LMFDB - Embedded newform 54.3.d.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,3,Mod(17,54)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("54.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	54.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47139342755$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	54.17
Dual form			54.3.d.a.35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(4.17423 + 7.22999i) q^{7} +2.82843i q^{8} -7.34847 q^{10} +(-0.825765 + 0.476756i) q^{11} +(4.84847 - 8.39780i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} -18.8776i q^{17} -24.6969 q^{19} +(9.00000 - 5.19615i) q^{20} +(0.674235 - 1.16781i) q^{22} +(-0.825765 - 0.476756i) q^{23} +(1.00000 + 1.73205i) q^{25} +13.7135i q^{26} +16.6969 q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(4.89898 + 2.82843i) q^{32} +(13.3485 + 23.1202i) q^{34} +43.3799i q^{35} +46.6969 q^{37} +(30.2474 - 17.4634i) q^{38} +(-7.34847 + 12.7279i) q^{40} +(9.45459 + 5.45861i) q^{41} +(-22.5227 - 39.0105i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(-39.2196 + 22.6435i) q^{47} +(-10.3485 + 17.9241i) q^{49} +(-2.44949 - 1.41421i) q^{50} +(-9.69694 - 16.7956i) q^{52} -94.3879i q^{53} -4.95459 q^{55} +(-20.4495 + 11.8065i) q^{56} +(9.67423 - 16.7563i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} -4.30686i q^{62} -8.00000 q^{64} +(43.6362 - 25.1934i) q^{65} +(-37.5227 + 64.9912i) q^{67} +(-32.6969 - 18.8776i) q^{68} +(-30.6742 - 53.1293i) q^{70} +18.0204i q^{71} -7.90918 q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(-6.89388 - 3.98018i) q^{77} +(21.8712 + 37.8820i) q^{79} -20.7846i q^{80} -15.4393 q^{82} +(112.871 - 65.1662i) q^{83} +(49.0454 - 84.9491i) q^{85} +(55.1691 + 31.8519i) q^{86} +(-1.34847 - 2.33562i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(-1.65153 + 0.953512i) q^{92} +(32.0227 - 55.4650i) q^{94} +(-111.136 - 64.1645i) q^{95} +(54.9393 + 95.1576i) q^{97} -29.2699i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7} - 18 q^{11} - 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 36 q^{20} - 12 q^{22} - 18 q^{23} + 4 q^{25} + 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} + 128 q^{37} + 72 q^{38}+ \cdots + 14 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 + 18 * q^5 + 2 * q^7 - 18 * q^11 - 10 * q^13 - 36 * q^14 - 8 * q^16 - 40 * q^19 + 36 * q^20 - 12 * q^22 - 18 * q^23 + 4 * q^25 + 8 * q^28 - 18 * q^29 + 38 * q^31 + 24 * q^34 + 128 * q^37 + 72 * q^38 + 126 * q^41 - 46 * q^43 - 24 * q^46 - 54 * q^47 - 12 * q^49 + 20 * q^52 - 108 * q^55 - 72 * q^56 + 24 * q^58 - 126 * q^59 + 62 * q^61 - 32 * q^64 - 90 * q^65 - 106 * q^67 - 72 * q^68 - 108 * q^70 - 208 * q^73 - 72 * q^74 - 40 * q^76 + 90 * q^77 + 14 * q^79 + 144 * q^82 + 378 * q^83 + 108 * q^85 + 108 * q^86 + 24 * q^88 + 412 * q^91 - 36 * q^92 + 84 * q^94 - 180 * q^95 + 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.877200	−	0.480125i	$-0.159409\pi$
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.0227998	+	0.999740i	$0.492742\pi$
$6$		0			0
$7$	4.17423	+	7.22999i	0.596319	+	1.03286i	0.993359	+	0.115054i	$0.0367041\pi$
$7$	4.17423	+	7.22999i	0.596319	+	1.03286i	−0.397040	+	0.917801i	$0.629963\pi$
$8$			2.82843i			0.353553i
$9$		0			0
$10$	−7.34847			−0.734847
$11$	−0.825765	+	0.476756i	−0.0750696	+	0.0433414i	−0.537065	−	0.843541i	$-0.680467\pi$
$11$	−0.825765	+	0.476756i	−0.0750696	+	0.0433414i	0.461995	+	0.886882i	$0.347134\pi$
$12$		0			0
$13$	4.84847	−	8.39780i	0.372959	−	0.645984i	−0.617060	−	0.786916i	$-0.711676\pi$
$13$	4.84847	−	8.39780i	0.372959	−	0.645984i	0.990019	+	0.140932i	$0.0450098\pi$
$14$	−10.2247	−	5.90326i	−0.730339	−	0.421661i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	18.8776i		−	1.11045i	−0.831701	−	0.555223i	$-0.812633\pi$
$17$		−	18.8776i		−	1.11045i	0.831701	−	0.555223i	$-0.187367\pi$
$18$		0			0
$19$	−24.6969			−1.29984			−0.649919	−	0.760003i	$-0.725197\pi$
$19$	−24.6969			−1.29984			−0.649919	+	0.760003i	$0.725197\pi$
$20$	9.00000	−	5.19615i	0.450000	−	0.259808i
$21$		0			0
$22$	0.674235	−	1.16781i	0.0306470	−	0.0530822i
$23$	−0.825765	−	0.476756i	−0.0359028	−	0.0207285i	0.481941	−	0.876204i	$-0.339932\pi$
$23$	−0.825765	−	0.476756i	−0.0359028	−	0.0207285i	−0.517844	+	0.855475i	$0.673265\pi$
$24$		0			0
$25$	1.00000	+	1.73205i	0.0400000	+	0.0692820i
$26$			13.7135i			0.527444i
$27$		0			0
$28$	16.6969			0.596319
$29$	−11.8485	+	6.84072i	−0.408568	+	0.235887i	−0.690174	−	0.723643i	$-0.742466\pi$
$29$	−11.8485	+	6.84072i	−0.408568	+	0.235887i	0.281606	+	0.959530i	$0.409133\pi$
$30$		0			0
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	−0.889540	−	0.456858i	$-0.848975\pi$
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	0.840420	+	0.541935i	$0.182308\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$		0			0
$34$	13.3485	+	23.1202i	0.392602	+	0.680007i
$35$			43.3799i			1.23943i
$36$		0			0
$37$	46.6969			1.26208			0.631040	−	0.775751i	$-0.282628\pi$
$37$	46.6969			1.26208			0.631040	+	0.775751i	$0.282628\pi$
$38$	30.2474	−	17.4634i	0.795985	−	0.459562i
$39$		0			0
$40$	−7.34847	+	12.7279i	−0.183712	+	0.318198i
$41$	9.45459	+	5.45861i	0.230600	+	0.133137i	0.610849	−	0.791747i	$-0.290828\pi$
$41$	9.45459	+	5.45861i	0.230600	+	0.133137i	−0.380249	+	0.924884i	$0.624162\pi$
$42$		0			0
$43$	−22.5227	−	39.0105i	−0.523784	−	0.907220i	−0.999617	−	0.0276845i	$-0.991187\pi$
$43$	−22.5227	−	39.0105i	−0.523784	−	0.907220i	0.475833	−	0.879536i	$-0.342147\pi$
$44$			1.90702i			0.0433414i
$45$		0			0
$46$	1.34847			0.0293145
$47$	−39.2196	+	22.6435i	−0.834460	+	0.481776i	−0.855377	−	0.518005i	$-0.826675\pi$
$47$	−39.2196	+	22.6435i	−0.834460	+	0.481776i	0.0209170	+	0.999781i	$0.493341\pi$
$48$		0			0
$49$	−10.3485	+	17.9241i	−0.211193	+	0.365797i
$50$	−2.44949	−	1.41421i	−0.0489898	−	0.0282843i
$51$		0			0
$52$	−9.69694	−	16.7956i	−0.186480	−	0.322992i
$53$		−	94.3879i		−	1.78090i	−0.455077	−	0.890452i	$-0.650388\pi$
$53$		−	94.3879i		−	1.78090i	0.455077	−	0.890452i	$-0.349612\pi$
$54$		0			0
$55$	−4.95459			−0.0900835
$56$	−20.4495	+	11.8065i	−0.365169	+	0.210831i
$57$		0			0
$58$	9.67423	−	16.7563i	0.166797	−	0.288901i
$59$	16.2650	+	9.39063i	0.275679	+	0.159163i	0.631466	−	0.775404i	$-0.282454\pi$
$59$	16.2650	+	9.39063i	0.275679	+	0.159163i	−0.355787	+	0.934567i	$0.615787\pi$
$60$		0			0
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	0.807375	−	0.590039i	$-0.200888\pi$
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	−0.914676	+	0.404187i	$0.867554\pi$
$62$		−	4.30686i		−	0.0694654i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	43.6362	−	25.1934i	0.671327	−	0.387591i
$66$		0			0
$67$	−37.5227	+	64.9912i	−0.560040	+	0.970018i	0.437452	+	0.899242i	$0.355881\pi$
$67$	−37.5227	+	64.9912i	−0.560040	+	0.970018i	−0.997492	+	0.0707765i	$0.977452\pi$
$68$	−32.6969	−	18.8776i	−0.480837	−	0.277612i
$69$		0			0
$70$	−30.6742	−	53.1293i	−0.438203	−	0.758990i
$71$			18.0204i			0.253808i	0.991915	+	0.126904i	$0.0405041\pi$
$71$			18.0204i			0.253808i	−0.991915	+	0.126904i	$0.959496\pi$
$72$		0			0
$73$	−7.90918			−0.108345			−0.0541725	−	0.998532i	$-0.517252\pi$
$73$	−7.90918			−0.108345			−0.0541725	+	0.998532i	$0.517252\pi$
$74$	−57.1918	+	33.0197i	−0.772863	+	0.446212i
$75$		0			0
$76$	−24.6969	+	42.7764i	−0.324960	+	0.562847i
