LMFDB - Embedded newform 820.2.x.a.793.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			793.15
Character	$\chi$	$=$	820.793
Dual form			820.2.x.a.577.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.585707 - 1.41402i) q^{3} +(-1.11869 - 1.93611i) q^{5} +(1.32779 + 0.549988i) q^{7} +(0.464917 + 0.464917i) q^{9} +(5.38595 - 2.23093i) q^{11} +(1.03084 - 2.48866i) q^{13} +(-3.39293 + 0.447852i) q^{15} +(1.27250 + 3.07210i) q^{17} +(-5.44669 - 2.25609i) q^{19} +(1.55539 - 1.55539i) q^{21} +(-0.656229 + 0.656229i) q^{23} +(-2.49708 + 4.33181i) q^{25} +(5.17177 - 2.14222i) q^{27} +(-1.75067 + 0.725150i) q^{29} -4.97291i q^{31} -8.92252i q^{33} +(-0.420540 - 3.18602i) q^{35} +(5.97617 - 5.97617i) q^{37} +(-2.91525 - 2.91525i) q^{39} +(-6.38615 - 0.465961i) q^{41} +8.73974i q^{43} +(0.380036 - 1.42023i) q^{45} +(-5.18025 - 12.5062i) q^{47} +(-3.48921 - 3.48921i) q^{49} +5.08932 q^{51} +(3.13796 + 1.29979i) q^{53} +(-10.3445 - 7.93210i) q^{55} +(-6.38032 + 6.38032i) q^{57} +10.4117i q^{59} +(-1.06609 - 1.06609i) q^{61} +(0.361612 + 0.873010i) q^{63} +(-5.97152 + 0.788214i) q^{65} +(0.282897 + 0.682973i) q^{67} +(0.543564 + 1.31228i) q^{69} +(5.84810 + 14.1186i) q^{71} -7.69510i q^{73} +(4.66272 + 6.06809i) q^{75} +8.37839 q^{77} +(1.10679 + 2.67203i) q^{79} -6.59523i q^{81} +(0.371199 + 0.371199i) q^{83} +(4.52440 - 5.90043i) q^{85} +2.90020i q^{87} +(-15.0374 + 6.22868i) q^{89} +(2.73747 - 2.73747i) q^{91} +(-7.03179 - 2.91266i) q^{93} +(1.72509 + 13.0693i) q^{95} +(3.44613 - 1.42744i) q^{97} +(3.54122 + 1.46682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.585707	−	1.41402i	0.338158	−	0.816386i	−0.659735	−	0.751499i	$-0.729331\pi$
$3$	0.585707	−	1.41402i	0.338158	−	0.816386i	0.997893	−	0.0648869i	$-0.0206687\pi$
$4$		0			0
$5$	−1.11869	−	1.93611i	−0.500292	−	0.865857i
$5$	−1.11869	−	1.93611i	−0.500292	−	0.865857i
$6$		0			0
$7$	1.32779	+	0.549988i	0.501857	+	0.207876i	0.619227	−	0.785212i	$-0.287446\pi$
$7$	1.32779	+	0.549988i	0.501857	+	0.207876i	−0.117370	+	0.993088i	$0.537446\pi$
$8$		0			0
$9$	0.464917	+	0.464917i	0.154972	+	0.154972i
$10$		0			0
$11$	5.38595	−	2.23093i	1.62393	−	0.672652i	0.629393	−	0.777087i	$-0.283303\pi$
$11$	5.38595	−	2.23093i	1.62393	−	0.672652i	0.994532	+	0.104435i	$0.0333034\pi$
$12$		0			0
$13$	1.03084	−	2.48866i	0.285903	−	0.690230i	−0.714049	−	0.700096i	$-0.753140\pi$
$13$	1.03084	−	2.48866i	0.285903	−	0.690230i	0.999951	+	0.00986577i	$0.00314042\pi$
$14$		0			0
$15$	−3.39293	+	0.447852i	−0.876051	+	0.115635i
$16$		0			0
$17$	1.27250	+	3.07210i	0.308627	+	0.745093i	0.999750	+	0.0223550i	$0.00711642\pi$
$17$	1.27250	+	3.07210i	0.308627	+	0.745093i	−0.691123	+	0.722737i	$0.742884\pi$
$18$		0			0
$19$	−5.44669	−	2.25609i	−1.24956	−	0.517583i	−0.342867	−	0.939384i	$-0.611398\pi$
$19$	−5.44669	−	2.25609i	−1.24956	−	0.517583i	−0.906688	+	0.421801i	$0.861398\pi$
$20$		0			0
$21$	1.55539	−	1.55539i	0.339414	−	0.339414i
$22$		0			0
$23$	−0.656229	+	0.656229i	−0.136833	+	0.136833i	−0.772206	−	0.635373i	$-0.780847\pi$
$23$	−0.656229	+	0.656229i	−0.136833	+	0.136833i	0.635373	+	0.772206i	$0.280847\pi$
$24$		0			0
$25$	−2.49708	+	4.33181i	−0.499416	+	0.866362i
$26$		0			0
$27$	5.17177	−	2.14222i	0.995308	−	0.412270i
$28$		0			0
$29$	−1.75067	+	0.725150i	−0.325090	+	0.134657i	−0.539259	−	0.842140i	$-0.681296\pi$
$29$	−1.75067	+	0.725150i	−0.325090	+	0.134657i	0.214169	+	0.976797i	$0.431296\pi$
$30$		0			0
$31$		−	4.97291i		−	0.893160i	−0.894744	−	0.446580i	$-0.852642\pi$
$31$		−	4.97291i		−	0.893160i	0.894744	−	0.446580i	$-0.147358\pi$
$32$		0			0
$33$		−	8.92252i		−	1.55321i
$34$		0			0
$35$	−0.420540	−	3.18602i	−0.0710842	−	0.538535i
$36$		0			0
$37$	5.97617	−	5.97617i	0.982476	−	0.982476i	−0.0173729	−	0.999849i	$-0.505530\pi$
