LMFDB - Embedded newform 120.2.d.a.109.4

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			109.4
Root			$-2.02852i$ of defining polynomial
Character	$\chi$	$=$	120.109
Dual form			120.2.d.a.109.3

$q$-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} +(0.321037 + 3.14594i) 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} +(-4.43594 - 0.567801i) 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} +(0.321037 + 3.14594i) 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} +(2.20613 - 5.92731i) 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} +(2.96311 + 6.42028i) 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} +(-4.43594 - 0.567801i) 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} +(-12.7632 + 1.30246i) 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} +(7.45539 + 4.94137i) 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} +(0.321037 + 3.14594i) 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} + q^{10} + q^{12} - 8 q^{13} - 10 q^{14} + q^{16} - q^{18} - 13 q^{20} + 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} + 6 q^{27} - 2 q^{28} + 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} + 25 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} - 13 q^{60} + 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} - 24 q^{68} - 6 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} + 15 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} + 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 + q^10 + q^12 - 8 * q^13 - 10 * q^14 + q^16 - q^18 - 13 * q^20 + 10 * q^22 - q^24 + 2 * q^25 - 14 * q^26 + 6 * q^27 - 2 * q^28 + 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 + 25 * 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 - 13 * q^60 + 28 * q^62 - 23 * q^64 - 12 * q^65 + 10 * q^66 - 24 * q^68 - 6 * 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 + 15 * 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 + 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	$0.278107\pi$
$7$			4.05705i			1.53342i	−0.641994	+	0.766710i	$0.721893\pi$
$8$	1.79387	−	2.18678i	0.634229	−	0.773145i
$9$	1.00000			0.333333
$10$	0.321037	+	3.14594i	0.101521	+	0.994833i
$11$		−	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	$-0.740565\pi$
$13$	−4.94567			−1.37168			−0.685841	+	0.727752i	$0.740565\pi$
$14$	−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	$-0.815191\pi$
$17$		−	4.52323i		−	1.09704i	0.836136	−	0.548522i	$-0.184809\pi$
$18$	−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	$-0.0965881\pi$
$20$	−4.43594	−	0.567801i	−0.991907	−	0.126964i
$21$			4.05705i			0.885320i
$22$	1.35793	+	0.316523i	0.289511	+	0.0674829i
$23$			3.53729i			0.737577i	0.929513	+	0.368788i	$0.120227\pi$
$23$			3.53729i			0.737577i	−0.929513	+	0.368788i	$0.879773\pi$
$24$	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	$-0.249105\pi$
$30$	0.321037	+	3.14594i	0.0586130	+	0.574367i
$31$	−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	$-0.475232\pi$
$37$	0.945668			0.155467			0.0777334	+	0.996974i	$0.475232\pi$
$38$	3.58774	+	0.836276i	0.582009	+	0.135662i
$39$	−4.94567			−0.791941
$40$	2.20613	−	5.92731i	0.348820	−	0.937190i
$41$	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	$-0.723160\pi$
$43$	−8.45963			−1.29008			−0.645041	+	0.764148i	$0.723160\pi$
$44$	−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	$-0.939157\pi$
$47$		−	2.60492i		−	0.379967i	0.981787	−	0.189984i	$-0.0608435\pi$
$48$	2.43594	+	3.17272i	0.351598	+	0.457943i
$49$	−9.45963			−1.35138
$50$	2.96311	+	6.42028i	0.419047	+	0.907964i
$51$		−	4.52323i		−	0.633379i
$52$	8.87189	+	4.37357i	1.23031	+	0.606505i
$53$	−0.229815			−0.0315675			−0.0157838	−	0.999875i	$-0.505024\pi$
$53$	−0.229815			−0.0315675			−0.0157838	+	0.999875i	$0.505024\pi$
$54$	−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	$0.798196\pi$
$60$	−4.43594	−	0.567801i	−0.572678	−	0.0733028i
$61$			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	$-0.327140\pi$
$67$	8.45963			1.03351			0.516754	+	0.856134i	$0.327140\pi$
$68$	−4.00000	+	8.11409i	−0.485071	+	0.983978i
$69$			3.53729i			0.425840i
