LMFDB - Embedded newform 1764.2.j.i.589.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(589,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1764.589"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			589.3
Character	$\chi$	$=$	1764.589
Dual form			1764.2.j.i.1177.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.47192 - 0.912932i) q^{3} +(1.94623 - 3.37097i) q^{5} +(1.33311 + 2.68753i) q^{9} +(-2.18778 - 3.78935i) q^{11} +(0.792201 - 1.37213i) q^{13} +(-5.94217 + 3.18503i) q^{15} +5.33356 q^{17} +4.64323 q^{19} +(-0.183900 + 0.318523i) q^{23} +(-5.07564 - 8.79126i) q^{25} +(0.491301 - 5.17287i) q^{27} +(-5.08750 - 8.81180i) q^{29} +(-1.14776 + 1.98798i) q^{31} +(-0.239175 + 7.57493i) q^{33} +10.8803 q^{37} +(-2.41872 + 1.29645i) q^{39} +(0.690443 - 1.19588i) q^{41} +(3.81699 + 6.61122i) q^{43} +(11.6541 + 0.736684i) q^{45} +(-3.80432 - 6.58928i) q^{47} +(-7.85058 - 4.86918i) q^{51} -0.925693 q^{53} -17.0317 q^{55} +(-6.83447 - 4.23895i) q^{57} +(-0.460475 + 0.797565i) q^{59} +(3.27780 + 5.67731i) q^{61} +(-3.08361 - 5.34097i) q^{65} +(-7.50420 + 12.9976i) q^{67} +(0.561476 - 0.300954i) q^{69} -4.91059 q^{71} -7.56707 q^{73} +(-0.554885 + 17.5738i) q^{75} +(-0.987715 - 1.71077i) q^{79} +(-5.44564 + 7.16554i) q^{81} +(0.253011 + 0.438227i) q^{83} +(10.3803 - 17.9793i) q^{85} +(-0.556181 + 17.6148i) q^{87} +12.2197 q^{89} +(3.50431 - 1.87833i) q^{93} +(9.03679 - 15.6522i) q^{95} +(-4.45315 - 7.71308i) q^{97} +(7.26745 - 10.9314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93}+ \cdots - 4 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.47192	−	0.912932i	−0.849815	−	0.527082i
$3$	−1.47192	−	0.912932i	−0.849815	−	0.527082i
$4$		0			0
$5$	1.94623	−	3.37097i	0.870381	−	1.50754i	0.00877856	−	0.999961i	$-0.497206\pi$
$5$	1.94623	−	3.37097i	0.870381	−	1.50754i	0.861603	−	0.507583i	$-0.169461\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.33311	+	2.68753i	0.444370	+	0.895844i
$10$		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	$-0.762820\pi$
$13$	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
$17$	5.33356			1.29358			0.646789	−	0.762669i	$-0.276111\pi$
$17$	5.33356			1.29358			0.646789	+	0.762669i	$0.276111\pi$
$18$		0			0
$19$	4.64323			1.06523			0.532614	−	0.846358i	$-0.321210\pi$
$19$	4.64323			1.06523			0.532614	+	0.846358i	$0.321210\pi$
$20$		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	−0.756302	−	0.654222i	$-0.772996\pi$
$29$	−5.08750	−	8.81180i	−0.944724	−	1.63631i	−0.188422	−	0.982088i	$-0.560337\pi$
$30$		0			0
$31$	−1.14776	+	1.98798i	−0.206144	+	0.357052i	−0.950497	−	0.310735i	$-0.899425\pi$
$31$	−1.14776	+	1.98798i	−0.206144	+	0.357052i	0.744353	+	0.667787i	$0.232758\pi$
$32$		0			0
$33$	−0.239175	+	7.57493i	−0.0416351	+	1.31863i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	10.8803			1.78872			0.894359	−	0.447351i	$-0.147632\pi$
$37$	10.8803			1.78872			0.894359	+	0.447351i	$0.147632\pi$
$38$		0			0
$39$	−2.41872	+	1.29645i	−0.387305	+	0.207597i
$40$		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
$45$	11.6541	+	0.736684i	1.73730	+	0.109818i
$46$		0			0
$47$	−3.80432	−	6.58928i	−0.554918	−	0.961145i	−0.997910	−	0.0646200i	$-0.979416\pi$
$47$	−3.80432	−	6.58928i	−0.554918	−	0.961145i	0.442992	−	0.896525i	$-0.353917\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−7.85058	−	4.86918i	−1.09930	−	0.681821i
$52$		0			0
$53$	−0.925693			−0.127154			−0.0635769	−	0.997977i	$-0.520251\pi$
$53$	−0.925693			−0.127154			−0.0635769	+	0.997977i	$0.520251\pi$
$54$		0			0
$55$	−17.0317			−2.29656
$56$		0			0
$57$	−6.83447	−	4.23895i	−0.905247	−	0.561463i
$58$		0			0
$59$	−0.460475	+	0.797565i	−0.0599487	+	0.103834i	−0.894442	−	0.447184i	$-0.852427\pi$
$59$	−0.460475	+	0.797565i	−0.0599487	+	0.103834i	0.834493	+	0.551018i	$0.185760\pi$
$60$		0			0
$61$	3.27780	+	5.67731i	0.419679	+	0.726905i	0.995907	−	0.0903836i	$-0.0288093\pi$
$61$	3.27780	+	5.67731i	0.419679	+	0.726905i	−0.576228	+	0.817289i	$0.695476\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.08361	−	5.34097i	−0.382475	−	0.662466i
$66$		0			0
$67$	−7.50420	+	12.9976i	−0.916783	+	1.58792i	−0.112514	+	0.993650i	$0.535890\pi$
