LMFDB - Embedded newform 216.3.p.b.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45504 - 1.37217i) q^{2} +(0.234289 - 3.99313i) q^{4} +(-8.07964 + 4.66478i) q^{5} +(-4.91220 - 2.83606i) q^{7} +(-5.13836 - 6.13166i) q^{8} +O(q^{10})$	\(q+(1.45504 - 1.37217i) q^{2} +(0.234289 - 3.99313i) q^{4} +(-8.07964 + 4.66478i) q^{5} +(-4.91220 - 2.83606i) q^{7} +(-5.13836 - 6.13166i) q^{8} +(-5.35532 + 17.8741i) q^{10} +(1.85519 - 3.21328i) q^{11} +(-11.0919 + 6.40390i) q^{13} +(-11.0390 + 2.61380i) q^{14} +(-15.8902 - 1.87110i) q^{16} -11.1817 q^{17} -13.1532 q^{19} +(16.7341 + 33.3560i) q^{20} +(-1.70980 - 7.22109i) q^{22} +(20.2104 - 11.6685i) q^{23} +(31.0204 - 53.7288i) q^{25} +(-7.35189 + 24.5379i) q^{26} +(-12.4757 + 18.9506i) q^{28} +(14.6837 + 8.47767i) q^{29} +(3.32057 - 1.91713i) q^{31} +(-25.6884 + 19.0816i) q^{32} +(-16.2699 + 15.3433i) q^{34} +52.9184 q^{35} -13.8029i q^{37} +(-19.1384 + 18.0484i) q^{38} +(70.1190 + 25.5722i) q^{40} +(-3.05861 - 5.29766i) q^{41} +(-11.3997 + 19.7448i) q^{43} +(-12.3964 - 8.16085i) q^{44} +(13.3958 - 44.7103i) q^{46} +(-49.8977 - 28.8084i) q^{47} +(-8.41350 - 14.5726i) q^{49} +(-28.5893 - 120.743i) q^{50} +(22.9729 + 45.7917i) q^{52} -60.0402i q^{53} +34.6162i q^{55} +(7.85093 + 44.6927i) q^{56} +(32.9983 - 7.81327i) q^{58} +(55.3504 + 95.8696i) q^{59} +(-73.2932 - 42.3159i) q^{61} +(2.20093 - 7.34589i) q^{62} +(-11.1944 + 63.0134i) q^{64} +(59.7456 - 103.482i) q^{65} +(16.0918 + 27.8718i) q^{67} +(-2.61976 + 44.6502i) q^{68} +(76.9985 - 72.6132i) q^{70} +38.7881i q^{71} -13.6313 q^{73} +(-18.9400 - 20.0838i) q^{74} +(-3.08164 + 52.5223i) q^{76} +(-18.2261 + 10.5229i) q^{77} +(4.14976 + 2.39586i) q^{79} +(137.115 - 59.0066i) q^{80} +(-11.7197 - 3.51138i) q^{82} +(2.70708 - 4.68879i) q^{83} +(90.3444 - 52.1604i) q^{85} +(10.5063 + 44.3718i) q^{86} +(-29.2354 + 5.13562i) q^{88} -98.2333 q^{89} +72.6474 q^{91} +(-41.8587 - 83.4366i) q^{92} +(-112.133 + 26.5507i) q^{94} +(106.273 - 61.3566i) q^{95} +(42.1665 - 73.0345i) q^{97} +(-32.2381 - 9.65898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.45504	−	1.37217i	0.727521	−	0.686086i
$2$	1.45504	−	1.37217i	0.727521	−	0.686086i
$3$		0			0
$3$		0			0
$4$	0.234289	−	3.99313i	0.0585723	−	0.998283i
$5$	−8.07964	+	4.66478i	−1.61593	+	0.932956i	−0.627969	+	0.778239i	$0.716113\pi$
$5$	−8.07964	+	4.66478i	−1.61593	+	0.932956i	−0.987959	+	0.154718i	$0.950553\pi$
$6$		0			0
$7$	−4.91220	−	2.83606i	−0.701744	−	0.405152i	0.106253	−	0.994339i	$-0.466115\pi$
$7$	−4.91220	−	2.83606i	−0.701744	−	0.405152i	−0.807996	+	0.589187i	$0.799448\pi$
$8$	−5.13836	−	6.13166i	−0.642295	−	0.766457i
$9$		0			0
$10$	−5.35532	+	17.8741i	−0.535532	+	1.78741i
$11$	1.85519	−	3.21328i	0.168654	−	0.292116i	−0.769293	−	0.638896i	$-0.779391\pi$
$11$	1.85519	−	3.21328i	0.168654	−	0.292116i	0.937947	+	0.346779i	$0.112725\pi$
$12$		0			0
$13$	−11.0919	+	6.40390i	−0.853221	+	0.492608i	−0.861736	−	0.507356i	$-0.830623\pi$
$13$	−11.0919	+	6.40390i	−0.853221	+	0.492608i	0.00851505	+	0.999964i	$0.497290\pi$
$14$	−11.0390	+	2.61380i	−0.788502	+	0.186700i
$15$		0			0
$16$	−15.8902	−	1.87110i	−0.993139	−	0.116944i
$17$	−11.1817			−0.657749			−0.328875	−	0.944374i	$-0.606669\pi$
$17$	−11.1817			−0.657749			−0.328875	+	0.944374i	$0.606669\pi$
$18$		0			0
$19$	−13.1532			−0.692271			−0.346136	−	0.938185i	$-0.612506\pi$
$19$	−13.1532			−0.692271			−0.346136	+	0.938185i	$0.612506\pi$
$20$	16.7341	+	33.3560i	0.836706	+	1.66780i
$21$		0			0
$22$	−1.70980	−	7.22109i	−0.0777181	−	0.328232i
$23$	20.2104	−	11.6685i	0.878713	−	0.507325i	0.00847922	−	0.999964i	$-0.497301\pi$
$23$	20.2104	−	11.6685i	0.878713	−	0.507325i	0.870234	+	0.492639i	$0.163968\pi$
$24$		0			0
$25$	31.0204	−	53.7288i	1.24081	−	2.14915i
$26$	−7.35189	+	24.5379i	−0.282765	+	0.943765i
$27$		0			0
$28$	−12.4757	+	18.9506i	−0.445559	+	0.676808i
$29$	14.6837	+	8.47767i	0.506336	+	0.292333i	0.731326	−	0.682028i	$-0.238902\pi$
$29$	14.6837	+	8.47767i	0.506336	+	0.292333i	−0.224990	+	0.974361i	$0.572235\pi$
$30$		0			0
$31$	3.32057	−	1.91713i	0.107115	−	0.0618429i	−0.445485	−	0.895289i	$-0.646969\pi$
$31$	3.32057	−	1.91713i	0.107115	−	0.0618429i	0.552600	+	0.833446i	$0.313636\pi$
$32$	−25.6884	+	19.0816i	−0.802762	+	0.596299i
$33$		0			0
$34$	−16.2699	+	15.3433i	−0.478526	+	0.451272i
$35$	52.9184			1.51196
$36$		0			0
$37$		−	13.8029i		−	0.373052i	−0.982450	−	0.186526i	$-0.940277\pi$
$37$		−	13.8029i		−	0.373052i	0.982450	−	0.186526i	$-0.0597229\pi$
$38$	−19.1384	+	18.0484i	−0.503641	+	0.474957i
$39$		0			0
$40$	70.1190	+	25.5722i	1.75297	+	0.639306i
$41$	−3.05861	−	5.29766i	−0.0746001	−	0.129211i	0.826312	−	0.563212i	$-0.190435\pi$
$41$	−3.05861	−	5.29766i	−0.0746001	−	0.129211i	−0.900912	+	0.434001i	$0.857101\pi$
$42$		0			0
$43$	−11.3997	+	19.7448i	−0.265109	+	0.459182i	−0.967592	−	0.252518i	$-0.918741\pi$
$43$	−11.3997	+	19.7448i	−0.265109	+	0.459182i	0.702483	+	0.711700i	$0.252074\pi$
$44$	−12.3964	−	8.16085i	−0.281737	−	0.185474i
$45$		0			0
$46$	13.3958	−	44.7103i	0.291213	−	0.971962i
$47$	−49.8977	−	28.8084i	−1.06165	−	0.612945i	−0.135764	−	0.990741i	$-0.543349\pi$
$47$	−49.8977	−	28.8084i	−1.06165	−	0.612945i	−0.925889	+	0.377796i	$0.876682\pi$
$48$		0			0
$49$	−8.41350	−	14.5726i	−0.171704	−	0.297400i
$50$	−28.5893	−	120.743i	−0.571786	−	2.41486i
$51$		0			0
$52$	22.9729	+	45.7917i	0.441787	+	0.880610i
$53$		−	60.0402i		−	1.13283i	−0.824119	−	0.566417i	$-0.808329\pi$
$53$		−	60.0402i		−	1.13283i	0.824119	−	0.566417i	$-0.191671\pi$
$54$		0			0
$55$			34.6162i			0.629385i
$56$	7.85093	+	44.6927i	0.140195	+	0.798084i
$57$		0			0
$58$	32.9983	−	7.81327i	0.568936	−	0.134712i
$59$	55.3504	+	95.8696i	0.938142	+	1.62491i	0.768933	+	0.639329i	$0.220788\pi$
$59$	55.3504	+	95.8696i	0.938142	+	1.62491i	0.169208	+	0.985580i	$0.445879\pi$
$60$		0			0
$61$	−73.2932	−	42.3159i	−1.20153	−	0.693703i	−0.240633	−	0.970616i	$-0.577355\pi$
$61$	−73.2932	−	42.3159i	−1.20153	−	0.693703i	−0.960895	+	0.276913i	$0.910688\pi$
$62$	2.20093	−	7.34589i	0.0354989	−	0.118482i
$63$		0			0
$64$	−11.1944	+	63.0134i	−0.174913	+	0.984584i
$65$	59.7456	−	103.482i	0.919163	−	1.59204i
$66$		0			0
$67$	16.0918	+	27.8718i	0.240176	+	0.415997i	0.960764	−	0.277366i	$-0.0894616\pi$
$67$	16.0918	+	27.8718i	0.240176	+	0.415997i	−0.720588	+	0.693363i	$0.756128\pi$
$68$	−2.61976	+	44.6502i	−0.0385259	+	0.656620i
$69$		0			0
$70$	76.9985	−	72.6132i	1.09998	−	1.03733i
$71$			38.7881i			0.546311i	0.961970	+	0.273156i	$0.0880674\pi$
$71$			38.7881i			0.546311i	−0.961970	+	0.273156i	$0.911933\pi$
$72$		0			0
$73$	−13.6313			−0.186730			−0.0933652	−	0.995632i	$-0.529762\pi$
$73$	−13.6313			−0.186730			−0.0933652	+	0.995632i	$0.529762\pi$
$74$	−18.9400	−	20.0838i	−0.255946	−	0.271403i
$75$		0			0
$76$	−3.08164	+	52.5223i	−0.0405479	+	0.691083i
$77$	−18.2261	+	10.5229i	−0.236703	+	0.136661i
$78$		0			0
$79$	4.14976	+	2.39586i	0.0525286	+	0.0303274i	0.526034	−	0.850463i	$-0.323678\pi$
$79$	4.14976	+	2.39586i	0.0525286	+	0.0303274i	−0.473506	+	0.880791i	$0.657012\pi$
$80$	137.115	−	59.0066i	1.71394	−	0.737582i
$81$		0			0
$82$	−11.7197	−	3.51138i	−0.142923	−	0.0428217i
$83$	2.70708	−	4.68879i	0.0326154	−	0.0564915i	−0.849257	−	0.527980i	$-0.822950\pi$
$83$	2.70708	−	4.68879i	0.0326154	−	0.0564915i	0.881872	+	0.471488i	$0.156283\pi$
$84$		0			0
$85$	90.3444	−	52.1604i	1.06288	−	0.613651i
