LMFDB - Embedded newform 1764.2.i.j.373.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1764.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.6
Character	$\chi$	$=$	1764.373
Dual form			1764.2.i.j.1537.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0546616 + 1.73119i) q^{3} +(1.94623 + 3.37097i) q^{5} +(-2.99402 - 0.189259i) q^{9} +O(q^{10})$	\(q+(-0.0546616 + 1.73119i) q^{3} +(1.94623 + 3.37097i) q^{5} +(-2.99402 - 0.189259i) q^{9} +(-2.18778 + 3.78935i) q^{11} +(0.792201 - 1.37213i) q^{13} +(-5.94217 + 3.18503i) q^{15} +(-2.66678 - 4.61900i) q^{17} +(-2.32161 + 4.02115i) q^{19} +(-0.183900 - 0.318523i) q^{23} +(-5.07564 + 8.79126i) q^{25} +(0.491301 - 5.17287i) q^{27} +(-5.08750 - 8.81180i) q^{29} +2.29552 q^{31} +(-6.44049 - 3.99460i) q^{33} +(-5.44017 + 9.42265i) q^{37} +(2.33212 + 1.44645i) q^{39} +(0.690443 - 1.19588i) q^{41} +(3.81699 + 6.61122i) q^{43} +(-5.18908 - 10.4611i) q^{45} +7.60865 q^{47} +(8.14212 - 4.36422i) q^{51} +(0.462847 + 0.801674i) q^{53} -17.0317 q^{55} +(-6.83447 - 4.23895i) q^{57} +0.920949 q^{59} -6.55560 q^{61} +6.16722 q^{65} +15.0084 q^{67} +(0.561476 - 0.300954i) q^{69} -4.91059 q^{71} +(3.78353 + 6.55327i) q^{73} +(-14.9419 - 9.26743i) q^{75} +1.97543 q^{79} +(8.92836 + 1.13329i) q^{81} +(0.253011 + 0.438227i) q^{83} +(10.3803 - 17.9793i) q^{85} +(15.5330 - 8.32575i) q^{87} +(-6.10987 + 10.5826i) q^{89} +(-0.125477 + 3.97398i) q^{93} -18.0736 q^{95} +(-4.45315 - 7.71308i) q^{97} +(7.26745 - 10.9314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} - 12 q^{37} + 8 q^{51} - 16 q^{53} + 52 q^{57} + 72 q^{65} - 24 q^{67} + 48 q^{71} - 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93} - 64 q^{95} - 4 q^{99}+O(q^{100}) $ 24 * q - 4 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 - 12 * q^37 + 8 * q^51 - 16 * q^53 + 52 * q^57 + 72 * q^65 - 24 * q^67 + 48 * q^71 - 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 64 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0546616	+	1.73119i	−0.0315589	+	0.999502i
$3$	−0.0546616	+	1.73119i	−0.0315589	+	0.999502i
$4$		0			0
$5$	1.94623	+	3.37097i	0.870381	+	1.50754i	0.861603	+	0.507583i	$0.169461\pi$
$5$	1.94623	+	3.37097i	0.870381	+	1.50754i	0.00877856	+	0.999961i	$0.497206\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.99402	−	0.189259i	−0.998008	−	0.0630863i
$10$		0			0
$11$	−2.18778	+	3.78935i	−0.659642	+	1.14253i	0.321067	+	0.947057i	$0.395959\pi$
$11$	−2.18778	+	3.78935i	−0.659642	+	1.14253i	−0.980708	+	0.195476i	$0.937375\pi$
$12$		0			0
$13$	0.792201	−	1.37213i	0.219717	−	0.380561i	−0.735004	−	0.678062i	$-0.762820\pi$
$13$	0.792201	−	1.37213i	0.219717	−	0.380561i	0.954721	+	0.297501i	$0.0961533\pi$
$14$		0			0
$15$	−5.94217	+	3.18503i	−1.53426	+	0.822371i
$16$		0			0
$17$	−2.66678	−	4.61900i	−0.646789	−	1.12027i	−0.983885	−	0.178801i	$-0.942778\pi$
$17$	−2.66678	−	4.61900i	−0.646789	−	1.12027i	0.337096	−	0.941470i	$-0.390555\pi$
$18$		0			0
$19$	−2.32161	+	4.02115i	−0.532614	+	0.922515i	0.466660	+	0.884437i	$0.345457\pi$
$19$	−2.32161	+	4.02115i	−0.532614	+	0.922515i	−0.999275	+	0.0380786i	$0.987876\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.183900	−	0.318523i	−0.0383457	−	0.0664167i	0.846216	−	0.532841i	$-0.178875\pi$
$23$	−0.183900	−	0.318523i	−0.0383457	−	0.0664167i	−0.884561	+	0.466424i	$0.845542\pi$
$24$		0			0
$25$	−5.07564	+	8.79126i	−1.01513	+	1.75825i
$26$		0			0
$27$	0.491301	−	5.17287i	0.0945509	−	0.995520i
$28$		0			0
$29$	−5.08750	−	8.81180i	−0.944724	−	1.63631i	−0.756302	−	0.654222i	$-0.772996\pi$
$29$	−5.08750	−	8.81180i	−0.944724	−	1.63631i	−0.188422	−	0.982088i	$-0.560337\pi$
$30$		0			0
$31$	2.29552			0.412288			0.206144	−	0.978522i	$-0.433908\pi$
$31$	2.29552			0.412288			0.206144	+	0.978522i	$0.433908\pi$
$32$		0			0
$33$	−6.44049	−	3.99460i	−1.12115	−	0.695370i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.44017	+	9.42265i	−0.894359	+	1.54907i	−0.0597623	+	0.998213i	$0.519034\pi$
$37$	−5.44017	+	9.42265i	−0.894359	+	1.54907i	−0.834596	+	0.550862i	$0.814299\pi$
$38$		0			0
$39$	2.33212	+	1.44645i	0.373437	+	0.231618i
$40$		0			0
$41$	0.690443	−	1.19588i	0.107829	−	0.186766i	−0.807061	−	0.590467i	$-0.798943\pi$
$41$	0.690443	−	1.19588i	0.107829	−	0.186766i	0.914891	+	0.403702i	$0.132277\pi$
$42$		0			0
$43$	3.81699	+	6.61122i	0.582086	+	1.00820i	0.995232	+	0.0975372i	$0.0310965\pi$
$43$	3.81699	+	6.61122i	0.582086	+	1.00820i	−0.413146	+	0.910665i	$0.635570\pi$
$44$		0			0
$45$	−5.18908	−	10.4611i	−0.773542	−	1.55945i
$46$		0			0
$47$	7.60865			1.10984			0.554918	−	0.831905i	$-0.312750\pi$
$47$	7.60865			1.10984			0.554918	+	0.831905i	$0.312750\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	8.14212	−	4.36422i	1.14013	−	0.611112i
$52$		0			0
$53$	0.462847	+	0.801674i	0.0635769	+	0.110118i	0.896062	−	0.443929i	$-0.146416\pi$
$53$	0.462847	+	0.801674i	0.0635769	+	0.110118i	−0.832485	+	0.554048i	$0.813083\pi$
$54$		0			0
$55$	−17.0317			−2.29656
$56$		0			0
$57$	−6.83447	−	4.23895i	−0.905247	−	0.561463i
$58$		0			0
$59$	0.920949			0.119897			0.0599487	−	0.998201i	$-0.480906\pi$
$59$	0.920949			0.119897			0.0599487	+	0.998201i	$0.480906\pi$
$60$		0			0
$61$	−6.55560			−0.839358			−0.419679	−	0.907673i	$-0.637857\pi$
$61$	−6.55560			−0.839358			−0.419679	+	0.907673i	$0.637857\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.16722			0.764950
$66$		0			0
$67$	15.0084			1.83357			0.916783	−	0.399385i	$-0.130776\pi$
$67$	15.0084			1.83357			0.916783	+	0.399385i	$0.130776\pi$
$68$		0			0
$69$	0.561476	−	0.300954i	0.0675938	−	0.0362306i
$70$		0			0
$71$	−4.91059			−0.582780			−0.291390	−	0.956604i	$-0.594118\pi$
$71$	−4.91059			−0.582780			−0.291390	+	0.956604i	$0.594118\pi$
$72$		0			0
$73$	3.78353	+	6.55327i	0.442829	+	0.767003i	0.997898	−	0.0648016i	$-0.0206415\pi$
$73$	3.78353	+	6.55327i	0.442829	+	0.767003i	−0.555069	+	0.831804i	$0.687308\pi$
$74$		0			0
$75$	−14.9419	−	9.26743i	−1.72534	−	1.07011i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.97543			0.222253			0.111127	−	0.993806i	$-0.464554\pi$
$79$	1.97543			0.222253			0.111127	+	0.993806i	$0.464554\pi$
$80$		0			0
$81$	8.92836	+	1.13329i	0.992040	+	0.125921i
$82$		0			0
$83$	0.253011	+	0.438227i	0.0277715	+	0.0481017i	0.879577	−	0.475756i	$-0.157826\pi$
$83$	0.253011	+	0.438227i	0.0277715	+	0.0481017i	−0.851806	+	0.523858i	$0.824492\pi$
