LMFDB - Embedded newform 120.2.d.b.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(109,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.d (of order $2$, degree $1$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.839056.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 8x^{2} + 1 $ x^6 + 6x^4 + 8x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.3
Root			$2.02852i$ of defining polynomial
Character	$\chi$	$=$	120.109
Dual form			120.2.d.b.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +(-1.67896 + 2.67975i) q^{10} -0.985939i q^{11} +(1.79387 + 0.884323i) q^{12} +4.94567 q^{13} +(-5.58774 - 1.30246i) q^{14} +(2.11491 + 0.726062i) q^{15} +(2.43594 + 3.17272i) q^{16} +4.52323i q^{17} +(0.321037 - 1.37729i) q^{18} -2.60492i q^{19} +(3.15180 + 3.17272i) q^{20} +4.05705i q^{21} +(-1.35793 - 0.316523i) q^{22} -3.53729i q^{23} +(1.79387 - 2.18678i) q^{24} +(3.94567 + 3.07111i) q^{25} +(1.58774 - 6.81163i) q^{26} -1.00000 q^{27} +(-3.58774 + 7.27782i) q^{28} -7.59434i q^{29} +(1.67896 - 2.67975i) q^{30} -3.28415 q^{31} +(5.15180 - 2.33645i) q^{32} +0.985939i q^{33} +(6.22982 + 1.45212i) q^{34} +(-2.94567 + 8.58028i) q^{35} +(-1.79387 - 0.884323i) q^{36} -0.945668 q^{37} +(-3.58774 - 0.836276i) q^{38} -4.94567 q^{39} +(5.38161 - 3.32239i) q^{40} +0.568295 q^{41} +(5.58774 + 1.30246i) q^{42} +8.45963 q^{43} +(-0.871889 + 1.76865i) q^{44} +(-2.11491 - 0.726062i) q^{45} +(-4.87189 - 1.13560i) q^{46} +2.60492i q^{47} +(-2.43594 - 3.17272i) q^{48} -9.45963 q^{49} +(5.49652 - 4.44840i) q^{50} -4.52323i q^{51} +(-8.87189 - 4.37357i) q^{52} +0.229815 q^{53} +(-0.321037 + 1.37729i) q^{54} +(-0.715853 + 2.08517i) q^{55} +(8.87189 + 7.27782i) q^{56} +2.60492i q^{57} +(-10.4596 - 2.43806i) q^{58} +9.10003i q^{59} +(-3.15180 - 3.17272i) q^{60} +11.0183i q^{61} +(-1.05433 + 4.52323i) q^{62} -4.05705i q^{63} +(-1.56406 - 7.84562i) q^{64} +(-10.4596 - 3.59086i) q^{65} +(1.35793 + 0.316523i) q^{66} -8.45963 q^{67} +(4.00000 - 8.11409i) q^{68} +3.53729i q^{69} +(10.8719 + 6.81163i) q^{70} +1.43171 q^{71} +(-1.79387 + 2.18678i) q^{72} -11.9507i q^{73} +(-0.303594 + 1.30246i) q^{74} +(-3.94567 - 3.07111i) q^{75} +(-2.30359 + 4.67289i) q^{76} -4.00000 q^{77} +(-1.58774 + 6.81163i) q^{78} +3.28415 q^{79} +(-2.84820 - 8.47866i) q^{80} +1.00000 q^{81} +(0.182443 - 0.782708i) q^{82} +9.89134 q^{83} +(3.58774 - 7.27782i) q^{84} +(3.28415 - 9.56622i) q^{85} +(2.71585 - 11.6514i) q^{86} +7.59434i q^{87} +(2.15604 + 1.76865i) q^{88} +12.3510 q^{89} +(-1.67896 + 2.67975i) q^{90} -20.0648i q^{91} +(-3.12811 + 6.34545i) q^{92} +3.28415 q^{93} +(3.58774 + 0.836276i) q^{94} +(-1.89134 + 5.50917i) q^{95} +(-5.15180 + 2.33645i) q^{96} -3.23797i q^{97} +(-3.03689 + 13.0287i) q^{98} -0.985939i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + q^2 - 6 * q^3 + q^4 - q^6 + q^8 + 6 * q^9	$ 6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9} - 11 q^{10} - q^{12} + 8 q^{13} - 10 q^{14} + q^{16} + q^{18} + 9 q^{20} - 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} - 6 q^{27} + 2 q^{28} + 11 q^{30} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} + q^{36} + 16 q^{37} + 2 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{41} + 10 q^{42} + 22 q^{44} - 2 q^{46} - q^{48} - 6 q^{49} - 15 q^{50} - 26 q^{52} - 24 q^{53} - q^{54} - 8 q^{55} + 26 q^{56} - 12 q^{58} - 9 q^{60} - 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} + 24 q^{68} + 38 q^{70} + 16 q^{71} + q^{72} + 18 q^{74} - 2 q^{75} + 6 q^{76} - 24 q^{77} + 14 q^{78} + 16 q^{79} - 27 q^{80} + 6 q^{81} + 50 q^{82} + 16 q^{83} - 2 q^{84} + 16 q^{85} + 20 q^{86} - 18 q^{88} - 20 q^{89} - 11 q^{90} - 46 q^{92} + 16 q^{93} - 2 q^{94} + 32 q^{95} - 21 q^{96} - 21 q^{98}+O(q^{100}) $ 6 * q + q^2 - 6 * q^3 + q^4 - q^6 + q^8 + 6 * q^9 - 11 * q^10 - q^12 + 8 * q^13 - 10 * q^14 + q^16 + q^18 + 9 * q^20 - 10 * q^22 - q^24 + 2 * q^25 - 14 * q^26 - 6 * q^27 + 2 * q^28 + 11 * q^30 - 16 * q^31 + 21 * q^32 + 12 * q^34 + 4 * q^35 + q^36 + 16 * q^37 + 2 * q^38 - 8 * q^39 - 3 * q^40 - 4 * q^41 + 10 * q^42 + 22 * q^44 - 2 * q^46 - q^48 - 6 * q^49 - 15 * q^50 - 26 * q^52 - 24 * q^53 - q^54 - 8 * q^55 + 26 * q^56 - 12 * q^58 - 9 * q^60 - 28 * q^62 - 23 * q^64 - 12 * q^65 + 10 * q^66 + 24 * q^68 + 38 * q^70 + 16 * q^71 + q^72 + 18 * q^74 - 2 * q^75 + 6 * q^76 - 24 * q^77 + 14 * q^78 + 16 * q^79 - 27 * q^80 + 6 * q^81 + 50 * q^82 + 16 * q^83 - 2 * q^84 + 16 * q^85 + 20 * q^86 - 18 * q^88 - 20 * q^89 - 11 * q^90 - 46 * q^92 + 16 * q^93 - 2 * q^94 + 32 * q^95 - 21 * q^96 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	0.321037	−	1.37729i	0.227007	−	0.973893i
$2$	0.321037	−	1.37729i	0.227007	−	0.973893i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.79387	−	0.884323i	−0.896935	−	0.442162i
$5$	−2.11491	−	0.726062i	−0.945815	−	0.324705i
$5$	−2.11491	−	0.726062i	−0.945815	−	0.324705i
$6$	−0.321037	+	1.37729i	−0.131063	+	0.562277i
$7$		−	4.05705i		−	1.53342i	−0.641994	−	0.766710i	$-0.721893\pi$
$7$		−	4.05705i		−	1.53342i	0.641994	−	0.766710i	$-0.278107\pi$
$8$	−1.79387	+	2.18678i	−0.634229	+	0.773145i
$9$	1.00000			0.333333
$10$	−1.67896	+	2.67975i	−0.530935	+	0.847413i
$11$		−	0.985939i		−	0.297272i	−0.988892	−	0.148636i	$-0.952512\pi$
$11$		−	0.985939i		−	0.297272i	0.988892	−	0.148636i	$-0.0474882\pi$
$12$	1.79387	+	0.884323i	0.517846	+	0.255282i
$13$	4.94567			1.37168			0.685841	−	0.727752i	$-0.259435\pi$
$13$	4.94567			1.37168			0.685841	+	0.727752i	$0.259435\pi$
$14$	−5.58774	−	1.30246i	−1.49339	−	0.348097i
$15$	2.11491	+	0.726062i	0.546067	+	0.187468i
$16$	2.43594	+	3.17272i	0.608986	+	0.793181i
$17$			4.52323i			1.09704i	0.836136	+	0.548522i	$0.184809\pi$
$17$			4.52323i			1.09704i	−0.836136	+	0.548522i	$0.815191\pi$
$18$	0.321037	−	1.37729i	0.0756691	−	0.324631i
$19$		−	2.60492i		−	0.597610i	−0.954314	−	0.298805i	$-0.903412\pi$
$19$		−	2.60492i		−	0.597610i	0.954314	−	0.298805i	$-0.0965881\pi$
$20$	3.15180	+	3.17272i	0.704763	+	0.709443i
$21$			4.05705i			0.885320i
$22$	−1.35793	−	0.316523i	−0.289511	−	0.0674829i
$23$		−	3.53729i		−	0.737577i	−0.929513	−	0.368788i	$-0.879773\pi$
$23$		−	3.53729i		−	0.737577i	0.929513	−	0.368788i	$-0.120227\pi$
$24$	1.79387	−	2.18678i	0.366172	−	0.446376i
$25$	3.94567	+	3.07111i	0.789134	+	0.614222i
$26$	1.58774	−	6.81163i	0.311382	−	1.33587i
$27$	−1.00000			−0.192450
$28$	−3.58774	+	7.27782i	−0.678019	+	1.37538i
$29$		−	7.59434i		−	1.41023i	−0.709091	−	0.705117i	$-0.750895\pi$
$29$		−	7.59434i		−	1.41023i	0.709091	−	0.705117i	$-0.249105\pi$
$30$	1.67896	−	2.67975i	0.306535	−	0.489254i
$31$	−3.28415			−0.589850			−0.294925	−	0.955520i	$-0.595295\pi$
$31$	−3.28415			−0.589850			−0.294925	+	0.955520i	$0.595295\pi$
$32$	5.15180	−	2.33645i	0.910718	−	0.413029i
$33$			0.985939i			0.171630i
$34$	6.22982	+	1.45212i	1.06840	+	0.249037i
$35$	−2.94567	+	8.58028i	−0.497909	+	1.45033i
$36$	−1.79387	−	0.884323i	−0.298978	−	0.147387i
$37$	−0.945668			−0.155467			−0.0777334	−	0.996974i	$-0.524768\pi$
$37$	−0.945668			−0.155467			−0.0777334	+	0.996974i	$0.524768\pi$
$38$	−3.58774	−	0.836276i	−0.582009	−	0.135662i
$39$	−4.94567			−0.791941
$40$	5.38161	−	3.32239i	0.850908	−	0.525315i
$41$	0.568295			0.0887527			0.0443763	−	0.999015i	$-0.485870\pi$
$41$	0.568295			0.0887527			0.0443763	+	0.999015i	$0.485870\pi$
$42$	5.58774	+	1.30246i	0.862207	+	0.200974i
$43$	8.45963			1.29008			0.645041	−	0.764148i	$-0.276840\pi$
$43$	8.45963			1.29008			0.645041	+	0.764148i	$0.276840\pi$
$44$	−0.871889	+	1.76865i	−0.131442	+	0.266634i
$45$	−2.11491	−	0.726062i	−0.315272	−	0.108235i
$46$	−4.87189	−	1.13560i	−0.718321	−	0.167435i
$47$			2.60492i			0.379967i	0.981787	+	0.189984i	$0.0608435\pi$
$47$			2.60492i			0.379967i	−0.981787	+	0.189984i	$0.939157\pi$
$48$	−2.43594	−	3.17272i	−0.351598	−	0.457943i
$49$	−9.45963			−1.35138
$50$	5.49652	−	4.44840i	0.777325	−	0.629099i
$51$		−	4.52323i		−	0.633379i
$52$	−8.87189	−	4.37357i	−1.23031	−	0.606505i
$53$	0.229815			0.0315675			0.0157838	−	0.999875i	$-0.494976\pi$
$53$	0.229815			0.0315675			0.0157838	+	0.999875i	$0.494976\pi$
$54$	−0.321037	+	1.37729i	−0.0436876	+	0.187426i
$55$	−0.715853	+	2.08517i	−0.0965256	+	0.281164i
$56$	8.87189	+	7.27782i	1.18556	+	0.972539i
$57$			2.60492i			0.345030i
$58$	−10.4596	−	2.43806i	−1.37342	−	0.320133i
$59$			9.10003i			1.18472i	0.805672	+	0.592362i	$0.201804\pi$
$59$			9.10003i			1.18472i	−0.805672	+	0.592362i	$0.798196\pi$
$60$	−3.15180	−	3.17272i	−0.406895	−	0.409597i
$61$			11.0183i			1.41075i	0.708832	+	0.705377i	$0.249222\pi$
