LMFDB - Embedded newform 1224.2.l.c.1189.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(1189,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("1224.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.l (of order $2$, degree $1$, 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:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{16} - 2x^{14} + 2x^{12} - 4x^{11} + 4x^{10} + 8x^{8} - 16x^{7} + 16x^{6} - 64x^{4} - 128x^{2} + 512 $ x^18 - x^16 - 2x^14 + 2x^12 - 4x^11 + 4x^10 + 8x^8 - 16x^7 + 16x^6 - 64x^4 - 128*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1189.6
Root			$-0.943929 - 1.05309i$ of defining polynomial
Character	$\chi$	$=$	1224.1189
Dual form			1224.2.l.c.1189.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.943929 + 1.05309i) q^{2} +(-0.217998 - 1.98808i) q^{4} +1.57273 q^{5} -1.68207i q^{7} +(2.29941 + 1.64704i) q^{8} +(-1.48454 + 1.65622i) q^{10} +3.33403 q^{11} -0.177520i q^{13} +(1.77138 + 1.58776i) q^{14} +(-3.90495 + 0.866796i) q^{16} +(3.53017 - 2.13024i) q^{17} -2.58556i q^{19} +(-0.342852 - 3.12672i) q^{20} +(-3.14709 + 3.51104i) q^{22} +3.40373i q^{23} -2.52653 q^{25} +(0.186944 + 0.167566i) q^{26} +(-3.34410 + 0.366689i) q^{28} -2.46715 q^{29} -4.84803i q^{31} +(2.77318 - 4.93046i) q^{32} +(-1.08889 + 5.72838i) q^{34} -2.64545i q^{35} +5.33914 q^{37} +(2.72283 + 2.44058i) q^{38} +(3.61634 + 2.59034i) q^{40} +4.79275i q^{41} -5.48185i q^{43} +(-0.726812 - 6.62833i) q^{44} +(-3.58443 - 3.21288i) q^{46} -5.72051 q^{47} +4.17063 q^{49} +(2.38486 - 2.66066i) q^{50} +(-0.352924 + 0.0386989i) q^{52} -4.52038i q^{53} +5.24353 q^{55} +(2.77044 - 3.86777i) q^{56} +(2.32881 - 2.59813i) q^{58} -6.32370i q^{59} +6.28670 q^{61} +(5.10541 + 4.57619i) q^{62} +(2.57454 + 7.57442i) q^{64} -0.279190i q^{65} -15.8300i q^{67} +(-5.00466 - 6.55388i) q^{68} +(2.78589 + 2.49711i) q^{70} +13.3194i q^{71} +4.38096i q^{73} +(-5.03977 + 5.62260i) q^{74} +(-5.14031 + 0.563647i) q^{76} -5.60809i q^{77} -7.47987i q^{79} +(-6.14143 + 1.36324i) q^{80} +(-5.04720 - 4.52401i) q^{82} -6.58394i q^{83} +(5.55199 - 3.35029i) q^{85} +(5.77289 + 5.17448i) q^{86} +(7.66629 + 5.49128i) q^{88} +8.64940 q^{89} -0.298601 q^{91} +(6.76689 - 0.742005i) q^{92} +(5.39975 - 6.02421i) q^{94} -4.06638i q^{95} +13.1686i q^{97} +(-3.93677 + 4.39205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{4} - 4 q^{5} + 8 q^{10} - 6 q^{14} + 10 q^{16} + 2 q^{17} - 2 q^{20} - 2 q^{22} + 22 q^{25} - 2 q^{26} + 10 q^{28} + 12 q^{29} - 30 q^{34} + 16 q^{37} + 34 q^{38} + 10 q^{40} + 12 q^{44} - 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 18 * q + 2 * q^4 - 4 * q^5 + 8 * q^10 - 6 * q^14 + 10 * q^16 + 2 * q^17 - 2 * q^20 - 2 * q^22 + 22 * q^25 - 2 * q^26 + 10 * q^28 + 12 * q^29 - 30 * q^34 + 16 * q^37 + 34 * q^38 + 10 * q^40 + 12 * q^44 - 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 - 14 * q^56 + 6 * q^58 + 16 * q^61 - 6 * q^62 + 2 * q^64 - 12 * q^68 - 32 * q^70 - 6 * q^74 - 62 * q^80 - 34 * q^82 - 16 * q^85 - 14 * q^86 - 16 * q^88 - 20 * q^89 - 2 * q^92 + 12 * q^94 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.943929	+	1.05309i	−0.667458	+	0.744647i
$2$	−0.943929	+	1.05309i	−0.667458	+	0.744647i
$3$		0			0
$3$		0			0
$4$	−0.217998	−	1.98808i	−0.108999	−	0.994042i
$5$	1.57273			0.703346			0.351673	−	0.936123i	$-0.385613\pi$
$5$	1.57273			0.703346			0.351673	+	0.936123i	$0.385613\pi$
$6$		0			0
$7$		−	1.68207i		−	0.635764i	−0.948130	−	0.317882i	$-0.897028\pi$
$7$		−	1.68207i		−	0.635764i	0.948130	−	0.317882i	$-0.102972\pi$
$8$	2.29941	+	1.64704i	0.812963	+	0.582316i
$9$		0			0
$10$	−1.48454	+	1.65622i	−0.469454	+	0.523744i
$11$	3.33403			1.00525			0.502624	−	0.864505i	$-0.332368\pi$
$11$	3.33403			1.00525			0.502624	+	0.864505i	$0.332368\pi$
$12$		0			0
$13$		−	0.177520i		−	0.0492351i	−0.999697	−	0.0246175i	$-0.992163\pi$
$13$		−	0.177520i		−	0.0492351i	0.999697	−	0.0246175i	$-0.00783680\pi$
$14$	1.77138	+	1.58776i	0.473420	+	0.424346i
$15$		0			0
$16$	−3.90495	+	0.866796i	−0.976238	+	0.216699i
$17$	3.53017	−	2.13024i	0.856191	−	0.516659i
$17$	3.53017	−	2.13024i	0.856191	−	0.516659i
$18$		0			0
$19$		−	2.58556i		−	0.593168i	−0.955007	−	0.296584i	$-0.904152\pi$
$19$		−	2.58556i		−	0.593168i	0.955007	−	0.296584i	$-0.0958475\pi$
$20$	−0.342852	−	3.12672i	−0.0766639	−	0.699155i
$21$		0			0
$22$	−3.14709	+	3.51104i	−0.670961	+	0.748556i
$23$			3.40373i			0.709726i	0.934918	+	0.354863i	$0.115473\pi$
$23$			3.40373i			0.709726i	−0.934918	+	0.354863i	$0.884527\pi$
$24$		0			0
$25$	−2.52653			−0.505305
$26$	0.186944	+	0.167566i	0.0366628	+	0.0328624i
$27$		0			0
$28$	−3.34410	+	0.366689i	−0.631976	+	0.0692976i
$29$	−2.46715			−0.458138			−0.229069	−	0.973410i	$-0.573568\pi$
$29$	−2.46715			−0.458138			−0.229069	+	0.973410i	$0.573568\pi$
$30$		0			0
$31$		−	4.84803i		−	0.870731i	−0.900254	−	0.435366i	$-0.856619\pi$
$31$		−	4.84803i		−	0.870731i	0.900254	−	0.435366i	$-0.143381\pi$
$32$	2.77318	−	4.93046i	0.490234	−	0.871591i
$33$		0			0
$34$	−1.08889	+	5.72838i	−0.186743	+	0.982409i
$35$		−	2.64545i		−	0.447162i
$36$		0			0
$37$	5.33914			0.877750			0.438875	−	0.898548i	$-0.355377\pi$
$37$	5.33914			0.877750			0.438875	+	0.898548i	$0.355377\pi$
$38$	2.72283	+	2.44058i	0.441701	+	0.395915i
$39$		0			0
$40$	3.61634	+	2.59034i	0.571794	+	0.409569i
$41$			4.79275i			0.748502i	0.927327	+	0.374251i	$0.122100\pi$
$41$			4.79275i			0.748502i	−0.927327	+	0.374251i	$0.877900\pi$
$42$		0			0
$43$		−	5.48185i		−	0.835975i	−0.908453	−	0.417987i	$-0.862736\pi$
$43$		−	5.48185i		−	0.835975i	0.908453	−	0.417987i	$-0.137264\pi$
$44$	−0.726812	−	6.62833i	−0.109571	−	0.999259i
$45$		0			0
$46$	−3.58443	−	3.21288i	−0.528496	−	0.473713i
$47$	−5.72051			−0.834422			−0.417211	−	0.908810i	$-0.636992\pi$
$47$	−5.72051			−0.834422			−0.417211	+	0.908810i	$0.636992\pi$
$48$		0			0
$49$	4.17063			0.595804
$50$	2.38486	−	2.66066i	0.337270	−	0.376274i
$51$		0			0
$52$	−0.352924	+	0.0386989i	−0.0489417	+	0.00536657i
$53$		−	4.52038i		−	0.620922i	−0.950586	−	0.310461i	$-0.899517\pi$
$53$		−	4.52038i		−	0.620922i	0.950586	−	0.310461i	$-0.100483\pi$
$54$		0			0
$55$	5.24353			0.707037
$56$	2.77044	−	3.86777i	0.370216	−	0.516853i
$57$		0			0
$58$	2.32881	−	2.59813i	0.305788	−	0.341152i
$59$		−	6.32370i		−	0.823276i	−0.911348	−	0.411638i	$-0.864957\pi$
$59$		−	6.32370i		−	0.823276i	0.911348	−	0.411638i	$-0.135043\pi$
$60$		0			0
$61$	6.28670			0.804929			0.402464	−	0.915436i	$-0.368154\pi$
$61$	6.28670			0.804929			0.402464	+	0.915436i	$0.368154\pi$
$62$	5.10541	+	4.57619i	0.648387	+	0.581177i
$63$		0			0
$64$	2.57454	+	7.57442i	0.321817	+	0.946802i
$65$		−	0.279190i		−	0.0346293i
$66$		0			0
$67$		−	15.8300i		−	1.93395i	−0.254875	−	0.966974i	$-0.582034\pi$