$70$	−12.7632	+	1.30246i	−1.52550	+	0.155674i
$71$	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	$0.246533\pi$
$73$			11.9507i			1.39873i	−0.714767	+	0.699363i	$0.753467\pi$
$74$	−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	$0.440853\pi$
$80$	7.45539	+	4.94137i	0.833538	+	0.552462i
$81$	1.00000			0.111111
$82$	−0.182443	+	0.782708i	−0.0201475	+	0.0864356i
$83$	−9.89134			−1.08572			−0.542858	−	0.839825i	$-0.682658\pi$
$83$	−9.89134			−1.08572			−0.542858	+	0.839825i	$0.682658\pi$
$84$	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	$0.272837\pi$
$90$	0.321037	+	3.14594i	0.0338403	+	0.331611i
$91$		−	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	$0.0525633\pi$
$97$			3.23797i			0.328766i	−0.986397	+	0.164383i	$0.947437\pi$
$98$	3.03689	−	13.0287i	0.306772	−	1.31610i
$99$		−	0.985939i		−	0.0990906i
$100$	−9.79387	+	2.01992i	−0.979387	+	0.201992i
$101$			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	$-0.733540\pi$
$103$		−	15.0754i		−	1.48542i	0.669612	−	0.742711i	$-0.266460\pi$
$104$	−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	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$	−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	$0.935996\pi$
$110$	3.10170	−	0.316523i	0.295736	−	0.0301793i
$111$	0.945668			0.0897588
$112$	−12.8719	+	9.88274i	−1.21628	+	0.933831i
$113$		−	1.28526i		−	0.120907i	−0.998171	−	0.0604537i	$-0.980745\pi$
$113$		−	1.28526i		−	0.120907i	0.998171	−	0.0604537i	$-0.0192548\pi$
$114$	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
$120$	2.20613	−	5.92731i	0.201391	−	0.541087i
$121$	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	$0.0162878\pi$
$127$			1.15280i			0.102294i	−0.998691	+	0.0511472i	$0.983712\pi$
$128$	11.3078	+	0.364570i	0.999481	+	0.0322237i
$129$	−8.45963			−0.744829
$130$	−1.58774	−	15.5588i	−0.139254	−	1.36459i
$131$		−	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	$0.269052\pi$
$137$			17.5135i			1.49628i	−0.663544	+	0.748138i	$0.730948\pi$
$138$	−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	$0.746392\pi$
$140$	2.30359	−	17.9968i	0.194689	−	1.52101i
$141$		−	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	$-0.141500\pi$
$150$	2.96311	+	6.42028i	0.241937	+	0.524214i
$151$	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	$-0.383809\pi$
$157$	8.94567			0.713942			0.356971	+	0.934115i	$0.383809\pi$
$158$	−1.05433	+	4.52323i	−0.0838782	+	0.359849i
$159$	−0.229815			−0.0182255
$160$	−9.19917	+	8.68189i	−0.727258	+	0.686364i
$161$	−14.3510			−1.13101
$162$	−0.321037	+	1.37729i	−0.0252230	+	0.108210i
$163$	15.7827			1.23619			0.618097	−	0.786102i	$-0.287904\pi$
$163$	15.7827			1.23619			0.618097	+	0.786102i	$0.287904\pi$
$164$	−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	$-0.931626\pi$
$167$		−	5.50917i		−	0.426312i	0.977018	−	0.213156i	$-0.0683743\pi$
$168$	8.87189	+	7.27782i	0.684481	+	0.561496i
$169$	11.4596			0.881510
$170$	14.2298	−	1.45212i	1.09138	−	0.111373i
$171$		−	2.60492i		−	0.199203i
$172$	15.1755	+	7.48105i	1.15712	+	0.570425i
$173$	−10.3385			−0.786020			−0.393010	−	0.919534i	$-0.628566\pi$
$173$	−10.3385			−0.786020			−0.393010	+	0.919534i	$0.628566\pi$
$174$	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	$-0.206617\pi$
$180$	−4.43594	−	0.567801i	−0.330636	−	0.0423214i
$181$			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
$190$	8.19493	−	0.836276i	0.594523	−	0.0606698i
$191$	−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	$0.0119116\pi$
$193$			1.03951i			0.0748254i	−0.999300	+	0.0374127i	$0.988088\pi$
$194$	−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	$-0.611842\pi$
$197$	−9.66152			−0.688355			−0.344177	+	0.938905i	$0.611842\pi$
$198$	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	$0.804686\pi$
$200$	0.362165	−	14.1375i	0.0256090	−	0.999672i
$201$	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
$210$	−12.7632	+	1.30246i	−0.880746	+	0.0898784i
$211$			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
$220$	−0.559817	+	4.37357i	−0.0377428	+	0.294866i
$221$			22.3704i			1.50480i
$222$	−0.303594	+	1.30246i	−0.0203759	+	0.0874155i
