LMFDB - Embedded newform 54.3.d.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(17,54)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			35.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	54.35
Dual form			54.3.d.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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	0.0227998	−	0.999740i	$-0.492742\pi$
$5$	4.50000	−	2.59808i	0.900000	−	0.519615i	0.877200	+	0.480125i	$0.159409\pi$
$6$		0			0
$7$	4.17423	−	7.22999i	0.596319	−	1.03286i	−0.397040	−	0.917801i	$-0.629963\pi$
$7$	4.17423	−	7.22999i	0.596319	−	1.03286i	0.993359	−	0.115054i	$-0.0367041\pi$
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−7.34847			−0.734847
$11$	−0.825765	−	0.476756i	−0.0750696	−	0.0433414i	0.461995	−	0.886882i	$-0.347134\pi$
$11$	−0.825765	−	0.476756i	−0.0750696	−	0.0433414i	−0.537065	+	0.843541i	$0.680467\pi$
$12$		0			0
$13$	4.84847	+	8.39780i	0.372959	+	0.645984i	0.990019	−	0.140932i	$-0.0450098\pi$
$13$	4.84847	+	8.39780i	0.372959	+	0.645984i	−0.617060	+	0.786916i	$0.711676\pi$
$14$	−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	$0.187367\pi$
$17$			18.8776i			1.11045i	−0.831701	+	0.555223i	$0.812633\pi$
$18$		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	−0.517844	−	0.855475i	$-0.673265\pi$
$23$	−0.825765	+	0.476756i	−0.0359028	+	0.0207285i	0.481941	+	0.876204i	$0.339932\pi$
$24$		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	0.281606	−	0.959530i	$-0.409133\pi$
$29$	−11.8485	−	6.84072i	−0.408568	−	0.235887i	−0.690174	+	0.723643i	$0.742466\pi$
$30$		0			0
$31$	−1.52270	−	2.63740i	−0.0491195	−	0.0850774i	0.840420	−	0.541935i	$-0.182308\pi$
$31$	−1.52270	−	2.63740i	−0.0491195	−	0.0850774i	−0.889540	+	0.456858i	$0.848975\pi$
$32$	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	−0.380249	−	0.924884i	$-0.624162\pi$
$41$	9.45459	−	5.45861i	0.230600	−	0.133137i	0.610849	+	0.791747i	$0.290828\pi$
$42$		0			0
$43$	−22.5227	+	39.0105i	−0.523784	+	0.907220i	0.475833	+	0.879536i	$0.342147\pi$
$43$	−22.5227	+	39.0105i	−0.523784	+	0.907220i	−0.999617	+	0.0276845i	$0.991187\pi$
$44$		−	1.90702i		−	0.0433414i
$45$		0			0
$46$	1.34847			0.0293145
$47$	−39.2196	−	22.6435i	−0.834460	−	0.481776i	0.0209170	−	0.999781i	$-0.493341\pi$
$47$	−39.2196	−	22.6435i	−0.834460	−	0.481776i	−0.855377	+	0.518005i	$0.826675\pi$
$48$		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	$0.349612\pi$
$53$			94.3879i			1.78090i	−0.455077	+	0.890452i	$0.650388\pi$
$54$		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	−0.355787	−	0.934567i	$-0.615787\pi$
$59$	16.2650	−	9.39063i	0.275679	−	0.159163i	0.631466	+	0.775404i	$0.282454\pi$
$60$		0			0
$61$	−6.54541	+	11.3370i	−0.107302	+	0.185852i	−0.914676	−	0.404187i	$-0.867554\pi$
$61$	−6.54541	+	11.3370i	−0.107302	+	0.185852i	0.807375	+	0.590039i	$0.200888\pi$
$62$			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	−0.997492	−	0.0707765i	$-0.977452\pi$
$67$	−37.5227	−	64.9912i	−0.560040	−	0.970018i	0.437452	−	0.899242i	$-0.355881\pi$
$68$	−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	$-0.959496\pi$
$71$		−	18.0204i		−	0.253808i	0.991915	−	0.126904i	$-0.0405041\pi$
$72$		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	−0.693750	−	0.720216i	$-0.744043\pi$
$79$	21.8712	−	37.8820i	0.276850	−	0.479519i	0.970600	+	0.240697i	$0.0773761\pi$
$80$			20.7846i			0.259808i
$81$		0			0
$82$	−15.4393			−0.188284
