LMFDB - Embedded newform 1764.2.l.j.961.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(949,1764)]

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, 4]))

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

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

chi := DirichletCharacter("1764.949");

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.l (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			961.9
Character	$\chi$	$=$	1764.961
Dual form			1764.2.l.j.949.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.755620 + 1.55854i) q^{3} +3.47961 q^{5} +(-1.85808 + 2.35532i) q^{9} +O(q^{10})$	\(q+(0.755620 + 1.55854i) q^{3} +3.47961 q^{5} +(-1.85808 + 2.35532i) q^{9} +2.51576 q^{11} +(-0.292110 - 0.505949i) q^{13} +(2.62926 + 5.42310i) q^{15} +(-0.547519 - 0.948331i) q^{17} +(2.96834 - 5.14132i) q^{19} +6.38528 q^{23} +7.10769 q^{25} +(-5.07486 - 1.11616i) q^{27} +(0.918333 - 1.59060i) q^{29} +(-3.51872 + 6.09459i) q^{31} +(1.90096 + 3.92091i) q^{33} +(0.702576 - 1.21690i) q^{37} +(0.567817 - 0.837570i) q^{39} +(5.37855 + 9.31593i) q^{41} +(-5.67879 + 9.83596i) q^{43} +(-6.46539 + 8.19561i) q^{45} +(3.76565 + 6.52229i) q^{47} +(1.06429 - 1.56991i) q^{51} +(-5.82285 - 10.0855i) q^{53} +8.75386 q^{55} +(10.2559 + 0.741391i) q^{57} +(2.22775 - 3.85858i) q^{59} +(-6.17622 - 10.6975i) q^{61} +(-1.01643 - 1.76051i) q^{65} +(6.33536 - 10.9732i) q^{67} +(4.82485 + 9.95170i) q^{69} -4.93390 q^{71} +(-4.35558 - 7.54408i) q^{73} +(5.37071 + 11.0776i) q^{75} +(0.280206 + 0.485330i) q^{79} +(-2.09509 - 8.75275i) q^{81} +(-3.68472 + 6.38212i) q^{83} +(-1.90515 - 3.29982i) q^{85} +(3.17292 + 0.229368i) q^{87} +(-6.07256 + 10.5180i) q^{89} +(-12.1575 - 0.878855i) q^{93} +(10.3287 - 17.8898i) q^{95} +(-6.98486 + 12.0981i) q^{97} +(-4.67448 + 5.92543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} + 8 q^{11} - 28 q^{15} + 16 q^{23} + 24 q^{25} - 32 q^{29} - 12 q^{37} + 32 q^{51} - 16 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} - 8 q^{81} + 12 q^{85} + 32 q^{95} - 4 q^{99}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^11 - 28 * q^15 + 16 * q^23 + 24 * q^25 - 32 * q^29 - 12 * q^37 + 32 * q^51 - 16 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 - 8 * q^81 + 12 * q^85 + 32 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.755620	+	1.55854i	0.436257	+	0.899822i
$3$	0.755620	+	1.55854i	0.436257	+	0.899822i
$4$		0			0
$5$	3.47961			1.55613			0.778065	−	0.628184i	$-0.216202\pi$
$5$	3.47961			1.55613			0.778065	+	0.628184i	$0.216202\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.85808	+	2.35532i	−0.619359	+	0.785108i
$10$		0			0
$11$	2.51576			0.758530			0.379265	−	0.925288i	$-0.376177\pi$
$11$	2.51576			0.758530			0.379265	+	0.925288i	$0.376177\pi$
$12$		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	0.791959	−	0.610574i	$-0.209061\pi$
$17$	−0.547519	−	0.948331i	−0.132793	−	0.230004i	−0.924752	+	0.380570i	$0.875728\pi$
$18$		0			0
$19$	2.96834	−	5.14132i	0.680984	−	1.17950i	−0.293696	−	0.955899i	$-0.594885\pi$
$19$	2.96834	−	5.14132i	0.680984	−	1.17950i	0.974681	−	0.223601i	$-0.0717812\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.38528			1.33142			0.665712	−	0.746209i	$-0.268128\pi$
$23$	6.38528			1.33142			0.665712	+	0.746209i	$0.268128\pi$
$24$		0			0
$25$	7.10769			1.42154
$26$		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
$31$	−3.51872	+	6.09459i	−0.631980	+	1.09462i	0.355166	+	0.934803i	$0.384424\pi$
$31$	−3.51872	+	6.09459i	−0.631980	+	1.09462i	−0.987146	+	0.159818i	$0.948909\pi$
$32$		0			0
$33$	1.90096	+	3.92091i	0.330914	+	0.682542i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.702576	−	1.21690i	0.115503	−	0.200057i	−0.802478	−	0.596682i	$-0.796485\pi$
$37$	0.702576	−	1.21690i	0.115503	−	0.200057i	0.917981	+	0.396625i	$0.129819\pi$
$38$		0			0
$39$	0.567817	−	0.837570i	0.0909235	−	0.134118i
$40$		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
$45$	−6.46539	+	8.19561i	−0.963803	+	1.22173i
$46$		0			0
$47$	3.76565	+	6.52229i	0.549276	+	0.951374i	0.998324	+	0.0578664i	$0.0184298\pi$
$47$	3.76565	+	6.52229i	0.549276	+	0.951374i	−0.449048	+	0.893507i	$0.648237\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.06429	−	1.56991i	0.149031	−	0.219831i
$52$		0			0
$53$	−5.82285	−	10.0855i	−0.799830	−	1.38535i	−0.919727	−	0.392560i	$-0.871590\pi$
$53$	−5.82285	−	10.0855i	−0.799830	−	1.38535i	0.119897	−	0.992786i	$-0.461744\pi$
$54$		0			0
$55$	8.75386			1.18037
$56$		0			0
$57$	10.2559	+	0.741391i	1.35842	+	0.0981996i
$58$		0			0
$59$	2.22775	−	3.85858i	0.290029	−	0.502345i	−0.683787	−	0.729681i	$-0.739668\pi$
