LMFDB - Embedded newform 756.2.bx.a.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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, 17, 9]))

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

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

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (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			41.12
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.304497 + 1.70508i) q^{3} +(2.29372 + 1.92466i) q^{5} +(2.03395 - 1.69205i) q^{7} +(-2.81456 - 1.03838i) q^{9} +O(q^{10})$	\(q+(-0.304497 + 1.70508i) q^{3} +(2.29372 + 1.92466i) q^{5} +(2.03395 - 1.69205i) q^{7} +(-2.81456 - 1.03838i) q^{9} +(1.13089 + 1.34775i) q^{11} +(5.62290 + 0.991469i) q^{13} +(-3.98013 + 3.32492i) q^{15} +(-0.239581 + 0.414967i) q^{17} +(3.31971 - 1.91663i) q^{19} +(2.26575 + 3.98326i) q^{21} +(-1.03273 - 2.83740i) q^{23} +(0.688600 + 3.90524i) q^{25} +(2.62755 - 4.48286i) q^{27} +(-3.17989 + 0.560701i) q^{29} +(-1.20093 - 3.29953i) q^{31} +(-2.64237 + 1.51788i) q^{33} +(7.92195 + 0.0335647i) q^{35} +(-2.39449 + 4.14738i) q^{37} +(-3.40269 + 9.28557i) q^{39} +(-1.02337 + 5.80382i) q^{41} +(-6.64566 + 5.57637i) q^{43} +(-4.45729 - 7.79884i) q^{45} +(-11.2325 - 4.08830i) q^{47} +(1.27391 - 6.88311i) q^{49} +(-0.634599 - 0.534861i) q^{51} +5.83466i q^{53} +5.26795i q^{55} +(2.25716 + 6.24396i) q^{57} +(9.24397 + 7.75661i) q^{59} +(1.79593 - 4.93428i) q^{61} +(-7.48168 + 2.65038i) q^{63} +(10.9891 + 13.0963i) q^{65} +(1.55948 - 8.84425i) q^{67} +(5.15244 - 0.896900i) q^{69} +(-4.92623 - 2.84416i) q^{71} +(-10.4876 + 6.05500i) q^{73} +(-6.86841 - 0.0150215i) q^{75} +(4.58065 + 0.827718i) q^{77} +(-1.59538 - 9.04783i) q^{79} +(6.84353 + 5.84518i) q^{81} +(1.34781 + 7.64383i) q^{83} +(-1.34821 + 0.490707i) q^{85} +(0.0122314 - 5.59269i) q^{87} +(-1.42054 - 2.46044i) q^{89} +(13.1143 - 7.49765i) q^{91} +(5.99162 - 1.04298i) q^{93} +(11.3034 + 1.99309i) q^{95} +(6.65254 + 7.92818i) q^{97} +(-1.78350 - 4.96762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

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
$3$	−0.304497	+	1.70508i	−0.175802	+	0.984426i
$3$	−0.304497	+	1.70508i	−0.175802	+	0.984426i
$4$		0			0
$5$	2.29372	+	1.92466i	1.02578	+	0.860735i	0.990343	−	0.138637i	$-0.0442720\pi$
$5$	2.29372	+	1.92466i	1.02578	+	0.860735i	0.0354408	+	0.999372i	$0.488716\pi$
$6$		0			0
$7$	2.03395	−	1.69205i	0.768761	−	0.639536i
$7$	2.03395	−	1.69205i	0.768761	−	0.639536i
$8$		0			0
$9$	−2.81456	−	1.03838i	−0.938188	−	0.346127i
$10$		0			0
$11$	1.13089	+	1.34775i	0.340978	+	0.406361i	0.909097	−	0.416585i	$-0.136773\pi$
$11$	1.13089	+	1.34775i	0.340978	+	0.406361i	−0.568119	+	0.822946i	$0.692329\pi$
$12$		0			0
$13$	5.62290	+	0.991469i	1.55951	+	0.274984i	0.885820	−	0.464028i	$-0.153596\pi$
$13$	5.62290	+	0.991469i	1.55951	+	0.274984i	0.673692	+	0.739012i	$0.264708\pi$
$14$		0			0
$15$	−3.98013	+	3.32492i	−1.02766	+	0.858490i
$16$		0			0
$17$	−0.239581	+	0.414967i	−0.0581070	+	0.100644i	−0.893616	−	0.448833i	$-0.851840\pi$
$17$	−0.239581	+	0.414967i	−0.0581070	+	0.100644i	0.835509	+	0.549477i	$0.185173\pi$
$18$		0			0
$19$	3.31971	−	1.91663i	0.761593	−	0.439706i	−0.0682745	−	0.997667i	$-0.521749\pi$
$19$	3.31971	−	1.91663i	0.761593	−	0.439706i	0.829867	+	0.557961i	$0.188416\pi$
$20$		0			0
$21$	2.26575	+	3.98326i	0.494426	+	0.869219i
$22$		0			0
$23$	−1.03273	−	2.83740i	−0.215339	−	0.591638i	0.784246	−	0.620450i	$-0.213050\pi$
$23$	−1.03273	−	2.83740i	−0.215339	−	0.591638i	−0.999585	+	0.0288115i	$0.990828\pi$
$24$		0			0
$25$	0.688600	+	3.90524i	0.137720	+	0.781049i
$26$		0			0
$27$	2.62755	−	4.48286i	0.505671	−	0.862726i
$28$		0			0
$29$	−3.17989	+	0.560701i	−0.590491	+	0.104120i	−0.460906	−	0.887449i	$-0.652476\pi$
$29$	−3.17989	+	0.560701i	−0.590491	+	0.104120i	−0.129585	+	0.991568i	$0.541364\pi$
$30$		0			0
$31$	−1.20093	−	3.29953i	−0.215693	−	0.592612i	0.783907	−	0.620878i	$-0.213224\pi$
$31$	−1.20093	−	3.29953i	−0.215693	−	0.592612i	−0.999600	+	0.0282656i	$0.991002\pi$
$32$		0			0
$33$	−2.64237	+	1.51788i	−0.459977	+	0.264228i
$34$		0			0
$35$	7.92195	+	0.0335647i	1.33905	+	0.00567347i
$36$		0			0
$37$	−2.39449	+	4.14738i	−0.393652	+	0.681826i	−0.992928	−	0.118717i	$-0.962122\pi$
$37$	−2.39449	+	4.14738i	−0.393652	+	0.681826i	0.599276	+	0.800543i	$0.295455\pi$
$38$		0			0
$39$	−3.40269	+	9.28557i	−0.544866	+	1.48688i
$40$		0			0
$41$	−1.02337	+	5.80382i	−0.159824	+	0.906404i	0.794419	+	0.607370i	$0.207775\pi$
$41$	−1.02337	+	5.80382i	−0.159824	+	0.906404i	−0.954242	+	0.299034i	$0.903336\pi$
$42$		0			0
$43$	−6.64566	+	5.57637i	−1.01345	+	0.850388i	−0.988791	−	0.149308i	$-0.952295\pi$
$43$	−6.64566	+	5.57637i	−1.01345	+	0.850388i	−0.0246622	+	0.999696i	$0.507851\pi$
$44$		0			0
$45$	−4.45729	−	7.79884i	−0.664454	−	1.16258i
$46$		0			0
$47$	−11.2325	−	4.08830i	−1.63843	−	0.596339i	−0.651666	−	0.758506i	$-0.725930\pi$
$47$	−11.2325	−	4.08830i	−1.63843	−	0.596339i	−0.986763	+	0.162167i	$0.948152\pi$
$48$		0			0
$49$	1.27391	−	6.88311i	0.181987	−	0.983301i
$50$		0			0
$51$	−0.634599	−	0.534861i	−0.0888616	−	0.0748955i
$52$		0			0
$53$			5.83466i			0.801452i	0.916198	+	0.400726i	$0.131242\pi$
$53$			5.83466i			0.801452i	−0.916198	+	0.400726i	$0.868758\pi$
$54$		0			0
$55$			5.26795i			0.710330i
$56$		0			0
$57$	2.25716	+	6.24396i	0.298968	+	0.827032i
$58$		0			0
$59$	9.24397	+	7.75661i	1.20346	+	1.00982i	0.999524	+	0.0308407i	$0.00981846\pi$
$59$	9.24397	+	7.75661i	1.20346	+	1.00982i	0.203938	+	0.978984i	$0.434626\pi$
$60$		0			0
$61$	1.79593	−	4.93428i	0.229945	−	0.631770i	−0.770035	−	0.638001i	$-0.779761\pi$
$61$	1.79593	−	4.93428i	0.229945	−	0.631770i	0.999981	+	0.00623160i	$0.00198359\pi$
$62$		0			0
$63$	−7.48168	+	2.65038i	−0.942603	+	0.333916i
$64$		0			0
$65$	10.9891	+	13.0963i	1.36303	+	1.62440i
$66$		0			0
$67$	1.55948	−	8.84425i	0.190521	−	1.08050i	−0.728134	−	0.685435i	$-0.759612\pi$
$67$	1.55948	−	8.84425i	0.190521	−	1.08050i	0.918655	−	0.395062i	$-0.129277\pi$
$68$		0			0
$69$	5.15244	−	0.896900i	0.620281	−	0.107974i
$70$		0			0
$71$	−4.92623	−	2.84416i	−0.584636	−	0.337540i	0.178338	−	0.983969i	$-0.442928\pi$
$71$	−4.92623	−	2.84416i	−0.584636	−	0.337540i	−0.762974	+	0.646430i	$0.776261\pi$
$72$		0			0
$73$	−10.4876	+	6.05500i	−1.22748	+	0.708684i	−0.966501	−	0.256662i	$-0.917377\pi$
$73$	−10.4876	+	6.05500i	−1.22748	+	0.708684i	−0.260975	+	0.965345i	$0.584044\pi$
$74$		0			0
$75$	−6.86841	−	0.0150215i	−0.793096	−	0.00173453i
$76$		0			0
$77$	4.58065	+	0.827718i	0.522013	+	0.0943272i
$78$		0			0
$79$	−1.59538	−	9.04783i	−0.179494	−	1.01796i	−0.932828	−	0.360322i	$-0.882667\pi$
$79$	−1.59538	−	9.04783i	−0.179494	−	1.01796i	0.753334	−	0.657638i	$-0.228444\pi$