$77$	−6.89388	−	3.98018i	−0.0895309	−	0.0516907i
$78$		0			0
$79$	21.8712	+	37.8820i	0.276850	+	0.479519i	0.970600	−	0.240697i	$-0.0773761\pi$
$79$	21.8712	+	37.8820i	0.276850	+	0.479519i	−0.693750	+	0.720216i	$0.744043\pi$
$80$		−	20.7846i		−	0.259808i
$81$		0			0
$82$	−15.4393			−0.188284
$83$	112.871	−	65.1662i	1.35989	−	0.785135i	0.370284	−	0.928918i	$-0.379260\pi$
$83$	112.871	−	65.1662i	1.35989	−	0.785135i	0.989609	+	0.143783i	$0.0459269\pi$
$84$		0			0
$85$	49.0454	−	84.9491i	0.577005	−	0.999402i
$86$	55.1691	+	31.8519i	0.641502	+	0.370371i
$87$		0			0
$88$	−1.34847	−	2.33562i	−0.0153235	−	0.0265411i
$89$			145.300i			1.63258i	0.577642	+	0.816290i	$0.303973\pi$
$89$			145.300i			1.63258i	−0.577642	+	0.816290i	$0.696027\pi$
$90$		0			0
$91$	80.9546			0.889611
$92$	−1.65153	+	0.953512i	−0.0179514	+	0.0103643i
$93$		0			0
$94$	32.0227	−	55.4650i	0.340667	−	0.590053i
$95$	−111.136	−	64.1645i	−1.16985	−	0.675416i
$96$		0			0
$97$	54.9393	+	95.1576i	0.566384	+	0.981007i	0.996919	+	0.0784327i	$0.0249916\pi$
$97$	54.9393	+	95.1576i	0.566384	+	0.981007i	−0.430535	+	0.902574i	$0.641675\pi$
$98$		−	29.2699i		−	0.298672i
$99$		0			0
$100$	4.00000			0.0400000
$101$	−127.772	+	73.7695i	−1.26507	+	0.730391i	−0.974052	−	0.226326i	$-0.927329\pi$
$101$	−127.772	+	73.7695i	−1.26507	+	0.730391i	−0.291022	+	0.956716i	$0.593995\pi$
$102$		0			0
$103$	51.5681	−	89.3186i	0.500661	−	0.867171i	−0.499338	−	0.866407i	$-0.666424\pi$
$103$	51.5681	−	89.3186i	0.500661	−	0.867171i	1.00000		0.000763745i	$-0.000243108\pi$
$104$	23.7526	+	13.7135i	0.228390	+	0.131861i
$105$		0			0
$106$	66.7423	+	115.601i	0.629645	+	1.09058i
$107$			36.0408i			0.336830i	0.985716	+	0.168415i	$0.0538649\pi$
$107$			36.0408i			0.336830i	−0.985716	+	0.168415i	$0.946135\pi$
$108$		0			0
$109$	−148.272			−1.36030			−0.680149	−	0.733074i	$-0.738085\pi$
$109$	−148.272			−1.36030			−0.680149	+	0.733074i	$0.738085\pi$
$110$	6.06811	−	3.50343i	0.0551647	−	0.0318493i
$111$		0			0
$112$	16.6969	−	28.9199i	0.149080	−	0.258214i
$113$	148.166	+	85.5439i	1.31121	+	0.757025i	0.982296	−	0.187336i	$-0.0599852\pi$
$113$	148.166	+	85.5439i	1.31121	+	0.757025i	0.328910	+	0.944361i	$0.393319\pi$
$114$		0			0
$115$	−2.47730	−	4.29080i	−0.0215417	−	0.0373113i
$116$			27.3629i			0.235887i
$117$		0			0
$118$	−26.5607			−0.225091
$119$	136.485	−	78.7995i	1.14693	−	0.662180i
$120$		0			0
$121$	−60.0454	+	104.002i	−0.496243	+	0.859518i
$122$	16.0329	+	9.25660i	0.131417	+	0.0758738i
$123$		0			0
$124$	3.04541	+	5.27480i	0.0245597	+	0.0425387i
$125$		−	119.512i		−	0.956092i
$126$		0			0
$127$	−78.0908			−0.614888			−0.307444	−	0.951566i	$-0.599474\pi$
$127$	−78.0908			−0.614888			−0.307444	+	0.951566i	$0.599474\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−35.6288	+	61.7109i	−0.274068	+	0.474700i
$131$	−202.704	−	117.031i	−1.54736	−	0.893369i	−0.998342	−	0.0575598i	$-0.981668\pi$
$131$	−202.704	−	117.031i	−1.54736	−	0.893369i	−0.549019	−	0.835810i	$-0.684999\pi$
$132$		0			0
$133$	−103.091	−	178.559i	−0.775119	−	1.34255i
$134$		−	106.130i		−	0.792017i
$135$		0			0
$136$	53.3939			0.392602
$137$	−129.758	+	74.9156i	−0.947136	+	0.546829i	−0.892190	−	0.451660i	$-0.850832\pi$
$137$	−129.758	+	74.9156i	−0.947136	+	0.546829i	−0.0549460	+	0.998489i	$0.517499\pi$
$138$		0			0
$139$	42.2650	−	73.2052i	0.304065	−	0.526656i	−0.672988	−	0.739654i	$-0.734989\pi$
$139$	42.2650	−	73.2052i	0.304065	−	0.526656i	0.977053	+	0.212998i	$0.0683226\pi$
$140$	75.1362	+	43.3799i	0.536687	+	0.309857i
$141$		0			0
$142$	−12.7423	−	22.0704i	−0.0897348	−	0.155425i
$143$			9.24614i			0.0646584i
$144$		0			0
$145$	−71.0908			−0.490281
$146$	9.68673	−	5.59264i	0.0663475	−	0.0383057i
$147$		0			0
$148$	46.6969	−	80.8815i	0.315520	−	0.546496i
$149$	−100.030	−	57.7524i	−0.671343	−	0.387600i	0.125242	−	0.992126i	$-0.460029\pi$
$149$	−100.030	−	57.7524i	−0.671343	−	0.387600i	−0.796585	+	0.604526i	$0.793362\pi$
$150$		0			0
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	0.953112	−	0.302619i	$-0.0978610\pi$
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	−0.738632	+	0.674109i	$0.764528\pi$
$152$		−	69.8535i		−	0.459562i
$153$		0			0
$154$	11.2577			0.0731016
$155$	−13.7043	+	7.91220i	−0.0884151	+	0.0510465i
$156$		0			0
$157$	10.4092	−	18.0292i	0.0663005	−	0.114836i	−0.830970	−	0.556318i	$-0.812214\pi$
$157$	10.4092	−	18.0292i	0.0663005	−	0.114836i	0.897270	+	0.441482i	$0.145547\pi$
$158$	−53.5732	−	30.9305i	−0.339071	−	0.195763i
$159$		0			0
$160$	14.6969	+	25.4558i	0.0918559	+	0.159099i
$161$		−	7.96036i		−	0.0494433i
$162$		0			0
$163$	133.060			0.816320			0.408160	−	0.912910i	$-0.366171\pi$
$163$	133.060			0.816320			0.408160	+	0.912910i	$0.366171\pi$
$164$	18.9092	−	10.9172i	0.115300	−	0.0665684i
$165$		0			0
$166$	−92.1589	+	159.624i	−0.555174	+	0.961590i
$167$	255.053	+	147.255i	1.52726	+	0.881765i	0.999475	+	0.0323885i	$0.0103114\pi$
$167$	255.053	+	147.255i	1.52726	+	0.881765i	0.527787	+	0.849377i	$0.323022\pi$
$168$		0			0
$169$	37.4847	+	64.9254i	0.221803	+	0.384174i
$170$			138.721i			0.816008i
$171$		0			0
$172$	−90.0908			−0.523784
$173$	59.9847	−	34.6322i	0.346732	−	0.200186i	−0.316513	−	0.948588i	$-0.602512\pi$
$173$	59.9847	−	34.6322i	0.346732	−	0.200186i	0.663245	+	0.748402i	$0.269179\pi$
$174$		0			0
$175$	−8.34847	+	14.4600i	−0.0477055	+	0.0826284i
$176$	3.30306	+	1.90702i	0.0187674	+	0.0108354i
$177$		0			0
$178$	−102.742	−	177.955i	−0.577204	−	0.999747i
$179$			47.4829i			0.265268i	0.991165	+	0.132634i	$0.0423435\pi$
$179$			47.4829i			0.265268i	−0.991165	+	0.132634i	$0.957657\pi$
$180$		0			0
$181$	242.879			1.34187			0.670935	−	0.741516i	$-0.265893\pi$
$181$	242.879			1.34187			0.670935	+	0.741516i	$0.265893\pi$
$182$	−99.1487	+	57.2435i	−0.544773	+	0.314525i
$183$		0			0
$184$	1.34847	−	2.33562i	0.00732864	−	0.0126936i
$185$	210.136	+	121.322i	1.13587	+	0.655796i
$186$		0			0
$187$	9.00000	+	15.5885i	0.0481283	+	0.0833607i
$188$			90.5739i			0.481776i
$189$		0			0
$190$	181.485			0.955183
$191$	−6.52270	+	3.76588i	−0.0341503	+	0.0197167i	−0.516978	−	0.855999i	$-0.672943\pi$
$191$	−6.52270	+	3.76588i	−0.0341503	+	0.0197167i	0.482828	+	0.875715i	$0.339610\pi$
$192$		0			0
$193$	−172.727	+	299.172i	−0.894959	+	1.55011i	−0.0611031	+	0.998131i	$0.519462\pi$
$193$	−172.727	+	299.172i	−0.894959	+	1.55011i	−0.833856	+	0.551983i	$0.813871\pi$
$194$	−134.573	−	77.6959i	−0.693676	−	0.400494i
$195$		0			0
$196$	20.6969	+	35.8481i	0.105597	+	0.182899i
$197$			77.2247i			0.392004i	0.980604	+	0.196002i	$0.0627959\pi$
$197$			77.2247i			0.392004i	−0.980604	+	0.196002i	$0.937204\pi$
$198$		0			0
$199$	153.485			0.771280			0.385640	−	0.922649i	$-0.373981\pi$
$199$	153.485			0.771280			0.385640	+	0.922649i	$0.373981\pi$
$200$	−4.89898	+	2.82843i	−0.0244949	+	0.0141421i
$201$		0			0
$202$	104.326	−	180.698i	0.516464	−	0.894542i
$203$	−98.9166	−	57.1095i	−0.487274	−	0.281328i
$204$		0			0
$205$	28.3638	+	49.1275i	0.138360	+	0.239646i
$206$			145.857i			0.708042i
$207$		0			0
$208$	−38.7878			−0.186480
$209$	20.3939	−	11.7744i	0.0975784	−	0.0563369i
$210$		0			0
$211$	25.7804	−	44.6529i	0.122182	−	0.211625i	−0.798446	−	0.602066i	$-0.794344\pi$
$211$	25.7804	−	44.6529i	0.122182	−	0.211625i	0.920628	+	0.390441i	$0.127678\pi$
$212$	−163.485	−	94.3879i	−0.771154	−	0.445226i
