LMFDB - Embedded newform 756.2.bf.c.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38270 + 0.296888i) q^{2} +(1.82372 - 0.821014i) q^{4} +(-0.421763 - 0.243505i) q^{5} +(0.250520 + 2.63386i) q^{7} +(-2.27790 + 1.67665i) q^{8} +O(q^{10})$	\(q+(-1.38270 + 0.296888i) q^{2} +(1.82372 - 0.821014i) q^{4} +(-0.421763 - 0.243505i) q^{5} +(0.250520 + 2.63386i) q^{7} +(-2.27790 + 1.67665i) q^{8} +(0.655465 + 0.211478i) q^{10} +(-2.51153 + 1.45003i) q^{11} -1.17266i q^{13} +(-1.12836 - 3.56747i) q^{14} +(2.65187 - 2.99459i) q^{16} +(-0.0401295 + 0.0231688i) q^{17} +(-2.38246 + 4.12654i) q^{19} +(-0.969097 - 0.0978105i) q^{20} +(3.04219 - 2.75060i) q^{22} +(-6.02414 - 3.47804i) q^{23} +(-2.38141 - 4.12472i) q^{25} +(0.348150 + 1.62144i) q^{26} +(2.61932 + 4.59774i) q^{28} +0.465824 q^{29} +(-0.536070 - 0.928500i) q^{31} +(-2.77769 + 4.92793i) q^{32} +(0.0486085 - 0.0439494i) q^{34} +(0.535699 - 1.17187i) q^{35} +(0.196198 - 0.339825i) q^{37} +(2.06910 - 6.41309i) q^{38} +(1.36901 - 0.152471i) q^{40} -0.139187i q^{41} +6.47359i q^{43} +(-3.38982 + 4.70644i) q^{44} +(9.36217 + 3.02059i) q^{46} +(-3.81879 + 6.61433i) q^{47} +(-6.87448 + 1.31967i) q^{49} +(4.51736 + 4.99624i) q^{50} +(-0.962774 - 2.13861i) q^{52} +(5.03428 + 8.71964i) q^{53} +1.41236 q^{55} +(-4.98674 - 5.57964i) q^{56} +(-0.644094 + 0.138297i) q^{58} +(-3.65438 - 6.32958i) q^{59} +(-12.0409 - 6.95182i) q^{61} +(1.01688 + 1.12468i) q^{62} +(2.37766 - 7.63850i) q^{64} +(-0.285550 + 0.494587i) q^{65} +(-3.49182 + 2.01601i) q^{67} +(-0.0541628 + 0.0752000i) q^{68} +(-0.392797 + 1.77939i) q^{70} +6.95063i q^{71} +(-7.14246 + 4.12370i) q^{73} +(-0.170393 + 0.528124i) q^{74} +(-0.956981 + 9.48167i) q^{76} +(-4.44837 - 6.25176i) q^{77} +(-12.0015 - 6.92909i) q^{79} +(-1.84766 + 0.617263i) q^{80} +(0.0413228 + 0.192453i) q^{82} +6.34905 q^{83} +0.0225668 q^{85} +(-1.92193 - 8.95103i) q^{86} +(3.28981 - 7.51399i) q^{88} +(-9.16832 - 5.29333i) q^{89} +(3.08864 - 0.293776i) q^{91} +(-13.8418 - 1.39705i) q^{92} +(3.31652 - 10.2794i) q^{94} +(2.00967 - 1.16028i) q^{95} -8.51277i q^{97} +(9.11354 - 3.86566i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) $ 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.38270	+	0.296888i	−0.977716	+	0.209932i
$2$	−1.38270	+	0.296888i	−0.977716	+	0.209932i
$3$		0			0
$3$		0			0
$4$	1.82372	−	0.821014i	0.911858	−	0.410507i
$5$	−0.421763	−	0.243505i	−0.188618	−	0.108899i	0.402717	−	0.915324i	$-0.368066\pi$
$5$	−0.421763	−	0.243505i	−0.188618	−	0.108899i	−0.591336	+	0.806426i	$0.701399\pi$
$6$		0			0
$7$	0.250520	+	2.63386i	0.0946876	+	0.995507i
$7$	0.250520	+	2.63386i	0.0946876	+	0.995507i
$8$	−2.27790	+	1.67665i	−0.805359	+	0.592787i
$9$		0			0
$10$	0.655465	+	0.211478i	0.207276	+	0.0668752i
$11$	−2.51153	+	1.45003i	−0.757254	+	0.437201i	−0.828309	−	0.560272i	$-0.810697\pi$
$11$	−2.51153	+	1.45003i	−0.757254	+	0.437201i	0.0710549	+	0.997472i	$0.477363\pi$
$12$		0			0
$13$		−	1.17266i		−	0.325239i	−0.986689	−	0.162619i	$-0.948006\pi$
$13$		−	1.17266i		−	0.325239i	0.986689	−	0.162619i	$-0.0519942\pi$
$14$	−1.12836	−	3.56747i	−0.301566	−	0.953445i
$15$		0			0
$16$	2.65187	−	2.99459i	0.662968	−	0.748648i
$17$	−0.0401295	+	0.0231688i	−0.00973282	+	0.00561925i	−0.504859	−	0.863202i	$-0.668455\pi$
$17$	−0.0401295	+	0.0231688i	−0.00973282	+	0.00561925i	0.495126	+	0.868821i	$0.335122\pi$
$18$		0			0
$19$	−2.38246	+	4.12654i	−0.546574	+	0.946693i	0.451932	+	0.892052i	$0.350735\pi$
$19$	−2.38246	+	4.12654i	−0.546574	+	0.946693i	−0.998506	+	0.0546412i	$0.982598\pi$
$20$	−0.969097	−	0.0978105i	−0.216697	−	0.0218711i
$21$		0			0
$22$	3.04219	−	2.75060i	0.648597	−	0.586430i
$23$	−6.02414	−	3.47804i	−1.25612	−	0.725221i	−0.283802	−	0.958883i	$-0.591596\pi$
$23$	−6.02414	−	3.47804i	−1.25612	−	0.725221i	−0.972318	+	0.233661i	$0.924929\pi$
$24$		0			0
$25$	−2.38141	−	4.12472i	−0.476282	−	0.824945i
$26$	0.348150	+	1.62144i	0.0682779	+	0.317991i
$27$		0			0
$28$	2.61932	+	4.59774i	0.495004	+	0.868891i
$29$	0.465824			0.0865013			0.0432506	−	0.999064i	$-0.486229\pi$
$29$	0.465824			0.0865013			0.0432506	+	0.999064i	$0.486229\pi$
$30$		0			0
$31$	−0.536070	−	0.928500i	−0.0962810	−	0.166764i	0.813862	−	0.581059i	$-0.197361\pi$
$31$	−0.536070	−	0.928500i	−0.0962810	−	0.166764i	−0.910142	+	0.414295i	$0.864028\pi$
$32$	−2.77769	+	4.92793i	−0.491030	+	0.871143i
$33$		0			0
$34$	0.0486085	−	0.0439494i	0.00833628	−	0.00753726i
$35$	0.535699	−	1.17187i	0.0905497	−	0.198082i
$36$		0			0
$37$	0.196198	−	0.339825i	0.0322547	−	0.0558668i	−0.849447	−	0.527673i	$-0.823065\pi$
$37$	0.196198	−	0.339825i	0.0322547	−	0.0558668i	0.881702	+	0.471806i	$0.156398\pi$
$38$	2.06910	−	6.41309i	0.335653	−	1.04034i
$39$		0			0
$40$	1.36901	−	0.152471i	0.216459	−	0.0241077i
$41$		−	0.139187i		−	0.0217373i	−0.999941	−	0.0108686i	$-0.996540\pi$
$41$		−	0.139187i		−	0.0217373i	0.999941	−	0.0108686i	$-0.00345967\pi$
$42$		0			0
$43$			6.47359i			0.987213i	0.869685	+	0.493607i	$0.164322\pi$
$43$			6.47359i			0.987213i	−0.869685	+	0.493607i	$0.835678\pi$
$44$	−3.38982	+	4.70644i	−0.511034	+	0.709523i
$45$		0			0
$46$	9.36217	+	3.02059i	1.38038	+	0.445361i
$47$	−3.81879	+	6.61433i	−0.557027	+	0.964800i	0.440715	+	0.897647i	$0.354725\pi$
$47$	−3.81879	+	6.61433i	−0.557027	+	0.964800i	−0.997743	+	0.0671528i	$0.978609\pi$
$48$		0			0
$49$	−6.87448	+	1.31967i	−0.982069	+	0.188524i
$50$	4.51736	+	4.99624i	0.638851	+	0.706575i
$51$		0			0
$52$	−0.962774	−	2.13861i	−0.133513	−	0.296571i
$53$	5.03428	+	8.71964i	0.691512	+	1.19773i	0.971342	+	0.237685i	$0.0763885\pi$
$53$	5.03428	+	8.71964i	0.691512	+	1.19773i	−0.279830	+	0.960049i	$0.590278\pi$
$54$		0			0
$55$	1.41236			0.190443
$56$	−4.98674	−	5.57964i	−0.666381	−	0.745611i
$57$		0			0
$58$	−0.644094	+	0.138297i	−0.0845737	+	0.0181593i
$59$	−3.65438	−	6.32958i	−0.475760	−	0.824041i	0.523854	−	0.851808i	$-0.324494\pi$
$59$	−3.65438	−	6.32958i	−0.475760	−	0.824041i	−0.999614	+	0.0277670i	$0.991160\pi$
$60$		0			0
$61$	−12.0409	−	6.95182i	−1.54168	−	0.890090i	−0.998733	−	0.0503231i	$-0.983975\pi$
$61$	−12.0409	−	6.95182i	−1.54168	−	0.890090i	−0.542948	−	0.839767i	$-0.682692\pi$
$62$	1.01688	+	1.12468i	0.129144	+	0.142835i
$63$		0			0
$64$	2.37766	−	7.63850i	0.297208	−	0.954813i
$65$	−0.285550	+	0.494587i	−0.0354181	+	0.0613459i
$66$		0			0
$67$	−3.49182	+	2.01601i	−0.426594	+	0.246294i	−0.697895	−	0.716200i	$-0.745880\pi$
$67$	−3.49182	+	2.01601i	−0.426594	+	0.246294i	0.271300	+	0.962495i	$0.412546\pi$
$68$	−0.0541628	+	0.0752000i	−0.00656821	+	0.00911934i
$69$		0			0
$70$	−0.392797	+	1.77939i	−0.0469482	+	0.212677i
$71$			6.95063i			0.824888i	0.910983	+	0.412444i	$0.135325\pi$
$71$			6.95063i			0.824888i	−0.910983	+	0.412444i	$0.864675\pi$
$72$		0			0
$73$	−7.14246	+	4.12370i	−0.835961	+	0.482643i	−0.855889	−	0.517159i	$-0.826990\pi$
$73$	−7.14246	+	4.12370i	−0.835961	+	0.482643i	0.0199280	+	0.999801i	$0.493656\pi$
$74$	−0.170393	+	0.528124i	−0.0198078	+	0.0613932i
$75$		0			0
$76$	−0.956981	+	9.48167i	−0.109773	+	1.08762i
$77$	−4.44837	−	6.25176i	−0.506939	−	0.712454i
$78$		0			0
$79$	−12.0015	−	6.92909i	−1.35028	−	0.779584i	−0.361990	−	0.932182i	$-0.617903\pi$
$79$	−12.0015	−	6.92909i	−1.35028	−	0.779584i	−0.988288	+	0.152598i	$0.951236\pi$
$80$	−1.84766	+	0.617263i	−0.206575	+	0.0690121i
$81$		0			0
$82$	0.0413228	+	0.192453i	0.00456334	+	0.0212529i
