LMFDB - Embedded newform 1764.2.w.a.509.6

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			509.6
Root			$-0.744857 - 1.56371i$ of defining polynomial
Character	$\chi$	$=$	1764.509
Dual form			1764.2.w.a.1109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.981784 + 1.42692i) q^{3} +(-0.276914 - 0.479629i) q^{5} +(-1.07220 + 2.80185i) q^{9} +O(q^{10})$	\(q+(0.981784 + 1.42692i) q^{3} +(-0.276914 - 0.479629i) q^{5} +(-1.07220 + 2.80185i) q^{9} +(-4.03478 - 2.32948i) q^{11} +(-3.58265 - 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} +(-3.62264 - 6.27459i) q^{17} +(5.81722 + 3.35857i) q^{19} +(4.85295 - 2.80185i) q^{23} +(2.34664 - 4.06450i) q^{25} +(-5.05069 + 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} -0.959257i q^{31} +(-0.637299 - 8.04435i) q^{33} +(3.53478 - 6.12241i) q^{37} +(-0.565885 - 7.14292i) q^{39} +(2.39152 - 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(1.64076 - 0.261614i) q^{45} -9.80602 q^{47} +(5.39669 - 11.3295i) q^{51} +(7.30235 - 4.21601i) q^{53} +2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} +7.79910 q^{59} +6.20463i q^{61} +2.29112i q^{65} -3.37628 q^{67} +(8.76257 + 4.17396i) q^{69} +0.407556i q^{71} +(-7.47870 + 4.31783i) q^{73} +(8.10360 - 0.641993i) q^{75} +0.636352 q^{79} +(-6.70077 - 6.00830i) q^{81} +(-2.78840 - 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(2.10534 + 1.00286i) q^{87} +(-3.46568 + 6.00274i) q^{89} +(1.36878 - 0.941783i) q^{93} -3.72014i q^{95} +(-7.48798 + 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.797439	−	0.603399i	$-0.206187\pi$
$5$	−0.276914	−	0.479629i	−0.123840	−	0.214496i	−0.921279	+	0.388903i	$0.872854\pi$
$6$		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	−0.0872856	−	0.996183i	$-0.527819\pi$
$13$	−3.58265	−	2.06844i	−0.993648	−	0.573683i	−0.906363	+	0.422500i	$0.861153\pi$
$14$		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	$-0.825132\pi$
$17$	−3.62264	−	6.27459i	−0.878619	−	1.52181i	−0.0257612	−	0.999668i	$-0.508201\pi$
$18$		0			0
$19$	5.81722	+	3.35857i	1.33456	+	0.770510i	0.985995	−	0.166774i	$-0.0533351\pi$
$19$	5.81722	+	3.35857i	1.33456	+	0.770510i	0.348567	+	0.937284i	$0.386668\pi$
$20$		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	$-0.972546\pi$
$31$		−	0.959257i		−	0.172288i	0.996283	−	0.0861438i	$-0.0274545\pi$
$32$		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	−0.616607	−	0.787271i	$-0.711493\pi$
$41$	2.39152	−	4.14224i	0.373493	−	0.646909i	0.990100	+	0.140362i	$0.0448265\pi$
$42$		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	$-0.753654\pi$
$47$	−9.80602			−1.43035			−0.715177	+	0.698943i	$0.753654\pi$
$48$		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	$-0.330504\pi$
$59$	7.79910			1.01536			0.507678	+	0.861547i	$0.330504\pi$
$60$		0			0
$61$			6.20463i			0.794421i	0.917728	+	0.397211i	$0.130022\pi$
$61$			6.20463i			0.794421i	−0.917728	+	0.397211i	$0.869978\pi$
$62$		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	−0.869111	−	0.494617i	$-0.835308\pi$
$73$	−7.47870	+	4.31783i	−0.875316	+	0.505364i	−0.00620487	+	0.999981i	$0.501975\pi$
$74$		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	0.671432	−	0.741066i	$-0.265680\pi$
$83$	−2.78840	−	4.82965i	−0.306066	−	0.530123i	−0.977498	+	0.210944i	$0.932346\pi$
$84$		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	−0.989152	−	0.146895i	$-0.953072\pi$
$89$	−3.46568	+	6.00274i	−0.367362	+	0.636289i	0.621790	+	0.783184i	$0.286406\pi$
$90$		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	−0.829399	−	0.558656i	$-0.811317\pi$
