LMFDB - Embedded newform 1764.2.w.a.509.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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, 5, 5]))

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

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

chi := DirichletCharacter("1764.509");

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.w (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.3
Root			$0.744857 + 1.56371i$ of defining polynomial
Character	$\chi$	$=$	1764.509
Dual form			1764.2.w.a.1109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.981784 - 1.42692i) q^{3} +(0.276914 + 0.479629i) q^{5} +(-1.07220 + 2.80185i) q^{9} +O(q^{10})$	\(q+(-0.981784 - 1.42692i) q^{3} +(0.276914 + 0.479629i) q^{5} +(-1.07220 + 2.80185i) q^{9} +(-4.03478 - 2.32948i) q^{11} +(3.58265 + 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} +(3.62264 + 6.27459i) q^{17} +(-5.81722 - 3.35857i) q^{19} +(4.85295 - 2.80185i) q^{23} +(2.34664 - 4.06450i) q^{25} +(5.05069 - 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} +0.959257i q^{31} +(0.637299 + 8.04435i) q^{33} +(3.53478 - 6.12241i) q^{37} +(-0.565885 - 7.14292i) q^{39} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(-1.64076 + 0.261614i) q^{45} +9.80602 q^{47} +(5.39669 - 11.3295i) q^{51} +(7.30235 - 4.21601i) q^{53} -2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} -7.79910 q^{59} -6.20463i q^{61} +2.29112i q^{65} -3.37628 q^{67} +(-8.76257 - 4.17396i) q^{69} +0.407556i q^{71} +(7.47870 - 4.31783i) q^{73} +(-8.10360 + 0.641993i) q^{75} +0.636352 q^{79} +(-6.70077 - 6.00830i) q^{81} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(-2.10534 - 1.00286i) q^{87} +(3.46568 - 6.00274i) q^{89} +(1.36878 - 0.941783i) q^{93} -3.72014i q^{95} +(7.48798 - 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^9	$ 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.981784	−	1.42692i	−0.566833	−	0.823833i
$3$	−0.981784	−	1.42692i	−0.566833	−	0.823833i
$4$		0			0
$5$	0.276914	+	0.479629i	0.123840	+	0.214496i	0.921279	−	0.388903i	$-0.127146\pi$
$5$	0.276914	+	0.479629i	0.123840	+	0.214496i	−0.797439	+	0.603399i	$0.793813\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.07220	+	2.80185i	−0.357400	+	0.933951i
$10$		0			0
$11$	−4.03478	−	2.32948i	−1.21653	−	0.702365i	−0.252357	−	0.967634i	$-0.581206\pi$
$11$	−4.03478	−	2.32948i	−1.21653	−	0.702365i	−0.964174	+	0.265270i	$0.914539\pi$
$12$		0			0
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.906363	−	0.422500i	$-0.138847\pi$
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.0872856	+	0.996183i	$0.472181\pi$
$14$		0			0
$15$	0.412522	−	0.866025i	0.106513	−	0.223607i
$16$		0			0
$17$	3.62264	+	6.27459i	0.878619	+	1.52181i	0.852857	+	0.522144i	$0.174868\pi$
$17$	3.62264	+	6.27459i	0.878619	+	1.52181i	0.0257612	+	0.999668i	$0.491799\pi$
$18$		0			0
$19$	−5.81722	−	3.35857i	−1.33456	−	0.770510i	−0.348567	−	0.937284i	$-0.613332\pi$
$19$	−5.81722	−	3.35857i	−1.33456	−	0.770510i	−0.985995	+	0.166774i	$0.946665\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.85295	−	2.80185i	1.01191	−	0.584227i	0.100160	−	0.994971i	$-0.468064\pi$
$23$	4.85295	−	2.80185i	1.01191	−	0.584227i	0.911751	+	0.410744i	$0.134731\pi$
$24$		0			0
$25$	2.34664	−	4.06450i	0.469328	−	0.812899i
$26$		0			0
$27$	5.05069	−	1.22087i	0.972006	−	0.234957i
$28$		0			0
$29$	1.16599	−	0.673187i	0.216520	−	0.125008i	−0.387818	−	0.921736i	$-0.626771\pi$
$29$	1.16599	−	0.673187i	0.216520	−	0.125008i	0.604338	+	0.796728i	$0.293438\pi$
$30$		0			0
$31$			0.959257i			0.172288i	0.996283	+	0.0861438i	$0.0274545\pi$
$31$			0.959257i			0.172288i	−0.996283	+	0.0861438i	$0.972546\pi$
$32$		0			0
$33$	0.637299	+	8.04435i	0.110939	+	1.40034i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.53478	−	6.12241i	0.581114	−	1.00652i	−0.414234	−	0.910170i	$-0.635950\pi$
$37$	3.53478	−	6.12241i	0.581114	−	1.00652i	0.995348	−	0.0963482i	$-0.0307162\pi$
$38$		0			0
$39$	−0.565885	−	7.14292i	−0.0906141	−	1.14378i
$40$		0			0
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	−0.990100	−	0.140362i	$-0.955173\pi$
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	0.616607	+	0.787271i	$0.288507\pi$
$42$		0			0
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	0.776888	−	0.629639i	$-0.216797\pi$
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	−0.933727	+	0.357986i	$0.883464\pi$
$44$		0			0
$45$	−1.64076	+	0.261614i	−0.244590	+	0.0389991i
$46$		0			0
$47$	9.80602			1.43035			0.715177	−	0.698943i	$-0.246346\pi$
$47$	9.80602			1.43035			0.715177	+	0.698943i	$0.246346\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	5.39669	−	11.3295i	0.755688	−	1.58645i
$52$		0			0
$53$	7.30235	−	4.21601i	1.00305	−	0.579114i	0.0939038	−	0.995581i	$-0.470065\pi$
$53$	7.30235	−	4.21601i	1.00305	−	0.579114i	0.909151	+	0.416468i	$0.136732\pi$
$54$		0			0
$55$		−	2.58026i		−	0.347922i
$56$		0			0
$57$	0.918838	+	11.5981i	0.121703	+	1.53621i
$58$		0			0
$59$	−7.79910			−1.01536			−0.507678	−	0.861547i	$-0.669496\pi$
$59$	−7.79910			−1.01536			−0.507678	+	0.861547i	$0.669496\pi$
$60$		0			0
$61$		−	6.20463i		−	0.794421i	−0.917728	−	0.397211i	$-0.869978\pi$
$61$		−	6.20463i		−	0.794421i	0.917728	−	0.397211i	$-0.130022\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			2.29112i			0.284179i
$66$		0			0
$67$	−3.37628			−0.412478			−0.206239	−	0.978502i	$-0.566122\pi$
$67$	−3.37628			−0.412478			−0.206239	+	0.978502i	$0.566122\pi$
$68$		0			0
$69$	−8.76257	−	4.17396i	−1.05489	−	0.502486i
$70$		0			0
$71$			0.407556i			0.0483680i	0.999708	+	0.0241840i	$0.00769875\pi$
$71$			0.407556i			0.0483680i	−0.999708	+	0.0241840i	$0.992301\pi$
$72$		0			0
$73$	7.47870	−	4.31783i	0.875316	−	0.505364i	0.00620487	−	0.999981i	$-0.498025\pi$
$73$	7.47870	−	4.31783i	0.875316	−	0.505364i	0.869111	+	0.494617i	$0.164692\pi$
$74$		0			0
$75$	−8.10360	+	0.641993i	−0.935723	+	0.0741309i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.636352			0.0715952			0.0357976	−	0.999359i	$-0.488603\pi$
$79$	0.636352			0.0715952			0.0357976	+	0.999359i	$0.488603\pi$
$80$		0			0
$81$	−6.70077	−	6.00830i	−0.744530	−	0.667589i
$82$		0			0
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	0.977498	−	0.210944i	$-0.0676537\pi$
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	−0.671432	+	0.741066i	$0.734320\pi$
$84$		0			0
$85$	−2.00632	+	3.47504i	−0.217616	+	0.376921i
$86$		0			0
$87$	−2.10534	−	1.00286i	−0.225716	−	0.107517i
