LMFDB - Embedded newform 572.2.i.b.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (of order $3$, degree $2$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	572.133
Dual form			572.2.i.b.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.119562 - 0.207087i) q^{3} +3.94282 q^{5} +(-2.21053 + 3.82876i) q^{7} +(1.47141 - 2.54856i) q^{9} +O(q^{10})$	\(q+(-0.119562 - 0.207087i) q^{3} +3.94282 q^{5} +(-2.21053 + 3.82876i) q^{7} +(1.47141 - 2.54856i) q^{9} +(0.500000 + 0.866025i) q^{11} +(2.50000 + 2.59808i) q^{13} +(-0.471410 - 0.816506i) q^{15} +(-2.06238 + 3.57215i) q^{17} +(-0.619562 + 1.07311i) q^{19} +1.05718 q^{21} +(-2.82326 - 4.89003i) q^{23} +10.5458 q^{25} -1.42107 q^{27} +(-1.94966 - 3.37690i) q^{29} +1.95649 q^{31} +(0.119562 - 0.207087i) q^{33} +(-8.71574 + 15.0961i) q^{35} +(5.65335 + 9.79190i) q^{37} +(0.239123 - 0.828347i) q^{39} +(-2.06238 - 3.57215i) q^{41} +(5.83530 - 10.1070i) q^{43} +(5.80150 - 10.0485i) q^{45} +4.66019 q^{47} +(-6.27292 - 10.8650i) q^{49} +0.986327 q^{51} +0.535426 q^{53} +(1.97141 + 3.41458i) q^{55} +0.296303 q^{57} +(-4.94966 + 8.57306i) q^{59} +(0.612725 - 1.06127i) q^{61} +(6.50520 + 11.2673i) q^{63} +(9.85705 + 10.2437i) q^{65} +(3.01204 + 5.21700i) q^{67} +(-0.675107 + 1.16932i) q^{69} +(6.29467 - 10.9027i) q^{71} -10.7278 q^{73} +(-1.26088 - 2.18390i) q^{75} -4.42107 q^{77} +10.6134 q^{79} +(-4.24433 - 7.35139i) q^{81} -2.46457 q^{83} +(-8.13160 + 14.0843i) q^{85} +(-0.466208 + 0.807496i) q^{87} +(-8.91423 - 15.4399i) q^{89} +(-15.4737 + 3.82876i) q^{91} +(-0.233922 - 0.405164i) q^{93} +(-2.44282 + 4.23109i) q^{95} +(-0.978247 + 1.69437i) q^{97} +2.94282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 6 q^{5} - 5 q^{7}+O(q^{10}) $ 6 * q - q^3 + 6 * q^5 - 5 * q^7	$ 6 q - q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{11} + 15 q^{13} + 6 q^{15} + 5 q^{17} - 4 q^{19} + 24 q^{21} + q^{23} + 12 q^{25} + 8 q^{27} - 4 q^{29} + 14 q^{31} + q^{33} - 9 q^{35} + 8 q^{37} + 2 q^{39} + 5 q^{41} - 8 q^{43} + 18 q^{45} + 12 q^{47} - 12 q^{49} - 14 q^{51} + 22 q^{53} + 3 q^{55} + 20 q^{57} - 22 q^{59} - 6 q^{61} + 4 q^{63} + 15 q^{65} - 7 q^{67} + 23 q^{69} + 11 q^{71} + 4 q^{73} - 7 q^{75} - 10 q^{77} - 40 q^{79} + 9 q^{81} + 4 q^{83} - 24 q^{85} - 29 q^{87} - 27 q^{89} - 35 q^{91} - 37 q^{93} + 3 q^{95} - 7 q^{97}+O(q^{100}) $ 6 * q - q^3 + 6 * q^5 - 5 * q^7 + 3 * q^11 + 15 * q^13 + 6 * q^15 + 5 * q^17 - 4 * q^19 + 24 * q^21 + q^23 + 12 * q^25 + 8 * q^27 - 4 * q^29 + 14 * q^31 + q^33 - 9 * q^35 + 8 * q^37 + 2 * q^39 + 5 * q^41 - 8 * q^43 + 18 * q^45 + 12 * q^47 - 12 * q^49 - 14 * q^51 + 22 * q^53 + 3 * q^55 + 20 * q^57 - 22 * q^59 - 6 * q^61 + 4 * q^63 + 15 * q^65 - 7 * q^67 + 23 * q^69 + 11 * q^71 + 4 * q^73 - 7 * q^75 - 10 * q^77 - 40 * q^79 + 9 * q^81 + 4 * q^83 - 24 * q^85 - 29 * q^87 - 27 * q^89 - 35 * q^91 - 37 * q^93 + 3 * q^95 - 7 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.119562	−	0.207087i	−0.0690289	−	0.119562i	0.829445	−	0.558588i	$-0.188657\pi$
$3$	−0.119562	−	0.207087i	−0.0690289	−	0.119562i	−0.898474	+	0.439027i	$0.855323\pi$
$4$		0			0
$5$	3.94282			1.76328			0.881641	−	0.471920i	$-0.156439\pi$
$5$	3.94282			1.76328			0.881641	+	0.471920i	$0.156439\pi$
$6$		0			0
$7$	−2.21053	+	3.82876i	−0.835503	+	1.44713i	0.0581171	+	0.998310i	$0.481490\pi$
$7$	−2.21053	+	3.82876i	−0.835503	+	1.44713i	−0.893620	+	0.448824i	$0.851843\pi$
$8$		0			0
$9$	1.47141	−	2.54856i	0.490470	−	0.849519i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$		0			0
$15$	−0.471410	−	0.816506i	−0.121718	−	0.210821i
$16$		0			0
$17$	−2.06238	+	3.57215i	−0.500201	+	0.866374i	0.499799	+	0.866141i	$0.333407\pi$
$17$	−2.06238	+	3.57215i	−0.500201	+	0.866374i	−1.00000		0.000232150i	$0.999926\pi$
$18$		0			0
$19$	−0.619562	+	1.07311i	−0.142137	+	0.246189i	−0.928301	−	0.371829i	$-0.878731\pi$
$19$	−0.619562	+	1.07311i	−0.142137	+	0.246189i	0.786164	+	0.618018i	$0.212064\pi$
$20$		0			0
$21$	1.05718			0.230696
$22$		0			0
$23$	−2.82326	−	4.89003i	−0.588690	−	1.01964i	−0.994404	−	0.105641i	$-0.966311\pi$
$23$	−2.82326	−	4.89003i	−0.588690	−	1.01964i	0.405714	−	0.914000i	$-0.367023\pi$
$24$		0			0
$25$	10.5458			2.10917
$26$		0			0
$27$	−1.42107			−0.273484
$28$		0			0
$29$	−1.94966	−	3.37690i	−0.362042	−	0.627075i	0.626255	−	0.779619i	$-0.284587\pi$
$29$	−1.94966	−	3.37690i	−0.362042	−	0.627075i	−0.988297	+	0.152543i	$0.951254\pi$
$30$		0			0
$31$	1.95649			0.351397			0.175698	−	0.984444i	$-0.443782\pi$
$31$	1.95649			0.351397			0.175698	+	0.984444i	$0.443782\pi$
$32$		0			0
$33$	0.119562	−	0.207087i	0.0208130	−	0.0360492i
$34$		0			0
$35$	−8.71574	+	15.0961i	−1.47323	+	2.55171i
$36$		0			0
$37$	5.65335	+	9.79190i	0.929406	+	1.60978i	0.784318	+	0.620359i	$0.213013\pi$
$37$	5.65335	+	9.79190i	0.929406	+	1.60978i	0.145087	+	0.989419i	$0.453654\pi$
$38$		0			0
$39$	0.239123	−	0.828347i	0.0382904	−	0.132642i
$40$		0			0
$41$	−2.06238	−	3.57215i	−0.322090	−	0.557876i	0.658829	−	0.752293i	$-0.271052\pi$
$41$	−2.06238	−	3.57215i	−0.322090	−	0.557876i	−0.980919	+	0.194416i	$0.937719\pi$
$42$		0			0
$43$	5.83530	−	10.1070i	0.889874	−	1.54131i	0.0498516	−	0.998757i	$-0.484125\pi$
$43$	5.83530	−	10.1070i	0.889874	−	1.54131i	0.840023	−	0.542551i	$-0.182541\pi$
$44$		0			0
$45$	5.80150	−	10.0485i	0.864837	−	1.49794i
$46$		0			0
$47$	4.66019			0.679759			0.339879	−	0.940469i	$-0.389614\pi$
$47$	4.66019			0.679759			0.339879	+	0.940469i	$0.389614\pi$
$48$		0			0
$49$	−6.27292	−	10.8650i	−0.896131	−	1.55214i
$50$		0			0
$51$	0.986327			0.138113
$52$		0			0
$53$	0.535426			0.0735465			0.0367732	−	0.999324i	$-0.488292\pi$
$53$	0.535426			0.0735465			0.0367732	+	0.999324i	$0.488292\pi$
$54$		0			0
$55$	1.97141	+	3.41458i	0.265825	+	0.460422i
$56$		0			0
$57$	0.296303			0.0392463
$58$		0			0
$59$	−4.94966	+	8.57306i	−0.644390	+	1.11612i	0.340052	+	0.940407i	$0.389555\pi$
$59$	−4.94966	+	8.57306i	−0.644390	+	1.11612i	−0.984442	+	0.175710i	$0.943778\pi$
$60$		0			0
$61$	0.612725	−	1.06127i	0.0784514	−	0.135882i	−0.824131	−	0.566400i	$-0.808336\pi$
$61$	0.612725	−	1.06127i	0.0784514	−	0.135882i	0.902582	+	0.430518i	$0.141669\pi$
$62$		0			0
$63$	6.50520	+	11.2673i	0.819578	+	1.41955i
$64$		0			0
$65$	9.85705	+	10.2437i	1.22262	+	1.27058i
$66$		0			0
$67$	3.01204	+	5.21700i	0.367979	+	0.637358i	0.989249	−	0.146238i	$-0.0467165\pi$
$67$	3.01204	+	5.21700i	0.367979	+	0.637358i	−0.621270	+	0.783596i	$0.713383\pi$
$68$		0			0
$69$	−0.675107	+	1.16932i	−0.0812733	+	0.140770i
$70$		0			0