$213$		0			0
$214$	−25.4847	−	44.1408i	−0.119087	−	0.206265i
$215$		−	234.063i		−	1.08866i
$216$		0			0
$217$	−25.4245			−0.117164
$218$	181.596	−	104.844i	0.833009	−	0.480938i
$219$		0			0
$220$	−4.95459	+	8.58161i	−0.0225209	+	0.0390073i
$221$	−158.530	−	91.5274i	−0.717331	−	0.414151i
$222$		0			0
$223$	−156.614	−	271.263i	−0.702303	−	1.21642i	−0.967656	−	0.252273i	$-0.918822\pi$
$223$	−156.614	−	271.263i	−0.702303	−	1.21642i	0.265353	−	0.964151i	$-0.414511\pi$
$224$			47.2261i			0.210831i
$225$		0			0
$226$	−241.955			−1.07060
$227$	66.0528	−	38.1356i	0.290982	−	0.167998i	−0.347403	−	0.937716i	$-0.612936\pi$
$227$	66.0528	−	38.1356i	0.290982	−	0.167998i	0.638384	+	0.769718i	$0.279603\pi$
$228$		0			0
$229$	60.7724	−	105.261i	0.265382	−	0.459655i	−0.702282	−	0.711899i	$-0.747835\pi$
$229$	60.7724	−	105.261i	0.265382	−	0.459655i	0.967664	+	0.252244i	$0.0811686\pi$
$230$	6.06811	+	3.50343i	0.0263831	+	0.0152323i
$231$		0			0
$232$	−19.3485	−	33.5125i	−0.0833986	−	0.144451i
$233$		−	151.021i		−	0.648157i	−0.946030	−	0.324079i	$-0.894946\pi$
$233$		−	151.021i		−	0.648157i	0.946030	−	0.324079i	$-0.105054\pi$
$234$		0			0
$235$	−235.318			−1.00135
$236$	32.5301	−	18.7813i	0.137839	−	0.0795816i
$237$		0			0
$238$	−111.439	+	193.019i	−0.468232	+	0.811002i
$239$	75.9620	+	43.8567i	0.317833	+	0.183501i	0.650426	−	0.759570i	$-0.274590\pi$
$239$	75.9620	+	43.8567i	0.317833	+	0.183501i	−0.332593	+	0.943070i	$0.607924\pi$
$240$		0			0
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	0.577157	−	0.816633i	$-0.304162\pi$
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	−0.995804	+	0.0915158i	$0.970829\pi$
$242$		−	169.834i		−	0.701794i
$243$		0			0
$244$	−26.1816			−0.107302
$245$	−93.1362	+	53.7722i	−0.380148	+	0.219478i
$246$		0			0
$247$	−119.742	+	207.400i	−0.484787	+	0.839675i
$248$	−7.45969	−	4.30686i	−0.0300794	−	0.0173664i
$249$		0			0
$250$	84.5074	+	146.371i	0.338030	+	0.585484i
$251$			52.6261i			0.209666i	0.994490	+	0.104833i	$0.0334307\pi$
$251$			52.6261i			0.209666i	−0.994490	+	0.104833i	$0.966569\pi$
$252$		0			0
$253$	0.909185			0.00359362
$254$	95.6413	−	55.2185i	0.376541	−	0.217396i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	69.8939	+	40.3532i	0.271961	+	0.157017i	0.629778	−	0.776775i	$-0.283146\pi$
$257$	69.8939	+	40.3532i	0.271961	+	0.157017i	−0.357818	+	0.933791i	$0.616479\pi$
$258$		0			0
$259$	194.924	+	337.618i	0.752602	+	1.30355i
$260$		−	100.774i		−	0.387591i
$261$		0			0
$262$	331.015			1.26342
$263$	−401.614	+	231.872i	−1.52705	+	0.881641i	−0.527564	+	0.849515i	$0.676894\pi$
$263$	−401.614	+	231.872i	−1.52705	+	0.881641i	−0.999484	+	0.0321259i	$0.989772\pi$
$264$		0			0
$265$	245.227	−	424.746i	0.925385	−	1.60281i
$266$	252.520	+	145.792i	0.949323	+	0.548092i
$267$		0			0
$268$	75.0454	+	129.982i	0.280020	+	0.485009i
$269$		−	43.4762i		−	0.161622i	−0.996729	−	0.0808109i	$-0.974249\pi$
$269$		−	43.4762i		−	0.161622i	0.996729	−	0.0808109i	$-0.0257510\pi$
$270$		0			0
$271$	−342.636			−1.26434			−0.632169	−	0.774830i	$-0.717835\pi$
$271$	−342.636			−1.26434			−0.632169	+	0.774830i	$0.717835\pi$
$272$	−65.3939	+	37.7552i	−0.240419	+	0.138806i
$273$		0			0
$274$	105.947	−	183.505i	0.386667	−	0.669726i
$275$	−1.65153	−	0.953512i	−0.00600557	−	0.00346732i
$276$		0			0
$277$	24.5000	+	42.4352i	0.0884477	+	0.153196i	0.906855	−	0.421442i	$-0.138476\pi$
$277$	24.5000	+	42.4352i	0.0884477	+	0.153196i	−0.818407	+	0.574638i	$0.805143\pi$
$278$			119.544i			0.430013i
$279$		0			0
$280$	−122.697			−0.438203
$281$	17.8791	−	10.3225i	0.0636266	−	0.0367349i	−0.467849	−	0.883808i	$-0.654971\pi$
$281$	17.8791	−	10.3225i	0.0636266	−	0.0367349i	0.531476	+	0.847073i	$0.321638\pi$
$282$		0			0
$283$	−26.7043	+	46.2533i	−0.0943616	+	0.163439i	−0.909342	−	0.416049i	$-0.863414\pi$
$283$	−26.7043	+	46.2533i	−0.0943616	+	0.163439i	0.814980	+	0.579489i	$0.196748\pi$
$284$	31.2122	+	18.0204i	0.109902	+	0.0634521i
$285$		0			0
$286$	−6.53801	−	11.3242i	−0.0228602	−	0.0395950i
$287$			91.1421i			0.317568i
$288$		0			0
$289$	−67.3633			−0.233091
$290$	87.0681	−	50.2688i	0.300235	−	0.173341i
$291$		0			0
$292$	−7.90918	+	13.6991i	−0.0270862	+	0.0469148i
$293$	12.9245	+	7.46196i	0.0441109	+	0.0254674i	0.521893	−	0.853011i	$-0.325226\pi$
$293$	12.9245	+	7.46196i	0.0441109	+	0.0254674i	−0.477782	+	0.878478i	$0.658559\pi$
$294$		0			0
$295$	48.7951	+	84.5157i	0.165407	+	0.286494i
$296$			132.079i			0.446212i
$297$		0			0
$298$	163.348			0.548149
$299$	−8.00740	+	4.62307i	−0.0267806	+	0.0154618i
$300$		0			0
$301$	188.030	−	325.678i	0.624685	−	1.08199i
$302$	−79.3304	−	45.8014i	−0.262683	−	0.151660i
$303$		0			0
$304$	49.3939	+	85.5527i	0.162480	+	0.281423i
$305$		−	68.0219i		−	0.223023i
$306$		0			0
$307$	65.9092			0.214688			0.107344	−	0.994222i	$-0.465765\pi$
$307$	65.9092			0.214688			0.107344	+	0.994222i	$0.465765\pi$
$308$	−13.7878	+	7.96036i	−0.0447654	+	0.0258453i
$309$		0			0
$310$	11.1895	−	19.3809i	0.0360953	−	0.0625189i
$311$	216.659	+	125.088i	0.696652	+	0.402213i	0.806099	−	0.591780i	$-0.201575\pi$
$311$	216.659	+	125.088i	0.696652	+	0.402213i	−0.109447	+	0.993993i	$0.534908\pi$
$312$		0			0
$313$	213.197	+	369.268i	0.681140	+	1.17977i	0.974633	+	0.223808i	$0.0718490\pi$
$313$	213.197	+	369.268i	0.681140	+	1.17977i	−0.293493	+	0.955961i	$0.594818\pi$
$314$			29.4416i			0.0937631i
$315$		0			0
$316$	87.4847			0.276850
$317$	401.818	−	231.990i	1.26756	−	0.731829i	0.293038	−	0.956101i	$-0.405334\pi$
$317$	401.818	−	231.990i	1.26756	−	0.731829i	0.974527	+	0.224272i	$0.0720005\pi$
$318$		0			0
$319$	6.52270	−	11.2977i	0.0204473	−	0.0354158i
$320$	−36.0000	−	20.7846i	−0.112500	−	0.0649519i
$321$		0			0
$322$	5.62883	+	9.74941i	0.0174808	+	0.0302777i
$323$			466.219i			1.44340i
$324$		0			0
$325$	19.3939			0.0596735
$326$	−162.965	+	94.0878i	−0.499892	+	0.288613i
$327$		0			0
$328$	−15.4393	+	26.7416i	−0.0470710	+	0.0815293i
$329$	−327.424	−	189.038i	−0.995210	−	0.574585i
$330$		0			0
$331$	−236.401	−	409.459i	−0.714203	−	1.23704i	−0.963266	−	0.268549i	$-0.913456\pi$
$331$	−236.401	−	409.459i	−0.714203	−	1.23704i	0.249063	−	0.968487i	$-0.419877\pi$
$332$		−	260.665i		−	0.785135i
$333$		0			0
$334$	−416.499			−1.24700
$335$	−337.704	+	194.974i	−1.00807	+	0.582011i
$336$		0			0
$337$	−152.803	+	264.663i	−0.453422	+	0.785349i	−0.998596	−	0.0529735i	$-0.983130\pi$
$337$	−152.803	+	264.663i	−0.453422	+	0.785349i	0.545174	+	0.838323i	$0.316463\pi$
$338$	−91.8184	−	53.0114i	−0.271652	−	0.156838i
$339$		0			0
$340$	−98.0908	−	169.898i	−0.288502	−	0.499701i
$341$		−	2.90383i		−	0.00851564i
$342$		0			0
$343$	236.287			0.688884
$344$	110.338	−	63.7038i	0.320751	−	0.185186i
$345$		0			0
$346$	−48.9773	+	84.8312i	−0.141553	+	0.245177i
$347$	−115.766	−	66.8373i	−0.333618	−	0.192615i	0.323828	−	0.946116i	$-0.395030\pi$
$347$	−115.766	−	66.8373i	−0.333618	−	0.192615i	−0.657446	+	0.753501i	$0.728363\pi$
$348$		0			0
$349$	49.3786	+	85.5262i	0.141486	+	0.245061i	0.928056	−	0.372440i	$-0.121479\pi$
$349$	49.3786	+	85.5262i	0.141486	+	0.245061i	−0.786570	+	0.617500i	$0.788145\pi$
$350$		−	23.6130i		−	0.0674658i
$351$		0			0
$352$	−5.39388			−0.0153235
$353$	282.424	−	163.058i	0.800068	−	0.461919i	−0.0434270	−	0.999057i	$-0.513828\pi$
$353$	282.424	−	163.058i	0.800068	−	0.461919i	0.843495	+	0.537137i	$0.180494\pi$
