LMFDB - Embedded newform 441.2.f.g.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.2
Root			$-1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	441.295
Dual form			441.2.f.g.148.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23025 + 2.13086i) q^{2} +(1.66238 + 0.486291i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.82904 + 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(2.52704 + 1.61680i) q^{9} -9.00071 q^{10} +(-0.203210 + 0.351971i) q^{11} +(-1.66238 - 6.82226i) q^{12} +(0.243398 + 0.421578i) q^{13} +(1.50000 + 6.15585i) q^{15} +(-2.16372 + 3.74766i) q^{16} +4.85584 q^{17} +(-6.55408 + 3.39569i) q^{18} -1.97351 q^{19} +(7.41507 - 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.32383 - 4.02499i) q^{23} +(8.40183 + 2.45776i) q^{24} +(-4.19076 + 7.25860i) q^{25} -1.19777 q^{26} +(3.41468 + 3.91663i) q^{27} +(-3.82383 + 6.62307i) q^{29} +(-14.9626 - 4.37697i) q^{30} +(-3.51360 - 6.08573i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(-0.508974 + 0.486291i) q^{33} +(-5.97391 + 10.3471i) q^{34} +(0.554084 - 12.1496i) q^{36} +2.32743 q^{37} +(2.42792 - 4.20528i) q^{38} +(0.199612 + 0.819187i) q^{39} +(9.24411 + 16.0113i) q^{40} +(-3.75700 - 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +1.64766 q^{44} +(-0.499960 + 10.9628i) q^{45} +11.4356 q^{46} +(3.15811 - 5.47002i) q^{47} +(-5.41938 + 5.17786i) q^{48} +(-10.3114 - 17.8598i) q^{50} +(8.07227 + 2.36135i) q^{51} +(0.986757 - 1.70911i) q^{52} -3.56867 q^{53} +(-12.5467 + 2.45776i) q^{54} -1.48672 q^{55} +(-3.28074 - 0.959702i) q^{57} +(-9.40856 - 16.2961i) q^{58} +(-3.05919 - 5.29868i) q^{59} +(18.5723 - 17.7446i) q^{60} +(4.01356 - 6.95169i) q^{61} +17.2905 q^{62} -7.32743 q^{64} +(-0.890369 + 1.54216i) q^{65} +(-0.410052 - 1.68281i) q^{66} +(-1.80039 - 3.11836i) q^{67} +(-9.84299 - 17.0486i) q^{68} +(-1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(12.7719 + 8.17147i) q^{72} +1.97351 q^{73} +(-2.86333 + 4.95943i) q^{74} +(-10.4964 + 10.0287i) q^{75} +(4.00040 + 6.92889i) q^{76} +(-1.99115 - 0.582462i) q^{78} +(-4.08113 + 7.06872i) q^{79} -15.8301 q^{80} +(3.77188 + 8.17147i) q^{81} +18.4882 q^{82} +(-6.08600 + 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(2.86333 + 4.95943i) q^{86} +(-9.57742 + 9.15059i) q^{87} +(-1.02704 + 1.77889i) q^{88} +14.8301 q^{89} +(-22.7452 - 14.5524i) q^{90} +(-9.42101 + 16.3177i) q^{92} +(-2.88151 - 11.8255i) q^{93} +(7.77056 + 13.4590i) q^{94} +(-3.60963 - 6.25206i) q^{95} +(-0.221221 - 0.907869i) q^{96} +(4.74375 - 8.21642i) q^{97} +(-1.08259 + 0.560893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43}+ \cdots - 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9 - 8 * q^11 + 18 * q^15 - 6 * q^16 - 42 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 - 48 * q^30 - 16 * q^32 - 30 * q^36 - 12 * q^37 + 24 * q^39 - 6 * q^43 - 28 * q^44 + 24 * q^46 - 56 * q^50 - 18 * q^51 + 56 * q^53 - 6 * q^57 - 18 * q^58 + 108 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 + 60 * q^72 - 36 * q^74 + 36 * q^78 + 6 * q^79 - 48 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.23025	+	2.13086i	−0.869920	+	1.50675i	−0.00784213	+	0.999969i	$0.502496\pi$
$2$	−1.23025	+	2.13086i	−0.869920	+	1.50675i	−0.862078	+	0.506776i	$0.830837\pi$
$3$	1.66238	+	0.486291i	0.959778	+	0.280760i
$3$	1.66238	+	0.486291i	0.959778	+	0.280760i
$4$	−2.02704	−	3.51094i	−1.01352	−	1.75547i
$5$	1.82904	+	3.16799i	0.817970	+	1.41677i	0.907175	+	0.420753i	$0.138234\pi$
$5$	1.82904	+	3.16799i	0.817970	+	1.41677i	−0.0892047	+	0.996013i	$0.528433\pi$
$6$	−3.08137	+	2.94405i	−1.25796	+	1.20190i
$7$		0			0
$7$		0			0
$8$	5.05408			1.78689
$9$	2.52704	+	1.61680i	0.842347	+	0.538935i
$10$	−9.00071			−2.84628
$11$	−0.203210	+	0.351971i	−0.0612702	+	0.106123i	−0.895033	−	0.445999i	$-0.852848\pi$
$11$	−0.203210	+	0.351971i	−0.0612702	+	0.106123i	0.833763	+	0.552122i	$0.186182\pi$
$12$	−1.66238	−	6.82226i	−0.479889	−	1.96942i
$13$	0.243398	+	0.421578i	0.0675065	+	0.116925i	0.897803	−	0.440397i	$-0.145162\pi$
$13$	0.243398	+	0.421578i	0.0675065	+	0.116925i	−0.830297	+	0.557322i	$0.811829\pi$
$14$		0			0
$15$	1.50000	+	6.15585i	0.387298	+	1.58943i
$16$	−2.16372	+	3.74766i	−0.540929	+	0.936916i
$17$	4.85584			1.17771			0.588857	−	0.808237i	$-0.299578\pi$
$17$	4.85584			1.17771			0.588857	+	0.808237i	$0.299578\pi$
$18$	−6.55408	+	3.39569i	−1.54481	+	0.800373i
$19$	−1.97351			−0.452755			−0.226378	−	0.974040i	$-0.572688\pi$
$19$	−1.97351			−0.452755			−0.226378	+	0.974040i	$0.572688\pi$
$20$	7.41507	−	12.8433i	1.65806	−	2.87185i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−2.32383	−	4.02499i	−0.484552	−	0.839269i	0.515290	−	0.857016i	$-0.327684\pi$
$23$	−2.32383	−	4.02499i	−0.484552	−	0.839269i	−0.999843	+	0.0177464i	$0.994351\pi$
$24$	8.40183	+	2.45776i	1.71502	+	0.501687i
$25$	−4.19076	+	7.25860i	−0.838151	+	1.45172i
$26$	−1.19777			−0.234901
$27$	3.41468	+	3.91663i	0.657155	+	0.753756i
$28$		0			0
$29$	−3.82383	+	6.62307i	−0.710068	+	1.22987i	0.254764	+	0.967003i	$0.418002\pi$
$29$	−3.82383	+	6.62307i	−0.710068	+	1.22987i	−0.964831	+	0.262870i	$0.915331\pi$
$30$	−14.9626	−	4.37697i	−2.73179	−	0.799121i
$31$	−3.51360	−	6.08573i	−0.631061	−	1.09303i	−0.987335	−	0.158648i	$-0.949286\pi$
$31$	−3.51360	−	6.08573i	−0.631061	−	1.09303i	0.356274	−	0.934381i	$-0.384047\pi$
$32$	−0.269748	−	0.467216i	−0.0476851	−	0.0825930i
$33$	−0.508974	+	0.486291i	−0.0886010	+	0.0846524i
$34$	−5.97391	+	10.3471i	−1.02452	+	1.77452i
$35$		0			0
$36$	0.554084	−	12.1496i	0.0923474	−	2.02494i
$37$	2.32743			0.382627			0.191314	−	0.981529i	$-0.438725\pi$
$37$	2.32743			0.382627			0.191314	+	0.981529i	$0.438725\pi$
$38$	2.42792	−	4.20528i	0.393861	−	0.682187i
$39$	0.199612	+	0.819187i	0.0319635	+	0.131175i
$40$	9.24411	+	16.0113i	1.46162	+	2.53160i
$41$	−3.75700	−	6.50731i	−0.586744	−	1.01627i	−0.994655	−	0.103249i	$-0.967076\pi$
$41$	−3.75700	−	6.50731i	−0.586744	−	1.01627i	0.407911	−	0.913022i	$-0.366257\pi$
$42$		0			0
$43$	1.16372	−	2.01561i	0.177465	−	0.307378i	−0.763547	−	0.645753i	$-0.776544\pi$
$43$	1.16372	−	2.01561i	0.177465	−	0.307378i	0.941012	+	0.338374i	$0.109877\pi$
$44$	1.64766			0.248395
$45$	−0.499960	+	10.9628i	−0.0745297	+	1.63424i
$46$	11.4356			1.68609
$47$	3.15811	−	5.47002i	0.460658	−	0.797884i	−0.538335	−	0.842731i	$-0.680947\pi$
$47$	3.15811	−	5.47002i	0.460658	−	0.797884i	0.998994	+	0.0448469i	$0.0142800\pi$
$48$	−5.41938	+	5.17786i	−0.782220	+	0.747360i
$49$		0			0
$50$	−10.3114	−	17.8598i	−1.45825	−	2.52576i
$51$	8.07227	+	2.36135i	1.13034	+	0.330655i
$52$	0.986757	−	1.70911i	0.136839	−	0.237011i
$53$	−3.56867			−0.490195			−0.245097	−	0.969498i	$-0.578820\pi$
$53$	−3.56867			−0.490195			−0.245097	+	0.969498i	$0.578820\pi$
$54$	−12.5467	+	2.45776i	−1.70739	+	0.334458i
$55$	−1.48672			−0.200469
$56$		0			0
$57$	−3.28074	−	0.959702i	−0.434544	−	0.127116i
$58$	−9.40856	−	16.2961i	−1.23540	−	2.13978i
$59$	−3.05919	−	5.29868i	−0.398273	−	0.689829i	0.595240	−	0.803548i	$-0.297057\pi$
$59$	−3.05919	−	5.29868i	−0.398273	−	0.689829i	−0.993513	+	0.113719i	$0.963724\pi$
$60$	18.5723	−	17.7446i	2.39767	−	2.29082i
$61$	4.01356	−	6.95169i	0.513884	−	0.890073i	−0.485987	−	0.873966i	$-0.661540\pi$
$61$	4.01356	−	6.95169i	0.513884	−	0.890073i	0.999870	−	0.0161063i	$-0.00512703\pi$
$62$	17.2905			2.19589
$63$		0			0
$64$	−7.32743			−0.915929
$65$	−0.890369	+	1.54216i	−0.110437	+	0.191282i
$66$	−0.410052	−	1.68281i	−0.0504739	−	0.207140i
$67$	−1.80039	−	3.11836i	−0.219952	−	0.380969i	0.734841	−	0.678240i	$-0.237257\pi$
$67$	−1.80039	−	3.11836i	−0.219952	−	0.380969i	−0.954793	+	0.297271i	$0.903924\pi$
$68$	−9.84299	−	17.0486i	−1.19364	−	2.06744i
$69$	−1.90578	−	7.82115i	−0.229429	−	0.941555i
$70$		0			0
$71$	8.46050			1.00408			0.502039	−	0.864845i	$-0.332584\pi$
$71$	8.46050			1.00408			0.502039	+	0.864845i	$0.332584\pi$
$72$	12.7719	+	8.17147i	1.50518	+	0.963017i
$73$	1.97351			0.230982			0.115491	−	0.993309i	$-0.463156\pi$
$73$	1.97351			0.230982			0.115491	+	0.993309i	$0.463156\pi$
$74$	−2.86333	+	4.95943i	−0.332855	+	0.576522i
$75$	−10.4964	+	10.0287i	−1.21202	+	1.15801i
$76$	4.00040	+	6.92889i	0.458877	+	0.794798i
$77$		0			0