$67$		−	15.8300i		−	1.93395i	0.254875	−	0.966974i	$-0.417966\pi$
$68$	−5.00466	−	6.55388i	−0.606905	−	0.794775i
$69$		0			0
$70$	2.78589	+	2.49711i	0.332978	+	0.298462i
$71$			13.3194i			1.58073i	0.612638	+	0.790364i	$0.290108\pi$
$71$			13.3194i			1.58073i	−0.612638	+	0.790364i	$0.709892\pi$
$72$		0			0
$73$			4.38096i			0.512752i	0.966577	+	0.256376i	$0.0825286\pi$
$73$			4.38096i			0.512752i	−0.966577	+	0.256376i	$0.917471\pi$
$74$	−5.03977	+	5.62260i	−0.585861	+	0.653614i
$75$		0			0
$76$	−5.14031	+	0.563647i	−0.589634	+	0.0646547i
$77$		−	5.60809i		−	0.639101i
$78$		0			0
$79$		−	7.47987i		−	0.841551i	−0.907165	−	0.420776i	$-0.861758\pi$
$79$		−	7.47987i		−	0.841551i	0.907165	−	0.420776i	$-0.138242\pi$
$80$	−6.14143	+	1.36324i	−0.686633	+	0.152414i
$81$		0			0
$82$	−5.04720	−	4.52401i	−0.557370	−	0.499594i
$83$		−	6.58394i		−	0.722681i	−0.932434	−	0.361341i	$-0.882319\pi$
$83$		−	6.58394i		−	0.722681i	0.932434	−	0.361341i	$-0.117681\pi$
$84$		0			0
$85$	5.55199	−	3.35029i	0.602198	−	0.363390i
$86$	5.77289	+	5.17448i	0.622506	+	0.557978i
$87$		0			0
$88$	7.66629	+	5.49128i	0.817230	+	0.585372i
$89$	8.64940			0.916835			0.458417	−	0.888737i	$-0.348416\pi$
$89$	8.64940			0.916835			0.458417	+	0.888737i	$0.348416\pi$
$90$		0			0
$91$	−0.298601			−0.0313019
$92$	6.76689	−	0.742005i	0.705498	−	0.0773594i
$93$		0			0
$94$	5.39975	−	6.02421i	0.556942	−	0.621350i
$95$		−	4.06638i		−	0.417202i
$96$		0			0
$97$			13.1686i			1.33707i	0.743680	+	0.668536i	$0.233079\pi$
$97$			13.1686i			1.33707i	−0.743680	+	0.668536i	$0.766921\pi$
$98$	−3.93677	+	4.39205i	−0.397674	+	0.443664i
$99$		0			0
$100$	0.550777	+	5.02294i	0.0550777	+	0.502294i
$101$			1.10135i			0.109588i	0.998498	+	0.0547940i	$0.0174502\pi$
$101$			1.10135i			0.109588i	−0.998498	+	0.0547940i	$0.982550\pi$
$102$		0			0
$103$	9.03960			0.890698			0.445349	−	0.895357i	$-0.353080\pi$
$103$	9.03960			0.890698			0.445349	+	0.895357i	$0.353080\pi$
$104$	0.292381	−	0.408190i	0.0286704	−	0.0400263i
$105$		0			0
$106$	4.76037	+	4.26691i	0.462368	+	0.414439i
$107$	18.3379			1.77280			0.886398	−	0.462923i	$-0.153200\pi$
$107$	18.3379			1.77280			0.886398	+	0.462923i	$0.153200\pi$
$108$		0			0
$109$	1.67742			0.160668			0.0803340	−	0.996768i	$-0.474401\pi$
$109$	1.67742			0.160668			0.0803340	+	0.996768i	$0.474401\pi$
$110$	−4.94951	+	5.52191i	−0.471918	+	0.526493i
$111$		0			0
$112$	1.45802	+	6.56842i	0.137770	+	0.620658i
$113$			6.87985i			0.647202i	0.946194	+	0.323601i	$0.104894\pi$
$113$			6.87985i			0.647202i	−0.946194	+	0.323601i	$0.895106\pi$
$114$		0			0
$115$			5.35314i			0.499183i
$116$	0.537834	+	4.90490i	0.0499366	+	0.455409i
$117$		0			0
$118$	6.65943	+	5.96912i	0.613050	+	0.549502i
$119$	−3.58322	−	5.93800i	−0.328473	−	0.544336i
$120$		0			0
$121$	0.115770			0.0105245
$122$	−5.93419	+	6.62046i	−0.537256	+	0.599388i
$123$		0			0
$124$	−9.63828	+	1.05686i	−0.865543	+	0.0949088i
$125$	−11.8372			−1.05875
$126$		0			0
$127$	−4.19770			−0.372486			−0.186243	−	0.982504i	$-0.559631\pi$
$127$	−4.19770			−0.372486			−0.186243	+	0.982504i	$0.559631\pi$
$128$	−10.4067	−	4.43849i	−0.919833	−	0.392311i
$129$		0			0
$130$	0.294012	+	0.263536i	0.0257866	+	0.0231136i
$131$	3.59013			0.313671			0.156835	−	0.987625i	$-0.449871\pi$
$131$	3.59013			0.313671			0.156835	+	0.987625i	$0.449871\pi$
$132$		0			0
$133$	−4.34910			−0.377115
$134$	16.6705	+	14.9424i	1.44011	+	1.29083i
$135$		0			0
$136$	11.6259	+	0.916032i	0.996910	+	0.0785491i
$137$	11.9023			1.01688			0.508441	−	0.861097i	$-0.330222\pi$
$137$	11.9023			1.01688			0.508441	+	0.861097i	$0.330222\pi$
$138$		0			0
$139$	5.96225			0.505711			0.252856	−	0.967504i	$-0.418630\pi$
$139$	5.96225			0.505711			0.252856	+	0.967504i	$0.418630\pi$
$140$	−5.25937	+	0.576702i	−0.444498	+	0.0487402i
$141$		0			0
$142$	−14.0266	−	12.5726i	−1.17708	−	1.05507i
$143$		−	0.591856i		−	0.0494935i
$144$		0			0
$145$	−3.88016			−0.322230
$146$	−4.61354	−	4.13531i	−0.381820	−	0.342241i
$147$		0			0
$148$	−1.16392	−	10.6147i	−0.0956738	−	0.872520i
$149$			22.1583i			1.81528i	0.419751	+	0.907639i	$0.362117\pi$
$149$			22.1583i			1.81528i	−0.419751	+	0.907639i	$0.637883\pi$
$150$		0			0
$151$	−4.16246			−0.338736			−0.169368	−	0.985553i	$-0.554173\pi$
$151$	−4.16246			−0.338736			−0.169368	+	0.985553i	$0.554173\pi$
$152$	4.25851	−	5.94525i	0.345411	−	0.482224i
$153$		0			0
$154$	5.90582	+	5.29364i	0.475905	+	0.426573i
$155$		−	7.62463i		−	0.612425i
$156$		0			0
$157$		−	1.66640i		−	0.132993i	−0.997787	−	0.0664964i	$-0.978818\pi$
$157$		−	1.66640i		−	0.132993i	0.997787	−	0.0664964i	$-0.0211821\pi$
$158$	7.87698	+	7.06046i	0.626659	+	0.561700i
$159$		0			0
$160$	4.36146	−	7.75428i	0.344804	−	0.613030i
$161$	5.72532			0.451219
$162$		0			0
$163$	−5.18018			−0.405743			−0.202871	−	0.979205i	$-0.565027\pi$
$163$	−5.18018			−0.405743			−0.202871	+	0.979205i	$0.565027\pi$
$164$	9.52839	−	1.04481i	0.744042	−	0.0815859i
$165$		0			0
$166$	6.93348	+	6.21477i	0.538142	+	0.482359i
$167$		−	20.8328i		−	1.61209i	−0.591854	−	0.806046i	$-0.701604\pi$
$167$		−	20.8328i		−	1.61209i	0.591854	−	0.806046i	$-0.298396\pi$
$168$		0			0
$169$	12.9685			0.997576
$170$	−1.71253	+	9.00918i	−0.131345	+	0.690973i
$171$		0			0
$172$	−10.8984	+	1.19503i	−0.830994	+	0.0911204i
$173$	−21.8618			−1.66212			−0.831062	−	0.556179i	$-0.812267\pi$
$173$	−21.8618			−1.66212			−0.831062	+	0.556179i	$0.812267\pi$
$174$		0			0
$175$			4.24980i			0.321255i
$176$	−13.0192	+	2.88993i	−0.981362	+	0.217836i
$177$		0			0
$178$	−8.16442	+	9.10860i	−0.611949	+	0.682719i
$179$		−	4.38920i		−	0.328064i	−0.986455	−	0.164032i	$-0.947550\pi$
$179$		−	4.38920i		−	0.328064i	0.986455	−	0.164032i	$-0.0524500\pi$
$180$		0			0
$181$	−11.1107			−0.825852			−0.412926	−	0.910765i	$-0.635493\pi$
$181$	−11.1107			−0.825852			−0.412926	+	0.910765i	$0.635493\pi$
$182$	0.281858	−	0.314454i	0.0208927	−	0.0233089i
$183$		0			0
$184$	−5.60607	+	7.82655i	−0.413285	+	0.576981i
$185$	8.39702			0.617361
$186$		0			0
$187$	11.7697	−	7.10229i	0.860685	−	0.519371i
$188$	1.24706	+	11.3729i	0.0909512	+	0.829451i
$189$		0			0
$190$	4.28227	+	3.83838i	0.310669	+	0.278465i
$191$	−11.5334			−0.834530			−0.417265	−	0.908785i	$-0.637011\pi$
$191$	−11.5334			−0.834530			−0.417265	+	0.908785i	$0.637011\pi$
$192$		0			0
$193$			13.5081i			0.972334i	0.873866	+	0.486167i	$0.161605\pi$
$193$			13.5081i			0.972334i	−0.873866	+	0.486167i	$0.838395\pi$
$194$	−13.8678	−	12.4303i	−0.995647	−	0.892440i
$195$		0			0
$196$	−0.909188	−	8.29155i	−0.0649420	−	0.592254i
$197$	20.9839			1.49504			0.747519	−	0.664240i	$-0.231245\pi$
$197$	20.9839			1.49504			0.747519	+	0.664240i	$0.231245\pi$
$198$		0			0
$199$			27.9971i			1.98466i	0.123605	+	0.992332i	$0.460555\pi$
$199$			27.9971i			1.98466i	−0.123605	+	0.992332i	$0.539445\pi$