$88$		0			0
$89$	3.46568	−	6.00274i	0.367362	−	0.636289i	−0.621790	−	0.783184i	$-0.713594\pi$
$89$	3.46568	−	6.00274i	0.367362	−	0.636289i	0.989152	+	0.146895i	$0.0469278\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.36878	−	0.941783i	0.141936	−	0.0976584i
$94$		0			0
$95$		−	3.72014i		−	0.381678i
$96$		0			0
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	−0.0691107	−	0.997609i	$-0.522016\pi$
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	0.829399	+	0.558656i	$0.188683\pi$
$98$		0			0
$99$	10.8530	−	8.80719i	1.09076	−	0.885156i
$100$		0			0
$101$	2.34227	−	4.05692i	0.233064	−	0.403679i	−0.725644	−	0.688070i	$-0.758458\pi$
$101$	2.34227	−	4.05692i	0.233064	−	0.403679i	0.958708	+	0.284391i	$0.0917915\pi$
$102$		0			0
$103$	6.40804	−	3.69969i	0.631403	−	0.364541i	−0.149892	−	0.988702i	$-0.547893\pi$
$103$	6.40804	−	3.69969i	0.631403	−	0.364541i	0.781295	+	0.624162i	$0.214559\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.38260	−	2.53029i	−0.423682	−	0.244613i	0.272970	−	0.962023i	$-0.411994\pi$
$107$	−4.38260	−	2.53029i	−0.423682	−	0.244613i	−0.696651	+	0.717410i	$0.745327\pi$
$108$		0			0
$109$	−5.88142	−	10.1869i	−0.563337	−	0.975729i	−0.997202	−	0.0747510i	$-0.976184\pi$
$109$	−5.88142	−	10.1869i	−0.563337	−	0.975729i	0.433865	−	0.900978i	$-0.357150\pi$
$110$		0			0
$111$	−12.2066	+	0.967044i	−1.15860	+	0.0917877i
$112$		0			0
$113$	−1.51895	−	0.876965i	−0.142891	−	0.0824979i	0.426850	−	0.904322i	$-0.359623\pi$
$113$	−1.51895	−	0.876965i	−0.142891	−	0.0824979i	−0.569741	+	0.821824i	$0.692956\pi$
$114$		0			0
$115$	2.68770	+	1.55174i	0.250629	+	0.144701i
$116$		0			0
$117$	−9.63680	+	7.82028i	−0.890922	+	0.722985i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.35295	+	9.27159i	0.486632	+	0.842872i
$122$		0			0
$123$	8.25861	−	0.654273i	0.744654	−	0.0589938i
$124$		0			0
$125$	5.36840			0.480164
$126$		0			0
$127$	11.0822			0.983385			0.491693	−	0.870769i	$-0.336378\pi$
$127$	11.0822			0.983385			0.491693	+	0.870769i	$0.336378\pi$
$128$		0			0
$129$	−1.53211	+	3.21643i	−0.134895	+	0.283191i
$130$		0			0
$131$	9.23643	+	15.9980i	0.806990	+	1.39775i	0.914939	+	0.403592i	$0.132238\pi$
$131$	9.23643	+	15.9980i	0.806990	+	1.39775i	−0.107949	+	0.994156i	$0.534428\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.98417	+	2.08438i	0.170770	+	0.179395i
$136$		0			0
$137$	−19.0537	−	11.0007i	−1.62787	−	0.939851i	−0.984727	−	0.174104i	$-0.944297\pi$
$137$	−19.0537	−	11.0007i	−1.62787	−	0.939851i	−0.643142	−	0.765747i	$-0.722370\pi$
$138$		0			0
$139$	−8.55986	−	4.94204i	−0.726038	−	0.419178i	0.0909332	−	0.995857i	$-0.471015\pi$
$139$	−8.55986	−	4.94204i	−0.726038	−	0.419178i	−0.816971	+	0.576679i	$0.804348\pi$
$140$		0			0
$141$	−9.62739	−	13.9924i	−0.810773	−	1.17837i
$142$		0			0
$143$	−9.63680	−	16.6914i	−0.805870	−	1.39581i
$144$		0			0
$145$	0.645760	+	0.372830i	0.0536274	+	0.0309618i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.36677	−	3.67585i	0.521586	−	0.301138i	−0.215997	−	0.976394i	$-0.569300\pi$
$149$	6.36677	−	3.67585i	0.521586	−	0.301138i	0.737583	+	0.675256i	$0.235967\pi$
$150$		0			0
$151$	2.16599	−	3.75161i	0.176266	−	0.305302i	−0.764333	−	0.644822i	$-0.776931\pi$
$151$	2.16599	−	3.75161i	0.176266	−	0.305302i	0.940599	+	0.339520i	$0.110265\pi$
$152$		0			0
$153$	−21.4647	+	3.42248i	−1.73532	+	0.276691i
$154$		0			0
$155$	−0.460087	+	0.265632i	−0.0369551	+	0.0213360i
$156$		0			0
$157$			1.78000i			0.142059i	0.997474	+	0.0710296i	$0.0226285\pi$
$157$			1.78000i			0.142059i	−0.997474	+	0.0710296i	$0.977372\pi$
$158$		0			0
$159$	−13.1852	−	6.28065i	−1.04566	−	0.498088i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.81818	−	4.88122i	0.220737	−	0.382327i	−0.734295	−	0.678830i	$-0.762487\pi$
$163$	2.81818	−	4.88122i	0.220737	−	0.382327i	0.955032	+	0.296503i	$0.0958206\pi$
$164$		0			0
$165$	−3.68182	+	2.53326i	−0.286630	+	0.197214i
$166$		0			0
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	−0.943506	−	0.331355i	$-0.892494\pi$
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	0.758715	+	0.651423i	$0.225827\pi$
$168$		0			0
$169$	2.05692	+	3.56270i	0.158225	+	0.274054i
$170$		0			0
$171$	15.6475	−	12.6979i	1.19659	−	0.971036i
$172$		0			0
$173$	5.67531			0.431486			0.215743	−	0.976450i	$-0.430783\pi$
$173$	5.67531			0.431486			0.215743	+	0.976450i	$0.430783\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.65703	+	11.1287i	0.575538	+	0.836484i
$178$		0			0
$179$	10.9383	−	6.31525i	0.817570	−	0.472024i	−0.0320079	−	0.999488i	$-0.510190\pi$
$179$	10.9383	−	6.31525i	0.817570	−	0.472024i	0.849578	+	0.527463i	$0.176857\pi$
$180$		0			0
$181$		−	22.7424i		−	1.69043i	−0.534426	−	0.845215i	$-0.679472\pi$
$181$		−	22.7424i		−	1.69043i	0.534426	−	0.845215i	$-0.320528\pi$
$182$		0			0
$183$	−8.85351	+	6.09160i	−0.654470	+	0.450304i
$184$		0			0
$185$	3.91531			0.287860
$186$		0			0
$187$		−	33.7554i		−	2.46844i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	11.6090i		−	0.840001i	−0.907524	−	0.420000i	$-0.862030\pi$
$191$		−	11.6090i		−	0.840001i	0.907524	−	0.420000i	$-0.137970\pi$
$192$		0			0
$193$	6.33199			0.455787			0.227893	−	0.973686i	$-0.426816\pi$
$193$	6.33199			0.455787			0.227893	+	0.973686i	$0.426816\pi$
$194$		0			0
$195$	3.26925	−	2.24939i	0.234116	−	0.161082i
$196$		0			0
$197$			3.10030i			0.220888i	0.993882	+	0.110444i	$0.0352272\pi$
$197$			3.10030i			0.220888i	−0.993882	+	0.110444i	$0.964773\pi$
$198$		0			0
$199$	−13.6198	+	7.86341i	−0.965484	+	0.557422i	−0.897856	−	0.440288i	$-0.854876\pi$
$199$	−13.6198	+	7.86341i	−0.965484	+	0.557422i	−0.0676272	+	0.997711i	$0.521543\pi$
$200$		0			0
$201$	3.31478	+	4.81768i	0.233806	+	0.339813i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.64898			−0.185013
$206$		0			0
$207$	2.64705	+	16.6014i	0.183982	+	1.15388i
$208$		0			0
$209$	15.6475	+	27.1022i	1.08236	+	1.87470i
$210$		0			0
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	−0.719413	−	0.694582i	$-0.755589\pi$
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	0.961233	+	0.275739i	$0.0889225\pi$
$212$		0			0
$213$	0.581549	−	0.400132i	0.0398471	−	0.0274166i
$214$		0			0
$215$	0.569590	−	0.986559i	0.0388457	−	0.0672828i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−13.5037	−	6.43233i	−0.912493	−	0.434657i
$220$		0			0
$221$			29.9729i			2.01619i
$222$		0			0
$223$	21.3477	−	12.3251i	1.42955	−	0.825350i	0.432464	−	0.901651i	$-0.357644\pi$