$67$	−7.50420	+	12.9976i	−0.916783	+	1.58792i	−0.804269	+	0.594265i	$0.797443\pi$
$68$		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
$73$	−7.56707			−0.885658			−0.442829	−	0.896606i	$-0.646025\pi$
$73$	−7.56707			−0.885658			−0.442829	+	0.896606i	$0.646025\pi$
$74$		0			0
$75$	−0.554885	+	17.5738i	−0.0640726	+	2.02924i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.987715	−	1.71077i	−0.111127	−	0.192477i	0.805098	−	0.593142i	$-0.202113\pi$
$79$	−0.987715	−	1.71077i	−0.111127	−	0.192477i	−0.916225	+	0.400665i	$0.868779\pi$
$80$		0			0
$81$	−5.44564	+	7.16554i	−0.605071	+	0.796171i
$82$		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
$87$	−0.556181	+	17.6148i	−0.0596289	+	1.88851i
$88$		0			0
$89$	12.2197			1.29529			0.647645	−	0.761942i	$-0.275754\pi$
$89$	12.2197			1.29529			0.647645	+	0.761942i	$0.275754\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.50431	−	1.87833i	0.363380	−	0.194773i
$94$		0			0
$95$	9.03679	−	15.6522i	0.927155	−	1.60588i
$96$		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	0.998381	+	0.0568740i	$0.0181133\pi$
$101$	5.51180	+	9.54672i	0.548445	+	0.949935i	−0.449936	+	0.893061i	$0.648553\pi$
$102$		0			0
$103$	1.36543	−	2.36499i	0.134540	−	0.233029i	−0.790882	−	0.611969i	$-0.790378\pi$
$103$	1.36543	−	2.36499i	0.134540	−	0.233029i	0.925421	+	0.378939i	$0.123711\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.7921			−1.04331			−0.521655	−	0.853156i	$-0.674685\pi$
$107$	−10.7921			−1.04331			−0.521655	+	0.853156i	$0.674685\pi$
$108$		0			0
$109$	−9.98374			−0.956269			−0.478134	−	0.878287i	$-0.658687\pi$
$109$	−9.98374			−0.956269			−0.478134	+	0.878287i	$0.658687\pi$
$110$		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
$117$	4.74374	+	0.299862i	0.438559	+	0.0277223i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.07280	+	7.05429i	−0.370254	+	0.641299i
$122$		0			0
$123$	−2.10804	+	1.12992i	−0.190075	+	0.101881i
$124$		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
$129$	0.417286	−	13.2159i	0.0367399	−	1.16359i
$130$		0			0
$131$	2.54342	−	4.40532i	0.222219	−	0.384895i	−0.733262	−	0.679946i	$-0.762003\pi$
$131$	2.54342	−	4.40532i	0.222219	−	0.384895i	0.955482	+	0.295051i	$0.0953366\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−16.4814	−	11.7238i	−1.41850	−	1.00902i
$136$		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	$-0.698193\pi$
$139$	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
$143$	−6.93265			−0.579738
$144$		0			0
$145$	−39.6058			−3.28908
$146$		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
$157$	5.78991	−	10.0284i	0.462085	−	0.800355i	−0.536980	−	0.843595i	$-0.680435\pi$
$157$	5.78991	−	10.0284i	0.462085	−	0.800355i	0.999065	+	0.0432404i	$0.0137681\pi$
$158$		0			0
$159$	1.36255	+	0.845095i	0.108057	+	0.0670204i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	3.41155			0.267213			0.133607	−	0.991034i	$-0.457344\pi$
$163$	3.41155			0.267213			0.133607	+	0.991034i	$0.457344\pi$
$164$		0			0
$165$	25.0694	+	15.5488i	1.95165	+	1.21047i
$166$		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
$171$	6.18993	+	12.4788i	0.473355	+	0.954278i
$172$		0			0
$173$	−3.20256	−	5.54700i	−0.243486	−	0.421730i	0.718219	−	0.695817i	$-0.244958\pi$
$173$	−3.20256	−	5.54700i	−0.243486	−	0.421730i	−0.961705	+	0.274087i	$0.911624\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.40591	−	0.753572i	0.105674	−	0.0566419i
$178$		0			0
$179$	17.0808			1.27668			0.638338	−	0.769756i	$-0.279622\pi$
$179$	17.0808			1.27668			0.638338	+	0.769756i	$0.279622\pi$
$180$		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
$185$	21.1757	−	36.6773i	1.55687	−	2.69657i
$186$		0			0
$187$	−11.6687	−	20.2107i	−0.853298	−	1.47796i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.94048	+	15.4854i	0.646911	+	1.12048i	0.983857	+	0.178958i	$0.0572727\pi$
$191$	8.94048	+	15.4854i	0.646911	+	1.12048i	−0.336946	+	0.941524i	$0.609394\pi$
$192$		0			0
$193$	6.50664	−	11.2698i	0.468358	−	0.811220i	−0.530988	−	0.847380i	$-0.678179\pi$
$193$	6.50664	−	11.2698i	0.468358	−	0.811220i	0.999346	+	0.0361591i	$0.0115123\pi$
$194$		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