$200$	−5.80951	−	4.16128i	−0.410794	−	0.294247i
$201$		0			0
$202$	−1.15982	−	1.03959i	−0.0816044	−	0.0731454i
$203$			4.14993i			0.291268i
$204$		0			0
$205$			7.53770i			0.526456i
$206$	−8.53274	+	9.51951i	−0.594504	+	0.663256i
$207$		0			0
$208$	0.153873	+	0.693206i	0.0106692	+	0.0480652i
$209$		−	8.62034i		−	0.596282i
$210$		0			0
$211$	14.4756			0.996540			0.498270	−	0.867022i	$-0.333969\pi$
$211$	14.4756			0.996540			0.498270	+	0.867022i	$0.333969\pi$
$212$	−8.98689	+	0.985433i	−0.617222	+	0.0676798i
$213$		0			0
$214$	−17.3097	+	19.3115i	−1.18327	+	1.32011i
$215$		−	8.62147i		−	0.587979i
$216$		0			0
$217$	−8.15474			−0.553580
$218$	−1.58337	+	1.76648i	−0.107239	+	0.119641i
$219$		0			0
$220$	−1.14308	−	10.4246i	−0.0770663	−	0.702824i
$221$	−0.378159	−	0.626674i	−0.0254377	−	0.0421546i
$222$		0			0
$223$	−27.2591			−1.82540			−0.912702	−	0.408626i	$-0.866008\pi$
$223$	−27.2591			−1.82540			−0.912702	+	0.408626i	$0.866008\pi$
$224$	−8.29340	−	4.66470i	−0.554126	−	0.311673i
$225$		0			0
$226$	−7.24510	−	6.49409i	−0.481937	−	0.431980i
$227$	9.26818			0.615151			0.307575	−	0.951524i	$-0.400482\pi$
$227$	9.26818			0.615151			0.307575	+	0.951524i	$0.400482\pi$
$228$		0			0
$229$		−	19.8306i		−	1.31044i	−0.755437	−	0.655222i	$-0.772575\pi$
$229$		−	19.8306i		−	1.31044i	0.755437	−	0.655222i	$-0.227425\pi$
$230$	−5.63734	−	5.05298i	−0.371715	−	0.333184i
$231$		0			0
$232$	−5.67298	−	4.06349i	−0.372450	−	0.266781i
$233$		−	9.37047i		−	0.613880i	−0.951729	−	0.306940i	$-0.900695\pi$
$233$		−	9.37047i		−	0.613880i	0.951729	−	0.306940i	$-0.0993051\pi$
$234$		0			0
$235$	−8.99681			−0.586887
$236$	−12.5720	+	1.37855i	−0.818370	+	0.0897362i
$237$		0			0
$238$	9.63556	+	1.83160i	0.624580	+	0.118725i
$239$	7.48309			0.484041			0.242021	−	0.970271i	$-0.422190\pi$
$239$	7.48309			0.484041			0.242021	+	0.970271i	$0.422190\pi$
$240$		0			0
$241$		−	12.5710i		−	0.809768i	−0.914368	−	0.404884i	$-0.867312\pi$
$241$		−	12.5710i		−	0.809768i	0.914368	−	0.404884i	$-0.132688\pi$
$242$	−0.109279	+	0.121916i	−0.00702470	+	0.00783708i
$243$		0			0
$244$	−1.37049	−	12.4985i	−0.0877364	−	0.800133i
$245$	6.55926			0.419056
$246$		0			0
$247$	−0.458988			−0.0292047
$248$	7.98488	−	11.1476i	0.507040	−	0.707872i
$249$		0			0
$250$	11.1735	−	12.4656i	0.706671	−	0.788395i
$251$			1.95634i			0.123483i	0.998092	+	0.0617416i	$0.0196655\pi$
$251$			1.95634i			0.123483i	−0.998092	+	0.0617416i	$0.980335\pi$
$252$		0			0
$253$			11.3481i			0.713451i
$254$	3.96233	−	4.42056i	0.248619	−	0.277371i
$255$		0			0
$256$	14.4973	−	6.76960i	0.906083	−	0.423100i
$257$	−13.3326			−0.831664			−0.415832	−	0.909441i	$-0.636510\pi$
$257$	−13.3326			−0.831664			−0.415832	+	0.909441i	$0.636510\pi$
$258$		0			0
$259$		−	8.98083i		−	0.558042i
$260$	−0.555053	+	0.0608629i	−0.0344229	+	0.00377455i
$261$		0			0
$262$	−3.38882	+	3.78073i	−0.209362	+	0.233574i
$263$	−19.5100			−1.20304			−0.601518	−	0.798859i	$-0.705437\pi$
$263$	−19.5100			−1.20304			−0.601518	+	0.798859i	$0.705437\pi$
$264$		0			0
$265$		−	7.10933i		−	0.436723i
$266$	4.10524	−	4.58000i	0.251709	−	0.280818i
$267$		0			0
$268$	−31.4715	+	3.45092i	−1.92243	+	0.210798i
$269$	−6.00877			−0.366361			−0.183180	−	0.983079i	$-0.558639\pi$
$269$	−6.00877			−0.366361			−0.183180	+	0.983079i	$0.558639\pi$
$270$		0			0
$271$	−13.9230			−0.845760			−0.422880	−	0.906186i	$-0.638981\pi$
$271$	−13.9230			−0.845760			−0.422880	+	0.906186i	$0.638981\pi$
$272$	−11.9387	+	11.3784i	−0.723887	+	0.689918i
$273$		0			0
$274$	−11.2349	+	12.5342i	−0.678726	+	0.757218i
$275$	−8.42352			−0.507957
$276$		0			0
$277$	−27.7674			−1.66838			−0.834192	−	0.551474i	$-0.814066\pi$
$277$	−27.7674			−1.66838			−0.834192	+	0.551474i	$0.814066\pi$
$278$	−5.62793	+	6.27878i	−0.337541	+	0.376576i
$279$		0			0
$280$	4.35715	−	6.08295i	0.260389	−	0.363526i
$281$	−16.6843			−0.995302			−0.497651	−	0.867377i	$-0.665804\pi$
$281$	−16.6843			−0.995302			−0.497651	+	0.867377i	$0.665804\pi$
$282$		0			0
$283$	9.70263			0.576761			0.288381	−	0.957516i	$-0.406883\pi$
$283$	9.70263			0.576761			0.288381	+	0.957516i	$0.406883\pi$
$284$	26.4802	−	2.90361i	1.57131	−	0.172298i
$285$		0			0
$286$	0.623278	+	0.558670i	0.0368552	+	0.0330348i
$287$	8.06176			0.475871
$288$		0			0
$289$	7.92416	−	15.0402i	0.466127	−	0.884718i
$290$	3.66259	−	4.08616i	0.215075	−	0.239947i
$291$		0			0
$292$	8.70971	−	0.955040i	0.509697	−	0.0558895i
$293$			31.3940i			1.83406i	0.398824	+	0.917028i	$0.369418\pi$
$293$			31.3940i			1.83406i	−0.398824	+	0.917028i	$0.630582\pi$
$294$		0			0
$295$		−	9.94546i		−	0.579047i
$296$	12.2769	+	8.79377i	0.713578	+	0.511127i
$297$		0			0
$298$	−23.3347	−	20.9158i	−1.35174	−	1.21162i
$299$	0.604228			0.0349434
$300$		0			0
$301$	−9.22089			−0.531483
$302$	3.92906	−	4.38344i	0.226092	−	0.252239i
$303$		0			0
$304$	2.24115	+	10.0965i	0.128539	+	0.579074i
$305$	9.88727			0.566143
$306$		0			0
$307$		−	1.53330i		−	0.0875099i	−0.999042	−	0.0437549i	$-0.986068\pi$
$307$		−	1.53330i		−	0.0875099i	0.999042	−	0.0437549i	$-0.0139321\pi$
$308$	−11.1494	+	1.22255i	−0.635293	+	0.0696614i
$309$		0			0
$310$	8.02942	+	7.19710i	0.456040	+	0.408768i
$311$			1.74672i			0.0990472i	0.998773	+	0.0495236i	$0.0157703\pi$
$311$			1.74672i			0.0990472i	−0.998773	+	0.0495236i	$0.984230\pi$
$312$		0			0
$313$		−	31.9640i		−	1.80671i	−0.428894	−	0.903355i	$-0.641097\pi$
$313$		−	31.9640i		−	1.80671i	0.428894	−	0.903355i	$-0.358903\pi$
$314$	1.75487	+	1.57296i	0.0990328	+	0.0887672i
$315$		0			0
$316$	−14.8706	+	1.63060i	−0.836537	+	0.0917282i
$317$	3.80550			0.213738			0.106869	−	0.994273i	$-0.465917\pi$
$317$	3.80550			0.213738			0.106869	+	0.994273i	$0.465917\pi$
$318$		0			0
$319$	−8.22556			−0.460543
$320$	4.04905	+	11.9125i	0.226348	+	0.665929i
$321$		0			0
$322$	−5.40429	+	6.02928i	−0.301170	+	0.335999i
$323$	−5.50786	−	9.12746i	−0.306466	−	0.507865i
$324$		0			0
$325$			0.448508i			0.0248787i
$326$	4.88971	−	5.45519i	0.270816	−	0.302135i
$327$		0			0
$328$	−7.89384	+	11.0205i	−0.435864	+	0.608504i
$329$			9.62232i			0.530496i
$330$		0			0
$331$			10.4319i			0.573388i	0.958022	+	0.286694i	$0.0925563\pi$
$331$			10.4319i			0.573388i	−0.958022	+	0.286694i	$0.907444\pi$
$332$	−13.0894	+	1.43528i	−0.718375	+	0.0787715i
$333$		0			0
$334$	21.9388	+	19.6647i	1.20044	+	1.07600i
$335$		−	24.8964i		−	1.36023i
$336$		0			0
$337$			21.4237i			1.16702i	0.812105	+	0.583511i	$0.198321\pi$
$337$			21.4237i			1.16702i	−0.812105	+	0.583511i	$0.801679\pi$
$338$	−12.2413	+	13.6570i	−0.665840	+	0.742842i
$339$		0			0
$340$	−7.87098	−	10.3075i	−0.426864	−	0.559001i
$341$		−	16.1635i		−	0.875301i
$342$		0			0
$343$		−	18.7898i		−	1.01456i
$344$	9.02882	−	12.6050i	0.486801	−	0.679617i
$345$		0			0
