LMFDB - Embedded newform 360.2.bm.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.a.131.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.537760 - 1.30798i) q^{2} +(1.67034 - 0.458221i) q^{3} +(-1.42163 + 1.40676i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.49759 - 1.93836i) q^{6} +(3.22730 + 1.86328i) q^{7} +(2.60451 + 1.10297i) q^{8} +(2.58007 - 1.53077i) q^{9} +O(q^{10})$	\(q+(-0.537760 - 1.30798i) q^{2} +(1.67034 - 0.458221i) q^{3} +(-1.42163 + 1.40676i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.49759 - 1.93836i) q^{6} +(3.22730 + 1.86328i) q^{7} +(2.60451 + 1.10297i) q^{8} +(2.58007 - 1.53077i) q^{9} +(-0.863865 + 1.11970i) q^{10} +(5.12442 + 2.95858i) q^{11} +(-1.73000 + 3.00119i) q^{12} +(-3.79850 + 2.19307i) q^{13} +(0.701627 - 5.22325i) q^{14} +(-1.23200 - 1.21745i) q^{15} +(0.0420575 - 3.99978i) q^{16} -4.41825i q^{17} +(-3.38967 - 2.55149i) q^{18} -3.32963 q^{19} +(1.92910 + 0.527787i) q^{20} +(6.24449 + 1.63350i) q^{21} +(1.11407 - 8.29365i) q^{22} +(-3.05850 - 5.29747i) q^{23} +(4.85582 + 0.648885i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.91117 + 3.78903i) q^{26} +(3.60816 - 3.73915i) q^{27} +(-7.20922 + 1.89114i) q^{28} +(-0.255686 + 0.442860i) q^{29} +(-0.929876 + 2.26613i) q^{30} +(-1.46642 + 0.846640i) q^{31} +(-5.25425 + 2.09591i) q^{32} +(9.91520 + 2.59372i) q^{33} +(-5.77899 + 2.37596i) q^{34} -3.72657i q^{35} +(-1.51447 + 5.80572i) q^{36} +3.84855i q^{37} +(1.79054 + 4.35510i) q^{38} +(-5.33988 + 5.40372i) q^{39} +(-0.347059 - 2.80705i) q^{40} +(0.779241 - 0.449895i) q^{41} +(-1.22145 - 9.04610i) q^{42} +(0.403230 - 0.698415i) q^{43} +(-11.4470 + 3.00281i) q^{44} +(-2.61572 - 1.46902i) q^{45} +(-5.28425 + 6.84922i) q^{46} +(2.33110 - 4.03758i) q^{47} +(-1.76253 - 6.70026i) q^{48} +(3.44366 + 5.96459i) q^{49} +(1.40162 + 0.188277i) q^{50} +(-2.02454 - 7.37998i) q^{51} +(2.31495 - 8.46131i) q^{52} +2.70454 q^{53} +(-6.83105 - 2.70864i) q^{54} -5.91717i q^{55} +(6.35040 + 8.41254i) q^{56} +(-5.56162 + 1.52571i) q^{57} +(0.716750 + 0.0962794i) q^{58} +(-11.5962 + 6.69508i) q^{59} +(3.46410 - 0.00237231i) q^{60} +(-3.60020 - 2.07857i) q^{61} +(1.89597 + 1.46276i) q^{62} +(11.1789 - 0.132859i) q^{63} +(5.56694 + 5.74537i) q^{64} +(3.79850 + 2.19307i) q^{65} +(-1.93946 - 14.3637i) q^{66} +(2.43445 + 4.21659i) q^{67} +(6.21542 + 6.28112i) q^{68} +(-7.53614 - 7.44711i) q^{69} +(-4.87428 + 2.00400i) q^{70} +5.40772 q^{71} +(8.40819 - 1.14118i) q^{72} -6.12993 q^{73} +(5.03383 - 2.06959i) q^{74} +(-0.438339 + 1.67567i) q^{75} +(4.73350 - 4.68399i) q^{76} +(11.0254 + 19.0965i) q^{77} +(9.93954 + 4.07856i) q^{78} +(-5.58799 - 3.22623i) q^{79} +(-3.48494 + 1.96347i) q^{80} +(4.31349 - 7.89898i) q^{81} +(-1.00750 - 0.777297i) q^{82} +(-12.4965 - 7.21485i) q^{83} +(-11.1753 + 6.46226i) q^{84} +(-3.82632 + 2.20913i) q^{85} +(-1.13035 - 0.151838i) q^{86} +(-0.224154 + 0.856888i) q^{87} +(10.0834 + 13.3577i) q^{88} +10.2904i q^{89} +(-0.514820 + 4.21129i) q^{90} -16.3452 q^{91} +(11.8003 + 3.22847i) q^{92} +(-2.06148 + 2.08612i) q^{93} +(-6.53465 - 0.877784i) q^{94} +(1.66482 + 2.88355i) q^{95} +(-7.81599 + 5.90849i) q^{96} +(-4.30061 + 7.44888i) q^{97} +(5.94971 - 7.71175i) q^{98} +(17.7502 - 0.210958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.537760	−	1.30798i	−0.380254	−	0.924882i
$2$	−0.537760	−	1.30798i	−0.380254	−	0.924882i
$3$	1.67034	−	0.458221i	0.964371	−	0.264554i
$3$	1.67034	−	0.458221i	0.964371	−	0.264554i
$4$	−1.42163	+	1.40676i	−0.710814	+	0.703380i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.49759	−	1.93836i	−0.611387	−	0.791332i
$7$	3.22730	+	1.86328i	1.21981	+	0.704255i	0.964876	−	0.262704i	$-0.0846144\pi$
$7$	3.22730	+	1.86328i	1.21981	+	0.704255i	0.254929	+	0.966960i	$0.417948\pi$
$8$	2.60451	+	1.10297i	0.920833	+	0.389957i
$9$	2.58007	−	1.53077i	0.860022	−	0.510256i
$10$	−0.863865	+	1.11970i	−0.273178	+	0.354082i
$11$	5.12442	+	2.95858i	1.54507	+	0.892046i	0.998507	+	0.0546283i	$0.0173974\pi$
$11$	5.12442	+	2.95858i	1.54507	+	0.892046i	0.546563	+	0.837418i	$0.315936\pi$
$12$	−1.73000	+	3.00119i	−0.499407	+	0.866368i
$13$	−3.79850	+	2.19307i	−1.05352	+	0.608247i	−0.923631	−	0.383282i	$-0.874794\pi$
$13$	−3.79850	+	2.19307i	−1.05352	+	0.608247i	−0.129884	+	0.991529i	$0.541460\pi$
$14$	0.701627	−	5.22325i	0.187518	−	1.39597i
$15$	−1.23200	−	1.21745i	−0.318101	−	0.314343i
$16$	0.0420575	−	3.99978i	0.0105144	−	0.999945i
$17$		−	4.41825i		−	1.07158i	−0.844350	−	0.535792i	$-0.820013\pi$
$17$		−	4.41825i		−	1.07158i	0.844350	−	0.535792i	$-0.179987\pi$
$18$	−3.38967	−	2.55149i	−0.798954	−	0.601393i
$19$	−3.32963			−0.763870			−0.381935	−	0.924189i	$-0.624742\pi$
$19$	−3.32963			−0.763870			−0.381935	+	0.924189i	$0.624742\pi$
$20$	1.92910	+	0.527787i	0.431361	+	0.118017i
$21$	6.24449	+	1.63350i	1.36266	+	0.356459i
$22$	1.11407	−	8.29365i	0.237520	−	1.76821i
$23$	−3.05850	−	5.29747i	−0.637740	−	1.10460i	−0.985927	−	0.167174i	$-0.946536\pi$
$23$	−3.05850	−	5.29747i	−0.637740	−	1.10460i	0.348187	−	0.937425i	$-0.386797\pi$
$24$	4.85582	+	0.648885i	0.991189	+	0.132453i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.91117	+	3.78903i	0.963160	+	0.743089i
$27$	3.60816	−	3.73915i	0.694390	−	0.719599i
$28$	−7.20922	+	1.89114i	−1.36241	+	0.357392i
$29$	−0.255686	+	0.442860i	−0.0474796	+	0.0822371i	−0.888789	−	0.458318i	$-0.848452\pi$
$29$	−0.255686	+	0.442860i	−0.0474796	+	0.0822371i	0.841309	+	0.540555i	$0.181786\pi$
$30$	−0.929876	+	2.26613i	−0.169771	+	0.413736i
$31$	−1.46642	+	0.846640i	−0.263377	+	0.152061i	−0.625874	−	0.779924i	$-0.715258\pi$
$31$	−1.46642	+	0.846640i	−0.263377	+	0.152061i	0.362497	+	0.931985i	$0.381924\pi$
$32$	−5.25425	+	2.09591i	−0.928829	+	0.370508i
$33$	9.91520	+	2.59372i	1.72601	+	0.451509i
$34$	−5.77899	+	2.37596i	−0.991089	+	0.407473i
$35$		−	3.72657i		−	0.629905i
$36$	−1.51447	+	5.80572i	−0.252412	+	0.967620i
$37$			3.84855i			0.632698i	0.948643	+	0.316349i	$0.102457\pi$
$37$			3.84855i			0.632698i	−0.948643	+	0.316349i	$0.897543\pi$
$38$	1.79054	+	4.35510i	0.290464	+	0.706490i
$39$	−5.33988	+	5.40372i	−0.855065	+	0.865288i
$40$	−0.347059	−	2.80705i	−0.0548748	−	0.443834i
$41$	0.779241	−	0.449895i	0.121697	−	0.0702618i	−0.437916	−	0.899016i	$-0.644283\pi$
$41$	0.779241	−	0.449895i	0.121697	−	0.0702618i	0.559613	+	0.828754i	$0.310950\pi$
$42$	−1.22145	−	9.04610i	−0.188474	−	1.39584i
$43$	0.403230	−	0.698415i	0.0614920	−	0.106507i	−0.833641	−	0.552307i	$-0.813747\pi$
$43$	0.403230	−	0.698415i	0.0614920	−	0.106507i	0.895133	+	0.445800i	$0.147081\pi$
$44$	−11.4470	+	3.00281i	−1.72571	+	0.452691i
$45$	−2.61572	−	1.46902i	−0.389928	−	0.218988i
$46$	−5.28425	+	6.84922i	−0.779121	+	1.00986i
$47$	2.33110	−	4.03758i	0.340026	−	0.588942i	−0.644411	−	0.764679i	$-0.722898\pi$
$47$	2.33110	−	4.03758i	0.340026	−	0.588942i	0.984437	+	0.175737i	$0.0562309\pi$
$48$	−1.76253	−	6.70026i	−0.254400	−	0.967099i
$49$	3.44366	+	5.96459i	0.491951	+	0.852084i
$50$	1.40162	+	0.188277i	0.198220	+	0.0266264i
$51$	−2.02454	−	7.37998i	−0.283492	−	1.03340i
$52$	2.31495	−	8.46131i	0.321025	−	1.17337i
$53$	2.70454			0.371497			0.185749	−	0.982597i	$-0.440529\pi$
$53$	2.70454			0.371497			0.185749	+	0.982597i	$0.440529\pi$
$54$	−6.83105	−	2.70864i	−0.929589	−	0.368599i
$55$		−	5.91717i		−	0.797871i
$56$	6.35040	+	8.41254i	0.848608	+	1.12417i
$57$	−5.56162	+	1.52571i	−0.736654	+	0.202085i
$58$	0.716750	+	0.0962794i	0.0941139	+	0.0126421i
$59$	−11.5962	+	6.69508i	−1.50970	+	0.871625i	−0.509762	+	0.860315i	$0.670267\pi$
$59$	−11.5962	+	6.69508i	−1.50970	+	0.871625i	−0.999936	+	0.0113095i	$0.996400\pi$
$60$	3.46410	−	0.00237231i	0.447213	−	0.000306264i
$61$	−3.60020	−	2.07857i	−0.460958	−	0.266134i	0.251489	−	0.967860i	$-0.419080\pi$
$61$	−3.60020	−	2.07857i	−0.460958	−	0.266134i	−0.712447	+	0.701726i	$0.752413\pi$
$62$	1.89597	+	1.46276i	0.240789	+	0.185771i
$63$	11.1789	−	0.132859i	1.40841	−	0.0167387i
$64$	5.56694	+	5.74537i	0.695867	+	0.718171i
$65$	3.79850	+	2.19307i	0.471146	+	0.272016i
$66$	−1.93946	−	14.3637i	−0.238731	−	1.76805i
$67$	2.43445	+	4.21659i	0.297415	+	0.515138i	0.975544	−	0.219805i	$-0.0705421\pi$
$67$	2.43445	+	4.21659i	0.297415	+	0.515138i	−0.678129	+	0.734943i	$0.737209\pi$
$68$	6.21542	+	6.28112i	0.753730	+	0.761697i
$69$	−7.53614	−	7.44711i	−0.907244	−	0.896526i
$70$	−4.87428	+	2.00400i	−0.582588	+	0.239524i
$71$	5.40772			0.641779			0.320889	−	0.947117i	$-0.396018\pi$
$71$	5.40772			0.641779			0.320889	+	0.947117i	$0.396018\pi$
$72$	8.40819	−	1.14118i	0.990915	−	0.134489i
$73$	−6.12993			−0.717454			−0.358727	−	0.933443i	$-0.616789\pi$
$73$	−6.12993			−0.717454			−0.358727	+	0.933443i	$0.616789\pi$
$74$	5.03383	−	2.06959i	0.585171	−	0.240586i
$75$	−0.438339	+	1.67567i	−0.0506150	+	0.193489i
$76$	4.73350	−	4.68399i	0.542970	−	0.537291i
$77$	11.0254	+	19.0965i	1.25646	+	2.17625i
$78$	9.93954	+	4.07856i	1.12543	+	0.461806i
$79$	−5.58799	−	3.22623i	−0.628698	−	0.362979i	0.151550	−	0.988450i	$-0.451574\pi$
$79$	−5.58799	−	3.22623i	−0.628698	−	0.362979i	−0.780248	+	0.625471i	$0.784907\pi$
