LMFDB - Embedded newform 357.2.p.a.67.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (of order $6$, degree $2$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.14
Character	$\chi$	$=$	357.67
Dual form			357.2.p.a.16.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.113439 + 0.196482i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.974263 - 1.68747i) q^{4} +(-0.103638 + 0.0598352i) q^{5} +0.226878i q^{6} +(-2.28748 - 1.32945i) q^{7} +0.895833 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.113439 + 0.196482i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.974263 - 1.68747i) q^{4} +(-0.103638 + 0.0598352i) q^{5} +0.226878i q^{6} +(-2.28748 - 1.32945i) q^{7} +0.895833 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0235130 - 0.0135753i) q^{10} +(3.73272 + 2.15509i) q^{11} +(1.68747 - 0.974263i) q^{12} +5.22378 q^{13} +(0.00172503 - 0.600260i) q^{14} -0.119670 q^{15} +(-1.84690 - 3.19893i) q^{16} +(0.947524 - 4.01275i) q^{17} +(-0.113439 + 0.196482i) q^{18} +(-1.79673 - 3.11203i) q^{19} +0.233181i q^{20} +(-1.31629 - 2.29508i) q^{21} +0.977884i q^{22} +(1.22544 - 0.707507i) q^{23} +(0.775814 + 0.447916i) q^{24} +(-2.49284 + 4.31772i) q^{25} +(0.592580 + 1.02638i) q^{26} +1.00000i q^{27} +(-4.47202 + 2.56482i) q^{28} +9.62870i q^{29} +(-0.0135753 - 0.0235130i) q^{30} +(-5.32463 - 3.07418i) q^{31} +(1.31485 - 2.27739i) q^{32} +(2.15509 + 3.73272i) q^{33} +(0.895920 - 0.269031i) q^{34} +(0.316617 + 0.000909894i) q^{35} +1.94853 q^{36} +(-2.45201 + 1.41567i) q^{37} +(0.407638 - 0.706049i) q^{38} +(4.52393 + 2.61189i) q^{39} +(-0.0928419 + 0.0536023i) q^{40} -8.26223i q^{41} +(0.301624 - 0.518977i) q^{42} -4.00310 q^{43} +(7.27331 - 4.19925i) q^{44} +(-0.103638 - 0.0598352i) q^{45} +(0.278025 + 0.160518i) q^{46} +(2.75198 + 4.76657i) q^{47} -3.69381i q^{48} +(3.46510 + 6.08219i) q^{49} -1.13114 q^{50} +(2.82696 - 3.00139i) q^{51} +(5.08934 - 8.81500i) q^{52} +(-4.71623 + 8.16874i) q^{53} +(-0.196482 + 0.113439i) q^{54} -0.515801 q^{55} +(-2.04920 - 1.19097i) q^{56} -3.59346i q^{57} +(-1.89187 + 1.09227i) q^{58} +(-4.76861 + 8.25948i) q^{59} +(-0.116590 + 0.201940i) q^{60} +(-7.84116 + 4.52710i) q^{61} -1.39492i q^{62} +(0.00760334 - 2.64574i) q^{63} -6.79099 q^{64} +(-0.541380 + 0.312566i) q^{65} +(-0.488942 + 0.846872i) q^{66} +(-2.66902 + 4.62287i) q^{67} +(-5.84828 - 5.50840i) q^{68} +1.41501 q^{69} +(0.0357378 + 0.0623126i) q^{70} -2.27301i q^{71} +(0.447916 + 0.775814i) q^{72} +(8.55939 + 4.94177i) q^{73} +(-0.556307 - 0.321184i) q^{74} +(-4.31772 + 2.49284i) q^{75} -7.00195 q^{76} +(-5.67343 - 9.89221i) q^{77} +1.18516i q^{78} +(2.63292 - 1.52012i) q^{79} +(0.382817 + 0.221020i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.62338 - 0.937258i) q^{82} +1.58106 q^{83} +(-5.15530 - 0.0148153i) q^{84} +(0.141905 + 0.472567i) q^{85} +(-0.454107 - 0.786537i) q^{86} +(-4.81435 + 8.33870i) q^{87} +(3.34390 + 1.93060i) q^{88} +(2.13643 + 3.70041i) q^{89} -0.0271505i q^{90} +(-11.9493 - 6.94479i) q^{91} -2.75719i q^{92} +(-3.07418 - 5.32463i) q^{93} +(-0.624364 + 1.08143i) q^{94} +(0.372417 + 0.215015i) q^{95} +(2.27739 - 1.31485i) q^{96} -13.0140i q^{97} +(-0.801964 + 1.37079i) q^{98} +4.31018i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.113439	+	0.196482i	0.0802134	+	0.138934i	0.903342	−	0.428922i	$-0.141106\pi$
$2$	0.113439	+	0.196482i	0.0802134	+	0.138934i	−0.823128	+	0.567856i	$0.807773\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.974263	−	1.68747i	0.487132	−	0.843737i
$5$	−0.103638	+	0.0598352i	−0.0463481	+	0.0267591i	−0.522995	−	0.852336i	$-0.675185\pi$
$5$	−0.103638	+	0.0598352i	−0.0463481	+	0.0267591i	0.476647	+	0.879095i	$0.341852\pi$
$6$			0.226878i			0.0926224i
$7$	−2.28748	−	1.32945i	−0.864585	−	0.502487i
$7$	−2.28748	−	1.32945i	−0.864585	−	0.502487i
$8$	0.895833			0.316725
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.0235130	−	0.0135753i	−0.00743548	−	0.00429288i
$11$	3.73272	+	2.15509i	1.12546	+	0.649784i	0.942789	−	0.333390i	$-0.108193\pi$
$11$	3.73272	+	2.15509i	1.12546	+	0.649784i	0.182670	+	0.983174i	$0.441526\pi$
$12$	1.68747	−	0.974263i	0.487132	−	0.281246i
$13$	5.22378			1.44882			0.724409	−	0.689371i	$-0.242113\pi$
$13$	5.22378			1.44882			0.724409	+	0.689371i	$0.242113\pi$
$14$	0.00172503	−	0.600260i	0.000461033	−	0.160426i
$15$	−0.119670			−0.0308987
$16$	−1.84690	−	3.19893i	−0.461726	−	0.799733i
$17$	0.947524	−	4.01275i	0.229808	−	0.973236i
$17$	0.947524	−	4.01275i	0.229808	−	0.973236i
$18$	−0.113439	+	0.196482i	−0.0267378	+	0.0463112i
$19$	−1.79673	−	3.11203i	−0.412198	−	0.713948i	0.582932	−	0.812521i	$-0.301905\pi$
$19$	−1.79673	−	3.11203i	−0.412198	−	0.713948i	−0.995130	+	0.0985733i	$0.968572\pi$
$20$			0.233181i			0.0521408i
$21$	−1.31629	−	2.29508i	−0.287237	−	0.500828i
$22$			0.977884i			0.208485i
$23$	1.22544	−	0.707507i	0.255521	−	0.147525i	−0.366768	−	0.930312i	$-0.619536\pi$
$23$	1.22544	−	0.707507i	0.255521	−	0.147525i	0.622290	+	0.782787i	$0.286203\pi$
$24$	0.775814	+	0.447916i	0.158362	+	0.0914305i
$25$	−2.49284	+	4.31772i	−0.498568	+	0.863545i
$26$	0.592580	+	1.02638i	0.116215	+	0.201289i
$27$			1.00000i			0.192450i
$28$	−4.47202	+	2.56482i	−0.845133	+	0.484705i
$29$			9.62870i			1.78801i	0.448062	+	0.894003i	$0.352115\pi$
$29$			9.62870i			1.78801i	−0.448062	+	0.894003i	$0.647885\pi$
$30$	−0.0135753	−	0.0235130i	−0.00247849	−	0.00429288i
$31$	−5.32463	−	3.07418i	−0.956332	−	0.552139i	−0.0612899	−	0.998120i	$-0.519521\pi$
$31$	−5.32463	−	3.07418i	−0.956332	−	0.552139i	−0.895042	+	0.445981i	$0.852855\pi$
$32$	1.31485	−	2.27739i	0.232436	−	0.402590i
$33$	2.15509	+	3.73272i	0.375153	+	0.649784i
$34$	0.895920	−	0.269031i	0.153649	−	0.0461384i
$35$	0.316617		0.000909894i	0.0535180		0.000153800i
$36$	1.94853			0.324754
$37$	−2.45201	+	1.41567i	−0.403109	+	0.232735i	−0.687824	−	0.725877i	$-0.741434\pi$
$37$	−2.45201	+	1.41567i	−0.403109	+	0.232735i	0.284716	+	0.958612i	$0.408101\pi$
$38$	0.407638	−	0.706049i	0.0661276	−	0.114536i
$39$	4.52393	+	2.61189i	0.724409	+	0.418237i
$40$	−0.0928419	+	0.0536023i	−0.0146796	+	0.00847527i
$41$		−	8.26223i		−	1.29034i	−0.764038	−	0.645172i	$-0.776786\pi$
$41$		−	8.26223i		−	1.29034i	0.764038	−	0.645172i	$-0.223214\pi$
$42$	0.301624	−	0.518977i	0.0465415	−	0.0800800i
$43$	−4.00310			−0.610467			−0.305234	−	0.952277i	$-0.598735\pi$
$43$	−4.00310			−0.610467			−0.305234	+	0.952277i	$0.598735\pi$
$44$	7.27331	−	4.19925i	1.09649	−	0.633061i
$45$	−0.103638	−	0.0598352i	−0.0154494	−	0.00891970i
$46$	0.278025	+	0.160518i	0.0409925	+	0.0236670i
$47$	2.75198	+	4.76657i	0.401418	+	0.695276i	0.993897	−	0.110309i	$-0.0351841\pi$
$47$	2.75198	+	4.76657i	0.401418	+	0.695276i	−0.592479	+	0.805586i	$0.701851\pi$
$48$		−	3.69381i		−	0.533155i
$49$	3.46510	+	6.08219i	0.495014	+	0.868885i
$50$	−1.13114			−0.159967
$51$	2.82696	−	3.00139i	0.395853	−	0.420278i
$52$	5.08934	−	8.81500i	0.705765	−	1.22242i
$53$	−4.71623	+	8.16874i	−0.647823	+	1.12206i	0.335818	+	0.941927i	$0.390987\pi$
$53$	−4.71623	+	8.16874i	−0.647823	+	1.12206i	−0.983642	+	0.180136i	$0.942346\pi$
$54$	−0.196482	+	0.113439i	−0.0267378	+	0.0154371i
$55$	−0.515801			−0.0695505
$56$	−2.04920	−	1.19097i	−0.273835	−	0.159150i
$57$		−	3.59346i		−	0.475965i
$58$	−1.89187	+	1.09227i	−0.248414	+	0.143422i
$59$	−4.76861	+	8.25948i	−0.620821	+	1.07529i	0.368513	+	0.929623i	$0.379867\pi$
$59$	−4.76861	+	8.25948i	−0.620821	+	1.07529i	−0.989333	+	0.145670i	$0.953466\pi$
$60$	−0.116590	+	0.201940i	−0.0150518	+	0.0260704i
$61$	−7.84116	+	4.52710i	−1.00396	+	0.579635i	−0.909417	−	0.415885i	$-0.863472\pi$
$61$	−7.84116	+	4.52710i	−1.00396	+	0.579635i	−0.0945411	+	0.995521i	$0.530138\pi$
$62$		−	1.39492i		−	0.177156i
$63$	0.00760334	−	2.64574i	0.000957931	−	0.333332i
$64$	−6.79099			−0.848874
$65$	−0.541380	+	0.312566i	−0.0671499	+	0.0387690i
$66$	−0.488942	+	0.846872i	−0.0601846	+	0.104243i
$67$	−2.66902	+	4.62287i	−0.326072	+	0.564774i	−0.981729	−	0.190285i	$-0.939059\pi$
$67$	−2.66902	+	4.62287i	−0.326072	+	0.564774i	0.655656	+	0.755059i	$0.272392\pi$
$68$	−5.84828	−	5.50840i	−0.709208	−	0.667992i
$69$	1.41501			0.170348
$70$	0.0357378	+	0.0623126i	0.00427149	+	0.00744778i
$71$		−	2.27301i		−	0.269756i	−0.990862	−	0.134878i	$-0.956936\pi$
$71$		−	2.27301i		−	0.269756i	0.990862	−	0.134878i	$-0.0430643\pi$
$72$	0.447916	+	0.775814i	0.0527874	+	0.0914305i
$73$	8.55939	+	4.94177i	1.00180	+	0.578390i	0.908781	−	0.417274i	$-0.137015\pi$
$73$	8.55939	+	4.94177i	1.00180	+	0.578390i	0.0930201	+	0.995664i	$0.470348\pi$
$74$	−0.556307	−	0.321184i	−0.0646694	−	0.0373369i
$75$	−4.31772	+	2.49284i	−0.498568	+	0.287848i
$76$	−7.00195			−0.803179