$37$	5.97617	−	5.97617i	0.982476	−	0.982476i	0.999849	+	0.0173729i	$0.00553025\pi$
$38$		0			0
$39$	−2.91525	−	2.91525i	−0.466814	−	0.466814i
$40$		0			0
$41$	−6.38615	−	0.465961i	−0.997349	−	0.0727710i
$41$	−6.38615	−	0.465961i	−0.997349	−	0.0727710i
$42$		0			0
$43$			8.73974i			1.33280i	0.745596	+	0.666399i	$0.232165\pi$
$43$			8.73974i			1.33280i	−0.745596	+	0.666399i	$0.767835\pi$
$44$		0			0
$45$	0.380036	−	1.42023i	0.0566524	−	0.211715i
$46$		0			0
$47$	−5.18025	−	12.5062i	−0.755617	−	1.82422i	−0.524803	−	0.851223i	$-0.675861\pi$
$47$	−5.18025	−	12.5062i	−0.755617	−	1.82422i	−0.230814	−	0.972998i	$-0.574139\pi$
$48$		0			0
$49$	−3.48921	−	3.48921i	−0.498459	−	0.498459i
$50$		0			0
$51$	5.08932			0.712648
$52$		0			0
$53$	3.13796	+	1.29979i	0.431032	+	0.178539i	0.587642	−	0.809121i	$-0.300056\pi$
$53$	3.13796	+	1.29979i	0.431032	+	0.178539i	−0.156610	+	0.987661i	$0.550056\pi$
$54$		0			0
$55$	−10.3445	−	7.93210i	−1.39486	−	1.06956i
$56$		0			0
$57$	−6.38032	+	6.38032i	−0.845094	+	0.845094i
$58$		0			0
$59$			10.4117i			1.35549i	0.735296	+	0.677746i	$0.237043\pi$
$59$			10.4117i			1.35549i	−0.735296	+	0.677746i	$0.762957\pi$
$60$		0			0
$61$	−1.06609	−	1.06609i	−0.136499	−	0.136499i	0.635556	−	0.772055i	$-0.280771\pi$
$61$	−1.06609	−	1.06609i	−0.136499	−	0.136499i	−0.772055	+	0.635556i	$0.780771\pi$
$62$		0			0
$63$	0.361612	+	0.873010i	0.0455589	+	0.109989i
$64$		0			0
$65$	−5.97152	+	0.788214i	−0.740676	+	0.0977659i
$66$		0			0
$67$	0.282897	+	0.682973i	0.0345613	+	0.0834384i	0.940218	−	0.340574i	$-0.110621\pi$
$67$	0.282897	+	0.682973i	0.0345613	+	0.0834384i	−0.905656	+	0.424012i	$0.860621\pi$
$68$		0			0
$69$	0.543564	+	1.31228i	0.0654374	+	0.157980i
$70$		0			0
$71$	5.84810	+	14.1186i	0.694042	+	1.67557i	0.736473	+	0.676467i	$0.236490\pi$
$71$	5.84810	+	14.1186i	0.694042	+	1.67557i	−0.0424309	+	0.999099i	$0.513510\pi$
$72$		0			0
$73$		−	7.69510i		−	0.900643i	−0.892866	−	0.450322i	$-0.851309\pi$
$73$		−	7.69510i		−	0.900643i	0.892866	−	0.450322i	$-0.148691\pi$
$74$		0			0
$75$	4.66272	+	6.06809i	0.538404	+	0.700683i
$76$		0			0
$77$	8.37839			0.954806
$78$		0			0
$79$	1.10679	+	2.67203i	0.124524	+	0.300627i	0.973831	−	0.227271i	$-0.0729804\pi$
$79$	1.10679	+	2.67203i	0.124524	+	0.300627i	−0.849308	+	0.527898i	$0.822980\pi$
$80$		0			0
$81$		−	6.59523i		−	0.732803i
$82$		0			0
$83$	0.371199	+	0.371199i	0.0407444	+	0.0407444i	0.727185	−	0.686441i	$-0.240828\pi$
$83$	0.371199	+	0.371199i	0.0407444	+	0.0407444i	−0.686441	+	0.727185i	$0.740828\pi$
$84$		0			0
$85$	4.52440	−	5.90043i	0.490740	−	0.639991i
$86$		0			0
$87$			2.90020i			0.310934i
$88$		0			0
$89$	−15.0374	+	6.22868i	−1.59396	+	0.660239i	−0.990545	−	0.137189i	$-0.956193\pi$
$89$	−15.0374	+	6.22868i	−1.59396	+	0.660239i	−0.603414	+	0.797428i	$0.706193\pi$
$90$		0			0
$91$	2.73747	−	2.73747i	0.286965	−	0.286965i
$92$		0			0
$93$	−7.03179	−	2.91266i	−0.729163	−	0.302029i
$94$		0			0
$95$	1.72509	+	13.0693i	0.176990	+	1.34088i
$96$		0			0
$97$	3.44613	−	1.42744i	0.349902	−	0.144934i	−0.200809	−	0.979631i	$-0.564357\pi$
$97$	3.44613	−	1.42744i	0.349902	−	0.144934i	0.550710	+	0.834696i	$0.314357\pi$
$98$		0			0
$99$	3.54122	+	1.46682i	0.355906	+	0.147421i
$100$		0			0
$101$	0.184996	−	0.446620i	0.0184078	−	0.0444404i	−0.914408	−	0.404793i	$-0.867344\pi$
$101$	0.184996	−	0.446620i	0.0184078	−	0.0444404i	0.932816	+	0.360353i	$0.117344\pi$
$102$		0			0
$103$	10.3459			1.01941			0.509705	−	0.860349i	$-0.329755\pi$
$103$	10.3459			1.01941			0.509705	+	0.860349i	$0.329755\pi$
$104$		0			0
$105$	−4.75141	−	1.27142i	−0.463690	−	0.124078i
$106$		0			0
$107$	9.24683	+	9.24683i	0.893925	+	0.893925i	0.994890	−	0.100965i	$-0.0321929\pi$
$107$	9.24683	+	9.24683i	0.893925	+	0.893925i	−0.100965	+	0.994890i	$0.532193\pi$
$108$		0			0