$80$		0			0
$81$	6.84353	+	5.84518i	0.760392	+	0.649464i
$82$		0			0
$83$	1.34781	+	7.64383i	0.147942	+	0.839020i	0.964958	+	0.262405i	$0.0845155\pi$
$83$	1.34781	+	7.64383i	0.147942	+	0.839020i	−0.817016	+	0.576615i	$0.804373\pi$
$84$		0			0
$85$	−1.34821	+	0.490707i	−0.146233	+	0.0532246i
$86$		0			0
$87$	0.0122314	−	5.59269i	0.00131135	−	0.599599i
$88$		0			0
$89$	−1.42054	−	2.46044i	−0.150577	−	0.260806i	0.780863	−	0.624702i	$-0.214780\pi$
$89$	−1.42054	−	2.46044i	−0.150577	−	0.260806i	−0.931440	+	0.363896i	$0.881446\pi$
$90$		0			0
$91$	13.1143	−	7.49765i	1.37475	−	0.785967i
$92$		0			0
$93$	5.99162	−	1.04298i	0.621302	−	0.108152i
$94$		0			0
$95$	11.3034	+	1.99309i	1.15970	+	0.204486i
$96$		0			0
$97$	6.65254	+	7.92818i	0.675463	+	0.804985i	0.989516	−	0.144420i	$-0.0461317\pi$
$97$	6.65254	+	7.92818i	0.675463	+	0.804985i	−0.314054	+	0.949405i	$0.601687\pi$
$98$		0			0
$99$	−1.78350	−	4.96762i	−0.179248	−	0.499265i
$100$		0			0
$101$	11.8669	+	4.31919i	1.18080	+	0.429775i	0.856483	−	0.516175i	$-0.172644\pi$
$101$	11.8669	+	4.31919i	1.18080	+	0.429775i	0.324314	+	0.945950i	$0.394867\pi$
$102$		0			0
$103$	6.84051	−	8.15220i	0.674016	−	0.803261i	−0.315309	−	0.948989i	$-0.602108\pi$
$103$	6.84051	−	8.15220i	0.674016	−	0.803261i	0.989325	+	0.145728i	$0.0465526\pi$
$104$		0			0
$105$	−2.46944	+	13.4973i	−0.240993	+	1.31720i
$106$		0			0
$107$		−	18.7836i		−	1.81588i	−0.419101	−	0.907939i	$-0.637655\pi$
$107$		−	18.7836i		−	1.81588i	0.419101	−	0.907939i	$-0.362345\pi$
$108$		0			0
$109$	−13.7605			−1.31802			−0.659009	−	0.752135i	$-0.729024\pi$
$109$	−13.7605			−1.31802			−0.659009	+	0.752135i	$0.729024\pi$
$110$		0			0
$111$	−6.34249	−	5.34566i	−0.602002	−	0.507387i
$112$		0			0
$113$	−7.86347	+	9.37132i	−0.739733	+	0.881580i	−0.996387	−	0.0849237i	$-0.972935\pi$
$113$	−7.86347	+	9.37132i	−0.739733	+	0.881580i	0.256654	+	0.966503i	$0.417380\pi$
$114$		0			0
$115$	3.09224	−	8.49586i	0.288353	−	0.792243i
$116$		0			0
$117$	−14.7965	−	8.62927i	−1.36794	−	0.797776i
$118$		0			0
$119$	0.214850	+	1.24941i	0.0196953	+	0.114533i
$120$		0			0
$121$	1.37263	−	7.78456i	0.124784	−	0.707688i
$122$		0			0
$123$	−9.58433	−	3.51217i	−0.864190	−	0.316682i
$124$		0			0
$125$	1.54879	−	2.68258i	0.138528	−	0.239937i
$126$		0			0
$127$	−6.62493	−	11.4747i	−0.587867	−	1.01822i	−0.994511	−	0.104629i	$-0.966634\pi$
$127$	−6.62493	−	11.4747i	−0.587867	−	1.01822i	0.406644	−	0.913587i	$-0.366699\pi$
$128$		0			0
$129$	−7.48454	−	13.0293i	−0.658977	−	1.14717i
$130$		0			0
$131$	−13.6290	+	4.96054i	−1.19077	+	0.433405i	−0.859994	−	0.510305i	$-0.829533\pi$
$131$	−13.6290	+	4.96054i	−1.19077	+	0.433405i	−0.330776	+	0.943709i	$0.607310\pi$
$132$		0			0
$133$	3.50907	−	9.51546i	0.304275	−	0.825095i
$134$		0			0
$135$	14.6548	−	5.22530i	1.26129	−	0.449722i
$136$		0			0
$137$	10.3063	−	1.81729i	0.880530	−	0.155261i	0.284936	−	0.958547i	$-0.408028\pi$
$137$	10.3063	−	1.81729i	0.880530	−	0.155261i	0.595594	+	0.803285i	$0.296917\pi$
$138$		0			0
$139$	−5.11101	−	14.0424i	−0.433510	−	1.19106i	−0.943643	−	0.330964i	$-0.892626\pi$
$139$	−5.11101	−	14.0424i	−0.433510	−	1.19106i	0.510133	−	0.860096i	$-0.329596\pi$
$140$		0			0
$141$	10.3911	−	17.9074i	0.875090	−	1.50807i
$142$		0			0
$143$	5.02266	+	8.69950i	0.420016	+	0.727489i
$144$		0			0
$145$	−8.37295	−	4.83413i	−0.695336	−	0.401452i
$146$		0			0
$147$	11.3483	+	4.26800i	0.935993	+	0.352018i
$148$		0			0
$149$	−10.7037	−	1.88734i	−0.876878	−	0.154617i	−0.282949	−	0.959135i	$-0.591313\pi$
$149$	−10.7037	−	1.88734i	−0.876878	−	0.154617i	−0.593929	+	0.804518i	$0.702424\pi$
$150$		0			0
$151$	−11.8808	+	9.96917i	−0.966845	+	0.811279i	−0.982053	−	0.188605i	$-0.939603\pi$
$151$	−11.8808	+	9.96917i	−0.966845	+	0.811279i	0.0152080	+	0.999884i	$0.495159\pi$
$152$		0			0
$153$	1.10521	−	0.919175i	0.0893510	−	0.0743109i
$154$		0			0
$155$	3.59587	−	9.87958i	0.288828	−	0.793547i
$156$		0			0
$157$	−1.66401	+	1.98309i	−0.132803	+	0.158268i	−0.828348	−	0.560215i	$-0.810719\pi$
$157$	−1.66401	+	1.98309i	−0.132803	+	0.158268i	0.695545	+	0.718483i	$0.255163\pi$
$158$		0			0
$159$	−9.94853	−	1.77664i	−0.788970	−	0.140897i
$160$		0			0
$161$	−6.90155	−	4.02369i	−0.543918	−	0.317112i
$162$		0			0
$163$	1.22861			0.0962319			0.0481160	−	0.998842i	$-0.484678\pi$
$163$	1.22861			0.0962319			0.0481160	+	0.998842i	$0.484678\pi$
$164$		0			0
$165$	−8.98225	−	1.60408i	−0.699267	−	0.124877i
$166$		0			0
$167$	10.8958	+	9.14262i	0.843139	+	0.707477i	0.958267	−	0.285873i	$-0.0922836\pi$
$167$	10.8958	+	9.14262i	0.843139	+	0.707477i	−0.115129	+	0.993351i	$0.536728\pi$
$168$		0			0
$169$	18.4180	+	6.70360i	1.41677	+	0.515662i
$170$		0			0
$171$	−11.3337	+	1.94736i	−0.866711	+	0.148919i
$172$		0			0
$173$	1.22802	−	1.03043i	0.0933643	−	0.0783419i	−0.594911	−	0.803792i	$-0.702813\pi$
$173$	1.22802	−	1.03043i	0.0933643	−	0.0783419i	0.688275	+	0.725450i	$0.258368\pi$
$174$		0			0
$175$	8.00846	+	6.77792i	0.605383	+	0.512363i
$176$		0			0
$177$	−16.0404	+	13.3998i	−1.20567	+	1.00719i
$178$		0			0
$179$	−10.1047	−	5.83392i	−0.755257	−	0.436048i	0.0723330	−	0.997381i	$-0.476956\pi$
$179$	−10.1047	−	5.83392i	−0.755257	−	0.436048i	−0.827590	+	0.561333i	$0.810289\pi$
$180$		0			0
$181$	9.88823	−	5.70897i	0.734986	−	0.424345i	−0.0852573	−	0.996359i	$-0.527171\pi$
$181$	9.88823	−	5.70897i	0.734986	−	0.424345i	0.820244	+	0.572014i	$0.193838\pi$
$182$		0			0
$183$	7.86646	+	4.56467i	0.581506	+	0.337430i
$184$		0			0
$185$	−13.4746	+	4.90436i	−0.990674	+	0.360576i
$186$		0			0
$187$	−0.830213	+	0.146389i	−0.0607112	+	0.0107050i
$188$		0			0
$189$	−2.24094	−	13.5639i	−0.163004	−	0.986625i
$190$		0			0
$191$	14.4419	−	2.54649i	1.04498	−	0.184258i	0.375295	−	0.926905i	$-0.377541\pi$
$191$	14.4419	−	2.54649i	1.04498	−	0.184258i	0.669683	+	0.742647i	$0.266430\pi$
$192$		0			0
$193$	25.1475	−	9.15293i	1.81015	−	0.658842i	0.813101	−	0.582123i	$-0.197778\pi$
$193$	25.1475	−	9.15293i	1.81015	−	0.658842i	0.997053	−	0.0767188i	$-0.0244444\pi$
$194$		0			0
$195$	−25.6764	+	14.7495i	−1.83873	+	1.05623i
$196$		0			0
$197$	11.8651	−	6.85035i	0.845357	−	0.488067i	−0.0137246	−	0.999906i	$-0.504369\pi$
$197$	11.8651	−	6.85035i	0.845357	−	0.488067i	0.859082	+	0.511839i	$0.171035\pi$
$198$		0			0
$199$	1.43401	+	0.827928i	0.101654	+	0.0586902i	0.549965	−	0.835187i	$-0.314641\pi$
$199$	1.43401	+	0.827928i	0.101654	+	0.0586902i	−0.448311	+	0.893878i	$0.647974\pi$
$200$		0			0
$201$	14.6052	+	5.35208i	1.03017	+	0.377506i
$202$		0			0
$203$	−5.51901	+	6.52099i	−0.387358	+	0.457684i
$204$		0			0
$205$	−13.5177	+	11.3427i	−0.944118	+	0.792209i
$206$		0			0
$207$	−0.0396223	+	9.05840i	−0.00275394	+	0.629602i
$208$		0			0