$346$	20.6360	−	23.0225i	1.10940	−	1.23770i
$347$	−16.4230			−0.881632			−0.440816	−	0.897598i	$-0.645311\pi$
$347$	−16.4230			−0.881632			−0.440816	+	0.897598i	$0.645311\pi$
$348$		0			0
$349$			7.84717i			0.420050i	0.977696	+	0.210025i	$0.0673545\pi$
$349$			7.84717i			0.420050i	−0.977696	+	0.210025i	$0.932646\pi$
$350$	−4.47543	−	4.01151i	−0.239222	−	0.214424i
$351$		0			0
$352$	9.24588	−	16.4383i	0.492807	−	0.876165i
$353$	−15.0952			−0.803438			−0.401719	−	0.915763i	$-0.631587\pi$
$353$	−15.0952			−0.803438			−0.401719	+	0.915763i	$0.631587\pi$
$354$		0			0
$355$			20.9479i			1.11180i
$356$	−1.88555	−	17.1957i	−0.0999340	−	0.911372i
$357$		0			0
$358$	4.62222	+	4.14309i	0.244292	+	0.218969i
$359$	−17.8645			−0.942850			−0.471425	−	0.881906i	$-0.656260\pi$
$359$	−17.8645			−0.942850			−0.471425	+	0.881906i	$0.656260\pi$
$360$		0			0
$361$	12.3149			0.648151
$362$	10.4877	−	11.7006i	0.551222	−	0.614969i
$363$		0			0
$364$	0.0650944	+	0.593644i	0.00341187	+	0.0311154i
$365$			6.89006i			0.360642i
$366$		0			0
$367$		−	17.8393i		−	0.931205i	−0.884994	−	0.465602i	$-0.845838\pi$
$367$		−	17.8393i		−	0.931205i	0.884994	−	0.465602i	$-0.154162\pi$
$368$	−2.95034	−	13.2914i	−0.153797	−	0.692862i
$369$		0			0
$370$	−7.92619	+	8.84282i	−0.412063	+	0.459716i
$371$	−7.60361			−0.394760
$372$		0			0
$373$			4.99138i			0.258444i	0.991616	+	0.129222i	$0.0412480\pi$
$373$			4.99138i			0.258444i	−0.991616	+	0.129222i	$0.958752\pi$
$374$	−3.63040	+	19.0986i	−0.187723	+	0.987565i
$375$		0			0
$376$	−13.1538	−	9.42190i	−0.678354	−	0.485897i
$377$			0.437968i			0.0225565i
$378$		0			0
$379$	−1.52394			−0.0782793			−0.0391396	−	0.999234i	$-0.512462\pi$
$379$	−1.52394			−0.0782793			−0.0391396	+	0.999234i	$0.512462\pi$
$380$	−8.08431	+	0.886463i	−0.414717	+	0.0454746i
$381$		0			0
$382$	10.8867	−	12.1457i	0.557014	−	0.621430i
$383$	−17.0544			−0.871438			−0.435719	−	0.900083i	$-0.643506\pi$
$383$	−17.0544			−0.871438			−0.435719	+	0.900083i	$0.643506\pi$
$384$		0			0
$385$		−	8.82000i		−	0.449509i
$386$	−14.2252	−	12.7507i	−0.724046	−	0.648992i
$387$		0			0
$388$	26.1803	−	2.87074i	1.32911	−	0.145739i
$389$			18.6459i			0.945383i	0.881228	+	0.472691i	$0.156717\pi$
$389$			18.6459i			0.945383i	−0.881228	+	0.472691i	$0.843283\pi$
$390$		0			0
$391$	7.25075	+	12.0157i	0.366686	+	0.607661i
$392$	9.58996	+	6.86918i	0.484366	+	0.346946i
$393$		0			0
$394$	−19.8073	+	22.0979i	−0.997876	+	1.11328i
$395$		−	11.7638i		−	0.591901i
$396$		0			0
$397$	22.9158			1.15011			0.575057	−	0.818114i	$-0.304980\pi$
$397$	22.9158			1.15011			0.575057	+	0.818114i	$0.304980\pi$
$398$	−29.4835	−	26.4273i	−1.47787	−	1.32468i
$399$		0			0
$400$	9.86596	−	2.18998i	0.493298	−	0.109499i
$401$			31.7440i			1.58522i	0.609728	+	0.792610i	$0.291279\pi$
$401$			31.7440i			1.58522i	−0.609728	+	0.792610i	$0.708721\pi$
$402$		0			0
$403$	−0.860619			−0.0428705
$404$	2.18957	−	0.240091i	0.108935	−	0.0119450i
$405$		0			0
$406$	−4.37025	−	3.91724i	−0.216892	−	0.194409i
$407$	17.8009			0.882357
$408$		0			0
$409$	27.8277			1.37599			0.687996	−	0.725715i	$-0.258491\pi$
$409$	27.8277			1.37599			0.687996	+	0.725715i	$0.258491\pi$
$410$	−7.93787	−	7.11505i	−0.392024	−	0.351387i
$411$		0			0
$412$	−1.97061	−	17.9715i	−0.0970852	−	0.885391i
$413$	−10.6369			−0.523409
$414$		0			0
$415$		−	10.3547i		−	0.508295i
$416$	−0.875254	−	0.492294i	−0.0429128	−	0.0241367i
$417$		0			0
$418$	9.07800	+	8.13699i	0.444019	+	0.397993i
$419$	−24.9157			−1.21721			−0.608605	−	0.793473i	$-0.708271\pi$
$419$	−24.9157			−1.21721			−0.608605	+	0.793473i	$0.708271\pi$
$420$		0			0
$421$			33.7977i			1.64720i	0.567171	+	0.823600i	$0.308038\pi$
$421$			33.7977i			1.64720i	−0.567171	+	0.823600i	$0.691962\pi$
$422$	−13.6639	+	15.2441i	−0.665149	+	0.742071i
$423$		0			0
$424$	7.44523	−	10.3942i	0.361573	−	0.504786i
$425$	−8.91906	+	5.38210i	−0.432638	+	0.261070i
$426$		0			0
$427$		−	10.5747i		−	0.511745i
$428$	−3.99763	−	36.4574i	−0.193233	−	1.76223i
$429$		0			0
$430$	9.07918	+	8.13805i	0.437837	+	0.392452i
$431$			6.65096i			0.320366i	0.987087	+	0.160183i	$0.0512084\pi$
$431$			6.65096i			0.320366i	−0.987087	+	0.160183i	$0.948792\pi$
$432$		0			0
$433$	−19.5349			−0.938786			−0.469393	−	0.882989i	$-0.655527\pi$
$433$	−19.5349			−0.938786			−0.469393	+	0.882989i	$0.655527\pi$
$434$	7.69749	−	8.58768i	0.369491	−	0.412222i
$435$		0			0
$436$	−0.365675	−	3.33486i	−0.0175126	−	0.159711i
$437$	8.80054			0.420987
$438$		0			0
$439$		−	0.431972i		−	0.0206169i	−0.999947	−	0.0103085i	$-0.996719\pi$
$439$		−	0.431972i		−	0.0206169i	0.999947	−	0.0103085i	$-0.00328134\pi$
$440$	12.0570	+	8.63629i	0.574795	+	0.411719i
$441$		0			0
$442$	1.01690	+	0.193299i	0.0483690	+	0.00919432i
$443$		−	0.940818i		−	0.0446996i	−0.999750	−	0.0223498i	$-0.992885\pi$
$443$		−	0.940818i		−	0.0446996i	0.999750	−	0.0223498i	$-0.00711476\pi$
$444$		0			0
$445$	13.6032			0.644852
$446$	25.7306	−	28.7063i	1.21838	−	1.35928i
$447$		0			0
$448$	12.7407	−	4.33056i	0.601943	−	0.204600i
$449$			40.6689i			1.91928i	0.281227	+	0.959641i	$0.409259\pi$
$449$			40.6689i			1.91928i	−0.281227	+	0.959641i	$0.590741\pi$
$450$		0			0
$451$			15.9792i			0.752431i
$452$	13.6777	−	1.49979i	0.643346	−	0.0705443i
$453$		0			0
$454$	−8.74850	+	9.76023i	−0.410587	+	0.458070i
$455$	−0.469618			−0.0220161
$456$		0			0
$457$	−10.6020			−0.495940			−0.247970	−	0.968768i	$-0.579763\pi$
$457$	−10.6020			−0.495940			−0.247970	+	0.968768i	$0.579763\pi$
$458$	20.8834	+	18.7187i	0.975818	+	0.874666i
$459$		0			0
$460$	10.6425	−	1.16697i	0.496209	−	0.0544104i
$461$		−	6.90435i		−	0.321568i	−0.986990	−	0.160784i	$-0.948598\pi$
$461$		−	6.90435i		−	0.321568i	0.986990	−	0.160784i	$-0.0514022\pi$
$462$		0			0
$463$	5.01760			0.233188			0.116594	−	0.993180i	$-0.462802\pi$
$463$	5.01760			0.233188			0.116594	+	0.993180i	$0.462802\pi$
$464$	9.63411	−	2.13852i	0.447252	−	0.0992782i
$465$		0			0
$466$	9.86795	+	8.84505i	0.457124	+	0.409739i
$467$		−	35.3420i		−	1.63543i	−0.575621	−	0.817717i	$-0.695240\pi$
$467$		−	35.3420i		−	1.63543i	0.575621	−	0.817717i	$-0.304760\pi$
$468$		0			0
$469$	−26.6273			−1.22953
$470$	8.49235	−	9.47445i	0.391723	−	0.437024i
$471$		0			0
$472$	10.4154	−	14.5408i	0.479406	−	0.669292i
$473$		−	18.2767i		−	0.840363i
$474$		0			0
$475$			6.53248i			0.299731i
$476$	−11.0241	+	8.41822i	−0.505289	+	0.385848i
$477$		0			0
$478$	−7.06351	+	7.88037i	−0.323077	+	0.360440i
$479$			40.1158i			1.83294i	0.400106	+	0.916469i	$0.368973\pi$
$479$			40.1158i			1.83294i	−0.400106	+	0.916469i	$0.631027\pi$
$480$		0			0
$481$		−	0.947802i		−	0.0432161i
$482$	13.2384	+	11.8661i	0.602992	+	0.540487i
$483$		0			0
$484$	−0.0252376	−	0.230161i	−0.00114716	−	0.0104618i
$485$			20.7107i			0.940424i
$486$		0			0