$59$	2.22775	−	3.85858i	0.290029	−	0.502345i	0.973816	+	0.227337i	$0.0730018\pi$
$60$		0			0
$61$	−6.17622	−	10.6975i	−0.790784	−	1.36968i	−0.925482	−	0.378792i	$-0.876340\pi$
$61$	−6.17622	−	10.6975i	−0.790784	−	1.36968i	0.134698	−	0.990887i	$-0.456994\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.01643	−	1.76051i	−0.126072	−	0.218364i
$66$		0			0
$67$	6.33536	−	10.9732i	0.773988	−	1.34059i	−0.161374	−	0.986893i	$-0.551593\pi$
$67$	6.33536	−	10.9732i	0.773988	−	1.34059i	0.935362	−	0.353693i	$-0.115074\pi$
$68$		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	−0.999936	−	0.0113320i	$-0.996393\pi$
$73$	−4.35558	−	7.54408i	−0.509782	−	0.882968i	0.490154	−	0.871636i	$-0.336940\pi$
$74$		0			0
$75$	5.37071	+	11.0776i	0.620156	+	1.27913i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.280206	+	0.485330i	0.0315256	+	0.0546039i	0.881358	−	0.472450i	$-0.156630\pi$
$79$	0.280206	+	0.485330i	0.0315256	+	0.0546039i	−0.849832	+	0.527053i	$0.823297\pi$
$80$		0			0
$81$	−2.09509	−	8.75275i	−0.232788	−	0.972528i
$82$		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
$87$	3.17292	+	0.229368i	0.340173	+	0.0245909i
$88$		0			0
$89$	−6.07256	+	10.5180i	−0.643690	+	1.11490i	0.340913	+	0.940095i	$0.389264\pi$
$89$	−6.07256	+	10.5180i	−0.643690	+	1.11490i	−0.984602	+	0.174808i	$0.944069\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−12.1575	−	0.878855i	−1.26067	−	0.0911331i
$94$		0			0
$95$	10.3287	−	17.8898i	1.05970	−	1.83545i
$96$		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
$101$	−9.17649			−0.913095			−0.456548	−	0.889699i	$-0.650914\pi$
$101$	−9.17649			−0.913095			−0.456548	+	0.889699i	$0.650914\pi$
$102$		0			0
$103$	−0.479075			−0.0472047			−0.0236024	−	0.999721i	$-0.507514\pi$
$103$	−0.479075			−0.0472047			−0.0236024	+	0.999721i	$0.507514\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.67882	−	4.63986i	0.258972	−	0.448552i	−0.706995	−	0.707219i	$-0.749950\pi$
$107$	2.67882	−	4.63986i	0.258972	−	0.448552i	0.965967	+	0.258666i	$0.0832830\pi$
$108$		0			0
$109$	7.87535	+	13.6405i	0.754322	+	1.30652i	0.945711	+	0.325009i	$0.105367\pi$
$109$	7.87535	+	13.6405i	0.754322	+	1.30652i	−0.191389	+	0.981514i	$0.561299\pi$
$110$		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
$115$	22.2183			2.07187
$116$		0			0
$117$	1.73444	+	0.252080i	0.160349	+	0.0233048i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.67095			−0.424632
$122$		0			0
$123$	−10.4551	+	15.4220i	−0.942703	+	1.39055i
$124$		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
$129$	−19.6207	−	1.41837i	−1.72751	−	0.124880i
$130$		0			0
$131$	−1.59898			−0.139704			−0.0698518	−	0.997557i	$-0.522253\pi$
$131$	−1.59898			−0.139704			−0.0698518	+	0.997557i	$0.522253\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−17.6585	−	3.88379i	−1.51980	−	0.334263i
$136$		0			0
$137$	−7.65220			−0.653771			−0.326886	−	0.945064i	$-0.605999\pi$
$137$	−7.65220			−0.653771			−0.326886	+	0.945064i	$0.605999\pi$
$138$		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
$149$	−2.87468			−0.235503			−0.117752	−	0.993043i	$-0.537569\pi$
$149$	−2.87468			−0.235503			−0.117752	+	0.993043i	$0.537569\pi$
$150$		0			0
$151$	9.16152			0.745554			0.372777	−	0.927921i	$-0.378406\pi$
$151$	9.16152			0.745554			0.372777	+	0.927921i	$0.378406\pi$
$152$		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
$157$	−6.39409	+	11.0749i	−0.510304	+	0.883873i	0.489625	+	0.871933i	$0.337134\pi$
$157$	−6.39409	+	11.0749i	−0.510304	+	0.883873i	−0.999929	+	0.0119393i	$0.996200\pi$
$158$		0			0
$159$	11.3187	−	16.6959i	0.897633	−	1.32407i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−7.18390	+	12.4429i	−0.562686	+	0.974601i	0.434575	+	0.900636i	$0.356899\pi$
$163$	−7.18390	+	12.4429i	−0.562686	+	0.974601i	−0.997261	+	0.0739653i	$0.976435\pi$
$164$		0			0
$165$	6.61459	+	13.6432i	0.514945	+	1.06212i
$166$		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
$171$	6.59406	+	16.5444i	0.504260	+	1.26518i
$172$		0			0
$173$	−12.5583	−	21.7517i	−0.954792	−	1.65375i	−0.734844	−	0.678237i	$-0.762744\pi$
$173$	−12.5583	−	21.7517i	−0.954792	−	1.65375i	−0.219948	−	0.975512i	$-0.570589\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.69708	+	0.556417i	0.578548	+	0.0418229i
$178$		0			0
$179$	−3.41168	−	5.90920i	−0.255001	−	0.441675i	0.709895	−	0.704308i	$-0.248742\pi$
$179$	−3.41168	−	5.90920i	−0.255001	−	0.441675i	−0.964896	+	0.262633i	$0.915409\pi$
$180$		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
$185$	2.44469	−	4.23433i	0.179737	−	0.311314i
$186$		0			0
