LMFDB - Embedded newform 588.2.e.f.491.10

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			491.10
Character	$\chi$	$=$	588.491
Dual form			588.2.e.f.491.12

$q$-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} +(-2.08603 - 1.28394i) q^{6} +(2.32403 + 1.61211i) q^{8} +(0.523976 - 2.95389i) q^{9} +(1.07761 - 0.358837i) q^{10} +2.34545 q^{11} +(-0.790717 + 3.37265i) q^{12} +5.26858 q^{13} +(0.893604 + 1.06607i) q^{15} +(1.12471 - 3.83862i) q^{16} +1.18543i q^{17} +(-4.19757 + 0.616742i) q^{18} -7.12430i q^{19} +(-0.962960 - 1.28559i) q^{20} +(-1.04795 - 3.14708i) q^{22} -7.88711 q^{23} +(4.87864 - 0.445940i) q^{24} +4.35499 q^{25} +(-2.35401 - 7.06926i) q^{26} +(-2.59115 - 4.50399i) q^{27} +4.23132i q^{29} +(1.03116 - 1.67534i) q^{30} -4.89898i q^{31} +(-5.65310 + 0.205989i) q^{32} +(3.11335 - 2.60969i) q^{33} +(1.59058 - 0.529652i) q^{34} +(2.70302 + 5.35665i) 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} +(-2.77814 - 6.34681i) q^{48} +(-1.94582 - 5.84343i) q^{50} +(1.31898 + 1.57354i) q^{51} +(-8.43361 + 6.31712i) q^{52} +8.72001i q^{53} +(-4.88563 + 5.48914i) q^{54} +1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(5.67750 - 1.89056i) q^{58} +0.662173 q^{59} +(-2.70866 - 0.635044i) q^{60} +0.958124 q^{61} +(-6.57334 + 2.18887i) q^{62} +(2.80221 + 7.49317i) q^{64} +4.23132i q^{65} +(-4.89268 - 3.01141i) q^{66} -8.42629i q^{67} +(-1.42135 - 1.89756i) q^{68} +(-10.4693 + 8.77567i) q^{69} -9.67432 q^{71} +(5.97972 - 6.02021i) q^{72} -1.41421 q^{73} +(-0.468227 - 1.40612i) q^{74} +(5.78081 - 4.84562i) q^{75} +(8.54216 + 11.4041i) q^{76} +(-10.9904 - 6.76452i) 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} +(-0.495321 - 3.37117i) q^{90} +(12.6252 - 9.45679i) q^{92} +(-5.45090 - 6.50290i) q^{93} +(-2.72508 - 8.18360i) q^{94} +5.72170 q^{95} +(-7.27473 + 6.56341i) q^{96} -4.37827 q^{97} +(1.22896 - 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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

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	$0.0574752\pi$
$5$			0.803124i			0.359168i	−0.983743	+	0.179584i	$0.942525\pi$
$6$	−2.08603	−	1.28394i	−0.851617	−	0.524165i
$7$		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	$-0.384961\pi$
$11$	2.34545			0.707181			0.353590	+	0.935400i	$0.384961\pi$
$12$	−0.790717	+	3.37265i	−0.228260	+	0.973600i
$13$	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	$0.0459176\pi$
$17$			1.18543i			0.287509i	−0.989613	+	0.143754i	$0.954082\pi$
$18$	−4.19757	+	0.616742i	−0.989378	+	0.145368i
$19$		−	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	$-0.807303\pi$
$23$	−7.88711			−1.64458			−0.822288	+	0.569071i	$0.807303\pi$
$24$	4.87864	−	0.445940i	0.995848	−	0.0910271i
$25$	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	$0.128517\pi$
$29$			4.23132i			0.785737i	−0.919595	+	0.392868i	$0.871483\pi$
$30$	1.03116	−	1.67534i	0.188263	−	0.305873i
$31$		−	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
$36$	2.70302	+	5.35665i	0.450503	+	0.892775i
$37$	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	$-0.810863\pi$
$41$		−	7.16942i		−	1.11968i	0.828602	−	0.559838i	$-0.189137\pi$
$42$		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	$-0.353267\pi$
$47$	6.09907			0.889641			0.444821	+	0.895620i	$0.353267\pi$
$48$	−2.77814	−	6.34681i	−0.400990	−	0.916083i
$49$		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	$0.204393\pi$
$53$			8.72001i			1.19779i	−0.800829	+	0.598893i	$0.795607\pi$
$54$	−4.88563	+	5.48914i	−0.664850	+	0.746977i