$84$		0			0
$85$	10.3803	−	17.9793i	1.12591	−	1.95013i
$86$		0			0
$87$	15.5330	−	8.32575i	1.66531	−	0.892614i
$88$		0			0
$89$	−6.10987	+	10.5826i	−0.647645	+	1.12175i	0.336039	+	0.941848i	$0.390913\pi$
$89$	−6.10987	+	10.5826i	−0.647645	+	1.12175i	−0.983684	+	0.179906i	$0.942421\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.125477	+	3.97398i	−0.0130114	+	0.412083i
$94$		0			0
$95$	−18.0736			−1.85431
$96$		0			0
$97$	−4.45315	−	7.71308i	−0.452149	−	0.783145i	0.546370	−	0.837544i	$-0.316009\pi$
$97$	−4.45315	−	7.71308i	−0.452149	−	0.783145i	−0.998519	+	0.0543987i	$0.982676\pi$
$98$		0			0
$99$	7.26745	−	10.9314i	0.730406	−	1.09864i
$100$		0			0
$101$	5.51180	−	9.54672i	0.548445	−	0.949935i	−0.449936	−	0.893061i	$-0.648553\pi$
$101$	5.51180	−	9.54672i	0.548445	−	0.949935i	0.998381	−	0.0568740i	$-0.0181133\pi$
$102$		0			0
$103$	1.36543	+	2.36499i	0.134540	+	0.233029i	0.925421	−	0.378939i	$-0.123711\pi$
$103$	1.36543	+	2.36499i	0.134540	+	0.233029i	−0.790882	+	0.611969i	$0.790378\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.39605	−	9.34623i	0.521655	−	0.903534i	−0.478027	−	0.878345i	$-0.658648\pi$
$107$	5.39605	−	9.34623i	0.521655	−	0.903534i	0.999683	−	0.0251887i	$-0.00801867\pi$
$108$		0			0
$109$	4.99187	+	8.64617i	0.478134	+	0.828153i	0.999686	−	0.0250668i	$-0.00797984\pi$
$109$	4.99187	+	8.64617i	0.478134	+	0.828153i	−0.521551	+	0.853220i	$0.674647\pi$
$110$		0			0
$111$	−16.0150	−	9.93302i	−1.52008	−	0.942800i
$112$		0			0
$113$	−6.12019	+	10.6005i	−0.575739	+	0.997209i	0.420222	+	0.907421i	$0.361952\pi$
$113$	−6.12019	+	10.6005i	−0.575739	+	0.997209i	−0.995961	+	0.0897875i	$0.971381\pi$
$114$		0			0
$115$	0.715822	−	1.23984i	0.0667508	−	0.115616i
$116$		0			0
$117$	−2.63156	+	3.95826i	−0.243287	+	0.365942i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.07280	−	7.05429i	−0.370254	−	0.641299i
$122$		0			0
$123$	2.03256	+	1.26066i	0.183270	+	0.113670i
$124$		0			0
$125$	−20.0511			−1.79343
$126$		0			0
$127$	−13.2005			−1.17135			−0.585677	−	0.810544i	$-0.699171\pi$
$127$	−13.2005			−1.17135			−0.585677	+	0.810544i	$0.699171\pi$
$128$		0			0
$129$	−11.6539	+	6.24655i	−1.02607	+	0.549978i
$130$		0			0
$131$	2.54342	+	4.40532i	0.222219	+	0.384895i	0.955482	−	0.295051i	$-0.0953366\pi$
$131$	2.54342	+	4.40532i	0.222219	+	0.384895i	−0.733262	+	0.679946i	$0.762003\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	18.3938	−	8.41145i	1.58309	−	0.723942i
$136$		0			0
$137$	−6.67208	+	11.5564i	−0.570034	+	0.987328i	0.426527	+	0.904475i	$0.359737\pi$
$137$	−6.67208	+	11.5564i	−0.570034	+	0.987328i	−0.996562	+	0.0828538i	$0.973597\pi$
$138$		0			0
$139$	4.85642	−	8.41157i	0.411916	−	0.713460i	−0.583183	−	0.812341i	$-0.698193\pi$
$139$	4.85642	−	8.41157i	0.411916	−	0.713460i	0.995099	+	0.0988809i	$0.0315263\pi$
$140$		0			0
$141$	−0.415901	+	13.1720i	−0.0350251	+	1.10928i
$142$		0			0
$143$	3.46633	+	6.00386i	0.289869	+	0.502068i
$144$		0			0
$145$	19.8029	−	34.2996i	1.64454	−	2.84843i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.92116	−	11.9878i	−0.567004	−	0.982079i	−0.996860	−	0.0791820i	$-0.974769\pi$
$149$	−6.92116	−	11.9878i	−0.567004	−	0.982079i	0.429856	−	0.902897i	$-0.358564\pi$
$150$		0			0
$151$	−11.4380	+	19.8112i	−0.930809	+	1.61221i	−0.148867	+	0.988857i	$0.547563\pi$
$151$	−11.4380	+	19.8112i	−0.930809	+	1.61221i	−0.781942	+	0.623352i	$0.785771\pi$
$152$		0			0
$153$	7.11022	+	14.3341i	0.574827	+	1.15884i
$154$		0			0
$155$	4.46762	+	7.73815i	0.358848	+	0.621543i
$156$		0			0
$157$	−11.5798			−0.924170			−0.462085	−	0.886836i	$-0.652899\pi$
$157$	−11.5798			−0.924170			−0.462085	+	0.886836i	$0.652899\pi$
$158$		0			0
$159$	−1.41315	+	0.757454i	−0.112070	+	0.0600700i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.70577	+	2.95449i	−0.133607	+	0.231413i	−0.925064	−	0.379811i	$-0.875989\pi$
$163$	−1.70577	+	2.95449i	−0.133607	+	0.231413i	0.791458	+	0.611224i	$0.209323\pi$
$164$		0			0
$165$	0.930982	−	29.4851i	0.0724768	−	2.29542i
$166$		0			0
$167$	4.69996	−	8.14057i	0.363694	−	0.629936i	−0.624872	−	0.780727i	$-0.714849\pi$
$167$	4.69996	−	8.14057i	0.363694	−	0.629936i	0.988566	+	0.150791i	$0.0481821\pi$
$168$		0			0
$169$	5.24484	+	9.08432i	0.403449	+	0.698794i
$170$		0			0
$171$	7.71200	−	11.6000i	0.589752	−	0.887077i
$172$		0			0
$173$	6.40512			0.486972			0.243486	−	0.969904i	$-0.421709\pi$
$173$	6.40512			0.486972			0.243486	+	0.969904i	$0.421709\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.0503405	+	1.59434i	−0.00378383	+	0.119838i
$178$		0			0
$179$	−8.54038	−	14.7924i	−0.638338	−	1.10563i	−0.985797	−	0.167938i	$-0.946289\pi$
$179$	−8.54038	−	14.7924i	−0.638338	−	1.10563i	0.347460	−	0.937695i	$-0.387044\pi$
$180$		0			0
$181$	−1.35988			−0.101079			−0.0505395	−	0.998722i	$-0.516094\pi$
$181$	−1.35988			−0.101079			−0.0505395	+	0.998722i	$0.516094\pi$
$182$		0			0
$183$	0.358339	−	11.3490i	0.0264892	−	0.838940i
$184$		0			0
$185$	−42.3513			−3.11373
$186$		0			0
$187$	23.3374			1.70660
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−17.8810			−1.29382			−0.646911	−	0.762566i	$-0.723939\pi$
$191$	−17.8810			−1.29382			−0.646911	+	0.762566i	$0.723939\pi$
$192$		0			0
$193$	−13.0133			−0.936717			−0.468358	−	0.883539i	$-0.655154\pi$
$193$	−13.0133			−0.936717			−0.468358	+	0.883539i	$0.655154\pi$
$194$		0			0
$195$	−0.337110	+	10.6766i	−0.0241410	+	0.764569i
$196$		0			0
$197$	6.36486			0.453478			0.226739	−	0.973956i	$-0.427194\pi$
$197$	6.36486			0.453478			0.226739	+	0.973956i	$0.427194\pi$
$198$		0			0
$199$	11.5764	+	20.0510i	0.820631	+	1.42137i	0.905213	+	0.424958i	$0.139711\pi$
$199$	11.5764	+	20.0510i	0.820631	+	1.42137i	−0.0845818	+	0.996417i	$0.526955\pi$
$200$		0			0
$201$	−0.820382	+	25.9823i	−0.0578653	+	1.83265i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.37505			0.375410
$206$		0			0
$207$	0.490316	+	0.988471i	0.0340793	+	0.0687035i
$208$		0			0
$209$	−10.1584	−	17.5948i	−0.702669	−	1.21706i
$210$		0			0
$211$	−5.67737	+	9.83349i	−0.390846	+	0.676965i	−0.992561	−	0.121745i	$-0.961151\pi$
$211$	−5.67737	+	9.83349i	−0.390846	+	0.676965i	0.601715	+	0.798711i	$0.294484\pi$
$212$		0			0
$213$	0.268421	−	8.50116i	0.0183919	−	0.582490i
$214$		0			0
$215$	−14.8575	+	25.7339i	−1.01327	+	1.75504i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−11.5518	+	6.19180i	−0.780596	+	0.418403i
