LMFDB - Embedded newform 276.2.i.b.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 18 x^{18} - 58 x^{17} + 169 x^{16} - 363 x^{15} + 800 x^{14} - 1682 x^{13} + \cdots + 529 $ x^20 - 4x^19 + 18x^18 - 58x^17 + 169x^16 - 363x^15 + 800x^14 - 1682x^13 + 2817x^12 - 3731x^11 + 5829x^10 - 8312x^9 + 7737x^8 + 4348x^7 - 12995x^6 - 2574x^5 + 24401x^4 + 22582x^3 + 9558x^2 + 2829*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			133.1
Root			$0.753595 + 1.65014i$ of defining polynomial
Character	$\chi$	$=$	276.133
Dual form			276.2.i.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{3} +(-0.0513473 + 0.357128i) q^{5} +(1.38384 + 3.03019i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{3} +(-0.0513473 + 0.357128i) q^{5} +(1.38384 + 3.03019i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(5.30865 - 1.55876i) q^{11} +(-1.03954 + 2.27628i) q^{13} +(0.236274 + 0.272675i) q^{15} +(5.44601 - 3.49994i) q^{17} +(-6.00339 - 3.85814i) q^{19} +(3.19629 + 0.938514i) q^{21} +(-4.78128 + 0.373376i) q^{23} +(4.67256 + 1.37199i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(-1.82796 + 1.17476i) q^{29} +(-3.06854 - 3.54128i) q^{31} +(2.29840 - 5.03278i) q^{33} +(-1.15322 + 0.338617i) q^{35} +(0.985943 + 6.85738i) q^{37} +(1.03954 + 2.27628i) q^{39} +(-0.381471 + 2.65319i) q^{41} +(-8.40992 + 9.70557i) q^{43} +0.360801 q^{45} +2.55121 q^{47} +(-2.68300 + 3.09634i) q^{49} +(0.921302 - 6.40780i) q^{51} +(-3.84676 - 8.42323i) q^{53} +(0.284093 + 1.97591i) q^{55} +(-6.84717 + 2.01051i) q^{57} +(1.29656 - 2.83908i) q^{59} +(-3.85872 - 4.45320i) q^{61} +(2.80240 - 1.80100i) q^{63} +(-0.759547 - 0.488132i) q^{65} +(-8.62847 - 2.53355i) q^{67} +(-2.84889 + 3.85796i) q^{69} +(-12.5556 - 3.68667i) q^{71} +(6.35417 + 4.08358i) q^{73} +(4.09676 - 2.63282i) q^{75} +(12.0697 + 13.9291i) q^{77} +(-0.696228 + 1.52453i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-1.66925 - 11.6099i) q^{83} +(0.970290 + 2.12464i) q^{85} +(-0.309237 + 2.15079i) q^{87} +(-7.59228 + 8.76196i) q^{89} -8.33612 q^{91} -4.68579 q^{93} +(1.68611 - 1.94588i) q^{95} +(1.06799 - 7.42802i) q^{97} +(-2.29840 - 5.03278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$		0			0
$5$	−0.0513473	+	0.357128i	−0.0229632	+	0.159713i	−0.998076	−	0.0619946i	$-0.980254\pi$
$5$	−0.0513473	+	0.357128i	−0.0229632	+	0.159713i	0.975113	+	0.221707i	$0.0711629\pi$
$6$		0			0
$7$	1.38384	+	3.03019i	0.523042	+	1.14530i	0.968275	+	0.249888i	$0.0803939\pi$
$7$	1.38384	+	3.03019i	0.523042	+	1.14530i	−0.445232	+	0.895415i	$0.646879\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	5.30865	−	1.55876i	1.60062	−	0.469984i	0.644901	−	0.764267i	$-0.276899\pi$
$11$	5.30865	−	1.55876i	1.60062	−	0.469984i	0.955719	+	0.294282i	$0.0950806\pi$
$12$		0			0
$13$	−1.03954	+	2.27628i	−0.288317	+	0.631327i	−0.997263	−	0.0739361i	$-0.976444\pi$
$13$	−1.03954	+	2.27628i	−0.288317	+	0.631327i	0.708946	+	0.705263i	$0.249171\pi$
$14$		0			0
$15$	0.236274	+	0.272675i	0.0610058	+	0.0704044i
$16$		0			0
$17$	5.44601	−	3.49994i	1.32085	−	0.848860i	0.325536	−	0.945530i	$-0.394455\pi$
$17$	5.44601	−	3.49994i	1.32085	−	0.848860i	0.995317	+	0.0966694i	$0.0308189\pi$
$18$		0			0
$19$	−6.00339	−	3.85814i	−1.37727	−	0.885119i	−0.378098	−	0.925766i	$-0.623422\pi$
$19$	−6.00339	−	3.85814i	−1.37727	−	0.885119i	−0.999174	+	0.0406470i	$0.987058\pi$
$20$		0			0
$21$	3.19629	+	0.938514i	0.697487	+	0.204801i
$22$		0			0
$23$	−4.78128	+	0.373376i	−0.996965	+	0.0778542i
$23$	−4.78128	+	0.373376i	−0.996965	+	0.0778542i
$24$		0			0
$25$	4.67256	+	1.37199i	0.934512	+	0.274398i
$26$		0			0
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$		0			0
$29$	−1.82796	+	1.17476i	−0.339444	+	0.218148i	−0.699246	−	0.714881i	$-0.746481\pi$
$29$	−1.82796	+	1.17476i	−0.339444	+	0.218148i	0.359802	+	0.933029i	$0.382844\pi$
$30$		0			0
$31$	−3.06854	−	3.54128i	−0.551126	−	0.636033i	0.410019	−	0.912077i	$-0.365522\pi$
$31$	−3.06854	−	3.54128i	−0.551126	−	0.636033i	−0.961145	+	0.276044i	$0.910977\pi$
$32$		0			0
$33$	2.29840	−	5.03278i	0.400099	−	0.876095i
$34$		0			0
$35$	−1.15322	+	0.338617i	−0.194930	+	0.0572367i
$36$		0			0
$37$	0.985943	+	6.85738i	0.162088	+	1.12735i	0.894689	+	0.446689i	$0.147397\pi$
$37$	0.985943	+	6.85738i	0.162088	+	1.12735i	−0.732601	+	0.680658i	$0.761694\pi$
$38$		0			0
$39$	1.03954	+	2.27628i	0.166460	+	0.364497i
$40$		0			0
$41$	−0.381471	+	2.65319i	−0.0595757	+	0.414358i	0.938108	+	0.346342i	$0.112576\pi$
$41$	−0.381471	+	2.65319i	−0.0595757	+	0.414358i	−0.997684	+	0.0680167i	$0.978333\pi$
$42$		0			0
$43$	−8.40992	+	9.70557i	−1.28250	+	1.48009i	−0.487972	+	0.872860i	$0.662263\pi$
$43$	−8.40992	+	9.70557i	−1.28250	+	1.48009i	−0.794530	+	0.607226i	$0.792282\pi$
$44$		0			0
$45$	0.360801			0.0537850
$46$		0			0
$47$	2.55121			0.372132			0.186066	−	0.982537i	$-0.440426\pi$
$47$	2.55121			0.372132			0.186066	+	0.982537i	$0.440426\pi$
$48$		0			0
$49$	−2.68300	+	3.09634i	−0.383285	+	0.442335i
$50$		0			0
$51$	0.921302	−	6.40780i	0.129008	−	0.897271i
$52$		0			0
$53$	−3.84676	−	8.42323i	−0.528393	−	1.15702i	−0.966163	−	0.257932i	$-0.916959\pi$
$53$	−3.84676	−	8.42323i	−0.528393	−	1.15702i	0.437770	−	0.899087i	$-0.355768\pi$
$54$		0			0
$55$	0.284093	+	1.97591i	0.0383071	+	0.266432i
$56$		0			0
$57$	−6.84717	+	2.01051i	−0.906930	+	0.266299i
$58$		0			0
$59$	1.29656	−	2.83908i	0.168798	−	0.369617i	−0.806261	−	0.591559i	$-0.798513\pi$
$59$	1.29656	−	2.83908i	0.168798	−	0.369617i	0.975060	+	0.221943i	$0.0712398\pi$
$60$		0			0
$61$	−3.85872	−	4.45320i	−0.494058	−	0.570174i	0.452887	−	0.891568i	$-0.350394\pi$
$61$	−3.85872	−	4.45320i	−0.494058	−	0.570174i	−0.946946	+	0.321394i	$0.895849\pi$
$62$		0			0
$63$	2.80240	−	1.80100i	0.353070	−	0.226904i
$64$		0			0
$65$	−0.759547	−	0.488132i	−0.0942103	−	0.0605453i
$66$		0			0
$67$	−8.62847	−	2.53355i	−1.05414	−	0.309522i	−0.291648	−	0.956526i	$-0.594204\pi$
$67$	−8.62847	−	2.53355i	−1.05414	−	0.309522i	−0.762487	+	0.647004i	$0.776022\pi$
$68$		0			0
$69$	−2.84889	+	3.85796i	−0.342966	+	0.464443i
$70$		0			0
$71$	−12.5556	−	3.68667i	−1.49008	−	0.437527i	−0.567514	−	0.823364i	$-0.692095\pi$
$71$	−12.5556	−	3.68667i	−1.49008	−	0.437527i	−0.922567	+	0.385836i	$0.873913\pi$
$72$		0			0
$73$	6.35417	+	4.08358i	0.743699	+	0.477947i	0.856808	−	0.515636i	$-0.172444\pi$
$73$	6.35417	+	4.08358i	0.743699	+	0.477947i	−0.113108	+	0.993583i	$0.536081\pi$
$74$		0			0
$75$	4.09676	−	2.63282i	0.473053	−	0.304012i
$76$		0			0
$77$	12.0697	+	13.9291i	1.37547	+	1.58737i
$78$		0			0
$79$	−0.696228	+	1.52453i	−0.0783318	+	0.171523i	−0.944746	−	0.327803i	$-0.893692\pi$