$209$	6.33738	+	2.30662i	0.438366	+	0.159552i
$210$		0			0
$211$	17.2239	+	14.4526i	1.18574	+	0.994958i	0.999923	+	0.0123739i	$0.00393883\pi$
$211$	17.2239	+	14.4526i	1.18574	+	0.994958i	0.185821	+	0.982584i	$0.440506\pi$
$212$		0			0
$213$	6.34953	−	7.53355i	0.435063	−	0.516191i
$214$		0			0
$215$	−25.9759			−1.77154
$216$		0			0
$217$	−8.02561	−	4.67904i	−0.544814	−	0.317634i
$218$		0			0
$219$	−7.13079	−	19.7258i	−0.481854	−	1.33295i
$220$		0			0
$221$	−1.75857	+	2.09578i	−0.118294	+	0.140978i
$222$		0			0
$223$	0.783836	−	2.15357i	0.0524895	−	0.144214i	−0.910677	−	0.413119i	$-0.864439\pi$
$223$	0.783836	−	2.15357i	0.0524895	−	0.144214i	0.963167	+	0.268905i	$0.0866617\pi$
$224$		0			0
$225$	2.11703	−	11.7066i	0.141135	−	0.780439i
$226$		0			0
$227$	4.67966	−	3.92670i	0.310600	−	0.260625i	−0.474140	−	0.880450i	$-0.657241\pi$
$227$	4.67966	−	3.92670i	0.310600	−	0.260625i	0.784740	+	0.619825i	$0.212796\pi$
$228$		0			0
$229$	−10.2439	−	1.80627i	−0.676934	−	0.119362i	−0.175397	−	0.984498i	$-0.556121\pi$
$229$	−10.2439	−	1.80627i	−0.676934	−	0.119362i	−0.501537	+	0.865136i	$0.667232\pi$
$230$		0			0
$231$	−2.80612	+	7.55831i	−0.184629	+	0.497300i
$232$		0			0
$233$	−12.2591	−	7.07779i	−0.803120	−	0.463682i	0.0414409	−	0.999141i	$-0.486805\pi$
$233$	−12.2591	−	7.07779i	−0.803120	−	0.463682i	−0.844561	+	0.535459i	$0.820139\pi$
$234$		0			0
$235$	−17.8957	−	30.9962i	−1.16738	−	2.02197i
$236$		0			0
$237$	15.9130	+	0.0348024i	1.03366	+	0.00226066i
$238$		0			0
$239$	2.11075	+	5.79923i	0.136533	+	0.375121i	0.989050	−	0.147578i	$-0.0471476\pi$
$239$	2.11075	+	5.79923i	0.136533	+	0.375121i	−0.852518	+	0.522698i	$0.824925\pi$
$240$		0			0
$241$	0.845855	−	0.149147i	0.0544863	−	0.00960741i	−0.146339	−	0.989235i	$-0.546749\pi$
$241$	0.845855	−	0.149147i	0.0544863	−	0.00960741i	0.200825	+	0.979627i	$0.435638\pi$
$242$		0			0
$243$	−12.0503	+	9.88889i	−0.773027	+	0.634373i
$244$		0			0
$245$	16.1696	−	13.3361i	1.03304	−	0.852012i
$246$		0			0
$247$	20.5667	−	7.48565i	1.30863	−	0.476301i
$248$		0			0
$249$	−13.4437	−	0.0294019i	−0.851961	−	0.00186327i
$250$		0			0
$251$	6.68713	+	11.5825i	0.422088	+	0.731078i	0.996144	−	0.0877385i	$-0.0279640\pi$
$251$	6.68713	+	11.5825i	0.422088	+	0.731078i	−0.574056	+	0.818816i	$0.694631\pi$
$252$		0			0
$253$	2.65619	−	4.60066i	0.166993	−	0.289241i
$254$		0			0
$255$	−0.426167	−	2.44821i	−0.0266876	−	0.153313i
$256$		0			0
$257$	4.36965	−	24.7815i	0.272571	−	1.54583i	−0.474002	−	0.880524i	$-0.657191\pi$
$257$	4.36965	−	24.7815i	0.272571	−	1.54583i	0.746573	−	0.665303i	$-0.231698\pi$
$258$		0			0
$259$	2.14732	+	12.4872i	0.133428	+	0.775916i
$260$		0			0
$261$	9.53223	+	1.72381i	0.590030	+	0.106701i
$262$		0			0
$263$	1.84697	−	5.07450i	0.113889	−	0.312907i	−0.869632	−	0.493700i	$-0.835644\pi$
$263$	1.84697	−	5.07450i	0.113889	−	0.312907i	0.983521	+	0.180793i	$0.0578664\pi$
$264$		0			0
$265$	−11.2297	+	13.3831i	−0.689838	+	0.822117i
$266$		0			0
$267$	4.62779	−	1.67292i	0.283216	−	0.102381i
$268$		0			0
$269$	−22.7267			−1.38567			−0.692835	−	0.721096i	$-0.743639\pi$
$269$	−22.7267			−1.38567			−0.692835	+	0.721096i	$0.743639\pi$
$270$		0			0
$271$		−	16.4567i		−	0.999675i	−0.866119	−	0.499838i	$-0.833393\pi$
$271$		−	16.4567i		−	0.999675i	0.866119	−	0.499838i	$-0.166607\pi$
$272$		0			0
$273$	8.79078	+	24.6439i	0.532042	+	1.49152i
$274$		0			0
$275$	−4.48455	+	5.34448i	−0.270429	+	0.322284i
$276$		0			0
$277$	6.26828	+	2.28147i	0.376625	+	0.137080i	0.523394	−	0.852091i	$-0.324665\pi$
$277$	6.26828	+	2.28147i	0.376625	+	0.137080i	−0.146770	+	0.989171i	$0.546888\pi$
$278$		0			0
$279$	−0.0460756	+	10.5337i	−0.00275848	+	0.630639i
$280$		0			0
$281$	−12.1553	−	14.4861i	−0.725123	−	0.864168i	0.269995	−	0.962862i	$-0.412978\pi$
$281$	−12.1553	−	14.4861i	−0.725123	−	0.864168i	−0.995118	+	0.0986941i	$0.968533\pi$
$282$		0			0
$283$	−30.5059	−	5.37902i	−1.81339	−	0.319749i	−0.838917	−	0.544259i	$-0.816811\pi$
$283$	−30.5059	−	5.37902i	−1.81339	−	0.319749i	−0.974472	+	0.224510i	$0.927922\pi$
$284$		0			0
$285$	−6.84020	+	18.6662i	−0.405179	+	1.10569i
$286$		0			0
$287$	7.73889	+	13.5363i	0.456812	+	0.799021i
$288$		0			0
$289$	8.38520	+	14.5236i	0.493247	+	0.854329i
$290$		0			0
$291$	−15.5438	+	8.92896i	−0.911195	+	0.523425i
$292$		0			0
$293$	20.0316	−	7.29092i	1.17026	−	0.425940i	0.317508	−	0.948256i	$-0.397154\pi$
$293$	20.0316	−	7.29092i	1.17026	−	0.425940i	0.852752	+	0.522316i	$0.174932\pi$
$294$		0			0
$295$	6.27425	+	35.5830i	0.365301	+	2.07172i
$296$		0			0
$297$	9.01324	−	1.52837i	0.523001	−	0.0886851i
$298$		0			0
$299$	−2.99374	−	16.9783i	−0.173132	−	0.981882i
$300$		0			0
$301$	−4.08142	+	22.5869i	−0.235249	+	1.30188i
$302$		0			0
$303$	−10.9780	+	18.9187i	−0.630667	+	1.08685i
$304$		0			0
$305$	13.6162	−	7.86131i	0.779661	−	0.450137i
$306$		0			0
$307$	−0.374145	−	0.216013i	−0.0213536	−	0.0123285i	0.489285	−	0.872124i	$-0.337258\pi$
$307$	−0.374145	−	0.216013i	−0.0213536	−	0.0123285i	−0.510639	+	0.859795i	$0.670591\pi$
$308$		0			0
$309$	11.8172	+	14.1459i	0.672257	+	0.804733i
$310$		0			0
$311$	−0.0637120	+	0.361329i	−0.00361278	+	0.0204891i	−0.986561	−	0.163394i	$-0.947756\pi$
$311$	−0.0637120	+	0.361329i	−0.00361278	+	0.0204891i	0.982948	+	0.183883i	$0.0588669\pi$
$312$		0			0
$313$	3.12828	+	3.72814i	0.176821	+	0.210727i	0.847174	−	0.531315i	$-0.178302\pi$
$313$	3.12828	+	3.72814i	0.176821	+	0.210727i	−0.670353	+	0.742042i	$0.733857\pi$
$314$		0			0
$315$	−22.2620	−	8.32048i	−1.25432	−	0.468806i
$316$		0			0
$317$	−6.59649	+	18.1237i	−0.370496	+	1.01793i	0.604674	+	0.796473i	$0.293303\pi$
$317$	−6.59649	+	18.1237i	−0.370496	+	1.01793i	−0.975170	+	0.221456i	$0.928919\pi$
$318$		0			0
$319$	−4.35181	−	3.65160i	−0.243654	−	0.204450i
$320$		0			0
$321$	32.0274	+	5.71955i	1.78760	+	0.319234i
$322$		0			0
$323$			1.83676i			0.102200i
$324$		0			0
$325$			22.6415i			1.25593i
$326$		0			0
$327$	4.19004	−	23.4627i	0.231710	−	1.29749i
$328$		0			0
$329$	−29.7640	+	10.6906i	−1.64094	+	0.589392i
$330$		0			0
$331$	−9.62455	−	3.50305i	−0.529013	−	0.192545i	0.0636844	−	0.997970i	$-0.479715\pi$
$331$	−9.62455	−	3.50305i	−0.529013	−	0.192545i	−0.592698	+	0.805425i	$0.701937\pi$
$332$		0			0
$333$	11.0460	−	9.18668i	0.605318	−	0.503427i
$334$		0			0
$335$	20.5992	−	17.2848i	1.12545	−	0.944368i
$336$		0			0
$337$	−1.99460	+	11.3119i	−0.108653	+	0.616199i	0.881046	+	0.473031i	$0.156840\pi$
$337$	−1.99460	+	11.3119i	−0.108653	+	0.616199i	−0.989698	+	0.143168i	$0.954271\pi$
$338$		0			0
$339$	−13.5844	−	16.2614i	−0.737803	−	0.883195i
$340$		0			0
$341$	3.08881	−	5.34997i	0.167268	−	0.289717i
$342$		0			0
$343$	−9.05552	−	16.1554i	−0.488952	−	0.872311i
$344$		0			0
$345$	13.5445	+	7.85947i	0.729211	+	0.423139i