$220$		0			0
$221$	−8.45050			−0.568442
$222$		0			0
$223$	13.3206	+	23.0719i	0.892011	+	1.54501i	0.837461	+	0.546498i	$0.184039\pi$
$223$	13.3206	+	23.0719i	0.892011	+	1.54501i	0.0545504	+	0.998511i	$0.482627\pi$
$224$		0			0
$225$	16.8604	−	25.3606i	1.12403	−	1.69071i
$226$		0			0
$227$	−8.30136	+	14.3784i	−0.550981	+	0.954326i	0.447224	+	0.894422i	$0.352413\pi$
$227$	−8.30136	+	14.3784i	−0.550981	+	0.954326i	−0.998204	+	0.0599042i	$0.980920\pi$
$228$		0			0
$229$	−7.25072	−	12.5586i	−0.479141	−	0.829897i	0.520573	−	0.853817i	$-0.325718\pi$
$229$	−7.25072	−	12.5586i	−0.479141	−	0.829897i	−0.999714	+	0.0239205i	$0.992385\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.99020	+	13.8394i	−0.523456	+	0.906652i	0.476172	+	0.879352i	$0.342024\pi$
$233$	−7.99020	+	13.8394i	−0.523456	+	0.906652i	−0.999627	+	0.0272993i	$0.991309\pi$
$234$		0			0
$235$	14.8082	+	25.6485i	0.965980	+	1.67313i
$236$		0			0
$237$	−0.107980	+	3.41984i	−0.00701407	+	0.222143i
$238$		0			0
$239$	−9.58994	+	16.6103i	−0.620322	+	1.07443i	0.369104	+	0.929388i	$0.379665\pi$
$239$	−9.58994	+	16.6103i	−0.620322	+	1.07443i	−0.989426	+	0.145040i	$0.953669\pi$
$240$		0			0
$241$	11.6785	−	20.2277i	0.752276	−	1.30298i	−0.194441	−	0.980914i	$-0.562289\pi$
$241$	11.6785	−	20.2277i	0.752276	−	1.30298i	0.946717	−	0.322067i	$-0.104377\pi$
$242$		0			0
$243$	−2.44998	+	15.3947i	−0.157166	+	0.987572i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.67837	+	6.37112i	0.234049	+	0.405384i
$248$		0			0
$249$	−0.772484	+	0.414055i	−0.0489542	+	0.0262397i
$250$		0			0
$251$	30.4619			1.92274			0.961371	−	0.275257i	$-0.0887631\pi$
$251$	30.4619			1.92274			0.961371	+	0.275257i	$0.0887631\pi$
$252$		0			0
$253$	1.60933			0.101178
$254$		0			0
$255$	30.5581	+	18.9531i	1.91362	+	1.18689i
$256$		0			0
$257$	−3.40438	−	5.89657i	−0.212360	−	0.367818i	0.740093	−	0.672505i	$-0.234782\pi$
$257$	−3.40438	−	5.89657i	−0.212360	−	0.367818i	−0.952453	+	0.304687i	$0.901448\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	13.5644	+	27.3456i	0.839614	+	1.69265i
$262$		0			0
$263$	2.30000	−	3.98372i	0.141824	−	0.245647i	−0.786359	−	0.617769i	$-0.788037\pi$
$263$	2.30000	−	3.98372i	0.141824	−	0.245647i	0.928184	+	0.372122i	$0.121370\pi$
$264$		0			0
$265$	−1.80161	+	3.12049i	−0.110672	+	0.191690i
$266$		0			0
$267$	−17.9865	−	11.1558i	−1.10076	−	0.682724i
$268$		0			0
$269$	−4.25090	−	7.36277i	−0.259182	−	0.448916i	0.706841	−	0.707372i	$-0.250120\pi$
$269$	−4.25090	−	7.36277i	−0.259182	−	0.448916i	−0.966023	+	0.258456i	$0.916786\pi$
$270$		0			0
$271$	3.29191	−	5.70175i	0.199969	−	0.346357i	−0.748549	−	0.663079i	$-0.769249\pi$
$271$	3.29191	−	5.70175i	0.199969	−	0.346357i	0.948518	+	0.316723i	$0.102583\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−22.2088	−	38.4668i	−1.33924	−	2.31963i
$276$		0			0
$277$	5.63483	−	9.75982i	0.338564	−	0.586411i	−0.645599	−	0.763677i	$-0.723392\pi$
$277$	5.63483	−	9.75982i	0.338564	−	0.586411i	0.984163	+	0.177266i	$0.0567254\pi$
$278$		0			0
$279$	−6.87285	−	0.434448i	−0.411467	−	0.0260097i
$280$		0			0
$281$	7.50741	+	13.0032i	0.447854	+	0.775707i	0.998246	−	0.0592000i	$-0.0188550\pi$
$281$	7.50741	+	13.0032i	0.447854	+	0.775707i	−0.550392	+	0.834907i	$0.685522\pi$
$282$		0			0
$283$	−14.6731			−0.872227			−0.436114	−	0.899892i	$-0.643645\pi$
$283$	−14.6731			−0.872227			−0.436114	+	0.899892i	$0.643645\pi$
$284$		0			0
$285$	0.987931	−	31.2888i	0.0585200	−	1.85339i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5.72343	+	9.91327i	−0.336672	+	0.583133i
$290$		0			0
$291$	13.5962	−	7.28763i	0.797024	−	0.427209i
$292$		0			0
$293$	9.38981	−	16.2636i	0.548559	−	0.950132i	−0.449815	−	0.893122i	$-0.648510\pi$
$293$	9.38981	−	16.2636i	0.548559	−	0.950132i	0.998374	−	0.0570099i	$-0.0181567\pi$
$294$		0			0
$295$	1.79238	+	3.10449i	0.104356	+	0.180751i
$296$		0			0
$297$	18.5270	+	13.1788i	1.07504	+	0.764714i
$298$		0			0
$299$	−0.582741			−0.0337008
$300$		0			0
$301$		0			0
$302$		0			0
$303$	16.2259	+	10.0638i	0.932153	+	0.578151i
$304$		0			0
$305$	−12.7587	−	22.0987i	−0.730562	−	1.26537i
$306$		0			0
$307$	28.9425			1.65184			0.825919	−	0.563789i	$-0.190657\pi$
$307$	28.9425			1.65184			0.825919	+	0.563789i	$0.190657\pi$
$308$		0			0
$309$	−4.16888	+	2.23454i	−0.237159	+	0.127118i
$310$		0			0
$311$	13.5936			0.770824			0.385412	−	0.922745i	$-0.374059\pi$
$311$	13.5936			0.770824			0.385412	+	0.922745i	$0.374059\pi$
$312$		0			0
$313$	13.8644			0.783665			0.391832	−	0.920037i	$-0.371841\pi$
$313$	13.8644			0.783665			0.391832	+	0.920037i	$0.371841\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	23.0856			1.29662			0.648309	−	0.761377i	$-0.275476\pi$
$317$	23.0856			1.29662			0.648309	+	0.761377i	$0.275476\pi$
$318$		0			0
$319$	44.5214			2.49272
$320$		0			0
$321$	15.8851	+	9.85245i	0.886621	+	0.549910i
$322$		0			0
$323$	24.7649			1.37796
$324$		0			0
$325$	8.04184	+	13.9289i	0.446081	+	0.772635i
$326$		0			0
$327$	−15.2410	+	8.16925i	−0.842830	+	0.451761i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−15.6529			−0.860364			−0.430182	−	0.902742i	$-0.641551\pi$
$331$	−15.6529			−0.860364			−0.430182	+	0.902742i	$0.641551\pi$
$332$		0			0
$333$	18.0713	−	27.1821i	0.990303	−	1.48957i
$334$		0			0
$335$	29.2098	+	50.5929i	1.59590	+	2.76418i
$336$		0			0
$337$	3.56686	−	6.17799i	0.194299	−	0.336537i	−0.752371	−	0.658739i	$-0.771090\pi$
$337$	3.56686	−	6.17799i	0.194299	−	0.336537i	0.946671	+	0.322203i	$0.104423\pi$
$338$		0			0
$339$	−18.0169	−	11.1746i	−0.978542	−	0.606923i
$340$		0			0
$341$	−5.02211	+	8.69855i	−0.271962	+	0.471053i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.10727	+	1.30699i	0.113452	+	0.0703662i
$346$		0			0
$347$	5.55655			0.298291			0.149146	−	0.988815i	$-0.452348\pi$
$347$	5.55655			0.298291			0.149146	+	0.988815i	$0.452348\pi$
$348$		0			0
$349$	5.33296	+	9.23696i	0.285467	+	0.494443i	0.972722	−	0.231973i	$-0.0745181\pi$
$349$	5.33296	+	9.23696i	0.285467	+	0.494443i	−0.687256	+	0.726416i	$0.741185\pi$
$350$		0			0
$351$	−6.70866	−	4.77208i	−0.358082	−	0.254715i
$352$		0			0
$353$	−6.42132	+	11.1221i	−0.341772	+	0.591967i	−0.984762	−	0.173908i	$-0.944361\pi$
$353$	−6.42132	+	11.1221i	−0.341772	+	0.591967i	0.642989	+	0.765875i	$0.277694\pi$
$354$		0			0