$83$	112.871	+	65.1662i	1.35989	+	0.785135i	0.989609	−	0.143783i	$-0.0459269\pi$
$83$	112.871	+	65.1662i	1.35989	+	0.785135i	0.370284	+	0.928918i	$0.379260\pi$
$84$		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	$-0.696027\pi$
$89$		−	145.300i		−	1.63258i	0.577642	−	0.816290i	$-0.303973\pi$
$90$		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	−0.430535	−	0.902574i	$-0.641675\pi$
$97$	54.9393	−	95.1576i	0.566384	−	0.981007i	0.996919	−	0.0784327i	$-0.0249916\pi$
$98$			29.2699i			0.298672i
$99$		0			0
$100$	4.00000			0.0400000
$101$	−127.772	−	73.7695i	−1.26507	−	0.730391i	−0.291022	−	0.956716i	$-0.593995\pi$
$101$	−127.772	−	73.7695i	−1.26507	−	0.730391i	−0.974052	+	0.226326i	$0.927329\pi$
$102$		0			0
$103$	51.5681	+	89.3186i	0.500661	+	0.867171i	1.00000		0.000763745i	$0.000243108\pi$
$103$	51.5681	+	89.3186i	0.500661	+	0.867171i	−0.499338	+	0.866407i	$0.666424\pi$
$104$	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	$-0.946135\pi$
$107$		−	36.0408i		−	0.336830i	0.985716	−	0.168415i	$-0.0538649\pi$
$108$		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	0.328910	−	0.944361i	$-0.393319\pi$
$113$	148.166	−	85.5439i	1.31121	−	0.757025i	0.982296	+	0.187336i	$0.0599852\pi$
$114$		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	−0.549019	+	0.835810i	$0.684999\pi$
$131$	−202.704	+	117.031i	−1.54736	+	0.893369i	−0.998342	+	0.0575598i	$0.981668\pi$
$132$		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	−0.0549460	−	0.998489i	$-0.517499\pi$
$137$	−129.758	−	74.9156i	−0.947136	−	0.546829i	−0.892190	+	0.451660i	$0.850832\pi$
$138$		0			0
$139$	42.2650	+	73.2052i	0.304065	+	0.526656i	0.977053	−	0.212998i	$-0.0683226\pi$
$139$	42.2650	+	73.2052i	0.304065	+	0.526656i	−0.672988	+	0.739654i	$0.734989\pi$
$140$	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	−0.796585	−	0.604526i	$-0.793362\pi$
$149$	−100.030	+	57.7524i	−0.671343	+	0.387600i	0.125242	+	0.992126i	$0.460029\pi$
$150$		0			0
$151$	32.3865	−	56.0950i	0.214480	−	0.371490i	−0.738632	−	0.674109i	$-0.764528\pi$
$151$	32.3865	−	56.0950i	0.214480	−	0.371490i	0.953112	+	0.302619i	$0.0978610\pi$
$152$			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	0.897270	−	0.441482i	$-0.145547\pi$
$157$	10.4092	+	18.0292i	0.0663005	+	0.114836i	−0.830970	+	0.556318i	$0.812214\pi$
$158$	−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	0.527787	−	0.849377i	$-0.323022\pi$
$167$	255.053	−	147.255i	1.52726	−	0.881765i	0.999475	−	0.0323885i	$-0.0103114\pi$
$168$		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	0.663245	−	0.748402i	$-0.269179\pi$
$173$	59.9847	+	34.6322i	0.346732	+	0.200186i	−0.316513	+	0.948588i	$0.602512\pi$
$174$		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	$-0.957657\pi$
$179$		−	47.4829i		−	0.265268i	0.991165	−	0.132634i	$-0.0423435\pi$
$180$		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	0.482828	−	0.875715i	$-0.339610\pi$
$191$	−6.52270	−	3.76588i	−0.0341503	−	0.0197167i	−0.516978	+	0.855999i	$0.672943\pi$
$192$		0			0
$193$	−172.727	−	299.172i	−0.894959	−	1.55011i	−0.833856	−	0.551983i	$-0.813871\pi$
$193$	−172.727	−	299.172i	−0.894959	−	1.55011i	−0.0611031	−	0.998131i	$-0.519462\pi$
$194$	−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	$-0.937204\pi$
$197$		−	77.2247i		−	0.392004i	0.980604	−	0.196002i	$-0.0627959\pi$
$198$		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	0.920628	−	0.390441i	$-0.127678\pi$
