LMFDB - Embedded newform 588.2.e.f.491.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(491,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.15
Character	$\chi$	$=$	588.491
Dual form			588.2.e.f.491.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.446802 + 1.34178i) q^{2} +(-1.32740 - 1.11266i) q^{3} +(-1.60074 + 1.19902i) q^{4} -0.803124i q^{5} +(0.899858 - 2.27821i) q^{6} +(-2.32403 - 1.61211i) q^{8} +(0.523976 + 2.95389i) q^{9} +O(q^{10})$	\(q+(0.446802 + 1.34178i) q^{2} +(-1.32740 - 1.11266i) q^{3} +(-1.60074 + 1.19902i) q^{4} -0.803124i q^{5} +(0.899858 - 2.27821i) q^{6} +(-2.32403 - 1.61211i) q^{8} +(0.523976 + 2.95389i) q^{9} +(1.07761 - 0.358837i) q^{10} -2.34545 q^{11} +(3.45891 + 0.189500i) q^{12} +5.26858 q^{13} +(-0.893604 + 1.06607i) q^{15} +(1.12471 - 3.83862i) q^{16} -1.18543i q^{17} +(-3.72935 + 2.02286i) q^{18} -7.12430i q^{19} +(0.962960 + 1.28559i) q^{20} +(-1.04795 - 3.14708i) q^{22} +7.88711 q^{23} +(1.29118 + 4.72576i) q^{24} +4.35499 q^{25} +(2.35401 + 7.06926i) q^{26} +(2.59115 - 4.50399i) q^{27} -4.23132i q^{29} +(-1.82969 - 0.722698i) q^{30} -4.89898i q^{31} +(5.65310 - 0.205989i) q^{32} +(3.11335 + 2.60969i) q^{33} +(1.59058 - 0.529652i) q^{34} +(-4.38051 - 4.10014i) q^{36} +1.04795 q^{37} +(9.55923 - 3.18315i) q^{38} +(-6.99351 - 5.86214i) q^{39} +(-1.29472 + 1.86648i) q^{40} +7.16942i q^{41} +7.94315i q^{43} +(3.75445 - 2.81224i) q^{44} +(2.37234 - 0.420818i) q^{45} +(3.52398 + 10.5828i) q^{46} -6.09907 q^{47} +(-5.76402 + 3.84396i) q^{48} +(1.94582 + 5.84343i) q^{50} +(-1.31898 + 1.57354i) q^{51} +(-8.43361 + 6.31712i) q^{52} -8.72001i q^{53} +(7.20109 + 1.46435i) q^{54} +1.88369i q^{55} +(-7.92692 + 9.45679i) q^{57} +(5.67750 - 1.89056i) q^{58} -0.662173 q^{59} +(0.152192 - 2.77794i) q^{60} +0.958124 q^{61} +(6.57334 - 2.18887i) q^{62} +(2.80221 + 7.49317i) q^{64} -4.23132i q^{65} +(-2.11057 + 5.34344i) q^{66} -8.42629i q^{67} +(1.42135 + 1.89756i) q^{68} +(-10.4693 - 8.77567i) q^{69} +9.67432 q^{71} +(3.54425 - 7.70962i) q^{72} -1.41421 q^{73} +(0.468227 + 1.40612i) q^{74} +(-5.78081 - 4.84562i) q^{75} +(8.54216 + 11.4041i) q^{76} +(4.74097 - 12.0029i) q^{78} +6.92820i q^{79} +(-3.08289 - 0.903284i) q^{80} +(-8.45090 + 3.09553i) q^{81} +(-9.61978 + 3.20331i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(-10.6579 + 3.54901i) q^{86} +(-4.70802 + 5.61665i) q^{87} +(5.45090 + 3.78113i) q^{88} -16.3659i q^{89} +(1.62461 + 2.99513i) q^{90} +(-12.6252 + 9.45679i) q^{92} +(-5.45090 + 6.50290i) q^{93} +(-2.72508 - 8.18360i) q^{94} -5.72170 q^{95} +(-7.73312 - 6.01655i) q^{96} -4.37827 q^{97} +(-1.22896 - 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) $ 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.446802	+	1.34178i	0.315937	+	0.948780i
$2$	0.446802	+	1.34178i	0.315937	+	0.948780i
$3$	−1.32740	−	1.11266i	−0.766374	−	0.642394i
$3$	−1.32740	−	1.11266i	−0.766374	−	0.642394i
$4$	−1.60074	+	1.19902i	−0.800368	+	0.599509i
$5$		−	0.803124i		−	0.359168i	−0.983743	−	0.179584i	$-0.942525\pi$
$5$		−	0.803124i		−	0.359168i	0.983743	−	0.179584i	$-0.0574752\pi$
$6$	0.899858	−	2.27821i	0.367365	−	0.930077i
$7$		0			0
$7$		0			0
$8$	−2.32403	−	1.61211i	−0.821668	−	0.569967i
$9$	0.523976	+	2.95389i	0.174659	+	0.984629i
$10$	1.07761	−	0.358837i	0.340771	−	0.113474i
$11$	−2.34545			−0.707181			−0.353590	−	0.935400i	$-0.615039\pi$
$11$	−2.34545			−0.707181			−0.353590	+	0.935400i	$0.615039\pi$
$12$	3.45891	+	0.189500i	0.998503	+	0.0547038i
$13$	5.26858			1.46124			0.730621	−	0.682784i	$-0.239231\pi$
$13$	5.26858			1.46124			0.730621	+	0.682784i	$0.239231\pi$
$14$		0			0
$15$	−0.893604	+	1.06607i	−0.230727	+	0.275257i
$16$	1.12471	−	3.83862i	0.281178	−	0.959656i
$17$		−	1.18543i		−	0.287509i	−0.989613	−	0.143754i	$-0.954082\pi$
$17$		−	1.18543i		−	0.287509i	0.989613	−	0.143754i	$-0.0459176\pi$
$18$	−3.72935	+	2.02286i	−0.879015	+	0.476793i
$19$		−	7.12430i		−	1.63443i	−0.576336	−	0.817213i	$-0.695518\pi$
$19$		−	7.12430i		−	1.63443i	0.576336	−	0.817213i	$-0.304482\pi$
$20$	0.962960	+	1.28559i	0.215324	+	0.287467i
$21$		0			0
$22$	−1.04795	−	3.14708i	−0.223424	−	0.670959i
$23$	7.88711			1.64458			0.822288	−	0.569071i	$-0.192697\pi$
$23$	7.88711			1.64458			0.822288	+	0.569071i	$0.192697\pi$
$24$	1.29118	+	4.72576i	0.263562	+	0.964643i
$25$	4.35499			0.870998
$26$	2.35401	+	7.06926i	0.461660	+	1.38640i
$27$	2.59115	−	4.50399i	0.498666	−	0.866794i
$28$		0			0
$29$		−	4.23132i		−	0.785737i	−0.919595	−	0.392868i	$-0.871483\pi$
$29$		−	4.23132i		−	0.785737i	0.919595	−	0.392868i	$-0.128517\pi$
$30$	−1.82969	−	0.722698i	−0.334054	−	0.131946i
$31$		−	4.89898i		−	0.879883i	−0.898027	−	0.439941i	$-0.854999\pi$
$31$		−	4.89898i		−	0.879883i	0.898027	−	0.439941i	$-0.145001\pi$
$32$	5.65310	−	0.205989i	0.999337	−	0.0364141i
$33$	3.11335	+	2.60969i	0.541965	+	0.454289i
$34$	1.59058	−	0.529652i	0.272783	−	0.0908346i
$35$		0			0
$36$	−4.38051	−	4.10014i	−0.730085	−	0.683356i
$37$	1.04795			0.172282			0.0861412	−	0.996283i	$-0.472546\pi$
$37$	1.04795			0.172282			0.0861412	+	0.996283i	$0.472546\pi$
$38$	9.55923	−	3.18315i	1.55071	−	0.516375i
$39$	−6.99351	−	5.86214i	−1.11986	−	0.938693i
$40$	−1.29472	+	1.86648i	−0.204714	+	0.295117i
$41$			7.16942i			1.11968i	0.828602	+	0.559838i	$0.189137\pi$
$41$			7.16942i			1.11968i	−0.828602	+	0.559838i	$0.810863\pi$
$42$		0			0
$43$			7.94315i			1.21132i	0.795724	+	0.605659i	$0.207091\pi$
$43$			7.94315i			1.21132i	−0.795724	+	0.605659i	$0.792909\pi$
$44$	3.75445	−	2.81224i	0.566005	−	0.423961i
$45$	2.37234	−	0.420818i	0.353647	−	0.0627318i
$46$	3.52398	+	10.5828i	0.519582	+	1.56034i
$47$	−6.09907			−0.889641			−0.444821	−	0.895620i	$-0.646733\pi$
$47$	−6.09907			−0.889641			−0.444821	+	0.895620i	$0.646733\pi$
$48$	−5.76402	+	3.84396i	−0.831965	+	0.554828i
$49$		0			0
$50$	1.94582	+	5.84343i	0.275180	+	0.826386i
$51$	−1.31898	+	1.57354i	−0.184694	+	0.220339i
$52$	−8.43361	+	6.31712i	−1.16953	+	0.876027i
$53$		−	8.72001i		−	1.19779i	−0.800829	−	0.598893i	$-0.795607\pi$
$53$		−	8.72001i		−	1.19779i	0.800829	−	0.598893i	$-0.204393\pi$
$54$	7.20109	+	1.46435i	0.979944	+	0.199273i
$55$			1.88369i			0.253997i
$56$		0			0
$57$	−7.92692	+	9.45679i	−1.04995	+	1.25258i
$58$	5.67750	−	1.89056i	0.745492	−	0.248243i
$59$	−0.662173			−0.0862076			−0.0431038	−	0.999071i	$-0.513725\pi$
$59$	−0.662173			−0.0862076			−0.0431038	+	0.999071i	$0.513725\pi$
$60$	0.152192	−	2.77794i	0.0196479	−	0.358630i
$61$	0.958124			0.122675			0.0613376	−	0.998117i	$-0.480463\pi$
$61$	0.958124			0.122675			0.0613376	+	0.998117i	$0.480463\pi$
$62$	6.57334	−	2.18887i	0.834815	−	0.277987i
$63$		0			0
$64$	2.80221	+	7.49317i	0.350276	+	0.936647i
$65$		−	4.23132i		−	0.524831i
$66$	−2.11057	+	5.34344i	−0.259794	+	0.657732i
$67$		−	8.42629i		−	1.02943i	−0.857360	−	0.514717i	$-0.827897\pi$
$67$		−	8.42629i		−	1.02943i	0.857360	−	0.514717i	$-0.172103\pi$
$68$	1.42135	+	1.89756i	0.172364	+	0.230113i
$69$	−10.4693	−	8.77567i	−1.26036	−	1.05647i
$70$		0			0
$71$	9.67432			1.14813			0.574065	−	0.818810i	$-0.305366\pi$
$71$	9.67432			1.14813			0.574065	+	0.818810i	$0.305366\pi$
$72$	3.54425	−	7.70962i	0.417694	−	0.908588i
$73$	−1.41421			−0.165521			−0.0827606	−	0.996569i	$-0.526374\pi$
$73$	−1.41421			−0.165521			−0.0827606	+	0.996569i	$0.526374\pi$
$74$	0.468227	+	1.40612i	0.0544303	+	0.163458i
$75$	−5.78081	−	4.84562i	−0.667511	−	0.559525i
$76$	8.54216	+	11.4041i	0.979853	+	1.30814i
$77$		0			0
$78$	4.74097	−	12.0029i	0.536810	−	1.35907i
$79$			6.92820i			0.779484i	0.920924	+	0.389742i	$0.127436\pi$
$79$			6.92820i			0.779484i	−0.920924	+	0.389742i	$0.872564\pi$
$80$	−3.08289	−	0.903284i	−0.344678	−	0.100990i