$346$		0			0
$347$	4.80430	+	13.1997i	0.257908	+	0.708597i	0.999296	+	0.0375201i	$0.0119458\pi$
$347$	4.80430	+	13.1997i	0.257908	+	0.708597i	−0.741388	+	0.671077i	$0.765832\pi$
$348$		0			0
$349$	14.3317	−	2.52707i	0.767161	−	0.135271i	0.223646	−	0.974671i	$-0.428204\pi$
$349$	14.3317	−	2.52707i	0.767161	−	0.135271i	0.543515	+	0.839399i	$0.317093\pi$
$350$		0			0
$351$	19.2190	−	22.6015i	1.02584	−	1.20638i
$352$		0			0
$353$	−1.69990	−	9.64062i	−0.0904767	−	0.513119i	−0.996040	−	0.0889073i	$-0.971663\pi$
$353$	−1.69990	−	9.64062i	−0.0904767	−	0.513119i	0.905563	−	0.424211i	$-0.139449\pi$
$354$		0			0
$355$	−5.82536	−	16.0050i	−0.309178	−	0.849460i
$356$		0			0
$357$	−2.19576	−	0.0141056i	−0.116212	−	0.000746547i
$358$		0			0
$359$	−20.6740	+	11.9361i	−1.09113	+	0.629966i	−0.933878	−	0.357592i	$-0.883598\pi$
$359$	−20.6740	+	11.9361i	−1.09113	+	0.629966i	−0.157255	+	0.987558i	$0.550264\pi$
$360$		0			0
$361$	−2.15303	+	3.72916i	−0.113318	+	0.196272i
$362$		0			0
$363$	12.8553	+	4.71081i	0.674728	+	0.247254i
$364$		0			0
$365$	−35.7094	−	6.29653i	−1.86911	−	0.329575i
$366$		0			0
$367$	13.2057	+	15.7379i	0.689330	+	0.821511i	0.991274	−	0.131814i	$-0.0420802\pi$
$367$	13.2057	+	15.7379i	0.689330	+	0.821511i	−0.301945	+	0.953325i	$0.597636\pi$
$368$		0			0
$369$	8.90692	−	15.2726i	0.463675	−	0.795058i
$370$		0			0
$371$	9.87256	+	11.8674i	0.512558	+	0.616125i
$372$		0			0
$373$	23.0718	+	19.3596i	1.19461	+	1.00240i	0.999767	+	0.0215660i	$0.00686519\pi$
$373$	23.0718	+	19.3596i	1.19461	+	1.00240i	0.194846	+	0.980834i	$0.437579\pi$
$374$		0			0
$375$	4.10240	+	3.45764i	0.211847	+	0.178552i
$376$		0			0
$377$	−18.4361			−0.949510
$378$		0			0
$379$	−21.8030			−1.11994			−0.559972	−	0.828512i	$-0.689188\pi$
$379$	−21.8030			−1.11994			−0.559972	+	0.828512i	$0.689188\pi$
$380$		0			0
$381$	21.5825	−	7.80198i	1.10571	−	0.399708i
$382$		0			0
$383$	9.87748	+	8.28819i	0.504716	+	0.423507i	0.859265	−	0.511530i	$-0.170921\pi$
$383$	9.87748	+	8.28819i	0.504716	+	0.423507i	−0.354549	+	0.935037i	$0.615366\pi$
$384$		0			0
$385$	8.91366	+	10.7148i	0.454282	+	0.546074i
$386$		0			0
$387$	24.4950	−	8.79431i	1.24515	−	0.447040i
$388$		0			0
$389$	9.91895	+	11.8209i	0.502911	+	0.599346i	0.956452	−	0.291889i	$-0.0942839\pi$
$389$	9.91895	+	11.8209i	0.502911	+	0.599346i	−0.453541	+	0.891235i	$0.649839\pi$
$390$		0			0
$391$	1.42485	+	0.251239i	0.0720578	+	0.0127057i
$392$		0			0
$393$	−4.30811	−	24.7489i	−0.217315	−	1.24842i
$394$		0			0
$395$	13.7547	−	23.8238i	0.692072	−	1.19870i
$396$		0			0
$397$	−17.0189	+	9.82588i	−0.854155	+	0.493147i	−0.862051	−	0.506822i	$-0.830820\pi$
$397$	−17.0189	+	9.82588i	−0.854155	+	0.493147i	0.00789528	+	0.999969i	$0.497487\pi$
$398$		0			0
$399$	15.1561	+	8.88066i	0.758752	+	0.444589i
$400$		0			0
$401$	−8.38929	−	23.0494i	−0.418941	−	1.15103i	−0.952306	−	0.305146i	$-0.901295\pi$
$401$	−8.38929	−	23.0494i	−0.418941	−	1.15103i	0.533364	−	0.845886i	$-0.320927\pi$
$402$		0			0
$403$	−3.48133	−	19.7436i	−0.173417	−	0.983498i
$404$		0			0
$405$	4.44716	+	26.5787i	0.220981	+	1.32071i
$406$		0			0
$407$	−8.29755	+	1.46308i	−0.411294	+	0.0725223i
$408$		0			0
$409$	0.783041	+	2.15139i	0.0387189	+	0.106379i	0.957545	−	0.288282i	$-0.0930841\pi$
$409$	0.783041	+	2.15139i	0.0387189	+	0.106379i	−0.918827	+	0.394661i	$0.870862\pi$
$410$		0			0
$411$	−0.0396432	+	18.1264i	−0.00195546	+	0.894112i
$412$		0			0
$413$	31.9264	+	0.135270i	1.57099	+	0.00665618i
$414$		0			0
$415$	−11.6203	+	20.1269i	−0.570417	+	0.987992i
$416$		0			0
$417$	25.4996	−	4.43879i	1.24872	−	0.217368i
$418$		0			0
$419$	−4.61423	+	26.1686i	−0.225420	+	1.27842i	0.636461	+	0.771309i	$0.280398\pi$
$419$	−4.61423	+	26.1686i	−0.225420	+	1.27842i	−0.861881	+	0.507111i	$0.830713\pi$
$420$		0			0
$421$	−6.24308	+	5.23857i	−0.304269	+	0.255312i	−0.782119	−	0.623130i	$-0.785861\pi$
$421$	−6.24308	+	5.23857i	−0.304269	+	0.255312i	0.477849	+	0.878442i	$0.341416\pi$
$422$		0			0
$423$	27.3694	+	23.1704i	1.33074	+	1.12658i
$424$		0			0
$425$	−1.78552	−	0.649878i	−0.0866107	−	0.0315237i
$426$		0			0
$427$	−4.69623	−	13.0749i	−0.227267	−	0.632738i
$428$		0			0
$429$	−16.3627	+	5.91504i	−0.789998	+	0.285581i
$430$		0			0
$431$		−	0.797341i		−	0.0384065i	−0.999816	−	0.0192033i	$-0.993887\pi$
$431$		−	0.797341i		−	0.0384065i	0.999816	−	0.0192033i	$-0.00611297\pi$
$432$		0			0
$433$			13.1787i			0.633330i	0.948537	+	0.316665i	$0.102563\pi$
$433$			13.1787i			0.633330i	−0.948537	+	0.316665i	$0.897437\pi$
$434$		0			0
$435$	10.7921	−	12.8045i	0.517441	−	0.613931i
$436$		0			0
$437$	−8.86661	−	7.43997i	−0.424147	−	0.355902i
$438$		0			0
$439$	−5.32761	+	14.6375i	−0.254273	+	0.698609i	0.745222	+	0.666817i	$0.232344\pi$
$439$	−5.32761	+	14.6375i	−0.254273	+	0.698609i	−0.999495	+	0.0317921i	$0.989879\pi$
$440$		0			0
$441$	−10.7328	+	18.0501i	−0.511085	+	0.859530i
$442$		0			0
$443$	18.1741	+	21.6591i	0.863479	+	1.02905i	0.999266	+	0.0383163i	$0.0121994\pi$
$443$	18.1741	+	21.6591i	0.863479	+	1.02905i	−0.135787	+	0.990738i	$0.543356\pi$
$444$		0			0
$445$	1.47720	−	8.37762i	0.0700260	−	0.397137i
$446$		0			0
$447$	6.47730	−	17.6758i	0.306366	−	0.836039i
$448$		0			0
$449$	−31.0029	−	17.8995i	−1.46312	−	0.844731i	−0.463963	−	0.885855i	$-0.653573\pi$
$449$	−31.0029	−	17.8995i	−1.46312	−	0.844731i	−0.999154	+	0.0411240i	$0.986906\pi$
$450$		0			0
$451$	−8.97941	+	5.18426i	−0.422824	+	0.244117i
$452$		0			0
$453$	−13.3805	−	23.2932i	−0.628671	−	1.09441i
$454$		0			0
$455$	44.5111	+	8.04310i	2.08671	+	0.377066i
$456$		0			0
$457$	0.660415	+	3.74540i	0.0308929	+	0.175202i	0.996350	−	0.0853587i	$-0.0272036\pi$
$457$	0.660415	+	3.74540i	0.0308929	+	0.175202i	−0.965457	+	0.260561i	$0.916092\pi$
$458$		0			0
$459$	1.23073	+	2.16435i	0.0574455	+	0.101023i
$460$		0			0
$461$	−1.34839	−	7.64712i	−0.0628009	−	0.356162i	−0.999973	−	0.00729534i	$-0.997678\pi$
$461$	−1.34839	−	7.64712i	−0.0628009	−	0.356162i	0.937172	−	0.348866i	$-0.113433\pi$
$462$		0			0
$463$	−9.92418	+	3.61211i	−0.461216	+	0.167869i	−0.562169	−	0.827022i	$-0.690033\pi$
$463$	−9.92418	+	3.61211i	−0.461216	+	0.167869i	0.100953	+	0.994891i	$0.467811\pi$
$464$		0			0
$465$	15.7505	+	9.13954i	0.730412	+	0.423836i
$466$		0			0
$467$	14.5591	+	25.2171i	0.673714	+	1.16691i	0.976843	+	0.213957i	$0.0686353\pi$
$467$	14.5591	+	25.2171i	0.673714	+	1.16691i	−0.303129	+	0.952949i	$0.598031\pi$
$468$		0			0
$469$	−11.7930	−	20.6275i	−0.544552	−	0.952488i
$470$		0			0
$471$	−2.87464	−	3.44112i	−0.132456	−	0.158558i
$472$		0			0
$473$	−15.0311	−	2.65038i	−0.691130	−	0.121865i
$474$		0			0
$475$	9.77087	+	11.6445i	0.448318	+	0.534285i
$476$		0			0
$477$	6.05860	−	16.4220i	0.277404	−	0.751912i
$478$		0			0
