LMFDB - Embedded newform 273.2.cg.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	273.19
Dual form			273.2.cg.a.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38279 - 0.638467i) q^{2} -1.00000i q^{3} +(3.53801 + 2.04267i) q^{4} +(0.488495 - 0.130892i) q^{5} +(-0.638467 + 2.38279i) q^{6} +(-2.15177 + 1.53945i) q^{7} +(-3.63751 - 3.63751i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-2.38279 - 0.638467i) q^{2} -1.00000i q^{3} +(3.53801 + 2.04267i) q^{4} +(0.488495 - 0.130892i) q^{5} +(-0.638467 + 2.38279i) q^{6} +(-2.15177 + 1.53945i) q^{7} +(-3.63751 - 3.63751i) q^{8} -1.00000 q^{9} -1.24755 q^{10} +(-4.20987 - 4.20987i) q^{11} +(2.04267 - 3.53801i) q^{12} +(3.50782 + 0.833795i) q^{13} +(6.11010 - 2.29436i) q^{14} +(-0.130892 - 0.488495i) q^{15} +(2.25966 + 3.91384i) q^{16} +(0.466614 - 0.808199i) q^{17} +(2.38279 + 0.638467i) q^{18} +(-5.60973 - 5.60973i) q^{19} +(1.99567 + 0.534738i) q^{20} +(1.53945 + 2.15177i) q^{21} +(7.34338 + 12.7191i) q^{22} +(-7.03583 + 4.06214i) q^{23} +(-3.63751 + 3.63751i) q^{24} +(-4.10863 + 2.37212i) q^{25} +(-7.82605 - 4.22639i) q^{26} +1.00000i q^{27} +(-10.7575 + 1.05124i) q^{28} +(1.96458 - 3.40276i) q^{29} +1.24755i q^{30} +(-0.636987 + 2.37727i) q^{31} +(-0.222595 - 0.830735i) q^{32} +(-4.20987 + 4.20987i) q^{33} +(-1.62785 + 1.62785i) q^{34} +(-0.849626 + 1.03366i) q^{35} +(-3.53801 - 2.04267i) q^{36} +(0.314544 - 1.17389i) q^{37} +(9.78519 + 16.9484i) q^{38} +(0.833795 - 3.50782i) q^{39} +(-2.25303 - 1.30079i) q^{40} +(-7.84968 + 2.10332i) q^{41} +(-2.29436 - 6.11010i) q^{42} +(-0.152677 + 0.0881483i) q^{43} +(-6.29518 - 23.4939i) q^{44} +(-0.488495 + 0.130892i) q^{45} +(19.3585 - 5.18708i) q^{46} +(0.444356 + 1.65836i) q^{47} +(3.91384 - 2.25966i) q^{48} +(2.26019 - 6.62507i) q^{49} +(11.3045 - 3.02904i) q^{50} +(-0.808199 - 0.466614i) q^{51} +(10.7075 + 10.1153i) q^{52} +(0.750763 + 1.30036i) q^{53} +(0.638467 - 2.38279i) q^{54} +(-2.60754 - 1.50546i) q^{55} +(13.4268 + 2.22730i) q^{56} +(-5.60973 + 5.60973i) q^{57} +(-6.85375 + 6.85375i) q^{58} +(1.10912 + 4.13930i) q^{59} +(0.534738 - 1.99567i) q^{60} -7.79133i q^{61} +(3.03561 - 5.25784i) q^{62} +(2.15177 - 1.53945i) q^{63} -6.91705i q^{64} +(1.82269 - 0.0518399i) q^{65} +(12.7191 - 7.34338i) q^{66} +(5.39742 - 5.39742i) q^{67} +(3.30177 - 1.90628i) q^{68} +(4.06214 + 7.03583i) q^{69} +(2.68444 - 1.92055i) q^{70} +(6.54710 + 1.75429i) q^{71} +(3.63751 + 3.63751i) q^{72} +(-12.2371 - 3.27893i) q^{73} +(-1.49899 + 2.59632i) q^{74} +(2.37212 + 4.10863i) q^{75} +(-8.38844 - 31.3061i) q^{76} +(15.5395 + 2.57777i) q^{77} +(-4.22639 + 7.82605i) q^{78} +(4.64069 - 8.03790i) q^{79} +(1.61612 + 1.61612i) q^{80} +1.00000 q^{81} +20.0471 q^{82} +(-1.66068 - 1.66068i) q^{83} +(1.05124 + 10.7575i) q^{84} +(0.122152 - 0.455878i) q^{85} +(0.420078 - 0.112560i) q^{86} +(-3.40276 - 1.96458i) q^{87} +30.6269i q^{88} +(4.12627 + 1.10563i) q^{89} +1.24755 q^{90} +(-8.83159 + 3.60598i) q^{91} -33.1904 q^{92} +(2.37727 + 0.636987i) q^{93} -4.23524i q^{94} +(-3.47459 - 2.00606i) q^{95} +(-0.830735 + 0.222595i) q^{96} +(0.856967 - 3.19825i) q^{97} +(-9.61545 + 14.3431i) q^{98} +(4.20987 + 4.20987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.38279	−	0.638467i	−1.68489	−	0.451465i	−0.715826	−	0.698279i	$-0.753950\pi$
$2$	−2.38279	−	0.638467i	−1.68489	−	0.451465i	−0.969063	+	0.246814i	$0.920616\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	3.53801	+	2.04267i	1.76900	+	1.02133i
$5$	0.488495	−	0.130892i	0.218462	−	0.0585366i	−0.147928	−	0.988998i	$-0.547260\pi$
$5$	0.488495	−	0.130892i	0.218462	−	0.0585366i	0.366390	+	0.930461i	$0.380594\pi$
$6$	−0.638467	+	2.38279i	−0.260653	+	0.972771i
$7$	−2.15177	+	1.53945i	−0.813291	+	0.581857i
$7$	−2.15177	+	1.53945i	−0.813291	+	0.581857i
$8$	−3.63751	−	3.63751i	−1.28605	−	1.28605i
$9$	−1.00000			−0.333333
$10$	−1.24755			−0.394511
$11$	−4.20987	−	4.20987i	−1.26932	−	1.26932i	−0.946438	−	0.322886i	$-0.895347\pi$
$11$	−4.20987	−	4.20987i	−1.26932	−	1.26932i	−0.322886	−	0.946438i	$-0.604653\pi$
$12$	2.04267	−	3.53801i	0.589668	−	1.02133i
$13$	3.50782	+	0.833795i	0.972894	+	0.231253i
$13$	3.50782	+	0.833795i	0.972894	+	0.231253i
$14$	6.11010	−	2.29436i	1.63299	−	0.613193i
$15$	−0.130892	−	0.488495i	−0.0337962	−	0.126129i
$16$	2.25966	+	3.91384i	0.564915	+	0.978461i
$17$	0.466614	−	0.808199i	0.113171	−	0.196017i	−0.803876	−	0.594796i	$-0.797233\pi$
$17$	0.466614	−	0.808199i	0.113171	−	0.196017i	0.917047	+	0.398779i	$0.130566\pi$
$18$	2.38279	+	0.638467i	0.561630	+	0.150488i
$19$	−5.60973	−	5.60973i	−1.28696	−	1.28696i	−0.936624	−	0.350335i	$-0.886068\pi$
$19$	−5.60973	−	5.60973i	−1.28696	−	1.28696i	−0.350335	−	0.936624i	$-0.613932\pi$
$20$	1.99567	+	0.534738i	0.446245	+	0.119571i
$21$	1.53945	+	2.15177i	0.335935	+	0.469554i
$22$	7.34338	+	12.7191i	1.56561	+	2.71172i
$23$	−7.03583	+	4.06214i	−1.46707	+	0.847014i	−0.999321	−	0.0368468i	$-0.988269\pi$
$23$	−7.03583	+	4.06214i	−1.46707	+	0.847014i	−0.467750	+	0.883861i	$0.654935\pi$
$24$	−3.63751	+	3.63751i	−0.742503	+	0.742503i
$25$	−4.10863	+	2.37212i	−0.821726	+	0.474424i
$26$	−7.82605	−	4.22639i	−1.53481	−	0.828863i
$27$			1.00000i			0.192450i
$28$	−10.7575	+	1.05124i	−2.03299	+	0.198665i
$29$	1.96458	−	3.40276i	0.364814	−	0.631877i	−0.623932	−	0.781479i	$-0.714466\pi$
$29$	1.96458	−	3.40276i	0.364814	−	0.631877i	0.988746	+	0.149602i	$0.0477992\pi$
$30$			1.24755i			0.227771i
$31$	−0.636987	+	2.37727i	−0.114406	+	0.426970i	−0.999242	−	0.0389336i	$-0.987604\pi$
$31$	−0.636987	+	2.37727i	−0.114406	+	0.426970i	0.884836	+	0.465903i	$0.154271\pi$
$32$	−0.222595	−	0.830735i	−0.0393496	−	0.146855i
$33$	−4.20987	+	4.20987i	−0.732844	+	0.732844i
$34$	−1.62785	+	1.62785i	−0.279174	+	0.279174i
$35$	−0.849626	+	1.03366i	−0.143613	+	0.174721i
$36$	−3.53801	−	2.04267i	−0.589668	−	0.340445i
$37$	0.314544	−	1.17389i	0.0517107	−	0.192987i	−0.935239	−	0.354018i	$-0.884815\pi$
$37$	0.314544	−	1.17389i	0.0517107	−	0.192987i	0.986949	+	0.161031i	$0.0514819\pi$
$38$	9.78519	+	16.9484i	1.58737	+	2.74940i
$39$	0.833795	−	3.50782i	0.133514	−	0.561700i
$40$	−2.25303	−	1.30079i	−0.356235	−	0.205672i
$41$	−7.84968	+	2.10332i	−1.22591	+	0.328483i	−0.812987	−	0.582281i	$-0.802160\pi$
$41$	−7.84968	+	2.10332i	−1.22591	+	0.328483i	−0.412927	+	0.910764i	$0.635494\pi$
$42$	−2.29436	−	6.11010i	−0.354027	−	0.942809i
$43$	−0.152677	+	0.0881483i	−0.0232831	+	0.0134425i	−0.511596	−	0.859226i	$-0.670946\pi$
$43$	−0.152677	+	0.0881483i	−0.0232831	+	0.0134425i	0.488313	+	0.872668i	$0.337612\pi$
$44$	−6.29518	−	23.4939i	−0.949034	−	3.54184i
$45$	−0.488495	+	0.130892i	−0.0728206	+	0.0195122i
$46$	19.3585	−	5.18708i	2.85425	−	0.764793i
$47$	0.444356	+	1.65836i	0.0648160	+	0.241897i	0.990732	−	0.135834i	$-0.0433713\pi$
$47$	0.444356	+	1.65836i	0.0648160	+	0.241897i	−0.925916	+	0.377730i	$0.876705\pi$
$48$	3.91384	−	2.25966i	0.564915	−	0.326154i
$49$	2.26019	−	6.62507i	0.322884	−	0.946438i
$50$	11.3045	−	3.02904i	1.59870	−	0.428371i
$51$	−0.808199	−	0.466614i	−0.113171	−	0.0653390i
$52$	10.7075	+	10.1153i	1.48487	+	1.40274i
$53$	0.750763	+	1.30036i	0.103125	+	0.178618i	0.912971	−	0.408025i	$-0.133782\pi$
$53$	0.750763	+	1.30036i	0.103125	+	0.178618i	−0.809845	+	0.586643i	$0.800449\pi$
$54$	0.638467	−	2.38279i	0.0868844	−	0.324257i
$55$	−2.60754	−	1.50546i	−0.351601	−	0.202997i
$56$	13.4268	+	2.22730i	1.79424	+	0.297636i
$57$	−5.60973	+	5.60973i	−0.743026	+	0.743026i
$58$	−6.85375	+	6.85375i	−0.899941	+	0.899941i
$59$	1.10912	+	4.13930i	0.144395	+	0.538890i	0.999782	+	0.0208998i	$0.00665310\pi$
$59$	1.10912	+	4.13930i	0.144395	+	0.538890i	−0.855386	+	0.517991i	$0.826680\pi$
$60$	0.534738	−	1.99567i	0.0690344	−	0.257640i
$61$		−	7.79133i		−	0.997578i	−0.866723	−	0.498789i	$-0.833778\pi$
$61$		−	7.79133i		−	0.997578i	0.866723	−	0.498789i	$-0.166222\pi$
$62$	3.03561	−	5.25784i	0.385523	−	0.667746i
$63$	2.15177	−	1.53945i	0.271097	−	0.193952i
$64$		−	6.91705i		−	0.864631i
$65$	1.82269	−	0.0518399i	0.226077	−	0.00642995i
$66$	12.7191	−	7.34338i	1.56561	−	0.903908i
$67$	5.39742	−	5.39742i	0.659400	−	0.659400i	−0.295838	−	0.955238i	$-0.595599\pi$
$67$	5.39742	−	5.39742i	0.659400	−	0.659400i	0.955238	+	0.295838i	$0.0955989\pi$
$68$	3.30177	−	1.90628i	0.400398	−	0.231170i
$69$	4.06214	+	7.03583i	0.489024	+	0.847014i
$70$	2.68444	−	1.92055i	0.320852	−	0.229549i
$71$	6.54710	+	1.75429i	0.776998	+	0.208196i	0.625461	−	0.780256i	$-0.284911\pi$
$71$	6.54710	+	1.75429i	0.776998	+	0.208196i	0.151537	+	0.988452i	$0.451578\pi$
$72$	3.63751	+	3.63751i	0.428685	+	0.428685i
$73$	−12.2371	−	3.27893i	−1.43225	−	0.383770i	−0.542437	−	0.840097i	$-0.682498\pi$
$73$	−12.2371	−	3.27893i	−1.43225	−	0.383770i	−0.889812	+	0.456327i	$0.849165\pi$
$74$	−1.49899	+	2.59632i	−0.174254	+	0.301816i
$75$	2.37212	+	4.10863i	0.273909	+	0.474424i
$76$	−8.38844	−	31.3061i	−0.962220	−	3.59105i
$77$	15.5395	+	2.57777i	1.77089	+	0.293764i
$78$	−4.22639	+	7.82605i	−0.478544	+	0.886126i
