LMFDB - Embedded newform 675.2.l.c.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.1
Root			$0.500000 + 2.22827i$ of defining polynomial
Character	$\chi$	$=$	675.76
Dual form			675.2.l.c.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.318266 - 0.267057i) q^{2} +(-0.159815 + 1.72466i) q^{3} +(-0.317323 + 1.79963i) q^{4} +(0.409719 + 0.591580i) q^{6} +(0.229151 + 1.29958i) q^{7} +(0.795075 + 1.37711i) q^{8} +(-2.94892 - 0.551252i) q^{9} +(4.90067 + 1.78370i) q^{11} +(-3.05303 - 0.834881i) q^{12} +(0.0138336 + 0.0116078i) q^{13} +(0.419993 + 0.352416i) q^{14} +(-2.81355 - 1.02405i) q^{16} +(-1.56640 + 2.71308i) q^{17} +(-1.08575 + 0.612083i) q^{18} +(-0.208676 - 0.361438i) q^{19} +(-2.27796 + 0.187516i) q^{21} +(2.03606 - 0.741067i) q^{22} +(0.179619 - 1.01867i) q^{23} +(-2.50212 + 1.15115i) q^{24} +0.00750270 q^{26} +(1.42200 - 4.99779i) q^{27} -2.41147 q^{28} +(-5.98068 + 5.01839i) q^{29} +(0.647649 - 3.67300i) q^{31} +(-4.15744 + 1.51319i) q^{32} +(-3.85948 + 8.16694i) q^{33} +(0.226015 + 1.28180i) q^{34} +(1.92781 - 5.13202i) q^{36} +(2.21238 - 3.83195i) q^{37} +(-0.162939 - 0.0593049i) q^{38} +(-0.0222303 + 0.0220032i) q^{39} +(-2.81517 - 2.36221i) q^{41} +(-0.674919 + 0.668024i) q^{42} +(-7.80685 - 2.84146i) q^{43} +(-4.76508 + 8.25337i) q^{44} +(-0.214876 - 0.372177i) q^{46} +(1.23254 + 6.99008i) q^{47} +(2.21579 - 4.68877i) q^{48} +(4.94145 - 1.79854i) q^{49} +(-4.42881 - 3.13510i) q^{51} +(-0.0252794 + 0.0212119i) q^{52} +1.30057 q^{53} +(-0.882118 - 1.97038i) q^{54} +(-1.60747 + 1.34883i) q^{56} +(0.656707 - 0.302133i) q^{57} +(-0.563252 + 3.19436i) q^{58} +(3.47856 - 1.26609i) q^{59} +(1.20064 + 6.80919i) q^{61} +(-0.774775 - 1.34195i) q^{62} +(0.0406486 - 3.95868i) q^{63} +(2.07506 - 3.59410i) q^{64} +(0.952697 + 3.62996i) q^{66} +(8.44702 + 7.08789i) q^{67} +(-4.38548 - 3.67985i) q^{68} +(1.72816 + 0.472581i) q^{69} +(3.04214 - 5.26914i) q^{71} +(-1.58548 - 4.49927i) q^{72} +(-0.273486 - 0.473692i) q^{73} +(-0.319224 - 1.81041i) q^{74} +(0.716670 - 0.260847i) q^{76} +(-1.19507 + 6.77756i) q^{77} +(-0.00119904 + 0.0129396i) q^{78} +(0.374706 - 0.314416i) q^{79} +(8.39224 + 3.25120i) q^{81} -1.52681 q^{82} +(-3.53428 + 2.96561i) q^{83} +(0.385389 - 4.15898i) q^{84} +(-3.24348 + 1.18053i) q^{86} +(-7.69922 - 11.1167i) q^{87} +(1.44005 + 8.16694i) q^{88} +(1.68653 + 2.92116i) q^{89} +(-0.0119153 + 0.0206379i) q^{91} +(1.77623 + 0.646495i) q^{92} +(6.23118 + 1.70398i) q^{93} +(2.25902 + 1.89554i) q^{94} +(-1.94531 - 7.41201i) q^{96} +(9.34182 + 3.40014i) q^{97} +(1.09238 - 1.89206i) q^{98} +(-13.4684 - 7.96149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27}+ \cdots - 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	0.318266	−	0.267057i	0.225048	−	0.188837i	−0.523291	−	0.852154i	$-0.675296\pi$
$2$	0.318266	−	0.267057i	0.225048	−	0.188837i	0.748339	+	0.663316i	$0.230852\pi$
$3$	−0.159815	+	1.72466i	−0.0922690	+	0.995734i
$3$	−0.159815	+	1.72466i	−0.0922690	+	0.995734i
$4$	−0.317323	+	1.79963i	−0.158661	+	0.899813i
$5$		0			0
$5$		0			0
$6$	0.409719	+	0.591580i	0.167267	+	0.241512i
$7$	0.229151	+	1.29958i	0.0866110	+	0.491195i	0.996997	+	0.0774361i	$0.0246734\pi$
$7$	0.229151	+	1.29958i	0.0866110	+	0.491195i	−0.910386	+	0.413759i	$0.864216\pi$
$8$	0.795075	+	1.37711i	0.281102	+	0.486882i
$9$	−2.94892	−	0.551252i	−0.982973	−	0.183751i
$10$		0			0
$11$	4.90067	+	1.78370i	1.47761	+	0.537805i	0.950155	−	0.311778i	$-0.100925\pi$
$11$	4.90067	+	1.78370i	1.47761	+	0.537805i	0.527454	+	0.849584i	$0.323147\pi$
$12$	−3.05303	−	0.834881i	−0.881335	−	0.241009i
$13$	0.0138336	+	0.0116078i	0.00383676	+	0.00321942i	0.644704	−	0.764432i	$-0.276981\pi$
$13$	0.0138336	+	0.0116078i	0.00383676	+	0.00321942i	−0.640867	+	0.767652i	$0.721425\pi$
$14$	0.419993	+	0.352416i	0.112248	+	0.0941870i
$15$		0			0
$16$	−2.81355	−	1.02405i	−0.703389	−	0.256012i
$17$	−1.56640	+	2.71308i	−0.379907	+	0.658019i	−0.991048	−	0.133503i	$-0.957377\pi$
$17$	−1.56640	+	2.71308i	−0.379907	+	0.658019i	0.611141	+	0.791522i	$0.290711\pi$
$18$	−1.08575	+	0.612083i	−0.255915	+	0.144269i
$19$	−0.208676	−	0.361438i	−0.0478736	−	0.0829195i	0.841096	−	0.540886i	$-0.181911\pi$
$19$	−0.208676	−	0.361438i	−0.0478736	−	0.0829195i	−0.888969	+	0.457967i	$0.848578\pi$
$20$		0			0
$21$	−2.27796	+	0.187516i	−0.497092	+	0.0409194i
$22$	2.03606	−	0.741067i	0.434090	−	0.157996i
$23$	0.179619	−	1.01867i	0.0374532	−	0.212408i	−0.960338	−	0.278839i	$-0.910050\pi$
$23$	0.179619	−	1.01867i	0.0374532	−	0.212408i	0.997791	+	0.0664316i	$0.0211614\pi$
$24$	−2.50212	+	1.15115i	−0.510742	+	0.234978i
$25$		0			0
$26$	0.00750270			0.00147140
$27$	1.42200	−	4.99779i	0.273665	−	0.961825i
$28$	−2.41147			−0.455726
$29$	−5.98068	+	5.01839i	−1.11058	+	0.931891i	−0.998091	−	0.0617615i	$-0.980328\pi$
$29$	−5.98068	+	5.01839i	−1.11058	+	0.931891i	−0.112493	+	0.993652i	$0.535884\pi$
$30$		0			0
$31$	0.647649	−	3.67300i	0.116321	−	0.659691i	−0.869766	−	0.493464i	$-0.835730\pi$
$31$	0.647649	−	3.67300i	0.116321	−	0.659691i	0.986088	−	0.166227i	$-0.0531584\pi$
$32$	−4.15744	+	1.51319i	−0.734939	+	0.267496i
$33$	−3.85948	+	8.16694i	−0.671849	+	1.42168i
$34$	0.226015	+	1.28180i	0.0387613	+	0.219826i
$35$		0			0
$36$	1.92781	−	5.13202i	0.321301	−	0.855337i
$37$	2.21238	−	3.83195i	0.363713	−	0.629969i	−0.624856	−	0.780740i	$-0.714842\pi$
$37$	2.21238	−	3.83195i	0.363713	−	0.629969i	0.988569	+	0.150771i	$0.0481756\pi$
$38$	−0.162939	−	0.0593049i	−0.0264322	−	0.00962052i
$39$	−0.0222303	+	0.0220032i	−0.00355970	+	0.00352334i
$40$		0			0
$41$	−2.81517	−	2.36221i	−0.439655	−	0.368915i	0.395925	−	0.918283i	$-0.370424\pi$
$41$	−2.81517	−	2.36221i	−0.439655	−	0.368915i	−0.835580	+	0.549368i	$0.814868\pi$
$42$	−0.674919	+	0.668024i	−0.104142	+	0.103078i
$43$	−7.80685	−	2.84146i	−1.19053	−	0.433319i	−0.330622	−	0.943763i	$-0.607259\pi$
$43$	−7.80685	−	2.84146i	−1.19053	−	0.433319i	−0.859911	+	0.510445i	$0.829481\pi$
$44$	−4.76508	+	8.25337i	−0.718363	+	1.24424i
$45$		0			0
$46$	−0.214876	−	0.372177i	−0.0316818	−	0.0548745i
$47$	1.23254	+	6.99008i	0.179784	+	1.01961i	0.932475	+	0.361234i	$0.117644\pi$
$47$	1.23254	+	6.99008i	0.179784	+	1.01961i	−0.752691	+	0.658374i	$0.771245\pi$
$48$	2.21579	−	4.68877i	0.319821	−	0.676766i
$49$	4.94145	−	1.79854i	0.705921	−	0.256934i
$50$		0			0
$51$	−4.42881	−	3.13510i	−0.620158	−	0.439001i
$52$	−0.0252794	+	0.0212119i	−0.00350562	+	0.00294157i
$53$	1.30057			0.178648			0.0893238	−	0.996003i	$-0.471529\pi$
$53$	1.30057			0.178648			0.0893238	+	0.996003i	$0.471529\pi$
$54$	−0.882118	−	1.97038i	−0.120041	−	0.268135i
$55$		0			0
$56$	−1.60747	+	1.34883i	−0.214808	+	0.180245i
$57$	0.656707	−	0.302133i	0.0869830	−	0.0400185i
$58$	−0.563252	+	3.19436i	−0.0739586	+	0.419440i
$59$	3.47856	−	1.26609i	0.452871	−	0.164831i	−0.105507	−	0.994419i	$-0.533646\pi$
$59$	3.47856	−	1.26609i	0.452871	−	0.164831i	0.558377	+	0.829587i	$0.311424\pi$
$60$		0			0
$61$	1.20064	+	6.80919i	0.153727	+	0.871828i	0.959941	+	0.280204i	$0.0904020\pi$
$61$	1.20064	+	6.80919i	0.153727	+	0.871828i	−0.806214	+	0.591624i	$0.798487\pi$
$62$	−0.774775	−	1.34195i	−0.0983965	−	0.170428i
$63$	0.0406486	−	3.95868i	0.00512125	−	0.498747i
$64$	2.07506	−	3.59410i	0.259382	−	0.449263i
$65$		0			0
$66$	0.952697	+	3.62996i	0.117269	+	0.446817i
$67$	8.44702	+	7.08789i	1.03197	+	0.865923i	0.991084	−	0.133241i	$-0.0425383\pi$
$67$	8.44702	+	7.08789i	1.03197	+	0.865923i	0.0408835	+	0.999164i	$0.486983\pi$
$68$	−4.38548	−	3.67985i	−0.531817	−	0.446247i
$69$	1.72816	+	0.472581i	0.208046	+	0.0568921i
$70$		0			0
$71$	3.04214	−	5.26914i	0.361035	−	0.625332i	−0.627096	−	0.778942i	$-0.715757\pi$
$71$	3.04214	−	5.26914i	0.361035	−	0.625332i	0.988132	+	0.153610i	$0.0490900\pi$
$72$	−1.58548	−	4.49927i	−0.186850	−	0.530245i
$73$	−0.273486	−	0.473692i	−0.0320092	−	0.0554415i	0.849577	−	0.527465i	$-0.176857\pi$
$73$	−0.273486	−	0.473692i	−0.0320092	−	0.0554415i	−0.881586	+	0.472023i	$0.843524\pi$
$74$	−0.319224	−	1.81041i	−0.0371090	−	0.210456i
$75$		0			0
$76$	0.716670	−	0.260847i	0.0822077	−	0.0299212i
$77$	−1.19507	+	6.77756i	−0.136190	+	0.772374i
$78$	−0.00119904	+	0.0129396i	−0.000135765	+	0.00146512i
$79$	0.374706	−	0.314416i	0.0421577	−	0.0353745i	−0.621465	−	0.783442i	$-0.713462\pi$
$79$	0.374706	−	0.314416i	0.0421577	−	0.0353745i	0.663623	+	0.748067i	$0.269018\pi$
$80$		0			0
