LMFDB - Embedded newform 800.2.be.a.529.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(209,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

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

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

chi := DirichletCharacter("800.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			529.24
Character	$\chi$	$=$	800.529
Dual form			800.2.be.a.369.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.01785 + 1.46605i) q^{3} +(1.86593 - 1.23219i) q^{5} -0.110917i q^{7} +(0.995348 + 3.06337i) q^{9} +O(q^{10})$	\(q+(2.01785 + 1.46605i) q^{3} +(1.86593 - 1.23219i) q^{5} -0.110917i q^{7} +(0.995348 + 3.06337i) q^{9} +(1.63700 + 0.531893i) q^{11} +(-1.48445 - 4.56868i) q^{13} +(5.57162 + 0.249171i) q^{15} +(0.269588 + 0.371056i) q^{17} +(2.40052 + 3.30403i) q^{19} +(0.162610 - 0.223814i) q^{21} +(6.10792 + 1.98459i) q^{23} +(1.96339 - 4.59838i) q^{25} +(-0.170346 + 0.524271i) q^{27} +(-5.29624 + 7.28964i) q^{29} +(-2.87291 + 2.08729i) q^{31} +(2.52343 + 3.47320i) q^{33} +(-0.136671 - 0.206963i) q^{35} +(0.500287 + 1.53972i) q^{37} +(3.70252 - 11.3952i) q^{39} +(-3.51556 - 10.8198i) q^{41} -10.5304 q^{43} +(5.63191 + 4.48957i) q^{45} +(-1.82373 + 2.51014i) q^{47} +6.98770 q^{49} +1.14397i q^{51} +(3.71441 + 2.69868i) q^{53} +(3.70992 - 1.02463i) q^{55} +10.1863i q^{57} +(-3.38621 + 1.10025i) q^{59} +(-11.1816 - 3.63312i) q^{61} +(0.339779 - 0.110401i) q^{63} +(-8.39939 - 6.69570i) q^{65} +(-3.02574 + 2.19833i) q^{67} +(9.41535 + 12.9591i) q^{69} +(-9.04844 - 6.57408i) q^{71} +(9.85476 + 3.20201i) q^{73} +(10.7033 - 6.40039i) q^{75} +(0.0589960 - 0.181571i) q^{77} +(4.45472 + 3.23655i) q^{79} +(6.70522 - 4.87163i) q^{81} +(-9.91061 + 7.20048i) q^{83} +(0.960247 + 0.360180i) q^{85} +(-21.3740 + 6.94483i) q^{87} +(-2.07551 + 6.38776i) q^{89} +(-0.506744 + 0.164651i) q^{91} -8.85717 q^{93} +(8.55040 + 3.20718i) q^{95} +(-3.30362 + 4.54704i) q^{97} +5.54415i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9}+O(q^{10}) $ 112 * q - 30 * q^9	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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
$3$	2.01785	+	1.46605i	1.16500	+	0.846425i	0.990402	−	0.138214i	$-0.0441361\pi$
$3$	2.01785	+	1.46605i	1.16500	+	0.846425i	0.174602	+	0.984639i	$0.444136\pi$
$4$		0			0
$5$	1.86593	−	1.23219i	0.834470	−	0.551054i
$5$	1.86593	−	1.23219i	0.834470	−	0.551054i
$6$		0			0
$7$		−	0.110917i		−	0.0419227i	−0.999780	−	0.0209613i	$-0.993327\pi$
$7$		−	0.110917i		−	0.0419227i	0.999780	−	0.0209613i	$-0.00667269\pi$
$8$		0			0
$9$	0.995348	+	3.06337i	0.331783	+	1.02112i
$10$		0			0
$11$	1.63700	+	0.531893i	0.493574	+	0.160372i	0.545219	−	0.838294i	$-0.316446\pi$
$11$	1.63700	+	0.531893i	0.493574	+	0.160372i	−0.0516452	+	0.998665i	$0.516446\pi$
$12$		0			0
$13$	−1.48445	−	4.56868i	−0.411713	−	1.26712i	−0.915158	−	0.403096i	$-0.867934\pi$
$13$	−1.48445	−	4.56868i	−0.411713	−	1.26712i	0.503445	−	0.864027i	$-0.332066\pi$
$14$		0			0
$15$	5.57162	+	0.249171i	1.43859	+	0.0643356i
$16$		0			0
$17$	0.269588	+	0.371056i	0.0653848	+	0.0899944i	0.840457	−	0.541878i	$-0.182287\pi$
$17$	0.269588	+	0.371056i	0.0653848	+	0.0899944i	−0.775072	+	0.631873i	$0.782287\pi$
$18$		0			0
$19$	2.40052	+	3.30403i	0.550716	+	0.757996i	0.990109	−	0.140299i	$-0.0448064\pi$
$19$	2.40052	+	3.30403i	0.550716	+	0.757996i	−0.439393	+	0.898295i	$0.644806\pi$
$20$		0			0
$21$	0.162610	−	0.223814i	0.0354844	−	0.0488401i
$22$		0			0
$23$	6.10792	+	1.98459i	1.27359	+	0.413815i	0.866318	−	0.499492i	$-0.166480\pi$
$23$	6.10792	+	1.98459i	1.27359	+	0.413815i	0.407272	+	0.913307i	$0.366480\pi$
$24$		0			0
$25$	1.96339	−	4.59838i	0.392679	−	0.919676i
$26$		0			0
$27$	−0.170346	+	0.524271i	−0.0327831	+	0.100896i
$28$		0			0
$29$	−5.29624	+	7.28964i	−0.983486	+	1.35365i	−0.0485566	+	0.998820i	$0.515462\pi$
$29$	−5.29624	+	7.28964i	−0.983486	+	1.35365i	−0.934930	+	0.354833i	$0.884538\pi$
$30$		0			0
$31$	−2.87291	+	2.08729i	−0.515990	+	0.374889i	−0.815091	−	0.579333i	$-0.803313\pi$
$31$	−2.87291	+	2.08729i	−0.515990	+	0.374889i	0.299101	+	0.954221i	$0.403313\pi$
$32$		0			0
$33$	2.52343	+	3.47320i	0.439273	+	0.604607i
$34$		0			0
$35$	−0.136671	−	0.206963i	−0.0231017	−	0.0349832i
$36$		0			0
$37$	0.500287	+	1.53972i	0.0822467	+	0.253129i	0.983721	−	0.179704i	$-0.0575139\pi$
$37$	0.500287	+	1.53972i	0.0822467	+	0.253129i	−0.901474	+	0.432833i	$0.857514\pi$
$38$		0			0
$39$	3.70252	−	11.3952i	0.592877	−	1.82469i
$40$		0			0
$41$	−3.51556	−	10.8198i	−0.549039	−	1.68977i	−0.711188	−	0.703002i	$-0.751843\pi$
$41$	−3.51556	−	10.8198i	−0.549039	−	1.68977i	0.162149	−	0.986766i	$-0.448157\pi$
$42$		0			0
$43$	−10.5304			−1.60588			−0.802938	−	0.596063i	$-0.796731\pi$
$43$	−10.5304			−1.60588			−0.802938	+	0.596063i	$0.796731\pi$
$44$		0			0
$45$	5.63191	+	4.48957i	0.839556	+	0.669265i
$46$		0			0
$47$	−1.82373	+	2.51014i	−0.266018	+	0.366142i	−0.921040	−	0.389467i	$-0.872659\pi$
$47$	−1.82373	+	2.51014i	−0.266018	+	0.366142i	0.655022	+	0.755609i	$0.272659\pi$
$48$		0			0
$49$	6.98770			0.998242
$50$		0			0
$51$			1.14397i			0.160187i
$52$		0			0
$53$	3.71441	+	2.69868i	0.510213	+	0.370692i	0.812905	−	0.582397i	$-0.197885\pi$
$53$	3.71441	+	2.69868i	0.510213	+	0.370692i	−0.302691	+	0.953089i	$0.597885\pi$
$54$		0			0
$55$	3.70992	−	1.02463i	0.500246	−	0.138160i
$56$		0			0
$57$			10.1863i			1.34921i
$58$		0			0
$59$	−3.38621	+	1.10025i	−0.440847	+	0.143240i	−0.521026	−	0.853541i	$-0.674451\pi$
$59$	−3.38621	+	1.10025i	−0.440847	+	0.143240i	0.0801796	+	0.996780i	$0.474451\pi$
$60$		0			0
$61$	−11.1816	−	3.63312i	−1.43166	−	0.465174i	−0.512372	−	0.858764i	$-0.671233\pi$
$61$	−11.1816	−	3.63312i	−1.43166	−	0.465174i	−0.919286	+	0.393590i	$0.871233\pi$
$62$		0			0
$63$	0.339779	−	0.110401i	0.0428082	−	0.0139092i
$64$		0			0
$65$	−8.39939	−	6.69570i	−1.04182	−	0.830499i
$66$		0			0
$67$	−3.02574	+	2.19833i	−0.369653	+	0.268569i	−0.757067	−	0.653337i	$-0.773368\pi$
$67$	−3.02574	+	2.19833i	−0.369653	+	0.268569i	0.387414	+	0.921906i	$0.373368\pi$
$68$		0			0
$69$	9.41535	+	12.9591i	1.13348	+	1.56009i
$70$		0			0
$71$	−9.04844	−	6.57408i	−1.07385	−	0.780200i	−0.0972518	−	0.995260i	$-0.531005\pi$
$71$	−9.04844	−	6.57408i	−1.07385	−	0.780200i	−0.976601	+	0.215060i	$0.931005\pi$
$72$		0			0
$73$	9.85476	+	3.20201i	1.15341	+	0.374766i	0.822428	−	0.568870i	$-0.192619\pi$
$73$	9.85476	+	3.20201i	1.15341	+	0.374766i	0.330985	+	0.943636i	$0.392619\pi$
$74$		0			0
$75$	10.7033	−	6.40039i	1.23591	−	0.739053i
$76$		0			0
$77$	0.0589960	−	0.181571i	0.00672322	−	0.0206919i
$78$		0			0
$79$	4.45472	+	3.23655i	0.501196	+	0.364140i	0.809474	−	0.587156i	$-0.199753\pi$
$79$	4.45472	+	3.23655i	0.501196	+	0.364140i	−0.308278	+	0.951296i	$0.599753\pi$