$71$	6.29467	−	10.9027i	0.747040	−	1.29391i	−0.202196	−	0.979345i	$-0.564808\pi$
$71$	6.29467	−	10.9027i	0.747040	−	1.29391i	0.949236	−	0.314566i	$-0.101859\pi$
$72$		0			0
$73$	−10.7278			−1.25559			−0.627795	−	0.778378i	$-0.716043\pi$
$73$	−10.7278			−1.25559			−0.627795	+	0.778378i	$0.716043\pi$
$74$		0			0
$75$	−1.26088	−	2.18390i	−0.145594	−	0.252175i
$76$		0			0
$77$	−4.42107			−0.503827
$78$		0			0
$79$	10.6134			1.19410			0.597051	−	0.802203i	$-0.296339\pi$
$79$	10.6134			1.19410			0.597051	+	0.802203i	$0.296339\pi$
$80$		0			0
$81$	−4.24433	−	7.35139i	−0.471592	−	0.816821i
$82$		0			0
$83$	−2.46457			−0.270522			−0.135261	−	0.990810i	$-0.543187\pi$
$83$	−2.46457			−0.270522			−0.135261	+	0.990810i	$0.543187\pi$
$84$		0			0
$85$	−8.13160	+	14.0843i	−0.881996	+	1.52766i
$86$		0			0
$87$	−0.466208	+	0.807496i	−0.0499828	+	0.0865727i
$88$		0			0
$89$	−8.91423	−	15.4399i	−0.944906	−	1.63663i	−0.755938	−	0.654643i	$-0.772819\pi$
$89$	−8.91423	−	15.4399i	−0.944906	−	1.63663i	−0.188968	−	0.981983i	$-0.560514\pi$
$90$		0			0
$91$	−15.4737	+	3.82876i	−1.62209	+	0.401363i
$92$		0			0
$93$	−0.233922	−	0.405164i	−0.0242565	−	0.0420135i
$94$		0			0
$95$	−2.44282	+	4.23109i	−0.250628	+	0.434101i
$96$		0			0
$97$	−0.978247	+	1.69437i	−0.0993259	+	0.172037i	−0.911406	−	0.411509i	$-0.865002\pi$
$97$	−0.978247	+	1.69437i	−0.0993259	+	0.172037i	0.812080	+	0.583546i	$0.198335\pi$
$98$		0			0
$99$	2.94282			0.295765
$100$		0			0
$101$	−2.16991	−	3.75839i	−0.215914	−	0.373973i	0.737641	−	0.675193i	$-0.235940\pi$
$101$	−2.16991	−	3.75839i	−0.215914	−	0.373973i	−0.953555	+	0.301220i	$0.902606\pi$
$102$		0			0
$103$	−15.1111			−1.48894			−0.744470	−	0.667656i	$-0.767298\pi$
$103$	−15.1111			−1.48894			−0.744470	+	0.667656i	$0.767298\pi$
$104$		0			0
$105$	4.16827			0.406782
$106$		0			0
$107$	−3.63160	−	6.29012i	−0.351080	−	0.608088i	0.635359	−	0.772217i	$-0.280852\pi$
$107$	−3.63160	−	6.29012i	−0.351080	−	0.608088i	−0.986439	+	0.164129i	$0.947519\pi$
$108$		0			0
$109$	−17.4887			−1.67511			−0.837554	−	0.546354i	$-0.816015\pi$
$109$	−17.4887			−1.67511			−0.837554	+	0.546354i	$0.816015\pi$
$110$		0			0
$111$	1.35185	−	2.34147i	0.128312	−	0.222243i
$112$		0			0
$113$	2.80150	−	4.85235i	0.263543	−	0.456471i	−0.703638	−	0.710559i	$-0.748442\pi$
$113$	2.80150	−	4.85235i	0.263543	−	0.456471i	0.967181	+	0.254088i	$0.0817754\pi$
$114$		0			0
$115$	−11.1316	−	19.2805i	−1.03803	−	1.79792i
$116$		0			0
$117$	10.2999	−	2.54856i	0.952223	−	0.235614i
$118$		0			0
$119$	−9.11793	−	15.7927i	−0.835839	−	1.44772i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−0.493163	+	0.854184i	−0.0444671	+	0.0770192i
$124$		0			0
$125$	21.8662			1.95577
$126$		0			0
$127$	−3.52859	−	6.11170i	−0.313112	−	0.542325i	0.665923	−	0.746021i	$-0.268038\pi$
$127$	−3.52859	−	6.11170i	−0.313112	−	0.542325i	−0.979034	+	0.203695i	$0.934705\pi$
$128$		0			0
$129$	−2.79071			−0.245708
$130$		0			0
$131$	−8.74145			−0.763744			−0.381872	−	0.924215i	$-0.624720\pi$
$131$	−8.74145			−0.763744			−0.381872	+	0.924215i	$0.624720\pi$
$132$		0			0
$133$	−2.73912	−	4.74430i	−0.237512	−	0.411383i
$134$		0			0
$135$	−5.60301			−0.482230
$136$		0			0
$137$	−8.87592	+	15.3736i	−0.758321	+	1.31345i	0.185385	+	0.982666i	$0.440647\pi$
$137$	−8.87592	+	15.3736i	−0.758321	+	1.31345i	−0.943706	+	0.330785i	$0.892686\pi$
$138$		0			0
$139$	−1.57893	+	2.73479i	−0.133923	+	0.231962i	−0.925186	−	0.379515i	$-0.876091\pi$
$139$	−1.57893	+	2.73479i	−0.133923	+	0.231962i	0.791262	+	0.611477i	$0.209424\pi$
$140$		0			0
$141$	−0.557180	−	0.965064i	−0.0469230	−	0.0812730i
$142$		0			0
$143$	−1.00000	+	3.46410i	−0.0836242	+	0.289683i
$144$		0			0
$145$	−7.68715	−	13.3145i	−0.638383	−	1.10571i
$146$		0			0
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$		0			0
$149$	7.23229	−	12.5267i	0.592492	−	1.02623i	−0.401404	−	0.915901i	$-0.631478\pi$
$149$	7.23229	−	12.5267i	0.592492	−	1.02623i	0.993896	−	0.110325i	$-0.0351892\pi$
$150$		0			0
$151$	11.5458			0.939586			0.469793	−	0.882777i	$-0.344328\pi$
$151$	11.5458			0.939586			0.469793	+	0.882777i	$0.344328\pi$
$152$		0			0
$153$	6.06922	+	10.5122i	0.490667	+	0.849861i
$154$		0			0
$155$	7.71410			0.619611
$156$		0			0
$157$	−8.66019			−0.691158			−0.345579	−	0.938390i	$-0.612318\pi$
$157$	−8.66019			−0.691158			−0.345579	+	0.938390i	$0.612318\pi$
$158$		0			0
$159$	−0.0640165	−	0.110880i	−0.00507684	−	0.00879334i
$160$		0			0
$161$	24.9636			1.96741
$162$		0			0
$163$	5.05267	−	8.75148i	0.395755	−	0.685468i	−0.597442	−	0.801912i	$-0.703816\pi$
$163$	5.05267	−	8.75148i	0.395755	−	0.685468i	0.993197	+	0.116444i	$0.0371495\pi$
$164$		0			0
$165$	0.471410	−	0.816506i	0.0366992	−	0.0635649i
$166$		0			0
$167$	−5.08414	−	8.80598i	−0.393422	−	0.681427i	0.599476	−	0.800393i	$-0.295376\pi$
$167$	−5.08414	−	8.80598i	−0.393422	−	0.681427i	−0.992898	+	0.118965i	$0.962042\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	1.82326	+	3.15798i	0.139428	+	0.241496i
$172$		0			0
$173$	6.06922	−	10.5122i	0.461434	−	0.799227i	−0.537599	−	0.843201i	$-0.680668\pi$
$173$	6.06922	−	10.5122i	0.461434	−	0.799227i	0.999033	+	0.0439736i	$0.0140017\pi$
$174$		0			0
$175$	−23.3119	+	40.3774i	−1.76221	+	3.05225i
$176$		0			0
$177$	2.36716			0.177926
$178$		0			0
$179$	0.0744200	+	0.128899i	0.00556241	+	0.00963438i	0.868793	−	0.495175i	$-0.164896\pi$
$179$	0.0744200	+	0.128899i	0.00556241	+	0.00963438i	−0.863231	+	0.504809i	$0.831563\pi$
$180$		0			0
$181$	−4.08701			−0.303785			−0.151893	−	0.988397i	$-0.548537\pi$
$181$	−4.08701			−0.303785			−0.151893	+	0.988397i	$0.548537\pi$
$182$		0			0
$183$	−0.293034			−0.0216617
$184$		0			0
$185$	22.2902	+	38.6077i	1.63880	+	2.83849i
$186$		0			0
$187$	−4.12476			−0.301633
$188$		0			0
$189$	3.14132	−	5.44092i	0.228497	−	0.395768i
$190$		0			0
$191$	−7.32326	+	12.6843i	−0.529892	+	0.917801i	0.469500	+	0.882933i	$0.344434\pi$
$191$	−7.32326	+	12.6843i	−0.529892	+	0.917801i	−0.999392	+	0.0348678i	$0.988899\pi$
$192$		0			0
$193$	−0.796303	−	1.37924i	−0.0573192	−	0.0992797i	0.835942	−	0.548818i	$-0.184922\pi$
$193$	−0.796303	−	1.37924i	−0.0573192	−	0.0992797i	−0.893261	+	0.449538i	$0.851589\pi$
$194$		0			0
$195$	0.942820	−	3.26602i	0.0675167	−	0.233885i
$196$		0			0
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	0.980614	−	0.195947i	$-0.0627782\pi$
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	−0.660003	+	0.751263i	$0.729445\pi$
$198$		0			0
$199$	−7.56758	+	13.1074i	−0.536452	+	0.929162i	0.462640	+	0.886546i	$0.346902\pi$
