LMFDB - Embedded newform 144.3.q.e.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, 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("144.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.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:	$3.92371580679$
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			113.3
Root			$0.831167 - 1.43962i$ of defining polynomial
Character	$\chi$	$=$	144.113
Dual form			144.3.q.e.65.3

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.668833	−	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	$-0.334951\pi$
$5$	−0.0440114	−	0.0254100i	−0.00880228	−	0.00508200i	−0.504395	+	0.863473i	$0.668284\pi$
$6$		0			0
$7$	−4.52944	−	7.84521i	−0.647062	−	1.12074i	−0.983821	−	0.179154i	$-0.942664\pi$
$7$	−4.52944	−	7.84521i	−0.647062	−	1.12074i	0.336759	−	0.941591i	$-0.390669\pi$
$8$		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	$-0.721929\pi$
$11$	−3.29117	+	1.90016i	−0.299198	+	0.172742i	0.342885	+	0.939377i	$0.388596\pi$
$12$		0			0
$13$	0.216902	−	0.375686i	0.0166848	−	0.0288989i	−0.857562	−	0.514380i	$-0.828022\pi$
$13$	0.216902	−	0.375686i	0.0166848	−	0.0288989i	0.874247	+	0.485481i	$0.161355\pi$
$14$		0			0
$15$	−0.0448751	+	0.145706i	−0.00299167	+	0.00971373i
$16$		0			0
$17$		−	26.2355i		−	1.54327i	−0.636068	−	0.771633i	$-0.719440\pi$
$17$		−	26.2355i		−	1.54327i	0.636068	−	0.771633i	$-0.280560\pi$
$18$		0			0
$19$	−34.2225			−1.80118			−0.900592	−	0.434666i	$-0.856867\pi$
$19$	−34.2225			−1.80118			−0.900592	+	0.434666i	$0.856867\pi$
$20$		0			0
$21$	−19.9138	+	18.4934i	−0.948278	+	0.880640i
$22$		0			0
$23$	29.9930	+	17.3164i	1.30404	+	0.752889i	0.981095	−	0.193528i	$-0.0619931\pi$
$23$	29.9930	+	17.3164i	1.30404	+	0.752889i	0.322947	+	0.946417i	$0.395326\pi$
$24$		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	$-0.576548\pi$
$29$	14.0316	−	8.10114i	0.483848	−	0.279350i	0.722019	+	0.691874i	$0.243214\pi$
$30$		0			0
$31$	17.1675	−	29.7350i	0.553790	−	0.959193i	−0.444206	−	0.895925i	$-0.646514\pi$
$31$	17.1675	−	29.7350i	0.553790	−	0.959193i	0.997997	−	0.0632685i	$-0.0201524\pi$
$32$		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	$-0.370529\pi$
$37$	29.2761			0.791247			0.395623	+	0.918413i	$0.370529\pi$
$38$		0			0
$39$	−1.24376	−	0.383058i	−0.0318913	−	0.00982200i
$40$		0			0
$41$	48.7026	+	28.1185i	1.18787	+	0.685816i	0.957822	−	0.287363i	$-0.0927787\pi$
$41$	48.7026	+	28.1185i	1.18787	+	0.685816i	0.230047	+	0.973180i	$0.426112\pi$
$42$		0			0
$43$	3.94539	+	6.83362i	0.0917533	+	0.158921i	0.908249	−	0.418430i	$-0.137420\pi$
$43$	3.94539	+	6.83362i	0.0917533	+	0.158921i	−0.816496	+	0.577352i	$0.804086\pi$
$44$		0			0
$45$	0.456130	+	0.0337838i	0.0101362	+	0.000750752i
$46$		0			0
$47$	33.4489	−	19.3117i	0.711678	−	0.410887i	−0.100004	−	0.994987i	$-0.531886\pi$
$47$	33.4489	−	19.3117i	0.711678	−	0.410887i	0.811682	+	0.584100i	$0.198552\pi$
$48$		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	$-0.306678\pi$
$59$	8.54743	+	4.93486i	0.144872	+	0.0836417i	−0.425812	+	0.904812i	$0.640012\pi$
$60$		0			0
$61$	−36.5718	−	63.3442i	−0.599537	−	1.03843i	−0.992889	−	0.119041i	$-0.962018\pi$
$61$	−36.5718	−	63.3442i	−0.599537	−	1.03843i	0.393352	−	0.919388i	$-0.371315\pi$
$62$		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	$-0.772728\pi$
$67$	12.6797	−	21.9618i	0.189249	−	0.327789i	0.945000	+	0.327070i	$0.106061\pi$
$68$		0			0
