LMFDB - Embedded newform 1764.2.i.j.1537.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1764.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1537.7
Character	$\chi$	$=$	1764.1537
Dual form			1764.2.i.j.373.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0546616	+	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	−0.00877856	+	0.999961i	$0.502794\pi$
$5$	−1.94623	+	3.37097i	−0.870381	+	1.50754i	−0.861603	+	0.507583i	$0.830539\pi$
$6$		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	−0.980708	−	0.195476i	$-0.937375\pi$
$11$	−2.18778	−	3.78935i	−0.659642	−	1.14253i	0.321067	−	0.947057i	$-0.395959\pi$
$12$		0			0
$13$	−0.792201	−	1.37213i	−0.219717	−	0.380561i	0.735004	−	0.678062i	$-0.237180\pi$
$13$	−0.792201	−	1.37213i	−0.219717	−	0.380561i	−0.954721	+	0.297501i	$0.903847\pi$
$14$		0			0
$15$	−5.94217	−	3.18503i	−1.53426	−	0.822371i
$16$		0			0
$17$	2.66678	−	4.61900i	0.646789	−	1.12027i	−0.337096	−	0.941470i	$-0.609445\pi$
$17$	2.66678	−	4.61900i	0.646789	−	1.12027i	0.983885	−	0.178801i	$-0.0572219\pi$
$18$		0			0
$19$	2.32161	+	4.02115i	0.532614	+	0.922515i	0.999275	+	0.0380786i	$0.0121237\pi$
$19$	2.32161	+	4.02115i	0.532614	+	0.922515i	−0.466660	+	0.884437i	$0.654543\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.183900	+	0.318523i	−0.0383457	+	0.0664167i	−0.884561	−	0.466424i	$-0.845542\pi$
$23$	−0.183900	+	0.318523i	−0.0383457	+	0.0664167i	0.846216	+	0.532841i	$0.178875\pi$
$24$		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	−0.188422	+	0.982088i	$0.560337\pi$
$29$	−5.08750	+	8.81180i	−0.944724	+	1.63631i	−0.756302	+	0.654222i	$0.772996\pi$
$30$		0			0
$31$	−2.29552			−0.412288			−0.206144	−	0.978522i	$-0.566092\pi$
$31$	−2.29552			−0.412288			−0.206144	+	0.978522i	$0.566092\pi$
$32$		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	−0.834596	−	0.550862i	$-0.814299\pi$
$37$	−5.44017	−	9.42265i	−0.894359	−	1.54907i	−0.0597623	−	0.998213i	$-0.519034\pi$
$38$		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	$-0.201057\pi$
$41$	−0.690443	−	1.19588i	−0.107829	−	0.186766i	−0.914891	+	0.403702i	$0.867723\pi$
$42$		0			0
$43$	3.81699	−	6.61122i	0.582086	−	1.00820i	−0.413146	−	0.910665i	$-0.635570\pi$
$43$	3.81699	−	6.61122i	0.582086	−	1.00820i	0.995232	−	0.0975372i	$-0.0310965\pi$
$44$		0			0
$45$	5.18908	−	10.4611i	0.773542	−	1.55945i
$46$		0			0
$47$	−7.60865			−1.10984			−0.554918	−	0.831905i	$-0.687250\pi$
$47$	−7.60865			−1.10984			−0.554918	+	0.831905i	$0.687250\pi$
$48$		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	−0.832485	−	0.554048i	$-0.813083\pi$
$53$	0.462847	−	0.801674i	0.0635769	−	0.110118i	0.896062	+	0.443929i	$0.146416\pi$
$54$		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	$-0.519094\pi$
$59$	−0.920949			−0.119897			−0.0599487	+	0.998201i	$0.519094\pi$
$60$		0			0
$61$	6.55560			0.839358			0.419679	−	0.907673i	$-0.362143\pi$
$61$	6.55560			0.839358			0.419679	+	0.907673i	$0.362143\pi$
$62$		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	$-0.979359\pi$
$73$	−3.78353	+	6.55327i	−0.442829	+	0.767003i	0.555069	+	0.831804i	$0.312692\pi$
$74$		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	$-0.842174\pi$
$83$	−0.253011	+	0.438227i	−0.0277715	+	0.0481017i	0.851806	+	0.523858i	$0.175508\pi$
$84$		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	0.983684	+	0.179906i	$0.0575794\pi$
