LMFDB - Embedded newform 273.2.bl.d.88.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.7
Root			$0.871638i$ of defining polynomial
Character	$\chi$	$=$	273.88
Dual form			273.2.bl.d.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.754861 + 0.435819i) q^{2} -1.00000 q^{3} +(-0.620123 - 1.07408i) q^{4} +(-1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.48610 - 0.905145i) q^{7} -2.82432i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.754861 + 0.435819i) q^{2} -1.00000 q^{3} +(-0.620123 - 1.07408i) q^{4} +(-1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.48610 - 0.905145i) q^{7} -2.82432i q^{8} +1.00000 q^{9} -1.34871 q^{10} -3.61595i q^{11} +(0.620123 + 1.07408i) q^{12} +(-3.37483 + 1.26906i) q^{13} +(-1.48218 - 1.76675i) q^{14} +(1.34003 - 0.773665i) q^{15} +(-0.00935211 + 0.0161983i) q^{16} +(-2.31602 - 4.01147i) q^{17} +(0.754861 + 0.435819i) q^{18} -0.586956i q^{19} +(1.66196 + 0.959535i) q^{20} +(2.48610 + 0.905145i) q^{21} +(1.57590 - 2.72954i) q^{22} +(1.14261 - 1.97906i) q^{23} +2.82432i q^{24} +(-1.30289 + 2.25666i) q^{25} +(-3.10061 - 0.512855i) q^{26} -1.00000 q^{27} +(0.569488 + 3.23159i) q^{28} +(1.07556 + 1.86293i) q^{29} +1.34871 q^{30} +(8.99732 + 5.19461i) q^{31} +(-4.90599 + 2.83247i) q^{32} +3.61595i q^{33} -4.03747i q^{34} +(4.03172 - 0.710493i) q^{35} +(-0.620123 - 1.07408i) q^{36} +(-5.03139 - 2.90487i) q^{37} +(0.255807 - 0.443071i) q^{38} +(3.37483 - 1.26906i) q^{39} +(2.18508 + 3.78467i) q^{40} +(-1.60485 + 0.926561i) q^{41} +(1.48218 + 1.76675i) q^{42} +(3.93747 - 6.81990i) q^{43} +(-3.88384 + 2.24233i) q^{44} +(-1.34003 + 0.773665i) q^{45} +(1.72503 - 0.995945i) q^{46} +(-2.10152 + 1.21331i) q^{47} +(0.00935211 - 0.0161983i) q^{48} +(5.36143 + 4.50057i) q^{49} +(-1.96699 + 1.13565i) q^{50} +(2.31602 + 4.01147i) q^{51} +(3.45589 + 2.83788i) q^{52} +(6.49352 - 11.2471i) q^{53} +(-0.754861 - 0.435819i) q^{54} +(2.79753 + 4.84547i) q^{55} +(-2.55642 + 7.02156i) q^{56} +0.586956i q^{57} +1.87500i q^{58} +(4.68954 - 2.70751i) q^{59} +(-1.66196 - 0.959535i) q^{60} -9.70842 q^{61} +(4.52782 + 7.84241i) q^{62} +(-2.48610 - 0.905145i) q^{63} -4.90038 q^{64} +(3.54054 - 4.31156i) q^{65} +(-1.57590 + 2.72954i) q^{66} +1.92060i q^{67} +(-2.87244 + 4.97521i) q^{68} +(-1.14261 + 1.97906i) q^{69} +(3.35304 + 1.22078i) q^{70} +(-9.14766 - 5.28141i) q^{71} -2.82432i q^{72} +(1.96780 + 1.13611i) q^{73} +(-2.53200 - 4.38555i) q^{74} +(1.30289 - 2.25666i) q^{75} +(-0.630441 + 0.363985i) q^{76} +(-3.27296 + 8.98963i) q^{77} +(3.10061 + 0.512855i) q^{78} +(5.78378 + 10.0178i) q^{79} -0.0289416i q^{80} +1.00000 q^{81} -1.61525 q^{82} -9.45200i q^{83} +(-0.569488 - 3.23159i) q^{84} +(6.20707 + 3.58365i) q^{85} +(5.94449 - 3.43205i) q^{86} +(-1.07556 - 1.86293i) q^{87} -10.2126 q^{88} +(-10.9701 - 6.33357i) q^{89} -1.34871 q^{90} +(9.53886 - 0.100297i) q^{91} -2.83424 q^{92} +(-8.99732 - 5.19461i) q^{93} -2.11514 q^{94} +(0.454108 + 0.786537i) q^{95} +(4.90599 - 2.83247i) q^{96} +(-14.3826 - 8.30380i) q^{97} +(2.08570 + 5.73392i) q^{98} -3.61595i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.754861	+	0.435819i	0.533767	+	0.308171i	0.742549	−	0.669792i	$-0.233617\pi$
$2$	0.754861	+	0.435819i	0.533767	+	0.308171i	−0.208782	+	0.977962i	$0.566950\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.620123	−	1.07408i	−0.310062	−	0.537042i
$5$	−1.34003	+	0.773665i	−0.599278	+	0.345993i	−0.768758	−	0.639540i	$-0.779125\pi$
$5$	−1.34003	+	0.773665i	−0.599278	+	0.345993i	0.169479	+	0.985534i	$0.445791\pi$
$6$	−0.754861	−	0.435819i	−0.308171	−	0.177922i
$7$	−2.48610	−	0.905145i	−0.939659	−	0.342113i
$7$	−2.48610	−	0.905145i	−0.939659	−	0.342113i
$8$		−	2.82432i		−	0.998549i
$9$	1.00000			0.333333
$10$	−1.34871			−0.426500
$11$		−	3.61595i		−	1.09025i	−0.838355	−	0.545125i	$-0.816482\pi$
$11$		−	3.61595i		−	1.09025i	0.838355	−	0.545125i	$-0.183518\pi$
$12$	0.620123	+	1.07408i	0.179014	+	0.310062i
$13$	−3.37483	+	1.26906i	−0.936010	+	0.351973i
$13$	−3.37483	+	1.26906i	−0.936010	+	0.351973i
$14$	−1.48218	−	1.76675i	−0.396130	−	0.472184i
$15$	1.34003	−	0.773665i	0.345993	−	0.199759i
$16$	−0.00935211	+	0.0161983i	−0.00233803	+	0.00404958i
$17$	−2.31602	−	4.01147i	−0.561718	−	0.972924i	−0.997347	−	0.0727978i	$-0.976807\pi$
$17$	−2.31602	−	4.01147i	−0.561718	−	0.972924i	0.435629	−	0.900126i	$-0.356526\pi$
$18$	0.754861	+	0.435819i	0.177922	+	0.102724i
$19$		−	0.586956i		−	0.134657i	−0.997731	−	0.0673285i	$-0.978552\pi$
$19$		−	0.586956i		−	0.134657i	0.997731	−	0.0673285i	$-0.0214476\pi$
$20$	1.66196	+	0.959535i	0.371626	+	0.214559i
$21$	2.48610	+	0.905145i	0.542512	+	0.197519i
$22$	1.57590	−	2.72954i	0.335983	−	0.581940i
$23$	1.14261	−	1.97906i	0.238251	−	0.412663i	−0.721961	−	0.691933i	$-0.756759\pi$
$23$	1.14261	−	1.97906i	0.238251	−	0.412663i	0.960213	+	0.279270i	$0.0900925\pi$
$24$			2.82432i			0.576513i
$25$	−1.30289	+	2.25666i	−0.260577	+	0.451333i
$26$	−3.10061	−	0.512855i	−0.608079	−	0.100579i
$27$	−1.00000			−0.192450
$28$	0.569488	+	3.23159i	0.107623	+	0.610713i
$29$	1.07556	+	1.86293i	0.199727	+	0.345937i	0.948440	−	0.316957i	$-0.102661\pi$
$29$	1.07556	+	1.86293i	0.199727	+	0.345937i	−0.748713	+	0.662894i	$0.769328\pi$
$30$	1.34871			0.246240
$31$	8.99732	+	5.19461i	1.61597	+	0.932979i	0.987949	+	0.154781i	$0.0494670\pi$
$31$	8.99732	+	5.19461i	1.61597	+	0.932979i	0.628018	+	0.778199i	$0.283866\pi$
$32$	−4.90599	+	2.83247i	−0.867265	+	0.500716i
$33$			3.61595i			0.629456i
$34$		−	4.03747i		−	0.692420i
$35$	4.03172	−	0.710493i	0.681486	−	0.120095i
$36$	−0.620123	−	1.07408i	−0.103354	−	0.179014i
$37$	−5.03139	−	2.90487i	−0.827155	−	0.477558i	0.0257226	−	0.999669i	$-0.491811\pi$
$37$	−5.03139	−	2.90487i	−0.827155	−	0.477558i	−0.852878	+	0.522111i	$0.825145\pi$
$38$	0.255807	−	0.443071i	0.0414974	−	0.0718755i
$39$	3.37483	−	1.26906i	0.540406	−	0.203212i
$40$	2.18508	+	3.78467i	0.345491	+	0.598409i
$41$	−1.60485	+	0.926561i	−0.250636	+	0.144704i	−0.620055	−	0.784558i	$-0.712890\pi$
$41$	−1.60485	+	0.926561i	−0.250636	+	0.144704i	0.369420	+	0.929263i	$0.379556\pi$
$42$	1.48218	+	1.76675i	0.228706	+	0.272616i
$43$	3.93747	−	6.81990i	0.600459	−	1.04003i	−0.392293	−	0.919840i	$-0.628318\pi$
$43$	3.93747	−	6.81990i	0.600459	−	1.04003i	0.992752	−	0.120185i	$-0.0383487\pi$
$44$	−3.88384	+	2.24233i	−0.585511	+	0.338045i
$45$	−1.34003	+	0.773665i	−0.199759	+	0.115331i
$46$	1.72503	−	0.995945i	0.254342	−	0.146844i
$47$	−2.10152	+	1.21331i	−0.306538	+	0.176980i	−0.645376	−	0.763865i	$-0.723299\pi$
$47$	−2.10152	+	1.21331i	−0.306538	+	0.176980i	0.338838	+	0.940845i	$0.389966\pi$
$48$	0.00935211	−	0.0161983i	0.00134986	−	0.00233803i
$49$	5.36143	+	4.50057i	0.765918	+	0.642938i
$50$	−1.96699	+	1.13565i	−0.278175	+	0.160604i
$51$	2.31602	+	4.01147i	0.324308	+	0.561718i
$52$	3.45589	+	2.83788i	0.479245	+	0.393544i
$53$	6.49352	−	11.2471i	0.891954	−	1.54491i	0.0544233	−	0.998518i	$-0.482668\pi$
$53$	6.49352	−	11.2471i	0.891954	−	1.54491i	0.837530	−	0.546391i	$-0.183999\pi$
$54$	−0.754861	−	0.435819i	−0.102724	−	0.0593075i
$55$	2.79753	+	4.84547i	0.377219	+	0.653363i
$56$	−2.55642	+	7.02156i	−0.341616	+	0.938296i
$57$			0.586956i			0.0777443i
$58$			1.87500i			0.246200i
$59$	4.68954	−	2.70751i	0.610526	−	0.352487i	−0.162645	−	0.986685i	$-0.552003\pi$
$59$	4.68954	−	2.70751i	0.610526	−	0.352487i	0.773171	+	0.634197i	$0.218669\pi$
$60$	−1.66196	−	0.959535i	−0.214559	−	0.123875i
$61$	−9.70842			−1.24304			−0.621518	−	0.783400i	$-0.713484\pi$
$61$	−9.70842			−1.24304			−0.621518	+	0.783400i	$0.713484\pi$
$62$	4.52782	+	7.84241i	0.575034	+	0.995988i
$63$	−2.48610	−	0.905145i	−0.313220	−	0.114038i
$64$	−4.90038			−0.612547
$65$	3.54054	−	4.31156i	0.439150	−	0.534783i
$66$	−1.57590	+	2.72954i	−0.193980	+	0.335983i
$67$			1.92060i			0.234638i	0.993094	+	0.117319i	$0.0374300\pi$
$67$			1.92060i			0.234638i	−0.993094	+	0.117319i	$0.962570\pi$
$68$	−2.87244	+	4.97521i	−0.348334	+	0.603333i
$69$	−1.14261	+	1.97906i	−0.137554	+	0.238251i
$70$	3.35304	+	1.22078i	0.400765	+	0.145911i
$71$	−9.14766	−	5.28141i	−1.08563	−	0.626788i	−0.153219	−	0.988192i	$-0.548964\pi$
$71$	−9.14766	−	5.28141i	−1.08563	−	0.626788i	−0.932409	+	0.361405i	$0.882297\pi$
$72$		−	2.82432i		−	0.332850i
$73$	1.96780	+	1.13611i	0.230313	+	0.132971i	0.610717	−	0.791849i	$-0.290882\pi$
$73$	1.96780	+	1.13611i	0.230313	+	0.132971i	−0.380403	+	0.924821i	$0.624215\pi$
$74$	−2.53200	−	4.38555i	−0.294339	−	0.509810i
$75$	1.30289	−	2.25666i	0.150444	−	0.260577i
$76$	−0.630441	+	0.363985i	−0.0723165	+	0.0417520i
$77$	−3.27296	+	8.98963i	−0.372988	+	1.02446i
