LMFDB - Embedded newform 360.2.d.f.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(109,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, 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("360.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.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:	$2.87461447277$
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:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.4
Root			$-2.02852i$ of defining polynomial
Character	$\chi$	$=$	360.109
Dual form			360.2.d.f.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.321037 + 1.37729i) q^{2} +(-1.79387 + 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} -4.05705i q^{7} +(-1.79387 - 2.18678i) q^{8} +O(q^{10})$	\(q+(0.321037 + 1.37729i) q^{2} +(-1.79387 + 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} -4.05705i q^{7} +(-1.79387 - 2.18678i) q^{8} +(0.321037 - 3.14594i) q^{10} -0.985939i q^{11} -4.94567 q^{13} +(5.58774 - 1.30246i) q^{14} +(2.43594 - 3.17272i) q^{16} -4.52323i q^{17} +2.60492i q^{19} +(4.43594 - 0.567801i) q^{20} +(1.35793 - 0.316523i) q^{22} +3.53729i q^{23} +(3.94567 + 3.07111i) q^{25} +(-1.58774 - 6.81163i) q^{26} +(3.58774 + 7.27782i) q^{28} -7.59434i q^{29} -3.28415 q^{31} +(5.15180 + 2.33645i) q^{32} +(6.22982 - 1.45212i) q^{34} +(-2.94567 + 8.58028i) q^{35} +0.945668 q^{37} +(-3.58774 + 0.836276i) q^{38} +(2.20613 + 5.92731i) q^{40} -0.568295 q^{41} -8.45963 q^{43} +(0.871889 + 1.76865i) q^{44} +(-4.87189 + 1.13560i) q^{46} -2.60492i q^{47} -9.45963 q^{49} +(-2.96311 + 6.42028i) q^{50} +(8.87189 - 4.37357i) q^{52} +0.229815 q^{53} +(-0.715853 + 2.08517i) q^{55} +(-8.87189 + 7.27782i) q^{56} +(10.4596 - 2.43806i) q^{58} +9.10003i q^{59} -11.0183i q^{61} +(-1.05433 - 4.52323i) q^{62} +(-1.56406 + 7.84562i) q^{64} +(10.4596 + 3.59086i) q^{65} +8.45963 q^{67} +(4.00000 + 8.11409i) q^{68} +(-12.7632 - 1.30246i) q^{70} -1.43171 q^{71} -11.9507i q^{73} +(0.303594 + 1.30246i) q^{74} +(-2.30359 - 4.67289i) q^{76} -4.00000 q^{77} +3.28415 q^{79} +(-7.45539 + 4.94137i) q^{80} +(-0.182443 - 0.782708i) q^{82} +9.89134 q^{83} +(-3.28415 + 9.56622i) q^{85} +(-2.71585 - 11.6514i) q^{86} +(-2.15604 + 1.76865i) q^{88} -12.3510 q^{89} +20.0648i q^{91} +(-3.12811 - 6.34545i) q^{92} +(3.58774 - 0.836276i) q^{94} +(1.89134 - 5.50917i) q^{95} -3.23797i q^{97} +(-3.03689 - 13.0287i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{4} + q^{8}+O(q^{10}) $ 6 * q + q^2 + q^4 + q^8	$ 6 q + q^{2} + q^{4} + q^{8} + q^{10} - 8 q^{13} + 10 q^{14} + q^{16} + 13 q^{20} + 10 q^{22} + 2 q^{25} + 14 q^{26} - 2 q^{28} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} - 16 q^{37} + 2 q^{38} + 25 q^{40} + 4 q^{41} - 22 q^{44} - 2 q^{46} - 6 q^{49} - 15 q^{50} + 26 q^{52} - 24 q^{53} - 8 q^{55} - 26 q^{56} + 12 q^{58} - 28 q^{62} - 23 q^{64} + 12 q^{65} + 24 q^{68} - 6 q^{70} - 16 q^{71} - 18 q^{74} + 6 q^{76} - 24 q^{77} + 16 q^{79} - 15 q^{80} - 50 q^{82} + 16 q^{83} - 16 q^{85} - 20 q^{86} + 18 q^{88} + 20 q^{89} - 46 q^{92} - 2 q^{94} - 32 q^{95} - 21 q^{98}+O(q^{100}) $ 6 * q + q^2 + q^4 + q^8 + q^10 - 8 * q^13 + 10 * q^14 + q^16 + 13 * q^20 + 10 * q^22 + 2 * q^25 + 14 * q^26 - 2 * q^28 - 16 * q^31 + 21 * q^32 + 12 * q^34 + 4 * q^35 - 16 * q^37 + 2 * q^38 + 25 * q^40 + 4 * q^41 - 22 * q^44 - 2 * q^46 - 6 * q^49 - 15 * q^50 + 26 * q^52 - 24 * q^53 - 8 * q^55 - 26 * q^56 + 12 * q^58 - 28 * q^62 - 23 * q^64 + 12 * q^65 + 24 * q^68 - 6 * q^70 - 16 * q^71 - 18 * q^74 + 6 * q^76 - 24 * q^77 + 16 * q^79 - 15 * q^80 - 50 * q^82 + 16 * q^83 - 16 * q^85 - 20 * q^86 + 18 * q^88 + 20 * q^89 - 46 * q^92 - 2 * q^94 - 32 * q^95 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$	−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			0
$7$		−	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
$9$		0			0
$10$	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	$-0.0474882\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	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			0
$19$			2.60492i			0.597610i	0.954314	+	0.298805i	$0.0965881\pi$
$19$			2.60492i			0.597610i	−0.954314	+	0.298805i	$0.903412\pi$
$20$	4.43594	−	0.567801i	0.991907	−	0.126964i
$21$		0			0
$22$	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	$0.879773\pi$
$24$		0			0
$25$	3.94567	+	3.07111i	0.789134	+	0.614222i
$26$	−1.58774	−	6.81163i	−0.311382	−	1.33587i
$27$		0			0
$28$	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			0
$31$	−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			0
$34$	6.22982	−	1.45212i	1.06840	−	0.249037i
$35$	−2.94567	+	8.58028i	−0.497909	+	1.45033i
$36$		0			0
$37$	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
$39$		0			0
$40$	2.20613	+	5.92731i	0.348820	+	0.937190i
$41$	−0.568295			−0.0887527			−0.0443763	−	0.999015i	$-0.514130\pi$
$41$	−0.568295			−0.0887527			−0.0443763	+	0.999015i	$0.514130\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	−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	$-0.0608435\pi$
$48$		0			0
$49$	−9.45963			−1.35138
$50$	−2.96311	+	6.42028i	−0.419047	+	0.907964i
$51$		0			0
$52$	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			0
$55$	−0.715853	+	2.08517i	−0.0965256	+	0.281164i
$56$	−8.87189	+	7.27782i	−1.18556	+	0.972539i
$57$		0			0