$86$	10.5063	+	44.3718i	0.122166	+	0.515951i
$87$		0			0
$88$	−29.2354	+	5.13562i	−0.332220	+	0.0583594i
$89$	−98.2333			−1.10374			−0.551872	−	0.833929i	$-0.686086\pi$
$89$	−98.2333			−1.10374			−0.551872	+	0.833929i	$0.686086\pi$
$90$		0			0
$91$	72.6474			0.798323
$92$	−41.8587	−	83.4366i	−0.454986	−	0.906920i
$93$		0			0
$94$	−112.133	+	26.5507i	−1.19291	+	0.282454i
$95$	106.273	−	61.3566i	1.11866	−	0.645859i
$96$		0			0
$97$	42.1665	−	73.0345i	0.434706	−	0.752932i	−0.562566	−	0.826753i	$-0.690186\pi$
$97$	42.1665	−	73.0345i	0.434706	−	0.752932i	0.997272	+	0.0738200i	$0.0235190\pi$
$98$	−32.2381	−	9.65898i	−0.328960	−	0.0985610i
$99$		0			0
$100$	−207.279	−	136.457i	−2.07279	−	1.36457i
$101$	−92.9603	−	53.6706i	−0.920399	−	0.531393i	−0.0366366	−	0.999329i	$-0.511664\pi$
$101$	−92.9603	−	53.6706i	−0.920399	−	0.531393i	−0.883762	+	0.467936i	$0.844998\pi$
$102$		0			0
$103$	75.2912	−	43.4694i	0.730983	−	0.422033i	−0.0877989	−	0.996138i	$-0.527983\pi$
$103$	75.2912	−	43.4694i	0.730983	−	0.422033i	0.818782	+	0.574105i	$0.194650\pi$
$104$	96.2606	+	35.1060i	0.925583	+	0.337558i
$105$		0			0
$106$	−82.3854	−	87.3609i	−0.777221	−	0.824160i
$107$	−168.670			−1.57636			−0.788179	−	0.615446i	$-0.788976\pi$
$107$	−168.670			−1.57636			−0.788179	+	0.615446i	$0.788976\pi$
$108$		0			0
$109$			162.909i			1.49458i	0.664497	+	0.747291i	$0.268646\pi$
$109$			162.909i			1.49458i	−0.664497	+	0.747291i	$0.731354\pi$
$110$	47.4994	+	50.3680i	0.431812	+	0.457891i
$111$		0			0
$112$	72.7494	+	54.2569i	0.649549	+	0.484436i
$113$	−30.8328	−	53.4040i	−0.272857	−	0.472602i	0.696736	−	0.717328i	$-0.254635\pi$
$113$	−30.8328	−	53.4040i	−0.272857	−	0.472602i	−0.969592	+	0.244727i	$0.921302\pi$
$114$		0			0
$115$	−108.862	+	188.554i	−0.946624	+	1.63960i
$116$	37.2927	−	56.6479i	0.321489	−	0.488344i
$117$		0			0
$118$	212.087	+	63.5441i	1.79734	+	0.538509i
$119$	54.9270	+	31.7121i	0.461571	+	0.266488i
$120$		0			0
$121$	53.6166	+	92.8666i	0.443112	+	0.767492i
$122$	−164.709	+	38.9996i	−1.35008	+	0.319669i
$123$		0			0
$124$	−6.87738	−	13.7086i	−0.0554628	−	0.110553i
$125$			345.574i			2.76459i
$126$		0			0
$127$		−	108.522i		−	0.854507i	−0.904132	−	0.427254i	$-0.859481\pi$
$127$		−	108.522i		−	0.854507i	0.904132	−	0.427254i	$-0.140519\pi$
$128$	70.1768	+	107.048i	0.548256	+	0.836311i
$129$		0			0
$130$	−55.0633	−	232.552i	−0.423564	−	1.78886i
$131$	32.6404	+	56.5348i	0.249163	+	0.431563i	0.963294	−	0.268449i	$-0.0865111\pi$
$131$	32.6404	+	56.5348i	0.249163	+	0.431563i	−0.714131	+	0.700012i	$0.753178\pi$
$132$		0			0
$133$	64.6110	+	37.3032i	0.485797	+	0.280475i
$134$	61.6591	+	18.4739i	0.460142	+	0.137865i
$135$		0			0
$136$	57.4558	+	68.5626i	0.422469	+	0.504137i
$137$	−35.6297	+	61.7125i	−0.260071	+	0.450456i	−0.966261	−	0.257567i	$-0.917079\pi$
$137$	−35.6297	+	61.7125i	−0.260071	+	0.450456i	0.706190	+	0.708023i	$0.250413\pi$
$138$		0			0
$139$	−38.9742	−	67.5054i	−0.280390	−	0.485650i	0.691091	−	0.722768i	$-0.257131\pi$
$139$	−38.9742	−	67.5054i	−0.280390	−	0.485650i	−0.971481	+	0.237118i	$0.923797\pi$
$140$	12.3982	−	211.310i	0.0885588	−	1.50936i
$141$		0			0
$142$	53.2239	+	56.4383i	0.374816	+	0.397453i
$143$			47.5218i			0.332320i
$144$		0			0
$145$	−158.186			−1.09094
$146$	−19.8341	+	18.7045i	−0.135850	+	0.128113i
$147$		0			0
$148$	−55.1169	−	3.23388i	−0.372412	−	0.0218505i
$149$	127.047	−	73.3505i	0.852664	−	0.492286i	−0.00888514	−	0.999961i	$-0.502828\pi$
$149$	127.047	−	73.3505i	0.852664	−	0.492286i	0.861549	+	0.507675i	$0.169495\pi$
$150$		0			0
$151$	91.4191	+	52.7808i	0.605424	+	0.349542i	0.771173	−	0.636626i	$-0.219671\pi$
$151$	91.4191	+	52.7808i	0.605424	+	0.349542i	−0.165748	+	0.986168i	$0.553004\pi$
$152$	67.5857	+	80.6506i	0.444643	+	0.530596i
$153$		0			0
$154$	−12.0806	+	40.3206i	−0.0784454	+	0.261822i
$155$	−17.8860	+	30.9794i	−0.115393	+	0.199867i
$156$		0			0
$157$	−148.874	+	85.9525i	−0.948243	+	0.547468i	−0.892535	−	0.450979i	$-0.851075\pi$
$157$	−148.874	+	85.9525i	−0.948243	+	0.547468i	−0.0557082	+	0.998447i	$0.517742\pi$
$158$	9.32561	−	2.20810i	0.0590228	−	0.0139753i
$159$		0			0
$160$	118.541	−	274.003i	0.740884	−	1.71252i
$161$	−132.370			−0.822175
$162$		0			0
$163$	−83.1474			−0.510107			−0.255053	−	0.966927i	$-0.582093\pi$
$163$	−83.1474			−0.510107			−0.255053	+	0.966927i	$0.582093\pi$
$164$	−21.8709	+	10.9722i	−0.133359	+	0.0669039i
$165$		0			0
$166$	−2.49492	−	10.5370i	−0.0150297	−	0.0634757i
$167$	−202.139	+	116.705i	−1.21041	+	0.698831i	−0.962849	−	0.270041i	$-0.912963\pi$
$167$	−202.139	+	116.705i	−1.21041	+	0.698831i	−0.247562	+	0.968872i	$0.579630\pi$
$168$		0			0
$169$	−2.48015	+	4.29575i	−0.0146755	+	0.0254186i
$170$	59.8818	−	199.863i	0.352246	−	1.17567i
$171$		0			0
$172$	76.1728	+	50.1464i	0.442865	+	0.291549i
$173$	−38.5845	−	22.2768i	−0.223032	−	0.128767i	0.384322	−	0.923199i	$-0.374435\pi$
$173$	−38.5845	−	22.2768i	−0.223032	−	0.128767i	−0.607353	+	0.794432i	$0.707769\pi$
$174$		0			0
$175$	−304.757	+	175.951i	−1.74147	+	1.00544i
$176$	−35.4917	+	47.5885i	−0.201657	+	0.270389i
$177$		0			0
$178$	−142.933	+	134.793i	−0.802997	+	0.757264i
$179$	15.3758			0.0858984			0.0429492	−	0.999077i	$-0.486325\pi$
$179$	15.3758			0.0858984			0.0429492	+	0.999077i	$0.486325\pi$
$180$		0			0
$181$		−	240.627i		−	1.32943i	−0.747096	−	0.664716i	$-0.768553\pi$
$181$		−	240.627i		−	1.32943i	0.747096	−	0.664716i	$-0.231447\pi$
$182$	105.705	−	99.6848i	0.580797	−	0.547718i
$183$		0			0
$184$	−175.396	−	63.9664i	−0.953236	−	0.347643i
$185$	64.3876	+	111.523i	0.348041	+	0.602825i
$186$		0			0
$187$	−20.7442	+	35.9301i	−0.110932	+	0.192139i
$188$	−126.726	+	192.499i	−0.674077	+	1.02393i
$189$		0			0
$190$	70.4394	−	235.101i	0.370734	−	1.23737i
$191$	68.8601	+	39.7564i	0.360524	+	0.208149i	0.669311	−	0.742983i	$-0.266590\pi$
$191$	68.8601	+	39.7564i	0.360524	+	0.208149i	−0.308787	+	0.951131i	$0.599923\pi$
$192$		0			0
$193$	16.7549	+	29.0203i	0.0868128	+	0.150364i	0.906162	−	0.422930i	$-0.138998\pi$
$193$	16.7549	+	29.0203i	0.0868128	+	0.150364i	−0.819349	+	0.573294i	$0.805665\pi$
$194$	−38.8619	−	164.128i	−0.200319	−	0.846019i
$195$		0			0
$196$	−60.1615	+	30.1820i	−0.306947	+	0.153990i
$197$		−	183.151i		−	0.929699i	−0.885390	−	0.464849i	$-0.846108\pi$
$197$		−	183.151i		−	0.929699i	0.885390	−	0.464849i	$-0.153892\pi$
$198$		0			0
$199$			86.2656i			0.433496i	0.976228	+	0.216748i	$0.0695449\pi$
$199$			86.2656i			0.433496i	−0.976228	+	0.216748i	$0.930455\pi$
$200$	−488.841	+	85.8721i	−2.44420	+	0.429360i
$201$		0			0
$202$	−208.906	+	49.4645i	−1.03419	+	0.244874i
$203$	−48.0864	−	83.2881i	−0.236879	−	0.410286i
$204$		0			0
$205$	49.4249	+	28.5355i	0.241097	+	0.139197i
$206$	49.9043	−	166.562i	0.242254	−	0.808555i
$207$		0			0
$208$	188.235	−	81.0054i	0.904974	−	0.389449i
$209$	−24.4016	+	42.2648i	−0.116754	+	0.202224i
$210$		0			0
$211$	−115.005	−	199.195i	−0.545049	−	0.944053i	−0.998604	−	0.0528247i	$-0.983178\pi$
$211$	−115.005	−	199.195i	−0.545049	−	0.944053i	0.453554	−	0.891229i	$-0.350156\pi$
$212$	−239.748	−	14.0668i	−1.13089	−	0.0663527i
$213$		0			0
$214$	−245.422	+	231.445i	−1.14683	+	1.08152i
$215$		−	212.708i		−	0.989339i
$216$		0			0
$217$	−21.7484			−0.100223
$218$	223.540	+	237.040i	1.02541	+	1.08734i
$219$		0			0
$220$	138.227	+	8.11021i	0.628305	+	0.0368646i
$221$	124.026	−	71.6067i	0.561206	−	0.324012i
