LMFDB - Embedded newform 1764.2.j.i.1177.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(589,1764)]

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, 0]))

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

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

chi := DirichletCharacter("1764.589");

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.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.0856109166$
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			1177.12
Character	$\chi$	$=$	1764.1177
Dual form			1764.2.j.i.589.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72754 + 0.124883i) q^{3} +(1.73981 + 3.01343i) q^{5} +(2.96881 + 0.431481i) q^{9} +O(q^{10})$	\(q+(1.72754 + 0.124883i) q^{3} +(1.73981 + 3.01343i) q^{5} +(2.96881 + 0.431481i) q^{9} +(-1.25788 + 2.17871i) q^{11} +(0.292110 + 0.505949i) q^{13} +(2.62926 + 5.42310i) q^{15} -1.09504 q^{17} +5.93668 q^{19} +(-3.19264 - 5.52982i) q^{23} +(-3.55384 + 6.15544i) q^{25} +(5.07486 + 1.11616i) q^{27} +(0.918333 - 1.59060i) q^{29} +(3.51872 + 6.09459i) q^{31} +(-2.44513 + 3.60673i) q^{33} -1.40515 q^{37} +(0.441448 + 0.910529i) q^{39} +(-5.37855 - 9.31593i) q^{41} +(-5.67879 + 9.83596i) q^{43} +(3.86491 + 9.69699i) q^{45} +(-3.76565 + 6.52229i) q^{47} +(-1.89173 - 0.136752i) q^{51} +11.6457 q^{53} -8.75386 q^{55} +(10.2559 + 0.741391i) q^{57} +(-2.22775 - 3.85858i) q^{59} +(6.17622 - 10.6975i) q^{61} +(-1.01643 + 1.76051i) q^{65} +(6.33536 + 10.9732i) q^{67} +(-4.82485 - 9.95170i) q^{69} -4.93390 q^{71} -8.71115 q^{73} +(-6.90813 + 10.1900i) q^{75} +(0.280206 - 0.485330i) q^{79} +(8.62765 + 2.56197i) q^{81} +(3.68472 - 6.38212i) q^{83} +(-1.90515 - 3.29982i) q^{85} +(1.78510 - 2.63315i) q^{87} -12.1451 q^{89} +(5.31762 + 10.9681i) q^{93} +(10.3287 + 17.8898i) q^{95} +(6.98486 - 12.0981i) q^{97} +(-4.67448 + 5.92543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9}+O(q^{10}) $ 24 * q + 8 * q^9	$ 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93} + 32 q^{95} - 4 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.72754	+	0.124883i	0.997397	+	0.0721012i
$3$	1.72754	+	0.124883i	0.997397	+	0.0721012i
$4$		0			0
$5$	1.73981	+	3.01343i	0.778065	+	1.34765i	0.933056	+	0.359732i	$0.117132\pi$
$5$	1.73981	+	3.01343i	0.778065	+	1.34765i	−0.154991	+	0.987916i	$0.549535\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.96881	+	0.431481i	0.989603	+	0.143827i
$10$		0			0
$11$	−1.25788	+	2.17871i	−0.379265	+	0.656906i	−0.990956	−	0.134191i	$-0.957156\pi$
$11$	−1.25788	+	2.17871i	−0.379265	+	0.656906i	0.611690	+	0.791097i	$0.290490\pi$
$12$		0			0
$13$	0.292110	+	0.505949i	0.0810167	+	0.140325i	0.903687	−	0.428194i	$-0.140850\pi$
$13$	0.292110	+	0.505949i	0.0810167	+	0.140325i	−0.822670	+	0.568519i	$0.807517\pi$
$14$		0			0
$15$	2.62926	+	5.42310i	0.678873	+	1.40024i
$16$		0			0
$17$	−1.09504			−0.265586			−0.132793	−	0.991144i	$-0.542395\pi$
$17$	−1.09504			−0.265586			−0.132793	+	0.991144i	$0.542395\pi$
$18$		0			0
$19$	5.93668			1.36197			0.680984	−	0.732298i	$-0.261552\pi$
$19$	5.93668			1.36197			0.680984	+	0.732298i	$0.261552\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.19264	−	5.52982i	−0.665712	−	1.15305i	−0.979092	−	0.203419i	$-0.934795\pi$
$23$	−3.19264	−	5.52982i	−0.665712	−	1.15305i	0.313380	−	0.949628i	$-0.398539\pi$
$24$		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
$31$	3.51872	+	6.09459i	0.631980	+	1.09462i	0.987146	+	0.159818i	$0.0510909\pi$
$31$	3.51872	+	6.09459i	0.631980	+	1.09462i	−0.355166	+	0.934803i	$0.615576\pi$
$32$		0			0
$33$	−2.44513	+	3.60673i	−0.425642	+	0.627851i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.40515			−0.231006			−0.115503	−	0.993307i	$-0.536848\pi$
$37$	−1.40515			−0.231006			−0.115503	+	0.993307i	$0.536848\pi$
$38$		0			0
$39$	0.441448	+	0.910529i	0.0706883	+	0.145801i
$40$		0			0
$41$	−5.37855	−	9.31593i	−0.839989	−	1.45490i	−0.889903	−	0.456150i	$-0.849228\pi$
$41$	−5.37855	−	9.31593i	−0.839989	−	1.45490i	0.0499141	−	0.998754i	$-0.484105\pi$
$42$		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
$45$	3.86491	+	9.69699i	0.576147	+	1.44554i
$46$		0			0
$47$	−3.76565	+	6.52229i	−0.549276	+	0.951374i	0.449048	+	0.893507i	$0.351763\pi$
$47$	−3.76565	+	6.52229i	−0.549276	+	0.951374i	−0.998324	+	0.0578664i	$0.981570\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.89173	−	0.136752i	−0.264894	−	0.0191491i
$52$		0			0
$53$	11.6457			1.59966			0.799830	−	0.600227i	$-0.204923\pi$
$53$	11.6457			1.59966			0.799830	+	0.600227i	$0.204923\pi$
$54$		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	$-0.260332\pi$
$59$	−2.22775	−	3.85858i	−0.290029	−	0.502345i	−0.973816	+	0.227337i	$0.926998\pi$
$60$		0			0
$61$	6.17622	−	10.6975i	0.790784	−	1.36968i	−0.134698	−	0.990887i	$-0.543006\pi$
$61$	6.17622	−	10.6975i	0.790784	−	1.36968i	0.925482	−	0.378792i	$-0.123660\pi$
