LMFDB - Embedded newform 600.2.y.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(121,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 6]))

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

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

chi := DirichletCharacter("600.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.y (of order $5$, degree $4$, 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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			121.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	600.121
Dual form			600.2.y.b.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{3} +(-1.80902 + 1.31433i) q^{5} +3.23607 q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{3} +(-1.80902 + 1.31433i) q^{5} +3.23607 q^{7} +(0.309017 + 0.951057i) q^{9} +(-1.38197 + 4.25325i) q^{11} +(-0.118034 - 0.363271i) q^{13} -2.23607 q^{15} +(-2.73607 + 1.98787i) q^{17} +(0.381966 - 0.277515i) q^{19} +(2.61803 + 1.90211i) q^{21} +(0.236068 - 0.726543i) q^{23} +(1.54508 - 4.75528i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(7.35410 + 5.34307i) q^{29} +(-3.61803 + 2.62866i) q^{31} +(-3.61803 + 2.62866i) q^{33} +(-5.85410 + 4.25325i) q^{35} +(2.80902 + 8.64527i) q^{37} +(0.118034 - 0.363271i) q^{39} +(-0.263932 - 0.812299i) q^{41} -0.472136 q^{43} +(-1.80902 - 1.31433i) q^{45} +(-3.00000 - 2.17963i) q^{47} +3.47214 q^{49} -3.38197 q^{51} +(10.1631 + 7.38394i) q^{53} +(-3.09017 - 9.51057i) q^{55} +0.472136 q^{57} +(-2.76393 - 8.50651i) q^{59} +(1.59017 - 4.89404i) q^{61} +(1.00000 + 3.07768i) q^{63} +(0.690983 + 0.502029i) q^{65} +(-5.47214 + 3.97574i) q^{67} +(0.618034 - 0.449028i) q^{69} +(-8.09017 - 5.87785i) q^{71} +(4.26393 - 13.1230i) q^{73} +(4.04508 - 2.93893i) q^{75} +(-4.47214 + 13.7638i) q^{77} +(3.23607 + 2.35114i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(11.0902 - 8.05748i) q^{83} +(2.33688 - 7.19218i) q^{85} +(2.80902 + 8.64527i) q^{87} +(5.51722 - 16.9803i) q^{89} +(-0.381966 - 1.17557i) q^{91} -4.47214 q^{93} +(-0.326238 + 1.00406i) q^{95} +(2.73607 + 1.98787i) q^{97} -4.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 5 q^{5} + 4 q^{7} - q^{9}+O(q^{10}) $ 4 * q + q^3 - 5 * q^5 + 4 * q^7 - q^9	$ 4 q + q^{3} - 5 q^{5} + 4 q^{7} - q^{9} - 10 q^{11} + 4 q^{13} - 2 q^{17} + 6 q^{19} + 6 q^{21} - 8 q^{23} - 5 q^{25} + q^{27} + 16 q^{29} - 10 q^{31} - 10 q^{33} - 10 q^{35} + 9 q^{37} - 4 q^{39} - 10 q^{41} + 16 q^{43} - 5 q^{45} - 12 q^{47} - 4 q^{49} - 18 q^{51} + 25 q^{53} + 10 q^{55} - 16 q^{57} - 20 q^{59} - 16 q^{61} + 4 q^{63} + 5 q^{65} - 4 q^{67} - 2 q^{69} - 10 q^{71} + 26 q^{73} + 5 q^{75} + 4 q^{79} - q^{81} + 22 q^{83} + 25 q^{85} + 9 q^{87} - 7 q^{89} - 6 q^{91} + 30 q^{95} + 2 q^{97}+O(q^{100}) $ 4 * q + q^3 - 5 * q^5 + 4 * q^7 - q^9 - 10 * q^11 + 4 * q^13 - 2 * q^17 + 6 * q^19 + 6 * q^21 - 8 * q^23 - 5 * q^25 + q^27 + 16 * q^29 - 10 * q^31 - 10 * q^33 - 10 * q^35 + 9 * q^37 - 4 * q^39 - 10 * q^41 + 16 * q^43 - 5 * q^45 - 12 * q^47 - 4 * q^49 - 18 * q^51 + 25 * q^53 + 10 * q^55 - 16 * q^57 - 20 * q^59 - 16 * q^61 + 4 * q^63 + 5 * q^65 - 4 * q^67 - 2 * q^69 - 10 * q^71 + 26 * q^73 + 5 * q^75 + 4 * q^79 - q^81 + 22 * q^83 + 25 * q^85 + 9 * q^87 - 7 * q^89 - 6 * q^91 + 30 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$6$		0			0
$7$	3.23607			1.22312			0.611559	−	0.791199i	$-0.290543\pi$
$7$	3.23607			1.22312			0.611559	+	0.791199i	$0.290543\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−1.38197	+	4.25325i	−0.416678	+	1.28240i	0.494063	+	0.869426i	$0.335511\pi$
$11$	−1.38197	+	4.25325i	−0.416678	+	1.28240i	−0.910741	+	0.412978i	$0.864489\pi$
$12$		0			0
$13$	−0.118034	−	0.363271i	−0.0327367	−	0.100753i	0.933353	−	0.358960i	$-0.116869\pi$
$13$	−0.118034	−	0.363271i	−0.0327367	−	0.100753i	−0.966090	+	0.258207i	$0.916869\pi$
$14$		0			0
$15$	−2.23607			−0.577350
$16$		0			0
$17$	−2.73607	+	1.98787i	−0.663594	+	0.482129i	−0.867875	−	0.496783i	$-0.834514\pi$
$17$	−2.73607	+	1.98787i	−0.663594	+	0.482129i	0.204281	+	0.978912i	$0.434514\pi$
$18$		0			0
$19$	0.381966	−	0.277515i	0.0876290	−	0.0636662i	−0.543108	−	0.839663i	$-0.682753\pi$
$19$	0.381966	−	0.277515i	0.0876290	−	0.0636662i	0.630737	+	0.775997i	$0.282753\pi$
$20$		0			0
$21$	2.61803	+	1.90211i	0.571302	+	0.415075i
$22$		0			0
$23$	0.236068	−	0.726543i	0.0492236	−	0.151495i	−0.923423	−	0.383783i	$-0.874621\pi$
$23$	0.236068	−	0.726543i	0.0492236	−	0.151495i	0.972647	+	0.232288i	$0.0746212\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	7.35410	+	5.34307i	1.36562	+	0.992183i	0.998065	+	0.0621820i	$0.0198059\pi$
$29$	7.35410	+	5.34307i	1.36562	+	0.992183i	0.367558	+	0.930001i	$0.380194\pi$
$30$		0			0
$31$	−3.61803	+	2.62866i	−0.649818	+	0.472120i	−0.863209	−	0.504846i	$-0.831549\pi$
$31$	−3.61803	+	2.62866i	−0.649818	+	0.472120i	0.213391	+	0.976967i	$0.431549\pi$
$32$		0			0
$33$	−3.61803	+	2.62866i	−0.629819	+	0.457590i
$34$		0			0
$35$	−5.85410	+	4.25325i	−0.989524	+	0.718931i
$36$		0			0
$37$	2.80902	+	8.64527i	0.461800	+	1.42127i	0.862963	+	0.505267i	$0.168606\pi$
$37$	2.80902	+	8.64527i	0.461800	+	1.42127i	−0.401164	+	0.916006i	$0.631394\pi$
$38$		0			0
$39$	0.118034	−	0.363271i	0.0189006	−	0.0581700i
$40$		0			0
$41$	−0.263932	−	0.812299i	−0.0412193	−	0.126860i	0.928329	−	0.371759i	$-0.121245\pi$
$41$	−0.263932	−	0.812299i	−0.0412193	−	0.126860i	−0.969549	+	0.244899i	$0.921245\pi$
$42$		0			0
$43$	−0.472136			−0.0720001			−0.0360000	−	0.999352i	$-0.511462\pi$
$43$	−0.472136			−0.0720001			−0.0360000	+	0.999352i	$0.511462\pi$
$44$		0			0
$45$	−1.80902	−	1.31433i	−0.269672	−	0.195928i
$46$		0			0
$47$	−3.00000	−	2.17963i	−0.437595	−	0.317931i	0.347084	−	0.937834i	$-0.387172\pi$
$47$	−3.00000	−	2.17963i	−0.437595	−	0.317931i	−0.784679	+	0.619903i	$0.787172\pi$
$48$		0			0
$49$	3.47214			0.496019
$50$		0			0
$51$	−3.38197			−0.473570
$52$		0			0
$53$	10.1631	+	7.38394i	1.39601	+	1.01426i	0.995175	+	0.0981123i	$0.0312804\pi$
$53$	10.1631	+	7.38394i	1.39601	+	1.01426i	0.400836	+	0.916150i	$0.368720\pi$
$54$		0			0
$55$	−3.09017	−	9.51057i	−0.416678	−	1.28240i
$56$		0			0
$57$	0.472136			0.0625359
$58$		0			0
$59$	−2.76393	−	8.50651i	−0.359833	−	1.10745i	−0.953154	−	0.302487i	$-0.902183\pi$
$59$	−2.76393	−	8.50651i	−0.359833	−	1.10745i	0.593320	−	0.804966i	$-0.297817\pi$
$60$		0			0
$61$	1.59017	−	4.89404i	0.203600	−	0.626618i	−0.796168	−	0.605076i	$-0.793143\pi$
$61$	1.59017	−	4.89404i	0.203600	−	0.626618i	0.999768	−	0.0215414i	$-0.00685737\pi$
$62$		0			0
$63$	1.00000	+	3.07768i	0.125988	+	0.387752i
$64$		0			0
$65$	0.690983	+	0.502029i	0.0857059	+	0.0622690i
$66$		0			0
$67$	−5.47214	+	3.97574i	−0.668528	+	0.485714i	−0.869532	−	0.493876i	$-0.835579\pi$