$78$	3.10061	+	0.512855i	0.351075	+	0.0580694i
$79$	5.78378	+	10.0178i	0.650726	+	1.12709i	0.982947	+	0.183889i	$0.0588686\pi$
$79$	5.78378	+	10.0178i	0.650726	+	1.12709i	−0.332221	+	0.943202i	$0.607798\pi$
$80$		−	0.0289416i		−	0.00323577i
$81$	1.00000			0.111111
$82$	−1.61525			−0.178375
$83$		−	9.45200i		−	1.03749i	−0.854928	−	0.518746i	$-0.826399\pi$
$83$		−	9.45200i		−	1.03749i	0.854928	−	0.518746i	$-0.173601\pi$
$84$	−0.569488	−	3.23159i	−0.0621363	−	0.352595i
$85$	6.20707	+	3.58365i	0.673251	+	0.388702i
$86$	5.94449	−	3.43205i	0.641011	−	0.370088i
$87$	−1.07556	−	1.86293i	−0.115312	−	0.199727i
$88$	−10.2126			−1.08867
$89$	−10.9701	−	6.33357i	−1.16283	−	0.671358i	−0.210846	−	0.977519i	$-0.567622\pi$
$89$	−10.9701	−	6.33357i	−1.16283	−	0.671358i	−0.951980	+	0.306162i	$0.900955\pi$
$90$	−1.34871			−0.142167
$91$	9.53886	−	0.100297i	0.999945	−	0.0105140i
$92$	−2.83424			−0.295490
$93$	−8.99732	−	5.19461i	−0.932979	−	0.538656i
$94$	−2.11514			−0.218160
$95$	0.454108	+	0.786537i	0.0465905	+	0.0806970i
$96$	4.90599	−	2.83247i	0.500716	−	0.289088i
$97$	−14.3826	−	8.30380i	−1.46033	−	0.843124i	−0.461307	−	0.887241i	$-0.652619\pi$
$97$	−14.3826	−	8.30380i	−1.46033	−	0.843124i	−0.999026	+	0.0441172i	$0.985952\pi$
$98$	2.08570	+	5.73392i	0.210687	+	0.579213i
$99$		−	3.61595i		−	0.363417i
$100$	3.23180			0.323180
$101$	13.0991			1.30341			0.651705	−	0.758472i	$-0.274054\pi$
$101$	13.0991			1.30341			0.651705	+	0.758472i	$0.274054\pi$
$102$			4.03747i			0.399769i
$103$	−0.0841095	−	0.145682i	−0.00828756	−	0.0143545i	0.861852	−	0.507160i	$-0.169305\pi$
$103$	−0.0841095	−	0.145682i	−0.00828756	−	0.0143545i	−0.870139	+	0.492806i	$0.835971\pi$
$104$	3.58423	+	9.53162i	0.351463	+	0.934652i
$105$	−4.03172	+	0.710493i	−0.393456	+	0.0693370i
$106$	9.80341	−	5.66000i	0.952191	−	0.549748i
$107$	0.791312	−	1.37059i	0.0764990	−	0.132500i	−0.825238	−	0.564785i	$-0.808959\pi$
$107$	0.791312	−	1.37059i	0.0764990	−	0.132500i	0.901737	+	0.432285i	$0.142292\pi$
$108$	0.620123	+	1.07408i	0.0596714	+	0.103354i
$109$	−3.76860	−	2.17580i	−0.360966	−	0.208404i	0.308538	−	0.951212i	$-0.400160\pi$
$109$	−3.76860	−	2.17580i	−0.360966	−	0.208404i	−0.669504	+	0.742808i	$0.733494\pi$
$110$			4.87688i			0.464992i
$111$	5.03139	+	2.90487i	0.477558	+	0.275718i
$112$	0.0379121	−	0.0318057i	0.00358236	−	0.00300536i
$113$	6.62266	−	11.4708i	0.623007	−	1.07908i	−0.365915	−	0.930648i	$-0.619244\pi$
$113$	6.62266	−	11.4708i	0.623007	−	1.07908i	0.988923	−	0.148432i	$-0.0474226\pi$
$114$	−0.255807	+	0.443071i	−0.0239585	+	0.0414974i
$115$			3.53600i			0.329734i
$116$	1.33396	−	2.31049i	0.123855	−	0.214524i
$117$	−3.37483	+	1.26906i	−0.312003	+	0.117324i
$118$	4.71993			0.434505
$119$	2.12691	+	12.0693i	0.194974	+	1.10639i
$120$	−2.18508	−	3.78467i	−0.199470	−	0.345491i
$121$	−2.07510			−0.188645
$122$	−7.32851	−	4.23111i	−0.663492	−	0.383067i
$123$	1.60485	−	0.926561i	0.144704	−	0.0835452i
$124$		−	12.8852i		−	1.15712i
$125$		−	11.7686i		−	1.05262i
$126$	−1.48218	−	1.76675i	−0.132043	−	0.157395i
$127$	1.74707	+	3.02602i	0.155028	+	0.268516i	0.933069	−	0.359697i	$-0.117120\pi$
$127$	1.74707	+	3.02602i	0.155028	+	0.268516i	−0.778041	+	0.628213i	$0.783787\pi$
$128$	6.11288	+	3.52927i	0.540307	+	0.311946i
$129$	−3.93747	+	6.81990i	−0.346675	+	0.600459i
$130$	4.55168	−	1.71159i	0.399208	−	0.150117i
$131$	−3.04778	−	5.27892i	−0.266286	−	0.461221i	0.701614	−	0.712558i	$-0.252463\pi$
$131$	−3.04778	−	5.27892i	−0.266286	−	0.461221i	−0.967900	+	0.251336i	$0.919130\pi$
$132$	3.88384	−	2.24233i	0.338045	−	0.195170i
$133$	−0.531281	+	1.45923i	−0.0460679	+	0.126532i
$134$	−0.837033	+	1.44978i	−0.0723086	+	0.125242i
$135$	1.34003	−	0.773665i	0.115331	−	0.0665865i
$136$	−11.3297	+	6.54120i	−0.971513	+	0.560903i
$137$	−2.13982	+	1.23543i	−0.182818	+	0.105550i	−0.588616	−	0.808413i	$-0.700327\pi$
$137$	−2.13982	+	1.23543i	−0.182818	+	0.105550i	0.405798	+	0.913963i	$0.366994\pi$
$138$	−1.72503	+	0.995945i	−0.146844	+	0.0847805i
$139$	5.27760	−	9.14107i	0.447640	−	0.775335i	−0.550592	−	0.834775i	$-0.685598\pi$
$139$	5.27760	−	9.14107i	0.447640	−	0.775335i	0.998232	+	0.0594393i	$0.0189313\pi$
$140$	−3.26330	−	3.88982i	−0.275799	−	0.328750i
$141$	2.10152	−	1.21331i	0.176980	−	0.102179i
$142$	−4.60348	−	7.97346i	−0.386315	−	0.669118i
$143$	4.58885	+	12.2032i	0.383739	+	1.02049i
$144$	−0.00935211	+	0.0161983i	−0.000779342	+	0.00134986i
$145$	−2.88257	−	1.66425i	−0.239384	−	0.138208i
$146$	0.990275	+	1.71521i	0.0819558	+	0.141952i
$147$	−5.36143	−	4.50057i	−0.442203	−	0.371201i
$148$			7.20552i			0.592290i
$149$			12.0561i			0.987673i	0.869555	+	0.493836i	$0.164406\pi$
$149$			12.0561i			0.987673i	−0.869555	+	0.493836i	$0.835594\pi$
$150$	1.96699	−	1.13565i	0.160604	−	0.0927250i
$151$	−5.84616	−	3.37528i	−0.475754	−	0.274677i	0.242891	−	0.970053i	$-0.421904\pi$
$151$	−5.84616	−	3.37528i	−0.475754	−	0.274677i	−0.718645	+	0.695377i	$0.755237\pi$
$152$	−1.65775			−0.134462
$153$	−2.31602	−	4.01147i	−0.187239	−	0.324308i
$154$	−6.38848	+	5.35950i	−0.514799	+	0.431881i
$155$	−16.0755			−1.29122
$156$	−3.45589	−	2.83788i	−0.276692	−	0.227213i
$157$	−1.42832	+	2.47392i	−0.113992	+	0.197441i	−0.917376	−	0.398021i	$-0.869697\pi$
$157$	−1.42832	+	2.47392i	−0.113992	+	0.197441i	0.803384	+	0.595461i	$0.203031\pi$
$158$			10.0827i			0.802139i
$159$	−6.49352	+	11.2471i	−0.514970	+	0.891954i
$160$	4.38277	−	7.59118i	0.346489	−	0.600136i
$161$	−4.63199	+	3.88593i	−0.365052	+	0.306254i
$162$	0.754861	+	0.435819i	0.0593075	+	0.0342412i
$163$		−	17.1937i		−	1.34672i	−0.739316	−	0.673358i	$-0.764851\pi$
$163$		−	17.1937i		−	1.34672i	0.739316	−	0.673358i	$-0.235149\pi$
$164$	1.99041	+	1.14916i	0.155425	+	0.0897346i
$165$	−2.79753	−	4.84547i	−0.217788	−	0.377219i
$166$	4.11936	−	7.13495i	0.319725	−	0.553779i
$167$	11.8526	−	6.84312i	0.917185	−	0.529537i	0.0344489	−	0.999406i	$-0.489032\pi$
$167$	11.8526	−	6.84312i	0.917185	−	0.529537i	0.882736	+	0.469870i	$0.155699\pi$
$168$	2.55642	−	7.02156i	0.197232	−	0.541725i
$169$	9.77899	−	8.56571i	0.752230	−	0.658901i
$170$	3.12365	+	5.41032i	0.239573	+	0.414952i
$171$		−	0.586956i		−	0.0448857i
$172$	−9.76687			−0.744717
$173$	18.3145			1.39243			0.696214	−	0.717835i	$-0.254867\pi$
$173$	18.3145			1.39243			0.696214	+	0.717835i	$0.254867\pi$
$174$		−	1.87500i		−	0.142144i
$175$	5.28172	−	4.43100i	0.399260	−	0.334952i
$176$	0.0585724	+	0.0338168i	0.00441506	+	0.00254903i
$177$	−4.68954	+	2.70751i	−0.352487	+	0.203509i
$178$	−5.52059	−	9.56194i	−0.413785	−	0.716697i
$179$	−18.3626			−1.37249			−0.686243	−	0.727372i	$-0.740741\pi$
$179$	−18.3626			−1.37249			−0.686243	+	0.727372i	$0.740741\pi$
$180$	1.66196	+	0.959535i	0.123875	+	0.0715195i
$181$	−18.0249			−1.33978			−0.669889	−	0.742462i	$-0.733658\pi$
$181$	−18.0249			−1.33978			−0.669889	+	0.742462i	$0.733658\pi$
$182$	7.24423	+	4.08151i	0.536978	+	0.302542i
$183$	9.70842			0.717667
$184$	−5.58952	−	3.22711i	−0.412065	−	0.237906i
$185$	8.98959			0.660928
$186$	−4.52782	−	7.84241i	−0.331996	−	0.575034i
$187$	−14.5053	+	8.37462i	−1.06073	+	0.612413i
$188$	2.60640	+	1.50481i	0.190092	+	0.109749i
$189$	2.48610	+	0.905145i	0.180837	+	0.0658396i
$190$			0.791635i			0.0574313i
$191$	24.3981			1.76538			0.882691	−	0.469954i	$-0.155730\pi$
$191$	24.3981			1.76538			0.882691	+	0.469954i	$0.155730\pi$
$192$	4.90038			0.353654
$193$			12.0152i			0.864870i	0.901665	+	0.432435i	$0.142346\pi$
$193$			12.0152i			0.864870i	−0.901665	+	0.432435i	$0.857654\pi$
$194$	−7.23792	−	12.5364i	−0.519652	−	0.900064i
$195$	−3.54054	+	4.31156i	−0.253543	+	0.308757i
$196$	1.50925	−	8.54953i	0.107803	−	0.610681i
$197$	−18.2189	+	10.5187i	−1.29804	+	0.749424i	−0.980065	−	0.198675i	$-0.936336\pi$
$197$	−18.2189	+	10.5187i	−1.29804	+	0.749424i	−0.317975	+	0.948099i	$0.603003\pi$
$198$	1.57590	−	2.72954i	0.111994	−	0.193980i
$199$	−0.543838	−	0.941956i	−0.0385517	−	0.0667735i	0.846106	−	0.533015i	$-0.178941\pi$
$199$	−0.543838	−	0.941956i	−0.0385517	−	0.0667735i	−0.884657	+	0.466242i	$0.845608\pi$
$200$	6.37355	+	3.67977i	0.450678	+	0.260199i
$201$		−	1.92060i		−	0.135468i
$202$	9.88801	+	5.70885i	0.695718	+	0.401673i
$203$	−0.987740	−	5.60498i	−0.0693258	−	0.393392i
$204$	2.87244	−	4.97521i	0.201111	−	0.348334i
$205$	1.43370	−	2.48323i	0.100134	−	0.173437i
$206$		−	0.146626i		−	0.0102159i
$207$	1.14261	−	1.97906i	0.0794171	−	0.137554i
$208$	0.0110052	−	0.0665350i	0.000763073	−	0.00461337i
$209$	−2.12241			−0.146810
$210$	−3.35304	−	1.22078i	−0.231382	−	0.0842418i
$211$	10.2015	+	17.6694i	0.702297	+	1.21641i	0.967658	+	0.252266i	$0.0811757\pi$