$61$			11.0183i			1.41075i	−0.708832	+	0.705377i	$0.750778\pi$
$62$	−1.05433	+	4.52323i	−0.133900	+	0.574451i
$63$		−	4.05705i		−	0.511140i
$64$	−1.56406	−	7.84562i	−0.195507	−	0.980702i
$65$	−10.4596	−	3.59086i	−1.29736	−	0.445392i
$66$	1.35793	+	0.316523i	0.167149	+	0.0389612i
$67$	−8.45963			−1.03351			−0.516754	−	0.856134i	$-0.672860\pi$
$67$	−8.45963			−1.03351			−0.516754	+	0.856134i	$0.672860\pi$
$68$	4.00000	−	8.11409i	0.485071	−	0.983978i
$69$			3.53729i			0.425840i
$70$	10.8719	+	6.81163i	1.29944	+	0.814146i
$71$	1.43171			0.169912			0.0849561	−	0.996385i	$-0.472925\pi$
$71$	1.43171			0.169912			0.0849561	+	0.996385i	$0.472925\pi$
$72$	−1.79387	+	2.18678i	−0.211410	+	0.257715i
$73$		−	11.9507i		−	1.39873i	−0.714767	−	0.699363i	$-0.753467\pi$
$73$		−	11.9507i		−	1.39873i	0.714767	−	0.699363i	$-0.246533\pi$
$74$	−0.303594	+	1.30246i	−0.0352921	+	0.151408i
$75$	−3.94567	−	3.07111i	−0.455606	−	0.354621i
$76$	−2.30359	+	4.67289i	−0.264240	+	0.536018i
$77$	−4.00000			−0.455842
$78$	−1.58774	+	6.81163i	−0.179776	+	0.771266i
$79$	3.28415			0.369495			0.184748	−	0.982786i	$-0.440853\pi$
$79$	3.28415			0.369495			0.184748	+	0.982786i	$0.440853\pi$
$80$	−2.84820	−	8.47866i	−0.318439	−	0.947943i
$81$	1.00000			0.111111
$82$	0.182443	−	0.782708i	0.0201475	−	0.0864356i
$83$	9.89134			1.08572			0.542858	−	0.839825i	$-0.317342\pi$
$83$	9.89134			1.08572			0.542858	+	0.839825i	$0.317342\pi$
$84$	3.58774	−	7.27782i	0.391455	−	0.794075i
$85$	3.28415	−	9.56622i	0.356216	−	1.03760i
$86$	2.71585	−	11.6514i	0.292858	−	1.25640i
$87$			7.59434i			0.814199i
$88$	2.15604	+	1.76865i	0.229834	+	0.188538i
$89$	12.3510			1.30920			0.654600	−	0.755976i	$-0.272837\pi$
$89$	12.3510			1.30920			0.654600	+	0.755976i	$0.272837\pi$
$90$	−1.67896	+	2.67975i	−0.176978	+	0.282471i
$91$		−	20.0648i		−	2.10336i
$92$	−3.12811	+	6.34545i	−0.326128	+	0.661559i
$93$	3.28415			0.340550
$94$	3.58774	+	0.836276i	0.370047	+	0.0862553i
$95$	−1.89134	+	5.50917i	−0.194047	+	0.565229i
$96$	−5.15180	+	2.33645i	−0.525803	+	0.238463i
$97$		−	3.23797i		−	0.328766i	−0.986397	−	0.164383i	$-0.947437\pi$
$97$		−	3.23797i		−	0.328766i	0.986397	−	0.164383i	$-0.0525633\pi$
$98$	−3.03689	+	13.0287i	−0.306772	+	1.31610i
$99$		−	0.985939i		−	0.0990906i
$100$	−4.36217	−	8.99842i	−0.436217	−	0.899842i
$101$			4.35637i			0.433475i	0.976230	+	0.216738i	$0.0695416\pi$
$101$			4.35637i			0.433475i	−0.976230	+	0.216738i	$0.930458\pi$
$102$	−6.22982	−	1.45212i	−0.616844	−	0.143782i
$103$			15.0754i			1.48542i	0.669612	+	0.742711i	$0.266460\pi$
$103$			15.0754i			1.48542i	−0.669612	+	0.742711i	$0.733540\pi$
$104$	−8.87189	+	10.8151i	−0.869960	+	1.06051i
$105$	2.94567	−	8.58028i	0.287468	−	0.837350i
$106$	0.0737791	−	0.316523i	0.00716606	−	0.0307434i
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$	1.79387	+	0.884323i	0.172615	+	0.0850941i
$109$			4.17034i			0.399446i	0.979852	+	0.199723i	$0.0640042\pi$
$109$			4.17034i			0.399446i	−0.979852	+	0.199723i	$0.935996\pi$
$110$	2.64207	+	1.65535i	0.251912	+	0.157832i
$111$	0.945668			0.0897588
$112$	12.8719	−	9.88274i	1.21628	−	0.933831i
$113$			1.28526i			0.120907i	0.998171	+	0.0604537i	$0.0192548\pi$
$113$			1.28526i			0.120907i	−0.998171	+	0.0604537i	$0.980745\pi$
$114$	3.58774	+	0.836276i	0.336023	+	0.0783244i
$115$	−2.56829	+	7.48105i	−0.239495	+	0.697611i
$116$	−6.71585	+	13.6233i	−0.623551	+	1.26489i
$117$	4.94567			0.457227
$118$	12.5334	+	2.92145i	1.15379	+	0.268941i
$119$	18.3510			1.68223
$120$	−5.38161	+	3.32239i	−0.491272	+	0.303291i
$121$	10.0279			0.911630
$122$	15.1755	+	3.53729i	1.37392	+	0.320252i
$123$	−0.568295			−0.0512414
$124$	5.89134	+	2.90425i	0.529058	+	0.260809i
$125$	−6.11491	−	9.35991i	−0.546934	−	0.837176i
$126$	−5.58774	−	1.30246i	−0.497796	−	0.116032i
$127$		−	1.15280i		−	0.102294i	−0.998691	−	0.0511472i	$-0.983712\pi$
$127$		−	1.15280i		−	0.102294i	0.998691	−	0.0511472i	$-0.0162878\pi$
$128$	−11.3078	−	0.364570i	−0.999481	−	0.0322237i
$129$	−8.45963			−0.744829
$130$	−8.30359	+	13.2532i	−0.728273	+	1.16238i
$131$		−	3.89019i		−	0.339887i	−0.985454	−	0.169944i	$-0.945641\pi$
$131$		−	3.89019i		−	0.339887i	0.985454	−	0.169944i	$-0.0543586\pi$
$132$	0.871889	−	1.76865i	0.0758882	−	0.153941i
$133$	−10.5683			−0.916387
$134$	−2.71585	+	11.6514i	−0.234614	+	1.00653i
$135$	2.11491	+	0.726062i	0.182022	+	0.0624895i
$136$	−9.89134	−	8.11409i	−0.848175	−	0.695778i
$137$		−	17.5135i		−	1.49628i	−0.663544	−	0.748138i	$-0.730948\pi$
$137$		−	17.5135i		−	1.49628i	0.663544	−	0.748138i	$-0.269052\pi$
$138$	4.87189	+	1.13560i	0.414723	+	0.0966688i
$139$			16.8612i			1.43015i	0.699047	+	0.715076i	$0.253608\pi$
$139$			16.8612i			1.43015i	−0.699047	+	0.715076i	$0.746392\pi$
$140$	12.8719	−	12.7870i	1.08787	−	1.08070i
$141$		−	2.60492i		−	0.219374i
$142$	0.459630	−	1.97188i	0.0385713	−	0.165476i
$143$		−	4.87613i		−	0.407762i
$144$	2.43594	+	3.17272i	0.202995	+	0.264394i
$145$	−5.51396	+	16.0613i	−0.457910	+	1.33382i
$146$	−16.4596	−	3.83662i	−1.36221	−	0.317521i
$147$	9.45963			0.780217
$148$	1.69641	+	0.836276i	0.139444	+	0.0687415i
$149$		−	10.4986i		−	0.860078i	−0.902810	−	0.430039i	$-0.858500\pi$
$149$		−	10.4986i		−	0.860078i	0.902810	−	0.430039i	$-0.141500\pi$
$150$	−5.49652	+	4.44840i	−0.448789	+	0.363210i
$151$	4.71585			0.383771			0.191885	−	0.981417i	$-0.438540\pi$
$151$	4.71585			0.383771			0.191885	+	0.981417i	$0.438540\pi$
$152$	5.69641	+	4.67289i	0.462040	+	0.379022i
$153$			4.52323i			0.365682i
$154$	−1.28415	+	5.50917i	−0.103480	+	0.443942i
$155$	6.94567	+	2.38449i	0.557889	+	0.191527i
$156$	8.87189	+	4.37357i	0.710320	+	0.350166i
$157$	−8.94567			−0.713942			−0.356971	−	0.934115i	$-0.616191\pi$
$157$	−8.94567			−0.713942			−0.356971	+	0.934115i	$0.616191\pi$
$158$	1.05433	−	4.52323i	0.0838782	−	0.359849i
$159$	−0.229815			−0.0182255
$160$	−12.5920	+	1.20085i	−0.995483	+	0.0949352i
$161$	−14.3510			−1.13101
$162$	0.321037	−	1.37729i	0.0252230	−	0.108210i
$163$	−15.7827			−1.23619			−0.618097	−	0.786102i	$-0.712096\pi$
$163$	−15.7827			−1.23619			−0.618097	+	0.786102i	$0.712096\pi$
$164$	−1.01945	−	0.502556i	−0.0796054	−	0.0392430i
$165$	0.715853	−	2.08517i	0.0557291	−	0.162330i
$166$	3.17548	−	13.6233i	0.246465	−	1.05737i
$167$			5.50917i			0.426312i	0.977018	+	0.213156i	$0.0683743\pi$
$167$			5.50917i			0.426312i	−0.977018	+	0.213156i	$0.931626\pi$
$168$	−8.87189	−	7.27782i	−0.684481	−	0.561496i
$169$	11.4596			0.881510
$170$	−12.1212	−	7.59434i	−0.929650	−	0.582459i
$171$		−	2.60492i		−	0.199203i
$172$	−15.1755	−	7.48105i	−1.15712	−	0.570425i
$173$	10.3385			0.786020			0.393010	−	0.919534i	$-0.371434\pi$
$173$	10.3385			0.786020			0.393010	+	0.919534i	$0.371434\pi$
$174$	10.4596	+	2.43806i	0.792943	+	0.184829i
$175$	12.4596	−	16.0078i	0.941860	−	1.21007i
$176$	3.12811	−	2.40169i	0.235790	−	0.181034i
$177$		−	9.10003i		−	0.684000i
$178$	3.96511	−	17.0109i	0.297198	−	1.27502i
$179$		−	16.1746i		−	1.20895i	−0.796625	−	0.604474i	$-0.793383\pi$
$179$		−	16.1746i		−	1.20895i	0.796625	−	0.604474i	$-0.206617\pi$
$180$	3.15180	+	3.17272i	0.234921	+	0.236481i
$181$			8.11409i			0.603116i	0.953448	+	0.301558i	$0.0975067\pi$
$181$			8.11409i			0.603116i	−0.953448	+	0.301558i	$0.902493\pi$
$182$	−27.6351	−	6.44154i	−2.04845	−	0.477479i
$183$		−	11.0183i		−	0.814499i
$184$	7.73530	+	6.34545i	0.570254	+	0.467793i
$185$	2.00000	+	0.686614i	0.147043	+	0.0504808i
$186$	1.05433	−	4.52323i	0.0773074	−	0.331659i
$187$	4.45963			0.326120
$188$	2.30359	−	4.67289i	0.168007	−	0.340806i
$189$			4.05705i			0.295107i
$190$	6.98055	+	4.37357i	0.506423	+	0.317292i
$191$	−24.9193			−1.80309			−0.901547	−	0.432681i	$-0.857568\pi$
$191$	−24.9193			−1.80309			−0.901547	+	0.432681i	$0.857568\pi$
$192$	1.56406	+	7.84562i	0.112876	+	0.566209i
$193$		−	1.03951i		−	0.0748254i	−0.999300	−	0.0374127i	$-0.988088\pi$
$193$		−	1.03951i		−	0.0748254i	0.999300	−	0.0374127i	$-0.0119116\pi$
$194$	−4.45963	−	1.03951i	−0.320183	−	0.0746323i
$195$	10.4596	+	3.59086i	0.749030	+	0.257147i
$196$	16.9694	+	8.36537i	1.21210	+	0.597527i
$197$	9.66152			0.688355			0.344177	−	0.938905i	$-0.388158\pi$
$197$	9.66152			0.688355			0.344177	+	0.938905i	$0.388158\pi$
$198$	−1.35793	−	0.316523i	−0.0965036	−	0.0224943i
$199$	−23.0668			−1.63516			−0.817582	−	0.575813i	$-0.804686\pi$
$199$	−23.0668			−1.63516			−0.817582	+	0.575813i	$0.804686\pi$
$200$	−13.7939	+	3.11916i	−0.975374	+	0.220558i
$201$	8.45963			0.596696
$202$	6.00000	+	1.39856i	0.422159	+	0.0984020i
$203$	−30.8106			−2.16248
$204$	−4.00000	+	8.11409i	−0.280056	+	0.568100i