$83$	6.34905			0.696899			0.348450	−	0.937328i	$-0.386708\pi$
$83$	6.34905			0.696899			0.348450	+	0.937328i	$0.386708\pi$
$84$		0			0
$85$	0.0225668			0.00244772
$86$	−1.92193	−	8.95103i	−0.207247	−	0.965214i
$87$		0			0
$88$	3.28981	−	7.51399i	0.350695	−	0.800994i
$89$	−9.16832	−	5.29333i	−0.971840	−	0.561092i	−0.0720434	−	0.997401i	$-0.522952\pi$
$89$	−9.16832	−	5.29333i	−0.971840	−	0.561092i	−0.899797	+	0.436309i	$0.856285\pi$
$90$		0			0
$91$	3.08864	−	0.293776i	0.323777	−	0.0307961i
$92$	−13.8418	−	1.39705i	−1.44311	−	0.145653i
$93$		0			0
$94$	3.31652	−	10.2794i	0.342073	−	1.06024i
$95$	2.00967	−	1.16028i	0.206188	−	0.119042i
$96$		0			0
$97$		−	8.51277i		−	0.864341i	−0.901792	−	0.432171i	$-0.857748\pi$
$97$		−	8.51277i		−	0.864341i	0.901792	−	0.432171i	$-0.142252\pi$
$98$	9.11354	−	3.86566i	0.920607	−	0.390490i
$99$		0			0
$100$	−7.72947	−	5.56715i	−0.772947	−	0.556715i
$101$	15.8252	−	9.13670i	1.57467	−	0.909136i	0.579085	−	0.815267i	$-0.303410\pi$
$101$	15.8252	−	9.13670i	1.57467	−	0.909136i	0.995585	−	0.0938690i	$-0.0299235\pi$
$102$		0			0
$103$	−8.99009	+	15.5713i	−0.885820	+	1.53429i	−0.0410493	+	0.999157i	$0.513070\pi$
$103$	−8.99009	+	15.5713i	−0.885820	+	1.53429i	−0.844771	+	0.535128i	$0.820263\pi$
$104$	1.96615	+	2.67121i	0.192797	+	0.261934i
$105$		0			0
$106$	−9.54966	−	10.5620i	−0.927545	−	1.02587i
$107$	4.20572	+	2.42818i	0.406583	+	0.234741i	0.689320	−	0.724457i	$-0.257909\pi$
$107$	4.20572	+	2.42818i	0.406583	+	0.234741i	−0.282738	+	0.959197i	$0.591243\pi$
$108$		0			0
$109$	8.83866	+	15.3090i	0.846590	+	1.46634i	0.884234	+	0.467045i	$0.154681\pi$
$109$	8.83866	+	15.3090i	0.846590	+	1.46634i	−0.0376439	+	0.999291i	$0.511985\pi$
$110$	−1.95287	+	0.419313i	−0.186199	+	0.0399799i
$111$		0			0
$112$	8.55169	+	6.23447i	0.808059	+	0.589102i
$113$	−17.4915			−1.64546			−0.822732	−	0.568430i	$-0.807551\pi$
$113$	−17.4915			−1.64546			−0.822732	+	0.568430i	$0.807551\pi$
$114$		0			0
$115$	1.69384	+	2.93382i	0.157951	+	0.273580i
$116$	0.849529	−	0.382447i	0.0788768	−	0.0355094i
$117$		0			0
$118$	6.93209	+	7.66696i	0.638151	+	0.705801i
$119$	−0.0710766	−	0.0998913i	−0.00651558	−	0.00915702i
$120$		0			0
$121$	−1.29482	+	2.24269i	−0.117711	+	0.203881i
$122$	18.7129	+	6.03748i	1.69418	+	0.546608i
$123$		0			0
$124$	−1.73995	−	1.25320i	−0.156252	−	0.112541i
$125$			4.75459i			0.425264i
$126$		0			0
$127$			7.10449i			0.630421i	0.949022	+	0.315211i	$0.102075\pi$
$127$			7.10449i			0.630421i	−0.949022	+	0.315211i	$0.897925\pi$
$128$	−1.01981	+	11.2677i	−0.0901394	+	0.995929i
$129$		0			0
$130$	0.247993	−	0.768641i	0.0217504	−	0.0674143i
$131$	7.34587	−	12.7234i	0.641812	−	1.11165i	−0.343216	−	0.939256i	$-0.611516\pi$
$131$	7.34587	−	12.7234i	0.641812	−	1.11165i	0.985028	−	0.172394i	$-0.0551503\pi$
$132$		0			0
$133$	−11.4656	−	5.24129i	−0.994194	−	0.454478i
$134$	4.22961	−	3.82421i	0.365383	−	0.330361i
$135$		0			0
$136$	0.0525649	−	0.120059i	0.00450741	−	0.0102950i
$137$	5.97043	+	10.3411i	0.510088	+	0.883498i	0.999932	+	0.0116880i	$0.00372050\pi$
$137$	5.97043	+	10.3411i	0.510088	+	0.883498i	−0.489844	+	0.871810i	$0.662946\pi$
$138$		0			0
$139$	9.39809			0.797135			0.398568	−	0.917139i	$-0.369507\pi$
$139$	9.39809			0.797135			0.398568	+	0.917139i	$0.369507\pi$
$140$	0.0148416	−	2.57697i	0.00125435	−	0.217794i
$141$		0			0
$142$	−2.06356	−	9.61063i	−0.173170	−	0.806506i
$143$	1.70040	+	2.94518i	0.142195	+	0.246288i
$144$		0			0
$145$	−0.196467	−	0.113430i	−0.0163157	−	0.00941988i
$146$	8.65159	−	7.82235i	0.716011	−	0.647382i
$147$		0			0
$148$	0.0788082	−	0.780824i	0.00647800	−	0.0641833i
$149$	−6.35996	+	11.0158i	−0.521028	+	0.902447i	0.478673	+	0.877993i	$0.341118\pi$
$149$	−6.35996	+	11.0158i	−0.521028	+	0.902447i	−0.999701	+	0.0244538i	$0.992215\pi$
$150$		0			0
$151$	2.87775	−	1.66147i	0.234188	−	0.135209i	−0.378314	−	0.925677i	$-0.623496\pi$
$151$	2.87775	−	1.66147i	0.234188	−	0.135209i	0.612503	+	0.790468i	$0.290163\pi$
$152$	−1.49178	−	13.3944i	−0.120999	−	1.08643i
$153$		0			0
$154$	8.00684	+	7.32364i	0.645209	+	0.590156i
$155$			0.522143i			0.0419395i
$156$		0			0
$157$	8.22021	−	4.74594i	0.656045	−	0.378767i	−0.134724	−	0.990883i	$-0.543015\pi$
$157$	8.22021	−	4.74594i	0.656045	−	0.378767i	0.790768	+	0.612116i	$0.209681\pi$
$158$	18.6517	+	6.01774i	1.48385	+	0.478746i
$159$		0			0
$160$	2.37150	−	1.40204i	0.187484	−	0.110841i
$161$	7.65152	−	16.7381i	0.603024	−	1.31915i
$162$		0			0
$163$	−11.9144	−	6.87876i	−0.933205	−	0.538786i	−0.0453814	−	0.998970i	$-0.514450\pi$
$163$	−11.9144	−	6.87876i	−0.933205	−	0.538786i	−0.887824	+	0.460183i	$0.847784\pi$
$164$	−0.114274	−	0.253837i	−0.00892331	−	0.0198213i
$165$		0			0
$166$	−8.77883	+	1.88496i	−0.681369	+	0.146301i
$167$	11.0139			0.852280			0.426140	−	0.904657i	$-0.359873\pi$
$167$	11.0139			0.852280			0.426140	+	0.904657i	$0.359873\pi$
$168$		0			0
$169$	11.6249			0.894220
$170$	−0.0312032	+	0.00669982i	−0.00239317	+	0.000513853i
$171$		0			0
$172$	5.31491	+	11.8060i	0.405258	+	0.900198i
$173$	15.2097	+	8.78130i	1.15637	+	0.667630i	0.950431	−	0.310935i	$-0.100642\pi$
$173$	15.2097	+	8.78130i	1.15637	+	0.667630i	0.205938	+	0.978565i	$0.433975\pi$
$174$		0			0
$175$	10.2674	−	7.30564i	0.776140	−	0.552254i
$176$	−2.31800	+	11.3663i	−0.174726	+	0.856767i
$177$		0			0
$178$	14.2486	+	4.59712i	1.06797	+	0.344569i
$179$	8.95722	−	5.17145i	0.669494	−	0.386533i	−0.126391	−	0.991981i	$-0.540339\pi$
$179$	8.95722	−	5.17145i	0.669494	−	0.386533i	0.795885	+	0.605448i	$0.207006\pi$
$180$		0			0
$181$		−	11.4154i		−	0.848503i	−0.905544	−	0.424252i	$-0.860537\pi$
$181$		−	11.4154i		−	0.848503i	0.905544	−	0.424252i	$-0.139463\pi$
$182$	−4.18344	+	1.32318i	−0.310097	+	0.0980809i
$183$		0			0
$184$	19.5539	−	2.17777i	1.44153	−	0.160548i
$185$	−0.165498	+	0.0955503i	−0.0121677	+	0.00702500i
$186$		0			0
$187$	0.0671908	−	0.116378i	0.00491348	−	0.00851040i
$188$	−1.53392	+	15.1979i	−0.111873	+	1.10842i
$189$		0			0
$190$	−2.43429	+	2.20097i	−0.176602	+	0.159675i
$191$	12.6603	+	7.30943i	0.916068	+	0.528892i	0.882379	−	0.470540i	$-0.155941\pi$
$191$	12.6603	+	7.30943i	0.916068	+	0.528892i	0.0336895	+	0.999432i	$0.489274\pi$
$192$		0			0
$193$	0.0358245	+	0.0620498i	0.00257870	+	0.00446644i	0.867312	−	0.497765i	$-0.165846\pi$
$193$	0.0358245	+	0.0620498i	0.00257870	+	0.00446644i	−0.864733	+	0.502232i	$0.832513\pi$
$194$	2.52734	+	11.7706i	0.181452	+	0.845080i
$195$		0			0
$196$	−11.4536	+	8.05074i	−0.818116	+	0.575053i
$197$	1.90917			0.136023			0.0680113	−	0.997685i	$-0.478335\pi$
$197$	1.90917			0.136023			0.0680113	+	0.997685i	$0.478335\pi$
$198$		0			0
$199$	0.291782	+	0.505382i	0.0206839	+	0.0358256i	0.876182	−	0.481980i	$-0.160082\pi$
$199$	0.291782	+	0.505382i	0.0206839	+	0.0358256i	−0.855498	+	0.517806i	$0.826749\pi$
$200$	12.3404	+	5.40291i	0.872595	+	0.382043i
$201$		0			0
$202$	−19.1690	+	17.3316i	−1.34872	+	1.21945i
$203$	0.116698	+	1.22692i	0.00819060	+	0.0861126i
$204$		0			0
$205$	−0.0338926	+	0.0587038i	−0.00236716	+	0.00410005i
$206$	7.80766	−	24.1995i	0.543986	−	1.68606i
$207$		0			0
$208$	−3.51165	−	3.10976i	−0.243489	−	0.215623i
$209$		−	13.8186i		−	0.955850i
$210$		0			0
$211$		−	4.89200i		−	0.336779i	−0.985721	−	0.168390i	$-0.946143\pi$
$211$		−	4.89200i		−	0.336779i	0.985721	−	0.168390i	$-0.0538567\pi$
$212$	16.3400	+	11.7689i	1.12224	+	0.808292i
$213$		0			0
$214$	−6.53615	−	2.10881i	−0.446802	−	0.144155i