$67$	−5.47214	+	3.97574i	−0.668528	+	0.485714i	0.201004	+	0.979590i	$0.435579\pi$
$68$		0			0
$69$	0.618034	−	0.449028i	0.0744025	−	0.0540566i
$70$		0			0
$71$	−8.09017	−	5.87785i	−0.960127	−	0.697573i	−0.00694640	−	0.999976i	$-0.502211\pi$
$71$	−8.09017	−	5.87785i	−0.960127	−	0.697573i	−0.953180	+	0.302403i	$0.902211\pi$
$72$		0			0
$73$	4.26393	−	13.1230i	0.499055	−	1.53593i	−0.311484	−	0.950251i	$-0.600826\pi$
$73$	4.26393	−	13.1230i	0.499055	−	1.53593i	0.810540	−	0.585684i	$-0.199174\pi$
$74$		0			0
$75$	4.04508	−	2.93893i	0.467086	−	0.339358i
$76$		0			0
$77$	−4.47214	+	13.7638i	−0.509647	+	1.56853i
$78$		0			0
$79$	3.23607	+	2.35114i	0.364086	+	0.264524i	0.754754	−	0.656007i	$-0.227756\pi$
$79$	3.23607	+	2.35114i	0.364086	+	0.264524i	−0.390668	+	0.920532i	$0.627756\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	11.0902	−	8.05748i	1.21730	−	0.884423i	0.221431	−	0.975176i	$-0.428927\pi$
$83$	11.0902	−	8.05748i	1.21730	−	0.884423i	0.995873	+	0.0907527i	$0.0289273\pi$
$84$		0			0
$85$	2.33688	−	7.19218i	0.253470	−	0.780101i
$86$		0			0
$87$	2.80902	+	8.64527i	0.301158	+	0.926870i
$88$		0			0
$89$	5.51722	−	16.9803i	0.584824	−	1.79990i	−0.0151508	−	0.999885i	$-0.504823\pi$
$89$	5.51722	−	16.9803i	0.584824	−	1.79990i	0.599975	−	0.800019i	$-0.295177\pi$
$90$		0			0
$91$	−0.381966	−	1.17557i	−0.0400409	−	0.123233i
$92$		0			0
$93$	−4.47214			−0.463739
$94$		0			0
$95$	−0.326238	+	1.00406i	−0.0334713	+	0.103014i
$96$		0			0
$97$	2.73607	+	1.98787i	0.277806	+	0.201838i	0.717960	−	0.696085i	$-0.245076\pi$
$97$	2.73607	+	1.98787i	0.277806	+	0.201838i	−0.440154	+	0.897922i	$0.645076\pi$
$98$		0			0
$99$	−4.47214			−0.449467
$100$		0			0
$101$	2.90983			0.289539			0.144769	−	0.989465i	$-0.453756\pi$
$101$	2.90983			0.289539			0.144769	+	0.989465i	$0.453756\pi$
$102$		0			0
$103$	12.7082	+	9.23305i	1.25218	+	0.909760i	0.998346	−	0.0574892i	$-0.0183095\pi$
$103$	12.7082	+	9.23305i	1.25218	+	0.909760i	0.253830	+	0.967249i	$0.418309\pi$
$104$		0			0
$105$	−7.23607			−0.706168
$106$		0			0
$107$	−11.2361			−1.08623			−0.543116	−	0.839658i	$-0.682756\pi$
$107$	−11.2361			−1.08623			−0.543116	+	0.839658i	$0.682756\pi$
$108$		0			0
$109$	−3.35410	−	10.3229i	−0.321265	−	0.988751i	−0.973099	−	0.230389i	$-0.926000\pi$
$109$	−3.35410	−	10.3229i	−0.321265	−	0.988751i	0.651834	−	0.758362i	$-0.274000\pi$
$110$		0			0
$111$	−2.80902	+	8.64527i	−0.266620	+	0.820572i
$112$		0			0
$113$	0.281153	+	0.865300i	0.0264486	+	0.0814006i	0.963410	−	0.268034i	$-0.0863738\pi$
$113$	0.281153	+	0.865300i	0.0264486	+	0.0814006i	−0.936961	+	0.349434i	$0.886374\pi$
$114$		0			0
$115$	0.527864	+	1.62460i	0.0492236	+	0.151495i
$116$		0			0
$117$	0.309017	−	0.224514i	0.0285686	−	0.0207563i
$118$		0			0
$119$	−8.85410	+	6.43288i	−0.811654	+	0.589701i
$120$		0			0
$121$	−7.28115	−	5.29007i	−0.661923	−	0.480915i
$122$		0			0
$123$	0.263932	−	0.812299i	0.0237979	−	0.0732426i
$124$		0			0
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$		0			0
$127$	5.38197	−	16.5640i	0.477572	−	1.46982i	−0.364885	−	0.931053i	$-0.618892\pi$
$127$	5.38197	−	16.5640i	0.477572	−	1.46982i	0.842457	−	0.538764i	$-0.181108\pi$
$128$		0			0
$129$	−0.381966	−	0.277515i	−0.0336302	−	0.0244338i
$130$		0			0
$131$	−6.23607	+	4.53077i	−0.544848	+	0.395855i	−0.825882	−	0.563843i	$-0.809322\pi$
$131$	−6.23607	+	4.53077i	−0.544848	+	0.395855i	0.281034	+	0.959698i	$0.409322\pi$
$132$		0			0
$133$	1.23607	−	0.898056i	0.107181	−	0.0778713i
$134$		0			0
$135$	−0.690983	−	2.12663i	−0.0594703	−	0.183031i
$136$		0			0
$137$	3.26393	+	10.0453i	0.278857	+	0.858232i	0.988173	+	0.153342i	$0.0490037\pi$
$137$	3.26393	+	10.0453i	0.278857	+	0.858232i	−0.709317	+	0.704890i	$0.750996\pi$
$138$		0			0
$139$	5.76393	−	17.7396i	0.488890	−	1.50465i	−0.337376	−	0.941370i	$-0.609539\pi$
$139$	5.76393	−	17.7396i	0.488890	−	1.50465i	0.826266	−	0.563280i	$-0.190461\pi$
$140$		0			0
$141$	−1.14590	−	3.52671i	−0.0965020	−	0.297003i
$142$		0			0
$143$	1.70820			0.142847
$144$		0			0
$145$	−20.3262			−1.68800
$146$		0			0
$147$	2.80902	+	2.04087i	0.231684	+	0.168328i
$148$		0			0
$149$	0.381966			0.0312919			0.0156459	−	0.999878i	$-0.495020\pi$
$149$	0.381966			0.0312919			0.0156459	+	0.999878i	$0.495020\pi$
$150$		0			0
$151$	1.70820			0.139012			0.0695058	−	0.997582i	$-0.477858\pi$
$151$	1.70820			0.139012			0.0695058	+	0.997582i	$0.477858\pi$
$152$		0			0
$153$	−2.73607	−	1.98787i	−0.221198	−	0.160710i
$154$		0			0
$155$	3.09017	−	9.51057i	0.248208	−	0.763907i
$156$		0			0
$157$	18.6180			1.48588			0.742940	−	0.669358i	$-0.233431\pi$
$157$	18.6180			1.48588			0.742940	+	0.669358i	$0.233431\pi$
$158$		0			0
$159$	3.88197	+	11.9475i	0.307860	+	0.947495i
$160$		0			0
$161$	0.763932	−	2.35114i	0.0602063	−	0.185296i
$162$		0			0
$163$	−1.00000	−	3.07768i	−0.0783260	−	0.241063i	0.904225	−	0.427057i	$-0.140450\pi$
$163$	−1.00000	−	3.07768i	−0.0783260	−	0.241063i	−0.982551	+	0.185994i	$0.940450\pi$
$164$		0			0
$165$	3.09017	−	9.51057i	0.240569	−	0.740396i
$166$		0			0
$167$	5.23607	−	3.80423i	0.405179	−	0.294380i	−0.366468	−	0.930431i	$-0.619433\pi$
$167$	5.23607	−	3.80423i	0.405179	−	0.294380i	0.771647	+	0.636051i	$0.219433\pi$
$168$		0			0
$169$	10.3992	−	7.55545i	0.799937	−	0.581189i
$170$		0			0
$171$	0.381966	+	0.277515i	0.0292097	+	0.0212221i
$172$		0			0
$173$	3.48278	−	10.7189i	0.264791	−	0.814942i	−0.726951	−	0.686690i	$-0.759063\pi$
$173$	3.48278	−	10.7189i	0.264791	−	0.814942i	0.991742	−	0.128253i	$-0.0409368\pi$
$174$		0			0
$175$	5.00000	−	15.3884i	0.377964	−	1.16326i
$176$		0			0
$177$	2.76393	−	8.50651i	0.207750	−	0.639388i
$178$		0			0
$179$	−18.7082	−	13.5923i	−1.39832	−	1.01594i	−0.994894	−	0.100923i	$-0.967820\pi$
$179$	−18.7082	−	13.5923i	−1.39832	−	1.01594i	−0.403423	−	0.915014i	$-0.632180\pi$
$180$		0			0
$181$	−13.8262	+	10.0453i	−1.02770	+	0.746665i	−0.967846	−	0.251542i	$-0.919062\pi$
$181$	−13.8262	+	10.0453i	−1.02770	+	0.746665i	−0.0598499	+	0.998207i	$0.519062\pi$
$182$		0			0
$183$	4.16312	−	3.02468i	0.307747	−	0.223591i
$184$		0			0
$185$	−16.4443	−	11.9475i	−1.20901	−	0.878395i
$186$		0			0
$187$	−4.67376	−	14.3844i	−0.341779	−	1.05189i
$188$		0			0
$189$	−1.00000	+	3.07768i	−0.0727393	+	0.223869i
$190$		0			0
$191$	−3.90983	−	12.0332i	−0.282905	−	0.870693i	−0.987019	−	0.160606i	$-0.948655\pi$
$191$	−3.90983	−	12.0332i	−0.282905	−	0.870693i	0.704113	−	0.710088i	$-0.251345\pi$
$192$		0			0
$193$	−3.14590			−0.226447			−0.113223	−	0.993570i	$-0.536118\pi$
$193$	−3.14590			−0.226447			−0.113223	+	0.993570i	$0.536118\pi$
$194$		0			0
$195$	0.263932	+	0.812299i	0.0189006	+	0.0581700i
$196$		0			0
$197$	0.163119	+	0.118513i	0.0116217	+	0.00844369i	0.593581	−	0.804774i	$-0.297714\pi$