$97$	−7.48798	+	4.32318i	−0.760289	+	0.438953i	0.0691107	+	0.997609i	$0.477984\pi$
$98$		0			0
$99$	10.8530	−	8.80719i	1.09076	−	0.885156i
$100$		0			0
$101$	−2.34227	+	4.05692i	−0.233064	+	0.403679i	−0.958708	−	0.284391i	$-0.908209\pi$
$101$	−2.34227	+	4.05692i	−0.233064	+	0.403679i	0.725644	+	0.688070i	$0.241542\pi$
$102$		0			0
$103$	−6.40804	+	3.69969i	−0.631403	+	0.364541i	−0.781295	−	0.624162i	$-0.785441\pi$
$103$	−6.40804	+	3.69969i	−0.631403	+	0.364541i	0.149892	+	0.988702i	$0.452107\pi$
$104$		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	$-0.867762\pi$
$131$	−9.23643	−	15.9980i	−0.806990	−	1.39775i	0.107949	−	0.994156i	$-0.465572\pi$
$132$		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	0.816971	−	0.576679i	$-0.195652\pi$
$139$	8.55986	+	4.94204i	0.726038	+	0.419178i	−0.0909332	+	0.995857i	$0.528985\pi$
$140$		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	$-0.977372\pi$
$157$		−	1.78000i		−	0.142059i	0.997474	−	0.0710296i	$-0.0226285\pi$
$158$		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	−0.758715	−	0.651423i	$-0.774173\pi$
$167$	2.38803	−	4.13618i	0.184791	−	0.320067i	0.943506	+	0.331355i	$0.107506\pi$
$168$		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	$-0.569217\pi$
$173$	−5.67531			−0.431486			−0.215743	+	0.976450i	$0.569217\pi$
$174$		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	$0.320528\pi$
$181$			22.7424i			1.69043i	−0.534426	+	0.845215i	$0.679472\pi$
$182$		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	0.0676272	−	0.997711i	$-0.478457\pi$
$199$	13.6198	−	7.86341i	0.965484	−	0.557422i	0.897856	+	0.440288i	$0.145124\pi$
$200$		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	−0.997085	−	0.0763008i	$-0.975689\pi$
$223$	−21.3477	+	12.3251i	−1.42955	+	0.825350i	−0.432464	+	0.901651i	$0.642356\pi$
$224$		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	$-0.601257\pi$
$227$	10.0372	−	17.3849i	0.666190	−	1.15388i	0.978961	−	0.204047i	$-0.0654095\pi$
$228$		0			0
$229$	6.75865	−	3.90211i	0.446624	−	0.257859i	−0.259779	−	0.965668i	$-0.583650\pi$
$229$	6.75865	−	3.90211i	0.446624	−	0.257859i	0.706403	+	0.707809i	$0.250316\pi$
$230$		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	0.524191	−	0.851601i	$-0.324368\pi$
$241$	0.757259	+	0.437203i	0.0487793	+	0.0281628i	−0.475412	+	0.879763i	$0.657701\pi$
$242$		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	$-0.476665\pi$
$251$	2.32082			0.146489			0.0732445	+	0.997314i	$0.476665\pi$
$252$		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	$-0.888236\pi$
$257$	−12.3017	−	21.3072i	−0.767361	−	1.32911i	0.171628	−	0.985162i	$-0.445097\pi$
$258$		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	$-0.950275\pi$
$269$	−10.3106	−	17.8585i	−0.628648	−	1.08885i	0.359176	−	0.933270i	$-0.383058\pi$
$270$		0			0
$271$	12.0771	+	6.97270i	0.733630	+	0.423562i	0.819749	−	0.572723i	$-0.194113\pi$
$271$	12.0771	+	6.97270i	0.733630	+	0.423562i	−0.0861186	+	0.996285i	$0.527446\pi$
$272$		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	$-0.874526\pi$
$283$		−	12.9218i		−	0.768120i	0.923308	−	0.384060i	$-0.125474\pi$
$284$		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	−0.801984	−	0.597346i	$-0.796222\pi$
$293$	1.99115	−	3.44878i	0.116324	−	0.201480i	0.918308	+	0.395866i	$0.129555\pi$
$294$		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	$-0.780247\pi$
$307$		−	22.3162i		−	1.27365i	0.771008	−	0.636825i	$-0.219753\pi$
$308$		0			0