$58$	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	$0.798196\pi$
$60$		0			0
$61$		−	11.0183i		−	1.41075i	−0.708832	−	0.705377i	$-0.750778\pi$
$61$		−	11.0183i		−	1.41075i	0.708832	−	0.705377i	$-0.249222\pi$
$62$	−1.05433	−	4.52323i	−0.133900	−	0.574451i
$63$		0			0
$64$	−1.56406	+	7.84562i	−0.195507	+	0.980702i
$65$	10.4596	+	3.59086i	1.29736	+	0.445392i
$66$		0			0
$67$	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
$69$		0			0
$70$	−12.7632	−	1.30246i	−1.52550	−	0.155674i
$71$	−1.43171			−0.169912			−0.0849561	−	0.996385i	$-0.527075\pi$
$71$	−1.43171			−0.169912			−0.0849561	+	0.996385i	$0.527075\pi$
$72$		0			0
$73$		−	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
$75$		0			0
$76$	−2.30359	−	4.67289i	−0.264240	−	0.536018i
$77$	−4.00000			−0.455842
$78$		0			0
$79$	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
$81$		0			0
$82$	−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	$0.317342\pi$
$84$		0			0
$85$	−3.28415	+	9.56622i	−0.356216	+	1.03760i
$86$	−2.71585	−	11.6514i	−0.292858	−	1.25640i
$87$		0			0
$88$	−2.15604	+	1.76865i	−0.229834	+	0.188538i
$89$	−12.3510			−1.30920			−0.654600	−	0.755976i	$-0.727163\pi$
$89$	−12.3510			−1.30920			−0.654600	+	0.755976i	$0.727163\pi$
$90$		0			0
$91$			20.0648i			2.10336i
$92$	−3.12811	−	6.34545i	−0.326128	−	0.661559i
$93$		0			0
$94$	3.58774	−	0.836276i	0.370047	−	0.0862553i
$95$	1.89134	−	5.50917i	0.194047	−	0.565229i
$96$		0			0
$97$		−	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			0
$100$	−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	$0.930458\pi$
$102$		0			0
$103$			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
$105$		0			0
$106$	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	$0.438066\pi$
$108$		0			0
$109$		−	4.17034i		−	0.399446i	−0.979852	−	0.199723i	$-0.935996\pi$
$109$		−	4.17034i		−	0.399446i	0.979852	−	0.199723i	$-0.0640042\pi$
$110$	−3.10170	−	0.316523i	−0.295736	−	0.0301793i
$111$		0			0
$112$	−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	$-0.0192548\pi$
$114$		0			0
$115$	2.56829	−	7.48105i	0.239495	−	0.697611i
$116$	6.71585	+	13.6233i	0.623551	+	1.26489i
$117$		0			0
$118$	−12.5334	+	2.92145i	−1.15379	+	0.268941i
$119$	−18.3510			−1.68223
$120$		0			0
$121$	10.0279			0.911630
$122$	15.1755	−	3.53729i	1.37392	−	0.320252i
$123$		0			0
$124$	5.89134	−	2.90425i	0.529058	−	0.260809i
$125$	−6.11491	−	9.35991i	−0.546934	−	0.837176i
$126$		0			0
$127$		−	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
$129$		0			0
$130$	−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			0
$133$	10.5683			0.916387
$134$	2.71585	+	11.6514i	0.234614	+	1.00653i
$135$		0			0
$136$	−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	$0.730948\pi$
$138$		0			0
$139$		−	16.8612i		−	1.43015i	−0.699047	−	0.715076i	$-0.746392\pi$
$139$		−	16.8612i		−	1.43015i	0.699047	−	0.715076i	$-0.253608\pi$
$140$	−2.30359	−	17.9968i	−0.194689	−	1.52101i
$141$		0			0
$142$	−0.459630	−	1.97188i	−0.0385713	−	0.165476i
$143$			4.87613i			0.407762i
$144$		0			0
$145$	−5.51396	+	16.0613i	−0.457910	+	1.33382i
$146$	16.4596	−	3.83662i	1.36221	−	0.317521i
$147$		0			0
$148$	−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	$-0.141500\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−1.28415	−	5.50917i	−0.103480	−	0.443942i
$155$	6.94567	+	2.38449i	0.557889	+	0.191527i
$156$		0			0
$157$	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			0
$160$	−9.19917	−	8.68189i	−0.727258	−	0.686364i
$161$	14.3510			1.13101
$162$		0			0
$163$	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			0
$166$	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	$-0.0683743\pi$
$168$		0			0
$169$	11.4596			0.881510
$170$	−14.2298	−	1.45212i	−1.09138	−	0.111373i
$171$		0			0
$172$	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	$0.371434\pi$
$174$		0			0
$175$	12.4596	−	16.0078i	0.941860	−	1.21007i
$176$	−3.12811	−	2.40169i	−0.235790	−	0.181034i
$177$		0			0
$178$	−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	$-0.206617\pi$
$180$		0			0
$181$		−	8.11409i		−	0.603116i	−0.953448	−	0.301558i	$-0.902493\pi$
$181$		−	8.11409i		−	0.603116i	0.953448	−	0.301558i	$-0.0975067\pi$
$182$	−27.6351	+	6.44154i	−2.04845	+	0.477479i
$183$		0			0
$184$	7.73530	−	6.34545i	0.570254	−	0.467793i
$185$	−2.00000	−	0.686614i	−0.147043	−	0.0504808i
$186$		0			0
$187$	−4.45963			−0.326120
$188$	2.30359	+	4.67289i	0.168007	+	0.340806i
$189$		0			0
$190$	8.19493	+	0.836276i	0.594523	+	0.0606698i
$191$	24.9193			1.80309			0.901547	−	0.432681i	$-0.142432\pi$
$191$	24.9193			1.80309			0.901547	+	0.432681i	$0.142432\pi$
$192$		0			0
$193$		−	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
$195$		0			0
$196$	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	$0.388158\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	−6.00000	+	1.39856i	−0.422159	+	0.0984020i
$203$	−30.8106			−2.16248
$204$		0			0
$205$	1.20189	+	0.412617i	0.0839437	+	0.0288184i
$206$	−20.7632	+	4.83975i	−1.44664	+	0.337202i
$207$		0			0
$208$	−12.0474	+	15.6912i	−0.835335	+	1.08799i
$209$	2.56829			0.177653
$210$		0			0
$211$		−	6.44154i		−	0.443454i	−0.975109	−	0.221727i	$-0.928831\pi$
$211$		−	6.44154i		−	0.443454i	0.975109	−	0.221727i	$-0.0711694\pi$
