LMFDB - Embedded newform 294.2.j.a.251.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(41,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("294.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, degree $6$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.18
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(1.24168 - 1.20757i) q^{3} +(0.222521 + 0.974928i) q^{4} +(0.210425 + 0.101335i) q^{5} +(1.72369 - 0.169937i) q^{6} +(0.981077 - 2.45713i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.0835604 - 2.99884i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(1.24168 - 1.20757i) q^{3} +(0.222521 + 0.974928i) q^{4} +(0.210425 + 0.101335i) q^{5} +(1.72369 - 0.169937i) q^{6} +(0.981077 - 2.45713i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.0835604 - 2.99884i) q^{9} +(0.101335 + 0.210425i) q^{10} +(0.581717 + 0.463904i) q^{11} +(1.45359 + 0.941844i) q^{12} +(-0.948322 - 0.756262i) q^{13} +(2.29903 - 1.30937i) q^{14} +(0.383650 - 0.128276i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.52085 + 6.66329i) q^{17} +(1.93507 - 2.29249i) q^{18} +4.63573i q^{19} +(-0.0519706 + 0.227698i) q^{20} +(-1.74896 - 4.23570i) q^{21} +(0.165565 + 0.725390i) q^{22} +(1.86385 - 0.425411i) q^{23} +(0.549234 + 1.64266i) q^{24} +(-3.08344 - 3.86651i) q^{25} +(-0.269907 - 1.18254i) q^{26} +(-3.51754 - 3.82451i) q^{27} +(2.61383 + 0.409716i) q^{28} +(2.44707 + 0.558528i) q^{29} +(0.379928 + 0.138912i) q^{30} +2.55159i q^{31} +(-0.974928 - 0.222521i) q^{32} +(1.28251 - 0.126441i) q^{33} +(-5.34354 + 4.26133i) q^{34} +(0.455437 - 0.417623i) q^{35} +(2.94224 - 0.585838i) q^{36} +(0.0943376 - 0.413320i) q^{37} +(-2.89033 + 3.62436i) q^{38} +(-2.09075 + 0.206125i) q^{39} +(-0.182600 + 0.145618i) q^{40} +(-5.27160 - 2.53867i) q^{41} +(1.27352 - 4.40206i) q^{42} +(1.04498 - 0.503234i) q^{43} +(-0.322829 + 0.670361i) q^{44} +(0.321471 - 0.622561i) q^{45} +(1.72245 + 0.829491i) q^{46} +(-3.40572 + 4.27064i) q^{47} +(-0.594775 + 1.62673i) q^{48} +(-5.07498 - 4.82127i) q^{49} -4.94545i q^{50} +(6.15795 + 10.1102i) q^{51} +(0.526279 - 1.09283i) q^{52} +(-11.3114 + 2.58176i) q^{53} +(-0.365580 - 5.18328i) q^{54} +(0.0753979 + 0.156565i) q^{55} +(1.78812 + 1.95003i) q^{56} +(5.59796 + 5.75612i) q^{57} +(1.56496 + 1.96240i) q^{58} +(-9.60560 + 4.62582i) q^{59} +(0.210430 + 0.345487i) q^{60} +(10.0456 + 2.29284i) q^{61} +(-1.59089 + 1.99491i) q^{62} +(-7.28655 - 3.14741i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-0.122914 - 0.255235i) q^{65} +(1.08154 + 0.700774i) q^{66} +5.04647 q^{67} -6.83465 q^{68} +(1.80060 - 2.77895i) q^{69} +(0.616458 - 0.0425509i) q^{70} +(9.18658 - 2.09678i) q^{71} +(2.66560 + 1.37643i) q^{72} +(3.56590 - 2.84371i) q^{73} +(0.331457 - 0.264328i) q^{74} +(-8.49773 - 1.07752i) q^{75} +(-4.51951 + 1.03155i) q^{76} +(1.71058 - 0.974230i) q^{77} +(-1.76313 - 1.14241i) q^{78} +4.07803 q^{79} -0.233554 q^{80} +(-8.98604 - 0.501168i) q^{81} +(-2.53867 - 5.27160i) q^{82} +(-5.46146 - 6.84845i) q^{83} +(3.74032 - 2.64764i) q^{84} +(-0.995250 + 1.24800i) q^{85} +(1.13076 + 0.258088i) q^{86} +(3.71295 - 2.26149i) q^{87} +(-0.670361 + 0.322829i) q^{88} +(-8.77266 - 11.0006i) q^{89} +(0.639497 - 0.286304i) q^{90} +(-2.78861 + 1.58820i) q^{91} +(0.829491 + 1.72245i) q^{92} +(3.08121 + 3.16826i) q^{93} +(-5.32540 + 1.21549i) q^{94} +(-0.469763 + 0.975473i) q^{95} +(-1.47926 + 0.900991i) q^{96} -3.82421i q^{97} +(-0.961765 - 6.93361i) q^{98} +(1.43978 - 1.70571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	1.24168	−	1.20757i	0.716887	−	0.697190i
$3$	1.24168	−	1.20757i	0.716887	−	0.697190i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	0.210425	+	0.101335i	0.0941048	+	0.0453185i	0.480344	−	0.877080i	$-0.340512\pi$
$5$	0.210425	+	0.101335i	0.0941048	+	0.0453185i	−0.386239	+	0.922399i	$0.626226\pi$
$6$	1.72369	−	0.169937i	0.703695	−	0.0693764i
$7$	0.981077	−	2.45713i	0.370812	−	0.928708i
$7$	0.981077	−	2.45713i	0.370812	−	0.928708i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	0.0835604	−	2.99884i	0.0278535	−	0.999612i
$10$	0.101335	+	0.210425i	0.0320450	+	0.0665421i
$11$	0.581717	+	0.463904i	0.175394	+	0.139872i	0.707252	−	0.706961i	$-0.249935\pi$
$11$	0.581717	+	0.463904i	0.175394	+	0.139872i	−0.531858	+	0.846834i	$0.678506\pi$
$12$	1.45359	+	0.941844i	0.419616	+	0.271887i
$13$	−0.948322	−	0.756262i	−0.263017	−	0.209749i	0.483098	−	0.875566i	$-0.339512\pi$
$13$	−0.948322	−	0.756262i	−0.263017	−	0.209749i	−0.746115	+	0.665817i	$0.768083\pi$
$14$	2.29903	−	1.30937i	0.614442	−	0.349944i
$15$	0.383650	−	0.128276i	0.0990580	−	0.0331207i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−1.52085	+	6.66329i	−0.368861	+	1.61608i	0.361053	+	0.932545i	$0.382417\pi$
$17$	−1.52085	+	6.66329i	−0.368861	+	1.61608i	−0.729914	+	0.683539i	$0.760440\pi$
$18$	1.93507	−	2.29249i	0.456101	−	0.540344i
$19$			4.63573i			1.06351i	0.846898	+	0.531755i	$0.178467\pi$
$19$			4.63573i			1.06351i	−0.846898	+	0.531755i	$0.821533\pi$
$20$	−0.0519706	+	0.227698i	−0.0116210	+	0.0509148i
$21$	−1.74896	−	4.23570i	−0.381655	−	0.924305i
$22$	0.165565	+	0.725390i	0.0352987	+	0.154654i
$23$	1.86385	−	0.425411i	0.388639	−	0.0887044i	−0.0237364	−	0.999718i	$-0.507556\pi$
$23$	1.86385	−	0.425411i	0.388639	−	0.0887044i	0.412376	+	0.911014i	$0.364699\pi$
$24$	0.549234	+	1.64266i	0.112112	+	0.335307i
$25$	−3.08344	−	3.86651i	−0.616688	−	0.773302i
$26$	−0.269907	−	1.18254i	−0.0529331	−	0.231915i
$27$	−3.51754	−	3.82451i	−0.676951	−	0.736028i
$28$	2.61383	+	0.409716i	0.493968	+	0.0774291i
$29$	2.44707	+	0.558528i	0.454410	+	0.103716i	0.443599	−	0.896225i	$-0.353702\pi$
$29$	2.44707	+	0.558528i	0.454410	+	0.103716i	0.0108111	+	0.999942i	$0.496559\pi$
$30$	0.379928	+	0.138912i	0.0693651	+	0.0253617i
$31$			2.55159i			0.458278i	0.973394	+	0.229139i	$0.0735911\pi$
$31$			2.55159i			0.458278i	−0.973394	+	0.229139i	$0.926409\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	1.28251	−	0.126441i	0.223256	−	0.0220105i
$34$	−5.34354	+	4.26133i	−0.916410	+	0.730812i
$35$	0.455437	−	0.417623i	0.0769828	−	0.0705912i
$36$	2.94224	−	0.585838i	0.490374	−	0.0976397i
$37$	0.0943376	−	0.413320i	0.0155090	−	0.0679494i	−0.966581	−	0.256360i	$-0.917477\pi$
$37$	0.0943376	−	0.413320i	0.0155090	−	0.0679494i	0.982090	+	0.188411i	$0.0603337\pi$
$38$	−2.89033	+	3.62436i	−0.468874	+	0.587949i
$39$	−2.09075	+	0.206125i	−0.334789	+	0.0330064i
$40$	−0.182600	+	0.145618i	−0.0288715	+	0.0230243i
$41$	−5.27160	−	2.53867i	−0.823286	−	0.396474i	−0.0256933	−	0.999670i	$-0.508179\pi$
$41$	−5.27160	−	2.53867i	−0.823286	−	0.396474i	−0.797593	+	0.603196i	$0.793894\pi$
$42$	1.27352	−	4.40206i	0.196508	−	0.679253i
$43$	1.04498	−	0.503234i	0.159357	−	0.0767424i	−0.352505	−	0.935810i	$-0.614670\pi$
$43$	1.04498	−	0.503234i	0.159357	−	0.0767424i	0.511862	+	0.859067i	$0.328956\pi$
$44$	−0.322829	+	0.670361i	−0.0486683	+	0.101061i
$45$	0.321471	−	0.622561i	0.0479220	−	0.0928060i
$46$	1.72245	+	0.829491i	0.253962	+	0.122302i
$47$	−3.40572	+	4.27064i	−0.496775	+	0.622937i	−0.965499	−	0.260409i	$-0.916143\pi$
$47$	−3.40572	+	4.27064i	−0.496775	+	0.622937i	0.468723	+	0.883345i	$0.344714\pi$
$48$	−0.594775	+	1.62673i	−0.0858484	+	0.234798i
$49$	−5.07498	−	4.82127i	−0.724997	−	0.688752i
$50$		−	4.94545i		−	0.699393i
$51$	6.15795	+	10.1102i	0.862286	+	1.41572i
$52$	0.526279	−	1.09283i	0.0729818	−	0.151548i
$53$	−11.3114	+	2.58176i	−1.55374	+	0.354632i	−0.911314	−	0.411712i	$-0.864931\pi$
$53$	−11.3114	+	2.58176i	−1.55374	+	0.354632i	−0.642431	+	0.766344i	$0.722074\pi$
$54$	−0.365580	−	5.18328i	−0.0497492	−	0.705355i
$55$	0.0753979	+	0.156565i	0.0101666	+	0.0211113i
$56$	1.78812	+	1.95003i	0.238948	+	0.260584i
$57$	5.59796	+	5.75612i	0.741468	+	0.762417i
$58$	1.56496	+	1.96240i	0.205489	+	0.257676i
$59$	−9.60560	+	4.62582i	−1.25054	+	0.602230i	−0.937657	−	0.347561i	$-0.887010\pi$
$59$	−9.60560	+	4.62582i	−1.25054	+	0.602230i	−0.312886	+	0.949791i	$0.601296\pi$
$60$	0.210430	+	0.345487i	0.0271664	+	0.0446022i
$61$	10.0456	+	2.29284i	1.28621	+	0.293568i	0.810345	−	0.585953i	$-0.199280\pi$
$61$	10.0456	+	2.29284i	1.28621	+	0.293568i	0.475861	+	0.879521i	$0.342137\pi$
$62$	−1.59089	+	1.99491i	−0.202043	+	0.253354i
$63$	−7.28655	−	3.14741i	−0.918019	−	0.396536i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−0.122914	−	0.255235i	−0.0152457	−	0.0316579i
$66$	1.08154	+	0.700774i	0.133128	+	0.0862593i
$67$	5.04647			0.616524			0.308262	−	0.951301i	$-0.400253\pi$
$67$	5.04647			0.616524			0.308262	+	0.951301i	$0.400253\pi$
$68$	−6.83465			−0.828823
$69$	1.80060	−	2.77895i	0.216767	−	0.334546i
$70$	0.616458	−	0.0425509i	0.0736809	−	0.00508581i
$71$	9.18658	−	2.09678i	1.09025	−	0.248842i	0.360637	−	0.932706i	$-0.382559\pi$
$71$	9.18658	−	2.09678i	1.09025	−	0.248842i	0.729609	+	0.683864i	$0.239702\pi$
$72$	2.66560	+	1.37643i	0.314144	+	0.162214i
$73$	3.56590	−	2.84371i	0.417357	−	0.332831i	−0.392192	−	0.919883i	$-0.628283\pi$
$73$	3.56590	−	2.84371i	0.417357	−	0.332831i	0.809549	+	0.587052i	$0.199712\pi$
$74$	0.331457	−	0.264328i	0.0385311	−	0.0307275i
$75$	−8.49773	−	1.07752i	−0.981234	−	0.124422i
$76$	−4.51951	+	1.03155i	−0.518423	+	0.118327i
$77$	1.71058	−	0.974230i	0.194939	−	0.111024i
