LMFDB - Embedded newform 144.3.o.c.31.4

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			31.4
Root			$-1.07834i$ of defining polynomial
Character	$\chi$	$=$	144.31
Dual form			144.3.o.c.79.4

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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	0.388834	+	0.921308i	$0.372878\pi$
$5$	−3.01729	+	5.22611i	−0.603459	+	1.04522i	−0.992293	+	0.123914i	$0.960455\pi$
$6$		0			0
$7$	−10.2332	+	5.90815i	−1.46189	+	0.844021i	−0.999099	−	0.0424471i	$-0.986485\pi$
$7$	−10.2332	+	5.90815i	−1.46189	+	0.844021i	−0.462789	+	0.886468i	$0.653151\pi$
$8$		0			0
$9$	5.04032	+	7.45622i	0.560036	+	0.828469i
$10$		0			0
$11$	−5.28454	+	3.05103i	−0.480413	+	0.277366i	−0.720588	−	0.693363i	$-0.756128\pi$
$11$	−5.28454	+	3.05103i	−0.480413	+	0.277366i	0.240176	+	0.970729i	$0.422795\pi$
$12$		0			0
$13$	7.44868	−	12.9015i	0.572975	−	0.992422i	−0.423283	−	0.905997i	$-0.639123\pi$
$13$	7.44868	−	12.9015i	0.572975	−	0.992422i	0.996258	−	0.0864245i	$-0.0275441\pi$
$14$		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	$-0.919949\pi$
$19$		−	9.45610i		−	0.497689i	0.968543	−	0.248845i	$-0.0800509\pi$
$20$		0			0
$21$	−35.4267	+	1.25516i	−1.68698	+	0.0597695i
$22$		0			0
$23$	17.2673	+	9.96931i	0.750754	+	0.433448i	0.825966	−	0.563719i	$-0.190630\pi$
$23$	17.2673	+	9.96931i	0.750754	+	0.433448i	−0.0752122	+	0.997168i	$0.523963\pi$
$24$		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	0.937910	+	0.346877i	$0.112758\pi$
$29$	22.3114	+	38.6445i	0.769360	+	1.33257i	−0.168551	+	0.985693i	$0.553909\pi$
$30$		0			0
$31$	−5.42359	−	3.13131i	−0.174955	−	0.101010i	0.409965	−	0.912101i	$-0.365541\pi$
$31$	−5.42359	−	3.13131i	−0.174955	−	0.101010i	−0.584920	+	0.811091i	$0.698874\pi$
$32$		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	−0.738045	−	0.674752i	$-0.764251\pi$
$41$	8.82853	−	15.2915i	0.215330	−	0.372963i	0.953375	+	0.301789i	$0.0975839\pi$
$42$		0			0
$43$	−20.2696	+	11.7027i	−0.471386	+	0.272155i	−0.716820	−	0.697258i	$-0.754403\pi$
$43$	−20.2696	+	11.7027i	−0.471386	+	0.272155i	0.245433	+	0.969413i	$0.421070\pi$
$44$		0			0
$45$	−54.1751	+	3.84365i	−1.20389	+	0.0854145i
$46$		0			0
$47$	36.4261	−	21.0306i	0.775023	−	0.447460i	−0.0596404	−	0.998220i	$-0.518995\pi$
$47$	36.4261	−	21.0306i	0.775023	−	0.447460i	0.834664	+	0.550760i	$0.185662\pi$
$48$		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	0.752209	−	0.658925i	$-0.228988\pi$
$59$	32.9024	+	18.9962i	0.557668	+	0.321970i	−0.194541	+	0.980894i	$0.562322\pi$
$60$		0			0
$61$	−45.3815	−	78.6031i	−0.743960	−	1.28858i	−0.950679	−	0.310176i	$-0.899612\pi$
$61$	−45.3815	−	78.6031i	−0.743960	−	1.28858i	0.206720	−	0.978400i	$-0.433721\pi$
$62$		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	0.0448520	−	0.998994i	$-0.485718\pi$
$67$	−53.4577	−	30.8638i	−0.797876	−	0.460654i	−0.842728	+	0.538340i	$0.819052\pi$
$68$		0			0
$69$	31.7233	+	50.7106i	0.459759	+	0.734936i
$70$		0			0
$71$			39.5232i			0.556665i	0.960485	+	0.278333i	$0.0897817\pi$
$71$			39.5232i			0.556665i	−0.960485	+	0.278333i	$0.910218\pi$
$72$		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	0.0825131	−	0.996590i	$-0.473705\pi$
$79$	77.9605	−	45.0105i	0.986842	−	0.569753i	0.904329	+	0.426837i	$0.140372\pi$
$80$		0			0
$81$	−30.1903	+	75.1634i	−0.372720	+	0.927944i
$82$		0			0
$83$	−102.357	+	59.0957i	−1.23321	+	0.711996i	−0.967698	−	0.252111i	$-0.918875\pi$