$199$	−23.1529			−1.64126			−0.820631	−	0.571458i	$-0.806378\pi$
$199$	−23.1529			−1.64126			−0.820631	+	0.571458i	$0.806378\pi$
$200$		0			0
$201$	22.9116	−	12.2807i	1.61606	−	0.866214i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.68753	−	4.65493i	−0.187705	−	0.325114i
$206$		0			0
$207$	−1.10120	−	0.0696093i	−0.0765387	−	0.00483818i
$208$		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
$213$	7.22801	+	4.48304i	0.495255	+	0.307173i
$214$		0			0
$215$	29.7150			2.02655
$216$		0			0
$217$		0			0
$218$		0			0
$219$	11.1381	+	6.90822i	0.752645	+	0.466814i
$220$		0			0
$221$	4.22525	−	7.31835i	0.284221	−	0.492285i
$222$		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	−0.998204	−	0.0599042i	$-0.980920\pi$
$227$	−8.30136	−	14.3784i	−0.550981	−	0.954326i	0.447224	−	0.894422i	$-0.352413\pi$
$228$		0			0
$229$	−7.25072	+	12.5586i	−0.479141	+	0.829897i	−0.999714	−	0.0239205i	$-0.992385\pi$
$229$	−7.25072	+	12.5586i	−0.479141	+	0.829897i	0.520573	+	0.853817i	$0.325718\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.9804			1.04691			0.523456	−	0.852053i	$-0.324643\pi$
$233$	15.9804			1.04691			0.523456	+	0.852053i	$0.324643\pi$
$234$		0			0
$235$	−29.6164			−1.93196
$236$		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	0.946717	+	0.322067i	$0.104377\pi$
$241$	11.6785	+	20.2277i	0.752276	+	1.30298i	−0.194441	+	0.980914i	$0.562289\pi$
$242$		0			0
$243$	14.5572	−	5.57562i	0.933846	−	0.357676i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.67837	−	6.37112i	0.234049	−	0.405384i
$248$		0			0
$249$	0.0276599	−	0.876018i	0.00175288	−	0.0555154i
$250$		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
$255$	−31.6929	+	16.9875i	−1.98469	+	1.06380i
$256$		0			0
$257$	−3.40438	+	5.89657i	−0.212360	+	0.367818i	−0.952453	−	0.304687i	$-0.901448\pi$
$257$	−3.40438	+	5.89657i	−0.212360	+	0.367818i	0.740093	+	0.672505i	$0.234782\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	16.8998	−	25.4199i	1.04607	−	1.57345i
$262$		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
$269$	8.50179			0.518363			0.259182	−	0.965829i	$-0.416547\pi$
$269$	8.50179			0.518363			0.259182	+	0.965829i	$0.416547\pi$
$270$		0			0
$271$	−6.58381			−0.399938			−0.199969	−	0.979802i	$-0.564084\pi$
$271$	−6.58381			−0.399938			−0.199969	+	0.979802i	$0.564084\pi$
$272$		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	0.998246	−	0.0592000i	$-0.0188550\pi$
$281$	7.50741	+	13.0032i	0.447854	+	0.775707i	−0.550392	+	0.834907i	$0.685522\pi$
$282$		0			0
$283$	7.33657	−	12.7073i	0.436114	−	0.755371i	−0.561272	−	0.827631i	$-0.689688\pi$
$283$	7.33657	−	12.7073i	0.436114	−	0.755371i	0.997386	+	0.0722602i	$0.0230212\pi$
$284$		0			0
$285$	−27.5908	+	14.7888i	−1.63434	+	0.876014i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	11.4469			0.673344
$290$		0			0
$291$	−0.486833	+	15.4185i	−0.0285386	+	0.903848i
$292$		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
$297$	−20.6767	+	9.45542i	−1.19978	+	0.548659i
$298$		0			0
$299$	0.291371	+	0.504669i	0.0168504	+	0.0291858i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.602568	−	19.0839i	0.0346166	−	1.09634i
$304$		0			0
$305$	25.5174			1.46112
$306$		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
$311$	−6.79681	+	11.7724i	−0.385412	+	0.667553i	−0.991826	−	0.127596i	$-0.959274\pi$
$311$	−6.79681	+	11.7724i	−0.385412	+	0.667553i	0.606414	+	0.795149i	$0.292607\pi$
$312$		0			0
$313$	−6.93222	−	12.0070i	−0.391832	−	0.678673i	0.600859	−	0.799355i	$-0.294825\pi$
$313$	−6.93222	−	12.0070i	−0.391832	−	0.678673i	−0.992691	+	0.120682i	$0.961492\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.5428	−	19.9927i	−0.648309	−	1.12290i	−0.983527	−	0.180764i	$-0.942143\pi$
$317$	−11.5428	−	19.9927i	−0.648309	−	1.12290i	0.335217	−	0.942141i	$-0.391190\pi$
$318$		0			0
$319$	−22.2607	+	38.5566i	−1.24636	+	2.15876i
$320$		0			0
$321$	15.8851	+	9.85245i	0.886621	+	0.549910i
$322$		0			0
$323$	24.7649			1.37796
$324$		0			0
$325$	−16.0837			−0.892163
$326$		0			0
$327$	14.6953	+	9.11448i	0.812651	+	0.504032i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.82647	+	13.5558i	0.430182	+	0.745097i	0.996889	−	0.0788227i	$-0.0251161\pi$