$215$	1.57635	−	2.73032i	0.107506	−	0.186206i
$216$		0			0
$217$	2.31125	−	1.64454i	0.156898	−	0.111639i
$218$	−16.7663	−	18.5437i	−1.13555	−	1.25593i
$219$		0			0
$220$	2.57574	−	1.15957i	0.173656	−	0.0781780i
$221$	0.0271692	+	0.0470584i	0.00182760	+	0.00316549i
$222$		0			0
$223$	18.3383			1.22803			0.614013	−	0.789296i	$-0.289554\pi$
$223$	18.3383			1.22803			0.614013	+	0.789296i	$0.289554\pi$
$224$	−13.6754	−	6.08150i	−0.913723	−	0.406337i
$225$		0			0
$226$	24.1855	−	5.19302i	1.60880	−	0.345435i
$227$	8.05581	+	13.9531i	0.534683	+	0.926098i	0.999179	+	0.0405227i	$0.0129023\pi$
$227$	8.05581	+	13.9531i	0.534683	+	0.926098i	−0.464496	+	0.885575i	$0.653764\pi$
$228$		0			0
$229$	12.0728	+	6.97024i	0.797793	+	0.460606i	0.842699	−	0.538385i	$-0.180965\pi$
$229$	12.0728	+	6.97024i	0.797793	+	0.460606i	−0.0449057	+	0.998991i	$0.514299\pi$
$230$	−3.21309	−	3.55371i	−0.211865	−	0.234325i
$231$		0			0
$232$	−1.06110	+	0.781025i	−0.0696646	+	0.0512768i
$233$	−1.82721	+	3.16482i	−0.119704	+	0.207334i	−0.919651	−	0.392738i	$-0.871528\pi$
$233$	−1.82721	+	3.16482i	−0.119704	+	0.207334i	0.799946	+	0.600072i	$0.204861\pi$
$234$		0			0
$235$	3.22125	−	1.85979i	0.210131	−	0.121319i
$236$	−11.8612	−	8.54305i	−0.772100	−	0.556105i
$237$		0			0
$238$	0.127934	+	0.117018i	0.00829273	+	0.00758514i
$239$		−	16.3218i		−	1.05577i	−0.849315	−	0.527886i	$-0.822985\pi$
$239$		−	16.3218i		−	1.05577i	0.849315	−	0.527886i	$-0.177015\pi$
$240$		0			0
$241$	−2.32608	+	1.34296i	−0.149836	+	0.0865079i	−0.573044	−	0.819525i	$-0.694237\pi$
$241$	−2.32608	+	1.34296i	−0.149836	+	0.0865079i	0.423208	+	0.906033i	$0.360904\pi$
$242$	1.12452	−	3.48538i	0.0722867	−	0.224049i
$243$		0			0
$244$	−27.6667	−	2.79239i	−1.77118	−	0.178765i
$245$	3.22075	+	1.11738i	0.205766	+	0.0713869i
$246$		0			0
$247$	4.83905	+	2.79383i	0.307901	+	0.177767i
$248$	2.77789	+	1.21623i	0.176396	+	0.0772305i
$249$		0			0
$250$	−1.41158	−	6.57417i	−0.0892763	−	0.415787i
$251$	−30.3569			−1.91611			−0.958055	−	0.286585i	$-0.907480\pi$
$251$	−30.3569			−1.91611			−0.958055	+	0.286585i	$0.907480\pi$
$252$		0			0
$253$	20.1731			1.26827
$254$	−2.10924	−	9.82337i	−0.132345	−	0.616373i
$255$		0			0
$256$	−1.93514	−	15.8825i	−0.120946	−	0.992659i
$257$	−20.1221	−	11.6175i	−1.25518	−	0.724678i	−0.283046	−	0.959106i	$-0.591345\pi$
$257$	−20.1221	−	11.6175i	−1.25518	−	0.724678i	−0.972133	+	0.234428i	$0.924678\pi$
$258$		0			0
$259$	0.944203	+	0.431625i	0.0586699	+	0.0268199i
$260$	−0.114699	+	1.13643i	−0.00711333	+	0.0704781i
$261$		0			0
$262$	−6.37970	+	19.7736i	−0.394139	+	1.22162i
$263$	−8.24274	+	4.75895i	−0.508269	+	0.293449i	−0.732122	−	0.681174i	$-0.761470\pi$
$263$	−8.24274	+	4.75895i	−0.508269	+	0.293449i	0.223853	+	0.974623i	$0.428137\pi$
$264$		0			0
$265$		−	4.90349i		−	0.301219i
$266$	17.4096	+	3.84313i	1.06745	+	0.235638i
$267$		0			0
$268$	−4.71292	+	6.54346i	−0.287888	+	0.399705i
$269$	10.0770	−	5.81796i	0.614405	−	0.354727i	−0.160282	−	0.987071i	$-0.551240\pi$
$269$	10.0770	−	5.81796i	0.614405	−	0.354727i	0.774688	+	0.632344i	$0.217907\pi$
$270$		0			0
$271$	7.94241	−	13.7567i	0.482467	−	0.835657i	−0.517330	−	0.855786i	$-0.673074\pi$
$271$	7.94241	−	13.7567i	0.482467	−	0.835657i	0.999797	+	0.0201285i	$0.00640752\pi$
$272$	−0.0370373	+	0.181612i	−0.00224572	+	0.0110118i
$273$		0			0
$274$	−11.3254	−	12.5261i	−0.684195	−	0.756727i
$275$	11.9620	+	6.90624i	0.721333	+	0.416462i
$276$		0			0
$277$	7.38977	+	12.7995i	0.444008	+	0.769045i	0.997983	−	0.0634891i	$-0.0202228\pi$
$277$	7.38977	+	12.7995i	0.444008	+	0.769045i	−0.553974	+	0.832534i	$0.686889\pi$
$278$	−12.9947	+	2.79018i	−0.779372	+	0.167344i
$279$		0			0
$280$	0.744551	+	3.56758i	0.0444954	+	0.213204i
$281$	−24.2255			−1.44517			−0.722586	−	0.691281i	$-0.757047\pi$
$281$	−24.2255			−1.44517			−0.722586	+	0.691281i	$0.757047\pi$
$282$		0			0
$283$	−15.1171	−	26.1836i	−0.898619	−	1.55645i	−0.829261	−	0.558861i	$-0.811239\pi$
$283$	−15.1171	−	26.1836i	−0.898619	−	1.55645i	−0.0693572	−	0.997592i	$-0.522095\pi$
$284$	5.70656	+	12.6760i	0.338622	+	0.752180i
$285$		0			0
$286$	−3.22553	−	3.56747i	−0.190730	−	0.210949i
$287$	0.366598	−	0.0348690i	0.0216396	−	0.00205825i
$288$		0			0
$289$	−8.49893	+	14.7206i	−0.499937	+	0.865916i
$290$	0.305331	+	0.0985114i	0.0179297	+	0.00578479i
$291$		0			0
$292$	−9.64019	+	13.3845i	−0.564150	+	0.783269i
$293$			27.6085i			1.61290i	0.591300	+	0.806452i	$0.298615\pi$
$293$			27.6085i			1.61290i	−0.591300	+	0.806452i	$0.701385\pi$
$294$		0			0
$295$			3.55944i			0.207239i
$296$	0.122849	+	1.10304i	0.00714047	+	0.0641130i
$297$		0			0
$298$	5.52346	−	17.1197i	0.319965	−	0.991717i
$299$	−4.07857	+	7.06430i	−0.235870	+	0.408539i
$300$		0			0
$301$	−17.0506	+	1.62176i	−0.982778	+	0.0934769i
$302$	−3.48580	+	3.15169i	−0.200585	+	0.181359i
$303$		0			0
$304$	6.03932	+	18.0776i	0.346379	+	1.03682i
$305$	3.38561	+	5.86405i	0.193859	+	0.335774i
$306$		0			0
$307$	18.3244			1.04583			0.522913	−	0.852386i	$-0.324845\pi$
$307$	18.3244			1.04583			0.522913	+	0.852386i	$0.324845\pi$
$308$	−13.2453	−	7.74926i	−0.754724	−	0.441555i
$309$		0			0
$310$	−0.155018	−	0.721966i	−0.00880443	−	0.0410049i
$311$	−9.34254	−	16.1817i	−0.529767	−	0.917583i	−0.999397	−	0.0347196i	$-0.988946\pi$
$311$	−9.34254	−	16.1817i	−0.529767	−	0.917583i	0.469630	−	0.882863i	$-0.344387\pi$
$312$		0			0
$313$	24.3438	+	14.0549i	1.37599	+	0.794431i	0.991675	−	0.128769i	$-0.0411027\pi$
$313$	24.3438	+	14.0549i	1.37599	+	0.794431i	0.384320	+	0.923200i	$0.374436\pi$
$314$	−9.95707	+	9.00270i	−0.561910	+	0.508051i
$315$		0			0
$316$	−27.5763	−	2.78326i	−1.55129	−	0.156571i
$317$	3.14099	−	5.44035i	0.176416	−	0.305561i	−0.764235	−	0.644938i	$-0.776883\pi$
$317$	3.14099	−	5.44035i	0.176416	−	0.305561i	0.940650	+	0.339378i	$0.110216\pi$
$318$		0			0
$319$	−1.16993	+	0.675459i	−0.0655034	+	0.0378184i
$320$	−2.86282	+	2.64267i	−0.160037	+	0.147730i
$321$		0			0
$322$	−5.61041	+	25.4154i	−0.312656	+	1.41634i
$323$		−	0.220794i		−	0.0122853i
$324$		0			0
$325$	−4.83692	+	2.79260i	−0.268304	+	0.154905i
$326$	18.5162	+	5.97403i	1.02552	+	0.330871i
$327$		0			0
$328$	0.233368	+	0.317053i	0.0128856	+	0.0175063i
$329$	−18.3779	−	8.40114i	−1.01321	−	0.463170i
$330$		0			0
$331$	−17.2443	−	9.95600i	−0.947832	−	0.547231i	−0.0554253	−	0.998463i	$-0.517651\pi$
$331$	−17.2443	−	9.95600i	−0.947832	−	0.547231i	−0.892407	+	0.451232i	$0.850985\pi$
$332$	11.5789	−	5.21266i	0.635473	−	0.286082i
$333$		0			0
$334$	−15.2289	+	3.26989i	−0.833288	+	0.178920i
$335$	1.96363			0.107285
$336$		0			0
$337$	27.4718			1.49649			0.748243	−	0.663424i	$-0.230898\pi$
$337$	27.4718			1.49649			0.748243	+	0.663424i	$0.230898\pi$
$338$	−16.0737	+	3.45128i	−0.874293	+	0.187725i
$339$		0			0
$340$	0.0411555	−	0.0185277i	0.00223197	−	0.00100480i
$341$	2.69271	+	1.55464i	0.145818	+	0.0841882i
$342$		0			0
$343$	−5.19803	−	17.7758i	−0.280667	−	0.959805i
$344$	−10.8540	−	14.7462i	−0.585207	−	0.795062i
$345$		0			0
$346$	−23.6375	−	7.62634i	−1.27076	−	0.409994i
$347$	−7.37788	+	4.25962i	−0.396065	+	0.228668i	−0.684785	−	0.728745i	$-0.740104\pi$
$347$	−7.37788	+	4.25962i	−0.396065	+	0.228668i	0.288720	+	0.957414i	$0.406770\pi$
$348$		0			0
$349$			5.53420i			0.296239i	0.988969	+	0.148119i	$0.0473220\pi$
$349$			5.53420i			0.296239i	−0.988969	+	0.148119i	$0.952678\pi$