$212$	−0.412259	+	0.203231i	−0.0283140	+	0.0139580i
$213$		0			0
$214$	1.28415	+	5.50917i	0.0877825	+	0.376599i
$215$	17.8913	+	6.14222i	1.22018	+	0.418896i
$216$		0			0
$217$			13.3239i			0.904488i
$218$	5.74378	−	1.33883i	0.389018	−	0.0906772i
$219$		0			0
$220$	−0.559817	−	4.37357i	−0.0377428	−	0.294866i
$221$			22.3704i			1.50480i
$222$		0			0
$223$			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
$225$		0			0
$226$	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	$0.425071\pi$
$228$		0			0
$229$			4.17034i			0.275584i	0.990461	+	0.137792i	$0.0440005\pi$
$229$			4.17034i			0.275584i	−0.990461	+	0.137792i	$0.955999\pi$
$230$	11.1281	+	1.13560i	0.733766	+	0.0748793i
$231$		0			0
$232$	−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	$-0.287748\pi$
$234$		0			0
$235$	−1.89134	+	5.50917i	−0.123377	+	0.359379i
$236$	−8.04737	−	16.3243i	−0.523839	−	1.06262i
$237$		0			0
$238$	−5.89134	−	25.2747i	−0.381879	−	1.63831i
$239$	−8.91926			−0.576939			−0.288469	−	0.957489i	$-0.593146\pi$
$239$	−8.91926			−0.576939			−0.288469	+	0.957489i	$0.593146\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	9.74378	+	19.7655i	0.623781	+	1.26536i
$245$	20.0062	+	6.86828i	1.27815	+	0.438798i
$246$		0			0
$247$		−	12.8831i		−	0.819731i
$248$	5.89134	+	7.18172i	0.374100	+	0.456040i
$249$		0			0
$250$	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	$-0.0425591\pi$
$252$		0			0
$253$	3.48755			0.219261
$254$	1.58774	−	0.370091i	0.0996238	−	0.0232216i
$255$		0			0
$256$	−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	$-0.279854\pi$
$258$		0			0
$259$		−	3.83662i		−	0.238396i
$260$	−21.9387	+	2.80815i	−1.36058	+	0.174154i
$261$		0			0
$262$	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	$0.850685\pi$
$264$		0			0
$265$	−0.486038	−	0.166860i	−0.0298571	−	0.0102501i
$266$	3.39281	+	14.5556i	0.208027	+	0.892463i
$267$		0			0
$268$	−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			0
$271$	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
$273$		0			0
$274$	−24.1212	+	5.62246i	−1.45721	+	0.339665i
$275$	3.02792	−	3.89019i	0.182591	−	0.234587i
$276$		0			0
$277$	−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
$279$		0			0
$280$	24.0474	−	8.95037i	1.43711	−	0.534887i
$281$	−21.7827			−1.29945			−0.649723	−	0.760171i	$-0.725115\pi$
$281$	−21.7827			−1.29945			−0.649723	+	0.760171i	$0.725115\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	−6.71585	+	1.56542i	−0.397117	+	0.0925650i
$287$			2.30560i			0.136095i
$288$		0			0
$289$	−3.45963			−0.203508
$290$	−23.8913	−	2.43806i	−1.40295	−	0.143168i
$291$		0			0
$292$	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	$0.884686\pi$
$294$		0			0
$295$	6.60719	−	19.2457i	0.384685	−	1.12053i
$296$	−1.69641	−	2.06797i	−0.0986016	−	0.120198i
$297$		0			0
$298$	14.4596	−	3.37043i	0.837624	−	0.195244i
$299$		−	17.4943i		−	1.01172i
$300$		0			0
$301$			34.3211i			1.97824i
$302$	1.51396	+	6.49511i	0.0871187	+	0.373752i
$303$		0			0
$304$	8.26470	+	6.34545i	0.474013	+	0.363936i
$305$	−8.00000	+	23.3028i	−0.458079	+	1.33431i
$306$		0			0
$307$	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
$309$		0			0
$310$	−1.05433	+	10.3317i	−0.0598820	+	0.586803i
$311$	−5.13659			−0.291269			−0.145635	−	0.989338i	$-0.546522\pi$
$311$	−5.13659			−0.291269			−0.145635	+	0.989338i	$0.546522\pi$
$312$		0			0
$313$		−	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
$315$		0			0
$316$	−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			0
$319$	−7.48755			−0.419223
$320$	9.00424	−	15.4572i	0.503352	−	0.864081i
$321$		0			0
$322$	4.60719	+	19.7655i	0.256749	+	1.10149i
$323$	11.7827			0.655605
$324$		0			0
$325$	−19.5140	−	15.1887i	−1.08244	−	0.842516i
$326$	5.06682	+	21.7374i	0.280625	+	1.20392i
$327$		0			0
$328$	1.01945	+	1.24274i	0.0562895	+	0.0686187i
$329$	−10.5683			−0.582649
$330$		0			0
$331$		−	25.9077i		−	1.42402i	−0.702171	−	0.712008i	$-0.747786\pi$
$331$		−	25.9077i		−	1.42402i	0.702171	−	0.712008i	$-0.252214\pi$
$332$	−17.7438	+	8.74714i	−0.973816	+	0.480062i
$333$		0			0
$334$	7.58774	−	1.76865i	0.415183	−	0.0967760i
$335$	−17.8913	−	6.14222i	−0.977508	−	0.335585i
$336$		0			0
$337$			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
$339$		0			0
$340$	−2.56829	−	20.0648i	−0.139285	−	1.08817i
$341$			3.23797i			0.175346i
$342$		0			0
$343$			9.97884i			0.538806i
$344$	15.1755	+	18.4994i	0.818207	+	0.997420i
$345$		0			0
$346$	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	$0.712098\pi$
$348$		0			0
$349$			21.4380i			1.14755i	0.819012	+	0.573776i	$0.194522\pi$
$349$			21.4380i			1.14755i	−0.819012	+	0.573776i	$0.805478\pi$
$350$	26.0474	+	12.0215i	1.39229	+	0.642575i
$351$		0			0
$352$	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	$-0.0384093\pi$
$354$		0			0
$355$	3.02792	+	1.03951i	0.160706	+	0.0551713i
$356$	22.1560	−	10.9222i	1.17427	−	0.578878i
$357$		0			0
$358$	22.2772	−	5.19265i	1.17739	−	0.274440i
$359$	10.3510			0.546303			0.273152	−	0.961971i	$-0.411934\pi$
$359$	10.3510			0.546303			0.273152	+	0.961971i	$0.411934\pi$
$360$		0			0
$361$	12.2144			0.642862
$362$	11.1755	−	2.60492i	0.587370	−	0.136912i
$363$		0			0
$364$	−17.7438	−	35.9937i	−0.930027	−	1.88658i
$365$	−8.67696	+	25.2747i	−0.454173	+	1.32294i