$331$	7.82647	+	13.5558i	0.430182	+	0.745097i	−0.566707	+	0.823920i	$0.691783\pi$
$332$		0			0
$333$	14.5047	+	29.2413i	0.794852	+	1.60241i
$334$		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
$339$	18.6860	−	10.0158i	1.01488	−	0.543981i
$340$		0			0
$341$	10.0442			0.543925
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.0782560	−	2.47845i	0.00421316	−	0.133435i
$346$		0			0
$347$	−2.77827	+	4.81211i	−0.149146	+	0.258328i	−0.930912	−	0.365244i	$-0.880986\pi$
$347$	−2.77827	+	4.81211i	−0.149146	+	0.258328i	0.781766	+	0.623571i	$0.214319\pi$
$348$		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	0.642989	−	0.765875i	$-0.277694\pi$
$353$	−6.42132	−	11.1221i	−0.341772	−	0.591967i	−0.984762	+	0.173908i	$0.944361\pi$
$354$		0			0
$355$	−9.55715	+	16.5535i	−0.507241	+	0.878567i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	25.6835			1.35552			0.677761	−	0.735282i	$-0.262950\pi$
$359$	25.6835			1.35552			0.677761	+	0.735282i	$0.262950\pi$
$360$		0			0
$361$	2.55954			0.134713
$362$		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	0.554653	−	0.832082i	$-0.312851\pi$
$367$	−8.49197	−	14.7085i	−0.443277	−	0.767778i	−0.997930	+	0.0643031i	$0.979518\pi$
$368$		0			0
$369$	4.13441	+	0.261345i	0.215229	+	0.0136051i
$370$		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
$375$	29.5137	+	18.3053i	1.52408	+	0.945283i
$376$		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
$381$	19.4301	+	12.0512i	0.995434	+	0.617400i
$382$		0			0
$383$	−4.50360	+	7.80046i	−0.230123	+	0.398585i	−0.957844	−	0.287288i	$-0.907246\pi$
$383$	−4.50360	+	7.80046i	−0.230123	+	0.398585i	0.727721	+	0.685873i	$0.240580\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.6794	+	19.0718i	−0.644530	+	0.969472i
$388$		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
$395$	−7.68929			−0.386890
$396$		0			0
$397$	−13.9186			−0.698554			−0.349277	−	0.937020i	$-0.613573\pi$
$397$	−13.9186			−0.698554			−0.349277	+	0.937020i	$0.613573\pi$
$398$		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
$409$	−6.81225	+	11.7992i	−0.336844	+	0.583431i	−0.983837	−	0.179064i	$-0.942693\pi$
$409$	−6.81225	+	11.7992i	−0.336844	+	0.583431i	0.646993	+	0.762496i	$0.276026\pi$
$410$		0			0
$411$	−0.729413	+	23.1013i	−0.0359793	+	1.13950i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1.96967			0.0966873
$416$		0			0
$417$	−14.8275	+	7.94759i	−0.726104	+	0.389195i
$418$		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
$423$	12.6373	−	19.0085i	0.614447	−	0.924223i
$424$		0			0
$425$	−27.0712	−	46.8887i	−1.31315	−	2.27444i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	10.2043	+	6.32904i	0.492670	+	0.305569i
$430$		0			0
$431$	−1.58213			−0.0762086			−0.0381043	−	0.999274i	$-0.512132\pi$
$431$	−1.58213			−0.0762086			−0.0381043	+	0.999274i	$0.512132\pi$
$432$		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
$437$	−0.853887	+	1.47898i	−0.0408470	+	0.0707490i
$438$		0			0
$439$	−12.4806	−	21.6170i	−0.595665	−	1.03172i	−0.993453	−	0.114244i	$-0.963555\pi$
$439$	−12.4806	−	21.6170i	−0.595665	−	1.03172i	0.397788	−	0.917477i	$-0.369778\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.542263	−	0.939227i	−0.0257637	−	0.0446240i	0.852856	−	0.522146i	$-0.174868\pi$
$443$	−0.542263	−	0.939227i	−0.0257637	−	0.0446240i	−0.878620	+	0.477522i	$0.841535\pi$
$444$		0			0
$445$	23.7825	−	41.1924i	1.12740	−	1.95271i
$446$		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
$451$	−6.04216			−0.284514
$452$		0			0
$453$	−1.25044	+	39.6026i	−0.0587506	+	1.86069i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.1513	+	31.4390i	0.849083	+	1.47065i	0.882028	+	0.471197i	$0.156178\pi$
$457$	18.1513	+	31.4390i	0.849083	+	1.47065i	−0.0329453	+	0.999457i	$0.510489\pi$
$458$		0			0
$459$	2.62038	−	27.5898i	0.122309	−	1.28778i
$460$		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
$465$	0.488414	−	15.4686i	0.0226497	−	0.717338i
$466$		0			0
$467$	20.0979			0.930021			0.465010	−	0.885305i	$-0.346051\pi$
$467$	20.0979			0.930021			0.465010	+	0.885305i	$0.346051\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−17.6776	+	9.47525i	−0.814539	+	0.436597i
$472$		0			0
$473$	16.7015	−	28.9279i	0.767936	−	1.33010i