$350$	−12.0277	+	13.1498i	−0.642909	+	0.702884i
$351$		0			0
$352$	−0.169415	−	16.4044i	−0.00902982	−	0.874355i
$353$	14.9667	−	8.64101i	0.796595	−	0.459914i	−0.0456841	−	0.998956i	$-0.514547\pi$
$353$	14.9667	−	8.64101i	0.796595	−	0.459914i	0.842279	+	0.539042i	$0.181213\pi$
$354$		0			0
$355$	1.69251	−	2.93152i	0.0898293	−	0.155589i
$356$	−21.0663	−	2.12621i	−1.11651	−	0.112689i
$357$		0			0
$358$	−10.8498	+	9.80986i	−0.573430	+	0.518467i
$359$	−20.8753	−	12.0523i	−1.10175	−	0.636098i	−0.165073	−	0.986281i	$-0.552786\pi$
$359$	−20.8753	−	12.0523i	−1.10175	−	0.636098i	−0.936681	+	0.350183i	$0.886119\pi$
$360$		0			0
$361$	−1.85223	−	3.20815i	−0.0974857	−	0.168850i
$362$	3.38911	+	15.7841i	0.178128	+	0.829595i
$363$		0			0
$364$	5.39160	−	3.07158i	0.282597	−	0.160994i
$365$	4.01657			0.210237
$366$		0			0
$367$	−2.54588	−	4.40959i	−0.132894	−	0.230179i	0.791897	−	0.610655i	$-0.209094\pi$
$367$	−2.54588	−	4.40959i	−0.132894	−	0.230179i	−0.924791	+	0.380476i	$0.875760\pi$
$368$	−26.3906	+	8.81652i	−1.37570	+	0.459593i
$369$		0			0
$370$	0.200466	−	0.181252i	0.0104217	−	0.00942283i
$371$	−21.7051	+	15.4441i	−1.12688	+	0.801816i
$372$		0			0
$373$	−6.30359	+	10.9181i	−0.326388	+	0.565320i	−0.981792	−	0.189958i	$-0.939165\pi$
$373$	−6.30359	+	10.9181i	−0.326388	+	0.565320i	0.655405	+	0.755278i	$0.272498\pi$
$374$	−0.0583535	+	0.180864i	−0.00301739	+	0.00935225i
$375$		0			0
$376$	−2.39113	−	21.4696i	−0.123313	−	1.10721i
$377$		−	0.546255i		−	0.0281336i
$378$		0			0
$379$			12.1068i			0.621883i	0.950429	+	0.310942i	$0.100644\pi$
$379$			12.1068i			0.621883i	−0.950429	+	0.310942i	$0.899356\pi$
$380$	2.71245	−	3.76599i	0.139146	−	0.193191i
$381$		0			0
$382$	−19.6755	−	6.34806i	−1.00669	−	0.324795i
$383$	−0.646193	+	1.11924i	−0.0330189	+	0.0571905i	−0.882063	−	0.471132i	$-0.843845\pi$
$383$	−0.646193	+	1.11924i	−0.0330189	+	0.0571905i	0.849044	+	0.528323i	$0.177179\pi$
$384$		0			0
$385$	0.353824	+	3.71996i	0.0180326	+	0.189587i
$386$	−0.0679563	−	0.0751604i	−0.00345888	−	0.00382556i
$387$		0			0
$388$	−6.98910	−	15.5249i	−0.354818	−	0.788156i
$389$	15.0809	+	26.1208i	0.764630	+	1.32438i	0.940442	+	0.339954i	$0.110412\pi$
$389$	15.0809	+	26.1208i	0.764630	+	1.32438i	−0.175812	+	0.984424i	$0.556255\pi$
$390$		0			0
$391$	0.322327			0.0163008
$392$	13.4467	−	14.5322i	0.679163	−	0.733987i
$393$		0			0
$394$	−2.63980	+	0.566809i	−0.132991	+	0.0285554i
$395$	3.37454	+	5.84487i	0.169791	+	0.294087i
$396$		0			0
$397$	−3.80099	−	2.19450i	−0.190766	−	0.110139i	0.401575	−	0.915826i	$-0.368463\pi$
$397$	−3.80099	−	2.19450i	−0.190766	−	0.110139i	−0.592341	+	0.805687i	$0.701796\pi$
$398$	−0.553489	−	0.612165i	−0.0277439	−	0.0306850i
$399$		0			0
$400$	−18.6671	−	3.80690i	−0.933353	−	0.190345i
$401$	−6.56098	+	11.3640i	−0.327640	+	0.567489i	−0.982043	−	0.188657i	$-0.939587\pi$
$401$	−6.56098	+	11.3640i	−0.327640	+	0.567489i	0.654403	+	0.756146i	$0.272920\pi$
$402$		0			0
$403$	−1.08882	+	0.628630i	−0.0542379	+	0.0313143i
$404$	21.3594	−	29.6555i	1.06267	−	1.47542i
$405$		0			0
$406$	−0.525615	−	1.66181i	−0.0260858	−	0.0824742i
$407$			1.13797i			0.0564072i
$408$		0			0
$409$	−13.8601	+	8.00213i	−0.685338	+	0.395680i	−0.801863	−	0.597508i	$-0.796158\pi$
$409$	−13.8601	+	8.00213i	−0.685338	+	0.395680i	0.116525	+	0.993188i	$0.462824\pi$
$410$	0.0294349	−	0.0912320i	0.00145369	−	0.00450563i
$411$		0			0
$412$	−3.61112	+	35.7786i	−0.177907	+	1.76268i
$413$	15.7558	−	11.2108i	0.775290	−	0.551649i
$414$		0			0
$415$	−2.67780	−	1.54603i	−0.131448	−	0.0758914i
$416$	5.77881	+	3.25729i	0.283329	+	0.159702i
$417$		0			0
$418$	4.10257	+	19.1069i	0.200663	+	0.934550i
$419$	−18.2612			−0.892119			−0.446059	−	0.895003i	$-0.647173\pi$
$419$	−18.2612			−0.892119			−0.446059	+	0.895003i	$0.647173\pi$
$420$		0			0
$421$	22.6765			1.10518			0.552592	−	0.833452i	$-0.313639\pi$
$421$	22.6765			1.10518			0.552592	+	0.833452i	$0.313639\pi$
$422$	1.45238	+	6.76416i	0.0707006	+	0.329274i
$423$		0			0
$424$	−26.0874	−	11.4217i	−1.26692	−	0.554687i
$425$	0.191129	+	0.110349i	0.00927114	+	0.00535270i
$426$		0			0
$427$	15.2937	−	33.4557i	0.740112	−	1.61903i
$428$	9.66361	+	0.975344i	0.467108	+	0.0471450i
$429$		0			0
$430$	−1.36902	+	4.24321i	−0.0660201	+	0.204626i
$431$	20.9603	−	12.1015i	1.00962	−	0.582907i	0.0985425	−	0.995133i	$-0.468582\pi$
$431$	20.9603	−	12.1015i	1.00962	−	0.582907i	0.911082	+	0.412226i	$0.135249\pi$
$432$		0			0
$433$		−	31.0508i		−	1.49221i	−0.665830	−	0.746103i	$-0.731922\pi$
$433$		−	31.0508i		−	1.49221i	0.665830	−	0.746103i	$-0.268078\pi$
$434$	−2.70751	+	2.96009i	−0.129965	+	0.142089i
$435$		0			0
$436$	28.6881	+	20.6626i	1.37391	+	0.989559i
$437$	28.7045	−	16.5726i	1.37312	−	0.792774i
$438$		0			0
$439$	17.6459	−	30.5637i	0.842195	−	1.45872i	−0.0458405	−	0.998949i	$-0.514597\pi$
$439$	17.6459	−	30.5637i	0.842195	−	1.45872i	0.888035	−	0.459775i	$-0.152070\pi$
$440$	−3.21722	+	2.36804i	−0.153375	+	0.112892i
$441$		0			0
$442$	−0.0515379	−	0.0570014i	−0.00245141	−	0.00271128i
$443$	−12.9852	−	7.49702i	−0.616947	−	0.356194i	0.158733	−	0.987322i	$-0.449259\pi$
$443$	−12.9852	−	7.49702i	−0.616947	−	0.356194i	−0.775679	+	0.631127i	$0.782593\pi$
$444$		0			0
$445$	2.57791	+	4.46507i	0.122205	+	0.211664i
$446$	−25.3564	+	5.44443i	−1.20066	+	0.257801i
$447$		0			0
$448$	20.7144	+	4.34884i	0.978665	+	0.205463i
$449$	−5.15686			−0.243367			−0.121684	−	0.992569i	$-0.538829\pi$
$449$	−5.15686			−0.243367			−0.121684	+	0.992569i	$0.538829\pi$
$450$		0			0
$451$	0.201825	+	0.349571i	0.00950356	+	0.0164607i
$452$	−31.8995	+	14.3608i	−1.50043	+	0.675474i
$453$		0			0
$454$	−15.2813	−	16.9012i	−0.717185	−	0.793214i
$455$	−1.37421	−	0.628196i	−0.0644240	−	0.0294503i
$456$		0			0
$457$	−12.7402	+	22.0666i	−0.595961	+	1.03223i	0.397450	+	0.917624i	$0.369895\pi$
$457$	−12.7402	+	22.0666i	−0.595961	+	1.03223i	−0.993411	+	0.114610i	$0.963438\pi$
$458$	−18.7624	−	6.05347i	−0.876711	−	0.282860i
$459$		0			0
$460$	5.49779	+	3.95978i	0.256336	+	0.184626i
$461$		−	1.16194i		−	0.0541170i	−0.999634	−	0.0270585i	$-0.991386\pi$
$461$		−	1.16194i		−	0.0541170i	0.999634	−	0.0270585i	$-0.00861403\pi$
$462$		0			0
$463$			23.3409i			1.08474i	0.840139	+	0.542371i	$0.182473\pi$
$463$			23.3409i			1.08474i	−0.840139	+	0.542371i	$0.817527\pi$
$464$	1.23530	−	1.39495i	0.0573476	−	0.0647589i
$465$		0			0
$466$	1.58688	−	4.91847i	0.0735110	−	0.227844i
$467$	−9.08065	+	15.7281i	−0.420202	+	0.727812i	−0.995959	−	0.0898092i	$-0.971374\pi$
$467$	−9.08065	+	15.7281i	−0.420202	+	0.727812i	0.575757	+	0.817621i	$0.304708\pi$
$468$		0			0
$469$	−6.18466	−	8.69194i	−0.285581	−	0.401357i
$470$	−3.90187	+	3.52788i	−0.179980	+	0.162729i
$471$		0			0
$472$	18.9368	+	8.29101i	0.871639	+	0.381625i
$473$	−9.38691	−	16.2586i	−0.431611	−	0.747571i
$474$		0			0
$475$	22.6945			1.04129
$476$	−0.211636	−	0.123818i	−0.00970030	−	0.00567521i
$477$		0			0
$478$	4.84576	+	22.5682i	0.221640	+	1.03225i
$479$	−5.41667	−	9.38196i	−0.247494	−	0.428672i	0.715336	−	0.698781i	$-0.246274\pi$
$479$	−5.41667	−	9.38196i	−0.247494	−	0.428672i	−0.962830	+	0.270108i	$0.912940\pi$
$480$		0			0
$481$	−0.398500	−	0.230074i	−0.0181700	−	0.0104905i
$482$	2.81756	−	2.54750i	0.128336	−	0.116036i
$483$		0			0
$484$	−0.520100	+	5.15309i	−0.0236409	+	0.234232i
$485$	−2.07290	+	3.59037i	−0.0941257	+	0.163030i
$486$		0			0
$487$	−15.3315	+	8.85162i	−0.694734	+	0.401105i	−0.805383	−	0.592754i	$-0.798040\pi$