$223$	21.3477	−	12.3251i	1.42955	−	0.825350i	0.997085	+	0.0763008i	$0.0243109\pi$
$224$		0			0
$225$	8.87206	+	10.9329i	0.591470	+	0.728859i
$226$		0			0
$227$	−10.0372	+	17.3849i	−0.666190	+	1.15388i	0.312771	+	0.949829i	$0.398743\pi$
$227$	−10.0372	+	17.3849i	−0.666190	+	1.15388i	−0.978961	+	0.204047i	$0.934590\pi$
$228$		0			0
$229$	−6.75865	+	3.90211i	−0.446624	+	0.257859i	−0.706403	−	0.707809i	$-0.749684\pi$
$229$	−6.75865	+	3.90211i	−0.446624	+	0.257859i	0.259779	+	0.965668i	$0.416350\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.89843	+	3.98281i	0.451931	+	0.260922i	0.708645	−	0.705565i	$-0.249307\pi$
$233$	6.89843	+	3.98281i	0.451931	+	0.260922i	−0.256714	+	0.966487i	$0.582640\pi$
$234$		0			0
$235$	2.71542	+	4.70325i	0.177135	+	0.306806i
$236$		0			0
$237$	−0.624760	−	0.908023i	−0.0405825	−	0.0589824i
$238$		0			0
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.999999	+	0.00123146i	$0.000391987\pi$
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.501066	+	0.865409i	$0.332941\pi$
$240$		0			0
$241$	−0.757259	−	0.437203i	−0.0487793	−	0.0281628i	0.475412	−	0.879763i	$-0.342299\pi$
$241$	−0.757259	−	0.437203i	−0.0487793	−	0.0281628i	−0.524191	+	0.851601i	$0.675632\pi$
$242$		0			0
$243$	−1.99465	+	15.4603i	−0.127957	+	0.991780i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.8940	−	24.0652i	−0.884057	−	1.53123i
$248$		0			0
$249$	4.15391	−	8.72049i	0.263244	−	0.552639i
$250$		0			0
$251$	−2.32082			−0.146489			−0.0732445	−	0.997314i	$-0.523335\pi$
$251$	−2.32082			−0.146489			−0.0732445	+	0.997314i	$0.523335\pi$
$252$		0			0
$253$	−26.1075			−1.64136
$254$		0			0
$255$	6.92837	−	0.548888i	0.433872	−	0.0343727i
$256$		0			0
$257$	12.3017	+	21.3072i	0.767361	+	1.32911i	0.938989	+	0.343947i	$0.111764\pi$
$257$	12.3017	+	21.3072i	0.767361	+	1.32911i	−0.171628	+	0.985162i	$0.554903\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.635992	+	3.98874i	0.0393669	+	0.246897i
$262$		0			0
$263$	20.5268	+	11.8512i	1.26574	+	0.730775i	0.974179	−	0.225778i	$-0.0724922\pi$
$263$	20.5268	+	11.8512i	1.26574	+	0.730775i	0.291560	+	0.956552i	$0.405826\pi$
$264$		0			0
$265$	4.04424	+	2.33494i	0.248436	+	0.143434i
$266$		0			0
$267$	−11.9680	+	0.948141i	−0.732429	+	0.0580253i
$268$		0			0
$269$	10.3106	+	17.8585i	0.628648	+	1.08885i	0.987823	+	0.155580i	$0.0497245\pi$
$269$	10.3106	+	17.8585i	0.628648	+	1.08885i	−0.359176	+	0.933270i	$0.616942\pi$
$270$		0			0
$271$	−12.0771	−	6.97270i	−0.733630	−	0.423562i	0.0861186	−	0.996285i	$-0.472554\pi$
$271$	−12.0771	−	6.97270i	−0.733630	−	0.423562i	−0.819749	+	0.572723i	$0.805887\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−18.9363	+	10.9329i	−1.14190	+	0.659278i
$276$		0			0
$277$	−10.3940	+	18.0030i	−0.624518	+	1.08170i	0.364116	+	0.931354i	$0.381371\pi$
$277$	−10.3940	+	18.0030i	−0.624518	+	1.08170i	−0.988634	+	0.150343i	$0.951962\pi$
$278$		0			0
$279$	−2.68770	−	1.02852i	−0.160908	−	0.0615757i
$280$		0			0
$281$	−20.3371	+	11.7416i	−1.21321	+	0.700448i	−0.963457	−	0.267862i	$-0.913683\pi$
$281$	−20.3371	+	11.7416i	−1.21321	+	0.700448i	−0.249754	+	0.968309i	$0.580350\pi$
$282$		0			0
$283$			12.9218i			0.768120i	0.923308	+	0.384060i	$0.125474\pi$
$283$			12.9218i			0.768120i	−0.923308	+	0.384060i	$0.874526\pi$
$284$		0			0
$285$	−5.30834	+	3.65237i	−0.314439	+	0.216348i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−17.7470	+	30.7387i	−1.04394	+	1.80816i
$290$		0			0
$291$	−13.5204	−	6.44031i	−0.792581	−	0.377538i
$292$		0			0
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	−0.918308	−	0.395866i	$-0.870445\pi$
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	0.801984	+	0.597346i	$0.203778\pi$
$294$		0			0
$295$	−2.15968	−	3.74067i	−0.125741	−	0.217790i
$296$		0			0
$297$	−23.2224	−	6.83954i	−1.34750	−	0.396870i
$298$		0			0
$299$	23.1819			1.34064
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−8.08850	+	0.640797i	−0.464672	+	0.0368128i
$304$		0			0
$305$	2.97592	−	1.71815i	0.170401	−	0.0983808i
$306$		0			0
$307$			22.3162i			1.27365i	0.771008	+	0.636825i	$0.219753\pi$
$307$			22.3162i			1.27365i	−0.771008	+	0.636825i	$0.780247\pi$
$308$		0			0
$309$	−11.5705	−	5.51147i	−0.658221	−	0.313537i
$310$		0			0
$311$	16.3674			0.928111			0.464056	−	0.885806i	$-0.346394\pi$
$311$	16.3674			0.928111			0.464056	+	0.885806i	$0.346394\pi$
$312$		0			0
$313$		−	19.1157i		−	1.08048i	−0.841510	−	0.540242i	$-0.818333\pi$
$313$		−	19.1157i		−	1.08048i	0.841510	−	0.540242i	$-0.181667\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			24.1099i			1.35415i	0.735915	+	0.677074i	$0.236752\pi$
$317$			24.1099i			1.35415i	−0.735915	+	0.677074i	$0.763248\pi$
$318$		0			0
$319$	−6.27270			−0.351204
$320$		0			0
$321$	0.692237	+	8.73781i	0.0386369	+	0.487697i
$322$		0			0
$323$		−	48.6676i		−	2.70794i
$324$		0			0
$325$	16.8144	−	9.70778i	0.932693	−	0.538491i
$326$		0			0
$327$	−8.76163	+	18.3937i	−0.484519	+	1.01717i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	11.4015			0.626686			0.313343	−	0.949640i	$-0.398551\pi$
$331$	11.4015			0.626686			0.313343	+	0.949640i	$0.398551\pi$
$332$		0			0
$333$	13.3641	+	16.4684i	0.732349	+	0.902462i
$334$		0			0
$335$	−0.934938	−	1.61936i	−0.0510811	−	0.0884751i
$336$		0			0
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	−0.800981	−	0.598689i	$-0.795689\pi$
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	0.918971	+	0.394326i	$0.129022\pi$
$338$		0			0
$339$	0.239920	+	3.02841i	0.0130307	+	0.164480i
$340$		0			0
$341$	2.23457	−	3.87039i	0.121009	−	0.209593i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.424526	−	5.35861i	−0.0228557	−	0.288498i
$346$		0			0
$347$			5.33765i			0.286540i	0.989684	+	0.143270i	$0.0457617\pi$
$347$			5.33765i			0.286540i	−0.989684	+	0.143270i	$0.954238\pi$
$348$		0			0
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	−0.246240	−	0.969209i	$-0.579195\pi$
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	0.716239	+	0.697855i	$0.245862\pi$
$350$		0			0
$351$	20.6202	+	6.07312i	1.10062	+	0.324159i
$352$		0			0
$353$	−7.67564	+	13.2946i	−0.408533	+	0.707600i	−0.994726	−	0.102571i	$-0.967293\pi$
$353$	−7.67564	+	13.2946i	−0.408533	+	0.707600i	0.586192	+	0.810172i	$0.300626\pi$
$354$		0			0
$355$	−0.195475	+	0.112858i	−0.0103748	+	0.00598987i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.51381	+	0.874000i	0.0798960	+	0.0461280i	0.539416	−	0.842040i	$-0.318645\pi$
$359$	1.51381	+	0.874000i	0.0798960	+	0.0461280i	−0.459520	+	0.888168i	$0.651978\pi$
