LMFDB - Embedded newform 512.2.k.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(17,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	512.49
Dual form			512.2.k.a.209.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.166619 - 1.69171i) q^{3} +(0.195184 + 0.104328i) q^{5} +(0.644963 - 3.24245i) q^{7} +(0.108228 - 0.0215280i) q^{9} +O(q^{10})$	\(q+(-0.166619 - 1.69171i) q^{3} +(0.195184 + 0.104328i) q^{5} +(0.644963 - 3.24245i) q^{7} +(0.108228 - 0.0215280i) q^{9} +(-0.522808 - 0.637044i) q^{11} +(1.80133 + 3.37005i) q^{13} +(0.143972 - 0.347579i) q^{15} +(-2.55951 - 6.17920i) q^{17} +(-0.480908 + 1.58534i) q^{19} +(-5.59275 - 0.550838i) q^{21} +(-2.58984 - 1.73048i) q^{23} +(-2.75064 - 4.11662i) q^{25} +(-1.53481 - 5.05961i) q^{27} +(2.96488 + 2.43321i) q^{29} +(3.93798 + 3.93798i) q^{31} +(-0.990584 + 0.990584i) q^{33} +(0.464165 - 0.565587i) q^{35} +(-5.58699 + 1.69479i) q^{37} +(5.40101 - 3.60884i) q^{39} +(5.11430 - 7.65409i) q^{41} +(-0.0922358 + 0.936486i) q^{43} +(0.0233705 + 0.00708935i) q^{45} +(-7.58571 + 3.14210i) q^{47} +(-3.63034 - 1.50373i) q^{49} +(-10.0270 + 5.35953i) q^{51} +(5.84937 - 4.80045i) q^{53} +(-0.0355823 - 0.178885i) q^{55} +(2.76207 + 0.549409i) q^{57} +(-0.316370 + 0.591888i) q^{59} +(5.53776 - 0.545421i) q^{61} -0.364810i q^{63} +0.845710i q^{65} +(-11.7223 + 1.15455i) q^{67} +(-2.49595 + 4.66960i) q^{69} +(13.2927 + 2.64409i) q^{71} +(1.38356 + 6.95562i) q^{73} +(-6.50583 + 5.33920i) q^{75} +(-2.40277 + 1.28431i) q^{77} +(14.4395 + 5.98105i) q^{79} +(-7.99782 + 3.31281i) q^{81} +(1.58555 + 0.480972i) q^{83} +(0.145089 - 1.47311i) q^{85} +(3.62229 - 5.42114i) q^{87} +(6.28752 - 4.20119i) q^{89} +(12.0890 - 3.66716i) q^{91} +(6.00578 - 7.31807i) q^{93} +(-0.259261 + 0.259261i) q^{95} +(11.8042 + 11.8042i) q^{97} +(-0.0702969 - 0.0576912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{5}{32}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.166619	−	1.69171i	−0.0961976	−	0.976710i	−0.915222	−	0.402951i	$-0.867984\pi$
$3$	−0.166619	−	1.69171i	−0.0961976	−	0.976710i	0.819024	−	0.573759i	$-0.194516\pi$
$4$		0			0
$5$	0.195184	+	0.104328i	0.0872891	+	0.0466570i	0.514464	−	0.857512i	$-0.327991\pi$
$5$	0.195184	+	0.104328i	0.0872891	+	0.0466570i	−0.427175	+	0.904169i	$0.640491\pi$
$6$		0			0
$7$	0.644963	−	3.24245i	0.243773	−	1.22553i	−0.643919	−	0.765093i	$-0.722693\pi$
$7$	0.644963	−	3.24245i	0.243773	−	1.22553i	0.887692	−	0.460437i	$-0.152307\pi$
$8$		0			0
$9$	0.108228	−	0.0215280i	0.0360761	−	0.00717599i
$10$		0			0
$11$	−0.522808	−	0.637044i	−0.157633	−	0.192076i	0.688205	−	0.725516i	$-0.258399\pi$
$11$	−0.522808	−	0.637044i	−0.157633	−	0.192076i	−0.845838	+	0.533440i	$0.820899\pi$
$12$		0			0
$13$	1.80133	+	3.37005i	0.499598	+	0.934683i	0.997714	+	0.0675725i	$0.0215254\pi$
$13$	1.80133	+	3.37005i	0.499598	+	0.934683i	−0.498116	+	0.867110i	$0.665975\pi$
$14$		0			0
$15$	0.143972	−	0.347579i	0.0371734	−	0.0897444i
$16$		0			0
$17$	−2.55951	−	6.17920i	−0.620772	−	1.49868i	−0.850798	−	0.525492i	$-0.823881\pi$
$17$	−2.55951	−	6.17920i	−0.620772	−	1.49868i	0.230026	−	0.973184i	$-0.426119\pi$
$18$		0			0
$19$	−0.480908	+	1.58534i	−0.110328	+	0.363702i	−0.994666	−	0.103144i	$-0.967110\pi$
$19$	−0.480908	+	1.58534i	−0.110328	+	0.363702i	0.884339	+	0.466846i	$0.154610\pi$
$20$		0			0
$21$	−5.59275	−	0.550838i	−1.22044	−	0.120203i
$22$		0			0
$23$	−2.58984	−	1.73048i	−0.540019	−	0.360829i	0.255451	−	0.966822i	$-0.417776\pi$
$23$	−2.58984	−	1.73048i	−0.540019	−	0.360829i	−0.795470	+	0.605993i	$0.792776\pi$
$24$		0			0
$25$	−2.75064	−	4.11662i	−0.550128	−	0.823324i
$26$		0			0
$27$	−1.53481	−	5.05961i	−0.295375	−	0.973722i
$28$		0			0
$29$	2.96488	+	2.43321i	0.550564	+	0.451836i	0.868085	−	0.496415i	$-0.165350\pi$
$29$	2.96488	+	2.43321i	0.550564	+	0.451836i	−0.317521	+	0.948251i	$0.602850\pi$
$30$		0			0
$31$	3.93798	+	3.93798i	0.707282	+	0.707282i	0.965963	−	0.258681i	$-0.0832878\pi$
$31$	3.93798	+	3.93798i	0.707282	+	0.707282i	−0.258681	+	0.965963i	$0.583288\pi$
$32$		0			0
$33$	−0.990584	+	0.990584i	−0.172439	+	0.172439i
$34$		0			0
$35$	0.464165	−	0.565587i	0.0784583	−	0.0956017i
$36$		0			0
$37$	−5.58699	+	1.69479i	−0.918495	+	0.278622i	−0.713919	−	0.700228i	$-0.753082\pi$
$37$	−5.58699	+	1.69479i	−0.918495	+	0.278622i	−0.204576	+	0.978851i	$0.565582\pi$
$38$		0			0
$39$	5.40101	−	3.60884i	0.864854	−	0.577877i
$40$		0			0
$41$	5.11430	−	7.65409i	0.798719	−	1.19537i	−0.178668	−	0.983909i	$-0.557179\pi$
$41$	5.11430	−	7.65409i	0.798719	−	1.19537i	0.977387	−	0.211458i	$-0.0678212\pi$
$42$		0			0
$43$	−0.0922358	+	0.936486i	−0.0140658	+	0.142813i	−0.999653	−	0.0263581i	$-0.991609\pi$
$43$	−0.0922358	+	0.936486i	−0.0140658	+	0.142813i	0.985587	+	0.169171i	$0.0541090\pi$
$44$		0			0
$45$	0.0233705	+	0.00708935i	0.00348386	+	0.00105682i
$46$		0			0
$47$	−7.58571	+	3.14210i	−1.10649	+	0.458323i	−0.859727	−	0.510753i	$-0.829366\pi$
$47$	−7.58571	+	3.14210i	−1.10649	+	0.458323i	−0.246762	+	0.969076i	$0.579366\pi$
$48$		0			0
$49$	−3.63034	−	1.50373i	−0.518620	−	0.214819i
$50$		0			0
$51$	−10.0270	+	5.35953i	−1.40406	+	0.750484i
$52$		0			0
$53$	5.84937	−	4.80045i	0.803473	−	0.659393i	−0.140255	−	0.990115i	$-0.544792\pi$
$53$	5.84937	−	4.80045i	0.803473	−	0.659393i	0.943728	+	0.330722i	$0.107292\pi$
$54$		0			0
$55$	−0.0355823	−	0.178885i	−0.00479792	−	0.0241208i
$56$		0			0
$57$	2.76207	+	0.549409i	0.365845	+	0.0727710i
$58$		0			0
$59$	−0.316370	+	0.591888i	−0.0411879	+	0.0770572i	−0.901673	−	0.432418i	$-0.857660\pi$
$59$	−0.316370	+	0.591888i	−0.0411879	+	0.0770572i	0.860485	+	0.509475i	$0.170160\pi$
$60$		0			0
$61$	5.53776	−	0.545421i	0.709037	−	0.0698341i	0.262932	−	0.964814i	$-0.415311\pi$
$61$	5.53776	−	0.545421i	0.709037	−	0.0698341i	0.446105	+	0.894980i	$0.352811\pi$
$62$		0			0
$63$		−	0.364810i		−	0.0459617i
$64$		0			0
$65$			0.845710i			0.104897i
$66$		0			0
$67$	−11.7223	+	1.15455i	−1.43211	+	0.141050i	−0.784125	−	0.620603i	$-0.786888\pi$
$67$	−11.7223	+	1.15455i	−1.43211	+	0.141050i	−0.647984	+	0.761654i	$0.724388\pi$
$68$		0			0
$69$	−2.49595	+	4.66960i	−0.300477	+	0.562153i
$70$		0			0
$71$	13.2927	+	2.64409i	1.57756	+	0.313795i	0.904723	−	0.426000i	$-0.140078\pi$
$71$	13.2927	+	2.64409i	1.57756	+	0.313795i	0.672832	+	0.739795i	$0.265078\pi$
$72$		0			0
$73$	1.38356	+	6.95562i	0.161933	+	0.814093i	0.973297	+	0.229551i	$0.0737258\pi$
$73$	1.38356	+	6.95562i	0.161933	+	0.814093i	−0.811363	+	0.584542i	$0.801274\pi$
$74$		0			0
$75$	−6.50583	+	5.33920i	−0.751228	+	0.616517i
$76$		0			0
$77$	−2.40277	+	1.28431i	−0.273821	+	0.146361i
$78$		0			0
$79$	14.4395	+	5.98105i	1.62457	+	0.672921i	0.994608	−	0.103701i	$-0.0330686\pi$
$79$	14.4395	+	5.98105i	1.62457	+	0.672921i	0.629966	+	0.776622i	$0.283069\pi$
$80$		0			0