$197$	0.163119	+	0.118513i	0.0116217	+	0.00844369i	−0.581959	+	0.813218i	$0.697714\pi$
$198$		0			0
$199$	13.4164			0.951064			0.475532	−	0.879698i	$-0.342256\pi$
$199$	13.4164			0.951064			0.475532	+	0.879698i	$0.342256\pi$
$200$		0			0
$201$	−6.76393			−0.477091
$202$		0			0
$203$	23.7984	+	17.2905i	1.67032	+	1.21356i
$204$		0			0
$205$	1.54508	+	1.12257i	0.107913	+	0.0784037i
$206$		0			0
$207$	0.763932			0.0530969
$208$		0			0
$209$	0.652476	+	2.00811i	0.0451327	+	0.138904i
$210$		0			0
$211$	−6.94427	+	21.3723i	−0.478063	+	1.47133i	0.363718	+	0.931509i	$0.381507\pi$
$211$	−6.94427	+	21.3723i	−0.478063	+	1.47133i	−0.841781	+	0.539819i	$0.818493\pi$
$212$		0			0
$213$	−3.09017	−	9.51057i	−0.211735	−	0.651653i
$214$		0			0
$215$	0.854102	−	0.620541i	0.0582493	−	0.0423206i
$216$		0			0
$217$	−11.7082	+	8.50651i	−0.794805	+	0.577459i
$218$		0			0
$219$	11.1631	−	8.11048i	0.754334	−	0.548055i
$220$		0			0
$221$	1.04508	+	0.759299i	0.0703000	+	0.0510760i
$222$		0			0
$223$	−7.32624	+	22.5478i	−0.490601	+	1.50992i	0.333100	+	0.942891i	$0.391905\pi$
$223$	−7.32624	+	22.5478i	−0.490601	+	1.50992i	−0.823701	+	0.567024i	$0.808095\pi$
$224$		0			0
$225$	5.00000			0.333333
$226$		0			0
$227$	−5.23607	+	16.1150i	−0.347530	+	1.06959i	0.612685	+	0.790327i	$0.290089\pi$
$227$	−5.23607	+	16.1150i	−0.347530	+	1.06959i	−0.960215	+	0.279261i	$0.909911\pi$
$228$		0			0
$229$	−2.45492	−	1.78360i	−0.162225	−	0.117864i	0.503711	−	0.863872i	$-0.331968\pi$
$229$	−2.45492	−	1.78360i	−0.162225	−	0.117864i	−0.665936	+	0.746009i	$0.731968\pi$
$230$		0			0
$231$	−11.7082	+	8.50651i	−0.770343	+	0.559687i
$232$		0			0
$233$	−22.7254	+	16.5110i	−1.48879	+	1.08167i	−0.514204	+	0.857668i	$0.671912\pi$
$233$	−22.7254	+	16.5110i	−1.48879	+	1.08167i	−0.974589	+	0.224003i	$0.928088\pi$
$234$		0			0
$235$	8.29180			0.540897
$236$		0			0
$237$	1.23607	+	3.80423i	0.0802912	+	0.247111i
$238$		0			0
$239$	7.70820	−	23.7234i	0.498602	−	1.53454i	−0.312664	−	0.949864i	$-0.601222\pi$
$239$	7.70820	−	23.7234i	0.498602	−	1.53454i	0.811267	−	0.584676i	$-0.198778\pi$
$240$		0			0
$241$	2.95492	+	9.09429i	0.190343	+	0.585815i	0.999999	−	0.00108897i	$-0.000346631\pi$
$241$	2.95492	+	9.09429i	0.190343	+	0.585815i	−0.809657	+	0.586904i	$0.800347\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−6.28115	+	4.56352i	−0.401288	+	0.291553i
$246$		0			0
$247$	−0.145898	−	0.106001i	−0.00928327	−	0.00674469i
$248$		0			0
$249$	13.7082			0.868722
$250$		0			0
$251$	−4.18034			−0.263861			−0.131930	−	0.991259i	$-0.542118\pi$
$251$	−4.18034			−0.263861			−0.131930	+	0.991259i	$0.542118\pi$
$252$		0			0
$253$	2.76393	+	2.00811i	0.173767	+	0.126249i
$254$		0			0
$255$	6.11803	−	4.44501i	0.383126	−	0.278357i
$256$		0			0
$257$	−5.79837			−0.361693			−0.180846	−	0.983511i	$-0.557884\pi$
$257$	−5.79837			−0.361693			−0.180846	+	0.983511i	$0.557884\pi$
$258$		0			0
$259$	9.09017	+	27.9767i	0.564836	+	1.73839i
$260$		0			0
$261$	−2.80902	+	8.64527i	−0.173874	+	0.535128i
$262$		0			0
$263$	6.23607	+	19.1926i	0.384532	+	1.18347i	0.936819	+	0.349815i	$0.113755\pi$
$263$	6.23607	+	19.1926i	0.384532	+	1.18347i	−0.552286	+	0.833654i	$0.686245\pi$
$264$		0			0
$265$	−28.0902			−1.72557
$266$		0			0
$267$	14.4443	−	10.4944i	0.883975	−	0.642245i
$268$		0			0
$269$	−7.54508	+	5.48183i	−0.460032	+	0.334233i	−0.793544	−	0.608513i	$-0.791766\pi$
$269$	−7.54508	+	5.48183i	−0.460032	+	0.334233i	0.333512	+	0.942746i	$0.391766\pi$
$270$		0			0
$271$	3.00000	+	2.17963i	0.182237	+	0.132403i	0.675164	−	0.737668i	$-0.264073\pi$
$271$	3.00000	+	2.17963i	0.182237	+	0.132403i	−0.492927	+	0.870071i	$0.664073\pi$
$272$		0			0
$273$	0.381966	−	1.17557i	0.0231176	−	0.0711488i
$274$		0			0
$275$	18.0902	+	13.1433i	1.09088	+	0.792569i
$276$		0			0
$277$	−9.37132	+	28.8420i	−0.563068	+	1.73295i	0.110554	+	0.993870i	$0.464737\pi$
$277$	−9.37132	+	28.8420i	−0.563068	+	1.73295i	−0.673622	+	0.739076i	$0.735263\pi$
$278$		0			0
$279$	−3.61803	−	2.62866i	−0.216606	−	0.157373i
$280$		0			0
$281$	21.6353	−	15.7189i	1.29065	−	0.937713i	0.290833	−	0.956774i	$-0.406068\pi$
$281$	21.6353	−	15.7189i	1.29065	−	0.937713i	0.999818	+	0.0190610i	$0.00606767\pi$
$282$		0			0
$283$	−10.7082	+	7.77997i	−0.636537	+	0.462471i	−0.858659	−	0.512548i	$-0.828702\pi$
$283$	−10.7082	+	7.77997i	−0.636537	+	0.462471i	0.222122	+	0.975019i	$0.428702\pi$
$284$		0			0
$285$	−0.854102	+	0.620541i	−0.0505926	+	0.0367577i
$286$		0			0
$287$	−0.854102	−	2.62866i	−0.0504160	−	0.155165i
$288$		0			0
$289$	−1.71885	+	5.29007i	−0.101109	+	0.311180i
$290$		0			0
$291$	1.04508	+	3.21644i	0.0612640	+	0.188551i
$292$		0			0
$293$	24.7984			1.44874			0.724368	−	0.689413i	$-0.242132\pi$
$293$	24.7984			1.44874			0.724368	+	0.689413i	$0.242132\pi$
$294$		0			0
$295$	16.1803	+	11.7557i	0.942056	+	0.684444i
$296$		0			0
$297$	−3.61803	−	2.62866i	−0.209940	−	0.152530i
$298$		0			0
$299$	−0.291796			−0.0168750
$300$		0			0
$301$	−1.52786			−0.0880646
$302$		0			0
$303$	2.35410	+	1.71036i	0.135240	+	0.0982573i
$304$		0			0
$305$	3.55573	+	10.9434i	0.203600	+	0.626618i
$306$		0			0
$307$	18.3607			1.04790			0.523950	−	0.851749i	$-0.324458\pi$
$307$	18.3607			1.04790			0.523950	+	0.851749i	$0.324458\pi$
$308$		0			0
$309$	4.85410	+	14.9394i	0.276140	+	0.849872i
$310$		0			0
$311$	2.38197	−	7.33094i	0.135069	−	0.415699i	−0.860532	−	0.509397i	$-0.829869\pi$
$311$	2.38197	−	7.33094i	0.135069	−	0.415699i	0.995601	+	0.0936973i	$0.0298686\pi$
$312$		0			0
$313$	−2.90983	−	8.95554i	−0.164473	−	0.506197i	0.834524	−	0.550972i	$-0.185743\pi$
$313$	−2.90983	−	8.95554i	−0.164473	−	0.506197i	−0.998997	+	0.0447751i	$0.985743\pi$
$314$		0			0
$315$	−5.85410	−	4.25325i	−0.329841	−	0.239644i
$316$		0			0
$317$	−7.32624	+	5.32282i	−0.411483	+	0.298960i	−0.774202	−	0.632939i	$-0.781848\pi$
$317$	−7.32624	+	5.32282i	−0.411483	+	0.298960i	0.362719	+	0.931898i	$0.381848\pi$
$318$		0			0
$319$	−32.8885	+	23.8949i	−1.84140	+	1.33786i
$320$		0			0
$321$	−9.09017	−	6.60440i	−0.507364	−	0.368621i
$322$		0			0
$323$	−0.493422	+	1.51860i	−0.0274547	+	0.0844970i
$324$		0			0
$325$	−1.90983			−0.105938
$326$		0			0
$327$	3.35410	−	10.3229i	0.185482	−	0.570856i
$328$		0			0
$329$	−9.70820	−	7.05342i	−0.535231	−	0.388868i
$330$		0			0
$331$	−10.6180	+	7.71445i	−0.583620	+	0.424025i	−0.840027	−	0.542544i	$-0.817461\pi$
$331$	−10.6180	+	7.71445i	−0.583620	+	0.424025i	0.256407	+	0.966569i	$0.417461\pi$
$332$		0			0
$333$	−7.35410	+	5.34307i	−0.403002	+	0.292798i
$334$		0			0
$335$	4.67376	−	14.3844i	0.255355	−	0.785902i
$336$		0			0
$337$	−4.14590	−	12.7598i	−0.225841	−	0.695069i	−0.998205	−	0.0598879i	$-0.980926\pi$
$337$	−4.14590	−	12.7598i	−0.225841	−	0.695069i	0.772364	−	0.635181i	$-0.219074\pi$
$338$		0			0