$83$	−102.357	+	59.0957i	−1.23321	+	0.711996i	−0.265515	+	0.964107i	$0.585542\pi$
$84$		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	0.969688	+	0.244347i	$0.0785736\pi$
$97$	67.5561	+	117.011i	0.696455	+	1.20629i	−0.273233	+	0.961948i	$0.588093\pi$
$98$		0			0
$99$	−49.3849	−	24.0245i	−0.498838	−	0.242672i
$100$		0			0
$101$	−11.7439	−	20.3411i	−0.116277	−	0.201397i	0.802013	−	0.597307i	$-0.203763\pi$
$101$	−11.7439	−	20.3411i	−0.116277	−	0.201397i	−0.918289	+	0.395910i	$0.870429\pi$
$102$		0			0
$103$	27.2852	+	15.7531i	0.264905	+	0.152943i	0.626570	−	0.779365i	$-0.284458\pi$
$103$	27.2852	+	15.7531i	0.264905	+	0.152943i	−0.361665	+	0.932308i	$0.617792\pi$
$104$		0			0
$105$	100.333	−	188.931i	0.955553	−	1.79934i
$106$		0			0
$107$		−	208.386i		−	1.94753i	−0.227558	−	0.973765i	$-0.573074\pi$
$107$		−	208.386i		−	1.94753i	0.227558	−	0.973765i	$-0.426926\pi$
$108$		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	−0.857991	−	0.513664i	$-0.828288\pi$
$113$	1.79115	−	3.10236i	0.0158509	−	0.0274545i	0.873842	+	0.486210i	$0.161621\pi$
$114$		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	$-0.881340\pi$
$127$		−	92.5083i		−	0.728412i	0.931319	−	0.364206i	$-0.118660\pi$
$128$		0			0
$129$	−70.1720	+	2.48618i	−0.543969	+	0.0192727i
$130$		0			0
$131$	105.265	+	60.7749i	0.803552	+	0.463931i	0.844712	−	0.535222i	$-0.179772\pi$
$131$	105.265	+	60.7749i	0.803552	+	0.463931i	−0.0411598	+	0.999153i	$0.513105\pi$
$132$		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	−0.770348	−	0.637623i	$-0.779918\pi$
$137$	−128.420	−	222.430i	−0.937372	−	1.62358i	−0.167024	−	0.985953i	$-0.553416\pi$
$138$		0			0
$139$	111.156	+	64.1761i	0.799685	+	0.461698i	0.843361	−	0.537348i	$-0.180574\pi$
$139$	111.156	+	64.1761i	0.799685	+	0.461698i	−0.0436761	+	0.999046i	$0.513907\pi$
$140$		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	−0.827285	−	0.561783i	$-0.810116\pi$
$149$	10.8586	−	18.8076i	0.0728762	−	0.126225i	0.900161	+	0.435558i	$0.143449\pi$
$150$		0			0
$151$	242.937	−	140.260i	1.60886	−	0.928874i	0.619230	−	0.785209i	$-0.287445\pi$
$151$	242.937	−	140.260i	1.60886	−	0.928874i	0.989626	−	0.143665i	$-0.0458886\pi$
$152$		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	−0.648796	−	0.760963i	$-0.724727\pi$
$157$	52.5346	−	90.9926i	0.334615	−	0.579571i	0.983411	+	0.181392i	$0.0580603\pi$
$158$		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	$-0.852527\pi$
$163$		−	145.690i		−	0.893804i	0.894583	−	0.446902i	$-0.147473\pi$
$164$		0			0
$165$	51.8131	−	97.5658i	0.314019	−	0.591308i
$166$		0			0
$167$	212.778	+	122.847i	1.27412	+	0.735613i	0.975761	−	0.218840i	$-0.0702274\pi$
$167$	212.778	+	122.847i	1.27412	+	0.735613i	0.298359	+	0.954454i	$0.403561\pi$
$168$		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	0.922376	−	0.386294i	$-0.126245\pi$
$173$	21.9101	+	37.9494i	0.126648	+	0.219361i	−0.795728	+	0.605654i	$0.792911\pi$
$174$		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	$-0.949045\pi$
$179$		−	57.0637i		−	0.318791i	0.987215	−	0.159396i	$-0.0509546\pi$
$180$		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	−0.283306	−	0.959030i	$-0.591431\pi$
$191$	77.4667	−	44.7254i	0.405585	−	0.234164i	0.688891	+	0.724865i	$0.258098\pi$
$192$		0			0
$193$	−115.213	+	199.555i	−0.596959	+	1.03396i	0.396308	+	0.918118i	$0.370291\pi$
$193$	−115.213	+	199.555i	−0.596959	+	1.03396i	−0.993267	+	0.115846i	$0.963042\pi$
$194$		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	$-0.959779\pi$