$81$	−7.99782	+	3.31281i	−0.888647	+	0.368089i
$82$		0			0
$83$	1.58555	+	0.480972i	0.174037	+	0.0527935i	0.376100	−	0.926579i	$-0.377265\pi$
$83$	1.58555	+	0.480972i	0.174037	+	0.0527935i	−0.202064	+	0.979372i	$0.564765\pi$
$84$		0			0
$85$	0.145089	−	1.47311i	0.0157371	−	0.159781i
$86$		0			0
$87$	3.62229	−	5.42114i	0.388350	−	0.581207i
$88$		0			0
$89$	6.28752	−	4.20119i	0.666476	−	0.445325i	−0.175761	−	0.984433i	$-0.556239\pi$
$89$	6.28752	−	4.20119i	0.666476	−	0.445325i	0.842237	+	0.539108i	$0.181239\pi$
$90$		0			0
$91$	12.0890	−	3.66716i	1.26727	−	0.384422i
$92$		0			0
$93$	6.00578	−	7.31807i	0.622771	−	0.758848i
$94$		0			0
$95$	−0.259261	+	0.259261i	−0.0265996	+	0.0265996i
$96$		0			0
$97$	11.8042	+	11.8042i	1.19853	+	1.19853i	0.974605	+	0.223929i	$0.0718885\pi$
$97$	11.8042	+	11.8042i	1.19853	+	1.19853i	0.223929	+	0.974605i	$0.428112\pi$
$98$		0			0
$99$	−0.0702969	−	0.0576912i	−0.00706511	−	0.00579818i
$100$		0			0
$101$	−0.541479	−	1.78502i	−0.0538792	−	0.177616i	0.925871	−	0.377840i	$-0.123333\pi$
$101$	−0.541479	−	1.78502i	−0.0538792	−	0.177616i	−0.979750	+	0.200224i	$0.935833\pi$
$102$		0			0
$103$	−2.27883	−	3.41052i	−0.224540	−	0.336048i	0.702045	−	0.712132i	$-0.252270\pi$
$103$	−2.27883	−	3.41052i	−0.224540	−	0.336048i	−0.926586	+	0.376084i	$0.877270\pi$
$104$		0			0
$105$	−1.03415	−	0.690997i	−0.100923	−	0.0674344i
$106$		0			0
$107$	18.9422	+	1.86564i	1.83121	+	0.180358i	0.954010	−	0.299773i	$-0.0969110\pi$
$107$	18.9422	+	1.86564i	1.83121	+	0.180358i	0.877197	+	0.480131i	$0.159411\pi$
$108$		0			0
$109$	−4.68109	+	15.4315i	−0.448367	+	1.47807i	0.383735	+	0.923443i	$0.374638\pi$
$109$	−4.68109	+	15.4315i	−0.448367	+	1.47807i	−0.832101	+	0.554624i	$0.812862\pi$
$110$		0			0
$111$	3.79800	+	9.16919i	0.360490	+	0.870301i
$112$		0			0
$113$	−4.43804	+	10.7144i	−0.417496	+	1.00792i	0.565575	+	0.824697i	$0.308654\pi$
$113$	−4.43804	+	10.7144i	−0.417496	+	1.00792i	−0.983071	+	0.183227i	$0.941346\pi$
$114$		0			0
$115$	−0.324959	−	0.607955i	−0.0303026	−	0.0566921i
$116$		0			0
$117$	0.267505	+	0.325956i	0.0247309	+	0.0301346i
$118$		0			0
$119$	−21.6865	+	4.31372i	−1.98800	+	0.395438i
$120$		0			0
$121$	2.01350	−	10.1225i	0.183045	−	0.920230i
$122$		0			0
$123$	−13.8007	−	7.37660i	−1.24436	−	0.665126i
$124$		0			0
$125$	−0.215866	−	2.19173i	−0.0193077	−	0.196034i
$126$		0			0
$127$	2.34874			0.208417			0.104209	−	0.994555i	$-0.466769\pi$
$127$	2.34874			0.208417			0.104209	+	0.994555i	$0.466769\pi$
$128$		0			0
$129$	1.59963			0.140840
$130$		0			0
$131$	−0.477724	−	4.85041i	−0.0417389	−	0.423783i	−0.993235	−	0.116122i	$-0.962954\pi$
$131$	−0.477724	−	4.85041i	−0.0417389	−	0.423783i	0.951496	−	0.307661i	$-0.0995462\pi$
$132$		0			0
$133$	4.83022	+	2.58180i	0.418833	+	0.223871i
$134$		0			0
$135$	0.228288	−	1.14768i	0.0196479	−	0.0987766i
$136$		0			0
$137$	−7.34848	+	1.46170i	−0.627823	+	0.124882i	−0.498739	−	0.866752i	$-0.666204\pi$
$137$	−7.34848	+	1.46170i	−0.627823	+	0.124882i	−0.129084	+	0.991634i	$0.541204\pi$
$138$		0			0
$139$	14.5785	+	17.7640i	1.23653	+	1.50672i	0.791452	+	0.611231i	$0.209325\pi$
$139$	14.5785	+	17.7640i	1.23653	+	1.50672i	0.445082	+	0.895490i	$0.353175\pi$
$140$		0			0
$141$	6.57946	+	12.3093i	0.554090	+	1.03663i
$142$		0			0
$143$	1.20512	−	2.90941i	0.100777	−	0.243297i
$144$		0			0
$145$	0.324845	+	0.784246i	0.0269769	+	0.0651281i
$146$		0			0
$147$	−1.93900	+	6.39204i	−0.159926	+	0.527206i
$148$		0			0
$149$	−13.2615	−	1.30614i	−1.08642	−	0.107003i	−0.461083	−	0.887357i	$-0.652539\pi$
$149$	−13.2615	−	1.30614i	−1.08642	−	0.107003i	−0.625338	+	0.780354i	$0.715039\pi$
$150$		0			0
$151$	−1.52898	−	1.02163i	−0.124427	−	0.0831393i	0.491800	−	0.870708i	$-0.336339\pi$
$151$	−1.52898	−	1.02163i	−0.124427	−	0.0831393i	−0.616226	+	0.787569i	$0.711339\pi$
$152$		0			0
$153$	−0.410037	−	0.613664i	−0.0331496	−	0.0496118i
$154$		0			0
$155$	0.357790	+	1.17947i	0.0287383	+	0.0947376i
$156$		0			0
$157$	13.5924	+	11.1550i	1.08479	+	0.890267i	0.994405	−	0.105639i	$-0.0336889\pi$
$157$	13.5924	+	11.1550i	1.08479	+	0.890267i	0.0903892	+	0.995907i	$0.471189\pi$
$158$		0			0
$159$	−9.09560	−	9.09560i	−0.721328	−	0.721328i
$160$		0			0
$161$	−7.28133	+	7.28133i	−0.573849	+	0.573849i
$162$		0			0
$163$	12.9274	−	15.7521i	1.01255	−	1.23380i	0.0404666	−	0.999181i	$-0.487116\pi$
$163$	12.9274	−	15.7521i	1.01255	−	1.23380i	0.972087	−	0.234620i	$-0.0753845\pi$
$164$		0			0
$165$	−0.296692	+	0.0900007i	−0.0230975	+	0.00700654i
$166$		0			0
$167$	−13.0212	+	8.70048i	−1.00761	+	0.673264i	−0.945775	−	0.324823i	$-0.894695\pi$
$167$	−13.0212	+	8.70048i	−1.00761	+	0.673264i	−0.0618354	+	0.998086i	$0.519695\pi$
$168$		0			0
$169$	−0.890023	+	1.33201i	−0.0684633	+	0.102463i
$170$		0			0
$171$	−0.0179187	+	0.181932i	−0.00137028	+	0.0139127i
$172$		0			0
$173$	−22.0817	−	6.69841i	−1.67884	−	0.509270i	−0.700042	−	0.714101i	$-0.746836\pi$
$173$	−22.0817	−	6.69841i	−1.67884	−	0.509270i	−0.978797	+	0.204831i	$0.934336\pi$
$174$		0			0
$175$	−15.1220	+	6.26373i	−1.14312	+	0.473494i
$176$		0			0
$177$	1.05402	+	0.436588i	0.0792247	+	0.0328160i
$178$		0			0
$179$	0.313667	−	0.167659i	0.0234446	−	0.0125314i	−0.459633	−	0.888109i	$-0.652019\pi$
$179$	0.313667	−	0.167659i	0.0234446	−	0.0125314i	0.483077	+	0.875578i	$0.339519\pi$
$180$		0			0
$181$	6.76115	−	5.54873i	0.502552	−	0.412434i	−0.348665	−	0.937247i	$-0.613365\pi$
$181$	6.76115	−	5.54873i	0.502552	−	0.412434i	0.851217	+	0.524813i	$0.175865\pi$
$182$		0			0
$183$	−1.84539	−	9.27741i	−0.136415	−	0.685806i
$184$		0			0
$185$	−1.26731	−	0.252083i	−0.0931742	−	0.0185335i
$186$		0			0
$187$	−2.59829	+	4.86106i	−0.190006	+	0.355476i
$188$		0			0
$189$	−17.3954	+	1.71330i	−1.26533	+	0.124624i
$190$		0			0
$191$			0.247250i			0.0178904i	0.999960	+	0.00894518i	$0.00284738\pi$
$191$			0.247250i			0.0178904i	−0.999960	+	0.00894518i	$0.997153\pi$
$192$		0			0
$193$		−	5.65108i		−	0.406774i	−0.979098	−	0.203387i	$-0.934805\pi$
$193$		−	5.65108i		−	0.406774i	0.979098	−	0.203387i	$-0.0651949\pi$
$194$		0			0
$195$	1.43070	−	0.140911i	0.102454	−	0.0100909i
$196$		0			0
$197$	4.39882	−	8.22962i	0.313403	−	0.586336i	−0.675066	−	0.737757i	$-0.735885\pi$
$197$	4.39882	−	8.22962i	0.313403	−	0.586336i	0.988469	+	0.151421i	$0.0483849\pi$
$198$		0			0
$199$	−0.826820	−	0.164465i	−0.0586117	−	0.0116586i	0.165697	−	0.986177i	$-0.447013\pi$
$199$	−0.826820	−	0.164465i	−0.0586117	−	0.0116586i	−0.224309	+	0.974518i	$0.572013\pi$
$200$		0			0
$201$	3.90632	+	19.6384i	0.275531	+	1.38519i
$202$		0			0
$203$	9.80181	−	8.04414i	0.687952	−	0.564588i
$204$		0			0
$205$	1.79677	−	0.960392i	0.125492	−	0.0670767i
$206$		0			0
$207$	−0.317548	−	0.131533i	−0.0220711	−	0.00914215i
$208$		0			0
$209$	1.26135	−	0.522470i	0.0872496	−	0.0361400i
$210$		0			0