$78$	−1.76313	−	1.14241i	−0.199636	−	0.129352i
$79$	4.07803			0.458814			0.229407	−	0.973331i	$-0.426321\pi$
$79$	4.07803			0.458814			0.229407	+	0.973331i	$0.426321\pi$
$80$	−0.233554			−0.0261121
$81$	−8.98604	−	0.501168i	−0.998448	−	0.0556853i
$82$	−2.53867	−	5.27160i	−0.280349	−	0.582151i
$83$	−5.46146	−	6.84845i	−0.599473	−	0.751715i	0.385823	−	0.922573i	$-0.373918\pi$
$83$	−5.46146	−	6.84845i	−0.599473	−	0.751715i	−0.985296	+	0.170858i	$0.945346\pi$
$84$	3.74032	−	2.64764i	0.408102	−	0.288882i
$85$	−0.995250	+	1.24800i	−0.107950	+	0.135365i
$86$	1.13076	+	0.258088i	0.121933	+	0.0278303i
$87$	3.71295	−	2.26149i	0.398070	−	0.242457i
$88$	−0.670361	+	0.322829i	−0.0714607	+	0.0344137i
$89$	−8.77266	−	11.0006i	−0.929900	−	1.16606i	−0.985851	−	0.167624i	$-0.946390\pi$
$89$	−8.77266	−	11.0006i	−0.929900	−	1.16606i	0.0559507	−	0.998434i	$-0.482181\pi$
$90$	0.639497	−	0.286304i	0.0674089	−	0.0301791i
$91$	−2.78861	+	1.58820i	−0.292326	+	0.166489i
$92$	0.829491	+	1.72245i	0.0864804	+	0.179578i
$93$	3.08121	+	3.16826i	0.319507	+	0.328534i
$94$	−5.32540	+	1.21549i	−0.549273	+	0.125368i
$95$	−0.469763	+	0.975473i	−0.0481967	+	0.100081i
$96$	−1.47926	+	0.900991i	−0.150977	+	0.0919570i
$97$		−	3.82421i		−	0.388289i	−0.980973	−	0.194145i	$-0.937807\pi$
$97$		−	3.82421i		−	0.388289i	0.980973	−	0.194145i	$-0.0621931\pi$
$98$	−0.961765	−	6.93361i	−0.0971529	−	0.700401i
$99$	1.43978	−	1.70571i	0.144703	−	0.171430i
$100$	3.08344	−	3.86651i	0.308344	−	0.386651i
$101$	6.55700	+	3.15769i	0.652446	+	0.314201i	0.730666	−	0.682735i	$-0.239209\pi$
$101$	6.55700	+	3.15769i	0.652446	+	0.314201i	−0.0782203	+	0.996936i	$0.524924\pi$
$102$	−1.48914	+	11.7439i	−0.147447	+	1.16282i
$103$	−7.53504	+	15.6467i	−0.742450	+	1.54171i	0.0951712	+	0.995461i	$0.469660\pi$
$103$	−7.53504	+	15.6467i	−0.742450	+	1.54171i	−0.837621	+	0.546252i	$0.816054\pi$
$104$	1.09283	−	0.526279i	0.107161	−	0.0516059i
$105$	0.0612002	−	1.06853i	0.00597252	−	0.104278i
$106$	−10.4533	−	5.03406i	−1.01532	−	0.488951i
$107$	−8.40368	+	6.70171i	−0.812414	+	0.647879i	−0.938939	−	0.344085i	$-0.888189\pi$
$107$	−8.40368	+	6.70171i	−0.812414	+	0.647879i	0.126525	+	0.991963i	$0.459618\pi$
$108$	2.94590	−	4.28038i	0.283469	−	0.411880i
$109$	9.84939	−	12.3507i	0.943400	−	1.18299i	−0.0395692	−	0.999217i	$-0.512599\pi$
$109$	9.84939	−	12.3507i	0.943400	−	1.18299i	0.982969	−	0.183770i	$-0.0588300\pi$
$110$	−0.0386684	+	0.169418i	−0.00368689	+	0.0161533i
$111$	−0.381974	−	0.627132i	−0.0362554	−	0.0595247i
$112$	0.182189	+	2.63947i	0.0172152	+	0.249407i
$113$	14.9443	−	11.9177i	1.40584	−	1.12112i	0.429955	−	0.902850i	$-0.358529\pi$
$113$	14.9443	−	11.9177i	1.40584	−	1.12112i	0.975888	−	0.218272i	$-0.0700420\pi$
$114$	0.787782	+	7.99059i	0.0737826	+	0.748387i
$115$	0.435309	+	0.0993564i	0.0405928	+	0.00926503i
$116$			2.51000i			0.233048i
$117$	−2.34715	+	2.78067i	−0.216994	+	0.257073i
$118$	−10.3941	−	2.37239i	−0.956856	−	0.218396i
$119$	14.8805	+	10.2741i	1.36409	+	0.941828i
$120$	−0.0508871	+	0.401314i	−0.00464534	+	0.0366347i
$121$	−2.32454	−	10.1845i	−0.211322	−	0.925862i
$122$	6.42440	+	8.05594i	0.581637	+	0.729350i
$123$	−9.61128	+	3.21359i	−0.866620	+	0.289760i
$124$	−2.48761	+	0.567781i	−0.223394	+	0.0509883i
$125$	−0.516871	−	2.26456i	−0.0462304	−	0.202548i
$126$	−3.73448	−	7.00383i	−0.332694	−	0.623951i
$127$	0.399422	−	1.74998i	0.0354429	−	0.155286i	−0.954110	−	0.299457i	$-0.903194\pi$
$127$	0.399422	−	1.74998i	0.0354429	−	0.155286i	0.989553	+	0.144171i	$0.0460516\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.689841	−	1.88674i	0.0607371	−	0.166118i
$130$	0.0630377	−	0.276186i	0.00552877	−	0.0242231i
$131$	13.9518	−	6.71883i	1.21897	−	0.587027i	0.289949	−	0.957042i	$-0.406362\pi$
$131$	13.9518	−	6.71883i	1.21897	−	0.587027i	0.929026	+	0.370015i	$0.120647\pi$
$132$	0.408655	+	1.22221i	0.0355688	+	0.106380i
$133$	11.3906	+	4.54801i	0.987690	+	0.394363i
$134$	3.94549	+	3.14642i	0.340838	+	0.271809i
$135$	−0.352620	−	1.16122i	−0.0303487	−	0.0999421i
$136$	−5.34354	−	4.26133i	−0.458205	−	0.365406i
$137$	8.13144	+	16.8851i	0.694716	+	1.44259i	0.887244	+	0.461301i	$0.152617\pi$
$137$	8.13144	+	16.8851i	0.694716	+	1.44259i	−0.192528	+	0.981291i	$0.561669\pi$
$138$	3.14041	−	1.05002i	0.267330	−	0.0893833i
$139$	4.96817	−	10.3165i	0.421395	−	0.875035i	−0.576909	−	0.816809i	$-0.695741\pi$
$139$	4.96817	−	10.3165i	0.421395	−	0.875035i	0.998303	−	0.0582264i	$-0.0185445\pi$
$140$	0.508497	+	0.351088i	0.0429758	+	0.0296723i
$141$	0.928255	+	9.41542i	0.0781732	+	0.792922i
$142$	8.48968	+	4.08841i	0.712438	+	0.343092i
$143$	−0.200823	−	0.879861i	−0.0167936	−	0.0735777i
$144$	1.22586	+	2.73811i	0.102155	+	0.228176i
$145$	0.458326	+	0.365503i	0.0380619	+	0.0303533i
$146$	4.56096			0.377467
$147$	−12.1235	+	0.141885i	−0.999932	+	0.0117024i
$148$	0.423949			0.0348484
$149$	7.58273	+	6.04703i	0.621202	+	0.495392i	0.882778	−	0.469791i	$-0.155671\pi$
$149$	7.58273	+	6.04703i	0.621202	+	0.495392i	−0.261576	+	0.965183i	$0.584242\pi$
$150$	−5.97197	−	6.14069i	−0.487609	−	0.501385i
$151$	5.04408	+	22.0996i	0.410481	+	1.79844i	0.581925	+	0.813243i	$0.302300\pi$
$151$	5.04408	+	22.0996i	0.410481	+	1.79844i	−0.171443	+	0.985194i	$0.554843\pi$
$152$	−4.17665	−	2.01137i	−0.338771	−	0.163144i
$153$	19.8550	+	5.11757i	1.60518	+	0.413731i
$154$	1.94481	+	0.304847i	0.156717	+	0.0245653i
$155$	−0.258565	+	0.536917i	−0.0207685	+	0.0431262i
$156$	−0.666193	−	1.99247i	−0.0533382	−	0.159525i
$157$	7.14332	+	14.8333i	0.570099	+	1.18382i	0.964303	+	0.264800i	$0.0853061\pi$
$157$	7.14332	+	14.8333i	0.570099	+	1.18382i	−0.394204	+	0.919023i	$0.628980\pi$
$158$	3.18833	+	2.54261i	0.253650	+	0.202279i
$159$	−10.9276	+	16.8651i	−0.866613	+	1.33749i
$160$	−0.182600	−	0.145618i	−0.0144358	−	0.0115121i
$161$	0.783288	−	4.99708i	0.0617317	−	0.393825i
$162$	−6.71309	−	5.99453i	−0.527430	−	0.470975i
$163$	0.507536	−	0.244417i	0.0397533	−	0.0191442i	−0.413901	−	0.910322i	$-0.635834\pi$
$163$	0.507536	−	0.244417i	0.0397533	−	0.0191442i	0.453655	+	0.891177i	$0.350120\pi$
$164$	1.30198	−	5.70434i	0.101667	−	0.445434i
$165$	0.282684	+	0.103357i	0.0220069	+	0.00804631i
$166$		−	8.75950i		−	0.679869i
$167$	0.192729	−	0.844402i	0.0149138	−	0.0653418i	−0.966923	−	0.255067i	$-0.917903\pi$
$167$	0.192729	−	0.844402i	0.0149138	−	0.0653418i	0.981837	+	0.189725i	$0.0607597\pi$
$168$	4.57508	+	0.262039i	0.352975	+	0.0202167i
$169$	−2.56539	−	11.2397i	−0.197338	−	0.864593i
$170$	−1.55624	+	0.355201i	−0.119358	+	0.0272426i
$171$	13.9018	+	0.387364i	1.06310	+	0.0296224i
$172$	0.723146	+	0.906796i	0.0551393	+	0.0691425i
$173$	−4.57529	−	20.0457i	−0.347853	−	1.52404i	−0.782044	−	0.623223i	$-0.785823\pi$
$173$	−4.57529	−	20.0457i	−0.347853	−	1.52404i	0.434192	−	0.900821i	$-0.357034\pi$
$174$	4.31292	+	0.546884i	0.326961	+	0.0414592i
$175$	−12.5256	+	3.78307i	−0.946847	+	0.285973i
$176$	−0.725390	−	0.165565i	−0.0546783	−	0.0124800i
$177$	−6.34114	+	17.3432i	−0.476630	+	1.30360i
$178$		−	14.0703i		−	1.05461i
$179$	6.11415	+	1.39552i	0.456993	+	0.104306i	0.444820	−	0.895620i	$-0.353268\pi$
$179$	6.11415	+	1.39552i	0.456993	+	0.104306i	0.0121737	+	0.999926i	$0.496125\pi$
$180$	0.678487	+	0.174878i	0.0505714	+	0.0130346i
$181$	12.6136	−	10.0590i	0.937562	−	0.747681i	−0.0302007	−	0.999544i	$-0.509615\pi$
$181$	12.6136	−	10.0590i	0.937562	−	0.747681i	0.967763	+	0.251863i	$0.0810432\pi$
$182$	−3.17045	−	0.496965i	−0.235009	−	0.0368375i
$183$	15.2422	−	9.28375i	1.12674	−	0.686274i
$184$	−0.425411	+	1.86385i	−0.0313617	+	0.137405i
$185$	0.0617348	−	0.0774130i	0.00453883	−	0.00569152i
$186$	0.433609	+	4.39815i	0.0317937	+	0.322488i
$187$	−3.97583	+	3.17062i	−0.290742	+	0.231859i
$188$	−4.92141	−	2.37003i	−0.358931	−	0.172852i
$189$	−12.8483	+	4.89092i	−0.934577	+	0.355762i
$190$	−0.975473	+	0.469763i	−0.0707682	+	0.0340802i
$191$	3.52784	−	7.32563i	0.255265	−	0.530064i	−0.733473	−	0.679719i	$-0.762102\pi$
$191$	3.52784	−	7.32563i	0.255265	−	0.530064i	0.988738	+	0.149655i	$0.0478162\pi$
$192$	−1.71829	−	0.217882i	−0.124007	−	0.0157243i
$193$	−17.3479	−	8.35429i	−1.24873	−	0.601355i	−0.311556	−	0.950228i	$-0.600850\pi$
$193$	−17.3479	−	8.35429i	−1.24873	−	0.601355i	−0.937170	+	0.348873i	$0.886565\pi$
$194$	2.38435	−	2.98989i	0.171187	−	0.214661i
$195$	−0.460834	−	0.168493i	−0.0330010	−	0.0120660i
$196$	3.57110	−	6.02057i	0.255079	−	0.430041i
$197$		−	10.5099i		−	0.748796i	−0.927268	−	0.374398i	$-0.877849\pi$
$197$		−	10.5099i		−	0.748796i	0.927268	−	0.374398i	$-0.122151\pi$
$198$	2.18916	−	0.435890i	0.155577	−	0.0309774i
$199$	−10.7159	+	22.2518i	−0.759631	+	1.57739i	0.0557352	+	0.998446i	$0.482250\pi$
$199$	−10.7159	+	22.2518i	−0.759631	+	1.57739i	−0.815367	+	0.578945i	$0.803465\pi$
$200$	4.82146	−	1.10047i	0.340929	−	0.0778147i
$201$	6.26612	−	6.09395i	0.441978	−	0.429834i
$202$	3.15769	+	6.55700i	0.222174	+	0.461349i
$203$	3.77314	−	5.46481i	0.264823	−	0.383555i
$204$	−8.48647	+	8.25330i	−0.594172	+	0.577846i
$205$	−0.852019	−	1.06840i	−0.0595076	−	0.0746201i
$206$	−15.6467	+	7.53504i	−1.09016	+	0.524991i
$207$	−1.11999	−	5.62492i	−0.0778450	−	0.390959i
$208$	1.18254	+	0.269907i	0.0819943	+	0.0187147i
$209$	−2.15054	+	2.69669i	−0.148756	+	0.186534i