$187$	−1.37743	−	2.38577i	−0.100727	−	0.174465i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.10318	−	12.3031i	−0.513968	−	0.890218i	−0.999869	−	0.0162045i	$-0.994842\pi$
$191$	−7.10318	−	12.3031i	−0.513968	−	0.890218i	0.485901	−	0.874014i	$-0.338492\pi$
$192$		0			0
$193$	3.39260	−	5.87616i	0.244205	−	0.422975i	−0.717703	−	0.696349i	$-0.754806\pi$
$193$	3.39260	−	5.87616i	0.244205	−	0.422975i	0.961908	+	0.273374i	$0.0881397\pi$
$194$		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	0.993501	+	0.113819i	$0.0363086\pi$
$199$	8.39804	+	14.5458i	0.595321	+	1.03113i	−0.398180	+	0.917307i	$0.630358\pi$
$200$		0			0
$201$	21.8892	+	1.58236i	1.54395	+	0.111611i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	18.7153	+	32.4158i	1.30713	+	2.26402i
$206$		0			0
$207$	−11.8644	+	15.0394i	−0.824630	+	1.04531i
$208$		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
$213$	−3.72815	−	7.68967i	−0.255449	−	0.526888i
$214$		0			0
$215$	−19.7600	+	34.2253i	−1.34762	+	2.33415i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	8.46657	−	12.4888i	0.572118	−	0.843914i
$220$		0			0
$221$	−0.319872	+	0.554034i	−0.0215169	+	0.0372683i
$222$		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
$227$	−2.93134			−0.194560			−0.0972799	−	0.995257i	$-0.531014\pi$
$227$	−2.93134			−0.194560			−0.0972799	+	0.995257i	$0.531014\pi$
$228$		0			0
$229$	4.38401			0.289704			0.144852	−	0.989453i	$-0.453729\pi$
$229$	4.38401			0.289704			0.144852	+	0.989453i	$0.453729\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.543158	−	0.940778i	0.0355835	−	0.0616324i	−0.847685	−	0.530500i	$-0.822004\pi$
$233$	0.543158	−	0.940778i	0.0355835	−	0.0616324i	0.883269	+	0.468867i	$0.155338\pi$
$234$		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
$241$	12.9254			0.832599			0.416300	−	0.909227i	$-0.363327\pi$
$241$	12.9254			0.832599			0.416300	+	0.909227i	$0.363327\pi$
$242$		0			0
$243$	12.0584	−	9.87903i	0.773546	−	0.633740i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.46833			−0.220685
$248$		0			0
$249$	−12.7310	−	0.920317i	−0.806796	−	0.0583227i
$250$		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
$255$	3.70332	−	5.46266i	0.231911	−	0.342085i
$256$		0			0
$257$	−25.3597			−1.58190			−0.790948	−	0.611884i	$-0.790412\pi$
$257$	−25.3597			−1.58190			−0.790948	+	0.611884i	$0.790412\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2.04004	+	5.11843i	0.126275	+	0.316823i
$262$		0			0
$263$	8.87595			0.547315			0.273657	−	0.961827i	$-0.411767\pi$
$263$	8.87595			0.547315			0.273657	+	0.961827i	$0.411767\pi$
$264$		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	−0.997656	−	0.0684319i	$-0.978200\pi$
$269$	−9.15338	−	15.8541i	−0.558092	−	0.966643i	0.439564	−	0.898211i	$-0.355133\pi$
$270$		0			0
$271$	−2.34465	+	4.06106i	−0.142427	+	0.246692i	−0.928410	−	0.371557i	$-0.878824\pi$
$271$	−2.34465	+	4.06106i	−0.142427	+	0.246692i	0.785983	+	0.618248i	$0.212157\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	17.8812			1.07828
$276$		0			0
$277$	5.65614			0.339845			0.169922	−	0.985457i	$-0.445648\pi$
$277$	5.65614			0.339845			0.169922	+	0.985457i	$0.445648\pi$
$278$		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
$283$	11.9053	−	20.6206i	0.707697	−	1.22577i	−0.258013	−	0.966141i	$-0.583068\pi$
$283$	11.9053	−	20.6206i	0.707697	−	1.22577i	0.965710	−	0.259625i	$-0.0835989\pi$
$284$		0			0
$285$	35.6865	+	2.57975i	2.11388	+	0.152811i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.90045	−	13.6840i	0.464732	−	0.804940i
$290$		0			0
$291$	−24.1333	−	1.74458i	−1.41472	−	0.102269i
$292$		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
$297$	−12.7671	−	2.80798i	−0.740824	−	0.162936i
$298$		0			0
$299$	−1.86521	−	3.23063i	−0.107868	−	0.186832i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.93394	−	14.3019i	−0.398344	−	0.821623i
$304$		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
$311$	4.56635	−	7.90916i	0.258934	−	0.448487i	−0.707022	−	0.707191i	$-0.749962\pi$
$311$	4.56635	−	7.90916i	0.258934	−	0.448487i	0.965957	+	0.258704i	$0.0832954\pi$
$312$		0			0
$313$	−6.91980	−	11.9854i	−0.391130	−	0.677457i	0.601469	−	0.798896i	$-0.294582\pi$
$313$	−6.91980	−	11.9854i	−0.391130	−	0.677457i	−0.992599	+	0.121439i	$0.961249\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.915786	−	1.58619i	−0.0514357	−	0.0890892i	0.839161	−	0.543883i	$-0.183046\pi$
$317$	−0.915786	−	1.58619i	−0.0514357	−	0.0890892i	−0.890597	+	0.454794i	$0.849713\pi$
$318$		0			0
$319$	2.31031	−	4.00157i	0.129352	−	0.224045i
$320$		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
$327$	−15.3085	+	22.5811i	−0.846560	+	1.24874i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.103132	+	0.178630i	0.00566864	+	0.00981838i	0.868846	−	0.495083i	$-0.164862\pi$