$211$	−10.5462	−	3.19915i	−0.726028	−	0.220238i	−0.0944271	−	0.995532i	$-0.530102\pi$
$211$	−10.5462	−	3.19915i	−0.726028	−	0.220238i	−0.631601	+	0.775294i	$0.717602\pi$
$212$		0			0
$213$	2.25821	−	22.9280i	0.154730	−	1.57100i
$214$		0			0
$215$	−0.115705	+	0.173164i	−0.00789100	+	0.0118097i
$216$		0			0
$217$	15.3085	−	10.2288i	1.03921	−	0.694379i
$218$		0			0
$219$	11.5364	−	3.49952i	0.779556	−	0.236476i
$220$		0			0
$221$	16.2137	−	19.7564i	1.09065	−	1.32896i
$222$		0			0
$223$	8.66668	−	8.66668i	0.580364	−	0.580364i	−0.354639	−	0.935003i	$-0.615396\pi$
$223$	8.66668	−	8.66668i	0.580364	−	0.580364i	0.935003	+	0.354639i	$0.115396\pi$
$224$		0			0
$225$	−0.386320	−	0.386320i	−0.0257546	−	0.0257546i
$226$		0			0
$227$	8.41899	+	6.90929i	0.558788	+	0.458585i	0.870900	−	0.491460i	$-0.163537\pi$
$227$	8.41899	+	6.90929i	0.558788	+	0.458585i	−0.312112	+	0.950045i	$0.601037\pi$
$228$		0			0
$229$	4.71273	+	15.5358i	0.311426	+	1.02663i	0.963327	+	0.268330i	$0.0864717\pi$
$229$	4.71273	+	15.5358i	0.311426	+	1.02663i	−0.651901	+	0.758304i	$0.726028\pi$
$230$		0			0
$231$	2.57303	+	3.85081i	0.169293	+	0.253365i
$232$		0			0
$233$	−14.3058	−	9.55886i	−0.937207	−	0.626222i	−0.00967027	−	0.999953i	$-0.503078\pi$
$233$	−14.3058	−	9.55886i	−0.937207	−	0.626222i	−0.927537	+	0.373731i	$0.878078\pi$
$234$		0			0
$235$	−1.80842	−	0.178114i	−0.117968	−	0.0116189i
$236$		0			0
$237$	7.71232	−	25.4241i	0.500969	−	1.65147i
$238$		0			0
$239$	0.702155	+	1.69515i	0.0454186	+	0.109650i	0.944961	−	0.327184i	$-0.106100\pi$
$239$	0.702155	+	1.69515i	0.0454186	+	0.109650i	−0.899542	+	0.436834i	$0.856100\pi$
$240$		0			0
$241$	−2.19857	+	5.30782i	−0.141622	+	0.341907i	−0.978736	−	0.205122i	$-0.934241\pi$
$241$	−2.19857	+	5.30782i	−0.141622	+	0.341907i	0.837114	+	0.547028i	$0.184241\pi$
$242$		0			0
$243$	−0.540309	−	1.01085i	−0.0346609	−	0.0648459i
$244$		0			0
$245$	−0.551703	−	0.672252i	−0.0352470	−	0.0429486i
$246$		0			0
$247$	−6.20894	+	1.23504i	−0.395066	+	0.0785834i
$248$		0			0
$249$	0.549482	−	2.76243i	0.0348220	−	0.175062i
$250$		0			0
$251$	−5.02570	−	2.68629i	−0.317220	−	0.169557i	0.305101	−	0.952320i	$-0.401310\pi$
$251$	−5.02570	−	2.68629i	−0.317220	−	0.169557i	−0.622320	+	0.782763i	$0.713810\pi$
$252$		0			0
$253$	0.251601	+	2.55455i	0.0158180	+	0.160603i
$254$		0			0
$255$	−2.51626			−0.157574
$256$		0			0
$257$	24.8880			1.55247			0.776237	−	0.630442i	$-0.217126\pi$
$257$	24.8880			1.55247			0.776237	+	0.630442i	$0.217126\pi$
$258$		0			0
$259$	1.89188	+	19.2086i	0.117556	+	1.19356i
$260$		0			0
$261$	0.373266	+	0.199515i	0.0231046	+	0.0123497i
$262$		0			0
$263$	2.20391	−	11.0798i	0.135899	−	0.683211i	−0.851423	−	0.524480i	$-0.824260\pi$
$263$	2.20391	−	11.0798i	0.135899	−	0.683211i	0.987322	−	0.158731i	$-0.0507402\pi$
$264$		0			0
$265$	1.64253	−	0.326719i	0.100900	−	0.0200702i
$266$		0			0
$267$	−8.15482	−	9.93667i	−0.499067	−	0.608115i
$268$		0			0
$269$	−13.9234	−	26.0489i	−0.848925	−	1.58823i	−0.808089	−	0.589061i	$-0.799498\pi$
$269$	−13.9234	−	26.0489i	−0.848925	−	1.58823i	−0.0408364	−	0.999166i	$-0.513002\pi$
$270$		0			0
$271$	−5.82085	+	14.0528i	−0.353591	+	0.853645i	0.642580	+	0.766219i	$0.277864\pi$
$271$	−5.82085	+	14.0528i	−0.353591	+	0.853645i	−0.996171	+	0.0874259i	$0.972136\pi$
$272$		0			0
$273$	−8.21803	−	19.8401i	−0.497378	−	1.20078i
$274$		0			0
$275$	−1.18441	+	3.90448i	−0.0714227	+	0.235449i
$276$		0			0
$277$	−20.4107	−	2.01028i	−1.22636	−	0.120786i	−0.535978	−	0.844232i	$-0.680057\pi$
$277$	−20.4107	−	2.01028i	−1.22636	−	0.120786i	−0.690381	+	0.723446i	$0.742557\pi$
$278$		0			0
$279$	0.510978	+	0.341424i	0.0305914	+	0.0204405i
$280$		0			0
$281$	6.65174	+	9.95503i	0.396809	+	0.593867i	0.975046	−	0.222002i	$-0.0712591\pi$
$281$	6.65174	+	9.95503i	0.396809	+	0.593867i	−0.578237	+	0.815869i	$0.696259\pi$
$282$		0			0
$283$	0.565398	+	1.86387i	0.0336094	+	0.110795i	0.972140	−	0.234400i	$-0.0753126\pi$
$283$	0.565398	+	1.86387i	0.0336094	+	0.110795i	−0.938531	+	0.345196i	$0.887813\pi$
$284$		0			0
$285$	0.481793	+	0.395398i	0.0285390	+	0.0234213i
$286$		0			0
$287$	−21.5195	−	21.5195i	−1.27025	−	1.27025i
$288$		0			0
$289$	−19.6106	+	19.6106i	−1.15357	+	1.15357i
$290$		0			0
$291$	18.0025	−	21.9361i	1.05533	−	1.28592i
$292$		0			0
$293$	6.75779	−	2.04995i	0.394795	−	0.119760i	−0.0866443	−	0.996239i	$-0.527614\pi$
$293$	6.75779	−	2.04995i	0.394795	−	0.119760i	0.481439	+	0.876480i	$0.340114\pi$
$294$		0			0
$295$	−0.123501	+	0.0825208i	−0.00719051	+	0.00480455i
$296$		0			0
$297$	−2.42078	+	3.62295i	−0.140468	+	0.210225i
$298$		0			0
$299$	1.16663	−	11.8450i	0.0674682	−	0.685016i
$300$		0			0
$301$	2.97702	+	0.903068i	0.171592	+	0.0520520i
$302$		0			0
$303$	−2.92951	+	1.21344i	−0.168296	+	0.0697106i
$304$		0			0
$305$	1.13779	+	0.471286i	0.0651494	+	0.0269858i
$306$		0			0
$307$	−7.39409	+	3.95222i	−0.422003	+	0.225565i	−0.668708	−	0.743525i	$-0.733152\pi$
$307$	−7.39409	+	3.95222i	−0.422003	+	0.225565i	0.246705	+	0.969091i	$0.420652\pi$
$308$		0			0
$309$	−5.38992	+	4.42339i	−0.306622	+	0.251638i
$310$		0			0
$311$	4.92192	+	24.7442i	0.279096	+	1.40311i	0.824938	+	0.565224i	$0.191210\pi$
$311$	4.92192	+	24.7442i	0.279096	+	1.40311i	−0.545841	+	0.837888i	$0.683790\pi$
$312$		0			0
$313$	−25.9352	−	5.15884i	−1.46595	−	0.291595i	−0.603345	−	0.797480i	$-0.706166\pi$
$313$	−25.9352	−	5.15884i	−1.46595	−	0.291595i	−0.862601	+	0.505885i	$0.831166\pi$
$314$		0			0
$315$	0.0380599	−	0.0712051i	0.00214443	−	0.00401195i
$316$		0			0
$317$	−7.53596	+	0.742227i	−0.423262	+	0.0416876i	−0.307406	−	0.951578i	$-0.599461\pi$
$317$	−7.53596	+	0.742227i	−0.423262	+	0.0416876i	−0.115856	+	0.993266i	$0.536961\pi$
$318$		0			0
$319$		−	3.16086i		−	0.176974i
$320$		0			0
$321$		−	32.3555i		−	1.80591i
$322$		0			0
$323$	11.0270	−	1.08607i	0.613560	−	0.0604304i
$324$		0			0
$325$	8.91841	−	16.6852i	0.494704	−	0.925526i
$326$		0			0
$327$	26.8856	+	5.34787i	1.48678	+	0.295738i
$328$		0			0
$329$	5.29560	+	26.6228i	0.291956	+	1.46776i
$330$		0			0
$331$	−1.93625	+	1.58904i	−0.106426	+	0.0873415i	−0.686101	−	0.727506i	$-0.740679\pi$
$331$	−1.93625	+	1.58904i	−0.106426	+	0.0873415i	0.579675	+	0.814847i	$0.303179\pi$
$332$		0			0
$333$	−0.568185	+	0.303701i	−0.0311364	+	0.0166427i
$334$		0			0
$335$	−2.40846	−	0.997619i	−0.131588	−	0.0545057i
$336$		0			0
$337$	−1.52912	+	0.633380i	−0.0832962	+	0.0345024i	−0.423943	−	0.905689i	$-0.639354\pi$
$337$	−1.52912	+	0.633380i	−0.0832962	+	0.0345024i	0.340646	+	0.940192i	$0.389354\pi$
$338$		0			0
$339$	18.8651	+	5.72266i	1.02461	+	0.310812i
$340$		0			0
$341$	0.449857	−	4.56747i	0.0243611	−	0.247342i
$342$		0			0
$343$	5.63968	−	8.44038i	0.304514	−	0.455738i
$344$		0			0
$345$	−0.974341	+	0.651034i	−0.0524567	+	0.0350505i
$346$		0			0