$69$	30.5815	−	99.2960i	0.443211	−	1.43907i
$70$		0			0
$71$		−	97.8262i		−	1.37783i	−0.724840	−	0.688917i	$-0.758086\pi$
$71$		−	97.8262i		−	1.37783i	0.724840	−	0.688917i	$-0.241914\pi$
$72$		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	0.999239	+	0.0390112i	$0.0124208\pi$
$79$	42.1389	+	72.9868i	0.533404	+	0.923883i	−0.465835	+	0.884872i	$0.654246\pi$
$80$		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	$-0.757978\pi$
$83$	−40.6763	+	23.4845i	−0.490076	+	0.282946i	0.234530	+	0.972109i	$0.424645\pi$
$84$		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	$-0.791154\pi$
$89$		−	108.587i		−	1.22008i	0.792371	−	0.610039i	$-0.208846\pi$
$90$		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	0.649258	−	0.760568i	$-0.275080\pi$
$97$	−32.4021	−	56.1221i	−0.334043	−	0.578579i	−0.983300	+	0.181990i	$0.941746\pi$
$98$		0			0
$99$	19.2426	−	28.2765i	0.194370	−	0.285621i
$100$		0			0
$101$	−168.478	+	97.2705i	−1.66809	+	0.963075i	−0.699430	+	0.714701i	$0.746563\pi$
$101$	−168.478	+	97.2705i	−1.66809	+	0.963075i	−0.968664	+	0.248373i	$0.920104\pi$
$102$		0			0
$103$	12.4420	−	21.5502i	0.120796	−	0.209225i	−0.799286	−	0.600951i	$-0.794789\pi$
$103$	12.4420	−	21.5502i	0.120796	−	0.209225i	0.920082	+	0.391726i	$0.128122\pi$
$104$		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	$-0.243895\pi$
$109$	157.077			1.44108			0.720538	+	0.693416i	$0.243895\pi$
$110$		0			0
$111$	−19.5808	−	85.6179i	−0.176404	−	0.771332i
$112$		0			0
$113$	−32.5614	−	18.7994i	−0.288154	−	0.166366i	0.348955	−	0.937140i	$-0.386537\pi$
$113$	−32.5614	−	18.7994i	−0.288154	−	0.166366i	−0.637109	+	0.770774i	$0.719870\pi$
$114$		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	$-0.333372\pi$
$131$	−0.0274376	−	0.0158411i	−0.000209447	−	0.000120924i	−0.500105	+	0.865965i	$0.666705\pi$
$132$		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	−0.496662	−	0.867944i	$-0.665441\pi$
$137$	0.913705	−	0.527528i	0.00666938	−	0.00385057i	0.503331	+	0.864094i	$0.332108\pi$
$138$		0			0
$139$	−45.3655	+	78.5754i	−0.326371	+	0.565290i	−0.981789	−	0.189976i	$-0.939159\pi$
$139$	−45.3655	+	78.5754i	−0.326371	+	0.565290i	0.655418	+	0.755266i	$0.272492\pi$
$140$		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	$-0.314688\pi$
$149$	15.1086	+	8.72295i	0.101400	+	0.0585433i	−0.448442	+	0.893812i	$0.648021\pi$
$150$		0			0
$151$	−40.8713	−	70.7912i	−0.270671	−	0.468816i	0.698363	−	0.715744i	$-0.253912\pi$
$151$	−40.8713	−	70.7912i	−0.270671	−	0.468816i	−0.969034	+	0.246928i	$0.920579\pi$
$152$		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	−0.375920	−	0.926652i	$-0.622673\pi$
$157$	96.4835	−	167.114i	0.614544	−	1.06442i	0.990464	−	0.137770i	$-0.0439934\pi$
$158$		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	$-0.330620\pi$
$163$	165.401			1.01473			0.507364	+	0.861732i	$0.330620\pi$
$164$		0			0
$165$	−0.129173	−	0.564814i	−0.000782868	−	0.00342311i
$166$		0			0
$167$	215.643	+	124.502i	1.29128	+	0.745520i	0.978881	−	0.204432i	$-0.0655346\pi$
$167$	215.643	+	124.502i	1.29128	+	0.745520i	0.312398	+	0.949951i	$0.398868\pi$
$168$		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	$-0.794901\pi$
$173$	−117.476	+	67.8248i	−0.679052	+	0.392051i	0.120446	+	0.992720i	$0.461568\pi$
$174$		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	$-0.447955\pi$
$181$	58.9249			0.325552			0.162776	+	0.986663i	$0.447955\pi$