$211$	10.2015	+	17.6694i	0.702297	+	1.21641i	−0.265361	+	0.964149i	$0.585491\pi$
$212$	−16.1071			−1.10624
$213$	9.14766	+	5.28141i	0.626788	+	0.361876i
$214$	1.19466	−	0.689738i	0.0816654	−	0.0471495i
$215$			12.1851i			0.831019i
$216$			2.82432i			0.192171i
$217$	−17.6664	−	21.0582i	−1.19927	−	1.42952i
$218$	−1.89651	−	3.28485i	−0.128448	−	0.222478i
$219$	−1.96780	−	1.13611i	−0.132971	−	0.0767710i
$220$	3.46963	−	6.00958i	0.233922	−	0.405166i
$221$	12.9070	+	10.5989i	0.868217	+	0.712957i
$222$	2.53200	+	4.38555i	0.169937	+	0.294339i
$223$	−9.56277	+	5.52107i	−0.640371	+	0.369718i	−0.784757	−	0.619803i	$-0.787212\pi$
$223$	−9.56277	+	5.52107i	−0.640371	+	0.369718i	0.144387	+	0.989521i	$0.453879\pi$
$224$	14.7606	−	2.60120i	0.986234	−	0.173800i
$225$	−1.30289	+	2.25666i	−0.0868590	+	0.150444i
$226$	9.99837	−	5.77256i	0.665082	−	0.383985i
$227$	−10.4830	+	6.05235i	−0.695780	+	0.401709i	−0.805774	−	0.592224i	$-0.798250\pi$
$227$	−10.4830	+	6.05235i	−0.695780	+	0.401709i	0.109994	+	0.993932i	$0.464917\pi$
$228$	0.630441	−	0.363985i	0.0417520	−	0.0241055i
$229$	−12.4222	+	7.17199i	−0.820885	+	0.473938i	−0.850722	−	0.525617i	$-0.823835\pi$
$229$	−12.4222	+	7.17199i	−0.820885	+	0.473938i	0.0298364	+	0.999555i	$0.490501\pi$
$230$	−1.54106	+	2.66919i	−0.101614	+	0.176001i
$231$	3.27296	−	8.98963i	0.215345	−	0.591474i
$232$	5.26152	−	3.03774i	0.345435	−	0.199437i
$233$	10.5498	+	18.2727i	0.691137	+	1.19709i	0.971465	+	0.237181i	$0.0762234\pi$
$233$	10.5498	+	18.2727i	0.691137	+	1.19709i	−0.280328	+	0.959904i	$0.590443\pi$
$234$	−3.10061	−	0.512855i	−0.202693	−	0.0335264i
$235$	1.87740	−	3.25175i	0.122468	−	0.212120i
$236$	−5.81618	−	3.35798i	−0.378601	−	0.218586i
$237$	−5.78378	−	10.0178i	−0.375697	−	0.650726i
$238$	−3.65449	+	10.0376i	−0.236886	+	0.650639i
$239$			4.64324i			0.300346i	0.988660	+	0.150173i	$0.0479831\pi$
$239$			4.64324i			0.300346i	−0.988660	+	0.150173i	$0.952017\pi$
$240$			0.0289416i			0.00186817i
$241$	−6.96275	+	4.01995i	−0.448510	+	0.258948i	−0.707201	−	0.707013i	$-0.750042\pi$
$241$	−6.96275	+	4.01995i	−0.448510	+	0.258948i	0.258691	+	0.965960i	$0.416709\pi$
$242$	−1.56641	−	0.904367i	−0.100693	−	0.0581349i
$243$	−1.00000			−0.0641500
$244$	6.02042	+	10.4277i	0.385418	+	0.667563i
$245$	−10.6664	−	1.88294i	−0.681450	−	0.120296i
$246$	1.61525			0.102985
$247$	0.744881	+	1.98088i	0.0473957	+	0.126040i
$248$	14.6713	−	25.4114i	0.931625	−	1.61362i
$249$			9.45200i			0.598996i
$250$	5.12900	−	8.88368i	0.324386	−	0.561853i
$251$	6.22683	−	10.7852i	0.393034	−	0.680755i	−0.599814	−	0.800140i	$-0.704759\pi$
$251$	6.22683	−	10.7852i	0.393034	−	0.680755i	0.992848	+	0.119384i	$0.0380921\pi$
$252$	0.569488	+	3.23159i	0.0358744	+	0.203571i
$253$	−7.15620	−	4.13163i	−0.449906	−	0.259753i
$254$			3.04563i			0.191100i
$255$	−6.20707	−	3.58365i	−0.388702	−	0.224417i
$256$	7.97663	+	13.8159i	0.498539	+	0.863495i
$257$	−3.58628	+	6.21162i	−0.223706	+	0.387470i	−0.955930	−	0.293593i	$-0.905149\pi$
$257$	−3.58628	+	6.21162i	−0.223706	+	0.387470i	0.732225	+	0.681063i	$0.238482\pi$
$258$	−5.94449	+	3.43205i	−0.370088	+	0.213670i
$259$	9.87922	+	11.7759i	0.613865	+	0.731722i
$260$	−6.82655	−	1.12914i	−0.423365	−	0.0700265i
$261$	1.07556	+	1.86293i	0.0665757	+	0.115312i
$262$		−	5.31313i		−	0.328246i
$263$	17.3561			1.07022			0.535111	−	0.844782i	$-0.320270\pi$
$263$	17.3561			1.07022			0.535111	+	0.844782i	$0.320270\pi$
$264$	10.2126			0.628543
$265$			20.0952i			1.23444i
$266$	−1.03701	+	0.869977i	−0.0635829	+	0.0533417i
$267$	10.9701	+	6.33357i	0.671358	+	0.387608i
$268$	2.06288	−	1.19101i	0.126011	−	0.0727523i
$269$	−5.60458	−	9.70742i	−0.341717	−	0.591872i	0.643034	−	0.765837i	$-0.277675\pi$
$269$	−5.60458	−	9.70742i	−0.341717	−	0.591872i	−0.984752	+	0.173965i	$0.944342\pi$
$270$	1.34871			0.0820800
$271$	22.1978	+	12.8159i	1.34842	+	0.778510i	0.988026	−	0.154290i	$-0.0493091\pi$
$271$	22.1978	+	12.8159i	1.34842	+	0.778510i	0.360393	+	0.932800i	$0.382642\pi$
$272$	0.0866388			0.00525325
$273$	−9.53886	+	0.100297i	−0.577318	+	0.00607024i
$274$	−2.15369			−0.130109
$275$	8.15998	+	4.71117i	0.492066	+	0.284094i
$276$	2.83424			0.170601
$277$	6.20307	+	10.7440i	0.372706	+	0.645546i	0.989981	−	0.141202i	$-0.0450966\pi$
$277$	6.20307	+	10.7440i	0.372706	+	0.645546i	−0.617275	+	0.786748i	$0.711763\pi$
$278$	7.96771	−	4.60016i	0.477871	−	0.275899i
$279$	8.99732	+	5.19461i	0.538656	+	0.310993i
$280$	−2.00666	−	11.3869i	−0.119921	−	0.680497i
$281$			30.8640i			1.84119i	0.390513	+	0.920597i	$0.372298\pi$
$281$			30.8640i			1.84119i	−0.390513	+	0.920597i	$0.627702\pi$
$282$	2.11514			0.125955
$283$	10.7352			0.638139			0.319069	−	0.947731i	$-0.396630\pi$
$283$	10.7352			0.638139			0.319069	+	0.947731i	$0.396630\pi$
$284$			13.1005i			0.777371i
$285$	−0.454108	−	0.786537i	−0.0268990	−	0.0465905i
$286$	−1.85446	+	11.2116i	−0.109656	+	0.662959i
$287$	4.82850	−	0.850905i	0.285017	−	0.0502273i
$288$	−4.90599	+	2.83247i	−0.289088	+	0.166905i
$289$	−2.22793	+	3.85888i	−0.131054	+	0.226993i
$290$	−1.45062	−	2.51256i	−0.0851836	−	0.147542i
$291$	14.3826	+	8.30380i	0.843124	+	0.486778i
$292$		−	2.81811i		−	0.164917i
$293$	−0.0137087	−	0.00791474i	−0.000800872	−	0.000462384i	0.499600	−	0.866257i	$-0.333481\pi$
$293$	−0.0137087	−	0.00791474i	−0.000800872	−	0.000462384i	−0.500400	+	0.865794i	$0.666814\pi$
$294$	−2.08570	−	5.73392i	−0.121640	−	0.334409i
$295$	−4.18941	+	7.25626i	−0.243917	+	0.422476i
$296$	−8.20430	+	14.2103i	−0.476865	+	0.825955i
$297$			3.61595i			0.209819i
$298$	−5.25427	+	9.10067i	−0.304372	+	0.527188i
$299$	−1.34458	+	8.12905i	−0.0777592	+	0.470115i
$300$	−3.23180			−0.186588
$301$	−15.9620	+	13.3910i	−0.920032	+	0.771844i
$302$	−2.94203	−	5.09574i	−0.169295	−	0.293227i
$303$	−13.0991			−0.752525
$304$	0.00950771	+	0.00548928i	0.000545305	+	0.000314832i
$305$	13.0095	−	7.51106i	0.744924	−	0.430082i
$306$		−	4.03747i		−	0.230807i
$307$		−	22.7982i		−	1.30116i	−0.759437	−	0.650581i	$-0.774526\pi$
$307$		−	22.7982i		−	1.30116i	0.759437	−	0.650581i	$-0.225474\pi$
$308$	11.6853	−	2.05924i	0.665830	−	0.117336i
$309$	0.0841095	+	0.145682i	0.00478482	+	0.00828756i
$310$	−12.1348	−	7.00603i	−0.689210	−	0.397916i
$311$	1.79592	−	3.11062i	0.101837	−	0.176387i	−0.810604	−	0.585594i	$-0.800861\pi$
$311$	1.79592	−	3.11062i	0.101837	−	0.176387i	0.912442	+	0.409207i	$0.134195\pi$
$312$	−3.58423	−	9.53162i	−0.202917	−	0.539622i
$313$	4.08399	+	7.07368i	0.230841	+	0.399828i	0.958056	−	0.286582i	$-0.0925190\pi$
$313$	4.08399	+	7.07368i	0.230841	+	0.399828i	−0.727215	+	0.686410i	$0.759186\pi$
$314$	−2.15637	+	1.24498i	−0.121691	+	0.0702582i
$315$	4.03172	−	0.710493i	0.227162	−	0.0400317i
$316$	7.17331	−	12.4245i	0.403530	−	0.698935i
$317$	−19.6172	+	11.3260i	−1.10181	+	0.636131i	−0.936696	−	0.350143i	$-0.886133\pi$
$317$	−19.6172	+	11.3260i	−1.10181	+	0.636131i	−0.165116	+	0.986274i	$0.552800\pi$
$318$	−9.80341	+	5.66000i	−0.549748	+	0.317397i
$319$	6.73626	−	3.88918i	0.377158	−	0.217752i
$320$	6.56664	−	3.79125i	0.367086	−	0.211937i
$321$	−0.791312	+	1.37059i	−0.0441667	+	0.0764990i
$322$	−5.19007	+	0.914624i	−0.289231	+	0.0509700i
$323$	−2.35456	+	1.35940i	−0.131011	+	0.0756393i
$324$	−0.620123	−	1.07408i	−0.0344513	−	0.0596714i
$325$	1.53318	−	9.26930i	0.0850457	−	0.514168i
$326$	7.49336	−	12.9789i	0.415019	−	0.718833i
$327$	3.76860	+	2.17580i	0.208404	+	0.120322i
$328$	2.61691	+	4.53262i	0.144495	+	0.250272i
$329$	6.32282	−	1.11424i	0.348589	−	0.0614302i
$330$		−	4.87688i		−	0.268463i
$331$		−	17.9518i		−	0.986720i	−0.869825	−	0.493360i	$-0.835769\pi$
$331$		−	17.9518i		−	0.986720i	0.869825	−	0.493360i	$-0.164231\pi$
$332$	−10.1523	+	5.86141i	−0.557177	+	0.321686i
$333$	−5.03139	−	2.90487i	−0.275718	−	0.159186i
$334$	11.9295			0.652751
$335$	−1.48590	−	2.57365i	−0.0811833	−	0.140614i
$336$	−0.0379121	+	0.0318057i	−0.00206828	+	0.00173514i
$337$	−5.23244			−0.285029			−0.142515	−	0.989793i	$-0.545519\pi$
$337$	−5.23244			−0.285029			−0.142515	+	0.989793i	$0.545519\pi$
$338$	11.1149	−	2.20405i	0.604570	−	0.119885i
$339$	−6.62266	+	11.4708i	−0.359693	+	0.623007i
$340$		−	8.88922i		−	0.482086i
$341$	18.7834	−	32.5339i	1.01718	−	1.76181i
$342$	0.255807	−	0.443071i	0.0138325	−	0.0239585i
$343$	−9.25540	−	16.0417i	−0.499744	−	0.866173i
$344$	−19.2616	−	11.1207i	−1.03852	−	0.599588i
$345$		−	3.53600i		−	0.190372i
$346$	13.8249	+	7.98182i	0.743232	+	0.429105i
$347$	−8.15940	−	14.1325i	−0.438019	−	0.758672i	0.559517	−	0.828819i	$-0.310987\pi$
$347$	−8.15940	−	14.1325i	−0.438019	−	0.758672i	−0.997537	+	0.0701468i	$0.977653\pi$
$348$	−1.33396	+	2.31049i	−0.0715079	+	0.123855i
