LMFDB - Embedded newform 756.2.be.d.431.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(107,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,-4,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.13
Character	$\chi$	$=$	756.431
Dual form			756.2.be.d.107.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33158 + 0.476336i) q^{2} +(1.54621 + 1.26856i) q^{4} +(-2.47695 + 1.43007i) q^{5} +(-2.52686 + 0.784194i) q^{7} +(1.45464 + 2.42570i) q^{8} +(-3.97945 + 0.724388i) q^{10} +(0.887062 - 1.53644i) q^{11} -4.70960 q^{13} +(-3.73826 - 0.159419i) q^{14} +(0.781518 + 3.92291i) q^{16} +(6.08556 + 3.51350i) q^{17} +(-6.93224 + 4.00233i) q^{19} +(-5.64401 - 0.930975i) q^{20} +(1.91305 - 1.62335i) q^{22} +(-2.46180 - 4.26396i) q^{23} +(1.59019 - 2.75429i) q^{25} +(-6.27121 - 2.24335i) q^{26} +(-4.90185 - 1.99295i) q^{28} +7.21461i q^{29} +(-1.31172 - 0.757322i) q^{31} +(-0.827971 + 5.59593i) q^{32} +(6.42980 + 7.57728i) q^{34} +(5.13747 - 5.55600i) q^{35} +(1.38862 + 2.40515i) q^{37} +(-11.1373 + 2.02734i) q^{38} +(-7.07199 - 3.92811i) q^{40} -4.94219i q^{41} -7.39300i q^{43} +(3.32064 - 1.25036i) q^{44} +(-1.24700 - 6.85044i) q^{46} +(2.78654 + 4.82642i) q^{47} +(5.77008 - 3.96310i) q^{49} +(3.42943 - 2.91009i) q^{50} +(-7.28202 - 5.97440i) q^{52} +(2.87828 + 1.66178i) q^{53} +5.07423i q^{55} +(-5.57789 - 4.98870i) q^{56} +(-3.43658 + 9.60683i) q^{58} +(-0.717330 + 1.24245i) q^{59} +(7.30221 + 12.6478i) q^{61} +(-1.38592 - 1.63325i) q^{62} +(-3.76805 + 7.05704i) q^{64} +(11.6654 - 6.73505i) q^{65} +(2.58315 + 1.49138i) q^{67} +(4.95246 + 13.1525i) q^{68} +(9.48747 - 4.95109i) q^{70} +11.4553 q^{71} +(0.0244370 - 0.0423261i) q^{73} +(0.703391 + 3.86410i) q^{74} +(-15.7959 - 2.60552i) q^{76} +(-1.03662 + 4.57799i) q^{77} +(-1.15816 + 0.668665i) q^{79} +(-7.54581 - 8.59923i) q^{80} +(2.35414 - 6.58092i) q^{82} +9.02165 q^{83} -20.0982 q^{85} +(3.52155 - 9.84437i) q^{86} +(5.01729 - 0.0832119i) q^{88} +(5.61463 - 3.24161i) q^{89} +(11.9005 - 3.69324i) q^{91} +(1.60263 - 9.71589i) q^{92} +(1.41149 + 7.75409i) q^{94} +(11.4472 - 19.8271i) q^{95} -1.07208 q^{97} +(9.57109 - 2.52869i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64}+ \cdots - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.33158	+	0.476336i	0.941569	+	0.336820i
$2$	1.33158	+	0.476336i	0.941569	+	0.336820i
$3$		0			0
$3$		0			0
$4$	1.54621	+	1.26856i	0.773104	+	0.634279i
$5$	−2.47695	+	1.43007i	−1.10773	+	0.639546i	−0.938239	−	0.345987i	$-0.887544\pi$
$5$	−2.47695	+	1.43007i	−1.10773	+	0.639546i	−0.169487	+	0.985532i	$0.554211\pi$
$6$		0			0
$7$	−2.52686	+	0.784194i	−0.955065	+	0.296398i
$7$	−2.52686	+	0.784194i	−0.955065	+	0.296398i
$8$	1.45464	+	2.42570i	0.514292	+	0.857615i
$9$		0			0
$10$	−3.97945	+	0.724388i	−1.25841	+	0.229072i
$11$	0.887062	−	1.53644i	0.267459	−	0.463253i	−0.700746	−	0.713411i	$-0.747149\pi$
$11$	0.887062	−	1.53644i	0.267459	−	0.463253i	0.968205	+	0.250158i	$0.0804826\pi$
$12$		0			0
$13$	−4.70960			−1.30621			−0.653104	−	0.757268i	$-0.726534\pi$
$13$	−4.70960			−1.30621			−0.653104	+	0.757268i	$0.726534\pi$
$14$	−3.73826	−	0.159419i	−0.999092	−	0.0426066i
$15$		0			0
$16$	0.781518	+	3.92291i	0.195379	+	0.980728i
$17$	6.08556	+	3.51350i	1.47597	+	0.852149i	0.999632	−	0.0271159i	$-0.00863232\pi$
$17$	6.08556	+	3.51350i	1.47597	+	0.852149i	0.476333	+	0.879265i	$0.341966\pi$
$18$		0			0
$19$	−6.93224	+	4.00233i	−1.59036	+	0.918197i	−0.597121	+	0.802152i	$0.703689\pi$
$19$	−6.93224	+	4.00233i	−1.59036	+	0.918197i	−0.993244	+	0.116046i	$0.962978\pi$
$20$	−5.64401	−	0.930975i	−1.26204	−	0.208172i
$21$		0			0
$22$	1.91305	−	1.62335i	0.407864	−	0.346099i
$23$	−2.46180	−	4.26396i	−0.513320	−	0.889096i	−0.999881	−	0.0154494i	$-0.995082\pi$
$23$	−2.46180	−	4.26396i	−0.513320	−	0.889096i	0.486561	−	0.873647i	$-0.338251\pi$
$24$		0			0
$25$	1.59019	−	2.75429i	0.318038	−	0.550858i
$26$	−6.27121	−	2.24335i	−1.22988	−	0.439958i
$27$		0			0
$28$	−4.90185	−	1.99295i	−0.926363	−	0.376632i
$29$			7.21461i			1.33972i	0.742487	+	0.669860i	$0.233646\pi$
$29$			7.21461i			1.33972i	−0.742487	+	0.669860i	$0.766354\pi$
$30$		0			0
$31$	−1.31172	−	0.757322i	−0.235592	−	0.136019i	0.377557	−	0.925986i	$-0.376764\pi$
$31$	−1.31172	−	0.757322i	−0.235592	−	0.136019i	−0.613149	+	0.789967i	$0.710097\pi$
$32$	−0.827971	+	5.59593i	−0.146366	+	0.989231i
$33$		0			0
$34$	6.42980	+	7.57728i	1.10270	+	1.29949i
$35$	5.13747	−	5.55600i	0.868390	−	0.939135i
$36$		0			0
$37$	1.38862	+	2.40515i	0.228287	+	0.395405i	0.957301	−	0.289095i	$-0.0933542\pi$
$37$	1.38862	+	2.40515i	0.228287	+	0.395405i	−0.729013	+	0.684499i	$0.760021\pi$
$38$	−11.1373	+	2.02734i	−1.80671	+	0.328879i
$39$		0			0
$40$	−7.07199	−	3.92811i	−1.11818	−	0.621089i
$41$		−	4.94219i		−	0.771840i	−0.922532	−	0.385920i	$-0.873884\pi$
$41$		−	4.94219i		−	0.771840i	0.922532	−	0.385920i	$-0.126116\pi$
$42$		0			0
$43$		−	7.39300i		−	1.12742i	−0.825972	−	0.563711i	$-0.809373\pi$
$43$		−	7.39300i		−	1.12742i	0.825972	−	0.563711i	$-0.190627\pi$
$44$	3.32064	−	1.25036i	0.500605	−	0.188499i
$45$		0			0
$46$	−1.24700	−	6.85044i	−0.183860	−	1.01004i
$47$	2.78654	+	4.82642i	0.406458	+	0.704006i	0.994490	−	0.104832i	$-0.0334304\pi$
$47$	2.78654	+	4.82642i	0.406458	+	0.704006i	−0.588032	+	0.808838i	$0.700097\pi$
$48$		0			0
$49$	5.77008	−	3.96310i	0.824297	−	0.566158i
$50$	3.42943	−	2.91009i	0.484995	−	0.411549i
$51$		0			0
$52$	−7.28202	−	5.97440i	−1.00983	−	0.828501i
$53$	2.87828	+	1.66178i	0.395362	+	0.228262i	0.684481	−	0.729031i	$-0.260029\pi$
$53$	2.87828	+	1.66178i	0.395362	+	0.228262i	−0.289119	+	0.957293i	$0.593362\pi$
$54$		0			0
$55$			5.07423i			0.684210i
$56$	−5.57789	−	4.98870i	−0.745377	−	0.666643i
$57$		0			0
$58$	−3.43658	+	9.60683i	−0.451245	+	1.26144i
$59$	−0.717330	+	1.24245i	−0.0933884	+	0.161753i	−0.908935	−	0.416938i	$-0.863103\pi$
$59$	−0.717330	+	1.24245i	−0.0933884	+	0.161753i	0.815546	+	0.578692i	$0.196436\pi$
$60$		0			0
$61$	7.30221	+	12.6478i	0.934952	+	1.61938i	0.774719	+	0.632306i	$0.217891\pi$
$61$	7.30221	+	12.6478i	0.934952	+	1.61938i	0.160233	+	0.987079i	$0.448775\pi$
$62$	−1.38592	−	1.63325i	−0.176012	−	0.207423i
$63$		0			0
$64$	−3.76805	+	7.05704i	−0.471007	+	0.882130i
$65$	11.6654	−	6.73505i	1.44692	−	0.835380i
$66$		0			0
$67$	2.58315	+	1.49138i	0.315582	+	0.182201i	0.649422	−	0.760428i	$-0.275011\pi$
$67$	2.58315	+	1.49138i	0.315582	+	0.182201i	−0.333840	+	0.942630i	$0.608344\pi$
$68$	4.95246	+	13.1525i	0.600574	+	1.59497i
$69$		0			0
$70$	9.48747	−	4.95109i	1.13397	−	0.591769i
$71$	11.4553			1.35949			0.679747	−	0.733447i	$-0.262090\pi$
$71$	11.4553			1.35949			0.679747	+	0.733447i	$0.262090\pi$
$72$		0			0
$73$	0.0244370	−	0.0423261i	0.00286014	−	0.00495390i	−0.864592	−	0.502475i	$-0.832423\pi$
$73$	0.0244370	−	0.0423261i	0.00286014	−	0.00495390i	0.867452	+	0.497521i	$0.165756\pi$
$74$	0.703391	+	3.86410i	0.0817676	+	0.449193i
$75$		0			0
$76$	−15.7959	−	2.60552i	−1.81191	−	0.298873i
$77$	−1.03662	+	4.57799i	−0.118134	+	0.521711i
$78$		0			0
$79$	−1.15816	+	0.668665i	−0.130303	+	0.0752307i	−0.563735	−	0.825956i	$-0.690636\pi$
$79$	−1.15816	+	0.668665i	−0.130303	+	0.0752307i	0.433431	+	0.901187i	$0.357303\pi$
$80$	−7.54581	−	8.59923i	−0.843647	−	0.961424i
$81$		0			0
$82$	2.35414	−	6.58092i	0.259972	−	0.726741i