$211$	25.7804	+	44.6529i	0.122182	+	0.211625i	−0.798446	+	0.602066i	$0.794344\pi$
$212$	−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	0.265353	+	0.964151i	$0.414511\pi$
$223$	−156.614	+	271.263i	−0.702303	+	1.21642i	−0.967656	+	0.252273i	$0.918822\pi$
$224$		−	47.2261i		−	0.210831i
$225$		0			0
$226$	−241.955			−1.07060
$227$	66.0528	+	38.1356i	0.290982	+	0.167998i	0.638384	−	0.769718i	$-0.279603\pi$
$227$	66.0528	+	38.1356i	0.290982	+	0.167998i	−0.347403	+	0.937716i	$0.612936\pi$
$228$		0			0
$229$	60.7724	+	105.261i	0.265382	+	0.459655i	0.967664	−	0.252244i	$-0.0811686\pi$
$229$	60.7724	+	105.261i	0.265382	+	0.459655i	−0.702282	+	0.711899i	$0.747835\pi$
$230$	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	$0.105054\pi$
$233$			151.021i			0.648157i	−0.946030	+	0.324079i	$0.894946\pi$
$234$		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	−0.332593	−	0.943070i	$-0.607924\pi$
$239$	75.9620	−	43.8567i	0.317833	−	0.183501i	0.650426	+	0.759570i	$0.274590\pi$
$240$		0			0
$241$	−100.894	+	174.753i	−0.418647	+	0.725118i	−0.995804	−	0.0915158i	$-0.970829\pi$
$241$	−100.894	+	174.753i	−0.418647	+	0.725118i	0.577157	+	0.816633i	$0.304162\pi$
$242$			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	$-0.966569\pi$
$251$		−	52.6261i		−	0.209666i	0.994490	−	0.104833i	$-0.0334307\pi$
$252$		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	−0.357818	−	0.933791i	$-0.616479\pi$
$257$	69.8939	−	40.3532i	0.271961	−	0.157017i	0.629778	+	0.776775i	$0.283146\pi$
$258$		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	−0.999484	−	0.0321259i	$-0.989772\pi$
$263$	−401.614	−	231.872i	−1.52705	−	0.881641i	−0.527564	−	0.849515i	$-0.676894\pi$
$264$		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	$0.0257510\pi$
$269$			43.4762i			0.161622i	−0.996729	+	0.0808109i	$0.974249\pi$
$270$		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	−0.818407	−	0.574638i	$-0.805143\pi$
$277$	24.5000	−	42.4352i	0.0884477	−	0.153196i	0.906855	+	0.421442i	$0.138476\pi$
$278$		−	119.544i		−	0.430013i
$279$		0			0
$280$	−122.697			−0.438203
$281$	17.8791	+	10.3225i	0.0636266	+	0.0367349i	0.531476	−	0.847073i	$-0.321638\pi$
$281$	17.8791	+	10.3225i	0.0636266	+	0.0367349i	−0.467849	+	0.883808i	$0.654971\pi$
$282$		0			0
$283$	−26.7043	−	46.2533i	−0.0943616	−	0.163439i	0.814980	−	0.579489i	$-0.196748\pi$
$283$	−26.7043	−	46.2533i	−0.0943616	−	0.163439i	−0.909342	+	0.416049i	$0.863414\pi$
$284$	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	−0.477782	−	0.878478i	$-0.658559\pi$
$293$	12.9245	−	7.46196i	0.0441109	−	0.0254674i	0.521893	+	0.853011i	$0.325226\pi$
$294$		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	−0.109447	−	0.993993i	$-0.534908\pi$
$311$	216.659	−	125.088i	0.696652	−	0.402213i	0.806099	+	0.591780i	$0.201575\pi$
$312$		0			0
$313$	213.197	−	369.268i	0.681140	−	1.17977i	−0.293493	−	0.955961i	$-0.594818\pi$
$313$	213.197	−	369.268i	0.681140	−	1.17977i	0.974633	−	0.223808i	$-0.0718490\pi$
$314$		−	29.4416i		−	0.0937631i
$315$		0			0
$316$	87.4847			0.276850
$317$	401.818	+	231.990i	1.26756	+	0.731829i	0.974527	−	0.224272i	$-0.0720005\pi$
$317$	401.818	+	231.990i	1.26756	+	0.731829i	0.293038	+	0.956101i	$0.405334\pi$
$318$		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	0.249063	+	0.968487i	$0.419877\pi$
$331$	−236.401	+	409.459i	−0.714203	+	1.23704i	−0.963266	+	0.268549i	$0.913456\pi$