$62$		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	0.935362	+	0.353693i	$0.115074\pi$
$67$	6.33536	+	10.9732i	0.773988	+	1.34059i	−0.161374	+	0.986893i	$0.551593\pi$
$68$		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
$73$	−8.71115			−1.01956			−0.509782	−	0.860304i	$-0.670274\pi$
$73$	−8.71115			−1.01956			−0.509782	+	0.860304i	$0.670274\pi$
$74$		0			0
$75$	−6.90813	+	10.1900i	−0.797682	+	1.17664i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.280206	−	0.485330i	0.0315256	−	0.0546039i	−0.849832	−	0.527053i	$-0.823297\pi$
$79$	0.280206	−	0.485330i	0.0315256	−	0.0546039i	0.881358	+	0.472450i	$0.156630\pi$
$80$		0			0
$81$	8.62765	+	2.56197i	0.958628	+	0.284663i
$82$		0			0
$83$	3.68472	−	6.38212i	0.404451	−	0.700529i	−0.589807	−	0.807544i	$-0.700796\pi$
$83$	3.68472	−	6.38212i	0.404451	−	0.700529i	0.994257	+	0.107015i	$0.0341294\pi$
$84$		0			0
$85$	−1.90515	−	3.29982i	−0.206643	−	0.357916i
$86$		0			0
$87$	1.78510	−	2.63315i	0.191383	−	0.282303i
$88$		0			0
$89$	−12.1451			−1.28738			−0.643690	−	0.765287i	$-0.722597\pi$
$89$	−12.1451			−1.28738			−0.643690	+	0.765287i	$0.722597\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.31762	+	10.9681i	0.551412	+	1.13734i
$94$		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	$-0.582387\pi$
$97$	6.98486	−	12.0981i	0.709205	−	1.22838i	0.965152	−	0.261688i	$-0.0842793\pi$
$98$		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	$-0.984248\pi$
$101$	−4.58825	+	7.94708i	−0.456548	+	0.790764i	0.542228	+	0.840231i	$0.317581\pi$
$102$		0			0
$103$	−0.239538	−	0.414892i	−0.0236024	−	0.0408805i	0.853983	−	0.520301i	$-0.174180\pi$
$103$	−0.239538	−	0.414892i	−0.0236024	−	0.0408805i	−0.877585	+	0.479420i	$0.840847\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.35765			−0.517943			−0.258972	−	0.965885i	$-0.583384\pi$
$107$	−5.35765			−0.517943			−0.258972	+	0.965885i	$0.583384\pi$
$108$		0			0
$109$	−15.7507			−1.50864			−0.754322	−	0.656505i	$-0.772034\pi$
$109$	−15.7507			−1.50864			−0.754322	+	0.656505i	$0.772034\pi$
$110$		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
$117$	0.648911	+	1.62811i	0.0599918	+	0.150519i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.33548	+	4.04516i	0.212316	+	0.367742i
$122$		0			0
$123$	−8.12828	−	16.7654i	−0.732902	−	1.51168i
$124$		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
$129$	−11.0387	+	16.2829i	−0.971903	+	1.43363i
$130$		0			0
$131$	−0.799491	−	1.38476i	−0.0698518	−	0.120987i	0.828984	−	0.559272i	$-0.188919\pi$
$131$	−0.799491	−	1.38476i	−0.0698518	−	0.120987i	−0.898836	+	0.438285i	$0.855586\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	5.46581	+	17.2346i	0.470422	+	1.48332i
$136$		0			0
$137$	3.82610	−	6.62700i	0.326886	−	0.566182i	−0.655007	−	0.755623i	$-0.727334\pi$
$137$	3.82610	−	6.62700i	0.326886	−	0.566182i	0.981892	+	0.189441i	$0.0606675\pi$
$138$		0			0
$139$	−7.99424	−	13.8464i	−0.678062	−	1.17444i	−0.975564	−	0.219717i	$-0.929487\pi$
$139$	−7.99424	−	13.8464i	−0.678062	−	1.17444i	0.297501	−	0.954721i	$-0.403847\pi$
$140$		0			0
$141$	−7.31984	+	10.7973i	−0.616442	+	0.909294i
$142$		0			0
$143$	−1.46976			−0.122907
$144$		0			0
$145$	6.39088			0.530734
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.43734	+	2.48955i	0.117752	+	0.203952i	0.918876	−	0.394546i	$-0.129098\pi$
$149$	1.43734	+	2.48955i	0.117752	+	0.203952i	−0.801125	+	0.598497i	$0.795765\pi$
$150$		0			0
$151$	−4.58076	+	7.93411i	−0.372777	+	0.645669i	−0.989992	−	0.141126i	$-0.954928\pi$
$151$	−4.58076	+	7.93411i	−0.372777	+	0.645669i	0.617215	+	0.786795i	$0.288261\pi$
$152$		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	0.999929	+	0.0119393i	$0.00380048\pi$
$157$	6.39409	+	11.0749i	0.510304	+	0.883873i	−0.489625	+	0.871933i	$0.662866\pi$
$158$		0			0
$159$	20.1184	+	1.45435i	1.59550	+	0.115337i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	14.3678			1.12537			0.562686	−	0.826671i	$-0.309768\pi$
$163$	14.3678			1.12537			0.562686	+	0.826671i	$0.309768\pi$
$164$		0			0
$165$	−15.1227	−	1.09321i	−1.17730	−	0.0851062i
$166$		0			0
$167$	−2.38280	−	4.12714i	−0.184387	−	0.319367i	0.758983	−	0.651111i	$-0.225697\pi$
$167$	−2.38280	−	4.12714i	−0.184387	−	0.319367i	−0.943370	+	0.331743i	$0.892363\pi$
$168$		0			0
$169$	6.32934	−	10.9627i	0.486873	−	0.843288i
$170$		0			0
$171$	17.6249	+	2.56157i	1.34781	+	0.195888i
$172$		0			0
$173$	12.5583	−	21.7517i	0.954792	−	1.65375i	0.219948	−	0.975512i	$-0.429411\pi$
$173$	12.5583	−	21.7517i	0.954792	−	1.65375i	0.734844	−	0.678237i	$-0.237256\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.36667	−	6.94407i	−0.253054	−	0.521949i
$178$		0			0
$179$	6.82336			0.510002			0.255001	−	0.966941i	$-0.417924\pi$
$179$	6.82336			0.510002			0.255001	+	0.966941i	$0.417924\pi$
$180$		0			0
$181$	13.4735			1.00148			0.500739	−	0.865598i	$-0.333062\pi$
