+	0.0617536i
$767$	−0.0228638	−	0.0628177i	−0.000825563	−	0.00226822i
$768$	4.76119	−	4.81033i	0.171805	−	0.173578i
$769$	−24.0648	+	20.1928i	−0.867800	+	0.728170i	−0.963634	−	0.267227i	$-0.913893\pi$
$769$	−24.0648	+	20.1928i	−0.867800	+	0.728170i	0.0958338	+	0.995397i	$0.469448\pi$
$770$		0			0
$771$	16.9085	+	16.7358i	0.608945	+	0.602725i
$772$	−6.75377	−	18.5558i	−0.243073	−	0.667839i
$773$	−24.8675	+	14.3573i	−0.894422	+	0.516395i	−0.875386	−	0.483424i	$-0.839393\pi$
$773$	−24.8675	+	14.3573i	−0.894422	+	0.516395i	−0.0190355	+	0.999819i	$0.506060\pi$
$774$	−10.2155	−	1.69331i	−0.367190	−	0.0608649i

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.267057 - 0.318266i) q^{2} +(1.72466 - 0.159815i) q^{3} +(0.317323 + 1.79963i) q^{4} +(0.409719 - 0.591580i) q^{6} +(-1.29958 - 0.229151i) q^{7} +(1.37711 + 0.795075i) q^{8} +(2.94892 - 0.551252i) q^{9} +O(q^{10})\)	\(q+(0.267057 - 0.318266i) q^{2} +(1.72466 - 0.159815i) q^{3} +(0.317323 + 1.79963i) q^{4} +(0.409719 - 0.591580i) q^{6} +(-1.29958 - 0.229151i) q^{7} +(1.37711 + 0.795075i) q^{8} +(2.94892 - 0.551252i) q^{9} +(4.90067 - 1.78370i) q^{11} +(0.834881 + 3.05303i) q^{12} +(0.0116078 + 0.0138336i) q^{13} +(-0.419993 + 0.352416i) q^{14} +(-2.81355 + 1.02405i) q^{16} +(-2.71308 + 1.56640i) q^{17} +(0.612083 - 1.08575i) q^{18} +(0.208676 - 0.361438i) q^{19} +(-2.27796 - 0.187516i) q^{21} +(0.741067 - 2.03606i) q^{22} +(-1.01867 + 0.179619i) q^{23} +(2.50212 + 1.15115i) q^{24} +0.00750270 q^{26} +(4.99779 - 1.42200i) q^{27} -2.41147i q^{28} +(5.98068 + 5.01839i) q^{29} +(0.647649 + 3.67300i) q^{31} +(-1.51319 + 4.15744i) q^{32} +(8.16694 - 3.85948i) q^{33} +(-0.226015 + 1.28180i) q^{34} +(1.92781 + 5.13202i) q^{36} +(3.83195 - 2.21238i) q^{37} +(-0.0593049 - 0.162939i) q^{38} +(0.0222303 + 0.0220032i) q^{39} +(-2.81517 + 2.36221i) q^{41} +(-0.668024 + 0.674919i) q^{42} +(-2.84146 - 7.80685i) q^{43} +(4.76508 + 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(-6.99008 - 1.23254i) q^{47} +(-4.68877 + 2.21579i) q^{48} +(-4.94145 - 1.79854i) q^{49} +(-4.42881 + 3.13510i) q^{51} +(-0.0212119 + 0.0252794i) q^{52} +1.30057i q^{53} +(0.882118 - 1.97038i) q^{54} +(-1.60747 - 1.34883i) q^{56} +(0.302133 - 0.656707i) q^{57} +(3.19436 - 0.563252i) q^{58} +(-3.47856 - 1.26609i) q^{59} +(1.20064 - 6.80919i) q^{61} +(1.34195 + 0.774775i) q^{62} +(-3.95868 + 0.0406486i) q^{63} +(-2.07506 - 3.59410i) q^{64} +(0.952697 - 3.62996i) q^{66} +(-7.08789 - 8.44702i) q^{67} +(-3.67985 - 4.38548i) q^{68} +(-1.72816 + 0.472581i) q^{69} +(3.04214 + 5.26914i) q^{71} +(4.49927 + 1.58548i) q^{72} +(-0.473692 - 0.273486i) q^{73} +(0.319224 - 1.81041i) q^{74} +(0.716670 + 0.260847i) q^{76} +(-6.77756 + 1.19507i) q^{77} +(0.0129396 - 0.00119904i) q^{78} +(-0.374706 - 0.314416i) q^{79} +(8.39224 - 3.25120i) q^{81} +1.52681i q^{82} +(2.96561 - 3.53428i) q^{83} +(-0.385389 - 4.15898i) q^{84} +(-3.24348 - 1.18053i) q^{86} +(11.1167 + 7.69922i) q^{87} +(8.16694 + 1.44005i) q^{88} +(-1.68653 + 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(-0.646495 - 1.77623i) q^{92} +(1.70398 + 6.23118i) q^{93} +(-2.25902 + 1.89554i) q^{94} +(-1.94531 + 7.41201i) q^{96} +(-3.40014 - 9.34182i) q^{97} +(-1.89206 + 1.09238i) q^{98} +(13.4684 - 7.96149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4}+O(q^{10}) \) 24 * q + 12 * q^4	\( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Introduction

L-functions

Modular forms

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