LMFDB - Embedded newform 1764.2.j.i.1177.1

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			1177.1
Character	$\chi$	$=$	1764.1177
Dual form			1764.2.j.i.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	$-0.882868\pi$
$5$	−1.73981	−	3.01343i	−0.778065	−	1.34765i	0.154991	−	0.987916i	$-0.450465\pi$
$6$		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	0.822670	−	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
$17$	1.09504			0.265586			0.132793	−	0.991144i	$-0.457605\pi$
$17$	1.09504			0.265586			0.132793	+	0.991144i	$0.457605\pi$
$18$		0			0
$19$	−5.93668			−1.36197			−0.680984	−	0.732298i	$-0.738448\pi$
$19$	−5.93668			−1.36197			−0.680984	+	0.732298i	$0.738448\pi$
$20$		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	$-0.948909\pi$
$31$	−3.51872	−	6.09459i	−0.631980	−	1.09462i	0.355166	−	0.934803i	$-0.384424\pi$
$32$		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	$0.150772\pi$
$41$	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
$45$	−3.86491	−	9.69699i	−0.576147	−	1.44554i
$46$		0			0
$47$	3.76565	−	6.52229i	0.549276	−	0.951374i	−0.449048	−	0.893507i	$-0.648237\pi$
$47$	3.76565	−	6.52229i	0.549276	−	0.951374i	0.998324	−	0.0578664i	$-0.0184298\pi$
$48$		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	0.973816	−	0.227337i	$-0.0730018\pi$
$59$	2.22775	+	3.85858i	0.290029	+	0.502345i	−0.683787	+	0.729681i	$0.739668\pi$
$60$		0			0
$61$	−6.17622	+	10.6975i	−0.790784	+	1.36968i	0.134698	+	0.990887i	$0.456994\pi$
$61$	−6.17622	+	10.6975i	−0.790784	+	1.36968i	−0.925482	+	0.378792i	$0.876340\pi$
$62$		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	$-0.329726\pi$
$73$	8.71115			1.01956			0.509782	+	0.860304i	$0.329726\pi$
$74$		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	−0.994257	−	0.107015i	$-0.965871\pi$
$83$	−3.68472	+	6.38212i	−0.404451	+	0.700529i	0.589807	+	0.807544i	$0.299204\pi$
$84$		0			0
$85$	−1.90515	−	3.29982i	−0.206643	−	0.357916i
$86$		0			0
$87$	−1.78510	+	2.63315i	−0.191383	+	0.282303i
$88$		0			0
$89$	12.1451			1.28738			0.643690	−	0.765287i	$-0.277403\pi$
$89$	12.1451			1.28738			0.643690	+	0.765287i	$0.277403\pi$
$90$		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	$0.417613\pi$
$97$	−6.98486	+	12.0981i	−0.709205	+	1.22838i	−0.965152	+	0.261688i	$0.915721\pi$
$98$		0			0
$99$	−4.67448	+	5.92543i	−0.469803	+	0.595528i
$100$		0			0
$101$	4.58825	−	7.94708i	0.456548	−	0.790764i	−0.542228	−	0.840231i	$-0.682419\pi$
$101$	4.58825	−	7.94708i	0.456548	−	0.790764i	0.998776	+	0.0494676i	$0.0157525\pi$
$102$		0			0
$103$	0.239538	+	0.414892i	0.0236024	+	0.0408805i	0.877585	−	0.479420i	$-0.159153\pi$
$103$	0.239538	+	0.414892i	0.0236024	+	0.0408805i	−0.853983	+	0.520301i	$0.825820\pi$
$104$		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	0.898836	−	0.438285i	$-0.144414\pi$
$131$	0.799491	+	1.38476i	0.0698518	+	0.120987i	−0.828984	+	0.559272i	$0.811081\pi$
$132$		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	$0.0705134\pi$
$139$	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
$143$	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	$-0.996200\pi$
$157$	−6.39409	−	11.0749i	−0.510304	−	0.883873i	0.489625	−	0.871933i	$-0.337134\pi$
$158$		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	0.943370	−	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
$171$	−17.6249	−	2.56157i	−1.34781	−	0.195888i
$172$		0			0
$173$	−12.5583	+	21.7517i	−0.954792	+	1.65375i	−0.219948	+	0.975512i	$0.570589\pi$
$173$	−12.5583	+	21.7517i	−0.954792	+	1.65375i	−0.734844	+	0.678237i	$0.762744\pi$
$174$		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	$-0.666938\pi$
$181$	−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	0.485901	+	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	$-0.702975\pi$
$199$	−16.7961			−1.19064			−0.595321	+	0.803488i	$0.702975\pi$
$200$		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	−0.882148	−	0.470972i	$-0.843903\pi$
