LMFDB - Embedded newform 756.2.be.d.107.2

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			107.2
Character	$\chi$	$=$	756.107
Dual form			756.2.be.d.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−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	$-0.112456\pi$
$5$	2.47695	+	1.43007i	1.10773	+	0.639546i	0.169487	+	0.985532i	$0.445789\pi$
$6$		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	$-0.252851\pi$
$11$	−0.887062	−	1.53644i	−0.267459	−	0.463253i	−0.968205	+	0.250158i	$0.919517\pi$
$12$		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	$-0.991368\pi$
$17$	−6.08556	+	3.51350i	−1.47597	+	0.852149i	−0.476333	+	0.879265i	$0.658034\pi$
$18$		0			0
$19$	−6.93224	−	4.00233i	−1.59036	−	0.918197i	−0.993244	−	0.116046i	$-0.962978\pi$
$19$	−6.93224	−	4.00233i	−1.59036	−	0.918197i	−0.597121	−	0.802152i	$-0.703689\pi$
$20$	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	−0.486561	−	0.873647i	$-0.661749\pi$
$23$	2.46180	−	4.26396i	0.513320	−	0.889096i	0.999881	−	0.0154494i	$-0.00491789\pi$
$24$		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	−0.613149	−	0.789967i	$-0.710097\pi$
$31$	−1.31172	+	0.757322i	−0.235592	+	0.136019i	0.377557	+	0.925986i	$0.376764\pi$
$32$	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	−0.729013	−	0.684499i	$-0.760021\pi$
$37$	1.38862	−	2.40515i	0.228287	−	0.395405i	0.957301	+	0.289095i	$0.0933542\pi$
$38$	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	$0.190627\pi$
$43$			7.39300i			1.12742i	−0.825972	+	0.563711i	$0.809373\pi$
$44$	−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	$-0.966570\pi$
$47$	−2.78654	+	4.82642i	−0.406458	+	0.704006i	0.588032	+	0.808838i	$0.299903\pi$
$48$		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	$-0.739971\pi$
$53$	−2.87828	+	1.66178i	−0.395362	+	0.228262i	0.289119	+	0.957293i	$0.406638\pi$
$54$		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	$-0.136897\pi$
$59$	0.717330	+	1.24245i	0.0933884	+	0.161753i	−0.815546	+	0.578692i	$0.803564\pi$
$60$		0			0
$61$	7.30221	−	12.6478i	0.934952	−	1.61938i	0.160233	−	0.987079i	$-0.448775\pi$
$61$	7.30221	−	12.6478i	0.934952	−	1.61938i	0.774719	−	0.632306i	$-0.217891\pi$
$62$	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	$-0.608344\pi$
$67$	2.58315	−	1.49138i	0.315582	−	0.182201i	0.649422	+	0.760428i	$0.275011\pi$
$68$	−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	$-0.737910\pi$
$71$	−11.4553			−1.35949			−0.679747	+	0.733447i	$0.737910\pi$
$72$		0			0
$73$	0.0244370	+	0.0423261i	0.00286014	+	0.00495390i	0.867452	−	0.497521i	$-0.165756\pi$
$73$	0.0244370	+	0.0423261i	0.00286014	+	0.00495390i	−0.864592	+	0.502475i	$0.832423\pi$
$74$	−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	0.433431	−	0.901187i	$-0.357303\pi$
$79$	−1.15816	−	0.668665i	−0.130303	−	0.0752307i	−0.563735	+	0.825956i	$0.690636\pi$
$80$	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	$-0.664879\pi$
$83$	−9.02165			−0.990255			−0.495128	+	0.868820i	$0.664879\pi$
$84$		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	$-0.444983\pi$
$89$	−5.61463	−	3.24161i	−0.595149	−	0.343610i	−0.767131	+	0.641491i	$0.778316\pi$
$90$		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	$-0.568132\pi$
$101$	5.30278	−	3.06156i	0.527646	−	0.304637i	0.740058	+	0.672544i	$0.234798\pi$
$102$		0			0
$103$	−6.18578	−	3.57136i	−0.609503	−	0.351897i	0.163268	−	0.986582i	$-0.447796\pi$