$205$	−1.20189	−	0.412617i	−0.0839437	−	0.0288184i
$206$	20.7632	+	4.83975i	1.44664	+	0.337202i
$207$		−	3.53729i		−	0.245859i
$208$	12.0474	+	15.6912i	0.835335	+	1.08799i
$209$	−2.56829			−0.177653
$210$	−10.8719	−	6.81163i	−0.750232	−	0.470047i
$211$			6.44154i			0.443454i	0.975109	+	0.221727i	$0.0711694\pi$
$211$			6.44154i			0.443454i	−0.975109	+	0.221727i	$0.928831\pi$
$212$	−0.412259	−	0.203231i	−0.0283140	−	0.0139580i
$213$	−1.43171			−0.0980988
$214$	1.28415	−	5.50917i	0.0877825	−	0.376599i
$215$	−17.8913	−	6.14222i	−1.22018	−	0.418896i
$216$	1.79387	−	2.18678i	0.122057	−	0.148792i
$217$			13.3239i			0.904488i
$218$	5.74378	+	1.33883i	0.389018	+	0.0906772i
$219$			11.9507i			0.807554i
$220$	3.12811	−	3.10748i	0.210897	−	0.209506i
$221$			22.3704i			1.50480i
$222$	0.303594	−	1.30246i	0.0203759	−	0.0874155i
$223$			17.9796i			1.20401i	0.798494	+	0.602003i	$0.205630\pi$
$223$			17.9796i			1.20401i	−0.798494	+	0.602003i	$0.794370\pi$
$224$	−9.47908	−	20.9011i	−0.633347	−	1.39651i
$225$	3.94567	+	3.07111i	0.263045	+	0.204741i
$226$	1.77018	+	0.412617i	0.117751	+	0.0274469i
$227$	7.02792			0.466460			0.233230	−	0.972422i	$-0.425071\pi$
$227$	7.02792			0.466460			0.233230	+	0.972422i	$0.425071\pi$
$228$	2.30359	−	4.67289i	0.152559	−	0.309470i
$229$		−	4.17034i		−	0.275584i	−0.990461	−	0.137792i	$-0.955999\pi$
$229$		−	4.17034i		−	0.275584i	0.990461	−	0.137792i	$-0.0440005\pi$
$230$	9.47908	+	5.93899i	0.625032	+	0.391605i
$231$	4.00000			0.263181
$232$	16.6072	+	13.6233i	1.09032	+	0.894411i
$233$			23.9894i			1.57160i	0.618483	+	0.785799i	$0.287748\pi$
$233$			23.9894i			1.57160i	−0.618483	+	0.785799i	$0.712252\pi$
$234$	1.58774	−	6.81163i	0.103794	−	0.445290i
$235$	1.89134	−	5.50917i	0.123377	−	0.359379i
$236$	8.04737	−	16.3243i	0.523839	−	1.06262i
$237$	−3.28415			−0.213328
$238$	5.89134	−	25.2747i	0.381879	−	1.63831i
$239$	8.91926			0.576939			0.288469	−	0.957489i	$-0.406854\pi$
$239$	8.91926			0.576939			0.288469	+	0.957489i	$0.406854\pi$
$240$	2.84820	+	8.47866i	0.183851	+	0.547295i
$241$	−16.3510			−1.05326			−0.526629	−	0.850095i	$-0.676544\pi$
$241$	−16.3510			−1.05326			−0.526629	+	0.850095i	$0.676544\pi$
$242$	3.21933	−	13.8114i	0.206947	−	0.887830i
$243$	−1.00000			−0.0641500
$244$	9.74378	−	19.7655i	0.623781	−	1.26536i
$245$	20.0062	+	6.86828i	1.27815	+	0.438798i
$246$	−0.182443	+	0.782708i	−0.0116322	+	0.0499036i
$247$		−	12.8831i		−	0.819731i
$248$	5.89134	−	7.18172i	0.374100	−	0.456040i
$249$	−9.89134			−0.626838
$250$	−14.8544	+	5.41714i	−0.939478	+	0.342610i
$251$		−	4.22391i		−	0.266611i	−0.991075	−	0.133305i	$-0.957441\pi$
$251$		−	4.22391i		−	0.266611i	0.991075	−	0.133305i	$-0.0425591\pi$
$252$	−3.58774	+	7.27782i	−0.226006	+	0.458459i
$253$	−3.48755			−0.219261
$254$	−1.58774	−	0.370091i	−0.0996238	−	0.0232216i
$255$	−3.28415	+	9.56622i	−0.205661	+	0.599060i
$256$	−4.13235	+	15.4572i	−0.258272	+	0.966072i
$257$			24.6952i			1.54044i	0.637777	+	0.770221i	$0.279854\pi$
$257$			24.6952i			1.54044i	−0.637777	+	0.770221i	$0.720146\pi$
$258$	−2.71585	+	11.6514i	−0.169082	+	0.725384i
$259$			3.83662i			0.238396i
$260$	15.5877	+	15.6912i	0.966711	+	0.973129i
$261$		−	7.59434i		−	0.470078i
$262$	−5.35793	−	1.24889i	−0.331014	−	0.0771569i
$263$		−	14.6628i		−	0.904145i	−0.891981	−	0.452073i	$-0.850685\pi$
$263$		−	14.6628i		−	0.904145i	0.891981	−	0.452073i	$-0.149315\pi$
$264$	−2.15604	−	1.76865i	−0.132695	−	0.108853i
$265$	−0.486038	−	0.166860i	−0.0298571	−	0.0102501i
$266$	−3.39281	+	14.5556i	−0.208027	+	0.892463i
$267$	−12.3510			−0.755867
$268$	15.1755	+	7.48105i	0.926990	+	0.456978i
$269$			11.5381i			0.703490i	0.936096	+	0.351745i	$0.114412\pi$
$269$			11.5381i			0.703490i	−0.936096	+	0.351745i	$0.885588\pi$
$270$	1.67896	−	2.67975i	0.102178	−	0.163085i
$271$	5.63511			0.342309			0.171154	−	0.985244i	$-0.445250\pi$
$271$	5.63511			0.342309			0.171154	+	0.985244i	$0.445250\pi$
$272$	−14.3510	+	11.0183i	−0.870155	+	0.668085i
$273$			20.0648i			1.21438i
$274$	−24.1212	−	5.62246i	−1.45721	−	0.339665i
$275$	3.02792	−	3.89019i	0.182591	−	0.234587i
$276$	3.12811	−	6.34545i	0.188290	−	0.381951i
$277$	17.4053			1.04578			0.522892	−	0.852399i	$-0.324853\pi$
$277$	17.4053			1.04578			0.522892	+	0.852399i	$0.324853\pi$
$278$	23.2229	+	5.41308i	1.39281	+	0.324655i
$279$	−3.28415			−0.196617
$280$	−13.4791	−	21.8335i	−0.805529	−	1.30480i
$281$	21.7827			1.29945			0.649723	−	0.760171i	$-0.274885\pi$
$281$	21.7827			1.29945			0.649723	+	0.760171i	$0.274885\pi$
$282$	−3.58774	−	0.836276i	−0.213647	−	0.0497995i
$283$	21.5962			1.28376			0.641881	−	0.766804i	$-0.278154\pi$
$283$	21.5962			1.28376			0.641881	+	0.766804i	$0.278154\pi$
$284$	−2.56829	−	1.26609i	−0.152400	−	0.0751287i
$285$	1.89134	−	5.50917i	0.112033	−	0.326335i
$286$	−6.71585	−	1.56542i	−0.397117	−	0.0925650i
$287$		−	2.30560i		−	0.136095i
$288$	5.15180	−	2.33645i	0.303573	−	0.137676i
$289$	−3.45963			−0.203508
$290$	20.3510	+	12.7506i	1.19505	+	0.748742i
$291$			3.23797i			0.189813i
$292$	−10.5683	+	21.4380i	−0.618463	+	1.25457i
$293$	−32.0125			−1.87019			−0.935095	−	0.354398i	$-0.884686\pi$
$293$	−32.0125			−1.87019			−0.935095	+	0.354398i	$0.884686\pi$
$294$	3.03689	−	13.0287i	0.177115	−	0.759848i
$295$	6.60719	−	19.2457i	0.384685	−	1.12053i
$296$	1.69641	−	2.06797i	0.0986016	−	0.120198i
$297$			0.985939i			0.0572100i
$298$	−14.4596	−	3.37043i	−0.837624	−	0.195244i
$299$		−	17.4943i		−	1.01172i
$300$	4.36217	+	8.99842i	0.251850	+	0.519524i
$301$		−	34.3211i		−	1.97824i
$302$	1.51396	−	6.49511i	0.0871187	−	0.373752i
$303$		−	4.35637i		−	0.250267i
$304$	8.26470	−	6.34545i	0.474013	−	0.363936i
$305$	8.00000	−	23.3028i	0.458079	−	1.33431i
$306$	6.22982	+	1.45212i	0.356135	+	0.0830124i
$307$	−1.13659			−0.0648686			−0.0324343	−	0.999474i	$-0.510326\pi$
$307$	−1.13659			−0.0648686			−0.0324343	+	0.999474i	$0.510326\pi$
$308$	7.17548	+	3.53729i	0.408861	+	0.201556i
$309$		−	15.0754i		−	0.857609i
$310$	5.51396	−	8.80071i	0.313172	−	0.499847i
$311$	5.13659			0.291269			0.145635	−	0.989338i	$-0.453478\pi$
$311$	5.13659			0.291269			0.145635	+	0.989338i	$0.453478\pi$
$312$	8.87189	−	10.8151i	0.502272	−	0.612285i
$313$		−	23.0762i		−	1.30434i	−0.758071	−	0.652172i	$-0.773858\pi$
$313$		−	23.0762i		−	1.30434i	0.758071	−	0.652172i	$-0.226142\pi$
$314$	−2.87189	+	12.3208i	−0.162070	+	0.695303i
$315$	−2.94567	+	8.58028i	−0.165970	+	0.483444i
$316$	−5.89134	−	2.90425i	−0.331414	−	0.163377i
$317$	1.66152			0.0933203			0.0466601	−	0.998911i	$-0.485142\pi$
$317$	1.66152			0.0933203			0.0466601	+	0.998911i	$0.485142\pi$
$318$	−0.0737791	+	0.316523i	−0.00413733	+	0.0177497i
$319$	−7.48755			−0.419223
$320$	−2.38857	+	17.7284i	−0.133525	+	0.991045i
$321$	−4.00000			−0.223258
$322$	−4.60719	+	19.7655i	−0.256749	+	1.10149i
$323$	11.7827			0.655605
$324$	−1.79387	−	0.884323i	−0.0996595	−	0.0491291i
$325$	19.5140	+	15.1887i	1.08244	+	0.842516i
$326$	−5.06682	+	21.7374i	−0.280625	+	1.20392i
$327$		−	4.17034i		−	0.230620i
$328$	−1.01945	+	1.24274i	−0.0562895	+	0.0686187i
$329$	10.5683			0.582649
$330$	−2.64207	−	1.65535i	−0.145441	−	0.0911243i
$331$			25.9077i			1.42402i	0.702171	+	0.712008i	$0.252214\pi$
$331$			25.9077i			1.42402i	−0.702171	+	0.712008i	$0.747786\pi$
$332$	−17.7438	−	8.74714i	−0.973816	−	0.480062i
$333$	−0.945668			−0.0518223
$334$	7.58774	+	1.76865i	0.415183	+	0.0967760i
$335$	17.8913	+	6.14222i	0.977508	+	0.335585i
$336$	−12.8719	+	9.88274i	−0.702219	+	0.539148i
$337$			8.00696i			0.436167i	0.975930	+	0.218083i	$0.0699805\pi$
$337$			8.00696i			0.436167i	−0.975930	+	0.218083i	$0.930020\pi$
$338$	3.67896	−	15.7833i	0.200109	−	0.858496i
$339$		−	1.28526i		−	0.0698060i
$340$	−14.3510	+	14.2563i	−0.778290	+	0.773157i
$341$			3.23797i			0.175346i
$342$	−3.58774	−	0.836276i	−0.194003	−	0.0452206i
$343$			9.97884i			0.538806i
$344$	−15.1755	+	18.4994i	−0.818207	+	0.997420i
$345$	2.56829	−	7.48105i	0.138272	−	0.402766i
$346$	3.31903	−	14.2391i	0.178432	−	0.765499i
$347$	−23.0279			−1.23620			−0.618102	−	0.786098i	$-0.712098\pi$
$347$	−23.0279			−1.23620			−0.618102	+	0.786098i	$0.712098\pi$
$348$	6.71585	−	13.6233i	0.360007	−	0.730284i
$349$		−	21.4380i		−	1.14755i	−0.819012	−	0.573776i	$-0.805478\pi$
$349$		−	21.4380i		−	1.14755i	0.819012	−	0.573776i	$-0.194522\pi$
$350$	−18.0474	−	22.2996i	−0.964673	−	1.19197i
$351$	−4.94567			−0.263980
$352$	−2.30359	−	5.07936i	−0.122782	−	0.270731i
$353$			4.52323i			0.240747i	0.992729	+	0.120374i	$0.0384093\pi$
$353$			4.52323i			0.240747i	−0.992729	+	0.120374i	$0.961591\pi$