$210$	0.714064	−	0.797250i	0.0492751	−	0.0550155i
$211$	0.631462	+	0.791829i	0.0434717	+	0.0545117i	0.803092	−	0.595855i	$-0.203187\pi$
$211$	0.631462	+	0.791829i	0.0434717	+	0.0545117i	−0.759620	+	0.650367i	$0.774615\pi$
$212$	−5.03406	−	10.4533i	−0.345741	−	0.717938i
$213$	8.87483	−	13.6970i	0.608094	−	0.938500i
$214$	−10.7487			−0.734766
$215$	0.270884			0.0184741
$216$	4.97197	−	1.50980i	0.338300	−	0.102729i
$217$	6.26958	+	2.50330i	0.425607	+	0.169935i
$218$	15.4011	−	3.51521i	1.04310	−	0.238080i
$219$	0.993749	−	7.83705i	0.0671514	−	0.529579i
$220$	−0.135862	+	0.108347i	−0.00915984	+	0.00730472i
$221$	6.48145	−	5.16878i	0.435989	−	0.347690i
$222$	0.0923708	−	0.728468i	0.00619952	−	0.0488916i
$223$	4.03725	−	0.921477i	0.270355	−	0.0617067i	−0.0851943	−	0.996364i	$-0.527151\pi$
$223$	4.03725	−	0.921477i	0.270355	−	0.0617067i	0.355549	+	0.934658i	$0.384294\pi$
$224$	−1.50324	+	2.17721i	−0.100440	+	0.145471i
$225$	−11.8527	+	8.92364i	−0.790179	+	0.594909i
$226$	19.1145			1.27148
$227$	11.2914			0.749438			0.374719	−	0.927138i	$-0.377739\pi$
$227$	11.2914			0.749438			0.374719	+	0.927138i	$0.377739\pi$
$228$	−4.36614	+	6.73847i	−0.289154	+	0.446266i
$229$	−0.978738	−	2.03237i	−0.0646768	−	0.134303i	0.866124	−	0.499828i	$-0.166604\pi$
$229$	−0.978738	−	2.03237i	−0.0646768	−	0.134303i	−0.930801	+	0.365526i	$0.880889\pi$
$230$	0.278390	+	0.349091i	0.0183565	+	0.0230184i
$231$	0.947555	−	3.27533i	0.0623446	−	0.215501i
$232$	−1.56496	+	1.96240i	−0.102745	+	0.128838i
$233$	−24.3358	−	5.55449i	−1.59429	−	0.363887i	−0.669036	−	0.743230i	$-0.733293\pi$
$233$	−24.3358	−	5.55449i	−1.59429	−	0.363887i	−0.925256	+	0.379343i	$0.876150\pi$
$234$	−3.56879	+	0.710593i	−0.233299	+	0.0464529i
$235$	−1.14941	+	0.553528i	−0.0749795	+	0.0361082i
$236$	−6.64728	−	8.33543i	−0.432701	−	0.542590i
$237$	5.06362	−	4.92450i	0.328918	−	0.319880i
$238$	5.22822	+	17.3105i	0.338895	+	1.12207i
$239$	−1.70262	−	3.53554i	−0.110134	−	0.228695i	0.838616	−	0.544722i	$-0.183365\pi$
$239$	−1.70262	−	3.53554i	−0.110134	−	0.228695i	−0.948750	+	0.316028i	$0.897651\pi$
$240$	−0.290000	+	0.282032i	−0.0187194	+	0.0182051i
$241$	−7.08227	+	1.61648i	−0.456209	+	0.104127i	−0.444449	−	0.895804i	$-0.646601\pi$
$241$	−7.08227	+	1.61648i	−0.456209	+	0.104127i	−0.0117599	+	0.999931i	$0.503743\pi$
$242$	4.53252	−	9.41188i	0.291362	−	0.605019i
$243$	−11.7630	+	10.2290i	−0.754598	+	0.656188i
$244$			10.3039i			0.659642i
$245$	−0.579336	−	1.52879i	−0.0370124	−	0.0976706i
$246$	−9.51805	−	3.48005i	−0.606848	−	0.221880i
$247$	3.50583	−	4.39617i	0.223070	−	0.279722i
$248$	−2.29890	−	1.10709i	−0.145980	−	0.0703004i
$249$	−15.0514	−	1.90853i	−0.953842	−	0.120948i
$250$	1.00782	−	2.09277i	0.0637404	−	0.132358i
$251$	−13.7471	+	6.62024i	−0.867707	+	0.417866i	−0.814119	−	0.580697i	$-0.802780\pi$
$251$	−13.7471	+	6.62024i	−0.867707	+	0.417866i	−0.0535876	+	0.998563i	$0.517066\pi$
$252$	1.44709	−	7.80423i	0.0911578	−	0.491620i
$253$	1.28158	+	0.617178i	0.0805725	+	0.0388016i
$254$	1.40338	−	1.11915i	0.0880556	−	0.0702220i
$255$	0.271263	+	2.75146i	0.0169871	+	0.172303i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−4.56517	+	20.0013i	−0.284767	+	1.24765i	0.606835	+	0.794828i	$0.292439\pi$
$257$	−4.56517	+	20.0013i	−0.284767	+	1.24765i	−0.891602	+	0.452820i	$0.850418\pi$
$258$	1.71570	−	1.04500i	0.106815	−	0.0650589i
$259$	−0.923028	−	0.637298i	−0.0573542	−	0.0395998i
$260$	0.221484	−	0.176628i	0.0137359	−	0.0109540i
$261$	1.87941	−	7.29170i	0.116333	−	0.451345i
$262$	15.0971	+	3.44581i	0.932701	+	0.212883i
$263$		−	20.3888i		−	1.25723i	−0.777719	−	0.628613i	$-0.783623\pi$
$263$		−	20.3888i		−	1.25723i	0.777719	−	0.628613i	$-0.216377\pi$
$264$	−0.442539	+	1.21036i	−0.0272364	+	0.0744924i
$265$	−2.64183	−	0.602980i	−0.162286	−	0.0370408i
$266$	6.06989	+	10.6577i	0.372169	+	0.653466i
$267$	−24.1768	−	3.06565i	−1.47960	−	0.187615i
$268$	1.12294	+	4.91994i	0.0685948	+	0.300533i
$269$	−4.48759	−	5.62726i	−0.273613	−	0.343100i	0.625972	−	0.779846i	$-0.284702\pi$
$269$	−4.48759	−	5.62726i	−0.273613	−	0.343100i	−0.899585	+	0.436745i	$0.856131\pi$
$270$	0.448321	−	1.12774i	0.0272840	−	0.0686318i
$271$	−1.21533	+	0.277392i	−0.0738262	+	0.0168503i	−0.259274	−	0.965804i	$-0.583483\pi$
$271$	−1.21533	+	0.277392i	−0.0738262	+	0.0168503i	0.185448	+	0.982654i	$0.440626\pi$
$272$	−1.52085	−	6.66329i	−0.0922152	−	0.404021i
$273$	−1.54471	+	5.33948i	−0.0934904	+	0.323160i
$274$	−4.17028	+	18.2712i	−0.251936	+	1.10380i
$275$		−	3.67964i		−	0.221890i
$276$	3.10995	+	1.13708i	0.187197	+	0.0684441i
$277$	2.60355	−	11.4069i	0.156432	−	0.685373i	−0.834500	−	0.551008i	$-0.814243\pi$
$277$	2.60355	−	11.4069i	0.156432	−	0.685373i	0.990932	−	0.134365i	$-0.0428995\pi$
$278$	10.3165	−	4.96817i	0.618743	−	0.297971i
$279$	7.65179	+	0.213211i	0.458101	+	0.0127646i
$280$	0.178659	+	0.591534i	0.0106769	+	0.0353509i
$281$	11.3069	+	9.01699i	0.674516	+	0.537909i	0.899755	−	0.436395i	$-0.143745\pi$
$281$	11.3069	+	9.01699i	0.674516	+	0.537909i	−0.225239	+	0.974303i	$0.572316\pi$
$282$	−5.14468	+	7.94003i	−0.306361	+	0.472822i
$283$	7.14978	+	5.70176i	0.425011	+	0.338935i	0.812522	−	0.582930i	$-0.198094\pi$
$283$	7.14978	+	5.70176i	0.425011	+	0.338935i	−0.387512	+	0.921865i	$0.626665\pi$
$284$	4.08841	+	8.48968i	0.242603	+	0.503770i
$285$	0.594652	+	1.77850i	0.0352242	+	0.105349i
$286$	0.391575	−	0.813114i	0.0231543	−	0.0480804i
$287$	−11.4097	+	10.4624i	−0.673493	+	0.617575i
$288$	−0.748769	+	2.90506i	−0.0441216	+	0.171182i
$289$	−26.7699	−	12.8917i	−1.57470	−	0.758336i
$290$	0.130446	+	0.571523i	0.00766007	+	0.0335610i
$291$	−4.61799	−	4.74846i	−0.270711	−	0.278360i
$292$	3.56590	+	2.84371i	0.208678	+	0.166416i
$293$	−8.04047			−0.469729			−0.234865	−	0.972028i	$-0.575465\pi$
$293$	−8.04047			−0.469729			−0.234865	+	0.972028i	$0.575465\pi$
$294$	−9.56702	−	7.44796i	−0.557960	−	0.434374i
$295$	−2.49001			−0.144974
$296$	0.331457	+	0.264328i	0.0192655	+	0.0153638i
$297$	−0.272008	−	3.85659i	−0.0157835	−	0.223782i
$298$	2.15816	+	9.45551i	0.125019	+	0.547743i
$299$	−2.08925	−	1.00613i	−0.120825	−	0.0581860i
$300$	−0.840415	−	8.52445i	−0.0485214	−	0.492159i
$301$	−0.211309	−	3.06135i	−0.0121797	−	0.176453i
$302$	−9.83523	+	20.4231i	−0.565954	+	1.17522i
$303$	11.9548	−	3.99718i	0.686788	−	0.229632i
$304$	−2.01137	−	4.17665i	−0.115360	−	0.239547i
$305$	1.88149	+	1.50044i	0.107734	+	0.0859150i
$306$	12.3325	+	16.3805i	0.705004	+	0.936410i
$307$	−10.8187	−	8.62764i	−0.617457	−	0.492405i	0.264092	−	0.964497i	$-0.414928\pi$
$307$	−10.8187	−	8.62764i	−0.617457	−	0.492405i	−0.881549	+	0.472092i	$0.843499\pi$
$308$	1.33044	+	1.45091i	0.0758091	+	0.0826732i
$309$	9.53828	+	28.5273i	0.542614	+	1.62286i
$310$	−0.536917	+	0.258565i	−0.0304948	+	0.0146855i
$311$	−5.68124	+	24.8911i	−0.322153	+	1.41145i	0.511560	+	0.859248i	$0.329068\pi$
$311$	−5.68124	+	24.8911i	−0.322153	+	1.41145i	−0.833713	+	0.552198i	$0.813789\pi$
$312$	0.721432	−	1.97314i	0.0408430	−	0.111707i
$313$		−	2.48236i		−	0.140311i	−0.997536	−	0.0701556i	$-0.977650\pi$
$313$		−	2.48236i		−	0.140311i	0.997536	−	0.0701556i	$-0.0223496\pi$
$314$	−3.66351	+	16.0509i	−0.206744	+	0.905805i
$315$	−1.21433	−	1.40068i	−0.0684196	−	0.0789192i
$316$	0.907447	+	3.97578i	0.0510479	+	0.223655i
$317$	−0.323966	+	0.0739432i	−0.0181957	+	0.00415306i	−0.231609	−	0.972809i	$-0.574399\pi$
$317$	−0.323966	+	0.0739432i	−0.0181957	+	0.00415306i	0.213413	+	0.976962i	$0.431542\pi$
$318$	−19.0587	+	6.37240i	−1.06876	+	0.357346i
$319$	1.16440	+	1.46011i	0.0651939	+	0.0817506i
$320$	−0.0519706	−	0.227698i	−0.00290524	−	0.0127287i
$321$	−2.34195	+	18.4694i	−0.130715	+	1.03086i
$322$	3.72803	−	3.41850i	0.207755	−	0.190506i
$323$	−30.8892	−	7.05026i	−1.71872	−	0.392287i
$324$	−1.51098	−	8.87226i	−0.0839433	−	0.492903i
$325$			5.99858i			0.332742i
$326$	0.549199	+	0.125351i	0.0304173	+	0.00694256i
$327$	−2.68453	−	27.2295i	−0.148455	−	1.50580i
$328$	4.57453	−	3.64806i	0.252586	−	0.201431i
$329$	7.15224	+	12.5581i	0.394316	+	0.692352i
$330$	0.156569	+	0.257058i	0.00861885	+	0.0141506i
$331$	−0.966187	+	4.23314i	−0.0531064	+	0.232675i	−0.994515	−	0.104594i	$-0.966646\pi$
$331$	−0.966187	+	4.23314i	−0.0531064	+	0.232675i	0.941409	+	0.337268i	$0.109503\pi$
$332$	5.46146	−	6.84845i	0.299736	−	0.375858i
$333$	−1.23160	−	0.317440i	−0.0674910	−	0.0173956i
$334$	0.677158	−	0.540016i	0.0370524	−	0.0295483i
$335$	1.06190	+	0.511385i	0.0580179	+	0.0279399i
$336$	3.41356	+	3.05738i	0.186225	+	0.166794i
$337$	−17.7926	+	8.56846i	−0.969225	+	0.466754i	−0.850386	−	0.526160i	$-0.823631\pi$
$337$	−17.7926	+	8.56846i	−0.969225	+	0.466754i	−0.118839	+	0.992914i	$0.537917\pi$
$338$	5.00214	−	10.3870i	0.272080	−	0.564981i
$339$	4.16470	−	32.8443i	0.226195	−	1.78386i
$340$	−1.43818	−	0.692590i	−0.0779962	−	0.0375610i
$341$	−1.18369	+	1.48430i	−0.0641005	+	0.0803795i
$342$	10.6274	+	8.97049i	0.574661	+	0.485068i
$343$	−16.8254	+	7.73984i	−0.908487	+	0.417912i
$344$			1.15984i			0.0625341i
$345$	0.660496	−	0.402296i	0.0355599	−	0.0216589i
$346$	8.92116	−	18.5250i	0.479604	−	0.995909i
$347$	24.3096	−	5.54851i	1.30501	−	0.297860i	0.487170	−	0.873307i	$-0.338029\pi$
$347$	24.3096	−	5.54851i	1.30501	−	0.297860i	0.817839	+	0.575447i	$0.195172\pi$
