LMFDB - Embedded newform 756.2.be.d.107.13

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			107.13
Character	$\chi$	$=$	756.107
Dual form			756.2.be.d.431.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33158 - 0.476336i) q^{2} +(1.54621 - 1.26856i) q^{4} +(-2.47695 - 1.43007i) q^{5} +(-2.52686 - 0.784194i) q^{7} +(1.45464 - 2.42570i) q^{8} +O(q^{10})$	\(q+(1.33158 - 0.476336i) q^{2} +(1.54621 - 1.26856i) q^{4} +(-2.47695 - 1.43007i) q^{5} +(-2.52686 - 0.784194i) q^{7} +(1.45464 - 2.42570i) q^{8} +(-3.97945 - 0.724388i) q^{10} +(0.887062 + 1.53644i) q^{11} -4.70960 q^{13} +(-3.73826 + 0.159419i) q^{14} +(0.781518 - 3.92291i) q^{16} +(6.08556 - 3.51350i) q^{17} +(-6.93224 - 4.00233i) q^{19} +(-5.64401 + 0.930975i) q^{20} +(1.91305 + 1.62335i) q^{22} +(-2.46180 + 4.26396i) q^{23} +(1.59019 + 2.75429i) q^{25} +(-6.27121 + 2.24335i) q^{26} +(-4.90185 + 1.99295i) q^{28} -7.21461i q^{29} +(-1.31172 + 0.757322i) q^{31} +(-0.827971 - 5.59593i) q^{32} +(6.42980 - 7.57728i) q^{34} +(5.13747 + 5.55600i) q^{35} +(1.38862 - 2.40515i) q^{37} +(-11.1373 - 2.02734i) q^{38} +(-7.07199 + 3.92811i) q^{40} +4.94219i q^{41} +7.39300i q^{43} +(3.32064 + 1.25036i) q^{44} +(-1.24700 + 6.85044i) q^{46} +(2.78654 - 4.82642i) q^{47} +(5.77008 + 3.96310i) q^{49} +(3.42943 + 2.91009i) q^{50} +(-7.28202 + 5.97440i) q^{52} +(2.87828 - 1.66178i) q^{53} -5.07423i q^{55} +(-5.57789 + 4.98870i) q^{56} +(-3.43658 - 9.60683i) q^{58} +(-0.717330 - 1.24245i) q^{59} +(7.30221 - 12.6478i) q^{61} +(-1.38592 + 1.63325i) q^{62} +(-3.76805 - 7.05704i) q^{64} +(11.6654 + 6.73505i) q^{65} +(2.58315 - 1.49138i) q^{67} +(4.95246 - 13.1525i) q^{68} +(9.48747 + 4.95109i) q^{70} +11.4553 q^{71} +(0.0244370 + 0.0423261i) q^{73} +(0.703391 - 3.86410i) q^{74} +(-15.7959 + 2.60552i) q^{76} +(-1.03662 - 4.57799i) q^{77} +(-1.15816 - 0.668665i) q^{79} +(-7.54581 + 8.59923i) q^{80} +(2.35414 + 6.58092i) q^{82} +9.02165 q^{83} -20.0982 q^{85} +(3.52155 + 9.84437i) q^{86} +(5.01729 + 0.0832119i) q^{88} +(5.61463 + 3.24161i) q^{89} +(11.9005 + 3.69324i) q^{91} +(1.60263 + 9.71589i) q^{92} +(1.41149 - 7.75409i) q^{94} +(11.4472 + 19.8271i) q^{95} -1.07208 q^{97} +(9.57109 + 2.52869i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.169487	−	0.985532i	$-0.554211\pi$
$5$	−2.47695	−	1.43007i	−1.10773	−	0.639546i	−0.938239	+	0.345987i	$0.887544\pi$
$6$		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	0.968205	−	0.250158i	$-0.0804826\pi$
$11$	0.887062	+	1.53644i	0.267459	+	0.463253i	−0.700746	+	0.713411i	$0.747149\pi$
$12$		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	0.476333	−	0.879265i	$-0.341966\pi$
$17$	6.08556	−	3.51350i	1.47597	−	0.852149i	0.999632	+	0.0271159i	$0.00863232\pi$
$18$		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	$0.338251\pi$
$23$	−2.46180	+	4.26396i	−0.513320	+	0.889096i	−0.999881	+	0.0154494i	$0.995082\pi$
$24$		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	$-0.766354\pi$
$29$		−	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	$-0.710097\pi$
$31$	−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	$0.126116\pi$
$41$			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	$0.809373\pi$
$44$	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	−0.588032	−	0.808838i	$-0.700097\pi$
$47$	2.78654	−	4.82642i	0.406458	−	0.704006i	0.994490	+	0.104832i	$0.0334304\pi$