$349$	23.6336	−	13.6449i	1.26508	−	0.730394i	0.291027	−	0.956715i	$-0.406003\pi$
$349$	23.6336	−	13.6449i	1.26508	−	0.730394i	0.974053	+	0.226321i	$0.0726698\pi$
$350$	5.91808	−	1.04292i	0.316335	−	0.0557462i
$351$	3.37483	−	1.26906i	0.180135	−	0.0677373i
$352$	10.2421	+	17.7398i	0.545905	+	0.945536i
$353$		−	28.4112i		−	1.51217i	−0.654471	−	0.756087i	$-0.727109\pi$
$353$		−	28.4112i		−	1.51217i	0.654471	−	0.756087i	$-0.272891\pi$
$354$	−4.71993			−0.250862
$355$	16.3442			0.867458
$356$			15.7104i			0.832649i
$357$	−2.12691	−	12.0693i	−0.112568	−	0.638773i
$358$	−13.8612	−	8.00278i	−0.732588	−	0.422960i
$359$	−4.79342	+	2.76748i	−0.252987	+	0.146062i	−0.621131	−	0.783707i	$-0.713327\pi$
$359$	−4.79342	+	2.76748i	−0.252987	+	0.146062i	0.368144	+	0.929769i	$0.379993\pi$
$360$	2.18508	+	3.78467i	0.115164	+	0.199470i
$361$	18.6555			0.981867
$362$	−13.6063	−	7.85558i	−0.715129	−	0.412880i
$363$	2.07510			0.108914
$364$	−6.02300	−	10.1834i	−0.315691	−	0.533753i
$365$	−3.51587			−0.184029
$366$	7.32851	+	4.23111i	0.383067	+	0.221164i
$367$	−26.5753			−1.38722			−0.693611	−	0.720350i	$-0.743981\pi$
$367$	−26.5753			−1.38722			−0.693611	+	0.720350i	$0.743981\pi$
$368$	0.0213717	+	0.0370168i	0.00111408	+	0.00192964i
$369$	−1.60485	+	0.926561i	−0.0835452	+	0.0482348i
$370$	6.78589	+	3.91784i	0.352782	+	0.203679i
$371$	−26.3238	+	22.0839i	−1.36666	+	1.14654i
$372$			12.8852i			0.668066i
$373$	−16.1169			−0.834503			−0.417251	−	0.908791i	$-0.637007\pi$
$373$	−16.1169			−0.834503			−0.417251	+	0.908791i	$0.637007\pi$
$374$	−14.5993			−0.754911
$375$			11.7686i			0.607730i
$376$	3.42679	+	5.93537i	0.176723	+	0.306094i
$377$	−5.99401	−	4.92212i	−0.308707	−	0.253502i
$378$	1.48218	+	1.76675i	0.0762353	+	0.0908718i
$379$	7.43319	−	4.29156i	0.381817	−	0.220442i	−0.296791	−	0.954942i	$-0.595917\pi$
$379$	7.43319	−	4.29156i	0.381817	−	0.220442i	0.678609	+	0.734500i	$0.262583\pi$
$380$	0.563205	−	0.975500i	0.0288918	−	0.0500421i
$381$	−1.74707	−	3.02602i	−0.0895053	−	0.155028i
$382$	18.4171	+	10.6331i	0.942303	+	0.544039i
$383$			0.903701i			0.0461770i	0.999733	+	0.0230885i	$0.00734995\pi$
$383$			0.903701i			0.0461770i	−0.999733	+	0.0230885i	$0.992650\pi$
$384$	−6.11288	−	3.52927i	−0.311946	−	0.180102i
$385$	−2.56911	−	14.5785i	−0.130934	−	0.742990i
$386$	−5.23644	+	9.06977i	−0.266528	+	0.461639i
$387$	3.93747	−	6.81990i	0.200153	−	0.346675i
$388$			20.5975i			1.04568i
$389$	12.3500	−	21.3909i	0.626171	−	1.08456i	−0.362142	−	0.932123i	$-0.617955\pi$
$389$	12.3500	−	21.3909i	0.626171	−	1.08456i	0.988313	−	0.152437i	$-0.0487122\pi$
$390$	−4.55168	+	1.71159i	−0.230483	+	0.0866699i
$391$	−10.5853			−0.535320
$392$	12.7111	−	15.1424i	0.642005	−	0.764807i
$393$	3.04778	+	5.27892i	0.153740	+	0.266286i
$394$	−18.3369			−0.923802
$395$	−15.5008	−	8.94941i	−0.779932	−	0.450294i
$396$	−3.88384	+	2.24233i	−0.195170	+	0.112682i
$397$			15.8503i			0.795502i	0.917493	+	0.397751i	$0.130209\pi$
$397$			15.8503i			0.795502i	−0.917493	+	0.397751i	$0.869791\pi$
$398$		−	0.948061i		−	0.0475220i
$399$	0.531281	−	1.45923i	0.0265973	−	0.0730531i
$400$	−0.0243695	−	0.0422091i	−0.00121847	−	0.00211046i
$401$	−32.9726	−	19.0367i	−1.64657	−	0.950650i	−0.978420	−	0.206626i	$-0.933752\pi$
$401$	−32.9726	−	19.0367i	−1.64657	−	0.950650i	−0.668153	−	0.744024i	$-0.732915\pi$
$402$	0.837033	−	1.44978i	0.0417474	−	0.0723086i
$403$	−36.9567	−	6.11281i	−1.84095	−	0.304501i
$404$	−8.12307	−	14.0696i	−0.404138	−	0.699987i
$405$	−1.34003	+	0.773665i	−0.0665865	+	0.0384437i
$406$	1.69715	−	4.66145i	0.0842281	−	0.231344i
$407$	−10.5039	+	18.1932i	−0.520658	+	0.901806i
$408$	11.3297	−	6.54120i	0.560903	−	0.323838i
$409$	−5.12097	+	2.95660i	−0.253216	+	0.146194i	−0.621236	−	0.783624i	$-0.713369\pi$
$409$	−5.12097	+	2.95660i	−0.253216	+	0.146194i	0.368020	+	0.929818i	$0.380036\pi$
$410$	2.16448	−	1.24966i	0.106896	−	0.0617165i
$411$	2.13982	−	1.23543i	0.105550	−	0.0609392i
$412$	−0.104317	+	0.180682i	−0.00513931	+	0.00890154i
$413$	−14.1094	+	2.48643i	−0.694277	+	0.122349i
$414$	1.72503	−	0.995945i	0.0847805	−	0.0489480i
$415$	7.31268	+	12.6659i	0.358965	+	0.621746i
$416$	12.9623	−	15.7851i	0.635530	−	0.773929i
$417$	−5.27760	+	9.14107i	−0.258445	+	0.447640i
$418$	−1.60212	−	0.924985i	−0.0783623	−	0.0452425i
$419$	−6.63834	−	11.4979i	−0.324304	−	0.561711i	0.657067	−	0.753832i	$-0.271797\pi$
$419$	−6.63834	−	11.4979i	−0.324304	−	0.561711i	−0.981371	+	0.192121i	$0.938463\pi$
$420$	3.26330	+	3.88982i	0.159233	+	0.189804i
$421$		−	23.3548i		−	1.13824i	−0.822254	−	0.569121i	$-0.807284\pi$
$421$		−	23.3548i		−	1.13824i	0.822254	−	0.569121i	$-0.192716\pi$
$422$			17.7840i			0.865710i
$423$	−2.10152	+	1.21331i	−0.102179	+	0.0589933i
$424$	−31.7655	−	18.3398i	−1.54267	−	0.890659i
$425$	12.0701			0.585483
$426$	4.60348	+	7.97346i	0.223039	+	0.386315i
$427$	24.1361	+	8.78752i	1.16803	+	0.425258i
$428$	−1.96284			−0.0948776
$429$	−4.58885	−	12.2032i	−0.221552	−	0.589177i
$430$	−5.31051	+	9.19808i	−0.256096	+	0.443571i
$431$			7.22799i			0.348160i	0.984732	+	0.174080i	$0.0556951\pi$
$431$			7.22799i			0.348160i	−0.984732	+	0.174080i	$0.944305\pi$
$432$	0.00935211	−	0.0161983i	0.000449954	−	0.000779342i
$433$	−11.8710	+	20.5611i	−0.570482	+	0.988103i	0.426035	+	0.904707i	$0.359910\pi$
$433$	−11.8710	+	20.5611i	−0.570482	+	0.988103i	−0.996516	+	0.0833965i	$0.973423\pi$
$434$	−4.15811	−	23.5954i	−0.199596	−	1.13261i
$435$	2.88257	+	1.66425i	0.138208	+	0.0797947i
$436$			5.39706i			0.258472i
$437$	−1.16162	−	0.670664i	−0.0555680	−	0.0320822i
$438$	−0.990275	−	1.71521i	−0.0473172	−	0.0819558i
$439$	14.2287	−	24.6448i	0.679097	−	1.17623i	−0.296156	−	0.955140i	$-0.595705\pi$
$439$	14.2287	−	24.6448i	0.679097	−	1.17623i	0.975253	−	0.221091i	$-0.0709619\pi$
$440$	13.6852	−	7.90114i	0.652415	−	0.376672i
$441$	5.36143	+	4.50057i	0.255306	+	0.214313i
$442$	5.12378	+	13.6258i	0.243713	+	0.648112i
$443$	−10.4345	−	18.0731i	−0.495760	−	0.858681i	0.504228	−	0.863570i	$-0.331777\pi$
$443$	−10.4345	−	18.0731i	−0.495760	−	0.858681i	−0.999988	+	0.00488943i	$0.998444\pi$
$444$		−	7.20552i		−	0.341959i
$445$	19.6003			0.929141
$446$	−9.62475			−0.455745
$447$		−	12.0561i		−	0.570233i
$448$	12.1829	+	4.43555i	0.575586	+	0.209560i
$449$	5.13399	+	2.96411i	0.242288	+	0.139885i	0.616228	−	0.787568i	$-0.288660\pi$
$449$	5.13399	+	2.96411i	0.242288	+	0.139885i	−0.373940	+	0.927453i	$0.621993\pi$
$450$	−1.96699	+	1.13565i	−0.0927250	+	0.0535348i
$451$	3.35040	+	5.80306i	0.157764	+	0.273255i
$452$	−16.4275			−0.772683
$453$	5.84616	+	3.37528i	0.274677	+	0.158585i
$454$	−10.5509			−0.495179
$455$	−12.7047	+	7.51428i	−0.595607	+	0.352275i
$456$	1.65775			0.0776315
$457$	20.1511	+	11.6342i	0.942629	+	0.544227i	0.890783	−	0.454428i	$-0.150156\pi$
$457$	20.1511	+	11.6342i	0.942629	+	0.544227i	0.0518454	+	0.998655i	$0.483490\pi$
$458$	−12.5028			−0.584216
$459$	2.31602	+	4.01147i	0.108103	+	0.187239i
$460$	3.79796	−	2.19275i	0.177081	−	0.102238i
$461$	−6.80211	−	3.92720i	−0.316806	−	0.182908i	0.333162	−	0.942870i	$-0.391884\pi$
$461$	−6.80211	−	3.92720i	−0.316806	−	0.182908i	−0.649968	+	0.759962i	$0.725218\pi$
$462$	6.38848	−	5.35950i	0.297219	−	0.249347i
$463$			22.0674i			1.02556i	0.858520	+	0.512780i	$0.171384\pi$
$463$			22.0674i			1.02556i	−0.858520	+	0.512780i	$0.828616\pi$
$464$	−0.0402351			−0.00186787
$465$	16.0755			0.745485
$466$			18.3911i			0.851953i
$467$	−5.20349	−	9.01270i	−0.240789	−	0.417058i	0.720150	−	0.693818i	$-0.244073\pi$
$467$	−5.20349	−	9.01270i	−0.240789	−	0.417058i	−0.960939	+	0.276760i	$0.910739\pi$
$468$	3.45589	+	2.83788i	0.159748	+	0.131181i
$469$	1.73842	−	4.77480i	0.0802727	−	0.220480i
$470$	2.83435	−	1.63641i	0.130739	−	0.0754820i
$471$	1.42832	−	2.47392i	0.0658135	−	0.113992i
$472$	−7.64688	−	13.2448i	−0.351976	−	0.609640i
$473$	−24.6604	−	14.2377i	−1.13389	−	0.654650i
$474$		−	10.0827i		−	0.463115i
$475$	1.32456	+	0.764737i	0.0607751	+	0.0350885i
$476$	11.6445	−	9.76892i	0.533723	−	0.447758i
$477$	6.49352	−	11.2471i	0.297318	−	0.514970i
$478$	−2.02361	+	3.50500i	−0.0925579	+	0.160315i
$479$		−	29.2221i		−	1.33519i	−0.744525	−	0.667595i	$-0.767324\pi$
$479$		−	29.2221i		−	1.33519i	0.744525	−	0.667595i	$-0.232676\pi$
$480$	−4.38277	+	7.59118i	−0.200045	+	0.346489i
$481$	20.6665	+	3.41834i	0.942313	+	0.155863i
$482$	−7.00788			−0.319200
$483$	4.63199	−	3.88593i	0.210763	−	0.176816i
$484$	1.28682	+	2.22883i	0.0584916	+	0.101311i
$485$	25.6974			1.16686
$486$	−0.754861	−	0.435819i	−0.0342412	−	0.0197692i
$487$	35.5719	−	20.5375i	1.61192	−	0.930641i	0.622993	−	0.782228i	$-0.285917\pi$