$109$	5.89492	−	14.2316i	0.564631	−	1.36314i	−0.341396	−	0.939919i	$-0.610900\pi$
$109$	5.89492	−	14.2316i	0.564631	−	1.36314i	0.906027	−	0.423220i	$-0.139100\pi$
$110$		0			0
$111$	−4.95015	−	11.9507i	−0.469847	−	1.13431i
$112$		0			0
$113$	−1.65366	+	1.65366i	−0.155563	+	0.155563i	−0.780597	−	0.625034i	$-0.785085\pi$
$113$	−1.65366	+	1.65366i	−0.155563	+	0.155563i	0.625034	+	0.780597i	$0.285085\pi$
$114$		0			0
$115$	2.00465	+	0.536420i	0.186935	+	0.0500214i
$116$		0			0
$117$	1.63627	−	0.677767i	0.151274	−	0.0626596i
$118$		0			0
$119$			4.77895i			0.438086i
$120$		0			0
$121$	16.2532	−	16.2532i	1.47757	−	1.47757i
$122$		0			0
$123$	−4.39929	+	8.75723i	−0.396671	+	0.789613i
$124$		0			0
$125$	11.1803	−	0.0113103i	0.999999	−	0.00101163i
$126$		0			0
$127$	9.61037	+	9.61037i	0.852782	+	0.852782i	0.990475	−	0.137693i	$-0.0439686\pi$
$127$	9.61037	+	9.61037i	0.852782	+	0.852782i	−0.137693	+	0.990475i	$0.543969\pi$
$128$		0			0
$129$	12.3582	+	5.11892i	1.08808	+	0.450696i
$130$		0			0
$131$	−11.0900	+	11.0900i	−0.968939	+	0.968939i	−0.999532	−	0.0305931i	$-0.990260\pi$
$131$	−11.0900	+	11.0900i	−0.968939	+	0.968939i	0.0305931	+	0.999532i	$0.490260\pi$
$132$		0			0
$133$	−5.99122	−	5.99122i	−0.519505	−	0.519505i
$134$		0			0
$135$	−9.93317	−	7.61667i	−0.854911	−	0.655539i
$136$		0			0
$137$	4.08455	+	9.86097i	0.348966	+	0.842480i	0.996743	+	0.0806488i	$0.0256992\pi$
$137$	4.08455	+	9.86097i	0.348966	+	0.842480i	−0.647776	+	0.761831i	$0.724301\pi$
$138$		0			0
$139$			16.9717i			1.43952i	0.694224	+	0.719759i	$0.255748\pi$
$139$			16.9717i			1.43952i	−0.694224	+	0.719759i	$0.744252\pi$
$140$		0			0
$141$	−20.7182			−1.74479
$142$		0			0
$143$		−	15.7035i		−	1.31320i
$144$		0			0
$145$	3.36242	+	2.57827i	0.279234	+	0.214114i
$146$		0			0
$147$	−6.97747	+	2.89016i	−0.575492	+	0.238377i
$148$		0			0
$149$	−10.7689	−	4.46062i	−0.882222	−	0.365428i	−0.104864	−	0.994487i	$-0.533441\pi$
$149$	−10.7689	−	4.46062i	−0.882222	−	0.365428i	−0.777358	+	0.629058i	$0.783441\pi$
$150$		0			0
$151$	−7.32348	+	3.03348i	−0.595976	+	0.246861i	−0.660219	−	0.751073i	$-0.729537\pi$
$151$	−7.32348	+	3.03348i	−0.595976	+	0.246861i	0.0642431	+	0.997934i	$0.479537\pi$
$152$		0			0
$153$	−0.836660	+	2.01988i	−0.0676400	+	0.163297i
$154$		0			0
$155$	−9.62811	+	5.56312i	−0.773349	+	0.446841i
$156$		0			0
$157$	−9.09755	+	21.9634i	−0.726064	+	1.75287i	−0.0707784	+	0.997492i	$0.522548\pi$
$157$	−9.09755	+	21.9634i	−0.726064	+	1.75287i	−0.655286	+	0.755381i	$0.727452\pi$
$158$		0			0
$159$	3.67585	−	3.67585i	0.291514	−	0.291514i
$160$		0			0
$161$	−1.23225	+	0.510416i	−0.0971151	+	0.0402264i
$162$		0			0
$163$	15.3240	−	15.3240i	1.20027	−	1.20027i	0.226182	−	0.974085i	$-0.427376\pi$
$163$	15.3240	−	15.3240i	1.20027	−	1.20027i	0.974085	−	0.226182i	$-0.0726245\pi$
$164$		0			0
$165$	−17.2750	+	9.98151i	−1.34486	+	0.777059i
$166$		0			0
$167$	11.9269	+	4.94027i	0.922929	+	0.382290i	0.792991	−	0.609233i	$-0.208522\pi$
$167$	11.9269	+	4.94027i	0.922929	+	0.382290i	0.129937	+	0.991522i	$0.458522\pi$
$168$		0			0
$169$	4.06158	+	4.06158i	0.312429	+	0.312429i
$170$		0			0
$171$	−1.48336	−	3.58115i	−0.113435	−	0.273857i
$172$		0			0
$173$	12.8991			0.980699			0.490349	−	0.871526i	$-0.336869\pi$
$173$	12.8991			0.980699			0.490349	+	0.871526i	$0.336869\pi$
$174$		0			0
$175$	−5.69804	+	4.37837i	−0.430731	+	0.330973i
$176$		0			0
$177$	14.7224	+	6.09822i	1.10660	+	0.458370i
$178$		0			0
$179$	4.82469	−	11.6478i	0.360615	−	0.870601i	−0.634596	−	0.772844i	$-0.718833\pi$
$179$	4.82469	−	11.6478i	0.360615	−	0.870601i	0.995210	−	0.0977565i	$-0.0311666\pi$
$180$		0			0
$181$	2.55409	−	6.16613i	0.189844	−	0.458325i	−0.800085	−	0.599886i	$-0.795212\pi$
$181$	2.55409	−	6.16613i	0.189844	−	0.458325i	0.989929	+	0.141562i	$0.0452124\pi$