$222$		0			0
$223$	327.758	+	189.231i	1.46977	+	0.848570i	0.999425	−	0.0339138i	$-0.0107972\pi$
$223$	327.758	+	189.231i	1.46977	+	0.848570i	0.470342	+	0.882484i	$0.344131\pi$
$224$	180.303	−	20.8788i	0.804925	−	0.0932088i
$225$		0			0
$226$	−118.142	−	35.3971i	−0.522754	−	0.156624i
$227$	208.237	−	360.677i	0.917343	−	1.58889i	0.113910	−	0.993491i	$-0.463663\pi$
$227$	208.237	−	360.677i	0.917343	−	1.58889i	0.803434	−	0.595394i	$-0.203004\pi$
$228$		0			0
$229$	153.319	−	88.5187i	0.669515	−	0.386545i	−0.126378	−	0.991982i	$-0.540335\pi$
$229$	153.319	−	88.5187i	0.669515	−	0.386545i	0.795893	+	0.605438i	$0.207002\pi$
$230$	100.330	+	423.731i	0.436219	+	1.84231i
$231$		0			0
$232$	−23.4683	−	133.597i	−0.101156	−	0.575849i
$233$	144.457			0.619987			0.309993	−	0.950739i	$-0.399673\pi$
$233$	144.457			0.619987			0.309993	+	0.950739i	$0.399673\pi$
$234$		0			0
$235$	537.540			2.28740
$236$	395.788	−	198.560i	1.67707	−	0.841356i
$237$		0			0
$238$	123.435	−	29.2268i	0.518636	−	0.122802i
$239$	−157.611	+	90.9966i	−0.659459	+	0.380739i	−0.792071	−	0.610429i	$-0.790997\pi$
$239$	−157.611	+	90.9966i	−0.659459	+	0.380739i	0.132612	+	0.991168i	$0.457664\pi$
$240$		0			0
$241$	70.3168	−	121.792i	0.291771	−	0.505362i	−0.682458	−	0.730925i	$-0.739089\pi$
$241$	70.3168	−	121.792i	0.291771	−	0.505362i	0.974229	+	0.225563i	$0.0724222\pi$
$242$	205.443	+	61.5536i	0.848939	+	0.254354i
$243$		0			0
$244$	−186.145	+	282.755i	−0.762888	+	1.15883i
$245$	135.956	+	78.4942i	0.554922	+	0.320385i
$246$		0			0
$247$	145.893	−	84.2315i	0.590661	−	0.341018i
$248$	−28.8175	−	10.5097i	−0.116199	−	0.0423777i
$249$		0			0
$250$	474.186	+	502.824i	1.89675	+	2.01130i
$251$	−38.7781			−0.154494			−0.0772471	−	0.997012i	$-0.524613\pi$
$251$	−38.7781			−0.154494			−0.0772471	+	0.997012i	$0.524613\pi$
$252$		0			0
$253$		−	86.5889i		−	0.342249i
$254$	−148.911	−	157.905i	−0.586265	−	0.621671i
$255$		0			0
$256$	248.998	+	59.4643i	0.972648	+	0.232282i
$257$	74.9268	+	129.777i	0.291544	+	0.504969i	0.974175	−	0.225794i	$-0.0724977\pi$
$257$	74.9268	+	129.777i	0.291544	+	0.504969i	−0.682631	+	0.730763i	$0.739164\pi$
$258$		0			0
$259$	−39.1460	+	67.8028i	−0.151143	+	0.261787i
$260$	−399.221	−	262.817i	−1.53547	−	1.01083i
$261$		0			0
$262$	125.069	+	37.4722i	0.477361	+	0.143024i
$263$	−67.5653	−	39.0088i	−0.256902	−	0.148323i	0.366018	−	0.930608i	$-0.380721\pi$
$263$	−67.5653	−	39.0088i	−0.256902	−	0.148323i	−0.622921	+	0.782285i	$0.714054\pi$
$264$		0			0
$265$	280.074	+	485.103i	1.05688	+	1.83058i
$266$	145.198	−	34.3797i	0.545857	−	0.129247i
$267$		0			0
$268$	115.066	−	57.7265i	0.429350	−	0.215398i
$269$		−	240.267i		−	0.893187i	−0.894737	−	0.446594i	$-0.852637\pi$
$269$		−	240.267i		−	0.893187i	0.894737	−	0.446594i	$-0.147363\pi$
$270$		0			0
$271$		−	440.449i		−	1.62527i	−0.582772	−	0.812636i	$-0.698032\pi$
$271$		−	440.449i		−	1.62527i	0.582772	−	0.812636i	$-0.301968\pi$
$272$	177.680	+	20.9221i	0.653236	+	0.0769195i
$273$		0			0
$274$	32.8374	+	138.684i	0.119845	+	0.506147i
$275$	−115.097	−	199.354i	−0.418535	−	0.724925i
$276$		0			0
$277$	−111.638	−	64.4543i	−0.403026	−	0.232687i	0.284763	−	0.958598i	$-0.408085\pi$
$277$	−111.638	−	64.4543i	−0.403026	−	0.232687i	−0.687789	+	0.725911i	$0.741418\pi$
$278$	−149.338	−	44.7437i	−0.537187	−	0.160949i
$279$		0			0
$280$	−271.914	−	324.478i	−0.971122	−	1.15885i
$281$	−70.2020	+	121.593i	−0.249829	+	0.432717i	−0.963478	−	0.267787i	$-0.913708\pi$
$281$	−70.2020	+	121.593i	−0.249829	+	0.432717i	0.713649	+	0.700503i	$0.247041\pi$
$282$		0			0
$283$	−209.786	−	363.361i	−0.741295	−	1.28396i	−0.951906	−	0.306390i	$-0.900879\pi$
$283$	−209.786	−	363.361i	−0.741295	−	1.28396i	0.210611	−	0.977570i	$-0.432455\pi$
$284$	154.886	+	9.08764i	0.545373	+	0.0319987i
$285$		0			0
$286$	65.2080	+	69.1461i	0.228000	+	0.241770i
$287$			34.6976i			0.120898i
$288$		0			0
$289$	−163.969			−0.567366
$290$	−230.167	+	217.058i	−0.793679	+	0.748476i
$291$		0			0
$292$	−3.19367	+	54.4317i	−0.0109372	+	0.186410i
$293$	−329.166	+	190.044i	−1.12343	+	0.648615i	−0.942275	−	0.334839i	$-0.891318\pi$
$293$	−329.166	+	190.044i	−1.12343	+	0.648615i	−0.181158	+	0.983454i	$0.557985\pi$
$294$		0			0
$295$	−894.422	−	516.395i	−3.03194	−	1.75049i
$296$	−84.6348	+	70.9244i	−0.285928	+	0.239610i
$297$		0			0
$298$	84.2089	−	281.058i	0.282580	−	0.943148i
$299$	−149.448	+	258.851i	−0.499825	+	0.865722i
$300$		0			0
$301$	111.995	−	64.6604i	0.372077	−	0.214819i
$302$	205.443	−	48.6444i	0.680274	−	0.161074i
$303$		0			0
$304$	209.006	+	24.6108i	0.687521	+	0.0809567i
$305$	789.577			2.58878
$306$		0			0
$307$	306.165			0.997281			0.498640	−	0.866809i	$-0.333833\pi$
$307$	306.165			0.997281			0.498640	+	0.866809i	$0.333833\pi$
$308$	37.7490	+	75.2448i	0.122562	+	0.244301i
$309$		0			0
$310$	16.4843	+	69.6190i	0.0531751	+	0.224577i
$311$	492.156	−	284.146i	1.58249	−	0.913654i	0.588000	−	0.808861i	$-0.299915\pi$
$311$	492.156	−	284.146i	1.58249	−	0.913654i	0.994494	−	0.104793i	$-0.0334179\pi$
$312$		0			0
$313$	−156.683	+	271.382i	−0.500583	+	0.867036i	0.499417	+	0.866362i	$0.333548\pi$
$313$	−156.683	+	271.382i	−0.500583	+	0.867036i	−1.00000		0.000673622i	$0.999786\pi$
$314$	−98.6764	+	329.345i	−0.314256	+	1.04887i
$315$		0			0
$316$	10.5393	−	16.0092i	0.0333521	−	0.0506621i
$317$	−133.136	−	76.8660i	−0.419987	−	0.242480i	0.275085	−	0.961420i	$-0.411294\pi$
$317$	−133.136	−	76.8660i	−0.419987	−	0.242480i	−0.695072	+	0.718940i	$0.744627\pi$
$318$		0			0
$319$	54.4822	−	31.4553i	0.170791	−	0.0986061i
$320$	−203.496	−	561.345i	−0.635926	−	1.75420i
$321$		0			0
$322$	−192.604	+	181.635i	−0.598149	+	0.564083i
$323$	147.075			0.455341
$324$		0			0
$325$			794.605i			2.44494i
$326$	−120.983	+	114.092i	−0.371113	+	0.349977i
$327$		0			0
$328$	−16.7672	+	45.9756i	−0.0511196	+	0.140170i
$329$	163.405	+	283.026i	0.496672	+	0.860261i
$330$		0			0
$331$	306.335	−	530.588i	0.925484	−	1.60299i	0.134704	−	0.990886i	$-0.456992\pi$
$331$	306.335	−	530.588i	0.925484	−	1.60299i	0.790780	−	0.612100i	$-0.209675\pi$
$332$	−18.0887	−	11.9082i	−0.0544841	−	0.0358682i
$333$		0			0
$334$	−133.981	+	447.179i	−0.401141	+	1.33886i
$335$	−260.031	−	150.129i	−0.776213	−	0.448147i
$336$		0			0
$337$	−233.237	−	403.978i	−0.692098	−	1.19875i	−0.971149	−	0.238473i	$-0.923353\pi$
$337$	−233.237	−	403.978i	−0.692098	−	1.19875i	0.279051	−	0.960276i	$-0.409980\pi$
$338$	2.28578	+	9.65369i	0.00676267	+	0.0285612i
$339$		0			0
$340$	−187.116	−	372.978i	−0.550343	−	1.09699i
$341$		−	14.2266i		−	0.0417201i
$342$		0			0
$343$			373.379i			1.08857i
$344$	179.644	−	31.5571i	0.522221	−	0.0917358i
$345$		0			0
$346$	−86.7095	+	20.5309i	−0.250606	+	0.0593379i
$347$	−178.207	−	308.664i	−0.513565	−	0.889520i	−0.999876	−	0.0157348i	$-0.994991\pi$
$347$	−178.207	−	308.664i	−0.513565	−	0.889520i	0.486311	−	0.873786i	$-0.338342\pi$
$348$		0			0
$349$	125.660	+	72.5496i	0.360056	+	0.207878i	0.669105	−	0.743168i	$-0.266677\pi$
$349$	125.660	+	72.5496i	0.360056	+	0.207878i	−0.309049	+	0.951046i	$0.600011\pi$
$350$	−201.998	+	674.195i	−0.577137	+	1.92627i
$351$		0			0
$352$	13.6577	+	117.944i	0.0388002	+	0.335068i
$353$	209.033	−	362.055i	0.592160	−	1.02565i	−0.401780	−	0.915736i	$-0.631608\pi$
$353$	209.033	−	362.055i	0.592160	−	1.02565i	0.993941	−	0.109916i	$-0.0350582\pi$
$354$		0			0
$355$	−180.938	−	313.394i	−0.509684	−	0.882799i