$354$	−12.5334	−	2.92145i	−0.666143	−	0.155273i
$355$	−3.02792	−	1.03951i	−0.160706	−	0.0551713i
$356$	−22.1560	−	10.9222i	−1.17427	−	0.578878i
$357$	−18.3510			−0.971236
$358$	−22.2772	−	5.19265i	−1.17739	−	0.274440i
$359$	−10.3510			−0.546303			−0.273152	−	0.961971i	$-0.588066\pi$
$359$	−10.3510			−0.546303			−0.273152	+	0.961971i	$0.588066\pi$
$360$	5.38161	−	3.32239i	0.283636	−	0.175105i
$361$	12.2144			0.642862
$362$	11.1755	+	2.60492i	0.587370	+	0.136912i
$363$	−10.0279			−0.526330
$364$	−17.7438	+	35.9937i	−0.930027	+	1.88658i
$365$	−8.67696	+	25.2747i	−0.454173	+	1.32294i
$366$	−15.1755	−	3.53729i	−0.793235	−	0.184897i
$367$		−	0.485359i		−	0.0253355i	−0.999920	−	0.0126678i	$-0.995968\pi$
$367$		−	0.485359i		−	0.0253355i	0.999920	−	0.0126678i	$-0.00403238\pi$
$368$	11.2229	−	8.61665i	0.585032	−	0.449174i
$369$	0.568295			0.0295842
$370$	1.58774	−	2.53416i	0.0825427	−	0.131745i
$371$		−	0.932371i		−	0.0484063i
$372$	−5.89134	−	2.90425i	−0.305452	−	0.150578i
$373$	−30.0823			−1.55760			−0.778800	−	0.627272i	$-0.784171\pi$
$373$	−30.0823			−1.55760			−0.778800	+	0.627272i	$0.784171\pi$
$374$	1.43171	−	6.14222i	0.0740317	−	0.317606i
$375$	6.11491	+	9.35991i	0.315772	+	0.483344i
$376$	−5.69641	−	4.67289i	−0.293770	−	0.240986i
$377$		−	37.5591i		−	1.93439i
$378$	5.58774	+	1.30246i	0.287402	+	0.0669914i
$379$		−	33.6881i		−	1.73044i	−0.501392	−	0.865220i	$-0.667179\pi$
$379$		−	33.6881i		−	1.73044i	0.501392	−	0.865220i	$-0.332821\pi$
$380$	8.26470	−	8.21019i	0.423970	−	0.421174i
$381$			1.15280i			0.0590597i
$382$	−8.00000	+	34.3211i	−0.409316	+	1.75602i
$383$			5.17545i			0.264453i	0.991220	+	0.132227i	$0.0422127\pi$
$383$			5.17545i			0.264453i	−0.991220	+	0.132227i	$0.957787\pi$
$384$	11.3078	+	0.364570i	0.577050	+	0.0186044i
$385$	8.45963	+	2.90425i	0.431143	+	0.148014i
$386$	−1.43171	−	0.333720i	−0.0728719	−	0.0169859i
$387$	8.45963			0.430027
$388$	−2.86341	+	5.80850i	−0.145368	+	0.294882i
$389$			16.6408i			0.843722i	0.906660	+	0.421861i	$0.138623\pi$
$389$			16.6408i			0.843722i	−0.906660	+	0.421861i	$0.861377\pi$
$390$	8.30359	−	13.2532i	0.420469	−	0.671101i
$391$	16.0000			0.809155
$392$	16.9694	−	20.6862i	0.857082	−	1.04481i
$393$			3.89019i			0.196234i
$394$	3.10170	−	13.3067i	0.156262	−	0.670384i
$395$	−6.94567	−	2.38449i	−0.349474	−	0.119977i
$396$	−0.871889	+	1.76865i	−0.0438141	+	0.0888778i
$397$	20.4332			1.02551			0.512757	−	0.858534i	$-0.328624\pi$
$397$	20.4332			1.02551			0.512757	+	0.858534i	$0.328624\pi$
$398$	−7.40530	+	31.7698i	−0.371194	+	1.59247i
$399$	10.5683			0.529076
$400$	−0.132350	+	19.9996i	−0.00661751	+	0.999978i
$401$	−4.56829			−0.228130			−0.114065	−	0.993473i	$-0.536387\pi$
$401$	−4.56829			−0.228130			−0.114065	+	0.993473i	$0.536387\pi$
$402$	2.71585	−	11.6514i	0.135454	−	0.581118i
$403$	−16.2423			−0.809087
$404$	3.85244	−	7.81477i	0.191666	−	0.388799i
$405$	−2.11491	−	0.726062i	−0.105091	−	0.0360783i
$406$	−9.89134	+	42.4352i	−0.490899	+	2.10602i
$407$			0.932371i			0.0462159i
$408$	9.89134	+	8.11409i	0.489694	+	0.401708i
$409$	−19.8913			−0.983563			−0.491782	−	0.870719i	$-0.663654\pi$
$409$	−19.8913			−0.983563			−0.491782	+	0.870719i	$0.663654\pi$
$410$	−0.954146	+	1.52289i	−0.0471219	+	0.0752102i
$411$			17.5135i			0.863875i
$412$	13.3315	−	27.0433i	0.656797	−	1.33233i
$413$	36.9193			1.81668
$414$	−4.87189	−	1.13560i	−0.239440	−	0.0558118i
$415$	−20.9193	−	7.18172i	−1.02689	−	0.352537i
$416$	25.4791	−	11.5553i	1.24921	−	0.566545i
$417$		−	16.8612i		−	0.825698i
$418$	−0.824517	+	3.53729i	−0.0403284	+	0.173015i
$419$			0.387288i			0.0189203i	0.999955	+	0.00946013i	$0.00301130\pi$
$419$			0.387288i			0.0189203i	−0.999955	+	0.00946013i	$0.996989\pi$
$420$	−12.8719	+	12.7870i	−0.628084	+	0.623941i
$421$		−	12.0578i		−	0.587664i	−0.955857	−	0.293832i	$-0.905069\pi$
$421$		−	12.0578i		−	0.587664i	0.955857	−	0.293832i	$-0.0949306\pi$
$422$	8.87189	+	2.06797i	0.431877	+	0.100667i
$423$			2.60492i			0.126656i
$424$	−0.412259	+	0.502556i	−0.0200210	+	0.0244063i
$425$	−13.8913	+	17.8472i	−0.673829	+	0.865715i
$426$	−0.459630	+	1.97188i	−0.0222692	+	0.0955378i
$427$	44.7019			2.16328
$428$	−7.17548	−	3.53729i	−0.346840	−	0.170982i
$429$			4.87613i			0.235422i
$430$	−14.2034	+	22.6697i	−0.684949	+	1.09323i
$431$	40.4068			1.94633			0.973164	−	0.230113i	$-0.0739096\pi$
$431$	40.4068			1.94633			0.973164	+	0.230113i	$0.0739096\pi$
$432$	−2.43594	−	3.17272i	−0.117199	−	0.152648i
$433$		−	36.1859i		−	1.73898i	−0.493949	−	0.869491i	$-0.664447\pi$
$433$		−	36.1859i		−	1.73898i	0.493949	−	0.869491i	$-0.335553\pi$
$434$	18.3510	+	4.27748i	0.880875	+	0.205325i
$435$	5.51396	−	16.0613i	0.264374	−	0.770082i
$436$	3.68793	−	7.48105i	0.176620	−	0.358277i
$437$	−9.21438			−0.440783
$438$	16.4596	+	3.83662i	0.786472	+	0.183321i
$439$	25.4178			1.21312			0.606562	−	0.795036i	$-0.292548\pi$
$439$	25.4178			1.21312			0.606562	+	0.795036i	$0.292548\pi$
$440$	−3.27567	−	5.30594i	−0.156161	−	0.252951i
$441$	−9.45963			−0.450459
$442$	30.8106	+	7.18172i	1.46551	+	0.341600i
$443$	−7.02792			−0.333907			−0.166953	−	0.985965i	$-0.553393\pi$
$443$	−7.02792			−0.333907			−0.166953	+	0.985965i	$0.553393\pi$
$444$	−1.69641	−	0.836276i	−0.0805079	−	0.0396879i
$445$	−26.1212	−	8.96757i	−1.23826	−	0.425103i
$446$	24.7632	+	5.77213i	1.17257	+	0.273318i
$447$			10.4986i			0.496566i
$448$	−31.8300	+	6.34545i	−1.50383	+	0.299794i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	5.49652	−	4.44840i	0.259108	−	0.209700i
$451$		−	0.560304i		−	0.0263837i
$452$	1.13659	−	2.30560i	0.0534607	−	0.108446i
$453$	−4.71585			−0.221570
$454$	2.25622	−	9.67951i	0.105890	−	0.454282i
$455$	−14.5683	+	42.4352i	−0.682972	+	1.98939i
$456$	−5.69641	−	4.67289i	−0.266759	−	0.218828i
$457$			25.2747i			1.18230i	0.806562	+	0.591149i	$0.201326\pi$
$457$			25.2747i			1.18230i	−0.806562	+	0.591149i	$0.798674\pi$
$458$	−5.74378	−	1.33883i	−0.268389	−	0.0625595i
$459$		−	4.52323i		−	0.211126i
$460$	11.2229	−	11.1488i	0.523268	−	0.519817i
$461$		−	41.0902i		−	1.91376i	−0.290479	−	0.956881i	$-0.593815\pi$
$461$		−	41.0902i		−	1.91376i	0.290479	−	0.956881i	$-0.406185\pi$
$462$	1.28415	−	5.50917i	0.0597439	−	0.256310i
$463$			13.2106i			0.613951i	0.951717	+	0.306975i	$0.0993169\pi$
$463$			13.2106i			0.613951i	−0.951717	+	0.306975i	$0.900683\pi$
$464$	24.0947	−	18.4994i	1.11857	−	0.858813i
$465$	−6.94567	−	2.38449i	−0.322098	−	0.110578i
$466$	33.0404	+	7.70148i	1.53057	+	0.356764i
$467$	−1.89134			−0.0875206			−0.0437603	−	0.999042i	$-0.513934\pi$
$467$	−1.89134			−0.0875206			−0.0437603	+	0.999042i	$0.513934\pi$
$468$	−8.87189	−	4.37357i	−0.410103	−	0.202168i
$469$			34.3211i			1.58480i
$470$	−6.98055	−	4.37357i	−0.321989	−	0.201738i
$471$	8.94567			0.412195
$472$	−19.8998	−	16.3243i	−0.915963	−	0.751386i
$473$		−	8.34068i		−	0.383505i
$474$	−1.05433	+	4.52323i	−0.0484271	+	0.207759i
$475$	8.00000	−	10.2782i	0.367065	−	0.471594i
$476$	−32.9193	−	16.2282i	−1.50885	−	0.743818i
$477$	0.229815			0.0105225
$478$	2.86341	−	12.2844i	0.130969	−	0.561877i
$479$	−31.4876			−1.43870			−0.719352	−	0.694646i	$-0.755561\pi$
$479$	−31.4876			−1.43870			−0.719352	+	0.694646i	$0.755561\pi$
$480$	12.5920	−	1.20085i	0.574743	−	0.0548109i
$481$	−4.67696			−0.213251
$482$	−5.24926	+	22.5201i	−0.239097	+	1.02576i
$483$	14.3510			0.652992
$484$	−17.9888	−	8.86793i	−0.817673	−	0.403088i
$485$	−2.35097	+	6.84800i	−0.106752	+	0.310952i
$486$	−0.321037	+	1.37729i	−0.0145625	+	0.0624753i
$487$			12.9964i			0.588922i	0.955664	+	0.294461i	$0.0951401\pi$
$487$			12.9964i			0.588922i	−0.955664	+	0.294461i	$0.904860\pi$
$488$	−24.0947	−	19.7655i	−1.09072	−	0.894741i
$489$	15.7827			0.713717
$490$	15.8824	−	25.3495i	0.717492	−	1.14517i
$491$			14.9085i			0.672812i	0.941717	+	0.336406i	$0.109212\pi$
$491$			14.9085i			0.672812i	−0.941717	+	0.336406i	$0.890788\pi$
$492$	1.01945	+	0.502556i	0.0459602	+	0.0226570i
$493$	34.3510			1.54709
$494$	−17.7438	−	4.13594i	−0.798330	−	0.186085i
$495$	−0.715853	+	2.08517i	−0.0321752	+	0.0937214i
$496$	−8.00000	−	10.4197i	−0.359211	−	0.467858i
$497$		−	5.80850i		−	0.260547i
$498$	−3.17548	+	13.6233i	−0.142297	+	0.610473i
$499$			35.6599i			1.59636i	0.602420	+	0.798179i	$0.294203\pi$
$499$			35.6599i			1.59636i	−0.602420	+	0.798179i	$0.705797\pi$
$500$	2.69217	+	22.1980i	0.120397	+	0.992726i
$501$		−	5.50917i		−	0.246132i
$502$	−5.81756	−	1.35603i	−0.259650	−	0.0605226i
$503$			25.3090i			1.12847i	0.825613	+	0.564237i	$0.190830\pi$
$503$			25.3090i			1.12847i	−0.825613	+	0.564237i	$0.809170\pi$
$504$	8.87189	+	7.27782i	0.395185	+	0.324180i
