LMFDB - Embedded newform 600.2.k.f.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(301,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.180227832610816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 $ x^12 + x^10 - 8x^6 + 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.2
Root			$-1.37729 + 0.321037i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.f.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.37729	+	0.321037i	−0.973893	+	0.227007i
$2$	−1.37729	+	0.321037i	−0.973893	+	0.227007i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.79387	−	0.884323i	0.896935	−	0.442162i
$5$		0			0
$5$		0			0
$6$	−0.321037	−	1.37729i	−0.131063	−	0.562277i
$7$	−4.05705			−1.53342			−0.766710	−	0.641994i	$-0.778107\pi$
$7$	−4.05705			−1.53342			−0.766710	+	0.641994i	$0.778107\pi$
$8$	−2.18678	+	1.79387i	−0.773145	+	0.634229i
$9$	−1.00000			−0.333333
$10$		0			0
$11$			0.985939i			0.297272i	0.988892	+	0.148636i	$0.0474882\pi$
$11$			0.985939i			0.297272i	−0.988892	+	0.148636i	$0.952512\pi$
$12$	0.884323	+	1.79387i	0.255282	+	0.517846i
$13$		−	4.94567i		−	1.37168i	−0.727752	−	0.685841i	$-0.759435\pi$
$13$		−	4.94567i		−	1.37168i	0.727752	−	0.685841i	$-0.240565\pi$
$14$	5.58774	−	1.30246i	1.49339	−	0.348097i
$15$		0			0
$16$	2.43594	−	3.17272i	0.608986	−	0.793181i
$17$	4.52323			1.09704			0.548522	−	0.836136i	$-0.315191\pi$
$17$	4.52323			1.09704			0.548522	+	0.836136i	$0.315191\pi$
$18$	1.37729	−	0.321037i	0.324631	−	0.0756691i
$19$		−	2.60492i		−	0.597610i	−0.954314	−	0.298805i	$-0.903412\pi$
$19$		−	2.60492i		−	0.597610i	0.954314	−	0.298805i	$-0.0965881\pi$
$20$		0			0
$21$		−	4.05705i		−	0.885320i
$22$	−0.316523	−	1.35793i	−0.0674829	−	0.289511i
$23$	3.53729			0.737577			0.368788	−	0.929513i	$-0.379773\pi$
$23$	3.53729			0.737577			0.368788	+	0.929513i	$0.379773\pi$
$24$	−1.79387	−	2.18678i	−0.366172	−	0.446376i
$25$		0			0
$26$	1.58774	+	6.81163i	0.311382	+	1.33587i
$27$		−	1.00000i		−	0.192450i
$28$	−7.27782	+	3.58774i	−1.37538	+	0.678019i
$29$		−	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	$0.595295\pi$
$32$	−2.33645	+	5.15180i	−0.413029	+	0.910718i
$33$	−0.985939			−0.171630
$34$	−6.22982	+	1.45212i	−1.06840	+	0.249037i
$35$		0			0
$36$	−1.79387	+	0.884323i	−0.298978	+	0.147387i
$37$		−	0.945668i		−	0.155467i	−0.996974	−	0.0777334i	$-0.975232\pi$
$37$		−	0.945668i		−	0.155467i	0.996974	−	0.0777334i	$-0.0247683\pi$
$38$	0.836276	+	3.58774i	0.135662	+	0.582009i
$39$	4.94567			0.791941
$40$		0			0
$41$	0.568295			0.0887527			0.0443763	−	0.999015i	$-0.485870\pi$
$41$	0.568295			0.0887527			0.0443763	+	0.999015i	$0.485870\pi$
$42$	1.30246	+	5.58774i	0.200974	+	0.862207i
$43$		−	8.45963i		−	1.29008i	−0.764148	−	0.645041i	$-0.776840\pi$
$43$		−	8.45963i		−	1.29008i	0.764148	−	0.645041i	$-0.223160\pi$
$44$	0.871889	+	1.76865i	0.131442	+	0.266634i
$45$		0			0
$46$	−4.87189	+	1.13560i	−0.718321	+	0.167435i
$47$	2.60492			0.379967			0.189984	−	0.981787i	$-0.439157\pi$
$47$	2.60492			0.379967			0.189984	+	0.981787i	$0.439157\pi$
$48$	3.17272	+	2.43594i	0.457943	+	0.351598i
$49$	9.45963			1.35138
$50$		0			0
$51$			4.52323i			0.633379i
$52$	−4.37357	−	8.87189i	−0.606505	−	1.23031i
$53$		−	0.229815i		−	0.0315675i	−0.999875	−	0.0157838i	$-0.994976\pi$
$53$		−	0.229815i		−	0.0315675i	0.999875	−	0.0157838i	$-0.00502434\pi$
$54$	0.321037	+	1.37729i	0.0436876	+	0.187426i
$55$		0			0
$56$	8.87189	−	7.27782i	1.18556	−	0.972539i
$57$	2.60492			0.345030
$58$	2.43806	+	10.4596i	0.320133	+	1.37342i
$59$			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	$-0.249222\pi$
$62$	4.52323	−	1.05433i	0.574451	−	0.133900i
$63$	4.05705			0.511140
$64$	1.56406	−	7.84562i	0.195507	−	0.980702i
$65$		0			0
$66$	1.35793	−	0.316523i	0.167149	−	0.0389612i
$67$		−	8.45963i		−	1.03351i	−0.856134	−	0.516754i	$-0.827140\pi$
$67$		−	8.45963i		−	1.03351i	0.856134	−	0.516754i	$-0.172860\pi$
$68$	8.11409	−	4.00000i	0.983978	−	0.485071i
$69$			3.53729i			0.425840i
$70$		0			0
$71$	1.43171			0.169912			0.0849561	−	0.996385i	$-0.472925\pi$
$71$	1.43171			0.169912			0.0849561	+	0.996385i	$0.472925\pi$
$72$	2.18678	−	1.79387i	0.257715	−	0.211410i
$73$	11.9507			1.39873			0.699363	−	0.714767i	$-0.253467\pi$
$73$	11.9507			1.39873			0.699363	+	0.714767i	$0.253467\pi$
$74$	0.303594	+	1.30246i	0.0352921	+	0.151408i
$75$		0			0
$76$	−2.30359	−	4.67289i	−0.264240	−	0.536018i
$77$		−	4.00000i		−	0.455842i
$78$	−6.81163	+	1.58774i	−0.771266	+	0.179776i
$79$	−3.28415			−0.369495			−0.184748	−	0.982786i	$-0.559147\pi$
$79$	−3.28415			−0.369495			−0.184748	+	0.982786i	$0.559147\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−0.782708	+	0.182443i	−0.0864356	+	0.0201475i
$83$		−	9.89134i		−	1.08572i	−0.839825	−	0.542858i	$-0.817342\pi$
$83$		−	9.89134i		−	1.08572i	0.839825	−	0.542858i	$-0.182658\pi$
$84$	−3.58774	−	7.27782i	−0.391455	−	0.794075i
$85$		0			0
$86$	2.71585	+	11.6514i	0.292858	+	1.25640i
$87$	7.59434			0.814199
$88$	−1.76865	−	2.15604i	−0.188538	−	0.229834i
$89$	−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
$92$	6.34545	−	3.12811i	0.661559	−	0.326128i
$93$		−	3.28415i		−	0.340550i
$94$	−3.58774	+	0.836276i	−0.370047	+	0.0862553i
$95$		0			0
$96$	−5.15180	−	2.33645i	−0.525803	−	0.238463i
$97$	−3.23797			−0.328766			−0.164383	−	0.986397i	$-0.552563\pi$
$97$	−3.23797			−0.328766			−0.164383	+	0.986397i	$0.552563\pi$
$98$	−13.0287	+	3.03689i	−1.31610	+	0.306772i
$99$		−	0.985939i		−	0.0990906i
$100$		0			0
$101$		−	4.35637i		−	0.433475i	−0.976230	−	0.216738i	$-0.930458\pi$
$101$		−	4.35637i		−	0.433475i	0.976230	−	0.216738i	$-0.0695416\pi$
$102$	−1.45212	−	6.22982i	−0.143782	−	0.616844i
$103$	−15.0754			−1.48542			−0.742711	−	0.669612i	$-0.766460\pi$
$103$	−15.0754			−1.48542			−0.742711	+	0.669612i	$0.766460\pi$
$104$	8.87189	+	10.8151i	0.869960	+	1.06051i
$105$		0			0
$106$	0.0737791	+	0.316523i	0.00716606	+	0.0307434i
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$	−0.884323	−	1.79387i	−0.0850941	−	0.172615i