$199$		−	50.1566i		−	0.252043i	0.992028	−	0.126021i	$-0.0402208\pi$
$200$		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	0.505394	−	0.862889i	$-0.331347\pi$
$211$	2.28029	+	1.31653i	0.0108071	+	0.00623946i	−0.494587	+	0.869128i	$0.664681\pi$
$212$		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	−0.801739	−	0.597675i	$-0.796091\pi$
$223$	−152.757	+	88.1940i	−0.685007	+	0.395489i	0.116732	+	0.993163i	$0.462758\pi$
$224$		0			0
$225$	44.9471	−	92.3936i	0.199765	−	0.410638i
$226$		0			0
$227$	1.85772	−	1.07256i	0.00818380	−	0.00472492i	−0.495903	−	0.868378i	$-0.665163\pi$
$227$	1.85772	−	1.07256i	0.00818380	−	0.00472492i	0.504086	+	0.863653i	$0.331829\pi$
$228$		0			0
$229$	63.6447	−	110.236i	0.277925	−	0.481379i	−0.692944	−	0.720991i	$-0.743687\pi$
$229$	63.6447	−	110.236i	0.277925	−	0.481379i	0.970869	+	0.239612i	$0.0770201\pi$
$230$		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	0.944447	−	0.328662i	$-0.106598\pi$
$239$	270.558	+	156.207i	1.13204	+	0.653584i	0.187594	+	0.982247i	$0.439931\pi$
$240$		0			0
$241$	−14.7110	−	25.4801i	−0.0610413	−	0.105727i	0.833890	−	0.551931i	$-0.186109\pi$
$241$	−14.7110	−	25.4801i	−0.0610413	−	0.105727i	−0.894931	+	0.446204i	$0.852775\pi$
$242$		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	$0.127213\pi$
$251$			195.326i			0.778192i	−0.921197	+	0.389096i	$0.872787\pi$
$252$		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	0.0295596	+	0.999563i	$0.490590\pi$
$257$	−218.673	+	378.753i	−0.850867	+	1.47375i	−0.880427	+	0.474182i	$0.842744\pi$
$258$		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	−0.618133	−	0.786073i	$-0.712111\pi$
$263$	−64.8138	+	37.4203i	−0.246440	+	0.142282i	0.371693	+	0.928356i	$0.378777\pi$
$264$		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	$-0.922633\pi$
$271$		−	130.442i		−	0.481337i	0.970607	−	0.240668i	$-0.0773666\pi$
$272$		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	0.582194	−	0.813050i	$-0.302194\pi$
$277$	−114.408	−	198.160i	−0.413025	−	0.715379i	−0.995219	+	0.0976702i	$0.968861\pi$
$278$		0			0
$279$	−3.98890	−	56.2223i	−0.0142971	−	0.201514i
$280$		0			0
$281$	23.9532	+	41.4882i	0.0852429	+	0.147645i	0.905495	−	0.424358i	$-0.139500\pi$
$281$	23.9532	+	41.4882i	0.0852429	+	0.147645i	−0.820252	+	0.572003i	$0.806167\pi$
$282$		0			0
$283$	−307.250	−	177.391i	−1.08569	−	0.626824i	−0.153265	−	0.988185i	$-0.548979\pi$
$283$	−307.250	−	177.391i	−1.08569	−	0.626824i	−0.932426	+	0.361361i	$0.882312\pi$
$284$		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	−0.909769	−	0.415114i	$-0.863742\pi$
$293$	−27.9478	+	48.4071i	−0.0953851	+	0.165212i	0.814384	+	0.580326i	$0.197075\pi$
$294$		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	$0.0297976\pi$
$307$			57.3939i			0.186951i	−0.995622	+	0.0934754i	$0.970202\pi$
$308$		0			0
$309$	50.1280	+	80.1309i	0.162226	+	0.259323i
$310$		0			0
$311$	−215.498	−	124.418i	−0.692920	−	0.400058i	0.111785	−	0.993732i	$-0.464343\pi$
$311$	−215.498	−	124.418i	−0.692920	−	0.400058i	−0.804705	+	0.593675i	$0.797677\pi$
$312$		0			0
$313$	−307.856	−	533.222i	−0.983565	−	1.70358i	−0.648147	−	0.761515i	$-0.724456\pi$
$313$	−307.856	−	533.222i	−0.983565	−	1.70358i	−0.335417	−	0.942070i	$-0.608877\pi$
$314$		0			0
$315$	531.677	−	359.408i	1.68786	−	1.14098i
$316$		0			0
$317$	−128.314	−	222.246i	−0.404775	−	0.701090i	0.589521	−	0.807753i	$-0.299317\pi$
$317$	−128.314	−	222.246i	−0.404775	−	0.701090i	−0.994295	+	0.106663i	$0.965983\pi$