$223$	−0.495791	+	0.858736i	−0.0332006	+	0.0575052i	0.848948	+	0.528477i	$0.177237\pi$
$224$		0			0
$225$	−13.2066	+	16.7409i	−0.880443	+	1.11606i
$226$		0			0
$227$	1.46567	−	2.53861i	0.0972799	−	0.168494i	−0.813278	−	0.581875i	$-0.802319\pi$
$227$	1.46567	−	2.53861i	0.0972799	−	0.168494i	0.910558	+	0.413382i	$0.135652\pi$
$228$		0			0
$229$	−2.19201	−	3.79667i	−0.144852	−	0.250891i	0.784466	−	0.620172i	$-0.212937\pi$
$229$	−2.19201	−	3.79667i	−0.144852	−	0.250891i	−0.929318	+	0.369281i	$0.879604\pi$
$230$		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	−0.995564	−	0.0940877i	$-0.970007\pi$
$241$	−6.46271	+	11.1937i	−0.416300	+	0.721052i	0.579264	+	0.815140i	$0.303340\pi$
$242$		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	$-0.713125\pi$
$251$	−19.6654			−1.24127			−0.620634	+	0.784101i	$0.713125\pi$
$252$		0			0
$253$	16.0638			1.00992
$254$		0			0
$255$	2.87914	+	5.93850i	0.180299	+	0.371884i
$256$		0			0
$257$	12.6799	+	21.9622i	0.790948	+	1.36996i	0.925381	+	0.379039i	$0.123745\pi$
$257$	12.6799	+	21.9622i	0.790948	+	1.36996i	−0.134433	+	0.990923i	$0.542921\pi$
$258$		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	$-0.311534\pi$
$269$	18.3068			1.11618			0.558092	+	0.829779i	$0.311534\pi$
$270$		0			0
$271$	4.68930			0.284855			0.142427	−	0.989805i	$-0.454509\pi$
$271$	4.68930			0.284855			0.142427	+	0.989805i	$0.454509\pi$
$272$		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	$0.0835989\pi$
$283$	11.9053	+	20.6206i	0.707697	+	1.22577i	−0.258013	+	0.966141i	$0.583068\pi$
$284$		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	$-0.960411\pi$
$293$	−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
$297$	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	$-0.389494\pi$
$307$	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	0.965957	−	0.258704i	$-0.0832954\pi$
$311$	4.56635	+	7.90916i	0.258934	+	0.448487i	−0.707022	+	0.707191i	$0.749962\pi$
$312$		0			0
$313$	−6.91980	+	11.9854i	−0.391130	+	0.677457i	−0.992599	−	0.121439i	$-0.961249\pi$
$313$	−6.91980	+	11.9854i	−0.391130	+	0.677457i	0.601469	+	0.798896i	$0.294582\pi$
$314$		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	−0.990601	−	0.136780i	$-0.956325\pi$
$349$	−7.04006	+	12.1937i	−0.376846	+	0.652716i	0.613756	+	0.789496i	$0.289658\pi$
$350$		0			0
$351$	0.917699	+	2.89366i	0.0489831	+	0.154452i
$352$		0			0
$353$	1.68465	−	2.91790i	0.0896648	−	0.155304i	−0.817705	−	0.575638i	$-0.804754\pi$
$353$	1.68465	−	2.91790i	0.0896648	−	0.155304i	0.907369	+	0.420334i	$0.138087\pi$
$354$		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	−0.856251	−	0.516560i	$-0.827212\pi$
$367$	0.368367	−	0.638030i	0.0192286	−	0.0333049i	0.875480	+	0.483255i	$0.160546\pi$
$368$		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	0.599329	−	0.800503i	$-0.295434\pi$
$383$	−7.70273	−	13.3415i	−0.393591	−	0.681720i	−0.992920	+	0.118783i	$0.962101\pi$
$384$		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	$-0.569713\pi$
$397$	−8.65790			−0.434528			−0.217264	+	0.976113i	$0.569713\pi$
$398$		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	0.981951	−	0.189135i	$-0.0605682\pi$
$409$	6.61681	+	11.4607i	0.327180	+	0.566693i	−0.654771	+	0.755827i	$0.727235\pi$
$410$		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	0.953854	−	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
$423$	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	$-0.620009\pi$
$433$	−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	−0.973359	−	0.229288i	$-0.926360\pi$
$439$	−6.03657	+	10.4556i	−0.288110	+	0.499021i	0.685249	+	0.728309i	$0.259693\pi$
$440$		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	$0.480812\pi$
$461$	−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
$465$	23.8000	−	35.1066i	1.10370	−	1.62803i
$466$		0			0
$467$	2.85477			0.132103			0.0660515	−	0.997816i	$-0.478960\pi$