$81$	8.39224	+	3.25120i	0.932471	+	0.361244i
$82$	−1.52681			−0.168608
$83$	−3.53428	+	2.96561i	−0.387937	+	0.325518i	−0.815809	−	0.578321i	$-0.803708\pi$
$83$	−3.53428	+	2.96561i	−0.387937	+	0.325518i	0.427872	+	0.903839i	$0.359263\pi$
$84$	0.385389	−	4.15898i	0.0420493	−	0.453782i
$85$		0			0
$86$	−3.24348	+	1.18053i	−0.349754	+	0.127300i
$87$	−7.69922	−	11.1167i	−0.825443	−	1.19183i
$88$	1.44005	+	8.16694i	0.153510	+	0.870599i
$89$	1.68653	+	2.92116i	0.178772	+	0.309642i	0.941460	−	0.337124i	$-0.109454\pi$
$89$	1.68653	+	2.92116i	0.178772	+	0.309642i	−0.762688	+	0.646766i	$0.776121\pi$
$90$		0			0
$91$	−0.0119153	+	0.0206379i	−0.00124906	+	0.00216344i
$92$	1.77623	+	0.646495i	0.185185	+	0.0674018i
$93$	6.23118	+	1.70398i	0.646144	+	0.176694i
$94$	2.25902	+	1.89554i	0.233000	+	0.195510i
$95$		0			0
$96$	−1.94531	−	7.41201i	−0.198543	−	0.756485i
$97$	9.34182	+	3.40014i	0.948518	+	0.345232i	0.769524	−	0.638618i	$-0.220493\pi$
$97$	9.34182	+	3.40014i	0.948518	+	0.345232i	0.178994	+	0.983850i	$0.442716\pi$
$98$	1.09238	−	1.89206i	0.110347	−	0.191127i
$99$	−13.4684	−	7.96149i	−1.35363	−	0.800160i
$100$		0			0
$101$	2.39626	+	13.5898i	0.238436	+	1.35224i	0.835255	+	0.549863i	$0.185320\pi$
$101$	2.39626	+	13.5898i	0.238436	+	1.35224i	−0.596818	+	0.802377i	$0.703569\pi$
$102$	−2.24679	+	0.184950i	−0.222465	+	0.0183128i
$103$	4.28981	−	1.56136i	0.422687	−	0.153846i	−0.121914	−	0.992541i	$-0.538903\pi$
$103$	4.28981	−	1.56136i	0.422687	−	0.153846i	0.544601	+	0.838695i	$0.316681\pi$
$104$	−0.00498644	+	0.0282795i	−0.000488961	+	0.00277303i
$105$		0			0
$106$	0.413928	−	0.347327i	0.0402042	−	0.0337354i
$107$	11.2965			1.09207			0.546035	−	0.837762i	$-0.316136\pi$
$107$	11.2965			1.09207			0.546035	+	0.837762i	$0.316136\pi$
$108$	8.54292	+	4.14499i	0.822043	+	0.398851i
$109$	14.5032			1.38915			0.694577	−	0.719419i	$-0.255592\pi$
$109$	14.5032			1.38915			0.694577	+	0.719419i	$0.255592\pi$
$110$		0			0
$111$	6.25525	+	4.42801i	0.593722	+	0.420288i
$112$	0.686107	−	3.89110i	0.0648310	−	0.367675i
$113$	11.8011	−	4.29523i	1.11015	−	0.404062i	0.279102	−	0.960262i	$-0.409963\pi$
$113$	11.8011	−	4.29523i	1.11015	−	0.404062i	0.831049	+	0.556200i	$0.187741\pi$
$114$	0.128321	−	0.271536i	0.0120183	−	0.0254317i
$115$		0			0
$116$	−7.13341	−	12.3554i	−0.662321	−	1.14717i
$117$	−0.0343954	−	0.0418563i	−0.00317986	−	0.00386961i
$118$	0.768989	−	1.33193i	0.0707912	−	0.122614i
$119$	−3.88481	−	1.41395i	−0.356120	−	0.129617i
$120$		0			0
$121$	12.4085	+	10.4120i	1.12805	+	0.946544i
$122$	2.20056	+	1.84649i	0.199230	+	0.167174i
$123$	4.52391	−	4.47770i	0.407907	−	0.403740i
$124$	6.40452	+	2.33105i	0.575143	+	0.209335i
$125$		0			0
$126$	−1.04425	−	1.27077i	−0.0930295	−	0.113209i
$127$	−4.19749	−	7.27027i	−0.372467	−	0.645132i	0.617477	−	0.786589i	$-0.288155\pi$
$127$	−4.19749	−	7.27027i	−0.372467	−	0.645132i	−0.989944	+	0.141456i	$0.954821\pi$
$128$	−1.83594	−	10.4121i	−0.162276	−	0.920310i
$129$	6.14821	−	13.0101i	0.541319	−	1.14547i
$130$		0			0
$131$	−2.69761	+	15.2989i	−0.235691	+	1.33667i	0.605463	+	0.795874i	$0.292988\pi$
$131$	−2.69761	+	15.2989i	−0.235691	+	1.33667i	−0.841154	+	0.540796i	$0.818123\pi$
$132$	−13.4727	−	9.53717i	−1.17265	−	0.830104i
$133$	0.421899	−	0.354015i	0.0365833	−	0.0306970i
$134$	4.58126			0.395761
$135$		0			0
$136$	−4.98162			−0.427170
$137$	−9.19820	+	7.71820i	−0.785855	+	0.659411i	−0.944716	−	0.327890i	$-0.893662\pi$
$137$	−9.19820	+	7.71820i	−0.785855	+	0.659411i	0.158861	+	0.987301i	$0.449218\pi$
$138$	0.676219	−	0.311110i	0.0575636	−	0.0264834i
$139$	1.06709	−	6.05176i	0.0905093	−	0.513304i	−0.905522	−	0.424299i	$-0.860520\pi$
$139$	1.06709	−	6.05176i	0.0905093	−	0.513304i	0.996031	−	0.0890042i	$-0.0283685\pi$
$140$		0			0
$141$	−12.2525	+	1.00860i	−1.03185	+	0.0849392i
$142$	−0.438950	−	2.48941i	−0.0368359	−	0.208907i
$143$	0.0470893	+	0.0815610i	0.00393780	+	0.00682047i
$144$	7.73243	+	4.57082i	0.644369	+	0.380901i
$145$		0			0
$146$	−0.213544	−	0.0777237i	−0.0176730	−	0.00643246i
$147$	2.31216	+	8.80976i	0.190704	+	0.726617i
$148$	6.19404	+	5.19742i	0.509147	+	0.427225i
$149$	0.676280	+	0.567466i	0.0554030	+	0.0464886i	0.670069	−	0.742299i	$-0.266265\pi$
$149$	0.676280	+	0.567466i	0.0554030	+	0.0464886i	−0.614666	+	0.788788i	$0.710709\pi$
$150$		0			0
$151$	−7.72942	−	2.81328i	−0.629011	−	0.228941i	0.00778980	−	0.999970i	$-0.497520\pi$
$151$	−7.72942	−	2.81328i	−0.629011	−	0.228941i	−0.636801	+	0.771028i	$0.719743\pi$
$152$	0.331826	−	0.574740i	0.0269147	−	0.0466176i
$153$	6.11477	−	7.13717i	0.494350	−	0.577006i
$154$	1.42964	+	2.47621i	0.115204	+	0.199539i
$155$		0			0
$156$	−0.0325434	−	0.0469884i	−0.00260556	−	0.00376208i
$157$	11.8024	−	4.29571i	0.941932	−	0.342835i	0.175003	−	0.984568i	$-0.444006\pi$
$157$	11.8024	−	4.29571i	0.941932	−	0.342835i	0.766928	+	0.641733i	$0.221784\pi$
$158$	0.0352893	−	0.200135i	0.00280746	−	0.0159219i
$159$	−0.207851	+	2.24305i	−0.0164836	+	0.177886i
$160$		0			0
$161$	1.36501			0.107578
$162$	3.53922	−	1.20646i	0.278067	−	0.0947884i
$163$	−3.31466			−0.259624			−0.129812	−	0.991539i	$-0.541437\pi$
$163$	−3.31466			−0.259624			−0.129812	+	0.991539i	$0.541437\pi$
$164$	5.14440	−	4.31667i	0.401710	−	0.337075i
$165$		0			0
$166$	−0.332853	+	1.88770i	−0.0258344	+	0.146514i
$167$	−19.3229	+	7.03295i	−1.49525	+	0.544226i	−0.954826	−	0.297167i	$-0.903958\pi$
$167$	−19.3229	+	7.03295i	−1.49525	+	0.544226i	−0.540424	+	0.841393i	$0.681736\pi$
$168$	−2.06938	−	2.98791i	−0.159656	−	0.230522i
$169$	−2.25737	−	12.8022i	−0.173644	−	0.984783i
$170$		0			0
$171$	0.416126	+	1.18088i	0.0318219	+	0.0903044i
$172$	7.59085	−	13.1477i	0.578797	−	1.00251i
$173$	13.1870	+	4.79966i	1.00259	+	0.364911i	0.790581	−	0.612357i	$-0.209779\pi$
$173$	13.1870	+	4.79966i	1.00259	+	0.364911i	0.212005	+	0.977269i	$0.432001\pi$
$174$	−5.41917	−	1.48192i	−0.410827	−	0.112344i
$175$		0			0
$176$	−11.9617	−	10.0371i	−0.901648	−	0.756572i
$177$	1.62766	+	6.20169i	0.122342	+	0.466148i
$178$	1.31688	+	0.479305i	0.0987043	+	0.0359254i
$179$	−5.09500	+	8.82479i	−0.380818	+	0.659596i	−0.991179	−	0.132527i	$-0.957691\pi$
$179$	−5.09500	+	8.82479i	−0.380818	+	0.659596i	0.610361	+	0.792123i	$0.291024\pi$
$180$		0			0
$181$	−12.0274	−	20.8320i	−0.893987	−	1.54843i	−0.835054	−	0.550169i	$-0.814563\pi$
$181$	−12.0274	−	20.8320i	−0.893987	−	1.54843i	−0.0589331	−	0.998262i	$-0.518770\pi$
$182$	0.00171925	+	0.00975037i	0.000127440	+	0.000722746i
$183$	−11.9354	+	0.982498i	−0.882293	+	0.0726283i
$184$	1.54563	−	0.562565i	0.113946	−	0.0414728i
$185$		0			0
$186$	2.43823	−	1.12176i	0.178780	−	0.0822516i
$187$	−12.5157	+	10.5019i	−0.915240	+	0.767978i
$188$	−12.9706			−0.945981
$189$	6.82089	+	0.702760i	0.496146	+	0.0511182i
$190$		0			0
$191$	8.38541	−	7.03619i	0.606747	−	0.509121i	−0.286860	−	0.957973i	$-0.592611\pi$
$191$	8.38541	−	7.03619i	0.606747	−	0.509121i	0.893606	+	0.448852i	$0.148167\pi$
$192$	5.86699	+	4.15316i	0.423414	+	0.299729i
$193$	1.87644	−	10.6418i	0.135069	−	0.766013i	−0.839743	−	0.542984i	$-0.817294\pi$
$193$	1.87644	−	10.6418i	0.135069	−	0.766013i	0.974812	−	0.223029i	$-0.0715945\pi$
$194$	3.88121	−	1.41265i	0.278655	−	0.101422i
$195$		0			0
$196$	1.66867	+	9.46347i	0.119190	+	0.675962i
$197$	−11.0367	−	19.1161i	−0.786331	−	1.36196i	−0.928201	−	0.372080i	$-0.878645\pi$
$197$	−11.0367	−	19.1161i	−0.786331	−	1.36196i	0.141870	−	0.989885i	$-0.454689\pi$
$198$	−6.41270	+	1.06296i	−0.455731	+	0.0755413i
$199$	−6.44338	+	11.1603i	−0.456759	+	0.791130i	−0.998787	−	0.0492301i	$-0.984323\pi$
$199$	−6.44338	+	11.1603i	−0.456759	+	0.791130i	0.542028	+	0.840360i	$0.317657\pi$
$200$		0			0
$201$	−13.5742	+	13.4355i	−0.957448	+	0.947667i
$202$	4.39190	+	3.68524i	0.309013	+	0.259293i
$203$	−7.89228	−	6.62241i	−0.553929	−	0.464802i
$204$	7.04736	−	6.97537i	0.493414	−	0.488374i
$205$		0			0
$206$	0.948326	−	1.64255i	0.0660730	−	0.114442i
$207$	−1.09123	+	2.90496i	−0.0758456	+	0.201909i
$208$	−0.0270347	−	0.0468255i	−0.00187452	−	0.00324676i
$209$	−0.377957	−	2.14350i	−0.0261439	−	0.148269i
$210$		0			0
$211$	22.5485	−	8.20699i	1.55230	−	0.564992i	0.583347	−	0.812223i	$-0.301743\pi$
$211$	22.5485	−	8.20699i	1.55230	−	0.564992i	0.968957	+	0.247230i	$0.0795204\pi$
$212$	−0.412702	+	2.34055i	−0.0283445	+	0.160749i
$213$	8.60131	+	6.08875i	0.589352	+	0.417194i
$214$	3.59528	−	3.01680i	0.245768	−	0.206224i
$215$		0			0
