LMFDB - Embedded newform 756.2.ck.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11789 + 1.32299i) q^{3} +(-0.682386 + 3.87000i) q^{5} +(2.62129 + 0.358920i) q^{7} +(-0.500623 + 2.95793i) q^{9} +O(q^{10})$	\(q+(1.11789 + 1.32299i) q^{3} +(-0.682386 + 3.87000i) q^{5} +(2.62129 + 0.358920i) q^{7} +(-0.500623 + 2.95793i) q^{9} +(0.639761 - 0.112807i) q^{11} +(2.79383 - 3.32955i) q^{13} +(-5.88282 + 3.42346i) q^{15} +4.23325 q^{17} -1.27018i q^{19} +(2.45548 + 3.86919i) q^{21} +(-3.69805 + 4.40717i) q^{23} +(-9.81281 - 3.57157i) q^{25} +(-4.47297 + 2.64434i) q^{27} +(-0.340590 - 0.405899i) q^{29} +(-1.83445 - 5.04012i) q^{31} +(0.864428 + 0.720293i) q^{33} +(-3.17775 + 9.89949i) q^{35} +(1.16130 + 2.01143i) q^{37} +(7.52818 - 0.0258750i) q^{39} +(-6.14659 - 5.15760i) q^{41} +(-0.264517 - 0.0962762i) q^{43} +(-11.1056 - 3.95587i) q^{45} +(-8.79969 - 3.20283i) q^{47} +(6.74235 + 1.88167i) q^{49} +(4.73233 + 5.60056i) q^{51} +(8.85622 - 5.11314i) q^{53} +2.55285i q^{55} +(1.68044 - 1.41993i) q^{57} +(0.258559 + 0.216957i) q^{59} +(-4.56709 + 12.5480i) q^{61} +(-2.37394 + 7.57393i) q^{63} +(10.9789 + 13.0842i) q^{65} +(1.70373 - 9.66231i) q^{67} +(-9.96468 + 0.0342494i) q^{69} +(9.11650 + 5.26341i) q^{71} +(-2.00088 - 1.15521i) q^{73} +(-6.24452 - 16.9749i) q^{75} +(1.71749 - 0.0660776i) q^{77} +(-2.46001 - 13.9514i) q^{79} +(-8.49875 - 2.96162i) q^{81} +(12.6075 - 10.5789i) q^{83} +(-2.88871 + 16.3827i) q^{85} +(0.156258 - 0.904351i) q^{87} +4.00479 q^{89} +(8.51848 - 7.72498i) q^{91} +(4.61732 - 8.06129i) q^{93} +(4.91560 + 0.866753i) q^{95} +(3.15648 - 8.67235i) q^{97} +(0.0133968 + 1.94884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.11789	+	1.32299i	0.645417	+	0.763831i
$3$	1.11789	+	1.32299i	0.645417	+	0.763831i
$4$		0			0
$5$	−0.682386	+	3.87000i	−0.305172	+	1.73072i	0.317520	+	0.948251i	$0.397150\pi$
$5$	−0.682386	+	3.87000i	−0.305172	+	1.73072i	−0.622693	+	0.782467i	$0.713961\pi$
$6$		0			0
$7$	2.62129	+	0.358920i	0.990756	+	0.135659i
$7$	2.62129	+	0.358920i	0.990756	+	0.135659i
$8$		0			0
$9$	−0.500623	+	2.95793i	−0.166874	+	0.985978i
$10$		0			0
$11$	0.639761	−	0.112807i	0.192895	−	0.0340126i	−0.0763658	−	0.997080i	$-0.524332\pi$
$11$	0.639761	−	0.112807i	0.192895	−	0.0340126i	0.269261	+	0.963067i	$0.413221\pi$
$12$		0			0
$13$	2.79383	−	3.32955i	0.774868	−	0.923452i	−0.223821	−	0.974630i	$-0.571853\pi$
$13$	2.79383	−	3.32955i	0.774868	−	0.923452i	0.998690	+	0.0511781i	$0.0162976\pi$
$14$		0			0
$15$	−5.88282	+	3.42346i	−1.51894	+	0.883934i
$16$		0			0
$17$	4.23325			1.02671			0.513357	−	0.858175i	$-0.328402\pi$
$17$	4.23325			1.02671			0.513357	+	0.858175i	$0.328402\pi$
$18$		0			0
$19$		−	1.27018i		−	0.291399i	−0.989329	−	0.145700i	$-0.953457\pi$
$19$		−	1.27018i		−	0.291399i	0.989329	−	0.145700i	$-0.0465433\pi$
$20$		0			0
$21$	2.45548	+	3.86919i	0.535830	+	0.844326i
$22$		0			0
$23$	−3.69805	+	4.40717i	−0.771097	+	0.918957i	−0.998495	−	0.0548445i	$-0.982534\pi$
$23$	−3.69805	+	4.40717i	−0.771097	+	0.918957i	0.227398	+	0.973802i	$0.426978\pi$
$24$		0			0
$25$	−9.81281	−	3.57157i	−1.96256	−	0.714314i
$26$		0			0
$27$	−4.47297	+	2.64434i	−0.860824	+	0.508903i
$28$		0			0
$29$	−0.340590	−	0.405899i	−0.0632459	−	0.0753736i	0.733494	−	0.679696i	$-0.237888\pi$
$29$	−0.340590	−	0.405899i	−0.0632459	−	0.0753736i	−0.796740	+	0.604322i	$0.793444\pi$
$30$		0			0
$31$	−1.83445	−	5.04012i	−0.329477	−	0.905232i	−0.988244	−	0.152884i	$-0.951144\pi$
$31$	−1.83445	−	5.04012i	−0.329477	−	0.905232i	0.658767	−	0.752347i	$-0.271078\pi$
$32$		0			0
$33$	0.864428	+	0.720293i	0.150478	+	0.125387i
$34$		0			0
$35$	−3.17775	+	9.89949i	−0.537138	+	1.67332i
$36$		0			0
$37$	1.16130	+	2.01143i	0.190917	+	0.330677i	0.945554	−	0.325464i	$-0.105521\pi$
$37$	1.16130	+	2.01143i	0.190917	+	0.330677i	−0.754638	+	0.656142i	$0.772187\pi$
$38$		0			0
$39$	7.52818	−	0.0258750i	1.20547	−	0.00414331i
$40$		0			0
$41$	−6.14659	−	5.15760i	−0.959936	−	0.805482i	0.0210065	−	0.999779i	$-0.493313\pi$
$41$	−6.14659	−	5.15760i	−0.959936	−	0.805482i	−0.980943	+	0.194297i	$0.937757\pi$
$42$		0			0
$43$	−0.264517	−	0.0962762i	−0.0403384	−	0.0146820i	0.321772	−	0.946817i	$-0.395721\pi$
$43$	−0.264517	−	0.0962762i	−0.0403384	−	0.0146820i	−0.362111	+	0.932135i	$0.617944\pi$
$44$		0			0
$45$	−11.1056	−	3.95587i	−1.65552	−	0.589706i
$46$		0			0
$47$	−8.79969	−	3.20283i	−1.28357	−	0.467180i	−0.391957	−	0.919984i	$-0.628202\pi$
$47$	−8.79969	−	3.20283i	−1.28357	−	0.467180i	−0.891610	+	0.452803i	$0.850424\pi$
$48$		0			0
$49$	6.74235	+	1.88167i	0.963193	+	0.268810i
$50$		0			0
$51$	4.73233	+	5.60056i	0.662658	+	0.784235i
$52$		0			0
$53$	8.85622	−	5.11314i	1.21650	−	0.702344i	0.252329	−	0.967642i	$-0.418803\pi$
$53$	8.85622	−	5.11314i	1.21650	−	0.702344i	0.964167	+	0.265297i	$0.0854701\pi$
$54$		0			0
$55$			2.55285i			0.344227i
$56$		0			0
$57$	1.68044	−	1.41993i	0.222580	−	0.188074i
$58$		0			0
$59$	0.258559	+	0.216957i	0.0336616	+	0.0282454i	0.659463	−	0.751737i	$-0.270784\pi$
$59$	0.258559	+	0.216957i	0.0336616	+	0.0282454i	−0.625802	+	0.779982i	$0.715228\pi$
$60$		0			0
$61$	−4.56709	+	12.5480i	−0.584756	+	1.60660i	0.195197	+	0.980764i	$0.437465\pi$
$61$	−4.56709	+	12.5480i	−0.584756	+	1.60660i	−0.779953	+	0.625839i	$0.784757\pi$
$62$		0			0
$63$	−2.37394	+	7.57393i	−0.299089	+	0.954225i
$64$		0			0
$65$	10.9789	+	13.0842i	1.36177	+	1.62289i
$66$		0			0
$67$	1.70373	−	9.66231i	0.208143	−	1.18044i	−0.684273	−	0.729226i	$-0.739880\pi$
$67$	1.70373	−	9.66231i	0.208143	−	1.18044i	0.892416	−	0.451213i	$-0.149009\pi$
$68$		0			0
$69$	−9.96468	+	0.0342494i	−1.19961	+	0.00412314i
$70$		0			0
$71$	9.11650	+	5.26341i	1.08193	+	0.624652i	0.931416	−	0.363956i	$-0.118574\pi$
$71$	9.11650	+	5.26341i	1.08193	+	0.624652i	0.150513	+	0.988608i	$0.451907\pi$
$72$		0			0
$73$	−2.00088	−	1.15521i	−0.234185	−	0.135207i	0.378316	−	0.925676i	$-0.376503\pi$
$73$	−2.00088	−	1.15521i	−0.234185	−	0.135207i	−0.612501	+	0.790470i	$0.709837\pi$
$74$		0			0
$75$	−6.24452	−	16.9749i	−0.721055	−	1.96010i
$76$		0			0
$77$	1.71749	−	0.0660776i	0.195726	−	0.00753025i
$78$		0			0
$79$	−2.46001	−	13.9514i	−0.276772	−	1.56965i	−0.733275	−	0.679932i	$-0.762009\pi$
$79$	−2.46001	−	13.9514i	−0.276772	−	1.56965i	0.456503	−	0.889722i	$-0.349102\pi$
$80$		0			0
$81$	−8.49875	−	2.96162i	−0.944306	−	0.329069i
$82$		0			0
$83$	12.6075	−	10.5789i	1.38385	−	1.16119i	0.416085	−	0.909326i	$-0.363402\pi$
$83$	12.6075	−	10.5789i	1.38385	−	1.16119i	0.967763	−	0.251861i	$-0.0810425\pi$
$84$		0			0
$85$	−2.88871	+	16.3827i	−0.313325	+	1.77695i
$86$		0			0
$87$	0.156258	−	0.904351i	0.0167527	−	0.0969566i
$88$		0			0
$89$	4.00479			0.424507			0.212254	−	0.977215i	$-0.431920\pi$