$309$	−11.5705	−	5.51147i	−0.658221	−	0.313537i
$310$		0			0
$311$	−16.3674			−0.928111			−0.464056	−	0.885806i	$-0.653606\pi$
$311$	−16.3674			−0.928111			−0.464056	+	0.885806i	$0.653606\pi$
$312$		0			0
$313$			19.1157i			1.08048i	0.841510	+	0.540242i	$0.181667\pi$
$313$			19.1157i			1.08048i	−0.841510	+	0.540242i	$0.818333\pi$
$314$		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	−0.716239	−	0.697855i	$-0.754138\pi$
$349$	−8.78031	+	5.06931i	−0.469999	+	0.271354i	0.246240	+	0.969209i	$0.420805\pi$
$350$		0			0
$351$	20.6202	+	6.07312i	1.10062	+	0.324159i
$352$		0			0
$353$	7.67564	−	13.2946i	0.408533	−	0.707600i	−0.586192	−	0.810172i	$-0.699374\pi$
$353$	7.67564	−	13.2946i	0.408533	−	0.707600i	0.994726	+	0.102571i	$0.0327070\pi$
$354$		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	0.179219	−	0.983809i	$-0.442643\pi$
$367$	−11.1720	−	6.45018i	−0.583176	−	0.336697i	−0.762394	+	0.647113i	$0.775976\pi$
$368$		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	0.999784	−	0.0207978i	$-0.00662061\pi$
$383$	9.43059	+	16.3343i	0.481880	+	0.834641i	−0.517903	+	0.855439i	$0.673287\pi$
$384$		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	0.999802	−	0.0198756i	$-0.00632700\pi$
$397$	29.5384	+	17.0540i	1.48249	+	0.855917i	0.482688	+	0.875792i	$0.339660\pi$
$398$		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	$0.185219\pi$
$409$			22.2299i			1.09920i	−0.835429	+	0.549599i	$0.814781\pi$
$410$		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	−0.650155	−	0.759802i	$-0.725296\pi$
$419$	6.81490	−	11.8038i	0.332930	−	0.576651i	0.983085	+	0.183150i	$0.0586294\pi$
$420$		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	$0.155786\pi$
$433$			19.5648i			0.940223i	−0.882607	+	0.470112i	$0.844214\pi$
$434$		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	$-0.761278\pi$
$439$		−	28.5628i		−	1.36323i	0.731712	−	0.681614i	$-0.238722\pi$
$440$		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	0.816019	−	0.578025i	$-0.196176\pi$
$461$	−1.98765	−	3.44272i	−0.0925743	−	0.160343i	−0.908594	+	0.417681i	$0.862843\pi$
$462$		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	−0.998626	−	0.0524035i	$-0.983312\pi$
$467$	−9.80952	+	16.9906i	−0.453930	+	0.786230i	0.544696	+	0.838634i	$0.316645\pi$
$468$		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	$0.423905\pi$
$479$	−15.8237	+	27.4074i	−0.723002	+	1.25228i	−0.959791	+	0.280715i	$0.909428\pi$
$480$		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	$-0.292997\pi$
$503$	27.1572			1.21088			0.605440	+	0.795891i	$0.292997\pi$
$504$		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	0.974075	−	0.226225i	$-0.0726384\pi$
$509$	6.56799	+	11.3761i	0.291121	+	0.504236i	−0.682954	+	0.730461i	$0.739305\pi$
$510$		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	0.906804	−	0.421553i	$-0.138515\pi$
$521$	2.01609	+	3.49198i	0.0883266	+	0.152986i	−0.818477	+	0.574539i	$0.805181\pi$
$522$		0			0
$523$	0.516117	+	0.297980i	0.0225682	+	0.0130298i	0.511242	−	0.859437i	$-0.329186\pi$
$523$	0.516117	+	0.297980i	0.0225682	+	0.0130298i	−0.488673	+	0.872467i	$0.662519\pi$
$524$		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	$-0.512593\pi$
$563$	−1.87687			−0.0791007			−0.0395504	+	0.999218i	$0.512593\pi$
$564$		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	−0.211905	−	0.977290i	$-0.567967\pi$
$577$	12.6950	−	7.32947i	0.528501	−	0.305130i	0.740406	+	0.672160i	$0.234633\pi$
$578$		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	$0.202789\pi$