$223$		−	17.9796i		−	1.20401i	−0.798494	−	0.602003i	$-0.794370\pi$
$223$		−	17.9796i		−	1.20401i	0.798494	−	0.602003i	$-0.205630\pi$
$224$	−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	$-0.574929\pi$
$227$	−7.02792			−0.466460			−0.233230	+	0.972422i	$0.574929\pi$
$228$	−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	$-0.0440005\pi$
$230$	−11.1281	+	1.13560i	−0.733766	+	0.0748793i
$231$	4.00000			0.263181
$232$	−16.6072	−	13.6233i	−1.09032	−	0.894411i
$233$		−	23.9894i		−	1.57160i	−0.618483	−	0.785799i	$-0.712252\pi$
$233$		−	23.9894i		−	1.57160i	0.618483	−	0.785799i	$-0.287748\pi$
$234$	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	$0.406854\pi$
$240$	7.45539	+	4.94137i	0.481243	+	0.318964i
$241$	−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
$250$	10.9282	+	11.4269i	0.691162	+	0.722700i
$251$		−	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	$-0.720146\pi$
$257$		−	24.6952i		−	1.54044i	0.637777	−	0.770221i	$-0.279854\pi$
$258$	2.71585	−	11.6514i	0.169082	−	0.725384i
$259$			3.83662i			0.238396i
$260$	21.9387	+	2.80815i	1.36058	+	0.174154i
$261$		−	7.59434i		−	0.470078i
$262$	5.35793	+	1.24889i	0.331014	+	0.0771569i
$263$			14.6628i			0.904145i	0.891981	+	0.452073i	$0.149315\pi$
$263$			14.6628i			0.904145i	−0.891981	+	0.452073i	$0.850685\pi$
$264$	−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	$0.885588\pi$
$270$	0.321037	+	3.14594i	0.0195377	+	0.191456i
$271$	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	$-0.675147\pi$
$277$	−17.4053			−1.04578			−0.522892	+	0.852399i	$0.675147\pi$
$278$	−23.2229	−	5.41308i	−1.39281	−	0.324655i
$279$	−3.28415			−0.196617
$280$	24.0474	+	8.95037i	1.43711	+	0.534887i
$281$	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	$-0.721846\pi$
$283$	−21.5962			−1.28376			−0.641881	+	0.766804i	$0.721846\pi$
$284$	−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
$290$	23.8913	−	2.43806i	1.40295	−	0.143168i
$291$			3.23797i			0.189813i
$292$	10.5683	−	21.4380i	0.618463	−	1.25457i
$293$	32.0125			1.87019			0.935095	−	0.354398i	$-0.115314\pi$
$293$	32.0125			1.87019			0.935095	+	0.354398i	$0.115314\pi$
$294$	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
$300$	−9.79387	+	2.01992i	−0.565449	+	0.116620i
$301$		−	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	$-0.489674\pi$
$307$	1.13659			0.0648686			0.0324343	+	0.999474i	$0.489674\pi$
$308$	−7.17548	−	3.53729i	−0.408861	−	0.201556i
$309$		−	15.0754i		−	0.857609i
$310$	−1.05433	−	10.3317i	−0.0598820	−	0.586803i
$311$	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	$0.226142\pi$
$313$			23.0762i			1.30434i	−0.758071	+	0.652172i	$0.773858\pi$
$314$	−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	$-0.514858\pi$
$317$	−1.66152			−0.0933203			−0.0466601	+	0.998911i	$0.514858\pi$
$318$	0.0737791	−	0.316523i	0.00413733	−	0.0177497i
$319$	−7.48755			−0.419223
$320$	−9.00424	−	15.4572i	−0.503352	−	0.864081i
$321$	−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
$330$	3.10170	−	0.316523i	0.170743	−	0.0174240i
$331$			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	$-0.930020\pi$
$337$		−	8.00696i		−	0.436167i	0.975930	−	0.218083i	$-0.0699805\pi$
$338$	−3.67896	+	15.7833i	−0.200109	+	0.858496i
$339$		−	1.28526i		−	0.0698060i
$340$	−2.56829	+	20.0648i	−0.139285	+	1.08817i
$341$			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	$-0.287902\pi$
$347$	23.0279			1.23620			0.618102	+	0.786098i	$0.287902\pi$
$348$	−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	$-0.194522\pi$
$350$	−26.0474	+	12.0215i	−1.39229	+	0.642575i
$351$	−4.94567			−0.263980
$352$	2.30359	+	5.07936i	0.122782	+	0.270731i
$353$		−	4.52323i		−	0.240747i	−0.992729	−	0.120374i	$-0.961591\pi$
$353$		−	4.52323i		−	0.240747i	0.992729	−	0.120374i	$-0.0384093\pi$
$354$	−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	$0.588066\pi$
$360$	2.20613	−	5.92731i	0.116273	−	0.312397i
$361$	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	$0.00403238\pi$
$367$			0.485359i			0.0253355i	−0.999920	+	0.0126678i	$0.995968\pi$
$368$	−11.2229	+	8.61665i	−0.585032	+	0.449174i