$216$	8.01311	−	2.01536i	0.545223	−	0.137128i
$217$	4.92177			0.334112
$218$	4.61587	−	3.87317i	0.312626	−	0.262324i
$219$	0.860667	−	0.395969i	0.0581585	−	0.0267571i
$220$		0			0
$221$	−0.0531618	+	0.0193493i	−0.00357605	+	0.00130158i
$222$	3.17336	−	0.261224i	0.212982	−	0.0175322i
$223$	−3.76160	−	21.3331i	−0.251895	−	1.42857i	−0.803918	−	0.594740i	$-0.797255\pi$
$223$	−3.76160	−	21.3331i	−0.251895	−	1.42857i	0.552023	−	0.833829i	$-0.313856\pi$
$224$	−2.91919	−	5.05618i	−0.195047	−	0.337831i
$225$		0			0
$226$	2.60880	−	4.51858i	0.173535	−	0.300571i
$227$	20.3367	+	7.40196i	1.34979	+	0.491285i	0.912884	−	0.408220i	$-0.133850\pi$
$227$	20.3367	+	7.40196i	1.34979	+	0.491285i	0.436911	+	0.899505i	$0.356072\pi$
$228$	0.335338	+	1.27770i	0.0222083	+	0.0846178i
$229$	−8.27739	−	6.94555i	−0.546985	−	0.458975i	0.326934	−	0.945047i	$-0.393985\pi$
$229$	−8.27739	−	6.94555i	−0.546985	−	0.458975i	−0.873919	+	0.486072i	$0.838429\pi$
$230$		0			0
$231$	−11.4980	−	3.14424i	−0.756513	−	0.206876i
$232$	−11.6660	−	4.24606i	−0.765908	−	0.278768i
$233$	3.81950	−	6.61557i	0.250224	−	0.433400i	−0.713364	−	0.700794i	$-0.752829\pi$
$233$	3.81950	−	6.61557i	0.250224	−	0.433400i	0.963587	+	0.267394i	$0.0861625\pi$
$234$	−0.0221249	−	0.00413588i	−0.00144635	−	0.000270371i
$235$		0			0
$236$	1.17467	+	6.66187i	0.0764644	+	0.433651i
$237$	0.482377	+	0.696490i	0.0313338	+	0.0452419i
$238$	−1.61401	+	0.587451i	−0.104621	+	0.0380788i
$239$	−0.561143	+	3.18240i	−0.0362973	+	0.205852i	−0.997563	−	0.0697711i	$-0.977773\pi$
$239$	−0.561143	+	3.18240i	−0.0362973	+	0.205852i	0.961266	+	0.275623i	$0.0888842\pi$
$240$		0			0
$241$	−20.3346	+	17.0628i	−1.30987	+	1.09911i	−0.321518	+	0.946903i	$0.604193\pi$
$241$	−20.3346	+	17.0628i	−1.30987	+	1.09911i	−0.988349	+	0.152206i	$0.951362\pi$
$242$	6.72979			0.432608
$243$	−6.94842	+	13.9542i	−0.445741	+	0.895162i
$244$	−12.6350			−0.808873
$245$		0			0
$246$	0.244007	−	2.63324i	0.0155573	−	0.167889i
$247$	0.00130875	−	0.00742226i	8.32735e−5	−	0.000472267i
$248$	5.57306	−	2.02843i	0.353890	−	0.128805i
$249$	−4.54985	−	6.56938i	−0.288335	−	0.416318i
$250$		0			0
$251$	2.24965	+	3.89651i	0.141997	+	0.245945i	0.928248	−	0.371961i	$-0.121314\pi$
$251$	2.24965	+	3.89651i	0.141997	+	0.245945i	−0.786252	+	0.617906i	$0.787981\pi$
$252$	7.11124	+	1.32933i	0.447966	+	0.0837399i
$253$	2.69726	−	4.67179i	0.169575	−	0.293713i
$254$	−3.27749	−	1.19291i	−0.205648	−	0.0748498i
$255$		0			0
$256$	2.99340	+	2.51176i	0.187088	+	0.156985i
$257$	−10.5219	−	8.82895i	−0.656340	−	0.550735i	0.252647	−	0.967559i	$-0.418699\pi$
$257$	−10.5219	−	8.82895i	−0.656340	−	0.550735i	−0.908987	+	0.416824i	$0.863143\pi$
$258$	−1.51766	−	5.78258i	−0.0944854	−	0.360007i
$259$	5.48690	+	1.99707i	0.340939	+	0.124092i
$260$		0			0
$261$	20.4029	−	11.5020i	1.26291	−	0.711953i
$262$	3.22711	+	5.58952i	0.199372	+	0.345322i
$263$	4.20273	+	23.8349i	0.259151	+	1.46972i	0.785187	+	0.619258i	$0.212567\pi$
$263$	4.20273	+	23.8349i	0.259151	+	1.46972i	−0.526036	+	0.850462i	$0.676322\pi$
$264$	−14.3154	+	1.17841i	−0.881049	+	0.0725260i
$265$		0			0
$266$	0.0397339	−	0.225342i	0.00243624	−	0.0138166i
$267$	−5.30755	+	2.44185i	−0.324817	+	0.149439i
$268$	−15.4360	+	12.9523i	−0.942902	+	0.791189i
$269$	12.0062			0.732032			0.366016	−	0.930609i	$-0.380722\pi$
$269$	12.0062			0.732032			0.366016	+	0.930609i	$0.380722\pi$
$270$		0			0
$271$	3.71777			0.225839			0.112919	−	0.993604i	$-0.463980\pi$
$271$	3.71777			0.225839			0.112919	+	0.993604i	$0.463980\pi$
$272$	7.18547	−	6.02933i	0.435683	−	0.365582i
$273$	−0.0336891	−	0.0238481i	−0.00203896	−	0.00144335i
$274$	−0.866273	+	4.91288i	−0.0523335	+	0.296798i
$275$		0			0
$276$	−1.39885	+	2.96008i	−0.0842011	+	0.178176i
$277$	4.07780	+	23.1264i	0.245011	+	1.38953i	0.820466	+	0.571695i	$0.193714\pi$
$277$	4.07780	+	23.1264i	0.245011	+	1.38953i	−0.575455	+	0.817833i	$0.695175\pi$
$278$	−1.27654	−	2.21104i	−0.0765621	−	0.132609i
$279$	−3.93462	+	10.4744i	−0.235559	+	0.627084i
$280$		0			0
$281$	19.1432	+	6.96754i	1.14199	+	0.415649i	0.842630	−	0.538493i	$-0.181006\pi$
$281$	19.1432	+	6.96754i	1.14199	+	0.415649i	0.299356	+	0.954142i	$0.403228\pi$
$282$	−3.63020	+	3.59311i	−0.216175	+	0.213967i
$283$	−8.88607	−	7.45630i	−0.528222	−	0.443231i	0.339265	−	0.940691i	$-0.389822\pi$
$283$	−8.88607	−	7.45630i	−0.528222	−	0.443231i	−0.867487	+	0.497460i	$0.834266\pi$
$284$	8.51714	+	7.14673i	0.505399	+	0.424080i
$285$		0			0
$286$	0.0367683	+	0.0133826i	0.00217416	+	0.000791328i
$287$	2.42478	−	4.19984i	0.143130	−	0.247909i
$288$	13.0941	−	2.17046i	0.771578	−	0.127896i
$289$	3.59280	+	6.22291i	0.211341	+	0.366053i
$290$		0			0
$291$	−7.35706	+	15.5681i	−0.431279	+	0.912618i
$292$	0.939253	−	0.341860i	0.0549656	−	0.0200058i
$293$	−5.48280	+	31.0945i	−0.320308	+	1.81656i	0.220470	+	0.975394i	$0.429241\pi$
$293$	−5.48280	+	31.0945i	−0.320308	+	1.81656i	−0.540779	+	0.841165i	$0.681870\pi$
$294$	3.08858	+	2.18637i	0.180130	+	0.127511i
$295$		0			0
$296$	7.03603			0.408961
$297$	15.8833	−	21.9561i	0.921644	−	1.27402i
$298$	0.366782			0.0212471
$299$	0.0143093	−	0.0120069i	0.000827529	−	0.000694379i
$300$		0			0
$301$	1.90376	−	10.7968i	0.109731	−	0.622315i
$302$	−3.21131	+	1.16882i	−0.184790	+	0.0672581i
$303$	−23.8208	+	1.96088i	−1.36847	+	0.112649i
$304$	0.216991	+	1.23062i	0.0124453	+	0.0705809i
$305$		0			0
$306$	0.0400924	−	3.90451i	0.00229193	−	0.223206i
$307$	−4.06027	+	7.03259i	−0.231732	+	0.401371i	−0.958318	−	0.285704i	$-0.907773\pi$
$307$	−4.06027	+	7.03259i	−0.231732	+	0.401371i	0.726586	+	0.687075i	$0.241106\pi$
$308$	−11.8178	−	4.30134i	−0.673384	−	0.245092i
$309$	2.00725	+	7.64800i	0.114188	+	0.435079i
$310$		0			0
$311$	−18.2691	−	15.3296i	−1.03594	−	0.869259i	−0.0443970	−	0.999014i	$-0.514137\pi$
$311$	−18.2691	−	15.3296i	−1.03594	−	0.869259i	−0.991546	+	0.129754i	$0.958581\pi$
$312$	−0.0479757	−	0.0131194i	−0.00271609	−	0.000742740i
$313$	25.2876	+	9.20392i	1.42934	+	0.520236i	0.936742	−	0.350022i	$-0.113826\pi$
$313$	25.2876	+	9.20392i	1.42934	+	0.520236i	0.492596	+	0.870258i	$0.336048\pi$
$314$	2.60909	−	4.51908i	0.147240	−	0.255026i
$315$		0			0
$316$	0.446928	+	0.774102i	0.0251417	+	0.0435466i
$317$	1.44689	+	8.20574i	0.0812657	+	0.460881i	0.998100	+	0.0616130i	$0.0196244\pi$
$317$	1.44689	+	8.20574i	0.0812657	+	0.460881i	−0.916834	+	0.399268i	$0.869264\pi$
$318$	0.532870	+	0.769394i	0.0298819	+	0.0431455i
$319$	−38.2606	+	13.9257i	−2.14218	+	0.779692i
$320$		0			0
$321$	−1.80534	+	19.4826i	−0.100764	+	1.08741i
$322$	0.434435	−	0.364534i	0.0242101	−	0.0203147i
$323$	1.30748			0.0727501
$324$	−8.51398	+	14.0712i	−0.472999	+	0.781734i
$325$		0			0
$326$	−1.05494	+	0.885201i	−0.0584278	+	0.0490268i
$327$	−2.31782	+	25.0131i	−0.128176	+	1.38323i
$328$	1.01475	−	5.75493i	0.0560301	−	0.317763i
$329$	−8.80173	+	3.20357i	−0.485255	+	0.176618i
$330$		0			0
$331$	−1.11487	−	6.32272i	−0.0612786	−	0.347528i	−0.999996	−	0.00284030i	$-0.999096\pi$
$331$	−1.11487	−	6.32272i	−0.0612786	−	0.347528i	0.938717	−	0.344688i	$-0.112015\pi$
$332$	−4.21548	−	7.30143i	−0.231355	−	0.400718i
$333$	−8.63650	+	10.0805i	−0.473277	+	0.552410i
$334$	−4.27161	+	7.39865i	−0.233732	+	0.404836i
$335$		0			0
$336$	6.60119	+	1.80516i	0.360124	+	0.0984794i
$337$	−5.72610	−	4.80477i	−0.311921	−	0.261732i	0.473365	−	0.880867i	$-0.343039\pi$
$337$	−5.72610	−	4.80477i	−0.311921	−	0.261732i	−0.785285	+	0.619134i	$0.787484\pi$
$338$	−4.13735	−	3.47165i	−0.225042	−	0.188833i
$339$	5.52185	+	21.0393i	0.299906	+	1.14270i
$340$		0			0
$341$	9.72545	−	16.8450i	0.526663	−	0.912206i
$342$	0.447801	+	0.264706i	0.0242143	+	0.0143136i
$343$	8.08839	+	14.0095i	0.436732	+	0.756442i
$344$	−2.29403	−	13.0101i	−0.123686	−	0.701456i
$345$		0			0
$346$	5.47874	−	1.99410i	0.294539	−	0.107203i
$347$	5.46202	−	30.9766i	0.293216	−	1.66291i	−0.381148	−	0.924514i	$-0.624471\pi$
$347$	5.46202	−	30.9766i	0.293216	−	1.66291i	0.674364	−	0.738399i	$-0.264418\pi$
$348$	22.4490	−	10.3281i	1.20339	−	0.553647i
$349$	9.07988	−	7.61893i	0.486035	−	0.407832i	−0.366568	−	0.930391i	$-0.619467\pi$
$349$	9.07988	−	7.61893i	0.486035	−	0.407832i	0.852603	+	0.522560i	$0.175023\pi$
$350$		0			0
$351$	0.0776848	−	0.0526312i	0.00414651	−	0.00280925i
$352$	−23.0733			−1.22981
$353$	6.28699	−	5.27541i	0.334623	−	0.280782i	−0.459958	−	0.887941i	$-0.652135\pi$
