LMFDB - Embedded newform 126.2.l.a.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(5,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.l (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Root			$0.765614 + 1.55365i$ of defining polynomial
Character	$\chi$	$=$	126.101
Dual form			126.2.l.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.52765 + 0.816261i) q^{3} -1.00000 q^{4} +(-1.82207 + 3.15592i) q^{5} +(-0.816261 + 1.52765i) q^{6} +(-1.58246 - 2.12034i) q^{7} -1.00000i q^{8} +(1.66744 + 2.49392i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.52765 + 0.816261i) q^{3} -1.00000 q^{4} +(-1.82207 + 3.15592i) q^{5} +(-0.816261 + 1.52765i) q^{6} +(-1.58246 - 2.12034i) q^{7} -1.00000i q^{8} +(1.66744 + 2.49392i) q^{9} +(-3.15592 - 1.82207i) q^{10} +(4.38809 - 2.53346i) q^{11} +(-1.52765 - 0.816261i) q^{12} +(2.94391 - 1.69967i) q^{13} +(2.12034 - 1.58246i) q^{14} +(-5.35954 + 3.33386i) q^{15} +1.00000 q^{16} +(-0.774696 + 1.34181i) q^{17} +(-2.49392 + 1.66744i) q^{18} +(-0.707140 + 0.408267i) q^{19} +(1.82207 - 3.15592i) q^{20} +(-0.686700 - 4.53083i) q^{21} +(2.53346 + 4.38809i) q^{22} +(1.47275 + 0.850294i) q^{23} +(0.816261 - 1.52765i) q^{24} +(-4.13989 - 7.17050i) q^{25} +(1.69967 + 2.94391i) q^{26} +(0.511572 + 5.17091i) q^{27} +(1.58246 + 2.12034i) q^{28} +(-3.60693 - 2.08246i) q^{29} +(-3.33386 - 5.35954i) q^{30} -2.16996i q^{31} +1.00000i q^{32} +(8.77143 - 0.288426i) q^{33} +(-1.34181 - 0.774696i) q^{34} +(9.57497 - 1.13071i) q^{35} +(-1.66744 - 2.49392i) q^{36} +(-3.39979 - 5.88860i) q^{37} +(-0.408267 - 0.707140i) q^{38} +(5.88465 - 0.193502i) q^{39} +(3.15592 + 1.82207i) q^{40} +(1.01681 + 1.76117i) q^{41} +(4.53083 - 0.686700i) q^{42} +(3.06189 - 5.30335i) q^{43} +(-4.38809 + 2.53346i) q^{44} +(-10.9088 + 0.718194i) q^{45} +(-0.850294 + 1.47275i) q^{46} -6.74255 q^{47} +(1.52765 + 0.816261i) q^{48} +(-1.99165 + 6.71069i) q^{49} +(7.17050 - 4.13989i) q^{50} +(-2.27874 + 1.41747i) q^{51} +(-2.94391 + 1.69967i) q^{52} +(-11.4961 - 6.63726i) q^{53} +(-5.17091 + 0.511572i) q^{54} +18.4646i q^{55} +(-2.12034 + 1.58246i) q^{56} +(-1.41352 + 0.0464799i) q^{57} +(2.08246 - 3.60693i) q^{58} -2.17632 q^{59} +(5.35954 - 3.33386i) q^{60} +7.25382i q^{61} +2.16996 q^{62} +(2.64930 - 7.48206i) q^{63} -1.00000 q^{64} +12.3877i q^{65} +(0.288426 + 8.77143i) q^{66} +2.45641 q^{67} +(0.774696 - 1.34181i) q^{68} +(1.55579 + 2.50110i) q^{69} +(1.13071 + 9.57497i) q^{70} +6.74272i q^{71} +(2.49392 - 1.66744i) q^{72} +(3.76912 + 2.17610i) q^{73} +(5.88860 - 3.39979i) q^{74} +(-0.471313 - 14.3333i) q^{75} +(0.707140 - 0.408267i) q^{76} +(-12.3158 - 5.29511i) q^{77} +(0.193502 + 5.88465i) q^{78} +12.7530 q^{79} +(-1.82207 + 3.15592i) q^{80} +(-3.43930 + 8.31692i) q^{81} +(-1.76117 + 1.01681i) q^{82} +(0.768040 - 1.33028i) q^{83} +(0.686700 + 4.53083i) q^{84} +(-2.82310 - 4.88976i) q^{85} +(5.30335 + 3.06189i) q^{86} +(-3.81029 - 6.12546i) q^{87} +(-2.53346 - 4.38809i) q^{88} +(-6.01679 - 10.4214i) q^{89} +(-0.718194 - 10.9088i) q^{90} +(-8.26249 - 3.55243i) q^{91} +(-1.47275 - 0.850294i) q^{92} +(1.77125 - 3.31494i) q^{93} -6.74255i q^{94} -2.97557i q^{95} +(-0.816261 + 1.52765i) q^{96} +(-5.59509 - 3.23033i) q^{97} +(-6.71069 - 1.99165i) q^{98} +(13.6351 + 6.71916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 2 * q^7	$ 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 6 * q^97 - 24 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.52765	+	0.816261i	0.881990	+	0.471268i
$3$	1.52765	+	0.816261i	0.881990	+	0.471268i
$4$	−1.00000			−0.500000
$5$	−1.82207	+	3.15592i	−0.814855	+	1.41137i	0.0945763	+	0.995518i	$0.469850\pi$
$5$	−1.82207	+	3.15592i	−0.814855	+	1.41137i	−0.909432	+	0.415853i	$0.863483\pi$
$6$	−0.816261	+	1.52765i	−0.333237	+	0.623661i
$7$	−1.58246	−	2.12034i	−0.598113	−	0.801412i
$7$	−1.58246	−	2.12034i	−0.598113	−	0.801412i
$8$		−	1.00000i		−	0.353553i
$9$	1.66744	+	2.49392i	0.555812	+	0.831308i
$10$	−3.15592	−	1.82207i	−0.997990	−	0.576190i
$11$	4.38809	−	2.53346i	1.32306	−	0.763868i	0.338843	−	0.940843i	$-0.389965\pi$
$11$	4.38809	−	2.53346i	1.32306	−	0.763868i	0.984215	+	0.176975i	$0.0566313\pi$
$12$	−1.52765	−	0.816261i	−0.440995	−	0.235634i
$13$	2.94391	−	1.69967i	0.816495	−	0.471404i	−0.0327114	−	0.999465i	$-0.510414\pi$
$13$	2.94391	−	1.69967i	0.816495	−	0.471404i	0.849206	+	0.528061i	$0.177081\pi$
$14$	2.12034	−	1.58246i	0.566684	−	0.422930i
$15$	−5.35954	+	3.33386i	−1.38383	+	0.860799i
$16$	1.00000			0.250000
$17$	−0.774696	+	1.34181i	−0.187891	+	0.325438i	−0.944547	−	0.328376i	$-0.893499\pi$
$17$	−0.774696	+	1.34181i	−0.187891	+	0.325438i	0.756656	+	0.653814i	$0.226832\pi$
$18$	−2.49392	+	1.66744i	−0.587823	+	0.393019i
$19$	−0.707140	+	0.408267i	−0.162229	+	0.0936629i	−0.578916	−	0.815387i	$-0.696524\pi$
$19$	−0.707140	+	0.408267i	−0.162229	+	0.0936629i	0.416687	+	0.909050i	$0.363191\pi$
$20$	1.82207	−	3.15592i	0.407428	−	0.705685i
$21$	−0.686700	−	4.53083i	−0.149850	−	0.988709i
$22$	2.53346	+	4.38809i	0.540136	+	0.935543i
$23$	1.47275	+	0.850294i	0.307090	+	0.177299i	0.645624	−	0.763656i	$-0.276598\pi$
$23$	1.47275	+	0.850294i	0.307090	+	0.177299i	−0.338533	+	0.940954i	$0.609931\pi$
$24$	0.816261	−	1.52765i	0.166618	−	0.311831i
$25$	−4.13989	−	7.17050i	−0.827979	−	1.43410i
$26$	1.69967	+	2.94391i	0.333333	+	0.577349i
$27$	0.511572	+	5.17091i	0.0984521	+	0.995142i
$28$	1.58246	+	2.12034i	0.299057	+	0.400706i
$29$	−3.60693	−	2.08246i	−0.669789	−	0.386703i	0.126208	−	0.992004i	$-0.459719\pi$
$29$	−3.60693	−	2.08246i	−0.669789	−	0.386703i	−0.795997	+	0.605301i	$0.793053\pi$
$30$	−3.33386	−	5.35954i	−0.608677	−	0.978515i
$31$		−	2.16996i		−	0.389736i	−0.980830	−	0.194868i	$-0.937572\pi$
$31$		−	2.16996i		−	0.389736i	0.980830	−	0.194868i	$-0.0624278\pi$
$32$			1.00000i			0.176777i
$33$	8.77143	−	0.288426i	1.52691	−	0.0502086i
$34$	−1.34181	−	0.774696i	−0.230119	−	0.132859i
$35$	9.57497	−	1.13071i	1.61846	−	0.191125i
$36$	−1.66744	−	2.49392i	−0.277906	−	0.415654i
$37$	−3.39979	−	5.88860i	−0.558921	−	0.968080i	−0.997587	−	0.0694297i	$-0.977882\pi$
$37$	−3.39979	−	5.88860i	−0.558921	−	0.968080i	0.438666	−	0.898650i	$-0.355451\pi$
$38$	−0.408267	−	0.707140i	−0.0662297	−	0.114713i
$39$	5.88465	−	0.193502i	0.942298	−	0.0309851i
$40$	3.15592	+	1.82207i	0.498995	+	0.288095i
$41$	1.01681	+	1.76117i	0.158799	+	0.275049i	0.934436	−	0.356131i	$-0.115904\pi$
$41$	1.01681	+	1.76117i	0.158799	+	0.275049i	−0.775637	+	0.631180i	$0.782571\pi$
$42$	4.53083	−	0.686700i	0.699123	−	0.105960i
$43$	3.06189	−	5.30335i	0.466934	−	0.808753i	−0.532353	−	0.846523i	$-0.678692\pi$
$43$	3.06189	−	5.30335i	0.466934	−	0.808753i	0.999286	+	0.0377695i	$0.0120253\pi$
$44$	−4.38809	+	2.53346i	−0.661529	+	0.381934i
$45$	−10.9088	+	0.718194i	−1.62619	+	0.107062i
$46$	−0.850294	+	1.47275i	−0.125369	+	0.217146i
$47$	−6.74255			−0.983502			−0.491751	−	0.870736i	$-0.663643\pi$
$47$	−6.74255			−0.983502			−0.491751	+	0.870736i	$0.663643\pi$
$48$	1.52765	+	0.816261i	0.220497	+	0.117817i
$49$	−1.99165	+	6.71069i	−0.284521	+	0.958670i
$50$	7.17050	−	4.13989i	1.01406	−	0.585469i
$51$	−2.27874	+	1.41747i	−0.319087	+	0.198485i
$52$	−2.94391	+	1.69967i	−0.408247	+	0.235702i
$53$	−11.4961	−	6.63726i	−1.57911	−	0.911698i	−0.994984	−	0.100032i	$-0.968105\pi$
$53$	−11.4961	−	6.63726i	−1.57911	−	0.911698i	−0.584123	−	0.811665i	$-0.698561\pi$
$54$	−5.17091	+	0.511572i	−0.703672	+	0.0696161i
$55$			18.4646i			2.48977i
$56$	−2.12034	+	1.58246i	−0.283342	+	0.211465i
$57$	−1.41352	+	0.0464799i	−0.187225	+	0.00615641i
$58$	2.08246	−	3.60693i	0.273440	−	0.473612i
$59$	−2.17632			−0.283333			−0.141666	−	0.989914i	$-0.545246\pi$
$59$	−2.17632			−0.283333			−0.141666	+	0.989914i	$0.545246\pi$
$60$	5.35954	−	3.33386i	0.691914	−	0.430400i
$61$			7.25382i			0.928756i	0.885637	+	0.464378i	$0.153722\pi$
$61$			7.25382i			0.928756i	−0.885637	+	0.464378i	$0.846278\pi$
$62$	2.16996			0.275585
$63$	2.64930	−	7.48206i	0.333781	−	0.942651i
$64$	−1.00000			−0.125000
$65$			12.3877i			1.53650i
$66$	0.288426	+	8.77143i	0.0355028	+	1.07969i
$67$	2.45641			0.300098			0.150049	−	0.988679i	$-0.452057\pi$
$67$	2.45641			0.300098			0.150049	+	0.988679i	$0.452057\pi$
$68$	0.774696	−	1.34181i	0.0939457	−	0.162719i
$69$	1.55579	+	2.50110i	0.187295	+	0.301097i
$70$	1.13071	+	9.57497i	0.135146	+	1.14443i
$71$			6.74272i			0.800213i	0.916469	+	0.400107i	$0.131027\pi$
$71$			6.74272i			0.800213i	−0.916469	+	0.400107i	$0.868973\pi$
$72$	2.49392	−	1.66744i	0.293912	−	0.196509i
$73$	3.76912	+	2.17610i	0.441142	+	0.254694i	0.704082	−	0.710119i	$-0.251359\pi$
$73$	3.76912	+	2.17610i	0.441142	+	0.254694i	−0.262940	+	0.964812i	$0.584692\pi$
$74$	5.88860	−	3.39979i	0.684536	−	0.395217i
$75$	−0.471313	−	14.3333i	−0.0544225	−	1.65506i
$76$	0.707140	−	0.408267i	0.0811145	−	0.0468315i
$77$	−12.3158	−	5.29511i	−1.40351	−	0.603434i
$78$	0.193502	+	5.88465i	0.0219097	+	0.666305i
$79$	12.7530			1.43483			0.717414	−	0.696647i	$-0.245326\pi$
$79$	12.7530			1.43483			0.717414	+	0.696647i	$0.245326\pi$