$78$	−1.99115	−	0.582462i	−0.225453	−	0.0659509i
$79$	−4.08113	+	7.06872i	−0.459163	+	0.795293i	−0.998917	−	0.0465297i	$-0.985184\pi$
$79$	−4.08113	+	7.06872i	−0.459163	+	0.795293i	0.539754	+	0.841823i	$0.318517\pi$
$80$	−15.8301			−1.76986
$81$	3.77188	+	8.17147i	0.419098	+	0.907941i
$82$	18.4882			2.04168
$83$	−6.08600	+	10.5413i	−0.668025	+	1.15705i	0.310431	+	0.950596i	$0.399527\pi$
$83$	−6.08600	+	10.5413i	−0.668025	+	1.15705i	−0.978456	+	0.206457i	$0.933807\pi$
$84$		0			0
$85$	8.88151	+	15.3832i	0.963336	+	1.66855i
$86$	2.86333	+	4.95943i	0.308760	+	0.534789i
$87$	−9.57742	+	9.15059i	−1.02681	+	0.981047i
$88$	−1.02704	+	1.77889i	−0.109483	+	0.189630i
$89$	14.8301			1.57199			0.785996	−	0.618231i	$-0.212151\pi$
$89$	14.8301			1.57199			0.785996	+	0.618231i	$0.212151\pi$
$90$	−22.7452	−	14.5524i	−2.39755	−	1.53396i
$91$		0			0
$92$	−9.42101	+	16.3177i	−0.982208	+	1.70123i
$93$	−2.88151	−	11.8255i	−0.298799	−	1.22624i
$94$	7.77056	+	13.4590i	0.801472	+	1.38819i
$95$	−3.60963	−	6.25206i	−0.370340	−	0.641448i
$96$	−0.221221	−	0.907869i	−0.0225783	−	0.0926590i
$97$	4.74375	−	8.21642i	0.481655	−	0.834251i	−0.518123	−	0.855306i	$-0.673369\pi$
$97$	4.74375	−	8.21642i	0.481655	−	0.834251i	0.999778	+	0.0210547i	$0.00670241\pi$
$98$		0			0
$99$	−1.08259	+	0.560893i	−0.108804	+	0.0563719i
$100$	33.9794			3.39794
$101$	−4.35588	+	7.54461i	−0.433426	+	0.750716i	−0.997166	−	0.0752364i	$-0.976029\pi$
$101$	−4.35588	+	7.54461i	−0.433426	+	0.750716i	0.563739	+	0.825953i	$0.309362\pi$
$102$	−14.9626	+	14.2958i	−1.48152	+	1.41550i
$103$	−4.01356	−	6.95169i	−0.395468	−	0.684970i	0.597693	−	0.801725i	$-0.296084\pi$
$103$	−4.01356	−	6.95169i	−0.395468	−	0.684970i	−0.993161	+	0.116755i	$0.962751\pi$
$104$	1.23016	+	2.13069i	0.120627	+	0.208931i
$105$		0			0
$106$	4.39037	−	7.60434i	0.426430	−	0.738599i
$107$	12.8420			1.24148			0.620742	−	0.784015i	$-0.286831\pi$
$107$	12.8420			1.24148			0.620742	+	0.784015i	$0.286831\pi$
$108$	6.82935	−	19.9279i	0.657155	−	1.91756i
$109$	2.60078			0.249109			0.124555	−	0.992213i	$-0.460250\pi$
$109$	2.60078			0.249109			0.124555	+	0.992213i	$0.460250\pi$
$110$	1.82904	−	3.16799i	0.174392	−	0.302056i
$111$	3.86908	+	1.13181i	0.367237	+	0.107427i
$112$		0			0
$113$	6.97509	+	12.0812i	0.656162	+	1.13651i	0.981601	+	0.190942i	$0.0611544\pi$
$113$	6.97509	+	12.0812i	0.656162	+	1.13651i	−0.325440	+	0.945563i	$0.605512\pi$
$114$	6.08113	−	5.81012i	0.569550	−	0.544167i
$115$	8.50075	−	14.7237i	0.792699	−	1.37300i
$116$	31.0043			2.87867
$117$	−0.0665320	+	1.45887i	−0.00615088	+	0.134873i
$118$	15.0543			1.38586
$119$		0			0
$120$	7.58113	+	31.1122i	0.692059	+	2.84014i
$121$	5.41741	+	9.38323i	0.492492	+	0.853021i
$122$	9.87538	+	17.1047i	0.894075	+	1.54858i
$123$	−3.08113	−	12.6446i	−0.277816	−	1.14013i
$124$	−14.2444	+	24.6721i	−1.27919	+	2.21562i
$125$	−12.3698			−1.10639
$126$		0			0
$127$	−15.5438			−1.37929			−0.689643	−	0.724149i	$-0.742233\pi$
$127$	−15.5438			−1.37929			−0.689643	+	0.724149i	$0.742233\pi$
$128$	9.55408	−	16.5482i	0.844470	−	1.46266i
$129$	2.91472	−	2.78482i	0.256626	−	0.245190i
$130$	−2.19076	−	3.79450i	−0.192142	−	0.332800i
$131$	4.25696	+	7.37327i	0.371932	+	0.644205i	0.989863	−	0.142027i	$-0.0453621\pi$
$131$	4.25696	+	7.37327i	0.371932	+	0.644205i	−0.617931	+	0.786233i	$0.712029\pi$
$132$	2.73905	+	0.801244i	0.238404	+	0.0697393i
$133$		0			0
$134$	8.85973			0.765364
$135$	−6.16225	+	17.9813i	−0.530362	+	1.54758i
$136$	24.5418			2.10444
$137$	−0.188621	+	0.326702i	−0.0161150	+	0.0279120i	−0.873970	−	0.485979i	$-0.838463\pi$
$137$	−0.188621	+	0.326702i	−0.0161150	+	0.0279120i	0.857855	+	0.513891i	$0.171796\pi$
$138$	19.0104	+	5.56103i	1.61827	+	0.473386i
$139$	9.50067	+	16.4556i	0.805837	+	1.39575i	0.915725	+	0.401806i	$0.131617\pi$
$139$	9.50067	+	16.4556i	0.805837	+	1.39575i	−0.109888	+	0.993944i	$0.535049\pi$
$140$		0			0
$141$	7.91002	−	7.55750i	0.666144	−	0.636457i
$142$	−10.4086	+	18.0281i	−0.873467	+	1.51289i
$143$	−0.197844			−0.0165446
$144$	−11.5270	+	5.97220i	−0.960587	+	0.497683i
$145$	−27.9757			−2.32326
$146$	−2.42792	+	4.20528i	−0.200936	+	0.348032i
$147$		0			0
$148$	−4.71780	−	8.17147i	−0.387801	−	0.671691i
$149$	4.85087	+	8.40196i	0.397399	+	0.688315i	0.993404	−	0.114665i	$-0.0365795\pi$
$149$	4.85087	+	8.40196i	0.397399	+	0.688315i	−0.596005	+	0.802981i	$0.703246\pi$
$150$	−8.45640	−	34.7042i	−0.690462	−	2.83359i
$151$	6.41741	−	11.1153i	0.522242	−	0.904549i	−0.477424	−	0.878673i	$-0.658429\pi$
$151$	6.41741	−	11.1153i	0.522242	−	0.904549i	0.999665	−	0.0258756i	$-0.00823738\pi$
$152$	−9.97430			−0.809023
$153$	12.2709	+	7.85095i	0.992045	+	0.634711i
$154$		0			0
$155$	12.8530	−	22.2621i	1.03238	−	1.78813i
$156$	2.47150	−	2.36135i	0.197878	−	0.189059i
$157$	−10.4743	−	18.1420i	−0.835937	−	1.44789i	−0.893265	−	0.449531i	$-0.851591\pi$
$157$	−10.4743	−	18.1420i	−0.835937	−	1.44789i	0.0573276	−	0.998355i	$-0.481742\pi$
$158$	−10.0416	−	17.3926i	−0.798869	−	1.38368i
$159$	−5.93251	−	1.73541i	−0.470478	−	0.137627i
$160$	0.986757	−	1.70911i	0.0780100	−	0.135117i
$161$		0			0
$162$	−22.0526	−	2.01561i	−1.73262	−	0.158362i
$163$	−11.1623			−0.874295			−0.437148	−	0.899390i	$-0.644011\pi$
$163$	−11.1623			−0.874295			−0.437148	+	0.899390i	$0.644011\pi$
$164$	−15.2312	+	26.3812i	−1.18936	+	2.06002i
$165$	−2.47150	−	0.722977i	−0.192406	−	0.0562837i
$166$	−14.9746	−	25.9368i	−1.16226	−	2.01309i
$167$	−1.73012	−	2.99665i	−0.133880	−	0.231888i	0.791289	−	0.611443i	$-0.209410\pi$
$167$	−1.73012	−	2.99665i	−0.133880	−	0.231888i	−0.925169	+	0.379555i	$0.876077\pi$
$168$		0			0
$169$	6.38151	−	11.0531i	0.490886	−	0.850239i
$170$	−43.7060			−3.35210
$171$	−4.98715	−	3.19079i	−0.381377	−	0.244006i
$172$	−9.43560			−0.719458
$173$	3.02680	−	5.24258i	0.230124	−	0.398586i	−0.727721	−	0.685874i	$-0.759420\pi$
$173$	3.02680	−	5.24258i	0.230124	−	0.398586i	0.957844	+	0.287288i	$0.0927536\pi$
$174$	−7.71599	−	31.6657i	−0.584948	−	2.40057i
$175$		0			0
$176$	−0.879379	−	1.52313i	−0.0662857	−	0.114810i
$177$	−2.50885	−	10.2961i	−0.188577	−	0.773902i
$178$	−18.2448	+	31.6010i	−1.36751	+	2.36859i
$179$	9.13307			0.682638			0.341319	−	0.939948i	$-0.389126\pi$
$179$	9.13307			0.682638			0.341319	+	0.939948i	$0.389126\pi$
$180$	39.5033	−	20.4668i	2.94440	−	1.52550i
$181$	11.9478			0.888074			0.444037	−	0.896008i	$-0.353546\pi$
$181$	11.9478			0.888074			0.444037	+	0.896008i	$0.353546\pi$
$182$		0			0
$183$	10.0526	−	9.60462i	0.743111	−	0.709994i
$184$	−11.7448	−	20.3427i	−0.865841	−	1.49968i
$185$	4.25696	+	7.37327i	0.312978	+	0.542093i
$186$	28.7434	+	8.40819i	2.10757	+	0.616519i
$187$	−0.986757	+	1.70911i	−0.0721588	+	0.124983i
$188$	−25.6065			−1.86755
$189$		0			0
$190$	17.7630			1.28867
$191$	−4.57014	+	7.91571i	−0.330683	+	0.572760i	−0.982646	−	0.185491i	$-0.940613\pi$
$191$	−4.57014	+	7.91571i	−0.330683	+	0.572760i	0.651963	+	0.758251i	$0.273946\pi$
$192$	−12.1810	−	3.56326i	−0.879088	−	0.257156i
$193$	−8.47150	−	14.6731i	−0.609792	−	1.05619i	−0.991274	−	0.131814i	$-0.957920\pi$
$193$	−8.47150	−	14.6731i	−0.609792	−	1.05619i	0.381483	−	0.924376i	$-0.375414\pi$
$194$	11.6720	+	20.2165i	0.838003	+	1.45146i
$195$	−2.23008	+	2.13069i	−0.159699	+	0.152582i
$196$		0			0
$197$	−21.3173			−1.51880			−0.759398	−	0.650627i	$-0.774506\pi$
$197$	−21.3173			−1.51880			−0.759398	+	0.650627i	$0.774506\pi$
$198$	0.136673	−	2.99689i	0.00971293	−	0.212979i
$199$	9.97430			0.707060			0.353530	−	0.935423i	$-0.384981\pi$
$199$	9.97430			0.707060			0.353530	+	0.935423i	$0.384981\pi$
$200$	−21.1804	+	36.6856i	−1.49768	+	2.59406i
$201$	−1.47650	−	6.05943i	−0.104145	−	0.427399i
$202$	−10.7177	−	18.5635i	−0.754092	−	1.30613i
$203$		0			0
$204$	−8.07227	−	33.1278i	−0.565172	−	2.31941i
$205$	13.7434	−	23.8042i	0.959879	−	1.66256i
$206$	19.7508			1.37610
$207$	0.635211	−	13.9285i	0.0441502	−	0.968099i
$208$	−2.10658			−0.146065
$209$	0.401038	−	0.694619i	0.0277404	−	0.0480478i
$210$		0			0
$211$	−2.44592	−	4.23645i	−0.168384	−	0.291649i	0.769468	−	0.638685i	$-0.220521\pi$
$211$	−2.44592	−	4.23645i	−0.168384	−	0.291649i	−0.937852	+	0.347036i	$0.887188\pi$
$212$	7.23385	+	12.5294i	0.496823	+	0.860523i
$213$	14.0646	+	4.11427i	0.963691	+	0.281905i
