LMFDB - Embedded newform 576.3.q.j.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(65,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("576.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19269881856.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 $ x^8 - 2x^7 + 15x^6 - 2x^5 + 133x^4 - 84x^3 + 276x^2 + 144*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$-0.331167 + 0.573598i$ of defining polynomial
Character	$\chi$	$=$	576.65
Dual form			576.3.q.j.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.668833 - 2.92449i) q^{3} +(0.0440114 - 0.0254100i) q^{5} +(-4.52944 + 7.84521i) q^{7} +(-8.10532 - 3.91200i) q^{9} +O(q^{10})$	\(q+(0.668833 - 2.92449i) q^{3} +(0.0440114 - 0.0254100i) q^{5} +(-4.52944 + 7.84521i) q^{7} +(-8.10532 - 3.91200i) q^{9} +(3.29117 + 1.90016i) q^{11} +(-0.216902 - 0.375686i) q^{13} +(-0.0448751 - 0.145706i) q^{15} +26.2355i q^{17} +34.2225 q^{19} +(19.9138 + 18.4934i) q^{21} +(29.9930 - 17.3164i) q^{23} +(-12.4987 + 21.6484i) q^{25} +(-16.8617 + 21.0875i) q^{27} +(-14.0316 - 8.10114i) q^{29} +(17.1675 + 29.7350i) q^{31} +(7.75825 - 8.35413i) q^{33} +0.460372i q^{35} -29.2761 q^{37} +(-1.24376 + 0.383058i) q^{39} +(48.7026 - 28.1185i) q^{41} +(-3.94539 + 6.83362i) q^{43} +(-0.456130 + 0.0337838i) q^{45} +(33.4489 + 19.3117i) q^{47} +(-16.5316 - 28.6335i) q^{49} +(76.7256 + 17.5472i) q^{51} +50.5273i q^{53} +0.193132 q^{55} +(22.8891 - 100.083i) q^{57} +(-8.54743 + 4.93486i) q^{59} +(36.5718 - 63.3442i) q^{61} +(67.4030 - 45.8689i) q^{63} +(-0.0190923 - 0.0110230i) q^{65} +(-12.6797 - 21.9618i) q^{67} +(-30.5815 - 99.2960i) q^{69} +97.8262i q^{71} -77.0599 q^{73} +(54.9511 + 51.0316i) q^{75} +(-29.8143 + 17.2133i) q^{77} +(42.1389 - 72.9868i) q^{79} +(50.3926 + 63.4160i) q^{81} +(40.6763 + 23.4845i) q^{83} +(0.666644 + 1.15466i) q^{85} +(-33.0765 + 35.6170i) q^{87} +108.587i q^{89} +3.92978 q^{91} +(98.4420 - 30.3185i) q^{93} +(1.50618 - 0.869593i) q^{95} +(-32.4021 + 56.1221i) q^{97} +(-19.2426 - 28.2765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{3} + 6 q^{5} - 6 q^{7} - 22 q^{9}+O(q^{10}) $ 8 * q + 10 * q^3 + 6 * q^5 - 6 * q^7 - 22 * q^9	$ 8 q + 10 q^{3} + 6 q^{5} - 6 q^{7} - 22 q^{9} + 36 q^{11} - 14 q^{13} - 10 q^{15} + 4 q^{19} + 54 q^{21} + 102 q^{23} + 10 q^{25} - 20 q^{27} + 114 q^{29} + 50 q^{31} - 104 q^{33} - 120 q^{37} - 82 q^{39} + 264 q^{41} - 28 q^{43} - 206 q^{45} - 150 q^{47} + 94 q^{49} + 170 q^{51} + 244 q^{55} - 178 q^{57} - 108 q^{59} - 14 q^{61} + 210 q^{63} - 198 q^{65} - 20 q^{67} + 14 q^{69} - 76 q^{73} + 326 q^{75} - 66 q^{77} - 26 q^{79} + 194 q^{81} + 246 q^{83} + 224 q^{85} + 18 q^{87} + 108 q^{91} + 130 q^{93} + 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) $ 8 * q + 10 * q^3 + 6 * q^5 - 6 * q^7 - 22 * q^9 + 36 * q^11 - 14 * q^13 - 10 * q^15 + 4 * q^19 + 54 * q^21 + 102 * q^23 + 10 * q^25 - 20 * q^27 + 114 * q^29 + 50 * q^31 - 104 * q^33 - 120 * q^37 - 82 * q^39 + 264 * q^41 - 28 * q^43 - 206 * q^45 - 150 * q^47 + 94 * q^49 + 170 * q^51 + 244 * q^55 - 178 * q^57 - 108 * q^59 - 14 * q^61 + 210 * q^63 - 198 * q^65 - 20 * q^67 + 14 * q^69 - 76 * q^73 + 326 * q^75 - 66 * q^77 - 26 * q^79 + 194 * q^81 + 246 * q^83 + 224 * q^85 + 18 * q^87 + 108 * q^91 + 130 * q^93 + 456 * q^95 - 236 * q^97 - 634 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.668833	−	2.92449i	0.222944	−	0.974831i
$3$	0.668833	−	2.92449i	0.222944	−	0.974831i
$4$		0			0
$5$	0.0440114	−	0.0254100i	0.00880228	−	0.00508200i	−0.495592	−	0.868555i	$-0.665049\pi$
$5$	0.0440114	−	0.0254100i	0.00880228	−	0.00508200i	0.504395	+	0.863473i	$0.331716\pi$
$6$		0			0
$7$	−4.52944	+	7.84521i	−0.647062	+	1.12074i	0.336759	+	0.941591i	$0.390669\pi$
$7$	−4.52944	+	7.84521i	−0.647062	+	1.12074i	−0.983821	+	0.179154i	$0.942664\pi$
$8$		0			0
$9$	−8.10532	−	3.91200i	−0.900592	−	0.434666i
$10$		0			0
$11$	3.29117	+	1.90016i	0.299198	+	0.172742i	0.642082	−	0.766636i	$-0.278071\pi$
$11$	3.29117	+	1.90016i	0.299198	+	0.172742i	−0.342885	+	0.939377i	$0.611404\pi$
$12$		0			0
$13$	−0.216902	−	0.375686i	−0.0166848	−	0.0288989i	0.857562	−	0.514380i	$-0.171978\pi$
$13$	−0.216902	−	0.375686i	−0.0166848	−	0.0288989i	−0.874247	+	0.485481i	$0.838645\pi$
$14$		0			0
$15$	−0.0448751	−	0.145706i	−0.00299167	−	0.00971373i
$16$		0			0
$17$			26.2355i			1.54327i	0.636068	+	0.771633i	$0.280560\pi$
$17$			26.2355i			1.54327i	−0.636068	+	0.771633i	$0.719440\pi$
$18$		0			0
$19$	34.2225			1.80118			0.900592	−	0.434666i	$-0.143133\pi$
$19$	34.2225			1.80118			0.900592	+	0.434666i	$0.143133\pi$
$20$		0			0
$21$	19.9138	+	18.4934i	0.948278	+	0.880640i
$22$		0			0
$23$	29.9930	−	17.3164i	1.30404	−	0.752889i	0.322947	−	0.946417i	$-0.395326\pi$
$23$	29.9930	−	17.3164i	1.30404	−	0.752889i	0.981095	+	0.193528i	$0.0619931\pi$
$24$		0			0
$25$	−12.4987	+	21.6484i	−0.499948	+	0.865936i
$26$		0			0
$27$	−16.8617	+	21.0875i	−0.624508	+	0.781018i
$28$		0			0
$29$	−14.0316	−	8.10114i	−0.483848	−	0.279350i	0.238171	−	0.971223i	$-0.423452\pi$
$29$	−14.0316	−	8.10114i	−0.483848	−	0.279350i	−0.722019	+	0.691874i	$0.756786\pi$
$30$		0			0
$31$	17.1675	+	29.7350i	0.553790	+	0.959193i	0.997997	+	0.0632685i	$0.0201524\pi$
$31$	17.1675	+	29.7350i	0.553790	+	0.959193i	−0.444206	+	0.895925i	$0.646514\pi$
$32$		0			0
$33$	7.75825	−	8.35413i	0.235099	−	0.253155i
$34$		0			0
$35$			0.460372i			0.0131535i
$36$		0			0
$37$	−29.2761			−0.791247			−0.395623	−	0.918413i	$-0.629471\pi$
$37$	−29.2761			−0.791247			−0.395623	+	0.918413i	$0.629471\pi$
$38$		0			0
$39$	−1.24376	+	0.383058i	−0.0318913	+	0.00982200i
$40$		0			0
$41$	48.7026	−	28.1185i	1.18787	−	0.685816i	0.230047	−	0.973180i	$-0.426112\pi$
$41$	48.7026	−	28.1185i	1.18787	−	0.685816i	0.957822	+	0.287363i	$0.0927787\pi$
$42$		0			0
$43$	−3.94539	+	6.83362i	−0.0917533	+	0.158921i	−0.908249	−	0.418430i	$-0.862580\pi$
$43$	−3.94539	+	6.83362i	−0.0917533	+	0.158921i	0.816496	+	0.577352i	$0.195914\pi$
$44$		0			0
$45$	−0.456130	+	0.0337838i	−0.0101362	+	0.000750752i
$46$		0			0
$47$	33.4489	+	19.3117i	0.711678	+	0.410887i	0.811682	−	0.584100i	$-0.198552\pi$
$47$	33.4489	+	19.3117i	0.711678	+	0.410887i	−0.100004	+	0.994987i	$0.531886\pi$
$48$		0			0
$49$	−16.5316	−	28.6335i	−0.337379	−	0.584358i
$50$		0			0
$51$	76.7256	+	17.5472i	1.50442	+	0.344062i
$52$		0			0
$53$			50.5273i			0.953344i	0.879081	+	0.476672i	$0.158157\pi$
$53$			50.5273i			0.953344i	−0.879081	+	0.476672i	$0.841843\pi$
$54$		0			0
$55$	0.193132			0.00351149
$56$		0			0
$57$	22.8891	−	100.083i	0.401564	−	1.75585i
$58$		0			0
$59$	−8.54743	+	4.93486i	−0.144872	+	0.0836417i	−0.570684	−	0.821170i	$-0.693322\pi$
$59$	−8.54743	+	4.93486i	−0.144872	+	0.0836417i	0.425812	+	0.904812i	$0.359988\pi$
$60$		0			0
$61$	36.5718	−	63.3442i	0.599537	−	1.03843i	−0.393352	−	0.919388i	$-0.628685\pi$
$61$	36.5718	−	63.3442i	0.599537	−	1.03843i	0.992889	−	0.119041i	$-0.0379821\pi$
$62$		0			0
