LMFDB - Embedded newform 576.3.o.g.511.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(319,576)]

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([3, 0, 2]))

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

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

chi := DirichletCharacter("576.319");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.o (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			511.5
Root			$-1.59523 + 1.20633i$ of defining polynomial
Character	$\chi$	$=$	576.511
Dual form			576.3.o.g.319.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.262217 + 2.98852i) q^{3} +(-1.10093 - 1.90686i) q^{5} +(-7.23844 - 4.17912i) q^{7} +(-8.86248 + 1.56728i) q^{9} +O(q^{10})$	\(q+(0.262217 + 2.98852i) q^{3} +(-1.10093 - 1.90686i) q^{5} +(-7.23844 - 4.17912i) q^{7} +(-8.86248 + 1.56728i) q^{9} +(-4.54769 - 2.62561i) q^{11} +(7.37788 + 12.7789i) q^{13} +(5.41000 - 3.79015i) q^{15} +28.2789 q^{17} -19.1376i q^{19} +(10.5913 - 22.7281i) q^{21} +(-3.16702 + 1.82848i) q^{23} +(10.0759 - 17.4520i) q^{25} +(-7.00775 - 26.0747i) q^{27} +(12.3355 - 21.3657i) q^{29} +(32.9674 - 19.0338i) q^{31} +(6.65419 - 14.2793i) q^{33} +18.4036i q^{35} +4.21977 q^{37} +(-36.2553 + 25.3998i) q^{39} +(-9.92483 - 17.1903i) q^{41} +(20.1894 + 11.6564i) q^{43} +(12.7455 + 15.1740i) q^{45} +(-25.8538 - 14.9267i) q^{47} +(10.4300 + 18.0654i) q^{49} +(7.41521 + 84.5120i) q^{51} +32.1118 q^{53} +11.5624i q^{55} +(57.1930 - 5.01820i) q^{57} +(-7.96159 + 4.59663i) q^{59} +(40.8215 - 70.7049i) q^{61} +(70.7005 + 25.6927i) q^{63} +(16.2450 - 28.1372i) q^{65} +(6.86179 - 3.96166i) q^{67} +(-6.29489 - 8.98523i) q^{69} +62.9286i q^{71} +33.3218 q^{73} +(54.7978 + 25.5359i) q^{75} +(21.9454 + 38.0106i) q^{77} +(-53.7133 - 31.0114i) q^{79} +(76.0873 - 27.7800i) q^{81} +(-103.056 - 59.4995i) q^{83} +(-31.1329 - 53.9238i) q^{85} +(67.0864 + 31.2624i) q^{87} -107.361 q^{89} -123.332i q^{91} +(65.5274 + 93.5328i) q^{93} +(-36.4927 + 21.0690i) q^{95} +(1.78621 - 3.09380i) q^{97} +(44.4189 + 16.1419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} + 18 q^{9}+O(q^{10}) $ 16 * q - 6 * q^5 + 18 * q^9	$ 16 q - 6 q^{5} + 18 q^{9} + 46 q^{13} + 12 q^{17} + 66 q^{21} - 30 q^{25} - 42 q^{29} - 168 q^{33} - 56 q^{37} + 84 q^{41} - 174 q^{45} + 58 q^{49} + 72 q^{53} + 366 q^{57} + 34 q^{61} - 30 q^{65} + 54 q^{69} + 116 q^{73} + 330 q^{77} - 102 q^{81} + 140 q^{85} - 384 q^{89} + 486 q^{93} - 148 q^{97}+O(q^{100}) $ 16 * q - 6 * q^5 + 18 * q^9 + 46 * q^13 + 12 * q^17 + 66 * q^21 - 30 * q^25 - 42 * q^29 - 168 * q^33 - 56 * q^37 + 84 * q^41 - 174 * q^45 + 58 * q^49 + 72 * q^53 + 366 * q^57 + 34 * q^61 - 30 * q^65 + 54 * q^69 + 116 * q^73 + 330 * q^77 - 102 * q^81 + 140 * q^85 - 384 * q^89 + 486 * q^93 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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
$3$	0.262217	+	2.98852i	0.0874058	+	0.996173i
$3$	0.262217	+	2.98852i	0.0874058	+	0.996173i
$4$		0			0
$5$	−1.10093	−	1.90686i	−0.220185	−	0.381372i	0.734679	−	0.678415i	$-0.237333\pi$
$5$	−1.10093	−	1.90686i	−0.220185	−	0.381372i	−0.954864	+	0.297043i	$0.903999\pi$
$6$		0			0
$7$	−7.23844	−	4.17912i	−1.03406	−	0.597017i	−0.115917	−	0.993259i	$-0.536981\pi$
$7$	−7.23844	−	4.17912i	−1.03406	−	0.597017i	−0.918146	+	0.396242i	$0.870314\pi$
$8$		0			0
$9$	−8.86248	+	1.56728i	−0.984720	+	0.174143i
$10$		0			0
$11$	−4.54769	−	2.62561i	−0.413426	−	0.238692i	0.278835	−	0.960339i	$-0.410052\pi$
$11$	−4.54769	−	2.62561i	−0.413426	−	0.238692i	−0.692261	+	0.721648i	$0.743385\pi$
$12$		0			0
$13$	7.37788	+	12.7789i	0.567529	+	0.982990i	0.996809	+	0.0798182i	$0.0254340\pi$
$13$	7.37788	+	12.7789i	0.567529	+	0.982990i	−0.429280	+	0.903171i	$0.641233\pi$
$14$		0			0
$15$	5.41000	−	3.79015i	0.360667	−	0.252676i
$16$		0			0
$17$	28.2789			1.66346			0.831732	−	0.555178i	$-0.187350\pi$
$17$	28.2789			1.66346			0.831732	+	0.555178i	$0.187350\pi$
$18$		0			0
$19$		−	19.1376i		−	1.00724i	−0.863925	−	0.503620i	$-0.832001\pi$
$19$		−	19.1376i		−	1.00724i	0.863925	−	0.503620i	$-0.167999\pi$
$20$		0			0
$21$	10.5913	−	22.7281i	0.504349	−	1.08229i
$22$		0			0
$23$	−3.16702	+	1.82848i	−0.137696	+	0.0794990i	−0.567266	−	0.823535i	$-0.691999\pi$
$23$	−3.16702	+	1.82848i	−0.137696	+	0.0794990i	0.429569	+	0.903034i	$0.358665\pi$
$24$		0			0
$25$	10.0759	−	17.4520i	0.403037	−	0.698081i
$26$		0			0
$27$	−7.00775	−	26.0747i	−0.259546	−	0.965731i
$28$		0			0
$29$	12.3355	−	21.3657i	0.425362	−	0.736748i	−0.571092	−	0.820886i	$-0.693480\pi$
$29$	12.3355	−	21.3657i	0.425362	−	0.736748i	0.996454	+	0.0841375i	$0.0268135\pi$
$30$		0			0
$31$	32.9674	−	19.0338i	1.06347	−	0.613992i	0.137077	−	0.990560i	$-0.456229\pi$
$31$	32.9674	−	19.0338i	1.06347	−	0.613992i	0.926389	+	0.376568i	$0.122896\pi$
$32$		0			0
$33$	6.65419	−	14.2793i	0.201642	−	0.432707i
$34$		0			0
$35$			18.4036i			0.525817i
$36$		0			0
$37$	4.21977			0.114048			0.0570239	−	0.998373i	$-0.481839\pi$
$37$	4.21977			0.114048			0.0570239	+	0.998373i	$0.481839\pi$
$38$		0			0
$39$	−36.2553	+	25.3998i	−0.929622	+	0.651276i
$40$		0			0
$41$	−9.92483	−	17.1903i	−0.242069	−	0.419276i	0.719235	−	0.694767i	$-0.244493\pi$
$41$	−9.92483	−	17.1903i	−0.242069	−	0.419276i	−0.961303	+	0.275492i	$0.911159\pi$
$42$		0			0
$43$	20.1894	+	11.6564i	0.469521	+	0.271078i	0.716039	−	0.698060i	$-0.245953\pi$
$43$	20.1894	+	11.6564i	0.469521	+	0.271078i	−0.246518	+	0.969138i	$0.579286\pi$
$44$		0			0
$45$	12.7455	+	15.1740i	0.283234	+	0.337201i
$46$		0			0
$47$	−25.8538	−	14.9267i	−0.550082	−	0.317590i	0.199073	−	0.979985i	$-0.436207\pi$
$47$	−25.8538	−	14.9267i	−0.550082	−	0.317590i	−0.749155	+	0.662395i	$0.769540\pi$
$48$		0			0
$49$	10.4300	+	18.0654i	0.212858	+	0.368681i
$50$		0			0
$51$	7.41521	+	84.5120i	0.145396	+	1.65710i
$52$		0			0
$53$	32.1118			0.605883			0.302942	−	0.953009i	$-0.402031\pi$
$53$	32.1118			0.605883			0.302942	+	0.953009i	$0.402031\pi$
$54$		0			0
$55$			11.5624i			0.210225i
$56$		0			0
$57$	57.1930	−	5.01820i	1.00339	−	0.0880387i
$58$		0			0
$59$	−7.96159	+	4.59663i	−0.134942	+	0.0779089i	−0.565951	−	0.824439i	$-0.691491\pi$
$59$	−7.96159	+	4.59663i	−0.134942	+	0.0779089i	0.431009	+	0.902348i	$0.358158\pi$
$60$		0			0
$61$	40.8215	−	70.7049i	0.669205	−	1.15910i	−0.308922	−	0.951087i	$-0.599968\pi$
$61$	40.8215	−	70.7049i	0.669205	−	1.15910i	0.978127	−	0.208009i	$-0.0666985\pi$
$62$		0			0
$63$	70.7005	+	25.6927i	1.12223	+	0.407820i
$64$		0			0
$65$	16.2450	−	28.1372i	0.249923	−	0.432879i
$66$		0			0
$67$	6.86179	−	3.96166i	0.102415	−	0.0591292i	−0.447918	−	0.894075i	$-0.647834\pi$
$67$	6.86179	−	3.96166i	0.102415	−	0.0591292i	0.550333	+	0.834946i	$0.314501\pi$
$68$		0			0
$69$	−6.29489	−	8.98523i	−0.0912302	−	0.130221i