$356$	−23.0150	+	392.258i	−0.0646489	+	1.10185i
$357$		0			0
$358$	22.3724	−	21.0983i	0.0624929	−	0.0589337i
$359$			291.137i			0.810968i	0.914102	+	0.405484i	$0.132897\pi$
$359$			291.137i			0.810968i	−0.914102	+	0.405484i	$0.867103\pi$
$360$		0			0
$361$	−187.995			−0.520761
$362$	−330.182	−	350.122i	−0.912104	−	0.967189i
$363$		0			0
$364$	17.0205	−	290.091i	0.0467597	−	0.796953i
$365$	110.136	−	63.5871i	0.301743	−	0.174211i
$366$		0			0
$367$	321.962	+	185.885i	0.877281	+	0.506499i	0.869761	−	0.493473i	$-0.164273\pi$
$367$	321.962	+	185.885i	0.877281	+	0.506499i	0.00752022	+	0.999972i	$0.497606\pi$
$368$	−342.981	+	147.599i	−0.932012	+	0.401084i
$369$		0			0
$370$	246.715	+	73.9191i	0.666797	+	0.199781i
$371$	−170.278	+	294.930i	−0.458970	+	0.794959i
$372$		0			0
$373$	−424.454	+	245.059i	−1.13795	+	0.656994i	−0.945921	−	0.324396i	$-0.894839\pi$
$373$	−424.454	+	245.059i	−1.13795	+	0.656994i	−0.192025	+	0.981390i	$0.561506\pi$
$374$	19.1185	+	80.7444i	0.0511190	+	0.215894i
$375$		0			0
$376$	79.7489	+	453.984i	0.212098	+	1.20740i
$377$	−217.160			−0.576022
$378$		0			0
$379$	−249.848			−0.659230			−0.329615	−	0.944115i	$-0.606919\pi$
$379$	−249.848			−0.659230			−0.329615	+	0.944115i	$0.606919\pi$
$380$	−220.106	−	438.736i	−0.579227	−	1.15457i
$381$		0			0
$382$	154.747	−	36.6407i	0.405096	−	0.0959180i
$383$	−42.3609	+	24.4571i	−0.110603	+	0.0638566i	−0.554281	−	0.832330i	$-0.687007\pi$
$383$	−42.3609	+	24.4571i	−0.110603	+	0.0638566i	0.443678	+	0.896186i	$0.353673\pi$
$384$		0			0
$385$	98.1737	−	170.042i	0.254997	−	0.441667i
$386$	64.1998	+	19.2351i	0.166321	+	0.0498320i
$387$		0			0
$388$	−281.757	−	185.487i	−0.726178	−	0.478060i
$389$	446.299	+	257.671i	1.14730	+	0.662393i	0.948228	−	0.317592i	$-0.102874\pi$
$389$	446.299	+	257.671i	1.14730	+	0.662393i	0.199071	+	0.979985i	$0.436208\pi$
$390$		0			0
$391$	−225.987	+	130.474i	−0.577973	+	0.333693i
$392$	−46.1226	+	126.468i	−0.117660	+	0.322622i
$393$		0			0
$394$	−251.314	−	266.492i	−0.637853	−	0.676375i
$395$	−44.7047			−0.113177
$396$		0			0
$397$		−	560.274i		−	1.41127i	−0.708576	−	0.705634i	$-0.750662\pi$
$397$		−	560.274i		−	1.41127i	0.708576	−	0.705634i	$-0.249338\pi$
$398$	118.371	+	125.520i	0.297415	+	0.315377i
$399$		0			0
$400$	−593.452	+	795.721i	−1.48363	+	1.98930i
$401$	−226.974	−	393.131i	−0.566021	−	0.980377i	−0.996954	−	0.0779928i	$-0.975149\pi$
$401$	−226.974	−	393.131i	−0.566021	−	0.980377i	0.430933	−	0.902384i	$-0.358184\pi$
$402$		0			0
$403$	−24.5542	+	42.5292i	−0.0609286	+	0.105531i
$404$	−236.094	+	358.628i	−0.584390	+	0.887694i
$405$		0			0
$406$	−184.253	−	55.2048i	−0.453826	−	0.135972i
$407$	−44.3527	−	25.6070i	−0.108975	−	0.0629165i
$408$		0			0
$409$	233.772	+	404.905i	0.571570	+	0.989988i	0.996405	+	0.0847172i	$0.0269987\pi$
$409$	233.772	+	404.905i	0.571570	+	0.989988i	−0.424835	+	0.905271i	$0.639668\pi$
$410$	111.071	−	26.2991i	0.270904	−	0.0641442i
$411$		0			0
$412$	−155.939	−	310.832i	−0.378493	−	0.754447i
$413$		−	627.908i		−	1.52036i
$414$		0			0
$415$			50.5117i			0.121715i
$416$	162.736	−	376.156i	0.391192	−	0.904222i
$417$		0			0
$418$	22.4892	+	94.9801i	0.0538020	+	0.227225i
$419$	−92.4411	−	160.113i	−0.220623	−	0.382131i	0.734374	−	0.678745i	$-0.237476\pi$
$419$	−92.4411	−	160.113i	−0.220623	−	0.382131i	−0.954997	+	0.296614i	$0.904142\pi$
$420$		0			0
$421$	−326.113	−	188.282i	−0.774616	−	0.447225i	0.0599029	−	0.998204i	$-0.480921\pi$
$421$	−326.113	−	188.282i	−0.774616	−	0.447225i	−0.834519	+	0.550980i	$0.814254\pi$
$422$	−440.668	−	132.030i	−1.04424	−	0.312867i
$423$		0			0
$424$	−368.146	+	308.508i	−0.868269	+	0.727614i
$425$	−346.862	+	600.782i	−0.816145	+	1.41360i
$426$		0			0
$427$	240.021	+	415.728i	0.562110	+	0.973603i
$428$	−39.5177	+	673.523i	−0.0923310	+	1.57365i
$429$		0			0
$430$	−291.872	−	309.499i	−0.678772	−	0.719765i
$431$			300.981i			0.698332i	0.937061	+	0.349166i	$0.113535\pi$
$431$			300.981i			0.698332i	−0.937061	+	0.349166i	$0.886465\pi$
$432$		0			0
$433$	−670.846			−1.54930			−0.774649	−	0.632391i	$-0.782074\pi$
$433$	−670.846			−1.54930			−0.774649	+	0.632391i	$0.782074\pi$
$434$	−31.6448	+	29.8426i	−0.0729144	+	0.0687617i
$435$		0			0
$436$	650.519	+	38.1680i	1.49202	+	0.0875412i
$437$	−265.830	+	153.477i	−0.608308	+	0.351207i
$438$		0			0
$439$	513.168	+	296.277i	1.16895	+	0.674892i	0.953432	−	0.301609i	$-0.0975237\pi$
$439$	513.168	+	296.277i	1.16895	+	0.674892i	0.215515	+	0.976501i	$0.430857\pi$
$440$	212.255	−	177.871i	0.482397	−	0.404251i
$441$		0			0
$442$	82.2069	−	274.376i	0.185988	−	0.620761i
$443$	106.548	−	184.547i	0.240515	−	0.416584i	−0.720346	−	0.693615i	$-0.756017\pi$
$443$	106.548	−	184.547i	0.240515	−	0.416584i	0.960861	+	0.277031i	$0.0893503\pi$
$444$		0			0
$445$	793.689	−	458.237i	1.78357	−	1.02975i
$446$	736.559	−	174.401i	1.65148	−	0.391034i
$447$		0			0
$448$	233.699	−	277.786i	0.521650	−	0.620059i
$449$	−574.593			−1.27972			−0.639858	−	0.768493i	$-0.721007\pi$
$449$	−574.593			−1.27972			−0.639858	+	0.768493i	$0.721007\pi$
$450$		0			0
$451$	−22.6972			−0.0503263
$452$	−220.473	+	110.607i	−0.487772	+	0.244707i
$453$		0			0
$454$	−191.917	−	810.537i	−0.422726	−	1.78532i
$455$	−586.965	+	338.884i	−1.29003	+	0.744801i
$456$		0			0
$457$	200.997	−	348.138i	0.439819	−	0.761789i	−0.557856	−	0.829938i	$-0.688376\pi$
$457$	200.997	−	348.138i	0.439819	−	0.761789i	0.997675	+	0.0681485i	$0.0217092\pi$
$458$	101.622	−	339.178i	0.221883	−	0.740564i
$459$		0			0
$460$	727.417	+	478.876i	1.58134	+	1.04103i
$461$	126.646	+	73.1191i	0.274720	+	0.158610i	0.631031	−	0.775758i	$-0.282632\pi$
$461$	126.646	+	73.1191i	0.274720	+	0.158610i	−0.356311	+	0.934368i	$0.615966\pi$
$462$		0			0
$463$	−443.882	+	256.275i	−0.958708	+	0.553510i	−0.895775	−	0.444508i	$-0.853379\pi$
$463$	−443.882	+	256.275i	−0.958708	+	0.553510i	−0.0629326	+	0.998018i	$0.520045\pi$
$464$	−217.465	−	162.187i	−0.468675	−	0.349540i
$465$		0			0
$466$	210.191	−	198.220i	0.451053	−	0.425364i
$467$	294.463			0.630543			0.315271	−	0.949002i	$-0.397904\pi$
$467$	294.463			0.630543			0.315271	+	0.949002i	$0.397904\pi$
$468$		0			0
$469$		−	182.549i		−	0.389231i
$470$	782.143	−	737.597i	1.66413	−	1.56936i
$471$		0			0
$472$	303.430	−	832.003i	0.642859	−	1.76272i
$473$	42.2971	+	73.2607i	0.0894230	+	0.154885i
$474$		0			0
$475$	−408.016	+	706.704i	−0.858980	+	1.48780i
$476$	139.499	−	211.901i	0.293066	−	0.445170i
$477$		0			0
$478$	−104.467	+	348.673i	−0.218550	+	0.729441i
$479$	648.588	+	374.462i	1.35405	+	0.781758i	0.988813	−	0.149158i	$-0.0476564\pi$
$479$	648.588	+	374.462i	1.35405	+	0.781758i	0.365232	+	0.930917i	$0.380990\pi$
$480$		0			0
$481$	88.3925	+	153.100i	0.183768	+	0.318296i
$482$	−64.8060	−	273.699i	−0.134452	−	0.567841i
$483$		0			0
$484$	383.390	−	192.340i	0.792129	−	0.397397i
$485$			786.789i			1.62225i
$486$		0			0
$487$		−	81.6059i		−	0.167569i	−0.996484	−	0.0837843i	$-0.973299\pi$
$487$		−	81.6059i		−	0.167569i	0.996484	−	0.0837843i	$-0.0267007\pi$
$488$	117.141	+	666.843i	0.240043	+	1.36648i
$489$		0			0
$490$	305.529	−	72.3426i	0.623529	−	0.147638i
$491$	345.383	+	598.220i	0.703427	+	1.21837i	0.967256	+	0.253802i	$0.0816811\pi$
$491$	345.383	+	598.220i	0.703427	+	1.21837i	−0.263829	+	0.964569i	$0.584986\pi$
$492$		0			0
$493$	−164.190	−	94.7950i	−0.333042	−	0.192282i
$494$	96.7005	−	322.751i	0.195750	−	0.653341i