$83$	9.02165			0.990255			0.495128	−	0.868820i	$-0.335121\pi$
$83$	9.02165			0.990255			0.495128	+	0.868820i	$0.335121\pi$
$84$		0			0
$85$	−20.0982			−2.17995
$86$	3.52155	−	9.84437i	0.379739	−	1.06155i
$87$		0			0
$88$	5.01729	−	0.0832119i	0.534845	−	0.00887042i
$89$	5.61463	−	3.24161i	0.595149	−	0.343610i	−0.171982	−	0.985100i	$-0.555017\pi$
$89$	5.61463	−	3.24161i	0.595149	−	0.343610i	0.767131	+	0.641491i	$0.221684\pi$
$90$		0			0
$91$	11.9005	−	3.69324i	1.24751	−	0.387157i
$92$	1.60263	−	9.71589i	0.167086	−	1.01295i
$93$		0			0
$94$	1.41149	+	7.75409i	0.145585	+	0.799773i
$95$	11.4472	−	19.8271i	1.17446	−	2.03422i
$96$		0			0
$97$	−1.07208			−0.108853			−0.0544267	−	0.998518i	$-0.517333\pi$
$97$	−1.07208			−0.108853			−0.0544267	+	0.998518i	$0.517333\pi$
$98$	9.57109	−	2.52869i	0.966826	−	0.255436i
$99$		0			0
$100$	5.95274	−	2.24146i	0.595274	−	0.224146i
$101$	−5.30278	−	3.06156i	−0.527646	−	0.304637i	0.212411	−	0.977180i	$-0.431868\pi$
$101$	−5.30278	−	3.06156i	−0.527646	−	0.304637i	−0.740058	+	0.672544i	$0.765202\pi$
$102$		0			0
$103$	−6.18578	+	3.57136i	−0.609503	+	0.351897i	−0.772771	−	0.634685i	$-0.781130\pi$
$103$	−6.18578	+	3.57136i	−0.609503	+	0.351897i	0.163268	+	0.986582i	$0.447796\pi$
$104$	−6.85077	−	11.4241i	−0.671773	−	1.12022i
$105$		0			0
$106$	3.04109	+	3.58382i	0.295377	+	0.348091i
$107$	−1.29481	−	2.24267i	−0.125174	−	0.216807i	0.796627	−	0.604471i	$-0.206615\pi$
$107$	−1.29481	−	2.24267i	−0.125174	−	0.216807i	−0.921801	+	0.387664i	$0.873282\pi$
$108$		0			0
$109$	−1.37701	+	2.38505i	−0.131894	+	0.228447i	−0.924407	−	0.381409i	$-0.875439\pi$
$109$	−1.37701	+	2.38505i	−0.131894	+	0.228447i	0.792513	+	0.609855i	$0.208772\pi$
$110$	−2.41704	+	6.75675i	−0.230456	+	0.644231i
$111$		0			0
$112$	−5.05111	−	9.29980i	−0.477285	−	0.878748i
$113$			18.3520i			1.72641i	0.504854	+	0.863205i	$0.331546\pi$
$113$			18.3520i			1.72641i	−0.504854	+	0.863205i	$0.668454\pi$
$114$		0			0
$115$	12.1955	+	7.04107i	1.13724	+	0.656583i
$116$	−9.15216	+	11.1553i	−0.849757	+	1.03574i
$117$		0			0
$118$	−1.54701	+	1.31273i	−0.142413	+	0.120847i
$119$	−18.1326	−	4.10587i	−1.66222	−	0.376385i
$120$		0			0
$121$	3.92624	+	6.80045i	0.356931	+	0.618223i
$122$	3.69887	+	20.3199i	0.334880	+	1.83967i
$123$		0			0
$124$	−1.06748	−	2.83497i	−0.0958629	−	0.254588i
$125$		−	5.20436i		−	0.465492i
$126$		0			0
$127$		−	8.18873i		−	0.726632i	−0.931666	−	0.363316i	$-0.881645\pi$
$127$		−	8.18873i		−	0.726632i	0.931666	−	0.363316i	$-0.118355\pi$
$128$	−8.37898	+	7.60215i	−0.740605	+	0.671941i
$129$		0			0
$130$	18.7416	−	3.41158i	1.64375	−	0.299215i
$131$	−0.153906	−	0.266573i	−0.0134469	−	0.0232906i	0.859224	−	0.511600i	$-0.170947\pi$
$131$	−0.153906	−	0.266573i	−0.0134469	−	0.0232906i	−0.872671	+	0.488309i	$0.837614\pi$
$132$		0			0
$133$	14.3782	−	15.5496i	1.24675	−	1.34832i
$134$	2.72927	+	3.21634i	0.235773	+	0.277850i
$135$		0			0
$136$	0.329588	+	19.8726i	0.0282620	+	1.70406i
$137$	−3.64686	−	2.10552i	−0.311573	−	0.179887i	0.336057	−	0.941842i	$-0.390906\pi$
$137$	−3.64686	−	2.10552i	−0.311573	−	0.179887i	−0.647630	+	0.761955i	$0.724240\pi$
$138$		0			0
$139$		−	10.5488i		−	0.894736i	−0.894350	−	0.447368i	$-0.852361\pi$
$139$		−	10.5488i		−	0.894736i	0.894350	−	0.447368i	$-0.147639\pi$
$140$	14.9917	−	2.07355i	1.26703	−	0.175247i
$141$		0			0
$142$	15.2536	+	5.45657i	1.28006	+	0.457905i
$143$	−4.17771	+	7.23600i	−0.349357	+	0.605105i
$144$		0			0
$145$	−10.3174	−	17.8702i	−0.856813	−	1.48404i
$146$	0.0527013	−	0.0447204i	0.00436159	−	0.00370109i
$147$		0			0
$148$	−0.903989	+	5.48041i	−0.0743075	+	0.450487i
$149$	−14.8380	+	8.56672i	−1.21558	+	0.701813i	−0.963969	−	0.266016i	$-0.914293\pi$
$149$	−14.8380	+	8.56672i	−1.21558	+	0.701813i	−0.251607	+	0.967829i	$0.580959\pi$
$150$		0			0
$151$	−6.08270	−	3.51185i	−0.495003	−	0.285790i	0.231645	−	0.972800i	$-0.425589\pi$
$151$	−6.08270	−	3.51185i	−0.495003	−	0.285790i	−0.726648	+	0.687010i	$0.758923\pi$
$152$	−19.7924	−	10.9936i	−1.60537	−	0.891698i
$153$		0			0
$154$	−3.56100	+	5.60218i	−0.286954	+	0.451437i
$155$	4.33209			0.347962
$156$		0			0
$157$	−1.01600	+	1.75976i	−0.0810853	+	0.140444i	−0.903716	−	0.428132i	$-0.859172\pi$
$157$	−1.01600	+	1.75976i	−0.0810853	+	0.140444i	0.822631	+	0.568576i	$0.192505\pi$
$158$	−1.86069	+	0.338707i	−0.148029	+	0.0269460i
$159$		0			0
$160$	−5.95172	−	15.0449i	−0.470525	−	1.18940i
$161$	9.56439	+	8.84391i	0.753780	+	0.696997i
$162$		0			0
$163$	4.79027	−	2.76566i	0.375203	−	0.216623i	−0.300526	−	0.953774i	$-0.597162\pi$
$163$	4.79027	−	2.76566i	0.375203	−	0.216623i	0.675729	+	0.737150i	$0.263829\pi$
$164$	6.26946	−	7.64165i	0.489562	−	0.596713i
$165$		0			0
$166$	12.0130	+	4.29734i	0.932393	+	0.333538i
$167$	−6.37142			−0.493035			−0.246518	−	0.969138i	$-0.579286\pi$
$167$	−6.37142			−0.493035			−0.246518	+	0.969138i	$0.579286\pi$
$168$		0			0
$169$	9.18033			0.706180
$170$	−26.7623	−	9.57349i	−2.05258	−	0.734253i
$171$		0			0
$172$	9.37845	−	11.4311i	0.715100	−	0.871614i
$173$	18.3863	−	10.6153i	1.39788	−	0.807069i	0.403714	−	0.914885i	$-0.367719\pi$
$173$	18.3863	−	10.6153i	1.39788	−	0.807069i	0.994171	+	0.107816i	$0.0343859\pi$
$174$		0			0
$175$	−1.85829	+	8.20673i	−0.140474	+	0.620371i
$176$	6.72056	+	2.27911i	0.506581	+	0.171795i
$177$		0			0
$178$	9.02042	−	1.64201i	0.676109	−	0.123074i
$179$	−10.2453	+	17.7453i	−0.765768	+	1.32635i	0.174072	+	0.984733i	$0.444307\pi$
$179$	−10.2453	+	17.7453i	−0.765768	+	1.32635i	−0.939840	+	0.341616i	$0.889026\pi$
$180$		0			0
$181$	−16.5989			−1.23379			−0.616894	−	0.787046i	$-0.711609\pi$
$181$	−16.5989			−1.23379			−0.616894	+	0.787046i	$0.711609\pi$
$182$	17.6057	+	0.750800i	1.30502	+	0.0556530i
$183$		0			0
$184$	6.76206	−	12.1741i	0.498506	−	0.897486i
$185$	−6.87907	−	3.97163i	−0.505759	−	0.292000i
$186$		0			0
$187$	10.7965	−	6.23338i	0.789521	−	0.455830i
$188$	−1.81404	+	10.9975i	−0.132302	+	0.802078i
$189$		0			0
$190$	24.6873	−	20.9487i	1.79100	−	1.51978i
$191$	3.51133	+	6.08181i	0.254071	+	0.440064i	0.964643	−	0.263561i	$-0.0848969\pi$
$191$	3.51133	+	6.08181i	0.254071	+	0.440064i	−0.710572	+	0.703625i	$0.751564\pi$
$192$		0			0
$193$	8.66227	−	15.0035i	0.623524	−	1.07997i	−0.365301	−	0.930890i	$-0.619034\pi$
$193$	8.66227	−	15.0035i	0.623524	−	1.07997i	0.988824	−	0.149085i	$-0.0476329\pi$
$194$	−1.42756	−	0.510672i	−0.102493	−	0.0366641i
$195$		0			0
$196$	13.9492	+	1.19190i	0.996369	+	0.0851357i
$197$		−	4.41987i		−	0.314902i	−0.987527	−	0.157451i	$-0.949672\pi$
$197$		−	4.41987i		−	0.314902i	0.987527	−	0.157451i	$-0.0503277\pi$
$198$		0			0
$199$	0.539285	+	0.311356i	0.0382289	+	0.0220715i	0.518993	−	0.854779i	$-0.326307\pi$
$199$	0.539285	+	0.311356i	0.0382289	+	0.0220715i	−0.480764	+	0.876850i	$0.659641\pi$
$200$	8.99424	−	0.149170i	0.635989	−	0.0105479i
$201$		0			0
$202$	−5.60274	−	6.60262i	−0.394208	−	0.464559i
$203$	−5.65766	−	18.2303i	−0.397090	−	1.27952i
$204$		0			0
$205$	7.06767	+	12.2416i	0.493627	+	0.854988i
$206$	−9.93802	+	1.80904i	−0.692415	+	0.126042i
$207$		0			0
$208$	−3.68064	−	18.4753i	−0.255206	−	1.28103i
$209$			14.2013i			0.982321i
$210$		0			0
$211$			19.0072i			1.30851i	0.756275	+	0.654253i	$0.227017\pi$
$211$			19.0072i			1.30851i	−0.756275	+	0.654253i	$0.772983\pi$