$70$		0			0
$71$			62.9286i			0.886318i	0.896443	+	0.443159i	$0.146142\pi$
$71$			62.9286i			0.886318i	−0.896443	+	0.443159i	$0.853858\pi$
$72$		0			0
$73$	33.3218			0.456463			0.228232	−	0.973607i	$-0.426706\pi$
$73$	33.3218			0.456463			0.228232	+	0.973607i	$0.426706\pi$
$74$		0			0
$75$	54.7978	+	25.5359i	0.730637	+	0.340478i
$76$		0			0
$77$	21.9454	+	38.0106i	0.285006	+	0.493644i
$78$		0			0
$79$	−53.7133	−	31.0114i	−0.679916	−	0.392549i	0.119908	−	0.992785i	$-0.461740\pi$
$79$	−53.7133	−	31.0114i	−0.679916	−	0.392549i	−0.799823	+	0.600236i	$0.795073\pi$
$80$		0			0
$81$	76.0873	−	27.7800i	0.939349	−	0.342963i
$82$		0			0
$83$	−103.056	−	59.4995i	−1.24164	−	0.716861i	−0.272212	−	0.962237i	$-0.587755\pi$
$83$	−103.056	−	59.4995i	−1.24164	−	0.716861i	−0.969428	+	0.245376i	$0.921089\pi$
$84$		0			0
$85$	−31.1329	−	53.9238i	−0.366270	−	0.634398i
$86$		0			0
$87$	67.0864	+	31.2624i	0.771108	+	0.359338i
$88$		0			0
$89$	−107.361			−1.20630			−0.603152	−	0.797626i	$-0.706089\pi$
$89$	−107.361			−1.20630			−0.603152	+	0.797626i	$0.706089\pi$
$90$		0			0
$91$		−	123.332i		−	1.35530i
$92$		0			0
$93$	65.5274	+	93.5328i	0.704596	+	1.00573i
$94$		0			0
$95$	−36.4927	+	21.0690i	−0.384133	+	0.221779i
$96$		0			0
$97$	1.78621	−	3.09380i	0.0184145	−	0.0318949i	−0.856671	−	0.515863i	$-0.827471\pi$
$97$	1.78621	−	3.09380i	0.0184145	−	0.0318949i	0.875086	+	0.483968i	$0.160805\pi$
$98$		0			0
$99$	44.4189	+	16.1419i	0.448675	+	0.163049i
$100$		0			0
$101$	−7.54688	+	13.0716i	−0.0747216	+	0.129422i	−0.900965	−	0.433891i	$-0.857140\pi$
$101$	−7.54688	+	13.0716i	−0.0747216	+	0.129422i	0.826244	+	0.563313i	$0.190473\pi$
$102$		0			0
$103$	112.813	−	65.1324i	1.09527	−	0.632353i	0.160294	−	0.987069i	$-0.448756\pi$
$103$	112.813	−	65.1324i	1.09527	−	0.632353i	0.934974	+	0.354716i	$0.115422\pi$
$104$		0			0
$105$	−54.9995	+	4.82574i	−0.523804	+	0.0459594i
$106$		0			0
$107$			51.2733i			0.479190i	0.970873	+	0.239595i	$0.0770146\pi$
$107$			51.2733i			0.479190i	−0.970873	+	0.239595i	$0.922985\pi$
$108$		0			0
$109$	25.4737			0.233704			0.116852	−	0.993149i	$-0.462720\pi$
$109$	25.4737			0.233704			0.116852	+	0.993149i	$0.462720\pi$
$110$		0			0
$111$	1.10650	+	12.6108i	0.00996843	+	0.113611i
$112$		0			0
$113$	76.1529	+	131.901i	0.673919	+	1.16726i	0.976783	+	0.214229i	$0.0687238\pi$
$113$	76.1529	+	131.901i	0.673919	+	1.16726i	−0.302864	+	0.953034i	$0.597943\pi$
$114$		0			0
$115$	6.97330	+	4.02603i	0.0606374	+	0.0350090i
$116$		0			0
$117$	−85.4144	−	101.689i	−0.730038	−	0.869139i
$118$		0			0
$119$	−204.695	−	118.181i	−1.72013	−	0.993116i
$120$		0			0
$121$	−46.7124	−	80.9082i	−0.386053	−	0.668663i
$122$		0			0
$123$	48.7711	−	34.1681i	0.396513	−	0.277790i
$124$		0			0
$125$	−99.4176			−0.795341
$126$		0			0
$127$		−	147.428i		−	1.16085i	−0.814314	−	0.580425i	$-0.802886\pi$
$127$		−	147.428i		−	1.16085i	0.814314	−	0.580425i	$-0.197114\pi$
$128$		0			0
$129$	−29.5412	+	63.3929i	−0.229002	+	0.491418i
$130$		0			0
$131$	−112.889	+	65.1766i	−0.861750	+	0.497532i	−0.864598	−	0.502464i	$-0.832427\pi$
$131$	−112.889	+	65.1766i	−0.861750	+	0.497532i	0.00284803	+	0.999996i	$0.499093\pi$
$132$		0			0
$133$	−79.9782	+	138.526i	−0.601340	+	1.04155i
$134$		0			0
$135$	−42.0058	+	42.0691i	−0.311154	+	0.311623i
$136$		0			0
$137$	49.9179	−	86.4604i	0.364364	−	0.631098i	−0.624310	−	0.781177i	$-0.714620\pi$
$137$	49.9179	−	86.4604i	0.364364	−	0.631098i	0.988674	+	0.150079i	$0.0479530\pi$
$138$		0			0
$139$	82.7828	−	47.7947i	0.595560	−	0.343847i	−0.171733	−	0.985144i	$-0.554937\pi$
$139$	82.7828	−	47.7947i	0.595560	−	0.343847i	0.767293	+	0.641297i	$0.221603\pi$
$140$		0			0
$141$	37.8295	−	81.1787i	0.268294	−	0.575736i
$142$		0			0
$143$		−	77.4857i		−	0.541858i
$144$		0			0
$145$	−54.3218			−0.374633
$146$		0			0
$147$	−51.2538	+	35.9074i	−0.348665	+	0.244268i
$148$		0			0
$149$	−34.3382	−	59.4755i	−0.230458	−	0.399164i	0.727485	−	0.686123i	$-0.240689\pi$
$149$	−34.3382	−	59.4755i	−0.230458	−	0.399164i	−0.957943	+	0.286959i	$0.907356\pi$
$150$		0			0
$151$	91.2633	+	52.6909i	0.604393	+	0.348946i	0.770768	−	0.637116i	$-0.219873\pi$
$151$	91.2633	+	52.6909i	0.604393	+	0.348946i	−0.166375	+	0.986063i	$0.553206\pi$
$152$		0			0
$153$	−250.621	+	44.3210i	−1.63805	+	0.289680i
$154$		0			0
$155$	−72.5894	−	41.9095i	−0.468319	−	0.270384i
$156$		0			0
$157$	107.502	+	186.200i	0.684729	+	1.18598i	0.973522	+	0.228593i	$0.0734125\pi$
$157$	107.502	+	186.200i	0.684729	+	1.18598i	−0.288794	+	0.957391i	$0.593254\pi$
$158$		0			0
$159$	8.42027	+	95.9667i	0.0529577	+	0.603564i
$160$		0			0
$161$	30.5657			0.189849
$162$		0			0
$163$		−	33.7439i		−	0.207018i	−0.994629	−	0.103509i	$-0.966993\pi$
$163$		−	33.7439i		−	0.207018i	0.994629	−	0.103509i	$-0.0330071\pi$
$164$		0			0
$165$	−34.5544	+	3.03186i	−0.209421	+	0.0183749i
$166$		0			0
$167$	−131.565	+	75.9589i	−0.787812	+	0.454843i	−0.839192	−	0.543836i	$-0.816971\pi$
$167$	−131.565	+	75.9589i	−0.787812	+	0.454843i	0.0513797	+	0.998679i	$0.483638\pi$
$168$		0			0
$169$	−24.3663	+	42.2036i	−0.144179	+	0.249726i
$170$		0			0
$171$	29.9940	+	169.606i	0.175403	+	0.991851i
$172$		0			0
$173$	59.4003	−	102.884i	0.343354	−	0.594707i	−0.641699	−	0.766957i	$-0.721770\pi$
$173$	59.4003	−	102.884i	0.343354	−	0.594707i	0.985053	+	0.172249i	$0.0551035\pi$
$174$		0			0
$175$	−145.868	+	84.2170i	−0.833532	+	0.481240i
$176$		0			0
$177$	−15.8248	−	22.5881i	−0.0894055	−	0.127616i
$178$		0			0
$179$		−	218.189i		−	1.21894i	−0.792811	−	0.609468i	$-0.791383\pi$
$179$		−	218.189i		−	1.21894i	0.792811	−	0.609468i	$-0.208617\pi$
$180$		0			0
$181$	−184.078			−1.01701			−0.508503	−	0.861060i	$-0.669801\pi$
$181$	−184.078			−1.01701			−0.508503	+	0.861060i	$0.669801\pi$
$182$		0			0
$183$	222.007	+	103.456i	1.21315	+	0.565332i
$184$		0			0
$185$	−4.64565	−	8.04650i	−0.0251116	−	0.0434946i
$186$		0			0
$187$	−128.603	−	74.2492i	−0.687719	−	0.397055i
$188$		0			0
$189$	−58.2442	+	218.027i	−0.308170	+	1.15358i
$190$		0			0
$191$	215.775	+	124.578i	1.12971	+	0.652239i	0.943862	−	0.330339i	$-0.107163\pi$
$191$	215.775	+	124.578i	1.12971	+	0.652239i	0.185849	+	0.982578i	$0.440497\pi$
$192$		0			0
$193$	125.086	+	216.656i	0.648115	+	1.12257i	0.983573	+	0.180513i	$0.0577758\pi$
$193$	125.086	+	216.656i	0.648115	+	1.12257i	−0.335457	+	0.942055i	$0.608891\pi$
$194$		0			0
$195$	88.3481	+	41.1704i	0.453067	+	0.211130i
$196$		0			0
$197$	−255.674			−1.29784			−0.648919	−	0.760858i	$-0.724779\pi$
$197$	−255.674			−1.29784			−0.648919	+	0.760858i	$0.724779\pi$
$198$		0			0
$199$		−	309.110i		−	1.55332i	−0.629921	−	0.776659i	$-0.716913\pi$
$199$		−	309.110i		−	1.55332i	0.629921	−	0.776659i	$-0.283087\pi$
$200$		0			0
$201$	13.6388	+	19.4678i	0.0678545	+	0.0968546i