$353$	6.28699	−	5.27541i	0.334623	−	0.280782i	0.794580	+	0.607159i	$0.207691\pi$
$354$	2.17423	+	1.53911i	0.115559	+	0.0818026i
$355$		0			0
$356$	−5.79217	+	2.10818i	−0.306984	+	0.111733i
$357$	3.05944	−	6.47401i	0.161923	−	0.342641i
$358$	0.735157	+	4.16928i	0.0388542	+	0.220353i
$359$	−8.86365	−	15.3523i	−0.467806	−	0.810263i	0.531517	−	0.847047i	$-0.321622\pi$
$359$	−8.86365	−	15.3523i	−0.467806	−	0.810263i	−0.999323	+	0.0367840i	$0.988289\pi$
$360$		0			0
$361$	9.41291	−	16.3036i	0.495416	−	0.858086i
$362$	−9.39122	−	3.41812i	−0.493591	−	0.179653i
$363$	−19.9402	+	19.7365i	−1.04659	+	1.03590i
$364$	−0.0333594	−	0.0279919i	−0.00174851	−	0.00146717i
$365$		0			0
$366$	−3.53626	+	3.50013i	−0.184843	+	0.182955i
$367$	−19.0941	−	6.94969i	−0.996704	−	0.362771i	−0.208392	−	0.978045i	$-0.566823\pi$
$367$	−19.0941	−	6.94969i	−0.996704	−	0.362771i	−0.788313	+	0.615275i	$0.789045\pi$
$368$	−1.54854	+	2.68215i	−0.0807232	+	0.139817i
$369$	6.99953	+	8.51782i	0.364381	+	0.443420i
$370$		0			0
$371$	0.298028	+	1.69020i	0.0154728	+	0.0877509i
$372$	−5.04381	+	10.6731i	−0.261510	+	0.553374i
$373$	−9.09758	+	3.31125i	−0.471055	+	0.171450i	−0.566630	−	0.823972i	$-0.691753\pi$
$373$	−9.09758	+	3.31125i	−0.471055	+	0.171450i	0.0955754	+	0.995422i	$0.469531\pi$
$374$	−1.17871	+	6.68481i	−0.0609498	+	0.345663i
$375$		0			0
$376$	−8.64615	+	7.25498i	−0.445891	+	0.374147i
$377$	−0.140987			−0.00726119
$378$	2.35853	−	1.59790i	0.121310	−	0.0821870i
$379$	−4.12905			−0.212095			−0.106048	−	0.994361i	$-0.533820\pi$
$379$	−4.12905			−0.212095			−0.106048	+	0.994361i	$0.533820\pi$
$380$		0			0
$381$	13.2096	−	6.07736i	0.676748	−	0.311353i
$382$	0.789725	−	4.47876i	0.0404059	−	0.229153i
$383$	4.46371	−	1.62466i	0.228085	−	0.0830162i	−0.225450	−	0.974255i	$-0.572385\pi$
$383$	4.46371	−	1.62466i	0.228085	−	0.0830162i	0.453535	+	0.891239i	$0.350163\pi$
$384$	18.2508	−	1.50236i	0.931357	−	0.0766672i
$385$		0			0
$386$	−2.24476	−	3.88803i	−0.114255	−	0.197896i
$387$	21.4554	+	12.6828i	1.09064	+	0.644702i
$388$	−9.08336	+	15.7328i	−0.461138	+	0.798714i
$389$	20.4978	+	7.46059i	1.03928	+	0.378267i	0.804607	−	0.593807i	$-0.202376\pi$
$389$	20.4978	+	7.46059i	1.03928	+	0.378267i	0.234673	+	0.972074i	$0.424598\pi$
$390$		0			0
$391$	2.48238	+	2.08297i	0.125539	+	0.105340i
$392$	6.40561	+	5.37495i	0.323532	+	0.271476i
$393$	−25.9543	−	7.09745i	−1.30922	−	0.358019i
$394$	−8.61767	−	3.13658i	−0.434152	−	0.158018i
$395$		0			0
$396$	18.6015	−	21.7117i	0.934762	−	1.09106i
$397$	−17.4245	−	30.1802i	−0.874512	−	1.51470i	−0.857282	−	0.514847i	$-0.827849\pi$
$397$	−17.4245	−	30.1802i	−0.874512	−	1.51470i	−0.0172294	−	0.999852i	$-0.505485\pi$
$398$	0.929715	+	5.27268i	0.0466024	+	0.264295i
$399$	0.543131	+	0.784210i	0.0271906	+	0.0392596i
$400$		0			0
$401$	−3.26911	+	18.5401i	−0.163252	+	0.925847i	0.787597	+	0.616191i	$0.211325\pi$
$401$	−3.26911	+	18.5401i	−0.163252	+	0.925847i	−0.950849	+	0.309656i	$0.899786\pi$
$402$	−0.732152	+	7.90113i	−0.0365164	+	0.394072i
$403$	0.0515948	−	0.0432932i	0.00257012	−	0.00215659i
$404$	−25.2170			−1.25459
$405$		0			0
$406$	−4.28040			−0.212433
$407$	17.6772	−	14.8329i	0.876226	−	0.735241i
$408$	0.796135	−	8.59160i	0.0394145	−	0.425348i
$409$	−1.10439	+	6.26334i	−0.0546088	+	0.309702i	−0.999862	−	0.0166371i	$-0.994704\pi$
$409$	−1.10439	+	6.26334i	−0.0546088	+	0.309702i	0.945253	+	0.326339i	$0.105815\pi$
$410$		0			0
$411$	−11.8413	−	17.0973i	−0.584088	−	0.843346i
$412$	1.44862	+	8.21551i	0.0713682	+	0.404749i
$413$	2.44251	+	4.23055i	0.120188	+	0.208172i
$414$	0.428490	+	1.21597i	0.0210591	+	0.0597617i
$415$		0			0
$416$	−0.0750772	−	0.0273259i	−0.00368096	−	0.00133976i
$417$	10.2667	+	2.80753i	0.502763	+	0.137485i
$418$	−0.692727	−	0.581267i	−0.0338824	−	0.0284307i
$419$	−18.6286	−	15.6313i	−0.910069	−	0.763638i	0.0620632	−	0.998072i	$-0.480232\pi$
$419$	−18.6286	−	15.6313i	−0.910069	−	0.763638i	−0.972132	+	0.234434i	$0.924676\pi$
$420$		0			0
$421$	7.50818	+	2.73275i	0.365926	+	0.133186i	0.518438	−	0.855115i	$-0.326514\pi$
$421$	7.50818	+	2.73275i	0.365926	+	0.133186i	−0.152511	+	0.988302i	$0.548736\pi$
$422$	4.98469	−	8.63373i	0.242651	−	0.420283i
$423$	0.218637	−	21.2926i	0.0106305	−	1.03528i
$424$	1.03405	+	1.79103i	0.0502181	+	0.0869803i
$425$		0			0
$426$	4.36354	−	0.359197i	0.211414	−	0.0174031i
$427$	−8.57397	+	3.12067i	−0.414924	+	0.151020i
$428$	−3.58462	+	20.3294i	−0.173269	+	0.982659i
$429$	−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	$0.423593\pi$
$432$	−9.11887	+	12.6053i	−0.438732	+	0.606475i
$433$	6.10369			0.293325			0.146662	−	0.989187i	$-0.453147\pi$
$433$	6.10369			0.293325			0.146662	+	0.989187i	$0.453147\pi$
$434$	1.56643	−	1.31439i	0.0751911	−	0.0630928i
$435$		0			0
$436$	−4.60219	+	26.1003i	−0.220405	+	1.24998i
$437$	−0.405669	+	0.147651i	−0.0194058	+	0.00706312i
$438$	0.168174	−	0.355870i	0.00803569	−	0.0170041i
$439$	−2.62800	−	14.9041i	−0.125427	−	0.711334i	−0.981053	−	0.193739i	$-0.937938\pi$
$439$	−2.62800	−	14.9041i	−0.125427	−	0.711334i	0.855626	−	0.517595i	$-0.173173\pi$
$440$		0			0
$441$	−15.5634	+	2.57976i	−0.741113	+	0.122846i
$442$	−0.0117522	+	0.0203554i	−0.000558996	+	0.000968210i
$443$	−0.679204	−	0.247210i	−0.0322699	−	0.0117453i	0.325835	−	0.945427i	$-0.394355\pi$
$443$	−0.679204	−	0.247210i	−0.0322699	−	0.0117453i	−0.358105	+	0.933681i	$0.616577\pi$
$444$	−9.95369	+	9.85201i	−0.472381	+	0.467555i
$445$		0			0
$446$	−6.89432	−	5.78502i	−0.326456	−	0.273929i
$447$	−1.08677	+	1.07566i	−0.0514023	+	0.0508772i
$448$	5.14633	+	1.87311i	0.243141	+	0.0884962i
$449$	−0.834224	+	1.44492i	−0.0393695	+	0.0681899i	−0.885039	−	0.465517i	$-0.845868\pi$
$449$	−0.834224	+	1.44492i	−0.0393695	+	0.0681899i	0.845669	+	0.533707i	$0.179202\pi$
$450$		0			0
$451$	−9.58275	−	16.5978i	−0.451234	−	0.781560i
$452$	3.98507	+	22.6005i	0.187442	+	1.06304i
$453$	6.08723	−	12.8810i	0.286003	−	0.605204i
$454$	8.44922	−	3.07526i	0.396541	−	0.144329i
$455$		0			0
$456$	0.938202	+	0.664140i	0.0439353	+	0.0311012i
$457$	−8.49041	+	7.12430i	−0.397165	+	0.333261i	−0.819397	−	0.573227i	$-0.805691\pi$
$457$	−8.49041	+	7.12430i	−0.397165	+	0.333261i	0.422232	+	0.906488i	$0.361247\pi$
$458$	−4.48926			−0.209769
$459$	11.3320	+	11.6865i	0.528932	+	0.545481i
$460$		0			0
$461$	−16.7644	+	14.0670i	−0.780797	+	0.655166i	−0.943449	−	0.331517i	$-0.892439\pi$
$461$	−16.7644	+	14.0670i	−0.780797	+	0.655166i	0.162653	+	0.986683i	$0.447995\pi$
$462$	−4.49911	+	2.06992i	−0.209318	+	0.0963012i
$463$	−4.31546	+	24.4742i	−0.200556	+	1.13741i	0.703724	+	0.710473i	$0.251519\pi$
$463$	−4.31546	+	24.4742i	−0.200556	+	1.13741i	−0.904281	+	0.426938i	$0.859592\pi$
$464$	21.9660	−	7.99499i	1.01975	−	0.371158i
$465$		0			0
$466$	−0.551115	−	3.12553i	−0.0255299	−	0.144787i
$467$	−5.91777	−	10.2499i	−0.273842	−	0.474308i	0.696001	−	0.718041i	$-0.254961\pi$
$467$	−5.91777	−	10.2499i	−0.273842	−	0.474308i	−0.969842	+	0.243734i	$0.921628\pi$
$468$	0.0862400	−	0.0486170i	0.00398645	−	0.00224732i
$469$	−7.27564	+	12.6018i	−0.335958	+	0.581896i
$470$		0			0
$471$	5.52246	+	21.0416i	0.254462	+	0.969547i
$472$	4.50927	+	3.78373i	0.207556	+	0.174160i
$473$	−33.1905	−	27.8501i	−1.52610	−	1.28055i
$474$	0.339526	+	0.0928466i	0.0155950	+	0.00426459i
$475$		0			0
$476$	3.77733	−	6.54252i	0.173134	−	0.299876i
$477$	−3.83529	−	0.716944i	−0.175606	−	0.0328266i
$478$	0.671288	+	1.16270i	0.0307040	+	0.0531809i
$479$	0.501383	+	2.84349i	0.0229088	+	0.129922i	0.994117	−	0.108309i	$-0.0345436\pi$
$479$	0.501383	+	2.84349i	0.0229088	+	0.129922i	−0.971209	+	0.238231i	$0.923432\pi$
$480$		0			0
$481$	0.0750857	−	0.0273290i	0.00342361	−	0.00124609i
$482$	−1.91508	+	10.8610i	−0.0872297	+	0.494704i
$483$	−0.218148	+	2.35417i	−0.00992607	+	0.107119i
$484$	−22.6752	+	19.0267i	−1.03069	+	0.864852i
$485$		0			0
$486$	1.51512	+	6.29676i	0.0687271	+	0.285627i
$487$	−8.75903			−0.396910			−0.198455	−	0.980110i	$-0.563592\pi$
$487$	−8.75903			−0.396910			−0.198455	+	0.980110i	$0.563592\pi$
$488$	−8.42241	+	7.06724i	−0.381265	+	0.319919i
$489$	0.529731	−	5.71667i	0.0239553	−	0.258517i
$490$		0			0
$491$	21.2117	−	7.72044i	0.957272	−	0.348418i	0.184308	−	0.982869i	$-0.440996\pi$
$491$	21.2117	−	7.72044i	0.957272	−	0.348418i	0.772964	+	0.634450i	$0.218773\pi$
$492$	6.62264	+	9.56222i	0.298572	+	0.431098i
$493$	−4.24716	−	24.0869i	−0.191283	−	1.08482i