$80$	−1.82207	+	3.15592i	−0.203714	+	0.352843i
$81$	−3.43930	+	8.31692i	−0.382145	+	0.924102i
$82$	−1.76117	+	1.01681i	−0.194489	+	0.112288i
$83$	0.768040	−	1.33028i	0.0843034	−	0.146018i	−0.820791	−	0.571229i	$-0.806467\pi$
$83$	0.768040	−	1.33028i	0.0843034	−	0.146018i	0.905094	+	0.425211i	$0.139800\pi$
$84$	0.686700	+	4.53083i	0.0749251	+	0.494354i
$85$	−2.82310	−	4.88976i	−0.306209	−	0.530369i
$86$	5.30335	+	3.06189i	0.571875	+	0.330172i
$87$	−3.81029	−	6.12546i	−0.408506	−	0.656718i
$88$	−2.53346	−	4.38809i	−0.270068	−	0.467772i
$89$	−6.01679	−	10.4214i	−0.637778	−	1.10466i	−0.985919	−	0.167222i	$-0.946520\pi$
$89$	−6.01679	−	10.4214i	−0.637778	−	1.10466i	0.348141	−	0.937442i	$-0.386813\pi$
$90$	−0.718194	−	10.9088i	−0.0757043	−	1.14989i
$91$	−8.26249	−	3.55243i	−0.866145	−	0.372396i
$92$	−1.47275	−	0.850294i	−0.153545	−	0.0886493i
$93$	1.77125	−	3.31494i	0.183670	−	0.343743i
$94$		−	6.74255i		−	0.695441i
$95$		−	2.97557i		−	0.305287i
$96$	−0.816261	+	1.52765i	−0.0833092	+	0.155915i
$97$	−5.59509	−	3.23033i	−0.568095	−	0.327990i	0.188293	−	0.982113i	$-0.439705\pi$
$97$	−5.59509	−	3.23033i	−0.568095	−	0.327990i	−0.756388	+	0.654123i	$0.773038\pi$
$98$	−6.71069	−	1.99165i	−0.677882	−	0.201187i
$99$	13.6351	+	6.71916i	1.37038	+	0.675301i
$100$	4.13989	+	7.17050i	0.413989	+	0.717050i
$101$	5.95045	+	10.3065i	0.592092	+	1.02553i	0.993950	+	0.109831i	$0.0350311\pi$
$101$	5.95045	+	10.3065i	0.592092	+	1.02553i	−0.401858	+	0.915702i	$0.631636\pi$
$102$	−1.41747	−	2.27874i	−0.140350	−	0.225628i
$103$	12.7174	+	7.34240i	1.25308	+	0.723468i	0.971721	−	0.236134i	$-0.0758803\pi$
$103$	12.7174	+	7.34240i	1.25308	+	0.723468i	0.281363	+	0.959601i	$0.409214\pi$
$104$	−1.69967	−	2.94391i	−0.166666	−	0.288675i
$105$	15.5502	+	6.08833i	1.51754	+	0.594161i
$106$	6.63726	−	11.4961i	0.644668	−	1.11660i
$107$	−2.87453	+	1.65961i	−0.277891	+	0.160440i	−0.632468	−	0.774586i	$-0.717958\pi$
$107$	−2.87453	+	1.65961i	−0.277891	+	0.160440i	0.354577	+	0.935027i	$0.384625\pi$
$108$	−0.511572	−	5.17091i	−0.0492260	−	0.497571i
$109$	1.41837	−	2.45668i	0.135855	−	0.235308i	−0.790069	−	0.613018i	$-0.789955\pi$
$109$	1.41837	−	2.45668i	0.135855	−	0.235308i	0.925924	+	0.377711i	$0.123289\pi$
$110$	−18.4646			−1.76053
$111$	−0.387054	−	11.7708i	−0.0367376	−	1.11724i
$112$	−1.58246	−	2.12034i	−0.149528	−	0.200353i
$113$	−6.80465	+	3.92866i	−0.640127	+	0.369578i	−0.784664	−	0.619922i	$-0.787164\pi$
$113$	−6.80465	+	3.92866i	−0.640127	+	0.369578i	0.144536	+	0.989500i	$0.453831\pi$
$114$	−0.0464799	−	1.41352i	−0.00435324	−	0.132388i
$115$	−5.36692	+	3.09859i	−0.500468	+	0.288945i
$116$	3.60693	+	2.08246i	0.334895	+	0.193351i
$117$	9.14764	+	4.50780i	0.845699	+	0.416746i
$118$		−	2.17632i		−	0.200346i
$119$	4.07102	−	0.480749i	0.373190	−	0.0440702i
$120$	3.33386	+	5.35954i	0.304339	+	0.489257i
$121$	7.33687	−	12.7078i	0.666988	−	1.15526i
$122$	−7.25382			−0.656730
$123$	0.115761	+	3.52044i	0.0104378	+	0.317427i
$124$			2.16996i			0.194868i
$125$	11.9520			1.06902
$126$	7.48206	+	2.64930i	0.666555	+	0.236019i
$127$	−17.4279			−1.54647			−0.773237	−	0.634117i	$-0.781364\pi$
$127$	−17.4279			−1.54647			−0.773237	+	0.634117i	$0.781364\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	9.00642	−	5.60237i	0.792971	−	0.493261i
$130$	−12.3877			−1.08647
$131$	1.61603	−	2.79904i	0.141193	−	0.244554i	−0.786753	−	0.617268i	$-0.788240\pi$
$131$	1.61603	−	2.79904i	0.141193	−	0.244554i	0.927946	+	0.372714i	$0.121573\pi$
$132$	−8.77143	+	0.288426i	−0.763455	+	0.0251043i
$133$	1.98468	+	0.853307i	0.172094	+	0.0739911i
$134$			2.45641i			0.212201i
$135$	−17.2511	−	7.80729i	−1.48474	−	0.671944i
$136$	1.34181	+	0.774696i	0.115060	+	0.0664297i
$137$	12.6284	−	7.29101i	1.07892	−	0.622913i	0.148313	−	0.988940i	$-0.452616\pi$
$137$	12.6284	−	7.29101i	1.07892	−	0.622913i	0.930604	+	0.366027i	$0.119282\pi$
$138$	−2.50110	+	1.55579i	−0.212908	+	0.132438i
$139$	−4.97814	+	2.87413i	−0.422240	+	0.243780i	−0.696035	−	0.718008i	$-0.745054\pi$
$139$	−4.97814	+	2.87413i	−0.422240	+	0.243780i	0.273795	+	0.961788i	$0.411721\pi$
$140$	−9.57497	+	1.13071i	−0.809232	+	0.0955626i
$141$	−10.3003	−	5.50368i	−0.867438	−	0.463493i
$142$	−6.74272			−0.565836
$143$	8.61210	−	14.9166i	0.720180	−	1.24739i
$144$	1.66744	+	2.49392i	0.138953	+	0.207827i
$145$	13.1442	−	7.58878i	1.09156	−	0.630214i
$146$	−2.17610	+	3.76912i	−0.180096	+	0.311935i
$147$	−8.52021	+	8.62589i	−0.702735	+	0.711451i
$148$	3.39979	+	5.88860i	0.279461	+	0.484040i
$149$	4.95904	+	2.86310i	0.406261	+	0.234555i	0.689182	−	0.724589i	$-0.257970\pi$
$149$	4.95904	+	2.86310i	0.406261	+	0.234555i	−0.282921	+	0.959143i	$0.591303\pi$
$150$	14.3333	−	0.471313i	1.17031	−	0.0384825i
$151$	6.38483	+	11.0589i	0.519590	+	0.899957i	0.999741	+	0.0227705i	$0.00724870\pi$
$151$	6.38483	+	11.0589i	0.519590	+	0.899957i	−0.480151	+	0.877186i	$0.659418\pi$
$152$	0.408267	+	0.707140i	0.0331148	+	0.0573566i
$153$	−4.63814	+	0.305357i	−0.374971	+	0.0246866i
$154$	5.29511	−	12.3158i	0.426692	−	0.992432i
$155$	6.84821	+	3.95382i	0.550062	+	0.317578i
$156$	−5.88465	+	0.193502i	−0.471149	+	0.0154925i
$157$			12.7707i			1.01921i	0.860407	+	0.509607i	$0.170209\pi$
$157$			12.7707i			1.01921i	−0.860407	+	0.509607i	$0.829791\pi$
$158$			12.7530i			1.01458i
$159$	−12.1443	−	19.5232i	−0.963102	−	1.54829i
$160$	−3.15592	−	1.82207i	−0.249497	−	0.144047i
$161$	−0.527662	−	4.46829i	−0.0415856	−	0.352150i
$162$	−8.31692	−	3.43930i	−0.653439	−	0.270217i
$163$	−1.51018	−	2.61570i	−0.118286	−	0.204878i	0.800802	−	0.598929i	$-0.204407\pi$
$163$	−1.51018	−	2.61570i	−0.118286	−	0.204878i	−0.919089	+	0.394051i	$0.871073\pi$
$164$	−1.01681	−	1.76117i	−0.0793997	−	0.137524i
$165$	−15.0719	+	28.2075i	−1.17335	+	2.19595i
$166$	1.33028	+	0.768040i	0.103250	+	0.0596115i
$167$	−7.14766	−	12.3801i	−0.553103	−	0.958002i	−0.998048	−	0.0624443i	$-0.980110\pi$
$167$	−7.14766	−	12.3801i	−0.553103	−	0.958002i	0.444946	−	0.895557i	$-0.353223\pi$
$168$	−4.53083	+	0.686700i	−0.349561	+	0.0529800i
$169$	−0.722247	+	1.25097i	−0.0555575	+	0.0962284i
$170$	4.88976	−	2.82310i	0.375028	−	0.216522i
$171$	−2.19730	−	1.08279i	−0.168032	−	0.0828032i
$172$	−3.06189	+	5.30335i	−0.233467	+	0.404377i
$173$	2.19905			0.167191			0.0835954	−	0.996500i	$-0.473360\pi$
$173$	2.19905			0.167191			0.0835954	+	0.996500i	$0.473360\pi$
$174$	6.12546	−	3.81029i	0.464370	−	0.288858i
$175$	−8.65267	+	20.1250i	−0.654080	+	1.52131i
$176$	4.38809	−	2.53346i	0.330764	−	0.190967i
$177$	−3.32466	−	1.77644i	−0.249897	−	0.133526i
$178$	10.4214	−	6.01679i	0.781116	−	0.450977i
$179$	9.30715	+	5.37349i	0.695649	+	0.401633i	0.805725	−	0.592290i	$-0.201776\pi$
$179$	9.30715	+	5.37349i	0.695649	+	0.401633i	−0.110076	+	0.993923i	$0.535109\pi$
$180$	10.9088	−	0.718194i	0.813095	−	0.0535310i
$181$		−	14.4710i		−	1.07562i	−0.843065	−	0.537811i	$-0.819251\pi$
$181$		−	14.4710i		−	1.07562i	0.843065	−	0.537811i	$-0.180749\pi$
$182$	3.55243	−	8.26249i	0.263323	−	0.612457i
$183$	−5.92100	+	11.0813i	−0.437693	+	0.819153i
$184$	0.850294	−	1.47275i	0.0626845	−	0.108573i
$185$	24.7786			1.82176
$186$	3.31494	+	1.77125i	0.243063	+	0.129874i
$187$			7.85066i			0.574097i
$188$	6.74255			0.491751
$189$	10.1545	−	9.26746i	0.738633	−	0.674108i
$190$	2.97557			0.215871
$191$			8.33194i			0.602878i	0.953485	+	0.301439i	$0.0974670\pi$
$191$			8.33194i			0.602878i	−0.953485	+	0.301439i	$0.902533\pi$
$192$	−1.52765	−	0.816261i	−0.110249	−	0.0589085i
$193$	−9.56786			−0.688710			−0.344355	−	0.938840i	$-0.611902\pi$
$193$	−9.56786			−0.688710			−0.344355	+	0.938840i	$0.611902\pi$
$194$	3.23033	−	5.59509i	0.231924	−	0.401704i
$195$	−10.1116	+	18.9241i	−0.724105	+	1.35518i
$196$	1.99165	−	6.71069i	0.142260	−	0.479335i
$197$			2.37228i			0.169018i	0.996423	+	0.0845089i	$0.0269322\pi$
$197$			2.37228i			0.169018i	−0.996423	+	0.0845089i	$0.973068\pi$
$198$	−6.71916	+	13.6351i	−0.477510	+	0.969006i
$199$	19.4983	+	11.2573i	1.38220	+	0.798011i	0.992419	−	0.122898i	$-0.0392188\pi$
$199$	19.4983	+	11.2573i	1.38220	+	0.798011i	0.389777	+	0.920909i	$0.372552\pi$
$200$	−7.17050	+	4.13989i	−0.507031	+	0.292735i
$201$	3.75253	+	2.00507i	0.264683	+	0.141427i
$202$	−10.3065	+	5.95045i	−0.725161	+	0.418672i
$203$	1.29230	+	10.9433i	0.0907016	+	0.768069i
$204$	2.27874	−	1.41747i	0.159543	−	0.0992427i
$205$	−7.41083			−0.517594
$206$	−7.34240	+	12.7174i	−0.511569	+	0.886064i
$207$	0.335155	+	5.09074i	0.0232949	+	0.353831i
$208$	2.94391	−	1.69967i	0.204124	−	0.117851i
$209$	−2.06866	+	3.58302i	−0.143092	+	0.247843i
$210$	−6.08833	+	15.5502i	−0.420135	+	1.07306i
$211$	−7.27211	−	12.5957i	−0.500632	−	0.867121i	−1.00000		0.000730453i	$-0.999767\pi$
$211$	−7.27211	−	12.5957i	−0.500632	−	0.867121i	0.499367	−	0.866390i	$-0.333566\pi$
$212$	11.4961	+	6.63726i	0.789553	+	0.455849i
$213$	−5.50381	+	10.3005i	−0.377115	+	0.705780i
$214$	−1.65961	−	2.87453i	−0.113449	−	0.196499i
$215$	11.1580	+	19.3262i	0.760967	+	1.31803i
$216$	5.17091	−	0.511572i	0.351836	−	0.0348081i
$217$	−4.60104	+	3.43387i	−0.312339	+	0.233106i
$218$	2.45668	+	1.41837i	0.166388	+	0.0960640i