$505$	3.16300	−	9.21332i	0.140751	−	0.409988i
$506$	−1.11963	+	4.80338i	−0.0497738	+	0.213536i
$507$	−11.4596			−0.508940
$508$	−1.01945	+	2.06797i	−0.0452306	+	0.0917514i
$509$			13.7366i			0.608862i	0.952534	+	0.304431i	$0.0984663\pi$
$509$			13.7366i			0.608862i	−0.952534	+	0.304431i	$0.901534\pi$
$510$	12.1212	+	7.59434i	0.536734	+	0.336283i
$511$	−48.4846			−2.14483
$512$	19.9624	+	10.6538i	0.882221	+	0.470835i
$513$			2.60492i			0.115010i
$514$	34.0125	+	7.92806i	1.50023	+	0.349692i
$515$	10.9457	−	31.8831i	0.482324	−	1.40494i
$516$	15.1755	+	7.48105i	0.668063	+	0.329335i
$517$	2.56829			0.112953
$518$	5.28415	+	1.23170i	0.232172	+	0.0541176i
$519$	−10.3385			−0.453809
$520$	26.6157	−	16.4314i	1.16717	−	0.720565i
$521$	−30.9193			−1.35460			−0.677299	−	0.735708i	$-0.736850\pi$
$521$	−30.9193			−1.35460			−0.677299	+	0.735708i	$0.736850\pi$
$522$	−10.4596	−	2.43806i	−0.457806	−	0.106711i
$523$	21.8385			0.954932			0.477466	−	0.878650i	$-0.341555\pi$
$523$	21.8385			0.954932			0.477466	+	0.878650i	$0.341555\pi$
$524$	−3.44018	+	6.97849i	−0.150285	+	0.304857i
$525$	−12.4596	+	16.0078i	−0.543783	+	0.698636i
$526$	−20.1949	−	4.70729i	−0.880541	−	0.205248i
$527$		−	14.8550i		−	0.647092i
$528$	−3.12811	+	2.40169i	−0.136134	+	0.104520i
$529$	10.4876			0.455981
$530$	−0.385851	+	0.615848i	−0.0167603	+	0.0267507i
$531$			9.10003i			0.394908i
$532$	18.9582	+	9.34579i	0.821940	+	0.405191i
$533$	2.81060			0.121740
$534$	−3.96511	+	17.0109i	−0.171587	+	0.736133i
$535$	−8.45963	−	2.90425i	−0.365742	−	0.125562i
$536$	15.1755	−	18.4994i	0.655481	−	0.799052i
$537$			16.1746i			0.697986i
$538$	15.8913	+	3.70415i	0.685124	+	0.159697i
$539$			9.32662i			0.401726i
$540$	−3.15180	−	3.17272i	−0.135632	−	0.136532i
$541$			24.3423i			1.04656i	0.852162	+	0.523278i	$0.175291\pi$
$541$			24.3423i			1.04656i	−0.852162	+	0.523278i	$0.824709\pi$
$542$	1.80908	−	7.76120i	0.0777066	−	0.333372i
$543$		−	8.11409i		−	0.348209i
$544$	10.5683	+	23.3028i	0.453112	+	0.999098i
$545$	3.02792	−	8.81988i	0.129702	−	0.377802i
$546$	27.6351	+	6.44154i	1.18267	+	0.275673i
$547$	−33.3789			−1.42718			−0.713589	−	0.700564i	$-0.752932\pi$
$547$	−33.3789			−1.42718			−0.713589	+	0.700564i	$0.752932\pi$
$548$	−15.4876	+	31.4169i	−0.661596	+	1.34206i
$549$			11.0183i			0.470251i
$550$	−4.38585	−	5.41923i	−0.187013	−	0.231077i
$551$	−19.7827			−0.842770
$552$	−7.73530	−	6.34545i	−0.329236	−	0.270080i
$553$		−	13.3239i		−	0.566592i
$554$	5.58774	−	23.9722i	0.237400	−	1.01848i
$555$	−2.00000	−	0.686614i	−0.0848953	−	0.0291451i
$556$	14.9108	−	30.2469i	0.632358	−	1.28275i
$557$	−30.5808			−1.29575			−0.647875	−	0.761747i	$-0.724342\pi$
$557$	−30.5808			−1.29575			−0.647875	+	0.761747i	$0.724342\pi$
$558$	−1.05433	+	4.52323i	−0.0446334	+	0.191484i
$559$	41.8385			1.76958
$560$	−34.3983	+	11.5553i	−1.45360	+	0.488300i
$561$	−4.45963			−0.188286
$562$	6.99304	−	30.0011i	0.294984	−	1.26552i
$563$	7.02792			0.296192			0.148096	−	0.988973i	$-0.452686\pi$
$563$	7.02792			0.296192			0.148096	+	0.988973i	$0.452686\pi$
$564$	−2.30359	+	4.67289i	−0.0969988	+	0.196764i
$565$	0.933181	−	2.71821i	0.0392592	−	0.114356i
$566$	6.93318	−	29.7443i	0.291423	−	1.25025i
$567$		−	4.05705i		−	0.170380i
$568$	−2.56829	+	3.13083i	−0.107763	+	0.131367i
$569$	−24.3510			−1.02085			−0.510423	−	0.859924i	$-0.670511\pi$
$569$	−24.3510			−1.02085			−0.510423	+	0.859924i	$0.670511\pi$
$570$	−6.98055	−	4.37357i	−0.292383	−	0.183189i
$571$			20.0992i			0.841125i	0.907263	+	0.420563i	$0.138167\pi$
$571$			20.0992i			0.841125i	−0.907263	+	0.420563i	$0.861833\pi$
$572$	−4.31207	+	8.74714i	−0.180297	+	0.365736i
$573$	24.9193			1.04102
$574$	−3.17548	−	0.740182i	−0.132542	−	0.0308946i
$575$	10.8634	−	13.9570i	0.453036	−	0.582047i
$576$	−1.56406	−	7.84562i	−0.0651690	−	0.326901i
$577$		−	4.76899i		−	0.198536i	−0.995061	−	0.0992678i	$-0.968350\pi$
$577$		−	4.76899i		−	0.198536i	0.995061	−	0.0992678i	$-0.0316501\pi$
$578$	−1.11067	+	4.76492i	−0.0461977	+	0.198195i
$579$			1.03951i			0.0432004i
$580$	24.0947	−	23.9358i	1.00048	−	0.993881i
$581$		−	40.1296i		−	1.66486i
$582$	4.45963	+	1.03951i	0.184858	+	0.0430890i
$583$		−	0.226584i		−	0.00938413i
$584$	26.1336	+	21.4380i	1.08142	+	0.887112i
$585$	−10.4596	−	3.59086i	−0.432452	−	0.148464i
$586$	−10.2772	+	44.0906i	−0.424547	+	1.82136i
$587$	8.21733			0.339165			0.169583	−	0.985516i	$-0.445758\pi$
$587$	8.21733			0.339165			0.169583	+	0.985516i	$0.445758\pi$
$588$	−16.9694	−	8.36537i	−0.699804	−	0.344982i
$589$			8.55495i			0.352501i
$590$	−24.3859	−	15.2786i	−1.00395	−	0.629011i
$591$	−9.66152			−0.397422
$592$	−2.30359	−	3.00034i	−0.0946771	−	0.123313i
$593$			7.76120i			0.318714i	0.987221	+	0.159357i	$0.0509421\pi$
$593$			7.76120i			0.318714i	−0.987221	+	0.159357i	$0.949058\pi$
$594$	1.35793	+	0.316523i	0.0557164	+	0.0129871i
$595$	−38.8106	−	13.3239i	−1.59108	−	0.546228i
$596$	−9.28415	+	18.8331i	−0.380293	+	0.771434i
$597$	23.0668			0.944062
$598$	−24.0947	−	5.61631i	−0.985307	−	0.229668i
$599$	5.64903			0.230813			0.115407	−	0.993318i	$-0.463183\pi$
$599$	5.64903			0.230813			0.115407	+	0.993318i	$0.463183\pi$
$600$	13.7939	−	3.11916i	0.563132	−	0.127339i
$601$	−37.7299			−1.53903			−0.769516	−	0.638627i	$-0.779503\pi$
$601$	−37.7299			−1.53903			−0.769516	+	0.638627i	$0.779503\pi$
$602$	−47.2702	−	11.0183i	−1.92659	−	0.449074i
$603$	−8.45963			−0.344503
$604$	−8.45963	−	4.17034i	−0.344217	−	0.169689i
$605$	−21.2081	−	7.28090i	−0.862233	−	0.296010i
$606$	−6.00000	−	1.39856i	−0.243733	−	0.0568124i
$607$		−	0.113292i		−	0.00459837i	−0.999997	−	0.00229919i	$-0.999268\pi$
$607$		−	0.113292i		−	0.00459837i	0.999997	−	0.00229919i	$-0.000731854\pi$
$608$	−6.08627	−	13.4200i	−0.246831	−	0.544254i
$609$	30.8106			1.24851
$610$	−29.5264	−	18.4994i	−1.19549	−	0.749018i
$611$			12.8831i			0.521194i
$612$	4.00000	−	8.11409i	0.161690	−	0.327993i
$613$	−0.703366			−0.0284087			−0.0142044	−	0.999899i	$-0.504522\pi$
$613$	−0.703366			−0.0284087			−0.0142044	+	0.999899i	$0.504522\pi$
$614$	−0.364887	+	1.56542i	−0.0147256	+	0.0631750i
$615$	1.20189	+	0.412617i	0.0484649	+	0.0166383i
$616$	7.17548	−	8.74714i	0.289108	−	0.352432i
$617$			24.4809i			0.985564i	0.870153	+	0.492782i	$0.164020\pi$
$617$			24.4809i			0.985564i	−0.870153	+	0.492782i	$0.835980\pi$
$618$	−20.7632	−	4.83975i	−0.835219	−	0.194683i
$619$		−	39.4966i		−	1.58750i	−0.608243	−	0.793751i	$-0.708126\pi$
$619$		−	39.4966i		−	1.58750i	0.608243	−	0.793751i	$-0.291874\pi$
$620$	−10.3510	−	10.4197i	−0.415705	−	0.418465i
$621$			3.53729i			0.141947i
$622$	1.64903	−	7.07459i	0.0661202	−	0.283665i
$623$		−	50.1084i		−	2.00755i
$624$	−12.0474	−	15.6912i	−0.482281	−	0.628152i
$625$	6.13659	+	24.2351i	0.245464	+	0.969406i
$626$	−31.7827	−	7.40831i	−1.27029	−	0.296095i
$627$	2.56829			0.102568
$628$	16.0474	+	7.91086i	0.640360	+	0.315678i
$629$		−	4.27748i		−	0.170554i
$630$	10.8719	+	6.81163i	0.433146	+	0.271382i
$631$	17.3400			0.690294			0.345147	−	0.938549i	$-0.387829\pi$
$631$	17.3400			0.690294			0.345147	+	0.938549i	$0.387829\pi$
$632$	−5.89134	+	7.18172i	−0.234345	+	0.285674i
$633$		−	6.44154i		−	0.256028i
$634$	0.533409	−	2.28840i	0.0211844	−	0.0908840i
$635$	−0.837003	+	2.43806i	−0.0332155	+	0.0967516i
$636$	0.412259	+	0.203231i	0.0163471	+	0.00805863i
$637$	−46.7842			−1.85366
$638$	−2.40378	+	10.3126i	−0.0951666	+	0.408278i
$639$	1.43171			0.0566374
$640$	23.6503	+	8.98122i	0.934861	+	0.355014i
$641$	38.7019			1.52863			0.764317	−	0.644840i	$-0.223076\pi$
$641$	38.7019			1.52863			0.764317	+	0.644840i	$0.223076\pi$
$642$	−1.28415	+	5.50917i	−0.0506812	+	0.217430i
$643$	−1.13659			−0.0448227			−0.0224113	−	0.999749i	$-0.507134\pi$
$643$	−1.13659			−0.0448227			−0.0224113	+	0.999749i	$0.507134\pi$
$644$	25.7438	+	12.6909i	1.01445	+	0.500091i
$645$	17.8913	+	6.14222i	0.704471	+	0.241850i
$646$	3.78267	−	16.2282i	0.148827	−	0.638490i
$647$			6.54868i			0.257455i	0.991680	+	0.128728i	$0.0410893\pi$
$647$			6.54868i			0.257455i	−0.991680	+	0.128728i	$0.958911\pi$
$648$	−1.79387	+	2.18678i	−0.0704699	+	0.0859050i
$649$	8.97208			0.352185
$650$	27.1840	−	22.0003i	1.06624	−	0.862923i
$651$		−	13.3239i		−	0.522206i
$652$	28.3121	+	13.9570i	1.10879	+	0.546598i
$653$	8.74226			0.342111			0.171056	−	0.985261i	$-0.445282\pi$
$653$	8.74226			0.342111			0.171056	+	0.985261i	$0.445282\pi$
$654$	−5.74378	−	1.33883i	−0.224599	−	0.0523525i
$655$	−2.82452	+	8.22739i	−0.110363	+	0.321471i
$656$	1.38433	+	1.80304i	0.0540492	+	0.0703969i
$657$		−	11.9507i		−	0.466242i