$369$	0.568295			0.0295842
$370$	0.303594	+	2.97501i	0.0157831	+	0.154664i
$371$		−	0.932371i		−	0.0484063i
$372$	5.89134	+	2.90425i	0.305452	+	0.150578i
$373$	30.0823			1.55760			0.778800	−	0.627272i	$-0.215829\pi$
$373$	30.0823			1.55760			0.778800	+	0.627272i	$0.215829\pi$
$374$	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	$-0.332821\pi$
$380$	−1.47908	+	11.5553i	−0.0758751	+	0.592774i
$381$			1.15280i			0.0590597i
$382$	8.00000	−	34.3211i	0.409316	−	1.75602i
$383$		−	5.17545i		−	0.264453i	−0.991220	−	0.132227i	$-0.957787\pi$
$383$		−	5.17545i		−	0.264453i	0.991220	−	0.132227i	$-0.0422127\pi$
$384$	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	$0.861377\pi$
$390$	−1.58774	−	15.5588i	−0.0803984	−	0.787849i
$391$	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	$-0.671376\pi$
$397$	−20.4332			−1.02551			−0.512757	+	0.858534i	$0.671376\pi$
$398$	7.40530	−	31.7698i	0.371194	−	1.59247i
$399$	10.5683			0.529076
$400$	19.3552	+	5.03746i	0.967760	+	0.251873i
$401$	−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	$0.663654\pi$
$410$	0.182443	+	1.78782i	0.00901024	+	0.0882941i
$411$			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	$0.996989\pi$
$420$	2.30359	−	17.9968i	0.112404	−	0.878156i
$421$		−	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
$430$	−2.71585	−	26.6135i	−0.130970	−	1.28342i
$431$	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	$0.335553\pi$
$433$			36.1859i			1.73898i	−0.493949	+	0.869491i	$0.664447\pi$
$434$	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	$0.292548\pi$
$440$	−5.84396	−	2.17511i	−0.278600	−	0.103694i
$441$	−9.45963			−0.450459
$442$	−30.8106	−	7.18172i	−1.46551	−	0.341600i
$443$	7.02792			0.333907			0.166953	−	0.985965i	$-0.446607\pi$
$443$	7.02792			0.333907			0.166953	+	0.985965i	$0.446607\pi$
$444$	−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	$0.484972\pi$
$450$	2.96311	+	6.42028i	0.139682	+	0.302655i
$451$		−	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	$-0.798674\pi$
$457$		−	25.2747i		−	1.18230i	0.806562	−	0.591149i	$-0.201326\pi$
$458$	5.74378	+	1.33883i	0.268389	+	0.0625595i
$459$		−	4.52323i		−	0.211126i
$460$	2.00848	−	15.6912i	0.0936458	−	0.731608i
$461$		−	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	$-0.900683\pi$
$463$		−	13.2106i		−	0.613951i	0.951717	−	0.306975i	$-0.0993169\pi$
$464$	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	$-0.486066\pi$
$467$	1.89134			0.0875206			0.0437603	+	0.999042i	$0.486066\pi$
$468$	8.87189	+	4.37357i	0.410103	+	0.202168i
$469$			34.3211i			1.58480i
$470$	8.19493	−	0.836276i	0.378004	−	0.0385745i
$471$	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	$0.755561\pi$
$480$	−9.19917	+	8.68189i	−0.419883	+	0.396272i
$481$	−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	$-0.904860\pi$
$487$		−	12.9964i		−	0.588922i	0.955664	−	0.294461i	$-0.0951401\pi$
$488$	24.0947	+	19.7655i	1.09072	+	0.894741i
$489$	15.7827			0.713717
$490$	−3.03689	−	29.7594i	−0.137193	−	1.34439i
$491$			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	$0.705797\pi$
$500$	−19.2465	+	11.3829i	−0.860731	+	0.509059i
$501$		−	5.50917i		−	0.246132i
$502$	5.81756	+	1.35603i	0.259650	+	0.0605226i
$503$		−	25.3090i		−	1.12847i	−0.825613	−	0.564237i	$-0.809170\pi$
$503$		−	25.3090i		−	1.12847i	0.825613	−	0.564237i	$-0.190830\pi$
$504$	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	$0.901534\pi$
$510$	14.2298	−	1.45212i	0.630107	−	0.0643011i
$511$	−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
$520$	−10.9108	+	29.3145i	−0.478469	+	1.28553i
$521$	−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	$-0.658445\pi$
$523$	−21.8385			−0.954932			−0.477466	+	0.878650i	$0.658445\pi$
$524$	−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
$530$	−0.0737791	−	0.722984i	−0.00320476	−	0.0314044i
$531$			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
$540$	−4.43594	−	0.567801i	−0.190893	−	0.0244343i
$541$			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	$-0.247068\pi$
$547$	33.3789			1.42718			0.713589	+	0.700564i	$0.247068\pi$
$548$	15.4876	−	31.4169i	0.661596	−	1.34206i
