LMFDB - Embedded newform 144.3.o.c.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(31,144)]

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([3, 0, 2]))

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

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

chi := DirichletCharacter("144.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.o (of order $6$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Root			$1.07834i$ of defining polynomial
Character	$\chi$	$=$	144.79
Dual form			144.3.o.c.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.64956 - 1.40707i) q^{3} +(-3.01729 - 5.22611i) q^{5} +(-10.2332 - 5.90815i) q^{7} +(5.04032 - 7.45622i) q^{9} +O(q^{10})$	\(q+(2.64956 - 1.40707i) q^{3} +(-3.01729 - 5.22611i) q^{5} +(-10.2332 - 5.90815i) q^{7} +(5.04032 - 7.45622i) q^{9} +(-5.28454 - 3.05103i) q^{11} +(7.44868 + 12.9015i) q^{13} +(-15.3480 - 9.60134i) q^{15} +26.6919 q^{17} +9.45610i q^{19} +(-35.4267 - 1.25516i) q^{21} +(17.2673 - 9.96931i) q^{23} +(-5.70813 + 9.88677i) q^{25} +(2.86322 - 26.8478i) q^{27} +(22.3114 - 38.6445i) q^{29} +(-5.42359 + 3.13131i) q^{31} +(-18.2947 - 0.648178i) q^{33} +71.3065i q^{35} -6.65707 q^{37} +(37.8890 + 23.7024i) q^{39} +(8.82853 + 15.2915i) q^{41} +(-20.2696 - 11.7027i) q^{43} +(-54.1751 - 3.84365i) q^{45} +(36.4261 + 21.0306i) q^{47} +(45.3125 + 78.4835i) q^{49} +(70.7216 - 37.5572i) q^{51} -51.6192 q^{53} +36.8234i q^{55} +(13.3054 + 25.0545i) q^{57} +(32.9024 - 18.9962i) q^{59} +(-45.3815 + 78.6031i) q^{61} +(-95.6311 + 46.5221i) q^{63} +(44.9497 - 77.8552i) q^{65} +(-53.4577 + 30.8638i) q^{67} +(31.7233 - 50.7106i) q^{69} -39.5232i q^{71} +35.0355 q^{73} +(-1.21267 + 34.2273i) q^{75} +(36.0519 + 62.4437i) q^{77} +(77.9605 + 45.0105i) q^{79} +(-30.1903 - 75.1634i) q^{81} +(-102.357 - 59.0957i) q^{83} +(-80.5372 - 139.494i) q^{85} +(4.73997 - 133.785i) q^{87} -14.4499 q^{89} -176.032i q^{91} +(-9.96416 + 15.9280i) q^{93} +(49.4186 - 28.5318i) q^{95} +(67.5561 - 117.011i) q^{97} +(-49.3849 + 24.0245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9	$ 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9} - 18 q^{11} + 5 q^{13} + 21 q^{15} + 6 q^{17} - 33 q^{21} + 81 q^{23} - 23 q^{25} - 108 q^{27} + 69 q^{29} - 45 q^{31} + 72 q^{33} - 20 q^{37} + 141 q^{39} + 54 q^{41} - 117 q^{45} - 207 q^{47} + 41 q^{49} + 141 q^{51} - 252 q^{53} - 273 q^{57} + 306 q^{59} + 7 q^{61} - 441 q^{63} + 93 q^{65} - 12 q^{67} + 189 q^{69} + 74 q^{73} + 387 q^{75} + 207 q^{77} - 33 q^{79} + 117 q^{81} - 549 q^{83} - 30 q^{85} + 87 q^{87} - 168 q^{89} - 27 q^{93} + 684 q^{95} - 10 q^{97} - 585 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9 - 18 * q^11 + 5 * q^13 + 21 * q^15 + 6 * q^17 - 33 * q^21 + 81 * q^23 - 23 * q^25 - 108 * q^27 + 69 * q^29 - 45 * q^31 + 72 * q^33 - 20 * q^37 + 141 * q^39 + 54 * q^41 - 117 * q^45 - 207 * q^47 + 41 * q^49 + 141 * q^51 - 252 * q^53 - 273 * q^57 + 306 * q^59 + 7 * q^61 - 441 * q^63 + 93 * q^65 - 12 * q^67 + 189 * q^69 + 74 * q^73 + 387 * q^75 + 207 * q^77 - 33 * q^79 + 117 * q^81 - 549 * q^83 - 30 * q^85 + 87 * q^87 - 168 * q^89 - 27 * q^93 + 684 * q^95 - 10 * q^97 - 585 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	2.64956	−	1.40707i	0.883186	−	0.469023i
$3$	2.64956	−	1.40707i	0.883186	−	0.469023i
$4$		0			0
$5$	−3.01729	−	5.22611i	−0.603459	−	1.04522i	−0.992293	−	0.123914i	$-0.960455\pi$
$5$	−3.01729	−	5.22611i	−0.603459	−	1.04522i	0.388834	−	0.921308i	$-0.372878\pi$
$6$		0			0
$7$	−10.2332	−	5.90815i	−1.46189	−	0.844021i	−0.462789	−	0.886468i	$-0.653151\pi$
$7$	−10.2332	−	5.90815i	−1.46189	−	0.844021i	−0.999099	+	0.0424471i	$0.986485\pi$
$8$		0			0
$9$	5.04032	−	7.45622i	0.560036	−	0.828469i
$10$		0			0
$11$	−5.28454	−	3.05103i	−0.480413	−	0.277366i	0.240176	−	0.970729i	$-0.422795\pi$
$11$	−5.28454	−	3.05103i	−0.480413	−	0.277366i	−0.720588	+	0.693363i	$0.756128\pi$
$12$		0			0
$13$	7.44868	+	12.9015i	0.572975	+	0.992422i	0.996258	+	0.0864245i	$0.0275441\pi$
$13$	7.44868	+	12.9015i	0.572975	+	0.992422i	−0.423283	+	0.905997i	$0.639123\pi$
$14$		0			0
$15$	−15.3480	−	9.60134i	−1.02320	−	0.640089i
$16$		0			0
$17$	26.6919			1.57011			0.785055	−	0.619427i	$-0.212635\pi$
$17$	26.6919			1.57011			0.785055	+	0.619427i	$0.212635\pi$
$18$		0			0
$19$			9.45610i			0.497689i	0.968543	+	0.248845i	$0.0800509\pi$
$19$			9.45610i			0.497689i	−0.968543	+	0.248845i	$0.919949\pi$
$20$		0			0
$21$	−35.4267	−	1.25516i	−1.68698	−	0.0597695i
$22$		0			0
$23$	17.2673	−	9.96931i	0.750754	−	0.433448i	−0.0752122	−	0.997168i	$-0.523963\pi$
$23$	17.2673	−	9.96931i	0.750754	−	0.433448i	0.825966	+	0.563719i	$0.190630\pi$
$24$		0			0
$25$	−5.70813	+	9.88677i	−0.228325	+	0.395471i
$26$		0			0
$27$	2.86322	−	26.8478i	0.106045	−	0.994361i
$28$		0			0
$29$	22.3114	−	38.6445i	0.769360	−	1.33257i	−0.168551	−	0.985693i	$-0.553909\pi$
$29$	22.3114	−	38.6445i	0.769360	−	1.33257i	0.937910	−	0.346877i	$-0.112758\pi$
$30$		0			0
$31$	−5.42359	+	3.13131i	−0.174955	+	0.101010i	−0.584920	−	0.811091i	$-0.698874\pi$
$31$	−5.42359	+	3.13131i	−0.174955	+	0.101010i	0.409965	+	0.912101i	$0.365541\pi$
$32$		0			0
$33$	−18.2947	−	0.648178i	−0.554385	−	0.0196418i
$34$		0			0
$35$			71.3065i			2.03733i
$36$		0			0
$37$	−6.65707			−0.179921			−0.0899604	−	0.995945i	$-0.528674\pi$
$37$	−6.65707			−0.179921			−0.0899604	+	0.995945i	$0.528674\pi$
$38$		0			0
$39$	37.8890	+	23.7024i	0.971512	+	0.607755i
$40$		0			0
$41$	8.82853	+	15.2915i	0.215330	+	0.372963i	0.953375	−	0.301789i	$-0.0975839\pi$
$41$	8.82853	+	15.2915i	0.215330	+	0.372963i	−0.738045	+	0.674752i	$0.764251\pi$
$42$		0			0
$43$	−20.2696	−	11.7027i	−0.471386	−	0.272155i	0.245433	−	0.969413i	$-0.421070\pi$
$43$	−20.2696	−	11.7027i	−0.471386	−	0.272155i	−0.716820	+	0.697258i	$0.754403\pi$
$44$		0			0
$45$	−54.1751	−	3.84365i	−1.20389	−	0.0854145i
$46$		0			0
$47$	36.4261	+	21.0306i	0.775023	+	0.447460i	0.834664	−	0.550760i	$-0.185662\pi$
$47$	36.4261	+	21.0306i	0.775023	+	0.447460i	−0.0596404	+	0.998220i	$0.518995\pi$
$48$		0			0
$49$	45.3125	+	78.4835i	0.924744	+	1.60170i
$50$		0			0
$51$	70.7216	−	37.5572i	1.38670	−	0.736417i
$52$		0			0
$53$	−51.6192			−0.973948			−0.486974	−	0.873416i	$-0.661899\pi$
$53$	−51.6192			−0.973948			−0.486974	+	0.873416i	$0.661899\pi$
$54$		0			0
$55$			36.8234i			0.669517i
$56$		0			0
$57$	13.3054	+	25.0545i	0.233428	+	0.439552i
$58$		0			0
$59$	32.9024	−	18.9962i	0.557668	−	0.321970i	−0.194541	−	0.980894i	$-0.562322\pi$
$59$	32.9024	−	18.9962i	0.557668	−	0.321970i	0.752209	+	0.658925i	$0.228988\pi$
$60$		0			0
$61$	−45.3815	+	78.6031i	−0.743960	+	1.28858i	0.206720	+	0.978400i	$0.433721\pi$
$61$	−45.3815	+	78.6031i	−0.743960	+	1.28858i	−0.950679	+	0.310176i	$0.899612\pi$
$62$		0			0
$63$	−95.6311	+	46.5221i	−1.51795	+	0.738446i
$64$		0			0