$474$		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	0.991764	−	0.128080i	$-0.0408816\pi$
$479$	8.42528	+	14.5930i	0.384961	+	0.666772i	−0.606803	+	0.794852i	$0.707548\pi$
$480$		0			0
$481$	8.61941	−	14.9293i	0.393011	−	0.680716i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−34.6675			−1.57417
$486$		0			0
$487$	23.9831			1.08678			0.543389	−	0.839481i	$-0.317141\pi$
$487$	23.9831			1.08678			0.543389	+	0.839481i	$0.317141\pi$
$488$		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
$495$	−22.7052	−	45.7733i	−1.02052	−	2.05736i
$496$		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
$501$	−14.3498	+	7.69154i	−0.641100	+	0.343633i
$502$		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
$507$	0.573382	−	18.1596i	0.0254648	−	0.806496i
$508$		0			0
$509$	14.6844	−	25.4342i	0.650876	−	1.12735i	−0.332034	−	0.943267i	$-0.607735\pi$
$509$	14.6844	−	25.4342i	0.650876	−	1.12735i	0.982911	−	0.184083i	$-0.0589316\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.28122	−	24.0188i	0.100718	−	1.06046i
$514$		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
$521$	−16.5078			−0.723219			−0.361610	−	0.932330i	$-0.617773\pi$
$521$	−16.5078			−0.723219			−0.361610	+	0.932330i	$0.617773\pi$
$522$		0			0
$523$	44.6952			1.95439			0.977193	−	0.212352i	$-0.0681122\pi$
$523$	44.6952			1.95439			0.977193	+	0.212352i	$0.0681122\pi$
$524$		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
$535$	−21.0039	+	36.3798i	−0.908078	+	1.57284i
$536$		0			0
$537$	−25.1415	−	15.5936i	−1.08494	−	0.672912i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−20.0737			−0.863037			−0.431519	−	0.902104i	$-0.642022\pi$
$541$	−20.0737			−0.863037			−0.431519	+	0.902104i	$0.642022\pi$
$542$		0			0
$543$	2.00164	+	1.24148i	0.0858985	+	0.0532769i
$544$		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
$549$	−10.8883	+	16.3777i	−0.464701	+	0.698981i
$550$		0			0
$551$	−23.6224	−	40.9152i	−1.00635	−	1.74305i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−64.6529	+	34.6542i	−2.74436	+	1.47099i
$556$		0			0
$557$	14.6949			0.622642			0.311321	−	0.950305i	$-0.399229\pi$
$557$	14.6949			0.622642			0.311321	+	0.950305i	$0.399229\pi$
$558$		0			0
$559$	12.0953			0.511576
$560$		0			0
$561$	−1.27566	+	40.4013i	−0.0538583	+	1.70575i
$562$		0			0
$563$	13.3930	−	23.1974i	0.564448	−	0.977653i	−0.432653	−	0.901561i	$-0.642422\pi$
$563$	13.3930	−	23.1974i	0.564448	−	0.977653i	0.997101	−	0.0760922i	$-0.0242443\pi$
$564$		0			0
$565$	23.8226	+	41.2620i	1.00222	+	1.73590i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.24168	−	5.61475i	−0.135898	−	0.235383i	0.790042	−	0.613053i	$-0.210059\pi$
$569$	−3.24168	−	5.61475i	−0.135898	−	0.235383i	−0.925940	+	0.377670i	$0.876725\pi$
$570$		0			0
$571$	−7.81632	+	13.5383i	−0.327103	+	0.566559i	−0.981936	−	0.189215i	$-0.939406\pi$
$571$	−7.81632	+	13.5383i	−0.327103	+	0.566559i	0.654833	+	0.755774i	$0.272739\pi$
$572$		0			0
$573$	0.977402	−	30.9553i	0.0408315	−	1.29318i
$574$		0			0
$575$	3.73363			0.155703
$576$		0			0
$577$	29.1600			1.21395			0.606974	−	0.794722i	$-0.292383\pi$
$577$	29.1600			1.21395			0.606974	+	0.794722i	$0.292383\pi$
$578$		0			0
$579$	−19.8659	+	10.6482i	−0.825597	+	0.442524i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.02522	+	3.50778i	0.0838759	+	0.145277i
$584$		0			0
$585$	10.2432	−	15.4074i	0.423506	−	0.637018i
$586$		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
$591$	−9.36858	−	5.81069i	−0.385372	−	0.239020i
$592$		0			0
$593$	−31.6644			−1.30030			−0.650150	−	0.759805i	$-0.725294\pi$
$593$	−31.6644			−1.30030			−0.650150	+	0.759805i	$0.725294\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	34.0792	+	21.1370i	1.39477	+	0.865079i
$598$		0			0
$599$	5.15268	−	8.92470i	0.210533	−	0.364653i	−0.741349	−	0.671120i	$-0.765813\pi$
$599$	5.15268	−	8.92470i	0.210533	−	0.364653i	0.951881	+	0.306467i	$0.0991468\pi$
$600$		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	−0.579561	−	0.814929i	$-0.696776\pi$
$607$	10.2484	−	17.7507i	0.415969	−	0.720480i	0.995530	+	0.0944495i	$0.0301091\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.0551			−0.487699
$612$		0			0