$214$	−15.7989	+	27.3645i	−1.07999	+	1.87060i
$215$	8.51392			0.580644
$216$	17.2581	+	19.7950i	1.17426	+	1.34688i
$217$		0			0
$218$	−3.19961	+	5.54189i	−0.216705	+	0.375344i
$219$	3.28074	+	0.959702i	0.221692	+	0.0648507i
$220$	3.01364	+	5.21978i	0.203179	+	0.351917i
$221$	1.18190	+	2.04712i	0.0795034	+	0.137704i
$222$	−7.17167	+	6.85206i	−0.481331	+	0.459880i
$223$	11.7044	−	20.2727i	0.783786	−	1.35756i	−0.145936	−	0.989294i	$-0.546619\pi$
$223$	11.7044	−	20.2727i	0.783786	−	1.35756i	0.929722	−	0.368263i	$-0.120047\pi$
$224$		0			0
$225$	−22.3260	+	11.5672i	−1.48840	+	0.771144i
$226$	−34.3245			−2.28323
$227$	3.05919	−	5.29868i	0.203046	−	0.351686i	−0.746463	−	0.665427i	$-0.768249\pi$
$227$	3.05919	−	5.29868i	0.203046	−	0.351686i	0.949508	+	0.313742i	$0.101583\pi$
$228$	3.28074	+	13.4638i	0.217272	+	0.891664i
$229$	−0.730195	−	1.26473i	−0.0482526	−	0.0835760i	0.840890	−	0.541206i	$-0.182032\pi$
$229$	−0.730195	−	1.26473i	−0.0482526	−	0.0835760i	−0.889143	+	0.457630i	$0.848699\pi$
$230$	20.9161	+	36.2278i	1.37917	+	2.38879i
$231$		0			0
$232$	−19.3260	+	33.4736i	−1.26881	+	2.19765i
$233$	−13.2484			−0.867934			−0.433967	−	0.900929i	$-0.642887\pi$
$233$	−13.2484			−0.867934			−0.433967	+	0.900929i	$0.642887\pi$
$234$	−3.02680	−	1.93655i	−0.197868	−	0.126596i
$235$	23.1052			1.50722
$236$	−12.4022	+	21.4813i	−0.807316	+	1.39831i
$237$	−10.2219	+	9.76631i	−0.663981	+	0.634390i
$238$		0			0
$239$	−9.69436	−	16.7911i	−0.627076	−	1.08613i	−0.988136	−	0.153584i	$-0.950918\pi$
$239$	−9.69436	−	16.7911i	−0.627076	−	1.08613i	0.361060	−	0.932543i	$-0.382415\pi$
$240$	−26.3157	−	7.69802i	−1.69867	−	0.496905i
$241$	2.52684	−	4.37662i	0.162768	−	0.281923i	−0.773092	−	0.634294i	$-0.781291\pi$
$241$	2.52684	−	4.37662i	0.162768	−	0.281923i	0.935860	+	0.352371i	$0.114624\pi$
$242$	−26.6591			−1.71371
$243$	2.29661	+	15.4184i	0.147327	+	0.989088i
$244$	−32.5426			−2.08333
$245$		0			0
$246$	30.7345	+	8.99066i	1.95956	+	0.573223i
$247$	−0.480350	−	0.831990i	−0.0305639	−	0.0529383i
$248$	−17.7580	−	30.7578i	−1.12764	−	1.95312i
$249$	−15.2434	+	14.5640i	−0.966010	+	0.922959i
$250$	15.2180	−	26.3584i	0.962472	−	1.66705i
$251$	−15.0928			−0.952647			−0.476324	−	0.879270i	$-0.658031\pi$
$251$	−15.0928			−0.952647			−0.476324	+	0.879270i	$0.658031\pi$
$252$		0			0
$253$	1.88891			0.118755
$254$	19.1228	−	33.1216i	1.19987	−	2.07823i
$255$	7.28376	+	29.8918i	0.456127	+	1.87190i
$256$	16.1804	+	28.0253i	1.01128	+	1.75158i
$257$	3.85592	+	6.67865i	0.240526	+	0.416603i	0.960864	−	0.277020i	$-0.0893469\pi$
$257$	3.85592	+	6.67865i	0.240526	+	0.416603i	−0.720338	+	0.693623i	$0.756014\pi$
$258$	2.34822	+	9.63688i	0.146194	+	0.599966i
$259$		0			0
$260$	7.21926			0.447720
$261$	−20.3712	+	10.5544i	−1.26095	+	0.653300i
$262$	−20.9485			−1.29420
$263$	−2.10603	+	3.64776i	−0.129864	+	0.224930i	−0.923624	−	0.383301i	$-0.874787\pi$
$263$	−2.10603	+	3.64776i	−0.129864	+	0.224930i	0.793760	+	0.608231i	$0.208121\pi$
$264$	−2.57240	+	2.45776i	−0.158320	+	0.151264i
$265$	−6.52724	−	11.3055i	−0.400965	−	0.694492i
$266$		0			0
$267$	24.6534	+	7.21177i	1.50876	+	0.441353i
$268$	−7.29893	+	12.6421i	−0.445853	+	0.772240i
$269$	−20.7507			−1.26519			−0.632596	−	0.774482i	$-0.718011\pi$
$269$	−20.7507			−1.26519			−0.632596	+	0.774482i	$0.718011\pi$
$270$	−30.7345	−	35.2524i	−1.87044	−	2.14540i
$271$	28.4889			1.73057			0.865287	−	0.501276i	$-0.167136\pi$
$271$	28.4889			1.73057			0.865287	+	0.501276i	$0.167136\pi$
$272$	−10.5067	+	18.1981i	−0.637060	+	1.10342i
$273$		0			0
$274$	−0.464103	−	0.803851i	−0.0280375	−	0.0485624i
$275$	−1.70321	−	2.95005i	−0.102707	−	0.177895i
$276$	−23.5965	+	22.5449i	−1.42034	+	1.35704i
$277$	−8.58113	+	14.8629i	−0.515590	+	0.893028i	0.484246	+	0.874932i	$0.339094\pi$
$277$	−8.58113	+	14.8629i	−0.515590	+	0.893028i	−0.999836	+	0.0180962i	$0.994239\pi$
$278$	−46.7529			−2.80405
$279$	0.960429	−	21.0597i	0.0574994	−	1.26081i
$280$		0			0
$281$	−4.72140	+	8.17770i	−0.281655	+	0.487841i	−0.971793	−	0.235837i	$-0.924217\pi$
$281$	−4.72140	+	8.17770i	−0.281655	+	0.487841i	0.690138	+	0.723678i	$0.257550\pi$
$282$	6.37266	+	26.1528i	0.379486	+	1.55738i
$283$	8.43422	+	14.6085i	0.501362	+	0.868385i	0.999999	+	0.00157378i	$0.000500949\pi$
$283$	8.43422	+	14.6085i	0.501362	+	0.868385i	−0.498636	+	0.866811i	$0.666166\pi$
$284$	−17.1498	−	29.7043i	−1.01765	−	1.76263i
$285$	−2.96027	−	12.1487i	−0.175351	−	0.719625i
$286$	0.243398	−	0.421578i	0.0143924	−	0.0249284i
$287$		0			0
$288$	0.0737345	−	1.61680i	0.00434485	−	0.0952711i
$289$	6.57918			0.387011
$290$	34.4172	−	59.6124i	2.02105	−	3.50056i
$291$	11.8815	−	11.3520i	0.696507	−	0.665466i
$292$	−4.00040	−	6.92889i	−0.234105	−	0.405483i
$293$	−1.86143	−	3.22409i	−0.108746	−	0.188353i	0.806517	−	0.591211i	$-0.201350\pi$
$293$	−1.86143	−	3.22409i	−0.108746	−	0.188353i	−0.915262	+	0.402858i	$0.868017\pi$
$294$		0			0
$295$	11.1908	−	19.3830i	0.651551	−	1.12852i
$296$	11.7630			0.683712
$297$	−2.07244	+	0.405967i	−0.120255	+	0.0235566i
$298$	−23.8712			−1.38282
$299$	1.13123	−	1.95935i	0.0654209	−	0.113312i
$300$	56.4868	+	16.5239i	3.26126	+	0.954006i
$301$		0			0
$302$	15.7901	+	27.3492i	0.908617	+	1.57377i
$303$	−10.9100	+	10.4238i	−0.626764	+	0.598832i
$304$	4.27012	−	7.39607i	0.244908	−	0.424194i
$305$	29.3638			1.68137
$306$	−31.8256	+	16.4889i	−1.81935	+	0.942610i
$307$	−30.5691			−1.74467			−0.872335	−	0.488908i	$-0.837395\pi$
$307$	−30.5691			−1.74467			−0.872335	+	0.488908i	$0.837395\pi$
$308$		0			0
$309$	−3.29153	−	13.5081i	−0.187249	−	0.768451i
$310$	31.6249	+	54.7759i	1.79617	+	3.11106i
$311$	−5.21739	−	9.03678i	−0.295851	−	0.512429i	0.679332	−	0.733831i	$-0.262270\pi$
$311$	−5.21739	−	9.03678i	−0.295851	−	0.512429i	−0.975182	+	0.221403i	$0.928936\pi$
$312$	1.00885	+	4.14024i	0.0571151	+	0.234395i
$313$	−0.309930	+	0.536815i	−0.0175183	+	0.0303426i	−0.874652	−	0.484752i	$-0.838910\pi$
$313$	−0.309930	+	0.536815i	−0.0175183	+	0.0303426i	0.857133	+	0.515095i	$0.172243\pi$
$314$	51.5440			2.90879
$315$		0			0
$316$	33.0905			1.86148
$317$	−5.12422	+	8.87541i	−0.287805	+	0.498493i	−0.973285	−	0.229598i	$-0.926259\pi$
$317$	−5.12422	+	8.87541i	−0.287805	+	0.498493i	0.685481	+	0.728091i	$0.259592\pi$
$318$	10.9964	−	10.5063i	0.616648	−	0.589166i
$319$	−1.55408	−	2.69175i	−0.0870120	−	0.150709i
$320$	−13.4021	−	23.2132i	−0.749203	−	1.29766i
$321$	21.3484	+	6.24496i	1.19155	+	0.348560i
$322$		0			0
$323$	−9.58307			−0.533216
$324$	21.0438	−	29.8068i	1.16910	−	1.65593i
$325$	−4.08009			−0.226323
$326$	13.7324	−	23.7852i	0.760567	−	1.31734i
$327$	4.32349	+	1.26473i	0.239090	+	0.0699400i
$328$	−18.9882	−	32.8885i	−1.04845	−	1.81596i
$329$		0			0
$330$	4.58113	−	4.37697i	0.252183	−	0.240944i
$331$	10.1819	−	17.6356i	0.559648	−	0.969339i	−0.437878	−	0.899035i	$-0.644270\pi$
$331$	10.1819	−	17.6356i	0.559648	−	0.969339i	0.997526	−	0.0703042i	$-0.0223970\pi$
$332$	49.3463			2.70823
$333$	5.88151	+	3.76300i	0.322305	+	0.206211i
$334$	8.51392			0.465861
$335$	6.58596	−	11.4072i	0.359829	−	0.623242i
$336$		0			0
$337$	2.85594	+	4.94662i	0.155573	+	0.269460i	0.933267	−	0.359182i	$-0.116944\pi$
$337$	2.85594	+	4.94662i	0.155573	+	0.269460i	−0.777695	+	0.628642i	$0.783611\pi$
$338$	15.7017	+	27.1962i	0.854062	+	1.47928i
$339$	5.72030	+	23.4755i	0.310684	+	1.27502i
$340$	36.0064	−	62.3649i	1.95272	−	3.38221i
$341$	2.85600			0.154661
$342$	12.9346	−	6.70145i	0.699422	−	0.362373i
$343$		0			0
$344$	5.88151	−	10.1871i	0.317110	−	0.549251i
$345$	21.2915	−	20.3427i	1.14630	−	1.09521i
$346$	7.44746	+	12.8994i	0.400378	+	0.693475i
$347$	−4.44066	−	7.69145i	−0.238387	−	0.412899i	0.721865	−	0.692034i	$-0.243285\pi$
$347$	−4.44066	−	7.69145i	−0.238387	−	0.412899i	−0.960252	+	0.279136i	$0.909952\pi$
$348$	51.5410	+	15.0771i	2.76289	+	0.808217i
$349$	−10.4874	+	18.1648i	−0.561379	+	0.972337i	0.435997	+	0.899948i	$0.356396\pi$
$349$	−10.4874	+	18.1648i	−0.561379	+	0.972337i	−0.997376	+	0.0723893i	$0.976938\pi$
$350$		0			0
$351$	−0.820039	+	2.39285i	−0.0437704	+	0.127721i
$352$	0.219262			0.0116867
$353$	7.38268	−	12.7872i	0.392941	−	0.680593i	−0.599895	−	0.800078i	$-0.704791\pi$
