LMFDB - Embedded newform 144.3.q.c.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.q (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:	$3.92371580679$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	144.113
Dual form			144.3.q.c.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(-4.17423 - 7.22999i) q^{7} +(3.00000 - 8.48528i) q^{9} +O(q^{10})$	\(q+(2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(-4.17423 - 7.22999i) q^{7} +(3.00000 - 8.48528i) q^{9} +(-0.825765 + 0.476756i) q^{11} +(4.84847 - 8.39780i) q^{13} +(-15.5227 + 1.43027i) q^{15} +18.8776i q^{17} +24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(-0.825765 - 0.476756i) q^{23} +(1.00000 + 1.73205i) q^{25} +(-7.34847 - 25.9808i) q^{27} +(11.8485 - 6.84072i) q^{29} +(1.52270 - 2.63740i) q^{31} +(-1.19694 + 2.59808i) q^{33} +43.3799i q^{35} +46.6969 q^{37} +(-2.66913 - 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(22.5227 + 39.0105i) q^{43} +(-35.5454 + 30.3895i) q^{45} +(-39.2196 + 22.6435i) q^{47} +(-10.3485 + 17.9241i) q^{49} +(32.6969 + 46.2405i) q^{51} +94.3879i q^{53} +4.95459 q^{55} +(60.4949 - 42.7764i) q^{57} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} +(-73.8712 + 13.7296i) q^{63} +(-43.6362 + 25.1934i) q^{65} +(37.5227 - 64.9912i) q^{67} +(-2.84847 + 0.262459i) q^{69} +18.0204i q^{71} -7.90918 q^{73} +(5.44949 + 2.51059i) q^{75} +(6.89388 + 3.98018i) q^{77} +(-21.8712 - 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} +(112.871 - 65.1662i) q^{83} +(49.0454 - 84.9491i) q^{85} +(17.1742 - 37.2784i) q^{87} -145.300i q^{89} -80.9546 q^{91} +(-0.838264 - 9.09769i) q^{93} +(-111.136 - 64.1645i) q^{95} +(54.9393 + 95.1576i) q^{97} +(1.56811 + 8.43712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9	$ 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9} - 18 q^{11} - 10 q^{13} - 18 q^{15} + 40 q^{19} - 42 q^{21} - 18 q^{23} + 4 q^{25} + 18 q^{29} - 38 q^{31} + 54 q^{33} + 128 q^{37} + 102 q^{39} - 126 q^{41} + 46 q^{43} - 54 q^{45} - 54 q^{47} - 12 q^{49} + 72 q^{51} + 108 q^{55} + 144 q^{57} - 126 q^{59} + 62 q^{61} - 222 q^{63} + 90 q^{65} + 106 q^{67} + 18 q^{69} - 208 q^{73} + 12 q^{75} - 90 q^{77} - 14 q^{79} - 252 q^{81} + 378 q^{83} + 108 q^{85} + 54 q^{87} - 412 q^{91} + 222 q^{93} - 180 q^{95} + 14 q^{97} - 126 q^{99}+O(q^{100}) $ 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9 - 18 * q^11 - 10 * q^13 - 18 * q^15 + 40 * q^19 - 42 * q^21 - 18 * q^23 + 4 * q^25 + 18 * q^29 - 38 * q^31 + 54 * q^33 + 128 * q^37 + 102 * q^39 - 126 * q^41 + 46 * q^43 - 54 * q^45 - 54 * q^47 - 12 * q^49 + 72 * q^51 + 108 * q^55 + 144 * q^57 - 126 * q^59 + 62 * q^61 - 222 * q^63 + 90 * q^65 + 106 * q^67 + 18 * q^69 - 208 * q^73 + 12 * q^75 - 90 * q^77 - 14 * q^79 - 252 * q^81 + 378 * q^83 + 108 * q^85 + 54 * q^87 - 412 * q^91 + 222 * q^93 - 180 * q^95 + 14 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.44949	−	1.73205i	0.816497	−	0.577350i
$3$	2.44949	−	1.73205i	0.816497	−	0.577350i
$4$		0			0
$5$	−4.50000	−	2.59808i	−0.900000	−	0.519615i	−0.0227998	−	0.999740i	$-0.507258\pi$
$5$	−4.50000	−	2.59808i	−0.900000	−	0.519615i	−0.877200	+	0.480125i	$0.840591\pi$
$6$		0			0
$7$	−4.17423	−	7.22999i	−0.596319	−	1.03286i	−0.993359	−	0.115054i	$-0.963296\pi$
$7$	−4.17423	−	7.22999i	−0.596319	−	1.03286i	0.397040	−	0.917801i	$-0.370037\pi$
$8$		0			0
$9$	3.00000	−	8.48528i	0.333333	−	0.942809i
$10$		0			0
$11$	−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	$0.0450098\pi$
$14$		0			0
$15$	−15.5227	+	1.43027i	−1.03485	+	0.0953512i
$16$		0			0
$17$			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	$-0.274803\pi$
$19$	24.6969			1.29984			0.649919	+	0.760003i	$0.274803\pi$
$20$		0			0
$21$	−22.7474	−	10.4798i	−1.08321	−	0.499038i
$22$		0			0
$23$	−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
$26$		0			0
$27$	−7.34847	−	25.9808i	−0.272166	−	0.962250i
$28$		0			0
$29$	11.8485	−	6.84072i	0.408568	−	0.235887i	−0.281606	−	0.959530i	$-0.590867\pi$
$29$	11.8485	−	6.84072i	0.408568	−	0.235887i	0.690174	+	0.723643i	$0.257534\pi$
$30$		0			0
$31$	1.52270	−	2.63740i	0.0491195	−	0.0850774i	−0.840420	−	0.541935i	$-0.817692\pi$
$31$	1.52270	−	2.63740i	0.0491195	−	0.0850774i	0.889540	+	0.456858i	$0.151025\pi$
$32$		0			0
$33$	−1.19694	+	2.59808i	−0.0362709	+	0.0787296i
$34$		0			0
$35$			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	$0.282628\pi$
$38$		0			0
$39$	−2.66913	−	28.9681i	−0.0684393	−	0.742772i
$40$		0			0
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	0.380249	−	0.924884i	$-0.375838\pi$
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	−0.610849	+	0.791747i	$0.709172\pi$
$42$		0			0
$43$	22.5227	+	39.0105i	0.523784	+	0.907220i	0.999617	+	0.0276845i	$0.00881337\pi$
$43$	22.5227	+	39.0105i	0.523784	+	0.907220i	−0.475833	+	0.879536i	$0.657853\pi$
$44$		0			0
$45$	−35.5454	+	30.3895i	−0.789898	+	0.675323i
$46$		0			0
$47$	−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
$50$		0			0
$51$	32.6969	+	46.2405i	0.641116	+	0.906676i
$52$		0			0
$53$			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
$56$		0			0
$57$	60.4949	−	42.7764i	1.06131	−	0.750462i
$58$		0			0
$59$	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	$0.867554\pi$