$79$	4.64069	−	8.03790i	0.522118	−	0.904335i	−0.477551	−	0.878604i	$-0.658475\pi$
$79$	4.64069	−	8.03790i	0.522118	−	0.904335i	0.999669	−	0.0257307i	$-0.00819123\pi$
$80$	1.61612	+	1.61612i	0.180688	+	0.180688i
$81$	1.00000			0.111111
$82$	20.0471			2.21383
$83$	−1.66068	−	1.66068i	−0.182284	−	0.182284i	0.610067	−	0.792350i	$-0.291143\pi$
$83$	−1.66068	−	1.66068i	−0.182284	−	0.182284i	−0.792350	+	0.610067i	$0.791143\pi$
$84$	1.05124	+	10.7575i	0.114700	+	1.17374i
$85$	0.122152	−	0.455878i	0.0132492	−	0.0494469i
$86$	0.420078	−	0.112560i	0.0452982	−	0.0121376i
$87$	−3.40276	−	1.96458i	−0.364814	−	0.210626i
$88$			30.6269i			3.26484i
$89$	4.12627	+	1.10563i	0.437384	+	0.117197i	0.470790	−	0.882245i	$-0.343969\pi$
$89$	4.12627	+	1.10563i	0.437384	+	0.117197i	−0.0334062	+	0.999442i	$0.510636\pi$
$90$	1.24755			0.131504
$91$	−8.83159	+	3.60598i	−0.925802	+	0.378009i
$92$	−33.1904			−3.46034
$93$	2.37727	+	0.636987i	0.246511	+	0.0660525i
$94$		−	4.23524i		−	0.436831i
$95$	−3.47459	−	2.00606i	−0.356486	−	0.205817i
$96$	−0.830735	+	0.222595i	−0.0847865	+	0.0227185i
$97$	0.856967	−	3.19825i	0.0870119	−	0.324733i	−0.908676	−	0.417503i	$-0.862905\pi$
$97$	0.856967	−	3.19825i	0.0870119	−	0.324733i	0.995688	+	0.0927700i	$0.0295721\pi$
$98$	−9.61545	+	14.3431i	−0.971307	+	1.44887i
$99$	4.20987	+	4.20987i	0.423108	+	0.423108i
$100$	−19.3818			−1.93818
$101$	4.47385			0.445165			0.222583	−	0.974914i	$-0.428551\pi$
$101$	4.47385			0.445165			0.222583	+	0.974914i	$0.428551\pi$
$102$	1.62785	+	1.62785i	0.161181	+	0.161181i
$103$	−2.07621	+	3.59610i	−0.204575	+	0.354335i	−0.949997	−	0.312258i	$-0.898915\pi$
$103$	−2.07621	+	3.59610i	−0.204575	+	0.354335i	0.745422	+	0.666593i	$0.232248\pi$
$104$	−9.72678	−	15.7927i	−0.953789	−	1.54860i
$105$	1.03366	+	0.849626i	0.100875	+	0.0829150i
$106$	−0.958675	−	3.57782i	−0.0931148	−	0.347509i
$107$	−4.71528	−	8.16710i	−0.455843	−	0.789543i	0.542893	−	0.839802i	$-0.317329\pi$
$107$	−4.71528	−	8.16710i	−0.455843	−	0.789543i	−0.998736	+	0.0502584i	$0.983996\pi$
$108$	−2.04267	+	3.53801i	−0.196556	+	0.340445i
$109$	−6.64872	−	1.78152i	−0.636832	−	0.170638i	−0.0740637	−	0.997254i	$-0.523597\pi$
$109$	−6.64872	−	1.78152i	−0.636832	−	0.170638i	−0.562768	+	0.826615i	$0.690263\pi$
$110$	5.25204	+	5.25204i	0.500762	+	0.500762i
$111$	−1.17389	−	0.314544i	−0.111421	−	0.0298552i
$112$	−10.8874	−	4.94304i	−1.02876	−	0.467074i
$113$	−2.13688	−	3.70118i	−0.201020	−	0.348178i	0.747837	−	0.663882i	$-0.231092\pi$
$113$	−2.13688	−	3.70118i	−0.201020	−	0.348178i	−0.948857	+	0.315705i	$0.897759\pi$
$114$	16.9484	−	9.78519i	1.58737	−	0.916467i
$115$	−2.90527	+	2.90527i	−0.270918	+	0.270918i
$116$	13.9014	−	8.02599i	1.29072	−	0.745195i
$117$	−3.50782	−	0.833795i	−0.324298	−	0.0770844i
$118$		−	10.5712i		−	0.973160i
$119$	0.240138	+	2.45738i	0.0220134	+	0.225268i
$120$	−1.30079	+	2.25303i	−0.118745	+	0.205672i
$121$			24.4460i			2.22236i
$122$	−4.97451	+	18.5651i	−0.450371	+	1.68081i
$123$	2.10332	+	7.84968i	0.189650	+	0.707782i
$124$	−7.10963	+	7.10963i	−0.638464	+	0.638464i
$125$	−3.48457	+	3.48457i	−0.311670	+	0.311670i
$126$	−6.11010	+	2.29436i	−0.544331	+	0.204398i
$127$	9.06211	+	5.23201i	0.804132	+	0.464266i	0.844914	−	0.534902i	$-0.179652\pi$
$127$	9.06211	+	5.23201i	0.804132	+	0.464266i	−0.0407820	+	0.999168i	$0.512985\pi$
$128$	−4.86150	+	18.1434i	−0.429700	+	1.60366i
$129$	0.0881483	+	0.152677i	0.00776103	+	0.0134425i
$130$	−4.37619	−	1.04020i	−0.383817	−	0.0912319i
$131$	−13.7862	−	7.95947i	−1.20451	−	0.695422i	−0.242952	−	0.970038i	$-0.578116\pi$
$131$	−13.7862	−	7.95947i	−1.20451	−	0.695422i	−0.961554	+	0.274617i	$0.911449\pi$
$132$	−23.4939	+	6.29518i	−2.04488	+	0.547925i
$133$	20.7067	+	3.43492i	1.79550	+	0.297846i
$134$	−16.3070	+	9.41486i	−1.40871	+	0.813320i
$135$	0.130892	+	0.488495i	0.0112654	+	0.0420430i
$136$	−4.63714	+	1.24252i	−0.397632	+	0.106545i
$137$	18.6481	−	4.99674i	1.59321	−	0.426900i	0.650230	−	0.759737i	$-0.274673\pi$
$137$	18.6481	−	4.99674i	1.59321	−	0.426900i	0.942984	+	0.332837i	$0.108006\pi$
$138$	−5.18708	−	19.3585i	−0.441554	−	1.64790i
$139$	6.10481	−	3.52462i	0.517804	−	0.298954i	−0.218232	−	0.975897i	$-0.570029\pi$
$139$	6.10481	−	3.52462i	0.517804	−	0.298954i	0.736036	+	0.676943i	$0.236696\pi$
$140$	−5.11741	+	1.92160i	−0.432500	+	0.162405i
$141$	1.65836	−	0.444356i	0.139659	−	0.0374216i
$142$	−14.4803	−	8.36022i	−1.21516	−	0.701574i
$143$	−11.2573	−	18.2776i	−0.941382	−	1.52845i
$144$	−2.25966	−	3.91384i	−0.188305	−	0.326154i
$145$	0.514297	−	1.91938i	0.0427100	−	0.159396i
$146$	27.0651	+	15.6260i	2.23992	+	1.29322i
$147$	−6.62507	−	2.26019i	−0.546427	−	0.186417i
$148$	3.51074	−	3.51074i	0.288581	−	0.288581i
$149$	10.2955	−	10.2955i	0.843438	−	0.843438i	−0.145867	−	0.989304i	$-0.546597\pi$
$149$	10.2955	−	10.2955i	0.843438	−	0.843438i	0.989304	+	0.145867i	$0.0465970\pi$
$150$	−3.02904	−	11.3045i	−0.247320	−	0.923012i
$151$	1.32592	−	4.94839i	0.107902	−	0.402694i	−0.890757	−	0.454481i	$-0.849825\pi$
$151$	1.32592	−	4.94839i	0.107902	−	0.402694i	0.998658	+	0.0517866i	$0.0164916\pi$
$152$			40.8109i			3.31020i
$153$	−0.466614	+	0.808199i	−0.0377235	+	0.0653390i
$154$	−35.3817	−	16.0638i	−2.85114	−	1.29446i
$155$			1.24466i			0.0999735i
$156$	10.1153	−	10.7075i	0.809871	−	0.857287i
$157$	0.998876	−	0.576701i	0.0797190	−	0.0460258i	−0.459611	−	0.888121i	$-0.652011\pi$
$157$	0.998876	−	0.576701i	0.0797190	−	0.0460258i	0.539330	+	0.842095i	$0.318678\pi$
$158$	−16.1897	+	16.1897i	−1.28799	+	1.28799i
$159$	1.30036	−	0.750763i	0.103125	−	0.0595394i
$160$	−0.217473	−	0.376674i	−0.0171927	−	0.0297787i
$161$	8.88599	−	19.5721i	0.700314	−	1.54249i
$162$	−2.38279	−	0.638467i	−0.187210	−	0.0501627i
$163$	9.67442	+	9.67442i	0.757759	+	0.757759i	0.975914	−	0.218155i	$-0.0700039\pi$
$163$	9.67442	+	9.67442i	0.757759	+	0.757759i	−0.218155	+	0.975914i	$0.570004\pi$
$164$	−32.0686	−	8.59276i	−2.50414	−	0.670982i
$165$	−1.50546	+	2.60754i	−0.117200	+	0.202997i
$166$	2.89677	+	5.01735i	0.224833	+	0.389422i
$167$	0.561041	+	2.09383i	0.0434146	+	0.162026i	0.984230	−	0.176894i	$-0.0566051\pi$
$167$	0.561041	+	2.09383i	0.0434146	+	0.162026i	−0.940815	+	0.338920i	$0.889938\pi$
$168$	2.22730	−	13.4268i	0.171840	−	1.03590i
$169$	11.6096	+	5.84960i	0.893044	+	0.449970i
$170$	−0.582126	+	1.00827i	−0.0446470	+	0.0773309i
$171$	5.60973	+	5.60973i	0.428987	+	0.428987i
$172$	−0.720232			−0.0549171
$173$	2.77142			0.210707			0.105354	−	0.994435i	$-0.466403\pi$
$173$	2.77142			0.210707			0.105354	+	0.994435i	$0.466403\pi$
$174$	6.85375	+	6.85375i	0.519581	+	0.519581i
$175$	5.18905	−	11.4293i	0.392256	−	0.863972i
$176$	6.96390	−	25.9896i	0.524924	−	1.95904i
$177$	4.13930	−	1.10912i	0.311128	−	0.0833666i
$178$	−9.12614	−	5.26898i	−0.684033	−	0.394927i
$179$			9.13629i			0.682878i	0.939904	+	0.341439i	$0.110914\pi$
$179$			9.13629i			0.682878i	−0.939904	+	0.341439i	$0.889086\pi$
$180$	−1.99567	−	0.534738i	−0.148748	−	0.0398570i
$181$	−12.3155			−0.915405			−0.457703	−	0.889105i	$-0.651328\pi$
$181$	−12.3155			−0.915405			−0.457703	+	0.889105i	$0.651328\pi$
$182$	23.3461	−	2.95361i	1.73053	−	0.218936i
$183$	−7.79133			−0.575952
$184$	40.3689	+	10.8168i	2.97604	+	0.797427i
$185$		−	0.614613i		−	0.0451873i
$186$	−5.25784	−	3.03561i	−0.385523	−	0.222582i
$187$	−5.36680	+	1.43803i	−0.392459	+	0.105159i
$188$	−1.81535	+	6.77497i	−0.132398	+	0.494115i
$189$	−1.53945	−	2.15177i	−0.111978	−	0.156518i
$190$	6.99843	+	6.99843i	0.507720	+	0.507720i
$191$	−0.534713			−0.0386905			−0.0193452	−	0.999813i	$-0.506158\pi$
$191$	−0.534713			−0.0386905			−0.0193452	+	0.999813i	$0.506158\pi$
$192$	−6.91705			−0.499195
$193$	−4.77086	−	4.77086i	−0.343414	−	0.343414i	0.514235	−	0.857649i	$-0.328076\pi$
$193$	−4.77086	−	4.77086i	−0.343414	−	0.343414i	−0.857649	+	0.514235i	$0.828076\pi$
$194$	−4.08395	+	7.07361i	−0.293211	+	0.507856i
$195$	−0.0518399	−	1.82269i	−0.00371233	−	0.130526i
$196$	21.5294	−	18.8227i	1.53781	−	1.34448i
$197$	−0.252665	−	0.942958i	−0.0180016	−	0.0671830i	0.956341	−	0.292254i	$-0.0944053\pi$
$197$	−0.252665	−	0.942958i	−0.0180016	−	0.0671830i	−0.974342	+	0.225071i	$0.927739\pi$
$198$	−7.34338	−	12.7191i	−0.521871	−	0.903908i
$199$	−7.58524	+	13.1380i	−0.537703	+	0.931330i	0.461324	+	0.887232i	$0.347375\pi$
$199$	−7.58524	+	13.1380i	−0.537703	+	0.931330i	−0.999027	+	0.0440978i	$0.985959\pi$
$200$	23.5738	+	6.31658i	1.66692	+	0.446650i
$201$	−5.39742	−	5.39742i	−0.380705	−	0.380705i
$202$	−10.6603	−	2.85641i	−0.750053	−	0.200976i
$203$	1.01105	+	10.3463i	0.0709620	+	0.726169i
$204$	−1.90628	−	3.30177i	−0.133466	−	0.231170i
$205$	−3.55923	+	2.05492i	−0.248587	+	0.143522i
$206$	7.24317	−	7.24317i	0.504656	−	0.504656i
$207$	7.03583	−	4.06214i	0.489024	−	0.282338i
$208$	4.66313	+	15.6131i	0.323330	+	1.08258i
$209$			47.2324i			3.26714i
$210$	−1.92055	−	2.68444i	−0.132530	−	0.185244i
$211$	10.0981	−	17.4904i	0.695180	−	1.20409i	−0.274940	−	0.961461i	$-0.588658\pi$
$211$	10.0981	−	17.4904i	0.695180	−	1.20409i	0.970120	−	0.242626i	$-0.0780088\pi$