$331$	0.103132	+	0.178630i	0.00566864	+	0.00981838i	−0.863177	+	0.504901i	$0.831529\pi$
$332$		0			0
$333$	1.56075	+	3.91589i	0.0855284	+	0.214589i
$334$		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
$339$	13.4608	−	19.8556i	0.731090	−	1.07841i
$340$		0			0
$341$	−8.85224	+	15.3325i	−0.479376	+	0.830303i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	16.7886	+	34.6281i	0.903867	+	1.86431i
$346$		0			0
$347$	1.60907	−	2.78698i	0.0863792	−	0.149613i	−0.819599	−	0.572938i	$-0.805804\pi$
$347$	1.60907	−	2.78698i	0.0863792	−	0.149613i	0.905978	+	0.423325i	$0.139137\pi$
$348$		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
$353$	−3.36930			−0.179330			−0.0896648	−	0.995972i	$-0.528580\pi$
$353$	−3.36930			−0.179330			−0.0896648	+	0.995972i	$0.528580\pi$
$354$		0			0
$355$	−17.1681			−0.911186
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.28913	−	12.6251i	0.384706	−	0.666330i	−0.607023	−	0.794685i	$-0.707636\pi$
$359$	7.28913	−	12.6251i	0.384706	−	0.666330i	0.991728	+	0.128355i	$0.0409696\pi$
$360$		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
$367$	−0.736734			−0.0384572			−0.0192286	−	0.999815i	$-0.506121\pi$
$367$	−0.736734			−0.0384572			−0.0192286	+	0.999815i	$0.506121\pi$
$368$		0			0
$369$	−31.9358	−	4.64149i	−1.66251	−	0.241626i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	28.9029			1.49653			0.748267	−	0.663397i	$-0.230886\pi$
$373$	28.9029			1.49653			0.748267	+	0.663397i	$0.230886\pi$
$374$		0			0
$375$	5.54167	+	11.4302i	0.286171	+	0.590254i
$376$		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
$381$	15.6816	+	32.3448i	0.803394	+	1.65708i
$382$		0			0
$383$	15.4055			0.787182			0.393591	−	0.919286i	$-0.371233\pi$
$383$	15.4055			0.787182			0.393591	+	0.919286i	$0.371233\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.6152	−	31.6514i	−0.641267	−	1.60893i
$388$		0			0
$389$	−20.3139			−1.02996			−0.514978	−	0.857204i	$-0.672200\pi$
$389$	−20.3139			−1.02996			−0.514978	+	0.857204i	$0.672200\pi$
$390$		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	−0.736707	−	0.676212i	$-0.763620\pi$
$397$	4.32895	−	7.49796i	0.217264	−	0.376312i	0.953970	+	0.299901i	$0.0969535\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	35.0546			1.75054			0.875272	−	0.483631i	$-0.160682\pi$
$401$	35.0546			1.75054			0.875272	+	0.483631i	$0.160682\pi$
$402$		0			0
$403$	4.11141			0.204804
$404$		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
$409$	6.61681	−	11.4607i	0.327180	−	0.566693i	−0.654771	−	0.755827i	$-0.727235\pi$
$409$	6.61681	−	11.4607i	0.327180	−	0.566693i	0.981951	+	0.189135i	$0.0605682\pi$
$410$		0			0
$411$	−5.78215	−	11.9262i	−0.285212	−	0.588278i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.8214	+	22.2073i	−0.629377	+	1.09011i
$416$		0			0
$417$	−15.5396	+	22.9219i	−0.760976	+	1.12249i
$418$		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
$423$	−22.3590	−	3.24961i	−1.08713	−	0.158002i
$424$		0			0
$425$	−3.89160	−	6.74044i	−0.188770	−	0.326959i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.42849	−	2.10712i	0.0689682	−	0.101733i
$430$		0			0
$431$	7.48548	+	12.9652i	0.360563	+	0.624513i	0.988054	−	0.154111i	$-0.0492513\pi$
$431$	7.48548	+	12.9652i	0.360563	+	0.624513i	−0.627491	+	0.778624i	$0.715918\pi$
$432$		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
$437$	18.9537	−	32.8288i	0.906679	−	1.57041i
$438$		0			0
$439$	−6.03657	−	10.4556i	−0.288110	−	0.499021i	0.685249	−	0.728309i	$-0.259693\pi$
$439$	−6.03657	−	10.4556i	−0.288110	−	0.499021i	−0.973359	+	0.229288i	$0.926360\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.02894	−	10.4424i	−0.286444	−	0.496135i	0.686515	−	0.727116i	$-0.259140\pi$
$443$	−6.02894	−	10.4424i	−0.286444	−	0.496135i	−0.972958	+	0.230981i	$0.925806\pi$
$444$		0			0
$445$	−21.1301	+	36.5985i	−1.00166	+	1.73493i
$446$		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
$453$	6.92263	+	14.2786i	0.325253	+	0.670866i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.88323	−	4.99390i	−0.134872	−	0.233605i	0.790677	−	0.612234i	$-0.209729\pi$
$457$	−2.88323	−	4.99390i	−0.134872	−	0.233605i	−0.925548	+	0.378629i	$0.876396\pi$
$458$		0			0
$459$	1.72010	+	5.42376i	0.0802872	+	0.253160i
$460$		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
$465$	−42.3032	−	3.05807i	−1.96177	−	0.141815i
$466$		0			0
$467$	−1.42738	+	2.47230i	−0.0660515	+	0.114404i	−0.897160	−	0.441706i	$-0.854373\pi$
$467$	−1.42738	+	2.47230i	−0.0660515	+	0.114404i	0.831108	+	0.556110i	$0.187707\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−22.0921	−	1.59703i	−1.01795	−	0.0735871i
