LMFDB - Embedded newform 756.2.be.c.431.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			431.6
Character	$\chi$	$=$	756.431
Dual form			756.2.be.c.107.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.253271 + 1.39135i) q^{2} +(-1.87171 - 0.704776i) q^{4} +(2.47695 - 1.43007i) q^{5} +(2.52686 - 0.784194i) q^{7} +(1.45464 - 2.42570i) q^{8} +O(q^{10})$	\(q+(-0.253271 + 1.39135i) q^{2} +(-1.87171 - 0.704776i) q^{4} +(2.47695 - 1.43007i) q^{5} +(2.52686 - 0.784194i) q^{7} +(1.45464 - 2.42570i) q^{8} +(1.36239 + 3.80850i) q^{10} +(0.887062 - 1.53644i) q^{11} -4.70960 q^{13} +(0.451108 + 3.71436i) q^{14} +(3.00658 + 2.63827i) q^{16} +(-6.08556 - 3.51350i) q^{17} +(6.93224 - 4.00233i) q^{19} +(-5.64401 + 0.930975i) q^{20} +(1.91305 + 1.62335i) q^{22} +(-2.46180 - 4.26396i) q^{23} +(1.59019 - 2.75429i) q^{25} +(1.19280 - 6.55270i) q^{26} +(-5.28223 - 0.313090i) q^{28} -7.21461i q^{29} +(1.31172 + 0.757322i) q^{31} +(-4.43223 + 3.51501i) q^{32} +(6.42980 - 7.57728i) q^{34} +(5.13747 - 5.55600i) q^{35} +(1.38862 + 2.40515i) q^{37} +(3.81291 + 10.6588i) q^{38} +(0.134149 - 8.08858i) q^{40} +4.94219i q^{41} +7.39300i q^{43} +(-2.74316 + 2.25058i) q^{44} +(6.55615 - 2.34528i) q^{46} +(2.78654 + 4.82642i) q^{47} +(5.77008 - 3.96310i) q^{49} +(3.42943 + 2.91009i) q^{50} +(8.81500 + 3.31921i) q^{52} +(-2.87828 - 1.66178i) q^{53} -5.07423i q^{55} +(1.77345 - 7.27014i) q^{56} +(10.0380 + 1.82725i) q^{58} +(-0.717330 + 1.24245i) q^{59} +(7.30221 + 12.6478i) q^{61} +(-1.38592 + 1.63325i) q^{62} +(-3.76805 - 7.05704i) q^{64} +(-11.6654 + 6.73505i) q^{65} +(-2.58315 - 1.49138i) q^{67} +(8.91416 + 10.8652i) q^{68} +(6.42917 + 8.55518i) q^{70} +11.4553 q^{71} +(0.0244370 - 0.0423261i) q^{73} +(-3.69810 + 1.32290i) q^{74} +(-15.7959 + 2.60552i) q^{76} +(1.03662 - 4.57799i) q^{77} +(1.15816 - 0.668665i) q^{79} +(11.2201 + 2.23525i) q^{80} +(-6.87631 - 1.25171i) q^{82} +9.02165 q^{83} -20.0982 q^{85} +(-10.2862 - 1.87243i) q^{86} +(-2.43658 - 4.38671i) q^{88} +(-5.61463 + 3.24161i) q^{89} +(-11.9005 + 3.69324i) q^{91} +(1.60263 + 9.71589i) q^{92} +(-7.42099 + 2.65465i) q^{94} +(11.4472 - 19.8271i) q^{95} -1.07208 q^{97} +(4.05267 + 9.03193i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} - 2 q^{7}+O(q^{10}) $ 28 * q - 4 * q^4 - 2 * q^7	$ 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58} + 6 q^{61} + 8 q^{64} - 24 q^{67} + 128 q^{70} - 22 q^{73} - 48 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} - 16 q^{91} - 12 q^{94} - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	−0.253271	+	1.39135i	−0.179089	+	0.983833i
$2$	−0.253271	+	1.39135i	−0.179089	+	0.983833i
$3$		0			0
$3$		0			0
$4$	−1.87171	−	0.704776i	−0.935854	−	0.352388i
$5$	2.47695	−	1.43007i	1.10773	−	0.639546i	0.169487	−	0.985532i	$-0.445789\pi$
$5$	2.47695	−	1.43007i	1.10773	−	0.639546i	0.938239	+	0.345987i	$0.112456\pi$
$6$		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
$10$	1.36239	+	3.80850i	0.430824	+	1.20435i
$11$	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	$0.726534\pi$
$14$	0.451108	+	3.71436i	0.120564	+	0.992706i
$15$		0			0
$16$	3.00658	+	2.63827i	0.751645	+	0.659567i
$17$	−6.08556	−	3.51350i	−1.47597	−	0.852149i	−0.476333	−	0.879265i	$-0.658034\pi$
$17$	−6.08556	−	3.51350i	−1.47597	−	0.852149i	−0.999632	+	0.0271159i	$0.991368\pi$
$18$		0			0
$19$	6.93224	−	4.00233i	1.59036	−	0.918197i	0.597121	−	0.802152i	$-0.296311\pi$
$19$	6.93224	−	4.00233i	1.59036	−	0.918197i	0.993244	−	0.116046i	$-0.0370219\pi$
$20$	−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
$26$	1.19280	−	6.55270i	0.233928	−	1.28509i
$27$		0			0
$28$	−5.28223	−	0.313090i	−0.998248	−	0.0591684i
$29$		−	7.21461i		−	1.33972i	−0.742487	−	0.669860i	$-0.766354\pi$
$29$		−	7.21461i		−	1.33972i	0.742487	−	0.669860i	$-0.233646\pi$
$30$		0			0
$31$	1.31172	+	0.757322i	0.235592	+	0.136019i	0.613149	−	0.789967i	$-0.289903\pi$
$31$	1.31172	+	0.757322i	0.235592	+	0.136019i	−0.377557	+	0.925986i	$0.623236\pi$
$32$	−4.43223	+	3.51501i	−0.783516	+	0.621372i
$33$		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	$0.760021\pi$
$38$	3.81291	+	10.6588i	0.618535	+	1.72909i
$39$		0			0
$40$	0.134149	−	8.08858i	0.0212109	−	1.27892i
$41$			4.94219i			0.771840i	0.922532	+	0.385920i	$0.126116\pi$
$41$			4.94219i			0.771840i	−0.922532	+	0.385920i	$0.873884\pi$
$42$		0			0
$43$			7.39300i			1.12742i	0.825972	+	0.563711i	$0.190627\pi$
$43$			7.39300i			1.12742i	−0.825972	+	0.563711i	$0.809373\pi$
$44$	−2.74316	+	2.25058i	−0.413547	+	0.339288i
$45$		0			0
$46$	6.55615	−	2.34528i	0.966652	−	0.345793i
$47$	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
$52$	8.81500	+	3.31921i	1.22242	+	0.460292i
$53$	−2.87828	−	1.66178i	−0.395362	−	0.228262i	0.289119	−	0.957293i	$-0.406638\pi$
$53$	−2.87828	−	1.66178i	−0.395362	−	0.228262i	−0.684481	+	0.729031i	$0.739971\pi$
$54$		0			0
$55$		−	5.07423i		−	0.684210i
$56$	1.77345	−	7.27014i	0.236987	−	0.971513i
$57$		0			0
$58$	10.0380	+	1.82725i	1.31806	+	0.239930i