$355$	−9.55715	−	16.5535i	−0.507241	−	0.878567i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.8417	+	22.2426i	−0.677761	+	1.17392i	0.297892	+	0.954600i	$0.403716\pi$
$359$	−12.8417	+	22.2426i	−0.677761	+	1.17392i	−0.975653	+	0.219318i	$0.929617\pi$
$360$		0			0
$361$	−1.27977	−	2.21663i	−0.0673563	−	0.116665i
$362$		0			0
$363$	12.4349	−	6.66518i	0.652665	−	0.349831i
$364$		0			0
$365$	−14.7273	+	25.5084i	−0.770861	+	1.33517i
$366$		0			0
$367$	−8.49197	+	14.7085i	−0.443277	+	0.767778i	−0.997930	−	0.0643031i	$-0.979518\pi$
$367$	−8.49197	+	14.7085i	−0.443277	+	0.767778i	0.554653	+	0.832082i	$0.312851\pi$
$368$		0			0
$369$	−2.29354	+	3.44983i	−0.119397	+	0.179591i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.38503	+	7.59509i	0.227048	+	0.393259i	0.956932	−	0.290312i	$-0.0937592\pi$
$373$	4.38503	+	7.59509i	0.227048	+	0.393259i	−0.729884	+	0.683571i	$0.760426\pi$
$374$		0			0
$375$	1.09603	−	34.7123i	0.0565986	−	1.79254i
$376$		0			0
$377$	−16.1213			−0.830288
$378$		0			0
$379$	11.7002			0.601001			0.300500	−	0.953782i	$-0.402846\pi$
$379$	11.7002			0.601001			0.300500	+	0.953782i	$0.402846\pi$
$380$		0			0
$381$	0.721560	−	22.8525i	0.0369666	−	1.17077i
$382$		0			0
$383$	−4.50360	−	7.80046i	−0.230123	−	0.398585i	0.727721	−	0.685873i	$-0.240580\pi$
$383$	−4.50360	−	7.80046i	−0.230123	−	0.398585i	−0.957844	+	0.287288i	$0.907246\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.1769	−	20.5166i	−0.517322	−	1.04292i
$388$		0			0
$389$	4.89390	−	8.47649i	0.248131	−	0.429775i	−0.714876	−	0.699251i	$-0.753517\pi$
$389$	4.89390	−	8.47649i	0.248131	−	0.429775i	0.963007	+	0.269476i	$0.0868504\pi$
$390$		0			0
$391$	−0.980839	+	1.69886i	−0.0496032	+	0.0859152i
$392$		0			0
$393$	−7.76547	+	4.16233i	−0.391716	+	0.209962i
$394$		0			0
$395$	3.84465	+	6.65912i	0.193445	+	0.335057i
$396$		0			0
$397$	6.95929	−	12.0538i	0.349277	−	0.604965i	−0.636844	−	0.770992i	$-0.719761\pi$
$397$	6.95929	−	12.0538i	0.349277	−	0.604965i	0.986121	+	0.166027i	$0.0530940\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.7414	+	20.3367i	0.586336	+	1.01556i	0.994707	+	0.102748i	$0.0327636\pi$
$401$	11.7414	+	20.3367i	0.586336	+	1.01556i	−0.408371	+	0.912816i	$0.633903\pi$
$402$		0			0
$403$	1.81852	−	3.14976i	0.0905867	−	0.156901i
$404$		0			0
$405$	13.5564	+	32.3029i	0.673621	+	1.60514i
$406$		0			0
$407$	−23.8038	−	41.2295i	−1.17991	−	2.04367i
$408$		0			0
$409$	13.6245			0.673689			0.336844	−	0.941560i	$-0.390640\pi$
$409$	13.6245			0.673689			0.336844	+	0.941560i	$0.390640\pi$
$410$		0			0
$411$	−19.6416	−	12.1823i	−0.968847	−	0.600909i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.984835	+	1.70578i	−0.0483436	+	0.0837336i
$416$		0			0
$417$	14.2965	+	8.86717i	0.700105	+	0.434227i
$418$		0			0
$419$	3.97733	−	6.88894i	0.194305	−	0.336547i	−0.752367	−	0.658744i	$-0.771088\pi$
$419$	3.97733	−	6.88894i	0.194305	−	0.336547i	0.946673	+	0.322197i	$0.104421\pi$
$420$		0			0
$421$	1.30584	+	2.26178i	0.0636426	+	0.110232i	0.896091	−	0.443870i	$-0.146395\pi$
$421$	1.30584	+	2.26178i	0.0636426	+	0.110232i	−0.832448	+	0.554102i	$0.813062\pi$
$422$		0			0
$423$	−22.7805	−	1.44000i	−1.10762	−	0.0700154i
$424$		0			0
$425$	54.1424			2.62629
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−10.5833	+	5.67268i	−0.510965	+	0.273880i
$430$		0			0
$431$	0.791065	+	1.37017i	0.0381043	+	0.0659985i	0.884449	−	0.466638i	$-0.154535\pi$
$431$	0.791065	+	1.37017i	0.0381043	+	0.0659985i	−0.846344	+	0.532636i	$0.821201\pi$
$432$		0			0
$433$	−5.17110			−0.248507			−0.124254	−	0.992250i	$-0.539654\pi$
$433$	−5.17110			−0.248507			−0.124254	+	0.992250i	$0.539654\pi$
$434$		0			0
$435$	58.2966	+	36.1574i	2.79511	+	1.73361i
$436$		0			0
$437$	1.70777			0.0816939
$438$		0			0
$439$	24.9611			1.19133			0.595665	−	0.803233i	$-0.296889\pi$
$439$	24.9611			1.19133			0.595665	+	0.803233i	$0.296889\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.08453			0.0515274			0.0257637	−	0.999668i	$-0.491798\pi$
$443$	1.08453			0.0515274			0.0257637	+	0.999668i	$0.491798\pi$
$444$		0			0
$445$	−47.5649			−2.25479
$446$		0			0
$447$	21.1315	−	11.3266i	0.999484	−	0.535728i
$448$		0			0
$449$	4.23372			0.199802			0.0999008	−	0.994997i	$-0.468147\pi$
$449$	4.23372			0.199802			0.0999008	+	0.994997i	$0.468147\pi$
$450$		0			0
$451$	3.02108	+	5.23267i	0.142257	+	0.246397i
$452$		0			0
$453$	−33.6716	−	20.8842i	−1.58203	−	0.981225i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−36.3026			−1.69817			−0.849083	−	0.528260i	$-0.822845\pi$
$457$	−36.3026			−1.69817			−0.849083	+	0.528260i	$0.822845\pi$
$458$		0			0
$459$	−25.2037	+	11.5256i	−1.17641	+	0.537969i
$460$		0			0
$461$	1.71236	+	2.96589i	0.0797524	+	0.138135i	0.903143	−	0.429340i	$-0.141254\pi$
$461$	1.71236	+	2.96589i	0.0797524	+	0.138135i	−0.823391	+	0.567475i	$0.807920\pi$
$462$		0			0
$463$	2.38499	−	4.13092i	0.110840	−	0.191980i	−0.805269	−	0.592909i	$-0.797979\pi$
$463$	2.38499	−	4.13092i	0.110840	−	0.191980i	0.916109	+	0.400929i	$0.131313\pi$
$464$		0			0
$465$	−13.6404	+	7.31131i	−0.632558	+	0.339054i
$466$		0			0
$467$	−10.0490	+	17.4053i	−0.465010	+	0.805422i	−0.999202	−	0.0399417i	$-0.987283\pi$
$467$	−10.0490	+	17.4053i	−0.465010	+	0.805422i	0.534192	+	0.845363i	$0.320616\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.632971	−	20.0468i	0.0291658	−	0.923710i
$472$		0			0
$473$	−33.4030			−1.53587
$474$		0			0
$475$	−23.5673	−	40.8198i	−1.08134	−	1.87294i
$476$		0			0
$477$	−1.23405	−	2.48783i	−0.0565033	−	0.113910i
$478$		0			0
$479$	8.42528	−	14.5930i	0.384961	−	0.666772i	−0.606803	−	0.794852i	$-0.707548\pi$
$479$	8.42528	−	14.5930i	0.384961	−	0.666772i	0.991764	+	0.128080i	$0.0408816\pi$
$480$		0			0
$481$	8.61941	+	14.9293i	0.393011	+	0.680716i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	17.3337	−	30.0229i	0.787084	−	1.36327i
$486$		0			0
$487$	−11.9916	−	20.7700i	−0.543389	−	0.941178i	−0.998706	−	0.0508486i	$-0.983807\pi$
$487$	−11.9916	−	20.7700i	−0.543389	−	0.941178i	0.455317	−	0.890329i	$-0.349526\pi$
$488$		0			0
$489$	−5.02153	−	3.11451i	−0.227082	−	0.140843i
$490$		0			0
$491$	−1.07281	+	1.85816i	−0.0484153	+	0.0838577i	−0.889217	−	0.457485i	$-0.848750\pi$
$491$	−1.07281	+	1.85816i	−0.0484153	+	0.0838577i	0.840802	+	0.541342i	$0.182084\pi$
$492$		0			0
$493$	−27.1345	+	46.9983i	−1.22207	+	2.11670i
$494$		0			0