$48$		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	−0.289119	−	0.957293i	$-0.593362\pi$
$53$	2.87828	−	1.66178i	0.395362	−	0.228262i	0.684481	+	0.729031i	$0.260029\pi$
$54$		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	0.815546	−	0.578692i	$-0.196436\pi$
$59$	−0.717330	−	1.24245i	−0.0933884	−	0.161753i	−0.908935	+	0.416938i	$0.863103\pi$
$60$		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	$-0.262090\pi$
$71$	11.4553			1.35949			0.679747	+	0.733447i	$0.262090\pi$
$72$		0			0
$73$	0.0244370	+	0.0423261i	0.00286014	+	0.00495390i	0.867452	−	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	$-0.335121\pi$
$83$	9.02165			0.990255			0.495128	+	0.868820i	$0.335121\pi$
$84$		0			0
$85$	−20.0982			−2.17995
$86$	3.52155	+	9.84437i	0.379739	+	1.06155i
$87$		0			0
$88$	5.01729	+	0.0832119i	0.534845	+	0.00887042i
$89$	5.61463	+	3.24161i	0.595149	+	0.343610i	0.767131	−	0.641491i	$-0.221684\pi$
$89$	5.61463	+	3.24161i	0.595149	+	0.343610i	−0.171982	+	0.985100i	$0.555017\pi$
$90$		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	−0.740058	−	0.672544i	$-0.765202\pi$
$101$	−5.30278	+	3.06156i	−0.527646	+	0.304637i	0.212411	+	0.977180i	$0.431868\pi$
$102$		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	−0.921801	−	0.387664i	$-0.873282\pi$
$107$	−1.29481	+	2.24267i	−0.125174	+	0.216807i	0.796627	+	0.604471i	$0.206615\pi$
$108$		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	$-0.668454\pi$
$113$		−	18.3520i		−	1.72641i	0.504854	−	0.863205i	$-0.331546\pi$
$114$		0			0
$115$	12.1955	−	7.04107i	1.13724	−	0.656583i
$116$	−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	−0.872671	−	0.488309i	$-0.837614\pi$
$131$	−0.153906	+	0.266573i	−0.0134469	+	0.0232906i	0.859224	+	0.511600i	$0.170947\pi$
$132$		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	−0.647630	−	0.761955i	$-0.724240\pi$
$137$	−3.64686	+	2.10552i	−0.311573	+	0.179887i	0.336057	+	0.941842i	$0.390906\pi$
$138$		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	−0.251607	−	0.967829i	$-0.580959\pi$
$149$	−14.8380	−	8.56672i	−1.21558	−	0.701813i	−0.963969	+	0.266016i	$0.914293\pi$
$150$		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	$-0.579286\pi$
$167$	−6.37142			−0.493035			−0.246518	+	0.969138i	$0.579286\pi$
$168$		0			0
$169$	9.18033			0.706180
$170$	−26.7623	+	9.57349i	−2.05258	+	0.734253i
$171$		0			0
$172$	9.37845	+	11.4311i	0.715100	+	0.871614i
$173$	18.3863	+	10.6153i	1.39788	+	0.807069i	0.994171	−	0.107816i	$-0.0343859\pi$
$173$	18.3863	+	10.6153i	1.39788	+	0.807069i	0.403714	+	0.914885i	$0.367719\pi$
$174$		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	$-0.889026\pi$
$179$	−10.2453	−	17.7453i	−0.765768	−	1.32635i	0.174072	−	0.984733i	$-0.444307\pi$
$180$		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	−0.710572	−	0.703625i	$-0.751564\pi$
$191$	3.51133	−	6.08181i	0.254071	−	0.440064i	0.964643	+	0.263561i	$0.0848969\pi$
$192$		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	$0.0503277\pi$
$197$			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	$-0.659641\pi$
$199$	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	0.793232	−	0.608920i	$-0.208397\pi$
$227$	−1.96956	−	3.41138i	−0.130724	−	0.226421i	−0.923956	+	0.382499i	$0.875064\pi$
$228$		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	0.860648	−	0.509200i	$-0.170058\pi$
$233$	12.9746	+	7.49088i	0.849993	+	0.490744i	−0.0106555	+	0.999943i	$0.503392\pi$