$103$	−6.18578	−	3.57136i	−0.609503	−	0.351897i	−0.772771	+	0.634685i	$0.781130\pi$
$104$	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	$-0.793385\pi$
$107$	1.29481	−	2.24267i	0.125174	−	0.216807i	0.921801	+	0.387664i	$0.126718\pi$
$108$		0			0
$109$	−1.37701	−	2.38505i	−0.131894	−	0.228447i	0.792513	−	0.609855i	$-0.208772\pi$
$109$	−1.37701	−	2.38505i	−0.131894	−	0.228447i	−0.924407	+	0.381409i	$0.875439\pi$
$110$	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	$0.118355\pi$
$127$			8.18873i			0.726632i	−0.931666	+	0.363316i	$0.881645\pi$
$128$	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	$-0.829053\pi$
$131$	0.153906	−	0.266573i	0.0134469	−	0.0232906i	0.872671	+	0.488309i	$0.162386\pi$
$132$		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	$-0.609094\pi$
$137$	3.64686	−	2.10552i	0.311573	−	0.179887i	0.647630	+	0.761955i	$0.275760\pi$
$138$		0			0
$139$			10.5488i			0.894736i	0.894350	+	0.447368i	$0.147639\pi$
$139$			10.5488i			0.894736i	−0.894350	+	0.447368i	$0.852361\pi$
$140$	−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	$-0.0857075\pi$
$149$	14.8380	+	8.56672i	1.21558	+	0.701813i	0.251607	+	0.967829i	$0.419041\pi$
$150$		0			0
$151$	−6.08270	+	3.51185i	−0.495003	+	0.285790i	−0.726648	−	0.687010i	$-0.758923\pi$
$151$	−6.08270	+	3.51185i	−0.495003	+	0.285790i	0.231645	+	0.972800i	$0.425589\pi$
$152$	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	0.822631	−	0.568576i	$-0.192505\pi$
$157$	−1.01600	−	1.75976i	−0.0810853	−	0.140444i	−0.903716	+	0.428132i	$0.859172\pi$
$158$	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	0.675729	−	0.737150i	$-0.263829\pi$
$163$	4.79027	+	2.76566i	0.375203	+	0.216623i	−0.300526	+	0.953774i	$0.597162\pi$
$164$	−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	$-0.420714\pi$
$167$	6.37142			0.493035			0.246518	+	0.969138i	$0.420714\pi$
$168$		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	$-0.632281\pi$
$173$	−18.3863	−	10.6153i	−1.39788	−	0.807069i	−0.994171	+	0.107816i	$0.965614\pi$
$174$		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	0.939840	+	0.341616i	$0.110974\pi$
$179$	10.2453	+	17.7453i	0.765768	+	1.32635i	−0.174072	+	0.984733i	$0.555693\pi$
$180$		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	$-0.915103\pi$
$191$	−3.51133	+	6.08181i	−0.254071	+	0.440064i	0.710572	+	0.703625i	$0.248436\pi$
$192$		0			0
$193$	8.66227	+	15.0035i	0.623524	+	1.07997i	0.988824	+	0.149085i	$0.0476329\pi$
$193$	8.66227	+	15.0035i	0.623524	+	1.07997i	−0.365301	+	0.930890i	$0.619034\pi$
$194$	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	−0.480764	−	0.876850i	$-0.659641\pi$
$199$	0.539285	−	0.311356i	0.0382289	−	0.0220715i	0.518993	+	0.854779i	$0.326307\pi$
$200$	−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	$-0.772983\pi$
$211$		−	19.0072i		−	1.30851i	0.756275	−	0.654253i	$-0.227017\pi$
$212$	−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	$-0.852378\pi$
$223$		−	13.3599i		−	0.894643i	0.894373	−	0.447321i	$-0.147622\pi$
$224$	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	$-0.124936\pi$
$227$	1.96956	+	3.41138i	0.130724	+	0.226421i	−0.793232	+	0.608920i	$0.791603\pi$
$228$		0			0
$229$	−1.44488	+	2.50261i	−0.0954804	+	0.165377i	−0.909809	−	0.415027i	$-0.863772\pi$
$229$	−1.44488	+	2.50261i	−0.0954804	+	0.165377i	0.814329	+	0.580404i	$0.197105\pi$
$230$	−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	$-0.496608\pi$