$339$	−0.281153	+	0.865300i	−0.0152701	+	0.0469966i
$340$		0			0
$341$	−6.18034	−	19.0211i	−0.334684	−	1.03005i
$342$		0			0
$343$	−11.4164			−0.616428
$344$		0			0
$345$	−0.527864	+	1.62460i	−0.0284192	+	0.0874654i
$346$		0			0
$347$	18.5623	+	13.4863i	0.996477	+	0.723983i	0.961330	−	0.275399i	$-0.0888101\pi$
$347$	18.5623	+	13.4863i	0.996477	+	0.723983i	0.0351469	+	0.999382i	$0.488810\pi$
$348$		0			0
$349$	28.1459			1.50662			0.753308	−	0.657668i	$-0.228457\pi$
$349$	28.1459			1.50662			0.753308	+	0.657668i	$0.228457\pi$
$350$		0			0
$351$	0.381966			0.0203878
$352$		0			0
$353$	6.09017	+	4.42477i	0.324147	+	0.235507i	0.737943	−	0.674863i	$-0.235797\pi$
$353$	6.09017	+	4.42477i	0.324147	+	0.235507i	−0.413796	+	0.910370i	$0.635797\pi$
$354$		0			0
$355$	22.3607			1.18678
$356$		0			0
$357$	−10.9443			−0.579232
$358$		0			0
$359$	−7.65248	−	23.5519i	−0.403882	−	1.24302i	−0.921825	−	0.387606i	$-0.873302\pi$
$359$	−7.65248	−	23.5519i	−0.403882	−	1.24302i	0.517943	−	0.855415i	$-0.326698\pi$
$360$		0			0
$361$	−5.80244	+	17.8581i	−0.305392	+	0.939899i
$362$		0			0
$363$	−2.78115	−	8.55951i	−0.145973	−	0.449258i
$364$		0			0
$365$	9.53444	+	29.3440i	0.499055	+	1.53593i
$366$		0			0
$367$	−13.8541	+	10.0656i	−0.723178	+	0.525420i	−0.887398	−	0.461004i	$-0.847489\pi$
$367$	−13.8541	+	10.0656i	−0.723178	+	0.525420i	0.164220	+	0.986424i	$0.447489\pi$
$368$		0			0
$369$	0.690983	−	0.502029i	0.0359711	−	0.0261346i
$370$		0			0
$371$	32.8885	+	23.8949i	1.70749	+	1.24056i
$372$		0			0
$373$	5.56231	−	17.1190i	0.288005	−	0.886389i	−0.697476	−	0.716608i	$-0.745694\pi$
$373$	5.56231	−	17.1190i	0.288005	−	0.886389i	0.985482	−	0.169781i	$-0.0543062\pi$
$374$		0			0
$375$	−3.45492	+	10.6331i	−0.178411	+	0.549093i
$376$		0			0
$377$	1.07295	−	3.30220i	0.0552597	−	0.170072i
$378$		0			0
$379$	−14.9443	−	10.8576i	−0.767636	−	0.557720i	0.133607	−	0.991034i	$-0.457344\pi$
$379$	−14.9443	−	10.8576i	−0.767636	−	0.557720i	−0.901243	+	0.433314i	$0.857344\pi$
$380$		0			0
$381$	14.0902	−	10.2371i	0.721861	−	0.524463i
$382$		0			0
$383$	16.7984	−	12.2047i	0.858357	−	0.623633i	−0.0690806	−	0.997611i	$-0.522007\pi$
$383$	16.7984	−	12.2047i	0.858357	−	0.623633i	0.927437	+	0.373978i	$0.122007\pi$
$384$		0			0
$385$	−10.0000	−	30.7768i	−0.509647	−	1.56853i
$386$		0			0
$387$	−0.145898	−	0.449028i	−0.00741641	−	0.0228254i
$388$		0			0
$389$	−1.59017	+	4.89404i	−0.0806248	+	0.248138i	−0.983242	−	0.182307i	$-0.941643\pi$
$389$	−1.59017	+	4.89404i	−0.0806248	+	0.248138i	0.902617	+	0.430445i	$0.141643\pi$
$390$		0			0
$391$	0.798374	+	2.45714i	0.0403755	+	0.124263i
$392$		0			0
$393$	−7.70820			−0.388827
$394$		0			0
$395$	−8.94427			−0.450035
$396$		0			0
$397$	16.0902	+	11.6902i	0.807542	+	0.586714i	0.913117	−	0.407697i	$-0.133668\pi$
$397$	16.0902	+	11.6902i	0.807542	+	0.586714i	−0.105575	+	0.994411i	$0.533668\pi$
$398$		0			0
$399$	1.52786			0.0764889
$400$		0			0
$401$	32.0902			1.60251			0.801253	−	0.598325i	$-0.204167\pi$
$401$	32.0902			1.60251			0.801253	+	0.598325i	$0.204167\pi$
$402$		0			0
$403$	1.38197	+	1.00406i	0.0688406	+	0.0500156i
$404$		0			0
$405$	0.690983	−	2.12663i	0.0343352	−	0.105673i
$406$		0			0
$407$	−40.6525			−2.01507
$408$		0			0
$409$	1.89919	+	5.84510i	0.0939088	+	0.289021i	0.986968	−	0.160918i	$-0.0514455\pi$
$409$	1.89919	+	5.84510i	0.0939088	+	0.289021i	−0.893059	+	0.449940i	$0.851446\pi$
$410$		0			0
$411$	−3.26393	+	10.0453i	−0.160998	+	0.495501i
$412$		0			0
$413$	−8.94427	−	27.5276i	−0.440119	−	1.35455i
$414$		0			0
$415$	−9.47214	+	29.1522i	−0.464969	+	1.43103i
$416$		0			0
$417$	15.0902	−	10.9637i	0.738969	−	0.536892i
$418$		0			0
$419$	−3.23607	+	2.35114i	−0.158092	+	0.114861i	−0.664019	−	0.747716i	$-0.731151\pi$
$419$	−3.23607	+	2.35114i	−0.158092	+	0.114861i	0.505927	+	0.862576i	$0.331151\pi$
$420$		0			0
$421$	−26.2984	−	19.1069i	−1.28170	−	0.931213i	−0.282101	−	0.959385i	$-0.591031\pi$
$421$	−26.2984	−	19.1069i	−1.28170	−	0.931213i	−0.999603	+	0.0281720i	$0.991031\pi$
$422$		0			0
$423$	1.14590	−	3.52671i	0.0557155	−	0.171475i
$424$		0			0
$425$	5.22542	+	16.0822i	0.253470	+	0.780101i
$426$		0			0
$427$	5.14590	−	15.8374i	0.249027	−	0.766428i
$428$		0			0
$429$	1.38197	+	1.00406i	0.0667219	+	0.0484763i
$430$		0			0
$431$	−0.0901699	+	0.0655123i	−0.00434333	+	0.00315562i	−0.589955	−	0.807436i	$-0.700854\pi$
$431$	−0.0901699	+	0.0655123i	−0.00434333	+	0.00315562i	0.585611	+	0.810592i	$0.300854\pi$
$432$		0			0
$433$	−9.63525	+	7.00042i	−0.463041	+	0.336419i	−0.794723	−	0.606972i	$-0.792384\pi$
$433$	−9.63525	+	7.00042i	−0.463041	+	0.336419i	0.331682	+	0.943391i	$0.392384\pi$
$434$		0			0
$435$	−16.4443	−	11.9475i	−0.788442	−	0.572837i
$436$		0			0
$437$	−0.111456	−	0.343027i	−0.00533167	−	0.0164092i
$438$		0			0
$439$	−10.0902	+	31.0543i	−0.481578	+	1.48214i	0.355300	+	0.934752i	$0.384379\pi$
$439$	−10.0902	+	31.0543i	−0.481578	+	1.48214i	−0.836877	+	0.547391i	$0.815621\pi$
$440$		0			0
$441$	1.07295	+	3.30220i	0.0510928	+	0.157248i
$442$		0			0
$443$	−9.23607			−0.438819			−0.219409	−	0.975633i	$-0.570413\pi$
$443$	−9.23607			−0.438819			−0.219409	+	0.975633i	$0.570413\pi$
$444$		0			0
$445$	12.3369	+	37.9690i	0.584824	+	1.79990i
$446$		0			0
$447$	0.309017	+	0.224514i	0.0146160	+	0.0106191i
$448$		0			0
$449$	−12.6180			−0.595482			−0.297741	−	0.954647i	$-0.596233\pi$
$449$	−12.6180			−0.595482			−0.297741	+	0.954647i	$0.596233\pi$
$450$		0			0
$451$	3.81966			0.179861
$452$		0			0
$453$	1.38197	+	1.00406i	0.0649304	+	0.0471747i
$454$		0			0
$455$	2.23607	+	1.62460i	0.104828	+	0.0761624i
$456$		0			0
$457$	9.05573			0.423609			0.211805	−	0.977312i	$-0.432066\pi$
$457$	9.05573			0.423609			0.211805	+	0.977312i	$0.432066\pi$
$458$		0			0
$459$	−1.04508	−	3.21644i	−0.0487804	−	0.150131i
$460$		0			0
$461$	10.7188	−	32.9892i	0.499226	−	1.53646i	−0.311038	−	0.950397i	$-0.600677\pi$
$461$	10.7188	−	32.9892i	0.499226	−	1.53646i	0.810265	−	0.586064i	$-0.199323\pi$
$462$		0			0
$463$	−7.09017	−	21.8213i	−0.329508	−	1.01412i	−0.969364	−	0.245627i	$-0.921006\pi$
$463$	−7.09017	−	21.8213i	−0.329508	−	1.01412i	0.639856	−	0.768495i	$-0.278994\pi$
$464$		0			0
$465$	8.09017	−	5.87785i	0.375173	−	0.272579i
$466$		0			0
$467$	5.00000	−	3.63271i	0.231372	−	0.168102i	−0.466059	−	0.884754i	$-0.654326\pi$
$467$	5.00000	−	3.63271i	0.231372	−	0.168102i	0.697431	+	0.716652i	$0.254326\pi$
$468$		0			0
$469$	−17.7082	+	12.8658i	−0.817689	+	0.594086i
$470$		0			0
$471$	15.0623	+	10.9434i	0.694034	+	0.504246i
$472$		0			0
$473$	0.652476	−	2.00811i	0.0300009	−	0.0923332i
$474$		0			0
$475$	−0.729490	−	2.24514i	−0.0334713	−	0.103014i
$476$		0			0
$477$	−3.88197	+	11.9475i	−0.177743	+	0.547037i
$478$		0			0