$366$		0			0
$367$		−	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			0
$370$	0.303594	−	2.97501i	0.0157831	−	0.154664i
$371$		−	0.932371i		−	0.0484063i
$372$		0			0
$373$	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
$375$		0			0
$376$	−5.69641	+	4.67289i	−0.293770	+	0.240986i
$377$			37.5591i			1.93439i
$378$		0			0
$379$			33.6881i			1.73044i	0.501392	+	0.865220i	$0.332821\pi$
$379$			33.6881i			1.73044i	−0.501392	+	0.865220i	$0.667179\pi$
$380$	1.47908	+	11.5553i	0.0758751	+	0.592774i
$381$		0			0
$382$	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	$-0.0422127\pi$
$384$		0			0
$385$	8.45963	+	2.90425i	0.431143	+	0.148014i
$386$	1.43171	−	0.333720i	0.0728719	−	0.0169859i
$387$		0			0
$388$	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	$0.861377\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	16.9694	+	20.6862i	0.857082	+	1.04481i
$393$		0			0
$394$	3.10170	+	13.3067i	0.156262	+	0.670384i
$395$	−6.94567	−	2.38449i	−0.349474	−	0.119977i
$396$		0			0
$397$	−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
$399$		0			0
$400$	19.3552	−	5.03746i	0.967760	−	0.251873i
$401$	4.56829			0.228130			0.114065	−	0.993473i	$-0.463613\pi$
$401$	4.56829			0.228130			0.114065	+	0.993473i	$0.463613\pi$
$402$		0			0
$403$	16.2423			0.809087
$404$	−3.85244	−	7.81477i	−0.191666	−	0.388799i
$405$		0			0
$406$	−9.89134	−	42.4352i	−0.490899	−	2.10602i
$407$		−	0.932371i		−	0.0462159i
$408$		0			0
$409$	−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
$411$		0			0
$412$	−13.3315	−	27.0433i	−0.656797	−	1.33233i
$413$	36.9193			1.81668
$414$		0			0
$415$	−20.9193	−	7.18172i	−1.02689	−	0.352537i
$416$	−25.4791	−	11.5553i	−1.24921	−	0.566545i
$417$		0			0
$418$	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	$0.996989\pi$
$420$		0			0
$421$			12.0578i			0.587664i	0.955857	+	0.293832i	$0.0949306\pi$
$421$			12.0578i			0.587664i	−0.955857	+	0.293832i	$0.905069\pi$
$422$	8.87189	−	2.06797i	0.431877	−	0.100667i
$423$		0			0
$424$	−0.412259	−	0.502556i	−0.0200210	−	0.0244063i
$425$	13.8913	−	17.8472i	0.673829	−	0.865715i
$426$		0			0
$427$	−44.7019			−2.16328
$428$	−7.17548	+	3.53729i	−0.346840	+	0.170982i
$429$		0			0
$430$	−2.71585	+	26.6135i	−0.130970	+	1.28342i
$431$	−40.4068			−1.94633			−0.973164	−	0.230113i	$-0.926090\pi$
$431$	−40.4068			−1.94633			−0.973164	+	0.230113i	$0.926090\pi$
$432$		0			0
$433$		−	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
$435$		0			0
$436$	3.68793	+	7.48105i	0.176620	+	0.358277i
$437$	−9.21438			−0.440783
$438$		0			0
$439$	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
$441$		0			0
$442$	−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	$0.553393\pi$
$444$		0			0
$445$	26.1212	+	8.96757i	1.23826	+	0.425103i
$446$	−24.7632	+	5.77213i	−1.17257	+	0.273318i
$447$		0			0
$448$	31.8300	+	6.34545i	1.50383	+	0.299794i
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$		0			0
$451$			0.560304i			0.0263837i
$452$	1.13659	+	2.30560i	0.0534607	+	0.108446i
$453$		0			0
$454$	2.25622	+	9.67951i	0.105890	+	0.454282i
$455$	14.5683	−	42.4352i	0.682972	−	1.98939i
$456$		0			0
$457$			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
$459$		0			0
$460$	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	$-0.406185\pi$
$462$		0			0
$463$			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
$465$		0			0
$466$	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	$0.513934\pi$
$468$		0			0
$469$		−	34.3211i		−	1.58480i
$470$	−8.19493	−	0.836276i	−0.378004	−	0.0385745i
$471$		0			0
$472$	19.8998	−	16.3243i	0.915963	−	0.751386i
$473$			8.34068i			0.383505i
$474$		0			0
$475$	−8.00000	+	10.2782i	−0.367065	+	0.471594i
$476$	32.9193	−	16.2282i	1.50885	−	0.743818i
$477$		0			0
$478$	−2.86341	−	12.2844i	−0.130969	−	0.561877i
$479$	31.4876			1.43870			0.719352	−	0.694646i	$-0.244439\pi$
$479$	31.4876			1.43870			0.719352	+	0.694646i	$0.244439\pi$
$480$		0			0
$481$	−4.67696			−0.213251
$482$	−5.24926	−	22.5201i	−0.239097	−	1.02576i
$483$		0			0
$484$	−17.9888	+	8.86793i	−0.817673	+	0.403088i
$485$	−2.35097	+	6.84800i	−0.106752	+	0.310952i
$486$		0			0
$487$			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
$489$		0			0
$490$	−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	$0.890788\pi$
$492$		0			0
$493$	−34.3510			−1.54709
$494$	17.7438	−	4.13594i	0.798330	−	0.186085i
$495$		0			0
$496$	−8.00000	+	10.4197i	−0.359211	+	0.467858i
$497$			5.80850i			0.260547i
$498$		0			0
$499$		−	35.6599i		−	1.59636i	−0.602420	−	0.798179i	$-0.705797\pi$
$499$		−	35.6599i		−	1.59636i	0.602420	−	0.798179i	$-0.294203\pi$
$500$	19.2465	+	11.3829i	0.860731	+	0.509059i
$501$		0			0
$502$	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	$-0.190830\pi$
$504$		0			0
$505$	3.16300	−	9.21332i	0.140751	−	0.409988i
$506$	1.11963	+	4.80338i	0.0497738	+	0.213536i
$507$		0			0
$508$	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	$0.901534\pi$
$510$		0			0
$511$	−48.4846			−2.14483
$512$	19.9624	−	10.6538i	0.882221	−	0.470835i
$513$		0			0
$514$	34.0125	−	7.92806i	1.50023	−	0.349692i
$515$	10.9457	−	31.8831i	0.482324	−	1.40494i
$516$		0			0
$517$	−2.56829			−0.112953
$518$	5.28415	−	1.23170i	0.232172	−	0.0541176i
$519$		0			0