$65$	44.9497	−	77.8552i	0.691534	−	1.19777i
$66$		0			0
$67$	−53.4577	+	30.8638i	−0.797876	+	0.460654i	−0.842728	−	0.538340i	$-0.819052\pi$
$67$	−53.4577	+	30.8638i	−0.797876	+	0.460654i	0.0448520	+	0.998994i	$0.485718\pi$
$68$		0			0
$69$	31.7233	−	50.7106i	0.459759	−	0.734936i
$70$		0			0
$71$		−	39.5232i		−	0.556665i	−0.960485	−	0.278333i	$-0.910218\pi$
$71$		−	39.5232i		−	0.556665i	0.960485	−	0.278333i	$-0.0897817\pi$
$72$		0			0
$73$	35.0355			0.479938			0.239969	−	0.970780i	$-0.422863\pi$
$73$	35.0355			0.479938			0.239969	+	0.970780i	$0.422863\pi$
$74$		0			0
$75$	−1.21267	+	34.2273i	−0.0161689	+	0.456364i
$76$		0			0
$77$	36.0519	+	62.4437i	0.468206	+	0.810957i
$78$		0			0
$79$	77.9605	+	45.0105i	0.986842	+	0.569753i	0.904329	−	0.426837i	$-0.140372\pi$
$79$	77.9605	+	45.0105i	0.986842	+	0.569753i	0.0825131	+	0.996590i	$0.473705\pi$
$80$		0			0
$81$	−30.1903	−	75.1634i	−0.372720	−	0.927944i
$82$		0			0
$83$	−102.357	−	59.0957i	−1.23321	−	0.711996i	−0.265515	−	0.964107i	$-0.585542\pi$
$83$	−102.357	−	59.0957i	−1.23321	−	0.711996i	−0.967698	+	0.252111i	$0.918875\pi$
$84$		0			0
$85$	−80.5372	−	139.494i	−0.947496	−	1.64111i
$86$		0			0
$87$	4.73997	−	133.785i	0.0544824	−	1.53775i
$88$		0			0
$89$	−14.4499			−0.162359			−0.0811794	−	0.996700i	$-0.525869\pi$
$89$	−14.4499			−0.162359			−0.0811794	+	0.996700i	$0.525869\pi$
$90$		0			0
$91$		−	176.032i		−	1.93441i
$92$		0			0
$93$	−9.96416	+	15.9280i	−0.107141	+	0.171268i
$94$		0			0
$95$	49.4186	−	28.5318i	0.520196	−	0.300335i
$96$		0			0
$97$	67.5561	−	117.011i	0.696455	−	1.20629i	−0.273233	−	0.961948i	$-0.588093\pi$
$97$	67.5561	−	117.011i	0.696455	−	1.20629i	0.969688	−	0.244347i	$-0.0785736\pi$
$98$		0			0
$99$	−49.3849	+	24.0245i	−0.498838	+	0.242672i
$100$		0			0
$101$	−11.7439	+	20.3411i	−0.116277	+	0.201397i	−0.918289	−	0.395910i	$-0.870429\pi$
$101$	−11.7439	+	20.3411i	−0.116277	+	0.201397i	0.802013	+	0.597307i	$0.203763\pi$
$102$		0			0
$103$	27.2852	−	15.7531i	0.264905	−	0.152943i	−0.361665	−	0.932308i	$-0.617792\pi$
$103$	27.2852	−	15.7531i	0.264905	−	0.152943i	0.626570	+	0.779365i	$0.284458\pi$
$104$		0			0
$105$	100.333	+	188.931i	0.955553	+	1.79934i
$106$		0			0
$107$			208.386i			1.94753i	0.227558	+	0.973765i	$0.426926\pi$
$107$			208.386i			1.94753i	−0.227558	+	0.973765i	$0.573074\pi$
$108$		0			0
$109$	64.5228			0.591952			0.295976	−	0.955195i	$-0.404355\pi$
$109$	64.5228			0.591952			0.295976	+	0.955195i	$0.404355\pi$
$110$		0			0
$111$	−17.6383	+	9.36695i	−0.158904	+	0.0843869i
$112$		0			0
$113$	1.79115	+	3.10236i	0.0158509	+	0.0274545i	0.873842	−	0.486210i	$-0.161621\pi$
$113$	1.79115	+	3.10236i	0.0158509	+	0.0274545i	−0.857991	+	0.513664i	$0.828288\pi$
$114$		0			0
$115$	−104.201	−	60.1607i	−0.906098	−	0.523136i
$116$		0			0
$117$	133.740	+	9.48868i	1.14308	+	0.0810998i
$118$		0			0
$119$	−273.143	−	157.699i	−2.29532	−	1.32521i
$120$		0			0
$121$	−41.8824	−	72.5425i	−0.346136	−	0.599525i
$122$		0			0
$123$	44.9079	+	28.0933i	0.365104	+	0.228401i
$124$		0			0
$125$	−81.9723			−0.655778
$126$		0			0
$127$			92.5083i			0.728412i	0.931319	+	0.364206i	$0.118660\pi$
$127$			92.5083i			0.728412i	−0.931319	+	0.364206i	$0.881340\pi$
$128$		0			0
$129$	−70.1720	−	2.48618i	−0.543969	−	0.0192727i
$130$		0			0
$131$	105.265	−	60.7749i	0.803552	−	0.463931i	−0.0411598	−	0.999153i	$-0.513105\pi$
$131$	105.265	−	60.7749i	0.803552	−	0.463931i	0.844712	+	0.535222i	$0.179772\pi$
$132$		0			0
$133$	55.8680	−	96.7663i	0.420060	−	0.727566i
$134$		0			0
$135$	−148.948	+	66.0441i	−1.10332	+	0.489215i
$136$		0			0
$137$	−128.420	+	222.430i	−0.937372	+	1.62358i	−0.167024	+	0.985953i	$0.553416\pi$
$137$	−128.420	+	222.430i	−0.937372	+	1.62358i	−0.770348	+	0.637623i	$0.779918\pi$
$138$		0			0
$139$	111.156	−	64.1761i	0.799685	−	0.461698i	−0.0436761	−	0.999046i	$-0.513907\pi$
$139$	111.156	−	64.1761i	0.799685	−	0.461698i	0.843361	+	0.537348i	$0.180574\pi$
$140$		0			0
$141$	126.105	+	4.46786i	0.894358	+	0.0316870i
$142$		0			0
$143$		−	90.9045i		−	0.635696i
$144$		0			0
$145$	−269.281			−1.85711
$146$		0			0
$147$	230.490	+	144.189i	1.56796	+	0.980877i
$148$		0			0
$149$	10.8586	+	18.8076i	0.0728762	+	0.126225i	0.900161	−	0.435558i	$-0.143449\pi$
$149$	10.8586	+	18.8076i	0.0728762	+	0.126225i	−0.827285	+	0.561783i	$0.810116\pi$
$150$		0			0
$151$	242.937	+	140.260i	1.60886	+	0.928874i	0.989626	+	0.143665i	$0.0458886\pi$
$151$	242.937	+	140.260i	1.60886	+	0.928874i	0.619230	+	0.785209i	$0.287445\pi$
$152$		0			0
$153$	134.536	−	199.020i	0.879317	−	1.30079i
$154$		0			0
$155$	32.7291	+	18.8962i	0.211156	+	0.121911i
$156$		0			0
$157$	52.5346	+	90.9926i	0.334615	+	0.579571i	0.983411	−	0.181392i	$-0.0580603\pi$
$157$	52.5346	+	90.9926i	0.334615	+	0.579571i	−0.648796	+	0.760963i	$0.724727\pi$
$158$		0			0
$159$	−136.768	+	72.6318i	−0.860177	+	0.456804i
$160$		0			0
$161$	−235.601			−1.46336
$162$		0			0
$163$			145.690i			0.893804i	0.894583	+	0.446902i	$0.147473\pi$
$163$			145.690i			0.893804i	−0.894583	+	0.446902i	$0.852527\pi$
$164$		0			0
$165$	51.8131	+	97.5658i	0.314019	+	0.591308i
$166$		0			0
$167$	212.778	−	122.847i	1.27412	−	0.735613i	0.298359	−	0.954454i	$-0.403561\pi$
$167$	212.778	−	122.847i	1.27412	−	0.735613i	0.975761	+	0.218840i	$0.0702274\pi$
$168$		0			0
$169$	−26.4655	+	45.8396i	−0.156601	+	0.271241i
$170$		0			0
$171$	70.5067	+	47.6618i	0.412320	+	0.278724i
$172$		0			0
$173$	21.9101	−	37.9494i	0.126648	−	0.219361i	−0.795728	−	0.605654i	$-0.792911\pi$
$173$	21.9101	−	37.9494i	0.126648	−	0.219361i	0.922376	+	0.386294i	$0.126245\pi$
$174$		0			0
$175$	116.825	−	67.4490i	0.667572	−	0.385423i
$176$		0			0
$177$	60.4479	−	96.6275i	0.341514	−	0.545918i
$178$		0			0
$179$			57.0637i			0.318791i	0.987215	+	0.159396i	$0.0509546\pi$
$179$			57.0637i			0.318791i	−0.987215	+	0.159396i	$0.949045\pi$
$180$		0			0
$181$	92.7281			0.512310			0.256155	−	0.966636i	$-0.417544\pi$
$181$	92.7281			0.512310			0.256155	+	0.966636i	$0.417544\pi$
$182$		0			0
$183$	−9.64111	+	272.118i	−0.0526837	+	1.48699i
$184$		0			0
$185$	20.0863	+	34.7905i	0.108575	+	0.188057i
$186$		0			0
$187$	−141.054	−	81.4377i	−0.754300	−	0.435495i
$188$		0			0
$189$	−187.921	+	257.823i	−0.994288	+	1.36414i
$190$		0			0
$191$	77.4667	+	44.7254i	0.405585	+	0.234164i	0.688891	−	0.724865i	$-0.258098\pi$
$191$	77.4667	+	44.7254i	0.405585	+	0.234164i	−0.283306	+	0.959030i	$0.591431\pi$
$192$		0			0
$193$	−115.213	−	199.555i	−0.596959	−	1.03396i	−0.993267	−	0.115846i	$-0.963042\pi$
$193$	−115.213	−	199.555i	−0.596959	−	1.03396i	0.396308	−	0.918118i	$-0.370291\pi$
$194$		0			0
$195$	9.54937	−	269.529i	0.0489711	−	1.38220i
$196$		0			0
$197$	−95.9308			−0.486958			−0.243479	−	0.969906i	$-0.578289\pi$
$197$	−95.9308			−0.486958			−0.243479	+	0.969906i	$0.578289\pi$
$198$		0			0
$199$			50.1566i			0.252043i	0.992028	+	0.126021i	$0.0402208\pi$