$202$		0			0
$203$	−178.580	+	103.103i	−0.879702	+	0.507896i
$204$		0			0
$205$	−21.8530	+	37.8505i	−0.106600	+	0.184636i
$206$		0			0
$207$	25.2019	−	21.1685i	0.121748	−	0.102263i
$208$		0			0
$209$	−50.2478	+	87.0317i	−0.240420	+	0.416420i
$210$		0			0
$211$	341.158	−	196.968i	1.61686	−	0.933497i	0.629140	−	0.777292i	$-0.283407\pi$
$211$	341.158	−	196.968i	1.61686	−	0.933497i	0.987725	−	0.156205i	$-0.0499261\pi$
$212$		0			0
$213$	−188.063	+	16.5010i	−0.882926	+	0.0774693i
$214$		0			0
$215$		−	51.3311i		−	0.238750i
$216$		0			0
$217$	−318.177			−1.46626
$218$		0			0
$219$	8.73756	+	99.5829i	0.0398975	+	0.454716i
$220$		0			0
$221$	208.638	+	361.372i	0.944064	+	1.63517i
$222$		0			0
$223$	89.4002	+	51.6152i	0.400898	+	0.231458i	0.686871	−	0.726779i	$-0.258984\pi$
$223$	89.4002	+	51.6152i	0.400898	+	0.231458i	−0.285974	+	0.958238i	$0.592317\pi$
$224$		0			0
$225$	−61.9455	+	170.460i	−0.275313	+	0.757600i
$226$		0			0
$227$	122.210	+	70.5578i	0.538369	+	0.310828i	0.744418	−	0.667714i	$-0.232727\pi$
$227$	122.210	+	70.5578i	0.538369	+	0.310828i	−0.206049	+	0.978542i	$0.566061\pi$
$228$		0			0
$229$	−105.572	−	182.856i	−0.461012	−	0.798496i	0.538000	−	0.842945i	$-0.319180\pi$
$229$	−105.572	−	182.856i	−0.461012	−	0.798496i	−0.999012	+	0.0444490i	$0.985847\pi$
$230$		0			0
$231$	−107.841	+	75.5514i	−0.466844	+	0.327062i
$232$		0			0
$233$	−280.109			−1.20219			−0.601093	−	0.799179i	$-0.705268\pi$
$233$	−280.109			−1.20219			−0.601093	+	0.799179i	$0.705268\pi$
$234$		0			0
$235$			65.7328i			0.279714i
$236$		0			0
$237$	78.5936	−	168.655i	0.331619	−	0.711624i
$238$		0			0
$239$	−339.349	+	195.923i	−1.41987	+	0.819762i	−0.996287	−	0.0860949i	$-0.972561\pi$
$239$	−339.349	+	195.923i	−1.41987	+	0.819762i	−0.423583	+	0.905857i	$0.639228\pi$
$240$		0			0
$241$	−23.6786	+	41.0125i	−0.0982514	+	0.170176i	−0.910961	−	0.412493i	$-0.864658\pi$
$241$	−23.6786	+	41.0125i	−0.0982514	+	0.170176i	0.812710	+	0.582669i	$0.197992\pi$
$242$		0			0
$243$	102.973	+	220.104i	0.423755	+	0.905777i
$244$		0			0
$245$	22.9654	−	39.7772i	0.0937363	−	0.162356i
$246$		0			0
$247$	244.557	−	141.195i	0.990107	−	0.571639i
$248$		0			0
$249$	150.792	−	323.587i	0.605591	−	1.29955i
$250$		0			0
$251$			389.416i			1.55146i	0.631065	+	0.775730i	$0.282618\pi$
$251$			389.416i			1.55146i	−0.631065	+	0.775730i	$0.717382\pi$
$252$		0			0
$253$	19.2035			0.0759030
$254$		0			0
$255$	152.989	−	107.181i	0.599956	−	0.420318i
$256$		0			0
$257$	−32.5409	−	56.3625i	−0.126618	−	0.219310i	0.795746	−	0.605631i	$-0.207079\pi$
$257$	−32.5409	−	56.3625i	−0.126618	−	0.219310i	−0.922364	+	0.386321i	$0.873746\pi$
$258$		0			0
$259$	−30.5445	−	17.6349i	−0.117933	−	0.0680884i
$260$		0			0
$261$	−75.8370	+	208.686i	−0.290563	+	0.799565i
$262$		0			0
$263$	−124.773	−	72.0378i	−0.474423	−	0.273908i	0.243667	−	0.969859i	$-0.421650\pi$
$263$	−124.773	−	72.0378i	−0.474423	−	0.273908i	−0.718089	+	0.695951i	$0.754983\pi$
$264$		0			0
$265$	−35.3527	−	61.2327i	−0.133406	−	0.231067i
$266$		0			0
$267$	−28.1519	−	320.850i	−0.105438	−	1.20169i
$268$		0			0
$269$	72.4113			0.269187			0.134593	−	0.990901i	$-0.457027\pi$
$269$	72.4113			0.269187			0.134593	+	0.990901i	$0.457027\pi$
$270$		0			0
$271$			35.4695i			0.130884i	0.997856	+	0.0654419i	$0.0208457\pi$
$271$			35.4695i			0.130884i	−0.997856	+	0.0654419i	$0.979154\pi$
$272$		0			0
$273$	368.580	−	32.3398i	1.35011	−	0.118461i
$274$		0			0
$275$	−91.6443	+	52.9109i	−0.333252	+	0.192403i
$276$		0			0
$277$	166.922	−	289.118i	0.602607	−	1.04375i	−0.389818	−	0.920892i	$-0.627462\pi$
$277$	166.922	−	289.118i	0.602607	−	1.04375i	0.992425	−	0.122854i	$-0.0392047\pi$
$278$		0			0
$279$	−262.342	+	220.356i	−0.940295	+	0.789806i
$280$		0			0
$281$	−20.5385	+	35.5737i	−0.0730906	+	0.126597i	−0.900254	−	0.435364i	$-0.856620\pi$
$281$	−20.5385	+	35.5737i	−0.0730906	+	0.126597i	0.827164	+	0.561961i	$0.189953\pi$
$282$		0			0
$283$	−218.583	+	126.199i	−0.772378	+	0.445933i	−0.833722	−	0.552184i	$-0.813795\pi$
$283$	−218.583	+	126.199i	−0.772378	+	0.445933i	0.0613442	+	0.998117i	$0.480461\pi$
$284$		0			0
$285$	−72.5342	−	103.534i	−0.254506	−	0.363278i
$286$		0			0
$287$			165.908i			0.578077i
$288$		0			0
$289$	510.695			1.76711
$290$		0			0
$291$	9.71427	+	4.52687i	0.0333824	+	0.0155562i
$292$		0			0
$293$	−20.3415	−	35.2325i	−0.0694248	−	0.120247i	0.829223	−	0.558917i	$-0.188783\pi$
$293$	−20.3415	−	35.2325i	−0.0694248	−	0.120247i	−0.898648	+	0.438670i	$0.855450\pi$
$294$		0			0
$295$	17.5302	+	10.1211i	0.0594245	+	0.0343088i
$296$		0			0
$297$	−36.5930	+	136.979i	−0.123209	+	0.461210i
$298$		0			0
$299$	−46.7317	−	26.9806i	−0.156293	−	0.0902361i
$300$		0			0
$301$	−97.4266	−	168.748i	−0.323677	−	0.560624i
$302$		0			0
$303$	−41.0436	−	19.1264i	−0.135457	−	0.0631234i
$304$		0			0
$305$	−179.766			−0.589396
$306$		0			0
$307$		−	136.830i		−	0.445701i	−0.974853	−	0.222850i	$-0.928464\pi$
$307$		−	136.830i		−	0.445701i	0.974853	−	0.222850i	$-0.0715361\pi$
$308$		0			0
$309$	224.231	+	320.064i	0.725666	+	1.03580i
$310$		0			0
$311$	371.260	−	214.347i	1.19376	−	0.689219i	0.234605	−	0.972091i	$-0.424620\pi$
$311$	371.260	−	214.347i	1.19376	−	0.689219i	0.959158	+	0.282871i	$0.0912869\pi$
$312$		0			0
$313$	5.98705	−	10.3699i	0.0191280	−	0.0331306i	−0.856303	−	0.516474i	$-0.827244\pi$
$313$	5.98705	−	10.3699i	0.0191280	−	0.0331306i	0.875431	+	0.483343i	$0.160578\pi$
$314$		0			0
$315$	−28.8436	−	163.101i	−0.0915670	−	0.517782i
$316$		0			0
$317$	23.5266	−	40.7493i	0.0742164	−	0.128547i	−0.826529	−	0.562894i	$-0.809688\pi$
$317$	23.5266	−	40.7493i	0.0742164	−	0.128547i	0.900745	+	0.434348i	$0.143021\pi$
$318$		0			0
$319$	−112.196	+	64.7763i	−0.351711	+	0.203061i
$320$		0			0
$321$	−153.231	+	13.4448i	−0.477356	+	0.0418840i
$322$		0			0
$323$		−	541.189i		−	1.67551i
$324$		0			0
$325$	297.356			0.914941
$326$		0			0
$327$	6.67964	+	76.1286i	0.0204270	+	0.232809i
$328$		0			0
$329$	124.761	+	216.092i	0.379213	+	0.656816i
$330$		0			0
$331$	−73.1501	−	42.2332i	−0.220997	−	0.127593i	0.385415	−	0.922743i	$-0.374058\pi$
$331$	−73.1501	−	42.2332i	−0.220997	−	0.127593i	−0.606412	+	0.795151i	$0.707392\pi$
$332$		0			0
$333$	−37.3976	+	6.61357i	−0.112305	+	0.0198606i
$334$		0			0
$335$	−15.1086	−	8.72297i	−0.0451004	−	0.0260387i
$336$		0			0
$337$	−252.558	−	437.443i	−0.749430	−	1.29805i	−0.948096	−	0.317983i	$-0.896994\pi$
$337$	−252.558	−	437.443i	−0.749430	−	1.29805i	0.198667	−	0.980067i	$-0.436339\pi$
$338$		0			0
$339$	−374.219	+	262.171i	−1.10389	+	0.773366i
$340$		0			0
$341$	−199.901			−0.586219
$342$		0			0
$343$			235.200i			0.685714i
$344$		0			0
$345$	−10.2034	+	21.8955i	−0.0295750	+	0.0634653i
$346$		0			0