$182$		0			0
$183$	−2.13189	+	0.883060i	−0.157594	+	0.0652776i
$184$		0			0
$185$	−18.2560	−	4.88509i	−1.34221	−	0.359159i
$186$		0			0
$187$	13.7073	+	13.7073i	1.00238	+	1.00238i
$188$		0			0
$189$	8.04521			0.585203
$190$		0			0
$191$	5.94607	+	2.46294i	0.430242	+	0.178212i	0.587286	−	0.809379i	$-0.300196\pi$
$191$	5.94607	+	2.46294i	0.430242	+	0.178212i	−0.157044	+	0.987592i	$0.550196\pi$
$192$		0			0
$193$	1.12671	−	2.72011i	0.0811020	−	0.195798i	−0.878127	−	0.478428i	$-0.841207\pi$
$193$	1.12671	−	2.72011i	0.0811020	−	0.195798i	0.959229	+	0.282630i	$0.0912069\pi$
$194$		0			0
$195$	−2.38301	+	8.90551i	−0.170651	+	0.637737i
$196$		0			0
$197$	−0.561451			−0.0400018			−0.0200009	−	0.999800i	$-0.506367\pi$
$197$	−0.561451			−0.0400018			−0.0200009	+	0.999800i	$0.506367\pi$
$198$		0			0
$199$	−5.88064	+	14.1971i	−0.416868	+	1.00641i	0.566382	+	0.824143i	$0.308343\pi$
$199$	−5.88064	+	14.1971i	−0.416868	+	1.00641i	−0.983250	+	0.182265i	$0.941657\pi$
$200$		0			0
$201$	1.13143			0.0798051
$202$		0			0
$203$	−2.72334			−0.191141
$204$		0			0
$205$	6.24195	+	12.8856i	0.435956	+	0.899968i
$206$		0			0
$207$	−0.610184			−0.0424107
$208$		0			0
$209$	−34.3688			−2.37734
$210$		0			0
$211$	0.973221	−	2.34956i	0.0669993	−	0.161751i	−0.886833	−	0.462090i	$-0.847100\pi$
$211$	0.973221	−	2.34956i	0.0669993	−	0.161751i	0.953833	+	0.300339i	$0.0970998\pi$
$212$		0			0
$213$	23.3892			1.60260
$214$		0			0
$215$	16.9211	−	9.77703i	1.15401	−	0.666788i
$216$		0			0
$217$	2.73504	−	6.60297i	0.185666	−	0.448239i
$218$		0			0
$219$	−10.8810	−	4.50707i	−0.735272	−	0.304560i
$220$		0			0
$221$	8.95715			0.602523
$222$		0			0
$223$	1.88894	+	1.88894i	0.126493	+	0.126493i	0.767519	−	0.641026i	$-0.221491\pi$
$223$	1.88894	+	1.88894i	0.126493	+	0.126493i	−0.641026	+	0.767519i	$0.721491\pi$
$224$		0			0
$225$	−3.17487	+	0.852998i	−0.211658	+	0.0568665i
$226$		0			0
$227$	−14.2543	+	5.90434i	−0.946094	+	0.391885i	−0.801761	−	0.597644i	$-0.796103\pi$
$227$	−14.2543	+	5.90434i	−0.946094	+	0.391885i	−0.144332	+	0.989529i	$0.546103\pi$
$228$		0			0
$229$	5.28313	−	12.7546i	0.349119	−	0.842848i	−0.647605	−	0.761976i	$-0.724229\pi$
$229$	5.28313	−	12.7546i	0.349119	−	0.842848i	0.996724	−	0.0808722i	$-0.0257706\pi$
$230$		0			0
$231$	4.90728	−	11.8472i	0.322875	−	0.779490i
$232$		0			0
$233$	22.6023	+	9.36219i	1.48073	+	0.613337i	0.969276	−	0.245975i	$-0.0791081\pi$
$233$	22.6023	+	9.36219i	1.48073	+	0.613337i	0.511451	+	0.859312i	$0.329108\pi$
$234$		0			0
$235$	−18.4184	+	24.0201i	−1.20149	+	1.56690i
$236$		0			0
$237$	4.42656			0.287536
$238$		0			0
$239$	0.255794	+	0.617540i	0.0165459	+	0.0399454i	0.931937	−	0.362621i	$-0.118118\pi$
$239$	0.255794	+	0.617540i	0.0165459	+	0.0399454i	−0.915391	+	0.402567i	$0.868118\pi$
$240$		0			0
$241$	−13.3944	−	13.3944i	−0.862807	−	0.862807i	0.128856	−	0.991663i	$-0.458869\pi$
$241$	−13.3944	−	13.3944i	−0.862807	−	0.862807i	−0.991663	+	0.128856i	$0.958869\pi$
$242$		0			0
$243$	6.18952	+	2.56378i	0.397058	+	0.164467i
$244$		0			0
$245$	−2.85218	+	10.6588i	−0.182219	+	0.680969i
$246$		0			0
$247$	−11.2293	+	11.2293i	−0.714503	+	0.714503i
$248$		0			0
$249$	0.742297	−	0.307469i	0.0470411	−	0.0194851i
$250$		0			0
$251$	−9.79463	+	9.79463i	−0.618232	+	0.618232i	−0.945078	−	0.326846i	$-0.894014\pi$
$251$	−9.79463	+	9.79463i	−0.618232	+	0.618232i	0.326846	+	0.945078i	$0.394014\pi$
$252$		0			0
$253$	−2.07041	+	4.99842i	−0.130166	+	0.314248i
$254$		0			0
$255$	−5.69336	−	9.85351i	−0.356532	−	0.617051i
$256$		0			0
$257$	−0.627750	+	1.51552i	−0.0391580	+	0.0945358i	−0.942249	−	0.334914i	$-0.891293\pi$
$257$	−0.627750	+	1.51552i	−0.0391580	+	0.0945358i	0.903091	+	0.429450i	$0.141293\pi$
$258$		0			0
$259$	11.2219	−	4.64827i	0.697296	−	0.288829i
$260$		0			0