$479$	14.0785	+	5.12415i	0.643263	+	0.234128i	0.642994	−	0.765872i	$-0.277692\pi$
$479$	14.0785	+	5.12415i	0.643263	+	0.234128i	0.000268922		1.00000i	$0.499914\pi$
$480$		0			0
$481$	−17.5760	+	20.9463i	−0.801397	+	0.955067i
$482$		0			0
$483$	8.96220	−	10.5425i	0.407794	−	0.479698i
$484$		0			0
$485$			30.9889i			1.40714i
$486$		0			0
$487$	28.0319			1.27025			0.635124	−	0.772410i	$-0.280949\pi$
$487$	28.0319			1.27025			0.635124	+	0.772410i	$0.280949\pi$
$488$		0			0
$489$	−0.374108	+	2.09487i	−0.0169177	+	0.0947332i
$490$		0			0
$491$	−27.8740	+	33.2189i	−1.25794	+	1.49915i	−0.470975	+	0.882147i	$0.656098\pi$
$491$	−27.8740	+	33.2189i	−1.25794	+	1.49915i	−0.786961	+	0.617003i	$0.788347\pi$
$492$		0			0
$493$	0.529171	−	1.45389i	0.0238327	−	0.0654797i
$494$		0			0
$495$	5.47014	−	14.8270i	0.245865	−	0.666423i
$496$		0			0
$497$	−14.8322	+	2.55057i	−0.665314	+	0.114408i
$498$		0			0
$499$	−0.0601126	+	0.340916i	−0.00269101	+	0.0152615i	−0.986124	−	0.166012i	$-0.946911\pi$
$499$	−0.0601126	+	0.340916i	−0.00269101	+	0.0152615i	0.983433	+	0.181274i	$0.0580220\pi$
$500$		0			0
$501$	−18.9066	+	15.7942i	−0.844684	+	0.705632i
$502$		0			0
$503$	12.8079	−	22.1839i	0.571075	−	0.989131i	−0.425381	−	0.905014i	$-0.639860\pi$
$503$	12.8079	−	22.1839i	0.571075	−	0.989131i	0.996456	−	0.0841166i	$-0.0268068\pi$
$504$		0			0
$505$	18.9063	+	32.7467i	0.841320	+	1.45721i
$506$		0			0
$507$	−17.0384	+	29.3628i	−0.756701	+	1.30405i
$508$		0			0
$509$	7.20644	−	2.62293i	0.319420	−	0.116259i	−0.177334	−	0.984151i	$-0.556747\pi$
$509$	7.20644	−	2.62293i	0.319420	−	0.116259i	0.496754	+	0.867891i	$0.334525\pi$
$510$		0			0
$511$	−11.0858	+	30.0611i	−0.490407	+	1.32982i
$512$		0			0
$513$	0.130685	−	19.9178i	0.00576987	−	0.879393i
$514$		0			0
$515$	31.3805	−	5.53323i	1.38279	−	0.243823i
$516$		0			0
$517$	−7.19279	−	19.7620i	−0.316338	−	0.869133i
$518$		0			0
$519$	1.38303	+	2.40762i	0.0607082	+	0.105683i
$520$		0			0
$521$	−20.3323	−	35.2166i	−0.890774	−	1.54287i	−0.838949	−	0.544210i	$-0.816829\pi$
$521$	−20.3323	−	35.2166i	−0.890774	−	1.54287i	−0.0518254	−	0.998656i	$-0.516504\pi$
$522$		0			0
$523$	−3.47770	−	2.00785i	−0.152069	−	0.0877973i	0.422035	−	0.906580i	$-0.361316\pi$
$523$	−3.47770	−	2.00785i	−0.152069	−	0.0877973i	−0.574104	+	0.818782i	$0.694649\pi$
$524$		0			0
$525$	−13.9954	+	11.5912i	−0.610810	+	0.505880i
$526$		0			0
$527$	1.65692	+	0.292159i	0.0721764	+	0.0127266i
$528$		0			0
$529$	10.6347	−	8.92359i	0.462379	−	0.387982i
$530$		0			0
$531$	−17.9634	−	31.4302i	−0.779546	−	1.36396i
$532$		0			0
$533$	−11.5086	+	31.6197i	−0.498493	+	1.36960i
$534$		0			0
$535$	36.1521	−	43.0844i	1.56299	−	1.86270i
$536$		0			0
$537$	13.0241	−	15.4528i	0.562032	−	0.666837i
$538$		0			0
$539$	10.7173	−	6.06716i	0.461629	−	0.261331i
$540$		0			0
$541$	−26.9397			−1.15823			−0.579114	−	0.815247i	$-0.696601\pi$
$541$	−26.9397			−1.15823			−0.579114	+	0.815247i	$0.696601\pi$
$542$		0			0
$543$	6.72329	+	18.5985i	0.288524	+	0.798140i
$544$		0			0
$545$	−31.5628	−	26.4843i	−1.35200	−	1.13446i
$546$		0			0
$547$	29.5375	+	10.7508i	1.26293	+	0.459670i	0.884752	−	0.466063i	$-0.154328\pi$
$547$	29.5375	+	10.7508i	1.26293	+	0.459670i	0.378180	+	0.925732i	$0.376550\pi$
$548$		0			0
$549$	−10.1784	+	12.0230i	−0.434405	+	0.513128i
$550$		0			0
$551$	−9.48165	+	7.95605i	−0.403932	+	0.338939i
$552$		0			0
$553$	−18.5543	−	15.7034i	−0.789010	−	0.667775i
$554$		0			0
$555$	−4.25932	−	24.4686i	−0.180798	−	1.03863i
$556$		0			0
$557$	−1.87310	−	1.08144i	−0.0793660	−	0.0458220i	0.459792	−	0.888027i	$-0.347924\pi$
$557$	−1.87310	−	1.08144i	−0.0793660	−	0.0458220i	−0.539158	+	0.842205i	$0.681257\pi$
$558$		0			0
$559$	−42.8967	+	24.7664i	−1.81434	+	1.04751i
$560$		0			0
$561$	0.00319340	−	1.46015i	0.000134826	−	0.0616476i
$562$		0			0
$563$	−20.5708	+	7.48715i	−0.866954	+	0.315546i	−0.736933	−	0.675966i	$-0.763727\pi$
$563$	−20.5708	+	7.48715i	−0.866954	+	0.315546i	−0.130021	+	0.991511i	$0.541505\pi$
$564$		0			0
$565$	−36.0732	+	6.36069i	−1.51761	+	0.267596i
$566$		0			0
$567$	23.8098	+	0.309188i	0.999916	+	0.0129847i
$568$		0			0
$569$	−29.3971	+	5.18350i	−1.23239	+	0.217304i	−0.751652	−	0.659560i	$-0.770743\pi$
$569$	−29.3971	+	5.18350i	−1.23239	+	0.217304i	−0.480739	+	0.876864i	$0.659632\pi$
$570$		0			0
$571$	2.67688	−	0.974303i	0.112024	−	0.0407733i	−0.285400	−	0.958408i	$-0.592126\pi$
$571$	2.67688	−	0.974303i	0.112024	−	0.0407733i	0.397424	+	0.917635i	$0.369904\pi$
$572$		0			0
$573$	−0.0555505	+	25.3999i	−0.00232066	+	1.06110i
$574$		0			0
$575$	10.3696	−	5.98689i	0.432442	−	0.249671i
$576$		0			0
$577$	−3.66700	−	2.11714i	−0.152659	−	0.0881378i	0.421725	−	0.906724i	$-0.361425\pi$
$577$	−3.66700	−	2.11714i	−0.152659	−	0.0881378i	−0.574384	+	0.818586i	$0.694758\pi$
$578$		0			0
$579$	7.94909	+	45.6653i	0.330353	+	1.89779i
$580$		0			0
$581$	15.6752	+	13.2666i	0.650315	+	0.550391i
$582$		0			0
$583$	−7.86365	+	6.59839i	−0.325679	+	0.273277i
$584$		0			0
$585$	−17.3306	−	48.2714i	−0.716533	−	1.99578i
$586$		0			0
$587$	−43.4191	−	15.8033i	−1.79210	−	0.652271i	−0.999071	−	0.0430865i	$-0.986281\pi$
$587$	−43.4191	−	15.8033i	−1.79210	−	0.652271i	−0.793029	−	0.609185i	$-0.791497\pi$
$588$		0			0
$589$	−10.3107	−	8.65172i	−0.424846	−	0.356488i
$590$		0			0
$591$	8.06745	+	22.3169i	0.331851	+	0.917994i
$592$		0			0
$593$	−9.96844			−0.409355			−0.204677	−	0.978829i	$-0.565615\pi$
$593$	−9.96844			−0.409355			−0.204677	+	0.978829i	$0.565615\pi$
$594$		0			0
$595$	−1.91188	+	3.27931i	−0.0783795	+	0.134439i
$596$		0			0
$597$	−1.84833	+	2.19300i	−0.0756472	+	0.0897534i
$598$		0			0
$599$	18.0700	−	21.5350i	0.738322	−	0.879898i	−0.257951	−	0.966158i	$-0.583047\pi$
$599$	18.0700	−	21.5350i	0.738322	−	0.879898i	0.996273	+	0.0862603i	$0.0274917\pi$
$600$		0			0
$601$	0.185327	−	0.509183i	0.00755966	−	0.0207700i	−0.935855	−	0.352384i	$-0.885371\pi$
$601$	0.185327	−	0.509183i	0.00755966	−	0.0207700i	0.943415	+	0.331614i	$0.107593\pi$
$602$		0			0
$603$	−13.5730	+	23.2733i	−0.552733	+	0.947764i
$604$		0			0
$605$	18.1311	−	15.2138i	0.737133	−	0.618528i
$606$		0			0
$607$	42.7645	+	7.54053i	1.73576	+	0.306061i	0.949948	−	0.312409i	$-0.101136\pi$
$607$	42.7645	+	7.54053i	1.73576	+	0.306061i	0.785809	+	0.618469i	$0.212247\pi$
$608$		0			0
$609$	−9.43825	−	11.3959i	−0.382457	−	0.461787i
$610$		0			0
$611$	−59.1058	−	34.1248i	−2.39117	−	1.38054i
$612$		0			0
$613$	3.20257	+	5.54702i	0.129351	+	0.224042i	0.923425	−	0.383778i	$-0.125377\pi$
$613$	3.20257	+	5.54702i	0.129351	+	0.224042i	−0.794074	+	0.607820i	$0.792044\pi$
$614$		0			0
$615$	−15.2241	−	26.5025i	−0.613894	−	1.06869i
$616$		0			0
$617$	−3.01058	−	8.27150i	−0.121201	−	0.332998i	0.864224	−	0.503108i	$-0.167810\pi$
