LMFDB - Embedded newform 240.2.bl.a.229.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.13
Character	$\chi$	$=$	240.229
Dual form			240.2.bl.a.109.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.345118 - 1.37146i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.76179 - 0.946629i) q^{4} +(-0.561697 + 2.16437i) q^{5} +(-1.21380 + 0.725731i) q^{6} -4.51614 q^{7} +(-1.90629 + 2.08952i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.345118 - 1.37146i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.76179 - 0.946629i) q^{4} +(-0.561697 + 2.16437i) q^{5} +(-1.21380 + 0.725731i) q^{6} -4.51614 q^{7} +(-1.90629 + 2.08952i) q^{8} +1.00000i q^{9} +(2.77449 + 1.51731i) q^{10} +(-3.44000 - 3.44000i) q^{11} +(0.576403 + 1.91514i) q^{12} +(0.113618 + 0.113618i) q^{13} +(-1.55860 + 6.19370i) q^{14} +(1.92762 - 1.13326i) q^{15} +(2.20779 + 3.33552i) q^{16} -5.03305i q^{17} +(1.37146 + 0.345118i) q^{18} +(-0.992498 + 0.992498i) q^{19} +(3.03845 - 3.28144i) q^{20} +(3.19340 + 3.19340i) q^{21} +(-5.90502 + 3.53061i) q^{22} +8.00517 q^{23} +(2.82546 - 0.129563i) q^{24} +(-4.36899 - 2.43144i) q^{25} +(0.195033 - 0.116610i) q^{26} +(0.707107 - 0.707107i) q^{27} +(7.95648 + 4.27512i) q^{28} +(-1.01722 + 1.01722i) q^{29} +(-0.888962 - 3.03476i) q^{30} -6.42697 q^{31} +(5.33647 - 1.87673i) q^{32} +4.86490i q^{33} +(-6.90261 - 1.73700i) q^{34} +(2.53670 - 9.77461i) q^{35} +(0.946629 - 1.76179i) q^{36} +(-1.63459 + 1.63459i) q^{37} +(1.01864 + 1.70370i) q^{38} -0.160680i q^{39} +(-3.45173 - 5.29958i) q^{40} -3.35633i q^{41} +(5.48170 - 3.27751i) q^{42} +(-5.68196 + 5.68196i) q^{43} +(2.80414 + 9.31696i) q^{44} +(-2.16437 - 0.561697i) q^{45} +(2.76273 - 10.9787i) q^{46} -9.10261i q^{47} +(0.797427 - 3.91971i) q^{48} +13.3956 q^{49} +(-4.84243 + 5.15275i) q^{50} +(-3.55890 + 3.55890i) q^{51} +(-0.0926163 - 0.307724i) q^{52} +(-3.27113 + 3.27113i) q^{53} +(-0.725731 - 1.21380i) q^{54} +(9.37767 - 5.51320i) q^{55} +(8.60906 - 9.43655i) q^{56} +1.40360 q^{57} +(1.04401 + 1.74614i) q^{58} +(-5.30843 - 5.30843i) q^{59} +(-4.46883 + 0.171823i) q^{60} +(-5.87487 + 5.87487i) q^{61} +(-2.21806 + 8.81431i) q^{62} -4.51614i q^{63} +(-0.732149 - 7.96643i) q^{64} +(-0.309729 + 0.182092i) q^{65} +(6.67200 + 1.67896i) q^{66} +(1.87639 + 1.87639i) q^{67} +(-4.76443 + 8.86716i) q^{68} +(-5.66051 - 5.66051i) q^{69} +(-12.5300 - 6.85237i) q^{70} +0.635312i q^{71} +(-2.08952 - 1.90629i) q^{72} -6.14208 q^{73} +(1.67765 + 2.80590i) q^{74} +(1.37006 + 4.80863i) q^{75} +(2.68810 - 0.809042i) q^{76} +(15.5355 + 15.5355i) q^{77} +(-0.220365 - 0.0554535i) q^{78} +1.76500 q^{79} +(-8.45940 + 2.90492i) q^{80} -1.00000 q^{81} +(-4.60307 - 1.15833i) q^{82} +(6.39170 + 6.39170i) q^{83} +(-2.60312 - 8.64905i) q^{84} +(10.8934 + 2.82705i) q^{85} +(5.83162 + 9.75352i) q^{86} +1.43857 q^{87} +(13.7456 - 0.630310i) q^{88} -0.579554i q^{89} +(-1.51731 + 2.77449i) q^{90} +(-0.513114 - 0.513114i) q^{91} +(-14.1034 - 7.57793i) q^{92} +(4.54455 + 4.54455i) q^{93} +(-12.4838 - 3.14148i) q^{94} +(-1.59065 - 2.70562i) q^{95} +(-5.10050 - 2.44640i) q^{96} -15.2769i q^{97} +(4.62305 - 18.3714i) q^{98} +(3.44000 - 3.44000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.345118	−	1.37146i	0.244035	−	0.969766i
$2$	0.345118	−	1.37146i	0.244035	−	0.969766i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.76179	−	0.946629i	−0.880893	−	0.473315i
$5$	−0.561697	+	2.16437i	−0.251198	+	0.967936i
$5$	−0.561697	+	2.16437i	−0.251198	+	0.967936i
$6$	−1.21380	+	0.725731i	−0.495532	+	0.296278i
$7$	−4.51614			−1.70694			−0.853471	−	0.521140i	$-0.825507\pi$
$7$	−4.51614			−1.70694			−0.853471	+	0.521140i	$0.825507\pi$
$8$	−1.90629	+	2.08952i	−0.673974	+	0.738755i
$9$			1.00000i			0.333333i
$10$	2.77449	+	1.51731i	0.877370	+	0.479814i
$11$	−3.44000	−	3.44000i	−1.03720	−	1.03720i	−0.999281	−	0.0379186i	$-0.987927\pi$
$11$	−3.44000	−	3.44000i	−1.03720	−	1.03720i	−0.0379186	−	0.999281i	$-0.512073\pi$
$12$	0.576403	+	1.91514i	0.166393	+	0.552853i
$13$	0.113618	+	0.113618i	0.0315119	+	0.0315119i	0.722687	−	0.691175i	$-0.242907\pi$
$13$	0.113618	+	0.113618i	0.0315119	+	0.0315119i	−0.691175	+	0.722687i	$0.742907\pi$
$14$	−1.55860	+	6.19370i	−0.416554	+	1.65534i
$15$	1.92762	−	1.13326i	0.497709	−	0.292607i
$16$	2.20779	+	3.33552i	0.551946	+	0.833880i
$17$		−	5.03305i		−	1.22069i	−0.792134	−	0.610347i	$-0.791030\pi$
$17$		−	5.03305i		−	1.22069i	0.792134	−	0.610347i	$-0.208970\pi$
$18$	1.37146	+	0.345118i	0.323255	+	0.0813451i
$19$	−0.992498	+	0.992498i	−0.227695	+	0.227695i	−0.811729	−	0.584034i	$-0.801473\pi$
$19$	−0.992498	+	0.992498i	−0.227695	+	0.227695i	0.584034	+	0.811729i	$0.301473\pi$
$20$	3.03845	−	3.28144i	0.679417	−	0.733752i
$21$	3.19340	+	3.19340i	0.696856	+	0.696856i
$22$	−5.90502	+	3.53061i	−1.25895	+	0.752728i
$23$	8.00517			1.66919			0.834596	−	0.550862i	$-0.185701\pi$
$23$	8.00517			1.66919			0.834596	+	0.550862i	$0.185701\pi$
$24$	2.82546	−	0.129563i	0.576744	−	0.0264469i
$25$	−4.36899	−	2.43144i	−0.873799	−	0.486288i
$26$	0.195033	−	0.116610i	0.0382492	−	0.0228691i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	7.95648	+	4.27512i	1.50363	+	0.807921i
$29$	−1.01722	+	1.01722i	−0.188894	+	0.188894i	−0.795218	−	0.606324i	$-0.792643\pi$
$29$	−1.01722	+	1.01722i	−0.188894	+	0.188894i	0.606324	+	0.795218i	$0.292643\pi$
$30$	−0.888962	−	3.03476i	−0.162301	−	0.554068i
$31$	−6.42697			−1.15432			−0.577159	−	0.816632i	$-0.695839\pi$
$31$	−6.42697			−1.15432			−0.577159	+	0.816632i	$0.695839\pi$
$32$	5.33647	−	1.87673i	0.943363	−	0.331763i
$33$			4.86490i			0.846870i
$34$	−6.90261	−	1.73700i	−1.18379	−	0.297893i
$35$	2.53670	−	9.77461i	0.428781	−	1.65221i
$36$	0.946629	−	1.76179i	0.157772	−	0.293631i
$37$	−1.63459	+	1.63459i	−0.268726	+	0.268726i	−0.828587	−	0.559861i	$-0.810855\pi$
$37$	−1.63459	+	1.63459i	−0.268726	+	0.268726i	0.559861	+	0.828587i	$0.310855\pi$
$38$	1.01864	+	1.70370i	0.165245	+	0.276376i
$39$		−	0.160680i		−	0.0257293i
$40$	−3.45173	−	5.29958i	−0.545766	−	0.837937i
$41$		−	3.35633i		−	0.524171i	−0.965045	−	0.262086i	$-0.915590\pi$
$41$		−	3.35633i		−	0.524171i	0.965045	−	0.262086i	$-0.0844103\pi$
$42$	5.48170	−	3.27751i	0.845845	−	0.505730i
$43$	−5.68196	+	5.68196i	−0.866491	+	0.866491i	−0.992082	−	0.125591i	$-0.959917\pi$
$43$	−5.68196	+	5.68196i	−0.866491	+	0.866491i	0.125591	+	0.992082i	$0.459917\pi$
$44$	2.80414	+	9.31696i	0.422740	+	1.40458i
$45$	−2.16437	−	0.561697i	−0.322645	−	0.0837328i
$46$	2.76273	−	10.9787i	0.407342	−	1.61873i
$47$		−	9.10261i		−	1.32775i	−0.747842	−	0.663876i	$-0.768910\pi$
$47$		−	9.10261i		−	1.32775i	0.747842	−	0.663876i	$-0.231090\pi$
$48$	0.797427	−	3.91971i	0.115099	−	0.565761i
$49$	13.3956			1.91365
$50$	−4.84243	+	5.15275i	−0.684823	+	0.728709i
$51$	−3.55890	+	3.55890i	−0.498346	+	0.498346i
$52$	−0.0926163	−	0.307724i	−0.0128436	−	0.0426736i
$53$	−3.27113	+	3.27113i	−0.449324	+	0.449324i	−0.895130	−	0.445806i	$-0.852917\pi$
$53$	−3.27113	+	3.27113i	−0.449324	+	0.449324i	0.445806	+	0.895130i	$0.352917\pi$
$54$	−0.725731	−	1.21380i	−0.0987595	−	0.165177i
$55$	9.37767	−	5.51320i	1.26449	−	0.743399i
$56$	8.60906	−	9.43655i	1.15043	−	1.26101i
$57$	1.40360			0.185912
$58$	1.04401	+	1.74614i	0.137086	+	0.229279i
$59$	−5.30843	−	5.30843i	−0.691098	−	0.691098i	0.271375	−	0.962474i	$-0.412522\pi$
$59$	−5.30843	−	5.30843i	−0.691098	−	0.691098i	−0.962474	+	0.271375i	$0.912522\pi$
$60$	−4.46883	+	0.171823i	−0.576924	+	0.0221822i
$61$	−5.87487	+	5.87487i	−0.752199	+	0.752199i	−0.974889	−	0.222690i	$-0.928516\pi$
$61$	−5.87487	+	5.87487i	−0.752199	+	0.752199i	0.222690	+	0.974889i	$0.428516\pi$
$62$	−2.21806	+	8.81431i	−0.281694	+	1.11942i
$63$		−	4.51614i		−	0.568981i
$64$	−0.732149	−	7.96643i	−0.0915186	−	0.995803i
$65$	−0.309729	+	0.182092i	−0.0384172	+	0.0225857i
$66$	6.67200	+	1.67896i	0.821266	+	0.206666i
$67$	1.87639	+	1.87639i	0.229238	+	0.229238i	0.812374	−	0.583137i	$-0.198175\pi$
$67$	1.87639	+	1.87639i	0.229238	+	0.229238i	−0.583137	+	0.812374i	$0.698175\pi$
$68$	−4.76443	+	8.86716i	−0.577772	+	1.07530i
$69$	−5.66051	−	5.66051i	−0.681445	−	0.681445i
$70$	−12.5300	−	6.85237i	−1.49762	−	0.819015i
$71$			0.635312i			0.0753977i	0.999289	+	0.0376988i	$0.0120028\pi$
$71$			0.635312i			0.0753977i	−0.999289	+	0.0376988i	$0.987997\pi$
$72$	−2.08952	−	1.90629i	−0.246252	−	0.224658i
$73$	−6.14208			−0.718876			−0.359438	−	0.933169i	$-0.617032\pi$
$73$	−6.14208			−0.718876			−0.359438	+	0.933169i	$0.617032\pi$
$74$	1.67765	+	2.80590i	0.195023	+	0.326180i
$75$	1.37006	+	4.80863i	0.158201	+	0.555253i
$76$	2.68810	−	0.809042i	0.308346	−	0.0928035i
$77$	15.5355	+	15.5355i	1.77044	+	1.77044i
$78$	−0.220365	−	0.0554535i	−0.0249514	−	0.00627887i
$79$	1.76500			0.198578			0.0992888	−	0.995059i	$-0.468343\pi$
$79$	1.76500			0.198578			0.0992888	+	0.995059i	$0.468343\pi$