$347$	−21.5337	+	6.53217i	−1.15599	+	0.350665i	−0.809346	−	0.587332i	$-0.800178\pi$
$347$	−21.5337	+	6.53217i	−1.15599	+	0.350665i	−0.346643	+	0.937997i	$0.612678\pi$
$348$		0			0
$349$	−4.88505	+	5.95245i	−0.261491	+	0.318627i	−0.887161	−	0.461460i	$-0.847326\pi$
$349$	−4.88505	+	5.95245i	−0.261491	+	0.318627i	0.625670	+	0.780088i	$0.284826\pi$
$350$		0			0
$351$	14.2864	−	14.2864i	0.762552	−	0.762552i
$352$		0			0
$353$	1.98662	+	1.98662i	0.105737	+	0.105737i	0.757996	−	0.652259i	$-0.226179\pi$
$353$	1.98662	+	1.98662i	0.105737	+	0.105737i	−0.652259	+	0.757996i	$0.726179\pi$
$354$		0			0
$355$	2.31868	+	1.90289i	0.123063	+	0.100995i
$356$		0			0
$357$	10.9110	+	35.9686i	0.577469	+	1.90366i
$358$		0			0
$359$	−13.3605	−	19.9954i	−0.705139	−	1.05531i	−0.995157	−	0.0982937i	$-0.968662\pi$
$359$	−13.3605	−	19.9954i	−0.705139	−	1.05531i	0.290019	−	0.957021i	$-0.406338\pi$
$360$		0			0
$361$	13.5159	+	9.03103i	0.711363	+	0.475317i
$362$		0			0
$363$	−17.4599	−	1.71965i	−0.916407	−	0.0902582i
$364$		0			0
$365$	−0.455618	+	1.50197i	−0.0238481	+	0.0786168i
$366$		0			0
$367$	−1.68697	−	4.07271i	−0.0880593	−	0.212594i	0.873715	−	0.486439i	$-0.161704\pi$
$367$	−1.68697	−	4.07271i	−0.0880593	−	0.212594i	−0.961774	+	0.273845i	$0.911704\pi$
$368$		0			0
$369$	0.388735	−	0.938490i	0.0202368	−	0.0488558i
$370$		0			0
$371$	−11.7926	−	22.0624i	−0.612241	−	1.14542i
$372$		0			0
$373$	1.20223	+	1.46493i	0.0622493	+	0.0758510i	0.803204	−	0.595704i	$-0.203127\pi$
$373$	1.20223	+	1.46493i	0.0622493	+	0.0758510i	−0.740955	+	0.671555i	$0.765627\pi$
$374$		0			0
$375$	−3.67180	+	0.730367i	−0.189611	+	0.0377160i
$376$		0			0
$377$	−2.85933	+	14.3748i	−0.147263	+	0.740340i
$378$		0			0
$379$	−27.1607	−	14.5177i	−1.39515	−	0.745725i	−0.409153	−	0.912466i	$-0.634176\pi$
$379$	−27.1607	−	14.5177i	−1.39515	−	0.745725i	−0.986001	+	0.166741i	$0.946676\pi$
$380$		0			0
$381$	−0.391345	−	3.97340i	−0.0200492	−	0.203563i
$382$		0			0
$383$	−3.10397			−0.158606			−0.0793028	−	0.996851i	$-0.525269\pi$
$383$	−3.10397			−0.158606			−0.0793028	+	0.996851i	$0.525269\pi$
$384$		0			0
$385$	−0.602973			−0.0307304
$386$		0			0
$387$	0.0101781	+	0.103340i	0.000517382	+	0.00525307i
$388$		0			0
$389$	−0.523215	−	0.279664i	−0.0265281	−	0.0141796i	0.458079	−	0.888911i	$-0.348538\pi$
$389$	−0.523215	−	0.279664i	−0.0265281	−	0.0141796i	−0.484607	+	0.874732i	$0.661038\pi$
$390$		0			0
$391$	−4.06424	+	20.4323i	−0.205538	+	1.03331i
$392$		0			0
$393$	−8.12590	+	1.61634i	−0.409898	+	0.0815337i
$394$		0			0
$395$	2.19438	+	2.67386i	0.110411	+	0.134536i
$396$		0			0
$397$	13.0571	+	24.4282i	0.655318	+	1.22601i	0.961700	+	0.274106i	$0.0883818\pi$
$397$	13.0571	+	24.4282i	0.655318	+	1.22601i	−0.306381	+	0.951909i	$0.599118\pi$
$398$		0			0
$399$	3.56286	−	8.60151i	0.178366	−	0.430614i
$400$		0			0
$401$	−0.575782	−	1.39006i	−0.0287532	−	0.0694163i	0.908851	−	0.417121i	$-0.136961\pi$
$401$	−0.575782	−	1.39006i	−0.0287532	−	0.0694163i	−0.937604	+	0.347705i	$0.886961\pi$
$402$		0			0
$403$	−6.17758	+	20.3648i	−0.307727	+	1.01444i
$404$		0			0
$405$	−1.90667	−	0.187790i	−0.0947431	−	0.00933138i
$406$		0			0
$407$	4.00058	+	2.67310i	0.198301	+	0.132501i
$408$		0			0
$409$	4.77619	+	7.14807i	0.236167	+	0.353450i	0.930555	−	0.366151i	$-0.119325\pi$
$409$	4.77619	+	7.14807i	0.236167	+	0.353450i	−0.694388	+	0.719601i	$0.744325\pi$
$410$		0			0
$411$	3.69718	+	12.1880i	0.182368	+	0.601188i
$412$		0			0
$413$	1.71512	+	1.40756i	0.0843954	+	0.0692615i
$414$		0			0
$415$	0.259296	+	0.259296i	0.0127283	+	0.0127283i
$416$		0			0
$417$	27.6225	−	27.6225i	1.35268	−	1.35268i
$418$		0			0
$419$	5.90657	−	7.19718i	0.288555	−	0.351605i	−0.608477	−	0.793572i	$-0.708219\pi$
$419$	5.90657	−	7.19718i	0.288555	−	0.351605i	0.897032	+	0.441967i	$0.145719\pi$
$420$		0			0
$421$	−9.07622	+	2.75324i	−0.442348	+	0.134185i	−0.503599	−	0.863938i	$-0.667991\pi$
$421$	−9.07622	+	2.75324i	−0.442348	+	0.134185i	0.0612510	+	0.998122i	$0.480491\pi$
$422$		0			0
$423$	−0.753346	+	0.503369i	−0.0366289	+	0.0244747i
$424$		0			0
$425$	−18.3972	+	27.5333i	−0.892393	+	1.33556i
$426$		0			0
$427$	1.80315	−	18.3077i	0.0872604	−	0.885970i
$428$		0			0
$429$	−5.12268	−	1.55395i	−0.247325	−	0.0750254i
$430$		0			0
$431$	−1.53650	+	0.636439i	−0.0740106	+	0.0306562i	−0.419382	−	0.907810i	$-0.637753\pi$
$431$	−1.53650	+	0.636439i	−0.0740106	+	0.0306562i	0.345371	+	0.938466i	$0.387753\pi$
$432$		0			0
$433$	25.9255	+	10.7387i	1.24590	+	0.516068i	0.905553	−	0.424233i	$-0.139456\pi$
$433$	25.9255	+	10.7387i	1.24590	+	0.516068i	0.340345	+	0.940301i	$0.389456\pi$
$434$		0			0
$435$	1.27259	−	0.680215i	0.0610161	−	0.0326138i
$436$		0			0
$437$	3.98887	−	3.27358i	0.190813	−	0.156597i
$438$		0			0
$439$	1.96056	+	9.85642i	0.0935726	+	0.470421i	0.998950	+	0.0458134i	$0.0145880\pi$
$439$	1.96056	+	9.85642i	0.0935726	+	0.470421i	−0.905377	+	0.424608i	$0.860412\pi$
$440$		0			0
$441$	−0.425278	−	0.0845930i	−0.0202513	−	0.00402824i
$442$		0			0
$443$	−8.07938	+	15.1155i	−0.383863	+	0.718157i	−0.997442	−	0.0714761i	$-0.977229\pi$
$443$	−8.07938	+	15.1155i	−0.383863	+	0.718157i	0.613579	+	0.789633i	$0.289729\pi$
$444$		0			0
$445$	1.66553	−	0.164040i	0.0789536	−	0.00777625i
$446$		0			0
$447$			22.6522i			1.07141i
$448$		0			0
$449$			20.7935i			0.981305i	0.871355	+	0.490652i	$0.163242\pi$
$449$			20.7935i			0.981305i	−0.871355	+	0.490652i	$0.836758\pi$
$450$		0			0
$451$	−7.54978	+	0.743589i	−0.355505	+	0.0350142i
$452$		0			0
$453$	−1.47355	+	2.75682i	−0.0692334	+	0.129527i
$454$		0			0
$455$	2.74217	+	0.545451i	0.128555	+	0.0255712i
$456$		0			0
$457$	−4.04865	−	20.3539i	−0.189388	−	0.952116i	−0.952195	−	0.305490i	$-0.901180\pi$
$457$	−4.04865	−	20.3539i	−0.189388	−	0.952116i	0.762807	−	0.646626i	$-0.223820\pi$
$458$		0			0
$459$	−27.3360	+	22.4340i	−1.27593	+	1.04713i
$460$		0			0
$461$	−15.7332	+	8.40957i	−0.732768	+	0.391673i	−0.795177	−	0.606378i	$-0.792622\pi$
$461$	−15.7332	+	8.40957i	−0.732768	+	0.391673i	0.0624083	+	0.998051i	$0.480122\pi$
$462$		0			0
$463$	24.4398	+	10.1233i	1.13581	+	0.470469i	0.869753	−	0.493487i	$-0.164278\pi$
$463$	24.4398	+	10.1233i	1.13581	+	0.470469i	0.266060	+	0.963956i	$0.414278\pi$
$464$		0			0
$465$	1.93572	−	0.801800i	0.0897667	−	0.0371826i
$466$		0			0
$467$	29.4796	+	8.94253i	1.36415	+	0.413811i	0.885682	−	0.464293i	$-0.153692\pi$
$467$	29.4796	+	8.94253i	1.36415	+	0.413811i	0.478470	+	0.878104i	$0.341192\pi$
$468$		0			0
$469$	−3.81690	+	38.7537i	−0.176248	+	1.78948i
$470$		0			0
$471$	16.6063	−	24.8531i	0.765179	−	1.14517i
$472$		0			0
$473$	0.644804	−	0.430844i	0.0296481	−	0.0198102i
$474$		0			0
$475$	7.84905	−	2.38098i	0.360139	−	0.109247i
$476$		0			0
$477$	0.529724	−	0.645471i	0.0242544	−	0.0295541i
$478$		0			0
$479$	−1.33863	+	1.33863i	−0.0611636	+	0.0611636i	−0.737027	−	0.675863i	$-0.763771\pi$