$199$			50.1566i			0.252043i	−0.992028	+	0.126021i	$0.959779\pi$
$200$		0			0
$201$	−98.2118	+	156.994i	−0.488616	+	0.781065i
$202$		0			0
$203$	−456.635	+	263.639i	−2.24944	+	1.29871i
$204$		0			0
$205$	53.2766	−	92.2777i	0.259886	−	0.450135i
$206$		0			0
$207$	12.6996	−	178.998i	0.0613509	−	0.864722i
$208$		0			0
$209$	28.8508	−	49.9711i	0.138042	−	0.239096i
$210$		0			0
$211$	2.28029	−	1.31653i	0.0108071	−	0.00623946i	−0.494587	−	0.869128i	$-0.664681\pi$
$211$	2.28029	−	1.31653i	0.0108071	−	0.00623946i	0.505394	+	0.862889i	$0.331347\pi$
$212$		0			0
$213$	−55.6119	−	104.719i	−0.261089	−	0.491639i
$214$		0			0
$215$			141.242i			0.656938i
$216$		0			0
$217$	74.0010			0.341019
$218$		0			0
$219$	92.8286	−	49.2973i	0.423875	−	0.225102i
$220$		0			0
$221$	198.819	+	344.365i	0.899633	+	1.55821i
$222$		0			0
$223$	−152.757	−	88.1940i	−0.685007	−	0.395489i	0.116732	−	0.993163i	$-0.462758\pi$
$223$	−152.757	−	88.1940i	−0.685007	−	0.395489i	−0.801739	+	0.597675i	$0.796091\pi$
$224$		0			0
$225$	44.9471	+	92.3936i	0.199765	+	0.410638i
$226$		0			0
$227$	1.85772	+	1.07256i	0.00818380	+	0.00472492i	0.504086	−	0.863653i	$-0.331829\pi$
$227$	1.85772	+	1.07256i	0.00818380	+	0.00472492i	−0.495903	+	0.868378i	$0.665163\pi$
$228$		0			0
$229$	63.6447	+	110.236i	0.277925	+	0.481379i	0.970869	−	0.239612i	$-0.0770201\pi$
$229$	63.6447	+	110.236i	0.277925	+	0.481379i	−0.692944	+	0.720991i	$0.743687\pi$
$230$		0			0
$231$	183.384	+	114.721i	0.793870	+	0.496627i
$232$		0			0
$233$	262.526			1.12672			0.563360	−	0.826211i	$-0.309508\pi$
$233$	262.526			1.12672			0.563360	+	0.826211i	$0.309508\pi$
$234$		0			0
$235$		−	253.822i		−	1.08009i
$236$		0			0
$237$	269.894	+	9.56229i	1.13879	+	0.0403472i
$238$		0			0
$239$	270.558	−	156.207i	1.13204	−	0.653584i	0.187594	−	0.982247i	$-0.439931\pi$
$239$	270.558	−	156.207i	1.13204	−	0.653584i	0.944447	+	0.328662i	$0.106598\pi$
$240$		0			0
$241$	−14.7110	+	25.4801i	−0.0610413	+	0.105727i	−0.894931	−	0.446204i	$-0.852775\pi$
$241$	−14.7110	+	25.4801i	−0.0610413	+	0.105727i	0.833890	+	0.551931i	$0.186109\pi$
$242$		0			0
$243$	−185.751	−	156.670i	−0.764408	−	0.644733i
$244$		0			0
$245$	273.442	−	473.616i	1.11609	−	1.93312i
$246$		0			0
$247$	−121.998	+	70.4354i	−0.493918	+	0.285164i
$248$		0			0
$249$	−354.352	−	12.5546i	−1.42310	−	0.0504202i
$250$		0			0
$251$		−	195.326i		−	0.778192i	−0.921197	−	0.389096i	$-0.872787\pi$
$251$		−	195.326i		−	0.778192i	0.921197	−	0.389096i	$-0.127213\pi$
$252$		0			0
$253$	−121.667			−0.480896
$254$		0			0
$255$	−409.666	−	256.278i	−1.60653	−	1.00501i
$256$		0			0
$257$	−218.673	−	378.753i	−0.850867	−	1.47375i	−0.880427	−	0.474182i	$-0.842744\pi$
$257$	−218.673	−	378.753i	−0.850867	−	1.47375i	0.0295596	−	0.999563i	$-0.490590\pi$
$258$		0			0
$259$	68.1232	+	39.3310i	0.263024	+	0.151857i
$260$		0			0
$261$	−175.685	−	361.140i	−0.673124	−	1.38368i
$262$		0			0
$263$	−64.8138	−	37.4203i	−0.246440	−	0.142282i	0.371693	−	0.928356i	$-0.378777\pi$
$263$	−64.8138	−	37.4203i	−0.246440	−	0.142282i	−0.618133	+	0.786073i	$0.712111\pi$
$264$		0			0
$265$	155.750	+	269.768i	0.587738	+	1.01799i
$266$		0			0
$267$	−38.2859	+	20.3320i	−0.143393	+	0.0761499i
$268$		0			0
$269$	40.6759			0.151212			0.0756058	−	0.997138i	$-0.475911\pi$
$269$	40.6759			0.151212			0.0756058	+	0.997138i	$0.475911\pi$
$270$		0			0
$271$			130.442i			0.481337i	0.970607	+	0.240668i	$0.0773666\pi$
$271$			130.442i			0.481337i	−0.970607	+	0.240668i	$0.922633\pi$
$272$		0			0
$273$	−247.688	−	466.406i	−0.907283	−	1.70845i
$274$		0			0
$275$	60.3297	−	34.8314i	0.219381	−	0.126659i
$276$		0			0
$277$	−114.408	+	198.160i	−0.413025	+	0.715379i	−0.995219	−	0.0976702i	$-0.968861\pi$
$277$	−114.408	+	198.160i	−0.413025	+	0.715379i	0.582194	+	0.813050i	$0.302194\pi$
$278$		0			0
$279$	−3.98890	+	56.2223i	−0.0142971	+	0.201514i
$280$		0			0
$281$	23.9532	−	41.4882i	0.0852429	−	0.147645i	−0.820252	−	0.572003i	$-0.806167\pi$
$281$	23.9532	−	41.4882i	0.0852429	−	0.147645i	0.905495	+	0.424358i	$0.139500\pi$
$282$		0			0
$283$	−307.250	+	177.391i	−1.08569	+	0.626824i	−0.932426	−	0.361361i	$-0.882312\pi$
$283$	−307.250	+	177.391i	−1.08569	+	0.626824i	−0.153265	+	0.988185i	$0.548979\pi$
$284$		0			0
$285$	90.7912	−	145.132i	0.318566	−	0.509235i
$286$		0			0
$287$		−	208.641i		−	0.726973i
$288$		0			0
$289$	423.455			1.46524
$290$		0			0
$291$	14.3520	−	405.082i	0.0493196	−	1.39204i
$292$		0			0
$293$	−27.9478	−	48.4071i	−0.0953851	−	0.165212i	0.814384	−	0.580326i	$-0.197075\pi$
$293$	−27.9478	−	48.4071i	−0.0953851	−	0.165212i	−0.909769	+	0.415114i	$0.863742\pi$
$294$		0			0
$295$	−198.552	−	114.634i	−0.673059	−	0.388591i
$296$		0			0
$297$	−97.0441	+	133.142i	−0.326748	+	0.448290i
$298$		0			0
$299$	257.238	+	148.516i	0.860327	+	0.496710i
$300$		0			0
$301$	138.282	+	239.512i	0.459409	+	0.795720i
$302$		0			0
$303$	−2.49495	+	70.4194i	−0.00823415	+	0.232407i
$304$		0			0
$305$	547.718			1.79580
$306$		0			0
$307$		−	57.3939i		−	0.186951i	−0.995622	−	0.0934754i	$-0.970202\pi$
$307$		−	57.3939i		−	0.186951i	0.995622	−	0.0934754i	$-0.0297976\pi$
$308$		0			0
$309$	50.1280	−	80.1309i	0.162226	−	0.259323i
$310$		0			0
$311$	−215.498	+	124.418i	−0.692920	+	0.400058i	−0.804705	−	0.593675i	$-0.797677\pi$
$311$	−215.498	+	124.418i	−0.692920	+	0.400058i	0.111785	+	0.993732i	$0.464343\pi$
$312$		0			0
$313$	−307.856	+	533.222i	−0.983565	+	1.70358i	−0.335417	+	0.942070i	$0.608877\pi$
$313$	−307.856	+	533.222i	−0.983565	+	1.70358i	−0.648147	+	0.761515i	$0.724456\pi$
$314$		0			0
$315$	531.677	+	359.408i	1.68786	+	1.14098i
$316$		0			0
$317$	−128.314	+	222.246i	−0.404775	+	0.701090i	−0.994295	−	0.106663i	$-0.965983\pi$
$317$	−128.314	+	222.246i	−0.404775	+	0.701090i	0.589521	+	0.807753i	$0.299317\pi$
$318$		0			0
$319$	−235.811	+	136.146i	−0.739220	+	0.426789i
$320$		0			0
$321$	293.213	+	552.130i	0.913435	+	1.72003i
$322$		0			0
$323$			252.401i			0.781427i
$324$		0			0
$325$	−170.072			−0.523299
$326$		0			0
$327$	170.957	−	90.7879i	0.522804	−	0.277639i
$328$		0			0
$329$	−248.504	−	430.422i	−0.755331	−	1.30827i
$330$		0			0
$331$	125.743	+	72.5978i	0.379889	+	0.219329i	0.677770	−	0.735274i	$-0.262947\pi$
$331$	125.743	+	72.5978i	0.379889	+	0.219329i	−0.297881	+	0.954603i	$0.596280\pi$
$332$		0			0
$333$	−33.5538	+	49.6365i	−0.100762	+	0.149059i
$334$		0			0
$335$	322.595	+	186.250i	0.962971	+	0.555971i
$336$		0			0
$337$	21.8136	+	37.7823i	0.0647288	+	0.112114i	0.896574	−	0.442895i	$-0.146048\pi$
$337$	21.8136	+	37.7823i	0.0647288	+	0.112114i	−0.831845	+	0.555008i	$0.812715\pi$
$338$		0			0
$339$	9.11098	+	5.69962i	0.0268761	+	0.0168130i
$340$		0			0
$341$	38.2149			0.112067
$342$		0			0
$343$		−	491.852i		−	1.43397i
$344$		0			0
$345$	−360.738	−	12.7809i	−1.04562	−	0.0370460i
$346$		0			0