$62$		0			0
$63$	−73.8712	+	13.7296i	−1.17256	+	0.217930i
$64$		0			0
$65$	−43.6362	+	25.1934i	−0.671327	+	0.387591i
$66$		0			0
$67$	37.5227	−	64.9912i	0.560040	−	0.970018i	−0.437452	−	0.899242i	$-0.644119\pi$
$67$	37.5227	−	64.9912i	0.560040	−	0.970018i	0.997492	−	0.0707765i	$-0.0225477\pi$
$68$		0			0
$69$	−2.84847	+	0.262459i	−0.0412822	+	0.00380375i
$70$		0			0
$71$			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	$0.517252\pi$
$74$		0			0
$75$	5.44949	+	2.51059i	0.0726599	+	0.0334745i
$76$		0			0
$77$	6.89388	+	3.98018i	0.0895309	+	0.0516907i
$78$		0			0
$79$	−21.8712	−	37.8820i	−0.276850	−	0.479519i	0.693750	−	0.720216i	$-0.255957\pi$
$79$	−21.8712	−	37.8820i	−0.276850	−	0.479519i	−0.970600	+	0.240697i	$0.922624\pi$
$80$		0			0
$81$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$82$		0			0
$83$	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
$86$		0			0
$87$	17.1742	−	37.2784i	0.197405	−	0.428488i
$88$		0			0
$89$		−	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
$92$		0			0
$93$	−0.838264	−	9.09769i	−0.00901359	−	0.0978246i
$94$		0			0
$95$	−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	$0.641675\pi$
$98$		0			0
$99$	1.56811	+	8.43712i	0.0158395	+	0.0852234i
$100$		0			0
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.291022	−	0.956716i	$-0.406005\pi$
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.974052	+	0.226326i	$0.0726714\pi$
$102$		0			0
$103$	−51.5681	+	89.3186i	−0.500661	+	0.867171i	0.499338	+	0.866407i	$0.333576\pi$
$103$	−51.5681	+	89.3186i	−0.500661	+	0.867171i	−1.00000		0.000763745i	$0.999757\pi$
$104$		0			0
$105$	75.1362	+	106.259i	0.715583	+	1.01199i
$106$		0			0
$107$			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	$0.738085\pi$
$110$		0			0
$111$	114.384	−	80.8815i	1.03048	−	0.728662i
$112$		0			0
$113$	−148.166	−	85.5439i	−1.31121	−	0.757025i	−0.328910	−	0.944361i	$-0.606681\pi$
$113$	−148.166	−	85.5439i	−1.31121	−	0.757025i	−0.982296	+	0.187336i	$0.940015\pi$
$114$		0			0
$115$	2.47730	+	4.29080i	0.0215417	+	0.0373113i
$116$		0			0
$117$	−56.7122	−	66.3340i	−0.484720	−	0.566957i
$118$		0			0
$119$	136.485	−	78.7995i	1.14693	−	0.662180i
$120$		0			0
$121$	−60.0454	+	104.002i	−0.496243	+	0.859518i
$122$		0			0
$123$	−32.6135	+	3.00502i	−0.265151	+	0.0244311i
$124$		0			0
$125$			119.512i			0.956092i
$126$		0			0
$127$	78.0908			0.614888			0.307444	−	0.951566i	$-0.400526\pi$
$127$	78.0908			0.614888			0.307444	+	0.951566i	$0.400526\pi$
$128$		0			0
$129$	122.737	+	56.5453i	0.951452	+	0.438335i
$130$		0			0
$131$	−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
$134$		0			0
$135$	−34.4319	+	136.005i	−0.255051	+	1.00745i
$136$		0			0
$137$	129.758	−	74.9156i	0.947136	−	0.546829i	0.0549460	−	0.998489i	$-0.482501\pi$
$137$	129.758	−	74.9156i	0.947136	−	0.546829i	0.892190	+	0.451660i	$0.149168\pi$
$138$		0			0
$139$	−42.2650	+	73.2052i	−0.304065	+	0.526656i	−0.977053	−	0.212998i	$-0.931677\pi$
$139$	−42.2650	+	73.2052i	−0.304065	+	0.526656i	0.672988	+	0.739654i	$0.265011\pi$
$140$		0			0
$141$	−56.8485	+	123.395i	−0.403181	+	0.875144i
$142$		0			0
$143$			9.24614i			0.0646584i
$144$		0			0
$145$	−71.0908			−0.490281
$146$		0			0
$147$	5.69694	+	61.8289i	0.0387547	+	0.420605i
$148$		0			0
$149$	100.030	+	57.7524i	0.671343	+	0.387600i	0.796585	−	0.604526i	$-0.206638\pi$
$149$	100.030	+	57.7524i	0.671343	+	0.387600i	−0.125242	+	0.992126i	$0.539971\pi$
$150$		0			0
$151$	−32.3865	−	56.0950i	−0.214480	−	0.371490i	0.738632	−	0.674109i	$-0.235472\pi$
$151$	−32.3865	−	56.0950i	−0.214480	−	0.371490i	−0.953112	+	0.302619i	$0.902139\pi$
$152$		0			0
$153$	160.182	+	56.6328i	1.04694	+	0.370149i
$154$		0			0
$155$	−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	$0.145547\pi$
$158$		0			0
$159$	163.485	+	231.202i	1.02821	+	1.45410i
$160$		0			0
$161$			7.96036i			0.0494433i
$162$		0			0
$163$	−133.060			−0.816320			−0.408160	−	0.912910i	$-0.633829\pi$
$163$	−133.060			−0.816320			−0.408160	+	0.912910i	$0.633829\pi$
$164$		0			0
$165$	12.1362	−	8.58161i	0.0735529	−	0.0520097i
$166$		0			0
$167$	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
$170$		0			0
$171$	74.0908	−	209.560i	0.433280	−	1.22550i
$172$		0			0
$173$	−59.9847	+	34.6322i	−0.346732	+	0.200186i	−0.663245	−	0.748402i	$-0.730821\pi$
$173$	−59.9847	+	34.6322i	−0.346732	+	0.200186i	0.316513	+	0.948588i	$0.397488\pi$
$174$		0			0
$175$	8.34847	−	14.4600i	0.0477055	−	0.0826284i
$176$		0			0
$177$	56.1061	−	5.16964i	0.316984	−	0.0292070i
$178$		0			0
$179$			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	$0.265893\pi$
$182$		0			0
$183$	−35.6691	−	16.4328i	−0.194913	−	0.0897969i
$184$		0			0
$185$	−210.136	−	121.322i	−1.13587	−	0.655796i
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.0481283	−	0.0833607i
$188$		0			0
$189$	−157.166	+	161.579i	−0.831568	+	0.854916i
$190$		0			0
$191$	−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	$0.813871\pi$
$194$		0			0
$195$	−63.2503	+	137.291i	−0.324360	+	0.704057i
$196$		0			0
$197$		−	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	$-0.626019\pi$
$199$	−153.485			−0.771280			−0.385640	+	0.922649i	$0.626019\pi$
$200$		0			0