$233$	−12.9746	−	7.49088i	−0.849993	−	0.490744i	−0.860648	+	0.509200i	$0.829942\pi$
$234$		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	$-0.397985\pi$
$239$	9.74049			0.630060			0.315030	+	0.949082i	$0.397985\pi$
$240$		0			0
$241$	−3.01158	−	5.21621i	−0.193993	−	0.336006i	0.752577	−	0.658504i	$-0.228811\pi$
$241$	−3.01158	−	5.21621i	−0.193993	−	0.336006i	−0.946570	+	0.322499i	$0.895477\pi$
$242$	−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	$-0.470241\pi$
$251$	2.95805			0.186710			0.0933551	+	0.995633i	$0.470241\pi$
$252$		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	$-0.345368\pi$
$257$	−1.04960	−	0.605984i	−0.0654719	−	0.0378002i	−0.532379	+	0.846506i	$0.678702\pi$
$258$		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	$-0.275390\pi$
$263$	−5.43216	−	9.40878i	−0.334962	−	0.580171i	−0.983477	+	0.181031i	$0.942057\pi$
$264$		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	$-0.741662\pi$
$269$	−6.63128	+	3.82857i	−0.404316	+	0.233432i	0.284028	+	0.958816i	$0.408329\pi$
$270$		0			0
$271$	17.2222	+	9.94322i	1.04617	+	0.604008i	0.921575	−	0.388200i	$-0.126903\pi$
$271$	17.2222	+	9.94322i	1.04617	+	0.604008i	0.124597	+	0.992207i	$0.460236\pi$
$272$	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	0.748410	−	0.663237i	$-0.230818\pi$
$277$	−3.33158	−	5.77046i	−0.200175	−	0.346713i	−0.948585	+	0.316523i	$0.897484\pi$
$278$	−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	−0.681947	−	0.731401i	$-0.738867\pi$
$283$	−6.55255	+	3.78312i	−0.389509	+	0.224883i	0.292439	+	0.956284i	$0.405533\pi$
$284$	−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	$-0.985572\pi$
$307$		−	1.58786i		−	0.0906240i	0.998973	−	0.0453120i	$-0.0144282\pi$
$308$	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	0.997256	+	0.0740353i	$0.0235878\pi$
$311$	9.92410	+	17.1891i	0.562744	+	0.974702i	−0.434511	+	0.900666i	$0.643079\pi$
$312$		0			0
$313$	−5.26944	+	9.12693i	−0.297846	+	0.515885i	−0.975643	−	0.219365i	$-0.929602\pi$
$313$	−5.26944	+	9.12693i	−0.297846	+	0.515885i	0.677797	+	0.735249i	$0.262935\pi$
$314$	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	$-0.455990\pi$
$317$	−11.5912	−	6.69221i	−0.651029	−	0.375872i	−0.788850	+	0.614585i	$0.789323\pi$
$318$		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	−0.336053	−	0.941843i	$-0.609092\pi$
$331$	−24.0106	−	13.8625i	−1.31974	−	0.761952i	−0.983687	+	0.179891i	$0.942426\pi$
$332$	−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	$-0.178222\pi$
$347$	−0.676069	−	1.17099i	−0.0362933	−	0.0628618i	−0.883602	+	0.468240i	$0.844888\pi$
$348$		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	$-0.559756\pi$
$353$	10.7257	−	6.19247i	0.570870	−	0.329592i	0.757497	+	0.652839i	$0.226422\pi$
$354$		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	$-0.942417\pi$
$359$	−6.36683	+	11.0277i	−0.336028	+	0.582018i	0.647653	+	0.761935i	$0.275750\pi$
$360$		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	−0.764492	−	0.644633i	$-0.777010\pi$
$367$	−11.2735	+	6.50873i	−0.588469	+	0.339753i	0.176023	+	0.984386i	$0.443677\pi$
$368$	−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	−0.780242	−	0.625477i	$-0.784904\pi$
$373$	2.92708	−	5.06985i	0.151558	−	0.262507i	0.931801	+	0.362971i	$0.118238\pi$
$374$	−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	$-0.791691\pi$
$379$		−	23.7003i		−	1.21740i	0.793399	−	0.608701i	$-0.208309\pi$