$347$	424.751	−	245.230i	1.22407	−	0.706715i	0.258284	−	0.966069i	$-0.416843\pi$
$347$	424.751	−	245.230i	1.22407	−	0.706715i	0.965782	+	0.259354i	$0.0835097\pi$
$348$		0			0
$349$	−186.972	+	323.845i	−0.535736	+	0.927923i	0.463391	+	0.886154i	$0.346633\pi$
$349$	−186.972	+	323.845i	−0.535736	+	0.927923i	−0.999127	+	0.0417686i	$0.986701\pi$
$350$		0			0
$351$	281.503	−	281.927i	0.802003	−	0.803212i
$352$		0			0
$353$	297.026	−	514.465i	0.841434	−	1.45741i	−0.0472483	−	0.998883i	$-0.515045\pi$
$353$	297.026	−	514.465i	0.841434	−	1.45741i	0.888682	−	0.458523i	$-0.151621\pi$
$354$		0			0
$355$	119.996	−	69.2796i	0.338016	−	0.195154i
$356$		0			0
$357$	299.511	−	642.724i	0.838966	−	1.80035i
$358$		0			0
$359$		−	410.893i		−	1.14455i	−0.820062	−	0.572274i	$-0.806061\pi$
$359$		−	410.893i		−	1.14455i	0.820062	−	0.572274i	$-0.193939\pi$
$360$		0			0
$361$	−5.24690			−0.0145343
$362$		0			0
$363$	229.547	−	160.816i	0.632360	−	0.443020i
$364$		0			0
$365$	−36.6848	−	63.5400i	−0.100506	−	0.174082i
$366$		0			0
$367$	−466.176	−	269.147i	−1.27023	−	0.733370i	−0.295203	−	0.955435i	$-0.595387\pi$
$367$	−466.176	−	269.147i	−1.27023	−	0.733370i	−0.975032	+	0.222064i	$0.928721\pi$
$368$		0			0
$369$	114.901	+	136.794i	0.311384	+	0.370715i
$370$		0			0
$371$	−232.440	−	134.199i	−0.626522	−	0.361722i
$372$		0			0
$373$	74.9606	+	129.836i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$373$	74.9606	+	129.836i	0.200967	+	0.348085i	−0.747873	+	0.663841i	$0.768925\pi$
$374$		0			0
$375$	−26.0690	−	297.111i	−0.0695174	−	0.792297i
$376$		0			0
$377$	364.039			0.965621
$378$		0			0
$379$			184.361i			0.486442i	0.969971	+	0.243221i	$0.0782040\pi$
$379$			184.361i			0.486442i	−0.969971	+	0.243221i	$0.921796\pi$
$380$		0			0
$381$	440.591	−	38.6582i	1.15641	−	0.101465i
$382$		0			0
$383$	180.514	−	104.220i	0.471315	−	0.272114i	−0.245475	−	0.969403i	$-0.578944\pi$
$383$	180.514	−	104.220i	0.471315	−	0.272114i	0.716790	+	0.697289i	$0.245611\pi$
$384$		0			0
$385$	48.3206	−	83.6937i	0.125508	−	0.217386i
$386$		0			0
$387$	−197.197	−	71.6618i	−0.509554	−	0.185173i
$388$		0			0
$389$	150.914	−	261.390i	0.387953	−	0.671954i	−0.604221	−	0.796816i	$-0.706516\pi$
$389$	150.914	−	261.390i	0.387953	−	0.671954i	0.992174	+	0.124863i	$0.0398491\pi$
$390$		0			0
$391$	−89.5597	+	51.7073i	−0.229053	+	0.132244i
$392$		0			0
$393$	−224.383	−	320.281i	−0.570949	−	0.814965i
$394$		0			0
$395$			136.565i			0.345734i
$396$		0			0
$397$	246.672			0.621341			0.310670	−	0.950518i	$-0.399447\pi$
$397$	246.672			0.621341			0.310670	+	0.950518i	$0.399447\pi$
$398$		0			0
$399$	−434.960	−	202.692i	−1.09013	−	0.508001i
$400$		0			0
$401$	377.516	+	653.877i	0.941437	+	1.63062i	0.762734	+	0.646713i	$0.223857\pi$
$401$	377.516	+	653.877i	0.941437	+	1.63062i	0.178703	+	0.983903i	$0.442810\pi$
$402$		0			0
$403$	486.460	+	280.858i	1.20710	+	0.696917i
$404$		0			0
$405$	−136.739	−	114.504i	−0.337627	−	0.282726i
$406$		0			0
$407$	−19.1902	−	11.0794i	−0.0471503	−	0.0272222i
$408$		0			0
$409$	130.730	+	226.432i	0.319634	+	0.553622i	0.980412	−	0.196959i	$-0.0631067\pi$
$409$	130.730	+	226.432i	0.319634	+	0.553622i	−0.660778	+	0.750582i	$0.729773\pi$
$410$		0			0
$411$	271.478	+	126.509i	0.660530	+	0.307808i
$412$		0			0
$413$	76.8394			0.186052
$414$		0			0
$415$			262.018i			0.631369i
$416$		0			0
$417$	164.542	+	234.865i	0.394586	+	0.563226i
$418$		0			0
$419$	−340.246	+	196.441i	−0.812043	+	0.468833i	−0.847665	−	0.530532i	$-0.821992\pi$
$419$	−340.246	+	196.441i	−0.812043	+	0.468833i	0.0356217	+	0.999365i	$0.488659\pi$
$420$		0			0
$421$	−102.451	+	177.450i	−0.243351	+	0.421496i	−0.961667	−	0.274221i	$-0.911580\pi$
$421$	−102.451	+	177.450i	−0.243351	+	0.421496i	0.718316	+	0.695717i	$0.244913\pi$
$422$		0			0
$423$	252.524	+	91.7676i	0.596983	+	0.216945i
$424$		0			0
$425$	284.936	−	493.524i	0.670438	−	1.16123i
$426$		0			0
$427$	−590.968	+	341.196i	−1.38400	+	0.799053i
$428$		0			0
$429$	231.567	−	20.3181i	0.539784	−	0.0473615i
$430$		0			0
$431$			462.725i			1.07361i	0.843707	+	0.536803i	$0.180368\pi$
$431$			462.725i			1.07361i	−0.843707	+	0.536803i	$0.819632\pi$
$432$		0			0
$433$	190.574			0.440126			0.220063	−	0.975486i	$-0.429374\pi$
$433$	190.574			0.440126			0.220063	+	0.975486i	$0.429374\pi$
$434$		0			0
$435$	−14.2441	−	162.342i	−0.0327451	−	0.373200i
$436$		0			0
$437$	34.9926	+	60.6090i	0.0800747	+	0.138693i
$438$		0			0
$439$	379.279	+	218.977i	0.863962	+	0.498809i	0.865337	−	0.501190i	$-0.167104\pi$
$439$	379.279	+	218.977i	0.863962	+	0.498809i	−0.00137479	+	0.999999i	$0.500438\pi$
$440$		0			0
$441$	−120.750	−	143.757i	−0.273809	−	0.325980i
$442$		0			0
$443$	721.993	+	416.843i	1.62978	+	0.940954i	0.984157	+	0.177297i	$0.0567354\pi$
$443$	721.993	+	416.843i	1.62978	+	0.940954i	0.645623	+	0.763657i	$0.276598\pi$
$444$		0			0
$445$	118.196	+	204.722i	0.265610	+	0.460050i
$446$		0			0
$447$	168.740	−	118.216i	0.377493	−	0.264465i
$448$		0			0
$449$	−480.789			−1.07080			−0.535399	−	0.844599i	$-0.679839\pi$
$449$	−480.789			−1.07080			−0.535399	+	0.844599i	$0.679839\pi$
$450$		0			0
$451$			104.235i			0.231119i
$452$		0			0
$453$	−133.537	+	286.559i	−0.294784	+	0.632580i
$454$		0			0
$455$	−235.177	+	135.779i	−0.516872	+	0.298416i
$456$		0			0
$457$	109.313	−	189.336i	0.239197	−	0.414302i	−0.721287	−	0.692636i	$-0.756449\pi$
$457$	109.313	−	189.336i	0.239197	−	0.414302i	0.960484	+	0.278334i	$0.0897824\pi$
$458$		0			0
$459$	−198.171	−	737.364i	−0.431746	−	1.60646i
$460$		0			0
$461$	358.474	−	620.894i	0.777600	−	1.34684i	−0.155722	−	0.987801i	$-0.549770\pi$
$461$	358.474	−	620.894i	0.777600	−	1.34684i	0.933322	−	0.359042i	$-0.116896\pi$
$462$		0			0
$463$	−26.6250	+	15.3719i	−0.0575053	+	0.0332007i	−0.528477	−	0.848948i	$-0.677237\pi$
$463$	−26.6250	+	15.3719i	−0.0575053	+	0.0332007i	0.470972	+	0.882148i	$0.343903\pi$
$464$		0			0
$465$	106.213	−	227.924i	0.228415	−	0.490159i
$466$		0			0
$467$			458.639i			0.982096i	0.871133	+	0.491048i	$0.163386\pi$
$467$			458.639i			0.982096i	−0.871133	+	0.491048i	$0.836614\pi$
$468$		0			0
$469$	−66.2249			−0.141204
$470$		0			0
$471$	−528.272	+	370.098i	−1.12160	+	0.785770i
$472$		0			0
$473$	−61.2101	−	106.019i	−0.129408	−	0.224142i
$474$		0			0
$475$	−333.989	−	192.829i	−0.703135	−	0.405955i
$476$		0			0
$477$	−284.590	+	50.3283i	−0.596626	+	0.105510i
$478$		0			0
$479$	570.477	+	329.365i	1.19098	+	0.687610i	0.958528	−	0.284999i	$-0.0919932\pi$
$479$	570.477	+	329.365i	1.19098	+	0.687610i	0.232448	+	0.972609i	$0.425326\pi$
$480$		0			0
$481$	31.1329	+	53.9238i	0.0647254	+	0.112108i
$482$		0			0
$483$	8.01485	+	91.3461i	0.0165939	+	0.189122i
$484$		0			0
$485$	−7.86593			−0.0162184
$486$		0			0
$487$			715.589i			1.46938i	0.678402	+	0.734691i	$0.262673\pi$