$549$			11.0183i			0.470251i
$550$	6.33000	−	2.92145i	0.269912	−	0.124571i
$551$	−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	$-0.275658\pi$
$557$	30.5808			1.29575			0.647875	+	0.761747i	$0.275658\pi$
$558$	1.05433	−	4.52323i	0.0446334	−	0.191484i
$559$	41.8385			1.76958
$560$	−20.0474	+	30.2469i	−0.847156	+	1.27816i
$561$	−4.45963			−0.188286
$562$	−6.99304	+	30.0011i	−0.294984	+	1.26552i
$563$	−7.02792			−0.296192			−0.148096	−	0.988973i	$-0.547314\pi$
$563$	−7.02792			−0.296192			−0.148096	+	0.988973i	$0.547314\pi$
$564$	−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	$0.670511\pi$
$570$	8.19493	−	0.836276i	0.343248	−	0.0350278i
$571$			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	$0.0316501\pi$
$577$			4.76899i			0.198536i	−0.995061	+	0.0992678i	$0.968350\pi$
$578$	1.11067	−	4.76492i	0.0461977	−	0.198195i
$579$			1.03951i			0.0432004i
$580$	−4.31207	+	33.6881i	−0.179049	+	1.39882i
$581$		−	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	$-0.554242\pi$
$587$	−8.21733			−0.339165			−0.169583	+	0.985516i	$0.554242\pi$
$588$	16.9694	+	8.36537i	0.699804	+	0.344982i
$589$			8.55495i			0.352501i
$590$	−28.6282	+	2.92145i	−1.17860	+	0.120274i
$591$	−9.66152			−0.397422
$592$	2.30359	+	3.00034i	0.0946771	+	0.123313i
$593$		−	7.76120i		−	0.318714i	−0.987221	−	0.159357i	$-0.949058\pi$
$593$		−	7.76120i		−	0.318714i	0.987221	−	0.159357i	$-0.0509421\pi$
$594$	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	$0.463183\pi$
$600$	0.362165	−	14.1375i	0.0147853	−	0.577161i
$601$	−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	$0.000731854\pi$
$607$			0.113292i			0.00459837i	−0.999997	+	0.00229919i	$0.999268\pi$
$608$	6.08627	+	13.4200i	0.246831	+	0.544254i
$609$	30.8106			1.24851
$610$	−34.6630	+	3.53729i	−1.40347	+	0.143221i
$611$			12.8831i			0.521194i
$612$	−4.00000	+	8.11409i	−0.161690	+	0.327993i
$613$	0.703366			0.0284087			0.0142044	−	0.999899i	$-0.495478\pi$
$613$	0.703366			0.0284087			0.0142044	+	0.999899i	$0.495478\pi$
$614$	−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	$-0.835980\pi$
$617$		−	24.4809i		−	0.985564i	0.870153	−	0.492782i	$-0.164020\pi$
$618$	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	$-0.291874\pi$
$620$	14.5683	+	1.86474i	0.585077	+	0.0748898i
$621$			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
$630$	−12.7632	+	1.30246i	−0.508499	+	0.0518913i
$631$	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
$640$	24.1797	−	7.43916i	0.955787	−	0.294058i
$641$	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	$-0.492866\pi$
$643$	1.13659			0.0448227			0.0224113	+	0.999749i	$0.492866\pi$
$644$	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	$-0.958911\pi$
$647$		−	6.54868i		−	0.257455i	0.991680	−	0.128728i	$-0.0410893\pi$
$648$	1.79387	−	2.18678i	0.0704699	−	0.0859050i
$649$	8.97208			0.352185
$650$	−14.6546	−	31.7526i	−0.574799	−	1.24544i
$651$		−	13.3239i		−	0.522206i
$652$	−28.3121	−	13.9570i	−1.10879	−	0.546598i
$653$	−8.74226			−0.342111			−0.171056	−	0.985261i	$-0.554718\pi$
$653$	−8.74226			−0.342111			−0.171056	+	0.985261i	$0.554718\pi$
$654$	−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	$0.756687\pi$
$660$	−0.559817	+	4.37357i	−0.0217908	+	0.170241i
$661$		−	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
$670$	2.71585	+	26.6135i	0.104923	+	1.02817i
$671$	10.8634			0.419377
$672$	−9.47908	−	20.9011i	−0.365663	−	0.806277i
$673$		−	14.3634i		−	0.553670i	−0.960917	−	0.276835i	$-0.910714\pi$
$673$		−	14.3634i		−	0.553670i	0.960917	−	0.276835i	$-0.0892856\pi$
$674$	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	$-0.654704\pi$
$677$	−24.3076			−0.934217			−0.467109	+	0.884200i	$0.654704\pi$
$678$	1.77018	+	0.412617i	0.0679835	+	0.0158465i
$679$	−13.1366			−0.504136
$680$	−26.8106	−	9.97884i	−1.02814	−	0.382671i
$681$	−7.02792			−0.269311
$682$	−4.45963	−	1.03951i	−0.170768	−	0.0398048i
$683$	−38.5933			−1.47673			−0.738365	−	0.674401i	$-0.764402\pi$
$683$	−38.5933			−1.47673			−0.738365	+	0.674401i	$0.764402\pi$
$684$	−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