$109$			4.17034i			0.399446i	0.979852	+	0.199723i	$0.0640042\pi$
$109$			4.17034i			0.399446i	−0.979852	+	0.199723i	$0.935996\pi$
$110$		0			0
$111$	0.945668			0.0897588
$112$	−9.88274	+	12.8719i	−0.933831	+	1.21628i
$113$	−1.28526			−0.120907			−0.0604537	−	0.998171i	$-0.519255\pi$
$113$	−1.28526			−0.120907			−0.0604537	+	0.998171i	$0.519255\pi$
$114$	−3.58774	+	0.836276i	−0.336023	+	0.0783244i
$115$		0			0
$116$	−6.71585	−	13.6233i	−0.623551	−	1.26489i
$117$			4.94567i			0.457227i
$118$	−2.92145	−	12.5334i	−0.268941	−	1.15379i
$119$	−18.3510			−1.68223
$120$		0			0
$121$	10.0279			0.911630
$122$	3.53729	+	15.1755i	0.320252	+	1.37392i
$123$			0.568295i			0.0512414i
$124$	−5.89134	+	2.90425i	−0.529058	+	0.260809i
$125$		0			0
$126$	−5.58774	+	1.30246i	−0.497796	+	0.116032i
$127$	−1.15280			−0.102294			−0.0511472	−	0.998691i	$-0.516288\pi$
$127$	−1.15280			−0.102294			−0.0511472	+	0.998691i	$0.516288\pi$
$128$	0.364570	+	11.3078i	0.0322237	+	0.999481i
$129$	8.45963			0.744829
$130$		0			0
$131$			3.89019i			0.339887i	0.985454	+	0.169944i	$0.0543586\pi$
$131$			3.89019i			0.339887i	−0.985454	+	0.169944i	$0.945641\pi$
$132$	−1.76865	+	0.871889i	−0.153941	+	0.0758882i
$133$			10.5683i			0.916387i
$134$	2.71585	+	11.6514i	0.234614	+	1.00653i
$135$		0			0
$136$	−9.89134	+	8.11409i	−0.848175	+	0.695778i
$137$	−17.5135			−1.49628			−0.748138	−	0.663544i	$-0.769052\pi$
$137$	−17.5135			−1.49628			−0.748138	+	0.663544i	$0.769052\pi$
$138$	−1.13560	−	4.87189i	−0.0966688	−	0.414723i
$139$			16.8612i			1.43015i	0.699047	+	0.715076i	$0.253608\pi$
$139$			16.8612i			1.43015i	−0.699047	+	0.715076i	$0.746392\pi$
$140$		0			0
$141$			2.60492i			0.219374i
$142$	−1.97188	+	0.459630i	−0.165476	+	0.0385713i
$143$	4.87613			0.407762
$144$	−2.43594	+	3.17272i	−0.202995	+	0.264394i
$145$		0			0
$146$	−16.4596	+	3.83662i	−1.36221	+	0.317521i
$147$			9.45963i			0.780217i
$148$	−0.836276	−	1.69641i	−0.0687415	−	0.139444i
$149$		−	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	$0.438540\pi$
$152$	4.67289	+	5.69641i	0.379022	+	0.462040i
$153$	−4.52323			−0.365682
$154$	1.28415	+	5.50917i	0.103480	+	0.443942i
$155$		0			0
$156$	8.87189	−	4.37357i	0.710320	−	0.350166i
$157$		−	8.94567i		−	0.713942i	−0.934115	−	0.356971i	$-0.883809\pi$
$157$		−	8.94567i		−	0.713942i	0.934115	−	0.356971i	$-0.116191\pi$
$158$	4.52323	−	1.05433i	0.359849	−	0.0838782i
$159$	0.229815			0.0182255
$160$		0			0
$161$	−14.3510			−1.13101
$162$	−1.37729	+	0.321037i	−0.108210	+	0.0252230i
$163$			15.7827i			1.23619i	0.786102	+	0.618097i	$0.212096\pi$
$163$			15.7827i			1.23619i	−0.786102	+	0.618097i	$0.787904\pi$
$164$	1.01945	−	0.502556i	0.0796054	−	0.0392430i
$165$		0			0
$166$	3.17548	+	13.6233i	0.246465	+	1.05737i
$167$	5.50917			0.426312			0.213156	−	0.977018i	$-0.431626\pi$
$167$	5.50917			0.426312			0.213156	+	0.977018i	$0.431626\pi$
$168$	7.27782	+	8.87189i	0.561496	+	0.684481i
$169$	−11.4596			−0.881510
$170$		0			0
$171$			2.60492i			0.199203i
$172$	−7.48105	−	15.1755i	−0.570425	−	1.15712i
$173$		−	10.3385i		−	0.786020i	−0.919534	−	0.393010i	$-0.871434\pi$
$173$		−	10.3385i		−	0.786020i	0.919534	−	0.393010i	$-0.128566\pi$
$174$	−10.4596	+	2.43806i	−0.792943	+	0.184829i
$175$		0			0
$176$	3.12811	+	2.40169i	0.235790	+	0.181034i
$177$	−9.10003			−0.684000
$178$	17.0109	−	3.96511i	1.27502	−	0.297198i
$179$		−	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	$-0.0975067\pi$
$182$	−6.44154	−	27.6351i	−0.477479	−	2.04845i
$183$	11.0183			0.814499
$184$	−7.73530	+	6.34545i	−0.570254	+	0.467793i
$185$		0			0
$186$	1.05433	+	4.52323i	0.0773074	+	0.331659i
$187$			4.45963i			0.326120i
$188$	4.67289	−	2.30359i	0.340806	−	0.168007i
$189$			4.05705i			0.295107i
$190$		0			0
$191$	−24.9193			−1.80309			−0.901547	−	0.432681i	$-0.857568\pi$
$191$	−24.9193			−1.80309			−0.901547	+	0.432681i	$0.857568\pi$
$192$	7.84562	+	1.56406i	0.566209	+	0.112876i
$193$	1.03951			0.0748254			0.0374127	−	0.999300i	$-0.488088\pi$
$193$	1.03951			0.0748254			0.0374127	+	0.999300i	$0.488088\pi$
$194$	4.45963	−	1.03951i	0.320183	−	0.0746323i
$195$		0			0
$196$	16.9694	−	8.36537i	1.21210	−	0.597527i
$197$			9.66152i			0.688355i	0.938905	+	0.344177i	$0.111842\pi$
$197$			9.66152i			0.688355i	−0.938905	+	0.344177i	$0.888158\pi$
$198$	0.316523	+	1.35793i	0.0224943	+	0.0965036i
$199$	23.0668			1.63516			0.817582	−	0.575813i	$-0.195314\pi$
$199$	23.0668			1.63516			0.817582	+	0.575813i	$0.195314\pi$
$200$		0			0
$201$	8.45963			0.596696
$202$	1.39856	+	6.00000i	0.0984020	+	0.422159i
$203$			30.8106i			2.16248i
$204$	4.00000	+	8.11409i	0.280056	+	0.568100i
$205$		0			0
$206$	20.7632	−	4.83975i	1.44664	−	0.337202i
$207$	−3.53729			−0.245859
$208$	−15.6912	−	12.0474i	−1.08799	−	0.835335i
$209$	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	$-0.0711694\pi$
$212$	−0.203231	−	0.412259i	−0.0139580	−	0.0283140i
$213$			1.43171i			0.0980988i
$214$	−1.28415	−	5.50917i	−0.0877825	−	0.376599i
$215$		0			0
$216$	1.79387	+	2.18678i	0.122057	+	0.148792i
$217$	13.3239			0.904488
$218$	−1.33883	−	5.74378i	−0.0906772	−	0.389018i
$219$			11.9507i			0.807554i
$220$		0			0
$221$		−	22.3704i		−	1.50480i
$222$	−1.30246	+	0.303594i	−0.0874155	+	0.0203759i
$223$	−17.9796			−1.20401			−0.602003	−	0.798494i	$-0.705630\pi$
$223$	−17.9796			−1.20401			−0.602003	+	0.798494i	$0.705630\pi$
$224$	9.47908	−	20.9011i	0.633347	−	1.39651i
$225$		0			0
$226$	1.77018	−	0.412617i	0.117751	−	0.0274469i
$227$			7.02792i			0.466460i	0.972422	+	0.233230i	$0.0749295\pi$
$227$			7.02792i			0.466460i	−0.972422	+	0.233230i	$0.925071\pi$
$228$	4.67289	−	2.30359i	0.309470	−	0.152559i
$229$		−	4.17034i		−	0.275584i	−0.990461	−	0.137792i	$-0.955999\pi$
$229$		−	4.17034i		−	0.275584i	0.990461	−	0.137792i	$-0.0440005\pi$
$230$		0			0
$231$	4.00000			0.263181
$232$	13.6233	+	16.6072i	0.894411	+	1.09032i
$233$	−23.9894			−1.57160			−0.785799	−	0.618483i	$-0.787748\pi$
$233$	−23.9894			−1.57160			−0.785799	+	0.618483i	$0.787748\pi$
$234$	−1.58774	−	6.81163i	−0.103794	−	0.445290i