$80$		0			0
$81$	6.70522	−	4.87163i	0.745025	−	0.541292i
$82$		0			0
$83$	−9.91061	+	7.20048i	−1.08783	+	0.790356i	−0.979032	−	0.203708i	$-0.934701\pi$
$83$	−9.91061	+	7.20048i	−1.08783	+	0.790356i	−0.108800	+	0.994064i	$0.534701\pi$
$84$		0			0
$85$	0.960247	+	0.360180i	0.104153	+	0.0390670i
$86$		0			0
$87$	−21.3740	+	6.94483i	−2.29153	+	0.744564i
$88$		0			0
$89$	−2.07551	+	6.38776i	−0.220003	+	0.677101i	0.778757	+	0.627326i	$0.215850\pi$
$89$	−2.07551	+	6.38776i	−0.220003	+	0.677101i	−0.998760	+	0.0497752i	$0.984150\pi$
$90$		0			0
$91$	−0.506744	+	0.164651i	−0.0531212	+	0.0172601i
$92$		0			0
$93$	−8.85717			−0.918446
$94$		0			0
$95$	8.55040	+	3.20718i	0.877253	+	0.329050i
$96$		0			0
$97$	−3.30362	+	4.54704i	−0.335431	+	0.461682i	−0.943100	−	0.332509i	$-0.892105\pi$
$97$	−3.30362	+	4.54704i	−0.335431	+	0.461682i	0.607669	+	0.794191i	$0.292105\pi$
$98$		0			0
$99$			5.54415i			0.557208i
$100$		0			0
$101$		−	1.55640i		−	0.154868i	−0.996997	−	0.0774339i	$-0.975327\pi$
$101$		−	1.55640i		−	0.154868i	0.996997	−	0.0774339i	$-0.0246727\pi$
$102$		0			0
$103$	−2.77316	+	3.81692i	−0.273247	+	0.376092i	−0.923483	−	0.383640i	$-0.874670\pi$
$103$	−2.77316	+	3.81692i	−0.273247	+	0.376092i	0.650235	+	0.759733i	$0.274670\pi$
$104$		0			0
$105$	0.0276373	−	0.617988i	0.00269712	−	0.0603094i
$106$		0			0
$107$	11.5454			1.11614			0.558070	−	0.829794i	$-0.311542\pi$
$107$	11.5454			1.11614			0.558070	+	0.829794i	$0.311542\pi$
$108$		0			0
$109$	1.79379	−	0.582837i	0.171814	−	0.0558256i	−0.221847	−	0.975081i	$-0.571209\pi$
$109$	1.79379	−	0.582837i	0.171814	−	0.0558256i	0.393661	+	0.919256i	$0.371209\pi$
$110$		0			0
$111$	−1.24781	+	3.84038i	−0.118437	+	0.364512i
$112$		0			0
$113$	4.37045	−	1.42005i	0.411137	−	0.133587i	−0.0961433	−	0.995367i	$-0.530651\pi$
$113$	4.37045	−	1.42005i	0.411137	−	0.133587i	0.507281	+	0.861781i	$0.330651\pi$
$114$		0			0
$115$	13.8424	−	3.82305i	1.29081	−	0.356502i
$116$		0			0
$117$	12.5180	−	9.09485i	1.15729	−	0.840819i
$118$		0			0
$119$	0.0411565	−	0.0299019i	0.00377281	−	0.00274111i
$120$		0			0
$121$	−6.50233	−	4.72422i	−0.591121	−	0.429475i
$122$		0			0
$123$	8.76851	−	26.9867i	0.790630	−	2.43331i
$124$		0			0
$125$	−2.00254	−	10.9995i	−0.179113	−	0.983829i
$126$		0			0
$127$	7.73794	+	2.51421i	0.686631	+	0.223100i	0.631496	−	0.775379i	$-0.282441\pi$
$127$	7.73794	+	2.51421i	0.686631	+	0.223100i	0.0551347	+	0.998479i	$0.482441\pi$
$128$		0			0
$129$	−21.2488	−	15.4382i	−1.87085	−	1.35925i
$130$		0			0
$131$	−12.7817	−	17.5926i	−1.11675	−	1.53707i	−0.811085	−	0.584929i	$-0.801122\pi$
$131$	−12.7817	−	17.5926i	−1.11675	−	1.53707i	−0.305661	−	0.952140i	$-0.598878\pi$
$132$		0			0
$133$	0.366473	−	0.266258i	0.0317772	−	0.0230875i
$134$		0			0
$135$	0.328150	+	1.18815i	0.0282427	+	0.102260i
$136$		0			0
$137$	8.72303	−	2.83428i	0.745259	−	0.242149i	0.0883189	−	0.996092i	$-0.471851\pi$
$137$	8.72303	−	2.83428i	0.745259	−	0.242149i	0.656940	+	0.753943i	$0.271851\pi$
$138$		0			0
$139$	−13.0150	−	4.22884i	−1.10392	−	0.358685i	−0.300310	−	0.953842i	$-0.597090\pi$
$139$	−13.0150	−	4.22884i	−1.10392	−	0.358685i	−0.803610	+	0.595156i	$0.797090\pi$
$140$		0			0
$141$	−7.36000	+	2.39141i	−0.619824	+	0.201393i
$142$		0			0
$143$		−	8.26849i		−	0.691446i
$144$		0			0
$145$	−0.900150	+	20.1280i	−0.0747534	+	1.67154i
$146$		0			0
$147$	14.1001	+	10.2443i	1.16296	+	0.844938i
$148$		0			0
$149$		−	14.8397i		−	1.21572i	−0.794045	−	0.607859i	$-0.792028\pi$
$149$		−	14.8397i		−	1.21572i	0.794045	−	0.607859i	$-0.207972\pi$
$150$		0			0
$151$	8.87251			0.722035			0.361017	−	0.932559i	$-0.382430\pi$
$151$	8.87251			0.722035			0.361017	+	0.932559i	$0.382430\pi$
$152$		0			0
$153$	−0.868348	+	1.19518i	−0.0702017	+	0.0966244i
$154$		0			0
$155$	−2.78870	+	7.43473i	−0.223994	+	0.597172i
$156$		0			0
$157$	−4.71374			−0.376197			−0.188099	−	0.982150i	$-0.560232\pi$
$157$	−4.71374			−0.376197			−0.188099	+	0.982150i	$0.560232\pi$
$158$		0			0
$159$	3.53871	+	10.8910i	0.280638	+	0.863715i
$160$		0			0
$161$	0.220124	−	0.677473i	0.0173482	−	0.0533923i
$162$		0			0
$163$	−3.09987	−	9.54040i	−0.242800	−	0.747262i	−0.995990	−	0.0894595i	$-0.971486\pi$
$163$	−3.09987	−	9.54040i	−0.242800	−	0.747262i	0.753190	−	0.657803i	$-0.228514\pi$
$164$		0			0
$165$	8.98821	+	3.37140i	0.699731	+	0.262463i
$166$		0			0
$167$	−4.72830	−	6.50795i	−0.365887	−	0.503601i	0.585890	−	0.810391i	$-0.300745\pi$
$167$	−4.72830	−	6.50795i	−0.365887	−	0.503601i	−0.951777	+	0.306790i	$0.900745\pi$
$168$		0			0
$169$	−8.15199	+	5.92277i	−0.627076	+	0.455597i
$170$		0			0
$171$	−7.73210	+	10.6423i	−0.591288	+	0.813838i
$172$		0			0
$173$	3.07351	−	9.45929i	0.233675	−	0.719176i	−0.763620	−	0.645666i	$-0.776580\pi$
$173$	3.07351	−	9.45929i	0.233675	−	0.719176i	0.997294	−	0.0735104i	$-0.0234202\pi$
$174$		0			0
$175$	−0.510038	−	0.217774i	−0.0385553	−	0.0164621i
$176$		0			0
$177$	−8.44586	−	2.74423i	−0.634830	−	0.206269i
$178$		0			0
$179$	−7.39861	+	10.1833i	−0.552998	+	0.761136i	−0.990415	−	0.138122i	$-0.955893\pi$
$179$	−7.39861	+	10.1833i	−0.552998	+	0.761136i	0.437417	+	0.899259i	$0.355893\pi$
$180$		0			0
$181$	7.67562	+	10.5646i	0.570524	+	0.785259i	0.992617	−	0.121293i	$-0.0387042\pi$
$181$	7.67562	+	10.5646i	0.570524	+	0.785259i	−0.422092	+	0.906553i	$0.638704\pi$
$182$		0			0
$183$	−17.2364	−	23.7239i	−1.27415	−	1.75372i
$184$		0			0
$185$	2.83074	+	2.25657i	0.208120	+	0.165906i
$186$		0			0
$187$	0.243953	+	0.750811i	0.0178396	+	0.0549048i
$188$		0			0
$189$	0.0581506	+	0.0188943i	0.00422983	+	0.00137436i
$190$		0			0
$191$	−0.889107	−	2.73639i	−0.0643335	−	0.197998i	0.913723	−	0.406337i	$-0.133194\pi$
$191$	−0.889107	−	2.73639i	−0.0643335	−	0.197998i	−0.978057	+	0.208339i	$0.933194\pi$
$192$		0			0
$193$			15.9019i			1.14464i	0.820029	+	0.572322i	$0.193957\pi$
$193$			15.9019i			1.14464i	−0.820029	+	0.572322i	$0.806043\pi$
$194$		0			0
$195$	−7.13243	−	25.8248i	−0.510764	−	1.84935i
$196$		0			0
$197$	3.78454	+	2.74963i	0.269637	+	0.195903i	0.714385	−	0.699753i	$-0.246707\pi$
$197$	3.78454	+	2.74963i	0.269637	+	0.195903i	−0.444748	+	0.895656i	$0.646707\pi$
$198$		0			0
$199$	−28.0439			−1.98798			−0.993988	−	0.109488i	$-0.965079\pi$
$199$	−28.0439			−1.98798			−0.993988	+	0.109488i	$0.965079\pi$
$200$		0			0
$201$	−9.32834			−0.657971
$202$		0			0
$203$	0.808546	+	0.587443i	0.0567488	+	0.0412304i
$204$		0			0
$205$	−19.8919	−	15.8571i	−1.38931	−	1.10751i
$206$		0			0
$207$			20.6862i			1.43779i
$208$		0			0
$209$	2.17225	+	6.68551i	0.150258	+	0.462446i
$210$		0			0
$211$	−0.310359	−	0.100842i	−0.0213660	−	0.00694223i	0.298315	−	0.954468i	$-0.403576\pi$
$211$	−0.310359	−	0.100842i	−0.0213660	−	0.00694223i	−0.319680	+	0.947525i	$0.603576\pi$
$212$		0			0
