LMFDB - Embedded newform 1224.2.l.d.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.d.1189.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.943929 + 1.05309i) q^{2} +(-0.217998 - 1.98808i) q^{4} -1.57273 q^{5} +1.68207i q^{7} +(2.29941 + 1.64704i) q^{8} +(1.48454 - 1.65622i) q^{10} -3.33403 q^{11} -0.177520i q^{13} +(-1.77138 - 1.58776i) q^{14} +(-3.90495 + 0.866796i) q^{16} +(3.53017 + 2.13024i) q^{17} -2.58556i q^{19} +(0.342852 + 3.12672i) q^{20} +(3.14709 - 3.51104i) q^{22} -3.40373i q^{23} -2.52653 q^{25} +(0.186944 + 0.167566i) q^{26} +(3.34410 - 0.366689i) q^{28} +2.46715 q^{29} +4.84803i q^{31} +(2.77318 - 4.93046i) q^{32} +(-5.57556 + 1.70679i) q^{34} -2.64545i q^{35} -5.33914 q^{37} +(2.72283 + 2.44058i) q^{38} +(-3.61634 - 2.59034i) q^{40} -4.79275i q^{41} -5.48185i q^{43} +(0.726812 + 6.62833i) q^{44} +(3.58443 + 3.21288i) q^{46} -5.72051 q^{47} +4.17063 q^{49} +(2.38486 - 2.66066i) q^{50} +(-0.352924 + 0.0386989i) q^{52} -4.52038i q^{53} +5.24353 q^{55} +(-2.77044 + 3.86777i) q^{56} +(-2.32881 + 2.59813i) q^{58} -6.32370i q^{59} -6.28670 q^{61} +(-5.10541 - 4.57619i) q^{62} +(2.57454 + 7.57442i) q^{64} +0.279190i q^{65} -15.8300i q^{67} +(3.46553 - 7.48266i) q^{68} +(2.78589 + 2.49711i) q^{70} -13.3194i q^{71} -4.38096i q^{73} +(5.03977 - 5.62260i) q^{74} +(-5.14031 + 0.563647i) q^{76} -5.60809i q^{77} +7.47987i q^{79} +(6.14143 - 1.36324i) q^{80} +(5.04720 + 4.52401i) q^{82} -6.58394i q^{83} +(-5.55199 - 3.35029i) q^{85} +(5.77289 + 5.17448i) q^{86} +(-7.66629 - 5.49128i) q^{88} +8.64940 q^{89} +0.298601 q^{91} +(-6.76689 + 0.742005i) q^{92} +(5.39975 - 6.02421i) q^{94} +4.06638i q^{95} -13.1686i q^{97} +(-3.93677 + 4.39205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 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 + 6 * 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 + 36 * 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	$-0.614387\pi$
$5$	−1.57273			−0.703346			−0.351673	+	0.936123i	$0.614387\pi$
$6$		0			0
$7$			1.68207i			0.635764i	0.948130	+	0.317882i	$0.102972\pi$
$7$			1.68207i			0.635764i	−0.948130	+	0.317882i	$0.897028\pi$
$8$	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	$-0.667632\pi$
$11$	−3.33403			−1.00525			−0.502624	+	0.864505i	$0.667632\pi$
$12$		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	$-0.884527\pi$
$23$		−	3.40373i		−	0.709726i	0.934918	−	0.354863i	$-0.115473\pi$
$24$		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	$-0.426432\pi$
$29$	2.46715			0.458138			0.229069	+	0.973410i	$0.426432\pi$
$30$		0			0
$31$			4.84803i			0.870731i	0.900254	+	0.435366i	$0.143381\pi$
$31$			4.84803i			0.870731i	−0.900254	+	0.435366i	$0.856619\pi$
$32$	2.77318	−	4.93046i	0.490234	−	0.871591i
$33$		0			0
$34$	−5.57556	+	1.70679i	−0.956201	+	0.292712i
$35$		−	2.64545i		−	0.447162i
$36$		0			0
$37$	−5.33914			−0.877750			−0.438875	−	0.898548i	$-0.644623\pi$
$37$	−5.33914			−0.877750			−0.438875	+	0.898548i	$0.644623\pi$
$38$	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	$-0.877900\pi$
$41$		−	4.79275i		−	0.748502i	0.927327	−	0.374251i	$-0.122100\pi$
$42$		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	$-0.631846\pi$
$61$	−6.28670			−0.804929			−0.402464	+	0.915436i	$0.631846\pi$