$182$		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	−0.865049	−	0.501687i	$-0.832713\pi$
$191$	−164.852	+	95.1775i	−0.863101	+	0.498311i	0.00194880	+	0.999998i	$0.499380\pi$
$192$		0			0
$193$	5.29645	−	9.17373i	0.0274428	−	0.0475323i	−0.851978	−	0.523578i	$-0.824597\pi$
$193$	5.29645	−	9.17373i	0.0274428	−	0.0475323i	0.879421	+	0.476046i	$0.157930\pi$
$194$		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	$-0.749652\pi$
$211$	54.8335	−	94.9744i	0.259874	−	0.450116i	0.966208	+	0.257763i	$0.0829855\pi$
$212$		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	0.651610	−	0.758554i	$-0.274094\pi$
$223$	−73.8403	−	127.895i	−0.331123	−	0.573521i	−0.982732	+	0.185033i	$0.940761\pi$
$224$		0			0
$225$	185.995	+	126.572i	0.826642	+	0.562544i
$226$		0			0
$227$	346.255	−	199.911i	1.52535	−	0.880664i	0.525806	−	0.850605i	$-0.323764\pi$
$227$	346.255	−	199.911i	1.52535	−	0.880664i	0.999548	−	0.0300589i	$-0.00956949\pi$
$228$		0			0
$229$	39.1692	−	67.8430i	0.171044	−	0.296258i	−0.767741	−	0.640760i	$-0.778619\pi$
$229$	39.1692	−	67.8430i	0.171044	−	0.296258i	0.938785	+	0.344503i	$0.111953\pi$
$230$		0			0
$231$	30.3994	−	98.7046i	0.131599	−	0.427293i
$232$		0			0
$233$			352.995i			1.51500i	0.652835	+	0.757500i	$0.273580\pi$
$233$			352.995i			1.51500i	−0.652835	+	0.757500i	$0.726420\pi$
$234$		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	−0.216060	−	0.976380i	$-0.569321\pi$
$239$	−279.549	−	161.397i	−1.16966	−	0.675303i	−0.953600	+	0.301077i	$0.902654\pi$
$240$		0			0
$241$	−105.601	−	182.907i	−0.438180	−	0.758949i	0.559370	−	0.828918i	$-0.311043\pi$
$241$	−105.601	−	182.907i	−0.438180	−	0.758949i	−0.997549	+	0.0699691i	$0.977710\pi$
$242$		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	0.539813	−	0.841785i	$-0.318495\pi$
$257$	20.7432	+	11.9761i	0.0807127	+	0.0465995i	−0.459100	+	0.888384i	$0.651828\pi$
$258$		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	−0.255592	−	0.966785i	$-0.582270\pi$
$263$	119.369	−	68.9175i	0.453873	−	0.262044i	0.709464	+	0.704741i	$0.248937\pi$
$264$		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	−0.981359	−	0.192185i	$-0.938443\pi$
$277$	−182.021	−	315.270i	−0.657117	−	1.13816i	0.324242	−	0.945974i	$-0.394891\pi$
$278$		0			0
$279$	−22.8251	+	308.171i	−0.0818102	+	1.10456i
$280$		0			0
$281$	241.120	−	139.211i	0.858077	−	0.495411i	−0.00529060	−	0.999986i	$-0.501684\pi$
$281$	241.120	−	139.211i	0.858077	−	0.495411i	0.863368	+	0.504575i	$0.168351\pi$
$282$		0			0
$283$	13.7745	−	23.8581i	0.0486732	−	0.0843044i	−0.840662	−	0.541560i	$-0.817834\pi$
$283$	13.7745	−	23.8581i	0.0486732	−	0.0843044i	0.889336	+	0.457255i	$0.151167\pi$
$284$		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	$-0.0978267\pi$
$293$	342.145	+	197.537i	1.16773	+	0.674189i	0.214585	+	0.976705i	$0.431160\pi$
$294$		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	$-0.436095\pi$
$307$	122.443			0.398836			0.199418	+	0.979915i	$0.436095\pi$
$308$		0			0
$309$	−71.3449	−	21.9731i	−0.230890	−	0.0711102i
$310$		0			0
$311$	420.591	+	242.829i	1.35238	+	0.780799i	0.988583	−	0.150677i	$-0.0481455\pi$
$311$	420.591	+	242.829i	1.35238	+	0.780799i	0.363801	+	0.931477i	$0.381479\pi$
$312$		0			0
$313$	5.15434	+	8.92759i	0.0164676	+	0.0285226i	0.874142	−	0.485671i	$-0.161425\pi$
$313$	5.15434	+	8.92759i	0.0164676	+	0.0285226i	−0.857674	+	0.514194i	$0.828091\pi$
$314$		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	$-0.751665\pi$