$235$		0			0
$236$	8.04737	+	16.3243i	0.523839	+	1.06262i
$237$		−	3.28415i		−	0.213328i
$238$	25.2747	−	5.89134i	1.63831	−	0.381879i
$239$	−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	$0.676544\pi$
$242$	−13.8114	+	3.21933i	−0.887830	+	0.206947i
$243$			1.00000i			0.0641500i
$244$	−9.74378	−	19.7655i	−0.623781	−	1.26536i
$245$		0			0
$246$	−0.182443	−	0.782708i	−0.0116322	−	0.0499036i
$247$	−12.8831			−0.819731
$248$	7.18172	−	5.89134i	0.456040	−	0.374100i
$249$	9.89134			0.626838
$250$		0			0
$251$			4.22391i			0.266611i	0.991075	+	0.133305i	$0.0425591\pi$
$251$			4.22391i			0.266611i	−0.991075	+	0.133305i	$0.957441\pi$
$252$	7.27782	−	3.58774i	0.458459	−	0.226006i
$253$			3.48755i			0.219261i
$254$	1.58774	−	0.370091i	0.0996238	−	0.0232216i
$255$		0			0
$256$	−4.13235	−	15.4572i	−0.258272	−	0.966072i
$257$	24.6952			1.54044			0.770221	−	0.637777i	$-0.220146\pi$
$257$	24.6952			1.54044			0.770221	+	0.637777i	$0.220146\pi$
$258$	−11.6514	+	2.71585i	−0.725384	+	0.169082i
$259$			3.83662i			0.238396i
$260$		0			0
$261$			7.59434i			0.470078i
$262$	−1.24889	−	5.35793i	−0.0771569	−	0.331014i
$263$	14.6628			0.904145			0.452073	−	0.891981i	$-0.350685\pi$
$263$	14.6628			0.904145			0.452073	+	0.891981i	$0.350685\pi$
$264$	2.15604	−	1.76865i	0.132695	−	0.108853i
$265$		0			0
$266$	−3.39281	−	14.5556i	−0.208027	−	0.892463i
$267$		−	12.3510i		−	0.755867i
$268$	−7.48105	−	15.1755i	−0.456978	−	0.926990i
$269$			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	$0.445250\pi$
$272$	11.0183	−	14.3510i	0.668085	−	0.870155i
$273$	−20.0648			−1.21438
$274$	24.1212	−	5.62246i	1.45721	−	0.339665i
$275$		0			0
$276$	3.12811	+	6.34545i	0.188290	+	0.381951i
$277$			17.4053i			1.04578i	0.852399	+	0.522892i	$0.175147\pi$
$277$			17.4053i			1.04578i	−0.852399	+	0.522892i	$0.824853\pi$
$278$	−5.41308	−	23.2229i	−0.324655	−	1.39281i
$279$	3.28415			0.196617
$280$		0			0
$281$	21.7827			1.29945			0.649723	−	0.760171i	$-0.274885\pi$
$281$	21.7827			1.29945			0.649723	+	0.760171i	$0.274885\pi$
$282$	−0.836276	−	3.58774i	−0.0497995	−	0.213647i
$283$		−	21.5962i		−	1.28376i	−0.766804	−	0.641881i	$-0.778154\pi$
$283$		−	21.5962i		−	1.28376i	0.766804	−	0.641881i	$-0.221846\pi$
$284$	2.56829	−	1.26609i	0.152400	−	0.0751287i
$285$		0			0
$286$	−6.71585	+	1.56542i	−0.397117	+	0.0925650i
$287$	−2.30560			−0.136095
$288$	2.33645	−	5.15180i	0.137676	−	0.303573i
$289$	3.45963			0.203508
$290$		0			0
$291$		−	3.23797i		−	0.189813i
$292$	21.4380	−	10.5683i	1.25457	−	0.618463i
$293$			32.0125i			1.87019i	0.354398	+	0.935095i	$0.384686\pi$
$293$			32.0125i			1.87019i	−0.354398	+	0.935095i	$0.615314\pi$
$294$	−3.03689	−	13.0287i	−0.177115	−	0.759848i
$295$		0			0
$296$	1.69641	+	2.06797i	0.0986016	+	0.120198i
$297$	0.985939			0.0572100
$298$	3.37043	+	14.4596i	0.195244	+	0.837624i
$299$		−	17.4943i		−	1.01172i
$300$		0			0
$301$			34.3211i			1.97824i
$302$	−6.49511	+	1.51396i	−0.373752	+	0.0871187i
$303$	4.35637			0.250267
$304$	−8.26470	−	6.34545i	−0.474013	−	0.363936i
$305$		0			0
$306$	6.22982	−	1.45212i	0.356135	−	0.0830124i
$307$		−	1.13659i		−	0.0648686i	−0.999474	−	0.0324343i	$-0.989674\pi$
$307$		−	1.13659i		−	0.0648686i	0.999474	−	0.0324343i	$-0.0103260\pi$
$308$	−3.53729	−	7.17548i	−0.201556	−	0.408861i
$309$		−	15.0754i		−	0.857609i
$310$		0			0
$311$	5.13659			0.291269			0.145635	−	0.989338i	$-0.453478\pi$
$311$	5.13659			0.291269			0.145635	+	0.989338i	$0.453478\pi$
$312$	−10.8151	+	8.87189i	−0.612285	+	0.502272i
$313$	23.0762			1.30434			0.652172	−	0.758071i	$-0.273858\pi$
$313$	23.0762			1.30434			0.652172	+	0.758071i	$0.273858\pi$
$314$	2.87189	+	12.3208i	0.162070	+	0.695303i
$315$		0			0
$316$	−5.89134	+	2.90425i	−0.331414	+	0.163377i
$317$			1.66152i			0.0933203i	0.998911	+	0.0466601i	$0.0148578\pi$
$317$			1.66152i			0.0933203i	−0.998911	+	0.0466601i	$0.985142\pi$
$318$	−0.316523	+	0.0737791i	−0.0177497	+	0.00413733i
$319$	7.48755			0.419223
$320$		0			0
$321$	−4.00000			−0.223258
$322$	19.7655	−	4.60719i	1.10149	−	0.256749i
$323$		−	11.7827i		−	0.655605i
$324$	1.79387	−	0.884323i	0.0996595	−	0.0491291i
$325$		0			0
$326$	−5.06682	−	21.7374i	−0.280625	−	1.20392i
$327$	−4.17034			−0.230620
$328$	−1.24274	+	1.01945i	−0.0686187	+	0.0562895i
$329$	−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	$-0.252214\pi$
$332$	−8.74714	−	17.7438i	−0.480062	−	0.973816i
$333$			0.945668i			0.0518223i
$334$	−7.58774	+	1.76865i	−0.415183	+	0.0967760i
$335$		0			0
$336$	−12.8719	−	9.88274i	−0.702219	−	0.539148i
$337$	8.00696			0.436167			0.218083	−	0.975930i	$-0.430020\pi$
$337$	8.00696			0.436167			0.218083	+	0.975930i	$0.430020\pi$
$338$	15.7833	−	3.67896i	0.858496	−	0.200109i
$339$		−	1.28526i		−	0.0698060i
$340$		0			0
$341$		−	3.23797i		−	0.175346i
$342$	−0.836276	−	3.58774i	−0.0452206	−	0.194003i
$343$	−9.97884			−0.538806
$344$	15.1755	+	18.4994i	0.818207	+	0.997420i
$345$		0			0
$346$	3.31903	+	14.2391i	0.178432	+	0.765499i
$347$		−	23.0279i		−	1.23620i	−0.786098	−	0.618102i	$-0.787902\pi$
$347$		−	23.0279i		−	1.23620i	0.786098	−	0.618102i	$-0.212098\pi$
$348$	13.6233	−	6.71585i	0.730284	−	0.360007i
$349$		−	21.4380i		−	1.14755i	−0.819012	−	0.573776i	$-0.805478\pi$
$349$		−	21.4380i		−	1.14755i	0.819012	−	0.573776i	$-0.194522\pi$
$350$		0			0
$351$	−4.94567			−0.263980
$352$	−5.07936	−	2.30359i	−0.270731	−	0.122782i
$353$	−4.52323			−0.240747			−0.120374	−	0.992729i	$-0.538409\pi$
$353$	−4.52323			−0.240747			−0.120374	+	0.992729i	$0.538409\pi$
$354$	12.5334	−	2.92145i	0.666143	−	0.155273i
$355$		0			0
$356$	−22.1560	+	10.9222i	−1.17427	+	0.578878i
$357$		−	18.3510i		−	0.971236i
$358$	5.19265	+	22.2772i	0.274440	+	1.17739i
$359$	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
$362$	2.60492	+	11.1755i	0.136912	+	0.587370i
$363$			10.0279i			0.526330i
$364$	17.7438	+	35.9937i	0.930027	+	1.88658i
$365$		0			0
$366$	−15.1755	+	3.53729i	−0.793235	+	0.184897i
$367$	−0.485359			−0.0253355			−0.0126678	−	0.999920i	$-0.504032\pi$