$59$	−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	0.333840	−	0.942630i	$-0.391656\pi$
$67$	−2.58315	−	1.49138i	−0.315582	−	0.182201i	−0.649422	+	0.760428i	$0.724989\pi$
$68$	8.91416	+	10.8652i	1.08100	+	1.31760i
$69$		0			0
$70$	6.42917	+	8.55518i	0.768433	+	1.02254i
$71$	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	$0.165756\pi$
$74$	−3.69810	+	1.32290i	−0.429896	+	0.153784i
$75$		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	−0.433431	−	0.901187i	$-0.642697\pi$
$79$	1.15816	−	0.668665i	0.130303	−	0.0752307i	0.563735	+	0.825956i	$0.309364\pi$
$80$	11.2201	+	2.23525i	1.25444	+	0.249908i
$81$		0			0
$82$	−6.87631	−	1.25171i	−0.759362	−	0.138228i
$83$	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
$86$	−10.2862	−	1.87243i	−1.10919	−	0.201909i
$87$		0			0
$88$	−2.43658	−	4.38671i	−0.259740	−	0.467624i
$89$	−5.61463	+	3.24161i	−0.595149	+	0.343610i	−0.767131	−	0.641491i	$-0.778316\pi$
$89$	−5.61463	+	3.24161i	−0.595149	+	0.343610i	0.171982	+	0.985100i	$0.444983\pi$
$90$		0			0
$91$	−11.9005	+	3.69324i	−1.24751	+	0.387157i
$92$	1.60263	+	9.71589i	0.167086	+	1.01295i
$93$		0			0
$94$	−7.42099	+	2.65465i	−0.765416	+	0.273807i
$95$	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	$0.517333\pi$
$98$	4.05267	+	9.03193i	0.409382	+	0.912363i
$99$		0			0
$100$	−4.91753	+	4.03450i	−0.491753	+	0.403450i
$101$	5.30278	+	3.06156i	0.527646	+	0.304637i	0.740058	−	0.672544i	$-0.234798\pi$
$101$	5.30278	+	3.06156i	0.527646	+	0.304637i	−0.212411	+	0.977180i	$0.568132\pi$
$102$		0			0
$103$	6.18578	−	3.57136i	0.609503	−	0.351897i	−0.163268	−	0.986582i	$-0.552204\pi$
$103$	6.18578	−	3.57136i	0.609503	−	0.351897i	0.772771	+	0.634685i	$0.218870\pi$
$104$	−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	$0.208772\pi$
$110$	7.06004	+	1.28515i	0.673148	+	0.122535i
$111$		0			0
$112$	9.66614	+	4.30880i	0.913364	+	0.407144i
$113$		−	18.3520i		−	1.72641i	−0.504854	−	0.863205i	$-0.668454\pi$
$113$		−	18.3520i		−	1.72641i	0.504854	−	0.863205i	$-0.331546\pi$
$114$		0			0
$115$	−12.1955	−	7.04107i	−1.13724	−	0.656583i
$116$	−5.08469	+	13.5036i	−0.472101	+	1.25378i
$117$		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
$122$	−19.4469	+	6.95661i	−1.76064	+	0.629822i
$123$		0			0
$124$	−1.92141	−	2.34195i	−0.172548	−	0.210314i
$125$			5.20436i			0.465492i
$126$		0			0
$127$			8.18873i			0.726632i	0.931666	+	0.363316i	$0.118355\pi$
$127$			8.18873i			0.726632i	−0.931666	+	0.363316i	$0.881645\pi$
$128$	10.7731	−	3.45534i	0.952220	−	0.305412i
$129$		0			0
$130$	−6.41629	−	17.9365i	−0.562746	−	1.57314i
$131$	−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
$136$	−17.3750	+	9.65088i	−1.48989	+	0.827556i
$137$	3.64686	+	2.10552i	0.311573	+	0.179887i	0.647630	−	0.761955i	$-0.275760\pi$
$137$	3.64686	+	2.10552i	0.311573	+	0.179887i	−0.336057	+	0.941842i	$0.609094\pi$
$138$		0			0
$139$			10.5488i			0.894736i	0.894350	+	0.447368i	$0.147639\pi$
$139$			10.5488i			0.894736i	−0.894350	+	0.447368i	$0.852361\pi$
$140$	−13.5316	+	6.77844i	−1.14363	+	0.572883i
$141$		0			0
$142$	−2.90129	+	15.9383i	−0.243471	+	1.33751i
$143$	−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	0.251607	−	0.967829i	$-0.419041\pi$
$149$	14.8380	−	8.56672i	1.21558	−	0.701813i	0.963969	+	0.266016i	$0.0857075\pi$
$150$		0			0
$151$	6.08270	+	3.51185i	0.495003	+	0.285790i	0.726648	−	0.687010i	$-0.241077\pi$
$151$	6.08270	+	3.51185i	0.495003	+	0.285790i	−0.231645	+	0.972800i	$0.574411\pi$
$152$	0.375444	−	22.6375i	0.0304525	−	1.83614i
$153$		0			0
$154$	6.10704	+	2.60177i	0.492120	+	0.209657i
$155$	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	$0.192505\pi$
$158$	0.637019	+	1.78076i	0.0506785	+	0.141670i
$159$		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	−0.675729	−	0.737150i	$-0.736171\pi$
$163$	−4.79027	+	2.76566i	−0.375203	+	0.216623i	0.300526	+	0.953774i	$0.402838\pi$
$164$	3.48314	−	9.25033i	0.271987	−	0.722330i
$165$		0			0
$166$	−2.28492	+	12.5523i	−0.177344	+	0.974246i
$167$	−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
$170$	5.09028	−	27.9636i	0.390407	−	2.14471i
$171$		0			0
$172$	5.21041	−	13.8375i	0.397290	−	1.05510i
$173$	−18.3863	+	10.6153i	−1.39788	+	0.807069i	−0.994171	−	0.107816i	$-0.965614\pi$
$173$	−18.3863	+	10.6153i	−1.39788	+	0.807069i	−0.403714	+	0.914885i	$0.632281\pi$
$174$		0			0
$175$	1.85829	−	8.20673i	0.140474	−	0.620371i
$176$	6.72056	−	2.27911i	0.506581	−	0.171795i
$177$		0			0
$178$	−3.08819	−	8.63291i	−0.231469	−	0.647064i
$179$	−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	$0.711609\pi$
$182$	−2.12454	−	17.4932i	−0.157481	−	1.29668i
$183$		0			0
$184$	−13.9241	−	0.230932i	−1.02650	−	0.0170245i
$185$	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	$-0.0476329\pi$
$194$	0.271527	−	1.49164i	0.0194945	−	0.107094i
$195$		0			0
$196$	−13.5930	+	3.35116i	−0.970929	+	0.239369i
$197$			4.41987i			0.314902i	0.987527	+	0.157451i	$0.0503277\pi$
$197$			4.41987i			0.314902i	−0.987527	+	0.157451i	$0.949672\pi$