$212$			6.13424i			0.421302i
$213$	1.75429	−	6.54710i	0.120202	−	0.448600i
$214$	6.02110	+	22.4711i	0.411594	+	1.53609i
$215$	−0.0630443	+	0.0630443i	−0.00429958	+	0.00429958i
$216$	3.63751	−	3.63751i	0.247501	−	0.247501i
$217$	−2.28904	−	6.09593i	−0.155390	−	0.413819i
$218$	14.7051	+	8.48998i	0.995953	+	0.575014i
$219$	−3.27893	+	12.2371i	−0.221570	+	0.826909i
$220$	−6.15033	−	10.6527i	−0.414655	−	0.718204i
$221$	2.31067	−	2.44596i	0.155432	−	0.164533i
$222$	2.59632	+	1.49899i	0.174254	+	0.100605i
$223$	−18.5472	+	4.96970i	−1.24201	+	0.332796i	−0.819245	−	0.573444i	$-0.805607\pi$
$223$	−18.5472	+	4.96970i	−1.24201	+	0.332796i	−0.422765	+	0.906239i	$0.638941\pi$
$224$	1.75785	+	1.44487i	0.117451	+	0.0965396i
$225$	4.10863	−	2.37212i	0.273909	−	0.158141i
$226$	2.72865	+	10.1835i	0.181507	+	0.677394i
$227$	21.2116	−	5.68363i	1.40786	−	0.377236i	0.526701	−	0.850051i	$-0.323429\pi$
$227$	21.2116	−	5.68363i	1.40786	−	0.377236i	0.881162	+	0.472815i	$0.156762\pi$
$228$	−31.3061	+	8.38844i	−2.07330	+	0.555538i
$229$	6.80200	+	25.3854i	0.449489	+	1.67751i	0.703805	+	0.710394i	$0.251483\pi$
$229$	6.80200	+	25.3854i	0.449489	+	1.67751i	−0.254316	+	0.967121i	$0.581850\pi$
$230$	8.77757	−	5.06773i	0.578776	−	0.334156i
$231$	2.57777	−	15.5395i	0.169605	−	1.02243i
$232$	−19.5238	+	5.23138i	−1.28180	+	0.343457i
$233$	8.80891	+	5.08583i	0.577091	+	0.333184i	0.759976	−	0.649951i	$-0.225210\pi$
$233$	8.80891	+	5.08583i	0.577091	+	0.333184i	−0.182886	+	0.983134i	$0.558544\pi$
$234$	7.82605	+	4.22639i	0.511605	+	0.276288i
$235$	0.434132	+	0.751939i	0.0283197	+	0.0490511i
$236$	−4.53113	+	16.9104i	−0.294952	+	1.10077i
$237$	−8.03790	−	4.64069i	−0.522118	−	0.301445i
$238$	0.996760	−	6.00876i	0.0646104	−	0.389490i
$239$	−0.836974	+	0.836974i	−0.0541394	+	0.0541394i	−0.733658	−	0.679519i	$-0.762189\pi$
$239$	−0.836974	+	0.836974i	−0.0541394	+	0.0541394i	0.679519	+	0.733658i	$0.262189\pi$
$240$	1.61612	−	1.61612i	0.104320	−	0.104320i
$241$	3.31190	+	12.3602i	0.213338	+	0.796189i	0.986745	+	0.162279i	$0.0518844\pi$
$241$	3.31190	+	12.3602i	0.213338	+	0.796189i	−0.773407	+	0.633910i	$0.781449\pi$
$242$	15.6080	−	58.2498i	1.00332	−	3.74444i
$243$		−	1.00000i		−	0.0641500i
$244$	15.9151	−	27.5658i	1.01886	−	1.76472i
$245$	0.236924	−	3.53216i	0.0151365	−	0.225661i
$246$		−	20.0471i		−	1.27815i
$247$	−15.0005	−	24.3553i	−0.954461	−	1.54969i
$248$	10.9644	−	6.33028i	0.696239	−	0.401973i
$249$	−1.66068	+	1.66068i	−0.105241	+	0.105241i
$250$	10.5278	−	6.07823i	0.665837	−	0.384421i
$251$	−7.87428	−	13.6386i	−0.497020	−	0.860864i	0.502974	−	0.864301i	$-0.332239\pi$
$251$	−7.87428	−	13.6386i	−0.497020	−	0.860864i	−0.999994	+	0.00343776i	$0.998906\pi$
$252$	10.7575	−	1.05124i	0.677662	−	0.0662218i
$253$	46.7210	+	12.5188i	2.93732	+	0.787053i
$254$	−18.2526	−	18.2526i	−1.14527	−	1.14527i
$255$	−0.455878	−	0.122152i	−0.0285482	−	0.00764946i
$256$	16.2508	−	28.1473i	1.01568	−	1.75920i
$257$	−6.54782	−	11.3412i	−0.408442	−	0.707442i	0.586274	−	0.810113i	$-0.300594\pi$
$257$	−6.54782	−	11.3412i	−0.408442	−	0.707442i	−0.994715	+	0.102671i	$0.967261\pi$
$258$	−0.112560	−	0.420078i	−0.00700766	−	0.0261529i
$259$	1.13033	+	3.01017i	0.0702350	+	0.187043i
$260$	6.55458	+	3.53974i	0.406498	+	0.219526i
$261$	−1.96458	+	3.40276i	−0.121605	+	0.210626i
$262$	27.7678	+	27.7678i	1.71550	+	1.71550i
$263$	−10.0561			−0.620084			−0.310042	−	0.950723i	$-0.600343\pi$
$263$	−10.0561			−0.620084			−0.310042	+	0.950723i	$0.600343\pi$
$264$	30.6269			1.88495
$265$	0.536951	+	0.536951i	0.0329846	+	0.0329846i
$266$	−47.1467	−	21.4053i	−2.89075	−	1.31244i
$267$	1.10563	−	4.12627i	0.0676636	−	0.252524i
$268$	30.1213	−	8.07097i	1.83995	−	0.493013i
$269$	−25.4408	−	14.6883i	−1.55115	−	0.895559i	−0.998048	−	0.0624485i	$-0.980109\pi$
$269$	−25.4408	−	14.6883i	−1.55115	−	0.895559i	−0.553106	−	0.833111i	$-0.686558\pi$
$270$		−	1.24755i		−	0.0759237i
$271$	1.57149	+	0.421080i	0.0954612	+	0.0255788i	0.306233	−	0.951956i	$-0.400931\pi$
$271$	1.57149	+	0.421080i	0.0954612	+	0.0255788i	−0.210772	+	0.977535i	$0.567598\pi$
$272$	4.21755			0.255727
$273$	3.60598	+	8.83159i	0.218244	+	0.534512i
$274$	−47.6248			−2.87712
$275$	27.2831	+	7.31049i	1.64523	+	0.440839i
$276$			33.1904i			1.99783i
$277$	−26.6141	−	15.3657i	−1.59909	−	0.923233i	−0.991663	−	0.128856i	$-0.958870\pi$
$277$	−26.6141	−	15.3657i	−1.59909	−	0.923233i	−0.607424	−	0.794378i	$-0.707797\pi$
$278$	−16.7969	+	4.50070i	−1.00741	+	0.269934i
$279$	0.636987	−	2.37727i	0.0381354	−	0.142323i
$280$	6.85048	−	0.669436i	0.409394	−	0.0400064i
$281$	−3.89852	−	3.89852i	−0.232566	−	0.232566i	0.581197	−	0.813763i	$-0.302585\pi$
$281$	−3.89852	−	3.89852i	−0.232566	−	0.232566i	−0.813763	+	0.581197i	$0.802585\pi$
$282$	−4.23524			−0.252205
$283$	−7.33897			−0.436257			−0.218128	−	0.975920i	$-0.569995\pi$
$283$	−7.33897			−0.436257			−0.218128	+	0.975920i	$0.569995\pi$
$284$	19.5803	+	19.5803i	1.16187	+	1.16187i
$285$	−2.00606	+	3.47459i	−0.118829	+	0.205817i
$286$	15.1541	+	50.7392i	0.896081	+	3.00027i
$287$	13.6527	−	16.6100i	0.805895	−	0.980459i
$288$	0.222595	+	0.830735i	0.0131165	+	0.0489515i
$289$	8.06454	+	13.9682i	0.474385	+	0.821659i
$290$	−2.45092	+	4.24512i	−0.143923	+	0.249282i
$291$	−3.19825	−	0.856967i	−0.187484	−	0.0502363i
$292$	−36.5973	−	36.5973i	−2.14170	−	2.14170i
$293$	−21.1201	−	5.65910i	−1.23385	−	0.330608i	−0.417771	−	0.908552i	$-0.637188\pi$
$293$	−21.1201	−	5.65910i	−1.23385	−	0.330608i	−0.816076	+	0.577944i	$0.803855\pi$
$294$	14.3431	+	9.61545i	0.836507	+	0.560785i
$295$	1.08360	+	1.87685i	0.0630897	+	0.109275i
$296$	−5.41421	+	3.12589i	−0.314694	+	0.181689i
$297$	4.20987	−	4.20987i	0.244281	−	0.244281i
$298$	−31.1053	+	17.9586i	−1.80188	+	1.04032i
$299$	−28.0674	+	8.38279i	−1.62318	+	0.484790i
$300$			19.3818i			1.11901i
$301$	0.192826	−	0.424714i	0.0111143	−	0.0244801i
$302$	−6.31877	+	10.9444i	−0.363604	+	0.629781i
$303$		−	4.47385i		−	0.257016i
$304$	9.27953	−	34.6317i	0.532217	−	1.98626i
$305$	−1.01982	−	3.80603i	−0.0583949	−	0.217933i
$306$	1.62785	−	1.62785i	0.0930582	−	0.0930582i
$307$	−2.37972	+	2.37972i	−0.135818	+	0.135818i	−0.771747	−	0.635929i	$-0.780617\pi$
$307$	−2.37972	+	2.37972i	−0.135818	+	0.135818i	0.635929	+	0.771747i	$0.280617\pi$
$308$	49.7135	+	40.8623i	2.83269	+	2.32835i
$309$	3.59610	+	2.07621i	0.204575	+	0.118112i
$310$	0.794675	−	2.96577i	0.0451345	−	0.168444i
$311$	−6.25768	−	10.8386i	−0.354841	−	0.614602i	0.632250	−	0.774764i	$-0.282132\pi$
$311$	−6.25768	−	10.8386i	−0.354841	−	0.614602i	−0.987091	+	0.160162i	$0.948798\pi$
$312$	−15.7927	+	9.72678i	−0.894083	+	0.550671i
$313$	8.39852	+	4.84889i	0.474713	+	0.274075i	0.718210	−	0.695826i	$-0.244962\pi$
$313$	8.39852	+	4.84889i	0.474713	+	0.274075i	−0.243498	+	0.969901i	$0.578295\pi$
$314$	−2.74832	+	0.736410i	−0.155097	+	0.0415580i
$315$	0.849626	−	1.03366i	0.0478710	−	0.0582403i
$316$	32.8376	−	18.9588i	1.84726	−	1.06651i
$317$	6.03514	+	22.5235i	0.338967	+	1.26504i	0.899504	+	0.436913i	$0.143928\pi$
$317$	6.03514	+	22.5235i	0.338967	+	1.26504i	−0.560536	+	0.828130i	$0.689405\pi$
$318$	−3.57782	+	0.958675i	−0.200634	+	0.0537598i
$319$	−22.5958	+	6.05453i	−1.26512	+	0.338989i
$320$	−0.905386	−	3.37895i	−0.0506126	−	0.188889i
$321$	−8.16710	+	4.71528i	−0.455843	+	0.263181i
$322$	−33.6696	+	40.9627i	−1.87633	+	2.28276i
$323$	−7.15135	+	1.91620i	−0.397912	+	0.106620i
$324$	3.53801	+	2.04267i	0.196556	+	0.113482i
$325$	−16.3902	+	4.89521i	−0.909164	+	0.271537i
$326$	−16.8753	−	29.2289i	−0.934638	−	1.61884i
$327$	−1.78152	+	6.64872i	−0.0985182	+	0.367675i
$328$	36.2041	+	20.9025i	1.99904	+	1.15414i
$329$	−3.50911	−	2.88434i	−0.193464	−	0.159019i
$330$	5.25204	−	5.25204i	0.289115	−	0.289115i
$331$	16.9938	−	16.9938i	0.934065	−	0.934065i	−0.0638916	−	0.997957i	$-0.520351\pi$
$331$	16.9938	−	16.9938i	0.934065	−	0.934065i	0.997957	+	0.0638916i	$0.0203512\pi$
$332$	−2.48328	−	9.26773i	−0.136288	−	0.508633i
$333$	−0.314544	+	1.17389i	−0.0172369	+	0.0643290i
$334$		−	5.34738i		−	0.292595i
$335$	1.93014	−	3.34309i	0.105455	−	0.182653i
$336$	−4.94304	+	10.8874i	−0.269665	+	0.593958i
$337$			6.92235i			0.377085i	0.982065	+	0.188542i	$0.0603762\pi$
$337$			6.92235i			0.377085i	−0.982065	+	0.188542i	$0.939624\pi$
$338$	−23.9284	−	21.3507i	−1.30153	−	1.16133i
$339$	−3.70118	+	2.13688i	−0.201020	+	0.116059i
$340$	1.36338	−	1.36338i	0.0739398	−	0.0739398i
$341$	12.6896	−	7.32635i	0.687181	−	0.396744i
$342$	−9.78519	−	16.9484i	−0.529122	−	0.916467i
$343$	5.33556	+	17.7350i	0.288093	+	0.957602i
$344$	0.876006	+	0.234725i	0.0472311	+	0.0126555i
$345$	2.90527	+	2.90527i	0.156414	+	0.156414i
$346$	−6.60373	−	1.76946i	−0.355019	−	0.0951270i
$347$	−13.8236	+	23.9431i	−0.742088	+	1.28533i	0.209454	+	0.977818i	$0.432831\pi$
$347$	−13.8236	+	23.9431i	−0.742088	+	1.28533i	−0.951543	+	0.307516i	$0.900502\pi$
$348$	−8.02599	−	13.9014i	−0.430238	−	0.745195i
$349$	1.89736	+	7.08103i	0.101563	+	0.379039i	0.997933	−	0.0642689i	$-0.0204715\pi$