$317$	−144.879	+	83.6462i	−0.457033	+	0.263868i	0.253763	+	0.967266i	$0.418332\pi$
$318$		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	$-0.217117\pi$
$331$	−52.2422	−	90.4861i	−0.157831	−	0.273372i	−0.934086	+	0.357047i	$0.883784\pi$
$332$		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	−0.413401	−	0.910549i	$-0.635659\pi$
$337$	196.086	−	339.631i	0.581858	−	1.00781i	0.995259	−	0.0972586i	$-0.0310074\pi$
$338$		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	$-0.468270\pi$
$347$	−247.220	−	142.732i	−0.712449	−	0.411333i	−0.811967	+	0.583703i	$0.801603\pi$
$348$		0			0
$349$	151.562	+	262.514i	0.434276	+	0.752189i	0.997236	−	0.0742956i	$-0.0236708\pi$
$349$	151.562	+	262.514i	0.434276	+	0.752189i	−0.562960	+	0.826484i	$0.690337\pi$
$350$		0			0
$351$	11.5796	−	1.76078i	0.0329903	−	0.00501646i
$352$		0			0
$353$	308.183	−	177.929i	0.873039	−	0.504049i	0.00468222	−	0.999989i	$-0.498510\pi$
$353$	308.183	−	177.929i	0.873039	−	0.504049i	0.868357	+	0.495940i	$0.165176\pi$
$354$		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	$0.0661639\pi$
$359$			148.171i			0.412733i	−0.978475	+	0.206367i	$0.933836\pi$
$360$		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	0.983915	−	0.178636i	$-0.0571686\pi$
$367$	123.772	+	214.380i	0.337254	+	0.584141i	−0.646661	+	0.762777i	$0.723835\pi$
$368$		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	0.390597	+	0.920562i	$0.372269\pi$
$373$	−224.520	+	388.881i	−0.601931	+	1.04258i	−0.992528	+	0.122014i	$0.961065\pi$
$374$		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	$-0.803634\pi$
$379$	−618.282			−1.63135			−0.815675	+	0.578510i	$0.803634\pi$
$380$		0			0
$381$	32.3959	+	141.652i	0.0850285	+	0.371790i
$382$		0			0
$383$	370.803	+	214.083i	0.968155	+	0.558965i	0.898673	−	0.438619i	$-0.144532\pi$
$383$	370.803	+	214.083i	0.968155	+	0.558965i	0.0694818	+	0.997583i	$0.477865\pi$
$384$		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	0.504674	−	0.863310i	$-0.331613\pi$
$389$	585.313	−	337.930i	1.50466	−	0.868716i	0.999985	−	0.00540555i	$-0.00172065\pi$
$390$		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	$-0.414839\pi$
$397$	209.902			0.528721			0.264361	+	0.964424i	$0.414839\pi$
$398$		0			0
$399$	681.501	−	632.892i	1.70802	−	1.58619i
$400$		0			0
$401$	175.023	+	101.050i	0.436467	+	0.251994i	0.702098	−	0.712080i	$-0.252247\pi$
$401$	175.023	+	101.050i	0.436467	+	0.251994i	−0.265631	+	0.964075i	$0.585580\pi$
$402$		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	0.251957	+	0.967739i	$0.418926\pi$
$409$	−291.252	+	504.464i	−0.712108	+	1.23341i	−0.964064	+	0.265669i	$0.914407\pi$
$410$		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	−0.988888	−	0.148662i	$-0.952503\pi$
$419$	−675.460	−	389.977i	−1.61208	−	0.930733i	−0.623189	−	0.782071i	$-0.714163\pi$
$420$		0			0
$421$	−84.1068	−	145.677i	−0.199779	−	0.346027i	0.748678	−	0.662934i	$-0.230689\pi$
$421$	−84.1068	−	145.677i	−0.199779	−	0.346027i	−0.948457	+	0.316907i	$0.897356\pi$
$422$		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	$0.0679933\pi$
$431$			182.732i			0.423973i	−0.977273	+	0.211986i	$0.932007\pi$
$432$		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	0.731581	−	0.681754i	$-0.238783\pi$
$439$	−98.6108	−	170.799i	−0.224626	−	0.389063i	−0.956207	+	0.292691i	$0.905449\pi$
$440$		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	$-0.770029\pi$