$261$	−1.15105	−	0.476780i	−0.0712481	−	0.0295119i
$262$		0			0
$263$	−26.0735	+	10.8000i	−1.60776	+	0.665955i	−0.992486	−	0.122359i	$-0.960954\pi$
$263$	−26.0735	+	10.8000i	−1.60776	+	0.665955i	−0.615272	+	0.788315i	$0.710954\pi$
$264$		0			0
$265$	−0.993862	−	7.52951i	−0.0610525	−	0.462534i
$266$		0			0
$267$			24.9113i			1.52455i
$268$		0			0
$269$	13.9422			0.850074			0.425037	−	0.905176i	$-0.360261\pi$
$269$	13.9422			0.850074			0.425037	+	0.905176i	$0.360261\pi$
$270$		0			0
$271$			10.6195i			0.645092i	0.946554	+	0.322546i	$0.104539\pi$
$271$			10.6195i			0.645092i	−0.946554	+	0.322546i	$0.895461\pi$
$272$		0			0
$273$	−2.26748	−	5.47419i	−0.137234	−	0.331313i
$274$		0			0
$275$	−3.78516	+	28.9017i	−0.228254	+	1.74284i
$276$		0			0
$277$	−1.89578	−	1.89578i	−0.113907	−	0.113907i	0.647856	−	0.761763i	$-0.275666\pi$
$277$	−1.89578	−	1.89578i	−0.113907	−	0.113907i	−0.761763	+	0.647856i	$0.775666\pi$
$278$		0			0
$279$	2.31199	−	2.31199i	0.138415	−	0.138415i
$280$		0			0
$281$	−22.4999	−	9.31976i	−1.34223	−	0.555970i	−0.408112	−	0.912932i	$-0.633813\pi$
$281$	−22.4999	−	9.31976i	−1.34223	−	0.555970i	−0.934119	+	0.356961i	$0.883813\pi$
$282$		0			0
$283$	8.18447	+	8.18447i	0.486516	+	0.486516i	0.907205	−	0.420689i	$-0.138212\pi$
$283$	8.18447	+	8.18447i	0.486516	+	0.486516i	−0.420689	+	0.907205i	$0.638212\pi$
$284$		0			0
$285$	19.4906	+	5.21545i	1.15452	+	0.308937i
$286$		0			0
$287$	−8.22318	−	4.13100i	−0.485399	−	0.243845i
$288$		0			0
$289$	4.20231	−	4.20231i	0.247195	−	0.247195i
$290$		0			0
$291$		−	5.70896i		−	0.334665i
$292$		0			0
$293$	−13.5257	+	5.60255i	−0.790182	+	0.327304i	−0.741017	−	0.671486i	$-0.765656\pi$
$293$	−13.5257	+	5.60255i	−0.790182	+	0.327304i	−0.0491655	+	0.998791i	$0.515656\pi$
$294$		0			0
$295$	20.1583	−	11.6475i	1.17366	−	0.678142i
$296$		0			0
$297$	23.0758	−	23.0758i	1.33899	−	1.33899i
$298$		0			0
$299$	0.956667	+	2.30960i	0.0553255	+	0.133568i
$300$		0			0
$301$	−4.80675	+	11.6045i	−0.277056	+	0.668873i
$302$		0			0
$303$	−0.523177	−	0.523177i	−0.0300557	−	0.0300557i
$304$		0			0
$305$	−0.871453	+	3.25670i	−0.0498993	+	0.186478i
$306$		0			0
$307$	−20.0709			−1.14551			−0.572753	−	0.819728i	$-0.694125\pi$
$307$	−20.0709			−1.14551			−0.572753	+	0.819728i	$0.694125\pi$
$308$		0			0
$309$	6.05965	−	14.6293i	0.344722	−	0.832231i
$310$		0			0
$311$	9.94449	+	4.11914i	0.563900	+	0.233575i	0.646377	−	0.763018i	$-0.276283\pi$
$311$	9.94449	+	4.11914i	0.563900	+	0.233575i	−0.0824773	+	0.996593i	$0.526283\pi$
$312$		0			0
$313$	−4.49605	+	1.86232i	−0.254132	+	0.105265i	−0.506113	−	0.862467i	$-0.668918\pi$
$313$	−4.49605	+	1.86232i	−0.254132	+	0.105265i	0.251981	+	0.967732i	$0.418918\pi$
$314$		0			0
$315$	1.28572	−	1.67675i	0.0724419	−	0.0944740i
$316$		0			0
$317$	−13.7995	−	5.71595i	−0.775058	−	0.321040i	−0.0401387	−	0.999194i	$-0.512780\pi$
$317$	−13.7995	−	5.71595i	−0.775058	−	0.321040i	−0.734919	+	0.678155i	$0.762780\pi$
$318$		0			0
$319$	−7.81124	+	7.81124i	−0.437345	+	0.437345i
$320$		0			0
$321$	18.4912	−	7.65929i	1.03208	−	0.427500i
$322$		0			0
$323$		−	19.6036i		−	1.09077i
$324$		0			0
$325$	8.20633	+	10.6798i	0.455205	+	0.592407i
$326$		0			0
$327$	−16.6711	−	16.6711i	−0.921913	−	0.921913i
$328$		0			0
$329$		−	19.4547i		−	1.07257i
$330$		0			0
$331$	1.90951	+	4.60997i	0.104956	+	0.253387i	0.967630	−	0.252375i	$-0.0812115\pi$
$331$	1.90951	+	4.60997i	0.104956	+	0.253387i	−0.862673	+	0.505762i	$0.831212\pi$
$332$		0			0
$333$	5.55684			0.304513
$334$		0			0
$335$	1.00584	−	1.31175i	0.0549550	−	0.0716687i
$336$		0			0
$337$			24.1931i			1.31788i	0.752194	+	0.658941i	$0.228996\pi$
$337$			24.1931i			1.31788i	−0.752194	+	0.658941i	$0.771004\pi$
$338$		0			0
$339$	1.36975	+	3.30687i	0.0743947	+	0.179605i
$340$		0			0
