LMFDB - Embedded newform 1764.2.i.j.1537.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(373,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1764.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.i (of order $3$, degree $2$, not 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.9
Character	$\chi$	$=$	1764.1537
Dual form			1764.2.i.j.373.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.971923 - 1.43365i) q^{3} +(-1.73981 + 3.01343i) q^{5} +(-1.11073 - 2.78680i) q^{9} +O(q^{10})$	\(q+(0.971923 - 1.43365i) q^{3} +(-1.73981 + 3.01343i) q^{5} +(-1.11073 - 2.78680i) q^{9} +(-1.25788 - 2.17871i) q^{11} +(-0.292110 - 0.505949i) q^{13} +(2.62926 + 5.42310i) q^{15} +(-0.547519 + 0.948331i) q^{17} +(2.96834 + 5.14132i) q^{19} +(-3.19264 + 5.52982i) q^{23} +(-3.55384 - 6.15544i) q^{25} +(-5.07486 - 1.11616i) q^{27} +(0.918333 - 1.59060i) q^{29} +7.03743 q^{31} +(-4.34608 - 0.314176i) q^{33} +(0.702576 + 1.21690i) q^{37} +(-1.00927 - 0.0729591i) q^{39} +(5.37855 + 9.31593i) q^{41} +(-5.67879 + 9.83596i) q^{43} +(10.3303 + 1.50139i) q^{45} -7.53129 q^{47} +(0.827432 + 1.70666i) q^{51} +(-5.82285 + 10.0855i) q^{53} +8.75386 q^{55} +(10.2559 + 0.741391i) q^{57} -4.45551 q^{59} +12.3524 q^{61} +2.03286 q^{65} -12.6707 q^{67} +(4.82485 + 9.95170i) q^{69} -4.93390 q^{71} +(-4.35558 + 7.54408i) q^{73} +(-12.2788 - 0.887629i) q^{75} -0.560411 q^{79} +(-6.53256 + 6.19078i) q^{81} +(-3.68472 + 6.38212i) q^{83} +(-1.90515 - 3.29982i) q^{85} +(-1.38782 - 2.86251i) q^{87} +(-6.07256 - 10.5180i) q^{89} +(6.83984 - 10.0892i) q^{93} -20.6573 q^{95} +(-6.98486 + 12.0981i) q^{97} +(-4.67448 + 5.92543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} - 12 q^{37} + 8 q^{51} - 16 q^{53} + 52 q^{57} + 72 q^{65} - 24 q^{67} + 48 q^{71} - 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93} - 64 q^{95} - 4 q^{99}+O(q^{100}) $ 24 * q - 4 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 - 12 * q^37 + 8 * q^51 - 16 * q^53 + 52 * q^57 + 72 * q^65 - 24 * q^67 + 48 * q^71 - 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 64 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.971923	−	1.43365i	0.561140	−	0.827721i
$3$	0.971923	−	1.43365i	0.561140	−	0.827721i
$4$		0			0
$5$	−1.73981	+	3.01343i	−0.778065	+	1.34765i	0.154991	+	0.987916i	$0.450465\pi$
$5$	−1.73981	+	3.01343i	−0.778065	+	1.34765i	−0.933056	+	0.359732i	$0.882868\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.11073	−	2.78680i	−0.370243	−	0.928935i
$10$		0			0
$11$	−1.25788	−	2.17871i	−0.379265	−	0.656906i	0.611690	−	0.791097i	$-0.290490\pi$
$11$	−1.25788	−	2.17871i	−0.379265	−	0.656906i	−0.990956	+	0.134191i	$0.957156\pi$
$12$		0			0
$13$	−0.292110	−	0.505949i	−0.0810167	−	0.140325i	0.822670	−	0.568519i	$-0.192483\pi$
$13$	−0.292110	−	0.505949i	−0.0810167	−	0.140325i	−0.903687	+	0.428194i	$0.859150\pi$
$14$		0			0
$15$	2.62926	+	5.42310i	0.678873	+	1.40024i
$16$		0			0
$17$	−0.547519	+	0.948331i	−0.132793	+	0.230004i	−0.924752	−	0.380570i	$-0.875728\pi$
$17$	−0.547519	+	0.948331i	−0.132793	+	0.230004i	0.791959	+	0.610574i	$0.209061\pi$
$18$		0			0
$19$	2.96834	+	5.14132i	0.680984	+	1.17950i	0.974681	+	0.223601i	$0.0717812\pi$
$19$	2.96834	+	5.14132i	0.680984	+	1.17950i	−0.293696	+	0.955899i	$0.594885\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.19264	+	5.52982i	−0.665712	+	1.15305i	0.313380	+	0.949628i	$0.398539\pi$
$23$	−3.19264	+	5.52982i	−0.665712	+	1.15305i	−0.979092	+	0.203419i	$0.934795\pi$
$24$		0			0
$25$	−3.55384	−	6.15544i	−0.710769	−	1.23109i
$26$		0			0
$27$	−5.07486	−	1.11616i	−0.976657	−	0.214804i
$28$		0			0
$29$	0.918333	−	1.59060i	0.170530	−	0.295367i	−0.768075	−	0.640360i	$-0.778785\pi$
$29$	0.918333	−	1.59060i	0.170530	−	0.295367i	0.938605	+	0.344993i	$0.112119\pi$
$30$		0			0
$31$	7.03743			1.26396			0.631980	−	0.774985i	$-0.282242\pi$
$31$	7.03743			1.26396			0.631980	+	0.774985i	$0.282242\pi$
$32$		0			0
$33$	−4.34608	−	0.314176i	−0.756556	−	0.0546909i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.702576	+	1.21690i	0.115503	+	0.200057i	0.917981	−	0.396625i	$-0.129819\pi$
$37$	0.702576	+	1.21690i	0.115503	+	0.200057i	−0.802478	+	0.596682i	$0.796485\pi$
$38$		0			0
$39$	−1.00927	−	0.0729591i	−0.161612	−	0.0116828i
$40$		0			0
$41$	5.37855	+	9.31593i	0.839989	+	1.45490i	0.889903	+	0.456150i	$0.150772\pi$
$41$	5.37855	+	9.31593i	0.839989	+	1.45490i	−0.0499141	+	0.998754i	$0.515895\pi$
$42$		0			0
$43$	−5.67879	+	9.83596i	−0.866008	+	1.49997i	3.53909e−5		1.00000i	$0.499989\pi$
$43$	−5.67879	+	9.83596i	−0.866008	+	1.49997i	−0.866043	+	0.499969i	$0.833345\pi$
$44$		0			0
$45$	10.3303	+	1.50139i	1.53995	+	0.223814i
$46$		0			0
$47$	−7.53129			−1.09855			−0.549276	−	0.835641i	$-0.685096\pi$
$47$	−7.53129			−1.09855			−0.549276	+	0.835641i	$0.685096\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.827432	+	1.70666i	0.115864	+	0.238980i
$52$		0			0
$53$	−5.82285	+	10.0855i	−0.799830	+	1.38535i	0.119897	+	0.992786i	$0.461744\pi$
$53$	−5.82285	+	10.0855i	−0.799830	+	1.38535i	−0.919727	+	0.392560i	$0.871590\pi$
$54$		0			0
$55$	8.75386			1.18037
$56$		0			0
$57$	10.2559	+	0.741391i	1.35842	+	0.0981996i
$58$		0			0
$59$	−4.45551			−0.580058			−0.290029	−	0.957018i	$-0.593665\pi$
$59$	−4.45551			−0.580058			−0.290029	+	0.957018i	$0.593665\pi$
$60$		0			0
$61$	12.3524			1.58157			0.790784	−	0.612095i	$-0.209673\pi$
$61$	12.3524			1.58157			0.790784	+	0.612095i	$0.209673\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.03286			0.252145
$66$		0			0
$67$	−12.6707			−1.54798			−0.773988	−	0.633201i	$-0.781741\pi$
$67$	−12.6707			−1.54798			−0.773988	+	0.633201i	$0.781741\pi$
$68$		0			0
$69$	4.82485	+	9.95170i	0.580843	+	1.19804i
$70$		0			0
$71$	−4.93390			−0.585546			−0.292773	−	0.956182i	$-0.594578\pi$
$71$	−4.93390			−0.585546			−0.292773	+	0.956182i	$0.594578\pi$
$72$		0			0
$73$	−4.35558	+	7.54408i	−0.509782	+	0.882968i	0.490154	+	0.871636i	$0.336940\pi$
$73$	−4.35558	+	7.54408i	−0.509782	+	0.882968i	−0.999936	+	0.0113320i	$0.996393\pi$
$74$		0			0
$75$	−12.2788	−	0.887629i	−1.41784	−	0.102495i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.560411			−0.0630512			−0.0315256	−	0.999503i	$-0.510037\pi$
$79$	−0.560411			−0.0630512			−0.0315256	+	0.999503i	$0.510037\pi$
$80$		0			0
$81$	−6.53256	+	6.19078i	−0.725840	+	0.687864i
$82$		0			0