$472$		0			0
$473$	−14.2865	+	24.7449i	−0.656893	+	1.13777i
$474$		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
$479$	−4.37376			−0.199842			−0.0999211	−	0.994995i	$-0.531859\pi$
$479$	−4.37376			−0.199842			−0.0999211	+	0.994995i	$0.531859\pi$
$480$		0			0
$481$	−0.820918			−0.0374307
$482$		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	0.971230	+	0.238142i	$0.0765383\pi$
$487$	15.2678	+	26.4447i	0.691852	+	1.19832i	−0.279378	+	0.960181i	$0.590128\pi$
$488$		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
$493$	−2.01122			−0.0905808
$494$		0			0
$495$	−16.2654	+	20.6182i	−0.731074	+	0.926718i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−22.7703			−1.01934			−0.509670	−	0.860370i	$-0.670232\pi$
$499$	−22.7703			−1.01934			−0.509670	+	0.860370i	$0.670232\pi$
$500$		0			0
$501$	−4.63180	+	6.83223i	−0.206934	+	0.305242i
$502$		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
$507$	21.8684	+	1.58085i	0.971211	+	0.0702082i
$508$		0			0
$509$	24.4700			1.08461			0.542307	−	0.840180i	$-0.317551\pi$
$509$	24.4700			1.08461			0.542307	+	0.840180i	$0.317551\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−20.8024	+	22.7783i	−0.918450	+	1.00569i
$514$		0			0
$515$	−1.66700			−0.0734566
$516$		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	0.882276	+	0.470733i	$0.156011\pi$
$521$	19.3743	+	33.5573i	0.848805	+	1.47017i	−0.0334709	+	0.999440i	$0.510656\pi$
$522$		0			0
$523$	12.8473	−	22.2521i	0.561771	−	0.973016i	−0.435571	−	0.900154i	$-0.643454\pi$
$523$	12.8473	−	22.2521i	0.561771	−	0.973016i	0.997342	−	0.0728616i	$-0.0232131\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.70626			0.335690
$528$		0			0
$529$	17.7719			0.772689
$530$		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
$535$	9.32127	−	16.1449i	0.402993	−	0.698005i
$536$		0			0
$537$	6.63178	−	9.78234i	0.286182	−	0.422139i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.92878	−	8.53690i	0.211905	−	0.367030i	−0.740406	−	0.672160i	$-0.765367\pi$
$541$	4.92878	−	8.53690i	0.211905	−	0.367030i	0.952311	+	0.305130i	$0.0986999\pi$
$542$		0			0
$543$	−10.1809	−	20.9990i	−0.436902	−	0.901152i
$544$		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
$549$	36.6720	+	5.32985i	1.56512	+	0.227472i
$550$		0			0
$551$	−5.45185	−	9.44289i	−0.232257	−	0.402281i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	8.44662	+	0.610601i	0.358539	+	0.0259186i
$556$		0			0
$557$	10.1686	+	17.6125i	0.430857	+	0.746266i	0.996947	−	0.0780770i	$-0.0248780\pi$
$557$	10.1686	+	17.6125i	0.430857	+	0.746266i	−0.566090	+	0.824343i	$0.691545\pi$
$558$		0			0
$559$	6.63533			0.280644
$560$		0			0
$561$	2.67750	−	3.94951i	0.113044	−	0.166748i
$562$		0			0
$563$	10.0910	−	17.4781i	0.425284	−	0.736614i	−0.571163	−	0.820837i	$-0.693507\pi$
$563$	10.0910	−	17.4781i	0.425284	−	0.736614i	0.996447	+	0.0842230i	$0.0268408\pi$
$564$		0			0
$565$	−24.0957	−	41.7350i	−1.01371	−	1.75580i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.0525	−	20.8755i	−0.505266	−	0.875146i	−0.999981	−	0.00609110i	$-0.998061\pi$
$569$	−12.0525	−	20.8755i	−0.505266	−	0.875146i	0.494716	−	0.869055i	$-0.335272\pi$
$570$		0			0
$571$	−3.22763	+	5.59042i	−0.135072	+	0.233952i	−0.925625	−	0.378442i	$-0.876460\pi$
$571$	−3.22763	+	5.59042i	−0.135072	+	0.233952i	0.790553	+	0.612394i	$0.209793\pi$
$572$		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	0.608351	−	0.793668i	$-0.291831\pi$
$577$	−9.20385	−	15.9415i	−0.383161	−	0.663654i	−0.991512	+	0.130014i	$0.958498\pi$
$578$		0			0
$579$	11.7217	+	0.847356i	0.487139	+	0.0352149i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−14.6489	−	25.3726i	−0.606695	−	1.05083i
$584$		0			0
$585$	6.03517	+	0.877140i	0.249523	+	0.0362653i
$586$		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
$591$	14.0006	+	28.8776i	0.575909	+	1.18787i
$592$		0			0
$593$	−8.71630	+	15.0971i	−0.357935	+	0.619962i	−0.987616	−	0.156892i	$-0.949853\pi$
$593$	−8.71630	+	15.0971i	−0.357935	+	0.619962i	0.629680	+	0.776854i	$0.283186\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−16.3245	+	24.0798i	−0.668117	+	0.985520i
$598$		0			0
$599$	−1.72222	+	2.98297i	−0.0703680	+	0.121881i	−0.899063	−	0.437820i	$-0.855751\pi$
$599$	−1.72222	+	2.98297i	−0.0703680	+	0.121881i	0.828695	+	0.559701i	$0.189084\pi$
$600$		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
$605$	−16.2531			−0.660782
$606$		0			0
$607$	−19.9215			−0.808587			−0.404294	−	0.914629i	$-0.632483\pi$
$607$	−19.9215			−0.808587			−0.404294	+	0.914629i	$0.632483\pi$