$212$	2.34236	+	6.22072i	0.160874	+	0.427241i
$213$		0			0
$214$	−0.655873	−	3.60306i	−0.0448346	−	0.246300i
$215$	10.5725	+	18.3121i	0.721038	+	1.24887i
$216$		0			0
$217$	3.90842	+	0.885005i	0.265321	+	0.0600781i
$218$	−2.96969	+	2.51997i	−0.201133	+	0.170674i
$219$		0			0
$220$	−6.43696	+	7.84582i	−0.433980	+	0.528965i
$221$	−28.6606	−	16.5472i	−1.92792	−	1.11308i
$222$		0			0
$223$			13.3599i			0.894643i	0.894373	+	0.447321i	$0.147622\pi$
$223$			13.3599i			0.894643i	−0.894373	+	0.447321i	$0.852378\pi$
$224$	−2.29613	−	14.7894i	−0.153417	−	0.988162i
$225$		0			0
$226$	−8.74171	+	24.4371i	−0.581490	+	1.62553i
$227$	−1.96956	+	3.41138i	−0.130724	+	0.226421i	−0.923956	−	0.382499i	$-0.875064\pi$
$227$	−1.96956	+	3.41138i	−0.130724	+	0.226421i	0.793232	+	0.608920i	$0.208397\pi$
$228$		0			0
$229$	−1.44488	−	2.50261i	−0.0954804	−	0.165377i	0.814329	−	0.580404i	$-0.197105\pi$
$229$	−1.44488	−	2.50261i	−0.0954804	−	0.165377i	−0.909809	+	0.415027i	$0.863772\pi$
$230$	12.8854	+	15.1849i	0.849635	+	1.00126i
$231$		0			0
$232$	−17.5005	+	10.4947i	−1.14896	+	0.689008i
$233$	12.9746	−	7.49088i	0.849993	−	0.490744i	−0.0106555	−	0.999943i	$-0.503392\pi$
$233$	12.9746	−	7.49088i	0.849993	−	0.490744i	0.860648	+	0.509200i	$0.170058\pi$
$234$		0			0
$235$	−13.8042	−	7.96987i	−0.900488	−	0.519897i
$236$	−2.68526	+	1.01111i	−0.174796	+	0.0658179i
$237$		0			0
$238$	−22.1893	−	14.1045i	−1.43832	−	0.914261i
$239$	−9.74049			−0.630060			−0.315030	−	0.949082i	$-0.602015\pi$
$239$	−9.74049			−0.630060			−0.315030	+	0.949082i	$0.602015\pi$
$240$		0			0
$241$	−3.01158	+	5.21621i	−0.193993	+	0.336006i	−0.946570	−	0.322499i	$-0.895477\pi$
$241$	−3.01158	+	5.21621i	−0.193993	+	0.336006i	0.752577	+	0.658504i	$0.228811\pi$
$242$	1.98880	+	10.9256i	0.127845	+	0.702321i
$243$		0			0
$244$	−4.75374	+	28.8194i	−0.304327	+	1.84497i
$245$	−8.62469	+	18.0680i	−0.551011	+	1.15432i
$246$		0			0
$247$	32.6481	−	18.8494i	2.07735	−	1.19936i
$248$	−0.0710415	−	4.28347i	−0.00451114	−	0.272001i
$249$		0			0
$250$	2.47902	−	6.93002i	0.156787	−	0.438293i
$251$	−2.95805			−0.186710			−0.0933551	−	0.995633i	$-0.529759\pi$
$251$	−2.95805			−0.186710			−0.0933551	+	0.995633i	$0.529759\pi$
$252$		0			0
$253$	−8.73506			−0.549168
$254$	3.90059	−	10.9039i	0.244745	−	0.684174i
$255$		0			0
$256$	−14.7785	+	6.13165i	−0.923654	+	0.383228i
$257$	1.04960	−	0.605984i	0.0654719	−	0.0378002i	−0.466907	−	0.884307i	$-0.654632\pi$
$257$	1.04960	−	0.605984i	0.0654719	−	0.0378002i	0.532379	+	0.846506i	$0.321298\pi$
$258$		0			0
$259$	−5.39495	−	4.98855i	−0.335226	−	0.309973i
$260$	26.5810	+	4.38452i	1.64848	+	0.271916i
$261$		0			0
$262$	−0.0779598	−	0.428275i	−0.00481638	−	0.0264589i
$263$	5.43216	−	9.40878i	0.334962	−	0.580171i	−0.648516	−	0.761201i	$-0.724610\pi$
$263$	5.43216	−	9.40878i	0.334962	−	0.580171i	0.983477	+	0.181031i	$0.0579433\pi$
$264$		0			0
$265$	−9.50581			−0.583937
$266$	26.5526	−	13.8566i	1.62804	−	0.849604i
$267$		0			0
$268$	2.10218	+	5.58287i	0.128411	+	0.341028i
$269$	6.63128	+	3.82857i	0.404316	+	0.233432i	0.688345	−	0.725384i	$-0.258338\pi$
$269$	6.63128	+	3.82857i	0.404316	+	0.233432i	−0.284028	+	0.958816i	$0.591671\pi$
$270$		0			0
$271$	17.2222	−	9.94322i	1.04617	−	0.604008i	0.124597	−	0.992207i	$-0.460236\pi$
$271$	17.2222	−	9.94322i	1.04617	−	0.604008i	0.921575	+	0.388200i	$0.126903\pi$
$272$	−9.02718	+	26.6190i	−0.547353	+	1.61401i
$273$		0			0
$274$	−3.85316	−	4.54080i	−0.232778	−	0.274320i
$275$	−2.82119	−	4.88645i	−0.170124	−	0.294664i
$276$		0			0
$277$	−3.33158	+	5.77046i	−0.200175	+	0.346713i	−0.948585	−	0.316523i	$-0.897484\pi$
$277$	−3.33158	+	5.77046i	−0.200175	+	0.346713i	0.748410	+	0.663237i	$0.230818\pi$
$278$	5.02476	−	14.0465i	0.301365	−	0.842455i
$279$		0			0
$280$	20.9503	+	4.37999i	1.25202	+	0.261754i
$281$		−	9.71892i		−	0.579782i	−0.957060	−	0.289891i	$-0.906381\pi$
$281$		−	9.71892i		−	0.579782i	0.957060	−	0.289891i	$-0.0936190\pi$
$282$		0			0
$283$	−6.55255	−	3.78312i	−0.389509	−	0.224883i	0.292439	−	0.956284i	$-0.405533\pi$
$283$	−6.55255	−	3.78312i	−0.389509	−	0.224883i	−0.681947	+	0.731401i	$0.738867\pi$
$284$	17.7123	+	14.5317i	1.05103	+	0.862299i
$285$		0			0
$286$	−9.00971	+	7.64532i	−0.532756	+	0.452077i
$287$	3.87564	+	12.4882i	0.228772	+	0.737157i
$288$		0			0
$289$	16.1894	+	28.0408i	0.952316	+	1.64946i
$290$	−5.22618	−	28.7102i	−0.306892	−	1.68592i
$291$		0			0
$292$	0.0914779	−	0.0344452i	0.00535334	−	0.00201575i
$293$		−	5.44847i		−	0.318303i	−0.987254	−	0.159151i	$-0.949124\pi$
$293$		−	5.44847i		−	0.318303i	0.987254	−	0.159151i	$-0.0508758\pi$
$294$		0			0
$295$		−	4.10332i		−	0.238905i
$296$	−3.81425	+	6.86700i	−0.221699	+	0.399136i
$297$		0			0
$298$	−23.8386	+	4.33940i	−1.38093	+	0.251375i
$299$	11.5941	+	20.0815i	0.670503	+	1.16134i
$300$		0			0
$301$	5.79755	+	18.6811i	0.334165	+	1.07676i
$302$	−6.42678	−	7.57371i	−0.369819	−	0.435818i
$303$		0			0
$304$	−21.1184	−	24.0667i	−1.21123	−	1.38032i
$305$	−36.1744	−	20.8853i	−2.07134	−	1.19589i
$306$		0			0
$307$			1.58786i			0.0906240i	0.998973	+	0.0453120i	$0.0144282\pi$
$307$			1.58786i			0.0906240i	−0.998973	+	0.0453120i	$0.985572\pi$
$308$	−7.41028	+	5.76352i	−0.422240	+	0.328407i
$309$		0			0
$310$	5.76852	+	2.06353i	0.327630	+	0.117201i
$311$	−9.92410	+	17.1891i	−0.562744	+	0.974702i	0.434511	+	0.900666i	$0.356921\pi$
$311$	−9.92410	+	17.1891i	−0.562744	+	0.974702i	−0.997256	+	0.0740353i	$0.976412\pi$
$312$		0			0
$313$	−5.26944	−	9.12693i	−0.297846	−	0.515885i	0.677797	−	0.735249i	$-0.262935\pi$
$313$	−5.26944	−	9.12693i	−0.297846	−	0.515885i	−0.975643	+	0.219365i	$0.929602\pi$
$314$	−2.19112	+	1.85930i	−0.123652	+	0.104926i
$315$		0			0
$316$	−2.63900	−	0.435301i	−0.148455	−	0.0244876i
$317$	11.5912	−	6.69221i	0.651029	−	0.375872i	−0.137821	−	0.990457i	$-0.544010\pi$
$317$	11.5912	−	6.69221i	0.651029	−	0.375872i	0.788850	+	0.614585i	$0.210677\pi$
$318$		0			0
$319$	11.0848	+	6.39981i	0.620629	+	0.358320i
$320$	−0.758759	−	22.8685i	−0.0424159	−	1.27839i
$321$		0			0
$322$	8.52308	+	16.3322i	0.474972	+	0.910160i
$323$	−56.2487			−3.12976
$324$		0			0
$325$	−7.48916	+	12.9716i	−0.415424	+	0.719535i
$326$	7.69600	−	1.40092i	0.426242	−	0.0775899i
$327$		0			0
$328$	11.9883	−	7.18910i	0.661942	−	0.396952i
$329$	−10.8260	−	10.0105i	−0.596859	−	0.551898i
$330$		0			0
$331$	−24.0106	+	13.8625i	−1.31974	+	0.761952i	−0.983687	−	0.179891i	$-0.942426\pi$
$331$	−24.0106	+	13.8625i	−1.31974	+	0.761952i	−0.336053	+	0.941843i	$0.609092\pi$
$332$	13.9494	+	11.4445i	0.765570	+	0.628098i
$333$		0			0
$334$	−8.48405	−	3.03494i	−0.464227	−	0.166064i
$335$	−8.53112			−0.466105
$336$		0			0
$337$	19.2739			1.04992			0.524959	−	0.851128i	$-0.324081\pi$
$337$	19.2739			1.04992			0.524959	+	0.851128i	$0.324081\pi$
$338$	12.2243	+	4.37292i	0.664917	+	0.237856i
$339$		0			0
$340$	−31.0760	−	25.4957i	−1.68533	−	1.38270i
$341$	−2.32715	+	1.34358i	−0.126022	+	0.0727590i
$342$		0			0
$343$	−11.4724	+	14.5391i	−0.619449	+	0.785037i
$344$	17.9332	−	10.7541i	0.966894	−	0.579824i
$345$		0			0
$346$	29.5393	−	5.37710i	1.58804	−	0.289075i
$347$	0.676069	−	1.17099i	0.0362933	−	0.0628618i	−0.847308	−	0.531102i	$-0.821778\pi$
$347$	0.676069	−	1.17099i	0.0362933	−	0.0628618i	0.883602	+	0.468240i	$0.155112\pi$
$348$		0			0