$199$	−7.56758	+	13.1074i	−0.536452	+	0.929162i	−0.999092	+	0.0426154i	$0.986431\pi$
$200$		0			0
$201$	0.720248	−	1.24751i	0.0508024	−	0.0879924i
$202$		0			0
$203$	17.2391			1.20995
$204$		0			0
$205$	−8.13160	−	14.0843i	−0.567936	−	0.983693i
$206$		0			0
$207$	−16.6167			−1.15494
$208$		0			0
$209$	−1.23912			−0.0857119
$210$		0			0
$211$	0.141315	+	0.244765i	0.00972853	+	0.0168503i	0.870849	−	0.491551i	$-0.163570\pi$
$211$	0.141315	+	0.244765i	0.00972853	+	0.0168503i	−0.861120	+	0.508401i	$0.830237\pi$
$212$		0			0
$213$	−3.01040			−0.206269
$214$		0			0
$215$	23.0075	−	39.8502i	1.56910	−	2.71776i
$216$		0			0
$217$	−4.32489	+	7.49093i	−0.293593	+	0.508518i
$218$		0			0
$219$	1.28263	+	2.22158i	0.0866721	+	0.150121i
$220$		0			0
$221$	−14.4367	+	3.57215i	−0.971116	+	0.240289i
$222$		0			0
$223$	−3.19686	−	5.53712i	−0.214078	−	0.370793i	0.738909	−	0.673805i	$-0.235341\pi$
$223$	−3.19686	−	5.53712i	−0.214078	−	0.370793i	−0.952987	+	0.303012i	$0.902008\pi$
$224$		0			0
$225$	15.5172	−	26.8766i	1.03448	−	1.79178i
$226$		0			0
$227$	2.77975	−	4.81467i	0.184499	−	0.319561i	−0.758909	−	0.651197i	$-0.774267\pi$
$227$	2.77975	−	4.81467i	0.184499	−	0.319561i	0.943407	+	0.331636i	$0.107601\pi$
$228$		0			0
$229$	4.69002			0.309925			0.154963	−	0.987920i	$-0.450474\pi$
$229$	4.69002			0.309925			0.154963	+	0.987920i	$0.450474\pi$
$230$		0			0
$231$	0.528590	+	0.915545i	0.0347787	+	0.0602384i
$232$		0			0
$233$	18.7278			1.22690			0.613449	−	0.789735i	$-0.289782\pi$
$233$	18.7278			1.22690			0.613449	+	0.789735i	$0.289782\pi$
$234$		0			0
$235$	18.3743			1.19861
$236$		0			0
$237$	−1.26896	−	2.19790i	−0.0824276	−	0.142769i
$238$		0			0
$239$	4.74720			0.307071			0.153536	−	0.988143i	$-0.450934\pi$
$239$	4.74720			0.307071			0.153536	+	0.988143i	$0.450934\pi$
$240$		0			0
$241$	−6.43762	+	11.1503i	−0.414683	+	0.718253i	−0.995395	−	0.0958565i	$-0.969441\pi$
$241$	−6.43762	+	11.1503i	−0.414683	+	0.718253i	0.580712	+	0.814109i	$0.302774\pi$
$242$		0			0
$243$	−3.14652	+	5.44993i	−0.201849	+	0.349613i
$244$		0			0
$245$	−24.7330	−	42.8388i	−1.58013	−	2.73687i
$246$		0			0
$247$	−4.33693	+	1.07311i	−0.275952	+	0.0682805i
$248$		0			0
$249$	0.294668	+	0.510381i	0.0186739	+	0.0323441i
$250$		0			0
$251$	0.557180	−	0.965064i	0.0351689	−	0.0609143i	−0.847905	−	0.530148i	$-0.822136\pi$
$251$	0.557180	−	0.965064i	0.0351689	−	0.0609143i	0.883074	+	0.469234i	$0.155470\pi$
$252$		0			0
$253$	2.82326	−	4.89003i	0.177497	−	0.307433i
$254$		0			0
$255$	3.88891			0.243533
$256$		0			0
$257$	3.69166	+	6.39414i	0.230279	+	0.398855i	0.957890	−	0.287135i	$-0.0927027\pi$
$257$	3.69166	+	6.39414i	0.230279	+	0.398855i	−0.727611	+	0.685990i	$0.759369\pi$
$258$		0			0
$259$	−49.9877			−3.10608
$260$		0			0
$261$	−11.4750			−0.710283
$262$		0			0
$263$	15.5406	+	26.9172i	0.958276	+	1.65978i	0.726686	+	0.686970i	$0.241059\pi$
$263$	15.5406	+	26.9172i	0.958276	+	1.65978i	0.231590	+	0.972813i	$0.425607\pi$
$264$		0			0
$265$	2.11109			0.129683
$266$		0			0
$267$	−2.13160	+	3.69204i	−0.130452	+	0.225949i
$268$		0			0
$269$	5.91423	−	10.2437i	0.360597	−	0.624572i	−0.627462	−	0.778647i	$-0.715906\pi$
$269$	5.91423	−	10.2437i	0.360597	−	0.624572i	0.988059	+	0.154075i	$0.0492397\pi$
$270$		0			0
$271$	−6.75924	−	11.7074i	−0.410595	−	0.711171i	0.584360	−	0.811494i	$-0.301346\pi$
$271$	−6.75924	−	11.7074i	−0.410595	−	0.711171i	−0.994955	+	0.100324i	$0.968012\pi$
$272$		0			0
$273$	2.64295	+	2.74663i	0.159959	+	0.166234i
$274$		0			0
$275$	5.27292	+	9.13296i	0.317969	+	0.550738i
$276$		0			0
$277$	11.4766	−	19.8781i	0.689563	−	1.19436i	−0.282417	−	0.959292i	$-0.591136\pi$
$277$	11.4766	−	19.8781i	0.689563	−	1.19436i	0.971979	−	0.235066i	$-0.0755306\pi$
$278$		0			0
$279$	2.87880	−	4.98623i	0.172349	−	0.298518i
$280$		0			0
$281$	−7.40164			−0.441545			−0.220772	−	0.975325i	$-0.570858\pi$
$281$	−7.40164			−0.441545			−0.220772	+	0.975325i	$0.570858\pi$
$282$		0			0
$283$	14.5676	+	25.2318i	0.865953	+	1.49987i	0.866098	+	0.499875i	$0.166621\pi$
$283$	14.5676	+	25.2318i	0.865953	+	1.49987i	−0.000144886		1.00000i	$0.500046\pi$
$284$		0			0
$285$	1.16827			0.0692024
$286$		0			0
$287$	18.2359			1.07643
$288$		0			0
$289$	−0.00683653	−	0.0118412i	−0.000402149	−	0.000696542i
$290$		0			0
$291$	0.467843			0.0274254
$292$		0			0
$293$	−0.942820	+	1.63301i	−0.0550801	+	0.0954016i	−0.892251	−	0.451540i	$-0.850875\pi$
$293$	−0.942820	+	1.63301i	−0.0550801	+	0.0954016i	0.837171	+	0.546942i	$0.184208\pi$
$294$		0			0
$295$	−19.5156	+	33.8020i	−1.13624	+	1.96803i
$296$		0			0
$297$	−0.710533	−	1.23068i	−0.0412293	−	0.0714113i
$298$		0			0
$299$	5.64652	−	19.5601i	0.326547	−	1.13119i
$300$		0			0
$301$	25.7982	+	44.6839i	1.48699	+	2.57553i
$302$		0			0
$303$	−0.518875	+	0.898718i	−0.0298086	+	0.0516300i
$304$		0			0
$305$	2.41586	−	4.18440i	0.138332	−	0.239598i
$306$		0			0
$307$	25.7850			1.47163			0.735813	−	0.677185i	$-0.236800\pi$
$307$	25.7850			1.47163			0.735813	+	0.677185i	$0.236800\pi$
$308$		0			0
$309$	1.80671	+	3.12931i	0.102780	+	0.178020i
$310$		0			0
$311$	−2.73104			−0.154863			−0.0774316	−	0.996998i	$-0.524672\pi$
$311$	−2.73104			−0.154863			−0.0774316	+	0.996998i	$0.524672\pi$
$312$		0			0
$313$	−12.8285			−0.725107			−0.362554	−	0.931963i	$-0.618095\pi$
$313$	−12.8285			−0.725107			−0.362554	+	0.931963i	$0.618095\pi$
$314$		0			0
$315$	25.6488	+	44.4251i	1.44515	+	2.50307i
$316$		0			0
$317$	−5.34446			−0.300175			−0.150087	−	0.988673i	$-0.547955\pi$
$317$	−5.34446			−0.300175			−0.150087	+	0.988673i	$0.547955\pi$
$318$		0			0
$319$	1.94966	−	3.37690i	0.109160	−	0.189070i
$320$		0			0
$321$	−0.868400	+	1.50411i	−0.0484694	+	0.0839514i
$322$		0			0
$323$	−2.55555	−	4.42633i	−0.142194	−	0.246288i
$324$		0			0
$325$	26.3646	+	27.3989i	1.46244	+	1.51982i
$326$		0			0
$327$	2.09097	+	3.62167i	0.115631	+	0.200279i
$328$		0			0
$329$	−10.3015	+	17.8427i	−0.567940	+	0.983702i
$330$		0			0
$331$	0.521753	−	0.903703i	0.0286782	−	0.0496720i	−0.851330	−	0.524630i	$-0.824204\pi$
$331$	0.521753	−	0.903703i	0.0286782	−	0.0496720i	0.880008	+	0.474958i	$0.157537\pi$
$332$		0			0
$333$	33.2736			1.82338
$334$		0			0
$335$	11.8759	+	20.5697i	0.648851	+	1.12384i
$336$		0			0
$337$	−8.79071			−0.478861			−0.239430	−	0.970914i	$-0.576961\pi$
$337$	−8.79071			−0.478861			−0.239430	+	0.970914i	$0.576961\pi$
$338$		0			0
$339$	−1.33981			−0.0727685
$340$		0			0
$341$	0.978247	+	1.69437i	0.0529750	+	0.0917554i
$342$		0			0
$343$	24.5185			1.32387
$344$		0			0
$345$	−2.66182	+	4.61042i	−0.143308	+	0.248216i