$520$	−10.9108	−	29.3145i	−0.478469	−	1.28553i
$521$	30.9193			1.35460			0.677299	−	0.735708i	$-0.263150\pi$
$521$	30.9193			1.35460			0.677299	+	0.735708i	$0.263150\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	−20.1949	+	4.70729i	−0.880541	+	0.205248i
$527$			14.8550i			0.647092i
$528$		0			0
$529$	10.4876			0.455981
$530$	0.0737791	−	0.722984i	0.00320476	−	0.0314044i
$531$		0			0
$532$	−18.9582	+	9.34579i	−0.821940	+	0.405191i
$533$	2.81060			0.121740
$534$		0			0
$535$	−8.45963	−	2.90425i	−0.365742	−	0.125562i
$536$	−15.1755	−	18.4994i	−0.655481	−	0.799052i
$537$		0			0
$538$	−15.8913	+	3.70415i	−0.685124	+	0.159697i
$539$			9.32662i			0.401726i
$540$		0			0
$541$		−	24.3423i		−	1.04656i	−0.852162	−	0.523278i	$-0.824709\pi$
$541$		−	24.3423i		−	1.04656i	0.852162	−	0.523278i	$-0.175291\pi$
$542$	1.80908	+	7.76120i	0.0777066	+	0.333372i
$543$		0			0
$544$	10.5683	−	23.3028i	0.453112	−	0.999098i
$545$	−3.02792	+	8.81988i	−0.129702	+	0.377802i
$546$		0			0
$547$	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
$549$		0			0
$550$	6.33000	+	2.92145i	0.269912	+	0.124571i
$551$	19.7827			0.842770
$552$		0			0
$553$		−	13.3239i		−	0.566592i
$554$	−5.58774	−	23.9722i	−0.237400	−	1.01848i
$555$		0			0
$556$	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	$0.724342\pi$
$558$		0			0
$559$	41.8385			1.76958
$560$	20.0474	+	30.2469i	0.847156	+	1.27816i
$561$		0			0
$562$	−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	$0.452686\pi$
$564$		0			0
$565$	−0.933181	+	2.71821i	−0.0392592	+	0.114356i
$566$	−6.93318	−	29.7443i	−0.291423	−	1.25025i
$567$		0			0
$568$	2.56829	+	3.13083i	0.107763	+	0.131367i
$569$	24.3510			1.02085			0.510423	−	0.859924i	$-0.329489\pi$
$569$	24.3510			1.02085			0.510423	+	0.859924i	$0.329489\pi$
$570$		0			0
$571$		−	20.0992i		−	0.841125i	−0.907263	−	0.420563i	$-0.861833\pi$
$571$		−	20.0992i		−	0.841125i	0.907263	−	0.420563i	$-0.138167\pi$
$572$	−4.31207	−	8.74714i	−0.180297	−	0.365736i
$573$		0			0
$574$	−3.17548	+	0.740182i	−0.132542	+	0.0308946i
$575$	−10.8634	+	13.9570i	−0.453036	+	0.582047i
$576$		0			0
$577$		−	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
$579$		0			0
$580$	−4.31207	−	33.6881i	−0.179049	−	1.39882i
$581$		−	40.1296i		−	1.66486i
$582$		0			0
$583$		−	0.226584i		−	0.00938413i
$584$	−26.1336	+	21.4380i	−1.08142	+	0.887112i
$585$		0			0
$586$	−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	$0.445758\pi$
$588$		0			0
$589$		−	8.55495i		−	0.352501i
$590$	28.6282	+	2.92145i	1.17860	+	0.120274i
$591$		0			0
$592$	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	$-0.0509421\pi$
$594$		0			0
$595$	38.8106	+	13.3239i	1.59108	+	0.546228i
$596$	9.28415	+	18.8331i	0.380293	+	0.771434i
$597$		0			0
$598$	24.0947	−	5.61631i	0.985307	−	0.229668i
$599$	−5.64903			−0.230813			−0.115407	−	0.993318i	$-0.536817\pi$
$599$	−5.64903			−0.230813			−0.115407	+	0.993318i	$0.536817\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−8.45963	+	4.17034i	−0.344217	+	0.169689i
$605$	−21.2081	−	7.28090i	−0.862233	−	0.296010i
$606$		0			0
$607$		−	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
$609$		0			0
$610$	−34.6630	−	3.53729i	−1.40347	−	0.143221i
$611$			12.8831i			0.521194i
$612$		0			0
$613$	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
$615$		0			0
$616$	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	$-0.164020\pi$
$618$		0			0
$619$			39.4966i			1.58750i	0.608243	+	0.793751i	$0.291874\pi$
$619$			39.4966i			1.58750i	−0.608243	+	0.793751i	$0.708126\pi$
$620$	−14.5683	+	1.86474i	−0.585077	+	0.0748898i
$621$		0			0
$622$	−1.64903	−	7.07459i	−0.0661202	−	0.283665i
$623$			50.1084i			2.00755i
$624$		0			0
$625$	6.13659	+	24.2351i	0.245464	+	0.969406i
$626$	31.7827	−	7.40831i	1.27029	−	0.296095i
$627$		0			0
$628$	−16.0474	+	7.91086i	−0.640360	+	0.315678i
$629$		−	4.27748i		−	0.170554i
$630$		0			0
$631$	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
$633$		0			0
$634$	0.533409	+	2.28840i	0.0211844	+	0.0908840i
$635$	−0.837003	+	2.43806i	−0.0332155	+	0.0967516i
$636$		0			0
$637$	46.7842			1.85366
$638$	−2.40378	−	10.3126i	−0.0951666	−	0.408278i
$639$		0			0
$640$	24.1797	+	7.43916i	0.955787	+	0.294058i
$641$	−38.7019			−1.52863			−0.764317	−	0.644840i	$-0.776924\pi$
$641$	−38.7019			−1.52863			−0.764317	+	0.644840i	$0.776924\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	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	$-0.0410893\pi$
$648$		0			0
$649$	8.97208			0.352185
$650$	14.6546	−	31.7526i	0.574799	−	1.24544i
$651$		0			0
$652$	−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	$0.445282\pi$
$654$		0			0
$655$	−2.82452	+	8.22739i	−0.110363	+	0.321471i
$656$	−1.38433	+	1.80304i	−0.0540492	+	0.0703969i
$657$		0			0
$658$	−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			0
$661$			23.3028i			0.906373i	0.891416	+	0.453186i	$0.149713\pi$
$661$			23.3028i			0.906373i	−0.891416	+	0.453186i	$0.850287\pi$
$662$	35.6825	−	8.31732i	1.38684	−	0.323262i
$663$		0			0
$664$	−17.7438	−	21.6302i	−0.688592	−	0.839415i
$665$	−22.3510	−	7.67324i	−0.866733	−	0.297555i
$666$		0			0
$667$	26.8634			1.04016
$668$	4.87189	+	9.88274i	0.188499	+	0.382375i
$669$		0			0
$670$	2.71585	−	26.6135i	0.104923	−	1.02817i
$671$	−10.8634			−0.419377