$89$	6.10987	+	10.5826i	0.647645	+	1.12175i	−0.336039	+	0.941848i	$0.609087\pi$
$90$		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	$-0.683991\pi$
$97$	4.45315	−	7.71308i	0.452149	−	0.783145i	0.998519	+	0.0543987i	$0.0173242\pi$
$98$		0			0
$99$	7.26745	+	10.9314i	0.730406	+	1.09864i
$100$		0			0
$101$	−5.51180	−	9.54672i	−0.548445	−	0.949935i	−0.998381	−	0.0568740i	$-0.981887\pi$
$101$	−5.51180	−	9.54672i	−0.548445	−	0.949935i	0.449936	−	0.893061i	$-0.351447\pi$
$102$		0			0
$103$	−1.36543	+	2.36499i	−0.134540	+	0.233029i	−0.925421	−	0.378939i	$-0.876289\pi$
$103$	−1.36543	+	2.36499i	−0.134540	+	0.233029i	0.790882	+	0.611969i	$0.209622\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.39605	+	9.34623i	0.521655	+	0.903534i	0.999683	+	0.0251887i	$0.00801867\pi$
$107$	5.39605	+	9.34623i	0.521655	+	0.903534i	−0.478027	+	0.878345i	$0.658648\pi$
$108$		0			0
$109$	4.99187	−	8.64617i	0.478134	−	0.828153i	−0.521551	−	0.853220i	$-0.674647\pi$
$109$	4.99187	−	8.64617i	0.478134	−	0.828153i	0.999686	+	0.0250668i	$0.00797984\pi$
$110$		0			0
$111$	16.0150	−	9.93302i	1.52008	−	0.942800i
$112$		0			0
$113$	−6.12019	−	10.6005i	−0.575739	−	0.997209i	−0.995961	−	0.0897875i	$-0.971381\pi$
$113$	−6.12019	−	10.6005i	−0.575739	−	0.997209i	0.420222	−	0.907421i	$-0.361952\pi$
$114$		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	$-0.904663\pi$
$131$	−2.54342	+	4.40532i	−0.222219	+	0.384895i	0.733262	+	0.679946i	$0.237997\pi$
$132$		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	−0.996562	−	0.0828538i	$-0.973597\pi$
$137$	−6.67208	−	11.5564i	−0.570034	−	0.987328i	0.426527	−	0.904475i	$-0.359737\pi$
$138$		0			0
$139$	−4.85642	−	8.41157i	−0.411916	−	0.713460i	0.583183	−	0.812341i	$-0.301807\pi$
$139$	−4.85642	−	8.41157i	−0.411916	−	0.713460i	−0.995099	+	0.0988809i	$0.968474\pi$
$140$		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	0.429856	+	0.902897i	$0.358564\pi$
$149$	−6.92116	+	11.9878i	−0.567004	+	0.982079i	−0.996860	+	0.0791820i	$0.974769\pi$
$150$		0			0
$151$	−11.4380	−	19.8112i	−0.930809	−	1.61221i	−0.781942	−	0.623352i	$-0.785771\pi$
$151$	−11.4380	−	19.8112i	−0.930809	−	1.61221i	−0.148867	−	0.988857i	$-0.547563\pi$
$152$		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	$-0.347101\pi$
$157$	11.5798			0.924170			0.462085	+	0.886836i	$0.347101\pi$
$158$		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	0.791458	−	0.611224i	$-0.209323\pi$
$163$	−1.70577	−	2.95449i	−0.133607	−	0.231413i	−0.925064	+	0.379811i	$0.875989\pi$
$164$		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	$-0.285151\pi$
$167$	−4.69996	−	8.14057i	−0.363694	−	0.629936i	−0.988566	+	0.150791i	$0.951818\pi$
$168$		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	$-0.578291\pi$
$173$	−6.40512			−0.486972			−0.243486	+	0.969904i	$0.578291\pi$
$174$		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	0.347460	+	0.937695i	$0.387044\pi$
$179$	−8.54038	+	14.7924i	−0.638338	+	1.10563i	−0.985797	+	0.167938i	$0.946289\pi$
$180$		0			0
$181$	1.35988			0.101079			0.0505395	−	0.998722i	$-0.483906\pi$
$181$	1.35988			0.101079			0.0505395	+	0.998722i	$0.483906\pi$
$182$		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	0.0845818	+	0.996417i	$0.473045\pi$