$181$	13.4735			1.00148			0.500739	+	0.865598i	$0.333062\pi$
$182$		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	0.485901	+	0.874014i	$0.338492\pi$
$191$	−7.10318	+	12.3031i	−0.513968	+	0.890218i	−0.999869	+	0.0162045i	$0.994842\pi$
$192$		0			0
$193$	3.39260	+	5.87616i	0.244205	+	0.422975i	0.961908	−	0.273374i	$-0.0881397\pi$
$193$	3.39260	+	5.87616i	0.244205	+	0.422975i	−0.717703	+	0.696349i	$0.754806\pi$
$194$		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
$199$	16.7961			1.19064			0.595321	−	0.803488i	$-0.297025\pi$
$199$	16.7961			1.19064			0.595321	+	0.803488i	$0.297025\pi$
$200$		0			0
$201$	9.57425	+	19.7478i	0.675315	+	1.39290i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	18.7153	−	32.4158i	1.30713	−	2.26402i
$206$		0			0
$207$	−7.09233	−	17.7945i	−0.492951	−	1.23681i
$208$		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
$213$	−8.52353	−	0.616160i	−0.584022	−	0.0422186i
$214$		0			0
$215$	−39.5200			−2.69524
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−15.0489	−	1.08787i	−1.01691	−	0.0735117i
$220$		0			0
$221$	−0.319872	−	0.554034i	−0.0215169	−	0.0372683i
$222$		0			0
$223$	0.495791	−	0.858736i	0.0332006	−	0.0575052i	−0.848948	−	0.528477i	$-0.822763\pi$
$223$	0.495791	−	0.858736i	0.0332006	−	0.0575052i	0.882148	+	0.470972i	$0.156097\pi$
$224$		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	$-0.864348\pi$
$227$	−1.46567	+	2.53861i	−0.0972799	+	0.168494i	0.813278	+	0.581875i	$0.197681\pi$
$228$		0			0
$229$	2.19201	+	3.79667i	0.144852	+	0.250891i	0.929318	−	0.369281i	$-0.120396\pi$
$229$	2.19201	+	3.79667i	0.144852	+	0.250891i	−0.784466	+	0.620172i	$0.787063\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.08632			−0.0711670			−0.0355835	−	0.999367i	$-0.511329\pi$
$233$	−1.08632			−0.0711670			−0.0355835	+	0.999367i	$0.511329\pi$
$234$		0			0
$235$	−26.2060			−1.70949
$236$		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	$-0.696660\pi$
$241$	6.46271	−	11.1937i	0.416300	−	0.721052i	0.995564	+	0.0940877i	$0.0299934\pi$
$242$		0			0
$243$	14.5847	+	5.50336i	0.935608	+	0.353041i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.73416	+	3.00366i	0.110342	+	0.191118i
$248$		0			0
$249$	7.16253	−	10.5652i	0.453907	−	0.669544i
$250$		0			0
$251$	19.6654			1.24127			0.620634	−	0.784101i	$-0.286875\pi$
$251$	19.6654			1.24127			0.620634	+	0.784101i	$0.286875\pi$
$252$		0			0
$253$	16.0638			1.00992
$254$		0			0
$255$	−2.87914	−	5.93850i	−0.180299	−	0.371884i
$256$		0			0
$257$	−12.6799	−	21.9622i	−0.790948	−	1.36996i	−0.925381	−	0.379039i	$-0.876255\pi$
$257$	−12.6799	−	21.9622i	−0.790948	−	1.36996i	0.134433	−	0.990923i	$-0.457079\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.41267	−	4.32594i	0.211239	−	0.267769i
$262$		0			0
$263$	−4.43798	+	7.68680i	−0.273657	+	0.473988i	−0.969796	−	0.243919i	$-0.921567\pi$
$263$	−4.43798	+	7.68680i	−0.273657	+	0.473988i	0.696138	+	0.717908i	$0.254900\pi$
$264$		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
$269$	−18.3068			−1.11618			−0.558092	−	0.829779i	$-0.688466\pi$
$269$	−18.3068			−1.11618			−0.558092	+	0.829779i	$0.688466\pi$
$270$		0			0
$271$	−4.68930			−0.284855			−0.142427	−	0.989805i	$-0.545491\pi$
$271$	−4.68930			−0.284855			−0.142427	+	0.989805i	$0.545491\pi$
$272$		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	−0.938392	−	0.345572i	$-0.887685\pi$
$277$	−2.82807	+	4.89836i	−0.169922	+	0.294314i	0.768470	+	0.639886i	$0.221018\pi$
$278$		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	−0.965710	−	0.259625i	$-0.916401\pi$
$283$	−11.9053	−	20.6206i	−0.707697	−	1.22577i	0.258013	−	0.966141i	$-0.416932\pi$
$284$		0			0
$285$	15.6091	+	32.1953i	0.924603	+	1.90708i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−15.8009			−0.929464
$290$		0			0
$291$	13.5775	−	20.0278i	0.795927	−	1.17405i
$292$		0			0
$293$	10.3315	+	17.8946i	0.603570	+	1.04541i	0.992276	+	0.124052i	$0.0395889\pi$
$293$	10.3315	+	17.8946i	0.603570	+	1.04541i	−0.388706	+	0.921362i	$0.627078\pi$
$294$		0			0
$295$	7.75171	−	13.4264i	0.451322	−	0.781713i
$296$		0			0
$297$	−8.81535	+	9.65267i	−0.511518	+	0.560104i
$298$		0			0
$299$	1.86521	−	3.23063i	0.107868	−	0.186832i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−8.91885	+	13.1559i	−0.512374	+	0.755788i
$304$		0			0
$305$	42.9817			2.46112
$306$		0			0
$307$	−11.9227			−0.680464			−0.340232	−	0.940342i	$-0.610506\pi$
$307$	−11.9227			−0.680464			−0.340232	+	0.940342i	$0.610506\pi$
$308$		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	$-0.250038\pi$
$311$	−4.56635	−	7.90916i	−0.258934	−	0.448487i	−0.965957	+	0.258704i	$0.916705\pi$
$312$		0			0
$313$	6.91980	−	11.9854i	0.391130	−	0.677457i	−0.601469	−	0.798896i	$-0.705418\pi$
$313$	6.91980	−	11.9854i	0.391130	−	0.677457i	0.992599	+	0.121439i	$0.0387509\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.915786	+	1.58619i	−0.0514357	+	0.0890892i	−0.890597	−	0.454794i	$-0.849713\pi$