$380$	−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	$-0.695871\pi$
$383$	8.19122	−	14.1876i	0.418552	−	0.724953i	0.995794	+	0.0916198i	$0.0292044\pi$
$384$		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	$-0.604808\pi$
$389$	6.59701	−	3.80878i	0.334482	−	0.193113i	0.657829	+	0.753167i	$0.271475\pi$
$390$		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	−0.741520	−	0.670931i	$-0.765895\pi$
$397$	4.18986	−	7.25706i	0.210283	−	0.364221i	0.951803	+	0.306710i	$0.0992281\pi$
$398$	−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	$-0.145751\pi$
$401$	19.2770	+	11.1296i	0.962648	+	0.555785i	0.0656611	+	0.997842i	$0.479084\pi$
$402$		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	0.999586	−	0.0287748i	$-0.00916058\pi$
$409$	9.60372	+	16.6341i	0.474873	+	0.822505i	−0.524713	+	0.851279i	$0.675827\pi$
$410$	−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	$-0.861294\pi$
$419$	−37.1132			−1.81310			−0.906550	+	0.422098i	$0.861294\pi$
$420$		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	−0.923626	−	0.383295i	$-0.874789\pi$
$431$	−16.4788	−	28.5421i	−0.793756	−	1.37483i	0.129870	−	0.991531i	$-0.458544\pi$
$432$		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	0.780048	−	0.625719i	$-0.215194\pi$
$439$	13.1619	+	7.59904i	0.628184	+	0.362682i	−0.151864	+	0.988401i	$0.548528\pi$
$440$	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	0.223064	+	0.974804i	$0.428394\pi$
$443$	−15.4210	+	26.7099i	−0.732673	+	1.26903i	−0.955737	+	0.294223i	$0.904939\pi$
$444$		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	0.102446	+	0.994739i	$0.467333\pi$
$457$	−17.3211	+	30.0010i	−0.810246	+	1.40339i	−0.912692	+	0.408649i	$0.866000\pi$
$458$	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	$-0.775317\pi$
$463$		−	27.9163i		−	1.29738i	0.761053	−	0.648690i	$-0.224683\pi$
$464$	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	−0.0847796	+	0.996400i	$0.527019\pi$
$467$	−19.5636	+	33.8852i	−0.905297	+	1.56802i	−0.820518	+	0.571621i	$0.806315\pi$
$468$		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	0.983325	+	0.181857i	$0.0582106\pi$
$479$	14.2074	+	24.6080i	0.649155	+	1.12437i	−0.334170	+	0.942513i	$0.608456\pi$
$480$		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	$-0.929145\pi$
$487$	−28.0663	+	16.2041i	−1.27180	+	0.734276i	−0.296476	+	0.955040i	$0.595812\pi$
$488$	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	$-0.356569\pi$
$491$	19.3004			0.871017			0.435508	+	0.900185i	$0.356569\pi$
$492$		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	−0.0969381	−	0.995290i	$-0.530905\pi$
$499$	−22.5026	−	12.9919i	−1.00735	−	0.581596i	−0.910416	+	0.413694i	$0.864238\pi$
$500$	−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	$-0.629591\pi$
$503$	−17.7613			−0.791939			−0.395969	+	0.918264i	$0.629591\pi$
$504$		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	$-0.529229\pi$
$509$	−22.5593	−	13.0246i	−0.999923	−	0.577306i	−0.908226	+	0.418481i	$0.862563\pi$
$510$		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	$-0.931476\pi$
$521$	−29.2252	+	16.8732i	−1.28038	+	0.739228i	−0.303463	+	0.952843i	$0.598143\pi$
$522$		0			0
$523$	17.2979	+	9.98697i	0.756386	+	0.436700i	0.827997	−	0.560733i	$-0.189481\pi$
$523$	17.2979	+	9.98697i	0.756386	+	0.436700i	−0.0716106	+	0.997433i	$0.522814\pi$
$524$	−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	−0.769421	−	0.638743i	$-0.779455\pi$