$199$	−11.5764	+	20.0510i	−0.820631	+	1.42137i	−0.905213	+	0.424958i	$0.860289\pi$
$200$		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	0.601715	−	0.798711i	$-0.294484\pi$
$211$	−5.67737	−	9.83349i	−0.390846	−	0.676965i	−0.992561	+	0.121745i	$0.961151\pi$
$212$		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	−0.0545504	+	0.998511i	$0.517373\pi$
$223$	−13.3206	+	23.0719i	−0.892011	+	1.54501i	−0.837461	+	0.546498i	$0.815961\pi$
$224$		0			0
$225$	16.8604	+	25.3606i	1.12403	+	1.69071i
$226$		0			0
$227$	8.30136	+	14.3784i	0.550981	+	0.954326i	0.998204	+	0.0599042i	$0.0190795\pi$
$227$	8.30136	+	14.3784i	0.550981	+	0.954326i	−0.447224	+	0.894422i	$0.647587\pi$
$228$		0			0
$229$	7.25072	−	12.5586i	0.479141	−	0.829897i	−0.520573	−	0.853817i	$-0.674282\pi$
$229$	7.25072	−	12.5586i	0.479141	−	0.829897i	0.999714	+	0.0239205i	$0.00761485\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.99020	−	13.8394i	−0.523456	−	0.906652i	−0.999627	−	0.0272993i	$-0.991309\pi$
$233$	−7.99020	−	13.8394i	−0.523456	−	0.906652i	0.476172	−	0.879352i	$-0.342024\pi$
$234$		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	−0.989426	−	0.145040i	$-0.953669\pi$
$239$	−9.58994	−	16.6103i	−0.620322	−	1.07443i	0.369104	−	0.929388i	$-0.379665\pi$
$240$		0			0
$241$	−11.6785	−	20.2277i	−0.752276	−	1.30298i	−0.946717	−	0.322067i	$-0.895623\pi$
$241$	−11.6785	−	20.2277i	−0.752276	−	1.30298i	0.194441	−	0.980914i	$-0.437711\pi$
$242$		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	$-0.911237\pi$
$251$	−30.4619			−1.92274			−0.961371	+	0.275257i	$0.911237\pi$
$252$		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	$-0.765218\pi$
$257$	3.40438	−	5.89657i	0.212360	−	0.367818i	0.952453	+	0.304687i	$0.0985518\pi$
$258$		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	0.928184	−	0.372122i	$-0.121370\pi$
$263$	2.30000	+	3.98372i	0.141824	+	0.245647i	−0.786359	+	0.617769i	$0.788037\pi$
$264$		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	$-0.749880\pi$
$269$	4.25090	−	7.36277i	0.259182	−	0.448916i	0.966023	+	0.258456i	$0.0832138\pi$
$270$		0			0
$271$	−3.29191	−	5.70175i	−0.199969	−	0.346357i	0.748549	−	0.663079i	$-0.230751\pi$
$271$	−3.29191	−	5.70175i	−0.199969	−	0.346357i	−0.948518	+	0.316723i	$0.897417\pi$
$272$		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	0.984163	−	0.177266i	$-0.0567254\pi$
$277$	5.63483	+	9.75982i	0.338564	+	0.586411i	−0.645599	+	0.763677i	$0.723392\pi$
$278$		0			0
$279$	6.87285	−	0.434448i	0.411467	−	0.0260097i
$280$		0			0
$281$	7.50741	−	13.0032i	0.447854	−	0.775707i	−0.550392	−	0.834907i	$-0.685522\pi$
$281$	7.50741	−	13.0032i	0.447854	−	0.775707i	0.998246	+	0.0592000i	$0.0188550\pi$
$282$		0			0
$283$	14.6731			0.872227			0.436114	−	0.899892i	$-0.356355\pi$
$283$	14.6731			0.872227			0.436114	+	0.899892i	$0.356355\pi$
$284$		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	−0.998374	−	0.0570099i	$-0.981843\pi$
$293$	−9.38981	−	16.2636i	−0.548559	−	0.950132i	0.449815	−	0.893122i	$-0.351490\pi$
$294$		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	$-0.809343\pi$
$307$	−28.9425			−1.65184			−0.825919	+	0.563789i	$0.809343\pi$
$308$		0			0
$309$	−4.16888	−	2.23454i	−0.237159	−	0.127118i
$310$		0			0
$311$	−13.5936			−0.770824			−0.385412	−	0.922745i	$-0.625941\pi$
$311$	−13.5936			−0.770824			−0.385412	+	0.922745i	$0.625941\pi$