$617$	−3.01058	−	8.27150i	−0.121201	−	0.332998i	−0.985425	+	0.170110i	$0.945588\pi$
$618$		0			0
$619$	38.7697	−	6.83614i	1.55828	−	0.274768i	0.672938	−	0.739699i	$-0.265032\pi$
$619$	38.7697	−	6.83614i	1.55828	−	0.274768i	0.885347	+	0.464932i	$0.153921\pi$
$620$		0			0
$621$	−15.4332	−	2.82582i	−0.619313	−	0.113396i
$622$		0			0
$623$	−7.05250	−	2.60079i	−0.282552	−	0.104199i
$624$		0			0
$625$	27.3473	−	9.95359i	1.09389	−	0.398143i
$626$		0			0
$627$	−5.86267	+	10.1033i	−0.234132	+	0.403489i
$628$		0			0
$629$	−1.14735	−	1.98727i	−0.0457479	−	0.0792378i
$630$		0			0
$631$	0.945115	−	1.63699i	0.0376244	−	0.0651675i	−0.846600	−	0.532230i	$-0.821354\pi$
$631$	0.945115	−	1.63699i	0.0376244	−	0.0651675i	0.884224	+	0.467062i	$0.154688\pi$
$632$		0			0
$633$	−29.8874	+	24.9673i	−1.18792	+	0.992362i
$634$		0			0
$635$	6.88919	−	39.0705i	0.273389	−	1.55047i
$636$		0			0
$637$	13.9874	−	37.4400i	0.554203	−	1.48343i
$638$		0			0
$639$	10.9119	+	13.1204i	0.431667	+	0.519034i
$640$		0			0
$641$	−4.74098	+	13.0257i	−0.187257	+	0.514485i	−0.997425	−	0.0717125i	$-0.977154\pi$
$641$	−4.74098	+	13.0257i	−0.187257	+	0.514485i	0.810168	+	0.586198i	$0.199376\pi$
$642$		0			0
$643$	−12.2918	+	14.6489i	−0.484743	+	0.577694i	−0.951872	−	0.306495i	$-0.900844\pi$
$643$	−12.2918	+	14.6489i	−0.484743	+	0.577694i	0.467129	+	0.884189i	$0.345288\pi$
$644$		0			0
$645$	7.90959	−	44.2909i	0.311440	−	1.74395i
$646$		0			0
$647$	−28.5676			−1.12311			−0.561553	−	0.827441i	$-0.689796\pi$
$647$	−28.5676			−1.12311			−0.561553	+	0.827441i	$0.689796\pi$
$648$		0			0
$649$			21.2304i			0.833368i
$650$		0			0
$651$	10.4219	−	12.2595i	0.408466	−	0.480488i
$652$		0			0
$653$	30.9127	−	36.8403i	1.20971	−	1.44167i	0.345588	−	0.938386i	$-0.387680\pi$
$653$	30.9127	−	36.8403i	1.20971	−	1.44167i	0.864120	−	0.503286i	$-0.167876\pi$
$654$		0			0
$655$	−40.8085	−	14.8531i	−1.59452	−	0.580357i
$656$		0			0
$657$	35.8053	−	6.15208i	1.39690	−	0.240016i
$658$		0			0
$659$	−27.3110	−	32.5480i	−1.06389	−	1.26789i	−0.961987	−	0.273095i	$-0.911953\pi$
$659$	−27.3110	−	32.5480i	−1.06389	−	1.26789i	−0.101899	−	0.994795i	$-0.532492\pi$
$660$		0			0
$661$	−41.0962	−	7.24636i	−1.59846	−	0.281851i	−0.697770	−	0.716322i	$-0.745824\pi$
$661$	−41.0962	−	7.24636i	−1.59846	−	0.281851i	−0.900686	+	0.434471i	$0.856935\pi$
$662$		0			0
$663$	−3.03799	−	3.63665i	−0.117986	−	0.141236i
$664$		0			0
$665$	26.3629	−	15.0720i	1.02231	−	0.584469i
$666$		0			0
$667$	4.87490	+	8.44357i	0.188757	+	0.326936i
$668$		0			0
$669$	3.43333	+	1.99226i	0.132740	+	0.0770251i
$670$		0			0
$671$	8.68118	−	3.15969i	0.335133	−	0.121978i
$672$		0			0
$673$	6.07898	+	34.4756i	0.234328	+	1.32894i	0.844025	+	0.536303i	$0.180180\pi$
$673$	6.07898	+	34.4756i	0.234328	+	1.32894i	−0.609698	+	0.792634i	$0.708709\pi$
$674$		0			0
$675$	19.3160	+	7.17431i	0.743472	+	0.276139i
$676$		0			0
$677$	−2.37829	−	13.4880i	−0.0914051	−	0.518384i	−0.995790	−	0.0916662i	$-0.970781\pi$
$677$	−2.37829	−	13.4880i	−0.0914051	−	0.518384i	0.904385	−	0.426718i	$-0.140330\pi$
$678$		0			0
$679$	26.9458	+	4.86908i	1.03409	+	0.186858i
$680$		0			0
$681$	5.27038	+	9.17485i	0.201961	+	0.351581i
$682$		0			0
$683$	31.6078	−	18.2488i	1.20944	−	0.698269i	0.246801	−	0.969066i	$-0.420621\pi$
$683$	31.6078	−	18.2488i	1.20944	−	0.698269i	0.962636	+	0.270797i	$0.0872872\pi$
$684$		0			0
$685$	27.1376	+	15.6679i	1.03687	+	0.598639i
$686$		0			0
$687$	6.19906	−	16.9166i	0.236509	−	0.645407i
$688$		0			0
$689$	−5.78488	+	32.8077i	−0.220387	+	1.24987i
$690$		0			0
$691$	−25.4033	−	30.2744i	−0.966386	−	1.15169i	−0.988390	−	0.151936i	$-0.951449\pi$
$691$	−25.4033	−	30.2744i	−0.966386	−	1.15169i	0.0220045	−	0.999758i	$-0.492995\pi$
$692$		0			0
$693$	−12.0330	−	7.08612i	−0.457097	−	0.269179i
$694$		0			0
$695$	15.3036	−	42.0463i	0.580499	−	1.59491i
$696$		0			0
$697$	−2.16321	−	1.81515i	−0.0819376	−	0.0687538i
$698$		0			0
$699$	15.8010	−	18.7475i	0.597650	−	0.709096i
$700$		0			0
$701$		−	32.7621i		−	1.23741i	−0.785625	−	0.618703i	$-0.787658\pi$
$701$		−	32.7621i		−	1.23741i	0.785625	−	0.618703i	$-0.212342\pi$
$702$		0			0
$703$			18.3575i			0.692365i
$704$		0			0
$705$	58.3000	−	21.0752i	2.19571	−	0.793738i
$706$		0			0
$707$	31.4449	−	11.2944i	1.18261	−	0.424768i
$708$		0			0
$709$	−27.0200	−	9.83449i	−1.01476	−	0.369342i	−0.219500	−	0.975612i	$-0.570443\pi$
$709$	−27.0200	−	9.83449i	−1.01476	−	0.369342i	−0.795259	+	0.606270i	$0.792665\pi$
$710$		0			0
$711$	−4.90481	+	27.1223i	−0.183945	+	1.01717i
$712$		0			0
$713$	−8.12183	+	6.81503i	−0.304165	+	0.255225i
$714$		0			0
$715$	−5.22301	+	29.6212i	−0.195330	+	1.10777i
$716$		0			0
$717$	−10.5308	+	1.83313i	−0.393281	+	0.0684596i
$718$		0			0
$719$	0.570488	−	0.988114i	0.0212756	−	0.0368504i	−0.855192	−	0.518312i	$-0.826561\pi$
$719$	0.570488	−	0.988114i	0.0212756	−	0.0368504i	0.876467	+	0.481462i	$0.159894\pi$
$720$		0			0
$721$	0.119294	−	28.1557i	0.00444273	−	1.04857i
$722$		0			0
$723$	−0.00325357	+	1.48766i	−0.000121002	+	0.0553267i
$724$		0			0
$725$	−4.37935	−	12.0322i	−0.162645	−	0.446863i
$726$		0			0
$727$	4.35712	−	0.768279i	0.161597	−	0.0284939i	−0.0922643	−	0.995735i	$-0.529410\pi$
$727$	4.35712	−	0.768279i	0.161597	−	0.0284939i	0.253861	+	0.967241i	$0.418299\pi$
$728$		0			0
$729$	−13.1920	−	23.5578i	−0.488593	−	0.872512i
$730$		0			0
$731$	−0.721834	−	4.09372i	−0.0266980	−	0.151412i
$732$		0			0
$733$	6.31974	+	17.3633i	0.233425	+	0.641329i	1.00000		0.000825524i	$-0.000262772\pi$
$733$	6.31974	+	17.3633i	0.233425	+	0.641329i	−0.766575	+	0.642155i	$0.778041\pi$
$734$		0			0
$735$	17.8154	+	31.6313i	0.657132	+	1.16674i
$736$		0			0
$737$	13.6834	−	7.90013i	0.504035	−	0.291005i
$738$		0			0
$739$	−0.869188	+	1.50548i	−0.0319736	+	0.0553799i	−0.881569	−	0.472054i	$-0.843513\pi$
$739$	−0.869188	+	1.50548i	−0.0319736	+	0.0553799i	0.849596	+	0.527434i	$0.176846\pi$
$740$		0			0
$741$	6.50111	+	37.3471i	0.238824	+	1.37198i
$742$		0			0
$743$	−38.4757	−	6.78431i	−1.41154	−	0.248892i	−0.584662	−	0.811277i	$-0.698773\pi$
$743$	−38.4757	−	6.78431i	−1.41154	−	0.248892i	−0.826876	+	0.562385i	$0.809884\pi$
$744$		0			0
$745$	−20.9187	−	24.9300i	−0.766403	−	0.913363i
$746$		0			0
$747$	4.14371	−	22.9136i	0.151610	−	0.838364i
$748$		0			0
$749$	−31.7829	−	38.2049i	−1.16132	−	1.39598i
$750$		0			0
$751$	7.75855	+	6.51020i	0.283114	+	0.237560i	0.773274	−	0.634072i	$-0.218618\pi$
$751$	7.75855	+	6.51020i	0.283114	+	0.237560i	−0.490161	+	0.871632i	$0.663062\pi$
$752$		0			0
$753$	−21.7852	+	7.87524i	−0.793896	+	0.286990i
$754$		0			0
$755$	−46.4385			−1.69007
$756$		0			0
$757$	49.1982			1.78814			0.894069	−	0.447930i	$-0.147839\pi$
$757$	49.1982			1.78814			0.894069	+	0.447930i	$0.147839\pi$