$201$	−20.6566	−	224.187i	−0.102769	−	1.11536i
$202$		0			0
$203$	−98.9166	−	57.1095i	−0.487274	−	0.281328i
$204$		0			0
$205$	28.3638	+	49.1275i	0.138360	+	0.239646i
$206$		0			0
$207$	−6.52270	+	5.57658i	−0.0315106	+	0.0269400i
$208$		0			0
$209$	−20.3939	+	11.7744i	−0.0975784	+	0.0563369i
$210$		0			0
$211$	−25.7804	+	44.6529i	−0.122182	+	0.211625i	−0.920628	−	0.390441i	$-0.872322\pi$
$211$	−25.7804	+	44.6529i	−0.122182	+	0.211625i	0.798446	+	0.602066i	$0.205656\pi$
$212$		0			0
$213$	31.2122	+	44.1408i	0.146536	+	0.207234i
$214$		0			0
$215$		−	234.063i		−	1.08866i
$216$		0			0
$217$	−25.4245			−0.117164
$218$		0			0
$219$	−19.3735	+	13.6991i	−0.0884633	+	0.0625530i
$220$		0			0
$221$	158.530	+	91.5274i	0.717331	+	0.414151i
$222$		0			0
$223$	156.614	+	271.263i	0.702303	+	1.21642i	0.967656	+	0.252273i	$0.0811781\pi$
$223$	156.614	+	271.263i	0.702303	+	1.21642i	−0.265353	+	0.964151i	$0.585489\pi$
$224$		0			0
$225$	17.6969	−	3.28913i	0.0786531	−	0.0146184i
$226$		0			0
$227$	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	$0.0811686\pi$
$230$		0			0
$231$	23.7804	−	2.19113i	0.102945	−	0.00948541i
$232$		0			0
$233$			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
$236$		0			0
$237$	−119.187	−	54.9095i	−0.502898	−	0.231686i
$238$		0			0
$239$	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	$0.970829\pi$
$242$		0			0
$243$	−242.499	−	15.5885i	−0.997940	−	0.0641500i
$244$		0			0
$245$	93.1362	−	53.7722i	0.380148	−	0.219478i
$246$		0			0
$247$	119.742	−	207.400i	0.484787	−	0.839675i
$248$		0			0
$249$	163.606	−	355.123i	0.657051	−	1.42619i
$250$		0			0
$251$			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
$254$		0			0
$255$	−27.0000	−	293.031i	−0.105882	−	1.14914i
$256$		0			0
$257$	−69.8939	−	40.3532i	−0.271961	−	0.157017i	0.357818	−	0.933791i	$-0.383521\pi$
$257$	−69.8939	−	40.3532i	−0.271961	−	0.157017i	−0.629778	+	0.776775i	$0.716854\pi$
$258$		0			0
$259$	−194.924	−	337.618i	−0.752602	−	1.30355i
$260$		0			0
$261$	−22.5000	−	121.060i	−0.0862069	−	0.463830i
$262$		0			0
$263$	−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
$266$		0			0
$267$	−251.666	−	355.910i	−0.942570	−	1.33300i
$268$		0			0
$269$			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	$-0.282165\pi$
$271$	342.636			1.26434			0.632169	+	0.774830i	$0.282165\pi$
$272$		0			0
$273$	−198.297	+	140.217i	−0.726364	+	0.513617i
$274$		0			0
$275$	−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	$0.805143\pi$
$278$		0			0
$279$	−17.8110	−	20.8328i	−0.0638386	−	0.0746694i
$280$		0			0
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	−0.531476	−	0.847073i	$-0.678362\pi$
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	0.467849	+	0.883808i	$0.345029\pi$
$282$		0			0
$283$	26.7043	−	46.2533i	0.0943616	−	0.163439i	−0.814980	−	0.579489i	$-0.803252\pi$
$283$	26.7043	−	46.2533i	0.0943616	−	0.163439i	0.909342	+	0.416049i	$0.136586\pi$
$284$		0			0
$285$	−383.363	+	35.3232i	−1.34513	+	0.123941i
$286$		0			0
$287$			91.1421i			0.317568i
$288$		0			0
$289$	−67.3633			−0.233091
$290$		0			0
$291$	299.391	+	137.930i	1.02884	+	0.473986i
$292$		0			0
$293$	−12.9245	−	7.46196i	−0.0441109	−	0.0254674i	0.477782	−	0.878478i	$-0.341441\pi$
$293$	−12.9245	−	7.46196i	−0.0441109	−	0.0254674i	−0.521893	+	0.853011i	$0.674774\pi$
$294$		0			0
$295$	−48.7951	−	84.5157i	−0.165407	−	0.286494i
$296$		0			0
$297$	18.4546	+	17.9506i	0.0621367	+	0.0604397i
$298$		0			0
$299$	−8.00740	+	4.62307i	−0.0267806	+	0.0154618i
$300$		0			0
$301$	188.030	−	325.678i	0.624685	−	1.08199i
$302$		0			0
$303$	185.205	−	402.006i	0.611237	−	1.32675i
$304$		0			0
$305$			68.0219i			0.223023i
$306$		0			0
$307$	−65.9092			−0.214688			−0.107344	−	0.994222i	$-0.534235\pi$
$307$	−65.9092			−0.214688			−0.107344	+	0.994222i	$0.534235\pi$
$308$		0			0
$309$	28.3888	+	308.104i	0.0918731	+	0.997099i
$310$		0			0
$311$	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	$0.594818\pi$
$314$		0			0
$315$	368.091	+	130.140i	1.16854	+	0.413142i
$316$		0			0
$317$	−401.818	+	231.990i	−1.26756	+	0.731829i	−0.974527	−	0.224272i	$-0.927999\pi$
$317$	−401.818	+	231.990i	−1.26756	+	0.731829i	−0.293038	+	0.956101i	$0.594666\pi$
$318$		0			0
$319$	−6.52270	+	11.2977i	−0.0204473	+	0.0354158i
$320$		0			0
$321$	62.4245	+	88.2816i	0.194469	+	0.275020i
$322$		0			0
$323$			466.219i			1.44340i
$324$		0			0
$325$	19.3939			0.0596735
$326$		0			0
$327$	−363.192	+	256.815i	−1.11068	+	0.785368i
$328$		0			0
$329$	327.424	+	189.038i	0.995210	+	0.574585i
$330$		0			0
$331$	236.401	+	409.459i	0.714203	+	1.23704i	0.963266	+	0.268549i	$0.0865441\pi$
$331$	236.401	+	409.459i	0.714203	+	1.23704i	−0.249063	+	0.968487i	$0.580123\pi$
$332$		0			0
$333$	140.091	−	396.237i	0.420693	−	1.18990i
$334$		0			0
$335$	−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	$0.316463\pi$
$338$		0			0
$339$	−511.098	+	47.0928i	−1.50766	+	0.138917i
$340$		0			0
$341$			2.90383i			0.00851564i
$342$		0			0
$343$	−236.287			−0.688884
$344$		0			0
$345$	13.5000	+	6.21947i	0.0391304	+	0.0180275i
$346$		0			0
$347$	−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	$0.788145\pi$
$350$		0			0
$351$	−253.810	−	64.2560i	−0.723105	−	0.183065i
$352$		0			0