$312$		0			0
$313$	−13.8644			−0.783665			−0.391832	−	0.920037i	$-0.628159\pi$
$313$	−13.8644			−0.783665			−0.391832	+	0.920037i	$0.628159\pi$
$314$		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	0.946671	−	0.322203i	$-0.104423\pi$
$337$	3.56686	+	6.17799i	0.194299	+	0.336537i	−0.752371	+	0.658739i	$0.771090\pi$
$338$		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	$-0.925482\pi$
$349$	−5.33296	+	9.23696i	−0.285467	+	0.494443i	0.687256	+	0.726416i	$0.258815\pi$
$350$		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	$-0.0556394\pi$
$353$	6.42132	+	11.1221i	0.341772	+	0.591967i	−0.642989	+	0.765875i	$0.722306\pi$
$354$		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	−0.975653	−	0.219318i	$-0.929617\pi$
$359$	−12.8417	−	22.2426i	−0.677761	−	1.17392i	0.297892	−	0.954600i	$-0.403716\pi$
$360$		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	$-0.0204824\pi$
$367$	8.49197	+	14.7085i	0.443277	+	0.767778i	−0.554653	+	0.832082i	$0.687149\pi$
$368$		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	−0.729884	−	0.683571i	$-0.760426\pi$
$373$	4.38503	−	7.59509i	0.227048	−	0.393259i	0.956932	+	0.290312i	$0.0937592\pi$
$374$		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	$-0.759420\pi$
$383$	4.50360	−	7.80046i	0.230123	−	0.398585i	0.957844	+	0.287288i	$0.0927538\pi$
$384$		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	0.963007	−	0.269476i	$-0.0868504\pi$
$389$	4.89390	+	8.47649i	0.248131	+	0.429775i	−0.714876	+	0.699251i	$0.753517\pi$
$390$		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	$-0.280239\pi$
$397$	−6.95929	−	12.0538i	−0.349277	−	0.604965i	−0.986121	+	0.166027i	$0.946906\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.7414	−	20.3367i	0.586336	−	1.01556i	−0.408371	−	0.912816i	$-0.633903\pi$
$401$	11.7414	−	20.3367i	0.586336	−	1.01556i	0.994707	−	0.102748i	$-0.0327636\pi$
$402$		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	$-0.609360\pi$
$409$	−13.6245			−0.673689			−0.336844	+	0.941560i	$0.609360\pi$
$410$		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	$-0.228912\pi$
$419$	−3.97733	−	6.88894i	−0.194305	−	0.336547i	−0.946673	+	0.322197i	$0.895579\pi$
$420$		0			0
$421$	1.30584	−	2.26178i	0.0636426	−	0.110232i	−0.832448	−	0.554102i	$-0.813062\pi$
$421$	1.30584	−	2.26178i	0.0636426	−	0.110232i	0.896091	+	0.443870i	$0.146395\pi$
$422$		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	−0.846344	−	0.532636i	$-0.821201\pi$
$431$	0.791065	−	1.37017i	0.0381043	−	0.0659985i	0.884449	+	0.466638i	$0.154535\pi$
$432$		0			0
$433$	5.17110			0.248507			0.124254	−	0.992250i	$-0.460346\pi$
$433$	5.17110			0.248507			0.124254	+	0.992250i	$0.460346\pi$
$434$		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	$-0.703111\pi$
$439$	−24.9611			−1.19133			−0.595665	+	0.803233i	$0.703111\pi$
$440$		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	$-0.858746\pi$
$461$	−1.71236	+	2.96589i	−0.0797524	+	0.138135i	0.823391	+	0.567475i	$0.192080\pi$
$462$		0			0
$463$	2.38499	+	4.13092i	0.110840	+	0.191980i	0.916109	−	0.400929i	$-0.131313\pi$
$463$	2.38499	+	4.13092i	0.110840	+	0.191980i	−0.805269	+	0.592909i	$0.797979\pi$
$464$		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	$-0.0127172\pi$
$467$	10.0490	+	17.4053i	0.465010	+	0.805422i	−0.534192	+	0.845363i	$0.679384\pi$