$55$			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	$-0.486275\pi$
$59$	0.662173			0.0862076			0.0431038	+	0.999071i	$0.486275\pi$
$60$	−2.70866	−	0.635044i	−0.349686	−	0.0819838i
$61$	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
$66$	−4.89268	−	3.01141i	−0.602247	−	0.370679i
$67$		−	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	$-0.694634\pi$
$71$	−9.67432			−1.14813			−0.574065	+	0.818810i	$0.694634\pi$
$72$	5.97972	−	6.02021i	0.704717	−	0.709488i
$73$	−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
$78$	−10.9904	−	6.76452i	−1.24442	−	0.765931i
$79$			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	$-0.408201\pi$
$83$	5.18229			0.568830			0.284415	+	0.958701i	$0.408201\pi$
$84$		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	$0.334205\pi$
$89$			16.3659i			1.73478i	−0.497626	+	0.867392i	$0.665795\pi$
$90$	−0.495321	−	3.37117i	−0.0522114	−	0.355353i
$91$		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
$96$	−7.27473	+	6.56341i	−0.742474	+	0.669875i
$97$	−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	$-0.862876\pi$
$101$		−	8.39337i		−	0.835171i	0.908638	−	0.417586i	$-0.137124\pi$
$102$	1.52202	−	2.47284i	0.150702	−	0.244848i
$103$			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	$-0.404730\pi$
$107$	6.09990			0.589700			0.294850	+	0.955544i	$0.404730\pi$
$108$	9.54811	+	4.10288i	0.918767	+	0.394800i
$109$	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	$0.108352\pi$
$113$			7.09803i			0.667726i	−0.942622	+	0.333863i	$0.891648\pi$
$114$	−9.14715	+	14.8615i	−0.856709	+	1.39190i
$115$		−	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
$120$	0.358145	+	3.91815i	0.0326940	+	0.357677i
$121$	−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	$-0.651556\pi$
$131$	−10.4919			−0.916680			−0.458340	+	0.888777i	$0.651556\pi$
$132$	−1.85459	+	7.91039i	−0.161421	+	0.688511i
$133$		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	$-0.804477\pi$
$137$		−	13.4920i		−	1.15270i	0.817203	−	0.576350i	$-0.195523\pi$
$138$	16.4527	+	10.1265i	1.40055	+	0.862029i
$139$			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
$144$	−10.7495	−	5.33362i	−0.895795	−	0.444468i
$145$	−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	$0.229247\pi$
$149$			16.1013i			1.31907i	−0.751673	+	0.659536i	$0.770753\pi$
$150$	−9.08463	−	5.59153i	−0.741757	−	0.456547i
$151$			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
$156$	−4.16595	+	17.7691i	−0.333543	+	1.42266i
$157$	−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
$162$	−0.377643	+	12.7223i	−0.0296704	+	0.999560i
$163$			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	$-0.394999\pi$
$167$	8.37196			0.647842			0.323921	+	0.946084i	$0.394999\pi$
$168$		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	$0.161357\pi$
$173$			12.7711i			0.970970i	−0.874245	+	0.485485i	$0.838643\pi$
$174$	5.43275	−	8.82665i	0.411856	−	0.669147i
$175$		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	$-0.789508\pi$
$179$	−21.1177			−1.57841			−0.789206	+	0.614129i	$0.789508\pi$
$180$	−4.30205	+	2.17086i	−0.320656	+	0.161806i
$181$	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
$186$	−6.28998	+	10.2194i	−0.461204	+	0.749323i
$187$			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	$-0.429170\pi$
$191$	6.09990			0.441374			0.220687	+	0.975345i	$0.429170\pi$
$192$	12.0570	+	6.82852i	0.870139	+	0.492806i
$193$	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	$0.178253\pi$