$347$	−156.116	+	90.1337i	−0.449902	+	0.259751i	−0.707789	−	0.706424i	$-0.750307\pi$
$347$	−156.116	+	90.1337i	−0.449902	+	0.259751i	0.257887	+	0.966175i	$0.416974\pi$
$348$		0			0
$349$	46.5629	−	80.6493i	0.133418	−	0.231087i	−0.791574	−	0.611073i	$-0.790738\pi$
$349$	46.5629	−	80.6493i	0.133418	−	0.231087i	0.924992	+	0.379987i	$0.124071\pi$
$350$		0			0
$351$	367.703	−	163.040i	1.04759	−	0.464503i
$352$		0			0
$353$	−215.455	+	373.178i	−0.610353	+	1.05716i	0.380828	+	0.924646i	$0.375639\pi$
$353$	−215.455	+	373.178i	−0.610353	+	1.05716i	−0.991181	+	0.132516i	$0.957694\pi$
$354$		0			0
$355$	−206.553	+	119.253i	−0.581838	+	0.335925i
$356$		0			0
$357$	−945.603	−	33.5026i	−2.64875	−	0.0938447i
$358$		0			0
$359$			316.054i			0.880374i	0.897906	+	0.440187i	$0.145088\pi$
$359$			316.054i			0.880374i	−0.897906	+	0.440187i	$0.854912\pi$
$360$		0			0
$361$	271.582			0.752305
$362$		0			0
$363$	−213.042	−	133.274i	−0.586893	−	0.367146i
$364$		0			0
$365$	−105.712	−	183.099i	−0.289623	−	0.501642i
$366$		0			0
$367$	453.751	+	261.973i	1.23638	+	0.713824i	0.968352	−	0.249588i	$-0.0802951\pi$
$367$	453.751	+	261.973i	1.23638	+	0.713824i	0.268027	+	0.963411i	$0.413628\pi$
$368$		0			0
$369$	158.515	+	11.2464i	0.429580	+	0.0304782i
$370$		0			0
$371$	528.231	+	304.974i	1.42380	+	0.822033i
$372$		0			0
$373$	−163.567	−	283.306i	−0.438518	−	0.759535i	0.559058	−	0.829129i	$-0.311163\pi$
$373$	−163.567	−	283.306i	−0.438518	−	0.759535i	−0.997575	+	0.0695940i	$0.977830\pi$
$374$		0			0
$375$	−217.190	+	115.341i	−0.579174	+	0.307575i
$376$		0			0
$377$	664.763			1.76330
$378$		0			0
$379$			443.580i			1.17040i	0.810890	+	0.585198i	$0.198983\pi$
$379$			443.580i			1.17040i	−0.810890	+	0.585198i	$0.801017\pi$
$380$		0			0
$381$	130.165	+	245.106i	0.341641	+	0.643323i
$382$		0			0
$383$	−393.008	+	226.903i	−1.02613	+	0.592436i	−0.915873	−	0.401467i	$-0.868500\pi$
$383$	−393.008	+	226.903i	−1.02613	+	0.592436i	−0.110256	+	0.993903i	$0.535167\pi$
$384$		0			0
$385$	217.558	−	376.822i	0.565086	−	0.978758i
$386$		0			0
$387$	−189.423	+	92.1495i	−0.489465	+	0.238112i
$388$		0			0
$389$	82.4361	−	142.783i	0.211918	−	0.367053i	−0.740397	−	0.672170i	$-0.765362\pi$
$389$	82.4361	−	142.783i	0.211918	−	0.367053i	0.952315	+	0.305117i	$0.0986957\pi$
$390$		0			0
$391$	460.897	−	266.099i	1.17877	−	0.680561i
$392$		0			0
$393$	193.392	−	309.142i	0.492092	−	0.786621i
$394$		0			0
$395$		−	543.240i		−	1.37529i
$396$		0			0
$397$	−395.775			−0.996914			−0.498457	−	0.866915i	$-0.666100\pi$
$397$	−395.775			−0.996914			−0.498457	+	0.866915i	$0.666100\pi$
$398$		0			0
$399$	11.8689	−	334.998i	0.0297467	−	0.839594i
$400$		0			0
$401$	173.838	+	301.097i	0.433512	+	0.750864i	0.997173	−	0.0751418i	$-0.0239409\pi$
$401$	173.838	+	301.097i	0.433512	+	0.750864i	−0.563661	+	0.826006i	$0.690608\pi$
$402$		0			0
$403$	−80.7971	−	46.6483i	−0.200489	−	0.115752i
$404$		0			0
$405$	−301.719	+	384.568i	−0.744985	+	0.949551i
$406$		0			0
$407$	35.1795	+	20.3109i	0.0864362	+	0.0499040i
$408$		0			0
$409$	−32.7989	−	56.8094i	−0.0801930	−	0.138898i	0.823140	−	0.567839i	$-0.192220\pi$
$409$	−32.7989	−	56.8094i	−0.0801930	−	0.138898i	−0.903333	+	0.428941i	$0.858887\pi$
$410$		0			0
$411$	−27.2823	+	770.037i	−0.0663802	+	1.87357i
$412$		0			0
$413$	−448.930			−1.08700
$414$		0			0
$415$			713.236i			1.71864i
$416$		0			0
$417$	204.215	−	326.442i	0.489724	−	0.782836i
$418$		0			0
$419$	595.923	−	344.056i	1.42225	−	0.821137i	0.425760	−	0.904836i	$-0.360007\pi$
$419$	595.923	−	344.056i	1.42225	−	0.821137i	0.996491	+	0.0836989i	$0.0266734\pi$
$420$		0			0
$421$	−146.855	+	254.360i	−0.348823	+	0.604180i	−0.986041	−	0.166504i	$-0.946752\pi$
$421$	−146.855	+	254.360i	−0.348823	+	0.604180i	0.637217	+	0.770684i	$0.280085\pi$
$422$		0			0
$423$	340.408	−	165.600i	0.804747	−	0.391489i
$424$		0			0
$425$	−152.361	+	263.896i	−0.358496	+	0.620932i
$426$		0			0
$427$	928.798	−	536.242i	2.17517	−	1.25584i
$428$		0			0
$429$	−127.909	−	240.857i	−0.298156	−	0.561438i
$430$		0			0
$431$		−	555.264i		−	1.28832i	−0.764893	−	0.644158i	$-0.777208\pi$
$431$		−	555.264i		−	1.28832i	0.764893	−	0.644158i	$-0.222792\pi$
$432$		0			0
$433$	−559.107			−1.29124			−0.645620	−	0.763659i	$-0.723401\pi$
$433$	−559.107			−1.29124			−0.645620	+	0.763659i	$0.723401\pi$
$434$		0			0
$435$	−713.475	+	378.896i	−1.64017	+	0.871026i
$436$		0			0
$437$	94.2707	+	163.282i	0.215722	+	0.373642i
$438$		0			0
$439$	−518.563	−	299.393i	−1.18124	−	0.681988i	−0.224937	−	0.974373i	$-0.572218\pi$
$439$	−518.563	−	299.393i	−1.18124	−	0.681988i	−0.956301	+	0.292385i	$0.905551\pi$
$440$		0			0
$441$	813.579	+	57.7224i	1.84485	+	0.130890i
$442$		0			0
$443$	−528.448	−	305.100i	−1.19289	−	0.688713i	−0.233926	−	0.972254i	$-0.575157\pi$
$443$	−528.448	−	305.100i	−1.19289	−	0.688713i	−0.958960	+	0.283542i	$0.908491\pi$
$444$		0			0
$445$	43.5997	+	75.5169i	0.0979768	+	0.169701i
$446$		0			0
$447$	55.2339	+	34.5530i	0.123566	+	0.0772998i
$448$		0			0
$449$	−342.989			−0.763896			−0.381948	−	0.924184i	$-0.624747\pi$
$449$	−342.989			−0.763896			−0.381948	+	0.924184i	$0.624747\pi$
$450$		0			0
$451$		−	107.744i		−	0.238901i
$452$		0			0
$453$	841.032	+	29.7976i	1.85658	+	0.0657784i
$454$		0			0
$455$	−919.960	+	531.139i	−2.02189	+	1.16734i
$456$		0			0
$457$	140.770	−	243.821i	0.308030	−	0.533524i	−0.669901	−	0.742450i	$-0.733663\pi$
$457$	140.770	−	243.821i	0.308030	−	0.533524i	0.977931	+	0.208926i	$0.0669968\pi$
$458$		0			0
$459$	76.4247	−	716.616i	0.166503	−	1.56126i
$460$		0			0
$461$	49.0643	−	84.9819i	0.106430	−	0.184343i	−0.807891	−	0.589331i	$-0.799391\pi$
$461$	49.0643	−	84.9819i	0.106430	−	0.184343i	0.914322	+	0.404989i	$0.132725\pi$
$462$		0			0
$463$	−625.293	+	361.013i	−1.35052	+	0.779726i	−0.988323	−	0.152374i	$-0.951308\pi$
$463$	−625.293	+	361.013i	−1.35052	+	0.779726i	−0.362202	+	0.932100i	$0.617975\pi$
$464$		0			0
$465$	113.306	+	4.01441i	0.243669	+	0.00863314i
$466$		0			0
$467$		−	723.722i		−	1.54972i	−0.632130	−	0.774862i	$-0.717819\pi$
$467$		−	723.722i		−	1.54972i	0.632130	−	0.774862i	$-0.282181\pi$
$468$		0			0
$469$	729.392			1.55521
$470$		0			0
$471$	267.226	+	167.171i	0.567359	+	0.354927i
$472$		0			0
$473$	71.4104	+	123.686i	0.150973	+	0.261494i
$474$		0			0
$475$	−93.4903	−	53.9766i	−0.196822	−	0.113635i
$476$		0			0
$477$	−260.178	+	384.884i	−0.545446	+	0.806885i
$478$		0			0
$479$	303.671	+	175.325i	0.633969	+	0.366022i	0.782288	−	0.622917i	$-0.214053\pi$
$479$	303.671	+	175.325i	0.633969	+	0.366022i	−0.148318	+	0.988940i	$0.547386\pi$
$480$		0			0
$481$	−49.5863	−	85.8861i	−0.103090	−	0.178557i
$482$		0			0
$483$	−624.238	+	331.506i	−1.29242	+	0.686348i
$484$		0			0
$485$	−815.347			−1.68113
$486$		0			0
$487$		−	693.565i		−	1.42416i	−0.702099	−	0.712079i	$-0.747754\pi$