$79$	−0.696228	+	1.52453i	−0.0783318	+	0.171523i	0.866414	+	0.499326i	$0.166419\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	−1.66925	−	11.6099i	−0.183224	−	1.27435i	−0.849077	−	0.528270i	$-0.822841\pi$
$83$	−1.66925	−	11.6099i	−0.183224	−	1.27435i	0.665852	−	0.746084i	$-0.268068\pi$
$84$		0			0
$85$	0.970290	+	2.12464i	0.105243	+	0.230449i
$86$		0			0
$87$	−0.309237	+	2.15079i	−0.0331536	+	0.230589i
$88$		0			0
$89$	−7.59228	+	8.76196i	−0.804780	+	0.928766i	−0.998633	−	0.0522649i	$-0.983356\pi$
$89$	−7.59228	+	8.76196i	−0.804780	+	0.928766i	0.193853	+	0.981031i	$0.437901\pi$
$90$		0			0
$91$	−8.33612			−0.873863
$92$		0			0
$93$	−4.68579			−0.485894
$94$		0			0
$95$	1.68611	−	1.94588i	0.172991	−	0.199643i
$96$		0			0
$97$	1.06799	−	7.42802i	0.108438	−	0.754201i	−0.860954	−	0.508683i	$-0.830133\pi$
$97$	1.06799	−	7.42802i	0.108438	−	0.754201i	0.969392	−	0.245519i	$-0.0789582\pi$
$98$		0			0
$99$	−2.29840	−	5.03278i	−0.230997	−	0.505814i
$100$		0			0
$101$	−0.420621	−	2.92549i	−0.0418534	−	0.291097i	−0.999989	−	0.00478052i	$-0.998478\pi$
$101$	−0.420621	−	2.92549i	−0.0418534	−	0.291097i	0.958135	−	0.286316i	$-0.0924308\pi$
$102$		0			0
$103$	1.84043	−	0.540399i	0.181343	−	0.0532471i	−0.189800	−	0.981823i	$-0.560784\pi$
$103$	1.84043	−	0.540399i	0.181343	−	0.0532471i	0.371143	+	0.928576i	$0.378966\pi$
$104$		0			0
$105$	−0.499291	+	1.09329i	−0.0487258	+	0.106695i
$106$		0			0
$107$	−3.78258	−	4.36533i	−0.365676	−	0.422012i	0.542858	−	0.839825i	$-0.317342\pi$
$107$	−3.78258	−	4.36533i	−0.365676	−	0.422012i	−0.908533	+	0.417813i	$0.862797\pi$
$108$		0			0
$109$	4.10532	−	2.63833i	0.393219	−	0.252706i	−0.329059	−	0.944309i	$-0.606732\pi$
$109$	4.10532	−	2.63833i	0.393219	−	0.252706i	0.722278	+	0.691603i	$0.243095\pi$
$110$		0			0
$111$	5.82812	+	3.74550i	0.553180	+	0.355508i
$112$		0			0
$113$	4.87647	+	1.43186i	0.458739	+	0.134698i	0.502934	−	0.864325i	$-0.332254\pi$
$113$	4.87647	+	1.43186i	0.458739	+	0.134698i	−0.0441944	+	0.999023i	$0.514072\pi$
$114$		0			0
$115$	0.112163	−	1.72670i	0.0104592	−	0.161016i
$116$		0			0
$117$	2.40106	+	0.705014i	0.221978	+	0.0651785i
$118$		0			0
$119$	18.1419	+	11.6591i	1.66306	+	1.06879i
$120$		0			0
$121$	16.4983	−	10.6028i	1.49984	−	0.963890i
$122$		0			0
$123$	1.75534	+	2.02577i	0.158273	+	0.182657i
$124$		0			0
$125$	−1.47931	+	3.23924i	−0.132313	+	0.289726i
$126$		0			0
$127$	11.3726	−	3.33928i	1.00915	−	0.296314i	0.264945	−	0.964264i	$-0.414646\pi$
$127$	11.3726	−	3.33928i	1.00915	−	0.296314i	0.744206	+	0.667950i	$0.232828\pi$
$128$		0			0
$129$	1.82765	+	12.7116i	0.160916	+	1.11919i
$130$		0			0
$131$	3.10751	+	6.80449i	0.271504	+	0.594511i	0.995444	−	0.0953524i	$-0.0303978\pi$
$131$	3.10751	+	6.80449i	0.271504	+	0.594511i	−0.723939	+	0.689864i	$0.757671\pi$
$132$		0			0
$133$	3.38317	−	23.5304i	0.293358	−	2.04035i
$134$		0			0
$135$	0.236274	−	0.272675i	0.0203353	−	0.0234681i
$136$		0			0
$137$	−4.99573			−0.426814			−0.213407	−	0.976963i	$-0.568456\pi$
$137$	−4.99573			−0.426814			−0.213407	+	0.976963i	$0.568456\pi$
$138$		0			0
$139$	8.92692			0.757172			0.378586	−	0.925566i	$-0.376410\pi$
$139$	8.92692			0.757172			0.378586	+	0.925566i	$0.376410\pi$
$140$		0			0
$141$	1.67068	−	1.92807i	0.140697	−	0.162373i
$142$		0			0
$143$	−1.97039	+	13.7044i	−0.164773	+	1.14602i
$144$		0			0
$145$	−0.325680	−	0.713139i	−0.0270462	−	0.0592229i
$146$		0			0
$147$	0.583071	+	4.05535i	0.0480909	+	0.334480i
$148$		0			0
$149$	−3.75955	+	1.10390i	−0.307995	+	0.0904354i	−0.432078	−	0.901836i	$-0.642219\pi$
$149$	−3.75955	+	1.10390i	−0.307995	+	0.0904354i	0.124083	+	0.992272i	$0.460401\pi$
$150$		0			0
$151$	−8.76108	+	19.1841i	−0.712966	+	1.56118i	0.110540	+	0.993872i	$0.464742\pi$
$151$	−8.76108	+	19.1841i	−0.712966	+	1.56118i	−0.823507	+	0.567307i	$0.807985\pi$
$152$		0			0
$153$	−4.23937	−	4.89249i	−0.342732	−	0.395534i
$154$		0			0
$155$	1.42225	−	0.914028i	0.114238	−	0.0734165i
$156$		0			0
$157$	10.7795	+	6.92758i	0.860299	+	0.552881i	0.894771	−	0.446525i	$-0.147339\pi$
$157$	10.7795	+	6.92758i	0.860299	+	0.552881i	−0.0344719	+	0.999406i	$0.510975\pi$
$158$		0			0
$159$	−8.88494	−	2.60885i	−0.704622	−	0.206896i
$160$		0			0
$161$	−7.74792	−	13.9715i	−0.610622	−	1.10111i
$162$		0			0
$163$	−0.451340	−	0.132525i	−0.0353517	−	0.0103802i	0.264009	−	0.964520i	$-0.414955\pi$
$163$	−0.451340	−	0.132525i	−0.0353517	−	0.0103802i	−0.299361	+	0.954140i	$0.596773\pi$
$164$		0			0
$165$	1.67933	+	1.07924i	0.130736	+	0.0840189i
$166$		0			0
$167$	20.0276	−	12.8709i	1.54978	−	0.995983i	0.564421	−	0.825487i	$-0.309099\pi$
$167$	20.0276	−	12.8709i	1.54978	−	0.995983i	0.985358	−	0.170496i	$-0.0545370\pi$
$168$		0			0
$169$	4.41238	+	5.09216i	0.339414	+	0.391704i
$170$		0			0
$171$	−2.96450	+	6.49135i	−0.226701	+	0.496406i
$172$		0			0
$173$	0.753799	−	0.221335i	0.0573103	−	0.0168278i	−0.252952	−	0.967479i	$-0.581401\pi$
$173$	0.753799	−	0.221335i	0.0573103	−	0.0168278i	0.310262	+	0.950651i	$0.399583\pi$
$174$		0			0
$175$	2.30870	+	16.0573i	0.174521	+	1.21382i
$176$		0			0
$177$	−1.29656	−	2.83908i	−0.0974557	−	0.213398i
$178$		0			0
$179$	2.17857	−	15.1523i	0.162834	−	1.13254i	−0.730425	−	0.682993i	$-0.760678\pi$
$179$	2.17857	−	15.1523i	0.162834	−	1.13254i	0.893259	−	0.449543i	$-0.148413\pi$
$180$		0			0
$181$	5.80166	−	6.69547i	0.431234	−	0.497670i	−0.497993	−	0.867181i	$-0.665929\pi$
$181$	5.80166	−	6.69547i	0.431234	−	0.497670i	0.929226	+	0.369511i	$0.120475\pi$
$182$		0			0
$183$	−5.89243			−0.435581
$184$		0			0
$185$	−2.49959			−0.183774
$186$		0			0
$187$	23.4554	−	27.0690i	1.71523	−	1.97948i
$188$		0			0
$189$	0.474083	−	3.29732i	0.0344844	−	0.239844i
$190$		0			0
$191$	11.2219	+	24.5726i	0.811989	+	1.77801i	0.598614	+	0.801037i	$0.295718\pi$
$191$	11.2219	+	24.5726i	0.811989	+	1.77801i	0.213375	+	0.976970i	$0.431554\pi$
$192$		0			0
$193$	0.419447	+	2.91732i	0.0301925	+	0.209993i	0.999333	−	0.0365153i	$-0.0116258\pi$
$193$	0.419447	+	2.91732i	0.0301925	+	0.209993i	−0.969141	+	0.246508i	$0.920717\pi$
$194$		0			0
$195$	−0.866303	+	0.254370i	−0.0620372	+	0.0182158i
$196$		0			0
$197$	−1.44651	+	3.16741i	−0.103059	+	0.225669i	−0.954136	−	0.299372i	$-0.903223\pi$
$197$	−1.44651	+	3.16741i	−0.103059	+	0.225669i	0.851077	+	0.525041i	$0.175950\pi$
$198$		0			0
$199$	−15.1790	−	17.5175i	−1.07601	−	1.24178i	−0.968878	−	0.247539i	$-0.920378\pi$
$199$	−15.1790	−	17.5175i	−1.07601	−	1.24178i	−0.107133	−	0.994245i	$-0.534167\pi$
$200$		0			0
$201$	−7.56517	+	4.86184i	−0.533606	+	0.342928i
$202$		0			0
$203$	−6.08936	−	3.91339i	−0.427389	−	0.274666i
$204$		0			0
$205$	−0.927942	−	0.272468i	−0.0648103	−	0.0190300i
$206$		0			0
$207$	1.05002	+	4.67947i	0.0729815	+	0.325246i
$208$		0			0
$209$	−37.8838	−	11.1237i	−2.62048	−	0.769442i
$210$		0			0