$487$			715.589i			1.46938i	−0.678402	+	0.734691i	$0.737327\pi$
$488$		0			0
$489$	100.844	−	8.84825i	0.206226	−	0.0180946i
$490$		0			0
$491$	574.179	−	331.502i	1.16941	−	0.675157i	0.215866	−	0.976423i	$-0.430742\pi$
$491$	574.179	−	331.502i	1.16941	−	0.675157i	0.953540	+	0.301266i	$0.0974091\pi$
$492$		0			0
$493$	348.834	−	604.198i	0.707574	−	1.22555i
$494$		0			0
$495$	−18.1215	−	102.472i	−0.0366092	−	0.207013i
$496$		0			0
$497$	262.986	−	455.505i	0.529147	−	0.916509i
$498$		0			0
$499$	−458.706	+	264.834i	−0.919251	+	0.530730i	−0.883396	−	0.468627i	$-0.844749\pi$
$499$	−458.706	+	264.834i	−0.919251	+	0.530730i	−0.0358546	+	0.999357i	$0.511415\pi$
$500$		0			0
$501$	−261.503	−	373.266i	−0.521962	−	0.745041i
$502$		0			0
$503$		−	68.3537i		−	0.135892i	−0.997689	−	0.0679460i	$-0.978355\pi$
$503$		−	68.3537i		−	0.135892i	0.997689	−	0.0679460i	$-0.0216446\pi$
$504$		0			0
$505$	33.2342			0.0658103
$506$		0			0
$507$	−132.516	−	61.7525i	−0.261372	−	0.121800i
$508$		0			0
$509$	400.473	+	693.640i	0.786784	+	1.36275i	0.927927	+	0.372761i	$0.121589\pi$
$509$	400.473	+	693.640i	0.786784	+	1.36275i	−0.141143	+	0.989989i	$0.545078\pi$
$510$		0			0
$511$	−241.198	−	139.256i	−0.472012	−	0.272516i
$512$		0			0
$513$	−499.007	+	134.111i	−0.972723	+	0.261426i
$514$		0			0
$515$	−248.396	−	143.412i	−0.482323	−	0.278469i
$516$		0			0
$517$	78.3834	+	135.764i	0.151612	+	0.262600i
$518$		0			0
$519$	323.047	+	150.541i	0.622442	+	0.290059i
$520$		0			0
$521$	−208.227			−0.399668			−0.199834	−	0.979830i	$-0.564040\pi$
$521$	−208.227			−0.399668			−0.199834	+	0.979830i	$0.564040\pi$
$522$		0			0
$523$		−	30.5350i		−	0.0583843i	−0.999574	−	0.0291921i	$-0.990707\pi$
$523$		−	30.5350i		−	0.0583843i	0.999574	−	0.0291921i	$-0.00929347\pi$
$524$		0			0
$525$	−289.933	−	413.846i	−0.552254	−	0.788279i
$526$		0			0
$527$	932.283	−	538.254i	1.76904	−	1.02135i
$528$		0			0
$529$	−257.813	+	446.546i	−0.487360	+	0.844132i
$530$		0			0
$531$	63.3553	−	53.2156i	0.119313	−	0.100218i
$532$		0			0
$533$	146.448	−	253.656i	0.274762	−	0.475903i
$534$		0			0
$535$	97.7710	−	56.4481i	0.182749	−	0.105510i
$536$		0			0
$537$	652.063	−	57.2130i	1.21427	−	0.106542i
$538$		0			0
$539$		−	109.541i		−	0.203230i
$540$		0			0
$541$	−526.091			−0.972442			−0.486221	−	0.873836i	$-0.661625\pi$
$541$	−526.091			−0.972442			−0.486221	+	0.873836i	$0.661625\pi$
$542$		0			0
$543$	−48.2685	−	550.121i	−0.0888923	−	1.01311i
$544$		0			0
$545$	−28.0446	−	48.5747i	−0.0514580	−	0.0891279i
$546$		0			0
$547$	823.276	+	475.318i	1.50507	+	0.868955i	0.999983	+	0.00588962i	$0.00187474\pi$
$547$	823.276	+	475.318i	1.50507	+	0.868955i	0.505092	+	0.863066i	$0.331459\pi$
$548$		0			0
$549$	−250.965	+	690.600i	−0.457132	+	1.25792i
$550$		0			0
$551$	−408.888	−	236.071i	−0.742083	−	0.428442i
$552$		0			0
$553$	259.201	+	448.949i	0.468717	+	0.811842i
$554$		0			0
$555$	22.8289	−	15.9935i	0.0411332	−	0.0288172i
$556$		0			0
$557$	−978.257			−1.75630			−0.878148	−	0.478390i	$-0.841221\pi$
$557$	−978.257			−1.75630			−0.878148	+	0.478390i	$0.841221\pi$
$558$		0			0
$559$			343.997i			0.615379i
$560$		0			0
$561$	188.173	−	403.803i	0.335425	−	0.719792i
$562$		0			0
$563$	925.131	−	534.125i	1.64322	−	0.948712i	0.663538	−	0.748143i	$-0.269054\pi$
$563$	925.131	−	534.125i	1.64322	−	0.948712i	0.979680	−	0.200569i	$-0.0642792\pi$
$564$		0			0
$565$	167.677	−	290.426i	0.296774	−	0.514028i
$566$		0			0
$567$	−666.849	−	116.893i	−1.17610	−	0.206161i
$568$		0			0
$569$	−481.775	+	834.459i	−0.846705	+	1.46654i	0.0374271	+	0.999299i	$0.488084\pi$
$569$	−481.775	+	834.459i	−0.846705	+	1.46654i	−0.884132	+	0.467237i	$0.845250\pi$
$570$		0			0
$571$	−243.132	+	140.372i	−0.425800	+	0.245836i	−0.697556	−	0.716531i	$-0.745729\pi$
$571$	−243.132	+	140.372i	−0.425800	+	0.245836i	0.271756	+	0.962366i	$0.412396\pi$
$572$		0			0
$573$	−315.723	+	677.513i	−0.550999	+	1.18240i
$574$		0			0
$575$			73.6944i			0.128164i
$576$		0			0
$577$	−552.228			−0.957068			−0.478534	−	0.878069i	$-0.658832\pi$
$577$	−552.228			−0.957068			−0.478534	+	0.878069i	$0.658832\pi$
$578$		0			0
$579$	−614.680	+	430.633i	−1.06162	+	0.743754i
$580$		0			0
$581$	497.311	+	861.367i	0.855956	+	1.48256i
$582$		0			0
$583$	−146.034	−	84.3130i	−0.250488	−	0.144619i
$584$		0			0
$585$	−99.8721	+	274.826i	−0.170722	+	0.469787i
$586$		0			0
$587$	141.476	+	81.6811i	0.241015	+	0.139150i	0.615643	−	0.788025i	$-0.288896\pi$
$587$	141.476	+	81.6811i	0.241015	+	0.139150i	−0.374628	+	0.927175i	$0.622230\pi$
$588$		0			0
$589$	−364.260	−	630.917i	−0.618438	−	1.07117i
$590$		0			0
$591$	−67.0421	−	764.086i	−0.113438	−	1.29287i
$592$		0			0
$593$	−818.460			−1.38020			−0.690101	−	0.723713i	$-0.742434\pi$
$593$	−818.460			−1.38020			−0.690101	+	0.723713i	$0.742434\pi$
$594$		0			0
$595$			520.433i			0.874677i
$596$		0			0
$597$	923.782	−	81.0541i	1.54737	−	0.135769i
$598$		0			0
$599$	398.849	−	230.275i	0.665857	−	0.384433i	−0.128648	−	0.991690i	$-0.541064\pi$
$599$	398.849	−	230.275i	0.665857	−	0.384433i	0.794505	+	0.607257i	$0.207730\pi$
$600$		0			0
$601$	162.324	−	281.153i	0.270090	−	0.467809i	−0.698795	−	0.715322i	$-0.746280\pi$
$601$	162.324	−	281.153i	0.270090	−	0.467809i	0.968885	+	0.247513i	$0.0796132\pi$
$602$		0			0
$603$	−54.6035	+	45.8645i	−0.0905530	+	0.0760605i
$604$		0			0
$605$	−102.854	+	178.148i	−0.170006	+	0.294459i
$606$		0			0
$607$	−764.054	+	441.127i	−1.25874	+	0.726733i	−0.972829	−	0.231524i	$-0.925629\pi$
$607$	−764.054	+	441.127i	−1.25874	+	0.726733i	−0.285909	+	0.958257i	$0.592295\pi$
$608$		0			0
$609$	−354.952	−	506.653i	−0.582844	−	0.831942i
$610$		0			0
$611$		−	440.510i		−	0.720966i
$612$		0			0
$613$	−19.4869			−0.0317895			−0.0158947	−	0.999874i	$-0.505060\pi$
$613$	−19.4869			−0.0317895			−0.0158947	+	0.999874i	$0.505060\pi$
$614$		0			0
$615$	−118.847	−	55.3830i	−0.193247	−	0.0900537i
$616$		0			0
$617$	−48.3314	−	83.7124i	−0.0783329	−	0.135677i	0.824198	−	0.566302i	$-0.191626\pi$
$617$	−48.3314	−	83.7124i	−0.0783329	−	0.135677i	−0.902531	+	0.430625i	$0.858293\pi$
$618$		0			0
$619$	−363.937	−	210.119i	−0.587944	−	0.339449i	0.176340	−	0.984329i	$-0.443574\pi$
$619$	−363.937	−	210.119i	−0.587944	−	0.339449i	−0.764284	+	0.644880i	$0.776907\pi$
$620$		0			0
$621$	69.8707	+	69.7656i	0.112513	+	0.112344i
$622$		0			0
$623$	777.127	+	448.674i	1.24739	+	0.720184i
$624$		0			0
$625$	−142.447	−	246.725i	−0.227915	−	0.394760i
$626$		0			0
$627$	−273.272	−	127.345i	−0.435840	−	0.203102i
$628$		0			0
$629$	119.330			0.189714
$630$		0			0
$631$		−	483.230i		−	0.765816i	−0.923787	−	0.382908i	$-0.874923\pi$
$631$		−	483.230i		−	0.765816i	0.923787	−	0.382908i	$-0.125077\pi$
$632$		0			0
$633$	678.100	+	967.910i	1.07125	+	1.52908i
$634$		0			0