$349$	−34.3047			−1.83629			−0.918145	−	0.396245i	$-0.870313\pi$
$349$	−34.3047			−1.83629			−0.918145	+	0.396245i	$0.870313\pi$
$350$	−6.38363	+	10.0427i	−0.341219	+	0.536807i
$351$		0			0
$352$	7.86333	+	6.23606i	0.419117	+	0.332383i
$353$	−10.7257	−	6.19247i	−0.570870	−	0.329592i	0.186627	−	0.982431i	$-0.440244\pi$
$353$	−10.7257	−	6.19247i	−0.570870	−	0.329592i	−0.757497	+	0.652839i	$0.773578\pi$
$354$		0			0
$355$	−28.3742	+	16.3819i	−1.50595	+	0.869458i
$356$	12.7935	+	2.11029i	0.678057	+	0.111845i
$357$		0			0
$358$	−22.0951	+	18.7491i	−1.16776	+	0.990922i
$359$	6.36683	+	11.0277i	0.336028	+	0.582018i	0.983682	−	0.179917i	$-0.0575829\pi$
$359$	6.36683	+	11.0277i	0.336028	+	0.582018i	−0.647653	+	0.761935i	$0.724250\pi$
$360$		0			0
$361$	22.5373	−	39.0357i	1.18617	−	2.05451i
$362$	−22.1028	−	7.90666i	−1.16170	−	0.415565i
$363$		0			0
$364$	23.0858	+	9.38598i	1.21002	+	0.491959i
$365$			0.139786i			0.00731675i
$366$		0			0
$367$	−11.2735	−	6.50873i	−0.588469	−	0.339753i	0.176023	−	0.984386i	$-0.443677\pi$
$367$	−11.2735	−	6.50873i	−0.588469	−	0.339753i	−0.764492	+	0.644633i	$0.777010\pi$
$368$	14.8032	−	12.9898i	0.771669	−	0.677138i
$369$		0			0
$370$	−7.26819	−	8.56529i	−0.377855	−	0.445288i
$371$	−8.57618	−	1.94195i	−0.445253	−	0.100821i
$372$		0			0
$373$	2.92708	+	5.06985i	0.151558	+	0.262507i	0.931801	−	0.362971i	$-0.118238\pi$
$373$	2.92708	+	5.06985i	0.151558	+	0.262507i	−0.780242	+	0.625477i	$0.784904\pi$
$374$	17.3456	−	3.15747i	0.896921	−	0.163269i
$375$		0			0
$376$	−7.65405	+	13.7800i	−0.394728	+	0.710649i
$377$		−	33.9779i		−	1.74995i
$378$		0			0
$379$			23.7003i			1.21740i	0.793399	+	0.608701i	$0.208309\pi$
$379$			23.7003i			1.21740i	−0.793399	+	0.608701i	$0.791691\pi$
$380$	42.8517	−	16.1354i	2.19824	−	0.827730i
$381$		0			0
$382$	1.77864	+	9.77099i	0.0910029	+	0.499927i
$383$	−8.19122	−	14.1876i	−0.418552	−	0.724953i	0.577242	−	0.816573i	$-0.304129\pi$
$383$	−8.19122	−	14.1876i	−0.418552	−	0.724953i	−0.995794	+	0.0916198i	$0.970796\pi$
$384$		0			0
$385$	−3.97919	−	12.8219i	−0.202798	−	0.653464i
$386$	18.6812	−	15.8522i	0.950848	−	0.806855i
$387$		0			0
$388$	−1.65766	−	1.36000i	−0.0841550	−	0.0690435i
$389$	−6.59701	−	3.80878i	−0.334482	−	0.193113i	0.323348	−	0.946280i	$-0.395192\pi$
$389$	−6.59701	−	3.80878i	−0.334482	−	0.193113i	−0.657829	+	0.753167i	$0.728525\pi$
$390$		0			0
$391$		−	34.5981i		−	1.74970i
$392$	18.0067	+	8.23160i	0.909475	+	0.415759i
$393$		0			0
$394$	2.10534	−	5.88540i	0.106066	−	0.296502i
$395$	1.91247	−	3.31250i	0.0962270	−	0.166670i
$396$		0			0
$397$	4.18986	+	7.25706i	0.210283	+	0.364221i	0.951803	−	0.306710i	$-0.0992281\pi$
$397$	4.18986	+	7.25706i	0.210283	+	0.364221i	−0.741520	+	0.670931i	$0.765895\pi$
$398$	0.569791	+	0.671477i	0.0285610	+	0.0336581i
$399$		0			0
$400$	12.0476	+	4.08565i	0.602380	+	0.204282i
$401$	−19.2770	+	11.1296i	−0.962648	+	0.555785i	−0.896987	−	0.442057i	$-0.854249\pi$
$401$	−19.2770	+	11.1296i	−0.962648	+	0.555785i	−0.0656611	+	0.997842i	$0.520916\pi$
$402$		0			0
$403$	6.17767	+	3.56668i	0.307732	+	0.177669i
$404$	−4.31543	−	11.4607i	−0.214701	−	0.570191i
$405$		0			0
$406$	1.15015	−	26.9701i	0.0570808	−	1.33850i
$407$	4.92715			0.244230
$408$		0			0
$409$	9.60372	−	16.6341i	0.474873	−	0.822505i	−0.524713	−	0.851279i	$-0.675827\pi$
$409$	9.60372	−	16.6341i	0.474873	−	0.822505i	0.999586	+	0.0287748i	$0.00916058\pi$
$410$	3.58006	+	19.6672i	0.176807	+	0.971293i
$411$		0			0
$412$	−14.0950	−	2.32496i	−0.694410	−	0.114542i
$413$	0.838271	−	3.70203i	0.0412486	−	0.182165i
$414$		0			0
$415$	−22.3462	+	12.9016i	−1.09693	+	0.633314i
$416$	3.89941	−	26.3546i	0.191184	−	1.29214i
$417$		0			0
$418$	−6.76457	+	18.9101i	−0.330866	+	0.924923i
$419$	37.1132			1.81310			0.906550	−	0.422098i	$-0.138706\pi$
$419$	37.1132			1.81310			0.906550	+	0.422098i	$0.138706\pi$
$420$		0			0
$421$	−1.14540			−0.0558236			−0.0279118	−	0.999610i	$-0.508886\pi$
$421$	−1.14540			−0.0558236			−0.0279118	+	0.999610i	$0.508886\pi$
$422$	−9.05380	+	25.3095i	−0.440732	+	1.23205i
$423$		0			0
$424$	0.155885	+	9.39913i	0.00757044	+	0.456462i
$425$	19.3544	−	11.1743i	0.938826	−	0.542032i
$426$		0			0
$427$	−28.3700	−	26.2329i	−1.37292	−	1.26950i
$428$	0.842920	−	5.11018i	0.0407441	−	0.247010i
$429$		0			0
$430$	5.35540	+	29.4201i	0.258261	+	1.41876i
$431$	16.4788	−	28.5421i	0.793756	−	1.37483i	−0.129870	−	0.991531i	$-0.541456\pi$
$431$	16.4788	−	28.5421i	0.793756	−	1.37483i	0.923626	−	0.383295i	$-0.125211\pi$
$432$		0			0
$433$	28.0131			1.34623			0.673113	−	0.739540i	$-0.264957\pi$
$433$	28.0131			1.34623			0.673113	+	0.739540i	$0.264957\pi$
$434$	4.78282	+	3.04018i	0.229583	+	0.145933i
$435$		0			0
$436$	−5.15473	+	1.94097i	−0.246867	+	0.0929556i
$437$	34.1315	+	19.7058i	1.63273	+	0.942658i
$438$		0			0
$439$	13.1619	−	7.59904i	0.628184	−	0.362682i	−0.151864	−	0.988401i	$-0.548528\pi$
$439$	13.1619	−	7.59904i	0.628184	−	0.362682i	0.780048	+	0.625719i	$0.215194\pi$
$440$	−12.3086	+	7.38118i	−0.586788	+	0.351884i
$441$		0			0
$442$	−30.2818	−	35.6859i	−1.44036	−	1.69741i
$443$	15.4210	+	26.7099i	0.732673	+	1.26903i	0.955737	+	0.294223i	$0.0950608\pi$
$443$	15.4210	+	26.7099i	0.732673	+	1.26903i	−0.223064	+	0.974804i	$0.571606\pi$
$444$		0			0
$445$	−9.27144	+	16.0586i	−0.439508	+	0.761251i
$446$	−6.36378	+	17.7897i	−0.301334	+	0.842368i
$447$		0			0
$448$	3.98727	−	20.7871i	0.188381	−	0.982096i
$449$			24.0119i			1.13319i	0.823995	+	0.566596i	$0.191740\pi$
$449$			24.0119i			1.13319i	−0.823995	+	0.566596i	$0.808260\pi$
$450$		0			0
$451$	−7.59336	−	4.38403i	−0.357557	−	0.206436i
$452$	−23.2806	+	28.3760i	−1.09503	+	1.33469i
$453$		0			0
$454$	−4.24759	+	3.60435i	−0.199349	+	0.169160i
$455$	−24.1954	+	26.1665i	−1.13430	+	1.22671i
$456$		0			0
$457$	−17.3211	−	30.0010i	−0.810246	−	1.40339i	−0.912692	−	0.408649i	$-0.866000\pi$
$457$	−17.3211	−	30.0010i	−0.810246	−	1.40339i	0.102446	−	0.994739i	$-0.467333\pi$
$458$	−0.731891	−	4.02067i	−0.0341990	−	0.187873i
$459$		0			0
$460$	9.92476	+	26.3577i	0.462744	+	1.22893i
$461$		−	25.4518i		−	1.18541i	−0.805421	−	0.592704i	$-0.798061\pi$
$461$		−	25.4518i		−	1.18541i	0.805421	−	0.592704i	$-0.201939\pi$
$462$		0			0
$463$			27.9163i			1.29738i	0.761053	+	0.648690i	$0.224683\pi$
$463$			27.9163i			1.29738i	−0.761053	+	0.648690i	$0.775317\pi$
$464$	−28.3023	+	5.63835i	−1.31390	+	0.261754i
$465$		0			0
$466$	20.8449	−	3.79444i	0.965619	−	0.175774i
$467$	19.5636	+	33.8852i	0.905297	+	1.56802i	0.820518	+	0.571621i	$0.193685\pi$
$467$	19.5636	+	33.8852i	0.905297	+	1.56802i	0.0847796	+	0.996400i	$0.472981\pi$
$468$		0			0
$469$	−7.69680	−	1.74283i	−0.355405	−	0.0804763i
$470$	−14.5851	−	17.1880i	−0.672760	−	0.792822i
$471$		0			0
$472$	−4.05727	+	0.0672900i	−0.186751	+	0.00309727i
$473$	−11.3589	−	6.55805i	−0.522281	−	0.301539i
$474$		0			0
$475$			25.4579i			1.16809i
$476$	−22.8283	−	29.3509i	−1.04633	−	1.34529i
$477$		0			0
$478$	−12.9702	−	4.63974i	−0.593245	−	0.212217i
$479$	−14.2074	+	24.6080i	−0.649155	+	1.12437i	0.334170	+	0.942513i	$0.391544\pi$
$479$	−14.2074	+	24.6080i	−0.649155	+	1.12437i	−0.983325	+	0.181857i	$0.941789\pi$
$480$		0			0
$481$	−6.53983	−	11.3273i	−0.298190	−	0.516481i
$482$	−6.49483	+	5.51127i	−0.295831	+	0.251032i
$483$		0			0
$484$	−2.55599	+	15.4956i	−0.116181	+	0.704345i