$211$	−7.48193	−	4.80835i	−0.515078	−	0.331020i	0.257145	−	0.966373i	$-0.417218\pi$
$211$	−7.48193	−	4.80835i	−0.515078	−	0.331020i	−0.772222	+	0.635353i	$0.780855\pi$
$212$		0			0
$213$	−11.0084	+	7.07467i	−0.754283	+	0.484748i
$214$		0			0
$215$	−3.03431	−	3.50178i	−0.206938	−	0.238819i
$216$		0			0
$217$	6.48439	−	14.1988i	0.440189	−	0.963879i
$218$		0			0
$219$	7.24726	−	2.12799i	0.489724	−	0.143796i
$220$		0			0
$221$	2.30549	+	16.0350i	0.155084	+	1.07863i
$222$		0			0
$223$	0.346318	+	0.758330i	0.0231912	+	0.0507816i	0.920873	−	0.389862i	$-0.127477\pi$
$223$	0.346318	+	0.758330i	0.0231912	+	0.0507816i	−0.897682	+	0.440644i	$0.854750\pi$
$224$		0			0
$225$	0.693048	−	4.82025i	0.0462032	−	0.321350i
$226$		0			0
$227$	−17.7142	+	20.4433i	−1.17573	+	1.35687i	−0.254876	+	0.966974i	$0.582035\pi$
$227$	−17.7142	+	20.4433i	−1.17573	+	1.35687i	−0.920859	+	0.389897i	$0.872511\pi$
$228$		0			0
$229$	−7.85531			−0.519094			−0.259547	−	0.965731i	$-0.583573\pi$
$229$	−7.85531			−0.519094			−0.259547	+	0.965731i	$0.583573\pi$
$230$		0			0
$231$	18.4309			1.21266
$232$		0			0
$233$	−2.81791	+	3.25205i	−0.184608	+	0.213049i	−0.840508	−	0.541799i	$-0.817744\pi$
$233$	−2.81791	+	3.25205i	−0.184608	+	0.213049i	0.655901	+	0.754847i	$0.272289\pi$
$234$		0			0
$235$	−0.130998	+	0.911108i	−0.00854534	+	0.0594342i
$236$		0			0
$237$	0.696228	+	1.52453i	0.0452249	+	0.0990286i
$238$		0			0
$239$	2.26912	+	15.7821i	0.146777	+	1.02086i	0.921450	+	0.388496i	$0.127005\pi$
$239$	2.26912	+	15.7821i	0.146777	+	1.02086i	−0.774673	+	0.632362i	$0.782086\pi$
$240$		0			0
$241$	−5.42730	+	1.59360i	−0.349603	+	0.102653i	−0.451819	−	0.892109i	$-0.649225\pi$
$241$	−5.42730	+	1.59360i	−0.349603	+	0.102653i	0.102216	+	0.994762i	$0.467407\pi$
$242$		0			0
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$		0			0
$245$	−0.968028	−	1.11716i	−0.0618450	−	0.0713730i
$246$		0			0
$247$	15.0230	−	9.65470i	0.955891	−	0.614314i
$248$		0			0
$249$	−9.86731	−	6.34134i	−0.625316	−	0.401866i
$250$		0			0
$251$	−11.8738	−	3.48647i	−0.749468	−	0.220064i	−0.115377	−	0.993322i	$-0.536808\pi$
$251$	−11.8738	−	3.48647i	−0.749468	−	0.220064i	−0.634092	+	0.773258i	$0.718626\pi$
$252$		0			0
$253$	−24.8001	+	9.43499i	−1.55917	+	0.593173i
$254$		0			0
$255$	2.24110	+	0.658046i	0.140343	+	0.0412085i
$256$		0			0
$257$	5.16165	+	3.31719i	0.321975	+	0.206921i	0.691637	−	0.722246i	$-0.256890\pi$
$257$	5.16165	+	3.31719i	0.321975	+	0.206921i	−0.369662	+	0.929166i	$0.620526\pi$
$258$		0			0
$259$	−19.4148	+	12.4771i	−1.20637	+	0.775290i
$260$		0			0
$261$	1.42295	+	1.64217i	0.0880784	+	0.101648i
$262$		0			0
$263$	2.15350	−	4.71552i	0.132791	−	0.290771i	−0.831543	−	0.555460i	$-0.812542\pi$
$263$	2.15350	−	4.71552i	0.132791	−	0.290771i	0.964334	+	0.264689i	$0.0852694\pi$
$264$		0			0
$265$	3.20570	−	0.941277i	0.196924	−	0.0578222i
$266$		0			0
$267$	1.64996	+	11.4757i	0.100976	+	0.702303i
$268$		0			0
$269$	−8.19857	−	17.9524i	−0.499876	−	1.09457i	−0.976510	−	0.215473i	$-0.930871\pi$
$269$	−8.19857	−	17.9524i	−0.499876	−	1.09457i	0.476634	−	0.879102i	$-0.341857\pi$
$270$		0			0
$271$	−1.19194	+	8.29012i	−0.0724051	+	0.503589i	0.921057	+	0.389428i	$0.127327\pi$
$271$	−1.19194	+	8.29012i	−0.0724051	+	0.503589i	−0.993462	+	0.114161i	$0.963582\pi$
$272$		0			0
$273$	−5.45900	+	6.30002i	−0.330394	+	0.381295i
$274$		0			0
$275$	26.9436			1.62476
$276$		0			0
$277$	−0.192520			−0.0115674			−0.00578371	−	0.999983i	$-0.501841\pi$
$277$	−0.192520			−0.0115674			−0.00578371	+	0.999983i	$0.501841\pi$
$278$		0			0
$279$	−3.06854	+	3.54128i	−0.183709	+	0.212011i
$280$		0			0
$281$	−1.35433	+	9.41957i	−0.0807925	+	0.561924i	0.908712	+	0.417423i	$0.137067\pi$
$281$	−1.35433	+	9.41957i	−0.0807925	+	0.561924i	−0.989505	+	0.144501i	$0.953842\pi$
$282$		0			0
$283$	−4.03176	−	8.82832i	−0.239663	−	0.524789i	0.751133	−	0.660151i	$-0.229508\pi$
$283$	−4.03176	−	8.82832i	−0.239663	−	0.524789i	−0.990796	+	0.135362i	$0.956780\pi$
$284$		0			0
$285$	−0.366427	−	2.54855i	−0.0217053	−	0.150963i
$286$		0			0
$287$	−8.56755	+	2.51566i	−0.505727	+	0.148495i
$288$		0			0
$289$	10.3474	−	22.6577i	0.608672	−	1.33281i
$290$		0			0
$291$	−4.91434	−	5.67145i	−0.288084	−	0.332466i
$292$		0			0
$293$	27.7520	−	17.8351i	1.62129	−	1.04194i	0.666131	−	0.745835i	$-0.267949\pi$
$293$	27.7520	−	17.8351i	1.62129	−	1.04194i	0.955156	−	0.296103i	$-0.0956872\pi$
$294$		0			0
$295$	0.947341	+	0.608819i	0.0551563	+	0.0354468i
$296$		0			0
$297$	−5.30865	−	1.55876i	−0.308039	−	0.0904485i
$298$		0			0
$299$	4.12043	−	11.2717i	0.238291	−	0.651858i
$300$		0			0
$301$	−41.0477	−	12.0527i	−2.36595	−	0.694705i
$302$		0			0
$303$	−2.48638	−	1.59790i	−0.142839	−	0.0917970i
$304$		0			0
$305$	1.78850	−	1.14940i	0.102409	−	0.0658144i
$306$		0			0
$307$	19.6600	+	22.6889i	1.12206	+	1.29492i	0.950838	+	0.309689i	$0.100225\pi$
$307$	19.6600	+	22.6889i	1.12206	+	1.29492i	0.171219	+	0.985233i	$0.445230\pi$
$308$		0			0
$309$	0.796820	−	1.74479i	0.0453295	−	0.0992577i
$310$		0			0
$311$	2.47334	−	0.726237i	0.140250	−	0.0411811i	−0.210854	−	0.977518i	$-0.567624\pi$
$311$	2.47334	−	0.726237i	0.140250	−	0.0411811i	0.351104	+	0.936336i	$0.385806\pi$
$312$		0			0
$313$	2.34800	+	16.3307i	0.132717	+	0.923064i	0.941992	+	0.335635i	$0.108951\pi$
$313$	2.34800	+	16.3307i	0.132717	+	0.923064i	−0.809276	+	0.587429i	$0.800140\pi$
$314$		0			0
$315$	0.499291	+	1.09329i	0.0281319	+	0.0616002i
$316$		0			0
$317$	−0.259368	+	1.80394i	−0.0145675	+	0.101319i	−0.995808	−	0.0914686i	$-0.970844\pi$
$317$	−0.259368	+	1.80394i	−0.0145675	+	0.101319i	0.981240	+	0.192788i	$0.0617530\pi$
$318$		0			0
$319$	−7.87285	+	9.08576i	−0.440795	+	0.508705i
$320$		0			0
$321$	−5.77616			−0.322394
$322$		0			0
$323$	−46.1978			−2.57051
$324$		0			0
$325$	−7.98036	+	9.20983i	−0.442671	+	0.510869i
$326$		0			0
$327$	0.694498	−	4.83034i	0.0384058	−	0.267118i
$328$		0			0
$329$	3.53046	+	7.73063i	0.194641	+	0.426204i
$330$		0			0
$331$	−1.84730	−	12.8483i	−0.101537	−	0.706206i	−0.975466	−	0.220151i	$-0.929345\pi$
$331$	−1.84730	−	12.8483i	−0.101537	−	0.706206i	0.873929	−	0.486054i	$-0.161564\pi$
$332$		0			0
$333$	6.64727	−	1.95181i	0.364268	−	0.106959i
$334$		0			0
$335$	1.34785	−	2.95138i	0.0736409	−	0.161251i
$336$		0			0
$337$	15.3235	+	17.6843i	0.834725	+	0.963324i	0.999736	−	0.0229674i	$-0.00731140\pi$
$337$	15.3235	+	17.6843i	0.834725	+	0.963324i	−0.165011	+	0.986292i	$0.552766\pi$
$338$		0			0
$339$	4.27553	−	2.74772i	0.232215	−	0.149236i
$340$		0			0
$341$	−21.8098	−	14.0163i	−1.18107	−	0.759027i
$342$		0			0
$343$	9.27865	+	2.72446i	0.501000	+	0.147107i
$344$		0			0
$345$	−1.23150	−	1.21552i	−0.0663019	−	0.0654412i
$346$		0			0
