LMFDB - Embedded newform 216.3.p.b.19.11

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			19.11
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.460815 - 1.94619i) q^{2} +(-3.57530 - 1.79367i) q^{4} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(-5.13836 + 6.13166i) q^{8} +O(q^{10})$	\(q+(0.460815 - 1.94619i) q^{2} +(-3.57530 - 1.79367i) q^{4} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(-5.13836 + 6.13166i) q^{8} +(-5.35532 - 17.8741i) q^{10} +(1.85519 - 3.21328i) q^{11} +(11.0919 - 6.40390i) q^{13} +(7.78313 - 8.25318i) q^{14} +(9.56553 + 12.8258i) q^{16} -11.1817 q^{17} -13.1532 q^{19} +(-37.2542 + 2.18582i) q^{20} +(-5.39875 - 5.09127i) q^{22} +(-20.2104 + 11.6685i) q^{23} +(31.0204 - 53.7288i) q^{25} +(-7.35189 - 24.5379i) q^{26} +(-12.4757 - 18.9506i) q^{28} +(-14.6837 - 8.47767i) q^{29} +(-3.32057 + 1.91713i) q^{31} +(29.3693 - 12.7060i) q^{32} +(-5.15271 + 21.7618i) q^{34} +52.9184 q^{35} +13.8029i q^{37} +(-6.06117 + 25.5985i) q^{38} +(-12.9133 + 73.5109i) q^{40} +(-3.05861 - 5.29766i) q^{41} +(-11.3997 + 19.7448i) q^{43} +(-12.3964 + 8.16085i) q^{44} +(13.3958 + 44.7103i) q^{46} +(49.8977 + 28.8084i) q^{47} +(-8.41350 - 14.5726i) q^{49} +(-90.2718 - 85.1305i) q^{50} +(-51.1432 + 3.00073i) q^{52} +60.0402i q^{53} -34.6162i q^{55} +(-42.6305 + 15.5472i) q^{56} +(-23.2656 + 24.6707i) q^{58} +(55.3504 + 95.8696i) q^{59} +(73.2932 + 42.3159i) q^{61} +(2.20093 + 7.34589i) q^{62} +(-11.1944 - 63.0134i) q^{64} +(59.7456 - 103.482i) q^{65} +(16.0918 + 27.8718i) q^{67} +(39.9781 + 20.0563i) q^{68} +(24.3856 - 102.989i) q^{70} -38.7881i q^{71} -13.6313 q^{73} +(26.8631 + 6.36060i) q^{74} +(47.0264 + 23.5924i) q^{76} +(18.2261 - 10.5229i) q^{77} +(-4.14976 - 2.39586i) q^{79} +(137.115 + 59.0066i) q^{80} +(-11.7197 + 3.51138i) q^{82} +(2.70708 - 4.68879i) q^{83} +(-90.3444 + 52.1604i) q^{85} +(33.1740 + 31.2846i) q^{86} +(10.1701 + 27.8864i) q^{88} -98.2333 q^{89} +72.6474 q^{91} +(93.1876 - 5.46760i) q^{92} +(79.0602 - 83.8349i) q^{94} +(-106.273 + 61.3566i) q^{95} +(42.1665 - 73.0345i) q^{97} +(-32.2381 + 9.65898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.460815	−	1.94619i	0.230408	−	0.973094i
$2$	0.460815	−	1.94619i	0.230408	−	0.973094i
$3$		0			0
$3$		0			0
$4$	−3.57530	−	1.79367i	−0.893825	−	0.448416i
$5$	8.07964	−	4.66478i	1.61593	−	0.932956i	0.627969	−	0.778239i	$-0.283887\pi$
$5$	8.07964	−	4.66478i	1.61593	−	0.932956i	0.987959	−	0.154718i	$-0.0494468\pi$
$6$		0			0
$7$	4.91220	+	2.83606i	0.701744	+	0.405152i	0.807996	−	0.589187i	$-0.200552\pi$
$7$	4.91220	+	2.83606i	0.701744	+	0.405152i	−0.106253	+	0.994339i	$0.533885\pi$
$8$	−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	−0.00851505	−	0.999964i	$-0.502710\pi$
$13$	11.0919	−	6.40390i	0.853221	−	0.492608i	0.861736	+	0.507356i	$0.169377\pi$
$14$	7.78313	−	8.25318i	0.555938	−	0.589513i
$15$		0			0
$16$	9.56553	+	12.8258i	0.597845	+	0.801611i
$17$	−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	$0.612506\pi$
$20$	−37.2542	+	2.18582i	−1.86271	+	0.109291i
$21$		0			0
$22$	−5.39875	−	5.09127i	−0.245398	−	0.231422i
$23$	−20.2104	+	11.6685i	−0.878713	+	0.507325i	−0.870234	−	0.492639i	$-0.836032\pi$
$23$	−20.2104	+	11.6685i	−0.878713	+	0.507325i	−0.00847922	+	0.999964i	$0.502699\pi$
$24$		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	0.224990	−	0.974361i	$-0.427765\pi$
$29$	−14.6837	−	8.47767i	−0.506336	−	0.292333i	−0.731326	+	0.682028i	$0.761098\pi$
$30$		0			0
$31$	−3.32057	+	1.91713i	−0.107115	+	0.0618429i	−0.552600	−	0.833446i	$-0.686364\pi$
$31$	−3.32057	+	1.91713i	−0.107115	+	0.0618429i	0.445485	+	0.895289i	$0.353031\pi$
$32$	29.3693	−	12.7060i	0.917792	−	0.397063i
$33$		0			0
$34$	−5.15271	+	21.7618i	−0.151550	+	0.640052i
$35$	52.9184			1.51196
$36$		0			0
$37$			13.8029i			0.373052i	0.982450	+	0.186526i	$0.0597229\pi$
$37$			13.8029i			0.373052i	−0.982450	+	0.186526i	$0.940277\pi$
$38$	−6.06117	+	25.5985i	−0.159504	+	0.673645i
$39$		0			0
$40$	−12.9133	+	73.5109i	−0.322832	+	1.83777i
$41$	−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	0.925889	−	0.377796i	$-0.123318\pi$
$47$	49.8977	+	28.8084i	1.06165	+	0.612945i	0.135764	+	0.990741i	$0.456651\pi$
$48$		0			0
$49$	−8.41350	−	14.5726i	−0.171704	−	0.297400i
$50$	−90.2718	−	85.1305i	−1.80544	−	1.70261i
$51$		0			0
$52$	−51.1432	+	3.00073i	−0.983524	+	0.0577064i
$53$			60.0402i			1.13283i	0.824119	+	0.566417i	$0.191671\pi$
$53$			60.0402i			1.13283i	−0.824119	+	0.566417i	$0.808329\pi$
$54$		0			0
$55$		−	34.6162i		−	0.629385i
$56$	−42.6305	+	15.5472i	−0.761258	+	0.277629i
$57$		0			0
$58$	−23.2656	+	24.6707i	−0.401132	+	0.425357i