$197$			14.9111i			1.06237i	−0.847256	+	0.531185i	$0.821747\pi$
$198$	−9.84521	+	1.44654i	−0.699669	+	0.102801i
$199$			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
$204$	−3.99804	−	0.937339i	−0.279919	−	0.0656269i
$205$	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
$216$	1.23904	−	14.6446i	0.0843057	−	0.996440i
$217$		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
$222$	−2.18606	−	1.34550i	−0.146719	−	0.0903044i
$223$			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	$-0.593824\pi$
$227$	−8.75387			−0.581015			−0.290507	+	0.956873i	$0.593824\pi$
$228$	24.0278	+	5.63330i	1.59128	+	0.373075i
$229$	−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	$-0.892237\pi$
$233$		−	10.1391i		−	0.664234i	0.943238	−	0.332117i	$-0.107763\pi$
$234$	−22.1153	+	3.24936i	−1.44572	+	0.212417i
$235$			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	$-0.484606\pi$
$239$	1.49470			0.0966841			0.0483421	+	0.998831i	$0.484606\pi$
$240$	5.09727	−	2.23119i	0.329027	−	0.144023i
$241$	−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
$246$	−9.20508	+	14.9556i	−0.586895	+	0.953535i
$247$		−	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	$-0.823827\pi$
$251$	−26.9555			−1.70142			−0.850709	+	0.525636i	$0.823827\pi$
$252$		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	$-0.972250\pi$
$257$		−	2.79168i		−	0.174140i	0.996202	−	0.0870700i	$-0.0277504\pi$
$258$	10.1985	−	16.5696i	0.634931	−	1.03158i
$259$		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	$-0.343519\pi$
$263$	15.3103			0.944074			0.472037	+	0.881579i	$0.343519\pi$
$264$	11.4426	−	1.04593i	0.704245	−	0.0643726i
$265$	−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	$-0.614956\pi$
$269$		−	30.6864i		−	1.87098i	0.353347	−	0.935492i	$-0.385044\pi$
$270$	−4.40846	−	3.92377i	−0.268290	−	0.238793i
$271$			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
$276$	6.23647	−	26.6005i	0.375391	−	1.60116i
$277$	−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	$0.0272509\pi$
$281$			2.86670i			0.171013i	−0.996338	+	0.0855066i	$0.972749\pi$
$282$	−12.7228	−	7.83082i	−0.757634	−	0.466319i
$283$			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
$288$	−2.35362	+	16.8066i	−0.138689	+	0.990336i
$289$	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	$-0.837281\pi$
$293$		−	16.7482i		−	0.978441i	0.872160	−	0.489221i	$-0.162719\pi$
$294$		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
$300$	−3.44356	+	14.6879i	−0.198814	+	0.848004i
$301$		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
$306$	−0.731105	−	4.97593i	−0.0417945	−	0.284455i
$307$		−	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	$-0.600003\pi$
$311$	−10.8995			−0.618051			−0.309026	+	0.951054i	$0.600003\pi$
$312$	25.7035	−	2.34947i	1.45517	−	0.133013i
$313$	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	$-0.916016\pi$
$317$		−	9.28660i		−	0.521588i	0.965395	−	0.260794i	$-0.0839843\pi$
$318$	11.1959	−	18.1902i	0.627837	−	1.02005i
$319$			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
$324$	17.2393	−	5.17764i	0.957737	−	0.287647i
$325$	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
$330$	2.41854	−	3.92943i	0.133136	−	0.216308i
$331$		−	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
$342$	4.39386	+	29.9048i	0.237593	+	1.61706i
$343$		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	$-0.741470\pi$
$347$	−25.6286			−1.37581			−0.687907	+	0.725799i	$0.741470\pi$
$348$	−14.2708	−	3.34578i	−0.764994	−	0.179353i