$348$	3.03100	+	3.11663i	0.162479	+	0.167069i
$349$	8.67285	+	18.0094i	0.464247	+	0.964019i	0.993315	+	0.115439i	$0.0368275\pi$
$349$	8.67285	+	18.0094i	0.464247	+	0.964019i	−0.529068	+	0.848580i	$0.677458\pi$
$350$	−12.1516	−	4.85187i	−0.649531	−	0.259343i
$351$	0.443431	+	6.28705i	0.0236686	+	0.335578i
$352$	−0.463904	−	0.581717i	−0.0247262	−	0.0310056i
$353$	2.99449	−	1.44207i	0.159381	−	0.0767538i	−0.352493	−	0.935815i	$-0.614666\pi$
$353$	2.99449	−	1.44207i	0.159381	−	0.0767538i	0.511874	+	0.859061i	$0.328952\pi$
$354$	−15.7710	+	9.60584i	−0.838221	+	0.510544i
$355$	2.14556	+	0.489710i	0.113875	+	0.0259911i
$356$	8.77266	−	11.0006i	0.464950	−	0.583029i
$357$	30.8836	−	5.21197i	1.63453	−	0.275847i
$358$	3.91015	+	4.90317i	0.206658	+	0.259141i
$359$	−12.8925	−	26.7715i	−0.680439	−	1.41295i	−0.899363	−	0.437204i	$-0.855969\pi$
$359$	−12.8925	−	26.7715i	−0.680439	−	1.41295i	0.218924	−	0.975742i	$-0.429745\pi$
$360$	0.421428	+	0.559754i	0.0222112	+	0.0295016i
$361$	−2.49003			−0.131054
$362$	16.1334			0.847953
$363$	−15.1848	−	9.83887i	−0.796995	−	0.516407i
$364$	−2.16890	−	2.36529i	−0.113681	−	0.123975i
$365$	1.03852	−	0.237036i	0.0543587	−	0.0124070i
$366$	17.7052	+	2.24504i	0.925464	+	0.117350i
$367$	14.0017	−	11.1659i	0.730880	−	0.582858i	−0.185748	−	0.982597i	$-0.559471\pi$
$367$	14.0017	−	11.1659i	0.730880	−	0.582858i	0.916629	+	0.399740i	$0.130900\pi$
$368$	−1.49469	+	1.19198i	−0.0779161	+	0.0621360i
$369$	−8.05355	+	15.5965i	−0.419251	+	0.811924i
$370$	0.0965324	−	0.0220329i	0.00501848	−	0.00114544i
$371$	−4.75366	+	30.3266i	−0.246798	+	1.57448i
$372$	−2.40320	+	3.70897i	−0.124600	+	0.192301i
$373$	−31.5372			−1.63293			−0.816466	−	0.577393i	$-0.804070\pi$
$373$	−31.5372			−1.63293			−0.816466	+	0.577393i	$0.804070\pi$
$374$	−5.08528			−0.262954
$375$	−3.37640	−	2.18771i	−0.174357	−	0.112973i
$376$	−2.37003	−	4.92141i	−0.122225	−	0.253802i
$377$	−1.89822	−	2.38029i	−0.0977633	−	0.122591i
$378$	−13.0946	−	4.18691i	−0.673516	−	0.215352i
$379$	17.2401	−	21.6184i	0.885563	−	1.11046i	−0.107654	−	0.994188i	$-0.534334\pi$
$379$	17.2401	−	21.6184i	0.885563	−	1.11046i	0.993217	−	0.116273i	$-0.0370947\pi$
$380$	−1.05555	−	0.240922i	−0.0541485	−	0.0123590i
$381$	−1.61726	−	2.65525i	−0.0828550	−	0.136033i
$382$	7.32563	−	3.52784i	0.374812	−	0.180500i
$383$	−4.32920	−	5.42864i	−0.221212	−	0.277391i	0.658825	−	0.752296i	$-0.271054\pi$
$383$	−4.32920	−	5.42864i	−0.221212	−	0.277391i	−0.880037	+	0.474905i	$0.842482\pi$
$384$	−1.20757	−	1.24168i	−0.0616234	−	0.0633644i
$385$	0.458673	−	0.0316598i	0.0233761	−	0.00161353i
$386$	−8.35429	−	17.3479i	−0.425222	−	0.882983i
$387$	−1.42180	−	3.17576i	−0.0722740	−	0.161433i
$388$	3.72833	−	0.850966i	0.189277	−	0.0432013i
$389$	11.7658	−	24.4319i	0.596548	−	1.23875i	−0.356036	−	0.934472i	$-0.615872\pi$
$389$	11.7658	−	24.4319i	0.596548	−	1.23875i	0.952585	−	0.304273i	$-0.0984136\pi$
$390$	−0.255241	−	0.419059i	−0.0129246	−	0.0212199i
$391$			13.0663i			0.660793i
$392$	6.54576	−	2.48053i	0.330611	−	0.125285i
$393$	9.21029	−	25.1904i	0.464598	−	1.27069i
$394$	6.55279	−	8.21693i	0.330125	−	0.413963i
$395$	0.858118	+	0.413248i	0.0431766	+	0.0207927i
$396$	1.98333	+	1.02413i	0.0996659	+	0.0514643i
$397$	11.8978	−	24.7061i	0.597136	−	1.23996i	−0.355165	−	0.934804i	$-0.615575\pi$
$397$	11.8978	−	24.7061i	0.597136	−	1.23996i	0.952301	−	0.305161i	$-0.0987104\pi$
$398$	−22.2518	+	10.7159i	−1.11538	+	0.537140i
$399$	19.6356	−	8.10773i	0.983008	−	0.405894i
$400$	4.45570	+	2.14575i	0.222785	+	0.107288i
$401$	−11.5245	+	9.19046i	−0.575505	+	0.458950i	−0.867477	−	0.497477i	$-0.834260\pi$
$401$	−11.5245	+	9.19046i	−0.575505	+	0.458950i	0.291973	+	0.956427i	$0.405688\pi$
$402$	8.69857	−	0.857581i	0.433845	−	0.0427723i
$403$	1.92967	−	2.41973i	0.0961236	−	0.120535i
$404$	−1.61945	+	7.09526i	−0.0805704	+	0.353002i
$405$	−1.84010	−	1.01606i	−0.0914352	−	0.0504884i
$406$	6.35722	−	1.92005i	0.315503	−	0.0952904i
$407$	0.246619	−	0.196672i	0.0122244	−	0.00974866i
$408$	−11.7808	+	1.16146i	−0.583238	+	0.0575008i
$409$	−27.8338	−	6.35289i	−1.37629	−	0.314130i	−0.530521	−	0.847672i	$-0.678004\pi$
$409$	−27.8338	−	6.35289i	−1.37629	−	0.314130i	−0.845774	+	0.533542i	$0.820861\pi$
$410$		−	1.36653i		−	0.0674882i
$411$	30.4866	+	11.1467i	1.50379	+	0.549827i
$412$	−16.9311	−	3.86441i	−0.834135	−	0.190386i
$413$	1.94239	+	28.1405i	0.0955789	+	1.38470i
$414$	2.63144	−	5.09605i	0.129328	−	0.250457i
$415$	−0.455236	−	1.99452i	−0.0223467	−	0.0979072i
$416$	0.756262	+	0.948322i	0.0370788	+	0.0464953i
$417$	−6.28899	−	18.8093i	−0.307973	−	0.921093i
$418$	−3.36271	+	0.767518i	−0.164476	+	0.0375405i
$419$	3.76837	+	16.5103i	0.184097	+	0.806581i	0.979653	+	0.200701i	$0.0643218\pi$
$419$	3.76837	+	16.5103i	0.184097	+	0.806581i	−0.795556	+	0.605880i	$0.792821\pi$
$420$	1.05535	−	0.178104i	0.0514960	−	0.00869058i
$421$	−5.38581	+	23.5968i	−0.262488	+	1.15004i	0.656054	+	0.754714i	$0.272224\pi$
$421$	−5.38581	+	23.5968i	−0.262488	+	1.15004i	−0.918542	+	0.395322i	$0.870633\pi$
$422$			1.01279i			0.0493017i
$423$	12.5224	+	10.5701i	0.608858	+	0.513934i
$424$	2.58176	−	11.3114i	0.125381	−	0.549332i
$425$	30.4531	−	14.6655i	1.47719	−	0.711379i
$426$	15.4785	−	5.17534i	0.749937	−	0.250746i
$427$	15.4893	−	22.4339i	0.749580	−	1.08565i
$428$	−8.40368	−	6.70171i	−0.406207	−	0.323939i
$429$	−1.31185	−	0.850003i	−0.0633367	−	0.0410385i
$430$	0.211786	+	0.168893i	0.0102132	+	0.00814476i
$431$	3.68746	+	7.65710i	0.177619	+	0.368829i	0.970703	−	0.240283i	$-0.0772402\pi$
$431$	3.68746	+	7.65710i	0.177619	+	0.368829i	−0.793084	+	0.609112i	$0.791526\pi$
$432$	4.82859	+	1.91956i	0.232316	+	0.0923550i
$433$	0.413638	−	0.858927i	0.0198782	−	0.0412774i	−0.890793	−	0.454409i	$-0.849851\pi$
$433$	0.413638	−	0.858927i	0.0198782	−	0.0412774i	0.910672	+	0.413131i	$0.135565\pi$
$434$	3.34097	+	5.86618i	0.160372	+	0.281586i
$435$	1.01047	−	0.0996205i	0.0484481	−	0.00477644i
$436$	14.2328	+	6.85414i	0.681626	+	0.328254i
$437$	1.97209	+	8.64031i	0.0943380	+	0.413322i
$438$	5.66327	−	5.50766i	0.270601	−	0.263166i
$439$	15.3300	+	12.2253i	0.731663	+	0.583482i	0.916855	−	0.399220i	$-0.130719\pi$
$439$	15.3300	+	12.2253i	0.731663	+	0.583482i	−0.185192	+	0.982702i	$0.559291\pi$
$440$	−0.173774			−0.00828437
$441$	−14.8823	+	14.8162i	−0.708679	+	0.705531i
$442$	8.29008			0.394319
$443$	4.81609	+	3.84070i	0.228819	+	0.182477i	0.731188	−	0.682176i	$-0.238966\pi$
$443$	4.81609	+	3.84070i	0.228819	+	0.182477i	−0.502368	+	0.864654i	$0.667538\pi$
$444$	0.526411	−	0.511947i	0.0249824	−	0.0242959i
$445$	−0.731240	−	3.20377i	−0.0346641	−	0.151873i
$446$	3.73098	+	1.79675i	0.176667	+	0.0850785i
$447$	16.7176	−	1.64816i	0.790713	−	0.0779555i
$448$	−2.53275	+	0.764959i	−0.119661	+	0.0361409i
$449$	−14.1453	+	29.3731i	−0.667560	+	1.38620i	0.241854	+	0.970313i	$0.422244\pi$
$449$	−14.1453	+	29.3731i	−0.667560	+	1.38620i	−0.909415	+	0.415891i	$0.863470\pi$
$450$	−14.8306	−	0.413244i	−0.699121	−	0.0194805i
$451$	−1.88888	−	3.92231i	−0.0889441	−	0.184694i
$452$	14.9443	+	11.9177i	0.702921	+	0.560561i
$453$	32.9499	+	21.3496i	1.54812	+	1.00309i
$454$	8.82799	+	7.04009i	0.414318	+	0.330408i
$455$	−0.747733	+	0.0516121i	−0.0350543	+	0.00241961i
$456$	−7.61495	+	2.54610i	−0.356603	+	0.119232i
$457$	−8.45978	+	4.07401i	−0.395732	+	0.190574i	−0.621157	−	0.783686i	$-0.713337\pi$
$457$	−8.45978	+	4.07401i	−0.395732	+	0.190574i	0.225425	+	0.974260i	$0.427623\pi$
$458$	0.501954	−	2.19920i	0.0234548	−	0.102762i
$459$	30.8335	−	17.6219i	1.43918	−	0.822519i
$460$			0.446504i			0.0208183i
$461$	−6.73527	+	29.5091i	−0.313693	+	1.37438i	0.534714	+	0.845033i	$0.320419\pi$
$461$	−6.73527	+	29.5091i	−0.313693	+	1.37438i	−0.848407	+	0.529344i	$0.822438\pi$
$462$	2.78296	−	1.96997i	0.129475	−	0.0916511i
$463$	−4.03685	−	17.6866i	−0.187609	−	0.821967i	−0.977873	−	0.209201i	$-0.932914\pi$
$463$	−4.03685	−	17.6866i	−0.187609	−	0.821967i	0.790264	−	0.612766i	$-0.209943\pi$
$464$	−2.44707	+	0.558528i	−0.113602	+	0.0259290i
$465$	0.327307	+	0.978916i	0.0151785	+	0.0453962i
$466$	−15.5633	−	19.5158i	−0.720958	−	0.904052i
$467$	1.98871	+	8.71311i	0.0920266	+	0.403195i	0.999870	−	0.0161142i	$-0.00512955\pi$
$467$	1.98871	+	8.71311i	0.0920266	+	0.403195i	−0.907844	+	0.419309i	$0.862272\pi$
$468$	−3.23324	−	1.66954i	−0.149457	−	0.0771746i
$469$	4.95097	−	12.3998i	0.228615	−	0.572571i
$470$	−1.24377	−	0.283882i	−0.0573707	−	0.0130945i
$471$	26.7819	+	9.79219i	1.23405	+	0.451200i
$472$		−	10.6614i		−	0.490731i
$473$	0.841333	+	0.192029i	0.0386845	+	0.00882949i
$474$	7.02927	−	0.693007i	0.322865	−	0.0318309i
$475$	17.9241	−	14.2940i	0.822415	−	0.655854i
$476$	−6.70531	+	16.7936i	−0.307338	+	0.769734i
$477$	6.79709	+	34.1369i	0.311217	+	1.56302i
$478$	0.873205	−	3.82576i	0.0399395	−	0.174986i
$479$	18.5756	−	23.2930i	0.848740	−	1.06429i	−0.148417	−	0.988925i	$-0.547418\pi$
$479$	18.5756	−	23.2930i	0.848740	−	1.06429i	0.997156	−	0.0753610i	$-0.0240109\pi$
$480$	−0.402575	+	0.0396894i	−0.0183750	+	0.00181157i
$481$	−0.402040	+	0.320616i	−0.0183315	+	0.0146189i
$482$	−6.54500	−	3.15191i	−0.298117	−	0.143565i
$483$	−5.06171	−	7.15067i	−0.230316	−	0.325367i
$484$	9.41188	−	4.53252i	0.427813	−	0.206024i