$479$	−30.5066	−	22.1643i	−1.39388	−	1.01271i	−0.995427	−	0.0955257i	$-0.969547\pi$
$479$	−30.5066	−	22.1643i	−1.39388	−	1.01271i	−0.398454	−	0.917188i	$-0.630453\pi$
$480$		0			0
$481$	2.80902	−	2.04087i	0.128080	−	0.0930557i
$482$		0			0
$483$	2.00000	−	1.45309i	0.0910032	−	0.0661177i
$484$		0			0
$485$	−7.56231			−0.343387
$486$		0			0
$487$	4.09017	+	12.5882i	0.185343	+	0.570428i	0.999954	−	0.00957994i	$-0.00304944\pi$
$487$	4.09017	+	12.5882i	0.185343	+	0.570428i	−0.814611	+	0.580008i	$0.803049\pi$
$488$		0			0
$489$	1.00000	−	3.07768i	0.0452216	−	0.139178i
$490$		0			0
$491$	−6.18034	−	19.0211i	−0.278915	−	0.858412i	−0.988157	−	0.153447i	$-0.950963\pi$
$491$	−6.18034	−	19.0211i	−0.278915	−	0.858412i	0.709242	−	0.704965i	$-0.249037\pi$
$492$		0			0
$493$	−30.7426			−1.38458
$494$		0			0
$495$	8.09017	−	5.87785i	0.363626	−	0.264190i
$496$		0			0
$497$	−26.1803	−	19.0211i	−1.17435	−	0.853214i
$498$		0			0
$499$	−1.70820			−0.0764697			−0.0382349	−	0.999269i	$-0.512173\pi$
$499$	−1.70820			−0.0764697			−0.0382349	+	0.999269i	$0.512173\pi$
$500$		0			0
$501$	6.47214			0.289154
$502$		0			0
$503$	16.1803	+	11.7557i	0.721446	+	0.524161i	0.886846	−	0.462066i	$-0.152892\pi$
$503$	16.1803	+	11.7557i	0.721446	+	0.524161i	−0.165400	+	0.986227i	$0.552892\pi$
$504$		0			0
$505$	−5.26393	+	3.82447i	−0.234242	+	0.170187i
$506$		0			0
$507$	12.8541			0.570871
$508$		0			0
$509$	10.6074	+	32.6462i	0.470164	+	1.44702i	0.852370	+	0.522940i	$0.175165\pi$
$509$	10.6074	+	32.6462i	0.470164	+	1.44702i	−0.382205	+	0.924077i	$0.624835\pi$
$510$		0			0
$511$	13.7984	−	42.4670i	0.610404	−	1.87863i
$512$		0			0
$513$	0.145898	+	0.449028i	0.00644156	+	0.0198251i
$514$		0			0
$515$	−35.1246			−1.54778
$516$		0			0
$517$	13.4164	−	9.74759i	0.590053	−	0.428699i
$518$		0			0
$519$	9.11803	−	6.62464i	0.400237	−	0.290789i
$520$		0			0
$521$	−23.9615	−	17.4090i	−1.04977	−	0.762704i	−0.0776030	−	0.996984i	$-0.524727\pi$
$521$	−23.9615	−	17.4090i	−1.04977	−	0.762704i	−0.972169	+	0.234280i	$0.924727\pi$
$522$		0			0
$523$	12.0902	−	37.2097i	0.528666	−	1.62707i	−0.228284	−	0.973595i	$-0.573311\pi$
$523$	12.0902	−	37.2097i	0.528666	−	1.62707i	0.756950	−	0.653473i	$-0.226689\pi$
$524$		0			0
$525$	13.0902	−	9.51057i	0.571302	−	0.415075i
$526$		0			0
$527$	4.67376	−	14.3844i	0.203592	−	0.626593i
$528$		0			0
$529$	18.1353	+	13.1760i	0.788489	+	0.572871i
$530$		0			0
$531$	7.23607	−	5.25731i	0.314019	−	0.228148i
$532$		0			0
$533$	−0.263932	+	0.191758i	−0.0114322	+	0.00830595i
$534$		0			0
$535$	20.3262	−	14.7679i	0.878780	−	0.638471i
$536$		0			0
$537$	−7.14590	−	21.9928i	−0.308368	−	0.949060i
$538$		0			0
$539$	−4.79837	+	14.7679i	−0.206681	+	0.636097i
$540$		0			0
$541$	7.46149	+	22.9641i	0.320795	+	0.987304i	0.973303	+	0.229523i	$0.0737166\pi$
$541$	7.46149	+	22.9641i	0.320795	+	0.987304i	−0.652509	+	0.757781i	$0.726283\pi$
$542$		0			0
$543$	−17.0902			−0.733409
$544$		0			0
$545$	19.6353	+	14.2658i	0.841082	+	0.611082i
$546$		0			0
$547$	−24.3262	−	17.6740i	−1.04011	−	0.755688i	−0.0698069	−	0.997561i	$-0.522238\pi$
$547$	−24.3262	−	17.6740i	−1.04011	−	0.755688i	−0.970308	+	0.241873i	$0.922238\pi$
$548$		0			0
$549$	5.14590			0.219622
$550$		0			0
$551$	4.29180			0.182837
$552$		0			0
$553$	10.4721	+	7.60845i	0.445321	+	0.323544i
$554$		0			0
$555$	−6.28115	−	19.3314i	−0.266620	−	0.820572i
$556$		0			0
$557$	−23.5623			−0.998367			−0.499183	−	0.866496i	$-0.666367\pi$
$557$	−23.5623			−0.998367			−0.499183	+	0.866496i	$0.666367\pi$
$558$		0			0
$559$	0.0557281	+	0.171513i	0.00235705	+	0.00725424i
$560$		0			0
$561$	4.67376	−	14.3844i	0.197326	−	0.607308i
$562$		0			0
$563$	1.23607	+	3.80423i	0.0520941	+	0.160329i	0.973719	−	0.227753i	$-0.0731378\pi$
$563$	1.23607	+	3.80423i	0.0520941	+	0.160329i	−0.921625	+	0.388082i	$0.873138\pi$
$564$		0			0
$565$	−1.64590	−	1.19581i	−0.0692435	−	0.0503083i
$566$		0			0
$567$	−2.61803	+	1.90211i	−0.109947	+	0.0798812i
$568$		0			0
$569$	26.3885	−	19.1724i	1.10627	−	0.803749i	0.124194	−	0.992258i	$-0.460366\pi$
$569$	26.3885	−	19.1724i	1.10627	−	0.803749i	0.982071	+	0.188509i	$0.0603655\pi$
$570$		0			0
$571$	12.2361	+	8.89002i	0.512064	+	0.372036i	0.813606	−	0.581417i	$-0.197501\pi$
$571$	12.2361	+	8.89002i	0.512064	+	0.372036i	−0.301542	+	0.953453i	$0.597501\pi$
$572$		0			0
$573$	3.90983	−	12.0332i	0.163335	−	0.502695i
$574$		0			0
$575$	−3.09017	−	2.24514i	−0.128869	−	0.0936288i
$576$		0			0
$577$	8.43769	−	25.9686i	0.351266	−	1.08108i	−0.606877	−	0.794795i	$-0.707578\pi$
$577$	8.43769	−	25.9686i	0.351266	−	1.08108i	0.958143	−	0.286289i	$-0.0924219\pi$
$578$		0			0
$579$	−2.54508	−	1.84911i	−0.105770	−	0.0768465i
$580$		0			0
$581$	35.8885	−	26.0746i	1.48891	−	1.08175i
$582$		0			0
$583$	−45.4508	+	33.0220i	−1.88238	+	1.36763i
$584$		0			0
$585$	−0.263932	+	0.812299i	−0.0109122	+	0.0335844i
$586$		0			0
$587$	−7.18034	−	22.0988i	−0.296364	−	0.912116i	−0.982760	−	0.184887i	$-0.940808\pi$
$587$	−7.18034	−	22.0988i	−0.296364	−	0.912116i	0.686395	−	0.727229i	$-0.259192\pi$
$588$		0			0
$589$	−0.652476	+	2.00811i	−0.0268848	+	0.0827429i
$590$		0			0
$591$	0.0623059	+	0.191758i	0.00256292	+	0.00788786i
$592$		0			0
$593$	−15.0902			−0.619679			−0.309840	−	0.950789i	$-0.600275\pi$
$593$	−15.0902			−0.619679			−0.309840	+	0.950789i	$0.600275\pi$
$594$		0			0
$595$	7.56231	−	23.2744i	0.310024	−	0.954157i
$596$		0			0
$597$	10.8541	+	7.88597i	0.444229	+	0.322751i
$598$		0			0
$599$	33.1246			1.35343			0.676717	−	0.736243i	$-0.263402\pi$
$599$	33.1246			1.35343			0.676717	+	0.736243i	$0.263402\pi$
$600$		0			0
$601$	25.4377			1.03763			0.518813	−	0.854888i	$-0.326374\pi$
$601$	25.4377			1.03763			0.518813	+	0.854888i	$0.326374\pi$
$602$		0			0
$603$	−5.47214	−	3.97574i	−0.222843	−	0.161905i
$604$		0			0
$605$	20.1246			0.818182
$606$		0			0
$607$	−14.5836			−0.591930			−0.295965	−	0.955199i	$-0.595641\pi$
$607$	−14.5836			−0.591930			−0.295965	+	0.955199i	$0.595641\pi$
$608$		0			0
$609$	9.09017	+	27.9767i	0.368352	+	1.13367i
$610$		0			0
$611$	−0.437694	+	1.34708i	−0.0177072	+	0.0544972i
$612$		0			0
$613$	6.98936	+	21.5110i	0.282297	+	0.868822i	0.987196	+	0.159514i	$0.0509927\pi$
$613$	6.98936	+	21.5110i	0.282297	+	0.868822i	−0.704898	+	0.709308i	$0.749007\pi$
$614$		0			0
$615$	0.590170	+	1.81636i	0.0237979	+	0.0732426i
$616$		0			0
$617$	2.21885	−	1.61209i	0.0893274	−	0.0649002i	−0.542225	−	0.840233i	$-0.682418\pi$
$617$	2.21885	−	1.61209i	0.0893274	−	0.0649002i	0.631553	+	0.775333i	$0.282418\pi$
$618$		0			0
$619$	−15.2361	+	11.0697i	−0.612389	+	0.444927i	−0.850255	−	0.526371i	$-0.823552\pi$
$619$	−15.2361	+	11.0697i	−0.612389	+	0.444927i	0.237866	+	0.971298i	$0.423552\pi$
$620$		0			0
$621$	0.618034	+	0.449028i	0.0248008	+	0.0180189i