$349$	−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	$0.0884253\pi$
$353$			10.3049i			0.548474i	−0.961662	+	0.274237i	$0.911575\pi$
$354$	−1.38131	−	0.850188i	−0.0734159	−	0.0451870i
$355$		−	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	$-0.750522\pi$
$359$	−26.8394			−1.41653			−0.708265	+	0.705947i	$0.750522\pi$
$360$	4.83497	+	4.80246i	0.254825	+	0.253112i
$361$	−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
$366$	−1.99867	−	1.23017i	−0.104472	−	0.0643020i
$367$			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
$372$	16.5225	+	3.87371i	0.856654	+	0.200842i
$373$	−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	$-0.236553\pi$
$383$	28.8209			1.47268			0.736339	+	0.676613i	$0.236553\pi$
$384$	3.77527	−	19.2288i	0.192656	−	0.981266i
$385$		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	$-0.984179\pi$
$389$		−	1.95975i		−	0.0993630i	0.998765	−	0.0496815i	$-0.0158206\pi$
$390$	5.43275	−	8.82665i	0.275098	−	0.446955i
$391$		−	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
$396$	6.33980	+	12.5638i	0.318587	+	0.631353i
$397$	−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	$0.233146\pi$
$401$			26.7811i			1.33738i	−0.743539	+	0.668692i	$0.766854\pi$
$402$	−10.8188	+	17.5775i	−0.539593	+	0.876684i
$403$		−	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
$408$	0.528631	+	5.78329i	0.0261711	+	0.286315i
$409$	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
$414$	33.1067	−	4.86432i	1.62711	−	0.239068i
$415$			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	$-0.359067\pi$
$419$	17.5395			0.856861			0.428430	+	0.903575i	$0.359067\pi$
$420$		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
$426$	20.1809	+	12.4212i	0.977767	+	0.601810i
$427$		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	$-0.430424\pi$
$431$	9.00360			0.433688			0.216844	+	0.976206i	$0.430424\pi$
$432$	−20.2034	+	4.88073i	−0.972038	+	0.234824i
$433$	−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
$438$	2.95009	+	1.81576i	0.140961	+	0.0867604i
$439$			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	$-0.554839\pi$
$443$	−7.21640			−0.342861			−0.171431	+	0.985196i	$0.554839\pi$
$444$	−0.828634	+	3.53438i	−0.0393252	+	0.167734i
$445$	−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	$0.0333665\pi$
$449$			4.43423i			0.209264i	−0.994511	+	0.104632i	$0.966634\pi$
$450$	−18.2804	+	2.68591i	−0.861746	+	0.126615i
$451$		−	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
$456$	−3.17701	−	34.7569i	−0.148777	−	1.62764i
$457$	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	$0.0390726\pi$
$461$			5.25789i			0.244885i	−0.992476	+	0.122442i	$0.960927\pi$
$462$		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	$-0.284495\pi$
$467$	27.0767			1.25296			0.626481	+	0.779437i	$0.284495\pi$
$468$	14.2411	+	28.2219i	0.658293	+	1.30456i
$469$		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
$474$	8.89537	−	14.4524i	0.408578	−	0.663822i
$475$		−	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	$-0.386645\pi$
$479$	15.2605			0.697271			0.348635	+	0.937258i	$0.386645\pi$
$480$	−5.27123	−	5.84251i	−0.240598	−	0.266673i
$481$	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
$486$	13.6543	+	17.3078i	0.619373	+	0.785097i
$487$		−	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	$-0.529046\pi$
$491$	−4.03833			−0.182247			−0.0911235	+	0.995840i	$0.529046\pi$
$492$	24.1800	+	5.66898i	1.09012	+	0.255578i
$493$	−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