$367$	−0.485359			−0.0253355			−0.0126678	+	0.999920i	$0.504032\pi$
$368$	8.61665	−	11.2229i	0.449174	−	0.585032i
$369$	−0.568295			−0.0295842
$370$		0			0
$371$			0.932371i			0.0484063i
$372$	−2.90425	−	5.89134i	−0.150578	−	0.305452i
$373$			30.0823i			1.55760i	0.627272	+	0.778800i	$0.284171\pi$
$373$			30.0823i			1.55760i	−0.627272	+	0.778800i	$0.715829\pi$
$374$	−1.43171	−	6.14222i	−0.0740317	−	0.317606i
$375$		0			0
$376$	−5.69641	+	4.67289i	−0.293770	+	0.240986i
$377$	−37.5591			−1.93439
$378$	−1.30246	−	5.58774i	−0.0669914	−	0.287402i
$379$		−	33.6881i		−	1.73044i	−0.501392	−	0.865220i	$-0.667179\pi$
$379$		−	33.6881i		−	1.73044i	0.501392	−	0.865220i	$-0.332821\pi$
$380$		0			0
$381$		−	1.15280i		−	0.0590597i
$382$	34.3211	−	8.00000i	1.75602	−	0.409316i
$383$	−5.17545			−0.264453			−0.132227	−	0.991220i	$-0.542213\pi$
$383$	−5.17545			−0.264453			−0.132227	+	0.991220i	$0.542213\pi$
$384$	−11.3078	+	0.364570i	−0.577050	+	0.0186044i
$385$		0			0
$386$	−1.43171	+	0.333720i	−0.0728719	+	0.0169859i
$387$			8.45963i			0.430027i
$388$	−5.80850	+	2.86341i	−0.294882	+	0.145368i
$389$			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
$392$	−20.6862	+	16.9694i	−1.04481	+	0.857082i
$393$	−3.89019			−0.196234
$394$	−3.10170	−	13.3067i	−0.156262	−	0.670384i
$395$		0			0
$396$	−0.871889	−	1.76865i	−0.0438141	−	0.0888778i
$397$			20.4332i			1.02551i	0.858534	+	0.512757i	$0.171376\pi$
$397$			20.4332i			1.02551i	−0.858534	+	0.512757i	$0.828624\pi$
$398$	−31.7698	+	7.40530i	−1.59247	+	0.371194i
$399$	−10.5683			−0.529076
$400$		0			0
$401$	−4.56829			−0.228130			−0.114065	−	0.993473i	$-0.536387\pi$
$401$	−4.56829			−0.228130			−0.114065	+	0.993473i	$0.536387\pi$
$402$	−11.6514	+	2.71585i	−0.581118	+	0.135454i
$403$			16.2423i			0.809087i
$404$	−3.85244	−	7.81477i	−0.191666	−	0.388799i
$405$		0			0
$406$	−9.89134	−	42.4352i	−0.490899	−	2.10602i
$407$	0.932371			0.0462159
$408$	−8.11409	−	9.89134i	−0.401708	−	0.489694i
$409$	19.8913			0.983563			0.491782	−	0.870719i	$-0.336346\pi$
$409$	19.8913			0.983563			0.491782	+	0.870719i	$0.336346\pi$
$410$		0			0
$411$		−	17.5135i		−	0.863875i
$412$	−27.0433	+	13.3315i	−1.33233	+	0.656797i
$413$		−	36.9193i		−	1.81668i
$414$	4.87189	−	1.13560i	0.239440	−	0.0558118i
$415$		0			0
$416$	25.4791	+	11.5553i	1.24921	+	0.566545i
$417$	−16.8612			−0.825698
$418$	−3.53729	+	0.824517i	−0.173015	+	0.0403284i
$419$			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	$0.905069\pi$
$422$	2.06797	+	8.87189i	0.100667	+	0.431877i
$423$	−2.60492			−0.126656
$424$	0.412259	+	0.502556i	0.0200210	+	0.0244063i
$425$		0			0
$426$	−0.459630	−	1.97188i	−0.0222692	−	0.0955378i
$427$			44.7019i			2.16328i
$428$	3.53729	+	7.17548i	0.170982	+	0.346840i
$429$			4.87613i			0.235422i
$430$		0			0
$431$	40.4068			1.94633			0.973164	−	0.230113i	$-0.0739096\pi$
$431$	40.4068			1.94633			0.973164	+	0.230113i	$0.0739096\pi$
$432$	−3.17272	−	2.43594i	−0.152648	−	0.117199i
$433$	36.1859			1.73898			0.869491	−	0.493949i	$-0.164447\pi$
$433$	36.1859			1.73898			0.869491	+	0.493949i	$0.164447\pi$
$434$	−18.3510	+	4.27748i	−0.880875	+	0.205325i
$435$		0			0
$436$	3.68793	+	7.48105i	0.176620	+	0.358277i
$437$		−	9.21438i		−	0.440783i
$438$	−3.83662	−	16.4596i	−0.183321	−	0.786472i
$439$	−25.4178			−1.21312			−0.606562	−	0.795036i	$-0.707452\pi$
$439$	−25.4178			−1.21312			−0.606562	+	0.795036i	$0.707452\pi$
$440$		0			0
$441$	−9.45963			−0.450459
$442$	7.18172	+	30.8106i	0.341600	+	1.46551i
$443$			7.02792i			0.333907i	0.985965	+	0.166953i	$0.0533929\pi$
$443$			7.02792i			0.333907i	−0.985965	+	0.166953i	$0.946607\pi$
$444$	1.69641	−	0.836276i	0.0805079	−	0.0396879i
$445$		0			0
$446$	24.7632	−	5.77213i	1.17257	−	0.273318i
$447$	10.4986			0.496566
$448$	−6.34545	+	31.8300i	−0.299794	+	1.50383i
$449$	−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
$452$	−2.30560	+	1.13659i	−0.108446	+	0.0534607i
$453$			4.71585i			0.221570i
$454$	−2.25622	−	9.67951i	−0.105890	−	0.454282i
$455$		0			0
$456$	−5.69641	+	4.67289i	−0.266759	+	0.218828i
$457$	25.2747			1.18230			0.591149	−	0.806562i	$-0.298674\pi$
$457$	25.2747			1.18230			0.591149	+	0.806562i	$0.298674\pi$
$458$	1.33883	+	5.74378i	0.0625595	+	0.268389i
$459$		−	4.52323i		−	0.211126i
$460$		0			0
$461$			41.0902i			1.91376i	0.290479	+	0.956881i	$0.406185\pi$
$461$			41.0902i			1.91376i	−0.290479	+	0.956881i	$0.593815\pi$
$462$	−5.50917	+	1.28415i	−0.256310	+	0.0597439i
$463$	−13.2106			−0.613951			−0.306975	−	0.951717i	$-0.599317\pi$
$463$	−13.2106			−0.613951			−0.306975	+	0.951717i	$0.599317\pi$
$464$	−24.0947	−	18.4994i	−1.11857	−	0.858813i
$465$		0			0
$466$	33.0404	−	7.70148i	1.53057	−	0.356764i
$467$		−	1.89134i		−	0.0875206i	−0.999042	−	0.0437603i	$-0.986066\pi$
$467$		−	1.89134i		−	0.0875206i	0.999042	−	0.0437603i	$-0.0139338\pi$
$468$	4.37357	+	8.87189i	0.202168	+	0.410103i
$469$			34.3211i			1.58480i
$470$		0			0
$471$	8.94567			0.412195
$472$	−16.3243	−	19.8998i	−0.751386	−	0.915963i
$473$	8.34068			0.383505
$474$	1.05433	+	4.52323i	0.0484271	+	0.207759i
$475$		0			0
$476$	−32.9193	+	16.2282i	−1.50885	+	0.743818i
$477$			0.229815i			0.0105225i
$478$	12.2844	−	2.86341i	0.561877	−	0.130969i
$479$	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
$482$	22.5201	−	5.24926i	1.02576	−	0.239097i
$483$		−	14.3510i		−	0.652992i
$484$	17.9888	−	8.86793i	0.817673	−	0.403088i
$485$		0			0
$486$	−0.321037	−	1.37729i	−0.0145625	−	0.0624753i
$487$	12.9964			0.588922			0.294461	−	0.955664i	$-0.404860\pi$
$487$	12.9964			0.588922			0.294461	+	0.955664i	$0.404860\pi$
$488$	19.7655	+	24.0947i	0.894741	+	1.09072i
$489$	−15.7827			−0.713717
$490$		0			0
$491$		−	14.9085i		−	0.672812i	−0.941717	−	0.336406i	$-0.890788\pi$
$491$		−	14.9085i		−	0.672812i	0.941717	−	0.336406i	$-0.109212\pi$
$492$	0.502556	+	1.01945i	0.0226570	+	0.0459602i
$493$		−	34.3510i		−	1.54709i
$494$	17.7438	−	4.13594i	0.798330	−	0.186085i
$495$		0			0
$496$	−8.00000	+	10.4197i	−0.359211	+	0.467858i
$497$	−5.80850			−0.260547