$63$	67.4030	−	45.8689i	1.06989	−	0.728077i
$64$		0			0
$65$	−0.0190923	−	0.0110230i	−0.000293728	−	0.000169584i
$66$		0			0
$67$	−12.6797	−	21.9618i	−0.189249	−	0.327789i	0.755751	−	0.654859i	$-0.227272\pi$
$67$	−12.6797	−	21.9618i	−0.189249	−	0.327789i	−0.945000	+	0.327070i	$0.893939\pi$
$68$		0			0
$69$	−30.5815	−	99.2960i	−0.443211	−	1.43907i
$70$		0			0
$71$			97.8262i			1.37783i	0.724840	+	0.688917i	$0.241914\pi$
$71$			97.8262i			1.37783i	−0.724840	+	0.688917i	$0.758086\pi$
$72$		0			0
$73$	−77.0599			−1.05561			−0.527807	−	0.849364i	$-0.676986\pi$
$73$	−77.0599			−1.05561			−0.527807	+	0.849364i	$0.676986\pi$
$74$		0			0
$75$	54.9511	+	51.0316i	0.732681	+	0.680421i
$76$		0			0
$77$	−29.8143	+	17.2133i	−0.387199	+	0.223549i
$78$		0			0
$79$	42.1389	−	72.9868i	0.533404	−	0.923883i	−0.465835	−	0.884872i	$-0.654246\pi$
$79$	42.1389	−	72.9868i	0.533404	−	0.923883i	0.999239	−	0.0390112i	$-0.0124208\pi$
$80$		0			0
$81$	50.3926	+	63.4160i	0.622131	+	0.782913i
$82$		0			0
$83$	40.6763	+	23.4845i	0.490076	+	0.282946i	0.724606	−	0.689163i	$-0.242022\pi$
$83$	40.6763	+	23.4845i	0.490076	+	0.282946i	−0.234530	+	0.972109i	$0.575355\pi$
$84$		0			0
$85$	0.666644	+	1.15466i	0.00784287	+	0.0135843i
$86$		0			0
$87$	−33.0765	+	35.6170i	−0.380190	+	0.409390i
$88$		0			0
$89$			108.587i			1.22008i	0.792371	+	0.610039i	$0.208846\pi$
$89$			108.587i			1.22008i	−0.792371	+	0.610039i	$0.791154\pi$
$90$		0			0
$91$	3.92978			0.0431844
$92$		0			0
$93$	98.4420	−	30.3185i	1.05852	−	0.326005i
$94$		0			0
$95$	1.50618	−	0.869593i	0.0158545	−	0.00915361i
$96$		0			0
$97$	−32.4021	+	56.1221i	−0.334043	+	0.578579i	−0.983300	−	0.181990i	$-0.941746\pi$
$97$	−32.4021	+	56.1221i	−0.334043	+	0.578579i	0.649258	+	0.760568i	$0.275080\pi$
$98$		0			0
$99$	−19.2426	−	28.2765i	−0.194370	−	0.285621i
$100$		0			0
$101$	168.478	+	97.2705i	1.66809	+	0.963075i	0.968664	+	0.248373i	$0.0798960\pi$
$101$	168.478	+	97.2705i	1.66809	+	0.963075i	0.699430	+	0.714701i	$0.253437\pi$
$102$		0			0
$103$	12.4420	+	21.5502i	0.120796	+	0.209225i	0.920082	−	0.391726i	$-0.128122\pi$
$103$	12.4420	+	21.5502i	0.120796	+	0.209225i	−0.799286	+	0.600951i	$0.794789\pi$
$104$		0			0
$105$	1.34635	+	0.307912i	0.0128224	+	0.00293249i
$106$		0			0
$107$		−	23.2306i		−	0.217108i	−0.994091	−	0.108554i	$-0.965378\pi$
$107$		−	23.2306i		−	0.217108i	0.994091	−	0.108554i	$-0.0346221\pi$
$108$		0			0
$109$	−157.077			−1.44108			−0.720538	−	0.693416i	$-0.756105\pi$
$109$	−157.077			−1.44108			−0.720538	+	0.693416i	$0.756105\pi$
$110$		0			0
$111$	−19.5808	+	85.6179i	−0.176404	+	0.771332i
$112$		0			0
$113$	−32.5614	+	18.7994i	−0.288154	+	0.166366i	−0.637109	−	0.770774i	$-0.719870\pi$
$113$	−32.5614	+	18.7994i	−0.288154	+	0.166366i	0.348955	+	0.937140i	$0.386537\pi$
$114$		0			0
$115$	0.880021	−	1.52424i	0.00765236	−	0.0132543i
$116$		0			0
$117$	0.288382	+	3.89357i	0.00246481	+	0.0332784i
$118$		0			0
$119$	−205.823	−	118.832i	−1.72961	−	0.998589i
$120$		0			0
$121$	−53.2788	−	92.2816i	−0.440321	−	0.762658i
$122$		0			0
$123$	−49.6584	−	161.237i	−0.403727	−	1.31087i
$124$		0			0
$125$			2.54087i			0.0203269i
$126$		0			0
$127$	−48.4364			−0.381389			−0.190694	−	0.981649i	$-0.561074\pi$
$127$	−48.4364			−0.381389			−0.190694	+	0.981649i	$0.561074\pi$
$128$		0			0
$129$	17.3461	+	16.1088i	0.134466	+	0.124875i
$130$		0			0
$131$	0.0274376	−	0.0158411i	0.000209447	−	0.000120924i	−0.499895	−	0.866086i	$-0.666628\pi$
$131$	0.0274376	−	0.0158411i	0.000209447	−	0.000120924i	0.500105	+	0.865965i	$0.333295\pi$
$132$		0			0
$133$	−155.009	+	268.483i	−1.16548	+	2.01867i
$134$		0			0
$135$	−0.206274	+	1.35655i	−0.00152796	+	0.0100485i
$136$		0			0
$137$	0.913705	+	0.527528i	0.00666938	+	0.00385057i	0.503331	−	0.864094i	$-0.332108\pi$
$137$	0.913705	+	0.527528i	0.00666938	+	0.00385057i	−0.496662	+	0.867944i	$0.665441\pi$
$138$		0			0
$139$	45.3655	+	78.5754i	0.326371	+	0.565290i	0.981789	−	0.189976i	$-0.0608410\pi$
$139$	45.3655	+	78.5754i	0.326371	+	0.565290i	−0.655418	+	0.755266i	$0.727508\pi$
$140$		0			0
$141$	78.8487	−	84.9047i	0.559211	−	0.602161i
$142$		0			0
$143$		−	1.64860i		−	0.0115286i
$144$		0			0
$145$	−0.823399			−0.00567862
$146$		0			0
$147$	−94.7955	+	29.1955i	−0.644867	+	0.198609i
$148$		0			0
$149$	−15.1086	+	8.72295i	−0.101400	+	0.0585433i	−0.549842	−	0.835268i	$-0.685312\pi$
$149$	−15.1086	+	8.72295i	−0.101400	+	0.0585433i	0.448442	+	0.893812i	$0.351979\pi$
$150$		0			0
$151$	−40.8713	+	70.7912i	−0.270671	+	0.468816i	−0.969034	−	0.246928i	$-0.920579\pi$
$151$	−40.8713	+	70.7912i	−0.270671	+	0.468816i	0.698363	+	0.715744i	$0.253912\pi$
$152$		0			0
$153$	102.633	−	212.647i	0.670806	−	1.38985i
$154$		0			0
$155$	1.51113	+	0.872452i	0.00974923	+	0.00562872i
$156$		0			0
$157$	−96.4835	−	167.114i	−0.614544	−	1.06442i	−0.990464	−	0.137770i	$-0.956007\pi$
$157$	−96.4835	−	167.114i	−0.614544	−	1.06442i	0.375920	−	0.926652i	$-0.377327\pi$
$158$		0			0
$159$	147.767	+	33.7943i	0.929350	+	0.212543i
$160$		0			0
$161$			313.735i			1.94866i
$162$		0			0
$163$	−165.401			−1.01473			−0.507364	−	0.861732i	$-0.669380\pi$
$163$	−165.401			−1.01473			−0.507364	+	0.861732i	$0.669380\pi$
$164$		0			0
$165$	0.129173	−	0.564814i	0.000782868	−	0.00342311i
$166$		0			0
$167$	215.643	−	124.502i	1.29128	−	0.745520i	0.312398	−	0.949951i	$-0.398868\pi$
$167$	215.643	−	124.502i	1.29128	−	0.745520i	0.978881	+	0.204432i	$0.0655346\pi$
$168$		0			0
$169$	84.4059	−	146.195i	0.499443	−	0.865061i
$170$		0			0
$171$	−277.384	−	133.878i	−1.62213	−	0.782914i
$172$		0			0
$173$	117.476	+	67.8248i	0.679052	+	0.392051i	0.799498	−	0.600669i	$-0.205099\pi$
$173$	117.476	+	67.8248i	0.679052	+	0.392051i	−0.120446	+	0.992720i	$0.538432\pi$
$174$		0			0
$175$	−113.224	−	196.110i	−0.646995	−	1.12063i
$176$		0			0
$177$	8.71516	+	28.2975i	0.0492382	+	0.159873i
$178$		0			0
$179$			95.4526i			0.533255i	0.963800	+	0.266627i	$0.0859093\pi$
$179$			95.4526i			0.533255i	−0.963800	+	0.266627i	$0.914091\pi$
$180$		0			0
$181$	−58.9249			−0.325552			−0.162776	−	0.986663i	$-0.552045\pi$
$181$	−58.9249			−0.325552			−0.162776	+	0.986663i	$0.552045\pi$
$182$		0			0
$183$	−160.789	−	149.321i	−0.878630	−	0.815960i
$184$		0			0
$185$	−1.28848	+	0.743906i	−0.00696477	+	0.00402111i
$186$		0			0
$187$	−49.8517	+	86.3457i	−0.266587	+	0.461742i
$188$		0			0
$189$	−89.0619	−	227.798i	−0.471227	−	1.20528i
$190$		0			0
$191$	−164.852	−	95.1775i	−0.863101	−	0.498311i	0.00194880	−	0.999998i	$-0.499380\pi$
$191$	−164.852	−	95.1775i	−0.863101	−	0.498311i	−0.865049	+	0.501687i	$0.832713\pi$
$192$		0			0
$193$	5.29645	+	9.17373i	0.0274428	+	0.0475323i	0.879421	−	0.476046i	$-0.157930\pi$
$193$	5.29645	+	9.17373i	0.0274428	+	0.0475323i	−0.851978	+	0.523578i	$0.824597\pi$
$194$		0			0
$195$	−0.0450062	+	0.0484629i	−0.000230801	+	0.000248528i
$196$		0			0
$197$			215.874i			1.09581i	0.836541	+	0.547904i	$0.184574\pi$