$318$		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	−0.297881	−	0.954603i	$-0.596280\pi$
$331$	125.743	−	72.5978i	0.379889	−	0.219329i	0.677770	+	0.735274i	$0.262947\pi$
$332$		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	−0.831845	−	0.555008i	$-0.812715\pi$
$337$	21.8136	−	37.7823i	0.0647288	−	0.112114i	0.896574	+	0.442895i	$0.146048\pi$
$338$		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	0.257887	−	0.966175i	$-0.416974\pi$
$347$	−156.116	−	90.1337i	−0.449902	−	0.259751i	−0.707789	+	0.706424i	$0.750307\pi$
$348$		0			0
$349$	46.5629	+	80.6493i	0.133418	+	0.231087i	0.924992	−	0.379987i	$-0.124071\pi$
$349$	46.5629	+	80.6493i	0.133418	+	0.231087i	−0.791574	+	0.611073i	$0.790738\pi$
$350$		0			0
$351$	367.703	+	163.040i	1.04759	+	0.464503i
$352$		0			0
$353$	−215.455	−	373.178i	−0.610353	−	1.05716i	−0.991181	−	0.132516i	$-0.957694\pi$
$353$	−215.455	−	373.178i	−0.610353	−	1.05716i	0.380828	−	0.924646i	$-0.375639\pi$
$354$		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	$-0.854912\pi$
$359$		−	316.054i		−	0.880374i	0.897906	−	0.440187i	$-0.145088\pi$
$360$		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	0.268027	−	0.963411i	$-0.413628\pi$
$367$	453.751	−	261.973i	1.23638	−	0.713824i	0.968352	+	0.249588i	$0.0802951\pi$
$368$		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	−0.997575	−	0.0695940i	$-0.977830\pi$
$373$	−163.567	+	283.306i	−0.438518	+	0.759535i	0.559058	+	0.829129i	$0.311163\pi$
$374$		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	$-0.801017\pi$
$379$		−	443.580i		−	1.17040i	0.810890	−	0.585198i	$-0.198983\pi$
$380$		0			0
$381$	130.165	−	245.106i	0.341641	−	0.643323i
$382$		0			0
$383$	−393.008	−	226.903i	−1.02613	−	0.592436i	−0.110256	−	0.993903i	$-0.535167\pi$
$383$	−393.008	−	226.903i	−1.02613	−	0.592436i	−0.915873	+	0.401467i	$0.868500\pi$
$384$		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	0.952315	−	0.305117i	$-0.0986957\pi$
$389$	82.4361	+	142.783i	0.211918	+	0.367053i	−0.740397	+	0.672170i	$0.765362\pi$
$390$		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	−0.563661	−	0.826006i	$-0.690608\pi$
$401$	173.838	−	301.097i	0.433512	−	0.750864i	0.997173	+	0.0751418i	$0.0239409\pi$
$402$		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	−0.903333	−	0.428941i	$-0.858887\pi$
$409$	−32.7989	+	56.8094i	−0.0801930	+	0.138898i	0.823140	+	0.567839i	$0.192220\pi$
$410$		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	0.996491	−	0.0836989i	$-0.0266734\pi$
$419$	595.923	+	344.056i	1.42225	+	0.821137i	0.425760	+	0.904836i	$0.360007\pi$
$420$		0			0
$421$	−146.855	−	254.360i	−0.348823	−	0.604180i	0.637217	−	0.770684i	$-0.280085\pi$
$421$	−146.855	−	254.360i	−0.348823	−	0.604180i	−0.986041	+	0.166504i	$0.946752\pi$
$422$		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	$0.222792\pi$
$431$			555.264i			1.28832i	−0.764893	+	0.644158i	$0.777208\pi$
$432$		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	−0.956301	−	0.292385i	$-0.905551\pi$
$439$	−518.563	+	299.393i	−1.18124	+	0.681988i	−0.224937	+	0.974373i	$0.572218\pi$
$440$		0			0
$441$	813.579	−	57.7224i	1.84485	−	0.130890i
$442$		0			0
$443$	−528.448	+	305.100i	−1.19289	+	0.688713i	−0.958960	−	0.283542i	$-0.908491\pi$
$443$	−528.448	+	305.100i	−1.19289	+	0.688713i	−0.233926	+	0.972254i	$0.575157\pi$
$444$		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	0.977931	−	0.208926i	$-0.0669968\pi$