$495$		0			0
$496$	−56.3517	+	24.2505i	−0.113612	+	0.0488922i
$497$	110.005	−	190.535i	0.221339	−	0.383370i
$498$		0			0
$499$	432.927	+	749.851i	0.867588	+	1.50271i	0.864454	+	0.502712i	$0.167664\pi$
$499$	432.927	+	749.851i	0.867588	+	1.50271i	0.00313444	+	0.999995i	$0.499002\pi$
$500$	1379.92	+	80.9643i	2.75984	+	0.161929i
$501$		0			0
$502$	−56.4237	+	53.2102i	−0.112398	+	0.105996i
$503$		−	349.624i		−	0.695077i	−0.937666	−	0.347539i	$-0.887018\pi$
$503$		−	349.624i		−	0.695077i	0.937666	−	0.347539i	$-0.112982\pi$
$504$		0			0
$505$	1001.45			1.98306
$506$	−118.815	−	125.990i	−0.234812	−	0.248993i
$507$		0			0
$508$	−433.344	−	25.4256i	−0.853040	−	0.0500505i
$509$	−12.5795	+	7.26280i	−0.0247142	+	0.0142688i	−0.512306	−	0.858803i	$-0.671209\pi$
$509$	−12.5795	+	7.26280i	−0.0247142	+	0.0142688i	0.487592	+	0.873072i	$0.337875\pi$
$510$		0			0
$511$	66.9598	+	38.6593i	0.131037	+	0.0756542i
$512$	443.898	−	255.145i	0.866987	−	0.498330i
$513$		0			0
$514$	287.098	+	86.0185i	0.558556	+	0.167351i
$515$	−405.550	+	702.434i	−0.787477	+	1.36395i
$516$		0			0
$517$	−185.139	+	106.890i	−0.358103	+	0.206751i
$518$	36.0781	+	152.371i	0.0696488	+	0.294152i
$519$		0			0
$520$	−941.513	+	165.391i	−1.81060	+	0.318059i
$521$	−219.308			−0.420936			−0.210468	−	0.977601i	$-0.567499\pi$
$521$	−219.308			−0.420936			−0.210468	+	0.977601i	$0.567499\pi$
$522$		0			0
$523$	−802.128			−1.53371			−0.766853	−	0.641823i	$-0.778179\pi$
$523$	−802.128			−1.53371			−0.766853	+	0.641823i	$0.778179\pi$
$524$	233.398	−	117.092i	0.445416	−	0.223458i
$525$		0			0
$526$	−151.837	+	35.9517i	−0.288664	+	0.0683492i
$527$	−37.1297	+	21.4369i	−0.0704549	+	0.0406771i
$528$		0			0
$529$	7.80688	−	13.5219i	0.0147578	−	0.0255613i
$530$	1073.16	+	321.535i	2.02484	+	0.606669i
$531$		0			0
$532$	164.094	−	249.260i	0.308448	−	0.468535i
$533$	67.8514	+	39.1740i	0.127301	+	0.0734972i
$534$		0			0
$535$	1362.80	−	786.810i	2.54728	−	1.47067i
$536$	88.2148	−	241.885i	0.164580	−	0.451277i
$537$		0			0
$538$	−329.688	−	349.599i	−0.612803	−	0.649812i
$539$	−62.4345			−0.115834
$540$		0			0
$541$			780.008i			1.44179i	0.693045	+	0.720895i	$0.256269\pi$
$541$			780.008i			1.44179i	−0.693045	+	0.720895i	$0.743731\pi$
$542$	−604.371	−	640.871i	−1.11508	−	1.18242i
$543$		0			0
$544$	287.241	−	213.365i	0.528016	−	0.392216i
$545$	−759.937	−	1316.25i	−1.39438	−	2.41514i
$546$		0			0
$547$	−19.8872	+	34.4456i	−0.0363568	+	0.0629718i	−0.883631	−	0.468184i	$-0.844909\pi$
$547$	−19.8872	+	34.4456i	−0.0363568	+	0.0629718i	0.847274	+	0.531155i	$0.178242\pi$
$548$	238.078	+	156.733i	0.434450	+	0.286009i
$549$		0			0
$550$	−441.020	−	132.135i	−0.801854	−	0.240246i
$551$	−193.138	−	111.508i	−0.350522	−	0.202374i
$552$		0			0
$553$	−13.5896	−	23.5380i	−0.0245744	−	0.0425641i
$554$	−250.881	+	59.4031i	−0.452853	+	0.107226i
$555$		0			0
$556$	−278.689	+	139.814i	−0.501240	+	0.251463i
$557$			87.9243i			0.157853i	0.996880	+	0.0789266i	$0.0251493\pi$
$557$			87.9243i			0.157853i	−0.996880	+	0.0789266i	$0.974851\pi$
$558$		0			0
$559$		−	292.009i		−	0.522378i
$560$	−840.886	−	99.0156i	−1.50158	−	0.176813i
$561$		0			0
$562$	64.7003	+	273.253i	0.115125	+	0.486215i
$563$	−263.524	−	456.436i	−0.468071	−	0.810722i	0.531264	−	0.847207i	$-0.321717\pi$
$563$	−263.524	−	456.436i	−0.468071	−	0.810722i	−0.999334	+	0.0364845i	$0.988384\pi$
$564$		0			0
$565$	498.236	+	287.656i	0.881833	+	0.509127i
$566$	−803.841	−	240.842i	−1.42021	−	0.425516i
$567$		0			0
$568$	237.835	−	199.307i	0.418724	−	0.350893i
$569$	−464.624	+	804.752i	−0.816562	+	1.41433i	0.0916393	+	0.995792i	$0.470789\pi$
$569$	−464.624	+	804.752i	−0.816562	+	1.41433i	−0.908201	+	0.418534i	$0.862544\pi$
$570$		0			0
$571$	198.535	+	343.873i	0.347698	+	0.602230i	0.985840	−	0.167688i	$-0.0536302\pi$
$571$	198.535	+	343.873i	0.347698	+	0.602230i	−0.638142	+	0.769918i	$0.720297\pi$
$572$	189.761	+	11.1338i	0.331749	+	0.0194648i
$573$		0			0
$574$	47.6111	+	50.4864i	0.0829461	+	0.0879554i
$575$		−	1447.84i		−	2.51799i
$576$		0			0
$577$	351.123			0.608531			0.304266	−	0.952587i	$-0.401589\pi$
$577$	351.123			0.608531			0.304266	+	0.952587i	$0.401589\pi$
$578$	−238.581	+	224.993i	−0.412770	+	0.389262i
$579$		0			0
$580$	−37.0613	+	631.657i	−0.0638987	+	1.08906i
$581$	−26.5954	+	15.3549i	−0.0457753	+	0.0264284i
$582$		0			0
$583$	−192.926	−	111.386i	−0.330919	−	0.191056i
$584$	70.0427	+	83.5826i	0.119936	+	0.143121i
$585$		0			0
$586$	−218.177	+	728.194i	−0.372316	+	1.24265i
$587$	466.965	−	808.807i	0.795511	−	1.37787i	−0.127003	−	0.991902i	$-0.540536\pi$
$587$	466.965	−	808.807i	0.795511	−	1.37787i	0.922514	−	0.385964i	$-0.126131\pi$
$588$		0			0
$589$	−43.6759	+	25.2163i	−0.0741527	+	0.0428121i
$590$	−2010.00	+	475.925i	−3.40678	+	0.806652i
$591$		0			0
$592$	−25.8266	+	219.331i	−0.0436260	+	0.370492i
$593$	743.820			1.25433			0.627167	−	0.778885i	$-0.284214\pi$
$593$	743.820			1.25433			0.627167	+	0.778885i	$0.284214\pi$
$594$		0			0
$595$	−591.720			−0.994488
$596$	−263.133	−	524.500i	−0.441498	−	0.880034i
$597$		0			0
$598$	137.735	+	581.706i	0.230327	+	0.972753i
$599$	519.915	−	300.173i	0.867971	−	0.501124i	0.00129781	−	0.999999i	$-0.499587\pi$
$599$	519.915	−	300.173i	0.867971	−	0.501124i	0.866674	+	0.498876i	$0.166254\pi$
$600$		0			0
$601$	−47.0344	+	81.4660i	−0.0782603	+	0.135551i	−0.902499	−	0.430691i	$-0.858270\pi$
$601$	−47.0344	+	81.4660i	−0.0782603	+	0.135551i	0.824239	+	0.566242i	$0.191603\pi$
$602$	74.2323	−	247.760i	0.123309	−	0.411561i
$603$		0			0
$604$	232.179	−	352.683i	0.384403	−	0.583911i
$605$	−866.405	−	500.219i	−1.43207	−	0.826808i
$606$		0			0
$607$	−107.746	+	62.2074i	−0.177506	+	0.102483i	−0.586121	−	0.810224i	$-0.699346\pi$
$607$	−107.746	+	62.2074i	−0.177506	+	0.102483i	0.408614	+	0.912707i	$0.366012\pi$
$608$	337.883	−	250.983i	0.555729	−	0.412801i
$609$		0			0
$610$	1148.87	−	1083.44i	1.88339	−	1.77612i
$611$	737.945			1.20777
$612$		0			0
$613$		−	196.037i		−	0.319799i	−0.987133	−	0.159899i	$-0.948883\pi$
$613$		−	196.037i		−	0.319799i	0.987133	−	0.159899i	$-0.0511170\pi$
$614$	445.483	−	420.111i	0.725542	−	0.684220i
$615$		0			0
$616$	158.175	+	57.6861i	0.256778	+	0.0936463i
$617$	21.0476	+	36.4555i	0.0341128	+	0.0590850i	0.882578	−	0.470166i	$-0.155806\pi$
$617$	21.0476	+	36.4555i	0.0341128	+	0.0590850i	−0.848465	+	0.529252i	$0.822473\pi$
$618$		0			0
$619$	−304.862	+	528.036i	−0.492507	+	0.853047i	−0.999963	−	0.00863088i	$-0.997253\pi$
$619$	−304.862	+	528.036i	−0.492507	+	0.853047i	0.507456	+	0.861678i	$0.330586\pi$
$620$	119.515	+	78.6793i	0.192765	+	0.126902i
$621$		0			0
$622$	326.209	−	1088.77i	0.524452	−	1.75043i
$623$	482.542	+	278.596i	0.774546	+	0.447184i
$624$		0			0
$625$	−836.517	−	1448.89i	−1.33843	−	2.31822i
$626$	144.403	+	609.868i	0.230676	+	0.974229i
$627$		0			0
$628$	308.340	+	614.612i	0.490988	+	0.978681i
$629$			154.341i			0.245375i
$630$		0			0
$631$			897.433i			1.42224i	0.703071	+	0.711120i	$0.251812\pi$
$631$			897.433i			1.42224i	−0.703071	+	0.711120i	$0.748188\pi$
$632$	−6.63235	−	37.7557i	−0.0104942	−	0.0597401i
$633$		0			0
$634$	−299.191	+	70.8420i	−0.471911	+	0.111738i
$635$	506.233	+	876.822i	0.797218	+	1.38082i
$636$		0			0
$637$	186.643	+	107.758i	0.293003	+	0.169165i
$638$	36.1118	−	120.528i	0.0566015	−	0.188915i
$639$		0			0
$640$	−1066.36	−	537.548i	−1.66618	−	0.839918i