$353$	−282.424	+	163.058i	−0.800068	+	0.461919i	−0.843495	−	0.537137i	$-0.819506\pi$
$353$	−282.424	+	163.058i	−0.800068	+	0.461919i	0.0434270	+	0.999057i	$0.486172\pi$
$354$		0			0
$355$	46.8184	−	81.0918i	0.131883	−	0.228428i
$356$		0			0
$357$	197.833	−	429.417i	0.554155	−	1.20285i
$358$		0			0
$359$		−	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
$362$		0			0
$363$	33.0556	+	358.753i	0.0910623	+	0.988300i
$364$		0			0
$365$	35.5913	+	20.5487i	0.0975105	+	0.0562977i
$366$		0			0
$367$	93.6135	+	162.143i	0.255078	+	0.441808i	0.964917	−	0.262557i	$-0.0845656\pi$
$367$	93.6135	+	162.143i	0.255078	+	0.441808i	−0.709839	+	0.704364i	$0.751232\pi$
$368$		0			0
$369$	−74.6816	+	63.8490i	−0.202389	+	0.173033i
$370$		0			0
$371$	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	$0.960001\pi$
$374$		0			0
$375$	207.000	+	292.742i	0.552000	+	0.780646i
$376$		0			0
$377$		−	132.668i		−	0.351905i
$378$		0			0
$379$	489.666			1.29200			0.645998	−	0.763339i	$-0.276442\pi$
$379$	489.666			1.29200			0.645998	+	0.763339i	$0.276442\pi$
$380$		0			0
$381$	191.283	−	135.257i	0.502054	−	0.355006i
$382$		0			0
$383$	−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
$386$		0			0
$387$	398.583	−	74.0801i	1.02993	−	0.191421i
$388$		0			0
$389$	29.6816	−	17.1367i	0.0763024	−	0.0440532i	−0.461363	−	0.887211i	$-0.652640\pi$
$389$	29.6816	−	17.1367i	0.0763024	−	0.0440532i	0.537666	+	0.843158i	$0.319306\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.0230179	−	0.0398682i
$392$		0			0
$393$	−699.227	+	64.4270i	−1.77920	+	0.163936i
$394$		0			0
$395$			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	$0.496684\pi$
$398$		0			0
$399$	−561.792	−	258.819i	−1.40800	−	0.648669i
$400$		0			0
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.875364	−	0.483464i	$-0.160622\pi$
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.0189903	+	0.999820i	$0.493955\pi$
$402$		0			0
$403$	−14.7656	−	25.5747i	−0.0366391	−	0.0634608i
$404$		0			0
$405$	151.228	+	392.781i	0.373401	+	0.969831i
$406$		0			0
$407$	−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	$0.0360960\pi$
$410$		0			0
$411$	188.082	−	408.252i	0.457621	−	0.993314i
$412$		0			0
$413$		−	156.795i		−	0.379648i
$414$		0			0
$415$	−677.227			−1.63187
$416$		0			0
$417$	23.2673	+	252.521i	0.0557970	+	0.605565i
$418$		0			0
$419$	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	$0.942723\pi$
$422$		0			0
$423$	74.4773	+	400.720i	0.176069	+	0.947329i
$424$		0			0
$425$	−32.6969	+	18.8776i	−0.0769340	+	0.0444178i
$426$		0			0
$427$	−54.6441	+	94.6464i	−0.127972	+	0.221654i
$428$		0			0
$429$	16.0148	+	22.6483i	0.0373305	+	0.0527933i
$430$		0			0
$431$		−	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	$0.314640\pi$
$434$		0			0
$435$	−174.136	+	123.133i	−0.400313	+	0.283064i
$436$		0			0
$437$	−20.3939	−	11.7744i	−0.0466679	−	0.0269437i
$438$		0			0
$439$	−278.931	−	483.123i	−0.635379	−	1.10051i	−0.986435	−	0.164154i	$-0.947511\pi$
$439$	−278.931	−	483.123i	−0.635379	−	1.10051i	0.351056	−	0.936355i	$-0.385823\pi$
$440$		0			0
$441$	121.045	+	141.582i	0.274479	+	0.321047i
$442$		0			0
$443$	−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
$446$		0			0
$447$	345.053	−	31.7933i	0.771930	−	0.0711259i
$448$		0			0
$449$		−	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
$452$		0			0
$453$	−176.490	−	81.3092i	−0.389602	−	0.179490i
$454$		0			0
$455$	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	$-0.449626\pi$
$458$		0			0
$459$	490.454	−	138.721i	1.06853	−	0.302225i
$460$		0			0
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	−0.508619	−	0.860992i	$-0.669844\pi$
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	0.491331	+	0.870973i	$0.336511\pi$
$462$		0			0
$463$	−27.5987	+	47.8024i	−0.0596085	+	0.103245i	−0.894290	−	0.447488i	$-0.852319\pi$
$463$	−27.5987	+	47.8024i	−0.0596085	+	0.103245i	0.834681	+	0.550733i	$0.185652\pi$
$464$		0			0
$465$	−19.8643	+	43.1175i	−0.0427189	+	0.0927257i
$466$		0			0
$467$		−	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
$470$		0			0
$471$	−5.73036	−	62.1917i	−0.0121664	−	0.132042i
$472$		0			0
$473$	−37.1969	−	21.4757i	−0.0786405	−	0.0454031i
$474$		0			0
$475$	24.6969	+	42.7764i	0.0519936	+	0.0900555i
$476$		0			0
$477$	800.908	+	283.164i	1.67905	+	0.593635i
$478$		0			0
$479$	−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
$482$		0			0
$483$	13.7878	+	19.4988i	0.0285461	+	0.0403702i
$484$		0			0
$485$		−	570.946i		−	1.17721i
$486$		0			0
$487$	28.3337			0.0581800			0.0290900	−	0.999577i	$-0.490739\pi$
$487$	28.3337			0.0581800			0.0290900	+	0.999577i	$0.490739\pi$
$488$		0			0
$489$	−325.930	+	230.467i	−0.666523	+	0.471303i
$490$		0			0
$491$	−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
$494$		0			0
$495$	14.8638	−	42.0411i	0.0300278	−	0.0849315i
$496$		0			0
$497$	130.287	−	75.2214i	0.262147	−	0.151351i
$498$		0			0
$499$	−280.113	+	485.170i	−0.561349	+	0.972284i	0.436030	+	0.899932i	$0.356384\pi$
$499$	−280.113	+	485.170i	−0.561349	+	0.972284i	−0.997379	+	0.0723525i	$0.976949\pi$
$500$		0			0
$501$	879.802	−	81.0653i	1.75609	−	0.161807i
$502$		0			0
$503$		−	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
$506$		0			0