$498$	−10.8104	−	6.65373i	−0.484426	−	0.298161i
$499$			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	$-0.603654\pi$
$503$	−14.3498			−0.639827			−0.319914	+	0.947447i	$0.603654\pi$
$504$		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	$-0.913705\pi$
$509$		−	12.0835i		−	0.535593i	0.963476	−	0.267796i	$-0.0862955\pi$
$510$	1.98600	+	1.22237i	0.0879414	+	0.0541274i
$511$		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
$516$	−26.7895	−	6.28078i	−1.17934	−	0.276496i
$517$	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	$-0.754018\pi$
$521$		−	31.8700i		−	1.39625i	0.715976	−	0.698125i	$-0.245982\pi$
$522$	−2.60964	−	17.7613i	−0.114221	−	0.777391i
$523$		−	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
$528$	−6.51599	−	14.8861i	−0.283572	−	0.647836i
$529$	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
$534$	21.0128	−	34.1397i	0.909312	−	1.47737i
$535$			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
$540$	−3.29512	+	7.66832i	−0.141799	+	0.329992i
$541$	−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
$552$	−38.4784	+	3.51718i	−1.63775	+	0.149701i
$553$		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	$-0.731102\pi$
$557$		−	35.2982i		−	1.49563i	0.663906	−	0.747816i	$-0.268898\pi$
$558$	3.02141	+	20.5638i	0.127906	+	0.870536i
$559$			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	$-0.688159\pi$
$563$	−26.4463			−1.11458			−0.557290	+	0.830318i	$0.688159\pi$
$564$	−4.82264	+	20.5700i	−0.203070	+	0.866155i
$565$	−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	$-0.805222\pi$
$569$		−	27.4048i		−	1.14887i	0.818551	−	0.574434i	$-0.194778\pi$
$570$	−11.9356	−	7.34629i	−0.499928	−	0.307702i
$571$		−	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
$576$	23.6023	−	4.35116i	0.983428	−	0.181298i
$577$	−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
$582$	9.13319	+	5.62142i	0.378583	+	0.233015i
$583$			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	$-0.300655\pi$
$587$	28.4011			1.17224			0.586119	+	0.810225i	$0.300655\pi$
$588$		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	$-0.836887\pi$
$593$		−	23.8791i		−	0.980598i	0.871554	−	0.490299i	$-0.163113\pi$
$594$	−11.4590	+	12.8745i	−0.470169	+	0.528247i
$595$		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	$-0.205204\pi$
$599$	39.1249			1.59860			0.799300	+	0.600932i	$0.205204\pi$
$600$	21.2464	−	1.94207i	0.867382	−	0.0792845i
$601$	−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
$606$	−10.7765	+	17.5088i	−0.437767	+	0.711246i
$607$		−	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
$612$	−6.34993	+	3.20424i	−0.256681	+	0.129524i
$613$	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	$-0.906398\pi$
$617$		−	14.3990i		−	0.579680i	0.957075	−	0.289840i	$-0.0936021\pi$
$618$	3.29580	−	5.35473i	0.132577	−	0.215399i
$619$		−	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
$624$	−14.6368	−	33.4387i	−0.585943	−	1.33862i
$625$	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
$636$	−29.4096	−	6.89506i	−1.16616	−	0.273407i
$637$		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	$0.125151\pi$
$641$			19.3998i			0.766245i	−0.923698	+	0.383122i	$0.874849\pi$
$642$	−12.7246	−	7.83189i	−0.502198	−	0.309100i
$643$			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	$-0.148920\pi$
$647$	45.4057			1.78508			0.892542	+	0.450965i	$0.148920\pi$
$648$	−14.6498	−	20.8179i	−0.575498	−	0.817803i
$649$	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	$0.00614981\pi$