$59$	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	0.960895	−	0.276913i	$-0.0893115\pi$
$61$	73.2932	+	42.3159i	1.20153	+	0.693703i	0.240633	+	0.970616i	$0.422645\pi$
$62$	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	$0.756128\pi$
$68$	39.9781	+	20.0563i	0.587913	+	0.294946i
$69$		0			0
$70$	24.3856	−	102.989i	0.348366	−	1.47128i
$71$		−	38.7881i		−	0.546311i	−0.961970	−	0.273156i	$-0.911933\pi$
$71$		−	38.7881i		−	0.546311i	0.961970	−	0.273156i	$-0.0880674\pi$
$72$		0			0
$73$	−13.6313			−0.186730			−0.0933652	−	0.995632i	$-0.529762\pi$
$73$	−13.6313			−0.186730			−0.0933652	+	0.995632i	$0.529762\pi$
$74$	26.8631	+	6.36060i	0.363015	+	0.0859540i
$75$		0			0
$76$	47.0264	+	23.5924i	0.618769	+	0.310426i
$77$	18.2261	−	10.5229i	0.236703	−	0.136661i
$78$		0			0
$79$	−4.14976	−	2.39586i	−0.0525286	−	0.0303274i	0.473506	−	0.880791i	$-0.342988\pi$
$79$	−4.14976	−	2.39586i	−0.0525286	−	0.0303274i	−0.526034	+	0.850463i	$0.676322\pi$
$80$	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
$86$	33.1740	+	31.2846i	0.385744	+	0.363775i
$87$		0			0
$88$	10.1701	+	27.8864i	0.115569	+	0.316891i
$89$	−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
$92$	93.1876	−	5.46760i	1.01291	−	0.0594305i
$93$		0			0
$94$	79.0602	−	83.8349i	0.841066	−	0.891861i
$95$	−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	0.883762	−	0.467936i	$-0.155002\pi$
$101$	92.9603	+	53.6706i	0.920399	+	0.531393i	0.0366366	+	0.999329i	$0.488336\pi$
$102$		0			0
$103$	−75.2912	+	43.4694i	−0.730983	+	0.422033i	−0.818782	−	0.574105i	$-0.805350\pi$
$103$	−75.2912	+	43.4694i	−0.730983	+	0.422033i	0.0877989	+	0.996138i	$0.472017\pi$
$104$	−17.7276	+	100.917i	−0.170458	+	0.970357i
$105$		0			0
$106$	116.850	+	27.6674i	1.10235	+	0.261013i
$107$	−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	$-0.731354\pi$
$109$		−	162.909i		−	1.49458i	0.664497	−	0.747291i	$-0.268646\pi$
$110$	−67.3696	−	15.9517i	−0.612451	−	0.145015i
$111$		0			0
$112$	10.6131	+	90.1313i	0.0947598	+	0.804744i
$113$	−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
$122$	116.129	−	123.143i	0.951879	−	1.00937i
$123$		0			0
$124$	15.3107	−	0.898327i	0.123474	−	0.00724457i
$125$		−	345.574i		−	2.76459i
$126$		0			0
$127$			108.522i			0.854507i	0.904132	+	0.427254i	$0.140519\pi$
$127$			108.522i			0.854507i	−0.904132	+	0.427254i	$0.859481\pi$
$128$	−127.794	−	7.25100i	−0.998394	−	0.0566484i
$129$		0			0
$130$	−173.865	−	163.962i	−1.33742	−	1.26125i
$131$	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	$0.923797\pi$
$140$	−189.199	−	94.9180i	−1.35142	−	0.677986i
$141$		0			0
$142$	−75.4889	−	17.8741i	−0.531612	−	0.125874i
$143$		−	47.5218i		−	0.332320i
$144$		0			0
$145$	−158.186			−1.09094
$146$	−6.28152	+	26.5291i	−0.0430241	+	0.181706i
$147$		0			0
$148$	24.7578	−	49.3496i	0.167283	−	0.333443i
$149$	−127.047	+	73.3505i	−0.852664	+	0.492286i	−0.861549	−	0.507675i	$-0.830505\pi$
$149$	−127.047	+	73.3505i	−0.852664	+	0.492286i	0.00888514	+	0.999961i	$0.497172\pi$
$150$		0			0
$151$	−91.4191	−	52.7808i	−0.605424	−	0.349542i	0.165748	−	0.986168i	$-0.446996\pi$
$151$	−91.4191	−	52.7808i	−0.605424	−	0.349542i	−0.771173	+	0.636626i	$0.780329\pi$
$152$	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	0.0557082	−	0.998447i	$-0.482258\pi$
$157$	148.874	−	85.9525i	0.948243	−	0.547468i	0.892535	+	0.450979i	$0.148925\pi$
$158$	−6.57508	+	6.97216i	−0.0416144	+	0.0441276i
$159$		0			0
$160$	178.023	−	239.661i	1.11264	−	1.49788i
$161$	−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	$0.582093\pi$
$164$	1.43320	+	24.4268i	0.00873901	+	0.148944i
$165$		0			0
$166$	−7.87781	−	7.42915i	−0.0474567	−	0.0447539i
$167$	202.139	−	116.705i	1.21041	−	0.698831i	0.247562	−	0.968872i	$-0.420370\pi$
$167$	202.139	−	116.705i	1.21041	−	0.698831i	0.962849	+	0.270041i	$0.0870371\pi$
$168$		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	0.607353	−	0.794432i	$-0.292231\pi$
$173$	38.5845	+	22.2768i	0.223032	+	0.128767i	−0.384322	+	0.923199i	$0.625565\pi$
$174$		0			0
$175$	304.757	−	175.951i	1.74147	−	1.00544i
$176$	58.9587	−	6.94248i	0.334993	−	0.0394459i
$177$		0			0
$178$	−45.2674	+	191.180i	−0.254311	+	1.07405i
$179$	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	$0.231447\pi$
$181$			240.627i			1.32943i	−0.747096	+	0.664716i	$0.768553\pi$
$182$	33.4770	−	141.386i	0.183940	−	0.776844i
$183$		0			0
$184$	32.3013	−	183.880i	0.175550	−	0.999349i
$185$	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	0.308787	−	0.951131i	$-0.400077\pi$
$191$	−68.8601	−	39.7564i	−0.360524	−	0.208149i	−0.669311	+	0.742983i	$0.733410\pi$
$192$		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	$0.805665\pi$
$194$	−122.708	−	115.719i	−0.632515	−	0.596491i