$467$	2.85477			0.132103			0.0660515	+	0.997816i	$0.478960\pi$
$468$		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	−0.811731	−	0.584032i	$-0.801474\pi$
$479$	2.18688	−	3.78779i	0.0999211	−	0.173068i	0.911652	+	0.410964i	$0.134808\pi$
$480$		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	$-0.680417\pi$
$503$	−24.0843			−1.07387			−0.536933	+	0.843625i	$0.680417\pi$
$504$		0			0
$505$	−31.9306			−1.42089
$506$		0			0
$507$	−12.3033	+	18.1482i	−0.546407	+	0.805989i
$508$		0			0
$509$	−12.2350	−	21.1917i	−0.542307	−	0.939304i	−0.998771	−	0.0495618i	$-0.984218\pi$
$509$	−12.2350	−	21.1917i	−0.542307	−	0.939304i	0.456464	−	0.889742i	$-0.349116\pi$
$510$		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	$-0.822677\pi$
$521$	−38.7487			−1.69761			−0.848805	+	0.528707i	$0.822677\pi$
$522$		0			0
$523$	−25.6945			−1.12354			−0.561771	−	0.827293i	$-0.689880\pi$
$523$	−25.6945			−1.12354			−0.561771	+	0.827293i	$0.689880\pi$
$524$		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	0.996447	−	0.0842230i	$-0.0268408\pi$
$563$	10.0910	+	17.4781i	0.425284	+	0.736614i	−0.571163	+	0.820837i	$0.693507\pi$
$564$		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	$-0.374835\pi$
$577$	18.4077			0.766322			0.383161	+	0.923682i	$0.374835\pi$
$578$		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	$-0.439825\pi$
$587$	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
$591$	−32.0091	−	2.31392i	−1.31668	−	0.0951818i
$592$		0			0
$593$	17.4326			0.715871			0.357935	−	0.933746i	$-0.383481\pi$
$593$	17.4326			0.715871			0.357935	+	0.933746i	$0.383481\pi$
$594$		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	−0.503706	−	0.863875i	$-0.668031\pi$
$601$	12.1666	−	21.0731i	0.496284	−	0.859590i	0.999991	+	0.00428500i	$0.00136396\pi$
$602$		0			0
$603$	14.0738	+	35.3108i	0.573128	+	1.43797i
$604$		0			0
$605$	8.12655	−	14.0756i	0.330391	−	0.572254i
$606$		0			0
$607$	9.96073	+	17.2525i	0.404294	+	0.700257i	0.994239	−	0.107186i	$-0.0341840\pi$
$607$	9.96073	+	17.2525i	0.404294	+	0.700257i	−0.589945	+	0.807443i	$0.700851\pi$
$608$		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	$-0.471928\pi$
$619$	22.5584	−	39.0723i	0.906698	−	1.57045i	0.818621	−	0.574334i	$-0.194739\pi$
$620$		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	$0.0856285\pi$
$643$	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
$647$	−7.46655			−0.293540			−0.146770	−	0.989171i	$-0.546888\pi$
$647$	−7.46655			−0.293540			−0.146770	+	0.989171i	$0.546888\pi$
$648$		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	0.566551	−	0.824026i	$-0.308277\pi$
$661$	−11.0643	−	19.1640i	−0.430352	−	0.745392i	−0.996904	+	0.0786346i	$0.974944\pi$
$662$		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	−0.991732	−	0.128323i	$-0.959041\pi$
$677$	−10.0105	+	17.3387i	−0.384736	+	0.666382i	0.606997	+	0.794704i	$0.292374\pi$
$678$		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	$-0.520560\pi$
$691$	21.8693	−	37.8787i	0.831947	−	1.44097i	0.896492	−	0.443060i	$-0.146107\pi$
$692$		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	$-0.298269\pi$
$719$	31.7575			1.18435			0.592177	+	0.805808i	$0.298269\pi$
$720$		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	−0.913812	−	0.406138i	$-0.866875\pi$
$727$	−2.83596	+	4.91203i	−0.105180	+	0.182177i	0.808632	+	0.588315i	$0.200209\pi$
$728$		0			0
$729$	24.5084	+	11.3287i	0.907718	+	0.419580i
$730$		0			0
$731$	−6.21849	+	10.7707i	−0.229999	+	0.398370i
$732$		0			0
$733$	−11.9926	−	20.7719i	−0.442958	−	0.767226i	0.554949	−	0.831884i	$-0.312738\pi$
$733$	−11.9926	−	20.7719i	−0.442958	−	0.767226i	−0.997907	+	0.0646579i	$0.979404\pi$
$734$		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	0.961430	−	0.275050i	$-0.0886946\pi$
$761$	6.69005	+	11.5875i	0.242514	+	0.420047i	−0.718916	+	0.695097i	$0.755361\pi$