$332$			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	0.545174	−	0.838323i	$-0.316463\pi$
$337$	−152.803	−	264.663i	−0.453422	−	0.785349i	−0.998596	+	0.0529735i	$0.983130\pi$
$338$	−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	−0.657446	−	0.753501i	$-0.728363\pi$
$347$	−115.766	+	66.8373i	−0.333618	+	0.192615i	0.323828	+	0.946116i	$0.395030\pi$
$348$		0			0
$349$	49.3786	−	85.5262i	0.141486	−	0.245061i	−0.786570	−	0.617500i	$-0.788145\pi$
$349$	49.3786	−	85.5262i	0.141486	−	0.245061i	0.928056	+	0.372440i	$0.121479\pi$
$350$			23.6130i			0.0674658i
$351$		0			0
$352$	−5.39388			−0.0153235
$353$	282.424	+	163.058i	0.800068	+	0.461919i	0.843495	−	0.537137i	$-0.180494\pi$
$353$	282.424	+	163.058i	0.800068	+	0.461919i	−0.0434270	+	0.999057i	$0.513828\pi$
$354$		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	$0.198199\pi$
$359$			418.736i			1.16639i	−0.812331	+	0.583197i	$0.801801\pi$
$360$		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	−0.964917	−	0.262557i	$-0.915434\pi$
$367$	−93.6135	+	162.143i	−0.255078	+	0.441808i	0.709839	+	0.704364i	$0.248768\pi$
$368$		−	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	−0.992115	−	0.125331i	$-0.960001\pi$
$373$	−225.515	−	390.603i	−0.604597	−	1.04719i	0.387518	−	0.921862i	$-0.373333\pi$
$374$	−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	−0.611968	−	0.790883i	$-0.709622\pi$
$383$	−89.2492	+	51.5281i	−0.233027	+	0.134538i	0.378941	+	0.925421i	$0.376288\pi$
$384$		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	0.461363	−	0.887211i	$-0.347360\pi$
$389$	−29.6816	−	17.1367i	−0.0763024	−	0.0440532i	−0.537666	+	0.843158i	$0.680694\pi$
$390$		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	−0.875364	−	0.483464i	$-0.839378\pi$
$401$	−358.636	+	207.059i	−0.894355	+	0.516356i	−0.0189903	+	0.999820i	$0.506045\pi$
$402$		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	0.993577	−	0.113156i	$-0.0360960\pi$
$409$	163.106	+	282.508i	0.398792	+	0.690729i	−0.594785	+	0.803885i	$0.702763\pi$
$410$	−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	0.176903	−	0.984228i	$-0.443392\pi$
$419$	468.325	−	270.388i	1.11772	−	0.645317i	0.940818	+	0.338912i	$0.110059\pi$
$420$		0			0
$421$	−141.848	+	245.689i	−0.336932	+	0.583584i	−0.983854	−	0.178973i	$-0.942723\pi$
$421$	−141.848	+	245.689i	−0.336932	+	0.583584i	0.646922	+	0.762556i	$0.276056\pi$
$422$		−	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	$0.0965334\pi$
$431$			257.429i			0.597282i	−0.954365	+	0.298641i	$0.903467\pi$
$432$		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	−0.351056	−	0.936355i	$-0.614177\pi$
$439$	278.931	−	483.123i	0.635379	−	1.10051i	0.986435	−	0.164154i	$-0.0524894\pi$
$440$			14.0137i			0.0318493i
$441$		0			0
$442$	258.879			0.585698
$443$	−720.400	−	415.923i	−1.62619	−	0.938879i	−0.985217	−	0.171312i	$-0.945199\pi$
$443$	−720.400	−	415.923i	−1.62619	−	0.938879i	−0.640969	−	0.767567i	$-0.721467\pi$
$444$		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	$-0.697922\pi$
$449$		−	729.927i		−	1.62567i	0.582492	−	0.812836i	$-0.302078\pi$
$450$		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	0.157594	+	0.987504i	$0.449626\pi$
$457$	−354.818	+	614.563i	−0.776407	+	1.34478i	−0.934000	+	0.357272i	$0.883707\pi$
$458$		−	171.890i		−	0.375307i
$459$		0			0
$460$	−9.90918			−0.0215417
$461$	7.96990	+	4.60142i	0.0172883	+	0.00998140i	0.508619	−	0.860992i	$-0.330156\pi$