$758$		0			0
$759$	7.03566	+	5.92989i	0.255378	+	0.215241i
$760$		0			0
$761$	34.1183	+	28.6287i	1.23679	+	1.03779i	0.997768	+	0.0667745i	$0.0212708\pi$
$761$	34.1183	+	28.6287i	1.23679	+	1.03779i	0.239021	+	0.971014i	$0.423174\pi$
$762$		0			0
$763$	−27.9882	+	23.2835i	−1.01324	+	0.842920i
$764$		0			0
$765$	4.30415	+	0.0188268i	0.155617	+	0.000680683i
$766$		0			0
$767$	44.2875	+	52.7798i	1.59913	+	1.90577i
$768$		0			0
$769$	44.9461	+	7.92521i	1.62080	+	0.285791i	0.909064	−	0.416657i	$-0.136799\pi$
$769$	44.9461	+	7.92521i	1.62080	+	0.285791i	0.711735	+	0.702448i	$0.247910\pi$
$770$		0			0
$771$	40.9238	+	14.9965i	1.47383	+	0.540085i
$772$		0			0
$773$	21.4106	−	37.0843i	0.770087	−	1.33383i	−0.167427	−	0.985884i	$-0.553546\pi$
$773$	21.4106	−	37.0843i	0.770087	−	1.33383i	0.937515	−	0.347946i	$-0.113121\pi$
$774$		0			0
$775$	12.0585	−	6.96198i	0.433154	−	0.250082i
$776$		0			0
$777$	−21.9454	−	0.140978i	−0.787288	−	0.00505756i
$778$		0			0
$779$	7.72650	+	21.2284i	0.276831	+	0.760586i
$780$		0			0
$781$	−1.73784	−	9.85576i	−0.0621847	−	0.352667i
$782$		0			0
$783$	−5.84177	+	15.7283i	−0.208768	+	0.562083i
$784$		0			0
$785$	−7.63357	+	1.34601i	−0.272454	+	0.0480410i
$786$		0			0
$787$	3.17211	+	8.71531i	0.113074	+	0.310667i	0.983302	−	0.181981i	$-0.0582510\pi$
$787$	3.17211	+	8.71531i	0.113074	+	0.310667i	−0.870228	+	0.492649i	$0.836029\pi$
$788$		0			0
$789$	8.09000	+	4.69438i	0.288012	+	0.167125i
$790$		0			0
$791$	−0.137133	+	32.3662i	−0.00487590	+	1.15081i
$792$		0			0
$793$	14.9905	−	25.9644i	0.532329	−	0.922021i
$794$		0			0
$795$	−19.3998	−	23.2227i	−0.688038	−	0.823624i
$796$		0			0
$797$	−4.16201	+	23.6039i	−0.147426	+	0.836094i	0.817961	+	0.575273i	$0.195104\pi$
$797$	−4.16201	+	23.6039i	−0.147426	+	0.836094i	−0.965387	+	0.260821i	$0.916007\pi$
$798$		0			0
$799$	4.38761	−	3.68164i	0.155222	−	0.130247i
$800$		0			0
$801$	1.44331	+	8.40012i	0.0509969	+	0.296804i
$802$		0			0
$803$	−20.0209	−	7.28703i	−0.706524	−	0.257154i
$804$		0			0
$805$	−8.08599	−	22.5124i	−0.284994	−	0.793457i
$806$		0			0
$807$	6.92021	−	38.7507i	0.243603	−	1.36409i
$808$		0			0
$809$			17.5369i			0.616565i	0.951295	+	0.308283i	$0.0997542\pi$
$809$			17.5369i			0.616565i	−0.951295	+	0.308283i	$0.900246\pi$
$810$		0			0
$811$		−	19.1464i		−	0.672320i	−0.941805	−	0.336160i	$-0.890872\pi$
$811$		−	19.1464i		−	0.672320i	0.941805	−	0.336160i	$-0.109128\pi$
$812$		0			0
$813$	28.0600	+	5.01103i	0.984106	+	0.175744i
$814$		0			0
$815$	2.81808	+	2.36465i	0.0987132	+	0.0828302i
$816$		0			0
$817$	−11.3738	+	31.2492i	−0.397918	+	1.09327i
$818$		0			0
$819$	−44.6965	+	7.48494i	−1.56182	+	0.261545i
$820$		0			0
$821$	1.39605	+	1.66374i	0.0487224	+	0.0580651i	0.789855	−	0.613293i	$-0.210156\pi$
$821$	1.39605	+	1.66374i	0.0487224	+	0.0580651i	−0.741133	+	0.671358i	$0.765711\pi$
$822$		0			0
$823$	2.99650	−	16.9940i	0.104452	−	0.592374i	−0.886986	−	0.461796i	$-0.847205\pi$
$823$	2.99650	−	16.9940i	0.104452	−	0.592374i	0.991438	−	0.130579i	$-0.0416835\pi$
$824$		0			0
$825$	−7.74721	−	9.27388i	−0.269723	−	0.322875i
$826$		0			0
$827$	1.83611	+	1.06008i	0.0638479	+	0.0368626i	0.531584	−	0.847006i	$-0.321597\pi$
$827$	1.83611	+	1.06008i	0.0638479	+	0.0368626i	−0.467736	+	0.883868i	$0.654930\pi$
$828$		0			0
$829$	15.2933	−	8.82957i	0.531157	−	0.306663i	−0.210331	−	0.977630i	$-0.567454\pi$
$829$	15.2933	−	8.82957i	0.531157	−	0.306663i	0.741487	+	0.670967i	$0.234121\pi$
$830$		0			0
$831$	−5.79875	+	9.99319i	−0.201156	+	0.346660i
$832$		0			0
$833$	2.55106	+	2.17770i	0.0883890	+	0.0754527i
$834$		0			0
$835$	7.39538	+	41.9413i	0.255928	+	1.45144i
$836$		0			0
$837$	−17.9468	−	3.28606i	−0.620332	−	0.113583i
$838$		0			0
$839$	3.93947	+	22.3419i	0.136006	+	0.771327i	0.974154	+	0.225885i	$0.0725272\pi$
$839$	3.93947	+	22.3419i	0.136006	+	0.771327i	−0.838148	+	0.545442i	$0.816362\pi$
$840$		0			0
$841$	−17.4538	+	6.35265i	−0.601853	+	0.219057i
$842$		0			0
$843$	28.4011	−	16.3147i	0.978186	−	0.561907i
$844$		0			0
$845$	29.3436	+	50.8246i	1.00945	+	1.74842i
$846$		0			0
$847$	−10.3800	−	18.1560i	−0.356662	−	0.623847i
$848$		0			0
$849$	18.4606	−	50.3770i	0.633566	−	1.72893i
$850$		0			0
$851$	14.2406	+	2.51101i	0.488163	+	0.0860763i
$852$		0			0
$853$	−28.0862	−	33.4718i	−0.961652	−	1.14605i	−0.989221	−	0.146432i	$-0.953221\pi$
$853$	−28.0862	−	33.4718i	−0.961652	−	1.14605i	0.0275689	−	0.999620i	$-0.491223\pi$
$854$		0			0
$855$	−29.7444	−	17.3469i	−1.01724	−	0.593250i
$856$		0			0
$857$	−0.257117	−	0.0935830i	−0.00878295	−	0.00319673i	0.337625	−	0.941281i	$-0.390376\pi$
$857$	−0.257117	−	0.0935830i	−0.00878295	−	0.00319673i	−0.346408	+	0.938084i	$0.612599\pi$
$858$		0			0
$859$	−12.7085	+	15.1454i	−0.433609	+	0.516755i	−0.937960	−	0.346744i	$-0.887287\pi$
$859$	−12.7085	+	15.1454i	−0.433609	+	0.516755i	0.504351	+	0.863499i	$0.331732\pi$
$860$		0			0
$861$	−25.4368	+	9.07363i	−0.866885	+	0.309228i
$862$		0			0
$863$			36.1024i			1.22894i	0.788941	+	0.614469i	$0.210630\pi$
$863$			36.1024i			1.22894i	−0.788941	+	0.614469i	$0.789370\pi$
$864$		0			0
$865$	4.79995			0.163203
$866$		0			0
$867$	−27.3171	+	9.87500i	−0.927737	+	0.335373i
$868$		0			0
$869$	10.3900	−	12.3823i	0.352456	−	0.420041i
$870$		0			0
$871$	17.5376	−	48.1841i	0.594239	−	1.63266i
$872$		0			0
$873$	−10.4915	−	29.2222i	−0.355084	−	0.989023i
$874$		0			0
$875$	−1.38891	−	8.07687i	−0.0469538	−	0.273048i
$876$		0			0
$877$	4.63509	−	26.2869i	0.156516	−	0.887645i	−0.800871	−	0.598837i	$-0.795630\pi$
$877$	4.63509	−	26.2869i	0.156516	−	0.887645i	0.957387	−	0.288808i	$-0.0932590\pi$
$878$		0			0
$879$	6.33199	+	36.3755i	0.213573	+	1.22692i
$880$		0			0
$881$	18.6853	−	32.3639i	0.629523	−	1.09037i	−0.358124	−	0.933674i	$-0.616584\pi$
$881$	18.6853	−	32.3639i	0.629523	−	1.09037i	0.987647	−	0.156692i	$-0.0500830\pi$
$882$		0			0
$883$	−16.1419	−	27.9586i	−0.543219	−	0.940883i	−0.998717	−	0.0506462i	$-0.983872\pi$
$883$	−16.1419	−	27.9586i	−0.543219	−	0.940883i	0.455497	−	0.890237i	$-0.349461\pi$
$884$		0			0
$885$	−62.5822	−	0.136870i	−2.10368	−	0.00460082i
$886$		0			0
$887$	8.66270	−	3.15297i	0.290865	−	0.105866i	−0.192467	−	0.981304i	$-0.561649\pi$
$887$	8.66270	−	3.15297i	0.290865	−	0.105866i	0.483332	+	0.875437i	$0.339427\pi$
$888$		0			0
$889$	−32.8906	−	12.1293i	−1.10312	−	0.406802i
$890$		0			0
$891$	−0.138518	+	15.8336i	−0.00464054	+	0.530447i
$892$		0			0
$893$	−45.1244	+	7.95665i	−1.51003	+	0.266259i
$894$		0			0
$895$	−11.9489	−	32.8295i	−0.399409	−	1.09737i
$896$		0			0
$897$	29.8609	+	0.0653069i	0.997027	+	0.00218053i
$898$		0			0
$899$	5.66887	+	9.81878i	0.189068	+	0.327475i
$900$		0			0
$901$	−2.42119	−	1.39788i	−0.0806616	−	0.0465700i