$608$		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	−0.903186	−	0.429250i	$-0.858778\pi$
$613$	−20.3848	−	35.3075i	−0.823334	−	1.42606i	0.0798515	−	0.996807i	$-0.474555\pi$
$614$		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
$619$	−45.1168			−1.81340			−0.906698	−	0.421780i	$-0.861406\pi$
$619$	−45.1168			−1.81340			−0.906698	+	0.421780i	$0.861406\pi$
$620$		0			0
$621$	−32.4044	−	7.12697i	−1.30034	−	0.285996i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−10.0192			−0.400768
$626$		0			0
$627$	25.8013	+	1.86516i	1.03041	+	0.0744873i
$628$		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
$633$	20.9764	−	30.9417i	0.833738	−	1.22982i
$634$		0			0
$635$	72.2135			2.86570
$636$		0			0
$637$		0			0
$638$		0			0
$639$	9.16757	−	11.6209i	0.362664	−	0.459717i
$640$		0			0
$641$	14.2449			0.562640			0.281320	−	0.959614i	$-0.409228\pi$
$641$	14.2449			0.562640			0.281320	+	0.959614i	$0.409228\pi$
$642$		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	0.930032	−	0.367479i	$-0.119779\pi$
$647$	3.73327	+	6.46622i	0.146770	+	0.254213i	−0.783262	+	0.621692i	$0.786446\pi$
$648$		0			0
$649$	5.60449	−	9.70727i	0.219996	−	0.381043i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−40.1090			−1.56959			−0.784794	−	0.619757i	$-0.787231\pi$
$653$	−40.1090			−1.56959			−0.784794	+	0.619757i	$0.787231\pi$
$654$		0			0
$655$	−5.56383			−0.217397
$656$		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
$661$	−11.0643	+	19.1640i	−0.430352	+	0.745392i	−0.996904	−	0.0786346i	$-0.974944\pi$
$661$	−11.0643	+	19.1640i	−0.430352	+	0.745392i	0.566551	+	0.824026i	$0.308277\pi$
$662$		0			0
$663$	−1.10518	−	0.0798930i	−0.0429218	−	0.00310279i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.86382	−	10.1564i	0.227048	−	0.393259i
$668$		0			0
$669$	−1.71300	−	0.123832i	−0.0662285	−	0.00478761i
$670$		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
$675$	−36.0705	−	7.93329i	−1.38836	−	0.305353i
$676$		0			0
$677$	−10.0105	−	17.3387i	−0.384736	−	0.666382i	0.606997	−	0.794704i	$-0.292374\pi$
$677$	−10.0105	−	17.3387i	−0.384736	−	0.666382i	−0.991732	+	0.128323i	$0.959041\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.21498	−	4.56860i	−0.0848781	−	0.175069i
$682$		0			0
$683$	−10.7716	−	18.6569i	−0.412162	−	0.713886i	0.582964	−	0.812498i	$-0.301893\pi$
$683$	−10.7716	−	18.6569i	−0.412162	−	0.713886i	−0.995126	+	0.0986124i	$0.968560\pi$
$684$		0			0
$685$	−26.6267			−1.01735
$686$		0			0
$687$	3.31265	+	6.83265i	0.126385	+	0.260682i
$688$		0			0
$689$	−3.40182	+	5.89213i	−0.129599	+	0.224472i
$690$		0			0
$691$	21.8693	+	37.8787i	0.831947	+	1.44097i	0.896492	+	0.443060i	$0.146107\pi$
$691$	21.8693	+	37.8787i	0.831947	+	1.44097i	−0.0645449	+	0.997915i	$0.520560\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	27.8168	+	48.1802i	1.05515	+	1.82758i
$696$		0			0
$697$	5.88972	−	10.2013i	0.223089	−	0.386402i
$698$		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
$705$	−25.4702	+	37.5703i	−0.959263	+	1.41498i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−18.4050	−	31.8784i	−0.691214	−	1.19722i	−0.971440	−	0.237284i	$-0.923743\pi$
$709$	−18.4050	−	31.8784i	−0.691214	−	1.19722i	0.280226	−	0.959934i	$-0.409591\pi$
$710$		0			0
$711$	−1.66375	−	0.241807i	−0.0623956	−	0.00906847i
$712$		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
$717$	−3.72096	+	5.48868i	−0.138962	+	0.204978i
$718$		0			0
$719$	−15.8787	+	27.5028i	−0.592177	+	1.02568i	0.401762	+	0.915744i	$0.368398\pi$
$719$	−15.8787	+	27.5028i	−0.592177	+	1.02568i	−0.993939	+	0.109936i	$0.964935\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	9.76670	+	20.1447i	0.363227	+	0.749191i
$724$		0			0
$725$	6.52723	−	11.3055i	0.242415	−	0.419875i
$726$		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
$731$	12.4370			0.459999
$732$		0			0
$733$	23.9853			0.885917			0.442958	−	0.896542i	$-0.353929\pi$
$733$	23.9853			0.885917			0.442958	+	0.896542i	$0.353929\pi$
$734$		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	0.869008	−	0.494798i	$-0.164758\pi$
$739$	0.162996	+	0.282317i	0.00599590	+	0.0103852i	−0.863012	+	0.505184i	$0.831425\pi$
$740$		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
$745$	−10.0028			−0.366473
$746$		0			0
$747$	−8.18546	−	20.5372i	−0.299490	−	0.751416i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	31.3955			1.14564			0.572820	−	0.819681i	$-0.305850\pi$
$751$	31.3955			1.14564			0.572820	+	0.819681i	$0.305850\pi$
$752$		0			0
$753$	−14.8595	−	30.6492i	−0.541512	−	1.11692i
$754$		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
$759$	12.1382	+	25.0361i	0.440587	+	0.908753i
$760$		0			0