$487$			22.2766i			1.00945i	0.863281	+	0.504724i	$0.168406\pi$
$487$			22.2766i			1.00945i	−0.863281	+	0.504724i	$0.831594\pi$
$488$	14.4557	+	10.3544i	0.654377	+	0.468723i
$489$		0			0
$490$	−6.19148	+	6.90750i	−0.279702	+	0.312049i
$491$			23.2548i			1.04947i	0.851265	+	0.524736i	$0.175836\pi$
$491$			23.2548i			1.04947i	−0.851265	+	0.524736i	$0.824164\pi$
$492$		0			0
$493$	−8.70946	+	5.25562i	−0.392254	+	0.236701i
$494$	0.433252	−	0.483355i	0.0194929	−	0.0217472i
$495$		0			0
$496$	4.20225	+	18.9313i	0.188687	+	0.850041i
$497$	22.4043			1.00497
$498$		0			0
$499$	4.16978			0.186665			0.0933324	−	0.995635i	$-0.470248\pi$
$499$	4.16978			0.186665			0.0933324	+	0.995635i	$0.470248\pi$
$500$	2.58048	+	23.5333i	0.115403	+	1.05244i
$501$		0			0
$502$	−2.06021	−	1.84665i	−0.0919515	−	0.0824199i
$503$			2.70786i			0.120737i	0.998176	+	0.0603687i	$0.0192276\pi$
$503$			2.70786i			0.120737i	−0.998176	+	0.0603687i	$0.980772\pi$
$504$		0			0
$505$			1.73212i			0.0770782i
$506$	−11.9506	−	10.7118i	−0.531269	−	0.476199i
$507$		0			0
$508$	0.915091	+	8.34539i	0.0406006	+	0.370267i
$509$			15.0471i			0.666952i	0.942759	+	0.333476i	$0.108222\pi$
$509$			15.0471i			0.666952i	−0.942759	+	0.333476i	$0.891778\pi$
$510$		0			0
$511$	7.36910			0.325990
$512$	−6.55544	+	21.6570i	−0.289712	+	0.957114i
$513$		0			0
$514$	12.5850	−	14.0404i	0.555101	−	0.619296i
$515$	14.2168			0.626469
$516$		0			0
$517$	−19.0724			−0.838802
$518$	9.45763	+	8.47727i	0.415544	+	0.372470i
$519$		0			0
$520$	0.459837	−	0.641971i	0.0201652	−	0.0281523i
$521$			29.0171i			1.27126i	0.771993	+	0.635631i	$0.219260\pi$
$521$			29.0171i			1.27126i	−0.771993	+	0.635631i	$0.780740\pi$
$522$		0			0
$523$			29.2097i			1.27725i	0.769518	+	0.638625i	$0.220497\pi$
$523$			29.2097i			1.27725i	−0.769518	+	0.638625i	$0.779503\pi$
$524$	−0.782640	−	7.13747i	−0.0341898	−	0.311802i
$525$		0			0
$526$	18.4160	−	20.5457i	0.802976	−	0.895837i
$527$	−10.3275	−	17.1143i	−0.449871	−	0.745512i
$528$		0			0
$529$	11.4146			0.496289
$530$	7.48676	+	6.71070i	0.325204	+	0.291494i
$531$		0			0
$532$	0.948096	+	8.64638i	0.0411052	+	0.374868i
$533$	0.850807			0.0368526
$534$		0			0
$535$	28.8406			1.24689
$536$	26.0727	−	36.3997i	1.12617	−	1.57223i
$537$		0			0
$538$	5.67185	−	6.32777i	0.244531	−	0.272810i
$539$	13.9050			0.598931
$540$		0			0
$541$	30.5463			1.31329			0.656643	−	0.754202i	$-0.271976\pi$
$541$	30.5463			1.31329			0.656643	+	0.754202i	$0.271976\pi$
$542$	13.1423	−	14.6621i	0.564509	−	0.629793i
$543$		0			0
$544$	−0.713268	−	23.3129i	−0.0305811	−	0.999532i
$545$	2.63813			0.113005
$546$		0			0
$547$	−36.8589			−1.57597			−0.787986	−	0.615693i	$-0.788876\pi$
$547$	−36.8589			−1.57597			−0.787986	+	0.615693i	$0.788876\pi$
$548$	−2.59467	−	23.6628i	−0.110839	−	1.01082i
$549$		0			0
$550$	7.95120	−	8.87072i	0.339040	−	0.378249i
$551$			6.37897i			0.271753i
$552$		0			0
$553$	−12.5817			−0.535028
$554$	26.2105	−	29.2416i	1.11358	−	1.24236i
$555$		0			0
$556$	−1.29976	−	11.8534i	−0.0551220	−	0.502698i
$557$		−	11.1786i		−	0.473652i	−0.971552	−	0.236826i	$-0.923893\pi$
$557$		−	11.1786i		−	0.473652i	0.971552	−	0.236826i	$-0.0761071\pi$
$558$		0			0
$559$	−0.973137			−0.0411593
$560$	2.29306	+	10.3303i	0.0968996	+	0.436537i
$561$		0			0
$562$	15.7488	−	17.5701i	0.664322	−	0.741149i
$563$			1.85190i			0.0780483i	0.999238	+	0.0390242i	$0.0124249\pi$
$563$			1.85190i			0.0780483i	−0.999238	+	0.0390242i	$0.987575\pi$
$564$		0			0
$565$			10.8201i			0.455207i
$566$	−9.15859	+	10.2177i	−0.384964	+	0.429484i
$567$		0			0
$568$	−21.9376	+	30.6268i	−0.920482	+	1.28507i
$569$	3.17782			0.133221			0.0666106	−	0.997779i	$-0.478781\pi$
$569$	3.17782			0.133221			0.0666106	+	0.997779i	$0.478781\pi$
$570$		0			0
$571$	−20.2381			−0.846937			−0.423468	−	0.905911i	$-0.639188\pi$
$571$	−20.2381			−0.846937			−0.423468	+	0.905911i	$0.639188\pi$
$572$	−1.17666	+	0.129023i	−0.0491986	+	0.00539474i
$573$		0			0
$574$	−7.60973	+	8.48976i	−0.317624	+	0.354356i
$575$		−	8.59960i		−	0.358628i
$576$		0			0
$577$	−5.53369			−0.230371			−0.115185	−	0.993344i	$-0.536746\pi$
$577$	−5.53369			−0.230371			−0.115185	+	0.993344i	$0.536746\pi$
$578$	8.35885	+	22.5417i	0.347682	+	0.937612i
$579$		0			0
$580$	0.845867	+	7.71408i	0.0351227	+	0.320310i
$581$	−11.0747			−0.459455
$582$		0			0
$583$		−	15.0711i		−	0.624181i
$584$	−7.21560	+	10.0736i	−0.298584	+	0.416849i
$585$		0			0
$586$	−33.0607	−	29.6337i	−1.36572	−	1.22416i
$587$			32.8487i			1.35581i	0.735149	+	0.677905i	$0.237112\pi$
$587$			32.8487i			1.35581i	−0.735149	+	0.677905i	$0.762888\pi$
$588$		0			0
$589$	−12.5349			−0.516490
$590$	10.4735	+	9.38781i	0.431186	+	0.386490i
$591$		0			0
$592$	−20.8491	+	4.62795i	−0.856893	+	0.190208i
$593$	4.38985			0.180269			0.0901347	−	0.995930i	$-0.471270\pi$
$593$	4.38985			0.180269			0.0901347	+	0.995930i	$0.471270\pi$
$594$		0			0
$595$	−5.63543	−	9.33887i	−0.231030	−	0.382856i
$596$	44.0525	−	4.83046i	1.80446	−	0.197863i
$597$		0			0
$598$	−0.570348	+	0.636307i	−0.0233233	+	0.0260205i
$599$	24.8193			1.01409			0.507044	−	0.861920i	$-0.330738\pi$
$599$	24.8193			1.01409			0.507044	+	0.861920i	$0.330738\pi$
$600$		0			0
$601$			43.9610i			1.79321i	0.442834	+	0.896603i	$0.353973\pi$
$601$			43.9610i			1.79321i	−0.442834	+	0.896603i	$0.646027\pi$
$602$	8.70386	−	9.71042i	0.354743	−	0.395767i
$603$		0			0
$604$	0.907407	+	8.27532i	0.0369219	+	0.336718i
$605$	0.182075			0.00740240
$606$		0			0
$607$			44.7140i			1.81488i	0.420177	+	0.907442i	$0.361968\pi$
$607$			44.7140i			1.81488i	−0.420177	+	0.907442i	$0.638032\pi$
$608$	−12.7480	−	7.17023i	−0.517000	−	0.290791i
$609$		0			0
$610$	−9.33287	+	10.4122i	−0.377877	+	0.421577i
$611$			1.01550i			0.0410828i
$612$		0			0
$613$		−	39.2562i		−	1.58554i	−0.609518	−	0.792772i	$-0.708637\pi$
$613$		−	39.2562i		−	1.58554i	0.609518	−	0.792772i	$-0.291363\pi$
$614$	1.61470	+	1.44732i	0.0651640	+	0.0584092i
$615$		0			0
$616$	9.23673	−	12.8953i	0.372159	−	0.519565i
$617$		−	33.5704i		−	1.35149i	−0.737133	−	0.675747i	$-0.763821\pi$
$617$		−	33.5704i		−	1.35149i	0.737133	−	0.675747i	$-0.236179\pi$
$618$		0			0
$619$	29.2701			1.17647			0.588233	−	0.808692i	$-0.299824\pi$
$619$	29.2701			1.17647			0.588233	+	0.808692i	$0.299824\pi$
$620$	−15.1584	+	1.66215i	−0.608776	+	0.0667537i
$621$		0			0
$622$	−1.83945	−	1.64878i	−0.0737552	−	0.0661099i
$623$		−	14.5489i		−	0.582891i
$624$		0			0
$625$	−5.98405			−0.239362
$626$	33.6609	+	30.1717i	1.34536	+	1.20590i
$627$		0			0
$628$	−3.31293	+	0.363271i	−0.132200	+	0.0144961i
$629$	18.8481	−	11.3737i	0.751522	−	0.453497i
$630$		0			0
$631$	11.2429			0.447574			0.223787	−	0.974638i	$-0.428158\pi$
$631$	11.2429			0.447574			0.223787	+	0.974638i	$0.428158\pi$
$632$	12.3196	−	17.1993i	0.490048	−	0.684150i