$195$		0			0
$196$	3.94239	+	67.1924i	0.0201142	+	0.342818i
$197$			183.151i			0.929699i	0.885390	+	0.464849i	$0.153892\pi$
$197$			183.151i			0.929699i	−0.885390	+	0.464849i	$0.846108\pi$
$198$		0			0
$199$		−	86.2656i		−	0.433496i	−0.976228	−	0.216748i	$-0.930455\pi$
$199$		−	86.2656i		−	0.433496i	0.976228	−	0.216748i	$-0.0695449\pi$
$200$	170.053	+	466.285i	0.850265	+	2.33142i
$201$		0			0
$202$	147.291	−	156.186i	0.729162	−	0.773198i
$203$	−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	$-0.350156\pi$
$212$	107.692	−	214.662i	0.507981	−	1.01255i
$213$		0			0
$214$	−77.7258	+	328.264i	−0.363205	+	1.53395i
$215$			212.708i			0.989339i
$216$		0			0
$217$	−21.7484			−0.100223
$218$	−317.053	−	75.0711i	−1.45437	−	0.344363i
$219$		0			0
$220$	−62.0899	+	123.763i	−0.282227	+	0.562560i
$221$	−124.026	+	71.6067i	−0.561206	+	0.324012i
$222$		0			0
$223$	−327.758	−	189.231i	−1.46977	−	0.848570i	−0.470342	−	0.882484i	$-0.655869\pi$
$223$	−327.758	−	189.231i	−1.46977	−	0.848570i	−0.999425	+	0.0339138i	$0.989203\pi$
$224$	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	−0.795893	−	0.605438i	$-0.792998\pi$
$229$	−153.319	+	88.5187i	−0.669515	+	0.386545i	0.126378	+	0.991982i	$0.459665\pi$
$230$	316.797	+	298.754i	1.37738	+	1.29893i
$231$		0			0
$232$	127.433	−	46.4744i	0.549278	−	0.200321i
$233$	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
$236$	−25.9360	−	442.043i	−0.109898	−	1.87306i
$237$		0			0
$238$	−87.0289	+	92.2848i	−0.365668	+	0.387751i
$239$	157.611	−	90.9966i	0.659459	−	0.380739i	−0.132612	−	0.991168i	$-0.542336\pi$
$239$	157.611	−	90.9966i	0.659459	−	0.380739i	0.792071	+	0.610429i	$0.209003\pi$
$240$		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
$248$	5.30709	−	30.2115i	0.0213996	−	0.121821i
$249$		0			0
$250$	−672.552	−	159.246i	−2.69021	−	0.636982i
$251$	−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
$254$	211.205	+	50.0087i	0.831516	+	0.196885i
$255$		0			0
$256$	−73.0014	+	245.371i	−0.285162	+	0.958479i
$257$	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	0.622921	−	0.782285i	$-0.285946\pi$
$263$	67.5653	+	39.0088i	0.256902	+	0.148323i	−0.366018	+	0.930608i	$0.619279\pi$
$264$		0			0
$265$	280.074	+	485.103i	1.05688	+	1.83058i
$266$	−102.373	+	108.555i	−0.384860	+	0.408103i
$267$		0			0
$268$	−7.54027	−	128.513i	−0.0281353	−	0.479527i
$269$			240.267i			0.893187i	0.894737	+	0.446594i	$0.147363\pi$
$269$			240.267i			0.893187i	−0.894737	+	0.446594i	$0.852637\pi$
$270$		0			0
$271$			440.449i			1.62527i	0.582772	+	0.812636i	$0.301968\pi$
$271$			440.449i			1.62527i	−0.582772	+	0.812636i	$0.698032\pi$
$272$	−106.959	−	143.415i	−0.393232	−	0.527259i
$273$		0			0
$274$	103.685	+	97.7802i	0.378414	+	0.356862i
$275$	−115.097	−	199.354i	−0.418535	−	0.724925i
$276$		0			0
$277$	111.638	+	64.4543i	0.403026	+	0.232687i	0.687789	−	0.725911i	$-0.258582\pi$
$277$	111.638	+	64.4543i	0.403026	+	0.232687i	−0.284763	+	0.958598i	$0.591915\pi$
$278$	−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	$-0.432455\pi$
$284$	−69.5729	+	138.679i	−0.244975	+	0.488306i
$285$		0			0
$286$	−92.4863	−	21.8987i	−0.323379	−	0.0765690i
$287$		−	34.6976i		−	0.120898i
$288$		0			0
$289$	−163.969			−0.567366
$290$	−72.8944	+	307.859i	−0.251360	+	1.06158i
$291$		0			0
$292$	48.7360	+	24.4500i	0.166904	+	0.0837330i
$293$	329.166	−	190.044i	1.12343	−	0.648615i	0.181158	−	0.983454i	$-0.442015\pi$
$293$	329.166	−	190.044i	1.12343	−	0.648615i	0.942275	+	0.334839i	$0.108682\pi$
$294$		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
$302$	−144.849	+	153.597i	−0.479632	+	0.508598i
$303$		0			0
$304$	−125.817	−	168.699i	−0.413871	−	0.554932i
$305$	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	$0.333833\pi$
$308$	−84.0384	+	4.93079i	−0.272852	+	0.0160091i
$309$		0			0
$310$	52.0497	+	49.0853i	0.167902	+	0.158340i
$311$	−492.156	+	284.146i	−1.58249	+	0.913654i	−0.588000	+	0.808861i	$0.700085\pi$
$311$	−492.156	+	284.146i	−1.58249	+	0.913654i	−0.994494	+	0.104793i	$0.966582\pi$
$312$		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	0.695072	−	0.718940i	$-0.255373\pi$
$317$	133.136	+	76.8660i	0.419987	+	0.242480i	−0.275085	+	0.961420i	$0.588706\pi$
$318$		0			0
$319$	−54.4822	+	31.4553i	−0.170791	+	0.0986061i
$320$	−384.391	−	456.906i	−1.20122	−	1.42783i
$321$		0			0
$322$	−60.9982	+	257.617i	−0.189435	+	0.800054i
$323$	147.075			0.455341
$324$		0			0
$325$		−	794.605i		−	2.44494i
$326$	−38.3156	+	161.820i	−0.117532	+	0.496382i
$327$		0			0
$328$	48.1997	+	8.46698i	0.146950	+	0.0258140i
$329$	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	$-0.409980\pi$
$338$	7.21745	+	6.80639i	0.0213534	+	0.0201373i