$213$	−8.62043	−	26.5310i	−0.590662	−	1.81787i
$214$		0			0
$215$	−19.6491	+	12.9755i	−1.34005	+	0.884924i
$216$		0			0
$217$	0.231516	+	0.318655i	0.0157163	+	0.0216317i
$218$		0			0
$219$	15.1911	+	20.9087i	1.02652	+	1.41288i
$220$		0			0
$221$	1.29505	−	1.78248i	0.0871142	−	0.119902i
$222$		0			0
$223$	11.2099	+	3.64231i	0.750669	+	0.243907i	0.659269	−	0.751907i	$-0.270866\pi$
$223$	11.2099	+	3.64231i	0.750669	+	0.243907i	0.0914002	+	0.995814i	$0.470866\pi$
$224$		0			0
$225$	16.0408	+	1.43761i	1.06939	+	0.0958404i
$226$		0			0
$227$	−0.324287	+	0.998051i	−0.0215237	+	0.0662430i	−0.961241	−	0.275708i	$-0.911088\pi$
$227$	−0.324287	+	0.998051i	−0.0215237	+	0.0662430i	0.939718	+	0.341951i	$0.111088\pi$
$228$		0			0
$229$	−11.8902	+	16.3654i	−0.785723	+	1.08146i	0.208904	+	0.977936i	$0.433010\pi$
$229$	−11.8902	+	16.3654i	−0.785723	+	1.08146i	−0.994627	+	0.103519i	$0.966990\pi$
$230$		0			0
$231$	0.385237	−	0.279891i	0.0253468	−	0.0184155i
$232$		0			0
$233$	−15.4318	−	21.2400i	−1.01097	−	1.39148i	−0.918347	−	0.395777i	$-0.870475\pi$
$233$	−15.4318	−	21.2400i	−1.01097	−	1.39148i	−0.0926216	−	0.995701i	$-0.529525\pi$
$234$		0			0
$235$	−0.309961	+	6.93094i	−0.0202196	+	0.452125i
$236$		0			0
$237$	4.24401	+	13.0617i	0.275678	+	0.848449i
$238$		0			0
$239$	2.69865	−	8.30559i	0.174561	−	0.537244i	−0.825052	−	0.565057i	$-0.808854\pi$
$239$	2.69865	−	8.30559i	0.174561	−	0.537244i	0.999613	+	0.0278129i	$0.00885425\pi$
$240$		0			0
$241$	0.110550	+	0.340238i	0.00712115	+	0.0219166i	0.954554	−	0.298038i	$-0.0963323\pi$
$241$	0.110550	+	0.340238i	0.00712115	+	0.0219166i	−0.947433	+	0.319955i	$0.896332\pi$
$242$		0			0
$243$	22.3259			1.43221
$244$		0			0
$245$	13.0386	−	8.61020i	0.833003	−	0.550086i
$246$		0			0
$247$	11.5316	−	15.8719i	0.733737	−	1.00990i
$248$		0			0
$249$	−30.5544			−1.93631
$250$		0			0
$251$			20.0370i			1.26473i	0.774672	+	0.632363i	$0.217915\pi$
$251$			20.0370i			1.26473i	−0.774672	+	0.632363i	$0.782085\pi$
$252$		0			0
$253$	8.94308	+	6.49753i	0.562247	+	0.408496i
$254$		0			0
$255$	1.40959	+	2.13456i	0.0882718	+	0.133671i
$256$		0			0
$257$		−	18.7305i		−	1.16838i	−0.811617	−	0.584190i	$-0.801412\pi$
$257$		−	18.7305i		−	1.16838i	0.811617	−	0.584190i	$-0.198588\pi$
$258$		0			0
$259$	0.170782	−	0.0554903i	0.0106119	−	0.00344800i
$260$		0			0
$261$	−27.6024	−	8.96858i	−1.70855	−	0.555141i
$262$		0			0
$263$	15.6804	−	5.09486i	0.966892	−	0.314162i	0.217331	−	0.976098i	$-0.430265\pi$
$263$	15.6804	−	5.09486i	0.966892	−	0.314162i	0.749561	+	0.661936i	$0.230265\pi$
$264$		0			0
$265$	10.2561	+	0.458668i	0.630029	+	0.0281758i
$266$		0			0
$267$	−13.5528	+	9.84671i	−0.829420	+	0.602609i
$268$		0			0
$269$	0.0856192	+	0.117845i	0.00522029	+	0.00718512i	0.811619	−	0.584187i	$-0.198586\pi$
$269$	0.0856192	+	0.117845i	0.00522029	+	0.00718512i	−0.806399	+	0.591372i	$0.798586\pi$
$270$		0			0
$271$	12.4072	+	9.01437i	0.753684	+	0.547584i	0.896967	−	0.442098i	$-0.145766\pi$
$271$	12.4072	+	9.01437i	0.753684	+	0.547584i	−0.143282	+	0.989682i	$0.545766\pi$
$272$		0			0
$273$	−1.26392	−	0.410672i	−0.0764958	−	0.0248550i
$274$		0			0
$275$	5.65992	−	6.48323i	0.341306	−	0.390953i
$276$		0			0
$277$	−6.39942	+	19.6954i	−0.384504	+	1.18338i	0.552336	+	0.833622i	$0.313737\pi$
$277$	−6.39942	+	19.6954i	−0.384504	+	1.18338i	−0.936840	+	0.349759i	$0.886263\pi$
$278$		0			0
$279$	−9.25369	−	6.72320i	−0.554004	−	0.402507i
$280$		0			0
$281$	−8.56374	+	6.22192i	−0.510870	+	0.371169i	−0.813153	−	0.582049i	$-0.802251\pi$
$281$	−8.56374	+	6.22192i	−0.510870	+	0.371169i	0.302284	+	0.953218i	$0.402251\pi$
$282$		0			0
$283$	−16.6426	+	12.0915i	−0.989298	+	0.718767i	−0.959767	−	0.280797i	$-0.909401\pi$
$283$	−16.6426	+	12.0915i	−0.989298	+	0.718767i	−0.0295305	+	0.999564i	$0.509401\pi$
$284$		0			0
$285$	12.5515	+	19.0069i	0.743487	+	1.12587i
$286$		0			0
$287$	−1.20010	+	0.389936i	−0.0708396	+	0.0230172i
$288$		0			0
$289$	5.18828	−	15.9679i	0.305193	−	0.939288i
$290$		0			0
$291$	−13.3324	+	4.33195i	−0.781558	+	0.253944i
$292$		0			0
$293$	0.603128			0.0352351			0.0176176	−	0.999845i	$-0.494392\pi$
$293$	0.603128			0.0352351			0.0176176	+	0.999845i	$0.494392\pi$
$294$		0			0
$295$	−4.96271	+	6.22545i	−0.288940	+	0.362459i
$296$		0			0
$297$	−0.557713	+	0.767625i	−0.0323618	+	0.0445421i
$298$		0			0
$299$		−	30.8512i		−	1.78417i
$300$		0			0
$301$			1.16800i			0.0673226i
$302$		0			0
$303$	2.28177	−	3.14058i	0.131084	−	0.180422i
$304$		0			0
$305$	−25.3408	+	6.99875i	−1.45101	+	0.400747i
$306$		0			0
$307$	9.96251			0.568591			0.284295	−	0.958737i	$-0.408240\pi$
$307$	9.96251			0.568591			0.284295	+	0.958737i	$0.408240\pi$
$308$		0			0
$309$	−11.1916	+	3.63637i	−0.636668	+	0.206866i
$310$		0			0
$311$	7.52782	−	23.1683i	0.426864	−	1.31375i	−0.474335	−	0.880344i	$-0.657311\pi$
$311$	7.52782	−	23.1683i	0.426864	−	1.31375i	0.901198	−	0.433407i	$-0.142689\pi$
$312$		0			0
$313$	17.7993	−	5.78333i	1.00607	−	0.326893i	0.240784	−	0.970579i	$-0.422596\pi$
$313$	17.7993	−	5.78333i	1.00607	−	0.326893i	0.765290	+	0.643686i	$0.222596\pi$
$314$		0			0
$315$	0.497969	−	0.624675i	0.0280574	−	0.0351964i
$316$		0			0
$317$	23.0942	−	16.7789i	1.29710	−	0.942397i	0.297175	−	0.954823i	$-0.403955\pi$
$317$	23.0942	−	16.7789i	1.29710	−	0.942397i	0.999923	+	0.0124261i	$0.00395545\pi$
$318$		0			0
$319$	−12.5472	+	9.11611i	−0.702511	+	0.510404i
$320$		0			0
$321$	23.2969	+	16.9262i	1.30031	+	0.944728i
$322$		0			0
$323$	−0.578830	+	1.78145i	−0.0322069	+	0.0991228i
$324$		0			0
$325$	−23.9231	−	2.14403i	−1.32701	−	0.118930i
$326$		0			0
$327$	4.47406	+	1.45371i	0.247416	+	0.0803903i
$328$		0			0
$329$	0.278418	+	0.202282i	0.0153497	+	0.0111522i
$330$		0			0
$331$	−2.10228	−	2.89354i	−0.115552	−	0.159043i	0.747323	−	0.664461i	$-0.231339\pi$
$331$	−2.10228	−	2.89354i	−0.115552	−	0.159043i	−0.862875	+	0.505417i	$0.831339\pi$
$332$		0			0
$333$	−4.21878	+	3.06512i	−0.231188	+	0.167968i
$334$		0			0
$335$	−2.93705	+	7.83023i	−0.160468	+	0.427811i
$336$		0			0
$337$	−9.35059	+	3.03819i	−0.509359	+	0.165501i	−0.552411	−	0.833572i	$-0.686292\pi$
$337$	−9.35059	+	3.03819i	−0.509359	+	0.165501i	0.0430517	+	0.999073i	$0.486292\pi$
$338$		0			0
$339$	10.9008	+	3.54187i	0.592048	+	0.192368i
$340$		0			0
$341$	−5.81317	+	1.88881i	−0.314801	+	0.102285i
$342$		0			0
$343$		−	1.55147i		−	0.0837717i
$344$		0			0
$345$	33.5366	+	12.5793i	1.80555	+	0.677245i
$346$		0			0
$347$	12.7780	+	9.28373i	0.685957	+	0.498377i	0.875329	−	0.483529i	$-0.160645\pi$
$347$	12.7780	+	9.28373i	0.685957	+	0.498377i	−0.189372	+	0.981905i	$0.560645\pi$
$348$		0			0
$349$			7.78786i			0.416875i	0.978036	+	0.208437i	$0.0668377\pi$
$349$			7.78786i			0.416875i	−0.978036	+	0.208437i	$0.933162\pi$
$350$		0			0
$351$	2.64810			0.141345