$353$	7.38268	−	12.7872i	0.392941	−	0.680593i	0.992836	+	0.119485i	$0.0381245\pi$
$354$	25.0261	+	7.32078i	1.33012	+	0.389095i
$355$	15.4746	+	26.8028i	0.821306	+	1.42254i
$356$	−30.0613	−	52.0677i	−1.59325	−	2.75959i
$357$		0			0
$358$	−11.2360	+	19.4613i	−0.593840	+	1.02856i
$359$	7.21206			0.380638			0.190319	−	0.981722i	$-0.439048\pi$
$359$	7.21206			0.380638			0.190319	+	0.981722i	$0.439048\pi$
$360$	−2.52684	+	55.4071i	−0.133176	+	2.92021i
$361$	−15.1052			−0.795013
$362$	−14.6988	+	25.4591i	−0.772554	+	1.33810i
$363$	4.44284	+	18.2330i	0.233188	+	0.956983i
$364$		0			0
$365$	3.60963	+	6.25206i	0.188937	+	0.327248i
$366$	8.09884	+	33.2368i	0.423333	+	1.73732i
$367$	5.48711	−	9.50396i	0.286425	−	0.496103i	−0.686529	−	0.727103i	$-0.740866\pi$
$367$	5.48711	−	9.50396i	0.286425	−	0.496103i	0.972954	+	0.231000i	$0.0741998\pi$
$368$	20.1124			1.04843
$369$	1.02696	−	22.5186i	0.0534614	−	1.17227i
$370$	−20.9485			−1.08906
$371$		0			0
$372$	−35.6775	+	34.0875i	−1.84979	+	1.76736i
$373$	0.271884	+	0.470916i	0.0140776	+	0.0243831i	0.872978	−	0.487759i	$-0.162185\pi$
$373$	0.271884	+	0.470916i	0.0140776	+	0.0243831i	−0.858901	+	0.512142i	$0.828852\pi$
$374$	−2.42792	−	4.20528i	−0.125545	−	0.217450i
$375$	−20.5634	−	6.01534i	−1.06189	−	0.310631i
$376$	15.9614	−	27.6459i	0.823145	−	1.42573i
$377$	−3.72286			−0.191737
$378$		0			0
$379$	−22.6912			−1.16557			−0.582785	−	0.812626i	$-0.698037\pi$
$379$	−22.6912			−1.16557			−0.582785	+	0.812626i	$0.698037\pi$
$380$	−14.6337	+	25.3464i	−0.750695	+	1.30024i
$381$	−25.8397	−	7.55879i	−1.32381	−	0.387249i
$382$	−11.2448	−	19.4766i	−0.575336	−	0.996511i
$383$	−17.8569	−	30.9291i	−0.912447	−	1.58041i	−0.810596	−	0.585606i	$-0.800857\pi$
$383$	−17.8569	−	30.9291i	−0.912447	−	1.58041i	−0.101851	−	0.994800i	$-0.532477\pi$
$384$	23.9298	−	22.8633i	1.22116	−	1.16674i
$385$		0			0
$386$	41.6883			2.12188
$387$	6.19961	−	3.21204i	0.315144	−	0.163277i
$388$	−38.4632			−1.95267
$389$	−19.3296	+	33.4798i	−0.980048	+	1.69749i	−0.317892	+	0.948127i	$0.602975\pi$
$389$	−19.3296	+	33.4798i	−0.980048	+	1.69749i	−0.662156	+	0.749366i	$0.730359\pi$
$390$	−1.79665	−	7.37327i	−0.0909768	−	0.373360i
$391$	−11.2842	−	19.5447i	−0.570664	−	0.988420i
$392$		0			0
$393$	3.49115	+	14.3273i	0.176105	+	0.722718i
$394$	26.2257	−	45.4242i	1.32123	−	2.28844i
$395$	−29.8581			−1.50233
$396$	4.16372	+	2.66395i	0.209235	+	0.133869i
$397$	−11.9478			−0.599644			−0.299822	−	0.953995i	$-0.596927\pi$
$397$	−11.9478			−0.599644			−0.299822	+	0.953995i	$0.596927\pi$
$398$	−12.2709	+	21.2538i	−0.615085	+	1.06536i
$399$		0			0
$400$	−18.1352	−	31.4111i	−0.906761	−	1.57056i
$401$	−16.1783	−	28.0216i	−0.807906	−	1.39933i	−0.914312	−	0.405011i	$-0.867268\pi$
$401$	−16.1783	−	28.0216i	−0.807906	−	1.39933i	0.106406	−	0.994323i	$-0.466066\pi$
$402$	14.7283	+	4.30841i	0.734579	+	0.214884i
$403$	1.71041	−	2.96251i	0.0852015	−	0.147573i
$404$	35.3182			1.75715
$405$	−18.9882	+	26.8952i	−0.943530	+	1.33643i
$406$		0			0
$407$	−0.472958	+	0.819187i	−0.0234437	+	0.0406056i
$408$	40.7979	+	11.9345i	2.01980	+	0.590844i
$409$	−9.48751	−	16.4328i	−0.469127	−	0.812552i	0.530250	−	0.847841i	$-0.322098\pi$
$409$	−9.48751	−	16.4328i	−0.469127	−	0.812552i	−0.999377	+	0.0352893i	$0.988765\pi$
$410$	33.8157	+	58.5704i	1.67004	+	2.89259i
$411$	−0.472433	+	0.451379i	−0.0233034	+	0.0222649i
$412$	−16.2713	+	28.1827i	−0.801630	+	1.38846i
$413$		0			0
$414$	28.8982	+	18.4891i	1.42027	+	0.908691i
$415$	−44.5261			−2.18570
$416$	0.131312	−	0.227439i	0.00643811	−	0.0111511i
$417$	7.79153	+	31.9757i	0.381553	+	1.56586i
$418$	0.986757	+	1.70911i	0.0482639	+	0.0835955i
$419$	8.64523	+	14.9740i	0.422347	+	0.731526i	0.996169	−	0.0874539i	$-0.0278730\pi$
$419$	8.64523	+	14.9740i	0.422347	+	0.731526i	−0.573822	+	0.818980i	$0.694540\pi$
$420$		0			0
$421$	−9.30039	+	16.1087i	−0.453273	+	0.785092i	−0.998587	−	0.0531397i	$-0.983077\pi$
$421$	−9.30039	+	16.1087i	−0.453273	+	0.785092i	0.545314	+	0.838232i	$0.316410\pi$
$422$	12.0364			0.585922
$423$	16.8246	−	8.71690i	0.818042	−	0.423830i
$424$	−18.0364			−0.875924
$425$	−20.3496	+	35.2466i	−0.987103	+	1.70971i
$426$	−26.0699	+	24.9081i	−1.26309	+	1.20680i
$427$		0			0
$428$	−26.0313	−	45.0876i	−1.25827	−	2.17939i
$429$	−0.328893	−	0.0962098i	−0.0158791	−	0.00464505i
$430$	−10.4743	+	18.1420i	−0.505114	+	0.874883i
$431$	−15.8784			−0.764835			−0.382418	−	0.923990i	$-0.624908\pi$
$431$	−15.8784			−0.764835			−0.382418	+	0.923990i	$0.624908\pi$
$432$	−22.0666	+	4.32260i	−1.06168	+	0.207971i
$433$	40.4367			1.94326			0.971631	−	0.236501i	$-0.0760007\pi$
$433$	40.4367			1.94326			0.971631	+	0.236501i	$0.0760007\pi$
$434$		0			0
$435$	−46.5064	−	13.6043i	−2.22981	−	0.652278i
$436$	−5.27188	−	9.13117i	−0.252477	−	0.437304i
$437$	4.58611	+	7.94338i	0.219384	+	0.379984i
$438$	−6.08113	+	5.81012i	−0.290567	+	0.277618i
$439$	−6.23047	+	10.7915i	−0.297364	+	0.515050i	−0.975532	−	0.219857i	$-0.929441\pi$
$439$	−6.23047	+	10.7915i	−0.297364	+	0.515050i	0.678168	+	0.734907i	$0.262774\pi$
$440$	−7.51399			−0.358216
$441$		0			0
$442$	−5.81616			−0.276646
$443$	4.11537	−	7.12802i	0.195527	−	0.338663i	−0.751546	−	0.659680i	$-0.770692\pi$
$443$	4.11537	−	7.12802i	0.195527	−	0.338663i	0.947073	+	0.321018i	$0.104025\pi$
$444$	−3.86908	−	15.8783i	−0.183619	−	0.753553i
$445$	27.1249	+	46.9817i	1.28584	+	2.22715i
$446$	28.7988	+	49.8810i	1.36366	+	2.36193i
$447$	3.97822	+	16.3262i	0.188163	+	0.772204i
$448$		0			0
$449$	5.64474			0.266392			0.133196	−	0.991090i	$-0.457476\pi$
$449$	5.64474			0.266392			0.133196	+	0.991090i	$0.457476\pi$
$450$	2.81858	−	61.8040i	0.132869	−	2.91347i
$451$	3.05384			0.143800
$452$	28.2776	−	48.9783i	1.33007	−	2.30374i
$453$	16.0735	−	15.3571i	0.755197	−	0.721541i
$454$	7.52716	+	13.0374i	0.353267	+	0.611876i
$455$		0			0
$456$	−16.5811	−	4.85041i	−0.776482	−	0.227141i
$457$	−2.53443	+	4.38977i	−0.118556	+	0.205345i	−0.919196	−	0.393801i	$-0.871160\pi$
$457$	−2.53443	+	4.38977i	−0.118556	+	0.205345i	0.800640	+	0.599146i	$0.204493\pi$
$458$	3.59330			0.167904
$459$	16.5811	+	19.0185i	0.773941	+	0.887709i
$460$	−68.9255			−3.21367
$461$	3.88831	−	6.73475i	0.181097	−	0.313669i	−0.761158	−	0.648567i	$-0.775369\pi$
$461$	3.88831	−	6.73475i	0.181097	−	0.313669i	0.942254	+	0.334898i	$0.108702\pi$
$462$		0			0
$463$	4.58998	+	7.95008i	0.213314	+	0.369472i	0.952750	−	0.303756i	$-0.0982408\pi$
$463$	4.58998	+	7.95008i	0.213314	+	0.369472i	−0.739435	+	0.673228i	$0.764907\pi$
$464$	−16.5474	−	28.6609i	−0.768192	−	1.33055i
$465$	32.1925	−	30.7578i	1.49289	−	1.42636i
$466$	16.2989	−	28.2306i	0.755033	−	1.30776i
$467$	−13.7654			−0.636989			−0.318494	−	0.947925i	$-0.603177\pi$
$467$	−13.7654			−0.636989			−0.318494	+	0.947925i	$0.603177\pi$
$468$	5.25688	−	2.72361i	0.242999	−	0.125899i
$469$		0			0
$470$	−28.4253	+	49.2340i	−1.31116	+	2.27100i
$471$	−8.58998	−	35.2524i	−0.395805	−	1.62435i
$472$	−15.4614	−	26.7800i	−0.711669	−	1.23265i
$473$	0.472958	+	0.819187i	0.0217466	+	0.0376663i
$474$	−8.23518	−	33.7964i	−0.378254	−	1.55232i
$475$	8.27052	−	14.3250i	0.379477	−	0.657274i
$476$		0			0
$477$	−9.01819	−	5.76985i	−0.412914	−	0.264183i
$478$	47.7060			2.18202
$479$	−4.35588	+	7.54461i	−0.199025	+	0.344722i	−0.948213	−	0.317636i	$-0.897111\pi$
$479$	−4.35588	+	7.54461i	−0.199025	+	0.344722i	0.749187	+	0.662358i	$0.230444\pi$
$480$	2.47150	−	2.36135i	0.112808	−	0.107780i
$481$	0.566492	+	0.981194i	0.0258298	+	0.0447386i
$482$	6.21731	+	10.7687i	0.283191	+	0.490501i
$483$		0			0
$484$	21.9626	−	38.0404i	0.998302	−	1.72911i
$485$	34.7060			1.57592
$486$	−35.6798	−	14.0747i	−1.61847	−	0.638442i
$487$	−18.0364			−0.817306			−0.408653	−	0.912690i	$-0.634001\pi$
$487$	−18.0364			−0.817306			−0.408653	+	0.912690i	$0.634001\pi$
$488$	20.2849	−	35.1344i	0.918253	−	1.59046i
$489$	−18.5560	−	5.42810i	−0.839129	−	0.245467i
$490$		0			0
$491$	−1.02344	−	1.77266i	−0.0461874	−	0.0799989i	0.842007	−	0.539466i	$-0.181374\pi$
$491$	−1.02344	−	1.77266i	−0.0461874	−	0.0799989i	−0.888195	+	0.459467i	$0.848040\pi$
$492$	−38.1490	+	36.4489i	−1.71989	+	1.64324i
$493$	−18.5679	+	32.1606i	−0.836257	+	1.44844i
$494$	2.36381			0.106353
$495$	−3.75700	−	2.40373i	−0.168864	−	0.108040i
$496$	30.4097			1.36544