$339$		0			0
$340$	416.566	−	24.4412i	1.22520	−	0.0718860i
$341$			14.2266i			0.0417201i
$342$		0			0
$343$		−	373.379i		−	1.08857i
$344$	−62.4928	−	171.355i	−0.181665	−	0.498125i
$345$		0			0
$346$	61.1351	−	64.8272i	0.176691	−	0.187362i
$347$	−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	0.309049	−	0.951046i	$-0.399989\pi$
$349$	−125.660	−	72.5496i	−0.360056	−	0.207878i	−0.669105	+	0.743168i	$0.733323\pi$
$350$	−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
$356$	351.213	+	176.198i	0.986554	+	0.494937i
$357$		0			0
$358$	7.08541	−	29.9242i	0.0197916	−	0.0835872i
$359$		−	291.137i		−	0.810968i	−0.914102	−	0.405484i	$-0.867103\pi$
$359$		−	291.137i		−	0.810968i	0.914102	−	0.405484i	$-0.132897\pi$
$360$		0			0
$361$	−187.995			−0.520761
$362$	468.306	+	110.885i	1.29366	+	0.306311i
$363$		0			0
$364$	−259.736	−	130.305i	−0.713561	−	0.357981i
$365$	−110.136	+	63.5871i	−0.301743	+	0.174211i
$366$		0			0
$367$	−321.962	−	185.885i	−0.877281	−	0.506499i	−0.00752022	−	0.999972i	$-0.502394\pi$
$367$	−321.962	−	185.885i	−0.877281	−	0.506499i	−0.869761	+	0.493473i	$0.835727\pi$
$368$	−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	0.192025	−	0.981390i	$-0.438494\pi$
$373$	424.454	−	245.059i	1.13795	−	0.656994i	0.945921	+	0.324396i	$0.105161\pi$
$374$	60.3674	+	56.9293i	0.161410	+	0.152217i
$375$		0			0
$376$	−433.036	+	157.927i	−1.15169	+	0.420019i
$377$	−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	$0.606919\pi$
$380$	490.010	−	28.7504i	1.28950	−	0.0756589i
$381$		0			0
$382$	−109.105	+	115.694i	−0.285616	+	0.302865i
$383$	42.3609	−	24.4571i	0.110603	−	0.0638566i	−0.443678	−	0.896186i	$-0.646327\pi$
$383$	42.3609	−	24.4571i	0.110603	−	0.0638566i	0.554281	+	0.832330i	$0.312993\pi$
$384$		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	−0.199071	−	0.979985i	$-0.563792\pi$
$389$	−446.299	−	257.671i	−1.14730	−	0.662393i	−0.948228	+	0.317592i	$0.897126\pi$
$390$		0			0
$391$	225.987	−	130.474i	0.577973	−	0.333693i
$392$	132.586	+	23.2906i	0.338229	+	0.0594149i
$393$		0			0
$394$	356.446	+	84.3986i	0.904685	+	0.214210i
$395$	−44.7047			−0.113177
$396$		0			0
$397$			560.274i			1.41127i	0.708576	+	0.705634i	$0.249338\pi$
$397$			560.274i			1.41127i	−0.708576	+	0.705634i	$0.750662\pi$
$398$	−167.889	−	39.7525i	−0.421832	−	0.0998807i
$399$		0			0
$400$	985.841	−	116.084i	2.46460	−	0.290211i
$401$	−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	$0.639668\pi$
$410$	−78.3111	+	83.0405i	−0.191003	+	0.202538i
$411$		0			0
$412$	347.158	−	20.3688i	0.842617	−	0.0494389i
$413$			627.908i			1.52036i
$414$		0			0
$415$		−	50.5117i		−	0.121715i
$416$	244.393	−	329.012i	0.587483	−	0.790893i
$417$		0			0
$418$	71.0106	+	66.9663i	0.169882	+	0.160206i
$419$	−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	0.834519	−	0.550980i	$-0.185746\pi$
$421$	326.113	+	188.282i	0.774616	+	0.447225i	−0.0599029	+	0.998204i	$0.519079\pi$
$422$	−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
$428$	603.047	+	302.538i	1.40899	+	0.706865i
$429$		0			0
$430$	413.970	+	98.0190i	0.962720	+	0.227951i
$431$		−	300.981i		−	0.698332i	−0.937061	−	0.349166i	$-0.886465\pi$
$431$		−	300.981i		−	0.698332i	0.937061	−	0.349166i	$-0.113535\pi$
$432$		0			0
$433$	−670.846			−1.54930			−0.774649	−	0.632391i	$-0.782074\pi$
$433$	−670.846			−1.54930			−0.774649	+	0.632391i	$0.782074\pi$
$434$	−10.0220	+	42.3265i	−0.0230922	+	0.0975265i
$435$		0			0
$436$	−292.205	+	582.450i	−0.670195	+	1.33589i
$437$	265.830	−	153.477i	0.608308	−	0.351207i
$438$		0			0
$439$	−513.168	−	296.277i	−1.16895	−	0.674892i	−0.215515	−	0.976501i	$-0.569143\pi$
$439$	−513.168	−	296.277i	−1.16895	−	0.674892i	−0.953432	+	0.301609i	$0.902476\pi$
$440$	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
$446$	−519.315	+	550.678i	−1.16438	+	1.23470i
$447$		0			0
$448$	123.720	−	341.283i	0.276162	−	0.761792i
$449$	−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
$452$	14.4476	+	246.239i	0.0319637	+	0.544776i
$453$		0			0
$454$	−605.987	−	571.474i	−1.33477	−	1.25875i
$455$	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	0.356311	−	0.934368i	$-0.384034\pi$
$461$	−126.646	−	73.1191i	−0.274720	−	0.158610i	−0.631031	+	0.775758i	$0.717368\pi$
$462$		0			0
$463$	443.882	−	256.275i	0.958708	−	0.553510i	0.0629326	−	0.998018i	$-0.479955\pi$
$463$	443.882	−	256.275i	0.958708	−	0.553510i	0.895775	+	0.444508i	$0.146621\pi$
$464$	−31.7251	−	269.424i	−0.0683730	−	0.580655i
$465$		0			0
$466$	66.5679	−	281.140i	0.142850	−	0.603306i
$467$	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
$470$	247.707	−	1046.15i	0.527035	−	2.22586i
$471$		0			0