$622$		0			0
$623$	17.8541	−	54.9493i	0.715309	−	2.20150i
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$		0			0
$627$	−0.652476	+	2.00811i	−0.0260574	+	0.0801964i
$628$		0			0
$629$	−24.8713	−	18.0701i	−0.991685	−	0.720501i
$630$		0			0
$631$	−8.09017	+	5.87785i	−0.322065	+	0.233994i	−0.737056	−	0.675832i	$-0.763785\pi$
$631$	−8.09017	+	5.87785i	−0.322065	+	0.233994i	0.414991	+	0.909825i	$0.363785\pi$
$632$		0			0
$633$	−18.1803	+	13.2088i	−0.722604	+	0.525002i
$634$		0			0
$635$	12.0344	+	37.0382i	0.477572	+	1.46982i
$636$		0			0
$637$	−0.409830	−	1.26133i	−0.0162381	−	0.0499756i
$638$		0			0
$639$	3.09017	−	9.51057i	0.122245	−	0.376232i
$640$		0			0
$641$	5.56231	+	17.1190i	0.219698	+	0.676161i	0.998787	+	0.0492469i	$0.0156821\pi$
$641$	5.56231	+	17.1190i	0.219698	+	0.676161i	−0.779089	+	0.626914i	$0.784318\pi$
$642$		0			0
$643$	−36.3607			−1.43393			−0.716963	−	0.697112i	$-0.754468\pi$
$643$	−36.3607			−1.43393			−0.716963	+	0.697112i	$0.754468\pi$
$644$		0			0
$645$	1.05573			0.0415693
$646$		0			0
$647$	−6.61803	−	4.80828i	−0.260182	−	0.189033i	0.450045	−	0.893006i	$-0.351408\pi$
$647$	−6.61803	−	4.80828i	−0.260182	−	0.189033i	−0.710227	+	0.703973i	$0.751408\pi$
$648$		0			0
$649$	40.0000			1.57014
$650$		0			0
$651$	−14.4721			−0.567208
$652$		0			0
$653$	−1.88197	−	1.36733i	−0.0736470	−	0.0535077i	0.550353	−	0.834932i	$-0.314493\pi$
$653$	−1.88197	−	1.36733i	−0.0736470	−	0.0535077i	−0.624000	+	0.781425i	$0.714493\pi$
$654$		0			0
$655$	5.32624	−	16.3925i	0.208113	−	0.640507i
$656$		0			0
$657$	13.7984			0.538326
$658$		0			0
$659$	11.7639	+	36.2057i	0.458258	+	1.41037i	0.867268	+	0.497842i	$0.165874\pi$
$659$	11.7639	+	36.2057i	0.458258	+	1.41037i	−0.409010	+	0.912530i	$0.634126\pi$
$660$		0			0
$661$	−7.20163	+	22.1643i	−0.280111	+	0.862092i	0.707711	+	0.706502i	$0.249728\pi$
$661$	−7.20163	+	22.1643i	−0.280111	+	0.862092i	−0.987822	+	0.155590i	$0.950272\pi$
$662$		0			0
$663$	0.399187	+	1.22857i	0.0155031	+	0.0477137i
$664$		0			0
$665$	−1.05573	+	3.24920i	−0.0409394	+	0.125998i
$666$		0			0
$667$	5.61803	−	4.08174i	0.217531	−	0.158046i
$668$		0			0
$669$	−19.1803	+	13.9353i	−0.741555	+	0.538771i
$670$		0			0
$671$	18.6180	+	13.5268i	0.718741	+	0.522196i
$672$		0			0
$673$	7.42705	−	22.8581i	0.286292	−	0.881115i	−0.699717	−	0.714420i	$-0.746690\pi$
$673$	7.42705	−	22.8581i	0.286292	−	0.881115i	0.986008	−	0.166695i	$-0.0533096\pi$
$674$		0			0
$675$	4.04508	+	2.93893i	0.155695	+	0.113119i
$676$		0			0
$677$	1.20163	−	3.69822i	0.0461822	−	0.142134i	−0.925306	−	0.379220i	$-0.876192\pi$
$677$	1.20163	−	3.69822i	0.0461822	−	0.142134i	0.971489	+	0.237086i	$0.0761923\pi$
$678$		0			0
$679$	8.85410	+	6.43288i	0.339789	+	0.246871i
$680$		0			0
$681$	−13.7082	+	9.95959i	−0.525300	+	0.381652i
$682$		0			0
$683$	−35.5967	+	25.8626i	−1.36207	+	0.989603i	−0.363762	+	0.931492i	$0.618508\pi$
$683$	−35.5967	+	25.8626i	−1.36207	+	0.989603i	−0.998310	+	0.0581109i	$0.981492\pi$
$684$		0			0
$685$	−19.1074	−	13.8823i	−0.730056	−	0.530417i
$686$		0			0
$687$	−0.937694	−	2.88593i	−0.0357753	−	0.110105i
$688$		0			0
$689$	1.48278	−	4.56352i	0.0564894	−	0.173856i
$690$		0			0
$691$	−11.9787	−	36.8667i	−0.455692	−	1.40247i	−0.870321	−	0.492485i	$-0.836089\pi$
$691$	−11.9787	−	36.8667i	−0.455692	−	1.40247i	0.414629	−	0.909990i	$-0.363911\pi$
$692$		0			0
$693$	−14.4721			−0.549751
$694$		0			0
$695$	12.8885	+	39.6669i	0.488890	+	1.50465i
$696$		0			0
$697$	2.33688	+	1.69784i	0.0885157	+	0.0643104i
$698$		0			0
$699$	−28.0902			−1.06247
$700$		0			0
$701$	−31.6180			−1.19420			−0.597098	−	0.802168i	$-0.703680\pi$
$701$	−31.6180			−1.19420			−0.597098	+	0.802168i	$0.703680\pi$
$702$		0			0
$703$	3.47214	+	2.52265i	0.130954	+	0.0951437i
$704$		0			0
$705$	6.70820	+	4.87380i	0.252646	+	0.183558i
$706$		0			0
$707$	9.41641			0.354140
$708$		0			0
$709$	−10.2984	−	31.6951i	−0.386764	−	1.19034i	−0.935193	−	0.354139i	$-0.884774\pi$
$709$	−10.2984	−	31.6951i	−0.386764	−	1.19034i	0.548429	−	0.836197i	$-0.315226\pi$
$710$		0			0
$711$	−1.23607	+	3.80423i	−0.0463562	+	0.142670i
$712$		0			0
$713$	1.05573	+	3.24920i	0.0395373	+	0.121683i
$714$		0			0
$715$	−3.09017	+	2.24514i	−0.115566	+	0.0839635i
$716$		0			0
$717$	20.1803	−	14.6619i	0.753649	−	0.547558i
$718$		0			0
$719$	−0.618034	+	0.449028i	−0.0230488	+	0.0167459i	−0.599250	−	0.800562i	$-0.704534\pi$
$719$	−0.618034	+	0.449028i	−0.0230488	+	0.0167459i	0.576201	+	0.817308i	$0.304534\pi$
$720$		0			0
$721$	41.1246	+	29.8788i	1.53156	+	1.11274i
$722$		0			0
$723$	−2.95492	+	9.09429i	−0.109894	+	0.338220i
$724$		0			0
$725$	36.7705	−	26.7153i	1.36562	−	0.992183i
$726$		0			0
$727$	6.96556	−	21.4378i	0.258338	−	0.795083i	−0.734815	−	0.678267i	$-0.762731\pi$
$727$	6.96556	−	21.4378i	0.258338	−	0.795083i	0.993154	−	0.116816i	$-0.0372688\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	1.29180	−	0.938545i	0.0477788	−	0.0347133i
$732$		0			0
$733$	6.85410	−	4.97980i	0.253162	−	0.183933i	−0.453965	−	0.891020i	$-0.649991\pi$
$733$	6.85410	−	4.97980i	0.253162	−	0.183933i	0.707127	+	0.707087i	$0.249991\pi$
$734$		0			0
$735$	−7.76393			−0.286377
$736$		0			0
$737$	−9.34752	−	28.7687i	−0.344320	−	1.05971i
$738$		0			0
$739$	−3.96556	+	12.2047i	−0.145875	+	0.448958i	−0.997123	−	0.0758067i	$-0.975847\pi$
$739$	−3.96556	+	12.2047i	−0.145875	+	0.448958i	0.851247	+	0.524765i	$0.175847\pi$
$740$		0			0
$741$	−0.0557281	−	0.171513i	−0.00204722	−	0.00630070i
$742$		0			0
$743$	−35.1246			−1.28860			−0.644299	−	0.764774i	$-0.722851\pi$
$743$	−35.1246			−1.28860			−0.644299	+	0.764774i	$0.722851\pi$
$744$		0			0
$745$	−0.690983	+	0.502029i	−0.0253157	+	0.0183929i
$746$		0			0
$747$	11.0902	+	8.05748i	0.405768	+	0.294808i
$748$		0			0
$749$	−36.3607			−1.32859
$750$		0			0
$751$	27.5279			1.00451			0.502253	−	0.864721i	$-0.332505\pi$
$751$	27.5279			1.00451			0.502253	+	0.864721i	$0.332505\pi$
$752$		0			0
$753$	−3.38197	−	2.45714i	−0.123246	−	0.0895432i
$754$		0			0
$755$	−3.09017	+	2.24514i	−0.112463	+	0.0817090i
$756$		0			0
$757$	32.9230			1.19661			0.598303	−	0.801270i	$-0.295842\pi$
$757$	32.9230			1.19661			0.598303	+	0.801270i	$0.295842\pi$
$758$		0			0
$759$	1.05573	+	3.24920i	0.0383205	+	0.117938i
$760$		0			0
$761$	−8.15248	+	25.0907i	−0.295527	+	0.909539i	0.687517	+	0.726168i	$0.258701\pi$
$761$	−8.15248	+	25.0907i	−0.295527	+	0.909539i	−0.983044	+	0.183370i	$0.941299\pi$
$762$		0			0
$763$	−10.8541	−	33.4055i	−0.392945	−	1.20936i
$764$		0			0
$765$	7.56231			0.273416
$766$		0			0
$767$	−2.76393	+	2.00811i	−0.0997998	+	0.0725088i
$768$		0			0
$769$	−28.7426	+	20.8828i	−1.03649	+	0.753051i	−0.969597	−	0.244709i	$-0.921308\pi$
$769$	−28.7426	+	20.8828i	−1.03649	+	0.753051i	−0.0668897	+	0.997760i	$0.521308\pi$