$354$		0			0
$355$	−46.8184	+	81.0918i	−0.131883	+	0.228428i
$356$	251.666	+	145.300i	0.706928	+	0.408145i
$357$		0			0
$358$	−33.5755	−	58.1545i	−0.0937863	−	0.162443i
$359$		−	418.736i		−	1.16639i	−0.812331	−	0.583197i	$-0.801801\pi$
$359$		−	418.736i		−	1.16639i	0.812331	−	0.583197i	$-0.198199\pi$
$360$		0			0
$361$	248.939			0.689581
$362$	−297.464	+	171.741i	−0.821725	+	0.474423i
$363$		0			0
$364$	80.9546	−	140.217i	0.222403	−	0.385213i
$365$	−35.5913	−	20.5487i	−0.0975105	−	0.0562977i
$366$		0			0
$367$	−93.6135	−	162.143i	−0.255078	−	0.441808i	0.709839	−	0.704364i	$-0.248768\pi$
$367$	−93.6135	−	162.143i	−0.255078	−	0.441808i	−0.964917	+	0.262557i	$0.915434\pi$
$368$			3.81405i			0.0103643i
$369$		0			0
$370$	−343.151			−0.927435
$371$	682.423	−	393.997i	1.83942	−	1.06199i
$372$		0			0
$373$	−225.515	+	390.603i	−0.604597	+	1.04719i	0.387518	+	0.921862i	$0.373333\pi$
$373$	−225.515	+	390.603i	−0.604597	+	1.04719i	−0.992115	+	0.125331i	$0.960001\pi$
$374$	−22.0454	−	12.7279i	−0.0589449	−	0.0340319i
$375$		0			0
$376$	−64.0454	−	110.930i	−0.170334	−	0.295026i
$377$			132.668i			0.351905i
$378$		0			0
$379$	−489.666			−1.29200			−0.645998	−	0.763339i	$-0.723558\pi$
$379$	−489.666			−1.29200			−0.645998	+	0.763339i	$0.723558\pi$
$380$	−222.272	+	128.329i	−0.584927	+	0.337708i
$381$		0			0
$382$	5.32577	−	9.22450i	0.0139418	−	0.0241479i
$383$	−89.2492	−	51.5281i	−0.233027	−	0.134538i	0.378941	−	0.925421i	$-0.376288\pi$
$383$	−89.2492	−	51.5281i	−0.233027	−	0.134538i	−0.611968	+	0.790883i	$0.709622\pi$
$384$		0			0
$385$	−20.6816	−	35.8216i	−0.0537185	−	0.0930432i
$386$		−	488.546i		−	1.26566i
$387$		0			0
$388$	219.757			0.566384
$389$	−29.6816	+	17.1367i	−0.0763024	+	0.0440532i	−0.537666	−	0.843158i	$-0.680694\pi$
$389$	−29.6816	+	17.1367i	−0.0763024	+	0.0440532i	0.461363	+	0.887211i	$0.347360\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	−50.6969	−	29.2699i	−0.129329	−	0.0746681i
$393$		0			0
$394$	−54.6061	−	94.5806i	−0.138594	−	0.240052i
$395$			227.292i			0.575423i
$396$		0			0
$397$	8.27245			0.0208374			0.0104187	−	0.999946i	$-0.496684\pi$
$397$	8.27245			0.0208374			0.0104187	+	0.999946i	$0.496684\pi$
$398$	−187.980	+	108.530i	−0.472311	+	0.272689i
$399$		0			0
$400$	4.00000	−	6.92820i	0.0100000	−	0.0173205i
$401$	−358.636	−	207.059i	−0.894355	−	0.516356i	−0.0189903	−	0.999820i	$-0.506045\pi$
$401$	−358.636	−	207.059i	−0.894355	−	0.516356i	−0.875364	+	0.483464i	$0.839378\pi$
$402$		0			0
$403$	14.7656	+	25.5747i	0.0366391	+	0.0634608i
$404$			295.078i			0.730391i
$405$		0			0
$406$	161.530			0.397857
$407$	−38.5607	+	22.2630i	−0.0947438	+	0.0547003i
$408$		0			0
$409$	163.106	−	282.508i	0.398792	−	0.690729i	−0.594785	−	0.803885i	$-0.702763\pi$
$409$	163.106	−	282.508i	0.398792	−	0.690729i	0.993577	+	0.113156i	$0.0360960\pi$
$410$	−69.4768	−	40.1124i	−0.169456	−	0.0978352i
$411$		0			0
$412$	−103.136	−	178.637i	−0.250331	−	0.433585i
$413$			156.795i			0.379648i
$414$		0			0
$415$	677.227			1.63187
$416$	47.5051	−	27.4271i	0.114195	−	0.0659305i
$417$		0			0
$418$	−16.6515	+	28.8413i	−0.0398362	+	0.0689983i
$419$	468.325	+	270.388i	1.11772	+	0.645317i	0.940818	−	0.338912i	$-0.110059\pi$
$419$	468.325	+	270.388i	1.11772	+	0.645317i	0.176903	+	0.984228i	$0.443392\pi$
$420$		0			0
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	0.646922	−	0.762556i	$-0.276056\pi$
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	−0.983854	+	0.178973i	$0.942723\pi$
$422$			72.9179i			0.172791i
$423$		0			0
$424$	266.969			0.629645
$425$	32.6969	−	18.8776i	0.0769340	−	0.0444178i
$426$		0			0
$427$	54.6441	−	94.6464i	0.127972	−	0.221654i
$428$	62.4245	+	36.0408i	0.145852	+	0.0842075i
$429$		0			0
$430$	165.507	+	286.667i	0.384901	+	0.666668i
$431$		−	257.429i		−	0.597282i	−0.954365	−	0.298641i	$-0.903467\pi$
$431$		−	257.429i		−	0.597282i	0.954365	−	0.298641i	$-0.0965334\pi$
$432$		0			0
$433$	476.272			1.09994			0.549968	−	0.835186i	$-0.314640\pi$
$433$	476.272			1.09994			0.549968	+	0.835186i	$0.314640\pi$
$434$	31.1385	−	17.9778i	0.0717477	−	0.0414236i
$435$		0			0
$436$	−148.272	+	256.815i	−0.340074	+	0.589026i
$437$	20.3939	+	11.7744i	0.0466679	+	0.0269437i
$438$		0			0
$439$	278.931	+	483.123i	0.635379	+	1.10051i	0.986435	+	0.164154i	$0.0524894\pi$
$439$	278.931	+	483.123i	0.635379	+	1.10051i	−0.351056	+	0.936355i	$0.614177\pi$
$440$		−	14.0137i		−	0.0318493i
$441$		0			0
$442$	258.879			0.585698
$443$	−720.400	+	415.923i	−1.62619	+	0.938879i	−0.640969	+	0.767567i	$0.721467\pi$
$443$	−720.400	+	415.923i	−1.62619	+	0.938879i	−0.985217	+	0.171312i	$0.945199\pi$
$444$		0			0
$445$	−377.499	+	653.848i	−0.848313	+	1.46932i
$446$	383.623	+	221.485i	0.860142	+	0.496603i
$447$		0			0
$448$	−33.3939	−	57.8399i	−0.0745399	−	0.129107i
$449$			729.927i			1.62567i	0.582492	+	0.812836i	$0.302078\pi$
$449$			729.927i			1.62567i	−0.582492	+	0.812836i	$0.697922\pi$
$450$		0			0
$451$	−10.4097			−0.0230814
$452$	296.333	−	171.088i	0.655603	−	0.378513i
$453$		0			0
$454$	−53.9319	+	93.4128i	−0.118793	+	0.205755i
$455$	364.296	+	210.326i	0.800650	+	0.462255i
$456$		0			0
$457$	−354.818	−	614.563i	−0.776407	−	1.34478i	−0.934000	−	0.357272i	$-0.883707\pi$
$457$	−354.818	−	614.563i	−0.776407	−	1.34478i	0.157594	−	0.987504i	$-0.449626\pi$
$458$			171.890i			0.375307i
$459$		0			0
$460$	−9.90918			−0.0215417
$461$	7.96990	−	4.60142i	0.0172883	−	0.00998140i	−0.491331	−	0.870973i	$-0.663489\pi$
$461$	7.96990	−	4.60142i	0.0172883	−	0.00998140i	0.508619	+	0.860992i	$0.330156\pi$
$462$		0			0
$463$	27.5987	−	47.8024i	0.0596085	−	0.103245i	−0.834681	−	0.550733i	$-0.814348\pi$
$463$	27.5987	−	47.8024i	0.0596085	−	0.103245i	0.894290	+	0.447488i	$0.147681\pi$
$464$	47.3939	+	27.3629i	0.102142	+	0.0589717i
$465$		0			0
$466$	106.788	+	184.962i	0.229158	+	0.396914i
$467$		−	625.811i		−	1.34007i	−0.742331	−	0.670033i	$-0.766280\pi$
$467$		−	625.811i		−	1.34007i	0.742331	−	0.670033i	$-0.233720\pi$
$468$		0			0
$469$	−626.514			−1.33585
$470$	288.204	−	166.395i	0.613201	−	0.354032i
$471$		0			0
$472$	−26.5607	+	46.0045i	−0.0562727	+	0.0974672i
$473$	37.1969	+	21.4757i	0.0786405	+	0.0454031i
$474$		0			0
$475$	−24.6969	−	42.7764i	−0.0519936	−	0.0900555i
$476$		−	315.198i		−	0.662180i
$477$		0			0
$478$	−124.045			−0.259509
$479$	−267.856	+	154.647i	−0.559199	+	0.322854i	−0.752824	−	0.658222i	$-0.771309\pi$
$479$	−267.856	+	154.647i	−0.559199	+	0.322854i	0.193625	+	0.981076i	$0.437976\pi$
$480$		0			0
$481$	226.409	−	392.151i	0.470704	−	0.815283i
$482$	247.139	+	142.685i	0.512736	+	0.296028i
$483$		0			0
$484$	120.091	+	208.003i	0.248122	+	0.429759i
$485$			570.946i			1.17721i
$486$		0			0
$487$	−28.3337			−0.0581800			−0.0290900	−	0.999577i	$-0.509261\pi$
$487$	−28.3337			−0.0581800			−0.0290900	+	0.999577i	$0.509261\pi$
$488$	32.0658	−	18.5132i	0.0657086	−	0.0379369i
$489$		0			0
$490$	76.0454	−	131.715i	0.155195	−	0.268805i
$491$	−822.461	−	474.848i	−1.67507	−	0.967105i	−0.964727	−	0.263254i	$-0.915204\pi$
$491$	−822.461	−	474.848i	−1.67507	−	0.967105i	−0.710348	−	0.703851i	$-0.751462\pi$
$492$		0			0
$493$	129.136	+	223.670i	0.261940	+	0.453693i
$494$		−	338.682i		−	0.685592i
$495$		0			0
$496$	12.1816			0.0245597
$497$	−130.287	+	75.2214i	−0.262147	+	0.151351i