$487$	35.5719	−	20.5375i	1.61192	−	0.930641i	0.988925	−	0.148414i	$-0.0474168\pi$
$488$			27.4197i			1.24123i
$489$			17.1937i			0.777527i
$490$	−7.23102	−	6.06997i	−0.326664	−	0.274213i
$491$	−6.32263	−	10.9511i	−0.285336	−	0.494217i	0.687355	−	0.726322i	$-0.258772\pi$
$491$	−6.32263	−	10.9511i	−0.285336	−	0.494217i	−0.972691	+	0.232105i	$0.925439\pi$
$492$	−1.99041	−	1.14916i	−0.0897346	−	0.0518083i
$493$	4.98206	−	8.62918i	0.224381	−	0.388639i
$494$	−0.301023	+	1.81992i	−0.0135437	+	0.0818822i
$495$	2.79753	+	4.84547i	0.125740	+	0.217788i
$496$	−0.168288	+	0.0971611i	−0.00755635	+	0.00436266i
$497$	17.9616	+	21.4101i	0.805688	+	0.960374i
$498$	−4.11936	+	7.13495i	−0.184593	+	0.319725i
$499$	−12.8737	+	7.43261i	−0.576304	+	0.332729i	−0.759663	−	0.650317i	$-0.774636\pi$
$499$	−12.8737	+	7.43261i	−0.576304	+	0.332729i	0.183359	+	0.983046i	$0.441303\pi$
$500$	−12.6405	+	7.29800i	−0.565301	+	0.326377i
$501$	−11.8526	+	6.84312i	−0.529537	+	0.305728i
$502$	9.40079	−	5.42755i	0.419578	−	0.242243i
$503$	−13.9385	+	24.1422i	−0.621488	+	1.07645i	0.367721	+	0.929936i	$0.380138\pi$
$503$	−13.9385	+	24.1422i	−0.621488	+	1.07645i	−0.989209	+	0.146513i	$0.953195\pi$
$504$	−2.55642	+	7.02156i	−0.113872	+	0.312765i
$505$	−17.5532	+	10.1343i	−0.781106	+	0.450972i
$506$	−3.60129	−	6.23762i	−0.160097	−	0.277296i
$507$	−9.77899	+	8.56571i	−0.434300	+	0.380417i
$508$	2.16680	−	3.75301i	0.0961363	−	0.166513i
$509$	27.4136	+	15.8272i	1.21508	+	0.701530i	0.963863	−	0.266400i	$-0.0858342\pi$
$509$	27.4136	+	15.8272i	1.21508	+	0.701530i	0.251222	+	0.967929i	$0.419168\pi$
$510$	−3.12365	−	5.41032i	−0.138317	−	0.239573i
$511$	−3.86380	−	4.60562i	−0.170925	−	0.203741i
$512$		−	0.211612i		−	0.00935202i
$513$			0.586956i			0.0259148i
$514$	−5.41428	+	3.12594i	−0.238814	+	0.137879i
$515$	0.225418	+	0.130145i	0.00993310	+	0.00573488i
$516$	9.76687			0.429962
$517$	4.38728	+	7.59900i	0.192952	+	0.334203i
$518$	2.32525	+	13.1948i	0.102166	+	0.579744i
$519$	−18.3145			−0.803918
$520$	−12.1772	−	9.99963i	−0.534007	−	0.438513i
$521$	16.3636	−	28.3425i	0.716901	−	1.24171i	−0.245321	−	0.969442i	$-0.578893\pi$
$521$	16.3636	−	28.3425i	0.716901	−	1.24171i	0.962222	−	0.272267i	$-0.0877733\pi$
$522$			1.87500i			0.0820667i
$523$	1.52483	−	2.64108i	0.0666761	−	0.115486i	−0.830760	−	0.556631i	$-0.812094\pi$
$523$	1.52483	−	2.64108i	0.0666761	−	0.115486i	0.897436	+	0.441144i	$0.145427\pi$
$524$	−3.78000	+	6.54716i	−0.165130	+	0.286014i
$525$	−5.28172	+	4.43100i	−0.230513	+	0.193385i
$526$	13.1014	+	7.56411i	0.571249	+	0.329811i
$527$		−	48.1233i		−	2.09629i
$528$	−0.0585724	−	0.0338168i	−0.00254903	−	0.00147169i
$529$	8.88887	+	15.3960i	0.386473	+	0.669390i
$530$	−8.75789	+	15.1691i	−0.380418	+	0.658904i
$531$	4.68954	−	2.70751i	0.203509	−	0.117496i
$532$	1.89680	−	0.334265i	0.0822368	−	0.0144922i
$533$	4.24024	−	5.16364i	0.183665	−	0.223662i
$534$	5.52059	+	9.56194i	0.238899	+	0.413785i
$535$			2.44884i			0.105873i
$536$	5.42439			0.234298
$537$	18.3626			0.792405
$538$		−	9.77034i		−	0.421229i
$539$	16.2738	−	19.3867i	0.700964	−	0.835042i
$540$	−1.66196	−	0.959535i	−0.0715195	−	0.0412918i
$541$	31.3496	−	18.0997i	1.34782	−	0.778166i	0.359883	−	0.932998i	$-0.382817\pi$
$541$	31.3496	−	18.0997i	1.34782	−	0.778166i	0.987941	+	0.154831i	$0.0494833\pi$
$542$	11.1708	+	19.3484i	0.479828	+	0.831086i
$543$	18.0249			0.773521
$544$	22.7248	+	13.1202i	0.974317	+	0.562522i
$545$	6.73336			0.288425
$546$	−7.24423	−	4.08151i	−0.310024	−	0.174673i
$547$	−14.4610			−0.618310			−0.309155	−	0.951012i	$-0.600046\pi$
$547$	−14.4610			−0.618310			−0.309155	+	0.951012i	$0.600046\pi$
$548$	2.65391	+	1.53224i	0.113369	+	0.0654538i
$549$	−9.70842			−0.414345
$550$	4.10644	+	7.11256i	0.175099	+	0.303280i
$551$	1.09346	−	0.631309i	0.0465829	−	0.0268947i
$552$	5.58952	+	3.22711i	0.237906	+	0.137355i
$553$	−5.31152	−	30.1404i	−0.225869	−	1.28170i
$554$			10.8137i			0.459429i
$555$	−8.98959			−0.381587
$556$	−13.0910			−0.555184
$557$			23.5452i			0.997641i	0.866705	+	0.498821i	$0.166233\pi$
$557$			23.5452i			0.997641i	−0.866705	+	0.498821i	$0.833767\pi$
$558$	4.52782	+	7.84241i	0.191678	+	0.331996i
$559$	−4.63346	+	28.0129i	−0.195974	+	1.18482i
$560$	−0.0261963	+	0.0719518i	−0.00110700	+	0.00304052i
$561$	14.5053	−	8.37462i	0.612413	−	0.353577i
$562$	−13.4511	+	23.2981i	−0.567402	+	0.982770i
$563$	15.3255	+	26.5446i	0.645894	+	1.11872i	0.984094	+	0.177646i	$0.0568484\pi$
$563$	15.3255	+	26.5446i	0.645894	+	1.11872i	−0.338201	+	0.941074i	$0.609818\pi$
$564$	−2.60640	−	1.50481i	−0.109749	−	0.0633638i
$565$			20.4949i			0.862226i
$566$	8.10355	+	4.67859i	0.340618	+	0.196656i
$567$	−2.48610	−	0.905145i	−0.104407	−	0.0380125i
$568$	−14.9164	+	25.8360i	−0.625878	+	1.08405i
$569$	−9.13665	+	15.8251i	−0.383028	+	0.663425i	−0.991494	−	0.130156i	$-0.958452\pi$
$569$	−9.13665	+	15.8251i	−0.383028	+	0.663425i	0.608465	+	0.793581i	$0.291786\pi$
$570$		−	0.791635i		−	0.0331579i
$571$	9.31271	−	16.1301i	0.389725	−	0.675023i	−0.602688	−	0.797977i	$-0.705904\pi$
$571$	9.31271	−	16.1301i	0.389725	−	0.675023i	0.992412	+	0.122954i	$0.0392369\pi$
$572$	10.2617	−	12.4963i	0.429061	−	0.522497i
$573$	−24.3981			−1.01924
$574$	4.01568	+	1.46204i	0.167611	+	0.0610242i
$575$	2.97739	+	5.15699i	0.124166	+	0.215061i
$576$	−4.90038			−0.204182
$577$	17.9758	+	10.3783i	0.748341	+	0.432055i	0.825094	−	0.564995i	$-0.191122\pi$
$577$	17.9758	+	10.3783i	0.748341	+	0.432055i	−0.0767533	+	0.997050i	$0.524455\pi$
$578$	−3.36355	+	1.94195i	−0.139905	+	0.0807743i
$579$		−	12.0152i		−	0.499333i
$580$			4.12816i			0.171413i
$581$	−8.55543	+	23.4987i	−0.354939	+	0.974889i
$582$	7.23792	+	12.5364i	0.300021	+	0.519652i
$583$	−40.6690	−	23.4802i	−1.68434	−	0.972452i
$584$	3.20874	−	5.55769i	0.132778	−	0.229979i
$585$	3.54054	−	4.31156i	0.146383	−	0.178261i
$586$	−0.00689879	−	0.0119491i	−0.000284986	−	0.000493611i
$587$	12.5550	−	7.24864i	0.518201	−	0.299183i	−0.217998	−	0.975949i	$-0.569952\pi$
$587$	12.5550	−	7.24864i	0.518201	−	0.299183i	0.736198	+	0.676766i	$0.236619\pi$
$588$	−1.50925	+	8.54953i	−0.0622403	+	0.352577i
$589$	3.04901	−	5.28104i	0.125632	−	0.217601i
$590$	−6.32484	+	3.65165i	−0.260389	+	0.150336i
$591$	18.2189	−	10.5187i	0.749424	−	0.432680i
$592$	0.0941082	−	0.0543334i	0.00386782	−	0.00223309i
$593$	−4.53361	+	2.61748i	−0.186173	+	0.107487i	−0.590190	−	0.807265i	$-0.700947\pi$
$593$	−4.53361	+	2.61748i	−0.186173	+	0.107487i	0.404017	+	0.914752i	$0.367614\pi$
$594$	−1.57590	+	2.72954i	−0.0646600	+	0.111994i
$595$	−12.1877	−	14.5276i	−0.499647	−	0.595574i
$596$	12.9493	−	7.47626i	0.530422	−	0.306239i
$597$	0.543838	+	0.941956i	0.0222578	+	0.0385517i
$598$	−4.55777	+	5.55031i	−0.186381	+	0.226969i
$599$	−7.47791	+	12.9521i	−0.305539	+	0.529209i	−0.977381	−	0.211485i	$-0.932170\pi$
$599$	−7.47791	+	12.9521i	−0.305539	+	0.529209i	0.671842	+	0.740694i	$0.265503\pi$
$600$	−6.37355	−	3.67977i	−0.260199	−	0.150226i
$601$	−23.0757	−	39.9683i	−0.941278	−	1.63034i	−0.763038	−	0.646354i	$-0.776293\pi$
$601$	−23.0757	−	39.9683i	−0.941278	−	1.63034i	−0.178240	−	0.983987i	$-0.557040\pi$
$602$	−17.8851	+	3.15181i	−0.728943	+	0.128458i
$603$			1.92060i			0.0782127i
$604$			8.37237i			0.340667i
$605$	2.78069	−	1.60543i	0.113051	−	0.0652700i
$606$	−9.88801	−	5.70885i	−0.401673	−	0.231906i
$607$	−43.6180			−1.77040			−0.885201	−	0.465210i	$-0.845979\pi$
$607$	−43.6180			−1.77040			−0.885201	+	0.465210i	$0.845979\pi$
$608$	1.66254	+	2.87960i	0.0674249	+	0.116783i
$609$	0.987740	+	5.60498i	0.0400253	+	0.227125i
$610$	13.0939			0.530155
$611$	5.55252	−	6.76168i	0.224631	−	0.273548i
$612$	−2.87244	+	4.97521i	−0.116111	+	0.201111i
$613$		−	18.0262i		−	0.728073i	−0.931385	−	0.364036i	$-0.881398\pi$
$613$		−	18.0262i		−	0.728073i	0.931385	−	0.364036i	$-0.118602\pi$
$614$	9.93589	−	17.2095i	0.400980	−	0.694517i
$615$	−1.43370	+	2.48323i	−0.0578122	+	0.100134i
$616$	25.3896	+	9.24389i	1.02298	+	0.372447i
$617$	32.3120	+	18.6554i	1.30083	+	0.751036i	0.980547	−	0.196285i	$-0.0628876\pi$
$617$	32.3120	+	18.6554i	1.30083	+	0.751036i	0.320286	+	0.947321i	$0.396221\pi$
$618$			0.146626i			0.00589817i
$619$	0.272738	+	0.157465i	0.0109623	+	0.00632906i	0.505471	−	0.862844i	$-0.331319\pi$
$619$	0.272738	+	0.157465i	0.0109623	+	0.00632906i	−0.494509	+	0.869173i	$0.664652\pi$
$620$	9.96882	+	17.2665i	0.400357	+	0.693439i
$621$	−1.14261	+	1.97906i	−0.0458515	+	0.0794171i
$622$	2.71133	−	1.56539i	0.108715	−	0.0627664i
$623$	21.5399	+	25.6754i	0.862979	+	1.02866i
$624$	−0.0110052	+	0.0665350i	−0.000440560	+	0.00266353i
$625$	2.59055	+	4.48697i	0.103622	+	0.179479i