$497$		0			0
$498$	−12.2807	−	50.3990i	−0.550313	−	2.25843i
$499$	19.5438	+	33.8508i	0.874899	+	1.51537i	0.856870	+	0.515532i	$0.172406\pi$
$499$	19.5438	+	33.8508i	0.874899	+	1.51537i	0.0180291	+	0.999837i	$0.494261\pi$
$500$	25.0742	+	43.4297i	1.12135	+	1.94224i
$501$	−1.41887	−	5.82292i	−0.0633906	−	0.260149i
$502$	18.5679	−	32.1606i	0.828727	−	1.43540i
$503$	5.11846			0.228221			0.114111	−	0.993468i	$-0.463598\pi$
$503$	5.11846			0.228221			0.114111	+	0.993468i	$0.463598\pi$
$504$		0			0
$505$	−31.8683			−1.41812
$506$	−2.32383	+	4.02499i	−0.103307	+	0.178933i
$507$	15.9836	−	15.2712i	0.709855	−	0.678219i
$508$	31.5079	+	54.5732i	1.39794	+	2.42130i
$509$	14.7636	+	25.5713i	0.654386	+	1.13343i	0.982047	+	0.188634i	$0.0604060\pi$
$509$	14.7636	+	25.5713i	0.654386	+	1.13343i	−0.327662	+	0.944795i	$0.606261\pi$
$510$	−72.6562	−	21.2538i	−3.21727	−	0.941136i
$511$		0			0
$512$	−41.4078			−1.82998
$513$	−6.73891	−	7.72952i	−0.297530	−	0.341267i
$514$	−18.9750			−0.836952
$515$	14.6819	−	25.4298i	0.646962	−	1.12057i
$516$	−15.6856	−	4.58845i	−0.690520	−	0.201995i
$517$	1.28352	+	2.22313i	0.0564493	+	0.0977730i
$518$		0			0
$519$	7.58113	−	7.24327i	0.332775	−	0.317944i
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	1.06470			0.0466454			0.0233227	−	0.999728i	$-0.492575\pi$
$521$	1.06470			0.0466454			0.0233227	+	0.999728i	$0.492575\pi$
$522$	2.57179	−	56.3927i	0.112564	−	2.46824i
$523$	13.3819			0.585149			0.292574	−	0.956243i	$-0.405488\pi$
$523$	13.3819			0.585149			0.292574	+	0.956243i	$0.405488\pi$
$524$	17.2581	−	29.8918i	0.753922	−	1.30583i
$525$		0			0
$526$	−5.18190	−	8.97532i	−0.225942	−	0.391343i
$527$	−17.0615	−	29.5513i	−0.743210	−	1.28728i
$528$	−0.721181	−	2.95966i	−0.0313854	−	0.128803i
$529$	0.699612	−	1.21176i	0.0304179	−	0.0526853i
$530$	32.1206			1.39523
$531$	0.836219	−	18.3361i	0.0362888	−	0.795719i
$532$		0			0
$533$	1.82889	−	3.16774i	0.0792181	−	0.137210i
$534$	−45.6972	+	43.6606i	−1.97751	+	1.88938i
$535$	23.4885	+	40.6833i	1.01550	+	1.75889i
$536$	−9.09931	−	15.7605i	−0.393031	−	0.680749i
$537$	15.1827	+	4.44133i	0.655181	+	0.191658i
$538$	25.5286	−	44.2168i	1.10062	−	1.90632i
$539$		0			0
$540$	75.6224	−	14.8136i	3.25427	−	0.637475i
$541$	−34.0875			−1.46554			−0.732769	−	0.680478i	$-0.761772\pi$
$541$	−34.0875			−1.46554			−0.732769	+	0.680478i	$0.761772\pi$
$542$	−35.0485	+	60.7058i	−1.50546	+	2.60754i
$543$	19.8619	+	5.81012i	0.852354	+	0.249336i
$544$	−1.30985	−	2.26873i	−0.0561594	−	0.0972709i
$545$	4.75692	+	8.23922i	0.203764	+	0.352930i
$546$		0			0
$547$	2.97150	−	5.14678i	0.127052	−	0.220060i	−0.795481	−	0.605978i	$-0.792782\pi$
$547$	2.97150	−	5.14678i	0.127052	−	0.220060i	0.922533	+	0.385918i	$0.126115\pi$
$548$	1.52937			0.0653316
$549$	21.3820	−	11.0781i	0.912560	−	0.472800i
$550$	8.38151			0.357389
$551$	7.54638	−	13.0707i	0.321487	−	0.556831i
$552$	−9.63198	−	39.5287i	−0.409964	−	1.68245i
$553$		0			0
$554$	−21.1139	−	36.5704i	−0.897044	−	1.55373i
$555$	3.49115	+	14.3273i	0.148191	+	0.608161i
$556$	38.5165	−	66.7126i	1.63346	−	2.82924i
$557$	−30.0803			−1.27454			−0.637272	−	0.770639i	$-0.719937\pi$
$557$	−30.0803			−1.27454			−0.637272	+	0.770639i	$0.719937\pi$
$558$	43.6937	+	27.9553i	1.84970	+	1.18344i
$559$	1.13298			0.0479202
$560$		0			0
$561$	−2.47150	+	2.36135i	−0.104347	+	0.0996963i
$562$	−11.6170	−	20.1213i	−0.490035	−	0.848765i
$563$	−9.81060	−	16.9925i	−0.413468	−	0.716147i	0.581799	−	0.813333i	$-0.302349\pi$
$563$	−9.81060	−	16.9925i	−0.413468	−	0.716147i	−0.995266	+	0.0971860i	$0.969016\pi$
$564$	−42.5679	−	12.4522i	−1.79243	−	0.524333i
$565$	−25.5154	+	44.1940i	−1.07344	+	1.85926i
$566$	−41.5049			−1.74458
$567$		0			0
$568$	42.7601			1.79417
$569$	0.687159	−	1.19019i	0.0288072	−	0.0498955i	−0.851262	−	0.524740i	$-0.824162\pi$
$569$	0.687159	−	1.19019i	0.0288072	−	0.0498955i	0.880070	+	0.474845i	$0.157496\pi$
$570$	29.5290	+	8.63800i	1.23683	+	0.361806i
$571$	−8.69076	−	15.0528i	−0.363697	−	0.629941i	0.624869	−	0.780729i	$-0.285152\pi$
$571$	−8.69076	−	15.0528i	−0.363697	−	0.629941i	−0.988566	+	0.150788i	$0.951819\pi$
$572$	0.401038	+	0.694619i	0.0167683	+	0.0290435i
$573$	−11.4467	+	10.9365i	−0.478191	+	0.456880i
$574$		0			0
$575$	38.9545			1.62451
$576$	−18.5167	−	11.8470i	−0.771530	−	0.493626i
$577$	27.0548			1.12631			0.563153	−	0.826353i	$-0.309588\pi$
$577$	27.0548			1.12631			0.563153	+	0.826353i	$0.309588\pi$
$578$	−8.09406	+	14.0193i	−0.336668	+	0.583127i
$579$	−6.94750	−	28.5119i	−0.288728	−	1.18491i
$580$	56.7080	+	98.2211i	2.35467	+	4.07841i
$581$		0			0
$582$	9.57227	+	39.2837i	0.396783	+	1.62836i
$583$	0.725191	−	1.25607i	0.0300344	−	0.0520210i
$584$	9.97430			0.412740
$585$	−4.74338	+	2.45756i	−0.196115	+	0.101608i
$586$	9.16010			0.378400
$587$	3.75700	−	6.50731i	0.155068	−	0.268585i	−0.778016	−	0.628245i	$-0.783774\pi$
$587$	3.75700	−	6.50731i	0.155068	−	0.268585i	0.933084	+	0.359659i	$0.117107\pi$
$588$		0			0
$589$	6.93414	+	12.0103i	0.285716	+	0.494875i
$590$	27.5349	+	47.6919i	1.13359	+	1.96344i
$591$	−35.4376	−	10.3664i	−1.45771	−	0.426417i
$592$	−5.03590	+	8.72243i	−0.206974	+	0.358490i
$593$	−35.5808			−1.46113			−0.730565	−	0.682843i	$-0.760743\pi$
$593$	−35.5808			−1.46113			−0.730565	+	0.682843i	$0.760743\pi$
$594$	1.68456	−	4.91551i	0.0691184	−	0.201686i
$595$		0			0
$596$	19.6659	−	34.0623i	0.805545	−	1.39524i
$597$	16.5811	+	4.85041i	0.678620	+	0.198514i
$598$	2.78340	+	4.82100i	0.113822	+	0.197145i
$599$	5.74105	+	9.94379i	0.234573	+	0.406292i	0.959148	−	0.282903i	$-0.0912975\pi$
$599$	5.74105	+	9.94379i	0.234573	+	0.406292i	−0.724576	+	0.689195i	$0.757964\pi$
$600$	−53.0499	+	50.6857i	−2.16575	+	2.06924i
$601$	−0.190030	+	0.329142i	−0.00775150	+	0.0134260i	−0.869875	−	0.493272i	$-0.835801\pi$
$601$	−0.190030	+	0.329142i	−0.00775150	+	0.0134260i	0.862124	+	0.506698i	$0.169134\pi$
$602$		0			0
$603$	0.492129	−	10.7911i	0.0200411	−	0.439448i
$604$	−52.0335			−2.11721
$605$	−19.8173	+	34.3246i	−0.805688	+	1.39549i
$606$	−8.78959	−	36.0716i	−0.357053	−	1.46531i
$607$	−9.27044	−	16.0569i	−0.376275	−	0.651728i	0.614242	−	0.789118i	$-0.289462\pi$
$607$	−9.27044	−	16.0569i	−0.376275	−	0.651728i	−0.990517	+	0.137390i	$0.956129\pi$
$608$	0.532351	+	0.922058i	0.0215897	+	0.0373944i
$609$		0			0
$610$	−36.1249	+	62.5702i	−1.46265	+	2.53339i
$611$	3.07472			0.124390
$612$	2.69054	−	58.9966i	0.108759	−	2.38480i
$613$	7.32451			0.295834			0.147917	−	0.989000i	$-0.452743\pi$
$613$	7.32451			0.295834			0.147917	+	0.989000i	$0.452743\pi$
$614$	37.6077	−	65.1385i	1.51772	−	2.62877i
$615$	34.4226	−	32.8885i	1.38805	−	1.32619i
$616$		0			0
$617$	12.7427	+	22.0710i	0.513002	+	0.888546i	0.999886	+	0.0150791i	$0.00480000\pi$
$617$	12.7427	+	22.0710i	0.513002	+	0.888546i	−0.486884	+	0.873466i	$0.661867\pi$
$618$	32.8334	+	9.60462i	1.32075	+	0.386354i
$619$	16.4482	−	28.4891i	0.661108	−	1.14507i	−0.319217	−	0.947682i	$-0.603420\pi$
$619$	16.4482	−	28.4891i	0.661108	−	1.14507i	0.980325	−	0.197391i	$-0.0632468\pi$
$620$	−104.214			−4.18535
$621$	7.82927	−	22.8456i	0.314178	−	0.916764i
$622$	25.6748			1.02947
$623$		0			0
$624$	−3.50194	−	1.02441i	−0.140190	−	0.0410092i
$625$	−1.67111	−	2.89444i	−0.0668443	−	0.115778i
$626$	−0.762585	−	1.32084i	−0.0304790	−	0.0527912i
$627$	1.00447	−	0.959702i	0.0401145	−	0.0383268i
$628$	−42.4636	+	73.5490i	−1.69448	+	2.93493i
$629$	11.3016			0.450626
$630$		0			0
$631$	29.8683			1.18904			0.594519	−	0.804082i	$-0.297343\pi$
$631$	29.8683			1.18904			0.594519	+	0.804082i	$0.297343\pi$
$632$	−20.6264	+	35.7259i	−0.820472	+	1.42110i
$633$	−2.00590	−	8.23203i	−0.0797275	−	0.327194i
$634$	−12.6082	−	21.8380i	−0.500734	−	0.867297i
$635$	−28.4301	−	49.2424i	−1.12822	−	1.95413i
$636$	5.93251	+	24.3464i	0.235239	+	0.965399i
$637$		0			0
$638$	7.64766			0.302774
$639$	21.3801	+	13.6790i	0.845782	+	0.541132i
$640$	69.8991			2.76301
$641$	−5.73025	+	9.92509i	−0.226331	+	0.392017i	−0.956718	−	0.291016i	$-0.906007\pi$
$641$	−5.73025	+	9.92509i	−0.226331	+	0.392017i	0.730387	+	0.683034i	$0.239340\pi$
$642$	−39.5710	+	37.8075i	−1.56174	+	1.49214i
$643$	−8.69078	−	15.0529i	−0.342731	−	0.593627i	0.642208	−	0.766531i	$-0.278019\pi$