$347$	19.4290	+	5.70488i	1.04301	+	0.306254i	0.757988	−	0.652269i	$-0.226183\pi$
$347$	19.4290	+	5.70488i	1.04301	+	0.306254i	0.285017	+	0.958522i	$0.408001\pi$
$348$		0			0
$349$	11.0731	+	7.11623i	0.592728	+	0.380923i	0.802345	−	0.596861i	$-0.203585\pi$
$349$	11.0731	+	7.11623i	0.592728	+	0.380923i	−0.209617	+	0.977783i	$0.567222\pi$
$350$		0			0
$351$	2.10517	−	1.35291i	0.112366	−	0.0722130i
$352$		0			0
$353$	21.8331	+	25.1968i	1.16206	+	1.34109i	0.929639	+	0.368473i	$0.120119\pi$
$353$	21.8331	+	25.1968i	1.16206	+	1.34109i	0.232421	+	0.972615i	$0.425335\pi$
$354$		0			0
$355$	1.96131	−	4.29468i	0.104096	−	0.227938i
$356$		0			0
$357$	20.6918	−	6.07565i	1.09512	−	0.321557i
$358$		0			0
$359$	−0.545170	−	3.79174i	−0.0287730	−	0.200120i	0.970364	−	0.241646i	$-0.0776873\pi$
$359$	−0.545170	−	3.79174i	−0.0287730	−	0.200120i	−0.999137	+	0.0415256i	$0.986778\pi$
$360$		0			0
$361$	13.2625	+	29.0408i	0.698027	+	1.52847i
$362$		0			0
$363$	2.79101	−	19.4119i	0.146490	−	1.01886i
$364$		0			0
$365$	−1.78463	+	2.05957i	−0.0934119	+	0.107803i
$366$		0			0
$367$	10.1213			0.528326			0.264163	−	0.964478i	$-0.414904\pi$
$367$	10.1213			0.528326			0.264163	+	0.964478i	$0.414904\pi$
$368$		0			0
$369$	2.68047			0.139540
$370$		0			0
$371$	20.2007	−	23.3128i	1.04877	−	1.21034i
$372$		0			0
$373$	3.41275	−	23.7362i	0.176706	−	1.22901i	−0.687616	−	0.726075i	$-0.741343\pi$
$373$	3.41275	−	23.7362i	0.176706	−	1.22901i	0.864321	−	0.502940i	$-0.167748\pi$
$374$		0			0
$375$	1.47931	+	3.23924i	0.0763912	+	0.167273i
$376$		0			0
$377$	−0.773840	−	5.38218i	−0.0398548	−	0.277196i
$378$		0			0
$379$	−25.4893	+	7.48434i	−1.30930	+	0.384445i	−0.860620	−	0.509248i	$-0.829924\pi$
$379$	−25.4893	+	7.48434i	−1.30930	+	0.384445i	−0.448679	+	0.893693i	$0.648105\pi$
$380$		0			0
$381$	4.92378	−	10.7816i	0.252253	−	0.552357i
$382$		0			0
$383$	−10.1659	−	11.7321i	−0.519455	−	0.599483i	0.434039	−	0.900894i	$-0.357088\pi$
$383$	−10.1659	−	11.7321i	−0.519455	−	0.599483i	−0.953494	+	0.301411i	$0.902542\pi$
$384$		0			0
$385$	−5.59424	+	3.59520i	−0.285109	+	0.183228i
$386$		0			0
$387$	10.8036	+	6.94307i	0.549180	+	0.352936i
$388$		0			0
$389$	−32.0980	−	9.42482i	−1.62743	−	0.477857i	−0.664430	−	0.747350i	$-0.731326\pi$
$389$	−32.0980	−	9.42482i	−1.62743	−	0.477857i	−0.963002	+	0.269493i	$0.913144\pi$
$390$		0			0
$391$	−24.7321	+	18.7676i	−1.25076	+	0.949118i
$392$		0			0
$393$	7.17748	+	2.10750i	0.362056	+	0.106309i
$394$		0			0
$395$	−0.508702	−	0.326923i	−0.0255956	−	0.0164493i
$396$		0			0
$397$	−6.87708	+	4.41963i	−0.345151	+	0.221815i	−0.701718	−	0.712455i	$-0.747583\pi$
$397$	−6.87708	+	4.41963i	−0.345151	+	0.221815i	0.356567	+	0.934270i	$0.383947\pi$
$398$		0			0
$399$	−15.5676	−	17.9660i	−0.779356	−	0.899424i
$400$		0			0
$401$	12.9866	−	28.4368i	0.648521	−	1.42006i	−0.244321	−	0.969694i	$-0.578565\pi$
$401$	12.9866	−	28.4368i	0.648521	−	1.42006i	0.892842	−	0.450369i	$-0.148708\pi$
$402$		0			0
$403$	11.2508	−	3.30355i	0.560444	−	0.164561i
$404$		0			0
$405$	−0.0513473	−	0.357128i	−0.00255147	−	0.0177459i
$406$		0			0
$407$	15.9230	+	34.8666i	0.789276	+	1.72827i
$408$		0			0
$409$	1.55553	−	10.8190i	0.0769160	−	0.534963i	−0.914537	−	0.404501i	$-0.867445\pi$
$409$	1.55553	−	10.8190i	0.0769160	−	0.534963i	0.991453	−	0.130461i	$-0.0416458\pi$
$410$		0			0
$411$	−3.27151	+	3.77552i	−0.161371	+	0.186233i
$412$		0			0
$413$	10.3972			0.511612
$414$		0			0
$415$	4.23194			0.207738
$416$		0			0
$417$	5.84589	−	6.74652i	0.286274	−	0.330378i
$418$		0			0
$419$	−0.715143	+	4.97393i	−0.0349370	+	0.242992i	−0.999805	−	0.0197425i	$-0.993715\pi$
$419$	−0.715143	+	4.97393i	−0.0349370	+	0.242992i	0.964868	+	0.262735i	$0.0846244\pi$
$420$		0			0
$421$	5.20851	+	11.4051i	0.253847	+	0.555848i	0.993058	−	0.117626i	$-0.0375284\pi$
$421$	5.20851	+	11.4051i	0.253847	+	0.555848i	−0.739211	+	0.673474i	$0.764801\pi$
$422$		0			0
$423$	−0.363075	−	2.52524i	−0.0176533	−	0.122781i
$424$		0			0
$425$	30.2487	−	8.88182i	1.46728	−	0.430832i
$426$		0			0
$427$	8.15418	−	17.8552i	0.394608	−	0.864072i
$428$		0			0
$429$	9.06675	+	10.4636i	0.437747	+	0.505187i
$430$		0			0
$431$	31.6031	−	20.3101i	1.52227	−	0.978302i	0.530865	−	0.847456i	$-0.321867\pi$
$431$	31.6031	−	20.3101i	1.52227	−	0.978302i	0.991403	−	0.130846i	$-0.0417694\pi$
$432$		0			0
$433$	11.7369	+	7.54284i	0.564039	+	0.362486i	0.791375	−	0.611331i	$-0.209365\pi$
$433$	11.7369	+	7.54284i	0.564039	+	0.362486i	−0.227337	+	0.973816i	$0.573002\pi$
$434$		0			0
$435$	−0.752229	−	0.220874i	−0.0360666	−	0.0105901i
$436$		0			0
$437$	30.1444	+	16.2053i	1.44200	+	0.775206i
$438$		0			0
$439$	16.9879	+	4.98811i	0.810790	+	0.238069i	0.660746	−	0.750610i	$-0.270240\pi$
$439$	16.9879	+	4.98811i	0.810790	+	0.238069i	0.150044	+	0.988679i	$0.452058\pi$
$440$		0			0
$441$	3.44666	+	2.21503i	0.164127	+	0.105478i
$442$		0			0
$443$	12.8989	−	8.28962i	0.612846	−	0.393852i	−0.197078	−	0.980388i	$-0.563145\pi$
$443$	12.8989	−	8.28962i	0.612846	−	0.393852i	0.809923	+	0.586536i	$0.199509\pi$
$444$		0			0
$445$	−2.73930	−	3.16132i	−0.129855	−	0.149861i
$446$		0			0
$447$	−1.62771	+	3.56419i	−0.0769880	+	0.168580i
$448$		0			0
$449$	−15.8728	+	4.66067i	−0.749083	+	0.219951i	−0.633923	−	0.773396i	$-0.718556\pi$
$449$	−15.8728	+	4.66067i	−0.749083	+	0.219951i	−0.115160	+	0.993347i	$0.536738\pi$
$450$		0			0
$451$	2.11059	+	14.6795i	0.0993838	+	0.691230i
$452$		0			0
$453$	8.76108	+	19.1841i	0.411631	+	0.901347i
$454$		0			0
$455$	0.428038	−	2.97707i	0.0200667	−	0.139567i
$456$		0			0
$457$	−19.2541	+	22.2204i	−0.900670	+	1.03943i	0.0983492	+	0.995152i	$0.468644\pi$
$457$	−19.2541	+	22.2204i	−0.900670	+	1.03943i	−0.999019	+	0.0442767i	$0.985902\pi$
$458$		0			0
$459$	−6.47369			−0.302166
$460$		0			0
$461$	37.2999			1.73723			0.868615	−	0.495488i	$-0.165011\pi$
$461$	37.2999			1.73723			0.868615	+	0.495488i	$0.165011\pi$
$462$		0			0
$463$	−17.4230	+	20.1072i	−0.809716	+	0.934463i	−0.998872	−	0.0474845i	$-0.984880\pi$
$463$	−17.4230	+	20.1072i	−0.809716	+	0.934463i	0.189156	+	0.981947i	$0.439425\pi$
$464$		0			0
$465$	0.240603	−	1.67343i	0.0111577	−	0.0776034i
$466$		0			0
$467$	−2.99605	−	6.56044i	−0.138641	−	0.303581i	0.827558	−	0.561381i	$-0.189730\pi$
$467$	−2.99605	−	6.56044i	−0.138641	−	0.303581i	−0.966198	+	0.257800i	$0.917002\pi$
$468$		0			0
$469$	−4.26330	−	29.6519i	−0.196861	−	1.36920i
$470$		0			0
$471$	12.2946	−	3.61002i	0.566505	−	0.166341i
$472$		0			0
$473$	−29.5167	+	64.6325i	−1.35718	+	2.97181i
$474$		0			0
$475$	−22.7579	−	26.2640i	−1.04420	−	1.20507i
$476$		0			0
$477$	−7.79004	+	5.00635i	−0.356681	+	0.229225i
$478$		0			0
$479$	−21.0736	−	13.5432i	−0.962879	−	0.618805i	−0.0380857	−	0.999274i	$-0.512126\pi$