$80$	−8.45940	+	2.90492i	−0.945790	+	0.324779i
$81$	−1.00000			−0.111111
$82$	−4.60307	−	1.15833i	−0.508324	−	0.127916i
$83$	6.39170	+	6.39170i	0.701580	+	0.701580i	0.964750	−	0.263169i	$-0.0847678\pi$
$83$	6.39170	+	6.39170i	0.701580	+	0.701580i	−0.263169	+	0.964750i	$0.584768\pi$
$84$	−2.60312	−	8.64905i	−0.284024	−	0.943688i
$85$	10.8934	+	2.82705i	1.18155	+	0.306636i
$86$	5.83162	+	9.75352i	0.628840	+	1.05175i
$87$	1.43857			0.154231
$88$	13.7456	−	0.630310i	1.46528	−	0.0671913i
$89$		−	0.579554i		−	0.0614326i	−0.999528	−	0.0307163i	$-0.990221\pi$
$89$		−	0.579554i		−	0.0614326i	0.999528	−	0.0307163i	$-0.00977884\pi$
$90$	−1.51731	+	2.77449i	−0.159938	+	0.292457i
$91$	−0.513114	−	0.513114i	−0.0537889	−	0.0537889i
$92$	−14.1034	−	7.57793i	−1.47038	−	0.790053i
$93$	4.54455	+	4.54455i	0.471248	+	0.471248i
$94$	−12.4838	−	3.14148i	−1.28761	−	0.324019i
$95$	−1.59065	−	2.70562i	−0.163197	−	0.277590i
$96$	−5.10050	−	2.44640i	−0.520568	−	0.249685i
$97$		−	15.2769i		−	1.55113i	−0.631265	−	0.775567i	$-0.717464\pi$
$97$		−	15.2769i		−	1.55113i	0.631265	−	0.775567i	$-0.282536\pi$
$98$	4.62305	−	18.3714i	0.466999	−	1.85580i
$99$	3.44000	−	3.44000i	0.345733	−	0.345733i
$100$	5.39556	+	8.41949i	0.539556	+	0.841949i
$101$	−2.60639	−	2.60639i	−0.259346	−	0.259346i	0.565442	−	0.824788i	$-0.308706\pi$
$101$	−2.60639	−	2.60639i	−0.259346	−	0.259346i	−0.824788	+	0.565442i	$0.808706\pi$
$102$	3.65264	+	6.10913i	0.361665	+	0.604894i
$103$	9.26272			0.912683			0.456341	−	0.889805i	$-0.349160\pi$
$103$	9.26272			0.912683			0.456341	+	0.889805i	$0.349160\pi$
$104$	−0.453994	+	0.0208181i	−0.0445177	+	0.00204138i
$105$	−8.70541	+	5.11797i	−0.849561	+	0.499463i
$106$	3.35729	+	5.61514i	0.326089	+	0.545391i
$107$	−4.72776	+	4.72776i	−0.457050	+	0.457050i	−0.897686	−	0.440636i	$-0.854753\pi$
$107$	−4.72776	+	4.72776i	−0.457050	+	0.457050i	0.440636	+	0.897686i	$0.354753\pi$
$108$	−1.91514	+	0.576403i	−0.184284	+	0.0554644i
$109$	0.160713	−	0.160713i	0.0153935	−	0.0153935i	−0.699368	−	0.714762i	$-0.746535\pi$
$109$	0.160713	−	0.160713i	0.0153935	−	0.0153935i	0.714762	+	0.699368i	$0.246535\pi$
$110$	−4.32471	−	14.7638i	−0.412345	−	1.40767i
$111$	2.31167			0.219414
$112$	−9.97068	−	15.0637i	−0.942141	−	1.42338i
$113$		−	1.02489i		−	0.0964131i	−0.998837	−	0.0482066i	$-0.984649\pi$
$113$		−	1.02489i		−	0.0964131i	0.998837	−	0.0482066i	$-0.0153506\pi$
$114$	0.484409	−	1.92498i	0.0453691	−	0.180291i
$115$	−4.49648	+	17.3261i	−0.419298	+	1.61567i
$116$	2.75506	−	0.829197i	0.255801	−	0.0769890i
$117$	−0.113618	+	0.113618i	−0.0105040	+	0.0105040i
$118$	−9.11231	+	5.44824i	−0.838856	+	0.501551i
$119$			22.7300i			2.08365i
$120$	−1.30663	+	6.18811i	−0.119278	+	0.564895i
$121$			12.6672i			1.15157i
$122$	6.02960	+	10.0846i	0.545894	+	0.913021i
$123$	−2.37329	+	2.37329i	−0.213992	+	0.213992i
$124$	11.3229	+	6.08396i	1.01683	+	0.546355i
$125$	7.71658	−	8.09039i	0.690192	−	0.723626i
$126$	−6.19370	−	1.55860i	−0.551778	−	0.138851i
$127$			9.29167i			0.824502i	0.911070	+	0.412251i	$0.135257\pi$
$127$			9.29167i			0.824502i	−0.911070	+	0.412251i	$0.864743\pi$
$128$	−11.1783	−	1.74525i	−0.988030	−	0.154260i
$129$	8.03551			0.707487
$130$	0.142838	+	0.487624i	0.0125277	+	0.0427674i
$131$	−4.53759	+	4.53759i	−0.396451	+	0.396451i	−0.876979	−	0.480528i	$-0.840445\pi$
$131$	−4.53759	+	4.53759i	−0.396451	+	0.396451i	0.480528	+	0.876979i	$0.340445\pi$
$132$	4.60525	−	8.57091i	0.400836	−	0.746002i
$133$	4.48226	−	4.48226i	0.388662	−	0.388662i
$134$	3.22096	−	1.92581i	0.278249	−	0.166365i
$135$	1.13326	+	1.92762i	0.0975356	+	0.165903i
$136$	10.5166	+	9.59443i	0.901794	+	0.822716i
$137$	−0.448842			−0.0383471			−0.0191736	−	0.999816i	$-0.506104\pi$
$137$	−0.448842			−0.0383471			−0.0191736	+	0.999816i	$0.506104\pi$
$138$	−9.71668	+	5.80960i	−0.827139	+	0.494546i
$139$	−5.12669	−	5.12669i	−0.434840	−	0.434840i	0.455431	−	0.890271i	$-0.349485\pi$
$139$	−5.12669	−	5.12669i	−0.434840	−	0.434840i	−0.890271	+	0.455431i	$0.849485\pi$
$140$	−13.7221	+	14.8195i	−1.15973	+	1.25247i
$141$	−6.43652	+	6.43652i	−0.542053	+	0.542053i
$142$	0.871303	+	0.219258i	0.0731181	+	0.0183997i
$143$		−	0.781690i		−	0.0653682i
$144$	−3.33552	+	2.20779i	−0.277960	+	0.183982i
$145$	−1.63028	−	2.77302i	−0.135387	−	0.230287i
$146$	−2.11974	+	8.42360i	−0.175431	+	0.697142i
$147$	−9.47209	−	9.47209i	−0.781245	−	0.781245i
$148$	4.42716	−	1.33245i	0.363911	−	0.109527i
$149$	4.56510	+	4.56510i	0.373988	+	0.373988i	0.868927	−	0.494940i	$-0.164810\pi$
$149$	4.56510	+	4.56510i	0.373988	+	0.373988i	−0.494940	+	0.868927i	$0.664810\pi$
$150$	7.06766	−	0.219429i	0.577072	−	0.0179163i
$151$			6.84317i			0.556890i	0.960452	+	0.278445i	$0.0898189\pi$
$151$			6.84317i			0.556890i	−0.960452	+	0.278445i	$0.910181\pi$
$152$	−0.181855	−	3.96582i	−0.0147504	−	0.321671i
$153$	5.03305			0.406898
$154$	26.6679	−	15.9447i	2.14896	−	1.28486i
$155$	3.61001	−	13.9103i	0.289963	−	1.11730i
$156$	−0.152104	+	0.283083i	−0.0121781	+	0.0226648i
$157$	1.85978	+	1.85978i	0.148426	+	0.148426i	0.777415	−	0.628988i	$-0.216531\pi$
$157$	1.85978	+	1.85978i	0.148426	+	0.148426i	−0.628988	+	0.777415i	$0.716531\pi$
$158$	0.609132	−	2.42062i	0.0484600	−	0.192574i
$159$	4.62608			0.366872
$160$	1.06447	+	12.6042i	0.0841540	+	0.996453i
$161$	−36.1525			−2.84922
$162$	−0.345118	+	1.37146i	−0.0271150	+	0.107752i
$163$	−9.43033	−	9.43033i	−0.738641	−	0.738641i	0.233674	−	0.972315i	$-0.424925\pi$
$163$	−9.43033	−	9.43033i	−0.738641	−	0.738641i	−0.972315	+	0.233674i	$0.924925\pi$
$164$	−3.17720	+	5.91314i	−0.248098	+	0.461739i
$165$	−10.5294	−	2.73260i	−0.819715	−	0.212732i
$166$	10.9718	−	6.56005i	0.851580	−	0.509159i
$167$	−21.2570			−1.64492			−0.822459	−	0.568824i	$-0.807398\pi$
$167$	−21.2570			−1.64492			−0.822459	+	0.568824i	$0.807398\pi$
$168$	−12.7602	+	0.585125i	−0.984469	+	0.0451434i
$169$		−	12.9742i		−	0.998014i
$170$	7.63668	−	13.9641i	0.585706	−	1.07100i
$171$	−0.992498	−	0.992498i	−0.0758982	−	0.0758982i
$172$	15.3891	−	4.63170i	1.17341	−	0.353164i
$173$	−3.90989	−	3.90989i	−0.297263	−	0.297263i	0.542678	−	0.839941i	$-0.317410\pi$
$173$	−3.90989	−	3.90989i	−0.297263	−	0.297263i	−0.839941	+	0.542678i	$0.817410\pi$
$174$	0.496477	−	1.97294i	0.0376378	−	0.149568i
$175$	19.7310	+	10.9807i	1.49152	+	0.830065i
$176$	3.87940	−	19.0690i	0.292421	−	1.43738i
$177$			7.50725i			0.564279i
$178$	−0.794834	−	0.200015i	−0.0595753	−	0.0149917i
$179$	16.8281	−	16.8281i	1.25779	−	1.25779i	0.305651	−	0.952144i	$-0.401126\pi$
$179$	16.8281	−	16.8281i	1.25779	−	1.25779i	0.952144	−	0.305651i	$-0.0988740\pi$
$180$	3.28144	+	3.03845i	0.244584	+	0.226472i
$181$	−10.4003	−	10.4003i	−0.773050	−	0.773050i	0.205588	−	0.978639i	$-0.434089\pi$
$181$	−10.4003	−	10.4003i	−0.773050	−	0.773050i	−0.978639	+	0.205588i	$0.934089\pi$
$182$	−0.880798	+	0.526628i	−0.0652891	+	0.0390363i
$183$	8.30831			0.614168
$184$	−15.2601	+	16.7269i	−1.12499	+	1.23312i
$185$	−2.61972	−	4.45601i	−0.192606	−	0.327613i
$186$	7.80106	−	4.66425i	0.572002	−	0.341999i
$187$	−17.3137	+	17.3137i	−1.26610	+	1.26610i
$188$	−8.61680	+	16.0369i	−0.628445	+	1.16961i
$189$	−3.19340	+	3.19340i	−0.232285	+	0.232285i
$190$	−4.25960	+	1.24775i	−0.309024	+	0.0905213i
$191$	20.8245			1.50681			0.753404	−	0.657558i	$-0.228411\pi$
$191$	20.8245			1.50681			0.753404	+	0.657558i	$0.228411\pi$
$192$	−5.11541	+	6.15082i	−0.369173	+	0.443897i
$193$		−	5.82531i		−	0.419315i	−0.977775	−	0.209657i	$-0.932765\pi$
$193$		−	5.82531i		−	0.419315i	0.977775	−	0.209657i	$-0.0672349\pi$
$194$	−20.9516	−	5.27234i	−1.50424	−	0.378532i
$195$	0.347770	+	0.0902532i	0.0249043	+	0.00646317i
$196$	−23.6001	−	12.6806i	−1.68572	−	0.905760i
$197$	11.0656	−	11.0656i	0.788391	−	0.788391i	−0.192839	−	0.981230i	$-0.561770\pi$
$197$	11.0656	−	11.0656i	0.788391	−	0.788391i	0.981230	+	0.192839i	$0.0617695\pi$
$198$	−3.53061	−	5.90502i	−0.250909	−	0.419652i
$199$			7.04564i			0.499452i	0.968317	+	0.249726i	$0.0803406\pi$
$199$			7.04564i			0.499452i	−0.968317	+	0.249726i	$0.919659\pi$
$200$	13.4091	−	4.49406i	0.948165	−	0.317778i
$201$		−	2.65362i		−	0.187172i
$202$	−4.47407	+	2.67504i	−0.314794	+	0.188215i
$203$	4.59393	−	4.59393i	0.322430	−	0.322430i
$204$	9.63899	−	2.90107i	0.674865	−	0.203115i
$205$	7.26435	+	1.88524i	0.507364	+	0.131671i
$206$	3.19673	−	12.7034i	0.222727	−	0.885089i
$207$			8.00517i			0.556398i
$208$	−0.128130	+	0.629817i	−0.00888424	+	0.0436700i
$209$	6.82839			0.472329
$210$	4.01468	+	13.7054i	0.277039	+	0.945762i
$211$	0.158025	−	0.158025i	0.0108789	−	0.0108789i	−0.701646	−	0.712525i	$-0.747551\pi$
$211$	0.158025	−	0.158025i	0.0108789	−	0.0108789i	0.712525	+	0.701646i	$0.247551\pi$
$212$	8.85958	−	2.66649i	0.608479	−	0.183135i
$213$	0.449234	−	0.449234i	0.0307810	−	0.0307810i
$214$	4.85229	+	8.11556i	0.331695	+	0.554768i