$472$	−872.250	−	153.224i	−1.84799	−	0.324626i
$473$	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	−0.365232	−	0.930917i	$-0.619010\pi$
$479$	−648.588	−	374.462i	−1.35405	−	0.781758i	−0.988813	+	0.149158i	$0.952344\pi$
$480$		0			0
$481$	88.3925	+	153.100i	0.183768	+	0.318296i
$482$	−204.628	−	192.973i	−0.424539	−	0.400360i
$483$		0			0
$484$	−25.1236	−	428.196i	−0.0519082	−	0.884702i
$485$		−	786.789i		−	1.62225i
$486$		0			0
$487$			81.6059i			0.167569i	0.996484	+	0.0837843i	$0.0267007\pi$
$487$			81.6059i			0.167569i	−0.996484	+	0.0837843i	$0.973299\pi$
$488$	−636.074	+	231.975i	−1.30343	+	0.475358i
$489$		0			0
$490$	−215.415	+	228.425i	−0.439623	+	0.466173i
$491$	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	$0.499002\pi$
$500$	−619.844	+	1235.53i	−1.23969	+	2.47106i
$501$		0			0
$502$	−17.8695	+	75.4694i	−0.0355966	+	0.150337i
$503$			349.624i			0.695077i	0.937666	+	0.347539i	$0.112982\pi$
$503$			349.624i			0.695077i	−0.937666	+	0.347539i	$0.887018\pi$
$504$		0			0
$505$	1001.45			1.98306
$506$	168.518	+	39.9015i	0.333040	+	0.0788567i
$507$		0			0
$508$	194.653	−	388.000i	0.383175	−	0.763780i
$509$	12.5795	−	7.26280i	0.0247142	−	0.0142688i	−0.487592	−	0.873072i	$-0.662125\pi$
$509$	12.5795	−	7.26280i	0.0247142	−	0.0142688i	0.512306	+	0.858803i	$0.328791\pi$
$510$		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
$518$	113.918	+	107.430i	0.219919	+	0.207394i
$519$		0			0
$520$	327.524	+	898.069i	0.629854	+	1.72706i
$521$	−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	$0.778179\pi$
$524$	−15.2946	−	260.675i	−0.0291881	−	0.497471i
$525$		0			0
$526$	107.054	−	113.519i	0.203524	−	0.215815i
$527$	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
$536$	−253.586	−	44.5460i	−0.473107	−	0.0831083i
$537$		0			0
$538$	467.606	+	110.719i	0.869155	+	0.205797i
$539$	−62.4345			−0.115834
$540$		0			0
$541$		−	780.008i		−	1.44179i	−0.693045	−	0.720895i	$-0.743731\pi$
$541$		−	780.008i		−	1.44179i	0.693045	−	0.720895i	$-0.256269\pi$
$542$	857.196	+	202.965i	1.58154	+	0.374475i
$543$		0			0
$544$	−328.400	+	142.075i	−0.603677	+	0.261168i
$545$	−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
$554$	176.885	−	187.567i	0.319287	−	0.338569i
$555$		0			0
$556$	18.2625	+	311.259i	0.0328462	+	0.559818i
$557$		−	87.9243i		−	0.157853i	−0.996880	−	0.0789266i	$-0.974851\pi$
$557$		−	87.9243i		−	0.157853i	0.996880	−	0.0789266i	$-0.0251493\pi$
$558$		0			0
$559$			292.009i			0.522378i
$560$	506.193	+	678.720i	0.903916	+	1.21200i
$561$		0			0
$562$	204.294	+	192.658i	0.363512	+	0.342808i
$563$	−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	$0.720297\pi$
$572$	−85.2382	+	169.905i	−0.149018	+	0.297036i
$573$		0			0
$574$	−67.5281	−	15.9892i	−0.117645	−	0.0278557i
$575$			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	$0.401589\pi$
$578$	−75.5593	+	319.114i	−0.130725	+	0.552101i
$579$		0			0
$580$	565.562	+	283.732i	0.975106	+	0.489194i
$581$	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
$590$	1417.16	−	1502.75i	2.40197	−	2.54704i
$591$		0			0
$592$	−177.033	+	132.032i	−0.299043	+	0.223027i
$593$	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
$596$	585.797	−	34.3705i	0.982881	−	0.0576686i
$597$		0			0
$598$	434.905	+	410.135i	0.727265	+	0.685845i
$599$	−519.915	+	300.173i	−0.867971	+	0.501124i	−0.866674	−	0.498876i	$-0.833746\pi$
$599$	−519.915	+	300.173i	−0.867971	+	0.501124i	−0.00129781	+	0.999999i	$0.500413\pi$
$600$		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	−0.408614	−	0.912707i	$-0.633988\pi$
$607$	107.746	−	62.2074i	0.177506	−	0.102483i	0.586121	+	0.810224i	$0.300654\pi$
$608$	−386.299	+	167.124i	−0.635361	+	0.274875i
$609$		0			0
$610$	363.849	−	1536.67i	0.596474	−	2.51912i
$611$	737.945			1.20777
$612$		0			0
$613$			196.037i			0.319799i	0.987133	+	0.159899i	$0.0511170\pi$
$613$			196.037i			0.319799i	−0.987133	+	0.159899i	$0.948883\pi$
$614$	141.086	−	595.855i	0.229781	−	0.970448i
$615$		0			0
$616$	−29.1299	+	165.827i	−0.0472888	+	0.269199i
$617$	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
$626$	455.959	+	429.991i	0.728369	+	0.686886i
$627$		0			0
$628$	−686.440	+	40.2755i	−1.09306	+	0.0641330i
$629$		−	154.341i		−	0.245375i
$630$		0			0
$631$		−	897.433i		−	1.42224i	−0.703071	−	0.711120i	$-0.748188\pi$
$631$		−	897.433i		−	1.42224i	0.703071	−	0.711120i	$-0.251812\pi$
$632$	36.0136	−	13.1341i	0.0569835	−	0.0207818i
$633$		0			0
$634$	210.947	−	223.686i	0.332724	−	0.352818i
$635$	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	$0.881356\pi$
$644$	473.263	+	237.428i	0.734880	+	0.368677i
$645$		0			0
$646$	67.7744	−	286.236i	0.104914	−	0.443089i