$658$	3.39281	−	14.5556i	0.132266	−	0.567438i
$659$			35.5336i			1.38419i	0.721804	+	0.692097i	$0.243313\pi$
$659$			35.5336i			1.38419i	−0.721804	+	0.692097i	$0.756687\pi$
$660$	−3.12811	+	3.10748i	−0.121762	+	0.120958i
$661$		−	23.3028i		−	0.906373i	−0.891416	−	0.453186i	$-0.850287\pi$
$661$		−	23.3028i		−	0.906373i	0.891416	−	0.453186i	$-0.149713\pi$
$662$	35.6825	+	8.31732i	1.38684	+	0.323262i
$663$		−	22.3704i		−	0.868795i
$664$	−17.7438	+	21.6302i	−0.688592	+	0.839415i
$665$	22.3510	+	7.67324i	0.866733	+	0.297555i
$666$	−0.303594	+	1.30246i	−0.0117640	+	0.0504694i
$667$	−26.8634			−1.04016
$668$	4.87189	−	9.88274i	0.188499	−	0.382375i
$669$		−	17.9796i		−	0.695133i
$670$	14.2034	−	22.6697i	0.548726	−	0.875808i
$671$	10.8634			0.419377
$672$	9.47908	+	20.9011i	0.365663	+	0.806277i
$673$			14.3634i			0.553670i	0.960917	+	0.276835i	$0.0892856\pi$
$673$			14.3634i			0.553670i	−0.960917	+	0.276835i	$0.910714\pi$
$674$	11.0279	+	2.57053i	0.424780	+	0.0990130i
$675$	−3.94567	−	3.07111i	−0.151869	−	0.118207i
$676$	−20.5571	−	10.1340i	−0.790658	−	0.389770i
$677$	24.3076			0.934217			0.467109	−	0.884200i	$-0.345296\pi$
$677$	24.3076			0.934217			0.467109	+	0.884200i	$0.345296\pi$
$678$	−1.77018	−	0.412617i	−0.0679835	−	0.0158465i
$679$	−13.1366			−0.504136
$680$	15.0279	+	24.3423i	0.576295	+	0.933484i
$681$	−7.02792			−0.269311
$682$	4.45963	+	1.03951i	0.170768	+	0.0398048i
$683$	38.5933			1.47673			0.738365	−	0.674401i	$-0.235598\pi$
$683$	38.5933			1.47673			0.738365	+	0.674401i	$0.235598\pi$
$684$	−2.30359	+	4.67289i	−0.0880801	+	0.178673i
$685$	−12.7159	+	37.0393i	−0.485848	+	1.41520i
$686$	13.7438	+	3.20357i	0.524740	+	0.122313i
$687$			4.17034i			0.159108i
$688$	20.6072	+	26.8401i	0.785642	+	1.02327i
$689$	1.13659			0.0433006
$690$	−9.47908	−	5.93899i	−0.360862	−	0.226093i
$691$			13.4090i			0.510102i	0.966928	+	0.255051i	$0.0820923\pi$
$691$			13.4090i			0.510102i	−0.966928	+	0.255051i	$0.917908\pi$
$692$	−18.5459	−	9.14256i	−0.705009	−	0.347548i
$693$	−4.00000			−0.151947
$694$	−7.39281	+	31.7162i	−0.280627	+	1.20393i
$695$	12.2423	−	35.6599i	0.464377	−	1.35266i
$696$	−16.6072	−	13.6233i	−0.629494	−	0.516389i
$697$			2.57053i			0.0973657i
$698$	−29.5264	−	6.88240i	−1.11759	−	0.260503i
$699$		−	23.9894i		−	0.907362i
$700$	−36.5070	+	17.6975i	−1.37983	+	0.668903i
$701$		−	15.6013i		−	0.589253i	−0.955613	−	0.294626i	$-0.904805\pi$
$701$		−	15.6013i		−	0.589253i	0.955613	−	0.294626i	$-0.0951952\pi$
$702$	−1.58774	+	6.81163i	−0.0599254	+	0.257089i
$703$			2.46339i			0.0929086i
$704$	−7.73530	+	1.54206i	−0.291535	+	0.0581187i
$705$	−1.89134	+	5.50917i	−0.0712318	+	0.207487i
$706$	6.22982	+	1.45212i	0.234462	+	0.0546514i
$707$	17.6740			0.664699
$708$	−8.04737	+	16.3243i	−0.302439	+	0.613504i
$709$		−	15.7873i		−	0.592906i	−0.955047	−	0.296453i	$-0.904196\pi$
$709$		−	15.7873i		−	0.592906i	0.955047	−	0.296453i	$-0.0958038\pi$
$710$	−2.40378	+	3.83662i	−0.0902123	+	0.143986i
$711$	3.28415			0.123165
$712$	−22.1560	+	27.0089i	−0.830333	+	1.01220i
$713$			11.6170i			0.435060i
$714$	−5.89134	+	25.2747i	−0.220478	+	0.945880i
$715$	−3.54037	+	10.3126i	−0.132402	+	0.385668i
$716$	−14.3036	+	29.0152i	−0.534550	+	1.08435i
$717$	−8.91926			−0.333096
$718$	−3.32304	+	14.2563i	−0.124015	+	0.532041i
$719$	−22.5683			−0.841655			−0.420828	−	0.907141i	$-0.638260\pi$
$719$	−22.5683			−0.841655			−0.420828	+	0.907141i	$0.638260\pi$
$720$	−2.84820	−	8.47866i	−0.106146	−	0.315981i
$721$	61.1616			2.27778
$722$	3.92126	−	16.8228i	0.145934	−	0.626079i
$723$	16.3510			0.608099
$724$	7.17548	−	14.5556i	0.266675	−	0.540956i
$725$	23.3230	−	29.9647i	0.866196	−	1.11286i
$726$	−3.21933	+	13.8114i	−0.119481	+	0.512589i
$727$			2.79096i			0.103511i	0.998660	+	0.0517554i	$0.0164816\pi$
$727$			2.79096i			0.103511i	−0.998660	+	0.0517554i	$0.983518\pi$
$728$	43.8774	+	35.9937i	1.62621	+	1.33401i
$729$	1.00000			0.0370370
$730$	32.0250	+	20.0648i	1.18530	+	0.742632i
$731$			38.2649i			1.41528i
$732$	−9.74378	+	19.7655i	−0.360140	+	0.730553i
$733$	16.4860			0.608926			0.304463	−	0.952524i	$-0.401523\pi$
$733$	16.4860			0.608926			0.304463	+	0.952524i	$0.401523\pi$
$734$	−0.668481	−	0.155818i	−0.0246741	−	0.00575135i
$735$	−20.0062	−	6.86828i	−0.737941	−	0.253340i
$736$	−8.26470	−	18.2234i	−0.304641	−	0.671724i
$737$			8.34068i			0.307233i
$738$	0.182443	−	0.782708i	0.00671584	−	0.0288119i
$739$		−	14.8894i		−	0.547714i	−0.961770	−	0.273857i	$-0.911701\pi$
$739$		−	14.8894i		−	0.547714i	0.961770	−	0.273857i	$-0.0882995\pi$
$740$	−2.98055	−	3.00034i	−0.109567	−	0.110295i
$741$			12.8831i			0.473272i
$742$	−1.28415	−	0.299325i	−0.0471425	−	0.0109886i
$743$		−	41.4301i		−	1.51992i	−0.649968	−	0.759961i	$-0.725218\pi$
$743$		−	41.4301i		−	1.51992i	0.649968	−	0.759961i	$-0.274782\pi$
$744$	−5.89134	+	7.18172i	−0.215987	+	0.263295i
$745$	−7.62263	+	22.2035i	−0.279271	+	0.813475i
$746$	−9.65751	+	41.4321i	−0.353587	+	1.51694i
$747$	9.89134			0.361905
$748$	−8.00000	−	3.94376i	−0.292509	−	0.144198i
$749$		−	16.2282i		−	0.592965i
$750$	14.8544	−	5.41714i	0.542408	−	0.197806i
$751$	30.5544			1.11494			0.557472	−	0.830195i	$-0.311771\pi$
$751$	30.5544			1.11494			0.557472	+	0.830195i	$0.311771\pi$
$752$	−8.26470	+	6.34545i	−0.301383	+	0.231395i
$753$			4.22391i			0.153928i
$754$	−51.7299	−	12.0578i	−1.88389	−	0.439121i
$755$	−9.97359	−	3.42400i	−0.362976	−	0.124612i
$756$	3.58774	−	7.27782i	0.130485	−	0.264692i
$757$	−0.433223			−0.0157457			−0.00787287	−	0.999969i	$-0.502506\pi$
$757$	−0.433223			−0.0157457			−0.00787287	+	0.999969i	$0.502506\pi$
$758$	−46.3983	−	10.8151i	−1.68526	−	0.392823i
$759$	3.48755			0.126590
$760$	−8.65456	−	14.0187i	−0.313934	−	0.508511i
$761$	−14.9193			−0.540823			−0.270411	−	0.962745i	$-0.587160\pi$
$761$	−14.9193			−0.540823			−0.270411	+	0.962745i	$0.587160\pi$
$762$	1.58774	+	0.370091i	0.0575178	+	0.0134070i
$763$	16.9193			0.612518
$764$	44.7019	+	22.0367i	1.61726	+	0.797259i
$765$	3.28415	−	9.56622i	0.118739	−	0.345867i
$766$	7.12811	+	1.66151i	0.257549	+	0.0600328i
$767$			45.0057i			1.62506i
$768$	4.13235	−	15.4572i	0.149113	−	0.557762i
$769$	31.3789			1.13155			0.565776	−	0.824559i	$-0.308577\pi$
$769$	31.3789			1.13155			0.565776	+	0.824559i	$0.308577\pi$
$770$	6.71585	−	10.7190i	0.242023	−	0.386287i
$771$		−	24.6952i		−	0.889375i
$772$	−0.919260	+	1.86474i	−0.0330849	+	0.0671135i
$773$	−13.4192			−0.482656			−0.241328	−	0.970444i	$-0.577583\pi$
$773$	−13.4192			−0.482656			−0.241328	+	0.970444i	$0.577583\pi$
$774$	2.71585	−	11.6514i	0.0976193	−	0.418800i
$775$	−12.9582	−	10.0860i	−0.465471	−	0.362299i
$776$	7.08074	+	5.80850i	0.254184	+	0.208513i
$777$		−	3.83662i		−	0.137638i
$778$	22.9193	+	5.34231i	0.821695	+	0.191531i
$779$		−	1.48036i		−	0.0530395i
$780$	−15.5877	−	15.6912i	−0.558131	−	0.561836i
$781$		−	1.41157i		−	0.0505101i
$782$	5.13659	−	22.0367i	0.183684	−	0.788030i
$783$			7.59434i			0.271400i
$784$	−23.0431	−	30.0128i	−0.822969	−	1.07189i
$785$	18.9193	+	6.49511i	0.675257	+	0.231820i
$786$	5.35793	+	1.24889i	0.191111	+	0.0445465i
$787$	−36.4846			−1.30054			−0.650268	−	0.759705i	$-0.725343\pi$
$787$	−36.4846			−1.30054			−0.650268	+	0.759705i	$0.725343\pi$
$788$	−17.3315	−	8.54391i	−0.617410	−	0.304364i
$789$			14.6628i			0.522009i
$790$	−5.51396	+	8.80071i	−0.196178	+	0.313115i
$791$	5.21438			0.185402
$792$	2.15604	+	1.76865i	0.0766114	+	0.0628461i
$793$			54.4931i			1.93511i
$794$	6.55982	−	28.1425i	0.232799	−	0.998741i
$795$	0.486038	+	0.166860i	0.0172380	+	0.00591791i
$796$	41.3789	+	20.3985i	1.46664	+	0.723007i
$797$	26.0683			0.923388			0.461694	−	0.887039i	$-0.347242\pi$
$797$	26.0683			0.923388			0.461694	+	0.887039i	$0.347242\pi$
$798$	3.39281	−	14.5556i	0.120104	−	0.515264i
$799$	−11.7827			−0.416841
$800$	27.5028	+	6.60288i	0.972370	+	0.233447i
$801$	12.3510			0.436400
$802$	−1.46659	+	6.29188i	−0.0517871	+	0.222174i
$803$	−11.7827			−0.415801
$804$	−15.1755	−	7.48105i	−0.535198	−	0.263836i
$805$	30.3510	+	10.4197i	1.06973	+	0.367246i
$806$	−5.21438	+	22.3704i	−0.183669	+	0.787964i
$807$		−	11.5381i		−	0.406160i
$808$	−9.52645	−	7.81477i	−0.335139	−	0.274923i
$809$	−35.6212			−1.25237			−0.626187	−	0.779673i	$-0.715385\pi$
$809$	−35.6212			−1.25237			−0.626187	+	0.779673i	$0.715385\pi$
$810$	−1.67896	+	2.67975i	−0.0589928	+	0.0941570i
$811$		−	43.8935i		−	1.54131i	−0.637253	−	0.770654i	$-0.719929\pi$
$811$		−	43.8935i		−	1.54131i	0.637253	−	0.770654i	$-0.280071\pi$
$812$	55.2702	+	27.2465i	1.93960	+	0.956166i
$813$	−5.63511			−0.197632