$81$	−8.45090	+	3.09553i	−0.938989	+	0.343948i
$82$	−9.61978	+	3.20331i	−1.06233	+	0.353747i
$83$	−5.18229			−0.568830			−0.284415	−	0.958701i	$-0.591799\pi$
$83$	−5.18229			−0.568830			−0.284415	+	0.958701i	$0.591799\pi$
$84$		0			0
$85$	−0.952047			−0.103264
$86$	−10.6579	+	3.54901i	−1.14928	+	0.382700i
$87$	−4.70802	+	5.61665i	−0.504753	+	0.602169i
$88$	5.45090	+	3.78113i	0.581068	+	0.403069i
$89$		−	16.3659i		−	1.73478i	−0.497626	−	0.867392i	$-0.665795\pi$
$89$		−	16.3659i		−	1.73478i	0.497626	−	0.867392i	$-0.334205\pi$
$90$	1.62461	+	2.99513i	0.171249	+	0.315714i
$91$		0			0
$92$	−12.6252	+	9.45679i	−1.31627	+	0.985938i
$93$	−5.45090	+	6.50290i	−0.565232	+	0.674319i
$94$	−2.72508	−	8.18360i	−0.281070	−	0.844074i
$95$	−5.72170			−0.587034
$96$	−7.73312	−	6.01655i	−0.789258	−	0.614062i
$97$	−4.37827			−0.444546			−0.222273	−	0.974984i	$-0.571348\pi$
$97$	−4.37827			−0.444546			−0.222273	+	0.974984i	$0.571348\pi$
$98$		0			0
$99$	−1.22896	−	6.92820i	−0.123515	−	0.696311i
$100$	−6.97119	+	5.22171i	−0.697119	+	0.522171i
$101$			8.39337i			0.835171i	0.908638	+	0.417586i	$0.137124\pi$
$101$			8.39337i			0.835171i	−0.908638	+	0.417586i	$0.862876\pi$
$102$	−2.70066	−	1.06672i	−0.267405	−	0.105621i
$103$			2.56695i			0.252929i	0.991971	+	0.126465i	$0.0403630\pi$
$103$			2.56695i			0.252929i	−0.991971	+	0.126465i	$0.959637\pi$
$104$	−12.2443	−	8.49353i	−1.20065	−	0.832859i
$105$		0			0
$106$	11.7003	−	3.89612i	1.13644	−	0.378424i
$107$	−6.09990			−0.589700			−0.294850	−	0.955544i	$-0.595270\pi$
$107$	−6.09990			−0.589700			−0.294850	+	0.955544i	$0.595270\pi$
$108$	1.25263	+	10.3165i	0.120534	+	0.992709i
$109$	5.45090			0.522101			0.261051	−	0.965325i	$-0.415931\pi$
$109$	5.45090			0.522101			0.261051	+	0.965325i	$0.415931\pi$
$110$	−2.52749	+	0.841636i	−0.240987	+	0.0802468i
$111$	−1.39105	−	1.16601i	−0.132033	−	0.110673i
$112$		0			0
$113$		−	7.09803i		−	0.667726i	−0.942622	−	0.333863i	$-0.891648\pi$
$113$		−	7.09803i		−	0.667726i	0.942622	−	0.333863i	$-0.108352\pi$
$114$	−16.2307	−	6.41086i	−1.52014	−	0.600432i
$115$		−	6.33433i		−	0.590679i
$116$	5.07343	+	6.77323i	0.471056	+	0.628879i
$117$	2.76061	+	15.5628i	0.255219	+	1.43878i
$118$	−0.295860	−	0.888490i	−0.0272361	−	0.0817921i
$119$		0			0
$120$	3.79537	−	1.03698i	0.346469	−	0.0946629i
$121$	−5.49885			−0.499895
$122$	0.428092	+	1.28559i	0.0387576	+	0.116392i
$123$	7.97713	−	9.51669i	0.719274	−	0.858091i
$124$	5.87396	+	7.84197i	0.527498	+	0.704230i
$125$		−	7.51322i		−	0.672003i
$126$		0			0
$127$		−	4.16202i		−	0.369320i	−0.982802	−	0.184660i	$-0.940882\pi$
$127$		−	4.16202i		−	0.369320i	0.982802	−	0.184660i	$-0.0591184\pi$
$128$	−8.80214	+	7.10790i	−0.778007	+	0.628256i
$129$	8.83802	−	10.5437i	0.778144	−	0.928323i
$130$	5.67750	−	1.89056i	0.497949	−	0.165813i
$131$	10.4919			0.916680			0.458340	−	0.888777i	$-0.348444\pi$
$131$	10.4919			0.916680			0.458340	+	0.888777i	$0.348444\pi$
$132$	−8.11272	−	0.444463i	−0.706122	−	0.0386855i
$133$		0			0
$134$	11.3062	−	3.76488i	0.976707	−	0.325236i
$135$	−3.61727	−	2.08101i	−0.311325	−	0.179105i
$136$	−1.91104	+	2.75497i	−0.163871	+	0.236237i
$137$			13.4920i			1.15270i	0.817203	+	0.576350i	$0.195523\pi$
$137$			13.4920i			1.15270i	−0.817203	+	0.576350i	$0.804477\pi$
$138$	7.09728	−	17.9685i	0.604161	−	1.52958i
$139$			7.57264i			0.642303i	0.947028	+	0.321151i	$0.104070\pi$
$139$			7.57264i			0.642303i	−0.947028	+	0.321151i	$0.895930\pi$
$140$		0			0
$141$	8.09591	+	6.78619i	0.681798	+	0.571501i
$142$	4.32250	+	12.9808i	0.362736	+	1.08932i
$143$	−12.3572			−1.03336
$144$	11.9282	+	1.31093i	0.994015	+	0.109244i
$145$	−3.39828			−0.282212
$146$	−0.631873	−	1.89756i	−0.0522942	−	0.157043i
$147$		0			0
$148$	−1.67750	+	1.25651i	−0.137889	+	0.103285i
$149$		−	16.1013i		−	1.31907i	−0.751673	−	0.659536i	$-0.770753\pi$
$149$		−	16.1013i		−	1.31907i	0.751673	−	0.659536i	$-0.229247\pi$
$150$	3.91887	−	9.92160i	0.319975	−	0.810095i
$151$			17.3844i			1.41472i	0.706853	+	0.707360i	$0.250114\pi$
$151$			17.3844i			1.41472i	−0.706853	+	0.707360i	$0.749886\pi$
$152$	−11.4851	+	16.5571i	−0.931568	+	1.34296i
$153$	3.50163	−	0.621137i	0.283090	−	0.0502160i
$154$		0			0
$155$	−3.93449			−0.316026
$156$	18.2236	+	0.998394i	1.45905	+	0.0799355i
$157$	−3.92218			−0.313024			−0.156512	−	0.987676i	$-0.550025\pi$
$157$	−3.92218			−0.313024			−0.156512	+	0.987676i	$0.550025\pi$
$158$	−9.29611	+	3.09553i	−0.739559	+	0.246267i
$159$	−9.70241	+	11.5749i	−0.769451	+	0.917952i
$160$	−0.165435	−	4.54014i	−0.0130788	−	0.358930i
$161$		0			0
$162$	−7.92940	−	9.95614i	−0.622992	−	0.782228i
$163$			7.30910i			0.572493i	0.958156	+	0.286246i	$0.0924076\pi$
$163$			7.30910i			0.572493i	−0.958156	+	0.286246i	$0.907592\pi$
$164$	−8.59627	−	11.4764i	−0.671256	−	0.896153i
$165$	2.09591	−	2.50041i	0.163166	−	0.194656i
$166$	−2.31546	−	6.95348i	−0.179714	−	0.539695i
$167$	−8.37196			−0.647842			−0.323921	−	0.946084i	$-0.605001\pi$
$167$	−8.37196			−0.647842			−0.323921	+	0.946084i	$0.605001\pi$
$168$		0			0
$169$	14.7579			1.13523
$170$	−0.425376	−	1.27744i	−0.0326249	−	0.0979749i
$171$	21.0444	−	3.73296i	1.60930	−	0.285467i
$172$	−9.52398	−	12.7149i	−0.726196	−	0.969501i
$173$		−	12.7711i		−	0.970970i	−0.874245	−	0.485485i	$-0.838643\pi$
$173$		−	12.7711i		−	0.970970i	0.874245	−	0.485485i	$-0.161357\pi$
$174$	−9.63986	−	3.80759i	−0.730796	−	0.288653i
$175$		0			0
$176$	−2.63796	+	9.00331i	−0.198844	+	0.678650i
$177$	0.878968	+	0.736774i	0.0660673	+	0.0553793i
$178$	21.9594	−	7.31232i	1.64593	−	0.548082i
$179$	21.1177			1.57841			0.789206	−	0.614129i	$-0.210492\pi$
$179$	21.1177			1.57841			0.789206	+	0.614129i	$0.210492\pi$
$180$	−3.29292	+	3.51809i	−0.245440	+	0.262223i
$181$	12.4075			0.922239			0.461120	−	0.887338i	$-0.347448\pi$
$181$	12.4075			0.922239			0.461120	+	0.887338i	$0.347448\pi$
$182$		0			0
$183$	−1.27181	−	1.06607i	−0.0940151	−	0.0788059i
$184$	−18.3299	−	12.7149i	−1.35130	−	0.937354i
$185$		−	0.841636i		−	0.0618783i
$186$	−11.1609	−	4.40839i	−0.818358	−	0.323239i
$187$			2.78037i			0.203321i
$188$	9.76301	−	7.31290i	0.712041	−	0.533348i
$189$		0			0
$190$	−2.55646	−	7.67724i	−0.185465	−	0.556966i
$191$	−6.09990			−0.441374			−0.220687	−	0.975345i	$-0.570830\pi$
$191$	−6.09990			−0.441374			−0.220687	+	0.975345i	$0.570830\pi$
$192$	4.61770	−	13.0643i	0.333254	−	0.942837i
$193$	0.645008			0.0464287			0.0232144	−	0.999731i	$-0.492610\pi$
$193$	0.645008			0.0464287			0.0232144	+	0.999731i	$0.492610\pi$
$194$	−1.95622	−	5.87467i	−0.140448	−	0.421777i
$195$	−4.70802	+	5.61665i	−0.337149	+	0.402217i
$196$		0			0
$197$		−	14.9111i		−	1.06237i	−0.847256	−	0.531185i	$-0.821747\pi$
$197$		−	14.9111i		−	1.06237i	0.847256	−	0.531185i	$-0.178253\pi$
$198$	8.74701	−	4.74453i	0.621623	−	0.337179i
$199$			18.6992i			1.32555i	0.748817	+	0.662777i	$0.230622\pi$
$199$			18.6992i			1.32555i	−0.748817	+	0.662777i	$0.769378\pi$
$200$	−10.1211	−	7.02072i	−0.715671	−	0.496440i
$201$	−9.37559	+	11.1850i	−0.661303	+	0.788932i
$202$	−11.2620	+	3.75017i	−0.792394	+	0.263861i
$203$		0			0
$204$	0.224639	−	4.10030i	0.0157278	−	0.287078i
$205$	5.75794			0.402152
$206$	−3.44428	+	1.14692i	−0.239974	+	0.0799096i
$207$	4.13266	+	23.2976i	0.287240	+	1.61930i
$208$	5.92564	−	20.2241i	0.410869	−	1.40229i
$209$			16.7097i			1.15583i
$210$		0			0
$211$		−	11.7243i		−	0.807132i	−0.914950	−	0.403566i	$-0.867771\pi$
$211$		−	11.7243i		−	0.807132i	0.914950	−	0.403566i	$-0.132229\pi$
$212$	10.4555	+	13.9584i	0.718083	+	0.958670i
$213$	−12.8417	−	10.7642i	−0.879898	−	0.737553i
$214$	−2.72545	−	8.18472i	−0.186308	−	0.559496i
$215$	6.37933			0.435067
$216$	−13.2828	+	6.29020i	−0.903782	+	0.427994i
$217$		0			0