$80$	−3.48494	+	1.96347i	−0.389628	+	0.219522i
$81$	4.31349	−	7.89898i	0.479277	−	0.877664i
$82$	−1.00750	−	0.777297i	−0.111260	−	0.0858381i
$83$	−12.4965	−	7.21485i	−1.37167	−	0.791933i	−0.380529	−	0.924769i	$-0.624258\pi$
$83$	−12.4965	−	7.21485i	−1.37167	−	0.791933i	−0.991138	+	0.132836i	$0.957592\pi$
$84$	−11.1753	+	6.46226i	−1.21932	+	0.705090i
$85$	−3.82632	+	2.20913i	−0.415023	+	0.239613i
$86$	−1.13035	−	0.151838i	−0.121889	−	0.0163731i
$87$	−0.224154	+	0.856888i	−0.0240318	+	0.0918680i
$88$	10.0834	+	13.3577i	1.07489	+	1.42394i
$89$			10.2904i			1.09078i	0.838183	+	0.545389i	$0.183618\pi$
$89$			10.2904i			1.09078i	−0.838183	+	0.545389i	$0.816382\pi$
$90$	−0.514820	+	4.21129i	−0.0542668	+	0.443909i
$91$	−16.3452			−1.71345
$92$	11.8003	+	3.22847i	1.23027	+	0.336591i
$93$	−2.06148	+	2.08612i	−0.213765	+	0.216321i
$94$	−6.53465	−	0.877784i	−0.673998	−	0.0905365i
$95$	1.66482	+	2.88355i	0.170807	+	0.295846i
$96$	−7.81599	+	5.90849i	−0.797716	+	0.603033i
$97$	−4.30061	+	7.44888i	−0.436661	+	0.756319i	−0.997430	−	0.0716538i	$-0.977172\pi$
$97$	−4.30061	+	7.44888i	−0.436661	+	0.756319i	0.560769	+	0.827972i	$0.310506\pi$
$98$	5.94971	−	7.71175i	0.601011	−	0.779005i
$99$	17.7502	−	0.210958i	1.78397	−	0.0212021i
$100$	−0.507475	−	1.93455i	−0.0507475	−	0.193455i
$101$	−1.04803	+	1.81523i	−0.104282	+	0.180623i	−0.913445	−	0.406963i	$-0.866588\pi$
$101$	−1.04803	+	1.81523i	−0.104282	+	0.180623i	0.809162	+	0.587585i	$0.199921\pi$
$102$	−8.56416	+	6.61671i	−0.847978	+	0.655152i
$103$	12.6329	−	7.29360i	1.24475	−	0.718659i	0.274696	−	0.961531i	$-0.411423\pi$
$103$	12.6329	−	7.29360i	1.24475	−	0.718659i	0.970058	+	0.242872i	$0.0780894\pi$
$104$	−12.3121	+	1.52225i	−1.20730	+	0.149268i
$105$	−1.70759	−	6.22463i	−0.166644	−	0.607462i
$106$	−1.45439	−	3.53749i	−0.141263	−	0.343591i
$107$			0.161637i			0.0156260i	0.999969	+	0.00781301i	$0.00248698\pi$
$107$			0.161637i			0.0156260i	−0.999969	+	0.00781301i	$0.997513\pi$
$108$	0.130618	+	10.3915i	0.0125687	+	0.999921i
$109$			19.7734i			1.89395i	0.321312	+	0.946974i	$0.395876\pi$
$109$			19.7734i			1.89395i	−0.321312	+	0.946974i	$0.604124\pi$
$110$	−7.73954	+	3.18201i	−0.737936	+	0.303393i
$111$	1.76349	+	6.42838i	0.167383	+	0.610155i
$112$	7.58846	−	12.8301i	0.717042	−	1.21233i
$113$	7.48170	−	4.31956i	0.703820	−	0.406350i	−0.104949	−	0.994478i	$-0.533468\pi$
$113$	7.48170	−	4.31956i	0.703820	−	0.406350i	0.808768	+	0.588127i	$0.200135\pi$
$114$	4.98641	+	6.45402i	0.467020	+	0.604475i
$115$	−3.05850	+	5.29747i	−0.285206	+	0.493992i
$116$	−0.259508	−	0.989271i	−0.0240947	−	0.0918515i
$117$	−6.44331	+	11.4729i	−0.595684	+	1.06067i
$118$	14.9930	+	11.5673i	1.38022	+	1.06485i
$119$	8.23246	−	14.2590i	0.754668	−	1.30712i
$120$	−1.86596	−	4.52970i	−0.170338	−	0.413503i
$121$	12.0064	+	20.7957i	1.09149	+	1.89052i
$122$	−0.782695	+	5.82676i	−0.0708619	+	0.527530i
$123$	1.09545	−	1.10854i	0.0987730	−	0.0999539i
$124$	0.893691	−	3.26651i	0.0802558	−	0.293341i
$125$	1.00000			0.0894427
$126$	−6.18535	−	14.5504i	−0.551035	−	1.29625i
$127$		−	15.3149i		−	1.35898i	−0.733685	−	0.679489i	$-0.762201\pi$
$127$		−	15.3149i		−	1.35898i	0.733685	−	0.679489i	$-0.237799\pi$
$128$	4.52116	−	10.3711i	0.399618	−	0.916682i
$129$	0.353502	−	1.35136i	0.0311241	−	0.118980i
$130$	0.825808	−	6.14771i	0.0724281	−	0.539190i
$131$	−17.8355	+	10.2974i	−1.55830	+	0.899684i	−0.560879	+	0.827898i	$0.689537\pi$
$131$	−17.8355	+	10.2974i	−1.55830	+	0.899684i	−0.997420	+	0.0717862i	$0.977130\pi$
$132$	−17.7445	+	10.2610i	−1.54446	+	0.893104i
$133$	−10.7457	−	6.20405i	−0.931773	−	0.537959i
$134$	4.20607	−	5.45172i	0.363349	−	0.470957i
$135$	−5.04227	−	1.25518i	−0.433970	−	0.108029i
$136$	4.87318	−	11.5074i	0.417872	−	0.986750i
$137$	−11.9951	−	6.92539i	−1.02481	−	0.591676i	−0.109319	−	0.994007i	$-0.534867\pi$
$137$	−11.9951	−	6.92539i	−1.02481	−	0.591676i	−0.915494	+	0.402331i	$0.868200\pi$
$138$	−5.68804	+	13.8619i	−0.484198	+	1.18000i
$139$	−3.39880	−	5.88689i	−0.288282	−	0.499320i	0.685117	−	0.728433i	$-0.259751\pi$
$139$	−3.39880	−	5.88689i	−0.288282	−	0.499320i	−0.973400	+	0.229113i	$0.926418\pi$
$140$	5.24238	+	5.29780i	0.443062	+	0.447746i
$141$	2.04362	−	7.81229i	0.172104	−	0.657914i
$142$	−2.90806	−	7.07320i	−0.244039	−	0.593570i
$143$	−25.9535			−2.17034
$144$	−6.01423	−	10.3841i	−0.501186	−	0.865340i
$145$	0.511371			0.0424671
$146$	3.29643	+	8.01783i	0.272814	+	0.663560i
$147$	8.48517	+	8.38493i	0.699845	+	0.691577i
$148$	−5.41398	−	5.47121i	−0.445027	−	0.449731i
$149$	−7.07518	−	12.2546i	−0.579621	−	1.00393i	−0.995523	−	0.0945239i	$-0.969867\pi$
$149$	−7.07518	−	12.2546i	−0.579621	−	1.00393i	0.415901	−	0.909410i	$-0.363466\pi$
$150$	2.42746	−	0.327768i	0.198201	−	0.0267621i
$151$	14.6256	+	8.44412i	1.19022	+	0.687172i	0.958356	−	0.285576i	$-0.0921850\pi$
$151$	14.6256	+	8.44412i	1.19022	+	0.687172i	0.231862	+	0.972749i	$0.425518\pi$
$152$	−8.67206	−	3.67247i	−0.703397	−	0.297877i
$153$	−6.76333	−	11.3994i	−0.546782	−	0.921586i
$154$	19.0488	−	24.6903i	1.53500	−	1.98960i
$155$	1.46642	+	0.846640i	0.117786	+	0.0680037i
$156$	−0.0104053	−	15.1940i	−0.000833089	−	1.21649i
$157$	8.02095	−	4.63090i	0.640142	−	0.369586i	−0.144527	−	0.989501i	$-0.546166\pi$
$157$	8.02095	−	4.63090i	0.640142	−	0.369586i	0.784669	+	0.619915i	$0.212833\pi$
$158$	−1.21485	+	9.04392i	−0.0966481	+	0.719495i
$159$	4.51750	−	1.23928i	0.358261	−	0.0982811i
$160$	4.44224	+	3.50236i	0.351190	+	0.276886i
$161$		−	22.7954i		−	1.79653i
$162$	−12.6513	−	1.39421i	−0.993982	−	0.109540i
$163$	9.68862			0.758871			0.379436	−	0.925218i	$-0.376118\pi$
$163$	9.68862			0.758871			0.379436	+	0.925218i	$0.376118\pi$
$164$	−0.474898	+	1.73579i	−0.0370833	+	0.135542i
$165$	−2.71137	−	9.88368i	−0.211080	−	0.769443i
$166$	−2.71678	+	20.2250i	−0.210863	+	1.56977i
$167$	−2.47132	−	4.28046i	−0.191237	−	0.331232i	0.754424	−	0.656388i	$-0.227917\pi$
$167$	−2.47132	−	4.28046i	−0.191237	−	0.331232i	−0.945660	+	0.325156i	$0.894583\pi$
$168$	14.4621	+	11.1419i	1.11578	+	0.859617i
$169$	3.11908	−	5.40241i	0.239930	−	0.415570i
$170$	4.94714	+	3.81677i	0.379428	+	0.292733i
$171$	−8.59067	+	5.09690i	−0.656945	+	0.389770i
$172$	0.409258	+	1.56013i	0.0312056	+	0.118959i
$173$	7.67527	−	13.2940i	0.583540	−	1.01072i	−0.411516	−	0.911403i	$-0.635000\pi$
$173$	7.67527	−	13.2940i	0.583540	−	1.01072i	0.995056	−	0.0993184i	$-0.0316662\pi$
$174$	1.24133	−	0.167611i	0.0941053	−	0.0127066i
$175$	−3.22730	+	1.86328i	−0.243961	+	0.140851i
$176$	12.0492	−	20.3721i	0.908243	−	1.53560i
$177$	−16.3018	+	16.4967i	−1.22532	+	1.23997i
$178$	13.4596	−	5.53375i	1.00884	−	0.414772i
$179$		−	16.7784i		−	1.25407i	−0.778990	−	0.627037i	$-0.784267\pi$
$179$		−	16.7784i		−	1.25407i	0.778990	−	0.627037i	$-0.215733\pi$
$180$	5.78514	−	1.59129i	0.431199	−	0.118608i
$181$		−	7.76276i		−	0.577001i	−0.957480	−	0.288501i	$-0.906843\pi$
$181$		−	7.76276i		−	0.577001i	0.957480	−	0.288501i	$-0.0931568\pi$
$182$	8.78980	+	21.3792i	0.651544	+	1.58474i
$183$	−6.96600	−	1.82224i	−0.514941	−	0.134704i
$184$	−2.12295	−	17.1707i	−0.156506	−	1.26584i
$185$	3.33294	−	1.92427i	0.245043	−	0.141475i
$186$	3.83719	+	1.57454i	0.281356	+	0.115451i
$187$	13.0718	−	22.6410i	0.955902	−	1.65567i
$188$	2.36595	+	9.01924i	0.172554	+	0.657796i
$189$	18.6117	−	5.34433i	1.35380	−	0.388743i
$190$	2.87635	−	3.72820i	0.208673	−	0.270472i
$191$	−9.93534	+	17.2085i	−0.718896	+	1.24516i	0.242541	+	0.970141i	$0.422019\pi$
$191$	−9.93534	+	17.2085i	−0.718896	+	1.24516i	−0.961437	+	0.275024i	$0.911314\pi$
$192$	11.9313	+	7.04582i	0.861069	+	0.508489i
$193$	6.02978	+	10.4439i	0.434033	+	0.751768i	0.997216	−	0.0745645i	$-0.0237567\pi$
$193$	6.02978	+	10.4439i	0.434033	+	0.751768i	−0.563183	+	0.826332i	$0.690423\pi$
$194$	12.0557	+	1.61941i	0.865548	+	0.116267i
$195$	7.34970	+	1.92261i	0.526323	+	0.137681i
$196$	−13.2863	−	3.63503i	−0.949024	−	0.259645i
$197$	−6.02638			−0.429362			−0.214681	−	0.976684i	$-0.568871\pi$
$197$	−6.02638			−0.429362			−0.214681	+	0.976684i	$0.568871\pi$
$198$	−9.82130	−	23.1035i	−0.697969	−	1.64190i
$199$			20.6971i			1.46718i	0.679594	+	0.733588i	$0.262156\pi$
$199$			20.6971i			1.46718i	−0.679594	+	0.733588i	$0.737844\pi$
$200$	−2.25745	+	1.70409i	−0.159626	+	0.120497i
$201$	5.99849	+	5.92762i	0.423101	+	0.418102i
$202$	2.93788	+	0.394638i	0.206708	+	0.0277666i
$203$	−1.65035	+	0.952830i	−0.115832	+	0.0668755i
$204$	13.2600	+	7.64356i	0.928385	+	0.535156i
$205$	−0.779241	−	0.449895i	−0.0544245	−	0.0314220i
$206$	−16.3333	−	12.6014i	−1.13800	−	0.877979i
$207$	−16.0003	−	8.98598i	−1.11210	−	0.624568i
$208$	8.61203	+	15.2854i	0.597137	+	1.05985i
$209$	−17.0624	−	9.85099i	−1.18023	−	0.681407i
$210$	−7.22343	+	5.58086i	−0.498464	+	0.385116i
$211$	0.00520012	+	0.00900687i	0.000357991	+	0.000620059i	0.866204	−	0.499690i	$-0.166553\pi$
$211$	0.00520012	+	0.00900687i	0.000357991	+	0.000620059i	−0.865846	+	0.500310i	$0.833219\pi$
$212$	−3.84485	+	3.80464i	−0.264066	+	0.261304i
$213$	9.03274	−	2.47793i	0.618913	−	0.169785i
$214$	0.211418	−	0.0869217i	0.0144522	−	0.00594185i