$461$	7.96990	+	4.60142i	0.0172883	+	0.00998140i	−0.491331	+	0.870973i	$0.663489\pi$
$462$		0			0
$463$	27.5987	+	47.8024i	0.0596085	+	0.103245i	0.894290	−	0.447488i	$-0.147681\pi$
$463$	27.5987	+	47.8024i	0.0596085	+	0.103245i	−0.834681	+	0.550733i	$0.814348\pi$
$464$	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	$0.233720\pi$
$467$			625.811i			1.34007i	−0.742331	+	0.670033i	$0.766280\pi$
$468$		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	0.193625	−	0.981076i	$-0.437976\pi$
$479$	−267.856	−	154.647i	−0.559199	−	0.322854i	−0.752824	+	0.658222i	$0.771309\pi$
$480$		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	−0.710348	+	0.703851i	$0.751462\pi$
$491$	−822.461	+	474.848i	−1.67507	+	0.967105i	−0.964727	+	0.263254i	$0.915204\pi$
$492$		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	0.997379	+	0.0723525i	$0.0230507\pi$
$499$	280.113	+	485.170i	0.561349	+	0.972284i	−0.436030	+	0.899932i	$0.643616\pi$
$500$	−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	$0.351034\pi$
$503$			897.832i			1.78495i	−0.451094	+	0.892477i	$0.648966\pi$
$504$		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	−0.323126	−	0.946356i	$-0.604734\pi$
$509$	170.454	−	98.4114i	0.334879	−	0.193343i	0.658005	+	0.753013i	$0.271400\pi$
$510$		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	$0.117458\pi$
$521$			375.837i			0.721377i	−0.932686	+	0.360688i	$0.882542\pi$
$522$		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	−0.570513	−	0.821289i	$-0.693256\pi$
$547$	233.022	−	403.606i	0.426000	−	0.737854i	0.996513	+	0.0834344i	$0.0265889\pi$
$548$		−	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	$-0.785541\pi$
$557$		−	695.042i		−	1.24783i	0.781492	−	0.623916i	$-0.214459\pi$
$558$		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	−0.0162552	−	0.999868i	$-0.505174\pi$
$563$	473.780	−	273.537i	0.841528	−	0.485857i	0.857783	+	0.514011i	$0.171841\pi$
$564$		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	0.298082	−	0.954540i	$-0.403653\pi$
$569$	−215.954	−	124.681i	−0.379533	−	0.219123i	−0.677615	+	0.735417i	$0.736986\pi$
$570$		0			0
$571$	−36.9166	−	63.9414i	−0.0646525	−	0.111981i	0.831887	−	0.554945i	$-0.187261\pi$
$571$	−36.9166	−	63.9414i	−0.0646525	−	0.111981i	−0.896540	+	0.442963i	$0.853927\pi$
$572$	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	0.788349	−	0.615228i	$-0.210936\pi$
$587$	381.386	+	220.194i	0.649721	+	0.375117i	−0.138628	+	0.990345i	$0.544269\pi$
$588$		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	$0.0945789\pi$
$593$			347.232i			0.585551i	−0.956181	+	0.292776i	$0.905421\pi$
$594$		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	0.195107	−	0.980782i	$-0.437495\pi$
$599$	684.083	−	394.956i	1.14204	−	0.659359i	0.946936	+	0.321423i	$0.104161\pi$
$600$		0			0
$601$	353.455	−	612.201i	0.588111	−	1.01864i	−0.406369	−	0.913709i	$-0.633205\pi$
$601$	353.455	−	612.201i	0.588111	−	1.01864i	0.994480	−	0.104929i	$-0.0334614\pi$
$602$		−	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	0.650866	+	0.759193i	$0.274406\pi$
$607$	596.628	+	1033.39i	0.982913	+	1.70246i	0.332048	+	0.943263i	$0.392261\pi$
$608$	−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	−0.629122	−	0.777306i	$-0.716586\pi$
$617$	−166.909	+	96.3648i	−0.270516	+	0.156183i	0.358606	+	0.933489i	$0.383252\pi$
$618$		0			0
$619$	76.4773	−	132.463i	0.123550	−	0.213994i	−0.797615	−	0.603166i	$-0.793905\pi$