$83$	−3.68472	+	6.38212i	−0.404451	+	0.700529i	−0.994257	−	0.107015i	$-0.965871\pi$
$83$	−3.68472	+	6.38212i	−0.404451	+	0.700529i	0.589807	+	0.807544i	$0.299204\pi$
$84$		0			0
$85$	−1.90515	−	3.29982i	−0.206643	−	0.357916i
$86$		0			0
$87$	−1.38782	−	2.86251i	−0.148790	−	0.306894i
$88$		0			0
$89$	−6.07256	−	10.5180i	−0.643690	−	1.11490i	−0.984602	−	0.174808i	$-0.944069\pi$
$89$	−6.07256	−	10.5180i	−0.643690	−	1.11490i	0.340913	−	0.940095i	$-0.389264\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.83984	−	10.0892i	0.709259	−	1.04621i
$94$		0			0
$95$	−20.6573			−2.11940
$96$		0			0
$97$	−6.98486	+	12.0981i	−0.709205	+	1.22838i	0.255947	+	0.966691i	$0.417613\pi$
$97$	−6.98486	+	12.0981i	−0.709205	+	1.22838i	−0.965152	+	0.261688i	$0.915721\pi$
$98$		0			0
$99$	−4.67448	+	5.92543i	−0.469803	+	0.595528i
$100$		0			0
$101$	4.58825	+	7.94708i	0.456548	+	0.790764i	0.998776	−	0.0494676i	$-0.0157525\pi$
$101$	4.58825	+	7.94708i	0.456548	+	0.790764i	−0.542228	+	0.840231i	$0.682419\pi$
$102$		0			0
$103$	0.239538	−	0.414892i	0.0236024	−	0.0408805i	−0.853983	−	0.520301i	$-0.825820\pi$
$103$	0.239538	−	0.414892i	0.0236024	−	0.0408805i	0.877585	+	0.479420i	$0.159153\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.67882	+	4.63986i	0.258972	+	0.448552i	0.965967	−	0.258666i	$-0.0832830\pi$
$107$	2.67882	+	4.63986i	0.258972	+	0.448552i	−0.706995	+	0.707219i	$0.749950\pi$
$108$		0			0
$109$	7.87535	−	13.6405i	0.754322	−	1.30652i	−0.191389	−	0.981514i	$-0.561299\pi$
$109$	7.87535	−	13.6405i	0.754322	−	1.30652i	0.945711	−	0.325009i	$-0.105367\pi$
$110$		0			0
$111$	2.42746	+	0.175480i	0.230404	+	0.0166558i
$112$		0			0
$113$	−6.92483	−	11.9942i	−0.651433	−	1.12832i	−0.982775	−	0.184804i	$-0.940835\pi$
$113$	−6.92483	−	11.9942i	−0.651433	−	1.12832i	0.331342	−	0.943511i	$-0.392499\pi$
$114$		0			0
$115$	−11.1092	−	19.2416i	−1.03593	−	1.79429i
$116$		0			0
$117$	−1.08553	+	1.37603i	−0.100357	+	0.127214i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.33548	−	4.04516i	0.212316	−	0.367742i
$122$		0			0
$123$	18.5834	+	1.34338i	1.67561	+	0.121128i
$124$		0			0
$125$	7.33394			0.655968
$126$		0			0
$127$	20.7533			1.84156			0.920780	−	0.390083i	$-0.127554\pi$
$127$	20.7533			1.84156			0.920780	+	0.390083i	$0.127554\pi$
$128$		0			0
$129$	8.58201	+	17.7012i	0.755604	+	1.55851i
$130$		0			0
$131$	0.799491	−	1.38476i	0.0698518	−	0.120987i	−0.828984	−	0.559272i	$-0.811081\pi$
$131$	0.799491	−	1.38476i	0.0698518	−	0.120987i	0.898836	+	0.438285i	$0.144414\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	12.1927	−	13.3508i	1.04938	−	1.14906i
$136$		0			0
$137$	3.82610	+	6.62700i	0.326886	+	0.566182i	0.981892	−	0.189441i	$-0.0606675\pi$
$137$	3.82610	+	6.62700i	0.326886	+	0.566182i	−0.655007	+	0.755623i	$0.727334\pi$
$138$		0			0
$139$	7.99424	+	13.8464i	0.678062	+	1.17444i	0.975564	+	0.219717i	$0.0705134\pi$
$139$	7.99424	+	13.8464i	0.678062	+	1.17444i	−0.297501	+	0.954721i	$0.596153\pi$
$140$		0			0
$141$	−7.31984	+	10.7973i	−0.616442	+	0.909294i
$142$		0			0
$143$	−0.734878	+	1.27285i	−0.0614536	+	0.106441i
$144$		0			0
$145$	3.19544	+	5.53467i	0.265367	+	0.459629i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.43734	−	2.48955i	0.117752	−	0.203952i	−0.801125	−	0.598497i	$-0.795765\pi$
$149$	1.43734	−	2.48955i	0.117752	−	0.203952i	0.918876	+	0.394546i	$0.129098\pi$
$150$		0			0
$151$	−4.58076	−	7.93411i	−0.372777	−	0.645669i	0.617215	−	0.786795i	$-0.288261\pi$
$151$	−4.58076	−	7.93411i	−0.372777	−	0.645669i	−0.989992	+	0.141126i	$0.954928\pi$
$152$		0			0
$153$	3.25096	+	0.472488i	0.262824	+	0.0381984i
$154$		0			0
$155$	−12.2438	+	21.2068i	−0.983443	+	1.70337i
$156$		0			0
$157$	12.7882			1.02061			0.510304	−	0.859994i	$-0.329533\pi$
$157$	12.7882			1.02061			0.510304	+	0.859994i	$0.329533\pi$
$158$		0			0
$159$	8.79972	+	18.1503i	0.697863	+	1.43941i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−7.18390	−	12.4429i	−0.562686	−	0.974601i	−0.997261	−	0.0739653i	$-0.976435\pi$
$163$	−7.18390	−	12.4429i	−0.562686	−	0.974601i	0.434575	−	0.900636i	$-0.356899\pi$
$164$		0			0
$165$	8.50808	−	12.5500i	0.662353	−	0.977017i
$166$		0			0
$167$	2.38280	+	4.12714i	0.184387	+	0.319367i	0.943370	−	0.331743i	$-0.107637\pi$
$167$	2.38280	+	4.12714i	0.184387	+	0.319367i	−0.758983	+	0.651111i	$0.774303\pi$
$168$		0			0
$169$	6.32934	−	10.9627i	0.486873	−	0.843288i
$170$		0			0
$171$	11.0308	−	13.9828i	0.843548	−	1.06929i
$172$		0			0
$173$	25.1167			1.90958			0.954792	−	0.297275i	$-0.0960778\pi$
$173$	25.1167			1.90958			0.954792	+	0.297275i	$0.0960778\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.33041	+	6.38766i	−0.325494	+	0.480126i
$178$		0			0
$179$	−3.41168	+	5.90920i	−0.255001	+	0.441675i	−0.964896	−	0.262633i	$-0.915409\pi$
$179$	−3.41168	+	5.90920i	−0.255001	+	0.441675i	0.709895	+	0.704308i	$0.248742\pi$
$180$		0			0
$181$	−13.4735			−1.00148			−0.500739	−	0.865598i	$-0.666938\pi$
$181$	−13.4735			−1.00148			−0.500739	+	0.865598i	$0.666938\pi$
$182$		0			0
$183$	12.0056	−	17.7091i	0.887481	−	1.30910i
$184$		0			0
$185$	−4.88938			−0.359475
$186$		0			0
$187$	2.75485			0.201455
$188$		0			0
$189$		0			0
$190$		0			0
$191$	14.2064			1.02794			0.513968	−	0.857809i	$-0.328175\pi$
$191$	14.2064			1.02794			0.513968	+	0.857809i	$0.328175\pi$
$192$		0			0
$193$	−6.78520			−0.488410			−0.244205	−	0.969724i	$-0.578527\pi$
$193$	−6.78520			−0.488410			−0.244205	+	0.969724i	$0.578527\pi$
$194$		0			0
$195$	1.97578	−	2.91442i	0.141489	−	0.208706i
$196$		0			0
$197$	18.5287			1.32011			0.660057	−	0.751215i	$-0.270532\pi$
$197$	18.5287			1.32011			0.660057	+	0.751215i	$0.270532\pi$
$198$		0			0
$199$	8.39804	−	14.5458i	0.595321	−	1.03113i	−0.398180	−	0.917307i	$-0.630358\pi$
$199$	8.39804	−	14.5458i	0.595321	−	1.03113i	0.993501	−	0.113819i	$-0.0363086\pi$
$200$		0			0
$201$	−12.3150	+	18.1654i	−0.868631	+	1.28129i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−37.4305			−2.61426
$206$		0			0
$207$	18.9567	+	2.75513i	1.31758	+	0.191495i
$208$		0			0
$209$	7.46763	−	12.9343i	0.516547	−	0.894686i
$210$		0			0
$211$	−10.7912	−	18.6909i	−0.742896	−	1.28673i	−0.951171	−	0.308664i	$-0.900118\pi$
$211$	−10.7912	−	18.6909i	−0.742896	−	1.28673i	0.208275	−	0.978070i	$-0.433215\pi$
$212$		0			0
$213$	−4.79537	+	7.07351i	−0.328574	+	0.484669i
$214$		0			0
