LMFDB - Embedded newform 756.2.bf.c.271.6

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			271.6
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.434237 - 1.34590i) q^{2} +(-1.62288 + 1.16888i) q^{4} +(0.421763 + 0.243505i) q^{5} +(-0.250520 - 2.63386i) q^{7} +(2.27790 + 1.67665i) q^{8} +O(q^{10})$	\(q+(-0.434237 - 1.34590i) q^{2} +(-1.62288 + 1.16888i) q^{4} +(0.421763 + 0.243505i) q^{5} +(-0.250520 - 2.63386i) q^{7} +(2.27790 + 1.67665i) q^{8} +(0.144587 - 0.673389i) q^{10} +(-2.51153 + 1.45003i) q^{11} -1.17266i q^{13} +(-3.43612 + 1.48090i) q^{14} +(1.26745 - 3.79388i) q^{16} +(0.0401295 - 0.0231688i) q^{17} +(2.38246 - 4.12654i) q^{19} +(-0.969097 + 0.0978105i) q^{20} +(3.04219 + 2.75060i) q^{22} +(-6.02414 - 3.47804i) q^{23} +(-2.38141 - 4.12472i) q^{25} +(-1.57829 + 0.509215i) q^{26} +(3.48523 + 3.98161i) q^{28} -0.465824 q^{29} +(0.536070 + 0.928500i) q^{31} +(-5.65655 - 0.0584175i) q^{32} +(-0.0486085 - 0.0439494i) q^{34} +(0.535699 - 1.17187i) q^{35} +(0.196198 - 0.339825i) q^{37} +(-6.58845 - 1.41465i) q^{38} +(0.552461 + 1.26183i) q^{40} +0.139187i q^{41} -6.47359i q^{43} +(2.38099 - 5.28889i) q^{44} +(-2.06518 + 9.61817i) q^{46} +(-3.81879 + 6.61433i) q^{47} +(-6.87448 + 1.31967i) q^{49} +(-4.51736 + 4.99624i) q^{50} +(1.37070 + 1.90309i) q^{52} +(-5.03428 - 8.71964i) q^{53} -1.41236 q^{55} +(3.84542 - 6.41972i) q^{56} +(0.202278 + 0.626950i) q^{58} +(-3.65438 - 6.32958i) q^{59} +(-12.0409 - 6.95182i) q^{61} +(1.01688 - 1.12468i) q^{62} +(2.37766 + 7.63850i) q^{64} +(0.285550 - 0.494587i) q^{65} +(3.49182 - 2.01601i) q^{67} +(-0.0380437 + 0.0845064i) q^{68} +(-1.80984 - 0.212126i) q^{70} +6.95063i q^{71} +(-7.14246 + 4.12370i) q^{73} +(-0.542565 - 0.116498i) q^{74} +(0.956981 + 9.48167i) q^{76} +(4.44837 + 6.25176i) q^{77} +(12.0015 + 6.92909i) q^{79} +(1.45840 - 1.29149i) q^{80} +(0.187331 - 0.0604400i) q^{82} +6.34905 q^{83} +0.0225668 q^{85} +(-8.71279 + 2.81107i) q^{86} +(-8.15221 - 0.907937i) q^{88} +(9.16832 + 5.29333i) q^{89} +(-3.08864 + 0.293776i) q^{91} +(13.8418 - 1.39705i) q^{92} +(10.5605 + 2.26750i) q^{94} +(2.00967 - 1.16028i) q^{95} -8.51277i q^{97} +(4.76129 + 8.67929i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.434237	−	1.34590i	−0.307052	−	0.951693i
$2$	−0.434237	−	1.34590i	−0.307052	−	0.951693i
$3$		0			0
$3$		0			0
$4$	−1.62288	+	1.16888i	−0.811438	+	0.584438i
$5$	0.421763	+	0.243505i	0.188618	+	0.108899i	0.591336	−	0.806426i	$-0.298601\pi$
$5$	0.421763	+	0.243505i	0.188618	+	0.108899i	−0.402717	+	0.915324i	$0.631934\pi$
$6$		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
$10$	0.144587	−	0.673389i	0.0457226	−	0.212944i
$11$	−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	$-0.0519942\pi$
$14$	−3.43612	+	1.48090i	−0.918343	+	0.395786i
$15$		0			0
$16$	1.26745	−	3.79388i	0.316864	−	0.948471i
$17$	0.0401295	−	0.0231688i	0.00973282	−	0.00561925i	−0.495126	−	0.868821i	$-0.664878\pi$
$17$	0.0401295	−	0.0231688i	0.00973282	−	0.00561925i	0.504859	+	0.863202i	$0.331545\pi$
$18$		0			0
$19$	2.38246	−	4.12654i	0.546574	−	0.946693i	−0.451932	−	0.892052i	$-0.649265\pi$
$19$	2.38246	−	4.12654i	0.546574	−	0.946693i	0.998506	−	0.0546412i	$-0.0174015\pi$
$20$	−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
$26$	−1.57829	+	0.509215i	−0.309527	+	0.0998652i
$27$		0			0
$28$	3.48523	+	3.98161i	0.658646	+	0.752453i
$29$	−0.465824			−0.0865013			−0.0432506	−	0.999064i	$-0.513771\pi$
$29$	−0.465824			−0.0865013			−0.0432506	+	0.999064i	$0.513771\pi$
$30$		0			0
$31$	0.536070	+	0.928500i	0.0962810	+	0.166764i	0.910142	−	0.414295i	$-0.135972\pi$
$31$	0.536070	+	0.928500i	0.0962810	+	0.166764i	−0.813862	+	0.581059i	$0.802639\pi$
$32$	−5.65655	−	0.0584175i	−0.999947	−	0.0103269i
$33$		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	$0.156398\pi$
$38$	−6.58845	−	1.41465i	−1.06879	−	0.229486i
$39$		0			0
$40$	0.552461	+	1.26183i	0.0873517	+	0.199513i
$41$			0.139187i			0.0217373i	0.999941	+	0.0108686i	$0.00345967\pi$
$41$			0.139187i			0.0217373i	−0.999941	+	0.0108686i	$0.996540\pi$
$42$		0			0
$43$		−	6.47359i		−	0.987213i	−0.869685	−	0.493607i	$-0.835678\pi$
$43$		−	6.47359i		−	0.987213i	0.869685	−	0.493607i	$-0.164322\pi$
$44$	2.38099	−	5.28889i	0.358948	−	0.797330i
$45$		0			0
$46$	−2.06518	+	9.61817i	−0.304494	+	1.41812i
$47$	−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
$52$	1.37070	+	1.90309i	0.190082	+	0.263911i
$53$	−5.03428	−	8.71964i	−0.691512	−	1.19773i	−0.971342	−	0.237685i	$-0.923612\pi$
$53$	−5.03428	−	8.71964i	−0.691512	−	1.19773i	0.279830	−	0.960049i	$-0.409722\pi$
$54$		0			0
$55$	−1.41236			−0.190443
$56$	3.84542	−	6.41972i	0.513866	−	0.857871i
$57$		0			0
$58$	0.202278	+	0.626950i	0.0265604	+	0.0823226i
$59$	−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	−0.271300	−	0.962495i	$-0.587454\pi$
$67$	3.49182	−	2.01601i	0.426594	−	0.246294i	0.697895	+	0.716200i	$0.254120\pi$
$68$	−0.0380437	+	0.0845064i	−0.00461348	+	0.0102479i