$197$			215.874i			1.09581i	−0.836541	+	0.547904i	$0.815426\pi$
$198$		0			0
$199$	146.668			0.737026			0.368513	−	0.929623i	$-0.379867\pi$
$199$	146.668			0.737026			0.368513	+	0.929623i	$0.379867\pi$
$200$		0			0
$201$	−72.7079	+	22.3928i	−0.361731	+	0.111407i
$202$		0			0
$203$	127.110	−	73.3872i	0.626159	−	0.361513i
$204$		0			0
$205$	1.42898	−	2.47506i	0.00697063	−	0.0120735i
$206$		0			0
$207$	−310.845	+	23.0231i	−1.50166	+	0.111223i
$208$		0			0
$209$	112.632	+	65.0282i	0.538910	+	0.311140i
$210$		0			0
$211$	−54.8335	−	94.9744i	−0.259874	−	0.450116i	0.706334	−	0.707879i	$-0.250348\pi$
$211$	−54.8335	−	94.9744i	−0.259874	−	0.450116i	−0.966208	+	0.257763i	$0.917014\pi$
$212$		0			0
$213$	286.092	+	65.4294i	1.34316	+	0.307180i
$214$		0			0
$215$			0.401009i			0.00186516i
$216$		0			0
$217$	−311.036			−1.43335
$218$		0			0
$219$	−51.5402	+	225.361i	−0.235343	+	1.02905i
$220$		0			0
$221$	9.85631	−	5.69054i	0.0445987	−	0.0257491i
$222$		0			0
$223$	−73.8403	+	127.895i	−0.331123	+	0.573521i	−0.982732	−	0.185033i	$-0.940761\pi$
$223$	−73.8403	+	127.895i	−0.331123	+	0.573521i	0.651610	+	0.758554i	$0.274094\pi$
$224$		0			0
$225$	185.995	−	126.572i	0.826642	−	0.562544i
$226$		0			0
$227$	−346.255	−	199.911i	−1.52535	−	0.880664i	−0.999548	−	0.0300589i	$-0.990431\pi$
$227$	−346.255	−	199.911i	−1.52535	−	0.880664i	−0.525806	−	0.850605i	$-0.676236\pi$
$228$		0			0
$229$	−39.1692	−	67.8430i	−0.171044	−	0.296258i	0.767741	−	0.640760i	$-0.221381\pi$
$229$	−39.1692	−	67.8430i	−0.171044	−	0.296258i	−0.938785	+	0.344503i	$0.888047\pi$
$230$		0			0
$231$	30.3994	+	98.7046i	0.131599	+	0.427293i
$232$		0			0
$233$		−	352.995i		−	1.51500i	−0.652835	−	0.757500i	$-0.726420\pi$
$233$		−	352.995i		−	1.51500i	0.652835	−	0.757500i	$-0.273580\pi$
$234$		0			0
$235$	1.96284			0.00835251
$236$		0			0
$237$	−185.265	−	172.051i	−0.781711	−	0.725953i
$238$		0			0
$239$	−279.549	+	161.397i	−1.16966	+	0.675303i	−0.953600	−	0.301077i	$-0.902654\pi$
$239$	−279.549	+	161.397i	−1.16966	+	0.675303i	−0.216060	+	0.976380i	$0.569321\pi$
$240$		0			0
$241$	−105.601	+	182.907i	−0.438180	+	0.758949i	−0.997549	−	0.0699691i	$-0.977710\pi$
$241$	−105.601	+	182.907i	−0.438180	+	0.758949i	0.559370	+	0.828918i	$0.311043\pi$
$242$		0			0
$243$	219.164	−	104.958i	0.901909	−	0.431926i
$244$		0			0
$245$	−1.45516	−	0.840135i	−0.00593941	−	0.00342912i
$246$		0			0
$247$	−7.42293	−	12.8569i	−0.0300524	−	0.0520522i
$248$		0			0
$249$	95.8859	−	103.250i	0.385084	−	0.414661i
$250$		0			0
$251$		−	206.824i		−	0.824001i	−0.911184	−	0.412001i	$-0.864830\pi$
$251$		−	206.824i		−	0.824001i	0.911184	−	0.412001i	$-0.135170\pi$
$252$		0			0
$253$	131.616			0.520222
$254$		0			0
$255$	3.82267	−	1.17732i	0.0149909	−	0.00461694i
$256$		0			0
$257$	20.7432	−	11.9761i	0.0807127	−	0.0465995i	−0.459100	−	0.888384i	$-0.651828\pi$
$257$	20.7432	−	11.9761i	0.0807127	−	0.0465995i	0.539813	+	0.841785i	$0.318495\pi$
$258$		0			0
$259$	132.604	−	229.678i	0.511986	−	0.886786i
$260$		0			0
$261$	82.0389	+	120.554i	0.314325	+	0.461892i
$262$		0			0
$263$	119.369	+	68.9175i	0.453873	+	0.262044i	0.709464	−	0.704741i	$-0.248937\pi$
$263$	119.369	+	68.9175i	0.453873	+	0.262044i	−0.255592	+	0.966785i	$0.582270\pi$
$264$		0			0
$265$	1.28390	+	2.22377i	0.00484489	+	0.00839160i
$266$		0			0
$267$	317.562	+	72.6265i	1.18937	+	0.272009i
$268$		0			0
$269$		−	249.461i		−	0.927366i	−0.886001	−	0.463683i	$-0.846528\pi$
$269$		−	249.461i		−	0.927366i	0.886001	−	0.463683i	$-0.153472\pi$
$270$		0			0
$271$	−72.6700			−0.268155			−0.134078	−	0.990971i	$-0.542807\pi$
$271$	−72.6700			−0.268155			−0.134078	+	0.990971i	$0.542807\pi$
$272$		0			0
$273$	2.62837	−	11.4926i	0.00962771	−	0.0420975i
$274$		0			0
$275$	−82.2709	+	47.4991i	−0.299167	+	0.172724i
$276$		0			0
$277$	182.021	−	315.270i	0.657117	−	1.13816i	−0.324242	−	0.945974i	$-0.605109\pi$
$277$	182.021	−	315.270i	0.657117	−	1.13816i	0.981359	−	0.192185i	$-0.0615574\pi$
$278$		0			0
$279$	−22.8251	−	308.171i	−0.0818102	−	1.10456i
$280$		0			0
$281$	241.120	+	139.211i	0.858077	+	0.495411i	0.863368	−	0.504575i	$-0.168351\pi$
$281$	241.120	+	139.211i	0.858077	+	0.495411i	−0.00529060	+	0.999986i	$0.501684\pi$
$282$		0			0
$283$	−13.7745	−	23.8581i	−0.0486732	−	0.0843044i	0.840662	−	0.541560i	$-0.182166\pi$
$283$	−13.7745	−	23.8581i	−0.0486732	−	0.0843044i	−0.889336	+	0.457255i	$0.848833\pi$
$284$		0			0
$285$	−1.53574	−	4.98642i	−0.00538855	−	0.0174962i
$286$		0			0
$287$			509.443i			1.77506i
$288$		0			0
$289$	−399.303			−1.38167
$290$		0			0
$291$	142.457	+	132.296i	0.489544	+	0.454626i
$292$		0			0
$293$	−342.145	+	197.537i	−1.16773	+	0.674189i	−0.953144	−	0.302517i	$-0.902173\pi$
$293$	−342.145	+	197.537i	−1.16773	+	0.674189i	−0.214585	+	0.976705i	$0.568840\pi$
$294$		0			0
$295$	−0.250789	+	0.434380i	−0.000850133	+	0.00147247i
$296$		0			0
$297$	−95.5645	+	37.3627i	−0.321766	+	0.125800i
$298$		0			0
$299$	−13.0111	−	7.51195i	−0.0435153	−	0.0251236i
$300$		0			0
$301$	−35.7408	−	61.9049i	−0.118740	−	0.205664i
$302$		0			0
$303$	397.150	−	427.654i	1.31073	−	1.41140i
$304$		0			0
$305$		−	3.71715i		−	0.0121874i
$306$		0			0
$307$	−122.443			−0.398836			−0.199418	−	0.979915i	$-0.563905\pi$
$307$	−122.443			−0.398836			−0.199418	+	0.979915i	$0.563905\pi$
$308$		0			0
$309$	71.3449	−	21.9731i	0.230890	−	0.0711102i
$310$		0			0
$311$	420.591	−	242.829i	1.35238	−	0.780799i	0.363801	−	0.931477i	$-0.381479\pi$
$311$	420.591	−	242.829i	1.35238	−	0.780799i	0.988583	+	0.150677i	$0.0481455\pi$
$312$		0			0
$313$	5.15434	−	8.92759i	0.0164676	−	0.0285226i	−0.857674	−	0.514194i	$-0.828091\pi$
$313$	5.15434	−	8.92759i	0.0164676	−	0.0285226i	0.874142	+	0.485671i	$0.161425\pi$
$314$		0			0
$315$	1.80097	−	3.73146i	0.00571737	−	0.0118459i
$316$		0			0
$317$	144.879	+	83.6462i	0.457033	+	0.263868i	0.710796	−	0.703398i	$-0.248335\pi$
$317$	144.879	+	83.6462i	0.457033	+	0.263868i	−0.253763	+	0.967266i	$0.581668\pi$
$318$		0			0
$319$	−30.7869	−	53.3245i	−0.0965107	−	0.167162i
$320$		0			0
$321$	−67.9378	−	15.5374i	−0.211644	−	0.0484031i
$322$		0			0
$323$			897.845i			2.77971i
$324$		0			0
$325$	10.8440			0.0333661
$326$		0			0
$327$	−105.058	+	459.371i	−0.321280	+	1.40481i
$328$		0			0
$329$	−303.009	+	174.942i	−0.921000	+	0.531740i
$330$		0			0
$331$	52.2422	−	90.4861i	0.157831	−	0.273372i	−0.776255	−	0.630419i	$-0.782883\pi$
$331$	52.2422	−	90.4861i	0.157831	−	0.273372i	0.934086	+	0.357047i	$0.116216\pi$
$332$		0			0
$333$	237.293	+	114.528i	0.712590	+	0.343928i
$334$		0			0
$335$	−1.11610	−	0.644381i	−0.00333164	−	0.00192352i
$336$		0			0
$337$	196.086	+	339.631i	0.581858	+	1.00781i	0.995259	+	0.0972586i	$0.0310074\pi$
$337$	196.086	+	339.631i	0.581858	+	1.00781i	−0.413401	+	0.910549i	$0.635659\pi$
$338$		0			0
$339$	33.2004	+	107.799i	0.0979364	+	0.317992i
$340$		0			0
$341$			130.484i			0.382651i
$342$		0			0
$343$	−144.370			−0.420903