$215$	−19.7600	−	34.2253i	−1.34762	−	2.33415i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.58232	+	13.5767i	0.444792	+	0.917426i
$220$		0			0
$221$	0.639743			0.0430338
$222$		0			0
$223$	−0.495791	+	0.858736i	−0.0332006	+	0.0575052i	−0.882148	−	0.470972i	$-0.843903\pi$
$223$	−0.495791	+	0.858736i	−0.0332006	+	0.0575052i	0.848948	+	0.528477i	$0.177237\pi$
$224$		0			0
$225$	−13.2066	+	16.7409i	−0.880443	+	1.11606i
$226$		0			0
$227$	1.46567	+	2.53861i	0.0972799	+	0.168494i	0.910558	−	0.413382i	$-0.135652\pi$
$227$	1.46567	+	2.53861i	0.0972799	+	0.168494i	−0.813278	+	0.581875i	$0.802319\pi$
$228$		0			0
$229$	−2.19201	+	3.79667i	−0.144852	+	0.250891i	−0.929318	−	0.369281i	$-0.879604\pi$
$229$	−2.19201	+	3.79667i	−0.144852	+	0.250891i	0.784466	+	0.620172i	$0.212937\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.543158	+	0.940778i	0.0355835	+	0.0616324i	0.883269	−	0.468867i	$-0.155338\pi$
$233$	0.543158	+	0.940778i	0.0355835	+	0.0616324i	−0.847685	+	0.530500i	$0.822004\pi$
$234$		0			0
$235$	13.1030	−	22.6950i	0.854744	−	1.48046i
$236$		0			0
$237$	−0.544677	+	0.803436i	−0.0353805	+	0.0521888i
$238$		0			0
$239$	1.91423	+	3.31554i	0.123821	+	0.214464i	0.921271	−	0.388920i	$-0.127152\pi$
$239$	1.91423	+	3.31554i	0.123821	+	0.214464i	−0.797450	+	0.603384i	$0.793818\pi$
$240$		0			0
$241$	−6.46271	−	11.1937i	−0.416300	−	0.721052i	0.579264	−	0.815140i	$-0.303340\pi$
$241$	−6.46271	−	11.1937i	−0.416300	−	0.721052i	−0.995564	+	0.0940877i	$0.970007\pi$
$242$		0			0
$243$	2.52629	+	15.3824i	0.162062	+	0.986781i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.73416	−	3.00366i	0.110342	−	0.191118i
$248$		0			0
$249$	5.56849	+	11.4855i	0.352889	+	0.727867i
$250$		0			0
$251$	−19.6654			−1.24127			−0.620634	−	0.784101i	$-0.713125\pi$
$251$	−19.6654			−1.24127			−0.620634	+	0.784101i	$0.713125\pi$
$252$		0			0
$253$	16.0638			1.00992
$254$		0			0
$255$	−6.58247	−	0.475842i	−0.412210	−	0.0297984i
$256$		0			0
$257$	12.6799	−	21.9622i	0.790948	−	1.36996i	−0.134433	−	0.990923i	$-0.542921\pi$
$257$	12.6799	−	21.9622i	0.790948	−	1.36996i	0.925381	−	0.379039i	$-0.123745\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−5.45271	−	0.792487i	−0.337514	−	0.0490537i
$262$		0			0
$263$	−4.43798	−	7.68680i	−0.273657	−	0.473988i	0.696138	−	0.717908i	$-0.254900\pi$
$263$	−4.43798	−	7.68680i	−0.273657	−	0.473988i	−0.969796	+	0.243919i	$0.921567\pi$
$264$		0			0
$265$	−20.2612	−	35.0935i	−1.24464	−	2.15578i
$266$		0			0
$267$	−20.9812	−	1.51672i	−1.28403	−	0.0928216i
$268$		0			0
$269$	−9.15338	+	15.8541i	−0.558092	+	0.966643i	0.439564	+	0.898211i	$0.355133\pi$
$269$	−9.15338	+	15.8541i	−0.558092	+	0.966643i	−0.997656	+	0.0684319i	$0.978200\pi$
$270$		0			0
$271$	−2.34465	−	4.06106i	−0.142427	−	0.246692i	0.785983	−	0.618248i	$-0.212157\pi$
$271$	−2.34465	−	4.06106i	−0.142427	−	0.246692i	−0.928410	+	0.371557i	$0.878824\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.94062	+	15.4856i	−0.539140	+	0.933817i
$276$		0			0
$277$	−2.82807	−	4.89836i	−0.169922	−	0.294314i	0.768470	−	0.639886i	$-0.221018\pi$
$277$	−2.82807	−	4.89836i	−0.169922	−	0.294314i	−0.938392	+	0.345572i	$0.887685\pi$
$278$		0			0
$279$	−7.81669	−	19.6119i	−0.467973	−	1.17414i
$280$		0			0
$281$	−5.36370	+	9.29020i	−0.319971	+	0.554207i	−0.980482	−	0.196610i	$-0.937007\pi$
$281$	−5.36370	+	9.29020i	−0.319971	+	0.554207i	0.660510	+	0.750817i	$0.270340\pi$
$282$		0			0
$283$	−23.8106			−1.41539			−0.707697	−	0.706517i	$-0.750266\pi$
$283$	−23.8106			−1.41539			−0.707697	+	0.706517i	$0.750266\pi$
$284$		0			0
$285$	−20.0774	+	29.6155i	−1.18928	+	1.75427i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.90045	+	13.6840i	0.464732	+	0.804940i
$290$		0			0
$291$	10.5558	+	21.7723i	0.618792	+	1.27632i
$292$		0			0
$293$	−10.3315	−	17.8946i	−0.603570	−	1.04541i	−0.992276	−	0.124052i	$-0.960411\pi$
$293$	−10.3315	−	17.8946i	−0.603570	−	1.04541i	0.388706	−	0.921362i	$-0.372922\pi$
$294$		0			0
$295$	7.75171	−	13.4264i	0.451322	−	0.781713i
$296$		0			0
$297$	3.95178	+	12.4606i	0.229306	+	0.723040i
$298$		0			0
$299$	3.73041			0.215735
$300$		0			0
$301$		0			0
$302$		0			0
$303$	15.8528	+	1.14599i	0.910719	+	0.0658353i
$304$		0			0
$305$	−21.4908	+	37.2232i	−1.23056	+	2.13140i
$306$		0			0
$307$	11.9227			0.680464			0.340232	−	0.940342i	$-0.389494\pi$
$307$	11.9227			0.680464			0.340232	+	0.940342i	$0.389494\pi$
$308$		0			0
$309$	−0.361999	−	0.746657i	−0.0205934	−	0.0424758i
$310$		0			0
$311$	−9.13271			−0.517868			−0.258934	−	0.965895i	$-0.583371\pi$
$311$	−9.13271			−0.517868			−0.258934	+	0.965895i	$0.583371\pi$
$312$		0			0
$313$	13.8396			0.782260			0.391130	−	0.920335i	$-0.372084\pi$
$313$	13.8396			0.782260			0.391130	+	0.920335i	$0.372084\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.83157			0.102871			0.0514357	−	0.998676i	$-0.483620\pi$
$317$	1.83157			0.102871			0.0514357	+	0.998676i	$0.483620\pi$
$318$		0			0
$319$	−4.62061			−0.258705
$320$		0			0
$321$	9.25557	+	0.669079i	0.516595	+	0.0373444i
$322$		0			0
$323$	−6.50089			−0.361719
$324$		0			0
$325$	−2.07623	+	3.59613i	−0.115168	+	0.199477i
$326$		0			0
$327$	−11.9015	−	24.5481i	−0.658157	−	1.35751i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.206264			−0.0113373			−0.00566864	−	0.999984i	$-0.501804\pi$
$331$	−0.206264			−0.0113373			−0.00566864	+	0.999984i	$0.501804\pi$
$332$		0			0
$333$	2.61088	−	3.30959i	0.143076	−	0.181364i
$334$		0			0
$335$	22.0446	−	38.1824i	1.20442	−	2.08613i
$336$		0			0
$337$	0.756536	+	1.31036i	0.0412111	+	0.0713798i	0.885895	−	0.463885i	$-0.153545\pi$
$337$	0.756536	+	1.31036i	0.0412111	+	0.0713798i	−0.844684	+	0.535265i	$0.820212\pi$
$338$		0			0
$339$	−23.9259	−	1.72959i	−1.29948	−	0.0939382i
$340$		0			0
$341$	−8.85224	−	15.3325i	−0.479376	−	0.830303i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−38.3831	−	2.77469i	−2.06647	−	0.149384i
$346$		0			0
$347$	−3.21813			−0.172758			−0.0863792	−	0.996262i	$-0.527530\pi$
$347$	−3.21813			−0.172758			−0.0863792	+	0.996262i	$0.527530\pi$
$348$		0			0
$349$	−7.04006	+	12.1937i	−0.376846	+	0.652716i	−0.990601	−	0.136780i	$-0.956325\pi$
$349$	−7.04006	+	12.1937i	−0.376846	+	0.652716i	0.613756	+	0.789496i	$0.289658\pi$
$350$		0			0
$351$	0.917699	+	2.89366i	0.0489831	+	0.154452i
$352$		0			0
$353$	1.68465	+	2.91790i	0.0896648	+	0.155304i	0.907369	−	0.420334i	$-0.138087\pi$