$234$		0			0
$235$	−13.8042	+	7.96987i	−0.900488	+	0.519897i
$236$	−2.68526	−	1.01111i	−0.174796	−	0.0658179i
$237$		0			0
$238$	−22.1893	+	14.1045i	−1.43832	+	0.914261i
$239$	−9.74049			−0.630060			−0.315030	−	0.949082i	$-0.602015\pi$
$239$	−9.74049			−0.630060			−0.315030	+	0.949082i	$0.602015\pi$
$240$		0			0
$241$	−3.01158	−	5.21621i	−0.193993	−	0.336006i	0.752577	−	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	$-0.529759\pi$
$251$	−2.95805			−0.186710			−0.0933551	+	0.995633i	$0.529759\pi$
$252$		0			0
$253$	−8.73506			−0.549168
$254$	3.90059	+	10.9039i	0.244745	+	0.684174i
$255$		0			0
$256$	−14.7785	−	6.13165i	−0.923654	−	0.383228i
$257$	1.04960	+	0.605984i	0.0654719	+	0.0378002i	0.532379	−	0.846506i	$-0.321298\pi$
$257$	1.04960	+	0.605984i	0.0654719	+	0.0378002i	−0.466907	+	0.884307i	$0.654632\pi$
$258$		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	0.983477	−	0.181031i	$-0.0579433\pi$
$263$	5.43216	+	9.40878i	0.334962	+	0.580171i	−0.648516	+	0.761201i	$0.724610\pi$
$264$		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	−0.284028	−	0.958816i	$-0.591671\pi$
$269$	6.63128	−	3.82857i	0.404316	−	0.233432i	0.688345	+	0.725384i	$0.258338\pi$
$270$		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	$0.0936190\pi$
$281$			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	$-0.738867\pi$
$283$	−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	$0.0508758\pi$
$293$			5.44847i			0.318303i	−0.987254	+	0.159151i	$0.949124\pi$
$294$		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	$-0.976412\pi$
$311$	−9.92410	−	17.1891i	−0.562744	−	0.974702i	0.434511	−	0.900666i	$-0.356921\pi$
$312$		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	0.788850	−	0.614585i	$-0.210677\pi$
$317$	11.5912	+	6.69221i	0.651029	+	0.375872i	−0.137821	+	0.990457i	$0.544010\pi$
$318$		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	0.883602	−	0.468240i	$-0.155112\pi$
$347$	0.676069	+	1.17099i	0.0362933	+	0.0628618i	−0.847308	+	0.531102i	$0.821778\pi$
$348$		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	−0.757497	−	0.652839i	$-0.773578\pi$
$353$	−10.7257	+	6.19247i	−0.570870	+	0.329592i	0.186627	+	0.982431i	$0.440244\pi$
$354$		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	−0.647653	−	0.761935i	$-0.724250\pi$
$359$	6.36683	−	11.0277i	0.336028	−	0.582018i	0.983682	+	0.179917i	$0.0575829\pi$
$360$		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	−0.995794	−	0.0916198i	$-0.970796\pi$
$383$	−8.19122	+	14.1876i	−0.418552	+	0.724953i	0.577242	+	0.816573i	$0.304129\pi$
$384$		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	−0.657829	−	0.753167i	$-0.728525\pi$
$389$	−6.59701	+	3.80878i	−0.334482	+	0.193113i	0.323348	+	0.946280i	$0.395192\pi$
$390$		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	−0.0656611	−	0.997842i	$-0.520916\pi$
$401$	−19.2770	−	11.1296i	−0.962648	−	0.555785i	−0.896987	+	0.442057i	$0.854249\pi$
$402$		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	$-0.138706\pi$
$419$	37.1132			1.81310			0.906550	+	0.422098i	$0.138706\pi$
$420$		0			0
$421$	−1.14540			−0.0558236			−0.0279118	−	0.999610i	$-0.508886\pi$
$421$	−1.14540			−0.0558236			−0.0279118	+	0.999610i	$0.508886\pi$
$422$	−9.05380	−	25.3095i	−0.440732	−	1.23205i
$423$		0			0
$424$	0.155885	−	9.39913i	0.00757044	−	0.456462i
$425$	19.3544	+	11.1743i	0.938826	+	0.542032i