$218$	2.43547	+	7.31389i	0.164951	+	0.495359i
$219$	1.87723	+	1.57354i	0.126851	+	0.106330i
$220$	−2.25858	−	3.01529i	−0.152273	−	0.203291i
$221$		−	6.24553i		−	0.420120i
$222$	0.943009	−	2.38746i	0.0632906	−	0.160236i
$223$			0.683260i			0.0457545i	0.999738	+	0.0228772i	$0.00728269\pi$
$223$			0.683260i			0.0457545i	−0.999738	+	0.0228772i	$0.992717\pi$
$224$		0			0
$225$	2.28191	+	12.8642i	0.152128	+	0.857610i
$226$	9.52398	−	3.17141i	0.633525	−	0.210959i
$227$	8.75387			0.581015			0.290507	−	0.956873i	$-0.406176\pi$
$227$	8.75387			0.581015			0.290507	+	0.956873i	$0.406176\pi$
$228$	1.35005	−	24.6423i	0.0894094	−	1.63198i
$229$	−18.4985			−1.22242			−0.611209	−	0.791469i	$-0.709316\pi$
$229$	−18.4985			−1.22242			−0.611209	+	0.791469i	$0.709316\pi$
$230$	8.49926	−	2.83019i	0.560425	−	0.186617i
$231$		0			0
$232$	−6.82135	+	9.83371i	−0.447844	+	0.645615i
$233$			10.1391i			0.664234i	0.943238	+	0.332117i	$0.107763\pi$
$233$			10.1391i			0.664234i	−0.943238	+	0.332117i	$0.892237\pi$
$234$	−19.6484	+	10.6576i	−1.28445	+	0.696710i
$235$			4.89831i			0.319531i
$236$	1.05996	−	0.793958i	0.0689978	−	0.0516822i
$237$	7.70873	−	9.19649i	0.500736	−	0.597376i
$238$		0			0
$239$	−1.49470			−0.0966841			−0.0483421	−	0.998831i	$-0.515394\pi$
$239$	−1.49470			−0.0966841			−0.0483421	+	0.998831i	$0.515394\pi$
$240$	3.08718	+	4.62923i	0.199276	+	0.298815i
$241$	−10.3337			−0.665653			−0.332827	−	0.942988i	$-0.608002\pi$
$241$	−10.3337			−0.665653			−0.332827	+	0.942988i	$0.608002\pi$
$242$	−2.45690	−	7.37824i	−0.157935	−	0.474291i
$243$	14.6620	+	5.29396i	0.940567	+	0.339608i
$244$	−1.53370	+	1.14881i	−0.0981853	+	0.0735449i
$245$		0			0
$246$	16.3335	+	6.45146i	1.04138	+	0.411330i
$247$		−	37.5349i		−	2.38829i
$248$	−7.89769	+	11.3854i	−0.501504	+	0.722971i
$249$	6.87897	+	5.76613i	0.435937	+	0.365413i
$250$	10.0811	−	3.35692i	0.637583	−	0.212310i
$251$	26.9555			1.70142			0.850709	−	0.525636i	$-0.176173\pi$
$251$	26.9555			1.70142			0.850709	+	0.525636i	$0.176173\pi$
$252$		0			0
$253$	−18.4989			−1.16301
$254$	5.58451	−	1.85960i	0.350403	−	0.116682i
$255$	1.26375	+	1.05930i	0.0791389	+	0.0663362i
$256$	−13.4700	−	8.63469i	−0.841878	−	0.539668i
$257$			2.79168i			0.174140i	0.996202	+	0.0870700i	$0.0277504\pi$
$257$			2.79168i			0.174140i	−0.996202	+	0.0870700i	$0.972250\pi$
$258$	18.0962	+	7.14771i	1.12662	+	0.444997i
$259$		0			0
$260$	5.07343	+	6.77323i	0.314641	+	0.420058i
$261$	12.4989	−	2.21711i	0.773659	−	0.137236i
$262$	4.68779	+	14.0778i	0.289613	+	0.869728i
$263$	−15.3103			−0.944074			−0.472037	−	0.881579i	$-0.656481\pi$
$263$	−15.3103			−0.944074			−0.472037	+	0.881579i	$0.656481\pi$
$264$	−3.02841	−	11.0841i	−0.186386	−	0.682177i
$265$	−7.00325			−0.430206
$266$		0			0
$267$	−18.2097	+	21.7241i	−1.11442	+	1.32949i
$268$	10.1033	+	13.4883i	0.617155	+	0.823927i
$269$			30.6864i			1.87098i	0.353347	+	0.935492i	$0.385044\pi$
$269$			30.6864i			1.87098i	−0.353347	+	0.935492i	$0.614956\pi$
$270$	1.17605	−	5.78337i	0.0715724	−	0.351965i
$271$			19.6862i			1.19585i	0.801550	+	0.597927i	$0.204009\pi$
$271$			19.6862i			1.19585i	−0.801550	+	0.597927i	$0.795991\pi$
$272$	−4.55042	−	1.33327i	−0.275910	−	0.0808412i
$273$		0			0
$274$	−18.1033	+	6.02825i	−1.09366	+	0.364180i
$275$	−10.2144			−0.615953
$276$	27.2808	+	1.49461i	1.64211	+	0.0899647i
$277$	−13.1129			−0.787880			−0.393940	−	0.919136i	$-0.628888\pi$
$277$	−13.1129			−0.787880			−0.393940	+	0.919136i	$0.628888\pi$
$278$	−10.1608	+	3.38347i	−0.609404	+	0.202927i
$279$	14.4710	−	2.56695i	0.866358	−	0.153679i
$280$		0			0
$281$		−	2.86670i		−	0.171013i	−0.996338	−	0.0855066i	$-0.972749\pi$
$281$		−	2.86670i		−	0.171013i	0.996338	−	0.0855066i	$-0.0272509\pi$
$282$	−5.48830	+	13.8950i	−0.326824	+	0.827435i
$283$			1.99040i			0.118317i	0.998249	+	0.0591585i	$0.0188417\pi$
$283$			1.99040i			0.118317i	−0.998249	+	0.0591585i	$0.981158\pi$
$284$	−15.4860	+	11.5997i	−0.918927	+	0.688314i
$285$	7.59497	+	6.36630i	0.449887	+	0.377107i
$286$	−5.52122	−	16.5806i	−0.326477	−	0.980433i
$287$		0			0
$288$	3.57056	+	16.5907i	0.210397	+	0.977616i
$289$	15.5948			0.917339
$290$	−1.51836	−	4.55973i	−0.0891610	−	0.267757i
$291$	5.81171	+	4.87153i	0.340689	+	0.285574i
$292$	2.26378	−	1.69567i	0.132478	−	0.0992314i
$293$			16.7482i			0.978441i	0.872160	+	0.489221i	$0.162719\pi$
$293$			16.7482i			0.978441i	−0.872160	+	0.489221i	$0.837281\pi$
$294$		0			0
$295$			0.531807i			0.0309630i
$296$	−2.43547	−	1.68941i	−0.141559	−	0.0981952i
$297$	−6.07741	+	10.5639i	−0.352647	+	0.612980i
$298$	21.6044	−	7.19411i	1.25151	−	0.416743i
$299$	41.5539			2.40312
$300$	15.0635	+	0.825270i	0.869694	+	0.0476470i
$301$		0			0
$302$	−23.3260	+	7.76737i	−1.34226	+	0.446962i
$303$	9.33896	−	11.1413i	0.536509	−	0.640054i
$304$	−27.3475	−	8.01279i	−1.56849	−	0.459565i
$305$		−	0.769492i		−	0.0440610i
$306$	2.39796	+	4.42088i	0.137082	+	0.252725i
$307$		−	15.4869i		−	0.883885i	−0.897043	−	0.441942i	$-0.854290\pi$
$307$		−	15.4869i		−	0.883885i	0.897043	−	0.441942i	$-0.145710\pi$
$308$		0			0
$309$	2.85614	−	3.40737i	0.162480	−	0.193838i
$310$	−1.75794	−	5.27921i	−0.0998441	−	0.299839i
$311$	10.8995			0.618051			0.309026	−	0.951054i	$-0.399997\pi$
$311$	10.8995			0.618051			0.309026	+	0.951054i	$0.399997\pi$
$312$	6.80270	+	24.8981i	0.385127	+	1.40958i
$313$	33.8022			1.91062			0.955308	−	0.295613i	$-0.0955238\pi$
$313$	33.8022			1.91062			0.955308	+	0.295613i	$0.0955238\pi$
$314$	−1.75244	−	5.26270i	−0.0988958	−	0.296991i
$315$		0			0
$316$	−8.30704	−	11.0902i	−0.467307	−	0.623874i
$317$			9.28660i			0.521588i	0.965395	+	0.260794i	$0.0839843\pi$
$317$			9.28660i			0.521588i	−0.965395	+	0.260794i	$0.916016\pi$
$318$	−19.8661	−	7.84677i	−1.11403	−	0.440025i
$319$			9.92437i			0.555658i
$320$	6.01795	−	2.25052i	0.336413	−	0.125808i
$321$	8.09701	+	6.78712i	0.451931	+	0.378820i
$322$		0			0
$323$	−8.44536			−0.469912
$324$	9.81606	−	15.0879i	0.545336	−	0.838217i
$325$	22.9446			1.27274
$326$	−9.80719	+	3.26572i	−0.543170	+	0.180871i
$327$	−7.23552	−	6.06499i	−0.400125	−	0.335395i
$328$	11.5579	−	16.6619i	0.638178	−	0.920002i
$329$		0			0
$330$	4.29145	+	1.69505i	0.236236	+	0.0933096i
$331$		−	1.01495i		−	0.0557864i	−0.999611	−	0.0278932i	$-0.991120\pi$
$331$		−	1.01495i		−	0.0557864i	0.999611	−	0.0278932i	$-0.00887984\pi$
$332$	8.29548	−	6.21366i	0.455274	−	0.341019i
$333$	0.549103	+	3.09553i	0.0300906	+	0.169634i
$334$	−3.74061	−	11.2333i	−0.204677	−	0.614659i
$335$	−6.76735			−0.369740
$336$		0			0
$337$	−12.6597			−0.689620			−0.344810	−	0.938673i	$-0.612057\pi$
$337$	−12.6597			−0.689620			−0.344810	+	0.938673i	$0.612057\pi$
$338$	6.59387	+	19.8019i	0.358659	+	1.07708i
$339$	−7.89769	+	9.42191i	−0.428944	+	0.511728i
$340$	1.52398	−	1.14152i	0.0826492	−	0.0619077i
$341$			11.4903i			0.622236i
$342$	14.4115	+	26.5690i	0.779283	+	1.43669i
$343$		0			0
$344$	12.8052	−	18.4601i	0.690411	−	0.995302i
$345$	−7.04795	+	8.40818i	−0.379449	+	0.452681i
$346$	17.1360	−	5.70616i	0.921237	−	0.306765i
$347$	25.6286			1.37581			0.687907	−	0.725799i	$-0.258530\pi$
$347$	25.6286			1.37581			0.687907	+	0.725799i	$0.258530\pi$
$348$	0.801834	−	14.6358i	0.0429828	−	0.784560i
$349$	−28.1235			−1.50542			−0.752709	−	0.658354i	$-0.771253\pi$
$349$	−28.1235			−1.50542			−0.752709	+	0.658354i	$0.771253\pi$
$350$		0			0
$351$	13.6517	−	23.7297i	0.728672	−	1.26660i
$352$	−13.2591	+	0.483138i	−0.706712	+	0.0257513i
$353$		−	10.3049i		−	0.548474i	−0.961662	−	0.274237i	$-0.911575\pi$
$353$		−	10.3049i		−	0.548474i	0.961662	−	0.274237i	$-0.0884253\pi$
$354$	−0.595862	+	1.50857i	−0.0316697	+	0.0801797i
$355$		−	7.76968i		−	0.412372i
$356$	19.6230	+	26.1975i	1.04002	+	1.38847i