$89$	4.00479			0.424507			0.212254	+	0.977215i	$0.431920\pi$
$90$		0			0
$91$	8.51848	−	7.72498i	0.892980	−	0.809798i
$92$		0			0
$93$	4.61732	−	8.06129i	0.478793	−	0.835917i
$94$		0			0
$95$	4.91560	+	0.866753i	0.504330	+	0.0889270i
$96$		0			0
$97$	3.15648	−	8.67235i	0.320492	−	0.880543i	−0.669925	−	0.742429i	$-0.733674\pi$
$97$	3.15648	−	8.67235i	0.320492	−	0.880543i	0.990416	−	0.138114i	$-0.0441041\pi$
$98$		0			0
$99$	0.0133968	+	1.94884i	0.00134643	+	0.195866i
$100$		0			0
$101$	−9.22907	+	7.74411i	−0.918327	+	0.770568i	−0.973685	−	0.227899i	$-0.926814\pi$
$101$	−9.22907	+	7.74411i	−0.918327	+	0.770568i	0.0553581	+	0.998467i	$0.482370\pi$
$102$		0			0
$103$	12.3318	+	2.17442i	1.21508	+	0.214252i	0.744209	−	0.667947i	$-0.232827\pi$
$103$	12.3318	+	2.17442i	1.21508	+	0.214252i	0.470876	+	0.882199i	$0.343938\pi$
$104$		0			0
$105$	−16.6494	+	6.86244i	−1.62481	+	0.669705i
$106$		0			0
$107$	3.09467	+	1.78671i	0.299173	+	0.172728i	0.642071	−	0.766645i	$-0.278075\pi$
$107$	3.09467	+	1.78671i	0.299173	+	0.172728i	−0.342898	+	0.939373i	$0.611409\pi$
$108$		0			0
$109$	6.37741	+	11.0460i	0.610845	+	1.05801i	0.991098	+	0.133132i	$0.0425034\pi$
$109$	6.37741	+	11.0460i	0.610845	+	1.05801i	−0.380254	+	0.924882i	$0.624163\pi$
$110$		0			0
$111$	−1.36290	+	3.78496i	−0.129361	+	0.359253i
$112$		0			0
$113$	3.18210	+	8.74275i	0.299347	+	0.822449i	0.994609	+	0.103693i	$0.0330659\pi$
$113$	3.18210	+	8.74275i	0.299347	+	0.822449i	−0.695262	+	0.718756i	$0.744712\pi$
$114$		0			0
$115$	−14.5322	−	17.3189i	−1.35514	−	1.61499i
$116$		0			0
$117$	8.44995	+	9.93081i	0.781198	+	0.918104i
$118$		0			0
$119$	11.0966	+	1.51940i	1.01722	+	0.139283i
$120$		0			0
$121$	−9.94005	+	3.61788i	−0.903641	+	0.328898i
$122$		0			0
$123$	−0.0477670	−	13.8976i	−0.00430700	−	1.25310i
$124$		0			0
$125$	10.6939	−	18.5223i	0.956487	−	1.65668i
$126$		0			0
$127$	5.81728	+	10.0758i	0.516200	+	0.894084i	0.999823	+	0.0188080i	$0.00598712\pi$
$127$	5.81728	+	10.0758i	0.516200	+	0.894084i	−0.483623	+	0.875276i	$0.660680\pi$
$128$		0			0
$129$	−0.168329	−	0.457581i	−0.0148205	−	0.0402877i
$130$		0			0
$131$	−0.330003	−	0.276906i	−0.0288325	−	0.0241934i	0.628258	−	0.778005i	$-0.283768\pi$
$131$	−0.330003	−	0.276906i	−0.0288325	−	0.0241934i	−0.657090	+	0.753812i	$0.728213\pi$
$132$		0			0
$133$	0.455893	−	3.32951i	0.0395309	−	0.288706i
$134$		0			0
$135$	−7.18130	−	19.1149i	−0.618068	−	1.64515i
$136$		0			0
$137$	−4.94778	+	13.5939i	−0.422717	+	1.16141i	0.527429	+	0.849599i	$0.323156\pi$
$137$	−4.94778	+	13.5939i	−0.422717	+	1.16141i	−0.950146	+	0.311806i	$0.899066\pi$
$138$		0			0
$139$	−15.9851	−	2.81861i	−1.35584	−	0.239071i	−0.551965	−	0.833868i	$-0.686122\pi$
$139$	−15.9851	−	2.81861i	−1.35584	−	0.239071i	−0.803876	+	0.594796i	$0.797233\pi$
$140$		0			0
$141$	−5.59981	−	15.2224i	−0.471589	−	1.28195i
$142$		0			0
$143$	1.41178	−	2.44528i	0.118059	−	0.204485i
$144$		0			0
$145$	1.80324	−	1.04110i	0.149751	−	0.0864590i
$146$		0			0
$147$	5.04781	+	11.0236i	0.416336	+	0.909211i
$148$		0			0
$149$	0.174749	+	0.480118i	0.0143160	+	0.0393328i	0.946645	−	0.322279i	$-0.104449\pi$
$149$	0.174749	+	0.480118i	0.0143160	+	0.0393328i	−0.932329	+	0.361612i	$0.882227\pi$
$150$		0			0
$151$	−0.273788	−	1.55273i	−0.0222806	−	0.126359i	0.971639	−	0.236470i	$-0.0759905\pi$
$151$	−0.273788	−	1.55273i	−0.0222806	−	0.126359i	−0.993919	+	0.110111i	$0.964879\pi$
$152$		0			0
$153$	−2.11926	+	12.5217i	−0.171332	+	1.01232i
$154$		0			0
$155$	20.7571	−	3.66003i	1.66725	−	0.293981i
$156$		0			0
$157$	7.62298	−	9.08472i	0.608380	−	0.725040i	−0.370646	−	0.928774i	$-0.620864\pi$
$157$	7.62298	−	9.08472i	0.608380	−	0.725040i	0.979026	+	0.203735i	$0.0653080\pi$
$158$		0			0
$159$	16.6650	+	6.00077i	1.32162	+	0.475892i
$160$		0			0
$161$	−11.2755	+	10.2252i	−0.888633	+	0.805856i
$162$		0			0
$163$	11.9778	−	20.7461i	0.938172	−	1.62496i	0.169295	−	0.985565i	$-0.445851\pi$
$163$	11.9778	−	20.7461i	0.938172	−	1.62496i	0.768877	−	0.639397i	$-0.220816\pi$
$164$		0			0
$165$	−3.37741	+	2.85382i	−0.262931	+	0.222170i
$166$		0			0
$167$	−22.6351	+	8.23851i	−1.75156	+	0.637515i	−0.999761	−	0.0218801i	$-0.993035\pi$
$167$	−22.6351	+	8.23851i	−1.75156	+	0.637515i	−0.751797	+	0.659395i	$0.770813\pi$
$168$		0			0
$169$	−1.02303	−	5.80190i	−0.0786947	−	0.446300i
$170$		0			0
$171$	3.75711	+	0.635882i	0.287313	+	0.0486271i
$172$		0			0
$173$	13.9125	−	11.6740i	1.05775	−	0.887559i	0.0638639	−	0.997959i	$-0.479658\pi$
$173$	13.9125	−	11.6740i	1.05775	−	0.887559i	0.993887	+	0.110400i	$0.0352132\pi$
$174$		0			0
$175$	−24.4403	−	12.8841i	−1.84752	−	0.973950i
$176$		0			0
$177$	0.00200934	+	0.584608i	0.000151031	+	0.0439418i
$178$		0			0
$179$		−	15.1291i		−	1.13080i	−0.824817	−	0.565400i	$-0.808722\pi$
$179$		−	15.1291i		−	1.13080i	0.824817	−	0.565400i	$-0.191278\pi$
$180$		0			0
$181$	8.68681	−	5.01533i	0.645685	−	0.372787i	−0.141116	−	0.989993i	$-0.545069\pi$
$181$	8.68681	−	5.01533i	0.645685	−	0.372787i	0.786801	+	0.617206i	$0.211736\pi$
$182$		0			0
$183$	−21.7064	+	7.98508i	−1.60458	+	0.590274i
$184$		0			0
$185$	−8.57670	+	3.12166i	−0.630572	+	0.229509i
$186$		0			0
$187$	2.70827	−	0.477540i	0.198048	−	0.0349212i
$188$		0			0
$189$	−12.6741	+	5.32615i	−0.921903	+	0.387420i
$190$		0			0
$191$	−1.98847	+	0.350621i	−0.143881	+	0.0253701i	−0.245125	−	0.969492i	$-0.578829\pi$
$191$	−1.98847	+	0.350621i	−0.143881	+	0.0253701i	0.101244	+	0.994862i	$0.467718\pi$
$192$		0			0
$193$	−12.8234	+	4.66733i	−0.923048	+	0.335962i	−0.759451	−	0.650565i	$-0.774532\pi$
$193$	−12.8234	+	4.66733i	−0.923048	+	0.335962i	−0.163598	+	0.986527i	$0.552310\pi$
$194$		0			0
$195$	−5.03699	+	29.1517i	−0.360706	+	2.08760i
$196$		0			0
$197$	7.10485	−	4.10199i	0.506200	−	0.292255i	−0.225070	−	0.974343i	$-0.572261\pi$
$197$	7.10485	−	4.10199i	0.506200	−	0.292255i	0.731270	+	0.682088i	$0.238928\pi$
$198$		0			0
$199$			18.3216i			1.29878i	0.760455	+	0.649391i	$0.224976\pi$
$199$			18.3216i			1.29878i	−0.760455	+	0.649391i	$0.775024\pi$
$200$		0			0
$201$	14.6878	−	8.54743i	1.03599	−	0.602889i
$202$		0			0
$203$	−0.747100	−	1.18622i	−0.0524362	−	0.0832567i
$204$		0			0
$205$	24.1543	−	20.2678i	1.68701	−	1.41557i
$206$		0			0
$207$	−11.1848	−	13.1449i	−0.777396	−	0.913635i
$208$		0			0
$209$	−0.143285	−	0.812612i	−0.00991125	−	0.0562095i
$210$		0			0
$211$	4.56276	−	1.66071i	0.314113	−	0.114328i	−0.180153	−	0.983639i	$-0.557659\pi$
$211$	4.56276	−	1.66071i	0.314113	−	0.114328i	0.494266	+	0.869311i	$0.335437\pi$
$212$		0			0
$213$	3.22782	+	17.9450i	0.221167	+	1.22957i
$214$		0			0
$215$	0.553092	−	0.957983i	0.0377205	−	0.0653339i
$216$		0			0