$219$	3.98163	+	6.40091i	0.269054	+	0.432533i
$220$		−	18.4646i		−	1.24488i
$221$			5.26691i			0.354291i
$222$	11.7708	−	0.387054i	0.790007	−	0.0259774i
$223$	−22.5221	−	13.0031i	−1.50819	−	0.870753i	−0.999955	−	0.00953489i	$-0.996965\pi$
$223$	−22.5221	−	13.0031i	−1.50819	−	0.870753i	−0.508235	−	0.861219i	$-0.669702\pi$
$224$	2.12034	−	1.58246i	0.141671	−	0.105732i
$225$	10.9797	−	22.2809i	0.731978	−	1.48540i
$226$	−3.92866	−	6.80465i	−0.261331	−	0.452638i
$227$	−11.4390	−	19.8129i	−0.759231	−	1.31503i	−0.943243	−	0.332103i	$-0.892242\pi$
$227$	−11.4390	−	19.8129i	−0.759231	−	1.31503i	0.184012	−	0.982924i	$-0.441091\pi$
$228$	1.41352	−	0.0464799i	0.0936123	−	0.00307820i
$229$	−23.3224	−	13.4652i	−1.54118	−	0.889803i	−0.998764	−	0.0496960i	$-0.984175\pi$
$229$	−23.3224	−	13.4652i	−1.54118	−	0.889803i	−0.542420	−	0.840107i	$-0.682492\pi$
$230$	−3.09859	−	5.36692i	−0.204315	−	0.353884i
$231$	−14.4920	−	18.1420i	−0.953503	−	1.19365i
$232$	−2.08246	+	3.60693i	−0.136720	+	0.236806i
$233$	−3.82003	+	2.20550i	−0.250259	+	0.144487i	−0.619883	−	0.784694i	$-0.712820\pi$
$233$	−3.82003	+	2.20550i	−0.250259	+	0.144487i	0.369624	+	0.929181i	$0.379486\pi$
$234$	−4.50780	+	9.14764i	−0.294684	+	0.598000i
$235$	12.2854	−	21.2789i	0.801412	−	1.38809i
$236$	2.17632			0.141666
$237$	19.4822	+	10.4098i	1.26550	+	0.676189i
$238$	0.480749	+	4.07102i	0.0311623	+	0.263885i
$239$	16.1660	−	9.33343i	1.04569	−	0.603729i	0.124250	−	0.992251i	$-0.460347\pi$
$239$	16.1660	−	9.33343i	1.04569	−	0.603729i	0.921440	+	0.388522i	$0.127014\pi$
$240$	−5.35954	+	3.33386i	−0.345957	+	0.215200i
$241$	0.412458	−	0.238133i	0.0265688	−	0.0153395i	−0.486657	−	0.873593i	$-0.661784\pi$
$241$	0.412458	−	0.238133i	0.0265688	−	0.0153395i	0.513226	+	0.858254i	$0.328450\pi$
$242$	12.7078	+	7.33687i	0.816890	+	0.471632i
$243$	−12.0428	+	9.89799i	−0.772548	+	0.634956i
$244$		−	7.25382i		−	0.464378i
$245$	−17.5495	−	18.5128i	−1.12120	−	1.18274i
$246$	−3.52044	+	0.115761i	−0.224455	+	0.00738063i
$247$	−1.38784	+	2.40381i	−0.0883061	+	0.152951i
$248$	−2.16996			−0.137792
$249$	2.25916	−	1.40529i	0.143168	−	0.0890566i
$250$			11.9520i			0.755912i
$251$	−17.6939			−1.11683			−0.558415	−	0.829562i	$-0.688590\pi$
$251$	−17.6939			−1.11683			−0.558415	+	0.829562i	$0.688590\pi$
$252$	−2.64930	+	7.48206i	−0.166890	+	0.471325i
$253$	8.61675			0.541731
$254$		−	17.4279i		−	1.09352i
$255$	−0.321401	−	9.77424i	−0.0201269	−	0.612087i
$256$	1.00000			0.0625000
$257$	−11.5971	+	20.0867i	−0.723405	+	1.25297i	0.236222	+	0.971699i	$0.424091\pi$
$257$	−11.5971	+	20.0867i	−0.723405	+	1.25297i	−0.959627	+	0.281275i	$0.909243\pi$
$258$	5.60237	+	9.00642i	0.348788	+	0.560715i
$259$	−7.10579	+	16.5272i	−0.441532	+	1.02695i
$260$		−	12.3877i		−	0.768251i
$261$	−0.820829	−	12.4678i	−0.0508080	−	0.771735i
$262$	2.79904	+	1.61603i	0.172925	+	0.0998386i
$263$	2.98247	−	1.72193i	0.183907	−	0.106179i	−0.405220	−	0.914219i	$-0.632805\pi$
$263$	2.98247	−	1.72193i	0.183907	−	0.106179i	0.589127	+	0.808040i	$0.299472\pi$
$264$	−0.288426	−	8.77143i	−0.0177514	−	0.539844i
$265$	41.8933	−	24.1871i	2.57349	−	1.48580i
$266$	−0.853307	+	1.98468i	−0.0523196	+	0.121689i
$267$	−0.684991	−	20.8315i	−0.0419208	−	1.27487i
$268$	−2.45641			−0.150049
$269$	−4.00690	+	6.94015i	−0.244305	+	0.423148i	−0.961936	−	0.273275i	$-0.911893\pi$
$269$	−4.00690	+	6.94015i	−0.244305	+	0.423148i	0.717631	+	0.696423i	$0.245226\pi$
$270$	7.80729	−	17.2511i	0.475136	−	1.04987i
$271$	−1.55095	+	0.895442i	−0.0942136	+	0.0543942i	−0.546367	−	0.837546i	$-0.683989\pi$
$271$	−1.55095	+	0.895442i	−0.0942136	+	0.0543942i	0.452153	+	0.891940i	$0.350656\pi$
$272$	−0.774696	+	1.34181i	−0.0469729	+	0.0813594i
$273$	−9.72250	−	12.1712i	−0.588433	−	0.736636i
$274$	7.29101	+	12.6284i	0.440466	+	0.762910i
$275$	−36.3324	−	20.9765i	−2.19093	−	1.26493i
$276$	−1.55579	−	2.50110i	−0.0936476	−	0.150549i
$277$	12.2968	+	21.2986i	0.738841	+	1.27971i	0.953017	+	0.302915i	$0.0979599\pi$
$277$	12.2968	+	21.2986i	0.738841	+	1.27971i	−0.214176	+	0.976795i	$0.568707\pi$
$278$	−2.87413	−	4.97814i	−0.172379	−	0.298569i
$279$	5.41170	−	3.61827i	0.323990	−	0.216620i
$280$	−1.13071	−	9.57497i	−0.0675730	−	0.572214i
$281$	18.6262	+	10.7539i	1.11115	+	0.641521i	0.939126	−	0.343572i	$-0.111637\pi$
$281$	18.6262	+	10.7539i	1.11115	+	0.641521i	0.172021	+	0.985093i	$0.444970\pi$
$282$	5.50368	−	10.3003i	0.327739	−	0.613372i
$283$		−	19.9480i		−	1.18579i	−0.805281	−	0.592894i	$-0.797985\pi$
$283$		−	19.9480i		−	1.18579i	0.805281	−	0.592894i	$-0.202015\pi$
$284$		−	6.74272i		−	0.400107i
$285$	2.42884	−	4.54563i	0.143872	−	0.269260i
$286$	14.9166	+	8.61210i	0.882037	+	0.509244i
$287$	2.12521	−	4.94297i	0.125447	−	0.291774i
$288$	−2.49392	+	1.66744i	−0.146956	+	0.0982547i
$289$	7.29969	+	12.6434i	0.429394	+	0.743732i
$290$	7.58878	+	13.1442i	0.445629	+	0.771851i
$291$	−5.91056	−	9.50186i	−0.346483	−	0.557009i
$292$	−3.76912	−	2.17610i	−0.220571	−	0.127347i
$293$	−1.24656	−	2.15911i	−0.0728251	−	0.126137i	0.827313	−	0.561741i	$-0.189868\pi$
$293$	−1.24656	−	2.15911i	−0.0728251	−	0.126137i	−0.900138	+	0.435604i	$0.856535\pi$
$294$	−8.62589	−	8.52021i	−0.503072	−	0.496909i
$295$	3.96541	−	6.86829i	0.230875	−	0.399887i
$296$	−5.88860	+	3.39979i	−0.342268	+	0.197609i
$297$	15.3451	+	21.3943i	0.890415	+	1.24143i
$298$	−2.86310	+	4.95904i	−0.165855	+	0.287270i
$299$	5.78088			0.334317
$300$	0.471313	+	14.3333i	0.0272113	+	0.827531i
$301$	−16.0902	+	1.90010i	−0.927423	+	0.109520i
$302$	−11.0589	+	6.38483i	−0.636365	+	0.367406i
$303$	0.677439	+	20.6018i	0.0389178	+	1.18354i
$304$	−0.707140	+	0.408267i	−0.0405572	+	0.0234157i
$305$	−22.8925	−	13.2170i	−1.31082	−	0.756802i
$306$	−0.305357	−	4.63814i	−0.0174561	−	0.265145i
$307$			9.23124i			0.526854i	0.964679	+	0.263427i	$0.0848529\pi$
$307$			9.23124i			0.526854i	−0.964679	+	0.263427i	$0.915147\pi$
$308$	12.3158	+	5.29511i	0.701755	+	0.301717i
$309$	13.4345	+	21.5973i	0.764259	+	1.22863i
$310$	−3.95382	+	6.84821i	−0.224562	+	0.388952i
$311$	22.9714			1.30259			0.651294	−	0.758826i	$-0.274227\pi$
$311$	22.9714			1.30259			0.651294	+	0.758826i	$0.274227\pi$
$312$	−0.193502	−	5.88465i	−0.0109549	−	0.333153i
$313$			6.43336i			0.363635i	0.983332	+	0.181818i	$0.0581980\pi$
$313$			6.43336i			0.363635i	−0.983332	+	0.181818i	$0.941802\pi$
$314$	−12.7707			−0.720694
$315$	18.7856	+	21.9938i	1.05845	+	1.23921i
$316$	−12.7530			−0.717414
$317$			8.73533i			0.490625i	0.969444	+	0.245313i	$0.0788906\pi$
$317$			8.73533i			0.490625i	−0.969444	+	0.245313i	$0.921109\pi$
$318$	19.5232	−	12.1443i	1.09481	−	0.681016i
$319$	−21.1033			−1.18156
$320$	1.82207	−	3.15592i	0.101857	−	0.176421i
$321$	−5.74595	+	0.188941i	−0.320708	+	0.0105457i
$322$	4.46829	−	0.527662i	0.249008	−	0.0294054i
$323$		−	1.26513i		−	0.0703939i
$324$	3.43930	−	8.31692i	0.191072	−	0.462051i
$325$	−24.3750	−	14.0729i	−1.35208	−	0.780624i
$326$	2.61570	−	1.51018i	0.144870	−	0.0836410i
$327$	4.17207	−	2.59520i	0.230716	−	0.143515i
$328$	1.76117	−	1.01681i	0.0972444	−	0.0561441i
$329$	10.6698	+	14.2965i	0.588245	+	0.788189i
$330$	−28.2075	−	15.0719i	−1.55277	−	0.829682i
$331$	31.7007			1.74243			0.871215	−	0.490901i	$-0.163332\pi$
$331$	31.7007			1.74243			0.871215	+	0.490901i	$0.163332\pi$
$332$	−0.768040	+	1.33028i	−0.0421517	+	0.0730088i
$333$	9.01679	−	18.2977i	0.494117	−	1.00271i
$334$	12.3801	−	7.14766i	0.677410	−	0.391103i
$335$	−4.47575	+	7.75223i	−0.244536	+	0.423549i
$336$	−0.686700	−	4.53083i	−0.0374625	−	0.247177i
$337$	16.1308	+	27.9393i	0.878700	+	1.52195i	0.852768	+	0.522289i	$0.174922\pi$
$337$	16.1308	+	27.9393i	0.878700	+	1.52195i	0.0259314	+	0.999664i	$0.491745\pi$
$338$	−1.25097	−	0.722247i	−0.0680437	−	0.0392851i
$339$	−13.6019	+	0.447265i	−0.738756	+	0.0242921i
$340$	2.82310	+	4.88976i	0.153104	+	0.265185i
$341$	−5.49750	−	9.52196i	−0.297707	−	0.515643i
$342$	1.08279	−	2.19730i	0.0585507	−	0.118816i
$343$	17.3806	−	6.39643i	0.938465	−	0.345375i
$344$	−5.30335	−	3.06189i	−0.285937	−	0.165086i
$345$	−10.7280	+	0.352765i	−0.577579	+	0.0189922i
$346$			2.19905i			0.118222i
$347$		−	6.82421i		−	0.366343i	−0.983081	−	0.183171i	$-0.941364\pi$
$347$		−	6.82421i		−	0.366343i	0.983081	−	0.183171i	$-0.0586363\pi$
$348$	3.81029	+	6.12546i	0.204253	+	0.328359i
$349$	−4.18379	−	2.41551i	−0.223953	−	0.129299i	0.383826	−	0.923405i	$-0.374606\pi$
$349$	−4.18379	−	2.41551i	−0.223953	−	0.129299i	−0.607779	+	0.794106i	$0.707939\pi$
$350$	−20.1250	−	8.65267i	−1.07573	−	0.462504i
$351$	10.2949	+	14.3532i	0.549499	+	0.766117i
$352$	2.53346	+	4.38809i	0.135034	+	0.233886i
$353$	−17.2922	−	29.9510i	−0.920371	−	1.59413i	−0.798842	−	0.601541i	$-0.794554\pi$
$353$	−17.2922	−	29.9510i	−0.920371	−	1.59413i	−0.121529	−	0.992588i	$-0.538780\pi$
$354$	1.77644	−	3.32466i	0.0944169	−	0.176704i
$355$	−21.2795	−	12.2857i	−1.12940	−	0.652058i
$356$	6.01679	+	10.4214i	0.318889	+	0.552332i
$357$	6.61152	+	2.58860i	0.349918	+	0.137003i
$358$	−5.37349	+	9.30715i	−0.283998	+	0.491898i