$653$			0.987349i			0.0386380i	−0.999813	+	0.0193190i	$0.993850\pi$
$654$	−11.3707	−	6.99861i	−0.444630	−	0.273667i
$655$		−	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	$-0.458491\pi$
$659$	6.67629			0.260071			0.130036	+	0.991509i	$0.458491\pi$
$660$	−6.35303	−	1.48946i	−0.247291	−	0.0579773i
$661$	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
$666$	−4.39886	+	0.646317i	−0.170452	+	0.0250443i
$667$		−	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	$0.0685990\pi$
$677$			11.1282i			0.427691i	−0.976867	+	0.213846i	$0.931401\pi$
$678$	9.11341	−	14.8067i	0.349999	−	0.568647i
$679$		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	$-0.440743\pi$
$683$	9.67432			0.370178			0.185089	+	0.982722i	$0.440743\pi$
$684$	38.1624	−	19.2571i	1.45918	−	0.736313i
$685$	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
$690$	−8.13287	+	13.2136i	−0.309613	+	0.503032i
$691$			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
$696$	1.88692	+	20.6431i	0.0715234	+	0.782475i
$697$	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	$-0.777652\pi$
$701$		−	34.0535i		−	1.28618i	0.765790	−	0.643091i	$-0.222348\pi$
$702$	−25.7403	+	28.9199i	−0.971507	+	1.09151i
$703$		−	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
$708$	−0.523592	+	2.23328i	−0.0196778	+	0.0839318i
$709$	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	$-0.451788\pi$
$719$	8.09170			0.301769			0.150885	+	0.988551i	$0.451788\pi$
$720$	4.28356	−	8.63321i	0.159639	−	0.321741i
$721$		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
$726$	11.4707	+	7.06017i	0.425719	+	0.262028i
$727$		−	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
$732$	−0.757605	+	3.23142i	−0.0280019	+	0.119437i
$733$	−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
$738$	4.42169	+	30.0942i	0.162765	+	1.10778i
$739$		−	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	$-0.369125\pi$
$743$	21.7884			0.799340			0.399670	+	0.916659i	$0.369125\pi$
$744$	−2.18465	−	23.9004i	−0.0800932	−	0.876230i
$745$	−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
$750$	9.64649	−	15.6728i	0.352240	−	0.572289i
$751$			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	$-0.717831\pi$
$761$		−	42.7498i		−	1.54968i	0.632159	−	0.774839i	$-0.282169\pi$
$762$	−5.34377	+	8.68209i	−0.193584	+	0.314519i
$763$		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
$768$	−27.4876	+	3.52589i	−0.991873	+	0.127230i
$769$	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	$-0.993109\pi$
$773$		−	1.20376i		−	0.0432963i	0.999766	−	0.0216482i	$-0.00689136\pi$
$774$	−4.89888	−	33.3420i	−0.176086	−	1.19845i
$775$		−	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
$780$	−14.2708	−	3.34578i	−0.510976	−	0.119798i
$781$	−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
$786$	21.8864	+	13.4709i	0.780661	+	0.480492i
$787$			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
$792$	14.0252	−	14.1201i	0.498362	−	0.501736i
$793$	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	$-0.894392\pi$
$797$		−	18.3911i		−	0.651447i	0.945465	−	0.325724i	$-0.105608\pi$
$798$		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
$804$	28.4189	+	6.66281i	1.00226	+	0.234979i
$805$		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	$-0.924946\pi$
$809$		−	13.2891i		−	0.467220i	0.972330	−	0.233610i	$-0.0750538\pi$
$810$	−10.2176	−	0.303294i	−0.359010	−	0.0106567i
$811$		−	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