$353$	1.68465	+	2.91790i	0.0896648	+	0.155304i	−0.817705	+	0.575638i	$0.804754\pi$
$354$		0			0
$355$	8.58403	−	14.8680i	0.455593	−	0.789110i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.28913	+	12.6251i	0.384706	+	0.666330i	0.991728	−	0.128355i	$-0.0409696\pi$
$359$	7.28913	+	12.6251i	0.384706	+	0.666330i	−0.607023	+	0.794685i	$0.707636\pi$
$360$		0			0
$361$	−8.12211	+	14.0679i	−0.427479	+	0.740416i
$362$		0			0
$363$	−3.52946	−	7.27986i	−0.185249	−	0.382093i
$364$		0			0
$365$	−15.1557	−	26.2505i	−0.793286	−	1.37401i
$366$		0			0
$367$	0.368367	+	0.638030i	0.0192286	+	0.0333049i	0.875480	−	0.483255i	$-0.160546\pi$
$367$	0.368367	+	0.638030i	0.0192286	+	0.0333049i	−0.856251	+	0.516560i	$0.827212\pi$
$368$		0			0
$369$	19.9875	−	25.3365i	1.04051	−	1.31896i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−14.4514	+	25.0306i	−0.748267	+	1.29604i	0.200385	+	0.979717i	$0.435781\pi$
$373$	−14.4514	+	25.0306i	−0.748267	+	1.29604i	−0.948653	+	0.316320i	$0.897553\pi$
$374$		0			0
$375$	7.12803	−	10.5143i	0.368090	−	0.542958i
$376$		0			0
$377$	−1.07302			−0.0552632
$378$		0			0
$379$	−8.88267			−0.456272			−0.228136	−	0.973629i	$-0.573263\pi$
$379$	−8.88267			−0.456272			−0.228136	+	0.973629i	$0.573263\pi$
$380$		0			0
$381$	20.1706	−	29.7531i	1.03337	−	1.52430i
$382$		0			0
$383$	−7.70273	+	13.3415i	−0.393591	+	0.681720i	−0.992920	−	0.118783i	$-0.962101\pi$
$383$	−7.70273	+	13.3415i	−0.393591	+	0.681720i	0.599329	+	0.800503i	$0.295434\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	33.7185	+	4.90059i	1.71401	+	0.249111i
$388$		0			0
$389$	10.1570	+	17.5924i	0.514978	+	0.891968i	0.999849	+	0.0173821i	$0.00553318\pi$
$389$	10.1570	+	17.5924i	0.514978	+	0.891968i	−0.484871	+	0.874586i	$0.661133\pi$
$390$		0			0
$391$	−3.49606	−	6.05536i	−0.176804	−	0.306233i
$392$		0			0
$393$	−1.20822	−	2.49207i	−0.0609467	−	0.125708i
$394$		0			0
$395$	0.975006	−	1.68876i	0.0490579	−	0.0849708i
$396$		0			0
$397$	4.32895	+	7.49796i	0.217264	+	0.376312i	0.953970	−	0.299901i	$-0.0969535\pi$
$397$	4.32895	+	7.49796i	0.217264	+	0.376312i	−0.736707	+	0.676212i	$0.763620\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.5273	+	30.3582i	−0.875272	+	1.51602i	−0.0187988	+	0.999823i	$0.505984\pi$
$401$	−17.5273	+	30.3582i	−0.875272	+	1.51602i	−0.856473	+	0.516192i	$0.827349\pi$
$402$		0			0
$403$	−2.05570	−	3.56058i	−0.102402	−	0.177365i
$404$		0			0
$405$	−7.29010	−	30.4562i	−0.362248	−	1.51338i
$406$		0			0
$407$	1.76751	−	3.06142i	0.0876124	−	0.151749i
$408$		0			0
$409$	−13.2336			−0.654361			−0.327180	−	0.944962i	$-0.606098\pi$
$409$	−13.2336			−0.654361			−0.327180	+	0.944962i	$0.606098\pi$
$410$		0			0
$411$	13.2195	+	0.955629i	0.652070	+	0.0471377i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.8214	−	22.2073i	−0.629377	−	1.09011i
$416$		0			0
$417$	27.6208	+	1.99669i	1.35260	+	0.0977782i
$418$		0			0
$419$	4.43952	+	7.68947i	0.216885	+	0.375655i	0.953854	−	0.300271i	$-0.0970771\pi$
$419$	4.43952	+	7.68947i	0.216885	+	0.375655i	−0.736969	+	0.675926i	$0.763744\pi$
$420$		0			0
$421$	2.00273	−	3.46884i	0.0976073	−	0.169061i	−0.813087	−	0.582143i	$-0.802214\pi$
$421$	2.00273	−	3.46884i	0.0976073	−	0.169061i	0.910694	+	0.413082i	$0.135548\pi$
$422$		0			0
$423$	8.36524	+	20.9882i	0.406732	+	1.02048i
$424$		0			0
$425$	7.78319			0.377540
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.11058	+	2.29067i	0.0536192	+	0.110595i
$430$		0			0
$431$	7.48548	−	12.9652i	0.360563	−	0.624513i	−0.627491	−	0.778624i	$-0.715918\pi$
$431$	7.48548	−	12.9652i	0.360563	−	0.624513i	0.988054	+	0.154111i	$0.0492513\pi$
$432$		0			0
$433$	−15.3215			−0.736304			−0.368152	−	0.929766i	$-0.620009\pi$
$433$	−15.3215			−0.736304			−0.368152	+	0.929766i	$0.620009\pi$
$434$		0			0
$435$	11.0405	+	0.798113i	0.529353	+	0.0382666i
$436$		0			0
$437$	−37.9074			−1.81336
$438$		0			0
$439$	12.0731			0.576220			0.288110	−	0.957597i	$-0.406973\pi$
$439$	12.0731			0.576220			0.288110	+	0.957597i	$0.406973\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.0579			0.572887			0.286444	−	0.958097i	$-0.407527\pi$
$443$	12.0579			0.572887			0.286444	+	0.958097i	$0.407527\pi$
$444$		0			0
$445$	42.2603			2.00333
$446$		0			0
$447$	−2.17217	−	4.48030i	−0.102740	−	0.211911i
$448$		0			0
$449$	−16.9502			−0.799928			−0.399964	−	0.916531i	$-0.630977\pi$
$449$	−16.9502			−0.799928			−0.399964	+	0.916531i	$0.630977\pi$
$450$		0			0
$451$	13.5311	−	23.4366i	0.637157	−	1.10359i
$452$		0			0
$453$	−15.8269	−	1.14412i	−0.743614	−	0.0537554i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.76646			0.269743			0.134872	−	0.990863i	$-0.456938\pi$
$457$	5.76646			0.269743			0.134872	+	0.990863i	$0.456938\pi$
$458$		0			0
$459$	3.83707	−	4.20153i	0.179099	−	0.196111i
$460$		0			0
$461$	−17.9138	+	31.0277i	−0.834330	+	1.44510i	0.0602447	+	0.998184i	$0.480812\pi$
$461$	−17.9138	+	31.0277i	−0.834330	+	1.44510i	−0.894575	+	0.446918i	$0.852521\pi$
$462$		0			0
$463$	1.53947	+	2.66645i	0.0715455	+	0.123920i	0.899579	−	0.436758i	$-0.143874\pi$
$463$	1.53947	+	2.66645i	0.0715455	+	0.123920i	−0.828033	+	0.560679i	$0.810540\pi$
$464$		0			0
$465$	18.5033	+	38.1647i	0.858068	+	1.76985i
$466$		0			0
$467$	−1.42738	−	2.47230i	−0.0660515	−	0.114404i	0.831108	−	0.556110i	$-0.187707\pi$
$467$	−1.42738	−	2.47230i	−0.0660515	−	0.114404i	−0.897160	+	0.441706i	$0.854373\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	12.4291	−	18.3338i	0.572704	−	0.844779i
$472$		0			0
$473$	28.5730			1.31379
$474$		0			0
$475$	21.0981	−	36.5429i	0.968045	−	1.67670i
$476$		0			0
$477$	34.5738	+	5.02490i	1.58303	+	0.230074i
$478$		0			0
$479$	2.18688	+	3.78779i	0.0999211	+	0.173068i	0.911652	−	0.410964i	$-0.134808\pi$
$479$	2.18688	+	3.78779i	0.0999211	+	0.173068i	−0.811731	+	0.584032i	$0.801474\pi$
$480$		0			0
$481$	0.410459	−	0.710936i	0.0187153	−	0.0324159i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.3046	−	42.0968i	−1.10361	−	1.91152i
$486$		0			0
$487$	15.2678	−	26.4447i	0.691852	−	1.19832i	−0.279378	−	0.960181i	$-0.590128\pi$
$487$	15.2678	−	26.4447i	0.691852	−	1.19832i	0.971230	−	0.238142i	$-0.0765383\pi$
$488$		0			0
$489$	−24.8210	−	1.79429i	−1.12244	−	0.0811407i
$490$		0			0
$491$	−21.3502	−	36.9797i	−0.963522	−	1.66887i	−0.713534	−	0.700621i	$-0.752906\pi$
$491$	−21.3502	−	36.9797i	−0.963522	−	1.66887i	−0.249989	−	0.968249i	$-0.580427\pi$