$587$	22.2189	+	38.4843i	0.917074	+	1.58842i	0.113238	+	0.993568i	$0.463878\pi$
$588$		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	$-0.557482\pi$
$593$	18.5593	−	32.1457i	0.762140	−	1.32006i	0.941746	−	0.336326i	$-0.109184\pi$
$594$		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	−0.507682	−	0.861545i	$-0.669497\pi$
$601$	−0.377613	+	0.218015i	−0.0154032	+	0.00889301i	0.492279	+	0.870438i	$0.336164\pi$
$602$		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	−0.460504	−	0.887658i	$-0.652331\pi$
$607$	1.92117	−	1.10919i	0.0779778	−	0.0450205i	0.538482	+	0.842637i	$0.318998\pi$
$608$		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	0.914922	−	0.403630i	$-0.132252\pi$
$619$	25.4477	+	14.6922i	1.02283	+	0.590531i	0.107907	+	0.994161i	$0.465585\pi$
$620$		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	−0.0533976	−	0.998573i	$-0.517005\pi$
$643$	−23.9599	−	13.8333i	−0.944886	−	0.545530i	−0.891489	+	0.453043i	$0.850338\pi$
$644$		0			0
$645$	−1.96696	+	0.155828i	−0.0774488	+	0.00613574i
$646$		0			0
$647$	2.40729	+	4.16954i	0.0946402	+	0.163922i	0.909458	−	0.415795i	$-0.136497\pi$
$647$	2.40729	+	4.16954i	0.0946402	+	0.163922i	−0.814818	+	0.579717i	$0.803163\pi$
$648$		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	$-0.951689\pi$
$661$		−	7.77431i		−	0.302386i	0.988504	−	0.151193i	$-0.0483114\pi$
$662$		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	$-0.259700\pi$
$677$	35.6586			1.37047			0.685235	+	0.728322i	$0.259700\pi$
$678$		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	$-0.945057\pi$
$691$		−	9.02967i		−	0.343505i	0.985140	−	0.171752i	$-0.0549429\pi$
$692$		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	−0.624509	−	0.781018i	$-0.714701\pi$
$719$	9.76375	−	16.9113i	0.364127	−	0.630686i	0.988636	+	0.150332i	$0.0480342\pi$
$720$		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	−0.507866	−	0.861436i	$-0.669566\pi$
$727$	−0.425312	+	0.245554i	−0.0157740	+	0.00910710i	0.492092	+	0.870543i	$0.336232\pi$
$728$		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	−0.371450	−	0.928453i	$-0.621139\pi$
$733$	6.68424	−	3.85915i	0.246888	−	0.142541i	0.618338	+	0.785912i	$0.287806\pi$
$734$		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	0.792436	−	0.609955i	$-0.208813\pi$
$761$	−3.64190	−	6.30795i	−0.132019	−	0.228663i	−0.924455	+	0.381292i	$0.875479\pi$
$762$		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	0.978995	−	0.203886i	$-0.0653570\pi$
$769$	35.8261	+	20.6842i	1.29192	+	0.745892i	0.312927	+	0.949777i	$0.398690\pi$
$770$		0			0
$771$	18.3261	−	38.4727i	0.659997	−	1.38556i
$772$		0			0
$773$	8.55914	+	14.8249i	0.307851	+	0.533213i	0.977892	−	0.209111i	$-0.0670569\pi$
$773$	8.55914	+	14.8249i	0.307851	+	0.533213i	−0.670041	+	0.742324i	$0.733724\pi$
$774$		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	$-0.822271\pi$
$787$		−	29.7250i		−	1.05958i	0.848129	−	0.529790i	$-0.177729\pi$
$788$		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	$0.427034\pi$
$797$	−20.6019	+	35.6836i	−0.729757	+	1.26398i	−0.956986	+	0.290135i	$0.906300\pi$
$798$		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	$-0.804171\pi$
$811$		−	32.8713i		−	1.15427i	0.816650	−	0.577133i	$-0.195829\pi$
$812$		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	−0.282709	−	0.959206i	$-0.591233\pi$
$829$	11.7079	−	6.75957i	0.406633	−	0.234770i	0.689342	+	0.724436i	$0.257900\pi$
$830$		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	0.874714	−	0.484639i	$-0.161049\pi$