$468$		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	$-0.292452\pi$
$479$	−8.42528	−	14.5930i	−0.384961	−	0.666772i	−0.991764	+	0.128080i	$0.959118\pi$
$480$		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	0.455317	+	0.890329i	$0.349526\pi$
$487$	−11.9916	+	20.7700i	−0.543389	+	0.941178i	−0.998706	+	0.0508486i	$0.983807\pi$
$488$		0			0
$489$	5.02153	−	3.11451i	0.227082	−	0.140843i
$490$		0			0
$491$	−1.07281	−	1.85816i	−0.0484153	−	0.0838577i	0.840802	−	0.541342i	$-0.182084\pi$
$491$	−1.07281	−	1.85816i	−0.0484153	−	0.0838577i	−0.889217	+	0.457485i	$0.848750\pi$
$492$		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	−0.369062	−	0.929405i	$-0.620321\pi$
$499$	13.8577	−	24.0023i	0.620357	−	1.07449i	0.989419	−	0.145085i	$-0.0463455\pi$
$500$		0			0
$501$	13.8359	−	8.58149i	0.618145	−	0.383393i
$502$		0			0
$503$	22.4265			0.999949			0.499974	−	0.866040i	$-0.333343\pi$
$503$	22.4265			0.999949			0.499974	+	0.866040i	$0.333343\pi$
$504$		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	0.332034	+	0.943267i	$0.392265\pi$
$509$	−14.6844	+	25.4342i	−0.650876	+	1.12735i	−0.982911	+	0.184083i	$0.941068\pi$
$510$		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	$-0.951106\pi$
$521$	−8.25389	+	14.2962i	−0.361610	+	0.626326i	0.626616	+	0.779328i	$0.284439\pi$
$522$		0			0
$523$	22.3476	+	38.7072i	0.977193	+	1.69255i	0.672499	+	0.740098i	$0.265221\pi$
$523$	22.3476	+	38.7072i	0.977193	+	1.69255i	0.304695	+	0.952450i	$0.401446\pi$
$524$		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	0.997004	−	0.0773460i	$-0.0246446\pi$
$541$	10.0369	+	17.3844i	0.431519	+	0.747412i	−0.565486	+	0.824758i	$0.691311\pi$
$542$		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	−0.697738	−	0.716353i	$-0.745810\pi$
$547$	6.35012	−	10.9987i	0.271512	−	0.470272i	0.969249	+	0.246082i	$0.0791432\pi$
$548$		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	−0.978649	−	0.205541i	$-0.934105\pi$
$557$	−7.34743	+	12.7261i	−0.311321	+	0.539223i	0.667328	+	0.744764i	$0.267438\pi$
$558$		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	$-0.309089\pi$
$563$	26.7860			1.12890			0.564448	+	0.825469i	$0.309089\pi$
$564$		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	−0.384763	−	0.923016i	$-0.625717\pi$
$577$	14.5800	−	25.2533i	0.606974	−	1.05131i	0.991736	−	0.128294i	$-0.0409500\pi$
$578$		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	$-0.864007\pi$
$587$	−2.33110	+	4.03758i	−0.0962146	+	0.166649i	0.813900	+	0.581005i	$0.197340\pi$
$588$		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	−0.983086	−	0.183144i	$-0.941373\pi$
$593$	−15.8322	−	27.4222i	−0.650150	−	1.12609i	0.332936	−	0.942950i	$-0.391961\pi$
$594$		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	$-0.894077\pi$
$601$	−4.64993	+	8.05391i	−0.189674	+	0.328526i	0.755467	+	0.655186i	$0.227410\pi$
$602$		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	$-0.969891\pi$
$607$	−10.2484	+	17.7507i	−0.415969	+	0.720480i	0.579561	+	0.814929i	$0.303224\pi$
$608$		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	−0.684045	−	0.729440i	$-0.739781\pi$
$613$	7.17240	−	12.4230i	0.289691	−	0.501759i	0.973736	+	0.227681i	$0.0731143\pi$
$614$		0			0
$615$	0.293809	+	9.30522i	0.0118475	+	0.375223i
$616$		0			0