$485$	2.65550	−	1.53315i	0.120580	−	0.0696168i
$486$		0			0
$487$	−28.0663	−	16.2041i	−1.27180	−	0.734276i	−0.296476	−	0.955040i	$-0.595812\pi$
$487$	−28.0663	−	16.2041i	−1.27180	−	0.734276i	−0.975327	+	0.220764i	$0.929145\pi$
$488$	−20.0577	+	36.1110i	−0.907970	+	1.63467i
$489$		0			0
$490$	−20.0909	+	19.9508i	−0.907615	+	0.901283i
$491$	−19.3004			−0.871017			−0.435508	−	0.900185i	$-0.643431\pi$
$491$	−19.3004			−0.871017			−0.435508	+	0.900185i	$0.643431\pi$
$492$		0			0
$493$	−25.3485	+	43.9050i	−1.14164	+	1.97738i
$494$	52.4521	−	9.54798i	2.35993	−	0.429584i
$495$		0			0
$496$	1.94577	−	5.73762i	0.0873678	−	0.257627i
$497$	−28.9460	+	8.98318i	−1.29840	+	0.402951i
$498$		0			0
$499$	−22.5026	+	12.9919i	−1.00735	+	0.581596i	−0.910416	−	0.413694i	$-0.864238\pi$
$499$	−22.5026	+	12.9919i	−1.00735	+	0.581596i	−0.0969381	+	0.995290i	$0.530905\pi$
$500$	6.60204	−	8.04702i	0.295252	−	0.359874i
$501$		0			0
$502$	−3.93887	−	1.40902i	−0.175801	−	0.0628878i
$503$	17.7613			0.791939			0.395969	−	0.918264i	$-0.370409\pi$
$503$	17.7613			0.791939			0.395969	+	0.918264i	$0.370409\pi$
$504$		0			0
$505$	17.5130			0.779317
$506$	−11.6314	−	4.16082i	−0.517080	−	0.184971i
$507$		0			0
$508$	10.3879	−	12.6615i	0.460888	−	0.561762i
$509$	22.5593	−	13.0246i	0.999923	−	0.577306i	0.0916978	−	0.995787i	$-0.470771\pi$
$509$	22.5593	−	13.0246i	0.999923	−	0.577306i	0.908226	+	0.418481i	$0.137437\pi$
$510$		0			0
$511$	−0.0285571	+	0.126116i	−0.00126329	+	0.00557903i
$512$	−22.5994	+	1.12526i	−0.998763	+	0.0497300i
$513$		0			0
$514$	1.68627	−	0.306956i	0.0743782	−	0.0135392i
$515$	10.2146	−	17.6922i	0.450108	−	0.779610i
$516$		0			0
$517$	9.88731			0.434844
$518$	−4.80758	−	9.21246i	−0.211233	−	0.404772i
$519$		0			0
$520$	33.3062	+	18.4998i	1.46057	+	0.811271i
$521$	29.2252	+	16.8732i	1.28038	+	0.739228i	0.976918	−	0.213615i	$-0.0685238\pi$
$521$	29.2252	+	16.8732i	1.28038	+	0.739228i	0.303463	+	0.952843i	$0.401857\pi$
$522$		0			0
$523$	17.2979	−	9.98697i	0.756386	−	0.436700i	−0.0716106	−	0.997433i	$-0.522814\pi$
$523$	17.2979	−	9.98697i	0.756386	−	0.436700i	0.827997	+	0.560733i	$0.189481\pi$
$524$	0.100193	−	0.607417i	0.00437695	−	0.0265351i
$525$		0			0
$526$	11.7151	−	9.94101i	0.510803	−	0.433449i
$527$	−5.32170	−	9.21745i	−0.231817	−	0.401519i
$528$		0			0
$529$	−0.620877	+	1.07539i	−0.0269946	+	0.0467561i
$530$	−12.6577	−	4.52796i	−0.549817	−	0.196682i
$531$		0			0
$532$	41.9572	−	5.80325i	1.81908	−	0.251603i
$533$			23.2757i			1.00818i
$534$		0			0
$535$	6.41435	+	3.70333i	0.277316	+	0.160109i
$536$	0.139901	+	8.43538i	0.00604281	+	0.364353i
$537$		0			0
$538$	7.00639	+	8.25676i	0.302067	+	0.355974i
$539$	−0.970640	−	12.3809i	−0.0418084	−	0.533282i
$540$		0			0
$541$	3.91821	+	6.78654i	0.168457	+	0.291776i	0.937878	−	0.346966i	$-0.112788\pi$
$541$	3.91821	+	6.78654i	0.168457	+	0.291776i	−0.769421	+	0.638743i	$0.779455\pi$
$542$	27.6690	−	5.03665i	1.18849	−	0.216343i
$543$		0			0
$544$	−24.7000	+	31.1453i	−1.05900	+	1.33534i
$545$		−	7.87688i		−	0.337409i
$546$		0			0
$547$		−	42.3065i		−	1.80890i	−0.426584	−	0.904448i	$-0.640283\pi$
$547$		−	42.3065i		−	1.80890i	0.426584	−	0.904448i	$-0.359717\pi$
$548$	−2.96784	−	7.88183i	−0.126780	−	0.336695i
$549$		0			0
$550$	−1.42905	−	7.85053i	−0.0609349	−	0.334748i
$551$	−28.8753	−	50.0134i	−1.23013	−	2.13064i
$552$		0			0
$553$	2.40215	−	2.59785i	0.102150	−	0.110472i
$554$	−7.18493	+	6.09687i	−0.305259	+	0.259031i
$555$		0			0
$556$	13.3817	−	16.3106i	0.567512	−	0.691724i
$557$	9.26900	+	5.35146i	0.392740	+	0.226749i	0.683347	−	0.730094i	$-0.260524\pi$
$557$	9.26900	+	5.35146i	0.392740	+	0.226749i	−0.290607	+	0.956843i	$0.593857\pi$
$558$		0			0
$559$			34.8181i			1.47265i
$560$	25.8107	+	15.8117i	1.09070	+	0.668167i
$561$		0			0
$562$	4.62947	−	12.9415i	0.195282	−	0.545905i
$563$	4.57187	−	7.91870i	0.192681	−	0.333734i	−0.753457	−	0.657497i	$-0.771615\pi$
$563$	4.57187	−	7.91870i	0.192681	−	0.333734i	0.946138	+	0.323764i	$0.104948\pi$
$564$		0			0
$565$	−26.2446	−	45.4570i	−1.10412	−	1.91239i
$566$	−6.92320	−	8.15873i	−0.291004	−	0.342937i
$567$		0			0
$568$	16.6633	+	27.7871i	0.699177	+	1.16592i
$569$	−25.5092	+	14.7277i	−1.06940	+	0.617419i	−0.928018	−	0.372536i	$-0.878488\pi$
$569$	−25.5092	+	14.7277i	−1.06940	+	0.617419i	−0.141384	+	0.989955i	$0.545155\pi$
$570$		0			0
$571$	28.0410	+	16.1895i	1.17348	+	0.677508i	0.954497	−	0.298221i	$-0.0963931\pi$
$571$	28.0410	+	16.1895i	1.17348	+	0.677508i	0.218982	+	0.975729i	$0.429726\pi$
$572$	−15.6389	+	5.88869i	−0.653895	+	0.246219i
$573$		0			0
$574$	−0.787879	+	18.4752i	−0.0328854	+	0.771139i
$575$	−15.6589			−0.653021
$576$		0			0
$577$	−2.89208	+	5.00923i	−0.120399	+	0.208537i	−0.919925	−	0.392094i	$-0.871751\pi$
$577$	−2.89208	+	5.00923i	−0.120399	+	0.208537i	0.799526	+	0.600631i	$0.205084\pi$
$578$	8.20058	+	45.0501i	0.341099	+	1.87384i
$579$		0			0
$580$	6.71662	−	40.7193i	0.278893	−	1.69078i
$581$	−22.7965	+	7.07473i	−0.945758	+	0.293509i
$582$		0			0
$583$	5.10642	−	2.94820i	0.211486	−	0.122102i
$584$	0.138218	−	0.00229234i	0.00571949	−	9.48579e-5i
$585$		0			0
$586$	2.59530	−	7.25507i	0.107211	−	0.299704i
$587$	−30.3210			−1.25148			−0.625740	−	0.780032i	$-0.715203\pi$
$587$	−30.3210			−1.25148			−0.625740	+	0.780032i	$0.715203\pi$
$588$		0			0
$589$	12.1242			0.499569
$590$	1.95456	−	5.46390i	0.0804680	−	0.224945i
$591$		0			0
$592$	−8.34997	+	7.32709i	−0.343182	+	0.301141i
$593$	−15.6450	+	9.03263i	−0.642462	+	0.370926i	−0.785562	−	0.618782i	$-0.787626\pi$
$593$	−15.6450	+	9.03263i	−0.642462	+	0.370926i	0.143100	+	0.989708i	$0.454293\pi$
$594$		0			0
$595$	50.7854	−	15.7609i	2.08200	−	0.646133i
$596$	−33.8100	−	5.57694i	−1.38491	−	0.228440i
$597$		0			0
$598$	5.87288	+	32.2628i	0.240160	+	1.31932i
$599$	−1.36569	+	2.36544i	−0.0558006	+	0.0966494i	−0.892576	−	0.450896i	$-0.851104\pi$
$599$	−1.36569	+	2.36544i	−0.0558006	+	0.0966494i	0.836776	+	0.547546i	$0.184438\pi$
$600$		0			0
$601$	12.7951			0.521925			0.260962	−	0.965349i	$-0.415960\pi$
$601$	12.7951			0.521925			0.260962	+	0.965349i	$0.415960\pi$
$602$	−1.17859	+	27.6370i	−0.0480356	+	1.12640i
$603$		0			0
$604$	−4.95013	−	13.1463i	−0.201418	−	0.534915i
$605$	−19.4502	−	11.2296i	−0.790764	−	0.456548i
$606$		0			0
$607$	21.6019	−	12.4718i	0.876792	−	0.506216i	0.00719299	−	0.999974i	$-0.497710\pi$
$607$	21.6019	−	12.4718i	0.876792	−	0.506216i	0.869599	+	0.493758i	$0.164377\pi$
$608$	−16.6571	−	42.1062i	−0.675534	−	1.70763i
$609$		0			0
$610$	−38.2207	−	45.0416i	−1.54751	−	1.82368i
$611$	−13.1235	−	22.7305i	−0.530919	−	0.919578i
$612$		0			0
$613$	−14.8231	+	25.6744i	−0.598699	+	1.03698i	0.394314	+	0.918976i	$0.370982\pi$
$613$	−14.8231	+	25.6744i	−0.598699	+	1.03698i	−0.993013	+	0.118002i	$0.962351\pi$
$614$	−0.756355	+	2.11436i	−0.0305240	+	0.0853287i
$615$		0			0
$616$	−12.6127	+	4.14479i	−0.508182	+	0.166999i
$617$			26.3663i			1.06147i	0.847539	+	0.530734i	$0.178083\pi$
$617$			26.3663i			1.06147i	−0.847539	+	0.530734i	$0.821917\pi$
$618$		0			0
$619$	17.3094	+	9.99359i	0.695724	+	0.401676i	0.805753	−	0.592252i	$-0.201761\pi$
$619$	17.3094	+	9.99359i	0.695724	+	0.401676i	−0.110029	+	0.993928i	$0.535094\pi$
$620$	6.69831	+	5.49551i	0.269010	+	0.220705i
$621$		0			0
$622$	−21.4025	+	18.1614i	−0.858162	+	0.728205i