$215$	−0.806460			−0.0550001
$216$	13.5216	−	5.75897i	0.920030	−	0.391848i
$217$	−6.31012			−0.428359
$218$	25.8632	−	10.6333i	1.75168	−	0.720180i
$219$	−10.2391	+	2.80886i	−0.691891	+	0.189805i
$220$	8.32403	+	8.41201i	0.561206	+	0.567138i
$221$	9.68952	+	16.7827i	0.651788	+	1.12893i
$222$	7.45987	−	5.76353i	0.500674	−	0.386823i
$223$	−10.5355	−	6.08267i	−0.705508	−	0.407325i	0.103887	−	0.994589i	$-0.466872\pi$
$223$	−10.5355	−	6.08267i	−0.705508	−	0.407325i	−0.809396	+	0.587264i	$0.800205\pi$
$224$	−20.8623	−	3.02603i	−1.39392	−	0.202185i
$225$	0.0356518	+	2.99979i	0.00237679	+	0.199986i
$226$	−9.67327	−	7.46304i	−0.643456	−	0.496434i
$227$	11.6359	+	6.71798i	0.772301	+	0.445888i	0.833695	−	0.552225i	$-0.186221\pi$
$227$	11.6359	+	6.71798i	0.772301	+	0.445888i	−0.0613937	+	0.998114i	$0.519555\pi$
$228$	5.76025	−	9.99284i	0.381482	−	0.661792i
$229$	−22.8339	+	13.1832i	−1.50891	+	0.871168i	−0.508961	+	0.860790i	$0.669970\pi$
$229$	−22.8339	+	13.1832i	−1.50891	+	0.871168i	−0.999946	+	0.0103785i	$0.996696\pi$
$230$	8.57373	+	1.15169i	0.565335	+	0.0759401i
$231$	27.1665	+	26.8456i	1.78743	+	1.76631i
$232$	−1.15439	+	0.871422i	−0.0757897	+	0.0572116i
$233$		−	3.95152i		−	0.258873i	−0.991588	−	0.129436i	$-0.958683\pi$
$233$		−	3.95152i		−	0.258873i	0.991588	−	0.129436i	$-0.0413168\pi$
$234$	18.4713	+	2.25807i	1.20751	+	0.147615i
$235$	−4.66220			−0.304128
$236$	7.06715	−	25.8310i	0.460032	−	1.68145i
$237$	−10.8122	−	2.82836i	−0.702325	−	0.183722i
$238$	−23.0776	−	3.09996i	−1.49590	−	0.200941i
$239$	−8.04934	−	13.9419i	−0.520669	−	0.901825i	−0.999711	−	0.0240330i	$-0.992349\pi$
$239$	−8.04934	−	13.9419i	−0.520669	−	0.901825i	0.479042	−	0.877792i	$-0.340984\pi$
$240$	−4.92133	+	4.87653i	−0.317670	+	0.314779i
$241$	−0.985896	+	1.70762i	−0.0635072	+	0.109998i	−0.896031	−	0.443992i	$-0.853562\pi$
$241$	−0.985896	+	1.70762i	−0.0635072	+	0.109998i	0.832524	+	0.553990i	$0.186895\pi$
$242$	20.7439	−	26.8873i	1.33347	−	1.72838i
$243$	3.58551	−	15.1705i	0.230011	−	0.973188i
$244$	8.04220	−	2.10965i	0.514849	−	0.135056i
$245$	3.44366	−	5.96459i	0.220007	−	0.381063i
$246$	−2.03904	−	0.836693i	−0.130004	−	0.0533456i
$247$	12.6476	−	7.30211i	0.804749	−	0.464622i
$248$	−4.75313	+	0.587667i	−0.301824	+	0.0373169i
$249$	−24.1794	−	6.32509i	−1.53231	−	0.400836i
$250$	−0.537760	−	1.30798i	−0.0340109	−	0.0827240i
$251$		−	6.37572i		−	0.402432i	−0.979547	−	0.201216i	$-0.935511\pi$
$251$		−	6.37572i		−	0.402432i	0.979547	−	0.201216i	$-0.0644893\pi$
$252$	−15.7054	+	15.9149i	−0.989345	+	1.00255i
$253$		−	36.1953i		−	2.27558i
$254$	−20.0316	+	8.23574i	−1.25690	+	0.516756i
$255$	−5.37898	+	5.44329i	−0.336845	+	0.340872i
$256$	−15.9965	−	0.336442i	−0.999779	−	0.0210276i
$257$	−9.08207	+	5.24354i	−0.566524	+	0.327083i	−0.755760	−	0.654849i	$-0.772732\pi$
$257$	−9.08207	+	5.24354i	−0.566524	+	0.327083i	0.189236	+	0.981932i	$0.439399\pi$
$258$	−1.95765	+	0.264331i	−0.121878	+	0.0164566i
$259$	−7.17094	+	12.4204i	−0.445581	+	0.771768i
$260$	−8.48518	+	2.22585i	−0.526228	+	0.138041i
$261$	0.0182313	+	1.53401i	0.00112849	+	0.0949525i
$262$	23.0600	+	17.7911i	1.42465	+	1.09913i
$263$	−12.4917	+	21.6363i	−0.770274	+	1.33415i	0.167139	+	0.985933i	$0.446547\pi$
$263$	−12.4917	+	21.6363i	−0.770274	+	1.33415i	−0.937413	+	0.348220i	$0.886786\pi$
$264$	22.9634	+	17.6915i	1.41330	+	1.08884i
$265$	−1.35227	−	2.34220i	−0.0830693	−	0.143880i
$266$	−2.33616	+	17.3915i	−0.143239	+	1.06634i
$267$	4.71527	+	17.1884i	0.288570	+	1.05192i
$268$	−9.39261	−	2.56974i	−0.573745	−	0.156972i
$269$	24.3110			1.48227			0.741135	−	0.671356i	$-0.234288\pi$
$269$	24.3110			1.48227			0.741135	+	0.671356i	$0.234288\pi$
$270$	1.06978	+	7.27018i	0.0651046	+	0.442449i
$271$		−	4.31845i		−	0.262327i	−0.991361	−	0.131164i	$-0.958129\pi$
$271$		−	4.31845i		−	0.262327i	0.991361	−	0.131164i	$-0.0418713\pi$
$272$	−17.6720	−	0.185821i	−1.07152	−	0.0112670i
$273$	−27.3021	+	7.48973i	−1.65240	+	0.453299i
$274$	−2.60778	+	19.4136i	−0.157542	+	1.17282i
$275$	−5.12442	+	2.95858i	−0.309014	+	0.178409i
$276$	21.1899	−	0.0145114i	1.27548	−	0.000873484i
$277$	−0.545547	−	0.314972i	−0.0327788	−	0.0189248i	0.483521	−	0.875333i	$-0.339358\pi$
$277$	−0.545547	−	0.314972i	−0.0327788	−	0.0189248i	−0.516300	+	0.856408i	$0.672691\pi$
$278$	−5.87221	+	7.61130i	−0.352192	+	0.456496i
$279$	−2.48746	+	4.42914i	−0.148920	+	0.265166i
$280$	4.11028	−	9.70588i	0.245636	−	0.580037i
$281$	13.1889	+	7.61459i	0.786782	+	0.454249i	0.838828	−	0.544396i	$-0.183241\pi$
$281$	13.1889	+	7.61459i	0.786782	+	0.454249i	−0.0520467	+	0.998645i	$0.516574\pi$
$282$	−11.3173	+	1.52812i	−0.673936	+	0.0909981i
$283$	10.2282	+	17.7158i	0.608006	+	1.05310i	0.991569	+	0.129582i	$0.0413636\pi$
$283$	10.2282	+	17.7158i	0.608006	+	1.05310i	−0.383563	+	0.923515i	$0.625303\pi$
$284$	−7.68778	+	7.60737i	−0.456186	+	0.451414i
$285$	4.10211	+	4.05365i	0.242988	+	0.240117i
$286$	13.9567	+	33.9467i	0.825279	+	2.00731i
$287$	3.35313			0.197929
$288$	−10.3480	+	13.4506i	−0.609760	+	0.792586i
$289$	−2.52095			−0.148291
$290$	−0.274995	−	0.668864i	−0.0161483	−	0.0392770i
$291$	−3.77025	+	14.4128i	−0.221016	+	0.844892i
$292$	8.71448	−	8.62333i	0.509976	−	0.504642i
$293$	1.91946	+	3.32460i	0.112136	+	0.194225i	0.916631	−	0.399734i	$-0.130897\pi$
$293$	1.91946	+	3.32460i	0.112136	+	0.194225i	−0.804495	+	0.593959i	$0.797564\pi$
$294$	6.40434	−	15.6075i	0.373509	−	0.910249i
$295$	11.5962	+	6.69508i	0.675158	+	0.389802i
$296$	−4.24482	+	10.0236i	−0.246725	+	0.582609i
$297$	29.5523	−	8.48591i	1.71480	−	0.492402i
$298$	−12.2240	+	15.8442i	−0.708117	+	0.917831i
$299$	23.2354	+	13.4150i	1.34374	+	0.775808i
$300$	−1.73410	−	2.99881i	−0.100119	−	0.173137i
$301$	2.60269	−	1.50266i	0.150017	−	0.0866121i
$302$	3.17966	−	23.6710i	0.182969	−	1.36211i
$303$	−0.918780	+	3.51228i	−0.0527825	+	0.201775i
$304$	−0.140036	+	13.3178i	−0.00803162	+	0.763828i
$305$			4.15715i			0.238038i
$306$	−11.2731	+	14.9764i	−0.644442	+	0.856146i
$307$	−10.2525			−0.585143			−0.292572	−	0.956244i	$-0.594511\pi$
$307$	−10.2525			−0.585143			−0.292572	+	0.956244i	$0.594511\pi$
$308$	−42.5381	−	11.6381i	−2.42384	−	0.663142i
$309$	17.7591	−	17.9714i	1.01028	−	1.02236i
$310$	0.318805	−	2.37334i	0.0181069	−	0.134797i
$311$	−7.31106	−	12.6631i	−0.414572	−	0.718060i	0.580811	−	0.814038i	$-0.302735\pi$
$311$	−7.31106	−	12.6631i	−0.414572	−	0.718060i	−0.995383	+	0.0959781i	$0.969402\pi$
$312$	−19.8679	+	8.18434i	−1.12480	+	0.463347i
$313$	15.8650	−	27.4790i	0.896744	−	1.55321i	0.0651117	−	0.997878i	$-0.479260\pi$
$313$	15.8650	−	27.4790i	0.896744	−	1.55321i	0.831632	−	0.555327i	$-0.187407\pi$
$314$	−10.3705	−	8.00094i	−0.585240	−	0.451519i
$315$	−5.70452	−	9.61480i	−0.321413	−	0.541732i
$316$	12.4826	−	3.27446i	0.702199	−	0.184203i
$317$	−1.86120	+	3.22369i	−0.104535	+	0.181060i	−0.913548	−	0.406730i	$-0.866669\pi$
$317$	−1.86120	+	3.22369i	−0.104535	+	0.181060i	0.809013	+	0.587791i	$0.200002\pi$
$318$	−4.05028	−	5.24237i	−0.227128	−	0.293978i
$319$	−2.62048	+	1.51293i	−0.146719	+	0.0847080i
$320$	2.19217	−	7.69379i	0.122546	−	0.430096i
$321$	0.0740654	+	0.269988i	0.00413393	+	0.0150693i
$322$	−29.8159	+	12.2584i	−1.66158	+	0.683136i
$323$			14.7112i			0.818550i
$324$	4.97977	+	17.2975i	0.276654	+	0.960970i
$325$		−	4.38613i		−	0.243299i
$326$	−5.21015	−	12.6725i	−0.288563	−	0.701866i
$327$	9.06058	+	33.0283i	0.501051	+	1.82647i
$328$	2.52576	−	0.312280i	0.139462	−	0.0172428i
$329$	15.0463	−	8.68700i	0.829531	−	0.478930i
$330$	−11.4696	+	8.86146i	−0.631380	+	0.487808i
$331$	11.2035	−	19.4050i	0.615798	−	1.06659i	−0.374446	−	0.927249i	$-0.622167\pi$
$331$	11.2035	−	19.4050i	0.615798	−	1.06659i	0.990244	−	0.139345i	$-0.0444997\pi$
$332$	27.9149	−	7.32271i	1.53203	−	0.401886i
$333$	5.89124	+	9.92951i	0.322838	+	0.544134i
$334$	−4.26978	+	5.53430i	−0.233632	+	0.302824i
$335$	2.43445	−	4.21659i	0.133008	−	0.230377i
$336$	6.79626	−	24.9079i	0.370766	−	1.35884i
$337$	−6.16470	−	10.6776i	−0.335813	−	0.581644i	0.647828	−	0.761787i	$-0.275678\pi$
$337$	−6.16470	−	10.6776i	−0.335813	−	0.581644i	−0.983641	+	0.180142i	$0.942344\pi$
$338$	−8.74357	−	1.17450i	−0.475588	−	0.0638845i
$339$	10.5177	−	10.6434i	0.571241	−	0.578071i
$340$	2.33190	−	8.52327i	0.126465	−	0.462239i
$341$	−10.0194			−0.542582
$342$	11.2864	+	8.49553i	0.610297	+	0.459386i
$343$		−	0.419941i		−	0.0226747i
$344$	1.82054	−	1.37428i	0.0981571	−	0.0740961i
$345$	−2.68131	+	10.2500i	−0.144357	+	0.551844i
$346$	−21.5157	−	2.89015i	−1.15669	−	0.155376i
$347$	13.5052	−	7.79724i	0.724998	−	0.418578i	−0.0915912	−	0.995797i	$-0.529195\pi$
$347$	13.5052	−	7.79724i	0.724998	−	0.418578i	0.816590	+	0.577219i	$0.195862\pi$
$348$	−0.886771	−	1.53351i	−0.0475359	−	0.0822046i
$349$	16.3875	+	9.46135i	0.877205	+	0.506454i	0.869736	−	0.493518i	$-0.164289\pi$
$349$	16.3875	+	9.46135i	0.877205	+	0.506454i	0.00746892	+	0.999972i	$0.497623\pi$
$350$	4.17265	+	3.21925i	0.223038	+	0.172076i
$351$	−5.50540	+	22.1161i	−0.293856	+	1.18047i
$352$	−33.1259	−	4.80483i	−1.76562	−	0.256098i