$814$	1.28415	+	0.299325i	0.0450093	+	0.0104913i
$815$	33.3789	+	11.4592i	1.16921	+	0.401398i
$816$	14.3510	−	11.0183i	0.502384	−	0.385719i
$817$		−	22.0367i		−	0.770966i
$818$	−6.38585	+	27.3962i	−0.223276	+	0.957885i
$819$		−	20.0648i		−	0.701121i
$820$	1.79115	+	1.80304i	0.0625496	+	0.0629649i
$821$			28.8058i			1.00533i	0.864482	+	0.502665i	$0.167647\pi$
$821$			28.8058i			1.00533i	−0.864482	+	0.502665i	$0.832353\pi$
$822$	24.1212	+	5.62246i	0.841322	+	0.196106i
$823$		−	27.9585i		−	0.974571i	−0.873243	−	0.487286i	$-0.837987\pi$
$823$		−	27.9585i		−	0.974571i	0.873243	−	0.487286i	$-0.162013\pi$
$824$	−32.9666	−	27.0433i	−1.14845	−	0.942098i
$825$	−3.02792	+	3.89019i	−0.105419	+	0.135439i
$826$	11.8524	−	50.8486i	0.412399	−	1.76925i
$827$	−14.8634			−0.516851			−0.258426	−	0.966031i	$-0.583204\pi$
$827$	−14.8634			−0.516851			−0.258426	+	0.966031i	$0.583204\pi$
$828$	−3.12811	+	6.34545i	−0.108709	+	0.220520i
$829$			41.7678i			1.45065i	0.688404	+	0.725327i	$0.258312\pi$
$829$			41.7678i			1.45065i	−0.688404	+	0.725327i	$0.741688\pi$
$830$	−16.6072	+	26.5063i	−0.576444	+	0.920049i
$831$	−17.4053			−0.603783
$832$	−7.73530	−	38.8018i	−0.268173	−	1.34521i
$833$		−	42.7881i		−	1.48252i
$834$	−23.2229	−	5.41308i	−0.804142	−	0.187440i
$835$	4.00000	−	11.6514i	0.138426	−	0.403213i
$836$	4.60719	+	2.27120i	0.159343	+	0.0785512i
$837$	3.28415			0.113517
$838$	0.533409	+	0.124334i	0.0184263	+	0.00429504i
$839$	21.6490			0.747408			0.373704	−	0.927548i	$-0.378088\pi$
$839$	21.6490			0.747408			0.373704	+	0.927548i	$0.378088\pi$
$840$	13.4791	+	21.8335i	0.465072	+	0.753326i
$841$	−28.6740			−0.988759
$842$	−16.6072	−	3.87101i	−0.572322	−	0.133404i
$843$	−21.7827			−0.750235
$844$	5.69641	−	11.5553i	0.196078	−	0.397750i
$845$	−24.2361	−	8.32040i	−0.833746	−	0.286231i
$846$	3.58774	+	0.836276i	0.123349	+	0.0287518i
$847$		−	40.6838i		−	1.39791i
$848$	0.559817	+	0.729140i	0.0192242	+	0.0250388i
$849$	−21.5962			−0.741180
$850$	20.1212	+	24.8620i	0.690150	+	0.852761i
$851$			3.34510i			0.114669i
$852$	2.56829	+	1.26609i	0.0879883	+	0.0433755i
$853$	−49.1880			−1.68416			−0.842082	−	0.539350i	$-0.818670\pi$
$853$	−49.1880			−1.68416			−0.842082	+	0.539350i	$0.818670\pi$
$854$	14.3510	−	61.5676i	0.491080	−	2.10680i
$855$	−1.89134	+	5.50917i	−0.0646823	+	0.188410i
$856$	−7.17548	+	8.74714i	−0.245253	+	0.298971i
$857$		−	2.65849i		−	0.0908123i	−0.998969	−	0.0454062i	$-0.985542\pi$
$857$		−	2.65849i		−	0.0908123i	0.998969	−	0.0454062i	$-0.0144582\pi$
$858$	6.71585	+	1.56542i	0.229275	+	0.0534424i
$859$			4.57680i			0.156158i	0.996947	+	0.0780792i	$0.0248787\pi$
$859$			4.57680i			0.156158i	−0.996947	+	0.0780792i	$0.975121\pi$
$860$	26.6630	+	26.8401i	0.909202	+	0.915239i
$861$			2.30560i			0.0785746i
$862$	12.9721	−	55.6520i	0.441831	−	1.89552i
$863$			34.0218i			1.15812i	0.815287	+	0.579058i	$0.196579\pi$
$863$			34.0218i			1.15812i	−0.815287	+	0.579058i	$0.803421\pi$
$864$	−5.15180	+	2.33645i	−0.175268	+	0.0794876i
$865$	−21.8649	−	7.50638i	−0.743430	−	0.255224i
$866$	−49.8385	−	11.6170i	−1.69358	−	0.394761i
$867$	3.45963			0.117495
$868$	11.7827	−	23.9014i	0.399930	−	0.811267i
$869$		−	3.23797i		−	0.109841i
$870$	−20.3510	−	12.7506i	−0.689962	−	0.432286i
$871$	−41.8385			−1.41764
$872$	−9.11963	−	7.48105i	−0.308830	−	0.253340i
$873$		−	3.23797i		−	0.109589i
$874$	−2.95815	+	12.6909i	−0.100061	+	0.429276i
$875$	−37.9736	+	24.8085i	−1.28374	+	0.838679i
$876$	10.5683	−	21.4380i	0.357070	−	0.724324i
$877$	11.7563			0.396981			0.198490	−	0.980103i	$-0.436396\pi$
$877$	11.7563			0.396981			0.198490	+	0.980103i	$0.436396\pi$
$878$	8.16004	−	35.0077i	0.275388	−	1.18145i
$879$	32.0125			1.07975
$880$	−8.35944	+	2.80815i	−0.281797	+	0.0946628i
$881$	13.2702			0.447085			0.223543	−	0.974694i	$-0.428238\pi$
$881$	13.2702			0.447085			0.223543	+	0.974694i	$0.428238\pi$
$882$	−3.03689	+	13.0287i	−0.102257	+	0.438698i
$883$	−17.1366			−0.576692			−0.288346	−	0.957526i	$-0.593105\pi$
$883$	−17.1366			−0.576692			−0.288346	+	0.957526i	$0.593105\pi$
$884$	19.7827	−	40.1296i	0.665363	−	1.34970i
$885$	−6.60719	+	19.2457i	−0.222098	+	0.646938i
$886$	−2.25622	+	9.67951i	−0.0757993	+	0.325189i
$887$		−	32.0883i		−	1.07742i	−0.842492	−	0.538709i	$-0.818912\pi$
$887$		−	32.0883i		−	1.07742i	0.842492	−	0.538709i	$-0.181088\pi$
$888$	−1.69641	+	2.06797i	−0.0569277	+	0.0693966i
$889$	−4.67696			−0.156860
$890$	−20.7368	+	33.0976i	−0.695100	+	1.10943i
$891$		−	0.985939i		−	0.0330302i
$892$	15.8998	−	32.2531i	0.532365	−	1.07992i
$893$	6.78562			0.227072
$894$	14.4596	+	3.37043i	0.483602	+	0.112724i
$895$	−11.7438	+	34.2078i	−0.392551	+	1.14344i
$896$	−1.47908	+	45.8764i	−0.0494125	+	1.53262i
$897$			17.4943i			0.584117i
$898$	0.642074	−	2.75459i	0.0214263	−	0.0919217i
$899$			24.9409i			0.831827i
$900$	−4.36217	−	8.99842i	−0.145406	−	0.299947i
$901$			1.03951i			0.0346310i
$902$	−0.771702	−	0.179878i	−0.0256949	−	0.00598929i
$903$			34.3211i			1.14214i
$904$	−2.81060	−	2.30560i	−0.0934790	−	0.0766830i
$905$	5.89134	−	17.1606i	0.195835	−	0.570436i
$906$	−1.51396	+	6.49511i	−0.0502980	+	0.215786i
$907$	40.4596			1.34344			0.671720	−	0.740805i	$-0.265556\pi$
$907$	40.4596			1.34344			0.671720	+	0.740805i	$0.265556\pi$
$908$	−12.6072	−	6.21496i	−0.418384	−	0.206251i
$909$			4.35637i			0.144492i
$910$	53.7688	+	33.6881i	1.78242	+	1.11675i
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$	−8.26470	+	6.34545i	−0.273672	+	0.210119i
$913$		−	9.75225i		−	0.322752i
$914$	34.8106	+	8.11409i	1.15143	+	0.268390i
$915$	−8.00000	+	23.3028i	−0.264472	+	0.770366i
$916$	−3.68793	+	7.48105i	−0.121853	+	0.247181i
$917$	−15.7827			−0.521190
$918$	−6.22982	−	1.45212i	−0.205615	−	0.0479272i
$919$	−50.8495			−1.67737			−0.838685	−	0.544617i	$-0.816675\pi$
$919$	−50.8495			−1.67737			−0.838685	+	0.544617i	$0.816675\pi$
$920$	−11.7523	−	19.0363i	−0.387460	−	0.627610i
$921$	1.13659			0.0374519
$922$	−56.5933	−	13.1915i	−1.86380	−	0.434438i
$923$	7.08074			0.233065
$924$	−7.17548	−	3.53729i	−0.236056	−	0.116368i
$925$	−3.73129	−	2.90425i	−0.122684	−	0.0954911i
$926$	18.1949	+	4.24110i	0.597922	+	0.139371i
$927$			15.0754i			0.495141i
$928$	−17.7438	−	39.1245i	−0.582468	−	1.28432i
$929$	−12.6461			−0.414904			−0.207452	−	0.978245i	$-0.566517\pi$
$929$	−12.6461			−0.414904			−0.207452	+	0.978245i	$0.566517\pi$
$930$	−5.51396	+	8.80071i	−0.180810	+	0.288587i
$931$			24.6416i			0.807596i
$932$	21.2144	−	43.0339i	0.694900	−	1.40962i
$933$	−5.13659			−0.168164
$934$	−0.607188	+	2.60492i	−0.0198678	+	0.0852357i
$935$	−9.43171	−	3.23797i	−0.308450	−	0.105893i
$936$	−8.87189	+	10.8151i	−0.289987	+	0.353503i
$937$		−	40.7971i		−	1.33278i	−0.745603	−	0.666391i	$-0.767838\pi$
$937$		−	40.7971i		−	1.33278i	0.745603	−	0.666391i	$-0.232162\pi$
$938$	47.2702	+	11.0183i	1.54343	+	0.359762i
$939$			23.0762i			0.753063i
$940$	−8.26470	+	8.21019i	−0.269565	+	0.267787i
$941$			14.1086i			0.459928i	0.973199	+	0.229964i	$0.0738608\pi$
$941$			14.1086i			0.459928i	−0.973199	+	0.229964i	$0.926139\pi$
$942$	2.87189	−	12.3208i	0.0935712	−	0.401433i
$943$		−	2.01022i		−	0.0654619i
$944$	−28.8719	+	22.1672i	−0.939700	+	0.721480i
$945$	2.94567	−	8.58028i	0.0958226	−	0.279117i
$946$	−11.4876	−	2.67766i	−0.373493	−	0.0870584i
$947$	45.8385			1.48955			0.744776	−	0.667315i	$-0.232556\pi$
$947$	45.8385			1.48955			0.744776	+	0.667315i	$0.232556\pi$
$948$	5.89134	+	2.90425i	0.191342	+	0.0943256i
$949$		−	59.1043i		−	1.91861i
$950$	−11.5877	−	14.3180i	−0.375956	−	0.464538i
$951$	−1.66152			−0.0538785
$952$	−32.9193	+	40.1296i	−1.06692	+	1.30061i
$953$			21.9104i			0.709747i	0.934914	+	0.354873i	$0.115476\pi$
$953$			21.9104i			0.709747i	−0.934914	+	0.354873i	$0.884524\pi$
$954$	0.0737791	−	0.316523i	0.00238869	−	0.0102478i
$955$	52.7019	+	18.0929i	1.70539	+	0.585473i
$956$	−16.0000	−	7.88751i	−0.517477	−	0.255100i
$957$	7.48755			0.242038
$958$	−10.1087	+	43.3676i	−0.326596	+	1.40114i
$959$	−71.0529			−2.29442
$960$	2.38857	−	17.7284i	0.0770909	−	0.572180i
$961$	−20.2144			−0.652077
$962$	−1.50148	+	6.44154i	−0.0484095	+	0.207684i
$963$	4.00000			0.128898
$964$	29.3315	+	14.4595i	0.944705	+	0.465710i
$965$	−0.754747	+	2.19846i	−0.0242962	+	0.0707710i
$966$	4.60719	−	19.7655i	0.148234	−	0.635944i
$967$			14.0359i			0.451364i	0.974201	+	0.225682i	$0.0724610\pi$
$967$			14.0359i			0.451364i	−0.974201	+	0.225682i	$0.927539\pi$
$968$	−17.9888	+	21.9289i	−0.578182	+	0.704822i
$969$	−11.7827			−0.378514
$970$	8.67696	+	5.43643i	0.278600	+	0.174553i
$971$		−	21.6494i		−	0.694762i	−0.937724	−	0.347381i	$-0.887071\pi$