$77$	−5.67343	−	9.89221i	−0.646547	−	1.12732i
$78$			1.18516i			0.134193i
$79$	2.63292	−	1.52012i	0.296227	−	0.171027i	−0.344520	−	0.938779i	$-0.611958\pi$
$79$	2.63292	−	1.52012i	0.296227	−	0.171027i	0.640747	+	0.767752i	$0.278625\pi$
$80$	0.382817	+	0.221020i	0.0428003	+	0.0247107i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.62338	−	0.937258i	0.179272	−	0.103503i
$83$	1.58106			0.173544			0.0867718	−	0.996228i	$-0.472345\pi$
$83$	1.58106			0.173544			0.0867718	+	0.996228i	$0.472345\pi$
$84$	−5.15530	−	0.0148153i	−0.562489	−	0.00161648i
$85$	0.141905	+	0.472567i	0.0153917	+	0.0512571i
$86$	−0.454107	−	0.786537i	−0.0489677	−	0.0848145i
$87$	−4.81435	+	8.33870i	−0.516153	+	0.894003i
$88$	3.34390	+	1.93060i	0.356461	+	0.205803i
$89$	2.13643	+	3.70041i	0.226461	+	0.392242i	0.956757	−	0.290889i	$-0.0939510\pi$
$89$	2.13643	+	3.70041i	0.226461	+	0.392242i	−0.730296	+	0.683131i	$0.760618\pi$
$90$		−	0.0271505i		−	0.00286192i
$91$	−11.9493	−	6.94479i	−1.25263	−	0.728011i
$92$		−	2.75719i		−	0.287457i
$93$	−3.07418	−	5.32463i	−0.318777	−	0.552139i
$94$	−0.624364	+	1.08143i	−0.0643982	+	0.111541i
$95$	0.372417	+	0.215015i	0.0382092	+	0.0220601i
$96$	2.27739	−	1.31485i	0.232436	−	0.134197i
$97$		−	13.0140i		−	1.32137i	−0.750662	−	0.660687i	$-0.770265\pi$
$97$		−	13.0140i		−	1.32137i	0.750662	−	0.660687i	$-0.229735\pi$
$98$	−0.801964	+	1.37079i	−0.0810106	+	0.138470i
$99$			4.31018i			0.433189i
$100$	4.85736	+	8.41320i	0.485736	+	0.841320i
$101$	−5.18235	+	8.97609i	−0.515663	+	0.893154i	0.484172	+	0.874973i	$0.339121\pi$
$101$	−5.18235	+	8.97609i	−0.515663	+	0.893154i	−0.999835	+	0.0181812i	$0.994212\pi$
$102$	0.910405	+	0.214972i	0.0901435	+	0.0212854i
$103$	−8.58152	−	14.8636i	−0.845563	−	1.46456i	−0.885132	−	0.465341i	$-0.845932\pi$
$103$	−8.58152	−	14.8636i	−0.845563	−	1.46456i	0.0395688	−	0.999217i	$-0.487402\pi$
$104$	4.67964			0.458876
$105$	0.273743	+	0.159096i	0.0267146	+	0.0155262i
$106$	−2.14001			−0.207856
$107$	−1.38873	+	0.801783i	−0.134253	+	0.0775113i	−0.565622	−	0.824664i	$-0.691364\pi$
$107$	−1.38873	+	0.801783i	−0.134253	+	0.0775113i	0.431369	+	0.902176i	$0.358031\pi$
$108$	1.68747	+	0.974263i	0.162377	+	0.0937485i
$109$	−3.19828	−	1.84653i	−0.306340	−	0.176866i	0.338947	−	0.940805i	$-0.389929\pi$
$109$	−3.19828	−	1.84653i	−0.306340	−	0.176866i	−0.645288	+	0.763940i	$0.723262\pi$
$110$	−0.0585118	−	0.101345i	−0.00557888	−	0.00966291i
$111$	−2.83134			−0.268739
$112$	−0.0280853	+	9.77286i	−0.00265381	+	0.923448i
$113$		−	9.27139i		−	0.872179i	−0.899903	−	0.436090i	$-0.856363\pi$
$113$		−	9.27139i		−	0.872179i	0.899903	−	0.436090i	$-0.143637\pi$
$114$	0.706049	−	0.407638i	0.0661276	−	0.0381788i
$115$	−0.0846676	+	0.146649i	−0.00789529	+	0.0136750i
$116$	16.2482	+	9.38089i	1.50861	+	0.870994i
$117$	2.61189	+	4.52393i	0.241470	+	0.418237i
$118$	−2.16378			−0.199192
$119$	−7.50222	+	7.91939i	−0.687727	+	0.725969i
$120$	−0.107205			−0.00978639
$121$	3.78882	+	6.56243i	0.344438	+	0.596585i
$122$	−1.77899	−	1.02710i	−0.161062	−	0.0929890i
$123$	4.13112	−	7.15530i	0.372490	−	0.645172i
$124$	−10.3752	+	5.99012i	−0.931719	+	0.537928i
$125$		−	1.19499i		−	0.106883i
$126$	0.520703	−	0.298636i	0.0463879	−	0.0266046i
$127$	12.4278			1.10279			0.551395	−	0.834244i	$-0.314096\pi$
$127$	12.4278			1.10279			0.551395	+	0.834244i	$0.314096\pi$
$128$	−3.40007	−	5.88910i	−0.300527	−	0.520527i
$129$	−3.46679	−	2.00155i	−0.305234	−	0.176227i
$130$	−0.122827	−	0.0709142i	−0.0107726	−	0.00621959i
$131$	−4.86357	+	2.80798i	−0.424932	+	0.245335i	−0.697185	−	0.716891i	$-0.745565\pi$
$131$	−4.86357	+	2.80798i	−0.424932	+	0.245335i	0.272253	+	0.962226i	$0.412231\pi$
$132$	8.39850			0.730995
$133$	−0.0273223	+	9.50736i	−0.00236914	+	0.824392i
$134$	−1.21108			−0.104621
$135$	−0.0598352	−	0.103638i	−0.00514979	−	0.00891970i
$136$	0.848823	−	3.59476i	0.0727860	−	0.308248i
$137$	8.70427	−	15.0762i	0.743656	−	1.28805i	−0.207164	−	0.978306i	$-0.566423\pi$
$137$	8.70427	−	15.0762i	0.743656	−	1.28805i	0.950820	−	0.309744i	$-0.100243\pi$
$138$	0.160518	+	0.278025i	0.0136642	+	0.0236670i
$139$		−	17.1547i		−	1.45504i	−0.686087	−	0.727520i	$-0.740673\pi$
$139$		−	17.1547i		−	1.45504i	0.686087	−	0.727520i	$-0.259327\pi$
$140$	0.310003	−	0.533396i	0.0262001	−	0.0450802i
$141$			5.50397i			0.463518i
$142$	0.446605	−	0.257847i	0.0374782	−	0.0216381i
$143$	19.4989	+	11.2577i	1.63058	+	0.941418i
$144$	1.84690	−	3.19893i	0.153909	−	0.266578i
$145$	−0.576135	−	0.997895i	−0.0478454	−	0.0828707i
$146$			2.24235i			0.185578i
$147$	−0.0402329	+	6.99988i	−0.00331836	+	0.577341i
$148$			5.51695i			0.453490i
$149$	11.6019	+	20.0951i	0.950466	+	1.64626i	0.744418	+	0.667714i	$0.232727\pi$
$149$	11.6019	+	20.0951i	0.950466	+	1.64626i	0.206048	+	0.978542i	$0.433940\pi$
$150$	−0.979596	−	0.565570i	−0.0799836	−	0.0461786i
$151$	−6.96011	+	12.0553i	−0.566406	+	0.981044i	0.430511	+	0.902585i	$0.358333\pi$
$151$	−6.96011	+	12.0553i	−0.566406	+	0.981044i	−0.996917	+	0.0784587i	$0.975000\pi$
$152$	−1.60957	−	2.78785i	−0.130553	−	0.226125i
$153$	3.94891	−	1.18580i	0.319250	−	0.0958660i
$154$	1.30005	−	2.23689i	0.104761	−	0.180253i
$155$	0.735776			0.0590989
$156$	8.81500	−	5.08934i	0.705765	−	0.407473i
$157$	6.38886	−	11.0658i	0.509887	−	0.883150i	−0.490048	−	0.871696i	$-0.663021\pi$
$157$	6.38886	−	11.0658i	0.509887	−	0.883150i	0.999934	−	0.0114541i	$-0.00364605\pi$
$158$	0.597352	+	0.344881i	0.0475228	+	0.0274373i
$159$	−8.16874	+	4.71623i	−0.647823	+	0.374021i
$160$			0.314698i			0.0248791i
$161$	−3.74376	−	0.0107588i	−0.295050	−	0.000847915i
$162$	−0.226878			−0.0178252
$163$	17.8882	−	10.3278i	1.40111	−	0.808932i	0.406605	−	0.913604i	$-0.366713\pi$
$163$	17.8882	−	10.3278i	1.40111	−	0.808932i	0.994507	+	0.104672i	$0.0333792\pi$
$164$	−13.9423	−	8.04959i	−1.08871	−	0.628567i
$165$	−0.446696	−	0.257900i	−0.0347753	−	0.0200775i
$166$	0.179353	+	0.310649i	0.0139205	+	0.0241110i
$167$		−	4.63395i		−	0.358586i	−0.983796	−	0.179293i	$-0.942619\pi$
$167$		−	4.63395i		−	0.358586i	0.983796	−	0.179293i	$-0.0573810\pi$
$168$	−1.17917	−	2.05601i	−0.0909751	−	0.158624i
$169$	14.2879			1.09907
$170$	−0.0767534	+	0.0814892i	−0.00588672	+	0.00624994i
$171$	1.79673	−	3.11203i	0.137399	−	0.237983i
$172$	−3.90008	+	6.75513i	−0.297378	+	0.515074i
$173$	−18.7206	+	10.8084i	−1.42330	+	0.821744i	−0.996580	−	0.0826382i	$-0.973665\pi$
$173$	−18.7206	+	10.8084i	−1.42330	+	0.821744i	−0.426723	+	0.904382i	$0.640332\pi$
$174$	−2.18454			−0.165609
$175$	11.4425	−	6.56258i	0.864974	−	0.496084i
$176$		−	15.9210i		−	1.20009i
$177$	−8.25948	+	4.76861i	−0.620821	+	0.358431i
$178$	−0.484708	+	0.839540i	−0.0363304	+	0.0629261i
$179$	1.47478	−	2.55439i	0.110230	−	0.190924i	−0.805633	−	0.592415i	$-0.798175\pi$
$179$	1.47478	−	2.55439i	0.110230	−	0.190924i	0.915863	+	0.401491i	$0.131508\pi$
$180$	−0.201940	+	0.116590i	−0.0150518	+	0.00869013i
$181$		−	1.25305i		−	0.0931383i	−0.998915	−	0.0465691i	$-0.985171\pi$
$181$		−	1.25305i		−	0.0931383i	0.998915	−	0.0465691i	$-0.0148288\pi$
$182$	0.00901118	−	3.13563i	0.000667953	−	0.232428i
$183$	−9.05420			−0.669305
$184$	1.09779	−	0.633808i	0.0809299	−	0.0467249i
$185$	0.169414	−	0.293433i	0.0124556	−	0.0215736i
$186$	0.697462	−	1.20804i	0.0511404	−	0.0885778i
$187$	12.1847	−	12.9365i	0.891033	−	0.946011i
$188$	10.7246			0.782174
$189$	1.32945	−	2.28748i	0.0967036	−	0.166389i
$190$			0.0975643i			0.00707806i
$191$	−12.5310	−	21.7043i	−0.906712	−	1.57047i	−0.818603	−	0.574360i	$-0.805251\pi$
$191$	−12.5310	−	21.7043i	−0.906712	−	1.57047i	−0.0881093	−	0.996111i	$-0.528082\pi$
$192$	−5.88117	−	3.39550i	−0.424437	−	0.245049i
$193$	15.5498	+	8.97767i	1.11930	+	0.646227i	0.941222	−	0.337790i	$-0.109679\pi$
$193$	15.5498	+	8.97767i	1.11930	+	0.646227i	0.178076	+	0.984017i	$0.443013\pi$
$194$	2.55702	−	1.47630i	0.183583	−	0.105992i
$195$	−0.625132			−0.0447666
$196$	13.6395	+	0.0783949i	0.974247	+	0.00559964i
$197$			23.8247i			1.69744i	0.528843	+	0.848720i	$0.322626\pi$
$197$			23.8247i			1.69744i	−0.528843	+	0.848720i	$0.677374\pi$
$198$	−0.846872	+	0.488942i	−0.0601846	+	0.0347476i
$199$	9.20203	+	5.31279i	0.652314	+	0.376614i	0.789342	−	0.613953i	$-0.210422\pi$
$199$	9.20203	+	5.31279i	0.652314	+	0.376614i	−0.137028	+	0.990567i	$0.543755\pi$
$200$	−2.23317	+	3.86796i	−0.157909	+	0.273506i
$201$	−4.62287	+	2.66902i	−0.326072	+	0.188258i
$202$	−2.35152			−0.165452
$203$	12.8009	−	22.0254i	0.898449	−	1.54588i
$204$	−2.31056	−	7.69455i	−0.161771	−	0.538727i
$205$	0.494372	+	0.856277i	0.0345284	+	0.0598050i
$206$	1.94696	−	3.37223i	0.135651	−	0.234954i
$207$	1.22544	+	0.707507i	0.0851738	+	0.0491751i
$208$	−9.64783	−	16.7105i	−0.668957	−	1.15867i