$353$	4.83467	+	2.79130i	0.257324	+	0.148566i	0.623113	−	0.782132i	$-0.285868\pi$
$353$	4.83467	+	2.79130i	0.257324	+	0.148566i	−0.365789	+	0.930698i	$0.619201\pi$
$354$	30.3438	+	12.4512i	1.61275	+	0.661773i
$355$	−2.70386	−	4.68323i	−0.143506	−	0.248560i
$356$	−14.4761	−	14.6291i	−0.767231	−	0.775341i
$357$	7.21721	−	27.5897i	0.381975	−	1.46020i
$358$	−21.9458	+	9.02273i	−1.15987	+	0.476866i
$359$	28.3606			1.49681			0.748406	−	0.663240i	$-0.230819\pi$
$359$	28.3606			1.49681			0.748406	+	0.663240i	$0.230819\pi$
$360$	−5.19239	−	6.71112i	−0.273663	−	0.353707i
$361$	−7.91355			−0.416503
$362$	−10.1535	+	4.17450i	−0.533658	+	0.219407i
$363$	29.5839	+	29.2343i	1.55275	+	1.53441i
$364$	23.2368	−	22.9938i	1.21794	−	1.20520i
$365$	3.06496	+	5.30867i	0.160427	+	0.277869i
$366$	1.36258	+	10.0913i	0.0712231	+	0.527482i
$367$	1.17380	+	0.677693i	0.0612718	+	0.0353753i	0.530323	−	0.847796i	$-0.322071\pi$
$367$	1.17380	+	0.677693i	0.0612718	+	0.0353753i	−0.469051	+	0.883171i	$0.655404\pi$
$368$	−21.3173	+	12.0105i	−1.11124	+	0.626091i
$369$	1.32181	−	2.35360i	0.0688106	−	0.122523i
$370$	−4.30924	−	3.32463i	−0.224027	−	0.172839i
$371$	8.72837	+	5.03933i	0.453154	+	0.261629i
$372$	−0.00401699	−	5.86569i	−0.000208271	−	0.304122i
$373$	−26.7910	+	15.4678i	−1.38718	+	0.800890i	−0.992997	−	0.118140i	$-0.962307\pi$
$373$	−26.7910	+	15.4678i	−1.38718	+	0.800890i	−0.394186	+	0.919031i	$0.628973\pi$
$374$	−36.6434	−	4.92222i	−1.89479	−	0.254522i
$375$	1.67034	−	0.458221i	0.0862560	−	0.0236624i
$376$	10.5247	−	7.94480i	0.542769	−	0.409722i
$377$		−	2.24294i		−	0.115517i
$378$	−16.9989	−	21.4698i	−0.874330	−	1.10429i
$379$	30.1919			1.55085			0.775426	−	0.631438i	$-0.217535\pi$
$379$	30.1919			1.55085			0.775426	+	0.631438i	$0.217535\pi$
$380$	−6.42320	−	1.75734i	−0.329503	−	0.0901495i
$381$	−7.01762	−	25.5811i	−0.359523	−	1.31056i
$382$	27.8512	+	3.74119i	1.42499	+	0.191416i
$383$	−12.5398	−	21.7196i	−0.640754	−	1.10982i	−0.985265	−	0.171036i	$-0.945289\pi$
$383$	−12.5398	−	21.7196i	−0.640754	−	1.10982i	0.344511	−	0.938782i	$-0.388045\pi$
$384$	2.79962	−	19.3949i	0.142868	−	0.989742i
$385$	11.0254	−	19.0965i	0.561904	−	0.973247i
$386$	10.4178	−	13.5031i	0.530254	−	0.687292i
$387$	−0.0287518	−	2.41921i	−0.00146153	−	0.122975i
$388$	−4.36490	−	16.6395i	−0.221594	−	0.844741i
$389$	6.73906	−	11.6724i	0.341684	−	0.591814i	−0.643062	−	0.765814i	$-0.722336\pi$
$389$	6.73906	−	11.6724i	0.341684	−	0.591814i	0.984746	+	0.174001i	$0.0556695\pi$
$390$	−1.43763	−	10.6472i	−0.0727974	−	0.539140i
$391$	−23.4056	+	13.5132i	−1.18367	+	0.683392i
$392$	2.39030	+	19.3331i	0.120728	+	0.976467i
$393$	−25.0729	+	25.3727i	−1.26476	+	1.27988i
$394$	3.24074	+	7.88239i	0.163266	+	0.397109i
$395$			6.45245i			0.324658i
$396$	−24.9375	+	25.2702i	−1.25316	+	1.26988i
$397$			10.4143i			0.522678i	0.965247	+	0.261339i	$0.0841641\pi$
$397$			10.4143i			0.522678i	−0.965247	+	0.261339i	$0.915836\pi$
$398$	27.0714	−	11.1301i	1.35697	−	0.557899i
$399$	−20.7918	−	5.43895i	−1.04089	−	0.272288i
$400$	3.44288	+	2.03631i	0.172144	+	0.101816i
$401$	1.10934	−	0.640480i	0.0553980	−	0.0319841i	−0.472045	−	0.881574i	$-0.656484\pi$
$401$	1.10934	−	0.640480i	0.0553980	−	0.0319841i	0.527443	+	0.849590i	$0.323151\pi$
$402$	4.52747	−	11.0335i	0.225810	−	0.550303i
$403$	3.71347	−	6.43193i	0.184981	−	0.320397i
$404$	−1.06369	−	4.05491i	−0.0529207	−	0.201739i
$405$	−8.99746	+	0.213896i	−0.447087	+	0.0106286i
$406$	2.13377	+	1.64623i	0.105897	+	0.0817011i
$407$	−11.3863	+	19.7216i	−0.564396	+	0.977562i
$408$	2.86694	−	21.4542i	0.141935	−	1.06214i
$409$	6.00858	+	10.4072i	0.297105	+	0.514601i	0.975472	−	0.220122i	$-0.0706455\pi$
$409$	6.00858	+	10.4072i	0.297105	+	0.514601i	−0.678367	+	0.734723i	$0.737312\pi$
$410$	−0.169410	+	1.26117i	−0.00836655	+	0.0622846i
$411$	−23.2093	−	6.07133i	−1.14483	−	0.299477i
$412$	−7.69893	+	28.1402i	−0.379299	+	1.38637i
$413$	−49.8993			−2.45539
$414$	−3.14915	+	25.7604i	−0.154772	+	1.26606i
$415$			14.4297i			0.708326i
$416$	15.3618	−	19.4842i	0.753175	−	0.955294i
$417$	−8.37465	−	8.27571i	−0.410108	−	0.405263i
$418$	−3.70943	+	27.6148i	−0.181434	+	1.35068i
$419$	12.8707	−	7.43087i	0.628773	−	0.363022i	−0.151504	−	0.988457i	$-0.548412\pi$
$419$	12.8707	−	7.43087i	0.628773	−	0.363022i	0.780277	+	0.625435i	$0.215078\pi$
$420$	11.1841	+	6.44695i	0.545729	+	0.314579i
$421$	21.5373	+	12.4346i	1.04966	+	0.606023i	0.922555	−	0.385866i	$-0.126097\pi$
$421$	21.5373	+	12.4346i	1.04966	+	0.606023i	0.127108	+	0.991889i	$0.459431\pi$
$422$	0.00898440	−	0.0116452i	0.000437354	−	0.000566879i
$423$	−0.166216	−	13.9856i	−0.00808170	−	0.680004i
$424$	7.04400	+	2.98301i	0.342087	+	0.144868i
$425$	3.82632	+	2.20913i	0.185604	+	0.107158i
$426$	−8.09853	−	10.4821i	−0.392375	−	0.507860i
$427$	−7.74595	−	13.4164i	−0.374853	−	0.649264i
$428$	−0.227384	−	0.229787i	−0.0109910	−	0.0111072i
$429$	−43.3511	+	11.8924i	−2.09301	+	0.574172i
$430$	0.433682	+	1.05483i	0.0209140	+	0.0508686i
$431$	1.71934			0.0828179			0.0414089	−	0.999142i	$-0.486815\pi$
$431$	1.71934			0.0828179			0.0414089	+	0.999142i	$0.486815\pi$
$432$	−14.8040	−	14.5891i	−0.712258	−	0.701918i
$433$	12.6546			0.608140			0.304070	−	0.952650i	$-0.401654\pi$
$433$	12.6546			0.608140			0.304070	+	0.952650i	$0.401654\pi$
$434$	3.39333	+	8.25352i	0.162885	+	0.396182i
$435$	0.854163	−	0.234321i	0.0409540	−	0.0112348i
$436$	−27.8164	−	28.1104i	−1.33216	−	1.34624i
$437$	10.1837	+	17.6386i	0.487151	+	0.843770i
$438$	9.18009	+	11.8820i	0.438642	+	0.567744i
$439$	20.5696	+	11.8759i	0.981734	+	0.566805i	0.902793	−	0.430075i	$-0.141513\pi$
$439$	20.5696	+	11.8759i	0.981734	+	0.566805i	0.0789411	+	0.996879i	$0.474846\pi$
$440$	6.52643	−	15.4113i	0.311135	−	0.734706i
$441$	18.0153	+	10.1176i	0.857870	+	0.481790i
$442$	16.7409	−	21.6988i	0.796282	−	1.03211i
$443$	−5.63155	−	3.25138i	−0.267563	−	0.154478i	0.360217	−	0.932869i	$-0.382703\pi$
$443$	−5.63155	−	3.25138i	−0.267563	−	0.154478i	−0.627780	+	0.778391i	$0.716036\pi$
$444$	−11.5502	−	6.65797i	−0.548149	−	0.315973i
$445$	8.91173	−	5.14519i	0.422457	−	0.243905i
$446$	−2.29045	+	17.0512i	−0.108456	+	0.807399i
$447$	−17.4333	−	17.2273i	−0.824565	−	0.814823i
$448$	7.26094	+	28.9148i	0.343047	+	1.36610i
$449$			15.3330i			0.723610i	0.932254	+	0.361805i	$0.117839\pi$
$449$			15.3330i			0.723610i	−0.932254	+	0.361805i	$0.882161\pi$
$450$	3.90449	−	1.65980i	0.184060	−	0.0782436i
$451$	5.32421			0.250707
$452$	−4.55962	+	16.6658i	−0.214467	+	0.783892i
$453$	28.2990	+	7.40276i	1.32961	+	0.347812i
$454$	2.52968	−	18.8322i	0.118724	−	0.883838i
$455$	8.17261	+	14.1554i	0.383138	+	0.663615i
$456$	−16.1681	−	2.16055i	−0.757140	−	0.101177i
$457$	−10.8278	+	18.7543i	−0.506502	+	0.877288i	0.493469	+	0.869763i	$0.335729\pi$
$457$	−10.8278	+	18.7543i	−0.506502	+	0.877288i	−0.999972	+	0.00752469i	$0.997605\pi$
$458$	29.5225	+	22.7769i	1.37950	+	1.06430i
$459$	−16.5205	−	15.9417i	−0.771110	−	0.744097i
$460$	−3.10422	−	11.8336i	−0.144735	−	0.551745i
$461$	0.979212	−	1.69604i	0.0456064	−	0.0789927i	−0.842321	−	0.538976i	$-0.818811\pi$
$461$	0.979212	−	1.69604i	0.0456064	−	0.0789927i	0.887928	+	0.459983i	$0.152145\pi$
$462$	20.5044	−	49.9697i	0.953952	−	2.32480i
$463$	19.1528	−	11.0579i	0.890107	−	0.513903i	0.0161293	−	0.999870i	$-0.494866\pi$
$463$	19.1528	−	11.0579i	0.890107	−	0.513903i	0.873977	+	0.485967i	$0.161532\pi$
$464$	1.76059	+	1.04131i	0.0817333	+	0.0483417i
$465$	2.83737	+	0.742230i	0.131580	+	0.0344201i
$466$	−5.16852	+	2.12497i	−0.239427	+	0.0984373i
$467$			8.58702i			0.397360i	0.980064	+	0.198680i	$0.0636655\pi$
$467$			8.58702i			0.397360i	−0.980064	+	0.198680i	$0.936335\pi$
$468$	−6.97960	−	25.3744i	−0.322632	−	1.17293i
$469$			18.1443i			0.837825i
$470$	2.50714	+	6.09807i	0.115646	+	0.281283i
$471$	11.2757	−	11.4105i	0.519559	−	0.525770i
$472$	−37.5869	+	4.64717i	−1.73008	+	0.213903i
$473$	4.13264	−	2.38598i	0.190019	−	0.109707i
$474$	2.11491	+	15.6631i	0.0971408	+	0.719429i
$475$	1.66482	−	2.88355i	0.0763870	−	0.132306i
$476$	8.35553	+	31.8521i	0.382975	+	1.45994i
$477$	6.97789	−	4.14003i	0.319496	−	0.189559i
$478$	−13.9071	+	18.0258i	−0.636096	+	0.824479i
$479$	−3.43928	+	5.95700i	−0.157145	+	0.272182i	−0.933838	−	0.357697i	$-0.883562\pi$
$479$	−3.43928	+	5.95700i	−0.157145	+	0.272182i	0.776693	+	0.629879i	$0.216896\pi$
$480$	9.02490	+	3.81460i	0.411928	+	0.174112i
$481$	−8.44013	−	14.6187i	−0.384837	−	0.666557i
$482$	2.76371	+	0.371243i	0.125884	+	0.0169097i
$483$	−10.4453	−	38.0760i	−0.475279	−	1.73252i
$484$	−46.3233	−	12.6737i	−2.10560	−	0.576076i
$485$	8.60122			0.390561
$486$	−21.7709	+	3.46830i	−0.987547	+	0.157325i
$487$		−	28.1573i		−	1.27593i	−0.770065	−	0.637966i	$-0.779776\pi$
$487$		−	28.1573i		−	1.27593i	0.770065	−	0.637966i	$-0.220224\pi$
$488$	−7.08415	−	9.38456i	−0.320684	−	0.424819i
$489$	16.1833	−	4.43953i	0.731833	−	0.200762i
$490$	−9.65343	−	1.29672i	−0.436097	−	0.0585799i
$491$	1.45905	−	0.842385i	0.0658462	−	0.0380163i	−0.466715	−	0.884408i	$-0.654563\pi$
$491$	1.45905	−	0.842385i	0.0658462	−	0.0380163i	0.532562	+	0.846391i	$0.321229\pi$