$839$	0.511154	+	0.885345i	0.0176470	+	0.0305655i	−0.857067	+	0.515205i	$0.827716\pi$
$840$		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	−0.641596	−	0.767043i	$-0.721727\pi$
$853$	−8.70682	+	5.02689i	−0.298116	+	0.172117i	0.343480	+	0.939160i	$0.388394\pi$
$854$		0			0
$855$	10.4233	+	3.98874i	0.356469	+	0.136412i
$856$		0			0
$857$	14.1272	−	24.4690i	0.482575	−	0.835844i	−0.517225	−	0.855850i	$-0.673035\pi$
$857$	14.1272	−	24.4690i	0.482575	−	0.835844i	0.999800	+	0.0200052i	$0.00636826\pi$
$858$		0			0
$859$	26.9800	−	15.5769i	0.920544	−	0.531476i	0.0367356	−	0.999325i	$-0.488304\pi$
$859$	26.9800	−	15.5769i	0.920544	−	0.531476i	0.883809	+	0.467849i	$0.154971\pi$
$860$		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	$-0.566337\pi$
$881$	−12.2822			−0.413799			−0.206900	+	0.978362i	$0.566337\pi$
$882$		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	0.979872	−	0.199628i	$-0.0639734\pi$
$887$	9.44264	+	16.3551i	0.317053	+	0.549152i	−0.662819	+	0.748780i	$0.730640\pi$
$888$		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	$-0.285196\pi$
$929$	38.0849			1.24952			0.624762	+	0.780815i	$0.285196\pi$
$930$		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	$-0.789319\pi$
$937$		−	37.6261i		−	1.22919i	0.788842	−	0.614596i	$-0.210681\pi$
$938$		0			0
$939$	−27.2766	+	18.7675i	−0.890137	+	0.612454i
$940$		0			0
$941$	−1.67547			−0.0546189			−0.0273094	−	0.999627i	$-0.508694\pi$
$941$	−1.67547			−0.0546189			−0.0273094	+	0.999627i	$0.508694\pi$
$942$		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	$0.361113\pi$
$971$	−17.8733	+	30.9574i	−0.573580	+	0.993470i	−0.996194	+	0.0871606i	$0.972221\pi$
$972$		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	−0.975634	−	0.219404i	$-0.929589\pi$
$983$	−9.33713	+	16.1724i	−0.297808	+	0.515819i	0.677826	+	0.735222i	$0.262922\pi$
$984$		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	−0.434209	−	0.900812i	$-0.642972\pi$
$997$	−45.1982	−	26.0952i	−1.43144	−	0.826442i	−0.997231	+	0.0743700i	$0.976305\pi$
$998$		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.509.6		16
3.2	odd	2		5292.2.w.a.1097.6		16
7.2	even	3		252.2.x.a.41.1	✓	16
7.3	odd	6		1764.2.bm.b.1697.3		16
7.4	even	3		1764.2.bm.b.1697.6		16
7.5	odd	6		252.2.x.a.41.8	yes	16
7.6	odd	2	inner	1764.2.w.a.509.3		16
9.2	odd	6		1764.2.bm.b.1685.3		16
9.7	even	3		5292.2.bm.b.4625.6		16
21.2	odd	6		756.2.x.a.125.6		16
21.5	even	6		756.2.x.a.125.3		16
21.11	odd	6		5292.2.bm.b.2285.3		16
21.17	even	6		5292.2.bm.b.2285.6		16
21.20	even	2		5292.2.w.a.1097.3		16
28.19	even	6		1008.2.cc.c.545.1		16
28.23	odd	6		1008.2.cc.c.545.8		16
63.2	odd	6		252.2.x.a.209.8	yes	16
63.5	even	6		2268.2.f.b.1133.11		16
63.11	odd	6	inner	1764.2.w.a.1109.3		16
63.16	even	3		756.2.x.a.629.3		16
63.20	even	6		1764.2.bm.b.1685.6		16
63.23	odd	6		2268.2.f.b.1133.6		16
63.25	even	3		5292.2.w.a.521.3		16
63.34	odd	6		5292.2.bm.b.4625.3		16
63.38	even	6	inner	1764.2.w.a.1109.6		16
63.40	odd	6		2268.2.f.b.1133.5		16
63.47	even	6		252.2.x.a.209.1	yes	16
63.52	odd	6		5292.2.w.a.521.6		16
63.58	even	3		2268.2.f.b.1133.12		16
63.61	odd	6		756.2.x.a.629.6		16
84.23	even	6		3024.2.cc.c.881.6		16
84.47	odd	6		3024.2.cc.c.881.3		16
252.47	odd	6		1008.2.cc.c.209.8		16
252.79	odd	6		3024.2.cc.c.2897.3		16
252.187	even	6		3024.2.cc.c.2897.6		16
252.191	even	6		1008.2.cc.c.209.1		16

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

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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