$761$	−13.3801			−0.485028			−0.242514	−	0.970148i	$-0.577972\pi$
$761$	−13.3801			−0.485028			−0.242514	+	0.970148i	$0.577972\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.3121	+	1.64408i	0.408989	+	0.0594417i
$766$		0			0
$767$	−2.60300			−0.0939887
$768$		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	−0.999998	−	0.00189699i	$-0.999396\pi$
$773$	−13.9471	−	24.1571i	−0.501642	−	0.868869i	0.498356	−	0.866972i	$-0.333937\pi$
$774$		0			0
$775$	−25.0099	+	43.3185i	−0.898384	+	1.55605i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	63.8615			2.28808
$780$		0			0
$781$	−12.4125			−0.444155
$782$		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
$787$	−0.0522535	+	0.0905057i	−0.00186264	+	0.00322618i	−0.866955	−	0.498386i	$-0.833926\pi$
$787$	−0.0522535	+	0.0905057i	−0.00186264	+	0.00322618i	0.865093	+	0.501612i	$0.167260\pi$
$788$		0			0
$789$	6.70684	+	13.8335i	0.238770	+	0.492486i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.60827	+	6.24971i	−0.128133	+	0.221934i
$794$		0			0
$795$	39.3848	−	58.0953i	1.39683	−	2.06043i
$796$		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
$801$	−13.4899	−	33.8461i	−0.476644	−	1.19589i
$802$		0			0
$803$	−10.9576	−	18.9791i	−0.386685	−	0.669758i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	17.7928	−	26.2456i	0.626335	−	0.923888i
$808$		0			0
$809$	22.1259	+	38.3233i	0.777907	+	1.34737i	0.933146	+	0.359497i	$0.117052\pi$
$809$	22.1259	+	38.3233i	0.777907	+	1.34737i	−0.155239	+	0.987877i	$0.549615\pi$
$810$		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
$815$	−24.9972	+	43.2964i	−0.875613	+	1.51661i
$816$		0			0
$817$	33.7132	+	58.3930i	1.17948	+	2.04291i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.1783	−	40.1459i	−0.808927	−	1.40110i	−0.913608	−	0.406596i	$-0.866716\pi$
$821$	−23.1783	−	40.1459i	−0.808927	−	1.40110i	0.104681	−	0.994506i	$-0.466618\pi$
$822$		0			0
$823$	15.4915	−	26.8320i	0.539998	−	0.935305i	−0.458905	−	0.888485i	$-0.651758\pi$
$823$	15.4915	−	26.8320i	0.539998	−	0.935305i	0.998903	−	0.0468193i	$-0.0149085\pi$
$824$		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	0.954373	+	0.298619i	$0.0965258\pi$
$829$	21.1853	+	36.6941i	0.735798	+	1.27444i	−0.218575	+	0.975820i	$0.570141\pi$
$830$		0			0
$831$	4.27389	+	8.81531i	0.148260	+	0.305800i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.29123	+	14.3608i	0.286930	+	0.496977i
$836$		0			0
$837$	24.6595	−	27.0018i	0.852357	−	0.933318i
$838$		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
$843$	−18.5320	−	1.33967i	−0.638277	−	0.0461407i
$844$		0			0
$845$	22.0237	−	38.1461i	0.757637	−	1.31227i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	41.1338	+	2.97354i	1.41171	+	0.102052i
$850$		0			0
$851$	4.48615	−	7.77024i	0.153783	−	0.266360i
$852$		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
$857$	−12.1221			−0.414084			−0.207042	−	0.978332i	$-0.566384\pi$
$857$	−12.1221			−0.414084			−0.207042	+	0.978332i	$0.566384\pi$
$858$		0			0
$859$	−6.83252			−0.233123			−0.116561	−	0.993183i	$-0.537187\pi$
$859$	−6.83252			−0.233123			−0.116561	+	0.993183i	$0.537187\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.2595	+	45.4827i	−0.893882	+	1.54825i	−0.0587005	+	0.998276i	$0.518696\pi$
$863$	−26.2595	+	45.4827i	−0.893882	+	1.54825i	−0.835182	+	0.549974i	$0.814638\pi$
$864$		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
$871$	−7.40249			−0.250824
$872$		0			0
$873$	−15.5166	−	38.9309i	−0.525157	−	1.31761i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	32.1564			1.08584			0.542922	−	0.839783i	$-0.317318\pi$
$877$	32.1564			1.08584			0.542922	+	0.839783i	$0.317318\pi$
$878$		0			0
$879$	20.0828	−	29.6235i	0.677375	−	0.999175i
$880$		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
$885$	26.7828	+	1.93611i	0.900295	+	0.0650818i
$886$		0			0
$887$	44.4566			1.49270			0.746352	−	0.665551i	$-0.231803\pi$
$887$	44.4566			1.49270			0.746352	+	0.665551i	$0.231803\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.27075	−	22.0198i	−0.176577	−	0.737691i
$892$		0			0
$893$	44.7109			1.49619
$894$		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
$905$	−46.8826			−1.55843
$906$		0			0
$907$	−16.4478			−0.546142			−0.273071	−	0.961994i	$-0.588039\pi$
$907$	−16.4478			−0.546142			−0.273071	+	0.961994i	$0.588039\pi$
$908$		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
$913$	−9.26987	+	16.0559i	−0.306788	+	0.531372i
$914$		0			0
$915$	41.7749	−	61.6209i	1.38104	−	2.03712i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−29.2722	+	50.7009i	−0.965600	+	1.67247i	−0.257606	+	0.966250i	$0.582934\pi$