$209$		−	15.4884i		−	1.07136i
$210$	−0.000206435		0.0718332i	−1.42453e−5		0.00495696i
$211$			4.88194i			0.336087i	0.985780	+	0.168043i	$0.0537448\pi$
$211$			4.88194i			0.336087i	−0.985780	+	0.168043i	$0.946255\pi$
$212$	9.18969	+	15.9170i	0.631151	+	1.09318i
$213$	1.13650	−	1.96848i	0.0778719	−	0.134878i
$214$	−0.315072	−	0.181907i	−0.0215378	−	0.0124349i
$215$	0.414872	−	0.239526i	0.0282940	−	0.0163356i
$216$			0.895833i			0.0609537i
$217$	8.09299	+	14.1110i	0.549388	+	0.957915i
$218$		−	0.837873i		−	0.0567479i
$219$	4.94177	+	8.55939i	0.333934	+	0.578390i
$220$	−0.502525	+	0.870400i	−0.0338803	+	0.0586823i
$221$	4.94966	−	20.9618i	0.332950	−	1.41004i
$222$	−0.321184	−	0.556307i	−0.0215565	−	0.0373369i
$223$	1.97588			0.132315			0.0661574	−	0.997809i	$-0.478926\pi$
$223$	1.97588			0.132315			0.0661574	+	0.997809i	$0.478926\pi$
$224$	−6.03539	+	3.46145i	−0.403257	+	0.231278i
$225$	−4.98568			−0.332379
$226$	1.82166	−	1.05174i	0.121175	−	0.0699604i
$227$	8.28358	+	4.78253i	0.549800	+	0.317427i	0.749042	−	0.662523i	$-0.230514\pi$
$227$	8.28358	+	4.78253i	0.549800	+	0.317427i	−0.199241	+	0.979951i	$0.563848\pi$
$228$	−6.06386	−	3.50097i	−0.401589	−	0.231858i
$229$	3.82356	+	6.62260i	0.252668	+	0.437634i	0.964260	−	0.264960i	$-0.0853586\pi$
$229$	3.82356	+	6.62260i	0.252668	+	0.437634i	−0.711592	+	0.702593i	$0.752025\pi$
$230$	−0.0384184			−0.00253323
$231$	0.0327718	−	11.4036i	0.00215622	−	0.750303i
$232$			8.62571i			0.566305i
$233$	−5.57572	+	3.21914i	−0.365277	+	0.210893i	−0.671393	−	0.741101i	$-0.734304\pi$
$233$	−5.57572	+	3.21914i	−0.365277	+	0.210893i	0.306116	+	0.951994i	$0.400970\pi$
$234$	−0.592580	+	1.02638i	−0.0387382	+	0.0670965i
$235$	−0.570417	−	0.329331i	−0.0372099	−	0.0214832i
$236$	9.29177	+	16.0938i	0.604843	+	1.04762i
$237$	3.04024			0.197485
$238$	−2.40706	−	0.575683i	−0.156026	−	0.0373160i
$239$	−23.0422			−1.49048			−0.745239	−	0.666797i	$-0.767665\pi$
$239$	−23.0422			−1.49048			−0.745239	+	0.666797i	$0.767665\pi$
$240$	0.221020	+	0.382817i	0.0142668	+	0.0247107i
$241$	11.7978	+	6.81145i	0.759961	+	0.438764i	0.829282	−	0.558831i	$-0.188750\pi$
$241$	11.7978	+	6.81145i	0.759961	+	0.438764i	−0.0693205	+	0.997594i	$0.522083\pi$
$242$	−0.859600	+	1.48887i	−0.0552572	+	0.0957082i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$			17.6423i			1.12944i
$245$	−0.723043	−	0.423009i	−0.0461935	−	0.0270250i
$246$	1.87452			0.119515
$247$	−9.38572	−	16.2566i	−0.597199	−	1.03438i
$248$	−4.76998	−	2.75395i	−0.302894	−	0.174876i
$249$	1.36924	+	0.790529i	0.0867718	+	0.0500977i
$250$	0.234794	−	0.135558i	0.0148497	−	0.00857345i
$251$	−22.0330			−1.39071			−0.695356	−	0.718666i	$-0.744753\pi$
$251$	−22.0330			−1.39071			−0.695356	+	0.718666i	$0.744753\pi$
$252$	−4.45721	−	2.59048i	−0.280778	−	0.163185i
$253$	6.09896			0.383438
$254$	1.40980	+	2.44184i	0.0884586	+	0.153215i
$255$	−0.113391	+	0.480208i	−0.00710079	+	0.0300718i
$256$	−6.01959	+	10.4262i	−0.376225	+	0.651640i
$257$	4.99662	+	8.65440i	0.311680	+	0.539846i	0.978726	−	0.205170i	$-0.0657748\pi$
$257$	4.99662	+	8.65440i	0.311680	+	0.539846i	−0.667046	+	0.745017i	$0.732441\pi$
$258$		−	0.908215i		−	0.0565430i
$259$	7.49100	+	0.0215277i	0.465468	+	0.00133766i
$260$			1.21809i			0.0755425i
$261$	−8.33870	+	4.81435i	−0.516153	+	0.298001i
$262$	−1.10344	−	0.637069i	−0.0681705	−	0.0393583i
$263$	4.54049	−	7.86436i	0.279979	−	0.484937i	−0.691400	−	0.722472i	$-0.743006\pi$
$263$	4.54049	−	7.86436i	0.279979	−	0.484937i	0.971379	+	0.237535i	$0.0763393\pi$
$264$	1.93060	+	3.34390i	0.118820	+	0.205803i
$265$		−	1.12878i		−	0.0693407i
$266$	−1.87112	+	1.07314i	−0.114726	+	0.0657981i
$267$			4.27286i			0.261495i
$268$	5.20065	+	9.00779i	0.317680	+	0.550238i
$269$	1.69737	+	0.979976i	0.103490	+	0.0597502i	0.550852	−	0.834603i	$-0.314303\pi$
$269$	1.69737	+	0.979976i	0.103490	+	0.0597502i	−0.447361	+	0.894353i	$0.647636\pi$
$270$	0.0135753	−	0.0235130i	0.000826164	−	0.00143096i
$271$	−1.96090	−	3.39638i	−0.119116	−	0.206315i	0.800302	−	0.599598i	$-0.204673\pi$
$271$	−1.96090	−	3.39638i	−0.119116	−	0.206315i	−0.919418	+	0.393283i	$0.871339\pi$
$272$	−14.5865	+	4.38011i	−0.884437	+	0.265583i
$273$	−6.87599	−	11.9890i	−0.416154	−	0.725607i
$274$	3.94961			0.238605
$275$	−18.6102	+	10.7446i	−1.12224	+	0.647923i
$276$	1.37860	−	2.38780i	0.0829817	−	0.143729i
$277$	−5.86738	−	3.38753i	−0.352537	−	0.203537i	0.313265	−	0.949666i	$-0.398577\pi$
$277$	−5.86738	−	3.38753i	−0.352537	−	0.203537i	−0.665802	+	0.746129i	$0.731910\pi$
$278$	3.37058	−	1.94600i	0.202154	−	0.116714i
$279$		−	6.14836i		−	0.368092i
$280$	0.283635		0.000815113i	0.0169505		4.87123e-5i
$281$	15.3118			0.913425			0.456712	−	0.889614i	$-0.349027\pi$
$281$	15.3118			0.913425			0.456712	+	0.889614i	$0.349027\pi$
$282$	−1.08143	+	0.624364i	−0.0643982	+	0.0371803i
$283$	9.83031	+	5.67553i	0.584351	+	0.337375i	0.762861	−	0.646563i	$-0.223794\pi$
$283$	9.83031	+	5.67553i	0.584351	+	0.337375i	−0.178509	+	0.983938i	$0.557128\pi$
$284$	−3.83564	−	2.21451i	−0.227603	−	0.131407i
$285$	0.215015	+	0.372417i	0.0127364	+	0.0220601i
$286$			5.10825i			0.302057i
$287$	−10.9843	+	18.8997i	−0.648381	+	1.11561i
$288$	2.62971			0.154957
$289$	−15.2044	−	7.60436i	−0.894376	−	0.447316i
$290$	0.130712	−	0.226400i	0.00767568	−	0.0132947i
$291$	6.50701	−	11.2705i	0.381448	−	0.660687i
$292$	16.6782	−	9.62916i	0.976018	−	0.563504i
$293$	18.4766			1.07941			0.539707	−	0.841853i	$-0.318535\pi$
$293$	18.4766			1.07941			0.539707	+	0.841853i	$0.318535\pi$
$294$	−1.37991	+	0.786154i	−0.0804782	+	0.0458494i
$295$		−	1.14132i		−	0.0664504i
$296$	−2.19659	+	1.26820i	−0.127674	+	0.0737129i
$297$	−2.15509	+	3.73272i	−0.125051	+	0.216595i
$298$	−2.63222	+	4.55913i	−0.152480	+	0.264103i
$299$	6.40142	−	3.69586i	0.370204	−	0.213737i
$300$			9.71473i			0.560880i
$301$	9.15700	+	5.32194i	0.527801	+	0.306752i
$302$	−3.15819			−0.181733
$303$	−8.97609	+	5.18235i	−0.515663	+	0.297718i
$304$	−6.63677	+	11.4952i	−0.380645	+	0.659297i
$305$	0.541759	−	0.938354i	0.0310210	−	0.0537300i
$306$	0.680947	+	0.641374i	0.0389272	+	0.0366649i
$307$	2.97735			0.169926			0.0849631	−	0.996384i	$-0.472923\pi$
$307$	2.97735			0.169926			0.0849631	+	0.996384i	$0.472923\pi$
$308$	−22.2202	−	0.0638566i	−1.26612	−	0.00363857i
$309$		−	17.1630i		−	0.976372i
$310$	0.0834655	+	0.144567i	0.00474052	+	0.00821083i
$311$	−29.0675	−	16.7822i	−1.64827	−	0.951629i	−0.977760	−	0.209728i	$-0.932742\pi$
$311$	−29.0675	−	16.7822i	−1.64827	−	0.951629i	−0.670509	−	0.741901i	$-0.733924\pi$
$312$	4.05268	+	2.33982i	0.229438	+	0.132466i
$313$	21.1646	−	12.2194i	1.19629	−	0.690681i	0.236567	−	0.971615i	$-0.423978\pi$
$313$	21.1646	−	12.2194i	1.19629	−	0.690681i	0.959727	+	0.280934i	$0.0906443\pi$
$314$	2.89898			0.163599
$315$	0.157520	+	0.274653i	0.00887526	+	0.0154749i
$316$		−	5.92399i		−	0.333250i
$317$	15.5925	−	9.00232i	0.875760	−	0.505620i	0.00650207	−	0.999979i	$-0.497930\pi$
$317$	15.5925	−	9.00232i	0.875760	−	0.505620i	0.869258	+	0.494358i	$0.164597\pi$
$318$	−1.85331	−	1.07001i	−0.103928	−	0.0600030i
$319$	−20.7507	+	35.9413i	−1.16182	+	2.01233i
$320$	0.703802	−	0.406340i	0.0393437	−	0.0227151i
$321$	−1.60357			−0.0895023
$322$	−0.422574	−	0.736801i	−0.0235491	−	0.0410603i
$323$	−14.1902	+	4.26111i	−0.789566	+	0.237095i
$324$	0.974263	+	1.68747i	0.0541257	+	0.0937485i
$325$	−13.0221	+	22.5549i	−0.722334	+	1.25112i
$326$	4.05843	+	2.34314i	0.224776	+	0.129774i
$327$	−1.84653	−	3.19828i	−0.102113	−	0.176866i
$328$		−	7.40158i		−	0.408684i
$329$	0.0418485	−	14.5621i	0.00230718	−	0.802833i
$330$		−	0.117024i		−	0.00644194i
$331$	−11.3004	−	19.5728i	−0.621125	−	1.07582i	−0.989277	−	0.146054i	$-0.953343\pi$
$331$	−11.3004	−	19.5728i	−0.621125	−	1.07582i	0.368152	−	0.929766i	$-0.379991\pi$
$332$	1.54037	−	2.66799i	0.0845386	−	0.146425i
$333$	−2.45201	−	1.41567i	−0.134370	−	0.0775783i
$334$	0.910488	−	0.525671i	0.0498197	−	0.0287634i
$335$		−	0.638804i		−	0.0349016i
$336$	−4.91075	+	8.44950i	−0.267903	+	0.460958i
$337$		−	17.3246i		−	0.943731i	−0.881670	−	0.471866i	$-0.843581\pi$
$337$		−	17.3246i		−	0.943731i	0.881670	−	0.471866i	$-0.156419\pi$
$338$	1.62081	+	2.80732i	0.0881602	+	0.152698i
$339$	4.63570	−	8.02926i	0.251776	−	0.436090i
$340$	0.935697	+	0.220944i	0.0507453	+	0.0119824i
$341$	−13.2503	−	22.9501i	−0.717542	−	1.24282i
$342$	0.815276			0.0440851
$343$	0.159668	−	18.5196i	0.00862128	−	0.999963i
$344$	−3.58611			−0.193350
$345$	−0.146649	+	0.0846676i	−0.00789529	+	0.00455835i
$346$	−4.24729	−	2.45218i	−0.228336	−	0.131830i
$347$	−4.22355	−	2.43847i	−0.226732	−	0.130904i	0.382332	−	0.924025i	$-0.375121\pi$
$347$	−4.22355	−	2.43847i	−0.226732	−	0.130904i	−0.609063	+	0.793121i	$0.708455\pi$