$617$	−6.47499	−	11.2150i	−0.260673	−	0.451499i	0.705748	−	0.708463i	$-0.250611\pi$
$617$	−6.47499	−	11.2150i	−0.260673	−	0.451499i	−0.966421	+	0.256964i	$0.917278\pi$
$618$		0			0
$619$	17.6990	+	30.6556i	0.711383	+	1.23215i	0.964338	+	0.264674i	$0.0852642\pi$
$619$	17.6990	+	30.6556i	0.711383	+	1.23215i	−0.252955	+	0.967478i	$0.581402\pi$
$620$		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	0.868378	−	0.495902i	$-0.165163\pi$
$641$	0.119634	+	0.207213i	0.00472528	+	0.00818442i	−0.863653	+	0.504087i	$0.831829\pi$
$642$		0			0
$643$	−4.57211	−	7.91913i	−0.180307	−	0.312300i	0.761678	−	0.647955i	$-0.224376\pi$
$643$	−4.57211	−	7.91913i	−0.180307	−	0.312300i	−0.941985	+	0.335655i	$0.891042\pi$
$644$		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	$-0.872931\pi$
$647$	−3.15607	+	5.46648i	−0.124078	+	0.214909i	0.797294	+	0.603591i	$0.206264\pi$
$648$		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	−0.817985	−	0.575239i	$-0.804909\pi$
$653$	2.27888	−	3.94713i	0.0891793	−	0.154463i	0.907164	+	0.420776i	$0.138242\pi$
$654$		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	0.343829	+	0.939032i	$0.388276\pi$
$659$	−16.4631	+	28.5149i	−0.641311	+	1.11078i	−0.985140	+	0.171751i	$0.945058\pi$
$660$		0			0
$661$	0.541337			0.0210556			0.0105278	−	0.999945i	$-0.496649\pi$
$661$	0.541337			0.0210556			0.0105278	+	0.999945i	$0.496649\pi$
$662$		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	−0.998725	−	0.0504780i	$-0.983926\pi$
$673$	−11.8205	+	20.4737i	−0.455647	+	0.789204i	0.543078	+	0.839682i	$0.317259\pi$
$674$		0			0
$675$	−42.9824	+	30.5748i	−1.65439	+	1.17682i
$676$		0			0
$677$	−2.72989			−0.104918			−0.0524591	−	0.998623i	$-0.516706\pi$
$677$	−2.72989			−0.104918			−0.0524591	+	0.998623i	$0.516706\pi$
$678$		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	−0.380254	−	0.924882i	$-0.624164\pi$
$683$	15.9640	−	27.6504i	0.610844	−	1.05801i	0.991098	−	0.133131i	$-0.0425032\pi$
$684$		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	$-0.514427\pi$
$691$	−2.38206			−0.0906178			−0.0453089	+	0.998973i	$0.514427\pi$
$692$		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	0.986375	+	0.164510i	$0.0526043\pi$
$719$	17.0446	+	29.5222i	0.635658	+	1.10099i	−0.350718	+	0.936481i	$0.614062\pi$
$720$		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	$-0.700278\pi$
$727$	10.9453	−	18.9578i	0.405938	−	0.703105i	0.994430	+	0.105398i	$0.0336117\pi$
$728$		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	$-0.782037\pi$
$733$	4.34416	−	7.52430i	0.160455	−	0.277916i	0.935032	+	0.354563i	$0.115370\pi$
$734$		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	−0.920996	−	0.389572i	$-0.872623\pi$
$739$	−3.34692	+	5.79704i	−0.123119	+	0.213248i	0.797877	+	0.602820i	$0.205956\pi$
$740$		0			0
$741$	11.2307	+	6.01969i	0.412569	+	0.221139i
$742$		0			0
$743$	21.5001	+	37.2392i	0.788761	+	1.36617i	0.926726	+	0.375737i	$0.122611\pi$
$743$	21.5001	+	37.2392i	0.788761	+	1.36617i	−0.137965	+	0.990437i	$0.544056\pi$
$744$		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	−0.672109	−	0.740452i	$-0.734612\pi$
$751$	8.36369	−	14.4863i	0.305196	−	0.528614i	0.977305	+	0.211838i	$0.0679448\pi$
$752$		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	0.163514	−	0.986541i	$-0.447717\pi$