$541$	3.91821	−	6.78654i	0.168457	−	0.291776i	0.937878	+	0.346966i	$0.112788\pi$
$542$	−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	$0.359717\pi$
$547$			42.3065i			1.80890i	−0.426584	+	0.904448i	$0.640283\pi$
$548$	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	$-0.739476\pi$
$557$	−9.26900	+	5.35146i	−0.392740	+	0.226749i	0.290607	+	0.956843i	$0.406143\pi$
$558$		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	$-0.228385\pi$
$563$	−4.57187	−	7.91870i	−0.192681	−	0.333734i	−0.946138	+	0.323764i	$0.895052\pi$
$564$		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	$-0.121512\pi$
$569$	25.5092	+	14.7277i	1.06940	+	0.617419i	0.141384	+	0.989955i	$0.454845\pi$
$570$		0			0
$571$	28.0410	−	16.1895i	1.17348	−	0.677508i	0.218982	−	0.975729i	$-0.429726\pi$
$571$	28.0410	−	16.1895i	1.17348	−	0.677508i	0.954497	+	0.298221i	$0.0963931\pi$
$572$	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	0.799526	−	0.600631i	$-0.205084\pi$
$577$	−2.89208	−	5.00923i	−0.120399	−	0.208537i	−0.919925	+	0.392094i	$0.871751\pi$
$578$	−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	$-0.284797\pi$
$587$	30.3210			1.25148			0.625740	+	0.780032i	$0.284797\pi$
$588$		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	$-0.212374\pi$
$593$	15.6450	+	9.03263i	0.642462	+	0.370926i	−0.143100	+	0.989708i	$0.545707\pi$
$594$		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	$-0.148896\pi$
$599$	1.36569	+	2.36544i	0.0558006	+	0.0966494i	−0.836776	+	0.547546i	$0.815562\pi$
$600$		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	0.869599	−	0.493758i	$-0.164377\pi$
$607$	21.6019	+	12.4718i	0.876792	+	0.506216i	0.00719299	+	0.999974i	$0.497710\pi$
$608$	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	−0.993013	−	0.118002i	$-0.962351\pi$
$613$	−14.8231	−	25.6744i	−0.598699	−	1.03698i	0.394314	−	0.918976i	$-0.370982\pi$
$614$	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	−0.110029	−	0.993928i	$-0.535094\pi$
$619$	17.3094	−	9.99359i	0.695724	−	0.401676i	0.805753	+	0.592252i	$0.201761\pi$
$620$	−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	$0.0503344\pi$
$631$			7.91131i			0.314944i	−0.987523	+	0.157472i	$0.949666\pi$
$632$	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	$-0.915227\pi$
$641$	−30.8675	+	17.8214i	−1.21919	+	0.703902i	−0.254448	+	0.967086i	$0.581894\pi$
$642$		0			0
$643$			7.96178i			0.313982i	0.987600	+	0.156991i	$0.0501794\pi$
$643$			7.96178i			0.313982i	−0.987600	+	0.156991i	$0.949821\pi$
$644$	−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	−0.754336	−	0.656489i	$-0.772041\pi$
$647$	−24.0551	−	41.6647i	−0.945704	−	1.63801i	−0.191368	−	0.981518i	$-0.561292\pi$
$648$		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	$-0.561295\pi$
$653$	−29.0569	−	16.7760i	−1.13708	−	0.656495i	−0.945706	+	0.325022i	$0.894628\pi$
$654$		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	$-0.443268\pi$
$659$	9.10230			0.354575			0.177288	+	0.984159i	$0.443268\pi$
$660$		0			0
$661$	−7.12959	−	12.3488i	−0.277309	−	0.480313i	0.693406	−	0.720547i	$-0.256109\pi$
$661$	−7.12959	−	12.3488i	−0.277309	−	0.480313i	−0.970715	+	0.240234i	$0.922776\pi$
$662$	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	$-0.567368\pi$
$677$	−30.2292	−	17.4528i	−1.16180	−	0.670766i	−0.951735	+	0.306921i	$0.900701\pi$
$678$		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	−0.860130	−	0.510075i	$-0.829618\pi$