$626$			7.11953i			0.284554i
$627$	2.12241			0.0847607
$628$	3.54294			0.141379
$629$			26.9110i			1.07301i
$630$	3.35304	+	1.22078i	0.133588	+	0.0486370i
$631$	22.1441	+	12.7849i	0.881542	+	0.508958i	0.871166	−	0.490988i	$-0.163364\pi$
$631$	22.1441	+	12.7849i	0.881542	+	0.508958i	0.0103751	+	0.999946i	$0.496697\pi$
$632$	28.2935	−	16.3353i	1.12546	−	0.649782i
$633$	−10.2015	−	17.6694i	−0.405472	−	0.702297i
$634$	−19.7443			−0.784148
$635$	−4.68225	−	2.70330i	−0.185810	−	0.107277i
$636$	16.1071			0.638689
$637$	−23.8054	−	8.38471i	−0.943204	−	0.332214i
$638$	6.77992			0.268420
$639$	−9.14766	−	5.28141i	−0.361876	−	0.208929i
$640$	−10.9219			−0.431726
$641$	−7.67167	−	13.2877i	−0.303013	−	0.524834i	0.673804	−	0.738910i	$-0.264659\pi$
$641$	−7.67167	−	13.2877i	−0.303013	−	0.524834i	−0.976817	+	0.214076i	$0.931326\pi$
$642$	−1.19466	+	0.689738i	−0.0471495	+	0.0272218i
$643$	−13.2667	−	7.65954i	−0.523188	−	0.302063i	0.215050	−	0.976603i	$-0.431009\pi$
$643$	−13.2667	−	7.65954i	−0.523188	−	0.302063i	−0.738238	+	0.674540i	$0.764342\pi$
$644$	7.04622	+	2.56540i	0.277660	+	0.101091i
$645$		−	12.1851i		−	0.479789i
$646$	−2.36982			−0.0932393
$647$	18.4649			0.725932			0.362966	−	0.931802i	$-0.381764\pi$
$647$	18.4649			0.725932			0.362966	+	0.931802i	$0.381764\pi$
$648$		−	2.82432i		−	0.110950i
$649$	−9.79021	−	16.9571i	−0.384299	−	0.665626i
$650$	5.19708	−	6.32884i	0.203846	−	0.248238i
$651$	17.6664	+	21.0582i	0.692401	+	0.825337i
$652$	−18.4675	+	10.6622i	−0.723244	+	0.417565i
$653$	−16.1420	+	27.9588i	−0.631687	+	1.09411i	0.355520	+	0.934669i	$0.384304\pi$
$653$	−16.1420	+	27.9588i	−0.631687	+	1.09411i	−0.987207	+	0.159445i	$0.949029\pi$
$654$	1.89651	+	3.28485i	0.0741594	+	0.128448i
$655$	8.16822	+	4.71593i	0.319159	+	0.184266i
$656$		−	0.0346612i		−	0.00135329i
$657$	1.96780	+	1.13611i	0.0767710	+	0.0443238i
$658$	5.25846	+	1.91451i	0.204996	+	0.0746353i
$659$	−1.93680	+	3.35464i	−0.0754471	+	0.130678i	−0.901281	−	0.433236i	$-0.857372\pi$
$659$	−1.93680	+	3.35464i	−0.0754471	+	0.130678i	0.825834	+	0.563914i	$0.190705\pi$
$660$	−3.46963	+	6.00958i	−0.135055	+	0.233922i
$661$		−	25.1506i		−	0.978245i	−0.872215	−	0.489123i	$-0.837317\pi$
$661$		−	25.1506i		−	0.978245i	0.872215	−	0.489123i	$-0.162683\pi$
$662$	7.82373	−	13.5511i	0.304078	−	0.526679i
$663$	−12.9070	−	10.5989i	−0.501265	−	0.411626i
$664$	−26.6955			−1.03599
$665$	−0.417028	−	2.36645i	−0.0161717	−	0.0917669i
$666$	−2.53200	−	4.38555i	−0.0981130	−	0.169937i
$667$	4.91581			0.190341
$668$	−14.7002	−	8.48716i	−0.568768	−	0.328378i
$669$	9.56277	−	5.52107i	0.369718	−	0.213457i
$670$		−	2.59033i		−	0.100073i
$671$			35.1052i			1.35522i
$672$	−14.7606	+	2.60120i	−0.569403	+	0.100343i
$673$	5.11747	+	8.86372i	0.197264	+	0.341671i	0.947640	−	0.319339i	$-0.103461\pi$
$673$	5.11747	+	8.86372i	0.197264	+	0.341671i	−0.750376	+	0.661011i	$0.770128\pi$
$674$	−3.94976	−	2.28040i	−0.152139	−	0.0878376i
$675$	1.30289	−	2.25666i	0.0501481	−	0.0868590i
$676$	−15.2645	−	5.19167i	−0.587095	−	0.199679i
$677$	−14.7224	−	25.4999i	−0.565827	−	0.980041i	−0.996972	−	0.0777582i	$-0.975224\pi$
$677$	−14.7224	−	25.4999i	−0.565827	−	0.980041i	0.431146	−	0.902282i	$-0.358110\pi$
$678$	−9.99837	+	5.77256i	−0.383985	+	0.221694i
$679$	28.2405	+	33.6625i	1.08377	+	1.29185i
$680$	10.1214	−	17.5308i	0.388138	−	0.672274i
$681$	10.4830	−	6.05235i	0.401709	−	0.231927i
$682$	28.3578	−	16.3724i	1.08588	−	0.626931i
$683$	−16.3563	+	9.44329i	−0.625855	+	0.361338i	−0.779145	−	0.626844i	$-0.784346\pi$
$683$	−16.3563	+	9.44329i	−0.625855	+	0.361338i	0.153290	+	0.988181i	$0.451013\pi$
$684$	−0.630441	+	0.363985i	−0.0241055	+	0.0139173i
$685$	1.91161	−	3.31101i	0.0730390	−	0.126507i
$686$	0.00476324	−	16.1430i	0.000181861	−	0.616341i
$687$	12.4222	−	7.17199i	0.473938	−	0.273628i
$688$	0.0736473	+	0.127561i	0.00280778	+	0.00486321i
$689$	−7.64132	+	46.1977i	−0.291111	+	1.75999i
$690$	1.54106	−	2.66919i	0.0586670	−	0.101614i
$691$	−4.19565	−	2.42236i	−0.159610	−	0.0921508i	0.418068	−	0.908416i	$-0.362708\pi$
$691$	−4.19565	−	2.42236i	−0.159610	−	0.0921508i	−0.577678	+	0.816265i	$0.696041\pi$
$692$	−11.3573	−	19.6714i	−0.431738	−	0.747793i
$693$	−3.27296	+	8.98963i	−0.124329	+	0.341488i
$694$		−	14.2241i		−	0.539939i
$695$			16.3324i			0.619522i
$696$	−5.26152	+	3.03774i	−0.199437	+	0.115145i
$697$	7.43374	+	4.29187i	0.281573	+	0.162566i
$698$	23.7868			0.900344
$699$	−10.5498	−	18.2727i	−0.399028	−	0.691137i
$700$	−8.03459	−	2.92525i	−0.303679	−	0.110564i
$701$	3.10557			0.117296			0.0586479	−	0.998279i	$-0.481321\pi$
$701$	3.10557			0.117296			0.0586479	+	0.998279i	$0.481321\pi$
$702$	3.10061	+	0.512855i	0.117025	+	0.0193565i
$703$	−1.70503	+	2.95320i	−0.0643066	+	0.111382i
$704$			17.7195i			0.667830i
$705$	−1.87740	+	3.25175i	−0.0707068	+	0.122468i
$706$	12.3821	−	21.4465i	0.466008	−	0.807149i
$707$	−32.5658	−	11.8566i	−1.22476	−	0.445913i
$708$	5.81618	+	3.35798i	0.218586	+	0.126200i
$709$			16.5722i			0.622380i	0.950348	+	0.311190i	$0.100728\pi$
$709$			16.5722i			0.622380i	−0.950348	+	0.311190i	$0.899272\pi$
$710$	12.3376	+	7.12310i	0.463021	+	0.267325i
$711$	5.78378	+	10.0178i	0.216909	+	0.375697i
$712$	−17.8881	+	30.9830i	−0.670383	+	1.16114i
$713$	20.5609	−	11.8709i	0.770012	−	0.444567i
$714$	3.65449	−	10.0376i	0.136766	−	0.375647i
$715$	−15.5904	−	12.8024i	−0.583047	−	0.478783i
$716$	11.3871	+	19.7230i	0.425555	+	0.737084i
$717$		−	4.64324i		−	0.173405i
$718$	−4.82449			−0.180048
$719$	16.8098			0.626898			0.313449	−	0.949605i	$-0.398516\pi$
$719$	16.8098			0.626898			0.313449	+	0.949605i	$0.398516\pi$
$720$		−	0.0289416i		−	0.00107859i
$721$	0.0772417	+	0.438312i	0.00287663	+	0.0163236i
$722$	14.0823	+	8.13042i	0.524089	+	0.302583i
$723$	6.96275	−	4.01995i	0.258948	−	0.149503i
$724$	11.1776	+	19.3602i	0.415414	+	0.719517i
$725$	−5.60534			−0.208177
$726$	1.56641	+	0.904367i	0.0581349	+	0.0335642i
$727$	36.2622			1.34489			0.672444	−	0.740148i	$-0.265244\pi$
$727$	36.2622			1.34489			0.672444	+	0.740148i	$0.265244\pi$
$728$	−0.283271	−	26.9408i	−0.0104987	−	0.998494i
$729$	1.00000			0.0370370
$730$	−2.65399	−	1.53228i	−0.0982286	−	0.0567123i
$731$	−36.4771			−1.34915
$732$	−6.02042	−	10.4277i	−0.222521	−	0.385418i
$733$	1.19882	−	0.692138i	0.0442794	−	0.0255647i	−0.477697	−	0.878525i	$-0.658528\pi$
$733$	1.19882	−	0.692138i	0.0442794	−	0.0255647i	0.521976	+	0.852960i	$0.325195\pi$
$734$	−20.0607	−	11.5820i	−0.740454	−	0.427501i
$735$	10.6664	+	1.88294i	0.393436	+	0.0694531i
$736$			12.9457i			0.477184i
$737$	6.94478			0.255814
$738$	−1.61525			−0.0594583
$739$		−	42.2380i		−	1.55375i	−0.629654	−	0.776876i	$-0.716803\pi$
$739$		−	42.2380i		−	1.55375i	0.629654	−	0.776876i	$-0.283197\pi$
$740$	−5.57465	−	9.65558i	−0.204928	−	0.354946i
$741$	−0.744881	−	1.98088i	−0.0273639	−	0.0727694i
$742$	−29.4954	+	5.19785i	−1.08281	+	0.190819i
$743$	−10.7785	+	6.22298i	−0.395425	+	0.228299i	−0.684508	−	0.729005i	$-0.739983\pi$
$743$	−10.7785	+	6.22298i	−0.395425	+	0.228299i	0.289083	+	0.957304i	$0.406650\pi$
$744$	−14.6713	+	25.4114i	−0.537874	+	0.931625i
$745$	−9.32737	−	16.1555i	−0.341728	−	0.591891i
$746$	−12.1660	−	7.02407i	−0.445430	−	0.257169i
$747$		−	9.45200i		−	0.345831i
$748$	17.9901	+	10.3866i	0.657784	+	0.379772i
$749$	−3.20787	+	2.69118i	−0.117213	+	0.0983337i
$750$	−5.12900	+	8.88368i	−0.187284	+	0.324386i
$751$	15.0056	−	25.9904i	0.547560	−	0.948402i	−0.450881	−	0.892584i	$-0.648890\pi$
$751$	15.0056	−	25.9904i	0.547560	−	0.948402i	0.998441	−	0.0558181i	$-0.0177767\pi$
$752$		−	0.0453882i		−	0.00165514i
$753$	−6.22683	+	10.7852i	−0.226918	+	0.393034i
$754$	−2.37949	−	6.32782i	−0.0866558	−	0.230446i
$755$	10.4454			0.380145
$756$	−0.569488	−	3.23159i	−0.0207121	−	0.117532i
$757$	−19.8603	−	34.3991i	−0.721835	−	1.25026i	−0.960263	−	0.279095i	$-0.909965\pi$
$757$	−19.8603	−	34.3991i	−0.721835	−	1.25026i	0.238428	−	0.971160i	$-0.423368\pi$
$758$	7.48137			0.271736
$759$	7.15620	+	4.13163i	0.259753	+	0.149969i
$760$	2.22144	−	1.28255i	0.0805799	−	0.0465229i
$761$			7.50457i			0.272040i	0.990706	+	0.136020i	$0.0434312\pi$
$761$			7.50457i			0.272040i	−0.990706	+	0.136020i	$0.956569\pi$
$762$		−	3.04563i		−	0.110332i
$763$	7.39971	+	8.82039i	0.267887	+	0.319320i
$764$	−15.1298	−	26.2056i	−0.547377	−	0.948085i
$765$	6.20707	+	3.58365i	0.224417	+	0.129567i
$766$	−0.393850	+	0.682169i	−0.0142304	+	0.0246478i
$767$	−12.3904	+	15.0887i	−0.447392	+	0.544821i
$768$	−7.97663	−	13.8159i	−0.287832	−	0.498539i
$769$	13.1246	−	7.57747i	0.473284	−	0.273251i	−0.244329	−	0.969692i	$-0.578568\pi$