$623$	−11.6453	+	12.5941i	−0.466561	+	0.504570i
$624$		0			0
$625$	15.3935	+	26.6624i	0.615742	+	1.06650i
$626$	−2.66919	−	14.6633i	−0.106682	−	0.586062i
$627$		0			0
$628$	−3.80330	+	1.43210i	−0.151768	+	0.0571470i
$629$			19.5156i			0.778138i
$630$		0			0
$631$		−	7.91131i		−	0.314944i	−0.987523	−	0.157472i	$-0.949666\pi$
$631$		−	7.91131i		−	0.314944i	0.987523	−	0.157472i	$-0.0503344\pi$
$632$	−3.30669	−	1.83669i	−0.131533	−	0.0730596i
$633$		0			0
$634$	18.6224	−	3.38988i	0.739590	−	0.134629i
$635$	11.7104	+	20.2831i	0.464715	+	0.804909i
$636$		0			0
$637$	−27.1748	+	18.6646i	−1.07670	+	0.739520i
$638$	11.7118	+	13.8019i	0.463675	+	0.546424i
$639$		0			0
$640$	9.88275	−	30.8127i	0.390650	−	1.21798i
$641$	30.8675	+	17.8214i	1.21919	+	0.703902i	0.964746	−	0.263185i	$-0.0847728\pi$
$641$	30.8675	+	17.8214i	1.21919	+	0.703902i	0.254448	+	0.967086i	$0.418106\pi$
$642$		0			0
$643$		−	7.96178i		−	0.313982i	−0.987600	−	0.156991i	$-0.949821\pi$
$643$		−	7.96178i		−	0.313982i	0.987600	−	0.156991i	$-0.0501794\pi$
$644$	3.56952	+	25.8075i	0.140659	+	1.01696i
$645$		0			0
$646$	−74.8997	−	26.7933i	−2.94689	−	1.05417i
$647$	24.0551	−	41.6647i	0.945704	−	1.63801i	0.191368	−	0.981518i	$-0.438708\pi$
$647$	24.0551	−	41.6647i	0.945704	−	1.63801i	0.754336	−	0.656489i	$-0.227959\pi$
$648$		0			0
$649$	1.27263	+	2.20426i	0.0499552	+	0.0865249i
$650$	−16.1513	+	13.7054i	−0.633504	+	0.537569i
$651$		0			0
$652$	10.9152	+	1.80045i	0.427470	+	0.0705109i
$653$	29.0569	−	16.7760i	1.13708	−	0.656495i	0.191376	−	0.981517i	$-0.438705\pi$
$653$	29.0569	−	16.7760i	1.13708	−	0.656495i	0.945706	+	0.325022i	$0.105372\pi$
$654$		0			0
$655$	0.762436	+	0.440193i	0.0297909	+	0.0171998i
$656$	19.3878	−	3.86241i	0.756965	−	0.150802i
$657$		0			0
$658$	−9.64737	−	18.4866i	−0.376094	−	0.720684i
$659$	−9.10230			−0.354575			−0.177288	−	0.984159i	$-0.556732\pi$
$659$	−9.10230			−0.354575			−0.177288	+	0.984159i	$0.556732\pi$
$660$		0			0
$661$	−7.12959	+	12.3488i	−0.277309	+	0.480313i	−0.970715	−	0.240234i	$-0.922776\pi$
$661$	−7.12959	+	12.3488i	−0.277309	+	0.480313i	0.693406	+	0.720547i	$0.256109\pi$
$662$	−38.5752	+	7.02193i	−1.49927	+	0.272915i
$663$		0			0
$664$	13.1232	+	21.8838i	0.509281	+	0.849258i
$665$	−13.3772	+	59.0773i	−0.518745	+	2.29092i
$666$		0			0
$667$	30.7628	−	17.7609i	1.19114	−	0.687705i
$668$	−9.85154	−	8.08252i	−0.381167	−	0.312722i
$669$		0			0
$670$	−11.3599	−	4.06368i	−0.438870	−	0.156994i
$671$	25.9100			1.00025
$672$		0			0
$673$	1.00872			0.0388833			0.0194417	−	0.999811i	$-0.493811\pi$
$673$	1.00872			0.0388833			0.0194417	+	0.999811i	$0.493811\pi$
$674$	25.6648	+	9.18087i	0.988570	+	0.353634i
$675$		0			0
$676$	14.1947	+	11.6458i	0.545950	+	0.447915i
$677$	30.2292	−	17.4528i	1.16180	−	0.670766i	0.210066	−	0.977687i	$-0.432632\pi$
$677$	30.2292	−	17.4528i	1.16180	−	0.670766i	0.951735	+	0.306921i	$0.0992988\pi$
$678$		0			0
$679$	2.70901	−	0.840721i	0.103962	−	0.0322639i
$680$	−29.2356	−	48.7522i	−1.12113	−	1.86956i
$681$		0			0
$682$	−3.73878	+	0.680580i	−0.143165	+	0.0260607i
$683$	22.7839	−	39.4629i	0.871803	−	1.51001i	0.0116726	−	0.999932i	$-0.496284\pi$
$683$	22.7839	−	39.4629i	0.871803	−	1.51001i	0.860130	−	0.510075i	$-0.170382\pi$
$684$		0			0
$685$	12.0441			0.460183
$686$	−22.2018	+	13.8953i	−0.847670	+	0.530523i
$687$		0			0
$688$	29.0021	−	5.77776i	1.10569	−	0.220275i
$689$	−13.5555	−	7.82630i	−0.516425	−	0.298158i
$690$		0			0
$691$	−6.57653	+	3.79696i	−0.250183	+	0.144443i	−0.619848	−	0.784722i	$-0.712806\pi$
$691$	−6.57653	+	3.79696i	−0.250183	+	0.144443i	0.369665	+	0.929165i	$0.379472\pi$
$692$	41.8952	+	6.91059i	1.59262	+	0.262701i
$693$		0			0
$694$	1.45802	−	1.23723i	0.0553458	−	0.0469644i
$695$	15.0855	+	26.1288i	0.572225	+	0.991122i
$696$		0			0
$697$	17.3644	−	30.0760i	0.657723	−	1.13921i
$698$	−45.6795	−	16.3406i	−1.72899	−	0.618500i
$699$		0			0
$700$	−13.2840	+	10.3320i	−0.502089	+	0.390511i
$701$		−	44.3539i		−	1.67522i	−0.546267	−	0.837611i	$-0.683951\pi$
$701$		−	44.3539i		−	1.67522i	0.546267	−	0.837611i	$-0.316049\pi$
$702$		0			0
$703$	−19.2524	−	11.1154i	−0.726119	−	0.419225i
$704$	7.50019	+	12.0494i	0.282674	+	0.454129i
$705$		0			0
$706$	−11.3324	−	13.3548i	−0.426500	−	0.502614i
$707$	15.8003	+	3.57774i	0.594230	+	0.134555i
$708$		0			0
$709$	12.1387	+	21.0249i	0.455879	+	0.789605i	0.998738	−	0.0502185i	$-0.0159918\pi$
$709$	12.1387	+	21.0249i	0.455879	+	0.789605i	−0.542860	+	0.839823i	$0.682658\pi$
$710$	−45.5858	+	8.29808i	−1.71080	+	0.311422i
$711$		0			0
$712$	16.0304	+	8.90404i	0.600765	+	0.333693i
$713$			7.45748i			0.279285i
$714$		0			0
$715$		−	23.8976i		−	0.893720i
$716$	−38.3523	+	14.4412i	−1.43329	+	0.539695i
$717$		0			0
$718$	3.22506	+	17.7170i	0.120358	+	0.661192i
$719$	13.9425	+	24.1491i	0.519967	+	0.900610i	0.999731	+	0.0232120i	$0.00738927\pi$
$719$	13.9425	+	24.1491i	0.519967	+	0.900610i	−0.479763	+	0.877398i	$0.659277\pi$
$720$		0			0
$721$	12.8300	−	13.8752i	0.477813	−	0.516739i
$722$	48.6043	−	41.2438i	1.80886	−	1.53494i
$723$		0			0
$724$	−25.6654	−	21.0567i	−0.953846	−	0.782566i
$725$	19.8711	+	11.4726i	0.737996	+	0.426082i
$726$		0			0
$727$		−	0.853452i		−	0.0316528i	−0.999875	−	0.0158264i	$-0.994962\pi$
$727$		−	0.853452i		−	0.0316528i	0.999875	−	0.0158264i	$-0.00503791\pi$
$728$	26.2697	+	23.4948i	0.973618	+	0.870774i
$729$		0			0
$730$	−0.0665853	+	0.186137i	−0.00246443	+	0.00688923i
$731$	25.9753	−	44.9906i	0.960731	−	1.66404i
$732$		0			0
$733$	12.7372	+	22.0614i	0.470458	+	0.814857i	0.999429	−	0.0337825i	$-0.0107553\pi$
$733$	12.7372	+	22.0614i	0.470458	+	0.814857i	−0.528971	+	0.848640i	$0.677422\pi$
$734$	−11.9112	−	14.0368i	−0.439649	−	0.518109i
$735$		0			0
$736$	25.8991	−	10.2456i	0.954654	−	0.377658i
$737$	4.58283	−	2.64590i	0.168811	−	0.0974629i
$738$		0			0
$739$	30.3461	+	17.5203i	1.11630	+	0.644496i	0.940454	−	0.339921i	$-0.110401\pi$
$739$	30.3461	+	17.5203i	1.11630	+	0.644496i	0.175846	+	0.984418i	$0.443734\pi$
$740$	−5.59822	−	14.8675i	−0.205795	−	0.546539i
$741$		0			0
$742$	−10.4948	−	6.67100i	−0.385278	−	0.244900i
$743$	28.8253			1.05750			0.528750	−	0.848778i	$-0.322661\pi$
$743$	28.8253			1.05750			0.528750	+	0.848778i	$0.322661\pi$
$744$		0			0
$745$	24.5020	−	42.4387i	0.897684	−	1.55483i
$746$	1.48268	+	8.14517i	0.0542850	+	0.298216i
$747$		0			0
$748$	24.6011	+	4.05793i	0.899505	+	0.148373i
$749$	5.03049	+	4.65154i	0.183810	+	0.169964i
$750$		0			0
$751$	24.7734	−	14.3029i	0.903994	−	0.521921i	0.0255004	−	0.999675i	$-0.491882\pi$
$751$	24.7734	−	14.3029i	0.903994	−	0.521921i	0.878494	+	0.477753i	$0.158549\pi$
$752$	−16.7559	+	14.7033i	−0.611024	+	0.536173i
$753$		0			0
$754$	16.1849	−	45.2443i	0.589420	−	1.64770i
$755$	20.0887			0.731103
$756$		0			0
$757$	−27.4539			−0.997830			−0.498915	−	0.866651i	$-0.666268\pi$
$757$	−27.4539			−0.997830			−0.498915	+	0.866651i	$0.666268\pi$
$758$	−11.2893	+	31.5588i	−0.410046	+	1.14627i
$759$		0			0
$760$	64.7463	−	1.07382i	2.34859	−	0.0389515i
$761$	24.7788	−	14.3060i	0.898231	−	0.518594i	0.0216049	−	0.999767i	$-0.493122\pi$
$761$	24.7788	−	14.3060i	0.898231	−	0.518594i	0.876626	+	0.481173i	$0.159789\pi$
$762$		0			0
$763$	1.60917	−	7.10655i	0.0582560	−	0.257274i
$764$	−2.28588	+	13.8581i	−0.0827002	+	0.501368i