$217$	−2.99964	−	13.8700i	−0.203629	−	0.941560i
$218$		0			0
$219$	−0.708439	−	3.93855i	−0.0478719	−	0.266143i
$220$		0			0
$221$	11.8270	−	14.0948i	0.795568	−	0.948121i
$222$		0			0
$223$	20.2250	−	3.56621i	1.35436	−	0.238811i	0.551102	−	0.834438i	$-0.314207\pi$
$223$	20.2250	−	3.56621i	1.35436	−	0.238811i	0.803261	+	0.595627i	$0.203096\pi$
$224$		0			0
$225$	15.4770	−	27.2376i	1.03180	−	1.81584i
$226$		0			0
$227$	−0.608939	−	3.45347i	−0.0404167	−	0.229215i	0.957908	−	0.287076i	$-0.0926831\pi$
$227$	−0.608939	−	3.45347i	−0.0404167	−	0.229215i	−0.998325	+	0.0578610i	$0.981572\pi$
$228$		0			0
$229$	4.61818	+	12.6884i	0.305178	+	0.838470i	0.993579	+	0.113140i	$0.0360907\pi$
$229$	4.61818	+	12.6884i	0.305178	+	0.838470i	−0.688401	+	0.725330i	$0.741687\pi$
$230$		0			0
$231$	2.00739	+	2.19836i	0.132077	+	0.144641i
$232$		0			0
$233$	−4.98374	+	2.87737i	−0.326496	+	0.188502i	−0.654284	−	0.756249i	$-0.727030\pi$
$233$	−4.98374	+	2.87737i	−0.326496	+	0.188502i	0.327788	+	0.944751i	$0.393697\pi$
$234$		0			0
$235$	18.3997	−	31.8693i	1.20027	−	2.07892i
$236$		0			0
$237$	15.7076	−	18.8508i	1.02032	−	1.22449i
$238$		0			0
$239$	10.7739	+	1.89974i	0.696908	+	0.122884i	0.510869	−	0.859659i	$-0.329324\pi$
$239$	10.7739	+	1.89974i	0.696908	+	0.122884i	0.186039	+	0.982542i	$0.440435\pi$
$240$		0			0
$241$	5.92681	−	16.2838i	0.381779	−	1.04893i	−0.588827	−	0.808259i	$-0.700410\pi$
$241$	5.92681	−	16.2838i	0.381779	−	1.04893i	0.970607	−	0.240671i	$-0.0773675\pi$
$242$		0			0
$243$	−5.58250	−	14.5546i	−0.358118	−	0.933676i
$244$		0			0
$245$	−11.8829	+	24.8089i	−0.759174	+	1.58498i
$246$		0			0
$247$	−4.22913	−	3.54867i	−0.269093	−	0.225796i
$248$		0			0
$249$	28.0896	+	4.85347i	1.78011	+	0.307576i
$250$		0			0
$251$	−8.96226	−	15.5231i	−0.565693	−	0.979809i	−0.996985	−	0.0775963i	$-0.975275\pi$
$251$	−8.96226	−	15.5231i	−0.565693	−	0.979809i	0.431292	−	0.902212i	$-0.358058\pi$
$252$		0			0
$253$	−1.86871	+	3.23670i	−0.117485	+	0.203489i
$254$		0			0
$255$	−24.9035	+	14.4924i	−1.55952	+	0.907548i
$256$		0			0
$257$	−10.6659	+	3.88206i	−0.665319	+	0.242156i	−0.652531	−	0.757762i	$-0.726293\pi$
$257$	−10.6659	+	3.88206i	−0.665319	+	0.242156i	−0.0127881	+	0.999918i	$0.504071\pi$
$258$		0			0
$259$	2.32217	+	5.68936i	0.144292	+	0.353520i
$260$		0			0
$261$	1.37113	−	0.804240i	0.0848708	−	0.0497812i
$262$		0			0
$263$	0.155958	+	0.185863i	0.00961677	+	0.0114608i	0.770831	−	0.637039i	$-0.219841\pi$
$263$	0.155958	+	0.185863i	0.00961677	+	0.0114608i	−0.761215	+	0.648500i	$0.775397\pi$
$264$		0			0
$265$	13.7445	+	37.7627i	0.844319	+	2.31975i
$266$		0			0
$267$	4.47693	+	5.29831i	0.273984	+	0.324251i
$268$		0			0
$269$	−8.65220	−	14.9860i	−0.527534	−	0.913715i	−0.999485	−	0.0320906i	$-0.989784\pi$
$269$	−8.65220	−	14.9860i	−0.527534	−	0.913715i	0.471951	−	0.881625i	$-0.343550\pi$
$270$		0			0
$271$	−8.44600	−	4.87630i	−0.513058	−	0.296214i	0.221032	−	0.975267i	$-0.429058\pi$
$271$	−8.44600	−	4.87630i	−0.513058	−	0.296214i	−0.734090	+	0.679053i	$0.762391\pi$
$272$		0			0
$273$	19.7429	+	2.63419i	1.19489	+	0.159428i
$274$		0			0
$275$	−6.68075	−	1.17800i	−0.402864	−	0.0710359i
$276$		0			0
$277$	−18.7307	+	15.7169i	−1.12542	+	0.944336i	−0.998865	−	0.0476243i	$-0.984835\pi$
$277$	−18.7307	+	15.7169i	−1.12542	+	0.944336i	−0.126550	+	0.991960i	$0.540391\pi$
$278$		0			0
$279$	15.8267	−	2.90299i	0.947520	−	0.173797i
$280$		0			0
$281$	−4.28951	+	11.7853i	−0.255891	+	0.703054i	0.743520	+	0.668714i	$0.233155\pi$
$281$	−4.28951	+	11.7853i	−0.255891	+	0.703054i	−0.999410	+	0.0343397i	$0.989067\pi$
$282$		0			0
$283$	−22.5040	−	3.96806i	−1.33772	−	0.235876i	−0.541408	−	0.840760i	$-0.682109\pi$
$283$	−22.5040	−	3.96806i	−1.33772	−	0.235876i	−0.796314	+	0.604883i	$0.793220\pi$
$284$		0			0
$285$	4.34842	+	7.47225i	0.257578	+	0.442618i
$286$		0			0
$287$	−14.2608	−	15.7257i	−0.841791	−	0.928260i
$288$		0			0
$289$	0.920395			0.0541409
$290$		0			0
$291$	15.0021	−	5.51877i	0.879437	−	0.323516i
$292$		0			0
$293$	−0.331036	+	1.87740i	−0.0193393	+	0.109679i	−0.992949	−	0.118539i	$-0.962179\pi$
$293$	−0.331036	+	1.87740i	−0.0193393	+	0.109679i	0.973610	+	0.228218i	$0.0732899\pi$
$294$		0			0
$295$	−1.01606	+	0.852577i	−0.0591574	+	0.0496390i
$296$		0			0
$297$	−2.56333	+	2.19633i	−0.148740	+	0.127444i
$298$		0			0
$299$	4.34218	+	24.6257i	0.251115	+	1.42414i
$300$		0			0
$301$	−0.658820	−	0.347308i	−0.0379738	−	0.0200185i
$302$		0			0
$303$	−20.5625	−	3.55290i	−1.18129	−	0.204109i
$304$		0			0
$305$	−45.4442	−	26.2372i	−2.60212	−	1.50234i
$306$		0			0
$307$	−12.7896	−	7.38406i	−0.729939	−	0.421430i	0.0884610	−	0.996080i	$-0.471805\pi$
$307$	−12.7896	−	7.38406i	−0.729939	−	0.421430i	−0.818400	+	0.574649i	$0.805138\pi$
$308$		0			0
$309$	10.9089	+	18.7456i	0.620584	+	1.06640i
$310$		0			0
$311$	−2.02677	+	11.4944i	−0.114928	+	0.651788i	0.871858	+	0.489758i	$0.162915\pi$
$311$	−2.02677	+	11.4944i	−0.114928	+	0.651788i	−0.986786	+	0.162029i	$0.948196\pi$
$312$		0			0
$313$	1.14698	+	1.36692i	0.0648312	+	0.0772629i	0.797485	−	0.603338i	$-0.206163\pi$
$313$	1.14698	+	1.36692i	0.0648312	+	0.0772629i	−0.732654	+	0.680601i	$0.761719\pi$
$314$		0			0
$315$	−27.6912	−	14.3555i	−1.56022	−	0.808841i
$316$		0			0
$317$	−10.5347	+	28.9437i	−0.591685	+	1.62564i	0.175692	+	0.984445i	$0.443784\pi$
$317$	−10.5347	+	28.9437i	−0.591685	+	1.62564i	−0.767377	+	0.641196i	$0.778438\pi$
$318$		0			0
$319$	−0.263684	−	0.221257i	−0.0147635	−	0.0123880i
$320$		0			0
$321$	1.09571	+	6.09158i	0.0611566	+	0.339999i
$322$		0			0
$323$		−	5.37699i		−	0.299184i
$324$		0			0
$325$	−39.3070	+	22.6939i	−2.18036	+	1.25883i
$326$		0			0
$327$	−7.48451	+	20.7855i	−0.413894	+	1.14944i
$328$		0			0
$329$	−21.9170	−	11.5539i	−1.20832	−	0.636989i
$330$		0			0
$331$	11.6294	+	4.23276i	0.639210	+	0.232653i	0.641235	−	0.767345i	$-0.278422\pi$
$331$	11.6294	+	4.23276i	0.639210	+	0.232653i	−0.00202526	+	0.999998i	$0.500645\pi$
$332$		0			0
$333$	−6.53106	+	2.42808i	−0.357900	+	0.133058i
$334$		0			0
$335$	36.2306	+	13.1868i	1.97949	+	0.720475i
$336$		0			0
$337$	16.3396	+	13.7106i	0.890075	+	0.746862i	0.968225	−	0.250080i	$-0.0804569\pi$
$337$	16.3396	+	13.7106i	0.890075	+	0.746862i	−0.0781501	+	0.996942i	$0.524901\pi$
$338$		0			0
$339$	−8.00935	+	13.9834i	−0.435008	+	0.759473i
$340$		0			0
$341$	−1.74217	−	3.01753i	−0.0943439	−	0.163408i
$342$		0			0
$343$	16.9983	+	7.35237i	0.917823	+	0.396990i
$344$		0			0
$345$	6.66721	−	38.5867i	0.358951	−	2.07744i
$346$		0			0
$347$	−0.760701	−	2.09001i	−0.0408366	−	0.112198i	0.917598	−	0.397509i	$-0.130125\pi$
$347$	−0.760701	−	2.09001i	−0.0408366	−	0.112198i	−0.958435	+	0.285311i	$0.907903\pi$
$348$		0			0