$346$		0			0
$347$	13.8473	−	23.9843i	0.743364	−	1.28754i	−0.207591	−	0.978216i	$-0.566562\pi$
$347$	13.8473	−	23.9843i	0.743364	−	1.28754i	0.950955	−	0.309328i	$-0.100104\pi$
$348$		0			0
$349$	−6.15335	−	10.6579i	−0.329381	−	0.570505i	0.653008	−	0.757351i	$-0.273507\pi$
$349$	−6.15335	−	10.6579i	−0.329381	−	0.570505i	−0.982389	+	0.186846i	$0.940174\pi$
$350$		0			0
$351$	−3.55267	−	3.69204i	−0.189627	−	0.197066i
$352$		0			0
$353$	6.80438	+	11.7855i	0.362161	+	0.627281i	0.988316	−	0.152417i	$-0.0487058\pi$
$353$	6.80438	+	11.7855i	0.362161	+	0.627281i	−0.626155	+	0.779698i	$0.715372\pi$
$354$		0			0
$355$	24.8187	−	42.9873i	1.31724	−	2.28153i
$356$		0			0
$357$	−2.18031	+	3.77641i	−0.115394	+	0.199869i
$358$		0			0
$359$	−3.41780			−0.180384			−0.0901922	−	0.995924i	$-0.528748\pi$
$359$	−3.41780			−0.180384			−0.0901922	+	0.995924i	$0.528748\pi$
$360$		0			0
$361$	8.73229	+	15.1248i	0.459594	+	0.796040i
$362$		0			0
$363$	0.239123			0.0125507
$364$		0			0
$365$	−42.2977			−2.21396
$366$		0			0
$367$	−14.1774	−	24.5560i	−0.740056	−	1.28181i	−0.952469	−	0.304634i	$-0.901466\pi$
$367$	−14.1774	−	24.5560i	−0.740056	−	1.28181i	0.212414	−	0.977180i	$-0.431868\pi$
$368$		0			0
$369$	−12.1384			−0.631902
$370$		0			0
$371$	−1.18358	+	2.05002i	−0.0614483	+	0.106432i
$372$		0			0
$373$	−16.7661	+	29.0397i	−0.868115	+	1.50362i	−0.00419370	+	0.999991i	$0.501335\pi$
$373$	−16.7661	+	29.0397i	−0.868115	+	1.50362i	−0.863921	+	0.503627i	$0.831998\pi$
$374$		0			0
$375$	−2.61436	−	4.52820i	−0.135005	−	0.233835i
$376$		0			0
$377$	3.89931	−	13.5076i	0.200825	−	0.695678i
$378$		0			0
$379$	−0.00971516	−	0.0168272i	−0.000499034	−	0.000864353i	0.865776	−	0.500432i	$-0.166826\pi$
$379$	−0.00971516	−	0.0168272i	−0.000499034	−	0.000864353i	−0.866275	+	0.499568i	$0.833492\pi$
$380$		0			0
$381$	−0.843768	+	1.46145i	−0.0432275	+	0.0748723i
$382$		0			0
$383$	9.51887	−	16.4872i	0.486392	−	0.842455i	−0.513486	−	0.858098i	$-0.671646\pi$
$383$	9.51887	−	16.4872i	0.486392	−	0.842455i	0.999878	+	0.0156428i	$0.00497945\pi$
$384$		0			0
$385$	−17.4315			−0.888390
$386$		0			0
$387$	−17.1722	−	29.7432i	−0.872913	−	1.51193i
$388$		0			0
$389$	−8.73353			−0.442808			−0.221404	−	0.975182i	$-0.571064\pi$
$389$	−8.73353			−0.442808			−0.221404	+	0.975182i	$0.571064\pi$
$390$		0			0
$391$	23.2905			1.17785
$392$		0			0
$393$	1.04514	+	1.81024i	0.0527204	+	0.0913145i
$394$		0			0
$395$	41.8468			2.10554
$396$		0			0
$397$	18.2684	−	31.6418i	0.916865	−	1.58806i	0.112717	−	0.993627i	$-0.464045\pi$
$397$	18.2684	−	31.6418i	0.916865	−	1.58806i	0.804148	−	0.594429i	$-0.202622\pi$
$398$		0			0
$399$	−0.654988	+	1.13447i	−0.0327904	+	0.0567947i
$400$		0			0
$401$	16.0059	+	27.7230i	0.799296	+	1.38442i	0.920075	+	0.391742i	$0.128127\pi$
$401$	16.0059	+	27.7230i	0.799296	+	1.38442i	−0.120779	+	0.992679i	$0.538539\pi$
$402$		0			0
$403$	4.89123	+	5.08312i	0.243650	+	0.253208i
$404$		0			0
$405$	−16.7346	−	28.9852i	−0.831549	−	1.44029i
$406$		0			0
$407$	−5.65335	+	9.79190i	−0.280226	+	0.485366i
$408$		0			0
$409$	−15.5390	+	26.9143i	−0.768354	+	1.33083i	0.170101	+	0.985427i	$0.445590\pi$
$409$	−15.5390	+	26.9143i	−0.768354	+	1.33083i	−0.938455	+	0.345401i	$0.887743\pi$
$410$		0			0
$411$	4.24488			0.209385
$412$		0			0
$413$	−21.8828	−	37.9021i	−1.07678	−	1.86504i
$414$		0			0
$415$	−9.71737			−0.477007
$416$		0			0
$417$	0.755119			0.0369784
$418$		0			0
$419$	−7.14652	−	12.3781i	−0.349130	−	0.604711i	0.636965	−	0.770893i	$-0.280190\pi$
$419$	−7.14652	−	12.3781i	−0.349130	−	0.604711i	−0.986095	+	0.166181i	$0.946856\pi$
$420$		0			0
$421$	34.8033			1.69621			0.848104	−	0.529830i	$-0.177744\pi$
$421$	34.8033			1.69621			0.848104	+	0.529830i	$0.177744\pi$
$422$		0			0
$423$	6.85705	−	11.8768i	0.333401	−	0.577468i
$424$		0			0
$425$	−21.7495	+	37.6713i	−1.05501	+	1.82733i
$426$		0			0
$427$	2.70890	+	4.69195i	0.131093	+	0.227059i
$428$		0			0
$429$	0.836931	−	0.207087i	0.0404074	−	0.00999825i
$430$		0			0
$431$	−10.3873	−	17.9913i	−0.500337	−	0.866610i	−1.00000		0.000389670i	$-0.999876\pi$
$431$	−10.3873	−	17.9913i	−0.500337	−	0.866610i	0.499662	−	0.866220i	$-0.333457\pi$
$432$		0			0
$433$	−8.81642	+	15.2705i	−0.423690	+	0.733853i	−0.996297	−	0.0859771i	$-0.972599\pi$
$433$	−8.81642	+	15.2705i	−0.423690	+	0.733853i	0.572607	+	0.819830i	$0.305932\pi$
$434$		0			0
$435$	−1.83818	+	3.18381i	−0.0881338	+	0.152652i
$436$		0			0
$437$	6.99673			0.334699
$438$		0			0
$439$	−7.40219	−	12.8210i	−0.353287	−	0.611912i	0.633536	−	0.773713i	$-0.281603\pi$
$439$	−7.40219	−	12.8210i	−0.353287	−	0.611912i	−0.986823	+	0.161802i	$0.948270\pi$
$440$		0			0
$441$	−36.9201			−1.75810
$442$		0			0
$443$	−9.14884			−0.434675			−0.217337	−	0.976097i	$-0.569737\pi$
$443$	−9.14884			−0.434675			−0.217337	+	0.976097i	$0.569737\pi$
$444$		0			0
$445$	−35.1472	−	60.8767i	−1.66614	−	2.88583i
$446$		0			0
$447$	−3.45882			−0.163596
$448$		0			0
$449$	9.03091	−	15.6420i	0.426195	−	0.738192i	−0.570336	−	0.821411i	$-0.693187\pi$
$449$	9.03091	−	15.6420i	0.426195	−	0.738192i	0.996531	+	0.0832198i	$0.0265204\pi$
$450$		0			0
$451$	2.06238	−	3.57215i	0.0971138	−	0.168206i
$452$		0			0
$453$	−1.38044	−	2.39099i	−0.0648587	−	0.112338i
$454$		0			0
$455$	−61.0101	+	15.0961i	−2.86020	+	0.707716i
$456$		0			0
$457$	0.430782	+	0.746136i	0.0201511	+	0.0349028i	0.875925	−	0.482447i	$-0.160252\pi$
$457$	0.430782	+	0.746136i	0.0201511	+	0.0349028i	−0.855774	+	0.517350i	$0.826919\pi$
$458$		0			0
$459$	2.93078	−	5.07626i	0.136797	−	0.236940i
$460$		0			0
$461$	9.84050	−	17.0442i	0.458318	−	0.793830i	−0.540555	−	0.841309i	$-0.681786\pi$
$461$	9.84050	−	17.0442i	0.458318	−	0.793830i	0.998872	+	0.0474794i	$0.0151189\pi$
$462$		0			0
$463$	25.2085			1.17154			0.585769	−	0.810478i	$-0.300792\pi$
$463$	25.2085			1.17154			0.585769	+	0.810478i	$0.300792\pi$
$464$		0			0
$465$	−0.922310	−	1.59749i	−0.0427711	−	0.0740818i
$466$		0			0
$467$	−17.4315			−0.806632			−0.403316	−	0.915061i	$-0.632142\pi$
$467$	−17.4315			−0.806632			−0.403316	+	0.915061i	$0.632142\pi$
$468$		0			0
$469$	−26.6328			−1.22979
$470$		0			0
$471$	1.03543	+	1.79341i	0.0477099	+	0.0826360i
$472$		0			0
$473$	11.6706			0.536614
$474$		0			0
$475$	−6.53379	+	11.3169i	−0.299791	+	0.519253i
$476$		0			0
$477$	0.787832	−	1.36456i	0.0360723	−	0.0624791i
$478$		0			0
$479$	14.7684	+	25.5796i	0.674785	+	1.16876i	0.976532	+	0.215374i	$0.0690972\pi$
$479$	14.7684	+	25.5796i	0.674785	+	1.16876i	−0.301746	+	0.953388i	$0.597569\pi$
$480$		0			0