$443$	−244.803	+	141.337i	−0.552603	+	0.319045i	0.197568	+	0.980289i	$0.436696\pi$
$444$		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	$0.127073\pi$
$449$			349.046i			0.777386i	−0.921367	+	0.388693i	$0.872927\pi$
$450$		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	0.818561	−	0.574419i	$-0.194772\pi$
$457$	−40.2987	−	69.7995i	−0.0881811	−	0.152734i	−0.906742	+	0.421685i	$0.861439\pi$
$458$		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	$-0.453759\pi$
$461$	495.135	−	285.866i	1.07405	−	0.620100i	0.929284	+	0.369366i	$0.120425\pi$
$462$		0			0
$463$	−139.837	+	242.205i	−0.302024	+	0.523120i	−0.976594	−	0.215090i	$-0.930996\pi$
$463$	−139.837	+	242.205i	−0.302024	+	0.523120i	0.674571	+	0.738210i	$0.264329\pi$
$464$		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	−0.255361	−	0.966846i	$-0.582194\pi$
$479$	217.596	−	125.629i	0.454271	−	0.262274i	0.709632	+	0.704572i	$0.248861\pi$
$480$		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	$-0.549134\pi$
$491$	−533.397	−	307.957i	−1.08635	−	0.627204i	−0.932602	+	0.360906i	$0.882467\pi$
$492$		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	−0.0756679	−	0.997133i	$-0.524109\pi$
$499$	412.029	−	713.654i	0.825709	−	1.43017i	0.901377	−	0.433036i	$-0.142558\pi$
$500$		0			0
$501$	219.875	−	713.919i	0.438873	−	1.42499i
$502$		0			0
$503$		−	175.718i		−	0.349340i	−0.984627	−	0.174670i	$-0.944114\pi$
$503$		−	175.718i		−	0.349340i	0.984627	−	0.174670i	$-0.0558858\pi$
$504$		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	$-0.449610\pi$
$509$	−314.934	−	181.827i	−0.618730	−	0.357224i	−0.776374	+	0.630272i	$0.782943\pi$
$510$		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	$0.145099\pi$
$521$			458.709i			0.880440i	−0.897890	+	0.440220i	$0.854901\pi$
$522$		0			0
$523$	458.289			0.876270			0.438135	−	0.898909i	$-0.355639\pi$
$523$	458.289			0.876270			0.438135	+	0.898909i	$0.355639\pi$
$524$		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	$-0.775961\pi$
$541$	−824.876			−1.52472			−0.762362	+	0.647150i	$0.775961\pi$
$542$		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	$-0.156847\pi$
$547$	16.8719	+	29.2230i	0.0308444	+	0.0534241i	−0.850191	+	0.526474i	$0.823514\pi$
$548$		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	$-0.301326\pi$
$563$	97.8909	+	56.5173i	0.173874	+	0.100386i	−0.410537	+	0.911844i	$0.634659\pi$
$564$		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	−0.277545	−	0.960713i	$-0.589521\pi$
$569$	236.524	−	136.557i	0.415684	−	0.239995i	0.693229	+	0.720717i	$0.256187\pi$
$570$		0			0
$571$	−122.654	+	212.443i	−0.214806	+	0.372054i	−0.953212	−	0.302301i	$-0.902245\pi$
$571$	−122.654	+	212.443i	−0.214806	+	0.372054i	0.738407	+	0.674356i	$0.235579\pi$
$572$		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	0.701942	−	0.712234i	$-0.252317\pi$
$587$	980.129	−	565.878i	1.66973	−	0.964017i	0.967784	−	0.251782i	$-0.0810167\pi$
$588$		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	$0.0485553\pi$
$593$			180.213i			0.303900i	−0.988388	+	0.151950i	$0.951445\pi$
$594$		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	0.891541	−	0.452941i	$-0.149625\pi$
$599$	566.086	+	326.830i	0.945052	+	0.545626i	0.0535119	+	0.998567i	$0.482959\pi$
$600$		0			0
$601$	−178.947	−	309.945i	−0.297749	−	0.515716i	0.677872	−	0.735180i	$-0.262902\pi$
$601$	−178.947	−	309.945i	−0.297749	−	0.515716i	−0.975621	+	0.219464i	$0.929569\pi$