$426$		0			0
$427$	−28.3700	+	26.2329i	−1.37292	+	1.26950i
$428$	0.842920	+	5.11018i	0.0407441	+	0.247010i
$429$		0			0
$430$	5.35540	−	29.4201i	0.258261	−	1.41876i
$431$	16.4788	+	28.5421i	0.793756	+	1.37483i	0.923626	+	0.383295i	$0.125211\pi$
$431$	16.4788	+	28.5421i	0.793756	+	1.37483i	−0.129870	+	0.991531i	$0.541456\pi$
$432$		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	$-0.571606\pi$
$443$	15.4210	−	26.7099i	0.732673	−	1.26903i	0.955737	−	0.294223i	$-0.0950608\pi$
$444$		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	$-0.808260\pi$
$449$		−	24.0119i		−	1.13319i	0.823995	−	0.566596i	$-0.191740\pi$
$450$		0			0
$451$	−7.59336	+	4.38403i	−0.357557	+	0.206436i
$452$	−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	$0.201939\pi$
$461$			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	$-0.224683\pi$
$464$	−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	$-0.472981\pi$
$467$	19.5636	−	33.8852i	0.905297	−	1.56802i	0.820518	−	0.571621i	$-0.193685\pi$
$468$		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	$-0.941789\pi$
$479$	−14.2074	−	24.6080i	−0.649155	−	1.12437i	0.334170	−	0.942513i	$-0.391544\pi$
$480$		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	$-0.643431\pi$
$491$	−19.3004			−0.871017			−0.435508	+	0.900185i	$0.643431\pi$
$492$		0			0
$493$	−25.3485	−	43.9050i	−1.14164	−	1.97738i
$494$	52.4521	+	9.54798i	2.35993	+	0.429584i
$495$		0			0
$496$	1.94577	+	5.73762i	0.0873678	+	0.257627i
$497$	−28.9460	−	8.98318i	−1.29840	−	0.402951i
$498$		0			0
$499$	−22.5026	−	12.9919i	−1.00735	−	0.581596i	−0.0969381	−	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	$-0.370409\pi$
$503$	17.7613			0.791939			0.395969	+	0.918264i	$0.370409\pi$
$504$		0			0
$505$	17.5130			0.779317
$506$	−11.6314	+	4.16082i	−0.517080	+	0.184971i
$507$		0			0
$508$	10.3879	+	12.6615i	0.460888	+	0.561762i
$509$	22.5593	+	13.0246i	0.999923	+	0.577306i	0.908226	−	0.418481i	$-0.137437\pi$
$509$	22.5593	+	13.0246i	0.999923	+	0.577306i	0.0916978	+	0.995787i	$0.470771\pi$
$510$		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	0.303463	−	0.952843i	$-0.401857\pi$
$521$	29.2252	−	16.8732i	1.28038	−	0.739228i	0.976918	+	0.213615i	$0.0685238\pi$
$522$		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	−0.290607	−	0.956843i	$-0.593857\pi$
$557$	9.26900	−	5.35146i	0.392740	−	0.226749i	0.683347	+	0.730094i	$0.260524\pi$
$558$		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	0.946138	−	0.323764i	$-0.104948\pi$
$563$	4.57187	+	7.91870i	0.192681	+	0.333734i	−0.753457	+	0.657497i	$0.771615\pi$
$564$		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	$-0.545155\pi$
$569$	−25.5092	−	14.7277i	−1.06940	−	0.617419i	−0.928018	+	0.372536i	$0.878488\pi$
$570$		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	$-0.715203\pi$
$587$	−30.3210			−1.25148			−0.625740	+	0.780032i	$0.715203\pi$
$588$		0			0
$589$	12.1242			0.499569
$590$	1.95456	+	5.46390i	0.0804680	+	0.224945i
$591$		0			0
$592$	−8.34997	−	7.32709i	−0.343182	−	0.301141i
$593$	−15.6450	−	9.03263i	−0.642462	−	0.370926i	0.143100	−	0.989708i	$-0.454293\pi$
$593$	−15.6450	−	9.03263i	−0.642462	−	0.370926i	−0.785562	+	0.618782i	$0.787626\pi$
$594$		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	0.836776	−	0.547546i	$-0.184438\pi$
$599$	−1.36569	−	2.36544i	−0.0558006	−	0.0966494i	−0.892576	+	0.450896i	$0.851104\pi$