$348$	9.38089	+	16.2482i	0.502869	+	0.870994i
$349$	−18.7547			−1.00392			−0.501958	−	0.864892i	$-0.667387\pi$
$349$	−18.7547			−1.00392			−0.501958	+	0.864892i	$0.667387\pi$
$350$	2.58746	+	1.50380i	0.138305	+	0.0803814i
$351$			5.22378i			0.278825i
$352$	9.81598	−	5.66726i	0.523193	−	0.302066i
$353$	−3.36366	+	5.82603i	−0.179030	+	0.310088i	−0.941548	−	0.336878i	$-0.890629\pi$
$353$	−3.36366	+	5.82603i	−0.179030	+	0.310088i	0.762519	+	0.646966i	$0.223962\pi$
$354$	−1.87389	−	1.08189i	−0.0995962	−	0.0575019i
$355$	0.136006	+	0.235569i	0.00721843	+	0.0125027i
$356$	8.32578			0.441266
$357$	−10.4568	+	3.10729i	−0.553433	+	0.164455i
$358$	0.669189			0.0353677
$359$	8.26314	+	14.3122i	0.436112	+	0.755368i	0.997386	−	0.0722622i	$-0.0230218\pi$
$359$	8.26314	+	14.3122i	0.436112	+	0.755368i	−0.561274	+	0.827630i	$0.689688\pi$
$360$	−0.0928419	−	0.0536023i	−0.00489320	−	0.00282509i
$361$	3.04353	−	5.27155i	0.160186	−	0.277450i
$362$	0.246201	−	0.142144i	0.0129400	−	0.00747094i
$363$			7.57765i			0.397723i
$364$	−23.3609	+	13.3981i	−1.22444	+	0.702249i
$365$	−1.18277			−0.0619088
$366$	−1.02710	−	1.77899i	−0.0536873	−	0.0929890i
$367$	−18.8930	−	10.9079i	−0.986207	−	0.569387i	−0.0820689	−	0.996627i	$-0.526153\pi$
$367$	−18.8930	−	10.9079i	−0.986207	−	0.569387i	−0.904138	+	0.427240i	$0.859486\pi$
$368$	−4.52653	−	2.61339i	−0.235962	−	0.136233i
$369$	7.15530	−	4.13112i	0.372490	−	0.215057i
$370$	0.0768724			0.00399641
$371$	21.6482	−	12.4158i	1.12392	−	0.644596i
$372$	−11.9802			−0.621146
$373$	−2.04680	−	3.54516i	−0.105979	−	0.183561i	0.808159	−	0.588965i	$-0.200464\pi$
$373$	−2.04680	−	3.54516i	−0.105979	−	0.183561i	−0.914138	+	0.405404i	$0.867131\pi$
$374$	3.92401	+	0.926568i	0.202906	+	0.0479117i
$375$	0.597495	−	1.03489i	0.0308545	−	0.0534415i
$376$	2.46532	+	4.27005i	0.127139	+	0.220211i
$377$			50.2983i			2.59049i
$378$	0.600260	+	0.00172503i	0.0308740	+	8.87259e-5i
$379$			30.0701i			1.54460i	0.635258	+	0.772300i	$0.280894\pi$
$379$			30.0701i			1.54460i	−0.635258	+	0.772300i	$0.719106\pi$
$380$	0.725665	−	0.418963i	0.0372258	−	0.0214923i
$381$	10.7628	+	6.21391i	0.551395	+	0.318348i
$382$	2.84301	−	4.92423i	0.145461	−	0.251946i
$383$	−5.81446	−	10.0709i	−0.297105	−	0.514601i	0.678367	−	0.734723i	$-0.262688\pi$
$383$	−5.81446	−	10.0709i	−0.297105	−	0.514601i	−0.975472	+	0.220122i	$0.929355\pi$
$384$		−	6.80014i		−	0.347018i
$385$	1.17988	+	0.685733i	0.0601323	+	0.0349482i
$386$			4.07367i			0.207344i
$387$	−2.00155	−	3.46679i	−0.101745	−	0.176227i
$388$	−21.9608	−	12.6791i	−1.11489	−	0.643683i
$389$	−6.92068	+	11.9870i	−0.350893	+	0.607764i	−0.986406	−	0.164326i	$-0.947455\pi$
$389$	−6.92068	+	11.9870i	−0.350893	+	0.607764i	0.635514	+	0.772090i	$0.280788\pi$
$390$	−0.0709142	−	0.122827i	−0.00359088	−	0.00621959i
$391$	−1.67792	−	5.58776i	−0.0848560	−	0.282585i
$392$	3.10415	+	5.44863i	0.156783	+	0.275197i
$393$	−5.61597			−0.283288
$394$	−4.68112	+	2.70265i	−0.235831	+	0.136157i
$395$	−0.181913	+	0.315083i	−0.00915304	+	0.0158535i
$396$	7.27331	+	4.19925i	0.365498	+	0.211020i
$397$	−1.84608	+	1.06584i	−0.0926523	+	0.0534928i	−0.545610	−	0.838039i	$-0.683702\pi$
$397$	−1.84608	+	1.06584i	−0.0926523	+	0.0534928i	0.452958	+	0.891532i	$0.350369\pi$
$398$			2.41071i			0.120838i
$399$	−4.77734	+	8.21995i	−0.239166	+	0.411512i
$400$	18.4161			0.920807
$401$	−13.7407	+	7.93322i	−0.686180	+	0.396166i	−0.802179	−	0.597083i	$-0.796326\pi$
$401$	−13.7407	+	7.93322i	−0.686180	+	0.396166i	0.116000	+	0.993249i	$0.462993\pi$
$402$	−1.04883	−	0.605541i	−0.0523107	−	0.0302016i
$403$	−27.8147	−	16.0588i	−1.38555	−	0.799948i
$404$	10.0979	+	17.4901i	0.502391	+	0.870167i
$405$		−	0.119670i		−	0.00594647i
$406$	5.77972	+	0.0166098i	0.286843	+	0.000824330i
$407$	−12.2036			−0.604910
$408$	2.53248	−	2.68874i	0.125376	−	0.133112i
$409$	3.86442	−	6.69338i	0.191083	−	0.330966i	−0.754526	−	0.656270i	$-0.772133\pi$
$409$	3.86442	−	6.69338i	0.191083	−	0.330966i	0.945610	+	0.325304i	$0.105467\pi$
$410$	−0.112162	+	0.194270i	−0.00553928	+	0.00959432i
$411$	15.0762	−	8.70427i	0.743656	−	0.429350i
$412$	−33.4427			−1.64760
$413$	21.8887	−	12.5537i	1.07707	−	0.617728i
$414$			0.321035i			0.0157780i
$415$	−0.163857	+	0.0946028i	−0.00804342	+	0.00464387i
$416$	6.86851	−	11.8966i	0.336757	−	0.583280i
$417$	8.57733	−	14.8564i	0.420034	−	0.727520i
$418$	3.04320	−	1.75699i	0.148848	−	0.0859373i
$419$		−	9.50944i		−	0.464567i	−0.972648	−	0.232283i	$-0.925380\pi$
$419$		−	9.50944i		−	0.464567i	0.972648	−	0.232283i	$-0.0746196\pi$
$420$	0.535169	−	0.306932i	0.0261136	−	0.0149768i
$421$	10.9082			0.531632			0.265816	−	0.964024i	$-0.414359\pi$
$421$	10.9082			0.531632			0.265816	+	0.964024i	$0.414359\pi$
$422$	−0.959213	+	0.553802i	−0.0466937	+	0.0269586i
$423$	−2.75198	+	4.76657i	−0.133806	+	0.231759i
$424$	−4.22495	+	7.31783i	−0.205182	+	0.355385i
$425$	14.9639	+	14.0943i	0.725858	+	0.683674i
$426$	0.515695			0.0249855
$427$	23.9551	+	0.0688421i	1.15927	+	0.00333150i
$428$			3.12459i			0.151033i
$429$	11.2577	+	19.4989i	0.543528	+	0.941418i
$430$	0.0941251	+	0.0543432i	0.00453912	+	0.00262066i
$431$	14.2889	+	8.24968i	0.688270	+	0.397373i	0.802964	−	0.596028i	$-0.203255\pi$
$431$	14.2889	+	8.24968i	0.688270	+	0.397373i	−0.114694	+	0.993401i	$0.536589\pi$
$432$	3.19893	−	1.84690i	0.153909	−	0.0888592i
$433$	−7.53820			−0.362263			−0.181131	−	0.983459i	$-0.557976\pi$
$433$	−7.53820			−0.362263			−0.181131	+	0.983459i	$0.557976\pi$
$434$	−1.85449	+	3.19086i	−0.0890184	+	0.153166i
$435$		−	1.15227i		−	0.0552471i
$436$	−6.23194	+	3.59801i	−0.298456	+	0.172314i
$437$	−4.40356	−	2.54240i	−0.210651	−	0.121619i
$438$	−1.12118	+	1.94193i	−0.0535719	+	0.0927892i
$439$	−13.2208	+	7.63302i	−0.630993	+	0.364304i	−0.781137	−	0.624360i	$-0.785360\pi$
$439$	−13.2208	+	7.63302i	−0.630993	+	0.364304i	0.150143	+	0.988664i	$0.452026\pi$
$440$	−0.462071			−0.0220284
$441$	−3.53478	+	6.04196i	−0.168323	+	0.287712i
$442$	4.68009	−	1.40536i	0.222609	−	0.0668461i
$443$	−12.9711	−	22.4667i	−0.616277	−	1.06742i	−0.990159	−	0.139947i	$-0.955307\pi$
$443$	−12.9711	−	22.4667i	−0.616277	−	1.06742i	0.373882	−	0.927476i	$-0.378027\pi$
$444$	−2.75847	+	4.77782i	−0.130911	+	0.226745i
$445$	−0.442829	−	0.255667i	−0.0209921	−	0.0121198i
$446$	0.224142	+	0.388225i	0.0106134	+	0.0183830i
$447$			23.2038i			1.09750i
$448$	15.5342	+	9.02832i	0.733924	+	0.426548i
$449$		−	5.54961i		−	0.261902i	−0.991389	−	0.130951i	$-0.958197\pi$
$449$		−	5.54961i		−	0.261902i	0.991389	−	0.130951i	$-0.0418031\pi$
$450$	−0.565570	−	0.979596i	−0.0266612	−	0.0461786i
$451$	17.8058	−	30.8406i	0.838445	−	1.45223i
$452$	−15.6452	−	9.03278i	−0.735889	−	0.424866i
$453$	−12.0553	+	6.96011i	−0.566406	+	0.327015i
$454$			2.17010i			0.101848i
$455$	1.65394	+	0.00475309i	0.0775377	+	0.000222828i
$456$		−	3.21914i		−	0.150750i
$457$	−4.89863	−	8.48467i	−0.229148	−	0.396896i	0.728408	−	0.685144i	$-0.240261\pi$
$457$	−4.89863	−	8.48467i	−0.229148	−	0.396896i	−0.957556	+	0.288248i	$0.906927\pi$
$458$	−0.867481	+	1.50252i	−0.0405347	+	0.0702082i
$459$	4.01275	+	0.947524i	0.187299	+	0.0442266i
$460$	0.164977	+	0.285749i	0.00769209	+	0.0133231i
$461$	24.3852			1.13573			0.567865	−	0.823122i	$-0.307769\pi$
$461$	24.3852			1.13573			0.567865	+	0.823122i	$0.307769\pi$
$462$	2.24432	−	1.28717i	0.104415	−	0.0598848i
$463$	27.2282			1.26540			0.632701	−	0.774396i	$-0.281946\pi$
$463$	27.2282			1.26540			0.632701	+	0.774396i	$0.281946\pi$
$464$	30.8016	−	17.7833i	1.42993	−	0.825569i
$465$	0.637200	+	0.367888i	0.0295495	+	0.0170604i
$466$	−1.26501	−	0.730351i	−0.0586003	−	0.0338329i
$467$	−0.807533	−	1.39869i	−0.0373682	−	0.0647236i	0.846736	−	0.532013i	$-0.178564\pi$
$467$	−0.807533	−	1.39869i	−0.0373682	−	0.0647236i	−0.884105	+	0.467289i	$0.845231\pi$
$468$	10.1787			0.470510
$469$	12.2512	−	7.02638i	0.565709	−	0.324448i
$470$		−	0.149436i		−	0.00689295i
$471$	11.0658	−	6.38886i	0.509887	−	0.294383i
$472$	−4.27188	+	7.39911i	−0.196629	+	0.340572i
$473$	−14.9425	−	8.62705i	−0.687056	−	0.396672i
$474$	0.344881	+	0.597352i	0.0158409	+	0.0274373i
$475$	17.9158			0.822035
$476$	6.05463	+	20.3754i	0.277514	+	0.933903i
$477$	−9.43245			−0.431882
$478$	−2.61389	−	4.52738i	−0.119556	−	0.207078i
$479$	1.27988	+	0.738941i	0.0584794	+	0.0337631i	0.528955	−	0.848650i	$-0.322584\pi$
$479$	1.27988	+	0.738941i	0.0584794	+	0.0337631i	−0.470475	+	0.882413i	$0.655918\pi$
$480$	−0.157349	+	0.272536i	−0.00718197	+	0.0124395i
$481$	−12.8088	+	7.39516i	−0.584031	+	0.337190i
$482$			3.09073i			0.140779i
$483$	−3.23681	−	1.88120i	−0.147280	−	0.0855974i
$484$	14.7652			0.671147
$485$	0.778696	+	1.34874i	0.0353588	+	0.0612432i