$479$	−1.33863	+	1.33863i	−0.0611636	+	0.0611636i	0.675863	+	0.737027i	$0.263771\pi$
$480$		0			0
$481$	−15.7755	−	15.7755i	−0.719302	−	0.719302i
$482$		0			0
$483$	13.5311	+	11.1047i	0.615687	+	0.505282i
$484$		0			0
$485$	1.07248	+	3.53550i	0.0486990	+	0.160539i
$486$		0			0
$487$	4.92190	+	7.36614i	0.223032	+	0.333792i	0.926064	−	0.377367i	$-0.123171\pi$
$487$	4.92190	+	7.36614i	0.223032	+	0.333792i	−0.703031	+	0.711159i	$0.748171\pi$
$488$		0			0
$489$	−28.8020	−	19.2449i	−1.30247	−	0.870283i
$490$		0			0
$491$	−0.357218	−	0.0351829i	−0.0161210	−	0.00158778i	0.0899534	−	0.995946i	$-0.471328\pi$
$491$	−0.357218	−	0.0351829i	−0.0161210	−	0.00158778i	−0.106074	+	0.994358i	$0.533828\pi$
$492$		0			0
$493$	7.44668	−	24.5484i	0.335382	−	1.10561i
$494$		0			0
$495$	−0.00770204	−	0.0185944i	−0.000346181	−	0.000835755i
$496$		0			0
$497$	17.1466	−	41.3956i	0.769131	−	1.85685i
$498$		0			0
$499$	−6.79800	−	12.7182i	−0.304320	−	0.569343i	0.682554	−	0.730835i	$-0.260869\pi$
$499$	−6.79800	−	12.7182i	−0.304320	−	0.569343i	−0.986874	+	0.161492i	$0.948369\pi$
$500$		0			0
$501$	16.8883	+	20.5784i	0.754513	+	0.919377i
$502$		0			0
$503$	13.0679	−	2.59936i	0.582667	−	0.115900i	0.105048	−	0.994467i	$-0.466500\pi$
$503$	13.0679	−	2.59936i	0.582667	−	0.115900i	0.477618	+	0.878568i	$0.341500\pi$
$504$		0			0
$505$	0.0805394	−	0.404899i	0.00358396	−	0.0180178i
$506$		0			0
$507$	2.40168	+	1.28372i	0.106662	+	0.0570122i
$508$		0			0
$509$	3.30600	+	33.5664i	0.146536	+	1.48780i	0.734329	+	0.678793i	$0.237497\pi$
$509$	3.30600	+	33.5664i	0.146536	+	1.48780i	−0.587793	+	0.809011i	$0.700003\pi$
$510$		0			0
$511$	23.4456			1.03717
$512$		0			0
$513$	8.75930			0.386733
$514$		0			0
$515$	−0.0889797	−	0.903426i	−0.00392091	−	0.0398097i
$516$		0			0
$517$	5.96752	+	3.18971i	0.262451	+	0.140283i
$518$		0			0
$519$	−7.65254	+	38.4719i	−0.335909	+	1.68873i
$520$		0			0
$521$	−6.58242	+	1.30933i	−0.288381	+	0.0573626i	−0.337161	−	0.941447i	$-0.609467\pi$
$521$	−6.58242	+	1.30933i	−0.288381	+	0.0573626i	0.0487800	+	0.998810i	$0.484467\pi$
$522$		0			0
$523$	27.9118	+	34.0107i	1.22050	+	1.48718i	0.821477	+	0.570242i	$0.193150\pi$
$523$	27.9118	+	34.0107i	1.22050	+	1.48718i	0.399022	+	0.916941i	$0.369350\pi$
$524$		0			0
$525$	13.1160	+	24.5384i	0.572431	+	1.07094i
$526$		0			0
$527$	14.2543	−	34.4129i	0.620926	−	1.49905i
$528$		0			0
$529$	−5.08899	−	12.2859i	−0.221261	−	0.534170i
$530$		0			0
$531$	−0.0214981	+	0.0708699i	−0.000932940	+	0.00307549i
$532$		0			0
$533$	35.0072	+	3.44790i	1.51633	+	0.149345i
$534$		0			0
$535$	3.50257	+	2.34034i	0.151429	+	0.101182i
$536$		0			0
$537$	−0.335893	−	0.502700i	−0.0144949	−	0.0216931i
$538$		0			0
$539$	0.940025	+	3.09885i	0.0404898	+	0.133477i
$540$		0			0
$541$	−25.4097	−	20.8532i	−1.09245	−	0.896550i	−0.0973318	−	0.995252i	$-0.531031\pi$
$541$	−25.4097	−	20.8532i	−1.09245	−	0.896550i	−0.995117	+	0.0987024i	$0.968531\pi$
$542$		0			0
$543$	−10.5134	−	10.5134i	−0.451173	−	0.451173i
$544$		0			0
$545$	−2.52361	+	2.52361i	−0.108100	+	0.108100i
$546$		0			0
$547$	−21.2860	+	25.9371i	−0.910124	+	1.10899i	0.0835300	+	0.996505i	$0.473381\pi$
$547$	−21.2860	+	25.9371i	−0.910124	+	1.10899i	−0.993654	+	0.112484i	$0.964119\pi$
$548$		0			0
$549$	0.587601	−	0.178247i	0.0250782	−	0.00760738i
$550$		0			0
$551$	−5.28330	+	3.53019i	−0.225076	+	0.150391i
$552$		0			0
$553$	28.7062	−	42.9619i	1.22071	−	1.82693i
$554$		0			0
$555$	−0.215294	+	2.18592i	−0.00913873	+	0.0927871i
$556$		0			0
$557$	−18.5442	−	5.62533i	−0.785744	−	0.238353i	−0.128179	−	0.991751i	$-0.540913\pi$
$557$	−18.5442	−	5.62533i	−0.785744	−	0.238353i	−0.657565	+	0.753398i	$0.728413\pi$
$558$		0			0
$559$	−3.32215	+	1.37608i	−0.140512	+	0.0582019i
$560$		0			0
$561$	8.65643	+	3.58561i	0.365475	+	0.151385i
$562$		0			0
$563$	33.6888	−	18.0070i	1.41981	−	0.758906i	0.430209	−	0.902729i	$-0.358440\pi$
$563$	33.6888	−	18.0070i	1.41981	−	0.758906i	0.989603	+	0.143824i	$0.0459398\pi$
$564$		0			0
$565$	−1.98405	+	1.62827i	−0.0834695	+	0.0685016i
$566$		0			0
$567$	5.58330	+	28.0692i	0.234477	+	1.17879i
$568$		0			0
$569$	0.0331792	+	0.00659975i	0.00139094	+	0.000276676i	0.195786	−	0.980647i	$-0.437274\pi$
$569$	0.0331792	+	0.00659975i	0.00139094	+	0.000276676i	−0.194395	+	0.980923i	$0.562274\pi$
$570$		0			0
$571$	12.5838	−	23.5427i	0.526617	−	0.985231i	−0.468207	−	0.883619i	$-0.655100\pi$
$571$	12.5838	−	23.5427i	0.526617	−	0.985231i	0.994824	−	0.101612i	$-0.0324001\pi$
$572$		0			0
$573$	0.418275	−	0.0411965i	0.0174737	−	0.00172101i
$574$		0			0
$575$			15.4213i			0.643113i
$576$		0			0
$577$		−	10.4783i		−	0.436218i	−0.975924	−	0.218109i	$-0.930011\pi$
$577$		−	10.4783i		−	0.436218i	0.975924	−	0.218109i	$-0.0699889\pi$
$578$		0			0
$579$	−9.56000	+	0.941578i	−0.397300	+	0.0391306i
$580$		0			0
$581$	2.58215	−	4.83086i	0.107126	−	0.200418i
$582$		0			0
$583$	−6.11620	−	1.21659i	−0.253307	−	0.0503859i
$584$		0			0
$585$	0.0182064	+	0.0915298i	0.000752742	+	0.00378429i
$586$		0			0
$587$	−17.4465	+	14.3180i	−0.720093	+	0.590965i	−0.921424	−	0.388558i	$-0.872973\pi$
$587$	−17.4465	+	14.3180i	−0.720093	+	0.590965i	0.201331	+	0.979523i	$0.435473\pi$
$588$		0			0
$589$	−8.13684	+	4.34923i	−0.335273	+	0.179207i
$590$		0			0
$591$	−14.6551	−	6.07033i	−0.602829	−	0.249700i
$592$		0			0
$593$	−19.0787	+	7.90267i	−0.783470	+	0.324524i	−0.738315	−	0.674456i	$-0.764378\pi$
$593$	−19.0787	+	7.90267i	−0.783470	+	0.324524i	−0.0451548	+	0.998980i	$0.514378\pi$
$594$		0			0
$595$	−4.68291	−	1.42055i	−0.191981	−	0.0582367i
$596$		0			0
$597$	−0.140463	+	1.42614i	−0.00574877	+	0.0583682i
$598$		0			0
$599$	−22.7800	+	34.0927i	−0.930765	+	1.39299i	−0.0112483	+	0.999937i	$0.503581\pi$
$599$	−22.7800	+	34.0927i	−0.930765	+	1.39299i	−0.919517	+	0.393051i	$0.871419\pi$
$600$		0			0
$601$	25.8908	−	17.2997i	1.05611	−	0.705668i	0.0989075	−	0.995097i	$-0.468465\pi$
$601$	25.8908	−	17.2997i	1.05611	−	0.705668i	0.957200	+	0.289428i	$0.0934652\pi$
$602$		0			0
$603$	−1.24383	+	0.377312i	−0.0506528	+	0.0153654i
$604$		0			0
$605$	1.44907	−	1.76570i	0.0589130	−	0.0717857i
$606$		0			0
$607$	−2.46041	+	2.46041i	−0.0998648	+	0.0998648i	−0.755274	−	0.655409i	$-0.772496\pi$
$607$	−2.46041	+	2.46041i	−0.0998648	+	0.0998648i	0.655409	+	0.755274i	$0.272496\pi$
$608$		0			0
$609$	−15.2415	−	15.2415i	−0.617618	−	0.617618i
$610$		0			0
$611$	−24.2534	−	19.9042i	−0.981186	−	0.805239i
$612$		0			0
$613$	−7.10688	−	23.4282i	−0.287044	−	0.946257i	−0.975318	−	0.220806i	$-0.929131\pi$
$613$	−7.10688	−	23.4282i	−0.287044	−	0.946257i	0.688274	−	0.725451i	$-0.258369\pi$
$614$		0			0
$615$	−1.92408	−	2.87959i	−0.0775865	−	0.116116i
$616$		0			0
$617$	21.3693	+	14.2785i	0.860297	+	0.574832i	0.905596	−	0.424141i	$-0.139424\pi$