$487$	−15.3315	+	8.85162i	−0.694734	+	0.401105i	0.110649	+	0.993860i	$0.464707\pi$
$488$	39.0838	−	4.35288i	1.76924	−	0.197046i
$489$		0			0
$490$	−4.78506	−	0.588802i	−0.216167	−	0.0265994i
$491$			2.86819i			0.129440i	0.997903	+	0.0647199i	$0.0206154\pi$
$491$			2.86819i			0.129440i	−0.997903	+	0.0647199i	$0.979385\pi$
$492$		0			0
$493$	−0.0186932	+	0.0107926i	−0.000841901	+	0.000486072i
$494$	−7.52040	−	2.42637i	−0.338359	−	0.109167i
$495$		0			0
$496$	−4.20207	−	0.856955i	−0.188678	−	0.0384784i
$497$	−18.3070	+	1.74127i	−0.821182	+	0.0781067i
$498$		0			0
$499$	24.5923	+	14.1984i	1.10090	+	0.635606i	0.936458	−	0.350781i	$-0.114084\pi$
$499$	24.5923	+	14.1984i	1.10090	+	0.635606i	0.164444	+	0.986386i	$0.447417\pi$
$500$	3.90359	+	8.67102i	0.174574	+	0.387780i
$501$		0			0
$502$	41.9744	−	9.01260i	1.87341	−	0.402252i
$503$	0.613623			0.0273601			0.0136800	−	0.999906i	$-0.495645\pi$
$503$	0.613623			0.0273601			0.0136800	+	0.999906i	$0.495645\pi$
$504$		0			0
$505$	−8.89933			−0.396015
$506$	−27.8933	+	5.98914i	−1.24001	+	0.266250i
$507$		0			0
$508$	5.83288	+	12.9566i	0.258792	+	0.574854i
$509$	8.62877	+	4.98182i	0.382464	+	0.220816i	0.678890	−	0.734240i	$-0.262461\pi$
$509$	8.62877	+	4.98182i	0.382464	+	0.220816i	−0.296426	+	0.955056i	$0.595795\pi$
$510$		0			0
$511$	−12.6506	−	17.7792i	−0.559629	−	0.786505i
$512$	7.39105	+	21.3863i	0.326641	+	0.945148i
$513$		0			0
$514$	31.2718	+	10.0895i	1.37934	+	0.445028i
$515$	7.58338	−	4.37827i	0.334164	−	0.192929i
$516$		0			0
$517$		−	22.1494i		−	0.974131i
$518$	−1.43369	−	0.316486i	−0.0629929	−	0.0139056i
$519$		0			0
$520$	−0.178797	−	1.60539i	−0.00784077	−	0.0704009i
$521$	−37.1542	+	21.4510i	−1.62776	+	0.939786i	−0.642997	+	0.765869i	$0.722309\pi$
$521$	−37.1542	+	21.4510i	−1.62776	+	0.939786i	−0.984760	+	0.173917i	$0.944357\pi$
$522$		0			0
$523$	−0.342559	+	0.593329i	−0.0149790	+	0.0259445i	−0.873418	−	0.486972i	$-0.838101\pi$
$523$	−0.342559	+	0.593329i	−0.0149790	+	0.0259445i	0.858439	+	0.512916i	$0.171435\pi$
$524$	2.95067	−	29.2350i	0.128901	−	1.27714i
$525$		0			0
$526$	9.98436	−	9.02737i	0.435339	−	0.393612i
$527$	0.0430244	+	0.0248401i	0.00187417	+	0.00108205i
$528$		0			0
$529$	12.6935	+	21.9858i	0.551892	+	0.955906i
$530$	1.45579	+	6.78006i	0.0632354	+	0.294507i
$531$		0			0
$532$	−25.2132	−	0.145211i	−1.09313	−	0.00629569i
$533$	−0.163219			−0.00706981
$534$		0			0
$535$	−1.18255	−	2.04823i	−0.0511259	−	0.0885527i
$536$	4.57388	−	10.4468i	0.197562	−	0.451235i
$537$		0			0
$538$	−12.2062	+	11.0362i	−0.526245	+	0.475805i
$539$	15.3519	−	13.2826i	0.661252	−	0.572122i
$540$		0			0
$541$	−0.951285	+	1.64767i	−0.0408989	+	0.0708390i	−0.885750	−	0.464162i	$-0.846356\pi$
$541$	−0.951285	+	1.64767i	−0.0408989	+	0.0708390i	0.844851	+	0.535001i	$0.179689\pi$
$542$	−6.89778	+	21.3793i	−0.296285	+	0.918321i
$543$		0			0
$544$	−0.00270692	−	0.262111i	−0.000116058	−	0.0112379i
$545$		−	8.60903i		−	0.368770i
$546$		0			0
$547$			32.8931i			1.40641i	0.710989	+	0.703203i	$0.248247\pi$
$547$			32.8931i			1.40641i	−0.710989	+	0.703203i	$0.751753\pi$
$548$	19.3785	+	13.9574i	0.827810	+	0.596230i
$549$		0			0
$550$	−18.5902	−	5.99789i	−0.792688	−	0.255751i
$551$	−1.10981	+	1.92224i	−0.0472793	+	0.0818902i
$552$		0			0
$553$	15.2437	−	33.3463i	0.648226	−	1.41803i
$554$	−14.0178	−	15.5039i	−0.595561	−	0.658696i
$555$		0			0
$556$	17.1394	−	7.71596i	0.726874	−	0.327230i
$557$	11.8145	+	20.4633i	0.500596	+	0.867058i	1.00000		0.000688398i	$0.000219124\pi$
$557$	11.8145	+	20.4633i	0.500596	+	0.867058i	−0.499404	+	0.866369i	$0.666448\pi$
$558$		0			0
$559$	7.59135			0.321080
$560$	−2.08866	−	4.71185i	−0.0882621	−	0.199112i
$561$		0			0
$562$	33.4966	−	7.19226i	1.41297	−	0.303387i
$563$	−10.9592	−	18.9820i	−0.461877	−	0.799994i	0.537178	−	0.843469i	$-0.319490\pi$
$563$	−10.9592	−	18.9820i	−0.461877	−	0.799994i	−0.999055	+	0.0434752i	$0.986157\pi$
$564$		0			0
$565$	7.37728	+	4.25927i	0.310364	+	0.179189i
$566$	28.6760	+	31.7159i	1.20534	+	1.33312i
$567$		0			0
$568$	−11.6538	−	15.8328i	−0.488983	−	0.664331i
$569$	4.15511	−	7.19687i	0.174191	−	0.301708i	−0.765690	−	0.643210i	$-0.777602\pi$
$569$	4.15511	−	7.19687i	0.174191	−	0.301708i	0.939881	+	0.341502i	$0.110936\pi$
$570$		0			0
$571$	−22.1031	+	12.7613i	−0.924988	+	0.534042i	−0.885223	−	0.465167i	$-0.845994\pi$
$571$	−22.1031	+	12.7613i	−0.924988	+	0.534042i	−0.0397651	+	0.999209i	$0.512661\pi$
$572$	5.51908	+	3.97512i	0.230764	+	0.166208i
$573$		0			0
$574$	−0.496543	+	0.157052i	−0.0207253	+	0.00655523i
$575$			33.1306i			1.38164i
$576$		0			0
$577$	14.3610	−	8.29131i	0.597855	−	0.345172i	−0.170342	−	0.985385i	$-0.554487\pi$
$577$	14.3610	−	8.29131i	0.597855	−	0.345172i	0.768197	+	0.640213i	$0.221154\pi$
$578$	7.38110	−	22.8774i	0.307013	−	0.951573i
$579$		0			0
$580$	−0.451428	−	0.0455624i	−0.0187445	−	0.00189188i
$581$	1.59056	+	16.7225i	0.0659877	+	0.693768i
$582$		0			0
$583$	−25.2875	−	14.5997i	−1.04730	−	0.604659i
$584$	9.35579	−	21.3688i	0.387145	−	0.884248i
$585$		0			0
$586$	−8.19662	−	38.1742i	−0.338599	−	1.57696i
$587$	27.4851			1.13443			0.567216	−	0.823569i	$-0.308021\pi$
$587$	27.4851			1.13443			0.567216	+	0.823569i	$0.308021\pi$
$588$		0			0
$589$	5.10866			0.210499
$590$	−1.05676	−	4.92164i	−0.0435060	−	0.202621i
$591$		0			0
$592$	−0.497344	−	1.48870i	−0.0204407	−	0.0611853i
$593$	−31.4732	−	18.1711i	−1.29245	−	0.746197i	−0.313363	−	0.949633i	$-0.601456\pi$
$593$	−31.4732	−	18.1711i	−1.29245	−	0.746197i	−0.979088	+	0.203437i	$0.934789\pi$
$594$		0			0
$595$	0.00565344	+	0.0594380i	0.000231768	+	0.00243672i
$596$	−2.55465	+	25.3112i	−0.104643	+	1.03679i
$597$		0			0
$598$	3.54214	−	10.9787i	0.144849	−	0.448952i
$599$	−27.8050	+	16.0532i	−1.13608	+	0.655918i	−0.945458	−	0.325745i	$-0.894385\pi$
$599$	−27.8050	+	16.0532i	−1.13608	+	0.655918i	−0.190625	+	0.981663i	$0.561051\pi$
$600$		0			0
$601$		−	22.7728i		−	0.928923i	−0.885593	−	0.464462i	$-0.846248\pi$
$601$		−	22.7728i		−	0.928923i	0.885593	−	0.464462i	$-0.153752\pi$
$602$	23.0943	−	7.30452i	0.941254	−	0.297710i
$603$		0			0
$604$	3.88411	−	5.39273i	0.158042	−	0.219427i
$605$	1.09221	−	0.630590i	0.0444048	−	0.0256371i
$606$		0			0
$607$	−22.4667	+	38.9134i	−0.911893	+	1.57945i	−0.100506	+	0.994936i	$0.532046\pi$
$607$	−22.4667	+	38.9134i	−0.911893	+	1.57945i	−0.811387	+	0.584509i	$0.801287\pi$
$608$	−13.7176	−	23.2028i	−0.556321	−	0.940999i
$609$		0			0
$610$	−6.42224	−	7.10306i	−0.260029	−	0.287595i
$611$	7.75640	+	4.47816i	0.313790	+	0.181167i
$612$		0			0
$613$	−15.0988	−	26.1519i	−0.609836	−	1.05627i	−0.991267	−	0.131869i	$-0.957902\pi$
$613$	−15.0988	−	26.1519i	−0.609836	−	1.05627i	0.381432	−	0.924397i	$-0.375431\pi$
$614$	−25.3371	+	5.44028i	−1.02252	+	0.219552i
$615$		0			0
$616$	20.6150	+	6.78251i	0.830602	+	0.273275i
$617$	9.76529			0.393136			0.196568	−	0.980490i	$-0.437020\pi$
$617$	9.76529			0.393136			0.196568	+	0.980490i	$0.437020\pi$
$618$		0			0
$619$	23.9884	+	41.5491i	0.964174	+	1.67000i	0.711819	+	0.702363i	$0.247872\pi$
$619$	23.9884	+	41.5491i	0.964174	+	1.67000i	0.252355	+	0.967635i	$0.418795\pi$
$620$	0.428686	+	0.952240i	0.0172165	+	0.0382429i
$621$		0			0
$622$	17.7221	+	19.6008i	0.710591	+	0.785921i
$623$	11.6451	−	25.4742i	0.466550	−	1.02060i
$624$		0			0
$625$	−10.7493	+	18.6183i	−0.429971	+	0.744732i