$317$	−0.915786	+	1.58619i	−0.0514357	+	0.0890892i	0.839161	+	0.543883i	$0.183046\pi$
$318$		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
$325$	−4.15245			−0.230337
$326$		0			0
$327$	−27.2100	−	1.96699i	−1.50472	−	0.108775i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.103132	−	0.178630i	0.00566864	−	0.00981838i	−0.863177	−	0.504901i	$-0.831529\pi$
$331$	0.103132	−	0.178630i	0.00566864	−	0.00981838i	0.868846	+	0.495083i	$0.164862\pi$
$332$		0			0
$333$	−4.17163	−	0.606297i	−0.228604	−	0.0332249i
$334$		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
$339$	−10.4651	−	21.5852i	−0.568385	−	1.17235i
$340$		0			0
$341$	−17.7045			−0.958752
$342$		0			0
$343$		0			0
$344$		0			0
$345$	21.5945	−	31.8534i	1.16261	−	1.71493i
$346$		0			0
$347$	1.60907	+	2.78698i	0.0863792	+	0.149613i	0.905978	−	0.423325i	$-0.139137\pi$
$347$	1.60907	+	2.78698i	0.0863792	+	0.149613i	−0.819599	+	0.572938i	$0.805804\pi$
$348$		0			0
$349$	7.04006	−	12.1937i	0.376846	−	0.652716i	−0.613756	−	0.789496i	$-0.710342\pi$
$349$	7.04006	−	12.1937i	0.376846	−	0.652716i	0.990601	+	0.136780i	$0.0436753\pi$
$350$		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	$-0.861913\pi$
$353$	−1.68465	+	2.91790i	−0.0896648	+	0.155304i	0.817705	+	0.575638i	$0.195246\pi$
$354$		0			0
$355$	−8.58403	−	14.8680i	−0.455593	−	0.789110i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.5783			−0.769411			−0.384706	−	0.923039i	$-0.625697\pi$
$359$	−14.5783			−0.769411			−0.384706	+	0.923039i	$0.625697\pi$
$360$		0			0
$361$	16.2442			0.854959
$362$		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	$-0.839454\pi$
$367$	−0.368367	+	0.638030i	−0.0192286	+	0.0333049i	0.856251	+	0.516560i	$0.172788\pi$
$368$		0			0
$369$	−11.9482	−	29.9779i	−0.622001	−	1.56059i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−14.4514	−	25.0306i	−0.748267	−	1.29604i	−0.948653	−	0.316320i	$-0.897553\pi$
$373$	−14.4514	−	25.0306i	−0.748267	−	1.29604i	0.200385	−	0.979717i	$-0.435781\pi$
$374$		0			0
$375$	−12.6697	−	0.915884i	−0.654260	−	0.0472961i
$376$		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
$381$	35.8523	+	2.59174i	1.83677	+	0.132779i
$382$		0			0
$383$	7.70273	+	13.3415i	0.393591	+	0.681720i	0.992920	−	0.118783i	$-0.0378992\pi$
$383$	7.70273	+	13.3415i	0.393591	+	0.681720i	−0.599329	+	0.800503i	$0.704566\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−21.1033	+	26.7508i	−1.07274	+	1.35982i
$388$		0			0
$389$	10.1570	−	17.5924i	0.514978	−	0.891968i	−0.484871	−	0.874586i	$-0.661133\pi$
$389$	10.1570	−	17.5924i	0.514978	−	0.891968i	0.999849	−	0.0173821i	$-0.00553318\pi$
$390$		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
$395$	1.95001			0.0981158
$396$		0			0
$397$	8.65790			0.434528			0.217264	−	0.976113i	$-0.430287\pi$
$397$	8.65790			0.434528			0.217264	+	0.976113i	$0.430287\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.5273	−	30.3582i	−0.875272	−	1.51602i	−0.856473	−	0.516192i	$-0.827349\pi$
$401$	−17.5273	−	30.3582i	−0.875272	−	1.51602i	−0.0187988	−	0.999823i	$-0.505984\pi$
$402$		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
$409$	−6.61681	−	11.4607i	−0.327180	−	0.566693i	0.654771	−	0.755827i	$-0.272765\pi$
$409$	−6.61681	−	11.4607i	−0.327180	−	0.566693i	−0.981951	+	0.189135i	$0.939432\pi$
$410$		0			0
$411$	7.43735	−	10.9706i	0.366857	−	0.541140i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	25.6428			1.25875
$416$		0			0
$417$	−12.0812	−	24.9186i	−0.591619	−	1.22027i
$418$		0			0
$419$	−4.43952	−	7.68947i	−0.216885	−	0.375655i	0.736969	−	0.675926i	$-0.236256\pi$
$419$	−4.43952	−	7.68947i	−0.216885	−	0.375655i	−0.953854	+	0.300271i	$0.902923\pi$
$420$		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
$423$	−13.9937	+	17.7386i	−0.680398	+	0.862482i
$424$		0			0
$425$	3.89160	−	6.74044i	0.188770	−	0.326959i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.53907	−	0.183548i	−0.122587	−	0.00886176i
$430$		0			0
$431$	−14.9710			−0.721126			−0.360563	−	0.932735i	$-0.617415\pi$
$431$	−14.9710			−0.721126			−0.360563	+	0.932735i	$0.617415\pi$
$432$		0			0
$433$	15.3215			0.736304			0.368152	−	0.929766i	$-0.379991\pi$
$433$	15.3215			0.736304			0.368152	+	0.929766i	$0.379991\pi$
$434$		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	$-0.740307\pi$
$439$	6.03657	−	10.4556i	0.288110	−	0.499021i	0.973359	+	0.229288i	$0.0736399\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.02894	+	10.4424i	−0.286444	+	0.496135i	−0.972958	−	0.230981i	$-0.925806\pi$
$443$	−6.02894	+	10.4424i	−0.286444	+	0.496135i	0.686515	+	0.727116i	$0.259140\pi$
$444$		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
$451$	27.0623			1.27431
$452$		0			0
$453$	−8.90430	+	13.1345i	−0.418360	+	0.617111i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.88323	+	4.99390i	−0.134872	+	0.233605i	−0.925548	−	0.378629i	$-0.876396\pi$