$479$	−21.0736	−	13.5432i	−0.962879	−	0.618805i	−0.924793	+	0.380470i	$0.875762\pi$
$480$		0			0
$481$	−16.6343	−	4.88426i	−0.758457	−	0.222703i
$482$		0			0
$483$	−15.6327	−	3.29388i	−0.711314	−	0.149877i
$484$		0			0
$485$	2.59792	+	0.762818i	0.117965	+	0.0346378i
$486$		0			0
$487$	10.0136	+	6.43533i	0.453758	+	0.291613i	0.747487	−	0.664276i	$-0.231260\pi$
$487$	10.0136	+	6.43533i	0.453758	+	0.291613i	−0.293729	+	0.955889i	$0.594896\pi$
$488$		0			0
$489$	−0.395721	+	0.254314i	−0.0178951	+	0.0115005i
$490$		0			0
$491$	8.38698	+	9.67910i	0.378499	+	0.436812i	0.912752	−	0.408513i	$-0.133953\pi$
$491$	8.38698	+	9.67910i	0.378499	+	0.436812i	−0.534253	+	0.845325i	$0.679407\pi$
$492$		0			0
$493$	−5.84352	+	12.7955i	−0.263179	+	0.576282i
$494$		0			0
$495$	1.91537	−	0.562402i	0.0860893	−	0.0252781i
$496$		0			0
$497$	−6.20371	−	43.1477i	−0.278274	−	1.93544i
$498$		0			0
$499$	6.18692	+	13.5475i	0.276964	+	0.606467i	0.996083	−	0.0884196i	$-0.0281816\pi$
$499$	6.18692	+	13.5475i	0.276964	+	0.606467i	−0.719119	+	0.694887i	$0.755454\pi$
$500$		0			0
$501$	3.38806	−	23.5645i	0.151367	−	1.05278i
$502$		0			0
$503$	15.2487	−	17.5979i	0.679904	−	0.784651i	−0.305988	−	0.952035i	$-0.598987\pi$
$503$	15.2487	−	17.5979i	0.679904	−	0.784651i	0.985892	+	0.167384i	$0.0535321\pi$
$504$		0			0
$505$	1.06637			0.0474529
$506$		0			0
$507$	6.73789			0.299240
$508$		0			0
$509$	−6.21785	+	7.17578i	−0.275601	+	0.318061i	−0.876629	−	0.481168i	$-0.840213\pi$
$509$	−6.21785	+	7.17578i	−0.275601	+	0.318061i	0.601027	+	0.799228i	$0.294758\pi$
$510$		0			0
$511$	−3.58085	+	24.9053i	−0.158407	+	1.10175i
$512$		0			0
$513$	2.96450	+	6.49135i	0.130886	+	0.286600i
$514$		0			0
$515$	0.0984908	+	0.685019i	0.00434002	+	0.0301855i
$516$		0			0
$517$	13.5435	−	3.97672i	0.595641	−	0.174896i
$518$		0			0
$519$	0.326359	−	0.714627i	0.0143256	−	0.0313687i
$520$		0			0
$521$	−12.9050	−	14.8931i	−0.565378	−	0.652481i	0.399018	−	0.916943i	$-0.369351\pi$
$521$	−12.9050	−	14.8931i	−0.565378	−	0.652481i	−0.964396	+	0.264462i	$0.914806\pi$
$522$		0			0
$523$	−3.49191	+	2.24411i	−0.152691	+	0.0981283i	−0.614755	−	0.788718i	$-0.710745\pi$
$523$	−3.49191	+	2.24411i	−0.152691	+	0.0981283i	0.462065	+	0.886846i	$0.347109\pi$
$524$		0			0
$525$	13.6472	+	8.77053i	0.595613	+	0.382777i
$526$		0			0
$527$	−29.1056	−	8.54618i	−1.26786	−	0.372277i
$528$		0			0
$529$	22.7212	−	3.57042i	0.987877	−	0.155236i
$530$		0			0
$531$	−2.99470	−	0.879324i	−0.129959	−	0.0381594i
$532$		0			0
$533$	−5.64285	−	3.62644i	−0.244419	−	0.157079i
$534$		0			0
$535$	1.75321	−	1.12672i	0.0757978	−	0.0487123i
$536$		0			0
$537$	−10.0247	−	11.5691i	−0.432597	−	0.499244i
$538$		0			0
$539$	−9.41664	+	20.6196i	−0.405604	+	0.888148i
$540$		0			0
$541$	−31.1848	+	9.15670i	−1.34074	+	0.393677i	−0.871934	−	0.489623i	$-0.837134\pi$
$541$	−31.1848	+	9.15670i	−1.34074	+	0.393677i	−0.468807	+	0.883301i	$0.655316\pi$
$542$		0			0
$543$	−1.26082	−	8.76920i	−0.0541070	−	0.376322i
$544$		0			0
$545$	0.731426	+	1.60160i	0.0313308	+	0.0686050i
$546$		0			0
$547$	1.24813	−	8.68093i	0.0533662	−	0.371170i	−0.945585	−	0.325376i	$-0.894509\pi$
$547$	1.24813	−	8.68093i	0.0533662	−	0.371170i	0.998951	−	0.0457939i	$-0.0145817\pi$
$548$		0			0
$549$	−3.85872	+	4.45320i	−0.164686	+	0.190058i
$550$		0			0
$551$	15.5064			0.660594
$552$		0			0
$553$	−5.58307			−0.237416
$554$		0			0
$555$	−1.63688	+	1.88907i	−0.0694819	+	0.0801864i
$556$		0			0
$557$	−3.20542	+	22.2942i	−0.135818	+	0.944636i	0.801954	+	0.597385i	$0.203794\pi$
$557$	−3.20542	+	22.2942i	−0.135818	+	0.944636i	−0.937772	+	0.347250i	$0.887115\pi$
$558$		0			0
$559$	−13.3501	−	29.2327i	−0.564650	−	1.23641i
$560$		0			0
$561$	−5.09735	−	35.4529i	−0.215210	−	1.49682i
$562$		0			0
$563$	−23.7010	+	6.95923i	−0.998877	+	0.293297i	−0.739995	−	0.672612i	$-0.765172\pi$
$563$	−23.7010	+	6.95923i	−0.998877	+	0.293297i	−0.258882	+	0.965909i	$0.583354\pi$
$564$		0			0
$565$	−0.761752	+	1.66800i	−0.0320471	+	0.0701734i
$566$		0			0
$567$	−2.18149	−	2.51757i	−0.0916139	−	0.105728i
$568$		0			0
$569$	−5.62804	+	3.61692i	−0.235940	+	0.151629i	−0.653268	−	0.757126i	$-0.726603\pi$
$569$	−5.62804	+	3.61692i	−0.235940	+	0.151629i	0.417329	+	0.908756i	$0.362966\pi$
$570$		0			0
$571$	15.3233	+	9.84769i	0.641260	+	0.412113i	0.820463	−	0.571699i	$-0.193716\pi$
$571$	15.3233	+	9.84769i	0.641260	+	0.412113i	−0.179203	+	0.983812i	$0.557352\pi$
$572$		0			0
$573$	25.9195	+	7.61065i	1.08280	+	0.317939i
$574$		0			0
$575$	−22.8531	−	4.81523i	−0.953039	−	0.200809i
$576$		0			0
$577$	−7.96363	−	2.33833i	−0.331530	−	0.0973461i	0.111731	−	0.993738i	$-0.464360\pi$
$577$	−7.96363	−	2.33833i	−0.331530	−	0.0973461i	−0.443261	+	0.896392i	$0.646179\pi$
$578$		0			0
$579$	2.47944	+	1.59344i	0.103042	+	0.0662211i
$580$		0			0
$581$	32.8702	−	21.1244i	1.36369	−	0.876388i
$582$		0			0
$583$	−33.5509	−	38.7198i	−1.38954	−	1.60361i
$584$		0			0
$585$	−0.375068	+	0.821285i	−0.0155072	+	0.0339559i
$586$		0			0
$587$	−23.2207	+	6.81821i	−0.958420	+	0.281417i	−0.723288	−	0.690546i	$-0.757370\pi$
$587$	−23.2207	+	6.81821i	−0.958420	+	0.281417i	−0.235132	+	0.971964i	$0.575552\pi$
$588$		0			0
$589$	4.75886	+	33.0986i	0.196085	+	1.36380i
$590$		0			0
$591$	1.44651	+	3.16741i	0.0595014	+	0.130290i
$592$		0			0
$593$	4.97310	−	34.5887i	0.204221	−	1.42039i	−0.587362	−	0.809325i	$-0.699833\pi$
$593$	4.97310	−	34.5887i	0.204221	−	1.42039i	0.791582	−	0.611062i	$-0.209258\pi$
$594$		0			0
$595$	−5.09533	+	5.88032i	−0.208888	+	0.241070i
$596$		0			0
$597$	−23.1790			−0.948653
$598$		0			0
$599$	−27.3249			−1.11646			−0.558232	−	0.829685i	$-0.688520\pi$
$599$	−27.3249			−1.11646			−0.558232	+	0.829685i	$0.688520\pi$
$600$		0			0
$601$	−3.82299	+	4.41197i	−0.155943	+	0.179968i	−0.828345	−	0.560218i	$-0.810717\pi$
$601$	−3.82299	+	4.41197i	−0.155943	+	0.179968i	0.672402	+	0.740186i	$0.265263\pi$
$602$		0			0
$603$	−1.27980	+	8.90120i	−0.0521175	+	0.362485i
$604$		0			0
$605$	2.93942	+	6.43643i	0.119504	+	0.261678i
$606$		0			0
$607$	−0.410514	−	2.85519i	−0.0166622	−	0.115888i	0.979793	−	0.200015i	$-0.0640991\pi$
$607$	−0.410514	−	2.85519i	−0.0166622	−	0.115888i	−0.996455	+	0.0841266i	$0.973190\pi$
$608$		0			0
$609$	−6.94522	+	2.03930i	−0.281435	+	0.0826367i
$610$		0			0
$611$	−2.65209	+	5.80727i	−0.107292	+	0.234937i
$612$		0			0
$613$	−2.54314	−	2.93495i	−0.102717	−	0.118541i	0.702063	−	0.712114i	$-0.252262\pi$
$613$	−2.54314	−	2.93495i	−0.102717	−	0.118541i	−0.804780	+	0.593573i	$0.797717\pi$
$614$		0			0
$615$	−0.813590	+	0.522863i	−0.0328071	+	0.0210839i
$616$		0			0
$617$	−13.2686	−	8.52718i	−0.534172	−	0.343291i	0.245584	−	0.969375i	$-0.421020\pi$