$761$	25.8242	−	44.7288i	0.936127	−	1.62142i	0.772613	−	0.634878i	$-0.218950\pi$
$762$		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	0.997902	+	0.0647361i	$0.0206205\pi$
$769$	15.3910	+	26.6580i	0.555014	+	0.961313i	−0.442888	+	0.896577i	$0.646046\pi$
$770$		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	$-0.995057\pi$
$773$	−13.5259	+	23.4275i	−0.486491	+	0.842627i	0.513388	+	0.858156i	$0.328390\pi$
$774$		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	$-0.715866\pi$
$787$	−35.1995			−1.25473			−0.627363	+	0.778727i	$0.715866\pi$
$788$		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	−0.886497	−	0.462735i	$-0.846868\pi$
$797$	−23.8268	−	41.2692i	−0.843988	−	1.46183i	0.0425084	−	0.999096i	$-0.486465\pi$
$798$		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	−0.985762	−	0.168148i	$-0.946221\pi$
$809$	−9.87711	+	17.1077i	−0.347261	+	0.601473i	0.638501	+	0.769621i	$0.279555\pi$
$810$		0			0
$811$	−49.2424			−1.72913			−0.864567	−	0.502518i	$-0.832407\pi$
$811$	−49.2424			−1.72913			−0.864567	+	0.502518i	$0.832407\pi$
$812$		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	$-0.764013\pi$
$829$	6.22083	−	10.7748i	0.216058	−	0.374224i	0.953599	+	0.301078i	$0.0973465\pi$
$830$		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	$-0.991714\pi$
$839$	−13.8249	+	23.9455i	−0.477290	+	0.826690i	0.522372	+	0.852718i	$0.325047\pi$
$840$		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	0.190616	+	0.981665i	$0.438952\pi$
$853$	−22.0459	+	38.1847i	−0.754839	+	1.30742i	−0.945454	+	0.325754i	$0.894382\pi$
$854$		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	$-0.0155256\pi$
$857$	13.3838	+	23.1814i	0.457182	+	0.791862i	−0.541629	+	0.840618i	$0.682192\pi$
$858$		0			0
$859$	10.0951	−	17.4852i	0.344439	−	0.596587i	−0.640812	−	0.767698i	$-0.721402\pi$
$859$	10.0951	−	17.4852i	0.344439	−	0.596587i	0.985252	+	0.171111i	$0.0547357\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.74538	−	8.21923i	−0.161534	−	0.279786i	0.773885	−	0.633327i	$-0.218311\pi$
$863$	−4.74538	−	8.21923i	−0.161534	−	0.279786i	−0.935419	+	0.353541i	$0.884978\pi$
$864$		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	−0.999974	−	0.00717380i	$-0.997716\pi$
$877$	−14.6227	+	25.3273i	−0.493774	+	0.855242i	0.506200	+	0.862416i	$0.331050\pi$
$878$		0			0
$879$	27.6422	−	17.1445i	0.932347	−	0.578271i
$880$		0			0
$881$	37.2768			1.25589			0.627944	−	0.778259i	$-0.283897\pi$
$881$	37.2768			1.25589			0.627944	+	0.778259i	$0.283897\pi$
$882$		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	$-0.780060\pi$
$887$	4.96127	−	8.59316i	0.166583	−	0.288530i	0.937216	+	0.348749i	$0.113393\pi$
$888$		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	0.994670	−	0.103109i	$-0.0328789\pi$
$907$	12.2887	+	21.2847i	0.408040	+	0.706747i	−0.586630	+	0.809855i	$0.699546\pi$
$908$		0			0
$909$	18.3093	+	27.5400i	0.607280	+	0.913443i
$910$		0			0
$911$	9.73496	−	16.8614i	0.322534	−	0.558645i	−0.658476	−	0.752601i	$-0.728799\pi$
$911$	9.73496	−	16.8614i	0.322534	−	0.558645i	0.981010	+	0.193957i	$0.0621321\pi$
$912$		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	0.954310	−	0.298818i	$-0.0965923\pi$
$919$	6.61992	+	11.4660i	0.218371	+	0.378230i	−0.735939	+	0.677048i	$0.763259\pi$
$920$		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	$-0.325702\pi$