$457$	140.770	+	243.821i	0.308030	+	0.533524i	−0.669901	+	0.742450i	$0.733663\pi$
$458$		0			0
$459$	76.4247	+	716.616i	0.166503	+	1.56126i
$460$		0			0
$461$	49.0643	+	84.9819i	0.106430	+	0.184343i	0.914322	−	0.404989i	$-0.132725\pi$
$461$	49.0643	+	84.9819i	0.106430	+	0.184343i	−0.807891	+	0.589331i	$0.799391\pi$
$462$		0			0
$463$	−625.293	−	361.013i	−1.35052	−	0.779726i	−0.362202	−	0.932100i	$-0.617975\pi$
$463$	−625.293	−	361.013i	−1.35052	−	0.779726i	−0.988323	+	0.152374i	$0.951308\pi$
$464$		0			0
$465$	113.306	−	4.01441i	0.243669	−	0.00863314i
$466$		0			0
$467$			723.722i			1.54972i	0.632130	+	0.774862i	$0.282181\pi$
$467$			723.722i			1.54972i	−0.632130	+	0.774862i	$0.717819\pi$
$468$		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	−0.148318	−	0.988940i	$-0.547386\pi$
$479$	303.671	−	175.325i	0.633969	−	0.366022i	0.782288	+	0.622917i	$0.214053\pi$
$480$		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	$0.252246\pi$
$487$			693.565i			1.42416i	−0.702099	+	0.712079i	$0.747754\pi$
$488$		0			0
$489$	204.996	−	386.015i	0.419214	−	0.789396i
$490$		0			0
$491$	−450.850	−	260.298i	−0.918228	−	0.530139i	−0.0351585	−	0.999382i	$-0.511194\pi$
$491$	−450.850	−	260.298i	−0.918228	−	0.530139i	−0.883069	+	0.469243i	$0.844527\pi$
$492$		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	0.0940208	−	0.995570i	$-0.470028\pi$
$499$	−359.858	−	207.764i	−0.721158	−	0.416361i	−0.815179	+	0.579209i	$0.803361\pi$
$500$		0			0
$501$	390.913	+	624.884i	0.780266	+	1.24727i
$502$		0			0
$503$			153.470i			0.305109i	0.988295	+	0.152555i	$0.0487500\pi$
$503$			153.470i			0.305109i	−0.988295	+	0.152555i	$0.951250\pi$
$504$		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	0.425539	+	0.904940i	$0.360085\pi$
$509$	−290.604	+	503.341i	−0.570932	+	0.988883i	−0.996471	+	0.0839427i	$0.973249\pi$
$510$		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	$0.0899056\pi$
$523$			291.527i			0.557413i	−0.960376	+	0.278706i	$0.910094\pi$
$524$		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	0.588214	−	0.808705i	$-0.299831\pi$
$547$	865.726	−	499.827i	1.58268	−	0.913761i	0.994466	−	0.105056i	$-0.0335022\pi$
$548$		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	0.767705	−	0.640803i	$-0.221399\pi$
$563$	335.889	+	193.926i	0.596606	+	0.344451i	−0.171099	+	0.985254i	$0.554732\pi$
$564$		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	0.510664	−	0.859780i	$-0.329400\pi$
$569$	−278.389	−	482.184i	−0.489260	−	0.847423i	−0.999924	+	0.0123576i	$0.996066\pi$
$570$		0			0
$571$	−28.0470	−	16.1930i	−0.0491191	−	0.0283589i	0.475239	−	0.879857i	$-0.342361\pi$
$571$	−28.0470	−	16.1930i	−0.0491191	−	0.0283589i	−0.524358	+	0.851498i	$0.675695\pi$
$572$		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	−0.939787	−	0.341759i	$-0.888977\pi$
$587$	−653.747	+	377.441i	−1.11371	+	0.643000i	−0.173921	+	0.984760i	$0.555644\pi$
$588$		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	0.431055	−	0.902326i	$-0.358141\pi$
$599$	−80.7777	−	46.6370i	−0.134854	−	0.0778581i	−0.565909	+	0.824467i	$0.691475\pi$
$600$		0			0
$601$	215.014	+	372.414i	0.357760	+	0.619658i	0.987586	−	0.157078i	$-0.0502074\pi$
$601$	215.014	+	372.414i	0.357760	+	0.619658i	−0.629827	+	0.776736i	$0.716874\pi$
$602$		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	0.0556627	−	0.998450i	$-0.482273\pi$
$607$	−474.182	−	273.769i	−0.781189	−	0.451019i	−0.836851	+	0.547430i	$0.815606\pi$