$613$	−14.3448			−0.579381			−0.289691	−	0.957120i	$-0.593552\pi$
$613$	−14.3448			−0.579381			−0.289691	+	0.957120i	$0.593552\pi$
$614$		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	−0.964338	−	0.264674i	$-0.914736\pi$
$619$	−17.6990	−	30.6556i	−0.711383	−	1.23215i	0.252955	−	0.967478i	$-0.418598\pi$
$620$		0			0
$621$	1.55733	+	1.10778i	0.0624936	+	0.0444537i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−13.6460	+	23.6355i	−0.545839	+	0.945422i
$626$		0			0
$627$	−1.11055	+	35.1721i	−0.0443509	+	1.40464i
$628$		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
$633$	17.3339	−	9.29108i	0.688963	−	0.369287i
$634$		0			0
$635$	−25.6912	+	44.4985i	−1.01952	+	1.76587i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−6.54635	−	13.1974i	−0.258970	−	0.522080i
$640$		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	$-0.775624\pi$
$643$	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
$647$	−6.31214			−0.248156			−0.124078	−	0.992272i	$-0.539597\pi$
$647$	−6.31214			−0.248156			−0.124078	+	0.992272i	$0.539597\pi$
$648$		0			0
$649$	4.02968			0.158179
$650$		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	−0.985140	−	0.171751i	$-0.945058\pi$
$659$	−16.4631	−	28.5149i	−0.641311	−	1.11078i	0.343829	−	0.939032i	$-0.388276\pi$
$660$		0			0
$661$	0.270668	−	0.468811i	0.0105278	−	0.0182346i	−0.860714	−	0.509090i	$-0.829982\pi$
$661$	0.270668	−	0.468811i	0.0105278	−	0.0182346i	0.871241	+	0.490855i	$0.163316\pi$
$662$		0			0
$663$	−12.9004	+	6.91467i	−0.501010	+	0.268543i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.74235			0.144905
$668$		0			0
$669$	1.45625	−	46.1208i	0.0563017	−	1.78313i
$670$		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
$675$	−47.9697	+	21.9365i	−1.84636	+	0.844335i
$676$		0			0
$677$	−1.36494	−	2.36415i	−0.0524591	−	0.0908618i	0.838603	−	0.544742i	$-0.183373\pi$
$677$	−1.36494	−	2.36415i	−0.0524591	−	0.0908618i	−0.891062	+	0.453881i	$0.850039\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.907531	+	28.7424i	−0.0347767	+	1.10141i
$682$		0			0
$683$	−31.9279			−1.22169			−0.610844	−	0.791751i	$-0.709170\pi$
$683$	−31.9279			−1.22169			−0.610844	+	0.791751i	$0.709170\pi$
$684$		0			0
$685$	−51.9417			−1.98459
$686$		0			0
$687$	22.1377	−	11.8659i	0.844605	−	0.452712i
$688$		0			0
$689$	−0.733335	+	1.27017i	−0.0279378	+	0.0483897i
$690$		0			0
$691$	−1.19103	−	2.06292i	−0.0453089	−	0.0784773i	0.842482	−	0.538725i	$-0.181094\pi$
$691$	−1.19103	−	2.06292i	−0.0453089	−	0.0784773i	−0.887790	+	0.460248i	$0.847761\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.9034	−	32.7417i	−0.717048	−	1.24196i
$696$		0			0
$697$	3.68252	−	6.37831i	0.139485	−	0.241596i
$698$		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
$703$	50.5199			1.90539
$704$		0			0
$705$	43.5930	+	27.0377i	1.64181	+	1.01830i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−20.1600	−	34.9182i	−0.757126	−	1.31138i	−0.944310	−	0.329056i	$-0.893269\pi$
$709$	−20.1600	−	34.9182i	−0.757126	−	1.31138i	0.187184	−	0.982325i	$-0.440064\pi$
$710$		0			0
$711$	3.28102	−	4.93516i	0.123048	−	0.185083i
$712$		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
$717$	29.2797	−	15.6940i	1.09347	−	0.586105i
$718$		0			0
$719$	34.0893			1.27132			0.635658	−	0.771971i	$-0.280729\pi$
$719$	34.0893			1.27132			0.635658	+	0.771971i	$0.280729\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.27673	−	40.4353i	0.0474820	−	1.50380i
$724$		0			0
$725$	−51.6446	+	89.4510i	−1.91803	+	3.32213i
$726$		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	−0.935032	−	0.354563i	$-0.884630\pi$
$733$	−4.34416	+	7.52430i	−0.160455	+	0.277916i	0.774577	+	0.632480i	$0.217963\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	65.6702			2.41899
$738$		0			0
$739$	6.69385			0.246237			0.123119	−	0.992392i	$-0.460710\pi$
$739$	6.69385			0.246237			0.123119	+	0.992392i	$0.460710\pi$
$740$		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
$747$	−0.840458	+	1.26418i	−0.0307508	+	0.0462539i
$748$		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
$753$	−44.8376	−	27.8097i	−1.63397	−	1.01344i
$754$		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