$215$	−9.10633	−	15.4894i	−0.621047	−	1.05637i
$216$	0.129563	+	2.82546i	0.00881564	+	0.192248i
$217$	29.0251			1.97035
$218$	−0.164946	−	0.275876i	−0.0111715	−	0.0186847i
$219$	4.34311	+	4.34311i	0.293480	+	0.293480i
$220$	−21.7404	+	0.835900i	−1.46574	+	0.0563564i
$221$	0.571843	−	0.571843i	0.0384663	−	0.0384663i
$222$	0.797798	−	3.17035i	0.0535447	−	0.212780i
$223$		−	8.38138i		−	0.561259i	−0.959816	−	0.280629i	$-0.909457\pi$
$223$		−	8.38138i		−	0.561259i	0.959816	−	0.280629i	$-0.0905432\pi$
$224$	−24.1003	+	8.47561i	−1.61027	+	0.566300i
$225$	2.43144	−	4.36899i	0.162096	−	0.291266i
$226$	−1.40559	−	0.353707i	−0.0934982	−	0.0235282i
$227$	−6.73568	−	6.73568i	−0.447063	−	0.447063i	0.447314	−	0.894377i	$-0.352381\pi$
$227$	−6.73568	−	6.73568i	−0.447063	−	0.447063i	−0.894377	+	0.447314i	$0.852381\pi$
$228$	−2.47285	−	1.32869i	−0.163769	−	0.0879948i
$229$	−13.6770	−	13.6770i	−0.903800	−	0.903800i	0.0919626	−	0.995762i	$-0.470686\pi$
$229$	−13.6770	−	13.6770i	−0.903800	−	0.903800i	−0.995762	+	0.0919626i	$0.970686\pi$
$230$	22.2102	+	12.1463i	1.46450	+	0.800902i
$231$		−	21.9706i		−	1.44556i
$232$	−0.186385	−	4.06462i	−0.0122368	−	0.266855i
$233$	1.62741			0.106615			0.0533077	−	0.998578i	$-0.483024\pi$
$233$	1.62741			0.106615			0.0533077	+	0.998578i	$0.483024\pi$
$234$	0.116610	+	0.195033i	0.00762304	+	0.0127497i
$235$	19.7014	+	5.11291i	1.28518	+	0.333529i
$236$	4.32720	+	14.3774i	0.281677	+	0.935891i
$237$	−1.24804	−	1.24804i	−0.0810690	−	0.0810690i
$238$	31.1732	+	7.84453i	2.02066	+	0.508485i
$239$	−12.6908			−0.820902			−0.410451	−	0.911883i	$-0.634629\pi$
$239$	−12.6908			−0.820902			−0.410451	+	0.911883i	$0.634629\pi$
$240$	8.03579	+	3.92761i	0.518708	+	0.253526i
$241$	21.1033			1.35938			0.679692	−	0.733498i	$-0.262114\pi$
$241$	21.1033			1.35938			0.679692	+	0.733498i	$0.262114\pi$
$242$	17.3725	+	4.37169i	1.11675	+	0.281023i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	15.9116	−	4.78894i	1.01863	−	0.306581i
$245$	−7.52424	+	28.9930i	−0.480706	+	1.85229i
$246$	2.43579	+	4.07392i	0.155301	+	0.259744i
$247$	−0.225531			−0.0143502
$248$	12.2516	−	13.4292i	0.777980	−	0.852758i
$249$		−	9.03923i		−	0.572838i
$250$	−8.43248	−	13.3751i	−0.533317	−	0.845915i
$251$	17.4935	+	17.4935i	1.10418	+	1.10418i	0.993900	+	0.110282i	$0.0351755\pi$
$251$	17.4935	+	17.4935i	1.10418	+	1.10418i	0.110282	+	0.993900i	$0.464824\pi$
$252$	−4.27512	+	7.95648i	−0.269307	+	0.501211i
$253$	−27.5378	−	27.5378i	−1.73129	−	1.73129i
$254$	12.7431	+	3.20672i	0.799574	+	0.201208i
$255$	−5.70376	−	9.70181i	−0.357183	−	0.607551i
$256$	−6.25136	+	14.7282i	−0.390710	+	0.920514i
$257$			7.80177i			0.486661i	0.969943	+	0.243331i	$0.0782400\pi$
$257$			7.80177i			0.486661i	−0.969943	+	0.243331i	$0.921760\pi$
$258$	2.77320	−	11.0204i	0.172652	−	0.686097i
$259$	7.38207	−	7.38207i	0.458699	−	0.458699i
$260$	0.718051	−	0.0276084i	0.0445316	−	0.00171220i
$261$	−1.01722	−	1.01722i	−0.0629645	−	0.0629645i
$262$	4.65710	+	7.78911i	0.287717	+	0.481213i
$263$	−11.9238			−0.735252			−0.367626	−	0.929974i	$-0.619829\pi$
$263$	−11.9238			−0.735252			−0.367626	+	0.929974i	$0.619829\pi$
$264$	−10.1653	−	9.27388i	−0.625630	−	0.570768i
$265$	−5.24255	−	8.91732i	−0.322047	−	0.547787i
$266$	−4.60032	−	7.69414i	−0.282064	−	0.471758i
$267$	−0.409807	+	0.409807i	−0.0250798	+	0.0250798i
$268$	−1.52955	−	5.08205i	−0.0934324	−	0.310435i
$269$	−8.24368	+	8.24368i	−0.502626	+	0.502626i	−0.912253	−	0.409627i	$-0.865659\pi$
$269$	−8.24368	+	8.24368i	−0.502626	+	0.502626i	0.409627	+	0.912253i	$0.365659\pi$
$270$	3.03476	−	0.888962i	0.184689	−	0.0541005i
$271$	−26.8960			−1.63381			−0.816907	−	0.576770i	$-0.804313\pi$
$271$	−26.8960			−1.63381			−0.816907	+	0.576770i	$0.804313\pi$
$272$	16.7878	−	11.1119i	1.01791	−	0.673758i
$273$			0.725652i			0.0439185i
$274$	−0.154903	+	0.615567i	−0.00935806	+	0.0371878i
$275$	6.66519	+	23.3935i	0.401926	+	1.41068i
$276$	4.61421	+	15.3310i	0.277743	+	0.922818i
$277$	15.8294	−	15.8294i	0.951099	−	0.951099i	−0.0477597	−	0.998859i	$-0.515208\pi$
$277$	15.8294	−	15.8294i	0.951099	−	0.951099i	0.998859	+	0.0477597i	$0.0152082\pi$
$278$	−8.80035	+	5.26172i	−0.527810	+	0.315577i
$279$		−	6.42697i		−	0.384772i
$280$	15.5885	+	23.9337i	0.931592	+	1.43031i
$281$		−	27.8550i		−	1.66169i	−0.556503	−	0.830845i	$-0.687857\pi$
$281$		−	27.8550i		−	1.66169i	0.556503	−	0.830845i	$-0.312143\pi$
$282$	6.60605	+	11.0488i	0.393384	+	0.657945i
$283$	−2.62285	+	2.62285i	−0.155913	+	0.155913i	−0.780753	−	0.624840i	$-0.785164\pi$
$283$	−2.62285	+	2.62285i	−0.155913	+	0.155913i	0.624840	+	0.780753i	$0.285164\pi$
$284$	0.601405	−	1.11928i	0.0356868	−	0.0664173i
$285$	−0.788400	+	3.03792i	−0.0467008	+	0.179951i
$286$	−1.07205	−	0.269775i	−0.0633919	−	0.0159522i
$287$			15.1577i			0.894730i
$288$	1.87673	+	5.33647i	0.110588	+	0.314454i
$289$	−8.33160			−0.490094
$290$	−4.36571	+	1.27883i	−0.256363	+	0.0750957i
$291$	−10.8024	+	10.8024i	−0.633248	+	0.633248i
$292$	10.8210	+	5.81428i	0.633253	+	0.340255i
$293$	−7.75559	+	7.75559i	−0.453086	+	0.453086i	−0.896378	−	0.443291i	$-0.853811\pi$
$293$	−7.75559	+	7.75559i	−0.453086	+	0.453086i	0.443291	+	0.896378i	$0.353811\pi$
$294$	−16.2596	+	9.72157i	−0.948277	+	0.566974i
$295$	14.4711	−	8.50767i	0.842541	−	0.495336i
$296$	−0.299506	−	6.53152i	−0.0174084	−	0.379637i
$297$	−4.86490			−0.282290
$298$	7.83634	−	4.68534i	0.453947	−	0.271414i
$299$	0.909528	+	0.909528i	0.0525994	+	0.0525994i
$300$	2.13824	−	9.76872i	0.123451	−	0.563997i
$301$	25.6606	−	25.6606i	1.47905	−	1.47905i
$302$	9.38512	+	2.36170i	0.540053	+	0.135901i
$303$			3.68600i			0.211755i
$304$	−5.50172	−	1.11927i	−0.315545	−	0.0641946i
$305$	−9.41549	−	16.0153i	−0.539129	−	0.917032i
$306$	1.73700	−	6.90261i	0.0992975	−	0.394596i
$307$	2.60764	+	2.60764i	0.148826	+	0.148826i	0.777593	−	0.628767i	$-0.216440\pi$
$307$	2.60764	+	2.60764i	0.148826	+	0.148826i	−0.628767	+	0.777593i	$0.716440\pi$
$308$	−12.6639	−	42.0767i	−0.721594	−	2.39754i
$309$	−6.54973	−	6.54973i	−0.372601	−	0.372601i
$310$	−17.8315	−	9.75168i	−1.01276	−	0.553858i
$311$			20.1642i			1.14340i	0.820461	+	0.571702i	$0.193717\pi$
$311$			20.1642i			1.14340i	−0.820461	+	0.571702i	$0.806283\pi$
$312$	0.335743	+	0.306301i	0.0190077	+	0.0173409i
$313$	−23.2572			−1.31457			−0.657286	−	0.753641i	$-0.728296\pi$
$313$	−23.2572			−1.31457			−0.657286	+	0.753641i	$0.728296\pi$
$314$	3.19245	−	1.90876i	0.180160	−	0.107718i
$315$	9.77461	+	2.53670i	0.550737	+	0.142927i
$316$	−3.10955	−	1.67080i	−0.174926	−	0.0939897i
$317$	−17.1360	−	17.1360i	−0.962451	−	0.962451i	0.0368693	−	0.999320i	$-0.488261\pi$
$317$	−17.1360	−	17.1360i	−0.962451	−	0.962451i	−0.999320	+	0.0368693i	$0.988261\pi$
$318$	1.59654	−	6.34446i	0.0895297	−	0.355780i
$319$	6.99850			0.391841
$320$	17.6535	+	2.89007i	0.986863	+	0.161560i
$321$	6.68607			0.373180
$322$	−12.4769	+	49.5816i	−0.695309	+	2.76307i
$323$	4.99529	+	4.99529i	0.277945	+	0.277945i
$324$	1.76179	+	0.946629i	0.0978770	+	0.0525905i
$325$	−0.220140	−	0.772649i	−0.0122112	−	0.0428589i
$326$	−16.1879	+	9.67871i	−0.896563	+	0.536054i
$327$	−0.227282			−0.0125687
$328$	7.01311	+	6.39813i	0.387234	+	0.353278i
$329$			41.1087i			2.26640i
$330$	−7.38154	+	13.4976i	−0.406340	+	0.743018i
$331$	−2.06668	−	2.06668i	−0.113595	−	0.113595i	0.648025	−	0.761619i	$-0.275595\pi$
$331$	−2.06668	−	2.06668i	−0.113595	−	0.113595i	−0.761619	+	0.648025i	$0.775595\pi$
$332$	−5.21024	−	17.3114i	−0.285949	−	0.950086i
$333$	−1.63459	−	1.63459i	−0.0895752	−	0.0895752i
$334$	−7.33619	+	29.1531i	−0.401418	+	1.59519i
$335$	−5.11517	+	3.00724i	−0.279471	+	0.164303i
$336$	−3.60130	+	17.7020i	−0.196467	+	0.965722i
$337$			35.2657i			1.92105i	0.278201	+	0.960523i	$0.410262\pi$
$337$			35.2657i			1.92105i	−0.278201	+	0.960523i	$0.589738\pi$
$338$	−17.7935	−	4.47763i	−0.967840	−	0.243551i
$339$	−0.724704	+	0.724704i	−0.0393605	+	0.0393605i
$340$	−16.5157	−	15.2927i	−0.895687	−	0.829360i
$341$	22.1088	+	22.1088i	1.19726	+	1.19726i
$342$	−1.70370	+	1.01864i	−0.0921254	+	0.0550817i
$343$	−28.8833			−1.55955
$344$	−1.04110	−	22.7040i	−0.0561326	−	1.22412i
$345$	15.4309	−	9.07194i	0.830773	−	0.488417i
$346$	−6.71161	+	4.01287i	−0.360818	+	0.215733i
$347$	−2.03686	+	2.03686i	−0.109344	+	0.109344i	−0.759662	−	0.650318i	$-0.774636\pi$
$347$	−2.03686	+	2.03686i	−0.109344	+	0.109344i	0.650318	+	0.759662i	$0.274636\pi$
$348$	−2.53445	−	1.36179i	−0.135861	−	0.0729998i
$349$	−19.7731	+	19.7731i	−1.05843	+	1.05843i	−0.0602455	+	0.998184i	$0.519188\pi$
$349$	−19.7731	+	19.7731i	−1.05843	+	1.05843i	−0.998184	+	0.0602455i	$0.980812\pi$
$350$	21.8691	−	23.2706i	1.16895	−	1.24386i
$351$	0.160680			0.00857644
$352$	−24.8134	−	11.9015i	−1.32256	−	0.634351i
$353$		−	10.5799i		−	0.563110i	−0.959545	−	0.281555i	$-0.909150\pi$
$353$		−	10.5799i		−	0.563110i	0.959545	−	0.281555i	$-0.0908502\pi$