$919$	−29.2722	+	50.7009i	−0.965600	+	1.67247i	−0.707994	+	0.706219i	$0.750400\pi$
$920$		0			0
$921$	9.00902	+	18.5820i	0.296857	+	0.612296i
$922$		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
$927$	0.890160	−	1.12838i	0.0292367	−	0.0370608i
$928$		0			0
$929$	−0.318672	−	0.551956i	−0.0104553	−	0.0181091i	0.860750	−	0.509027i	$-0.169995\pi$
$929$	−0.318672	−	0.551956i	−0.0104553	−	0.0181091i	−0.871206	+	0.490918i	$0.836661\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	15.7771	+	1.14052i	0.516521	+	0.0373389i
$934$		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
$941$	−14.8153	+	25.6609i	−0.482965	+	0.836521i	−0.999809	−	0.0195594i	$-0.993774\pi$
$941$	−14.8153	+	25.6609i	−0.482965	+	0.836521i	0.516843	+	0.856080i	$0.327107\pi$
$942$		0			0
$943$	34.3436	+	59.4848i	1.11838	+	1.93709i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.1681	−	29.7360i	−0.557888	−	0.966290i	−0.997673	−	0.0681867i	$-0.978279\pi$
$947$	−17.1681	−	29.7360i	−0.557888	−	0.966290i	0.439785	−	0.898103i	$-0.355055\pi$
$948$		0			0
$949$	−2.54461	+	4.40740i	−0.0826017	+	0.143070i
$950$		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
$957$	7.98230	+	0.577036i	0.258031	+	0.0186529i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9.26272	−	16.0435i	−0.298798	−	0.517533i
$962$		0			0
$963$	5.95090	+	14.9307i	0.191765	+	0.481136i
$964$		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
$969$	−4.91220	−	10.1319i	−0.157803	−	0.325483i
$970$		0			0
$971$	11.9191	−	20.6446i	0.382503	−	0.662515i	−0.608916	−	0.793235i	$-0.708395\pi$
$971$	11.9191	−	20.6446i	0.382503	−	0.662515i	0.991419	+	0.130719i	$0.0417287\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	4.03587	−	5.95318i	0.129251	−	0.190654i
$976$		0			0
$977$	−19.0842	+	33.0547i	−0.610556	+	1.05751i	0.380591	+	0.924744i	$0.375721\pi$
$977$	−19.0842	+	33.0547i	−0.610556	+	1.05751i	−0.991147	+	0.132771i	$0.957613\pi$
$978$		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
$983$	7.57537			0.241617			0.120808	−	0.992676i	$-0.461451\pi$
$983$	7.57537			0.241617			0.120808	+	0.992676i	$0.461451\pi$
$984$		0			0
$985$	64.4726			2.05427
$986$		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	0.930846	−	0.365411i	$-0.119072\pi$
$991$	4.68952	+	8.12248i	0.148967	+	0.258019i	−0.781879	+	0.623431i	$0.785738\pi$
$992$		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
$997$	−8.43658			−0.267189			−0.133595	−	0.991036i	$-0.542652\pi$
$997$	−8.43658			−0.267189			−0.133595	+	0.991036i	$0.542652\pi$
$998$		0			0
$999$	−4.92372	+	5.39140i	−0.155780	+	0.170576i

Twists

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

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

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.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.755620 + 1.55854i) q^{3} +3.47961 q^{5} +(-1.85808 + 2.35532i) q^{9} +O(q^{10})\)	\(q+(0.755620 + 1.55854i) q^{3} +3.47961 q^{5} +(-1.85808 + 2.35532i) q^{9} +2.51576 q^{11} +(-0.292110 - 0.505949i) q^{13} +(2.62926 + 5.42310i) q^{15} +(-0.547519 - 0.948331i) q^{17} +(2.96834 - 5.14132i) q^{19} +6.38528 q^{23} +7.10769 q^{25} +(-5.07486 - 1.11616i) q^{27} +(0.918333 - 1.59060i) q^{29} +(-3.51872 + 6.09459i) q^{31} +(1.90096 + 3.92091i) q^{33} +(0.702576 - 1.21690i) q^{37} +(0.567817 - 0.837570i) q^{39} +(5.37855 + 9.31593i) q^{41} +(-5.67879 + 9.83596i) q^{43} +(-6.46539 + 8.19561i) q^{45} +(3.76565 + 6.52229i) q^{47} +(1.06429 - 1.56991i) q^{51} +(-5.82285 - 10.0855i) q^{53} +8.75386 q^{55} +(10.2559 + 0.741391i) q^{57} +(2.22775 - 3.85858i) q^{59} +(-6.17622 - 10.6975i) q^{61} +(-1.01643 - 1.76051i) q^{65} +(6.33536 - 10.9732i) q^{67} +(4.82485 + 9.95170i) q^{69} -4.93390 q^{71} +(-4.35558 - 7.54408i) q^{73} +(5.37071 + 11.0776i) q^{75} +(0.280206 + 0.485330i) q^{79} +(-2.09509 - 8.75275i) q^{81} +(-3.68472 + 6.38212i) q^{83} +(-1.90515 - 3.29982i) q^{85} +(3.17292 + 0.229368i) q^{87} +(-6.07256 + 10.5180i) q^{89} +(-12.1575 - 0.878855i) q^{93} +(10.3287 - 17.8898i) q^{95} +(-6.98486 + 12.0981i) q^{97} +(-4.67448 + 5.92543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} + 8 q^{11} - 28 q^{15} + 16 q^{23} + 24 q^{25} - 32 q^{29} - 12 q^{37} + 32 q^{51} - 16 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} - 8 q^{81} + 12 q^{85} + 32 q^{95} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^11 - 28 * q^15 + 16 * q^23 + 24 * q^25 - 32 * q^29 - 12 * q^37 + 32 * q^51 - 16 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 - 8 * q^81 + 12 * q^85 + 32 * q^95 - 4 * q^99

Introduction

L-functions

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