$360$		0			0
$361$	13.0600	+	22.6207i	0.687371	+	1.19056i
$362$		0			0
$363$	7.97437	−	16.7409i	0.418546	−	0.878671i
$364$		0			0
$365$	4.14191	+	2.39133i	0.216798	+	0.125168i
$366$		0			0
$367$	11.1720	+	6.45018i	0.583176	+	0.336697i	0.762394	−	0.647113i	$-0.224024\pi$
$367$	11.1720	+	6.45018i	0.583176	+	0.336697i	−0.179219	+	0.983809i	$0.557357\pi$
$368$		0			0
$369$	−9.04176	−	11.1420i	−0.470695	−	0.580030i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.34782	+	9.26269i	0.276900	+	0.479604i	0.970613	−	0.240647i	$-0.0773597\pi$
$373$	5.34782	+	9.26269i	0.276900	+	0.479604i	−0.693713	+	0.720251i	$0.744026\pi$
$374$		0			0
$375$	−5.27061	−	7.66028i	−0.272173	−	0.395575i
$376$		0			0
$377$	5.56980			0.286859
$378$		0			0
$379$	0.566797			0.0291144			0.0145572	−	0.999894i	$-0.495366\pi$
$379$	0.566797			0.0291144			0.0145572	+	0.999894i	$0.495366\pi$
$380$		0			0
$381$	−10.8803	−	15.8134i	−0.557415	−	0.810145i
$382$		0			0
$383$	−9.43059	−	16.3343i	−0.481880	−	0.834641i	0.517903	−	0.855439i	$-0.326713\pi$
$383$	−9.43059	−	16.3343i	−0.481880	−	0.834641i	−0.999784	+	0.0207978i	$0.993379\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.09379	−	0.971637i	0.309765	−	0.0493911i
$388$		0			0
$389$	−14.3182	−	8.26660i	−0.725960	−	0.419133i	0.0909822	−	0.995853i	$-0.470999\pi$
$389$	−14.3182	−	8.26660i	−0.725960	−	0.419133i	−0.816943	+	0.576719i	$0.804333\pi$
$390$		0			0
$391$	35.1610	+	20.3002i	1.77817	+	1.02663i
$392$		0			0
$393$	13.7596	−	28.8862i	0.694082	−	1.45712i
$394$		0			0
$395$	0.176215	+	0.305213i	0.00886632	+	0.0153569i
$396$		0			0
$397$	−29.5384	−	17.0540i	−1.48249	−	0.855917i	−0.482688	−	0.875792i	$-0.660340\pi$
$397$	−29.5384	−	17.0540i	−1.48249	−	0.855917i	−0.999802	+	0.0198756i	$0.993673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.6395	+	10.7615i	−0.930811	+	0.537404i	−0.887068	−	0.461639i	$-0.847262\pi$
$401$	−18.6395	+	10.7615i	−0.930811	+	0.537404i	−0.0437428	+	0.999043i	$0.513928\pi$
$402$		0			0
$403$	−1.98417	+	3.43668i	−0.0988386	+	0.171193i
$404$		0			0
$405$	1.02622	−	4.87766i	0.0509931	−	0.242373i
$406$		0			0
$407$	−28.5241	+	16.4684i	−1.41389	+	0.816308i
$408$		0			0
$409$		−	22.2299i		−	1.09920i	−0.835429	−	0.549599i	$-0.814781\pi$
$409$		−	22.2299i		−	1.09920i	0.835429	−	0.549599i	$-0.185219\pi$
$410$		0			0
$411$	3.00956	+	37.9884i	0.148451	+	1.87383i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.54429	+	2.67479i	−0.0758063	+	0.131300i
$416$		0			0
$417$	1.35204	+	17.0662i	0.0662098	+	0.835738i
$418$		0			0
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	−0.983085	−	0.183150i	$-0.941371\pi$
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	0.650155	+	0.759802i	$0.274704\pi$
$420$		0			0
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	0.978451	+	0.206480i	$0.0662009\pi$
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	−0.310408	+	0.950603i	$0.600466\pi$
$422$		0			0
$423$	−10.5140	+	27.4750i	−0.511209	+	1.33588i
$424$		0			0
$425$	34.0041			1.64944
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−14.3561	+	30.1383i	−0.693118	+	1.45509i
$430$		0			0
$431$	−30.1663	+	17.4165i	−1.45306	+	0.838925i	−0.998654	−	0.0518699i	$-0.983482\pi$
$431$	−30.1663	+	17.4165i	−1.45306	+	0.838925i	−0.454406	+	0.890795i	$0.650149\pi$
$432$		0			0
$433$		−	19.5648i		−	0.940223i	−0.882607	−	0.470112i	$-0.844214\pi$
$433$		−	19.5648i		−	0.940223i	0.882607	−	0.470112i	$-0.155786\pi$
$434$		0			0
$435$	−0.101999	−	1.28749i	−0.00489046	−	0.0617302i
$436$		0			0
$437$	−37.6409			−1.80061
$438$		0			0
$439$			28.5628i			1.36323i	0.731712	+	0.681614i	$0.238722\pi$
$439$			28.5628i			1.36323i	−0.731712	+	0.681614i	$0.761278\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	25.2431i		−	1.19934i	−0.800248	−	0.599669i	$-0.795299\pi$
$443$		−	25.2431i		−	1.19934i	0.800248	−	0.599669i	$-0.204701\pi$
$444$		0			0
$445$	3.83878			0.181976
$446$		0			0
$447$	−11.4959	−	5.47597i	−0.543739	−	0.259005i
$448$		0			0
$449$		−	15.1042i		−	0.712811i	−0.934331	−	0.356405i	$-0.884002\pi$
$449$		−	15.1042i		−	0.712811i	0.934331	−	0.356405i	$-0.115998\pi$
$450$		0			0
$451$	19.2985	−	11.1420i	0.908733	−	0.524657i
$452$		0			0
$453$	−7.47979	+	0.592572i	−0.351431	+	0.0278415i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.50276			0.163852			0.0819261	−	0.996638i	$-0.473893\pi$
$457$	3.50276			0.163852			0.0819261	+	0.996638i	$0.473893\pi$
$458$		0			0
$459$	25.9573	+	27.2682i	1.21158	+	1.27277i
$460$		0			0
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	0.908594	−	0.417681i	$-0.137157\pi$
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	−0.816019	+	0.578025i	$0.803824\pi$
$462$		0			0
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	−0.960989	−	0.276585i	$-0.910797\pi$
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	0.720025	+	0.693948i	$0.244130\pi$
$464$		0			0
$465$	0.830741	+	0.395715i	0.0385247	+	0.0183508i
$466$		0			0
$467$	9.80952	−	16.9906i	0.453930	−	0.786230i	−0.544696	−	0.838634i	$-0.683355\pi$
$467$	9.80952	−	16.9906i	0.453930	−	0.786230i	0.998626	+	0.0524035i	$0.0166882\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.53991	−	1.74757i	0.117033	−	0.0805239i
$472$		0			0
$473$			9.58312i			0.440632i
$474$		0			0
$475$	−27.3018	+	15.7627i	−1.25269	+	0.723243i
$476$		0			0
$477$	3.98307	+	24.9805i	0.182372	+	1.14378i
$478$		0			0
$479$	15.8237	−	27.4074i	0.723002	−	1.25228i	−0.236789	−	0.971561i	$-0.576095\pi$
$479$	15.8237	−	27.4074i	0.723002	−	1.25228i	0.959791	−	0.280715i	$-0.0905717\pi$
$480$		0			0
$481$	25.3277	−	14.6230i	1.15485	−	0.666751i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.14705	+	2.39430i	0.188308	+	0.108719i
$486$		0			0
$487$	9.72923	+	16.8515i	0.440874	+	0.763616i	0.997755	−	0.0669768i	$-0.0213353\pi$
$487$	9.72923	+	16.8515i	0.440874	+	0.763616i	−0.556881	+	0.830592i	$0.688002\pi$
$488$		0			0
$489$	−9.73196	+	0.770996i	−0.440094	+	0.0348656i
$490$		0			0
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.931156	−	0.364622i	$-0.118802\pi$
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.149806	+	0.988715i	$0.452135\pi$
$492$		0			0
$493$	8.44795	+	4.87743i	0.380476	+	0.219668i
$494$		0			0
$495$	7.22951	+	2.76656i	0.324942	+	0.124347i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4.50632	+	7.80517i	0.201730	+	0.349407i	0.949086	−	0.315017i	$-0.102010\pi$
$499$	4.50632	+	7.80517i	0.201730	+	0.349407i	−0.747356	+	0.664424i	$0.768677\pi$