$617$	−13.2686	−	8.52718i	−0.534172	−	0.343291i	−0.779756	+	0.626084i	$0.784657\pi$
$618$		0			0
$619$	−5.97278	−	1.75377i	−0.240066	−	0.0704898i	0.159486	−	0.987200i	$-0.449016\pi$
$619$	−5.97278	−	1.75377i	−0.240066	−	0.0704898i	−0.399552	+	0.916710i	$0.630834\pi$
$620$		0			0
$621$	4.22413	+	2.27085i	0.169508	+	0.0911260i
$622$		0			0
$623$	−37.0569	−	10.8809i	−1.48465	−	0.435933i
$624$		0			0
$625$	19.4029	+	12.4695i	0.776117	+	0.498780i
$626$		0			0
$627$	−33.2154	+	21.3462i	−1.32649	+	0.852486i
$628$		0			0
$629$	29.3699	+	33.8947i	1.17105	+	1.35147i
$630$		0			0
$631$	−5.48383	+	12.0079i	−0.218308	+	0.478027i	−0.986823	−	0.161804i	$-0.948269\pi$
$631$	−5.48383	+	12.0079i	−0.218308	+	0.478027i	0.768515	+	0.639832i	$0.220996\pi$
$632$		0			0
$633$	−8.53353	+	2.50567i	−0.339177	+	0.0995915i
$634$		0			0
$635$	0.608603	+	4.23293i	0.0241517	+	0.167979i
$636$		0			0
$637$	−4.25906	−	9.32605i	−0.168750	−	0.369511i
$638$		0			0
$639$	−1.86229	+	12.9525i	−0.0736711	+	0.512394i
$640$		0			0
$641$	15.3102	−	17.6689i	0.604715	−	0.697878i	−0.368015	−	0.929820i	$-0.619963\pi$
$641$	15.3102	−	17.6689i	0.604715	−	0.697878i	0.972730	+	0.231942i	$0.0745080\pi$
$642$		0			0
$643$	23.2890			0.918429			0.459215	−	0.888325i	$-0.348131\pi$
$643$	23.2890			0.918429			0.459215	+	0.888325i	$0.348131\pi$
$644$		0			0
$645$	−4.63352			−0.182444
$646$		0			0
$647$	−16.7674	+	19.3506i	−0.659195	+	0.760752i	−0.982646	−	0.185493i	$-0.940612\pi$
$647$	−16.7674	+	19.3506i	−0.659195	+	0.760752i	0.323450	+	0.946245i	$0.395157\pi$
$648$		0			0
$649$	2.45756	−	17.0927i	0.0964677	−	0.670948i
$650$		0			0
$651$	−6.48439	−	14.1988i	−0.254143	−	0.556496i
$652$		0			0
$653$	5.74961	+	39.9894i	0.225000	+	1.56491i	0.718728	+	0.695291i	$0.244725\pi$
$653$	5.74961	+	39.9894i	0.225000	+	1.56491i	−0.493728	+	0.869616i	$0.664366\pi$
$654$		0			0
$655$	−2.58964	+	0.760387i	−0.101186	+	0.0297108i
$656$		0			0
$657$	3.13772	−	6.87065i	0.122414	−	0.268049i
$658$		0			0
$659$	4.43932	+	5.12325i	0.172931	+	0.199573i	0.835598	−	0.549341i	$-0.185121\pi$
$659$	4.43932	+	5.12325i	0.172931	+	0.199573i	−0.662667	+	0.748914i	$0.730576\pi$
$660$		0			0
$661$	−20.9110	+	13.4387i	−0.813343	+	0.522704i	−0.879945	−	0.475076i	$-0.842421\pi$
$661$	−20.9110	+	13.4387i	−0.813343	+	0.522704i	0.0666018	+	0.997780i	$0.478784\pi$
$662$		0			0
$663$	13.6282	+	8.75833i	0.529276	+	0.340145i
$664$		0			0
$665$	8.22967	+	2.41645i	0.319133	+	0.0937059i
$666$		0			0
$667$	8.30137	−	6.29937i	0.321430	−	0.243913i
$668$		0			0
$669$	0.799898	+	0.234871i	0.0309258	+	0.00908065i
$670$		0			0
$671$	−27.4261	−	17.6257i	−1.05877	−	0.680431i
$672$		0			0
$673$	−12.1017	+	7.77730i	−0.466487	+	0.299793i	−0.752689	−	0.658377i	$-0.771243\pi$
$673$	−12.1017	+	7.77730i	−0.466487	+	0.299793i	0.286202	+	0.958169i	$0.407607\pi$
$674$		0			0
$675$	−3.18906	−	3.68037i	−0.122747	−	0.141657i
$676$		0			0
$677$	11.2772	−	24.6937i	0.433419	−	0.949055i	−0.559341	−	0.828938i	$-0.688946\pi$
$677$	11.2772	−	24.6937i	0.433419	−	0.949055i	0.992760	−	0.120117i	$-0.0383270\pi$
$678$		0			0
$679$	23.9862	−	7.04299i	0.920507	−	0.270285i
$680$		0			0
$681$	3.84967	+	26.7750i	0.147520	+	1.02602i
$682$		0			0
$683$	−6.50303	−	14.2396i	−0.248832	−	0.544865i	0.743461	−	0.668779i	$-0.233183\pi$
$683$	−6.50303	−	14.2396i	−0.248832	−	0.544865i	−0.992293	+	0.123914i	$0.960455\pi$
$684$		0			0
$685$	0.256517	−	1.78412i	0.00980102	−	0.0681676i
$686$		0			0
$687$	−5.14414	+	5.93665i	−0.196261	+	0.226497i
$688$		0			0
$689$	23.1725			0.882803
$690$		0			0
$691$	44.6487			1.69852			0.849258	−	0.527979i	$-0.177050\pi$
$691$	44.6487			1.69852			0.849258	+	0.527979i	$0.177050\pi$
$692$		0			0
$693$	12.0697	−	13.9291i	0.458489	−	0.529124i
$694$		0			0
$695$	−0.458374	+	3.18806i	−0.0173871	+	0.120930i
$696$		0			0
$697$	7.20851	+	15.7844i	0.273042	+	0.597878i
$698$		0			0
$699$	0.612391	+	4.25928i	0.0231628	+	0.161101i
$700$		0			0
$701$	−8.11021	+	2.38137i	−0.306318	+	0.0899432i	−0.431279	−	0.902218i	$-0.641938\pi$
$701$	−8.11021	+	2.38137i	−0.306318	+	0.0899432i	0.124961	+	0.992162i	$0.460119\pi$
$702$		0			0
$703$	20.5378	−	44.9714i	0.774596	−	1.69613i
$704$		0			0
$705$	0.602785	+	0.695651i	0.0227022	+	0.0261997i
$706$		0			0
$707$	8.28270	−	5.32297i	0.311503	−	0.200191i
$708$		0			0
$709$	−37.3850	−	24.0259i	−1.40402	−	0.902312i	−0.404101	−	0.914714i	$-0.632416\pi$
$709$	−37.3850	−	24.0259i	−1.40402	−	0.902312i	−0.999923	+	0.0124024i	$0.996052\pi$
$710$		0			0
$711$	1.60809	+	0.472179i	0.0603082	+	0.0177081i
$712$		0			0
$713$	15.9938	+	15.7861i	0.598971	+	0.591195i
$714$		0			0
$715$	−4.79305	−	1.40737i	−0.179250	−	0.0526326i
$716$		0			0
$717$	13.4133	+	8.62018i	0.500928	+	0.321927i
$718$		0			0
$719$	34.6032	−	22.2381i	1.29048	−	0.829343i	0.298340	−	0.954460i	$-0.403567\pi$
$719$	34.6032	−	22.2381i	1.29048	−	0.829343i	0.992142	+	0.125117i	$0.0399307\pi$
$720$		0			0
$721$	4.18437	+	4.82903i	0.155834	+	0.179842i
$722$		0			0
$723$	−2.34977	+	5.14527i	−0.0873887	+	0.191355i
$724$		0			0
$725$	−10.1530	+	2.98120i	−0.377074	+	0.110719i
$726$		0			0
$727$	−4.89298	−	34.0314i	−0.181470	−	1.26215i	−0.853289	−	0.521439i	$-0.825396\pi$
$727$	−4.89298	−	34.0314i	−0.181470	−	1.26215i	0.671818	−	0.740716i	$-0.265514\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	−11.8316	+	82.2909i	−0.437609	+	3.04364i
$732$		0			0
$733$	9.71756	−	11.2147i	0.358926	−	0.414223i	−0.547353	−	0.836902i	$-0.684365\pi$
$733$	9.71756	−	11.2147i	0.358926	−	0.414223i	0.906280	+	0.422678i	$0.138910\pi$
$734$		0			0
$735$	−1.47822			−0.0545250
$736$		0			0
$737$	−49.7547			−1.83274
$738$		0			0
$739$	28.7288	−	33.1548i	1.05681	−	1.21962i	0.0819859	−	0.996633i	$-0.473874\pi$
$739$	28.7288	−	33.1548i	1.05681	−	1.21962i	0.974821	−	0.222987i	$-0.0715808\pi$
$740$		0			0
$741$	2.54144	−	17.6761i	0.0933622	−	0.649348i
$742$		0			0
$743$	3.28917	+	7.20228i	0.120668	+	0.264226i	0.960321	−	0.278897i	$-0.0899689\pi$
$743$	3.28917	+	7.20228i	0.120668	+	0.264226i	−0.839653	+	0.543123i	$0.817242\pi$
$744$		0			0
$745$	−0.201193	−	1.39933i	−0.00737113	−	0.0512674i
$746$		0			0
$747$	−11.2542	+	3.30452i	−0.411769	+	0.120906i
$748$		0			0
$749$	7.99328	−	17.5028i	0.292068	−	0.639540i
$750$		0			0
$751$	16.3311	+	18.8471i	0.595932	+	0.687742i	0.970952	−	0.239275i	$-0.0769096\pi$
$751$	16.3311	+	18.8471i	0.595932	+	0.687742i	−0.375020	+	0.927017i	$0.622364\pi$
$752$		0			0
$753$	−10.4106	+	6.69048i	−0.379383	+	0.243815i
$754$		0			0
$755$	−6.40132	−	4.11388i	−0.232968	−	0.149719i
$756$		0			0
$757$	18.5745	+	5.45396i	0.675102	+	0.198228i	0.601274	−	0.799043i	$-0.294660\pi$
$757$	18.5745	+	5.45396i	0.675102	+	0.198228i	0.0738281	+	0.997271i	$0.476478\pi$
$758$		0			0