$487$		−	693.565i		−	1.42416i	0.702099	−	0.712079i	$-0.252246\pi$
$488$		0			0
$489$	204.996	+	386.015i	0.419214	+	0.789396i
$490$		0			0
$491$	−450.850	+	260.298i	−0.918228	+	0.530139i	−0.883069	−	0.469243i	$-0.844527\pi$
$491$	−450.850	+	260.298i	−0.918228	+	0.530139i	−0.0351585	+	0.999382i	$0.511194\pi$
$492$		0			0
$493$	595.534	−	1031.49i	1.20798	−	2.09228i
$494$		0			0
$495$	274.563	+	185.602i	0.554674	+	0.374953i
$496$		0			0
$497$	−233.509	+	404.450i	−0.469837	+	0.813782i
$498$		0			0
$499$	−359.858	+	207.764i	−0.721158	+	0.416361i	−0.815179	−	0.579209i	$-0.803361\pi$
$499$	−359.858	+	207.764i	−0.721158	+	0.416361i	0.0940208	+	0.995570i	$0.470028\pi$
$500$		0			0
$501$	390.913	−	624.884i	0.780266	−	1.24727i
$502$		0			0
$503$		−	153.470i		−	0.305109i	−0.988295	−	0.152555i	$-0.951250\pi$
$503$		−	153.470i		−	0.305109i	0.988295	−	0.152555i	$-0.0487500\pi$
$504$		0			0
$505$	141.740			0.280673
$506$		0			0
$507$	−5.62249	+	158.694i	−0.0110897	+	0.313005i
$508$		0			0
$509$	−290.604	−	503.341i	−0.570932	−	0.988883i	−0.996471	−	0.0839427i	$-0.973249\pi$
$509$	−290.604	−	503.341i	−0.570932	−	0.988883i	0.425539	−	0.904940i	$-0.360085\pi$
$510$		0			0
$511$	−358.526	−	206.995i	−0.701616	−	0.405078i
$512$		0			0
$513$	253.875	+	27.0749i	0.494883	+	0.0527776i
$514$		0			0
$515$	−164.655	−	95.0635i	−0.319718	−	0.184589i
$516$		0			0
$517$	−128.330	−	222.274i	−0.248221	−	0.429931i
$518$		0			0
$519$	4.65470	−	131.378i	0.00896860	−	0.253137i
$520$		0			0
$521$	−119.457			−0.229284			−0.114642	−	0.993407i	$-0.536572\pi$
$521$	−119.457			−0.229284			−0.114642	+	0.993407i	$0.536572\pi$
$522$		0			0
$523$		−	291.527i		−	0.557413i	−0.960376	−	0.278706i	$-0.910094\pi$
$523$		−	291.527i		−	0.557413i	0.960376	−	0.278706i	$-0.0899056\pi$
$524$		0			0
$525$	214.630	−	343.091i	0.408818	−	0.653506i
$526$		0			0
$527$	−144.766	+	83.5805i	−0.274698	+	0.158597i
$528$		0			0
$529$	−65.7259	+	113.841i	−0.124246	+	0.215200i
$530$		0			0
$531$	24.1988	−	341.074i	0.0455721	−	0.642325i
$532$		0			0
$533$	−131.522	+	227.802i	−0.246758	+	0.427397i
$534$		0			0
$535$	1089.05	−	628.761i	2.03560	−	1.17525i
$536$		0			0
$537$	80.2924	+	151.193i	0.149520	+	0.281552i
$538$		0			0
$539$		−	552.999i		−	1.02597i
$540$		0			0
$541$	−918.712			−1.69817			−0.849087	−	0.528254i	$-0.822847\pi$
$541$	−918.712			−1.69817			−0.849087	+	0.528254i	$0.822847\pi$
$542$		0			0
$543$	245.688	−	130.475i	0.452465	−	0.240285i
$544$		0			0
$545$	−194.684	−	337.203i	−0.357219	−	0.618721i
$546$		0			0
$547$	865.726	+	499.827i	1.58268	+	0.913761i	0.994466	+	0.105056i	$0.0335022\pi$
$547$	865.726	+	499.827i	1.58268	+	0.913761i	0.588214	+	0.808705i	$0.299831\pi$
$548$		0			0
$549$	357.344	+	734.559i	0.650901	+	1.33800i
$550$		0			0
$551$	365.427	+	210.979i	0.663206	+	0.382902i
$552$		0			0
$553$	−531.858	−	921.205i	−0.961768	−	1.66583i
$554$		0			0
$555$	102.173	+	63.9168i	0.184095	+	0.115165i
$556$		0			0
$557$	730.122			1.31081			0.655406	−	0.755277i	$-0.272497\pi$
$557$	730.122			1.31081			0.655406	+	0.755277i	$0.272497\pi$
$558$		0			0
$559$		−	348.678i		−	0.623752i
$560$		0			0
$561$	−488.320	−	17.3011i	−0.870445	−	0.0308397i
$562$		0			0
$563$	335.889	−	193.926i	0.596606	−	0.344451i	−0.171099	−	0.985254i	$-0.554732\pi$
$563$	335.889	−	193.926i	0.596606	−	0.344451i	0.767705	+	0.640803i	$0.221399\pi$
$564$		0			0
$565$	10.8088	−	18.7215i	0.0191307	−	0.0331353i
$566$		0			0
$567$	−135.133	+	947.533i	−0.238329	+	1.67113i
$568$		0			0
$569$	−278.389	+	482.184i	−0.489260	+	0.847423i	−0.999924	−	0.0123576i	$-0.996066\pi$
$569$	−278.389	+	482.184i	−0.489260	+	0.847423i	0.510664	+	0.859780i	$0.329400\pi$
$570$		0			0
$571$	−28.0470	+	16.1930i	−0.0491191	+	0.0283589i	−0.524358	−	0.851498i	$-0.675695\pi$
$571$	−28.0470	+	16.1930i	−0.0491191	+	0.0283589i	0.475239	+	0.879857i	$0.342361\pi$
$572$		0			0
$573$	268.184	+	9.50172i	0.468035	+	0.0165824i
$574$		0			0
$575$			227.624i			0.395869i
$576$		0			0
$577$	221.536			0.383945			0.191972	−	0.981400i	$-0.438512\pi$
$577$	221.536			0.383945			0.191972	+	0.981400i	$0.438512\pi$
$578$		0			0
$579$	−586.051	−	366.620i	−1.01218	−	0.633195i
$580$		0			0
$581$	698.292	+	1209.48i	1.20188	+	2.08172i
$582$		0			0
$583$	272.784	+	157.492i	0.467897	+	0.270140i
$584$		0			0
$585$	−353.944	−	727.570i	−0.605033	−	1.24371i
$586$		0			0
$587$	−653.747	−	377.441i	−1.11371	−	0.643000i	−0.173921	−	0.984760i	$-0.555644\pi$
$587$	−653.747	−	377.441i	−1.11371	−	0.643000i	−0.939787	+	0.341759i	$0.888977\pi$
$588$		0			0
$589$	−29.6100	−	51.2860i	−0.0502716	−	0.0870730i
$590$		0			0
$591$	−254.174	+	134.981i	−0.430075	+	0.228395i
$592$		0			0
$593$	697.420			1.17609			0.588044	−	0.808829i	$-0.299898\pi$
$593$	697.420			1.17609			0.588044	+	0.808829i	$0.299898\pi$
$594$		0			0
$595$			1903.30i			3.19883i
$596$		0			0
$597$	70.5737	+	132.893i	0.118214	+	0.222601i
$598$		0			0
$599$	−80.7777	+	46.6370i	−0.134854	+	0.0778581i	−0.565909	−	0.824467i	$-0.691475\pi$
$599$	−80.7777	+	46.6370i	−0.134854	+	0.0778581i	0.431055	+	0.902326i	$0.358141\pi$
$600$		0			0
$601$	215.014	−	372.414i	0.357760	−	0.619658i	−0.629827	−	0.776736i	$-0.716874\pi$
$601$	215.014	−	372.414i	0.357760	−	0.619658i	0.987586	+	0.157078i	$0.0502074\pi$
$602$		0			0
$603$	−39.3166	+	554.156i	−0.0652017	+	0.918998i
$604$		0			0
$605$	−252.743	+	437.764i	−0.417757	+	0.723577i
$606$		0			0
$607$	−474.182	+	273.769i	−0.781189	+	0.451019i	−0.836851	−	0.547430i	$-0.815606\pi$
$607$	−474.182	+	273.769i	−0.781189	+	0.451019i	0.0556627	+	0.998450i	$0.482273\pi$
$608$		0			0
$609$	−838.925	+	1341.04i	−1.37755	+	2.20204i
$610$		0			0
$611$			626.601i			1.02553i
$612$		0			0
$613$	−6.42863			−0.0104872			−0.00524358	−	0.999986i	$-0.501669\pi$
$613$	−6.42863			−0.0104872			−0.00524358	+	0.999986i	$0.501669\pi$
$614$		0			0
$615$	11.3184	−	319.459i	0.0184039	−	0.519446i
$616$		0			0
$617$	−517.155	−	895.739i	−0.838177	−	1.45177i	−0.891417	−	0.453184i	$-0.850288\pi$
$617$	−517.155	−	895.739i	−0.838177	−	1.45177i	0.0532398	−	0.998582i	$-0.483045\pi$
$618$		0			0
$619$	641.544	+	370.395i	1.03642	+	0.598377i	0.918817	−	0.394684i	$-0.129146\pi$
$619$	641.544	+	370.395i	1.03642	+	0.598377i	0.117602	+	0.993061i	$0.462479\pi$
$620$		0			0
$621$	−218.213	−	492.134i	−0.351390	−	0.792486i
$622$		0			0
$623$	147.869	+	85.3724i	0.237350	+	0.137034i
$624$		0			0
$625$	390.038	+	675.565i	0.624060	+	1.08090i
$626$		0			0
$627$	6.12923	−	172.996i	0.00977549	−	0.275911i
$628$		0			0
$629$	−177.689			−0.282495
$630$		0			0
$631$		−	693.165i		−	1.09852i	−0.835652	−	0.549259i	$-0.814910\pi$
$631$		−	693.165i		−	1.09852i	0.835652	−	0.549259i	$-0.185090\pi$
$632$		0			0
$633$	4.18932	−	6.69674i	0.00661820	−	0.0105794i
$634$		0			0
$635$	483.458	−	279.125i	0.761351	−	0.439566i
$636$		0			0
$637$	−675.036	+	1169.20i	−1.05971	+	1.83547i