$500$		0			0
$501$	8.24653	−	0.653316i	0.368428	−	0.0291880i
$502$		0			0
$503$	−27.1572			−1.21088			−0.605440	−	0.795891i	$-0.707003\pi$
$503$	−27.1572			−1.21088			−0.605440	+	0.795891i	$0.707003\pi$
$504$		0			0
$505$	2.59442			0.115450
$506$		0			0
$507$	3.06423	−	6.43286i	0.136087	−	0.285693i
$508$		0			0
$509$	−6.56799	−	11.3761i	−0.291121	−	0.504236i	0.682954	−	0.730461i	$-0.260695\pi$
$509$	−6.56799	−	11.3761i	−0.291121	−	0.504236i	−0.974075	+	0.226225i	$0.927362\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−33.4814	−	9.86104i	−1.47824	−	0.435376i
$514$		0			0
$515$	3.54895	+	2.04899i	0.156385	+	0.0902892i
$516$		0			0
$517$	−39.5651	−	22.8429i	−1.74007	−	1.00463i
$518$		0			0
$519$	−5.57193	−	8.09822i	−0.244581	−	0.355472i
$520$		0			0
$521$	−2.01609	−	3.49198i	−0.0883266	−	0.152986i	0.818477	−	0.574539i	$-0.194819\pi$
$521$	−2.01609	−	3.49198i	−0.0883266	−	0.152986i	−0.906804	+	0.421553i	$0.861485\pi$
$522$		0			0
$523$	−0.516117	−	0.297980i	−0.0225682	−	0.0130298i	0.488673	−	0.872467i	$-0.337481\pi$
$523$	−0.516117	−	0.297980i	−0.0225682	−	0.0130298i	−0.511242	+	0.859437i	$0.670814\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.01895	+	3.47504i	−0.262189	+	0.151375i
$528$		0			0
$529$	4.20077	−	7.27595i	0.182642	−	0.316346i
$530$		0			0
$531$	8.36220	−	21.8519i	0.362889	−	0.948294i
$532$		0			0
$533$	−17.1360	+	9.89347i	−0.742242	+	0.428534i
$534$		0			0
$535$		−	2.80269i		−	0.121171i
$536$		0			0
$537$	−19.7504	−	9.40792i	−0.852295	−	0.405982i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	7.05061	−	12.2120i	0.303129	−	0.525035i	−0.673714	−	0.738992i	$-0.735302\pi$
$541$	7.05061	−	12.2120i	0.303129	−	0.525035i	0.976843	+	0.213957i	$0.0686353\pi$
$542$		0			0
$543$	−32.4516	+	22.3281i	−1.39263	+	0.958192i
$544$		0			0
$545$	3.25729	−	5.64179i	0.139527	−	0.241668i
$546$		0			0
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	−0.911433	−	0.411450i	$-0.865023\pi$
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	0.0993905	−	0.995049i	$-0.468311\pi$
$548$		0			0
$549$	17.3845	+	6.65260i	0.741951	+	0.283926i
$550$		0			0
$551$	−9.04380			−0.385279
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−3.84399	−	5.58684i	−0.163168	−	0.237148i
$556$		0			0
$557$	36.1181	−	20.8528i	1.53037	−	0.883562i	0.531031	−	0.847353i	$-0.321805\pi$
$557$	36.1181	−	20.8528i	1.53037	−	0.883562i	0.999344	−	0.0362098i	$-0.0115285\pi$
$558$		0			0
$559$		−	8.50926i		−	0.359903i
$560$		0			0
$561$	−48.1663	+	33.1406i	−2.03358	+	1.39920i
$562$		0			0
$563$	1.87687			0.0791007			0.0395504	−	0.999218i	$-0.487407\pi$
$563$	1.87687			0.0791007			0.0395504	+	0.999218i	$0.487407\pi$
$564$		0			0
$565$		−	0.971375i		−	0.0408660i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	23.8320i		−	0.999089i	−0.866288	−	0.499545i	$-0.833501\pi$
$569$		−	23.8320i		−	0.999089i	0.866288	−	0.499545i	$-0.166499\pi$
$570$		0			0
$571$	29.7438			1.24474			0.622370	−	0.782723i	$-0.286170\pi$
$571$	29.7438			1.24474			0.622370	+	0.782723i	$0.286170\pi$
$572$		0			0
$573$	−16.5652	+	11.3976i	−0.692020	+	0.476140i
$574$		0			0
$575$		−	26.2997i		−	1.09678i
$576$		0			0
$577$	−12.6950	+	7.32947i	−0.528501	+	0.305130i	−0.740406	−	0.672160i	$-0.765367\pi$
$577$	−12.6950	+	7.32947i	−0.528501	+	0.305130i	0.211905	+	0.977290i	$0.432033\pi$
$578$		0			0
$579$	−6.21664	−	9.03524i	−0.258355	−	0.375492i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−39.2845			−1.62700
$584$		0			0
$585$	−6.41939	−	2.45654i	−0.265409	−	0.101566i
$586$		0			0
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.803836	−	0.594851i	$-0.797211\pi$
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.113238	−	0.993568i	$-0.536122\pi$
$588$		0			0
$589$	3.22174	−	5.58021i	0.132749	−	0.229929i
$590$		0			0
$591$	4.42389	−	3.04383i	0.181974	−	0.125206i
$592$		0			0
$593$	−18.5593	+	32.1457i	−0.762140	+	1.32006i	0.179606	+	0.983739i	$0.442518\pi$
$593$	−18.5593	+	32.1457i	−0.762140	+	1.32006i	−0.941746	+	0.336326i	$0.890816\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	24.5922	+	11.7142i	1.00649	+	0.479431i
$598$		0			0
$599$			13.9180i			0.568675i	0.958724	+	0.284338i	$0.0917737\pi$
$599$			13.9180i			0.568675i	−0.958724	+	0.284338i	$0.908226\pi$
$600$		0			0
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	−0.492279	−	0.870438i	$-0.663836\pi$
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	0.507682	+	0.861545i	$0.330503\pi$
$602$		0			0
$603$	3.62005	−	9.45984i	0.147420	−	0.385235i
$604$		0			0
$605$	−2.96461	+	5.13486i	−0.120529	+	0.208762i
$606$		0			0
$607$	−1.92117	+	1.10919i	−0.0779778	+	0.0450205i	−0.538482	−	0.842637i	$-0.681002\pi$
$607$	−1.92117	+	1.10919i	−0.0779778	+	0.0450205i	0.460504	+	0.887658i	$0.347669\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	35.1315	+	20.2832i	1.42127	+	0.820570i
$612$		0			0
$613$	−19.1011	−	33.0841i	−0.771488	−	1.33626i	−0.936748	−	0.350006i	$-0.886180\pi$
$613$	−19.1011	−	33.0841i	−0.771488	−	1.33626i	0.165260	−	0.986250i	$-0.447154\pi$
$614$		0			0
$615$	2.60073	+	3.77989i	0.104872	+	0.152420i
$616$		0			0
$617$	21.1043	+	12.1846i	0.849628	+	0.490533i	0.860525	−	0.509407i	$-0.170135\pi$
$617$	21.1043	+	12.1846i	0.849628	+	0.490533i	−0.0108970	+	0.999941i	$0.503469\pi$
$618$		0			0
$619$	−25.4477	−	14.6922i	−1.02283	−	0.590531i	−0.107907	−	0.994161i	$-0.534415\pi$
$619$	−25.4477	−	14.6922i	−1.02283	−	0.590531i	−0.914922	+	0.403630i	$0.867748\pi$
$620$		0			0
$621$	21.0901	−	20.0761i	0.846315	−	0.805627i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−10.2466	−	17.7476i	−0.409864	−	0.709906i
$626$		0			0
$627$	23.3102	−	48.9362i	0.930921	−	1.95432i
$628$		0			0
$629$	51.2209			2.04231
$630$		0			0
$631$	5.17077			0.205845			0.102923	−	0.994689i	$-0.467181\pi$
$631$	5.17077			0.205845			0.102923	+	0.994689i	$0.467181\pi$
$632$		0			0
$633$	−12.1301	+	0.960985i	−0.482128	+	0.0381957i
$634$		0			0
$635$	3.06881	+	5.31533i	0.121782	+	0.210933i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.14191	−	0.436981i	−0.0451733	−	0.0172867i
$640$		0			0
$641$	5.32405	+	3.07384i	0.210287	+	0.121410i	0.601445	−	0.798914i	$-0.294592\pi$
$641$	5.32405	+	3.07384i	0.210287	+	0.121410i	−0.391158	+	0.920324i	$0.627925\pi$
$642$		0			0
$643$	23.9599	+	13.8333i	0.944886	+	0.545530i	0.891489	−	0.453043i	$-0.149662\pi$
$643$	23.9599	+	13.8333i	0.944886	+	0.545530i	0.0533976	+	0.998573i	$0.482995\pi$
$644$		0			0