$357$		0			0
$358$	9.43543	+	28.3353i	0.498678	+	1.49757i
$359$	26.8394			1.41653			0.708265	−	0.705947i	$-0.249478\pi$
$359$	26.8394			1.41653			0.708265	+	0.705947i	$0.249478\pi$
$360$	−6.19178	−	2.84647i	−0.326336	−	0.150022i
$361$	−31.7556			−1.67135
$362$	5.54368	+	16.6481i	0.291369	+	0.875003i
$363$	7.29917	+	6.11835i	0.383107	+	0.321130i
$364$		0			0
$365$			1.13579i			0.0594499i
$366$	0.862175	−	2.18281i	0.0450666	−	0.114097i
$367$			13.3519i			0.696964i	0.937315	+	0.348482i	$0.113303\pi$
$367$			13.3519i			0.696964i	−0.937315	+	0.348482i	$0.886697\pi$
$368$	8.87073	−	30.2756i	0.462419	−	1.57823i
$369$	−21.1777	+	3.75661i	−1.10247	+	0.195561i
$370$	1.12929	−	0.376045i	0.0587089	−	0.0195496i
$371$		0			0
$372$	0.928355	−	16.9452i	0.0481330	−	0.878565i
$373$	−22.8059			−1.18084			−0.590422	−	0.807095i	$-0.701039\pi$
$373$	−22.8059			−1.18084			−0.590422	+	0.807095i	$0.701039\pi$
$374$	−3.73064	+	1.24227i	−0.192907	+	0.0642365i
$375$	−8.35966	+	9.97304i	−0.431691	+	0.515006i
$376$	14.1744	+	9.83237i	0.730990	+	0.507066i
$377$		−	22.2931i		−	1.14815i
$378$		0			0
$379$			1.98122i			0.101768i	0.998705	+	0.0508842i	$0.0162040\pi$
$379$			1.98122i			0.101768i	−0.998705	+	0.0508842i	$0.983796\pi$
$380$	9.15892	−	6.86041i	0.469843	−	0.351932i
$381$	−4.63091	+	5.52466i	−0.237249	+	0.283037i
$382$	−2.72545	−	8.18472i	−0.139446	−	0.418767i
$383$	−28.8209			−1.47268			−0.736339	−	0.676613i	$-0.763447\pi$
$383$	−28.8209			−1.47268			−0.736339	+	0.676613i	$0.763447\pi$
$384$	19.5926	+	0.358762i	0.999832	+	0.0183080i
$385$		0			0
$386$	0.288191	+	0.865458i	0.0146685	+	0.0440506i
$387$	−23.4632	+	4.16202i	−1.19270	+	0.211567i
$388$	7.00846	−	5.24963i	0.355801	−	0.266509i
$389$			1.95975i			0.0993630i	0.998765	+	0.0496815i	$0.0158206\pi$
$389$			1.95975i			0.0993630i	−0.998765	+	0.0496815i	$0.984179\pi$
$390$	−9.63986	−	3.80759i	−0.488133	−	0.192805i
$391$		−	9.34962i		−	0.472831i
$392$		0			0
$393$	−13.9269	−	11.6739i	−0.702520	−	0.588870i
$394$	20.0074	−	6.66230i	1.00796	−	0.335642i
$395$	5.56421			0.279966
$396$	10.2743	+	9.61668i	0.516302	+	0.483256i
$397$	−4.56310			−0.229015			−0.114508	−	0.993422i	$-0.536529\pi$
$397$	−4.56310			−0.229015			−0.114508	+	0.993422i	$0.536529\pi$
$398$	−25.0902	+	8.35485i	−1.25766	+	0.418791i
$399$		0			0
$400$	4.89811	−	16.7172i	0.244906	−	0.835858i
$401$		−	26.7811i		−	1.33738i	−0.743539	−	0.668692i	$-0.766854\pi$
$401$		−	26.7811i		−	1.33738i	0.743539	−	0.668692i	$-0.233146\pi$
$402$	−19.1969	−	7.58246i	−0.957453	−	0.378179i
$403$		−	25.8107i		−	1.28572i
$404$	−10.0638	−	13.4356i	−0.500693	−	0.668444i
$405$	2.48610	+	6.78712i	0.123535	+	0.337255i
$406$		0			0
$407$	−2.45792			−0.121835
$408$	5.60206	−	1.53061i	0.277343	−	0.0757763i
$409$	18.0424			0.892142			0.446071	−	0.894998i	$-0.352823\pi$
$409$	18.0424			0.892142			0.446071	+	0.894998i	$0.352823\pi$
$410$	2.57266	+	7.72587i	0.127054	+	0.381554i
$411$	15.0120	−	17.9093i	0.740488	−	0.883399i
$412$	−3.07782	−	4.10901i	−0.151633	−	0.202436i
$413$		0			0
$414$	−29.4138	+	15.9545i	−1.44561	+	0.784123i
$415$			4.16202i			0.204306i
$416$	29.7838	−	1.08527i	1.46027	−	0.0532098i
$417$	8.42577	−	10.0519i	0.412612	−	0.492244i
$418$	−22.4207	+	7.46593i	−1.09663	+	0.365171i
$419$	−17.5395			−0.856861			−0.428430	−	0.903575i	$-0.640933\pi$
$419$	−17.5395			−0.856861			−0.428430	+	0.903575i	$0.640933\pi$
$420$		0			0
$421$	15.4006			0.750582			0.375291	−	0.926907i	$-0.377543\pi$
$421$	15.4006			0.750582			0.375291	+	0.926907i	$0.377543\pi$
$422$	15.7314	−	5.23843i	0.765791	−	0.255003i
$423$	−3.19577	−	18.0160i	−0.155384	−	0.875967i
$424$	−14.0576	+	20.2656i	−0.682698	+	0.984182i
$425$		−	5.16254i		−	0.250420i
$426$	8.70551	−	22.0402i	0.421784	−	1.06785i
$427$		0			0
$428$	9.76434	−	7.31389i	0.471977	−	0.353530i
$429$	16.4029	+	13.7494i	0.791942	+	0.663826i
$430$	2.85030	+	8.55965i	0.137454	+	0.412783i
$431$	−9.00360			−0.433688			−0.216844	−	0.976206i	$-0.569576\pi$
$431$	−9.00360			−0.433688			−0.216844	+	0.976206i	$0.569576\pi$
$432$	−14.3748	−	15.0121i	−0.691610	−	0.722271i
$433$	−6.15889			−0.295977			−0.147989	−	0.988989i	$-0.547280\pi$
$433$	−6.15889			−0.295977			−0.147989	+	0.988989i	$0.547280\pi$
$434$		0			0
$435$	4.51087	+	3.78113i	0.216280	+	0.181291i
$436$	−8.72545	+	6.53572i	−0.417873	+	0.313004i
$437$		−	56.1901i		−	2.68794i
$438$	−1.27259	+	3.22188i	−0.0608068	+	0.153947i
$439$			29.2493i			1.39599i	0.716102	+	0.697996i	$0.245925\pi$
$439$			29.2493i			1.39599i	−0.716102	+	0.697996i	$0.754075\pi$
$440$	3.03671	−	4.37775i	0.144770	−	0.208701i
$441$		0			0
$442$	8.38012	−	2.79052i	0.398602	−	0.132731i
$443$	7.21640			0.342861			0.171431	−	0.985196i	$-0.445161\pi$
$443$	7.21640			0.342861			0.171431	+	0.985196i	$0.445161\pi$
$444$	3.62478	+	0.198587i	0.172024	+	0.00942451i
$445$	−13.1439			−0.623079
$446$	−0.916783	+	0.305282i	−0.0434109	+	0.0144555i
$447$	−17.9153	+	21.3729i	−0.847365	+	1.01090i
$448$		0			0
$449$		−	4.43423i		−	0.209264i	−0.994511	−	0.104632i	$-0.966634\pi$
$449$		−	4.43423i		−	0.209264i	0.994511	−	0.104632i	$-0.0333665\pi$
$450$	−16.2413	+	8.80955i	−0.765621	+	0.415286i
$451$		−	16.8155i		−	0.791813i
$452$	8.51066	+	11.3621i	0.400308	+	0.534427i
$453$	19.3429	−	23.0760i	0.908809	−	1.08421i
$454$	3.91125	+	11.7458i	0.183564	+	0.551256i
$455$		0			0
$456$	33.6678	−	9.19877i	1.57664	−	0.430772i
$457$	13.6620			0.639083			0.319541	−	0.947572i	$-0.396471\pi$
$457$	13.6620			0.639083			0.319541	+	0.947572i	$0.396471\pi$
$458$	−8.26518	−	24.8209i	−0.386207	−	1.15981i
$459$	−5.33917	−	3.07162i	−0.249211	−	0.143371i
$460$	7.59497	+	10.1396i	0.354117	+	0.472761i
$461$		−	5.25789i		−	0.244885i	−0.992476	−	0.122442i	$-0.960927\pi$
$461$		−	5.25789i		−	0.244885i	0.992476	−	0.122442i	$-0.0390726\pi$
$462$		0			0
$463$		−	15.8863i		−	0.738299i	−0.929370	−	0.369149i	$-0.879649\pi$
$463$		−	15.8863i		−	0.738299i	0.929370	−	0.369149i	$-0.120351\pi$
$464$	−16.2425	−	4.75902i	−0.754037	−	0.220932i
$465$	5.22264	+	4.37775i	0.242194	+	0.203013i
$466$	−13.6044	+	4.53017i	−0.630212	+	0.209856i
$467$	−27.0767			−1.25296			−0.626481	−	0.779437i	$-0.715505\pi$
$467$	−27.0767			−1.25296			−0.626481	+	0.779437i	$0.715505\pi$
$468$	−23.0791	−	21.6019i	−1.06683	−	0.998548i
$469$		0			0
$470$	−6.57245	+	2.18858i	−0.303164	+	0.100951i
$471$	5.20630	+	4.36405i	0.239894	+	0.201085i
$472$	1.53891	+	1.06750i	0.0708340	+	0.0491355i
$473$		−	18.6303i		−	0.856621i
$474$	15.7839	+	6.23440i	0.724980	+	0.286355i
$475$		−	31.0263i		−	1.42358i
$476$		0			0
$477$	25.7579	−	4.56908i	1.17937	−	0.209204i
$478$	−0.667835	−	2.00556i	−0.0305461	−	0.0917320i
$479$	−15.2605			−0.697271			−0.348635	−	0.937258i	$-0.613355\pi$
$479$	−15.2605			−0.697271			−0.348635	+	0.937258i	$0.613355\pi$
$480$	−4.83204	+	6.21065i	−0.220551	+	0.283476i
$481$	5.52122			0.251746
$482$	−4.61712	−	13.8655i	−0.210304	−	0.631558i
$483$		0			0
$484$	8.80221	−	6.59322i	0.400100	−	0.299692i
$485$			3.51629i			0.159667i
$486$	−0.552321	+	22.0385i	−0.0250538	+	0.999686i
$487$		−	6.06417i		−	0.274794i	−0.990516	−	0.137397i	$-0.956126\pi$
$487$		−	6.06417i		−	0.274794i	0.990516	−	0.137397i	$-0.0438736\pi$
$488$	−2.22671	−	1.54460i	−0.100798	−	0.0699208i
$489$	8.13254	−	9.70209i	0.367766	−	0.438744i
$490$		0			0
$491$	4.03833			0.182247			0.0911235	−	0.995840i	$-0.470954\pi$
$491$	4.03833			0.182247			0.0911235	+	0.995840i	$0.470954\pi$
$492$	−1.35860	+	24.7984i	−0.0612506	+	1.11800i
$493$	−5.01594			−0.225906
$494$	50.3636	−	16.7707i	2.26596	−	0.754549i
$495$	−5.56421	+	0.987009i	−0.250092	+	0.0443627i
$496$	−18.8053	−	5.50994i	−0.844384	−	0.247404i
$497$		0			0
$498$	−4.66333	+	11.8064i	−0.208969	+	0.529056i