$608$		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	0.0532398	+	0.998582i	$0.483045\pi$
$617$	−517.155	+	895.739i	−0.838177	+	1.45177i	−0.891417	+	0.453184i	$0.850288\pi$
$618$		0			0
$619$	641.544	−	370.395i	1.03642	−	0.598377i	0.117602	−	0.993061i	$-0.462479\pi$
$619$	641.544	−	370.395i	1.03642	−	0.598377i	0.918817	+	0.394684i	$0.129146\pi$
$620$		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	$0.185090\pi$
$631$			693.165i			1.09852i	−0.835652	+	0.549259i	$0.814910\pi$
$632$		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	0.941755	−	0.336299i	$-0.109175\pi$
$641$	115.145	+	199.438i	0.179634	+	0.311135i	−0.762121	+	0.647434i	$0.775842\pi$
$642$		0			0
$643$	662.916	+	382.735i	1.03097	+	0.595233i	0.917263	−	0.398281i	$-0.130393\pi$
$643$	662.916	+	382.735i	1.03097	+	0.595233i	0.113710	+	0.993514i	$0.463726\pi$
$644$		0			0
$645$	198.737	−	374.228i	0.308119	−	0.580198i
$646$		0			0
$647$		−	339.078i		−	0.524078i	−0.965057	−	0.262039i	$-0.915605\pi$
$647$		−	339.078i		−	0.524078i	0.965057	−	0.262039i	$-0.0843949\pi$
$648$		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	−0.803946	−	0.594702i	$-0.797270\pi$
$653$	73.8243	−	127.867i	0.113054	−	0.195815i	0.917000	+	0.398887i	$0.130603\pi$
$654$		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	0.244915	−	0.969544i	$-0.421240\pi$
$659$	795.428	−	459.241i	1.20702	−	0.696875i	0.962108	+	0.272669i	$0.0879064\pi$
$660$		0			0
$661$	−103.150	+	178.662i	−0.156052	+	0.270290i	−0.933442	−	0.358729i	$-0.883210\pi$
$661$	−103.150	+	178.662i	−0.156052	+	0.270290i	0.777389	+	0.629020i	$0.216543\pi$
$662$		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	0.504780	−	0.863248i	$-0.331573\pi$
$673$	−333.272	−	577.245i	−0.495204	−	0.857719i	−0.999985	+	0.00552878i	$0.998240\pi$
$674$		0			0
$675$	249.094	−	181.559i	0.369028	−	0.268976i
$676$		0			0
$677$	235.497	+	407.893i	0.347854	+	0.602500i	0.985868	−	0.167524i	$-0.0535773\pi$
$677$	235.497	+	407.893i	0.347854	+	0.602500i	−0.638014	+	0.770025i	$0.720244\pi$
$678$		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	$-0.768087\pi$
$683$		−	909.494i		−	1.33162i	0.746123	−	0.665808i	$-0.231913\pi$
$684$		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	−0.210539	−	0.977585i	$-0.567522\pi$
$691$	366.787	−	211.764i	0.530805	−	0.306461i	0.741344	+	0.671125i	$0.234189\pi$
$692$		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	0.829878	−	0.557945i	$-0.188410\pi$
$709$	−48.3932	−	83.8194i	−0.0682555	−	0.118222i	−0.898133	+	0.439723i	$0.855077\pi$
$710$		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	$-0.691942\pi$
$719$		−	1184.39i		−	1.64727i	0.567120	−	0.823635i	$-0.308058\pi$
$720$		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	−0.891818	−	0.452394i	$-0.850570\pi$
$727$	−687.700	+	397.044i	−0.945942	+	0.546140i	−0.0541243	+	0.998534i	$0.517237\pi$
$728$		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	−0.906659	−	0.421863i	$-0.861376\pi$
$733$	−64.4932	+	111.706i	−0.0879853	+	0.152395i	0.818674	+	0.574258i	$0.194710\pi$
$734$		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	$-0.996183\pi$
$739$		−	17.7228i		−	0.0239822i	0.999928	−	0.0119911i	$-0.00381697\pi$
$740$		0			0
$741$	−224.133	−	358.282i	−0.302473	−	0.483511i
$742$		0			0
$743$	−39.9367	−	23.0575i	−0.0537507	−	0.0310330i	0.472884	−	0.881125i	$-0.343213\pi$
$743$	−39.9367	−	23.0575i	−0.0537507	−	0.0310330i	−0.526635	+	0.850092i	$0.676546\pi$