$633$		0			0
$634$	−3.59212	+	4.00754i	−0.142661	+	0.159160i
$635$	−6.60185			−0.261986
$636$		0			0
$637$		−	0.740368i		−	0.0293344i
$638$	7.76434	−	8.66226i	0.307393	−	0.342942i
$639$		0			0
$640$	−16.3669	−	6.98054i	−0.646960	−	0.275930i
$641$		−	33.9330i		−	1.34027i	−0.742237	−	0.670137i	$-0.766235\pi$
$641$		−	33.9330i		−	1.34027i	0.742237	−	0.670137i	$-0.233765\pi$
$642$		0			0
$643$	−35.2361			−1.38958			−0.694788	−	0.719214i	$-0.744502\pi$
$643$	−35.2361			−1.38958			−0.694788	+	0.719214i	$0.744502\pi$
$644$	−1.24811	−	11.3824i	−0.0491824	−	0.448530i
$645$		0			0
$646$	14.8111	+	2.81539i	0.582734	+	0.110770i
$647$	41.8365			1.64476			0.822381	−	0.568937i	$-0.192645\pi$
$647$	41.8365			1.64476			0.822381	+	0.568937i	$0.192645\pi$
$648$		0			0
$649$		−	21.0834i		−	0.827596i
$650$	−0.472319	−	0.423359i	−0.0185259	−	0.0166055i
$651$		0			0
$652$	1.12927	+	10.2986i	0.0442255	+	0.403325i
$653$	−22.6804			−0.887554			−0.443777	−	0.896137i	$-0.646362\pi$
$653$	−22.6804			−0.887554			−0.443777	+	0.896137i	$0.646362\pi$
$654$		0			0
$655$	5.64629			0.220619
$656$	−4.15434	−	18.7155i	−0.162200	−	0.730716i
$657$		0			0
$658$	−10.1332	−	9.08279i	−0.395032	−	0.354084i
$659$			34.4905i			1.34356i	0.740751	+	0.671779i	$0.234470\pi$
$659$			34.4905i			1.34356i	−0.740751	+	0.671779i	$0.765530\pi$
$660$		0			0
$661$		−	0.923741i		−	0.0359293i	−0.999839	−	0.0179647i	$-0.994281\pi$
$661$		−	0.923741i		−	0.0359293i	0.999839	−	0.0179647i	$-0.00571864\pi$
$662$	−10.9857	−	9.84695i	−0.426972	−	0.382713i
$663$		0			0
$664$	10.8440	−	15.1391i	0.420829	−	0.587513i
$665$	−6.83996			−0.265242
$666$		0			0
$667$		−	8.39751i		−	0.325153i
$668$	−41.4174	+	4.54151i	−1.60249	+	0.175716i
$669$		0			0
$670$	26.2181	+	23.5004i	1.01289	+	0.907899i
$671$	20.9600			0.809154
$672$		0			0
$673$			3.91400i			0.150874i	0.997151	+	0.0754368i	$0.0240351\pi$
$673$			3.91400i			0.150874i	−0.997151	+	0.0754368i	$0.975965\pi$
$674$	−22.5611	−	20.2224i	−0.869020	−	0.778938i
$675$		0			0
$676$	−2.82710	−	25.7824i	−0.108735	−	0.991632i
$677$	22.1006			0.849394			0.424697	−	0.905336i	$-0.360381\pi$
$677$	22.1006			0.849394			0.424697	+	0.905336i	$0.360381\pi$
$678$		0			0
$679$	22.1506			0.850063
$680$	18.2843	+	1.44067i	0.701172	+	0.0552471i
$681$		0			0
$682$	17.0216	+	15.2572i	0.651791	+	0.584227i
$683$	42.9736			1.64434			0.822169	−	0.569244i	$-0.192764\pi$
$683$	42.9736			1.64434			0.822169	+	0.569244i	$0.192764\pi$
$684$		0			0
$685$	18.7191			0.715219
$686$	19.7874	+	17.7362i	0.755486	+	0.677173i
$687$		0			0
$688$	4.75165	+	21.4064i	0.181155	+	0.816111i
$689$	−0.802456			−0.0305711
$690$		0			0
$691$	17.7933			0.676890			0.338445	−	0.940986i	$-0.390099\pi$
$691$	17.7933			0.676890			0.338445	+	0.940986i	$0.390099\pi$
$692$	4.76583	+	43.4632i	0.181170	+	1.65222i
$693$		0			0
$694$	15.5021	−	17.2949i	0.588453	−	0.656505i
$695$	9.37699			0.355690
$696$		0			0
$697$	10.2097	+	16.9192i	0.386720	+	0.640861i
$698$	−8.26378	−	7.40717i	−0.312789	−	0.280366i
$699$		0			0
$700$	8.44896	−	0.926448i	0.319341	−	0.0350164i
$701$		−	18.7151i		−	0.706859i	−0.935461	−	0.353430i	$-0.885015\pi$
$701$		−	18.7151i		−	0.706859i	0.935461	−	0.353430i	$-0.114985\pi$
$702$		0			0
$703$		−	13.8047i		−	0.520653i
$704$	8.58358	+	25.2533i	0.323506	+	0.951771i
$705$		0			0
$706$	14.2488	−	15.8966i	0.536261	−	0.598278i
$707$	1.85255			0.0696721
$708$		0			0
$709$	−30.0583			−1.12886			−0.564431	−	0.825480i	$-0.690905\pi$
$709$	−30.0583			−1.12886			−0.564431	+	0.825480i	$0.690905\pi$
$710$	−22.0600	−	19.7733i	−0.827897	−	0.742079i
$711$		0			0
$712$	19.8885	+	14.2459i	0.745353	+	0.533887i
$713$	16.5014			0.617981
$714$		0			0
$715$		−	0.930829i		−	0.0348110i
$716$	−8.72609	+	0.956835i	−0.326109	+	0.0357586i
$717$		0			0
$718$	16.8628	−	18.8129i	0.629313	−	0.702091i
$719$			5.50072i			0.205142i	0.994726	+	0.102571i	$0.0327070\pi$
$719$			5.50072i			0.205142i	−0.994726	+	0.102571i	$0.967293\pi$
$720$		0			0
$721$		−	15.2053i		−	0.566274i
$722$	−11.6244	+	12.9687i	−0.432614	+	0.482644i
$723$		0			0
$724$	2.42211	+	22.0890i	0.0900170	+	0.820932i
$725$	6.23332			0.231500
$726$		0			0
$727$	−48.9745			−1.81636			−0.908182	−	0.418576i	$-0.862529\pi$
$727$	−48.9745			−1.81636			−0.908182	+	0.418576i	$0.862529\pi$
$728$	−0.686605	−	0.491807i	−0.0254473	−	0.0182276i
$729$		0			0
$730$	−7.25585	−	6.50372i	−0.268551	−	0.240714i
$731$	−11.6777	−	19.3519i	−0.431914	−	0.715754i
$732$		0			0
$733$			20.3595i			0.751996i	0.926621	+	0.375998i	$0.122700\pi$
$733$			20.3595i			0.751996i	−0.926621	+	0.375998i	$0.877300\pi$
$734$	18.7864	+	16.8390i	0.693419	+	0.621540i
$735$		0			0
$736$	16.7819	+	9.43916i	0.618591	+	0.347932i
$737$		−	52.7779i		−	1.94410i
$738$		0			0
$739$			13.0474i			0.479955i	0.970778	+	0.239977i	$0.0771400\pi$
$739$			13.0474i			0.479955i	−0.970778	+	0.239977i	$0.922860\pi$
$740$	−1.83053	−	16.6940i	−0.0672917	−	0.613683i
$741$		0			0
$742$	7.17727	−	8.00729i	0.263486	−	0.293957i
$743$			15.7329i			0.577186i	0.957452	+	0.288593i	$0.0931874\pi$
$743$			15.7329i			0.577186i	−0.957452	+	0.288593i	$0.906813\pi$
$744$		0			0
$745$			34.8490i			1.27677i
$746$	−5.25637	−	4.71151i	−0.192450	−	0.172501i
$747$		0			0
$748$	−16.6857	−	21.8508i	−0.610090	−	0.798946i
$749$		−	30.8458i		−	1.12708i
$750$		0			0
$751$		−	45.6534i		−	1.66591i	−0.553337	−	0.832957i	$-0.686646\pi$
$751$		−	45.6534i		−	1.66591i	0.553337	−	0.832957i	$-0.313354\pi$
$752$	22.3383	−	4.95852i	0.814595	−	0.180819i
$753$		0			0
$754$	−0.461219	−	0.413410i	−0.0167966	−	0.0150555i
$755$	−6.54642			−0.238249
$756$		0			0
$757$		−	33.5775i		−	1.22039i	−0.792250	−	0.610197i	$-0.791090\pi$
$757$		−	33.5775i		−	1.22039i	0.792250	−	0.610197i	$-0.208910\pi$
$758$	1.43849	−	1.60484i	0.0522482	−	0.0582905i
$759$		0			0
$760$	6.69749	−	9.35027i	0.242943	−	0.339170i
$761$	1.39682			0.0506348			0.0253174	−	0.999679i	$-0.491940\pi$
$761$	1.39682			0.0506348			0.0253174	+	0.999679i	$0.491940\pi$
$762$		0			0
$763$		−	2.82155i		−	0.102147i
$764$	2.51426	+	22.9294i	0.0909629	+	0.829558i
$765$		0			0
$766$	16.0981	−	17.9598i	0.581648	−	0.648914i
$767$	−1.12258			−0.0405340
$768$		0			0
$769$	20.8164			0.750658			0.375329	−	0.926892i	$-0.377530\pi$
$769$	20.8164			0.750658			0.375329	+	0.926892i	$0.377530\pi$
$770$	9.28826	+	8.32545i	0.334726	+	0.300028i
$771$		0			0
$772$	26.8552	−	2.94474i	0.966541	−	0.105983i
$773$		−	45.0123i		−	1.61898i	−0.587133	−	0.809490i	$-0.699744\pi$
$773$		−	45.0123i		−	1.61898i	0.587133	−	0.809490i	$-0.300256\pi$
$774$		0			0
$775$			12.2487i			0.439985i
$776$	−21.6892	+	30.2800i	−0.778598	+	1.08699i
$777$		0			0
$778$	−19.6358	−	17.6004i	−0.703977	−	0.631003i
$779$	12.3919			0.443988
$780$		0			0
$781$			44.4075i			1.58902i