$62$	−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	$-0.417966\pi$
$68$	3.46553	−	7.48266i	0.420257	−	0.907405i
$69$		0			0
$70$	2.78589	+	2.49711i	0.332978	+	0.298462i
$71$		−	13.3194i		−	1.58073i	−0.612638	−	0.790364i	$-0.709892\pi$
$71$		−	13.3194i		−	1.58073i	0.612638	−	0.790364i	$-0.290108\pi$
$72$		0			0
$73$		−	4.38096i		−	0.512752i	−0.966577	−	0.256376i	$-0.917471\pi$
$73$		−	4.38096i		−	0.512752i	0.966577	−	0.256376i	$-0.0825286\pi$
$74$	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	$0.138242\pi$
$79$			7.47987i			0.841551i	−0.907165	+	0.420776i	$0.861758\pi$
$80$	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	$-0.766921\pi$
$97$		−	13.1686i		−	1.33707i	0.743680	−	0.668536i	$-0.233079\pi$
$98$	−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	$-0.846800\pi$
$107$	−18.3379			−1.77280			−0.886398	+	0.462923i	$0.846800\pi$
$108$		0			0
$109$	−1.67742			−0.160668			−0.0803340	−	0.996768i	$-0.525599\pi$
$109$	−1.67742			−0.160668			−0.0803340	+	0.996768i	$0.525599\pi$
$110$	−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	$-0.895106\pi$
$113$		−	6.87985i		−	0.647202i	0.946194	−	0.323601i	$-0.104894\pi$
$114$		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	$-0.550129\pi$
$131$	−3.59013			−0.313671			−0.156835	+	0.987625i	$0.550129\pi$
$132$		0			0
$133$	4.34910			0.377115
$134$	16.6705	+	14.9424i	1.44011	+	1.29083i
$135$		0			0
$136$	4.60870	+	10.7126i	0.395193	+	0.918598i
$137$	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	$-0.581370\pi$
$139$	−5.96225			−0.505711			−0.252856	+	0.967504i	$0.581370\pi$
$140$	−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	$-0.434973\pi$
$163$	5.18018			0.405743			0.202871	+	0.979205i	$0.434973\pi$
$164$	−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	$0.298396\pi$
$167$			20.8328i			1.61209i	−0.591854	+	0.806046i	$0.701604\pi$
$168$		0			0
$169$	12.9685			0.997576
$170$	8.76884	−	2.68432i	0.672539	−	0.205878i
$171$		0			0
$172$	−10.8984	+	1.19503i	−0.830994	+	0.0911204i
$173$	21.8618			1.66212			0.831062	−	0.556179i	$-0.187733\pi$
$173$	21.8618			1.66212			0.831062	+	0.556179i	$0.187733\pi$
$174$		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	$-0.364507\pi$
$181$	11.1107			0.825852			0.412926	+	0.910765i	$0.364507\pi$
$182$	−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	$-0.838395\pi$
$193$		−	13.5081i		−	0.972334i	0.873866	−	0.486167i	$-0.161605\pi$
$194$	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	$-0.768755\pi$
$197$	−20.9839			−1.49504			−0.747519	+	0.664240i	$0.768755\pi$
$198$		0			0
$199$		−	27.9971i		−	1.98466i	−0.123605	−	0.992332i	$-0.539445\pi$
$199$		−	27.9971i		−	1.98466i	0.123605	−	0.992332i	$-0.460555\pi$
$200$	−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	$-0.666031\pi$
$211$	−14.4756			−0.996540			−0.498270	+	0.867022i	$0.666031\pi$
$212$	−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	$-0.599518\pi$
$227$	−9.26818			−0.615151			−0.307575	+	0.951524i	$0.599518\pi$
$228$		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	$0.0993051\pi$
$233$			9.37047i			0.613880i	−0.951729	+	0.306940i	$0.900695\pi$
$234$		0			0
$235$	8.99681			0.586887
$236$	−12.5720	+	1.37855i	−0.818370	+	0.0897362i
$237$		0			0
$238$	−2.87095	−	9.37851i	−0.186096	−	0.607918i