$645$	−1.96696	+	0.155828i	−0.0774488	+	0.00613574i
$646$		0			0
$647$	−2.40729	−	4.16954i	−0.0946402	−	0.163922i	0.814818	−	0.579717i	$-0.196837\pi$
$647$	−2.40729	−	4.16954i	−0.0946402	−	0.163922i	−0.909458	+	0.415795i	$0.863503\pi$
$648$		0			0
$649$	31.4676	+	18.1679i	1.23521	+	0.713151i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.1759	+	12.2259i	−0.828677	+	0.478437i	−0.853400	−	0.521257i	$-0.825463\pi$
$653$	−21.1759	+	12.2259i	−0.828677	+	0.478437i	0.0247223	+	0.999694i	$0.492130\pi$
$654$		0			0
$655$	−5.11539	+	8.86011i	−0.199875	+	0.346193i
$656$		0			0
$657$	4.07926	+	25.5838i	0.159147	+	0.998120i
$658$		0			0
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	−0.846386	−	0.532570i	$-0.821226\pi$
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	0.0380267	+	0.999277i	$0.487893\pi$
$660$		0			0
$661$			7.77431i			0.302386i	0.988504	+	0.151193i	$0.0483114\pi$
$661$			7.77431i			0.302386i	−0.988504	+	0.151193i	$0.951689\pi$
$662$		0			0
$663$	42.7689	−	29.4269i	1.66101	−	1.14285i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.77234	−	6.53389i	0.146066	−	0.252993i
$668$		0			0
$669$	−38.5458	−	18.3609i	−1.49027	−	0.709873i
$670$		0			0
$671$	−14.4536	+	25.0343i	−0.557973	+	0.966438i
$672$		0			0
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	−0.996790	−	0.0800548i	$-0.974490\pi$
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	0.429066	−	0.903273i	$-0.358843\pi$
$674$		0			0
$675$	6.88992	−	23.3935i	0.265193	−	0.900414i
$676$		0			0
$677$	−35.6586			−1.37047			−0.685235	−	0.728322i	$-0.740300\pi$
$677$	−35.6586			−1.37047			−0.685235	+	0.728322i	$0.740300\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	34.6612	−	2.74597i	1.32822	−	0.105226i
$682$		0			0
$683$	11.3423	−	6.54846i	0.433999	−	0.250570i	−0.267050	−	0.963683i	$-0.586049\pi$
$683$	11.3423	−	6.54846i	0.433999	−	0.250570i	0.701049	+	0.713113i	$0.252715\pi$
$684$		0			0
$685$		−	12.1850i		−	0.465563i
$686$		0			0
$687$	12.2035	+	5.81302i	0.465594	+	0.221781i
$688$		0			0
$689$	34.8823			1.32891
$690$		0			0
$691$			9.02967i			0.343505i	0.985140	+	0.171752i	$0.0549429\pi$
$691$			9.02967i			0.343505i	−0.985140	+	0.171752i	$0.945057\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	5.47407i		−	0.207643i
$696$		0			0
$697$	−34.6545			−1.31263
$698$		0			0
$699$	−1.08962	−	13.7538i	−0.0412131	−	0.520215i
$700$		0			0
$701$		−	0.259274i		−	0.00979264i	−0.999988	−	0.00489632i	$-0.998441\pi$
$701$		−	0.259274i		−	0.00979264i	0.999988	−	0.00489632i	$-0.00155855\pi$
$702$		0			0
$703$	−41.1252	+	23.7436i	−1.55107	+	0.895508i
$704$		0			0
$705$	4.04520	−	8.49226i	0.152351	−	0.319837i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	6.17149			0.231775			0.115888	−	0.993262i	$-0.463029\pi$
$709$	6.17149			0.231775			0.115888	+	0.993262i	$0.463029\pi$
$710$		0			0
$711$	−0.682297	+	1.78296i	−0.0255881	+	0.0668664i
$712$		0			0
$713$	2.68770	+	4.65523i	0.100655	+	0.174340i
$714$		0			0
$715$	5.33712	−	9.24417i	0.199597	−	0.345712i
$716$		0			0
$717$	−3.66541	−	46.2668i	−0.136887	−	1.72787i
$718$		0			0
$719$	−9.76375	+	16.9113i	−0.364127	+	0.630686i	−0.988636	−	0.150332i	$-0.951966\pi$
$719$	−9.76375	+	16.9113i	−0.364127	+	0.630686i	0.624509	+	0.781018i	$0.285299\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	0.119610	+	1.50979i	0.00444835	+	0.0561496i
$724$		0			0
$725$		−	6.31890i		−	0.234678i
$726$		0			0
$727$	0.425312	−	0.245554i	0.0157740	−	0.00910710i	−0.492092	−	0.870543i	$-0.663768\pi$
$727$	0.425312	−	0.245554i	0.0157740	−	0.00910710i	0.507866	+	0.861436i	$0.330434\pi$
$728$		0			0
$729$	24.0189	−	12.3325i	0.889591	−	0.456759i
$730$		0			0
$731$	7.45149	−	12.9064i	0.275603	−	0.477359i
$732$		0			0
$733$	−6.68424	+	3.85915i	−0.246888	+	0.142541i	−0.618338	−	0.785912i	$-0.712194\pi$
$733$	−6.68424	+	3.85915i	−0.246888	+	0.142541i	0.371450	+	0.928453i	$0.378861\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.6225	+	7.86498i	0.501793	+	0.289710i
$738$		0			0
$739$	−5.45417	−	9.44690i	−0.200635	−	0.347510i	0.748098	−	0.663588i	$-0.230967\pi$
$739$	−5.45417	−	9.44690i	−0.200635	−	0.347510i	−0.948733	+	0.316078i	$0.897634\pi$
$740$		0			0
$741$	−20.6982	+	43.4525i	−0.760366	+	1.59627i
$742$		0			0
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.905490	−	0.424367i	$-0.139503\pi$
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.0852322	+	0.996361i	$0.472837\pi$
$744$		0			0
$745$	3.52609	+	2.03579i	0.129186	+	0.0745855i
$746$		0			0
$747$	−16.5217	+	2.63433i	−0.604497	+	0.0963852i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	23.0367	+	39.9008i	0.840622	+	1.45600i	0.889370	+	0.457188i	$0.151143\pi$
$751$	23.0367	+	39.9008i	0.840622	+	1.45600i	−0.0487482	+	0.998811i	$0.515523\pi$
$752$		0			0
$753$	2.27855	+	3.31163i	0.0830349	+	0.120682i
$754$		0			0
$755$	2.39917			0.0873149
$756$		0			0
$757$	40.6419			1.47715			0.738577	−	0.674169i	$-0.235498\pi$
$757$	40.6419			1.47715			0.738577	+	0.674169i	$0.235498\pi$
$758$		0			0
$759$	25.6319	+	37.2532i	0.930378	+	1.35221i
$760$		0			0
$761$	3.64190	+	6.30795i	0.132019	+	0.228663i	0.924455	−	0.381292i	$-0.124521\pi$
$761$	3.64190	+	6.30795i	0.132019	+	0.228663i	−0.792436	+	0.609955i	$0.791187\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−7.58538	−	9.34735i	−0.274250	−	0.337954i
$766$		0			0
$767$	−27.9415	−	16.1320i	−1.00891	−	0.582493i
$768$		0			0
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.312927	−	0.949777i	$-0.601310\pi$
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.978995	+	0.203886i	$0.934643\pi$
$770$		0			0
$771$	18.3261	−	38.4727i	0.659997	−	1.38556i
$772$		0			0
$773$	−8.55914	−	14.8249i	−0.307851	−	0.533213i	0.670041	−	0.742324i	$-0.266276\pi$
$773$	−8.55914	−	14.8249i	−0.307851	−	0.533213i	−0.977892	+	0.209111i	$0.932943\pi$
$774$		0			0
$775$	3.89890	+	2.25103i	0.140053	+	0.0808594i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	27.8241	−	16.0642i	0.996900	−	0.575561i
$780$		0			0
$781$	0.949393	−	1.64440i	0.0339719	−	0.0588411i
$782$		0			0
$783$	5.06720	−	4.82359i	0.181087	−	0.172381i
$784$		0			0
$785$	−0.853737	+	0.492906i	−0.0304712	+	0.0175926i
$786$		0			0
$787$			29.7250i			1.05958i	0.848129	+	0.529790i	$0.177729\pi$
$787$			29.7250i			1.05958i	−0.848129	+	0.529790i	$0.822271\pi$
$788$		0			0
$789$	−3.24224	−	40.9255i	−0.115427	−	1.45698i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	12.8339	−	22.2290i	0.455746	−	0.789375i