$492$		0			0
$493$	1.00561	+	1.74177i	0.0452904	+	0.0784453i
$494$		0			0
$495$	−9.72318	−	24.3953i	−0.437025	−	1.09649i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	11.3852	−	19.7197i	0.509670	−	0.882774i	−0.490267	−	0.871572i	$-0.663101\pi$
$499$	11.3852	−	19.7197i	0.509670	−	0.882774i	0.999937	−	0.0112020i	$-0.00356578\pi$
$500$		0			0
$501$	8.23279	+	0.595143i	0.367814	+	0.0265890i
$502$		0			0
$503$	−24.0843			−1.07387			−0.536933	−	0.843625i	$-0.680417\pi$
$503$	−24.0843			−1.07387			−0.536933	+	0.843625i	$0.680417\pi$
$504$		0			0
$505$	−31.9306			−1.42089
$506$		0			0
$507$	−9.56515	−	19.7290i	−0.424803	−	0.876197i
$508$		0			0
$509$	−12.2350	+	21.1917i	−0.542307	+	0.939304i	0.456464	+	0.889742i	$0.349116\pi$
$509$	−12.2350	+	21.1917i	−0.542307	+	0.939304i	−0.998771	+	0.0495618i	$0.984218\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−9.32540	−	29.4046i	−0.411727	−	1.29824i
$514$		0			0
$515$	0.833498	+	1.44366i	0.0367283	+	0.0636153i
$516$		0			0
$517$	9.47346	+	16.4085i	0.416642	+	0.721646i
$518$		0			0
$519$	24.4115	−	36.0086i	1.07154	−	1.58060i
$520$		0			0
$521$	19.3743	−	33.5573i	0.848805	−	1.47017i	−0.0334709	−	0.999440i	$-0.510656\pi$
$521$	19.3743	−	33.5573i	0.848805	−	1.47017i	0.882276	−	0.470733i	$-0.156011\pi$
$522$		0			0
$523$	12.8473	+	22.2521i	0.561771	+	0.973016i	0.997342	+	0.0728616i	$0.0232131\pi$
$523$	12.8473	+	22.2521i	0.561771	+	0.973016i	−0.435571	+	0.900154i	$0.643454\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.85313	+	6.67381i	−0.167845	+	0.290716i
$528$		0			0
$529$	−8.88593	−	15.3909i	−0.386345	−	0.669169i
$530$		0			0
$531$	4.94887	+	12.4166i	0.214763	+	0.538836i
$532$		0			0
$533$	3.14226	−	5.44255i	0.136106	−	0.235743i
$534$		0			0
$535$	−18.6425			−0.805987
$536$		0			0
$537$	5.15586	+	10.6345i	0.222492	+	0.458911i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.92878	+	8.53690i	0.211905	+	0.367030i	0.952311	−	0.305130i	$-0.0986999\pi$
$541$	4.92878	+	8.53690i	0.211905	+	0.367030i	−0.740406	+	0.672160i	$0.765367\pi$
$542$		0			0
$543$	−13.0952	+	19.3164i	−0.561970	+	0.828945i
$544$		0			0
$545$	27.4032	+	47.4636i	1.17382	+	2.03312i
$546$		0			0
$547$	−3.94133	+	6.82659i	−0.168519	+	0.291884i	−0.937899	−	0.346907i	$-0.887232\pi$
$547$	−3.94133	+	6.82659i	−0.168519	+	0.291884i	0.769380	+	0.638791i	$0.220565\pi$
$548$		0			0
$549$	−13.7202	−	34.4238i	−0.585565	−	1.46917i
$550$		0			0
$551$	10.9037			0.464514
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.75211	+	7.00969i	−0.201716	+	0.297545i
$556$		0			0
$557$	10.1686	−	17.6125i	0.430857	−	0.746266i	−0.566090	−	0.824343i	$-0.691545\pi$
$557$	10.1686	−	17.6125i	0.430857	−	0.746266i	0.996947	+	0.0780770i	$0.0248780\pi$
$558$		0			0
$559$	6.63533			0.280644
$560$		0			0
$561$	2.67750	−	3.94951i	0.113044	−	0.166748i
$562$		0			0
$563$	−20.1820			−0.850568			−0.425284	−	0.905060i	$-0.639826\pi$
$563$	−20.1820			−0.850568			−0.425284	+	0.905060i	$0.639826\pi$
$564$		0			0
$565$	48.1914			2.02743
$566$		0			0
$567$		0			0
$568$		0			0
$569$	24.1049			1.01053			0.505266	−	0.862964i	$-0.331394\pi$
$569$	24.1049			1.01053			0.505266	+	0.862964i	$0.331394\pi$
$570$		0			0
$571$	6.45527			0.270144			0.135072	−	0.990836i	$-0.456873\pi$
$571$	6.45527			0.270144			0.135072	+	0.990836i	$0.456873\pi$
$572$		0			0
$573$	13.8075	−	20.3670i	0.576816	−	0.850844i
$574$		0			0
$575$	45.3846			1.89267
$576$		0			0
$577$	−9.20385	+	15.9415i	−0.383161	+	0.663654i	−0.991512	−	0.130014i	$-0.958498\pi$
$577$	−9.20385	+	15.9415i	−0.383161	+	0.663654i	0.608351	+	0.793668i	$0.291831\pi$
$578$		0			0
$579$	−6.59470	+	9.72764i	−0.274066	+	0.404267i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	29.2978			1.21339
$584$		0			0
$585$	−2.25796	−	5.66518i	−0.0933550	−	0.234226i
$586$		0			0
$587$	22.8848	−	39.6376i	0.944557	−	1.63602i	0.187921	−	0.982184i	$-0.439825\pi$
$587$	22.8848	−	39.6376i	0.944557	−	1.63602i	0.756636	−	0.653837i	$-0.226842\pi$
$588$		0			0
$589$	20.8895	+	36.1817i	0.860737	+	1.49084i
$590$		0			0
$591$	18.0085	−	26.5637i	0.740769	−	1.09269i
$592$		0			0
$593$	−8.71630	−	15.0971i	−0.357935	−	0.619962i	0.629680	−	0.776854i	$-0.283186\pi$
$593$	−8.71630	−	15.0971i	−0.357935	−	0.619962i	−0.987616	+	0.156892i	$0.949853\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.6914	−	26.1773i	−0.519426	−	1.07137i
$598$		0			0
$599$	3.44444			0.140736			0.0703680	−	0.997521i	$-0.477583\pi$
$599$	3.44444			0.140736			0.0703680	+	0.997521i	$0.477583\pi$
$600$		0			0
$601$	12.1666	−	21.0731i	0.496284	−	0.859590i	−0.503706	−	0.863875i	$-0.668031\pi$
$601$	12.1666	−	21.0731i	0.496284	−	0.859590i	0.999991	+	0.00428500i	$0.00136396\pi$
$602$		0			0
$603$	14.0738	+	35.3108i	0.573128	+	1.43797i
$604$		0			0
$605$	8.12655	+	14.0756i	0.330391	+	0.572254i
$606$		0			0
$607$	9.96073	−	17.2525i	0.404294	−	0.700257i	−0.589945	−	0.807443i	$-0.700851\pi$
$607$	9.96073	−	17.2525i	0.404294	−	0.700257i	0.994239	+	0.107186i	$0.0341840\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.19997	+	3.81045i	0.0890011	+	0.154154i
$612$		0			0
$613$	−20.3848	+	35.3075i	−0.823334	+	1.42606i	0.0798515	+	0.996807i	$0.474555\pi$
$613$	−20.3848	+	35.3075i	−0.823334	+	1.42606i	−0.903186	+	0.429250i	$0.858778\pi$
$614$		0			0
$615$	−36.3796	+	53.6625i	−1.46697	+	2.16388i
$616$		0			0
$617$	−11.5453	−	19.9970i	−0.464796	−	0.805050i	0.534396	−	0.845234i	$-0.320539\pi$
$617$	−11.5453	−	19.9970i	−0.464796	−	0.805050i	−0.999192	+	0.0401838i	$0.987206\pi$
$618$		0			0
$619$	22.5584	+	39.0723i	0.906698	+	1.57045i	0.818621	+	0.574334i	$0.194739\pi$
$619$	22.5584	+	39.0723i	0.906698	+	1.57045i	0.0880774	+	0.996114i	$0.471928\pi$
$620$		0			0
$621$	22.3743	−	24.4996i	0.897852	−	0.983134i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5.00960	−	8.67688i	0.200384	−	0.347075i
$626$		0			0
$627$	−11.2854	−	23.2772i	−0.450695	−	0.929601i
$628$		0			0
$629$	−1.53870			−0.0613518
$630$		0			0
$631$	−36.7010			−1.46104			−0.730521	−	0.682890i	$-0.760723\pi$
$631$	−36.7010			−1.46104			−0.730521	+	0.682890i	$0.760723\pi$
$632$		0			0
$633$	−37.2845	−	2.69527i	−1.48193	−	0.107127i
$634$		0			0
$635$	−36.1067	+	62.5387i	−1.43285	+	2.48177i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	5.48023	+	13.7498i	0.216795	+	0.543934i
$640$		0			0