$499$			38.5012i			1.72355i	0.507290	+	0.861776i	$0.330647\pi$
$499$			38.5012i			1.72355i	−0.507290	+	0.861776i	$0.669353\pi$
$500$	9.00848	+	12.0267i	0.402872	+	0.537849i
$501$	11.1129	+	9.31514i	0.496489	+	0.416170i
$502$	12.0438	+	36.1684i	0.537541	+	1.61427i
$503$	14.3498			0.639827			0.319914	−	0.947447i	$-0.396346\pi$
$503$	14.3498			0.639827			0.319914	+	0.947447i	$0.396346\pi$
$504$		0			0
$505$	6.74091			0.299967
$506$	−8.26532	−	24.8213i	−0.367438	−	1.10344i
$507$	−19.5897	−	16.4206i	−0.870008	−	0.729263i
$508$	4.99034	+	6.66230i	0.221410	+	0.295592i
$509$			12.0835i			0.535593i	0.963476	+	0.267796i	$0.0862955\pi$
$509$			12.0835i			0.535593i	−0.963476	+	0.267796i	$0.913705\pi$
$510$	−0.856707	+	2.16897i	−0.0379356	+	0.0960435i
$511$		0			0
$512$	5.56740	−	21.9318i	0.246047	−	0.969258i
$513$	−32.0878	−	18.4601i	−1.41671	−	0.815033i
$514$	−3.74581	+	1.24733i	−0.165221	+	0.0550172i
$515$	2.06158			0.0908440
$516$	−1.50522	+	27.4747i	−0.0662638	+	1.20950i
$517$	14.3051			0.629137
$518$		0			0
$519$	−14.2099	+	16.9524i	−0.623746	+	0.744126i
$520$	−6.82135	+	9.83371i	−0.299136	+	0.431237i
$521$			31.8700i			1.39625i	0.715976	+	0.698125i	$0.245982\pi$
$521$			31.8700i			1.39625i	−0.715976	+	0.698125i	$0.754018\pi$
$522$	8.55938	+	15.7801i	0.374634	+	0.690675i
$523$		−	36.6085i		−	1.60078i	−0.599481	−	0.800389i	$-0.704626\pi$
$523$		−	36.6085i		−	1.60078i	0.599481	−	0.800389i	$-0.295374\pi$
$524$	−16.7947	+	12.5800i	−0.733682	+	0.549558i
$525$		0			0
$526$	−6.84068	−	20.5430i	−0.298268	−	0.895719i
$527$	−5.80740			−0.252974
$528$	13.5192	−	9.01583i	0.588350	−	0.392364i
$529$	39.2065			1.70463
$530$	−3.12907	−	9.39681i	−0.135918	−	0.408171i
$531$	−0.346963	−	1.95599i	−0.0150569	−	0.0848825i
$532$		0			0
$533$			37.7727i			1.63612i
$534$	−37.2850	−	14.7270i	−1.61348	−	0.637300i
$535$			4.89898i			0.211801i
$536$	−13.5841	+	19.5829i	−0.586743	+	0.845853i
$537$	−28.0316	−	23.4968i	−1.20965	−	1.01396i
$538$	−41.1744	+	13.7108i	−1.77515	+	0.591113i
$539$		0			0
$540$	8.28546	−	1.00602i	0.356549	−	0.0432921i
$541$	−36.2065			−1.55664			−0.778320	−	0.627867i	$-0.783928\pi$
$541$	−36.2065			−1.55664			−0.778320	+	0.627867i	$0.783928\pi$
$542$	−26.4146	+	8.79585i	−1.13460	+	0.377814i
$543$	−16.4697	−	13.8053i	−0.706781	−	0.592442i
$544$	−0.244186	−	6.70136i	−0.0104694	−	0.287318i
$545$		−	4.37775i		−	0.187522i
$546$		0			0
$547$			31.3917i			1.34221i	0.741361	+	0.671106i	$0.234180\pi$
$547$			31.3917i			1.34221i	−0.741361	+	0.671106i	$0.765820\pi$
$548$	−16.1771	−	21.5971i	−0.691053	−	0.922584i
$549$	0.502034	+	2.83019i	0.0214263	+	0.120790i
$550$	−4.56383	−	13.7055i	−0.194602	−	0.584404i
$551$	−30.1452			−1.28423
$552$	10.1837	+	37.2726i	0.433447	+	1.58643i
$553$		0			0
$554$	−5.85888	−	17.5946i	−0.248920	−	0.747525i
$555$	−0.936455	+	1.11719i	−0.0397503	+	0.0474219i
$556$	−9.07973	−	12.1218i	−0.385066	−	0.514079i
$557$			35.2982i			1.49563i	0.663906	+	0.747816i	$0.268898\pi$
$557$			35.2982i			1.49563i	−0.663906	+	0.747816i	$0.731102\pi$
$558$	9.90996	+	18.2700i	0.419522	+	0.773431i
$559$			41.8491i			1.77003i
$560$		0			0
$561$	3.09361	−	3.69066i	0.130612	−	0.155820i
$562$	3.84648	−	1.28085i	0.162254	−	0.0540293i
$563$	26.4463			1.11458			0.557290	−	0.830318i	$-0.311841\pi$
$563$	26.4463			1.11458			0.557290	+	0.830318i	$0.311841\pi$
$564$	−21.0962	−	1.15577i	−0.888309	−	0.0486668i
$565$	−5.70060			−0.239826
$566$	−2.67067	+	0.889314i	−0.112257	+	0.0373807i
$567$		0			0
$568$	−22.4834	−	15.5961i	−0.943382	−	0.654396i
$569$			27.4048i			1.14887i	0.818551	+	0.574434i	$0.194778\pi$
$569$			27.4048i			1.14887i	−0.818551	+	0.574434i	$0.805222\pi$
$570$	−5.14871	+	13.0352i	−0.215656	+	0.545986i
$571$		−	28.0937i		−	1.17569i	−0.808975	−	0.587843i	$-0.799977\pi$
$571$		−	28.0937i		−	1.17569i	0.808975	−	0.587843i	$-0.200023\pi$
$572$	19.7806	−	14.8165i	0.827070	−	0.619509i
$573$	8.09701	+	6.78712i	0.338257	+	0.283536i
$574$		0			0
$575$	34.3483			1.43242
$576$	−20.6657	+	12.2037i	−0.861071	+	0.508486i
$577$	−22.8309			−0.950461			−0.475231	−	0.879861i	$-0.657635\pi$
$577$	−22.8309			−0.950461			−0.475231	+	0.879861i	$0.657635\pi$
$578$	6.96777	+	20.9247i	0.289821	+	0.870353i
$579$	−0.856183	−	0.717675i	−0.0355818	−	0.0298255i
$580$	5.43974	−	4.07459i	0.225873	−	0.169188i
$581$		0			0
$582$	−3.93982	+	9.97464i	−0.163311	+	0.413462i
$583$			20.4524i			0.847051i
$584$	3.28667	+	2.27987i	0.136003	+	0.0943415i
$585$	12.4989	−	2.21711i	0.516764	−	0.0916664i
$586$	−22.4724	+	7.48314i	−0.928326	+	0.309126i
$587$	−28.4011			−1.17224			−0.586119	−	0.810225i	$-0.699345\pi$
$587$	−28.4011			−1.17224			−0.586119	+	0.810225i	$0.699345\pi$
$588$		0			0
$589$	−34.9018			−1.43810
$590$	−0.713567	+	0.237612i	−0.0293771	+	0.00978235i
$591$	−16.5910	+	19.7930i	−0.682461	+	0.814173i
$592$	1.17865	−	4.02270i	0.0484420	−	0.165332i
$593$			23.8791i			0.980598i	0.871554	+	0.490299i	$0.163113\pi$
$593$			23.8791i			0.980598i	−0.871554	+	0.490299i	$0.836887\pi$
$594$	−16.8898	−	3.43456i	−0.692998	−	0.140922i
$595$		0			0
$596$	19.3058	+	25.7740i	0.790796	+	1.05574i
$597$	20.8059	−	24.8213i	0.851528	−	1.01587i
$598$	18.5664	+	55.7561i	0.759235	+	2.28004i
$599$	−39.1249			−1.59860			−0.799300	−	0.600932i	$-0.794796\pi$
$599$	−39.1249			−1.59860			−0.799300	+	0.600932i	$0.794796\pi$
$600$	5.62309	+	20.5807i	0.229562	+	0.840202i
$601$	−4.88356			−0.199204			−0.0996022	−	0.995027i	$-0.531757\pi$
$601$	−4.88356			−0.199204			−0.0996022	+	0.995027i	$0.531757\pi$
$602$		0			0
$603$	24.8903	−	4.41518i	1.01361	−	0.179800i
$604$	−20.8442	−	27.8278i	−0.848138	−	1.13230i
$605$			4.41626i			0.179546i
$606$	19.1219	+	7.55284i	0.776773	+	0.306813i
$607$		−	31.7259i		−	1.28771i	−0.765145	−	0.643857i	$-0.777333\pi$
$607$		−	31.7259i		−	1.28771i	0.765145	−	0.643857i	$-0.222667\pi$
$608$	−1.46753	−	40.2744i	−0.0595161	−	1.63334i
$609$		0			0
$610$	1.03249	−	0.343811i	0.0418042	−	0.0139205i
$611$	−32.1335			−1.29998
$612$	−4.86042	+	5.19279i	−0.196471	+	0.209906i
$613$	32.9668			1.33152			0.665758	−	0.746168i	$-0.268108\pi$
$613$	32.9668			1.33152			0.665758	+	0.746168i	$0.268108\pi$
$614$	20.7800	−	6.91958i	0.838612	−	0.279252i
$615$	−7.64308	−	6.40662i	−0.308199	−	0.258340i
$616$		0			0
$617$			14.3990i			0.579680i	0.957075	+	0.289840i	$0.0936021\pi$
$617$			14.3990i			0.579680i	−0.957075	+	0.289840i	$0.906398\pi$
$618$	5.84806	+	2.30989i	0.235243	+	0.0929174i
$619$		−	24.6919i		−	0.992453i	−0.868193	−	0.496226i	$-0.834719\pi$
$619$		−	24.6919i		−	0.992453i	0.868193	−	0.496226i	$-0.165281\pi$
$620$	6.29808	−	4.71752i	0.252937	−	0.189460i
$621$	20.4367	−	35.5235i	0.820095	−	1.42551i
$622$	4.86990	+	14.6246i	0.195265	+	0.586395i
$623$		0			0
$624$	−30.3682	+	20.2522i	−1.21570	+	0.810738i
$625$	15.7409			0.629637
$626$	15.1029	+	45.3551i	0.603634	+	1.81275i
$627$	18.5922	−	22.1805i	0.742502	−	0.885802i
$628$	6.27838	−	4.70277i	0.250535	−	0.187661i
$629$		−	1.24227i		−	0.0495327i
$630$		0			0
$631$		−	15.8863i		−	0.632423i	−0.948689	−	0.316212i	$-0.897589\pi$
$631$		−	15.8863i		−	0.632423i	0.948689	−	0.316212i	$-0.102411\pi$
$632$	11.1690	−	16.1013i	0.444280	−	0.640477i
$633$	−13.0451	+	15.5628i	−0.518497	+	0.618565i
$634$	−12.4606	+	4.14927i	−0.494872	+	0.164789i
$635$	−3.34262			−0.132648
$636$	1.65244	−	30.1618i	0.0655235	−	1.19599i
$637$		0			0
$638$	−13.3163	+	4.43423i	−0.527197	+	0.175553i
$639$	5.06912	+	28.5768i	0.200531	+	1.13048i
$640$	5.70853	+	7.06921i	0.225649	+	0.279435i
$641$		−	19.3998i		−	0.766245i	−0.923698	−	0.383122i	$-0.874849\pi$
$641$		−	19.3998i		−	0.766245i	0.923698	−	0.383122i	$-0.125151\pi$
$642$	−5.48905	+	13.8969i	−0.216635	+	0.548466i