$486$	−0.196482	−	0.113439i	−0.00891260	−	0.00514569i
$487$	−34.0547	−	19.6615i	−1.54317	−	0.890948i	−0.998636	−	0.0522082i	$-0.983374\pi$
$487$	−34.0547	−	19.6615i	−1.54317	−	0.890948i	−0.544532	−	0.838740i	$-0.683293\pi$
$488$	−7.02437	+	4.05552i	−0.317978	+	0.183585i
$489$	20.6555			0.934075
$490$	0.00109235	−	0.190051i	4.93471e−5	−	0.00858561i
$491$	4.73990			0.213909			0.106954	−	0.994264i	$-0.465890\pi$
$491$	4.73990			0.213909			0.106954	+	0.994264i	$0.465890\pi$
$492$	−8.04959	−	13.9423i	−0.362903	−	0.628567i
$493$	38.6376	+	9.12343i	1.74015	+	0.410899i
$494$	2.12941	−	3.68825i	0.0958068	−	0.165942i
$495$	−0.257900	−	0.446696i	−0.0115918	−	0.0200775i
$496$			22.7108i			1.01975i
$497$	−3.02186	+	5.19945i	−0.135549	+	0.233227i
$498$			0.358707i			0.0160740i
$499$	−29.7378	+	17.1691i	−1.33125	+	0.768595i	−0.985491	−	0.169730i	$-0.945710\pi$
$499$	−29.7378	+	17.1691i	−1.33125	+	0.768595i	−0.345755	+	0.938325i	$0.612377\pi$
$500$	−2.01651	−	1.16423i	−0.0901812	−	0.0520661i
$501$	2.31698	−	4.01312i	0.103515	−	0.179293i
$502$	−2.49940	−	4.32909i	−0.111554	−	0.193217i
$503$		−	3.02700i		−	0.134967i	−0.997720	−	0.0674836i	$-0.978503\pi$
$503$		−	3.02700i		−	0.134967i	0.997720	−	0.0674836i	$-0.0214970\pi$
$504$	0.00681132	−	2.37014i	0.000303400	−	0.105574i
$505$		−	1.24035i		−	0.0551947i
$506$	0.691859	+	1.19834i	0.0307569	+	0.0532725i
$507$	12.3737	+	7.14396i	0.549535	+	0.317274i
$508$	12.1080	−	20.9716i	0.537204	−	0.930465i
$509$	2.28760	+	3.96223i	0.101396	+	0.175623i	0.912260	−	0.409612i	$-0.134336\pi$
$509$	2.28760	+	3.96223i	0.101396	+	0.175623i	−0.810864	+	0.585235i	$0.801002\pi$
$510$	−0.107215	+	0.0321950i	−0.00474756	+	0.00142562i
$511$	−13.0095	−	22.6835i	−0.575509	−	1.00346i
$512$	−16.3317			−0.721766
$513$	3.11203	−	1.79673i	0.137399	−	0.0793275i
$514$	−1.13362	+	1.96349i	−0.0500019	+	0.0866058i
$515$	1.77874	+	1.02695i	0.0783805	+	0.0452530i
$516$	−6.75513	+	3.90008i	−0.297378	+	0.171691i
$517$			23.7231i			1.04334i
$518$	0.845540	+	1.47429i	0.0371509	+	0.0647765i
$519$	−21.6167			−0.948868
$520$	−0.484986	+	0.280007i	−0.0212680	+	0.0122791i
$521$	31.2918	+	18.0663i	1.37092	+	0.791500i	0.991044	−	0.133538i	$-0.0426340\pi$
$521$	31.2918	+	18.0663i	1.37092	+	0.791500i	0.379874	+	0.925038i	$0.375967\pi$
$522$	−1.89187	−	1.09227i	−0.0828047	−	0.0478073i
$523$	−0.871285	−	1.50911i	−0.0380986	−	0.0659887i	0.846347	−	0.532631i	$-0.178797\pi$
$523$	−0.871285	−	1.50911i	−0.0380986	−	0.0659887i	−0.884446	+	0.466643i	$0.845463\pi$
$524$			10.9429i			0.478041i
$525$	13.1908	+	0.0379078i	0.575694	+	0.00165443i
$526$	2.06027			0.0898321
$527$	−17.3811	+	18.4536i	−0.757134	+	0.803851i
$528$	7.96049	−	13.7880i	0.346436	−	0.600044i
$529$	−10.4989	+	18.1846i	−0.456473	+	0.790634i
$530$	0.221786	−	0.128048i	0.00963375	−	0.00556205i
$531$	−9.53723			−0.413880
$532$	16.0168	+	9.30877i	0.694416	+	0.403587i
$533$		−	43.1601i		−	1.86947i
$534$	−0.839540	+	0.484708i	−0.0363304	+	0.0209754i
$535$	0.0959496	−	0.166190i	0.00414826	−	0.00718500i
$536$	−2.39099	+	4.14132i	−0.103275	+	0.178878i
$537$	2.55439	−	1.47478i	0.110230	−	0.0636414i
$538$			0.444670i			0.0191711i
$539$	−0.173411	+	30.1708i	−0.00746935	+	1.29955i
$540$	−0.233181			−0.0100345
$541$	17.9757	−	10.3782i	0.772834	−	0.446196i	−0.0610509	−	0.998135i	$-0.519445\pi$
$541$	17.9757	−	10.3782i	0.772834	−	0.446196i	0.833885	+	0.551939i	$0.186112\pi$
$542$	0.444884	−	0.770562i	0.0191094	−	0.0330985i
$543$	0.626524	−	1.08517i	0.0268867	−	0.0465691i
$544$	−7.89277	−	7.43407i	−0.338400	−	0.318733i
$545$	0.441950			0.0189310
$546$	1.57562	−	2.71103i	0.0674302	−	0.116021i
$547$		−	26.0552i		−	1.11404i	−0.830499	−	0.557020i	$-0.811945\pi$
$547$		−	26.0552i		−	1.11404i	0.830499	−	0.557020i	$-0.188055\pi$
$548$	−16.9605	−	29.3765i	−0.724517	−	1.25490i
$549$	−7.84116	−	4.52710i	−0.334653	−	0.193212i
$550$	−4.22223	−	2.43771i	−0.180037	−	0.103944i
$551$	29.9648	−	17.3002i	1.27654	−	0.737012i
$552$	1.26762			0.0539533
$553$	−8.04368	−	0.0231160i	−0.342052	−	0.000982991i
$554$		−	1.53711i		−	0.0653056i
$555$	0.293433	−	0.169414i	0.0124556	−	0.00719122i
$556$	−28.9480	−	16.7132i	−1.22767	−	0.708796i
$557$	9.48337	−	16.4257i	0.401823	−	0.695978i	−0.592123	−	0.805848i	$-0.701710\pi$
$557$	9.48337	−	16.4257i	0.401823	−	0.695978i	0.993946	+	0.109870i	$0.0350433\pi$
$558$	1.20804	−	0.697462i	0.0511404	−	0.0295259i
$559$	−20.9113			−0.884456
$560$	−0.581850	−	1.01452i	−0.0245876	−	0.0428711i
$561$	17.0205	−	5.11100i	0.718606	−	0.215787i
$562$	1.73695	+	3.00849i	0.0732689	+	0.126905i
$563$	12.7116	−	22.0171i	0.535730	−	0.927911i	−0.463398	−	0.886150i	$-0.653370\pi$
$563$	12.7116	−	22.0171i	0.535730	−	0.927911i	0.999128	−	0.0417606i	$-0.0132967\pi$
$564$	9.28780	+	5.36231i	0.391087	+	0.225794i
$565$	0.554755	+	0.960864i	0.0233387	+	0.0404239i
$566$			2.57530i			0.108248i
$567$	2.29508	−	1.31629i	0.0963843	−	0.0552788i
$568$		−	2.03623i		−	0.0854385i
$569$	−1.50866	−	2.61307i	−0.0632462	−	0.109546i	0.832668	−	0.553772i	$-0.186812\pi$
$569$	−1.50866	−	2.61307i	−0.0632462	−	0.109546i	−0.895915	+	0.444226i	$0.853479\pi$
$570$	−0.0487821	+	0.0844931i	−0.00204326	+	0.00353903i
$571$	−16.8672	−	9.73830i	−0.705872	−	0.407535i	0.103659	−	0.994613i	$-0.466945\pi$
$571$	−16.8672	−	9.73830i	−0.705872	−	0.407535i	−0.809531	+	0.587078i	$0.800278\pi$
$572$	37.9942	−	21.9360i	1.58862	−	0.917189i
$573$		−	25.0620i		−	1.04698i
$574$	−4.95948	−	0.0142526i	−0.207005	−	0.000594891i
$575$			7.05480i			0.294206i
$576$	−3.39550	−	5.88117i	−0.141479	−	0.245049i
$577$	6.51749	−	11.2886i	0.271326	−	0.469951i	−0.697875	−	0.716219i	$-0.745871\pi$
$577$	6.51749	−	11.2886i	0.271326	−	0.469951i	0.969202	+	0.246268i	$0.0792044\pi$
$578$	−0.230650	−	3.85002i	−0.00959376	−	0.160140i
$579$	8.97767	+	15.5498i	0.373099	+	0.646227i
$580$	−2.24523			−0.0932280
$581$	−3.61663	−	2.10194i	−0.150043	−	0.0872034i
$582$	2.95259			0.122389
$583$	−35.2087	+	20.3278i	−1.45820	+	0.841891i
$584$	7.66778	+	4.42700i	0.317295	+	0.183190i
$585$	−0.541380	−	0.312566i	−0.0223833	−	0.0129230i
$586$	2.09596	+	3.63031i	0.0865834	+	0.149967i
$587$	21.2227			0.875954			0.437977	−	0.898986i	$-0.355695\pi$
$587$	21.2227			0.875954			0.437977	+	0.898986i	$0.355695\pi$
$588$	11.7729	+	6.88762i	0.485507	+	0.284041i
$589$			22.0939i			0.910362i
$590$	0.224249	−	0.129470i	0.00923220	−	0.00533021i
$591$	−11.9123	+	20.6328i	−0.490009	+	0.848720i
$592$	9.05727	+	5.22922i	0.372252	+	0.214920i
$593$	8.12508	+	14.0731i	0.333657	+	0.577911i	0.983226	−	0.182392i	$-0.0583839\pi$
$593$	8.12508	+	14.0731i	0.333657	+	0.577911i	−0.649569	+	0.760303i	$0.725051\pi$
$594$	−0.977884			−0.0401231
$595$	0.303653	−	1.26964i	0.0124486	−	0.0520503i
$596$	45.2133			1.85201
$597$	5.31279	+	9.20203i	0.217438	+	0.376614i
$598$	1.45234	+	0.838509i	0.0593906	+	0.0342892i
$599$	16.0131	−	27.7356i	0.654280	−	1.13325i	−0.327794	−	0.944749i	$-0.606305\pi$
$599$	16.0131	−	27.7356i	0.654280	−	1.13325i	0.982074	−	0.188496i	$-0.0603614\pi$
$600$	−3.86796	+	2.23317i	−0.157909	+	0.0911687i
$601$			19.0735i			0.778026i	0.921232	+	0.389013i	$0.127184\pi$
$601$			19.0735i			0.778026i	−0.921232	+	0.389013i	$0.872816\pi$
$602$	−0.00690547	+	2.40290i	−0.000281446	+	0.0979349i
$603$	−5.33803			−0.217382
$604$	13.5620	+	23.4900i	0.551828	+	0.955795i
$605$	−0.785329	−	0.453410i	−0.0319281	−	0.0184337i
$606$	−2.03647	−	1.17576i	−0.0827261	−	0.0477619i
$607$	19.4216	−	11.2131i	0.788298	−	0.455124i	−0.0510652	−	0.998695i	$-0.516262\pi$
$607$	19.4216	−	11.2131i	0.788298	−	0.455124i	0.839363	+	0.543571i	$0.182928\pi$
$608$	−9.44975			−0.383238
$609$	22.0986	−	12.6741i	0.895482	−	0.513581i
$610$	0.245826			0.00995321
$611$	14.3758	+	24.8996i	0.581581	+	1.00733i
$612$	1.84628	−	7.81896i	0.0746313	−	0.316063i
$613$	−3.67217	+	6.36038i	−0.148317	+	0.256893i	−0.930606	−	0.366023i	$-0.880719\pi$
$613$	−3.67217	+	6.36038i	−0.148317	+	0.256893i	0.782288	+	0.622917i	$0.214052\pi$
$614$	0.337747	+	0.584995i	0.0136304	+	0.0236085i
$615$			0.988744i			0.0398700i
$616$	−5.08244	−	8.86176i	−0.204777	−	0.357051i
$617$		−	42.4010i		−	1.70700i	−0.521094	−	0.853499i	$-0.674476\pi$
$617$		−	42.4010i		−	1.70700i	0.521094	−	0.853499i	$-0.325524\pi$
$618$	3.37223	−	1.94696i	0.135651	−	0.0783181i
$619$	−13.5723	−	7.83595i	−0.545516	−	0.314954i	0.201796	−	0.979428i	$-0.435322\pi$
$619$	−13.5723	−	7.83595i	−0.545516	−	0.314954i	−0.747311	+	0.664474i	$0.768656\pi$
$620$	0.716839	−	1.24160i	0.0287890	−	0.0498639i
$621$	0.707507	+	1.22544i	0.0283913	+	0.0491751i
$622$		−	7.61499i		−	0.305333i
$623$	0.0324880	−	11.3049i	0.00130160	−	0.452920i
$624$		−	19.2957i		−	0.772445i
$625$	−12.3927	−	21.4648i	−0.495708	−	0.858591i