$349$	1.89736	+	7.08103i	0.101563	+	0.379039i	−0.896369	+	0.443308i	$0.853805\pi$
$350$	−19.6617	+	23.9206i	−1.05096	+	1.27861i
$351$	−0.833795	+	3.50782i	−0.0445047	+	0.187233i
$352$	−2.56019	+	4.43438i	−0.136459	+	0.236353i
$353$	−18.1569	−	18.1569i	−0.966396	−	0.966396i	0.0330576	−	0.999453i	$-0.489476\pi$
$353$	−18.1569	−	18.1569i	−0.966396	−	0.966396i	−0.999453	+	0.0330576i	$0.989476\pi$
$354$	−10.5712			−0.561854
$355$	3.42785			0.181931
$356$	12.3403	+	12.3403i	0.654037	+	0.654037i
$357$	2.45738	−	0.240138i	0.130059	−	0.0127095i
$358$	5.83322	−	21.7699i	0.308295	−	1.15057i
$359$	−2.21189	+	0.592674i	−0.116739	+	0.0312801i	−0.316716	−	0.948521i	$-0.602580\pi$
$359$	−2.21189	+	0.592674i	−0.116739	+	0.0312801i	0.199977	+	0.979801i	$0.435913\pi$
$360$	2.25303	+	1.30079i	0.118745	+	0.0685574i
$361$			43.9381i			2.31253i
$362$	29.3453	+	7.86305i	1.54236	+	0.413273i
$363$	24.4460			1.28308
$364$	−38.6120	−	5.28204i	−2.02382	−	0.276854i
$365$	−6.40697			−0.335356
$366$	18.5651	+	4.97451i	0.970415	+	0.260022i
$367$		−	26.9876i		−	1.40874i	−0.709832	−	0.704371i	$-0.751229\pi$
$367$		−	26.9876i		−	1.40874i	0.709832	−	0.704371i	$-0.248771\pi$
$368$	−31.7971	−	18.3581i	−1.65754	−	0.956981i
$369$	7.84968	−	2.10332i	0.408638	−	0.109494i
$370$	−0.392410	+	1.46450i	−0.0204004	+	0.0761355i
$371$	−3.61730	−	1.64231i	−0.187801	−	0.0852643i
$372$	7.10963	+	7.10963i	0.368617	+	0.368617i
$373$	−16.7708			−0.868361			−0.434180	−	0.900826i	$-0.642962\pi$
$373$	−16.7708			−0.868361			−0.434180	+	0.900826i	$0.642962\pi$
$374$	13.7061			0.708726
$375$	3.48457	+	3.48457i	0.179943	+	0.179943i
$376$	4.41595	−	7.64865i	0.227735	−	0.394449i
$377$	9.72861	−	10.2982i	0.501049	−	0.530384i
$378$	2.29436	+	6.11010i	0.118009	+	0.314270i
$379$	−6.13097	−	22.8811i	−0.314927	−	1.17532i	−0.924058	−	0.382253i	$-0.875148\pi$
$379$	−6.13097	−	22.8811i	−0.314927	−	1.17532i	0.609131	−	0.793070i	$-0.291518\pi$
$380$	−8.19542	−	14.1949i	−0.420416	−	0.728183i
$381$	5.23201	−	9.06211i	0.268044	−	0.464266i
$382$	1.27411	+	0.341397i	0.0651892	+	0.0174674i
$383$	14.2007	+	14.2007i	0.725620	+	0.725620i	0.969744	−	0.244124i	$-0.0785005\pi$
$383$	14.2007	+	14.2007i	0.725620	+	0.725620i	−0.244124	+	0.969744i	$0.578501\pi$
$384$	18.1434	+	4.86150i	0.925874	+	0.248087i
$385$	7.92840	−	0.774771i	0.404069	−	0.0394860i
$386$	8.32193	+	14.4140i	0.423575	+	0.733653i
$387$	0.152677	−	0.0881483i	0.00776103	−	0.00448083i
$388$	9.56492	−	9.56492i	0.485585	−	0.485585i
$389$	28.3573	−	16.3721i	1.43777	−	0.830099i	0.440078	−	0.897959i	$-0.354951\pi$
$389$	28.3573	−	16.3721i	1.43777	−	0.830099i	0.997695	+	0.0678608i	$0.0216174\pi$
$390$	−1.04020	+	4.37619i	−0.0526728	+	0.221597i
$391$			7.58180i			0.383428i
$392$	−32.3202	+	15.8773i	−1.63242	+	0.801924i
$393$	−7.95947	+	13.7862i	−0.401502	+	0.695422i
$394$			2.40819i			0.121323i
$395$	1.21486	−	4.53391i	0.0611261	−	0.228126i
$396$	6.29518	+	23.4939i	0.316345	+	1.18061i
$397$	2.58612	−	2.58612i	0.129793	−	0.129793i	−0.639226	−	0.769019i	$-0.720745\pi$
$397$	2.58612	−	2.58612i	0.129793	−	0.129793i	0.769019	+	0.639226i	$0.220745\pi$
$398$	26.4622	−	26.4622i	1.32643	−	1.32643i
$399$	3.43492	−	20.7067i	0.171961	−	1.03663i
$400$	−18.5682	−	10.7204i	−0.928411	−	0.536018i
$401$	−1.45628	+	5.43493i	−0.0727234	+	0.271407i	−0.992707	−	0.120548i	$-0.961535\pi$
$401$	−1.45628	+	5.43493i	−0.0727234	+	0.271407i	0.919984	+	0.391956i	$0.128201\pi$
$402$	9.41486	+	16.3070i	0.469570	+	0.813320i
$403$	−4.21659	+	7.80790i	−0.210043	+	0.388939i
$404$	15.8285	+	9.13860i	0.787499	+	0.454663i
$405$	0.488495	−	0.130892i	0.0242735	−	0.00650407i
$406$	4.19666	−	25.2987i	0.208277	−	1.25555i
$407$	−6.26613	+	3.61775i	−0.310601	+	0.179325i
$408$	1.24252	+	4.63714i	0.0615139	+	0.229573i
$409$	−9.87215	+	2.64523i	−0.488146	+	0.130798i	−0.494493	−	0.869181i	$-0.664646\pi$
$409$	−9.87215	+	2.64523i	−0.488146	+	0.130798i	0.00634701	+	0.999980i	$0.497980\pi$
$410$	9.79289	−	2.62400i	0.483637	−	0.129590i
$411$	−4.99674	−	18.6481i	−0.246471	−	0.919843i
$412$	−14.6913	+	8.48202i	−0.723788	+	0.417879i
$413$	−8.75880	−	7.19936i	−0.430993	−	0.354257i
$414$	−19.3585	+	5.18708i	−0.951416	+	0.254931i
$415$	−1.02861	−	0.593866i	−0.0504923	−	0.0291517i
$416$	−0.0881589	−	3.09966i	−0.00432235	−	0.151974i
$417$	−3.52462	−	6.10481i	−0.172601	−	0.298954i
$418$	30.1564	−	112.545i	1.47500	−	5.50476i
$419$	12.7783	+	7.37756i	0.624261	+	0.360417i	0.778526	−	0.627612i	$-0.215968\pi$
$419$	12.7783	+	7.37756i	0.624261	+	0.360417i	−0.154265	+	0.988029i	$0.549301\pi$
$420$	1.92160	+	5.11741i	0.0937646	+	0.249704i
$421$	−15.6726	+	15.6726i	−0.763838	+	0.763838i	−0.977014	−	0.213176i	$-0.931619\pi$
$421$	−15.6726	+	15.6726i	−0.763838	+	0.763838i	0.213176	+	0.977014i	$0.431619\pi$
$422$	−35.2287	+	35.2287i	−1.71490	+	1.71490i
$423$	−0.444356	−	1.65836i	−0.0216053	−	0.0806323i
$424$	1.99916	−	7.46098i	0.0970879	−	0.362337i
$425$			4.42746i			0.214763i
$426$	−8.36022	+	14.4803i	−0.405054	+	0.701574i
$427$	11.9944	+	16.7651i	0.580448	+	0.811321i
$428$		−	38.5270i		−	1.86227i
$429$	−18.2776	+	11.2573i	−0.882452	+	0.543507i
$430$	0.190473	−	0.109970i	0.00918543	−	0.00530321i
$431$	17.8538	−	17.8538i	0.859990	−	0.859990i	−0.131347	−	0.991336i	$-0.541930\pi$
$431$	17.8538	−	17.8538i	0.859990	−	0.859990i	0.991336	+	0.131347i	$0.0419302\pi$
$432$	−3.91384	+	2.25966i	−0.188305	+	0.108718i
$433$	−12.7247	−	22.0399i	−0.611512	−	1.05917i	−0.990986	−	0.133967i	$-0.957228\pi$
$433$	−12.7247	−	22.0399i	−0.611512	−	1.05917i	0.379474	−	0.925203i	$-0.376105\pi$
$434$	1.56225	+	15.9868i	0.0749903	+	0.767391i
$435$	−1.91938	−	0.514297i	−0.0920273	−	0.0246586i
$436$	−19.8842	−	19.8842i	−0.952278	−	0.952278i
$437$	62.2565	+	16.6816i	2.97813	+	0.797989i
$438$	15.6260	−	27.0651i	0.746640	−	1.29322i
$439$	−6.29997	−	10.9119i	−0.300681	−	0.520795i	0.675609	−	0.737260i	$-0.263881\pi$
$439$	−6.29997	−	10.9119i	−0.300681	−	0.520795i	−0.976290	+	0.216465i	$0.930547\pi$
$440$	4.00881	+	14.9611i	0.191113	+	0.713242i
$441$	−2.26019	+	6.62507i	−0.107628	+	0.315479i
$442$	−7.06751	+	4.35292i	−0.336167	+	0.207047i
$443$	−5.24317	+	9.08144i	−0.249111	+	0.431472i	−0.963279	−	0.268501i	$-0.913472\pi$
$443$	−5.24317	+	9.08144i	−0.249111	+	0.431472i	0.714169	+	0.699974i	$0.246805\pi$
$444$	−3.51074	−	3.51074i	−0.166612	−	0.166612i
$445$	2.16038			0.102412
$446$	47.3670			2.24289
$447$	−10.2955	−	10.2955i	−0.486959	−	0.486959i
$448$	10.6484	+	14.8839i	0.503092	+	0.703196i
$449$	−1.45535	+	5.43146i	−0.0686824	+	0.256326i	−0.991727	−	0.128368i	$-0.959026\pi$
$449$	−1.45535	+	5.43146i	−0.0686824	+	0.256326i	0.923044	+	0.384694i	$0.125693\pi$
$450$	−11.3045	+	3.02904i	−0.532901	+	0.142790i
$451$	41.9008	+	24.1915i	1.97303	+	1.13913i
$452$		−	17.4597i		−	0.821237i
$453$	−4.94839	−	1.32592i	−0.232496	−	0.0622970i
$454$	−54.1716			−2.54240
$455$	−3.84220	+	2.91749i	−0.180125	+	0.136774i
$456$	40.8109			1.91114
$457$	−11.4453	−	3.06675i	−0.535387	−	0.143457i	−0.0190122	−	0.999819i	$-0.506052\pi$
$457$	−11.4453	−	3.06675i	−0.535387	−	0.143457i	−0.516375	+	0.856363i	$0.672719\pi$
$458$		−	64.8310i		−	3.02935i
$459$	0.808199	+	0.466614i	0.0377235	+	0.0217797i
$460$	−16.2134	+	4.34436i	−0.755952	+	0.202557i
$461$	2.12757	−	7.94019i	0.0990907	−	0.369812i	−0.898517	−	0.438938i	$-0.855355\pi$
$461$	2.12757	−	7.94019i	0.0990907	−	0.369812i	0.997608	+	0.0691268i	$0.0220213\pi$
$462$	−16.0638	+	35.3817i	−0.747354	+	1.64610i
$463$	−21.3807	−	21.3807i	−0.993646	−	0.993646i	0.00633382	−	0.999980i	$-0.497984\pi$
$463$	−21.3807	−	21.3807i	−0.993646	−	0.993646i	−0.999980	+	0.00633382i	$0.997984\pi$
$464$	17.7572			0.824356
$465$	1.24466			0.0577197
$466$	−17.7427	−	17.7427i	−0.821913	−	0.821913i
$467$	−14.3612	+	24.8744i	−0.664559	+	1.15105i	0.314846	+	0.949143i	$0.398047\pi$
$467$	−14.3612	+	24.8744i	−0.664559	+	1.15105i	−0.979405	+	0.201907i	$0.935286\pi$
$468$	−10.7075	−	10.1153i	−0.494955	−	0.467579i
$469$	−3.30493	+	19.9230i	−0.152607	+	0.919961i
$470$	−0.554358	−	2.06889i	−0.0255706	−	0.0954309i
$471$	−0.576701	−	0.998876i	−0.0265730	−	0.0460258i
$472$	11.0223	−	19.0912i	0.507342	−	0.878742i
$473$	1.01384	+	0.271659i	0.0466166	+	0.0124909i
$474$	16.1897	+	16.1897i	0.743619	+	0.743619i
$475$	36.3552	+	9.74136i	1.66809	+	0.446964i
$476$	−4.17001	+	9.18477i	−0.191132	+	0.420983i
$477$	−0.750763	−	1.30036i	−0.0343751	−	0.0595394i
$478$	2.52872	−	1.45995i	0.115661	−	0.0667768i
$479$	12.0866	−	12.0866i	0.552252	−	0.552252i	−0.374838	−	0.927090i	$-0.622302\pi$
$479$	12.0866	−	12.0866i	0.552252	−	0.552252i	0.927090	+	0.374838i	$0.122302\pi$
$480$	−0.376674	+	0.217473i	−0.0171927	+	0.00992624i
$481$	2.08215	−	3.85554i	0.0949379	−	0.175798i
$482$		−	31.5663i		−	1.43780i
$483$	−19.5721	−	8.88599i	−0.890560	−	0.404327i
$484$	−49.9351	+	86.4902i	−2.26978	+	3.93137i
$485$		−	1.67450i		−	0.0760350i
$486$	−0.638467	+	2.38279i	−0.0289615	+	0.108086i
$487$	−3.91992	−	14.6293i	−0.177628	−	0.662918i	−0.996089	−	0.0883554i	$-0.971839\pi$