$239$	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	$0.132688\pi$
$241$			12.5710i			0.809768i	−0.914368	+	0.404884i	$0.867312\pi$
$242$	−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	$-0.441361\pi$
$269$	6.00877			0.366361			0.183180	+	0.983079i	$0.441361\pi$
$270$		0			0
$271$	−13.9230			−0.845760			−0.422880	−	0.906186i	$-0.638981\pi$
$271$	−13.9230			−0.845760			−0.422880	+	0.906186i	$0.638981\pi$
$272$	−15.6316	−	5.25855i	−0.947806	−	0.318847i
$273$		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	$-0.185934\pi$
$277$	27.7674			1.66838			0.834192	+	0.551474i	$0.185934\pi$
$278$	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	$-0.593117\pi$
$283$	−9.70263			−0.576761			−0.288381	+	0.957516i	$0.593117\pi$
$284$	−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	$-0.984230\pi$
$311$		−	1.74672i		−	0.0990472i	0.998773	−	0.0495236i	$-0.0157703\pi$
$312$		0			0
$313$			31.9640i			1.80671i	0.428894	+	0.903355i	$0.358903\pi$
$313$			31.9640i			1.80671i	−0.428894	+	0.903355i	$0.641097\pi$
$314$	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	$-0.534083\pi$
$317$	−3.80550			−0.213738			−0.106869	+	0.994273i	$0.534083\pi$
$318$		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	$-0.801679\pi$
$337$		−	21.4237i		−	1.16702i	0.812105	−	0.583511i	$-0.198321\pi$
$338$	−12.2413	+	13.6570i	−0.665840	+	0.742842i
$339$		0			0
$340$	−5.45033	+	11.7682i	−0.295586	+	0.638219i
$341$		−	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	$-0.354689\pi$
$347$	16.4230			0.881632			0.440816	+	0.897598i	$0.354689\pi$
$348$		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	$0.154162\pi$
$367$			17.8393i			0.931205i	−0.884994	+	0.465602i	$0.845838\pi$
$368$	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	$0.958752\pi$
$374$	18.5891	−	5.69049i	0.961219	−	0.294248i
$375$		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	$-0.487538\pi$
$379$	1.52394			0.0782793			0.0391396	+	0.999234i	$0.487538\pi$
$380$	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	$-0.695020\pi$
$397$	−22.9158			−1.15011			−0.575057	+	0.818114i	$0.695020\pi$
$398$	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	$-0.708721\pi$
$401$		−	31.7440i		−	1.58522i	0.609728	−	0.792610i	$-0.291279\pi$
$402$		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	$-0.291729\pi$
$419$	24.9157			1.21721			0.608605	+	0.793473i	$0.291729\pi$
$420$		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	$-0.948792\pi$
$431$		−	6.65096i		−	0.320366i	0.987087	−	0.160183i	$-0.0512084\pi$
$432$		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	$0.00328134\pi$
$439$			0.431972i			0.0206169i	−0.999947	+	0.0103085i	$0.996719\pi$
$440$	12.0570	+	8.63629i	0.574795	+	0.411719i
$441$		0			0
$442$	0.302989	+	0.989771i	0.0144117	+	0.0470786i
$443$		−	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	$-0.590741\pi$
$449$		−	40.6689i		−	1.91928i	0.281227	−	0.959641i	$-0.409259\pi$
$450$		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
$476$	12.5864	+	5.82927i	0.576896	+	0.267184i
$477$		0			0
$478$	−7.06351	+	7.88037i	−0.323077	+	0.360440i
$479$		−	40.1158i		−	1.83294i	−0.400106	−	0.916469i	$-0.631027\pi$
$479$		−	40.1158i		−	1.83294i	0.400106	−	0.916469i	$-0.368973\pi$
$480$		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	$-0.831594\pi$