$495$	50.9934	+	3.22341i	2.29198	+	0.144881i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	13.8577	+	24.0023i	0.620357	+	1.07449i	0.989419	+	0.145085i	$0.0463455\pi$
$499$	13.8577	+	24.0023i	0.620357	+	1.07449i	−0.369062	+	0.929405i	$0.620321\pi$
$500$		0			0
$501$	13.8359	+	8.58149i	0.618145	+	0.383393i
$502$		0			0
$503$	−22.4265			−0.999949			−0.499974	−	0.866040i	$-0.666657\pi$
$503$	−22.4265			−0.999949			−0.499974	+	0.866040i	$0.666657\pi$
$504$		0			0
$505$	42.9090			1.90943
$506$		0			0
$507$	−16.0134	+	8.58323i	−0.711178	+	0.381195i
$508$		0			0
$509$	14.6844	+	25.4342i	0.650876	+	1.12735i	0.982911	+	0.184083i	$0.0589316\pi$
$509$	14.6844	+	25.4342i	0.650876	+	1.12735i	−0.332034	+	0.943267i	$0.607735\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	19.6603	+	13.9850i	0.868023	+	0.617453i
$514$		0			0
$515$	−5.31488	+	9.20563i	−0.234201	+	0.405649i
$516$		0			0
$517$	−16.6461	+	28.8318i	−0.732093	+	1.26802i
$518$		0			0
$519$	−0.350114	+	11.0885i	−0.0153683	+	0.486730i
$520$		0			0
$521$	8.25389	+	14.2962i	0.361610	+	0.626326i	0.988226	−	0.153002i	$-0.0488940\pi$
$521$	8.25389	+	14.2962i	0.361610	+	0.626326i	−0.626616	+	0.779328i	$0.715561\pi$
$522$		0			0
$523$	−22.3476	+	38.7072i	−0.977193	+	1.69255i	−0.304695	+	0.952450i	$0.598554\pi$
$523$	−22.3476	+	38.7072i	−0.977193	+	1.69255i	−0.672499	+	0.740098i	$0.734779\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.12166	−	10.6030i	−0.266664	−	0.461875i
$528$		0			0
$529$	11.4324	−	19.8014i	0.497059	−	0.860932i
$530$		0			0
$531$	−2.75734	−	0.174298i	−0.119659	−	0.00756388i
$532$		0			0
$533$	−1.09394	−	1.89476i	−0.0473838	−	0.0820711i
$534$		0			0
$535$	42.0078			1.81616
$536$		0			0
$537$	26.0752	−	13.9764i	1.12523	−	0.603127i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	10.0369	−	17.3844i	0.431519	−	0.747412i	−0.565486	−	0.824758i	$-0.691311\pi$
$541$	10.0369	−	17.3844i	0.431519	−	0.747412i	0.997004	+	0.0773460i	$0.0246446\pi$
$542$		0			0
$543$	0.0743332	−	2.35421i	0.00318994	−	0.101029i
$544$		0			0
$545$	−19.4307	+	33.6549i	−0.832319	+	1.44162i
$546$		0			0
$547$	6.35012	+	10.9987i	0.271512	+	0.470272i	0.969249	−	0.246082i	$-0.0791432\pi$
$547$	6.35012	+	10.9987i	0.271512	+	0.470272i	−0.697738	+	0.716353i	$0.745810\pi$
$548$		0			0
$549$	19.6276	+	1.24071i	0.837686	+	0.0529520i
$550$		0			0
$551$	47.2448			2.01270
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.31499	−	73.3181i	0.0982659	−	3.11218i
$556$		0			0
$557$	−7.34743	−	12.7261i	−0.311321	−	0.539223i	0.667328	−	0.744764i	$-0.267438\pi$
$557$	−7.34743	−	12.7261i	−0.311321	−	0.539223i	−0.978649	+	0.205541i	$0.934105\pi$
$558$		0			0
$559$	12.0953			0.511576
$560$		0			0
$561$	−1.27566	+	40.4013i	−0.0538583	+	1.70575i
$562$		0			0
$563$	−26.7860			−1.12890			−0.564448	−	0.825469i	$-0.690911\pi$
$563$	−26.7860			−1.12890			−0.564448	+	0.825469i	$0.690911\pi$
$564$		0			0
$565$	−47.6452			−2.00445
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.48336			0.271797			0.135898	−	0.990723i	$-0.456608\pi$
$569$	6.48336			0.271797			0.135898	+	0.990723i	$0.456608\pi$
$570$		0			0
$571$	15.6326			0.654205			0.327103	−	0.944989i	$-0.393928\pi$
$571$	15.6326			0.654205			0.327103	+	0.944989i	$0.393928\pi$
$572$		0			0
$573$	0.977402	−	30.9553i	0.0408315	−	1.29318i
$574$		0			0
$575$	3.73363			0.155703
$576$		0			0
$577$	−14.5800	−	25.2533i	−0.606974	−	1.05131i	−0.991736	−	0.128294i	$-0.959050\pi$
$577$	−14.5800	−	25.2533i	−0.606974	−	1.05131i	0.384763	−	0.923016i	$-0.374283\pi$
$578$		0			0
$579$	0.711327	−	22.5284i	0.0295617	−	0.936250i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.05043			−0.167752
$584$		0			0
$585$	−18.4648	−	1.16720i	−0.763426	−	0.0482579i
$586$		0			0
$587$	2.33110	+	4.03758i	0.0962146	+	0.166649i	0.910115	−	0.414356i	$-0.135993\pi$
$587$	2.33110	+	4.03758i	0.0962146	+	0.166649i	−0.813900	+	0.581005i	$0.802660\pi$
$588$		0			0
$589$	−5.32932	+	9.23065i	−0.219591	+	0.380342i
$590$		0			0
$591$	−0.347913	+	11.0188i	−0.0143112	+	0.453252i
$592$		0			0
$593$	15.8322	−	27.4222i	0.650150	−	1.12609i	−0.332936	−	0.942950i	$-0.608039\pi$
$593$	15.8322	−	27.4222i	0.650150	−	1.12609i	0.983086	−	0.183144i	$-0.0586275\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−35.3448	+	18.9450i	−1.44657	+	0.775365i
$598$		0			0
$599$	−10.3054			−0.421065			−0.210533	−	0.977587i	$-0.567520\pi$
$599$	−10.3054			−0.421065			−0.210533	+	0.977587i	$0.567520\pi$
$600$		0			0
$601$	4.64993	+	8.05391i	0.189674	+	0.328526i	0.945142	−	0.326661i	$-0.105923\pi$
$601$	4.64993	+	8.05391i	0.189674	+	0.328526i	−0.755467	+	0.655186i	$0.772590\pi$
$602$		0			0
$603$	−44.9355	−	2.84047i	−1.82991	−	0.115673i
$604$		0			0
$605$	15.8532	−	27.4586i	0.644525	−	1.11635i
$606$		0			0
$607$	10.2484	+	17.7507i	0.415969	+	0.720480i	0.995530	−	0.0944495i	$-0.0301091\pi$
$607$	10.2484	+	17.7507i	0.415969	+	0.720480i	−0.579561	+	0.814929i	$0.696776\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.02757	−	10.4401i	0.243850	−	0.422360i
$612$		0			0
$613$	7.17240	+	12.4230i	0.289691	+	0.501759i	0.973736	−	0.227681i	$-0.0731143\pi$
$613$	7.17240	+	12.4230i	0.289691	+	0.501759i	−0.684045	+	0.729440i	$0.739781\pi$
$614$		0			0
$615$	−0.293809	+	9.30522i	−0.0118475	+	0.375223i
$616$		0			0
$617$	−6.47499	+	11.2150i	−0.260673	+	0.451499i	−0.966421	−	0.256964i	$-0.917278\pi$
$617$	−6.47499	+	11.2150i	−0.260673	+	0.451499i	0.705748	+	0.708463i	$0.250611\pi$
$618$		0			0
$619$	−17.6990	+	30.6556i	−0.711383	+	1.23215i	0.252955	+	0.967478i	$0.418598\pi$
$619$	−17.6990	+	30.6556i	−0.711383	+	1.23215i	−0.964338	+	0.264674i	$0.914736\pi$
$620$		0			0
$621$	−1.73803	+	0.794798i	−0.0697448	+	0.0318942i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−13.6460	−	23.6355i	−0.545839	−	0.945422i
$626$		0			0
$627$	31.0152	−	16.6243i	1.23863	−	0.663910i
$628$		0			0
$629$	58.0310			2.31385
$630$		0			0
$631$	33.1936			1.32141			0.660707	−	0.750644i	$-0.270256\pi$
$631$	33.1936			1.32141			0.660707	+	0.750644i	$0.270256\pi$
$632$		0			0
$633$	−16.7133	−	10.3661i	−0.664293	−	0.412016i
$634$		0			0
$635$	−25.6912	−	44.4985i	−1.01952	−	1.76587i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	14.7024	+	0.929373i	0.581619	+	0.0367654i
$640$		0			0
$641$	0.119634	−	0.207213i	0.00472528	−	0.00818442i	−0.863653	−	0.504087i	$-0.831829\pi$
$641$	0.119634	−	0.207213i	0.00472528	−	0.00818442i	0.868378	+	0.495902i	$0.165163\pi$