$498$	−13.6233	+	3.17548i	−0.610473	+	0.142297i
$499$			35.6599i			1.59636i	0.602420	+	0.798179i	$0.294203\pi$
$499$			35.6599i			1.59636i	−0.602420	+	0.798179i	$0.705797\pi$
$500$		0			0
$501$			5.50917i			0.246132i
$502$	−1.35603	−	5.81756i	−0.0605226	−	0.259650i
$503$	−25.3090			−1.12847			−0.564237	−	0.825613i	$-0.690830\pi$
$503$	−25.3090			−1.12847			−0.564237	+	0.825613i	$0.690830\pi$
$504$	−8.87189	+	7.27782i	−0.395185	+	0.324180i
$505$		0			0
$506$	−1.11963	−	4.80338i	−0.0497738	−	0.213536i
$507$		−	11.4596i		−	0.508940i
$508$	−2.06797	+	1.01945i	−0.0917514	+	0.0452306i
$509$			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
$512$	10.6538	+	19.9624i	0.470835	+	0.882221i
$513$	−2.60492			−0.115010
$514$	−34.0125	+	7.92806i	−1.50023	+	0.349692i
$515$		0			0
$516$	15.1755	−	7.48105i	0.668063	−	0.329335i
$517$			2.56829i			0.112953i
$518$	−1.23170	−	5.28415i	−0.0541176	−	0.232172i
$519$	10.3385			0.453809
$520$		0			0
$521$	−30.9193			−1.35460			−0.677299	−	0.735708i	$-0.736850\pi$
$521$	−30.9193			−1.35460			−0.677299	+	0.735708i	$0.736850\pi$
$522$	−2.43806	−	10.4596i	−0.106711	−	0.457806i
$523$		−	21.8385i		−	0.954932i	−0.878650	−	0.477466i	$-0.841555\pi$
$523$		−	21.8385i		−	0.954932i	0.878650	−	0.477466i	$-0.158445\pi$
$524$	3.44018	+	6.97849i	0.150285	+	0.304857i
$525$		0			0
$526$	−20.1949	+	4.70729i	−0.880541	+	0.205248i
$527$	−14.8550			−0.647092
$528$	−2.40169	+	3.12811i	−0.104520	+	0.136134i
$529$	−10.4876			−0.455981
$530$		0			0
$531$		−	9.10003i		−	0.394908i
$532$	9.34579	+	18.9582i	0.405191	+	0.821940i
$533$		−	2.81060i		−	0.121740i
$534$	3.96511	+	17.0109i	0.171587	+	0.736133i
$535$		0			0
$536$	15.1755	+	18.4994i	0.655481	+	0.799052i
$537$	16.1746			0.697986
$538$	−3.70415	−	15.8913i	−0.159697	−	0.685124i
$539$			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	$-0.175291\pi$
$542$	−7.76120	+	1.80908i	−0.333372	+	0.0777066i
$543$	8.11409			0.348209
$544$	−10.5683	+	23.3028i	−0.453112	+	0.999098i
$545$		0			0
$546$	27.6351	−	6.44154i	1.18267	−	0.275673i
$547$		−	33.3789i		−	1.42718i	−0.700564	−	0.713589i	$-0.747068\pi$
$547$		−	33.3789i		−	1.42718i	0.700564	−	0.713589i	$-0.252932\pi$
$548$	−31.4169	+	15.4876i	−1.34206	+	0.661596i
$549$			11.0183i			0.470251i
$550$		0			0
$551$	−19.7827			−0.842770
$552$	−6.34545	−	7.73530i	−0.270080	−	0.329236i
$553$	13.3239			0.566592
$554$	−5.58774	−	23.9722i	−0.237400	−	1.01848i
$555$		0			0
$556$	14.9108	+	30.2469i	0.632358	+	1.28275i
$557$		−	30.5808i		−	1.29575i	−0.761747	−	0.647875i	$-0.775658\pi$
$557$		−	30.5808i		−	1.29575i	0.761747	−	0.647875i	$-0.224342\pi$
$558$	−4.52323	+	1.05433i	−0.191484	+	0.0446334i
$559$	−41.8385			−1.76958
$560$		0			0
$561$	−4.45963			−0.188286
$562$	−30.0011	+	6.99304i	−1.26552	+	0.294984i
$563$		−	7.02792i		−	0.296192i	−0.988973	−	0.148096i	$-0.952686\pi$
$563$		−	7.02792i		−	0.296192i	0.988973	−	0.148096i	$-0.0473144\pi$
$564$	2.30359	+	4.67289i	0.0969988	+	0.196764i
$565$		0			0
$566$	6.93318	+	29.7443i	0.291423	+	1.25025i
$567$	−4.05705			−0.170380
$568$	−3.13083	+	2.56829i	−0.131367	+	0.107763i
$569$	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	$-0.138167\pi$
$572$	8.74714	−	4.31207i	0.365736	−	0.180297i
$573$		−	24.9193i		−	1.04102i
$574$	3.17548	−	0.740182i	0.132542	−	0.0308946i
$575$		0			0
$576$	−1.56406	+	7.84562i	−0.0651690	+	0.326901i
$577$	−4.76899			−0.198536			−0.0992678	−	0.995061i	$-0.531650\pi$
$577$	−4.76899			−0.198536			−0.0992678	+	0.995061i	$0.531650\pi$
$578$	−4.76492	+	1.11067i	−0.198195	+	0.0461977i
$579$			1.03951i			0.0432004i
$580$		0			0
$581$			40.1296i			1.66486i
$582$	1.03951	+	4.45963i	0.0430890	+	0.184858i
$583$	0.226584			0.00938413
$584$	−26.1336	+	21.4380i	−1.08142	+	0.887112i
$585$		0			0
$586$	−10.2772	−	44.0906i	−0.424547	−	1.82136i
$587$			8.21733i			0.339165i	0.985516	+	0.169583i	$0.0542420\pi$
$587$			8.21733i			0.339165i	−0.985516	+	0.169583i	$0.945758\pi$
$588$	8.36537	+	16.9694i	0.344982	+	0.699804i
$589$			8.55495i			0.352501i
$590$		0			0
$591$	−9.66152			−0.397422
$592$	−3.00034	−	2.30359i	−0.123313	−	0.0946771i
$593$	−7.76120			−0.318714			−0.159357	−	0.987221i	$-0.550942\pi$
$593$	−7.76120			−0.318714			−0.159357	+	0.987221i	$0.550942\pi$
$594$	−1.35793	+	0.316523i	−0.0557164	+	0.0129871i
$595$		0			0
$596$	−9.28415	−	18.8331i	−0.380293	−	0.771434i
$597$			23.0668i			0.944062i
$598$	5.61631	+	24.0947i	0.229668	+	0.985307i
$599$	−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	$0.779503\pi$
$602$	−11.0183	−	47.2702i	−0.449074	−	1.92659i
$603$			8.45963i			0.344503i
$604$	8.45963	−	4.17034i	0.344217	−	0.169689i
$605$		0			0
$606$	−6.00000	+	1.39856i	−0.243733	+	0.0568124i
$607$	−0.113292			−0.00459837			−0.00229919	−	0.999997i	$-0.500732\pi$
$607$	−0.113292			−0.00459837			−0.00229919	+	0.999997i	$0.500732\pi$
$608$	13.4200	+	6.08627i	0.544254	+	0.246831i
$609$	−30.8106			−1.24851
$610$		0			0
$611$		−	12.8831i		−	0.521194i
$612$	−8.11409	+	4.00000i	−0.327993	+	0.161690i
$613$			0.703366i			0.0284087i	0.999899	+	0.0142044i	$0.00452154\pi$
$613$			0.703366i			0.0284087i	−0.999899	+	0.0142044i	$0.995478\pi$
$614$	0.364887	+	1.56542i	0.0147256	+	0.0631750i
$615$		0			0
$616$	7.17548	+	8.74714i	0.289108	+	0.352432i
$617$	24.4809			0.985564			0.492782	−	0.870153i	$-0.335980\pi$
$617$	24.4809			0.985564			0.492782	+	0.870153i	$0.335980\pi$
$618$	4.83975	+	20.7632i	0.194683	+	0.835219i
$619$		−	39.4966i		−	1.58750i	−0.608243	−	0.793751i	$-0.708126\pi$
$619$		−	39.4966i		−	1.58750i	0.608243	−	0.793751i	$-0.291874\pi$
$620$		0			0
$621$		−	3.53729i		−	0.141947i
$622$	−7.07459	+	1.64903i	−0.283665	+	0.0661202i
$623$	50.1084			2.00755
$624$	12.0474	−	15.6912i	0.482281	−	0.628152i
$625$		0			0
$626$	−31.7827	+	7.40831i	−1.27029	+	0.296095i
$627$			2.56829i			0.102568i
$628$	−7.91086	−	16.0474i	−0.315678	−	0.640360i
$629$		−	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	$0.387829\pi$
$632$	7.18172	−	5.89134i	0.285674	−	0.234345i
$633$	6.44154			0.256028