$507$	204.272	+	94.1087i	0.402904	+	0.185619i
$508$		0			0
$509$	−170.454	−	98.4114i	−0.334879	−	0.193343i	0.323126	−	0.946356i	$-0.395266\pi$
$509$	−170.454	−	98.4114i	−0.334879	−	0.193343i	−0.658005	+	0.753013i	$0.728600\pi$
$510$		0			0
$511$	33.0148	+	57.1833i	0.0646082	+	0.111905i
$512$		0			0
$513$	−181.485	−	641.645i	−0.353771	−	1.25077i
$514$		0			0
$515$	464.113	−	267.956i	0.901190	−	0.520302i
$516$		0			0
$517$	21.5908	−	37.3964i	0.0417617	−	0.0723334i
$518$		0			0
$519$	−86.9472	+	188.728i	−0.167528	+	0.363637i
$520$		0			0
$521$			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	$-0.527783\pi$
$523$	−91.1827			−0.174345			−0.0871727	+	0.996193i	$0.527783\pi$
$524$		0			0
$525$	−4.59592	−	49.8795i	−0.00875413	−	0.0950086i
$526$		0			0
$527$	49.7878	+	28.7450i	0.0944739	+	0.0545445i
$528$		0			0
$529$	−264.045	−	457.340i	−0.499141	−	0.864537i
$530$		0			0
$531$	128.477	−	109.842i	0.241953	−	0.206858i
$532$		0			0
$533$	−91.6806	+	52.9318i	−0.172009	+	0.0993092i
$534$		0			0
$535$	93.6367	−	162.184i	0.175022	−	0.303147i
$536$		0			0
$537$	82.2429	+	116.309i	0.153152	+	0.216590i
$538$		0			0
$539$		−	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	$0.511431\pi$
$542$		0			0
$543$	594.929	−	420.678i	1.09563	−	0.774729i
$544$		0			0
$545$	667.226	+	385.223i	1.22427	+	0.706831i
$546$		0			0
$547$	−233.022	−	403.606i	−0.426000	−	0.737854i	0.570513	−	0.821289i	$-0.306744\pi$
$547$	−233.022	−	403.606i	−0.426000	−	0.737854i	−0.996513	+	0.0834344i	$0.973411\pi$
$548$		0			0
$549$	−115.834	+	21.5287i	−0.210990	+	0.0392144i
$550$		0			0
$551$	292.621	−	168.945i	0.531072	−	0.306615i
$552$		0			0
$553$	−182.591	+	316.257i	−0.330182	+	0.571893i
$554$		0			0
$555$	−724.863	+	66.7891i	−1.30606	+	0.120341i
$556$		0			0
$557$		−	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
$560$		0			0
$561$	−49.0454	−	22.5953i	−0.0874250	−	0.0402768i
$562$		0			0
$563$	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
$566$		0			0
$567$	−105.114	+	668.006i	−0.185386	+	1.17814i
$568$		0			0
$569$	215.954	−	124.681i	0.379533	−	0.219123i	−0.298082	−	0.954540i	$-0.596347\pi$
$569$	215.954	−	124.681i	0.379533	−	0.219123i	0.677615	+	0.735417i	$0.263014\pi$
$570$		0			0
$571$	36.9166	−	63.9414i	0.0646525	−	0.111981i	−0.831887	−	0.554945i	$-0.812739\pi$
$571$	36.9166	−	63.9414i	0.0646525	−	0.111981i	0.896540	+	0.442963i	$0.146073\pi$
$572$		0			0
$573$	−9.45459	+	20.5222i	−0.0165002	+	0.0358153i
$574$		0			0
$575$		−	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	$0.512114\pi$
$578$		0			0
$579$	95.0880	+	1031.99i	0.164228	+	1.78237i
$580$		0			0
$581$	−942.302	−	544.038i	−1.62186	−	0.936382i
$582$		0			0
$583$	−45.0000	−	77.9423i	−0.0771870	−	0.133692i
$584$		0			0
$585$	82.8643	+	445.846i	0.141648	+	0.762130i
$586$		0			0
$587$	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
$590$		0			0
$591$	−133.757	−	189.161i	−0.226323	−	0.320070i
$592$		0			0
$593$			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
$596$		0			0
$597$	−375.959	+	265.843i	−0.629747	+	0.445299i
$598$		0			0
$599$	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	$0.633205\pi$
$602$		0			0
$603$	−438.901	−	513.364i	−0.727862	−	0.851351i
$604$		0			0
$605$	540.409	−	312.005i	0.893237	−	0.515711i
$606$		0			0
$607$	−596.628	+	1033.39i	−0.982913	+	1.70246i	−0.332048	+	0.943263i	$0.607739\pi$
$607$	−596.628	+	1033.39i	−0.982913	+	1.70246i	−0.650866	+	0.759193i	$0.725594\pi$
$608$		0			0
$609$	−341.212	+	31.4394i	−0.560282	+	0.0516246i
$610$		0			0
$611$			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	$0.328461\pi$
$614$		0			0
$615$	154.568	+	71.2098i	0.251330	+	0.115788i
$616$		0			0
$617$	166.909	+	96.3648i	0.270516	+	0.156183i	0.629122	−	0.777306i	$-0.283414\pi$
$617$	166.909	+	96.3648i	0.270516	+	0.156183i	−0.358606	+	0.933489i	$0.616748\pi$
$618$		0			0
$619$	−76.4773	−	132.463i	−0.123550	−	0.213994i	0.797615	−	0.603166i	$-0.206095\pi$
$619$	−76.4773	−	132.463i	−0.123550	−	0.213994i	−0.921165	+	0.389172i	$0.872761\pi$
$620$		0			0
$621$	−6.31837	+	24.9574i	−0.0101745	+	0.0401891i
$622$		0			0
$623$	−1050.51	+	606.515i	−1.68622	+	0.973539i
$624$		0			0
$625$	335.500	−	581.103i	0.536800	−	0.929765i
$626$		0			0
$627$	−29.5607	+	64.1645i	−0.0471463	+	0.102336i
$628$		0			0
$629$			881.525i			1.40147i
$630$		0			0
$631$	−44.8786			−0.0711229			−0.0355615	−	0.999367i	$-0.511322\pi$
$631$	−44.8786			−0.0711229			−0.0355615	+	0.999367i	$0.511322\pi$
$632$		0			0
$633$	14.1924	+	154.030i	0.0224208	+	0.243333i
$634$		0			0
$635$	−351.409	−	202.886i	−0.553399	−	0.319505i
$636$		0			0
$637$	100.348	+	173.809i	0.157533	+	0.272855i
$638$		0			0
$639$	152.908	+	54.0612i	0.239293	+	0.0846028i
$640$		0			0
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	−0.654161	−	0.756355i	$-0.726978\pi$
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	0.327942	+	0.944698i	$0.393645\pi$
$642$		0			0
$643$	395.704	−	685.380i	0.615403	−	1.06591i	−0.374910	−	0.927061i	$-0.622326\pi$
$643$	395.704	−	685.380i	0.615403	−	1.06591i	0.990314	−	0.138849i	$-0.0443402\pi$
$644$		0			0
$645$	−405.409	−	573.334i	−0.628541	−	0.888891i
$646$		0			0
$647$			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