$638$		0			0
$639$	−294.694	−	199.210i	−0.461180	−	0.311752i
$640$		0			0
$641$	115.145	−	199.438i	0.179634	−	0.311135i	−0.762121	−	0.647434i	$-0.775842\pi$
$641$	115.145	−	199.438i	0.179634	−	0.311135i	0.941755	+	0.336299i	$0.109175\pi$
$642$		0			0
$643$	662.916	−	382.735i	1.03097	−	0.595233i	0.113710	−	0.993514i	$-0.463726\pi$
$643$	662.916	−	382.735i	1.03097	−	0.595233i	0.917263	+	0.398281i	$0.130393\pi$
$644$		0			0
$645$	198.737	+	374.228i	0.308119	+	0.580198i
$646$		0			0
$647$			339.078i			0.524078i	0.965057	+	0.262039i	$0.0843949\pi$
$647$			339.078i			0.524078i	−0.965057	+	0.262039i	$0.915605\pi$
$648$		0			0
$649$	−231.832			−0.357214
$650$		0			0
$651$	196.070	−	104.124i	0.301183	−	0.159945i
$652$		0			0
$653$	73.8243	+	127.867i	0.113054	+	0.195815i	0.917000	−	0.398887i	$-0.130603\pi$
$653$	73.8243	+	127.867i	0.113054	+	0.195815i	−0.803946	+	0.594702i	$0.797270\pi$
$654$		0			0
$655$	−635.233	−	366.752i	−0.969821	−	0.559926i
$656$		0			0
$657$	176.590	−	261.232i	0.268783	−	0.397614i
$658$		0			0
$659$	795.428	+	459.241i	1.20702	+	0.696875i	0.962108	−	0.272669i	$-0.0879064\pi$
$659$	795.428	+	459.241i	1.20702	+	0.696875i	0.244915	+	0.969544i	$0.421240\pi$
$660$		0			0
$661$	−103.150	−	178.662i	−0.156052	−	0.270290i	0.777389	−	0.629020i	$-0.216543\pi$
$661$	−103.150	−	178.662i	−0.156052	−	0.270290i	−0.933442	+	0.358729i	$0.883210\pi$
$662$		0			0
$663$	1011.33	+	632.662i	1.52538	+	0.954242i
$664$		0			0
$665$	−674.281			−1.01396
$666$		0			0
$667$		−	889.718i		−	1.33391i
$668$		0			0
$669$	−528.832	−	18.7364i	−0.790482	−	0.0280066i
$670$		0			0
$671$	479.641	−	276.921i	0.714815	−	0.412699i
$672$		0			0
$673$	−333.272	+	577.245i	−0.495204	+	0.857719i	−0.999985	−	0.00552878i	$-0.998240\pi$
$673$	−333.272	+	577.245i	−0.495204	+	0.857719i	0.504780	+	0.863248i	$0.331573\pi$
$674$		0			0
$675$	249.094	+	181.559i	0.369028	+	0.268976i
$676$		0			0
$677$	235.497	−	407.893i	0.347854	−	0.602500i	−0.638014	−	0.770025i	$-0.720244\pi$
$677$	235.497	−	407.893i	0.347854	−	0.602500i	0.985868	+	0.167524i	$0.0535773\pi$
$678$		0			0
$679$	−1382.63	+	798.263i	−2.03628	+	1.17565i
$680$		0			0
$681$	6.43130	+	0.227860i	0.00944391	+	0.000334596i
$682$		0			0
$683$			909.494i			1.33162i	0.746123	+	0.665808i	$0.231913\pi$
$683$			909.494i			1.33162i	−0.746123	+	0.665808i	$0.768087\pi$
$684$		0			0
$685$	1549.92			2.26266
$686$		0			0
$687$	323.740	+	202.524i	0.471237	+	0.294795i
$688$		0			0
$689$	−384.495	−	665.965i	−0.558048	−	0.966567i
$690$		0			0
$691$	366.787	+	211.764i	0.530805	+	0.306461i	0.741344	−	0.671125i	$-0.234189\pi$
$691$	366.787	+	211.764i	0.530805	+	0.306461i	−0.210539	+	0.977585i	$0.567522\pi$
$692$		0			0
$693$	647.307	+	45.9256i	0.934065	+	0.0662707i
$694$		0			0
$695$	−670.782	−	387.276i	−0.965154	−	0.557232i
$696$		0			0
$697$	235.650	+	408.158i	0.338092	+	0.585592i
$698$		0			0
$699$	695.578	−	369.392i	0.995104	−	0.528457i
$700$		0			0
$701$	−66.5738			−0.0949697			−0.0474849	−	0.998872i	$-0.515121\pi$
$701$	−66.5738			−0.0949697			−0.0474849	+	0.998872i	$0.515121\pi$
$702$		0			0
$703$		−	62.9499i		−	0.0895446i
$704$		0			0
$705$	−357.145	−	672.517i	−0.506589	−	0.953924i
$706$		0			0
$707$	240.356	−	138.770i	0.339967	−	0.196280i
$708$		0			0
$709$	−48.3932	+	83.8194i	−0.0682555	+	0.118222i	−0.898133	−	0.439723i	$-0.855077\pi$
$709$	−48.3932	+	83.8194i	−0.0682555	+	0.118222i	0.829878	+	0.557945i	$0.188410\pi$
$710$		0			0
$711$	728.554	−	354.423i	1.02469	−	0.498485i
$712$		0			0
$713$	−62.4340	+	108.139i	−0.0875652	+	0.151667i
$714$		0			0
$715$	−475.077	+	274.286i	−0.664443	+	0.383616i
$716$		0			0
$717$	497.065	−	794.572i	0.693257	−	1.10819i
$718$		0			0
$719$			1184.39i			1.64727i	0.567120	+	0.823635i	$0.308058\pi$
$719$			1184.39i			1.64727i	−0.567120	+	0.823635i	$0.691942\pi$
$720$		0			0
$721$	−372.287			−0.516348
$722$		0			0
$723$	−3.12528	+	88.2104i	−0.00432266	+	0.122006i
$724$		0			0
$725$	254.713	+	441.176i	0.351329	+	0.608519i
$726$		0			0
$727$	−687.700	−	397.044i	−0.945942	−	0.546140i	−0.0541243	−	0.998534i	$-0.517237\pi$
$727$	−687.700	−	397.044i	−0.945942	−	0.546140i	−0.891818	+	0.452394i	$0.850570\pi$
$728$		0			0
$729$	−712.604	−	153.742i	−0.977509	−	0.210895i
$730$		0			0
$731$	−541.034	−	312.366i	−0.740128	−	0.427313i
$732$		0			0
$733$	−64.4932	−	111.706i	−0.0879853	−	0.152395i	0.818674	−	0.574258i	$-0.194710\pi$
$733$	−64.4932	−	111.706i	−0.0879853	−	0.152395i	−0.906659	+	0.421863i	$0.861376\pi$
$734$		0			0
$735$	58.0916	−	1639.62i	0.0790361	−	2.23078i
$736$		0			0
$737$	376.666			0.511080
$738$		0			0
$739$			17.7228i			0.0239822i	0.999928	+	0.0119911i	$0.00381697\pi$
$739$			17.7228i			0.0239822i	−0.999928	+	0.0119911i	$0.996183\pi$
$740$		0			0
$741$	−224.133	+	358.282i	−0.302473	+	0.483511i
$742$		0			0
$743$	−39.9367	+	23.0575i	−0.0537507	+	0.0310330i	−0.526635	−	0.850092i	$-0.676546\pi$
$743$	−39.9367	+	23.0575i	−0.0537507	+	0.0310330i	0.472884	+	0.881125i	$0.343213\pi$
$744$		0			0
$745$	65.5269	−	113.496i	0.0879556	−	0.152343i
$746$		0			0
$747$	−956.541	+	465.333i	−1.28051	+	0.622935i
$748$		0			0
$749$	1231.17	−	2132.45i	1.64376	−	2.84707i
$750$		0			0
$751$	205.122	−	118.427i	0.273132	−	0.157693i	−0.357178	−	0.934036i	$-0.616261\pi$
$751$	205.122	−	118.427i	0.273132	−	0.157693i	0.630310	+	0.776343i	$0.282928\pi$
$752$		0			0
$753$	−274.837	−	517.528i	−0.364990	−	0.687288i
$754$		0			0
$755$		−	1692.82i		−	2.24215i
$756$		0			0
$757$	193.736			0.255925			0.127963	−	0.991779i	$-0.459156\pi$
$757$	193.736			0.255925			0.127963	+	0.991779i	$0.459156\pi$
$758$		0			0
$759$	−322.363	+	171.193i	−0.424720	+	0.225551i
$760$		0			0
$761$	−41.0648	−	71.1263i	−0.0539616	−	0.0934642i	0.837783	−	0.546004i	$-0.183852\pi$
$761$	−41.0648	−	71.1263i	−0.0539616	−	0.0934642i	−0.891744	+	0.452539i	$0.850518\pi$
$762$		0			0
$763$	−660.276	−	381.210i	−0.865368	−	0.499620i
$764$		0			0
$765$	−1446.03	−	102.594i	−1.89024	−	0.134110i
$766$		0			0
$767$	490.159	+	282.993i	0.639060	+	0.368961i
$768$		0			0
$769$	659.227	+	1141.82i	0.857253	+	1.48481i	0.874539	+	0.484955i	$0.161164\pi$
$769$	659.227	+	1141.82i	0.857253	+	1.48481i	−0.0172867	+	0.999851i	$0.505503\pi$
$770$		0			0
$771$	−1112.32	−	695.839i	−1.44269	−	0.902515i
$772$		0			0
$773$	−1.74554			−0.00225814			−0.00112907	−	0.999999i	$-0.500359\pi$
$773$	−1.74554			−0.00225814			−0.00112907	+	0.999999i	$0.500359\pi$
$774$		0			0
$775$		−	71.4958i		−	0.0922526i
$776$		0			0
$777$	235.838	+	8.35569i	0.303523	+	0.0107538i
$778$		0			0
$779$	−144.598	+	83.4835i	−0.185620	+	0.107167i
$780$		0			0
$781$	−120.587	+	208.862i	−0.154400	+	0.267429i
$782$		0			0
$783$	−973.637	−	709.660i	−1.24347	−	0.906335i
$784$		0			0
$785$	317.025	−	549.103i	0.403853	−	0.699494i
$786$		0			0
$787$	−1026.21	+	592.484i	−1.30395	+	0.752838i	−0.981080	−	0.193603i	$-0.937983\pi$