$642$		0			0
$643$	4.57211	−	7.91913i	0.180307	−	0.312300i	−0.761678	−	0.647955i	$-0.775624\pi$
$643$	4.57211	−	7.91913i	0.180307	−	0.312300i	0.941985	+	0.335655i	$0.108958\pi$
$644$		0			0
$645$	−43.7382	−	27.1278i	−1.72219	−	1.06816i
$646$		0			0
$647$	3.15607	+	5.46648i	0.124078	+	0.214909i	0.921372	−	0.388682i	$-0.127069\pi$
$647$	3.15607	+	5.46648i	0.124078	+	0.214909i	−0.797294	+	0.603591i	$0.793736\pi$
$648$		0			0
$649$	−2.01484	+	3.48980i	−0.0790893	+	0.136987i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.27888	+	3.94713i	0.0891793	+	0.154463i	0.907164	−	0.420776i	$-0.138242\pi$
$653$	2.27888	+	3.94713i	0.0891793	+	0.154463i	−0.817985	+	0.575239i	$0.804909\pi$
$654$		0			0
$655$	−9.90015	+	17.1476i	−0.386831	+	0.670011i
$656$		0			0
$657$	−10.0877	−	20.3367i	−0.393560	−	0.793411i
$658$		0			0
$659$	−16.4631	−	28.5149i	−0.641311	−	1.11078i	−0.985140	−	0.171751i	$-0.945058\pi$
$659$	−16.4631	−	28.5149i	−0.641311	−	1.11078i	0.343829	−	0.939032i	$-0.388276\pi$
$660$		0			0
$661$	−0.541337			−0.0210556			−0.0105278	−	0.999945i	$-0.503351\pi$
$661$	−0.541337			−0.0210556			−0.0105278	+	0.999945i	$0.503351\pi$
$662$		0			0
$663$	0.461918	−	14.6294i	0.0179394	−	0.568159i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.87118	+	3.24097i	−0.0724523	+	0.125491i
$668$		0			0
$669$	−40.6699	+	21.7993i	−1.57239	+	0.842808i
$670$		0			0
$671$	14.3422	−	24.8415i	0.553676	−	0.958994i
$672$		0			0
$673$	−11.8205	−	20.4737i	−0.455647	−	0.789204i	0.543078	−	0.839682i	$-0.317259\pi$
$673$	−11.8205	−	20.4737i	−0.455647	−	0.789204i	−0.998725	+	0.0504780i	$0.983926\pi$
$674$		0			0
$675$	42.9824	+	30.5748i	1.65439	+	1.17682i
$676$		0			0
$677$	2.72989			0.104918			0.0524591	−	0.998623i	$-0.483294\pi$
$677$	2.72989			0.104918			0.0524591	+	0.998623i	$0.483294\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−24.4379	−	15.1572i	−0.936463	−	0.580824i
$682$		0			0
$683$	15.9640	+	27.6504i	0.610844	+	1.05801i	0.991098	+	0.133131i	$0.0425032\pi$
$683$	15.9640	+	27.6504i	0.610844	+	1.05801i	−0.380254	+	0.924882i	$0.624164\pi$
$684$		0			0
$685$	−51.9417			−1.98459
$686$		0			0
$687$	22.1377	−	11.8659i	0.844605	−	0.452712i
$688$		0			0
$689$	1.46667			0.0558756
$690$		0			0
$691$	2.38206			0.0906178			0.0453089	−	0.998973i	$-0.485573\pi$
$691$	2.38206			0.0906178			0.0453089	+	0.998973i	$0.485573\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	37.8069			1.43410
$696$		0			0
$697$	−7.36504			−0.278971
$698$		0			0
$699$	−23.5219	−	14.5890i	−0.889680	−	0.551808i
$700$		0			0
$701$	50.3767			1.90270			0.951350	−	0.308111i	$-0.0996968\pi$
$701$	50.3767			1.90270			0.951350	+	0.308111i	$0.0996968\pi$
$702$		0			0
$703$	−25.2599	−	43.7515i	−0.952697	−	1.65012i
$704$		0			0
$705$	−45.2119	+	24.2338i	−1.70278	+	0.912697i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	40.3201			1.51425			0.757126	−	0.653268i	$-0.226603\pi$
$709$	40.3201			1.51425			0.757126	+	0.653268i	$0.226603\pi$
$710$		0			0
$711$	−5.91449	−	0.373868i	−0.221811	−	0.0140211i
$712$		0			0
$713$	−0.422146	−	0.731178i	−0.0158095	−	0.0273828i
$714$		0			0
$715$	−13.4926	+	23.3698i	−0.504593	+	0.873981i
$716$		0			0
$717$	−28.2313	−	17.5099i	−1.05432	−	0.653920i
$718$		0			0
$719$	−17.0446	+	29.5222i	−0.635658	+	1.10099i	0.350718	+	0.936481i	$0.385938\pi$
$719$	−17.0446	+	29.5222i	−0.635658	+	1.10099i	−0.986375	+	0.164510i	$0.947396\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	34.3796	+	21.3233i	1.27859	+	0.793022i
$724$		0			0
$725$	103.289			3.83606
$726$		0			0
$727$	−10.9453	−	18.9578i	−0.405938	−	0.703105i	0.588492	−	0.808503i	$-0.299722\pi$
$727$	−10.9453	−	18.9578i	−0.405938	−	0.703105i	−0.994430	+	0.105398i	$0.966388\pi$
$728$		0			0
$729$	−26.5172	−	5.08288i	−0.982120	−	0.188255i
$730$		0			0
$731$	20.3581	−	35.2613i	0.752973	−	1.30419i
$732$		0			0
$733$	−4.34416	−	7.52430i	−0.160455	−	0.277916i	0.774577	−	0.632480i	$-0.217963\pi$
$733$	−4.34416	−	7.52430i	−0.160455	−	0.277916i	−0.935032	+	0.354563i	$0.884630\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−32.8351	+	56.8721i	−1.20950	+	2.09491i
$738$		0			0
$739$	−3.34692	−	5.79704i	−0.123119	−	0.213248i	0.797877	−	0.602820i	$-0.205956\pi$
$739$	−3.34692	−	5.79704i	−0.123119	−	0.213248i	−0.920996	+	0.389572i	$0.872623\pi$
$740$		0			0
$741$	−11.2307	+	6.01969i	−0.412569	+	0.221139i
$742$		0			0
$743$	21.5001	−	37.2392i	0.788761	−	1.36617i	−0.137965	−	0.990437i	$-0.544056\pi$
$743$	21.5001	−	37.2392i	0.788761	−	1.36617i	0.926726	−	0.375737i	$-0.122611\pi$
$744$		0			0
$745$	26.9404	−	46.6621i	0.987019	−	1.70957i
$746$		0			0
$747$	−0.674582	−	1.35995i	−0.0246816	−	0.0497579i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	8.36369	+	14.4863i	0.305196	+	0.528614i	0.977305	−	0.211838i	$-0.0679448\pi$
$751$	8.36369	+	14.4863i	0.305196	+	0.528614i	−0.672109	+	0.740452i	$0.734612\pi$
$752$		0			0
$753$	−1.66510	+	52.7354i	−0.0606796	+	1.92178i
$754$		0			0
$755$	−89.0438			−3.24064
$756$		0			0
$757$	−4.68561			−0.170301			−0.0851507	−	0.996368i	$-0.527137\pi$
$757$	−4.68561			−0.170301			−0.0851507	+	0.996368i	$0.527137\pi$
$758$		0			0
$759$	−0.0879685	+	2.78605i	−0.00319306	+	0.101127i
$760$		0			0
$761$	−25.8242	−	44.7288i	−0.936127	−	1.62142i	−0.772613	−	0.634878i	$-0.781050\pi$
$761$	−25.8242	−	44.7288i	−0.936127	−	1.62142i	−0.163514	−	0.986541i	$-0.552283\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−34.4817	+	51.8658i	−1.24669	+	1.87521i
$766$		0			0
$767$	0.729576	−	1.26366i	0.0263435	−	0.0456282i
$768$		0			0
$769$	−15.3910	+	26.6580i	−0.555014	+	0.961313i	0.442888	+	0.896577i	$0.353954\pi$
$769$	−15.3910	+	26.6580i	−0.555014	+	0.961313i	−0.997902	+	0.0647361i	$0.979379\pi$
$770$		0			0
$771$	10.3942	−	5.57131i	0.374336	−	0.200646i
$772$		0			0
$773$	13.5259	+	23.4275i	0.486491	+	0.842627i	0.999879	−	0.0155292i	$-0.00494329\pi$
$773$	13.5259	+	23.4275i	0.486491	+	0.842627i	−0.513388	+	0.858156i	$0.671610\pi$
$774$		0			0
$775$	−11.6512	+	20.1805i	−0.418525	+	0.724907i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.20588	+	5.55275i	0.114863	+	0.198948i
$780$		0			0
$781$	10.7433	−	18.6080i	0.384426	−	0.665845i
$782$		0			0
$783$	−48.0818	+	21.9877i	−1.71830	+	0.785777i
$784$		0			0
$785$	−22.5370	−	39.0352i	−0.804380	−	1.39323i
$786$		0			0