$626$	4.80178	+	2.77231i	0.191918	+	0.110804i
$627$	7.74422	−	13.4134i	0.309275	−	0.535679i
$628$	−12.4489	−	21.5621i	−0.496764	−	0.860420i
$629$	3.35740	+	11.1807i	0.133868	+	0.445804i
$630$	−0.0360954	+	0.0621062i	−0.00143808	+	0.00247437i
$631$	0.246131			0.00979830			0.00489915	−	0.999988i	$-0.498441\pi$
$631$	0.246131			0.00979830			0.00489915	+	0.999988i	$0.498441\pi$
$632$	2.35866	−	1.36177i	0.0938224	−	0.0541684i
$633$	−2.44097	+	4.22788i	−0.0970198	+	0.168043i
$634$	3.53758	+	2.04242i	0.140495	+	0.0811150i
$635$	−1.28799	+	0.743621i	−0.0511123	+	0.0295097i
$636$			18.3794i			0.728790i
$637$	18.1009	+	31.7721i	0.717185	+	1.25886i
$638$	−9.41575			−0.372773
$639$	1.96848	−	1.13650i	0.0778719	−	0.0449594i
$640$	0.704750	+	0.406888i	0.0278577	+	0.0160836i
$641$	−3.82475	−	2.20822i	−0.151069	−	0.0872195i	0.422560	−	0.906335i	$-0.361131\pi$
$641$	−3.82475	−	2.20822i	−0.151069	−	0.0872195i	−0.573629	+	0.819115i	$0.694465\pi$
$642$	−0.181907	−	0.315072i	−0.00717928	−	0.0124349i
$643$			12.4711i			0.491811i	0.969294	+	0.245906i	$0.0790853\pi$
$643$			12.4711i			0.491811i	−0.969294	+	0.245906i	$0.920915\pi$
$644$	−3.66556	+	6.30701i	−0.144443	+	0.248531i
$645$	0.479053			0.0188627
$646$	−2.44696	−	2.30475i	−0.0962742	−	0.0906791i
$647$	−12.9174	+	22.3736i	−0.507836	+	0.879597i	0.492123	+	0.870526i	$0.336221\pi$
$647$	−12.9174	+	22.3736i	−0.507836	+	0.879597i	−0.999959	+	0.00907170i	$0.997112\pi$
$648$	−0.447916	+	0.775814i	−0.0175958	+	0.0304768i
$649$	−35.5998	+	20.5536i	−1.39742	+	0.806799i
$650$	−5.90883			−0.231763
$651$	−0.0467480	+	16.2670i	−0.00183220	+	0.637552i
$652$		−	40.2478i		−	1.57623i
$653$	4.05208	−	2.33947i	0.158570	−	0.0915505i	−0.418615	−	0.908164i	$-0.637484\pi$
$653$	4.05208	−	2.33947i	0.158570	−	0.0915505i	0.577185	+	0.816613i	$0.304151\pi$
$654$	0.418937	−	0.725619i	0.0163817	−	0.0283740i
$655$	0.336032	−	0.582025i	0.0131299	−	0.0227416i
$656$	−26.4303	+	15.2595i	−1.03193	+	0.595785i
$657$			9.88353i			0.385593i
$658$	2.86593	−	1.64368i	0.111726	−	0.0640774i
$659$	32.2523			1.25637			0.628186	−	0.778063i	$-0.283798\pi$
$659$	32.2523			1.25637			0.628186	+	0.778063i	$0.283798\pi$
$660$	−0.870400	+	0.502525i	−0.0338803	+	0.0195608i
$661$	−2.00869	+	3.47915i	−0.0781289	+	0.135323i	−0.902443	−	0.430810i	$-0.858228\pi$
$661$	−2.00869	+	3.47915i	−0.0781289	+	0.135323i	0.824314	+	0.566133i	$0.191561\pi$
$662$	2.56380	−	4.44064i	0.0996450	−	0.172590i
$663$	14.7674	−	15.6786i	0.573519	−	0.608906i
$664$	1.41636			0.0549655
$665$	−0.566043	−	0.986954i	−0.0219502	−	0.0382724i
$666$		−	0.642369i		−	0.0248913i
$667$	6.81237	+	11.7994i	0.263776	+	0.456874i
$668$	−7.81968	−	4.51469i	−0.302552	−	0.174679i
$669$	1.71116	+	0.987940i	0.0661574	+	0.0381960i
$670$	0.125513	−	0.0724652i	0.00484901	−	0.00279958i
$671$	−39.0252			−1.50655
$672$	−6.95753	−	0.0199946i	−0.268392	−	0.000771307i
$673$			36.5941i			1.41060i	0.708910	+	0.705299i	$0.249187\pi$
$673$			36.5941i			1.41060i	−0.708910	+	0.705299i	$0.750813\pi$
$674$	3.40397	−	1.96528i	0.131116	−	0.0756999i
$675$	−4.31772	−	2.49284i	−0.166189	−	0.0959494i
$676$	13.9202	−	24.1105i	0.535392	−	0.927326i
$677$	−31.0298	+	17.9151i	−1.19257	+	0.688532i	−0.958889	−	0.283781i	$-0.908411\pi$
$677$	−31.0298	+	17.9151i	−1.19257	+	0.688532i	−0.233683	+	0.972313i	$0.575078\pi$
$678$	2.10347			0.0807834
$679$	−17.3016	+	29.7693i	−0.663973	+	1.14244i
$680$	0.127123	+	0.423341i	0.00487494	+	0.0162344i
$681$	4.78253	+	8.28358i	0.183267	+	0.317427i
$682$	3.00619	−	5.20687i	0.115113	−	0.199381i
$683$	32.7458	+	18.9058i	1.25298	+	0.723409i	0.971701	−	0.236216i	$-0.0759073\pi$
$683$	32.7458	+	18.9058i	1.25298	+	0.723409i	0.281281	+	0.959625i	$0.409241\pi$
$684$	−3.50097	−	6.06386i	−0.133863	−	0.231858i
$685$			2.08329i			0.0795983i
$686$	3.65687	−	2.06947i	0.139620	−	0.0790126i
$687$			7.64712i			0.291756i
$688$	7.39335	+	12.8057i	0.281869	+	0.488211i
$689$	−24.6365	+	42.6718i	−0.938578	+	1.62566i
$690$	−0.0332713	−	0.0192092i	−0.00126662	−	0.000731281i
$691$	10.1330	−	5.85028i	0.385477	−	0.222555i	−0.294722	−	0.955583i	$-0.595227\pi$
$691$	10.1330	−	5.85028i	0.385477	−	0.222555i	0.680199	+	0.733028i	$0.261894\pi$
$692$			42.1207i			1.60119i
$693$	5.73019	−	9.85943i	0.217672	−	0.374529i
$694$		−	1.10647i		−	0.0420009i
$695$	1.02645	+	1.77787i	0.0389355	+	0.0674383i
$696$	−4.31285	+	7.47008i	−0.163478	+	0.283153i
$697$	−33.1543	−	7.82866i	−1.25581	−	0.296532i
$698$	−2.12751	−	3.68496i	−0.0805275	−	0.139478i
$699$	−6.43828			−0.243518
$700$	0.0738644	−	25.7026i	0.00279181	−	0.971469i
$701$	−23.8211			−0.899711			−0.449856	−	0.893101i	$-0.648525\pi$
$701$	−23.8211			−0.899711			−0.449856	+	0.893101i	$0.648525\pi$
$702$	−1.02638	+	0.592580i	−0.0387382	+	0.0223655i
$703$	8.81121	+	5.08716i	0.332321	+	0.191866i
$704$	−25.3489	−	14.6352i	−0.955373	−	0.551585i
$705$	−0.329331	−	0.570417i	−0.0124033	−	0.0214832i
$706$	−1.52628			−0.0574423
$707$	23.7878	−	13.6429i	0.894632	−	0.513094i
$708$			18.5835i			0.698412i
$709$	12.5730	−	7.25905i	0.472191	−	0.272619i	−0.244966	−	0.969532i	$-0.578777\pi$
$709$	12.5730	−	7.25905i	0.472191	−	0.272619i	0.717156	+	0.696912i	$0.245443\pi$
$710$	−0.0308567	+	0.0534453i	−0.00115803	+	0.00200577i
$711$	2.63292	+	1.52012i	0.0987424	+	0.0570089i
$712$	1.91388	+	3.31494i	0.0717258	+	0.124233i
$713$	−8.70001			−0.325818
$714$	−1.79673	−	1.70209i	−0.0672411	−	0.0636990i
$715$	−2.69443			−0.100766
$716$	−2.87365	−	4.97730i	−0.107393	−	0.186010i
$717$	−19.9552	−	11.5211i	−0.745239	−	0.430264i
$718$	−1.87472	+	3.24712i	−0.0699640	+	0.121181i
$719$	23.9018	−	13.7997i	0.891387	−	0.514643i	0.0169913	−	0.999856i	$-0.494591\pi$
$719$	23.9018	−	13.7997i	0.891387	−	0.514643i	0.874396	+	0.485213i	$0.161258\pi$
$720$			0.442039i			0.0164738i
$721$	−0.130497	+	45.4090i	−0.00485994	+	1.69112i
$722$	1.38102			0.0513962
$723$	6.81145	+	11.7978i	0.253320	+	0.438764i
$724$	−2.11448	−	1.22080i	−0.0785842	−	0.0453706i
$725$	−41.5741	−	24.0028i	−1.54402	−	0.891442i
$726$	−1.48887	+	0.859600i	−0.0552572	+	0.0319027i
$727$	22.8158			0.846190			0.423095	−	0.906085i	$-0.360944\pi$
$727$	22.8158			0.846190			0.423095	+	0.906085i	$0.360944\pi$
$728$	−10.7046	−	6.22137i	−0.396737	−	0.230579i
$729$	−1.00000			−0.0370370
$730$	−0.134172	−	0.232392i	−0.00496591	−	0.00860121i
$731$	−3.79304	+	16.0635i	−0.140291	+	0.594129i
$732$	−8.82117	+	15.2787i	−0.326040	+	0.564718i
$733$	−16.8696	−	29.2189i	−0.623091	−	1.07923i	−0.988907	−	0.148538i	$-0.952543\pi$
$733$	−16.8696	−	29.2189i	−0.623091	−	1.07923i	0.365815	−	0.930687i	$-0.380790\pi$
$734$		−	4.94951i		−	0.182690i
$735$	−0.414670	−	0.727858i	−0.0152953	−	0.0268474i
$736$		−	3.72107i		−	0.137161i
$737$	−19.9254	+	11.5039i	−0.733962	+	0.423753i
$738$	1.62338	+	0.937258i	0.0597574	+	0.0345009i
$739$	−7.19971	+	12.4703i	−0.264846	+	0.458726i	−0.967523	−	0.252782i	$-0.918654\pi$
$739$	−7.19971	+	12.4703i	−0.264846	+	0.458726i	0.702677	+	0.711509i	$0.251988\pi$
$740$	−0.330107	−	0.571763i	−0.0121350	−	0.0210184i
$741$		−	18.7714i		−	0.689586i
$742$	4.89523	+	2.84505i	0.179710	+	0.104445i
$743$			29.7992i			1.09323i	0.837385	+	0.546613i	$0.184083\pi$
$743$			29.7992i			1.09323i	−0.837385	+	0.546613i	$0.815917\pi$
$744$	−2.75395	−	4.76998i	−0.100965	−	0.174876i
$745$	−2.40479	−	1.38841i	−0.0881046	−	0.0508672i
$746$	0.464373	−	0.804317i	0.0170019	−	0.0294482i
$747$	0.790529	+	1.36924i	0.0289239	+	0.0500977i
$748$	−9.95892	−	33.1649i	−0.364134	−	1.21263i
$749$	4.24262	+	0.0121925i	0.155022	+	0.000445503i
$750$	0.271116			0.00989977
$751$	16.2013	−	9.35385i	0.591196	−	0.341327i	−0.174374	−	0.984679i	$-0.555790\pi$
$751$	16.2013	−	9.35385i	0.591196	−	0.341327i	0.765570	+	0.643352i	$0.222457\pi$
$752$	10.1653	−	17.6068i	0.370690	−	0.642054i
$753$	−19.0812	−	11.0165i	−0.695356	−	0.401464i
$754$	−9.88270	+	5.70578i	−0.359907	+	0.207792i
$755$		−	1.66584i		−	0.0606260i
$756$	−2.56482	−	4.47202i	−0.0932815	−	0.162646i
$757$	−35.3576			−1.28509			−0.642546	−	0.766247i	$-0.722122\pi$
$757$	−35.3576			−1.28509			−0.642546	+	0.766247i	$0.722122\pi$
$758$	−5.90824	+	3.41112i	−0.214597	+	0.123898i
$759$	5.28186	+	3.04948i	0.191719	+	0.110689i
$760$	0.333623	+	0.192618i	0.0121018	+	0.00698697i
$761$	−11.4051	−	19.7541i	−0.413433	−	0.716087i	0.581830	−	0.813311i	$-0.302337\pi$
$761$	−11.4051	−	19.7541i	−0.413433	−	0.716087i	−0.995263	+	0.0972239i	$0.969004\pi$
$762$			2.81960i			0.102143i
$763$	4.86112	+	8.47587i	0.175984	+	0.306847i
$764$	−48.8340			−1.76675
$765$	−0.338303	+	0.359177i	−0.0122314	+	0.0129861i
$766$	1.31917	−	2.28487i	0.0476636	−	0.0825558i
$767$	−24.9102	+	43.1457i	−0.899455	+	1.55790i
$768$	−10.4262	+	6.01959i	−0.376225	+	0.217213i