$481$	−11.3067	+	39.1676i	−0.515541	+	1.78589i
$482$		0			0
$483$	−2.98469	−	5.16964i	−0.135808	−	0.235227i
$484$		0			0
$485$	−3.85705	+	6.68061i	−0.175140	+	0.303351i
$486$		0			0
$487$	0.703697	−	1.21884i	0.0318875	−	0.0552308i	−0.849641	−	0.527361i	$-0.823181\pi$
$487$	0.703697	−	1.21884i	0.0318875	−	0.0552308i	0.881529	+	0.472130i	$0.156515\pi$
$488$		0			0
$489$	−2.41642			−0.109274
$490$		0			0
$491$	−7.05950	−	12.2274i	−0.318591	−	0.551816i	0.661603	−	0.749854i	$-0.269876\pi$
$491$	−7.05950	−	12.2274i	−0.318591	−	0.551816i	−0.980194	+	0.198038i	$0.936543\pi$
$492$		0			0
$493$	16.0837			0.724375
$494$		0			0
$495$	11.6030			0.521517
$496$		0			0
$497$	27.8291	+	48.2015i	1.24831	+	2.16213i
$498$		0			0
$499$	9.93955			0.444955			0.222478	−	0.974938i	$-0.428586\pi$
$499$	9.93955			0.444955			0.222478	+	0.974938i	$0.428586\pi$
$500$		0			0
$501$	−1.21574	+	2.10571i	−0.0543150	+	0.0940764i
$502$		0			0
$503$	−10.2157	+	17.6942i	−0.455497	+	0.788944i	−0.998717	−	0.0506466i	$-0.983872\pi$
$503$	−10.2157	+	17.6942i	−0.455497	+	0.788944i	0.543220	+	0.839591i	$0.317205\pi$
$504$		0			0
$505$	−8.55555	−	14.8186i	−0.380717	−	0.659421i
$506$		0			0
$507$	2.74992	−	1.44961i	0.122128	−	0.0643793i
$508$		0			0
$509$	9.06307	+	15.6977i	0.401714	+	0.695788i	0.993933	−	0.109989i	$-0.0350814\pi$
$509$	9.06307	+	15.6977i	0.401714	+	0.695788i	−0.592219	+	0.805777i	$0.701748\pi$
$510$		0			0
$511$	23.7141	−	41.0740i	1.04905	−	1.81701i
$512$		0			0
$513$	0.880438	−	1.52496i	0.0388723	−	0.0673288i
$514$		0			0
$515$	−59.5803			−2.62542
$516$		0			0
$517$	2.33009	+	4.03584i	0.102477	+	0.177496i
$518$		0			0
$519$	−2.90258			−0.127409
$520$		0			0
$521$	7.39372			0.323925			0.161962	−	0.986797i	$-0.448218\pi$
$521$	7.39372			0.323925			0.161962	+	0.986797i	$0.448218\pi$
$522$		0			0
$523$	1.30834	+	2.26611i	0.0572098	+	0.0990902i	0.893212	−	0.449636i	$-0.148446\pi$
$523$	1.30834	+	2.26611i	0.0572098	+	0.0990902i	−0.836002	+	0.548726i	$0.815113\pi$
$524$		0			0
$525$	11.1488			0.486575
$526$		0			0
$527$	−4.03504	+	6.98889i	−0.175769	+	0.304441i
$528$		0			0
$529$	−4.44158	+	7.69304i	−0.193112	+	0.334480i
$530$		0			0
$531$	14.5659	+	25.2290i	0.632108	+	1.09484i
$532$		0			0
$533$	4.12476	−	14.2886i	0.178663	−	0.618908i
$534$		0			0
$535$	−14.3187	−	24.8008i	−0.619053	−	1.07223i
$536$		0			0
$537$	0.0177955	−	0.0308228i	0.000767935	−	0.00133010i
$538$		0			0
$539$	6.27292	−	10.8650i	0.270194	−	0.467989i
$540$		0			0
$541$	−18.0859			−0.777574			−0.388787	−	0.921328i	$-0.627106\pi$
$541$	−18.0859			−0.777574			−0.388787	+	0.921328i	$0.627106\pi$
$542$		0			0
$543$	0.488650	+	0.846367i	0.0209700	+	0.0363211i
$544$		0			0
$545$	−68.9546			−2.95369
$546$		0			0
$547$	−8.98057			−0.383981			−0.191991	−	0.981397i	$-0.561494\pi$
$547$	−8.98057			−0.383981			−0.191991	+	0.981397i	$0.561494\pi$
$548$		0			0
$549$	−1.80314	−	3.12313i	−0.0769561	−	0.133292i
$550$		0			0
$551$	4.83173			0.205839
$552$		0			0
$553$	−23.4613	+	40.6362i	−0.997676	+	1.72803i
$554$		0			0
$555$	5.33009	−	9.23200i	0.226250	−	0.391876i
$556$		0			0
$557$	−17.1328	−	29.6750i	−0.725942	−	1.25737i	−0.958585	−	0.284806i	$-0.908071\pi$
$557$	−17.1328	−	29.6750i	−0.725942	−	1.25737i	0.232643	−	0.972562i	$-0.425263\pi$
$558$		0			0
$559$	40.8471	−	10.1070i	1.72765	−	0.427482i
$560$		0			0
$561$	0.493163	+	0.854184i	0.0208214	+	0.0360637i
$562$		0			0
$563$	−15.6791	+	27.1569i	−0.660794	+	1.14453i	0.319614	+	0.947548i	$0.396447\pi$
$563$	−15.6791	+	27.1569i	−0.660794	+	1.14453i	−0.980407	+	0.196980i	$0.936886\pi$
$564$		0			0
$565$	11.0458	−	19.1319i	0.464702	−	0.804887i
$566$		0			0
$567$	37.5289			1.57607
$568$		0			0
$569$	−3.34213	−	5.78874i	−0.140110	−	0.242677i	0.787428	−	0.616406i	$-0.211412\pi$
$569$	−3.34213	−	5.78874i	−0.140110	−	0.242677i	−0.927538	+	0.373730i	$0.878079\pi$
$570$		0			0
$571$	21.1273			0.884148			0.442074	−	0.896979i	$-0.354243\pi$
$571$	21.1273			0.884148			0.442074	+	0.896979i	$0.354243\pi$
$572$		0			0
$573$	3.50232			0.146312
$574$		0			0
$575$	−29.7736	−	51.5694i	−1.24165	−	2.15059i
$576$		0			0
$577$	−31.8252			−1.32490			−0.662450	−	0.749106i	$-0.730483\pi$
$577$	−31.8252			−1.32490			−0.662450	+	0.749106i	$0.730483\pi$
$578$		0			0
$579$	−0.190415	+	0.329808i	−0.00791336	+	0.0137063i
$580$		0			0
$581$	5.44802	−	9.43625i	0.226022	−	0.391482i
$582$		0			0
$583$	0.267713	+	0.463693i	0.0110875	+	0.0192042i
$584$		0			0
$585$	40.6105	−	10.0485i	1.67904	−	0.415454i
$586$		0			0
$587$	20.2713	+	35.1109i	0.836685	+	1.44918i	0.892651	+	0.450749i	$0.148843\pi$
$587$	20.2713	+	35.1109i	0.836685	+	1.44918i	−0.0559656	+	0.998433i	$0.517824\pi$
$588$		0			0
$589$	−1.21217	+	2.09954i	−0.0499465	+	0.0865099i
$590$		0			0
$591$	1.07605	−	1.86378i	0.0442630	−	0.0766657i
$592$		0			0
$593$	−5.79536			−0.237987			−0.118993	−	0.992895i	$-0.537967\pi$
$593$	−5.79536			−0.237987			−0.118993	+	0.992895i	$0.537967\pi$
$594$		0			0
$595$	−35.9503	−	62.2678i	−1.47382	−	2.55273i
$596$		0			0
$597$	3.61917			0.148123
$598$		0			0
$599$	11.4211			0.466652			0.233326	−	0.972399i	$-0.425039\pi$
$599$	11.4211			0.466652			0.233326	+	0.972399i	$0.425039\pi$
$600$		0			0
$601$	8.32558	+	14.4203i	0.339608	+	0.588218i	0.984359	−	0.176175i	$-0.0563724\pi$
$601$	8.32558	+	14.4203i	0.339608	+	0.588218i	−0.644751	+	0.764392i	$0.723039\pi$
$602$		0			0
$603$	17.7278			0.721931
$604$		0			0
$605$	−1.97141	+	3.41458i	−0.0801492	+	0.138823i
$606$		0			0
$607$	−7.61109	+	13.1828i	−0.308925	+	0.535073i	−0.978127	−	0.208007i	$-0.933302\pi$
$607$	−7.61109	+	13.1828i	−0.308925	+	0.535073i	0.669203	+	0.743080i	$0.266636\pi$
$608$		0			0
$609$	−2.06114	−	3.57000i	−0.0835215	−	0.144664i
$610$		0			0
$611$	11.6505	+	12.1075i	0.471328	+	0.489818i
$612$		0			0
$613$	−3.53379	−	6.12071i	−0.142729	−	0.247213i	0.785795	−	0.618487i	$-0.212254\pi$
$613$	−3.53379	−	6.12071i	−0.142729	−	0.247213i	−0.928523	+	0.371274i	$0.878921\pi$
$614$		0			0
$615$	−1.94445	+	3.36789i	−0.0784080	+	0.135807i
$616$		0			0
$617$	16.2862	−	28.2085i	0.655658	−	1.13563i	−0.326071	−	0.945345i	$-0.605725\pi$
$617$	16.2862	−	28.2085i	0.655658	−	1.13563i	0.981729	−	0.190287i	$-0.0609418\pi$
$618$		0			0
$619$	−8.36062			−0.336042			−0.168021	−	0.985783i	$-0.553738\pi$
$619$	−8.36062			−0.336042			−0.168021	+	0.985783i	$0.553738\pi$
$620$		0			0
$621$	4.01204	+	6.94905i	0.160998	+	0.278856i
$622$		0			0
$623$	78.8208			3.15789
$624$		0			0
$625$	33.4854			1.33942
$626$		0			0
$627$	0.148152	+	0.256606i	0.00591661	+	0.0102479i