$602$		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	0.472206	+	0.881488i	$0.343458\pi$
$607$	−320.064	+	554.367i	−0.527288	+	0.913290i	−0.999494	+	0.0318015i	$0.989876\pi$
$608$		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	$-0.435669\pi$
$613$	246.093			0.401457			0.200729	+	0.979647i	$0.435669\pi$
$614$		0			0
$615$	−6.28256	+	5.83445i	−0.0102155	+	0.00948690i
$616$		0			0
$617$	309.912	+	178.928i	0.502289	+	0.289997i	0.729658	−	0.683812i	$-0.239679\pi$
$617$	309.912	+	178.928i	0.502289	+	0.289997i	−0.227369	+	0.973809i	$0.573013\pi$
$618$		0			0
$619$	40.5053	+	70.1573i	0.0654368	+	0.113340i	0.896888	−	0.442258i	$-0.145823\pi$
$619$	40.5053	+	70.1573i	0.0654368	+	0.113340i	−0.831451	+	0.555598i	$0.812489\pi$
$620$		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	−0.983012	−	0.183542i	$-0.941244\pi$
$641$	−843.278	+	486.867i	−1.31557	+	0.759542i	−0.332554	+	0.943084i	$0.607910\pi$
$642$		0			0
$643$	341.530	−	591.547i	0.531151	−	0.919980i	−0.468188	−	0.883629i	$-0.655093\pi$
$643$	341.530	−	591.547i	0.531151	−	0.919980i	0.999339	−	0.0363512i	$-0.0115735\pi$
$644$		0			0
$645$	−1.17275	+	0.268208i	−0.00181822	+	0.000415827i
$646$		0			0
$647$			390.640i			0.603771i	0.953344	+	0.301885i	$0.0976160\pi$
$647$			390.640i			0.603771i	−0.953344	+	0.301885i	$0.902384\pi$
$648$		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	$-0.174087\pi$
$653$	542.529	+	313.230i	0.830826	+	0.479678i	−0.0233093	+	0.999728i	$0.507420\pi$
$654$		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	$-0.681020\pi$
$659$	−51.4518	+	29.7057i	−0.0780755	+	0.0450769i	0.460454	+	0.887684i	$0.347687\pi$
$660$		0			0
$661$	425.950	−	737.767i	0.644402	−	1.11614i	−0.340037	−	0.940412i	$-0.610440\pi$
$661$	425.950	−	737.767i	0.644402	−	1.11614i	0.984439	−	0.175725i	$-0.0562270\pi$
$662$		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	0.978959	−	0.204056i	$-0.0654124\pi$
$673$	210.489	+	364.577i	0.312762	+	0.541720i	−0.666197	+	0.745776i	$0.732079\pi$
$674$		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	$-0.580566\pi$
$677$	313.326	−	180.899i	0.462816	−	0.267207i	0.713227	+	0.700933i	$0.247233\pi$
$678$		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	$-0.333272\pi$
$691$	−345.384	−	598.222i	−0.499832	−	0.865734i	−1.00000		0.000194148i	$0.999938\pi$
$692$		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	$-0.0630848\pi$
$709$	226.667	+	392.598i	0.319699	+	0.553735i	−0.660726	+	0.750627i	$0.729751\pi$
$710$		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	$-0.905925\pi$
$719$		−	418.833i		−	0.582522i	0.956644	−	0.291261i	$-0.0940748\pi$
$720$		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	−0.999795	−	0.0202365i	$-0.993558\pi$
$727$	−376.166	−	651.539i	−0.517423	−	0.896203i	0.482372	−	0.875966i	$-0.339775\pi$
$728$		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	$-0.719833\pi$
$733$	255.863	−	443.168i	0.349063	−	0.604595i	0.986083	+	0.166252i	$0.0531665\pi$
$734$		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	$-0.397710\pi$
$739$	466.830			0.631705			0.315853	+	0.948808i	$0.397710\pi$
$740$		0			0
$741$	42.5646	+	13.1092i	0.0574421	+	0.0176912i
$742$		0			0
$743$	546.320	+	315.418i	0.735290	+	0.424520i	0.820354	−	0.571856i	$-0.193776\pi$
$743$	546.320	+	315.418i	0.735290	+	0.424520i	−0.0850643	+	0.996375i	$0.527110\pi$
$744$		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	−0.920081	−	0.391727i	$-0.871878\pi$