$744$		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	0.630310	−	0.776343i	$-0.282928\pi$
$751$	205.122	+	118.427i	0.273132	+	0.157693i	−0.357178	+	0.934036i	$0.616261\pi$
$752$		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	−0.891744	−	0.452539i	$-0.850518\pi$
$761$	−41.0648	+	71.1263i	−0.0539616	+	0.0934642i	0.837783	+	0.546004i	$0.183852\pi$
$762$		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	−0.0172867	−	0.999851i	$-0.505503\pi$
$769$	659.227	−	1141.82i	0.857253	−	1.48481i	0.874539	−	0.484955i	$-0.161164\pi$
$770$		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	−0.322875	−	0.946442i	$-0.604649\pi$
$787$	−1026.21	−	592.484i	−1.30395	−	0.752838i	−0.981080	+	0.193603i	$0.937983\pi$
$788$		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	−0.671934	−	0.740611i	$-0.734536\pi$
$797$	243.421	−	421.617i	0.305421	−	0.529005i	0.977355	+	0.211606i	$0.0678695\pi$
$798$		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	$-0.936477\pi$
$811$		−	321.548i		−	0.396483i	0.980153	−	0.198241i	$-0.0635230\pi$
$812$		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	0.999830	−	0.0184511i	$-0.00587351\pi$
$821$	397.311	+	688.163i	0.483936	+	0.838201i	−0.515894	+	0.856652i	$0.672540\pi$
$822$		0			0
$823$	1020.29	+	589.063i	1.23972	+	0.715750i	0.969036	−	0.246919i	$-0.0794181\pi$
$823$	1020.29	+	589.063i	1.23972	+	0.715750i	0.270680	+	0.962669i	$0.412751\pi$
$824$		0			0
$825$	110.837	+	177.176i	0.134348	+	0.214758i
$826$		0			0
$827$		−	722.570i		−	0.873725i	−0.899528	−	0.436862i	$-0.856090\pi$
$827$		−	722.570i		−	0.873725i	0.899528	−	0.436862i	$-0.143910\pi$
$828$		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	−0.772239	−	0.635332i	$-0.780863\pi$
$839$	−510.234	+	294.584i	−0.608145	+	0.351113i	0.164094	+	0.986445i	$0.447530\pi$
$840$		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	0.757683	−	0.652623i	$-0.226331\pi$
$853$	−158.954	−	275.316i	−0.186347	−	0.322762i	−0.944029	+	0.329861i	$0.892998\pi$
$854$		0			0
$855$	36.3460	+	512.285i	0.0425099	+	0.599164i
$856$		0			0
$857$	270.238	+	468.066i	0.315330	+	0.546168i	0.979508	−	0.201407i	$-0.0645513\pi$
$857$	270.238	+	468.066i	0.315330	+	0.546168i	−0.664177	+	0.747575i	$0.731218\pi$
$858$		0			0
$859$	878.889	+	507.427i	1.02315	+	0.590718i	0.915016	−	0.403418i	$-0.132178\pi$
$859$	878.889	+	507.427i	1.02315	+	0.590718i	0.108138	+	0.994136i	$0.465511\pi$
$860$		0			0
$861$	−293.572	+	552.807i	−0.340967	+	0.642052i
$862$		0			0
$863$		−	894.091i		−	1.03603i	−0.855373	−	0.518013i	$-0.826672\pi$
$863$		−	894.091i		−	1.03603i	0.855373	−	0.518013i	$-0.173328\pi$
$864$		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	−0.994281	−	0.106797i	$-0.965941\pi$
$877$	−354.879	+	614.669i	−0.404652	+	0.700877i	0.589629	+	0.807674i	$0.299274\pi$
$878$		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	$0.199450\pi$
$883$			1035.56i			1.17277i	−0.810032	+	0.586386i	$0.800550\pi$
$884$		0			0
$885$	−687.375	+	24.3536i	−0.776695	+	0.0275182i
$886$		0			0
$887$	−721.263	−	416.421i	−0.813149	−	0.469472i	0.0348996	−	0.999391i	$-0.488889\pi$
$887$	−721.263	−	416.421i	−0.813149	−	0.469472i	−0.848048	+	0.529919i	$0.822222\pi$
$888$		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	−0.504731	−	0.863277i	$-0.668408\pi$
$907$	−8.59611	+	4.96297i	−0.00947752	+	0.00547185i	0.495254	+	0.868748i	$0.335075\pi$
$908$		0			0
$909$	92.4744	−	190.091i	0.101732	−	0.209121i
$910$		0			0