$69$		0			0
$70$	−1.80984	−	0.212126i	−0.216317	−	0.0253540i
$71$			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	$0.493656\pi$
$74$	−0.542565	−	0.116498i	−0.0630719	−	0.0135426i
$75$		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	0.988288	−	0.152598i	$-0.0487640\pi$
$79$	12.0015	+	6.92909i	1.35028	+	0.779584i	0.361990	+	0.932182i	$0.382097\pi$
$80$	1.45840	−	1.29149i	0.163054	−	0.144393i
$81$		0			0
$82$	0.187331	−	0.0604400i	0.0206872	−	0.00667448i
$83$	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
$86$	−8.71279	+	2.81107i	−0.939524	+	0.303126i
$87$		0			0
$88$	−8.15221	−	0.907937i	−0.869029	−	0.0967864i
$89$	9.16832	+	5.29333i	0.971840	+	0.561092i	0.899797	−	0.436309i	$-0.143715\pi$
$89$	9.16832	+	5.29333i	0.971840	+	0.561092i	0.0720434	+	0.997401i	$0.477048\pi$
$90$		0			0
$91$	−3.08864	+	0.293776i	−0.323777	+	0.0307961i
$92$	13.8418	−	1.39705i	1.44311	−	0.145653i
$93$		0			0
$94$	10.5605	+	2.26750i	1.08923	+	0.233875i
$95$	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	$-0.142252\pi$
$98$	4.76129	+	8.67929i	0.480963	+	0.876741i
$99$		0			0
$100$	8.68603	+	3.91034i	0.868603	+	0.391034i
$101$	−15.8252	+	9.13670i	−1.57467	+	0.909136i	−0.579085	+	0.815267i	$0.696590\pi$
$101$	−15.8252	+	9.13670i	−1.57467	+	0.909136i	−0.995585	+	0.0938690i	$0.970077\pi$
$102$		0			0
$103$	8.99009	−	15.5713i	0.885820	−	1.53429i	0.0410493	−	0.999157i	$-0.486930\pi$
$103$	8.99009	−	15.5713i	0.885820	−	1.53429i	0.844771	−	0.535128i	$-0.179737\pi$
$104$	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	$0.511985\pi$
$110$	0.613299	+	1.90089i	0.0584758	+	0.181243i
$111$		0			0
$112$	−10.3101	−	2.38786i	−0.974213	−	0.225632i
$113$	17.4915			1.64546			0.822732	−	0.568430i	$-0.192449\pi$
$113$	17.4915			1.64546			0.822732	+	0.568430i	$0.192449\pi$
$114$		0			0
$115$	−1.69384	−	2.93382i	−0.157951	−	0.273580i
$116$	0.755974	−	0.544490i	0.0701904	−	0.0505546i
$117$		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
$122$	−4.12783	+	19.2246i	−0.373716	+	1.74051i
$123$		0			0
$124$	−1.95528	−	0.880241i	−0.175589	−	0.0790480i
$125$		−	4.75459i		−	0.425264i
$126$		0			0
$127$		−	7.10449i		−	0.630421i	−0.949022	−	0.315211i	$-0.897925\pi$
$127$		−	7.10449i		−	0.630421i	0.949022	−	0.315211i	$-0.102075\pi$
$128$	9.24817	−	6.51701i	0.817430	−	0.576028i
$129$		0			0
$130$	−0.789659	−	0.169553i	−0.0692577	−	0.0148707i
$131$	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
$136$	0.130257	+	0.0145071i	0.0111694	+	0.00124397i
$137$	−5.97043	−	10.3411i	−0.510088	−	0.883498i	−0.999932	−	0.0116880i	$-0.996279\pi$
$137$	−5.97043	−	10.3411i	−0.510088	−	0.883498i	0.489844	−	0.871810i	$-0.337054\pi$
$138$		0			0
$139$	−9.39809			−0.797135			−0.398568	−	0.917139i	$-0.630493\pi$
$139$	−9.39809			−0.797135			−0.398568	+	0.917139i	$0.630493\pi$
$140$	0.500398	+	2.52797i	0.0422913	+	0.213652i
$141$		0			0
$142$	9.35483	−	3.01822i	0.785040	−	0.253283i
$143$	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	$-0.658882\pi$
$149$	6.35996	−	11.0158i	0.521028	−	0.902447i	0.999701	−	0.0244538i	$-0.00778465\pi$
$150$		0			0
$151$	−2.87775	+	1.66147i	−0.234188	+	0.135209i	−0.612503	−	0.790468i	$-0.709837\pi$
$151$	−2.87775	+	1.66147i	−0.234188	+	0.135209i	0.378314	+	0.925677i	$0.376504\pi$
$152$	12.3458	−	5.40529i	1.00138	−	0.438427i
$153$		0			0
$154$	6.48258	−	8.70180i	0.522381	−	0.701211i
$155$			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	$0.209681\pi$
$158$	4.11433	−	19.1617i	0.327318	−	1.52442i
$159$		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	0.887824	−	0.460183i	$-0.152216\pi$
$163$	11.9144	+	6.87876i	0.933205	+	0.538786i	0.0453814	+	0.998970i	$0.485550\pi$
$164$	−0.162692	−	0.225883i	−0.0127041	−	0.0176385i
$165$		0			0
$166$	−2.75699	−	8.54517i	−0.213984	−	0.663234i
$167$	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
$170$	−0.00979936	−	0.0303726i	−0.000751576	−	0.00232947i
$171$		0			0
$172$	7.56683	+	10.5058i	0.576965	+	0.801063i
$173$	−15.2097	−	8.78130i	−1.15637	−	0.667630i	−0.205938	−	0.978565i	$-0.566025\pi$
$173$	−15.2097	−	8.78130i	−1.15637	−	0.667630i	−0.950431	+	0.310935i	$0.899358\pi$
$174$		0			0
$175$	−10.2674	+	7.30564i	−0.776140	+	0.552254i
$176$	2.31800	+	11.3663i	0.174726	+	0.856767i
$177$		0			0
$178$	3.14305	−	14.6382i	0.235582	−	1.09718i
$179$	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	$-0.139463\pi$
$182$	1.73659	+	4.02942i	0.128725	+	0.298681i
$183$		0			0
$184$	−7.89093	−	18.0230i	−0.581727	−	1.32868i
$185$	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	$0.832513\pi$
$194$	−11.4573	+	3.69656i	−0.822587	+	0.265398i
$195$		0			0
$196$	9.61390	−	10.1771i	0.686707	−	0.726934i
$197$	−1.90917			−0.136023			−0.0680113	−	0.997685i	$-0.521665\pi$
$197$	−1.90917			−0.136023			−0.0680113	+	0.997685i	$0.521665\pi$
$198$		0			0
$199$	−0.291782	−	0.505382i	−0.0206839	−	0.0358256i	0.855498	−	0.517806i	$-0.173251\pi$