$359$	23.5112	−	13.5742i	1.24087	−	0.716417i	0.271600	−	0.962410i	$-0.412447\pi$
$359$	23.5112	−	13.5742i	1.24087	−	0.716417i	0.969272	+	0.245993i	$0.0791140\pi$
$360$	0.718194	+	10.9088i	0.0378521	+	0.574945i
$361$	−9.16664	+	15.8771i	−0.482455	+	0.835636i
$362$	14.4710			0.760580
$363$	21.5811	−	13.4243i	1.13271	−	0.704595i
$364$	8.26249	+	3.55243i	0.433072	+	0.186198i
$365$	−13.7352	+	7.93003i	−0.718934	+	0.415077i
$366$	−11.0813	−	5.92100i	−0.579229	−	0.309496i
$367$	−10.3307	+	5.96444i	−0.539259	+	0.311341i	−0.744778	−	0.667312i	$-0.767445\pi$
$367$	−10.3307	+	5.96444i	−0.539259	+	0.311341i	0.205520	+	0.978653i	$0.434112\pi$
$368$	1.47275	+	0.850294i	0.0767725	+	0.0443246i
$369$	−2.69675	+	5.47250i	−0.140387	+	0.284887i
$370$			24.7786i			1.28818i
$371$	4.11884	+	34.8787i	0.213840	+	1.81081i
$372$	−1.77125	+	3.31494i	−0.0918350	+	0.171871i
$373$	−4.81925	+	8.34718i	−0.249531	+	0.432201i	−0.963396	−	0.268083i	$-0.913610\pi$
$373$	−4.81925	+	8.34718i	−0.249531	+	0.432201i	0.713865	+	0.700284i	$0.246943\pi$
$374$	−7.85066			−0.405948
$375$	18.2585	+	9.75596i	0.942865	+	0.503795i
$376$			6.74255i			0.347720i
$377$	−14.1580			−0.729173
$378$	9.26746	+	10.1545i	0.476666	+	0.522292i
$379$	−16.0145			−0.822612			−0.411306	−	0.911497i	$-0.634927\pi$
$379$	−16.0145			−0.822612			−0.411306	+	0.911497i	$0.634927\pi$
$380$			2.97557i			0.152643i
$381$	−26.6237	−	14.2257i	−1.36397	−	0.728804i
$382$	−8.33194			−0.426299
$383$	−3.18472	+	5.51610i	−0.162732	+	0.281860i	−0.935847	−	0.352405i	$-0.885364\pi$
$383$	−3.18472	+	5.51610i	−0.162732	+	0.281860i	0.773116	+	0.634265i	$0.218697\pi$
$384$	0.816261	−	1.52765i	0.0416546	−	0.0779576i
$385$	39.1512	−	29.2195i	1.99533	−	1.48916i
$386$		−	9.56786i		−	0.486991i
$387$	18.3317	−	1.20688i	0.931850	−	0.0613494i
$388$	5.59509	+	3.23033i	0.284048	+	0.163995i
$389$	−15.2013	+	8.77645i	−0.770735	+	0.444984i	−0.833137	−	0.553067i	$-0.813457\pi$
$389$	−15.2013	+	8.77645i	−0.770735	+	0.444984i	0.0624020	+	0.998051i	$0.480124\pi$
$390$	−18.9241	−	10.1116i	−0.958257	−	0.512020i
$391$	−2.28187	+	1.31744i	−0.115399	+	0.0666258i
$392$	6.71069	+	1.99165i	0.338941	+	0.100593i
$393$	4.75348	−	2.95686i	0.239781	−	0.149154i
$394$	−2.37228			−0.119514
$395$	−23.2369	+	40.2476i	−1.16918	+	2.02507i
$396$	−13.6351	−	6.71916i	−0.685191	−	0.337650i
$397$	11.5693	−	6.67955i	0.580647	−	0.335237i	−0.180743	−	0.983530i	$-0.557850\pi$
$397$	11.5693	−	6.67955i	0.580647	−	0.335237i	0.761391	+	0.648293i	$0.224517\pi$
$398$	−11.2573	+	19.4983i	−0.564279	+	0.977360i
$399$	2.33538	+	2.92357i	0.116915	+	0.146362i
$400$	−4.13989	−	7.17050i	−0.206995	−	0.358525i
$401$	3.66182	+	2.11415i	0.182863	+	0.105576i	0.588637	−	0.808398i	$-0.299665\pi$
$401$	3.66182	+	2.11415i	0.182863	+	0.105576i	−0.405774	+	0.913973i	$0.632998\pi$
$402$	−2.00507	+	3.75253i	−0.100004	+	0.187159i
$403$	−3.68821	−	6.38817i	−0.183723	−	0.318217i
$404$	−5.95045	−	10.3065i	−0.296046	−	0.512767i
$405$	−19.9809	−	26.0082i	−0.992858	−	1.29236i
$406$	−10.9433	+	1.29230i	−0.543107	+	0.0641357i
$407$	−29.8371	−	17.2265i	−1.47897	−	0.853884i
$408$	1.41747	+	2.27874i	0.0701752	+	0.112814i
$409$			38.4154i			1.89952i	0.312982	+	0.949759i	$0.398672\pi$
$409$			38.4154i			1.89952i	−0.312982	+	0.949759i	$0.601328\pi$
$410$		−	7.41083i		−	0.365995i
$411$	25.2432	−	0.830057i	1.24515	−	0.0409437i
$412$	−12.7174	−	7.34240i	−0.626542	−	0.361734i
$413$	3.44394	+	4.61453i	0.169465	+	0.227066i
$414$	−5.09074	+	0.335155i	−0.250196	+	0.0164720i
$415$	2.79885	+	4.84775i	0.137390	+	0.237967i
$416$	1.69967	+	2.94391i	0.0833332	+	0.144337i
$417$	−9.95089	+	0.327210i	−0.487297	+	0.0160235i
$418$	−3.58302	−	2.06866i	−0.175251	−	0.101181i
$419$	7.03301	+	12.1815i	0.343585	+	0.595107i	0.985096	−	0.172007i	$-0.0550253\pi$
$419$	7.03301	+	12.1815i	0.343585	+	0.595107i	−0.641511	+	0.767114i	$0.721692\pi$
$420$	−15.5502	−	6.08833i	−0.758770	−	0.297080i
$421$	10.5504	−	18.2738i	0.514195	−	0.890612i	−0.485670	−	0.874143i	$-0.661424\pi$
$421$	10.5504	−	18.2738i	0.514195	−	0.890612i	0.999864	−	0.0164691i	$-0.00524252\pi$
$422$	12.5957	−	7.27211i	0.613147	−	0.354001i
$423$	−11.2428	−	16.8154i	−0.546642	−	0.817592i
$424$	−6.63726	+	11.4961i	−0.322334	+	0.558299i
$425$	12.8286			0.622280
$426$	−10.3005	−	5.50381i	−0.499062	−	0.266661i
$427$	15.3805	−	11.4789i	0.744316	−	0.555501i
$428$	2.87453	−	1.65961i	0.138946	−	0.0802202i
$429$	25.3321	−	15.7576i	1.22305	−	0.760786i
$430$	−19.3262	+	11.1580i	−0.931991	+	0.538085i
$431$	10.0928	+	5.82709i	0.486154	+	0.280681i	0.722977	−	0.690872i	$-0.242773\pi$
$431$	10.0928	+	5.82709i	0.486154	+	0.280681i	−0.236824	+	0.971553i	$0.576106\pi$
$432$	0.511572	+	5.17091i	0.0246130	+	0.248785i
$433$			17.9149i			0.860936i	0.902606	+	0.430468i	$0.141652\pi$
$433$			17.9149i			0.860936i	−0.902606	+	0.430468i	$0.858348\pi$
$434$	−3.43387	−	4.60104i	−0.164831	−	0.220857i
$435$	26.2741	−	0.863957i	1.25975	−	0.0414236i
$436$	−1.41837	+	2.45668i	−0.0679275	+	0.117654i
$437$	−1.38859			−0.0664252
$438$	−6.40091	+	3.98163i	−0.305847	+	0.190250i
$439$			19.0275i			0.908135i	0.890967	+	0.454068i	$0.150028\pi$
$439$			19.0275i			0.908135i	−0.890967	+	0.454068i	$0.849972\pi$
$440$	18.4646			0.880266
$441$	−20.0569	+	6.22264i	−0.955090	+	0.296316i
$442$	−5.26691			−0.250521
$443$		−	7.67734i		−	0.364761i	−0.983228	−	0.182381i	$-0.941620\pi$
$443$		−	7.67734i		−	0.364761i	0.983228	−	0.182381i	$-0.0583803\pi$
$444$	0.387054	+	11.7708i	0.0183688	+	0.558619i
$445$	43.8521			2.07879
$446$	13.0031	−	22.5221i	0.615716	−	1.06645i
$447$	5.23865	+	8.42170i	0.247780	+	0.398333i
$448$	1.58246	+	2.12034i	0.0747642	+	0.100176i
$449$			30.1018i			1.42059i	0.703903	+	0.710296i	$0.251439\pi$
$449$			30.1018i			1.42059i	−0.703903	+	0.710296i	$0.748561\pi$
$450$	22.2809	+	10.9797i	1.05033	+	0.517587i
$451$	8.92373	+	5.15212i	0.420202	+	0.242604i
$452$	6.80465	−	3.92866i	0.320064	−	0.184789i
$453$	0.726892	+	22.1058i	0.0341523	+	1.03862i
$454$	19.8129	−	11.4390i	0.929864	−	0.536857i
$455$	26.2660	−	19.6030i	1.23137	−	0.919003i
$456$	0.0464799	+	1.41352i	0.00217662	+	0.0661939i
$457$	−39.4876			−1.84715			−0.923576	−	0.383415i	$-0.874748\pi$
$457$	−39.4876			−1.84715			−0.923576	+	0.383415i	$0.874748\pi$
$458$	13.4652	−	23.3224i	0.629186	−	1.08978i
$459$	−7.33471	−	3.31945i	−0.342355	−	0.154939i
$460$	5.36692	−	3.09859i	0.250234	−	0.144473i
$461$	11.3776	−	19.7066i	0.529909	−	0.917830i	−0.469482	−	0.882942i	$-0.655559\pi$
$461$	11.3776	−	19.7066i	0.529909	−	0.917830i	0.999391	−	0.0348879i	$-0.0111074\pi$
$462$	18.1420	−	14.4920i	0.844040	−	0.674229i
$463$	6.63866	+	11.4985i	0.308525	+	0.534381i	0.978040	−	0.208418i	$-0.0668314\pi$
$463$	6.63866	+	11.4985i	0.308525	+	0.534381i	−0.669515	+	0.742798i	$0.733498\pi$
$464$	−3.60693	−	2.08246i	−0.167447	−	0.0966757i
$465$	7.23434	+	11.6300i	0.335484	+	0.539327i
$466$	−2.20550	−	3.82003i	−0.102168	−	0.176960i
$467$	−11.5873	−	20.0698i	−0.536195	−	0.928717i	−0.999104	−	0.0423116i	$-0.986528\pi$
$467$	−11.5873	−	20.0698i	−0.536195	−	0.928717i	0.462909	−	0.886406i	$-0.346806\pi$
$468$	−9.14764	−	4.50780i	−0.422850	−	0.208373i
$469$	−3.88716	−	5.20841i	−0.179493	−	0.240502i
$470$	21.2789	+	12.2854i	0.981525	+	0.566684i
$471$	−10.4242	+	19.5092i	−0.480324	+	0.898937i
$472$			2.17632i			0.100173i
$473$		−	31.0287i		−	1.42670i
$474$	−10.4098	+	19.4822i	−0.478138	+	0.894846i
$475$	5.85497	+	3.38037i	0.268644	+	0.155102i
$476$	−4.07102	+	0.480749i	−0.186595	+	0.0220351i
$477$	−2.61616	−	39.7375i	−0.119786	−	1.81946i
$478$	9.33343	+	16.1660i	0.426901	+	0.739414i
$479$	−12.3567	−	21.4025i	−0.564594	−	0.977905i	−0.997087	−	0.0762684i	$-0.975699\pi$
$479$	−12.3567	−	21.4025i	−0.564594	−	0.977905i	0.432493	−	0.901637i	$-0.357634\pi$
$480$	−3.33386	−	5.35954i	−0.152169	−	0.244629i
$481$	−20.0174	−	11.5570i	−0.912713	−	0.526955i
$482$	0.238133	+	0.412458i	0.0108467	+	0.0187870i
$483$	2.84120	−	7.25669i	0.129279	−	0.330191i
$484$	−7.33687	+	12.7078i	−0.333494	+	0.577629i
$485$	20.3893	−	11.7718i	0.925831	−	0.534529i
$486$	−9.89799	−	12.0428i	−0.448982	−	0.546274i
$487$	16.9877	−	29.4236i	0.769788	−	1.33331i	−0.167889	−	0.985806i	$-0.553695\pi$
$487$	16.9877	−	29.4236i	0.769788	−	1.33331i	0.937678	−	0.347506i	$-0.112971\pi$
$488$	7.25382			0.328365
$489$	−0.171929	−	5.22858i	−0.00777488	−	0.236445i
$490$	18.5128	−	17.5495i	0.836325	−	0.792805i
$491$	−25.5933	+	14.7763i	−1.15501	+	0.666845i	−0.950103	−	0.311937i	$-0.899022\pi$
$491$	−25.5933	+	14.7763i	−1.15501	+	0.666845i	−0.204906	+	0.978782i	$0.565689\pi$
$492$	−0.115761	−	3.52044i	−0.00521890	−	0.158714i
$493$	5.58854	−	3.22655i	0.251695	−	0.145316i
$494$	−2.40381	−	1.38784i	−0.108152	−	0.0624418i
$495$	−46.0493	+	30.7886i	−2.06976	+	1.38384i
$496$		−	2.16996i		−	0.0974339i
$497$	14.2968	−	10.6701i	0.641300	−	0.478618i
$498$	1.40529	+	2.25916i	0.0629726	+	0.101235i
$499$	5.38644	−	9.32959i	0.241130	−	0.417650i	−0.719906	−	0.694071i	$-0.755815\pi$
$499$	5.38644	−	9.32959i	0.241130	−	0.417650i	0.961037	+	0.276421i	$0.0891486\pi$
$500$	−11.9520			−0.534510
$501$	−0.813737	−	24.7468i	−0.0363551	−	1.10561i