$765$		0			0
$766$	−4.14919	−	22.7937i	−0.149916	−	0.823570i
$767$	3.37834	−	5.85145i	0.121985	−	0.211284i
$768$		0			0
$769$	4.97212			0.179299			0.0896496	−	0.995973i	$-0.471425\pi$
$769$	4.97212			0.179299			0.0896496	+	0.995973i	$0.471425\pi$
$770$	0.808930	−	18.9688i	0.0291518	−	0.683588i
$771$		0			0
$772$	32.4265	−	12.2099i	1.16705	−	0.439445i
$773$	36.9413	+	21.3281i	1.32869	+	0.767117i	0.985096	−	0.172003i	$-0.0550240\pi$
$773$	36.9413	+	21.3281i	1.32869	+	0.767117i	0.343589	+	0.939120i	$0.388357\pi$
$774$		0			0
$775$	−4.17177	+	2.40857i	−0.149854	+	0.0865184i
$776$	−1.55949	−	2.60055i	−0.0559825	−	0.0933544i
$777$		0			0
$778$	−6.97018	−	8.21409i	−0.249893	−	0.294489i
$779$	19.7803	+	34.2604i	0.708702	+	1.22751i
$780$		0			0
$781$	10.1616	−	17.6003i	0.363609	−	0.629789i
$782$	16.4803	−	46.0701i	0.589335	−	1.64746i
$783$		0			0
$784$	20.0563	+	19.5383i	0.716297	+	0.697795i
$785$		−	5.81177i		−	0.207431i
$786$		0			0
$787$	3.83610	+	2.21477i	0.136742	+	0.0789481i	0.566810	−	0.823848i	$-0.308177\pi$
$787$	3.83610	+	2.21477i	0.136742	+	0.0789481i	−0.430068	+	0.902796i	$0.641511\pi$
$788$	5.60686	−	6.83403i	0.199736	−	0.243452i
$789$		0			0
$790$	4.12448	−	3.49988i	0.146742	−	0.124520i
$791$	−14.3915	−	46.3730i	−0.511704	−	1.64883i
$792$		0			0
$793$	−34.3905	−	59.5661i	−1.22124	−	2.11525i
$794$	2.12234	+	11.6591i	0.0753190	+	0.413767i
$795$		0			0
$796$	0.438873	+	1.16554i	0.0155554	+	0.0413114i
$797$		−	1.10654i		−	0.0391957i	−0.999808	−	0.0195979i	$-0.993761\pi$
$797$		−	1.10654i		−	0.0391957i	0.999808	−	0.0195979i	$-0.00623859\pi$
$798$		0			0
$799$			39.1620i			1.38545i
$800$	14.0962	+	11.1791i	0.498376	+	0.395240i
$801$		0			0
$802$	−30.9703	+	5.63760i	−1.09360	+	0.199070i
$803$	−0.0433543	−	0.0750918i	−0.00152994	−	0.00264993i
$804$		0			0
$805$	−36.3379	−	8.22819i	−1.28074	−	0.290006i
$806$	6.52713	+	7.69197i	0.229908	+	0.270938i
$807$		0			0
$808$	−0.287194	−	17.3164i	−0.0101034	−	0.609190i
$809$	−40.2345	−	23.2294i	−1.41457	−	0.816702i	−0.418755	−	0.908099i	$-0.637533\pi$
$809$	−40.2345	−	23.2294i	−1.41457	−	0.816702i	−0.995815	+	0.0913970i	$0.970867\pi$
$810$		0			0
$811$			12.2358i			0.429657i	0.976652	+	0.214829i	$0.0689193\pi$
$811$			12.2358i			0.429657i	−0.976652	+	0.214829i	$0.931081\pi$
$812$	14.3783	−	35.3650i	0.504581	−	1.24107i
$813$		0			0
$814$	6.56089	+	2.34698i	0.229959	+	0.0822616i
$815$	−7.91017	+	13.7008i	−0.277081	+	0.479919i
$816$		0			0
$817$	29.5892	+	51.2500i	1.03520	+	1.79301i
$818$	20.7115	−	17.5751i	0.724162	−	0.614498i
$819$		0			0
$820$	−4.60105	+	27.8937i	−0.160676	+	0.974092i
$821$	10.1503	−	5.86030i	0.354249	−	0.204526i	−0.312306	−	0.949982i	$-0.601101\pi$
$821$	10.1503	−	5.86030i	0.354249	−	0.204526i	0.666555	+	0.745456i	$0.267768\pi$
$822$		0			0
$823$	29.5545	+	17.0633i	1.03021	+	0.594790i	0.917044	−	0.398787i	$-0.130569\pi$
$823$	29.5545	+	17.0633i	1.03021	+	0.594790i	0.113162	+	0.993577i	$0.463902\pi$
$824$	−17.6611	−	9.80981i	−0.615255	−	0.341741i
$825$		0			0
$826$	2.87964	−	4.53025i	0.100195	−	0.157628i
$827$	−29.7930			−1.03600			−0.518001	−	0.855380i	$-0.673324\pi$
$827$	−29.7930			−1.03600			−0.518001	+	0.855380i	$0.673324\pi$
$828$		0			0
$829$	21.6981	−	37.5822i	0.753605	−	1.30528i	−0.192459	−	0.981305i	$-0.561646\pi$
$829$	21.6981	−	37.5822i	0.753605	−	1.30528i	0.946065	−	0.323978i	$-0.105020\pi$
$830$	−35.9012	+	6.53518i	−1.24615	+	0.226839i
$831$		0			0
$832$	17.7460	−	33.2358i	0.615233	−	1.15224i
$833$	49.0385	−	3.84454i	1.69908	−	0.133205i
$834$		0			0
$835$	15.7817	−	9.11156i	0.546148	−	0.315319i
$836$	−18.0151	+	21.9581i	−0.623066	+	0.759436i
$837$		0			0
$838$	49.4192	+	17.6784i	1.70716	+	0.610689i
$839$	52.4272			1.80999			0.904995	−	0.425423i	$-0.139875\pi$
$839$	52.4272			1.80999			0.904995	+	0.425423i	$0.139875\pi$
$840$		0			0
$841$	−23.0506			−0.794850
$842$	−1.52520	−	0.545598i	−0.0525618	−	0.0188025i
$843$		0			0
$844$	−24.1117	+	29.3890i	−0.829959	+	1.01161i
$845$	−22.7392	+	13.1285i	−0.782253	+	0.451634i
$846$		0			0
$847$	−15.2540	−	14.1049i	−0.524132	−	0.484649i
$848$	−4.26957	+	12.5899i	−0.146618	+	0.432340i
$849$		0			0
$850$	31.0946	−	5.66023i	1.06654	−	0.194144i
$851$	6.83698	−	11.8420i	0.234369	−	0.405938i
$852$		0			0
$853$	12.6354			0.432628			0.216314	−	0.976324i	$-0.430597\pi$
$853$	12.6354			0.432628			0.216314	+	0.976324i	$0.430597\pi$
$854$	−25.2813	−	48.4449i	−0.865107	−	1.65775i
$855$		0			0
$856$	3.55658	−	6.40309i	0.121561	−	0.218853i
$857$	10.6106	+	6.12603i	0.362451	+	0.209261i	0.670155	−	0.742221i	$-0.266227\pi$
$857$	10.6106	+	6.12603i	0.362451	+	0.209261i	−0.307704	+	0.951482i	$0.599561\pi$
$858$		0			0
$859$	−45.0377	+	26.0026i	−1.53667	+	0.887196i	−0.537637	+	0.843176i	$0.680683\pi$
$859$	−45.0377	+	26.0026i	−1.53667	+	0.887196i	−0.999031	+	0.0440193i	$0.985984\pi$
$860$	−6.88270	+	41.7261i	−0.234698	+	1.42285i
$861$		0			0
$862$	35.5385	−	30.1567i	1.21045	−	1.02714i
$863$	−6.94583	−	12.0305i	−0.236439	−	0.409524i	0.723251	−	0.690585i	$-0.242647\pi$
$863$	−6.94583	−	12.0305i	−0.236439	−	0.409524i	−0.959690	+	0.281061i	$0.909314\pi$
$864$		0			0
$865$	−30.3613	+	52.5873i	−1.03232	+	1.78802i
$866$	37.3017	+	13.3437i	1.26756	+	0.453436i
$867$		0			0
$868$	4.92055	+	6.32647i	0.167014	+	0.214734i
$869$			2.37259i			0.0804846i
$870$		0			0
$871$	−12.1656	−	7.02382i	−0.412216	−	0.237993i
$872$	−7.78848	+	0.129172i	−0.263751	+	0.00437433i
$873$		0			0
$874$	36.0622	+	42.4980i	1.21982	+	1.43751i
$875$	4.08123	+	13.1507i	0.137971	+	0.444575i
$876$		0			0
$877$	−19.2703	−	33.3771i	−0.650711	−	1.12706i	−0.982951	−	0.183870i	$-0.941138\pi$
$877$	−19.2703	−	33.3771i	−0.650711	−	1.12706i	0.332240	−	0.943195i	$-0.392196\pi$
$878$	21.1458	−	3.84923i	0.713637	−	0.129905i
$879$		0			0
$880$	−19.9058	+	3.96560i	−0.671023	+	0.133680i
$881$		−	2.21967i		−	0.0747826i	−0.999301	−	0.0373913i	$-0.988095\pi$
$881$		−	2.21967i		−	0.0747826i	0.999301	−	0.0373913i	$-0.0119048\pi$
$882$		0			0
$883$		−	43.9289i		−	1.47833i	−0.673527	−	0.739163i	$-0.735221\pi$
$883$		−	43.9289i		−	1.47833i	0.673527	−	0.739163i	$-0.264779\pi$
$884$	−23.3241	−	61.9430i	−0.784475	−	2.08337i
$885$		0			0
$886$	7.81136	+	42.9120i	0.262428	+	1.44166i
$887$	−7.80639	−	13.5211i	−0.262113	−	0.453993i	0.704690	−	0.709515i	$-0.251086\pi$
$887$	−7.80639	−	13.5211i	−0.262113	−	0.453993i	−0.966803	+	0.255522i	$0.917753\pi$
$888$		0			0
$889$	6.42155	+	20.6918i	0.215372	+	0.693981i
$890$	−19.9949	+	16.9670i	−0.670232	+	0.568735i
$891$		0			0
$892$	−16.9478	+	20.6571i	−0.567453	+	0.691652i
$893$	−38.6338	−	22.3053i	−1.29283	−	0.746417i
$894$		0			0
$895$		−	58.6058i		−	1.95897i
$896$	15.2110	−	25.7803i	0.508164	−	0.861261i
$897$		0			0
$898$	−11.4377	+	31.9738i	−0.381683	+	1.06698i
$899$	5.46378	−	9.46355i	0.182227	−	0.315627i
$900$		0			0
$901$	11.6773	+	20.2257i	0.389027	+	0.673815i
$902$	−8.02289	−	9.45467i	−0.267133	−	0.314806i
$903$		0			0
$904$	−44.5164	+	26.6955i	−1.48059	+	0.887879i
$905$	41.1147	−	23.7376i	1.36670	−	0.789064i
$906$		0			0
$907$	−0.925872	−	0.534552i	−0.0307431	−	0.0177495i	0.484550	−	0.874764i	$-0.338983\pi$
$907$	−0.925872	−	0.534552i	−0.0307431	−	0.0177495i	−0.515293	+	0.857014i	$0.672317\pi$
$908$	−7.37288	+	2.77620i	−0.244678	+	0.0921313i
$909$		0			0
$910$	−44.6822	+	23.3177i	−1.48120	+	0.772973i