$782$	−19.4978	−	3.70629i	−0.697241	−	0.132537i
$783$		0			0
$784$	−16.2861	+	3.61508i	−0.581647	+	0.129110i
$785$		−	2.62079i		−	0.0935400i
$786$		0			0
$787$	16.8464			0.600509			0.300255	−	0.953859i	$-0.402928\pi$
$787$	16.8464			0.600509			0.300255	+	0.953859i	$0.402928\pi$
$788$	−4.57444	−	41.7177i	−0.162958	−	1.48613i
$789$		0			0
$790$	12.3883	+	11.1042i	0.440758	+	0.395069i
$791$	11.5724			0.411468
$792$		0			0
$793$		−	1.11601i		−	0.0396307i
$794$	−21.6309	+	24.1324i	−0.767653	+	0.856429i
$795$		0			0
$796$	55.6606	−	6.10331i	1.97284	−	0.216326i
$797$		−	6.68748i		−	0.236883i	−0.992961	−	0.118441i	$-0.962210\pi$
$797$		−	6.68748i		−	0.236883i	0.992961	−	0.118441i	$-0.0377897\pi$
$798$		0			0
$799$	−20.1944	+	12.1861i	−0.714425	+	0.431112i
$800$	−7.00652	+	12.4569i	−0.247718	+	0.440419i
$801$		0			0
$802$	−33.4293	−	29.9641i	−1.18043	−	1.05807i
$803$			14.6063i			0.515444i
$804$		0			0
$805$	9.00438			0.317363
$806$	0.812363	−	0.906310i	0.0286143	−	0.0319234i
$807$		0			0
$808$	−1.81396	+	2.53244i	−0.0638148	+	0.0890910i
$809$			16.7530i			0.589004i	0.955651	+	0.294502i	$0.0951537\pi$
$809$			16.7530i			0.589004i	−0.955651	+	0.294502i	$0.904846\pi$
$810$		0			0
$811$	−10.8001			−0.379243			−0.189622	−	0.981857i	$-0.560726\pi$
$811$	−10.8001			−0.379243			−0.189622	+	0.981857i	$0.560726\pi$
$812$	8.25041	−	0.904676i	0.289533	−	0.0317479i
$813$		0			0
$814$	−16.8028	+	18.7459i	−0.588936	+	0.657044i
$815$	−8.14701			−0.285377
$816$		0			0
$817$	−14.1737			−0.495874
$818$	−26.2674	+	29.3051i	−0.918417	+	1.02463i
$819$		0			0
$820$	14.9856	−	1.64320i	0.523319	−	0.0573831i
$821$	−38.5393			−1.34503			−0.672516	−	0.740083i	$-0.734786\pi$
$821$	−38.5393			−1.34503			−0.672516	+	0.740083i	$0.734786\pi$
$822$		0			0
$823$			18.0592i			0.629505i	0.949174	+	0.314752i	$0.101921\pi$
$823$			18.0592i			0.629505i	−0.949174	+	0.314752i	$0.898079\pi$
$824$	20.7857	+	14.8886i	0.724105	+	0.518668i
$825$		0			0
$826$	10.0405	−	11.2016i	0.349354	−	0.389755i
$827$	−27.1647			−0.944611			−0.472305	−	0.881435i	$-0.656578\pi$
$827$	−27.1647			−0.944611			−0.472305	+	0.881435i	$0.656578\pi$
$828$		0			0
$829$			24.5873i			0.853952i	0.904263	+	0.426976i	$0.140421\pi$
$829$			24.5873i			0.853952i	−0.904263	+	0.426976i	$0.859579\pi$
$830$	10.9045	+	9.77414i	0.378500	+	0.339265i
$831$		0			0
$832$	1.34461	−	0.457030i	0.0466159	−	0.0158447i
$833$	14.7230	−	8.88443i	0.510122	−	0.307827i
$834$		0			0
$835$		−	32.7644i		−	1.13386i
$836$	−17.1380	+	1.87922i	−0.592729	+	0.0649941i
$837$		0			0
$838$	23.5186	−	26.2384i	0.812437	−	0.906392i
$839$			5.06106i			0.174727i	0.996176	+	0.0873637i	$0.0278442\pi$
$839$			5.06106i			0.174727i	−0.996176	+	0.0873637i	$0.972156\pi$
$840$		0			0
$841$	−22.9132			−0.790109
$842$	−35.5921	−	31.9026i	−1.22658	−	1.09944i
$843$		0			0
$844$	−3.15565	−	28.7787i	−0.108622	−	0.990603i
$845$	20.3959			0.701641
$846$		0			0
$847$		−	0.194734i		−	0.00669113i
$848$	3.91825	+	17.6519i	0.134553	+	0.606168i
$849$		0			0
$850$	2.75111	−	14.4729i	0.0943623	−	0.496416i
$851$			18.1730i			0.622962i
$852$		0			0
$853$	19.5592			0.669695			0.334847	−	0.942272i	$-0.391315\pi$
$853$	19.5592			0.669695			0.334847	+	0.942272i	$0.391315\pi$
$854$	11.1361	+	9.98175i	0.381070	+	0.341568i
$855$		0			0
$856$	42.1664	+	30.2033i	1.44122	+	1.03233i
$857$		−	15.7887i		−	0.539333i	−0.962954	−	0.269666i	$-0.913087\pi$
$857$		−	15.7887i		−	0.539333i	0.962954	−	0.269666i	$-0.0869134\pi$
$858$		0			0
$859$			32.5990i			1.11226i	0.831094	+	0.556132i	$0.187715\pi$
$859$			32.5990i			1.11226i	−0.831094	+	0.556132i	$0.812285\pi$
$860$	−17.1402	+	1.87946i	−0.584476	+	0.0640891i
$861$		0			0
$862$	−7.00406	−	6.27803i	−0.238559	−	0.213831i
$863$	−43.1734			−1.46964			−0.734819	−	0.678263i	$-0.762733\pi$
$863$	−43.1734			−1.46964			−0.734819	+	0.678263i	$0.762733\pi$
$864$		0			0
$865$	−34.3827			−1.16905
$866$	18.4395	−	20.5720i	0.626600	−	0.699064i
$867$		0			0
$868$	1.77772	+	16.2123i	0.0603396	+	0.550281i
$869$		−	24.9381i		−	0.845968i
$870$		0			0
$871$	−2.81014			−0.0952181
$872$	3.85708	+	2.76278i	0.130617	+	0.0935595i
$873$		0			0
$874$	−8.30708	+	9.26777i	−0.280991	+	0.313487i
$875$			19.9110i			0.673115i
$876$		0			0
$877$	49.3608			1.66680			0.833399	−	0.552672i	$-0.186392\pi$
$877$	49.3608			1.66680			0.833399	+	0.552672i	$0.186392\pi$
$878$	0.454906	+	0.407751i	0.0153523	+	0.0137609i
$879$		0			0
$880$	−20.4757	+	4.54507i	−0.690237	+	0.153214i
$881$		−	44.3363i		−	1.49373i	−0.664977	−	0.746864i	$-0.731559\pi$
$881$		−	44.3363i		−	1.49373i	0.664977	−	0.746864i	$-0.268441\pi$
$882$		0			0
$883$			12.1954i			0.410407i	0.978719	+	0.205203i	$0.0657856\pi$
$883$			12.1954i			0.410407i	−0.978719	+	0.205203i	$0.934214\pi$
$884$	−1.16344	+	0.888426i	−0.0391308	+	0.0298810i
$885$		0			0
$886$	0.990767	+	0.888065i	0.0332855	+	0.0298351i
$887$			39.8250i			1.33719i	0.743626	+	0.668596i	$0.233104\pi$
$887$			39.8250i			1.33719i	−0.743626	+	0.668596i	$0.766896\pi$
$888$		0			0
$889$			7.06085i			0.236813i
$890$	−12.8404	+	14.3254i	−0.430412	+	0.480187i
$891$		0			0
$892$	5.94243	+	54.1934i	0.198967	+	1.81453i
$893$			14.7907i			0.494953i
$894$		0			0
$895$		−	6.90301i		−	0.230742i
$896$	−7.46587	+	17.5049i	−0.249417	+	0.584797i
$897$		0			0
$898$	−42.8280	−	38.3885i	−1.42919	−	1.28104i
$899$			11.9608i			0.398915i
$900$		0			0
$901$	−9.62949	−	15.9577i	−0.320805	−	0.531628i
$902$	−16.8275	−	15.0832i	−0.560295	−	0.502216i
$903$		0			0
$904$	−11.3314	+	15.8196i	−0.376876	+	0.526151i
$905$	−17.4741			−0.580860
$906$		0			0
$907$	−31.3002			−1.03931			−0.519653	−	0.854377i	$-0.673939\pi$
$907$	−31.3002			−1.03931			−0.519653	+	0.854377i	$0.673939\pi$
$908$	−2.02044	−	18.4259i	−0.0670508	−	0.611486i
$909$		0			0
$910$	0.443286	−	0.494551i	0.0146948	−	0.0163942i
$911$			19.0074i			0.629745i	0.949134	+	0.314872i	$0.101962\pi$
$911$			19.0074i			0.629745i	−0.949134	+	0.314872i	$0.898038\pi$
$912$		0			0
$913$		−	21.9511i		−	0.726474i
$914$	10.0075	−	11.1648i	0.331019	−	0.369300i
$915$		0			0
$916$	−39.4249	+	4.32303i	−1.30264	+	0.142837i
$917$		−	6.03886i		−	0.199421i
$918$		0			0
$919$	60.5097			1.99603			0.998016	−	0.0629608i	$-0.0200543\pi$
$919$	60.5097			1.99603			0.998016	+	0.0629608i	$0.0200543\pi$
$920$	−8.81682	+	12.3090i	−0.290682	+	0.405817i
$921$		0			0
$922$	7.27090	+	6.51721i	0.239454	+	0.214633i
$923$	2.36446			0.0778272
$924$		0			0
$925$	−13.4895			−0.443531
$926$	−4.73626	+	5.28399i	−0.155643	+	0.173643i
$927$		0			0
$928$	−6.84186	+	12.1642i	−0.224595	+	0.399309i
$929$			35.6403i			1.16932i	0.811279	+	0.584660i	$0.198772\pi$
$929$			35.6403i			1.16932i	−0.811279	+	0.584660i	$0.801228\pi$
$930$		0			0
$931$		−	10.7834i		−	0.353412i
$932$	−18.6293	+	2.04274i	−0.610222	+	0.0669123i