$628$		0			0
$629$	−46.6375			−1.85956
$630$		0			0
$631$	−11.3977	+	19.7414i	−0.453734	+	0.785891i	−0.998614	−	0.0526230i	$-0.983242\pi$
$631$	−11.3977	+	19.7414i	−0.453734	+	0.785891i	0.544880	+	0.838514i	$0.316575\pi$
$632$		0			0
$633$	0.0337917	−	0.0585290i	0.00134310	−	0.00232632i
$634$		0			0
$635$	−13.9126	−	24.0973i	−0.552105	−	0.956273i
$636$		0			0
$637$	12.5458	−	43.4600i	0.497084	−	1.72195i
$638$		0			0
$639$	−18.5241	−	32.0846i	−0.732801	−	1.26925i
$640$		0			0
$641$	3.45361	−	5.98184i	0.136410	−	0.236268i	−0.789725	−	0.613460i	$-0.789777\pi$
$641$	3.45361	−	5.98184i	0.136410	−	0.236268i	0.926135	+	0.377192i	$0.123110\pi$
$642$		0			0
$643$	−17.7616	+	30.7639i	−0.700448	+	1.21321i	0.267862	+	0.963457i	$0.413683\pi$
$643$	−17.7616	+	30.7639i	−0.700448	+	1.21321i	−0.968309	+	0.249754i	$0.919650\pi$
$644$		0			0
$645$	−11.0033			−0.433253
$646$		0			0
$647$	−11.4737	−	19.8731i	−0.451079	−	0.781292i	0.547374	−	0.836888i	$-0.315627\pi$
$647$	−11.4737	−	19.8731i	−0.451079	−	0.781292i	−0.998453	+	0.0555961i	$0.982294\pi$
$648$		0			0
$649$	−9.89931			−0.388582
$650$		0			0
$651$	2.06837			0.0810656
$652$		0			0
$653$	−4.47429	−	7.74970i	−0.175092	−	0.303269i	0.765101	−	0.643911i	$-0.222689\pi$
$653$	−4.47429	−	7.74970i	−0.175092	−	0.303269i	−0.940193	+	0.340641i	$0.889356\pi$
$654$		0			0
$655$	−34.4660			−1.34670
$656$		0			0
$657$	−15.7850	+	27.3403i	−0.615830	+	1.06665i
$658$		0			0
$659$	−18.8662	+	32.6772i	−0.734923	+	1.27292i	0.219834	+	0.975537i	$0.429448\pi$
$659$	−18.8662	+	32.6772i	−0.734923	+	1.27292i	−0.954757	+	0.297387i	$0.903885\pi$
$660$		0			0
$661$	2.73392	+	4.73529i	0.106337	+	0.184181i	0.914284	−	0.405074i	$-0.132754\pi$
$661$	2.73392	+	4.73529i	0.106337	+	0.184181i	−0.807947	+	0.589256i	$0.799421\pi$
$662$		0			0
$663$	2.46582	+	2.56255i	0.0957644	+	0.0995213i
$664$		0			0
$665$	−10.7999	−	18.7059i	−0.418801	−	0.725385i
$666$		0			0
$667$	−11.0088	+	19.0677i	−0.426261	+	0.738306i
$668$		0			0
$669$	−0.764444	+	1.32406i	−0.0295551	+	0.0511909i
$670$		0			0
$671$	1.22545			0.0473080
$672$		0			0
$673$	23.1884	+	40.1635i	0.893847	+	1.54819i	0.835225	+	0.549908i	$0.185337\pi$
$673$	23.1884	+	40.1635i	0.893847	+	1.54819i	0.0586212	+	0.998280i	$0.481330\pi$
$674$		0			0
$675$	−14.9863			−0.576824
$676$		0			0
$677$	29.4088			1.13027			0.565135	−	0.824998i	$-0.308824\pi$
$677$	29.4088			1.13027			0.565135	+	0.824998i	$0.308824\pi$
$678$		0			0
$679$	−4.32489	−	7.49093i	−0.165974	−	0.287476i
$680$		0			0
$681$	−1.32941			−0.0509430
$682$		0			0
$683$	−21.8074	+	37.7715i	−0.834437	+	1.44529i	0.0600514	+	0.998195i	$0.480874\pi$
$683$	−21.8074	+	37.7715i	−0.834437	+	1.44529i	−0.894488	+	0.447092i	$0.852460\pi$
$684$		0			0
$685$	−34.9962	+	60.6152i	−1.33714	+	2.31599i
$686$		0			0
$687$	−0.560747	−	0.971242i	−0.0213938	−	0.0370552i
$688$		0			0
$689$	1.33857	+	1.39108i	0.0509953	+	0.0529959i
$690$		0			0
$691$	−22.3856	−	38.7731i	−0.851590	−	1.47500i	−0.879773	−	0.475394i	$-0.842305\pi$
$691$	−22.3856	−	38.7731i	−0.851590	−	1.47500i	0.0281830	−	0.999603i	$-0.491028\pi$
$692$		0			0
$693$	−6.50520	+	11.2673i	−0.247112	+	0.428011i
$694$		0			0
$695$	−6.22545	+	10.7828i	−0.236145	+	0.409015i
$696$		0			0
$697$	17.0137			0.644439
$698$		0			0
$699$	−2.23912	−	3.87828i	−0.0846914	−	0.146690i
$700$		0			0
$701$	14.3445			0.541783			0.270891	−	0.962610i	$-0.412682\pi$
$701$	14.3445			0.541783			0.270891	+	0.962610i	$0.412682\pi$
$702$		0			0
$703$	−14.0104			−0.528412
$704$		0			0
$705$	−2.19686	−	3.80507i	−0.0827385	−	0.143307i
$706$		0			0
$707$	19.1866			0.721586
$708$		0			0
$709$	0.927903	−	1.60718i	0.0348481	−	0.0603587i	−0.848075	−	0.529876i	$-0.822239\pi$
$709$	0.927903	−	1.60718i	0.0348481	−	0.0603587i	0.882923	+	0.469517i	$0.155572\pi$
$710$		0			0
$711$	15.6167	−	27.0489i	0.585671	−	1.01441i
$712$		0			0
$713$	−5.52369	−	9.56730i	−0.206864	−	0.358298i
$714$		0			0
$715$	−3.94282	+	13.6583i	−0.147453	+	0.510793i
$716$		0			0
$717$	−0.567583	−	0.983083i	−0.0211968	−	0.0367139i
$718$		0			0
$719$	−9.29467	+	16.0988i	−0.346633	+	0.600385i	−0.985649	−	0.168808i	$-0.946008\pi$
$719$	−9.29467	+	16.0988i	−0.346633	+	0.600385i	0.639016	+	0.769193i	$0.279342\pi$
$720$		0			0
$721$	33.4036	−	57.8567i	1.24401	−	2.15470i
$722$		0			0
$723$	3.07877			0.114501
$724$		0			0
$725$	−20.5607	−	35.6123i	−0.763607	−	1.32261i
$726$		0			0
$727$	12.5732			0.466313			0.233157	−	0.972439i	$-0.425095\pi$
$727$	12.5732			0.466313			0.233157	+	0.972439i	$0.425095\pi$
$728$		0			0
$729$	−23.9611			−0.887450
$730$		0			0
$731$	24.0692	+	41.6891i	0.890232	+	1.54193i
$732$		0			0
$733$	−28.6512			−1.05825			−0.529127	−	0.848542i	$-0.677481\pi$
$733$	−28.6512			−1.05825			−0.529127	+	0.848542i	$0.677481\pi$
$734$		0			0
$735$	−5.91423	+	10.2437i	−0.218150	+	0.377846i
$736$		0			0
$737$	−3.01204	+	5.21700i	−0.110950	+	0.192171i
$738$		0			0
$739$	−3.43762	−	5.95413i	−0.126455	−	0.219026i	0.795846	−	0.605499i	$-0.207027\pi$
$739$	−3.43762	−	5.95413i	−0.126455	−	0.219026i	−0.922301	+	0.386473i	$0.873693\pi$
$740$		0			0
$741$	0.740758	+	0.769818i	0.0272124	+	0.0282800i
$742$		0			0
$743$	14.3788	+	24.9048i	0.527507	+	0.913669i	0.999486	+	0.0320593i	$0.0102065\pi$
$743$	14.3788	+	24.9048i	0.527507	+	0.913669i	−0.471979	+	0.881610i	$0.656460\pi$
$744$		0			0
$745$	28.5156	−	49.3905i	1.04473	−	1.80953i
$746$		0			0
$747$	−3.62640	+	6.28111i	−0.132683	+	0.229814i
$748$		0			0
$749$	32.1111			1.17331
$750$		0			0
$751$	15.0377	+	26.0461i	0.548735	+	0.950437i	0.998362	+	0.0572206i	$0.0182238\pi$
$751$	15.0377	+	26.0461i	0.548735	+	0.950437i	−0.449626	+	0.893217i	$0.648443\pi$
$752$		0			0
$753$	−0.266469			−0.00971068
$754$		0			0
$755$	45.5231			1.65676
$756$		0			0
$757$	7.05718	+	12.2234i	0.256498	+	0.444267i	0.965301	−	0.261139i	$-0.0840981\pi$
$757$	7.05718	+	12.2234i	0.256498	+	0.444267i	−0.708804	+	0.705406i	$0.750765\pi$
$758$		0			0
$759$	−1.35021			−0.0490096
$760$		0			0
$761$	5.35705	−	9.27868i	0.194193	−	0.336352i	−0.752443	−	0.658658i	$-0.771125\pi$
$761$	5.35705	−	9.27868i	0.194193	−	0.336352i	0.946636	+	0.322306i	$0.104458\pi$
$762$		0			0
$763$	38.6592	−	66.9598i	1.39956	−	2.42411i
$764$		0			0
$765$	23.9298	+	41.4477i	0.865185	+	1.49854i
$766$		0			0
$767$	−34.6476	+	8.57306i	−1.25105	+	0.309555i
$768$		0			0
$769$	−4.56363	−	7.90443i	−0.164569	−	0.285041i	0.771933	−	0.635703i	$-0.219290\pi$
$769$	−4.56363	−	7.90443i	−0.164569	−	0.285041i	−0.936502	+	0.350662i	$0.885957\pi$
$770$		0			0
$771$	0.882761	−	1.52899i	0.0317919	−	0.0550651i