$344$		0			0
$345$	−3.86905	−	3.59308i	−0.0112146	−	0.0104147i
$346$		0			0
$347$	247.220	−	142.732i	0.712449	−	0.411333i	−0.0995180	−	0.995036i	$-0.531730\pi$
$347$	247.220	−	142.732i	0.712449	−	0.411333i	0.811967	+	0.583703i	$0.198397\pi$
$348$		0			0
$349$	−151.562	+	262.514i	−0.434276	+	0.752189i	−0.997236	−	0.0742956i	$-0.976329\pi$
$349$	−151.562	+	262.514i	−0.434276	+	0.752189i	0.562960	+	0.826484i	$0.309663\pi$
$350$		0			0
$351$	11.5796	+	1.76078i	0.0329903	+	0.00501646i
$352$		0			0
$353$	308.183	+	177.929i	0.873039	+	0.504049i	0.868357	−	0.495940i	$-0.165176\pi$
$353$	308.183	+	177.929i	0.873039	+	0.504049i	0.00468222	+	0.999989i	$0.498510\pi$
$354$		0			0
$355$	2.48576	+	4.30547i	0.00700215	+	0.0121281i
$356$		0			0
$357$	−485.185	+	522.450i	−1.35906	+	1.46345i
$358$		0			0
$359$		−	148.171i		−	0.412733i	−0.978475	−	0.206367i	$-0.933836\pi$
$359$		−	148.171i		−	0.412733i	0.978475	−	0.206367i	$-0.0661639\pi$
$360$		0			0
$361$	810.179			2.24426
$362$		0			0
$363$	−305.511	+	94.0925i	−0.841629	+	0.259208i
$364$		0			0
$365$	−3.39151	+	1.95809i	−0.00929181	+	0.00536463i
$366$		0			0
$367$	123.772	−	214.380i	0.337254	−	0.584141i	−0.646661	−	0.762777i	$-0.723835\pi$
$367$	123.772	−	214.380i	0.337254	−	0.584141i	0.983915	+	0.178636i	$0.0571686\pi$
$368$		0			0
$369$	−504.750	+	37.3849i	−1.36789	+	0.101314i
$370$		0			0
$371$	−396.397	−	228.860i	−1.06846	−	0.616873i
$372$		0			0
$373$	224.520	+	388.881i	0.601931	+	1.04258i	0.992528	+	0.122014i	$0.0389353\pi$
$373$	224.520	+	388.881i	0.601931	+	1.04258i	−0.390597	+	0.920562i	$0.627731\pi$
$374$		0			0
$375$	7.43075	+	1.69942i	0.0198153	+	0.00453177i
$376$		0			0
$377$			7.02862i			0.0186436i
$378$		0			0
$379$	618.282			1.63135			0.815675	−	0.578510i	$-0.196366\pi$
$379$	618.282			1.63135			0.815675	+	0.578510i	$0.196366\pi$
$380$		0			0
$381$	−32.3959	+	141.652i	−0.0850285	+	0.371790i
$382$		0			0
$383$	370.803	−	214.083i	0.968155	−	0.558965i	0.0694818	−	0.997583i	$-0.477865\pi$
$383$	370.803	−	214.083i	0.968155	−	0.558965i	0.898673	+	0.438619i	$0.144532\pi$
$384$		0			0
$385$	−0.874780	+	1.51516i	−0.00227216	+	0.00393549i
$386$		0			0
$387$	58.7118	−	39.9544i	0.151710	−	0.103241i
$388$		0			0
$389$	−585.313	−	337.930i	−1.50466	−	0.868716i	−0.999985	−	0.00540555i	$-0.998279\pi$
$389$	−585.313	−	337.930i	−1.50466	−	0.868716i	−0.504674	−	0.863310i	$-0.668387\pi$
$390$		0			0
$391$	454.306	+	786.881i	1.16191	+	2.01248i
$392$		0			0
$393$	−0.0279760	−	0.0908360i	−7.11857e−5	−	0.000231135i
$394$		0			0
$395$		−	4.28300i		−	0.0108430i
$396$		0			0
$397$	−209.902			−0.528721			−0.264361	−	0.964424i	$-0.585161\pi$
$397$	−209.902			−0.528721			−0.264361	+	0.964424i	$0.585161\pi$
$398$		0			0
$399$	681.501	+	632.892i	1.70802	+	1.58619i
$400$		0			0
$401$	175.023	−	101.050i	0.436467	−	0.251994i	−0.265631	−	0.964075i	$-0.585580\pi$
$401$	175.023	−	101.050i	0.436467	−	0.251994i	0.702098	+	0.712080i	$0.252247\pi$
$402$		0			0
$403$	7.44734	−	12.8992i	0.0184797	−	0.0320079i
$404$		0			0
$405$	3.82925	+	1.51055i	0.00945493	+	0.00372975i
$406$		0			0
$407$	−96.3528	−	55.6293i	−0.236739	−	0.136681i
$408$		0			0
$409$	−291.252	−	504.464i	−0.712108	−	1.23341i	−0.964064	−	0.265669i	$-0.914407\pi$
$409$	−291.252	−	504.464i	−0.712108	−	1.23341i	0.251957	−	0.967739i	$-0.418926\pi$
$410$		0			0
$411$	2.15387	−	2.31930i	0.00524056	−	0.00564306i
$412$		0			0
$413$		−	89.4085i		−	0.216486i
$414$		0			0
$415$	2.38696			0.00575172
$416$		0			0
$417$	260.135	−	80.1173i	0.623825	−	0.192128i
$418$		0			0
$419$	675.460	−	389.977i	1.61208	−	0.930733i	0.623189	−	0.782071i	$-0.285837\pi$
$419$	675.460	−	389.977i	1.61208	−	0.930733i	0.988888	−	0.148662i	$-0.0474968\pi$
$420$		0			0
$421$	84.1068	−	145.677i	0.199779	−	0.346027i	−0.748678	−	0.662934i	$-0.769311\pi$
$421$	84.1068	−	145.677i	0.199779	−	0.346027i	0.948457	+	0.316907i	$0.102644\pi$
$422$		0			0
$423$	−195.567	−	287.380i	−0.462332	−	0.679384i
$424$		0			0
$425$	−567.957	−	327.910i	−1.33637	−	0.771553i
$426$		0			0
$427$	331.299	+	573.827i	0.775876	+	1.34386i
$428$		0			0
$429$	−4.82131	−	1.10264i	−0.0112385	−	0.00257024i
$430$		0			0
$431$		−	182.732i		−	0.423973i	−0.977273	−	0.211986i	$-0.932007\pi$
$431$		−	182.732i		−	0.423973i	0.977273	−	0.211986i	$-0.0679933\pi$
$432$		0			0
$433$	447.193			1.03278			0.516389	−	0.856354i	$-0.327276\pi$
$433$	447.193			1.03278			0.516389	+	0.856354i	$0.327276\pi$
$434$		0			0
$435$	−0.550717	+	2.40803i	−0.00126602	+	0.00553569i
$436$		0			0
$437$	1026.43	−	592.612i	2.34882	−	1.35609i
$438$		0			0
$439$	−98.6108	+	170.799i	−0.224626	+	0.389063i	−0.956207	−	0.292691i	$-0.905449\pi$
$439$	−98.6108	+	170.799i	−0.224626	+	0.389063i	0.731581	+	0.681754i	$0.238783\pi$
$440$		0			0
$441$	21.9796	+	296.756i	0.0498403	+	0.672915i
$442$		0			0
$443$	244.803	+	141.337i	0.552603	+	0.319045i	0.750171	−	0.661244i	$-0.229971\pi$
$443$	244.803	+	141.337i	0.552603	+	0.319045i	−0.197568	+	0.980289i	$0.563304\pi$
$444$		0			0
$445$	2.75919	+	4.77906i	0.00620043	+	0.0107395i
$446$		0			0
$447$	15.4051	+	50.0192i	0.0344633	+	0.111900i
$448$		0			0
$449$		−	349.046i		−	0.777386i	−0.921367	−	0.388693i	$-0.872927\pi$
$449$		−	349.046i		−	0.777386i	0.921367	−	0.388693i	$-0.127073\pi$
$450$		0			0
$451$	213.718			0.473877
$452$		0			0
$453$	179.692	+	166.875i	0.396672	+	0.368378i
$454$		0			0
$455$	0.172955	−	0.0998556i	0.000380121	−	0.000219463i
$456$		0			0
$457$	−40.2987	+	69.7995i	−0.0881811	+	0.152734i	−0.906742	−	0.421685i	$-0.861439\pi$
$457$	−40.2987	+	69.7995i	−0.0881811	+	0.152734i	0.818561	+	0.574419i	$0.194772\pi$
$458$		0			0
$459$	−553.242	−	442.376i	−1.20532	−	0.963782i
$460$		0			0
$461$	−495.135	−	285.866i	−1.07405	−	0.620100i	−0.144761	−	0.989467i	$-0.546241\pi$
$461$	−495.135	−	285.866i	−1.07405	−	0.620100i	−0.929284	+	0.369366i	$0.879575\pi$
$462$		0			0
$463$	−139.837	−	242.205i	−0.302024	−	0.523120i	0.674571	−	0.738210i	$-0.264329\pi$
$463$	−139.837	−	242.205i	−0.302024	−	0.523120i	−0.976594	+	0.215090i	$0.930996\pi$
$464$		0			0
$465$	3.56217	−	3.83577i	0.00766059	−	0.00824896i
$466$		0			0
$467$			506.702i			1.08501i	0.840051	+	0.542507i	$0.182525\pi$
$467$			506.702i			1.08501i	−0.840051	+	0.542507i	$0.817475\pi$
$468$		0			0
$469$	229.727			0.489823
$470$		0			0
$471$	−553.256	+	170.394i	−1.17464	+	0.361770i
$472$		0			0
$473$	−25.9699	+	14.9938i	−0.0549048	+	0.0316993i
$474$		0			0
$475$	−427.737	+	740.862i	−0.900499	+	1.55971i
$476$		0			0
$477$	197.662	−	409.540i	0.414387	−	0.858574i
$478$		0			0
$479$	217.596	+	125.629i	0.454271	+	0.262274i	0.709632	−	0.704572i	$-0.248861\pi$
$479$	217.596	+	125.629i	0.454271	+	0.262274i	−0.255361	+	0.966846i	$0.582194\pi$
$480$		0			0
$481$	6.35006	+	10.9986i	0.0132018	+	0.0228662i
$482$		0			0
$483$	917.516	+	209.836i	1.89962	+	0.434444i
$484$		0			0
$485$			3.29335i			0.00679041i
$486$		0			0