$199$	−0.291782	−	0.505382i	−0.0206839	−	0.0358256i	−0.876182	+	0.481980i	$0.839918\pi$
$200$	1.49112	−	13.3885i	0.105438	−	0.946711i
$201$		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
$206$	−24.8612	−	5.33810i	−1.73216	−	0.371923i
$207$		0			0
$208$	−4.44895	−	1.48630i	−0.308479	−	0.103056i
$209$			13.8186i			0.955850i
$210$		0			0
$211$			4.89200i			0.336779i	0.985721	+	0.168390i	$0.0538567\pi$
$211$			4.89200i			0.336779i	−0.985721	+	0.168390i	$0.946143\pi$
$212$	18.3622	+	8.26643i	1.26112	+	0.567741i
$213$		0			0
$214$	1.44179	−	6.71487i	0.0985589	−	0.459019i
$215$	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
$220$	2.29209	−	1.65087i	0.154532	−	0.111302i
$221$	−0.0271692	−	0.0470584i	−0.00182760	−	0.00316549i
$222$		0			0
$223$	−18.3383			−1.22803			−0.614013	−	0.789296i	$-0.710446\pi$
$223$	−18.3383			−1.22803			−0.614013	+	0.789296i	$0.710446\pi$
$224$	1.26321	+	14.9132i	0.0844021	+	0.996432i
$225$		0			0
$226$	−7.59547	−	23.5418i	−0.505243	−	1.56598i
$227$	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	−0.799946	−	0.600072i	$-0.795139\pi$
$233$	1.82721	−	3.16482i	0.119704	−	0.207334i	0.919651	+	0.392738i	$0.128472\pi$
$234$		0			0
$235$	−3.22125	+	1.85979i	−0.210131	+	0.121319i
$236$	13.3291	+	6.00060i	0.867651	+	0.390606i
$237$		0			0
$238$	−0.103579	+	0.139038i	−0.00671405	+	0.00901251i
$239$		−	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	$0.360904\pi$
$242$	3.58069	+	0.768832i	0.230175	+	0.0494224i
$243$		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
$248$	−0.335660	+	3.01383i	−0.0213144	+	0.191379i
$249$		0			0
$250$	−6.39919	+	2.06462i	−0.404720	+	0.130578i
$251$	−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
$254$	−9.56191	+	3.08503i	−0.599967	+	0.193572i
$255$		0			0
$256$	−12.7871	−	9.61715i	−0.799195	−	0.601072i
$257$	20.1221	+	11.6175i	1.25518	+	0.724678i	0.972133	−	0.234428i	$-0.0753217\pi$
$257$	20.1221	+	11.6175i	1.25518	+	0.724678i	0.283046	+	0.959106i	$0.408655\pi$
$258$		0			0
$259$	−0.944203	−	0.431625i	−0.0586699	−	0.0268199i
$260$	0.114699	+	1.13643i	0.00711333	+	0.0704781i
$261$		0			0
$262$	−20.3143	−	4.36180i	−1.25502	−	0.269473i
$263$	−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
$266$	−2.07545	+	17.7075i	−0.127254	+	1.08572i
$267$		0			0
$268$	−3.31034	+	7.35324i	−0.202211	+	0.449171i
$269$	−10.0770	+	5.81796i	−0.614405	+	0.354727i	−0.774688	−	0.632344i	$-0.782093\pi$
$269$	−10.0770	+	5.81796i	−0.614405	+	0.354727i	0.160282	+	0.987071i	$0.448760\pi$
$270$		0			0
$271$	−7.94241	+	13.7567i	−0.482467	+	0.835657i	−0.999797	−	0.0201285i	$-0.993592\pi$
$271$	−7.94241	+	13.7567i	−0.482467	+	0.835657i	0.517330	+	0.855786i	$0.326926\pi$
$272$	−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	$0.686889\pi$
$278$	4.08100	+	12.6489i	0.244762	+	0.758628i
$279$		0			0
$280$	3.18509	−	1.77122i	0.190346	−	0.105851i
$281$	24.2255			1.44517			0.722586	−	0.691281i	$-0.242953\pi$
$281$	24.2255			1.44517			0.722586	+	0.691281i	$0.242953\pi$
$282$		0			0
$283$	15.1171	+	26.1836i	0.898619	+	1.55645i	0.829261	+	0.558861i	$0.188761\pi$
$283$	15.1171	+	26.1836i	0.898619	+	1.55645i	0.0693572	+	0.997592i	$0.477905\pi$
$284$	−8.12443	−	11.2800i	−0.482096	−	0.669345i
$285$		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
$290$	−0.0673522	+	0.313680i	−0.00395506	+	0.0184199i
$291$		0			0
$292$	6.77123	−	15.0409i	0.396256	−	0.880202i
$293$		−	27.6085i		−	1.61290i	−0.591300	−	0.806452i	$-0.701385\pi$
$293$		−	27.6085i		−	1.61290i	0.591300	−	0.806452i	$-0.298615\pi$
$294$		0			0
$295$		−	3.55944i		−	0.207239i
$296$	1.01669	−	0.445131i	0.0590937	−	0.0258727i
$297$		0			0
$298$	−17.5878	−	3.77639i	−1.01884	−	0.218760i
$299$	−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
$304$	−12.6360	−	14.2690i	−0.724722	−	0.818382i
$305$	−3.38561	−	5.86405i	−0.193859	−	0.335774i
$306$		0			0
$307$	−18.3244			−1.04583			−0.522913	−	0.852386i	$-0.675155\pi$
$307$	−18.3244			−1.04583			−0.522913	+	0.852386i	$0.675155\pi$
$308$	−14.5267	−	4.94624i	−0.827735	−	0.281838i
$309$		0			0
$310$	0.702750	−	0.226734i	0.0399135	−	0.0128776i
$311$	−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	−0.940650	−	0.339378i	$-0.889784\pi$
$317$	−3.14099	+	5.44035i	−0.176416	+	0.305561i	0.764235	+	0.644938i	$0.223117\pi$
$318$		0			0
$319$	1.16993	−	0.675459i	0.0655034	−	0.0378184i
$320$	−0.857204	+	3.80061i	−0.0479192	+	0.212461i
$321$		0			0
$322$	25.8503	+	3.02985i	1.44058	+	0.168847i
$323$		−	0.220794i		−	0.0122853i
$324$		0			0
$325$	−4.83692	+	2.79260i	−0.268304	+	0.154905i
$326$	4.08444	−	19.0225i	0.226216	−	1.05356i
$327$		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	0.892407	−	0.451232i	$-0.149015\pi$
$331$	17.2443	+	9.95600i	0.947832	+	0.547231i	0.0554253	+	0.998463i	$0.482349\pi$
$332$	−10.3037	+	7.42126i	−0.565490	+	0.407295i
$333$		0			0
$334$	−4.78264	−	14.8236i	−0.261694	−	0.811109i
$335$	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	$0.230898\pi$