$641$	478.777	−	829.266i	0.746922	−	1.29371i	−0.202370	−	0.979309i	$-0.564864\pi$
$641$	478.777	−	829.266i	0.746922	−	1.29371i	0.949292	−	0.314397i	$-0.101802\pi$
$642$		0			0
$643$	−96.6408	−	167.387i	−0.150297	−	0.260321i	0.781040	−	0.624481i	$-0.214690\pi$
$643$	−96.6408	−	167.387i	−0.150297	−	0.260321i	−0.931337	+	0.364160i	$0.881356\pi$
$644$	−31.0129	+	528.572i	−0.0481567	+	0.820763i
$645$		0			0
$646$	214.000	−	201.812i	0.331270	−	0.312403i
$647$			462.896i			0.715450i	0.933827	+	0.357725i	$0.116447\pi$
$647$			462.896i			0.715450i	−0.933827	+	0.357725i	$0.883553\pi$
$648$		0			0
$649$	410.741			0.632884
$650$	1090.33	+	1156.18i	1.67744	+	1.77874i
$651$		0			0
$652$	−19.4805	+	332.019i	−0.0298781	+	0.509231i
$653$	−175.738	+	101.463i	−0.269125	+	0.155379i	−0.628490	−	0.777818i	$-0.716327\pi$
$653$	−175.738	+	101.463i	−0.269125	+	0.155379i	0.359365	+	0.933197i	$0.382993\pi$
$654$		0			0
$655$	−527.445	−	304.520i	−0.805259	−	0.464917i
$656$	38.6895	+	89.9039i	0.0589779	+	0.137049i
$657$		0			0
$658$	626.121	+	187.594i	0.951552	+	0.285098i
$659$	−423.773	+	733.996i	−0.643054	+	1.11380i	0.341693	+	0.939812i	$0.389000\pi$
$659$	−423.773	+	733.996i	−0.643054	+	1.11380i	−0.984747	+	0.173991i	$0.944334\pi$
$660$		0			0
$661$	−552.689	+	319.095i	−0.836141	+	0.482746i	−0.855951	−	0.517058i	$-0.827027\pi$
$661$	−552.689	+	319.095i	−0.836141	+	0.482746i	0.0198096	+	0.999804i	$0.493694\pi$
$662$	−282.328	−	1192.37i	−0.426477	−	1.80117i
$663$		0			0
$664$	−42.6600	+	7.49386i	−0.0642470	+	0.0112859i
$665$	−696.044			−1.04668
$666$		0			0
$667$	395.686			0.593232
$668$	418.659	+	834.509i	0.626735	+	1.24927i
$669$		0			0
$670$	−584.360	+	138.364i	−0.872178	+	0.206513i
$671$	−271.946	+	157.008i	−0.405284	+	0.233991i
$672$		0			0
$673$	216.850	−	375.595i	0.322214	−	0.558091i	−0.658730	−	0.752379i	$-0.728906\pi$
$673$	216.850	−	375.595i	0.322214	−	0.558091i	0.980945	+	0.194288i	$0.0622396\pi$
$674$	−893.697	−	267.764i	−1.32596	−	0.397276i
$675$		0			0
$676$	16.5724	+	10.9100i	0.0245154	+	0.0161391i
$677$	−304.392	−	175.741i	−0.449619	−	0.259588i	0.258050	−	0.966131i	$-0.416920\pi$
$677$	−304.392	−	175.741i	−0.449619	−	0.259588i	−0.707669	+	0.706544i	$0.750253\pi$
$678$		0			0
$679$	−414.261	+	239.173i	−0.610104	+	0.352244i
$680$	−784.052	−	285.942i	−1.15302	−	0.420503i
$681$		0			0
$682$	−19.5213	−	20.7002i	−0.0286236	−	0.0303522i
$683$	−174.129			−0.254948			−0.127474	−	0.991842i	$-0.540687\pi$
$683$	−174.129			−0.254948			−0.127474	+	0.991842i	$0.540687\pi$
$684$		0			0
$685$		−	664.819i		−	0.970539i
$686$	512.340	+	543.282i	0.746851	+	0.791956i
$687$		0			0
$688$	218.088	−	292.419i	0.316988	−	0.425028i
$689$	384.491	+	665.958i	0.558043	+	0.966558i
$690$		0			0
$691$	147.131	−	254.838i	0.212925	−	0.368796i	−0.739704	−	0.672932i	$-0.765034\pi$
$691$	147.131	−	254.838i	0.212925	−	0.368796i	0.952629	+	0.304136i	$0.0983678\pi$
$692$	−97.9940	+	148.854i	−0.141610	+	0.215107i
$693$		0			0
$694$	−682.838	−	204.588i	−0.983916	−	0.294795i
$695$	629.796	+	363.613i	0.906181	+	0.523184i
$696$		0			0
$697$	34.2005	+	59.2370i	0.0490682	+	0.0849886i
$698$	282.390	−	66.8639i	0.404571	−	0.0957935i
$699$		0			0
$700$	631.196	+	1258.16i	0.901708	+	1.79737i
$701$			579.128i			0.826146i	0.910698	+	0.413073i	$0.135545\pi$
$701$			579.128i			0.826146i	−0.910698	+	0.413073i	$0.864455\pi$
$702$		0			0
$703$			181.552i			0.258253i
$704$	181.712	+	152.873i	0.258113	+	0.217149i
$705$		0			0
$706$	−192.651	−	813.634i	−0.272876	−	1.15246i
$707$	304.427	+	527.282i	0.430589	+	0.745803i
$708$		0			0
$709$	−702.992	−	405.872i	−0.991526	−	0.572458i	−0.0857956	−	0.996313i	$-0.527343\pi$
$709$	−702.992	−	405.872i	−0.991526	−	0.572458i	−0.905730	+	0.423855i	$0.860677\pi$
$710$	−693.302	−	207.723i	−0.976482	−	0.292567i
$711$		0			0
$712$	504.758	+	602.333i	0.708930	+	0.845973i
$713$	44.7400	−	77.4920i	0.0627490	−	0.108684i
$714$		0			0
$715$	−221.679	−	383.959i	−0.310040	−	0.537005i
$716$	3.60239	−	61.3977i	0.00503127	−	0.0857509i
$717$		0			0
$718$	399.490	+	423.617i	0.556393	+	0.589996i
$719$			441.412i			0.613924i	0.951722	+	0.306962i	$0.0993125\pi$
$719$			441.412i			0.613924i	−0.951722	+	0.306962i	$0.900687\pi$
$720$		0			0
$721$	−493.128			−0.683950
$722$	−273.540	+	257.961i	−0.378864	+	0.357287i
$723$		0			0
$724$	−960.856	−	56.3764i	−1.32715	−	0.0778679i
$725$	910.990	−	525.961i	1.25654	−	0.725463i
$726$		0			0
$727$	−30.1778	−	17.4232i	−0.0415101	−	0.0239658i	0.479101	−	0.877760i	$-0.340963\pi$
$727$	−30.1778	−	17.4232i	−0.0415101	−	0.0239658i	−0.520611	+	0.853794i	$0.674296\pi$
$728$	−373.289	−	445.449i	−0.512760	−	0.611881i
$729$		0			0
$730$	73.0001	−	243.648i	0.100000	−	0.333764i
$731$	127.468	−	220.781i	0.174375	−	0.302026i
$732$		0			0
$733$	−889.135	+	513.342i	−1.21301	+	0.700331i	−0.963413	−	0.268020i	$-0.913631\pi$
$733$	−889.135	+	513.342i	−1.21301	+	0.700331i	−0.249595	+	0.968350i	$0.580297\pi$
$734$	723.534	−	171.317i	0.985742	−	0.233402i
$735$		0			0
$736$	−296.520	+	685.391i	−0.402880	+	0.931238i
$737$	119.413			0.162026
$738$		0			0
$739$	1155.74			1.56393			0.781963	−	0.623324i	$-0.214218\pi$
$739$	1155.74			1.56393			0.781963	+	0.623324i	$0.214218\pi$
$740$	460.410	−	230.980i	0.622176	−	0.312135i
$741$		0			0
$742$	156.933	+	662.785i	0.211500	+	0.893241i
$743$	−703.173	+	405.977i	−0.946397	+	0.546403i	−0.891960	−	0.452115i	$-0.850670\pi$
$743$	−703.173	+	405.977i	−0.946397	+	0.546403i	−0.0544372	+	0.998517i	$0.517336\pi$
$744$		0			0
$745$	−684.328	+	1185.29i	−0.918562	+	1.59100i
$746$	−281.336	+	938.994i	−0.377125	+	1.25871i
$747$		0			0
$748$	138.613	+	91.2525i	0.185312	+	0.121995i
$749$	828.543	+	478.360i	1.10620	+	0.638665i
$750$		0			0
$751$	189.525	−	109.422i	0.252363	−	0.145702i	−0.368483	−	0.929635i	$-0.620123\pi$
$751$	189.525	−	109.422i	0.252363	−	0.145702i	0.620846	+	0.783933i	$0.286789\pi$
$752$	738.981	+	551.136i	0.982688	+	0.732893i
$753$		0			0
$754$	−315.977	+	297.981i	−0.419068	+	0.395201i
$755$	−984.844			−1.30443
$756$		0			0
$757$		−	985.851i		−	1.30231i	−0.758944	−	0.651156i	$-0.774284\pi$
$757$		−	985.851i		−	1.30231i	0.758944	−	0.651156i	$-0.225716\pi$
$758$	−363.539	+	342.834i	−0.479603	+	0.452288i
$759$		0			0
$760$	−922.285	−	336.355i	−1.21353	−	0.442573i
$761$	−216.932	−	375.738i	−0.285062	−	0.493742i	0.687562	−	0.726125i	$-0.258681\pi$
$761$	−216.932	−	375.738i	−0.285062	−	0.493742i	−0.972624	+	0.232384i	$0.925348\pi$
$762$		0			0
$763$	462.022	−	800.245i	0.605533	−	1.04881i
$764$	174.886	−	265.653i	0.228908	−	0.347713i
$765$		0			0
$766$	−28.0775	+	93.7125i	−0.0366548	+	0.122340i
$767$	−1227.88	−	708.916i	−1.60089	−	0.924272i
$768$		0			0
$769$	−318.366	−	551.425i	−0.414000	−	0.717068i	0.581323	−	0.813673i	$-0.302535\pi$
$769$	−318.366	−	551.425i	−0.414000	−	0.717068i	−0.995323	+	0.0966044i	$0.969202\pi$
$770$	−90.4798	−	382.129i	−0.117506	−	0.496271i
$771$		0			0
$772$	119.807	−	60.1053i	0.155191	−	0.0778565i
$773$		−	815.596i		−	1.05510i	−0.849523	−	0.527552i	$-0.823110\pi$
$773$		−	815.596i		−	1.05510i	0.849523	−	0.527552i	$-0.176890\pi$
$774$		0			0
$775$		−	237.880i		−	0.306942i
$776$	−664.489	+	116.727i	−0.856300	+	0.150422i
$777$		0			0
$778$	1002.95	−	237.477i	1.28914	−	0.305241i
$779$	40.2303	+	69.6809i	0.0516435	+	0.0894492i
$780$		0			0
$781$	124.637	+	71.9592i	0.159586	+	0.0921373i
$782$	−149.788	+	499.938i	−0.191545	+	0.639307i