$641$	−7.12245	−	12.3365i	−0.281320	−	0.487261i	0.690390	−	0.723437i	$-0.257439\pi$
$641$	−7.12245	−	12.3365i	−0.281320	−	0.487261i	−0.971710	+	0.236177i	$0.924106\pi$
$642$		0			0
$643$	18.0592	+	31.2795i	0.712187	+	1.23354i	0.964035	+	0.265777i	$0.0856285\pi$
$643$	18.0592	+	31.2795i	0.712187	+	1.23354i	−0.251848	+	0.967767i	$0.581038\pi$
$644$		0			0
$645$	−68.2724	−	4.93537i	−2.68822	−	0.194330i
$646$		0			0
$647$	3.73327	−	6.46622i	0.146770	−	0.254213i	−0.783262	−	0.621692i	$-0.786446\pi$
$647$	3.73327	−	6.46622i	0.146770	−	0.254213i	0.930032	+	0.367479i	$0.119779\pi$
$648$		0			0
$649$	5.60449	+	9.70727i	0.219996	+	0.381043i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.0545	−	34.7354i	0.784794	−	1.35930i	−0.144329	−	0.989530i	$-0.546102\pi$
$653$	20.0545	−	34.7354i	0.784794	−	1.35930i	0.929122	−	0.369773i	$-0.120564\pi$
$654$		0			0
$655$	2.78192	+	4.81842i	0.108698	+	0.188271i
$656$		0			0
$657$	25.8617	+	3.75870i	1.00896	+	0.146641i
$658$		0			0
$659$	−3.96459	+	6.86688i	−0.154439	+	0.267496i	−0.932855	−	0.360253i	$-0.882690\pi$
$659$	−3.96459	+	6.86688i	−0.154439	+	0.267496i	0.778416	+	0.627749i	$0.216024\pi$
$660$		0			0
$661$	22.1286			0.860704			0.430352	−	0.902661i	$-0.358389\pi$
$661$	22.1286			0.860704			0.430352	+	0.902661i	$0.358389\pi$
$662$		0			0
$663$	0.621781	−	0.917170i	0.0241480	−	0.0356200i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.86382	+	10.1564i	0.227048	+	0.393259i
$668$		0			0
$669$	0.749259	+	1.54542i	0.0289680	+	0.0597493i
$670$		0			0
$671$	−15.5379	−	26.9124i	−0.599834	−	1.03894i
$672$		0			0
$673$	6.60773	−	11.4449i	0.254709	−	0.441169i	−0.710107	−	0.704094i	$-0.751354\pi$
$673$	6.60773	−	11.4449i	0.254709	−	0.441169i	0.964817	+	0.262924i	$0.0846869\pi$
$674$		0			0
$675$	11.1648	+	35.2046i	0.429735	+	1.35503i
$676$		0			0
$677$	20.0210			0.769471			0.384736	−	0.923027i	$-0.374293\pi$
$677$	20.0210			0.769471			0.384736	+	0.923027i	$0.374293\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	5.06402	+	0.366074i	0.194053	+	0.0140280i
$682$		0			0
$683$	−10.7716	+	18.6569i	−0.412162	+	0.713886i	−0.995126	−	0.0986124i	$-0.968560\pi$
$683$	−10.7716	+	18.6569i	−0.412162	+	0.713886i	0.582964	+	0.812498i	$0.301893\pi$
$684$		0			0
$685$	−26.6267			−1.01735
$686$		0			0
$687$	3.31265	+	6.83265i	0.126385	+	0.260682i
$688$		0			0
$689$	6.80365			0.259198
$690$		0			0
$691$	−43.7386			−1.66389			−0.831947	−	0.554855i	$-0.812774\pi$
$691$	−43.7386			−1.66389			−0.831947	+	0.554855i	$0.812774\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−55.6337			−2.11031
$696$		0			0
$697$	−11.7794			−0.446178
$698$		0			0
$699$	1.87666	+	0.135662i	0.0709818	+	0.00513123i
$700$		0			0
$701$	16.2894			0.615244			0.307622	−	0.951509i	$-0.400467\pi$
$701$	16.2894			0.615244			0.307622	+	0.951509i	$0.400467\pi$
$702$		0			0
$703$	−4.17097	+	7.22434i	−0.157311	+	0.272471i
$704$		0			0
$705$	−19.8017	−	40.8430i	−0.745777	−	1.53824i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	36.8100			1.38243			0.691214	−	0.722650i	$-0.257076\pi$
$709$	36.8100			1.38243			0.691214	+	0.722650i	$0.257076\pi$
$710$		0			0
$711$	0.622466	+	1.56176i	0.0233443	+	0.0585704i
$712$		0			0
$713$	−22.4680	+	38.9157i	−0.841433	+	1.45741i
$714$		0			0
$715$	−2.55709	−	4.42901i	−0.0956298	−	0.165636i
$716$		0			0
$717$	6.61382	+	0.478109i	0.246998	+	0.0178553i
$718$		0			0
$719$	−15.8787	−	27.5028i	−0.592177	−	1.02568i	−0.993939	−	0.109936i	$-0.964935\pi$
$719$	−15.8787	−	27.5028i	−0.592177	−	1.02568i	0.401762	−	0.915744i	$-0.368398\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−22.3292	−	1.61416i	−0.830432	−	0.0600314i
$724$		0			0
$725$	−13.0545			−0.484830
$726$		0			0
$727$	−2.83596	+	4.91203i	−0.105180	+	0.182177i	−0.913812	−	0.406138i	$-0.866875\pi$
$727$	−2.83596	+	4.91203i	−0.105180	+	0.182177i	0.808632	+	0.588315i	$0.200209\pi$
$728$		0			0
$729$	24.5084	+	11.3287i	0.907718	+	0.419580i
$730$		0			0
$731$	−6.21849	−	10.7707i	−0.229999	−	0.398370i
$732$		0			0
$733$	−11.9926	+	20.7719i	−0.442958	+	0.767226i	−0.997907	−	0.0646579i	$-0.979404\pi$
$733$	−11.9926	+	20.7719i	−0.442958	+	0.767226i	0.554949	+	0.831884i	$0.312738\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.9382	+	27.6059i	0.587093	+	1.01687i
$738$		0			0
$739$	0.162996	−	0.282317i	0.00599590	−	0.0103852i	−0.863012	−	0.505184i	$-0.831425\pi$
$739$	0.162996	−	0.282317i	0.00599590	−	0.0103852i	0.869008	+	0.494798i	$0.164758\pi$
$740$		0			0
$741$	−2.62074	−	5.40552i	−0.0962752	−	0.198577i
$742$		0			0
$743$	13.3464	+	23.1166i	0.489631	+	0.848066i	0.999929	−	0.0119319i	$-0.00379815\pi$
$743$	13.3464	+	23.1166i	0.489631	+	0.848066i	−0.510298	+	0.859998i	$0.670465\pi$
$744$		0			0
$745$	5.00139	+	8.66266i	0.183237	+	0.317375i
$746$		0			0
$747$	21.8785	+	3.17978i	0.800491	+	0.116342i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−15.6978	+	27.1893i	−0.572820	+	0.992153i	0.423455	+	0.905917i	$0.360817\pi$
$751$	−15.6978	+	27.1893i	−0.572820	+	0.992153i	−0.996275	+	0.0862357i	$0.972516\pi$
$752$		0			0
$753$	−19.1132	+	28.1934i	−0.696525	+	1.02742i
$754$		0			0
$755$	31.8785			1.16018
$756$		0			0
$757$	−0.144979			−0.00526933			−0.00263467	−	0.999997i	$-0.500839\pi$
$757$	−0.144979			−0.00526933			−0.00263467	+	0.999997i	$0.500839\pi$
$758$		0			0
$759$	15.6128	−	23.0300i	0.566709	−	0.835936i
$760$		0			0
$761$	6.69005	−	11.5875i	0.242514	−	0.420047i	−0.718916	−	0.695097i	$-0.755361\pi$
$761$	6.69005	−	11.5875i	0.242514	−	0.420047i	0.961430	+	0.275050i	$0.0886946\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−7.07985	+	8.97450i	−0.255972	+	0.324474i
$766$		0			0
$767$	1.30150	+	2.25426i	0.0469944	+	0.0813966i
$768$		0			0
$769$	5.98750	+	10.3707i	0.215915	+	0.373975i	0.953555	−	0.301218i	$-0.0973933\pi$
$769$	5.98750	+	10.3707i	0.215915	+	0.373975i	−0.737640	+	0.675194i	$0.764060\pi$
$770$		0			0
$771$	−19.1623	−	39.5241i	−0.690113	−	1.42342i
$772$		0			0
$773$	−13.9471	+	24.1571i	−0.501642	+	0.868869i	0.498356	+	0.866972i	$0.333937\pi$
$773$	−13.9471	+	24.1571i	−0.501642	+	0.868869i	−0.999998	+	0.00189699i	$0.999396\pi$
$774$		0			0
$775$	−25.0099	−	43.3185i	−0.898384	−	1.55605i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−31.9308	+	55.3057i	−1.14404	+	1.98153i
$780$		0			0
$781$	6.20626	+	10.7495i	0.222077	+	0.384649i
$782$		0			0
$783$	−6.43577	+	7.04707i	−0.229996	+	0.251842i