$349$	11.8201	+	14.0867i	0.632718	+	0.754043i	0.983201	−	0.182525i	$-0.0584272\pi$
$349$	11.8201	+	14.0867i	0.632718	+	0.754043i	−0.350484	+	0.936569i	$0.613983\pi$
$350$		0			0
$351$	−3.69225	+	22.2808i	−0.197078	+	1.18926i
$352$		0			0
$353$	−26.2308	−	9.54724i	−1.39613	−	0.508148i	−0.469100	−	0.883145i	$-0.655421\pi$
$353$	−26.2308	−	9.54724i	−1.39613	−	0.508148i	−0.927026	+	0.374997i	$0.877644\pi$
$354$		0			0
$355$	−26.5904	+	31.6892i	−1.41127	+	1.68189i
$356$		0			0
$357$	10.3947	+	16.3792i	0.550144	+	0.866881i
$358$		0			0
$359$			17.1001i			0.902507i	0.892396	+	0.451253i	$0.149023\pi$
$359$			17.1001i			0.902507i	−0.892396	+	0.451253i	$0.850977\pi$
$360$		0			0
$361$	17.3866			0.915086
$362$		0			0
$363$	−15.8984	−	9.10621i	−0.834448	−	0.477952i
$364$		0			0
$365$	5.83603	−	6.95511i	0.305472	−	0.364047i
$366$		0			0
$367$	−23.2623	+	4.10177i	−1.21428	+	0.214110i	−0.743862	−	0.668333i	$-0.767008\pi$
$367$	−23.2623	+	4.10177i	−1.21428	+	0.214110i	−0.470418	+	0.882443i	$0.655897\pi$
$368$		0			0
$369$	18.3330	−	15.5992i	0.954377	−	0.812062i
$370$		0			0
$371$	25.0500	−	10.2244i	1.30053	−	0.530823i
$372$		0			0
$373$	0.125883	−	0.713915i	0.00651795	−	0.0369651i	−0.981375	−	0.192100i	$-0.938470\pi$
$373$	0.125883	−	0.713915i	0.00651795	−	0.0369651i	0.987893	+	0.155135i	$0.0495813\pi$
$374$		0			0
$375$	36.4595	−	6.55808i	1.88276	−	0.338658i
$376$		0			0
$377$	−2.30301			−0.118611
$378$		0			0
$379$	8.15560			0.418925			0.209462	−	0.977817i	$-0.432829\pi$
$379$	8.15560			0.418925			0.209462	+	0.977817i	$0.432829\pi$
$380$		0			0
$381$	−6.82714	+	18.9599i	−0.349765	+	0.971346i
$382$		0			0
$383$	0.822617	−	4.66529i	0.0420338	−	0.238385i	−0.956551	−	0.291564i	$-0.905824\pi$
$383$	0.822617	−	4.66529i	0.0420338	−	0.238385i	0.998585	+	0.0531790i	$0.0169354\pi$
$384$		0			0
$385$	−0.916270	+	6.69178i	−0.0466974	+	0.341045i
$386$		0			0
$387$	0.417202	−	0.734225i	0.0212076	−	0.0373228i
$388$		0			0
$389$	30.2267	−	5.32978i	1.53255	−	0.270231i	0.657201	−	0.753715i	$-0.271740\pi$
$389$	30.2267	−	5.32978i	1.53255	−	0.270231i	0.875353	+	0.483485i	$0.160629\pi$
$390$		0			0
$391$	−15.6548	+	18.6566i	−0.791696	+	0.943506i
$392$		0			0
$393$	−0.00256455	−	0.746143i	−0.000129365	−	0.0376380i
$394$		0			0
$395$	55.6706			2.80109
$396$		0			0
$397$			30.3514i			1.52329i	0.647992	+	0.761647i	$0.275609\pi$
$397$			30.3514i			1.52329i	−0.647992	+	0.761647i	$0.724391\pi$
$398$		0			0
$399$	4.91457	−	3.11890i	0.246036	−	0.156140i
$400$		0			0
$401$	3.04703	−	3.63131i	0.152161	−	0.181339i	−0.684579	−	0.728939i	$-0.740014\pi$
$401$	3.04703	−	3.63131i	0.152161	−	0.181339i	0.836740	+	0.547600i	$0.184458\pi$
$402$		0			0
$403$	−21.9065	−	7.97331i	−1.09124	−	0.397179i
$404$		0			0
$405$	17.2609	−	30.8692i	0.857702	−	1.53390i
$406$		0			0
$407$	0.969858	+	1.15583i	0.0480741	+	0.0572925i
$408$		0			0
$409$	3.67133	+	10.0869i	0.181536	+	0.498765i	0.996765	−	0.0803734i	$-0.0256113\pi$
$409$	3.67133	+	10.0869i	0.181536	+	0.498765i	−0.815229	+	0.579139i	$0.803389\pi$
$410$		0			0
$411$	−23.5157	+	8.65067i	−1.15995	+	0.426706i
$412$		0			0
$413$	0.599890	+	0.661510i	0.0295187	+	0.0325508i
$414$		0			0
$415$	32.3373	+	56.0098i	1.58737	+	2.74941i
$416$		0			0
$417$	−14.1407	−	24.2991i	−0.692472	−	1.18993i
$418$		0			0
$419$	−8.97960	−	7.53478i	−0.438682	−	0.368098i	0.396534	−	0.918020i	$-0.370213\pi$
$419$	−8.97960	−	7.53478i	−0.438682	−	0.368098i	−0.835216	+	0.549922i	$0.814657\pi$
$420$		0			0
$421$	−15.3936	−	5.60280i	−0.750236	−	0.273064i	−0.0615311	−	0.998105i	$-0.519598\pi$
$421$	−15.3936	−	5.60280i	−0.750236	−	0.273064i	−0.688705	+	0.725041i	$0.741821\pi$
$422$		0			0
$423$	13.8791	−	24.4255i	0.674824	−	1.18761i
$424$		0			0
$425$	−41.5401	−	15.1193i	−2.01499	−	0.733396i
$426$		0			0
$427$	−16.4754	+	31.2527i	−0.797300	+	1.51242i
$428$		0			0
$429$	4.81332	−	0.865786i	0.232389	−	0.0418006i
$430$		0			0
$431$	−7.17094	+	4.14015i	−0.345412	+	0.199424i	−0.662663	−	0.748918i	$-0.730574\pi$
$431$	−7.17094	+	4.14015i	−0.345412	+	0.199424i	0.317251	+	0.948342i	$0.397240\pi$
$432$		0			0
$433$		−	5.95449i		−	0.286154i	−0.989712	−	0.143077i	$-0.954300\pi$
$433$		−	5.95449i		−	0.286154i	0.989712	−	0.143077i	$-0.0456997\pi$
$434$		0			0
$435$	3.39321	+	1.22184i	0.162692	+	0.0585826i
$436$		0			0
$437$	5.59789	+	4.69719i	0.267784	+	0.224697i
$438$		0			0
$439$	9.17660	−	25.2125i	0.437975	−	1.20333i	−0.502832	−	0.864384i	$-0.667709\pi$
$439$	9.17660	−	25.2125i	0.437975	−	1.20333i	0.940807	−	0.338943i	$-0.110069\pi$
$440$		0			0
$441$	−8.94123	+	19.0014i	−0.425773	+	0.904830i
$442$		0			0
$443$	−9.94463	−	11.8515i	−0.472484	−	0.563084i	0.476189	−	0.879343i	$-0.342018\pi$
$443$	−9.94463	−	11.8515i	−0.472484	−	0.563084i	−0.948673	+	0.316259i	$0.897573\pi$
$444$		0			0
$445$	−2.73281	+	15.4986i	−0.129548	+	0.734702i
$446$		0			0
$447$	−0.439842	+	0.767912i	−0.0208038	+	0.0363210i
$448$		0			0
$449$	−6.95141	−	4.01340i	−0.328058	−	0.189404i	0.326921	−	0.945052i	$-0.393989\pi$
$449$	−6.95141	−	4.01340i	−0.328058	−	0.189404i	−0.654978	+	0.755648i	$0.727322\pi$
$450$		0			0
$451$	−4.51416	−	2.60625i	−0.212564	−	0.122724i
$452$		0			0
$453$	1.74818	−	2.09801i	0.0821369	−	0.0985730i
$454$		0			0
$455$	24.0828	+	38.2380i	1.12902	+	1.79262i
$456$		0			0
$457$	5.90878	+	33.5104i	0.276401	+	1.56755i	0.734475	+	0.678635i	$0.237428\pi$
$457$	5.90878	+	33.5104i	0.276401	+	1.56755i	−0.458074	+	0.888914i	$0.651461\pi$
$458$		0			0
$459$	−18.9352	+	11.1941i	−0.883820	+	0.522498i
$460$		0			0
$461$	11.2017	−	9.39934i	0.521715	−	0.437771i	−0.343514	−	0.939148i	$-0.611617\pi$
$461$	11.2017	−	9.39934i	0.521715	−	0.437771i	0.865229	+	0.501377i	$0.167173\pi$
$462$		0			0
$463$	5.10869	−	28.9728i	0.237421	−	1.34648i	−0.600033	−	0.799975i	$-0.704846\pi$
$463$	5.10869	−	28.9728i	0.237421	−	1.34648i	0.837454	−	0.546507i	$-0.184043\pi$
$464$		0			0
$465$	28.0464	+	23.3699i	1.30062	+	1.08375i
$466$		0			0
$467$	−14.2525			−0.659527			−0.329763	−	0.944064i	$-0.606969\pi$
$467$	−14.2525			−0.659527			−0.329763	+	0.944064i	$0.606969\pi$
$468$		0			0
$469$	7.93396	−	24.7162i	0.366356	−	1.14129i
$470$		0			0
$471$	20.5407	−	0.0706000i	0.946466	−	0.00325308i
$472$		0			0
$473$	−0.180088	−	0.0317544i	−0.00828046	−	0.00146007i
$474$		0			0
$475$	−4.53654	+	12.4640i	−0.208151	+	0.571889i
$476$		0			0
$477$	10.6907	+	28.7559i	0.489494	+	1.31664i
$478$		0			0
$479$	−2.86649	+	2.40527i	−0.130973	+	0.109900i	−0.705921	−	0.708290i	$-0.749467\pi$
$479$	−2.86649	+	2.40527i	−0.130973	+	0.109900i	0.574948	+	0.818190i	$0.305022\pi$
$480$		0			0
$481$	9.94164	+	1.75298i	0.453300	+	0.0799290i
$482$		0			0
$483$	−26.1326	−	3.48674i	−1.18908	−	0.158652i
$484$		0			0