$626$	−37.8329	−	12.2063i	−1.51211	−	0.487863i
$627$		0			0
$628$	11.0948	−	15.4042i	0.442732	−	0.614693i
$629$			0.0181826i			0.000724989i
$630$		0			0
$631$			12.7354i			0.506987i	0.967337	+	0.253493i	$0.0815796\pi$
$631$			12.7354i			0.506987i	−0.967337	+	0.253493i	$0.918420\pi$
$632$	38.9560	−	4.33865i	1.54959	−	0.172582i
$633$		0			0
$634$	−2.72787	+	8.45489i	−0.108337	+	0.335787i
$635$	1.72998	−	2.99641i	0.0686521	−	0.118909i
$636$		0			0
$637$	1.54753	+	8.06146i	0.0613154	+	0.319407i
$638$	1.41712	−	1.28129i	0.0561045	−	0.0507269i
$639$		0			0
$640$	3.17385	−	4.50395i	0.125457	−	0.178034i
$641$	−22.4179	−	38.8289i	−0.885452	−	1.53365i	−0.845195	−	0.534459i	$-0.820515\pi$
$641$	−22.4179	−	38.8289i	−0.885452	−	1.53365i	−0.0402575	−	0.999189i	$-0.512818\pi$
$642$		0			0
$643$	−24.9324			−0.983236			−0.491618	−	0.870811i	$-0.663594\pi$
$643$	−24.9324			−0.983236			−0.491618	+	0.870811i	$0.663594\pi$
$644$	0.211986	−	36.8075i	0.00835343	−	1.45042i
$645$		0			0
$646$	0.0655512	+	0.305292i	0.00257908	+	0.0120116i
$647$	23.4210	+	40.5664i	0.920775	+	1.59483i	0.798219	+	0.602367i	$0.205776\pi$
$647$	23.4210	+	40.5664i	0.920775	+	1.59483i	0.122556	+	0.992462i	$0.460891\pi$
$648$		0			0
$649$	18.3562	+	10.5979i	0.720543	+	0.416006i
$650$	5.85892	−	5.29734i	0.229806	−	0.207779i
$651$		0			0
$652$	−27.3760	−	2.76304i	−1.07213	−	0.108209i
$653$	12.1952	−	21.1227i	0.477236	−	0.826597i	−0.522424	−	0.852686i	$-0.674972\pi$
$653$	12.1952	−	21.1227i	0.477236	−	0.826597i	0.999660	+	0.0260892i	$0.00830540\pi$
$654$		0			0
$655$	−6.19644	+	3.57751i	−0.242115	+	0.139785i
$656$	−0.416807	−	0.369105i	−0.0162736	−	0.0144111i
$657$		0			0
$658$	27.9054	+	6.16007i	1.08786	+	0.240144i
$659$		−	36.2942i		−	1.41382i	−0.707302	−	0.706911i	$-0.750088\pi$
$659$		−	36.2942i		−	1.41382i	0.707302	−	0.706911i	$-0.249912\pi$
$660$		0			0
$661$	−17.1034	+	9.87464i	−0.665244	+	0.384079i	−0.794272	−	0.607562i	$-0.792148\pi$
$661$	−17.1034	+	9.87464i	−0.665244	+	0.384079i	0.129028	+	0.991641i	$0.458814\pi$
$662$	26.7995	+	8.64653i	1.04159	+	0.336057i
$663$		0			0
$664$	−14.4625	+	10.6452i	−0.561254	+	0.413113i
$665$	3.55949	+	5.00252i	0.138031	+	0.193989i
$666$		0			0
$667$	−2.80619	−	1.62015i	−0.108656	−	0.0627326i
$668$	20.0862	−	9.04255i	0.777158	−	0.349867i
$669$		0			0
$670$	−2.71511	+	0.582978i	−0.104894	+	0.0225224i
$671$	40.3214			1.55659
$672$		0			0
$673$	−9.01232			−0.347399			−0.173700	−	0.984799i	$-0.555572\pi$
$673$	−9.01232			−0.347399			−0.173700	+	0.984799i	$0.555572\pi$
$674$	−37.9853	+	8.15606i	−1.46314	+	0.314160i
$675$		0			0
$676$	21.2004	−	9.54417i	0.815401	−	0.367083i
$677$	14.1790	+	8.18626i	0.544944	+	0.314624i	0.747080	−	0.664734i	$-0.231455\pi$
$677$	14.1790	+	8.18626i	0.544944	+	0.314624i	−0.202136	+	0.979357i	$0.564788\pi$
$678$		0			0
$679$	22.4215	−	2.13262i	0.860458	−	0.0818424i
$680$	−0.0514050	+	0.0378368i	−0.00197129	+	0.00145097i
$681$		0			0
$682$	−4.18476	−	1.35016i	−0.160243	−	0.0517003i
$683$	18.9098	−	10.9176i	0.723564	−	0.417750i	−0.0924991	−	0.995713i	$-0.529486\pi$
$683$	18.9098	−	10.9176i	0.723564	−	0.417750i	0.816063	+	0.577963i	$0.196152\pi$
$684$		0			0
$685$		−	5.81532i		−	0.222192i
$686$	12.4647	+	23.0354i	0.475906	+	0.879496i
$687$		0			0
$688$	19.3858	+	17.1671i	0.739075	+	0.654491i
$689$	10.2252	−	5.90353i	0.389549	−	0.224906i
$690$		0			0
$691$	6.17352	−	10.6929i	0.234852	−	0.406775i	−0.724378	−	0.689403i	$-0.757873\pi$
$691$	6.17352	−	10.6929i	0.234852	−	0.406775i	0.959230	+	0.282628i	$0.0912062\pi$
$692$	34.9477	+	3.52725i	1.32851	+	0.134086i
$693$		0			0
$694$	8.93676	−	8.08018i	0.339235	−	0.306719i
$695$	−3.96377	−	2.28848i	−0.150354	−	0.0868071i
$696$		0			0
$697$	0.00322478	+	0.00558548i	0.000122147	+	0.000211565i
$698$	−1.64304	−	7.65213i	−0.0621898	−	0.289637i
$699$		0			0
$700$	12.7267	−	21.7531i	0.481025	−	0.822188i
$701$	31.7226			1.19815			0.599074	−	0.800694i	$-0.295536\pi$
$701$	31.7226			1.19815			0.599074	+	0.800694i	$0.295536\pi$
$702$		0			0
$703$	0.934867	+	1.61924i	0.0352592	+	0.0610707i
$704$	5.10451	+	22.6320i	0.192383	+	0.852975i
$705$		0			0
$706$	−18.1290	+	16.3913i	−0.682293	+	0.616896i
$707$	28.0294	+	39.3926i	1.05415	+	1.48151i
$708$		0			0
$709$	−17.7550	+	30.7526i	−0.666804	+	1.15494i	0.311989	+	0.950086i	$0.399005\pi$
$709$	−17.7550	+	30.7526i	−0.666804	+	1.15494i	−0.978793	+	0.204852i	$0.934329\pi$
$710$	−1.46990	+	4.55590i	−0.0551645	+	0.170980i
$711$		0			0
$712$	29.7596	−	3.31442i	1.11529	−	0.124213i
$713$			7.45789i			0.279300i
$714$		0			0
$715$		−	1.65622i		−	0.0619393i
$716$	12.0896	−	16.7853i	0.451809	−	0.627295i
$717$		0			0
$718$	32.4424	+	10.4671i	1.21074	+	0.390630i
$719$	6.27192	−	10.8633i	0.233903	−	0.405132i	−0.725050	−	0.688696i	$-0.758183\pi$
$719$	6.27192	−	10.8633i	0.233903	−	0.405132i	0.958953	+	0.283564i	$0.0915168\pi$
$720$		0			0
$721$	−43.2649	−	19.7778i	−1.61127	−	0.736562i
$722$	3.51354	+	3.88601i	0.130760	+	0.144622i
$723$		0			0
$724$	−9.37223	−	20.8185i	−0.348316	−	0.773714i
$725$	−1.10932	−	1.92139i	−0.0411990	−	0.0713588i
$726$		0			0
$727$	8.90679			0.330335			0.165167	−	0.986266i	$-0.447184\pi$
$727$	8.90679			0.330335			0.165167	+	0.986266i	$0.447184\pi$
$728$	−6.54305	+	5.84777i	−0.242502	+	0.216733i
$729$		0			0
$730$	−5.55370	+	1.19247i	−0.205552	+	0.0441353i
$731$	−0.149985	−	0.259782i	−0.00554740	−	0.00960837i
$732$		0			0
$733$	−14.4986	−	8.37078i	−0.535519	−	0.309182i	0.207742	−	0.978184i	$-0.433388\pi$
$733$	−14.4986	−	8.37078i	−0.535519	−	0.309182i	−0.743261	+	0.669002i	$0.766722\pi$
$734$	4.82934	+	5.34130i	0.178254	+	0.197151i
$735$		0			0
$736$	33.8727	−	20.0256i	1.24856	−	0.738155i
$737$	5.84654	−	10.1265i	0.215360	−	0.373015i
$738$		0			0
$739$	−20.0208	+	11.5590i	−0.736476	+	0.425205i	−0.820787	−	0.571235i	$-0.806465\pi$
$739$	−20.0208	+	11.5590i	−0.736476	+	0.425205i	0.0843103	+	0.996440i	$0.473131\pi$
$740$	−0.223373	+	0.310133i	−0.00821136	+	0.0114007i
$741$		0			0
$742$	25.4265	−	27.7985i	0.933437	−	1.02051i
$743$			25.7365i			0.944181i	0.881550	+	0.472091i	$0.156501\pi$
$743$			25.7365i			0.944181i	−0.881550	+	0.472091i	$0.843499\pi$
$744$		0			0
$745$	5.36479	−	3.09736i	0.196551	−	0.113479i
$746$	5.47451	−	16.9680i	0.200436	−	0.621242i
$747$		0			0
$748$	0.0269891	−	0.267405i	0.000986818	−	0.00977729i
$749$	−5.34187	+	11.6856i	−0.195188	+	0.426983i
$750$		0			0
$751$	19.0832	+	11.0177i	0.696355	+	0.402041i	0.805988	−	0.591931i	$-0.201634\pi$
$751$	19.0832	+	11.0177i	0.696355	+	0.402041i	−0.109633	+	0.993972i	$0.534968\pi$
$752$	9.68028	+	28.9761i	0.353003	+	1.05665i
$753$		0			0
$754$	0.162176	+	0.755306i	0.00590612	+	0.0275066i
$755$	−1.61831			−0.0588962
$756$		0			0
$757$	−5.29374			−0.192404			−0.0962021	−	0.995362i	$-0.530670\pi$
$757$	−5.29374			−0.192404			−0.0962021	+	0.995362i	$0.530670\pi$
$758$	−3.59436	−	16.7400i	−0.130553	−	0.608025i
$759$		0			0
$760$	−2.63243	+	6.01252i	−0.0954883	+	0.218097i
$761$	36.0460	+	20.8112i	1.30667	+	0.754405i	0.981538	−	0.191265i	$-0.0612589\pi$
$761$	36.0460	+	20.8112i	1.30667	+	0.754405i	0.325129	+	0.945670i	$0.394592\pi$
$762$		0			0
$763$	−38.1076	+	27.1150i	−1.37959	+	0.981630i
$764$	29.0899	+	2.93604i	1.05244	+	0.106222i
$765$		0			0
$766$	0.561202	−	1.73942i	0.0202771	−	0.0628477i
$767$	−7.42247	+	4.28537i	−0.268010	+	0.154736i
$768$		0			0
$769$		−	4.29112i		−	0.154742i	−0.997002	−	0.0773709i	$-0.975347\pi$