$338$	−5.04794	−	15.6459i	−0.274572	−	0.851022i
$339$		0			0
$340$	−0.0366232	+	0.0263778i	−0.00198617	+	0.00143054i
$341$	−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
$346$	−5.21413	+	24.2838i	−0.280313	+	1.30551i
$347$	−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	$0.952678\pi$
$350$	14.2911	+	10.6464i	0.763892	+	0.569076i
$351$		0			0
$352$	14.2913	−	8.05546i	0.761729	−	0.429358i
$353$	−14.9667	+	8.64101i	−0.796595	+	0.459914i	−0.842279	−	0.539042i	$-0.818787\pi$
$353$	−14.9667	+	8.64101i	−0.796595	+	0.459914i	0.0456841	+	0.998956i	$0.485453\pi$
$354$		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
$362$	−15.3640	+	4.95701i	−0.807514	+	0.260535i
$363$		0			0
$364$	4.66909	−	4.08700i	0.244727	−	0.214217i
$365$	−4.01657			−0.210237
$366$		0			0
$367$	2.54588	+	4.40959i	0.132894	+	0.230179i	0.924791	−	0.380476i	$-0.124240\pi$
$367$	2.54588	+	4.40959i	0.132894	+	0.230179i	−0.791897	+	0.610655i	$0.790906\pi$
$368$	−20.8306	+	18.4466i	−1.08587	+	0.961598i
$369$		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	$0.272498\pi$
$374$	0.185809	+	0.0398963i	0.00960798	+	0.00206299i
$375$		0			0
$376$	−19.7888	+	8.66401i	−1.02053	+	0.446812i
$377$			0.546255i			0.0281336i
$378$		0			0
$379$		−	12.1068i		−	0.621883i	−0.950429	−	0.310942i	$-0.899356\pi$
$379$		−	12.1068i		−	0.621883i	0.950429	−	0.310942i	$-0.100644\pi$
$380$	−1.90521	+	4.23205i	−0.0977355	+	0.217099i
$381$		0			0
$382$	4.34017	−	20.2135i	0.222062	−	1.03421i
$383$	−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
$388$	9.95038	+	13.8152i	0.505154	+	0.701359i
$389$	−15.0809	−	26.1208i	−0.764630	−	1.32438i	−0.940442	−	0.339954i	$-0.889588\pi$
$389$	−15.0809	−	26.1208i	−0.764630	−	1.32438i	0.175812	−	0.984424i	$-0.443745\pi$
$390$		0			0
$391$	−0.322327			−0.0163008
$392$	−17.8720	−	8.52005i	−0.902673	−	0.430327i
$393$		0			0
$394$	0.829031	+	2.56954i	0.0417660	+	0.129452i
$395$	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	−0.654403	−	0.756146i	$-0.727080\pi$
$401$	6.56098	−	11.3640i	0.327640	−	0.567489i	0.982043	+	0.188657i	$0.0604134\pi$
$402$		0			0
$403$	1.08882	−	0.628630i	0.0542379	−	0.0313143i
$404$	15.0027	−	33.3255i	0.746413	−	1.65801i
$405$		0			0
$406$	1.60063	−	0.689836i	0.0794378	−	0.0342360i
$407$			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	$0.462824\pi$
$410$	0.0937266	+	0.0201246i	0.00462883	+	0.000993885i
$411$		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
$416$	−0.0685042	+	6.63324i	−0.00335869	+	0.325221i
$417$		0			0
$418$	18.5984	−	6.00053i	0.909676	−	0.293496i
$419$	−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	$0.313639\pi$
$422$	6.58413	−	2.12429i	0.320510	−	0.103409i
$423$		0			0
$424$	3.15222	−	28.3032i	0.153085	−	1.37453i
$425$	−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
$430$	−4.35924	−	0.936000i	−0.210221	−	0.0451379i
$431$	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	$-0.268078\pi$
$434$	−3.21701	−	2.39658i	−0.154422	−	0.115039i
$435$		0			0
$436$	−32.2384	−	14.5133i	−1.54394	−	0.695062i
$437$	−28.7045	+	16.5726i	−1.37312	+	0.792774i
$438$		0			0
$439$	−17.6459	+	30.5637i	−0.842195	+	1.45872i	0.0458405	+	0.998949i	$0.485403\pi$
$439$	−17.6459	+	30.5637i	−0.842195	+	1.45872i	−0.888035	+	0.459775i	$0.847930\pi$
$440$	−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
$446$	7.96318	+	24.6815i	0.377068	+	1.16870i
$447$		0			0
$448$	19.5231	−	8.17603i	0.922381	−	0.386281i
$449$	5.15686			0.243367			0.121684	−	0.992569i	$-0.461171\pi$
$449$	5.15686			0.243367			0.121684	+	0.992569i	$0.461171\pi$
$450$		0			0
$451$	−0.201825	−	0.349571i	−0.00950356	−	0.0164607i
$452$	−28.3866	+	20.4454i	−1.33519	+	0.961672i
$453$		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	$0.963438\pi$
$458$	4.13876	−	19.2755i	0.193391	−	0.900684i
$459$		0			0
$460$	6.17817	+	2.78133i	0.288058	+	0.129680i
$461$			1.16194i			0.0541170i	0.999634	+	0.0270585i	$0.00861403\pi$
$461$			1.16194i			0.0541170i	−0.999634	+	0.0270585i	$0.991386\pi$
$462$		0			0
$463$		−	23.3409i		−	1.08474i	−0.840139	−	0.542371i	$-0.817527\pi$
$463$		−	23.3409i		−	1.08474i	0.840139	−	0.542371i	$-0.182473\pi$
$464$	−0.590410	+	1.76728i	−0.0274091	+	0.0820439i
$465$		0			0
$466$	−5.05296	−	1.08495i	−0.234074	−	0.0502595i
$467$	−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
$472$	2.28819	−	20.5453i	0.105323	−	0.945674i
$473$	9.38691	+	16.2586i	0.431611	+	0.747571i
$474$		0			0
$475$	−22.6945			−1.04129
$476$	0.232109	+	0.0790315i	0.0106387	+	0.00362240i
$477$		0			0
$478$	−21.9675	+	7.08755i	−1.00477	+	0.324177i
$479$	−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	−0.110649	−	0.993860i	$-0.535293\pi$
$487$	15.3315	−	8.85162i	0.694734	−	0.401105i	0.805383	+	0.592754i	$0.201960\pi$
$488$	−15.7722	−	36.0240i	−0.713974	−	1.63073i
$489$		0			0
$490$	−0.105312	+	4.82000i	−0.00475753	+	0.217746i
$491$			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
$494$	−1.65891	+	7.72604i	−0.0746378	+	0.347611i