$759$	−9.11014	+	24.9213i	−0.330677	+	0.904585i
$760$		0			0
$761$	12.8610	+	3.77632i	0.466209	+	0.136891i	0.506396	−	0.862301i	$-0.330977\pi$
$761$	12.8610	+	3.77632i	0.466209	+	0.136891i	−0.0401873	+	0.999192i	$0.512795\pi$
$762$		0			0
$763$	13.6758	+	8.78887i	0.495096	+	0.318179i
$764$		0			0
$765$	1.96493	−	1.26278i	0.0710421	−	0.0456560i
$766$		0			0
$767$	5.11471	+	5.90269i	0.184682	+	0.213134i
$768$		0			0
$769$	4.21544	−	9.23052i	0.152013	−	0.332861i	−0.818271	−	0.574833i	$-0.805067\pi$
$769$	4.21544	−	9.23052i	0.152013	−	0.332861i	0.970283	+	0.241972i	$0.0777942\pi$
$770$		0			0
$771$	5.88713	−	1.72862i	0.212020	−	0.0622546i
$772$		0			0
$773$	1.15306	+	8.01974i	0.0414728	+	0.288450i	0.999994	+	0.00342899i	$0.00109148\pi$
$773$	1.15306	+	8.01974i	0.0414728	+	0.288450i	−0.958521	+	0.285021i	$0.907999\pi$
$774$		0			0
$775$	−9.47934	−	20.7569i	−0.340508	−	0.745609i
$776$		0			0
$777$	−3.28440	+	22.8435i	−0.117827	+	0.819505i
$778$		0			0
$779$	12.5265	−	14.4563i	0.448808	−	0.517952i
$780$		0			0
$781$	−72.4002			−2.59068
$782$		0			0
$783$	2.17290			0.0776533
$784$		0			0
$785$	−3.02753	+	3.49396i	−0.108057	+	0.124705i
$786$		0			0
$787$	4.62383	−	32.1594i	0.164822	−	1.14636i	−0.724565	−	0.689206i	$-0.757960\pi$
$787$	4.62383	−	32.1594i	0.164822	−	1.14636i	0.889387	−	0.457155i	$-0.151131\pi$
$788$		0			0
$789$	−2.15350	−	4.71552i	−0.0766668	−	0.167877i
$790$		0			0
$791$	2.40945	+	16.7581i	0.0856701	+	0.595849i
$792$		0			0
$793$	14.1480	−	4.15424i	0.502412	−	0.147521i
$794$		0			0
$795$	1.38791	−	3.03911i	0.0492242	−	0.107786i
$796$		0			0
$797$	15.0401	+	17.3572i	0.532747	+	0.614823i	0.956776	−	0.290826i	$-0.0939300\pi$
$797$	15.0401	+	17.3572i	0.532747	+	0.614823i	−0.424029	+	0.905649i	$0.639385\pi$
$798$		0			0
$799$	13.8939	−	8.92907i	0.491531	−	0.315888i
$800$		0			0
$801$	9.75327	+	6.26804i	0.344615	+	0.221470i
$802$		0			0
$803$	40.0974	+	11.7737i	1.41501	+	0.415483i
$804$		0			0
$805$	5.38744	−	2.04961i	0.189882	−	0.0722391i
$806$		0			0
$807$	−18.9364	−	5.56023i	−0.666593	−	0.195729i
$808$		0			0
$809$	−24.7196	−	15.8864i	−0.869097	−	0.558534i	0.0283797	−	0.999597i	$-0.490965\pi$
$809$	−24.7196	−	15.8864i	−0.869097	−	0.558534i	−0.897476	+	0.441063i	$0.854602\pi$
$810$		0			0
$811$	−26.1106	+	16.7803i	−0.916869	+	0.589236i	−0.911747	−	0.410751i	$-0.865266\pi$
$811$	−26.1106	+	16.7803i	−0.916869	+	0.589236i	−0.00512117	+	0.999987i	$0.501630\pi$
$812$		0			0
$813$	5.48470	+	6.32968i	0.192357	+	0.221992i
$814$		0			0
$815$	0.0705036	−	0.154381i	0.00246963	−	0.00540775i
$816$		0			0
$817$	87.9335	−	25.8196i	3.07640	−	0.903313i
$818$		0			0
$819$	1.18635	+	8.25127i	0.0414546	+	0.288323i
$820$		0			0
$821$	−10.0509	−	22.0085i	−0.350780	−	0.768102i	−0.999972	−	0.00747695i	$-0.997620\pi$
$821$	−10.0509	−	22.0085i	−0.350780	−	0.768102i	0.649192	−	0.760625i	$-0.275107\pi$
$822$		0			0
$823$	4.52695	−	31.4856i	0.157800	−	1.09752i	−0.744877	−	0.667202i	$-0.767492\pi$
$823$	4.52695	−	31.4856i	0.157800	−	1.09752i	0.902677	−	0.430319i	$-0.141599\pi$
$824$		0			0
$825$	17.6443	−	20.3626i	0.614296	−	0.708935i
$826$		0			0
$827$	23.1346			0.804470			0.402235	−	0.915536i	$-0.368233\pi$
$827$	23.1346			0.804470			0.402235	+	0.915536i	$0.368233\pi$
$828$		0			0
$829$	−1.06791			−0.0370899			−0.0185450	−	0.999828i	$-0.505903\pi$
$829$	−1.06791			−0.0370899			−0.0185450	+	0.999828i	$0.505903\pi$
$830$		0			0
$831$	−0.126074	+	0.145497i	−0.00437345	+	0.00504723i
$832$		0			0
$833$	−3.77462	+	26.2531i	−0.130783	+	0.909615i
$834$		0			0
$835$	3.56822	+	7.81330i	0.123483	+	0.270390i
$836$		0			0
$837$	0.666858	+	4.63810i	0.0230500	+	0.160316i
$838$		0			0
$839$	−28.1845	+	8.27573i	−0.973039	+	0.285710i	−0.729348	−	0.684143i	$-0.760176\pi$
$839$	−28.1845	+	8.27573i	−0.973039	+	0.285710i	−0.243691	+	0.969853i	$0.578358\pi$
$840$		0			0
$841$	−10.0856	+	22.0845i	−0.347781	+	0.761534i
$842$		0			0
$843$	6.23194	+	7.19204i	0.214639	+	0.247707i
$844$		0			0
$845$	−2.04512	+	1.31432i	−0.0703542	+	0.0452139i
$846$		0			0
$847$	54.9594	+	35.3203i	1.88843	+	1.21362i
$848$		0			0
$849$	−9.31224	−	2.73432i	−0.319595	−	0.0938416i
$850$		0			0
$851$	−7.27444	−	32.4189i	−0.249365	−	1.11131i
$852$		0			0
$853$	46.7465	+	13.7260i	1.60057	+	0.469969i	0.955704	−	0.294328i	$-0.0950959\pi$
$853$	46.7465	+	13.7260i	1.60057	+	0.469969i	0.644864	+	0.764298i	$0.276914\pi$
$854$		0			0
$855$	−2.16603	−	1.39202i	−0.0740766	−	0.0476061i
$856$		0			0
$857$	−3.19603	+	2.05396i	−0.109174	+	0.0701621i	−0.594089	−	0.804400i	$-0.702487\pi$
$857$	−3.19603	+	2.05396i	−0.109174	+	0.0701621i	0.484914	+	0.874562i	$0.338851\pi$
$858$		0			0
$859$	−10.6626	−	12.3053i	−0.363803	−	0.419851i	0.544107	−	0.839016i	$-0.316868\pi$
$859$	−10.6626	−	12.3053i	−0.363803	−	0.419851i	−0.907910	+	0.419165i	$0.862323\pi$
$860$		0			0
$861$	−3.70934	+	8.12233i	−0.126414	+	0.276808i
$862$		0			0
$863$	22.5069	−	6.60861i	0.766142	−	0.224960i	0.124766	−	0.992186i	$-0.460182\pi$
$863$	22.5069	−	6.60861i	0.766142	−	0.224960i	0.641376	+	0.767227i	$0.278364\pi$
$864$		0			0
$865$	0.0403396	+	0.280568i	0.00137159	+	0.00953960i
$866$		0			0
$867$	−10.3474	−	22.6577i	−0.351417	−	0.769496i
$868$		0			0
$869$	−1.31966	+	9.17844i	−0.0447664	+	0.311357i
$870$		0			0
$871$	14.7367	−	17.0071i	0.499335	−	0.576263i
$872$		0			0
$873$	−7.50440			−0.253986
$874$		0			0
$875$	−11.8626			−0.401030
$876$		0			0
$877$	5.65272	−	6.52358i	0.190879	−	0.220286i	−0.652241	−	0.758012i	$-0.726171\pi$
$877$	5.65272	−	6.52358i	0.190879	−	0.220286i	0.843120	+	0.537726i	$0.180716\pi$
$878$		0			0
$879$	4.69480	−	32.6530i	0.158352	−	1.10136i
$880$		0			0
$881$	−5.84942	−	12.8084i	−0.197072	−	0.431527i	0.785136	−	0.619323i	$-0.212593\pi$
$881$	−5.84942	−	12.8084i	−0.197072	−	0.431527i	−0.982208	+	0.187796i	$0.939866\pi$
$882$		0			0
$883$	6.94781	+	48.3230i	0.233812	+	1.62620i	0.681366	+	0.731943i	$0.261386\pi$
$883$	6.94781	+	48.3230i	0.233812	+	1.62620i	−0.447554	+	0.894257i	$0.647705\pi$
$884$		0			0
$885$	1.08049	−	0.317261i	0.0363203	−	0.0106646i
$886$		0			0
$887$	8.08595	−	17.7058i	0.271500	−	0.594501i	−0.723943	−	0.689859i	$-0.757672\pi$
$887$	8.08595	−	17.7058i	0.271500	−	0.594501i	0.995443	+	0.0953581i	$0.0303996\pi$
$888$		0			0
$889$	25.8565	+	29.8399i	0.867198	+	1.00080i
$890$		0			0
$891$	−4.65446	+	2.99124i	−0.155930	+	0.100210i
$892$		0			0
$893$	−15.3159	−	9.84292i	−0.512526	−	0.329381i
$894$		0			0
$895$	5.29946	+	1.55606i	0.177141	+	0.0520134i
$896$		0			0
$897$	−5.82025	−	10.4954i	−0.194333	−	0.350431i
$898$		0			0
$899$	9.76934	+	2.86854i	0.325826	+	0.0956711i
$900$		0			0
$901$	−50.4303	−	32.4096i	−1.68008	−	1.07972i
$902$		0			0
$903$	−35.9893	+	23.1289i	−1.19765	+	0.769683i