$783$		0			0
$784$	106.426	+	247.304i	0.135747	+	0.315439i
$785$	801.899	−	1388.93i	1.02153	−	1.76934i
$786$		0			0
$787$	22.2735	+	38.5788i	0.0283017	+	0.0490201i	0.879829	−	0.475290i	$-0.157657\pi$
$787$	22.2735	+	38.5788i	0.0283017	+	0.0490201i	−0.851528	+	0.524310i	$0.824323\pi$
$788$	−731.345	−	42.9103i	−0.928103	−	0.0544546i
$789$		0			0
$790$	−65.0472	+	61.3426i	−0.0823383	+	0.0776488i
$791$			349.775i			0.442193i
$792$		0			0
$793$	1083.95			1.36689
$794$	−768.792	−	815.221i	−0.968252	−	1.02673i
$795$		0			0
$796$	344.470	+	20.2111i	0.432751	+	0.0253909i
$797$	131.223	−	75.7614i	0.164646	−	0.0950582i	−0.415413	−	0.909633i	$-0.636363\pi$
$797$	131.223	−	75.7614i	0.164646	−	0.0950582i	0.580059	+	0.814575i	$0.303030\pi$
$798$		0			0
$799$	557.943	+	322.128i	0.698301	+	0.403164i
$800$	228.368	+	1972.12i	0.285460	+	2.46516i
$801$		0			0
$802$	−869.700	−	260.574i	−1.08441	−	0.324905i
$803$	−25.2887	+	43.8013i	−0.0314927	+	0.0545470i
$804$		0			0
$805$	1069.50	−	617.478i	1.32858	−	0.767053i
$806$	22.6299	+	95.5743i	0.0280768	+	0.118579i
$807$		0			0
$808$	148.574	+	845.780i	0.183878	+	1.04676i
$809$	214.614			0.265284			0.132642	−	0.991164i	$-0.457654\pi$
$809$	214.614			0.265284			0.132642	+	0.991164i	$0.457654\pi$
$810$		0			0
$811$	−958.317			−1.18165			−0.590824	−	0.806800i	$-0.701197\pi$
$811$	−958.317			−1.18165			−0.590824	+	0.806800i	$0.701197\pi$
$812$	−343.846	+	172.502i	−0.423456	+	0.212441i
$813$		0			0
$814$	−99.6722	+	23.6002i	−0.122447	+	0.0289929i
$815$	671.801	−	387.864i	0.824295	−	0.475907i
$816$		0			0
$817$	149.942	−	259.706i	0.183527	−	0.317878i
$818$	895.747	+	268.378i	1.09505	+	0.328091i
$819$		0			0
$820$	125.526	−	190.674i	0.153080	−	0.232530i
$821$	−980.237	−	565.940i	−1.19395	−	0.689330i	−0.234754	−	0.972055i	$-0.575428\pi$
$821$	−980.237	−	565.940i	−1.19395	−	0.689330i	−0.959201	+	0.282725i	$0.908762\pi$
$822$		0			0
$823$	−786.212	+	453.920i	−0.955300	+	0.551543i	−0.894723	−	0.446621i	$-0.852627\pi$
$823$	−786.212	+	453.920i	−0.955300	+	0.551543i	−0.0605770	+	0.998164i	$0.519294\pi$
$824$	−653.413	−	238.298i	−0.792977	−	0.289197i
$825$		0			0
$826$	−861.598	−	913.633i	−1.04310	−	1.10609i
$827$	10.7818			0.0130373			0.00651865	−	0.999979i	$-0.497925\pi$
$827$	10.7818			0.0130373			0.00651865	+	0.999979i	$0.497925\pi$
$828$		0			0
$829$			112.915i			0.136206i	0.997678	+	0.0681030i	$0.0216946\pi$
$829$			112.915i			0.136206i	−0.997678	+	0.0681030i	$0.978305\pi$
$830$	69.3107	+	73.4965i	0.0835068	+	0.0885501i
$831$		0			0
$832$	−279.364	−	770.625i	−0.335774	−	0.926232i
$833$	94.0775	+	162.947i	0.112938	+	0.195615i
$834$		0			0
$835$	1088.80	−	1885.87i	1.30396	−	2.25852i
$836$	163.052	+	107.341i	0.195038	+	0.128398i
$837$		0			0
$838$	−354.208	−	106.126i	−0.422682	−	0.126641i
$839$	−257.467	−	148.649i	−0.306874	−	0.177174i	0.338653	−	0.940911i	$-0.390029\pi$
$839$	−257.467	−	148.649i	−0.306874	−	0.177174i	−0.645527	+	0.763738i	$0.723362\pi$
$840$		0			0
$841$	−276.758	−	479.360i	−0.329082	−	0.569988i
$842$	−732.863	+	173.526i	−0.870383	+	0.206088i
$843$		0			0
$844$	−822.358	+	412.563i	−0.974357	+	0.488818i
$845$		−	46.2775i		−	0.0547662i
$846$		0			0
$847$		−	608.240i		−	0.718111i
$848$	−112.341	+	954.052i	−0.132478	+	1.12506i
$849$		0			0
$850$	319.678	+	1350.12i	0.376092	+	1.58837i
$851$	−161.059	−	278.963i	−0.189259	−	0.327806i
$852$		0			0
$853$	1353.97	+	781.714i	1.58730	+	0.916429i	0.993749	+	0.111634i	$0.0356083\pi$
$853$	1353.97	+	781.714i	1.58730	+	0.916429i	0.593552	+	0.804795i	$0.297725\pi$
$854$	919.691	+	275.552i	1.07692	+	0.322660i
$855$		0			0
$856$	866.690	+	1034.23i	1.01249	+	1.20821i
$857$	−14.3592	+	24.8709i	−0.0167552	+	0.0290208i	−0.874281	−	0.485419i	$-0.838667\pi$
$857$	−14.3592	+	24.8709i	−0.0167552	+	0.0290208i	0.857526	+	0.514440i	$0.172000\pi$
$858$		0			0
$859$	602.824	+	1044.12i	0.701774	+	1.21551i	0.967843	+	0.251555i	$0.0809418\pi$
$859$	602.824	+	1044.12i	0.701774	+	1.21551i	−0.266069	+	0.963954i	$0.585725\pi$
$860$	−849.371	−	49.8352i	−0.987641	−	0.0579479i
$861$		0			0
$862$	412.998	+	437.940i	0.479116	+	0.508051i
$863$			740.816i			0.858419i	0.903205	+	0.429210i	$0.141208\pi$
$863$			740.816i			0.858419i	−0.903205	+	0.429210i	$0.858792\pi$
$864$		0			0
$865$	415.665			0.480537
$866$	−976.109	+	920.516i	−1.12715	+	1.06295i
$867$		0			0
$868$	−5.09542	+	86.8443i	−0.00587030	+	0.100051i
$869$	15.3972	−	8.88956i	0.0177183	−	0.0102296i
$870$		0			0
$871$	−356.976	−	206.100i	−0.409846	−	0.236625i
$872$	998.905	−	837.088i	1.14553	−	0.959963i
$873$		0			0
$874$	−176.197	+	588.081i	−0.201598	+	0.672861i
$875$	980.069	−	1697.53i	1.12008	−	1.94003i
$876$		0			0
$877$	−1084.73	+	626.268i	−1.23686	+	0.714102i	−0.968451	−	0.249203i	$-0.919832\pi$
$877$	−1084.73	+	626.268i	−1.23686	+	0.714102i	−0.268410	+	0.963305i	$0.586498\pi$
$878$	1153.22	−	273.058i	1.31347	−	0.311000i
$879$		0			0
$880$	64.7703	−	550.059i	0.0736026	−	0.625067i
$881$	−814.978			−0.925060			−0.462530	−	0.886604i	$-0.653058\pi$
$881$	−814.978			−0.925060			−0.462530	+	0.886604i	$0.653058\pi$
$882$		0			0
$883$	−895.745			−1.01443			−0.507217	−	0.861819i	$-0.669326\pi$
$883$	−895.745			−1.01443			−0.507217	+	0.861819i	$0.669326\pi$
$884$	−256.877	−	512.031i	−0.290585	−	0.579220i
$885$		0			0
$886$	−98.1980	−	414.726i	−0.110833	−	0.468088i
$887$	1453.92	−	839.424i	1.63915	−	0.946363i	0.658021	−	0.752999i	$-0.271394\pi$
$887$	1453.92	−	839.424i	1.63915	−	0.946363i	0.981127	−	0.193363i	$-0.0619396\pi$
$888$		0			0
$889$	−307.776	+	533.084i	−0.346205	+	0.599645i
$890$	526.071	−	1755.83i	0.591091	−	1.97284i
$891$		0			0
$892$	832.415	−	1264.45i	0.933201	−	1.41754i
$893$	656.312	+	378.922i	0.734951	+	0.424324i
$894$		0			0
$895$	−124.231	+	71.7248i	−0.138806	+	0.0801394i
$896$	−41.1286	−	724.866i	−0.0459024	−	0.809002i
$897$		0			0
$898$	−836.056	+	788.440i	−0.931020	+	0.877995i
$899$	65.0112			0.0723150
$900$		0			0
$901$			671.354i			0.745121i
$902$	−33.0253	+	31.1444i	−0.0366134	+	0.0345282i
$903$		0			0
$904$	−169.025	+	463.465i	−0.186974	+	0.512683i
$905$	1122.47	+	1944.18i	1.24030	+	2.14827i
$906$		0			0
$907$	−195.810	+	339.153i	−0.215888	+	0.373928i	−0.953547	−	0.301245i	$-0.902598\pi$
$907$	−195.810	+	339.153i	−0.215888	+	0.373928i	0.737659	+	0.675173i	$0.235931\pi$
$908$	−1391.44	−	916.021i	−1.53243	−	1.00883i
$909$		0			0
$910$	−389.051	+	1298.51i	−0.427528	+	1.42693i
$911$	−1375.58	−	794.190i	−1.50996	−	0.871778i	−0.999932	−	0.0116223i	$-0.996300\pi$
$911$	−1375.58	−	794.190i	−1.50996	−	0.871778i	−0.510031	−	0.860156i	$-0.670366\pi$
$912$		0			0
$913$	−10.0443	−	17.3972i	−0.0110014	−	0.0190550i
$914$	−185.245	−	782.358i	−0.202675	−	0.855971i
$915$		0			0
$916$	−317.546	−	632.962i	−0.346666	−	0.691006i
$917$		−	370.281i		−	0.403796i
$918$		0			0
$919$		−	995.618i		−	1.08337i	−0.840581	−	0.541686i	$-0.817786\pi$
$919$		−	995.618i		−	1.08337i	0.840581	−	0.541686i	$-0.182214\pi$
$920$	1715.52	−	301.357i	1.86470	−	0.327561i
$921$		0			0
$922$	284.607	−	67.3887i	0.308684	−	0.0730897i
$923$	−248.395	−	430.233i	−0.269117	−	0.466124i
$924$		0			0
$925$	−741.615	−	428.172i	−0.801746	−	0.462888i
$926$	−294.212	+	981.973i	−0.317724	+	1.06045i
$927$		0			0
$928$	−538.969	+	62.4116i	−0.580786	+	0.0672539i
$929$	−729.805	+	1264.06i	−0.785581	+	1.36067i	0.143070	+	0.989713i	$0.454303\pi$