$492$	0.00213458	+	3.11696i	9.62344e−5	+	0.140524i
$493$	1.95667	+	1.12968i	0.0881239	+	0.0508784i
$494$	−16.3524	−	12.6161i	−0.735729	−	0.567624i
$495$	−9.05782	−	15.2667i	−0.407119	−	0.686186i
$496$	3.32470	+	5.90097i	0.149283	+	0.264962i
$497$	17.4524	+	10.0761i	0.782846	+	0.451976i
$498$	4.72959	+	35.0275i	0.211938	+	1.56962i
$499$	−7.19745	−	12.4663i	−0.322202	−	0.558070i	0.658740	−	0.752371i	$-0.271090\pi$
$499$	−7.19745	−	12.4663i	−0.322202	−	0.558070i	−0.980942	+	0.194300i	$0.937756\pi$
$500$	−1.42163	+	1.40676i	−0.0635772	+	0.0629122i
$501$	−6.08935	−	6.01741i	−0.272052	−	0.268838i
$502$	−8.33932	+	3.42860i	−0.372202	+	0.153026i
$503$	30.3439			1.35297			0.676484	−	0.736458i	$-0.263503\pi$
$503$	30.3439			1.35297			0.676484	+	0.736458i	$0.263503\pi$
$504$	29.2621	+	11.9839i	1.30344	+	0.533806i
$505$	2.09605			0.0932731
$506$	−47.3427	+	19.4644i	−2.10464	+	0.865296i
$507$	2.73443	−	10.4531i	0.121440	−	0.464238i
$508$	21.5444	+	21.7721i	0.955878	+	0.965982i
$509$	18.3083	+	31.7109i	0.811501	+	1.40556i	0.911813	+	0.410605i	$0.134683\pi$
$509$	18.3083	+	31.7109i	0.811501	+	1.40556i	−0.100312	+	0.994956i	$0.531984\pi$
$510$	10.0123	+	4.10842i	0.443353	+	0.181924i
$511$	−19.7831	−	11.4218i	−0.875154	−	0.505270i
$512$	8.16219	+	21.1040i	0.360721	+	0.932674i
$513$	−12.0138	+	12.4500i	−0.530424	+	0.549680i
$514$	11.7424	+	9.05941i	0.517936	+	0.399594i
$515$	−12.6329	−	7.29360i	−0.556671	−	0.321394i
$516$	1.39849	+	2.41842i	0.0615649	+	0.106465i
$517$	23.8910	−	13.7935i	1.05073	−	0.606637i
$518$	20.1019	+	2.70025i	0.883228	+	0.118642i
$519$	6.72873	−	25.7224i	0.295359	−	1.12909i
$520$	7.47436	+	9.90148i	0.327772	+	0.434209i
$521$			9.86643i			0.432256i	0.976365	+	0.216128i	$0.0693428\pi$
$521$			9.86643i			0.432256i	−0.976365	+	0.216128i	$0.930657\pi$
$522$	1.99665	−	0.848772i	0.0873908	−	0.0371498i
$523$	−41.1369			−1.79879			−0.899395	−	0.437138i	$-0.855992\pi$
$523$	−41.1369			−1.79879			−0.899395	+	0.437138i	$0.855992\pi$
$524$	10.8696	−	39.7293i	0.474842	−	1.73558i
$525$	−4.53689	+	4.59114i	−0.198006	+	0.200374i
$526$	35.0175	+	4.70381i	1.52683	+	0.205096i
$527$	3.74067	+	6.47903i	0.162946	+	0.282231i
$528$	10.7913	−	39.5495i	0.469632	−	1.72117i
$529$	−7.20879	+	12.4860i	−0.313426	+	0.542869i
$530$	−2.33636	+	3.02828i	−0.101485	+	0.131540i
$531$	−19.6704	+	35.0249i	−0.853622	+	1.51995i
$532$	24.0040	−	6.29680i	1.04071	−	0.273001i
$533$	−1.97330	+	3.41785i	−0.0854731	+	0.148044i
$534$	19.9465	−	15.4107i	0.863168	−	0.666888i
$535$	0.139982	−	0.0808184i	0.00605193	−	0.00349408i
$536$	1.68979	+	13.6673i	0.0729879	+	0.590336i
$537$	−7.68820	−	28.0256i	−0.331770	−	1.20939i
$538$	−13.0735	−	31.7984i	−0.563638	−	1.37092i
$539$			40.7534i			1.75537i
$540$	8.93398	−	5.30886i	0.384457	−	0.228457i
$541$		−	36.3958i		−	1.56478i	−0.622789	−	0.782390i	$-0.714001\pi$
$541$		−	36.3958i		−	1.56478i	0.622789	−	0.782390i	$-0.285999\pi$
$542$	−5.64845	+	2.32229i	−0.242622	+	0.0997509i
$543$	−3.55706	−	12.9664i	−0.152648	−	0.556443i
$544$	9.26026	+	23.2146i	0.397030	+	0.995318i
$545$	17.1243	−	9.88669i	0.733523	−	0.423499i
$546$	24.4784	+	31.6829i	1.04758	+	1.35590i
$547$	2.44245	−	4.23045i	0.104432	−	0.180881i	−0.809074	−	0.587707i	$-0.800031\pi$
$547$	2.44245	−	4.23045i	0.104432	−	0.180881i	0.913506	+	0.406825i	$0.133364\pi$
$548$	26.7950	−	7.02892i	1.14462	−	0.300261i
$549$	−12.4706	+	0.148210i	−0.532231	+	0.00632545i
$550$	6.62548	+	5.11163i	0.282511	+	0.217961i
$551$	0.851339	−	1.47456i	0.0362683	−	0.0628185i
$552$	−11.4140	−	27.7082i	−0.485814	−	1.17934i
$553$	−12.0228	−	20.8240i	−0.511259	−	0.885527i
$554$	−0.118604	+	0.882945i	−0.00503900	+	0.0375127i
$555$	4.68540	−	4.74142i	0.198884	−	0.201262i
$556$	13.1133	+	3.58769i	0.556127	+	0.152152i
$557$	−12.6214			−0.534786			−0.267393	−	0.963588i	$-0.586162\pi$
$557$	−12.6214			−0.534786			−0.267393	+	0.963588i	$0.586162\pi$
$558$	7.13089	+	0.871735i	0.301875	+	0.0369035i
$559$			3.53724i			0.149609i
$560$	−14.9054	−	0.156730i	−0.629870	−	0.00662306i
$561$	11.4597	−	43.8079i	0.483830	−	1.84957i
$562$	2.86730	−	21.3456i	0.120950	−	0.900410i
$563$	8.05487	−	4.65048i	0.339472	−	0.195994i	−0.320566	−	0.947226i	$-0.603873\pi$
$563$	8.05487	−	4.65048i	0.339472	−	0.195994i	0.660039	+	0.751232i	$0.270540\pi$
$564$	8.08474	+	13.9811i	0.340429	+	0.588709i
$565$	−7.48170	−	4.31956i	−0.314758	−	0.181725i
$566$	17.6716	−	22.9052i	0.742794	−	0.962778i
$567$	28.6390	−	17.4551i	1.20272	−	0.733046i
$568$	14.0845	+	5.96453i	0.590971	+	0.250266i
$569$	2.39000	+	1.37987i	0.100194	+	0.0578472i	0.549260	−	0.835652i	$-0.314910\pi$
$569$	2.39000	+	1.37987i	0.100194	+	0.0578472i	−0.449066	+	0.893499i	$0.648243\pi$
$570$	3.09614	−	7.54537i	0.129683	−	0.316041i
$571$	−2.31318	−	4.00655i	−0.0968036	−	0.167669i	0.813556	−	0.581486i	$-0.197529\pi$
$571$	−2.31318	−	4.00655i	−0.0968036	−	0.167669i	−0.910360	+	0.413817i	$0.864195\pi$
$572$	36.8962	−	36.5103i	1.54271	−	1.52657i
$573$	−8.71009	+	33.2966i	−0.363869	+	1.39099i
$574$	−1.80318	−	4.38583i	−0.0752632	−	0.183061i
$575$	6.11699			0.255096
$576$	23.1579	+	6.30173i	0.964912	+	0.262572i
$577$	4.89661			0.203849			0.101924	−	0.994792i	$-0.467500\pi$
$577$	4.89661			0.203849			0.101924	+	0.994792i	$0.467500\pi$
$578$	1.35567	+	3.29736i	0.0563883	+	0.137152i
$579$	14.8574	+	14.6819i	0.617452	+	0.610158i
$580$	−0.726980	+	0.719376i	−0.0301862	+	0.0298705i
$581$	−26.8866	−	46.5690i	−1.11545	−	1.93201i
$582$	20.8791	−	2.81920i	0.865468	−	0.116860i
$583$	13.8592	+	8.00161i	0.573989	+	0.331393i
$584$	−15.9654	−	6.76110i	−0.660655	−	0.279776i
$585$	13.1575	−	0.156374i	0.543995	−	0.00646526i
$586$	3.31631	−	4.29845i	0.136995	−	0.177568i
$587$	15.0805	+	8.70674i	0.622440	+	0.359366i	0.777818	−	0.628489i	$-0.216326\pi$
$587$	15.0805	+	8.70674i	0.622440	+	0.359366i	−0.155379	+	0.987855i	$0.549660\pi$
$588$	−23.8583	+	0.0163389i	−0.983901	+	0.000673803i
$589$	4.88265	−	2.81900i	0.201186	−	0.116155i
$590$	2.52106	−	18.7680i	0.103790	−	0.772665i
$591$	−10.0661	+	2.76141i	−0.414064	+	0.113589i
$592$	15.3933	+	0.161860i	0.632663	+	0.00665242i
$593$			39.9553i			1.64077i	0.571814	+	0.820383i	$0.306240\pi$
$593$			39.9553i			1.64077i	−0.571814	+	0.820383i	$0.693760\pi$
$594$	−26.9914	−	34.0904i	−1.10747	−	1.39875i
$595$	−16.4649			−0.674996
$596$	27.2975	+	7.46838i	1.11815	+	0.305917i
$597$	9.48384	+	34.5711i	0.388148	+	1.41490i
$598$	5.05146	−	37.6055i	0.206570	−	1.53780i
$599$	−3.19993	−	5.54244i	−0.130746	−	0.226458i	0.793219	−	0.608937i	$-0.208404\pi$
$599$	−3.19993	−	5.54244i	−0.130746	−	0.226458i	−0.923964	+	0.382479i	$0.875070\pi$
$600$	−2.98986	+	3.88082i	−0.122060	+	0.158434i
$601$	4.34886	−	7.53245i	0.177394	−	0.307255i	−0.763593	−	0.645697i	$-0.776567\pi$
$601$	4.34886	−	7.53245i	0.177394	−	0.307255i	0.940987	+	0.338442i	$0.109900\pi$
$602$	−3.36508	−	2.59620i	−0.137150	−	0.105813i
$603$	12.7357	+	7.15250i	0.518636	+	0.291272i
$604$	−32.6711	+	8.57035i	−1.32937	+	0.348723i
$605$	12.0064	−	20.7957i	0.488131	−	0.845467i
$606$	5.08808	−	0.687018i	0.206689	−	0.0279082i
$607$	−17.4808	+	10.0925i	−0.709523	+	0.409643i	−0.810884	−	0.585206i	$-0.801013\pi$
$607$	−17.4808	+	10.0925i	−0.709523	+	0.409643i	0.101361	+	0.994850i	$0.467680\pi$
$608$	17.4947	−	6.97861i	0.709505	−	0.283020i
$609$	−2.32004	+	2.34777i	−0.0940126	+	0.0951366i
$610$	5.43747	−	2.23555i	0.220157	−	0.0905147i
$611$			20.4490i			0.827279i
$612$	25.6511	+	6.69133i	1.03689	+	0.270481i
$613$			22.9023i			0.925015i	0.886615	+	0.462507i	$0.153050\pi$
$613$			22.9023i			0.925015i	−0.886615	+	0.462507i	$0.846950\pi$
$614$	5.51340	+	13.4101i	0.222503	+	0.541189i
$615$	−1.50775	−	0.394413i	−0.0607983	−	0.0159043i
$616$	7.65289	+	61.8976i	0.308344	+	2.49392i
$617$	14.8150	−	8.55344i	0.596429	−	0.344349i	−0.171206	−	0.985235i	$-0.554766\pi$
$617$	14.8150	−	8.55344i	0.596429	−	0.344349i	0.767636	+	0.640887i	$0.221433\pi$
$618$	−33.0564	−	13.5643i	−1.32972	−	0.545635i
$619$	15.2798	−	26.4653i	0.614145	−	1.06373i	−0.376388	−	0.926462i	$-0.622834\pi$
$619$	15.2798	−	26.4653i	0.614145	−	1.06373i	0.990534	−	0.137269i	$-0.0438325\pi$
$620$	−3.27573	+	0.859296i	−0.131556	+	0.0345102i
$621$	−30.8435	−	7.67794i	−1.23771	−	0.308105i
$622$	−12.6315	+	16.3725i	−0.506479	+	0.656475i
$623$	−19.1739	+	33.2102i	−0.768186	+	1.33054i
$624$	21.3891	+	21.5856i	0.856249	+	0.864116i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−44.4736	−	5.97403i	−1.77752	−	0.238770i
$627$	−33.0140	−	8.63614i	−1.31845	−	0.344894i
$628$	−4.88826	+	17.8670i	−0.195063	+	0.712970i
$629$	17.0039			0.677988
$630$	−9.50831	+	12.6319i	−0.378820	+	0.503265i
$631$		−	25.0243i		−	0.996201i	−0.867119	−	0.498100i	$-0.834031\pi$
$631$		−	25.0243i		−	0.996201i	0.867119	−	0.498100i	$-0.165969\pi$
$632$	−10.9956	−	14.5661i	−0.437380	−	0.579408i
$633$	0.0128131	+	0.0126617i	0.000509275	+	0.000503259i
$634$	5.21740	+	0.700841i	0.207209	+	0.0278339i
$635$	−13.2631	+	7.65746i	−0.526330	+	0.303877i
$636$	−4.67884	+	8.11683i	−0.185528	+	0.321853i
$637$	−26.1615	−	15.1043i	−1.03656	−	0.598456i