$485$	0.387527	−	0.804708i	0.0175967	−	0.0365399i
$486$	−15.5743	+	0.663199i	−0.706467	+	0.0300833i
$487$	5.17753	+	2.49337i	0.234616	+	0.112985i	0.547498	−	0.836807i	$-0.315580\pi$
$487$	5.17753	+	2.49337i	0.234616	+	0.112985i	−0.312882	+	0.949792i	$0.601295\pi$
$488$	−6.42440	+	8.05594i	−0.290819	+	0.364675i
$489$	0.335050	−	0.916373i	0.0151515	−	0.0414398i
$490$	0.500240	−	1.55646i	0.0225985	−	0.0703139i
$491$		−	22.7588i		−	1.02709i	−0.858063	−	0.513545i	$-0.828332\pi$
$491$		−	22.7588i		−	1.02709i	0.858063	−	0.513545i	$-0.171668\pi$
$492$	−5.27173	−	8.65522i	−0.237668	−	0.390207i
$493$	−7.44327	+	15.4561i	−0.335228	+	0.696108i
$494$	5.48193	−	1.25122i	0.246644	−	0.0562948i
$495$	0.475814	−	0.213023i	0.0213863	−	0.00957468i
$496$	−1.10709	−	2.29890i	−0.0497099	−	0.103224i
$497$	3.86069	−	24.6297i	0.173176	−	1.10479i
$498$	−10.5777	−	10.8765i	−0.473997	−	0.487389i
$499$	21.2945	+	26.7025i	0.953273	+	1.19537i	0.980656	+	0.195741i	$0.0627112\pi$
$499$	21.2945	+	26.7025i	0.953273	+	1.19537i	−0.0273831	+	0.999625i	$0.508717\pi$
$500$	2.09277	−	1.00782i	0.0935915	−	0.0450713i
$501$	−0.780364	−	1.28122i	−0.0348641	−	0.0572405i
$502$	−14.8755	−	3.39524i	−0.663928	−	0.151537i
$503$	−1.10362	+	1.38390i	−0.0492080	+	0.0617049i	−0.805826	−	0.592152i	$-0.798279\pi$
$503$	−1.10362	+	1.38390i	−0.0492080	+	0.0617049i	0.756619	+	0.653857i	$0.226850\pi$
$504$	5.99723	−	5.19935i	0.267138	−	0.231597i
$505$	1.05977	+	1.32891i	0.0471592	+	0.0591357i
$506$	0.617178	+	1.28158i	0.0274369	+	0.0569733i
$507$	−16.7581	−	10.8583i	−0.744254	−	0.482233i
$508$	1.79498			0.0796396
$509$	33.2094			1.47198			0.735990	−	0.676993i	$-0.236717\pi$
$509$	33.2094			1.47198			0.735990	+	0.676993i	$0.236717\pi$
$510$	−1.50342	+	2.32031i	−0.0665728	+	0.102745i
$511$	−3.48894	−	11.5518i	−0.154342	−	0.511020i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	17.7294	−	16.3064i	0.782773	−	0.719945i
$514$	−16.0398	+	12.7913i	−0.707486	+	0.564201i
$515$	−3.17112	+	2.52888i	−0.139736	+	0.111436i
$516$	1.99294	+	0.252707i	0.0877341	+	0.0111248i
$517$	−3.96233	+	0.904377i	−0.174263	+	0.0397744i
$518$	−0.324304	−	1.07376i	−0.0142491	−	0.0471782i
$519$	−29.8876	−	19.3654i	−1.31192	−	0.850047i
$520$	0.283289			0.0124230
$521$	−19.7709			−0.866177			−0.433088	−	0.901351i	$-0.642576\pi$
$521$	−19.7709			−0.866177			−0.433088	+	0.901351i	$0.642576\pi$
$522$	6.01568	−	4.52908i	0.263299	−	0.198233i
$523$	4.24252	+	8.80969i	0.185513	+	0.385221i	0.972896	−	0.231243i	$-0.0742791\pi$
$523$	4.24252	+	8.80969i	0.185513	+	0.385221i	−0.787383	+	0.616463i	$0.788565\pi$
$524$	9.65495	+	12.1069i	0.421778	+	0.528893i
$525$	−10.9845	+	19.8229i	−0.479405	+	0.865142i
$526$	12.7122	−	15.9406i	0.554278	−	0.695042i
$527$	−17.0020	−	3.88058i	−0.740617	−	0.169041i
$528$	−1.10064	+	0.670377i	−0.0478991	+	0.0291744i
$529$	−17.4293	+	8.39352i	−0.757797	+	0.364936i
$530$	−1.68951	−	2.11858i	−0.0733877	−	0.0920253i
$531$	13.0694	+	29.1922i	0.567164	+	1.26683i
$532$	−1.89934	+	12.1170i	−0.0823467	+	0.525340i
$533$	3.07928	+	6.39419i	0.133378	+	0.276963i
$534$	−16.9908	−	17.4708i	−0.735263	−	0.756036i
$535$	−2.44746	+	0.558617i	−0.105813	+	0.0241511i
$536$	−2.18958	+	4.54671i	−0.0945755	+	0.196388i
$537$	9.27703	−	5.65047i	0.400333	−	0.243836i
$538$		−	7.19754i		−	0.310308i
$539$	−0.715596	−	5.15892i	−0.0308229	−	0.222210i
$540$	1.05364	−	0.602175i	0.0453416	−	0.0259135i
$541$	−17.9547	+	22.5145i	−0.771933	+	0.967974i	−0.999984	−	0.00567535i	$-0.998193\pi$
$541$	−17.9547	+	22.5145i	−0.771933	+	0.967974i	0.228050	+	0.973649i	$0.426765\pi$
$542$	−1.12314	−	0.540874i	−0.0482428	−	0.0232325i
$543$	3.51518	−	27.7219i	0.150851	−	1.18966i
$544$	2.96544	−	6.15780i	0.127142	−	0.264014i
$545$	3.32412	−	1.60081i	0.142390	−	0.0685712i
$546$	−4.53682	+	3.21146i	−0.194158	+	0.137438i
$547$	30.3340	+	14.6081i	1.29699	+	0.624597i	0.949700	−	0.313160i	$-0.101388\pi$
$547$	30.3340	+	14.6081i	1.29699	+	0.624597i	0.347290	+	0.937758i	$0.387102\pi$
$548$	−14.6523	+	11.6849i	−0.625917	+	0.499152i
$549$	7.71526	−	29.9335i	0.329279	−	1.27753i
$550$	2.29422	−	2.87686i	0.0978257	−	0.122670i
$551$	−2.58919	+	11.3440i	−0.110303	+	0.483270i
$552$	1.72250	+	2.82802i	0.0733143	+	0.120369i
$553$	4.00086	−	10.0202i	0.170134	−	0.426104i
$554$	9.14761	−	7.29498i	0.388645	−	0.309934i
$555$	−0.0168263	−	0.170671i	−0.000714236	−	0.00724460i
$556$	11.1634	+	2.54797i	0.473433	+	0.108058i
$557$			16.8259i			0.712938i	0.934307	+	0.356469i	$0.116019\pi$
$557$			16.8259i			0.712938i	−0.934307	+	0.356469i	$0.883981\pi$
$558$	5.84947	+	4.93751i	0.247628	+	0.209021i
$559$	−1.37155	−	0.313047i	−0.0580104	−	0.0132405i
$560$	−0.229134	+	0.573872i	−0.00968269	+	0.0242505i
$561$	−1.10799	+	8.73800i	−0.0467794	+	0.368919i
$562$	3.21813	+	14.0995i	0.135748	+	0.594753i
$563$	−18.1178	−	22.7190i	−0.763573	−	0.957490i	0.236326	−	0.971674i	$-0.424057\pi$
$563$	−18.1178	−	22.7190i	−0.763573	−	0.957490i	−0.999899	+	0.0141836i	$0.995485\pi$
$564$	−8.97280	+	3.00011i	−0.377823	+	0.126327i
$565$	4.35233	−	0.993392i	0.183104	−	0.0417923i
$566$	2.03494	+	8.91564i	0.0855347	+	0.374752i
$567$	−10.0474	+	21.5882i	−0.421952	+	0.906618i
$568$	−2.09678	+	9.18658i	−0.0879788	+	0.385460i
$569$			5.02274i			0.210564i	0.994442	+	0.105282i	$0.0335746\pi$
$569$			5.02274i			0.210564i	−0.994442	+	0.105282i	$0.966425\pi$
$570$	−0.643959	+	1.76125i	−0.0269725	+	0.0737705i
$571$	−7.01956	+	30.7547i	−0.293759	+	1.28704i	0.585489	+	0.810680i	$0.300903\pi$
$571$	−7.01956	+	30.7547i	−0.293759	+	1.28704i	−0.879248	+	0.476364i	$0.841955\pi$
$572$	0.813114	−	0.391575i	0.0339980	−	0.0163726i
$573$	−4.46573	−	13.3562i	−0.186559	−	0.557964i
$574$	−15.4436	+	1.06599i	−0.644605	+	0.0444938i
$575$	−7.39192	−	5.89486i	−0.308264	−	0.245833i
$576$	−2.39668	+	1.80441i	−0.0998618	+	0.0751839i
$577$	−33.2625	−	26.5260i	−1.38474	−	1.10429i	−0.981980	−	0.188985i	$-0.939480\pi$
$577$	−33.2625	−	26.5260i	−1.38474	−	1.10429i	−0.402758	−	0.915307i	$-0.631948\pi$
$578$	−12.8917	−	26.7699i	−0.536225	−	1.11348i
$579$	−31.6289	+	10.5753i	−1.31445	+	0.439496i
$580$	−0.254352	+	0.528167i	−0.0105614	+	0.0219309i
$581$	−22.1856	+	6.70065i	−0.920415	+	0.277990i
$582$	−0.649874	−	6.59176i	−0.0269381	−	0.273237i
$583$	−7.77775	−	3.74557i	−0.322121	−	0.155126i
$584$	1.01491	+	4.44660i	0.0419972	+	0.184002i
$585$	−0.775677	+	0.347273i	−0.0320703	+	0.0143580i
$586$	−6.28630	−	5.01315i	−0.259684	−	0.207091i
$587$	2.91560			0.120340			0.0601698	−	0.998188i	$-0.480836\pi$
$587$	2.91560			0.120340			0.0601698	+	0.998188i	$0.480836\pi$
$588$	−2.83607	−	11.7880i	−0.116957	−	0.486129i
$589$	−11.8285			−0.487384
$590$	−1.94677	−	1.55250i	−0.0801473	−	0.0639153i
$591$	−12.6914	−	13.0499i	−0.522053	−	0.536802i
$592$	0.0943376	+	0.413320i	0.00387725	+	0.0169873i
$593$	−15.0451	−	7.24532i	−0.617826	−	0.297530i	0.0986701	−	0.995120i	$-0.468541\pi$
$593$	−15.0451	−	7.24532i	−0.617826	−	0.297530i	−0.716497	+	0.697591i	$0.754255\pi$
$594$	2.19188	−	3.18480i	0.0899339	−	0.130674i
$595$	2.09009	+	3.66985i	0.0856854	+	0.150449i
$596$	−4.20810	+	8.73821i	−0.172370	+	0.357931i
$597$	13.5648	+	40.5700i	0.555171	+	1.66042i
$598$	−1.00613	−	2.08925i	−0.0411437	−	0.0854358i
$599$	10.3831	+	8.28022i	0.424240	+	0.338320i	0.812224	−	0.583346i	$-0.198257\pi$
$599$	10.3831	+	8.28022i	0.424240	+	0.338320i	−0.387983	+	0.921666i	$0.626828\pi$
$600$	4.65784	−	7.18867i	0.190156	−	0.293476i
$601$	25.4370	+	20.2853i	1.03760	+	0.827455i	0.985241	−	0.171173i	$-0.0547558\pi$
$601$	25.4370	+	20.2853i	1.03760	+	0.827455i	0.0523552	+	0.998629i	$0.483327\pi$
$602$	1.74351	−	2.52521i	0.0710603	−	0.102920i
$603$	0.421685	−	15.1335i	0.0171723	−	0.616285i
$604$	−20.4231	+	9.83523i	−0.831003	+	0.400190i
$605$	0.542906	−	2.37862i	0.0220723	−	0.0967048i
$606$	11.8389	+	4.32861i	0.480921	+	0.175838i
$607$		−	28.5588i		−	1.15917i	−0.814913	−	0.579583i	$-0.803215\pi$
$607$		−	28.5588i		−	1.15917i	0.814913	−	0.579583i	$-0.196785\pi$
$608$	1.03155	−	4.51951i	0.0418348	−	0.183290i
$609$	−1.91408	−	11.3419i	−0.0775625	−	0.459597i
$610$	0.535501	+	2.34619i	0.0216818	+	0.0949943i
$611$	6.45944	−	1.47432i	0.261321	−	0.0596448i
$612$	−0.571105	+	20.4960i	−0.0230856	+	0.828501i
$613$	21.0968	+	26.4545i	0.852091	+	1.06849i	0.996873	+	0.0790252i	$0.0251807\pi$
$613$	21.0968	+	26.4545i	0.852091	+	1.06849i	−0.144781	+	0.989464i	$0.546248\pi$
$614$	−3.07917	−	13.4907i	−0.124265	−	0.544441i
$615$	−2.34810	−	0.297742i	−0.0946846	−	0.0120061i
$616$	0.135557	+	1.96388i	0.00546174	+	0.0791271i
$617$	−31.1080	−	7.10019i	−1.25236	−	0.285843i	−0.455625	−	0.890172i	$-0.650584\pi$
$617$	−31.1080	−	7.10019i	−1.25236	−	0.285843i	−0.796735	+	0.604329i	$0.793441\pi$
$618$	−10.3292	+	28.2506i	−0.415500	+	1.13640i
$619$			0.289617i			0.0116407i	0.999983	+	0.00582034i	$0.00185268\pi$
$619$			0.289617i			0.0116407i	−0.999983	+	0.00582034i	$0.998147\pi$
$620$	−0.580991	−	0.132607i	−0.0233332	−	0.00532564i
$621$	−8.18316	−	5.63191i	−0.328379	−	0.226001i
$622$	−19.9611	+	15.9185i	−0.800368	+	0.638272i
$623$	−35.6365	+	10.7632i	−1.42775	+	0.431217i
$624$	1.79427	−	1.09286i	0.0718283	−	0.0437493i
$625$	−5.38162	+	23.5784i	−0.215265	+	0.943136i
$626$	1.54773	−	1.94079i	0.0618596	−	0.0775694i