$352$		0			0
$353$	−6.60894	+	9.09643i	−0.351759	+	0.484154i	−0.947830	−	0.318778i	$-0.896728\pi$
$353$	−6.60894	+	9.09643i	−0.351759	+	0.484154i	0.596071	+	0.802932i	$0.296728\pi$
$354$		0			0
$355$	−24.9843	−	1.11733i	−1.32603	−	0.0593019i
$356$		0			0
$357$	0.126885			0.00671548
$358$		0			0
$359$	3.14405	+	9.67639i	0.165937	+	0.510700i	0.999104	−	0.0423204i	$-0.0134750\pi$
$359$	3.14405	+	9.67639i	0.165937	+	0.510700i	−0.833167	+	0.553021i	$0.813475\pi$
$360$		0			0
$361$	0.717206	−	2.20733i	0.0377477	−	0.116175i
$362$		0			0
$363$	−6.19476	−	19.0655i	−0.325141	−	1.00068i
$364$		0			0
$365$	22.3338	−	6.16826i	1.16900	−	0.322862i
$366$		0			0
$367$	7.13356	+	9.81851i	0.372369	+	0.512522i	0.953543	−	0.301257i	$-0.0974064\pi$
$367$	7.13356	+	9.81851i	0.372369	+	0.512522i	−0.581174	+	0.813779i	$0.697406\pi$
$368$		0			0
$369$	29.6458	−	21.5389i	1.54330	−	1.12127i
$370$		0			0
$371$	0.299329	−	0.411991i	0.0155404	−	0.0213895i
$372$		0			0
$373$	2.30235	−	7.08589i	0.119211	−	0.366894i	−0.873591	−	0.486661i	$-0.838215\pi$
$373$	2.30235	−	7.08589i	0.119211	−	0.366894i	0.992802	+	0.119767i	$0.0382148\pi$
$374$		0			0
$375$	12.0851	−	25.1312i	0.624070	−	1.29777i
$376$		0			0
$377$	41.1660	+	13.3757i	2.12016	+	0.688881i
$378$		0			0
$379$	3.70220	−	5.09564i	0.190169	−	0.261746i	−0.703277	−	0.710916i	$-0.748281\pi$
$379$	3.70220	−	5.09564i	0.190169	−	0.261746i	0.893446	+	0.449171i	$0.148281\pi$
$380$		0			0
$381$	11.9280	+	16.4175i	0.611091	+	0.841094i
$382$		0			0
$383$	16.8385	+	23.1761i	0.860405	+	1.18425i	0.981473	+	0.191601i	$0.0613681\pi$
$383$	16.8385	+	23.1761i	0.860405	+	1.18425i	−0.121068	+	0.992644i	$0.538632\pi$
$384$		0			0
$385$	−0.113648	−	0.411494i	−0.00579206	−	0.0209717i
$386$		0			0
$387$	−10.4814	−	32.2586i	−0.532802	−	1.63979i
$388$		0			0
$389$	−0.660483	−	0.214604i	−0.0334878	−	0.0108808i	0.292225	−	0.956350i	$-0.405604\pi$
$389$	−0.660483	−	0.214604i	−0.0334878	−	0.0108808i	−0.325713	+	0.945469i	$0.605604\pi$
$390$		0			0
$391$	0.910232	+	2.80141i	0.0460324	+	0.141673i
$392$		0			0
$393$		−	54.2378i		−	2.73593i
$394$		0			0
$395$	12.3003	+	0.550085i	0.618893	+	0.0276778i
$396$		0			0
$397$	16.9780	+	12.3352i	0.852099	+	0.619086i	0.925724	−	0.378200i	$-0.123457\pi$
$397$	16.9780	+	12.3352i	0.852099	+	0.619086i	−0.0736250	+	0.997286i	$0.523457\pi$
$398$		0			0
$399$	1.12983			0.0565625
$400$		0			0
$401$	18.7715			0.937404			0.468702	−	0.883356i	$-0.344722\pi$
$401$	18.7715			0.937404			0.468702	+	0.883356i	$0.344722\pi$
$402$		0			0
$403$	13.8009	+	10.0269i	0.687470	+	0.499476i
$404$		0			0
$405$	6.50869	−	17.3523i	0.323419	−	0.862241i
$406$		0			0
$407$			2.78663i			0.138128i
$408$		0			0
$409$	11.2943	+	34.7602i	0.558465	+	1.71878i	0.686611	+	0.727025i	$0.259097\pi$
$409$	11.2943	+	34.7602i	0.558465	+	1.71878i	−0.128146	+	0.991755i	$0.540903\pi$
$410$		0			0
$411$	21.7569	+	7.06926i	1.07319	+	0.348701i
$412$		0			0
$413$	0.122036	+	0.375588i	0.00600499	+	0.0184815i
$414$		0			0
$415$	−9.62012	+	25.6474i	−0.472233	+	1.25898i
$416$		0			0
$417$	−20.0626	−	27.6138i	−0.982471	−	1.35226i
$418$		0			0
$419$	−6.06690	−	8.35037i	−0.296387	−	0.407942i	0.634688	−	0.772768i	$-0.281128\pi$
$419$	−6.06690	−	8.35037i	−0.296387	−	0.407942i	−0.931076	+	0.364826i	$0.881128\pi$
$420$		0			0
$421$	−7.12906	+	9.81232i	−0.347449	+	0.478223i	−0.946599	−	0.322414i	$-0.895506\pi$
$421$	−7.12906	+	9.81232i	−0.347449	+	0.478223i	0.599149	+	0.800637i	$0.295506\pi$
$422$		0			0
$423$	−9.50473	−	3.08828i	−0.462136	−	0.150157i
$424$		0			0
$425$	2.23557	−	0.511139i	0.108441	−	0.0247939i
$426$		0			0
$427$	−0.402975	+	1.24023i	−0.0195013	+	0.0600189i
$428$		0			0
$429$	12.1220	−	16.6845i	0.585257	−	0.805538i
$430$		0			0
$431$	24.8747	−	18.0726i	1.19817	−	0.870525i	0.204070	−	0.978956i	$-0.434583\pi$
$431$	24.8747	−	18.0726i	1.19817	−	0.870525i	0.994104	+	0.108432i	$0.0345828\pi$
$432$		0			0
$433$	2.65013	+	3.64760i	0.127357	+	0.175292i	0.867934	−	0.496680i	$-0.165448\pi$
$433$	2.65013	+	3.64760i	0.127357	+	0.175292i	−0.740577	+	0.671972i	$0.765448\pi$
$434$		0			0
$435$	−31.3250	+	39.2955i	−1.50192	+	1.88407i
$436$		0			0
$437$	8.10505	+	24.9448i	0.387717	+	1.19327i
$438$		0			0
$439$	−3.68407	+	11.3384i	−0.175831	+	0.541153i	−0.999670	−	0.0256706i	$-0.991828\pi$
$439$	−3.68407	+	11.3384i	−0.175831	+	0.541153i	0.823839	+	0.566824i	$0.191828\pi$
$440$		0			0
$441$	6.95519	+	21.4059i	0.331200	+	1.01933i
$442$		0			0
$443$	4.00502			0.190284			0.0951422	−	0.995464i	$-0.469669\pi$
$443$	4.00502			0.190284			0.0951422	+	0.995464i	$0.469669\pi$
$444$		0			0
$445$	3.99820	+	14.4765i	0.189533	+	0.686254i
$446$		0			0
$447$	21.7558	−	29.9443i	1.02902	−	1.41632i
$448$		0			0
$449$	6.20695			0.292924			0.146462	−	0.989216i	$-0.453211\pi$
$449$	6.20695			0.292924			0.146462	+	0.989216i	$0.453211\pi$
$450$		0			0
$451$		−	19.5819i		−	0.922076i
$452$		0			0
$453$	17.9034	+	13.0076i	0.841174	+	0.611148i
$454$		0			0
$455$	−0.742667	+	0.931635i	−0.0348168	+	0.0436757i
$456$		0			0
$457$			34.1526i			1.59759i	0.601604	+	0.798795i	$0.294529\pi$
$457$			34.1526i			1.59759i	−0.601604	+	0.798795i	$0.705471\pi$
$458$		0			0
$459$	−0.240457	+	0.0781294i	−0.0112236	+	0.00364677i
$460$		0			0
$461$	12.3750	+	4.02087i	0.576359	+	0.187271i	0.582669	−	0.812710i	$-0.302008\pi$
$461$	12.3750	+	4.02087i	0.576359	+	0.187271i	−0.00630961	+	0.999980i	$0.502008\pi$
$462$		0			0
$463$	0.474013	−	0.154016i	0.0220292	−	0.00715774i	−0.297982	−	0.954572i	$-0.596313\pi$
$463$	0.474013	−	0.154016i	0.0220292	−	0.00715774i	0.320011	+	0.947414i	$0.396313\pi$
$464$		0			0
$465$	−16.5269	+	10.9138i	−0.766415	+	0.506113i
$466$		0			0
$467$	22.0431	−	16.0152i	1.02003	−	0.741096i	0.0537419	−	0.998555i	$-0.482885\pi$
$467$	22.0431	−	16.0152i	1.02003	−	0.741096i	0.966289	+	0.257459i	$0.0828852\pi$
$468$		0			0
$469$	0.243832	+	0.335606i	0.0112591	+	0.0154968i
$470$		0			0
$471$	−9.51161	−	6.91059i	−0.438272	−	0.318423i
$472$		0			0
$473$	−17.2383	−	5.60106i	−0.792618	−	0.257537i
$474$		0			0
$475$	19.9063	−	4.55138i	0.913365	−	0.208831i
$476$		0			0
$477$	−4.56990	+	14.0647i	−0.209242	+	0.643979i
$478$		0			0
$479$	−23.5204	−	17.0886i	−1.07468	−	0.780797i	−0.0979285	−	0.995193i	$-0.531222\pi$
$479$	−23.5204	−	17.0886i	−1.07468	−	0.780797i	−0.976747	+	0.214396i	$0.931222\pi$
$480$		0			0
$481$	6.29185	−	4.57130i	0.286884	−	0.208433i
$482$		0			0
$483$	1.43739	−	1.04432i	0.0654034	−	0.0475183i
$484$		0			0
$485$	−0.561484	+	12.5551i	−0.0254957	+	0.570100i
$486$		0			0
$487$	24.7645	−	8.04647i	1.12219	−	0.364620i	0.311584	−	0.950219i	$-0.399140\pi$
$487$	24.7645	−	8.04647i	1.12219	−	0.364620i	0.810601	+	0.585598i	$0.199140\pi$
$488$		0			0
$489$	7.73167	−	23.7956i	0.349638	−	1.07608i
$490$		0			0