$487$		−	22.2766i		−	1.00945i	0.863281	−	0.504724i	$-0.168406\pi$
$488$	−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	$-0.529752\pi$
$499$	−4.16978			−0.186665			−0.0933324	+	0.995635i	$0.529752\pi$
$500$	−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	$-0.980772\pi$
$503$		−	2.70786i		−	0.120737i	0.998176	−	0.0603687i	$-0.0192276\pi$
$504$		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	$-0.780740\pi$
$521$		−	29.0171i		−	1.27126i	0.771993	−	0.635631i	$-0.219260\pi$
$522$		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	$-0.728024\pi$
$541$	−30.5463			−1.31329			−0.656643	+	0.754202i	$0.728024\pi$
$542$	13.1423	−	14.6621i	0.564509	−	0.629793i
$543$		0			0
$544$	20.2929	−	11.4978i	0.870049	−	0.492965i
$545$	2.63813			0.113005
$546$		0			0
$547$	36.8589			1.57597			0.787986	−	0.615693i	$-0.211124\pi$
$547$	36.8589			1.57597			0.787986	+	0.615693i	$0.211124\pi$
$548$	−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	$-0.360812\pi$
$571$	20.2381			0.846937			0.423468	+	0.905911i	$0.360812\pi$
$572$	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	$0.536746\pi$
$578$	−23.3185	−	5.85202i	−0.969923	−	0.243412i
$579$		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	$-0.646027\pi$
$601$		−	43.9610i		−	1.79321i	0.442834	−	0.896603i	$-0.353973\pi$
$602$	−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	$-0.638032\pi$
$607$		−	44.7140i		−	1.81488i	0.420177	−	0.907442i	$-0.361968\pi$
$608$	−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	$0.236179\pi$
$617$			33.5704i			1.35149i	−0.737133	+	0.675747i	$0.763821\pi$
$618$		0			0
$619$	−29.2701			−1.17647			−0.588233	−	0.808692i	$-0.700176\pi$
$619$	−29.2701			−1.17647			−0.588233	+	0.808692i	$0.700176\pi$
$620$	−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	$0.233765\pi$
$641$			33.9330i			1.34027i	−0.742237	+	0.670137i	$0.766235\pi$
$642$		0			0
$643$	35.2361			1.38958			0.694788	−	0.719214i	$-0.255498\pi$
$643$	35.2361			1.38958			0.694788	+	0.719214i	$0.255498\pi$
$644$	−1.24811	−	11.3824i	−0.0491824	−	0.448530i
$645$		0			0
$646$	4.41301	+	14.4159i	0.173628	+	0.567188i
$647$	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	$-0.353638\pi$
$653$	22.6804			0.887554			0.443777	+	0.896137i	$0.353638\pi$
$654$		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	$-0.975965\pi$
$673$		−	3.91400i		−	0.150874i	0.997151	−	0.0754368i	$-0.0240351\pi$
$674$	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	$-0.639619\pi$
$677$	−22.1006			−0.849394			−0.424697	+	0.905336i	$0.639619\pi$
$678$		0			0
$679$	22.1506			0.850063
$680$	−7.24824	−	16.8480i	−0.277957	−	0.646092i
$681$		0			0
$682$	17.0216	+	15.2572i	0.651791	+	0.584227i
$683$	−42.9736			−1.64434			−0.822169	−	0.569244i	$-0.807236\pi$
$683$	−42.9736			−1.64434			−0.822169	+	0.569244i	$0.807236\pi$
$684$		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	$-0.609901\pi$
$691$	−17.7933			−0.676890			−0.338445	+	0.940986i	$0.609901\pi$
$692$	−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	$-0.309095\pi$
$709$	30.0583			1.12886			0.564431	+	0.825480i	$0.309095\pi$
$710$	−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	$-0.967293\pi$
$719$		−	5.50072i		−	0.205142i	0.994726	−	0.102571i	$-0.0327070\pi$