$672$		0			0
$673$			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
$675$		0			0
$676$	−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	$0.345296\pi$
$678$		0			0
$679$	−13.1366			−0.504136
$680$	26.8106	−	9.97884i	1.02814	−	0.382671i
$681$		0			0
$682$	−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	$0.235598\pi$
$684$		0			0
$685$	12.7159	−	37.0393i	0.485848	−	1.41520i
$686$	−13.7438	+	3.20357i	−0.524740	+	0.122313i
$687$		0			0
$688$	−20.6072	+	26.8401i	−0.785642	+	1.02327i
$689$	−1.13659			−0.0433006
$690$		0			0
$691$		−	13.4090i		−	0.510102i	−0.966928	−	0.255051i	$-0.917908\pi$
$691$		−	13.4090i		−	0.510102i	0.966928	−	0.255051i	$-0.0820923\pi$
$692$	−18.5459	+	9.14256i	−0.705009	+	0.347548i
$693$		0			0
$694$	−7.39281	−	31.7162i	−0.280627	−	1.20393i
$695$	−12.2423	+	35.6599i	−0.464377	+	1.35266i
$696$		0			0
$697$			2.57053i			0.0973657i
$698$	−29.5264	+	6.88240i	−1.11759	+	0.260503i
$699$		0			0
$700$	−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	$-0.0951952\pi$
$702$		0			0
$703$			2.46339i			0.0929086i
$704$	7.73530	+	1.54206i	0.291535	+	0.0581187i
$705$		0			0
$706$	6.22982	−	1.45212i	0.234462	−	0.0546514i
$707$	17.6740			0.664699
$708$		0			0
$709$			15.7873i			0.592906i	0.955047	+	0.296453i	$0.0958038\pi$
$709$			15.7873i			0.592906i	−0.955047	+	0.296453i	$0.904196\pi$
$710$	−0.459630	+	4.50406i	−0.0172496	+	0.169034i
$711$		0			0
$712$	22.1560	+	27.0089i	0.830333	+	1.01220i
$713$		−	11.6170i		−	0.435060i
$714$		0			0
$715$	3.54037	−	10.3126i	0.132402	−	0.385668i
$716$	14.3036	+	29.0152i	0.534550	+	1.08435i
$717$		0			0
$718$	3.32304	+	14.2563i	0.124015	+	0.532041i
$719$	22.5683			0.841655			0.420828	−	0.907141i	$-0.361740\pi$
$719$	22.5683			0.841655			0.420828	+	0.907141i	$0.361740\pi$
$720$		0			0
$721$	61.1616			2.27778
$722$	3.92126	+	16.8228i	0.145934	+	0.626079i
$723$		0			0
$724$	7.17548	+	14.5556i	0.266675	+	0.540956i
$725$	23.3230	−	29.9647i	0.866196	−	1.11286i
$726$		0			0
$727$			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
$729$		0			0
$730$	−37.5962	−	3.83662i	−1.39150	−	0.142000i
$731$			38.2649i			1.41528i
$732$		0			0
$733$	−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
$735$		0			0
$736$	−8.26470	+	18.2234i	−0.304641	+	0.671724i
$737$		−	8.34068i		−	0.307233i
$738$		0			0
$739$			14.8894i			0.547714i	0.961770	+	0.273857i	$0.0882995\pi$
$739$			14.8894i			0.547714i	−0.961770	+	0.273857i	$0.911701\pi$
$740$	4.19493	−	0.536951i	0.154209	−	0.0197387i
$741$		0			0
$742$	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	$0.725218\pi$
$744$		0			0
$745$	−7.62263	+	22.2035i	−0.279271	+	0.813475i
$746$	9.65751	+	41.4321i	0.353587	+	1.51694i
$747$		0			0
$748$	8.00000	−	3.94376i	0.292509	−	0.144198i
$749$		−	16.2282i		−	0.592965i
$750$		0			0
$751$	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
$753$		0			0
$754$	−51.7299	+	12.0578i	−1.88389	+	0.439121i
$755$	−9.97359	−	3.42400i	−0.362976	−	0.124612i
$756$		0			0
$757$	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
$759$		0			0
$760$	−15.4402	+	5.74680i	−0.560074	+	0.208458i
$761$	14.9193			0.540823			0.270411	−	0.962745i	$-0.412840\pi$
$761$	14.9193			0.540823			0.270411	+	0.962745i	$0.412840\pi$
$762$		0			0
$763$	−16.9193			−0.612518
$764$	−44.7019	+	22.0367i	−1.61726	+	0.797259i
$765$		0			0
$766$	7.12811	−	1.66151i	0.257549	−	0.0600328i
$767$		−	45.0057i		−	1.62506i
$768$		0			0
$769$	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
$771$		0			0
$772$	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	$0.577583\pi$
$774$		0			0
$775$	−12.9582	−	10.0860i	−0.465471	−	0.362299i
$776$	−7.08074	+	5.80850i	−0.254184	+	0.208513i
$777$		0			0
$778$	−22.9193	+	5.34231i	−0.821695	+	0.191531i
$779$		−	1.48036i		−	0.0530395i
$780$		0			0
$781$			1.41157i			0.0505101i
$782$	5.13659	+	22.0367i	0.183684	+	0.788030i
$783$		0			0
$784$	−23.0431	+	30.0128i	−0.822969	+	1.07189i
$785$	−18.9193	−	6.49511i	−0.675257	−	0.231820i
$786$		0			0
$787$	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
$789$		0			0
$790$	1.05433	−	10.3317i	0.0375115	−	0.367586i
$791$	−5.21438			−0.185402
$792$		0			0
$793$			54.4931i			1.93511i
$794$	−6.55982	−	28.1425i	−0.232799	−	0.998741i
$795$		0			0
$796$	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	$0.347242\pi$
$798$		0			0
$799$	−11.7827			−0.416841
$800$	13.1518	+	25.0406i	0.464986	+	0.885318i
$801$		0			0
$802$	1.46659	+	6.29188i	0.0517871	+	0.222174i
$803$	−11.7827			−0.415801
$804$		0			0
$805$	−30.3510	−	10.4197i	−1.06973	−	0.367246i
$806$	5.21438	+	22.3704i	0.183669	+	0.787964i
$807$		0			0
$808$	9.52645	−	7.81477i	0.335139	−	0.274923i
$809$	35.6212			1.25237			0.626187	−	0.779673i	$-0.284615\pi$
$809$	35.6212			1.25237			0.626187	+	0.779673i	$0.284615\pi$
$810$		0			0
$811$			43.8935i			1.54131i	0.637253	+	0.770654i	$0.280071\pi$
$811$			43.8935i			1.54131i	−0.637253	+	0.770654i	$0.719929\pi$
$812$	55.2702	−	27.2465i	1.93960	−	0.956166i
$813$		0			0
$814$	1.28415	−	0.299325i	0.0450093	−	0.0104913i
$815$	−33.3789	−	11.4592i	−1.16921	−	0.401398i
$816$		0			0
$817$		−	22.0367i		−	0.770966i
$818$	−6.38585	−	27.3962i	−0.223276	−	0.957885i
$819$		0			0
$820$	−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	$0.832353\pi$