$650$		0			0
$651$	−62.2770	+	44.0365i	−0.0956636	+	0.0676444i
$652$		0			0
$653$	−665.379	−	384.156i	−1.01896	−	0.588295i	−0.105155	−	0.994456i	$-0.533534\pi$
$653$	−665.379	−	384.156i	−1.01896	−	0.588295i	−0.913802	+	0.406161i	$0.866867\pi$
$654$		0			0
$655$	608.113	+	1053.28i	0.928417	+	1.60807i
$656$		0			0
$657$	−23.7276	+	67.1117i	−0.0361150	+	0.102149i
$658$		0			0
$659$	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	$0.889053\pi$
$662$		0			0
$663$	546.848	−	50.3868i	0.824808	−	0.0759981i
$664$		0			0
$665$			1071.35i			1.61105i
$666$		0			0
$667$	−13.0454			−0.0195583
$668$		0			0
$669$	853.464	+	393.192i	1.27573	+	0.587731i
$670$		0			0
$671$	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	$0.970754\pi$
$674$		0			0
$675$	37.6515	−	38.7087i	0.0557800	−	0.0573462i
$676$		0			0
$677$	−303.227	+	175.068i	−0.447897	+	0.258594i	−0.706942	−	0.707272i	$-0.749926\pi$
$677$	−303.227	+	175.068i	−0.447897	+	0.258594i	0.259044	+	0.965865i	$0.416592\pi$
$678$		0			0
$679$	458.659	−	794.421i	0.675492	−	1.16999i
$680$		0			0
$681$	95.7429	−	207.820i	0.140592	−	0.305168i
$682$		0			0
$683$			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
$686$		0			0
$687$	−33.4559	−	363.097i	−0.0486985	−	0.528525i
$688$		0			0
$689$	792.650	+	457.637i	1.15044	+	0.664205i
$690$		0			0
$691$	188.159	+	325.902i	0.272300	+	0.471638i	0.969450	−	0.245287i	$-0.0788823\pi$
$691$	188.159	+	325.902i	0.272300	+	0.471638i	−0.697150	+	0.716925i	$0.745549\pi$
$692$		0			0
$693$	54.4546	−	46.5559i	0.0785781	−	0.0671803i
$694$		0			0
$695$	380.385	−	219.616i	0.547317	−	0.315994i
$696$		0			0
$697$	103.045	−	178.480i	0.147841	−	0.256069i
$698$		0			0
$699$	261.576	+	369.924i	0.374214	+	0.529218i
$700$		0			0
$701$		−	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
$704$		0			0
$705$	576.409	−	407.582i	0.817601	−	0.578131i
$706$		0			0
$707$	−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	$0.941831\pi$
$710$		0			0
$711$	−387.053	+	71.9371i	−0.544378	+	0.101177i
$712$		0			0
$713$	−2.51479	+	1.45192i	−0.00352706	+	0.00203635i
$714$		0			0
$715$	24.0222	−	41.6077i	0.0335975	−	0.0581925i
$716$		0			0
$717$	262.030	−	24.1435i	0.365453	−	0.0336730i
$718$		0			0
$719$		−	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
$722$		0			0
$723$	−549.820	−	253.303i	−0.760470	−	0.350350i
$724$		0			0
$725$	23.6969	+	13.6814i	0.0326854	+	0.0188709i
$726$		0			0
$727$	−222.296	−	385.027i	−0.305771	−	0.529611i	0.671662	−	0.740858i	$-0.265581\pi$
$727$	−222.296	−	385.027i	−0.305771	−	0.529611i	−0.977433	+	0.211247i	$0.932248\pi$
$728$		0			0
$729$	−621.000	+	381.838i	−0.851852	+	0.523783i
$730$		0			0
$731$	−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	$0.00415584\pi$
$734$		0			0
$735$	135.000	−	293.031i	0.183673	−	0.398682i
$736$		0			0
$737$			71.5567i			0.0970918i
$738$		0			0
$739$	−933.362			−1.26301			−0.631504	−	0.775373i	$-0.717562\pi$
$739$	−933.362			−1.26301			−0.631504	+	0.775373i	$0.717562\pi$
$740$		0			0
$741$	−65.9194	−	715.424i	−0.0889600	−	0.965484i
$742$		0			0
$743$	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
$746$		0			0
$747$	−214.340	−	1153.24i	−0.286934	−	1.54383i
$748$		0			0
$749$	260.574	−	150.443i	0.347896	−	0.200858i
$750$		0			0
$751$	404.916	−	701.334i	0.539169	−	0.933867i	−0.459781	−	0.888033i	$-0.652072\pi$
$751$	404.916	−	701.334i	0.539169	−	0.933867i	0.998949	−	0.0458347i	$-0.0145947\pi$
$752$		0			0
$753$	91.1510	+	128.907i	0.121050	+	0.171191i
$754$		0			0
$755$			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	$0.349458\pi$
$758$		0			0
$759$	2.22704	−	1.57475i	0.00293417	−	0.00207477i
$760$		0			0
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.152479	−	0.988307i	$-0.548726\pi$
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.932138	+	0.362103i	$0.882059\pi$
$762$		0			0
$763$	618.924	+	1072.01i	0.811172	+	1.40499i
$764$		0			0
$765$	−573.681	−	671.011i	−0.749910	−	0.877139i
$766$		0			0
$767$	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	$0.0262440\pi$
$770$		0			0
$771$	−241.098	+	22.2149i	−0.312708	+	0.0288131i
$772$		0			0
$773$			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
$776$		0			0
$777$	−1062.24	−	489.374i	−1.36710	−	0.629825i
$778$		0			0
$779$	−233.499	−	134.811i	−0.299743	−	0.173056i
$780$		0			0
$781$	−8.59133	−	14.8806i	−0.0110004	−	0.0190533i
$782$		0			0
$783$	−264.795	−	257.563i	−0.338180	−	0.328944i
$784$		0			0
$785$	−93.6827	+	54.0877i	−0.119341	+	0.0689015i
$786$		0			0
$787$	410.977	−	711.833i	0.522207	−	0.904489i	−0.477459	−	0.878654i	$-0.658442\pi$
$787$	410.977	−	711.833i	0.522207	−	0.904489i	0.999666	−	0.0258350i	$-0.00822444\pi$
$788$		0			0
$789$	−582.135	+	1263.58i	−0.737813	+	1.60150i
$790$		0			0
$791$			1428.32i			1.80572i
$792$		0			0
$793$	−126.941			−0.160077
$794$		0			0
$795$	−135.000	−	1465.16i	−0.169811	−	1.84296i
$796$		0			0
$797$	1145.33	+	661.257i	1.43705	+	0.829683i	0.997644	−	0.0686043i	$-0.0218546\pi$
$797$	1145.33	+	661.257i	1.43705	+	0.829683i	0.439409	+	0.898287i	$0.355188\pi$
$798$		0			0
$799$	−427.454	−	740.372i	−0.534986	−	0.926624i
$800$		0			0
$801$	−1232.91	−	435.899i	−1.53921	−	0.544193i
$802$		0			0
$803$	6.53113	−	3.77075i	0.00813341	−	0.00469583i