$816$	7.52369	−	3.29329i	0.263382	−	0.115288i
$817$	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	$-0.838035\pi$
$821$		−	27.9169i		−	0.974306i	0.873317	−	0.487153i	$-0.161965\pi$
$822$	−17.3229	+	28.1447i	−0.604204	+	0.981658i
$823$			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	$-0.296619\pi$
$827$	34.2989			1.19269			0.596344	+	0.802729i	$0.296619\pi$
$828$	−21.3190	−	42.2485i	−0.740886	−	1.46824i
$829$	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
$834$	9.72279	−	15.7967i	0.336673	−	0.546996i
$835$			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	$-0.801101\pi$
$839$	−46.9847			−1.62209			−0.811046	+	0.584983i	$0.801101\pi$
$840$		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
$846$	−25.6013	+	3.76156i	−0.880191	+	0.129325i
$847$		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
$852$	7.64965	−	32.6281i	0.262073	−	1.11782i
$853$	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	$-0.827320\pi$
$857$		−	30.2271i		−	1.03254i	0.856426	−	0.516269i	$-0.172680\pi$
$858$	−25.7775	−	15.8659i	−0.880028	−	0.541652i
$859$		−	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	$-0.351700\pi$
$863$	26.3936			0.898450			0.449225	+	0.893419i	$0.351700\pi$
$864$	15.5758	+	24.9278i	0.529899	+	0.848061i
$865$	−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
$870$	7.08890	+	4.36317i	0.240336	+	0.147925i
$871$		−	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
$876$	1.11824	−	4.76965i	0.0377819	−	0.161151i
$877$	−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	$0.215091\pi$
$881$			37.1298i			1.25093i	−0.780251	+	0.625467i	$0.784909\pi$
$882$		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	$-0.644579\pi$
$887$	−26.1343			−0.877504			−0.438752	+	0.898608i	$0.644579\pi$
$888$	5.11259	−	0.467324i	0.171567	−	0.0156824i
$889$		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
$894$	20.6731	−	33.5878i	0.691412	−	1.12334i
$895$		−	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
$900$	11.7716	+	23.3282i	0.392387	+	0.777606i
$901$	−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
$906$	22.3204	−	36.2643i	0.741547	−	1.20480i
$907$			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	$-0.477240\pi$
$911$	4.31270			0.142886			0.0714430	+	0.997445i	$0.477240\pi$
$912$	−45.2165	+	19.7923i	−1.49727	+	0.655388i
$913$	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
$918$	−6.50699	−	5.79157i	−0.214763	−	0.191150i
$919$		−	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	$-0.875978\pi$
$929$		−	23.1549i		−	0.759687i	0.925051	−	0.379843i	$-0.124022\pi$
$930$	−8.20745	−	5.05163i	−0.269133	−	0.165650i
$931$		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
$936$	31.5047	−	31.7179i	1.02976	−	1.03673i
$937$	−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	$0.125970\pi$
$941$			23.6509i			0.770996i	−0.922709	+	0.385498i	$0.874030\pi$
$942$	8.18178	+	5.03583i	0.266577	+	0.164076i
$943$			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	$-0.115532\pi$
$947$	57.5371			1.86970			0.934852	+	0.355037i	$0.115532\pi$
$948$	−23.3664	−	5.47825i	−0.758906	−	0.177925i
$949$	−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	$-0.926151\pi$
$953$		−	14.1961i		−	0.459855i	0.973208	−	0.229928i	$-0.0738490\pi$
$954$	−5.37800	−	36.6029i	−0.174119	−	1.18506i
$955$			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
$960$	−5.48415	+	9.68327i	−0.177000	+	0.312526i
$961$	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	$-0.655936\pi$