$643$			37.0568i			1.46138i	0.682710	+	0.730690i	$0.260801\pi$
$643$			37.0568i			1.46138i	−0.682710	+	0.730690i	$0.739199\pi$
$644$		0			0
$645$	−8.46792	−	7.09803i	−0.333424	−	0.279485i
$646$	−3.77340	−	11.3318i	−0.148462	−	0.445843i
$647$	−45.4057			−1.78508			−0.892542	−	0.450965i	$-0.851080\pi$
$647$	−45.4057			−1.78508			−0.892542	+	0.450965i	$0.851080\pi$
$648$	24.6305	+	6.42966i	0.967576	+	0.252581i
$649$	1.55310			0.0609644
$650$	10.2517	+	30.7866i	0.402105	+	1.20755i
$651$		0			0
$652$	−8.76374	−	11.6999i	−0.343215	−	0.458205i
$653$		−	0.987349i		−	0.0386380i	−0.999813	−	0.0193190i	$-0.993850\pi$
$653$		−	0.987349i		−	0.0386380i	0.999813	−	0.0193190i	$-0.00614981\pi$
$654$	4.90503	−	12.4183i	0.191802	−	0.485594i
$655$		−	8.42629i		−	0.329242i
$656$	27.5207	+	8.06354i	1.07450	+	0.314828i
$657$	−0.741015	−	4.17743i	−0.0289097	−	0.162977i
$658$		0			0
$659$	−6.67629			−0.260071			−0.130036	−	0.991509i	$-0.541509\pi$
$659$	−6.67629			−0.260071			−0.130036	+	0.991509i	$0.541509\pi$
$660$	−0.356959	+	6.51552i	−0.0138946	+	0.253616i
$661$	2.71141			0.105462			0.0527309	−	0.998609i	$-0.483207\pi$
$661$	2.71141			0.105462			0.0527309	+	0.998609i	$0.483207\pi$
$662$	1.36183	−	0.453479i	0.0529291	−	0.0176250i
$663$	−6.94915	+	8.29031i	−0.269883	+	0.321969i
$664$	12.0438	+	8.35442i	0.467390	+	0.324214i
$665$		0			0
$666$	−3.90818	+	2.11986i	−0.151439	+	0.0821431i
$667$		−	33.3729i		−	1.29220i
$668$	13.4013	−	10.0381i	0.518512	−	0.388387i
$669$	0.760236	−	0.906959i	0.0293924	−	0.0350651i
$670$	−3.02367	−	9.08028i	−0.116814	−	0.350802i
$671$	−2.24723			−0.0867535
$672$		0			0
$673$	37.2088			1.43430			0.717148	−	0.696921i	$-0.245447\pi$
$673$	37.2088			1.43430			0.717148	+	0.696921i	$0.245447\pi$
$674$	−5.65639	−	16.9865i	−0.217876	−	0.654297i
$675$	11.2844	−	19.6149i	0.434337	−	0.754976i
$676$	−23.6236	+	17.6950i	−0.908599	+	0.680578i
$677$		−	11.1282i		−	0.427691i	−0.976867	−	0.213846i	$-0.931401\pi$
$677$		−	11.1282i		−	0.427691i	0.976867	−	0.213846i	$-0.0685990\pi$
$678$	−16.1708	−	6.38722i	−0.621037	−	0.245300i
$679$		0			0
$680$	2.21258	+	1.53480i	0.0848487	+	0.0588570i
$681$	−11.6199	−	9.74008i	−0.445275	−	0.373241i
$682$	−15.4175	+	5.13390i	−0.590365	+	0.196587i
$683$	−9.67432			−0.370178			−0.185089	−	0.982722i	$-0.559257\pi$
$683$	−9.67432			−0.370178			−0.185089	+	0.982722i	$0.559257\pi$
$684$	−29.2106	+	31.2081i	−1.11690	+	1.19327i
$685$	10.8357			0.414013
$686$		0			0
$687$	24.5549	+	20.5826i	0.936829	+	0.785274i
$688$	30.4907	+	8.93376i	1.16245	+	0.340596i
$689$		−	45.9421i		−	1.75025i
$690$	−14.4310	−	5.70000i	−0.549377	−	0.216995i
$691$			8.32473i			0.316688i	0.987384	+	0.158344i	$0.0506154\pi$
$691$			8.32473i			0.316688i	−0.987384	+	0.158344i	$0.949385\pi$
$692$	15.3128	+	20.4432i	0.582105	+	0.777133i
$693$		0			0
$694$	11.4509	+	34.3879i	0.434670	+	1.30535i
$695$	6.08177			0.230695
$696$	19.9962	−	5.46341i	0.757955	−	0.207090i
$697$	8.49885			0.321917
$698$	−12.5656	−	37.7355i	−0.475617	−	1.42831i
$699$	11.2814	−	13.4586i	0.426700	−	0.509052i
$700$		0			0
$701$			34.0535i			1.28618i	0.765790	+	0.643091i	$0.222348\pi$
$701$			34.0535i			1.28618i	−0.765790	+	0.643091i	$0.777652\pi$
$702$	37.9395	+	7.71504i	1.43193	+	0.291185i
$703$		−	7.46593i		−	0.281583i
$704$	−6.57245	−	17.5749i	−0.247708	−	0.662378i
$705$	5.45016	−	6.50202i	0.205265	−	0.244880i
$706$	13.8269	−	4.60425i	0.520382	−	0.173283i
$707$		0			0
$708$	−2.29040	−	0.125482i	−0.0860785	−	0.00471589i
$709$	9.64271			0.362140			0.181070	−	0.983470i	$-0.442044\pi$
$709$	9.64271			0.362140			0.181070	+	0.983470i	$0.442044\pi$
$710$	10.4252	−	3.47151i	0.391250	−	0.130283i
$711$	−20.4651	+	3.63021i	−0.767502	+	0.136144i
$712$	−26.3836	+	38.0348i	−0.988769	+	1.42542i
$713$		−	38.6388i		−	1.44703i
$714$		0			0
$715$			9.92437i			0.371150i
$716$	−33.8039	+	25.3205i	−1.26331	+	0.946272i
$717$	1.98406	+	1.66309i	0.0740962	+	0.0621093i
$718$	11.9919	+	36.0125i	0.447534	+	1.34398i
$719$	−8.09170			−0.301769			−0.150885	−	0.988551i	$-0.548212\pi$
$719$	−8.09170			−0.301769			−0.150885	+	0.988551i	$0.548212\pi$
$720$	1.05284	−	9.57981i	0.0392369	−	0.357018i
$721$		0			0
$722$	−14.1885	−	42.6090i	−0.528040	−	1.58574i
$723$	13.7170	+	11.4979i	0.510139	+	0.427612i
$724$	−19.8611	+	14.8768i	−0.738131	+	0.552891i
$725$		−	18.4274i		−	0.684376i
$726$	−4.94818	+	12.5276i	−0.183644	+	0.464941i
$727$		−	36.9501i		−	1.37040i	−0.728353	−	0.685202i	$-0.759714\pi$
$727$		−	36.9501i		−	1.37040i	0.728353	−	0.685202i	$-0.240286\pi$
$728$		0			0
$729$	−13.5719	−	23.3410i	−0.502664	−	0.864482i
$730$	−1.52398	+	0.507473i	−0.0564049	+	0.0187824i
$731$	9.41605			0.348265
$732$	3.31407	+	0.181564i	0.122492	+	0.00671081i
$733$	−37.9552			−1.40191			−0.700954	−	0.713207i	$-0.747242\pi$
$733$	−37.9552			−1.40191			−0.700954	+	0.713207i	$0.747242\pi$
$734$	−17.9153	+	5.96566i	−0.661266	+	0.220197i
$735$		0			0
$736$	44.5867	−	1.62466i	1.64349	−	0.0598857i
$737$			19.7635i			0.727996i
$738$	−14.5028	−	26.7373i	−0.533854	−	0.984213i
$739$		−	22.1318i		−	0.814131i	−0.913399	−	0.407065i	$-0.866552\pi$
$739$		−	22.1318i		−	0.814131i	0.913399	−	0.407065i	$-0.133448\pi$
$740$	1.00914	+	1.34724i	0.0370966	+	0.0495254i
$741$	−41.7636	+	49.8238i	−1.53422	+	1.83032i
$742$		0			0
$743$	−21.7884			−0.799340			−0.399670	−	0.916659i	$-0.630875\pi$
$743$	−21.7884			−0.799340			−0.399670	+	0.916659i	$0.630875\pi$
$744$	23.1514	−	6.32548i	0.848772	−	0.231903i
$745$	−12.9314			−0.473769
$746$	−10.1897	−	30.6004i	−0.373072	−	1.12036i
$747$	−2.71540	−	15.3079i	−0.0993512	−	0.560087i
$748$	−3.33371	−	4.45064i	−0.121893	−	0.162731i
$749$		0			0
$750$	−17.1167	−	6.76083i	−0.625014	−	0.246871i
$751$			5.12830i			0.187134i	0.995613	+	0.0935671i	$0.0298270\pi$
$751$			5.12830i			0.187134i	−0.995613	+	0.0935671i	$0.970173\pi$
$752$	−6.85971	+	23.4120i	−0.250148	+	0.853749i
$753$	−35.7808	−	29.9923i	−1.30392	−	1.09298i
$754$	29.9123	−	9.96058i	1.08934	−	0.362743i
$755$	13.9618			0.508122
$756$		0			0
$757$	−30.4486			−1.10667			−0.553337	−	0.832958i	$-0.686646\pi$
$757$	−30.4486			−1.10667			−0.553337	+	0.832958i	$0.686646\pi$
$758$	−2.65836	+	0.885213i	−0.0965559	+	0.0321524i
$759$	24.5554	+	20.5829i	0.891303	+	0.747113i
$760$	13.2974	+	9.22400i	0.482347	+	0.334590i
$761$			42.7498i			1.54968i	0.632159	+	0.774839i	$0.282169\pi$
$761$			42.7498i			1.54968i	−0.632159	+	0.774839i	$0.717831\pi$
$762$	−9.48197	−	3.74523i	−0.343496	−	0.135675i
$763$		0			0
$764$	9.76434	−	7.31389i	0.353261	−	0.264607i
$765$	−0.498850	−	2.81224i	−0.0180360	−	0.101677i
$766$	−12.8772	−	38.6712i	−0.465273	−	1.39725i
$767$	−3.48871			−0.125970
$768$	8.27265	+	26.4493i	0.298513	+	0.954405i
$769$	7.77655			0.280430			0.140215	−	0.990121i	$-0.455221\pi$
$769$	7.77655			0.280430			0.140215	+	0.990121i	$0.455221\pi$
$770$		0			0
$771$	3.10619	−	3.70567i	0.111867	−	0.133456i
$772$	−1.03249	+	0.773376i	−0.0371600	+	0.0278344i
$773$			1.20376i			0.0432963i	0.999766	+	0.0216482i	$0.00689136\pi$
$773$			1.20376i			0.0432963i	−0.999766	+	0.0216482i	$0.993109\pi$
$774$	−16.0679	−	29.6228i	−0.577549	−	1.06477i
$775$		−	21.3350i		−	0.766376i
$776$	10.1752	+	7.05825i	0.365269	+	0.253376i
$777$		0			0
$778$	−2.62954	+	0.875618i	−0.0942737	+	0.0313924i
$779$	51.0771			1.83003
$780$	0.801834	−	14.6358i	0.0287103	−	0.524045i
$781$	−22.6907			−0.811936
$782$	12.5451	−	4.17743i	0.448612	−	0.149384i
$783$	−19.0579	−	10.9640i	−0.681072	−	0.391820i
$784$		0			0
$785$			3.15000i			0.112428i
$786$	9.44121	−	23.9028i	0.336757	−	0.852583i
$787$			22.5045i			0.802199i	0.916035	+	0.401099i	$0.131372\pi$
$787$			22.5045i			0.802199i	−0.916035	+	0.401099i	$0.868628\pi$
$788$	17.8787	+	23.8687i	0.636901	+	0.850288i