$600$		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	$-0.821917\pi$
$617$		−	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	$-0.535094\pi$
$619$	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	0.254448	−	0.967086i	$-0.418106\pi$
$641$	30.8675	−	17.8214i	1.21919	−	0.703902i	0.964746	+	0.263185i	$0.0847728\pi$
$642$		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	$0.227959\pi$
$647$	24.0551	+	41.6647i	0.945704	+	1.63801i	0.191368	+	0.981518i	$0.438708\pi$
$648$		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	$-0.105372\pi$
$653$	29.0569	+	16.7760i	1.13708	+	0.656495i	0.191376	+	0.981517i	$0.438705\pi$
$654$		0			0
$655$	0.762436	−	0.440193i	0.0297909	−	0.0171998i
$656$	19.3878	+	3.86241i	0.756965	+	0.150802i
$657$		0			0
$658$	−9.64737	+	18.4866i	−0.376094	+	0.720684i
$659$	−9.10230			−0.354575			−0.177288	−	0.984159i	$-0.556732\pi$
$659$	−9.10230			−0.354575			−0.177288	+	0.984159i	$0.556732\pi$
$660$		0			0
$661$	−7.12959	−	12.3488i	−0.277309	−	0.480313i	0.693406	−	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	0.951735	−	0.306921i	$-0.0992988\pi$
$677$	30.2292	+	17.4528i	1.16180	+	0.670766i	0.210066	+	0.977687i	$0.432632\pi$
$678$		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	$0.170382\pi$
$683$	22.7839	+	39.4629i	0.871803	+	1.51001i	0.0116726	+	0.999932i	$0.496284\pi$
$684$		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	$0.316049\pi$
$701$			44.3539i			1.67522i	−0.546267	+	0.837611i	$0.683951\pi$
$702$		0			0
$703$	−19.2524	+	11.1154i	−0.726119	+	0.419225i
$704$	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	$-0.659277\pi$
$719$	13.9425	−	24.1491i	0.519967	−	0.900610i	0.999731	−	0.0232120i	$-0.00738927\pi$
$720$		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	$-0.322661\pi$
$743$	28.8253			1.05750			0.528750	+	0.848778i	$0.322661\pi$
$744$		0			0
$745$	24.5020	+	42.4387i	0.897684	+	1.55483i
$746$	1.48268	−	8.14517i	0.0542850	−	0.298216i
$747$		0			0
$748$	24.6011	−	4.05793i	0.899505	−	0.148373i
$749$	5.03049	−	4.65154i	0.183810	−	0.169964i
$750$		0			0
$751$	24.7734	+	14.3029i	0.903994	+	0.521921i	0.878494	−	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	0.876626	−	0.481173i	$-0.159789\pi$
$761$	24.7788	+	14.3060i	0.898231	+	0.518594i	0.0216049	+	0.999767i	$0.493122\pi$
$762$		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	0.343589	−	0.939120i	$-0.388357\pi$
$773$	36.9413	−	21.3281i	1.32869	−	0.767117i	0.985096	+	0.172003i	$0.0550240\pi$
$774$		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	$0.00623859\pi$
$797$			1.10654i			0.0391957i	−0.999808	+	0.0195979i	$0.993761\pi$
$798$		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	−0.995815	−	0.0913970i	$-0.970867\pi$
$809$	−40.2345	+	23.2294i	−1.41457	+	0.816702i	−0.418755	+	0.908099i	$0.637533\pi$
$810$		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	0.666555	−	0.745456i	$-0.267768\pi$
$821$	10.1503	+	5.86030i	0.354249	+	0.204526i	−0.312306	+	0.949982i	$0.601101\pi$
$822$		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	$-0.673324\pi$
$827$	−29.7930			−1.03600			−0.518001	+	0.855380i	$0.673324\pi$
$828$		0			0
$829$	21.6981	+	37.5822i	0.753605	+	1.30528i	0.946065	+	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	$-0.139875\pi$
$839$	52.4272			1.80999			0.904995	+	0.425423i	$0.139875\pi$
$840$		0			0
$841$	−23.0506			−0.794850