$485$	31.4081	+	18.1335i	1.42617	+	0.823398i
$486$		0			0
$487$	11.0027	+	19.0573i	0.498581	+	0.863568i	0.999999	−	0.00163760i	$-0.000521265\pi$
$487$	11.0027	+	19.0573i	0.498581	+	0.863568i	−0.501418	+	0.865205i	$0.667188\pi$
$488$		0			0
$489$	40.8369	−	7.34546i	1.84671	−	0.332173i
$490$		0			0
$491$	−8.03487	−	22.0756i	−0.362609	−	0.996259i	−0.978104	−	0.208118i	$-0.933266\pi$
$491$	−8.03487	−	22.0756i	−0.362609	−	0.996259i	0.615495	−	0.788141i	$-0.288956\pi$
$492$		0			0
$493$	−1.44180	−	1.71827i	−0.0649355	−	0.0773871i
$494$		0			0
$495$	−7.55118	−	1.27802i	−0.339400	−	0.0574426i
$496$		0			0
$497$	22.0079	+	17.0690i	0.987188	+	0.765651i
$498$		0			0
$499$	−4.45052	+	1.61986i	−0.199233	+	0.0725147i	−0.439709	−	0.898140i	$-0.644918\pi$
$499$	−4.45052	+	1.61986i	−0.199233	+	0.0725147i	0.240477	+	0.970655i	$0.422696\pi$
$500$		0			0
$501$	−36.2032	−	20.7363i	−1.61744	−	0.926430i
$502$		0			0
$503$	−9.45110	+	16.3698i	−0.421404	+	0.729893i	−0.996077	−	0.0884900i	$-0.971796\pi$
$503$	−9.45110	+	16.3698i	−0.421404	+	0.729893i	0.574673	+	0.818383i	$0.305129\pi$
$504$		0			0
$505$	−23.6719	−	41.0010i	−1.05339	−	1.82452i
$506$		0			0
$507$	6.53223	−	7.83938i	0.290107	−	0.348159i
$508$		0			0
$509$	−28.0651	−	23.5494i	−1.24396	−	1.04381i	−0.997204	−	0.0747321i	$-0.976190\pi$
$509$	−28.0651	−	23.5494i	−1.24396	−	1.04381i	−0.246759	−	0.969077i	$-0.579366\pi$
$510$		0			0
$511$	−4.83026	−	3.74629i	−0.213678	−	0.165726i
$512$		0			0
$513$	3.35879	+	5.68148i	0.148294	+	0.250844i
$514$		0			0
$515$	−16.8300	+	46.2402i	−0.741620	+	2.03758i
$516$		0			0
$517$	−5.99100	−	1.05638i	−0.263484	−	0.0464593i
$518$		0			0
$519$	30.9974	+	5.35589i	1.36063	+	0.235098i
$520$		0			0
$521$	16.4028	−	28.4105i	0.718621	−	1.24469i	−0.242925	−	0.970045i	$-0.578107\pi$
$521$	16.4028	−	28.4105i	0.718621	−	1.24469i	0.961546	−	0.274643i	$-0.0885598\pi$
$522$		0			0
$523$	3.12916	−	1.80662i	0.136829	−	0.0789980i	−0.430023	−	0.902818i	$-0.641495\pi$
$523$	3.12916	−	1.80662i	0.136829	−	0.0789980i	0.566852	+	0.823820i	$0.308161\pi$
$524$		0			0
$525$	−10.2761	−	46.7375i	−0.448485	−	2.03979i
$526$		0			0
$527$	−7.76569	−	21.3361i	−0.338279	−	0.929414i
$528$		0			0
$529$	−1.75362	−	9.94526i	−0.0762442	−	0.432403i
$530$		0			0
$531$	−0.771186	+	0.656188i	−0.0334666	+	0.0284761i
$532$		0			0
$533$	−34.3450	+	6.05596i	−1.48765	+	0.262313i
$534$		0			0
$535$	−9.02633	+	10.7572i	−0.390242	+	0.465073i
$536$		0			0
$537$	20.0157	−	16.9127i	0.863740	−	0.729837i
$538$		0			0
$539$	4.52576	+	0.443232i	0.194938	+	0.0190913i
$540$		0			0
$541$	8.45105	−	14.6376i	0.363339	−	0.629321i	−0.625169	−	0.780489i	$-0.714970\pi$
$541$	8.45105	−	14.6376i	0.363339	−	0.629321i	0.988508	+	0.151168i	$0.0483034\pi$
$542$		0			0
$543$	16.3462	+	5.88598i	0.701482	+	0.252591i
$544$		0			0
$545$	−47.0999	+	17.1430i	−2.01754	+	0.734323i
$546$		0			0
$547$	1.82850	+	10.3699i	0.0781810	+	0.443386i	0.998621	+	0.0525021i	$0.0167196\pi$
$547$	1.82850	+	10.3699i	0.0781810	+	0.443386i	−0.920440	+	0.390884i	$0.872169\pi$
$548$		0			0
$549$	−34.8297	−	19.7909i	−1.48649	−	0.844657i
$550$		0			0
$551$	−0.515565	+	0.432610i	−0.0219638	+	0.0184298i
$552$		0			0
$553$	−1.44097	−	37.4536i	−0.0612762	−	1.59269i
$554$		0			0
$555$	−13.7178	−	7.85723i	−0.582288	−	0.333521i
$556$		0			0
$557$			4.74008i			0.200844i	0.994945	+	0.100422i	$0.0320192\pi$
$557$			4.74008i			0.200844i	−0.994945	+	0.100422i	$0.967981\pi$
$558$		0			0
$559$	−1.05957	+	0.611744i	−0.0448151	+	0.0258740i
$560$		0			0
$561$	3.65934	+	3.04918i	0.154497	+	0.128736i
$562$		0			0
$563$	15.4903	−	5.63801i	0.652839	−	0.237614i	0.00569722	−	0.999984i	$-0.498187\pi$
$563$	15.4903	−	5.63801i	0.652839	−	0.237614i	0.647142	+	0.762370i	$0.275964\pi$
$564$		0			0
$565$	−36.0059	+	6.34881i	−1.51478	+	0.267097i
$566$		0			0
$567$	−21.2147	−	10.8136i	−0.890935	−	0.454131i
$568$		0			0
$569$	−31.0763	+	5.47959i	−1.30279	+	0.229716i	−0.781629	−	0.623744i	$-0.785611\pi$
$569$	−31.0763	+	5.47959i	−1.30279	+	0.229716i	−0.521158	+	0.853460i	$0.674500\pi$
$570$		0			0
$571$	31.0241	−	11.2918i	1.29832	−	0.472549i	0.401870	−	0.915697i	$-0.368361\pi$
$571$	31.0241	−	11.2918i	1.29832	−	0.472549i	0.896449	+	0.443148i	$0.146138\pi$
$572$		0			0
$573$	−2.68677	−	2.23878i	−0.112241	−	0.0935262i
$574$		0			0
$575$	52.0288	−	30.0388i	2.16975	−	1.25271i
$576$		0			0
$577$			15.9807i			0.665285i	0.943053	+	0.332642i	$0.107940\pi$
$577$			15.9807i			0.665285i	−0.943053	+	0.332642i	$0.892060\pi$
$578$		0			0
$579$	−20.5101	−	11.7477i	−0.852369	−	0.488217i
$580$		0			0
$581$	36.8448	−	23.2054i	1.52858	−	0.962721i
$582$		0			0
$583$	5.08906	−	4.27023i	0.210768	−	0.176855i
$584$		0			0
$585$	−44.1984	+	25.9247i	−1.82738	+	1.07185i
$586$		0			0
$587$	−2.71350	−	15.3890i	−0.111998	−	0.635174i	−0.988193	−	0.153216i	$-0.951037\pi$
$587$	−2.71350	−	15.3890i	−0.111998	−	0.635174i	0.876195	−	0.481958i	$-0.160074\pi$
$588$		0			0
$589$	−6.40186	+	2.33009i	−0.263784	+	0.0960095i
$590$		0			0
$591$	13.3694	+	4.81408i	0.549943	+	0.198025i
$592$		0			0
$593$	−0.551611	+	0.955418i	−0.0226520	+	0.0392343i	−0.877129	−	0.480255i	$-0.840544\pi$
$593$	−0.551611	+	0.955418i	−0.0226520	+	0.0392343i	0.854477	+	0.519489i	$0.173878\pi$
$594$		0			0
$595$	−13.4522	+	41.9070i	−0.551487	+	1.71802i
$596$		0			0
$597$	−24.2393	+	20.4816i	−0.992049	+	0.838255i
$598$		0			0
$599$	−0.973078	+	1.15967i	−0.0397589	+	0.0473828i	−0.785557	−	0.618789i	$-0.787624\pi$
$599$	−0.973078	+	1.15967i	−0.0397589	+	0.0473828i	0.745799	+	0.666172i	$0.232068\pi$
$600$		0			0
$601$	−40.4782	+	7.13740i	−1.65114	+	0.291141i	−0.920243	−	0.391347i	$-0.872009\pi$
$601$	−40.4782	+	7.13740i	−1.65114	+	0.291141i	−0.730897	+	0.682488i	$0.760898\pi$
$602$		0			0
$603$	27.7276	+	9.87669i	1.12915	+	0.402210i
$604$		0			0
$605$	−7.21827	−	40.9368i	−0.293464	−	1.66432i
$606$		0			0
$607$	12.3909	+	34.0439i	0.502933	+	1.38180i	0.888398	+	0.459075i	$0.151819\pi$
$607$	12.3909	+	34.0439i	0.502933	+	1.38180i	−0.385464	+	0.922723i	$0.625959\pi$
$608$		0			0
$609$	0.734188	−	2.31448i	0.0297508	−	0.0937876i
$610$		0			0
$611$	−35.2488	+	20.3509i	−1.42601	+	0.823310i
$612$		0			0
$613$	4.15491	−	7.19651i	0.167815	−	0.290664i	−0.769836	−	0.638241i	$-0.779662\pi$
$613$	4.15491	−	7.19651i	0.167815	−	0.290664i	0.937651	+	0.347577i	$0.112996\pi$
$614$		0			0
$615$	53.8162	+	9.29864i	2.17008	+	0.374957i
$616$		0			0
$617$	−29.6763	−	5.23273i	−1.19472	−	0.210662i	−0.459306	−	0.888278i	$-0.651902\pi$
$617$	−29.6763	−	5.23273i	−1.19472	−	0.210662i	−0.735416	+	0.677616i	$0.763013\pi$
$618$		0			0
$619$	7.51408	−	20.6448i	0.302016	−	0.829783i	−0.692133	−	0.721770i	$-0.743329\pi$