$769$		−	4.29112i		−	0.154742i	0.997002	−	0.0773709i	$-0.0246526\pi$
$770$	−1.59365	−	5.03855i	−0.0574310	−	0.181577i
$771$		0			0
$772$	0.116277	+	0.0837488i	0.00418491	+	0.00301418i
$773$	−40.4039	+	23.3272i	−1.45323	+	0.839021i	−0.998663	−	0.0516925i	$-0.983538\pi$
$773$	−40.4039	+	23.3272i	−1.45323	+	0.839021i	−0.454564	+	0.890714i	$0.650205\pi$
$774$		0			0
$775$	−2.55320	+	4.42228i	−0.0917138	+	0.158853i
$776$	14.2730	+	19.3913i	0.512370	+	0.696105i
$777$		0			0
$778$	−28.6073	−	31.6399i	−1.02562	−	1.13435i
$779$	0.574359	+	0.331606i	0.0205785	+	0.0118810i
$780$		0			0
$781$	−10.0786	−	17.4567i	−0.360642	−	0.624650i
$782$	−0.445682	+	0.0956951i	−0.0159376	+	0.00342205i
$783$		0			0
$784$	−14.2784	+	24.0858i	−0.509942	+	0.860209i
$785$	−4.62264			−0.164989
$786$		0			0
$787$	−21.1595	−	36.6493i	−0.754254	−	1.30641i	−0.945744	−	0.324912i	$-0.894665\pi$
$787$	−21.1595	−	36.6493i	−0.754254	−	1.30641i	0.191490	−	0.981495i	$-0.438668\pi$
$788$	3.48178	−	1.56745i	0.124033	−	0.0558382i
$789$		0			0
$790$	−6.40124	−	7.07984i	−0.227746	−	0.251889i
$791$	−4.38197	−	46.0703i	−0.155805	−	1.63807i
$792$		0			0
$793$	−8.15216	+	14.1200i	−0.289492	+	0.501414i
$794$	5.90714	+	1.90587i	0.209637	+	0.0676367i
$795$		0			0
$796$	0.947053	+	0.682115i	0.0335674	+	0.0241769i
$797$		−	7.72777i		−	0.273732i	−0.990590	−	0.136866i	$-0.956297\pi$
$797$		−	7.72777i		−	0.273732i	0.990590	−	0.136866i	$-0.0437029\pi$
$798$		0			0
$799$		−	0.353906i		−	0.0125203i
$800$	26.9411	−	0.278232i	0.952513	−	0.00983700i
$801$		0			0
$802$	5.69804	−	17.6608i	0.201205	−	0.623625i
$803$	11.9590	−	20.7136i	0.422023	−	0.730966i
$804$		0			0
$805$	−7.30294	+	5.19633i	−0.257395	+	0.183146i
$806$	1.31888	−	1.19246i	0.0464555	−	0.0420027i
$807$		0			0
$808$	−20.7292	+	47.3460i	−0.729251	+	1.66562i
$809$	1.09641	+	1.89904i	0.0385477	+	0.0667666i	0.884656	−	0.466245i	$-0.154394\pi$
$809$	1.09641	+	1.89904i	0.0385477	+	0.0667666i	−0.846108	+	0.533012i	$0.821060\pi$
$810$		0			0
$811$	4.83311			0.169713			0.0848567	−	0.996393i	$-0.472957\pi$
$811$	4.83311			0.169713			0.0848567	+	0.996393i	$0.472957\pi$
$812$	1.22014	+	2.14173i	0.0428185	+	0.0751601i
$813$		0			0
$814$	−0.337850	−	1.57347i	−0.0118416	−	0.0551502i
$815$	3.35003	+	5.80242i	0.117346	+	0.203250i
$816$		0			0
$817$	−26.7135	−	15.4231i	−0.934589	−	0.539585i
$818$	16.7886	−	15.1794i	0.587000	−	0.530737i
$819$		0			0
$820$	−0.0136139	+	0.134885i	−0.000475418	+	0.00471040i
$821$	−19.6615	+	34.0547i	−0.686191	+	1.18852i	0.286870	+	0.957970i	$0.407385\pi$
$821$	−19.6615	+	34.0547i	−0.686191	+	1.18852i	−0.973061	+	0.230548i	$0.925948\pi$
$822$		0			0
$823$	−13.3558	+	7.71099i	−0.465555	+	0.268788i	−0.714377	−	0.699761i	$-0.753290\pi$
$823$	−13.3558	+	7.71099i	−0.465555	+	0.268788i	0.248822	+	0.968549i	$0.419956\pi$
$824$	−5.62914	−	50.5431i	−0.196101	−	1.76075i
$825$		0			0
$826$	−18.4571	+	20.1789i	−0.642205	+	0.702114i
$827$		−	10.7035i		−	0.372196i	−0.982531	−	0.186098i	$-0.940416\pi$
$827$		−	10.7035i		−	0.372196i	0.982531	−	0.186098i	$-0.0595843\pi$
$828$		0			0
$829$	−23.7020	+	13.6843i	−0.823203	+	0.475276i	−0.851520	−	0.524323i	$-0.824319\pi$
$829$	−23.7020	+	13.6843i	−0.823203	+	0.475276i	0.0283169	+	0.999599i	$0.490985\pi$
$830$	4.16158	+	1.34268i	0.144451	+	0.0466052i
$831$		0			0
$832$	−8.95740	−	2.78820i	−0.310542	−	0.0966634i
$833$	0.245294	−	0.212231i	0.00849893	−	0.00735336i
$834$		0			0
$835$	−4.64525	−	2.68194i	−0.160756	−	0.0928123i
$836$	−11.3452	−	25.2011i	−0.392383	−	0.871599i
$837$		0			0
$838$	25.2498	−	5.42153i	0.872239	−	0.187284i
$839$	9.67322			0.333957			0.166978	−	0.985961i	$-0.446599\pi$
$839$	9.67322			0.333957			0.166978	+	0.985961i	$0.446599\pi$
$840$		0			0
$841$	−28.7830			−0.992518
$842$	−31.3547	+	6.73237i	−1.08056	+	0.232013i
$843$		0			0
$844$	−4.01640	−	8.92161i	−0.138250	−	0.307095i
$845$	−4.90294	−	2.83071i	−0.168666	−	0.0973794i
$846$		0			0
$847$	−6.23132	−	2.84854i	−0.214111	−	0.0978769i
$848$	39.4620	+	8.04775i	1.35513	+	0.276361i
$849$		0			0
$850$	−0.297036	−	0.0958349i	−0.0101882	−	0.00328711i
$851$	−2.36385	+	1.36477i	−0.0810316	+	0.0467836i
$852$		0			0
$853$		−	40.8757i		−	1.39956i	−0.714359	−	0.699779i	$-0.753282\pi$
$853$		−	40.8757i		−	1.39956i	0.714359	−	0.699779i	$-0.246718\pi$
$854$	−11.2140	+	50.7997i	−0.383734	+	1.73833i
$855$		0			0
$856$	−13.6514	+	1.52040i	−0.466596	+	0.0519663i
$857$	−21.4624	+	12.3913i	−0.733141	+	0.423279i	−0.819570	−	0.572979i	$-0.805788\pi$
$857$	−21.4624	+	12.3913i	−0.733141	+	0.423279i	0.0864289	+	0.996258i	$0.472454\pi$
$858$		0			0
$859$	2.84935	−	4.93522i	0.0972185	−	0.168387i	−0.813314	−	0.581825i	$-0.802339\pi$
$859$	2.84935	−	4.93522i	0.0972185	−	0.168387i	0.910532	+	0.413438i	$0.135672\pi$
$860$	0.633185	−	6.27354i	0.0215914	−	0.213926i
$861$		0			0
$862$	−25.3891	+	22.9556i	−0.864755	+	0.781869i
$863$	−11.4093	−	6.58713i	−0.388375	−	0.224229i	0.293081	−	0.956088i	$-0.405320\pi$
$863$	−11.4093	−	6.58713i	−0.388375	−	0.224229i	−0.681456	+	0.731859i	$0.738653\pi$
$864$		0			0
$865$	−4.27658	−	7.40726i	−0.145408	−	0.251854i
$866$	9.21861	+	42.9339i	0.313261	+	1.45895i
$867$		0			0
$868$	2.86486	−	4.89674i	0.0972398	−	0.166206i
$869$	40.1896			1.36334
$870$		0			0
$871$	2.36410	+	4.09474i	0.0801044	+	0.138745i
$872$	−45.8015	−	20.0530i	−1.55103	−	0.679081i
$873$		0			0
$874$	−34.7696	+	31.4369i	−1.17610	+	1.06337i
$875$	−12.5230	+	1.19112i	−0.423353	+	0.0402672i
$876$		0			0
$877$	14.6431	−	25.3625i	0.494461	−	0.856432i	−0.505519	−	0.862816i	$-0.668699\pi$
$877$	14.6431	−	25.3625i	0.494461	−	0.856432i	0.999980	+	0.00638414i	$0.00203215\pi$
$878$	−15.3250	+	47.4992i	−0.517195	+	1.60302i
$879$		0			0
$880$	3.74540	−	4.22944i	0.126257	−	0.142574i
$881$		−	41.7794i		−	1.40758i	−0.710406	−	0.703792i	$-0.751489\pi$
$881$		−	41.7794i		−	1.40758i	0.710406	−	0.703792i	$-0.248511\pi$
$882$		0			0
$883$			15.9004i			0.535090i	0.963545	+	0.267545i	$0.0862124\pi$
$883$			15.9004i			0.535090i	−0.963545	+	0.267545i	$0.913788\pi$
$884$	0.0881844	+	0.0635148i	0.00296596	+	0.00213624i
$885$		0			0
$886$	20.1804	+	6.51097i	0.677975	+	0.218740i
$887$	−2.54513	+	4.40830i	−0.0854572	+	0.148016i	−0.905586	−	0.424163i	$-0.860568\pi$
$887$	−2.54513	+	4.40830i	−0.0854572	+	0.148016i	0.820129	+	0.572179i	$0.193902\pi$
$888$		0			0
$889$	−18.7123	+	1.77982i	−0.627589	+	0.0596931i
$890$	−4.89009	−	5.40849i	−0.163916	−	0.181293i
$891$		0			0
$892$	33.4439	−	15.0560i	1.11978	−	0.504113i
$893$	−18.1962	−	31.5168i	−0.608913	−	1.05467i
$894$		0			0
$895$	−5.03710			−0.168372
$896$	−29.9329	+	0.136728i	−0.999990	+	0.00456777i
$897$		0			0
$898$	7.13039	−	1.53101i	0.237944	−	0.0510905i
$899$	−0.249714	−	0.432517i	−0.00832842	−	0.0144253i
$900$		0			0
$901$	−0.404046	−	0.233276i	−0.0134607	−	0.00777156i
$902$	−0.382847	−	0.423432i	−0.0127474	−	0.0140987i
$903$		0			0
$904$	39.8439	−	29.3272i	1.32519	−	0.975409i
$905$	−2.77972	+	4.81461i	−0.0924009	+	0.160043i
$906$		0			0
$907$	−30.1139	+	17.3863i	−0.999916	+	0.577302i	−0.908223	−	0.418486i	$-0.862561\pi$
$907$	−30.1139	+	17.3863i	−0.999916	+	0.577302i	−0.0916923	+	0.995787i	$0.529228\pi$
$908$	26.1472	+	18.8325i	0.867724	+	0.624978i
$909$		0			0
$910$	2.08662	+	0.460619i	0.0691709	+	0.0152694i
$911$			26.6242i			0.882098i	0.897483	+	0.441049i	$0.145394\pi$
$911$			26.6242i			0.882098i	−0.897483	+	0.441049i	$0.854606\pi$
$912$		0			0