$789$	20.3229	+	17.0352i	0.723514	+	0.606468i
$790$	2.48610	+	7.46593i	0.0884514	+	0.265626i
$791$		0			0
$792$	−8.31288	+	18.0826i	−0.295385	+	0.642536i
$793$	5.04795			0.179258
$794$	−2.03880	−	6.12267i	−0.0723544	−	0.217285i
$795$	9.29611	+	7.79224i	0.329699	+	0.276362i
$796$	−22.4207	−	29.9325i	−0.794681	−	1.06093i
$797$			18.3911i			0.651447i	0.945465	+	0.325724i	$0.105608\pi$
$797$			18.3911i			0.651447i	−0.945465	+	0.325724i	$0.894392\pi$
$798$		0			0
$799$			7.23003i			0.255780i
$800$	24.6192	−	0.897081i	0.870421	−	0.0317166i
$801$	48.3431	−	8.57535i	1.70812	−	0.302995i
$802$	35.9343	−	11.9658i	1.26888	−	0.422529i
$803$	3.31697			0.117053
$804$	1.59678	−	29.1458i	0.0563140	−	1.02789i
$805$		0			0
$806$	34.6322	−	11.5323i	1.21987	−	0.406206i
$807$	34.1436	−	40.7331i	1.20191	−	1.43387i
$808$	13.5310	−	19.5064i	0.476020	−	0.686233i
$809$			13.2891i			0.467220i	0.972330	+	0.233610i	$0.0750538\pi$
$809$			13.2891i			0.467220i	−0.972330	+	0.233610i	$0.924946\pi$
$810$	−7.99601	+	6.36829i	−0.280951	+	0.223759i
$811$		−	6.46254i		−	0.226930i	−0.993542	−	0.113465i	$-0.963805\pi$
$811$		−	6.46254i		−	0.226930i	0.993542	−	0.113465i	$-0.0361950\pi$
$812$		0			0
$813$	21.9041	−	26.1315i	0.768210	−	0.916472i
$814$	−1.09821	−	3.29799i	−0.0384921	−	0.115594i
$815$	5.87011			0.205621
$816$	4.55675	+	6.83285i	0.159518	+	0.239197i
$817$	56.5894			1.97981
$818$	8.06140	+	24.2090i	0.281860	+	0.846446i
$819$		0			0
$820$	−9.21694	+	6.90387i	−0.321869	+	0.241094i
$821$			27.9169i			0.974306i	0.873317	+	0.487153i	$0.161965\pi$
$821$			27.9169i			0.974306i	−0.873317	+	0.487153i	$0.838035\pi$
$822$	30.7377	+	12.1409i	1.07210	+	0.423462i
$823$			44.9950i			1.56843i	0.620492	+	0.784213i	$0.286933\pi$
$823$			44.9950i			1.56843i	−0.620492	+	0.784213i	$0.713067\pi$
$824$	4.13820	−	5.96566i	0.144161	−	0.207824i
$825$	13.5586	+	11.3652i	0.472051	+	0.395685i
$826$		0			0
$827$	−34.2989			−1.19269			−0.596344	−	0.802729i	$-0.703381\pi$
$827$	−34.2989			−1.19269			−0.596344	+	0.802729i	$0.703381\pi$
$828$	−34.5496	−	32.3382i	−1.20068	−	1.12383i
$829$	23.0157			0.799368			0.399684	−	0.916653i	$-0.369120\pi$
$829$	23.0157			0.799368			0.399684	+	0.916653i	$0.369120\pi$
$830$	−5.58451	+	1.85960i	−0.193841	+	0.0645476i
$831$	17.4061	+	14.5902i	0.603811	+	0.506129i
$832$	14.7637	+	39.4784i	0.511838	+	1.36867i
$833$		0			0
$834$	17.2521	+	6.81430i	0.597391	+	0.235960i
$835$			6.72372i			0.232684i
$836$	−20.0352	−	26.7478i	−0.692933	−	0.925093i
$837$	−22.0650	−	12.6940i	−0.762677	−	0.438768i
$838$	−7.83668	−	23.5341i	−0.270714	−	0.812972i
$839$	46.9847			1.62209			0.811046	−	0.584983i	$-0.198899\pi$
$839$	46.9847			1.62209			0.811046	+	0.584983i	$0.198899\pi$
$840$		0			0
$841$	11.0959			0.382617
$842$	6.88104	+	20.6642i	0.237136	+	0.712137i
$843$	−3.18967	+	3.80526i	−0.109858	+	0.131060i
$844$	14.0576	+	18.7675i	0.483883	+	0.646003i
$845$		−	11.8525i		−	0.407737i
$846$	22.7456	−	12.3376i	0.782009	−	0.424175i
$847$		0			0
$848$	−33.4728	−	9.80751i	−1.14946	−	0.336791i
$849$	2.21464	−	2.64205i	0.0760062	−	0.0906751i
$850$	6.92698	−	2.30663i	0.237593	−	0.0791168i
$851$	8.26532			0.283332
$852$	33.4626	+	1.83328i	1.14641	+	0.0628072i
$853$	12.7498			0.436545			0.218272	−	0.975888i	$-0.429958\pi$
$853$	12.7498			0.436545			0.218272	+	0.975888i	$0.429958\pi$
$854$		0			0
$855$	−2.99803	−	16.9012i	−0.102531	−	0.578010i
$856$	14.1763	+	9.83371i	0.484538	+	0.336109i
$857$			30.2271i			1.03254i	0.856426	+	0.516269i	$0.172680\pi$
$857$			30.2271i			1.03254i	−0.856426	+	0.516269i	$0.827320\pi$
$858$	−11.1197	+	28.1524i	−0.379621	+	0.961105i
$859$		−	18.3576i		−	0.626353i	−0.949695	−	0.313177i	$-0.898607\pi$
$859$		−	18.3576i		−	0.626353i	0.949695	−	0.313177i	$-0.101393\pi$
$860$	−10.2116	+	7.64893i	−0.348214	+	0.260826i
$861$		0			0
$862$	−4.02283	−	12.0808i	−0.137018	−	0.411475i
$863$	−26.3936			−0.898450			−0.449225	−	0.893419i	$-0.648300\pi$
$863$	−26.3936			−0.898450			−0.449225	+	0.893419i	$0.648300\pi$
$864$	13.7202	−	25.9953i	0.466772	−	0.884378i
$865$	−10.2568			−0.348741
$866$	−2.75180	−	8.26386i	−0.0935101	−	0.280817i
$867$	−20.7005	−	17.3517i	−0.703025	−	0.589293i
$868$		0			0
$869$		−	16.2498i		−	0.551236i
$870$	−3.05797	+	7.74200i	−0.103675	+	0.262478i
$871$		−	44.3946i		−	1.50425i
$872$	−12.6680	−	8.78744i	−0.428994	−	0.297580i
$873$	−2.29411	−	12.9329i	−0.0776439	−	0.437713i
$874$	75.3947	−	25.1059i	2.55026	−	0.849218i
$875$		0			0
$876$	−4.89164	−	0.267993i	−0.165273	−	0.00905464i
$877$	−0.937324			−0.0316512			−0.0158256	−	0.999875i	$-0.505038\pi$
$877$	−0.937324			−0.0316512			−0.0158256	+	0.999875i	$0.505038\pi$
$878$	−39.2460	+	13.0686i	−1.32449	+	0.441045i
$879$	18.6351	−	22.2316i	0.628545	−	0.749852i
$880$	7.23077	+	2.11861i	0.243749	+	0.0714183i
$881$		−	37.1298i		−	1.25093i	−0.780251	−	0.625467i	$-0.784909\pi$
$881$		−	37.1298i		−	1.25093i	0.780251	−	0.625467i	$-0.215091\pi$
$882$		0			0
$883$		−	5.76235i		−	0.193918i	−0.995288	−	0.0969592i	$-0.969088\pi$
$883$		−	5.76235i		−	0.193918i	0.995288	−	0.0969592i	$-0.0309116\pi$
$884$	7.48850	+	9.99745i	0.251866	+	0.336251i
$885$	0.591721	−	0.705920i	0.0198905	−	0.0237293i
$886$	3.22430	+	9.68280i	0.108322	+	0.325300i
$887$	26.1343			0.877504			0.438752	−	0.898608i	$-0.355421\pi$
$887$	26.1343			0.877504			0.438752	+	0.898608i	$0.355421\pi$
$888$	1.35310	+	4.95238i	0.0454070	+	0.166191i
$889$		0			0
$890$	−5.87270	−	17.6361i	−0.196853	−	0.591165i
$891$	19.8212	−	7.26043i	0.664035	−	0.243234i
$892$	−0.819241	−	1.09372i	−0.0274302	−	0.0366204i
$893$			43.4516i			1.45405i
$894$	−36.6823	−	14.4889i	−1.22684	−	0.484582i
$895$		−	16.9601i		−	0.566915i
$896$		0			0
$897$	−55.1586	−	46.2353i	−1.84169	−	1.54375i
$898$	5.94975	−	1.98122i	0.198546	−	0.0661142i
$899$	−20.7292			−0.691356
$900$	−19.0771	−	17.8561i	−0.635903	−	0.595202i
$901$	−10.3370			−0.344374
$902$	22.5627	−	7.51322i	0.751257	−	0.250163i
$903$		0			0
$904$	−11.4428	+	16.4960i	−0.380582	+	0.548649i
$905$		−	9.96473i		−	0.331239i
$906$	39.6053	+	15.6435i	1.31580	+	0.519720i
$907$			40.8329i			1.35584i	0.735138	+	0.677918i	$0.237117\pi$
$907$			40.8329i			1.35584i	−0.735138	+	0.677918i	$0.762883\pi$
$908$	−14.0126	+	10.4960i	−0.465026	+	0.348324i
$909$	−24.7931	+	4.39793i	−0.822334	+	0.145870i
$910$		0			0
$911$	−4.31270			−0.142886			−0.0714430	−	0.997445i	$-0.522760\pi$
$911$	−4.31270			−0.142886			−0.0714430	+	0.997445i	$0.522760\pi$
$912$	27.3855	+	41.0646i	0.906825	+	1.35979i
$913$	12.1548			0.402266
$914$	6.10422	+	18.3314i	0.201910	+	0.606349i
$915$	−0.856183	+	1.02142i	−0.0283045	+	0.0337672i
$916$	29.6113	−	22.1801i	0.978384	−	0.732850i
$917$		0			0
$918$	1.73588	−	8.53639i	0.0572927	−	0.281743i
$919$		−	17.2821i		−	0.570085i	−0.958515	−	0.285043i	$-0.907992\pi$
$919$		−	17.2821i		−	0.570085i	0.958515	−	0.285043i	$-0.0920077\pi$
$920$	−10.2116	+	14.7212i	−0.336667	+	0.485342i
$921$	−17.2317	+	20.5573i	−0.567803	+	0.677386i
$922$	7.05493	−	2.34924i	0.232342	−	0.0773680i
$923$	50.9699			1.67770
$924$		0			0
$925$	4.56383			0.150058
$926$	21.3159	−	7.09803i	0.700483	−	0.233256i
$927$	−7.58248	+	1.34502i	−0.249041	+	0.0441763i
$928$	−0.871607	−	23.9201i	−0.0286119	−	0.785216i
$929$			23.1549i			0.759687i	0.925051	+	0.379843i	$0.124022\pi$
$929$			23.1549i			0.759687i	−0.925051	+	0.379843i	$0.875978\pi$
$930$	−3.54048	+	8.96360i	−0.116097	+	0.293928i
$931$		0			0
$932$	−12.1570	−	16.2300i	−0.398214	−	0.531632i
$933$	−14.4679	−	12.1274i	−0.473658	−	0.397033i
$934$	−12.0979	−	36.3310i	−0.395857	−	1.18879i
$935$	2.23298			0.0730263
$936$	18.6732	−	40.6188i	0.610352	−	1.32767i
$937$	−3.10294			−0.101369			−0.0506843	−	0.998715i	$-0.516140\pi$