$619$	7.51408	−	20.6448i	0.302016	−	0.829783i	0.994149	−	0.108013i	$-0.0344488\pi$
$620$		0			0
$621$	4.88724	−	29.4920i	0.196118	−	1.18347i
$622$		0			0
$623$	10.4977	+	1.43740i	0.420583	+	0.0575882i
$624$		0			0
$625$	24.3866	+	20.4628i	0.975465	+	0.818512i
$626$		0			0
$627$	0.914902	−	1.09798i	0.0365377	−	0.0438491i
$628$		0			0
$629$	4.91607	+	8.51489i	0.196017	+	0.339511i
$630$		0			0
$631$	13.1731	−	22.8165i	0.524414	−	0.908311i	−0.475182	−	0.879887i	$-0.657618\pi$
$631$	13.1731	−	22.8165i	0.524414	−	0.908311i	0.999596	−	0.0284238i	$-0.00904880\pi$
$632$		0			0
$633$	7.29779	+	4.18000i	0.290061	+	0.166140i
$634$		0			0
$635$	−42.9631	+	15.6373i	−1.70494	+	0.620546i
$636$		0			0
$637$	25.1021	−	17.1920i	0.994581	−	0.681171i
$638$		0			0
$639$	−20.1328	+	24.3310i	−0.796440	+	0.962520i
$640$		0			0
$641$	−27.9668	−	33.3296i	−1.10462	−	1.31644i	−0.944193	−	0.329393i	$-0.893156\pi$
$641$	−27.9668	−	33.3296i	−1.10462	−	1.31644i	−0.160431	−	0.987047i	$-0.551288\pi$
$642$		0			0
$643$	−6.28983	−	17.2812i	−0.248047	−	0.681503i	−0.999758	−	0.0220101i	$-0.992993\pi$
$643$	−6.28983	−	17.2812i	−0.248047	−	0.681503i	0.751711	−	0.659493i	$-0.229229\pi$
$644$		0			0
$645$	1.88570	−	0.339187i	0.0742495	−	0.0133555i
$646$		0			0
$647$	−16.2772	−	28.1929i	−0.639922	−	1.10838i	−0.985449	−	0.169969i	$-0.945633\pi$
$647$	−16.2772	−	28.1929i	−0.639922	−	1.10838i	0.345527	−	0.938409i	$-0.387700\pi$
$648$		0			0
$649$	0.189891	+	0.109633i	0.00745385	+	0.00430348i
$650$		0			0
$651$	14.9967	−	19.4737i	0.587767	−	0.763236i
$652$		0			0
$653$	−22.5933	−	3.98381i	−0.884145	−	0.155899i	−0.286903	−	0.957960i	$-0.592626\pi$
$653$	−22.5933	−	3.98381i	−0.884145	−	0.155899i	−0.597242	+	0.802061i	$0.703737\pi$
$654$		0			0
$655$	1.29682	−	1.08816i	0.0506708	−	0.0425178i
$656$		0			0
$657$	4.41872	−	5.34015i	0.172391	−	0.208339i
$658$		0			0
$659$	3.24389	−	8.91251i	0.126364	−	0.347182i	−0.860338	−	0.509725i	$-0.829747\pi$
$659$	3.24389	−	8.91251i	0.126364	−	0.347182i	0.986702	+	0.162543i	$0.0519695\pi$
$660$		0			0
$661$	24.9854	+	4.40561i	0.971821	+	0.171358i	0.636949	−	0.770906i	$-0.280196\pi$
$661$	24.9854	+	4.40561i	0.971821	+	0.171358i	0.334871	+	0.942264i	$0.391307\pi$
$662$		0			0
$663$	31.8687	−	0.109535i	1.23768	−	0.00425399i
$664$		0			0
$665$	12.5741	+	4.03632i	0.487604	+	0.156522i
$666$		0			0
$667$	3.04838			0.118034
$668$		0			0
$669$	27.3274	+	22.7708i	1.05654	+	0.880372i
$670$		0			0
$671$	−1.50634	+	8.54290i	−0.0581517	+	0.329795i
$672$		0			0
$673$	−7.51664	+	6.30721i	−0.289745	+	0.243125i	−0.776061	−	0.630658i	$-0.782785\pi$
$673$	−7.51664	+	6.30721i	−0.289745	+	0.243125i	0.486315	+	0.873783i	$0.338341\pi$
$674$		0			0
$675$	53.3369	−	9.97285i	2.05294	−	0.383855i
$676$		0			0
$677$	−6.52377	−	36.9981i	−0.250729	−	1.42195i	−0.806803	−	0.590821i	$-0.798804\pi$
$677$	−6.52377	−	36.9981i	−0.250729	−	1.42195i	0.556074	−	0.831133i	$-0.312307\pi$
$678$		0			0
$679$	11.3867	−	21.5998i	0.436982	−	0.828926i
$680$		0			0
$681$	3.88818	−	4.66623i	0.148995	−	0.178810i
$682$		0			0
$683$	−2.32361	−	1.34154i	−0.0889104	−	0.0513324i	0.454886	−	0.890550i	$-0.349680\pi$
$683$	−2.32361	−	1.34154i	−0.0889104	−	0.0513324i	−0.543796	+	0.839217i	$0.683013\pi$
$684$		0			0
$685$	−49.2321	−	28.4242i	−1.88106	−	1.08603i
$686$		0			0
$687$	−11.6240	+	20.2941i	−0.443482	+	0.774267i
$688$		0			0
$689$	7.71827	−	43.7725i	0.294043	−	1.66760i
$690$		0			0
$691$	15.9156	+	18.9675i	0.605459	+	0.721558i	0.978498	−	0.206258i	$-0.0661287\pi$
$691$	15.9156	+	18.9675i	0.605459	+	0.721558i	−0.373039	+	0.927816i	$0.621684\pi$
$692$		0			0
$693$	−0.664362	+	5.11330i	−0.0252370	+	0.194238i
$694$		0			0
$695$	21.8161	−	59.9391i	0.827530	−	2.27362i
$696$		0			0
$697$	−26.0200	−	21.8334i	−0.985580	−	0.826999i
$698$		0			0
$699$	−9.37804	−	3.37687i	−0.354710	−	0.127725i
$700$		0			0
$701$			39.7674i			1.50200i	0.660305	+	0.750998i	$0.270427\pi$
$701$			39.7674i			1.50200i	−0.660305	+	0.750998i	$0.729573\pi$
$702$		0			0
$703$	2.55488	−	1.47506i	0.0963592	−	0.0556330i
$704$		0			0
$705$	62.7318	−	11.2838i	2.36262	−	0.424971i
$706$		0			0
$707$	−26.9716	+	16.9871i	−1.01437	+	0.638865i
$708$		0			0
$709$	33.8905	+	12.3351i	1.27279	+	0.463256i	0.888040	−	0.459766i	$-0.152067\pi$
$709$	33.8905	+	12.3351i	1.27279	+	0.463256i	0.384746	+	0.923022i	$0.374289\pi$
$710$		0			0
$711$	42.4988	−	0.292147i	1.59383	−	0.0109564i
$712$		0			0
$713$	28.9965	+	10.5539i	1.08593	+	0.395246i
$714$		0			0
$715$	8.49987	+	7.13223i	0.317877	+	0.266730i
$716$		0			0
$717$	9.53079	+	16.3776i	0.355934	+	0.611631i
$718$		0			0
$719$	−14.2473	−	24.6770i	−0.531333	−	0.920296i	−0.999331	−	0.0365666i	$-0.988358\pi$
$719$	−14.2473	−	24.6770i	−0.531333	−	0.920296i	0.467998	−	0.883730i	$-0.344975\pi$
$720$		0			0
$721$	31.5447	+	10.1259i	1.17479	+	0.377109i
$722$		0			0
$723$	28.1689	−	10.3624i	1.04761	−	0.385382i
$724$		0			0
$725$	1.89245	+	5.19945i	0.0702837	+	0.193103i
$726$		0			0
$727$	−13.6895	−	16.3145i	−0.507716	−	0.605072i	0.449915	−	0.893071i	$-0.351454\pi$
$727$	−13.6895	−	16.3145i	−0.507716	−	0.605072i	−0.957631	+	0.287999i	$0.907010\pi$
$728$		0			0
$729$	13.0150	−	23.6561i	0.482035	−	0.876152i
$730$		0			0
$731$	−1.11977	−	0.407561i	−0.0414160	−	0.0150742i
$732$		0			0
$733$	30.0632	−	35.8280i	1.11041	−	1.32334i	0.169175	−	0.985586i	$-0.445890\pi$
$733$	30.0632	−	35.8280i	1.11041	−	1.32334i	0.941236	−	0.337750i	$-0.109666\pi$
$734$		0			0
$735$	−46.1059	+	12.0127i	−1.70064	+	0.443094i
$736$		0			0
$737$		−	6.37376i		−	0.234780i
$738$		0			0
$739$	8.16282			0.300274			0.150137	−	0.988665i	$-0.452028\pi$
$739$	8.16282			0.300274			0.150137	+	0.988665i	$0.452028\pi$
$740$		0			0
$741$	−0.0328659	−	9.56215i	−0.00120736	−	0.351274i
$742$		0			0
$743$	−11.9198	+	14.2055i	−0.437295	+	0.521148i	−0.939012	−	0.343884i	$-0.888257\pi$
$743$	−11.9198	+	14.2055i	−0.437295	+	0.521148i	0.501717	+	0.865032i	$0.332702\pi$
$744$		0			0
$745$	−1.97730	+	0.348652i	−0.0724428	+	0.0127736i
$746$		0			0
$747$	24.9801	+	42.5881i	0.913976	+	1.55822i
$748$		0			0
$749$	7.47075	+	5.79423i	0.272975	+	0.211716i
$750$		0			0
$751$	−1.93571	+	10.9779i	−0.0706350	+	0.400591i	0.928907	+	0.370314i	$0.120750\pi$
$751$	−1.93571	+	10.9779i	−0.0706350	+	0.400591i	−0.999542	+	0.0302768i	$0.990361\pi$
$752$		0			0
$753$	10.5181	−	29.2102i	0.383300	−	1.06448i
$754$		0			0
$755$	6.19590			0.225492
$756$		0			0
$757$	14.8985			0.541494			0.270747	−	0.962651i	$-0.412729\pi$
$757$	14.8985			0.541494			0.270747	+	0.962651i	$0.412729\pi$
$758$		0			0
$759$	−6.37115	+	1.14600i	−0.231258	+	0.0415971i
$760$		0			0
$761$	−5.84310	+	33.1379i	−0.211812	+	1.20125i	0.674541	+	0.738237i	$0.264341\pi$