$491$	−23.4217	+	7.61016i	−1.05700	+	0.343442i	−0.785414	−	0.618971i	$-0.787550\pi$
$491$	−23.4217	+	7.61016i	−1.05700	+	0.343442i	−0.271591	+	0.962413i	$0.587550\pi$
$492$		0			0
$493$	−4.13267			−0.186126
$494$		0			0
$495$	6.83147	+	10.3450i	0.307052	+	0.464973i
$496$		0			0
$497$	−0.729177	+	1.00363i	−0.0327081	+	0.0450188i
$498$		0			0
$499$			18.4619i			0.826469i	0.910625	+	0.413234i	$0.135601\pi$
$499$			18.4619i			0.826469i	−0.910625	+	0.413234i	$0.864399\pi$
$500$		0			0
$501$		−	20.0640i		−	0.896393i
$502$		0			0
$503$	−14.1453	+	19.4694i	−0.630709	+	0.868097i	−0.998077	−	0.0619786i	$-0.980259\pi$
$503$	−14.1453	+	19.4694i	−0.630709	+	0.868097i	0.367368	+	0.930076i	$0.380259\pi$
$504$		0			0
$505$	−1.91779	−	2.90414i	−0.0853406	−	0.129232i
$506$		0			0
$507$	−25.1325			−1.11618
$508$		0			0
$509$	0.950881	−	0.308960i	0.0421471	−	0.0136944i	−0.287868	−	0.957670i	$-0.592946\pi$
$509$	0.950881	−	0.308960i	0.0421471	−	0.0136944i	0.330015	+	0.943976i	$0.392946\pi$
$510$		0			0
$511$	0.355157	−	1.09306i	0.0157112	−	0.0483541i
$512$		0			0
$513$	−2.14112	+	0.695693i	−0.0945330	+	0.0307156i
$514$		0			0
$515$	−0.471327	+	10.5392i	−0.0207691	+	0.464412i
$516$		0			0
$517$	−4.32057	+	3.13908i	−0.190018	+	0.138056i
$518$		0			0
$519$	20.0697	−	14.5815i	0.880961	−	0.640056i
$520$		0			0
$521$	−13.1276	−	9.53774i	−0.575129	−	0.417856i	0.261836	−	0.965112i	$-0.415672\pi$
$521$	−13.1276	−	9.53774i	−0.575129	−	0.417856i	−0.836965	+	0.547257i	$0.815672\pi$
$522$		0			0
$523$	0.338728	−	1.04250i	0.0148115	−	0.0455852i	−0.943378	−	0.331721i	$-0.892371\pi$
$523$	0.338728	−	1.04250i	0.0148115	−	0.0455852i	0.958189	+	0.286136i	$0.0923708\pi$
$524$		0			0
$525$	−0.709912	−	1.18718i	−0.0309831	−	0.0518126i
$526$		0			0
$527$	−1.54901	−	0.503303i	−0.0674758	−	0.0219242i
$528$		0			0
$529$	14.7608	+	10.7243i	0.641773	+	0.466275i
$530$		0			0
$531$	−6.74091	−	9.27806i	−0.292530	−	0.402634i
$532$		0			0
$533$	−44.2135	+	32.1230i	−1.91510	+	1.39140i
$534$		0			0
$535$	21.5430	−	14.2262i	0.931384	−	0.615053i
$536$		0			0
$537$	−29.8585	+	9.70162i	−1.28849	+	0.418656i
$538$		0			0
$539$	11.4389	+	3.71671i	0.492706	+	0.160090i
$540$		0			0
$541$	22.8256	−	7.41649i	0.981349	−	0.318860i	0.225961	−	0.974136i	$-0.427448\pi$
$541$	22.8256	−	7.41649i	0.981349	−	0.318860i	0.755389	+	0.655277i	$0.227448\pi$
$542$		0			0
$543$			32.5706i			1.39774i
$544$		0			0
$545$	2.62891	−	3.29783i	0.112610	−	0.141263i
$546$		0			0
$547$	20.6852	+	15.0286i	0.884434	+	0.642579i	0.934421	−	0.356171i	$-0.115918\pi$
$547$	20.6852	+	15.0286i	0.884434	+	0.642579i	−0.0499871	+	0.998750i	$0.515918\pi$
$548$		0			0
$549$		−	37.8696i		−	1.61623i
$550$		0			0
$551$	−36.7989			−1.56769
$552$		0			0
$553$	0.358988	−	0.494105i	0.0152657	−	0.0210115i
$554$		0			0
$555$	2.40376	+	8.70342i	0.102034	+	0.369440i
$556$		0			0
$557$	−39.1180			−1.65748			−0.828742	−	0.559631i	$-0.810943\pi$
$557$	−39.1180			−1.65748			−0.828742	+	0.559631i	$0.810943\pi$
$558$		0			0
$559$	15.6319	+	48.1101i	0.661160	+	2.03484i
$560$		0			0
$561$	−0.608468	+	1.87267i	−0.0256895	+	0.0790642i
$562$		0			0
$563$	9.45014	+	29.0845i	0.398276	+	1.22577i	0.926381	+	0.376588i	$0.122903\pi$
$563$	9.45014	+	29.0845i	0.398276	+	1.22577i	−0.528105	+	0.849179i	$0.677097\pi$
$564$		0			0
$565$	6.40519	−	8.03495i	0.269468	−	0.338033i
$566$		0			0
$567$	−0.540347	−	0.743723i	−0.0226924	−	0.0312334i
$568$		0			0
$569$	0.511882	−	0.371904i	0.0214592	−	0.0155910i	−0.577004	−	0.816741i	$-0.695778\pi$
$569$	0.511882	−	0.371904i	0.0214592	−	0.0155910i	0.598463	+	0.801150i	$0.295778\pi$
$570$		0			0
$571$	2.91121	−	4.00694i	0.121830	−	0.167685i	−0.743746	−	0.668463i	$-0.766953\pi$
$571$	2.91121	−	4.00694i	0.121830	−	0.167685i	0.865576	+	0.500778i	$0.166953\pi$
$572$		0			0
$573$	2.21761	−	6.82510i	0.0926419	−	0.285122i
$574$		0			0
$575$	21.1181	−	24.1900i	0.880687	−	1.00879i
$576$		0			0
$577$	−15.2638	−	4.95951i	−0.635440	−	0.206467i	−0.0264569	−	0.999650i	$-0.508422\pi$
$577$	−15.2638	−	4.95951i	−0.635440	−	0.206467i	−0.608984	+	0.793183i	$0.708422\pi$
$578$		0			0
$579$	−23.3130	+	32.0876i	−0.968855	+	1.33352i
$580$		0			0
$581$	0.798656	+	1.09926i	0.0331338	+	0.0456048i
$582$		0			0
$583$	4.64508	+	6.39340i	0.192379	+	0.264788i
$584$		0			0
$585$	12.1511	−	32.3949i	0.502385	−	1.33937i
$586$		0			0
$587$	−7.22818	−	22.2461i	−0.298339	−	0.918193i	−0.982079	−	0.188468i	$-0.939648\pi$
$587$	−7.22818	−	22.2461i	−0.298339	−	0.918193i	0.683740	−	0.729725i	$-0.260352\pi$
$588$		0			0
$589$	−13.7929	−	4.48160i	−0.568328	−	0.184661i
$590$		0			0
$591$	3.60552	+	11.0967i	0.148311	+	0.456455i
$592$		0			0
$593$			7.54773i			0.309948i	0.987919	+	0.154974i	$0.0495294\pi$
$593$			7.54773i			0.309948i	−0.987919	+	0.154974i	$0.950471\pi$
$594$		0			0
$595$	0.0399501	−	0.106508i	0.00163780	−	0.00436639i
$596$		0			0
$597$	−56.5882	−	41.1137i	−2.31600	−	1.68267i
$598$		0			0
$599$	−0.302745			−0.0123698			−0.00618491	−	0.999981i	$-0.501969\pi$
$599$	−0.302745			−0.0123698			−0.00618491	+	0.999981i	$0.501969\pi$
$600$		0			0
$601$	−32.7273			−1.33497			−0.667487	−	0.744622i	$-0.732630\pi$
$601$	−32.7273			−1.33497			−0.667487	+	0.744622i	$0.732630\pi$
$602$		0			0
$603$	−9.74595	−	7.08085i	−0.396886	−	0.288354i
$604$		0			0
$605$	−17.9541	−	0.802930i	−0.729936	−	0.0326438i
$606$		0			0
$607$		−	26.9091i		−	1.09221i	−0.837718	−	0.546103i	$-0.816111\pi$
$607$		−	26.9091i		−	1.09221i	0.837718	−	0.546103i	$-0.183889\pi$
$608$		0			0
$609$	0.770300	+	2.37074i	0.0312141	+	0.0960672i
$610$		0			0
$611$	14.1753	+	4.60583i	0.573470	+	0.186332i
$612$		0			0
$613$	2.61296	+	8.04187i	0.105537	+	0.324808i	0.989856	−	0.142074i	$-0.0453772\pi$
$613$	2.61296	+	8.04187i	0.105537	+	0.324808i	−0.884319	+	0.466882i	$0.845377\pi$
$614$		0			0
$615$	−16.8914	−	61.1598i	−0.681128	−	2.46620i
$616$		0			0
$617$	−11.3137	−	15.5720i	−0.455472	−	0.626904i	0.518090	−	0.855326i	$-0.326643\pi$
$617$	−11.3137	−	15.5720i	−0.455472	−	0.626904i	−0.973562	+	0.228422i	$0.926643\pi$
$618$		0			0
$619$	19.2261	+	26.4625i	0.772763	+	1.06362i	0.996044	+	0.0888631i	$0.0283233\pi$
$619$	19.2261	+	26.4625i	0.772763	+	1.06362i	−0.223281	+	0.974754i	$0.571677\pi$
$620$		0			0
$621$	−2.08092	+	2.86414i	−0.0835045	+	0.114934i
$622$		0			0
$623$	0.708511	+	0.230209i	0.0283859	+	0.00922313i
$624$		0			0
$625$	−17.2902	−	18.0569i	−0.691607	−	0.722274i
$626$		0			0
$627$	−5.41803	+	16.6750i	−0.216375	+	0.665934i
$628$		0			0
$629$	−0.436453	+	0.600727i	−0.0174025	+	0.0239525i
$630$		0			0
$631$	−29.3548	+	21.3275i	−1.16860	+	0.849035i	−0.990840	−	0.135040i	$-0.956884\pi$
$631$	−29.3548	+	21.3275i	−1.16860	+	0.849035i	−0.177756	+	0.984075i	$0.556884\pi$
$632$		0			0
$633$	−0.478417	−	0.658485i	−0.0190154	−	0.0261724i