$759$	−2.36881	−	1.46921i	−0.0859823	−	0.0533289i
$760$		0			0
$761$	−25.8242	+	44.7288i	−0.936127	+	1.62142i	−0.163514	+	0.986541i	$0.552283\pi$
$761$	−25.8242	+	44.7288i	−0.936127	+	1.62142i	−0.772613	+	0.634878i	$0.781050\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	62.1580	+	3.92915i	2.24733	+	0.142059i
$766$		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
$773$	−27.0517			−0.972982			−0.486491	−	0.873686i	$-0.661723\pi$
$773$	−27.0517			−0.972982			−0.486491	+	0.873686i	$0.661723\pi$
$774$		0			0
$775$	23.3025			0.837050
$776$		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
$787$	−17.5997	+	30.4837i	−0.627363	+	1.08662i	0.360716	+	0.932676i	$0.382532\pi$
$787$	−17.5997	+	30.4837i	−0.627363	+	1.08662i	−0.988079	+	0.153949i	$0.950801\pi$
$788$		0			0
$789$	0.251444	−	7.96348i	0.00895163	−	0.283507i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	10.3867			0.368842
$794$		0			0
$795$	5.50063	−	2.94836i	0.195087	−	0.104568i
$796$		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
$801$	16.2903	+	32.8409i	0.575588	+	1.16038i
$802$		0			0
$803$	16.5551	+	28.6743i	0.584217	+	1.01189i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.5140	−	7.76156i	−0.440513	−	0.273220i
$808$		0			0
$809$	19.7542			0.694521			0.347261	−	0.937769i	$-0.387112\pi$
$809$	19.7542			0.694521			0.347261	+	0.937769i	$0.387112\pi$
$810$		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
$815$	6.63967	−	11.5002i	0.232577	−	0.402836i
$816$		0			0
$817$	17.7231	+	30.6974i	0.620054	+	1.07397i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.00013	−	8.66048i	−0.174506	−	0.302253i	0.765484	−	0.643455i	$-0.222499\pi$
$821$	−5.00013	−	8.66048i	−0.174506	−	0.302253i	−0.939990	+	0.341202i	$0.889166\pi$
$822$		0			0
$823$	17.5138	−	30.3348i	0.610493	−	1.05741i	−0.380664	−	0.924713i	$-0.624305\pi$
$823$	17.5138	−	30.3348i	0.610493	−	1.05741i	0.991157	−	0.132692i	$-0.0423621\pi$
$824$		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
$829$	12.4417			0.432117			0.216058	−	0.976380i	$-0.430680\pi$
$829$	12.4417			0.432117			0.216058	+	0.976380i	$0.430680\pi$
$830$		0			0
$831$	0.616018	−	19.5099i	0.0213694	−	0.676791i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.2944	−	31.6869i	−0.633105	−	1.09657i
$836$		0			0
$837$	9.71968	+	6.91392i	0.335961	+	0.238980i
$838$		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
$843$	0.820733	−	25.9935i	0.0282676	−	0.895263i
$844$		0			0
$845$	40.8307			1.40462
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−22.3998	+	12.0064i	−0.768758	+	0.412058i
$850$		0			0
$851$	−2.00089	+	3.46564i	−0.0685896	+	0.118801i
$852$		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	0.541629	−	0.840618i	$-0.317808\pi$
$857$	−13.3838	−	23.1814i	−0.457182	−	0.791862i	−0.998811	+	0.0487557i	$0.984474\pi$
$858$		0			0
$859$	−10.0951	+	17.4852i	−0.344439	+	0.596587i	−0.985252	−	0.171111i	$-0.945264\pi$
$859$	−10.0951	+	17.4852i	−0.344439	+	0.596587i	0.640812	+	0.767698i	$0.278598\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.49075			0.323069			0.161534	−	0.986867i	$-0.448356\pi$
$863$	9.49075			0.323069			0.161534	+	0.986867i	$0.448356\pi$
$864$		0			0
$865$	−24.9317			−0.847703
$866$		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
$873$	14.7926	−	22.2504i	0.500654	−	0.753061i
$874$		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
$879$	−28.6687	+	15.3665i	−0.966970	+	0.518301i
$880$		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
$885$	0.195949	−	6.20590i	0.00658674	−	0.208609i
$886$		0			0
$887$	−4.96127	+	8.59316i	−0.166583	+	0.288530i	−0.937216	−	0.348749i	$-0.886607\pi$
$887$	−4.96127	+	8.59316i	−0.166583	+	0.288530i	0.770633	+	0.637279i	$0.219940\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	39.0667	+	4.95879i	1.30878	+	0.166126i
$892$		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
$899$	23.3569			0.778997
$900$		0			0
$901$	−4.93724			−0.164483
$902$		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	0.981010	−	0.193957i	$-0.0621321\pi$
$911$	9.73496	+	16.8614i	0.322534	+	0.558645i	−0.658476	+	0.752601i	$0.728799\pi$
$912$		0			0
$913$	1.10707	−	1.91749i	0.0366385	−	0.0634598i