$495$		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	−0.164444	−	0.986386i	$-0.552583\pi$
$499$	−24.5923	−	14.1984i	−1.10090	−	0.635606i	−0.936458	+	0.350781i	$0.885916\pi$
$500$	5.55753	+	7.71612i	0.248540	+	0.345075i
$501$		0			0
$502$	13.1821	+	40.8572i	0.588345	+	1.82355i
$503$	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
$506$	−8.75989	−	27.1509i	−0.389425	−	1.20700i
$507$		0			0
$508$	8.30427	+	11.5297i	0.368442	+	0.511548i
$509$	−8.62877	−	4.98182i	−0.382464	−	0.220816i	0.296426	−	0.955056i	$-0.404205\pi$
$509$	−8.62877	−	4.98182i	−0.382464	−	0.220816i	−0.678890	+	0.734240i	$0.737539\pi$
$510$		0			0
$511$	12.6506	+	17.7792i	0.559629	+	0.786505i
$512$	−7.39105	+	21.3863i	−0.326641	+	0.945148i
$513$		0			0
$514$	6.89818	−	32.1270i	0.304266	−	1.41706i
$515$	7.58338	−	4.37827i	0.334164	−	0.192929i
$516$		0			0
$517$		−	22.1494i		−	0.974131i
$518$	−0.170915	+	1.45823i	−0.00750959	+	0.0640708i
$519$		0			0
$520$	1.47971	−	0.647851i	0.0648894	−	0.0284102i
$521$	37.1542	−	21.4510i	1.62776	−	0.939786i	0.642997	−	0.765869i	$-0.277691\pi$
$521$	37.1542	−	21.4510i	1.62776	−	0.939786i	0.984760	−	0.173917i	$-0.0556426\pi$
$522$		0			0
$523$	0.342559	−	0.593329i	0.0149790	−	0.0259445i	−0.858439	−	0.512916i	$-0.828565\pi$
$523$	0.342559	−	0.593329i	0.0149790	−	0.0259445i	0.873418	+	0.486972i	$0.161899\pi$
$524$	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
$530$	−6.59960	+	2.12928i	−0.286668	+	0.0924900i
$531$		0			0
$532$	24.7337	−	4.89590i	1.07234	−	0.212264i
$533$	0.163219			0.00706981
$534$		0			0
$535$	1.18255	+	2.04823i	0.0511259	+	0.0885527i
$536$	11.3342	+	1.26232i	0.489562	+	0.0545240i
$537$		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	$0.179689\pi$
$542$	21.9639	+	4.71601i	0.943431	+	0.202570i
$543$		0			0
$544$	−0.228348	+	0.128711i	−0.00979033	+	0.00551844i
$545$			8.60903i			0.368770i
$546$		0			0
$547$		−	32.8931i		−	1.40641i	−0.710989	−	0.703203i	$-0.751753\pi$
$547$		−	32.8931i		−	1.40641i	0.710989	−	0.703203i	$-0.248247\pi$
$548$	21.7767	+	9.80360i	0.930255	+	0.418789i
$549$		0			0
$550$	4.10076	−	19.0985i	0.174857	−	0.814363i
$551$	−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
$556$	15.2519	−	10.9852i	0.646826	−	0.465876i
$557$	−11.8145	−	20.4633i	−0.500596	−	0.867058i	−1.00000		0.000688398i	$-0.999781\pi$
$557$	−11.8145	−	20.4633i	−0.500596	−	0.867058i	0.499404	−	0.866369i	$-0.333552\pi$
$558$		0			0
$559$	−7.59135			−0.321080
$560$	−3.76696	−	3.51767i	−0.159183	−	0.148649i
$561$		0			0
$562$	−10.5196	−	32.6050i	−0.443743	−	1.37536i
$563$	−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	−0.939881	−	0.341502i	$-0.889064\pi$
$569$	−4.15511	+	7.19687i	−0.174191	+	0.301708i	0.765690	+	0.643210i	$0.222398\pi$
$570$		0			0
$571$	22.1031	−	12.7613i	0.924988	−	0.534042i	0.0397651	−	0.999209i	$-0.487339\pi$
$571$	22.1031	−	12.7613i	0.924988	−	0.534042i	0.885223	+	0.465167i	$0.154006\pi$
$572$	−6.20209	−	2.79210i	−0.259322	−	0.116744i
$573$		0			0
$574$	−0.206121	−	0.478262i	−0.00860331	−	0.0199623i
$575$			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	$0.221154\pi$
$578$	23.5029	+	5.04646i	0.977593	+	0.209905i
$579$		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
$584$	−23.1838	−	2.58205i	−0.959354	−	0.106846i
$585$		0			0
$586$	−37.1581	+	11.9886i	−1.53499	+	0.495245i
$587$	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
$590$	−4.79064	+	1.54564i	−0.197228	+	0.0636331i
$591$		0			0
$592$	−1.04058	−	1.17506i	−0.0427677	−	0.0482948i
$593$	31.4732	+	18.1711i	1.29245	+	0.746197i	0.979088	−	0.203437i	$-0.0652111\pi$
$593$	31.4732	+	18.1711i	1.29245	+	0.746197i	0.313363	+	0.949633i	$0.398544\pi$
$594$		0			0
$595$	−0.00565344	−	0.0594380i	−0.000231768	−	0.00243672i
$596$	2.55465	+	25.3112i	0.104643	+	1.03679i
$597$		0			0
$598$	11.2789	+	2.42176i	0.461228	+	0.0990331i
$599$	−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	$-0.153752\pi$
$602$	9.58671	+	22.2441i	0.390725	+	0.906600i
$603$		0			0
$604$	2.72818	−	6.06010i	0.111008	−	0.246582i
$605$	−1.09221	+	0.630590i	−0.0444048	+	0.0256371i
$606$		0			0
$607$	22.4667	−	38.9134i	0.911893	−	1.57945i	0.100506	−	0.994936i	$-0.467954\pi$
$607$	22.4667	−	38.9134i	0.911893	−	1.57945i	0.811387	−	0.584509i	$-0.198713\pi$
$608$	−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	$-0.375431\pi$
$614$	7.95712	+	24.6627i	0.321123	+	0.995305i
$615$		0			0
$616$	−0.349091	+	21.6993i	−0.0140653	+	0.874289i
$617$	−9.76529			−0.393136			−0.196568	−	0.980490i	$-0.562980\pi$
$617$	−9.76529			−0.393136			−0.196568	+	0.980490i	$0.562980\pi$
$618$		0			0
$619$	−23.9884	−	41.5491i	−0.964174	−	1.67000i	−0.711819	−	0.702363i	$-0.752128\pi$
$619$	−23.9884	−	41.5491i	−0.964174	−	1.67000i	−0.252355	−	0.967635i	$-0.581205\pi$
$620$	−0.610320	−	0.847373i	−0.0245111	−	0.0340313i
$621$		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
$626$	8.34547	−	38.8674i	0.333552	−	1.55346i
$627$		0			0