$794$		0			0
$795$	−0.638793	−	8.06322i	−0.0226557	−	0.285973i
$796$		0			0
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	−0.227229	−	0.973841i	$-0.572966\pi$
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	0.956986	−	0.290135i	$-0.0937002\pi$
$798$		0			0
$799$	35.5236	+	61.5288i	1.25674	+	2.17673i
$800$		0			0
$801$	13.1029	+	16.1465i	0.462968	+	0.570508i
$802$		0			0
$803$	−40.2332			−1.41980
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.3598	−	32.2455i	0.540691	−	1.13510i
$808$		0			0
$809$	10.7589	−	6.21165i	0.378262	−	0.218390i	−0.298800	−	0.954316i	$-0.596586\pi$
$809$	10.7589	−	6.21165i	0.378262	−	0.218390i	0.677062	+	0.735926i	$0.263253\pi$
$810$		0			0
$811$			32.8713i			1.15427i	0.816650	+	0.577133i	$0.195829\pi$
$811$			32.8713i			1.15427i	−0.816650	+	0.577133i	$0.804171\pi$
$812$		0			0
$813$	1.90759	+	24.0787i	0.0669021	+	0.844477i
$814$		0			0
$815$	3.12157			0.109344
$816$		0			0
$817$			13.8167i			0.483384i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	13.5575i		−	0.473159i	−0.971612	−	0.236579i	$-0.923974\pi$
$821$		−	13.5575i		−	0.473159i	0.971612	−	0.236579i	$-0.0760263\pi$
$822$		0			0
$823$	−24.5130			−0.854470			−0.427235	−	0.904141i	$-0.640512\pi$
$823$	−24.5130			−0.854470			−0.427235	+	0.904141i	$0.640512\pi$
$824$		0			0
$825$	34.1917	+	16.2869i	1.19040	+	0.567036i
$826$		0			0
$827$		−	14.7323i		−	0.512292i	−0.966638	−	0.256146i	$-0.917547\pi$
$827$		−	14.7323i		−	0.512292i	0.966638	−	0.256146i	$-0.0824527\pi$
$828$		0			0
$829$	−11.7079	+	6.75957i	−0.406633	+	0.234770i	−0.689342	−	0.724436i	$-0.742100\pi$
$829$	−11.7079	+	6.75957i	−0.406633	+	0.234770i	0.282709	+	0.959206i	$0.408767\pi$
$830$		0			0
$831$	35.8936	−	2.84360i	1.24513	−	0.0986434i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.64511			−0.0915378
$836$		0			0
$837$	1.17113	+	4.84491i	0.0404802	+	0.167465i
$838$		0			0
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	0.857067	−	0.515205i	$-0.172284\pi$
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	−0.874714	+	0.484639i	$0.838951\pi$
$840$		0			0
$841$	−13.5936	+	23.5449i	−0.468746	+	0.811892i
$842$		0			0
$843$	36.7210	+	17.4917i	1.26474	+	0.602446i
$844$		0			0
$845$	−1.13918	+	1.97312i	−0.0391890	+	0.0678773i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	18.4383	−	12.6864i	0.632802	−	0.435396i
$850$		0			0
$851$		−	39.6157i		−	1.35801i
$852$		0			0
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	−0.343480	−	0.939160i	$-0.611606\pi$
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	0.641596	+	0.767043i	$0.278273\pi$
$854$		0			0
$855$	10.4233	+	3.98874i	0.356469	+	0.136412i
$856$		0			0
$857$	−14.1272	+	24.4690i	−0.482575	+	0.835844i	−0.999800	−	0.0200052i	$-0.993632\pi$
$857$	−14.1272	+	24.4690i	−0.482575	+	0.835844i	0.517225	+	0.855850i	$0.326965\pi$
$858$		0			0
$859$	−26.9800	+	15.5769i	−0.920544	+	0.531476i	−0.883809	−	0.467849i	$-0.845029\pi$
$859$	−26.9800	+	15.5769i	−0.920544	+	0.531476i	−0.0367356	+	0.999325i	$0.511696\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−49.4703	−	28.5617i	−1.68399	−	0.972252i	−0.958963	−	0.283530i	$-0.908495\pi$
$863$	−49.4703	−	28.5617i	−1.68399	−	0.972252i	−0.725026	−	0.688722i	$-0.758172\pi$
$864$		0			0
$865$	1.57157	+	2.72204i	0.0534351	+	0.0925522i
$866$		0			0
$867$	61.2854	−	4.85522i	2.08136	−	0.164892i
$868$		0			0
$869$	−2.56754	−	1.48237i	−0.0870978	−	0.0502859i
$870$		0			0
$871$	−12.0960	−	6.98365i	−0.409858	−	0.236632i
$872$		0			0
$873$	4.08432	+	25.6155i	0.138233	+	0.866955i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	15.6691	+	27.1397i	0.529108	+	0.916443i	0.999424	+	0.0339441i	$0.0108068\pi$
$877$	15.6691	+	27.1397i	0.529108	+	0.916443i	−0.470315	+	0.882498i	$0.655860\pi$
$878$		0			0
$879$	6.87601	−	0.544739i	0.231922	−	0.0183736i
$880$		0			0
$881$	12.2822			0.413799			0.206900	−	0.978362i	$-0.433663\pi$
$881$	12.2822			0.413799			0.206900	+	0.978362i	$0.433663\pi$
$882$		0			0
$883$	3.61496			0.121653			0.0608266	−	0.998148i	$-0.480626\pi$
$883$	3.61496			0.121653			0.0608266	+	0.998148i	$0.480626\pi$
$884$		0			0
$885$	−3.21730	+	6.75422i	−0.108148	+	0.227041i
$886$		0			0
$887$	−9.44264	−	16.3551i	−0.317053	−	0.549152i	0.662819	−	0.748780i	$-0.269360\pi$
$887$	−9.44264	−	16.3551i	−0.317053	−	0.549152i	−0.979872	+	0.199628i	$0.936027\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	13.0399	+	39.8515i	0.436854	+	1.33507i
$892$		0			0
$893$	−57.0438	−	32.9342i	−1.90890	−	1.10210i
$894$		0			0
$895$	6.05795	+	3.49756i	0.202495	+	0.116911i
$896$		0			0
$897$	−22.7596	−	33.0787i	−0.759922	−	1.10447i
$898$		0			0
$899$	0.645760	+	1.11849i	0.0215373	+	0.0373037i
$900$		0			0
$901$	52.9075	+	30.5462i	1.76260	+	1.01764i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.9079	−	6.29769i	0.362591	−	0.209342i
$906$		0			0
$907$	28.8802	−	50.0219i	0.958950	−	1.66095i	0.233891	−	0.972263i	$-0.424854\pi$
$907$	28.8802	−	50.0219i	0.958950	−	1.66095i	0.725059	−	0.688687i	$-0.241813\pi$
$908$		0			0
$909$	8.85553	+	10.9125i	0.293719	+	0.361945i
$910$		0			0
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.941200	−	0.337850i	$-0.890300\pi$
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.178013	+	0.984028i	$0.556967\pi$
$912$		0			0
$913$		−	25.9821i		−	0.859881i
$914$		0			0
$915$	−5.37336	−	2.55955i	−0.177638	−	0.0846160i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	15.9047	−	27.5478i	0.524649	−	0.908719i	−0.474939	−	0.880019i	$-0.657530\pi$
$919$	15.9047	−	27.5478i	0.524649	−	0.908719i	0.999588	−	0.0287001i	$-0.00913677\pi$
$920$		0			0
$921$	31.8434	−	21.9096i	1.04927	−	0.721947i
$922$		0			0
$923$	−0.843006	+	1.46013i	−0.0277479	+	0.0480607i
$924$		0			0
$925$	−16.5897	−	28.7342i	−0.545465	−	0.944774i
$926$		0			0
$927$	3.49527	+	21.9212i	0.114800	+	0.719987i
$928$		0			0
$929$	−38.0849			−1.24952			−0.624762	−	0.780815i	$-0.714804\pi$
$929$	−38.0849			−1.24952			−0.624762	+	0.780815i	$0.714804\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−16.0693	−	23.3550i	−0.526084	−	0.764608i
$934$		0			0
$935$	16.1901	−	9.34735i	0.529472	−	0.305691i
$936$		0			0
$937$			37.6261i			1.22919i	0.788842	+	0.614596i	$0.210681\pi$
$937$			37.6261i			1.22919i	−0.788842	+	0.614596i	$0.789319\pi$
$938$		0			0
$939$	−27.2766	+	18.7675i	−0.890137	+	0.612454i
$940$		0			0
$941$	1.67547			0.0546189			0.0273094	−	0.999627i	$-0.491306\pi$
$941$	1.67547			0.0546189			0.0273094	+	0.999627i	$0.491306\pi$