$787$	35.1995			1.25473			0.627363	−	0.778727i	$-0.284134\pi$
$787$	35.1995			1.25473			0.627363	+	0.778727i	$0.284134\pi$
$788$		0			0
$789$	6.77085	+	4.19950i	0.241049	+	0.149506i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−5.19335	+	8.99514i	−0.184421	+	0.319427i
$794$		0			0
$795$	−5.30367	−	3.28950i	−0.188102	−	0.116667i
$796$		0			0
$797$	23.8268	−	41.2692i	0.843988	−	1.46183i	−0.0425084	−	0.999096i	$-0.513535\pi$
$797$	23.8268	−	41.2692i	0.843988	−	1.46183i	0.886497	−	0.462735i	$-0.153132\pi$
$798$		0			0
$799$	−20.2906	−	35.1443i	−0.717829	−	1.24332i
$800$		0			0
$801$	20.2960	−	30.5282i	0.717122	−	1.07866i
$802$		0			0
$803$	−33.1102			−1.16843
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.9787	−	6.95664i	0.456872	−	0.244885i
$808$		0			0
$809$	−9.87711	−	17.1077i	−0.347261	−	0.601473i	0.638501	−	0.769621i	$-0.279555\pi$
$809$	−9.87711	−	17.1077i	−0.347261	−	0.601473i	−0.985762	+	0.168148i	$0.946221\pi$
$810$		0			0
$811$	49.2424			1.72913			0.864567	−	0.502518i	$-0.167593\pi$
$811$	49.2424			1.72913			0.864567	+	0.502518i	$0.167593\pi$
$812$		0			0
$813$	9.69086	+	6.01057i	0.339873	+	0.210800i
$814$		0			0
$815$	−13.2793			−0.465155
$816$		0			0
$817$	−35.4463			−1.24011
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.0003			0.349012			0.174506	−	0.984656i	$-0.444167\pi$
$821$	10.0003			0.349012			0.174506	+	0.984656i	$0.444167\pi$
$822$		0			0
$823$	−35.0276			−1.22099			−0.610493	−	0.792021i	$-0.709029\pi$
$823$	−35.0276			−1.22099			−0.610493	+	0.792021i	$0.709029\pi$
$824$		0			0
$825$	67.8072	−	36.3449i	2.36074	−	1.26537i
$826$		0			0
$827$	−22.7079			−0.789631			−0.394816	−	0.918760i	$-0.629192\pi$
$827$	−22.7079			−0.789631			−0.394816	+	0.918760i	$0.629192\pi$
$828$		0			0
$829$	−6.22083	−	10.7748i	−0.216058	−	0.374224i	0.737541	−	0.675302i	$-0.235987\pi$
$829$	−6.22083	−	10.7748i	−0.216058	−	0.374224i	−0.953599	+	0.301078i	$0.902653\pi$
$830$		0			0
$831$	16.5881	+	10.2884i	0.575434	+	0.356902i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	36.5888			1.26621
$836$		0			0
$837$	1.12779	−	11.8745i	0.0389822	−	0.410441i
$838$		0			0
$839$	13.8249	+	23.9455i	0.477290	+	0.826690i	0.999661	−	0.0260281i	$-0.00828595\pi$
$839$	13.8249	+	23.9455i	0.477290	+	0.826690i	−0.522372	+	0.852718i	$0.674953\pi$
$840$		0			0
$841$	−37.2652	+	64.5453i	−1.28501	+	2.22570i
$842$		0			0
$843$	−22.9214	+	12.2860i	−0.789454	+	0.423151i
$844$		0			0
$845$	−20.4153	+	35.3604i	−0.702309	+	1.21643i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.802057	−	25.4020i	0.0275265	−	0.871793i
$850$		0			0
$851$	4.00178			0.137179
$852$		0			0
$853$	22.0459	+	38.1847i	0.754839	+	1.30742i	0.945454	+	0.325754i	$0.105618\pi$
$853$	22.0459	+	38.1847i	0.754839	+	1.30742i	−0.190616	+	0.981665i	$0.561048\pi$
$854$		0			0
$855$	54.1127	+	3.42059i	1.85062	+	0.116982i
$856$		0			0
$857$	−13.3838	+	23.1814i	−0.457182	+	0.791862i	−0.998811	−	0.0487557i	$-0.984474\pi$
$857$	−13.3838	+	23.1814i	−0.457182	+	0.791862i	0.541629	+	0.840618i	$0.317808\pi$
$858$		0			0
$859$	−10.0951	−	17.4852i	−0.344439	−	0.596587i	0.640812	−	0.767698i	$-0.278598\pi$
$859$	−10.0951	−	17.4852i	−0.344439	−	0.596587i	−0.985252	+	0.171111i	$0.945264\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.74538	+	8.21923i	−0.161534	+	0.279786i	−0.935419	−	0.353541i	$-0.884978\pi$
$863$	−4.74538	+	8.21923i	−0.161534	+	0.279786i	0.773885	+	0.633327i	$0.218311\pi$
$864$		0			0
$865$	12.4659	+	21.5915i	0.423852	+	0.734133i
$866$		0			0
$867$	−16.8489	−	10.4502i	−0.572218	−	0.354908i
$868$		0			0
$869$	−4.32182	+	7.48560i	−0.146608	+	0.253932i
$870$		0			0
$871$	11.8897	−	20.5935i	0.402866	−	0.697784i
$872$		0			0
$873$	11.8731	+	23.9360i	0.401843	+	0.810110i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.6227	−	25.3273i	−0.493774	−	0.855242i	0.506200	−	0.862416i	$-0.331050\pi$
$877$	−14.6227	−	25.3273i	−0.493774	−	0.855242i	−0.999974	+	0.00717380i	$0.997716\pi$
$878$		0			0
$879$	27.6422	+	17.1445i	0.932347	+	0.578271i
$880$		0			0
$881$	−37.2768			−1.25589			−0.627944	−	0.778259i	$-0.716103\pi$
$881$	−37.2768			−1.25589			−0.627944	+	0.778259i	$0.716103\pi$
$882$		0			0
$883$	−56.9436			−1.91630			−0.958152	−	0.286260i	$-0.907588\pi$
$883$	−56.9436			−1.91630			−0.958152	+	0.286260i	$0.907588\pi$
$884$		0			0
$885$	−5.47244	+	2.93325i	−0.183954	+	0.0986002i
$886$		0			0
$887$	−4.96127	−	8.59316i	−0.166583	−	0.288530i	0.770633	−	0.637279i	$-0.219940\pi$
$887$	−4.96127	−	8.59316i	−0.166583	−	0.288530i	−0.937216	+	0.348749i	$0.886607\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−23.8278	+	31.3533i	−0.798260	+	1.05038i
$892$		0			0
$893$	−17.6643	+	30.5955i	−0.591114	+	1.02384i
$894$		0			0
$895$	33.2431	−	57.5787i	1.11119	−	1.92465i
$896$		0			0
$897$	0.0318536	−	1.00884i	0.00106356	−	0.0336840i
$898$		0			0
$899$	−11.6785	−	20.2277i	−0.389499	−	0.674632i
$900$		0			0
$901$	2.46862	−	4.27577i	0.0822416	−	0.142447i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.64664	−	4.58412i	−0.0879774	−	0.152381i
$906$		0			0
$907$	12.2887	−	21.2847i	0.408040	−	0.706747i	−0.586630	−	0.809855i	$-0.699546\pi$
$907$	12.2887	−	21.2847i	0.408040	−	0.706747i	0.994670	+	0.103109i	$0.0328789\pi$
$908$		0			0
$909$	−18.3093	+	27.5400i	−0.607280	+	0.913443i
$910$		0			0
$911$	9.73496	+	16.8614i	0.322534	+	0.558645i	0.981010	−	0.193957i	$-0.0621321\pi$
$911$	9.73496	+	16.8614i	0.322534	+	0.558645i	−0.658476	+	0.752601i	$0.728799\pi$
$912$		0			0
$913$	−2.21413			−0.0732770
$914$		0			0
$915$	38.9545	−	20.8798i	1.28780	−	0.690264i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	6.61992	−	11.4660i	0.218371	−	0.378230i	−0.735939	−	0.677048i	$-0.763259\pi$
$919$	6.61992	−	11.4660i	0.218371	−	0.378230i	0.954310	+	0.298818i	$0.0965923\pi$
$920$		0			0
$921$	−1.58204	+	50.1050i	−0.0521301	+	1.65101i
$922$		0			0
$923$	−3.89017	+	6.73798i	−0.128047	+	0.221783i
$924$		0			0
$925$	−55.2247	−	95.6519i	−1.81578	−	3.14502i
$926$		0			0
$927$	−3.64053	−	7.33925i	−0.119571	−	0.241053i
$928$		0			0
$929$	−31.7363			−1.04124			−0.520618	−	0.853790i	$-0.674298\pi$
$929$	−31.7363			−1.04124			−0.520618	+	0.853790i	$0.674298\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.743049	+	23.5331i	−0.0243263	+	0.770440i
$934$		0			0
$935$	45.4199	+	78.6696i	1.48539	+	2.57277i
$936$		0			0
$937$	13.5019			0.441087			0.220543	−	0.975377i	$-0.429217\pi$