$617$	21.3693	+	14.2785i	0.860297	+	0.574832i	−0.0452990	+	0.998973i	$0.514424\pi$
$618$		0			0
$619$	−21.8475	−	2.15179i	−0.878124	−	0.0864876i	−0.351100	−	0.936338i	$-0.614192\pi$
$619$	−21.8475	−	2.15179i	−0.878124	−	0.0864876i	−0.527024	+	0.849850i	$0.676692\pi$
$620$		0			0
$621$	−4.78060	+	15.7595i	−0.191839	+	0.632408i
$622$		0			0
$623$	−9.56691	−	23.0966i	−0.383290	−	0.925344i
$624$		0			0
$625$	−9.28684	+	22.4204i	−0.371474	+	0.896817i
$626$		0			0
$627$	−1.09403	−	2.04679i	−0.0436915	−	0.0817410i
$628$		0			0
$629$	24.7724	+	30.1853i	0.987741	+	1.20357i
$630$		0			0
$631$	15.9785	−	3.17832i	0.636094	−	0.126527i	0.133499	−	0.991049i	$-0.457379\pi$
$631$	15.9785	−	3.17832i	0.636094	−	0.126527i	0.502595	+	0.864522i	$0.332379\pi$
$632$		0			0
$633$	−3.65484	+	18.3741i	−0.145267	+	0.730306i
$634$		0			0
$635$	0.458438	+	0.245040i	0.0181925	+	0.00972412i
$636$		0			0
$637$	−1.47177	−	14.9431i	−0.0583136	−	0.592068i
$638$		0			0
$639$	1.49557			0.0591639
$640$		0			0
$641$	−2.84184			−0.112246			−0.0561230	−	0.998424i	$-0.517874\pi$
$641$	−2.84184			−0.112246			−0.0561230	+	0.998424i	$0.517874\pi$
$642$		0			0
$643$	1.60434	+	16.2891i	0.0632690	+	0.642381i	0.973563	+	0.228419i	$0.0733555\pi$
$643$	1.60434	+	16.2891i	0.0632690	+	0.642381i	−0.910294	+	0.413963i	$0.864144\pi$
$644$		0			0
$645$	0.312223	+	0.166887i	0.0122938	+	0.00657116i
$646$		0			0
$647$	−2.77448	+	13.9483i	−0.109076	+	0.548363i	0.887143	+	0.461494i	$0.152686\pi$
$647$	−2.77448	+	13.9483i	−0.109076	+	0.548363i	−0.996220	+	0.0868695i	$0.972314\pi$
$648$		0			0
$649$	0.542459	−	0.107902i	0.0212934	−	0.00423552i
$650$		0			0
$651$	−19.8550	−	24.1933i	−0.778177	−	0.948211i
$652$		0			0
$653$	8.72703	+	16.3271i	0.341515	+	0.638930i	0.992784	−	0.119917i	$-0.0382629\pi$
$653$	8.72703	+	16.3271i	0.341515	+	0.638930i	−0.651269	+	0.758847i	$0.725763\pi$
$654$		0			0
$655$	0.412791	−	0.996565i	0.0161291	−	0.0389390i
$656$		0			0
$657$	0.299481	+	0.723010i	0.0116838	+	0.0282073i
$658$		0			0
$659$	3.09573	−	10.2053i	0.120593	−	0.397540i	−0.875773	−	0.482724i	$-0.839648\pi$
$659$	3.09573	−	10.2053i	0.120593	−	0.397540i	0.996365	+	0.0851833i	$0.0271476\pi$
$660$		0			0
$661$	14.3070	+	1.40911i	0.556476	+	0.0548081i	0.372346	−	0.928094i	$-0.378553\pi$
$661$	14.3070	+	1.40911i	0.556476	+	0.0548081i	0.184130	+	0.982902i	$0.441053\pi$
$662$		0			0
$663$	−36.1237	−	24.1371i	−1.40293	−	0.937407i
$664$		0			0
$665$	0.673427	+	1.00786i	0.0261144	+	0.0390830i
$666$		0			0
$667$	−3.46795	−	11.4323i	−0.134279	−	0.442660i
$668$		0			0
$669$	−16.1056	−	13.2175i	−0.622677	−	0.511018i
$670$		0			0
$671$	−3.24264	−	3.24264i	−0.125181	−	0.125181i
$672$		0			0
$673$	−17.0049	+	17.0049i	−0.655492	+	0.655492i	−0.954310	−	0.298818i	$-0.903408\pi$
$673$	−17.0049	+	17.0049i	−0.655492	+	0.655492i	0.298818	+	0.954310i	$0.403408\pi$
$674$		0			0
$675$	−16.6068	+	20.2354i	−0.639195	+	0.778861i
$676$		0			0
$677$	−34.3615	+	10.4234i	−1.32062	+	0.400605i	−0.870414	−	0.492320i	$-0.836149\pi$
$677$	−34.3615	+	10.4234i	−1.32062	+	0.400605i	−0.450205	+	0.892925i	$0.648649\pi$
$678$		0			0
$679$	45.8878	−	30.6612i	1.76101	−	1.17667i
$680$		0			0
$681$	10.2858	−	15.3937i	0.394151	−	0.589889i
$682$		0			0
$683$	2.56948	−	26.0884i	0.0983185	−	0.998244i	−0.811811	−	0.583920i	$-0.801518\pi$
$683$	2.56948	−	26.0884i	0.0983185	−	0.998244i	0.910129	−	0.414324i	$-0.135982\pi$
$684$		0			0
$685$	−1.58680	−	0.481352i	−0.0606287	−	0.0183915i
$686$		0			0
$687$	25.4969	−	10.5611i	0.972766	−	0.402933i
$688$		0			0
$689$	26.7144	+	11.0655i	1.01774	+	0.421561i
$690$		0			0
$691$	−17.8856	+	9.56004i	−0.680399	+	0.363681i	−0.775112	−	0.631824i	$-0.782307\pi$
$691$	−17.8856	+	9.56004i	−0.680399	+	0.363681i	0.0947128	+	0.995505i	$0.469807\pi$
$692$		0			0
$693$	−0.232400	+	0.190725i	−0.00882813	+	0.00724506i
$694$		0			0
$695$	0.992215	+	4.98820i	0.0376369	+	0.189213i
$696$		0			0
$697$	−60.3863	−	12.0116i	−2.28729	−	0.454971i
$698$		0			0
$699$	−13.7872	+	25.7941i	−0.521480	+	0.975621i
$700$		0			0
$701$	−28.2255	+	2.77997i	−1.06606	+	0.104998i	−0.615804	−	0.787899i	$-0.711169\pi$
$701$	−28.2255	+	2.77997i	−1.06606	+	0.104998i	−0.450260	+	0.892898i	$0.648669\pi$
$702$		0			0
$703$		−	9.67231i		−	0.364798i
$704$		0			0
$705$			3.08900i			0.116339i
$706$		0			0
$707$	−6.13706	+	0.604448i	−0.230808	+	0.0227326i
$708$		0			0
$709$	8.91824	−	16.6849i	0.334932	−	0.626613i	−0.656927	−	0.753954i	$-0.728144\pi$
$709$	8.91824	−	16.6849i	0.334932	−	0.626613i	0.991859	+	0.127341i	$0.0406442\pi$
$710$		0			0
$711$	1.69153	+	0.336466i	0.0634373	+	0.0126185i
$712$		0			0
$713$	−3.38416	−	17.0133i	−0.126738	−	0.637154i
$714$		0			0
$715$	0.538754	−	0.442144i	0.0201483	−	0.0165352i
$716$		0			0
$717$	2.75072	−	1.47029i	0.102727	−	0.0549090i
$718$		0			0
$719$	4.80783	+	1.99147i	0.179302	+	0.0742692i	0.470528	−	0.882385i	$-0.344063\pi$
$719$	4.80783	+	1.99147i	0.179302	+	0.0742692i	−0.291227	+	0.956654i	$0.594063\pi$
$720$		0			0
$721$	−12.5282	+	5.18935i	−0.466574	+	0.193261i
$722$		0			0
$723$	9.34563	+	2.83496i	0.347568	+	0.105433i
$724$		0			0
$725$	1.86131	−	18.8982i	0.0691272	−	0.701861i
$726$		0			0
$727$	12.0364	−	18.0138i	0.446407	−	0.668095i	−0.538212	−	0.842809i	$-0.680900\pi$
$727$	12.0364	−	18.0138i	0.446407	−	0.668095i	0.984619	+	0.174714i	$0.0559002\pi$
$728$		0			0
$729$	−23.2136	+	15.5108i	−0.859762	+	0.574475i
$730$		0			0
$731$	6.02281	−	1.82700i	0.222762	−	0.0675740i
$732$		0			0
$733$	11.0032	−	13.4074i	0.406411	−	0.495214i	−0.529076	−	0.848575i	$-0.677461\pi$
$733$	11.0032	−	13.4074i	0.406411	−	0.495214i	0.935487	+	0.353361i	$0.114961\pi$
$734$		0			0
$735$	−1.04533	+	1.04533i	−0.0385577	+	0.0385577i
$736$		0			0
$737$	6.86402	+	6.86402i	0.252839	+	0.252839i
$738$		0			0
$739$	−37.9190	−	31.1193i	−1.39487	−	1.14474i	−0.971017	−	0.239012i	$-0.923177\pi$
$739$	−37.9190	−	31.1193i	−1.39487	−	1.14474i	−0.423855	−	0.905730i	$-0.639323\pi$
$740$		0			0
$741$	3.12385	+	10.2980i	0.114758	+	0.378305i
$742$		0			0
$743$	−10.3834	−	15.5399i	−0.380932	−	0.570105i	0.590615	−	0.806954i	$-0.298885\pi$
$743$	−10.3834	−	15.5399i	−0.380932	−	0.570105i	−0.971546	+	0.236849i	$0.923885\pi$
$744$		0			0
$745$	−2.45216	−	1.63848i	−0.0898403	−	0.0600294i
$746$		0			0
$747$	0.181956	+	0.0179211i	0.00665742	+	0.000655699i
$748$		0			0
$749$	18.2662	−	60.2157i	0.667433	−	2.20023i
$750$		0			0
$751$	−5.16089	−	12.4595i	−0.188323	−	0.454653i	0.801314	−	0.598244i	$-0.204135\pi$
$751$	−5.16089	−	12.4595i	−0.188323	−	0.454653i	−0.989637	+	0.143592i	$0.954135\pi$
$752$		0			0
$753$	−3.70706	+	8.94963i	−0.135093	+	0.326143i
$754$		0			0
$755$	−0.191848	−	0.358922i	−0.00698206	−	0.0130625i
$756$		0			0
$757$	−19.8765	−	24.2196i	−0.722423	−	0.880275i	0.274260	−	0.961656i	$-0.411567\pi$
$757$	−19.8765	−	24.2196i	−0.722423	−	0.880275i	−0.996683	+	0.0813806i	$0.974067\pi$