$822$		0			0
$823$		−	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
$825$		0			0
$826$	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	$0.583204\pi$
$828$		0			0
$829$		−	41.7678i		−	1.45065i	−0.688404	−	0.725327i	$-0.741688\pi$
$829$		−	41.7678i		−	1.45065i	0.688404	−	0.725327i	$-0.258312\pi$
$830$	3.17548	−	31.1175i	0.110223	−	1.08011i
$831$		0			0
$832$	7.73530	−	38.8018i	0.268173	−	1.34521i
$833$			42.7881i			1.48252i
$834$		0			0
$835$	−4.00000	+	11.6514i	−0.138426	+	0.403213i
$836$	−4.60719	+	2.27120i	−0.159343	+	0.0785512i
$837$		0			0
$838$	−0.533409	+	0.124334i	−0.0184263	+	0.00429504i
$839$	−21.6490			−0.747408			−0.373704	−	0.927548i	$-0.621912\pi$
$839$	−21.6490			−0.747408			−0.373704	+	0.927548i	$0.621912\pi$
$840$		0			0
$841$	−28.6740			−0.988759
$842$	−16.6072	+	3.87101i	−0.572322	+	0.133404i
$843$		0			0
$844$	5.69641	+	11.5553i	0.196078	+	0.397750i
$845$	−24.2361	−	8.32040i	−0.833746	−	0.286231i
$846$		0			0
$847$		−	40.6838i		−	1.39791i
$848$	0.559817	−	0.729140i	0.0192242	−	0.0250388i
$849$		0			0
$850$	29.0404	+	13.4028i	0.996078	+	0.459714i
$851$			3.34510i			0.114669i
$852$		0			0
$853$	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
$855$		0			0
$856$	−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	$0.985542\pi$
$858$		0			0
$859$		−	4.57680i		−	0.156158i	−0.996947	−	0.0780792i	$-0.975121\pi$
$859$		−	4.57680i		−	0.156158i	0.996947	−	0.0780792i	$-0.0248787\pi$
$860$	−37.5264	+	4.80338i	−1.27964	+	0.163794i
$861$		0			0
$862$	−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	$-0.196579\pi$
$864$		0			0
$865$	−21.8649	−	7.50638i	−0.743430	−	0.255224i
$866$	49.8385	−	11.6170i	1.69358	−	0.394761i
$867$		0			0
$868$	−11.7827	−	23.9014i	−0.399930	−	0.811267i
$869$		−	3.23797i		−	0.109841i
$870$		0			0
$871$	−41.8385			−1.41764
$872$	−9.11963	+	7.48105i	−0.308830	+	0.253340i
$873$		0			0
$874$	−2.95815	−	12.6909i	−0.100061	−	0.429276i
$875$	−37.9736	+	24.8085i	−1.28374	+	0.838679i
$876$		0			0
$877$	−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
$879$		0			0
$880$	4.87189	+	7.35056i	0.164231	+	0.247787i
$881$	−13.2702			−0.447085			−0.223543	−	0.974694i	$-0.571762\pi$
$881$	−13.2702			−0.447085			−0.223543	+	0.974694i	$0.571762\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−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	$0.818912\pi$
$888$		0			0
$889$	−4.67696			−0.156860
$890$	−3.96511	+	38.8554i	−0.132911	+	1.30244i
$891$		0			0
$892$	−15.8998	−	32.2531i	−0.532365	−	1.07992i
$893$	6.78562			0.227072
$894$		0			0
$895$	−11.7438	+	34.2078i	−0.392551	+	1.14344i
$896$	1.47908	+	45.8764i	0.0494125	+	1.53262i
$897$		0			0
$898$	−0.642074	−	2.75459i	−0.0214263	−	0.0919217i
$899$			24.9409i			0.831827i
$900$		0			0
$901$		−	1.03951i		−	0.0346310i
$902$	−0.771702	+	0.179878i	−0.0256949	+	0.00598929i
$903$		0			0
$904$	−2.81060	+	2.30560i	−0.0934790	+	0.0766830i
$905$	−5.89134	+	17.1606i	−0.195835	+	0.570436i
$906$		0			0
$907$	−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
$909$		0			0
$910$	63.1227	+	6.44154i	2.09250	+	0.213535i
$911$	−16.0000			−0.530104			−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000			−0.530104			−0.265052	+	0.964234i	$0.585389\pi$
$912$		0			0
$913$		−	9.75225i		−	0.322752i
$914$	−34.8106	+	8.11409i	−1.15143	+	0.268390i
$915$		0			0
$916$	−3.68793	−	7.48105i	−0.121853	−	0.247181i
$917$	−15.7827			−0.521190
$918$		0			0
$919$	−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
$921$		0			0
$922$	56.5933	−	13.1915i	1.86380	−	0.434438i
$923$	7.08074			0.233065
$924$		0			0
$925$	3.73129	+	2.90425i	0.122684	+	0.0954911i
$926$	−18.1949	+	4.24110i	−0.597922	+	0.139371i
$927$		0			0
$928$	17.7438	−	39.1245i	0.582468	−	1.28432i
$929$	12.6461			0.414904			0.207452	−	0.978245i	$-0.433483\pi$
$929$	12.6461			0.414904			0.207452	+	0.978245i	$0.433483\pi$
$930$		0			0
$931$		−	24.6416i		−	0.807596i
$932$	21.2144	+	43.0339i	0.694900	+	1.40962i
$933$		0			0
$934$	−0.607188	−	2.60492i	−0.0198678	−	0.0852357i
$935$	9.43171	+	3.23797i	0.308450	+	0.105893i
$936$		0			0
$937$		−	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
$939$		0			0
$940$	−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	$0.926139\pi$
$942$		0			0
$943$		−	2.01022i		−	0.0654619i
$944$	28.8719	+	22.1672i	0.939700	+	0.721480i
$945$		0			0
$946$	−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	$0.232556\pi$
$948$		0			0
$949$			59.1043i			1.91861i
$950$	−16.7243	−	7.71867i	−0.542609	−	0.250427i
$951$		0			0
$952$	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			0
$955$	−52.7019	−	18.0929i	−1.70539	−	0.585473i
$956$	16.0000	−	7.88751i	0.517477	−	0.255100i
$957$		0			0
$958$	10.1087	+	43.3676i	0.326596	+	1.40114i
$959$	71.0529			2.29442
$960$		0			0
$961$	−20.2144			−0.652077
$962$	−1.50148	−	6.44154i	−0.0484095	−	0.207684i
$963$		0			0
$964$	29.3315	−	14.4595i	0.944705	−	0.465710i
$965$	−0.754747	+	2.19846i	−0.0242962	+	0.0707710i
$966$		0			0
$967$			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
$969$		0			0
$970$	−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	$-0.112929\pi$
$972$		0			0
$973$	−68.4068			−2.19302
$974$	−17.8998	+	4.17231i	−0.573547	+	0.133690i
$975$		0			0