$772$		0			0
$773$	−14.6814	+	25.4289i	−0.528053	+	0.914614i	0.471412	+	0.881913i	$0.343744\pi$
$773$	−14.6814	+	25.4289i	−0.528053	+	0.914614i	−0.999465	+	0.0327014i	$0.989589\pi$
$774$		0			0
$775$	20.6328			0.741154
$776$		0			0
$777$	5.97661	+	10.3518i	0.214410	+	0.371369i
$778$		0			0
$779$	5.11109			0.183124
$780$		0			0
$781$	12.5893			0.450482
$782$		0			0
$783$	2.77059	+	4.79881i	0.0990129	+	0.171495i
$784$		0			0
$785$	−34.1456			−1.21871
$786$		0			0
$787$	3.26320	−	5.65203i	0.116321	−	0.201473i	−0.801986	−	0.597342i	$-0.796223\pi$
$787$	3.26320	−	5.65203i	0.116321	−	0.201473i	0.918307	+	0.395869i	$0.129557\pi$
$788$		0			0
$789$	3.71613	−	6.43652i	0.132298	−	0.229146i
$790$		0			0
$791$	12.3856	+	21.4526i	0.440383	+	0.762765i
$792$		0			0
$793$	4.28908	−	1.06127i	0.152310	−	0.0376868i
$794$		0			0
$795$	−0.252405	−	0.437179i	−0.00895190	−	0.0155051i
$796$		0			0
$797$	−14.6569	+	25.3865i	−0.519175	+	0.899237i	0.480577	+	0.876953i	$0.340427\pi$
$797$	−14.6569	+	25.3865i	−0.519175	+	0.899237i	−0.999752	+	0.0222845i	$0.992906\pi$
$798$		0			0
$799$	−9.61109	+	16.6469i	−0.340016	+	0.588925i
$800$		0			0
$801$	−52.4660			−1.85379
$802$		0			0
$803$	−5.36389	−	9.29052i	−0.189287	−	0.327855i
$804$		0			0
$805$	98.4271			3.46910
$806$		0			0
$807$	−2.82846			−0.0995665
$808$		0			0
$809$	−0.642950	−	1.11362i	−0.0226049	−	0.0391529i	0.854502	−	0.519449i	$-0.173863\pi$
$809$	−0.642950	−	1.11362i	−0.0226049	−	0.0391529i	−0.877107	+	0.480296i	$0.840529\pi$
$810$		0			0
$811$	7.88426			0.276854			0.138427	−	0.990373i	$-0.455795\pi$
$811$	7.88426			0.276854			0.138427	+	0.990373i	$0.455795\pi$
$812$		0			0
$813$	−1.61629	+	2.79950i	−0.0566858	+	0.0981828i
$814$		0			0
$815$	19.9218	−	34.5055i	0.697829	−	1.20867i
$816$		0			0
$817$	7.23065	+	12.5239i	0.252968	+	0.438154i
$818$		0			0
$819$	−13.0104	+	45.0694i	−0.454620	+	1.57485i
$820$		0			0
$821$	−19.7821	−	34.2636i	−0.690399	−	1.19581i	−0.971707	−	0.236189i	$-0.924102\pi$
$821$	−19.7821	−	34.2636i	−0.690399	−	1.19581i	0.281308	−	0.959618i	$-0.409232\pi$
$822$		0			0
$823$	15.2488	−	26.4118i	0.531541	−	0.920656i	−0.467781	−	0.883844i	$-0.654946\pi$
$823$	15.2488	−	26.4118i	0.531541	−	0.920656i	0.999322	−	0.0368118i	$-0.0117202\pi$
$824$		0			0
$825$	1.26088	−	2.18390i	0.0438981	−	0.0760337i
$826$		0			0
$827$	37.9248			1.31877			0.659387	−	0.751804i	$-0.270816\pi$
$827$	37.9248			1.31877			0.659387	+	0.751804i	$0.270816\pi$
$828$		0			0
$829$	9.27455	+	16.0640i	0.322118	+	0.557925i	0.980925	−	0.194387i	$-0.0622717\pi$
$829$	9.27455	+	16.0640i	0.322118	+	0.557925i	−0.658806	+	0.752312i	$0.728938\pi$
$830$		0			0
$831$	−5.48865			−0.190399
$832$		0			0
$833$	51.7486			1.79298
$834$		0			0
$835$	−20.0458	−	34.7204i	−0.693715	−	1.20155i
$836$		0			0
$837$	−2.78031			−0.0961015
$838$		0			0
$839$	−16.8599	+	29.2023i	−0.582069	+	1.00817i	0.413164	+	0.910656i	$0.364423\pi$
$839$	−16.8599	+	29.2023i	−0.582069	+	1.00817i	−0.995234	+	0.0975173i	$0.968910\pi$
$840$		0			0
$841$	6.89768	−	11.9471i	0.237851	−	0.411970i
$842$		0			0
$843$	0.884952	+	1.53278i	0.0304794	+	0.0527918i
$844$		0			0
$845$	−1.97141	+	51.2187i	−0.0678186	+	1.76198i
$846$		0			0
$847$	−2.21053	−	3.82876i	−0.0759548	−	0.131558i
$848$		0			0
$849$	3.48345	−	6.03351i	0.119552	−	0.207070i
$850$		0			0
$851$	31.9218	−	55.2901i	1.09426	−	1.89532i
$852$		0			0
$853$	−1.07223			−0.0367124			−0.0183562	−	0.999832i	$-0.505843\pi$
$853$	−1.07223			−0.0367124			−0.0183562	+	0.999832i	$0.505843\pi$
$854$		0			0
$855$	7.18878	+	12.4513i	0.245851	+	0.425827i
$856$		0			0
$857$	31.0837			1.06180			0.530900	−	0.847434i	$-0.321854\pi$
$857$	31.0837			1.06180			0.530900	+	0.847434i	$0.321854\pi$
$858$		0			0
$859$	−49.6512			−1.69408			−0.847038	−	0.531532i	$-0.821616\pi$
$859$	−49.6512			−1.69408			−0.847038	+	0.531532i	$0.821616\pi$
$860$		0			0
$861$	−2.18031	−	3.77641i	−0.0743047	−	0.128700i
$862$		0			0
$863$	41.5724			1.41514			0.707570	−	0.706643i	$-0.249791\pi$
$863$	41.5724			1.41514			0.707570	+	0.706643i	$0.249791\pi$
$864$		0			0
$865$	23.9298	−	41.4477i	0.813639	−	1.40926i
$866$		0			0
$867$	−0.00163477	+	0.00283151i	−5.55198e−5	+	9.61631e-5i
$868$		0			0
$869$	5.30671	+	9.19149i	0.180018	+	0.311800i
$870$		0			0
$871$	−6.02408	+	20.8680i	−0.204118	+	0.707086i
$872$		0			0
$873$	2.87880	+	4.98623i	0.0974327	+	0.168758i
$874$		0			0
$875$	−48.3360	+	83.7204i	−1.63405	+	2.83027i
$876$		0			0
$877$	−12.5699	+	21.7717i	−0.424456	+	0.735179i	−0.996369	−	0.0851351i	$-0.972868\pi$
$877$	−12.5699	+	21.7717i	−0.424456	+	0.735179i	0.571914	+	0.820314i	$0.306201\pi$
$878$		0			0
$879$	0.450900			0.0152085
$880$		0			0
$881$	27.1911	+	47.0964i	0.916092	+	1.58672i	0.805295	+	0.592874i	$0.202007\pi$
$881$	27.1911	+	47.0964i	0.916092	+	1.58672i	0.110796	+	0.993843i	$0.464660\pi$
$882$		0			0
$883$	5.38907			0.181357			0.0906784	−	0.995880i	$-0.471096\pi$
$883$	5.38907			0.181357			0.0906784	+	0.995880i	$0.471096\pi$
$884$		0			0
$885$	9.33327			0.313734
$886$		0			0
$887$	12.7134	+	22.0203i	0.426875	+	0.739368i	0.996593	−	0.0824712i	$-0.0262812\pi$
$887$	12.7134	+	22.0203i	0.426875	+	0.739368i	−0.569719	+	0.821840i	$0.692948\pi$
$888$		0			0
$889$	31.2003			1.04642
$890$		0			0
$891$	4.24433	−	7.35139i	0.142190	−	0.246281i
$892$		0			0
$893$	−2.88727	+	5.00091i	−0.0966190	+	0.167349i
$894$		0			0
$895$	0.293425	+	0.508226i	0.00980810	+	0.0169881i
$896$		0			0
$897$	−4.72575	+	1.16932i	−0.157788	+	0.0390424i
$898$		0			0
$899$	−3.81449	−	6.60689i	−0.127220	−	0.220352i
$900$		0			0
$901$	−1.10425	+	1.91262i	−0.0367880	+	0.0637187i
$902$		0			0
$903$	6.16896	−	10.6849i	0.205290	−	0.355573i
$904$		0			0
$905$	−16.1144			−0.535659
$906$		0			0
$907$	−2.39248	−	4.14389i	−0.0794409	−	0.137596i	0.823568	−	0.567218i	$-0.191980\pi$
$907$	−2.39248	−	4.14389i	−0.0794409	−	0.137596i	−0.903009	+	0.429622i	$0.858647\pi$
$908$		0			0
$909$	−12.7713			−0.423597
$910$		0			0
$911$	−5.44187			−0.180297			−0.0901487	−	0.995928i	$-0.528734\pi$
$911$	−5.44187			−0.180297			−0.0901487	+	0.995928i	$0.528734\pi$
$912$		0			0
$913$	−1.23229	−	2.13438i	−0.0407827	−	0.0706378i
$914$		0			0
$915$	−1.15538			−0.0381957
$916$		0			0
$917$	19.3233	−	33.4689i	0.638110	−	1.10524i
$918$		0			0
$919$	19.8937	−	34.4569i	0.656233	−	1.13663i	−0.325350	−	0.945594i	$-0.605482\pi$
$919$	19.8937	−	34.4569i	0.656233	−	1.13663i	0.981583	−	0.191036i	$-0.0611846\pi$
$920$		0			0
$921$	−3.08289	−	5.33972i	−0.101585	−	0.175950i
$922$		0			0