$634$		0			0
$635$	17.5364	−	4.84331i	0.695913	−	0.192201i
$636$		0			0
$637$	−10.3729	−	31.9245i	−0.410990	−	1.26490i
$638$		0			0
$639$	11.1325	−	34.2622i	0.440393	−	1.35539i
$640$		0			0
$641$	−0.0519999	−	0.160039i	−0.00205387	−	0.00632117i	0.950024	−	0.312176i	$-0.101058\pi$
$641$	−0.0519999	−	0.160039i	−0.00205387	−	0.00632117i	−0.952078	+	0.305855i	$0.901058\pi$
$642$		0			0
$643$	−6.95566			−0.274305			−0.137152	−	0.990550i	$-0.543795\pi$
$643$	−6.95566			−0.274305			−0.137152	+	0.990550i	$0.543795\pi$
$644$		0			0
$645$	−58.6716	−	2.62387i	−2.31019	−	0.103315i
$646$		0			0
$647$	−15.2526	+	20.9935i	−0.599643	+	0.825338i	−0.995676	−	0.0928983i	$-0.970387\pi$
$647$	−15.2526	+	20.9935i	−0.599643	+	0.825338i	0.396032	+	0.918237i	$0.370387\pi$
$648$		0			0
$649$	−6.12843			−0.240562
$650$		0			0
$651$			0.982411i			0.0385037i
$652$		0			0
$653$	14.9322	+	10.8488i	0.584340	+	0.424548i	0.840286	−	0.542143i	$-0.182387\pi$
$653$	14.9322	+	10.8488i	0.584340	+	0.424548i	−0.255946	+	0.966691i	$0.582387\pi$
$654$		0			0
$655$	−45.5273	−	17.0769i	−1.77890	−	0.667250i
$656$		0			0
$657$			33.3758i			1.30212i
$658$		0			0
$659$	−8.10100	+	2.63217i	−0.315570	+	0.102535i	−0.462520	−	0.886609i	$-0.653055\pi$
$659$	−8.10100	+	2.63217i	−0.315570	+	0.102535i	0.146950	+	0.989144i	$0.453055\pi$
$660$		0			0
$661$	38.1202	+	12.3860i	1.48270	+	0.481760i	0.934920	−	0.354859i	$-0.115471\pi$
$661$	38.1202	+	12.3860i	1.48270	+	0.481760i	0.547785	+	0.836619i	$0.315471\pi$
$662$		0			0
$663$	5.22641	−	1.69816i	0.202977	−	0.0659512i
$664$		0			0
$665$	0.355731	−	0.948385i	0.0137947	−	0.0367768i
$666$		0			0
$667$	−46.8159	+	34.0138i	−1.81272	+	1.31702i
$668$		0			0
$669$	17.2800	+	23.7839i	0.668084	+	0.919539i
$670$		0			0
$671$	−16.3718	−	11.8948i	−0.632028	−	0.459195i
$672$		0			0
$673$	42.8082	+	13.9092i	1.65014	+	0.536162i	0.978770	−	0.204964i	$-0.0657076\pi$
$673$	42.8082	+	13.9092i	1.65014	+	0.536162i	0.671367	+	0.741125i	$0.265708\pi$
$674$		0			0
$675$	2.07634	+	1.81267i	0.0799184	+	0.0697695i
$676$		0			0
$677$	13.9190	−	42.8382i	0.534950	−	1.64641i	−0.208808	−	0.977957i	$-0.566958\pi$
$677$	13.9190	−	42.8382i	0.534950	−	1.64641i	0.743758	−	0.668450i	$-0.233042\pi$
$678$		0			0
$679$	0.504344	+	0.366427i	0.0193549	+	0.0140622i
$680$		0			0
$681$	−2.11756	+	1.53849i	−0.0811449	+	0.0589552i
$682$		0			0
$683$	5.91153	−	4.29498i	0.226199	−	0.164343i	−0.468914	−	0.883244i	$-0.655355\pi$
$683$	5.91153	−	4.29498i	0.226199	−	0.164343i	0.695112	+	0.718901i	$0.255355\pi$
$684$		0			0
$685$	12.7842	−	16.0370i	0.488458	−	0.612744i
$686$		0			0
$687$	−47.9850	+	15.5913i	−1.83074	+	0.594844i
$688$		0			0
$689$	6.81552	−	20.9760i	0.259650	−	0.799122i
$690$		0			0
$691$	33.1194	−	10.7611i	1.25992	−	0.409373i	0.398455	−	0.917188i	$-0.369546\pi$
$691$	33.1194	−	10.7611i	1.25992	−	0.409373i	0.861467	+	0.507814i	$0.169546\pi$
$692$		0			0
$693$	0.614940			0.0233596
$694$		0			0
$695$	−29.4959	+	8.14632i	−1.11884	+	0.309008i
$696$		0			0
$697$	3.06700	−	4.22136i	0.116171	−	0.159896i
$698$		0			0
$699$		−	65.4828i		−	2.47679i
$700$		0			0
$701$		−	22.3659i		−	0.844750i	−0.906421	−	0.422375i	$-0.861197\pi$
$701$		−	22.3659i		−	0.844750i	0.906421	−	0.422375i	$-0.138803\pi$
$702$		0			0
$703$	−3.88635	+	5.34910i	−0.146576	+	0.201745i
$704$		0			0
$705$	−10.7866	+	13.5312i	−0.406246	+	0.509613i
$706$		0			0
$707$	−0.172631			−0.00649248
$708$		0			0
$709$	−17.1971	+	5.58767i	−0.645849	+	0.209849i	−0.613583	−	0.789630i	$-0.710272\pi$
$709$	−17.1971	+	5.58767i	−0.645849	+	0.209849i	−0.0322662	+	0.999479i	$0.510272\pi$
$710$		0			0
$711$	−5.48073	+	16.8679i	−0.205543	+	0.632597i
$712$		0			0
$713$	−21.6899	+	7.04749i	−0.812294	+	0.263930i
$714$		0			0
$715$	−10.1884	−	15.4284i	−0.381024	−	0.576991i
$716$		0			0
$717$	17.6219	−	12.8030i	0.658101	−	0.478139i
$718$		0			0
$719$	31.8411	−	23.1339i	1.18747	−	0.862749i	0.194477	−	0.980907i	$-0.437699\pi$
$719$	31.8411	−	23.1339i	1.18747	−	0.862749i	0.992995	+	0.118158i	$0.0376991\pi$
$720$		0			0
$721$	0.423362	+	0.307590i	0.0157668	+	0.0114553i
$722$		0			0
$723$	−0.275733	+	0.848620i	−0.0102546	+	0.0315605i
$724$		0			0
$725$	23.1219	+	38.6665i	0.858728	+	1.43604i
$726$		0			0
$727$	16.7936	+	5.45658i	0.622841	+	0.202373i	0.603401	−	0.797438i	$-0.293812\pi$
$727$	16.7936	+	5.45658i	0.622841	+	0.202373i	0.0194399	+	0.999811i	$0.493812\pi$
$728$		0			0
$729$	24.9346	+	18.1161i	0.923505	+	0.670966i
$730$		0			0
$731$	−2.83888	−	3.90738i	−0.105000	−	0.144520i
$732$		0			0
$733$	7.26956	−	5.28165i	0.268507	−	0.195082i	−0.445382	−	0.895341i	$-0.646932\pi$
$733$	7.26956	−	5.28165i	0.268507	−	0.195082i	0.713889	+	0.700259i	$0.246932\pi$
$734$		0			0
$735$	38.9328	+	1.74113i	1.43606	+	0.0642225i
$736$		0			0
$737$	−6.12241	+	1.98929i	−0.225522	+	0.0732765i
$738$		0			0
$739$	−20.0852	−	6.52609i	−0.738848	−	0.240066i	−0.0846720	−	0.996409i	$-0.526984\pi$
$739$	−20.0852	−	6.52609i	−0.738848	−	0.240066i	−0.654176	+	0.756343i	$0.726984\pi$
$740$		0			0
$741$	46.5379	−	15.1211i	1.70961	−	0.555487i
$742$		0			0
$743$			8.50903i			0.312166i	0.987744	+	0.156083i	$0.0498868\pi$
$743$			8.50903i			0.312166i	−0.987744	+	0.156083i	$0.950113\pi$
$744$		0			0
$745$	−18.2854	−	27.6899i	−0.669927	−	1.01448i
$746$		0			0
$747$	−31.9222	−	23.1929i	−1.16797	−	0.848582i
$748$		0			0
$749$		−	1.28058i		−	0.0467916i
$750$		0			0
$751$	17.1075			0.624262			0.312131	−	0.950039i	$-0.398957\pi$
$751$	17.1075			0.624262			0.312131	+	0.950039i	$0.398957\pi$
$752$		0			0
$753$	−29.3753	+	40.4317i	−1.07050	+	1.47341i
$754$		0			0
$755$	16.5555	−	10.9327i	0.602516	−	0.397880i
$756$		0			0
$757$	2.28693			0.0831199			0.0415599	−	0.999136i	$-0.486767\pi$
$757$	2.28693			0.0831199			0.0415599	+	0.999136i	$0.486767\pi$
$758$		0			0
$759$	8.52006	+	26.2220i	0.309258	+	0.951800i
$760$		0			0
$761$	−6.05917	+	18.6482i	−0.219645	+	0.675997i	0.779146	+	0.626842i	$0.215653\pi$
$761$	−6.05917	+	18.6482i	−0.219645	+	0.675997i	−0.998791	+	0.0491552i	$0.984347\pi$
$762$		0			0
$763$	−0.0646465	−	0.198961i	−0.00234036	−	0.00720289i
$764$		0			0
$765$	−0.147585	+	3.30009i	−0.00533593	+	0.119315i
$766$		0			0
$767$	10.0533	+	13.8372i	0.363005	+	0.499633i
$768$		0			0
$769$	15.2893	−	11.1083i	0.551345	−	0.400576i	−0.276936	−	0.960888i	$-0.589319\pi$
$769$	15.2893	−	11.1083i	0.551345	−	0.400576i	0.828281	+	0.560313i	$0.189319\pi$
$770$		0			0
$771$	27.4599	−	37.7954i	0.988946	−	1.36117i
$772$		0			0
$773$	−2.33908	+	7.19893i	−0.0841307	+	0.258928i	−0.984269	−	0.176677i	$-0.943465\pi$
$773$	−2.33908	+	7.19893i	−0.0841307	+	0.258928i	0.900138	+	0.435604i	$0.143465\pi$
$774$		0			0
$775$	3.95750	+	17.3089i	0.142158	+	0.621754i
$776$		0			0
$777$	0.425963	+	0.138404i	0.0152813	+	0.00496521i