$976$	−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	$-0.0336802\pi$
$978$		0			0
$979$			12.1773i			0.389188i
$980$	−41.9624	+	5.37118i	−1.34044	+	0.171576i
$981$		0			0
$982$	−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	$-0.328873\pi$
$984$		0			0
$985$	−20.4332	−	7.01486i	−0.651057	−	0.223512i
$986$	−11.0279	−	47.3113i	−0.351201	−	1.50670i
$987$		0			0
$988$	11.3928	+	23.1106i	0.362454	+	0.735246i
$989$		−	29.9242i		−	0.951534i
$990$		0			0
$991$	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
$993$		0			0
$994$	−8.00000	+	1.86474i	−0.253745	+	0.0591460i
$995$	48.7842	+	16.7479i	1.54656	+	0.530945i
$996$		0			0
$997$	−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			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.3	✓	6	3.2	odd	2
120.2.d.a.109.4	yes	6	120.29	odd	2
120.2.d.b.109.3	yes	6	24.5	odd	2
120.2.d.b.109.4	yes	6	15.14	odd	2
360.2.d.e.109.3		6	5.4	even	2
360.2.d.e.109.4		6	8.5	even	2
360.2.d.f.109.3		6	40.29	even	2	inner
360.2.d.f.109.4		6	1.1	even	1	trivial
480.2.d.a.49.5		6	120.59	even	2
480.2.d.a.49.6		6	12.11	even	2
480.2.d.b.49.1		6	24.11	even	2
480.2.d.b.49.2		6	60.59	even	2
600.2.k.f.301.1		12	120.53	even	4
600.2.k.f.301.2		12	15.8	even	4
600.2.k.f.301.11		12	15.2	even	4
600.2.k.f.301.12		12	120.77	even	4
1440.2.d.e.1009.1		6	4.3	odd	2
1440.2.d.e.1009.2		6	40.19	odd	2
1440.2.d.f.1009.5		6	20.19	odd	2
1440.2.d.f.1009.6		6	8.3	odd	2
1800.2.k.u.901.1		12	40.37	odd	4
1800.2.k.u.901.2		12	5.2	odd	4
1800.2.k.u.901.11		12	5.3	odd	4
1800.2.k.u.901.12		12	40.13	odd	4
2400.2.k.f.1201.1		12	120.107	odd	4
2400.2.k.f.1201.6		12	60.23	odd	4
2400.2.k.f.1201.7		12	60.47	odd	4
2400.2.k.f.1201.12		12	120.83	odd	4
3840.2.f.l.769.3		12	48.5	odd	4
3840.2.f.l.769.4		12	240.29	odd	4
3840.2.f.l.769.9		12	240.149	odd	4
3840.2.f.l.769.10		12	48.29	odd	4
3840.2.f.m.769.3		12	240.59	even	4
3840.2.f.m.769.4		12	48.35	even	4
3840.2.f.m.769.9		12	48.11	even	4
3840.2.f.m.769.10		12	240.179	even	4
7200.2.k.u.3601.1		12	40.27	even	4
7200.2.k.u.3601.2		12	20.7	even	4
7200.2.k.u.3601.11		12	40.3	even	4
7200.2.k.u.3601.12		12	20.3	even	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.321037 + 1.37729i) q^{2} +(-1.79387 + 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} -4.05705i q^{7} +(-1.79387 - 2.18678i) q^{8} +O(q^{10})\)	\(q+(0.321037 + 1.37729i) q^{2} +(-1.79387 + 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} -4.05705i q^{7} +(-1.79387 - 2.18678i) q^{8} +(0.321037 - 3.14594i) q^{10} -0.985939i q^{11} -4.94567 q^{13} +(5.58774 - 1.30246i) q^{14} +(2.43594 - 3.17272i) q^{16} -4.52323i q^{17} +2.60492i q^{19} +(4.43594 - 0.567801i) q^{20} +(1.35793 - 0.316523i) q^{22} +3.53729i q^{23} +(3.94567 + 3.07111i) q^{25} +(-1.58774 - 6.81163i) q^{26} +(3.58774 + 7.27782i) q^{28} -7.59434i q^{29} -3.28415 q^{31} +(5.15180 + 2.33645i) q^{32} +(6.22982 - 1.45212i) q^{34} +(-2.94567 + 8.58028i) q^{35} +0.945668 q^{37} +(-3.58774 + 0.836276i) q^{38} +(2.20613 + 5.92731i) q^{40} -0.568295 q^{41} -8.45963 q^{43} +(0.871889 + 1.76865i) q^{44} +(-4.87189 + 1.13560i) q^{46} -2.60492i q^{47} -9.45963 q^{49} +(-2.96311 + 6.42028i) q^{50} +(8.87189 - 4.37357i) q^{52} +0.229815 q^{53} +(-0.715853 + 2.08517i) q^{55} +(-8.87189 + 7.27782i) q^{56} +(10.4596 - 2.43806i) q^{58} +9.10003i q^{59} -11.0183i q^{61} +(-1.05433 - 4.52323i) q^{62} +(-1.56406 + 7.84562i) q^{64} +(10.4596 + 3.59086i) q^{65} +8.45963 q^{67} +(4.00000 + 8.11409i) q^{68} +(-12.7632 - 1.30246i) q^{70} -1.43171 q^{71} -11.9507i q^{73} +(0.303594 + 1.30246i) q^{74} +(-2.30359 - 4.67289i) q^{76} -4.00000 q^{77} +3.28415 q^{79} +(-7.45539 + 4.94137i) q^{80} +(-0.182443 - 0.782708i) q^{82} +9.89134 q^{83} +(-3.28415 + 9.56622i) q^{85} +(-2.71585 - 11.6514i) q^{86} +(-2.15604 + 1.76865i) q^{88} -12.3510 q^{89} +20.0648i q^{91} +(-3.12811 - 6.34545i) q^{92} +(3.58774 - 0.836276i) q^{94} +(1.89134 - 5.50917i) q^{95} -3.23797i q^{97} +(-3.03689 - 13.0287i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{4} + q^{8}+O(q^{10}) \) 6 * q + q^2 + q^4 + q^8	\( 6 q + q^{2} + q^{4} + q^{8} + q^{10} - 8 q^{13} + 10 q^{14} + q^{16} + 13 q^{20} + 10 q^{22} + 2 q^{25} + 14 q^{26} - 2 q^{28} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} - 16 q^{37} + 2 q^{38} + 25 q^{40} + 4 q^{41} - 22 q^{44} - 2 q^{46} - 6 q^{49} - 15 q^{50} + 26 q^{52} - 24 q^{53} - 8 q^{55} - 26 q^{56} + 12 q^{58} - 28 q^{62} - 23 q^{64} + 12 q^{65} + 24 q^{68} - 6 q^{70} - 16 q^{71} - 18 q^{74} + 6 q^{76} - 24 q^{77} + 16 q^{79} - 15 q^{80} - 50 q^{82} + 16 q^{83} - 16 q^{85} - 20 q^{86} + 18 q^{88} + 20 q^{89} - 46 q^{92} - 2 q^{94} - 32 q^{95} - 21 q^{98}+O(q^{100}) \) 6 * q + q^2 + q^4 + q^8 + q^10 - 8 * q^13 + 10 * q^14 + q^16 + 13 * q^20 + 10 * q^22 + 2 * q^25 + 14 * q^26 - 2 * q^28 - 16 * q^31 + 21 * q^32 + 12 * q^34 + 4 * q^35 - 16 * q^37 + 2 * q^38 + 25 * q^40 + 4 * q^41 - 22 * q^44 - 2 * q^46 - 6 * q^49 - 15 * q^50 + 26 * q^52 - 24 * q^53 - 8 * q^55 - 26 * q^56 + 12 * q^58 - 28 * q^62 - 23 * q^64 + 12 * q^65 + 24 * q^68 - 6 * q^70 - 16 * q^71 - 18 * q^74 + 6 * q^76 - 24 * q^77 + 16 * q^79 - 15 * q^80 - 50 * q^82 + 16 * q^83 - 16 * q^85 - 20 * q^86 + 18 * q^88 + 20 * q^89 - 46 * q^92 - 2 * q^94 - 32 * q^95 - 21 * q^98

Introduction

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