$643$	−8.69078	−	15.0529i	−0.342731	−	0.593627i	−0.984939	+	0.172903i	$0.944685\pi$
$644$		0			0
$645$	14.1534	+	4.14024i	0.557290	+	0.163022i
$646$	11.7896	−	20.4202i	0.463855	−	0.803421i
$647$	−25.3439			−0.996372			−0.498186	−	0.867070i	$-0.666000\pi$
$647$	−25.3439			−0.996372			−0.498186	+	0.867070i	$0.666000\pi$
$648$	19.0634	+	41.2993i	0.748882	+	1.62239i
$649$	2.48664			0.0976091
$650$	5.01954	−	8.69410i	0.196883	−	0.341011i
$651$		0			0
$652$	22.6264	+	39.1900i	0.886116	+	1.53480i
$653$	−7.04163	−	12.1965i	−0.275560	−	0.477284i	0.694716	−	0.719284i	$-0.255530\pi$
$653$	−7.04163	−	12.1965i	−0.275560	−	0.477284i	−0.970276	+	0.242000i	$0.922197\pi$
$654$	−8.01396	+	7.65681i	−0.313370	+	0.299405i
$655$	−15.5723	+	26.9720i	−0.608459	+	1.05388i
$656$	32.5163			1.26955
$657$	4.98715	+	3.19079i	0.194567	+	0.124484i
$658$		0			0
$659$	−19.0854	+	33.0569i	−0.743462	+	1.28771i	0.207449	+	0.978246i	$0.433484\pi$
$659$	−19.0854	+	33.0569i	−0.743462	+	1.28771i	−0.950910	+	0.309467i	$0.899849\pi$
$660$	2.47150	+	10.1428i	0.0962028	+	0.394807i
$661$	−0.176866	−	0.306341i	−0.00687930	−	0.0119153i	0.862565	−	0.505946i	$-0.168856\pi$
$661$	−0.176866	−	0.306341i	−0.00687930	−	0.0119153i	−0.869445	+	0.494031i	$0.835523\pi$
$662$	25.0526	+	43.3924i	0.973698	+	1.68649i
$663$	0.969283	+	3.97784i	0.0376438	+	0.154487i
$664$	−30.7591	+	53.2764i	−1.19369	+	2.06752i
$665$		0			0
$666$	−15.2542	+	7.90324i	−0.591087	+	0.306244i
$667$	35.5438			1.37626
$668$	−7.01403	+	12.1487i	−0.271381	+	0.470046i
$669$	29.3157	−	28.0092i	1.13341	−	1.08290i
$670$	16.2048	+	28.0675i	0.626045	+	1.08434i
$671$	1.63119	+	2.82531i	0.0629715	+	0.109070i
$672$		0			0
$673$	10.5555	−	18.2827i	0.406886	−	0.704748i	−0.587653	−	0.809113i	$-0.699948\pi$
$673$	10.5555	−	18.2827i	0.406886	−	0.704748i	0.994539	+	0.104365i	$0.0332811\pi$
$674$	−14.0541			−0.541343
$675$	−42.7393	+	8.37215i	−1.64504	+	0.322244i
$676$	−51.7424			−1.99009
$677$	10.5732	−	18.3133i	0.406361	−	0.703837i	−0.588118	−	0.808775i	$-0.700131\pi$
$677$	10.5732	−	18.3133i	0.406361	−	0.703837i	0.994479	+	0.104938i	$0.0334643\pi$
$678$	−57.0605	−	16.6917i	−2.19140	−	0.641041i
$679$		0			0
$680$	44.8879	+	77.7482i	1.72137	+	2.98151i
$681$	7.66225	−	7.32078i	0.293618	−	0.280533i
$682$	−3.51360	+	6.08573i	−0.134543	+	0.233035i
$683$	34.7716			1.33050			0.665249	−	0.746622i	$-0.268326\pi$
$683$	34.7716			1.33050			0.665249	+	0.746622i	$0.268326\pi$
$684$	−1.09349	+	23.9775i	−0.0418107	+	0.916801i
$685$	−1.37998			−0.0527264
$686$		0			0
$687$	−0.598835	−	2.45756i	−0.0228470	−	0.0937618i
$688$	5.03590	+	8.72243i	0.191992	+	0.332539i
$689$	−0.868609	−	1.50447i	−0.0330914	−	0.0573159i
$690$	17.1534	+	70.3959i	0.653019	+	2.67993i
$691$	17.3246	−	30.0071i	0.659059	−	1.14152i	−0.321801	−	0.946807i	$-0.604288\pi$
$691$	17.3246	−	30.0071i	0.659059	−	1.14152i	0.980860	−	0.194716i	$-0.0623785\pi$
$692$	−24.5418			−0.932940
$693$		0			0
$694$	21.8525			0.829511
$695$	−34.7542	+	60.1960i	−1.31830	+	2.28336i
$696$	−48.4051	+	46.2479i	−1.83479	+	1.75302i
$697$	−18.2434	−	31.5985i	−0.691017	−	1.19688i
$698$	−25.8044	−	44.6945i	−0.976710	−	1.69171i
$699$	−22.0240	−	6.44260i	−0.833024	−	0.243681i
$700$		0			0
$701$	−48.6050			−1.83579			−0.917894	−	0.396826i	$-0.870111\pi$
$701$	−48.6050			−1.83579			−0.917894	+	0.396826i	$0.870111\pi$
$702$	−4.08998	−	4.69120i	−0.154366	−	0.177058i
$703$	−4.59322			−0.173236
$704$	1.48901	−	2.57904i	0.0561192	−	0.0972012i
$705$	38.4098	+	11.2359i	1.44660	+	0.423167i
$706$	18.1651	+	31.4629i	0.683654	+	1.18412i
$707$		0			0
$708$	−31.0634	+	29.6791i	−1.16743	+	1.11541i
$709$	−2.05408	+	3.55778i	−0.0771428	+	0.133615i	−0.902016	−	0.431702i	$-0.857913\pi$
$709$	−2.05408	+	3.55778i	−0.0771428	+	0.133615i	0.824873	+	0.565318i	$0.191246\pi$
$710$	−76.1506			−2.85788
$711$	−21.7419	+	11.2646i	−0.815386	+	0.422454i
$712$	74.9528			2.80898
$713$	−16.3300	+	28.2844i	−0.611564	+	1.05926i
$714$		0			0
$715$	−0.361864	−	0.626767i	−0.0135330	−	0.0234398i
$716$	−18.5131	−	32.0657i	−0.691868	−	1.19835i
$717$	−7.95037	−	32.6276i	−0.296912	−	1.21850i
$718$	−8.87266	+	15.3679i	−0.331125	+	0.573525i
$719$	−48.2816			−1.80060			−0.900299	−	0.435271i	$-0.856653\pi$
$719$	−48.2816			−1.80060			−0.900299	+	0.435271i	$0.856653\pi$
$720$	−40.0032	−	25.5941i	−1.49083	−	0.953837i
$721$		0			0
$722$	18.5833	−	32.1872i	0.691597	−	1.19788i
$723$	6.32889	−	6.04684i	0.235374	−	0.224884i
$724$	−24.2187	−	41.9481i	−0.900082	−	1.55899i
$725$	−32.0495	−	55.5114i	−1.19029	−	2.06164i
$726$	−44.3177	−	12.9641i	−1.64478	−	0.481143i
$727$	−20.5151	+	35.5332i	−0.760863	+	1.31785i	0.181543	+	0.983383i	$0.441891\pi$
$727$	−20.5151	+	35.5332i	−0.760863	+	1.31785i	−0.942406	+	0.334470i	$0.891443\pi$
$728$		0			0
$729$	−3.67996	+	26.7480i	−0.136295	+	0.990668i
$730$	−17.7630			−0.657439
$731$	5.65082	−	9.78750i	0.209003	−	0.362004i
$732$	−54.0983	−	15.8252i	−1.99953	−	0.584916i
$733$	15.2714	+	26.4508i	0.564062	+	0.976983i	0.997136	+	0.0756253i	$0.0240953\pi$
$733$	15.2714	+	26.4508i	0.564062	+	0.976983i	−0.433075	+	0.901358i	$0.642571\pi$
$734$	13.5011	+	23.3845i	0.498334	+	0.863139i
$735$		0			0
$736$	−1.25370	+	2.17147i	−0.0462118	+	0.0800413i
$737$	1.46343			0.0539061
$738$	46.7205	+	29.8918i	1.71981	+	1.10033i
$739$	23.8200			0.876234			0.438117	−	0.898918i	$-0.355646\pi$
$739$	23.8200			0.876234			0.438117	+	0.898918i	$0.355646\pi$
$740$	17.2581	−	29.8918i	0.634419	−	1.09885i
$741$	−0.393936	−	1.61668i	−0.0144716	−	0.0593901i
$742$		0			0
$743$	−5.26089	−	9.11213i	−0.193003	−	0.334292i	0.753241	−	0.657745i	$-0.228490\pi$
$743$	−5.26089	−	9.11213i	−0.193003	−	0.334292i	−0.946244	+	0.323453i	$0.895156\pi$
$744$	−14.5634	−	59.7669i	−0.533921	−	2.19116i
$745$	−17.7449	+	30.7350i	−0.650121	+	1.12604i
$746$	−1.33794			−0.0489855
$747$	−32.4227	+	16.7983i	−1.18629	+	0.614619i
$748$	8.00079			0.292538
$749$		0			0
$750$	38.1160	−	36.4174i	1.39180	−	1.32977i
$751$	5.13521	+	8.89445i	0.187386	+	0.324563i	0.944378	−	0.328862i	$-0.106665\pi$
$751$	5.13521	+	8.89445i	0.187386	+	0.324563i	−0.756992	+	0.653425i	$0.773332\pi$
$752$	13.6665	+	23.6711i	0.498367	+	0.863197i
$753$	−25.0900	−	7.33948i	−0.914330	−	0.267465i
$754$	4.58005	−	7.93288i	0.166796	−	0.288899i
$755$	46.9507			1.70871
$756$		0			0
$757$	8.03930			0.292193			0.146097	−	0.989270i	$-0.453329\pi$
$757$	8.03930			0.292193			0.146097	+	0.989270i	$0.453329\pi$
$758$	27.9159	−	48.3518i	1.01395	−	1.75622i
$759$	3.14009	+	0.918558i	0.113978	+	0.0333416i
$760$	−18.2434	−	31.5985i	−0.661757	−	1.14620i
$761$	13.8302	+	23.9547i	0.501345	+	0.868355i	0.999999	+	0.00155404i	$0.000494668\pi$
$761$	13.8302	+	23.9547i	0.501345	+	0.868355i	−0.498654	+	0.866801i	$0.666172\pi$
$762$	47.8961	−	45.7616i	1.73509	−	1.65777i
$763$		0			0
$764$	37.0554			1.34062
$765$	−2.42773	+	53.2338i	−0.0877747	+	1.92467i
$766$	87.8742			3.17502
$767$	1.48920	−	2.57938i	0.0537720	−	0.0931359i
$768$	13.2696	+	54.4573i	0.478827	+	1.96506i
$769$	−16.9613	−	29.3778i	−0.611640	−	1.05939i	−0.990964	−	0.134128i	$-0.957177\pi$
$769$	−16.9613	−	29.3778i	−0.611640	−	1.05939i	0.379324	−	0.925264i	$-0.376157\pi$
$770$		0			0
$771$	3.16225	+	12.9776i	0.113886	+	0.467376i
$772$	−34.3442	+	59.4858i	−1.23607	+	2.14094i
$773$	28.5956			1.02851			0.514256	−	0.857637i	$-0.328068\pi$
$773$	28.5956			1.02851			0.514256	+	0.857637i	$0.328068\pi$
$774$	−0.782679	+	17.1621i	−0.0281328	+	0.616880i
$775$	58.8986			2.11570
$776$	23.9753	−	41.5265i	0.860664	−	1.49071i
$777$		0			0
$778$	−47.5605	−	82.3772i	−1.70513	−	2.95337i
$779$	7.41449	+	12.8423i	0.265652	+	0.460122i
$780$	12.0012	+	3.51066i	0.429711	+	0.125702i
$781$	−1.71926	+	2.97785i	−0.0615200	+	0.106556i
$782$	55.5294			1.98573
$783$	−38.9973	+	7.63912i	−1.39365	+	0.273000i
$784$		0			0
$785$	38.3157	−	66.3647i	1.36754	−	2.36866i
$786$	−34.8245	−	10.1871i	−1.24215	−	0.363361i
$787$	23.0017	+	39.8402i	0.819923	+	1.42015i	0.905738	+	0.423838i	$0.139317\pi$
$787$	23.0017	+	39.8402i	0.819923	+	1.42015i	−0.0858145	+	0.996311i	$0.527349\pi$
$788$	43.2111	+	74.8438i	1.53933	+	2.66620i
$789$	−5.27491	+	5.03983i	−0.187792	+	0.179423i
$790$	36.7330	−	63.6235i	1.30690	−	2.26362i
$791$		0			0