$635$	−281.124	+	162.307i	−0.442715	+	0.255602i
$636$		0			0
$637$	−153.903	+	266.568i	−0.241606	+	0.418475i
$638$		0			0
$639$	−98.6268	−	557.703i	−0.154346	−	0.872775i
$640$		0			0
$641$	−45.2967	+	78.4562i	−0.0706657	+	0.122397i	−0.899193	−	0.437552i	$-0.855846\pi$
$641$	−45.2967	+	78.4562i	−0.0706657	+	0.122397i	0.828528	+	0.559948i	$0.189179\pi$
$642$		0			0
$643$	453.773	−	261.986i	0.705713	−	0.407444i	−0.103759	−	0.994602i	$-0.533087\pi$
$643$	453.773	−	261.986i	0.705713	−	0.407444i	0.809472	+	0.587159i	$0.199754\pi$
$644$		0			0
$645$	153.404	−	13.4599i	0.237836	−	0.0208681i
$646$		0			0
$647$			31.3018i			0.0483799i	0.999707	+	0.0241900i	$0.00770066\pi$
$647$			31.3018i			0.0483799i	−0.999707	+	0.0241900i	$0.992299\pi$
$648$		0			0
$649$	48.2758			0.0743848
$650$		0			0
$651$	−83.4316	−	950.879i	−0.128159	−	1.46064i
$652$		0			0
$653$	−445.115	−	770.961i	−0.681646	−	1.18065i	−0.974478	−	0.224481i	$-0.927931\pi$
$653$	−445.115	−	770.961i	−0.681646	−	1.18065i	0.292833	−	0.956164i	$-0.405402\pi$
$654$		0			0
$655$	248.565	+	143.509i	0.379489	+	0.219098i
$656$		0			0
$657$	−295.314	+	52.2247i	−0.449489	+	0.0794897i
$658$		0			0
$659$	41.1783	+	23.7743i	0.0624860	+	0.0360763i	0.530918	−	0.847423i	$-0.321847\pi$
$659$	41.1783	+	23.7743i	0.0624860	+	0.0360763i	−0.468432	+	0.883500i	$0.655181\pi$
$660$		0			0
$661$	24.8421	+	43.0278i	0.0375826	+	0.0650950i	0.884205	−	0.467099i	$-0.154701\pi$
$661$	24.8421	+	43.0278i	0.0375826	+	0.0650950i	−0.846622	+	0.532194i	$0.821368\pi$
$662$		0			0
$663$	−1025.26	+	718.277i	−1.54639	+	1.08337i
$664$		0			0
$665$	352.200			0.529624
$666$		0			0
$667$			90.2207i			0.135263i
$668$		0			0
$669$	−130.811	+	280.709i	−0.195532	+	0.419594i
$670$		0			0
$671$	−371.287	+	214.362i	−0.553333	+	0.319467i
$672$		0			0
$673$	−16.4365	+	28.4688i	−0.0244227	+	0.0423013i	−0.877978	−	0.478700i	$-0.841108\pi$
$673$	−16.4365	+	28.4688i	−0.0244227	+	0.0423013i	0.853556	+	0.521002i	$0.174441\pi$
$674$		0			0
$675$	−525.666	−	140.428i	−0.778765	−	0.208041i
$676$		0			0
$677$	−457.417	+	792.269i	−0.675653	+	1.17026i	0.300625	+	0.953742i	$0.402805\pi$
$677$	−457.417	+	792.269i	−0.675653	+	1.17026i	−0.976278	+	0.216522i	$0.930529\pi$
$678$		0			0
$679$	−25.8587	+	14.9296i	−0.0380836	+	0.0219876i
$680$		0			0
$681$	−178.818	+	383.728i	−0.262581	+	0.563477i
$682$		0			0
$683$			870.646i			1.27474i	0.770559	+	0.637369i	$0.219977\pi$
$683$			870.646i			1.27474i	−0.770559	+	0.637369i	$0.780023\pi$
$684$		0			0
$685$	−219.824			−0.320910
$686$		0			0
$687$	518.784	−	363.451i	0.755145	−	0.529041i
$688$		0			0
$689$	236.917	+	410.352i	0.343856	+	0.595577i
$690$		0			0
$691$	−800.188	−	461.988i	−1.15801	−	0.668580i	−0.207187	−	0.978301i	$-0.566431\pi$
$691$	−800.188	−	461.988i	−1.15801	−	0.668580i	−0.950827	+	0.309722i	$0.899764\pi$
$692$		0			0
$693$	−254.065	−	302.474i	−0.366616	−	0.436470i
$694$		0			0
$695$	−182.275	−	105.237i	−0.262267	−	0.151420i
$696$		0			0
$697$	−280.663	−	486.123i	−0.402673	−	0.697450i
$698$		0			0
$699$	−73.4495	−	837.112i	−0.105078	−	1.19758i
$700$		0			0
$701$	−1191.44			−1.69963			−0.849815	−	0.527082i	$-0.823286\pi$
$701$	−1191.44			−1.69963			−0.849815	+	0.527082i	$0.823286\pi$
$702$		0			0
$703$		−	80.7561i		−	0.114874i
$704$		0			0
$705$	−196.444	+	17.2363i	−0.278644	+	0.0244486i
$706$		0			0
$707$	109.255	−	63.0786i	0.154534	−	0.0892201i
$708$		0			0
$709$	−655.954	+	1136.15i	−0.925182	+	1.60246i	−0.133914	+	0.990993i	$0.542754\pi$
$709$	−655.954	+	1136.15i	−0.925182	+	1.60246i	−0.791268	+	0.611469i	$0.790579\pi$
$710$		0			0
$711$	524.637	+	190.654i	0.737886	+	0.268149i
$712$		0			0
$713$	−69.6056	+	120.560i	−0.0976236	+	0.169089i
$714$		0			0
$715$	−147.754	+	85.3059i	−0.206649	+	0.119309i
$716$		0			0
$717$	−674.503	−	962.776i	−0.940730	−	1.34278i
$718$		0			0
$719$			245.763i			0.341813i	0.985287	+	0.170906i	$0.0546695\pi$
$719$			245.763i			0.341813i	−0.985287	+	0.170906i	$0.945330\pi$
$720$		0			0
$721$	−1088.78			−1.51010
$722$		0			0
$723$	−128.776	−	60.0097i	−0.178113	−	0.0830010i
$724$		0			0
$725$	−248.583	−	430.559i	−0.342873	−	0.593874i
$726$		0			0
$727$	1041.96	+	601.573i	1.43323	+	0.827473i	0.997365	−	0.0725411i	$-0.0231108\pi$
$727$	1041.96	+	601.573i	1.43323	+	0.827473i	0.435860	+	0.900014i	$0.356444\pi$
$728$		0			0
$729$	−630.783	+	365.450i	−0.865271	+	0.501304i
$730$		0			0
$731$	570.934	+	329.629i	0.781032	+	0.450929i
$732$		0			0
$733$	510.693	+	884.546i	0.696716	+	1.20675i	0.969599	+	0.244700i	$0.0786896\pi$
$733$	510.693	+	884.546i	0.696716	+	1.20675i	−0.272883	+	0.962047i	$0.587977\pi$
$734$		0			0
$735$	124.897	+	58.2023i	0.169928	+	0.0791867i
$736$		0			0
$737$	−41.6070			−0.0564546
$738$		0			0
$739$			259.300i			0.350879i	0.984490	+	0.175439i	$0.0561346\pi$
$739$			259.300i			0.350879i	−0.984490	+	0.175439i	$0.943865\pi$
$740$		0			0
$741$	486.090	+	693.838i	0.655992	+	0.936354i
$742$		0			0
$743$	100.270	−	57.8907i	0.134953	−	0.0779149i	−0.431004	−	0.902350i	$-0.641840\pi$
$743$	100.270	−	57.8907i	0.134953	−	0.0779149i	0.565956	+	0.824435i	$0.308507\pi$
$744$		0			0
$745$	−75.6076	+	130.956i	−0.101487	+	0.175780i
$746$		0			0
$747$	1006.59	+	365.795i	1.34750	+	0.489686i
$748$		0			0
$749$	214.277	−	371.139i	0.286084	−	0.495513i
$750$		0			0
$751$	−543.581	+	313.837i	−0.723809	+	0.417891i	−0.816153	−	0.577836i	$-0.803897\pi$
$751$	−543.581	+	313.837i	−0.723809	+	0.417891i	0.0923438	+	0.995727i	$0.470564\pi$
$752$		0			0
$753$	−1163.78	+	102.112i	−1.54552	+	0.135607i
$754$		0			0
$755$		−	232.035i		−	0.307331i
$756$		0			0
$757$	−49.5546			−0.0654618			−0.0327309	−	0.999464i	$-0.510420\pi$
$757$	−49.5546			−0.0654618			−0.0327309	+	0.999464i	$0.510420\pi$
$758$		0			0
$759$	5.03548	+	57.3899i	0.00663436	+	0.0756125i
$760$		0			0
$761$	−13.0738	−	22.6446i	−0.0171798	−	0.0297563i	0.857308	−	0.514804i	$-0.172135\pi$
$761$	−13.0738	−	22.6446i	−0.0171798	−	0.0297563i	−0.874488	+	0.485048i	$0.838802\pi$
$762$		0			0
$763$	−184.390	−	106.458i	−0.241664	−	0.139525i
$764$		0			0
$765$	360.429	+	429.105i	0.471149	+	0.560921i
$766$		0			0
$767$	−117.479	−	67.8267i	−0.153167	−	0.0884312i
$768$		0			0
$769$	93.5875	+	162.098i	0.121700	+	0.210791i	0.920438	−	0.390888i	$-0.127832\pi$
$769$	93.5875	+	162.098i	0.121700	+	0.210791i	−0.798738	+	0.601679i	$0.794499\pi$
$770$		0			0
$771$	159.908	−	112.028i	0.207403	−	0.145303i
$772$		0			0
$773$	877.069			1.13463			0.567315	−	0.823501i	$-0.307982\pi$
$773$	877.069			1.13463			0.567315	+	0.823501i	$0.307982\pi$
$774$		0			0
$775$		−	767.131i		−	0.989847i
$776$		0			0
$777$	44.6929	−	95.9071i	0.0575198	−	0.123433i
$778$		0			0
$779$	−328.981	+	189.937i	−0.422312	+	0.243822i
$780$		0			0
$781$	165.226	−	286.179i	0.211557	−	0.366427i