$638$	3.38808	+	2.61394i	0.134135	+	0.103487i
$639$	13.9523	−	8.27798i	0.551944	−	0.327472i
$640$	−11.2422	+	1.27010i	−0.444387	+	0.0502051i
$641$	−22.2700	−	12.8576i	−0.879614	−	0.507845i	−0.00908283	−	0.999959i	$-0.502891\pi$
$641$	−22.2700	−	12.8576i	−0.879614	−	0.507845i	−0.870531	+	0.492113i	$0.836225\pi$
$642$	0.313310	−	0.242065i	0.0123654	−	0.00955354i
$643$	6.10909	+	10.5812i	0.240919	+	0.417284i	0.960976	−	0.276631i	$-0.0892179\pi$
$643$	6.10909	+	10.5812i	0.240919	+	0.417284i	−0.720057	+	0.693914i	$0.755885\pi$
$644$	32.0676	+	32.4066i	1.26364	+	1.27700i
$645$	−1.34706	+	0.369537i	−0.0530405	+	0.0145505i
$646$	19.2419	−	7.91107i	0.757063	−	0.311257i
$647$	−8.68944			−0.341617			−0.170809	−	0.985304i	$-0.554638\pi$
$647$	−8.68944			−0.341617			−0.170809	+	0.985304i	$0.554638\pi$
$648$	19.9468	−	15.8153i	0.783585	−	0.621285i
$649$	−79.2318			−3.11012
$650$	−5.73698	+	2.35869i	−0.225023	+	0.0925153i
$651$	−10.5400	+	2.89143i	−0.413097	+	0.113324i
$652$	−13.7736	+	13.6296i	−0.539416	+	0.533774i
$653$	2.81801	+	4.88093i	0.110277	+	0.191006i	0.915882	−	0.401448i	$-0.131493\pi$
$653$	2.81801	+	4.88093i	0.110277	+	0.191006i	−0.805605	+	0.592453i	$0.798160\pi$
$654$	38.3279	−	29.6123i	1.49874	−	1.15793i
$655$	17.8355	+	10.2974i	0.696892	+	0.402351i
$656$	−1.76671	−	3.13571i	−0.0689783	−	0.122429i
$657$	−15.8156	+	9.38350i	−0.617026	+	0.366085i
$658$	−19.4537	−	15.0088i	−0.758386	−	0.585104i
$659$	0.804284	+	0.464354i	0.0313305	+	0.0180886i	0.515583	−	0.856839i	$-0.327575\pi$
$659$	0.804284	+	0.464354i	0.0313305	+	0.0180886i	−0.484253	+	0.874928i	$0.660909\pi$
$660$	17.7585	+	10.2367i	0.691249	+	0.398462i
$661$	−0.608542	+	0.351342i	−0.0236695	+	0.0136656i	−0.511788	−	0.859112i	$-0.671017\pi$
$661$	−0.608542	+	0.351342i	−0.0236695	+	0.0136656i	0.488119	+	0.872777i	$0.337683\pi$
$662$	−31.4061	−	4.21871i	−1.22063	−	0.163965i
$663$	23.8750	+	23.5929i	0.927228	+	0.916274i
$664$	−24.5895	−	32.5743i	−0.954257	−	1.26413i
$665$			12.4081i			0.481166i
$666$	9.81954	−	13.0453i	0.380500	−	0.505496i
$667$	3.12805			0.121119
$668$	9.53488	+	2.60867i	0.368916	+	0.100932i
$669$	−20.3850	−	5.33253i	−0.788131	−	0.206168i
$670$	−6.82437	−	0.916701i	−0.263648	−	0.0354153i
$671$	−12.2993	−	21.3030i	−0.474808	−	0.822392i
$672$	−36.2338	+	4.50507i	−1.39775	+	0.173787i
$673$	−1.58948	+	2.75306i	−0.0612700	+	0.106123i	−0.895033	−	0.445999i	$-0.852848\pi$
$673$	−1.58948	+	2.75306i	−0.0612700	+	0.106123i	0.833763	+	0.552122i	$0.186182\pi$
$674$	−10.6509	+	13.8053i	−0.410259	+	0.531759i
$675$	1.43412	+	4.99433i	0.0551992	+	0.192232i
$676$	3.16571	+	12.0680i	0.121758	+	0.464155i
$677$	10.6625	−	18.4679i	0.409791	−	0.709780i	−0.585075	−	0.810979i	$-0.698935\pi$
$677$	10.6625	−	18.4679i	0.409791	−	0.709780i	0.994866	+	0.101200i	$0.0322682\pi$
$678$	−19.5774	−	8.03331i	−0.751864	−	0.308518i
$679$	−27.7587	+	16.0265i	−1.06528	+	0.615041i
$680$	−12.4023	+	1.53339i	−0.475605	+	0.0588029i
$681$	22.5142	+	5.88950i	0.862746	+	0.225686i
$682$	5.38804	+	13.1052i	0.206319	+	0.501824i
$683$		−	50.1446i		−	1.91873i	−0.282170	−	0.959365i	$-0.591054\pi$
$683$		−	50.1446i		−	1.91873i	0.282170	−	0.959365i	$-0.408946\pi$
$684$	5.04264	−	19.3309i	0.192810	−	0.739136i
$685$			13.8508i			0.529211i
$686$	−0.549275	+	0.225827i	−0.0209714	+	0.00862213i
$687$	−32.0996	+	32.4833i	−1.22468	+	1.23932i
$688$	−2.77654	−	1.64220i	−0.105855	−	0.0626084i
$689$	−10.2732	+	5.93124i	−0.391378	+	0.225962i
$690$	14.8488	−	2.00495i	0.565283	−	0.0763272i
$691$	17.2695	−	29.9117i	0.656963	−	1.13789i	−0.324434	−	0.945908i	$-0.605174\pi$
$691$	17.2695	−	29.9117i	0.656963	−	1.13789i	0.981398	−	0.191986i	$-0.0614927\pi$
$692$	7.79001	+	29.6963i	0.296132	+	1.12889i
$693$	57.6785	+	32.3929i	2.19102	+	1.23051i
$694$	−17.4612	−	13.4715i	−0.662819	−	0.511372i
$695$	−3.39880	+	5.88689i	−0.128924	+	0.223303i
$696$	−1.52893	+	1.98454i	−0.0579538	+	0.0752237i
$697$	−1.98775	−	3.44288i	−0.0752914	−	0.130408i
$698$	3.56271	−	26.5225i	0.134850	−	1.00389i
$699$	−1.81067	−	6.60038i	−0.0684859	−	0.249649i
$700$	1.96684	−	7.18894i	0.0743394	−	0.271716i
$701$	−33.9751			−1.28322			−0.641611	−	0.767030i	$-0.721734\pi$
$701$	−33.9751			−1.28322			−0.641611	+	0.767030i	$0.721734\pi$
$702$	31.8880	−	4.69219i	1.20353	−	0.177095i
$703$		−	12.8143i		−	0.483299i
$704$	11.5292	+	45.9119i	0.434521	+	1.73037i
$705$	−7.78745	+	2.13632i	−0.293292	+	0.0804584i
$706$	1.05107	−	7.82471i	0.0395577	−	0.294487i
$707$	−6.76459	+	3.90554i	−0.254409	+	0.146883i
$708$	−0.0317656	−	46.3848i	−0.00119383	−	1.74325i
$709$	0.930498	+	0.537223i	0.0349456	+	0.0201758i	0.517371	−	0.855761i	$-0.326911\pi$
$709$	0.930498	+	0.537223i	0.0349456	+	0.0201758i	−0.482425	+	0.875937i	$0.660244\pi$
$710$	−4.67154	+	6.05505i	−0.175320	+	0.227242i
$711$	−19.3560	+	0.230042i	−0.725906	+	0.00862724i
$712$	−11.3499	+	26.8014i	−0.425357	+	1.00442i
$713$	8.97010	+	5.17889i	0.335933	+	0.193951i
$714$	−39.9680	+	5.39667i	−1.49576	+	0.201965i
$715$	12.9767	+	22.4764i	0.485303	+	0.840569i
$716$	23.6031	+	23.8526i	0.882090	+	0.891414i
$717$	−19.8336	−	19.5993i	−0.740699	−	0.731948i
$718$	−15.2512	−	37.0951i	−0.569168	−	1.38438i
$719$	11.6734			0.435343			0.217672	−	0.976022i	$-0.430154\pi$
$719$	11.6734			0.435343			0.217672	+	0.976022i	$0.430154\pi$
$720$	−5.98576	+	10.4005i	−0.223076	+	0.387604i
$721$	54.3602			2.02448
$722$	4.25559	+	10.3508i	0.158377	+	0.385216i
$723$	−0.864313	+	3.30407i	−0.0321441	+	0.122880i
$724$	10.9203	+	11.0358i	0.405851	+	0.410141i
$725$	−0.255686	−	0.442860i	−0.00949592	−	0.0164474i
$726$	22.3290	−	54.4162i	0.828706	−	2.01957i
$727$	−36.5594	−	21.1076i	−1.35591	−	0.782837i	−0.366844	−	0.930282i	$-0.619562\pi$
$727$	−36.5594	−	21.1076i	−1.35591	−	0.782837i	−0.989070	+	0.147445i	$0.952895\pi$
$728$	−42.5713	−	18.0282i	−1.57780	−	0.668170i
$729$	−0.962418	−	26.9828i	−0.0356451	−	0.999365i
$730$	5.29543	−	6.86370i	0.195993	−	0.254037i
$731$	−3.08577	−	1.78157i	−0.114131	−	0.0658938i
$732$	12.4665	−	7.20893i	0.460776	−	0.266450i
$733$	25.3075	−	14.6113i	0.934755	−	0.539681i	0.0464428	−	0.998921i	$-0.485211\pi$
$733$	25.3075	−	14.6113i	0.934755	−	0.539681i	0.888312	+	0.459240i	$0.151878\pi$
$734$	0.255188	−	1.89974i	0.00941916	−	0.0701208i
$735$	3.01897	−	11.5408i	0.111357	−	0.425690i
$736$	27.1731	+	21.4239i	1.00161	+	0.789696i
$737$			28.8101i			1.06123i
$738$	−3.78928	−	0.463230i	−0.139485	−	0.0170517i
$739$	−11.5598			−0.425235			−0.212617	−	0.977136i	$-0.568199\pi$
$739$	−11.5598			−0.425235			−0.212617	+	0.977136i	$0.568199\pi$
$740$	−2.03122	+	7.42425i	−0.0746689	+	0.272921i
$741$	17.7798	−	17.9924i	0.653159	−	0.660967i
$742$	1.89758	−	14.1265i	0.0696623	−	0.518600i
$743$	17.2122	+	29.8125i	0.631456	+	1.09371i	0.987254	+	0.159151i	$0.0508756\pi$
$743$	17.2122	+	29.8125i	0.631456	+	1.09371i	−0.355799	+	0.934563i	$0.615791\pi$
$744$	−7.67005	+	3.15959i	−0.281198	+	0.115836i
$745$	−7.07518	+	12.2546i	−0.259215	+	0.448973i
$746$	34.6386	+	26.7241i	1.26821	+	0.978439i
$747$	−43.2860	+	0.514445i	−1.58375	+	0.0188226i
$748$	13.2672	+	50.5759i	0.485096	+	1.84924i
$749$	−0.301175	+	0.521651i	−0.0110047	+	0.0190607i
$750$	−1.49759	−	1.93836i	−0.0546841	−	0.0707789i
$751$	9.12070	−	5.26584i	0.332819	−	0.192153i	−0.324273	−	0.945964i	$-0.605120\pi$
$751$	9.12070	−	5.26584i	0.332819	−	0.192153i	0.657092	+	0.753810i	$0.271786\pi$
$752$	−16.0514	−	9.49369i	−0.585334	−	0.346199i
$753$	−2.92149	−	10.6496i	−0.106465	−	0.388093i
$754$	−2.93373	+	1.20616i	−0.106840	+	0.0439259i
$755$		−	16.8882i		−	0.614626i
$756$	−18.9407	+	33.7798i	−0.688868	+	1.22856i
$757$			41.2042i			1.49759i	0.662801	+	0.748796i	$0.269368\pi$
$757$			41.2042i			1.49759i	−0.662801	+	0.748796i	$0.730632\pi$
$758$	−16.2360	−	39.4904i	−0.589717	−	1.43436i
$759$	−16.5854	−	60.4584i	−0.602013	−	2.19450i
$760$	1.15558	+	9.34646i	0.0419172	+	0.339032i
$761$	−25.2952	+	14.6042i	−0.916950	+	0.529402i	−0.882661	−	0.470010i	$-0.844250\pi$
$761$	−25.2952	+	14.6042i	−0.916950	+	0.529402i	−0.0342895	+	0.999412i	$0.510917\pi$
$762$	−29.6858	+	22.9354i	−1.07540	+	0.830862i
$763$	−36.8434	+	63.8147i	−1.33382	+	2.31025i
$764$	−10.0839	−	38.4408i	−0.364822	−	1.39074i
$765$	−6.49049	+	11.5569i	−0.234664	+	0.417841i
$766$	−21.6654	+	28.0817i	−0.782802	+	1.01463i
$767$	29.3655	−	50.8625i	1.06033	−	1.83654i
$768$	−26.8737	+	6.76795i	−0.969721	+	0.244217i
$769$	−5.94893	−	10.3039i	−0.214524	−	0.371567i	0.738601	−	0.674143i	$-0.235487\pi$
$769$	−5.94893	−	10.3039i	−0.214524	−	0.371567i	−0.953125	+	0.302576i	$0.902153\pi$
$770$	−30.9068	−	4.15164i	−1.11381	−	0.149615i
$771$	−12.7674	+	12.9201i	−0.459808	+	0.465305i
$772$	−23.2642	−	6.36489i	−0.837295	−	0.229077i
$773$	22.8720			0.822650			0.411325	−	0.911489i	$-0.365066\pi$
$773$	22.8720			0.822650			0.411325	+	0.911489i	$0.365066\pi$
$774$	−3.14882	+	1.33856i	−0.113182	+	0.0481135i
$775$		−	1.69328i		−	0.0608244i
$776$	−19.4168	+	14.6572i	−0.697024	+	0.526164i
$777$	−6.28660	+	24.0322i	−0.225530	+	0.862151i
$778$	−18.8913	−	2.53762i	−0.677284	−	0.0909780i
$779$	−2.59459	+	1.49798i	−0.0929607	+	0.0536709i