$341$	−11.0942	−	26.7838i	−0.600786	−	1.45043i
$342$		0			0
$343$	−6.56383	−	15.8465i	−0.354413	−	0.855629i
$344$		0			0
$345$	1.93265	−	2.52043i	0.104050	−	0.135696i
$346$		0			0
$347$	−2.39315	−	5.77758i	−0.128471	−	0.310157i	0.846536	−	0.532332i	$-0.178684\pi$
$347$	−2.39315	−	5.77758i	−0.128471	−	0.310157i	−0.975007	+	0.222175i	$0.928684\pi$
$348$		0			0
$349$	−10.7368	−	10.7368i	−0.574726	−	0.574726i	0.358719	−	0.933445i	$-0.383214\pi$
$349$	−10.7368	−	10.7368i	−0.574726	−	0.574726i	−0.933445	+	0.358719i	$0.883214\pi$
$350$		0			0
$351$		−	15.0791i		−	0.804861i
$352$		0			0
$353$	−14.8910	+	14.8910i	−0.792566	+	0.792566i	−0.981911	−	0.189344i	$-0.939364\pi$
$353$	−14.8910	+	14.8910i	−0.792566	+	0.792566i	0.189344	+	0.981911i	$0.439364\pi$
$354$		0			0
$355$	20.7930	−	27.1169i	1.10358	−	1.43921i
$356$		0			0
$357$	6.75754	+	2.79907i	0.357647	+	0.148142i
$358$		0			0
$359$	−18.7718			−0.990736			−0.495368	−	0.868683i	$-0.664967\pi$
$359$	−18.7718			−0.990736			−0.495368	+	0.868683i	$0.664967\pi$
$360$		0			0
$361$	11.1414	+	11.1414i	0.586390	+	0.586390i
$362$		0			0
$363$	−13.4628	−	32.5020i	−0.706613	−	1.70591i
$364$		0			0
$365$	−14.8986	+	8.60841i	−0.779828	+	0.450585i
$366$		0			0
$367$		−	13.7074i		−	0.715520i	−0.933814	−	0.357760i	$-0.883541\pi$
$367$		−	13.7074i		−	0.715520i	0.933814	−	0.357760i	$-0.116459\pi$
$368$		0			0
$369$	−2.75239	−	3.18566i	−0.143284	−	0.165839i
$370$		0			0
$371$	3.45168	+	3.45168i	0.179203	+	0.179203i
$372$		0			0
$373$	3.32790	−	3.32790i	0.172312	−	0.172312i	−0.615682	−	0.787994i	$-0.711120\pi$
$373$	3.32790	−	3.32790i	0.172312	−	0.172312i	0.787994	+	0.615682i	$0.211120\pi$
$374$		0			0
$375$	6.53240	−	15.8159i	0.337332	−	0.816727i
$376$		0			0
$377$			5.10433i			0.262886i
$378$		0			0
$379$		−	7.57513i		−	0.389108i	−0.980892	−	0.194554i	$-0.937674\pi$
$379$		−	7.57513i		−	0.389108i	0.980892	−	0.194554i	$-0.0623260\pi$
$380$		0			0
$381$	19.2181	−	7.96041i	0.984574	−	0.407824i
$382$		0			0
$383$	−4.32487	+	1.79142i	−0.220990	+	0.0915372i	−0.490432	−	0.871480i	$-0.663161\pi$
$383$	−4.32487	+	1.79142i	−0.220990	+	0.0915372i	0.269441	+	0.963017i	$0.413161\pi$
$384$		0			0
$385$	−9.37279	−	16.2215i	−0.477682	−	0.826725i
$386$		0			0
$387$	−4.06325	+	4.06325i	−0.206547	+	0.206547i
$388$		0			0
$389$	24.9178	−	24.9178i	1.26338	−	1.26338i	0.313939	−	0.949443i	$-0.398351\pi$
$389$	24.9178	−	24.9178i	1.26338	−	1.26338i	0.949443	−	0.313939i	$-0.101649\pi$
$390$		0			0
$391$	−2.85105	−	1.18094i	−0.144184	−	0.0597230i
$392$		0			0
$393$	9.18602	+	22.1770i	0.463373	+	1.11868i
$394$		0			0
$395$	3.93520	−	5.13203i	0.198001	−	0.258221i
$396$		0			0
$397$	7.93034	−	19.1455i	0.398012	−	0.960887i	−0.590125	−	0.807312i	$-0.700921\pi$
$397$	7.93034	−	19.1455i	0.398012	−	0.960887i	0.988137	−	0.153575i	$-0.0490785\pi$
$398$		0			0
$399$	−11.9808	+	4.96262i	−0.599791	+	0.248442i
$400$		0			0
$401$	5.12785	+	5.12785i	0.256072	+	0.256072i	0.823455	−	0.567382i	$-0.192044\pi$
$401$	5.12785	+	5.12785i	0.256072	+	0.256072i	−0.567382	+	0.823455i	$0.692044\pi$
$402$		0			0
$403$	−12.3759	−	5.12626i	−0.616486	−	0.255357i
$404$		0			0
$405$	−12.7691	+	7.37800i	−0.634503	+	0.366616i
$406$		0			0
$407$	18.8549	−	45.5198i	0.934603	−	2.25633i
$408$		0			0
$409$	−3.74666			−0.185261			−0.0926303	−	0.995701i	$-0.529527\pi$
$409$	−3.74666			−0.185261			−0.0926303	+	0.995701i	$0.529527\pi$
$410$		0			0
$411$	16.3360			0.805794
$412$		0			0
$413$	−5.72633	+	13.8246i	−0.281774	+	0.680263i
$414$		0			0
$415$	0.303428	−	1.13394i	0.0148947	−	0.0556629i
$416$		0			0
$417$	23.9983	+	9.94042i	1.17520	+	0.486785i
$418$		0			0
$419$	26.1687	+	26.1687i	1.27842	+	1.27842i	0.941550	+	0.336873i	$0.109369\pi$
$419$	26.1687	+	26.1687i	1.27842	+	1.27842i	0.336873	+	0.941550i	$0.390631\pi$
$420$		0			0