$758$		0			0
$759$	4.27964	−	0.851273i	0.155341	−	0.0308993i
$760$		0			0
$761$	−4.27756	+	21.5047i	−0.155061	+	0.779546i	0.822479	+	0.568796i	$0.192591\pi$
$761$	−4.27756	+	21.5047i	−0.155061	+	0.779546i	−0.977540	+	0.210750i	$0.932409\pi$
$762$		0			0
$763$	47.0166	+	25.1309i	1.70212	+	0.909800i
$764$		0			0
$765$	−0.0160104	−	0.162556i	−0.000578856	−	0.00587723i
$766$		0			0
$767$	−2.56458			−0.0926015
$768$		0			0
$769$	7.55712			0.272517			0.136258	−	0.990673i	$-0.456492\pi$
$769$	7.55712			0.272517			0.136258	+	0.990673i	$0.456492\pi$
$770$		0			0
$771$	−4.14682	−	42.1034i	−0.149344	−	1.51632i
$772$		0			0
$773$	−18.6051	−	9.94461i	−0.669178	−	0.357683i	0.101565	−	0.994829i	$-0.467615\pi$
$773$	−18.6051	−	9.94461i	−0.669178	−	0.357683i	−0.770743	+	0.637146i	$0.780115\pi$
$774$		0			0
$775$	5.37921	−	27.0431i	0.193227	−	0.971418i
$776$		0			0
$777$	32.1802	−	6.40104i	1.15446	−	0.229636i
$778$		0			0
$779$	9.67483	+	11.7888i	0.346637	+	0.422378i
$780$		0			0
$781$	−5.26514	−	9.85039i	−0.188402	−	0.352475i
$782$		0			0
$783$	7.76056	−	18.7357i	0.277340	−	0.669558i
$784$		0			0
$785$	1.48925	+	3.59536i	0.0531535	+	0.128324i
$786$		0			0
$787$	3.87908	−	12.7876i	0.138274	−	0.455829i	−0.860266	−	0.509846i	$-0.829703\pi$
$787$	3.87908	−	12.7876i	0.138274	−	0.455829i	0.998540	+	0.0540170i	$0.0172025\pi$
$788$		0			0
$789$	−19.1111	−	1.88228i	−0.680372	−	0.0670108i
$790$		0			0
$791$	31.8784	+	21.3005i	1.13347	+	0.757358i
$792$		0			0
$793$	11.8134	+	17.6800i	0.419506	+	0.627836i
$794$		0			0
$795$	−0.826391	−	2.72425i	−0.0293091	−	0.0966191i
$796$		0			0
$797$	3.35856	+	2.75630i	0.118966	+	0.0976332i	0.691995	−	0.721902i	$-0.256732\pi$
$797$	3.35856	+	2.75630i	0.118966	+	0.0976332i	−0.573029	+	0.819535i	$0.694232\pi$
$798$		0			0
$799$	38.8314	+	38.8314i	1.37376	+	1.37376i
$800$		0			0
$801$	0.590045	−	0.590045i	0.0208482	−	0.0208482i
$802$		0			0
$803$	3.70770	−	4.51784i	0.130842	−	0.159431i
$804$		0			0
$805$	−2.18085	+	0.661554i	−0.0768649	+	0.0233167i
$806$		0			0
$807$	−41.7473	+	27.8946i	−1.46957	+	0.981937i
$808$		0			0
$809$	9.73562	−	14.5704i	0.342286	−	0.512268i	−0.619892	−	0.784687i	$-0.712824\pi$
$809$	9.73562	−	14.5704i	0.342286	−	0.512268i	0.962179	+	0.272419i	$0.0878238\pi$
$810$		0			0
$811$	2.17589	−	22.0921i	0.0764057	−	0.775760i	−0.878280	−	0.478146i	$-0.841309\pi$
$811$	2.17589	−	22.0921i	0.0764057	−	0.775760i	0.954686	−	0.297614i	$-0.0961910\pi$
$812$		0			0
$813$	24.7431	+	7.50574i	0.867778	+	0.263238i
$814$		0			0
$815$	4.16662	−	1.72587i	0.145950	−	0.0604546i
$816$		0			0
$817$	−1.44029	−	0.596588i	−0.0503894	−	0.0208720i
$818$		0			0
$819$	1.22943	−	0.657142i	0.0429596	−	0.0229624i
$820$		0			0
$821$	20.9081	−	17.1588i	0.729698	−	0.598847i	−0.194437	−	0.980915i	$-0.562288\pi$
$821$	20.9081	−	17.1588i	0.729698	−	0.598847i	0.924134	+	0.382068i	$0.124788\pi$
$822$		0			0
$823$	−6.29705	−	31.6574i	−0.219501	−	1.10351i	−0.920619	−	0.390462i	$-0.872315\pi$
$823$	−6.29705	−	31.6574i	−0.219501	−	1.10351i	0.701118	−	0.713046i	$-0.252685\pi$
$824$		0			0
$825$	6.80260	+	1.35312i	0.236836	+	0.0471096i
$826$		0			0
$827$	17.5338	−	32.8035i	0.609711	−	1.14069i	−0.367820	−	0.929897i	$-0.619896\pi$
$827$	17.5338	−	32.8035i	0.609711	−	1.14069i	0.977531	−	0.210792i	$-0.0676044\pi$
$828$		0			0
$829$	15.9589	−	1.57182i	0.554276	−	0.0545914i	0.182998	−	0.983113i	$-0.441420\pi$
$829$	15.9589	−	1.57182i	0.554276	−	0.0545914i	0.371278	+	0.928522i	$0.378920\pi$
$830$		0			0
$831$			34.8640i			1.20942i
$832$		0			0
$833$			26.2814i			0.910597i
$834$		0			0
$835$	−3.44924	+	0.339720i	−0.119366	+	0.0117565i
$836$		0			0
$837$	13.8806	−	25.9687i	0.479782	−	0.897609i
$838$		0			0
$839$	−21.3833	−	4.25339i	−0.738232	−	0.146843i	−0.188369	−	0.982098i	$-0.560320\pi$
$839$	−21.3833	−	4.25339i	−0.738232	−	0.146843i	−0.549863	+	0.835255i	$0.685320\pi$
$840$		0			0
$841$	−2.78764	−	14.0144i	−0.0961255	−	0.483255i
$842$		0			0
$843$	15.7327	−	12.9115i	0.541864	−	0.444696i
$844$		0			0
$845$	−0.312685	+	0.167134i	−0.0107567	+	0.00574957i
$846$		0			0
$847$	−31.5232	−	13.0573i	−1.08315	−	0.448655i
$848$		0			0
$849$	3.05892	−	1.26705i	0.104982	−	0.0434849i
$850$		0			0
$851$	17.4022	+	5.27890i	0.596540	+	0.180958i
$852$		0			0
$853$	−0.947579	+	9.62093i	−0.0324445	+	0.329414i	0.965238	+	0.261373i	$0.0841751\pi$
$853$	−0.947579	+	9.62093i	−0.0324445	+	0.329414i	−0.997682	+	0.0680418i	$0.978325\pi$
$854$		0			0
$855$	−0.0224781	+	0.0336408i	−0.000768734	+	0.00115049i
$856$		0			0
$857$	−19.9925	+	13.3586i	−0.682930	+	0.456320i	−0.848024	−	0.529958i	$-0.822208\pi$
$857$	−19.9925	+	13.3586i	−0.682930	+	0.456320i	0.165093	+	0.986278i	$0.447208\pi$
$858$		0			0
$859$	−0.904584	+	0.274403i	−0.0308640	+	0.00936250i	−0.305679	−	0.952135i	$-0.598883\pi$
$859$	−0.904584	+	0.274403i	−0.0308640	+	0.00936250i	0.274815	+	0.961497i	$0.411383\pi$
$860$		0			0
$861$	−32.8192	+	39.9903i	−1.11847	+	1.36286i
$862$		0			0
$863$	−14.2985	+	14.2985i	−0.486728	+	0.486728i	−0.907272	−	0.420544i	$-0.861839\pi$
$863$	−14.2985	+	14.2985i	−0.486728	+	0.486728i	0.420544	+	0.907272i	$0.361839\pi$
$864$		0			0
$865$	−3.61117	−	3.61117i	−0.122783	−	0.122783i
$866$		0			0
$867$	36.4431	+	29.9081i	1.23767	+	1.01573i
$868$		0			0
$869$	−3.73892	−	12.3256i	−0.126834	−	0.418116i
$870$		0			0
$871$	−25.0066	−	37.4250i	−0.847317	−	1.26810i
$872$		0			0
$873$	1.53167	+	1.02343i	0.0518392	+	0.0346378i
$874$		0			0
$875$	−7.24579	−	0.713648i	−0.244952	−	0.0241257i
$876$		0			0
$877$	−10.6957	+	35.2589i	−0.361167	+	1.19061i	0.568649	+	0.822581i	$0.307466\pi$
$877$	−10.6957	+	35.2589i	−0.361167	+	1.19061i	−0.929815	+	0.368026i	$0.880034\pi$
$878$		0			0
$879$	−4.59391	−	11.0907i	−0.154949	−	0.374079i
$880$		0			0
$881$	15.6106	−	37.6874i	0.525935	−	1.26972i	−0.408230	−	0.912879i	$-0.633854\pi$
$881$	15.6106	−	37.6874i	0.525935	−	1.26972i	0.934165	−	0.356841i	$-0.116146\pi$
$882$		0			0
$883$	−8.56955	−	16.0325i	−0.288388	−	0.539536i	0.695455	−	0.718570i	$-0.255203\pi$
$883$	−8.56955	−	16.0325i	−0.288388	−	0.539536i	−0.983843	+	0.179033i	$0.942703\pi$
$884$		0			0
$885$	0.160179	+	0.195179i	0.00538436	+	0.00656086i
$886$		0			0
$887$	−1.90133	+	0.378198i	−0.0638404	+	0.0126986i	−0.226907	−	0.973916i	$-0.572861\pi$
$887$	−1.90133	+	0.378198i	−0.0638404	+	0.0126986i	0.163067	+	0.986615i	$0.447861\pi$
$888$		0			0
$889$	1.51485	−	7.61568i	0.0508065	−	0.255422i
$890$		0			0
$891$	6.29173	+	3.36300i	0.210781	+	0.112665i
$892$		0			0
$893$	−1.33328	−	13.5370i	−0.0446164	−	0.452998i
$894$		0			0
$895$	0.0787145			0.00263113
$896$		0			0
$897$	−20.2328			−0.675553
$898$		0			0
$899$	2.09369	+	21.2576i	0.0698284	+	0.708980i
$900$		0			0
$901$	−44.6345	−	23.8576i	−1.48699	−	0.794813i
$902$		0			0