$804$		0			0
$805$	20.6816	−	35.8216i	0.0256915	−	0.0444989i
$806$		0			0
$807$	75.3031	+	106.495i	0.0933123	+	0.131964i
$808$		0			0
$809$		−	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	$-0.382052\pi$
$811$	587.362			0.724244			0.362122	+	0.932131i	$0.382052\pi$
$812$		0			0
$813$	839.283	−	593.462i	1.03233	−	0.729966i
$814$		0			0
$815$	598.771	+	345.701i	0.734688	+	0.424172i
$816$		0			0
$817$	556.242	+	963.439i	0.680835	+	1.17924i
$818$		0			0
$819$	−242.864	+	686.922i	−0.296537	+	0.838733i
$820$		0			0
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.906967	−	0.421202i	$-0.861608\pi$
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.0887121	+	0.996057i	$0.528275\pi$
$822$		0			0
$823$	−807.871	+	1399.27i	−0.981617	+	1.70021i	−0.325520	+	0.945535i	$0.605539\pi$
$823$	−807.871	+	1399.27i	−0.981617	+	1.70021i	−0.656097	+	0.754676i	$0.727794\pi$
$824$		0			0
$825$	−5.69694	+	0.524918i	−0.00690538	+	0.000636264i
$826$		0			0
$827$			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	$0.322558\pi$
$830$		0			0
$831$	133.512	+	61.5095i	0.160665	+	0.0740186i
$832$		0			0
$833$	−338.363	−	195.354i	−0.406198	−	0.234519i
$834$		0			0
$835$	−765.158	−	1325.29i	−0.916357	−	1.58718i
$836$		0			0
$837$	−79.7112	−	20.1802i	−0.0952344	−	0.0241101i
$838$		0			0
$839$	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
$842$		0			0
$843$	−25.9155	+	56.2523i	−0.0307421	+	0.0667287i
$844$		0			0
$845$		−	389.552i		−	0.461009i
$846$		0			0
$847$	1002.57			1.18368
$848$		0			0
$849$	−14.7010	−	159.550i	−0.0173157	−	0.187927i
$850$		0			0
$851$	−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	$0.773306\pi$
$854$		0			0
$855$	−877.863	+	750.529i	−1.02674	+	0.877811i
$856$		0			0
$857$	691.061	−	398.984i	0.806372	−	0.465559i	−0.0393225	−	0.999227i	$-0.512520\pi$
$857$	691.061	−	398.984i	0.806372	−	0.465559i	0.845694	+	0.533668i	$0.179187\pi$
$858$		0			0
$859$	−233.901	+	405.128i	−0.272294	+	0.471627i	−0.969449	−	0.245293i	$-0.921116\pi$
$859$	−233.901	+	405.128i	−0.272294	+	0.471627i	0.697155	+	0.716921i	$0.254449\pi$
$860$		0			0
$861$	157.863	+	223.252i	0.183348	+	0.259293i
$862$		0			0
$863$		−	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
$866$		0			0
$867$	−165.006	+	116.677i	−0.190318	+	0.134575i
$868$		0			0
$869$	36.1209	+	20.8544i	0.0415661	+	0.0239982i
$870$		0			0
$871$	−363.855	−	630.216i	−0.417744	−	0.723554i
$872$		0			0
$873$	972.257	−	180.702i	1.11370	−	0.206990i
$874$		0			0
$875$	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	$0.0983146\pi$
$878$		0			0
$879$	−44.5829	+	4.10789i	−0.0507200	+	0.00467336i
$880$		0			0
$881$		−	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	$-0.213976\pi$
$883$	1381.79			1.56488			0.782439	+	0.622728i	$0.213976\pi$
$884$		0			0
$885$	−265.909	−	122.505i	−0.300462	−	0.138423i
$886$		0			0
$887$	−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
$890$		0			0
$891$	76.2957	+	12.0055i	0.0856293	+	0.0134742i
$892$		0			0
$893$	−968.605	+	559.224i	−1.08466	+	0.626231i
$894$		0			0
$895$	123.364	−	213.673i	0.137837	−	0.238741i
$896$		0			0
$897$	−11.6066	+	25.1934i	−0.0129394	+	0.0280863i
$898$		0			0
$899$		−	41.6655i		−	0.0463465i
$900$		0			0
$901$	−1781.82			−1.97760
$902$		0			0
$903$	−103.512	−	1123.42i	−0.114632	−	1.24410i
$904$		0			0
$905$	−1092.95	−	631.017i	−1.20768	−	0.697256i
$906$		0			0
$907$	590.037	+	1021.97i	0.650537	+	1.12676i	0.982993	+	0.183644i	$0.0587894\pi$
$907$	590.037	+	1021.97i	0.650537	+	1.12676i	−0.332456	+	0.943119i	$0.607877\pi$
$908$		0			0
$909$	−242.637	−	1305.49i	−0.266928	−	1.43619i
$910$		0			0
$911$	−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
$914$		0			0
$915$	117.817	+	166.619i	0.128762	+	0.182097i
$916$		0			0
$917$			1954.07i			2.13093i
$918$		0			0
$919$	−1316.63			−1.43268			−0.716340	−	0.697751i	$-0.754184\pi$
$919$	−1316.63			−1.43268			−0.716340	+	0.697751i	$0.754184\pi$
$920$		0			0
$921$	−161.444	+	114.158i	−0.175292	+	0.123950i
$922$		0			0
$923$	151.332	+	87.3713i	0.163956	+	0.0946602i
$924$		0			0
$925$	46.6969	+	80.8815i	0.0504832	+	0.0874394i
$926$		0			0
$927$	603.189	+	705.526i	0.650689	+	0.761085i
$928$		0			0
$929$	543.424	−	313.746i	0.584956	−	0.337724i	−0.178145	−	0.984004i	$-0.557009\pi$
$929$	543.424	−	313.746i	0.584956	−	0.337724i	0.763100	+	0.646280i	$0.223676\pi$
$930$		0			0
$931$	−255.576	+	442.670i	−0.274517	+	0.475478i
$932$		0			0
$933$	747.363	−	68.8623i	0.801032	−	0.0738074i
$934$		0			0
$935$			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	$0.419343\pi$
$938$		0			0
$939$	1161.81	+	535.250i	1.23729	+	0.570021i
$940$		0			0
$941$	805.984	+	465.335i	0.856518	+	0.494511i	0.862845	−	0.505469i	$-0.168680\pi$
$941$	805.984	+	465.335i	0.856518	+	0.494511i	−0.00632656	+	0.999980i	$0.502014\pi$
$942$		0			0
$943$	5.20485	+	9.01506i	0.00551946	+	0.00955998i
$944$		0			0
$945$	1127.04	−	318.776i	1.19264	−	0.337329i
$946$		0			0
$947$	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
$950$		0			0
$951$	−582.431	+	1264.23i	−0.612440	+	1.32936i
$952$		0			0
$953$			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
$956$		0			0
$957$	3.59082	+	38.9711i	0.00375216	+	0.0407222i