$751$	−90.7172	+	157.127i	−0.120795	+	0.209223i	0.799286	+	0.600950i	$0.205211\pi$
$752$		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	$-0.866003\pi$
$757$	−1381.82			−1.82539			−0.912696	+	0.408640i	$0.866003\pi$
$758$		0			0
$759$	88.0292	+	384.910i	0.115980	+	0.507128i
$760$		0			0
$761$	−590.093	−	340.690i	−0.775418	−	0.447688i	0.0593862	−	0.998235i	$-0.481086\pi$
$761$	−590.093	−	340.690i	−0.775418	−	0.447688i	−0.834804	+	0.550548i	$0.814419\pi$
$762$		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	−0.893903	−	0.448261i	$-0.852043\pi$
$769$	−45.1754	+	78.2461i	−0.0587457	+	0.101750i	0.835157	+	0.550012i	$0.185377\pi$
$770$		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	$-0.987633\pi$
$787$	−366.731	+	635.196i	−0.465986	+	0.807111i	0.533260	+	0.845951i	$0.320967\pi$
$788$		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	$-0.121164\pi$
$797$	853.500	+	492.768i	1.07089	+	0.618279i	0.142466	+	0.989800i	$0.454497\pi$
$798$		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	$-0.908308\pi$
$809$		−	459.662i		−	0.568185i	0.958797	−	0.284093i	$-0.0916923\pi$
$810$		0			0
$811$	−912.030			−1.12457			−0.562287	−	0.826942i	$-0.690078\pi$
$811$	−912.030			−1.12457			−0.562287	+	0.826942i	$0.690078\pi$
$812$		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	$-0.616213\pi$
$821$	224.455	−	129.589i	0.273393	−	0.157843i	0.630428	+	0.776247i	$0.282879\pi$
$822$		0			0
$823$	721.885	−	1250.34i	0.877139	−	1.51925i	0.0226714	−	0.999743i	$-0.492783\pi$
$823$	721.885	−	1250.34i	0.877139	−	1.51925i	0.854467	−	0.519506i	$-0.173884\pi$
$824$		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	$-0.582446\pi$
$829$	−424.655			−0.512250			−0.256125	+	0.966644i	$0.582446\pi$
$830$		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	−0.468567	−	0.883428i	$-0.655230\pi$
$839$	52.2029	−	30.1394i	0.0622204	−	0.0359230i	0.530787	+	0.847505i	$0.321896\pi$
$840$		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	−0.966122	−	0.258087i	$-0.916908\pi$
$853$	−602.705	−	1043.92i	−0.706571	−	1.22382i	0.259550	−	0.965730i	$-0.416426\pi$
$854$		0			0
$855$	−15.6099	−	1.15617i	−0.0182572	−	0.00135224i
$856$		0			0
$857$	174.400	−	100.690i	0.203500	−	0.117491i	−0.394787	−	0.918773i	$-0.629182\pi$
$857$	174.400	−	100.690i	0.203500	−	0.117491i	0.598287	+	0.801282i	$0.295848\pi$
$858$		0			0
$859$	−706.859	+	1224.31i	−0.822885	+	1.42528i	0.0806394	+	0.996743i	$0.474304\pi$
$859$	−706.859	+	1224.31i	−0.822885	+	1.42528i	−0.903525	+	0.428536i	$0.859030\pi$
$860$		0			0
$861$	−1489.86	+	340.732i	−1.73039	+	0.395740i
$862$		0			0
$863$		−	299.383i		−	0.346909i	−0.984842	−	0.173455i	$-0.944507\pi$
$863$		−	299.383i		−	0.346909i	0.984842	−	0.173455i	$-0.0554930\pi$
$864$		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	$-0.742408\pi$
$877$	247.122	−	428.029i	0.281782	−	0.488060i	0.971824	+	0.235709i	$0.0757413\pi$
$878$		0			0
$879$	348.859	−	1132.72i	0.396882	−	1.28865i
$880$		0			0
$881$			211.533i			0.240105i	0.992768	+	0.120053i	$0.0383063\pi$
$881$			211.533i			0.240105i	−0.992768	+	0.120053i	$0.961694\pi$
$882$		0			0
$883$	410.167			0.464515			0.232258	−	0.972654i	$-0.425389\pi$
$883$	410.167			0.464515			0.232258	+	0.972654i	$0.425389\pi$
$884$		0			0
$885$	−1.10261	+	1.02396i	−0.00124588	+	0.00115702i
$886$		0			0
$887$	734.748	+	424.207i	0.828352	+	0.478249i	0.853288	−	0.521440i	$-0.174605\pi$