$784$		0			0
$785$	−22.2489	+	38.5363i	−0.794099	+	1.37542i
$786$		0			0
$787$	0.104507			0.00372527			0.00186264	−	0.999998i	$-0.499407\pi$
$787$	0.104507			0.00372527			0.00186264	+	0.999998i	$0.499407\pi$
$788$		0			0
$789$	−15.3336	−	1.10846i	−0.545890	−	0.0394621i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.60827	−	6.24971i	−0.128133	−	0.221934i
$794$		0			0
$795$	−70.0043	−	5.06057i	−2.48280	−	0.179480i
$796$		0			0
$797$	17.5235	+	30.3516i	0.620715	+	1.07511i	0.989353	+	0.145537i	$0.0464910\pi$
$797$	17.5235	+	30.3516i	0.620715	+	1.07511i	−0.368638	+	0.929573i	$0.620176\pi$
$798$		0			0
$799$	4.12353	−	7.14216i	0.145880	−	0.252671i
$800$		0			0
$801$	−22.5666	+	28.6057i	−0.797351	+	1.01073i
$802$		0			0
$803$	21.9152			0.773369
$804$		0			0
$805$		0			0
$806$		0			0
$807$	13.8330	+	28.5318i	0.486943	+	1.00437i
$808$		0			0
$809$	22.1259	−	38.3233i	0.777907	−	1.34737i	−0.155239	−	0.987877i	$-0.549615\pi$
$809$	22.1259	−	38.3233i	0.777907	−	1.34737i	0.933146	−	0.359497i	$-0.117052\pi$
$810$		0			0
$811$	0.903637			0.0317310			0.0158655	−	0.999874i	$-0.494950\pi$
$811$	0.903637			0.0317310			0.0158655	+	0.999874i	$0.494950\pi$
$812$		0			0
$813$	−8.10098	−	0.585614i	−0.284114	−	0.0205384i
$814$		0			0
$815$	49.9943			1.75123
$816$		0			0
$817$	−67.4264			−2.35895
$818$		0			0
$819$		0			0
$820$		0			0
$821$	46.3565			1.61785			0.808927	−	0.587910i	$-0.200049\pi$
$821$	46.3565			1.61785			0.808927	+	0.587910i	$0.200049\pi$
$822$		0			0
$823$	−30.9829			−1.08000			−0.539998	−	0.841666i	$-0.681575\pi$
$823$	−30.9829			−1.08000			−0.539998	+	0.841666i	$0.681575\pi$
$824$		0			0
$825$	13.5114	+	27.8686i	0.470407	+	0.970259i
$826$		0			0
$827$	25.0923			0.872544			0.436272	−	0.899815i	$-0.356299\pi$
$827$	25.0923			0.872544			0.436272	+	0.899815i	$0.356299\pi$
$828$		0			0
$829$	21.1853	−	36.6941i	0.735798	−	1.27444i	−0.218575	−	0.975820i	$-0.570141\pi$
$829$	21.1853	−	36.6941i	0.735798	−	1.27444i	0.954373	−	0.298619i	$-0.0965258\pi$
$830$		0			0
$831$	−9.77123	−	0.706356i	−0.338960	−	0.0245032i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−16.5825			−0.573860
$836$		0			0
$837$	−35.7140	−	7.85487i	−1.23446	−	0.271504i
$838$		0			0
$839$	1.36843	−	2.37020i	0.0472435	−	0.0818282i	−0.841437	−	0.540356i	$-0.818290\pi$
$839$	1.36843	−	2.37020i	0.0472435	−	0.0818282i	0.888680	+	0.458528i	$0.151623\pi$
$840$		0			0
$841$	12.8133	+	22.1933i	0.441839	+	0.765287i
$842$		0			0
$843$	8.10583	+	16.7191i	0.279180	+	0.575835i
$844$		0			0
$845$	22.0237	+	38.1461i	0.757637	+	1.31227i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−23.1421	+	34.1362i	−0.794234	+	1.17155i
$850$		0			0
$851$	−8.97230			−0.307566
$852$		0			0
$853$	−4.59273	+	7.95485i	−0.157252	+	0.272369i	−0.933877	−	0.357595i	$-0.883597\pi$
$853$	−4.59273	+	7.95485i	−0.157252	+	0.272369i	0.776625	+	0.629964i	$0.216930\pi$
$854$		0			0
$855$	22.9447	+	57.5680i	0.784694	+	1.96878i
$856$		0			0
$857$	6.06106	+	10.4981i	0.207042	+	0.358607i	0.950781	−	0.309862i	$-0.100283\pi$
$857$	6.06106	+	10.4981i	0.207042	+	0.358607i	−0.743739	+	0.668470i	$0.766950\pi$
$858$		0			0
$859$	3.41626	−	5.91714i	0.116561	−	0.201890i	−0.801841	−	0.597537i	$-0.796146\pi$
$859$	3.41626	−	5.91714i	0.116561	−	0.201890i	0.918403	+	0.395647i	$0.129480\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.2595	−	45.4827i	−0.893882	−	1.54825i	−0.835182	−	0.549974i	$-0.814638\pi$
$863$	−26.2595	−	45.4827i	−0.893882	−	1.54825i	−0.0587005	−	0.998276i	$-0.518696\pi$
$864$		0			0
$865$	−43.6981	+	75.6873i	−1.48578	+	2.57345i
$866$		0			0
$867$	27.2967	+	1.97326i	0.927045	+	0.0670155i
$868$		0			0
$869$	0.704930	+	1.22097i	0.0239131	+	0.0414187i
$870$		0			0
$871$	3.70125	+	6.41074i	0.125412	+	0.217220i
$872$		0			0
$873$	41.4734	+	6.02767i	1.40366	+	0.204006i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.0782	+	27.8482i	−0.542922	+	0.940368i	0.455813	+	0.890076i	$0.349349\pi$
$877$	−16.0782	+	27.8482i	−0.542922	+	0.940368i	−0.998735	+	0.0502923i	$0.983985\pi$
$878$		0			0
$879$	−35.6961	−	2.58044i	−1.20400	−	0.0870362i
$880$		0			0
$881$	−16.9101			−0.569715			−0.284858	−	0.958570i	$-0.591946\pi$
$881$	−16.9101			−0.569715			−0.284858	+	0.958570i	$0.591946\pi$
$882$		0			0
$883$	−13.9999			−0.471135			−0.235567	−	0.971858i	$-0.575695\pi$
$883$	−13.9999			−0.471135			−0.235567	+	0.971858i	$0.575695\pi$
$884$		0			0
$885$	−11.7147	−	24.1627i	−0.393785	−	0.812219i
$886$		0			0
$887$	−22.2283	+	38.5005i	−0.746352	+	1.29272i	0.203208	+	0.979136i	$0.434863\pi$
$887$	−22.2283	+	38.5005i	−0.746352	+	1.29272i	−0.949560	+	0.313585i	$0.898470\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	21.7051	+	6.44530i	0.727148	+	0.215926i
$892$		0			0
$893$	−22.3555	−	38.7208i	−0.748097	−	1.29574i
$894$		0			0
$895$	−11.8713	−	20.5617i	−0.396814	−	0.687303i
$896$		0			0
$897$	3.62567	−	5.34812i	0.121058	−	0.178569i
$898$		0			0
$899$	6.46271	−	11.1937i	0.215543	−	0.373332i
$900$		0			0
$901$	−6.37624	−	11.0440i	−0.212423	−	0.367928i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.4413	−	40.6015i	0.779215	−	1.34964i
$906$		0			0
$907$	8.22392	+	14.2442i	0.273071	+	0.472972i	0.969647	−	0.244511i	$-0.0786273\pi$
$907$	8.22392	+	14.2442i	0.273071	+	0.472972i	−0.696576	+	0.717483i	$0.745294\pi$
$908$		0			0
$909$	17.0506	−	21.6136i	0.565534	−	0.716878i
$910$		0			0
$911$	−25.1577	+	43.5745i	−0.833513	+	1.44369i	0.0617228	+	0.998093i	$0.480341\pi$
$911$	−25.1577	+	43.5745i	−0.833513	+	1.44369i	−0.895236	+	0.445593i	$0.852993\pi$
$912$		0			0
$913$	18.5397			0.613576
$914$		0			0
$915$	32.4778	+	66.9886i	1.07368	+	2.21457i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−29.2722	−	50.7009i	−0.965600	−	1.67247i	−0.707994	−	0.706219i	$-0.750400\pi$
$919$	−29.2722	−	50.7009i	−0.965600	−	1.67247i	−0.257606	−	0.966250i	$-0.582934\pi$
$920$		0			0
$921$	11.5879	−	17.0930i	0.381836	−	0.563234i
$922$		0			0
$923$	1.44124	+	2.49630i	0.0474391	+	0.0821669i
$924$		0			0
$925$	4.99370	−	8.64933i	0.164192	−	0.284388i
$926$		0			0
$927$	−1.42228	−	0.206712i	−0.0467139	−	0.00678932i
$928$		0			0
$929$	0.637344			0.0209106			0.0104553	−	0.999945i	$-0.496672\pi$
$929$	0.637344			0.0209106			0.0104553	+	0.999945i	$0.496672\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−8.87629	+	13.0931i	−0.290597	+	0.428650i
$934$		0			0