$942$		0			0
$943$			26.8028i			0.872820i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			22.2085i			0.721679i	0.932628	+	0.360839i	$0.117510\pi$
$947$			22.2085i			0.721679i	−0.932628	+	0.360839i	$0.882490\pi$
$948$		0			0
$949$	35.7248			1.15968
$950$		0			0
$951$	34.4029	−	23.6707i	1.11559	−	0.767576i
$952$		0			0
$953$		−	27.1505i		−	0.879491i	−0.898122	−	0.439746i	$-0.855069\pi$
$953$		−	27.1505i		−	0.879491i	0.898122	−	0.439746i	$-0.144931\pi$
$954$		0			0
$955$	5.56803	−	3.21470i	0.180177	−	0.104025i
$956$		0			0
$957$	6.15844	+	8.95065i	0.199074	+	0.289333i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.0798			0.970317
$962$		0			0
$963$	11.7885	−	9.56641i	0.379880	−	0.308273i
$964$		0			0
$965$	1.75341	+	3.03700i	0.0564444	+	0.0977646i
$966$		0			0
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	0.460153	+	0.887840i	$0.347795\pi$
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	−0.998968	+	0.0454157i	$0.985539\pi$
$968$		0			0
$969$	−69.4447	+	47.7811i	−2.23089	+	1.53495i
$970$		0			0
$971$	17.8733	−	30.9574i	0.573580	−	0.993470i	−0.422614	−	0.906310i	$-0.638887\pi$
$971$	17.8733	−	30.9574i	0.573580	−	0.993470i	0.996194	−	0.0871606i	$-0.0277793\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−30.3603	−	14.4618i	−0.972308	−	0.463149i
$976$		0			0
$977$			45.6910i			1.46178i	0.682493	+	0.730892i	$0.260896\pi$
$977$			45.6910i			1.46178i	−0.682493	+	0.730892i	$0.739104\pi$
$978$		0			0
$979$	−27.9665	+	16.1465i	−0.893814	+	0.516044i
$980$		0			0
$981$	34.8483	−	5.55646i	1.11262	−	0.177404i
$982$		0			0
$983$	9.33713	−	16.1724i	0.297808	−	0.515819i	−0.677826	−	0.735222i	$-0.737078\pi$
$983$	9.33713	−	16.1724i	0.297808	−	0.515819i	0.975634	+	0.219404i	$0.0704111\pi$
$984$		0			0
$985$	−1.48699	+	0.858517i	−0.0473796	+	0.0273546i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.98215	−	5.76320i	−0.317414	−	0.183259i
$990$		0			0
$991$	−24.2806	−	42.0552i	−0.771299	−	1.33593i	−0.936851	−	0.349727i	$-0.886274\pi$
$991$	−24.2806	−	42.0552i	−0.771299	−	1.33593i	0.165553	−	0.986201i	$-0.447059\pi$
$992$		0			0
$993$	−11.1939	−	16.2691i	−0.355226	−	0.516284i
$994$		0			0
$995$	−7.54303	−	4.35497i	−0.239130	−	0.138062i
$996$		0			0
$997$	45.1982	+	26.0952i	1.43144	+	0.826442i	0.997231	−	0.0743700i	$-0.0236946\pi$
$997$	45.1982	+	26.0952i	1.43144	+	0.826442i	0.434209	+	0.900812i	$0.357028\pi$
$998$		0			0
$999$	10.3784	−	35.2379i	0.328358	−	1.11488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.a.509.3		16
3.2	odd	2		5292.2.w.a.1097.3		16
7.2	even	3		252.2.x.a.41.8	yes	16
7.3	odd	6		1764.2.bm.b.1697.6		16
7.4	even	3		1764.2.bm.b.1697.3		16
7.5	odd	6		252.2.x.a.41.1	✓	16
7.6	odd	2	inner	1764.2.w.a.509.6		16
9.2	odd	6		1764.2.bm.b.1685.6		16
9.7	even	3		5292.2.bm.b.4625.3		16
21.2	odd	6		756.2.x.a.125.3		16
21.5	even	6		756.2.x.a.125.6		16
21.11	odd	6		5292.2.bm.b.2285.6		16
21.17	even	6		5292.2.bm.b.2285.3		16
21.20	even	2		5292.2.w.a.1097.6		16
28.19	even	6		1008.2.cc.c.545.8		16
28.23	odd	6		1008.2.cc.c.545.1		16
63.2	odd	6		252.2.x.a.209.1	yes	16
63.5	even	6		2268.2.f.b.1133.6		16
63.11	odd	6	inner	1764.2.w.a.1109.6		16
63.16	even	3		756.2.x.a.629.6		16
63.20	even	6		1764.2.bm.b.1685.3		16
63.23	odd	6		2268.2.f.b.1133.11		16
63.25	even	3		5292.2.w.a.521.6		16
63.34	odd	6		5292.2.bm.b.4625.6		16
63.38	even	6	inner	1764.2.w.a.1109.3		16
63.40	odd	6		2268.2.f.b.1133.12		16
63.47	even	6		252.2.x.a.209.8	yes	16
63.52	odd	6		5292.2.w.a.521.3		16
63.58	even	3		2268.2.f.b.1133.5		16
63.61	odd	6		756.2.x.a.629.3		16
84.23	even	6		3024.2.cc.c.881.3		16
84.47	odd	6		3024.2.cc.c.881.6		16
252.47	odd	6		1008.2.cc.c.209.1		16
252.79	odd	6		3024.2.cc.c.2897.6		16
252.187	even	6		3024.2.cc.c.2897.3		16
252.191	even	6		1008.2.cc.c.209.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.1	✓	16	7.5	odd	6
252.2.x.a.41.8	yes	16	7.2	even	3
252.2.x.a.209.1	yes	16	63.2	odd	6
252.2.x.a.209.8	yes	16	63.47	even	6
756.2.x.a.125.3		16	21.2	odd	6
756.2.x.a.125.6		16	21.5	even	6
756.2.x.a.629.3		16	63.61	odd	6
756.2.x.a.629.6		16	63.16	even	3
1008.2.cc.c.209.1		16	252.47	odd	6
1008.2.cc.c.209.8		16	252.191	even	6
1008.2.cc.c.545.1		16	28.23	odd	6
1008.2.cc.c.545.8		16	28.19	even	6
1764.2.w.a.509.3		16	1.1	even	1	trivial
1764.2.w.a.509.6		16	7.6	odd	2	inner
1764.2.w.a.1109.3		16	63.38	even	6	inner
1764.2.w.a.1109.6		16	63.11	odd	6	inner
1764.2.bm.b.1685.3		16	63.20	even	6
1764.2.bm.b.1685.6		16	9.2	odd	6
1764.2.bm.b.1697.3		16	7.4	even	3
1764.2.bm.b.1697.6		16	7.3	odd	6
2268.2.f.b.1133.5		16	63.58	even	3
2268.2.f.b.1133.6		16	63.5	even	6
2268.2.f.b.1133.11		16	63.23	odd	6
2268.2.f.b.1133.12		16	63.40	odd	6
3024.2.cc.c.881.3		16	84.23	even	6
3024.2.cc.c.881.6		16	84.47	odd	6
3024.2.cc.c.2897.3		16	252.187	even	6
3024.2.cc.c.2897.6		16	252.79	odd	6
5292.2.w.a.521.3		16	63.52	odd	6
5292.2.w.a.521.6		16	63.25	even	3
5292.2.w.a.1097.3		16	3.2	odd	2
5292.2.w.a.1097.6		16	21.20	even	2
5292.2.bm.b.2285.3		16	21.17	even	6
5292.2.bm.b.2285.6		16	21.11	odd	6
5292.2.bm.b.4625.3		16	9.7	even	3
5292.2.bm.b.4625.6		16	63.34	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.981784 - 1.42692i) q^{3} +(0.276914 + 0.479629i) q^{5} +(-1.07220 + 2.80185i) q^{9} +O(q^{10})\)	\(q+(-0.981784 - 1.42692i) q^{3} +(0.276914 + 0.479629i) q^{5} +(-1.07220 + 2.80185i) q^{9} +(-4.03478 - 2.32948i) q^{11} +(3.58265 + 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} +(3.62264 + 6.27459i) q^{17} +(-5.81722 - 3.35857i) q^{19} +(4.85295 - 2.80185i) q^{23} +(2.34664 - 4.06450i) q^{25} +(5.05069 - 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} +0.959257i q^{31} +(0.637299 + 8.04435i) q^{33} +(3.53478 - 6.12241i) q^{37} +(-0.565885 - 7.14292i) q^{39} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(-1.64076 + 0.261614i) q^{45} +9.80602 q^{47} +(5.39669 - 11.3295i) q^{51} +(7.30235 - 4.21601i) q^{53} -2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} -7.79910 q^{59} -6.20463i q^{61} +2.29112i q^{65} -3.37628 q^{67} +(-8.76257 - 4.17396i) q^{69} +0.407556i q^{71} +(7.47870 - 4.31783i) q^{73} +(-8.10360 + 0.641993i) q^{75} +0.636352 q^{79} +(-6.70077 - 6.00830i) q^{81} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(-2.10534 - 1.00286i) q^{87} +(3.46568 - 6.00274i) q^{89} +(1.36878 - 0.941783i) q^{93} -3.72014i q^{95} +(7.48798 - 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

Introduction

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