$887$	734.748	+	424.207i	0.828352	+	0.478249i	−0.0249363	+	0.999689i	$0.507938\pi$
$888$		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	0.986152	+	0.165844i	$0.0530347\pi$
$907$	577.488	+	1000.24i	0.636701	+	1.10280i	−0.349451	+	0.936955i	$0.613632\pi$
$908$		0			0
$909$	985.043	−	1447.49i	1.08366	−	1.59240i
$910$		0			0
$911$	−454.824	+	262.593i	−0.499258	+	0.288247i	−0.728407	−	0.685145i	$-0.759739\pi$
$911$	−454.824	+	262.593i	−0.499258	+	0.288247i	0.229149	+	0.973391i	$0.426406\pi$
$912$		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	−0.758134	−	0.652099i	$-0.773889\pi$
$929$	−531.821	+	307.047i	−0.572466	+	0.330513i	0.185668	+	0.982613i	$0.440555\pi$
$930$		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	$-0.0694851\pi$
$941$	1201.52	+	693.697i	1.27685	+	0.737191i	0.300584	+	0.953755i	$0.402818\pi$
$942$		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	$-0.893700\pi$
$947$	−1073.21	+	619.615i	−1.13327	+	0.654293i	−0.188514	+	0.982071i	$0.560367\pi$
$948$		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	$0.0777518\pi$
$953$			460.952i			0.483686i	−0.970315	+	0.241843i	$0.922248\pi$
$954$		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	−0.860932	−	0.508719i	$-0.830119\pi$
$967$	9.76447	−	16.9126i	0.0100977	−	0.0174897i	0.871030	+	0.491230i	$0.163452\pi$
$968$		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	0.879613	−	0.475690i	$-0.157802\pi$
$977$	886.588	+	511.872i	0.907460	+	0.523922i	0.0278467	+	0.999612i	$0.491135\pi$
$978$		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	0.225202	−	0.974312i	$-0.427696\pi$
$983$	1161.49	−	670.589i	1.18158	−	0.682187i	0.956380	+	0.292126i	$0.0943625\pi$
$984$		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	0.849615	+	0.527404i	$0.176835\pi$
$997$	878.908	+	1522.31i	0.881553	+	1.52689i	0.0319379	+	0.999490i	$0.489832\pi$
$998$		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	144.3.q.e.113.3		8
3.2	odd	2		432.3.q.e.17.3		8
4.3	odd	2		72.3.m.b.41.2	✓	8
8.3	odd	2		576.3.q.i.257.3		8
8.5	even	2		576.3.q.j.257.2		8
9.2	odd	6	inner	144.3.q.e.65.3		8
9.4	even	3		1296.3.e.i.161.5		8
9.5	odd	6		1296.3.e.i.161.4		8
9.7	even	3		432.3.q.e.305.3		8
12.11	even	2		216.3.m.b.17.3		8
24.5	odd	2		1728.3.q.i.449.2		8
24.11	even	2		1728.3.q.j.449.2		8
36.7	odd	6		216.3.m.b.89.3		8
36.11	even	6		72.3.m.b.65.2	yes	8
36.23	even	6		648.3.e.c.161.4		8
36.31	odd	6		648.3.e.c.161.5		8
72.11	even	6		576.3.q.i.65.3		8
72.29	odd	6		576.3.q.j.65.2		8
72.43	odd	6		1728.3.q.j.1601.2		8
72.61	even	6		1728.3.q.i.1601.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.2	✓	8	4.3	odd	2
72.3.m.b.65.2	yes	8	36.11	even	6
144.3.q.e.65.3		8	9.2	odd	6	inner
144.3.q.e.113.3		8	1.1	even	1	trivial
216.3.m.b.17.3		8	12.11	even	2
216.3.m.b.89.3		8	36.7	odd	6
432.3.q.e.17.3		8	3.2	odd	2
432.3.q.e.305.3		8	9.7	even	3
576.3.q.i.65.3		8	72.11	even	6
576.3.q.i.257.3		8	8.3	odd	2
576.3.q.j.65.2		8	72.29	odd	6
576.3.q.j.257.2		8	8.5	even	2
648.3.e.c.161.4		8	36.23	even	6
648.3.e.c.161.5		8	36.31	odd	6
1296.3.e.i.161.4		8	9.5	odd	6
1296.3.e.i.161.5		8	9.4	even	3
1728.3.q.i.449.2		8	24.5	odd	2
1728.3.q.i.1601.2		8	72.61	even	6
1728.3.q.j.449.2		8	24.11	even	2
1728.3.q.j.1601.2		8	72.43	odd	6

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.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

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