$198$		0			0
$199$	−0.539285	−	0.311356i	−0.0382289	−	0.0220715i	0.480764	−	0.876850i	$-0.340359\pi$
$199$	−0.539285	−	0.311356i	−0.0382289	−	0.0220715i	−0.518993	+	0.854779i	$0.673693\pi$
$200$	−4.36793	−	7.86382i	−0.308860	−	0.556056i
$201$		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
$206$	3.40234	+	9.51110i	0.237052	+	0.662670i
$207$		0			0
$208$	−14.1598	−	12.4252i	−0.981805	−	0.861532i
$209$		−	14.2013i		−	0.982321i
$210$		0			0
$211$		−	19.0072i		−	1.30851i	−0.756275	−	0.654253i	$-0.772983\pi$
$211$		−	19.0072i		−	1.30851i	0.756275	−	0.654253i	$-0.227017\pi$
$212$	4.21612	+	5.13890i	0.289564	+	0.352941i
$213$		0			0
$214$	3.44828	−	1.23353i	0.235719	−	0.0843222i
$215$	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
$220$	−3.57620	+	9.49749i	−0.241107	+	0.640320i
$221$	28.6606	+	16.5472i	1.92792	+	1.11308i
$222$		0			0
$223$		−	13.3599i		−	0.894643i	−0.894373	−	0.447321i	$-0.852378\pi$
$223$		−	13.3599i		−	0.894643i	0.894373	−	0.447321i	$-0.147622\pi$
$224$	−8.44320	+	12.3577i	−0.564135	+	0.825683i
$225$		0			0
$226$	25.5340	+	4.64802i	1.69850	+	0.309182i
$227$	−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	−0.860648	−	0.509200i	$-0.829942\pi$
$233$	−12.9746	+	7.49088i	−0.849993	+	0.490744i	0.0106555	+	0.999943i	$0.496608\pi$
$234$		0			0
$235$	13.8042	+	7.96987i	0.900488	+	0.519897i
$236$	2.21828	−	1.81995i	0.144398	−	0.118469i
$237$		0			0
$238$	10.3052	−	24.1890i	0.667985	−	1.56794i
$239$	−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	$0.228811\pi$
$242$	−10.4562	+	3.74042i	−0.672151	+	0.240443i
$243$		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
$248$	3.74511	−	2.08021i	0.237815	−	0.132094i
$249$		0			0
$250$	−7.24108	−	1.31811i	−0.457966	−	0.0833647i
$251$	−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
$254$	−11.3934	−	2.07396i	−0.714884	−	0.130132i
$255$		0			0
$256$	2.07907	+	15.8643i	0.129942	+	0.991522i
$257$	−1.04960	+	0.605984i	−0.0654719	+	0.0378002i	−0.532379	−	0.846506i	$-0.678702\pi$
$257$	−1.04960	+	0.605984i	−0.0654719	+	0.0378002i	0.466907	+	0.884307i	$0.345368\pi$
$258$		0			0
$259$	5.39495	+	4.98855i	0.335226	+	0.309973i
$260$	26.5810	−	4.38452i	1.64848	−	0.271916i
$261$		0			0
$262$	0.409877	−	0.146622i	0.0253223	−	0.00905835i
$263$	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
$266$	17.9933	+	23.9434i	1.10324	+	1.46806i
$267$		0			0
$268$	3.78381	+	4.61198i	0.231133	+	0.281721i
$269$	−6.63128	−	3.82857i	−0.404316	−	0.233432i	0.284028	−	0.958816i	$-0.408329\pi$
$269$	−6.63128	−	3.82857i	−0.404316	−	0.233432i	−0.688345	+	0.725384i	$0.741662\pi$
$270$		0			0
$271$	−17.2222	+	9.94322i	−1.04617	+	0.604008i	−0.921575	−	0.388200i	$-0.873097\pi$
$271$	−17.2222	+	9.94322i	−1.04617	+	0.604008i	−0.124597	+	0.992207i	$0.539764\pi$
$272$	−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	$0.230818\pi$
$278$	−14.6770	−	2.67170i	−0.880271	−	0.160238i
$279$		0			0
$280$	−6.00404	−	20.5439i	−0.358810	−	1.22773i
$281$			9.71892i			0.579782i	0.957060	+	0.289891i	$0.0936190\pi$
$281$			9.71892i			0.579782i	−0.957060	+	0.289891i	$0.906381\pi$
$282$		0			0
$283$	6.55255	+	3.78312i	0.389509	+	0.224883i	0.681947	−	0.731401i	$-0.261133\pi$
$283$	6.55255	+	3.78312i	0.389509	+	0.224883i	−0.292439	+	0.956284i	$0.594467\pi$
$284$	−21.4410	−	8.07342i	−1.27229	−	0.479069i
$285$		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
$290$	27.4768	−	9.82909i	1.61350	−	0.577184i
$291$		0			0
$292$	−0.0755694	+	0.0619996i	−0.00442236	+	0.00362825i
$293$			5.44847i			0.318303i	0.987254	+	0.159151i	$0.0508758\pi$
$293$			5.44847i			0.318303i	−0.987254	+	0.159151i	$0.949124\pi$
$294$		0			0
$295$			4.10332i			0.238905i
$296$	7.85412	+	0.130261i	0.456511	+	0.00757126i
$297$		0			0
$298$	8.16128	+	22.8145i	0.472770	+	1.32161i
$299$	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
$304$	31.4016	+	6.25578i	1.80100	+	0.358794i
$305$	36.1744	+	20.8853i	2.07134	+	1.19589i
$306$		0			0
$307$		−	1.58786i		−	0.0906240i	−0.998973	−	0.0453120i	$-0.985572\pi$
$307$		−	1.58786i		−	0.0906240i	0.998973	−	0.0453120i	$-0.0144282\pi$
$308$	−5.16671	+	7.83808i	−0.294400	+	0.446616i
$309$		0			0
$310$	−1.09719	+	6.02745i	−0.0623162	+	0.342336i
$311$	−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	−0.788850	−	0.614585i	$-0.789323\pi$
$317$	−11.5912	+	6.69221i	−0.651029	+	0.375872i	0.137821	+	0.990457i	$0.455990\pi$
$318$		0			0
$319$	−11.0848	−	6.39981i	−0.620629	−	0.358320i
$320$	−19.4253	−	12.0914i	−1.08591	−	0.675927i
$321$		0			0
$322$	14.7273	−	11.0675i	0.820723	−	0.616768i
$323$	−56.2487			−3.12976
$324$		0			0
$325$	−7.48916	+	12.9716i	−0.415424	+	0.719535i
$326$	−2.63477	−	7.36540i	−0.145926	−	0.407932i
$327$		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	0.336053	−	0.941843i	$-0.390908\pi$
$331$	24.0106	−	13.8625i	1.31974	−	0.761952i	0.983687	+	0.179891i	$0.0575744\pi$
$332$	−16.8859	−	6.35824i	−0.926734	−	0.348954i
$333$		0			0
$334$	1.61369	−	8.86487i	0.0882974	−	0.485064i