$627$	0.586145	+	5.94535i	0.0234084	+	0.237435i
$628$	−12.8718	+	10.2649i	−0.513642	+	0.409616i
$629$	2.61060	+	1.25720i	0.104091	+	0.0501277i
$630$	−0.0760917	−	1.85221i	−0.00303157	−	0.0737939i
$631$	−6.24227	+	3.00612i	−0.248501	+	0.119672i	−0.553989	−	0.832524i	$-0.686895\pi$
$631$	−6.24227	+	3.00612i	−0.248501	+	0.119672i	0.305488	+	0.952196i	$0.401181\pi$
$632$	−1.76939	+	3.67418i	−0.0703826	+	0.146151i
$633$	1.74026	+	0.220668i	0.0691693	+	0.00877076i
$634$	−0.299390	−	0.144178i	−0.0118903	−	0.00572606i
$635$	0.261383	−	0.327764i	0.0103727	−	0.0130069i
$636$	−18.8738	−	6.90077i	−0.748396	−	0.273634i
$637$	1.16657	+	8.41012i	0.0462213	+	0.333221i
$638$			1.86755i			0.0739372i
$639$	−5.52026	−	27.7243i	−0.218378	−	1.09675i
$640$	0.101335	−	0.210425i	0.00400562	−	0.00831777i
$641$	−4.56459	+	1.04184i	−0.180290	+	0.0411501i	−0.311713	−	0.950176i	$-0.600903\pi$
$641$	−4.56459	+	1.04184i	−0.180290	+	0.0411501i	0.131422	+	0.991326i	$0.458046\pi$
$642$	−13.3465	+	12.9798i	−0.526744	+	0.512271i
$643$	−9.78702	−	20.3229i	−0.385962	−	0.801459i	−0.999926	−	0.0121250i	$-0.996140\pi$
$643$	−9.78702	−	20.3229i	−0.385962	−	0.801459i	0.613964	−	0.789334i	$-0.289574\pi$
$644$	5.04609	−	0.348305i	0.198844	−	0.0137252i
$645$	0.336352	−	0.327111i	0.0132439	−	0.0128800i
$646$	−19.7544	−	24.7712i	−0.777227	−	0.974611i
$647$	−3.76852	+	1.81482i	−0.148156	+	0.0713481i	−0.506493	−	0.862244i	$-0.669058\pi$
$647$	−3.76852	+	1.81482i	−0.148156	+	0.0713481i	0.358337	+	0.933592i	$0.383344\pi$
$648$	4.35043	−	7.87869i	0.170901	−	0.309504i
$649$	−7.73368	−	1.76516i	−0.303574	−	0.0692887i
$650$	−3.74006	+	4.68988i	−0.146697	+	0.183952i
$651$	10.8077	−	4.46263i	0.423589	−	0.174904i
$652$	0.351226	+	0.440424i	0.0137551	+	0.0172483i
$653$	−12.9364	−	26.8628i	−0.506241	−	1.05122i	−0.984885	−	0.173212i	$-0.944586\pi$
$653$	−12.9364	−	26.8628i	−0.506241	−	1.05122i	0.478643	−	0.878010i	$-0.341129\pi$
$654$	14.8785	−	22.9627i	0.581795	−	0.897912i
$655$	3.61666			0.141315
$656$	5.85104			0.228445
$657$	−8.22985	−	10.9312i	−0.321077	−	0.426466i
$658$	−2.23802	+	14.2777i	−0.0872469	+	0.556602i
$659$	43.3209	−	9.88771i	1.68754	−	0.385171i	0.732297	−	0.680985i	$-0.238448\pi$
$659$	43.3209	−	9.88771i	1.68754	−	0.385171i	0.955245	+	0.295815i	$0.0955912\pi$
$660$	−0.0378623	+	0.298595i	−0.00147379	+	0.0116228i
$661$	20.0267	−	15.9708i	0.778950	−	0.621192i	−0.151145	−	0.988512i	$-0.548296\pi$
$661$	20.0267	−	15.9708i	0.778950	−	0.621192i	0.930095	+	0.367320i	$0.119725\pi$
$662$	−3.39472	+	2.70720i	−0.131939	+	0.105218i
$663$	1.80626	−	14.2448i	0.0701492	−	0.553221i
$664$	8.53988	−	1.94917i	0.331412	−	0.0756425i
$665$	1.93599	+	2.11128i	0.0750745	+	0.0818720i
$666$	−0.764980	−	1.01607i	−0.0296424	−	0.0393720i
$667$	4.79858			0.185802
$668$	0.866118			0.0335111
$669$	3.90025	−	6.01944i	0.150792	−	0.232725i
$670$	0.511385	+	1.06190i	0.0197565	+	0.0410248i
$671$	4.78004	+	5.99398i	0.184531	+	0.231395i
$672$	0.762582	+	4.51868i	0.0294172	+	0.174312i
$673$	−3.30569	+	4.14521i	−0.127425	+	0.159786i	−0.841451	−	0.540333i	$-0.818298\pi$
$673$	−3.30569	+	4.14521i	−0.127425	+	0.159786i	0.714026	+	0.700119i	$0.246870\pi$
$674$	−19.2532	−	4.39441i	−0.741604	−	0.169266i
$675$	−3.94139	+	25.3933i	−0.151704	+	0.977387i
$676$	10.3870	−	5.00214i	0.399502	−	0.192390i
$677$	−26.3508	−	33.0428i	−1.01274	−	1.26994i	−0.962523	−	0.271201i	$-0.912579\pi$
$677$	−26.3508	−	33.0428i	−1.01274	−	1.26994i	−0.0502202	−	0.998738i	$-0.515992\pi$
$678$	23.7342	−	23.0820i	0.911505	−	0.886461i
$679$	−9.39658	−	3.75184i	−0.360607	−	0.143982i
$680$	−0.692590	−	1.43818i	−0.0265596	−	0.0551516i
$681$	14.0204	−	13.6352i	0.537262	−	0.522500i
$682$	−1.85089	+	0.422455i	−0.0708744	+	0.0161766i
$683$	−11.3497	+	23.5679i	−0.434284	+	0.901800i	0.562880	+	0.826539i	$0.309693\pi$
$683$	−11.3497	+	23.5679i	−0.434284	+	0.901800i	−0.997164	+	0.0752611i	$0.976021\pi$
$684$	2.71579	+	13.6395i	0.103841	+	0.521518i
$685$			4.37704i			0.167238i
$686$	−17.9804	−	4.43923i	−0.686493	−	0.169491i
$687$	−3.66951	−	1.34167i	−0.140000	−	0.0511879i
$688$	−0.723146	+	0.906796i	−0.0275697	+	0.0345713i
$689$	12.6794	+	6.10606i	0.483046	+	0.232622i
$690$	0.767224	+	0.0972850i	0.0292077	+	0.00370358i
$691$	−18.1001	+	37.5852i	−0.688560	+	1.42981i	0.204042	+	0.978962i	$0.434592\pi$
$691$	−18.1001	+	37.5852i	−0.688560	+	1.42981i	−0.892601	+	0.450847i	$0.851122\pi$
$692$	18.5250	−	8.92116i	0.704214	−	0.339132i
$693$	−2.77862	−	5.21116i	−0.105551	−	0.197956i
$694$	22.4655	+	10.8188i	0.852778	+	0.410676i
$695$	2.09085	−	1.66740i	0.0793105	−	0.0632480i
$696$	0.426542	+	4.32648i	0.0161680	+	0.163995i
$697$	24.9332	−	31.2653i	0.944413	−	1.18426i
$698$	−4.44794	+	19.4877i	−0.168357	+	0.737621i
$699$	−36.9248	+	22.4902i	−1.39663	+	0.850658i
$700$	−6.47543	−	11.3698i	−0.244748	−	0.429736i
$701$	31.3391	−	24.9921i	1.18366	−	0.943937i	0.184417	−	0.982848i	$-0.440960\pi$
$701$	31.3391	−	24.9921i	1.18366	−	0.943937i	0.999243	+	0.0389109i	$0.0123888\pi$
$702$	−3.57323	+	5.19189i	−0.134863	+	0.195955i
$703$	1.91604	+	0.437324i	0.0722648	+	0.0164940i
$704$		−	0.744045i		−	0.0280422i
$705$	−0.758786	+	2.07530i	−0.0285775	+	0.0781604i
$706$	3.24031	+	0.739579i	0.121951	+	0.0278344i
$707$	14.1918	−	13.0135i	0.533736	−	0.489422i
$708$	−18.3194	−	2.32293i	−0.688486	−	0.0873010i
$709$	5.28405	+	23.1509i	0.198447	+	0.869451i	0.971862	+	0.235552i	$0.0756896\pi$
$709$	5.28405	+	23.1509i	0.198447	+	0.869451i	−0.773415	+	0.633900i	$0.781453\pi$
$710$	1.37214	+	1.72061i	0.0514954	+	0.0645732i
$711$	0.340761	−	12.2293i	0.0127796	−	0.458636i
$712$	13.7175	−	3.13093i	0.514085	−	0.117336i
$713$	1.08547	+	4.75577i	0.0406513	+	0.178105i
$714$	27.3954	+	15.1807i	1.02525	+	0.568124i
$715$	0.0469029	−	0.205495i	0.00175407	−	0.00768507i
$716$			6.27139i			0.234373i
$717$	−6.38352	−	2.33399i	−0.238397	−	0.0871643i
$718$	6.61201	−	28.9691i	0.246758	−	1.08112i
$719$	5.58243	−	2.68835i	0.208189	−	0.100259i	−0.326883	−	0.945065i	$-0.605998\pi$
$719$	5.58243	−	2.68835i	0.208189	−	0.100259i	0.535073	+	0.844806i	$0.320284\pi$
$720$	−0.0195158	+	0.700389i	−0.000727312	+	0.0261020i
$721$	31.0535	+	33.8652i	1.15649	+	1.26120i
$722$	−1.94678	−	1.55251i	−0.0724517	−	0.0577783i
$723$	−6.84193	+	10.5595i	−0.254454	+	0.392711i
$724$	12.6136	+	10.0590i	0.468781	+	0.373840i
$725$	−5.38584	−	11.1838i	−0.200025	−	0.415357i
$726$	−5.73752	−	17.1599i	−0.212939	−	0.636864i
$727$	2.65081	−	5.50446i	0.0983131	−	0.204149i	−0.846011	−	0.533165i	$-0.821003\pi$
$727$	2.65081	−	5.50446i	0.0983131	−	0.204149i	0.944324	+	0.329016i	$0.106717\pi$
$728$	−0.220986	−	3.20155i	−0.00819029	−	0.118657i
$729$	−2.25380	+	26.9058i	−0.0834739	+	0.996510i
$730$	0.959738	+	0.462185i	0.0355215	+	0.0171062i
$731$	1.76394	+	7.72832i	0.0652416	+	0.285842i
$732$	12.4427	+	12.7942i	0.459895	+	0.472888i
$733$	11.3759	+	9.07195i	0.420177	+	0.335080i	0.810647	−	0.585536i	$-0.199116\pi$
$733$	11.3759	+	9.07195i	0.420177	+	0.335080i	−0.390469	+	0.920616i	$0.627687\pi$
$734$	17.9088			0.661025
$735$	−2.56547	−	1.19868i	−0.0946287	−	0.0442141i
$736$	−1.91178			−0.0704692
$737$	2.93562	+	2.34108i	0.108135	+	0.0862347i
$738$	−16.0208	+	7.17256i	−0.589734	+	0.264026i
$739$	8.10441	+	35.5078i	0.298126	+	1.30617i	0.872915	+	0.487872i	$0.162227\pi$
$739$	8.10441	+	35.5078i	0.298126	+	1.30617i	−0.574789	+	0.818301i	$0.694916\pi$
$740$	0.0892094	+	0.0429610i	0.00327940	+	0.00157928i
$741$	−0.955540	−	9.69218i	−0.0351026	−	0.356051i
$742$	−22.6249	+	20.7464i	−0.830585	+	0.761624i
$743$	−16.3169	+	33.8823i	−0.598608	+	1.24302i	0.352976	+	0.935632i	$0.385170\pi$
$743$	−16.3169	+	33.8823i	−0.598608	+	1.24302i	−0.951584	+	0.307390i	$0.900545\pi$
$744$	−4.19140	+	1.40142i	−0.153664	+	0.0513785i
$745$	0.982818	+	2.04084i	0.0360077	+	0.0747707i
$746$	−24.6567	−	19.6631i	−0.902748	−	0.719917i
$747$	−20.9937	+	15.8058i	−0.768121	+	0.578302i
$748$	−3.97583	−	3.17062i	−0.145371	−	0.115929i
$749$	8.22231	+	27.2238i	0.300437	+	0.994737i
$750$	−1.27576	−	3.81557i	−0.0465842	−	0.139325i
$751$	45.7383	−	22.0264i	1.66902	−	0.803756i	0.670956	−	0.741498i	$-0.265884\pi$
$751$	45.7383	−	22.0264i	1.66902	−	0.803756i	0.998060	−	0.0622580i	$-0.0198302\pi$
$752$	1.21549	−	5.32540i	0.0443243	−	0.194197i
$753$	−9.07513	+	24.8208i	−0.330716	+	0.904519i
$754$		−	3.04451i		−	0.110874i
$755$	−1.17806	+	5.16143i	−0.0428741	+	0.187844i
$756$	−7.62731	−	11.4378i	−0.277403	−	0.415990i
$757$	−2.94881	−	12.9196i	−0.107176	−	0.469570i	−0.999823	−	0.0188130i	$-0.994011\pi$
$757$	−2.94881	−	12.9196i	−0.107176	−	0.469570i	0.892647	−	0.450757i	$-0.148846\pi$
$758$	26.9577	−	6.15291i	0.979147	−	0.223484i
$759$	2.33661	−	0.781258i	0.0848134	−	0.0283579i
$760$	−0.675048	−	0.846484i	−0.0244866	−	0.0307052i
$761$	5.51014	+	24.1415i	0.199742	+	0.875129i	0.971090	+	0.238714i	$0.0767260\pi$
$761$	5.51014	+	24.1415i	0.199742	+	0.875129i	−0.771347	+	0.636414i	$0.780417\pi$
$762$	0.391094	−	3.08431i	0.0141679	−	0.111733i
$763$	−20.6844	−	36.3183i	−0.748824	−	1.31481i
$764$	7.92698	+	1.80928i	0.286788	+	0.0654575i
$765$	3.65940	+	3.08888i	0.132306	+	0.111679i
$766$		−	6.94349i		−	0.250879i
$767$	12.6075	+	2.87759i	0.455232	+	0.103904i
$768$	−0.169937	−	1.72369i	−0.00613207	−	0.0621985i