$780$	−13.1532	+	7.60602i	−0.470960	+	0.272339i
$781$	27.7114	+	15.9992i	0.991593	+	0.572497i
$782$	30.2616	+	23.3472i	1.08215	+	0.834893i
$783$	0.733366	+	2.55395i	0.0262084	+	0.0912709i
$784$	24.0019	−	13.5230i	0.857209	−	0.482965i
$785$	−8.02095	−	4.63090i	−0.286280	−	0.165284i
$786$	46.6702	+	19.1505i	1.66467	+	0.683076i
$787$	15.1722	+	26.2791i	0.540832	+	0.936748i	0.998857	+	0.0478086i	$0.0152238\pi$
$787$	15.1722	+	26.2791i	0.540832	+	0.936748i	−0.458025	+	0.888939i	$0.651443\pi$
$788$	8.56728	−	8.47767i	0.305197	−	0.302004i
$789$	−10.9512	+	41.8640i	−0.389874	+	1.49040i
$790$	8.43969	−	3.46987i	0.300271	−	0.123452i
$791$	32.1943			1.14470
$792$	46.4634	+	19.0285i	1.65100	+	0.676147i
$793$	18.2338			0.647502
$794$	13.6217	−	5.60039i	0.483416	−	0.198750i
$795$	−3.33200	−	3.29263i	−0.118174	−	0.116778i
$796$	−29.1158	−	29.4236i	−1.03198	−	1.04289i
$797$	1.97218	+	3.41592i	0.0698584	+	0.120998i	0.898839	−	0.438279i	$-0.144412\pi$
$797$	1.97218	+	3.41592i	0.0698584	+	0.120998i	−0.828980	+	0.559278i	$0.811079\pi$
$798$	4.06697	+	30.1202i	0.143969	+	1.06624i
$799$	−17.8391	−	10.2994i	−0.631100	−	0.364366i
$800$	0.812015	−	5.59827i	0.0287091	−	0.197929i
$801$	15.7522	+	26.5499i	0.556577	+	0.938094i
$802$	−1.43430	−	1.10658i	−0.0506468	−	0.0390746i
$803$	−31.4123	−	18.1359i	−1.10852	−	0.640002i
$804$	−16.8664	+	0.0115505i	−0.594830	+	0.000407356i
$805$	−19.7414	+	11.3977i	−0.695792	+	0.401716i
$806$	−10.4098	−	1.39832i	−0.366669	−	0.0492538i
$807$	40.6077	−	11.1398i	1.42946	−	0.392140i
$808$	−4.73173	+	3.57186i	−0.166462	+	0.125657i
$809$		−	1.21675i		−	0.0427785i	−0.999771	−	0.0213893i	$-0.993191\pi$
$809$		−	1.21675i		−	0.0427785i	0.999771	−	0.0213893i	$-0.00680893\pi$
$810$	5.11824	+	11.6535i	0.179837	+	0.409462i
$811$	−28.4463			−0.998883			−0.499442	−	0.866348i	$-0.666461\pi$
$811$	−28.4463			−0.998883			−0.499442	+	0.866348i	$0.666461\pi$
$812$	1.00578	−	3.67621i	0.0352961	−	0.129010i
$813$	−1.97881	−	7.21328i	−0.0693998	−	0.252981i
$814$	31.9185	+	4.28754i	1.11874	+	0.150278i
$815$	−4.84431	−	8.39059i	−0.169689	−	0.293909i
$816$	−29.6034	+	7.78731i	−1.03633	+	0.272611i
$817$	−1.34261	+	2.32546i	−0.0469719	+	0.0813577i
$818$	10.3812	−	13.4557i	0.362970	−	0.470466i
$819$	−42.1718	+	25.0208i	−1.47360	+	0.874297i
$820$	1.74069	−	0.456621i	0.0607874	−	0.0159459i
$821$	−20.0669	+	34.7570i	−0.700341	+	1.21303i	0.268005	+	0.963417i	$0.413635\pi$
$821$	−20.0669	+	34.7570i	−0.700341	+	1.21303i	−0.968347	+	0.249609i	$0.919698\pi$
$822$	4.53984	+	33.6222i	0.158345	+	1.17271i
$823$	26.2706	−	15.1673i	0.915736	−	0.528700i	0.0334636	−	0.999440i	$-0.489346\pi$
$823$	26.2706	−	15.1673i	0.915736	−	0.528700i	0.882272	+	0.470740i	$0.156013\pi$
$824$	40.9470	−	5.06261i	1.42646	−	0.176364i
$825$	−7.20383	+	7.28995i	−0.250805	+	0.253804i
$826$	26.8338	+	65.2674i	0.933669	+	2.27094i
$827$		−	51.9742i		−	1.80732i	−0.428252	−	0.903659i	$-0.640870\pi$
$827$		−	51.9742i		−	1.80732i	0.428252	−	0.903659i	$-0.359130\pi$
$828$	35.3876	−	9.73389i	1.22981	−	0.338276i
$829$		−	14.1029i		−	0.489815i	−0.969546	−	0.244908i	$-0.921242\pi$
$829$		−	14.1029i		−	0.489815i	0.969546	−	0.244908i	$-0.0787576\pi$
$830$	18.8738	−	7.75971i	0.655118	−	0.269343i
$831$	−1.05558	−	0.276129i	−0.0366175	−	0.00957880i
$832$	−33.7460	−	9.61513i	−1.16993	−	0.333345i
$833$	26.3530	−	15.2149i	0.913079	−	0.527166i
$834$	−6.32092	+	15.4042i	−0.218876	+	0.533405i
$835$	−2.47132	+	4.28046i	−0.0855237	+	0.148131i
$836$	38.1144	−	9.99826i	1.31821	−	0.345797i
$837$	−2.12537	+	8.53798i	−0.0734637	+	0.295116i
$838$	−16.6408	−	12.8385i	−0.574846	−	0.443500i
$839$	1.69288	−	2.93215i	0.0584445	−	0.101229i	−0.835323	−	0.549760i	$-0.814719\pi$
$839$	1.69288	−	2.93215i	0.0584445	−	0.101229i	0.893767	+	0.448531i	$0.148053\pi$
$840$	2.41811	−	18.0955i	0.0834329	−	0.624355i
$841$	14.3692	+	24.8883i	0.495491	+	0.858216i
$842$	4.68228	−	34.8572i	0.161362	−	1.20126i
$843$	25.5190	+	6.67554i	0.878923	+	0.229918i
$844$	−0.0200631	−	0.00548911i	−0.000690602	−	0.000188943i
$845$	−6.23817			−0.214600
$846$	−18.2035	+	7.73830i	−0.625850	+	0.266048i
$847$			89.4856i			3.07476i
$848$	0.113746	−	10.8176i	0.00390606	−	0.371477i
$849$	25.2024	+	24.9047i	0.864944	+	0.854726i
$850$	0.831855	−	6.19273i	0.0285324	−	0.212409i
$851$	20.3876	−	11.7708i	0.698877	−	0.403497i
$852$	−9.35534	+	16.2296i	−0.320509	+	0.556016i
$853$	7.01390	+	4.04948i	0.240151	+	0.138651i	0.615246	−	0.788335i	$-0.289057\pi$
$853$	7.01390	+	4.04948i	0.240151	+	0.138651i	−0.375095	+	0.926986i	$0.622390\pi$
$854$	−13.3829	+	17.3463i	−0.457954	+	0.593580i
$855$	8.70938	+	4.89129i	0.297855	+	0.167279i
$856$	−0.178280	+	0.420984i	−0.00609348	+	0.0143889i
$857$	−29.2288	−	16.8752i	−0.998436	−	0.576447i	−0.0906507	−	0.995883i	$-0.528895\pi$
$857$	−29.2288	−	16.8752i	−0.998436	−	0.576447i	−0.907785	+	0.419436i	$0.862228\pi$
$858$	38.8676	+	50.3072i	1.32692	+	1.71746i
$859$	−4.78873	−	8.29433i	−0.163389	−	0.282999i	0.772693	−	0.634780i	$-0.218909\pi$
$859$	−4.78873	−	8.29433i	−0.163389	−	0.282999i	−0.936082	+	0.351781i	$0.885576\pi$
$860$	1.14649	−	1.13449i	0.0390949	−	0.0386859i
$861$	5.60086	−	1.53647i	0.190877	−	0.0523629i
$862$	−0.924594	−	2.24887i	−0.0314918	−	0.0765968i
$863$	1.65377			0.0562950			0.0281475	−	0.999604i	$-0.491039\pi$
$863$	1.65377			0.0562950			0.0281475	+	0.999604i	$0.491039\pi$
$864$	−11.1212	+	27.2088i	−0.378353	+	0.925662i
$865$	−15.3505			−0.521934
$866$	−6.80512	−	16.5520i	−0.231248	−	0.562458i
$867$	−4.21085	+	1.15515i	−0.143008	+	0.0392311i
$868$	8.97065	−	8.87682i	0.304484	−	0.301299i
$869$	−19.0901	−	33.0651i	−0.647588	−	1.12166i
$870$	−0.765822	−	0.991221i	−0.0259638	−	0.0336055i
$871$	−18.4945	−	10.6778i	−0.626663	−	0.361804i
$872$	−21.8094	+	51.5000i	−0.738558	+	1.74401i
$873$	0.306649	+	25.8018i	0.0103785	+	0.873260i
$874$	17.5946	−	22.8054i	0.595147	−	0.771404i
$875$	3.22730	+	1.86328i	0.109103	+	0.0629905i
$876$	10.6047	−	18.3970i	0.358301	−	0.621579i
$877$	34.2779	−	19.7904i	1.15748	−	0.668273i	0.206783	−	0.978387i	$-0.433700\pi$
$877$	34.2779	−	19.7904i	1.15748	−	0.668273i	0.950699	+	0.310114i	$0.100367\pi$
$878$	4.47191	−	33.2910i	0.150920	−	1.12352i
$879$	4.72955	+	4.67368i	0.159524	+	0.157639i
$880$	−23.6674	−	0.248861i	−0.797826	−	0.00838911i
$881$			1.03774i			0.0349624i	0.999847	+	0.0174812i	$0.00556473\pi$
$881$			1.03774i			0.0349624i	−0.999847	+	0.0174812i	$0.994435\pi$
$882$	3.54573	−	29.0045i	0.119391	−	0.976631i
$883$	18.7650			0.631492			0.315746	−	0.948844i	$-0.397745\pi$
$883$	18.7650			0.631492			0.315746	+	0.948844i	$0.397745\pi$
$884$	−37.3842	−	10.2280i	−1.25737	−	0.344005i
$885$	22.4374	+	5.86942i	0.754226	+	0.197298i
$886$	−1.22432	+	9.11442i	−0.0411318	+	0.306205i
$887$	5.67677	+	9.83246i	0.190607	+	0.330142i	0.945452	−	0.325762i	$-0.105621\pi$
$887$	5.67677	+	9.83246i	0.190607	+	0.330142i	−0.754844	+	0.655904i	$0.772288\pi$
$888$	−2.49727	+	18.6878i	−0.0838028	+	0.627123i
$889$	28.5360	−	49.4259i	0.957068	−	1.65769i
$890$	−11.5222	−	8.88950i	−0.386225	−	0.297977i
$891$	45.4739	−	27.7158i	1.52343	−	0.928515i
$892$	23.5344	−	6.17360i	0.787990	−	0.206707i
$893$	−7.76170	+	13.4437i	−0.259735	+	0.449875i
$894$	−13.1581	+	32.0665i	−0.440072	+	1.07246i
$895$	−14.5305	+	8.38918i	−0.485701	+	0.280419i
$896$	33.9154	−	25.0464i	1.13303	−	0.836741i
$897$	44.9580	+	11.7606i	1.50111	+	0.392675i
$898$	20.0553	−	8.24548i	0.669254	−	0.275155i
$899$		−	0.865894i		−	0.0288792i
$900$	−4.27066	−	4.21443i	−0.142355	−	0.140481i
$901$		−	11.9493i		−	0.398090i
$902$	−2.86314	−	6.96396i	−0.0953323	−	0.231875i
$903$	3.65882	−	3.70257i	0.121758	−	0.123214i
$904$	24.2505	−	2.99828i	0.806560	−	0.0997214i
$905$	−6.72275	+	3.88138i	−0.223472	+	0.129021i
$906$	−5.53542	−	40.9955i	−0.183902	−	1.36199i
$907$	−18.9547	+	32.8305i	−0.629380	+	1.09012i	0.358297	+	0.933608i	$0.383358\pi$
$907$	−18.9547	+	32.8305i	−0.629380	+	1.09012i	−0.987676	+	0.156510i	$0.949976\pi$
$908$	−25.9925	+	6.81841i	−0.862592	+	0.226277i
$909$	0.0747281	+	6.28771i	0.00247857	+	0.208550i
$910$	14.1201	−	18.3018i	0.468076	−	0.606699i
$911$	20.7850	−	36.0006i	0.688636	−	1.19275i	−0.283643	−	0.958930i	$-0.591543\pi$
$911$	20.7850	−	36.0006i	0.688636	−	1.19275i	0.972279	−	0.233823i	$-0.0751236\pi$
$912$	5.86859	+	22.3094i	0.194328	+	0.738738i
$913$	−42.6915	−	73.9438i	−1.41288	−	2.44718i
$914$	30.3530	+	4.07724i	1.00399	+	0.134863i
$915$	1.90489	+	6.94385i	0.0629738	+	0.229557i
$916$	13.9158	−	50.8634i	0.459791	−	1.68057i
$917$	−76.7476			−2.53443
$918$	−11.9674	+	30.1813i	−0.394985	+	0.996132i
$919$			27.5954i			0.910287i	0.890418	+	0.455143i	$0.150412\pi$
$919$			27.5954i			0.910287i	−0.890418	+	0.455143i	$0.849588\pi$
$920$	−13.8088	+	10.4239i	−0.455263	+	0.343666i
$921$	−17.1252	+	4.69793i	−0.564295	+	0.154802i
$922$	−2.74497	−	0.368726i	−0.0904009	−	0.0121433i
$923$	−20.5413	+	11.8595i	−0.676124	+	0.390360i
$924$	−76.3859	+	0.0523112i	−2.51291	+	0.00172091i
$925$	−3.33294	−	1.92427i	−0.109586	−	0.0632698i
$926$	−24.7631	−	19.1050i	−0.813766	−	0.627830i