$457$	−2.88323	+	4.99390i	−0.134872	+	0.233605i	0.790677	+	0.612234i	$0.209729\pi$
$458$		0			0
$459$	−5.55716	−	1.22223i	−0.259386	−	0.0570490i
$460$		0			0
$461$	17.9138	−	31.0277i	0.834330	−	1.44510i	−0.0602447	−	0.998184i	$-0.519188\pi$
$461$	17.9138	−	31.0277i	0.834330	−	1.44510i	0.894575	−	0.446918i	$-0.147479\pi$
$462$		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
$465$	−23.8000	+	35.1066i	−1.10370	+	1.62803i
$466$		0			0
$467$	−2.85477			−0.132103			−0.0660515	−	0.997816i	$-0.521040\pi$
$467$	−2.85477			−0.132103			−0.0660515	+	0.997816i	$0.521040\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	9.66300	+	19.9309i	0.445248	+	0.918366i
$472$		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
$479$	−2.18688	+	3.78779i	−0.0999211	+	0.173068i	−0.911652	−	0.410964i	$-0.865192\pi$
$479$	−2.18688	+	3.78779i	−0.0999211	+	0.173068i	0.811731	+	0.584032i	$0.198526\pi$
$480$		0			0
$481$	−0.410459	−	0.710936i	−0.0187153	−	0.0324159i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	48.6092			2.20723
$486$		0			0
$487$	−30.5357			−1.38370			−0.691852	−	0.722039i	$-0.743205\pi$
$487$	−30.5357			−1.38370			−0.691852	+	0.722039i	$0.743205\pi$
$488$		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
$495$	−25.9885	−	3.77713i	−1.16810	−	0.169769i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	11.3852	+	19.7197i	0.509670	+	0.882774i	0.999937	+	0.0112020i	$0.00356578\pi$
$499$	11.3852	+	19.7197i	0.509670	+	0.882774i	−0.490267	+	0.871572i	$0.663101\pi$
$500$		0			0
$501$	−3.60099	−	7.42738i	−0.160880	−	0.331831i
$502$		0			0
$503$	24.0843			1.07387			0.536933	−	0.843625i	$-0.319583\pi$
$503$	24.0843			1.07387			0.536933	+	0.843625i	$0.319583\pi$
$504$		0			0
$505$	−31.9306			−1.42089
$506$		0			0
$507$	12.3033	−	18.1482i	0.546407	−	0.805989i
$508$		0			0
$509$	12.2350	+	21.1917i	0.542307	+	0.939304i	0.998771	+	0.0495618i	$0.0157825\pi$
$509$	12.2350	+	21.1917i	0.542307	+	0.939304i	−0.456464	+	0.889742i	$0.650884\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	30.1278	+	6.62627i	1.33018	+	0.292557i
$514$		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
$521$	38.7487			1.69761			0.848805	−	0.528707i	$-0.177323\pi$
$521$	38.7487			1.69761			0.848805	+	0.528707i	$0.177323\pi$
$522$		0			0
$523$	25.6945			1.12354			0.561771	−	0.827293i	$-0.310120\pi$
$523$	25.6945			1.12354			0.561771	+	0.827293i	$0.310120\pi$
$524$		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
$535$	−9.32127	−	16.1449i	−0.402993	−	0.698005i
$536$		0			0
$537$	11.7876	+	0.852121i	0.508674	+	0.0367717i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−9.85757			−0.423810			−0.211905	−	0.977290i	$-0.567967\pi$
$541$	−9.85757			−0.423810			−0.211905	+	0.977290i	$0.567967\pi$
$542$		0			0
$543$	23.2761	+	1.68261i	0.998872	+	0.0722078i
$544$		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
$549$	22.9518	−	29.0940i	0.979559	−	1.24170i
$550$		0			0
$551$	5.45185	−	9.44289i	0.232257	−	0.402281i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−3.69452	−	7.62029i	−0.156823	−	0.323463i
$556$		0			0
$557$	−20.3372			−0.861714			−0.430857	−	0.902420i	$-0.641789\pi$
$557$	−20.3372			−0.861714			−0.430857	+	0.902420i	$0.641789\pi$
$558$		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	$-0.306493\pi$
$563$	−10.0910	−	17.4781i	−0.425284	−	0.736614i	−0.996447	+	0.0842230i	$0.973159\pi$
$564$		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	0.494716	+	0.869055i	$0.335272\pi$
$569$	−12.0525	+	20.8755i	−0.505266	+	0.875146i	−0.999981	+	0.00609110i	$0.998061\pi$
$570$		0			0
$571$	−3.22763	−	5.59042i	−0.135072	−	0.233952i	0.790553	−	0.612394i	$-0.209793\pi$
$571$	−3.22763	−	5.59042i	−0.135072	−	0.233952i	−0.925625	+	0.378442i	$0.876460\pi$
$572$		0			0
$573$	−13.8075	+	20.3670i	−0.576816	+	0.850844i
$574$		0			0
$575$	45.3846			1.89267
$576$		0			0
$577$	−18.4077			−0.766322			−0.383161	−	0.923682i	$-0.625165\pi$
$577$	−18.4077			−0.766322			−0.383161	+	0.923682i	$0.625165\pi$
$578$		0			0
$579$	5.12703	+	10.5750i	0.213072	+	0.439482i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−14.6489	+	25.3726i	−0.606695	+	1.05083i
$584$		0			0
$585$	−3.77721	+	4.78804i	−0.156168	+	0.197961i
$586$		0			0
$587$	−22.8848	+	39.6376i	−0.944557	+	1.63602i	−0.187921	+	0.982184i	$0.560175\pi$
$587$	−22.8848	+	39.6376i	−0.944557	+	1.63602i	−0.756636	+	0.653837i	$0.773158\pi$
$588$		0			0
$589$	20.8895	+	36.1817i	0.860737	+	1.49084i
$590$		0			0
$591$	32.0091	+	2.31392i	1.31668	+	0.0951818i
$592$		0			0
$593$	−17.4326			−0.715871			−0.357935	−	0.933746i	$-0.616519\pi$
$593$	−17.4326			−0.715871			−0.357935	+	0.933746i	$0.616519\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	29.0159	+	2.09754i	1.18754	+	0.0858468i
$598$		0			0
$599$	−1.72222	−	2.98297i	−0.0703680	−	0.121881i	0.828695	−	0.559701i	$-0.189084\pi$