$487$	−3.91992	−	14.6293i	−0.177628	−	0.662918i	0.818461	−	0.574563i	$-0.194828\pi$
$488$	−28.3410	+	28.3410i	−1.28294	+	1.28294i
$489$	9.67442	−	9.67442i	0.437492	−	0.437492i
$490$	−2.81971	+	8.26513i	−0.127381	+	0.373380i
$491$	4.15520	+	2.39900i	0.187521	+	0.108266i	0.590822	−	0.806802i	$-0.298804\pi$
$491$	4.15520	+	2.39900i	0.187521	+	0.108266i	−0.403300	+	0.915068i	$0.632137\pi$
$492$	−8.59276	+	32.0686i	−0.387391	+	1.44576i
$493$	−1.83341	−	3.17555i	−0.0825724	−	0.143020i
$494$	20.1931	+	67.6109i	0.908531	+	3.04196i
$495$	2.60754	+	1.50546i	0.117200	+	0.0676656i
$496$	−10.7436	+	2.87875i	−0.482403	+	0.129259i
$497$	−16.7885	+	6.30411i	−0.753066	+	0.282778i
$498$	5.01735	−	2.89677i	0.224833	−	0.129807i
$499$	3.91188	+	14.5993i	0.175120	+	0.653556i	0.996531	+	0.0832201i	$0.0265205\pi$
$499$	3.91188	+	14.5993i	0.175120	+	0.653556i	−0.821411	+	0.570336i	$0.806813\pi$
$500$	−19.4463	+	5.21061i	−0.869664	+	0.233026i
$501$	2.09383	−	0.561041i	0.0935456	−	0.0250655i
$502$	10.0549	+	37.5255i	0.448774	+	1.67485i
$503$	13.9638	−	8.06201i	0.622615	−	0.359467i	−0.155271	−	0.987872i	$-0.549625\pi$
$503$	13.9638	−	8.06201i	0.622615	−	0.359467i	0.777887	+	0.628405i	$0.216292\pi$
$504$	−13.4268	−	2.22730i	−0.598078	−	0.0992120i
$505$	2.18546	−	0.585591i	0.0972515	−	0.0260585i
$506$	−103.334	−	59.6596i	−4.59373	−	2.65219i
$507$	5.84960	−	11.6096i	0.259790	−	0.515599i
$508$	21.3745	+	37.0218i	0.948342	+	1.64258i
$509$	8.57960	−	32.0195i	0.380284	−	1.41924i	−0.465184	−	0.885214i	$-0.654012\pi$
$509$	8.57960	−	32.0195i	0.380284	−	1.41924i	0.845468	−	0.534026i	$-0.179321\pi$
$510$	1.00827	+	0.582126i	0.0446470	+	0.0257770i
$511$	31.3792	−	11.7830i	1.38813	−	0.521248i
$512$	−30.1297	+	30.1297i	−1.33156	+	1.33156i
$513$	5.60973	−	5.60973i	0.247675	−	0.247675i
$514$	8.36113	+	31.2042i	0.368794	+	1.37636i
$515$	−0.543518	+	2.02844i	−0.0239503	+	0.0893837i
$516$			0.720232i			0.0317064i
$517$	5.11080	−	8.85217i	0.224773	−	0.389318i
$518$	−0.771437	−	7.89428i	−0.0338950	−	0.346855i
$519$		−	2.77142i		−	0.121652i
$520$	−6.81862	−	6.44148i	−0.299016	−	0.282478i
$521$	−8.41886	+	4.86063i	−0.368837	+	0.212948i	−0.672950	−	0.739688i	$-0.734973\pi$
$521$	−8.41886	+	4.86063i	−0.368837	+	0.212948i	0.304113	+	0.952636i	$0.401640\pi$
$522$	6.85375	−	6.85375i	0.299980	−	0.299980i
$523$	−16.8431	+	9.72437i	−0.736497	+	0.425217i	−0.820794	−	0.571224i	$-0.806469\pi$
$523$	−16.8431	+	9.72437i	−0.736497	+	0.425217i	0.0842971	+	0.996441i	$0.473136\pi$
$524$	−32.5171	−	56.3213i	−1.42052	−	2.46041i
$525$	−11.4293	−	5.18905i	−0.498815	−	0.226469i
$526$	23.9615	+	6.42047i	1.04477	+	0.279946i
$527$	1.62408	+	1.62408i	0.0707460	+	0.0707460i
$528$	−25.9896	−	6.96390i	−1.13105	−	0.303065i
$529$	21.5019	−	37.2424i	0.934865	−	1.61923i
$530$	−0.936617	−	1.62227i	−0.0406840	−	0.0704668i
$531$	−1.10912	−	4.13930i	−0.0481317	−	0.179630i
$532$	66.2441	+	54.4498i	2.87204	+	2.36070i
$533$	−29.2890	+	0.833021i	−1.26865	+	0.0360821i
$534$	−5.26898	+	9.12614i	−0.228011	+	0.394927i
$535$	−3.37240	−	3.37240i	−0.145801	−	0.145801i
$536$	−39.2663			−1.69605
$537$	9.13629			0.394260
$538$	51.2422	+	51.2422i	2.20921	+	2.20921i
$539$	−37.4058	+	18.3756i	−1.61118	+	0.791492i
$540$	−0.534738	+	1.99567i	−0.0230115	+	0.0858799i
$541$	−10.2493	+	2.74629i	−0.440652	+	0.118072i	−0.472322	−	0.881426i	$-0.656584\pi$
$541$	−10.2493	+	2.74629i	−0.440652	+	0.118072i	0.0316700	+	0.999498i	$0.489917\pi$
$542$	−3.47569	−	2.00669i	−0.149294	−	0.0861947i
$543$			12.3155i			0.528509i
$544$	−0.775265	−	0.207732i	−0.0332392	−	0.00890642i
$545$	−3.48105			−0.149112
$546$	−2.95361	−	23.3461i	−0.126403	−	0.999122i
$547$	−23.4548			−1.00285			−0.501427	−	0.865200i	$-0.667192\pi$
$547$	−23.4548			−1.00285			−0.501427	+	0.865200i	$0.667192\pi$
$548$	76.1838	+	20.4134i	3.25441	+	0.872017i
$549$			7.79133i			0.332526i
$550$	−60.3425	−	34.8388i	−2.57301	−	1.48553i
$551$	−30.1093	+	8.06777i	−1.28270	+	0.343699i
$552$	10.8168	−	40.3689i	0.460395	−	1.71822i
$553$	2.38828	+	24.4398i	0.101560	+	1.03929i
$554$	53.6054	+	53.6054i	2.27748	+	2.27748i
$555$	−0.614613			−0.0260889
$556$	28.7985			1.22133
$557$	14.1726	+	14.1726i	0.600512	+	0.600512i	0.940448	−	0.339936i	$-0.110406\pi$
$557$	14.1726	+	14.1726i	0.600512	+	0.600512i	−0.339936	+	0.940448i	$0.610406\pi$
$558$	−3.03561	+	5.25784i	−0.128508	+	0.222582i
$559$	−0.609062	+	0.181907i	−0.0257606	+	0.00769383i
$560$	−5.96546	−	0.989578i	−0.252087	−	0.0418173i
$561$	1.43803	+	5.36680i	0.0607136	+	0.226586i
$562$	6.80029	+	11.7785i	0.286853	+	0.496844i
$563$	−22.8772	+	39.6245i	−0.964159	+	1.66997i	−0.252299	+	0.967649i	$0.581187\pi$
$563$	−22.8772	+	39.6245i	−0.964159	+	1.66997i	−0.711859	+	0.702322i	$0.752147\pi$
$564$	6.77497	+	1.81535i	0.285278	+	0.0764399i
$565$	−1.52831	−	1.52831i	−0.0642964	−	0.0642964i
$566$	17.4872	+	4.68569i	0.735044	+	0.196954i
$567$	−2.15177	+	1.53945i	−0.0903657	+	0.0646508i
$568$	−17.4339	−	30.1964i	−0.731510	−	1.26701i
$569$	20.8891	−	12.0603i	0.875717	−	0.505595i	0.00647287	−	0.999979i	$-0.497940\pi$
$569$	20.8891	−	12.0603i	0.875717	−	0.505595i	0.869244	+	0.494384i	$0.164606\pi$
$570$	6.99843	−	6.99843i	0.293132	−	0.293132i
$571$	15.0931	−	8.71402i	0.631628	−	0.364671i	−0.149754	−	0.988723i	$-0.547848\pi$
$571$	15.0931	−	8.71402i	0.631628	−	0.364671i	0.781382	+	0.624053i	$0.214515\pi$
$572$	−2.49321	−	87.6613i	−0.104247	−	3.66530i
$573$			0.534713i			0.0223380i
$574$	−43.1366	+	30.8614i	−1.80049	+	1.28813i
$575$	19.2717	−	33.3796i	0.803687	−	1.39203i
$576$			6.91705i			0.288210i
$577$	5.64807	−	21.0789i	0.235132	−	0.877525i	−0.742957	−	0.669339i	$-0.766577\pi$
$577$	5.64807	−	21.0789i	0.235132	−	0.877525i	0.978089	−	0.208186i	$-0.0667559\pi$
$578$	−10.2979	−	38.4323i	−0.428336	−	1.59857i
$579$	−4.77086	+	4.77086i	−0.198270	+	0.198270i
$580$	5.74025	−	5.74025i	0.238351	−	0.238351i
$581$	6.12994	+	1.01686i	0.254313	+	0.0421866i
$582$	7.07361	+	4.08395i	0.293211	+	0.169285i
$583$	2.31373	−	8.63496i	0.0958249	−	0.357623i
$584$	32.5856	+	56.4399i	1.34840	+	2.33550i
$585$	−1.82269	+	0.0518399i	−0.0753589	+	0.00214332i
$586$	46.7116	+	26.9689i	1.92964	+	1.11408i
$587$	−13.4282	+	3.59809i	−0.554243	+	0.148509i	−0.525060	−	0.851065i	$-0.675957\pi$
$587$	−13.4282	+	3.59809i	−0.554243	+	0.148509i	−0.0291829	+	0.999574i	$0.509291\pi$
$588$	−18.8227	−	21.5294i	−0.776236	−	0.887857i
$589$	16.9091	−	9.76250i	0.696729	−	0.402257i
$590$	−1.38369	−	5.16399i	−0.0569655	−	0.212598i
$591$	−0.942958	+	0.252665i	−0.0387881	+	0.0103932i
$592$	5.30520	−	1.42152i	0.218042	−	0.0584243i
$593$	−8.72592	−	32.5656i	−0.358331	−	1.33731i	−0.876241	−	0.481873i	$-0.839957\pi$
$593$	−8.72592	−	32.5656i	−0.358331	−	1.33731i	0.517911	−	0.855435i	$-0.326710\pi$
$594$	−12.7191	+	7.34338i	−0.521871	+	0.301303i
$595$	0.438958	+	1.16899i	0.0179955	+	0.0479239i
$596$	57.4557	−	15.3952i	2.35348	−	0.630612i
$597$	13.1380	+	7.58524i	0.537703	+	0.310443i
$598$	72.2309	−	2.05435i	2.95374	−	0.0840086i
$599$	−6.39544	−	11.0772i	−0.261311	−	0.452603i	0.705280	−	0.708929i	$-0.250821\pi$
$599$	−6.39544	−	11.0772i	−0.261311	−	0.452603i	−0.966590	+	0.256326i	$0.917488\pi$
$600$	6.31658	−	23.5738i	0.257873	−	0.962396i
$601$	−26.5897	−	15.3516i	−1.08462	−	0.626205i	−0.152480	−	0.988307i	$-0.548726\pi$
$601$	−26.5897	−	15.3516i	−1.08462	−	0.626205i	−0.932138	+	0.362102i	$0.882059\pi$
$602$	−0.730630	+	0.888891i	−0.0297783	+	0.0362285i
$603$	−5.39742	+	5.39742i	−0.219800	+	0.219800i
$604$	14.7990	−	14.7990i	0.602164	−	0.602164i
$605$	3.19979	+	11.9418i	0.130090	+	0.485502i
$606$	−2.85641	+	10.6603i	−0.116034	+	0.433044i
$607$			26.8554i			1.09003i	0.838427	+	0.545014i	$0.183476\pi$
$607$			26.8554i			1.09003i	−0.838427	+	0.545014i	$0.816524\pi$
$608$	−3.41150	+	5.90889i	−0.138355	+	0.239637i
$609$	10.3463	−	1.01105i	0.419254	−	0.0409699i
$610$			9.72010i			0.393555i
$611$	0.175988	+	6.18773i	0.00711971	+	0.250329i
$612$	−3.30177	+	1.90628i	−0.133466	+	0.0770567i
$613$	−7.54924	+	7.54924i	−0.304911	+	0.304911i	−0.842932	−	0.538021i	$-0.819172\pi$
$613$	−7.54924	+	7.54924i	−0.304911	+	0.304911i	0.538021	+	0.842932i	$0.319172\pi$
$614$	7.18975	−	4.15100i	0.290155	−	0.167521i
$615$	2.05492	+	3.55923i	0.0828624	+	0.143522i
$616$	−47.1485	−	65.9019i	−1.89967	−	2.65526i
$617$	−8.37021	−	2.24279i	−0.336972	−	0.0902913i	0.0863653	−	0.996264i	$-0.472475\pi$
$617$	−8.37021	−	2.24279i	−0.336972	−	0.0902913i	−0.423337	+	0.905972i	$0.639141\pi$
$618$	−7.24317	−	7.24317i	−0.291363	−	0.291363i
$619$	−5.25761	−	1.40877i	−0.211321	−	0.0566233i	0.151605	−	0.988441i	$-0.451556\pi$
$619$	−5.25761	−	1.40877i	−0.211321	−	0.0566233i	−0.362926	+	0.931818i	$0.618222\pi$
$620$	−2.54243	+	4.40362i	−0.102106	+	0.176854i
$621$	−4.06214	−	7.03583i	−0.163008	−	0.282338i
$622$	7.99065	+	29.8215i	0.320396	+	1.19573i
$623$	−10.5808	+	3.97313i	−0.423912	+	0.159180i
$624$	15.6131	−	4.66313i	0.625026	−	0.186674i
$625$	10.6145	−	18.3849i	0.424580	−	0.735394i
$626$	−16.9161	−	16.9161i	−0.676102	−	0.676102i