$782$		0			0
$783$	−643.549	−	171.919i	−0.821902	−	0.219565i
$784$		0			0
$785$	236.704	−	409.984i	0.301534	−	0.522272i
$786$		0			0
$787$	577.106	−	333.192i	0.733298	−	0.423370i	−0.0863293	−	0.996267i	$-0.527514\pi$
$787$	577.106	−	333.192i	0.733298	−	0.423370i	0.819628	+	0.572897i	$0.194180\pi$
$788$		0			0
$789$	182.569	−	391.776i	0.231392	−	0.496548i
$790$		0			0
$791$		−	1273.01i		−	1.60936i
$792$		0			0
$793$	1204.70			1.51917
$794$		0			0
$795$	173.725	−	121.708i	0.218522	−	0.153092i
$796$		0			0
$797$	−90.8816	−	157.412i	−0.114030	−	0.197505i	0.803362	−	0.595491i	$-0.203043\pi$
$797$	−90.8816	−	157.412i	−0.114030	−	0.197505i	−0.917391	+	0.397986i	$0.869709\pi$
$798$		0			0
$799$	−731.118	−	422.111i	−0.915041	−	0.528299i
$800$		0			0
$801$	951.486	−	168.265i	1.18787	−	0.210069i
$802$		0			0
$803$	−151.537	−	87.4900i	−0.188714	−	0.108954i
$804$		0			0
$805$	−33.6505	−	58.2844i	−0.0418019	−	0.0724030i
$806$		0			0
$807$	18.9875	+	216.402i	0.0235285	+	0.268157i
$808$		0			0
$809$	114.921			0.142053			0.0710266	−	0.997474i	$-0.477372\pi$
$809$	114.921			0.142053			0.0710266	+	0.997474i	$0.477372\pi$
$810$		0			0
$811$			1378.48i			1.69973i	0.526997	+	0.849867i	$0.323318\pi$
$811$			1378.48i			1.69973i	−0.526997	+	0.849867i	$0.676682\pi$
$812$		0			0
$813$	−106.001	+	9.30072i	−0.130383	+	0.0114400i
$814$		0			0
$815$	−64.3449	+	37.1496i	−0.0789508	+	0.0455823i
$816$		0			0
$817$	223.075	−	386.377i	0.273041	−	0.472921i
$818$		0			0
$819$	193.296	+	1093.03i	0.236015	+	1.33459i
$820$		0			0
$821$	160.807	−	278.526i	0.195867	−	0.339252i	−0.751317	−	0.659941i	$-0.770581\pi$
$821$	160.807	−	278.526i	0.195867	−	0.339252i	0.947184	+	0.320689i	$0.103915\pi$
$822$		0			0
$823$	56.6805	−	32.7245i	0.0688706	−	0.0397625i	−0.465169	−	0.885222i	$-0.654007\pi$
$823$	56.6805	−	32.7245i	0.0688706	−	0.0397625i	0.534040	+	0.845459i	$0.320673\pi$
$824$		0			0
$825$	−182.156	−	260.007i	−0.220795	−	0.315159i
$826$		0			0
$827$		−	778.406i		−	0.941240i	−0.882336	−	0.470620i	$-0.844030\pi$
$827$		−	778.406i		−	0.941240i	0.882336	−	0.470620i	$-0.155970\pi$
$828$		0			0
$829$	81.3426			0.0981214			0.0490607	−	0.998796i	$-0.484377\pi$
$829$	81.3426			0.0981214			0.0490607	+	0.998796i	$0.484377\pi$
$830$		0			0
$831$	907.803	+	423.038i	1.09242	+	0.509071i
$832$		0			0
$833$	294.950	+	510.869i	0.354082	+	0.613288i
$834$		0			0
$835$	289.686	+	167.250i	0.346929	+	0.200299i
$836$		0			0
$837$	−727.328	−	726.233i	−0.868970	−	0.867662i
$838$		0			0
$839$	553.733	+	319.698i	0.659992	+	0.381046i	0.792274	−	0.610166i	$-0.208897\pi$
$839$	553.733	+	319.698i	0.659992	+	0.381046i	−0.132282	+	0.991212i	$0.542231\pi$
$840$		0			0
$841$	116.171	+	201.214i	0.138135	+	0.239256i
$842$		0			0
$843$	−111.698	−	52.0515i	−0.132501	−	0.0617456i
$844$		0			0
$845$	107.302			0.126984
$846$		0			0
$847$			780.866i			0.921920i
$848$		0			0
$849$	−434.464	−	620.148i	−0.511736	−	0.730445i
$850$		0			0
$851$	−13.3641	+	7.71575i	−0.0157040	+	0.00906668i
$852$		0			0
$853$	38.8069	−	67.2155i	0.0454946	−	0.0787989i	−0.842381	−	0.538882i	$-0.818847\pi$
$853$	38.8069	−	67.2155i	0.0454946	−	0.0787989i	0.887876	+	0.460083i	$0.152180\pi$
$854$		0			0
$855$	290.394	−	243.918i	0.339643	−	0.285285i
$856$		0			0
$857$	436.010	−	755.192i	0.508763	−	0.881204i	−0.491185	−	0.871055i	$-0.663436\pi$
$857$	436.010	−	755.192i	0.508763	−	0.881204i	0.999948	−	0.0101489i	$-0.00323056\pi$
$858$		0			0
$859$	−136.909	+	79.0444i	−0.159382	+	0.0920191i	−0.577570	−	0.816342i	$-0.695999\pi$
$859$	−136.909	+	79.0444i	−0.159382	+	0.0920191i	0.418188	+	0.908361i	$0.362665\pi$
$860$		0			0
$861$	−495.819	+	43.5040i	−0.575865	+	0.0505273i
$862$		0			0
$863$			685.963i			0.794859i	0.917633	+	0.397429i	$0.130098\pi$
$863$			685.963i			0.794859i	−0.917633	+	0.397429i	$0.869902\pi$
$864$		0			0
$865$	−261.581			−0.302406
$866$		0			0
$867$	133.913	+	1526.22i	0.154456	+	1.76035i
$868$		0			0
$869$	162.848	+	282.060i	0.187396	+	0.324580i
$870$		0			0
$871$	101.251	+	58.4573i	0.116247	+	0.0671151i
$872$		0			0
$873$	−10.9814	+	30.2183i	−0.0125789	+	0.0346143i
$874$		0			0
$875$	719.629	+	415.478i	0.822433	+	0.474832i
$876$		0			0
$877$	−458.905	−	794.847i	−0.523267	−	0.906325i	−0.999633	−	0.0270780i	$-0.991380\pi$
$877$	−458.905	−	794.847i	−0.523267	−	0.906325i	0.476366	−	0.879247i	$-0.341954\pi$
$878$		0			0
$879$	99.9590	−	70.0294i	0.113719	−	0.0796694i
$880$		0			0
$881$	−657.430			−0.746231			−0.373116	−	0.927785i	$-0.621711\pi$
$881$	−657.430			−0.746231			−0.373116	+	0.927785i	$0.621711\pi$
$882$		0			0
$883$		−	618.879i		−	0.700882i	−0.936585	−	0.350441i	$-0.886032\pi$
$883$		−	618.879i		−	0.700882i	0.936585	−	0.350441i	$-0.113968\pi$
$884$		0			0
$885$	−25.6503	+	55.0434i	−0.0289834	+	0.0621959i
$886$		0			0
$887$	−110.844	+	63.9959i	−0.124965	+	0.0721487i	−0.561180	−	0.827694i	$-0.689652\pi$
$887$	−110.844	+	63.9959i	−0.124965	+	0.0721487i	0.436214	+	0.899843i	$0.356319\pi$
$888$		0			0
$889$	−616.119	+	1067.15i	−0.693047	+	1.20039i
$890$		0			0
$891$	−418.960	−	73.4404i	−0.470214	−	0.0824247i
$892$		0			0
$893$	−285.661	+	494.780i	−0.319890	+	0.554065i
$894$		0			0
$895$	−416.056	+	240.210i	−0.464867	+	0.268391i
$896$		0			0
$897$	68.3781	−	146.733i	0.0762298	−	0.163582i
$898$		0			0
$899$		−	939.164i		−	1.04468i
$900$		0			0
$901$	908.086			1.00786
$902$		0			0
$903$	478.759	−	335.410i	0.530187	−	0.371440i
$904$		0			0
$905$	202.656	+	351.011i	0.223930	+	0.387858i
$906$		0			0
$907$	13.7946	+	7.96431i	0.0152090	+	0.00878094i	0.507585	−	0.861602i	$-0.330538\pi$
$907$	13.7946	+	7.96431i	0.0152090	+	0.00878094i	−0.492376	+	0.870382i	$0.663872\pi$
$908$		0			0
$909$	46.3972	−	127.675i	0.0510421	−	0.140456i
$910$		0			0
$911$	43.9255	+	25.3604i	0.0482168	+	0.0278380i	0.523915	−	0.851771i	$-0.324471\pi$
$911$	43.9255	+	25.3604i	0.0482168	+	0.0278380i	−0.475698	+	0.879609i	$0.657804\pi$
$912$		0			0
$913$	312.445	+	541.170i	0.342218	+	0.592738i
$914$		0			0
$915$	−47.1377	−	537.233i	−0.0515166	−	0.587140i
$916$		0			0
$917$	1089.52			1.18814
$918$		0			0
$919$			1065.04i			1.15892i	0.815002	+	0.579458i	$0.196736\pi$
$919$			1065.04i			1.15892i	−0.815002	+	0.579458i	$0.803264\pi$
$920$		0			0
$921$	408.919	−	35.8792i	0.443995	−	0.0389568i
$922$		0			0
$923$	−804.156	+	464.279i	−0.871241	+	0.503011i
$924$		0			0
$925$	42.5181	−	73.6434i	0.0459655	−	0.0796145i
$926$		0			0
$927$	−897.719	+	754.044i	−0.968413	+	0.813424i
$928$		0			0
$929$	171.699	−	297.392i	0.184822	−	0.320121i	−0.758695	−	0.651446i	$-0.774163\pi$
$929$	171.699	−	297.392i	0.184822	−	0.320121i	0.943516	+	0.331326i	$0.107496\pi$
$930$		0			0
$931$	345.727	−	199.606i	0.371351	−	0.214399i
$932$		0			0
$933$	737.932	+	1053.31i	0.790923	+	1.12895i