$335$	−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	$0.324081\pi$
$338$	−2.32511	+	12.7731i	−0.126469	+	0.694763i
$339$		0			0
$340$	37.6179	+	14.1647i	2.04012	+	0.768190i
$341$	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
$346$	−10.1129	−	28.2703i	−0.543675	−	1.51982i
$347$	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	$0.870313\pi$
$350$	10.9478	+	4.66406i	0.585184	+	0.249305i
$351$		0			0
$352$	1.46892	+	9.92787i	0.0782939	+	0.529158i
$353$	10.7257	+	6.19247i	0.570870	+	0.329592i	0.757497	−	0.652839i	$-0.226422\pi$
$353$	10.7257	+	6.19247i	0.570870	+	0.329592i	−0.186627	+	0.982431i	$0.559756\pi$
$354$		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
$362$	4.20402	−	23.0949i	0.220958	−	1.21384i
$363$		0			0
$364$	24.8772	+	1.47453i	1.30392	+	0.0772862i
$365$		−	0.139786i		−	0.00731675i
$366$		0			0
$367$	11.2735	+	6.50873i	0.588469	+	0.339753i	0.764492	−	0.644633i	$-0.222990\pi$
$367$	11.2735	+	6.50873i	0.588469	+	0.339753i	−0.176023	+	0.984386i	$0.556323\pi$
$368$	3.84787	−	19.3148i	0.200584	−	1.00685i
$369$		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	$0.784904\pi$
$374$	−5.93837	−	16.6005i	−0.307066	−	0.858391i
$375$		0			0
$376$	15.7609	+	0.261394i	0.812804	+	0.0134804i
$377$			33.9779i			1.74995i
$378$		0			0
$379$		−	23.7003i		−	1.21740i	−0.793399	−	0.608701i	$-0.791691\pi$
$379$		−	23.7003i		−	1.21740i	0.793399	−	0.608701i	$-0.208309\pi$
$380$	−35.3995	+	29.0429i	−1.81596	+	1.48987i
$381$		0			0
$382$	−9.35124	+	3.34515i	−0.478451	+	0.171153i
$383$	−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
$388$	2.00663	+	0.755578i	0.101871	+	0.0383587i
$389$	6.59701	+	3.80878i	0.334482	+	0.193113i	0.657829	−	0.753167i	$-0.271475\pi$
$389$	6.59701	+	3.80878i	0.334482	+	0.193113i	−0.323348	+	0.946280i	$0.604808\pi$
$390$		0			0
$391$			34.5981i			1.74970i
$392$	−1.21993	−	19.7614i	−0.0616158	−	0.998100i
$393$		0			0
$394$	−6.14958	−	1.11942i	−0.309811	−	0.0563957i
$395$	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	0.0656611	−	0.997842i	$-0.479084\pi$
$401$	19.2770	−	11.1296i	0.962648	−	0.555785i	0.896987	+	0.442057i	$0.145751\pi$
$402$		0			0
$403$	−6.17767	−	3.56668i	−0.307732	−	0.177669i
$404$	−7.76754	−	9.46762i	−0.386450	−	0.471032i
$405$		0			0
$406$	26.7977	−	3.25457i	1.32995	−	0.161522i
$407$	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	$0.00916058\pi$
$410$	−18.8223	+	6.73317i	−0.929568	+	0.332528i
$411$		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
$416$	20.8741	−	16.5543i	1.02343	−	0.811641i
$417$		0			0
$418$	19.7589	+	3.59676i	0.966440	+	0.175923i
$419$	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	$0.508886\pi$
$422$	26.4456	+	4.81395i	1.28735	+	0.234340i
$423$		0			0
$424$	−8.21783	+	4.56456i	−0.399093	+	0.221675i
$425$	−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
$430$	−28.1562	+	10.0721i	−1.35781	+	0.485721i
$431$	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	$0.264957\pi$
$434$	−2.22124	+	5.21384i	−0.106623	+	0.250272i
$435$		0			0
$436$	4.25829	−	3.49364i	0.203935	−	0.167315i
$437$	−34.1315	−	19.7058i	−1.63273	−	0.942658i
$438$		0			0
$439$	−13.1619	+	7.59904i	−0.628184	+	0.362682i	−0.780048	−	0.625719i	$-0.784806\pi$
$439$	−13.1619	+	7.59904i	−0.628184	+	0.362682i	0.151864	+	0.988401i	$0.451472\pi$
$440$	−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
$446$	18.5882	+	3.38366i	0.880179	+	0.160221i
$447$		0			0
$448$	−15.0554	−	14.8773i	−0.711303	−	0.702885i
$449$		−	24.0119i		−	1.13319i	−0.823995	−	0.566596i	$-0.808260\pi$
$449$		−	24.0119i		−	1.13319i	0.823995	−	0.566596i	$-0.191740\pi$
$450$		0			0
$451$	7.59336	+	4.38403i	0.357557	+	0.206436i
$452$	−12.9340	+	34.3495i	−0.608366	+	1.61567i
$453$		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	$-0.467333\pi$
$458$	3.84794	−	1.37650i	0.179803	−	0.0643195i
$459$		0			0
$460$	17.8640	+	21.7739i	0.832915	+	1.01521i
$461$			25.4518i			1.18541i	0.805421	+	0.592704i	$0.201939\pi$
$461$			25.4518i			1.18541i	−0.805421	+	0.592704i	$0.798061\pi$
$462$		0			0
$463$		−	27.9163i		−	1.29738i	−0.761053	−	0.648690i	$-0.775317\pi$
$463$		−	27.9163i		−	1.29738i	0.761053	−	0.648690i	$-0.224683\pi$
$464$	19.0341	−	21.6913i	0.883636	−	1.00699i
$465$		0			0
$466$	−7.13635	−	19.9494i	−0.330585	−	0.924138i
$467$	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
$472$	1.97036	+	3.54735i	0.0906932	+	0.163280i
$473$	11.3589	+	6.55805i	0.522281	+	0.301539i
$474$		0			0
$475$		−	25.4579i		−	1.16809i
$476$	31.0453	+	20.4645i	1.42296	+	0.937987i
$477$		0			0
$478$	2.46698	−	13.5524i	0.112837	−	0.619873i
$479$	−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	0.975327	−	0.220764i	$-0.0708551\pi$
$487$	28.0663	+	16.2041i	1.27180	+	0.734276i	0.296476	+	0.955040i	$0.404188\pi$
$488$	41.3019	+	0.684993i	1.86965	+	0.0310082i
$489$		0			0
$490$	22.9546	+	16.5761i	1.03698	+	0.748830i
$491$	−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
$494$	−17.9573	−	50.1989i	−0.807936	−	2.25855i