$647$		−	462.896i		−	0.715450i	−0.933827	−	0.357725i	$-0.883553\pi$
$647$		−	462.896i		−	0.715450i	0.933827	−	0.357725i	$-0.116447\pi$
$648$		0			0
$649$	410.741			0.632884
$650$	−1546.45	−	366.166i	−2.37916	−	0.563332i
$651$		0			0
$652$	297.277	+	149.139i	0.455946	+	0.228740i
$653$	175.738	−	101.463i	0.269125	−	0.155379i	−0.359365	−	0.933197i	$-0.617007\pi$
$653$	175.738	−	101.463i	0.269125	−	0.155379i	0.628490	+	0.777818i	$0.283673\pi$
$654$		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	−0.0198096	−	0.999804i	$-0.506306\pi$
$661$	552.689	−	319.095i	0.836141	−	0.482746i	0.855951	+	0.517058i	$0.172973\pi$
$662$	−891.461	−	840.689i	−1.34662	−	1.26992i
$663$		0			0
$664$	14.8401	+	40.6916i	0.0223496	+	0.0612825i
$665$	−696.044			−1.04668
$666$		0			0
$667$	395.686			0.593232
$668$	−932.036	+	54.6854i	−1.39526	+	0.0818644i
$669$		0			0
$670$	412.006	−	436.888i	0.614935	−	0.652072i
$671$	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	0.707669	−	0.706544i	$-0.249747\pi$
$677$	304.392	+	175.741i	0.449619	+	0.259588i	−0.258050	+	0.966131i	$0.583080\pi$
$678$		0			0
$679$	414.261	−	239.173i	0.610104	−	0.352244i
$680$	144.393	−	821.980i	0.212342	−	1.20879i
$681$		0			0
$682$	27.6876	+	6.55581i	0.0405976	+	0.00961263i
$683$	−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
$686$	−726.666	−	172.059i	−1.05928	−	0.250814i
$687$		0			0
$688$	−362.287	+	42.6598i	−0.526579	+	0.0620055i
$689$	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
$698$	−199.101	+	211.125i	−0.285245	+	0.302472i
$699$		0			0
$700$	−1405.19	+	82.4471i	−2.00742	+	0.117782i
$701$		−	579.128i		−	0.826146i	−0.910698	−	0.413073i	$-0.864455\pi$
$701$		−	579.128i		−	0.826146i	0.910698	−	0.413073i	$-0.135545\pi$
$702$		0			0
$703$		−	181.552i		−	0.258253i
$704$	−223.247	−	80.9308i	−0.317113	−	0.114958i
$705$		0			0
$706$	−608.302	−	573.657i	−0.861618	−	0.812546i
$707$	304.427	+	527.282i	0.430589	+	0.745803i
$708$		0			0
$709$	702.992	+	405.872i	0.991526	+	0.572458i	0.905730	−	0.423855i	$-0.139323\pi$
$709$	702.992	+	405.872i	0.991526	+	0.572458i	0.0857956	+	0.996313i	$0.472657\pi$
$710$	−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
$716$	−54.9731	−	27.5791i	−0.0767781	−	0.0385183i
$717$		0			0
$718$	−566.608	−	134.160i	−0.789148	−	0.186853i
$719$		−	441.412i		−	0.613924i	−0.951722	−	0.306962i	$-0.900687\pi$
$719$		−	441.412i		−	0.613924i	0.951722	−	0.306962i	$-0.0993125\pi$
$720$		0			0
$721$	−493.128			−0.683950
$722$	−86.6307	+	365.873i	−0.119987	+	0.506749i
$723$		0			0
$724$	431.605	−	860.314i	0.596139	−	1.18828i
$725$	−910.990	+	525.961i	−1.25654	+	0.725463i
$726$		0			0
$727$	30.1778	+	17.4232i	0.0415101	+	0.0239658i	0.520611	−	0.853794i	$-0.325704\pi$
$727$	30.1778	+	17.4232i	0.0415101	+	0.0239658i	−0.479101	+	0.877760i	$0.659037\pi$
$728$	−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	0.249595	−	0.968350i	$-0.419703\pi$
$733$	889.135	−	513.342i	1.21301	−	0.700331i	0.963413	+	0.268020i	$0.0863692\pi$
$734$	−510.132	+	540.941i	−0.695003	+	0.736976i
$735$		0			0
$736$	−445.306	+	599.489i	−0.605036	+	0.814523i
$737$	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	$0.214218\pi$
$740$	−30.1707	−	514.217i	−0.0407712	−	0.694887i
$741$		0			0
$742$	495.522	+	467.301i	0.667820	+	0.629785i
$743$	703.173	−	405.977i	0.946397	−	0.546403i	0.0544372	−	0.998517i	$-0.482664\pi$
$743$	703.173	−	405.977i	0.946397	−	0.546403i	0.891960	+	0.452115i	$0.149330\pi$
$744$		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	−0.620846	−	0.783933i	$-0.713211\pi$
$751$	−189.525	+	109.422i	−0.252363	+	0.145702i	0.368483	+	0.929635i	$0.379877\pi$
$752$	107.807	+	915.545i	0.143360	+	1.21748i
$753$		0			0
$754$	−100.071	+	422.635i	−0.132720	+	0.560524i
$755$	−984.844			−1.30443
$756$		0			0
$757$			985.851i			1.30231i	0.758944	+	0.651156i	$0.225716\pi$
$757$			985.851i			1.30231i	−0.758944	+	0.651156i	$0.774284\pi$
$758$	−115.134	+	486.251i	−0.151891	+	0.641493i
$759$		0			0
$760$	169.850	−	966.900i	0.223487	−	1.27224i
$761$	−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	$0.969202\pi$
$770$	−285.694	−	269.422i	−0.371031	−	0.349899i
$771$		0			0
$772$	−7.85097	−	133.809i	−0.0101697	−	0.173327i
$773$			815.596i			1.05510i	0.849523	+	0.527552i	$0.176890\pi$
$773$			815.596i			1.05510i	−0.849523	+	0.527552i	$0.823110\pi$
$774$		0			0
$775$			237.880i			0.306942i
$776$	231.156	+	633.828i	0.297881	+	0.816788i
$777$		0			0
$778$	−707.138	+	749.844i	−0.908917	+	0.963809i
$779$	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	$0.824323\pi$
$788$	328.511	−	654.818i	0.416892	−	0.830988i
$789$		0			0
$790$	−20.6006	+	87.0038i	−0.0260767	+	0.110131i
$791$		−	349.775i		−	0.442193i