$690$	−11.1281	+	1.13560i	−0.423640	+	0.0432316i
$691$			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
$700$	−8.19493	−	39.7342i	−0.309739	−	1.50181i
$701$		−	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	$-0.0958038\pi$
$710$	0.459630	+	4.50406i	0.0172496	+	0.169034i
$711$	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	$0.638260\pi$
$720$	7.45539	+	4.94137i	0.277846	+	0.184154i
$721$	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	$-0.983518\pi$
$727$		−	2.79096i		−	0.103511i	0.998660	−	0.0517554i	$-0.0164816\pi$
$728$	−43.8774	−	35.9937i	−1.62621	−	1.33401i
$729$	1.00000			0.0370370
$730$	−37.5962	+	3.83662i	−1.39150	+	0.142000i
$731$			38.2649i			1.41528i
$732$	9.74378	−	19.7655i	0.360140	−	0.730553i
$733$	−16.4860			−0.608926			−0.304463	−	0.952524i	$-0.598477\pi$
$733$	−16.4860			−0.608926			−0.304463	+	0.952524i	$0.598477\pi$
$734$	−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	$-0.0882995\pi$
$740$	−4.19493	−	0.536951i	−0.154209	−	0.0197387i
$741$			12.8831i			0.473272i
$742$	1.28415	+	0.299325i	0.0471425	+	0.0109886i
$743$			41.4301i			1.51992i	0.649968	+	0.759961i	$0.274782\pi$
$743$			41.4301i			1.51992i	−0.649968	+	0.759961i	$0.725218\pi$
$744$	−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
$750$	10.9282	+	11.4269i	0.399042	+	0.417251i
$751$	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	$-0.497494\pi$
$757$	0.433223			0.0157457			0.00787287	+	0.999969i	$0.497494\pi$
$758$	46.3983	+	10.8151i	1.68526	+	0.392823i
$759$	3.48755			0.126590
$760$	−15.4402	−	5.74680i	−0.560074	−	0.208458i
$761$	−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	$0.308577\pi$
$770$	1.28415	+	12.5838i	0.0462775	+	0.453487i
$771$		−	24.6952i		−	0.889375i
$772$	0.919260	−	1.86474i	0.0330849	−	0.0671135i
$773$	13.4192			0.482656			0.241328	−	0.970444i	$-0.422417\pi$
$773$	13.4192			0.482656			0.241328	+	0.970444i	$0.422417\pi$
$774$	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
$780$	21.9387	+	2.80815i	0.785532	+	0.100548i
$781$		−	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	$-0.274657\pi$
$787$	36.4846			1.30054			0.650268	+	0.759705i	$0.274657\pi$
$788$	17.3315	+	8.54391i	0.617410	+	0.304364i
$789$			14.6628i			0.522009i
$790$	1.05433	+	10.3317i	0.0375115	+	0.367586i
$791$	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	$-0.652758\pi$
$797$	−26.0683			−0.923388			−0.461694	+	0.887039i	$0.652758\pi$
$798$	−3.39281	+	14.5556i	−0.120104	+	0.515264i
$799$	−11.7827			−0.416841
$800$	−13.1518	+	25.0406i	−0.464986	+	0.885318i
$801$	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	$0.715385\pi$
$810$	0.321037	+	3.14594i	0.0112801	+	0.110537i
$811$		−	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
$820$	−2.52092	−	0.322678i	−0.0880344	−	0.0112684i
$821$			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	$0.162013\pi$
$823$			27.9585i			0.974571i	−0.873243	+	0.487286i	$0.837987\pi$
$824$	−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	$-0.416796\pi$
$827$	14.8634			0.516851			0.258426	+	0.966031i	$0.416796\pi$
$828$	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	$0.741688\pi$
$830$	−3.17548	−	31.1175i	−0.110223	−	1.08011i
$831$	−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	$0.378088\pi$
$840$	24.0474	+	8.95037i	0.829713	+	0.308817i
$841$	−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
$850$	29.0404	−	13.4028i	0.996078	−	0.459714i
$851$			3.34510i			0.114669i
$852$	−2.56829	−	1.26609i	−0.0879883	−	0.0433755i
$853$	49.1880			1.68416			0.842082	−	0.539350i	$-0.181330\pi$
$853$	49.1880			1.68416			0.842082	+	0.539350i	$0.181330\pi$
$854$	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	$0.0144582\pi$
$857$			2.65849i			0.0908123i	−0.998969	+	0.0454062i	$0.985542\pi$
$858$	−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	$0.975121\pi$
$860$	37.5264	+	4.80338i	1.27964	+	0.163794i
$861$			2.30560i			0.0785746i
$862$	−12.9721	+	55.6520i	−0.441831	+	1.89552i
$863$		−	34.0218i		−	1.15812i	−0.815287	−	0.579058i	$-0.803421\pi$
$863$		−	34.0218i		−	1.15812i	0.815287	−	0.579058i	$-0.196579\pi$