$498$		0			0
$499$	280.113	−	485.170i	0.561349	−	0.972284i	−0.436030	−	0.899932i	$-0.643616\pi$
$499$	280.113	−	485.170i	0.561349	−	0.972284i	0.997379	−	0.0723525i	$-0.0230507\pi$
$500$	−207.000	−	119.512i	−0.414000	−	0.239023i
$501$		0			0
$502$	−37.2122	−	64.4535i	−0.0741280	−	0.128393i
$503$		−	897.832i		−	1.78495i	−0.451094	−	0.892477i	$-0.648966\pi$
$503$		−	897.832i		−	1.78495i	0.451094	−	0.892477i	$-0.351034\pi$
$504$		0			0
$505$	−766.635			−1.51809
$506$	−1.11352	+	0.642891i	−0.00220063	+	0.00127053i
$507$		0			0
$508$	−78.0908	+	135.257i	−0.153722	+	0.266254i
$509$	170.454	+	98.4114i	0.334879	+	0.193343i	0.658005	−	0.753013i	$-0.271400\pi$
$509$	170.454	+	98.4114i	0.334879	+	0.193343i	−0.323126	+	0.946356i	$0.604734\pi$
$510$		0			0
$511$	−33.0148	−	57.1833i	−0.0646082	−	0.111905i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−114.136			−0.222055
$515$	464.113	−	267.956i	0.901190	−	0.520302i
$516$		0			0
$517$	21.5908	−	37.3964i	0.0417617	−	0.0723334i
$518$	−477.464	−	275.664i	−0.921746	−	0.532170i
$519$		0			0
$520$	71.2577	+	123.422i	0.137034	+	0.237350i
$521$		−	375.837i		−	0.721377i	−0.932686	−	0.360688i	$-0.882542\pi$
$521$		−	375.837i		−	0.721377i	0.932686	−	0.360688i	$-0.117458\pi$
$522$		0			0
$523$	91.1827			0.174345			0.0871727	−	0.996193i	$-0.472217\pi$
$523$	91.1827			0.174345			0.0871727	+	0.996193i	$0.472217\pi$
$524$	−405.409	+	234.063i	−0.773681	+	0.446685i
$525$		0			0
$526$	327.916	−	567.967i	0.623415	−	1.07979i
$527$	49.7878	+	28.7450i	0.0944739	+	0.0545445i
$528$		0			0
$529$	−264.045	−	457.340i	−0.499141	−	0.864537i
$530$			693.607i			1.30869i
$531$		0			0
$532$	−412.363			−0.775119
$533$	91.6806	−	52.9318i	0.172009	−	0.0993092i
$534$		0			0
$535$	−93.6367	+	162.184i	−0.175022	+	0.303147i
$536$	−183.823	−	106.130i	−0.342953	−	0.198004i
$537$		0			0
$538$	30.7423	+	53.2473i	0.0571419	+	0.0989727i
$539$		−	19.7348i		−	0.0366137i
$540$		0			0
$541$	−38.8490			−0.0718096			−0.0359048	−	0.999355i	$-0.511431\pi$
$541$	−38.8490			−0.0718096			−0.0359048	+	0.999355i	$0.511431\pi$
$542$	419.641	−	242.280i	0.774246	−	0.447011i
$543$		0			0
$544$	53.3939	−	92.4809i	0.0981505	−	0.170002i
$545$	−667.226	−	385.223i	−1.22427	−	0.706831i
$546$		0			0
$547$	233.022	+	403.606i	0.426000	+	0.737854i	0.996513	−	0.0834344i	$-0.0265889\pi$
$547$	233.022	+	403.606i	0.426000	+	0.737854i	−0.570513	+	0.821289i	$0.693256\pi$
$548$			299.662i			0.546829i
$549$		0			0
$550$	2.69694			0.00490352
$551$	292.621	−	168.945i	0.531072	−	0.306615i
$552$		0			0
$553$	−182.591	+	316.257i	−0.330182	+	0.571893i
$554$	−60.0125	−	34.6482i	−0.108326	−	0.0625419i
$555$		0			0
$556$	−84.5301	−	146.410i	−0.152033	−	0.263328i
$557$			695.042i			1.24783i	0.781492	+	0.623916i	$0.214459\pi$
$557$			695.042i			1.24783i	−0.781492	+	0.623916i	$0.785541\pi$
$558$		0			0
$559$	−436.803			−0.781400
$560$	150.272	−	86.7598i	0.268344	−	0.154928i
$561$		0			0
$562$	−14.5982	+	25.2848i	−0.0259755	+	0.0449908i
$563$	473.780	+	273.537i	0.841528	+	0.485857i	0.857783	−	0.514011i	$-0.171841\pi$
$563$	473.780	+	273.537i	0.841528	+	0.485857i	−0.0162552	+	0.999868i	$0.505174\pi$
$564$		0			0
$565$	444.499	+	769.895i	0.786724	+	1.36265i
$566$		−	75.5313i		−	0.133447i
$567$		0			0
$568$	−50.9694			−0.0897348
$569$	−215.954	+	124.681i	−0.379533	+	0.219123i	−0.677615	−	0.735417i	$-0.736986\pi$
$569$	−215.954	+	124.681i	−0.379533	+	0.219123i	0.298082	+	0.954540i	$0.403653\pi$
$570$		0			0
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	−0.896540	−	0.442963i	$-0.853927\pi$
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	0.831887	+	0.554945i	$0.187261\pi$
$572$	16.0148	+	9.24614i	0.0279979	+	0.0161646i
$573$		0			0
$574$	−64.4472	−	111.626i	−0.112277	−	0.194470i
$575$		−	1.90702i		−	0.00331656i
$576$		0			0
$577$	−43.9092			−0.0760991			−0.0380496	−	0.999276i	$-0.512114\pi$
$577$	−43.9092			−0.0760991			−0.0380496	+	0.999276i	$0.512114\pi$
$578$	82.5028	−	47.6330i	0.142738	−	0.0824101i
$579$		0			0
$580$	−71.0908	+	123.133i	−0.122570	+	0.212298i
$581$	942.302	+	544.038i	1.62186	+	0.936382i
$582$		0			0
$583$	45.0000	+	77.9423i	0.0771870	+	0.133692i
$584$		−	22.3706i		−	0.0383057i
$585$		0			0
$586$	−21.1056			−0.0360164
$587$	381.386	−	220.194i	0.649721	−	0.375117i	−0.138628	−	0.990345i	$-0.544269\pi$
$587$	381.386	−	220.194i	0.649721	−	0.375117i	0.788349	+	0.615228i	$0.210936\pi$
$588$		0			0
$589$	37.6061	−	65.1357i	0.0638474	−	0.110587i
$590$	−119.523	−	69.0068i	−0.202582	−	0.116961i
$591$		0			0
$592$	−93.3939	−	161.763i	−0.157760	−	0.273248i
$593$		−	347.232i		−	0.585551i	−0.956181	−	0.292776i	$-0.905421\pi$
$593$		−	347.232i		−	0.585551i	0.956181	−	0.292776i	$-0.0945789\pi$
$594$		0			0
$595$	818.908			1.37632
$596$	−200.060	+	115.505i	−0.335671	+	0.193800i
$597$		0			0
$598$	6.53801	−	11.3242i	0.0109331	−	0.0189367i
$599$	684.083	+	394.956i	1.14204	+	0.659359i	0.946936	−	0.321423i	$-0.104161\pi$
$599$	684.083	+	394.956i	1.14204	+	0.659359i	0.195107	+	0.980782i	$0.437495\pi$
$600$		0			0
$601$	353.455	+	612.201i	0.588111	+	1.01864i	0.994480	+	0.104929i	$0.0334614\pi$
$601$	353.455	+	612.201i	0.588111	+	1.01864i	−0.406369	+	0.913709i	$0.633205\pi$
$602$			531.829i			0.883438i
$603$		0			0
$604$	129.546			0.214480
$605$	−540.409	+	312.005i	−0.893237	+	0.515711i
$606$		0			0
$607$	596.628	−	1033.39i	0.982913	−	1.70246i	0.332048	−	0.943263i	$-0.392261\pi$
$607$	596.628	−	1033.39i	0.982913	−	1.70246i	0.650866	−	0.759193i	$-0.274406\pi$
$608$	−120.990	−	69.8535i	−0.198996	−	0.114891i
$609$		0			0
$610$	48.0987	+	83.3094i	0.0788504	+	0.136573i
$611$			439.145i			0.718731i
$612$		0			0
$613$	629.181			1.02640			0.513198	−	0.858270i	$-0.328461\pi$
$613$	629.181			1.02640			0.513198	+	0.858270i	$0.328461\pi$
$614$	−80.7219	+	46.6048i	−0.131469	+	0.0759036i
$615$		0			0
$616$	11.2577	−	19.4988i	0.0182754	−	0.0316539i
$617$	−166.909	−	96.3648i	−0.270516	−	0.156183i	0.358606	−	0.933489i	$-0.383252\pi$
$617$	−166.909	−	96.3648i	−0.270516	−	0.156183i	−0.629122	+	0.777306i	$0.716586\pi$
$618$		0			0
$619$	76.4773	+	132.463i	0.123550	+	0.213994i	0.921165	−	0.389172i	$-0.127239\pi$
$619$	76.4773	+	132.463i	0.123550	+	0.213994i	−0.797615	+	0.603166i	$0.793905\pi$
$620$			31.6488i			0.0510465i
$621$		0			0
$622$	−353.803			−0.568814
$623$	−1050.51	+	606.515i	−1.68622	+	0.973539i
$624$		0			0
$625$	335.500	−	581.103i	0.536800	−	0.929765i
$626$	−522.224	−	301.506i	−0.834223	−	0.481639i
$627$		0			0
$628$	−20.8184	−	36.0585i	−0.0331503	−	0.0574180i
$629$		−	881.525i		−	1.40147i
$630$		0			0
$631$	44.8786			0.0711229			0.0355615	−	0.999367i	$-0.488678\pi$
$631$	44.8786			0.0711229			0.0355615	+	0.999367i	$0.488678\pi$
$632$	−107.146	+	61.8610i	−0.169535	+	0.0978814i
$633$		0			0
$634$	−328.083	+	568.256i	−0.517481	+	0.896303i
$635$	−351.409	−	202.886i	−0.553399	−	0.319505i
$636$		0			0
$637$	100.348	+	173.809i	0.157533	+	0.272855i
$638$			18.4490i			0.0289169i
$639$		0			0
$640$	58.7878			0.0918559
$641$	209.106	−	120.727i	0.326219	−	0.188342i	−0.327942	−	0.944698i	$-0.606355\pi$
$641$	209.106	−	120.727i	0.326219	−	0.188342i	0.654161	+	0.756355i	$0.273022\pi$
$642$		0			0
$643$	−395.704	+	685.380i	−0.615403	+	1.06591i	0.374910	+	0.927061i	$0.377674\pi$
$643$	−395.704	+	685.380i	−0.615403	+	1.06591i	−0.990314	+	0.138849i	$0.955660\pi$