$761$	−5.84310	+	33.1379i	−0.211812	+	1.20125i	−0.886353	+	0.463009i	$0.846770\pi$
$762$		0			0
$763$	12.7524	+	31.2438i	0.461669	+	1.13110i
$764$		0			0
$765$	−47.0128	−	16.7462i	−1.69975	−	0.605459i
$766$		0			0
$767$	1.44474	−	0.254747i	0.0521666	−	0.00919838i
$768$		0			0
$769$	2.31424	−	2.75800i	0.0834536	−	0.0994561i	−0.722702	−	0.691160i	$-0.757100\pi$
$769$	2.31424	−	2.75800i	0.0834536	−	0.0994561i	0.806155	+	0.591704i	$0.201544\pi$
$770$		0			0
$771$	−17.0593	−	9.77115i	−0.614375	−	0.351900i
$772$		0			0
$773$	−39.3835			−1.41653			−0.708263	−	0.705948i	$-0.750521\pi$
$773$	−39.3835			−1.41653			−0.708263	+	0.705948i	$0.750521\pi$
$774$		0			0
$775$			56.0096i			2.01192i
$776$		0			0
$777$	−4.93106	+	9.43232i	−0.176901	+	0.338383i
$778$		0			0
$779$	−6.55108	+	7.80728i	−0.234717	+	0.279725i
$780$		0			0
$781$	6.42613	+	2.33892i	0.229945	+	0.0836931i
$782$		0			0
$783$	2.59678	+	0.914941i	0.0928015	+	0.0326973i
$784$		0			0
$785$	29.9561	+	35.7003i	1.06918	+	1.27420i
$786$		0			0
$787$	−6.31085	−	17.3389i	−0.224958	−	0.618066i	0.774945	−	0.632029i	$-0.217778\pi$
$787$	−6.31085	−	17.3389i	−0.224958	−	0.618066i	−0.999903	+	0.0139628i	$0.995555\pi$
$788$		0			0
$789$	−0.0715515	+	0.414107i	−0.00254730	+	0.0147426i
$790$		0			0
$791$	5.20327	+	24.0594i	0.185007	+	0.855455i
$792$		0			0
$793$	29.0195	+	50.2632i	1.03051	+	1.78490i
$794$		0			0
$795$	−34.5949	+	60.3987i	−1.22696	+	2.14212i
$796$		0			0
$797$	−10.3259	−	8.66449i	−0.365763	−	0.306912i	0.441319	−	0.897350i	$-0.354511\pi$
$797$	−10.3259	−	8.66449i	−0.365763	−	0.306912i	−0.807083	+	0.590438i	$0.798955\pi$
$798$		0			0
$799$	−37.2513	−	13.5584i	−1.31786	−	0.479660i
$800$		0			0
$801$	−2.00489	+	11.8459i	−0.0708394	+	0.418555i
$802$		0			0
$803$	−1.41040	−	0.513344i	−0.0497719	−	0.0181155i
$804$		0			0
$805$	−31.8772	−	50.6137i	−1.12352	−	1.78390i
$806$		0			0
$807$	10.1542	−	28.1996i	0.357445	−	0.992674i
$808$		0			0
$809$	32.7992	−	18.9366i	1.15316	−	0.665777i	0.203504	−	0.979074i	$-0.434767\pi$
$809$	32.7992	−	18.9366i	1.15316	−	0.665777i	0.949655	+	0.313297i	$0.101434\pi$
$810$		0			0
$811$		−	17.3724i		−	0.610028i	−0.952348	−	0.305014i	$-0.901339\pi$
$811$		−	17.3724i		−	0.610028i	0.952348	−	0.305014i	$-0.0986612\pi$
$812$		0			0
$813$	−2.99042	−	16.6252i	−0.104879	−	0.583071i
$814$		0			0
$815$	72.1141	+	60.5109i	2.52605	+	2.11960i
$816$		0			0
$817$	−0.122288	+	0.335984i	−0.00427832	+	0.0117546i
$818$		0			0
$819$	18.5854	+	29.0644i	0.649427	+	1.01559i
$820$		0			0
$821$	10.6175	+	12.6535i	0.370555	+	0.441610i	0.918809	−	0.394701i	$-0.129152\pi$
$821$	10.6175	+	12.6535i	0.370555	+	0.441610i	−0.548255	+	0.836312i	$0.684707\pi$
$822$		0			0
$823$	1.18804	−	6.73770i	0.0414124	−	0.234861i	−0.957075	−	0.289840i	$-0.906398\pi$
$823$	1.18804	−	6.73770i	0.0414124	−	0.234861i	0.998488	+	0.0549785i	$0.0175090\pi$
$824$		0			0
$825$	−5.90989	−	10.1555i	−0.205756	−	0.353568i
$826$		0			0
$827$	−16.7920	−	9.69487i	−0.583915	−	0.337124i	0.178772	−	0.983890i	$-0.442787\pi$
$827$	−16.7920	−	9.69487i	−0.583915	−	0.337124i	−0.762688	+	0.646767i	$0.776121\pi$
$828$		0			0
$829$	−9.76285	−	5.63658i	−0.339078	−	0.195767i	0.320786	−	0.947152i	$-0.396053\pi$
$829$	−9.76285	−	5.63658i	−0.339078	−	0.195767i	−0.659864	+	0.751385i	$0.729386\pi$
$830$		0			0
$831$	−41.7322	−	7.21071i	−1.44767	−	0.250137i
$832$		0			0
$833$	28.5421	+	7.96557i	0.988924	+	0.275991i
$834$		0			0
$835$	−16.4372	−	93.2198i	−0.568831	−	3.22600i
$836$		0			0
$837$	21.5332	+	17.6934i	0.744297	+	0.611573i
$838$		0			0
$839$	−26.2914	+	22.0611i	−0.907679	+	0.761633i	−0.971676	−	0.236317i	$-0.924060\pi$
$839$	−26.2914	+	22.0611i	−0.907679	+	0.761633i	0.0639972	+	0.997950i	$0.479615\pi$
$840$		0			0
$841$	4.98704	−	28.2829i	0.171967	−	0.975274i
$842$		0			0
$843$	−20.3871	+	7.49976i	−0.702170	+	0.258306i
$844$		0			0
$845$	23.1515			0.796435
$846$		0			0
$847$	−27.3543	+	5.91585i	−0.939905	+	0.203271i
$848$		0			0
$849$	−19.9074	−	34.2085i	−0.683219	−	1.17403i
$850$		0			0
$851$	−13.1593	−	2.32033i	−0.451094	−	0.0795400i
$852$		0			0
$853$	−8.19387	+	22.5125i	−0.280553	+	0.770812i	0.716744	+	0.697336i	$0.245632\pi$
$853$	−8.19387	+	22.5125i	−0.280553	+	0.770812i	−0.997297	+	0.0734762i	$0.976591\pi$
$854$		0			0
$855$	−5.02466	+	14.1061i	−0.171840	+	0.482419i
$856$		0			0
$857$	31.1092	−	26.1037i	1.06267	−	0.891685i	0.0683004	−	0.997665i	$-0.478242\pi$
$857$	31.1092	−	26.1037i	1.06267	−	0.891685i	0.994368	+	0.105980i	$0.0337979\pi$
$858$		0			0
$859$	−6.56312	−	1.15725i	−0.223931	−	0.0394850i	0.0605569	−	0.998165i	$-0.480712\pi$
$859$	−6.56312	−	1.15725i	−0.223931	−	0.0394850i	−0.284488	+	0.958680i	$0.591823\pi$
$860$		0			0
$861$	4.86290	−	36.4467i	0.165727	−	1.24210i
$862$		0			0
$863$	−15.5521	−	8.97900i	−0.529399	−	0.305649i	0.211373	−	0.977406i	$-0.432207\pi$
$863$	−15.5521	−	8.97900i	−0.529399	−	0.305649i	−0.740772	+	0.671757i	$0.765540\pi$
$864$		0			0
$865$	35.6847	+	61.8078i	1.21332	+	2.10153i
$866$		0			0
$867$	1.02891	+	1.21768i	0.0349434	+	0.0413545i
$868$		0			0
$869$	−3.14763	−	8.64804i	−0.106776	−	0.293365i
$870$		0			0
$871$	−27.4113	−	32.6675i	−0.928795	−	1.10690i
$872$		0			0
$873$	24.0720	+	13.6782i	0.814715	+	0.462938i
$874$		0			0
$875$	34.6797	−	44.7141i	1.17239	−	1.51161i
$876$		0			0
$877$	−23.5354	+	8.56618i	−0.794734	+	0.289259i	−0.707302	−	0.706911i	$-0.750088\pi$
$877$	−23.5354	+	8.56618i	−0.794734	+	0.289259i	−0.0874314	+	0.996171i	$0.527866\pi$
$878$		0			0
$879$	−2.85385	+	1.66078i	−0.0962580	+	0.0560166i
$880$		0			0
$881$	−6.86863	+	11.8968i	−0.231410	+	0.400814i	−0.958223	−	0.286021i	$-0.907667\pi$
$881$	−6.86863	+	11.8968i	−0.231410	+	0.400814i	0.726813	+	0.686835i	$0.241001\pi$
$882$		0			0
$883$	−21.8188	−	37.7913i	−0.734261	−	1.27178i	−0.955047	−	0.296455i	$-0.904195\pi$
$883$	−21.8188	−	37.7913i	−0.734261	−	1.27178i	0.220786	−	0.975322i	$-0.429138\pi$
$884$		0			0
$885$	−2.26380	−	0.391152i	−0.0760970	−	0.0131484i
$886$		0			0
$887$	3.94260	+	3.30823i	0.132379	+	0.111080i	0.706573	−	0.707640i	$-0.250240\pi$
$887$	3.94260	+	3.30823i	0.132379	+	0.111080i	−0.574194	+	0.818719i	$0.694684\pi$
$888$		0			0
$889$	11.6324	+	28.4996i	0.390137	+	0.955846i
$890$		0			0
$891$	−5.77126	−	0.936010i	−0.193345	−	0.0313575i
$892$		0			0
$893$	−4.06817	+	11.1772i	−0.136136	+	0.374031i
$894$		0			0
$895$	58.5496	+	10.3239i	1.95710	+	0.345089i
$896$		0			0
$897$	−27.7256	+	33.2736i	−0.925730	+	1.11097i
$898$		0			0
$899$	−1.42098	+	2.46121i	−0.0473924	+	0.0820861i
$900$		0			0
$901$	37.4906	−	21.6452i	1.24899	−	0.721106i
$902$		0			0
$903$	−0.277005	−	1.25987i	−0.00921815	−	0.0419258i
$904$		0			0
$905$	13.4816	+	37.0404i	0.448143	+	1.23126i