$923$	44.0627	−	10.9027i	1.45034	−	0.358866i
$924$		0			0
$925$	59.6193	+	103.264i	1.96027	+	3.39529i
$926$		0			0
$927$	−22.2346	+	38.5115i	−0.730280	+	1.26488i
$928$		0			0
$929$	27.5397	−	47.7001i	0.903548	−	1.56499i	0.0806927	−	0.996739i	$-0.474287\pi$
$929$	27.5397	−	47.7001i	0.903548	−	1.56499i	0.822855	−	0.568251i	$-0.192380\pi$
$930$		0			0
$931$	15.5458			0.509494
$932$		0			0
$933$	0.326528	+	0.565563i	0.0106900	+	0.0185157i
$934$		0			0
$935$	−16.2632			−0.531864
$936$		0			0
$937$	7.94609			0.259587			0.129794	−	0.991541i	$-0.458568\pi$
$937$	7.94609			0.259587			0.129794	+	0.991541i	$0.458568\pi$
$938$		0			0
$939$	1.53379	+	2.65661i	0.0500534	+	0.0866950i
$940$		0			0
$941$	−32.3365			−1.05414			−0.527071	−	0.849822i	$-0.676710\pi$
$941$	−32.3365			−1.05414			−0.527071	+	0.849822i	$0.676710\pi$
$942$		0			0
$943$	−11.6453	+	20.1702i	−0.379222	+	0.656832i
$944$		0			0
$945$	12.3856	−	21.4526i	0.402905	−	0.697852i
$946$		0			0
$947$	−0.0578683	−	0.100231i	−0.00188047	−	0.00325706i	0.865084	−	0.501628i	$-0.167265\pi$
$947$	−0.0578683	−	0.100231i	−0.00188047	−	0.00325706i	−0.866964	+	0.498371i	$0.833932\pi$
$948$		0			0
$949$	−26.8194	−	27.8716i	−0.870596	−	0.904750i
$950$		0			0
$951$	0.638992	+	1.10677i	0.0207207	+	0.0358894i
$952$		0			0
$953$	14.0253	−	24.2926i	0.454325	−	0.786913i	−0.544324	−	0.838875i	$-0.683214\pi$
$953$	14.0253	−	24.2926i	0.454325	−	0.786913i	0.998649	+	0.0519614i	$0.0165473\pi$
$954$		0			0
$955$	−28.8743	+	50.0117i	−0.934350	+	1.61834i
$956$		0			0
$957$	−0.932417			−0.0301407
$958$		0			0
$959$	−39.2411	−	67.9675i	−1.26716	−	2.19479i
$960$		0			0
$961$	−27.1721			−0.876520
$962$		0			0
$963$	−21.3743			−0.688777
$964$		0			0
$965$	−3.13968	−	5.43809i	−0.101070	−	0.175058i
$966$		0			0
$967$	−47.5095			−1.52780			−0.763901	−	0.645334i	$-0.776718\pi$
$967$	−47.5095			−1.52780			−0.763901	+	0.645334i	$0.776718\pi$
$968$		0			0
$969$	−0.611090	+	1.05844i	−0.0196310	+	0.0340020i
$970$		0			0
$971$	15.2947	−	26.4911i	0.490829	−	0.850141i	−0.509115	−	0.860699i	$-0.670027\pi$
$971$	15.2947	−	26.4911i	0.490829	−	0.850141i	0.999944	+	0.0105573i	$0.00336055\pi$
$972$		0			0
$973$	−6.98057	−	12.0907i	−0.223787	−	0.387610i
$974$		0			0
$975$	2.52175	−	8.73561i	0.0807607	−	0.279763i
$976$		0			0
$977$	7.17619	+	12.4295i	0.229587	+	0.397656i	0.957686	−	0.287816i	$-0.0929293\pi$
$977$	7.17619	+	12.4295i	0.229587	+	0.397656i	−0.728099	+	0.685472i	$0.759596\pi$
$978$		0			0
$979$	8.91423	−	15.4399i	0.284900	−	0.493461i
$980$		0			0
$981$	−25.7330	+	44.5708i	−0.821591	+	1.42304i
$982$		0			0
$983$	54.8643			1.74990			0.874950	−	0.484213i	$-0.160894\pi$
$983$	54.8643			1.74990			0.874950	+	0.484213i	$0.160894\pi$
$984$		0			0
$985$	17.7427	+	30.7312i	0.565329	+	0.979179i
$986$		0			0
$987$	4.92666			0.156817
$988$		0			0
$989$	−65.8982			−2.09544
$990$		0			0
$991$	9.00589	+	15.5987i	0.286082	+	0.495508i	0.972871	−	0.231349i	$-0.0743138\pi$
$991$	9.00589	+	15.5987i	0.286082	+	0.495508i	−0.686789	+	0.726857i	$0.740981\pi$
$992$		0			0
$993$	−0.249527			−0.00791849
$994$		0			0
$995$	−29.8376	+	51.6803i	−0.945916	+	1.63837i
$996$		0			0
$997$	−5.03379	+	8.71878i	−0.159422	+	0.276127i	−0.934660	−	0.355542i	$-0.884296\pi$
$997$	−5.03379	+	8.71878i	−0.159422	+	0.276127i	0.775239	+	0.631669i	$0.217630\pi$
$998$		0			0
$999$	−8.03379	−	13.9149i	−0.254178	−	0.440249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.b.133.2	✓	6
13.3	even	3		7436.2.a.n.1.2		3
13.9	even	3	inner	572.2.i.b.529.2	yes	6
13.10	even	6		7436.2.a.m.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.b.133.2	✓	6	1.1	even	1	trivial
572.2.i.b.529.2	yes	6	13.9	even	3	inner
7436.2.a.m.1.2		3	13.10	even	6
7436.2.a.n.1.2		3	13.3	even	3

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.119562 - 0.207087i) q^{3} +3.94282 q^{5} +(-2.21053 + 3.82876i) q^{7} +(1.47141 - 2.54856i) q^{9} +O(q^{10})\)	\(q+(-0.119562 - 0.207087i) q^{3} +3.94282 q^{5} +(-2.21053 + 3.82876i) q^{7} +(1.47141 - 2.54856i) q^{9} +(0.500000 + 0.866025i) q^{11} +(2.50000 + 2.59808i) q^{13} +(-0.471410 - 0.816506i) q^{15} +(-2.06238 + 3.57215i) q^{17} +(-0.619562 + 1.07311i) q^{19} +1.05718 q^{21} +(-2.82326 - 4.89003i) q^{23} +10.5458 q^{25} -1.42107 q^{27} +(-1.94966 - 3.37690i) q^{29} +1.95649 q^{31} +(0.119562 - 0.207087i) q^{33} +(-8.71574 + 15.0961i) q^{35} +(5.65335 + 9.79190i) q^{37} +(0.239123 - 0.828347i) q^{39} +(-2.06238 - 3.57215i) q^{41} +(5.83530 - 10.1070i) q^{43} +(5.80150 - 10.0485i) q^{45} +4.66019 q^{47} +(-6.27292 - 10.8650i) q^{49} +0.986327 q^{51} +0.535426 q^{53} +(1.97141 + 3.41458i) q^{55} +0.296303 q^{57} +(-4.94966 + 8.57306i) q^{59} +(0.612725 - 1.06127i) q^{61} +(6.50520 + 11.2673i) q^{63} +(9.85705 + 10.2437i) q^{65} +(3.01204 + 5.21700i) q^{67} +(-0.675107 + 1.16932i) q^{69} +(6.29467 - 10.9027i) q^{71} -10.7278 q^{73} +(-1.26088 - 2.18390i) q^{75} -4.42107 q^{77} +10.6134 q^{79} +(-4.24433 - 7.35139i) q^{81} -2.46457 q^{83} +(-8.13160 + 14.0843i) q^{85} +(-0.466208 + 0.807496i) q^{87} +(-8.91423 - 15.4399i) q^{89} +(-15.4737 + 3.82876i) q^{91} +(-0.233922 - 0.405164i) q^{93} +(-2.44282 + 4.23109i) q^{95} +(-0.978247 + 1.69437i) q^{97} +2.94282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 6 q^{5} - 5 q^{7}+O(q^{10}) \) 6 * q - q^3 + 6 * q^5 - 5 * q^7	\( 6 q - q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{11} + 15 q^{13} + 6 q^{15} + 5 q^{17} - 4 q^{19} + 24 q^{21} + q^{23} + 12 q^{25} + 8 q^{27} - 4 q^{29} + 14 q^{31} + q^{33} - 9 q^{35} + 8 q^{37} + 2 q^{39} + 5 q^{41} - 8 q^{43} + 18 q^{45} + 12 q^{47} - 12 q^{49} - 14 q^{51} + 22 q^{53} + 3 q^{55} + 20 q^{57} - 22 q^{59} - 6 q^{61} + 4 q^{63} + 15 q^{65} - 7 q^{67} + 23 q^{69} + 11 q^{71} + 4 q^{73} - 7 q^{75} - 10 q^{77} - 40 q^{79} + 9 q^{81} + 4 q^{83} - 24 q^{85} - 29 q^{87} - 27 q^{89} - 35 q^{91} - 37 q^{93} + 3 q^{95} - 7 q^{97}+O(q^{100}) \) 6 * q - q^3 + 6 * q^5 - 5 * q^7 + 3 * q^11 + 15 * q^13 + 6 * q^15 + 5 * q^17 - 4 * q^19 + 24 * q^21 + q^23 + 12 * q^25 + 8 * q^27 - 4 * q^29 + 14 * q^31 + q^33 - 9 * q^35 + 8 * q^37 + 2 * q^39 + 5 * q^41 - 8 * q^43 + 18 * q^45 + 12 * q^47 - 12 * q^49 - 14 * q^51 + 22 * q^53 + 3 * q^55 + 20 * q^57 - 22 * q^59 - 6 * q^61 + 4 * q^63 + 15 * q^65 - 7 * q^67 + 23 * q^69 + 11 * q^71 + 4 * q^73 - 7 * q^75 - 10 * q^77 - 40 * q^79 + 9 * q^81 + 4 * q^83 - 24 * q^85 - 29 * q^87 - 27 * q^89 - 35 * q^91 - 37 * q^93 + 3 * q^95 - 7 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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