$644$	−13.7878	−	7.96036i	−0.0214096	−	0.0123608i
$645$		0			0
$646$	−329.666	−	570.999i	−0.510319	−	0.883899i
$647$			294.028i			0.454448i	0.973842	+	0.227224i	$0.0729650\pi$
$647$			294.028i			0.454448i	−0.973842	+	0.227224i	$0.927035\pi$
$648$		0			0
$649$	−17.9082			−0.0275935
$650$	−23.7526	+	13.7135i	−0.0365424	+	0.0210978i
$651$		0			0
$652$	133.060	−	230.467i	0.204080	−	0.353477i
$653$	665.379	+	384.156i	1.01896	+	0.588295i	0.913802	−	0.406161i	$-0.133133\pi$
$653$	665.379	+	384.156i	1.01896	+	0.588295i	0.105155	+	0.994456i	$0.466466\pi$
$654$		0			0
$655$	−608.113	−	1053.28i	−0.928417	−	1.60807i
$656$		−	43.6689i		−	0.0665684i
$657$		0			0
$658$	534.681			0.812585
$659$	373.204	−	215.469i	0.566318	−	0.326964i	−0.189359	−	0.981908i	$-0.560641\pi$
$659$	373.204	−	215.469i	0.566318	−	0.326964i	0.755678	+	0.654944i	$0.227308\pi$
$660$		0			0
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	0.174157	+	0.984718i	$0.444280\pi$
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	−0.939869	+	0.341534i	$0.889053\pi$
$662$	579.062	+	334.322i	0.874717	+	0.505018i
$663$		0			0
$664$	184.318	+	319.248i	0.277587	+	0.480795i
$665$		−	1071.35i		−	1.61105i
$666$		0			0
$667$	13.0454			0.0195583
$668$	510.106	−	294.510i	0.763631	−	0.440883i
$669$		0			0
$670$	275.734	−	477.586i	0.411544	−	0.712815i
$671$	10.8099	+	6.24112i	0.0161102	+	0.00930123i
$672$		0			0
$673$	−281.606	−	487.755i	−0.418433	−	0.724748i	0.577349	−	0.816498i	$-0.304087\pi$
$673$	−281.606	−	487.755i	−0.418433	−	0.724748i	−0.995782	+	0.0917499i	$0.970754\pi$
$674$		−	432.192i		−	0.641235i
$675$		0			0
$676$	149.939			0.221803
$677$	303.227	−	175.068i	0.447897	−	0.258594i	−0.259044	−	0.965865i	$-0.583408\pi$
$677$	303.227	−	175.068i	0.447897	−	0.258594i	0.706942	+	0.707272i	$0.250074\pi$
$678$		0			0
$679$	−458.659	+	794.421i	−0.675492	+	1.16999i
$680$	240.272	+	138.721i	0.353342	+	0.204002i
$681$		0			0
$682$	2.05332	+	3.55645i	0.00301073	+	0.00521474i
$683$			502.818i			0.736190i	0.929788	+	0.368095i	$0.119990\pi$
$683$			502.818i			0.736190i	−0.929788	+	0.368095i	$0.880010\pi$
$684$		0			0
$685$	−778.546			−1.13656
$686$	−289.392	+	167.080i	−0.421854	+	0.243557i
$687$		0			0
$688$	−90.0908	+	156.042i	−0.130946	+	0.226805i
$689$	−792.650	−	457.637i	−1.15044	−	0.664205i
$690$		0			0
$691$	−188.159	−	325.902i	−0.272300	−	0.471638i	0.697150	−	0.716925i	$-0.254451\pi$
$691$	−188.159	−	325.902i	−0.272300	−	0.471638i	−0.969450	+	0.245287i	$0.921118\pi$
$692$		−	138.529i		−	0.200186i
$693$		0			0
$694$	189.044			0.272398
$695$	380.385	−	219.616i	0.547317	−	0.315994i
$696$		0			0
$697$	103.045	−	178.480i	0.147841	−	0.256069i
$698$	−120.952	−	69.8318i	−0.173284	−	0.100046i
$699$		0			0
$700$	16.6969	+	28.9199i	0.0238528	+	0.0413142i
$701$			489.681i			0.698546i	0.937021	+	0.349273i	$0.113571\pi$
$701$			489.681i			0.698546i	−0.937021	+	0.349273i	$0.886429\pi$
$702$		0			0
$703$	−1153.27			−1.64050
$704$	6.60612	−	3.81405i	0.00938370	−	0.00541768i
$705$		0			0
$706$	−230.598	+	399.408i	−0.326626	+	0.565733i
$707$	−1066.70	−	615.862i	−1.50878	−	0.871092i
$708$		0			0
$709$	−237.014	−	410.521i	−0.334294	−	0.579014i	0.649055	−	0.760741i	$-0.275164\pi$
$709$	−237.014	−	410.521i	−0.334294	−	0.579014i	−0.983349	+	0.181728i	$0.941831\pi$
$710$		−	132.422i		−	0.186510i
$711$		0			0
$712$	−410.969			−0.577204
$713$	2.51479	−	1.45192i	0.00352706	−	0.00203635i
$714$		0			0
$715$	−24.0222	+	41.6077i	−0.0335975	+	0.0581925i
$716$	82.2429	+	47.4829i	0.114864	+	0.0663170i
$717$		0			0
$718$	296.091	+	512.844i	0.412383	+	0.714268i
$719$		−	108.122i		−	0.150379i	−0.997169	−	0.0751894i	$-0.976044\pi$
$719$		−	108.122i		−	0.150379i	0.997169	−	0.0751894i	$-0.0239561\pi$
$720$		0			0
$721$	861.030			1.19422
$722$	−304.886	+	176.026i	−0.422280	+	0.243804i
$723$		0			0
$724$	242.879	−	420.678i	0.335468	−	0.581047i
$725$	−23.6969	−	13.6814i	−0.0326854	−	0.0188709i
$726$		0			0
$727$	222.296	+	385.027i	0.305771	+	0.529611i	0.977433	−	0.211247i	$-0.0677524\pi$
$727$	222.296	+	385.027i	0.305771	+	0.529611i	−0.671662	+	0.740858i	$0.734419\pi$
$728$			228.974i			0.314525i
$729$		0			0
$730$	58.1204			0.0796170
$731$	−736.423	+	425.174i	−1.00742	+	0.581634i
$732$		0			0
$733$	358.181	−	620.388i	0.488651	−	0.846368i	−0.511264	−	0.859424i	$-0.670823\pi$
$733$	358.181	−	620.388i	0.488651	−	0.846368i	0.999915	+	0.0130556i	$0.00415584\pi$
$734$	229.305	+	132.390i	0.312405	+	0.180367i
$735$		0			0
$736$	−2.69694	−	4.67123i	−0.00366432	−	0.00634679i
$737$		−	71.5567i		−	0.0970918i
$738$		0			0
$739$	933.362			1.26301			0.631504	−	0.775373i	$-0.282438\pi$
$739$	933.362			1.26301			0.631504	+	0.775373i	$0.282438\pi$
$740$	420.272	−	242.644i	0.567936	−	0.327898i
$741$		0			0
$742$	−557.196	+	965.093i	−0.750939	+	1.30066i
$743$	13.7793	+	7.95550i	0.0185455	+	0.0107073i	0.509244	−	0.860622i	$-0.329925\pi$
$743$	13.7793	+	7.95550i	0.0185455	+	0.0107073i	−0.490699	+	0.871329i	$0.663258\pi$
$744$		0			0
$745$	−300.090	−	519.772i	−0.402806	−	0.697680i
$746$		−	637.852i		−	0.855030i
$747$		0			0
$748$	36.0000			0.0481283
$749$	−260.574	+	150.443i	−0.347896	+	0.200858i
$750$		0			0
$751$	−404.916	+	701.334i	−0.539169	+	0.933867i	0.459781	+	0.888033i	$0.347928\pi$
$751$	−404.916	+	701.334i	−0.539169	+	0.933867i	−0.998949	+	0.0458347i	$0.985405\pi$
$752$	156.879	+	90.5739i	0.208615	+	0.120444i
$753$		0			0
$754$	−93.8105	−	162.484i	−0.124417	−	0.215497i
$755$			336.570i			0.445788i
$756$		0			0
$757$	689.637			0.911013			0.455506	−	0.890232i	$-0.349458\pi$
$757$	689.637			0.911013			0.455506	+	0.890232i	$0.349458\pi$
$758$	599.716	−	346.246i	0.791182	−	0.456789i
$759$		0			0
$760$	181.485	−	314.341i	0.238796	−	0.413606i
$761$	825.393	+	476.541i	1.08462	+	0.626204i	0.932138	−	0.362103i	$-0.117941\pi$
$761$	825.393	+	476.541i	1.08462	+	0.626204i	0.152479	+	0.988307i	$0.451274\pi$
$762$		0			0
$763$	−618.924	−	1072.01i	−0.811172	−	1.40499i
$764$			15.0635i			0.0197167i
$765$		0			0
$766$	145.743			0.190266
$767$	157.721	−	91.0604i	0.205634	−	0.118723i
$768$		0			0
$769$	328.348	−	568.715i	0.426980	−	0.739552i	−0.569623	−	0.821906i	$-0.692911\pi$
$769$	328.348	−	568.715i	0.426980	−	0.739552i	0.996603	+	0.0823545i	$0.0262440\pi$
$770$	50.6594	+	29.2482i	0.0657915	+	0.0379847i
$771$		0			0
$772$	345.454	+	598.344i	0.447479	+	0.775057i
$773$		−	278.021i		−	0.359665i	−0.983697	−	0.179832i	$-0.942445\pi$
$773$		−	278.021i		−	0.359665i	0.983697	−	0.179832i	$-0.0575555\pi$
$774$		0			0
$775$	−6.09082			−0.00785912
$776$	−269.146	+	155.392i	−0.346838	+	0.200247i
$777$		0			0
$778$	24.2350	−	41.9762i	0.0311503	−	0.0539539i
$779$	−233.499	−	134.811i	−0.299743	−	0.173056i
$780$		0			0
$781$	−8.59133	−	14.8806i	−0.0110004	−	0.0190533i
$782$		−	25.4558i		−	0.0325522i
$783$		0			0
$784$	82.7878			0.105597
$785$	93.6827	−	54.0877i	0.119341	−	0.0689015i
$786$		0			0
$787$	−410.977	+	711.833i	−0.522207	+	0.904489i	0.477459	+	0.878654i	$0.341558\pi$
$787$	−410.977	+	711.833i	−0.522207	+	0.904489i	−0.999666	+	0.0258350i	$0.991776\pi$
$788$	133.757	+	77.2247i	0.169743	+	0.0980009i
$789$		0			0
$790$	−160.720	−	278.375i	−0.203443	−	0.352373i
$791$			1428.32i			1.80572i
$792$		0			0
$793$	−126.941			−0.160077
$794$	−10.1316	+	5.84950i	−0.0127602	+	0.00736713i
$795$		0			0