$628$	−7.79297	+	17.3105i	−0.310973	+	0.690764i
$629$		−	0.0181826i		−	0.000724989i
$630$		0			0
$631$		−	12.7354i		−	0.506987i	−0.967337	−	0.253493i	$-0.918420\pi$
$631$		−	12.7354i		−	0.506987i	0.967337	−	0.253493i	$-0.0815796\pi$
$632$	15.7206	+	35.9062i	0.625333	+	1.42827i
$633$		0			0
$634$	8.68609	+	1.86504i	0.344969	+	0.0740704i
$635$	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
$640$	5.48746	−	0.496658i	0.216911	−	0.0196321i
$641$	22.4179	+	38.8289i	0.885452	+	1.53365i	0.845195	+	0.534459i	$0.179485\pi$
$641$	22.4179	+	38.8289i	0.885452	+	1.53365i	0.0402575	+	0.999189i	$0.487182\pi$
$642$		0			0
$643$	24.9324			0.983236			0.491618	−	0.870811i	$-0.336406\pi$
$643$	24.9324			0.983236			0.491618	+	0.870811i	$0.336406\pi$
$644$	−7.14730	−	36.1075i	−0.281643	−	1.42284i
$645$		0			0
$646$	−0.297167	+	0.0958772i	−0.0116919	+	0.00377224i
$647$	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	−0.999660	−	0.0260892i	$-0.991695\pi$
$653$	−12.1952	+	21.1227i	−0.477236	+	0.826597i	0.522424	+	0.852686i	$0.325028\pi$
$654$		0			0
$655$	6.19644	−	3.57751i	0.242115	−	0.139785i
$656$	0.528058	+	0.176413i	0.0206172	+	0.00688776i
$657$		0			0
$658$	3.32669	−	28.3829i	0.129688	−	1.10648i
$659$		−	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	$0.458814\pi$
$662$	5.91163	−	27.5323i	0.229762	−	1.07007i
$663$		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
$668$	−17.8742	+	12.8739i	−0.691573	+	0.498105i
$669$		0			0
$670$	−0.852681	−	2.64284i	−0.0329419	−	0.102102i
$671$	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	$0.555572\pi$
$674$	−11.9293	−	36.9743i	−0.459499	−	1.42420i
$675$		0			0
$676$	−18.8657	+	13.5880i	−0.725604	+	0.522616i
$677$	−14.1790	−	8.18626i	−0.544944	−	0.314624i	0.202136	−	0.979357i	$-0.435212\pi$
$677$	−14.1790	−	8.18626i	−0.544944	−	0.314624i	−0.747080	+	0.664734i	$0.768545\pi$
$678$		0			0
$679$	−22.4215	+	2.13262i	−0.860458	+	0.0818424i
$680$	0.0514050	+	0.0378368i	0.00197129	+	0.00145097i
$681$		0			0
$682$	−0.923105	+	4.29919i	−0.0353475	+	0.164624i
$683$	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
$686$	21.6673	−	14.7149i	0.827260	−	0.561819i
$687$		0			0
$688$	−24.5601	−	8.20498i	−0.936343	−	0.312812i
$689$	−10.2252	+	5.90353i	−0.389549	+	0.224906i
$690$		0			0
$691$	−6.17352	+	10.6929i	−0.234852	+	0.406775i	−0.959230	−	0.282628i	$-0.908794\pi$
$691$	−6.17352	+	10.6929i	−0.234852	+	0.406775i	0.724378	+	0.689403i	$0.242127\pi$
$692$	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
$698$	7.44846	−	2.40315i	0.281928	−	0.0909607i
$699$		0			0
$700$	8.12328	−	23.8574i	0.307031	−	0.901726i
$701$	−31.7226			−1.19815			−0.599074	−	0.800694i	$-0.704464\pi$
$701$	−31.7226			−1.19815			−0.599074	+	0.800694i	$0.704464\pi$
$702$		0			0
$703$	−0.934867	−	1.61924i	−0.0352592	−	0.0610707i
$704$	−17.0476	−	15.7366i	−0.642507	−	0.593097i
$705$		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	$0.934329\pi$
$710$	4.68047	+	1.00497i	0.175655	+	0.0377160i
$711$		0			0
$712$	12.0094	+	27.4298i	0.450073	+	1.02797i
$713$		−	7.45789i		−	0.279300i
$714$		0			0
$715$			1.65622i			0.0619393i
$716$	−8.49167	+	18.8625i	−0.317349	+	0.704925i
$717$		0			0
$718$	−7.15639	+	33.3295i	−0.267074	+	1.24385i
$719$	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
$724$	13.3432	+	18.5258i	0.495898	+	0.688508i
$725$	1.10932	+	1.92139i	0.0411990	+	0.0713588i
$726$		0			0
$727$	−8.90679			−0.330335			−0.165167	−	0.986266i	$-0.552816\pi$
$727$	−8.90679			−0.330335			−0.165167	+	0.986266i	$0.552816\pi$
$728$	−7.52817	−	4.50939i	−0.279013	−	0.167129i
$729$		0			0
$730$	1.74414	+	5.40588i	0.0645536	+	0.200081i
$731$	−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	−0.0843103	−	0.996440i	$-0.526869\pi$
$739$	20.0208	−	11.5590i	0.736476	−	0.425205i	0.820787	+	0.571235i	$0.193535\pi$
$740$	−0.156896	+	0.348513i	−0.00576762	+	0.0128116i
$741$		0			0
$742$	30.2113	+	22.5065i	1.10909	+	0.826240i
$743$			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
$746$	17.4320	+	3.74292i	0.638229	+	0.137038i
$747$		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	0.109633	−	0.993972i	$-0.465032\pi$
$751$	−19.0832	−	11.0177i	−0.696355	−	0.402041i	−0.805988	+	0.591931i	$0.798366\pi$
$752$	20.2539	+	22.8714i	0.738583	+	0.834034i
$753$		0			0
$754$	0.735203	−	0.237204i	0.0267745	−	0.00863846i
$755$	−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	$0.530670\pi$
$758$	−16.2945	+	5.25721i	−0.591842	+	0.190950i
$759$		0			0
$760$	6.52321	+	0.726510i	0.236622	+	0.0263533i
$761$	−36.0460	−	20.8112i	−1.30667	−	0.754405i	−0.325129	−	0.945670i	$-0.605408\pi$
$761$	−36.0460	−	20.8112i	−1.30667	−	0.754405i	−0.981538	+	0.191265i	$0.938741\pi$
$762$		0			0
$763$	38.1076	−	27.1150i	1.37959	−	0.981630i
$764$	−29.0899	+	2.93604i	−1.05244	+	0.106222i
$765$		0			0
$766$	1.78698	+	0.383694i	0.0645663	+	0.0138634i
$767$	−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	$-0.0246526\pi$