$769$	11.7968			0.425404			0.212702	−	0.977117i	$-0.431774\pi$
$769$	11.7968			0.425404			0.212702	+	0.977117i	$0.431774\pi$
$770$	−0.000889771		0.309614i	−3.20651e−5		0.0111577i
$771$			9.99323i			0.359898i
$772$	30.2992	−	17.4932i	1.09049	−	0.629595i
$773$	5.66039	−	9.80409i	0.203590	−	0.352629i	−0.746092	−	0.665842i	$-0.768072\pi$
$773$	5.66039	−	9.80409i	0.203590	−	0.352629i	0.949683	+	0.313214i	$0.101406\pi$
$774$	0.454107	−	0.786537i	0.0163226	−	0.0282715i
$775$	26.5469	−	15.3269i	0.953593	−	0.550557i
$776$		−	11.6584i		−	0.418512i
$777$	6.47663	+	3.76414i	0.232348	+	0.135038i
$778$	−3.14030			−0.112585
$779$	−25.7123	+	14.8450i	−0.921238	+	0.531877i
$780$	−0.609043	+	1.05489i	−0.0218072	+	0.0377712i
$781$	4.89853	−	8.48451i	0.175283	−	0.303600i
$782$	0.907552	−	0.963550i	0.0324540	−	0.0344565i
$783$	−9.62870			−0.344102
$784$	13.0568	−	22.3178i	0.466315	−	0.797066i
$785$			1.52911i			0.0545764i
$786$	−0.637069	−	1.10344i	−0.0227235	−	0.0393583i
$787$	−22.7112	−	13.1123i	−0.809566	−	0.467403i	0.0372393	−	0.999306i	$-0.488144\pi$
$787$	−22.7112	−	13.1123i	−0.809566	−	0.467403i	−0.846805	+	0.531903i	$0.821477\pi$
$788$	40.2035	+	23.2115i	1.43219	+	0.826876i
$789$	7.86436	−	4.54049i	0.279979	−	0.161646i
$790$	−0.0825441			−0.00293679
$791$	−12.3259	+	21.2081i	−0.438258	+	0.754073i
$792$			3.86120i			0.137202i
$793$	−40.9605	+	23.6486i	−1.45455	+	0.839786i
$794$	−0.418835	−	0.241815i	−0.0148639	−	0.00858168i
$795$	0.564392	−	0.977556i	0.0200169	−	0.0346703i
$796$	17.9304	−	10.3521i	0.635526	−	0.366921i
$797$	−42.7086			−1.51281			−0.756407	−	0.654101i	$-0.773047\pi$
$797$	−42.7086			−1.51281			−0.756407	+	0.654101i	$0.773047\pi$
$798$	−2.15701	−	0.00619882i	−0.0763572	−	0.000219436i
$799$	21.7347	−	6.52659i	0.768917	−	0.230894i
$800$	6.55544	+	11.3544i	0.231770	+	0.401437i
$801$	−2.13643	+	3.70041i	−0.0754870	+	0.130747i
$802$	−3.11747	−	1.79987i	−0.110082	−	0.0635556i
$803$	21.2999	+	36.8925i	0.751657	+	1.30191i
$804$			10.4013i			0.366826i
$805$	0.388638	−	0.222893i	0.0136977	−	0.00785596i
$806$		−	7.28679i		−	0.256666i
$807$	0.979976	+	1.69737i	0.0344968	+	0.0597502i
$808$	−4.64252	+	8.04107i	−0.163323	+	0.282884i
$809$	13.1203	+	7.57498i	0.461284	+	0.266322i	0.712584	−	0.701587i	$-0.247525\pi$
$809$	13.1203	+	7.57498i	0.461284	+	0.266322i	−0.251300	+	0.967909i	$0.580858\pi$
$810$	0.0235130	−	0.0135753i	0.000826164	−	0.000476986i
$811$			2.92328i			0.102650i	0.998682	+	0.0513251i	$0.0163445\pi$
$811$			2.92328i			0.102650i	−0.998682	+	0.0513251i	$0.983656\pi$
$812$	−24.6959	−	43.0598i	−0.866655	−	1.51110i
$813$		−	3.92180i		−	0.137543i
$814$	−1.38436	−	2.39778i	−0.0485219	−	0.0840423i
$815$	−1.23593	+	2.14069i	−0.0432926	+	0.0749850i
$816$	−14.8223	−	3.49997i	−0.518886	−	0.122524i
$817$	7.19249	+	12.4578i	0.251633	+	0.435842i
$818$	1.75350			0.0613098
$819$	0.0397182	−	13.8208i	0.00138787	−	0.482937i
$820$	1.92659			0.0672796
$821$	40.4388	−	23.3474i	1.41132	−	0.814828i	0.415811	−	0.909451i	$-0.363498\pi$
$821$	40.4388	−	23.3474i	1.41132	−	0.814828i	0.995513	+	0.0946227i	$0.0301645\pi$
$822$	3.42046	+	1.97481i	0.119302	+	0.0688792i
$823$	−21.8508	−	12.6156i	−0.761673	−	0.439752i	0.0682234	−	0.997670i	$-0.478267\pi$
$823$	−21.8508	−	12.6156i	−0.761673	−	0.439752i	−0.829896	+	0.557918i	$0.811600\pi$
$824$	−7.68761	−	13.3153i	−0.267811	−	0.463862i
$825$	−21.4892			−0.748157
$826$	4.94961	+	2.87665i	0.172219	+	0.100092i
$827$		−	4.10089i		−	0.142602i	−0.997455	−	0.0713010i	$-0.977285\pi$
$827$		−	4.10089i		−	0.142602i	0.997455	−	0.0713010i	$-0.0227151\pi$
$828$	2.38780	−	1.37860i	0.0829817	−	0.0479095i
$829$	−2.70159	+	4.67929i	−0.0938301	+	0.162518i	−0.909120	−	0.416535i	$-0.863244\pi$
$829$	−2.70159	+	4.67929i	−0.0938301	+	0.162518i	0.815290	+	0.579053i	$0.196578\pi$
$830$	−0.0371755	−	0.0214633i	−0.00129038	−	0.000745001i
$831$	−3.38753	−	5.86738i	−0.117512	−	0.203537i
$832$	−35.4747			−1.22986
$833$	27.6896	−	8.14157i	0.959388	−	0.282089i
$834$	3.89201			0.134769
$835$	0.277273	+	0.480252i	0.00959544	+	0.0166198i
$836$	−26.1363	−	15.0898i	−0.903944	−	0.521893i
$837$	3.07418	−	5.32463i	0.106259	−	0.184046i
$838$	1.86843	−	1.07874i	0.0645439	−	0.0372645i
$839$		−	9.31077i		−	0.321443i	−0.987000	−	0.160722i	$-0.948618\pi$
$839$		−	9.31077i		−	0.321443i	0.987000	−	0.160722i	$-0.0513822\pi$
$840$	0.245228	+	0.142524i	0.00846117	+	0.00491753i
$841$	−63.7119			−2.19696
$842$	1.23741	+	2.14326i	0.0426440	+	0.0738616i
$843$	13.2604	+	7.65589i	0.456712	+	0.263683i
$844$	8.23814	+	4.75629i	0.283569	+	0.163718i
$845$	−1.48076	+	0.854920i	−0.0509399	+	0.0294101i
$846$	−1.24873			−0.0429321
$847$	0.0576154	−	20.0485i	0.00197969	−	0.688874i
$848$	34.8417			1.19647
$849$	5.67553	+	9.83031i	0.194784	+	0.337375i
$850$	−1.07178	+	4.53898i	−0.0367618	+	0.155686i
$851$	−2.00319	+	3.46963i	−0.0686686	+	0.118938i
$852$	−2.21451	−	3.83564i	−0.0758678	−	0.131407i
$853$		−	7.55700i		−	0.258747i	−0.991596	−	0.129373i	$-0.958703\pi$
$853$		−	7.55700i		−	0.258747i	0.991596	−	0.129373i	$-0.0412966\pi$
$854$	2.70391	+	4.71454i	0.0925258	+	0.161328i
$855$			0.430030i			0.0147067i
$856$	−1.24407	+	0.718263i	−0.0425214	+	0.0245497i
$857$	−0.391745	−	0.226174i	−0.0133818	−	0.00772596i	0.493294	−	0.869863i	$-0.335793\pi$
$857$	−0.391745	−	0.226174i	−0.0133818	−	0.00772596i	−0.506676	+	0.862137i	$0.669126\pi$
$858$	−2.55413	+	4.42388i	−0.0871964	+	0.151029i
$859$	13.4600	+	23.3134i	0.459250	+	0.795444i	0.998921	−	0.0464318i	$-0.0147850\pi$
$859$	13.4600	+	23.3134i	0.459250	+	0.795444i	−0.539672	+	0.841875i	$0.681452\pi$
$860$		−	0.933447i		−	0.0318303i
$861$	−18.9625	+	10.8755i	−0.646240	+	0.370634i
$862$			3.74334i			0.127499i
$863$	9.49552	+	16.4467i	0.323231	+	0.559853i	0.981153	−	0.193233i	$-0.0618975\pi$
$863$	9.49552	+	16.4467i	0.323231	+	0.559853i	−0.657921	+	0.753087i	$0.728564\pi$
$864$	2.27739	+	1.31485i	0.0774785	+	0.0447322i
$865$	1.29344	−	2.24030i	0.0439783	−	0.0761726i
$866$	−0.855125	−	1.48112i	−0.0290583	−	0.0503305i
$867$	−9.36521	−	14.1878i	−0.318059	−	0.481842i
$868$	31.6966	+	0.0910898i	1.07585	+	0.00309179i
$869$	13.1040			0.444522
$870$	0.226400	−	0.130712i	0.00767568	−	0.00443156i
$871$	−13.9424	+	24.1489i	−0.472419	+	0.818254i
$872$	−2.86513	−	1.65418i	−0.0970255	−	0.0560177i
$873$	11.2705	−	6.50701i	0.381448	−	0.220229i
$874$		−	1.15363i		−	0.0390220i
$875$	−1.58868	+	2.73351i	−0.0537073	+	0.0924095i
$876$	19.2583			0.650678
$877$	11.7115	−	6.76161i	0.395468	−	0.228324i	−0.289059	−	0.957311i	$-0.593342\pi$
$877$	11.7115	−	6.76161i	0.395468	−	0.228324i	0.684527	+	0.728988i	$0.260009\pi$
$878$	−2.99950	−	1.73176i	−0.101228	−	0.0584441i
$879$	16.0012	+	9.23829i	0.539707	+	0.311600i
$880$	0.952634	+	1.65001i	0.0321133	+	0.0556219i
$881$		−	2.52287i		−	0.0849976i	−0.999097	−	0.0424988i	$-0.986468\pi$
$881$		−	2.52287i		−	0.0849976i	0.999097	−	0.0424988i	$-0.0135319\pi$
$882$	−1.58812	−	0.00912796i	−0.0534747	−	0.000307354i
$883$	−22.9238			−0.771446			−0.385723	−	0.922615i	$-0.626048\pi$
$883$	−22.9238			−0.771446			−0.385723	+	0.922615i	$0.626048\pi$
$884$	−30.5501	−	28.7747i	−1.02751	−	0.967798i
$885$	0.570661	−	0.988415i	0.0191826	−	0.0332252i
$886$	2.94286	−	5.09718i	0.0988673	−	0.171243i
$887$	−16.5305	+	9.54388i	−0.555039	+	0.320452i	−0.751152	−	0.660129i	$-0.770501\pi$
$887$	−16.5305	+	9.54388i	−0.555039	+	0.320452i	0.196113	+	0.980581i	$0.437168\pi$
$888$	−2.53641			−0.0851163
$889$	−28.4284	−	16.5222i	−0.953456	−	0.554138i
$890$		−	0.116010i		−	0.00388868i
$891$	−3.73272	+	2.15509i	−0.125051	+	0.0721982i
$892$	1.92503	−	3.33425i	0.0644547	−	0.111639i
$893$	9.88914	−	17.1285i	0.330927	−	0.573183i
$894$	−4.55913	+	2.63222i	−0.152480	+	0.0880345i
$895$			0.352975i			0.0117986i
$896$	−0.0517038	+	17.9914i	−0.00172730	+	0.601051i
$897$	7.39173			0.246803
$898$	1.09040	−	0.629541i	0.0363870	−	0.0210081i
$899$	29.6003	−	51.2693i	0.987227	−	1.70993i
$900$	−4.85736	+	8.41320i	−0.161912	+	0.280440i
$901$	28.3104	+	26.6651i	0.943157	+	0.888345i
$902$	8.07950			0.269018
$903$	5.26923	+	9.18744i	0.175349	+	0.305739i
$904$		−	8.30561i		−	0.276241i
$905$	0.0749763	+	0.129863i	0.00249230	+	0.00431678i
$906$	−2.73507	−	1.57909i	−0.0908667	−	0.0524619i
$907$	42.5740	+	24.5801i	1.41365	+	0.816170i	0.995730	−	0.0923154i	$-0.0294268\pi$
$907$	42.5740	+	24.5801i	1.41365	+	0.816170i	0.417917	+	0.908485i	$0.362760\pi$
$908$	16.1408	−	9.31888i	0.535650	−	0.309258i
$909$	−10.3647			−0.343775
$910$	0.186687	+	0.325508i	0.00618861	+	0.0107905i
$911$			37.3460i			1.23733i	0.785656	+	0.618664i	$0.212326\pi$
$911$			37.3460i			1.23733i	−0.785656	+	0.618664i	$0.787674\pi$
$912$	−11.4952	+	6.63677i	−0.380645	+	0.219766i