$914$		0			0
$915$	−37.5596	−	23.2957i	−1.24168	−	0.770131i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−13.2398			−0.436742			−0.218371	−	0.975866i	$-0.570074\pi$
$919$	−13.2398			−0.436742			−0.218371	+	0.975866i	$0.570074\pi$
$920$		0			0
$921$	−42.6012	−	26.4226i	−1.40376	−	0.870653i
$922$		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
$927$	8.17624	+	0.516839i	0.268543	+	0.0169752i
$928$		0			0
$929$	15.8682	+	27.4845i	0.520618	+	0.901737i	0.999713	+	0.0239734i	$0.00763170\pi$
$929$	15.8682	+	27.4845i	0.520618	+	0.901737i	−0.479095	+	0.877763i	$0.659035\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	20.7518	−	11.1231i	0.679384	−	0.364153i
$934$		0			0
$935$	−90.8398			−2.97078
$936$		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
$941$	−19.8286	+	34.3441i	−0.646394	+	1.11959i	0.337584	+	0.941295i	$0.390390\pi$
$941$	−19.8286	+	34.3441i	−0.646394	+	1.11959i	−0.983978	+	0.178291i	$0.942943\pi$
$942$		0			0
$943$	0.253944	+	0.439845i	0.00826957	+	0.0143233i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	30.5172	+	52.8573i	0.991675	+	1.71763i	0.607350	+	0.794434i	$0.292232\pi$
$947$	30.5172	+	52.8573i	0.991675	+	1.71763i	0.384325	+	0.923198i	$0.374434\pi$
$948$		0			0
$949$	−5.99464	+	10.3830i	−0.194594	+	0.337047i
$950$		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
$955$	69.6010			2.25224
$956$		0			0
$957$	67.9656	−	36.4299i	2.19702	−	1.17761i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12.8653	+	22.2833i	0.415009	+	0.718817i
$962$		0			0
$963$	−14.3870	−	29.0041i	−0.463616	−	0.934643i
$964$		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
$969$	−36.4520	−	22.6087i	−1.17101	−	0.726296i
$970$		0			0
$971$	−1.17880			−0.0378296			−0.0189148	−	0.999821i	$-0.506021\pi$
$971$	−1.17880			−0.0378296			−0.0189148	+	0.999821i	$0.506021\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	23.6739	+	14.6833i	0.758173	+	0.470243i
$976$		0			0
$977$	−4.10487	+	7.10984i	−0.131326	+	0.227464i	−0.924188	−	0.381938i	$-0.875257\pi$
$977$	−4.10487	+	7.10984i	−0.131326	+	0.227464i	0.792862	+	0.609402i	$0.208590\pi$
$978$		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	0.853759	−	0.520668i	$-0.174317\pi$
$983$	−0.753481	−	1.30507i	−0.0240323	−	0.0416252i	−0.877791	+	0.479043i	$0.840984\pi$
$984$		0			0
$985$	12.3875	−	21.4558i	0.394698	−	0.683638i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.80777			−0.0892820
$990$		0			0
$991$	32.4459			1.03068			0.515339	−	0.856987i	$-0.327666\pi$
$991$	32.4459			1.03068			0.515339	+	0.856987i	$0.327666\pi$
$992$		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	0.749665	−	0.661818i	$-0.230215\pi$
$997$	−6.26198	−	10.8461i	−0.198319	−	0.343498i	−0.947983	+	0.318320i	$0.896881\pi$
$998$		0			0
$999$	5.34552	−	56.2826i	0.169125	−	1.78070i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.47192 - 0.912932i) q^{3} +(1.94623 - 3.37097i) q^{5} +(1.33311 + 2.68753i) q^{9} +(-2.18778 - 3.78935i) q^{11} +(0.792201 - 1.37213i) q^{13} +(-5.94217 + 3.18503i) q^{15} +5.33356 q^{17} +4.64323 q^{19} +(-0.183900 + 0.318523i) q^{23} +(-5.07564 - 8.79126i) q^{25} +(0.491301 - 5.17287i) q^{27} +(-5.08750 - 8.81180i) q^{29} +(-1.14776 + 1.98798i) q^{31} +(-0.239175 + 7.57493i) q^{33} +10.8803 q^{37} +(-2.41872 + 1.29645i) q^{39} +(0.690443 - 1.19588i) q^{41} +(3.81699 + 6.61122i) q^{43} +(11.6541 + 0.736684i) q^{45} +(-3.80432 - 6.58928i) q^{47} +(-7.85058 - 4.86918i) q^{51} -0.925693 q^{53} -17.0317 q^{55} +(-6.83447 - 4.23895i) q^{57} +(-0.460475 + 0.797565i) q^{59} +(3.27780 + 5.67731i) q^{61} +(-3.08361 - 5.34097i) q^{65} +(-7.50420 + 12.9976i) q^{67} +(0.561476 - 0.300954i) q^{69} -4.91059 q^{71} -7.56707 q^{73} +(-0.554885 + 17.5738i) q^{75} +(-0.987715 - 1.71077i) q^{79} +(-5.44564 + 7.16554i) q^{81} +(0.253011 + 0.438227i) q^{83} +(10.3803 - 17.9793i) q^{85} +(-0.556181 + 17.6148i) q^{87} +12.2197 q^{89} +(3.50431 - 1.87833i) q^{93} +(9.03679 - 15.6522i) q^{95} +(-4.45315 - 7.71308i) q^{97} +(7.26745 - 10.9314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93}+ \cdots - 4 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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