$683$	−22.7839	−	39.4629i	−0.871803	−	1.51001i	−0.0116726	−	0.999932i	$-0.503716\pi$
$684$		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	0.369665	−	0.929165i	$-0.379472\pi$
$691$	−6.57653	−	3.79696i	−0.250183	−	0.144443i	−0.619848	+	0.784722i	$0.712806\pi$
$692$	−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	−0.542860	−	0.839823i	$-0.682658\pi$
$709$	12.1387	−	21.0249i	0.455879	−	0.789605i	0.998738	+	0.0502185i	$0.0159918\pi$
$710$	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	0.479763	+	0.877398i	$0.340723\pi$
$719$	−13.9425	+	24.1491i	−0.519967	+	0.900610i	−0.999731	+	0.0232120i	$0.992611\pi$
$720$		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	$0.00503791\pi$
$727$			0.853452i			0.0316528i	−0.999875	+	0.0158264i	$0.994962\pi$
$728$	−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	−0.528971	−	0.848640i	$-0.677422\pi$
$733$	12.7372	−	22.0614i	0.470458	−	0.814857i	0.999429	+	0.0337825i	$0.0107553\pi$
$734$	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	$-0.443734\pi$
$739$	30.3461	−	17.5203i	1.11630	−	0.644496i	0.940454	+	0.339921i	$0.110401\pi$
$740$	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	$-0.677339\pi$
$743$	−28.8253			−1.05750			−0.528750	+	0.848778i	$0.677339\pi$
$744$		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	0.878494	−	0.477753i	$-0.158549\pi$
$751$	24.7734	+	14.3029i	0.903994	+	0.521921i	0.0255004	+	0.999675i	$0.491882\pi$
$752$	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	$-0.506878\pi$
$761$	−24.7788	−	14.3060i	−0.898231	−	0.518594i	−0.876626	+	0.481173i	$0.840211\pi$
$762$		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	$-0.944976\pi$
$773$	−36.9413	+	21.3281i	−1.32869	+	0.767117i	−0.343589	+	0.939120i	$0.611643\pi$
$774$		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	−0.430068	−	0.902796i	$-0.641511\pi$
$787$	3.83610	−	2.21477i	0.136742	−	0.0789481i	0.566810	+	0.823848i	$0.308177\pi$
$788$	−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	$-0.362467\pi$
$809$	40.2345	−	23.2294i	1.41457	−	0.816702i	0.995815	+	0.0913970i	$0.0291332\pi$
$810$		0			0
$811$		−	12.2358i		−	0.429657i	−0.976652	−	0.214829i	$-0.931081\pi$
$811$		−	12.2358i		−	0.429657i	0.976652	−	0.214829i	$-0.0689193\pi$
$812$	−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	$-0.398899\pi$
$821$	−10.1503	−	5.86030i	−0.354249	−	0.204526i	−0.666555	+	0.745456i	$0.732232\pi$
$822$		0			0
$823$	29.5545	−	17.0633i	1.03021	−	0.594790i	0.113162	−	0.993577i	$-0.463902\pi$
$823$	29.5545	−	17.0633i	1.03021	−	0.594790i	0.917044	+	0.398787i	$0.130569\pi$
$824$	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	$-0.326676\pi$
$827$	29.7930			1.03600			0.518001	+	0.855380i	$0.326676\pi$
$828$		0			0
$829$	21.6981	+	37.5822i	0.753605	+	1.30528i	0.946065	+	0.323978i	$0.105020\pi$
$829$	21.6981	+	37.5822i	0.753605	+	1.30528i	−0.192459	+	0.981305i	$0.561646\pi$
$830$	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	$-0.860125\pi$
$839$	−52.4272			−1.80999			−0.904995	+	0.425423i	$0.860125\pi$
$840$		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	$-0.733773\pi$
$857$	−10.6106	+	6.12603i	−0.362451	+	0.209261i	0.307704	+	0.951482i	$0.400439\pi$
$858$		0			0
$859$	−45.0377	−	26.0026i	−1.53667	−	0.887196i	−0.999031	−	0.0440193i	$-0.985984\pi$
$859$	−45.0377	−	26.0026i	−1.53667	−	0.887196i	−0.537637	−	0.843176i	$-0.680683\pi$
$860$	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	$-0.757353\pi$