$627$	47.2324			1.88628
$628$	4.71204			0.188031
$629$	−0.801970	−	0.801970i	−0.0319766	−	0.0319766i
$630$	−2.68444	+	1.92055i	−0.106951	+	0.0765164i
$631$	1.72756	−	6.44735i	0.0687731	−	0.256665i	−0.922976	−	0.384857i	$-0.874251\pi$
$631$	1.72756	−	6.44735i	0.0687731	−	0.256665i	0.991749	+	0.128192i	$0.0409174\pi$
$632$	−46.1185	+	12.3574i	−1.83449	+	0.491551i
$633$	−17.4904	−	10.0981i	−0.695180	−	0.401363i
$634$		−	57.5219i		−	2.28449i
$635$	5.11162	+	1.36966i	0.202849	+	0.0543531i
$636$	6.13424			0.243239
$637$	13.4523	−	21.3550i	0.532999	−	0.846116i
$638$	57.7068			2.28463
$639$	−6.54710	−	1.75429i	−0.258999	−	0.0693987i
$640$			9.49928i			0.375492i
$641$	−3.17545	−	1.83335i	−0.125423	−	0.0724129i	0.435976	−	0.899958i	$-0.356403\pi$
$641$	−3.17545	−	1.83335i	−0.125423	−	0.0724129i	−0.561399	+	0.827545i	$0.689737\pi$
$642$	22.4711	−	6.02110i	0.886862	−	0.237634i
$643$	4.98038	−	18.5870i	0.196407	−	0.733001i	−0.795491	−	0.605965i	$-0.792787\pi$
$643$	4.98038	−	18.5870i	0.196407	−	0.733001i	0.991898	−	0.127036i	$-0.0405462\pi$
$644$	71.4180	−	51.0950i	2.81426	−	2.01342i
$645$	0.0630443	+	0.0630443i	0.00248237	+	0.00248237i
$646$	18.2636			0.718573
$647$	2.14470			0.0843167			0.0421583	−	0.999111i	$-0.486577\pi$
$647$	2.14470			0.0843167			0.0421583	+	0.999111i	$0.486577\pi$
$648$	−3.63751	−	3.63751i	−0.142895	−	0.142895i
$649$	12.7566	−	22.0952i	0.500742	−	0.867311i
$650$	42.1799	−	1.19966i	1.65443	−	0.0470544i
$651$	−6.09593	+	2.28904i	−0.238918	+	0.0897144i
$652$	14.4665	+	53.9898i	0.566553	+	2.11440i
$653$	11.3978	+	19.7415i	0.446029	+	0.772544i	0.998123	−	0.0612374i	$-0.0195047\pi$
$653$	11.3978	+	19.7415i	0.446029	+	0.772544i	−0.552095	+	0.833781i	$0.686171\pi$
$654$	8.48998	−	14.7051i	0.331984	−	0.575014i
$655$	−7.77632	−	2.08366i	−0.303846	−	0.0814153i
$656$	−25.9696	−	25.9696i	−1.01394	−	1.01394i
$657$	12.2371	+	3.27893i	0.477416	+	0.127923i
$658$	6.51993	+	9.11323i	0.254173	+	0.355271i
$659$	−16.2426	−	28.1330i	−0.632721	−	1.09591i	−0.986993	−	0.160763i	$-0.948605\pi$
$659$	−16.2426	−	28.1330i	−0.632721	−	1.09591i	0.354272	−	0.935142i	$-0.384729\pi$
$660$	−10.6527	+	6.15033i	−0.414655	+	0.239401i
$661$	−24.4397	+	24.4397i	−0.950596	+	0.950596i	−0.998836	−	0.0482402i	$-0.984639\pi$
$661$	−24.4397	+	24.4397i	−0.950596	+	0.950596i	0.0482402	+	0.998836i	$0.484639\pi$
$662$	−51.3428	+	29.6428i	−1.99549	+	1.15210i
$663$	−2.44596	−	2.31067i	−0.0949930	−	0.0897390i
$664$			12.0815i			0.468853i
$665$	10.5647	−	1.03240i	0.409683	−	0.0400346i
$666$	1.49899	−	2.59632i	0.0580845	−	0.100605i
$667$			31.9216i			1.23601i
$668$	−2.29204	+	8.55402i	−0.0886818	+	0.330965i
$669$	4.96970	+	18.5472i	0.192140	+	0.717075i
$670$	−6.73357	+	6.73357i	−0.260141	+	0.260141i
$671$	−32.8005	+	32.8005i	−1.26625	+	1.26625i
$672$	1.44487	−	1.75785i	0.0557372	−	0.0678104i
$673$	−14.0303	−	8.10040i	−0.540828	−	0.312247i	0.204586	−	0.978849i	$-0.434415\pi$
$673$	−14.0303	−	8.10040i	−0.540828	−	0.312247i	−0.745415	+	0.666601i	$0.767748\pi$
$674$	4.41969	−	16.4945i	0.170240	−	0.635345i
$675$	−2.37212	−	4.10863i	−0.0913029	−	0.158141i
$676$	29.1259	+	44.4105i	1.12023	+	1.70809i
$677$	16.1987	+	9.35233i	0.622567	+	0.359439i	0.777868	−	0.628428i	$-0.216301\pi$
$677$	16.1987	+	9.35233i	0.622567	+	0.359439i	−0.155301	+	0.987867i	$0.549635\pi$
$678$	10.1835	−	2.72865i	0.391094	−	0.104793i
$679$	3.07955	+	8.20113i	0.118182	+	0.314731i
$680$	−2.10259	+	1.21393i	−0.0806306	+	0.0465521i
$681$	−5.68363	−	21.2116i	−0.217797	−	0.812830i
$682$	−34.9144	+	9.35527i	−1.33694	+	0.358232i
$683$	−6.89832	+	1.84840i	−0.263957	+	0.0707270i	−0.388370	−	0.921503i	$-0.626962\pi$
$683$	−6.89832	+	1.84840i	−0.263957	+	0.0707270i	0.124413	+	0.992230i	$0.460295\pi$
$684$	8.38844	+	31.3061i	0.320740	+	1.19702i
$685$	8.45547	−	4.88177i	0.323067	−	0.186523i
$686$	−1.39029	−	45.6655i	−0.0530817	−	1.74352i
$687$	25.3854	−	6.80200i	0.968514	−	0.259512i
$688$	−0.689998	−	0.398370i	−0.0263059	−	0.0151877i
$689$	1.54931	+	5.18741i	0.0590239	+	0.197624i
$690$	−5.06773	−	8.77757i	−0.192925	−	0.334156i
$691$	−12.0995	+	45.1559i	−0.460286	+	1.71781i	0.211778	+	0.977318i	$0.432074\pi$
$691$	−12.0995	+	45.1559i	−0.460286	+	1.71781i	−0.672064	+	0.740493i	$0.734592\pi$
$692$	9.80532	+	5.66110i	0.372742	+	0.215203i
$693$	−15.5395	−	2.57777i	−0.590298	−	0.0979214i
$694$	48.2256	−	48.2256i	1.83062	−	1.83062i
$695$	2.52083	−	2.52083i	0.0956205	−	0.0956205i
$696$	5.23138	+	19.5238i	0.198295	+	0.740046i
$697$	−1.96287	+	7.32554i	−0.0743491	+	0.277475i
$698$		−	18.0840i		−	0.684491i
$699$	5.08583	−	8.80891i	0.192364	−	0.333184i
$700$	41.7051	−	29.8373i	1.57631	−	1.12775i
$701$		−	12.2740i		−	0.463581i	−0.972766	−	0.231790i	$-0.925542\pi$
$701$		−	12.2740i		−	0.463581i	0.972766	−	0.231790i	$-0.0744584\pi$
$702$	4.22639	−	7.82605i	0.159515	−	0.295375i
$703$	−8.34973	+	4.82072i	−0.314916	+	0.181817i
$704$	−29.1199	+	29.1199i	−1.09750	+	1.09750i
$705$	0.751939	−	0.434132i	0.0283197	−	0.0163504i
$706$	31.6716	+	54.8568i	1.19198	+	2.06456i
$707$	−9.62668	+	6.88727i	−0.362049	+	0.259023i
$708$	16.9104	+	4.53113i	0.635533	+	0.170290i
$709$	−31.1400	−	31.1400i	−1.16949	−	1.16949i	−0.982330	−	0.187156i	$-0.940073\pi$
$709$	−31.1400	−	31.1400i	−1.16949	−	1.16949i	−0.187156	−	0.982330i	$-0.559927\pi$
$710$	−8.16786	−	2.18857i	−0.306534	−	0.0821356i
$711$	−4.64069	+	8.03790i	−0.174039	+	0.301445i
$712$	−10.9876	−	19.0311i	−0.411778	−	0.713221i
$713$	−5.17505	−	19.3136i	−0.193807	−	0.723299i
$714$	−6.00876	−	0.996760i	−0.224872	−	0.0373028i
$715$	−7.89153	−	7.45505i	−0.295126	−	0.278803i
$716$	−18.6624	+	32.3242i	−0.697447	+	1.20801i
$717$	0.836974	+	0.836974i	0.0312574	+	0.0312574i
$718$	5.64888			0.210814
$719$	0.534003			0.0199150			0.00995748	−	0.999950i	$-0.496830\pi$
$719$	0.534003			0.0199150			0.00995748	+	0.999950i	$0.496830\pi$
$720$	−1.61612	−	1.61612i	−0.0602294	−	0.0602294i
$721$	−1.06850	−	10.9342i	−0.0397930	−	0.407211i
$722$	28.0530	−	104.695i	1.04403	−	3.89635i
$723$	12.3602	−	3.31190i	0.459680	−	0.123171i
$724$	−43.5724	−	25.1565i	−1.61936	−	0.934935i
$725$			18.6409i			0.692306i
$726$	−58.2498	−	15.6080i	−2.16185	−	0.579266i
$727$	17.0326			0.631703			0.315851	−	0.948809i	$-0.397710\pi$
$727$	17.0326			0.631703			0.315851	+	0.948809i	$0.397710\pi$
$728$	45.2418	+	19.0082i	1.67677	+	0.704491i
$729$	−1.00000			−0.0370370
$730$	15.2665	+	4.09064i	0.565038	+	0.151401i
$731$			0.164525i			0.00608518i
$732$	−27.5658	−	15.9151i	−1.01886	−	0.588240i
$733$	−27.9251	+	7.48252i	−1.03144	+	0.276373i	−0.734561	−	0.678542i	$-0.762612\pi$
$733$	−27.9251	+	7.48252i	−1.03144	+	0.276373i	−0.296877	+	0.954916i	$0.595945\pi$
$734$	−17.2307	+	64.3059i	−0.635997	+	2.37357i
$735$	−3.53216	−	0.236924i	−0.130286	−	0.00873907i
$736$	4.94070	+	4.94070i	0.182116	+	0.182116i
$737$	−45.4449			−1.67398
$738$	−20.0471			−0.737942
$739$	−10.0479	−	10.0479i	−0.369617	−	0.369617i	0.497721	−	0.867337i	$-0.334170\pi$
$739$	−10.0479	−	10.0479i	−0.369617	−	0.369617i	−0.867337	+	0.497721i	$0.834170\pi$
$740$	1.25545	−	2.17451i	0.0461513	−	0.0799364i
$741$	−24.3553	+	15.0005i	−0.894713	+	0.551058i
$742$	7.57072	+	6.22281i	0.277930	+	0.228446i
$743$	12.9109	+	48.1840i	0.473654	+	1.76770i	0.626470	+	0.779446i	$0.284499\pi$
$743$	12.9109	+	48.1840i	0.473654	+	1.76770i	−0.152816	+	0.988255i	$0.548834\pi$
$744$	−6.33028	−	10.9644i	−0.232080	−	0.401973i
$745$	3.68169	−	6.37688i	0.134887	−	0.233631i
$746$	39.9614	+	10.7076i	1.46309	+	0.392034i
$747$	1.66068	+	1.66068i	0.0607612	+	0.0607612i
$748$	−21.9252	−	5.87484i	−0.801664	−	0.214805i
$749$	22.7190	+	10.3148i	0.830135	+	0.376893i
$750$	−6.07823	−	10.5278i	−0.221946	−	0.384421i
$751$	−4.94920	+	2.85742i	−0.180599	+	0.104269i	−0.587574	−	0.809170i	$-0.699917\pi$
$751$	−4.94920	+	2.85742i	−0.180599	+	0.104269i	0.406975	+	0.913439i	$0.366584\pi$
$752$	−5.48647	+	5.48647i	−0.200071	+	0.200071i
$753$	−13.6386	+	7.87428i	−0.497020	+	0.286955i
$754$	−29.7563	+	18.3271i	−1.08366	+	0.667433i
$755$		−	2.59082i		−	0.0942894i
$756$	−1.05124	−	10.7575i	−0.0382332	−	0.391248i
$757$	−8.98844	+	15.5684i	−0.326690	+	0.565844i	−0.981853	−	0.189643i	$-0.939267\pi$
$757$	−8.98844	+	15.5684i	−0.326690	+	0.565844i	0.655163	+	0.755488i	$0.272600\pi$
$758$			58.4353i			2.12247i
$759$	12.5188	−	46.7210i	0.454405	−	1.69586i
$760$	5.34181	+	19.9359i	0.193768	+	0.723152i
$761$	−24.9471	+	24.9471i	−0.904330	+	0.904330i	−0.995807	−	0.0914770i	$-0.970841\pi$
$761$	−24.9471	+	24.9471i	−0.904330	+	0.904330i	0.0914770	+	0.995807i	$0.470841\pi$
$762$	−18.2526	+	18.2526i	−0.661224	+	0.661224i
$763$	17.0490	−	6.40195i	0.617217	−	0.231766i
$764$	−1.89182	−	1.09224i	−0.0684436	−	0.0395159i
$765$	−0.122152	+	0.455878i	−0.00441642	+	0.0164823i
$766$	−24.7706	−	42.9039i	−0.894997	−	1.55018i
$767$	0.439269	+	15.4447i	0.0158611	+	0.557675i
$768$	−28.1473	−	16.2508i	−1.01568	−	0.586401i
$769$	31.5109	−	8.44333i	1.13631	−	0.304474i	0.358845	−	0.933397i	$-0.383171\pi$
$769$	31.5109	−	8.44333i	1.13631	−	0.304474i	0.777468	+	0.628923i	$0.216504\pi$