$487$	313.224			0.643170			0.321585	−	0.946881i	$-0.395784\pi$
$487$	313.224			0.643170			0.321585	+	0.946881i	$0.395784\pi$
$488$		0			0
$489$	−110.625	+	483.713i	−0.226228	+	0.989188i
$490$		0			0
$491$	533.397	−	307.957i	1.08635	−	0.627204i	0.153747	−	0.988110i	$-0.450866\pi$
$491$	533.397	−	307.957i	1.08635	−	0.627204i	0.932602	+	0.360906i	$0.117533\pi$
$492$		0			0
$493$	212.538	−	368.126i	0.431111	−	0.746706i
$494$		0			0
$495$	−1.56540	−	0.755532i	−0.00316242	−	0.00152633i
$496$		0			0
$497$	−767.467	−	443.098i	−1.54420	−	0.891544i
$498$		0			0
$499$	−412.029	−	713.654i	−0.825709	−	1.43017i	−0.901377	−	0.433036i	$-0.857442\pi$
$499$	−412.029	−	713.654i	−0.825709	−	1.43017i	0.0756679	−	0.997133i	$-0.475891\pi$
$500$		0			0
$501$	−219.875	−	713.919i	−0.438873	−	1.42499i
$502$		0			0
$503$			175.718i			0.349340i	0.984627	+	0.174670i	$0.0558858\pi$
$503$			175.718i			0.349340i	−0.984627	+	0.174670i	$0.944114\pi$
$504$		0			0
$505$	9.88657			0.0195774
$506$		0			0
$507$	−371.094	−	344.625i	−0.731940	−	0.679733i
$508$		0			0
$509$	314.934	−	181.827i	0.618730	−	0.357224i	−0.157644	−	0.987496i	$-0.550390\pi$
$509$	314.934	−	181.827i	0.618730	−	0.357224i	0.776374	+	0.630272i	$0.217057\pi$
$510$		0			0
$511$	349.038	−	604.551i	0.683049	−	1.18307i
$512$		0			0
$513$	−577.050	+	721.667i	−1.12485	+	1.40676i
$514$		0			0
$515$	1.09518	+	0.632301i	0.00212656	+	0.00122777i
$516$		0			0
$517$	73.3907	+	127.116i	0.141955	+	0.245873i
$518$		0			0
$519$	276.925	−	298.194i	0.533574	−	0.574556i
$520$		0			0
$521$		−	458.709i		−	0.880440i	−0.897890	−	0.440220i	$-0.854901\pi$
$521$		−	458.709i		−	0.880440i	0.897890	−	0.440220i	$-0.145099\pi$
$522$		0			0
$523$	−458.289			−0.876270			−0.438135	−	0.898909i	$-0.644361\pi$
$523$	−458.289			−0.876270			−0.438135	+	0.898909i	$0.644361\pi$
$524$		0			0
$525$	−649.251	+	199.959i	−1.23667	+	0.380873i
$526$		0			0
$527$	−780.113	+	450.398i	−1.48029	+	0.854646i
$528$		0			0
$529$	335.219	−	580.616i	0.633683	−	1.09757i
$530$		0			0
$531$	88.5848	−	6.56114i	0.166826	−	0.0123562i
$532$		0			0
$533$	−21.1274	−	12.1979i	−0.0396387	−	0.0228854i
$534$		0			0
$535$	−0.590289	−	1.02241i	−0.00110334	−	0.00191105i
$536$		0			0
$537$	279.150	+	63.8418i	0.519833	+	0.118886i
$538$		0			0
$539$		−	125.651i		−	0.233118i
$540$		0			0
$541$	824.876			1.52472			0.762362	−	0.647150i	$-0.224039\pi$
$541$	824.876			1.52472			0.762362	+	0.647150i	$0.224039\pi$
$542$		0			0
$543$	−39.4109	+	172.325i	−0.0725800	+	0.317358i
$544$		0			0
$545$	−6.91319	+	3.99133i	−0.0126847	+	0.00732354i
$546$		0			0
$547$	−16.8719	+	29.2230i	−0.0308444	+	0.0534241i	−0.881036	−	0.473050i	$-0.843153\pi$
$547$	−16.8719	+	29.2230i	−0.0308444	+	0.0534241i	0.850191	+	0.526474i	$0.176486\pi$
$548$		0			0
$549$	−544.228	+	370.357i	−0.991309	+	0.674602i
$550$		0			0
$551$	−480.196	−	277.241i	−0.871499	−	0.503160i
$552$		0			0
$553$	381.731	+	661.178i	0.690291	+	1.19562i
$554$		0			0
$555$	1.31377	+	4.26571i	0.00236715	+	0.00768596i
$556$		0			0
$557$			541.032i			0.971332i	0.874145	+	0.485666i	$0.161423\pi$
$557$			541.032i			0.971332i	−0.874145	+	0.485666i	$0.838577\pi$
$558$		0			0
$559$	3.42306			0.00612354
$560$		0			0
$561$	219.175	+	203.542i	0.390686	+	0.362820i
$562$		0			0
$563$	−97.8909	+	56.5173i	−0.173874	+	0.100386i	−0.584411	−	0.811458i	$-0.698674\pi$
$563$	−97.8909	+	56.5173i	−0.173874	+	0.100386i	0.410537	+	0.911844i	$0.365341\pi$
$564$		0			0
$565$	−0.955383	+	1.65477i	−0.00169094	+	0.00292880i
$566$		0			0
$567$	−725.762	+	108.102i	−1.28000	+	0.190656i
$568$		0			0
$569$	236.524	+	136.557i	0.415684	+	0.239995i	0.693229	−	0.720717i	$-0.256187\pi$
$569$	236.524	+	136.557i	0.415684	+	0.239995i	−0.277545	+	0.960713i	$0.589521\pi$
$570$		0			0
$571$	122.654	+	212.443i	0.214806	+	0.372054i	0.953212	−	0.302301i	$-0.0977548\pi$
$571$	122.654	+	212.443i	0.214806	+	0.372054i	−0.738407	+	0.674356i	$0.764421\pi$
$572$		0			0
$573$	−388.604	+	418.451i	−0.678193	+	0.730282i
$574$		0			0
$575$			865.733i			1.50562i
$576$		0			0
$577$	632.666			1.09648			0.548238	−	0.836323i	$-0.315299\pi$
$577$	632.666			1.09648			0.548238	+	0.836323i	$0.315299\pi$
$578$		0			0
$579$	30.3709	−	9.35375i	0.0524541	−	0.0161550i
$580$		0			0
$581$	−368.482	+	212.743i	−0.634220	+	0.366167i
$582$		0			0
$583$	−96.0099	+	166.294i	−0.164682	+	0.285238i
$584$		0			0
$585$	0.111628	+	0.164034i	0.000190817	+	0.000280400i
$586$		0			0
$587$	−980.129	−	565.878i	−1.66973	−	0.964017i	−0.967784	−	0.251782i	$-0.918983\pi$
$587$	−980.129	−	565.878i	−1.66973	−	0.964017i	−0.701942	−	0.712234i	$-0.747683\pi$
$588$		0			0
$589$	587.515	+	1017.61i	0.997478	+	1.72768i
$590$		0			0
$591$	631.322	+	144.384i	1.06823	+	0.244304i
$592$		0			0
$593$		−	180.213i		−	0.303900i	−0.988388	−	0.151950i	$-0.951445\pi$
$593$		−	180.213i		−	0.303900i	0.988388	−	0.151950i	$-0.0485553\pi$
$594$		0			0
$595$	−12.0781			−0.0202993
$596$		0			0
$597$	98.0965	−	428.930i	0.164316	−	0.718476i
$598$		0			0
$599$	566.086	−	326.830i	0.945052	−	0.545626i	0.0535119	−	0.998567i	$-0.482959\pi$
$599$	566.086	−	326.830i	0.945052	−	0.545626i	0.891541	+	0.452941i	$0.149625\pi$
$600$		0			0
$601$	−178.947	+	309.945i	−0.297749	+	0.515716i	−0.975621	−	0.219464i	$-0.929569\pi$
$601$	−178.947	+	309.945i	−0.297749	+	0.515716i	0.677872	+	0.735180i	$0.262902\pi$
$602$		0			0
$603$	16.8583	+	227.611i	0.0279573	+	0.377464i
$604$		0			0
$605$	−4.68975	−	2.70763i	−0.00775164	−	0.00447541i
$606$		0			0
$607$	−320.064	−	554.367i	−0.527288	−	0.913290i	−0.999494	−	0.0318015i	$-0.989876\pi$
$607$	−320.064	−	554.367i	−0.527288	−	0.913290i	0.472206	−	0.881488i	$-0.343458\pi$
$608$		0			0
$609$	−129.605	−	420.817i	−0.212816	−	0.690997i
$610$		0			0
$611$		−	16.7550i		−	0.0274223i
$612$		0			0
$613$	−246.093			−0.401457			−0.200729	−	0.979647i	$-0.564331\pi$
$613$	−246.093			−0.401457			−0.200729	+	0.979647i	$0.564331\pi$
$614$		0			0
$615$	−6.28256	−	5.83445i	−0.0102155	−	0.00948690i
$616$		0			0
$617$	309.912	−	178.928i	0.502289	−	0.289997i	−0.227369	−	0.973809i	$-0.573013\pi$
$617$	309.912	−	178.928i	0.502289	−	0.289997i	0.729658	+	0.683812i	$0.239679\pi$
$618$		0			0
$619$	−40.5053	+	70.1573i	−0.0654368	+	0.113340i	−0.896888	−	0.442258i	$-0.854177\pi$
$619$	−40.5053	+	70.1573i	−0.0654368	+	0.113340i	0.831451	+	0.555598i	$0.187511\pi$
$620$		0			0
$621$	−140.572	+	924.462i	−0.226364	+	1.48867i
$622$		0			0
$623$	−851.888	−	491.838i	−1.36740	−	0.789467i
$624$		0			0
$625$	−312.403	−	541.098i	−0.499845	−	0.865757i
$626$		0			0
$627$	265.507	−	285.899i	0.423456	−	0.455979i
$628$		0			0
$629$		−	768.075i		−	1.22110i
$630$		0			0
$631$	252.241			0.399748			0.199874	−	0.979822i	$-0.435947\pi$
$631$	252.241			0.399748			0.199874	+	0.979822i	$0.435947\pi$
$632$		0			0
$633$	−314.426	+	96.8382i	−0.496724	+	0.152983i
$634$		0			0
$635$	−2.13175	+	1.23077i	−0.00335709	+	0.00193822i
$636$		0			0
$637$	−7.17147	+	12.4214i	−0.0112582	+	0.0194998i