$911$	35.4745			1.17532			0.587661	−	0.809107i	$-0.300049\pi$
$911$	35.4745			1.17532			0.587661	+	0.809107i	$0.300049\pi$
$912$		0			0
$913$	8.00276	−	13.8612i	0.264853	−	0.458739i
$914$	−8.77384	−	48.1994i	−0.290213	−	1.59429i
$915$		0			0
$916$	0.940617	−	5.70246i	0.0310789	−	0.188415i
$917$	0.597945	+	0.552902i	0.0197459	+	0.0182584i
$918$		0			0
$919$	−37.2941	+	21.5318i	−1.23022	+	0.710267i	−0.967075	−	0.254490i	$-0.918092\pi$
$919$	−37.2941	+	21.5318i	−1.23022	+	0.710267i	−0.263143	+	0.964757i	$0.584759\pi$
$920$	0.660497	+	39.8248i	0.0217759	+	1.31299i
$921$		0			0
$922$	12.1236	−	33.8911i	0.399269	−	1.11614i
$923$	−53.9499			−1.77578
$924$		0			0
$925$	8.83265			0.290416
$926$	−13.2975	+	37.1728i	−0.436984	+	1.22157i
$927$		0			0
$928$	−40.3725	−	5.97349i	−1.32529	−	0.196089i
$929$	1.25933	−	0.727077i	0.0413174	−	0.0238546i	−0.479199	−	0.877706i	$-0.659073\pi$
$929$	1.25933	−	0.727077i	0.0413174	−	0.0238546i	0.520516	+	0.853852i	$0.325739\pi$
$930$		0			0
$931$	−24.1379	+	50.5669i	−0.791088	+	1.65726i
$932$	29.5640	+	4.87656i	0.968401	+	0.159737i
$933$		0			0
$934$	9.90979	+	54.4397i	0.324258	+	1.78132i
$935$	−17.8283	+	30.8796i	−0.583049	+	1.00987i
$936$		0			0
$937$	−31.7757			−1.03807			−0.519034	−	0.854754i	$-0.673708\pi$
$937$	−31.7757			−1.03807			−0.519034	+	0.854754i	$0.673708\pi$
$938$	−9.41873	−	5.98698i	−0.307533	−	0.195482i
$939$		0			0
$940$	−11.2339	−	29.8345i	−0.366411	−	0.973095i
$941$	23.5114	+	13.5743i	0.766450	+	0.442510i	0.831607	−	0.555365i	$-0.187421\pi$
$941$	23.5114	+	13.5743i	0.766450	+	0.442510i	−0.0651568	+	0.997875i	$0.520755\pi$
$942$		0			0
$943$	−21.0733	+	12.1667i	−0.686240	+	0.396201i
$944$	−5.43463	−	1.84302i	−0.176882	−	0.0599853i
$945$		0			0
$946$	−12.0014	−	14.1432i	−0.390199	−	0.459835i
$947$	−25.5373	−	44.2319i	−0.829852	−	1.43735i	−0.898154	−	0.439680i	$-0.855092\pi$
$947$	−25.5373	−	44.2319i	−0.829852	−	1.43735i	0.0683027	−	0.997665i	$-0.478242\pi$
$948$		0			0
$949$	−0.115089	+	0.199339i	−0.00373593	+	0.00647082i
$950$	−12.1265	+	33.8992i	−0.393436	+	1.09983i
$951$		0			0
$952$	−16.4168	−	49.9570i	−0.532072	−	1.61911i
$953$		−	18.8458i		−	0.610476i	−0.952276	−	0.305238i	$-0.901264\pi$
$953$		−	18.8458i		−	0.610476i	0.952276	−	0.305238i	$-0.0987361\pi$
$954$		0			0
$955$	−17.3948	−	10.0429i	−0.562883	−	0.324980i
$956$	−15.0608	−	12.3564i	−0.487102	−	0.399634i
$957$		0			0
$958$	−30.6400	+	26.0000i	−0.989935	+	0.840022i
$959$	10.8663	+	2.46051i	0.350890	+	0.0794539i
$960$		0			0
$961$	−14.3529	−	24.8600i	−0.462998	−	0.801936i
$962$	−3.31269	−	18.1984i	−0.106805	−	0.586739i
$963$		0			0
$964$	−11.2736	+	4.24498i	−0.363098	+	0.136722i
$965$			49.5505i			1.59509i
$966$		0			0
$967$			9.75651i			0.313748i	0.987619	+	0.156874i	$0.0501417\pi$
$967$			9.75651i			0.313748i	−0.987619	+	0.156874i	$0.949858\pi$
$968$	−10.7846	+	19.4161i	−0.346630	+	0.624057i
$969$		0			0
$970$	4.26630	−	0.776604i	0.136983	−	0.0249353i
$971$	27.7505	+	48.0653i	0.890557	+	1.54249i	0.839209	+	0.543809i	$0.183018\pi$
$971$	27.7505	+	48.0653i	0.890557	+	1.54249i	0.0513476	+	0.998681i	$0.483648\pi$
$972$		0			0
$973$	8.27229	+	26.6553i	0.265198	+	0.854531i
$974$	−29.6539	−	34.9460i	−0.950171	−	1.11974i
$975$		0			0
$976$	−43.9094	+	38.5304i	−1.40551	+	1.23333i
$977$	18.5299	+	10.6982i	0.592824	+	0.342267i	0.766213	−	0.642586i	$-0.222139\pi$
$977$	18.5299	+	10.6982i	0.592824	+	0.342267i	−0.173389	+	0.984853i	$0.555472\pi$
$978$		0			0
$979$		−	11.5020i		−	0.367606i
$980$	−36.2559	+	16.9960i	−1.15815	+	0.542917i
$981$		0			0
$982$	−25.7001	−	9.19349i	−0.820122	−	0.293376i
$983$	1.01003	−	1.74942i	0.0322149	−	0.0557979i	−0.849468	−	0.527639i	$-0.823077\pi$
$983$	1.01003	−	1.74942i	0.0322149	−	0.0557979i	0.881683	+	0.471842i	$0.156411\pi$
$984$		0			0
$985$	6.32071	+	10.9478i	0.201395	+	0.348826i
$986$	−54.6671	+	46.3885i	−1.74096	+	1.47731i
$987$		0			0
$988$	74.3922	+	12.2709i	2.36673	+	0.390391i
$989$	−31.5234	+	18.2001i	−1.00239	+	0.578728i
$990$		0			0
$991$	−26.8179	−	15.4834i	−0.851900	−	0.491845i	0.00939132	−	0.999956i	$-0.497011\pi$
$991$	−26.8179	−	15.4834i	−0.851900	−	0.491845i	−0.861292	+	0.508111i	$0.830344\pi$
$992$	5.32399	−	6.71325i	0.169037	−	0.213146i
$993$		0			0
$994$	−42.8229	−	1.82619i	−1.35826	−	0.0579233i
$995$	−1.78104			−0.0564629
$996$		0			0
$997$	4.71534	−	8.16720i	0.149336	−	0.258658i	−0.781646	−	0.623722i	$-0.785620\pi$
$997$	4.71534	−	8.16720i	0.149336	−	0.258658i	0.930982	+	0.365064i	$0.118953\pi$
$998$	−36.1525	+	6.58092i	−1.14439	+	0.208315i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.d.431.13	yes	28
3.2	odd	2	inner	756.2.be.d.431.2	yes	28
4.3	odd	2		756.2.be.c.431.9	yes	28
7.2	even	3		756.2.be.c.107.6	✓	28
12.11	even	2		756.2.be.c.431.6	yes	28
21.2	odd	6		756.2.be.c.107.9	yes	28
28.23	odd	6	inner	756.2.be.d.107.2	yes	28
84.23	even	6	inner	756.2.be.d.107.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.6	✓	28	7.2	even	3
756.2.be.c.107.9	yes	28	21.2	odd	6
756.2.be.c.431.6	yes	28	12.11	even	2
756.2.be.c.431.9	yes	28	4.3	odd	2
756.2.be.d.107.2	yes	28	28.23	odd	6	inner
756.2.be.d.107.13	yes	28	84.23	even	6	inner
756.2.be.d.431.2	yes	28	3.2	odd	2	inner
756.2.be.d.431.13	yes	28	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33158 + 0.476336i) q^{2} +(1.54621 + 1.26856i) q^{4} +(-2.47695 + 1.43007i) q^{5} +(-2.52686 + 0.784194i) q^{7} +(1.45464 + 2.42570i) q^{8} +(-3.97945 + 0.724388i) q^{10} +(0.887062 - 1.53644i) q^{11} -4.70960 q^{13} +(-3.73826 - 0.159419i) q^{14} +(0.781518 + 3.92291i) q^{16} +(6.08556 + 3.51350i) q^{17} +(-6.93224 + 4.00233i) q^{19} +(-5.64401 - 0.930975i) q^{20} +(1.91305 - 1.62335i) q^{22} +(-2.46180 - 4.26396i) q^{23} +(1.59019 - 2.75429i) q^{25} +(-6.27121 - 2.24335i) q^{26} +(-4.90185 - 1.99295i) q^{28} +7.21461i q^{29} +(-1.31172 - 0.757322i) q^{31} +(-0.827971 + 5.59593i) q^{32} +(6.42980 + 7.57728i) q^{34} +(5.13747 - 5.55600i) q^{35} +(1.38862 + 2.40515i) q^{37} +(-11.1373 + 2.02734i) q^{38} +(-7.07199 - 3.92811i) q^{40} -4.94219i q^{41} -7.39300i q^{43} +(3.32064 - 1.25036i) q^{44} +(-1.24700 - 6.85044i) q^{46} +(2.78654 + 4.82642i) q^{47} +(5.77008 - 3.96310i) q^{49} +(3.42943 - 2.91009i) q^{50} +(-7.28202 - 5.97440i) q^{52} +(2.87828 + 1.66178i) q^{53} +5.07423i q^{55} +(-5.57789 - 4.98870i) q^{56} +(-3.43658 + 9.60683i) q^{58} +(-0.717330 + 1.24245i) q^{59} +(7.30221 + 12.6478i) q^{61} +(-1.38592 - 1.63325i) q^{62} +(-3.76805 + 7.05704i) q^{64} +(11.6654 - 6.73505i) q^{65} +(2.58315 + 1.49138i) q^{67} +(4.95246 + 13.1525i) q^{68} +(9.48747 - 4.95109i) q^{70} +11.4553 q^{71} +(0.0244370 - 0.0423261i) q^{73} +(0.703391 + 3.86410i) q^{74} +(-15.7959 - 2.60552i) q^{76} +(-1.03662 + 4.57799i) q^{77} +(-1.15816 + 0.668665i) q^{79} +(-7.54581 - 8.59923i) q^{80} +(2.35414 - 6.58092i) q^{82} +9.02165 q^{83} -20.0982 q^{85} +(3.52155 - 9.84437i) q^{86} +(5.01729 - 0.0832119i) q^{88} +(5.61463 - 3.24161i) q^{89} +(11.9005 - 3.69324i) q^{91} +(1.60263 - 9.71589i) q^{92} +(1.41149 + 7.75409i) q^{94} +(11.4472 - 19.8271i) q^{95} -1.07208 q^{97} +(9.57109 - 2.52869i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64}+ \cdots - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Introduction

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