$842$	−1.52520	+	0.545598i	−0.0525618	+	0.0188025i
$843$		0			0
$844$	−24.1117	−	29.3890i	−0.829959	−	1.01161i
$845$	−22.7392	−	13.1285i	−0.782253	−	0.451634i
$846$		0			0
$847$	−15.2540	+	14.1049i	−0.524132	+	0.484649i
$848$	−4.26957	−	12.5899i	−0.146618	−	0.432340i
$849$		0			0
$850$	31.0946	+	5.66023i	1.06654	+	0.194144i
$851$	6.83698	+	11.8420i	0.234369	+	0.405938i
$852$		0			0
$853$	12.6354			0.432628			0.216314	−	0.976324i	$-0.430597\pi$
$853$	12.6354			0.432628			0.216314	+	0.976324i	$0.430597\pi$
$854$	−25.2813	+	48.4449i	−0.865107	+	1.65775i
$855$		0			0
$856$	3.55658	+	6.40309i	0.121561	+	0.218853i
$857$	10.6106	−	6.12603i	0.362451	−	0.209261i	−0.307704	−	0.951482i	$-0.599561\pi$
$857$	10.6106	−	6.12603i	0.362451	−	0.209261i	0.670155	+	0.742221i	$0.266227\pi$
$858$		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	−0.959690	−	0.281061i	$-0.909314\pi$
$863$	−6.94583	+	12.0305i	−0.236439	+	0.409524i	0.723251	+	0.690585i	$0.242647\pi$
$864$		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	$0.0119048\pi$
$881$			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	$0.735221\pi$
$884$	−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	−0.966803	−	0.255522i	$-0.917753\pi$
$887$	−7.80639	+	13.5211i	−0.262113	+	0.453993i	0.704690	+	0.709515i	$0.251086\pi$
$888$		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	$-0.300049\pi$
$911$	35.4745			1.17532			0.587661	+	0.809107i	$0.300049\pi$
$912$		0			0
$913$	8.00276	+	13.8612i	0.264853	+	0.458739i
$914$	−8.77384	+	48.1994i	−0.290213	+	1.59429i
$915$		0			0
$916$	0.940617	+	5.70246i	0.0310789	+	0.188415i
$917$	0.597945	−	0.552902i	0.0197459	−	0.0182584i
$918$		0			0
$919$	−37.2941	−	21.5318i	−1.23022	−	0.710267i	−0.263143	−	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	0.520516	−	0.853852i	$-0.325739\pi$
$929$	1.25933	+	0.727077i	0.0413174	+	0.0238546i	−0.479199	+	0.877706i	$0.659073\pi$
$930$		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	−0.0651568	−	0.997875i	$-0.520755\pi$
$941$	23.5114	−	13.5743i	0.766450	−	0.442510i	0.831607	+	0.555365i	$0.187421\pi$
$942$		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	$0.478242\pi$
$947$	−25.5373	+	44.2319i	−0.829852	+	1.43735i	−0.898154	+	0.439680i	$0.855092\pi$
$948$		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	$0.0987361\pi$
$953$			18.8458i			0.610476i	−0.952276	+	0.305238i	$0.901264\pi$
$954$		0			0
$955$	−17.3948	+	10.0429i	−0.562883	+	0.324980i
$956$	−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	$-0.483648\pi$
$971$	27.7505	−	48.0653i	0.890557	−	1.54249i	0.839209	−	0.543809i	$-0.183018\pi$
$972$		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	−0.173389	−	0.984853i	$-0.555472\pi$
$977$	18.5299	−	10.6982i	0.592824	−	0.342267i	0.766213	+	0.642586i	$0.222139\pi$
$978$		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	0.881683	−	0.471842i	$-0.156411\pi$
$983$	1.01003	+	1.74942i	0.0322149	+	0.0557979i	−0.849468	+	0.527639i	$0.823077\pi$
$984$		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.107.13	yes	28
3.2	odd	2	inner	756.2.be.d.107.2	yes	28
4.3	odd	2		756.2.be.c.107.9	yes	28
7.4	even	3		756.2.be.c.431.6	yes	28
12.11	even	2		756.2.be.c.107.6	✓	28
21.11	odd	6		756.2.be.c.431.9	yes	28
28.11	odd	6	inner	756.2.be.d.431.2	yes	28
84.11	even	6	inner	756.2.be.d.431.13	yes	28

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more