$971$	−29.3240			−0.941051			−0.470526	+	0.882386i	$0.655936\pi$
$972$	17.1224	−	26.0542i	0.549202	−	0.835690i
$973$		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	$0.0609436\pi$
$977$			11.8959i			0.380585i	−0.981727	+	0.190292i	$0.939056\pi$
$978$	9.38442	−	15.2470i	0.300081	−	0.487545i
$979$			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	$-0.576786\pi$
$983$	−14.9803			−0.477796			−0.238898	+	0.971045i	$0.576786\pi$
$984$	−3.19713	−	34.9770i	−0.101921	−	1.11503i
$985$	−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
$990$	−1.16175	−	7.90693i	−0.0369229	−	0.251299i
$991$			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
$996$	−4.09772	+	17.4781i	−0.129841	+	0.553813i
$997$	−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.491.10	yes	24
3.2	odd	2	inner	588.2.e.f.491.15	yes	24
4.3	odd	2	inner	588.2.e.f.491.13	yes	24
7.2	even	3		588.2.n.d.263.4		24
7.3	odd	6		588.2.n.h.275.12		24
7.4	even	3		588.2.n.h.275.11		24
7.5	odd	6		588.2.n.d.263.3		24
7.6	odd	2	inner	588.2.e.f.491.9	✓	24
12.11	even	2	inner	588.2.e.f.491.12	yes	24
21.2	odd	6		588.2.n.d.263.10		24
21.5	even	6		588.2.n.d.263.9		24
21.11	odd	6		588.2.n.h.275.1		24
21.17	even	6		588.2.n.h.275.2		24
21.20	even	2	inner	588.2.e.f.491.16	yes	24
28.3	even	6		588.2.n.d.275.9		24
28.11	odd	6		588.2.n.d.275.10		24
28.19	even	6		588.2.n.h.263.2		24
28.23	odd	6		588.2.n.h.263.1		24
28.27	even	2	inner	588.2.e.f.491.14	yes	24
84.11	even	6		588.2.n.d.275.4		24
84.23	even	6		588.2.n.h.263.11		24
84.47	odd	6		588.2.n.h.263.12		24
84.59	odd	6		588.2.n.d.275.3		24
84.83	odd	2	inner	588.2.e.f.491.11	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
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} +(-2.08603 - 1.28394i) q^{6} +(2.32403 + 1.61211i) q^{8} +(0.523976 - 2.95389i) q^{9} +(1.07761 - 0.358837i) q^{10} +2.34545 q^{11} +(-0.790717 + 3.37265i) q^{12} +5.26858 q^{13} +(0.893604 + 1.06607i) q^{15} +(1.12471 - 3.83862i) q^{16} +1.18543i q^{17} +(-4.19757 + 0.616742i) q^{18} -7.12430i q^{19} +(-0.962960 - 1.28559i) q^{20} +(-1.04795 - 3.14708i) q^{22} -7.88711 q^{23} +(4.87864 - 0.445940i) q^{24} +4.35499 q^{25} +(-2.35401 - 7.06926i) q^{26} +(-2.59115 - 4.50399i) q^{27} +4.23132i q^{29} +(1.03116 - 1.67534i) q^{30} -4.89898i q^{31} +(-5.65310 + 0.205989i) q^{32} +(3.11335 - 2.60969i) q^{33} +(1.59058 - 0.529652i) q^{34} +(2.70302 + 5.35665i) 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} +(-2.77814 - 6.34681i) q^{48} +(-1.94582 - 5.84343i) q^{50} +(1.31898 + 1.57354i) q^{51} +(-8.43361 + 6.31712i) q^{52} +8.72001i q^{53} +(-4.88563 + 5.48914i) q^{54} +1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(5.67750 - 1.89056i) q^{58} +0.662173 q^{59} +(-2.70866 - 0.635044i) q^{60} +0.958124 q^{61} +(-6.57334 + 2.18887i) q^{62} +(2.80221 + 7.49317i) q^{64} +4.23132i q^{65} +(-4.89268 - 3.01141i) q^{66} -8.42629i q^{67} +(-1.42135 - 1.89756i) q^{68} +(-10.4693 + 8.77567i) q^{69} -9.67432 q^{71} +(5.97972 - 6.02021i) q^{72} -1.41421 q^{73} +(-0.468227 - 1.40612i) q^{74} +(5.78081 - 4.84562i) q^{75} +(8.54216 + 11.4041i) q^{76} +(-10.9904 - 6.76452i) 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} +(-0.495321 - 3.37117i) q^{90} +(12.6252 - 9.45679i) q^{92} +(-5.45090 - 6.50290i) q^{93} +(-2.72508 - 8.18360i) q^{94} +5.72170 q^{95} +(-7.27473 + 6.56341i) q^{96} -4.37827 q^{97} +(1.22896 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) \) 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

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