$933$		0			0
$934$	37.2183	+	33.3603i	1.21782	+	1.09158i
$935$	18.5105	−	11.1700i	0.605359	−	0.365297i
$936$		0			0
$937$	−44.8079			−1.46381			−0.731906	−	0.681406i	$-0.761369\pi$
$937$	−44.8079			−1.46381			−0.731906	+	0.681406i	$0.761369\pi$
$938$	25.1343	−	28.0410i	0.820663	−	0.915570i
$939$		0			0
$940$	1.96129	+	17.8864i	0.0639701	+	0.583390i
$941$	−51.2637			−1.67115			−0.835575	−	0.549377i	$-0.814865\pi$
$941$	−51.2637			−1.67115			−0.835575	+	0.549377i	$0.814865\pi$
$942$		0			0
$943$	−16.3132			−0.531231
$944$	5.48136	+	24.6938i	0.178403	+	0.803713i
$945$		0			0
$946$	19.2470	+	17.2519i	0.625774	+	0.560907i
$947$	−32.5760			−1.05858			−0.529289	−	0.848442i	$-0.677541\pi$
$947$	−32.5760			−1.05858			−0.529289	+	0.848442i	$0.677541\pi$
$948$		0			0
$949$	0.777706			0.0252454
$950$	−6.87929	−	6.16620i	−0.223194	−	0.200058i
$951$		0			0
$952$	1.54083	−	19.5556i	0.0499387	−	0.633800i
$953$	−36.4757			−1.18156			−0.590782	−	0.806831i	$-0.701181\pi$
$953$	−36.4757			−1.18156			−0.590782	+	0.806831i	$0.701181\pi$
$954$		0			0
$955$	−18.1390			−0.586963
$956$	−1.63130	−	14.8770i	−0.0527600	−	0.481157i
$957$		0			0
$958$	−42.2456	−	37.8664i	−1.36489	−	1.22341i
$959$		−	20.0205i		−	0.646497i
$960$		0			0
$961$	7.49665			0.241827
$962$	0.998121	+	0.894658i	0.0321807	+	0.0288449i
$963$		0			0
$964$	−24.9922	+	2.74045i	−0.804944	+	0.0882639i
$965$			21.2446i			0.683887i
$966$		0			0
$967$	22.8837			0.735891			0.367946	−	0.929847i	$-0.380061\pi$
$967$	22.8837			0.735891			0.367946	+	0.929847i	$0.380061\pi$
$968$	0.266202	+	0.190678i	0.00855607	+	0.00612861i
$969$		0			0
$970$	−21.8102	−	19.5494i	−0.700284	−	0.627694i
$971$		−	34.4721i		−	1.10626i	−0.833094	−	0.553131i	$-0.813433\pi$
$971$		−	34.4721i		−	1.10626i	0.833094	−	0.553131i	$-0.186567\pi$
$972$		0			0
$973$		−	10.0289i		−	0.321513i
$974$	−23.4592	−	21.0275i	−0.751682	−	0.673764i
$975$		0			0
$976$	−24.5493	+	5.44928i	−0.785803	+	0.174427i
$977$	−16.3524			−0.523160			−0.261580	−	0.965182i	$-0.584244\pi$
$977$	−16.3524			−0.523160			−0.261580	+	0.965182i	$0.584244\pi$
$978$		0			0
$979$	28.8374			0.921647
$980$	−1.42991	−	13.0404i	−0.0456767	−	0.416559i
$981$		0			0
$982$	−24.4894	−	21.9508i	−0.781487	−	0.700479i
$983$			39.1096i			1.24740i	0.781662	+	0.623702i	$0.214372\pi$
$983$			39.1096i			1.24740i	−0.781662	+	0.623702i	$0.785628\pi$
$984$		0			0
$985$	33.0019			1.05153
$986$	2.68646	−	14.1328i	0.0855543	−	0.450079i
$987$		0			0
$988$	0.100058	+	0.912506i	0.00318328	+	0.0290307i
$989$	18.6587			0.593313
$990$		0			0
$991$		−	28.4092i		−	0.902449i	−0.892411	−	0.451224i	$-0.850987\pi$
$991$		−	28.4092i		−	0.902449i	0.892411	−	0.451224i	$-0.149013\pi$
$992$	−23.9030	−	13.4445i	−0.758921	−	0.426862i
$993$		0			0
$994$	−21.1481	+	23.5937i	−0.670776	+	0.748348i
$995$			44.0319i			1.39590i
$996$		0			0
$997$	9.78760			0.309976			0.154988	−	0.987916i	$-0.450466\pi$
$997$	9.78760			0.309976			0.154988	+	0.987916i	$0.450466\pi$
$998$	−3.93597	+	4.39115i	−0.124591	+	0.138999i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.l.c.1189.6		18
3.2	odd	2		408.2.l.a.373.13	✓	18
4.3	odd	2		4896.2.l.c.3025.16		18
8.3	odd	2		4896.2.l.d.3025.4		18
8.5	even	2		1224.2.l.d.1189.5		18
12.11	even	2		1632.2.l.b.1393.4		18
17.16	even	2		1224.2.l.d.1189.6		18
24.5	odd	2		408.2.l.b.373.14	yes	18
24.11	even	2		1632.2.l.a.1393.16		18
51.50	odd	2		408.2.l.b.373.13	yes	18
68.67	odd	2		4896.2.l.d.3025.3		18
136.67	odd	2		4896.2.l.c.3025.15		18
136.101	even	2	inner	1224.2.l.c.1189.5		18
204.203	even	2		1632.2.l.a.1393.15		18
408.101	odd	2		408.2.l.a.373.14	yes	18
408.203	even	2		1632.2.l.b.1393.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.l.a.373.13	✓	18	3.2	odd	2
408.2.l.a.373.14	yes	18	408.101	odd	2
408.2.l.b.373.13	yes	18	51.50	odd	2
408.2.l.b.373.14	yes	18	24.5	odd	2
1224.2.l.c.1189.5		18	136.101	even	2	inner
1224.2.l.c.1189.6		18	1.1	even	1	trivial
1224.2.l.d.1189.5		18	8.5	even	2
1224.2.l.d.1189.6		18	17.16	even	2
1632.2.l.a.1393.15		18	204.203	even	2
1632.2.l.a.1393.16		18	24.11	even	2
1632.2.l.b.1393.3		18	408.203	even	2
1632.2.l.b.1393.4		18	12.11	even	2
4896.2.l.c.3025.15		18	136.67	odd	2
4896.2.l.c.3025.16		18	4.3	odd	2
4896.2.l.d.3025.3		18	68.67	odd	2
4896.2.l.d.3025.4		18	8.3	odd	2

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:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.943929 + 1.05309i) q^{2} +(-0.217998 - 1.98808i) q^{4} +1.57273 q^{5} -1.68207i q^{7} +(2.29941 + 1.64704i) q^{8} +(-1.48454 + 1.65622i) q^{10} +3.33403 q^{11} -0.177520i q^{13} +(1.77138 + 1.58776i) q^{14} +(-3.90495 + 0.866796i) q^{16} +(3.53017 - 2.13024i) q^{17} -2.58556i q^{19} +(-0.342852 - 3.12672i) q^{20} +(-3.14709 + 3.51104i) q^{22} +3.40373i q^{23} -2.52653 q^{25} +(0.186944 + 0.167566i) q^{26} +(-3.34410 + 0.366689i) q^{28} -2.46715 q^{29} -4.84803i q^{31} +(2.77318 - 4.93046i) q^{32} +(-1.08889 + 5.72838i) q^{34} -2.64545i q^{35} +5.33914 q^{37} +(2.72283 + 2.44058i) q^{38} +(3.61634 + 2.59034i) q^{40} +4.79275i q^{41} -5.48185i q^{43} +(-0.726812 - 6.62833i) q^{44} +(-3.58443 - 3.21288i) q^{46} -5.72051 q^{47} +4.17063 q^{49} +(2.38486 - 2.66066i) q^{50} +(-0.352924 + 0.0386989i) q^{52} -4.52038i q^{53} +5.24353 q^{55} +(2.77044 - 3.86777i) q^{56} +(2.32881 - 2.59813i) q^{58} -6.32370i q^{59} +6.28670 q^{61} +(5.10541 + 4.57619i) q^{62} +(2.57454 + 7.57442i) q^{64} -0.279190i q^{65} -15.8300i q^{67} +(-5.00466 - 6.55388i) q^{68} +(2.78589 + 2.49711i) q^{70} +13.3194i q^{71} +4.38096i q^{73} +(-5.03977 + 5.62260i) q^{74} +(-5.14031 + 0.563647i) q^{76} -5.60809i q^{77} -7.47987i q^{79} +(-6.14143 + 1.36324i) q^{80} +(-5.04720 - 4.52401i) q^{82} -6.58394i q^{83} +(5.55199 - 3.35029i) q^{85} +(5.77289 + 5.17448i) q^{86} +(7.66629 + 5.49128i) q^{88} +8.64940 q^{89} -0.298601 q^{91} +(6.76689 - 0.742005i) q^{92} +(5.39975 - 6.02421i) q^{94} -4.06638i q^{95} +13.1686i q^{97} +(-3.93677 + 4.39205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{4} - 4 q^{5} + 8 q^{10} - 6 q^{14} + 10 q^{16} + 2 q^{17} - 2 q^{20} - 2 q^{22} + 22 q^{25} - 2 q^{26} + 10 q^{28} + 12 q^{29} - 30 q^{34} + 16 q^{37} + 34 q^{38} + 10 q^{40} + 12 q^{44} - 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 18 * q + 2 * q^4 - 4 * q^5 + 8 * q^10 - 6 * q^14 + 10 * q^16 + 2 * q^17 - 2 * q^20 - 2 * q^22 + 22 * q^25 - 2 * q^26 + 10 * q^28 + 12 * q^29 - 30 * q^34 + 16 * q^37 + 34 * q^38 + 10 * q^40 + 12 * q^44 - 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 - 14 * q^56 + 6 * q^58 + 16 * q^61 - 6 * q^62 + 2 * q^64 - 12 * q^68 - 32 * q^70 - 6 * q^74 - 62 * q^80 - 34 * q^82 - 16 * q^85 - 14 * q^86 - 16 * q^88 - 20 * q^89 - 2 * q^92 + 12 * q^94 + 60 * q^98

Introduction

L-functions

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