$913$	5.90165	+	3.40732i	0.195316	+	0.112766i
$914$	1.11139	−	1.92498i	0.0367615	−	0.0636728i
$915$	0.938354	−	0.541759i	0.0310210	−	0.0179100i
$916$	14.9006			0.492330
$917$	14.8584	+	0.0427001i	0.490667	+	0.00141008i
$918$	0.269031	+	0.895920i	0.00887934	+	0.0295698i
$919$	−10.2671	−	17.7831i	−0.338679	−	0.586609i	0.645506	−	0.763756i	$-0.276647\pi$
$919$	−10.2671	−	17.7831i	−0.338679	−	0.586609i	−0.984185	+	0.177146i	$0.943313\pi$
$920$	−0.0758480	+	0.131373i	−0.00250063	+	0.00433122i
$921$	2.57846	+	1.48867i	0.0849631	+	0.0490535i
$922$	2.76623	+	4.79124i	0.0911008	+	0.157791i
$923$		−	11.8737i		−	0.390828i
$924$	−19.2114	−	11.1654i	−0.632008	−	0.367316i
$925$		−	14.1162i		−	0.464137i
$926$	3.08874	+	5.34985i	0.101502	+	0.175807i
$927$	8.58152	−	14.8636i	0.281854	−	0.488186i
$928$	21.9284	+	12.6603i	0.719833	+	0.415596i
$929$	30.4443	−	17.5770i	0.998844	−	0.576683i	0.0909380	−	0.995857i	$-0.471013\pi$
$929$	30.4443	−	17.5770i	0.998844	−	0.576683i	0.907906	+	0.419174i	$0.137680\pi$
$930$			0.166931i			0.00547389i
$931$	12.7021	−	21.7115i	0.416295	−	0.711567i
$932$			12.5452i			0.410931i
$933$	−16.7822	−	29.0675i	−0.549423	−	0.951629i
$934$	0.183211	−	0.317331i	0.00599486	−	0.0103834i
$935$	−0.488734	+	2.06978i	−0.0159833	+	0.0676891i
$936$	2.33982	+	4.05268i	0.0764794	+	0.132466i
$937$	27.0553			0.883859			0.441930	−	0.897050i	$-0.354294\pi$
$937$	27.0553			0.883859			0.441930	+	0.897050i	$0.354294\pi$
$938$	2.77032	+	1.61008i	0.0904542	+	0.0525709i
$939$	24.4388			0.797529
$940$	−1.11147	+	0.641710i	−0.0362523	+	0.0209303i
$941$	−40.4807	−	23.3715i	−1.31963	−	0.761891i	−0.335964	−	0.941875i	$-0.609062\pi$
$941$	−40.4807	−	23.3715i	−1.31963	−	0.761891i	−0.983669	+	0.179984i	$0.942395\pi$
$942$	2.51059	+	1.44949i	0.0817995	+	0.0472270i
$943$	−5.84558	−	10.1248i	−0.190358	−	0.329710i
$944$	35.2287			1.14660
$945$	−0.000909894		0.316617i	−2.95989e−5		0.0102995i
$946$		−	3.91457i		−	0.127274i
$947$	−19.4130	+	11.2081i	−0.630838	+	0.364214i	−0.781076	−	0.624436i	$-0.785329\pi$
$947$	−19.4130	+	11.2081i	−0.630838	+	0.364214i	0.150239	+	0.988650i	$0.451996\pi$
$948$	2.96199	−	5.13032i	0.0962011	−	0.166625i
$949$	44.7124	+	25.8147i	1.45143	+	0.837981i
$950$	2.03235	+	3.52014i	0.0659382	+	0.114208i
$951$	18.0046			0.583840
$952$	−6.72073	+	7.09445i	−0.217820	+	0.229932i
$953$	−18.6418			−0.603867			−0.301934	−	0.953329i	$-0.597632\pi$
$953$	−18.6418			−0.603867			−0.301934	+	0.953329i	$0.597632\pi$
$954$	−1.07001	−	1.85331i	−0.0346427	−	0.0600030i
$955$	2.59737	+	1.49959i	0.0840488	+	0.0485256i
$956$	−22.4492	+	38.8832i	−0.726059	+	1.25757i
$957$	−35.9413	+	20.7507i	−1.16182	+	0.670776i
$958$			0.335299i			0.0108330i
$959$	−39.9540	+	22.9146i	−1.29018	+	0.739951i
$960$	0.812680			0.0262291
$961$	3.40114	+	5.89095i	0.109714	+	0.190031i
$962$	−2.90603	−	1.67780i	−0.0936942	−	0.0540944i
$963$	−1.38873	−	0.801783i	−0.0447512	−	0.0258371i
$964$	22.9883	−	13.2723i	0.740402	−	0.427472i
$965$	−2.14872			−0.0691698
$966$	0.00244094	−	0.849375i	7.85359e−5	−	0.0273282i
$967$	18.6151			0.598620			0.299310	−	0.954156i	$-0.403244\pi$
$967$	18.6151			0.598620			0.299310	+	0.954156i	$0.403244\pi$
$968$	3.39415	+	5.87884i	0.109092	+	0.188953i
$969$	−14.4197	−	3.40489i	−0.463226	−	0.109381i
$970$	−0.176669	+	0.305999i	−0.00567249	+	0.00982505i
$971$	0.948979	+	1.64368i	0.0304542	+	0.0527482i	0.880851	−	0.473394i	$-0.156971\pi$
$971$	0.948979	+	1.64368i	0.0304542	+	0.0527482i	−0.850397	+	0.526142i	$0.823638\pi$
$972$			1.94853i			0.0624990i
$973$	−22.8063	+	39.2409i	−0.731138	+	1.25800i
$974$		−	8.92152i		−	0.285864i
$975$	−22.5549	+	13.0221i	−0.722334	+	0.417040i
$976$	28.9638	+	16.7222i	0.927107	+	0.535266i
$977$	11.7732	−	20.3918i	0.376659	−	0.652392i	−0.613915	−	0.789372i	$-0.710406\pi$
$977$	11.7732	−	20.3918i	0.376659	−	0.652392i	0.990574	+	0.136980i	$0.0437395\pi$
$978$	2.34314	+	4.05843i	0.0749253	+	0.129774i
$979$			18.4168i			0.588603i
$980$	−1.41825	+	0.807995i	−0.0453044	+	0.0258104i
$981$		−	3.69306i		−	0.117910i
$982$	0.537689	+	0.931304i	0.0171583	+	0.0297191i
$983$	−10.7557	−	6.20979i	−0.343052	−	0.198061i	0.318569	−	0.947900i	$-0.396798\pi$
$983$	−10.7557	−	6.20979i	−0.343052	−	0.198061i	−0.661621	+	0.749838i	$0.730131\pi$
$984$	3.70079	−	6.40995i	0.117977	−	0.204342i
$985$	−1.42555	−	2.46913i	−0.0454219	−	0.0786731i
$986$	2.59042	+	8.62654i	0.0824958	+	0.274725i
$987$	7.31727	−	12.5902i	0.232911	−	0.400750i
$988$	−36.5767			−1.16366
$989$	−4.90555	+	2.83222i	−0.155988	+	0.0900594i
$990$	0.0585118	−	0.101345i	0.00185963	−	0.00322097i
$991$	27.9571	+	16.1410i	0.888087	+	0.512737i	0.873316	−	0.487154i	$-0.161965\pi$
$991$	27.9571	+	16.1410i	0.888087	+	0.512737i	0.0147704	+	0.999891i	$0.495298\pi$
$992$	−14.0022	+	8.08419i	−0.444571	+	0.256673i
$993$		−	22.6007i		−	0.717213i
$994$	−1.36439	−	0.00392100i	−0.0432760	−	0.000124367i
$995$	−1.27157			−0.0403114
$996$	2.66799	−	1.54037i	0.0845386	−	0.0488084i
$997$	40.4862	+	23.3747i	1.28221	+	0.740285i	0.977252	−	0.212081i	$-0.0680239\pi$
$997$	40.4862	+	23.3747i	1.28221	+	0.740285i	0.304959	+	0.952366i	$0.401357\pi$
$998$	−6.74684	−	3.89529i	−0.213567	−	0.123303i
$999$	−1.41567	−	2.45201i	−0.0447899	−	0.0775783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.67.14	yes	48
7.2	even	3	inner	357.2.p.a.16.13	✓	48
17.16	even	2	inner	357.2.p.a.67.13	yes	48
119.16	even	6	inner	357.2.p.a.16.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.13	✓	48	7.2	even	3	inner
357.2.p.a.16.14	yes	48	119.16	even	6	inner
357.2.p.a.67.13	yes	48	17.16	even	2	inner
357.2.p.a.67.14	yes	48	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.113439 + 0.196482i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.974263 - 1.68747i) q^{4} +(-0.103638 + 0.0598352i) q^{5} +0.226878i q^{6} +(-2.28748 - 1.32945i) q^{7} +0.895833 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.113439 + 0.196482i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.974263 - 1.68747i) q^{4} +(-0.103638 + 0.0598352i) q^{5} +0.226878i q^{6} +(-2.28748 - 1.32945i) q^{7} +0.895833 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0235130 - 0.0135753i) q^{10} +(3.73272 + 2.15509i) q^{11} +(1.68747 - 0.974263i) q^{12} +5.22378 q^{13} +(0.00172503 - 0.600260i) q^{14} -0.119670 q^{15} +(-1.84690 - 3.19893i) q^{16} +(0.947524 - 4.01275i) q^{17} +(-0.113439 + 0.196482i) q^{18} +(-1.79673 - 3.11203i) q^{19} +0.233181i q^{20} +(-1.31629 - 2.29508i) q^{21} +0.977884i q^{22} +(1.22544 - 0.707507i) q^{23} +(0.775814 + 0.447916i) q^{24} +(-2.49284 + 4.31772i) q^{25} +(0.592580 + 1.02638i) q^{26} +1.00000i q^{27} +(-4.47202 + 2.56482i) q^{28} +9.62870i q^{29} +(-0.0135753 - 0.0235130i) q^{30} +(-5.32463 - 3.07418i) q^{31} +(1.31485 - 2.27739i) q^{32} +(2.15509 + 3.73272i) q^{33} +(0.895920 - 0.269031i) q^{34} +(0.316617 + 0.000909894i) q^{35} +1.94853 q^{36} +(-2.45201 + 1.41567i) q^{37} +(0.407638 - 0.706049i) q^{38} +(4.52393 + 2.61189i) q^{39} +(-0.0928419 + 0.0536023i) q^{40} -8.26223i q^{41} +(0.301624 - 0.518977i) q^{42} -4.00310 q^{43} +(7.27331 - 4.19925i) q^{44} +(-0.103638 - 0.0598352i) q^{45} +(0.278025 + 0.160518i) q^{46} +(2.75198 + 4.76657i) q^{47} -3.69381i q^{48} +(3.46510 + 6.08219i) q^{49} -1.13114 q^{50} +(2.82696 - 3.00139i) q^{51} +(5.08934 - 8.81500i) q^{52} +(-4.71623 + 8.16874i) q^{53} +(-0.196482 + 0.113439i) q^{54} -0.515801 q^{55} +(-2.04920 - 1.19097i) q^{56} -3.59346i q^{57} +(-1.89187 + 1.09227i) q^{58} +(-4.76861 + 8.25948i) q^{59} +(-0.116590 + 0.201940i) q^{60} +(-7.84116 + 4.52710i) q^{61} -1.39492i q^{62} +(0.00760334 - 2.64574i) q^{63} -6.79099 q^{64} +(-0.541380 + 0.312566i) q^{65} +(-0.488942 + 0.846872i) q^{66} +(-2.66902 + 4.62287i) q^{67} +(-5.84828 - 5.50840i) q^{68} +1.41501 q^{69} +(0.0357378 + 0.0623126i) q^{70} -2.27301i q^{71} +(0.447916 + 0.775814i) q^{72} +(8.55939 + 4.94177i) q^{73} +(-0.556307 - 0.321184i) q^{74} +(-4.31772 + 2.49284i) q^{75} -7.00195 q^{76} +(-5.67343 - 9.89221i) q^{77} +1.18516i q^{78} +(2.63292 - 1.52012i) q^{79} +(0.382817 + 0.221020i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.62338 - 0.937258i) q^{82} +1.58106 q^{83} +(-5.15530 - 0.0148153i) q^{84} +(0.141905 + 0.472567i) q^{85} +(-0.454107 - 0.786537i) q^{86} +(-4.81435 + 8.33870i) q^{87} +(3.34390 + 1.93060i) q^{88} +(2.13643 + 3.70041i) q^{89} -0.0271505i q^{90} +(-11.9493 - 6.94479i) q^{91} -2.75719i q^{92} +(-3.07418 - 5.32463i) q^{93} +(-0.624364 + 1.08143i) q^{94} +(0.372417 + 0.215015i) q^{95} +(2.27739 - 1.31485i) q^{96} -13.0140i q^{97} +(-0.801964 + 1.37079i) q^{98} +4.31018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

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