$495$		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	0.0969381	−	0.995290i	$-0.469095\pi$
$499$	22.5026	−	12.9919i	1.00735	−	0.581596i	0.910416	+	0.413694i	$0.135762\pi$
$500$	3.66791	−	9.74104i	0.164034	−	0.435633i
$501$		0			0
$502$	0.749186	−	4.11568i	0.0334378	−	0.183692i
$503$	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
$506$	2.21233	−	12.1535i	0.0983502	−	0.540290i
$507$		0			0
$508$	5.77122	−	15.3269i	0.256056	−	0.680022i
$509$	−22.5593	+	13.0246i	−0.999923	+	0.577306i	−0.908226	−	0.418481i	$-0.862563\pi$
$509$	−22.5593	+	13.0246i	−0.999923	+	0.577306i	−0.0916978	+	0.995787i	$0.529229\pi$
$510$		0			0
$511$	0.0285571	−	0.126116i	0.00126329	−	0.00557903i
$512$	−22.5994	−	1.12526i	−0.998763	−	0.0497300i
$513$		0			0
$514$	−0.577304	−	1.61383i	−0.0254638	−	0.0711831i
$515$	10.2146	−	17.6922i	0.450108	−	0.779610i
$516$		0			0
$517$	9.88731			0.434844
$518$	−8.30720	+	6.24281i	−0.364997	+	0.274293i
$519$		0			0
$520$	−0.631790	+	38.0940i	−0.0277058	+	1.67053i
$521$	−29.2252	−	16.8732i	−1.28038	−	0.739228i	−0.303463	−	0.952843i	$-0.598143\pi$
$521$	−29.2252	−	16.8732i	−1.28038	−	0.739228i	−0.976918	+	0.213615i	$0.931476\pi$
$522$		0			0
$523$	−17.2979	+	9.98697i	−0.756386	+	0.436700i	−0.827997	−	0.560733i	$-0.810519\pi$
$523$	−17.2979	+	9.98697i	−0.756386	+	0.436700i	0.0716106	+	0.997433i	$0.477186\pi$
$524$	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
$530$	2.40754	−	13.2259i	0.104577	−	0.574497i
$531$		0			0
$532$	−37.8708	+	18.9708i	−1.64191	+	0.822489i
$533$		−	23.2757i		−	1.00818i
$534$		0			0
$535$	−6.41435	−	3.70333i	−0.277316	−	0.160109i
$536$	−7.37520	+	4.09653i	−0.318560	+	0.176943i
$537$		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	$0.779455\pi$
$542$	−9.47263	−	26.4804i	−0.406884	−	1.13743i
$543$		0			0
$544$	39.3226	−	5.81815i	1.68594	−	0.249451i
$545$			7.87688i			0.337409i
$546$		0			0
$547$			42.3065i			1.80890i	0.426584	+	0.904448i	$0.359717\pi$
$547$			42.3065i			1.80890i	−0.426584	+	0.904448i	$0.640283\pi$
$548$	−5.34195	−	6.51114i	−0.228197	−	0.278142i
$549$		0			0
$550$	7.51329	−	2.68767i	0.320368	−	0.114603i
$551$	−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
$556$	7.43453	−	19.7442i	0.315294	−	0.837342i
$557$	−9.26900	−	5.35146i	−0.392740	−	0.226749i	0.290607	−	0.956843i	$-0.406143\pi$
$557$	−9.26900	−	5.35146i	−0.392740	−	0.226749i	−0.683347	+	0.730094i	$0.739476\pi$
$558$		0			0
$559$		−	34.8181i		−	1.47265i
$560$	30.1044	−	3.15054i	1.27214	−	0.133135i
$561$		0			0
$562$	−13.5224	−	2.46152i	−0.570408	−	0.103833i
$563$	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	0.141384	−	0.989955i	$-0.454845\pi$
$569$	25.5092	−	14.7277i	1.06940	−	0.617419i	0.928018	+	0.372536i	$0.121512\pi$
$570$		0			0
$571$	−28.0410	−	16.1895i	−1.17348	−	0.677508i	−0.218982	−	0.975729i	$-0.570274\pi$
$571$	−28.0410	−	16.1895i	−1.17348	−	0.677508i	−0.954497	+	0.298221i	$0.903607\pi$
$572$	12.9192	−	10.5993i	0.540179	−	0.443180i
$573$		0			0
$574$	−18.3571	+	2.22946i	−0.766210	+	0.0930560i
$575$	−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	$0.205084\pi$
$578$	−43.1149	+	15.4232i	−1.79334	+	0.641519i
$579$		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
$584$	−0.0671236	−	0.120846i	−0.00277759	−	0.00500065i
$585$		0			0
$586$	−7.58073	−	1.37994i	−0.313157	−	0.0570047i
$587$	−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
$590$	−5.70916	−	1.03925i	−0.235042	−	0.0427853i
$591$		0			0
$592$	−2.17046	+	10.8948i	−0.0892052	+	0.447775i
$593$	15.6450	−	9.03263i	0.642462	−	0.370926i	−0.143100	−	0.989708i	$-0.545707\pi$
$593$	15.6450	−	9.03263i	0.642462	−	0.370926i	0.785562	+	0.618782i	$0.212374\pi$
$594$		0			0
$595$	−50.7854	+	15.7609i	−2.08200	+	0.646133i
$596$	−33.8100	+	5.57694i	−1.38491	+	0.228440i
$597$		0			0
$598$	−30.8769	+	11.0454i	−1.26265	+	0.451678i
$599$	−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	$0.415960\pi$
$602$	−27.4603	+	3.33504i	−1.11920	+	0.135926i
$603$		0			0
$604$	−8.90997	−	10.8601i	−0.362541	−	0.441891i
$605$	19.4502	+	11.2296i	0.790764	+	0.456548i
$606$		0			0
$607$	−21.6019	+	12.4718i	−0.876792	+	0.506216i	−0.869599	−	0.493758i	$-0.835623\pi$
$607$	−21.6019	+	12.4718i	−0.876792	+	0.506216i	−0.00719299	+	0.999974i	$0.502290\pi$
$608$	−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	$0.962351\pi$
$614$	2.20927	+	0.402158i	0.0891589	+	0.0162298i
$615$		0			0
$616$	−9.59694	−	9.17385i	−0.386672	−	0.369625i
$617$		−	26.3663i		−	1.06147i	−0.847539	−	0.530734i	$-0.821917\pi$
$617$		−	26.3663i		−	1.06147i	0.847539	−	0.530734i	$-0.178083\pi$
$618$		0			0
$619$	−17.3094	−	9.99359i	−0.695724	−	0.401676i	0.110029	−	0.993928i	$-0.464906\pi$
$619$	−17.3094	−	9.99359i	−0.695724	−	0.401676i	−0.805753	+	0.592252i	$0.798239\pi$
$620$	−8.10840	−	3.05315i	−0.325641	−	0.122617i
$621$		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
$626$	14.0333	−	5.02004i	0.560885	−	0.200641i
$627$		0			0
$628$	3.14188	−	2.57770i	0.125375	−	0.102861i
$629$		−	19.5156i		−	0.778138i
$630$		0			0