$720$		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	$-0.906813\pi$
$743$		−	15.7329i		−	0.577186i	0.957452	−	0.288593i	$-0.0931874\pi$
$744$		0			0
$745$		−	34.8490i		−	1.27677i
$746$	−5.25637	−	4.71151i	−0.192450	−	0.172501i
$747$		0			0
$748$	−11.5542	+	24.9474i	−0.422462	+	0.912168i
$749$		−	30.8458i		−	1.12708i
$750$		0			0
$751$			45.6534i			1.66591i	0.553337	+	0.832957i	$0.313354\pi$
$751$			45.6534i			1.66591i	−0.553337	+	0.832957i	$0.686646\pi$
$752$	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
$782$	5.80945	+	18.9777i	0.207745	+	0.678641i
$783$		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	$-0.597072\pi$
$787$	−16.8464			−0.600509			−0.300255	+	0.953859i	$0.597072\pi$
$788$	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	$-0.904846\pi$
$809$		−	16.7530i		−	0.589004i	0.955651	−	0.294502i	$-0.0951537\pi$
$810$		0			0
$811$	10.8001			0.379243			0.189622	−	0.981857i	$-0.439274\pi$
$811$	10.8001			0.379243			0.189622	+	0.981857i	$0.439274\pi$
$812$	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	$-0.265214\pi$
$821$	38.5393			1.34503			0.672516	+	0.740083i	$0.265214\pi$
$822$		0			0
$823$		−	18.0592i		−	0.629505i	−0.949174	−	0.314752i	$-0.898079\pi$
$823$		−	18.0592i		−	0.629505i	0.949174	−	0.314752i	$-0.101921\pi$
$824$	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	$-0.343422\pi$
$827$	27.1647			0.944611			0.472305	+	0.881435i	$0.343422\pi$
$828$		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	$-0.972156\pi$
$839$		−	5.06106i		−	0.174727i	0.996176	−	0.0873637i	$-0.0278442\pi$
$840$		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
$850$	14.0868	−	4.31225i	0.483173	−	0.147909i
$851$			18.1730i			0.622962i
$852$		0			0
$853$	−19.5592			−0.669695			−0.334847	−	0.942272i	$-0.608685\pi$
$853$	−19.5592			−0.669695			−0.334847	+	0.942272i	$0.608685\pi$
$854$	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	$0.0869134\pi$
$857$			15.7887i			0.539333i	−0.962954	+	0.269666i	$0.913087\pi$
$858$		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	$-0.813608\pi$
$877$	−49.3608			−1.66680			−0.833399	+	0.552672i	$0.813608\pi$
$878$	−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	$0.268441\pi$
$881$			44.3363i			1.49373i	−0.664977	+	0.746864i	$0.731559\pi$
$882$		0			0
$883$			12.1954i			0.410407i	0.978719	+	0.205203i	$0.0657856\pi$
$883$			12.1954i			0.410407i	−0.978719	+	0.205203i	$0.934214\pi$
$884$	−1.32832	−	0.615199i	−0.0446762	−	0.0206914i
$885$		0			0
$886$	0.990767	+	0.888065i	0.0332855	+	0.0298351i
$887$		−	39.8250i		−	1.33719i	−0.743626	−	0.668596i	$-0.766896\pi$
$887$		−	39.8250i		−	1.33719i	0.743626	−	0.668596i	$-0.233104\pi$
$888$		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	$-0.326061\pi$
$907$	31.3002			1.03931			0.519653	+	0.854377i	$0.326061\pi$
$908$	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	$-0.898038\pi$
$911$		−	19.0074i		−	0.629745i	0.949134	−	0.314872i	$-0.101962\pi$
$912$		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	$-0.801228\pi$
$929$		−	35.6403i		−	1.16932i	0.811279	−	0.584660i	$-0.198772\pi$
$930$		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	$-0.185135\pi$
$941$	51.2637			1.67115			0.835575	+	0.549377i	$0.185135\pi$
$942$		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	$-0.322459\pi$