$792$		0			0
$793$	1083.95			1.36689
$794$	1090.40	+	258.183i	1.37330	+	0.325167i
$795$		0			0
$796$	−154.732	+	308.425i	−0.194387	+	0.387469i
$797$	−131.223	+	75.7614i	−0.164646	+	0.0950582i	−0.580059	−	0.814575i	$-0.696970\pi$
$797$	−131.223	+	75.7614i	−0.164646	+	0.0950582i	0.415413	+	0.909633i	$0.363637\pi$
$798$		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
$806$	71.4548	+	67.3852i	0.0886536	+	0.0836045i
$807$		0			0
$808$	−806.754	+	294.221i	−0.998458	+	0.364135i
$809$	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	$0.701197\pi$
$812$	22.5323	+	384.031i	0.0277491	+	0.472944i
$813$		0			0
$814$	70.2745	−	74.5186i	0.0863323	−	0.0915462i
$815$	−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	0.959201	−	0.282725i	$-0.0912383\pi$
$821$	980.237	+	565.940i	1.19395	+	0.689330i	0.234754	+	0.972055i	$0.424572\pi$
$822$		0			0
$823$	786.212	−	453.920i	0.955300	−	0.551543i	0.0605770	−	0.998164i	$-0.480706\pi$
$823$	786.212	−	453.920i	0.955300	−	0.551543i	0.894723	+	0.446621i	$0.147373\pi$
$824$	120.334	−	685.022i	0.146037	−	0.831337i
$825$		0			0
$826$	1222.03	+	289.350i	1.47945	+	0.350302i
$827$	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	$-0.978305\pi$
$829$		−	112.915i		−	0.136206i	0.997678	−	0.0681030i	$-0.0216946\pi$
$830$	−98.3052	−	23.2765i	−0.118440	−	0.0280440i
$831$		0			0
$832$	−527.699	−	627.248i	−0.634253	−	0.753904i
$833$	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	0.645527	−	0.763738i	$-0.276638\pi$
$839$	257.467	+	148.649i	0.306874	+	0.177174i	−0.338653	+	0.940911i	$0.609971\pi$
$840$		0			0
$841$	−276.758	−	479.360i	−0.329082	−	0.569988i
$842$	516.709	−	547.915i	0.613669	−	0.650730i
$843$		0			0
$844$	53.8891	+	918.464i	0.0638496	+	1.08823i
$845$			46.2775i			0.0547662i
$846$		0			0
$847$			608.240i			0.718111i
$848$	−770.062	+	574.316i	−0.908092	+	0.677259i
$849$		0			0
$850$	1009.40	+	951.907i	1.18752	+	1.11989i
$851$	−161.059	−	278.963i	−0.189259	−	0.327806i
$852$		0			0
$853$	−1353.97	−	781.714i	−1.58730	−	0.916429i	−0.993749	−	0.111634i	$-0.964392\pi$
$853$	−1353.97	−	781.714i	−1.58730	−	0.916429i	−0.593552	−	0.804795i	$-0.702275\pi$
$854$	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	$0.585725\pi$
$860$	381.527	−	760.494i	0.443636	−	0.884296i
$861$		0			0
$862$	−585.766	−	138.697i	−0.679543	−	0.160901i
$863$		−	740.816i		−	0.858419i	−0.903205	−	0.429210i	$-0.858792\pi$
$863$		−	740.816i		−	0.858419i	0.903205	−	0.429210i	$-0.141208\pi$
$864$		0			0
$865$	415.665			0.480537
$866$	−309.136	+	1305.59i	−0.356970	+	1.50761i
$867$		0			0
$868$	77.7571	+	39.0094i	0.0895819	+	0.0449417i
$869$	−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	0.268410	−	0.963305i	$-0.413502\pi$
$877$	1084.73	−	626.268i	1.23686	−	0.714102i	0.968451	+	0.249203i	$0.0801685\pi$
$878$	−813.087	+	862.192i	−0.926067	+	0.981995i
$879$		0			0
$880$	443.980	−	331.122i	0.504522	−	0.376275i
$881$	−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	$0.669326\pi$
$884$	571.870	−	33.5534i	0.646912	−	0.0379563i
$885$		0			0
$886$	−310.064	−	292.405i	−0.349959	−	0.330028i
$887$	−1453.92	+	839.424i	−1.63915	+	0.946363i	−0.658021	+	0.752999i	$0.728606\pi$
$887$	−1453.92	+	839.424i	−1.63915	+	0.946363i	−0.981127	+	0.193363i	$0.938060\pi$
$888$		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
$896$	−607.188	−	398.051i	−0.677665	−	0.444254i
$897$		0			0
$898$	−264.781	+	1118.27i	−0.294856	+	1.24528i
$899$	65.0112			0.0723150
$900$		0			0
$901$		−	671.354i		−	0.745121i
$902$	−10.4592	+	44.1730i	−0.0115956	+	0.0489722i
$903$		0			0
$904$	485.885	+	85.3528i	0.537483	+	0.0944169i
$905$	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	$0.00369956\pi$
$911$	1375.58	+	794.190i	1.50996	+	0.871778i	0.510031	+	0.860156i	$0.329634\pi$
$912$		0			0
$913$	−10.0443	−	17.3972i	−0.0110014	−	0.0190550i
$914$	−584.919	−	551.606i	−0.639955	−	0.603508i
$915$		0			0
$916$	706.934	−	41.4780i	0.771762	−	0.0452816i
$917$			370.281i			0.403796i
$918$		0			0
$919$			995.618i			1.08337i	0.840581	+	0.541686i	$0.182214\pi$
$919$			995.618i			1.08337i	−0.840581	+	0.541686i	$0.817786\pi$
$920$	−596.778	−	1636.36i	−0.648672	−	1.77866i
$921$		0			0
$922$	−200.664	+	212.783i	−0.217640	+	0.230784i
$923$	−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
$932$	−516.477	−	259.108i	−0.554160	−	0.278012i
$933$		0			0
$934$	135.693	−	573.081i	0.145282	−	0.613578i
$935$			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	$0.422921\pi$
$938$	355.275	+	84.1214i	0.378758	+	0.0896817i
$939$		0			0
$940$	−1921.87	−	964.167i	−2.04454	−	1.02571i
$941$	994.500	−	574.175i	1.05685	−	0.610175i	0.132294	−	0.991211i	$-0.457766\pi$