$494$	−0.00156564	−	0.00271176i	−7.04413e−5	−	0.000122008i
$495$		0			0
$496$	−5.58354	+	9.67097i	−0.250708	+	0.434239i
$497$	7.54478	+	2.74608i	0.338430	+	0.123178i
$498$	−3.20246	−	0.875741i	−0.143505	−	0.0392429i
$499$	−19.4061	−	16.2836i	−0.868734	−	0.728955i	0.0950968	−	0.995468i	$-0.469684\pi$
$499$	−19.4061	−	16.2836i	−0.868734	−	0.728955i	−0.963831	+	0.266513i	$0.914128\pi$
$500$		0			0
$501$	−9.04139	−	34.4494i	−0.403940	−	1.53909i
$502$	1.75657	+	0.639340i	0.0783997	+	0.0285352i
$503$	1.87207	−	3.24252i	0.0834714	−	0.144577i	−0.821267	−	0.570543i	$-0.806733\pi$
$503$	1.87207	−	3.24252i	0.0834714	−	0.144577i	0.904739	+	0.425967i	$0.140066\pi$
$504$	5.48386	−	3.09147i	0.244270	−	0.137705i
$505$		0			0
$506$	−0.389187	−	2.20719i	−0.0173015	−	0.0981216i
$507$	22.4402	−	1.84723i	0.996604	−	0.0820382i
$508$	14.4157	−	5.24690i	0.639595	−	0.232793i
$509$	4.22831	−	23.9800i	0.187417	−	1.06289i	−0.735394	−	0.677640i	$-0.763003\pi$
$509$	4.22831	−	23.9800i	0.187417	−	1.06289i	0.922811	−	0.385253i	$-0.125886\pi$
$510$		0			0
$511$	0.552932	−	0.463965i	0.0244603	−	0.0205246i
$512$	22.7690			1.00626
$513$	−2.10313	+	0.528954i	−0.0928554	+	0.0233539i
$514$	−5.70660			−0.251707
$515$		0			0
$516$	21.4623	+	15.1929i	0.944824	+	0.668828i
$517$	−6.42792	+	36.4546i	−0.282700	+	1.60327i
$518$	2.27962	−	0.829715i	0.100161	−	0.0364556i
$519$	−10.3853	+	21.9760i	−0.455862	+	0.964639i
$520$		0			0
$521$	−9.81046	−	16.9922i	−0.429804	−	0.744443i	0.567051	−	0.823682i	$-0.308084\pi$
$521$	−9.81046	−	16.9922i	−0.429804	−	0.744443i	−0.996856	+	0.0792397i	$0.974751\pi$
$522$	3.42188	−	9.10941i	0.149772	−	0.398708i
$523$	10.4077	−	18.0267i	0.455097	−	0.788251i	−0.543597	−	0.839346i	$-0.682938\pi$
$523$	10.4077	−	18.0267i	0.455097	−	0.788251i	0.998694	+	0.0510956i	$0.0162713\pi$
$524$	−26.6763	−	9.70937i	−1.16536	−	0.424156i
$525$		0			0
$526$	7.70284	+	6.46345i	0.335860	+	0.281820i
$527$	8.95067	+	7.51051i	0.389897	+	0.327163i
$528$	19.2222	−	19.0258i	0.836539	−	0.827993i
$529$	20.6075	+	7.50052i	0.895978	+	0.326109i
$530$		0			0
$531$	−10.9559	+	1.81604i	−0.475447	+	0.0788095i
$532$	0.503217	+	0.871598i	0.0218172	+	0.0377886i
$533$	−0.0115240	−	0.0653558i	−0.000499159	−	0.00283087i
$534$	−1.03710	+	2.19457i	−0.0448795	+	0.0949685i
$535$		0			0
$536$	−3.04479	+	17.2679i	−0.131515	+	0.745859i
$537$	−14.4055	−	10.1975i	−0.621645	−	0.440054i
$538$	3.82117	−	3.20634i	0.164742	−	0.138235i
$539$	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	$0.728759\pi$
$542$	1.18324	−	0.992856i	0.0508245	−	0.0426468i
$543$	37.8503	−	17.4139i	1.62431	−	0.747301i
$544$	2.40681	−	13.6497i	0.103191	−	0.585227i
$545$		0			0
$546$	−0.0170909	+	0.00140688i	−0.000731421	+	6.02089e-5i
$547$	−3.93273	−	22.3036i	−0.168151	−	0.953633i	−0.945756	−	0.324879i	$-0.894676\pi$
$547$	−3.93273	−	22.3036i	−0.168151	−	0.953633i	0.777604	−	0.628754i	$-0.216435\pi$
$548$	−10.9711	−	19.0025i	−0.468661	−	0.811745i
$549$	0.212980	−	20.7416i	0.00908976	−	0.885231i
$550$		0			0
$551$	3.06186	+	1.11443i	0.130440	+	0.0474761i
$552$	0.723220	+	2.75560i	0.0307823	+	0.117286i
$553$	0.494473	+	0.414912i	0.0210271	+	0.0176439i
$554$	7.47387	+	6.27132i	0.317534	+	0.266443i
$555$		0			0
$556$	10.5523	+	3.84072i	0.447517	+	0.162883i
$557$	18.2259	−	31.5682i	0.772256	−	1.33759i	−0.164067	−	0.986449i	$-0.552461\pi$
$557$	18.2259	−	31.5682i	0.772256	−	1.33759i	0.936324	−	0.351138i	$-0.114205\pi$
$558$	1.54500	+	4.38440i	0.0654049	+	0.185606i
$559$	−0.0750139	−	0.129928i	−0.00317275	−	0.00549537i
$560$		0			0
$561$	−16.1121	−	23.2637i	−0.680253	−	0.982196i
$562$	7.95334	−	2.89478i	0.335491	−	0.122109i
$563$	−4.60450	+	26.1134i	−0.194056	+	1.10055i	0.719700	+	0.694285i	$0.244279\pi$
$563$	−4.60450	+	26.1134i	−0.194056	+	1.10055i	−0.913756	+	0.406263i	$0.866832\pi$
$564$	2.07290	−	22.3700i	0.0872847	−	0.941945i
$565$		0			0
$566$	−4.81938			−0.202574
$567$	−2.30210	+	11.6514i	−0.0966791	+	0.489313i
$568$	9.67492			0.405950
$569$	17.5941	−	14.7632i	0.737581	−	0.618904i	−0.194606	−	0.980882i	$-0.562343\pi$
$569$	17.5941	−	14.7632i	0.737581	−	0.618904i	0.932187	+	0.361978i	$0.117898\pi$
$570$		0			0
$571$	−0.833165	+	4.72511i	−0.0348669	+	0.197740i	−0.997266	−	0.0739009i	$-0.976455\pi$
$571$	−0.833165	+	4.72511i	−0.0348669	+	0.197740i	0.962399	+	0.271641i	$0.0875662\pi$
$572$	−0.161722	+	0.0588619i	−0.00676193	+	0.00246114i
$573$	10.7949	+	15.5865i	0.450965	+	0.651134i
$574$	−0.349871	−	1.98422i	−0.0146033	−	0.0828197i
$575$		0			0
$576$	−8.10043	+	9.45484i	−0.337518	+	0.393952i
$577$	−2.15666	+	3.73545i	−0.0897831	+	0.155509i	−0.907419	−	0.420226i	$-0.861951\pi$
$577$	−2.15666	+	3.73545i	−0.0897831	+	0.155509i	0.817636	+	0.575735i	$0.195284\pi$
$578$	2.80533	+	1.02106i	0.116686	+	0.0424704i
$579$	18.0536	+	4.93693i	0.750283	+	0.205172i
$580$		0			0
$581$	−4.66393	−	3.91351i	−0.193493	−	0.162360i
$582$	1.81606	+	6.91954i	0.0752782	+	0.286824i
$583$	6.37369	+	2.31983i	0.263971	+	0.0960777i
$584$	0.434885	−	0.753242i	0.0179957	−	0.0311694i
$585$		0			0
$586$	6.55900	+	11.3605i	0.270950	+	0.469299i
$587$	−7.26235	−	41.1868i	−0.299749	−	1.69996i	−0.647246	−	0.762281i	$-0.724079\pi$
$587$	−7.26235	−	41.1868i	−0.299749	−	1.69996i	0.347497	−	0.937681i	$-0.387032\pi$
$588$	−16.5880	+	1.36548i	−0.684076	+	0.0563116i
$589$	−1.46271	+	0.532383i	−0.0602699	+	0.0219365i
$590$		0			0
$591$	34.7326	−	15.9795i	1.42871	−	0.657309i
$592$	−10.1488	+	8.51582i	−0.417111	+	0.349998i
$593$	31.5370			1.29507			0.647536	−	0.762035i	$-0.275800\pi$
$593$	31.5370			1.29507			0.647536	+	0.762035i	$0.275800\pi$
$594$	−0.808405	−	11.2296i	−0.0331693	−	0.460757i
$595$		0			0
$596$	−1.23583	+	1.03698i	−0.0506214	+	0.0424764i
$597$	−18.2179	−	12.8962i	−0.745611	−	0.527807i
$598$	0.00134763	−	0.00764279i	5.51087e−5	−	0.000312537i
$599$	11.8686	−	4.31982i	0.484938	−	0.176503i	−0.0879695	−	0.996123i	$-0.528038\pi$
$599$	11.8686	−	4.31982i	0.484938	−	0.176503i	0.572907	+	0.819620i	$0.305816\pi$
$600$		0			0
$601$	3.56725	+	20.2309i	0.145511	+	0.825235i	0.966955	+	0.254946i	$0.0820577\pi$
$601$	3.56725	+	20.2309i	0.145511	+	0.825235i	−0.821444	+	0.570289i	$0.806831\pi$
$602$	−2.27744	−	3.94465i	−0.0928216	−	0.160772i
$603$	−21.0023	−	25.5580i	−0.855282	−	1.04080i
$604$	7.51556	−	13.0173i	0.305804	−	0.529668i
$605$		0			0
$606$	−7.05769	+	6.98559i	−0.286699	+	0.283770i
$607$	−9.89160	−	8.30003i	−0.401487	−	0.336888i	0.419581	−	0.907718i	$-0.362177\pi$
$607$	−9.89160	−	8.30003i	−0.401487	−	0.336888i	−0.821068	+	0.570830i	$0.806622\pi$
$608$	1.41448	+	1.18689i	0.0573648	+	0.0481348i
$609$	12.6827	−	12.5532i	0.513930	−	0.508680i
$610$		0			0
$611$	−0.0640889	+	0.111005i	−0.00259276	+	0.00449079i
$612$	10.9039	+	13.2691i	0.440763	+	0.536371i
$613$	−15.5799	−	26.9851i	−0.629265	−	1.08992i	−0.987699	−	0.156364i	$-0.950023\pi$
$613$	−15.5799	−	26.9851i	−0.629265	−	1.08992i	0.358434	−	0.933555i	$-0.383311\pi$
$614$	0.585856	+	3.32255i	0.0236432	+	0.134087i
$615$		0			0
$616$	−10.2836	+	3.74293i	−0.414339	+	0.150807i
$617$	1.23998	−	7.03230i	0.0499199	−	0.283110i	−0.949621	−	0.313400i	$-0.898532\pi$
$617$	1.23998	−	7.03230i	0.0499199	−	0.283110i	0.999541	+	0.0302901i	$0.00964312\pi$
$618$	2.68129	+	1.89805i	0.107857	+	0.0763506i
$619$	−7.68412	+	6.44774i	−0.308851	+	0.259157i	−0.784017	−	0.620740i	$-0.786832\pi$
$619$	−7.68412	+	6.44774i	−0.308851	+	0.259157i	0.475166	+	0.879896i	$0.342388\pi$
$620$		0			0
$621$	−4.83569	−	2.34625i	−0.194049	−	0.0941520i
$622$	−9.90827			−0.397285
$623$	−3.40981	+	2.86117i	−0.136611	+	0.114630i
$624$	0.0850787	−	0.0391423i	0.00340587	−	0.00156695i
$625$		0			0
$626$	10.5061	−	3.82392i	0.419909	−	0.152835i
$627$	3.75722	−	0.309286i	0.150049	−	0.0123517i
$628$	3.98552	+	22.6030i	0.159039	+	0.901957i
$629$	6.93093	+	12.0047i	0.276354	+	0.478660i
$630$		0			0
$631$	3.53780	−	6.12765i	0.140838	−	0.243938i	−0.786975	−	0.616985i	$-0.788354\pi$
$631$	3.53780	−	6.12765i	0.140838	−	0.243938i	0.927812	+	0.373047i	$0.121687\pi$
$632$	0.730905	+	0.266028i	0.0290738	+	0.0105820i
$633$	10.5507	+	40.2002i	0.419353	+	1.59781i
$634$	2.65189	+	2.22520i	0.105320	+	0.0883741i
$635$		0			0
$636$	−3.97070	−	1.08582i	−0.157448	−	0.0430557i
$637$	0.0892352	+	0.0324790i	0.00353563	+	0.00128686i
$638$	−8.45809	+	14.6498i	−0.334859	+	0.579993i
$639$	−11.8756	+	13.8613i	−0.469793	+	0.548344i
$640$		0			0