$935$	−4.79291	+	8.30156i	−0.156745	+	0.271490i
$936$		0			0
$937$	19.0780			0.623250			0.311625	−	0.950205i	$-0.399127\pi$
$937$	19.0780			0.623250			0.311625	+	0.950205i	$0.399127\pi$
$938$		0			0
$939$	13.4510	−	19.8412i	0.438958	−	0.647493i
$940$		0			0
$941$	29.6306			0.965931			0.482965	−	0.875639i	$-0.339560\pi$
$941$	29.6306			0.965931			0.482965	+	0.875639i	$0.339560\pi$
$942$		0			0
$943$	−68.6872			−2.23676
$944$		0			0
$945$		0			0
$946$		0			0
$947$	34.3362			1.11578			0.557888	−	0.829916i	$-0.311612\pi$
$947$	34.3362			1.11578			0.557888	+	0.829916i	$0.311612\pi$
$948$		0			0
$949$	5.08923			0.165203
$950$		0			0
$951$	1.78015	−	2.62584i	0.0577252	−	0.0851488i
$952$		0			0
$953$	53.6361			1.73744			0.868722	−	0.495301i	$-0.164942\pi$
$953$	53.6361			1.73744			0.868722	+	0.495301i	$0.164942\pi$
$954$		0			0
$955$	−24.7163	+	42.8099i	−0.799800	+	1.38529i
$956$		0			0
$957$	−4.49088	+	6.62436i	−0.145170	+	0.214135i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	18.5254			0.597595
$962$		0			0
$963$	9.95493	−	12.6190i	0.320793	−	0.406641i
$964$		0			0
$965$	11.8049	−	20.4467i	0.380014	−	0.658204i
$966$		0			0
$967$	14.5629	+	25.2236i	0.468310	+	0.811136i	0.999344	−	0.0362139i	$-0.0115298\pi$
$967$	14.5629	+	25.2236i	0.468310	+	0.811136i	−0.531034	+	0.847350i	$0.678196\pi$
$968$		0			0
$969$	−6.31837	+	9.32004i	−0.202975	+	0.299403i
$970$		0			0
$971$	11.9191	+	20.6446i	0.382503	+	0.662515i	0.991419	−	0.130719i	$-0.0417287\pi$
$971$	11.9191	+	20.6446i	0.382503	+	0.662515i	−0.608916	+	0.793235i	$0.708395\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3.13768	+	6.47176i	0.100486	+	0.207262i
$976$		0			0
$977$	38.1683			1.22111			0.610556	−	0.791973i	$-0.290946\pi$
$977$	38.1683			1.22111			0.610556	+	0.791973i	$0.290946\pi$
$978$		0			0
$979$	−15.2771	+	26.4607i	−0.488258	+	0.845688i
$980$		0			0
$981$	−46.7608	−	6.79613i	−1.49296	−	0.216984i
$982$		0			0
$983$	−3.78769	−	6.56046i	−0.120808	−	0.209246i	0.799278	−	0.600961i	$-0.205215\pi$
$983$	−3.78769	−	6.56046i	−0.120808	−	0.209246i	−0.920087	+	0.391715i	$0.871882\pi$
$984$		0			0
$985$	−32.2363	+	55.8349i	−1.02713	+	1.77905i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−36.2607	−	62.8054i	−1.15302	−	1.99709i
$990$		0			0
$991$	4.68952	−	8.12248i	0.148967	−	0.258019i	−0.781879	−	0.623431i	$-0.785738\pi$
$991$	4.68952	−	8.12248i	0.148967	−	0.258019i	0.930846	+	0.365411i	$0.119072\pi$
$992$		0			0
$993$	−0.200473	+	0.295711i	−0.00636181	+	0.00938411i
$994$		0			0
$995$	29.2219	+	50.6138i	0.926397	+	1.60457i
$996$		0			0
$997$	4.21829	+	7.30629i	0.133595	+	0.231393i	0.925060	−	0.379822i	$-0.124015\pi$
$997$	4.21829	+	7.30629i	0.133595	+	0.231393i	−0.791465	+	0.611214i	$0.790681\pi$
$998$		0			0
$999$	−2.20723	−	6.95977i	−0.0698336	−	0.220197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.i.j.1537.9		24
3.2	odd	2		5292.2.i.j.2125.11		24
7.2	even	3		1764.2.l.j.961.9		24
7.3	odd	6		1764.2.j.i.1177.12	yes	24
7.4	even	3		1764.2.j.i.1177.1	yes	24
7.5	odd	6		1764.2.l.j.961.4		24
7.6	odd	2	inner	1764.2.i.j.1537.4		24
9.4	even	3		1764.2.l.j.949.9		24
9.5	odd	6		5292.2.l.j.361.2		24
21.2	odd	6		5292.2.l.j.3313.2		24
21.5	even	6		5292.2.l.j.3313.11		24
21.11	odd	6		5292.2.j.i.3529.11		24
21.17	even	6		5292.2.j.i.3529.2		24
21.20	even	2		5292.2.i.j.2125.2		24
63.4	even	3		1764.2.j.i.589.1	✓	24
63.5	even	6		5292.2.i.j.1549.2		24
63.13	odd	6		1764.2.l.j.949.4		24
63.23	odd	6		5292.2.i.j.1549.11		24
63.31	odd	6		1764.2.j.i.589.12	yes	24
63.32	odd	6		5292.2.j.i.1765.11		24
63.40	odd	6	inner	1764.2.i.j.373.4		24
63.41	even	6		5292.2.l.j.361.11		24
63.58	even	3	inner	1764.2.i.j.373.9		24
63.59	even	6		5292.2.j.i.1765.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.4		24	63.40	odd	6	inner
1764.2.i.j.373.9		24	63.58	even	3	inner
1764.2.i.j.1537.4		24	7.6	odd	2	inner
1764.2.i.j.1537.9		24	1.1	even	1	trivial
1764.2.j.i.589.1	✓	24	63.4	even	3
1764.2.j.i.589.12	yes	24	63.31	odd	6
1764.2.j.i.1177.1	yes	24	7.4	even	3
1764.2.j.i.1177.12	yes	24	7.3	odd	6
1764.2.l.j.949.4		24	63.13	odd	6
1764.2.l.j.949.9		24	9.4	even	3
1764.2.l.j.961.4		24	7.5	odd	6
1764.2.l.j.961.9		24	7.2	even	3
5292.2.i.j.1549.2		24	63.5	even	6
5292.2.i.j.1549.11		24	63.23	odd	6
5292.2.i.j.2125.2		24	21.20	even	2
5292.2.i.j.2125.11		24	3.2	odd	2
5292.2.j.i.1765.2		24	63.59	even	6
5292.2.j.i.1765.11		24	63.32	odd	6
5292.2.j.i.3529.2		24	21.17	even	6
5292.2.j.i.3529.11		24	21.11	odd	6
5292.2.l.j.361.2		24	9.5	odd	6
5292.2.l.j.361.11		24	63.41	even	6
5292.2.l.j.3313.2		24	21.2	odd	6
5292.2.l.j.3313.11		24	21.5	even	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.971923 - 1.43365i) q^{3} +(-1.73981 + 3.01343i) q^{5} +(-1.11073 - 2.78680i) q^{9} +O(q^{10})\)	\(q+(0.971923 - 1.43365i) q^{3} +(-1.73981 + 3.01343i) q^{5} +(-1.11073 - 2.78680i) q^{9} +(-1.25788 - 2.17871i) q^{11} +(-0.292110 - 0.505949i) q^{13} +(2.62926 + 5.42310i) q^{15} +(-0.547519 + 0.948331i) q^{17} +(2.96834 + 5.14132i) q^{19} +(-3.19264 + 5.52982i) q^{23} +(-3.55384 - 6.15544i) q^{25} +(-5.07486 - 1.11616i) q^{27} +(0.918333 - 1.59060i) q^{29} +7.03743 q^{31} +(-4.34608 - 0.314176i) q^{33} +(0.702576 + 1.21690i) q^{37} +(-1.00927 - 0.0729591i) q^{39} +(5.37855 + 9.31593i) q^{41} +(-5.67879 + 9.83596i) q^{43} +(10.3303 + 1.50139i) q^{45} -7.53129 q^{47} +(0.827432 + 1.70666i) q^{51} +(-5.82285 + 10.0855i) q^{53} +8.75386 q^{55} +(10.2559 + 0.741391i) q^{57} -4.45551 q^{59} +12.3524 q^{61} +2.03286 q^{65} -12.6707 q^{67} +(4.82485 + 9.95170i) q^{69} -4.93390 q^{71} +(-4.35558 + 7.54408i) q^{73} +(-12.2788 - 0.887629i) q^{75} -0.560411 q^{79} +(-6.53256 + 6.19078i) q^{81} +(-3.68472 + 6.38212i) q^{83} +(-1.90515 - 3.29982i) q^{85} +(-1.38782 - 2.86251i) q^{87} +(-6.07256 - 10.5180i) q^{89} +(6.83984 - 10.0892i) q^{93} -20.6573 q^{95} +(-6.98486 + 12.0981i) q^{97} +(-4.67448 + 5.92543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} - 12 q^{37} + 8 q^{51} - 16 q^{53} + 52 q^{57} + 72 q^{65} - 24 q^{67} + 48 q^{71} - 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93} - 64 q^{95} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 - 12 * q^37 + 8 * q^51 - 16 * q^53 + 52 * q^57 + 72 * q^65 - 24 * q^67 + 48 * q^71 - 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 64 * q^95 - 4 * q^99

Introduction

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