$941$	994.500	−	574.175i	1.05685	−	0.610175i	0.924561	+	0.381035i	$0.124432\pi$
$942$		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
$950$	1187.36	+	1119.73i	1.24985	+	1.17867i
$951$		0			0
$952$	476.683	−	173.845i	0.500717	−	0.182610i
$953$	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
$956$	−726.723	+	42.6391i	−0.760170	+	0.0446015i
$957$		0			0
$958$	−1027.65	+	1089.72i	−1.07271	+	1.13749i
$959$	−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	−0.498433	−	0.866928i	$-0.666091\pi$
$967$	3.02820	−	1.74833i	0.00313154	−	0.00180800i	0.501565	+	0.865120i	$0.332758\pi$
$968$	−844.927	−	148.424i	−0.872859	−	0.153331i
$969$		0			0
$970$	−1531.24	−	362.564i	−1.57860	−	0.373778i
$971$	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
$974$	158.821	+	37.6052i	0.163060	+	0.0386091i
$975$		0			0
$976$	158.354	+	1344.82i	0.162248	+	1.37789i
$977$	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	0.721828	−	0.692073i	$-0.243302\pi$
$983$	475.171	+	274.340i	0.483389	+	0.279085i	−0.238439	+	0.971158i	$0.576636\pi$
$984$		0			0
$985$	854.358	+	1479.79i	0.867368	+	1.50233i
$986$	260.150	−	275.861i	0.263844	−	0.279778i
$987$		0			0
$988$	672.695	−	39.4691i	0.680865	−	0.0399485i
$989$		−	532.067i		−	0.537985i
$990$		0			0
$991$		−	494.677i		−	0.499169i	−0.968353	−	0.249585i	$-0.919706\pi$
$991$		−	494.677i		−	0.499169i	0.968353	−	0.249585i	$-0.0802941\pi$
$992$	−73.1638	+	98.4960i	−0.0737538	+	0.0992903i
$993$		0			0
$994$	−320.125	−	301.893i	−0.322057	−	0.303715i
$995$	−402.410	−	696.995i	−0.404433	−	0.700498i
$996$		0			0
$997$	112.086	+	64.7128i	0.112423	+	0.0649075i	0.555157	−	0.831745i	$-0.312658\pi$
$997$	112.086	+	64.7128i	0.112423	+	0.0649075i	−0.442734	+	0.896653i	$0.645991\pi$
$998$	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.19.11		40
3.2	odd	2		72.3.p.b.43.10	yes	40
4.3	odd	2		864.3.t.b.559.20		40
8.3	odd	2	inner	216.3.p.b.19.14		40
8.5	even	2		864.3.t.b.559.1		40
9.2	odd	6		648.3.b.f.163.19		20
9.4	even	3	inner	216.3.p.b.91.14		40
9.5	odd	6		72.3.p.b.67.7	yes	40
9.7	even	3		648.3.b.e.163.2		20
12.11	even	2		288.3.t.b.79.3		40
24.5	odd	2		288.3.t.b.79.4		40
24.11	even	2		72.3.p.b.43.7	✓	40
36.7	odd	6		2592.3.b.f.1135.20		20
36.11	even	6		2592.3.b.e.1135.1		20
36.23	even	6		288.3.t.b.175.4		40
36.31	odd	6		864.3.t.b.847.1		40
72.5	odd	6		288.3.t.b.175.3		40
72.11	even	6		648.3.b.f.163.20		20
72.13	even	6		864.3.t.b.847.20		40
72.29	odd	6		2592.3.b.e.1135.20		20
72.43	odd	6		648.3.b.e.163.1		20
72.59	even	6		72.3.p.b.67.10	yes	40
72.61	even	6		2592.3.b.f.1135.1		20
72.67	odd	6	inner	216.3.p.b.91.11		40

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

\(f(q)\)	\(=\)	\(q+(0.460815 - 1.94619i) q^{2} +(-3.57530 - 1.79367i) q^{4} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(-5.13836 + 6.13166i) q^{8} +O(q^{10})\)	\(q+(0.460815 - 1.94619i) q^{2} +(-3.57530 - 1.79367i) q^{4} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(-5.13836 + 6.13166i) q^{8} +(-5.35532 - 17.8741i) q^{10} +(1.85519 - 3.21328i) q^{11} +(11.0919 - 6.40390i) q^{13} +(7.78313 - 8.25318i) q^{14} +(9.56553 + 12.8258i) q^{16} -11.1817 q^{17} -13.1532 q^{19} +(-37.2542 + 2.18582i) q^{20} +(-5.39875 - 5.09127i) q^{22} +(-20.2104 + 11.6685i) q^{23} +(31.0204 - 53.7288i) q^{25} +(-7.35189 - 24.5379i) q^{26} +(-12.4757 - 18.9506i) q^{28} +(-14.6837 - 8.47767i) q^{29} +(-3.32057 + 1.91713i) q^{31} +(29.3693 - 12.7060i) q^{32} +(-5.15271 + 21.7618i) q^{34} +52.9184 q^{35} +13.8029i q^{37} +(-6.06117 + 25.5985i) q^{38} +(-12.9133 + 73.5109i) q^{40} +(-3.05861 - 5.29766i) q^{41} +(-11.3997 + 19.7448i) q^{43} +(-12.3964 + 8.16085i) q^{44} +(13.3958 + 44.7103i) q^{46} +(49.8977 + 28.8084i) q^{47} +(-8.41350 - 14.5726i) q^{49} +(-90.2718 - 85.1305i) q^{50} +(-51.1432 + 3.00073i) q^{52} +60.0402i q^{53} -34.6162i q^{55} +(-42.6305 + 15.5472i) q^{56} +(-23.2656 + 24.6707i) q^{58} +(55.3504 + 95.8696i) q^{59} +(73.2932 + 42.3159i) q^{61} +(2.20093 + 7.34589i) q^{62} +(-11.1944 - 63.0134i) q^{64} +(59.7456 - 103.482i) q^{65} +(16.0918 + 27.8718i) q^{67} +(39.9781 + 20.0563i) q^{68} +(24.3856 - 102.989i) q^{70} -38.7881i q^{71} -13.6313 q^{73} +(26.8631 + 6.36060i) q^{74} +(47.0264 + 23.5924i) q^{76} +(18.2261 - 10.5229i) q^{77} +(-4.14976 - 2.39586i) q^{79} +(137.115 + 59.0066i) q^{80} +(-11.7197 + 3.51138i) q^{82} +(2.70708 - 4.68879i) q^{83} +(-90.3444 + 52.1604i) q^{85} +(33.1740 + 31.2846i) q^{86} +(10.1701 + 27.8864i) q^{88} -98.2333 q^{89} +72.6474 q^{91} +(93.1876 - 5.46760i) q^{92} +(79.0602 - 83.8349i) q^{94} +(-106.273 + 61.3566i) q^{95} +(42.1665 - 73.0345i) q^{97} +(-32.2381 + 9.65898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more