$769$	6.36474	−	5.07571i	0.229519	−	0.183035i	−0.501977	−	0.864881i	$-0.667394\pi$
$769$	6.36474	−	5.07571i	0.229519	−	0.183035i	0.731496	+	0.681846i	$0.238823\pi$
$770$	0.378344	+	0.261225i	0.0136346	+	0.00941390i
$771$	18.4844	+	30.3481i	0.665701	+	1.09296i
$772$	4.28457	−	18.7719i	0.154205	−	0.675616i
$773$	2.23433	−	2.80176i	0.0803633	−	0.100772i	−0.740025	−	0.672580i	$-0.765186\pi$
$773$	2.23433	−	2.80176i	0.0803633	−	0.100772i	0.820388	+	0.571807i	$0.193758\pi$
$774$	0.868449	−	3.36939i	0.0312158	−	0.121110i
$775$	9.86574	−	7.86766i	0.354388	−	0.282615i
$776$	3.44549	+	1.65926i	0.123686	+	0.0595640i
$777$	−1.91569	+	0.323296i	−0.0687250	+	0.0115982i
$778$	24.4319	−	11.7658i	0.875925	−	0.421823i
$779$	11.7686	−	24.4378i	0.421654	−	0.875573i
$780$	0.0617235	−	0.486773i	0.00221006	−	0.0174293i
$781$	6.31670	+	3.04196i	0.226029	+	0.108850i
$782$	−8.14673	+	10.2157i	−0.291327	+	0.365312i
$783$	−6.47158	−	11.3235i	−0.231275	−	0.404669i
$784$	6.66426	+	2.14186i	0.238009	+	0.0764951i
$785$			3.84515i			0.137239i
$786$	22.9069	−	13.9521i	0.817061	−	0.497656i
$787$	10.2785	−	21.3435i	0.366389	−	0.760815i	−0.633528	−	0.773720i	$-0.718394\pi$
$787$	10.2785	−	21.3435i	0.366389	−	0.760815i	0.999917	+	0.0129053i	$0.00410799\pi$
$788$	10.2463	−	2.33866i	0.365011	−	0.0833114i
$789$	−24.6208	−	25.3164i	−0.876524	−	0.901288i
$790$	0.413248	+	0.858118i	0.0147027	+	0.0305305i
$791$	−14.6218	−	48.4123i	−0.519891	−	1.72134i
$792$	0.912095	+	2.03728i	0.0324099	+	0.0723915i
$793$	−7.79247	−	9.77145i	−0.276719	−	0.346994i
$794$	24.7061	−	11.8978i	0.876788	−	0.422239i
$795$	−4.00846	+	2.44148i	−0.142165	+	0.0865902i
$796$	−24.0785	−	5.49575i	−0.853438	−	0.194792i
$797$	29.8739	−	37.4607i	1.05819	−	1.32693i	0.115480	−	0.993310i	$-0.463159\pi$
$797$	29.8739	−	37.4607i	1.05819	−	1.32693i	0.942709	−	0.333617i	$-0.108269\pi$
$798$	20.4068	+	5.90370i	0.722392	+	0.208989i
$799$	−23.2769	−	29.1883i	−0.823477	−	1.03261i
$800$	2.14575	+	4.45570i	0.0758638	+	0.157533i
$801$	−33.7220	+	25.3886i	−1.19151	+	0.897061i
$802$	−14.7404			−0.520500
$803$	3.39355			0.119756
$804$	7.33551	+	4.75298i	0.258703	+	0.167625i
$805$	0.671203	−	0.972134i	0.0236568	−	0.0342632i
$806$	3.01735	−	0.688690i	0.106282	−	0.0242581i
$807$	−12.3675	−	1.56821i	−0.435356	−	0.0552037i
$808$	−5.68995	+	4.53759i	−0.200172	+	0.159632i
$809$	7.29382	−	5.81662i	0.256437	−	0.204502i	−0.486830	−	0.873497i	$-0.661847\pi$
$809$	7.29382	−	5.81662i	0.256437	−	0.204502i	0.743267	+	0.668995i	$0.233275\pi$
$810$	−0.805143	−	1.94167i	−0.0282899	−	0.0682233i
$811$	−35.7475	+	8.15912i	−1.25526	+	0.286506i	−0.797908	−	0.602779i	$-0.794060\pi$
$811$	−35.7475	+	8.15912i	−1.25526	+	0.286506i	−0.457355	+	0.889284i	$0.651203\pi$
$812$	6.16740	+	2.46251i	0.216433	+	0.0864170i
$813$	−1.17409	+	1.81203i	−0.0411771	+	0.0635506i
$814$	0.315437			0.0110561
$815$	0.131566			0.00460856
$816$	−9.93479	−	6.43717i	−0.347787	−	0.225346i
$817$	2.33286	+	4.84423i	0.0816164	+	0.169478i
$818$	−17.8004	−	22.3210i	−0.622376	−	0.780435i
$819$	4.52973	+	8.49530i	0.158282	+	0.296850i
$820$	0.852019	−	1.06840i	0.0297538	−	0.0373101i
$821$	53.6843	+	12.2531i	1.87359	+	0.427635i	0.998421	−	0.0561758i	$-0.0178907\pi$
$821$	53.6843	+	12.2531i	1.87359	+	0.427635i	0.875172	+	0.483811i	$0.160748\pi$
$822$	16.8855	+	27.7229i	0.588950	+	0.966948i
$823$	−49.5397	+	23.8571i	−1.72684	+	0.831605i	−0.739473	+	0.673186i	$0.764925\pi$
$823$	−49.5397	+	23.8571i	−1.72684	+	0.831605i	−0.987372	+	0.158418i	$0.949361\pi$
$824$	−10.8278	−	13.5777i	−0.377206	−	0.473001i
$825$	−4.44341	−	4.56895i	−0.154700	−	0.159070i
$826$	−16.0267	+	23.2122i	−0.557640	+	0.807655i
$827$	7.21703	+	14.9863i	0.250961	+	0.521125i	0.987949	−	0.154780i	$-0.0494670\pi$
$827$	7.21703	+	14.9863i	0.250961	+	0.521125i	−0.736988	+	0.675906i	$0.763753\pi$
$828$	5.23467	−	2.34358i	0.181917	−	0.0814449i
$829$	4.93053	−	1.12536i	0.171244	−	0.0390854i	−0.136039	−	0.990703i	$-0.543437\pi$
$829$	4.93053	−	1.12536i	0.171244	−	0.0390854i	0.307283	+	0.951618i	$0.400580\pi$
$830$	0.887645	−	1.84321i	0.0308106	−	0.0639789i
$831$	−10.5418	−	17.3077i	−0.365691	−	0.600398i
$832$			1.21295i			0.0420515i
$833$	39.8438	−	26.4836i	1.38050	−	0.917602i
$834$	6.81045	−	18.6268i	0.235827	−	0.644993i
$835$	0.126123	−	0.158153i	0.00436466	−	0.00547310i
$836$	−3.10762	−	1.49655i	−0.107479	−	0.0517592i
$837$	9.75857	−	8.97531i	0.337306	−	0.310232i
$838$	−7.34777	+	15.2578i	−0.253825	+	0.527072i
$839$	−15.4522	+	7.44140i	−0.533470	+	0.256906i	−0.681168	−	0.732127i	$-0.738528\pi$
$839$	−15.4522	+	7.44140i	−0.533470	+	0.256906i	0.147698	+	0.989032i	$0.452814\pi$
$840$	0.936155	+	0.518756i	0.0323004	+	0.0178988i
$841$	−20.4519	−	9.84911i	−0.705238	−	0.339625i
$842$	−18.9231	+	15.0907i	−0.652134	+	0.520060i
$843$	24.9283	−	2.45765i	0.858576	−	0.0846460i
$844$	−0.631462	+	0.791829i	−0.0217358	+	0.0272559i
$845$	0.599156	−	2.62508i	0.0206116	−	0.0903053i
$846$	3.20006	+	16.0716i	0.110020	+	0.552552i
$847$	−27.3052	−	4.28006i	−0.938216	−	0.147065i
$848$	9.07107	−	7.23393i	0.311502	−	0.248414i
$849$	15.7630	−	1.55406i	0.540986	−	0.0533352i
$850$	32.9530	+	7.52130i	1.13028	+	0.257978i
$851$		−	0.810498i		−	0.0277835i
$852$	15.3284	+	5.60446i	0.525142	+	0.192006i
$853$	38.6363	+	8.81848i	1.32288	+	0.301939i	0.824915	−	0.565257i	$-0.191223\pi$
$853$	38.6363	+	8.81848i	1.32288	+	0.301939i	0.497967	+	0.867196i	$0.334080\pi$
$854$	26.0973	−	7.88208i	0.893032	−	0.269719i
$855$	2.88603	+	1.49025i	0.0987001	+	0.0509656i
$856$	−2.39181	−	10.4792i	−0.0817504	−	0.358172i
$857$	−26.2313	−	32.8930i	−0.896044	−	1.12360i	−0.991749	−	0.128194i	$-0.959082\pi$
$857$	−26.2313	−	32.8930i	−0.896044	−	1.12360i	0.0957046	−	0.995410i	$-0.469490\pi$
$858$	−0.495678	−	1.48248i	−0.0169222	−	0.0506112i
$859$	47.0556	−	10.7401i	1.60552	−	0.366449i	0.676487	−	0.736455i	$-0.263501\pi$
$859$	47.0556	−	10.7401i	1.60552	−	0.366449i	0.929029	+	0.370006i	$0.120644\pi$
$860$	0.0602773	+	0.264092i	0.00205544	+	0.00900547i
$861$	−1.53320	+	26.7690i	−0.0522513	+	0.912284i
$862$	−1.89115	+	8.28566i	−0.0644127	+	0.282211i
$863$			29.9701i			1.02019i	0.860117	+	0.510096i	$0.170390\pi$
$863$			29.9701i			1.02019i	−0.860117	+	0.510096i	$0.829610\pi$
$864$	2.57832	+	4.51135i	0.0877161	+	0.153479i
$865$	1.06858	−	4.68174i	0.0363327	−	0.159184i
$866$	0.858927	−	0.413638i	0.0291875	−	0.0140560i
$867$	−48.8074	+	16.3191i	−1.65759	+	0.554224i
$868$	−1.04543	+	6.66943i	−0.0354841	+	0.226375i
$869$	2.37226	+	1.89181i	0.0804734	+	0.0641754i
$870$	0.852126	+	0.552128i	0.0288898	+	0.0187189i
$871$	−4.78568	−	3.81645i	−0.162156	−	0.129315i
$872$	6.85414	+	14.2328i	0.232111	+	0.481983i
$873$	−11.4682	−	0.319552i	−0.388139	−	0.0108152i
$874$	−3.84530	+	7.98484i	−0.130069	+	0.270091i
$875$	−6.07141	−	0.951689i	−0.205251	−	0.0321729i
$876$	7.86169	−	0.775075i	0.265622	−	0.0261874i
$877$	−13.6284	−	6.56310i	−0.460199	−	0.221620i	0.189396	−	0.981901i	$-0.439347\pi$
$877$	−13.6284	−	6.56310i	−0.460199	−	0.221620i	−0.649595	+	0.760281i	$0.725061\pi$
$878$	4.36316	+	19.1163i	0.147250	+	0.645142i
$879$	−9.98373	+	9.70942i	−0.336743	+	0.327490i
$880$	−0.135862	−	0.108347i	−0.00457992	−	0.00365236i
$881$	40.7353			1.37241			0.686204	−	0.727409i	$-0.259276\pi$
$881$	40.7353			1.37241			0.686204	+	0.727409i	$0.259276\pi$
$882$	−20.8731	+	2.30480i	−0.702835	+	0.0776067i
$883$	−9.94285			−0.334604			−0.167302	−	0.985906i	$-0.553505\pi$
$883$	−9.94285			−0.334604			−0.167302	+	0.985906i	$0.553505\pi$
$884$	6.48145	+	5.16878i	0.217995	+	0.173845i
$885$	−3.09181	+	3.00686i	−0.103930	+	0.101075i
$886$	1.37073	+	6.00557i	0.0460506	+	0.201761i
$887$	3.58295	+	1.72546i	0.120304	+	0.0579352i	0.493068	−	0.869991i	$-0.335876\pi$
$887$	3.58295	+	1.72546i	0.120304	+	0.0579352i	−0.372764	+	0.927926i	$0.621590\pi$
$888$	0.730759	−	0.0720446i	0.0245227	−	0.00241766i
$889$	−3.90807	−	2.69830i	−0.131072	−	0.0904980i
$890$	1.42581	−	2.96073i	0.0477933	−	0.0992439i
$891$	−4.99484	−	4.46020i	−0.167333	−	0.149422i
$892$	1.79675	+	3.73098i	0.0601596	+	0.124923i
$893$	−19.7975	−	15.7880i	−0.662499	−	0.528326i
$894$	14.0979	+	9.13464i	0.471505	+	0.305508i
$895$	1.14515	+	0.913230i	0.0382783	+	0.0305259i
$896$	−2.45713	−	0.981077i	−0.0820870	−	0.0327755i
$897$	−3.80916	+	1.27362i	−0.127184	+	0.0425248i
$898$	−29.3731	+	14.1453i	−0.980194	+	0.472036i
$899$	−1.42513	+	6.24392i	−0.0475308	+	0.208246i
$900$	−11.3374	−	9.56982i	−0.377913	−	0.318994i
$901$		−	79.2978i		−	2.64179i
$902$	0.968730	−	4.24428i	0.0322552	−	0.141319i
$903$	−3.95917	−	3.54606i	−0.131753	−	0.118006i
$904$	4.25338	+	18.6353i	0.141465	+	0.619799i
$905$	3.67355	−	0.838463i	0.122113	−	0.0278715i
$906$	12.4500	+	37.2357i	0.413623	+	1.23707i
$907$	17.9286	+	22.4817i	0.595308	+	0.746493i	0.984638	−	0.174605i	$-0.0558650\pi$
$907$	17.9286	+	22.4817i	0.595308	+	0.746493i	−0.389330	+	0.921098i	$0.627294\pi$
$908$	2.51258	+	11.0083i	0.0833828	+	0.365324i
$909$	10.0173	−	19.3995i	0.332252	−	0.643441i
$910$	−0.616781	−	0.425852i	−0.0204461	−	0.0141169i
$911$	−5.10850	−	1.16598i	−0.169252	−	0.0386307i	0.137055	−	0.990563i	$-0.456236\pi$
$911$	−5.10850	−	1.16598i	−0.169252	−	0.0386307i	−0.306307	+	0.951933i	$0.599093\pi$
$912$	−7.54108	−	2.75722i	−0.249710	−	0.0913006i