$770$		0			0
$771$	−4.69098	−	3.40820i	−0.168942	−	0.122743i
$772$		0			0
$773$	14.1180	−	43.4508i	0.507790	−	1.56282i	−0.288238	−	0.957559i	$-0.593069\pi$
$773$	14.1180	−	43.4508i	0.507790	−	1.56282i	0.796028	−	0.605259i	$-0.206931\pi$
$774$		0			0
$775$	6.90983	+	21.2663i	0.248208	+	0.763907i
$776$		0			0
$777$	−9.09017	+	27.9767i	−0.326108	+	1.00366i
$778$		0			0
$779$	−0.326238	−	0.237026i	−0.0116887	−	0.00849233i
$780$		0			0
$781$	36.1803	−	26.2866i	1.29463	−	0.940607i
$782$		0			0
$783$	−7.35410	+	5.34307i	−0.262814	+	0.190946i
$784$		0			0
$785$	−33.6803	+	24.4702i	−1.20210	+	0.873379i
$786$		0			0
$787$	−7.20163	−	22.1643i	−0.256710	−	0.790073i	−0.993488	−	0.113938i	$-0.963654\pi$
$787$	−7.20163	−	22.1643i	−0.256710	−	0.790073i	0.736778	−	0.676135i	$-0.236346\pi$
$788$		0			0
$789$	−6.23607	+	19.1926i	−0.222010	+	0.683276i
$790$		0			0
$791$	0.909830	+	2.80017i	0.0323498	+	0.0995625i
$792$		0			0
$793$	−1.96556			−0.0697990
$794$		0			0
$795$	−22.7254	−	16.5110i	−0.805988	−	0.585584i
$796$		0			0
$797$	−10.0172	−	7.27794i	−0.354828	−	0.257798i	0.396064	−	0.918223i	$-0.370376\pi$
$797$	−10.0172	−	7.27794i	−0.354828	−	0.257798i	−0.750892	+	0.660425i	$0.770376\pi$
$798$		0			0
$799$	12.5410			0.443669
$800$		0			0
$801$	17.8541			0.630844
$802$		0			0
$803$	49.9230	+	36.2712i	1.76174	+	1.27998i
$804$		0			0
$805$	1.70820	+	5.25731i	0.0602063	+	0.185296i
$806$		0			0
$807$	−9.32624			−0.328299
$808$		0			0
$809$	11.9894	+	36.8994i	0.421523	+	1.29732i	0.906284	+	0.422669i	$0.138907\pi$
$809$	11.9894	+	36.8994i	0.421523	+	1.29732i	−0.484761	+	0.874647i	$0.661093\pi$
$810$		0			0
$811$	16.7426	−	51.5286i	0.587914	−	1.80941i	0.000673838	−	1.00000i	$-0.499786\pi$
$811$	16.7426	−	51.5286i	0.587914	−	1.80941i	0.587240	−	0.809413i	$-0.300214\pi$
$812$		0			0
$813$	1.14590	+	3.52671i	0.0401884	+	0.123687i
$814$		0			0
$815$	5.85410	+	4.25325i	0.205060	+	0.148985i
$816$		0			0
$817$	−0.180340	+	0.131025i	−0.00630929	+	0.00458397i
$818$		0			0
$819$	1.00000	−	0.726543i	0.0349428	−	0.0253875i
$820$		0			0
$821$	−25.3262	−	18.4006i	−0.883892	−	0.642185i	0.0503864	−	0.998730i	$-0.483955\pi$
$821$	−25.3262	−	18.4006i	−0.883892	−	0.642185i	−0.934278	+	0.356545i	$0.883955\pi$
$822$		0			0
$823$	−10.6738	+	32.8505i	−0.372064	+	1.14510i	0.573374	+	0.819294i	$0.305634\pi$
$823$	−10.6738	+	32.8505i	−0.372064	+	1.14510i	−0.945438	+	0.325802i	$0.894366\pi$
$824$		0			0
$825$	6.90983	+	21.2663i	0.240569	+	0.740396i
$826$		0			0
$827$	−4.79837	+	14.7679i	−0.166856	+	0.513529i	−0.999168	−	0.0407774i	$-0.987017\pi$
$827$	−4.79837	+	14.7679i	−0.166856	+	0.513529i	0.832312	+	0.554307i	$0.187017\pi$
$828$		0			0
$829$	−35.5795	−	25.8500i	−1.23573	−	0.897809i	−0.238422	−	0.971162i	$-0.576630\pi$
$829$	−35.5795	−	25.8500i	−1.23573	−	0.897809i	−0.997306	+	0.0733527i	$0.976630\pi$
$830$		0			0
$831$	−24.5344	+	17.8253i	−0.851090	+	0.618353i
$832$		0			0
$833$	−9.50000	+	6.90215i	−0.329155	+	0.239145i
$834$		0			0
$835$	−4.47214	+	13.7638i	−0.154765	+	0.476317i
$836$		0			0
$837$	−1.38197	−	4.25325i	−0.0477677	−	0.147014i
$838$		0			0
$839$	1.90983	−	5.87785i	0.0659347	−	0.202926i	−0.912661	−	0.408716i	$-0.865977\pi$
$839$	1.90983	−	5.87785i	0.0659347	−	0.202926i	0.978596	+	0.205790i	$0.0659765\pi$
$840$		0			0
$841$	16.5729	+	51.0063i	0.571481	+	1.75884i
$842$		0			0
$843$	26.7426			0.921066
$844$		0			0
$845$	−8.88197	+	27.3359i	−0.305549	+	0.940383i
$846$		0			0
$847$	−23.5623	−	17.1190i	−0.809610	−	0.588216i
$848$		0			0
$849$	−13.2361			−0.454261
$850$		0			0
$851$	6.94427			0.238047
$852$		0			0
$853$	1.54508	+	1.12257i	0.0529027	+	0.0384361i	0.613922	−	0.789366i	$-0.289591\pi$
$853$	1.54508	+	1.12257i	0.0529027	+	0.0384361i	−0.561020	+	0.827802i	$0.689591\pi$
$854$		0			0
$855$	−1.05573			−0.0361051
$856$		0			0
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$		0			0
$859$	−9.12461	−	28.0827i	−0.311328	−	0.958168i	−0.977240	−	0.212138i	$-0.931957\pi$
$859$	−9.12461	−	28.0827i	−0.311328	−	0.958168i	0.665912	−	0.746030i	$-0.268043\pi$
$860$		0			0
$861$	0.854102	−	2.62866i	0.0291077	−	0.0895843i
$862$		0			0
$863$	−7.90983	−	24.3440i	−0.269254	−	0.828678i	−0.990683	−	0.136189i	$-0.956514\pi$
$863$	−7.90983	−	24.3440i	−0.269254	−	0.828678i	0.721429	−	0.692488i	$-0.243486\pi$
$864$		0			0
$865$	7.78773	+	23.9682i	0.264791	+	0.814942i
$866$		0			0
$867$	−4.50000	+	3.26944i	−0.152828	+	0.111036i
$868$		0			0
$869$	−14.4721	+	10.5146i	−0.490934	+	0.356684i
$870$		0			0
$871$	2.09017	+	1.51860i	0.0708227	+	0.0514557i
$872$		0			0
$873$	−1.04508	+	3.21644i	−0.0353708	+	0.108860i
$874$		0			0
$875$	11.1803	+	34.4095i	0.377964	+	1.16326i
$876$		0			0
$877$	1.77051	−	5.44907i	0.0597859	−	0.184002i	−0.916703	−	0.399569i	$-0.869160\pi$
$877$	1.77051	−	5.44907i	0.0597859	−	0.184002i	0.976489	+	0.215567i	$0.0691599\pi$
$878$		0			0
$879$	20.0623	+	14.5761i	0.676685	+	0.491640i
$880$		0			0
$881$	12.3820	−	8.99602i	0.417159	−	0.303084i	−0.359335	−	0.933209i	$-0.616996\pi$
$881$	12.3820	−	8.99602i	0.417159	−	0.303084i	0.776494	+	0.630125i	$0.216996\pi$
$882$		0			0
$883$	−16.0902	+	11.6902i	−0.541477	+	0.393406i	−0.824633	−	0.565668i	$-0.808619\pi$
$883$	−16.0902	+	11.6902i	−0.541477	+	0.393406i	0.283156	+	0.959074i	$0.408619\pi$
$884$		0			0
$885$	6.18034	+	19.0211i	0.207750	+	0.639388i
$886$		0			0
$887$	6.32624	+	19.4702i	0.212414	+	0.653744i	0.999327	+	0.0366797i	$0.0116781\pi$
$887$	6.32624	+	19.4702i	0.212414	+	0.653744i	−0.786913	+	0.617064i	$0.788322\pi$
$888$		0			0
$889$	17.4164	−	53.6022i	0.584128	−	1.79776i
$890$		0			0
$891$	−1.38197	−	4.25325i	−0.0462976	−	0.142489i
$892$		0			0
$893$	−1.75078			−0.0585875
$894$		0			0
$895$	51.7082			1.72841
$896$		0			0
$897$	−0.236068	−	0.171513i	−0.00788208	−	0.00572667i
$898$		0			0
$899$	−40.6525			−1.35584
$900$		0			0
$901$	−42.4853			−1.41539
$902$		0			0
$903$	−1.23607	−	0.898056i	−0.0411338	−	0.0298854i
$904$		0			0
$905$	11.8090	−	36.3444i	0.392545	−	1.20813i
$906$		0			0
$907$	−10.3607			−0.344021			−0.172010	−	0.985095i	$-0.555026\pi$
$907$	−10.3607			−0.344021			−0.172010	+	0.985095i	$0.555026\pi$
$908$		0			0
$909$	0.899187	+	2.76741i	0.0298241	+	0.0917893i
$910$		0			0
$911$	0.437694	−	1.34708i	0.0145015	−	0.0446309i	−0.943544	−	0.331247i	$-0.892531\pi$
$911$	0.437694	−	1.34708i	0.0145015	−	0.0446309i	0.958045	+	0.286616i	$0.0925305\pi$
$912$		0			0
$913$	18.9443	+	58.3045i	0.626964	+	1.92960i
$914$		0			0
$915$	−3.55573	+	10.9434i	−0.117549	+	0.361778i
$916$		0			0
$917$	−20.1803	+	14.6619i	−0.666414	+	0.484178i
$918$		0			0
$919$	−20.3262	+	14.7679i	−0.670501	+	0.487147i	−0.870193	−	0.492711i	$-0.836006\pi$