$354$	10.2959	+	2.59089i	0.547219	+	0.137704i
$355$	−1.37505	−	0.356853i	−0.0729801	−	0.0189398i
$356$	−0.548623	+	1.02105i	−0.0290770	+	0.0541156i
$357$	16.0725	−	16.0725i	0.850648	−	0.850648i
$358$	−17.2714	−	28.8868i	−0.912820	−	1.52671i
$359$			32.7257i			1.72719i	0.504183	+	0.863597i	$0.331794\pi$
$359$			32.7257i			1.72719i	−0.504183	+	0.863597i	$0.668206\pi$
$360$	5.29958	−	3.45173i	0.279312	−	0.181922i
$361$			17.0299i			0.896310i
$362$	−17.8529	+	10.6743i	−0.938330	+	0.561026i
$363$	8.95708	−	8.95708i	0.470125	−	0.470125i
$364$	0.418269	+	1.38973i	0.0219232	+	0.0728414i
$365$	3.44999	−	13.2937i	0.180581	−	0.695826i
$366$	2.86735	−	11.3945i	0.149879	−	0.595600i
$367$		−	22.0267i		−	1.14978i	−0.818230	−	0.574891i	$-0.805044\pi$
$367$		−	22.0267i		−	1.14978i	0.818230	−	0.574891i	$-0.194956\pi$
$368$	17.6737	+	26.7014i	0.921305	+	1.39191i
$369$	3.35633			0.174724
$370$	−7.01534	+	2.05498i	−0.364710	+	0.106833i
$371$	14.7729	−	14.7729i	0.766971	−	0.766971i
$372$	−3.70453	−	12.3085i	−0.192071	−	0.638168i
$373$	−9.69407	+	9.69407i	−0.501940	+	0.501940i	−0.912040	−	0.410100i	$-0.865494\pi$
$373$	−9.69407	+	9.69407i	−0.501940	+	0.501940i	0.410100	+	0.912040i	$0.365494\pi$
$374$	17.7697	+	29.7203i	0.918850	+	1.53680i
$375$	−11.1772	+	0.264320i	−0.577189	+	0.0136494i
$376$	19.0201	+	17.3522i	0.980884	+	0.894871i
$377$	−0.231149			−0.0119048
$378$	3.27751	+	5.48170i	0.168577	+	0.281948i
$379$	−7.44766	−	7.44766i	−0.382560	−	0.382560i	0.489463	−	0.872024i	$-0.337193\pi$
$379$	−7.44766	−	7.44766i	−0.382560	−	0.382560i	−0.872024	+	0.489463i	$0.837193\pi$
$380$	0.241171	+	6.27247i	0.0123718	+	0.321771i
$381$	6.57020	−	6.57020i	0.336602	−	0.336602i
$382$	7.18691	−	28.5599i	0.367714	−	1.46125i
$383$		−	7.30581i		−	0.373309i	−0.982426	−	0.186655i	$-0.940235\pi$
$383$		−	7.30581i		−	0.373309i	0.982426	−	0.186655i	$-0.0597645\pi$
$384$	6.67017	+	9.13832i	0.340385	+	0.466338i
$385$	−42.3509	+	24.8984i	−2.15840	+	1.26894i
$386$	−7.98916	−	2.01042i	−0.406637	−	0.102328i
$387$	−5.68196	−	5.68196i	−0.288830	−	0.288830i
$388$	−14.4616	+	26.9147i	−0.734175	+	1.36638i
$389$	−10.6571	−	10.6571i	−0.540338	−	0.540338i	0.383290	−	0.923628i	$-0.374791\pi$
$389$	−10.6571	−	10.6571i	−0.540338	−	0.540338i	−0.923628	+	0.383290i	$0.874791\pi$
$390$	0.243800	−	0.445804i	0.0123453	−	0.0225741i
$391$		−	40.2904i		−	2.03757i
$392$	−25.5358	+	27.9902i	−1.28975	+	1.41372i
$393$	6.41712			0.323701
$394$	−11.3571	−	18.9949i	−0.572160	−	0.956951i
$395$	−0.991393	+	3.82011i	−0.0498824	+	0.192210i
$396$	−9.31696	+	2.80414i	−0.468195	+	0.140913i
$397$	3.10102	+	3.10102i	0.155636	+	0.155636i	0.780630	−	0.624994i	$-0.214899\pi$
$397$	3.10102	+	3.10102i	0.155636	+	0.155636i	−0.624994	+	0.780630i	$0.714899\pi$
$398$	9.66279	+	2.43158i	0.484352	+	0.121884i
$399$	−6.33888			−0.317341
$400$	−1.53570	−	19.9410i	−0.0767848	−	0.997048i
$401$	−9.88608			−0.493687			−0.246844	−	0.969055i	$-0.579393\pi$
$401$	−9.88608			−0.493687			−0.246844	+	0.969055i	$0.579393\pi$
$402$	−3.63932	−	0.915811i	−0.181513	−	0.0456765i
$403$	−0.730217	−	0.730217i	−0.0363747	−	0.0363747i
$404$	2.12462	+	7.05920i	0.105704	+	0.351208i
$405$	0.561697	−	2.16437i	0.0279109	−	0.107548i
$406$	−4.71492	−	7.88582i	−0.233998	−	0.391367i
$407$	11.2460			0.557444
$408$	−0.652097	−	14.2207i	−0.0322836	−	0.704028i
$409$			11.6903i			0.578048i	0.957322	+	0.289024i	$0.0933307\pi$
$409$			11.6903i			0.578048i	−0.957322	+	0.289024i	$0.906669\pi$
$410$	5.09258	−	9.31210i	0.251505	−	0.459892i
$411$	0.317379	+	0.317379i	0.0156552	+	0.0156552i
$412$	−16.3189	−	8.76836i	−0.803976	−	0.431986i
$413$	23.9736	+	23.9736i	1.17966	+	1.17966i
$414$	10.9787	+	2.76273i	0.539576	+	0.135781i
$415$	−17.4242	+	10.2438i	−0.855321	+	0.502849i
$416$	0.819547	+	0.393086i	0.0401816	+	0.0192727i
$417$			7.25024i			0.355046i
$418$	2.35660	−	9.36484i	0.115265	−	0.458049i
$419$	5.66521	−	5.66521i	0.276764	−	0.276764i	−0.555052	−	0.831816i	$-0.687302\pi$
$419$	5.66521	−	5.66521i	0.276764	−	0.276764i	0.831816	+	0.555052i	$0.187302\pi$
$420$	20.1819	−	0.775977i	0.984776	−	0.0378638i
$421$	19.7440	+	19.7440i	0.962263	+	0.962263i	0.999313	−	0.0370502i	$-0.0117961\pi$
$421$	19.7440	+	19.7440i	0.962263	+	0.962263i	−0.0370502	+	0.999313i	$0.511796\pi$
$422$	−0.162187	−	0.271261i	−0.00789514	−	0.0132048i
$423$	9.10261			0.442584
$424$	−0.599368	−	13.0708i	−0.0291079	−	0.634773i
$425$	−12.2376	+	21.9894i	−0.593609	+	1.06664i
$426$	−0.461066	−	0.771143i	−0.0223387	−	0.0373620i
$427$	26.5317	−	26.5317i	1.28396	−	1.28396i
$428$	12.8048	−	3.85387i	0.618941	−	0.186284i
$429$	−0.552738	+	0.552738i	−0.0266864	+	0.0266864i
$430$	−24.3858	+	7.14326i	−1.17599	+	0.344479i
$431$	−10.8449			−0.522382			−0.261191	−	0.965287i	$-0.584115\pi$
$431$	−10.8449			−0.522382			−0.261191	+	0.965287i	$0.584115\pi$
$432$	3.91971	+	0.797427i	0.188587	+	0.0383662i
$433$			15.4885i			0.744330i	0.928167	+	0.372165i	$0.121384\pi$
$433$			15.4885i			0.744330i	−0.928167	+	0.372165i	$0.878616\pi$
$434$	10.0171	−	39.8067i	0.480836	−	1.91078i
$435$	−0.808040	+	3.11360i	−0.0387426	+	0.149286i
$436$	−0.435277	+	0.131006i	−0.0208460	+	0.00627407i
$437$	−7.94511	+	7.94511i	−0.380066	+	0.380066i
$438$	7.45527	−	4.45750i	0.356227	−	0.212988i
$439$		−	10.4685i		−	0.499633i	−0.968293	−	0.249816i	$-0.919630\pi$
$439$		−	10.4685i		−	0.499633i	0.968293	−	0.249816i	$-0.0803702\pi$
$440$	−6.35661	+	30.1045i	−0.303040	+	1.43518i
$441$			13.3956i			0.637884i
$442$	−0.586905	−	0.981612i	−0.0279162	−	0.0466905i
$443$	15.6375	−	15.6375i	0.742961	−	0.742961i	−0.230186	−	0.973147i	$-0.573933\pi$
$443$	15.6375	−	15.6375i	0.742961	−	0.742961i	0.973147	+	0.230186i	$0.0739334\pi$
$444$	−4.07266	−	2.18829i	−0.193280	−	0.103852i
$445$	1.25437	+	0.325534i	0.0594628	+	0.0154318i
$446$	−11.4947	−	2.89257i	−0.544290	−	0.136967i
$447$		−	6.45603i		−	0.305360i
$448$	3.30649	+	35.9775i	0.156217	+	1.69978i
$449$	22.2119			1.04825			0.524123	−	0.851642i	$-0.324393\pi$
$449$	22.2119			1.04825			0.524123	+	0.851642i	$0.324393\pi$
$450$	−5.15275	−	4.84243i	−0.242903	−	0.228274i
$451$	−11.5458	+	11.5458i	−0.543670	+	0.543670i
$452$	−0.970187	+	1.80563i	−0.0456337	+	0.0849297i
$453$	4.83885	−	4.83885i	0.227349	−	0.227349i
$454$	−11.5623	+	6.91308i	−0.542645	+	0.324447i
$455$	1.39878	−	0.822354i	0.0655759	−	0.0385525i
$456$	−2.67567	+	2.93285i	−0.125300	+	0.137343i
$457$	28.4752			1.33201			0.666006	−	0.745946i	$-0.268002\pi$
$457$	28.4752			1.33201			0.666006	+	0.745946i	$0.268002\pi$
$458$	−23.4776	+	14.0372i	−1.09703	+	0.655916i
$459$	−3.55890	−	3.55890i	−0.166115	−	0.166115i
$460$	24.3233	−	26.2685i	1.13408	−	1.22477i
$461$	22.7778	−	22.7778i	1.06087	−	1.06087i	0.0628456	−	0.998023i	$-0.479982\pi$
$461$	22.7778	−	22.7778i	1.06087	−	1.06087i	0.998023	−	0.0628456i	$-0.0200176\pi$
$462$	−30.1317	−	7.58245i	−1.40185	−	0.352767i
$463$			24.5804i			1.14235i	0.820829	+	0.571174i	$0.193512\pi$
$463$			24.5804i			1.14235i	−0.820829	+	0.571174i	$0.806488\pi$
$464$	−5.63877	−	1.14715i	−0.261774	−	0.0532553i
$465$	−12.3888	+	7.28343i	−0.574515	+	0.337761i
$466$	0.561650	−	2.23193i	0.0260179	−	0.103392i
$467$	−15.6837	−	15.6837i	−0.725757	−	0.725757i	0.244015	−	0.969772i	$-0.421536\pi$
$467$	−15.6837	−	15.6837i	−0.725757	−	0.725757i	−0.969772	+	0.244015i	$0.921536\pi$
$468$	0.307724	−	0.0926163i	0.0142245	−	0.00428119i
$469$	−8.47405	−	8.47405i	−0.391295	−	0.391295i
$470$	13.8115	−	25.2551i	0.637075	−	1.16493i
$471$		−	2.63012i		−	0.121190i
$472$	21.2114	−	0.972661i	0.976334	−	0.0447703i
$473$	39.0919			1.79745
$474$	−2.14236	+	1.28091i	−0.0984017	+	0.0588343i
$475$	6.74941	−	1.92302i	0.309684	−	0.0882342i
$476$	21.5169	−	40.0454i	0.986224	−	1.83548i
$477$	−3.27113	−	3.27113i	−0.149775	−	0.149775i
$478$	−4.37984	+	17.4049i	−0.200329	+	0.796083i
$479$	−9.45943			−0.432212			−0.216106	−	0.976370i	$-0.569336\pi$
$479$	−9.45943			−0.432212			−0.216106	+	0.976370i	$0.569336\pi$
$480$	8.15985	−	9.66524i	0.372444	−	0.441156i
$481$	−0.371438			−0.0169361
$482$	7.28314	−	28.9423i	0.331738	−	1.31828i
$483$	25.5637	+	25.5637i	1.16319	+	1.16319i
$484$	11.9912	−	22.3169i	0.545053	−	1.01441i
$485$	33.0649	+	8.58099i	1.50140	+	0.389643i
$486$	1.21380	−	0.725731i	0.0550592	−	0.0329198i
$487$	−9.95957			−0.451311			−0.225656	−	0.974207i	$-0.572452\pi$
$487$	−9.95957			−0.451311			−0.225656	+	0.974207i	$0.572452\pi$
$488$	−1.07645	−	23.4748i	−0.0487286	−	1.06265i
$489$			13.3365i			0.603097i
$490$	37.1658	+	20.3252i	1.67898	+	0.918198i
$491$	4.35184	+	4.35184i	0.196396	+	0.196396i	0.798453	−	0.602057i	$-0.205652\pi$
$491$	4.35184	+	4.35184i	0.196396	+	0.196396i	−0.602057	+	0.798453i	$0.705652\pi$
$492$	6.42785	−	1.93460i	0.289790	−	0.0872186i
$493$	5.11973	+	5.11973i	0.230581	+	0.230581i
$494$	−0.0778347	+	0.309305i	−0.00350195	+	0.0139163i