$641$	−0.870188	−	4.93508i	−0.0343704	−	0.194924i	0.962788	−	0.270258i	$-0.0871089\pi$
$641$	−0.870188	−	4.93508i	−0.0343704	−	0.194924i	−0.997158	+	0.0753337i	$0.975998\pi$
$642$	4.62838	+	6.68277i	0.182667	+	0.263748i
$643$	1.53960	−	0.560367i	0.0607157	−	0.0220987i	−0.311484	−	0.950251i	$-0.600826\pi$
$643$	1.53960	−	0.560367i	0.0607157	−	0.0220987i	0.372199	+	0.928153i	$0.378604\pi$
$644$	−0.433147	+	2.45650i	−0.0170684	+	0.0967997i
$645$		0			0
$646$	0.416126	−	0.349171i	0.0163722	−	0.0137379i
$647$	−34.4927			−1.35605			−0.678024	−	0.735040i	$-0.737164\pi$
$647$	−34.4927			−1.35605			−0.678024	+	0.735040i	$0.737164\pi$
$648$	2.19521	+	14.1420i	0.0862359	+	0.555550i
$649$	19.3056			0.757813
$650$		0			0
$651$	−0.786571	+	8.48840i	−0.0308282	+	0.332687i
$652$	1.05182	−	5.96515i	0.0411923	−	0.233613i
$653$	36.4230	−	13.2569i	1.42534	−	0.518783i	0.489751	−	0.871862i	$-0.337088\pi$
$653$	36.4230	−	13.2569i	1.42534	−	0.518783i	0.935593	+	0.353080i	$0.114866\pi$
$654$	5.94223	+	8.57980i	0.232360	+	0.335497i
$655$		0			0
$656$	5.50161	+	9.52907i	0.214802	+	0.372048i
$657$	0.545365	+	1.54764i	0.0212767	+	0.0603792i
$658$	−1.94575	+	3.37015i	−0.0758534	+	0.131382i
$659$	−8.82552	−	3.21223i	−0.343794	−	0.125131i	0.164352	−	0.986402i	$-0.447447\pi$
$659$	−8.82552	−	3.21223i	−0.343794	−	0.125131i	−0.508146	+	0.861271i	$0.669669\pi$
$660$		0			0
$661$	−18.4980	−	15.5217i	−0.719489	−	0.603723i	0.207755	−	0.978181i	$-0.433384\pi$
$661$	−18.4980	−	15.5217i	−0.719489	−	0.603723i	−0.927244	+	0.374458i	$0.877829\pi$
$662$	−2.04335	−	1.71457i	−0.0794169	−	0.0666387i
$663$	−0.0248750	−	0.0947785i	−0.000966065	−	0.00368089i
$664$	−6.89399	−	2.50921i	−0.267539	−	0.0973761i
$665$		0			0
$666$	−0.0566265	+	5.51472i	−0.00219423	+	0.213691i
$667$	4.03784	+	6.99375i	0.156346	+	0.270799i
$668$	−6.52510	−	37.0057i	−0.252464	−	1.43179i
$669$	37.3935	−	3.07815i	1.44572	−	0.119008i
$670$		0			0
$671$	−6.26159	+	35.5112i	−0.241726	+	1.37090i
$672$	9.18674	−	4.22656i	0.354386	−	0.163043i
$673$	20.2742	−	17.0121i	0.781514	−	0.655768i	−0.162115	−	0.986772i	$-0.551832\pi$
$673$	20.2742	−	17.0121i	0.781514	−	0.655768i	0.943630	+	0.331003i	$0.107387\pi$
$674$	−3.10557			−0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	−23.7986	+	19.9694i	−0.914654	+	0.767486i	−0.972999	−	0.230811i	$-0.925862\pi$
$677$	−23.7986	+	19.9694i	−0.914654	+	0.767486i	0.0583448	+	0.998296i	$0.481418\pi$
$678$	7.37609	+	5.22143i	0.283277	+	0.200528i
$679$	−2.27807	+	12.9196i	−0.0874245	+	0.495809i
$680$		0			0
$681$	−16.0160	+	33.8910i	−0.613734	+	1.29871i
$682$	−1.40328	−	7.95842i	−0.0537345	−	0.304744i
$683$	19.0681	+	33.0268i	0.729619	+	1.26374i	0.957044	+	0.289942i	$0.0936359\pi$
$683$	19.0681	+	33.0268i	0.729619	+	1.26374i	−0.227425	+	0.973796i	$0.573031\pi$
$684$	−2.25719	+	0.374149i	−0.0863060	+	0.0143060i
$685$		0			0
$686$	6.31558	+	2.29868i	0.241130	+	0.0877642i
$687$	13.3016	−	13.1657i	0.507487	−	0.502303i
$688$	19.0552	+	15.9892i	0.726472	+	0.609583i
$689$	0.0179917	+	0.0150968i	0.000685428	+	0.000575142i
$690$		0			0
$691$	−30.9436	−	11.2626i	−1.17715	−	0.428448i	−0.321957	−	0.946754i	$-0.604341\pi$
$691$	−30.9436	−	11.2626i	−1.17715	−	0.428448i	−0.855195	+	0.518306i	$0.826563\pi$
$692$	−12.8221	+	22.2085i	−0.487424	+	0.844242i
$693$	7.26030	−	19.3277i	0.275796	−	0.734198i
$694$	−6.53414	−	11.3175i	−0.248033	−	0.429605i
$695$		0			0
$696$	9.18742	−	19.4413i	0.348248	−	0.736919i
$697$	10.8185	−	3.93762i	0.409781	−	0.149148i
$698$	0.855130	−	4.84968i	0.0323672	−	0.183563i
$699$	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	$0.513873\pi$
$702$	0.0106689	−	0.0374969i	0.000402671	−	0.00141523i
$703$	−1.84668			−0.0696490
$704$	16.5800	−	13.9123i	0.624881	−	0.524338i
$705$		0			0
$706$	0.592100	−	3.35796i	0.0222840	−	0.126379i
$707$	−17.1120	+	6.22826i	−0.643563	+	0.234238i
$708$	−11.6772	+	0.961241i	−0.438857	+	0.0361257i
$709$	−1.93654	−	10.9826i	−0.0727281	−	0.412462i	−0.999336	−	0.0364329i	$-0.988400\pi$
$709$	−1.93654	−	10.9826i	−0.0727281	−	0.412462i	0.926608	−	0.376029i	$-0.122711\pi$
$710$		0			0
$711$	−1.27830	+	0.720629i	−0.0479400	+	0.0270257i
$712$	−2.68184	+	4.64508i	−0.100506	+	0.174082i
$713$	−3.62525	−	1.31948i	−0.135767	−	0.0494151i
$714$	−0.755212	−	2.87750i	−0.0282631	−	0.107688i
$715$		0			0
$716$	−14.2646	−	11.9694i	−0.533092	−	0.447317i
$717$	−5.39888	−	1.47637i	−0.201625	−	0.0551362i
$718$	−6.92093	−	2.51901i	−0.258287	−	0.0940087i
$719$	16.0850	−	27.8600i	0.599869	−	1.03900i	−0.392971	−	0.919551i	$-0.628553\pi$
$719$	16.0850	−	27.8600i	0.599869	−	1.03900i	0.992840	−	0.119453i	$-0.0381140\pi$
$720$		0			0
$721$	3.01213	+	5.21717i	0.112178	+	0.194297i
$722$	−1.35819	−	7.70267i	−0.0505465	−	0.286664i
$723$	−26.1777	−	37.7972i	−0.973560	−	1.40569i
$724$	41.3064	−	15.0343i	1.53514	−	0.558745i
$725$		0			0
$726$	−1.07552	+	11.6066i	−0.0399163	+	0.430762i
$727$	4.11022	−	3.44888i	0.152440	−	0.127912i	−0.563378	−	0.826199i	$-0.690499\pi$
$727$	4.11022	−	3.44888i	0.152440	−	0.127912i	0.715818	+	0.698287i	$0.246054\pi$
$728$	−0.0378942			−0.00140445
$729$	−22.9558	−	14.2138i	−0.850215	−	0.526435i
$730$		0			0
$731$	19.9377	−	16.7297i	0.737424	−	0.618772i
$732$	2.01926	−	21.7911i	0.0746338	−	0.805422i
$733$	2.53463	−	14.3746i	0.0936187	−	0.530938i	−0.901543	−	0.432689i	$-0.857565\pi$
$733$	2.53463	−	14.3746i	0.0936187	−	0.530938i	0.995162	−	0.0982489i	$-0.0313241\pi$
$734$	−7.93296	+	2.88736i	−0.292811	+	0.106574i
$735$		0			0
$736$	0.794682	+	4.50687i	0.0292924	+	0.166125i
$737$	28.7534	+	49.8023i	1.05915	+	1.83449i
$738$	4.50245	+	0.841659i	0.165737	+	0.0309819i
$739$	21.6083	−	37.4266i	0.794873	−	1.37676i	−0.128047	−	0.991768i	$-0.540871\pi$
$739$	21.6083	−	37.4266i	0.794873	−	1.37676i	0.922920	−	0.384992i	$-0.125796\pi$
$740$		0			0
$741$	0.0125917	+	0.00344333i	0.000462569	+	0.000126494i
$742$	0.546231	+	0.458343i	0.0200528	+	0.0168263i
$743$	−6.21431	−	5.21443i	−0.227981	−	0.191299i	0.521641	−	0.853165i	$-0.325320\pi$
$743$	−6.21431	−	5.21443i	−0.227981	−	0.191299i	−0.749622	+	0.661866i	$0.769765\pi$
$744$	2.60770	+	9.93582i	0.0956028	+	0.364265i
$745$		0			0
$746$	−2.01116	+	3.48342i	−0.0736336	+	0.127537i
$747$	12.0571	−	6.79706i	0.441146	−	0.248692i
$748$	−14.9280	−	25.8561i	−0.545823	−	0.945393i
$749$	2.58860	+	14.6807i	0.0945854	+	0.536420i
$750$		0			0
$751$	−8.22744	+	2.99454i	−0.300223	+	0.109272i	−0.487740	−	0.872989i	$-0.662178\pi$
$751$	−8.22744	+	2.99454i	−0.300223	+	0.109272i	0.187516	+	0.982261i	$0.439956\pi$
$752$	3.69037	−	20.9291i	0.134574	−	0.763207i
$753$	−7.07968	+	3.25717i	−0.257998	+	0.118698i
$754$	−0.0448713	+	0.0376515i	−0.00163412	+	0.00137119i
$755$		0			0
$756$	−3.42913	+	12.0520i	−0.124716	+	0.438329i
$757$	32.1511			1.16855			0.584276	−	0.811555i	$-0.301378\pi$
$757$	32.1511			1.16855			0.584276	+	0.811555i	$0.301378\pi$
$758$	−1.31414	+	1.10269i	−0.0477316	+	0.0400515i
$759$	7.62620	+	5.39848i	0.276813	+	0.195952i
$760$		0			0
$761$	23.0656	−	8.39520i	0.836128	−	0.304326i	0.111756	−	0.993736i	$-0.464352\pi$
$761$	23.0656	−	8.39520i	0.836128	−	0.304326i	0.724371	+	0.689410i	$0.242130\pi$
$762$	2.58116	−	5.46192i	0.0935054	−	0.197865i
$763$	3.32342	+	18.8481i	0.120316	+	0.682346i
$764$	10.0016	+	17.3233i	0.361846	+	0.626736i
$765$		0			0
$766$	0.986770	−	1.70914i	0.0356535	−	0.0617536i
$767$	0.0628177	+	0.0228638i	0.00226822	+	0.000825563i
$768$	−4.81033	+	4.76119i	−0.173578	+	0.171805i
$769$	24.0648	+	20.1928i	0.867800	+	0.728170i	0.963634	−	0.267227i	$-0.0861073\pi$
$769$	24.0648	+	20.1928i	0.867800	+	0.728170i	−0.0958338	+	0.995397i	$0.530552\pi$
$770$		0			0
$771$	16.9085	−	16.7358i	0.608945	−	0.602725i
$772$	18.5558	+	6.75377i	0.667839	+	0.243073i
$773$	14.3573	−	24.8675i	0.516395	−	0.894422i	−0.483424	−	0.875386i	$-0.660607\pi$
$773$	14.3573	−	24.8675i	0.516395	−	0.894422i	0.999819	−	0.0190355i	$-0.00605954\pi$
$774$	10.2155	−	1.69331i	0.367190	−	0.0608649i
$775$		0			0
$776$	2.74507	+	15.5681i	0.0985424	+	0.558862i
$777$	−4.32116	+	9.14389i	−0.155021	+	0.328035i
$778$	8.51615	−	3.09962i	0.305319	−	0.111127i
$779$	−0.266332	+	1.51044i	−0.00954233	+	0.0541173i
$780$		0			0
$781$	24.3071	−	20.3961i	0.869776	−	0.729829i
$782$	1.34633			0.0481446
$783$	16.5763	+	37.0263i	0.592388	+	1.32321i
$784$	−15.7448			−0.562315
$785$		0			0
$786$	−10.1558	+	4.67239i	−0.362245	+	0.166659i