$770$	−19.3864	−	3.21591i	−0.698637	−	0.115893i
$771$	−11.3412	+	6.54782i	−0.408442	+	0.235814i
$772$	−7.13404	−	26.6246i	−0.256760	−	0.958241i
$773$	29.2744	−	7.84405i	1.05293	−	0.282131i	0.309466	−	0.950911i	$-0.399850\pi$
$773$	29.2744	−	7.84405i	1.05293	−	0.282131i	0.743461	+	0.668780i	$0.233183\pi$
$774$	−0.420078	+	0.112560i	−0.0150994	+	0.00404587i
$775$	−3.02202	−	11.2783i	−0.108554	−	0.405129i
$776$	−14.7509	+	8.51642i	−0.529526	+	0.305722i
$777$	3.01017	−	1.13033i	0.107989	−	0.0405502i
$778$	−78.0226	+	20.9061i	−2.79725	+	0.749520i
$779$	55.8336	+	32.2355i	2.00045	+	1.15496i
$780$	3.53974	−	6.55458i	0.126743	−	0.234692i
$781$	−20.1771	−	34.9478i	−0.721994	−	1.25053i
$782$	4.84073	−	18.0659i	0.173104	−	0.646034i
$783$	3.40276	+	1.96458i	0.121605	+	0.0702085i
$784$	31.0367	−	6.12437i	1.10846	−	0.218727i
$785$	0.412461	−	0.412461i	0.0147213	−	0.0147213i
$786$	27.7678	−	27.7678i	0.990444	−	0.990444i
$787$	−3.06522	−	11.4395i	−0.109263	−	0.407776i	0.889531	−	0.456875i	$-0.151031\pi$
$787$	−3.06522	−	11.4395i	−0.109263	−	0.407776i	−0.998794	+	0.0490996i	$0.984365\pi$
$788$	1.03222	−	3.85230i	0.0367714	−	0.137233i
$789$			10.0561i			0.358006i
$790$	−5.78950	+	10.0277i	−0.205981	+	0.356770i
$791$	10.2958	+	4.67446i	0.366078	+	0.166205i
$792$		−	30.6269i		−	1.08828i
$793$	6.49638	−	27.3306i	0.230693	−	0.970537i
$794$	−7.81332	+	4.51103i	−0.277285	+	0.160090i
$795$	0.536951	−	0.536951i	0.0190437	−	0.0190437i
$796$	−53.6733	+	30.9883i	−1.90240	+	1.09835i
$797$	−9.50469	−	16.4626i	−0.336673	−	0.583135i	0.647132	−	0.762378i	$-0.275968\pi$
$797$	−9.50469	−	16.4626i	−0.336673	−	0.583135i	−0.983805	+	0.179243i	$0.942635\pi$
$798$	−21.4053	+	47.1467i	−0.757738	+	1.66897i
$799$	1.54763	+	0.414686i	0.0547512	+	0.0146705i
$800$	2.88516	+	2.88516i	0.102006	+	0.102006i
$801$	−4.12627	−	1.10563i	−0.145795	−	0.0390656i
$802$	6.94005	−	12.0205i	0.245062	−	0.424459i
$803$	37.7129	+	65.3206i	1.33086	+	2.30512i
$804$	−8.07097	−	30.1213i	−0.284641	−	1.06230i
$805$	1.77894	−	10.7240i	0.0626994	−	0.377970i
$806$	15.0323	−	15.9125i	0.529492	−	0.560492i
$807$	−14.6883	+	25.4408i	−0.517051	+	0.895559i
$808$	−16.2737	−	16.2737i	−0.572506	−	0.572506i
$809$	−37.1649			−1.30665			−0.653325	−	0.757078i	$-0.726626\pi$
$809$	−37.1649			−1.30665			−0.653325	+	0.757078i	$0.726626\pi$
$810$	−1.24755			−0.0438345
$811$	21.6751	+	21.6751i	0.761116	+	0.761116i	0.976524	−	0.215408i	$-0.0691082\pi$
$811$	21.6751	+	21.6751i	0.761116	+	0.761116i	−0.215408	+	0.976524i	$0.569108\pi$
$812$	−17.5570	+	38.6706i	−0.616130	+	1.35707i
$813$	0.421080	−	1.57149i	0.0147679	−	0.0551146i
$814$	17.2407	−	4.61963i	0.604286	−	0.161918i
$815$	5.99221	+	3.45960i	0.209898	+	0.121185i
$816$		−	4.21755i		−	0.147644i
$817$	1.35097	+	0.361990i	0.0472643	+	0.0126644i
$818$	25.2122			0.881523
$819$	8.83159	−	3.60598i	0.308601	−	0.126003i
$820$	−16.7901			−0.586335
$821$	−2.42187	−	0.648939i	−0.0845239	−	0.0226481i	0.216309	−	0.976325i	$-0.430598\pi$
$821$	−2.42187	−	0.648939i	−0.0845239	−	0.0226481i	−0.300833	+	0.953677i	$0.597265\pi$
$822$			47.6248i			1.66111i
$823$	17.3695	+	10.0283i	0.605463	+	0.349564i	0.771188	−	0.636608i	$-0.219663\pi$
$823$	17.3695	+	10.0283i	0.605463	+	0.349564i	−0.165725	+	0.986172i	$0.552996\pi$
$824$	20.6331	−	5.52862i	0.718788	−	0.192599i
$825$	7.31049	−	27.2831i	0.254519	−	0.949876i
$826$	16.2739	+	22.7468i	0.566240	+	0.791462i
$827$	−19.4069	−	19.4069i	−0.674842	−	0.674842i	0.283986	−	0.958828i	$-0.408343\pi$
$827$	−19.4069	−	19.4069i	−0.674842	−	0.674842i	−0.958828	+	0.283986i	$0.908343\pi$
$828$	33.1904			1.15345
$829$	−36.6766			−1.27383			−0.636916	−	0.770933i	$-0.719790\pi$
$829$	−36.6766			−1.27383			−0.636916	+	0.770933i	$0.719790\pi$
$830$	2.07179	+	2.07179i	0.0719129	+	0.0719129i
$831$	−15.3657	+	26.6141i	−0.533029	+	0.923233i
$832$	5.76740	−	24.2637i	0.199949	−	0.841194i
$833$	−4.29974	−	4.91803i	−0.148977	−	0.170400i
$834$	4.50070	+	16.7969i	0.155847	+	0.581628i
$835$	0.548132	+	0.949392i	0.0189689	+	0.0328551i
$836$	−96.4803	+	167.109i	−3.33684	+	5.77958i
$837$	−2.37727	−	0.636987i	−0.0821704	−	0.0220175i
$838$	−25.7377	−	25.7377i	−0.889095	−	0.889095i
$839$	−7.31939	−	1.96122i	−0.252693	−	0.0677090i	0.130249	−	0.991481i	$-0.458422\pi$
$839$	−7.31939	−	1.96122i	−0.252693	−	0.0677090i	−0.382942	+	0.923772i	$0.625089\pi$
$840$	−0.669436	−	6.85048i	−0.0230977	−	0.236364i
$841$	6.78081	+	11.7447i	0.233821	+	0.404990i
$842$	47.3511	−	27.3382i	1.63183	−	0.942136i
$843$	−3.89852	+	3.89852i	−0.134272	+	0.134272i
$844$	71.4541	−	41.2541i	2.45955	−	1.42002i
$845$	6.43689	+	1.33791i	0.221436	+	0.0460253i
$846$			4.23524i			0.145610i
$847$	−37.6334	−	52.6021i	−1.29310	−	1.80743i
$848$	−3.39294	+	5.87674i	−0.116514	+	0.201808i
$849$			7.33897i			0.251873i
$850$	2.82679	−	10.5497i	0.0969580	−	0.361852i
$851$	2.55544	+	9.53704i	0.0875994	+	0.326925i
$852$	19.5803	−	19.5803i	0.670809	−	0.670809i
$853$	−30.8352	+	30.8352i	−1.05578	+	1.05578i	−0.0574283	+	0.998350i	$0.518290\pi$
$853$	−30.8352	+	30.8352i	−1.05578	+	1.05578i	−0.998350	+	0.0574283i	$0.981710\pi$
$854$	−17.8761	−	47.6058i	−0.611707	−	1.62904i
$855$	3.47459	+	2.00606i	0.118829	+	0.0686057i
$856$	−12.5560	+	46.8598i	−0.429156	+	1.60163i
$857$	7.54118	+	13.0617i	0.257602	+	0.446180i	0.965599	−	0.260036i	$-0.0837344\pi$
$857$	7.54118	+	13.0617i	0.257602	+	0.446180i	−0.707997	+	0.706215i	$0.750401\pi$
$858$	50.7392	−	15.1541i	1.73221	−	0.517353i
$859$	39.8801	+	23.0248i	1.36069	+	0.785596i	0.989716	−	0.143047i	$-0.0456901\pi$
$859$	39.8801	+	23.0248i	1.36069	+	0.785596i	0.370975	+	0.928643i	$0.379023\pi$
$860$	−0.351830	+	0.0942725i	−0.0119973	+	0.00321467i
$861$	−16.6100	−	13.6527i	−0.566068	−	0.465284i
$862$	−53.9411	+	31.1429i	−1.83724	+	1.06073i
$863$	−6.88082	−	25.6796i	−0.234226	−	0.874142i	−0.978496	−	0.206264i	$-0.933869\pi$
$863$	−6.88082	−	25.6796i	−0.234226	−	0.874142i	0.744271	−	0.667878i	$-0.232797\pi$
$864$	0.830735	−	0.222595i	0.0282622	−	0.00757283i
$865$	1.35383	−	0.362757i	0.0460315	−	0.0123341i
$866$	16.2487	+	60.6408i	0.552152	+	2.06066i
$867$	13.9682	−	8.06454i	0.474385	−	0.273886i
$868$	4.35334	−	26.2432i	0.147762	−	0.890752i
$869$	−53.3752	+	14.3018i	−1.81063	+	0.485157i
$870$	4.24512	+	2.45092i	0.143923	+	0.0830941i
$871$	23.4335	−	14.4328i	0.794014	−	0.489038i
$872$	17.7045	+	30.6651i	0.599549	+	1.03845i
$873$	−0.856967	+	3.19825i	−0.0290040	+	0.108244i
$874$	−137.694	−	79.4975i	−4.65756	−	2.68904i
$875$	2.13366	−	12.8623i	0.0721309	−	0.434825i
$876$	−36.5973	+	36.5973i	−1.23651	+	1.23651i
$877$	37.2596	−	37.2596i	1.25817	−	1.25817i	0.306198	−	0.951968i	$-0.400943\pi$
$877$	37.2596	−	37.2596i	1.25817	−	1.25817i	0.951968	−	0.306198i	$-0.0990568\pi$
$878$	8.04464	+	30.0230i	0.271494	+	1.01323i
$879$	−5.65910	+	21.1201i	−0.190877	+	0.712362i
$880$		−	13.6073i		−	0.458703i
$881$	−19.2420	+	33.3282i	−0.648280	+	1.12285i	0.335253	+	0.942128i	$0.391178\pi$
$881$	−19.2420	+	33.3282i	−0.648280	+	1.12285i	−0.983533	+	0.180727i	$0.942155\pi$
$882$	9.61545	−	14.3431i	0.323769	−	0.482958i
$883$		−	17.6170i		−	0.592859i	−0.955055	−	0.296429i	$-0.904204\pi$
$883$		−	17.6170i		−	0.592859i	0.955055	−	0.296429i	$-0.0957959\pi$
$884$	13.1714	−	3.93387i	0.443004	−	0.132310i
$885$	1.87685	−	1.08360i	0.0630897	−	0.0364248i
$886$	18.2916	−	18.2916i	0.614518	−	0.614518i
$887$	−11.6202	+	6.70890i	−0.390167	+	0.225263i	−0.682232	−	0.731135i	$-0.738991\pi$
$887$	−11.6202	+	6.70890i	−0.390167	+	0.225263i	0.292066	+	0.956398i	$0.405657\pi$
$888$	3.12589	+	5.41421i	0.104898	+	0.181689i
$889$	−27.5539	+	2.69260i	−0.924130	+	0.0903069i
$890$	−5.14774	−	1.37933i	−0.172553	−	0.0462354i
$891$	−4.20987	−	4.20987i	−0.141036	−	0.141036i
$892$	−75.7715	−	20.3029i	−2.53702	−	0.679792i
$893$	6.81023	−	11.7957i	0.227896	−	0.394727i
$894$	17.9586	+	31.1053i	0.600627	+	1.04032i
$895$	1.19587	+	4.46303i	0.0399734	+	0.149183i
$896$	−17.4700	−	46.5243i	−0.583631	−	1.55427i
$897$	8.38279	+	28.0674i	0.279893	+	0.937143i
$898$	6.93561	−	12.0128i	0.231444	−	0.400874i
$899$	6.83786	+	6.83786i	0.228055	+	0.228055i
$900$	19.3818			0.646061
$901$	1.40127			0.0466829
$902$	−84.3955	−	84.3955i	−2.81006	−	2.81006i
$903$	−0.424714	−	0.192826i	−0.0141336	−	0.00641685i
$904$	−5.69016	+	21.2360i	−0.189252	+	0.706298i
$905$	−6.01607	+	1.61200i	−0.199981	+	0.0535848i
$906$	10.9444	+	6.31877i	0.363604	+	0.209927i
$907$		−	14.7112i		−	0.488479i	−0.969715	−	0.244239i	$-0.921462\pi$
$907$		−	14.7112i		−	0.488479i	0.969715	−	0.244239i	$-0.0785382\pi$
$908$	86.6565	+	23.2195i	2.87580	+	0.770568i
$909$	−4.47385			−0.148388
$910$	11.0179	−	4.49865i	0.365239	−	0.149129i
$911$	−25.5134			−0.845296			−0.422648	−	0.906294i	$-0.638899\pi$
$911$	−25.5134			−0.845296			−0.422648	+	0.906294i	$0.638899\pi$
$912$	−34.6317	−	9.27953i	−1.14677	−	0.307276i
$913$			13.9825i			0.462754i
$914$	25.3137	+	14.6149i	0.837302	+	0.483416i
$915$	−3.80603	+	1.01982i	−0.125823	+	0.0337143i