$864$	−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
$870$	23.8913	−	2.43806i	0.809992	−	0.0826581i
$871$	−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	$-0.563604\pi$
$877$	−11.7563			−0.396981			−0.198490	+	0.980103i	$0.563604\pi$
$878$	−8.16004	+	35.0077i	−0.275388	+	1.18145i
$879$	32.0125			1.07975
$880$	4.87189	−	7.35056i	0.164231	−	0.247787i
$881$	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	$-0.406895\pi$
$883$	17.1366			0.576692			0.288346	+	0.957526i	$0.406895\pi$
$884$	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	$0.181088\pi$
$887$			32.0883i			1.07742i	−0.842492	+	0.538709i	$0.818912\pi$
$888$	1.69641	−	2.06797i	0.0569277	−	0.0693966i
$889$	−4.67696			−0.156860
$890$	3.96511	+	38.8554i	0.132911	+	1.30244i
$891$		−	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
$900$	−9.79387	+	2.01992i	−0.326462	+	0.0673308i
$901$			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	$-0.734444\pi$
$907$	−40.4596			−1.34344			−0.671720	+	0.740805i	$0.734444\pi$
$908$	12.6072	+	6.21496i	0.418384	+	0.206251i
$909$			4.35637i			0.144492i
$910$	63.1227	−	6.44154i	2.09250	−	0.213535i
$911$	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	$0.816675\pi$
$920$	20.9666	+	7.80373i	0.691249	+	0.257281i
$921$	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	$0.566517\pi$
$930$	−1.05433	−	10.3317i	−0.0345729	−	0.338791i
$931$			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	$0.232162\pi$
$937$			40.7971i			1.33278i	−0.745603	+	0.666391i	$0.767838\pi$
$938$	−47.2702	−	11.0183i	−1.54343	−	0.359762i
$939$			23.0762i			0.753063i
$940$	−1.47908	+	11.5553i	−0.0482422	+	0.376892i
$941$			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	$-0.767444\pi$
$947$	−45.8385			−1.48955			−0.744776	+	0.667315i	$0.767444\pi$
$948$	−5.89134	−	2.90425i	−0.191342	−	0.0943256i
$949$		−	59.1043i		−	1.91861i
$950$	16.7243	−	7.71867i	0.542609	−	0.250427i
$951$	−1.66152			−0.0538785
$952$	32.9193	−	40.1296i	1.06692	−	1.30061i
$953$		−	21.9104i		−	0.709747i	−0.934914	−	0.354873i	$-0.884524\pi$
$953$		−	21.9104i		−	0.709747i	0.934914	−	0.354873i	$-0.115476\pi$
$954$	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
$960$	−9.00424	−	15.4572i	−0.290611	−	0.498878i
$961$	−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	$-0.927539\pi$
$967$		−	14.0359i		−	0.451364i	0.974201	−	0.225682i	$-0.0724610\pi$
$968$	17.9888	−	21.9289i	0.578182	−	0.704822i
$969$	−11.7827			−0.378514
$970$	−10.1865	+	1.03951i	−0.327067	+	0.0333766i
$971$		−	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	$-0.966320\pi$
$977$		−	6.60225i		−	0.211225i	0.994407	−	0.105612i	$-0.0336802\pi$
$978$	−5.06682	+	21.7374i	−0.162019	+	0.695084i
$979$		−	12.1773i		−	0.389188i
$980$	41.9624	+	5.37118i	1.34044	+	0.171576i
$981$			4.17034i			0.133149i
$982$	−20.5334	−	4.78619i	−0.655247	−	0.152733i
$983$		−	53.8600i		−	1.71787i	−0.512087	−	0.858934i	$-0.671127\pi$
$983$		−	53.8600i		−	1.71787i	0.512087	−	0.858934i	$-0.328873\pi$
$984$	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
$990$	3.10170	−	0.316523i	0.0985786	−	0.0100598i
$991$	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	$-0.584931\pi$
$997$	−16.6506			−0.527328			−0.263664	+	0.964615i	$0.584931\pi$
$998$	−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.a.109.4	yes	6
3.2	odd	2		360.2.d.f.109.3		6
4.3	odd	2		480.2.d.a.49.5		6
5.2	odd	4		600.2.k.f.301.1		12
5.3	odd	4		600.2.k.f.301.12		12
5.4	even	2		120.2.d.b.109.3	yes	6
8.3	odd	2		480.2.d.b.49.2		6
8.5	even	2		120.2.d.b.109.4	yes	6
12.11	even	2		1440.2.d.e.1009.2		6
15.2	even	4		1800.2.k.u.901.12		12
15.8	even	4		1800.2.k.u.901.1		12
15.14	odd	2		360.2.d.e.109.4		6
16.3	odd	4		3840.2.f.m.769.3		12
16.5	even	4		3840.2.f.l.769.4		12
16.11	odd	4		3840.2.f.m.769.10		12
16.13	even	4		3840.2.f.l.769.9		12
20.3	even	4		2400.2.k.f.1201.1		12
20.7	even	4		2400.2.k.f.1201.12		12
20.19	odd	2		480.2.d.b.49.1		6
24.5	odd	2		360.2.d.e.109.3		6
24.11	even	2		1440.2.d.f.1009.5		6
40.3	even	4		2400.2.k.f.1201.7		12
40.13	odd	4		600.2.k.f.301.11		12
40.19	odd	2		480.2.d.a.49.6		6
40.27	even	4		2400.2.k.f.1201.6		12
40.29	even	2	inner	120.2.d.a.109.3	✓	6