$902$		0			0
$903$	−37.2695	−	13.8368i	−1.24025	−	0.460459i
$904$		0			0
$905$	33.6687	+	5.93670i	1.11919	+	0.197343i
$906$		0			0
$907$	11.0554	−	9.27655i	0.367087	−	0.308023i	−0.440521	−	0.897742i	$-0.645206\pi$
$907$	11.0554	−	9.27655i	0.367087	−	0.308023i	0.807608	+	0.589720i	$0.200762\pi$
$908$		0			0
$909$	−28.9151	−	24.4789i	−0.959052	−	0.811915i
$910$		0			0
$911$	6.87678	−	18.8938i	0.227838	−	0.625980i	−0.772117	−	0.635481i	$-0.780802\pi$
$911$	6.87678	−	18.8938i	0.227838	−	0.625980i	0.999955	+	0.00950081i	$0.00302425\pi$
$912$		0			0
$913$	−8.77772	+	10.4609i	−0.290500	+	0.346205i
$914$		0			0
$915$	9.25803	+	25.6104i	0.306061	+	0.846653i
$916$		0			0
$917$	−19.3272	+	33.1505i	−0.638239	+	1.09472i
$918$		0			0
$919$	10.7251			0.353788			0.176894	−	0.984230i	$-0.443395\pi$
$919$	10.7251			0.353788			0.176894	+	0.984230i	$0.443395\pi$
$920$		0			0
$921$	0.482244	−	0.572170i	0.0158905	−	0.0188536i
$922$		0			0
$923$	−24.8798	−	20.8766i	−0.818929	−	0.687163i
$924$		0			0
$925$	−17.8454	−	6.49519i	−0.586753	−	0.213561i
$926$		0			0
$927$	−27.7181	+	15.8418i	−0.910383	+	0.520314i
$928$		0			0
$929$	6.17170	−	5.17867i	0.202487	−	0.169907i	−0.535905	−	0.844278i	$-0.680030\pi$
$929$	6.17170	−	5.17867i	0.202487	−	0.169907i	0.738393	+	0.674371i	$0.235585\pi$
$930$		0			0
$931$	−8.96339	−	25.2915i	−0.293763	−	0.828896i
$932$		0			0
$933$	−0.596693	−	0.218657i	−0.0195348	−	0.00715852i
$934$		0			0
$935$	−2.18603	−	1.26210i	−0.0714907	−	0.0412752i
$936$		0			0
$937$	16.0358	−	9.25829i	0.523868	−	0.302455i	−0.214648	−	0.976691i	$-0.568860\pi$
$937$	16.0358	−	9.25829i	0.523868	−	0.302455i	0.738516	+	0.674236i	$0.235527\pi$
$938$		0			0
$939$	−7.30932	+	4.19875i	−0.238531	+	0.137021i
$940$		0			0
$941$	−5.56030	+	2.02378i	−0.181261	+	0.0659735i	−0.431056	−	0.902325i	$-0.641859\pi$
$941$	−5.56030	+	2.02378i	−0.181261	+	0.0659735i	0.249795	+	0.968299i	$0.419637\pi$
$942$		0			0
$943$	17.5246	−	3.09006i	0.570680	−	0.100626i
$944$		0			0
$945$	20.9657	−	35.4248i	0.682016	−	1.15237i
$946$		0			0
$947$	−18.2373	+	3.21572i	−0.592631	+	0.104497i	−0.461917	−	0.886923i	$-0.652838\pi$
$947$	−18.2373	+	3.21572i	−0.592631	+	0.104497i	−0.130714	+	0.991420i	$0.541727\pi$
$948$		0			0
$949$	−64.9739	+	23.6486i	−2.10914	+	0.767665i
$950$		0			0
$951$	−28.8937	−	16.7661i	−0.936942	−	0.543679i
$952$		0			0
$953$	−43.1462	+	24.9105i	−1.39764	+	0.806929i	−0.994145	−	0.108051i	$-0.965539\pi$
$953$	−43.1462	+	24.9105i	−1.39764	+	0.806929i	−0.403497	+	0.914981i	$0.632206\pi$
$954$		0			0
$955$	38.0268	+	21.9548i	1.23052	+	0.710441i
$956$		0			0
$957$	7.55137	−	6.30826i	0.244101	−	0.203917i
$958$		0			0
$959$	17.8876	−	21.1352i	0.577622	−	0.682490i
$960$		0			0
$961$	14.3027	−	12.0014i	0.461379	−	0.387143i
$962$		0			0
$963$	−19.5045	+	52.8676i	−0.628525	+	1.70363i
$964$		0			0
$965$	75.2976	+	27.4061i	2.42391	+	0.882233i
$966$		0			0
$967$	43.6545	+	36.6305i	1.40383	+	1.17796i	0.959367	+	0.282161i	$0.0910512\pi$
$967$	43.6545	+	36.6305i	1.40383	+	1.17796i	0.444466	+	0.895795i	$0.353393\pi$
$968$		0			0
$969$	−3.13181	−	0.559288i	−0.100608	−	0.0179669i
$970$		0			0
$971$	40.8234			1.31008			0.655042	−	0.755593i	$-0.272651\pi$
$971$	40.8234			1.31008			0.655042	+	0.755593i	$0.272651\pi$
$972$		0			0
$973$	−34.1560	−	19.9134i	−1.09499	−	0.638395i
$974$		0			0
$975$	−38.6055	−	6.89428i	−1.23637	−	0.220794i
$976$		0			0
$977$	−30.7345	+	36.6280i	−0.983285	+	1.17183i	0.00184087	+	0.999998i	$0.499414\pi$
$977$	−30.7345	+	36.6280i	−0.983285	+	1.17183i	−0.985126	+	0.171835i	$0.945030\pi$
$978$		0			0
$979$	1.70958	−	4.69703i	0.0546383	−	0.150118i
$980$		0			0
$981$	38.7298	+	14.2887i	1.23655	+	0.456202i
$982$		0			0
$983$	−24.5247	+	20.5787i	−0.782216	+	0.656357i	−0.943806	−	0.330501i	$-0.892782\pi$
$983$	−24.5247	+	20.5787i	−0.782216	+	0.656357i	0.161590	+	0.986858i	$0.448338\pi$
$984$		0			0
$985$	40.4000	+	7.12360i	1.28725	+	0.226977i
$986$		0			0
$987$	−9.16524	−	54.0051i	−0.291733	−	1.71900i
$988$		0			0
$989$	22.6855	+	13.0975i	0.721358	+	0.416476i
$990$		0			0
$991$	2.37500	+	4.11363i	0.0754445	+	0.130674i	0.901279	−	0.433238i	$-0.142629\pi$
$991$	2.37500	+	4.11363i	0.0754445	+	0.130674i	−0.825835	+	0.563912i	$0.809296\pi$
$992$		0			0
$993$	8.90362	−	15.3439i	0.282548	−	0.486925i
$994$		0			0
$995$	1.69575	+	4.65903i	0.0537588	+	0.147701i
$996$		0			0
$997$	56.9369	−	10.0395i	1.80321	−	0.317955i	0.831749	−	0.555151i	$-0.187340\pi$
$997$	56.9369	−	10.0395i	1.80321	−	0.317955i	0.971462	+	0.237197i	$0.0762286\pi$
$998$		0			0
$999$	12.3005	+	21.6316i	0.389170	+	0.684394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.12	✓	144
7.6	odd	2	inner	756.2.bx.a.41.13	yes	144
27.2	odd	18	inner	756.2.bx.a.461.13	yes	144
189.83	even	18	inner	756.2.bx.a.461.12	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.12	✓	144	1.1	even	1	trivial
756.2.bx.a.41.13	yes	144	7.6	odd	2	inner
756.2.bx.a.461.12	yes	144	189.83	even	18	inner
756.2.bx.a.461.13	yes	144	27.2	odd	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.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.304497 + 1.70508i) q^{3} +(2.29372 + 1.92466i) q^{5} +(2.03395 - 1.69205i) q^{7} +(-2.81456 - 1.03838i) q^{9} +O(q^{10})\)	\(q+(-0.304497 + 1.70508i) q^{3} +(2.29372 + 1.92466i) q^{5} +(2.03395 - 1.69205i) q^{7} +(-2.81456 - 1.03838i) q^{9} +(1.13089 + 1.34775i) q^{11} +(5.62290 + 0.991469i) q^{13} +(-3.98013 + 3.32492i) q^{15} +(-0.239581 + 0.414967i) q^{17} +(3.31971 - 1.91663i) q^{19} +(2.26575 + 3.98326i) q^{21} +(-1.03273 - 2.83740i) q^{23} +(0.688600 + 3.90524i) q^{25} +(2.62755 - 4.48286i) q^{27} +(-3.17989 + 0.560701i) q^{29} +(-1.20093 - 3.29953i) q^{31} +(-2.64237 + 1.51788i) q^{33} +(7.92195 + 0.0335647i) q^{35} +(-2.39449 + 4.14738i) q^{37} +(-3.40269 + 9.28557i) q^{39} +(-1.02337 + 5.80382i) q^{41} +(-6.64566 + 5.57637i) q^{43} +(-4.45729 - 7.79884i) q^{45} +(-11.2325 - 4.08830i) q^{47} +(1.27391 - 6.88311i) q^{49} +(-0.634599 - 0.534861i) q^{51} +5.83466i q^{53} +5.26795i q^{55} +(2.25716 + 6.24396i) q^{57} +(9.24397 + 7.75661i) q^{59} +(1.79593 - 4.93428i) q^{61} +(-7.48168 + 2.65038i) q^{63} +(10.9891 + 13.0963i) q^{65} +(1.55948 - 8.84425i) q^{67} +(5.15244 - 0.896900i) q^{69} +(-4.92623 - 2.84416i) q^{71} +(-10.4876 + 6.05500i) q^{73} +(-6.86841 - 0.0150215i) q^{75} +(4.58065 + 0.827718i) q^{77} +(-1.59538 - 9.04783i) q^{79} +(6.84353 + 5.84518i) q^{81} +(1.34781 + 7.64383i) q^{83} +(-1.34821 + 0.490707i) q^{85} +(0.0122314 - 5.59269i) q^{87} +(-1.42054 - 2.46044i) q^{89} +(13.1143 - 7.49765i) q^{91} +(5.99162 - 1.04298i) q^{93} +(11.3034 + 1.99309i) q^{95} +(6.65254 + 7.92818i) q^{97} +(-1.78350 - 4.96762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more