$792$	−5.47150	+	2.83480i	−0.194421	+	0.100730i
$793$	3.90757			0.138762
$794$	14.6988	−	25.4591i	0.521642	−	0.903511i
$795$	−5.35301	−	21.9682i	−0.189852	−	0.779133i
$796$	−20.2183	−	35.0192i	−0.716620	−	1.24122i
$797$	−18.4558	−	31.9664i	−0.653739	−	1.13231i	−0.982208	−	0.187795i	$-0.939866\pi$
$797$	−18.4558	−	31.9664i	−0.653739	−	1.13231i	0.328469	−	0.944515i	$-0.393467\pi$
$798$		0			0
$799$	15.3353	−	26.5615i	0.542524	−	0.939679i
$800$	4.52179			0.159869
$801$	37.4764	+	23.9775i	1.32416	+	0.847202i
$802$	79.6136			2.81125
$803$	−0.401038	+	0.694619i	−0.0141523	+	0.0245126i
$804$	−18.2814	+	17.4666i	−0.644734	+	0.616001i
$805$		0			0
$806$	4.20847	+	7.28928i	0.148237	+	0.256754i
$807$	−34.4956	−	10.0909i	−1.21430	−	0.355216i
$808$	−22.0150	+	38.1311i	−0.774484	+	1.34145i
$809$	47.6887			1.67665			0.838323	−	0.545174i	$-0.183537\pi$
$809$	47.6887			1.67665			0.838323	+	0.545174i	$0.183537\pi$
$810$	−33.9496	−	73.5490i	−1.19287	−	2.58425i
$811$	6.02728			0.211646			0.105823	−	0.994385i	$-0.466252\pi$
$811$	6.02728			0.211646			0.105823	+	0.994385i	$0.466252\pi$
$812$		0			0
$813$	47.3594	+	13.8539i	1.66097	+	0.485877i
$814$	−1.16372	−	2.01561i	−0.0407882	−	0.0706472i
$815$	−20.4162	−	35.3619i	−0.715148	−	1.23867i
$816$	−26.3157	+	25.1429i	−0.921232	+	0.880177i
$817$	−2.29661	+	3.97784i	−0.0803481	+	0.139167i
$818$	46.6881			1.63241
$819$		0			0
$820$	−111.434			−3.89143
$821$	19.6321	−	34.0038i	0.685165	−	1.18674i	−0.288220	−	0.957564i	$-0.593064\pi$
$821$	19.6321	−	34.0038i	0.685165	−	1.18674i	0.973385	−	0.229176i	$-0.0736031\pi$
$822$	−0.380613	−	1.56200i	−0.0132754	−	0.0544809i
$823$	−11.3815	−	19.7134i	−0.396735	−	0.687165i	0.596586	−	0.802549i	$-0.296523\pi$
$823$	−11.3815	−	19.7134i	−0.396735	−	0.687165i	−0.993321	+	0.115384i	$0.963190\pi$
$824$	−20.2849	−	35.1344i	−0.706657	−	1.22397i
$825$	−1.39681	−	5.73237i	−0.0486306	−	0.199575i
$826$		0			0
$827$	−28.9286			−1.00595			−0.502973	−	0.864302i	$-0.667760\pi$
$827$	−28.9286			−1.00595			−0.502973	+	0.864302i	$0.667760\pi$
$828$	−50.1898	+	26.0035i	−1.74422	+	0.903684i
$829$	−33.9767			−1.18006			−0.590029	−	0.807382i	$-0.700884\pi$
$829$	−33.9767			−1.18006			−0.590029	+	0.807382i	$0.700884\pi$
$830$	54.7783	−	94.8788i	1.90138	−	3.29329i
$831$	−21.4928	+	20.5350i	−0.745579	+	0.712351i
$832$	−1.78348	−	3.08908i	−0.0618312	−	0.107095i
$833$		0			0
$834$	−77.7213	−	22.7355i	−2.69127	−	0.787267i
$835$	6.32889	−	10.9620i	0.219020	−	0.379354i
$836$	−3.25169			−0.112462
$837$	11.8377	−	34.5423i	0.409172	−	1.19396i
$838$	−42.5432			−1.46963
$839$	−19.0206	+	32.9446i	−0.656663	+	1.13737i	0.324811	+	0.945779i	$0.394699\pi$
$839$	−19.0206	+	32.9446i	−0.656663	+	1.13737i	−0.981474	+	0.191595i	$0.938634\pi$
$840$		0			0
$841$	−14.7434	−	25.5363i	−0.508392	−	0.880561i
$842$	−22.8837	−	39.6356i	−0.788623	−	1.36593i
$843$	−11.8255	+	11.2985i	−0.407293	+	0.389141i
$844$	−9.91595	+	17.1749i	−0.341321	+	0.591185i
$845$	46.6881			1.60612
$846$	−2.12405	+	46.5749i	−0.0730264	+	1.60128i
$847$		0			0
$848$	7.72159	−	13.3742i	0.265161	−	0.459272i
$849$	6.91693	+	28.3864i	0.237388	+	0.974219i
$850$	−50.0704	−	86.7245i	−1.71740	−	2.97463i
$851$	−5.40856	−	9.36790i	−0.185403	−	0.321127i
$852$	−14.0646	−	57.7198i	−0.481846	−	1.97745i
$853$	−4.90746	+	8.49996i	−0.168028	+	0.291033i	−0.937726	−	0.347374i	$-0.887073\pi$
$853$	−4.90746	+	8.49996i	−0.168028	+	0.291033i	0.769698	+	0.638408i	$0.220407\pi$
$854$		0			0
$855$	0.986679	−	21.6353i	0.0337437	−	0.739912i
$856$	64.9046			2.21840
$857$	−13.3680	+	23.1541i	−0.456642	+	0.790928i	−0.998781	−	0.0493613i	$-0.984281\pi$
$857$	−13.3680	+	23.1541i	−0.456642	+	0.790928i	0.542139	+	0.840289i	$0.317615\pi$
$858$	0.609631	−	0.582462i	0.0208125	−	0.0198849i
$859$	9.24411	+	16.0113i	0.315405	+	0.546297i	0.979523	−	0.201330i	$-0.0645263\pi$
$859$	9.24411	+	16.0113i	0.315405	+	0.546297i	−0.664119	+	0.747627i	$0.731193\pi$
$860$	−17.2581	−	29.8918i	−0.588495	−	1.01930i
$861$		0			0
$862$	19.5344	−	33.8346i	0.665345	−	1.15241i
$863$	−9.14786			−0.311397			−0.155698	−	0.987805i	$-0.549763\pi$
$863$	−9.14786			−0.311397			−0.155698	+	0.987805i	$0.549763\pi$
$864$	0.908813	−	2.65189i	0.0309184	−	0.0902193i
$865$	22.1445			0.752937
$866$	−49.7473	+	86.1649i	−1.69048	+	2.92800i
$867$	10.9371	+	3.19940i	0.371444	+	0.108657i
$868$		0			0
$869$	−1.65865	−	2.87287i	−0.0562660	−	0.0974555i
$870$	86.2036	−	82.3619i	2.92257	−	2.79233i
$871$	0.876423	−	1.51801i	0.0296964	−	0.0514358i
$872$	13.1445			0.445130
$873$	25.2720	−	13.0935i	0.855328	−	0.443149i
$874$	−22.5683			−0.763385
$875$		0			0
$876$	−3.28074	−	13.4638i	−0.110846	−	0.454901i
$877$	−11.3442	−	19.6487i	−0.383065	−	0.663488i	0.608434	−	0.793605i	$-0.291798\pi$
$877$	−11.3442	−	19.6487i	−0.383065	−	0.663488i	−0.991499	+	0.130117i	$0.958465\pi$
$878$	−15.3301	−	26.5525i	−0.517366	−	0.896104i
$879$	−1.52656	−	6.26487i	−0.0514897	−	0.211309i
$880$	3.21683	−	5.57172i	0.108439	−	0.187823i
$881$	15.3696			0.517815			0.258907	−	0.965902i	$-0.416638\pi$
$881$	15.3696			0.517815			0.258907	+	0.965902i	$0.416638\pi$
$882$		0			0
$883$	29.6372			0.997370			0.498685	−	0.866783i	$-0.333817\pi$
$883$	29.6372			0.997370			0.498685	+	0.866783i	$0.333817\pi$
$884$	4.79153	−	8.29918i	0.161157	−	0.279132i
$885$	28.0291	−	26.7800i	0.942188	−	0.900199i
$886$	10.1259	+	17.5385i	0.340185	+	0.589219i
$887$	9.38252	+	16.2510i	0.315034	+	0.545655i	0.979445	−	0.201712i	$-0.0646506\pi$
$887$	9.38252	+	16.2510i	0.315034	+	0.545655i	−0.664410	+	0.747368i	$0.731317\pi$
$888$	19.5547	+	5.72026i	0.656212	+	0.191959i
$889$		0			0
$890$	−133.482			−4.47432
$891$	−3.64260	−	0.332935i	−0.122032	−	0.0111537i
$892$	−94.9014			−3.17753
$893$	−6.23258	+	10.7952i	−0.208565	+	0.361246i
$894$	−39.6831	−	11.6083i	−1.32720	−	0.388241i
$895$	16.7047	+	28.9335i	0.558378	+	0.967139i
$896$		0			0
$897$	2.83336	−	2.70709i	0.0946031	−	0.0903871i
$898$	−6.94445	+	12.0281i	−0.231739	+	0.401384i
$899$	53.7416			1.79238
$900$	85.8673	+	54.9380i	2.86224	+	1.83127i
$901$	−17.3289			−0.577310
$902$	−3.75700	+	6.50731i	−0.125094	+	0.216670i
$903$		0			0
$904$	35.2527	+	61.0595i	1.17249	+	2.03081i
$905$	21.8530	+	37.8505i	0.726419	+	1.25819i
$906$	12.9495	+	53.1435i	0.430218	+	1.76557i
$907$	15.5541	−	26.9405i	0.516465	−	0.894543i	−0.483352	−	0.875426i	$-0.660581\pi$
$907$	15.5541	−	26.9405i	0.516465	−	0.894543i	0.999817	−	0.0191175i	$-0.00608567\pi$
$908$	−24.8045			−0.823165
$909$	−23.2056	+	12.0229i	−0.769683	+	0.398775i
$910$		0			0
$911$	−8.73764	+	15.1340i	−0.289491	+	0.501413i	−0.973688	−	0.227884i	$-0.926819\pi$
$911$	−8.73764	+	15.1340i	−0.289491	+	0.501413i	0.684197	+	0.729297i	$0.260153\pi$
$912$	10.6952	−	10.2186i	0.354154	−	0.338371i
$913$	−2.47347	−	4.28418i	−0.0818600	−	0.141786i
$914$	−6.23599	−	10.8010i	−0.206268	−	0.357267i
$915$	48.8139	+	14.2794i	1.61374	+	0.472061i
$916$	−2.96027	+	5.12734i	−0.0978101	+	0.169412i
$917$		0			0
$918$	−60.9248	+	11.9345i	−2.01082	+	0.393896i
$919$	42.1986			1.39200			0.696002	−	0.718040i	$-0.254960\pi$
$919$	42.1986			1.39200			0.696002	+	0.718040i	$0.254960\pi$
$920$	42.9635	−	74.4150i	1.41647	−	2.45339i
$921$	−50.8176	−	14.8655i	−1.67450	−	0.489834i
$922$	9.56720	+	16.5709i	0.315079	+	0.545733i
$923$	2.05927	+	3.56676i	0.0677818	+	0.117401i
$924$		0			0
$925$	−9.75370	+	16.8939i	−0.320700	+	0.555468i
$926$	−22.5873			−0.742266
$927$	1.09709	−	24.0564i	0.0360332	−	0.790114i
$928$	4.12588			0.135439
$929$	−24.2056	+	41.9253i	−0.794159	+	1.37552i	0.129213	+	0.991617i	$0.458755\pi$
$929$	−24.2056	+	41.9253i	−0.794159	+	1.37552i	−0.923372	+	0.383907i	$0.874578\pi$
$930$	25.9357	+	106.438i	0.850465	+	3.49022i
$931$		0			0
$932$	26.8551	+	46.5145i	0.879670	+	1.52363i
$933$	−4.27880	−	17.5598i	−0.140082	−	0.574881i
$934$	16.9350	−	29.3322i	0.554129	−	0.959780i
$935$	−7.21926			−0.236095
$936$	−0.336258	+	7.37327i	−0.0109909	+	0.241003i
$937$	−22.6750			−0.740762			−0.370381	−	0.928880i	$-0.620773\pi$
$937$	−22.6750			−0.740762			−0.370381	+	0.928880i	$0.620773\pi$
$938$		0			0
$939$	−0.776271	+	0.741676i	−0.0253327	+	0.0242037i
$940$	−46.8353	−	81.1211i	−1.52760	−	2.64588i
$941$	24.9753	+	43.2584i	0.814170	+	1.41018i	0.909922	+	0.414779i	$0.136141\pi$