40.37	odd	4		600.2.k.f.301.2		12
60.23	odd	4		7200.2.k.u.3601.1		12
60.47	odd	4		7200.2.k.u.3601.11		12
60.59	even	2		1440.2.d.f.1009.6		6
80.19	odd	4		3840.2.f.m.769.9		12
80.29	even	4		3840.2.f.l.769.3		12
80.59	odd	4		3840.2.f.m.769.4		12
80.69	even	4		3840.2.f.l.769.10		12
120.29	odd	2		360.2.d.f.109.4		6
120.53	even	4		1800.2.k.u.901.2		12
120.59	even	2		1440.2.d.e.1009.1		6
120.77	even	4		1800.2.k.u.901.11		12
120.83	odd	4		7200.2.k.u.3601.2		12
120.107	odd	4		7200.2.k.u.3601.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.3	✓	6	40.29	even	2	inner
120.2.d.a.109.4	yes	6	1.1	even	1	trivial
120.2.d.b.109.3	yes	6	5.4	even	2
120.2.d.b.109.4	yes	6	8.5	even	2
360.2.d.e.109.3		6	24.5	odd	2
360.2.d.e.109.4		6	15.14	odd	2
360.2.d.f.109.3		6	3.2	odd	2
360.2.d.f.109.4		6	120.29	odd	2
480.2.d.a.49.5		6	4.3	odd	2
480.2.d.a.49.6		6	40.19	odd	2
480.2.d.b.49.1		6	20.19	odd	2
480.2.d.b.49.2		6	8.3	odd	2
600.2.k.f.301.1		12	5.2	odd	4
600.2.k.f.301.2		12	40.37	odd	4
600.2.k.f.301.11		12	40.13	odd	4
600.2.k.f.301.12		12	5.3	odd	4
1440.2.d.e.1009.1		6	120.59	even	2
1440.2.d.e.1009.2		6	12.11	even	2
1440.2.d.f.1009.5		6	24.11	even	2
1440.2.d.f.1009.6		6	60.59	even	2
1800.2.k.u.901.1		12	15.8	even	4
1800.2.k.u.901.2		12	120.53	even	4
1800.2.k.u.901.11		12	120.77	even	4
1800.2.k.u.901.12		12	15.2	even	4
2400.2.k.f.1201.1		12	20.3	even	4
2400.2.k.f.1201.6		12	40.27	even	4
2400.2.k.f.1201.7		12	40.3	even	4
2400.2.k.f.1201.12		12	20.7	even	4
3840.2.f.l.769.3		12	80.29	even	4
3840.2.f.l.769.4		12	16.5	even	4
3840.2.f.l.769.9		12	16.13	even	4
3840.2.f.l.769.10		12	80.69	even	4
3840.2.f.m.769.3		12	16.3	odd	4
3840.2.f.m.769.4		12	80.59	odd	4
3840.2.f.m.769.9		12	80.19	odd	4
3840.2.f.m.769.10		12	16.11	odd	4
7200.2.k.u.3601.1		12	60.23	odd	4
7200.2.k.u.3601.2		12	120.83	odd	4
7200.2.k.u.3601.11		12	60.47	odd	4
7200.2.k.u.3601.12		12	120.107	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} +(0.321037 + 3.14594i) 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} +(-4.43594 - 0.567801i) 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} +(0.321037 + 3.14594i) 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} +(2.20613 - 5.92731i) 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} +(2.96311 + 6.42028i) 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} +(-4.43594 - 0.567801i) 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} +(-12.7632 + 1.30246i) 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} +(7.45539 + 4.94137i) 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} +(0.321037 + 3.14594i) 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	\( 6 q - q^{2} + 6 q^{3} + q^{4} - q^{6} - q^{8} + 6 q^{9} + q^{10} + q^{12} - 8 q^{13} - 10 q^{14} + q^{16} - q^{18} - 13 q^{20} + 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} + 6 q^{27} - 2 q^{28} + q^{30} - 16 q^{31} - 21 q^{32} + 12 q^{34} - 4 q^{35} + q^{36} - 16 q^{37} - 2 q^{38} - 8 q^{39} + 25 q^{40} - 4 q^{41} - 10 q^{42} + 22 q^{44} - 2 q^{46} + q^{48} - 6 q^{49} + 15 q^{50} + 26 q^{52} + 24 q^{53} - q^{54} - 8 q^{55} + 26 q^{56} + 12 q^{58} - 13 q^{60} + 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} - 24 q^{68} - 6 q^{70} + 16 q^{71} - q^{72} + 18 q^{74} + 2 q^{75} + 6 q^{76} + 24 q^{77} - 14 q^{78} + 16 q^{79} + 15 q^{80} + 6 q^{81} - 50 q^{82} - 16 q^{83} - 2 q^{84} - 16 q^{85} + 20 q^{86} + 18 q^{88} - 20 q^{89} + q^{90} + 46 q^{92} - 16 q^{93} - 2 q^{94} + 32 q^{95} - 21 q^{96} + 21 q^{98}+O(q^{100}) \) 6 * q - q^2 + 6 * q^3 + q^4 - q^6 - q^8 + 6 * q^9 + q^10 + q^12 - 8 * q^13 - 10 * q^14 + q^16 - q^18 - 13 * q^20 + 10 * q^22 - q^24 + 2 * q^25 - 14 * q^26 + 6 * q^27 - 2 * q^28 + 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 + 25 * 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 - 13 * q^60 + 28 * q^62 - 23 * q^64 - 12 * q^65 + 10 * q^66 - 24 * q^68 - 6 * 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 + 15 * 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 + q^90 + 46 * q^92 - 16 * q^93 - 2 * q^94 + 32 * q^95 - 21 * q^96 + 21 * q^98

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