$619$	76.4773	−	132.463i	0.123550	−	0.213994i	0.921165	+	0.389172i	$0.127239\pi$
$620$		−	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	0.654161	−	0.756355i	$-0.273022\pi$
$641$	209.106	+	120.727i	0.326219	+	0.188342i	−0.327942	+	0.944698i	$0.606355\pi$
$642$		0			0
$643$	−395.704	−	685.380i	−0.615403	−	1.06591i	−0.990314	−	0.138849i	$-0.955660\pi$
$643$	−395.704	−	685.380i	−0.615403	−	1.06591i	0.374910	−	0.927061i	$-0.377674\pi$
$644$	−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	$-0.927035\pi$
$647$		−	294.028i		−	0.454448i	0.973842	−	0.227224i	$-0.0729650\pi$
$648$		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	0.105155	−	0.994456i	$-0.466466\pi$
$653$	665.379	−	384.156i	1.01896	−	0.588295i	0.913802	+	0.406161i	$0.133133\pi$
$654$		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	0.755678	−	0.654944i	$-0.227308\pi$
$659$	373.204	+	215.469i	0.566318	+	0.326964i	−0.189359	+	0.981908i	$0.560641\pi$
$660$		0			0
$661$	−506.136	−	876.653i	−0.765712	−	1.32625i	−0.939869	−	0.341534i	$-0.889053\pi$
$661$	−506.136	−	876.653i	−0.765712	−	1.32625i	0.174157	−	0.984718i	$-0.444280\pi$
$662$	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	−0.995782	−	0.0917499i	$-0.970754\pi$
$673$	−281.606	+	487.755i	−0.418433	+	0.724748i	0.577349	+	0.816498i	$0.304087\pi$
$674$			432.192i			0.641235i
$675$		0			0
$676$	149.939			0.221803
$677$	303.227	+	175.068i	0.447897	+	0.258594i	0.706942	−	0.707272i	$-0.250074\pi$
$677$	303.227	+	175.068i	0.447897	+	0.258594i	−0.259044	+	0.965865i	$0.583408\pi$
$678$		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	$-0.880010\pi$
$683$		−	502.818i		−	0.736190i	0.929788	−	0.368095i	$-0.119990\pi$
$684$		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	−0.969450	−	0.245287i	$-0.921118\pi$
$691$	−188.159	+	325.902i	−0.272300	+	0.471638i	0.697150	+	0.716925i	$0.254451\pi$
$692$			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	$-0.886429\pi$
$701$		−	489.681i		−	0.698546i	0.937021	−	0.349273i	$-0.113571\pi$
$702$		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	−0.983349	−	0.181728i	$-0.941831\pi$
$709$	−237.014	+	410.521i	−0.334294	+	0.579014i	0.649055	+	0.760741i	$0.275164\pi$
$710$			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	$0.0239561\pi$
$719$			108.122i			0.150379i	−0.997169	+	0.0751894i	$0.976044\pi$
$720$		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	−0.671662	−	0.740858i	$-0.734419\pi$
$727$	222.296	−	385.027i	0.305771	−	0.529611i	0.977433	+	0.211247i	$0.0677524\pi$
$728$		−	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	0.999915	−	0.0130556i	$-0.00415584\pi$
$733$	358.181	+	620.388i	0.488651	+	0.846368i	−0.511264	+	0.859424i	$0.670823\pi$
$734$	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	−0.490699	−	0.871329i	$-0.663258\pi$
$743$	13.7793	−	7.95550i	0.0185455	−	0.0107073i	0.509244	+	0.860622i	$0.329925\pi$
$744$		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	−0.998949	−	0.0458347i	$-0.985405\pi$
$751$	−404.916	−	701.334i	−0.539169	−	0.933867i	0.459781	−	0.888033i	$-0.347928\pi$
$752$	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	0.152479	−	0.988307i	$-0.451274\pi$
$761$	825.393	−	476.541i	1.08462	−	0.626204i	0.932138	+	0.362103i	$0.117941\pi$
$762$		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	0.996603	−	0.0823545i	$-0.0262440\pi$
$769$	328.348	+	568.715i	0.426980	+	0.739552i	−0.569623	+	0.821906i	$0.692911\pi$