$911$	−1444.63	+	834.057i	−1.58576	+	0.915540i	−0.591767	+	0.806109i	$0.701569\pi$
$911$	−1444.63	+	834.057i	−1.58576	+	0.915540i	−0.993994	+	0.109431i	$0.965097\pi$
$912$		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	$-0.574850\pi$
$919$		−	1787.42i		−	1.94496i	0.232988	−	0.972480i	$-0.425150\pi$
$920$		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	0.992093	−	0.125501i	$-0.0400539\pi$
$929$	359.857	+	623.291i	0.387360	+	0.670926i	−0.604734	+	0.796428i	$0.706721\pi$
$930$		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	0.114127	+	0.993466i	$0.463593\pi$
$941$	−755.908	+	1309.27i	−0.803303	+	1.39136i	−0.917431	+	0.397896i	$0.869741\pi$
$942$		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	−0.0599968	−	0.998199i	$-0.519109\pi$
$947$	733.423	−	423.442i	0.774470	−	0.447140i	0.834467	+	0.551058i	$0.185776\pi$
$948$		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	0.404931	−	0.914347i	$-0.367296\pi$
$967$	−178.365	−	102.979i	−0.184452	−	0.106493i	−0.589383	+	0.807854i	$0.700629\pi$
$968$		0			0
$969$	355.145	−	668.751i	0.366507	−	0.690145i
$970$		0			0
$971$		−	1364.48i		−	1.40523i	−0.711568	−	0.702617i	$-0.752015\pi$
$971$		−	1364.48i		−	1.40523i	0.711568	−	0.702617i	$-0.247985\pi$
$972$		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	−0.516620	−	0.856215i	$-0.672810\pi$
$977$	472.081	−	817.668i	0.483194	−	0.836917i	0.999814	+	0.0192983i	$0.00614322\pi$
$978$		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	−0.987537	−	0.157390i	$-0.949692\pi$
$983$	−1322.14	+	763.336i	−1.34500	+	0.776537i	−0.357465	+	0.933927i	$0.616359\pi$
$984$		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	$0.0978338\pi$
$991$			599.630i			0.605075i	−0.953137	+	0.302538i	$0.902166\pi$
$992$		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	0.975681	−	0.219196i	$-0.0703434\pi$
$997$	297.117	+	514.622i	0.298011	+	0.516170i	−0.677670	+	0.735366i	$0.737010\pi$
$998$		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.31.4	yes	8
3.2	odd	2		432.3.o.a.415.4		8
4.3	odd	2		144.3.o.a.31.1	✓	8
8.3	odd	2		576.3.o.f.319.4		8
8.5	even	2		576.3.o.d.319.1		8
9.2	odd	6		432.3.o.b.127.4		8
9.4	even	3		1296.3.g.j.1135.7		8
9.5	odd	6		1296.3.g.k.1135.1		8
9.7	even	3		144.3.o.a.79.1	yes	8
12.11	even	2		432.3.o.b.415.4		8
24.5	odd	2		1728.3.o.e.1279.1		8
24.11	even	2		1728.3.o.f.1279.1		8
36.7	odd	6	inner	144.3.o.c.79.4	yes	8
36.11	even	6		432.3.o.a.127.4		8
36.23	even	6		1296.3.g.k.1135.2		8
36.31	odd	6		1296.3.g.j.1135.8		8
72.11	even	6		1728.3.o.e.127.1		8
72.29	odd	6		1728.3.o.f.127.1		8
72.43	odd	6		576.3.o.d.511.1		8
72.61	even	6		576.3.o.f.511.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.1	✓	8	4.3	odd	2
144.3.o.a.79.1	yes	8	9.7	even	3
144.3.o.c.31.4	yes	8	1.1	even	1	trivial
144.3.o.c.79.4	yes	8	36.7	odd	6	inner
432.3.o.a.127.4		8	36.11	even	6
432.3.o.a.415.4		8	3.2	odd	2
432.3.o.b.127.4		8	9.2	odd	6
432.3.o.b.415.4		8	12.11	even	2
576.3.o.d.319.1		8	8.5	even	2
576.3.o.d.511.1		8	72.43	odd	6
576.3.o.f.319.4		8	8.3	odd	2
576.3.o.f.511.4		8	72.61	even	6
1296.3.g.j.1135.7		8	9.4	even	3
1296.3.g.j.1135.8		8	36.31	odd	6
1296.3.g.k.1135.1		8	9.5	odd	6
1296.3.g.k.1135.2		8	36.23	even	6
1728.3.o.e.127.1		8	72.11	even	6
1728.3.o.e.1279.1		8	24.5	odd	2
1728.3.o.f.127.1		8	72.29	odd	6
1728.3.o.f.1279.1		8	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
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

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