$631$			7.91131i			0.314944i	0.987523	+	0.157472i	$0.0503344\pi$
$631$			7.91131i			0.314944i	−0.987523	+	0.157472i	$0.949666\pi$
$632$	0.0627250	−	3.78202i	0.00249507	−	0.150441i
$633$		0			0
$634$	−6.37548	−	17.8224i	−0.253203	−	0.707819i
$635$	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
$640$	21.7432	−	23.9650i	0.859474	−	0.947301i
$641$	−30.8675	−	17.8214i	−1.21919	−	0.703902i	−0.254448	−	0.967086i	$-0.581894\pi$
$641$	−30.8675	−	17.8214i	−1.21919	−	0.703902i	−0.964746	+	0.263185i	$0.915227\pi$
$642$		0			0
$643$			7.96178i			0.313982i	0.987600	+	0.156991i	$0.0501794\pi$
$643$			7.96178i			0.313982i	−0.987600	+	0.156991i	$0.949821\pi$
$644$	11.6688	+	23.2940i	0.459814	+	0.917911i
$645$		0			0
$646$	14.2462	−	78.2617i	0.560507	−	3.07916i
$647$	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	−0.945706	−	0.325022i	$-0.894628\pi$
$653$	−29.0569	+	16.7760i	−1.13708	+	0.656495i	−0.191376	+	0.981517i	$0.561295\pi$
$654$		0			0
$655$	−0.762436	−	0.440193i	−0.0297909	−	0.0171998i
$656$	−13.0388	+	14.8591i	−0.509081	+	0.580150i
$657$		0			0
$658$	−16.6701	+	12.5274i	−0.649866	+	0.488371i
$659$	−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	$0.256109\pi$
$662$	13.2064	+	36.9181i	0.513282	+	1.43486i
$663$		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
$668$	11.9254	+	4.49042i	0.461409	+	0.173740i
$669$		0			0
$670$	2.16068	−	11.8698i	0.0834744	−	0.458569i
$671$	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	$0.493811\pi$
$674$	−4.88152	+	26.8168i	−0.188029	+	1.03294i
$675$		0			0
$676$	−17.1829	−	6.47008i	−0.660881	−	0.248849i
$677$	−30.2292	+	17.4528i	−1.16180	+	0.670766i	−0.951735	−	0.306921i	$-0.900701\pi$
$677$	−30.2292	+	17.4528i	−1.16180	+	0.670766i	−0.210066	+	0.977687i	$0.567368\pi$
$678$		0			0
$679$	−2.70901	+	0.840721i	−0.103962	+	0.0322639i
$680$	−29.2356	+	48.7522i	−1.12113	+	1.86956i
$681$		0			0
$682$	1.27999	+	3.57817i	0.0490135	+	0.137015i
$683$	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
$686$	17.3233	+	19.6444i	0.661408	+	0.750026i
$687$		0			0
$688$	−19.5047	+	22.2277i	−0.743611	+	0.847422i
$689$	13.5555	+	7.82630i	0.516425	+	0.298158i
$690$		0			0
$691$	6.57653	−	3.79696i	0.250183	−	0.144443i	−0.369665	−	0.929165i	$-0.620528\pi$
$691$	6.57653	−	3.79696i	0.250183	−	0.144443i	0.619848	+	0.784722i	$0.287194\pi$
$692$	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
$698$	8.68838	−	47.7299i	0.328860	−	1.80660i
$699$		0			0
$700$	−9.26209	+	14.0509i	−0.350074	+	0.531075i
$701$			44.3539i			1.67522i	0.546267	+	0.837611i	$0.316049\pi$
$701$			44.3539i			1.67522i	−0.546267	+	0.837611i	$0.683951\pi$
$702$		0			0
$703$	19.2524	+	11.1154i	0.726119	+	0.419225i
$704$	−14.1852	−	0.470653i	−0.534624	−	0.0177384i
$705$		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	$0.682658\pi$
$710$	15.6065	+	43.6275i	0.585703	+	1.63731i
$711$		0			0
$712$	−0.304083	+	18.3348i	−0.0113960	+	0.687125i
$713$		−	7.45748i		−	0.279285i
$714$		0			0
$715$			23.8976i			0.893720i
$716$	31.6826	−	25.9935i	1.18404	−	0.971421i
$717$		0			0
$718$	−16.9559	+	6.06550i	−0.632788	+	0.226362i
$719$	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
$724$	31.0683	+	11.6985i	1.15465	+	0.434772i
$725$	−19.8711	−	11.4726i	−0.737996	−	0.426082i
$726$		0			0
$727$			0.853452i			0.0316528i	0.999875	+	0.0158264i	$0.00503791\pi$
$727$			0.853452i			0.0316528i	−0.999875	+	0.0158264i	$0.994962\pi$
$728$	−8.35225	+	34.2394i	−0.309555	+	1.26900i
$729$		0			0
$730$	0.194492	+	0.0354038i	0.00719846	+	0.00131035i
$731$	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	−0.175846	−	0.984418i	$-0.556266\pi$
$739$	−30.3461	−	17.5203i	−1.11630	−	0.644496i	−0.940454	+	0.339921i	$0.889599\pi$
$740$	−10.0765	−	12.2819i	−0.370419	−	0.451493i
$741$		0			0
$742$	4.87402	−	11.4406i	0.178931	−	0.419998i
$743$	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
$746$	−7.79527	+	2.78854i	−0.285405	+	0.102096i
$747$		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	−0.878494	−	0.477753i	$-0.841451\pi$
$751$	−24.7734	+	14.3029i	−0.903994	+	0.521921i	−0.0255004	+	0.999675i	$0.508118\pi$
$752$	−4.35545	+	21.8627i	−0.158827	+	0.797249i
$753$		0			0
$754$	−47.2752	−	8.60561i	−1.72166	−	0.313398i
$755$	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	$0.666268\pi$
$758$	32.9754	+	6.00259i	1.19772	+	0.218024i
$759$		0			0
$760$	−31.4432	−	56.6088i	−1.14056	−	2.05342i
$761$	−24.7788	+	14.3060i	−0.898231	+	0.518594i	−0.876626	−	0.481173i	$-0.840211\pi$
$761$	−24.7788	+	14.3060i	−0.898231	+	0.518594i	−0.0216049	+	0.999767i	$0.506878\pi$
$762$		0			0
$763$	−1.60917	+	7.10655i	−0.0582560	+	0.257274i
$764$	−2.28588	−	13.8581i	−0.0827002	−	0.501368i
$765$		0			0
$766$	21.8145	−	7.80355i	0.788191	−	0.281954i
$767$	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	$0.471425\pi$
$770$	18.8476	−	2.28903i	0.679219	−	0.0824909i
$771$		0			0
$772$	−26.7873	+	21.9772i	−0.964097	+	0.790977i
$773$	−36.9413	−	21.3281i	−1.32869	−	0.767117i	−0.343589	−	0.939120i	$-0.611643\pi$