$495$	5.51320	+	9.37767i	0.247800	+	0.421495i
$496$	−14.1894	−	21.4373i	−0.637121	−	0.962562i
$497$		−	2.86916i		−	0.128700i
$498$	−12.3969	−	3.11960i	−0.555519	−	0.139793i
$499$	3.09455	−	3.09455i	0.138531	−	0.138531i	−0.634440	−	0.772972i	$-0.718769\pi$
$499$	3.09455	−	3.09455i	0.138531	−	0.138531i	0.772972	+	0.634440i	$0.218769\pi$
$500$	−21.2536	+	6.94880i	−0.950489	+	0.310760i
$501$	15.0310	+	15.0310i	0.671535	+	0.671535i
$502$	30.0290	−	17.9543i	1.34026	−	0.801339i
$503$	−5.84356			−0.260552			−0.130276	−	0.991478i	$-0.541586\pi$
$503$	−5.84356			−0.260552			−0.130276	+	0.991478i	$0.541586\pi$
$504$	9.43655	+	8.60906i	0.420338	+	0.383478i
$505$	7.10520	−	4.17720i	0.316177	−	0.185883i
$506$	−47.2707	+	28.2631i	−2.10144	+	1.25645i
$507$	−9.17413	+	9.17413i	−0.407438	+	0.407438i
$508$	8.79576	−	16.3699i	0.390249	−	0.726298i
$509$	2.16459	−	2.16459i	0.0959436	−	0.0959436i	−0.657506	−	0.753449i	$-0.728389\pi$
$509$	2.16459	−	2.16459i	0.0959436	−	0.0959436i	0.753449	+	0.657506i	$0.228389\pi$
$510$	−15.2741	+	4.47419i	−0.676348	+	0.198120i
$511$	27.7385			1.22708
$512$	18.0417	+	13.6564i	0.797336	+	0.603536i
$513$			1.40360i			0.0619706i
$514$	10.6998	+	2.69253i	0.471948	+	0.118763i
$515$	−5.20284	+	20.0479i	−0.229264	+	0.883418i
$516$	−14.1569	−	7.60665i	−0.623221	−	0.334864i
$517$	−31.3130	+	31.3130i	−1.37714	+	1.37714i
$518$	−7.57650	−	12.6719i	−0.332892	−	0.556770i
$519$			5.52941i			0.242714i
$520$	0.209949	−	0.994303i	0.00920685	−	0.0436031i
$521$			4.80746i			0.210619i	0.994440	+	0.105309i	$0.0335833\pi$
$521$			4.80746i			0.210619i	−0.994440	+	0.105309i	$0.966417\pi$
$522$	−1.74614	+	1.04401i	−0.0764264	+	0.0456953i
$523$	23.6204	−	23.6204i	1.03285	−	1.03285i	0.0334047	−	0.999442i	$-0.489365\pi$
$523$	23.6204	−	23.6204i	1.03285	−	1.03285i	0.999442	−	0.0334047i	$-0.0106350\pi$
$524$	12.2897	−	3.69885i	0.536877	−	0.161585i
$525$	−6.18738	−	21.7165i	−0.270039	−	0.947785i
$526$	−4.11512	+	16.3530i	−0.179428	+	0.713023i
$527$			32.3473i			1.40907i
$528$	−16.2270	+	10.7407i	−0.706187	+	0.467427i
$529$	41.0827			1.78620
$530$	−14.0390	+	4.11241i	−0.609816	+	0.178631i
$531$	5.30843	−	5.30843i	0.230366	−	0.230366i
$532$	−12.1398	+	3.65375i	−0.526329	+	0.158410i
$533$	0.381339	−	0.381339i	0.0165176	−	0.0165176i
$534$	0.420600	+	0.703464i	0.0182012	+	0.0304419i
$535$	−7.57706	−	12.8882i	−0.327585	−	0.557205i
$536$	−7.49768	+	0.343810i	−0.323851	+	0.0148503i
$537$	−23.7986			−1.02698
$538$	8.46080	+	14.1509i	0.364771	+	0.610088i
$539$	−46.0808	−	46.0808i	−1.98484	−	1.98484i
$540$	−0.171823	−	4.46883i	−0.00739408	−	0.192308i
$541$	−22.9002	+	22.9002i	−0.984558	+	0.984558i	−0.999883	−	0.0153248i	$-0.995122\pi$
$541$	−22.9002	+	22.9002i	−0.984558	+	0.984558i	0.0153248	+	0.999883i	$0.495122\pi$
$542$	−9.28229	+	36.8866i	−0.398708	+	1.58442i
$543$			14.7083i			0.631193i
$544$	−9.44570	−	26.8587i	−0.404981	−	1.15156i
$545$	0.257570	+	0.438114i	0.0110331	+	0.0187667i
$546$	0.995201	+	0.250436i	0.0425907	+	0.0107177i
$547$	24.1611	+	24.1611i	1.03306	+	1.03306i	0.999435	+	0.0336209i	$0.0107039\pi$
$547$	24.1611	+	24.1611i	1.03306	+	1.03306i	0.0336209	+	0.999435i	$0.489296\pi$
$548$	0.790764	+	0.424887i	0.0337797	+	0.0181503i
$549$	−5.87487	−	5.87487i	−0.250733	−	0.250733i
$550$	34.3834	−	1.06750i	1.46612	−	0.0455184i
$551$		−	2.01918i		−	0.0860201i
$552$	22.6183	−	1.03717i	0.962697	−	0.0441450i
$553$	−7.97098			−0.338961
$554$	−16.2464	−	27.1724i	−0.690242	−	1.15445i
$555$	−1.29846	+	5.00330i	−0.0551164	+	0.212378i
$556$	4.17906	+	13.8852i	0.177232	+	0.588864i
$557$	−4.87106	−	4.87106i	−0.206393	−	0.206393i	0.596339	−	0.802733i	$-0.296621\pi$
$557$	−4.87106	−	4.87106i	−0.206393	−	0.206393i	−0.802733	+	0.596339i	$0.796621\pi$
$558$	−8.81431	−	2.21806i	−0.373139	−	0.0938981i
$559$	−1.29114			−0.0546095
$560$	38.2039	−	13.1190i	1.61441	−	0.554380i
$561$	24.4853			1.03377
$562$	−38.2019	−	9.61327i	−1.61145	−	0.405511i
$563$	1.64374	+	1.64374i	0.0692752	+	0.0692752i	0.740896	−	0.671620i	$-0.234401\pi$
$563$	1.64374	+	1.64374i	0.0692752	+	0.0692752i	−0.671620	+	0.740896i	$0.734401\pi$
$564$	17.4328	−	5.24678i	0.734052	−	0.220929i
$565$	2.21823	+	0.575675i	0.0933217	+	0.0242188i
$566$	2.69194	+	4.50233i	0.113151	+	0.189247i
$567$	4.51614			0.189660
$568$	−1.32749	−	1.21109i	−0.0557004	−	0.0508161i
$569$		−	30.0890i		−	1.26140i	−0.776028	−	0.630699i	$-0.782768\pi$
$569$		−	30.0890i		−	1.26140i	0.776028	−	0.630699i	$-0.217232\pi$
$570$	3.89428	+	2.12970i	0.163114	+	0.0892032i
$571$	12.4422	+	12.4422i	0.520688	+	0.520688i	0.917779	−	0.397091i	$-0.129980\pi$
$571$	12.4422	+	12.4422i	0.520688	+	0.520688i	−0.397091	+	0.917779i	$0.629980\pi$
$572$	−0.739970	+	1.37717i	−0.0309397	+	0.0575824i
$573$	−14.7251	−	14.7251i	−0.615151	−	0.615151i
$574$	20.7881	+	5.23119i	0.867679	+	0.218346i
$575$	−34.9745	−	19.4641i	−1.45854	−	0.811708i
$576$	7.96643	−	0.732149i	0.331934	−	0.0305062i
$577$		−	38.4529i		−	1.60081i	−0.599457	−	0.800407i	$-0.704617\pi$
$577$		−	38.4529i		−	1.60081i	0.599457	−	0.800407i	$-0.295383\pi$
$578$	−2.87539	+	11.4264i	−0.119600	+	0.475277i
$579$	−4.11912	+	4.11912i	−0.171185	+	0.171185i
$580$	0.247179	+	6.42873i	0.0102636	+	0.266939i
$581$	−28.8659	−	28.8659i	−1.19756	−	1.19756i
$582$	11.0869	+	18.5431i	0.459568	+	0.768638i
$583$	22.5054			0.932078
$584$	11.7086	−	12.8340i	0.484504	−	0.531074i
$585$	−0.182092	−	0.309729i	−0.00752858	−	0.0128057i
$586$	7.95986	+	13.3131i	0.328819	+	0.549957i
$587$	20.0374	−	20.0374i	0.827031	−	0.827031i	−0.160074	−	0.987105i	$-0.551173\pi$
$587$	20.0374	−	20.0374i	0.827031	−	0.827031i	0.987105	+	0.160074i	$0.0511734\pi$
$588$	7.72125	+	25.6544i	0.318419	+	1.05797i
$589$	6.37875	−	6.37875i	0.262832	−	0.262832i
$590$	−6.67366	−	22.7827i	−0.274750	−	0.937948i
$591$	−15.6491			−0.643719
$592$	−9.06106	−	1.84339i	−0.372407	−	0.0757627i
$593$			39.5143i			1.62266i	0.584590	+	0.811329i	$0.301255\pi$
$593$			39.5143i			1.62266i	−0.584590	+	0.811329i	$0.698745\pi$
$594$	−1.67896	+	6.67200i	−0.0688887	+	0.273755i
$595$	−49.1961	−	12.7674i	−2.01684	−	0.523411i
$596$	−3.72128	−	12.3642i	−0.152429	−	0.506457i
$597$	4.98202	−	4.98202i	0.203901	−	0.203901i
$598$	1.56127	−	0.933484i	0.0638452	−	0.0381730i
$599$		−	46.6476i		−	1.90597i	−0.303022	−	0.952984i	$-0.597996\pi$
$599$		−	46.6476i		−	1.90597i	0.303022	−	0.952984i	$-0.402004\pi$
$600$	−12.6594	−	6.30387i	−0.516819	−	0.257354i
$601$		−	39.8224i		−	1.62439i	−0.583386	−	0.812195i	$-0.698273\pi$
$601$		−	39.8224i		−	1.62439i	0.583386	−	0.812195i	$-0.301727\pi$
$602$	−26.3364	−	44.0483i	−1.07339	−	1.79527i
$603$	−1.87639	+	1.87639i	−0.0764125	+	0.0764125i
$604$	6.47795	−	12.0562i	0.263584	−	0.490560i
$605$	−27.4165	−	7.11514i	−1.11464	−	0.289271i
$606$	5.05518	+	1.27210i	0.205353	+	0.0516757i
$607$		−	29.2165i		−	1.18586i	−0.805254	−	0.592930i	$-0.797971\pi$
$607$		−	29.2165i		−	1.18586i	0.805254	−	0.592930i	$-0.202029\pi$
$608$	−3.43378	+	7.15909i	−0.139258	+	0.290339i
$609$	−6.49679			−0.263263
$610$	−25.2137	+	7.38577i	−1.02087	+	0.299041i
$611$	1.03422	−	1.03422i	0.0418400	−	0.0418400i
$612$	−8.86716	−	4.76443i	−0.358434	−	0.192591i
$613$	19.6885	−	19.6885i	0.795212	−	0.795212i	−0.187124	−	0.982336i	$-0.559917\pi$
$613$	19.6885	−	19.6885i	0.795212	−	0.795212i	0.982336	+	0.187124i	$0.0599167\pi$
$614$	4.47622	−	2.67633i	0.180645	−	0.108008i
$615$	−3.80360	−	6.46973i	−0.153376	−	0.260885i
$616$	−62.0769	+	2.84657i	−2.50115	+	0.114692i
$617$	10.8873			0.438306			0.219153	−	0.975691i	$-0.429671\pi$
$617$	10.8873			0.438306			0.219153	+	0.975691i	$0.429671\pi$
$618$	−11.2431	+	6.72224i	−0.452264	+	0.270408i
$619$	31.2108	+	31.2108i	1.25447	+	1.25447i	0.953696	+	0.300773i	$0.0972445\pi$
$619$	31.2108	+	31.2108i	1.25447	+	1.25447i	0.300773	+	0.953696i	$0.402755\pi$
$620$	−19.5280	+	21.0897i	−0.784263	+	0.846983i
$621$	5.66051	−	5.66051i	0.227148	−	0.227148i
$622$	27.6543	+	6.95902i	1.10884	+	0.279031i
$623$			2.61735i			0.104862i
$624$	0.535950	−	0.354746i	0.0214552	−	0.0142012i
$625$	13.1762	+	21.2459i	0.527048	+	0.849835i
$626$	−8.02647	+	31.8962i	−0.320802	+	1.27483i
$627$	−4.82840	−	4.82840i	−0.192828	−	0.192828i
$628$	−1.51601	−	5.03705i	−0.0604955	−	0.201000i
$629$	8.22700	+	8.22700i	0.328032	+	0.328032i
$630$	6.85237	−	12.5300i	0.273005	−	0.499207i
$631$		−	15.8570i		−	0.631257i	−0.948883	−	0.315629i	$-0.897785\pi$
$631$		−	15.8570i		−	0.631257i	0.948883	−	0.315629i	$-0.102215\pi$
$632$	−3.36459	+	3.68799i	−0.133836	+	0.146700i
$633$	−0.223481			−0.00888257
$634$	−29.4151	+	17.5873i	−1.16822	+	0.698480i
$635$	−20.1106	−	5.21910i	−0.798065	−	0.207114i
$636$	−8.15016	−	4.37918i	−0.323175	−	0.173646i
$637$	1.52197	+	1.52197i	0.0603027	+	0.0603027i
$638$	2.41531	−	9.59813i	0.0956230	−	0.379994i
$639$	−0.635312			−0.0251326
$640$	10.0562	−	23.2136i	0.397505	−	0.917600i