$599$	−1.72222	−	2.98297i	−0.0703680	−	0.121881i	−0.899063	+	0.437820i	$0.855751\pi$
$600$		0			0
$601$	−12.1666	+	21.0731i	−0.496284	+	0.859590i	−0.999991	−	0.00428500i	$-0.998636\pi$
$601$	−12.1666	+	21.0731i	−0.496284	+	0.859590i	0.503706	+	0.863875i	$0.331969\pi$
$602$		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	$-0.299149\pi$
$607$	−9.96073	−	17.2525i	−0.404294	−	0.700257i	−0.994239	+	0.107186i	$0.965816\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.39993			−0.178002
$612$		0			0
$613$	40.7696			1.64667			0.823334	−	0.567557i	$-0.192111\pi$
$613$	40.7696			1.64667			0.823334	+	0.567557i	$0.192111\pi$
$614$		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	−0.0880774	+	0.996114i	$0.528072\pi$
$619$	−22.5584	+	39.0723i	−0.906698	+	1.57045i	−0.818621	+	0.574334i	$0.805261\pi$
$620$		0			0
$621$	−10.0301	−	31.6265i	−0.402493	−	1.26913i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5.00960	+	8.67688i	0.200384	+	0.347075i
$626$		0			0
$627$	−14.5159	+	21.4120i	−0.579711	+	0.855114i
$628$		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
$633$	−16.3081	−	33.6369i	−0.648188	−	1.33695i
$634$		0			0
$635$	36.1067	+	62.5387i	1.43285	+	2.48177i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−14.6478	−	2.12889i	−0.579458	−	0.0842174i
$640$		0			0
$641$	−7.12245	+	12.3365i	−0.281320	+	0.487261i	−0.971710	−	0.236177i	$-0.924106\pi$
$641$	−7.12245	+	12.3365i	−0.281320	+	0.487261i	0.690390	+	0.723437i	$0.257439\pi$
$642$		0			0
$643$	−18.0592	−	31.2795i	−0.712187	−	1.23354i	−0.964035	−	0.265777i	$-0.914372\pi$
$643$	−18.0592	−	31.2795i	−0.712187	−	1.23354i	0.251848	−	0.967767i	$-0.418962\pi$
$644$		0			0
$645$	−68.2724	−	4.93537i	−2.68822	−	0.194330i
$646$		0			0
$647$	7.46655			0.293540			0.146770	−	0.989171i	$-0.453112\pi$
$647$	7.46655			0.293540			0.146770	+	0.989171i	$0.453112\pi$
$648$		0			0
$649$	11.2090			0.439991
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.0545	+	34.7354i	0.784794	+	1.35930i	0.929122	+	0.369773i	$0.120564\pi$
$653$	20.0545	+	34.7354i	0.784794	+	1.35930i	−0.144329	+	0.989530i	$0.546102\pi$
$654$		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
$661$	11.0643	+	19.1640i	0.430352	+	0.745392i	0.996904	−	0.0786346i	$-0.0250560\pi$
$661$	11.0643	+	19.1640i	0.430352	+	0.745392i	−0.566551	+	0.824026i	$0.691723\pi$
$662$		0			0
$663$	−0.483402	−	0.997064i	−0.0187738	−	0.0387227i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−11.7276			−0.454096
$668$		0			0
$669$	0.963742	−	1.42159i	0.0372604	−	0.0549617i
$670$		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
$675$	−24.9057	+	27.2713i	−0.958621	+	1.04967i
$676$		0			0
$677$	10.0105	−	17.3387i	0.384736	−	0.666382i	−0.606997	−	0.794704i	$-0.707626\pi$
$677$	10.0105	−	17.3387i	0.384736	−	0.666382i	0.991732	+	0.128323i	$0.0409593\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.84904	+	4.20253i	−0.109175	+	0.161041i
$682$		0			0
$683$	21.5431			0.824324			0.412162	−	0.911111i	$-0.364774\pi$
$683$	21.5431			0.824324			0.412162	+	0.911111i	$0.364774\pi$
$684$		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	0.0645449	+	0.997915i	$0.479440\pi$
$691$	−21.8693	+	37.8787i	−0.831947	+	1.44097i	−0.896492	+	0.443060i	$0.853893\pi$
$692$		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
$703$	−8.34195			−0.314623
$704$		0			0
$705$	−45.2719	−	3.27268i	−1.70504	−	0.123256i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−18.4050	+	31.8784i	−0.691214	+	1.19722i	0.280226	+	0.959934i	$0.409591\pi$
$709$	−18.4050	+	31.8784i	−0.691214	+	1.19722i	−0.971440	+	0.237284i	$0.923743\pi$
$710$		0			0
$711$	1.04129	−	1.31995i	0.0390513	−	0.0495020i
$712$		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
$717$	2.89285	+	5.96679i	0.108036	+	0.222834i
$718$		0			0
$719$	−31.7575			−1.18435			−0.592177	−	0.805808i	$-0.701731\pi$
$719$	−31.7575			−1.18435			−0.592177	+	0.805808i	$0.701731\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	12.5625	−	18.5306i	0.467205	−	0.689160i
$724$		0			0
$725$	6.52723	+	11.3055i	0.242415	+	0.419875i
$726$		0			0
$727$	2.83596	−	4.91203i	0.105180	−	0.182177i	−0.808632	−	0.588315i	$-0.799791\pi$
$727$	2.83596	−	4.91203i	0.105180	−	0.182177i	0.913812	+	0.406138i	$0.133125\pi$
$728$		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	$-0.0205956\pi$
$733$	11.9926	+	20.7719i	0.442958	+	0.767226i	−0.554949	+	0.831884i	$0.687262\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−31.8765			−1.17419
$738$		0			0
$739$	−0.325992			−0.0119918			−0.00599590	−	0.999982i	$-0.501909\pi$
$739$	−0.325992			−0.0119918			−0.00599590	+	0.999982i	$0.501909\pi$
$740$		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
$747$	13.6930	−	17.3574i	0.501000	−	0.635074i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−15.6978	−	27.1893i	−0.572820	−	0.992153i	−0.996275	−	0.0862357i	$-0.972516\pi$