$773$	−36.9413	−	21.3281i	−1.32869	−	0.767117i	−0.985096	+	0.172003i	$0.944976\pi$
$774$		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
$782$	−48.1380	−	8.76268i	−1.72141	−	0.313353i
$783$		0			0
$784$	27.8039	+	3.30763i	0.992998	+	0.118129i
$785$			5.81177i			0.207431i
$786$		0			0
$787$	−3.83610	−	2.21477i	−0.136742	−	0.0789481i	0.430068	−	0.902796i	$-0.358489\pi$
$787$	−3.83610	−	2.21477i	−0.136742	−	0.0789481i	−0.566810	+	0.823848i	$0.691823\pi$
$788$	3.11502	−	8.27270i	0.110968	−	0.294703i
$789$		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
$794$	−11.1583	+	3.99157i	−0.395992	+	0.141655i
$795$		0			0
$796$	0.789948	+	0.962844i	0.0279990	+	0.0341271i
$797$			1.10654i			0.0391957i	0.999808	+	0.0195979i	$0.00623859\pi$
$797$			1.10654i			0.0391957i	−0.999808	+	0.0195979i	$0.993761\pi$
$798$		0			0
$799$		−	39.1620i		−	1.38545i
$800$	2.63326	+	17.7972i	0.0930999	+	0.629226i
$801$		0			0
$802$	10.6028	+	29.6399i	0.374400	+	1.04662i
$803$	−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
$808$	15.1401	−	8.40950i	0.532626	−	0.295845i
$809$	40.2345	+	23.2294i	1.41457	+	0.816702i	0.995815	−	0.0913970i	$-0.0291332\pi$
$809$	40.2345	+	23.2294i	1.41457	+	0.816702i	0.418755	+	0.908099i	$0.362467\pi$
$810$		0			0
$811$		−	12.2358i		−	0.429657i	−0.976652	−	0.214829i	$-0.931081\pi$
$811$		−	12.2358i		−	0.429657i	0.976652	−	0.214829i	$-0.0689193\pi$
$812$	−2.25882	+	38.1093i	−0.0792691	+	1.33737i
$813$		0			0
$814$	−1.24790	+	6.85539i	−0.0437390	+	0.240281i
$815$	−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	−0.666555	−	0.745456i	$-0.732232\pi$
$821$	−10.1503	+	5.86030i	−0.354249	+	0.204526i	0.312306	+	0.949982i	$0.398899\pi$
$822$		0			0
$823$	−29.5545	−	17.0633i	−1.03021	−	0.594790i	−0.113162	−	0.993577i	$-0.536098\pi$
$823$	−29.5545	−	17.0633i	−1.03021	−	0.594790i	−0.917044	+	0.398787i	$0.869431\pi$
$824$	0.335016	−	20.1999i	0.0116708	−	0.703697i
$825$		0			0
$826$	−4.93851	−	2.10394i	−0.171833	−	0.0732056i
$827$	−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	$-0.105020\pi$
$830$	12.2910	+	34.3590i	0.426626	+	1.19262i
$831$		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
$836$	−10.0087	+	26.5806i	−0.346158	+	0.919309i
$837$		0			0
$838$	−9.39969	+	51.6375i	−0.324707	+	1.78379i
$839$	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
$842$	0.290097	−	1.59366i	0.00999741	−	0.0549211i
$843$		0			0
$844$	−13.3958	+	35.5759i	−0.461102	+	1.22457i
$845$	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
$850$	−10.6454	−	29.7589i	−0.365135	−	1.02072i
$851$	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	$0.430597\pi$
$854$	−43.6844	+	32.8286i	−1.49485	+	1.12337i
$855$		0			0
$856$	−7.32353	−	0.121461i	−0.250313	−	0.00415145i
$857$	−10.6106	−	6.12603i	−0.362451	−	0.209261i	0.307704	−	0.951482i	$-0.400439\pi$
$857$	−10.6106	−	6.12603i	−0.362451	−	0.209261i	−0.670155	+	0.742221i	$0.733773\pi$
$858$		0			0
$859$	45.0377	−	26.0026i	1.53667	−	0.887196i	0.537637	−	0.843176i	$-0.319317\pi$
$859$	45.0377	−	26.0026i	1.53667	−	0.887196i	0.999031	−	0.0440193i	$-0.0140163\pi$
$860$	−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
$866$	−7.09491	+	38.9761i	−0.241095	+	1.32446i
$867$		0			0
$868$	−6.69170	−	4.41103i	−0.227131	−	0.149720i
$869$		−	2.37259i		−	0.0804846i
$870$		0			0
$871$	12.1656	+	7.02382i	0.412216	+	0.237993i
$872$	3.78238	+	6.80961i	0.128087	+	0.230603i
$873$		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	$-0.392196\pi$
$878$	−7.23939	−	20.2374i	−0.244318	−	0.682981i
$879$		0			0
$880$	13.3872	−	15.2561i	0.451282	−	0.514283i
$881$			2.21967i			0.0747826i	0.999301	+	0.0373913i	$0.0119048\pi$
$881$			2.21967i			0.0747826i	−0.999301	+	0.0373913i	$0.988095\pi$
$882$		0			0
$883$			43.9289i			1.47833i	0.673527	+	0.739163i	$0.264779\pi$
$883$			43.9289i			1.47833i	−0.673527	+	0.739163i	$0.735221\pi$
$884$	−41.9821	−	51.1708i	−1.41201	−	1.72106i
$885$		0			0
$886$	−41.0685	+	14.6911i	−1.37972	+	0.493558i
$887$	−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
$892$	−9.41571	+	25.0058i	−0.315261	+	0.837255i
$893$	38.6338	+	22.3053i	1.29283	+	0.746417i
$894$		0			0
$895$			58.6058i			1.95897i
$896$	24.5126	−	17.1794i	0.818909	−	0.573924i
$897$		0			0
$898$	33.4090	+	6.08152i	1.11487	+	0.202943i
$899$	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	0.515293	−	0.857014i	$-0.327683\pi$
$907$	0.925872	+	0.534552i	0.0307431	+	0.0177495i	−0.484550	+	0.874764i	$0.661017\pi$
$908$	6.09070	−	4.99701i	0.202127	−	0.165831i
$909$		0			0
$910$	−30.2788	−	40.2915i	−1.00373	−	1.33565i
$911$	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
$914$	46.1288	−	16.5013i	1.52581	−	0.545815i
$915$		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	0.263143	−	0.964757i	$-0.415241\pi$
$919$	37.2941	−	21.5318i	1.23022	−	0.710267i	0.967075	+	0.254490i	$0.0819076\pi$
$920$	−34.8196	+	19.3404i	−1.14797	+	0.637635i
$921$		0			0
$922$	−35.4123	−	6.44619i	−1.16624	−	0.212294i
$923$	−53.9499			−1.77578