$796$	153.485	−	265.843i	0.192820	−	0.333974i
$797$	−1145.33	−	661.257i	−1.43705	−	0.829683i	−0.439409	−	0.898287i	$-0.644812\pi$
$797$	−1145.33	−	661.257i	−1.43705	−	0.829683i	−0.997644	+	0.0686043i	$0.978145\pi$
$798$		0			0
$799$	427.454	+	740.372i	0.534986	+	0.926624i
$800$			11.3137i			0.0141421i
$801$		0			0
$802$	585.650			0.730238
$803$	6.53113	−	3.77075i	0.00813341	−	0.00469583i
$804$		0			0
$805$	20.6816	−	35.8216i	0.0256915	−	0.0444989i
$806$	−36.1681	−	20.8817i	−0.0448736	−	0.0259078i
$807$		0			0
$808$	−208.652	−	361.395i	−0.258232	−	0.447271i
$809$			235.681i			0.291324i	0.989334	+	0.145662i	$0.0465311\pi$
$809$			235.681i			0.291324i	−0.989334	+	0.145662i	$0.953469\pi$
$810$		0			0
$811$	−587.362			−0.724244			−0.362122	−	0.932131i	$-0.617948\pi$
$811$	−587.362			−0.724244			−0.362122	+	0.932131i	$0.617948\pi$
$812$	−197.833	+	114.219i	−0.243637	+	0.140664i
$813$		0			0
$814$	31.4847	−	54.5331i	0.0386790	−	0.0669940i
$815$	598.771	+	345.701i	0.734688	+	0.424172i
$816$		0			0
$817$	556.242	+	963.439i	0.680835	+	1.17924i
$818$			461.334i			0.563978i
$819$		0			0
$820$	113.455			0.138360
$821$	817.453	−	471.956i	0.995679	−	0.574856i	0.0887121	−	0.996057i	$-0.471725\pi$
$821$	817.453	−	471.956i	0.995679	−	0.574856i	0.906967	+	0.421202i	$0.138392\pi$
$822$		0			0
$823$	807.871	−	1399.27i	0.981617	−	1.70021i	0.325520	−	0.945535i	$-0.394461\pi$
$823$	807.871	−	1399.27i	0.981617	−	1.70021i	0.656097	−	0.754676i	$-0.272206\pi$
$824$	252.631	+	145.857i	0.306591	+	0.177010i
$825$		0			0
$826$	−110.871	−	192.034i	−0.134226	−	0.232486i
$827$			582.354i			0.704177i	0.935967	+	0.352088i	$0.114528\pi$
$827$			582.354i			0.704177i	−0.935967	+	0.352088i	$0.885472\pi$
$828$		0			0
$829$	877.121			1.05805			0.529024	−	0.848607i	$-0.322558\pi$
$829$	877.121			1.05805			0.529024	+	0.848607i	$0.322558\pi$
$830$	−829.430	+	478.872i	−0.999314	+	0.576954i
$831$		0			0
$832$	−38.7878	+	67.1824i	−0.0466199	+	0.0807480i
$833$	338.363	+	195.354i	0.406198	+	0.234519i
$834$		0			0
$835$	765.158	+	1325.29i	0.916357	+	1.58718i
$836$		−	47.0976i		−	0.0563369i
$837$		0			0
$838$	−764.772			−0.912616
$839$	984.778	−	568.562i	1.17375	−	0.677666i	0.219191	−	0.975682i	$-0.429658\pi$
$839$	984.778	−	568.562i	1.17375	−	0.677666i	0.954561	+	0.298016i	$0.0963247\pi$
$840$		0			0
$841$	−326.909	+	566.223i	−0.388715	+	0.673274i
$842$	347.456	+	200.604i	0.412656	+	0.238247i
$843$		0			0
$844$	−51.5607	−	89.3058i	−0.0610909	−	0.105813i
$845$			389.552i			0.461009i
$846$		0			0
$847$	−1002.57			−1.18368
$848$	−326.969	+	188.776i	−0.385577	+	0.222613i
$849$		0			0
$850$	−26.6969	+	46.2405i	−0.0314082	+	0.0544005i
$851$	−38.5607	−	22.2630i	−0.0453122	−	0.0261610i
$852$		0			0
$853$	159.909	+	276.970i	0.187466	+	0.324701i	0.944405	−	0.328785i	$-0.106639\pi$
$853$	159.909	+	276.970i	0.187466	+	0.324701i	−0.756939	+	0.653486i	$0.773306\pi$
$854$			154.557i			0.180980i
$855$		0			0
$856$	−101.939			−0.119087
$857$	−691.061	+	398.984i	−0.806372	+	0.465559i	−0.845694	−	0.533668i	$-0.820813\pi$
$857$	−691.061	+	398.984i	−0.806372	+	0.465559i	0.0393225	+	0.999227i	$0.487480\pi$
$858$		0			0
$859$	233.901	−	405.128i	0.272294	−	0.471627i	−0.697155	−	0.716921i	$-0.745551\pi$
$859$	233.901	−	405.128i	0.272294	−	0.471627i	0.969449	+	0.245293i	$0.0788843\pi$
$860$	−405.409	−	234.063i	−0.471405	−	0.272166i
$861$		0			0
$862$	182.030	+	315.284i	0.211171	+	0.365759i
$863$		−	1304.85i		−	1.51199i	−0.654578	−	0.755994i	$-0.727154\pi$
$863$		−	1304.85i		−	1.51199i	0.654578	−	0.755994i	$-0.272846\pi$
$864$		0			0
$865$	359.908			0.416079
$866$	−583.312	+	336.775i	−0.673571	+	0.388886i
$867$		0			0
$868$	−25.4245	+	44.0365i	−0.0292909	+	0.0507333i
$869$	−36.1209	−	20.8544i	−0.0415661	−	0.0239982i
$870$		0			0
$871$	363.855	+	630.216i	0.417744	+	0.723554i
$872$		−	419.378i		−	0.480938i
$873$		0			0
$874$	−33.3031			−0.0381042
$875$	864.067	−	498.869i	0.987505	−	0.570136i
$876$		0			0
$877$	186.878	−	323.682i	0.213088	−	0.369079i	−0.739592	−	0.673056i	$-0.764981\pi$
$877$	186.878	−	323.682i	0.213088	−	0.369079i	0.952679	+	0.303977i	$0.0983146\pi$
$878$	−683.240	−	394.469i	−0.778177	−	0.449281i
$879$		0			0
$880$	9.90918	+	17.1632i	0.0112604	+	0.0195036i
$881$			229.979i			0.261043i	0.991445	+	0.130522i	$0.0416652\pi$
$881$			229.979i			0.261043i	−0.991445	+	0.130522i	$0.958335\pi$
$882$		0			0
$883$	−1381.79			−1.56488			−0.782439	−	0.622728i	$-0.786024\pi$
$883$	−1381.79			−1.56488			−0.782439	+	0.622728i	$0.786024\pi$
$884$	−317.060	+	183.055i	−0.358665	+	0.207076i
$885$		0			0
$886$	588.204	−	1018.80i	0.663888	−	1.14989i
$887$	−758.794	−	438.090i	−0.855461	−	0.493901i	0.00702852	−	0.999975i	$-0.497763\pi$
$887$	−758.794	−	438.090i	−0.855461	−	0.493901i	−0.862490	+	0.506075i	$0.831096\pi$
$888$		0			0
$889$	−325.969	−	564.596i	−0.366670	−	0.635091i
$890$		−	1067.73i		−	1.19970i
$891$		0			0
$892$	−626.454			−0.702303
$893$	968.605	−	559.224i	1.08466	−	0.626231i
$894$		0			0
$895$	−123.364	+	213.673i	−0.137837	+	0.238741i
$896$	81.7980	+	47.2261i	0.0912924	+	0.0527077i
$897$		0			0
$898$	−516.136	−	893.974i	−0.574762	−	0.995517i
$899$		−	41.6655i		−	0.0463465i
$900$		0			0
$901$	−1781.82			−1.97760
$902$	12.7492	−	7.36077i	0.0141344	−	0.00816050i
$903$		0			0
$904$	−241.955	+	419.078i	−0.267649	+	0.463581i
$905$	1092.95	+	631.017i	1.20768	+	0.697256i
$906$		0			0
$907$	−590.037	−	1021.97i	−0.650537	−	1.12676i	−0.982993	−	0.183644i	$-0.941211\pi$
$907$	−590.037	−	1021.97i	−0.650537	−	1.12676i	0.332456	−	0.943119i	$-0.392123\pi$
$908$		−	152.542i		−	0.167998i
$909$		0			0
$910$	−594.892			−0.653728
$911$	−1100.13	+	635.158i	−1.20760	+	0.697210i	−0.962235	−	0.272220i	$-0.912242\pi$
$911$	−1100.13	+	635.158i	−1.20760	+	0.697210i	−0.245368	+	0.969430i	$0.578909\pi$
$912$		0			0
$913$	−62.1367	+	107.624i	−0.0680578	+	0.117880i
$914$	869.123	+	501.788i	0.950900	+	0.549002i
$915$		0			0
$916$	−121.545	−	210.522i	−0.132691	−	0.229827i
$917$		−	1954.07i		−	2.13093i
$918$		0			0
$919$	1316.63			1.43268			0.716340	−	0.697751i	$-0.245816\pi$
$919$	1316.63			1.43268			0.716340	+	0.697751i	$0.245816\pi$
$920$	12.1362	−	7.00685i	0.0131915	−	0.00761614i
$921$		0			0
$922$	−6.50740	+	11.2711i	−0.00705791	+	0.0122247i
$923$	151.332	+	87.3713i	0.163956	+	0.0946602i
$924$		0			0
$925$	46.6969	+	80.8815i	0.0504832	+	0.0874394i
$926$			78.0610i			0.0842991i
$927$		0			0
$928$	−77.3939			−0.0833986
$929$	−543.424	+	313.746i	−0.584956	+	0.337724i	−0.763100	−	0.646280i	$-0.776324\pi$
$929$	−543.424	+	313.746i	−0.584956	+	0.337724i	0.178145	+	0.984004i	$0.442991\pi$
$930$		0			0
$931$	255.576	−	442.670i	0.274517	−	0.475478i
$932$	−261.576	−	151.021i	−0.280660	−	0.162039i
$933$		0			0
$934$	442.515	+	766.459i	0.473785	+	0.820620i
$935$			93.5307i			0.100033i
$936$		0			0
$937$	469.789			0.501375			0.250688	−	0.968068i	$-0.419343\pi$
$937$	469.789			0.501375			0.250688	+	0.968068i	$0.419343\pi$
$938$	767.320	−	443.012i	0.818039	−	0.472295i
$939$		0			0
$940$	−235.318	+	407.582i	−0.250338	+	0.433598i
$941$	−805.984	−	465.335i	−0.856518	−	0.494511i	0.00632656	−	0.999980i	$-0.497986\pi$
$941$	−805.984	−	465.335i	−0.856518	−	0.494511i	−0.862845	+	0.505469i	$0.831320\pi$
$942$		0			0
$943$	−5.20485	−	9.01506i	−0.00551946	−	0.00955998i
$944$		−	75.1250i		−	0.0795816i
$945$		0			0