$502$		−	17.6939i		−	0.789718i
$503$	20.2016			0.900743			0.450372	−	0.892841i	$-0.351292\pi$
$503$	20.2016			0.900743			0.450372	+	0.892841i	$0.351292\pi$
$504$	−7.48206	−	2.64930i	−0.333277	−	0.118009i
$505$	−43.3686			−1.92988
$506$			8.61675i			0.383061i
$507$	−2.12446	+	1.32150i	−0.0943505	+	0.0586900i
$508$	17.4279			0.773237
$509$	−0.529272	+	0.916725i	−0.0234595	+	0.0406331i	−0.877517	−	0.479546i	$-0.840801\pi$
$509$	−0.529272	+	0.916725i	−0.0234595	+	0.0406331i	0.854057	+	0.520179i	$0.174135\pi$
$510$	9.77424	−	0.321401i	0.432811	−	0.0142319i
$511$	−1.35041	−	11.4354i	−0.0597387	−	0.505872i
$512$			1.00000i			0.0441942i
$513$	−2.47287	−	3.44770i	−0.109180	−	0.152220i
$514$	−20.0867	−	11.5971i	−0.885987	−	0.511525i
$515$	−46.3441	+	26.7568i	−2.04216	+	1.17904i
$516$	−9.00642	+	5.60237i	−0.396485	+	0.246631i
$517$	−29.5869	+	17.0820i	−1.30123	+	0.751265i
$518$	−16.5272	−	7.10579i	−0.726162	−	0.312210i
$519$	3.35939	+	1.79500i	0.147461	+	0.0787918i
$520$	12.3877			0.543236
$521$	5.05068	−	8.74804i	0.221275	−	0.383259i	−0.733921	−	0.679235i	$-0.762312\pi$
$521$	5.05068	−	8.74804i	0.221275	−	0.383259i	0.955195	+	0.295976i	$0.0956450\pi$
$522$	12.4678	−	0.820829i	0.545699	−	0.0359267i
$523$	−8.02992	+	4.63608i	−0.351124	+	0.202722i	−0.665180	−	0.746683i	$-0.731645\pi$
$523$	−8.02992	+	4.63608i	−0.351124	+	0.202722i	0.314056	+	0.949404i	$0.398312\pi$
$524$	−1.61603	+	2.79904i	−0.0705965	+	0.122277i
$525$	−29.6455	+	23.6811i	−1.29384	+	1.03353i
$526$	1.72193	+	2.98247i	0.0750797	+	0.130042i
$527$	2.91168	+	1.68106i	0.126835	+	0.0732280i
$528$	8.77143	−	0.288426i	0.381728	−	0.0125521i
$529$	−10.0540	−	17.4140i	−0.437130	−	0.757132i
$530$	24.1871	+	41.8933i	1.05062	+	1.81973i
$531$	−3.62888	−	5.42757i	−0.157480	−	0.235537i
$532$	−1.98468	−	0.853307i	−0.0860469	−	0.0369956i
$533$	5.98682	+	3.45649i	0.259318	+	0.149717i
$534$	20.8315	−	0.684991i	0.901468	−	0.0296425i
$535$		−	12.0957i		−	0.522943i
$536$		−	2.45641i		−	0.106101i
$537$	9.83192	+	15.8059i	0.424278	+	0.682074i
$538$	−6.94015	−	4.00690i	−0.299211	−	0.172750i
$539$	8.26177	+	34.4928i	0.355859	+	1.48571i
$540$	17.2511	+	7.80729i	0.742369	+	0.335972i
$541$	−2.87498	−	4.97960i	−0.123605	−	0.214090i	0.797582	−	0.603211i	$-0.206112\pi$
$541$	−2.87498	−	4.97960i	−0.123605	−	0.214090i	−0.921187	+	0.389121i	$0.872779\pi$
$542$	−0.895442	−	1.55095i	−0.0384625	−	0.0666191i
$543$	11.8121	−	22.1067i	0.506907	−	0.948689i
$544$	−1.34181	−	0.774696i	−0.0575298	−	0.0332148i
$545$	5.16874	+	8.95251i	0.221404	+	0.383484i
$546$	12.1712	−	9.72250i	0.520880	−	0.416085i
$547$	18.3094	−	31.7128i	0.782853	−	1.35594i	−0.147421	−	0.989074i	$-0.547097\pi$
$547$	18.3094	−	31.7128i	0.782853	−	1.35594i	0.930273	−	0.366867i	$-0.119570\pi$
$548$	−12.6284	+	7.29101i	−0.539459	+	0.311457i
$549$	−18.0905	+	12.0953i	−0.772082	+	0.516214i
$550$	20.9765	−	36.3324i	0.894442	−	1.54922i
$551$	3.40080			0.144879
$552$	2.50110	−	1.55579i	0.106454	−	0.0662189i
$553$	−20.1811	−	27.0407i	−0.858190	−	1.14989i
$554$	−21.2986	+	12.2968i	−0.904892	+	0.522440i
$555$	37.8531	+	20.2258i	1.60677	+	0.858538i
$556$	4.97814	−	2.87413i	0.211120	−	0.121890i
$557$	−0.323902	−	0.187005i	−0.0137242	−	0.00792365i	0.493122	−	0.869960i	$-0.335856\pi$
$557$	−0.323902	−	0.187005i	−0.0137242	−	0.00792365i	−0.506846	+	0.862036i	$0.669189\pi$
$558$	3.61827	+	5.41170i	0.153173	+	0.229096i
$559$		−	20.8168i		−	0.880457i
$560$	9.57497	−	1.13071i	0.404616	−	0.0477813i
$561$	−6.40818	+	11.9931i	−0.270554	+	0.506348i
$562$	−10.7539	+	18.6262i	−0.453624	+	0.785700i
$563$	−4.37923			−0.184562			−0.0922812	−	0.995733i	$-0.529416\pi$
$563$	−4.37923			−0.184562			−0.0922812	+	0.995733i	$0.529416\pi$
$564$	10.3003	+	5.50368i	0.433719	+	0.231747i
$565$		−	28.6332i		−	1.20461i
$566$	19.9480			0.838478
$567$	23.0772	−	5.86871i	0.969152	−	0.246463i
$568$	6.74272			0.282918
$569$		−	36.8641i		−	1.54542i	−0.634757	−	0.772712i	$-0.718900\pi$
$569$		−	36.8641i		−	1.54542i	0.634757	−	0.772712i	$-0.281100\pi$
$570$	4.54563	+	2.42884i	0.190396	+	0.101733i
$571$	31.6595			1.32491			0.662454	−	0.749103i	$-0.269515\pi$
$571$	31.6595			1.32491			0.662454	+	0.749103i	$0.269515\pi$
$572$	−8.61210	+	14.9166i	−0.360090	+	0.623694i
$573$	−6.80104	+	12.7283i	−0.284117	+	0.531732i
$574$	4.94297	+	2.12521i	0.206315	+	0.0887045i
$575$		−	14.0805i		−	0.587198i
$576$	−1.66744	−	2.49392i	−0.0694766	−	0.103913i
$577$	12.2923	+	7.09699i	0.511737	+	0.295452i	0.733547	−	0.679638i	$-0.237863\pi$
$577$	12.2923	+	7.09699i	0.511737	+	0.295452i	−0.221810	+	0.975090i	$0.571197\pi$
$578$	−12.6434	+	7.29969i	−0.525898	+	0.303627i
$579$	−14.6164	−	7.80987i	−0.607435	−	0.324567i
$580$	−13.1442	+	7.58878i	−0.545781	+	0.315107i
$581$	−4.03604	+	0.476618i	−0.167443	+	0.0197734i
$582$	9.50186	−	5.91056i	0.393865	−	0.245001i
$583$	−67.2610			−2.78567
$584$	2.17610	−	3.76912i	0.0900478	−	0.155967i
$585$	−30.8939	+	20.6557i	−1.27731	+	0.854007i
$586$	2.15911	−	1.24656i	0.0891921	−	0.0514951i
$587$	−2.32227	+	4.02230i	−0.0958505	+	0.166018i	−0.909963	−	0.414689i	$-0.863890\pi$
$587$	−2.32227	+	4.02230i	−0.0958505	+	0.166018i	0.814113	+	0.580707i	$0.197224\pi$
$588$	8.52021	−	8.62589i	0.351368	−	0.355726i
$589$	0.885922	+	1.53446i	0.0365038	+	0.0632264i
$590$	6.86829	+	3.96541i	0.282763	+	0.163253i
$591$	−1.93640	+	3.62402i	−0.0796528	+	0.149072i
$592$	−3.39979	−	5.88860i	−0.139730	−	0.242020i
$593$	11.5215	+	19.9558i	0.473132	+	0.819488i	0.999527	−	0.0307518i	$-0.00979014\pi$
$593$	11.5215	+	19.9558i	0.473132	+	0.819488i	−0.526395	+	0.850240i	$0.676457\pi$
$594$	−21.3943	+	15.3451i	−0.877821	+	0.629618i
$595$	−5.90049	+	13.7238i	−0.241896	+	0.562620i
$596$	−4.95904	−	2.86310i	−0.203130	−	0.117277i
$597$	20.5977	+	33.1130i	0.843006	+	1.35522i
$598$			5.78088i			0.236398i
$599$			28.9622i			1.18336i	0.806171	+	0.591682i	$0.201536\pi$
$599$			28.9622i			1.18336i	−0.806171	+	0.591682i	$0.798464\pi$
$600$	−14.3333	+	0.471313i	−0.585153	+	0.0192413i
$601$	5.04993	+	2.91558i	0.205991	+	0.118929i	0.599447	−	0.800414i	$-0.295387\pi$
$601$	5.04993	+	2.91558i	0.205991	+	0.118929i	−0.393456	+	0.919344i	$0.628721\pi$
$602$	−1.90010	−	16.0902i	−0.0774422	−	0.655787i
$603$	4.09591	+	6.12609i	0.166798	+	0.249474i
$604$	−6.38483	−	11.0589i	−0.259795	−	0.449978i
$605$	26.7366	+	46.3092i	1.08700	+	1.88273i
$606$	−20.6018	+	0.677439i	−0.836892	+	0.0275191i
$607$	16.3750	+	9.45411i	0.664641	+	0.383731i	0.794043	−	0.607862i	$-0.207972\pi$
$607$	16.3750	+	9.45411i	0.664641	+	0.383731i	−0.129402	+	0.991592i	$0.541306\pi$
$608$	−0.408267	−	0.707140i	−0.0165574	−	0.0286783i
$609$	−6.95840	+	17.7724i	−0.281969	+	0.720174i
$610$	13.2170	−	22.8925i	0.535140	−	0.926889i
$611$	−19.8495	+	11.4601i	−0.803024	+	0.463626i
$612$	4.63814	−	0.305357i	0.187486	−	0.0123433i
$613$	−16.5880	+	28.7313i	−0.669984	+	1.16045i	0.307924	+	0.951411i	$0.400366\pi$
$613$	−16.5880	+	28.7313i	−0.669984	+	1.16045i	−0.977908	+	0.209036i	$0.932967\pi$
$614$	−9.23124			−0.372542
$615$	−11.3212	−	6.04916i	−0.456513	−	0.243926i
$616$	−5.29511	+	12.3158i	−0.213346	+	0.496216i
$617$	34.0222	−	19.6427i	1.36968	−	0.790786i	0.378794	−	0.925481i	$-0.376339\pi$
$617$	34.0222	−	19.6427i	1.36968	−	0.790786i	0.990887	+	0.134695i	$0.0430054\pi$
$618$	−21.5973	+	13.4345i	−0.868773	+	0.540413i
$619$	−8.46727	+	4.88858i	−0.340329	+	0.196489i	−0.660417	−	0.750899i	$-0.729621\pi$
$619$	−8.46727	+	4.88858i	−0.340329	+	0.196489i	0.320089	+	0.947388i	$0.396287\pi$
$620$	−6.84821	−	3.95382i	−0.275031	−	0.158789i
$621$	−3.64337	+	8.05046i	−0.146204	+	0.323054i
$622$			22.9714i			0.921069i
$623$	−12.5755	+	29.2490i	−0.503827	+	1.17184i
$624$	5.88465	−	0.193502i	0.235574	−	0.00774627i
$625$	−1.07796	+	1.86708i	−0.0431185	+	0.0746834i
$626$	−6.43336			−0.257129
$627$	−6.08487	+	3.78505i	−0.243006	+	0.151160i
$628$		−	12.7707i		−	0.509607i
$629$	10.5352			0.420066
$630$	−21.9938	+	18.7856i	−0.876256	+	0.748435i
$631$	11.6364			0.463237			0.231618	−	0.972807i	$-0.425598\pi$
$631$	11.6364			0.463237			0.231618	+	0.972807i	$0.425598\pi$
$632$		−	12.7530i		−	0.507288i
$633$	−0.827905	−	25.1777i	−0.0329063	−	1.00072i
$634$	−8.73533			−0.346924
$635$	31.7549	−	55.0010i	1.26015	−	2.18265i
$636$	12.1443	+	19.5232i	0.481551	+	0.774146i
$637$	5.54272	+	23.1408i	0.219610	+	0.916873i
$638$		−	21.1033i		−	0.835489i
$639$	−16.8158	+	11.2431i	−0.665223	+	0.444768i
$640$	3.15592	+	1.82207i	0.124749	+	0.0720237i
$641$	25.2233	−	14.5627i	0.996262	−	0.575192i	0.0891220	−	0.996021i	$-0.471594\pi$
$641$	25.2233	−	14.5627i	0.996262	−	0.575192i	0.907140	+	0.420828i	$0.138261\pi$
$642$	−0.188941	−	5.74595i	−0.00745690	−	0.226775i
$643$	33.9410	−	19.5959i	1.33850	−	0.772785i	0.351918	−	0.936031i	$-0.385530\pi$
$643$	33.9410	−	19.5959i	1.33850	−	0.772785i	0.986585	+	0.163245i	$0.0521962\pi$
$644$	0.527662	+	4.46829i	0.0207928	+	0.176075i
$645$	1.27030	+	38.6315i	0.0500179	+	1.52111i
$646$	1.26513			0.0497760
$647$	10.1800	−	17.6323i	0.400218	−	0.693199i	−0.593534	−	0.804809i	$-0.702268\pi$