$937$	−3.10294			−0.101369			−0.0506843	+	0.998715i	$0.516140\pi$
$938$		0			0
$939$	−44.8691	−	37.6104i	−1.46425	−	1.22737i
$940$	−5.87316	−	7.84091i	−0.191562	−	0.255742i
$941$		−	23.6509i		−	0.770996i	−0.922709	−	0.385498i	$-0.874030\pi$
$941$		−	23.6509i		−	0.770996i	0.922709	−	0.385498i	$-0.125970\pi$
$942$	−3.52941	+	8.93557i	−0.114994	+	0.291137i
$943$			56.5461i			1.84139i
$944$	−0.744755	+	2.54183i	−0.0242397	+	0.0827296i
$945$		0			0
$946$	24.9977	−	8.32404i	0.812745	−	0.270638i
$947$	−57.5371			−1.86970			−0.934852	−	0.355037i	$-0.884468\pi$
$947$	−57.5371			−1.86970			−0.934852	+	0.355037i	$0.884468\pi$
$948$	−1.31289	+	23.9641i	−0.0426408	+	0.778317i
$949$	−7.45090			−0.241866
$950$	41.6304	−	13.8626i	1.35067	−	0.449762i
$951$	10.3328	−	12.3270i	0.335065	−	0.399731i
$952$		0			0
$953$			14.1961i			0.459855i	0.973208	+	0.229928i	$0.0738490\pi$
$953$			14.1961i			0.459855i	−0.973208	+	0.229928i	$0.926151\pi$
$954$	17.6394	+	32.5200i	0.571096	+	1.05287i
$955$			4.89898i			0.158527i
$956$	2.39262	−	1.79217i	0.0773829	−	0.0579630i
$957$	11.0424	−	13.1736i	0.356952	−	0.425842i
$958$	−6.81842	−	20.4762i	−0.220293	−	0.661557i
$959$		0			0
$960$	−10.4923	−	3.70859i	−0.338637	−	0.119694i
$961$	7.00000			0.225806
$962$	2.46689	+	7.40826i	0.0795358	+	0.238852i
$963$	−3.19621	−	18.0184i	−0.102996	−	0.580636i
$964$	16.5415	−	12.3903i	0.532767	−	0.399065i
$965$		−	0.518021i		−	0.0166757i
$966$		0			0
$967$			31.5730i			1.01532i	0.861558	+	0.507660i	$0.169489\pi$
$967$			31.5730i			1.01532i	−0.861558	+	0.507660i	$0.830511\pi$
$968$	12.7795	+	8.86475i	0.410748	+	0.284924i
$969$	11.2104	+	9.39681i	0.360129	+	0.301869i
$970$	−4.71809	+	1.57109i	−0.151489	+	0.0504446i
$971$	29.3240			0.941051			0.470526	−	0.882386i	$-0.344064\pi$
$971$	29.3240			0.941051			0.470526	+	0.882386i	$0.344064\pi$
$972$	−29.8175	+	9.10575i	−0.956398	+	0.292067i
$973$		0			0
$974$	8.13677	−	2.70948i	0.260719	−	0.0868174i
$975$	−30.4567	−	25.5296i	−0.975394	−	0.817600i
$976$	1.07761	−	3.67788i	0.0344936	−	0.117726i
$977$		−	11.8959i		−	0.380585i	−0.981727	−	0.190292i	$-0.939056\pi$
$977$		−	11.8959i		−	0.380585i	0.981727	−	0.190292i	$-0.0609436\pi$
$978$	16.6517	+	6.57715i	0.532462	+	0.210314i
$979$			38.3855i			1.22681i
$980$		0			0
$981$	2.85614	+	16.1013i	0.0911896	+	0.514076i
$982$	1.80433	+	5.41854i	0.0575785	+	0.172912i
$983$	14.9803			0.477796			0.238898	−	0.971045i	$-0.423214\pi$
$983$	14.9803			0.477796			0.238898	+	0.971045i	$0.423214\pi$
$984$	−33.8810	+	9.25704i	−1.08009	+	0.295104i
$985$	−11.9754			−0.381569
$986$	−2.24113	−	6.73027i	−0.0713721	−	0.214336i
$987$		0			0
$988$	45.0051	+	60.0835i	1.43180	+	1.91151i
$989$			62.6485i			1.99211i
$990$	−3.81044	−	7.02493i	−0.121104	−	0.223267i
$991$			20.7846i			0.660245i	0.943938	+	0.330122i	$0.107090\pi$
$991$			20.7846i			0.660245i	−0.943938	+	0.330122i	$0.892910\pi$
$992$	−1.00914	−	27.6944i	−0.0320401	−	0.879299i
$993$	−1.12929	+	1.34724i	−0.0358369	+	0.0427533i
$994$		0			0
$995$	15.0178			0.476096
$996$	−17.9251	−	0.982042i	−0.567979	−	0.0311172i
$997$	−19.6382			−0.621949			−0.310975	−	0.950418i	$-0.600655\pi$
$997$	−19.6382			−0.621949			−0.310975	+	0.950418i	$0.600655\pi$
$998$	−51.6601	+	17.2024i	−1.63527	+	0.544533i
$999$	2.71540	−	4.71997i	0.0859114	−	0.149333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.f.491.15	yes	24
3.2	odd	2	inner	588.2.e.f.491.10	yes	24
4.3	odd	2	inner	588.2.e.f.491.12	yes	24
7.2	even	3		588.2.n.d.263.10		24
7.3	odd	6		588.2.n.h.275.2		24
7.4	even	3		588.2.n.h.275.1		24
7.5	odd	6		588.2.n.d.263.9		24
7.6	odd	2	inner	588.2.e.f.491.16	yes	24
12.11	even	2	inner	588.2.e.f.491.13	yes	24
21.2	odd	6		588.2.n.d.263.4		24
21.5	even	6		588.2.n.d.263.3		24
21.11	odd	6		588.2.n.h.275.11		24
21.17	even	6		588.2.n.h.275.12		24
21.20	even	2	inner	588.2.e.f.491.9	✓	24
28.3	even	6		588.2.n.d.275.3		24
28.11	odd	6		588.2.n.d.275.4		24
28.19	even	6		588.2.n.h.263.12		24
28.23	odd	6		588.2.n.h.263.11		24
28.27	even	2	inner	588.2.e.f.491.11	yes	24
84.11	even	6		588.2.n.d.275.10		24
84.23	even	6		588.2.n.h.263.1		24
84.47	odd	6		588.2.n.h.263.2		24
84.59	odd	6		588.2.n.d.275.9		24
84.83	odd	2	inner	588.2.e.f.491.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.9	✓	24	21.20	even	2	inner
588.2.e.f.491.10	yes	24	3.2	odd	2	inner
588.2.e.f.491.11	yes	24	28.27	even	2	inner
588.2.e.f.491.12	yes	24	4.3	odd	2	inner
588.2.e.f.491.13	yes	24	12.11	even	2	inner
588.2.e.f.491.14	yes	24	84.83	odd	2	inner
588.2.e.f.491.15	yes	24	1.1	even	1	trivial
588.2.e.f.491.16	yes	24	7.6	odd	2	inner
588.2.n.d.263.3		24	21.5	even	6
588.2.n.d.263.4		24	21.2	odd	6
588.2.n.d.263.9		24	7.5	odd	6
588.2.n.d.263.10		24	7.2	even	3
588.2.n.d.275.3		24	28.3	even	6
588.2.n.d.275.4		24	28.11	odd	6
588.2.n.d.275.9		24	84.59	odd	6
588.2.n.d.275.10		24	84.11	even	6
588.2.n.h.263.1		24	84.23	even	6
588.2.n.h.263.2		24	84.47	odd	6
588.2.n.h.263.11		24	28.23	odd	6
588.2.n.h.263.12		24	28.19	even	6
588.2.n.h.275.1		24	7.4	even	3
588.2.n.h.275.2		24	7.3	odd	6
588.2.n.h.275.11		24	21.11	odd	6
588.2.n.h.275.12		24	21.17	even	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.446802 + 1.34178i) q^{2} +(-1.32740 - 1.11266i) q^{3} +(-1.60074 + 1.19902i) q^{4} -0.803124i q^{5} +(0.899858 - 2.27821i) q^{6} +(-2.32403 - 1.61211i) q^{8} +(0.523976 + 2.95389i) q^{9} +O(q^{10})\)	\(q+(0.446802 + 1.34178i) q^{2} +(-1.32740 - 1.11266i) q^{3} +(-1.60074 + 1.19902i) q^{4} -0.803124i q^{5} +(0.899858 - 2.27821i) q^{6} +(-2.32403 - 1.61211i) q^{8} +(0.523976 + 2.95389i) q^{9} +(1.07761 - 0.358837i) q^{10} -2.34545 q^{11} +(3.45891 + 0.189500i) q^{12} +5.26858 q^{13} +(-0.893604 + 1.06607i) q^{15} +(1.12471 - 3.83862i) q^{16} -1.18543i q^{17} +(-3.72935 + 2.02286i) q^{18} -7.12430i q^{19} +(0.962960 + 1.28559i) q^{20} +(-1.04795 - 3.14708i) q^{22} +7.88711 q^{23} +(1.29118 + 4.72576i) q^{24} +4.35499 q^{25} +(2.35401 + 7.06926i) q^{26} +(2.59115 - 4.50399i) q^{27} -4.23132i q^{29} +(-1.82969 - 0.722698i) q^{30} -4.89898i q^{31} +(5.65310 - 0.205989i) q^{32} +(3.11335 + 2.60969i) q^{33} +(1.59058 - 0.529652i) q^{34} +(-4.38051 - 4.10014i) q^{36} +1.04795 q^{37} +(9.55923 - 3.18315i) q^{38} +(-6.99351 - 5.86214i) q^{39} +(-1.29472 + 1.86648i) q^{40} +7.16942i q^{41} +7.94315i q^{43} +(3.75445 - 2.81224i) q^{44} +(2.37234 - 0.420818i) q^{45} +(3.52398 + 10.5828i) q^{46} -6.09907 q^{47} +(-5.76402 + 3.84396i) q^{48} +(1.94582 + 5.84343i) q^{50} +(-1.31898 + 1.57354i) q^{51} +(-8.43361 + 6.31712i) q^{52} -8.72001i q^{53} +(7.20109 + 1.46435i) q^{54} +1.88369i q^{55} +(-7.92692 + 9.45679i) q^{57} +(5.67750 - 1.89056i) q^{58} -0.662173 q^{59} +(0.152192 - 2.77794i) q^{60} +0.958124 q^{61} +(6.57334 - 2.18887i) q^{62} +(2.80221 + 7.49317i) q^{64} -4.23132i q^{65} +(-2.11057 + 5.34344i) q^{66} -8.42629i q^{67} +(1.42135 + 1.89756i) q^{68} +(-10.4693 - 8.77567i) q^{69} +9.67432 q^{71} +(3.54425 - 7.70962i) q^{72} -1.41421 q^{73} +(0.468227 + 1.40612i) q^{74} +(-5.78081 - 4.84562i) q^{75} +(8.54216 + 11.4041i) q^{76} +(4.74097 - 12.0029i) q^{78} +6.92820i q^{79} +(-3.08289 - 0.903284i) q^{80} +(-8.45090 + 3.09553i) q^{81} +(-9.61978 + 3.20331i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(-10.6579 + 3.54901i) q^{86} +(-4.70802 + 5.61665i) q^{87} +(5.45090 + 3.78113i) q^{88} -16.3659i q^{89} +(1.62461 + 2.99513i) q^{90} +(-12.6252 + 9.45679i) q^{92} +(-5.45090 + 6.50290i) q^{93} +(-2.72508 - 8.18360i) q^{94} -5.72170 q^{95} +(-7.73312 - 6.01655i) q^{96} -4.37827 q^{97} +(-1.22896 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) \) 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

Introduction

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