$903$	1.03170	−	5.18672i	0.0343329	−	0.172603i
$904$		0			0
$905$	1.89856	−	0.377647i	0.0631103	−	0.0125534i
$906$		0			0
$907$	−24.1258	−	29.3974i	−0.801085	−	0.976125i	0.198907	−	0.980018i	$-0.436261\pi$
$907$	−24.1258	−	29.3974i	−0.801085	−	0.976125i	−0.999992	+	0.00389302i	$0.998761\pi$
$908$		0			0
$909$	−0.0970312	−	0.181533i	−0.00321832	−	0.00602106i
$910$		0			0
$911$	−9.64456	+	23.2840i	−0.319538	+	0.771434i	0.679740	+	0.733453i	$0.262093\pi$
$911$	−9.64456	+	23.2840i	−0.319538	+	0.771434i	−0.999278	+	0.0379809i	$0.987907\pi$
$912$		0			0
$913$	−0.522539	−	1.26152i	−0.0172935	−	0.0417502i
$914$		0			0
$915$	0.607704	−	2.00333i	0.0200901	−	0.0662281i
$916$		0			0
$917$	−16.0353	−	1.57934i	−0.529533	−	0.0521545i
$918$		0			0
$919$	−21.4335	−	14.3214i	−0.707027	−	0.472420i	0.149341	−	0.988786i	$-0.452285\pi$
$919$	−21.4335	−	14.3214i	−0.707027	−	0.472420i	−0.856368	+	0.516365i	$0.827285\pi$
$920$		0			0
$921$	7.91802	+	11.8502i	0.260908	+	0.390476i
$922$		0			0
$923$	15.0338	+	49.5600i	0.494845	+	1.63129i
$924$		0			0
$925$	22.3446	+	18.3377i	0.734686	+	0.602941i
$926$		0			0
$927$	−0.320056	−	0.320056i	−0.0105120	−	0.0105120i
$928$		0			0
$929$	−18.1305	+	18.1305i	−0.594843	+	0.594843i	−0.938936	−	0.344092i	$-0.888187\pi$
$929$	−18.1305	+	18.1305i	−0.594843	+	0.594843i	0.344092	+	0.938936i	$0.388187\pi$
$930$		0			0
$931$	4.12979	−	5.03216i	0.135348	−	0.164922i
$932$		0			0
$933$	41.0399	−	12.4493i	1.34359	−	0.407572i
$934$		0			0
$935$	−1.01429	+	0.677727i	−0.0331708	+	0.0221641i
$936$		0			0
$937$	−12.6708	+	18.9632i	−0.413938	+	0.619501i	−0.978588	−	0.205829i	$-0.934011\pi$
$937$	−12.6708	+	18.9632i	−0.413938	+	0.619501i	0.564650	+	0.825330i	$0.309011\pi$
$938$		0			0
$939$	−4.40596	+	44.7345i	−0.143783	+	1.45986i
$940$		0			0
$941$	53.9836	+	16.3757i	1.75982	+	0.533834i	0.994015	−	0.109244i	$-0.0348431\pi$
$941$	53.9836	+	16.3757i	1.75982	+	0.533834i	0.765800	+	0.643079i	$0.222343\pi$
$942$		0			0
$943$	−26.4904	+	10.9727i	−0.862647	+	0.357320i
$944$		0			0
$945$	−3.57406	−	1.48042i	−0.116264	−	0.0481581i
$946$		0			0
$947$	29.6506	−	15.8486i	0.963516	−	0.515010i	0.0869086	−	0.996216i	$-0.472301\pi$
$947$	29.6506	−	15.8486i	0.963516	−	0.515010i	0.876607	+	0.481206i	$0.159801\pi$
$948$		0			0
$949$	−20.9485	+	17.1920i	−0.680017	+	0.558076i
$950$		0			0
$951$	2.51127	+	12.6250i	0.0814335	+	0.409394i
$952$		0			0
$953$	38.9549	+	7.74861i	1.26187	+	0.251002i	0.780301	−	0.625404i	$-0.215066\pi$
$953$	38.9549	+	7.74861i	1.26187	+	0.251002i	0.481572	+	0.876406i	$0.340066\pi$
$954$		0			0
$955$	−0.0257951	+	0.0482592i	−0.000834710	+	0.00156163i
$956$		0			0
$957$	−5.34727	+	0.526660i	−0.172853	+	0.0170245i
$958$		0			0
$959$			24.7698i			0.799859i
$960$		0			0
$961$			0.0153601i			0.000495486i
$962$		0			0
$963$	2.09024	−	0.205871i	0.0673571	−	0.00663410i
$964$		0			0
$965$	0.589567	−	1.10300i	0.0189788	−	0.0355069i
$966$		0			0
$967$	−23.7029	−	4.71479i	−0.762233	−	0.151618i	−0.201358	−	0.979518i	$-0.564535\pi$
$967$	−23.7029	−	4.71479i	−0.762233	−	0.151618i	−0.560875	+	0.827900i	$0.689535\pi$
$968$		0			0
$969$	−3.67463	−	18.4736i	−0.118046	−	0.593457i
$970$		0			0
$971$	4.66037	−	3.82466i	0.149558	−	0.122739i	−0.556639	−	0.830755i	$-0.687909\pi$
$971$	4.66037	−	3.82466i	0.149558	−	0.122739i	0.706197	+	0.708015i	$0.250409\pi$
$972$		0			0
$973$	67.0014	−	35.8130i	2.14797	−	1.14811i
$974$		0			0
$975$	−29.7125	−	12.3073i	−0.951561	−	0.394149i
$976$		0			0
$977$	36.4675	−	15.1053i	1.16670	−	0.483262i	0.286598	−	0.958051i	$-0.407476\pi$
$977$	36.4675	−	15.1053i	1.16670	−	0.483262i	0.880100	+	0.474789i	$0.157476\pi$
$978$		0			0
$979$	−5.96350	−	1.80901i	−0.190594	−	0.0578162i
$980$		0			0
$981$	−0.174418	+	1.77090i	−0.00556874	+	0.0565404i
$982$		0			0
$983$	11.9931	−	17.9490i	0.382521	−	0.572483i	−0.589385	−	0.807852i	$-0.700630\pi$
$983$	11.9931	−	17.9490i	0.382521	−	0.572483i	0.971906	+	0.235369i	$0.0756300\pi$
$984$		0			0
$985$	1.71716	−	1.14737i	0.0547133	−	0.0365583i
$986$		0			0
$987$	44.1558	−	13.3945i	1.40549	−	0.426352i
$988$		0			0
$989$	1.85944	−	2.26574i	0.0591268	−	0.0720462i
$990$		0			0
$991$	−20.0205	+	20.0205i	−0.635974	+	0.635974i	−0.949560	−	0.313586i	$-0.898470\pi$
$991$	−20.0205	+	20.0205i	−0.635974	+	0.635974i	0.313586	+	0.949560i	$0.398470\pi$
$992$		0			0
$993$	3.01081	+	3.01081i	0.0955453	+	0.0955453i
$994$		0			0
$995$	−0.144224	−	0.118362i	−0.00457221	−	0.00375231i
$996$		0			0
$997$	−13.7769	−	45.4164i	−0.436319	−	1.43835i	−0.849445	−	0.527678i	$-0.823063\pi$
$997$	−13.7769	−	45.4164i	−0.436319	−	1.43835i	0.413125	−	0.910674i	$-0.364437\pi$
$998$		0			0
$999$	17.1500	+	25.6668i	0.542601	+	0.812060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.49.4		240
4.3	odd	2		128.2.k.a.53.7	yes	240
128.29	even	32	inner	512.2.k.a.209.4		240
128.99	odd	32		128.2.k.a.29.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.29.7	✓	240	128.99	odd	32
128.2.k.a.53.7	yes	240	4.3	odd	2
512.2.k.a.49.4		240	1.1	even	1	trivial
512.2.k.a.209.4		240	128.29	even	32	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.166619 - 1.69171i) q^{3} +(0.195184 + 0.104328i) q^{5} +(0.644963 - 3.24245i) q^{7} +(0.108228 - 0.0215280i) q^{9} +O(q^{10})\)	\(q+(-0.166619 - 1.69171i) q^{3} +(0.195184 + 0.104328i) q^{5} +(0.644963 - 3.24245i) q^{7} +(0.108228 - 0.0215280i) q^{9} +(-0.522808 - 0.637044i) q^{11} +(1.80133 + 3.37005i) q^{13} +(0.143972 - 0.347579i) q^{15} +(-2.55951 - 6.17920i) q^{17} +(-0.480908 + 1.58534i) q^{19} +(-5.59275 - 0.550838i) q^{21} +(-2.58984 - 1.73048i) q^{23} +(-2.75064 - 4.11662i) q^{25} +(-1.53481 - 5.05961i) q^{27} +(2.96488 + 2.43321i) q^{29} +(3.93798 + 3.93798i) q^{31} +(-0.990584 + 0.990584i) q^{33} +(0.464165 - 0.565587i) q^{35} +(-5.58699 + 1.69479i) q^{37} +(5.40101 - 3.60884i) q^{39} +(5.11430 - 7.65409i) q^{41} +(-0.0922358 + 0.936486i) q^{43} +(0.0233705 + 0.00708935i) q^{45} +(-7.58571 + 3.14210i) q^{47} +(-3.63034 - 1.50373i) q^{49} +(-10.0270 + 5.35953i) q^{51} +(5.84937 - 4.80045i) q^{53} +(-0.0355823 - 0.178885i) q^{55} +(2.76207 + 0.549409i) q^{57} +(-0.316370 + 0.591888i) q^{59} +(5.53776 - 0.545421i) q^{61} -0.364810i q^{63} +0.845710i q^{65} +(-11.7223 + 1.15455i) q^{67} +(-2.49595 + 4.66960i) q^{69} +(13.2927 + 2.64409i) q^{71} +(1.38356 + 6.95562i) q^{73} +(-6.50583 + 5.33920i) q^{75} +(-2.40277 + 1.28431i) q^{77} +(14.4395 + 5.98105i) q^{79} +(-7.99782 + 3.31281i) q^{81} +(1.58555 + 0.480972i) q^{83} +(0.145089 - 1.47311i) q^{85} +(3.62229 - 5.42114i) q^{87} +(6.28752 - 4.20119i) q^{89} +(12.0890 - 3.66716i) q^{91} +(6.00578 - 7.31807i) q^{93} +(-0.259261 + 0.259261i) q^{95} +(11.8042 + 11.8042i) q^{97} +(-0.0702969 - 0.0576912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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