$769$	13.1246	−	7.57747i	0.473284	−	0.273251i	0.717613	+	0.696442i	$0.245234\pi$
$770$	4.41428	−	12.1244i	0.159080	−	0.436934i
$771$	3.58628	−	6.21162i	0.129157	−	0.223706i
$772$	12.9053	−	7.45088i	0.464472	−	0.268163i
$773$	9.02753	−	5.21205i	0.324698	−	0.187464i	−0.328787	−	0.944404i	$-0.606640\pi$
$773$	9.02753	−	5.21205i	0.324698	−	0.187464i	0.653485	+	0.756940i	$0.273306\pi$
$774$	5.94449	−	3.43205i	0.213670	−	0.123363i
$775$	−23.4450	+	13.5360i	−0.842168	+	0.486226i
$776$	−23.4526	+	40.6211i	−0.841900	+	1.45821i
$777$	−9.87922	−	11.7759i	−0.354415	−	0.422460i
$778$	18.6451	−	10.7648i	0.668459	−	0.385935i
$779$	0.543851	+	0.941977i	0.0194855	+	0.0337498i
$780$	6.82655	+	1.12914i	0.244430	+	0.0404298i
$781$	−19.0973	+	33.0775i	−0.683355	+	1.18361i
$782$	−7.99041	−	4.61326i	−0.285736	−	0.164970i
$783$	−1.07556	−	1.86293i	−0.0384375	−	0.0665757i
$784$	−0.123042	+	0.0447563i	−0.00439437	+	0.00159844i
$785$		−	4.42016i		−	0.157762i
$786$			5.31313i			0.189513i
$787$	−12.0557	+	6.96037i	−0.429740	+	0.248110i	−0.699236	−	0.714891i	$-0.746476\pi$
$787$	−12.0557	+	6.96037i	−0.429740	+	0.248110i	0.269496	+	0.963001i	$0.413143\pi$
$788$	22.5959	+	13.0457i	0.804945	+	0.464735i
$789$	−17.3561			−0.617893
$790$	−7.80065	−	13.5111i	−0.277535	−	0.480704i
$791$	−26.8473	+	22.5231i	−0.954581	+	0.800829i
$792$	−10.2126			−0.362889
$793$	32.7643	−	12.3205i	1.16349	−	0.437515i
$794$	−6.90785	+	11.9647i	−0.245150	+	0.424613i
$795$		−	20.0952i		−	0.712704i
$796$	−0.674494	+	1.16826i	−0.0239068	+	0.0414078i
$797$	21.6516	−	37.5016i	0.766938	−	1.32838i	−0.172278	−	0.985048i	$-0.555113\pi$
$797$	21.6516	−	37.5016i	0.766938	−	1.32838i	0.939216	−	0.343327i	$-0.111554\pi$
$798$	1.03701	−	0.869977i	0.0367096	−	0.0307969i
$799$	9.73434	+	5.62012i	0.344376	+	0.198826i
$800$		−	14.7616i		−	0.521900i
$801$	−10.9701	−	6.33357i	−0.387608	−	0.223786i
$802$	−16.5932	−	28.7402i	−0.585925	−	1.01485i
$803$	4.10811	−	7.11545i	0.144972	−	0.251099i
$804$	−2.06288	+	1.19101i	−0.0727523	+	0.0420036i
$805$	3.20059	−	8.79086i	0.112806	−	0.309837i
$806$	−25.2331	−	20.7208i	−0.888798	−	0.729858i
$807$	5.60458	+	9.70742i	0.197291	+	0.341717i
$808$		−	36.9961i		−	1.30152i
$809$	6.93270			0.243741			0.121870	−	0.992546i	$-0.461111\pi$
$809$	6.93270			0.243741			0.121870	+	0.992546i	$0.461111\pi$
$810$	−1.34871			−0.0473889
$811$		−	9.46114i		−	0.332226i	−0.986107	−	0.166113i	$-0.946878\pi$
$811$		−	9.46114i		−	0.332226i	0.986107	−	0.166113i	$-0.0531216\pi$
$812$	−5.40770	+	4.53669i	−0.189773	+	0.159207i
$813$	−22.1978	−	12.8159i	−0.778510	−	0.449473i
$814$	−15.8579	+	9.15558i	−0.555820	+	0.320903i
$815$	13.3022	+	23.0401i	0.465955	+	0.807058i
$816$	−0.0866388			−0.00303296
$817$	−4.00298	−	2.31112i	−0.140047	−	0.0808560i
$818$	−5.15417			−0.180211
$819$	9.53886	−	0.100297i	0.333315	−	0.00350465i
$820$	−3.55627			−0.124190
$821$	18.1928	+	10.5036i	0.634934	+	0.366579i	0.782660	−	0.622449i	$-0.213862\pi$
$821$	18.1928	+	10.5036i	0.634934	+	0.366579i	−0.147727	+	0.989028i	$0.547196\pi$
$822$	2.15369			0.0751187
$823$	16.3656	+	28.3461i	0.570469	+	0.988082i	0.996518	+	0.0833815i	$0.0265720\pi$
$823$	16.3656	+	28.3461i	0.570469	+	0.988082i	−0.426048	+	0.904700i	$0.640095\pi$
$824$	−0.411453	+	0.237552i	−0.0143336	+	0.00827553i
$825$	−8.15998	−	4.71117i	−0.284094	−	0.164022i
$826$	−11.7342	−	4.27222i	−0.408287	−	0.148650i
$827$			5.50483i			0.191422i	0.995409	+	0.0957109i	$0.0305124\pi$
$827$			5.50483i			0.191422i	−0.995409	+	0.0957109i	$0.969488\pi$
$828$	−2.83424			−0.0984968
$829$	20.3249			0.705913			0.352956	−	0.935640i	$-0.385176\pi$
$829$	20.3249			0.705913			0.352956	+	0.935640i	$0.385176\pi$
$830$			12.7480i			0.442491i
$831$	−6.20307	−	10.7440i	−0.215182	−	0.372706i
$832$	16.5380	−	6.21886i	0.573351	−	0.215600i
$833$	5.63671	−	31.9306i	0.195300	−	1.10633i
$834$	−7.96771	+	4.60016i	−0.275899	+	0.159290i
$835$	−10.5886	+	18.3399i	−0.366433	+	0.634680i
$836$	1.31615	+	2.27964i	0.0455201	+	0.0788431i
$837$	−8.99732	−	5.19461i	−0.310993	−	0.179552i
$838$		−	11.5725i		−	0.399764i
$839$	−48.2439	−	27.8536i	−1.66556	−	0.961614i	−0.969985	−	0.243166i	$-0.921814\pi$
$839$	−48.2439	−	27.8536i	−1.66556	−	0.961614i	−0.695580	−	0.718448i	$-0.744853\pi$
$840$	2.00666	+	11.3869i	0.0692364	+	0.392885i
$841$	12.1863	−	21.1073i	0.420218	−	0.727839i
$842$	10.1785	−	17.6296i	0.350773	−	0.607557i
$843$		−	30.8640i		−	1.06301i
$844$	12.6523	−	21.9145i	0.435511	−	0.754327i
$845$	−6.47711	+	19.0439i	−0.222819	+	0.655132i
$846$	−2.11514			−0.0727201
$847$	5.15891	+	1.87826i	0.177262	+	0.0645379i
$848$	0.121456	+	0.210368i	0.00417082	+	0.00722408i
$849$	−10.7352			−0.368430
$850$	9.11121	+	5.26036i	0.312512	+	0.180429i
$851$	−11.4979	+	6.63829i	−0.394141	+	0.227558i
$852$		−	13.1005i		−	0.448815i
$853$			32.5630i			1.11493i	0.830199	+	0.557467i	$0.188227\pi$
$853$			32.5630i			1.11493i	−0.830199	+	0.557467i	$0.811773\pi$
$854$	14.3897	+	17.1524i	0.492404	+	0.586941i
$855$	0.454108	+	0.786537i	0.0155302	+	0.0268990i
$856$	−3.87100	−	2.23492i	−0.132308	−	0.0763880i
$857$	−3.97771	+	6.88960i	−0.135876	+	0.235344i	−0.925932	−	0.377691i	$-0.876718\pi$
$857$	−3.97771	+	6.88960i	−0.135876	+	0.235344i	0.790056	+	0.613035i	$0.210052\pi$
$858$	1.85446	−	11.2116i	0.0633101	−	0.382759i
$859$	15.3344	+	26.5599i	0.523201	+	0.906211i	0.999635	+	0.0270012i	$0.00859580\pi$
$859$	15.3344	+	26.5599i	0.523201	+	0.906211i	−0.476434	+	0.879210i	$0.658071\pi$
$860$	13.0879	−	7.55628i	0.446293	−	0.257667i
$861$	−4.82850	+	0.850905i	−0.164555	+	0.0289988i
$862$	−3.15010	+	5.45613i	−0.107293	+	0.185836i
$863$	20.2659	−	11.7005i	0.689860	−	0.398291i	−0.113699	−	0.993515i	$-0.536270\pi$
$863$	20.2659	−	11.7005i	0.689860	−	0.398291i	0.803560	+	0.595224i	$0.202937\pi$
$864$	4.90599	−	2.83247i	0.166905	−	0.0963628i
$865$	−24.5420	+	14.1693i	−0.834451	+	0.481771i
$866$	−17.9218	+	10.3472i	−0.609009	+	0.351612i
$867$	2.22793	−	3.85888i	0.0756643	−	0.131054i
$868$	−11.6630	+	32.0339i	−0.395867	+	1.08730i
$869$	36.2239	−	20.9139i	1.22881	−	0.709454i
$870$	1.45062	+	2.51256i	0.0491808	+	0.0851836i
$871$	−2.43735	−	6.48169i	−0.0825864	−	0.219624i
$872$	−6.14516	+	10.6437i	−0.208101	+	0.360442i
$873$	−14.3826	−	8.30380i	−0.486778	−	0.281041i
$874$	−0.584577	−	1.01252i	−0.0197736	−	0.0342489i
$875$	−10.6523	+	29.2581i	−0.360114	+	0.989103i
$876$			2.81811i			0.0952150i
$877$			12.4552i			0.420583i	0.977639	+	0.210291i	$0.0674413\pi$
$877$			12.4552i			0.420583i	−0.977639	+	0.210291i	$0.932559\pi$
$878$	21.4813	−	12.4023i	0.724960	−	0.418556i
$879$	0.0137087	+	0.00791474i	0.000462384	+	0.000266957i
$880$	−0.104651			−0.00352780
$881$	0.980893	+	1.69896i	0.0330471	+	0.0572393i	0.882076	−	0.471107i	$-0.156146\pi$
$881$	0.980893	+	1.69896i	0.0330471	+	0.0572393i	−0.849029	+	0.528347i	$0.822812\pi$
$882$	2.08570	+	5.73392i	0.0702291	+	0.193071i
$883$	−32.7262			−1.10132			−0.550662	−	0.834728i	$-0.685625\pi$
$883$	−32.7262			−1.10132			−0.550662	+	0.834728i	$0.685625\pi$
$884$	3.38017	−	20.4358i	0.113688	−	0.687330i
$885$	4.18941	−	7.25626i	0.140825	−	0.243917i
$886$		−	18.1903i		−	0.611114i
$887$	−14.3599	+	24.8720i	−0.482157	+	0.835120i	−0.999790	−	0.0204826i	$-0.993480\pi$
$887$	−14.3599	+	24.8720i	−0.482157	+	0.835120i	0.517634	+	0.855602i	$0.326813\pi$
$888$	8.20430	−	14.2103i	0.275318	−	0.476865i
$889$	−1.60442	−	9.10436i	−0.0538106	−	0.305350i
$890$	14.7955	+	8.54217i	0.495945	+	0.286334i
$891$		−	3.61595i		−	0.121139i
$892$	11.8602	+	6.84749i	0.397109	+	0.229271i
$893$	0.712162	+	1.23350i	0.0238316	+	0.0412775i
$894$	5.25427	−	9.10067i	0.175729	−	0.304372i
$895$	24.6064	−	14.2065i	0.822501	−	0.474871i
$896$	−12.0027	−	14.3072i	−0.400984	−	0.477969i
$897$	1.34458	−	8.12905i	0.0448943	−	0.271421i
$898$	2.58363	+	4.47498i	0.0862170	+	0.149332i
$899$			22.3485i			0.745365i
$900$	3.23180			0.107727
$901$	−60.1566			−2.00411
$902$			5.84067i			0.194473i
$903$	15.9620	−	13.3910i	0.531181	−	0.445625i
$904$	−32.3972	−	18.7045i	−1.07751	−	0.622103i
$905$	24.1538	−	13.9452i	0.802899	−	0.463554i
$906$	2.94203	+	5.09574i	0.0977423	+	0.169295i
$907$	27.6669			0.918665			0.459333	−	0.888264i	$-0.348089\pi$
$907$	27.6669			0.918665			0.459333	+	0.888264i	$0.348089\pi$
$908$	13.0015	+	7.50641i	0.431469	+	0.249109i
$909$	13.0991			0.434470
$910$	−12.8652	+	0.135272i	−0.426477	+	0.00448421i
$911$	−34.4320			−1.14078			−0.570392	−	0.821373i	$-0.693209\pi$
$911$	−34.4320			−1.14078			−0.570392	+	0.821373i	$0.693209\pi$
$912$	−0.00950771	−	0.00548928i	−0.000314832	−	0.000181768i
$913$	−34.1780			−1.13113
$914$	10.1409	+	17.5645i	0.335430	+	0.580981i