$778$		0			0
$779$	27.3097	−	37.5886i	0.978473	−	1.34675i
$780$		0			0
$781$	−11.3156	−	15.5746i	−0.404903	−	0.557302i
$782$		0			0
$783$	−2.91956	−	4.01843i	−0.104336	−	0.143607i
$784$		0			0
$785$	−8.79551	+	5.80824i	−0.313925	+	0.207305i
$786$		0			0
$787$	−12.5994	−	38.7769i	−0.449119	−	1.38225i	−0.877903	−	0.478839i	$-0.841058\pi$
$787$	−12.5994	−	38.7769i	−0.449119	−	1.38225i	0.428784	−	0.903407i	$-0.358942\pi$
$788$		0			0
$789$	39.1099	+	12.7076i	1.39235	+	0.452401i
$790$		0			0
$791$	−0.157507	−	0.484757i	−0.00560031	−	0.0172360i
$792$		0			0
$793$			56.4783i			2.00560i
$794$		0			0
$795$	20.0229	+	15.9615i	0.710138	+	0.566097i
$796$		0			0
$797$	4.00819	+	2.91212i	0.141977	+	0.103153i	0.656507	−	0.754320i	$-0.272033\pi$
$797$	4.00819	+	2.91212i	0.141977	+	0.103153i	−0.514529	+	0.857473i	$0.672033\pi$
$798$		0			0
$799$	−1.42306			−0.0503443
$800$		0			0
$801$	−21.6339			−0.764396
$802$		0			0
$803$	14.4291	+	10.4834i	0.509192	+	0.369950i
$804$		0			0
$805$	−0.424042	−	1.53535i	−0.0149455	−	0.0541141i
$806$		0			0
$807$			0.363315i			0.0127893i
$808$		0			0
$809$	7.58506	+	23.3444i	0.266676	+	0.820746i	0.991302	+	0.131603i	$0.0420126\pi$
$809$	7.58506	+	23.3444i	0.266676	+	0.820746i	−0.724626	+	0.689142i	$0.757987\pi$
$810$		0			0
$811$	0.736311	+	0.239242i	0.0258554	+	0.00840092i	0.321916	−	0.946768i	$-0.395673\pi$
$811$	0.736311	+	0.239242i	0.0258554	+	0.00840092i	−0.296061	+	0.955169i	$0.595673\pi$
$812$		0			0
$813$	11.8203	+	36.3792i	0.414557	+	1.27588i
$814$		0			0
$815$	−17.5398	−	13.9821i	−0.614391	−	0.489771i
$816$		0			0
$817$	−25.2785	−	34.7928i	−0.884382	−	1.21725i
$818$		0			0
$819$	−1.00877	−	1.38846i	−0.0352494	−	0.0485166i
$820$		0			0
$821$	−4.17446	+	5.74566i	−0.145690	+	0.200525i	−0.875625	−	0.482992i	$-0.839550\pi$
$821$	−4.17446	+	5.74566i	−0.145690	+	0.200525i	0.729935	+	0.683516i	$0.239550\pi$
$822$		0			0
$823$	−7.47765	−	2.42963i	−0.260654	−	0.0846917i	0.175775	−	0.984430i	$-0.443757\pi$
$823$	−7.47765	−	2.42963i	−0.260654	−	0.0846917i	−0.436429	+	0.899739i	$0.643757\pi$
$824$		0			0
$825$	20.9256	−	4.78442i	0.728536	−	0.166572i
$826$		0			0
$827$	1.01952	−	3.13777i	0.0354523	−	0.109111i	−0.931764	−	0.363064i	$-0.881731\pi$
$827$	1.01952	−	3.13777i	0.0354523	−	0.109111i	0.967217	+	0.253953i	$0.0817308\pi$
$828$		0			0
$829$	19.0835	−	26.2662i	0.662798	−	0.912263i	−0.336772	−	0.941586i	$-0.609335\pi$
$829$	19.0835	−	26.2662i	0.662798	−	0.912263i	0.999570	+	0.0293232i	$0.00933521\pi$
$830$		0			0
$831$	−41.7875	+	30.3604i	−1.44959	+	1.05319i
$832$		0			0
$833$	1.88380	+	2.59283i	0.0652699	+	0.0898362i
$834$		0			0
$835$	−16.8418	−	6.31720i	−0.582833	−	0.218616i
$836$		0			0
$837$	−0.604918	−	1.86175i	−0.0209090	−	0.0643514i
$838$		0			0
$839$	−3.32108	+	10.2212i	−0.114656	+	0.352876i	−0.991875	−	0.127215i	$-0.959396\pi$
$839$	−3.32108	+	10.2212i	−0.114656	+	0.352876i	0.877219	+	0.480091i	$0.159396\pi$
$840$		0			0
$841$	−16.1273	−	49.6347i	−0.556114	−	1.71154i
$842$		0			0
$843$	−26.4020			−0.909332
$844$		0			0
$845$	−7.91304	+	21.0963i	−0.272217	+	0.725735i
$846$		0			0
$847$	−0.523996	+	0.721219i	−0.0180047	+	0.0247814i
$848$		0			0
$849$	−51.3090			−1.76092
$850$		0			0
$851$			10.3974i			0.356418i
$852$		0			0
$853$	−18.7063	−	13.5909i	−0.640491	−	0.465344i	0.219528	−	0.975606i	$-0.429548\pi$
$853$	−18.7063	−	13.5909i	−0.640491	−	0.465344i	−0.860019	+	0.510262i	$0.829548\pi$
$854$		0			0
$855$	−1.31415	+	29.3853i	−0.0449430	+	1.00495i
$856$		0			0
$857$			15.8941i			0.542932i	0.962448	+	0.271466i	$0.0875084\pi$
$857$			15.8941i			0.542932i	−0.962448	+	0.271466i	$0.912492\pi$
$858$		0			0
$859$	−3.46524	+	1.12593i	−0.118233	+	0.0384161i	−0.367536	−	0.930009i	$-0.619798\pi$
$859$	−3.46524	+	1.12593i	−0.118233	+	0.0384161i	0.249303	+	0.968425i	$0.419798\pi$
$860$		0			0
$861$	−2.99328	−	0.972577i	−0.102011	−	0.0331453i
$862$		0			0
$863$	−39.8580	+	12.9507i	−1.35678	+	0.440845i	−0.894968	−	0.446131i	$-0.852802\pi$
$863$	−39.8580	+	12.9507i	−1.35678	+	0.440845i	−0.461815	+	0.886976i	$0.652802\pi$
$864$		0			0
$865$	−5.92073	−	21.4375i	−0.201311	−	0.728898i
$866$		0			0
$867$	33.8789	−	24.6145i	1.15059	−	0.835951i
$868$		0			0
$869$	5.57088	+	7.66766i	0.188979	+	0.260108i
$870$		0			0
$871$	14.5350	+	10.5603i	0.492500	+	0.357823i
$872$		0			0
$873$	−17.2175	−	5.59430i	−0.582723	−	0.189338i
$874$		0			0
$875$	−1.22004	+	0.222116i	−0.0412447	+	0.00750888i
$876$		0			0
$877$	−8.84000	+	27.2067i	−0.298505	+	0.918705i	0.683516	+	0.729936i	$0.260450\pi$
$877$	−8.84000	+	27.2067i	−0.298505	+	0.918705i	−0.982021	+	0.188770i	$0.939550\pi$
$878$		0			0
$879$	1.21702	+	0.884217i	0.0410491	+	0.0298239i
$880$		0			0
$881$	15.5718	−	11.3135i	0.524626	−	0.381163i	−0.293718	−	0.955892i	$-0.594893\pi$
$881$	15.5718	−	11.3135i	0.524626	−	0.381163i	0.818344	+	0.574729i	$0.194893\pi$
$882$		0			0
$883$	10.5069	−	7.63372i	0.353586	−	0.256895i	−0.396786	−	0.917911i	$-0.629874\pi$
$883$	10.5069	−	7.63372i	0.353586	−	0.256895i	0.750372	+	0.661016i	$0.229874\pi$
$884$		0			0
$885$	−19.1408	+	5.28641i	−0.643411	+	0.177701i
$886$		0			0
$887$	−16.0762	+	5.22346i	−0.539785	+	0.175387i	−0.566205	−	0.824264i	$-0.691589\pi$
$887$	−16.0762	+	5.22346i	−0.539785	+	0.175387i	0.0264205	+	0.999651i	$0.491589\pi$
$888$		0			0
$889$	0.278868	−	0.858269i	0.00935295	−	0.0287854i
$890$		0			0
$891$	13.5676	−	4.40839i	0.454533	−	0.147687i
$892$		0			0
$893$	−12.6715			−0.424035
$894$		0			0
$895$	−1.25747	+	28.1179i	−0.0420326	+	0.939877i
$896$		0			0
$897$	45.2294	−	62.2529i	1.51017	−	2.07856i
$898$		0			0
$899$		−	31.9973i		−	1.06717i
$900$		0			0
$901$			2.10579i			0.0701540i
$902$		0			0
$903$	−1.71235	+	2.35685i	−0.0569836	+	0.0784312i
$904$		0			0
$905$	27.3398	+	10.2549i	0.908806	+	0.340885i
$906$		0			0
$907$	−36.2209			−1.20269			−0.601347	−	0.798988i	$-0.705369\pi$
$907$	−36.2209			−1.20269			−0.601347	+	0.798988i	$0.705369\pi$
$908$		0			0
$909$	4.76783	−	1.54916i	0.158139	−	0.0513825i
$910$		0			0
$911$	3.31491	−	10.2022i	0.109828	−	0.338015i	−0.881005	−	0.473106i	$-0.843133\pi$
$911$	3.31491	−	10.2022i	0.109828	−	0.338015i	0.990833	+	0.135091i	$0.0431327\pi$
$912$		0			0
$913$	−20.0536	+	6.51579i	−0.663676	+	0.215641i
$914$		0			0
$915$	−61.3944	−	23.0285i	−2.02964	−	0.761299i
$916$		0			0
$917$	−1.95131	+	1.41771i	−0.0644381	+	0.0468170i
$918$		0			0
$919$	32.1024	−	23.3238i	1.05896	−	0.769380i	0.0850654	−	0.996375i	$-0.472890\pi$
$919$	32.1024	−	23.3238i	1.05896	−	0.769380i	0.973896	+	0.226995i	$0.0728901\pi$
$920$		0			0
$921$	20.1028	+	14.6056i	0.662411	+	0.481270i
$922$		0			0
$923$	−16.6029	+	51.0983i	−0.546490	+	1.68192i
$924$		0			0
$925$	8.06250	+	0.722577i	0.265093	+	0.0237582i
$926$		0			0