$421$	−27.3502	+	11.3288i	−1.33297	+	0.552133i	−0.931500	−	0.363741i	$-0.881499\pi$
$421$	−27.3502	+	11.3288i	−1.33297	+	0.552133i	−0.401467	+	0.915874i	$0.631499\pi$
$422$		0			0
$423$	3.40597	−	8.22274i	0.165604	−	0.399803i
$424$		0			0
$425$	−16.4853	−	2.15902i	−0.799654	−	0.104728i
$426$		0			0
$427$	−0.829207	−	2.00188i	−0.0401281	−	0.0968779i
$428$		0			0
$429$	−22.2051	−	9.19767i	−1.07207	−	0.444068i
$430$		0			0
$431$	6.13925	−	6.13925i	0.295717	−	0.295717i	−0.543617	−	0.839334i	$-0.682945\pi$
$431$	6.13925	−	6.13925i	0.295717	−	0.295717i	0.839334	+	0.543617i	$0.182945\pi$
$432$		0			0
$433$	25.5931	−	25.5931i	1.22993	−	1.22993i	0.265937	−	0.963991i	$-0.414319\pi$
$433$	25.5931	−	25.5931i	1.22993	−	1.22993i	0.963991	−	0.265937i	$-0.0856812\pi$
$434$		0			0
$435$	5.61513	−	3.24442i	0.269225	−	0.155558i
$436$		0			0
$437$	5.05479	−	2.09376i	0.241803	−	0.100158i
$438$		0			0
$439$	5.83888	−	2.41854i	0.278674	−	0.115431i	−0.238969	−	0.971027i	$-0.576809\pi$
$439$	5.83888	−	2.41854i	0.278674	−	0.115431i	0.517643	+	0.855596i	$0.326809\pi$
$440$		0			0
$441$		−	3.24439i		−	0.154495i
$442$		0			0
$443$		−	7.14463i		−	0.339452i	−0.985491	−	0.169726i	$-0.945712\pi$
$443$		−	7.14463i		−	0.339452i	0.985491	−	0.169726i	$-0.0542882\pi$
$444$		0			0
$445$	28.8816	+	22.1461i	1.36912	+	1.04983i
$446$		0			0
$447$	−12.6148	+	12.6148i	−0.596661	+	0.596661i
$448$		0			0
$449$	5.03157	+	5.03157i	0.237454	+	0.237454i	0.815795	−	0.578341i	$-0.196300\pi$
$449$	5.03157	+	5.03157i	0.237454	+	0.237454i	−0.578341	+	0.815795i	$0.696300\pi$
$450$		0			0
$451$	−35.4350	+	11.7374i	−1.66857	+	0.552694i
$452$		0			0
$453$			12.1323i			0.570025i
$454$		0			0
$455$	−8.36242	−	2.23768i	−0.392036	−	0.104904i
$456$		0			0
$457$	−8.30209	−	20.0430i	−0.388355	−	0.937572i	−0.990289	−	0.139026i	$-0.955603\pi$
$457$	−8.30209	−	20.0430i	−0.388355	−	0.937572i	0.601934	−	0.798546i	$-0.294397\pi$
$458$		0			0
$459$	13.1622	+	13.1622i	0.614359	+	0.614359i
$460$		0			0
$461$	4.14903			0.193240			0.0966198	−	0.995321i	$-0.469197\pi$
$461$	4.14903			0.193240			0.0966198	+	0.995321i	$0.469197\pi$
$462$		0			0
$463$	12.1599	+	5.03680i	0.565119	+	0.234080i	0.646906	−	0.762570i	$-0.276063\pi$
$463$	12.1599	+	5.03680i	0.565119	+	0.234080i	−0.0817870	+	0.996650i	$0.526063\pi$
$464$		0			0
$465$	2.22712	+	16.8727i	0.103280	+	0.782454i
$466$		0			0
$467$	−2.08551	+	2.08551i	−0.0965060	+	0.0965060i	−0.753711	−	0.657205i	$-0.771738\pi$
$467$	−2.08551	+	2.08551i	−0.0965060	+	0.0965060i	0.657205	+	0.753711i	$0.271738\pi$
$468$		0			0
$469$			1.06243i			0.0490586i
$470$		0			0
$471$	25.7283	+	25.7283i	1.18550	+	1.18550i
$472$		0			0
$473$	19.4978	+	47.0718i	0.896508	+	2.16436i
$474$		0			0
$475$	23.3738	−	17.9604i	1.07246	−	0.824079i
$476$		0			0
$477$	0.854599	+	2.06318i	0.0391294	+	0.0944667i
$478$		0			0
$479$	−1.23851	−	2.99002i	−0.0565889	−	0.136618i	0.893056	−	0.449945i	$-0.148556\pi$
$479$	−1.23851	−	2.99002i	−0.0565889	−	0.136618i	−0.949645	+	0.313327i	$0.898556\pi$
$480$		0			0
$481$	−8.71220	−	21.0331i	−0.397242	−	0.959028i
$482$		0			0
$483$			2.04138i			0.0928862i
$484$		0			0
$485$	−6.61882	−	5.07526i	−0.300545	−	0.230455i
$486$		0			0
$487$	2.77307			0.125660			0.0628299	−	0.998024i	$-0.479987\pi$
$487$	2.77307			0.125660			0.0628299	+	0.998024i	$0.479987\pi$
$488$		0			0
$489$	−12.6931	−	30.6438i	−0.574001	−	1.38576i
$490$		0			0
$491$		−	16.1389i		−	0.728337i	−0.931333	−	0.364168i	$-0.881353\pi$
$491$		−	16.1389i		−	0.728337i	0.931333	−	0.364168i	$-0.118647\pi$
$492$		0			0
$493$	−4.45546	−	4.45546i	−0.200664	−	0.200664i
$494$		0			0
$495$	−1.12158	−	8.49711i	−0.0504113	−	0.381917i
$496$		0			0
$497$			21.9629i			0.985169i
$498$		0			0
$499$	−16.2476	+	6.72999i	−0.727344	+	0.301276i	−0.715460	−	0.698654i	$-0.753783\pi$