$641$	−10.9256			−0.431535			−0.215767	−	0.976445i	$-0.569225\pi$
$641$	−10.9256			−0.431535			−0.215767	+	0.976445i	$0.569225\pi$
$642$	2.30748	−	9.16965i	0.0910691	−	0.361897i
$643$	−34.9865	−	34.9865i	−1.37973	−	1.37973i	−0.845058	−	0.534675i	$-0.820434\pi$
$643$	−34.9865	−	34.9865i	−1.37973	−	1.37973i	−0.534675	−	0.845058i	$-0.679566\pi$
$644$	63.6930	+	34.2230i	2.50986	+	1.34858i
$645$	−4.51352	+	17.3918i	−0.177720	+	0.684802i
$646$	8.57479	−	5.12686i	0.337371	−	0.201714i
$647$	−8.60364			−0.338244			−0.169122	−	0.985595i	$-0.554093\pi$
$647$	−8.60364			−0.338244			−0.169122	+	0.985595i	$0.554093\pi$
$648$	1.90629	−	2.08952i	0.0748860	−	0.0820839i
$649$			36.5220i			1.43361i
$650$	−1.13563	+	0.0352578i	−0.0445430	+	0.00138293i
$651$	−20.5239	−	20.5239i	−0.804393	−	0.804393i
$652$	7.68721	+	25.5413i	0.301054	+	1.00027i
$653$	−9.44853	−	9.44853i	−0.369750	−	0.369750i	0.497636	−	0.867386i	$-0.334201\pi$
$653$	−9.44853	−	9.44853i	−0.369750	−	0.369750i	−0.867386	+	0.497636i	$0.834201\pi$
$654$	−0.0784393	+	0.311708i	−0.00306722	+	0.0121887i
$655$	−7.27227	−	12.3698i	−0.284151	−	0.483327i
$656$	11.1951	−	7.41006i	0.437096	−	0.289314i
$657$		−	6.14208i		−	0.239625i
$658$	56.3788	+	14.1874i	2.19788	+	0.553081i
$659$	−4.77731	+	4.77731i	−0.186098	+	0.186098i	−0.794007	−	0.607909i	$-0.792009\pi$
$659$	−4.77731	+	4.77731i	−0.186098	+	0.186098i	0.607909	+	0.794007i	$0.292009\pi$
$660$	15.9639	+	14.7817i	0.621393	+	0.575378i
$661$	14.2928	+	14.2928i	0.555927	+	0.555927i	0.928145	−	0.372218i	$-0.121403\pi$
$661$	14.2928	+	14.2928i	0.555927	+	0.555927i	−0.372218	+	0.928145i	$0.621403\pi$
$662$	−3.54761	+	2.12111i	−0.137882	+	0.0824394i
$663$	−0.808709			−0.0314076
$664$	−25.5400	+	1.17115i	−0.991143	+	0.0454494i
$665$	7.18360	+	12.2189i	0.278568	+	0.473831i
$666$	−2.80590	+	1.67765i	−0.108727	+	0.0650075i
$667$	−8.14304	+	8.14304i	−0.315300	+	0.315300i
$668$	37.4504	+	20.1225i	1.44900	+	0.778564i
$669$	−5.92653	+	5.92653i	−0.229133	+	0.229133i
$670$	2.35896	+	8.05308i	0.0911347	+	0.311118i
$671$	40.4191			1.56036
$672$	23.0346	+	11.0483i	0.888579	+	0.426197i
$673$			19.6076i			0.755818i	0.925843	+	0.377909i	$0.123357\pi$
$673$			19.6076i			0.755818i	−0.925843	+	0.377909i	$0.876643\pi$
$674$	48.3654	+	12.1708i	1.86297	+	0.468803i
$675$	−4.80863	+	1.37006i	−0.185084	+	0.0527336i
$676$	−12.2817	+	22.8577i	−0.472375	+	0.879144i
$677$	1.22231	−	1.22231i	0.0469773	−	0.0469773i	−0.683228	−	0.730205i	$-0.739424\pi$
$677$	1.22231	−	1.22231i	0.0469773	−	0.0469773i	0.730205	+	0.683228i	$0.239424\pi$
$678$	0.743791	+	1.24401i	0.0285651	+	0.0477758i
$679$			68.9927i			2.64770i
$680$	−26.6731	+	17.3727i	−1.02287	+	0.666214i
$681$			9.52569i			0.365025i
$682$	37.9514	−	22.6911i	1.45323	−	0.868887i
$683$	−27.1537	+	27.1537i	−1.03901	+	1.03901i	−0.0398011	+	0.999208i	$0.512672\pi$
$683$	−27.1537	+	27.1537i	−1.03901	+	1.03901i	−0.999208	+	0.0398011i	$0.987328\pi$
$684$	0.809042	+	2.68810i	0.0309345	+	0.102782i
$685$	0.252113	−	0.971460i	0.00963274	−	0.0371176i
$686$	−9.96815	+	39.6122i	−0.380586	+	1.51240i
$687$			19.3422i			0.737950i
$688$	−31.4969	−	6.40773i	−1.20081	−	0.244293i
$689$	−0.743316			−0.0283181
$690$	−7.11629	−	24.2937i	−0.270912	−	0.924847i
$691$	14.8065	−	14.8065i	0.563266	−	0.563266i	−0.366968	−	0.930234i	$-0.619604\pi$
$691$	14.8065	−	14.8065i	0.563266	−	0.563266i	0.930234	+	0.366968i	$0.119604\pi$
$692$	3.18717	+	10.5896i	0.121158	+	0.402556i
$693$	−15.5355	+	15.5355i	−0.590147	+	0.590147i
$694$	2.09051	+	3.49643i	0.0793547	+	0.132723i
$695$	13.9757	−	8.21641i	0.530129	−	0.311666i
$696$	−2.74233	+	3.00591i	−0.103948	+	0.113939i
$697$	−16.8926			−0.639853
$698$	20.2939	+	33.9420i	0.768135	+	1.28472i
$699$	−1.15076	−	1.15076i	−0.0435256	−	0.0435256i
$700$	−24.3672	−	38.0237i	−0.920992	−	1.43716i
$701$	−0.259714	+	0.259714i	−0.00980927	+	0.00980927i	−0.711994	−	0.702185i	$-0.752208\pi$
$701$	−0.259714	+	0.259714i	−0.00980927	+	0.00980927i	0.702185	+	0.711994i	$0.252208\pi$
$702$	0.0554535	−	0.220365i	0.00209296	−	0.00831715i
$703$		−	3.24466i		−	0.122375i
$704$	−24.8859	+	29.9231i	−0.937924	+	1.12777i
$705$	−10.3156	−	17.5464i	−0.388509	−	0.660835i
$706$	−14.5098	−	3.65131i	−0.546085	−	0.137419i
$707$	11.7708	+	11.7708i	0.442688	+	0.442688i
$708$	7.10658	−	13.2262i	0.267082	−	0.497070i
$709$	−16.6998	−	16.6998i	−0.627173	−	0.627173i	0.320183	−	0.947356i	$-0.396256\pi$
$709$	−16.6998	−	16.6998i	−0.627173	−	0.627173i	−0.947356	+	0.320183i	$0.896256\pi$
$710$	−0.963963	+	1.76267i	−0.0361769	+	0.0661517i
$711$			1.76500i			0.0661925i
$712$	1.21099	+	1.10480i	0.0453837	+	0.0414040i
$713$	−51.4489			−1.92678
$714$	−16.4959	−	27.5897i	−0.617342	−	1.03252i
$715$	1.69187	+	0.439073i	0.0632722	+	0.0164204i
$716$	−45.5776	+	13.7176i	−1.70332	+	0.512650i
$717$	8.97378	+	8.97378i	0.335132	+	0.335132i
$718$	44.8818	+	11.2942i	1.67497	+	0.421496i
$719$	0.0356124			0.00132812			0.000664059	−	1.00000i	$-0.499789\pi$
$719$	0.0356124			0.00132812			0.000664059		1.00000i	$0.499789\pi$
$720$	−2.90492	−	8.45940i	−0.108260	−	0.315263i
$721$	−41.8318			−1.55790
$722$	23.3558	+	5.87733i	0.869212	+	0.218731i
$723$	−14.9223	−	14.9223i	−0.554966	−	0.554966i
$724$	8.47791	+	28.1684i	0.315079	+	1.04687i
$725$	6.91755	−	1.97093i	0.256912	−	0.0731983i
$726$	−9.19299	−	15.3755i	−0.341184	−	0.570638i
$727$	−35.1597			−1.30400			−0.652000	−	0.758219i	$-0.726070\pi$
$727$	−35.1597			−1.30400			−0.652000	+	0.758219i	$0.726070\pi$
$728$	2.05030	−	0.0940176i	0.0759892	−	0.00348453i
$729$		−	1.00000i		−	0.0370370i
$730$	−17.0411	−	9.31942i	−0.630721	−	0.344927i
$731$	28.5976	+	28.5976i	1.05772	+	1.05772i
$732$	−14.6375	−	7.86489i	−0.541017	−	0.290695i
$733$	27.9959	+	27.9959i	1.03405	+	1.03405i	0.999399	+	0.0346524i	$0.0110324\pi$
$733$	27.9959	+	27.9959i	1.03405	+	1.03405i	0.0346524	+	0.999399i	$0.488968\pi$
$734$	−30.2086	−	7.60180i	−1.11502	−	0.280588i
$735$	25.8216	−	15.1807i	0.952443	−	0.559947i
$736$	42.7193	−	15.0236i	1.57465	−	0.553776i
$737$		−	12.9096i		−	0.475530i
$738$	1.15833	−	4.60307i	0.0426388	−	0.169441i
$739$	22.3803	−	22.3803i	0.823274	−	0.823274i	−0.163302	−	0.986576i	$-0.552215\pi$
$739$	22.3803	−	22.3803i	0.823274	−	0.823274i	0.986576	+	0.163302i	$0.0522145\pi$
$740$	0.397197	+	10.3305i	0.0146013	+	0.379755i
$741$	0.159474	+	0.159474i	0.00585843	+	0.00585843i
$742$	−15.1620	−	25.3588i	−0.556614	−	0.930950i
$743$	−11.3806			−0.417514			−0.208757	−	0.977968i	$-0.566942\pi$
$743$	−11.3806			−0.417514			−0.208757	+	0.977968i	$0.566942\pi$
$744$	−18.1591	+	0.832697i	−0.665746	+	0.0305281i
$745$	−12.4448	+	7.31637i	−0.455941	+	0.268051i
$746$	9.94940	+	16.6406i	0.364273	+	0.609256i
$747$	−6.39170	+	6.39170i	−0.233860	+	0.233860i
$748$	46.8927	−	14.1134i	1.71457	−	0.516037i
$749$	21.3513	−	21.3513i	0.780158	−	0.780158i
$750$	−3.49496	+	15.4203i	−0.127618	+	0.563069i
$751$	54.6781			1.99523			0.997616	−	0.0690113i	$-0.0219845\pi$
$751$	54.6781			1.99523			0.997616	+	0.0690113i	$0.0219845\pi$
$752$	30.3619	−	20.0966i	1.10719	−	0.732848i
$753$		−	24.7396i		−	0.901561i
$754$	−0.0797737	+	0.317011i	−0.00290519	+	0.0115448i
$755$	−14.8112	−	3.84379i	−0.539033	−	0.139890i
$756$	8.64905	−	2.60312i	0.314563	−	0.0946746i
$757$	−32.3418	+	32.3418i	−1.17548	+	1.17548i	−0.194602	+	0.980882i	$0.562342\pi$
$757$	−32.3418	+	32.3418i	−1.17548	+	1.17548i	−0.980882	+	0.194602i	$0.937658\pi$
$758$	−12.7845	+	7.64382i	−0.464353	+	0.277636i
$759$			38.9443i			1.41359i
$760$	8.68566	+	1.83399i	0.315062	+	0.0665258i
$761$			0.392110i			0.0142140i	0.999975	+	0.00710700i	$0.00226225\pi$
$761$			0.392110i			0.0142140i	−0.999975	+	0.00710700i	$0.997738\pi$
$762$	−6.74325	−	11.2782i	−0.244282	−	0.408568i
$763$	−0.725803	+	0.725803i	−0.0262758	+	0.0262758i
$764$	−36.6883	−	19.7131i	−1.32734	−	0.713194i
$765$	−2.82705	+	10.8934i	−0.102212	+	0.393851i
$766$	−10.0196	−	2.52137i	−0.362023	−	0.0911007i
$767$		−	1.20626i		−	0.0435556i
$768$	14.8348	−	5.99404i	0.535305	−	0.216291i
$769$	−4.36080			−0.157255			−0.0786273	−	0.996904i	$-0.525054\pi$
$769$	−4.36080			−0.157255			−0.0786273	+	0.996904i	$0.525054\pi$
$770$	19.5310	+	66.6754i	0.703848	+	2.40281i
$771$	5.51668	−	5.51668i	0.198679	−	0.198679i
$772$	−5.51441	+	10.2630i	−0.198468	+	0.369372i
$773$	17.2357	−	17.2357i	0.619923	−	0.619923i	−0.325588	−	0.945512i	$-0.605562\pi$
$773$	17.2357	−	17.2357i	0.619923	−	0.619923i	0.945512	+	0.325588i	$0.105562\pi$
$774$	−9.75352	+	5.83162i	−0.350583	+	0.209613i
$775$	28.0794	+	15.6268i	1.00864	+	0.561330i
$776$	31.9213	+	29.1221i	1.14591	+	1.04542i
$777$	−10.4398			−0.374526
$778$	−18.2938	+	10.9378i	−0.655863	+	0.392140i
$779$	3.33115	+	3.33115i	0.119351	+	0.119351i
$780$	−0.527260	−	0.488216i	−0.0188790	−	0.0174809i
$781$	2.18548	−	2.18548i	0.0782024	−	0.0782024i
$782$	−55.2565	−	13.9050i	−1.97597	−	0.497240i