$770$	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	$0.0575555\pi$
$773$			278.021i			0.359665i	−0.983697	+	0.179832i	$0.942445\pi$
$774$		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	−0.999666	−	0.0258350i	$-0.991776\pi$
$787$	−410.977	−	711.833i	−0.522207	−	0.904489i	0.477459	−	0.878654i	$-0.341558\pi$
$788$	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	−0.997644	−	0.0686043i	$-0.978145\pi$
$797$	−1145.33	+	661.257i	−1.43705	+	0.829683i	−0.439409	+	0.898287i	$0.644812\pi$
$798$		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	$-0.953469\pi$
$809$		−	235.681i		−	0.291324i	0.989334	−	0.145662i	$-0.0465311\pi$
$810$		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	0.906967	−	0.421202i	$-0.138392\pi$
$821$	817.453	+	471.956i	0.995679	+	0.574856i	0.0887121	+	0.996057i	$0.471725\pi$
$822$		0			0
$823$	807.871	+	1399.27i	0.981617	+	1.70021i	0.656097	+	0.754676i	$0.272206\pi$
$823$	807.871	+	1399.27i	0.981617	+	1.70021i	0.325520	+	0.945535i	$0.394461\pi$
$824$	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	$-0.885472\pi$
$827$		−	582.354i		−	0.704177i	0.935967	−	0.352088i	$-0.114528\pi$
$828$		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	0.954561	−	0.298016i	$-0.0963247\pi$
$839$	984.778	+	568.562i	1.17375	+	0.677666i	0.219191	+	0.975682i	$0.429658\pi$
$840$		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	−0.756939	−	0.653486i	$-0.773306\pi$
$853$	159.909	−	276.970i	0.187466	−	0.324701i	0.944405	+	0.328785i	$0.106639\pi$
$854$		−	154.557i		−	0.180980i
$855$		0			0
$856$	−101.939			−0.119087
$857$	−691.061	−	398.984i	−0.806372	−	0.465559i	0.0393225	−	0.999227i	$-0.487480\pi$
$857$	−691.061	−	398.984i	−0.806372	−	0.465559i	−0.845694	+	0.533668i	$0.820813\pi$
$858$		0			0
$859$	233.901	+	405.128i	0.272294	+	0.471627i	0.969449	−	0.245293i	$-0.0788843\pi$
$859$	233.901	+	405.128i	0.272294	+	0.471627i	−0.697155	+	0.716921i	$0.745551\pi$
$860$	−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	$0.272846\pi$
$863$			1304.85i			1.51199i	−0.654578	+	0.755994i	$0.727154\pi$
$864$		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	0.952679	−	0.303977i	$-0.0983146\pi$
$877$	186.878	+	323.682i	0.213088	+	0.369079i	−0.739592	+	0.673056i	$0.764981\pi$
$878$	−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	$-0.958335\pi$
$881$		−	229.979i		−	0.261043i	0.991445	−	0.130522i	$-0.0416652\pi$
$882$		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	−0.862490	−	0.506075i	$-0.831096\pi$
$887$	−758.794	+	438.090i	−0.855461	+	0.493901i	0.00702852	+	0.999975i	$0.497763\pi$
$888$		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	0.332456	+	0.943119i	$0.392123\pi$
$907$	−590.037	+	1021.97i	−0.650537	+	1.12676i	−0.982993	+	0.183644i	$0.941211\pi$
$908$			152.542i			0.167998i
$909$		0			0
$910$	−594.892			−0.653728
$911$	−1100.13	−	635.158i	−1.20760	−	0.697210i	−0.245368	−	0.969430i	$-0.578909\pi$
$911$	−1100.13	−	635.158i	−1.20760	−	0.697210i	−0.962235	+	0.272220i	$0.912242\pi$
$912$		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	0.178145	−	0.984004i	$-0.442991\pi$
$929$	−543.424	−	313.746i	−0.584956	−	0.337724i	−0.763100	+	0.646280i	$0.776324\pi$
$930$		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	−0.862845	−	0.505469i	$-0.831320\pi$
$941$	−805.984	+	465.335i	−0.856518	+	0.494511i	0.00632656	+	0.999980i	$0.497986\pi$