$770$	4.85304	−	2.09156i	0.174892	−	0.0753745i
$771$		0			0
$772$	−0.130667	−	0.0588248i	−0.00470282	−	0.00211715i
$773$	40.4039	−	23.3272i	1.45323	−	0.839021i	0.454564	−	0.890714i	$-0.349795\pi$
$773$	40.4039	−	23.3272i	1.45323	−	0.839021i	0.998663	+	0.0516925i	$0.0164616\pi$
$774$		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
$782$	0.139967	+	0.433819i	0.00500519	+	0.0155134i
$783$		0			0
$784$	−3.70641	+	27.7536i	−0.132372	+	0.991200i
$785$	4.62264			0.164989
$786$		0			0
$787$	21.1595	+	36.6493i	0.754254	+	1.30641i	0.945744	+	0.324912i	$0.105335\pi$
$787$	21.1595	+	36.6493i	0.754254	+	1.30641i	−0.191490	+	0.981495i	$0.561332\pi$
$788$	3.09834	−	2.23158i	0.110374	−	0.0794968i
$789$		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
$794$	−1.30304	+	6.06867i	−0.0462432	+	0.215369i
$795$		0			0
$796$	1.06426	+	0.479115i	0.0377215	+	0.0169818i
$797$			7.72777i			0.273732i	0.990590	+	0.136866i	$0.0437029\pi$
$797$			7.72777i			0.273732i	−0.990590	+	0.136866i	$0.956297\pi$
$798$		0			0
$799$			0.353906i			0.0125203i
$800$	13.2296	+	23.4708i	0.467738	+	0.829819i
$801$		0			0
$802$	−18.1437	−	3.89575i	−0.640677	−	0.137564i
$803$	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
$808$	−51.3674	−	5.72095i	−1.80710	−	0.201262i
$809$	−1.09641	−	1.89904i	−0.0385477	−	0.0667666i	0.846108	−	0.533012i	$-0.178940\pi$
$809$	−1.09641	−	1.89904i	−0.0385477	−	0.0667666i	−0.884656	+	0.466245i	$0.845606\pi$
$810$		0			0
$811$	−4.83311			−0.169713			−0.0848567	−	0.996393i	$-0.527043\pi$
$811$	−4.83311			−0.169713			−0.0848567	+	0.996393i	$0.527043\pi$
$812$	−1.62350	−	1.85473i	−0.0569737	−	0.0650882i
$813$		0			0
$814$	1.53159	−	0.494150i	0.0536823	−	0.0173199i
$815$	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	$-0.592615\pi$
$821$	19.6615	−	34.0547i	0.686191	−	1.18852i	0.973061	−	0.230548i	$-0.0740520\pi$
$822$		0			0
$823$	13.3558	−	7.71099i	0.465555	−	0.268788i	−0.248822	−	0.968549i	$-0.580044\pi$
$823$	13.3558	−	7.71099i	0.465555	−	0.268788i	0.714377	+	0.699761i	$0.246710\pi$
$824$	46.5862	−	20.3966i	1.62291	−	0.710549i
$825$		0			0
$826$	21.9304	+	16.3375i	0.763055	+	0.568453i
$827$		−	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	$0.490985\pi$
$830$	0.917993	−	4.27538i	0.0318640	−	0.148401i
$831$		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
$836$	−16.1522	−	22.4258i	−0.558635	−	0.775613i
$837$		0			0
$838$	7.92970	+	24.5777i	0.273927	+	0.849023i
$839$	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
$842$	−9.84697	−	30.5202i	−0.339349	−	1.05180i
$843$		0			0
$844$	−5.71814	−	7.93911i	−0.196827	−	0.273275i
$845$	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
$850$	−0.0655224	+	0.305158i	−0.00224740	+	0.0104668i
$851$	−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	$-0.246718\pi$
$854$	51.6690	+	6.05600i	1.76808	+	0.207232i
$855$		0			0
$856$	5.50901	+	12.5827i	0.188294	+	0.430067i
$857$	21.4624	−	12.3913i	0.733141	−	0.423279i	−0.0864289	−	0.996258i	$-0.527546\pi$
$857$	21.4624	−	12.3913i	0.733141	−	0.423279i	0.819570	+	0.572979i	$0.194212\pi$
$858$		0			0
$859$	−2.84935	+	4.93522i	−0.0972185	+	0.168387i	−0.910532	−	0.413438i	$-0.864328\pi$
$859$	−2.84935	+	4.93522i	−0.0972185	+	0.168387i	0.813314	+	0.581825i	$0.197661\pi$
$860$	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
$866$	−41.7912	+	13.4834i	−1.42012	+	0.458185i
$867$		0			0
$868$	−1.82860	+	5.37045i	−0.0620667	+	0.182285i
$869$	−40.1896			−1.36334
$870$		0			0
$871$	−2.36410	−	4.09474i	−0.0801044	−	0.138745i
$872$	−5.53432	+	49.6917i	−0.187416	+	1.68277i
$873$		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	$0.00203215\pi$
$878$	48.7981	+	10.4777i	1.64685	+	0.353606i
$879$		0			0
$880$	−1.79010	+	5.35833i	−0.0603443	+	0.180629i
$881$			41.7794i			1.40758i	0.710406	+	0.703792i	$0.248511\pi$
$881$			41.7794i			1.40758i	−0.710406	+	0.703792i	$0.751489\pi$
$882$		0			0
$883$		−	15.9004i		−	0.535090i	−0.963545	−	0.267545i	$-0.913788\pi$
$883$		−	15.9004i		−	0.535090i	0.963545	−	0.267545i	$-0.0862124\pi$
$884$	0.0990977	+	0.0446125i	0.00333302	+	0.00150048i
$885$		0			0
$886$	−4.45155	+	20.7323i	−0.149553	+	0.696514i
$887$	−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
$892$	29.7608	−	21.4352i	0.996467	−	0.717705i
$893$	18.1962	+	31.5168i	0.608913	+	1.05467i
$894$		0			0
$895$	5.03710			0.168372
$896$	−19.4818	−	22.7258i	−0.650840	−	0.759215i
$897$		0			0
$898$	−2.23930	−	6.94061i	−0.0747265	−	0.231611i
$899$	−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	0.0916923	−	0.995787i	$-0.470772\pi$
$907$	30.1139	−	17.3863i	0.999916	−	0.577302i	0.908223	+	0.418486i	$0.137439\pi$
$908$	−29.3830	−	13.2279i	−0.975109	−	0.438982i
$909$		0			0
$910$	−0.248753	+	2.12233i	−0.00824609	+	0.0703546i
$911$			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
$914$	35.2317	+	7.56482i	1.16536	+	0.250222i
$915$		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	0.470941	−	0.882165i	$-0.343915\pi$