$783$			1.43857i			0.0514103i
$784$	29.5745	+	44.6811i	1.05623	+	1.59576i
$785$	−5.06988	+	2.98062i	−0.180952	+	0.106383i
$786$	2.21466	−	8.80080i	0.0789945	−	0.313914i
$787$	24.9814	+	24.9814i	0.890490	+	0.890490i	0.994569	−	0.104079i	$-0.0331895\pi$
$787$	24.9814	+	24.9814i	0.890490	+	0.890490i	−0.104079	+	0.994569i	$0.533189\pi$
$788$	−29.9703	+	9.02021i	−1.06765	+	0.321332i
$789$	8.43139	+	8.43139i	0.300165	+	0.300165i
$790$	4.89696	+	2.67804i	0.174226	+	0.0952804i
$791$			4.62853i			0.164572i
$792$	0.630310	+	13.7456i	0.0223971	+	0.488427i
$793$	−1.33498			−0.0474064
$794$	5.32314	−	3.18270i	0.188911	−	0.112950i
$795$	−2.59845	+	10.0125i	−0.0921576	+	0.355108i
$796$	6.66961	−	12.4129i	0.236398	−	0.439964i
$797$	−18.8067	−	18.8067i	−0.666166	−	0.666166i	0.290660	−	0.956826i	$-0.406125\pi$
$797$	−18.8067	−	18.8067i	−0.666166	−	0.666166i	−0.956826	+	0.290660i	$0.906125\pi$
$798$	−2.18766	+	8.69350i	−0.0774424	+	0.307746i
$799$	−45.8139			−1.62078
$800$	−27.8782	−	4.77585i	−0.985641	−	0.168852i
$801$	0.579554			0.0204775
$802$	−3.41187	+	13.5583i	−0.120477	+	0.478761i
$803$	21.1288	+	21.1288i	0.745618	+	0.745618i
$804$	−2.51199	+	4.67511i	−0.0885911	+	0.164878i
$805$	20.3067	−	78.2474i	0.715718	−	2.75786i
$806$	−1.25347	+	0.749450i	−0.0441517	+	0.0263982i
$807$	11.6583			0.410392
$808$	10.4146	−	0.477568i	0.366385	−	0.0168008i
$809$		−	48.5593i		−	1.70726i	−0.520883	−	0.853628i	$-0.674397\pi$
$809$		−	48.5593i		−	1.70726i	0.520883	−	0.853628i	$-0.325603\pi$
$810$	−2.77449	−	1.51731i	−0.0974856	−	0.0533127i
$811$	−14.4543	−	14.4543i	−0.507560	−	0.507560i	0.406217	−	0.913777i	$-0.366848\pi$
$811$	−14.4543	−	14.4543i	−0.507560	−	0.507560i	−0.913777	+	0.406217i	$0.866848\pi$
$812$	−12.4423	+	3.74477i	−0.436638	+	0.131416i
$813$	19.0183	+	19.0183i	0.667002	+	0.667002i
$814$	3.88121	−	15.4234i	0.136036	−	0.540591i
$815$	25.7077	−	15.1137i	0.900502	−	0.529411i
$816$	−19.7281	−	4.01349i	−0.690621	−	0.140500i
$817$		−	11.2787i		−	0.394591i
$818$	16.0327	+	4.03453i	0.560571	+	0.141064i
$819$	0.513114	−	0.513114i	0.0179296	−	0.0179296i
$820$	−11.0136	−	10.1980i	−0.384612	−	0.356131i
$821$	−29.1579	−	29.1579i	−1.01762	−	1.01762i	−0.999842	−	0.0177763i	$-0.994341\pi$
$821$	−29.1579	−	29.1579i	−1.01762	−	1.01762i	−0.0177763	−	0.999842i	$-0.505659\pi$
$822$	0.544805	−	0.325738i	0.0190023	−	0.0113614i
$823$	−7.17233			−0.250012			−0.125006	−	0.992156i	$-0.539895\pi$
$823$	−7.17233			−0.250012			−0.125006	+	0.992156i	$0.539895\pi$
$824$	−17.6574	+	19.3546i	−0.615124	+	0.674249i
$825$	11.8287	−	21.2547i	0.411822	−	0.739994i
$826$	41.1525	−	24.6050i	1.43188	−	0.856119i
$827$	21.6132	−	21.6132i	0.751564	−	0.751564i	−0.223207	−	0.974771i	$-0.571653\pi$
$827$	21.6132	−	21.6132i	0.751564	−	0.751564i	0.974771	+	0.223207i	$0.0716526\pi$
$828$	7.57793	−	14.1034i	0.263351	−	0.490127i
$829$	−21.3762	+	21.3762i	−0.742424	+	0.742424i	−0.973044	−	0.230620i	$-0.925925\pi$
$829$	−21.3762	+	21.3762i	−0.742424	+	0.742424i	0.230620	+	0.973044i	$0.425925\pi$
$830$	8.03553	+	27.4319i	0.278917	+	0.952174i
$831$	−22.3862			−0.776569
$832$	0.821942	−	0.988312i	0.0284957	−	0.0342635i
$833$		−	67.4205i		−	2.33598i
$834$	9.94339	+	2.50219i	0.344311	+	0.0866437i
$835$	11.9400	−	46.0081i	0.413201	−	1.59217i
$836$	−12.0302	−	6.46395i	−0.416072	−	0.223560i
$837$	−4.54455	+	4.54455i	−0.157083	+	0.157083i
$838$	−5.81443	−	9.72476i	−0.200856	−	0.335936i
$839$			1.15350i			0.0398234i	0.999802	+	0.0199117i	$0.00633851\pi$
$839$			1.15350i			0.0398234i	−0.999802	+	0.0199117i	$0.993661\pi$
$840$	5.90092	−	27.9464i	0.203601	−	0.964243i
$841$			26.9305i			0.928638i
$842$	33.8920	−	20.2640i	1.16800	−	0.698344i
$843$	−19.6965	+	19.6965i	−0.678382	+	0.678382i
$844$	−0.427997	+	0.128815i	−0.0147323	+	0.00443400i
$845$	28.0809	+	7.28755i	0.966013	+	0.250700i
$846$	3.14148	−	12.4838i	0.108006	−	0.429203i
$847$		−	57.2070i		−	1.96566i
$848$	−18.1329	−	3.68896i	−0.622685	−	0.126679i
$849$	3.70928			0.127302
$850$	25.9341	+	24.3722i	0.889531	+	0.835960i
$851$	−13.0852	+	13.0852i	−0.448555	+	0.448555i
$852$	−1.21671	+	0.366196i	−0.0416839	+	0.0125457i
$853$	−27.6979	+	27.6979i	−0.948358	+	0.948358i	−0.998730	−	0.0503728i	$-0.983959\pi$
$853$	−27.6979	+	27.6979i	−0.948358	+	0.948358i	0.0503728	+	0.998730i	$0.483959\pi$
$854$	−27.2305	−	45.5437i	−0.931810	−	1.55847i
$855$	2.70562	−	1.59065i	0.0925301	−	0.0543991i
$856$	−0.866266	−	18.8912i	−0.0296084	−	0.645688i
$857$	−49.0796			−1.67653			−0.838263	−	0.545266i	$-0.816429\pi$
$857$	−49.0796			−1.67653			−0.838263	+	0.545266i	$0.816429\pi$
$858$	0.567296	+	0.948816i	0.0193672	+	0.0323921i
$859$	−28.4421	−	28.4421i	−0.970433	−	0.970433i	0.0291421	−	0.999575i	$-0.490722\pi$
$859$	−28.4421	−	28.4421i	−0.970433	−	0.970433i	−0.999575	+	0.0291421i	$0.990722\pi$
$860$	1.38068	+	35.9094i	0.0470809	+	1.22450i
$861$	10.7181	−	10.7181i	0.365272	−	0.365272i
$862$	−3.74278	+	14.8734i	−0.127480	+	0.506589i
$863$			24.2991i			0.827151i	0.910470	+	0.413576i	$0.135720\pi$
$863$			24.2991i			0.827151i	−0.910470	+	0.413576i	$0.864280\pi$
$864$	2.44640	−	5.10050i	0.0832282	−	0.173523i
$865$	10.6586	−	6.26627i	0.362404	−	0.213060i
$866$	21.2418	+	5.34536i	0.721826	+	0.181643i
$867$	5.89133	+	5.89133i	0.200080	+	0.200080i
$868$	−51.1361	−	27.4760i	−1.73567	−	0.932597i
$869$	−6.07159	−	6.07159i	−0.205965	−	0.205965i
$870$	3.99130	+	2.18275i	0.135318	+	0.0740022i
$871$			0.426382i			0.0144474i
$872$	0.0294474	+	0.642177i	0.000997214	+	0.0217469i
$873$	15.2769			0.517045
$874$	8.15437	+	13.6384i	0.275826	+	0.461325i
$875$	−34.8492	+	36.5374i	−1.17812	+	1.23519i
$876$	−3.54032	−	11.7629i	−0.119616	−	0.397433i
$877$	14.7778	+	14.7778i	0.499010	+	0.499010i	0.911130	−	0.412120i	$-0.135211\pi$
$877$	14.7778	+	14.7778i	0.499010	+	0.499010i	−0.412120	+	0.911130i	$0.635211\pi$
$878$	−14.3570	−	3.61286i	−0.484527	−	0.121928i
$879$	10.9681			0.369943
$880$	39.0933	+	19.1074i	1.31783	+	0.644112i
$881$	29.8866			1.00691			0.503453	−	0.864023i	$-0.332063\pi$
$881$	29.8866			1.00691			0.503453	+	0.864023i	$0.332063\pi$
$882$	18.3714	+	4.62305i	0.618598	+	0.155666i
$883$	16.5411	+	16.5411i	0.556653	+	0.556653i	0.928353	−	0.371700i	$-0.121225\pi$
$883$	16.5411	+	16.5411i	0.556653	+	0.556653i	−0.371700	+	0.928353i	$0.621225\pi$
$884$	−1.54879	+	0.466142i	−0.0520914	+	0.0156781i
$885$	−16.2485	−	4.21680i	−0.546186	−	0.141746i
$886$	−16.0494	−	26.8430i	−0.539190	−	0.901807i
$887$	36.8915			1.23870			0.619348	−	0.785116i	$-0.287397\pi$
$887$	36.8915			1.23870			0.619348	+	0.785116i	$0.287397\pi$
$888$	−4.40670	+	4.83026i	−0.147879	+	0.162093i
$889$		−	41.9625i		−	1.40738i
$890$	0.879361	−	1.60797i	0.0294763	−	0.0538991i
$891$	3.44000	+	3.44000i	0.115244	+	0.115244i
$892$	−7.93406	+	14.7662i	−0.265652	+	0.494409i
$893$	9.03432	+	9.03432i	0.302322	+	0.302322i
$894$	−8.85417	−	2.22809i	−0.296128	−	0.0745186i
$895$	26.9700	+	45.8746i	0.901508	+	1.53342i
$896$	50.4828	+	7.88179i	1.68651	+	0.263312i
$897$		−	1.28627i		−	0.0429472i
$898$	7.66575	−	30.4627i	0.255809	−	1.01655i
$899$	6.53766	−	6.53766i	0.218043	−	0.218043i
$900$	−8.41949	+	5.39556i	−0.280650	+	0.179852i
$901$	16.4638	+	16.4638i	0.548487	+	0.548487i
$902$	11.8499	+	19.8192i	0.394558	+	0.659908i
$903$	−36.2895			−1.20764
$904$	2.14151	+	1.95372i	0.0712257	+	0.0649799i
$905$	28.3520	−	16.6683i	0.942452	−	0.554074i
$906$	−4.96630	−	8.30626i	−0.164994	−	0.275957i
$907$	−19.6564	+	19.6564i	−0.652679	+	0.652679i	−0.953637	−	0.300958i	$-0.902694\pi$
$907$	−19.6564	+	19.6564i	−0.652679	+	0.652679i	0.300958	+	0.953637i	$0.402694\pi$
$908$	5.49064	+	18.2430i	0.182213	+	0.605416i
$909$	2.60639	−	2.60639i	0.0864486	−	0.0864486i
$910$	−0.645077	−	2.20218i	−0.0213841	−	0.0730015i
$911$	−10.4327			−0.345650			−0.172825	−	0.984953i	$-0.555289\pi$
$911$	−10.4327			−0.345650			−0.172825	+	0.984953i	$0.555289\pi$
$912$	3.09886	+	4.68175i	0.102613	+	0.155028i
$913$		−	43.9749i		−	1.45536i
$914$	9.82730	−	39.0525i	0.325058	−	1.29174i
$915$	−4.66675	+	17.9823i	−0.154278	+	0.594475i
$916$	11.1489	+	37.0429i	0.368370	+	1.22393i
$917$	20.4924	−	20.4924i	0.676719	−	0.676719i
$918$	−6.10913	+	3.65264i	−0.201631	+	0.120555i
$919$			21.6666i			0.714715i	0.933968	+	0.357357i	$0.116322\pi$
$919$			21.6666i			0.714715i	−0.933968	+	0.357357i	$0.883678\pi$
$920$	−27.6317	−	42.4240i	−0.910989	−	1.39868i
$921$		−	3.68777i		−	0.121516i
$922$	−23.3778	−	39.0998i	−0.769905	−	1.28768i
$923$	−0.0721827	+	0.0721827i	−0.00237592	+	0.00237592i
$924$	−20.7980	+	38.7075i	−0.684204	+	1.27338i
$925$	11.1160	−	3.16712i	0.365490	−	0.104134i
$926$	33.7109	+	8.48314i	1.10781	+	0.278773i
$927$			9.26272i			0.304228i
$928$	−3.51932	+	7.33743i	−0.115527	+	0.240863i
$929$	6.46931			0.212251			0.106126	−	0.994353i	$-0.466155\pi$
$929$	6.46931			0.212251			0.106126	+	0.994353i	$0.466155\pi$