$941$	24.9753	+	43.2584i	0.814170	+	1.41018i	−0.0957523	+	0.995405i	$0.530526\pi$
$942$	85.6859	+	25.0654i	2.79180	+	0.816674i
$943$	−17.4613	+	30.2438i	−0.568617	+	0.984873i
$944$	26.4769			0.861749
$945$		0			0
$946$	−2.32743			−0.0756713
$947$	−8.85613	+	15.3393i	−0.287786	+	0.498459i	−0.973281	−	0.229618i	$-0.926252\pi$
$947$	−8.85613	+	15.3393i	−0.287786	+	0.498459i	0.685495	+	0.728077i	$0.259586\pi$
$948$	55.0091	+	16.0916i	1.78661	+	0.522631i
$949$	0.480350	+	0.831990i	0.0155928	+	0.0270075i
$950$	20.3496	+	35.2466i	0.660230	+	1.14355i
$951$	−12.8345	+	12.2625i	−0.416186	+	0.397638i
$952$		0			0
$953$	38.0229			1.23168			0.615842	−	0.787870i	$-0.288816\pi$
$953$	38.0229			1.23168			0.615842	+	0.787870i	$0.288816\pi$
$954$	23.3894	−	12.1181i	0.757259	−	0.392339i
$955$	−33.4358			−1.08196
$956$	−39.3017	+	68.0726i	−1.27111	+	2.20163i
$957$	−1.27451	−	5.23046i	−0.0411990	−	0.169077i
$958$	−10.7177	−	18.5635i	−0.346272	−	0.599761i
$959$		0			0
$960$	−10.9911	−	45.1066i	−0.354738	−	1.45581i
$961$	−9.19076	+	15.9189i	−0.296476	+	0.513512i
$962$	−2.78771			−0.0898795
$963$	32.4523	+	20.7630i	1.04576	+	0.669080i
$964$	−20.4881			−0.659876
$965$	30.9894	−	53.6752i	0.997583	−	1.72786i
$966$		0			0
$967$	15.5064	+	26.8579i	0.498652	+	0.863691i	0.999999	−	0.00155529i	$-0.000495066\pi$
$967$	15.5064	+	26.8579i	0.498652	+	0.863691i	−0.501346	+	0.865247i	$0.667162\pi$
$968$	27.3801	+	47.4236i	0.880028	+	1.52425i
$969$	−15.9307	−	4.66016i	−0.511769	−	0.149706i
$970$	−42.6972	+	73.9537i	−1.37092	+	2.37451i
$971$	−14.5675			−0.467494			−0.233747	−	0.972297i	$-0.575099\pi$
$971$	−14.5675			−0.467494			−0.233747	+	0.972297i	$0.575099\pi$
$972$	49.4776	−	39.3169i	1.58699	−	1.26109i
$973$		0			0
$974$	22.1893	−	38.4330i	0.710991	−	1.23147i
$975$	−6.78268	−	1.98411i	−0.217220	−	0.0635424i
$976$	17.3684	+	30.0830i	0.555949	+	0.962932i
$977$	23.9399	+	41.4651i	0.765904	+	1.32659i	0.939767	+	0.341815i	$0.111042\pi$
$977$	23.9399	+	41.4651i	0.765904	+	1.32659i	−0.173863	+	0.984770i	$0.555625\pi$
$978$	34.3950	−	32.8622i	1.09983	−	1.05082i
$979$	−3.01364	+	5.21978i	−0.0963163	+	0.166825i
$980$		0			0
$981$	6.57227	+	4.20495i	0.209836	+	0.134254i
$982$	5.03638			0.160717
$983$	22.2128	−	38.4737i	0.708479	−	1.22712i	−0.256942	−	0.966427i	$-0.582715\pi$
$983$	22.2128	−	38.4737i	0.708479	−	1.22712i	0.965421	−	0.260695i	$-0.0839517\pi$
$984$	−15.5723	−	63.9071i	−0.496426	−	2.03728i
$985$	−38.9902	−	67.5329i	−1.24233	−	2.15178i
$986$	−45.6864	−	79.1313i	−1.45495	−	2.52005i
$987$		0			0
$988$	−1.94738	+	3.37296i	−0.0619544	+	0.107308i
$989$	−10.8171			−0.343964
$990$	9.74407	−	5.04844i	0.309687	−	0.160450i
$991$	−41.6156			−1.32196			−0.660981	−	0.750403i	$-0.729860\pi$
$991$	−41.6156			−1.32196			−0.660981	+	0.750403i	$0.729860\pi$
$992$	−1.89557	+	3.28322i	−0.0601844	+	0.104242i
$993$	25.5023	−	24.3657i	0.809290	−	0.773223i
$994$		0			0
$995$	18.2434	+	31.5985i	0.578354	+	1.00174i
$996$	82.0325	+	23.9967i	2.59930	+	0.760363i
$997$	−6.51407	+	11.2827i	−0.206303	+	0.357327i	−0.950547	−	0.310581i	$-0.899477\pi$
$997$	−6.51407	+	11.2827i	−0.206303	+	0.357327i	0.744244	+	0.667908i	$0.232810\pi$
$998$	−96.1751			−3.04437
$999$	7.94742	+	9.11568i	0.251445	+	0.288407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.g.295.2	yes	12
3.2	odd	2		1323.2.f.g.883.5		12
7.2	even	3		441.2.h.g.214.5		12
7.3	odd	6		441.2.g.g.79.2		12
7.4	even	3		441.2.g.g.79.1		12
7.5	odd	6		441.2.h.g.214.6		12
7.6	odd	2	inner	441.2.f.g.295.1	yes	12
9.2	odd	6		3969.2.a.bd.1.2		6
9.4	even	3	inner	441.2.f.g.148.2	yes	12
9.5	odd	6		1323.2.f.g.442.5		12
9.7	even	3		3969.2.a.be.1.5		6
21.2	odd	6		1323.2.h.g.802.1		12
21.5	even	6		1323.2.h.g.802.2		12
21.11	odd	6		1323.2.g.g.667.6		12
21.17	even	6		1323.2.g.g.667.5		12
21.20	even	2		1323.2.f.g.883.6		12
63.4	even	3		441.2.h.g.373.5		12
63.5	even	6		1323.2.g.g.361.5		12
63.13	odd	6	inner	441.2.f.g.148.1	✓	12
63.20	even	6		3969.2.a.bd.1.1		6
63.23	odd	6		1323.2.g.g.361.6		12
63.31	odd	6		441.2.h.g.373.6		12
63.32	odd	6		1323.2.h.g.226.1		12
63.34	odd	6		3969.2.a.be.1.6		6
63.40	odd	6		441.2.g.g.67.2		12
63.41	even	6		1323.2.f.g.442.6		12
63.58	even	3		441.2.g.g.67.1		12
63.59	even	6		1323.2.h.g.226.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.1	✓	12	63.13	odd	6	inner
441.2.f.g.148.2	yes	12	9.4	even	3	inner
441.2.f.g.295.1	yes	12	7.6	odd	2	inner
441.2.f.g.295.2	yes	12	1.1	even	1	trivial
441.2.g.g.67.1		12	63.58	even	3
441.2.g.g.67.2		12	63.40	odd	6
441.2.g.g.79.1		12	7.4	even	3
441.2.g.g.79.2		12	7.3	odd	6
441.2.h.g.214.5		12	7.2	even	3
441.2.h.g.214.6		12	7.5	odd	6
441.2.h.g.373.5		12	63.4	even	3
441.2.h.g.373.6		12	63.31	odd	6
1323.2.f.g.442.5		12	9.5	odd	6
1323.2.f.g.442.6		12	63.41	even	6
1323.2.f.g.883.5		12	3.2	odd	2
1323.2.f.g.883.6		12	21.20	even	2
1323.2.g.g.361.5		12	63.5	even	6
1323.2.g.g.361.6		12	63.23	odd	6
1323.2.g.g.667.5		12	21.17	even	6
1323.2.g.g.667.6		12	21.11	odd	6
1323.2.h.g.226.1		12	63.32	odd	6
1323.2.h.g.226.2		12	63.59	even	6
1323.2.h.g.802.1		12	21.2	odd	6
1323.2.h.g.802.2		12	21.5	even	6
3969.2.a.bd.1.1		6	63.20	even	6
3969.2.a.bd.1.2		6	9.2	odd	6
3969.2.a.be.1.5		6	9.7	even	3
3969.2.a.be.1.6		6	63.34	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23025 + 2.13086i) q^{2} +(1.66238 + 0.486291i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.82904 + 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(2.52704 + 1.61680i) q^{9} -9.00071 q^{10} +(-0.203210 + 0.351971i) q^{11} +(-1.66238 - 6.82226i) q^{12} +(0.243398 + 0.421578i) q^{13} +(1.50000 + 6.15585i) q^{15} +(-2.16372 + 3.74766i) q^{16} +4.85584 q^{17} +(-6.55408 + 3.39569i) q^{18} -1.97351 q^{19} +(7.41507 - 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.32383 - 4.02499i) q^{23} +(8.40183 + 2.45776i) q^{24} +(-4.19076 + 7.25860i) q^{25} -1.19777 q^{26} +(3.41468 + 3.91663i) q^{27} +(-3.82383 + 6.62307i) q^{29} +(-14.9626 - 4.37697i) q^{30} +(-3.51360 - 6.08573i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(-0.508974 + 0.486291i) q^{33} +(-5.97391 + 10.3471i) q^{34} +(0.554084 - 12.1496i) q^{36} +2.32743 q^{37} +(2.42792 - 4.20528i) q^{38} +(0.199612 + 0.819187i) q^{39} +(9.24411 + 16.0113i) q^{40} +(-3.75700 - 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +1.64766 q^{44} +(-0.499960 + 10.9628i) q^{45} +11.4356 q^{46} +(3.15811 - 5.47002i) q^{47} +(-5.41938 + 5.17786i) q^{48} +(-10.3114 - 17.8598i) q^{50} +(8.07227 + 2.36135i) q^{51} +(0.986757 - 1.70911i) q^{52} -3.56867 q^{53} +(-12.5467 + 2.45776i) q^{54} -1.48672 q^{55} +(-3.28074 - 0.959702i) q^{57} +(-9.40856 - 16.2961i) q^{58} +(-3.05919 - 5.29868i) q^{59} +(18.5723 - 17.7446i) q^{60} +(4.01356 - 6.95169i) q^{61} +17.2905 q^{62} -7.32743 q^{64} +(-0.890369 + 1.54216i) q^{65} +(-0.410052 - 1.68281i) q^{66} +(-1.80039 - 3.11836i) q^{67} +(-9.84299 - 17.0486i) q^{68} +(-1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(12.7719 + 8.17147i) q^{72} +1.97351 q^{73} +(-2.86333 + 4.95943i) q^{74} +(-10.4964 + 10.0287i) q^{75} +(4.00040 + 6.92889i) q^{76} +(-1.99115 - 0.582462i) q^{78} +(-4.08113 + 7.06872i) q^{79} -15.8301 q^{80} +(3.77188 + 8.17147i) q^{81} +18.4882 q^{82} +(-6.08600 + 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(2.86333 + 4.95943i) q^{86} +(-9.57742 + 9.15059i) q^{87} +(-1.02704 + 1.77889i) q^{88} +14.8301 q^{89} +(-22.7452 - 14.5524i) q^{90} +(-9.42101 + 16.3177i) q^{92} +(-2.88151 - 11.8255i) q^{93} +(7.77056 + 13.4590i) q^{94} +(-3.60963 - 6.25206i) q^{95} +(-0.221221 - 0.907869i) q^{96} +(4.74375 - 8.21642i) q^{97} +(-1.08259 + 0.560893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43}+ \cdots - 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9 - 8 * q^11 + 18 * q^15 - 6 * q^16 - 42 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 - 48 * q^30 - 16 * q^32 - 30 * q^36 - 12 * q^37 + 24 * q^39 - 6 * q^43 - 28 * q^44 + 24 * q^46 - 56 * q^50 - 18 * q^51 + 56 * q^53 - 6 * q^57 - 18 * q^58 + 108 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 + 60 * q^72 - 36 * q^74 + 36 * q^78 + 6 * q^79 - 48 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Introduction

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