$919$	−1.74511	−	1.00754i	−0.0575659	−	0.0332357i	−0.528507	+	0.848929i	$0.677248\pi$
$920$	1.06060	−	9.52293i	0.0349669	−	0.313962i
$921$		0			0
$922$	1.56385	−	0.504558i	0.0515027	−	0.0166167i
$923$	8.15076			0.268285
$924$		0			0
$925$	−1.86891			−0.0614494
$926$	−31.4144	+	10.1355i	−1.03234	+	0.333072i
$927$		0			0
$928$	2.63496	+	0.0272123i	0.0864966	+	0.000893286i
$929$	30.2534	+	17.4668i	0.992581	+	0.573067i	0.906045	−	0.423182i	$-0.139087\pi$
$929$	30.2534	+	17.4668i	0.992581	+	0.573067i	0.0865362	+	0.996249i	$0.472420\pi$
$930$		0			0
$931$	−10.9325	+	31.5119i	−0.358298	+	1.03276i
$932$	0.733949	+	7.27189i	0.0240413	+	0.238199i
$933$		0			0
$934$	25.1116	+	5.39187i	0.821677	+	0.176427i
$935$	−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	$0.735826\pi$
$938$	−9.01285	+	12.0983i	−0.294280	+	0.395023i
$939$		0			0
$940$	3.05382	−	6.78345i	0.0996047	−	0.221252i
$941$	0.227297	−	0.131230i	0.00740966	−	0.00427797i	−0.496291	−	0.868156i	$-0.665305\pi$
$941$	0.227297	−	0.131230i	0.00740966	−	0.00427797i	0.503700	+	0.863878i	$0.331972\pi$
$942$		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
$950$	9.85478	+	30.5444i	0.319731	+	0.990991i
$951$		0			0
$952$	0.00557782	−	0.346713i	0.000180778	−	0.0112370i
$953$	33.2031			1.07555			0.537777	−	0.843087i	$-0.319264\pi$
$953$	33.2031			1.07555			0.537777	+	0.843087i	$0.319264\pi$
$954$		0			0
$955$	3.55977	+	6.16570i	0.115191	+	0.199517i
$956$	19.0782	+	26.4883i	0.617034	+	0.856694i
$957$		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
$962$	−0.136613	+	0.636247i	−0.00440457	+	0.0205134i
$963$		0			0
$964$	2.20518	−	4.89837i	0.0710242	−	0.157766i
$965$			0.0348938i			0.00112327i
$966$		0			0
$967$		−	31.4179i		−	1.01033i	−0.863022	−	0.505166i	$-0.831431\pi$
$967$		−	31.4179i		−	1.01033i	0.863022	−	0.505166i	$-0.168569\pi$
$968$	−6.70969	+	2.93767i	−0.215657	+	0.0944201i
$969$		0			0
$970$	−5.73240	−	1.23084i	−0.184056	−	0.0395199i
$971$	−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
$976$	−41.6357	+	36.8707i	−1.33273	+	1.18020i
$977$	28.2780	+	48.9789i	0.904694	+	1.56698i	0.821328	+	0.570456i	$0.193234\pi$
$977$	28.2780	+	48.9789i	0.904694	+	1.56698i	0.0833656	+	0.996519i	$0.473433\pi$
$978$		0			0
$979$	−30.7020			−0.981240
$980$	6.53296	−	1.95128i	0.208688	−	0.0623315i
$981$		0			0
$982$	3.86029	−	1.24548i	0.123187	−	0.0397447i
$983$	−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	−0.601402	−	0.798946i	$-0.705391\pi$
$991$	−6.61700	+	3.82033i	−0.210196	+	0.121357i	0.391207	+	0.920303i	$0.372058\pi$
$992$	−2.97807	−	5.28342i	−0.0945537	−	0.167749i
$993$		0			0
$994$	−10.2932	−	23.8832i	−0.326479	−	0.757530i
$995$		−	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	$0.414460\pi$
$998$	−8.43064	+	39.2641i	−0.266867	+	1.24288i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.434237 - 1.34590i) q^{2} +(-1.62288 + 1.16888i) q^{4} +(0.421763 + 0.243505i) q^{5} +(-0.250520 - 2.63386i) q^{7} +(2.27790 + 1.67665i) q^{8} +O(q^{10})\)	\(q+(-0.434237 - 1.34590i) q^{2} +(-1.62288 + 1.16888i) q^{4} +(0.421763 + 0.243505i) q^{5} +(-0.250520 - 2.63386i) q^{7} +(2.27790 + 1.67665i) q^{8} +(0.144587 - 0.673389i) q^{10} +(-2.51153 + 1.45003i) q^{11} -1.17266i q^{13} +(-3.43612 + 1.48090i) q^{14} +(1.26745 - 3.79388i) q^{16} +(0.0401295 - 0.0231688i) q^{17} +(2.38246 - 4.12654i) q^{19} +(-0.969097 + 0.0978105i) q^{20} +(3.04219 + 2.75060i) q^{22} +(-6.02414 - 3.47804i) q^{23} +(-2.38141 - 4.12472i) q^{25} +(-1.57829 + 0.509215i) q^{26} +(3.48523 + 3.98161i) q^{28} -0.465824 q^{29} +(0.536070 + 0.928500i) q^{31} +(-5.65655 - 0.0584175i) q^{32} +(-0.0486085 - 0.0439494i) q^{34} +(0.535699 - 1.17187i) q^{35} +(0.196198 - 0.339825i) q^{37} +(-6.58845 - 1.41465i) q^{38} +(0.552461 + 1.26183i) q^{40} +0.139187i q^{41} -6.47359i q^{43} +(2.38099 - 5.28889i) q^{44} +(-2.06518 + 9.61817i) q^{46} +(-3.81879 + 6.61433i) q^{47} +(-6.87448 + 1.31967i) q^{49} +(-4.51736 + 4.99624i) q^{50} +(1.37070 + 1.90309i) q^{52} +(-5.03428 - 8.71964i) q^{53} -1.41236 q^{55} +(3.84542 - 6.41972i) q^{56} +(0.202278 + 0.626950i) q^{58} +(-3.65438 - 6.32958i) q^{59} +(-12.0409 - 6.95182i) q^{61} +(1.01688 - 1.12468i) q^{62} +(2.37766 + 7.63850i) q^{64} +(0.285550 - 0.494587i) q^{65} +(3.49182 - 2.01601i) q^{67} +(-0.0380437 + 0.0845064i) q^{68} +(-1.80984 - 0.212126i) q^{70} +6.95063i q^{71} +(-7.14246 + 4.12370i) q^{73} +(-0.542565 - 0.116498i) q^{74} +(0.956981 + 9.48167i) q^{76} +(4.44837 + 6.25176i) q^{77} +(12.0015 + 6.92909i) q^{79} +(1.45840 - 1.29149i) q^{80} +(0.187331 - 0.0604400i) q^{82} +6.34905 q^{83} +0.0225668 q^{85} +(-8.71279 + 2.81107i) q^{86} +(-8.15221 - 0.907937i) q^{88} +(9.16832 + 5.29333i) q^{89} +(-3.08864 + 0.293776i) q^{91} +(13.8418 - 1.39705i) q^{92} +(10.5605 + 2.26750i) q^{94} +(2.00967 - 1.16028i) q^{95} -8.51277i q^{97} +(4.76129 + 8.67929i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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