$927$	21.4289	−	38.1560i	0.703816	−	1.25321i
$928$	0.415241	−	2.86279i	0.0136310	−	0.0939758i
$929$	−8.18403	−	4.72505i	−0.268509	−	0.155024i	0.359701	−	0.933068i	$-0.382879\pi$
$929$	−8.18403	−	4.72505i	−0.268509	−	0.155024i	−0.628210	+	0.778044i	$0.716212\pi$
$930$	−0.555002	−	4.11037i	−0.0181992	−	0.134784i
$931$	−11.4661	−	19.8599i	−0.375786	−	0.650881i
$932$	5.55884	+	5.61760i	0.182086	+	0.184011i
$933$	−18.0145	−	17.8016i	−0.589767	−	0.582800i
$934$	11.2317	−	4.61776i	0.367511	−	0.151098i
$935$	−26.1435			−0.854985
$936$	−29.4359	+	22.7745i	−0.962141	+	0.744408i
$937$	37.8644			1.23698			0.618488	−	0.785794i	$-0.287745\pi$
$937$	37.8644			1.23698			0.618488	+	0.785794i	$0.287745\pi$
$938$	23.7324	−	9.75726i	0.774890	−	0.318586i
$939$	13.9085	−	53.1690i	0.453887	−	1.73510i
$940$	6.62792	−	6.55859i	0.216179	−	0.213918i
$941$	20.1834	+	34.9587i	0.657960	+	1.13962i	0.981143	+	0.193284i	$0.0619139\pi$
$941$	20.1834	+	34.9587i	0.657960	+	1.13962i	−0.323182	+	0.946337i	$0.604753\pi$
$942$	−20.9884	−	8.61232i	−0.683840	−	0.280605i
$943$	−4.76661	−	2.75200i	−0.155222	−	0.0896176i
$944$	26.2911	+	46.6639i	0.855703	+	1.51878i
$945$	−13.9342	−	13.4460i	−0.453279	−	0.437400i
$946$	−5.34318	−	4.12233i	−0.173722	−	0.134028i
$947$	37.9584	+	21.9153i	1.23348	+	0.712151i	0.967754	−	0.251897i	$-0.0810544\pi$
$947$	37.9584	+	21.9153i	1.23348	+	0.712151i	0.265728	+	0.964048i	$0.414388\pi$
$948$	19.3497	−	11.1892i	0.628449	−	0.363409i
$949$	23.2845	−	13.4433i	0.755848	−	0.436389i
$950$	−4.66689	−	0.626893i	−0.151414	−	0.0203391i
$951$	−1.63167	+	6.23749i	−0.0529105	+	0.202264i
$952$	37.1687	−	28.0577i	1.20465	−	0.909355i
$953$			50.6972i			1.64224i	0.570754	+	0.821121i	$0.306651\pi$
$953$			50.6972i			1.64224i	−0.570754	+	0.821121i	$0.693349\pi$
$954$	−9.16751	−	6.90061i	−0.296809	−	0.223416i
$955$	19.8707			0.643000
$956$	31.0560	+	8.49668i	1.00442	+	0.274802i
$957$	−3.68383	+	3.72787i	−0.119081	+	0.120505i
$958$	9.64115	+	1.29507i	0.311492	+	0.0418419i
$959$	−25.8079	−	44.7007i	−0.833382	−	1.44346i
$960$	0.136203	−	13.8557i	0.00439592	−	0.447192i
$961$	−14.0664	+	24.3637i	−0.453755	+	0.785927i
$962$	−14.5823	+	18.9009i	−0.470151	+	0.609389i
$963$	0.247429	+	0.417034i	0.00797327	+	0.0134387i
$964$	−1.00063	−	3.81452i	−0.0322283	−	0.122858i
$965$	6.02978	−	10.4439i	0.194106	−	0.336201i
$966$	−44.1857	+	34.1380i	−1.42165	+	1.09837i
$967$	−4.07877	+	2.35488i	−0.131165	+	0.0757279i	−0.564147	−	0.825675i	$-0.690795\pi$
$967$	−4.07877	+	2.35488i	−0.131165	+	0.0757279i	0.432982	+	0.901403i	$0.357461\pi$
$968$	8.33387	+	67.4054i	0.267861	+	2.16649i
$969$	6.74096	+	24.5726i	0.216551	+	0.789386i
$970$	−4.62539	−	11.2502i	−0.148512	−	0.361223i
$971$		−	33.2090i		−	1.06573i	−0.846201	−	0.532864i	$-0.821116\pi$
$971$		−	33.2090i		−	1.06573i	0.846201	−	0.532864i	$-0.178884\pi$
$972$	16.2440	+	26.6108i	0.521026	+	0.853541i
$973$		−	25.3317i		−	0.812098i
$974$	−36.8293	+	15.1419i	−1.18009	+	0.485177i
$975$	−2.00982	−	7.32633i	−0.0643657	−	0.234630i
$976$	−8.46525	+	14.3126i	−0.270966	+	0.458134i
$977$	−2.92167	+	1.68683i	−0.0934725	+	0.0539664i	−0.546008	−	0.837780i	$-0.683853\pi$
$977$	−2.92167	+	1.68683i	−0.0934725	+	0.0539664i	0.452535	+	0.891747i	$0.350520\pi$
$978$	−14.5095	−	18.7800i	−0.463964	−	0.600519i
$979$	−30.4450	+	52.7322i	−0.973025	+	1.68533i
$980$	3.49514	+	13.3238i	0.111648	+	0.425614i
$981$	30.2685	+	51.0167i	0.966399	+	1.62884i
$982$	−1.88644	−	1.45541i	−0.0601989	−	0.0464441i
$983$	−20.8933	+	36.1882i	−0.666391	+	1.15422i	0.312515	+	0.949913i	$0.398829\pi$
$983$	−20.8933	+	36.1882i	−0.666391	+	1.15422i	−0.978906	+	0.204311i	$0.934505\pi$
$984$	4.07578	−	1.67897i	0.129931	−	0.0535236i
$985$	3.01319	+	5.21900i	0.0960082	+	0.166291i
$986$	0.425387	−	3.16678i	0.0135471	−	0.100851i
$987$	21.1519	−	21.4048i	0.673272	−	0.681322i
$988$	−7.70792	+	28.1730i	−0.245221	+	0.896304i
$989$	−4.93311			−0.156864
$990$	−15.0976	+	20.0573i	−0.479833	+	0.637462i
$991$		−	12.0603i		−	0.383107i	−0.981482	−	0.191554i	$-0.938647\pi$
$991$		−	12.0603i		−	0.383107i	0.981482	−	0.191554i	$-0.0613526\pi$
$992$	5.93048	−	7.52195i	0.188293	−	0.238822i
$993$	9.82182	−	37.5466i	0.311686	−	1.19150i
$994$	3.79421	−	28.2459i	0.120345	−	0.895906i
$995$	17.9242	−	10.3485i	0.568235	−	0.328071i
$996$	43.2720	−	25.0226i	1.37112	−	0.792872i
$997$	−15.4574	−	8.92433i	−0.489540	−	0.282636i	0.234843	−	0.972033i	$-0.424542\pi$
$997$	−15.4574	−	8.92433i	−0.489540	−	0.282636i	−0.724384	+	0.689397i	$0.757876\pi$
$998$	−12.4352	+	16.1180i	−0.393631	+	0.510207i
$999$	14.3903	+	13.8862i	0.455288	+	0.439339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.a.11.8	✓	48
3.2	odd	2		1080.2.bm.b.251.17		48
4.3	odd	2		1440.2.cc.a.911.2		48
8.3	odd	2		360.2.bm.b.11.1	yes	48
8.5	even	2		1440.2.cc.b.911.2		48
9.4	even	3		1080.2.bm.a.611.24		48
9.5	odd	6		360.2.bm.b.131.1	yes	48
12.11	even	2		4320.2.cc.b.1871.2		48
24.5	odd	2		4320.2.cc.a.1871.23		48
24.11	even	2		1080.2.bm.a.251.24		48
36.23	even	6		1440.2.cc.b.1391.2		48
36.31	odd	6		4320.2.cc.a.3311.23		48
72.5	odd	6		1440.2.cc.a.1391.2		48
72.13	even	6		4320.2.cc.b.3311.2		48
72.59	even	6	inner	360.2.bm.a.131.8	yes	48
72.67	odd	6		1080.2.bm.b.611.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.8	✓	48	1.1	even	1	trivial
360.2.bm.a.131.8	yes	48	72.59	even	6	inner
360.2.bm.b.11.1	yes	48	8.3	odd	2
360.2.bm.b.131.1	yes	48	9.5	odd	6
1080.2.bm.a.251.24		48	24.11	even	2
1080.2.bm.a.611.24		48	9.4	even	3
1080.2.bm.b.251.17		48	3.2	odd	2
1080.2.bm.b.611.17		48	72.67	odd	6
1440.2.cc.a.911.2		48	4.3	odd	2
1440.2.cc.a.1391.2		48	72.5	odd	6
1440.2.cc.b.911.2		48	8.5	even	2
1440.2.cc.b.1391.2		48	36.23	even	6
4320.2.cc.a.1871.23		48	24.5	odd	2
4320.2.cc.a.3311.23		48	36.31	odd	6
4320.2.cc.b.1871.2		48	12.11	even	2
4320.2.cc.b.3311.2		48	72.13	even	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537760 - 1.30798i) q^{2} +(1.67034 - 0.458221i) q^{3} +(-1.42163 + 1.40676i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.49759 - 1.93836i) q^{6} +(3.22730 + 1.86328i) q^{7} +(2.60451 + 1.10297i) q^{8} +(2.58007 - 1.53077i) q^{9} +O(q^{10})\)	\(q+(-0.537760 - 1.30798i) q^{2} +(1.67034 - 0.458221i) q^{3} +(-1.42163 + 1.40676i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.49759 - 1.93836i) q^{6} +(3.22730 + 1.86328i) q^{7} +(2.60451 + 1.10297i) q^{8} +(2.58007 - 1.53077i) q^{9} +(-0.863865 + 1.11970i) q^{10} +(5.12442 + 2.95858i) q^{11} +(-1.73000 + 3.00119i) q^{12} +(-3.79850 + 2.19307i) q^{13} +(0.701627 - 5.22325i) q^{14} +(-1.23200 - 1.21745i) q^{15} +(0.0420575 - 3.99978i) q^{16} -4.41825i q^{17} +(-3.38967 - 2.55149i) q^{18} -3.32963 q^{19} +(1.92910 + 0.527787i) q^{20} +(6.24449 + 1.63350i) q^{21} +(1.11407 - 8.29365i) q^{22} +(-3.05850 - 5.29747i) q^{23} +(4.85582 + 0.648885i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.91117 + 3.78903i) q^{26} +(3.60816 - 3.73915i) q^{27} +(-7.20922 + 1.89114i) q^{28} +(-0.255686 + 0.442860i) q^{29} +(-0.929876 + 2.26613i) q^{30} +(-1.46642 + 0.846640i) q^{31} +(-5.25425 + 2.09591i) q^{32} +(9.91520 + 2.59372i) q^{33} +(-5.77899 + 2.37596i) q^{34} -3.72657i q^{35} +(-1.51447 + 5.80572i) q^{36} +3.84855i q^{37} +(1.79054 + 4.35510i) q^{38} +(-5.33988 + 5.40372i) q^{39} +(-0.347059 - 2.80705i) q^{40} +(0.779241 - 0.449895i) q^{41} +(-1.22145 - 9.04610i) q^{42} +(0.403230 - 0.698415i) q^{43} +(-11.4470 + 3.00281i) q^{44} +(-2.61572 - 1.46902i) q^{45} +(-5.28425 + 6.84922i) q^{46} +(2.33110 - 4.03758i) q^{47} +(-1.76253 - 6.70026i) q^{48} +(3.44366 + 5.96459i) q^{49} +(1.40162 + 0.188277i) q^{50} +(-2.02454 - 7.37998i) q^{51} +(2.31495 - 8.46131i) q^{52} +2.70454 q^{53} +(-6.83105 - 2.70864i) q^{54} -5.91717i q^{55} +(6.35040 + 8.41254i) q^{56} +(-5.56162 + 1.52571i) q^{57} +(0.716750 + 0.0962794i) q^{58} +(-11.5962 + 6.69508i) q^{59} +(3.46410 - 0.00237231i) q^{60} +(-3.60020 - 2.07857i) q^{61} +(1.89597 + 1.46276i) q^{62} +(11.1789 - 0.132859i) q^{63} +(5.56694 + 5.74537i) q^{64} +(3.79850 + 2.19307i) q^{65} +(-1.93946 - 14.3637i) q^{66} +(2.43445 + 4.21659i) q^{67} +(6.21542 + 6.28112i) q^{68} +(-7.53614 - 7.44711i) q^{69} +(-4.87428 + 2.00400i) q^{70} +5.40772 q^{71} +(8.40819 - 1.14118i) q^{72} -6.12993 q^{73} +(5.03383 - 2.06959i) q^{74} +(-0.438339 + 1.67567i) q^{75} +(4.73350 - 4.68399i) q^{76} +(11.0254 + 19.0965i) q^{77} +(9.93954 + 4.07856i) q^{78} +(-5.58799 - 3.22623i) q^{79} +(-3.48494 + 1.96347i) q^{80} +(4.31349 - 7.89898i) q^{81} +(-1.00750 - 0.777297i) q^{82} +(-12.4965 - 7.21485i) q^{83} +(-11.1753 + 6.46226i) q^{84} +(-3.82632 + 2.20913i) q^{85} +(-1.13035 - 0.151838i) q^{86} +(-0.224154 + 0.856888i) q^{87} +(10.0834 + 13.3577i) q^{88} +10.2904i q^{89} +(-0.514820 + 4.21129i) q^{90} -16.3452 q^{91} +(11.8003 + 3.22847i) q^{92} +(-2.06148 + 2.08612i) q^{93} +(-6.53465 - 0.877784i) q^{94} +(1.66482 + 2.88355i) q^{95} +(-7.81599 + 5.90849i) q^{96} +(-4.30061 + 7.44888i) q^{97} +(5.94971 - 7.71175i) q^{98} +(17.7502 - 0.210958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

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