$787$	−1026.21	+	592.484i	−1.30395	+	0.752838i	−0.322875	+	0.946442i	$0.604649\pi$
$788$		0			0
$789$	−224.381	−	7.94977i	−0.284386	−	0.0100758i
$790$		0			0
$791$		−	42.3295i		−	0.0535139i
$792$		0			0
$793$	−1352.13			−1.70508
$794$		0			0
$795$	792.251	+	495.614i	0.996543	+	0.623414i
$796$		0			0
$797$	243.421	+	421.617i	0.305421	+	0.529005i	0.977355	−	0.211606i	$-0.0678695\pi$
$797$	243.421	+	421.617i	0.305421	+	0.529005i	−0.671934	+	0.740611i	$0.734536\pi$
$798$		0			0
$799$	972.280	+	561.346i	1.21687	+	0.702561i
$800$		0			0
$801$	−72.8323	+	107.742i	−0.0909267	+	0.134509i
$802$		0			0
$803$	−185.147	−	106.894i	−0.230569	−	0.133119i
$804$		0			0
$805$	710.876	+	1231.27i	0.883076	+	1.52953i
$806$		0			0
$807$	107.773	−	57.2338i	0.133548	−	0.0709216i
$808$		0			0
$809$	1104.99			1.36587			0.682936	−	0.730478i	$-0.260703\pi$
$809$	1104.99			1.36587			0.682936	+	0.730478i	$0.260703\pi$
$810$		0			0
$811$			321.548i			0.396483i	0.980153	+	0.198241i	$0.0635230\pi$
$811$			321.548i			0.396483i	−0.980153	+	0.198241i	$0.936477\pi$
$812$		0			0
$813$	183.541	+	345.614i	0.225758	+	0.425110i
$814$		0			0
$815$	761.392	−	439.590i	0.934224	−	0.539374i
$816$		0			0
$817$	110.662	−	191.671i	0.135449	−	0.234604i
$818$		0			0
$819$	−1312.53	−	887.255i	−1.60260	−	1.08334i
$820$		0			0
$821$	397.311	−	688.163i	0.483936	−	0.838201i	−0.515894	−	0.856652i	$-0.672540\pi$
$821$	397.311	−	688.163i	0.483936	−	0.838201i	0.999830	+	0.0184511i	$0.00587351\pi$
$822$		0			0
$823$	1020.29	−	589.063i	1.23972	−	0.715750i	0.270680	−	0.962669i	$-0.412751\pi$
$823$	1020.29	−	589.063i	1.23972	−	0.715750i	0.969036	+	0.246919i	$0.0794181\pi$
$824$		0			0
$825$	110.837	−	177.176i	0.134348	−	0.214758i
$826$		0			0
$827$			722.570i			0.873725i	0.899528	+	0.436862i	$0.143910\pi$
$827$			722.570i			0.873725i	−0.899528	+	0.436862i	$0.856090\pi$
$828$		0			0
$829$	1435.00			1.73100			0.865501	−	0.500906i	$-0.167000\pi$
$829$	1435.00			1.73100			0.865501	+	0.500906i	$0.167000\pi$
$830$		0			0
$831$	−24.3054	+	686.016i	−0.0292484	+	0.825531i
$832$		0			0
$833$	1209.47	+	2094.87i	1.45195	+	2.51485i
$834$		0			0
$835$	−1284.03	−	741.334i	−1.53776	−	0.887825i
$836$		0			0
$837$	68.5398	+	154.577i	0.0818874	+	0.184680i
$838$		0			0
$839$	−510.234	−	294.584i	−0.608145	−	0.351113i	0.164094	−	0.986445i	$-0.447530\pi$
$839$	−510.234	−	294.584i	−0.608145	−	0.351113i	−0.772239	+	0.635332i	$0.780863\pi$
$840$		0			0
$841$	−575.101	−	996.103i	−0.683829	−	1.18443i
$842$		0			0
$843$	5.08876	−	143.629i	0.00603649	−	0.170379i
$844$		0			0
$845$	319.417			0.378009
$846$		0			0
$847$			989.791i			1.16858i
$848$		0			0
$849$	−564.477	+	902.330i	−0.664872	+	1.06282i
$850$		0			0
$851$	−114.950	+	66.3663i	−0.135076	+	0.0779863i
$852$		0			0
$853$	−158.954	+	275.316i	−0.186347	+	0.322762i	−0.944029	−	0.329861i	$-0.892998\pi$
$853$	−158.954	+	275.316i	−0.186347	+	0.322762i	0.757683	+	0.652623i	$0.226331\pi$
$854$		0			0
$855$	36.3460	−	512.285i	0.0425099	−	0.599164i
$856$		0			0
$857$	270.238	−	468.066i	0.315330	−	0.546168i	−0.664177	−	0.747575i	$-0.731218\pi$
$857$	270.238	−	468.066i	0.315330	−	0.546168i	0.979508	+	0.201407i	$0.0645513\pi$
$858$		0			0
$859$	878.889	−	507.427i	1.02315	−	0.590718i	0.108138	−	0.994136i	$-0.465511\pi$
$859$	878.889	−	507.427i	1.02315	−	0.590718i	0.915016	+	0.403418i	$0.132178\pi$
$860$		0			0
$861$	−293.572	−	552.807i	−0.340967	−	0.642052i
$862$		0			0
$863$			894.091i			1.03603i	0.855373	+	0.518013i	$0.173328\pi$
$863$			894.091i			1.03603i	−0.855373	+	0.518013i	$0.826672\pi$
$864$		0			0
$865$	−264.437			−0.305707
$866$		0			0
$867$	1121.97	−	595.830i	1.29408	−	0.687232i
$868$		0			0
$869$	−274.657	−	475.720i	−0.316061	−	0.547434i
$870$		0			0
$871$	−796.378	−	459.789i	−0.914326	−	0.527886i
$872$		0			0
$873$	−531.952	−	1093.48i	−0.609338	−	1.25256i
$874$		0			0
$875$	838.840	+	484.304i	0.958674	+	0.553491i
$876$		0			0
$877$	−354.879	−	614.669i	−0.404652	−	0.700877i	0.589629	−	0.807674i	$-0.299274\pi$
$877$	−354.879	−	614.669i	−0.404652	−	0.700877i	−0.994281	+	0.106797i	$0.965941\pi$
$878$		0			0
$879$	−142.161	−	88.9329i	−0.161731	−	0.101175i
$880$		0			0
$881$	−1318.63			−1.49674			−0.748371	−	0.663281i	$-0.769163\pi$
$881$	−1318.63			−1.49674			−0.748371	+	0.663281i	$0.769163\pi$
$882$		0			0
$883$		−	1035.56i		−	1.17277i	−0.810032	−	0.586386i	$-0.800550\pi$
$883$		−	1035.56i		−	1.17277i	0.810032	−	0.586386i	$-0.199450\pi$
$884$		0			0
$885$	−687.375	−	24.3536i	−0.776695	−	0.0275182i
$886$		0			0
$887$	−721.263	+	416.421i	−0.813149	+	0.469472i	−0.848048	−	0.529919i	$-0.822222\pi$
$887$	−721.263	+	416.421i	−0.813149	+	0.469472i	0.0348996	+	0.999391i	$0.488889\pi$
$888$		0			0
$889$	546.553	−	946.657i	0.614795	−	1.06486i
$890$		0			0
$891$	−69.7839	+	489.316i	−0.0783209	+	0.549176i
$892$		0			0
$893$	−198.868	+	344.449i	−0.222696	+	0.385721i
$894$		0			0
$895$	298.221	−	172.178i	0.333208	−	0.192377i
$896$		0			0
$897$	890.539	+	31.5516i	0.992797	+	0.0351746i
$898$		0			0
$899$			279.456i			0.310852i
$900$		0			0
$901$	−1377.81			−1.52920
$902$		0			0
$903$	703.396	+	440.028i	0.778955	+	0.487296i
$904$		0			0
$905$	−279.788	−	484.607i	−0.309158	−	0.535477i
$906$		0			0
$907$	−8.59611	−	4.96297i	−0.00947752	−	0.00547185i	0.495254	−	0.868748i	$-0.335075\pi$
$907$	−8.59611	−	4.96297i	−0.00947752	−	0.00547185i	−0.504731	+	0.863277i	$0.668408\pi$
$908$		0			0
$909$	92.4744	+	190.091i	0.101732	+	0.209121i
$910$		0			0
$911$	−1444.63	−	834.057i	−1.58576	−	0.915540i	−0.993994	−	0.109431i	$-0.965097\pi$
$911$	−1444.63	−	834.057i	−1.58576	−	0.915540i	−0.591767	−	0.806109i	$-0.701569\pi$
$912$		0			0
$913$	360.605	+	624.587i	0.394968	+	0.684104i
$914$		0			0
$915$	1451.21	−	770.676i	1.58602	−	0.842269i
$916$		0			0
$917$	−1436.27			−1.56627
$918$		0			0
$919$			1787.42i			1.94496i	0.232988	+	0.972480i	$0.425150\pi$
$919$			1787.42i			1.94496i	−0.232988	+	0.972480i	$0.574850\pi$
$920$		0			0
$921$	−80.7571	−	152.068i	−0.0876841	−	0.165112i
$922$		0			0
$923$	509.908	−	294.396i	0.552447	−	0.318955i
$924$		0			0
$925$	37.9994	−	65.8169i	0.0410804	−	0.0711534i
$926$		0			0
$927$	20.0675	−	282.845i	0.0216478	−	0.305119i
$928$		0			0
$929$	359.857	−	623.291i	0.387360	−	0.670926i	−0.604734	−	0.796428i	$-0.706721\pi$
$929$	359.857	−	623.291i	0.387360	−	0.670926i	0.992093	+	0.125501i	$0.0400539\pi$
$930$		0			0
$931$	−742.147	+	428.479i	−0.797151	+	0.460235i
$932$		0			0
$933$	−395.910	+	632.873i	−0.424341	+	0.678320i
$934$		0			0
$935$			982.886i			1.05121i
$936$		0			0
$937$	1352.51			1.44345			0.721724	−	0.692181i	$-0.243350\pi$
$937$	1352.51			1.44345			0.721724	+	0.692181i	$0.243350\pi$
$938$		0			0
$939$	−65.4026	+	1845.98i	−0.0696514	+	1.96590i
$940$		0			0
$941$	−755.908	−	1309.27i	−0.803303	−	1.39136i	−0.917431	−	0.397896i	$-0.869741\pi$