$924$		0			0
$925$	8.83265			0.290416
$926$	38.8413	+	7.07037i	1.27640	+	0.232347i
$927$		0			0
$928$	25.3594	+	31.9769i	0.832464	+	1.04969i
$929$	−1.25933	+	0.727077i	−0.0413174	+	0.0238546i	−0.520516	−	0.853852i	$-0.674261\pi$
$929$	−1.25933	+	0.727077i	−0.0413174	+	0.0238546i	0.479199	+	0.877706i	$0.340927\pi$
$930$		0			0
$931$	24.1379	−	50.5669i	0.791088	−	1.65726i
$932$	29.5640	−	4.87656i	0.968401	−	0.159737i
$933$		0			0
$934$	−52.1011	+	18.6377i	−1.70480	+	0.609845i
$935$	−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	$0.673708\pi$
$938$	4.37426	−	10.2675i	0.142825	−	0.335247i
$939$		0			0
$940$	−20.2205	−	24.6462i	−0.659520	−	0.803869i
$941$	−23.5114	−	13.5743i	−0.766450	−	0.442510i	0.0651568	−	0.997875i	$-0.479245\pi$
$941$	−23.5114	−	13.5743i	−0.766450	−	0.442510i	−0.831607	+	0.555365i	$0.812579\pi$
$942$		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
$950$	35.4208	+	6.44773i	1.14920	+	0.209192i
$951$		0			0
$952$	−36.3361	+	38.0118i	−1.17766	+	1.23197i
$953$			18.8458i			0.610476i	0.952276	+	0.305238i	$0.0987361\pi$
$953$			18.8458i			0.610476i	−0.952276	+	0.305238i	$0.901264\pi$
$954$		0			0
$955$	17.3948	+	10.0429i	0.562883	+	0.324980i
$956$	18.2313	+	6.86486i	0.589644	+	0.222025i
$957$		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
$962$	17.4166	−	6.23031i	0.561534	−	0.200873i
$963$		0			0
$964$	9.31306	−	7.64073i	0.299953	−	0.246091i
$965$		−	49.5505i		−	1.59509i
$966$		0			0
$967$		−	9.75651i		−	0.313748i	−0.987619	−	0.156874i	$-0.949858\pi$
$967$		−	9.75651i		−	0.313748i	0.987619	−	0.156874i	$-0.0501417\pi$
$968$	22.2071	+	0.368306i	0.713764	+	0.0118378i
$969$		0			0
$970$	−1.46059	−	4.08302i	−0.0468967	−	0.131098i
$971$	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
$976$	−11.4136	+	57.2918i	−0.365341	+	1.83387i
$977$	−18.5299	−	10.6982i	−0.592824	−	0.342267i	0.173389	−	0.984853i	$-0.444528\pi$
$977$	−18.5299	−	10.6982i	−0.592824	−	0.342267i	−0.766213	+	0.642586i	$0.777861\pi$
$978$		0			0
$979$			11.5020i			0.367606i
$980$	−28.8768	+	27.7396i	−0.922436	+	0.886109i
$981$		0			0
$982$	4.88823	−	26.8537i	0.155990	−	0.856935i
$983$	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	0.861292	−	0.508111i	$-0.169656\pi$
$991$	26.8179	+	15.4834i	0.851900	+	0.491845i	−0.00939132	+	0.999956i	$0.502989\pi$
$992$	−8.47584	+	1.25408i	−0.269108	+	0.0398171i
$993$		0			0
$994$	5.16758	+	42.5491i	0.163906	+	1.34958i
$995$	−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	$0.118953\pi$
$998$	12.3770	+	34.5994i	0.391787	+	1.09523i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.253271 + 1.39135i) q^{2} +(-1.87171 - 0.704776i) q^{4} +(2.47695 - 1.43007i) q^{5} +(2.52686 - 0.784194i) q^{7} +(1.45464 - 2.42570i) q^{8} +O(q^{10})\)	\(q+(-0.253271 + 1.39135i) q^{2} +(-1.87171 - 0.704776i) q^{4} +(2.47695 - 1.43007i) q^{5} +(2.52686 - 0.784194i) q^{7} +(1.45464 - 2.42570i) q^{8} +(1.36239 + 3.80850i) q^{10} +(0.887062 - 1.53644i) q^{11} -4.70960 q^{13} +(0.451108 + 3.71436i) q^{14} +(3.00658 + 2.63827i) q^{16} +(-6.08556 - 3.51350i) q^{17} +(6.93224 - 4.00233i) q^{19} +(-5.64401 + 0.930975i) q^{20} +(1.91305 + 1.62335i) q^{22} +(-2.46180 - 4.26396i) q^{23} +(1.59019 - 2.75429i) q^{25} +(1.19280 - 6.55270i) q^{26} +(-5.28223 - 0.313090i) q^{28} -7.21461i q^{29} +(1.31172 + 0.757322i) q^{31} +(-4.43223 + 3.51501i) q^{32} +(6.42980 - 7.57728i) q^{34} +(5.13747 - 5.55600i) q^{35} +(1.38862 + 2.40515i) q^{37} +(3.81291 + 10.6588i) q^{38} +(0.134149 - 8.08858i) q^{40} +4.94219i q^{41} +7.39300i q^{43} +(-2.74316 + 2.25058i) q^{44} +(6.55615 - 2.34528i) q^{46} +(2.78654 + 4.82642i) q^{47} +(5.77008 - 3.96310i) q^{49} +(3.42943 + 2.91009i) q^{50} +(8.81500 + 3.31921i) q^{52} +(-2.87828 - 1.66178i) q^{53} -5.07423i q^{55} +(1.77345 - 7.27014i) q^{56} +(10.0380 + 1.82725i) q^{58} +(-0.717330 + 1.24245i) q^{59} +(7.30221 + 12.6478i) q^{61} +(-1.38592 + 1.63325i) q^{62} +(-3.76805 - 7.05704i) q^{64} +(-11.6654 + 6.73505i) q^{65} +(-2.58315 - 1.49138i) q^{67} +(8.91416 + 10.8652i) q^{68} +(6.42917 + 8.55518i) q^{70} +11.4553 q^{71} +(0.0244370 - 0.0423261i) q^{73} +(-3.69810 + 1.32290i) q^{74} +(-15.7959 + 2.60552i) q^{76} +(1.03662 - 4.57799i) q^{77} +(1.15816 - 0.668665i) q^{79} +(11.2201 + 2.23525i) q^{80} +(-6.87631 - 1.25171i) q^{82} +9.02165 q^{83} -20.0982 q^{85} +(-10.2862 - 1.87243i) q^{86} +(-2.43658 - 4.38671i) q^{88} +(-5.61463 + 3.24161i) q^{89} +(-11.9005 + 3.69324i) q^{91} +(1.60263 + 9.71589i) q^{92} +(-7.42099 + 2.65465i) q^{94} +(11.4472 - 19.8271i) q^{95} -1.07208 q^{97} +(4.05267 + 9.03193i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} - 2 q^{7}+O(q^{10}) \) 28 * q - 4 * q^4 - 2 * q^7	\( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58} + 6 q^{61} + 8 q^{64} - 24 q^{67} + 128 q^{70} - 22 q^{73} - 48 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} - 16 q^{91} - 12 q^{94} - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

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