$634$	−0.533409	−	2.28840i	−0.0211844	−	0.0908840i
$635$		0			0
$636$	0.412259	−	0.203231i	0.0163471	−	0.00805863i
$637$		−	46.7842i		−	1.85366i
$638$	−10.3126	+	2.40378i	−0.408278	+	0.0951666i
$639$	−1.43171			−0.0566374
$640$		0			0
$641$	38.7019			1.52863			0.764317	−	0.644840i	$-0.223076\pi$
$641$	38.7019			1.52863			0.764317	+	0.644840i	$0.223076\pi$
$642$	5.50917	−	1.28415i	0.217430	−	0.0506812i
$643$			1.13659i			0.0448227i	0.999749	+	0.0224113i	$0.00713435\pi$
$643$			1.13659i			0.0448227i	−0.999749	+	0.0224113i	$0.992866\pi$
$644$	−25.7438	+	12.6909i	−1.01445	+	0.500091i
$645$		0			0
$646$	3.78267	+	16.2282i	0.148827	+	0.638490i
$647$	6.54868			0.257455			0.128728	−	0.991680i	$-0.458911\pi$
$647$	6.54868			0.257455			0.128728	+	0.991680i	$0.458911\pi$
$648$	−2.18678	+	1.79387i	−0.0859050	+	0.0704699i
$649$	−8.97208			−0.352185
$650$		0			0
$651$			13.3239i			0.522206i
$652$	13.9570	+	28.3121i	0.546598	+	1.10879i
$653$		−	8.74226i		−	0.342111i	−0.985261	−	0.171056i	$-0.945282\pi$
$653$		−	8.74226i		−	0.342111i	0.985261	−	0.171056i	$-0.0547178\pi$
$654$	5.74378	−	1.33883i	0.224599	−	0.0523525i
$655$		0			0
$656$	1.38433	−	1.80304i	0.0540492	−	0.0703969i
$657$	−11.9507			−0.466242
$658$	14.5556	−	3.39281i	0.567438	−	0.132266i
$659$			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	$0.850287\pi$
$662$	8.31732	+	35.6825i	0.323262	+	1.38684i
$663$	22.3704			0.868795
$664$	17.7438	+	21.6302i	0.688592	+	0.839415i
$665$		0			0
$666$	−0.303594	−	1.30246i	−0.0117640	−	0.0504694i
$667$		−	26.8634i		−	1.04016i
$668$	9.88274	−	4.87189i	0.382375	−	0.188499i
$669$		−	17.9796i		−	0.695133i
$670$		0			0
$671$	10.8634			0.419377
$672$	20.9011	+	9.47908i	0.806277	+	0.365663i
$673$	−14.3634			−0.553670			−0.276835	−	0.960917i	$-0.589286\pi$
$673$	−14.3634			−0.553670			−0.276835	+	0.960917i	$0.589286\pi$
$674$	−11.0279	+	2.57053i	−0.424780	+	0.0990130i
$675$		0			0
$676$	−20.5571	+	10.1340i	−0.790658	+	0.389770i
$677$			24.3076i			0.934217i	0.884200	+	0.467109i	$0.154704\pi$
$677$			24.3076i			0.934217i	−0.884200	+	0.467109i	$0.845296\pi$
$678$	0.412617	+	1.77018i	0.0158465	+	0.0679835i
$679$	13.1366			0.504136
$680$		0			0
$681$	−7.02792			−0.269311
$682$	1.03951	+	4.45963i	0.0398048	+	0.170768i
$683$		−	38.5933i		−	1.47673i	−0.674401	−	0.738365i	$-0.735598\pi$
$683$		−	38.5933i		−	1.47673i	0.674401	−	0.738365i	$-0.264402\pi$
$684$	2.30359	+	4.67289i	0.0880801	+	0.178673i
$685$		0			0
$686$	13.7438	−	3.20357i	0.524740	−	0.122313i
$687$	4.17034			0.159108
$688$	−26.8401	−	20.6072i	−1.02327	−	0.785642i
$689$	−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	$-0.0820923\pi$
$692$	−9.14256	−	18.5459i	−0.347548	−	0.705009i
$693$			4.00000i			0.151947i
$694$	7.39281	+	31.7162i	0.280627	+	1.20393i
$695$		0			0
$696$	−16.6072	+	13.6233i	−0.629494	+	0.516389i
$697$	2.57053			0.0973657
$698$	6.88240	+	29.5264i	0.260503	+	1.11759i
$699$		−	23.9894i		−	0.907362i
$700$		0			0
$701$			15.6013i			0.589253i	0.955613	+	0.294626i	$0.0951952\pi$
$701$			15.6013i			0.589253i	−0.955613	+	0.294626i	$0.904805\pi$
$702$	6.81163	−	1.58774i	0.257089	−	0.0599254i
$703$	−2.46339			−0.0929086
$704$	7.73530	+	1.54206i	0.291535	+	0.0581187i
$705$		0			0
$706$	6.22982	−	1.45212i	0.234462	−	0.0546514i
$707$			17.6740i			0.664699i
$708$	−16.3243	+	8.04737i	−0.613504	+	0.302439i
$709$		−	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			0
$711$	3.28415			0.123165
$712$	27.0089	−	22.1560i	1.01220	−	0.830333i
$713$	−11.6170			−0.435060
$714$	5.89134	+	25.2747i	0.220478	+	0.945880i
$715$		0			0
$716$	−14.3036	−	29.0152i	−0.534550	−	1.08435i
$717$		−	8.91926i		−	0.333096i
$718$	−14.2563	+	3.32304i	−0.532041	+	0.124015i
$719$	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
$722$	−16.8228	+	3.92126i	−0.626079	+	0.145934i
$723$		−	16.3510i		−	0.608099i
$724$	−7.17548	−	14.5556i	−0.266675	−	0.540956i
$725$		0			0
$726$	−3.21933	−	13.8114i	−0.119481	−	0.512589i
$727$	2.79096			0.103511			0.0517554	−	0.998660i	$-0.483518\pi$
$727$	2.79096			0.103511			0.0517554	+	0.998660i	$0.483518\pi$
$728$	−35.9937	−	43.8774i	−1.33401	−	1.62621i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		−	38.2649i		−	1.41528i
$732$	19.7655	−	9.74378i	0.730553	−	0.360140i
$733$		−	16.4860i		−	0.608926i	−0.952524	−	0.304463i	$-0.901523\pi$
$733$		−	16.4860i		−	0.608926i	0.952524	−	0.304463i	$-0.0984769\pi$
$734$	0.668481	−	0.155818i	0.0246741	−	0.00575135i
$735$		0			0
$736$	−8.26470	+	18.2234i	−0.304641	+	0.671724i
$737$	8.34068			0.307233
$738$	0.782708	−	0.182443i	0.0288119	−	0.00671584i
$739$		−	14.8894i		−	0.547714i	−0.961770	−	0.273857i	$-0.911701\pi$
$739$		−	14.8894i		−	0.547714i	0.961770	−	0.273857i	$-0.0882995\pi$
$740$		0			0
$741$		−	12.8831i		−	0.473272i
$742$	−0.299325	−	1.28415i	−0.0109886	−	0.0471425i
$743$	41.4301			1.51992			0.759961	−	0.649968i	$-0.225218\pi$
$743$	41.4301			1.51992			0.759961	+	0.649968i	$0.225218\pi$
$744$	5.89134	+	7.18172i	0.215987	+	0.263295i
$745$		0			0
$746$	−9.65751	−	41.4321i	−0.353587	−	1.51694i
$747$			9.89134i			0.361905i
$748$	3.94376	+	8.00000i	0.144198	+	0.292509i
$749$		−	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	$0.311771\pi$
$752$	6.34545	−	8.26470i	0.231395	−	0.301383i
$753$	−4.22391			−0.153928
$754$	51.7299	−	12.0578i	1.88389	−	0.439121i
$755$		0			0
$756$	3.58774	+	7.27782i	0.130485	+	0.264692i
$757$		−	0.433223i		−	0.0157457i	−0.999969	−	0.00787287i	$-0.997494\pi$
$757$		−	0.433223i		−	0.0157457i	0.999969	−	0.00787287i	$-0.00250604\pi$
$758$	10.8151	+	46.3983i	0.392823	+	1.68526i
$759$	−3.48755			−0.126590
$760$		0			0
$761$	−14.9193			−0.540823			−0.270411	−	0.962745i	$-0.587160\pi$
$761$	−14.9193			−0.540823			−0.270411	+	0.962745i	$0.587160\pi$
$762$	0.370091	+	1.58774i	0.0134070	+	0.0575178i
$763$		−	16.9193i		−	0.612518i
$764$	−44.7019	+	22.0367i	−1.61726	+	0.797259i
$765$		0			0
$766$	7.12811	−	1.66151i	0.257549	−	0.0600328i
$767$	45.0057			1.62506
$768$	15.4572	−	4.13235i	0.557762	−	0.149113i