$937$	13.5019			0.441087			0.220543	+	0.975377i	$0.429217\pi$
$938$		0			0
$939$	−0.757852	+	24.0020i	−0.0247316	+	0.783274i
$940$		0			0
$941$	39.6572			1.29279			0.646394	−	0.763004i	$-0.276276\pi$
$941$	39.6572			1.29279			0.646394	+	0.763004i	$0.276276\pi$
$942$		0			0
$943$	−0.507889			−0.0165391
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−61.0344			−1.98335			−0.991675	−	0.128764i	$-0.958899\pi$
$947$	−61.0344			−1.98335			−0.991675	+	0.128764i	$0.958899\pi$
$948$		0			0
$949$	11.9893			0.389188
$950$		0			0
$951$	−1.26190	+	39.9656i	−0.0409198	+	1.29597i
$952$		0			0
$953$	5.22726			0.169328			0.0846638	−	0.996410i	$-0.473018\pi$
$953$	5.22726			0.169328			0.0846638	+	0.996410i	$0.473018\pi$
$954$		0			0
$955$	−34.8005	−	60.2762i	−1.12612	−	1.95049i
$956$		0			0
$957$	−2.43361	+	77.0749i	−0.0786674	+	2.49148i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−25.7306			−0.830018
$962$		0			0
$963$	−17.9247	+	26.9616i	−0.577617	+	0.868825i
$964$		0			0
$965$	−25.3269	−	43.8674i	−0.815301	−	1.41214i
$966$		0			0
$967$	10.2035	−	17.6729i	0.328121	−	0.568323i	−0.654018	−	0.756479i	$-0.726918\pi$
$967$	10.2035	−	17.6729i	0.328121	−	0.568323i	0.982139	+	0.188156i	$0.0602511\pi$
$968$		0			0
$969$	−1.35369	+	42.8727i	−0.0434868	+	1.37727i
$970$		0			0
$971$	0.589402	−	1.02087i	0.0189148	−	0.0327614i	−0.856413	−	0.516291i	$-0.827312\pi$
$971$	0.589402	−	1.02087i	0.0189148	−	0.0327614i	0.875328	+	0.483530i	$0.160646\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−24.5531	+	13.1606i	−0.786328	+	0.421476i
$976$		0			0
$977$	8.20973			0.262653			0.131326	−	0.991339i	$-0.458076\pi$
$977$	8.20973			0.262653			0.131326	+	0.991339i	$0.458076\pi$
$978$		0			0
$979$	−26.7342	−	46.3049i	−0.854427	−	1.47991i
$980$		0			0
$981$	−13.3094	−	26.8316i	−0.424937	−	0.856667i
$982$		0			0
$983$	−0.753481	+	1.30507i	−0.0240323	+	0.0416252i	−0.877791	−	0.479043i	$-0.840984\pi$
$983$	−0.753481	+	1.30507i	−0.0240323	+	0.0416252i	0.853759	+	0.520668i	$0.174317\pi$
$984$		0			0
$985$	12.3875	+	21.4558i	0.394698	+	0.683638i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.40389	−	2.43160i	0.0446410	−	0.0773204i
$990$		0			0
$991$	−16.2229	−	28.0990i	−0.515339	−	0.892593i	−0.999842	−	0.0178030i	$-0.994333\pi$
$991$	−16.2229	−	28.0990i	−0.515339	−	0.892593i	0.484503	−	0.874790i	$-0.339001\pi$
$992$		0			0
$993$	0.855615	−	27.0982i	0.0271521	−	0.859935i
$994$		0			0
$995$	−45.0608	+	78.0476i	−1.42852	+	2.47428i
$996$		0			0
$997$	−6.26198	+	10.8461i	−0.198319	+	0.343498i	−0.947983	−	0.318320i	$-0.896881\pi$
$997$	−6.26198	+	10.8461i	−0.198319	+	0.343498i	0.749665	+	0.661818i	$0.230215\pi$
$998$		0			0
$999$	46.0694	+	32.7707i	1.45757	+	1.03682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.i.j.373.6		24
3.2	odd	2		5292.2.i.j.1549.1		24
7.2	even	3		1764.2.j.i.589.3	✓	24
7.3	odd	6		1764.2.l.j.949.2		24
7.4	even	3		1764.2.l.j.949.11		24
7.5	odd	6		1764.2.j.i.589.10	yes	24
7.6	odd	2	inner	1764.2.i.j.373.7		24
9.2	odd	6		5292.2.l.j.3313.12		24
9.7	even	3		1764.2.l.j.961.11		24
21.2	odd	6		5292.2.j.i.1765.1		24
21.5	even	6		5292.2.j.i.1765.12		24
21.11	odd	6		5292.2.l.j.361.12		24
21.17	even	6		5292.2.l.j.361.1		24
21.20	even	2		5292.2.i.j.1549.12		24
63.2	odd	6		5292.2.j.i.3529.1		24
63.11	odd	6		5292.2.i.j.2125.1		24
63.16	even	3		1764.2.j.i.1177.3	yes	24
63.20	even	6		5292.2.l.j.3313.1		24
63.25	even	3	inner	1764.2.i.j.1537.6		24
63.34	odd	6		1764.2.l.j.961.2		24
63.38	even	6		5292.2.i.j.2125.12		24
63.47	even	6		5292.2.j.i.3529.12		24
63.52	odd	6	inner	1764.2.i.j.1537.7		24
63.61	odd	6		1764.2.j.i.1177.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.6		24	1.1	even	1	trivial
1764.2.i.j.373.7		24	7.6	odd	2	inner
1764.2.i.j.1537.6		24	63.25	even	3	inner
1764.2.i.j.1537.7		24	63.52	odd	6	inner
1764.2.j.i.589.3	✓	24	7.2	even	3
1764.2.j.i.589.10	yes	24	7.5	odd	6
1764.2.j.i.1177.3	yes	24	63.16	even	3
1764.2.j.i.1177.10	yes	24	63.61	odd	6
1764.2.l.j.949.2		24	7.3	odd	6
1764.2.l.j.949.11		24	7.4	even	3
1764.2.l.j.961.2		24	63.34	odd	6
1764.2.l.j.961.11		24	9.7	even	3
5292.2.i.j.1549.1		24	3.2	odd	2
5292.2.i.j.1549.12		24	21.20	even	2
5292.2.i.j.2125.1		24	63.11	odd	6
5292.2.i.j.2125.12		24	63.38	even	6
5292.2.j.i.1765.1		24	21.2	odd	6
5292.2.j.i.1765.12		24	21.5	even	6
5292.2.j.i.3529.1		24	63.2	odd	6
5292.2.j.i.3529.12		24	63.47	even	6
5292.2.l.j.361.1		24	21.17	even	6
5292.2.l.j.361.12		24	21.11	odd	6
5292.2.l.j.3313.1		24	63.20	even	6
5292.2.l.j.3313.12		24	9.2	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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0546616 + 1.73119i) q^{3} +(1.94623 + 3.37097i) q^{5} +(-2.99402 - 0.189259i) q^{9} +O(q^{10})\)	\(q+(-0.0546616 + 1.73119i) q^{3} +(1.94623 + 3.37097i) q^{5} +(-2.99402 - 0.189259i) q^{9} +(-2.18778 + 3.78935i) q^{11} +(0.792201 - 1.37213i) q^{13} +(-5.94217 + 3.18503i) q^{15} +(-2.66678 - 4.61900i) q^{17} +(-2.32161 + 4.02115i) q^{19} +(-0.183900 - 0.318523i) q^{23} +(-5.07564 + 8.79126i) q^{25} +(0.491301 - 5.17287i) q^{27} +(-5.08750 - 8.81180i) q^{29} +2.29552 q^{31} +(-6.44049 - 3.99460i) q^{33} +(-5.44017 + 9.42265i) q^{37} +(2.33212 + 1.44645i) q^{39} +(0.690443 - 1.19588i) q^{41} +(3.81699 + 6.61122i) q^{43} +(-5.18908 - 10.4611i) q^{45} +7.60865 q^{47} +(8.14212 - 4.36422i) q^{51} +(0.462847 + 0.801674i) q^{53} -17.0317 q^{55} +(-6.83447 - 4.23895i) q^{57} +0.920949 q^{59} -6.55560 q^{61} +6.16722 q^{65} +15.0084 q^{67} +(0.561476 - 0.300954i) q^{69} -4.91059 q^{71} +(3.78353 + 6.55327i) q^{73} +(-14.9419 - 9.26743i) q^{75} +1.97543 q^{79} +(8.92836 + 1.13329i) q^{81} +(0.253011 + 0.438227i) q^{83} +(10.3803 - 17.9793i) q^{85} +(15.5330 - 8.32575i) q^{87} +(-6.10987 + 10.5826i) q^{89} +(-0.125477 + 3.97398i) q^{93} -18.0736 q^{95} +(-4.45315 - 7.71308i) q^{97} +(7.26745 - 10.9314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} - 12 q^{37} + 8 q^{51} - 16 q^{53} + 52 q^{57} + 72 q^{65} - 24 q^{67} + 48 q^{71} - 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93} - 64 q^{95} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 - 12 * q^37 + 8 * q^51 - 16 * q^53 + 52 * q^57 + 72 * q^65 - 24 * q^67 + 48 * q^71 - 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 64 * q^95 - 4 * q^99

Introduction

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