$787$	6.74033	−	38.2263i	0.240267	−	1.36262i	−0.590966	−	0.806697i	$-0.701253\pi$
$787$	6.74033	−	38.2263i	0.240267	−	1.36262i	0.831233	−	0.555925i	$-0.187636\pi$
$788$	37.9040	−	13.7959i	1.35027	−	0.491459i
$789$	−41.7787	+	3.43913i	−1.48736	+	0.122436i
$790$		0			0
$791$	8.28623	+	14.3522i	0.294625	+	0.510305i
$792$	0.255448	−	24.8775i	0.00907694	−	0.883983i
$793$	−0.0624304	+	0.108133i	−0.00221697	+	0.00383990i
$794$	−13.6054	−	4.95197i	−0.482839	−	0.175739i
$795$		0			0
$796$	−18.0397	−	15.1371i	−0.639399	−	0.536520i
$797$	3.09030	+	2.59307i	0.109464	+	0.0918512i	0.695877	−	0.718161i	$-0.255016\pi$
$797$	3.09030	+	2.59307i	0.109464	+	0.0918512i	−0.586413	+	0.810012i	$0.699460\pi$
$798$	0.382289	+	0.104540i	0.0135329	+	0.00370069i
$799$	−20.8953	−	7.60526i	−0.739222	−	0.269055i
$800$		0			0
$801$	−3.36315	−	9.54397i	−0.118831	−	0.337220i
$802$	3.91080	+	6.77371i	0.138095	+	0.239188i
$803$	−0.495343	−	2.80923i	−0.0174803	−	0.0991355i
$804$	−19.8715	−	28.6918i	−0.700813	−	1.01188i
$805$		0			0
$806$	0.00485912	−	0.0275575i	0.000171155	−	0.000970670i
$807$	−1.91877	+	20.7067i	−0.0675438	+	0.728909i
$808$	−16.8095	+	14.1049i	−0.591357	+	0.496207i
$809$	−29.9454			−1.05283			−0.526413	−	0.850229i	$-0.676463\pi$
$809$	−29.9454			−1.05283			−0.526413	+	0.850229i	$0.676463\pi$
$810$		0			0
$811$	20.2173			0.709927			0.354963	−	0.934880i	$-0.384493\pi$
$811$	20.2173			0.709927			0.354963	+	0.934880i	$0.384493\pi$
$812$	14.4223	−	12.1017i	0.506122	−	0.424687i
$813$	−0.594154	+	6.41190i	−0.0208379	+	0.224875i
$814$	1.66481	−	9.44162i	0.0583516	−	0.330929i
$815$		0			0
$816$	9.25021	+	13.3561i	0.323822	+	0.467557i
$817$	0.602092	+	3.41463i	0.0210645	+	0.119463i
$818$	1.32117	+	2.28834i	0.0461938	+	0.0800099i
$819$	0.0465138	−	0.0542910i	0.00162533	−	0.00189708i
$820$		0			0
$821$	−25.2530	−	9.19133i	−0.881334	−	0.320779i	−0.138586	−	0.990350i	$-0.544256\pi$
$821$	−25.2530	−	9.19133i	−0.881334	−	0.320779i	−0.742748	+	0.669571i	$0.766478\pi$
$822$	−8.33461	−	2.27918i	−0.290703	−	0.0794954i
$823$	−17.6606	−	14.8190i	−0.615611	−	0.516559i	0.280809	−	0.959764i	$-0.409397\pi$
$823$	−17.6606	−	14.8190i	−0.615611	−	0.516559i	−0.896421	+	0.443204i	$0.853842\pi$
$824$	5.56089	+	4.66614i	0.193723	+	0.162553i
$825$		0			0
$826$	1.90716	+	0.694150i	0.0663587	+	0.0241526i
$827$	−2.55476	+	4.42498i	−0.0888378	+	0.153872i	−0.907020	−	0.421087i	$-0.861649\pi$
$827$	−2.55476	+	4.42498i	−0.0888378	+	0.153872i	0.818182	+	0.574959i	$0.194982\pi$
$828$	−4.88158	−	2.88561i	−0.169647	−	0.100282i
$829$	15.2991	+	26.4988i	0.531360	+	0.920343i	0.999330	+	0.0365985i	$0.0116523\pi$
$829$	15.2991	+	26.4988i	0.531360	+	0.920343i	−0.467970	+	0.883744i	$0.655014\pi$
$830$		0			0
$831$	−40.5368	+	3.33690i	−1.40621	+	0.115756i
$832$	0.0704252	−	0.0256327i	0.00244155	−	0.000888653i
$833$	−2.86069	+	16.2238i	−0.0991170	+	0.562120i
$834$	4.01731	−	1.84825i	0.139108	−	0.0639997i
$835$		0			0
$836$	3.97744			0.137563
$837$	−17.4359	−	8.45984i	−0.602674	−	0.292415i
$838$	−10.1033			−0.349013
$839$	−43.1350	+	36.1945i	−1.48918	+	1.24957i	−0.593539	+	0.804805i	$0.702270\pi$
$839$	−43.1350	+	36.1945i	−1.48918	+	1.24957i	−0.895645	+	0.444769i	$0.853286\pi$
$840$		0			0
$841$	5.54853	−	31.4673i	0.191329	−	1.08508i
$842$	3.11939	−	1.13537i	0.107501	−	0.0391273i
$843$	−15.0760	+	31.9020i	−0.519246	+	1.09876i
$844$	7.61436	+	43.1832i	0.262097	+	1.48643i
$845$		0			0
$846$	−5.61674	−	6.83509i	−0.193108	−	0.234995i
$847$	−10.6878	+	18.5118i	−0.367237	+	0.636073i
$848$	−3.65924	−	1.33185i	−0.125659	−	0.0457360i
$849$	14.2797	−	14.1338i	0.490079	−	0.485072i
$850$		0			0
$851$	−3.50612	−	2.94198i	−0.120188	−	0.100850i
$852$	−13.6869	+	13.5470i	−0.468904	+	0.464114i
$853$	−42.7983	−	15.5773i	−1.46539	−	0.533357i	−0.518542	−	0.855052i	$-0.673525\pi$
$853$	−42.7983	−	15.5773i	−1.46539	−	0.533357i	−0.946843	+	0.321695i	$0.895747\pi$
$854$	−1.89540	+	3.28294i	−0.0648594	+	0.112340i
$855$		0			0
$856$	8.98154	+	15.5565i	0.306983	+	0.531710i
$857$	3.03696	+	17.2235i	0.103741	+	0.588343i	0.991716	+	0.128451i	$0.0410006\pi$
$857$	3.03696	+	17.2235i	0.103741	+	0.588343i	−0.887975	+	0.459892i	$0.847888\pi$
$858$	−0.0289565	+	0.0612742i	−0.000988559	+	0.00209187i
$859$	−17.2396	+	6.27471i	−0.588208	+	0.214090i	−0.618941	−	0.785437i	$-0.712438\pi$
$859$	−17.2396	+	6.27471i	−0.588208	+	0.214090i	0.0307329	+	0.999528i	$0.490216\pi$
$860$		0			0
$861$	6.85579	+	4.85312i	0.233645	+	0.165394i
$862$	3.14167	−	2.63618i	0.107006	−	0.0897886i
$863$	−4.65373			−0.158415			−0.0792073	−	0.996858i	$-0.525239\pi$
$863$	−4.65373			−0.158415			−0.0792073	+	0.996858i	$0.525239\pi$
$864$	1.65068	+	22.9298i	0.0561574	+	0.780087i
$865$		0			0
$866$	1.94259	−	1.63003i	0.0660120	−	0.0553907i
$867$	−11.3066	+	5.20185i	−0.383992	+	0.176664i
$868$	−1.56179	+	8.85735i	−0.0530106	+	0.300638i
$869$	2.39713	−	0.872486i	0.0813172	−	0.0295971i
$870$		0			0
$871$	0.0345781	+	0.196102i	0.00117164	+	0.00664468i
$872$	11.5311	+	19.9725i	0.390493	+	0.676354i
$873$	−25.6739	−	15.1765i	−0.868931	−	0.513645i
$874$	−0.0896791	+	0.155329i	−0.00303344	+	0.00525407i
$875$		0			0
$876$	0.439487	+	1.67453i	0.0148489	+	0.0565770i
$877$	2.80916	+	2.35716i	0.0948585	+	0.0795958i	0.688984	−	0.724777i	$-0.258057\pi$
$877$	2.80916	+	2.35716i	0.0948585	+	0.0795958i	−0.594125	+	0.804373i	$0.702502\pi$
$878$	−4.81664	−	4.04164i	−0.162554	−	0.136399i
$879$	−52.7512	−	14.4253i	−1.77925	−	0.486554i
$880$		0			0
$881$	−19.1504	+	33.1694i	−0.645193	+	1.11751i	0.339064	+	0.940763i	$0.389890\pi$
$881$	−19.1504	+	33.1694i	−0.645193	+	1.11751i	−0.984257	+	0.176744i	$0.943444\pi$
$882$	−4.26434	+	4.97735i	−0.143588	+	0.167596i
$883$	11.3071	+	19.5844i	0.380513	+	0.659069i	0.991136	−	0.132853i	$-0.0424139\pi$
$883$	11.3071	+	19.5844i	0.380513	+	0.659069i	−0.610622	+	0.791922i	$0.709081\pi$
$884$	−0.0179521	−	0.101811i	−0.000603794	−	0.00342429i
$885$		0			0
$886$	−0.282186	+	0.102707i	−0.00948023	+	0.00345052i
$887$	0.329334	−	1.86774i	0.0110579	−	0.0627127i	−0.978779	−	0.204916i	$-0.934308\pi$
$887$	0.329334	−	1.86774i	0.0110579	−	0.0627127i	0.989837	+	0.142204i	$0.0454188\pi$
$888$	−1.12446	+	12.1348i	−0.0377344	+	0.407216i
$889$	8.48645	−	7.12097i	0.284626	−	0.238830i
$890$		0			0
$891$	35.3285	+	30.9023i	1.18355	+	1.03527i
$892$	39.5852			1.32541
$893$	2.26928	−	1.90415i	0.0759384	−	0.0637199i
$894$	−0.0586171	+	0.632575i	−0.00196045	+	0.0211565i
$895$		0			0
$896$	13.1107	−	4.77190i	0.437997	−	0.159418i
$897$	0.0184211	+	0.0265976i	0.000615062	+	0.000888069i
$898$	0.120370	+	0.682653i	0.00401680	+	0.0227804i
$899$	14.5592	+	25.2172i	0.485575	+	0.841041i
$900$		0			0
$901$	−2.03722	+	3.52856i	−0.0678695	+	0.117553i
$902$	−7.48241	−	2.72338i	−0.249137	−	0.0906785i
$903$	18.3165	+	5.00882i	0.609535	+	0.166683i
$904$	15.2977	+	12.8363i	0.508795	+	0.426930i
$905$		0			0
$906$	−1.50261	−	5.72522i	−0.0499208	−	0.190208i
$907$	6.13708	+	2.23371i	0.203778	+	0.0741693i	0.441893	−	0.897068i	$-0.354307\pi$
$907$	6.13708	+	2.23371i	0.203778	+	0.0741693i	−0.238115	+	0.971237i	$0.576529\pi$
$908$	−19.7740	+	34.2497i	−0.656225	+	1.13661i
$909$	0.425067	−	41.3963i	0.0140986	−	1.37303i
$910$		0			0
$911$	−7.47332	−	42.3833i	−0.247602	−	1.40422i	−0.814371	−	0.580344i	$-0.802918\pi$
$911$	−7.47332	−	42.3833i	−0.247602	−	1.40422i	0.566769	−	0.823877i	$-0.308193\pi$
$912$	−2.15708	+	0.177566i	−0.0714281	+	0.00587980i
$913$	−22.6101	+	8.22940i	−0.748285	+	0.272353i
$914$	−0.799615	+	4.53484i	−0.0264489	+	0.149999i
$915$		0			0
$916$	15.1260	−	12.6922i	0.499777	−	0.419363i
$917$	−20.5003			−0.676980
$918$	6.72755	+	0.693143i	0.222042	+	0.0228771i
$919$	−16.7911			−0.553887			−0.276943	−	0.960886i	$-0.589321\pi$
$919$	−16.7911			−0.553887			−0.276943	+	0.960886i	$0.589321\pi$
$920$		0			0
$921$	−11.4800	−	8.12650i	−0.378277	−	0.267777i
$922$	−1.57885	+	8.95409i	−0.0519966	+	0.294887i
$923$	0.103247	−	0.0375788i	0.00339841	−	0.00123692i
$924$	9.30703	−	19.6944i	0.306179	−	0.647897i
$925$		0			0
$926$	5.16253	+	8.94176i	0.169651	+	0.293844i
$927$	−13.5110	+	2.23957i	−0.443760	+	0.0735570i
$928$	17.2706	−	29.9135i	0.566935	−	0.981960i
$929$	10.9004	+	3.96744i	0.357632	+	0.130167i	0.514587	−	0.857438i	$-0.327945\pi$
$929$	10.9004	+	3.96744i	0.357632	+	0.130167i	−0.156955	+	0.987606i	$0.550168\pi$
$930$		0			0
$931$	−1.68122	−	1.41071i	−0.0550998	−	0.0462343i
$932$	10.6935	+	8.97294i	0.350278	+	0.293918i