$769$	−31.3789			−1.13155			−0.565776	−	0.824559i	$-0.691423\pi$
$769$	−31.3789			−1.13155			−0.565776	+	0.824559i	$0.691423\pi$
$770$		0			0
$771$			24.6952i			0.889375i
$772$	1.86474	−	0.919260i	0.0671135	−	0.0330849i
$773$			13.4192i			0.482656i	0.970444	+	0.241328i	$0.0775829\pi$
$773$			13.4192i			0.482656i	−0.970444	+	0.241328i	$0.922417\pi$
$774$	−2.71585	−	11.6514i	−0.0976193	−	0.418800i
$775$		0			0
$776$	7.08074	−	5.80850i	0.254184	−	0.208513i
$777$	−3.83662			−0.137638
$778$	−5.34231	−	22.9193i	−0.191531	−	0.821695i
$779$		−	1.48036i		−	0.0530395i
$780$		0			0
$781$			1.41157i			0.0505101i
$782$	−22.0367	+	5.13659i	−0.788030	+	0.183684i
$783$	−7.59434			−0.271400
$784$	23.0431	−	30.0128i	0.822969	−	1.07189i
$785$		0			0
$786$	5.35793	−	1.24889i	0.191111	−	0.0445465i
$787$		−	36.4846i		−	1.30054i	−0.759705	−	0.650268i	$-0.774657\pi$
$787$		−	36.4846i		−	1.30054i	0.759705	−	0.650268i	$-0.225343\pi$
$788$	8.54391	+	17.3315i	0.304364	+	0.617410i
$789$			14.6628i			0.522009i
$790$		0			0
$791$	5.21438			0.185402
$792$	1.76865	+	2.15604i	0.0628461	+	0.0766114i
$793$	−54.4931			−1.93511
$794$	−6.55982	−	28.1425i	−0.232799	−	0.998741i
$795$		0			0
$796$	41.3789	−	20.3985i	1.46664	−	0.723007i
$797$			26.0683i			0.923388i	0.887039	+	0.461694i	$0.152758\pi$
$797$			26.0683i			0.923388i	−0.887039	+	0.461694i	$0.847242\pi$
$798$	14.5556	−	3.39281i	0.515264	−	0.120104i
$799$	11.7827			0.416841
$800$		0			0
$801$	12.3510			0.436400
$802$	6.29188	−	1.46659i	0.222174	−	0.0517871i
$803$			11.7827i			0.415801i
$804$	15.1755	−	7.48105i	0.535198	−	0.263836i
$805$		0			0
$806$	−5.21438	−	22.3704i	−0.183669	−	0.787964i
$807$	−11.5381			−0.406160
$808$	7.81477	+	9.52645i	0.274923	+	0.335139i
$809$	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	$0.719929\pi$
$812$	27.2465	+	55.2702i	0.956166	+	1.93960i
$813$			5.63511i			0.197632i
$814$	−1.28415	+	0.299325i	−0.0450093	+	0.0104913i
$815$		0			0
$816$	14.3510	+	11.0183i	0.502384	+	0.385719i
$817$	−22.0367			−0.770966
$818$	−27.3962	+	6.38585i	−0.957885	+	0.223276i
$819$		−	20.0648i		−	0.701121i
$820$		0			0
$821$		−	28.8058i		−	1.00533i	−0.864482	−	0.502665i	$-0.832353\pi$
$821$		−	28.8058i		−	1.00533i	0.864482	−	0.502665i	$-0.167647\pi$
$822$	5.62246	+	24.1212i	0.196106	+	0.841322i
$823$	27.9585			0.974571			0.487286	−	0.873243i	$-0.337987\pi$
$823$	27.9585			0.974571			0.487286	+	0.873243i	$0.337987\pi$
$824$	32.9666	−	27.0433i	1.14845	−	0.942098i
$825$		0			0
$826$	11.8524	+	50.8486i	0.412399	+	1.76925i
$827$		−	14.8634i		−	0.516851i	−0.966031	−	0.258426i	$-0.916796\pi$
$827$		−	14.8634i		−	0.516851i	0.966031	−	0.258426i	$-0.0832037\pi$
$828$	−6.34545	+	3.12811i	−0.220520	+	0.108709i
$829$			41.7678i			1.45065i	0.688404	+	0.725327i	$0.258312\pi$
$829$			41.7678i			1.45065i	−0.688404	+	0.725327i	$0.741688\pi$
$830$		0			0
$831$	−17.4053			−0.603783
$832$	−38.8018	−	7.73530i	−1.34521	−	0.268173i
$833$	42.7881			1.48252
$834$	23.2229	−	5.41308i	0.804142	−	0.187440i
$835$		0			0
$836$	4.60719	−	2.27120i	0.159343	−	0.0785512i
$837$			3.28415i			0.113517i
$838$	−0.124334	−	0.533409i	−0.00429504	−	0.0184263i
$839$	−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
$842$	−3.87101	−	16.6072i	−0.133404	−	0.572322i
$843$			21.7827i			0.750235i
$844$	−5.69641	−	11.5553i	−0.196078	−	0.397750i
$845$		0			0
$846$	3.58774	−	0.836276i	0.123349	−	0.0287518i
$847$	−40.6838			−1.39791
$848$	−0.729140	−	0.559817i	−0.0250388	−	0.0192242i
$849$	21.5962			0.741180
$850$		0			0
$851$		−	3.34510i		−	0.114669i
$852$	1.26609	+	2.56829i	0.0433755	+	0.0879883i
$853$			49.1880i			1.68416i	0.539350	+	0.842082i	$0.318670\pi$
$853$			49.1880i			1.68416i	−0.539350	+	0.842082i	$0.681330\pi$
$854$	−14.3510	−	61.5676i	−0.491080	−	2.10680i
$855$		0			0
$856$	−7.17548	−	8.74714i	−0.245253	−	0.298971i
$857$	−2.65849			−0.0908123			−0.0454062	−	0.998969i	$-0.514458\pi$
$857$	−2.65849			−0.0908123			−0.0454062	+	0.998969i	$0.514458\pi$
$858$	−1.56542	−	6.71585i	−0.0534424	−	0.229275i
$859$			4.57680i			0.156158i	0.996947	+	0.0780792i	$0.0248787\pi$
$859$			4.57680i			0.156158i	−0.996947	+	0.0780792i	$0.975121\pi$
$860$		0			0
$861$		−	2.30560i		−	0.0785746i
$862$	−55.6520	+	12.9721i	−1.89552	+	0.441831i
$863$	−34.0218			−1.15812			−0.579058	−	0.815287i	$-0.696579\pi$
$863$	−34.0218			−1.15812			−0.579058	+	0.815287i	$0.696579\pi$
$864$	5.15180	+	2.33645i	0.175268	+	0.0794876i
$865$		0			0
$866$	−49.8385	+	11.6170i	−1.69358	+	0.394761i
$867$			3.45963i			0.117495i
$868$	23.9014	−	11.7827i	0.811267	−	0.399930i
$869$		−	3.23797i		−	0.109841i
$870$		0			0
$871$	−41.8385			−1.41764
$872$	−7.48105	−	9.11963i	−0.253340	−	0.308830i
$873$	3.23797			0.109589
$874$	2.95815	+	12.6909i	0.100061	+	0.429276i
$875$		0			0
$876$	10.5683	+	21.4380i	0.357070	+	0.724324i
$877$			11.7563i			0.396981i	0.980103	+	0.198490i	$0.0636039\pi$
$877$			11.7563i			0.396981i	−0.980103	+	0.198490i	$0.936396\pi$
$878$	35.0077	−	8.16004i	1.18145	−	0.275388i
$879$	−32.0125			−1.07975
$880$		0			0
$881$	13.2702			0.447085			0.223543	−	0.974694i	$-0.428238\pi$
$881$	13.2702			0.447085			0.223543	+	0.974694i	$0.428238\pi$
$882$	13.0287	−	3.03689i	0.438698	−	0.102257i
$883$			17.1366i			0.576692i	0.957526	+	0.288346i	$0.0931054\pi$
$883$			17.1366i			0.576692i	−0.957526	+	0.288346i	$0.906895\pi$
$884$	−19.7827	−	40.1296i	−0.665363	−	1.34970i
$885$		0			0
$886$	−2.25622	−	9.67951i	−0.0757993	−	0.325189i
$887$	−32.0883			−1.07742			−0.538709	−	0.842492i	$-0.681088\pi$
$887$	−32.0883			−1.07742			−0.538709	+	0.842492i	$0.681088\pi$
$888$	−2.06797	+	1.69641i	−0.0693966	+	0.0569277i
$889$	4.67696			0.156860
$890$		0			0
$891$			0.985939i			0.0330302i
$892$	−32.2531	+	15.8998i	−1.07992	+	0.532365i
$893$		−	6.78562i		−	0.227072i
$894$	−14.4596	+	3.37043i	−0.483602	+	0.112724i
$895$		0			0
$896$	−1.47908	−	45.8764i	−0.0494125	−	1.53262i
$897$	17.4943			0.584117
$898$	2.75459	−	0.642074i	0.0919217	−	0.0214263i
$899$			24.9409i			0.831827i
$900$		0			0
$901$		−	1.03951i		−	0.0346310i