$647$	10.1800	−	17.6323i	0.400218	−	0.693199i	0.993752	+	0.111610i	$0.0356009\pi$
$648$	8.31692	+	3.43930i	0.326720	+	0.135109i
$649$	−9.54988	+	5.51362i	−0.374865	+	0.216429i
$650$	14.0729	−	24.3750i	0.551985	−	0.956065i
$651$	−9.83171	+	1.49011i	−0.385335	+	0.0584019i
$652$	1.51018	+	2.61570i	0.0591431	+	0.102439i
$653$	−13.1105	−	7.56933i	−0.513052	−	0.296211i	0.221035	−	0.975266i	$-0.429056\pi$
$653$	−13.1105	−	7.56933i	−0.513052	−	0.296211i	−0.734087	+	0.679055i	$0.762390\pi$
$654$	2.59520	+	4.17207i	0.101480	+	0.163141i
$655$	5.88904	+	10.2001i	0.230104	+	0.398552i
$656$	1.01681	+	1.76117i	0.0396999	+	0.0687622i
$657$	0.857740	+	13.0284i	0.0334636	+	0.508287i
$658$	−14.2965	+	10.6698i	−0.557334	+	0.415952i
$659$	−9.17413	−	5.29668i	−0.357373	−	0.206330i	0.310555	−	0.950556i	$-0.399485\pi$
$659$	−9.17413	−	5.29668i	−0.357373	−	0.206330i	−0.667928	+	0.744226i	$0.732819\pi$
$660$	15.0719	−	28.2075i	0.586674	−	1.09797i
$661$		−	17.0415i		−	0.662836i	−0.943484	−	0.331418i	$-0.892473\pi$
$661$		−	17.0415i		−	0.662836i	0.943484	−	0.331418i	$-0.107527\pi$
$662$			31.7007i			1.23208i
$663$	−4.29917	+	8.04600i	−0.166966	+	0.312481i
$664$	−1.33028	−	0.768040i	−0.0516251	−	0.0298057i
$665$	−6.30921	+	4.70872i	−0.244661	+	0.182596i
$666$	18.2977	+	9.01679i	0.709021	+	0.349393i
$667$	−3.54141	−	6.13389i	−0.137124	−	0.237505i
$668$	7.14766	+	12.3801i	0.276551	+	0.479001i
$669$	−23.7919	−	38.2481i	−0.919849	−	1.47876i
$670$	−7.75223	−	4.47575i	−0.299495	−	0.172913i
$671$	18.3773	+	31.8304i	0.709447	+	1.22880i
$672$	4.53083	−	0.686700i	0.174781	−	0.0264900i
$673$	−12.5048	+	21.6590i	−0.482025	+	0.834891i	−0.999787	−	0.0206331i	$-0.993432\pi$
$673$	−12.5048	+	21.6590i	−0.482025	+	0.834891i	0.517762	+	0.855524i	$0.326765\pi$
$674$	−27.9393	+	16.1308i	−1.07618	+	0.621335i
$675$	34.9602	−	25.0752i	1.34562	−	0.965146i
$676$	0.722247	−	1.25097i	0.0277787	−	0.0481142i
$677$	39.7068			1.52606			0.763028	−	0.646365i	$-0.223712\pi$
$677$	39.7068			1.52606			0.763028	+	0.646365i	$0.223712\pi$
$678$	−0.447265	−	13.6019i	−0.0171771	−	0.522379i
$679$	2.00462	+	16.9753i	0.0769304	+	0.651453i
$680$	−4.88976	+	2.82310i	−0.187514	+	0.108261i
$681$	−1.30229	−	39.6043i	−0.0499038	−	1.51764i
$682$	9.52196	−	5.49750i	0.364615	−	0.210510i
$683$	2.31868	+	1.33869i	0.0887218	+	0.0512236i	0.543705	−	0.839277i	$-0.317021\pi$
$683$	2.31868	+	1.33869i	0.0887218	+	0.0512236i	−0.454983	+	0.890500i	$0.650355\pi$
$684$	2.19730	+	1.08279i	0.0840158	+	0.0414016i
$685$			53.1390i			2.03034i
$686$	6.39643	+	17.3806i	0.244217	+	0.663595i
$687$	−24.6373	−	39.6072i	−0.939973	−	1.51111i
$688$	3.06189	−	5.30335i	0.116733	−	0.202188i
$689$	−45.1246			−1.71911
$690$	−0.352765	−	10.7280i	−0.0134295	−	0.408410i
$691$		−	19.2080i		−	0.730706i	−0.930869	−	0.365353i	$-0.880948\pi$
$691$		−	19.2080i		−	0.730706i	0.930869	−	0.365353i	$-0.119052\pi$
$692$	−2.19905			−0.0835954
$693$	−7.33015	−	39.5438i	−0.278449	−	1.50215i
$694$	6.82421			0.259043
$695$		−	20.9475i		−	0.794583i
$696$	−6.12546	+	3.81029i	−0.232185	+	0.144429i
$697$	−3.15088			−0.119348
$698$	2.41551	−	4.18379i	0.0914284	−	0.158359i
$699$	−7.63594	+	0.251088i	−0.288818	+	0.00949704i
$700$	8.65267	−	20.1250i	0.327040	−	0.760653i
$701$		−	34.1916i		−	1.29140i	−0.763591	−	0.645700i	$-0.776566\pi$
$701$		−	34.1916i		−	1.29140i	0.763591	−	0.645700i	$-0.223434\pi$
$702$	−14.3532	+	10.2949i	−0.541727	+	0.388554i
$703$	4.80825	+	2.77604i	0.181346	+	0.104700i
$704$	−4.38809	+	2.53346i	−0.165382	+	0.0954835i
$705$	36.1370	−	22.4787i	1.36100	−	0.846598i
$706$	29.9510	−	17.2922i	1.12722	−	0.650800i
$707$	12.4369	−	28.9265i	0.467736	−	1.08789i
$708$	3.32466	+	1.77644i	0.124948	+	0.0667628i
$709$	−23.4568			−0.880937			−0.440468	−	0.897768i	$-0.645188\pi$
$709$	−23.4568			−0.880937			−0.440468	+	0.897768i	$0.645188\pi$
$710$	12.2857	−	21.2795i	0.461075	−	0.798605i
$711$	21.2649	+	31.8051i	0.797495	+	1.19278i
$712$	−10.4214	+	6.01679i	−0.390558	+	0.225489i
$713$	1.84510	−	3.19581i	0.0690996	−	0.119684i
$714$	−2.58860	+	6.61152i	−0.0968758	+	0.247430i
$715$	31.3837	+	54.3582i	1.17368	+	2.03288i
$716$	−9.30715	−	5.37349i	−0.347825	−	0.200817i
$717$	32.3145	−	1.06258i	1.20681	−	0.0396828i
$718$	13.5742	+	23.5112i	0.506584	+	0.877429i
$719$	−7.98801	−	13.8356i	−0.297902	−	0.515982i	0.677753	−	0.735289i	$-0.262954\pi$
$719$	−7.98801	−	13.8356i	−0.297902	−	0.515982i	−0.975656	+	0.219307i	$0.929620\pi$
$720$	−10.9088	+	0.718194i	−0.406548	+	0.0267655i
$721$	−4.55643	−	38.5842i	−0.169690	−	1.43695i
$722$	−15.8771	−	9.16664i	−0.590884	−	0.341147i
$723$	0.824471	−	0.0271106i	0.0306624	−	0.00100826i
$724$			14.4710i			0.537811i
$725$			34.4846i			1.28073i
$726$	13.4243	+	21.5811i	0.498224	+	0.800949i
$727$	21.6787	+	12.5162i	0.804019	+	0.464201i	0.844875	−	0.534964i	$-0.179675\pi$
$727$	21.6787	+	12.5162i	0.804019	+	0.464201i	−0.0408555	+	0.999165i	$0.513008\pi$
$728$	−3.55243	+	8.26249i	−0.131662	+	0.306228i
$729$	−26.4766	+	5.29058i	−0.980614	+	0.195948i
$730$	−7.93003	−	13.7352i	−0.293504	−	0.508363i
$731$	4.74407	+	8.21697i	0.175466	+	0.303916i
$732$	5.92100	−	11.0813i	0.218847	−	0.409577i
$733$	10.1433	+	5.85625i	0.374652	+	0.216305i	0.675489	−	0.737370i	$-0.263933\pi$
$733$	10.1433	+	5.85625i	0.374652	+	0.216305i	−0.300837	+	0.953676i	$0.597266\pi$
$734$	−5.96444	−	10.3307i	−0.220151	−	0.381313i
$735$	−11.6982	−	42.6061i	−0.431494	−	1.57155i
$736$	−0.850294	+	1.47275i	−0.0313423	+	0.0542864i
$737$	10.7789	−	6.22322i	0.397047	−	0.229235i
$738$	−5.47250	−	2.69675i	−0.201445	−	0.0992689i
$739$	−8.20255	+	14.2072i	−0.301736	+	0.522622i	−0.976529	−	0.215385i	$-0.930899\pi$
$739$	−8.20255	+	14.2072i	−0.301736	+	0.522622i	0.674793	+	0.738007i	$0.264233\pi$
$740$	−24.7786			−0.910880
$741$	−4.08227	+	2.53934i	−0.149966	+	0.0932850i
$742$	−34.8787	+	4.11884i	−1.28044	+	0.151208i
$743$	8.02860	−	4.63532i	0.294541	−	0.170053i	−0.345447	−	0.938438i	$-0.612273\pi$
$743$	8.02860	−	4.63532i	0.294541	−	0.170053i	0.639988	+	0.768385i	$0.278939\pi$
$744$	−3.31494	−	1.77125i	−0.121531	−	0.0649372i
$745$	−18.0715	+	10.4336i	−0.662087	+	0.382256i
$746$	−8.34718	−	4.81925i	−0.305612	−	0.176445i
$747$	4.59829	−	0.302733i	0.168242	−	0.0110764i
$748$		−	7.85066i		−	0.287048i
$749$	8.06775	+	3.46870i	0.294789	+	0.126744i
$750$	−9.75596	+	18.2585i	−0.356237	+	0.666706i
$751$	−10.0756	+	17.4515i	−0.367665	+	0.636815i	−0.989200	−	0.146572i	$-0.953176\pi$
$751$	−10.0756	+	17.4515i	−0.367665	+	0.636815i	0.621535	+	0.783386i	$0.286509\pi$
$752$	−6.74255			−0.245875
$753$	−27.0301	−	14.4428i	−0.985032	−	0.526326i
$754$		−	14.1580i		−	0.515603i
$755$	−46.5345			−1.69356
$756$	−10.1545	+	9.26746i	−0.369316	+	0.337054i
$757$	47.4297			1.72386			0.861932	−	0.507024i	$-0.169255\pi$
$757$	47.4297			1.72386			0.861932	+	0.507024i	$0.169255\pi$
$758$		−	16.0145i		−	0.581675i
$759$	13.1634	+	7.03352i	0.477801	+	0.255300i
$760$	−2.97557			−0.107935
$761$	−24.0809	+	41.7094i	−0.872933	+	1.51196i	−0.0139853	+	0.999902i	$0.504452\pi$
$761$	−24.0809	+	41.7094i	−0.872933	+	1.51196i	−0.858948	+	0.512063i	$0.828882\pi$
$762$	14.2257	−	26.6237i	0.515342	−	0.964476i
$763$	−7.45350	+	0.880188i	−0.269835	+	0.0318649i
$764$		−	8.33194i		−	0.301439i
$765$	7.48734	−	15.1940i	0.270705	−	0.549339i
$766$	−5.51610	−	3.18472i	−0.199305	−	0.115069i
$767$	−6.40690	+	3.69902i	−0.231340	+	0.133564i
$768$	1.52765	+	0.816261i	0.0551244	+	0.0294543i
$769$	9.84984	−	5.68681i	0.355194	−	0.205071i	−0.311776	−	0.950155i	$-0.600924\pi$
$769$	9.84984	−	5.68681i	0.355194	−	0.205071i	0.666971	+	0.745084i	$0.267591\pi$
$770$	29.2195	+	39.1512i	1.05300	+	1.41091i
$771$	−34.1123	+	21.2193i	−1.22852	+	0.764193i
$772$	9.56786			0.344355
$773$	2.13778	−	3.70275i	0.0768906	−	0.133179i	−0.825016	−	0.565109i	$-0.808834\pi$
$773$	2.13778	−	3.70275i	0.0768906	−	0.133179i	0.901907	+	0.431931i	$0.142167\pi$
$774$	1.20688	+	18.3317i	0.0433806	+	0.658918i
$775$	−15.5597	+	8.98339i	−0.558920	+	0.322693i
$776$	−3.23033	+	5.59509i	−0.115962	+	0.200852i
$777$	−24.3456	+	19.4476i	−0.873395	+	0.697677i
$778$	−8.77645	−	15.2013i	−0.314651	−	0.544992i
$779$	−1.43806	−	0.830263i	−0.0515238	−	0.0297473i
$780$	10.1116	−	18.9241i	0.362052	−	0.677590i
$781$	17.0824	+	29.5876i	0.611257	+	1.05873i
$782$	−1.31744	−	2.28187i	−0.0471115	−	0.0815996i
$783$	8.92300	−	19.7164i	0.318882	−	0.704607i
$784$	−1.99165	+	6.71069i	−0.0711302	+	0.239667i
$785$	−40.3034	−	23.2692i	−1.43849	−	0.830513i
$786$	2.95686	+	4.75348i	0.105468	+	0.169551i
$787$		−	26.4016i		−	0.941115i	−0.882369	−	0.470557i	$-0.844053\pi$
$787$		−	26.4016i		−	0.941115i	0.882369	−	0.470557i	$-0.155947\pi$
$788$		−	2.37228i		−	0.0845089i
$789$	5.96172	−	0.196036i	0.212243	−	0.00697906i
$790$	−40.2476	−	23.2369i	−1.43194	−	0.826733i
$791$	19.0982	+	8.21118i	0.679053	+	0.291956i
$792$	6.71916	−	13.6351i	0.238755	−	0.484503i
$793$	12.3291	+	21.3546i	0.437819	+	0.758324i
$794$	6.67955	+	11.5693i	0.237048	+	0.410580i
$795$	83.7414	−	2.75362i	2.97000	−	0.0976610i
$796$	−19.4983	−	11.2573i	−0.691098	−	0.399006i