$915$	−13.0095	+	7.51106i	−0.430082	+	0.248308i
$916$	15.4066	+	8.89503i	0.509050	+	0.293900i
$917$	2.79892	+	15.8826i	0.0924286	+	0.524490i
$918$			4.03747i			0.133256i
$919$	31.4316			1.03683			0.518417	−	0.855128i	$-0.326522\pi$
$919$	31.4316			1.03683			0.518417	+	0.855128i	$0.326522\pi$
$920$	9.98680			0.329255
$921$			22.7982i			0.751226i
$922$	−3.42310	−	5.92898i	−0.112734	−	0.195261i
$923$	37.5742	+	6.21495i	1.23677	+	0.204568i
$924$	−11.6853	+	2.05924i	−0.384417	+	0.0677441i
$925$	13.1106	−	7.56943i	0.431075	−	0.248881i
$926$	−9.61740	+	16.6578i	−0.316047	+	0.547410i
$927$	−0.0841095	−	0.145682i	−0.00276252	−	0.00478482i
$928$	−10.5534	−	6.09301i	−0.346432	−	0.200013i
$929$			46.6395i			1.53019i	0.643915	+	0.765097i	$0.277309\pi$
$929$			46.6395i			1.53019i	−0.643915	+	0.765097i	$0.722691\pi$
$930$	12.1348	+	7.00603i	0.397916	+	0.229737i
$931$	2.64164	−	3.14692i	0.0865762	−	0.103136i
$932$	13.0843	−	22.6627i	0.428590	−	0.742340i
$933$	−1.79592	+	3.11062i	−0.0587957	+	0.101837i
$934$		−	9.07112i		−	0.296816i
$935$	12.9583	−	22.4444i	0.423782	−	0.734012i
$936$	3.58423	+	9.53162i	0.117154	+	0.311551i
$937$	3.16478			0.103389			0.0516945	−	0.998663i	$-0.483538\pi$
$937$	3.16478			0.103389			0.0516945	+	0.998663i	$0.483538\pi$
$938$	3.39321	−	2.84668i	0.110792	−	0.0929473i
$939$	−4.08399	−	7.07368i	−0.133276	−	0.230841i
$940$	−4.65687			−0.151890
$941$	15.6164	+	9.01615i	0.509081	+	0.293918i	0.732456	−	0.680814i	$-0.238374\pi$
$941$	15.6164	+	9.01615i	0.509081	+	0.293918i	−0.223375	+	0.974733i	$0.571707\pi$
$942$	2.15637	−	1.24498i	0.0702582	−	0.0405636i
$943$			4.23480i			0.137904i
$944$			0.101284i			0.00329650i
$945$	−4.03172	+	0.710493i	−0.131152	+	0.0231123i
$946$	−12.4101	−	21.4950i	−0.403488	−	0.698862i
$947$	−38.6552	−	22.3176i	−1.25612	−	0.725224i	−0.283805	−	0.958882i	$-0.591597\pi$
$947$	−38.6552	−	22.3176i	−1.25612	−	0.725224i	−0.972319	+	0.233658i	$0.924930\pi$
$948$	−7.17331	+	12.4245i	−0.232978	+	0.403530i
$949$	−8.08277	−	1.33693i	−0.262378	−	0.0433985i
$950$	0.666574	+	1.15454i	0.0216265	+	0.0374582i
$951$	19.6172	−	11.3260i	0.636131	−	0.367271i
$952$	34.0875	−	6.00709i	1.10478	−	0.194691i
$953$	19.2233	−	33.2957i	0.622702	−	1.07855i	−0.366278	−	0.930505i	$-0.619368\pi$
$953$	19.2233	−	33.2957i	0.622702	−	1.07855i	0.988980	−	0.148047i	$-0.0472986\pi$
$954$	9.80341	−	5.66000i	0.317397	−	0.183249i
$955$	−32.6941	+	18.8759i	−1.05795	+	0.610810i
$956$	4.98723	−	2.87938i	0.161299	−	0.0931258i
$957$	−6.73626	+	3.88918i	−0.217752	+	0.125719i
$958$	12.7355	−	22.0586i	0.411466	−	0.712681i
$959$	6.43807	−	1.13455i	0.207896	−	0.0366366i
$960$	−6.56664	+	3.79125i	−0.211937	+	0.122362i
$961$	38.4679	+	66.6284i	1.24090	+	2.14930i
$962$	14.1106	+	11.5872i	0.454944	+	0.373588i
$963$	0.791312	−	1.37059i	0.0254997	−	0.0441667i
$964$	8.63553	+	4.98572i	0.278132	+	0.160579i
$965$	−9.29571	−	16.1006i	−0.299239	−	0.518298i
$966$	5.19007	−	0.914624i	0.166988	−	0.0294275i
$967$		−	34.6858i		−	1.11542i	−0.830036	−	0.557710i	$-0.811680\pi$
$967$		−	34.6858i		−	1.11542i	0.830036	−	0.557710i	$-0.188320\pi$
$968$			5.86075i			0.188372i
$969$	2.35456	−	1.35940i	0.0756393	−	0.0436704i
$970$	19.3980	+	11.1994i	0.622832	+	0.359592i
$971$	−3.78467			−0.121456			−0.0607280	−	0.998154i	$-0.519342\pi$
$971$	−3.78467			−0.121456			−0.0607280	+	0.998154i	$0.519342\pi$
$972$	0.620123	+	1.07408i	0.0198905	+	0.0344513i
$973$	−21.3946	+	17.9487i	−0.685881	+	0.575407i
$974$	35.8025			1.14719
$975$	−1.53318	+	9.26930i	−0.0491012	+	0.296855i
$976$	0.0907942	−	0.157260i	0.00290625	−	0.00503377i
$977$			0.253036i			0.00809533i	0.999992	+	0.00404767i	$0.00128842\pi$
$977$			0.253036i			0.00809533i	−0.999992	+	0.00404767i	$0.998712\pi$
$978$	−7.49336	+	12.9789i	−0.239611	+	0.415019i
$979$	−22.9019	+	39.6672i	−0.731948	+	1.26777i
$980$	4.59204	+	12.6243i	0.146687	+	0.403267i
$981$	−3.76860	−	2.17580i	−0.120322	−	0.0694680i
$982$		−	11.0221i		−	0.351729i
$983$	6.88388	+	3.97441i	0.219562	+	0.126764i	0.605747	−	0.795657i	$-0.292874\pi$
$983$	6.88388	+	3.97441i	0.219562	+	0.126764i	−0.386186	+	0.922421i	$0.626208\pi$
$984$	−2.61691	−	4.53262i	−0.0834240	−	0.144495i
$985$	16.2758	−	28.1906i	0.518591	−	0.898227i
$986$	7.52152	−	4.34255i	0.239534	−	0.138295i
$987$	−6.32282	+	1.11424i	−0.201258	+	0.0354668i
$988$	1.66571	−	2.02846i	0.0529934	−	0.0645338i
$989$	−8.99801	−	15.5850i	−0.286120	−	0.495575i
$990$			4.87688i			0.154997i
$991$	28.4261			0.902985			0.451493	−	0.892275i	$-0.350892\pi$
$991$	28.4261			0.902985			0.451493	+	0.892275i	$0.350892\pi$
$992$	−58.8544			−1.86863
$993$			17.9518i			0.569683i
$994$	4.22759	+	23.9897i	0.134091	+	0.760906i
$995$	1.45752	+	0.841497i	0.0462064	+	0.0266773i
$996$	10.1523	−	5.86141i	0.321686	−	0.185726i
$997$	22.4318	+	38.8530i	0.710422	+	1.23049i	0.964699	+	0.263355i	$0.0848290\pi$
$997$	22.4318	+	38.8530i	0.710422	+	1.23049i	−0.254278	+	0.967131i	$0.581838\pi$
$998$	−12.9571			−0.410150
$999$	5.03139	+	2.90487i	0.159186	+	0.0919061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.d.88.7	yes	20
3.2	odd	2		819.2.do.g.361.4		20
7.2	even	3		273.2.t.d.205.4	yes	20
13.4	even	6		273.2.t.d.4.7	✓	20
21.2	odd	6		819.2.bm.g.478.7		20
39.17	odd	6		819.2.bm.g.550.4		20
91.30	even	6	inner	273.2.bl.d.121.7	yes	20
273.212	odd	6		819.2.do.g.667.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.7	✓	20	13.4	even	6
273.2.t.d.205.4	yes	20	7.2	even	3
273.2.bl.d.88.7	yes	20	1.1	even	1	trivial
273.2.bl.d.121.7	yes	20	91.30	even	6	inner
819.2.bm.g.478.7		20	21.2	odd	6
819.2.bm.g.550.4		20	39.17	odd	6
819.2.do.g.361.4		20	3.2	odd	2
819.2.do.g.667.4		20	273.212	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.754861 + 0.435819i) q^{2} -1.00000 q^{3} +(-0.620123 - 1.07408i) q^{4} +(-1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.48610 - 0.905145i) q^{7} -2.82432i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.754861 + 0.435819i) q^{2} -1.00000 q^{3} +(-0.620123 - 1.07408i) q^{4} +(-1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.48610 - 0.905145i) q^{7} -2.82432i q^{8} +1.00000 q^{9} -1.34871 q^{10} -3.61595i q^{11} +(0.620123 + 1.07408i) q^{12} +(-3.37483 + 1.26906i) q^{13} +(-1.48218 - 1.76675i) q^{14} +(1.34003 - 0.773665i) q^{15} +(-0.00935211 + 0.0161983i) q^{16} +(-2.31602 - 4.01147i) q^{17} +(0.754861 + 0.435819i) q^{18} -0.586956i q^{19} +(1.66196 + 0.959535i) q^{20} +(2.48610 + 0.905145i) q^{21} +(1.57590 - 2.72954i) q^{22} +(1.14261 - 1.97906i) q^{23} +2.82432i q^{24} +(-1.30289 + 2.25666i) q^{25} +(-3.10061 - 0.512855i) q^{26} -1.00000 q^{27} +(0.569488 + 3.23159i) q^{28} +(1.07556 + 1.86293i) q^{29} +1.34871 q^{30} +(8.99732 + 5.19461i) q^{31} +(-4.90599 + 2.83247i) q^{32} +3.61595i q^{33} -4.03747i q^{34} +(4.03172 - 0.710493i) q^{35} +(-0.620123 - 1.07408i) q^{36} +(-5.03139 - 2.90487i) q^{37} +(0.255807 - 0.443071i) q^{38} +(3.37483 - 1.26906i) q^{39} +(2.18508 + 3.78467i) q^{40} +(-1.60485 + 0.926561i) q^{41} +(1.48218 + 1.76675i) q^{42} +(3.93747 - 6.81990i) q^{43} +(-3.88384 + 2.24233i) q^{44} +(-1.34003 + 0.773665i) q^{45} +(1.72503 - 0.995945i) q^{46} +(-2.10152 + 1.21331i) q^{47} +(0.00935211 - 0.0161983i) q^{48} +(5.36143 + 4.50057i) q^{49} +(-1.96699 + 1.13565i) q^{50} +(2.31602 + 4.01147i) q^{51} +(3.45589 + 2.83788i) q^{52} +(6.49352 - 11.2471i) q^{53} +(-0.754861 - 0.435819i) q^{54} +(2.79753 + 4.84547i) q^{55} +(-2.55642 + 7.02156i) q^{56} +0.586956i q^{57} +1.87500i q^{58} +(4.68954 - 2.70751i) q^{59} +(-1.66196 - 0.959535i) q^{60} -9.70842 q^{61} +(4.52782 + 7.84241i) q^{62} +(-2.48610 - 0.905145i) q^{63} -4.90038 q^{64} +(3.54054 - 4.31156i) q^{65} +(-1.57590 + 2.72954i) q^{66} +1.92060i q^{67} +(-2.87244 + 4.97521i) q^{68} +(-1.14261 + 1.97906i) q^{69} +(3.35304 + 1.22078i) q^{70} +(-9.14766 - 5.28141i) q^{71} -2.82432i q^{72} +(1.96780 + 1.13611i) q^{73} +(-2.53200 - 4.38555i) q^{74} +(1.30289 - 2.25666i) q^{75} +(-0.630441 + 0.363985i) q^{76} +(-3.27296 + 8.98963i) q^{77} +(3.10061 + 0.512855i) q^{78} +(5.78378 + 10.0178i) q^{79} -0.0289416i q^{80} +1.00000 q^{81} -1.61525 q^{82} -9.45200i q^{83} +(-0.569488 - 3.23159i) q^{84} +(6.20707 + 3.58365i) q^{85} +(5.94449 - 3.43205i) q^{86} +(-1.07556 - 1.86293i) q^{87} -10.2126 q^{88} +(-10.9701 - 6.33357i) q^{89} -1.34871 q^{90} +(9.53886 - 0.100297i) q^{91} -2.83424 q^{92} +(-8.99732 - 5.19461i) q^{93} -2.11514 q^{94} +(0.454108 + 0.786537i) q^{95} +(4.90599 - 2.83247i) q^{96} +(-14.3826 - 8.30380i) q^{97} +(2.08570 + 5.73392i) q^{98} -3.61595i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

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