$863$	6.94583	−	12.0305i	0.236439	−	0.409524i	0.959690	+	0.281061i	$0.0906864\pi$
$864$		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	0.332240	+	0.943195i	$0.392196\pi$
$877$	−19.2703	+	33.3771i	−0.650711	+	1.12706i	−0.982951	+	0.183870i	$0.941138\pi$
$878$	−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	$0.264779\pi$
$883$			43.9289i			1.47833i	−0.673527	+	0.739163i	$0.735221\pi$
$884$	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	$-0.748914\pi$
$887$	7.80639	−	13.5211i	0.262113	−	0.453993i	0.966803	+	0.255522i	$0.0822474\pi$
$888$		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	−0.515293	−	0.857014i	$-0.672317\pi$
$907$	−0.925872	+	0.534552i	−0.0307431	+	0.0177495i	0.484550	+	0.874764i	$0.338983\pi$
$908$	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	$-0.699951\pi$
$911$	−35.4745			−1.17532			−0.587661	+	0.809107i	$0.699951\pi$
$912$		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	−0.263143	−	0.964757i	$-0.584759\pi$
$919$	−37.2941	−	21.5318i	−1.23022	−	0.710267i	−0.967075	+	0.254490i	$0.918092\pi$
$920$	−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	$-0.340927\pi$
$929$	−1.25933	−	0.727077i	−0.0413174	−	0.0238546i	−0.520516	+	0.853852i	$0.674261\pi$
$930$		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	$-0.812579\pi$
$941$	−23.5114	+	13.5743i	−0.766450	+	0.442510i	0.0651568	+	0.997875i	$0.479245\pi$
$942$		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	−0.0683027	−	0.997665i	$-0.521758\pi$
$947$	25.5373	−	44.2319i	0.829852	−	1.43735i	0.898154	−	0.439680i	$-0.144908\pi$
$948$		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	$-0.949858\pi$
$967$		−	9.75651i		−	0.313748i	0.987619	−	0.156874i	$-0.0501417\pi$
$968$	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	−0.0513476	+	0.998681i	$0.516352\pi$
$971$	−27.7505	+	48.0653i	−0.890557	+	1.54249i	−0.839209	+	0.543809i	$0.816982\pi$
$972$		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	$-0.777861\pi$
$977$	−18.5299	+	10.6982i	−0.592824	+	0.342267i	0.173389	+	0.984853i	$0.444528\pi$
$978$		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	$-0.176923\pi$
$983$	−1.01003	−	1.74942i	−0.0322149	−	0.0557979i	−0.881683	+	0.471842i	$0.843589\pi$
$984$		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	$-0.830344\pi$
$991$	−26.8179	+	15.4834i	−0.851900	+	0.491845i	0.00939132	+	0.999956i	$0.497011\pi$
$992$	−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	0.930982	−	0.365064i	$-0.118953\pi$
$997$	4.71534	+	8.16720i	0.149336	+	0.258658i	−0.781646	+	0.623722i	$0.785620\pi$
$998$	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.107.2	yes	28
3.2	odd	2	inner	756.2.be.d.107.13	yes	28
4.3	odd	2		756.2.be.c.107.6	✓	28
7.4	even	3		756.2.be.c.431.9	yes	28
12.11	even	2		756.2.be.c.107.9	yes	28
21.11	odd	6		756.2.be.c.431.6	yes	28
28.11	odd	6	inner	756.2.be.d.431.13	yes	28
84.11	even	6	inner	756.2.be.d.431.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.6	✓	28	4.3	odd	2
756.2.be.c.107.9	yes	28	12.11	even	2
756.2.be.c.431.6	yes	28	21.11	odd	6
756.2.be.c.431.9	yes	28	7.4	even	3
756.2.be.d.107.2	yes	28	1.1	even	1	trivial
756.2.be.d.107.13	yes	28	3.2	odd	2	inner
756.2.be.d.431.2	yes	28	84.11	even	6	inner
756.2.be.d.431.13	yes	28	28.11	odd	6	inner

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)

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

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