$916$	−27.7885	+	103.708i	−0.918157	+	3.42661i
$917$	41.9179	−	4.09626i	1.38425	−	0.135270i
$918$	−1.62785	−	1.62785i	−0.0537272	−	0.0537272i
$919$	−34.4074			−1.13500			−0.567498	−	0.823375i	$-0.692089\pi$
$919$	−34.4074			−1.13500			−0.567498	+	0.823375i	$0.692089\pi$
$920$	21.1359			0.696829
$921$	2.37972	+	2.37972i	0.0784144	+	0.0784144i
$922$	−10.1391	+	17.5614i	−0.333914	+	0.578355i
$923$	21.5033	+	11.6127i	0.707790	+	0.382236i
$924$	40.8623	−	49.7135i	1.34427	−	1.63545i
$925$	1.49227	+	5.56924i	0.0490656	+	0.183115i
$926$	37.2949	+	64.5967i	1.22559	+	2.12278i
$927$	2.07621	−	3.59610i	0.0681917	−	0.118112i
$928$	−3.26410	−	0.874612i	−0.107149	−	0.0287106i
$929$	−20.4339	−	20.4339i	−0.670414	−	0.670414i	0.287398	−	0.957811i	$-0.407210\pi$
$929$	−20.4339	−	20.4339i	−0.670414	−	0.670414i	−0.957811	+	0.287398i	$0.907210\pi$
$930$	−2.96577	−	0.794675i	−0.0972513	−	0.0260584i
$931$	−49.8439	+	24.4858i	−1.63357	+	0.802489i
$932$	20.7773	+	35.9874i	0.680584	+	1.17881i
$933$	−10.8386	+	6.25768i	−0.354841	+	0.204867i
$934$	50.1013	−	50.1013i	1.63937	−	1.63937i
$935$	−2.43343	+	1.40494i	−0.0795817	+	0.0459465i
$936$	9.72678	+	15.7927i	0.317930	+	0.516199i
$937$		−	49.8602i		−	1.62886i	−0.580261	−	0.814431i	$-0.697049\pi$
$937$		−	49.8602i		−	1.62886i	0.580261	−	0.814431i	$-0.302951\pi$
$938$	20.5952	−	45.3624i	0.672456	−	1.48113i
$939$	4.84889	−	8.39852i	0.158238	−	0.274075i
$940$			3.54715i			0.115695i
$941$	7.54766	−	28.1682i	0.246047	−	0.918258i	−0.726808	−	0.686841i	$-0.758997\pi$
$941$	7.54766	−	28.1682i	0.246047	−	0.918258i	0.972854	−	0.231418i	$-0.0743364\pi$
$942$	0.736410	+	2.74832i	0.0239935	+	0.0895450i
$943$	46.6850	−	46.6850i	1.52027	−	1.52027i
$944$	−13.6943	+	13.6943i	−0.445712	+	0.445712i
$945$	−1.03366	−	0.849626i	−0.0336251	−	0.0276383i
$946$	−2.24234	−	1.29461i	−0.0729046	−	0.0420915i
$947$	13.3721	−	49.9055i	0.434536	−	1.62171i	−0.307639	−	0.951503i	$-0.599539\pi$
$947$	13.3721	−	49.9055i	0.434536	−	1.62171i	0.742175	−	0.670206i	$-0.233794\pi$
$948$	−18.9588	−	32.8376i	−0.615752	−	1.06651i
$949$	−40.1917	−	21.7052i	−1.30468	−	0.704579i
$950$	−80.4075	−	46.4233i	−2.60876	−	1.50617i
$951$	22.5235	−	6.03514i	0.730373	−	0.195703i
$952$	8.06525	−	9.81226i	0.261396	−	0.318017i
$953$	−4.92386	+	2.84279i	−0.159500	+	0.0920871i	−0.577625	−	0.816302i	$-0.696020\pi$
$953$	−4.92386	+	2.84279i	−0.159500	+	0.0920871i	0.418126	+	0.908389i	$0.362687\pi$
$954$	0.958675	+	3.57782i	0.0310383	+	0.115836i
$955$	−0.261205	+	0.0699896i	−0.00845239	+	0.00226481i
$956$	−4.67088	+	1.25156i	−0.151067	+	0.0404783i
$957$	6.05453	+	22.5958i	0.195715	+	0.730419i
$958$	−36.5168	+	21.0830i	−1.17980	+	0.681160i
$959$	−32.4341	+	39.4596i	−1.04735	+	1.27422i
$960$	−3.37895	+	0.905386i	−0.109055	+	0.0292212i
$961$	21.6011	+	12.4714i	0.696811	+	0.402304i
$962$	−7.42297	+	7.85757i	−0.239326	+	0.253338i
$963$	4.71528	+	8.16710i	0.151948	+	0.263181i
$964$	−13.5302	+	50.4955i	−0.435779	+	1.62635i
$965$	−2.95501	−	1.70607i	−0.0951251	−	0.0549205i
$966$	40.9627	+	33.6696i	1.31795	+	1.08330i
$967$	24.1174	−	24.1174i	0.775562	−	0.775562i	−0.203511	−	0.979073i	$-0.565235\pi$
$967$	24.1174	−	24.1174i	0.775562	−	0.775562i	0.979073	+	0.203511i	$0.0652352\pi$
$968$	88.9226	−	88.9226i	2.85808	−	2.85808i
$969$	1.91620	+	7.15135i	0.0615572	+	0.229735i
$970$	−1.06911	+	3.98998i	−0.0343271	+	0.128111i
$971$			29.7856i			0.955864i	0.878397	+	0.477932i	$0.158613\pi$
$971$			29.7856i			0.955864i	−0.878397	+	0.477932i	$0.841387\pi$
$972$	2.04267	−	3.53801i	0.0655187	−	0.113482i
$973$	−7.71016	+	16.9822i	−0.247176	+	0.544424i
$974$			37.3614i			1.19714i
$975$	4.89521	+	16.3902i	0.156772	+	0.524906i
$976$	30.4941	−	17.6058i	0.976091	−	0.563546i
$977$	−18.7696	+	18.7696i	−0.600493	+	0.600493i	−0.940443	−	0.339950i	$-0.889590\pi$
$977$	−18.7696	+	18.7696i	−0.600493	+	0.600493i	0.339950	+	0.940443i	$0.389590\pi$
$978$	−29.2289	+	16.8753i	−0.934638	+	0.539614i
$979$	−12.7165	−	22.0256i	−0.406421	−	0.703942i
$980$	8.05327	−	12.0128i	0.257252	−	0.383736i
$981$	6.64872	+	1.78152i	0.212277	+	0.0568795i
$982$	−8.36929	−	8.36929i	−0.267075	−	0.267075i
$983$	−18.8288	−	5.04516i	−0.600545	−	0.160915i	−0.0542768	−	0.998526i	$-0.517285\pi$
$983$	−18.8288	−	5.04516i	−0.600545	−	0.160915i	−0.546268	+	0.837610i	$0.683952\pi$
$984$	20.9025	−	36.2041i	0.666346	−	1.15414i
$985$	−0.246851	−	0.427559i	−0.00786533	−	0.0136232i
$986$	2.34114	+	8.73725i	0.0745570	+	0.278251i
$987$	−2.88434	+	3.50911i	−0.0918095	+	0.111696i
$988$	−3.32225	−	116.810i	−0.105695	−	3.71623i
$989$	0.716141	−	1.24039i	0.0227720	−	0.0394422i
$990$	−5.25204	−	5.25204i	−0.166921	−	0.166921i
$991$	33.0137			1.04871			0.524357	−	0.851499i	$-0.324306\pi$
$991$	33.0137			1.04871			0.524357	+	0.851499i	$0.324306\pi$
$992$	2.11667			0.0672043
$993$	−16.9938	−	16.9938i	−0.539283	−	0.539283i
$994$	44.0284	−	4.30250i	1.39650	−	0.136467i
$995$	−1.98569	+	7.41071i	−0.0629507	+	0.234935i
$996$	−9.26773	+	2.48328i	−0.293659	+	0.0786858i
$997$	28.4195	+	16.4080i	0.900054	+	0.519646i	0.877218	−	0.480093i	$-0.159397\pi$
$997$	28.4195	+	16.4080i	0.900054	+	0.519646i	0.0228361	+	0.999739i	$0.492730\pi$
$998$		−	37.2848i		−	1.18023i
$999$	1.17389	+	0.314544i	0.0371404	+	0.00995173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.19.1	yes	36
3.2	odd	2		819.2.gh.c.19.9		36
7.3	odd	6		273.2.bt.a.136.9	✓	36
13.11	odd	12		273.2.bt.a.271.9	yes	36
21.17	even	6		819.2.et.c.136.1		36
39.11	even	12		819.2.et.c.271.1		36
91.24	even	12	inner	273.2.cg.a.115.1	yes	36
273.206	odd	12		819.2.gh.c.388.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.9	✓	36	7.3	odd	6
273.2.bt.a.271.9	yes	36	13.11	odd	12
273.2.cg.a.19.1	yes	36	1.1	even	1	trivial
273.2.cg.a.115.1	yes	36	91.24	even	12	inner
819.2.et.c.136.1		36	21.17	even	6
819.2.et.c.271.1		36	39.11	even	12
819.2.gh.c.19.9		36	3.2	odd	2
819.2.gh.c.388.9		36	273.206	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38279 - 0.638467i) q^{2} -1.00000i q^{3} +(3.53801 + 2.04267i) q^{4} +(0.488495 - 0.130892i) q^{5} +(-0.638467 + 2.38279i) q^{6} +(-2.15177 + 1.53945i) q^{7} +(-3.63751 - 3.63751i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-2.38279 - 0.638467i) q^{2} -1.00000i q^{3} +(3.53801 + 2.04267i) q^{4} +(0.488495 - 0.130892i) q^{5} +(-0.638467 + 2.38279i) q^{6} +(-2.15177 + 1.53945i) q^{7} +(-3.63751 - 3.63751i) q^{8} -1.00000 q^{9} -1.24755 q^{10} +(-4.20987 - 4.20987i) q^{11} +(2.04267 - 3.53801i) q^{12} +(3.50782 + 0.833795i) q^{13} +(6.11010 - 2.29436i) q^{14} +(-0.130892 - 0.488495i) q^{15} +(2.25966 + 3.91384i) q^{16} +(0.466614 - 0.808199i) q^{17} +(2.38279 + 0.638467i) q^{18} +(-5.60973 - 5.60973i) q^{19} +(1.99567 + 0.534738i) q^{20} +(1.53945 + 2.15177i) q^{21} +(7.34338 + 12.7191i) q^{22} +(-7.03583 + 4.06214i) q^{23} +(-3.63751 + 3.63751i) q^{24} +(-4.10863 + 2.37212i) q^{25} +(-7.82605 - 4.22639i) q^{26} +1.00000i q^{27} +(-10.7575 + 1.05124i) q^{28} +(1.96458 - 3.40276i) q^{29} +1.24755i q^{30} +(-0.636987 + 2.37727i) q^{31} +(-0.222595 - 0.830735i) q^{32} +(-4.20987 + 4.20987i) q^{33} +(-1.62785 + 1.62785i) q^{34} +(-0.849626 + 1.03366i) q^{35} +(-3.53801 - 2.04267i) q^{36} +(0.314544 - 1.17389i) q^{37} +(9.78519 + 16.9484i) q^{38} +(0.833795 - 3.50782i) q^{39} +(-2.25303 - 1.30079i) q^{40} +(-7.84968 + 2.10332i) q^{41} +(-2.29436 - 6.11010i) q^{42} +(-0.152677 + 0.0881483i) q^{43} +(-6.29518 - 23.4939i) q^{44} +(-0.488495 + 0.130892i) q^{45} +(19.3585 - 5.18708i) q^{46} +(0.444356 + 1.65836i) q^{47} +(3.91384 - 2.25966i) q^{48} +(2.26019 - 6.62507i) q^{49} +(11.3045 - 3.02904i) q^{50} +(-0.808199 - 0.466614i) q^{51} +(10.7075 + 10.1153i) q^{52} +(0.750763 + 1.30036i) q^{53} +(0.638467 - 2.38279i) q^{54} +(-2.60754 - 1.50546i) q^{55} +(13.4268 + 2.22730i) q^{56} +(-5.60973 + 5.60973i) q^{57} +(-6.85375 + 6.85375i) q^{58} +(1.10912 + 4.13930i) q^{59} +(0.534738 - 1.99567i) q^{60} -7.79133i q^{61} +(3.03561 - 5.25784i) q^{62} +(2.15177 - 1.53945i) q^{63} -6.91705i q^{64} +(1.82269 - 0.0518399i) q^{65} +(12.7191 - 7.34338i) q^{66} +(5.39742 - 5.39742i) q^{67} +(3.30177 - 1.90628i) q^{68} +(4.06214 + 7.03583i) q^{69} +(2.68444 - 1.92055i) q^{70} +(6.54710 + 1.75429i) q^{71} +(3.63751 + 3.63751i) q^{72} +(-12.2371 - 3.27893i) q^{73} +(-1.49899 + 2.59632i) q^{74} +(2.37212 + 4.10863i) q^{75} +(-8.38844 - 31.3061i) q^{76} +(15.5395 + 2.57777i) q^{77} +(-4.22639 + 7.82605i) q^{78} +(4.64069 - 8.03790i) q^{79} +(1.61612 + 1.61612i) q^{80} +1.00000 q^{81} +20.0471 q^{82} +(-1.66068 - 1.66068i) q^{83} +(1.05124 + 10.7575i) q^{84} +(0.122152 - 0.455878i) q^{85} +(0.420078 - 0.112560i) q^{86} +(-3.40276 - 1.96458i) q^{87} +30.6269i q^{88} +(4.12627 + 1.10563i) q^{89} +1.24755 q^{90} +(-8.83159 + 3.60598i) q^{91} -33.1904 q^{92} +(2.37727 + 0.636987i) q^{93} -4.23524i q^{94} +(-3.47459 - 2.00606i) q^{95} +(-0.830735 + 0.222595i) q^{96} +(0.856967 - 3.19825i) q^{97} +(-9.61545 + 14.3431i) q^{98} +(4.20987 + 4.20987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more