$942$		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	0.501659	−	0.865065i	$-0.332723\pi$
$947$	3.14465	+	1.81556i	0.00332064	+	0.00191717i	−0.498339	+	0.866982i	$0.666056\pi$
$948$		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	$0.123239\pi$
$953$			719.641i			0.755132i	−0.925983	+	0.377566i	$0.876761\pi$
$954$		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	0.857162	−	0.515047i	$-0.172226\pi$
$967$	−16.8870	−	29.2491i	−0.0174633	−	0.0302473i	−0.874625	+	0.484800i	$0.838892\pi$
$968$	−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	$-0.833433\pi$
$971$		−	970.472i		−	0.999456i	0.866182	−	0.499728i	$-0.166567\pi$
$972$		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	0.398406	−	0.917209i	$-0.369563\pi$
$977$	1359.92	−	785.151i	1.39194	−	0.803635i	0.993529	+	0.113574i	$0.0362300\pi$
$978$		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	0.801192	−	0.598408i	$-0.204200\pi$
$983$	671.930	+	387.939i	0.683551	+	0.394648i	−0.117641	+	0.993056i	$0.537533\pi$
$984$		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	0.364290	+	0.931286i	$0.381312\pi$
$997$	−622.499	+	1078.20i	−0.624372	+	1.08144i	−0.988662	+	0.150159i	$0.952022\pi$
$998$		−	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.35.1		4
3.2	odd	2		18.3.d.a.11.2	yes	4
4.3	odd	2		432.3.q.d.305.1		4
5.2	odd	4		1350.3.k.a.899.4		8
5.3	odd	4		1350.3.k.a.899.1		8
5.4	even	2		1350.3.i.b.251.2		4
8.3	odd	2		1728.3.q.c.1601.1		4
8.5	even	2		1728.3.q.d.1601.2		4
9.2	odd	6		162.3.b.a.161.1		4
9.4	even	3		18.3.d.a.5.2	✓	4
9.5	odd	6	inner	54.3.d.a.17.1		4
9.7	even	3		162.3.b.a.161.4		4
12.11	even	2		144.3.q.c.65.2		4
15.2	even	4		450.3.k.a.299.1		8
15.8	even	4		450.3.k.a.299.4		8
15.14	odd	2		450.3.i.b.101.1		4
24.5	odd	2		576.3.q.f.65.2		4
24.11	even	2		576.3.q.e.65.1		4
36.7	odd	6		1296.3.e.g.161.4		4
36.11	even	6		1296.3.e.g.161.2		4
36.23	even	6		432.3.q.d.17.1		4
36.31	odd	6		144.3.q.c.113.2		4
45.4	even	6		450.3.i.b.401.1		4
45.13	odd	12		450.3.k.a.149.1		8
45.14	odd	6		1350.3.i.b.1151.2		4
45.22	odd	12		450.3.k.a.149.4		8
45.23	even	12		1350.3.k.a.449.4		8
45.32	even	12		1350.3.k.a.449.1		8
72.5	odd	6		1728.3.q.d.449.2		4
72.13	even	6		576.3.q.f.257.2		4
72.59	even	6		1728.3.q.c.449.1		4
72.67	odd	6		576.3.q.e.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	9.4	even	3
18.3.d.a.11.2	yes	4	3.2	odd	2
54.3.d.a.17.1		4	9.5	odd	6	inner
54.3.d.a.35.1		4	1.1	even	1	trivial
144.3.q.c.65.2		4	12.11	even	2
144.3.q.c.113.2		4	36.31	odd	6
162.3.b.a.161.1		4	9.2	odd	6
162.3.b.a.161.4		4	9.7	even	3
432.3.q.d.17.1		4	36.23	even	6
432.3.q.d.305.1		4	4.3	odd	2
450.3.i.b.101.1		4	15.14	odd	2
450.3.i.b.401.1		4	45.4	even	6
450.3.k.a.149.1		8	45.13	odd	12
450.3.k.a.149.4		8	45.22	odd	12
450.3.k.a.299.1		8	15.2	even	4
450.3.k.a.299.4		8	15.8	even	4
576.3.q.e.65.1		4	24.11	even	2
576.3.q.e.257.1		4	72.67	odd	6
576.3.q.f.65.2		4	24.5	odd	2
576.3.q.f.257.2		4	72.13	even	6
1296.3.e.g.161.2		4	36.11	even	6
1296.3.e.g.161.4		4	36.7	odd	6
1350.3.i.b.251.2		4	5.4	even	2
1350.3.i.b.1151.2		4	45.14	odd	6
1350.3.k.a.449.1		8	45.32	even	12
1350.3.k.a.449.4		8	45.23	even	12
1350.3.k.a.899.1		8	5.3	odd	4
1350.3.k.a.899.4		8	5.2	odd	4
1728.3.q.c.449.1		4	72.59	even	6
1728.3.q.c.1601.1		4	8.3	odd	2
1728.3.q.d.449.2		4	72.5	odd	6
1728.3.q.d.1601.2		4	8.5	even	2

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

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