$904$		0			0
$905$	2.09324	+	2.41573i	0.0695818	+	0.0803016i
$906$		0			0
$907$	−12.2446	+	26.8120i	−0.406576	+	0.890277i	0.589985	+	0.807414i	$0.299134\pi$
$907$	−12.2446	+	26.8120i	−0.406576	+	0.890277i	−0.996561	+	0.0828631i	$0.973594\pi$
$908$		0			0
$909$	−2.83585	+	0.832680i	−0.0940591	+	0.0276183i
$910$		0			0
$911$	−6.05770	−	42.1322i	−0.200701	−	1.39590i	−0.802212	−	0.597039i	$-0.796344\pi$
$911$	−6.05770	−	42.1322i	−0.200701	−	1.39590i	0.601511	−	0.798864i	$-0.294565\pi$
$912$		0			0
$913$	−26.9586	−	59.0310i	−0.892198	−	1.95364i
$914$		0			0
$915$	0.302560	−	2.10435i	0.0100023	−	0.0695678i
$916$		0			0
$917$	−16.3186	+	18.8327i	−0.538887	+	0.621909i
$918$		0			0
$919$	−2.55302			−0.0842163			−0.0421081	−	0.999113i	$-0.513407\pi$
$919$	−2.55302			−0.0842163			−0.0421081	+	0.999113i	$0.513407\pi$
$920$		0			0
$921$	30.0217			0.989248
$922$		0			0
$923$	21.4440	−	24.7477i	0.705839	−	0.814582i
$924$		0			0
$925$	−4.80137	+	33.3942i	−0.157868	+	1.09800i
$926$		0			0
$927$	−0.796820	−	1.74479i	−0.0261710	−	0.0573065i
$928$		0			0
$929$	5.11143	+	35.5508i	0.167701	+	1.16638i	0.883621	+	0.468202i	$0.155098\pi$
$929$	5.11143	+	35.5508i	0.167701	+	1.16638i	−0.715921	+	0.698181i	$0.753993\pi$
$930$		0			0
$931$	28.0532	−	8.23717i	0.919407	−	0.269962i
$932$		0			0
$933$	1.07084	−	2.34481i	0.0350577	−	0.0767656i
$934$		0			0
$935$	8.46274	+	9.76652i	0.276761	+	0.319399i
$936$		0			0
$937$	5.70758	−	3.66804i	0.186458	−	0.119830i	−0.444081	−	0.895986i	$-0.646470\pi$
$937$	5.70758	−	3.66804i	0.186458	−	0.119830i	0.630540	+	0.776157i	$0.282834\pi$
$938$		0			0
$939$	13.8795	+	8.91982i	0.452941	+	0.291087i
$940$		0			0
$941$	14.5435	+	4.27035i	0.474104	+	0.139209i	0.510051	−	0.860144i	$-0.329627\pi$
$941$	14.5435	+	4.27035i	0.474104	+	0.139209i	−0.0359471	+	0.999354i	$0.511445\pi$
$942$		0			0
$943$	0.833282	−	12.8281i	0.0271354	−	0.417739i
$944$		0			0
$945$	1.15322	+	0.338617i	0.0375143	+	0.0110152i
$946$		0			0
$947$	29.8816	+	19.2038i	0.971023	+	0.624039i	0.927028	−	0.374993i	$-0.122355\pi$
$947$	29.8816	+	19.2038i	0.971023	+	0.624039i	0.0439954	+	0.999032i	$0.485991\pi$
$948$		0			0
$949$	−15.9008	+	10.2188i	−0.516162	+	0.331717i
$950$		0			0
$951$	1.19348	+	1.37735i	0.0387012	+	0.0446636i
$952$		0			0
$953$	15.9049	−	34.8268i	0.515209	−	1.12815i	−0.456013	−	0.889973i	$-0.650723\pi$
$953$	15.9049	−	34.8268i	0.515209	−	1.12815i	0.971222	−	0.238177i	$-0.0765498\pi$
$954$		0			0
$955$	−9.35178	+	2.74593i	−0.302616	+	0.0888562i
$956$		0			0
$957$	1.71093	+	11.8998i	0.0553067	+	0.384666i
$958$		0			0
$959$	−6.91329	−	15.1380i	−0.223242	−	0.488831i
$960$		0			0
$961$	1.28700	−	8.95132i	0.0415163	−	0.288752i
$962$		0			0
$963$	−3.78258	+	4.36533i	−0.121892	+	0.140671i
$964$		0			0
$965$	−1.06339			−0.0342319
$966$		0			0
$967$	−8.92604			−0.287042			−0.143521	−	0.989647i	$-0.545842\pi$
$967$	−8.92604			−0.287042			−0.143521	+	0.989647i	$0.545842\pi$
$968$		0			0
$969$	−30.2531	+	34.9140i	−0.971870	+	1.12160i
$970$		0			0
$971$	−8.46912	+	58.9040i	−0.271787	+	1.89032i	0.158078	+	0.987427i	$0.449470\pi$
$971$	−8.46912	+	58.9040i	−0.271787	+	1.89032i	−0.429865	+	0.902893i	$0.641439\pi$
$972$		0			0
$973$	12.3534	+	27.0502i	0.396033	+	0.867191i
$974$		0			0
$975$	1.73430	+	12.0623i	0.0555420	+	0.386303i
$976$		0			0
$977$	37.7732	−	11.0912i	1.20847	−	0.354839i	0.385385	−	0.922756i	$-0.374069\pi$
$977$	37.7732	−	11.0912i	1.20847	−	0.354839i	0.823086	+	0.567916i	$0.192250\pi$
$978$		0			0
$979$	−26.6470	+	58.3487i	−0.851641	+	1.86483i
$980$		0			0
$981$	−3.19573	−	3.68806i	−0.102032	−	0.117751i
$982$		0			0
$983$	−40.7214	+	26.1700i	−1.29881	+	0.834695i	−0.993082	−	0.117424i	$-0.962536\pi$
$983$	−40.7214	+	26.1700i	−1.29881	+	0.834695i	−0.305728	+	0.952119i	$0.598900\pi$
$984$		0			0
$985$	−1.05690	−	0.679227i	−0.0336756	−	0.0216420i
$986$		0			0
$987$	8.15438	+	2.39434i	0.259557	+	0.0762128i
$988$		0			0
$989$	36.5863	−	49.5450i	1.16338	−	1.57544i
$990$		0			0
$991$	16.6825	+	4.89841i	0.529936	+	0.155603i	0.535745	−	0.844380i	$-0.320031\pi$
$991$	16.6825	+	4.89841i	0.529936	+	0.155603i	−0.00580887	+	0.999983i	$0.501849\pi$
$992$		0			0
$993$	−10.9198	−	7.01774i	−0.346530	−	0.222701i
$994$		0			0
$995$	7.03540	−	4.52138i	0.223037	−	0.143337i
$996$		0			0
$997$	−36.8079	−	42.4786i	−1.16572	−	1.34531i	−0.927377	−	0.374128i	$-0.877942\pi$
$997$	−36.8079	−	42.4786i	−1.16572	−	1.34531i	−0.238340	−	0.971182i	$-0.576603\pi$
$998$		0			0
$999$	2.87795	−	6.30184i	0.0910544	−	0.199381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.133.1	✓	20
3.2	odd	2		828.2.q.b.685.2		20
23.3	even	11		6348.2.a.r.1.7		10
23.9	even	11	inner	276.2.i.b.193.1	yes	20
23.20	odd	22		6348.2.a.q.1.4		10
69.32	odd	22		828.2.q.b.469.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.133.1	✓	20	1.1	even	1	trivial
276.2.i.b.193.1	yes	20	23.9	even	11	inner
828.2.q.b.469.2		20	69.32	odd	22
828.2.q.b.685.2		20	3.2	odd	2
6348.2.a.q.1.4		10	23.20	odd	22
6348.2.a.r.1.7		10	23.3	even	11

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{3} +(-0.0513473 + 0.357128i) q^{5} +(1.38384 + 3.03019i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{3} +(-0.0513473 + 0.357128i) q^{5} +(1.38384 + 3.03019i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(5.30865 - 1.55876i) q^{11} +(-1.03954 + 2.27628i) q^{13} +(0.236274 + 0.272675i) q^{15} +(5.44601 - 3.49994i) q^{17} +(-6.00339 - 3.85814i) q^{19} +(3.19629 + 0.938514i) q^{21} +(-4.78128 + 0.373376i) q^{23} +(4.67256 + 1.37199i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(-1.82796 + 1.17476i) q^{29} +(-3.06854 - 3.54128i) q^{31} +(2.29840 - 5.03278i) q^{33} +(-1.15322 + 0.338617i) q^{35} +(0.985943 + 6.85738i) q^{37} +(1.03954 + 2.27628i) q^{39} +(-0.381471 + 2.65319i) q^{41} +(-8.40992 + 9.70557i) q^{43} +0.360801 q^{45} +2.55121 q^{47} +(-2.68300 + 3.09634i) q^{49} +(0.921302 - 6.40780i) q^{51} +(-3.84676 - 8.42323i) q^{53} +(0.284093 + 1.97591i) q^{55} +(-6.84717 + 2.01051i) q^{57} +(1.29656 - 2.83908i) q^{59} +(-3.85872 - 4.45320i) q^{61} +(2.80240 - 1.80100i) q^{63} +(-0.759547 - 0.488132i) q^{65} +(-8.62847 - 2.53355i) q^{67} +(-2.84889 + 3.85796i) q^{69} +(-12.5556 - 3.68667i) q^{71} +(6.35417 + 4.08358i) q^{73} +(4.09676 - 2.63282i) q^{75} +(12.0697 + 13.9291i) q^{77} +(-0.696228 + 1.52453i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-1.66925 - 11.6099i) q^{83} +(0.970290 + 2.12464i) q^{85} +(-0.309237 + 2.15079i) q^{87} +(-7.59228 + 8.76196i) q^{89} -8.33612 q^{91} -4.68579 q^{93} +(1.68611 - 1.94588i) q^{95} +(1.06799 - 7.42802i) q^{97} +(-2.29840 - 5.03278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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