$933$	29.3580	−	29.0581i	0.961137	−	0.951318i
$934$	−4.62072	−	1.68180i	−0.151195	−	0.0550303i
$935$		0			0
$936$	0.0302937	−	0.0806452i	0.000990182	−	0.00263597i
$937$	23.8976	+	41.3919i	0.780702	+	1.35222i	0.931533	+	0.363656i	$0.118472\pi$
$937$	23.8976	+	41.3919i	0.780702	+	1.35222i	−0.150832	+	0.988559i	$0.548195\pi$
$938$	1.04980	+	5.95372i	0.0342772	+	0.194396i
$939$	−19.9150	+	42.1416i	−0.649901	+	1.37524i
$940$		0			0
$941$	1.95534	−	11.0893i	0.0637422	−	0.361500i	−0.936207	−	0.351448i	$-0.885689\pi$
$941$	1.95534	−	11.0893i	0.0637422	−	0.361500i	0.999949	−	0.0100518i	$-0.00319964\pi$
$942$	7.37691	+	5.22202i	0.240353	+	0.170142i
$943$	−2.91197	+	2.44343i	−0.0948268	+	0.0795691i
$944$	−11.0837			−0.360743
$945$		0			0
$946$	−18.0010			−0.585261
$947$	−5.61656	+	4.71285i	−0.182514	+	0.153147i	−0.729467	−	0.684016i	$-0.760232\pi$
$947$	−5.61656	+	4.71285i	−0.182514	+	0.153147i	0.546954	+	0.837163i	$0.315787\pi$
$948$	−1.40649	+	0.647087i	−0.0456807	+	0.0210164i
$949$	0.00171521	−	0.00972746i	5.56782e−5	−	0.000315767i
$950$		0			0
$951$	−14.3834	+	1.18401i	−0.466413	+	0.0383940i
$952$	−1.14154	−	6.47401i	−0.0369976	−	0.209824i
$953$	−12.4377	−	21.5427i	−0.402895	−	0.697835i	0.591179	−	0.806541i	$-0.298663\pi$
$953$	−12.4377	−	21.5427i	−0.402895	−	0.697835i	−0.994074	+	0.108705i	$0.965329\pi$
$954$	−1.41210	+	0.796060i	−0.0457186	+	0.0257734i
$955$		0			0
$956$	−5.54906	−	2.01969i	−0.179469	−	0.0653215i
$957$	−17.9026	−	68.2122i	−0.578708	−	2.20499i
$958$	0.918945	+	0.771086i	0.0296898	+	0.0249127i
$959$	−12.1382	−	10.1852i	−0.391963	−	0.328896i
$960$		0			0
$961$	16.0590	+	5.84499i	0.518031	+	0.188548i
$962$	0.0165988	−	0.0287500i	0.000535168	−	0.000926937i
$963$	−33.3124	−	6.22720i	−1.07348	−	0.200669i
$964$	−24.2540	−	42.0091i	−0.781167	−	1.35302i
$965$		0			0
$966$	0.559269	+	0.807511i	0.0179942	+	0.0259812i
$967$	−31.9777	+	11.6389i	−1.02833	+	0.374283i	−0.800446	−	0.599404i	$-0.795404\pi$
$967$	−31.9777	+	11.6389i	−1.02833	+	0.374283i	−0.227888	+	0.973687i	$0.573182\pi$
$968$	−4.47275	+	25.3662i	−0.143760	+	0.815301i
$969$	−0.208954	+	2.25496i	−0.00671258	+	0.0724397i
$970$		0			0
$971$	−34.2476			−1.09906			−0.549530	−	0.835474i	$-0.685193\pi$
$971$	−34.2476			−1.09906			−0.549530	+	0.835474i	$0.685193\pi$
$972$	−22.9074	−	16.9325i	−0.734756	−	0.543111i
$973$	8.10928			0.259971
$974$	−2.78770	+	2.33916i	−0.0893236	+	0.0749514i
$975$		0			0
$976$	3.59488	−	20.3876i	0.115069	−	0.652590i
$977$	−22.0051	+	8.00919i	−0.704004	+	0.256237i	−0.669120	−	0.743155i	$-0.733329\pi$
$977$	−22.0051	+	8.00919i	−0.704004	+	0.256237i	−0.0348848	+	0.999391i	$0.511106\pi$
$978$	−1.35808	−	1.96089i	−0.0434266	−	0.0627022i
$979$	3.05467	+	17.3239i	0.0976278	+	0.553675i
$980$		0			0
$981$	−42.7687	−	7.99491i	−1.36550	−	0.255258i
$982$	4.68917	−	8.12188i	0.149637	−	0.259180i
$983$	−31.2007	−	11.3561i	−0.995149	−	0.362205i	−0.207437	−	0.978248i	$-0.566512\pi$
$983$	−31.2007	−	11.3561i	−0.995149	−	0.362205i	−0.787712	+	0.616044i	$0.788734\pi$
$984$	9.76314	+	2.66982i	0.311237	+	0.0851108i
$985$		0			0
$986$	−7.78428	−	6.53178i	−0.247902	−	0.208014i
$987$	−4.11843	−	15.6920i	−0.131091	−	0.499482i
$988$	0.0129420	+	0.00471050i	0.000411740	+	0.000149861i
$989$	−4.29678	+	7.44223i	−0.136630	+	0.236649i
$990$		0			0
$991$	14.0903	+	24.4051i	0.447594	+	0.775255i	0.998229	−	0.0594912i	$-0.0189478\pi$
$991$	14.0903	+	24.4051i	0.447594	+	0.775255i	−0.550635	+	0.834746i	$0.685614\pi$
$992$	2.86537	+	16.2503i	0.0909755	+	0.515948i
$993$	11.0827	−	0.912305i	0.351700	−	0.0289511i
$994$	3.13460	−	1.14090i	0.0994236	−	0.0361872i
$995$		0			0
$996$	13.2662	−	6.10341i	0.420355	−	0.193394i
$997$	34.4342	−	28.8938i	1.09054	−	0.915075i	0.0937901	−	0.995592i	$-0.470102\pi$
$997$	34.4342	−	28.8938i	1.09054	−	0.915075i	0.996753	+	0.0805175i	$0.0256573\pi$
$998$	−10.5249			−0.333161
$999$	−16.0053	−	16.5061i	−0.506385	−	0.522228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.c.76.1		12
5.2	odd	4		675.2.u.b.49.3		24
5.3	odd	4		675.2.u.b.49.2		24
5.4	even	2		27.2.e.a.22.2	yes	12
15.14	odd	2		81.2.e.a.37.1		12
20.19	odd	2		432.2.u.c.49.1		12
27.16	even	9	inner	675.2.l.c.151.1		12
45.4	even	6		243.2.e.d.28.2		12
45.14	odd	6		243.2.e.a.28.1		12
45.29	odd	6		243.2.e.b.190.2		12
45.34	even	6		243.2.e.c.190.1		12
135.4	even	18		729.2.a.a.1.4		6
135.14	odd	18		729.2.c.b.487.4		12
135.29	odd	18		243.2.e.b.55.2		12
135.34	even	18		243.2.e.d.217.2		12
135.43	odd	36		675.2.u.b.124.3		24
135.49	even	18		729.2.c.e.244.3		12
135.59	odd	18		729.2.c.b.244.4		12
135.74	odd	18		243.2.e.a.217.1		12
135.79	even	18		243.2.e.c.55.1		12
135.94	even	18		729.2.c.e.487.3		12
135.97	odd	36		675.2.u.b.124.2		24
135.104	odd	18		729.2.a.d.1.3		6
135.119	odd	18		81.2.e.a.46.1		12
135.124	even	18		27.2.e.a.16.2	✓	12
540.259	odd	18		432.2.u.c.97.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.2	✓	12	135.124	even	18
27.2.e.a.22.2	yes	12	5.4	even	2
81.2.e.a.37.1		12	15.14	odd	2
81.2.e.a.46.1		12	135.119	odd	18
243.2.e.a.28.1		12	45.14	odd	6
243.2.e.a.217.1		12	135.74	odd	18
243.2.e.b.55.2		12	135.29	odd	18
243.2.e.b.190.2		12	45.29	odd	6
243.2.e.c.55.1		12	135.79	even	18
243.2.e.c.190.1		12	45.34	even	6
243.2.e.d.28.2		12	45.4	even	6
243.2.e.d.217.2		12	135.34	even	18
432.2.u.c.49.1		12	20.19	odd	2
432.2.u.c.97.1		12	540.259	odd	18
675.2.l.c.76.1		12	1.1	even	1	trivial
675.2.l.c.151.1		12	27.16	even	9	inner
675.2.u.b.49.2		24	5.3	odd	4
675.2.u.b.49.3		24	5.2	odd	4
675.2.u.b.124.2		24	135.97	odd	36
675.2.u.b.124.3		24	135.43	odd	36
729.2.a.a.1.4		6	135.4	even	18
729.2.a.d.1.3		6	135.104	odd	18
729.2.c.b.244.4		12	135.59	odd	18
729.2.c.b.487.4		12	135.14	odd	18
729.2.c.e.244.3		12	135.49	even	18
729.2.c.e.487.3		12	135.94	even	18

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.318266 - 0.267057i) q^{2} +(-0.159815 + 1.72466i) q^{3} +(-0.317323 + 1.79963i) q^{4} +(0.409719 + 0.591580i) q^{6} +(0.229151 + 1.29958i) q^{7} +(0.795075 + 1.37711i) q^{8} +(-2.94892 - 0.551252i) q^{9} +(4.90067 + 1.78370i) q^{11} +(-3.05303 - 0.834881i) q^{12} +(0.0138336 + 0.0116078i) q^{13} +(0.419993 + 0.352416i) q^{14} +(-2.81355 - 1.02405i) q^{16} +(-1.56640 + 2.71308i) q^{17} +(-1.08575 + 0.612083i) q^{18} +(-0.208676 - 0.361438i) q^{19} +(-2.27796 + 0.187516i) q^{21} +(2.03606 - 0.741067i) q^{22} +(0.179619 - 1.01867i) q^{23} +(-2.50212 + 1.15115i) q^{24} +0.00750270 q^{26} +(1.42200 - 4.99779i) q^{27} -2.41147 q^{28} +(-5.98068 + 5.01839i) q^{29} +(0.647649 - 3.67300i) q^{31} +(-4.15744 + 1.51319i) q^{32} +(-3.85948 + 8.16694i) q^{33} +(0.226015 + 1.28180i) q^{34} +(1.92781 - 5.13202i) q^{36} +(2.21238 - 3.83195i) q^{37} +(-0.162939 - 0.0593049i) q^{38} +(-0.0222303 + 0.0220032i) q^{39} +(-2.81517 - 2.36221i) q^{41} +(-0.674919 + 0.668024i) q^{42} +(-7.80685 - 2.84146i) q^{43} +(-4.76508 + 8.25337i) q^{44} +(-0.214876 - 0.372177i) q^{46} +(1.23254 + 6.99008i) q^{47} +(2.21579 - 4.68877i) q^{48} +(4.94145 - 1.79854i) q^{49} +(-4.42881 - 3.13510i) q^{51} +(-0.0252794 + 0.0212119i) q^{52} +1.30057 q^{53} +(-0.882118 - 1.97038i) q^{54} +(-1.60747 + 1.34883i) q^{56} +(0.656707 - 0.302133i) q^{57} +(-0.563252 + 3.19436i) q^{58} +(3.47856 - 1.26609i) q^{59} +(1.20064 + 6.80919i) q^{61} +(-0.774775 - 1.34195i) q^{62} +(0.0406486 - 3.95868i) q^{63} +(2.07506 - 3.59410i) q^{64} +(0.952697 + 3.62996i) q^{66} +(8.44702 + 7.08789i) q^{67} +(-4.38548 - 3.67985i) q^{68} +(1.72816 + 0.472581i) q^{69} +(3.04214 - 5.26914i) q^{71} +(-1.58548 - 4.49927i) q^{72} +(-0.273486 - 0.473692i) q^{73} +(-0.319224 - 1.81041i) q^{74} +(0.716670 - 0.260847i) q^{76} +(-1.19507 + 6.77756i) q^{77} +(-0.00119904 + 0.0129396i) q^{78} +(0.374706 - 0.314416i) q^{79} +(8.39224 + 3.25120i) q^{81} -1.52681 q^{82} +(-3.53428 + 2.96561i) q^{83} +(0.385389 - 4.15898i) q^{84} +(-3.24348 + 1.18053i) q^{86} +(-7.69922 - 11.1167i) q^{87} +(1.44005 + 8.16694i) q^{88} +(1.68653 + 2.92116i) q^{89} +(-0.0119153 + 0.0206379i) q^{91} +(1.77623 + 0.646495i) q^{92} +(6.23118 + 1.70398i) q^{93} +(2.25902 + 1.89554i) q^{94} +(-1.94531 - 7.41201i) q^{96} +(9.34182 + 3.40014i) q^{97} +(1.09238 - 1.89206i) q^{98} +(-13.4684 - 7.96149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27}+ \cdots - 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

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