$927$	−14.4529	−	4.69603i	−0.474695	−	0.154238i
$928$		0			0
$929$	17.2005	+	12.4969i	0.564331	+	0.410011i	0.833042	−	0.553210i	$-0.186597\pi$
$929$	17.2005	+	12.4969i	0.564331	+	0.410011i	−0.268710	+	0.963221i	$0.586597\pi$
$930$		0			0
$931$	16.7741	+	23.0875i	0.549748	+	0.756664i
$932$		0			0
$933$	49.1558	−	35.7138i	1.60929	−	1.16922i
$934$		0			0
$935$	1.38035	+	1.10036i	0.0451421	+	0.0359857i
$936$		0			0
$937$	28.5238	−	9.26796i	0.931833	−	0.302771i	0.196521	−	0.980500i	$-0.437036\pi$
$937$	28.5238	−	9.26796i	0.931833	−	0.302771i	0.735312	+	0.677729i	$0.237036\pi$
$938$		0			0
$939$	44.3948	+	14.4248i	1.44877	+	0.470734i
$940$		0			0
$941$	−20.6829	+	6.72027i	−0.674242	+	0.219075i	−0.626073	−	0.779765i	$-0.715339\pi$
$941$	−20.6829	+	6.72027i	−0.674242	+	0.219075i	−0.0481695	+	0.998839i	$0.515339\pi$
$942$		0			0
$943$		−	73.0634i		−	2.37927i
$944$		0			0
$945$	0.131786	−	0.0363974i	0.00428701	−	0.00118401i
$946$		0			0
$947$	19.0805	+	13.8628i	0.620034	+	0.450481i	0.852934	−	0.522020i	$-0.174821\pi$
$947$	19.0805	+	13.8628i	0.620034	+	0.450481i	−0.232899	+	0.972501i	$0.574821\pi$
$948$		0			0
$949$		−	49.7764i		−	1.61581i
$950$		0			0
$951$	71.1992			2.30879
$952$		0			0
$953$	16.3647	−	22.5241i	0.530106	−	0.729629i	−0.457040	−	0.889446i	$-0.651091\pi$
$953$	16.3647	−	22.5241i	0.530106	−	0.729629i	0.987147	+	0.159817i	$0.0510905\pi$
$954$		0			0
$955$	−5.03078	−	4.01036i	−0.162792	−	0.129772i
$956$		0			0
$957$	−38.6831			−1.25045
$958$		0			0
$959$	−0.314370	−	0.967532i	−0.0101515	−	0.0312432i
$960$		0			0
$961$	−5.68270	+	17.4895i	−0.183313	+	0.564179i
$962$		0			0
$963$	11.4917	+	35.3679i	0.370316	+	1.13971i
$964$		0			0
$965$	19.5942	+	29.6718i	0.630761	+	0.955170i
$966$		0			0
$967$	−35.9696	−	49.5079i	−1.15671	−	1.59207i	−0.722707	−	0.691154i	$-0.757103\pi$
$967$	−35.9696	−	49.5079i	−1.15671	−	1.59207i	−0.433998	−	0.900914i	$-0.642897\pi$
$968$		0			0
$969$	−3.77969	+	2.74611i	−0.121421	+	0.0882177i
$970$		0			0
$971$	19.9841	−	27.5058i	0.641321	−	0.882703i	−0.357364	−	0.933965i	$-0.616324\pi$
$971$	19.9841	−	27.5058i	0.641321	−	0.882703i	0.998685	+	0.0512621i	$0.0163244\pi$
$972$		0			0
$973$	−0.469050	+	1.44359i	−0.0150371	+	0.0462793i
$974$		0			0
$975$	−45.1298	−	39.3988i	−1.44531	−	1.26177i
$976$		0			0
$977$	50.4988	+	16.4081i	1.61560	+	0.524940i	0.970898	−	0.239494i	$-0.0769816\pi$
$977$	50.4988	+	16.4081i	1.61560	+	0.524940i	0.644702	+	0.764434i	$0.276982\pi$
$978$		0			0
$979$	−6.79521	+	9.35280i	−0.217176	+	0.298917i
$980$		0			0
$981$	3.57088	+	4.91490i	0.114010	+	0.156921i
$982$		0			0
$983$	−18.0867	−	24.8942i	−0.576877	−	0.794003i	0.416472	−	0.909149i	$-0.363266\pi$
$983$	−18.0867	−	24.8942i	−0.576877	−	0.794003i	−0.993349	+	0.115146i	$0.963266\pi$
$984$		0			0
$985$	10.4498	+	0.467327i	0.332957	+	0.0148903i
$986$		0			0
$987$	0.265248	+	0.816350i	0.00844294	+	0.0259847i
$988$		0			0
$989$	−64.3191	−	20.8985i	−2.04523	−	0.664535i
$990$		0			0
$991$	3.86953	+	11.9092i	0.122920	+	0.378308i	0.993516	−	0.113690i	$-0.0362669\pi$
$991$	3.86953	+	11.9092i	0.122920	+	0.378308i	−0.870597	+	0.491997i	$0.836267\pi$
$992$		0			0
$993$		−	8.92077i		−	0.283092i
$994$		0			0
$995$	−52.3279	+	34.5555i	−1.65891	+	1.09548i
$996$		0			0
$997$	9.99182	+	7.25948i	0.316444	+	0.229910i	0.734657	−	0.678439i	$-0.237343\pi$
$997$	9.99182	+	7.25948i	0.316444	+	0.229910i	−0.418212	+	0.908349i	$0.637343\pi$
$998$		0			0
$999$	−0.892455			−0.0282360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.529.24		112
4.3	odd	2		200.2.o.a.29.2	✓	112
8.3	odd	2		200.2.o.a.29.9	yes	112
8.5	even	2	inner	800.2.be.a.529.5		112
20.3	even	4		1000.2.t.b.101.30		224
20.7	even	4		1000.2.t.b.101.27		224
20.19	odd	2		1000.2.o.a.149.27		112
25.19	even	10	inner	800.2.be.a.369.5		112
40.3	even	4		1000.2.t.b.101.14		224
40.19	odd	2		1000.2.o.a.149.20		112
40.27	even	4		1000.2.t.b.101.43		224
100.19	odd	10		200.2.o.a.69.9	yes	112
100.31	odd	10		1000.2.o.a.349.20		112
100.67	even	20		1000.2.t.b.901.43		224
100.83	even	20		1000.2.t.b.901.14		224
200.19	odd	10		200.2.o.a.69.2	yes	112
200.67	even	20		1000.2.t.b.901.27		224
200.69	even	10	inner	800.2.be.a.369.24		112
200.83	even	20		1000.2.t.b.901.30		224
200.131	odd	10		1000.2.o.a.349.27		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.2	✓	112	4.3	odd	2
200.2.o.a.29.9	yes	112	8.3	odd	2
200.2.o.a.69.2	yes	112	200.19	odd	10
200.2.o.a.69.9	yes	112	100.19	odd	10
800.2.be.a.369.5		112	25.19	even	10	inner
800.2.be.a.369.24		112	200.69	even	10	inner
800.2.be.a.529.5		112	8.5	even	2	inner
800.2.be.a.529.24		112	1.1	even	1	trivial
1000.2.o.a.149.20		112	40.19	odd	2
1000.2.o.a.149.27		112	20.19	odd	2
1000.2.o.a.349.20		112	100.31	odd	10
1000.2.o.a.349.27		112	200.131	odd	10
1000.2.t.b.101.14		224	40.3	even	4
1000.2.t.b.101.27		224	20.7	even	4
1000.2.t.b.101.30		224	20.3	even	4
1000.2.t.b.101.43		224	40.27	even	4
1000.2.t.b.901.14		224	100.83	even	20
1000.2.t.b.901.27		224	200.67	even	20
1000.2.t.b.901.30		224	200.83	even	20
1000.2.t.b.901.43		224	100.67	even	20

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.01785 + 1.46605i) q^{3} +(1.86593 - 1.23219i) q^{5} -0.110917i q^{7} +(0.995348 + 3.06337i) q^{9} +O(q^{10})\)	\(q+(2.01785 + 1.46605i) q^{3} +(1.86593 - 1.23219i) q^{5} -0.110917i q^{7} +(0.995348 + 3.06337i) q^{9} +(1.63700 + 0.531893i) q^{11} +(-1.48445 - 4.56868i) q^{13} +(5.57162 + 0.249171i) q^{15} +(0.269588 + 0.371056i) q^{17} +(2.40052 + 3.30403i) q^{19} +(0.162610 - 0.223814i) q^{21} +(6.10792 + 1.98459i) q^{23} +(1.96339 - 4.59838i) q^{25} +(-0.170346 + 0.524271i) q^{27} +(-5.29624 + 7.28964i) q^{29} +(-2.87291 + 2.08729i) q^{31} +(2.52343 + 3.47320i) q^{33} +(-0.136671 - 0.206963i) q^{35} +(0.500287 + 1.53972i) q^{37} +(3.70252 - 11.3952i) q^{39} +(-3.51556 - 10.8198i) q^{41} -10.5304 q^{43} +(5.63191 + 4.48957i) q^{45} +(-1.82373 + 2.51014i) q^{47} +6.98770 q^{49} +1.14397i q^{51} +(3.71441 + 2.69868i) q^{53} +(3.70992 - 1.02463i) q^{55} +10.1863i q^{57} +(-3.38621 + 1.10025i) q^{59} +(-11.1816 - 3.63312i) q^{61} +(0.339779 - 0.110401i) q^{63} +(-8.39939 - 6.69570i) q^{65} +(-3.02574 + 2.19833i) q^{67} +(9.41535 + 12.9591i) q^{69} +(-9.04844 - 6.57408i) q^{71} +(9.85476 + 3.20201i) q^{73} +(10.7033 - 6.40039i) q^{75} +(0.0589960 - 0.181571i) q^{77} +(4.45472 + 3.23655i) q^{79} +(6.70522 - 4.87163i) q^{81} +(-9.91061 + 7.20048i) q^{83} +(0.960247 + 0.360180i) q^{85} +(-21.3740 + 6.94483i) q^{87} +(-2.07551 + 6.38776i) q^{89} +(-0.506744 + 0.164651i) q^{91} -8.85717 q^{93} +(8.55040 + 3.20718i) q^{95} +(-3.30362 + 4.54704i) q^{97} +5.54415i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 112 * q - 30 * q^9	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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