$638$		0			0
$639$	382.696	−	792.913i	0.598898	−	1.24087i
$640$		0			0
$641$	−843.278	−	486.867i	−1.31557	−	0.759542i	−0.332554	−	0.943084i	$-0.607910\pi$
$641$	−843.278	−	486.867i	−1.31557	−	0.759542i	−0.983012	+	0.183542i	$0.941244\pi$
$642$		0			0
$643$	−341.530	−	591.547i	−0.531151	−	0.919980i	−0.999339	−	0.0363512i	$-0.988426\pi$
$643$	−341.530	−	591.547i	−0.531151	−	0.919980i	0.468188	−	0.883629i	$-0.344907\pi$
$644$		0			0
$645$	1.17275	+	0.268208i	0.00181822	+	0.000415827i
$646$		0			0
$647$		−	390.640i		−	0.603771i	−0.953344	−	0.301885i	$-0.902384\pi$
$647$		−	390.640i		−	0.603771i	0.953344	−	0.301885i	$-0.0976160\pi$
$648$		0			0
$649$	−37.5081			−0.0577937
$650$		0			0
$651$	−208.031	+	909.624i	−0.319557	+	1.39727i
$652$		0			0
$653$	−542.529	+	313.230i	−0.830826	+	0.479678i	−0.854135	−	0.520051i	$-0.825913\pi$
$653$	−542.529	+	313.230i	−0.830826	+	0.479678i	0.0233093	+	0.999728i	$0.492580\pi$
$654$		0			0
$655$	0.000805043	−	0.00139438i	1.22907e−6	−	2.12882e-6i
$656$		0			0
$657$	624.595	+	301.458i	0.950678	+	0.458840i
$658$		0			0
$659$	51.4518	+	29.7057i	0.0780755	+	0.0450769i	0.538530	−	0.842607i	$-0.318980\pi$
$659$	51.4518	+	29.7057i	0.0780755	+	0.0450769i	−0.460454	+	0.887684i	$0.652313\pi$
$660$		0			0
$661$	−425.950	−	737.767i	−0.644402	−	1.11614i	−0.984439	−	0.175725i	$-0.943773\pi$
$661$	−425.950	−	737.767i	−0.644402	−	1.11614i	0.340037	−	0.940412i	$-0.389560\pi$
$662$		0			0
$663$	−10.0497	−	32.6307i	−0.0151580	−	0.0492168i
$664$		0			0
$665$			15.7551i			0.0236918i
$666$		0			0
$667$	−561.132			−0.841277
$668$		0			0
$669$	324.642	+	301.486i	0.485264	+	0.450652i
$670$		0			0
$671$	240.728	−	138.985i	0.358760	−	0.207130i
$672$		0			0
$673$	210.489	−	364.577i	0.312762	−	0.541720i	−0.666197	−	0.745776i	$-0.732079\pi$
$673$	210.489	−	364.577i	0.312762	−	0.541720i	0.978959	+	0.204056i	$0.0654124\pi$
$674$		0			0
$675$	−245.761	−	628.596i	−0.364090	−	0.931253i
$676$		0			0
$677$	−313.326	−	180.899i	−0.462816	−	0.267207i	0.250412	−	0.968139i	$-0.419434\pi$
$677$	−313.326	−	180.899i	−0.462816	−	0.267207i	−0.713227	+	0.700933i	$0.752767\pi$
$678$		0			0
$679$	−293.527	−	508.403i	−0.432293	−	0.748753i
$680$		0			0
$681$	−816.224	+	878.915i	−1.19857	+	1.29062i
$682$		0			0
$683$			705.769i			1.03334i	0.856186	+	0.516668i	$0.172828\pi$
$683$			705.769i			1.03334i	−0.856186	+	0.516668i	$0.827172\pi$
$684$		0			0
$685$	0.0536179			7.82743e−5
$686$		0			0
$687$	−224.604	+	69.1743i	−0.326934	+	0.100690i
$688$		0			0
$689$	18.9824	−	10.9595i	0.0275506	−	0.0159063i
$690$		0			0
$691$	345.384	−	598.222i	0.499832	−	0.865734i	−0.500168	−	0.865928i	$-0.666728\pi$
$691$	345.384	−	598.222i	0.499832	−	0.865734i	1.00000		0.000194148i	$6.17992e-5\pi$
$692$		0			0
$693$	308.993	−	22.8860i	0.445878	−	0.0330245i
$694$		0			0
$695$	3.99320	+	2.30547i	0.00574561	+	0.00331723i
$696$		0			0
$697$	737.703	+	1277.74i	1.05840	+	1.83320i
$698$		0			0
$699$	−1032.33	−	236.095i	−1.47687	−	0.337761i
$700$		0			0
$701$		−	1213.04i		−	1.73045i	−0.501384	−	0.865225i	$-0.667176\pi$
$701$		−	1213.04i		−	1.73045i	0.501384	−	0.865225i	$-0.332824\pi$
$702$		0			0
$703$	−1001.90			−1.42518
$704$		0			0
$705$	1.31281	−	5.74032i	0.00186215	−	0.00814229i
$706$		0			0
$707$	−1526.22	+	881.161i	−2.15872	+	1.24634i
$708$		0			0
$709$	−226.667	+	392.598i	−0.319699	+	0.553735i	−0.980425	−	0.196892i	$-0.936915\pi$
$709$	−226.667	+	392.598i	−0.319699	+	0.553735i	0.660726	+	0.750627i	$0.270249\pi$
$710$		0			0
$711$	−627.074	+	426.734i	−0.881960	+	0.600189i
$712$		0			0
$713$	1029.81	+	594.560i	1.44433	+	0.833885i
$714$		0			0
$715$	−0.0418908	−	0.0725570i	−5.85885e−5	−	0.000101478i
$716$		0			0
$717$	285.035	+	925.486i	0.397538	+	1.29078i
$718$		0			0
$719$			418.833i			0.582522i	0.956644	+	0.291261i	$0.0940748\pi$
$719$			418.833i			0.582522i	−0.956644	+	0.291261i	$0.905925\pi$
$720$		0			0
$721$	−225.421			−0.312650
$722$		0			0
$723$	464.280	+	431.164i	0.642158	+	0.596355i
$724$		0			0
$725$	350.753	−	202.508i	0.483798	−	0.279321i
$726$		0			0
$727$	−376.166	+	651.539i	−0.517423	+	0.896203i	0.482372	+	0.875966i	$0.339775\pi$
$727$	−376.166	+	651.539i	−0.517423	+	0.896203i	−0.999795	+	0.0202365i	$0.993558\pi$
$728$		0			0
$729$	−160.365	−	711.143i	−0.219980	−	0.975504i
$730$		0			0
$731$	−179.284	−	103.509i	−0.245258	−	0.141600i
$732$		0			0
$733$	−255.863	−	443.168i	−0.349063	−	0.604595i	0.637020	−	0.770847i	$-0.280167\pi$
$733$	−255.863	−	443.168i	−0.349063	−	0.604595i	−0.986083	+	0.166252i	$0.946833\pi$
$734$		0			0
$735$	−3.43022	+	3.69368i	−0.00466697	+	0.00502542i
$736$		0			0
$737$		−	96.3737i		−	0.130765i
$738$		0			0
$739$	−466.830			−0.631705			−0.315853	−	0.948808i	$-0.602290\pi$
$739$	−466.830			−0.631705			−0.315853	+	0.948808i	$0.602290\pi$
$740$		0			0
$741$	−42.5646	+	13.1092i	−0.0574421	+	0.0176912i
$742$		0			0
$743$	546.320	−	315.418i	0.735290	−	0.424520i	−0.0850643	−	0.996375i	$-0.527110\pi$
$743$	546.320	−	315.418i	0.735290	−	0.424520i	0.820354	+	0.571856i	$0.193776\pi$
$744$		0			0
$745$	−0.443300	+	0.767818i	−0.000595034	+	0.00103063i
$746$		0			0
$747$	−237.824	−	349.475i	−0.318372	−	0.467838i
$748$		0			0
$749$	182.249	+	105.222i	0.243323	+	0.140483i
$750$		0			0
$751$	−90.7172	−	157.127i	−0.120795	−	0.209223i	0.799286	−	0.600950i	$-0.205211\pi$
$751$	−90.7172	−	157.127i	−0.120795	−	0.209223i	−0.920081	+	0.391727i	$0.871878\pi$
$752$		0			0
$753$	−604.856	−	138.331i	−0.803262	−	0.183706i
$754$		0			0
$755$			4.15416i			0.00550220i
$756$		0			0
$757$	1381.82			1.82539			0.912696	−	0.408640i	$-0.133997\pi$
$757$	1381.82			1.82539			0.912696	+	0.408640i	$0.133997\pi$
$758$		0			0
$759$	88.0292	−	384.910i	0.115980	−	0.507128i
$760$		0			0
$761$	−590.093	+	340.690i	−0.775418	+	0.447688i	−0.834804	−	0.550548i	$-0.814419\pi$
$761$	−590.093	+	340.690i	−0.775418	+	0.447688i	0.0593862	+	0.998235i	$0.481086\pi$
$762$		0			0
$763$	711.471	−	1232.30i	0.932466	−	1.61508i
$764$		0			0
$765$	−0.886337	−	11.9668i	−0.00115861	−	0.0156429i
$766$		0			0
$767$	3.70791	+	2.14076i	0.00483430	+	0.00279109i
$768$		0			0
$769$	−45.1754	−	78.2461i	−0.0587457	−	0.101750i	0.835157	−	0.550012i	$-0.185377\pi$
$769$	−45.1754	−	78.2461i	−0.0587457	−	0.101750i	−0.893903	+	0.448261i	$0.852043\pi$
$770$		0			0
$771$	−21.1502	−	68.6732i	−0.0274322	−	0.0890703i
$772$		0			0
$773$		−	87.4025i		−	0.113069i	−0.998401	−	0.0565346i	$-0.981995\pi$
$773$		−	87.4025i		−	0.113069i	0.998401	−	0.0565346i	$-0.0180051\pi$
$774$		0			0
$775$	−858.286			−1.10747
$776$		0			0
$777$	−583.000	−	541.417i	−0.750322	−	0.696804i
$778$		0			0
$779$	1666.72	−	962.284i	2.13957	−	1.23528i
$780$		0			0
$781$	−185.885	+	321.963i	−0.238010	+	0.412245i
$782$		0			0
$783$	407.429	−	159.292i	0.520344	−	0.203438i
$784$		0			0
$785$	−8.49274	−	4.90329i	−0.0108188	−	0.00624622i
$786$		0			0
$787$	366.731	+	635.196i	0.465986	+	0.807111i	0.999245	−	0.0388408i	$-0.0123665\pi$