$929$	−729.805	+	1264.06i	−0.785581	+	1.36067i	−0.928651	+	0.370954i	$0.879031\pi$
$930$		0			0
$931$	110.664	+	191.676i	0.118866	+	0.205881i
$932$	33.8447	−	576.836i	0.0363141	−	0.618923i
$933$		0			0
$934$	428.456	−	404.054i	0.458733	−	0.432606i
$935$		−	387.069i		−	0.413978i
$936$		0			0
$937$	449.372			0.479585			0.239793	−	0.970824i	$-0.422921\pi$
$937$	449.372			0.479585			0.239793	+	0.970824i	$0.422921\pi$
$938$	−250.489	−	265.617i	−0.267046	−	0.283173i
$939$		0			0
$940$	125.940	−	2146.47i	0.133979	−	2.28348i
$941$	−994.500	+	574.175i	−1.05685	+	0.610175i	−0.924561	−	0.381035i	$-0.875568\pi$
$941$	−994.500	+	574.175i	−1.05685	+	0.610175i	−0.132294	+	0.991211i	$0.542234\pi$
$942$		0			0
$943$	−123.631	−	71.3786i	−0.131104	−	0.0756931i
$944$	−700.148	−	1626.96i	−0.741682	−	1.72347i
$945$		0			0
$946$	162.070	+	48.5585i	0.171322	+	0.0513303i
$947$	−162.539	+	281.526i	−0.171636	+	0.297282i	−0.938992	−	0.343939i	$-0.888239\pi$
$947$	−162.539	+	281.526i	−0.171636	+	0.297282i	0.767356	+	0.641221i	$0.221572\pi$
$948$		0			0
$949$	151.197	−	87.2936i	0.159322	−	0.0919848i
$950$	376.039	+	1588.15i	0.395831	+	1.67174i
$951$		0			0
$952$	−87.7870	−	499.742i	−0.0922132	−	0.524939i
$953$	1073.20			1.12613			0.563064	−	0.826414i	$-0.309623\pi$
$953$	1073.20			1.12613			0.563064	+	0.826414i	$0.309623\pi$
$954$		0			0
$955$	−741.819			−0.776774
$956$	326.435	+	650.680i	0.341459	+	0.680627i
$957$		0			0
$958$	1457.55	−	345.116i	1.52145	−	0.360246i
$959$	350.041	−	202.096i	0.365006	−	0.210736i
$960$		0			0
$961$	−473.149	+	819.518i	−0.492351	+	0.852777i
$962$	338.695	+	101.478i	0.352074	+	0.105486i
$963$		0			0
$964$	−469.858	−	309.319i	−0.487405	−	0.320870i
$965$	−270.746	−	156.316i	−0.280566	−	0.161985i
$966$		0			0
$967$	−3.02820	+	1.74833i	−0.00313154	+	0.00180800i	−0.501565	−	0.865120i	$-0.667242\pi$
$967$	−3.02820	+	1.74833i	−0.00313154	+	0.00180800i	0.498433	+	0.866928i	$0.333909\pi$
$968$	293.925	−	805.941i	0.303641	−	0.832583i
$969$		0			0
$970$	1079.61	+	1144.81i	1.11300	+	1.18022i
$971$	810.426			0.834630			0.417315	−	0.908762i	$-0.362971\pi$
$971$	810.426			0.834630			0.417315	+	0.908762i	$0.362971\pi$
$972$		0			0
$973$			442.134i			0.454402i
$974$	−111.977	−	118.740i	−0.114967	−	0.121910i
$975$		0			0
$976$	1085.47	+	809.547i	1.11216	+	0.829454i
$977$	546.820	+	947.119i	0.559692	+	0.969416i	0.997522	+	0.0703577i	$0.0224141\pi$
$977$	546.820	+	947.119i	0.559692	+	0.969416i	−0.437829	+	0.899058i	$0.644253\pi$
$978$		0			0
$979$	−182.241	+	315.651i	−0.186150	+	0.322422i
$980$	345.291	−	524.500i	0.352338	−	0.535204i
$981$		0			0
$982$	1323.41	+	396.511i	1.34766	+	0.403779i
$983$	−475.171	−	274.340i	−0.483389	−	0.279085i	0.238439	−	0.971158i	$-0.423364\pi$
$983$	−475.171	−	274.340i	−0.483389	−	0.279085i	−0.721828	+	0.692073i	$0.756698\pi$
$984$		0			0
$985$	854.358	+	1479.79i	0.867368	+	1.50233i
$986$	−368.978	+	87.3660i	−0.374217	+	0.0886064i
$987$		0			0
$988$	−302.166	−	602.305i	−0.305836	−	0.609621i
$989$			532.067i			0.537985i
$990$		0			0
$991$			494.677i			0.499169i	0.968353	+	0.249585i	$0.0802941\pi$
$991$			494.677i			0.499169i	−0.968353	+	0.249585i	$0.919706\pi$
$992$	−48.7181	+	112.610i	−0.0491110	+	0.113518i
$993$		0			0
$994$	−101.384	−	428.183i	−0.101996	−	0.430767i
$995$	−402.410	−	696.995i	−0.404433	−	0.700498i
$996$		0			0
$997$	−112.086	−	64.7128i	−0.112423	−	0.0649075i	0.442734	−	0.896653i	$-0.354009\pi$
$997$	−112.086	−	64.7128i	−0.112423	−	0.0649075i	−0.555157	+	0.831745i	$0.687342\pi$
$998$	1658.85	+	497.014i	1.66217	+	0.498010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.19.14		40
3.2	odd	2		72.3.p.b.43.7	✓	40
4.3	odd	2		864.3.t.b.559.1		40
8.3	odd	2	inner	216.3.p.b.19.11		40
8.5	even	2		864.3.t.b.559.20		40
9.2	odd	6		648.3.b.f.163.20		20
9.4	even	3	inner	216.3.p.b.91.11		40
9.5	odd	6		72.3.p.b.67.10	yes	40
9.7	even	3		648.3.b.e.163.1		20
12.11	even	2		288.3.t.b.79.4		40
24.5	odd	2		288.3.t.b.79.3		40
24.11	even	2		72.3.p.b.43.10	yes	40
36.7	odd	6		2592.3.b.f.1135.1		20
36.11	even	6		2592.3.b.e.1135.20		20
36.23	even	6		288.3.t.b.175.3		40
36.31	odd	6		864.3.t.b.847.20		40
72.5	odd	6		288.3.t.b.175.4		40
72.11	even	6		648.3.b.f.163.19		20
72.13	even	6		864.3.t.b.847.1		40
72.29	odd	6		2592.3.b.e.1135.1		20
72.43	odd	6		648.3.b.e.163.2		20
72.59	even	6		72.3.p.b.67.7	yes	40
72.61	even	6		2592.3.b.f.1135.20		20
72.67	odd	6	inner	216.3.p.b.91.14		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.7	✓	40	3.2	odd	2
72.3.p.b.43.10	yes	40	24.11	even	2
72.3.p.b.67.7	yes	40	72.59	even	6
72.3.p.b.67.10	yes	40	9.5	odd	6
216.3.p.b.19.11		40	8.3	odd	2	inner
216.3.p.b.19.14		40	1.1	even	1	trivial
216.3.p.b.91.11		40	9.4	even	3	inner
216.3.p.b.91.14		40	72.67	odd	6	inner
288.3.t.b.79.3		40	24.5	odd	2
288.3.t.b.79.4		40	12.11	even	2
288.3.t.b.175.3		40	36.23	even	6
288.3.t.b.175.4		40	72.5	odd	6
648.3.b.e.163.1		20	9.7	even	3
648.3.b.e.163.2		20	72.43	odd	6
648.3.b.f.163.19		20	72.11	even	6
648.3.b.f.163.20		20	9.2	odd	6
864.3.t.b.559.1		40	4.3	odd	2
864.3.t.b.559.20		40	8.5	even	2
864.3.t.b.847.1		40	72.13	even	6
864.3.t.b.847.20		40	36.31	odd	6
2592.3.b.e.1135.1		20	72.29	odd	6
2592.3.b.e.1135.20		20	36.11	even	6
2592.3.b.f.1135.1		20	36.7	odd	6
2592.3.b.f.1135.20		20	72.61	even	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45504 - 1.37217i) q^{2} +(0.234289 - 3.99313i) q^{4} +(-8.07964 + 4.66478i) q^{5} +(-4.91220 - 2.83606i) q^{7} +(-5.13836 - 6.13166i) q^{8} +O(q^{10})\)	\(q+(1.45504 - 1.37217i) q^{2} +(0.234289 - 3.99313i) q^{4} +(-8.07964 + 4.66478i) q^{5} +(-4.91220 - 2.83606i) q^{7} +(-5.13836 - 6.13166i) q^{8} +(-5.35532 + 17.8741i) q^{10} +(1.85519 - 3.21328i) q^{11} +(-11.0919 + 6.40390i) q^{13} +(-11.0390 + 2.61380i) q^{14} +(-15.8902 - 1.87110i) q^{16} -11.1817 q^{17} -13.1532 q^{19} +(16.7341 + 33.3560i) q^{20} +(-1.70980 - 7.22109i) q^{22} +(20.2104 - 11.6685i) q^{23} +(31.0204 - 53.7288i) q^{25} +(-7.35189 + 24.5379i) q^{26} +(-12.4757 + 18.9506i) q^{28} +(14.6837 + 8.47767i) q^{29} +(3.32057 - 1.91713i) q^{31} +(-25.6884 + 19.0816i) q^{32} +(-16.2699 + 15.3433i) q^{34} +52.9184 q^{35} -13.8029i q^{37} +(-19.1384 + 18.0484i) q^{38} +(70.1190 + 25.5722i) q^{40} +(-3.05861 - 5.29766i) q^{41} +(-11.3997 + 19.7448i) q^{43} +(-12.3964 - 8.16085i) q^{44} +(13.3958 - 44.7103i) q^{46} +(-49.8977 - 28.8084i) q^{47} +(-8.41350 - 14.5726i) q^{49} +(-28.5893 - 120.743i) q^{50} +(22.9729 + 45.7917i) q^{52} -60.0402i q^{53} +34.6162i q^{55} +(7.85093 + 44.6927i) q^{56} +(32.9983 - 7.81327i) q^{58} +(55.3504 + 95.8696i) q^{59} +(-73.2932 - 42.3159i) q^{61} +(2.20093 - 7.34589i) q^{62} +(-11.1944 + 63.0134i) q^{64} +(59.7456 - 103.482i) q^{65} +(16.0918 + 27.8718i) q^{67} +(-2.61976 + 44.6502i) q^{68} +(76.9985 - 72.6132i) q^{70} +38.7881i q^{71} -13.6313 q^{73} +(-18.9400 - 20.0838i) q^{74} +(-3.08164 + 52.5223i) q^{76} +(-18.2261 + 10.5229i) q^{77} +(4.14976 + 2.39586i) q^{79} +(137.115 - 59.0066i) q^{80} +(-11.7197 - 3.51138i) q^{82} +(2.70708 - 4.68879i) q^{83} +(90.3444 - 52.1604i) q^{85} +(10.5063 + 44.3718i) q^{86} +(-29.2354 + 5.13562i) q^{88} -98.2333 q^{89} +72.6474 q^{91} +(-41.8587 - 83.4366i) q^{92} +(-112.133 + 26.5507i) q^{94} +(106.273 - 61.3566i) q^{95} +(42.1665 - 73.0345i) q^{97} +(-32.2381 - 9.65898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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