$919$	−20.3262	+	14.7679i	−0.670501	+	0.487147i	0.199692	+	0.979859i	$0.436006\pi$
$920$		0			0
$921$	14.8541	+	10.7921i	0.489459	+	0.355613i
$922$		0			0
$923$	−1.18034	+	3.63271i	−0.0388514	+	0.119572i
$924$		0			0
$925$	45.4508			1.49441
$926$		0			0
$927$	−4.85410	+	14.9394i	−0.159430	+	0.490674i
$928$		0			0
$929$	−1.79180	−	1.30182i	−0.0587869	−	0.0427112i	0.558004	−	0.829838i	$-0.311567\pi$
$929$	−1.79180	−	1.30182i	−0.0587869	−	0.0427112i	−0.616791	+	0.787127i	$0.711567\pi$
$930$		0			0
$931$	1.32624	−	0.963568i	0.0434657	−	0.0315797i
$932$		0			0
$933$	6.23607	−	4.53077i	0.204160	−	0.148331i
$934$		0			0
$935$	27.3607	+	19.8787i	0.894790	+	0.650103i
$936$		0			0
$937$	10.4828	+	32.2627i	0.342457	+	1.05398i	0.962931	+	0.269748i	$0.0869405\pi$
$937$	10.4828	+	32.2627i	0.342457	+	1.05398i	−0.620473	+	0.784227i	$0.713060\pi$
$938$		0			0
$939$	2.90983	−	8.95554i	0.0949587	−	0.292253i
$940$		0			0
$941$	4.31559	+	13.2820i	0.140684	+	0.432982i	0.996431	−	0.0844135i	$-0.0269016\pi$
$941$	4.31559	+	13.2820i	0.140684	+	0.432982i	−0.855746	+	0.517395i	$0.826902\pi$
$942$		0			0
$943$	−0.652476			−0.0212475
$944$		0			0
$945$	−2.23607	−	6.88191i	−0.0727393	−	0.223869i
$946$		0			0
$947$	33.2705	+	24.1724i	1.08115	+	0.785499i	0.977882	−	0.209155i	$-0.0670714\pi$
$947$	33.2705	+	24.1724i	1.08115	+	0.785499i	0.103264	+	0.994654i	$0.467071\pi$
$948$		0			0
$949$	−5.27051			−0.171088
$950$		0			0
$951$	−9.05573			−0.293652
$952$		0			0
$953$	9.44427	+	6.86167i	0.305930	+	0.222271i	0.730148	−	0.683289i	$-0.239451\pi$
$953$	9.44427	+	6.86167i	0.305930	+	0.222271i	−0.424218	+	0.905560i	$0.639451\pi$
$954$		0			0
$955$	22.8885	+	16.6295i	0.740656	+	0.538118i
$956$		0			0
$957$	−40.6525			−1.31411
$958$		0			0
$959$	10.5623	+	32.5074i	0.341075	+	1.04972i
$960$		0			0
$961$	−3.39919	+	10.4616i	−0.109651	+	0.337472i
$962$		0			0
$963$	−3.47214	−	10.6861i	−0.111888	−	0.344356i
$964$		0			0
$965$	5.69098	−	4.13474i	0.183199	−	0.133102i
$966$		0			0
$967$	28.9443	−	21.0292i	0.930785	−	0.676255i	−0.0153999	−	0.999881i	$-0.504902\pi$
$967$	28.9443	−	21.0292i	0.930785	−	0.676255i	0.946185	+	0.323627i	$0.104902\pi$
$968$		0			0
$969$	−1.29180	+	0.938545i	−0.0414985	+	0.0301504i
$970$		0			0
$971$	−1.85410	−	1.34708i	−0.0595010	−	0.0432300i	0.557637	−	0.830085i	$-0.311708\pi$
$971$	−1.85410	−	1.34708i	−0.0595010	−	0.0432300i	−0.617138	+	0.786855i	$0.711708\pi$
$972$		0			0
$973$	18.6525	−	57.4064i	0.597971	−	1.84037i
$974$		0			0
$975$	−1.54508	−	1.12257i	−0.0494823	−	0.0359510i
$976$		0			0
$977$	4.86068	−	14.9596i	0.155507	−	0.478601i	−0.842705	−	0.538376i	$-0.819038\pi$
$977$	4.86068	−	14.9596i	0.155507	−	0.478601i	0.998212	+	0.0597745i	$0.0190382\pi$
$978$		0			0
$979$	64.5967	+	46.9323i	2.06452	+	1.49996i
$980$		0			0
$981$	8.78115	−	6.37988i	0.280361	−	0.203694i
$982$		0			0
$983$	9.79837	−	7.11894i	0.312520	−	0.227059i	−0.420457	−	0.907312i	$-0.638130\pi$
$983$	9.79837	−	7.11894i	0.312520	−	0.227059i	0.732977	+	0.680254i	$0.238130\pi$
$984$		0			0
$985$	−0.450850			−0.0143653
$986$		0			0
$987$	−3.70820	−	11.4127i	−0.118033	−	0.363270i
$988$		0			0
$989$	−0.111456	+	0.343027i	−0.00354410	+	0.0109076i
$990$		0			0
$991$	−6.56231	−	20.1967i	−0.208459	−	0.641569i	−0.999554	−	0.0298762i	$-0.990489\pi$
$991$	−6.56231	−	20.1967i	−0.208459	−	0.641569i	0.791095	−	0.611693i	$-0.209511\pi$
$992$		0			0
$993$	−13.1246			−0.416497
$994$		0			0
$995$	−24.2705	+	17.6336i	−0.769427	+	0.559021i
$996$		0			0
$997$	−12.5623	−	9.12705i	−0.397852	−	0.289057i	0.370813	−	0.928707i	$-0.379079\pi$
$997$	−12.5623	−	9.12705i	−0.397852	−	0.289057i	−0.768666	+	0.639651i	$0.779079\pi$
$998$		0			0
$999$	−9.09017			−0.287600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.y.b.121.1	✓	4
25.6	even	5	inner	600.2.y.b.481.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.y.b.121.1	✓	4	1.1	even	1	trivial
600.2.y.b.481.1	yes	4	25.6	even	5	inner

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.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(-1.80902 + 1.31433i) q^{5} +3.23607 q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{3} +(-1.80902 + 1.31433i) q^{5} +3.23607 q^{7} +(0.309017 + 0.951057i) q^{9} +(-1.38197 + 4.25325i) q^{11} +(-0.118034 - 0.363271i) q^{13} -2.23607 q^{15} +(-2.73607 + 1.98787i) q^{17} +(0.381966 - 0.277515i) q^{19} +(2.61803 + 1.90211i) q^{21} +(0.236068 - 0.726543i) q^{23} +(1.54508 - 4.75528i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(7.35410 + 5.34307i) q^{29} +(-3.61803 + 2.62866i) q^{31} +(-3.61803 + 2.62866i) q^{33} +(-5.85410 + 4.25325i) q^{35} +(2.80902 + 8.64527i) q^{37} +(0.118034 - 0.363271i) q^{39} +(-0.263932 - 0.812299i) q^{41} -0.472136 q^{43} +(-1.80902 - 1.31433i) q^{45} +(-3.00000 - 2.17963i) q^{47} +3.47214 q^{49} -3.38197 q^{51} +(10.1631 + 7.38394i) q^{53} +(-3.09017 - 9.51057i) q^{55} +0.472136 q^{57} +(-2.76393 - 8.50651i) q^{59} +(1.59017 - 4.89404i) q^{61} +(1.00000 + 3.07768i) q^{63} +(0.690983 + 0.502029i) q^{65} +(-5.47214 + 3.97574i) q^{67} +(0.618034 - 0.449028i) q^{69} +(-8.09017 - 5.87785i) q^{71} +(4.26393 - 13.1230i) q^{73} +(4.04508 - 2.93893i) q^{75} +(-4.47214 + 13.7638i) q^{77} +(3.23607 + 2.35114i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(11.0902 - 8.05748i) q^{83} +(2.33688 - 7.19218i) q^{85} +(2.80902 + 8.64527i) q^{87} +(5.51722 - 16.9803i) q^{89} +(-0.381966 - 1.17557i) q^{91} -4.47214 q^{93} +(-0.326238 + 1.00406i) q^{95} +(2.73607 + 1.98787i) q^{97} -4.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 5 q^{5} + 4 q^{7} - q^{9}+O(q^{10}) \) 4 * q + q^3 - 5 * q^5 + 4 * q^7 - q^9	\( 4 q + q^{3} - 5 q^{5} + 4 q^{7} - q^{9} - 10 q^{11} + 4 q^{13} - 2 q^{17} + 6 q^{19} + 6 q^{21} - 8 q^{23} - 5 q^{25} + q^{27} + 16 q^{29} - 10 q^{31} - 10 q^{33} - 10 q^{35} + 9 q^{37} - 4 q^{39} - 10 q^{41} + 16 q^{43} - 5 q^{45} - 12 q^{47} - 4 q^{49} - 18 q^{51} + 25 q^{53} + 10 q^{55} - 16 q^{57} - 20 q^{59} - 16 q^{61} + 4 q^{63} + 5 q^{65} - 4 q^{67} - 2 q^{69} - 10 q^{71} + 26 q^{73} + 5 q^{75} + 4 q^{79} - q^{81} + 22 q^{83} + 25 q^{85} + 9 q^{87} - 7 q^{89} - 6 q^{91} + 30 q^{95} + 2 q^{97}+O(q^{100}) \) 4 * q + q^3 - 5 * q^5 + 4 * q^7 - q^9 - 10 * q^11 + 4 * q^13 - 2 * q^17 + 6 * q^19 + 6 * q^21 - 8 * q^23 - 5 * q^25 + q^27 + 16 * q^29 - 10 * q^31 - 10 * q^33 - 10 * q^35 + 9 * q^37 - 4 * q^39 - 10 * q^41 + 16 * q^43 - 5 * q^45 - 12 * q^47 - 4 * q^49 - 18 * q^51 + 25 * q^53 + 10 * q^55 - 16 * q^57 - 20 * q^59 - 16 * q^61 + 4 * q^63 + 5 * q^65 - 4 * q^67 - 2 * q^69 - 10 * q^71 + 26 * q^73 + 5 * q^75 + 4 * q^79 - q^81 + 22 * q^83 + 25 * q^85 + 9 * q^87 - 7 * q^89 - 6 * q^91 + 30 * q^95 + 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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