$934$		0			0
$935$			326.971i			0.349702i
$936$		0			0
$937$	−267.742			−0.285744			−0.142872	−	0.989741i	$-0.545634\pi$
$937$	−267.742			−0.285744			−0.142872	+	0.989741i	$0.545634\pi$
$938$		0			0
$939$	32.5605	+	15.1733i	0.0346757	+	0.0161590i
$940$		0			0
$941$	610.126	+	1056.77i	0.648380	+	1.12303i	0.983510	+	0.180855i	$0.0578865\pi$
$941$	610.126	+	1056.77i	0.648380	+	1.12303i	−0.335130	+	0.942172i	$0.608780\pi$
$942$		0			0
$943$	62.8642	+	36.2946i	0.0666640	+	0.0384885i
$944$		0			0
$945$	479.868	−	128.968i	0.507797	−	0.136474i
$946$		0			0
$947$	−1395.84	−	805.888i	−1.47396	−	0.850991i	−0.474390	−	0.880315i	$-0.657331\pi$
$947$	−1395.84	−	805.888i	−1.47396	−	0.850991i	−0.999570	+	0.0293240i	$0.990665\pi$
$948$		0			0
$949$	245.845	+	425.815i	0.259056	+	0.448699i
$950$		0			0
$951$	127.949	+	59.6245i	0.134542	+	0.0626967i
$952$		0			0
$953$	242.459			0.254416			0.127208	−	0.991876i	$-0.459398\pi$
$953$	242.459			0.254416			0.127208	+	0.991876i	$0.459398\pi$
$954$		0			0
$955$		−	548.603i		−	0.574453i
$956$		0			0
$957$	−223.005	−	318.314i	−0.233025	−	0.332617i
$958$		0			0
$959$	−722.656	+	417.226i	−0.753552	+	0.435063i
$960$		0			0
$961$	244.068	−	422.739i	0.253973	−	0.439895i
$962$		0			0
$963$	−80.3598	−	454.409i	−0.0834473	−	0.471868i
$964$		0			0
$965$	275.421	−	477.043i	0.285411	−	0.494346i
$966$		0			0
$967$	1543.81	−	891.320i	1.59650	−	0.921737i	0.604340	−	0.796726i	$-0.293437\pi$
$967$	1543.81	−	891.320i	1.59650	−	0.921737i	0.992155	−	0.125011i	$-0.0398966\pi$
$968$		0			0
$969$	1617.35	−	141.909i	1.66910	−	0.146449i
$970$		0			0
$971$			645.136i			0.664404i	0.943208	+	0.332202i	$0.107792\pi$
$971$			645.136i			0.664404i	−0.943208	+	0.332202i	$0.892208\pi$
$972$		0			0
$973$	−798.958			−0.821129
$974$		0			0
$975$	77.9719	+	888.654i	0.0799712	+	0.911440i
$976$		0			0
$977$	−689.779	−	1194.73i	−0.706017	−	1.22286i	−0.966323	−	0.257331i	$-0.917157\pi$
$977$	−689.779	−	1194.73i	−0.706017	−	1.22286i	0.260306	−	0.965526i	$-0.416176\pi$
$978$		0			0
$979$	488.244	+	281.888i	0.498717	+	0.287935i
$980$		0			0
$981$	−225.760	+	39.9245i	−0.230133	+	0.0406977i
$982$		0			0
$983$	−639.804	−	369.391i	−0.650869	−	0.375779i	0.137920	−	0.990443i	$-0.455958\pi$
$983$	−639.804	−	369.391i	−0.650869	−	0.375779i	−0.788789	+	0.614664i	$0.789292\pi$
$984$		0			0
$985$	281.478	+	487.534i	0.285764	+	0.494959i
$986$		0			0
$987$	−613.082	+	429.514i	−0.621157	+	0.435171i
$988$		0			0
$989$	−85.2536			−0.0862018
$990$		0			0
$991$		−	1533.69i		−	1.54762i	−0.633416	−	0.773811i	$-0.718348\pi$
$991$		−	1533.69i		−	1.54762i	0.633416	−	0.773811i	$-0.281652\pi$
$992$		0			0
$993$	107.034	−	229.685i	0.107788	−	0.231304i
$994$		0			0
$995$	−589.430	+	340.307i	−0.592391	+	0.342017i
$996$		0			0
$997$	871.274	−	1509.09i	0.873896	−	1.51363i	0.0159621	−	0.999873i	$-0.494919\pi$
$997$	871.274	−	1509.09i	0.873896	−	1.51363i	0.857934	−	0.513760i	$-0.171748\pi$
$998$		0			0
$999$	−29.5711	−	110.029i	−0.0296007	−	0.110139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.o.g.511.5		16
3.2	odd	2		1728.3.o.g.127.3		16
4.3	odd	2	inner	576.3.o.g.511.4		16
8.3	odd	2		36.3.f.c.7.2	✓	16
8.5	even	2		36.3.f.c.7.8	yes	16
9.4	even	3	inner	576.3.o.g.319.4		16
9.5	odd	6		1728.3.o.g.1279.4		16
12.11	even	2		1728.3.o.g.127.4		16
24.5	odd	2		108.3.f.c.19.1		16
24.11	even	2		108.3.f.c.19.7		16
36.23	even	6		1728.3.o.g.1279.3		16
36.31	odd	6	inner	576.3.o.g.319.5		16
72.5	odd	6		108.3.f.c.91.7		16
72.11	even	6		324.3.d.g.163.5		8
72.13	even	6		36.3.f.c.31.2	yes	16
72.29	odd	6		324.3.d.g.163.6		8
72.43	odd	6		324.3.d.i.163.4		8
72.59	even	6		108.3.f.c.91.1		16
72.61	even	6		324.3.d.i.163.3		8
72.67	odd	6		36.3.f.c.31.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.2	✓	16	8.3	odd	2
36.3.f.c.7.8	yes	16	8.5	even	2
36.3.f.c.31.2	yes	16	72.13	even	6
36.3.f.c.31.8	yes	16	72.67	odd	6
108.3.f.c.19.1		16	24.5	odd	2
108.3.f.c.19.7		16	24.11	even	2
108.3.f.c.91.1		16	72.59	even	6
108.3.f.c.91.7		16	72.5	odd	6
324.3.d.g.163.5		8	72.11	even	6
324.3.d.g.163.6		8	72.29	odd	6
324.3.d.i.163.3		8	72.61	even	6
324.3.d.i.163.4		8	72.43	odd	6
576.3.o.g.319.4		16	9.4	even	3	inner
576.3.o.g.319.5		16	36.31	odd	6	inner
576.3.o.g.511.4		16	4.3	odd	2	inner
576.3.o.g.511.5		16	1.1	even	1	trivial
1728.3.o.g.127.3		16	3.2	odd	2
1728.3.o.g.127.4		16	12.11	even	2
1728.3.o.g.1279.3		16	36.23	even	6
1728.3.o.g.1279.4		16	9.5	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.262217 + 2.98852i) q^{3} +(-1.10093 - 1.90686i) q^{5} +(-7.23844 - 4.17912i) q^{7} +(-8.86248 + 1.56728i) q^{9} +O(q^{10})\)	\(q+(0.262217 + 2.98852i) q^{3} +(-1.10093 - 1.90686i) q^{5} +(-7.23844 - 4.17912i) q^{7} +(-8.86248 + 1.56728i) q^{9} +(-4.54769 - 2.62561i) q^{11} +(7.37788 + 12.7789i) q^{13} +(5.41000 - 3.79015i) q^{15} +28.2789 q^{17} -19.1376i q^{19} +(10.5913 - 22.7281i) q^{21} +(-3.16702 + 1.82848i) q^{23} +(10.0759 - 17.4520i) q^{25} +(-7.00775 - 26.0747i) q^{27} +(12.3355 - 21.3657i) q^{29} +(32.9674 - 19.0338i) q^{31} +(6.65419 - 14.2793i) q^{33} +18.4036i q^{35} +4.21977 q^{37} +(-36.2553 + 25.3998i) q^{39} +(-9.92483 - 17.1903i) q^{41} +(20.1894 + 11.6564i) q^{43} +(12.7455 + 15.1740i) q^{45} +(-25.8538 - 14.9267i) q^{47} +(10.4300 + 18.0654i) q^{49} +(7.41521 + 84.5120i) q^{51} +32.1118 q^{53} +11.5624i q^{55} +(57.1930 - 5.01820i) q^{57} +(-7.96159 + 4.59663i) q^{59} +(40.8215 - 70.7049i) q^{61} +(70.7005 + 25.6927i) q^{63} +(16.2450 - 28.1372i) q^{65} +(6.86179 - 3.96166i) q^{67} +(-6.29489 - 8.98523i) q^{69} +62.9286i q^{71} +33.3218 q^{73} +(54.7978 + 25.5359i) q^{75} +(21.9454 + 38.0106i) q^{77} +(-53.7133 - 31.0114i) q^{79} +(76.0873 - 27.7800i) q^{81} +(-103.056 - 59.4995i) q^{83} +(-31.1329 - 53.9238i) q^{85} +(67.0864 + 31.2624i) q^{87} -107.361 q^{89} -123.332i q^{91} +(65.5274 + 93.5328i) q^{93} +(-36.4927 + 21.0690i) q^{95} +(1.78621 - 3.09380i) q^{97} +(44.4189 + 16.1419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} + 18 q^{9}+O(q^{10}) \) 16 * q - 6 * q^5 + 18 * q^9	\( 16 q - 6 q^{5} + 18 q^{9} + 46 q^{13} + 12 q^{17} + 66 q^{21} - 30 q^{25} - 42 q^{29} - 168 q^{33} - 56 q^{37} + 84 q^{41} - 174 q^{45} + 58 q^{49} + 72 q^{53} + 366 q^{57} + 34 q^{61} - 30 q^{65} + 54 q^{69} + 116 q^{73} + 330 q^{77} - 102 q^{81} + 140 q^{85} - 384 q^{89} + 486 q^{93} - 148 q^{97}+O(q^{100}) \) 16 * q - 6 * q^5 + 18 * q^9 + 46 * q^13 + 12 * q^17 + 66 * q^21 - 30 * q^25 - 42 * q^29 - 168 * q^33 - 56 * q^37 + 84 * q^41 - 174 * q^45 + 58 * q^49 + 72 * q^53 + 366 * q^57 + 34 * q^61 - 30 * q^65 + 54 * q^69 + 116 * q^73 + 330 * q^77 - 102 * q^81 + 140 * q^85 - 384 * q^89 + 486 * q^93 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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