$929$	31.7363			1.04124			0.520618	+	0.853790i	$0.325702\pi$
$930$		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	$-0.570783\pi$
$937$	−13.5019			−0.441087			−0.220543	+	0.975377i	$0.570783\pi$
$938$		0			0
$939$	−0.757852	−	24.0020i	−0.0247316	−	0.783274i
$940$		0			0
$941$	−39.6572			−1.29279			−0.646394	−	0.763004i	$-0.723724\pi$
$941$	−39.6572			−1.29279			−0.646394	+	0.763004i	$0.723724\pi$
$942$		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	0.982139	−	0.188156i	$-0.0602511\pi$
$967$	10.2035	+	17.6729i	0.328121	+	0.568323i	−0.654018	+	0.756479i	$0.726918\pi$
$968$		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	$-0.172688\pi$
$971$	−0.589402	−	1.02087i	−0.0189148	−	0.0327614i	−0.875328	+	0.483530i	$0.839354\pi$
$972$		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	$-0.159016\pi$
$983$	0.753481	+	1.30507i	0.0240323	+	0.0416252i	−0.853759	+	0.520668i	$0.825683\pi$
$984$		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	0.484503	+	0.874790i	$0.339001\pi$
$991$	−16.2229	+	28.0990i	−0.515339	+	0.892593i	−0.999842	+	0.0178030i	$0.994333\pi$
$992$		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	$-0.103119\pi$
$997$	6.26198	+	10.8461i	0.198319	+	0.343498i	−0.749665	+	0.661818i	$0.769785\pi$
$998$		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.1537.7		24
3.2	odd	2		5292.2.i.j.2125.12		24
7.2	even	3		1764.2.l.j.961.2		24
7.3	odd	6		1764.2.j.i.1177.3	yes	24
7.4	even	3		1764.2.j.i.1177.10	yes	24
7.5	odd	6		1764.2.l.j.961.11		24
7.6	odd	2	inner	1764.2.i.j.1537.6		24
9.4	even	3		1764.2.l.j.949.2		24
9.5	odd	6		5292.2.l.j.361.1		24
21.2	odd	6		5292.2.l.j.3313.1		24
21.5	even	6		5292.2.l.j.3313.12		24
21.11	odd	6		5292.2.j.i.3529.12		24
21.17	even	6		5292.2.j.i.3529.1		24
21.20	even	2		5292.2.i.j.2125.1		24
63.4	even	3		1764.2.j.i.589.10	yes	24
63.5	even	6		5292.2.i.j.1549.1		24
63.13	odd	6		1764.2.l.j.949.11		24
63.23	odd	6		5292.2.i.j.1549.12		24
63.31	odd	6		1764.2.j.i.589.3	✓	24
63.32	odd	6		5292.2.j.i.1765.12		24
63.40	odd	6	inner	1764.2.i.j.373.6		24
63.41	even	6		5292.2.l.j.361.12		24
63.58	even	3	inner	1764.2.i.j.373.7		24
63.59	even	6		5292.2.j.i.1765.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.6		24	63.40	odd	6	inner
1764.2.i.j.373.7		24	63.58	even	3	inner
1764.2.i.j.1537.6		24	7.6	odd	2	inner
1764.2.i.j.1537.7		24	1.1	even	1	trivial
1764.2.j.i.589.3	✓	24	63.31	odd	6
1764.2.j.i.589.10	yes	24	63.4	even	3
1764.2.j.i.1177.3	yes	24	7.3	odd	6
1764.2.j.i.1177.10	yes	24	7.4	even	3
1764.2.l.j.949.2		24	9.4	even	3
1764.2.l.j.949.11		24	63.13	odd	6
1764.2.l.j.961.2		24	7.2	even	3
1764.2.l.j.961.11		24	7.5	odd	6
5292.2.i.j.1549.1		24	63.5	even	6
5292.2.i.j.1549.12		24	63.23	odd	6
5292.2.i.j.2125.1		24	21.20	even	2
5292.2.i.j.2125.12		24	3.2	odd	2
5292.2.j.i.1765.1		24	63.59	even	6
5292.2.j.i.1765.12		24	63.32	odd	6
5292.2.j.i.3529.1		24	21.17	even	6
5292.2.j.i.3529.12		24	21.11	odd	6
5292.2.l.j.361.1		24	9.5	odd	6
5292.2.l.j.361.12		24	63.41	even	6
5292.2.l.j.3313.1		24	21.2	odd	6
5292.2.l.j.3313.12		24	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

L-functions

Modular forms

Varieties

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Representations

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Database

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