$930$	5.71333	+	19.5043i	0.187347	+	0.639571i
$931$	−13.2951	+	13.2951i	−0.435728	+	0.435728i
$932$	−2.86716	−	1.54056i	−0.0939168	−	0.0504626i
$933$	14.2582	−	14.2582i	0.466793	−	0.466793i
$934$	−26.9223	+	16.0968i	−0.880925	+	0.526704i
$935$	−27.7482	−	47.1983i	−0.907463	−	1.54355i
$936$	−0.0208181	−	0.453994i	−0.000680461	−	0.0148392i
$937$	−20.4235			−0.667208			−0.333604	−	0.942713i	$-0.608265\pi$
$937$	−20.4235			−0.667208			−0.333604	+	0.942713i	$0.608265\pi$
$938$	−14.5463	+	8.69724i	−0.474955	+	0.283975i
$939$	16.4453	+	16.4453i	0.536672	+	0.536672i
$940$	−29.8697	−	27.6578i	−0.974242	−	0.902098i
$941$	−28.2871	+	28.2871i	−0.922134	+	0.922134i	−0.997180	−	0.0750464i	$-0.976090\pi$
$941$	−28.2871	+	28.2871i	−0.922134	+	0.922134i	0.0750464	+	0.997180i	$0.476090\pi$
$942$	−3.60710	−	0.907703i	−0.117526	−	0.0295746i
$943$		−	26.8680i		−	0.874943i
$944$	5.98648	−	29.4262i	0.194843	−	0.957742i
$945$	−5.11797	−	8.70541i	−0.166488	−	0.283187i
$946$	13.4913	−	53.6129i	0.438641	−	1.74311i
$947$	8.81881	+	8.81881i	0.286573	+	0.286573i	0.835723	−	0.549151i	$-0.185049\pi$
$947$	8.81881	+	8.81881i	0.286573	+	0.286573i	−0.549151	+	0.835723i	$0.685049\pi$
$948$	1.01735	+	3.38021i	0.0330420	+	0.109784i
$949$	−0.697849	−	0.697849i	−0.0226531	−	0.0226531i
$950$	−0.307992	−	9.92020i	−0.00999257	−	0.321854i
$951$			24.2339i			0.785838i
$952$	−47.4947	−	43.3298i	−1.53931	−	1.40433i
$953$	43.7042			1.41572			0.707858	−	0.706354i	$-0.249661\pi$
$953$	43.7042			1.41572			0.707858	+	0.706354i	$0.249661\pi$
$954$	−5.61514	+	3.35729i	−0.181797	+	0.108696i
$955$	−11.6970	+	45.0719i	−0.378508	+	1.45849i
$956$	22.3586	+	12.0135i	0.723127	+	0.388545i
$957$	−4.94868	−	4.94868i	−0.159968	−	0.159968i
$958$	−3.26462	+	12.9732i	−0.105475	+	0.419145i
$959$	2.02703			0.0654564
$960$	−10.4393	−	14.5265i	−0.336928	−	0.468842i
$961$	10.3059			0.332449
$962$	−0.128190	+	0.509411i	−0.00413301	+	0.0164241i
$963$	−4.72776	−	4.72776i	−0.152350	−	0.152350i
$964$	−37.1795	−	19.9770i	−1.19747	−	0.643416i
$965$	12.6081	+	3.27206i	0.405870	+	0.105331i
$966$	43.8820	−	26.2370i	1.41188	−	0.844161i
$967$	24.4130			0.785068			0.392534	−	0.919738i	$-0.371599\pi$
$967$	24.4130			0.785068			0.392534	+	0.919738i	$0.371599\pi$
$968$	−26.4684	−	24.1473i	−0.850725	−	0.776125i
$969$		−	7.06441i		−	0.226942i
$970$	23.1797	−	42.3856i	0.744257	−	1.36092i
$971$	−3.61271	−	3.61271i	−0.115937	−	0.115937i	0.646758	−	0.762695i	$-0.276124\pi$
$971$	−3.61271	−	3.61271i	−0.115937	−	0.115937i	−0.762695	+	0.646758i	$0.776124\pi$
$972$	−0.576403	−	1.91514i	−0.0184881	−	0.0614281i
$973$	23.1529	+	23.1529i	0.742247	+	0.742247i
$974$	−3.43723	+	13.6591i	−0.110136	+	0.437666i
$975$	−0.390683	+	0.702008i	−0.0125119	+	0.0224823i
$976$	−32.5662	−	6.62527i	−1.04242	−	0.212070i
$977$			52.1693i			1.66904i	0.550975	+	0.834522i	$0.314256\pi$
$977$			52.1693i			1.66904i	−0.550975	+	0.834522i	$0.685744\pi$
$978$	18.2904	+	4.60267i	0.584864	+	0.147177i
$979$	−1.99367	+	1.99367i	−0.0637179	+	0.0637179i
$980$	40.7017	−	43.9567i	1.30017	−	1.40415i
$981$	0.160713	+	0.160713i	0.00513117	+	0.00513117i
$982$	7.47026	−	4.46646i	0.238386	−	0.142531i
$983$	43.2396			1.37913			0.689564	−	0.724225i	$-0.257802\pi$
$983$	43.2396			1.37913			0.689564	+	0.724225i	$0.257802\pi$
$984$	−0.434856	−	9.48318i	−0.0138627	−	0.302313i
$985$	17.7345	+	30.1656i	0.565069	+	0.961155i
$986$	8.78841	−	5.25458i	0.279880	−	0.167340i
$987$	29.0683	−	29.0683i	0.925253	−	0.925253i
$988$	0.397337	+	0.213494i	0.0126410	+	0.00679214i
$989$	−45.4851	+	45.4851i	−1.44634	+	1.44634i
$990$	14.7638	−	4.32471i	0.469224	−	0.137448i
$991$	−48.9048			−1.55351			−0.776756	−	0.629802i	$-0.783136\pi$
$991$	−48.9048			−1.55351			−0.776756	+	0.629802i	$0.783136\pi$
$992$	−34.2973	+	12.0617i	−1.08894	+	0.382960i
$993$			2.92273i			0.0927499i
$994$	−3.93493	−	0.990200i	−0.124808	−	0.0314072i
$995$	−15.2494	−	3.95751i	−0.483438	−	0.125462i
$996$	−8.55680	+	15.9252i	−0.271133	+	0.504609i
$997$	−41.0281	+	41.0281i	−1.29937	+	1.29937i	−0.370565	+	0.928806i	$0.620836\pi$
$997$	−41.0281	+	41.0281i	−1.29937	+	1.29937i	−0.928806	+	0.370565i	$0.879164\pi$
$998$	−3.17606	−	5.31203i	−0.100536	−	0.168149i
$999$			2.31167i			0.0731379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.229.13	yes	48
3.2	odd	2		720.2.bm.h.469.12		48
4.3	odd	2		960.2.bl.a.49.18		48
5.4	even	2	inner	240.2.bl.a.229.12	yes	48
8.3	odd	2		1920.2.bl.b.1249.12		48
8.5	even	2		1920.2.bl.a.1249.13		48
15.14	odd	2		720.2.bm.h.469.13		48
16.3	odd	4		960.2.bl.a.529.12		48
16.5	even	4		1920.2.bl.a.289.12		48
16.11	odd	4		1920.2.bl.b.289.13		48
16.13	even	4	inner	240.2.bl.a.109.12	✓	48
20.19	odd	2		960.2.bl.a.49.12		48
40.19	odd	2		1920.2.bl.b.1249.13		48
40.29	even	2		1920.2.bl.a.1249.12		48
48.29	odd	4		720.2.bm.h.109.13		48
80.19	odd	4		960.2.bl.a.529.18		48
80.29	even	4	inner	240.2.bl.a.109.13	yes	48
80.59	odd	4		1920.2.bl.b.289.12		48
80.69	even	4		1920.2.bl.a.289.13		48
240.29	odd	4		720.2.bm.h.109.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.12	✓	48	16.13	even	4	inner
240.2.bl.a.109.13	yes	48	80.29	even	4	inner
240.2.bl.a.229.12	yes	48	5.4	even	2	inner
240.2.bl.a.229.13	yes	48	1.1	even	1	trivial
720.2.bm.h.109.12		48	240.29	odd	4
720.2.bm.h.109.13		48	48.29	odd	4
720.2.bm.h.469.12		48	3.2	odd	2
720.2.bm.h.469.13		48	15.14	odd	2
960.2.bl.a.49.12		48	20.19	odd	2
960.2.bl.a.49.18		48	4.3	odd	2
960.2.bl.a.529.12		48	16.3	odd	4
960.2.bl.a.529.18		48	80.19	odd	4
1920.2.bl.a.289.12		48	16.5	even	4
1920.2.bl.a.289.13		48	80.69	even	4
1920.2.bl.a.1249.12		48	40.29	even	2
1920.2.bl.a.1249.13		48	8.5	even	2
1920.2.bl.b.289.12		48	80.59	odd	4
1920.2.bl.b.289.13		48	16.11	odd	4
1920.2.bl.b.1249.12		48	8.3	odd	2
1920.2.bl.b.1249.13		48	40.19	odd	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.345118 - 1.37146i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.76179 - 0.946629i) q^{4} +(-0.561697 + 2.16437i) q^{5} +(-1.21380 + 0.725731i) q^{6} -4.51614 q^{7} +(-1.90629 + 2.08952i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.345118 - 1.37146i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.76179 - 0.946629i) q^{4} +(-0.561697 + 2.16437i) q^{5} +(-1.21380 + 0.725731i) q^{6} -4.51614 q^{7} +(-1.90629 + 2.08952i) q^{8} +1.00000i q^{9} +(2.77449 + 1.51731i) q^{10} +(-3.44000 - 3.44000i) q^{11} +(0.576403 + 1.91514i) q^{12} +(0.113618 + 0.113618i) q^{13} +(-1.55860 + 6.19370i) q^{14} +(1.92762 - 1.13326i) q^{15} +(2.20779 + 3.33552i) q^{16} -5.03305i q^{17} +(1.37146 + 0.345118i) q^{18} +(-0.992498 + 0.992498i) q^{19} +(3.03845 - 3.28144i) q^{20} +(3.19340 + 3.19340i) q^{21} +(-5.90502 + 3.53061i) q^{22} +8.00517 q^{23} +(2.82546 - 0.129563i) q^{24} +(-4.36899 - 2.43144i) q^{25} +(0.195033 - 0.116610i) q^{26} +(0.707107 - 0.707107i) q^{27} +(7.95648 + 4.27512i) q^{28} +(-1.01722 + 1.01722i) q^{29} +(-0.888962 - 3.03476i) q^{30} -6.42697 q^{31} +(5.33647 - 1.87673i) q^{32} +4.86490i q^{33} +(-6.90261 - 1.73700i) q^{34} +(2.53670 - 9.77461i) q^{35} +(0.946629 - 1.76179i) q^{36} +(-1.63459 + 1.63459i) q^{37} +(1.01864 + 1.70370i) q^{38} -0.160680i q^{39} +(-3.45173 - 5.29958i) q^{40} -3.35633i q^{41} +(5.48170 - 3.27751i) q^{42} +(-5.68196 + 5.68196i) q^{43} +(2.80414 + 9.31696i) q^{44} +(-2.16437 - 0.561697i) q^{45} +(2.76273 - 10.9787i) q^{46} -9.10261i q^{47} +(0.797427 - 3.91971i) q^{48} +13.3956 q^{49} +(-4.84243 + 5.15275i) q^{50} +(-3.55890 + 3.55890i) q^{51} +(-0.0926163 - 0.307724i) q^{52} +(-3.27113 + 3.27113i) q^{53} +(-0.725731 - 1.21380i) q^{54} +(9.37767 - 5.51320i) q^{55} +(8.60906 - 9.43655i) q^{56} +1.40360 q^{57} +(1.04401 + 1.74614i) q^{58} +(-5.30843 - 5.30843i) q^{59} +(-4.46883 + 0.171823i) q^{60} +(-5.87487 + 5.87487i) q^{61} +(-2.21806 + 8.81431i) q^{62} -4.51614i q^{63} +(-0.732149 - 7.96643i) q^{64} +(-0.309729 + 0.182092i) q^{65} +(6.67200 + 1.67896i) q^{66} +(1.87639 + 1.87639i) q^{67} +(-4.76443 + 8.86716i) q^{68} +(-5.66051 - 5.66051i) q^{69} +(-12.5300 - 6.85237i) q^{70} +0.635312i q^{71} +(-2.08952 - 1.90629i) q^{72} -6.14208 q^{73} +(1.67765 + 2.80590i) q^{74} +(1.37006 + 4.80863i) q^{75} +(2.68810 - 0.809042i) q^{76} +(15.5355 + 15.5355i) q^{77} +(-0.220365 - 0.0554535i) q^{78} +1.76500 q^{79} +(-8.45940 + 2.90492i) q^{80} -1.00000 q^{81} +(-4.60307 - 1.15833i) q^{82} +(6.39170 + 6.39170i) q^{83} +(-2.60312 - 8.64905i) q^{84} +(10.8934 + 2.82705i) q^{85} +(5.83162 + 9.75352i) q^{86} +1.43857 q^{87} +(13.7456 - 0.630310i) q^{88} -0.579554i q^{89} +(-1.51731 + 2.77449i) q^{90} +(-0.513114 - 0.513114i) q^{91} +(-14.1034 - 7.57793i) q^{92} +(4.54455 + 4.54455i) q^{93} +(-12.4838 - 3.14148i) q^{94} +(-1.59065 - 2.70562i) q^{95} +(-5.10050 - 2.44640i) q^{96} -15.2769i q^{97} +(4.62305 - 18.3714i) q^{98} +(3.44000 - 3.44000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more