$941$	−755.908	−	1309.27i	−0.803303	−	1.39136i	0.114127	−	0.993466i	$-0.463593\pi$
$942$		0			0
$943$	304.891	+	176.029i	0.323320	+	0.186669i
$944$		0			0
$945$	1914.42	+	204.166i	2.02584	+	0.216049i
$946$		0			0
$947$	733.423	+	423.442i	0.774470	+	0.447140i	0.834467	−	0.551058i	$-0.185776\pi$
$947$	733.423	+	423.442i	0.774470	+	0.447140i	−0.0599968	+	0.998199i	$0.519109\pi$
$948$		0			0
$949$	260.968	+	452.010i	0.274993	+	0.476301i
$950$		0			0
$951$	−27.2596	+	769.398i	−0.0286642	+	0.809041i
$952$		0			0
$953$	−198.475			−0.208263			−0.104131	−	0.994564i	$-0.533206\pi$
$953$	−198.475			−0.208263			−0.104131	+	0.994564i	$0.533206\pi$
$954$		0			0
$955$		−	539.799i		−	0.565234i
$956$		0			0
$957$	−433.230	+	692.529i	−0.452696	+	0.723645i
$958$		0			0
$959$	2628.30	−	1517.45i	2.74067	−	1.58232i
$960$		0			0
$961$	−460.890	+	798.284i	−0.479594	+	0.830681i
$962$		0			0
$963$	1553.77	+	1050.33i	1.61347	+	1.09069i
$964$		0			0
$965$	−695.264	+	1204.23i	−0.720481	+	1.24791i
$966$		0			0
$967$	−178.365	+	102.979i	−0.184452	+	0.106493i	−0.589383	−	0.807854i	$-0.700629\pi$
$967$	−178.365	+	102.979i	−0.184452	+	0.106493i	0.404931	+	0.914347i	$0.367296\pi$
$968$		0			0
$969$	355.145	+	668.751i	0.366507	+	0.690145i
$970$		0			0
$971$			1364.48i			1.40523i	0.711568	+	0.702617i	$0.247985\pi$
$971$			1364.48i			1.40523i	−0.711568	+	0.702617i	$0.752015\pi$
$972$		0			0
$973$	−1516.65			−1.55873
$974$		0			0
$975$	−450.616	+	239.303i	−0.462170	+	0.245439i
$976$		0			0
$977$	472.081	+	817.668i	0.483194	+	0.836917i	0.999814	−	0.0192983i	$-0.00614322\pi$
$977$	472.081	+	817.668i	0.483194	+	0.836917i	−0.516620	+	0.856215i	$0.672810\pi$
$978$		0			0
$979$	76.3612	+	44.0872i	0.0779992	+	0.0450329i
$980$		0			0
$981$	325.216	−	481.096i	0.331514	−	0.490414i
$982$		0			0
$983$	−1322.14	−	763.336i	−1.34500	−	0.776537i	−0.357465	−	0.933927i	$-0.616359\pi$
$983$	−1322.14	−	763.336i	−1.34500	−	0.776537i	−0.987537	+	0.157390i	$0.949692\pi$
$984$		0			0
$985$	289.452	+	501.345i	0.293859	+	0.508979i
$986$		0			0
$987$	−1264.06	−	790.765i	−1.28071	−	0.801180i
$988$		0			0
$989$	−466.670			−0.471860
$990$		0			0
$991$		−	599.630i		−	0.605075i	−0.953137	−	0.302538i	$-0.902166\pi$
$991$		−	599.630i		−	0.605075i	0.953137	−	0.302538i	$-0.0978338\pi$
$992$		0			0
$993$	435.314	+	15.4231i	0.438383	+	0.0155318i
$994$		0			0
$995$	262.124	−	151.337i	0.263441	−	0.152098i
$996$		0			0
$997$	297.117	−	514.622i	0.298011	−	0.516170i	−0.677670	−	0.735366i	$-0.737010\pi$
$997$	297.117	−	514.622i	0.298011	−	0.516170i	0.975681	+	0.219196i	$0.0703434\pi$
$998$		0			0
$999$	−19.0607	+	178.727i	−0.0190797	+	0.178906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.o.c.79.4	yes	8
3.2	odd	2		432.3.o.a.127.4		8
4.3	odd	2		144.3.o.a.79.1	yes	8
8.3	odd	2		576.3.o.f.511.4		8
8.5	even	2		576.3.o.d.511.1		8
9.2	odd	6		1296.3.g.k.1135.2		8
9.4	even	3		144.3.o.a.31.1	✓	8
9.5	odd	6		432.3.o.b.415.4		8
9.7	even	3		1296.3.g.j.1135.8		8
12.11	even	2		432.3.o.b.127.4		8
24.5	odd	2		1728.3.o.e.127.1		8
24.11	even	2		1728.3.o.f.127.1		8
36.7	odd	6		1296.3.g.j.1135.7		8
36.11	even	6		1296.3.g.k.1135.1		8
36.23	even	6		432.3.o.a.415.4		8
36.31	odd	6	inner	144.3.o.c.31.4	yes	8
72.5	odd	6		1728.3.o.f.1279.1		8
72.13	even	6		576.3.o.f.319.4		8
72.59	even	6		1728.3.o.e.1279.1		8
72.67	odd	6		576.3.o.d.319.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.1	✓	8	9.4	even	3
144.3.o.a.79.1	yes	8	4.3	odd	2
144.3.o.c.31.4	yes	8	36.31	odd	6	inner
144.3.o.c.79.4	yes	8	1.1	even	1	trivial
432.3.o.a.127.4		8	3.2	odd	2
432.3.o.a.415.4		8	36.23	even	6
432.3.o.b.127.4		8	12.11	even	2
432.3.o.b.415.4		8	9.5	odd	6
576.3.o.d.319.1		8	72.67	odd	6
576.3.o.d.511.1		8	8.5	even	2
576.3.o.f.319.4		8	72.13	even	6
576.3.o.f.511.4		8	8.3	odd	2
1296.3.g.j.1135.7		8	36.7	odd	6
1296.3.g.j.1135.8		8	9.7	even	3
1296.3.g.k.1135.1		8	36.11	even	6
1296.3.g.k.1135.2		8	9.2	odd	6
1728.3.o.e.127.1		8	24.5	odd	2
1728.3.o.e.1279.1		8	72.59	even	6
1728.3.o.f.127.1		8	24.11	even	2
1728.3.o.f.1279.1		8	72.5	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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.64956 - 1.40707i) q^{3} +(-3.01729 - 5.22611i) q^{5} +(-10.2332 - 5.90815i) q^{7} +(5.04032 - 7.45622i) q^{9} +O(q^{10})\)	\(q+(2.64956 - 1.40707i) q^{3} +(-3.01729 - 5.22611i) q^{5} +(-10.2332 - 5.90815i) q^{7} +(5.04032 - 7.45622i) q^{9} +(-5.28454 - 3.05103i) q^{11} +(7.44868 + 12.9015i) q^{13} +(-15.3480 - 9.60134i) q^{15} +26.6919 q^{17} +9.45610i q^{19} +(-35.4267 - 1.25516i) q^{21} +(17.2673 - 9.96931i) q^{23} +(-5.70813 + 9.88677i) q^{25} +(2.86322 - 26.8478i) q^{27} +(22.3114 - 38.6445i) q^{29} +(-5.42359 + 3.13131i) q^{31} +(-18.2947 - 0.648178i) q^{33} +71.3065i q^{35} -6.65707 q^{37} +(37.8890 + 23.7024i) q^{39} +(8.82853 + 15.2915i) q^{41} +(-20.2696 - 11.7027i) q^{43} +(-54.1751 - 3.84365i) q^{45} +(36.4261 + 21.0306i) q^{47} +(45.3125 + 78.4835i) q^{49} +(70.7216 - 37.5572i) q^{51} -51.6192 q^{53} +36.8234i q^{55} +(13.3054 + 25.0545i) q^{57} +(32.9024 - 18.9962i) q^{59} +(-45.3815 + 78.6031i) q^{61} +(-95.6311 + 46.5221i) q^{63} +(44.9497 - 77.8552i) q^{65} +(-53.4577 + 30.8638i) q^{67} +(31.7233 - 50.7106i) q^{69} -39.5232i q^{71} +35.0355 q^{73} +(-1.21267 + 34.2273i) q^{75} +(36.0519 + 62.4437i) q^{77} +(77.9605 + 45.0105i) q^{79} +(-30.1903 - 75.1634i) q^{81} +(-102.357 - 59.0957i) q^{83} +(-80.5372 - 139.494i) q^{85} +(4.73997 - 133.785i) q^{87} -14.4499 q^{89} -176.032i q^{91} +(-9.96416 + 15.9280i) q^{93} +(49.4186 - 28.5318i) q^{95} +(67.5561 - 117.011i) q^{97} +(-49.3849 + 24.0245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9	\( 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9} - 18 q^{11} + 5 q^{13} + 21 q^{15} + 6 q^{17} - 33 q^{21} + 81 q^{23} - 23 q^{25} - 108 q^{27} + 69 q^{29} - 45 q^{31} + 72 q^{33} - 20 q^{37} + 141 q^{39} + 54 q^{41} - 117 q^{45} - 207 q^{47} + 41 q^{49} + 141 q^{51} - 252 q^{53} - 273 q^{57} + 306 q^{59} + 7 q^{61} - 441 q^{63} + 93 q^{65} - 12 q^{67} + 189 q^{69} + 74 q^{73} + 387 q^{75} + 207 q^{77} - 33 q^{79} + 117 q^{81} - 549 q^{83} - 30 q^{85} + 87 q^{87} - 168 q^{89} - 27 q^{93} + 684 q^{95} - 10 q^{97} - 585 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9 - 18 * q^11 + 5 * q^13 + 21 * q^15 + 6 * q^17 - 33 * q^21 + 81 * q^23 - 23 * q^25 - 108 * q^27 + 69 * q^29 - 45 * q^31 + 72 * q^33 - 20 * q^37 + 141 * q^39 + 54 * q^41 - 117 * q^45 - 207 * q^47 + 41 * q^49 + 141 * q^51 - 252 * q^53 - 273 * q^57 + 306 * q^59 + 7 * q^61 - 441 * q^63 + 93 * q^65 - 12 * q^67 + 189 * q^69 + 74 * q^73 + 387 * q^75 + 207 * q^77 - 33 * q^79 + 117 * q^81 - 549 * q^83 - 30 * q^85 + 87 * q^87 - 168 * q^89 - 27 * q^93 + 684 * q^95 - 10 * q^97 - 585 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more