$762$		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	0.953555	−	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
$773$	27.8942			1.00328			0.501642	−	0.865075i	$-0.332730\pi$
$773$	27.8942			1.00328			0.501642	+	0.865075i	$0.332730\pi$
$774$		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	0.865093	−	0.501612i	$-0.167260\pi$
$787$	−0.0522535	−	0.0905057i	−0.00186264	−	0.00322618i	−0.866955	+	0.498386i	$0.833926\pi$
$788$		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	$0.0464910\pi$
$797$	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
$801$	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	$-0.494950\pi$
$811$	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	0.104681	+	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	$-0.763193\pi$
$829$	−42.3707			−1.47160			−0.735798	+	0.677202i	$0.763193\pi$
$830$		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	−0.841437	−	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
$843$	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	−0.933877	−	0.357595i	$-0.883597\pi$
$853$	−4.59273	+	7.95485i	−0.157252	+	0.272369i	0.776625	+	0.629964i	$0.216930\pi$
$854$		0			0
$855$	22.9447	+	57.5680i	0.784694	+	1.96878i
$856$		0			0
$857$	6.06106	−	10.4981i	0.207042	−	0.358607i	−0.743739	−	0.668470i	$-0.766950\pi$
$857$	6.06106	−	10.4981i	0.207042	−	0.358607i	0.950781	+	0.309862i	$0.100283\pi$
$858$		0			0
$859$	3.41626	+	5.91714i	0.116561	+	0.201890i	0.918403	−	0.395647i	$-0.129480\pi$
$859$	3.41626	+	5.91714i	0.116561	+	0.201890i	−0.801841	+	0.597537i	$0.796146\pi$
$860$		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	$-0.591946\pi$
$881$	−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
$885$	−15.0681	+	22.2266i	−0.506510	+	0.747138i
$886$		0			0
$887$	−22.2283	−	38.5005i	−0.746352	−	1.29272i	−0.949560	−	0.313585i	$-0.898470\pi$
$887$	−22.2283	−	38.5005i	−0.746352	−	1.29272i	0.203208	−	0.979136i	$-0.434863\pi$
$888$		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	−0.871206	−	0.490918i	$-0.836661\pi$
$929$	−0.318672	+	0.551956i	−0.0104553	+	0.0181091i	0.860750	+	0.509027i	$0.169995\pi$
$930$		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	$-0.399127\pi$
$937$	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	0.516843	−	0.856080i	$-0.327107\pi$
$941$	−14.8153	−	25.6609i	−0.482965	−	0.836521i	−0.999809	+	0.0195594i	$0.993774\pi$
$942$		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	$-0.624938\pi$
$971$	−23.8383			−0.765007			−0.382503	+	0.923954i	$0.624938\pi$
$972$		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	−0.920087	−	0.391715i	$-0.871882\pi$
$983$	−3.78769	+	6.56046i	−0.120808	+	0.209246i	0.799278	+	0.600961i	$0.205215\pi$
$984$		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	−0.791465	−	0.611214i	$-0.790681\pi$
$997$	4.21829	−	7.30629i	0.133595	−	0.231393i	0.925060	+	0.379822i	$0.124015\pi$
$998$		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.1177.1	yes	24
3.2	odd	2		5292.2.j.i.3529.11		24
7.2	even	3		1764.2.i.j.1537.9		24
7.3	odd	6		1764.2.l.j.961.4		24
7.4	even	3		1764.2.l.j.961.9		24
7.5	odd	6		1764.2.i.j.1537.4		24
7.6	odd	2	inner	1764.2.j.i.1177.12	yes	24
9.4	even	3	inner	1764.2.j.i.589.1	✓	24
9.5	odd	6		5292.2.j.i.1765.11		24
21.2	odd	6		5292.2.i.j.2125.11		24
21.5	even	6		5292.2.i.j.2125.2		24
21.11	odd	6		5292.2.l.j.3313.2		24
21.17	even	6		5292.2.l.j.3313.11		24
21.20	even	2		5292.2.j.i.3529.2		24
63.4	even	3		1764.2.i.j.373.9		24
63.5	even	6		5292.2.l.j.361.11		24
63.13	odd	6	inner	1764.2.j.i.589.12	yes	24
63.23	odd	6		5292.2.l.j.361.2		24
63.31	odd	6		1764.2.i.j.373.4		24
63.32	odd	6		5292.2.i.j.1549.11		24
63.40	odd	6		1764.2.l.j.949.4		24
63.41	even	6		5292.2.j.i.1765.2		24
63.58	even	3		1764.2.l.j.949.9		24
63.59	even	6		5292.2.i.j.1549.2		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

L-functions

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