$797$	−26.7253	−	46.2896i	−0.946660	−	1.63966i	−0.752393	−	0.658715i	$-0.771100\pi$
$797$	−26.7253	−	46.2896i	−0.946660	−	1.63966i	−0.194267	−	0.980949i	$-0.562233\pi$
$798$	−2.92357	+	2.33538i	−0.103493	+	0.0826717i
$799$	5.22343	−	9.04724i	0.184792	−	0.320068i
$800$	7.17050	−	4.13989i	0.253516	−	0.146367i
$801$	15.9575	−	32.3824i	0.563831	−	1.14418i
$802$	−2.11415	+	3.66182i	−0.0746533	+	0.129303i
$803$	22.0523			0.778209
$804$	−3.75253	−	2.00507i	−0.132342	−	0.0707133i
$805$	15.0630	+	6.47628i	0.530901	+	0.228259i
$806$	6.38817	−	3.68821i	0.225014	−	0.129912i
$807$	−11.7861	+	7.33145i	−0.414891	+	0.258079i
$808$	10.3065	−	5.95045i	0.362581	−	0.209336i
$809$	8.76550	+	5.06076i	0.308179	+	0.177927i	0.646111	−	0.763243i	$-0.276394\pi$
$809$	8.76550	+	5.06076i	0.308179	+	0.177927i	−0.337933	+	0.941170i	$0.609728\pi$
$810$	26.0082	−	19.9809i	0.913835	−	0.702057i
$811$		−	44.8854i		−	1.57614i	−0.615586	−	0.788070i	$-0.711080\pi$
$811$		−	44.8854i		−	1.57614i	0.615586	−	0.788070i	$-0.288920\pi$
$812$	−1.29230	−	10.9433i	−0.0453508	−	0.384034i
$813$	−3.10023	+	0.101943i	−0.108730	+	0.00357530i
$814$	17.2265	−	29.8371i	0.603787	−	1.04579i
$815$	11.0066			0.385544
$816$	−2.27874	+	1.41747i	−0.0797717	+	0.0496213i
$817$			5.00028i			0.174938i
$818$	−38.4154			−1.34316
$819$	−4.91771	−	26.5295i	−0.171839	−	0.927015i
$820$	7.41083			0.258797
$821$			34.4709i			1.20304i	0.798857	+	0.601521i	$0.205438\pi$
$821$			34.4709i			1.20304i	−0.798857	+	0.601521i	$0.794562\pi$
$822$	0.830057	+	25.2432i	0.0289516	+	0.880456i
$823$	−28.9121			−1.00781			−0.503906	−	0.863758i	$-0.668104\pi$
$823$	−28.9121			−1.00781			−0.503906	+	0.863758i	$0.668104\pi$
$824$	7.34240	−	12.7174i	0.255785	−	0.443032i
$825$	−38.3810	−	61.7015i	−1.33625	−	2.14817i
$826$	−4.61453	+	3.44394i	−0.160560	+	0.119830i
$827$			18.8795i			0.656506i	0.944590	+	0.328253i	$0.106460\pi$
$827$			18.8795i			0.656506i	−0.944590	+	0.328253i	$0.893540\pi$
$828$	−0.335155	−	5.09074i	−0.0116474	−	0.176916i
$829$	15.6663	+	9.04494i	0.544113	+	0.314144i	0.746744	−	0.665111i	$-0.231616\pi$
$829$	15.6663	+	9.04494i	0.544113	+	0.314144i	−0.202631	+	0.979255i	$0.564949\pi$
$830$	−4.84775	+	2.79885i	−0.168268	+	0.0971495i
$831$	1.39995	+	42.5742i	0.0485636	+	1.47688i
$832$	−2.94391	+	1.69967i	−0.102062	+	0.0589254i
$833$	−7.46157	−	7.87116i	−0.258528	−	0.272720i
$834$	−0.327210	−	9.95089i	−0.0113303	−	0.344571i
$835$	52.0942			1.80279
$836$	2.06866	−	3.58302i	0.0715461	−	0.123921i
$837$	11.2206	−	1.11009i	0.387842	−	0.0383703i
$838$	−12.1815	+	7.03301i	−0.420804	+	0.242951i
$839$	2.53049	−	4.38294i	0.0873623	−	0.151316i	−0.819033	−	0.573746i	$-0.805490\pi$
$839$	2.53049	−	4.38294i	0.0873623	−	0.151316i	0.906395	+	0.422430i	$0.138823\pi$
$840$	6.08833	−	15.5502i	0.210067	−	0.536532i
$841$	−5.82673	−	10.0922i	−0.200922	−	0.348007i
$842$	18.2738	+	10.5504i	0.629758	+	0.363591i
$843$	19.6764	+	31.6320i	0.677692	+	1.08946i
$844$	7.27211	+	12.5957i	0.250316	+	0.433560i
$845$	−2.63197	−	4.55871i	−0.0905426	−	0.156824i
$846$	16.8154	−	11.2428i	0.578125	−	0.386535i
$847$	−38.5552	+	4.55300i	−1.32477	+	0.156443i
$848$	−11.4961	−	6.63726i	−0.394777	−	0.227924i
$849$	16.2828	−	30.4736i	0.558824	−	1.04585i
$850$			12.8286i			0.440019i
$851$		−	11.5633i		−	0.396384i
$852$	5.50381	−	10.3005i	0.188558	−	0.352890i
$853$	37.0163	+	21.3714i	1.26741	+	0.731742i	0.974498	−	0.224397i	$-0.0720412\pi$
$853$	37.0163	+	21.3714i	1.26741	+	0.731742i	0.292916	+	0.956138i	$0.405374\pi$
$854$	11.4789	+	15.3805i	0.392799	+	0.526311i
$855$	7.42084	−	4.96158i	0.253787	−	0.169682i
$856$	1.65961	+	2.87453i	0.0567243	+	0.0982493i
$857$	0.537523	+	0.931017i	0.0183614	+	0.0318030i	0.875060	−	0.484014i	$-0.160822\pi$
$857$	0.537523	+	0.931017i	0.0183614	+	0.0318030i	−0.856699	+	0.515817i	$0.827488\pi$
$858$	15.7576	+	25.3321i	0.537957	+	0.864824i
$859$	−20.9983	−	12.1234i	−0.716452	−	0.413644i	0.0969931	−	0.995285i	$-0.469078\pi$
$859$	−20.9983	−	12.1234i	−0.716452	−	0.413644i	−0.813446	+	0.581641i	$0.802411\pi$
$860$	−11.1580	−	19.3262i	−0.380484	−	0.659017i
$861$	7.28133	−	5.81640i	0.248147	−	0.198223i
$862$	−5.82709	+	10.0928i	−0.198471	+	0.343762i
$863$	−38.7211	+	22.3556i	−1.31808	+	0.760994i	−0.983420	−	0.181344i	$-0.941955\pi$
$863$	−38.7211	+	22.3556i	−1.31808	+	0.760994i	−0.334661	+	0.942339i	$0.608622\pi$
$864$	−5.17091	+	0.511572i	−0.175918	+	0.0174040i
$865$	−4.00683	+	6.94004i	−0.136236	+	0.235968i
$866$	−17.9149			−0.608774
$867$	0.831045	+	25.2732i	0.0282238	+	0.858323i
$868$	4.60104	−	3.43387i	0.156169	−	0.116553i
$869$	55.9614	−	32.3093i	1.89836	−	1.09602i
$870$	0.863957	+	26.2741i	0.0292909	+	0.890776i
$871$	7.23145	−	4.17508i	0.245028	−	0.141467i
$872$	−2.45668	−	1.41837i	−0.0831938	−	0.0480320i
$873$	−1.27328	−	19.3401i	−0.0430939	−	0.654563i
$874$		−	1.38859i		−	0.0469697i
$875$	−18.9136	−	25.3423i	−0.639395	−	0.856725i
$876$	−3.98163	−	6.40091i	−0.134527	−	0.216267i
$877$	2.08435	−	3.61020i	0.0703835	−	0.121908i	−0.828686	−	0.559714i	$-0.810911\pi$
$877$	2.08435	−	3.61020i	0.0703835	−	0.121908i	0.899069	+	0.437806i	$0.144244\pi$
$878$	−19.0275			−0.642149
$879$	−0.141917	−	4.31589i	−0.00478675	−	0.145571i
$880$			18.4646i			0.622442i
$881$	−32.0880			−1.08107			−0.540536	−	0.841321i	$-0.681779\pi$
$881$	−32.0880			−1.08107			−0.540536	+	0.841321i	$0.681779\pi$
$882$	−6.22264	−	20.0569i	−0.209527	−	0.675351i
$883$	−29.5080			−0.993022			−0.496511	−	0.868031i	$-0.665386\pi$
$883$	−29.5080			−0.993022			−0.496511	+	0.868031i	$0.665386\pi$
$884$		−	5.26691i		−	0.177145i
$885$	11.6641	−	7.25555i	0.392084	−	0.243893i
$886$	7.67734			0.257925
$887$	12.4214	−	21.5145i	0.417071	−	0.722387i	−0.578573	−	0.815631i	$-0.696390\pi$
$887$	12.4214	−	21.5145i	0.417071	−	0.722387i	0.995643	+	0.0932433i	$0.0297234\pi$
$888$	−11.7708	+	0.387054i	−0.395004	+	0.0129887i
$889$	27.5789	+	36.9530i	0.924967	+	1.23936i
$890$			43.8521i			1.46993i
$891$	5.97865	+	45.2087i	0.200292	+	1.51455i
$892$	22.5221	+	13.0031i	0.754095	+	0.435377i
$893$	4.76792	−	2.75276i	0.159552	−	0.0921176i
$894$	−8.42170	+	5.23865i	−0.281664	+	0.175207i
$895$	−33.9166	+	19.5818i	−1.13371	+	0.654546i
$896$	−2.12034	+	1.58246i	−0.0708354	+	0.0528662i
$897$	8.83116	+	4.71870i	0.294864	+	0.157553i
$898$	−30.1018			−1.00451
$899$	−4.51885	+	7.82687i	−0.150712	+	0.261041i
$900$	−10.9797	+	22.2809i	−0.365989	+	0.742698i
$901$	17.8119	−	10.2837i	0.593401	−	0.342600i
$902$	−5.15212	+	8.92373i	−0.171547	+	0.297128i
$903$	−26.1312	−	10.2311i	−0.869591	−	0.340470i
$904$	3.92866	+	6.80465i	0.130665	+	0.226319i
$905$	45.6694	+	26.3673i	1.51810	+	0.876477i
$906$	−22.1058	+	0.726892i	−0.734415	+	0.0241494i
$907$	−20.4561	−	35.4311i	−0.679235	−	1.17647i	−0.975212	−	0.221274i	$-0.928979\pi$
$907$	−20.4561	−	35.4311i	−0.679235	−	1.17647i	0.295977	−	0.955195i	$-0.404355\pi$
$908$	11.4390	+	19.8129i	0.379616	+	0.657513i
$909$	−15.7816	+	32.0254i	−0.523442	+	1.06221i
$910$	19.6030	+	26.2660i	0.649833	+	0.870711i
$911$	2.21678	+	1.27986i	0.0734452	+	0.0424036i	0.536273	−	0.844045i	$-0.319832\pi$
$911$	2.21678	+	1.27986i	0.0734452	+	0.0424036i	−0.462828	+	0.886448i	$0.653165\pi$
$912$	−1.41352	+	0.0464799i	−0.0468062	+	0.00153910i
$913$		−	7.78320i		−	0.257586i
$914$		−	39.4876i		−	1.30613i
$915$	−24.1832	−	38.8771i	−0.799473	−	1.28524i
$916$	23.3224	+	13.4652i	0.770592	+	0.444902i
$917$	−8.49221	+	1.00285i	−0.280438	+	0.0331170i
$918$	3.31945	−	7.33471i	0.109558	−	0.242081i
$919$	5.12246	+	8.87236i	0.168974	+	0.292672i	0.938060	−	0.346474i	$-0.112621\pi$
$919$	5.12246	+	8.87236i	0.168974	+	0.292672i	−0.769085	+	0.639146i	$0.779288\pi$
$920$	3.09859	+	5.36692i	0.102158	+	0.176942i
$921$	−7.53509	+	14.1021i	−0.248290	+	0.464680i
$922$	19.7066	+	11.3776i	0.649004	+	0.374703i
$923$	11.4604	+	19.8500i	0.377223	+	0.653370i
$924$	14.4920	+	18.1420i	0.476752	+	0.596827i
$925$	−28.1495	+	48.7564i	−0.925550	+	1.60310i
$926$	−11.4985	+	6.63866i	−0.377864	+	0.218160i
$927$	2.89410	+	43.9592i	0.0950548	+	1.44381i
$928$	2.08246	−	3.60693i	0.0683601	−	0.118403i
$929$	−29.5704			−0.970173			−0.485087	−	0.874466i	$-0.661212\pi$
$929$	−29.5704			−0.970173			−0.485087	+	0.874466i	$0.661212\pi$
$930$	−11.6300	+	7.23434i	−0.381362	+	0.237223i
$931$	−1.33138	−	5.55852i	−0.0436343	−	0.182173i
$932$	3.82003	−	2.20550i	0.125129	−	0.0722435i
$933$	35.0923	+	18.7506i	1.14887	+	0.613868i
$934$	20.0698	−	11.5873i	0.656702	−	0.379147i
$935$	−24.7761	−	14.3045i	−0.810264	−	0.467806i
$936$	4.50780	−	9.14764i	0.147342	−	0.299000i
$937$		−	17.9991i		−	0.588005i	−0.955805	−	0.294002i	$-0.905013\pi$
$937$		−	17.9991i		−	0.588005i	0.955805	−	0.294002i	$-0.0949874\pi$
$938$	5.20841	−	3.88716i	0.170061	−	0.126920i
$939$	−5.25130	+	9.82793i	−0.171370	+	0.320722i
$940$	−12.2854	+	21.2789i	−0.400706	+	0.694043i
$941$	29.7237			0.968965			0.484483	−	0.874801i	$-0.339008\pi$
$941$	29.7237			0.968965			0.484483	+	0.874801i	$0.339008\pi$
$942$	−19.5092	−	10.4242i	−0.635645	−	0.339640i
$943$			3.45836i			0.112620i
$944$	−2.17632			−0.0708331
$945$	10.7451	+	48.9328i	0.349538	+	1.59179i