$902$	−0.179878	−	0.771702i	−0.00598929	−	0.0256949i
$903$	−34.3211			−1.14214
$904$	2.81060	−	2.30560i	0.0934790	−	0.0766830i
$905$		0			0
$906$	−1.51396	−	6.49511i	−0.0502980	−	0.215786i
$907$			40.4596i			1.34344i	0.740805	+	0.671720i	$0.234444\pi$
$907$			40.4596i			1.34344i	−0.740805	+	0.671720i	$0.765556\pi$
$908$	6.21496	+	12.6072i	0.206251	+	0.418384i
$909$			4.35637i			0.144492i
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$	6.34545	−	8.26470i	0.210119	−	0.273672i
$913$	9.75225			0.322752
$914$	−34.8106	+	8.11409i	−1.15143	+	0.268390i
$915$		0			0
$916$	−3.68793	−	7.48105i	−0.121853	−	0.247181i
$917$		−	15.7827i		−	0.521190i
$918$	1.45212	+	6.22982i	0.0479272	+	0.205615i
$919$	50.8495			1.67737			0.838685	−	0.544617i	$-0.183325\pi$
$919$	50.8495			1.67737			0.838685	+	0.544617i	$0.183325\pi$
$920$		0			0
$921$	1.13659			0.0374519
$922$	−13.1915	−	56.5933i	−0.434438	−	1.86380i
$923$		−	7.08074i		−	0.233065i
$924$	7.17548	−	3.53729i	0.236056	−	0.116368i
$925$		0			0
$926$	18.1949	−	4.24110i	0.597922	−	0.139371i
$927$	15.0754			0.495141
$928$	39.1245	+	17.7438i	1.28432	+	0.582468i
$929$	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
$932$	−43.0339	+	21.2144i	−1.40962	+	0.694900i
$933$			5.13659i			0.168164i
$934$	0.607188	+	2.60492i	0.0198678	+	0.0852357i
$935$		0			0
$936$	−8.87189	−	10.8151i	−0.289987	−	0.353503i
$937$	−40.7971			−1.33278			−0.666391	−	0.745603i	$-0.732162\pi$
$937$	−40.7971			−1.33278			−0.666391	+	0.745603i	$0.732162\pi$
$938$	−11.0183	−	47.2702i	−0.359762	−	1.54343i
$939$			23.0762i			0.753063i
$940$		0			0
$941$		−	14.1086i		−	0.459928i	−0.973199	−	0.229964i	$-0.926139\pi$
$941$		−	14.1086i		−	0.459928i	0.973199	−	0.229964i	$-0.0738608\pi$
$942$	−12.3208	+	2.87189i	−0.401433	+	0.0935712i
$943$	2.01022			0.0654619
$944$	28.8719	+	22.1672i	0.939700	+	0.721480i
$945$		0			0
$946$	−11.4876	+	2.67766i	−0.373493	+	0.0870584i
$947$			45.8385i			1.48955i	0.667315	+	0.744776i	$0.267444\pi$
$947$			45.8385i			1.48955i	−0.667315	+	0.744776i	$0.732556\pi$
$948$	−2.90425	−	5.89134i	−0.0943256	−	0.191342i
$949$		−	59.1043i		−	1.91861i
$950$		0			0
$951$	−1.66152			−0.0538785
$952$	40.1296	−	32.9193i	1.30061	−	1.06692i
$953$	−21.9104			−0.709747			−0.354873	−	0.934914i	$-0.615476\pi$
$953$	−21.9104			−0.709747			−0.354873	+	0.934914i	$0.615476\pi$
$954$	−0.0737791	−	0.316523i	−0.00238869	−	0.0102478i
$955$		0			0
$956$	−16.0000	+	7.88751i	−0.517477	+	0.255100i
$957$			7.48755i			0.242038i
$958$	−43.3676	+	10.1087i	−1.40114	+	0.326596i
$959$	71.0529			2.29442
$960$		0			0
$961$	−20.2144			−0.652077
$962$	6.44154	−	1.50148i	0.207684	−	0.0484095i
$963$		−	4.00000i		−	0.128898i
$964$	−29.3315	+	14.4595i	−0.944705	+	0.465710i
$965$		0			0
$966$	4.60719	+	19.7655i	0.148234	+	0.635944i
$967$	14.0359			0.451364			0.225682	−	0.974201i	$-0.427539\pi$
$967$	14.0359			0.451364			0.225682	+	0.974201i	$0.427539\pi$
$968$	−21.9289	+	17.9888i	−0.704822	+	0.578182i
$969$	11.7827			0.378514
$970$		0			0
$971$			21.6494i			0.694762i	0.937724	+	0.347381i	$0.112929\pi$
$971$			21.6494i			0.694762i	−0.937724	+	0.347381i	$0.887071\pi$
$972$	0.884323	+	1.79387i	0.0283647	+	0.0575384i
$973$		−	68.4068i		−	2.19302i
$974$	−17.8998	+	4.17231i	−0.573547	+	0.133690i
$975$		0			0
$976$	−34.9582	−	26.8401i	−1.11898	−	0.859130i
$977$	6.60225			0.211225			0.105612	−	0.994407i	$-0.466320\pi$
$977$	6.60225			0.211225			0.105612	+	0.994407i	$0.466320\pi$
$978$	21.7374	−	5.06682i	0.695084	−	0.162019i
$979$		−	12.1773i		−	0.389188i
$980$		0			0
$981$		−	4.17034i		−	0.133149i
$982$	4.78619	+	20.5334i	0.152733	+	0.655247i
$983$	−53.8600			−1.71787			−0.858934	−	0.512087i	$-0.828873\pi$
$983$	−53.8600			−1.71787			−0.858934	+	0.512087i	$0.828873\pi$
$984$	−1.01945	−	1.24274i	−0.0324988	−	0.0396170i
$985$		0			0
$986$	11.0279	+	47.3113i	0.351201	+	1.50670i
$987$		−	10.5683i		−	0.336393i
$988$	−23.1106	+	11.3928i	−0.735246	+	0.362454i
$989$		−	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	$0.343557\pi$
$992$	7.67324	−	16.9193i	0.243626	−	0.537187i
$993$	25.9077			0.822156
$994$	8.00000	−	1.86474i	0.253745	−	0.0591460i
$995$		0			0
$996$	17.7438	−	8.74714i	0.562233	−	0.277164i
$997$			16.6506i			0.527328i	0.964615	+	0.263664i	$0.0849311\pi$
$997$			16.6506i			0.527328i	−0.964615	+	0.263664i	$0.915069\pi$
$998$	−11.4482	−	49.1142i	−0.362385	−	1.55468i
$999$	−0.945668			−0.0299196

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.3	✓	6	5.2	odd	4
120.2.d.a.109.4	yes	6	40.13	odd	4
120.2.d.b.109.3	yes	6	40.37	odd	4
120.2.d.b.109.4	yes	6	5.3	odd	4
360.2.d.e.109.3		6	15.8	even	4
360.2.d.e.109.4		6	120.77	even	4
360.2.d.f.109.3		6	120.53	even	4
360.2.d.f.109.4		6	15.2	even	4
480.2.d.a.49.5		6	40.3	even	4
480.2.d.a.49.6		6	20.7	even	4
480.2.d.b.49.1		6	40.27	even	4
480.2.d.b.49.2		6	20.3	even	4
600.2.k.f.301.1		12	8.5	even	2	inner
600.2.k.f.301.2		12	1.1	even	1	trivial
600.2.k.f.301.11		12	5.4	even	2	inner
600.2.k.f.301.12		12	40.29	even	2	inner
1440.2.d.e.1009.1		6	60.47	odd	4
1440.2.d.e.1009.2		6	120.83	odd	4
1440.2.d.f.1009.5		6	60.23	odd	4
1440.2.d.f.1009.6		6	120.107	odd	4
1800.2.k.u.901.1		12	120.29	odd	2
1800.2.k.u.901.2		12	15.14	odd	2
1800.2.k.u.901.11		12	3.2	odd	2
1800.2.k.u.901.12		12	24.5	odd	2
2400.2.k.f.1201.1		12	40.19	odd	2
2400.2.k.f.1201.6		12	4.3	odd	2
2400.2.k.f.1201.7		12	20.19	odd	2
2400.2.k.f.1201.12		12	8.3	odd	2
3840.2.f.l.769.3		12	80.37	odd	4
3840.2.f.l.769.4		12	80.13	odd	4
3840.2.f.l.769.9		12	80.53	odd	4
3840.2.f.l.769.10		12	80.77	odd	4
3840.2.f.m.769.3		12	80.43	even	4
3840.2.f.m.769.4		12	80.67	even	4
3840.2.f.m.769.9		12	80.27	even	4
3840.2.f.m.769.10		12	80.3	even	4
7200.2.k.u.3601.1		12	120.59	even	2
7200.2.k.u.3601.2		12	60.59	even	2
7200.2.k.u.3601.11		12	24.11	even	2
7200.2.k.u.3601.12		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.k (of order \(2\), degree \(1\), minimal)

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

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