$946$	−60.7423			−0.0642097
$947$	3.14465	−	1.81556i	0.00332064	−	0.00191717i	−0.498339	−	0.866982i	$-0.666056\pi$
$947$	3.14465	−	1.81556i	0.00332064	−	0.00191717i	0.501659	+	0.865065i	$0.332723\pi$
$948$		0			0
$949$	−38.3474	+	66.4197i	−0.0404083	+	0.0699892i
$950$	60.4949	+	34.9267i	0.0636788	+	0.0367650i
$951$		0			0
$952$	222.879	+	386.037i	0.234116	+	0.405501i
$953$		−	719.641i		−	0.755132i	−0.925983	−	0.377566i	$-0.876761\pi$
$953$		−	719.641i		−	0.755132i	0.925983	−	0.377566i	$-0.123239\pi$
$954$		0			0
$955$	−39.1362			−0.0409803
$956$	151.924	−	87.7133i	0.158916	−	0.0917504i
$957$		0			0
$958$	218.704	−	378.806i	0.228292	−	0.395413i
$959$	−1083.28	−	625.431i	−1.12959	−	0.652170i
$960$		0			0
$961$	475.863	+	824.218i	0.495175	+	0.857667i
$962$			640.380i			0.665676i
$963$		0			0
$964$	−403.576			−0.418647
$965$	−1554.54	+	897.516i	−1.61093	+	0.930068i
$966$		0			0
$967$	−16.8870	+	29.2491i	−0.0174633	+	0.0302473i	−0.874625	−	0.484800i	$-0.838892\pi$
$967$	−16.8870	+	29.2491i	−0.0174633	+	0.0302473i	0.857162	+	0.515047i	$0.172226\pi$
$968$	−294.161	−	169.834i	−0.303886	−	0.175448i
$969$		0			0
$970$	−403.720	−	699.263i	−0.416206	−	0.720890i
$971$			970.472i			0.999456i	0.866182	+	0.499728i	$0.166567\pi$
$971$			970.472i			0.999456i	−0.866182	+	0.499728i	$0.833433\pi$
$972$		0			0
$973$	705.697			0.725279
$974$	34.7015	−	20.0349i	0.0356278	−	0.0205697i
$975$		0			0
$976$	−26.1816	+	45.3479i	−0.0268254	+	0.0464630i
$977$	1359.92	+	785.151i	1.39194	+	0.803635i	0.993529	−	0.113574i	$-0.0362300\pi$
$977$	1359.92	+	785.151i	1.39194	+	0.803635i	0.398406	+	0.917209i	$0.369563\pi$
$978$		0			0
$979$	−69.2724	−	119.983i	−0.0707584	−	0.122557i
$980$			215.089i			0.219478i
$981$		0			0
$982$	1343.07			1.36769
$983$	671.930	−	387.939i	0.683551	−	0.394648i	−0.117641	−	0.993056i	$-0.537533\pi$
$983$	671.930	−	387.939i	0.683551	−	0.394648i	0.801192	+	0.598408i	$0.204200\pi$
$984$		0			0
$985$	−200.636	+	347.511i	−0.203691	+	0.352803i
$986$	−316.318	−	182.626i	−0.320809	−	0.185219i
$987$		0			0
$988$	239.485	+	414.800i	0.242393	+	0.419838i
$989$			42.9513i			0.0434290i
$990$		0			0
$991$	870.454			0.878359			0.439180	−	0.898399i	$-0.355269\pi$
$991$	870.454			0.878359			0.439180	+	0.898399i	$0.355269\pi$
$992$	−14.9194	+	8.61371i	−0.0150397	+	0.00868318i
$993$		0			0
$994$	106.379	−	184.254i	0.107021	−	0.185366i
$995$	690.681	+	398.765i	0.694152	+	0.400769i
$996$		0			0
$997$	−622.499	−	1078.20i	−0.624372	−	1.08144i	−0.988662	−	0.150159i	$-0.952022\pi$
$997$	−622.499	−	1078.20i	−0.624372	−	1.08144i	0.364290	−	0.931286i	$-0.381312\pi$
$998$			792.279i			0.793867i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.3.d.a.17.1		4
3.2	odd	2		18.3.d.a.5.2	✓	4
4.3	odd	2		432.3.q.d.17.1		4
5.2	odd	4		1350.3.k.a.449.1		8
5.3	odd	4		1350.3.k.a.449.4		8
5.4	even	2		1350.3.i.b.1151.2		4
8.3	odd	2		1728.3.q.c.449.1		4
8.5	even	2		1728.3.q.d.449.2		4
9.2	odd	6	inner	54.3.d.a.35.1		4
9.4	even	3		162.3.b.a.161.1		4
9.5	odd	6		162.3.b.a.161.4		4
9.7	even	3		18.3.d.a.11.2	yes	4
12.11	even	2		144.3.q.c.113.2		4
15.2	even	4		450.3.k.a.149.4		8
15.8	even	4		450.3.k.a.149.1		8
15.14	odd	2		450.3.i.b.401.1		4
24.5	odd	2		576.3.q.f.257.2		4
24.11	even	2		576.3.q.e.257.1		4
36.7	odd	6		144.3.q.c.65.2		4
36.11	even	6		432.3.q.d.305.1		4
36.23	even	6		1296.3.e.g.161.4		4
36.31	odd	6		1296.3.e.g.161.2		4
45.2	even	12		1350.3.k.a.899.4		8
45.7	odd	12		450.3.k.a.299.1		8
45.29	odd	6		1350.3.i.b.251.2		4
45.34	even	6		450.3.i.b.101.1		4
45.38	even	12		1350.3.k.a.899.1		8
45.43	odd	12		450.3.k.a.299.4		8
72.11	even	6		1728.3.q.c.1601.1		4
72.29	odd	6		1728.3.q.d.1601.2		4
72.43	odd	6		576.3.q.e.65.1		4
72.61	even	6		576.3.q.f.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	3.2	odd	2
18.3.d.a.11.2	yes	4	9.7	even	3
54.3.d.a.17.1		4	1.1	even	1	trivial
54.3.d.a.35.1		4	9.2	odd	6	inner
144.3.q.c.65.2		4	36.7	odd	6
144.3.q.c.113.2		4	12.11	even	2
162.3.b.a.161.1		4	9.4	even	3
162.3.b.a.161.4		4	9.5	odd	6
432.3.q.d.17.1		4	4.3	odd	2
432.3.q.d.305.1		4	36.11	even	6
450.3.i.b.101.1		4	45.34	even	6
450.3.i.b.401.1		4	15.14	odd	2
450.3.k.a.149.1		8	15.8	even	4
450.3.k.a.149.4		8	15.2	even	4
450.3.k.a.299.1		8	45.7	odd	12
450.3.k.a.299.4		8	45.43	odd	12
576.3.q.e.65.1		4	72.43	odd	6
576.3.q.e.257.1		4	24.11	even	2
576.3.q.f.65.2		4	72.61	even	6
576.3.q.f.257.2		4	24.5	odd	2
1296.3.e.g.161.2		4	36.31	odd	6
1296.3.e.g.161.4		4	36.23	even	6
1350.3.i.b.251.2		4	45.29	odd	6
1350.3.i.b.1151.2		4	5.4	even	2
1350.3.k.a.449.1		8	5.2	odd	4
1350.3.k.a.449.4		8	5.3	odd	4
1350.3.k.a.899.1		8	45.38	even	12
1350.3.k.a.899.4		8	45.2	even	12
1728.3.q.c.449.1		4	8.3	odd	2
1728.3.q.c.1601.1		4	72.11	even	6
1728.3.q.d.449.2		4	8.5	even	2
1728.3.q.d.1601.2		4	72.29	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(4.17423 + 7.22999i) q^{7} +2.82843i q^{8} -7.34847 q^{10} +(-0.825765 + 0.476756i) q^{11} +(4.84847 - 8.39780i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} -18.8776i q^{17} -24.6969 q^{19} +(9.00000 - 5.19615i) q^{20} +(0.674235 - 1.16781i) q^{22} +(-0.825765 - 0.476756i) q^{23} +(1.00000 + 1.73205i) q^{25} +13.7135i q^{26} +16.6969 q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(4.89898 + 2.82843i) q^{32} +(13.3485 + 23.1202i) q^{34} +43.3799i q^{35} +46.6969 q^{37} +(30.2474 - 17.4634i) q^{38} +(-7.34847 + 12.7279i) q^{40} +(9.45459 + 5.45861i) q^{41} +(-22.5227 - 39.0105i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(-39.2196 + 22.6435i) q^{47} +(-10.3485 + 17.9241i) q^{49} +(-2.44949 - 1.41421i) q^{50} +(-9.69694 - 16.7956i) q^{52} -94.3879i q^{53} -4.95459 q^{55} +(-20.4495 + 11.8065i) q^{56} +(9.67423 - 16.7563i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} -4.30686i q^{62} -8.00000 q^{64} +(43.6362 - 25.1934i) q^{65} +(-37.5227 + 64.9912i) q^{67} +(-32.6969 - 18.8776i) q^{68} +(-30.6742 - 53.1293i) q^{70} +18.0204i q^{71} -7.90918 q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(-6.89388 - 3.98018i) q^{77} +(21.8712 + 37.8820i) q^{79} -20.7846i q^{80} -15.4393 q^{82} +(112.871 - 65.1662i) q^{83} +(49.0454 - 84.9491i) q^{85} +(55.1691 + 31.8519i) q^{86} +(-1.34847 - 2.33562i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(-1.65153 + 0.953512i) q^{92} +(32.0227 - 55.4650i) q^{94} +(-111.136 - 64.1645i) q^{95} +(54.9393 + 95.1576i) q^{97} -29.2699i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7} - 18 q^{11} - 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 36 q^{20} - 12 q^{22} - 18 q^{23} + 4 q^{25} + 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} + 128 q^{37} + 72 q^{38}+ \cdots + 14 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 + 18 * q^5 + 2 * q^7 - 18 * q^11 - 10 * q^13 - 36 * q^14 - 8 * q^16 - 40 * q^19 + 36 * q^20 - 12 * q^22 - 18 * q^23 + 4 * q^25 + 8 * q^28 - 18 * q^29 + 38 * q^31 + 24 * q^34 + 128 * q^37 + 72 * q^38 + 126 * q^41 - 46 * q^43 - 24 * q^46 - 54 * q^47 - 12 * q^49 + 20 * q^52 - 108 * q^55 - 72 * q^56 + 24 * q^58 - 126 * q^59 + 62 * q^61 - 32 * q^64 - 90 * q^65 - 106 * q^67 - 72 * q^68 - 108 * q^70 - 208 * q^73 - 72 * q^74 - 40 * q^76 + 90 * q^77 + 14 * q^79 + 144 * q^82 + 378 * q^83 + 108 * q^85 + 108 * q^86 + 24 * q^88 + 412 * q^91 - 36 * q^92 + 84 * q^94 - 180 * q^95 + 14 * q^97

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