$946$	31.0287			1.00883
$947$			22.1959i			0.721270i	0.932707	+	0.360635i	$0.117440\pi$
$947$			22.1959i			0.721270i	−0.932707	+	0.360635i	$0.882560\pi$
$948$	−19.4822	−	10.4098i	−0.632752	−	0.338094i
$949$	14.7946			0.480254
$950$	−3.38037	+	5.85497i	−0.109674	+	0.189960i
$951$	−7.13031	+	13.3445i	−0.231216	+	0.432726i
$952$	−0.480749	−	4.07102i	−0.0155812	−	0.131943i
$953$			2.12319i			0.0687769i	0.999409	+	0.0343884i	$0.0109483\pi$
$953$			2.12319i			0.0687769i	−0.999409	+	0.0343884i	$0.989052\pi$
$954$	39.7375	−	2.61616i	1.28655	−	0.0847014i
$955$	−26.2950	−	15.1814i	−0.850885	−	0.491258i
$956$	−16.1660	+	9.33343i	−0.522845	+	0.301865i
$957$	−32.2385	−	17.2258i	−1.04212	−	0.556832i
$958$	21.4025	−	12.3567i	0.691484	−	0.399228i
$959$	−35.4433	−	15.2387i	−1.14452	−	0.492084i
$960$	5.35954	−	3.33386i	0.172979	−	0.107600i
$961$	26.2913			0.848106
$962$	11.5570	−	20.0174i	0.372613	−	0.645385i
$963$	−8.93203	−	4.40156i	−0.287831	−	0.141838i
$964$	−0.412458	+	0.238133i	−0.0132844	+	0.00766974i
$965$	17.4333	−	30.1954i	0.561199	−	0.972025i
$966$	7.25669	+	2.84120i	0.233480	+	0.0914142i
$967$	−2.23409	−	3.86955i	−0.0718434	−	0.124436i	0.827866	−	0.560926i	$-0.189555\pi$
$967$	−2.23409	−	3.86955i	−0.0718434	−	0.124436i	−0.899709	+	0.436490i	$0.856222\pi$
$968$	−12.7078	−	7.33687i	−0.408445	−	0.235816i
$969$	1.03268	−	1.93268i	0.0331744	−	0.0620867i
$970$	11.7718	+	20.3893i	0.377969	+	0.654661i
$971$	−0.916026	−	1.58660i	−0.0293967	−	0.0509165i	0.850953	−	0.525242i	$-0.176025\pi$
$971$	−0.916026	−	1.58660i	−0.0293967	−	0.0509165i	−0.880349	+	0.474326i	$0.842692\pi$
$972$	12.0428	−	9.89799i	0.386274	−	0.317478i
$973$	13.9718	+	6.00713i	0.447916	+	0.192580i
$974$	29.4236	+	16.9877i	0.942794	+	0.544322i
$975$	−25.7493	−	41.3948i	−0.824638	−	1.32570i
$976$			7.25382i			0.232189i
$977$			30.9498i			0.990173i	0.868844	+	0.495087i	$0.164864\pi$
$977$			30.9498i			0.990173i	−0.868844	+	0.495087i	$0.835136\pi$
$978$	5.22858	−	0.171929i	0.167192	−	0.00549767i
$979$	−52.8044	−	30.4866i	−1.68764	−	0.974357i
$980$	17.5495	+	18.5128i	0.560598	+	0.591371i
$981$	8.49182	−	0.559068i	0.271123	−	0.0178497i
$982$	−14.7763	−	25.5933i	−0.471531	−	0.816715i
$983$	16.2825	+	28.2020i	0.519330	+	0.899505i	0.999748	+	0.0224656i	$0.00715163\pi$
$983$	16.2825	+	28.2020i	0.519330	+	0.899505i	−0.480418	+	0.877040i	$0.659515\pi$
$984$	3.52044	−	0.115761i	0.112228	−	0.00369032i
$985$	−7.48673	−	4.32246i	−0.238547	−	0.137725i
$986$	3.22655	+	5.58854i	0.102754	+	0.177975i
$987$	4.63010	+	30.5494i	0.147378	+	0.972397i
$988$	1.38784	−	2.40381i	0.0441530	−	0.0764753i
$989$	9.01881	−	5.20701i	0.286782	−	0.165573i
$990$	−30.7886	−	46.0493i	−0.978525	−	1.46354i
$991$	1.45730	−	2.52411i	0.0462926	−	0.0801811i	−0.841951	−	0.539555i	$-0.818593\pi$
$991$	1.45730	−	2.52411i	0.0462926	−	0.0801811i	0.888243	+	0.459373i	$0.151926\pi$
$992$	2.16996			0.0688962
$993$	48.4277	+	25.8761i	1.53681	+	0.821152i
$994$	10.6701	+	14.2968i	0.338434	+	0.453468i
$995$	−71.0545	+	41.0234i	−2.25258	+	1.30053i
$996$	−2.25916	+	1.40529i	−0.0715841	+	0.0445283i
$997$	39.9943	−	23.0907i	1.26663	−	0.731290i	0.292282	−	0.956332i	$-0.405585\pi$
$997$	39.9943	−	23.0907i	1.26663	−	0.731290i	0.974349	+	0.225042i	$0.0722520\pi$
$998$	9.32959	+	5.38644i	0.295323	+	0.170505i
$999$	28.7102	−	20.5924i	0.908350	−	0.651515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.l.a.101.8	yes	16
3.2	odd	2		378.2.l.a.143.4		16
4.3	odd	2		1008.2.ca.c.353.2		16
7.2	even	3		882.2.t.a.803.5		16
7.3	odd	6		882.2.m.a.587.2		16
7.4	even	3		882.2.m.b.587.3		16
7.5	odd	6		126.2.t.a.47.8	yes	16
7.6	odd	2		882.2.l.b.227.5		16
9.2	odd	6		1134.2.k.b.647.4		16
9.4	even	3		378.2.t.a.17.4		16
9.5	odd	6		126.2.t.a.59.8	yes	16
9.7	even	3		1134.2.k.a.647.5		16
12.11	even	2		3024.2.ca.c.2033.8		16
21.2	odd	6		2646.2.t.b.1979.1		16
21.5	even	6		378.2.t.a.89.4		16
21.11	odd	6		2646.2.m.b.1763.8		16
21.17	even	6		2646.2.m.a.1763.5		16
21.20	even	2		2646.2.l.a.521.1		16
28.19	even	6		1008.2.df.c.929.1		16
36.23	even	6		1008.2.df.c.689.1		16
36.31	odd	6		3024.2.df.c.17.8		16
63.4	even	3		2646.2.m.a.881.5		16
63.5	even	6	inner	126.2.l.a.5.4	✓	16
63.13	odd	6		2646.2.t.b.2285.1		16
63.23	odd	6		882.2.l.b.509.1		16
63.31	odd	6		2646.2.m.b.881.8		16
63.32	odd	6		882.2.m.a.293.2		16
63.40	odd	6		378.2.l.a.341.8		16
63.41	even	6		882.2.t.a.815.5		16
63.47	even	6		1134.2.k.a.971.5		16
63.58	even	3		2646.2.l.a.1097.5		16
63.59	even	6		882.2.m.b.293.3		16
63.61	odd	6		1134.2.k.b.971.4		16
84.47	odd	6		3024.2.df.c.1601.8		16
252.103	even	6		3024.2.ca.c.2609.8		16
252.131	odd	6		1008.2.ca.c.257.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.4	✓	16	63.5	even	6	inner
126.2.l.a.101.8	yes	16	1.1	even	1	trivial
126.2.t.a.47.8	yes	16	7.5	odd	6
126.2.t.a.59.8	yes	16	9.5	odd	6
378.2.l.a.143.4		16	3.2	odd	2
378.2.l.a.341.8		16	63.40	odd	6
378.2.t.a.17.4		16	9.4	even	3
378.2.t.a.89.4		16	21.5	even	6
882.2.l.b.227.5		16	7.6	odd	2
882.2.l.b.509.1		16	63.23	odd	6
882.2.m.a.293.2		16	63.32	odd	6
882.2.m.a.587.2		16	7.3	odd	6
882.2.m.b.293.3		16	63.59	even	6
882.2.m.b.587.3		16	7.4	even	3
882.2.t.a.803.5		16	7.2	even	3
882.2.t.a.815.5		16	63.41	even	6
1008.2.ca.c.257.2		16	252.131	odd	6
1008.2.ca.c.353.2		16	4.3	odd	2
1008.2.df.c.689.1		16	36.23	even	6
1008.2.df.c.929.1		16	28.19	even	6
1134.2.k.a.647.5		16	9.7	even	3
1134.2.k.a.971.5		16	63.47	even	6
1134.2.k.b.647.4		16	9.2	odd	6
1134.2.k.b.971.4		16	63.61	odd	6
2646.2.l.a.521.1		16	21.20	even	2
2646.2.l.a.1097.5		16	63.58	even	3
2646.2.m.a.881.5		16	63.4	even	3
2646.2.m.a.1763.5		16	21.17	even	6
2646.2.m.b.881.8		16	63.31	odd	6
2646.2.m.b.1763.8		16	21.11	odd	6
2646.2.t.b.1979.1		16	21.2	odd	6
2646.2.t.b.2285.1		16	63.13	odd	6
3024.2.ca.c.2033.8		16	12.11	even	2
3024.2.ca.c.2609.8		16	252.103	even	6
3024.2.df.c.17.8		16	36.31	odd	6
3024.2.df.c.1601.8		16	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.52765 + 0.816261i) q^{3} -1.00000 q^{4} +(-1.82207 + 3.15592i) q^{5} +(-0.816261 + 1.52765i) q^{6} +(-1.58246 - 2.12034i) q^{7} -1.00000i q^{8} +(1.66744 + 2.49392i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.52765 + 0.816261i) q^{3} -1.00000 q^{4} +(-1.82207 + 3.15592i) q^{5} +(-0.816261 + 1.52765i) q^{6} +(-1.58246 - 2.12034i) q^{7} -1.00000i q^{8} +(1.66744 + 2.49392i) q^{9} +(-3.15592 - 1.82207i) q^{10} +(4.38809 - 2.53346i) q^{11} +(-1.52765 - 0.816261i) q^{12} +(2.94391 - 1.69967i) q^{13} +(2.12034 - 1.58246i) q^{14} +(-5.35954 + 3.33386i) q^{15} +1.00000 q^{16} +(-0.774696 + 1.34181i) q^{17} +(-2.49392 + 1.66744i) q^{18} +(-0.707140 + 0.408267i) q^{19} +(1.82207 - 3.15592i) q^{20} +(-0.686700 - 4.53083i) q^{21} +(2.53346 + 4.38809i) q^{22} +(1.47275 + 0.850294i) q^{23} +(0.816261 - 1.52765i) q^{24} +(-4.13989 - 7.17050i) q^{25} +(1.69967 + 2.94391i) q^{26} +(0.511572 + 5.17091i) q^{27} +(1.58246 + 2.12034i) q^{28} +(-3.60693 - 2.08246i) q^{29} +(-3.33386 - 5.35954i) q^{30} -2.16996i q^{31} +1.00000i q^{32} +(8.77143 - 0.288426i) q^{33} +(-1.34181 - 0.774696i) q^{34} +(9.57497 - 1.13071i) q^{35} +(-1.66744 - 2.49392i) q^{36} +(-3.39979 - 5.88860i) q^{37} +(-0.408267 - 0.707140i) q^{38} +(5.88465 - 0.193502i) q^{39} +(3.15592 + 1.82207i) q^{40} +(1.01681 + 1.76117i) q^{41} +(4.53083 - 0.686700i) q^{42} +(3.06189 - 5.30335i) q^{43} +(-4.38809 + 2.53346i) q^{44} +(-10.9088 + 0.718194i) q^{45} +(-0.850294 + 1.47275i) q^{46} -6.74255 q^{47} +(1.52765 + 0.816261i) q^{48} +(-1.99165 + 6.71069i) q^{49} +(7.17050 - 4.13989i) q^{50} +(-2.27874 + 1.41747i) q^{51} +(-2.94391 + 1.69967i) q^{52} +(-11.4961 - 6.63726i) q^{53} +(-5.17091 + 0.511572i) q^{54} +18.4646i q^{55} +(-2.12034 + 1.58246i) q^{56} +(-1.41352 + 0.0464799i) q^{57} +(2.08246 - 3.60693i) q^{58} -2.17632 q^{59} +(5.35954 - 3.33386i) q^{60} +7.25382i q^{61} +2.16996 q^{62} +(2.64930 - 7.48206i) q^{63} -1.00000 q^{64} +12.3877i q^{65} +(0.288426 + 8.77143i) q^{66} +2.45641 q^{67} +(0.774696 - 1.34181i) q^{68} +(1.55579 + 2.50110i) q^{69} +(1.13071 + 9.57497i) q^{70} +6.74272i q^{71} +(2.49392 - 1.66744i) q^{72} +(3.76912 + 2.17610i) q^{73} +(5.88860 - 3.39979i) q^{74} +(-0.471313 - 14.3333i) q^{75} +(0.707140 - 0.408267i) q^{76} +(-12.3158 - 5.29511i) q^{77} +(0.193502 + 5.88465i) q^{78} +12.7530 q^{79} +(-1.82207 + 3.15592i) q^{80} +(-3.43930 + 8.31692i) q^{81} +(-1.76117 + 1.01681i) q^{82} +(0.768040 - 1.33028i) q^{83} +(0.686700 + 4.53083i) q^{84} +(-2.82310 - 4.88976i) q^{85} +(5.30335 + 3.06189i) q^{86} +(-3.81029 - 6.12546i) q^{87} +(-2.53346 - 4.38809i) q^{88} +(-6.01679 - 10.4214i) q^{89} +(-0.718194 - 10.9088i) q^{90} +(-8.26249 - 3.55243i) q^{91} +(-1.47275 - 0.850294i) q^{92} +(1.77125 - 3.31494i) q^{93} -6.74255i q^{94} -2.97557i q^{95} +(-0.816261 + 1.52765i) q^{96} +(-5.59509 - 3.23033i) q^{97} +(-6.71069 - 1.99165i) q^{98} +(13.6351 + 6.71916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 2 * q^7	\( 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 6 * q^97 - 24 * q^98 + 18 * q^99

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