$913$		−	6.51746i		−	0.215696i
$914$	−9.15422	−	2.08939i	−0.302795	−	0.0691109i
$915$	4.14811	−	0.408957i	0.137132	−	0.0135197i
$916$	1.76362	−	1.40644i	0.0582718	−	0.0464702i
$917$	−2.82126	−	40.8731i	−0.0931661	−	1.34975i
$918$	35.0937	+	5.44703i	1.15826	+	0.179779i
$919$	2.70140	−	11.8356i	0.0891111	−	0.390421i	−0.910629	−	0.413225i	$-0.864402\pi$
$919$	2.70140	−	11.8356i	0.0891111	−	0.390421i	0.999740	+	0.0228040i	$0.00725935\pi$
$920$	−0.278390	+	0.349091i	−0.00917826	+	0.0115092i
$921$	−23.8519	+	2.35153i	−0.785947	+	0.0774855i
$922$	−23.6645	+	18.8718i	−0.779348	+	0.621510i
$923$	−10.2975	−	4.95904i	−0.338948	−	0.163229i
$924$	3.40406	+	0.194969i	0.111985	+	0.00641400i
$925$	−1.88899	+	0.909690i	−0.0621096	+	0.0299104i
$926$	7.87129	−	16.3449i	0.258666	−	0.537126i
$927$	46.2922	+	23.9038i	1.52043	+	0.785104i
$928$	−2.26143	−	1.08905i	−0.0742352	−	0.0357498i
$929$	−34.1840	+	42.8654i	−1.12154	+	1.40637i	−0.219022	+	0.975720i	$0.570287\pi$
$929$	−34.1840	+	42.8654i	−1.12154	+	1.40637i	−0.902520	+	0.430649i	$0.858285\pi$
$930$	−0.354446	+	0.969420i	−0.0116227	+	0.0317885i
$931$	22.3501	−	23.5262i	0.732495	−	0.771041i
$932$		−	24.9617i		−	0.817646i
$933$	23.0034	+	37.7674i	0.753098	+	1.23645i
$934$	−3.87770	+	8.05213i	−0.126882	+	0.263474i
$935$	−1.15791	+	0.264285i	−0.0378677	+	0.00864305i
$936$	−1.48691	−	3.32119i	−0.0486011	−	0.108557i
$937$	6.22444	+	12.9252i	0.203344	+	0.422247i	0.977555	−	0.210679i	$-0.0675676\pi$
$937$	6.22444	+	12.9252i	0.203344	+	0.422247i	−0.774212	+	0.632927i	$0.781853\pi$
$938$	11.6020	−	6.60769i	0.378819	−	0.215749i
$939$	−2.99762	−	3.08231i	−0.0978235	−	0.100587i
$940$	−0.795419	−	0.997424i	−0.0259437	−	0.0325324i
$941$	−36.0583	+	17.3648i	−1.17547	+	0.566075i	−0.916587	−	0.399835i	$-0.869068\pi$
$941$	−36.0583	+	17.3648i	−1.17547	+	0.566075i	−0.258880	+	0.965910i	$0.583353\pi$
$942$	14.8336	+	24.3541i	0.483306	+	0.793499i
$943$	−10.9054	−	2.48910i	−0.355130	−	0.0810562i
$944$	6.64728	−	8.33543i	0.216351	−	0.271295i
$945$	−3.19922	−	0.272816i	−0.104071	−	0.00887470i
$946$	0.538053	+	0.674697i	0.0174936	+	0.0219363i
$947$	2.01018	+	4.17418i	0.0653220	+	0.135643i	0.931074	−	0.364831i	$-0.118873\pi$
$947$	2.01018	+	4.17418i	0.0653220	+	0.135643i	−0.865752	+	0.500474i	$0.833159\pi$
$948$	5.92779	+	3.84087i	0.192526	+	0.124745i
$949$	−5.53221			−0.179583
$950$	22.9258			0.743811
$951$	−0.312972	+	0.483025i	−0.0101488	+	0.0156632i
$952$	−15.7131	+	8.94908i	−0.509264	+	0.290041i
$953$	32.3102	−	7.37459i	1.04663	−	0.238887i	0.335568	−	0.942016i	$-0.391072\pi$
$953$	32.3102	−	7.37459i	1.04663	−	0.238887i	0.711062	+	0.703129i	$0.248215\pi$
$954$	−15.9698	+	30.9272i	−0.517042	+	1.00130i
$955$	1.48469	−	1.18400i	0.0480434	−	0.0383133i
$956$	3.06802	−	2.44667i	0.0992269	−	0.0791308i
$957$	3.20900	+	0.406906i	0.103732	+	0.0131534i
$958$	29.0459	−	6.62955i	0.938432	−	0.214191i
$959$	49.4665	−	3.41441i	1.59736	−	0.110257i
$960$	−0.339492	−	0.219971i	−0.0109571	−	0.00709954i
$961$	24.4894			0.789981
$962$	−0.514229			−0.0165794
$963$	19.3951	+	25.7612i	0.624999	+	0.830144i
$964$	−3.15191	−	6.54500i	−0.101516	−	0.210800i
$965$	−2.80383	−	3.51590i	−0.0902586	−	0.113181i
$966$	0.500961	−	8.74655i	0.0161182	−	0.281415i
$967$	−2.39260	+	3.00022i	−0.0769408	+	0.0964807i	−0.818812	−	0.574061i	$-0.805367\pi$
$967$	−2.39260	+	3.00022i	−0.0769408	+	0.0964807i	0.741871	+	0.670542i	$0.233938\pi$
$968$	10.1845	+	2.32454i	0.327342	+	0.0747136i
$969$	−46.8683	+	28.5466i	−1.50563	+	0.917050i
$970$	0.804708	−	0.387527i	0.0258376	−	0.0124427i
$971$	−11.9815	−	15.0243i	−0.384503	−	0.482152i	0.551484	−	0.834185i	$-0.314062\pi$
$971$	−11.9815	−	15.0243i	−0.384503	−	0.482152i	−0.935987	+	0.352033i	$0.885490\pi$
$972$	−12.5900	−	9.19193i	−0.403825	−	0.294831i
$973$	−20.4748	−	22.3287i	−0.656394	−	0.715826i
$974$	2.49337	+	5.17753i	0.0798926	+	0.165899i
$975$	7.24370	+	7.44835i	0.231984	+	0.238538i
$976$	−10.0456	+	2.29284i	−0.321551	+	0.0733920i
$977$	−20.0870	+	41.7110i	−0.642639	+	1.33445i	0.284117	+	0.958790i	$0.408300\pi$
$977$	−20.0870	+	41.7110i	−0.642639	+	1.33445i	−0.926756	+	0.375664i	$0.877415\pi$
$978$	0.833302	−	0.507549i	0.0266461	−	0.0162296i
$979$		−	10.4689i		−	0.334587i
$980$	1.36154	−	0.904998i	0.0434929	−	0.0289091i
$981$	−36.2148	−	30.5687i	−1.15625	−	0.975984i
$982$	14.1899	−	17.7935i	0.452817	−	0.567814i
$983$	38.6138	+	18.5954i	1.23159	+	0.593101i	0.932516	−	0.361129i	$-0.117609\pi$
$983$	38.6138	+	18.5954i	1.23159	+	0.593101i	0.299072	+	0.954231i	$0.403323\pi$
$984$	1.27483	−	10.0538i	0.0406403	−	0.320503i
$985$	1.06502	−	2.21153i	0.0339343	−	0.0704653i
$986$	−15.4561	+	7.44327i	−0.492223	+	0.237042i
$987$	24.0456	+	6.95641i	0.765380	+	0.221425i
$988$	5.06607	+	2.43969i	0.161173	+	0.0776169i
$989$	1.73359	−	1.38250i	0.0551251	−	0.0439608i
$990$	0.504824	+	0.130117i	0.0160444	+	0.00413539i
$991$	−29.7133	+	37.2593i	−0.943873	+	1.18358i	0.0389892	+	0.999240i	$0.487586\pi$
$991$	−29.7133	+	37.2593i	−0.943873	+	1.18358i	−0.982863	+	0.184340i	$0.940985\pi$
$992$	0.567781	−	2.48761i	0.0180271	−	0.0789818i
$993$	3.91211	+	6.42296i	0.124147	+	0.203827i
$994$	18.3748	−	16.8492i	0.582813	−	0.534424i
$995$	−4.50979	+	3.59644i	−0.142970	+	0.114015i
$996$	−1.48856	−	15.0987i	−0.0471669	−	0.478420i
$997$	8.60138	+	1.96321i	0.272409	+	0.0621755i	0.356543	−	0.934279i	$-0.383955\pi$
$997$	8.60138	+	1.96321i	0.272409	+	0.0621755i	−0.0841343	+	0.996454i	$0.526812\pi$
$998$			34.1537i			1.08112i
$999$	−1.91258	+	1.09307i	−0.0605115	+	0.0345834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.18	yes	120
3.2	odd	2	inner	294.2.j.a.251.6	yes	120
49.41	odd	14	inner	294.2.j.a.41.6	✓	120
147.41	even	14	inner	294.2.j.a.41.18	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.6	✓	120	49.41	odd	14	inner
294.2.j.a.41.18	yes	120	147.41	even	14	inner
294.2.j.a.251.6	yes	120	3.2	odd	2	inner
294.2.j.a.251.18	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(1.24168 - 1.20757i) q^{3} +(0.222521 + 0.974928i) q^{4} +(0.210425 + 0.101335i) q^{5} +(1.72369 - 0.169937i) q^{6} +(0.981077 - 2.45713i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.0835604 - 2.99884i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(1.24168 - 1.20757i) q^{3} +(0.222521 + 0.974928i) q^{4} +(0.210425 + 0.101335i) q^{5} +(1.72369 - 0.169937i) q^{6} +(0.981077 - 2.45713i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.0835604 - 2.99884i) q^{9} +(0.101335 + 0.210425i) q^{10} +(0.581717 + 0.463904i) q^{11} +(1.45359 + 0.941844i) q^{12} +(-0.948322 - 0.756262i) q^{13} +(2.29903 - 1.30937i) q^{14} +(0.383650 - 0.128276i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.52085 + 6.66329i) q^{17} +(1.93507 - 2.29249i) q^{18} +4.63573i q^{19} +(-0.0519706 + 0.227698i) q^{20} +(-1.74896 - 4.23570i) q^{21} +(0.165565 + 0.725390i) q^{22} +(1.86385 - 0.425411i) q^{23} +(0.549234 + 1.64266i) q^{24} +(-3.08344 - 3.86651i) q^{25} +(-0.269907 - 1.18254i) q^{26} +(-3.51754 - 3.82451i) q^{27} +(2.61383 + 0.409716i) q^{28} +(2.44707 + 0.558528i) q^{29} +(0.379928 + 0.138912i) q^{30} +2.55159i q^{31} +(-0.974928 - 0.222521i) q^{32} +(1.28251 - 0.126441i) q^{33} +(-5.34354 + 4.26133i) q^{34} +(0.455437 - 0.417623i) q^{35} +(2.94224 - 0.585838i) q^{36} +(0.0943376 - 0.413320i) q^{37} +(-2.89033 + 3.62436i) q^{38} +(-2.09075 + 0.206125i) q^{39} +(-0.182600 + 0.145618i) q^{40} +(-5.27160 - 2.53867i) q^{41} +(1.27352 - 4.40206i) q^{42} +(1.04498 - 0.503234i) q^{43} +(-0.322829 + 0.670361i) q^{44} +(0.321471 - 0.622561i) q^{45} +(1.72245 + 0.829491i) q^{46} +(-3.40572 + 4.27064i) q^{47} +(-0.594775 + 1.62673i) q^{48} +(-5.07498 - 4.82127i) q^{49} -4.94545i q^{50} +(6.15795 + 10.1102i) q^{51} +(0.526279 - 1.09283i) q^{52} +(-11.3114 + 2.58176i) q^{53} +(-0.365580 - 5.18328i) q^{54} +(0.0753979 + 0.156565i) q^{55} +(1.78812 + 1.95003i) q^{56} +(5.59796 + 5.75612i) q^{57} +(1.56496 + 1.96240i) q^{58} +(-9.60560 + 4.62582i) q^{59} +(0.210430 + 0.345487i) q^{60} +(10.0456 + 2.29284i) q^{61} +(-1.59089 + 1.99491i) q^{62} +(-7.28655 - 3.14741i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-0.122914 - 0.255235i) q^{65} +(1.08154 + 0.700774i) q^{66} +5.04647 q^{67} -6.83465 q^{68} +(1.80060 - 2.77895i) q^{69} +(0.616458 - 0.0425509i) q^{70} +(9.18658 - 2.09678i) q^{71} +(2.66560 + 1.37643i) q^{72} +(3.56590 - 2.84371i) q^{73} +(0.331457 - 0.264328i) q^{74} +(-8.49773 - 1.07752i) q^{75} +(-4.51951 + 1.03155i) q^{76} +(1.71058 - 0.974230i) q^{77} +(-1.76313 - 1.14241i) q^{78} +4.07803 q^{79} -0.233554 q^{80} +(-8.98604 - 0.501168i) q^{81} +(-2.53867 - 5.27160i) q^{82} +(-5.46146 - 6.84845i) q^{83} +(3.74032 - 2.64764i) q^{84} +(-0.995250 + 1.24800i) q^{85} +(1.13076 + 0.258088i) q^{86} +(3.71295 - 2.26149i) q^{87} +(-0.670361 + 0.322829i) q^{88} +(-8.77266 - 11.0006i) q^{89} +(0.639497 - 0.286304i) q^{90} +(-2.78861 + 1.58820i) q^{91} +(0.829491 + 1.72245i) q^{92} +(3.08121 + 3.16826i) q^{93} +(-5.32540 + 1.21549i) q^{94} +(-0.469763 + 0.975473i) q^{95} +(-1.47926 + 0.900991i) q^{96} -3.82421i q^{97} +(-0.961765 - 6.93361i) q^{98} +(1.43978 - 1.70571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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