$751$	−15.6978	−	27.1893i	−0.572820	−	0.992153i	0.423455	−	0.905917i	$-0.360817\pi$
$752$		0			0
$753$	33.9728	+	2.45587i	1.23804	+	0.0894969i
$754$		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
$759$	27.7510	+	2.00610i	1.00730	+	0.0728168i
$760$		0			0
$761$	−6.69005	−	11.5875i	−0.242514	−	0.420047i	0.718916	−	0.695097i	$-0.244639\pi$
$761$	−6.69005	−	11.5875i	−0.242514	−	0.420047i	−0.961430	+	0.275050i	$0.911305\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−4.23222	−	10.6186i	−0.153016	−	0.383915i
$766$		0			0
$767$	1.30150	−	2.25426i	0.0469944	−	0.0813966i
$768$		0			0
$769$	−5.98750	−	10.3707i	−0.215915	−	0.373975i	0.737640	−	0.675194i	$-0.235940\pi$
$769$	−5.98750	−	10.3707i	−0.215915	−	0.373975i	−0.953555	+	0.301218i	$0.902607\pi$
$770$		0			0
$771$	−19.1623	−	39.5241i	−0.690113	−	1.42342i
$772$		0			0
$773$	−27.8942			−1.00328			−0.501642	−	0.865075i	$-0.667270\pi$
$773$	−27.8942			−1.00328			−0.501642	+	0.865075i	$0.667270\pi$
$774$		0			0
$775$	−50.0199			−1.79677
$776$		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
$787$	0.0522535	+	0.0905057i	0.00186264	+	0.00322618i	0.866955	−	0.498386i	$-0.166074\pi$
$787$	0.0522535	+	0.0905057i	0.00186264	+	0.00322618i	−0.865093	+	0.501612i	$0.832740\pi$
$788$		0			0
$789$	−8.62674	+	12.7250i	−0.307120	+	0.453024i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	7.21654			0.256267
$794$		0			0
$795$	30.6196	+	63.1558i	1.08596	+	2.23991i
$796$		0			0
$797$	−17.5235	−	30.3516i	−0.620715	−	1.07511i	−0.989353	−	0.145537i	$-0.953509\pi$
$797$	−17.5235	−	30.3516i	−0.620715	−	1.07511i	0.368638	−	0.929573i	$-0.379824\pi$
$798$		0			0
$799$	4.12353	−	7.14216i	0.145880	−	0.252671i
$800$		0			0
$801$	−36.0565	−	5.24039i	−1.27399	−	0.185160i
$802$		0			0
$803$	10.9576	−	18.9791i	0.386685	−	0.669758i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−31.6257	−	2.28620i	−1.11328	−	0.0804782i
$808$		0			0
$809$	−44.2519			−1.55581			−0.777907	−	0.628380i	$-0.783718\pi$
$809$	−44.2519			−1.55581			−0.777907	+	0.628380i	$0.783718\pi$
$810$		0			0
$811$	−0.903637			−0.0317310			−0.0158655	−	0.999874i	$-0.505050\pi$
$811$	−0.903637			−0.0317310			−0.0158655	+	0.999874i	$0.505050\pi$
$812$		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	0.104681	+	0.994506i	$0.466618\pi$
$821$	−23.1783	+	40.1459i	−0.808927	+	1.40110i	−0.913608	+	0.406596i	$0.866716\pi$
$822$		0			0
$823$	15.4915	+	26.8320i	0.539998	+	0.935305i	0.998903	+	0.0468193i	$0.0149085\pi$
$823$	15.4915	+	26.8320i	0.539998	+	0.935305i	−0.458905	+	0.888485i	$0.651758\pi$
$824$		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
$829$	42.3707			1.47160			0.735798	−	0.677202i	$-0.236807\pi$
$829$	42.3707			1.47160			0.735798	+	0.677202i	$0.236807\pi$
$830$		0			0
$831$	−5.49734	+	8.10895i	−0.190700	+	0.281296i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.29123	−	14.3608i	0.286930	−	0.496977i
$836$		0			0
$837$	11.0545	+	34.8566i	0.382098	+	1.20482i
$838$		0			0
$839$	−1.36843	+	2.37020i	−0.0472435	+	0.0818282i	−0.888680	−	0.458528i	$-0.848377\pi$
$839$	−1.36843	+	2.37020i	−0.0472435	+	0.0818282i	0.841437	+	0.540356i	$0.181710\pi$
$840$		0			0
$841$	12.8133	+	22.1933i	0.441839	+	0.765287i
$842$		0			0
$843$	−10.4262	+	15.3794i	−0.359098	+	0.529694i
$844$		0			0
$845$	44.0473			1.51527
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−17.9918	−	37.1097i	−0.617475	−	1.27360i
$850$		0			0
$851$	4.48615	+	7.77024i	0.153783	+	0.266360i
$852$		0			0
$853$	4.59273	−	7.95485i	0.157252	−	0.272369i	−0.776625	−	0.629964i	$-0.783070\pi$
$853$	4.59273	−	7.95485i	0.157252	−	0.272369i	0.933877	+	0.357595i	$0.116403\pi$
$854$		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	$-0.899717\pi$
$857$	−6.06106	+	10.4981i	−0.207042	+	0.358607i	0.743739	+	0.668470i	$0.233050\pi$
$858$		0			0
$859$	−3.41626	−	5.91714i	−0.116561	−	0.201890i	0.801841	−	0.597537i	$-0.203854\pi$
$859$	−3.41626	−	5.91714i	−0.116561	−	0.201890i	−0.918403	+	0.395647i	$0.870520\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	52.5189			1.78776			0.893882	−	0.448302i	$-0.147971\pi$
$863$	52.5189			1.78776			0.893882	+	0.448302i	$0.147971\pi$
$864$		0			0
$865$	87.3962			2.97156
$866$		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
$873$	25.9568	−	32.9032i	0.878506	−	1.11360i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.0782	−	27.8482i	−0.542922	−	0.940368i	−0.998735	−	0.0502923i	$-0.983985\pi$
$877$	−16.0782	−	27.8482i	−0.542922	−	0.940368i	0.455813	−	0.890076i	$-0.349349\pi$
$878$		0			0
$879$	15.6133	+	32.2039i	0.526623	+	1.08621i
$880$		0			0
$881$	16.9101			0.569715			0.284858	−	0.958570i	$-0.408054\pi$
$881$	16.9101			0.569715			0.284858	+	0.958570i	$0.408054\pi$
$882$		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
$885$	15.0681	−	22.2266i	0.506510	−	0.747138i
$886$		0			0