$913$	−15.9458	+	9.20632i	−0.527730	+	0.304685i
$914$	11.0645	−	34.2939i	0.365982	−	1.13434i
$915$		0			0
$916$	27.7400	+	2.79979i	0.916556	+	0.0925076i
$917$	35.3521	+	16.1606i	1.16743	+	0.533669i
$918$		0			0
$919$	1.74511	+	1.00754i	0.0575659	+	0.0332357i	0.528507	−	0.848929i	$-0.322752\pi$
$919$	1.74511	+	1.00754i	0.0575659	+	0.0332357i	−0.470941	+	0.882165i	$0.656085\pi$
$920$	−8.77740	−	3.84296i	−0.289382	−	0.126699i
$921$		0			0
$922$	0.344966	+	1.60661i	0.0113609	+	0.0529110i
$923$	8.15076			0.268285
$924$		0			0
$925$	−1.86891			−0.0614494
$926$	−6.92963	−	32.2734i	−0.227722	−	1.06057i
$927$		0			0
$928$	−1.29391	+	2.29554i	−0.0424747	+	0.0753549i
$929$	−30.2534	−	17.4668i	−0.992581	−	0.573067i	−0.0865362	−	0.996249i	$-0.527580\pi$
$929$	−30.2534	−	17.4668i	−0.992581	−	0.573067i	−0.906045	+	0.423182i	$0.860913\pi$
$930$		0			0
$931$	10.9325	−	31.5119i	0.358298	−	1.03276i
$932$	−0.733949	+	7.27189i	−0.0240413	+	0.238199i
$933$		0			0
$934$	7.88631	−	24.4432i	0.258048	−	0.799807i
$935$	−0.0566772	+	0.0327226i	−0.00185354	+	0.00107014i
$936$		0			0
$937$			45.1738i			1.47576i	0.674931	+	0.737881i	$0.264174\pi$
$937$			45.1738i			1.47576i	−0.674931	+	0.737881i	$0.735826\pi$
$938$	11.1321	+	10.1822i	0.363474	+	0.332460i
$939$		0			0
$940$	4.34773	−	6.03641i	0.141807	−	0.196886i
$941$	−0.227297	+	0.131230i	−0.00740966	+	0.00427797i	−0.503700	−	0.863878i	$-0.668028\pi$
$941$	−0.227297	+	0.131230i	−0.00740966	+	0.00427797i	0.496291	+	0.868156i	$0.334695\pi$
$942$		0			0
$943$	−0.484096	+	0.838480i	−0.0157643	+	0.0273047i
$944$	−28.6455	−	5.84186i	−0.932330	−	0.190136i
$945$		0			0
$946$	17.8063	+	19.6939i	0.578931	+	0.640304i
$947$	26.5793	+	15.3456i	0.863711	+	0.498664i	0.865253	−	0.501335i	$-0.167157\pi$
$947$	26.5793	+	15.3456i	0.863711	+	0.498664i	−0.00154195	+	0.999999i	$0.500491\pi$
$948$		0			0
$949$	4.83572	+	8.37571i	0.156974	+	0.271887i
$950$	−31.3796	+	6.73771i	−1.01809	+	0.218600i
$951$		0			0
$952$	0.329389	+	0.108372i	0.0106755	+	0.00351234i
$953$	−33.2031			−1.07555			−0.537777	−	0.843087i	$-0.680736\pi$
$953$	−33.2031			−1.07555			−0.537777	+	0.843087i	$0.680736\pi$
$954$		0			0
$955$	−3.55977	−	6.16570i	−0.115191	−	0.199517i
$956$	−13.4005	−	29.7664i	−0.433402	−	0.962714i
$957$		0			0
$958$	10.2750	+	11.3643i	0.331971	+	0.367163i
$959$	−25.7413	+	18.3159i	−0.831230	+	0.591453i
$960$		0			0
$961$	14.9253	−	25.8513i	0.481460	−	0.833913i
$962$	0.619312	+	0.199814i	0.0199674	+	0.00644225i
$963$		0			0
$964$	−3.13952	+	4.35893i	−0.101117	+	0.140392i
$965$		−	0.0348938i		−	0.00112327i
$966$		0			0
$967$			31.4179i			1.01033i	0.863022	+	0.505166i	$0.168569\pi$
$967$			31.4179i			1.01033i	−0.863022	+	0.505166i	$0.831431\pi$
$968$	−0.810750	−	7.27959i	−0.0260585	−	0.233975i
$969$		0			0
$970$	1.80026	−	5.57983i	0.0578030	−	0.179157i
$971$	−0.674219	+	1.16778i	−0.0216367	+	0.0374759i	−0.876641	−	0.481145i	$-0.840221\pi$
$971$	−0.674219	+	1.16778i	−0.0216367	+	0.0374759i	0.855004	+	0.518621i	$0.173554\pi$
$972$		0			0
$973$	2.35441	+	24.7533i	0.0754788	+	0.793554i
$974$	18.5709	−	16.7909i	0.595048	−	0.538014i
$975$		0			0
$976$	−52.7488	+	17.6222i	−1.68845	+	0.564074i
$977$	−28.2780	−	48.9789i	−0.904694	−	1.56698i	−0.821328	−	0.570456i	$-0.806766\pi$
$977$	−28.2780	−	48.9789i	−0.904694	−	1.56698i	−0.0833656	−	0.996519i	$-0.526567\pi$
$978$		0			0
$979$	30.7020			0.981240
$980$	6.79111	−	0.606492i	0.216934	−	0.0193737i
$981$		0			0
$982$	−0.851532	−	3.96585i	−0.0271735	−	0.126555i
$983$	−25.5636	−	44.2775i	−0.815353	−	1.41223i	−0.909074	−	0.416634i	$-0.863210\pi$
$983$	−25.5636	−	44.2775i	−0.815353	−	1.41223i	0.0937214	−	0.995598i	$-0.470124\pi$
$984$		0			0
$985$	−0.805216	−	0.464892i	−0.0256563	−	0.0148127i
$986$	0.0226430	−	0.0204727i	0.000721099	−	0.000651982i
$987$		0			0
$988$	11.1188	+	1.12222i	0.353737	+	0.0357025i
$989$	22.5154	−	38.9978i	0.715948	−	1.24006i
$990$		0			0
$991$	6.61700	−	3.82033i	0.210196	−	0.121357i	−0.391207	−	0.920303i	$-0.627942\pi$
$991$	6.61700	−	3.82033i	0.210196	−	0.121357i	0.601402	+	0.798946i	$0.294609\pi$
$992$	6.06461	−	0.0626317i	0.192552	−	0.00198856i
$993$		0			0
$994$	24.7961	−	7.84279i	0.786485	−	0.248758i
$995$		−	0.284202i		−	0.00900981i
$996$		0			0
$997$	−13.7883	+	7.96070i	−0.436681	+	0.252118i	−0.702189	−	0.711991i	$-0.747794\pi$
$997$	−13.7883	+	7.96070i	−0.436681	+	0.252118i	0.265508	+	0.964109i	$0.414460\pi$
$998$	−38.2190	−	12.3309i	−1.20980	−	0.390328i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.c.271.1	yes	32
3.2	odd	2		756.2.bf.b.271.16	yes	32
4.3	odd	2		756.2.bf.b.271.11	✓	32
7.3	odd	6		756.2.bf.b.703.11	yes	32
12.11	even	2	inner	756.2.bf.c.271.6	yes	32
21.17	even	6	inner	756.2.bf.c.703.6	yes	32
28.3	even	6	inner	756.2.bf.c.703.1	yes	32
84.59	odd	6		756.2.bf.b.703.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.11	✓	32	4.3	odd	2
756.2.bf.b.271.16	yes	32	3.2	odd	2
756.2.bf.b.703.11	yes	32	7.3	odd	6
756.2.bf.b.703.16	yes	32	84.59	odd	6
756.2.bf.c.271.1	yes	32	1.1	even	1	trivial
756.2.bf.c.271.6	yes	32	12.11	even	2	inner
756.2.bf.c.703.1	yes	32	28.3	even	6	inner
756.2.bf.c.703.6	yes	32	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.38270 + 0.296888i) q^{2} +(1.82372 - 0.821014i) q^{4} +(-0.421763 - 0.243505i) q^{5} +(0.250520 + 2.63386i) q^{7} +(-2.27790 + 1.67665i) q^{8} +O(q^{10})\)	\(q+(-1.38270 + 0.296888i) q^{2} +(1.82372 - 0.821014i) q^{4} +(-0.421763 - 0.243505i) q^{5} +(0.250520 + 2.63386i) q^{7} +(-2.27790 + 1.67665i) q^{8} +(0.655465 + 0.211478i) q^{10} +(-2.51153 + 1.45003i) q^{11} -1.17266i q^{13} +(-1.12836 - 3.56747i) q^{14} +(2.65187 - 2.99459i) q^{16} +(-0.0401295 + 0.0231688i) q^{17} +(-2.38246 + 4.12654i) q^{19} +(-0.969097 - 0.0978105i) q^{20} +(3.04219 - 2.75060i) q^{22} +(-6.02414 - 3.47804i) q^{23} +(-2.38141 - 4.12472i) q^{25} +(0.348150 + 1.62144i) q^{26} +(2.61932 + 4.59774i) q^{28} +0.465824 q^{29} +(-0.536070 - 0.928500i) q^{31} +(-2.77769 + 4.92793i) q^{32} +(0.0486085 - 0.0439494i) q^{34} +(0.535699 - 1.17187i) q^{35} +(0.196198 - 0.339825i) q^{37} +(2.06910 - 6.41309i) q^{38} +(1.36901 - 0.152471i) q^{40} -0.139187i q^{41} +6.47359i q^{43} +(-3.38982 + 4.70644i) q^{44} +(9.36217 + 3.02059i) q^{46} +(-3.81879 + 6.61433i) q^{47} +(-6.87448 + 1.31967i) q^{49} +(4.51736 + 4.99624i) q^{50} +(-0.962774 - 2.13861i) q^{52} +(5.03428 + 8.71964i) q^{53} +1.41236 q^{55} +(-4.98674 - 5.57964i) q^{56} +(-0.644094 + 0.138297i) q^{58} +(-3.65438 - 6.32958i) q^{59} +(-12.0409 - 6.95182i) q^{61} +(1.01688 + 1.12468i) q^{62} +(2.37766 - 7.63850i) q^{64} +(-0.285550 + 0.494587i) q^{65} +(-3.49182 + 2.01601i) q^{67} +(-0.0541628 + 0.0752000i) q^{68} +(-0.392797 + 1.77939i) q^{70} +6.95063i q^{71} +(-7.14246 + 4.12370i) q^{73} +(-0.170393 + 0.528124i) q^{74} +(-0.956981 + 9.48167i) q^{76} +(-4.44837 - 6.25176i) q^{77} +(-12.0015 - 6.92909i) q^{79} +(-1.84766 + 0.617263i) q^{80} +(0.0413228 + 0.192453i) q^{82} +6.34905 q^{83} +0.0225668 q^{85} +(-1.92193 - 8.95103i) q^{86} +(3.28981 - 7.51399i) q^{88} +(-9.16832 - 5.29333i) q^{89} +(3.08864 - 0.293776i) q^{91} +(-13.8418 - 1.39705i) q^{92} +(3.31652 - 10.2794i) q^{94} +(2.00967 - 1.16028i) q^{95} -8.51277i q^{97} +(9.11354 - 3.86566i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) \) 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

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