$787$	366.731	+	635.196i	0.465986	+	0.807111i	−0.533260	+	0.845951i	$0.679033\pi$
$788$		0			0
$789$	281.386	−	302.998i	0.356637	−	0.384028i
$790$		0			0
$791$		−	340.602i		−	0.430597i
$792$		0			0
$793$	−31.7300			−0.0400126
$794$		0			0
$795$	7.36213	−	2.26741i	0.00926054	−	0.00285209i
$796$		0			0
$797$	−853.500	+	492.768i	−1.07089	+	0.618279i	−0.928425	−	0.371521i	$-0.878836\pi$
$797$	−853.500	+	492.768i	−1.07089	+	0.618279i	−0.142466	+	0.989800i	$0.545503\pi$
$798$		0			0
$799$	−506.653	+	877.549i	−0.634109	+	1.09831i
$800$		0			0
$801$	424.792	−	880.133i	0.530327	−	1.09879i
$802$		0			0
$803$	−253.617	−	146.426i	−0.315837	−	0.182349i
$804$		0			0
$805$	7.97200	+	13.8079i	0.00990310	+	0.0171527i
$806$		0			0
$807$	−729.548	−	166.848i	−0.904025	−	0.206751i
$808$		0			0
$809$			459.662i			0.568185i	0.958797	+	0.284093i	$0.0916923\pi$
$809$			459.662i			0.568185i	−0.958797	+	0.284093i	$0.908308\pi$
$810$		0			0
$811$	912.030			1.12457			0.562287	−	0.826942i	$-0.309922\pi$
$811$	912.030			1.12457			0.562287	+	0.826942i	$0.309922\pi$
$812$		0			0
$813$	−48.6041	+	212.523i	−0.0597836	+	0.261406i
$814$		0			0
$815$	−7.27951	+	4.20283i	−0.00893191	+	0.00515684i
$816$		0			0
$817$	−135.021	+	233.864i	−0.165265	+	0.286247i
$818$		0			0
$819$	−31.8521	−	15.3733i	−0.0388915	−	0.0187708i
$820$		0			0
$821$	−224.455	−	129.589i	−0.273393	−	0.157843i	0.357036	−	0.934091i	$-0.383787\pi$
$821$	−224.455	−	129.589i	−0.273393	−	0.157843i	−0.630428	+	0.776247i	$0.717121\pi$
$822$		0			0
$823$	721.885	+	1250.34i	0.877139	+	1.51925i	0.854467	+	0.519506i	$0.173884\pi$
$823$	721.885	+	1250.34i	0.877139	+	1.51925i	0.0226714	+	0.999743i	$0.492783\pi$
$824$		0			0
$825$	83.8853	+	272.370i	0.101679	+	0.330145i
$826$		0			0
$827$		−	1148.68i		−	1.38897i	−0.719505	−	0.694487i	$-0.755631\pi$
$827$		−	1148.68i		−	1.38897i	0.719505	−	0.694487i	$-0.244369\pi$
$828$		0			0
$829$	424.655			0.512250			0.256125	−	0.966644i	$-0.417554\pi$
$829$	424.655			0.512250			0.256125	+	0.966644i	$0.417554\pi$
$830$		0			0
$831$	−800.264	−	743.183i	−0.963013	−	0.894324i
$832$		0			0
$833$	751.216	−	433.715i	0.901820	−	0.520666i
$834$		0			0
$835$	6.32718	−	10.9590i	0.00757746	−	0.0131245i
$836$		0			0
$837$	−916.510	−	139.363i	−1.09499	−	0.166503i
$838$		0			0
$839$	52.2029	+	30.1394i	0.0622204	+	0.0359230i	0.530787	−	0.847505i	$-0.321896\pi$
$839$	52.2029	+	30.1394i	0.0622204	+	0.0359230i	−0.468567	+	0.883428i	$0.655230\pi$
$840$		0			0
$841$	−289.243	−	500.984i	−0.343928	−	0.595700i
$842$		0			0
$843$	568.389	−	612.045i	0.674246	−	0.726031i
$844$		0			0
$845$		−	8.57901i		−	0.0101527i
$846$		0			0
$847$	965.291			1.13966
$848$		0			0
$849$	−78.9858	+	24.3263i	−0.0930340	+	0.0286529i
$850$		0			0
$851$	−878.078	+	506.959i	−1.03182	+	0.595721i
$852$		0			0
$853$	602.705	−	1043.92i	0.706571	−	1.22382i	−0.259550	−	0.965730i	$-0.583574\pi$
$853$	602.705	−	1043.92i	0.706571	−	1.22382i	0.966122	−	0.258087i	$-0.0830923\pi$
$854$		0			0
$855$	−15.6099	+	1.15617i	−0.0182572	+	0.00135224i
$856$		0			0
$857$	174.400	+	100.690i	0.203500	+	0.117491i	0.598287	−	0.801282i	$-0.295848\pi$
$857$	174.400	+	100.690i	0.203500	+	0.117491i	−0.394787	+	0.918773i	$0.629182\pi$
$858$		0			0
$859$	706.859	+	1224.31i	0.822885	+	1.42528i	0.903525	+	0.428536i	$0.140970\pi$
$859$	706.859	+	1224.31i	0.822885	+	1.42528i	−0.0806394	+	0.996743i	$0.525696\pi$
$860$		0			0
$861$	1489.86	+	340.732i	1.73039	+	0.395740i
$862$		0			0
$863$			299.383i			0.346909i	0.984842	+	0.173455i	$0.0554930\pi$
$863$			299.383i			0.346909i	−0.984842	+	0.173455i	$0.944507\pi$
$864$		0			0
$865$	6.89371			0.00796961
$866$		0			0
$867$	−267.067	+	1167.76i	−0.308035	+	1.34690i
$868$		0			0
$869$	277.373	−	160.141i	0.319186	−	0.184282i
$870$		0			0
$871$	−5.50050	+	9.52714i	−0.00631515	+	0.0109382i
$872$		0			0
$873$	482.179	−	328.131i	0.552325	−	0.375866i
$874$		0			0
$875$	−19.9336	−	11.5087i	−0.0227813	−	0.0131528i
$876$		0			0
$877$	−247.122	−	428.029i	−0.281782	−	0.488060i	0.690042	−	0.723769i	$-0.257592\pi$
$877$	−247.122	−	428.029i	−0.281782	−	0.488060i	−0.971824	+	0.235709i	$0.924259\pi$
$878$		0			0
$879$	348.859	+	1132.72i	0.396882	+	1.28865i
$880$		0			0
$881$		−	211.533i		−	0.240105i	−0.992768	−	0.120053i	$-0.961694\pi$
$881$		−	211.533i		−	0.240105i	0.992768	−	0.120053i	$-0.0383063\pi$
$882$		0			0
$883$	−410.167			−0.464515			−0.232258	−	0.972654i	$-0.574611\pi$
$883$	−410.167			−0.464515			−0.232258	+	0.972654i	$0.574611\pi$
$884$		0			0
$885$	1.10261	+	1.02396i	0.00124588	+	0.00115702i
$886$		0			0
$887$	734.748	−	424.207i	0.828352	−	0.478249i	−0.0249363	−	0.999689i	$-0.507938\pi$
$887$	734.748	−	424.207i	0.828352	−	0.478249i	0.853288	+	0.521440i	$0.174605\pi$
$888$		0			0
$889$	219.390	−	379.994i	0.246782	−	0.427440i
$890$		0			0
$891$	45.3502	+	304.467i	0.0508981	+	0.341714i
$892$		0			0
$893$	1144.70	+	660.895i	1.28186	+	0.740084i
$894$		0			0
$895$	2.42545	+	4.20100i	0.00271000	+	0.00469385i
$896$		0			0
$897$	−30.6709	+	33.0266i	−0.0341927	+	0.0368189i
$898$		0			0
$899$		−	556.305i		−	0.618805i
$900$		0			0
$901$	−1325.61			−1.47126
$902$		0			0
$903$	−204.945	+	63.1197i	−0.226960	+	0.0699000i
$904$		0			0
$905$	−2.59337	+	1.49728i	−0.00286560	+	0.00165445i
$906$		0			0
$907$	−577.488	+	1000.24i	−0.636701	+	1.10280i	0.349451	+	0.936955i	$0.386368\pi$
$907$	−577.488	+	1000.24i	−0.636701	+	1.10280i	−0.986152	+	0.165844i	$0.946965\pi$
$908$		0			0
$909$	−985.043	−	1447.49i	−1.08366	−	1.59240i
$910$		0			0
$911$	−454.824	−	262.593i	−0.499258	−	0.288247i	0.229149	−	0.973391i	$-0.426406\pi$
$911$	−454.824	−	262.593i	−0.499258	−	0.288247i	−0.728407	+	0.685145i	$0.759739\pi$
$912$		0			0
$913$	89.2486	+	154.583i	0.0977531	+	0.169313i
$914$		0			0
$915$	−10.8708	−	2.48615i	−0.0118806	−	0.00271711i
$916$		0			0
$917$			0.287005i			0.000312982i
$918$		0			0
$919$	1548.07			1.68452			0.842260	−	0.539072i	$-0.181225\pi$
$919$	1548.07			1.68452			0.842260	+	0.539072i	$0.181225\pi$
$920$		0			0
$921$	−81.8937	+	358.083i	−0.0889182	+	0.388798i
$922$		0			0
$923$	36.7519	−	21.2187i	0.0398179	−	0.0229889i
$924$		0			0
$925$	365.914	−	633.781i	0.395583	−	0.685169i
$926$		0			0
$927$	−16.5422	−	223.344i	−0.0178449	−	0.240932i
$928$		0			0
$929$	−531.821	−	307.047i	−0.572466	−	0.330513i	0.185668	−	0.982613i	$-0.440555\pi$
$929$	−531.821	−	307.047i	−0.572466	−	0.330513i	−0.758134	+	0.652099i	$0.773889\pi$
$930$		0			0
$931$	−565.752	−	979.911i	−0.607682	−	1.05254i
$932$		0			0
$933$	−428.845	−	1392.43i	−0.459641	−	1.49242i
$934$		0			0
$935$			5.06692i			0.00541917i
$936$		0			0
$937$	−1763.19			−1.88174			−0.940868	−	0.338774i	$-0.889988\pi$
$937$	−1763.19			−1.88174			−0.940868	+	0.338774i	$0.889988\pi$
$938$		0			0
$939$	−22.6613	−	21.0449i	−0.0241334	−	0.0224120i
$940$		0			0
$941$	−1201.52	+	693.697i	−1.27685	+	0.737191i	−0.976268	−	0.216564i	$-0.930515\pi$