$947$	32.5760			1.05858			0.529289	+	0.848442i	$0.322459\pi$
$948$		0			0
$949$	−0.777706			−0.0252454
$950$	−6.87929	−	6.16620i	−0.223194	−	0.200058i
$951$		0			0
$952$	−18.0194	+	7.75218i	−0.584012	+	0.251250i
$953$	−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	$-0.785628\pi$
$983$		−	39.1096i		−	1.24740i	0.781662	−	0.623702i	$-0.214372\pi$
$984$		0			0
$985$	33.0019			1.05153
$986$	−13.7557	+	4.21091i	−0.438072	+	0.134103i
$987$		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	$0.149013\pi$
$991$			28.4092i			0.902449i	−0.892411	+	0.451224i	$0.850987\pi$
$992$	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	$-0.549534\pi$
$997$	−9.78760			−0.309976			−0.154988	+	0.987916i	$0.549534\pi$
$998$	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.d.1189.6		18
3.2	odd	2		408.2.l.b.373.13	yes	18
4.3	odd	2		4896.2.l.d.3025.3		18
8.3	odd	2		4896.2.l.c.3025.15		18
8.5	even	2		1224.2.l.c.1189.5		18
12.11	even	2		1632.2.l.a.1393.15		18
17.16	even	2		1224.2.l.c.1189.6		18
24.5	odd	2		408.2.l.a.373.14	yes	18
24.11	even	2		1632.2.l.b.1393.3		18
51.50	odd	2		408.2.l.a.373.13	✓	18
68.67	odd	2		4896.2.l.c.3025.16		18
136.67	odd	2		4896.2.l.d.3025.4		18
136.101	even	2	inner	1224.2.l.d.1189.5		18
204.203	even	2		1632.2.l.b.1393.4		18
408.101	odd	2		408.2.l.b.373.14	yes	18
408.203	even	2		1632.2.l.a.1393.16		18

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

\(f(q)\)	\(=\)	\(q+(-0.943929 + 1.05309i) q^{2} +(-0.217998 - 1.98808i) q^{4} -1.57273 q^{5} +1.68207i q^{7} +(2.29941 + 1.64704i) q^{8} +(1.48454 - 1.65622i) q^{10} -3.33403 q^{11} -0.177520i q^{13} +(-1.77138 - 1.58776i) q^{14} +(-3.90495 + 0.866796i) q^{16} +(3.53017 + 2.13024i) q^{17} -2.58556i q^{19} +(0.342852 + 3.12672i) q^{20} +(3.14709 - 3.51104i) q^{22} -3.40373i q^{23} -2.52653 q^{25} +(0.186944 + 0.167566i) q^{26} +(3.34410 - 0.366689i) q^{28} +2.46715 q^{29} +4.84803i q^{31} +(2.77318 - 4.93046i) q^{32} +(-5.57556 + 1.70679i) q^{34} -2.64545i q^{35} -5.33914 q^{37} +(2.72283 + 2.44058i) q^{38} +(-3.61634 - 2.59034i) q^{40} -4.79275i q^{41} -5.48185i q^{43} +(0.726812 + 6.62833i) q^{44} +(3.58443 + 3.21288i) q^{46} -5.72051 q^{47} +4.17063 q^{49} +(2.38486 - 2.66066i) q^{50} +(-0.352924 + 0.0386989i) q^{52} -4.52038i q^{53} +5.24353 q^{55} +(-2.77044 + 3.86777i) q^{56} +(-2.32881 + 2.59813i) q^{58} -6.32370i q^{59} -6.28670 q^{61} +(-5.10541 - 4.57619i) q^{62} +(2.57454 + 7.57442i) q^{64} +0.279190i q^{65} -15.8300i q^{67} +(3.46553 - 7.48266i) q^{68} +(2.78589 + 2.49711i) q^{70} -13.3194i q^{71} -4.38096i q^{73} +(5.03977 - 5.62260i) q^{74} +(-5.14031 + 0.563647i) q^{76} -5.60809i q^{77} +7.47987i q^{79} +(6.14143 - 1.36324i) q^{80} +(5.04720 + 4.52401i) q^{82} -6.58394i q^{83} +(-5.55199 - 3.35029i) q^{85} +(5.77289 + 5.17448i) q^{86} +(-7.66629 - 5.49128i) q^{88} +8.64940 q^{89} +0.298601 q^{91} +(-6.76689 + 0.742005i) q^{92} +(5.39975 - 6.02421i) q^{94} +4.06638i q^{95} -13.1686i q^{97} +(-3.93677 + 4.39205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 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 + 6 * 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 + 36 * 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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