$887$	22.2283	+	38.5005i	0.746352	+	1.29272i	0.949560	+	0.313585i	$0.101530\pi$
$887$	22.2283	+	38.5005i	0.746352	+	1.29272i	−0.203208	+	0.979136i	$0.565137\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−16.4343	+	15.5745i	−0.550571	+	0.521766i
$892$		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
$899$	12.9254			0.431087
$900$		0			0
$901$	−12.7525			−0.424847
$902$		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	−0.696576	−	0.717483i	$-0.745294\pi$
$907$	8.22392	−	14.2442i	0.273071	−	0.472972i	0.969647	+	0.244511i	$0.0786273\pi$
$908$		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
$915$	74.2527	+	5.36768i	2.45472	+	0.177450i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	58.5444			1.93120			0.965600	−	0.260031i	$-0.0837329\pi$
$919$	58.5444			1.93120			0.965600	+	0.260031i	$0.0837329\pi$
$920$		0			0
$921$	−20.5970	−	1.48894i	−0.678693	−	0.0490623i
$922$		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
$927$	−0.532124	−	1.33509i	−0.0174772	−	0.0438501i
$928$		0			0
$929$	0.318672	−	0.551956i	0.0104553	−	0.0181091i	−0.860750	−	0.509027i	$-0.830005\pi$
$929$	0.318672	−	0.551956i	0.0104553	−	0.0181091i	0.871206	+	0.490918i	$0.163339\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−6.90085	−	14.2337i	−0.225924	−	0.465989i
$934$		0			0
$935$	9.58581			0.313490
$936$		0			0
$937$	−19.0780			−0.623250			−0.311625	−	0.950205i	$-0.600873\pi$
$937$	−19.0780			−0.623250			−0.311625	+	0.950205i	$0.600873\pi$
$938$		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	$-0.00622634\pi$
$941$	14.8153	+	25.6609i	0.482965	+	0.836521i	−0.516843	+	0.856080i	$0.672893\pi$
$942$		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	0.439785	+	0.898103i	$0.355055\pi$
$947$	−17.1681	+	29.7360i	−0.557888	+	0.966290i	−0.997673	+	0.0681867i	$0.978279\pi$
$948$		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
$955$	−49.4326			−1.59960
$956$		0			0
$957$	3.49142	+	7.20140i	0.112862	+	0.232788i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9.26272	+	16.0435i	−0.298798	+	0.517533i
$962$		0			0
$963$	−15.9058	−	2.31173i	−0.512558	−	0.0744943i
$964$		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
$969$	−11.2306	−	0.811851i	−0.360778	−	0.0260804i
$970$		0			0
$971$	23.8383			0.765007			0.382503	−	0.923954i	$-0.375062\pi$
$971$	23.8383			0.765007			0.382503	+	0.923954i	$0.375062\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.17354	−	0.518571i	−0.229737	−	0.0166076i
$976$		0			0
$977$	−19.0842	−	33.0547i	−0.610556	−	1.05751i	−0.991147	−	0.132771i	$-0.957613\pi$
$977$	−19.0842	−	33.0547i	−0.610556	−	1.05751i	0.380591	−	0.924744i	$-0.375721\pi$
$978$		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	$-0.794785\pi$
$983$	3.78769	−	6.56046i	0.120808	−	0.209246i	0.920087	+	0.391715i	$0.128118\pi$
$984$		0			0
$985$	32.2363	+	55.8349i	1.02713	+	1.77905i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	72.5214			2.30605
$990$		0			0
$991$	−9.37904			−0.297935			−0.148967	−	0.988842i	$-0.547595\pi$
$991$	−9.37904			−0.297935			−0.148967	+	0.988842i	$0.547595\pi$
$992$		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	$-0.875985\pi$
$997$	−4.21829	+	7.30629i	−0.133595	+	0.231393i	0.791465	+	0.611214i	$0.209319\pi$
$998$		0			0
$999$	−7.13095	−	1.56837i	−0.225613	−	0.0496210i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72754 + 0.124883i) q^{3} +(1.73981 + 3.01343i) q^{5} +(2.96881 + 0.431481i) q^{9} +O(q^{10})\)	\(q+(1.72754 + 0.124883i) q^{3} +(1.73981 + 3.01343i) q^{5} +(2.96881 + 0.431481i) q^{9} +(-1.25788 + 2.17871i) q^{11} +(0.292110 + 0.505949i) q^{13} +(2.62926 + 5.42310i) q^{15} -1.09504 q^{17} +5.93668 q^{19} +(-3.19264 - 5.52982i) q^{23} +(-3.55384 + 6.15544i) q^{25} +(5.07486 + 1.11616i) q^{27} +(0.918333 - 1.59060i) q^{29} +(3.51872 + 6.09459i) q^{31} +(-2.44513 + 3.60673i) q^{33} -1.40515 q^{37} +(0.441448 + 0.910529i) q^{39} +(-5.37855 - 9.31593i) q^{41} +(-5.67879 + 9.83596i) q^{43} +(3.86491 + 9.69699i) q^{45} +(-3.76565 + 6.52229i) q^{47} +(-1.89173 - 0.136752i) q^{51} +11.6457 q^{53} -8.75386 q^{55} +(10.2559 + 0.741391i) q^{57} +(-2.22775 - 3.85858i) q^{59} +(6.17622 - 10.6975i) q^{61} +(-1.01643 + 1.76051i) q^{65} +(6.33536 + 10.9732i) q^{67} +(-4.82485 - 9.95170i) q^{69} -4.93390 q^{71} -8.71115 q^{73} +(-6.90813 + 10.1900i) q^{75} +(0.280206 - 0.485330i) q^{79} +(8.62765 + 2.56197i) q^{81} +(3.68472 - 6.38212i) q^{83} +(-1.90515 - 3.29982i) q^{85} +(1.78510 - 2.63315i) q^{87} -12.1451 q^{89} +(5.31762 + 10.9681i) q^{93} +(10.3287 + 17.8898i) q^{95} +(6.98486 - 12.0981i) q^{97} +(-4.67448 + 5.92543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9}+O(q^{10}) \) 24 * q + 8 * q^9	\( 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93} + 32 q^{95} - 4 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Introduction

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