$906$		0			0
$907$	5.59203	+	31.7140i	0.185680	+	1.05305i	0.925078	+	0.379777i	$0.123999\pi$
$907$	5.59203	+	31.7140i	0.185680	+	1.05305i	−0.739398	+	0.673269i	$0.764890\pi$
$908$		0			0
$909$	−18.2863	−	31.1759i	−0.606518	−	1.03404i
$910$		0			0
$911$	−48.2615	+	8.50980i	−1.59897	+	0.281942i	−0.900882	−	0.434065i	$-0.857079\pi$
$911$	−48.2615	+	8.50980i	−1.59897	+	0.281942i	−0.698093	+	0.716007i	$0.745968\pi$
$912$		0			0
$913$	6.87238	−	8.19018i	0.227443	−	0.271056i
$914$		0			0
$915$	−16.0901	−	89.4527i	−0.531924	−	2.95722i
$916$		0			0
$917$	−0.765648	−	0.844295i	−0.0252839	−	0.0278811i
$918$		0			0
$919$	15.9356	−	27.6012i	0.525666	−	0.910480i	−0.473887	−	0.880586i	$-0.657150\pi$
$919$	15.9356	−	27.6012i	0.525666	−	0.910480i	0.999553	−	0.0298944i	$-0.00951709\pi$
$920$		0			0
$921$	−4.52832	−	25.1751i	−0.149213	−	0.829548i
$922$		0			0
$923$	42.9947	−	15.6488i	1.41519	−	0.515087i
$924$		0			0
$925$	−4.21165	−	23.8855i	−0.138478	−	0.785349i
$926$		0			0
$927$	−12.6054	+	35.3880i	−0.414015	+	1.16229i
$928$		0			0
$929$	21.6257	−	18.1461i	0.709517	−	0.595356i	−0.214946	−	0.976626i	$-0.568958\pi$
$929$	21.6257	−	18.1461i	0.709517	−	0.595356i	0.924464	+	0.381270i	$0.124513\pi$
$930$		0			0
$931$	2.39006	−	8.56400i	0.0783310	−	0.280674i
$932$		0			0
$933$	−17.4727	+	10.1681i	−0.572032	+	0.332889i
$934$		0			0
$935$			10.8069i			0.353422i
$936$		0			0
$937$	−49.2056	+	28.4089i	−1.60748	+	0.928077i	−0.617545	+	0.786536i	$0.711873\pi$
$937$	−49.2056	+	28.4089i	−1.60748	+	0.928077i	−0.989932	+	0.141542i	$0.954794\pi$
$938$		0			0
$939$	−0.526221	+	3.04552i	−0.0171726	+	0.0993868i
$940$		0			0
$941$	8.60541	−	3.13211i	0.280528	−	0.102104i	−0.197924	−	0.980217i	$-0.563420\pi$
$941$	8.60541	−	3.13211i	0.280528	−	0.102104i	0.478453	+	0.878113i	$0.341198\pi$
$942$		0			0
$943$	45.4608	−	8.01597i	1.48041	−	0.261036i
$944$		0			0
$945$	−11.9636	−	52.6832i	−0.389176	−	1.71378i
$946$		0			0
$947$	−5.95384	+	1.04982i	−0.193474	+	0.0341147i	−0.269545	−	0.962988i	$-0.586873\pi$
$947$	−5.95384	+	1.04982i	−0.193474	+	0.0341147i	0.0760715	+	0.997102i	$0.475762\pi$
$948$		0			0
$949$	−9.43644	+	3.43458i	−0.306320	+	0.111491i
$950$		0			0
$951$	−50.0690	+	18.4188i	−1.62360	+	0.597269i
$952$		0			0
$953$	8.78832	−	5.07394i	0.284682	−	0.164361i	−0.350859	−	0.936428i	$-0.614110\pi$
$953$	8.78832	−	5.07394i	0.284682	−	0.164361i	0.635541	+	0.772067i	$0.280777\pi$
$954$		0			0
$955$		−	7.93465i		−	0.256759i
$956$		0			0
$957$	−0.00204917	−	0.596195i	−6.62402e−5	−	0.0192722i
$958$		0			0
$959$	−17.8487	+	33.8577i	−0.576364	+	1.09332i
$960$		0			0
$961$	1.70982	−	1.43471i	0.0551556	−	0.0462810i
$962$		0			0
$963$	−6.83423	+	8.25936i	−0.220230	+	0.266154i
$964$		0			0
$965$	−9.31209	−	52.8115i	−0.299767	−	1.70006i
$966$		0			0
$967$	−30.7394	+	11.1882i	−0.988512	+	0.359789i	−0.785144	−	0.619313i	$-0.787411\pi$
$967$	−30.7394	+	11.1882i	−0.988512	+	0.359789i	−0.203368	+	0.979102i	$0.565189\pi$
$968$		0			0
$969$	7.11372	−	6.01091i	0.228526	−	0.193098i
$970$		0			0
$971$	−9.68760	+	16.7794i	−0.310890	+	0.538477i	−0.978555	−	0.205984i	$-0.933960\pi$
$971$	−9.68760	+	16.7794i	−0.310890	+	0.538477i	0.667665	+	0.744461i	$0.267294\pi$
$972$		0			0
$973$	−40.8901	−	13.1258i	−1.31087	−	0.420793i
$974$		0			0
$975$	−73.9650	−	26.6335i	−2.36878	−	0.852956i
$976$		0			0
$977$	34.6734	−	41.3222i	1.10930	−	1.32201i	0.167488	−	0.985874i	$-0.446434\pi$
$977$	34.6734	−	41.3222i	1.10930	−	1.32201i	0.941812	−	0.336139i	$-0.109121\pi$
$978$		0			0
$979$	2.56211	−	0.451769i	0.0818853	−	0.0144386i
$980$		0			0
$981$	−35.8660	+	13.3341i	−1.14511	+	0.425724i
$982$		0			0
$983$	5.47759	+	31.0649i	0.174708	+	0.990817i	0.938481	+	0.345332i	$0.112234\pi$
$983$	5.47759	+	31.0649i	0.174708	+	0.990817i	−0.763773	+	0.645485i	$0.776655\pi$
$984$		0			0
$985$	11.0265	+	30.2949i	0.351332	+	0.965277i
$986$		0			0
$987$	−9.21514	−	41.9121i	−0.293321	−	1.33408i
$988$		0			0
$989$	1.40250	−	0.809735i	0.0445969	−	0.0257481i
$990$		0			0
$991$	−9.68664	+	16.7777i	−0.307706	+	0.532963i	−0.977860	−	0.209259i	$-0.932895\pi$
$991$	−9.68664	+	16.7777i	−0.307706	+	0.532963i	0.670154	+	0.742222i	$0.266228\pi$
$992$		0			0
$993$	7.40054	+	20.1174i	0.234849	+	0.638406i
$994$		0			0
$995$	−70.9045	−	12.5024i	−2.24782	−	0.396352i
$996$		0			0
$997$	−13.7696	+	37.8316i	−0.436086	+	1.19814i	0.505931	+	0.862574i	$0.331149\pi$
$997$	−13.7696	+	37.8316i	−0.436086	+	1.19814i	−0.942017	+	0.335564i	$0.891073\pi$
$998$		0			0
$999$	−10.5134	−	5.92621i	−0.332628	−	0.187497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.18	yes	144
7.3	odd	6		756.2.ca.a.437.9	yes	144
27.11	odd	18		756.2.ca.a.173.9	✓	144
189.38	even	18	inner	756.2.ck.a.605.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.9	✓	144	27.11	odd	18
756.2.ca.a.437.9	yes	144	7.3	odd	6
756.2.ck.a.5.18	yes	144	1.1	even	1	trivial
756.2.ck.a.605.18	yes	144	189.38	even	18	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.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11789 + 1.32299i) q^{3} +(-0.682386 + 3.87000i) q^{5} +(2.62129 + 0.358920i) q^{7} +(-0.500623 + 2.95793i) q^{9} +O(q^{10})\)	\(q+(1.11789 + 1.32299i) q^{3} +(-0.682386 + 3.87000i) q^{5} +(2.62129 + 0.358920i) q^{7} +(-0.500623 + 2.95793i) q^{9} +(0.639761 - 0.112807i) q^{11} +(2.79383 - 3.32955i) q^{13} +(-5.88282 + 3.42346i) q^{15} +4.23325 q^{17} -1.27018i q^{19} +(2.45548 + 3.86919i) q^{21} +(-3.69805 + 4.40717i) q^{23} +(-9.81281 - 3.57157i) q^{25} +(-4.47297 + 2.64434i) q^{27} +(-0.340590 - 0.405899i) q^{29} +(-1.83445 - 5.04012i) q^{31} +(0.864428 + 0.720293i) q^{33} +(-3.17775 + 9.89949i) q^{35} +(1.16130 + 2.01143i) q^{37} +(7.52818 - 0.0258750i) q^{39} +(-6.14659 - 5.15760i) q^{41} +(-0.264517 - 0.0962762i) q^{43} +(-11.1056 - 3.95587i) q^{45} +(-8.79969 - 3.20283i) q^{47} +(6.74235 + 1.88167i) q^{49} +(4.73233 + 5.60056i) q^{51} +(8.85622 - 5.11314i) q^{53} +2.55285i q^{55} +(1.68044 - 1.41993i) q^{57} +(0.258559 + 0.216957i) q^{59} +(-4.56709 + 12.5480i) q^{61} +(-2.37394 + 7.57393i) q^{63} +(10.9789 + 13.0842i) q^{65} +(1.70373 - 9.66231i) q^{67} +(-9.96468 + 0.0342494i) q^{69} +(9.11650 + 5.26341i) q^{71} +(-2.00088 - 1.15521i) q^{73} +(-6.24452 - 16.9749i) q^{75} +(1.71749 - 0.0660776i) q^{77} +(-2.46001 - 13.9514i) q^{79} +(-8.49875 - 2.96162i) q^{81} +(12.6075 - 10.5789i) q^{83} +(-2.88871 + 16.3827i) q^{85} +(0.156258 - 0.904351i) q^{87} +4.00479 q^{89} +(8.51848 - 7.72498i) q^{91} +(4.61732 - 8.06129i) q^{93} +(4.91560 + 0.866753i) q^{95} +(3.15648 - 8.67235i) q^{97} +(0.0133968 + 1.94884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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