$958$		0			0
$959$	−1083.28	−	625.431i	−1.12959	−	0.652170i
$960$		0			0
$961$	475.863	+	824.218i	0.495175	+	0.857667i
$962$		0			0
$963$	305.816	+	108.122i	0.317566	+	0.112277i
$964$		0			0
$965$	1554.54	−	897.516i	1.61093	−	0.930068i
$966$		0			0
$967$	16.8870	−	29.2491i	0.0174633	−	0.0302473i	−0.857162	−	0.515047i	$-0.827774\pi$
$967$	16.8870	−	29.2491i	0.0174633	−	0.0302473i	0.874625	+	0.484800i	$0.161108\pi$
$968$		0			0
$969$	807.514	+	1142.00i	0.833348	+	1.17853i
$970$		0			0
$971$			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
$974$		0			0
$975$	47.5051	−	33.5912i	0.0487232	−	0.0344525i
$976$		0			0
$977$	−1359.92	−	785.151i	−1.39194	−	0.803635i	−0.398406	−	0.917209i	$-0.630437\pi$
$977$	−1359.92	−	785.151i	−1.39194	−	0.803635i	−0.993529	+	0.113574i	$0.963770\pi$
$978$		0			0
$979$	69.2724	+	119.983i	0.0707584	+	0.122557i
$980$		0			0
$981$	−444.817	+	1258.13i	−0.453433	+	1.28250i
$982$		0			0
$983$	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
$986$		0			0
$987$	1129.45	−	104.068i	1.14432	−	0.105438i
$988$		0			0
$989$		−	42.9513i		−	0.0434290i
$990$		0			0
$991$	−870.454			−0.878359			−0.439180	−	0.898399i	$-0.644731\pi$
$991$	−870.454			−0.878359			−0.439180	+	0.898399i	$0.644731\pi$
$992$		0			0
$993$	1288.27	+	593.507i	1.29735	+	0.597690i
$994$		0			0
$995$	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	$-0.381312\pi$
$998$		0			0
$999$	−343.151	−	1213.22i	−0.343495	−	1.21444i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	4.3	odd	2
18.3.d.a.11.2	yes	4	36.11	even	6
54.3.d.a.17.1		4	12.11	even	2
54.3.d.a.35.1		4	36.7	odd	6
144.3.q.c.65.2		4	9.2	odd	6	inner
144.3.q.c.113.2		4	1.1	even	1	trivial
162.3.b.a.161.1		4	36.23	even	6
162.3.b.a.161.4		4	36.31	odd	6
432.3.q.d.17.1		4	3.2	odd	2
432.3.q.d.305.1		4	9.7	even	3
450.3.i.b.101.1		4	180.119	even	6
450.3.i.b.401.1		4	20.19	odd	2
450.3.k.a.149.1		8	20.3	even	4
450.3.k.a.149.4		8	20.7	even	4
450.3.k.a.299.1		8	180.47	odd	12
450.3.k.a.299.4		8	180.83	odd	12
576.3.q.e.65.1		4	72.29	odd	6
576.3.q.e.257.1		4	8.5	even	2
576.3.q.f.65.2		4	72.11	even	6
576.3.q.f.257.2		4	8.3	odd	2
1296.3.e.g.161.2		4	9.5	odd	6
1296.3.e.g.161.4		4	9.4	even	3
1350.3.i.b.251.2		4	180.79	odd	6
1350.3.i.b.1151.2		4	60.59	even	2
1350.3.k.a.449.1		8	60.47	odd	4
1350.3.k.a.449.4		8	60.23	odd	4
1350.3.k.a.899.1		8	180.43	even	12
1350.3.k.a.899.4		8	180.7	even	12
1728.3.q.c.449.1		4	24.5	odd	2
1728.3.q.c.1601.1		4	72.61	even	6
1728.3.q.d.449.2		4	24.11	even	2
1728.3.q.d.1601.2		4	72.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(-4.17423 - 7.22999i) q^{7} +(3.00000 - 8.48528i) q^{9} +O(q^{10})\)	\(q+(2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(-4.17423 - 7.22999i) q^{7} +(3.00000 - 8.48528i) q^{9} +(-0.825765 + 0.476756i) q^{11} +(4.84847 - 8.39780i) q^{13} +(-15.5227 + 1.43027i) q^{15} +18.8776i q^{17} +24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(-0.825765 - 0.476756i) q^{23} +(1.00000 + 1.73205i) q^{25} +(-7.34847 - 25.9808i) q^{27} +(11.8485 - 6.84072i) q^{29} +(1.52270 - 2.63740i) q^{31} +(-1.19694 + 2.59808i) q^{33} +43.3799i q^{35} +46.6969 q^{37} +(-2.66913 - 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(22.5227 + 39.0105i) q^{43} +(-35.5454 + 30.3895i) q^{45} +(-39.2196 + 22.6435i) q^{47} +(-10.3485 + 17.9241i) q^{49} +(32.6969 + 46.2405i) q^{51} +94.3879i q^{53} +4.95459 q^{55} +(60.4949 - 42.7764i) q^{57} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} +(-73.8712 + 13.7296i) q^{63} +(-43.6362 + 25.1934i) q^{65} +(37.5227 - 64.9912i) q^{67} +(-2.84847 + 0.262459i) q^{69} +18.0204i q^{71} -7.90918 q^{73} +(5.44949 + 2.51059i) q^{75} +(6.89388 + 3.98018i) q^{77} +(-21.8712 - 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} +(112.871 - 65.1662i) q^{83} +(49.0454 - 84.9491i) q^{85} +(17.1742 - 37.2784i) q^{87} -145.300i q^{89} -80.9546 q^{91} +(-0.838264 - 9.09769i) q^{93} +(-111.136 - 64.1645i) q^{95} +(54.9393 + 95.1576i) q^{97} +(1.56811 + 8.43712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9	\( 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9} - 18 q^{11} - 10 q^{13} - 18 q^{15} + 40 q^{19} - 42 q^{21} - 18 q^{23} + 4 q^{25} + 18 q^{29} - 38 q^{31} + 54 q^{33} + 128 q^{37} + 102 q^{39} - 126 q^{41} + 46 q^{43} - 54 q^{45} - 54 q^{47} - 12 q^{49} + 72 q^{51} + 108 q^{55} + 144 q^{57} - 126 q^{59} + 62 q^{61} - 222 q^{63} + 90 q^{65} + 106 q^{67} + 18 q^{69} - 208 q^{73} + 12 q^{75} - 90 q^{77} - 14 q^{79} - 252 q^{81} + 378 q^{83} + 108 q^{85} + 54 q^{87} - 412 q^{91} + 222 q^{93} - 180 q^{95} + 14 q^{97} - 126 q^{99}+O(q^{100}) \) 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9 - 18 * q^11 - 10 * q^13 - 18 * q^15 + 40 * q^19 - 42 * q^21 - 18 * q^23 + 4 * q^25 + 18 * q^29 - 38 * q^31 + 54 * q^33 + 128 * q^37 + 102 * q^39 - 126 * q^41 + 46 * q^43 - 54 * q^45 - 54 * q^47 - 12 * q^49 + 72 * q^51 + 108 * q^55 + 144 * q^57 - 126 * q^59 + 62 * q^61 - 222 * q^63 + 90 * q^65 + 106 * q^67 + 18 * q^69 - 208 * q^73 + 12 * q^75 - 90 * q^77 - 14 * q^79 - 252 * q^81 + 378 * q^83 + 108 * q^85 + 54 * q^87 - 412 * q^91 + 222 * q^93 - 180 * q^95 + 14 * q^97 - 126 * q^99

Introduction

L-functions

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