$941$	−1201.52	+	693.697i	−1.27685	+	0.737191i	−0.300584	+	0.953755i	$0.597182\pi$
$942$		0			0
$943$	973.824	−	1686.71i	1.03269	−	1.78867i
$944$		0			0
$945$	−9.70808	−	7.76265i	−0.0102731	−	0.00821445i
$946$		0			0
$947$	1073.21	+	619.615i	1.13327	+	0.654293i	0.944755	−	0.327778i	$-0.106300\pi$
$947$	1073.21	+	619.615i	1.13327	+	0.654293i	0.188514	+	0.982071i	$0.439633\pi$
$948$		0			0
$949$	16.7145	+	28.9503i	0.0176127	+	0.0305061i
$950$		0			0
$951$	341.523	−	367.754i	0.359120	−	0.386702i
$952$		0			0
$953$		−	460.952i		−	0.483686i	−0.970315	−	0.241843i	$-0.922248\pi$
$953$		−	460.952i		−	0.483686i	0.970315	−	0.241843i	$-0.0777518\pi$
$954$		0			0
$955$	−9.67383			−0.0101297
$956$		0			0
$957$	−176.539	+	54.3710i	−0.184471	+	0.0568140i
$958$		0			0
$959$	−8.27714	+	4.77881i	−0.00863101	+	0.00498312i
$960$		0			0
$961$	−108.946	+	188.700i	−0.113368	+	0.196358i
$962$		0			0
$963$	−90.8780	+	188.292i	−0.0943697	+	0.195526i
$964$		0			0
$965$	0.466208	+	0.269166i	0.000483117	+	0.000278928i
$966$		0			0
$967$	9.76447	+	16.9126i	0.0100977	+	0.0174897i	0.871030	−	0.491230i	$-0.163452\pi$
$967$	9.76447	+	16.9126i	0.0100977	+	0.0174897i	−0.860932	+	0.508719i	$0.830119\pi$
$968$		0			0
$969$	2625.74	+	600.508i	2.70974	+	0.619720i
$970$		0			0
$971$			509.199i			0.524406i	0.965013	+	0.262203i	$0.0844491\pi$
$971$			509.199i			0.524406i	−0.965013	+	0.262203i	$0.915551\pi$
$972$		0			0
$973$	−821.921			−0.844728
$974$		0			0
$975$	7.25282	−	31.7132i	0.00743879	−	0.0325263i
$976$		0			0
$977$	886.588	−	511.872i	0.907460	−	0.523922i	0.0278467	−	0.999612i	$-0.491135\pi$
$977$	886.588	−	511.872i	0.907460	−	0.523922i	0.879613	+	0.475690i	$0.157802\pi$
$978$		0			0
$979$	−206.333	+	357.379i	−0.210759	+	0.365045i
$980$		0			0
$981$	1273.16	+	614.485i	1.29782	+	0.626387i
$982$		0			0
$983$	1161.49	+	670.589i	1.18158	+	0.682187i	0.956380	−	0.292126i	$-0.0943625\pi$
$983$	1161.49	+	670.589i	1.18158	+	0.682187i	0.225202	+	0.974312i	$0.427696\pi$
$984$		0			0
$985$	5.48536	+	9.50092i	0.00556889	+	0.00964560i
$986$		0			0
$987$	308.955	+	1003.16i	0.313025	+	1.01637i
$988$		0			0
$989$			273.281i			0.276320i
$990$		0			0
$991$	−505.274			−0.509863			−0.254931	−	0.966959i	$-0.582053\pi$
$991$	−505.274			−0.509863			−0.254931	+	0.966959i	$0.582053\pi$
$992$		0			0
$993$	−229.685	−	213.302i	−0.231304	−	0.214806i
$994$		0			0
$995$	6.45507	−	3.72683i	0.00648750	−	0.00374556i
$996$		0			0
$997$	−878.908	+	1522.31i	−0.881553	+	1.52689i	−0.0319379	+	0.999490i	$0.510168\pi$
$997$	−878.908	+	1522.31i	−0.881553	+	1.52689i	−0.849615	+	0.527404i	$0.823165\pi$
$998$		0			0
$999$	493.646	−	617.360i	0.494140	−	0.617978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.q.j.65.2		8
3.2	odd	2		1728.3.q.i.1601.2		8
4.3	odd	2		576.3.q.i.65.3		8
8.3	odd	2		72.3.m.b.65.2	yes	8
8.5	even	2		144.3.q.e.65.3		8
9.4	even	3		1728.3.q.i.449.2		8
9.5	odd	6	inner	576.3.q.j.257.2		8
12.11	even	2		1728.3.q.j.1601.2		8
24.5	odd	2		432.3.q.e.305.3		8
24.11	even	2		216.3.m.b.89.3		8
36.23	even	6		576.3.q.i.257.3		8
36.31	odd	6		1728.3.q.j.449.2		8
72.5	odd	6		144.3.q.e.113.3		8
72.11	even	6		648.3.e.c.161.5		8
72.13	even	6		432.3.q.e.17.3		8
72.29	odd	6		1296.3.e.i.161.5		8
72.43	odd	6		648.3.e.c.161.4		8
72.59	even	6		72.3.m.b.41.2	✓	8
72.61	even	6		1296.3.e.i.161.4		8
72.67	odd	6		216.3.m.b.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.2	✓	8	72.59	even	6
72.3.m.b.65.2	yes	8	8.3	odd	2
144.3.q.e.65.3		8	8.5	even	2
144.3.q.e.113.3		8	72.5	odd	6
216.3.m.b.17.3		8	72.67	odd	6
216.3.m.b.89.3		8	24.11	even	2
432.3.q.e.17.3		8	72.13	even	6
432.3.q.e.305.3		8	24.5	odd	2
576.3.q.i.65.3		8	4.3	odd	2
576.3.q.i.257.3		8	36.23	even	6
576.3.q.j.65.2		8	1.1	even	1	trivial
576.3.q.j.257.2		8	9.5	odd	6	inner
648.3.e.c.161.4		8	72.43	odd	6
648.3.e.c.161.5		8	72.11	even	6
1296.3.e.i.161.4		8	72.61	even	6
1296.3.e.i.161.5		8	72.29	odd	6
1728.3.q.i.449.2		8	9.4	even	3
1728.3.q.i.1601.2		8	3.2	odd	2
1728.3.q.j.449.2		8	36.31	odd	6
1728.3.q.j.1601.2		8	12.11	even	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.668833 - 2.92449i) q^{3} +(0.0440114 - 0.0254100i) q^{5} +(-4.52944 + 7.84521i) q^{7} +(-8.10532 - 3.91200i) q^{9} +O(q^{10})\)	\(q+(0.668833 - 2.92449i) q^{3} +(0.0440114 - 0.0254100i) q^{5} +(-4.52944 + 7.84521i) q^{7} +(-8.10532 - 3.91200i) q^{9} +(3.29117 + 1.90016i) q^{11} +(-0.216902 - 0.375686i) q^{13} +(-0.0448751 - 0.145706i) q^{15} +26.2355i q^{17} +34.2225 q^{19} +(19.9138 + 18.4934i) q^{21} +(29.9930 - 17.3164i) q^{23} +(-12.4987 + 21.6484i) q^{25} +(-16.8617 + 21.0875i) q^{27} +(-14.0316 - 8.10114i) q^{29} +(17.1675 + 29.7350i) q^{31} +(7.75825 - 8.35413i) q^{33} +0.460372i q^{35} -29.2761 q^{37} +(-1.24376 + 0.383058i) q^{39} +(48.7026 - 28.1185i) q^{41} +(-3.94539 + 6.83362i) q^{43} +(-0.456130 + 0.0337838i) q^{45} +(33.4489 + 19.3117i) q^{47} +(-16.5316 - 28.6335i) q^{49} +(76.7256 + 17.5472i) q^{51} +50.5273i q^{53} +0.193132 q^{55} +(22.8891 - 100.083i) q^{57} +(-8.54743 + 4.93486i) q^{59} +(36.5718 - 63.3442i) q^{61} +(67.4030 - 45.8689i) q^{63} +(-0.0190923 - 0.0110230i) q^{65} +(-12.6797 - 21.9618i) q^{67} +(-30.5815 - 99.2960i) q^{69} +97.8262i q^{71} -77.0599 q^{73} +(54.9511 + 51.0316i) q^{75} +(-29.8143 + 17.2133i) q^{77} +(42.1389 - 72.9868i) q^{79} +(50.3926 + 63.4160i) q^{81} +(40.6763 + 23.4845i) q^{83} +(0.666644 + 1.15466i) q^{85} +(-33.0765 + 35.6170i) q^{87} +108.587i q^{89} +3.92978 q^{91} +(98.4420 - 30.3185i) q^{93} +(1.50618 - 0.869593i) q^{95} +(-32.4021 + 56.1221i) q^{97} +(-19.2426 - 28.2765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{3} + 6 q^{5} - 6 q^{7} - 22 q^{9}+O(q^{10}) \) 8 * q + 10 * q^3 + 6 * q^5 - 6 * q^7 - 22 * q^9	\( 8 q + 10 q^{3} + 6 q^{5} - 6 q^{7} - 22 q^{9} + 36 q^{11} - 14 q^{13} - 10 q^{15} + 4 q^{19} + 54 q^{21} + 102 q^{23} + 10 q^{25} - 20 q^{27} + 114 q^{29} + 50 q^{31} - 104 q^{33} - 120 q^{37} - 82 q^{39} + 264 q^{41} - 28 q^{43} - 206 q^{45} - 150 q^{47} + 94 q^{49} + 170 q^{51} + 244 q^{55} - 178 q^{57} - 108 q^{59} - 14 q^{61} + 210 q^{63} - 198 q^{65} - 20 q^{67} + 14 q^{69} - 76 q^{73} + 326 q^{75} - 66 q^{77} - 26 q^{79} + 194 q^{81} + 246 q^{83} + 224 q^{85} + 18 q^{87} + 108 q^{91} + 130 q^{93} + 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) \) 8 * q + 10 * q^3 + 6 * q^5 - 6 * q^7 - 22 * q^9 + 36 * q^11 - 14 * q^13 - 10 * q^15 + 4 * q^19 + 54 * q^21 + 102 * q^23 + 10 * q^25 - 20 * q^27 + 114 * q^29 + 50 * q^31 - 104 * q^33 - 120 * q^37 - 82 * q^39 + 264 * q^41 - 28 * q^43 - 206 * q^45 - 150 * q^47 + 94 * q^49 + 170 * q^51 + 244 * q^55 - 178 * q^57 - 108 * q^59 - 14 * q^61 + 210 * q^63 - 198 * q^65 - 20 * q^67 + 14 * q^69 - 76 * q^73 + 326 * q^75 - 66 * q^77 - 26 * q^79 + 194 * q^81 + 246 * q^83 + 224 * q^85 + 18 * q^87 + 108 * q^91 + 130 * q^93 + 456 * q^95 - 236 * q^97 - 634 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more