$971$		−	21.6494i		−	0.694762i	0.937724	−	0.347381i	$-0.112929\pi$
$972$	1.79387	+	0.884323i	0.0575384	+	0.0283647i
$973$	68.4068			2.19302
$974$	17.8998	+	4.17231i	0.573547	+	0.133690i
$975$	−19.5140	−	15.1887i	−0.624947	−	0.486427i
$976$	−34.9582	+	26.8401i	−1.11898	+	0.859130i
$977$			6.60225i			0.211225i	0.994407	+	0.105612i	$0.0336802\pi$
$977$			6.60225i			0.211225i	−0.994407	+	0.105612i	$0.966320\pi$
$978$	5.06682	−	21.7374i	0.162019	−	0.695084i
$979$		−	12.1773i		−	0.389188i
$980$	−29.8148	−	30.0128i	−0.952400	−	0.958723i
$981$			4.17034i			0.133149i
$982$	20.5334	+	4.78619i	0.655247	+	0.152733i
$983$			53.8600i			1.71787i	0.512087	+	0.858934i	$0.328873\pi$
$983$			53.8600i			1.71787i	−0.512087	+	0.858934i	$0.671127\pi$
$984$	1.01945	−	1.24274i	0.0324988	−	0.0396170i
$985$	−20.4332	−	7.01486i	−0.651057	−	0.223512i
$986$	11.0279	−	47.3113i	0.351201	−	1.50670i
$987$	−10.5683			−0.336393
$988$	−11.3928	+	23.1106i	−0.362454	+	0.735246i
$989$		−	29.9242i		−	0.951534i
$990$	2.64207	+	1.65535i	0.0839706	+	0.0526106i
$991$	29.7129			0.943861			0.471931	−	0.881636i	$-0.343557\pi$
$991$	29.7129			0.943861			0.471931	+	0.881636i	$0.343557\pi$
$992$	−16.9193	+	7.67324i	−0.537187	+	0.243626i
$993$		−	25.9077i		−	0.822156i
$994$	−8.00000	−	1.86474i	−0.253745	−	0.0591460i
$995$	48.7842	+	16.7479i	1.54656	+	0.530945i
$996$	17.7438	+	8.74714i	0.562233	+	0.277164i
$997$	16.6506			0.527328			0.263664	−	0.964615i	$-0.415069\pi$
$997$	16.6506			0.527328			0.263664	+	0.964615i	$0.415069\pi$
$998$	49.1142	+	11.4482i	1.55468	+	0.362385i
$999$	0.945668			0.0299196

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.d.b.109.3	yes	6
3.2	odd	2		360.2.d.e.109.4		6
4.3	odd	2		480.2.d.b.49.1		6
5.2	odd	4		600.2.k.f.301.12		12
5.3	odd	4		600.2.k.f.301.1		12
5.4	even	2		120.2.d.a.109.4	yes	6
8.3	odd	2		480.2.d.a.49.6		6
8.5	even	2		120.2.d.a.109.3	✓	6
12.11	even	2		1440.2.d.f.1009.6		6
15.2	even	4		1800.2.k.u.901.1		12
15.8	even	4		1800.2.k.u.901.12		12
15.14	odd	2		360.2.d.f.109.3		6
16.3	odd	4		3840.2.f.m.769.9		12
16.5	even	4		3840.2.f.l.769.10		12
16.11	odd	4		3840.2.f.m.769.4		12
16.13	even	4		3840.2.f.l.769.3		12
20.3	even	4		2400.2.k.f.1201.12		12
20.7	even	4		2400.2.k.f.1201.1		12
20.19	odd	2		480.2.d.a.49.5		6
24.5	odd	2		360.2.d.f.109.4		6
24.11	even	2		1440.2.d.e.1009.1		6
40.3	even	4		2400.2.k.f.1201.6		12
40.13	odd	4		600.2.k.f.301.2		12
40.19	odd	2		480.2.d.b.49.2		6
40.27	even	4		2400.2.k.f.1201.7		12
40.29	even	2	inner	120.2.d.b.109.4	yes	6
40.37	odd	4		600.2.k.f.301.11		12
60.23	odd	4		7200.2.k.u.3601.11		12
60.47	odd	4		7200.2.k.u.3601.1		12
60.59	even	2		1440.2.d.e.1009.2		6
80.19	odd	4		3840.2.f.m.769.3		12
80.29	even	4		3840.2.f.l.769.9		12
80.59	odd	4		3840.2.f.m.769.10		12
80.69	even	4		3840.2.f.l.769.4		12
120.29	odd	2		360.2.d.e.109.3		6
120.53	even	4		1800.2.k.u.901.11		12
120.59	even	2		1440.2.d.f.1009.5		6
120.77	even	4		1800.2.k.u.901.2		12
120.83	odd	4		7200.2.k.u.3601.12		12
120.107	odd	4		7200.2.k.u.3601.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.3	✓	6	8.5	even	2
120.2.d.a.109.4	yes	6	5.4	even	2
120.2.d.b.109.3	yes	6	1.1	even	1	trivial
120.2.d.b.109.4	yes	6	40.29	even	2	inner
360.2.d.e.109.3		6	120.29	odd	2
360.2.d.e.109.4		6	3.2	odd	2
360.2.d.f.109.3		6	15.14	odd	2
360.2.d.f.109.4		6	24.5	odd	2
480.2.d.a.49.5		6	20.19	odd	2
480.2.d.a.49.6		6	8.3	odd	2
480.2.d.b.49.1		6	4.3	odd	2
480.2.d.b.49.2		6	40.19	odd	2
600.2.k.f.301.1		12	5.3	odd	4
600.2.k.f.301.2		12	40.13	odd	4
600.2.k.f.301.11		12	40.37	odd	4
600.2.k.f.301.12		12	5.2	odd	4
1440.2.d.e.1009.1		6	24.11	even	2
1440.2.d.e.1009.2		6	60.59	even	2
1440.2.d.f.1009.5		6	120.59	even	2
1440.2.d.f.1009.6		6	12.11	even	2
1800.2.k.u.901.1		12	15.2	even	4
1800.2.k.u.901.2		12	120.77	even	4
1800.2.k.u.901.11		12	120.53	even	4
1800.2.k.u.901.12		12	15.8	even	4
2400.2.k.f.1201.1		12	20.7	even	4
2400.2.k.f.1201.6		12	40.3	even	4
2400.2.k.f.1201.7		12	40.27	even	4
2400.2.k.f.1201.12		12	20.3	even	4
3840.2.f.l.769.3		12	16.13	even	4
3840.2.f.l.769.4		12	80.69	even	4
3840.2.f.l.769.9		12	80.29	even	4
3840.2.f.l.769.10		12	16.5	even	4
3840.2.f.m.769.3		12	80.19	odd	4
3840.2.f.m.769.4		12	16.11	odd	4
3840.2.f.m.769.9		12	16.3	odd	4
3840.2.f.m.769.10		12	80.59	odd	4
7200.2.k.u.3601.1		12	60.47	odd	4
7200.2.k.u.3601.2		12	120.107	odd	4
7200.2.k.u.3601.11		12	60.23	odd	4
7200.2.k.u.3601.12		12	120.83	odd	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +(-1.67896 + 2.67975i) q^{10} -0.985939i q^{11} +(1.79387 + 0.884323i) q^{12} +4.94567 q^{13} +(-5.58774 - 1.30246i) q^{14} +(2.11491 + 0.726062i) q^{15} +(2.43594 + 3.17272i) q^{16} +4.52323i q^{17} +(0.321037 - 1.37729i) q^{18} -2.60492i q^{19} +(3.15180 + 3.17272i) q^{20} +4.05705i q^{21} +(-1.35793 - 0.316523i) q^{22} -3.53729i q^{23} +(1.79387 - 2.18678i) q^{24} +(3.94567 + 3.07111i) q^{25} +(1.58774 - 6.81163i) q^{26} -1.00000 q^{27} +(-3.58774 + 7.27782i) q^{28} -7.59434i q^{29} +(1.67896 - 2.67975i) q^{30} -3.28415 q^{31} +(5.15180 - 2.33645i) q^{32} +0.985939i q^{33} +(6.22982 + 1.45212i) q^{34} +(-2.94567 + 8.58028i) q^{35} +(-1.79387 - 0.884323i) q^{36} -0.945668 q^{37} +(-3.58774 - 0.836276i) q^{38} -4.94567 q^{39} +(5.38161 - 3.32239i) q^{40} +0.568295 q^{41} +(5.58774 + 1.30246i) q^{42} +8.45963 q^{43} +(-0.871889 + 1.76865i) q^{44} +(-2.11491 - 0.726062i) q^{45} +(-4.87189 - 1.13560i) q^{46} +2.60492i q^{47} +(-2.43594 - 3.17272i) q^{48} -9.45963 q^{49} +(5.49652 - 4.44840i) q^{50} -4.52323i q^{51} +(-8.87189 - 4.37357i) q^{52} +0.229815 q^{53} +(-0.321037 + 1.37729i) q^{54} +(-0.715853 + 2.08517i) q^{55} +(8.87189 + 7.27782i) q^{56} +2.60492i q^{57} +(-10.4596 - 2.43806i) q^{58} +9.10003i q^{59} +(-3.15180 - 3.17272i) q^{60} +11.0183i q^{61} +(-1.05433 + 4.52323i) q^{62} -4.05705i q^{63} +(-1.56406 - 7.84562i) q^{64} +(-10.4596 - 3.59086i) q^{65} +(1.35793 + 0.316523i) q^{66} -8.45963 q^{67} +(4.00000 - 8.11409i) q^{68} +3.53729i q^{69} +(10.8719 + 6.81163i) q^{70} +1.43171 q^{71} +(-1.79387 + 2.18678i) q^{72} -11.9507i q^{73} +(-0.303594 + 1.30246i) q^{74} +(-3.94567 - 3.07111i) q^{75} +(-2.30359 + 4.67289i) q^{76} -4.00000 q^{77} +(-1.58774 + 6.81163i) q^{78} +3.28415 q^{79} +(-2.84820 - 8.47866i) q^{80} +1.00000 q^{81} +(0.182443 - 0.782708i) q^{82} +9.89134 q^{83} +(3.58774 - 7.27782i) q^{84} +(3.28415 - 9.56622i) q^{85} +(2.71585 - 11.6514i) q^{86} +7.59434i q^{87} +(2.15604 + 1.76865i) q^{88} +12.3510 q^{89} +(-1.67896 + 2.67975i) q^{90} -20.0648i q^{91} +(-3.12811 + 6.34545i) q^{92} +3.28415 q^{93} +(3.58774 + 0.836276i) q^{94} +(-1.89134 + 5.50917i) q^{95} +(-5.15180 + 2.33645i) q^{96} -3.23797i q^{97} +(-3.03689 + 13.0287i) q^{98} -0.985939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + q^2 - 6 * q^3 + q^4 - q^6 + q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9} - 11 q^{10} - q^{12} + 8 q^{13} - 10 q^{14} + q^{16} + q^{18} + 9 q^{20} - 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} - 6 q^{27} + 2 q^{28} + 11 q^{30} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} + q^{36} + 16 q^{37} + 2 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{41} + 10 q^{42} + 22 q^{44} - 2 q^{46} - q^{48} - 6 q^{49} - 15 q^{50} - 26 q^{52} - 24 q^{53} - q^{54} - 8 q^{55} + 26 q^{56} - 12 q^{58} - 9 q^{60} - 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} + 24 q^{68} + 38 q^{70} + 16 q^{71} + q^{72} + 18 q^{74} - 2 q^{75} + 6 q^{76} - 24 q^{77} + 14 q^{78} + 16 q^{79} - 27 q^{80} + 6 q^{81} + 50 q^{82} + 16 q^{83} - 2 q^{84} + 16 q^{85} + 20 q^{86} - 18 q^{88} - 20 q^{89} - 11 q^{90} - 46 q^{92} + 16 q^{93} - 2 q^{94} + 32 q^{95} - 21 q^{96} - 21 q^{98}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + q^4 - q^6 + q^8 + 6 * q^9 - 11 * q^10 - q^12 + 8 * q^13 - 10 * q^14 + q^16 + q^18 + 9 * q^20 - 10 * q^22 - q^24 + 2 * q^25 - 14 * q^26 - 6 * q^27 + 2 * q^28 + 11 * q^30 - 16 * q^31 + 21 * q^32 + 12 * q^34 + 4 * q^35 + q^36 + 16 * q^37 + 2 * q^38 - 8 * q^39 - 3 * q^40 - 4 * q^41 + 10 * q^42 + 22 * q^44 - 2 * q^46 - q^48 - 6 * q^49 - 15 * q^50 - 26 * q^52 - 24 * q^53 - q^54 - 8 * q^55 + 26 * q^56 - 12 * q^58 - 9 * q^60 - 28 * q^62 - 23 * q^64 - 12 * q^65 + 10 * q^66 + 24 * q^68 + 38 * q^70 + 16 * q^71 + q^72 + 18 * q^74 - 2 * q^75 + 6 * q^76 - 24 * q^77 + 14 * q^78 + 16 * q^79 - 27 * q^80 + 6 * q^81 + 50 * q^82 + 16 * q^83 - 2 * q^84 + 16 * q^85 + 20 * q^86 - 18 * q^88 - 20 * q^89 - 11 * q^90 - 46 * q^92 + 16 * q^93 - 2 * q^94 + 32 * q^95 - 21 * q^96 - 21 * q^98

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