$499$	−16.2476	+	6.72999i	−0.727344	+	0.301276i	−0.0118841	+	0.999929i	$0.503783\pi$
$500$		0			0
$501$	13.9713	−	13.9713i	0.624191	−	0.624191i
$502$		0			0
$503$	10.7293	+	4.44424i	0.478398	+	0.198159i	0.608834	−	0.793298i	$-0.291638\pi$
$503$	10.7293	+	4.44424i	0.478398	+	0.198159i	−0.130436	+	0.991457i	$0.541638\pi$
$504$		0			0
$505$	−1.07166	+	0.141454i	−0.0476883	+	0.00629464i
$506$		0			0
$507$	8.12205	−	3.36426i	0.360713	−	0.149412i
$508$		0			0
$509$	8.20280	+	3.39771i	0.363583	+	0.150601i	0.556993	−	0.830517i	$-0.311955\pi$
$509$	8.20280	+	3.39771i	0.363583	+	0.150601i	−0.193410	+	0.981118i	$0.561955\pi$
$510$		0			0
$511$	4.23221	−	10.2175i	0.187222	−	0.451994i
$512$		0			0
$513$	−33.0021			−1.45708
$514$		0			0
$515$	−11.5738	−	20.0308i	−0.510003	−	0.882663i
$516$		0			0
$517$	−55.8011	−	55.8011i	−2.45413	−	2.45413i
$518$		0			0
$519$	7.55508	−	18.2396i	0.331631	−	0.800628i
$520$		0			0
$521$	6.75827	+	16.3159i	0.296085	+	0.714813i	0.999990	+	0.00451847i	$0.00143828\pi$
$521$	6.75827	+	16.3159i	0.296085	+	0.714813i	−0.703905	+	0.710295i	$0.748562\pi$
$522$		0			0
$523$	29.5055	−	29.5055i	1.29019	−	1.29019i	0.355515	−	0.934671i	$-0.384305\pi$
$523$	29.5055	−	29.5055i	1.29019	−	1.29019i	0.934671	−	0.355515i	$-0.115695\pi$
$524$		0			0
$525$	2.85372	+	10.6216i	0.124547	+	0.463564i
$526$		0			0
$527$	15.2772	−	6.32804i	0.665487	−	0.275654i
$528$		0			0
$529$			22.1387i			0.962553i
$530$		0			0
$531$	−4.84059	+	4.84059i	−0.210064	+	0.210064i
$532$		0			0
$533$	−7.74270	+	15.4126i	−0.335374	+	0.667595i
$534$		0			0
$535$	7.55862	−	28.2472i	0.326788	−	1.22123i
$536$		0			0
$537$	−13.6444	−	13.6444i	−0.588801	−	0.588801i
$538$		0			0
$539$	−26.5769	−	11.0085i	−1.14475	−	0.474171i
$540$		0			0
$541$	−12.7554	+	12.7554i	−0.548396	+	0.548396i	−0.925977	−	0.377581i	$-0.876756\pi$
$541$	−12.7554	+	12.7554i	−0.548396	+	0.548396i	0.377581	+	0.925977i	$0.376756\pi$
$542$		0			0
$543$	−7.22308	−	7.22308i	−0.309972	−	0.309972i
$544$		0			0
$545$	−34.1486	+	4.50746i	−1.46276	+	0.193078i
$546$		0			0
$547$	11.6872	+	28.2153i	0.499707	+	1.20640i	0.949642	+	0.313338i	$0.101447\pi$
$547$	11.6872	+	28.2153i	0.499707	+	1.20640i	−0.449935	+	0.893061i	$0.648553\pi$
$548$		0			0
$549$		−	0.991288i		−	0.0423072i
$550$		0			0
$551$	11.1713			0.475915
$552$		0			0
$553$			4.15661i			0.176757i
$554$		0			0
$555$	−17.6003	+	22.9532i	−0.747090	+	0.974307i
$556$		0			0
$557$	29.8644	−	12.3702i	1.26539	−	0.524143i	0.353833	−	0.935309i	$-0.384878\pi$
$557$	29.8644	−	12.3702i	1.26539	−	0.524143i	0.911561	+	0.411165i	$0.134878\pi$
$558$		0			0
$559$	21.7502	+	9.00925i	0.919937	+	0.381050i
$560$		0			0
$561$	27.4108	−	11.3539i	1.15729	−	0.479364i
$562$		0			0
$563$	−9.46592	+	22.8528i	−0.398941	+	0.963129i	0.588977	+	0.808150i	$0.299531\pi$
$563$	−9.46592	+	22.8528i	−0.398941	+	0.963129i	−0.987918	+	0.154979i	$0.950469\pi$
$564$		0			0
$565$	5.05161	+	1.35175i	0.212523	+	0.0568685i
$566$		0			0
$567$	3.62730	−	8.75707i	0.152332	−	0.367762i
$568$		0			0
$569$	−29.4293	+	29.4293i	−1.23374	+	1.23374i	−0.271225	+	0.962516i	$0.587429\pi$
$569$	−29.4293	+	29.4293i	−1.23374	+	1.23374i	−0.962516	+	0.271225i	$0.912571\pi$
$570$		0			0
$571$	16.2622	−	6.73603i	0.680552	−	0.281894i	−0.0155054	−	0.999880i	$-0.504936\pi$
$571$	16.2622	−	6.73603i	0.680552	−	0.281894i	0.696058	+	0.717986i	$0.254936\pi$
$572$		0			0
$573$	6.96530	−	6.96530i	0.290980	−	0.290980i
$574$		0			0
$575$	−1.20401	−	4.48132i	−0.0502105	−	0.186884i
$576$		0			0
$577$	17.4315	+	7.22036i	0.725683	+	0.300588i	0.714777	−	0.699353i	$-0.246528\pi$
$577$	17.4315	+	7.22036i	0.725683	+	0.300588i	0.0109063	+	0.999941i	$0.496528\pi$
$578$		0			0
$579$	−3.18637	−	3.18637i	−0.132421	−	0.132421i
$580$		0			0
$581$	0.288719	+	0.697028i	0.0119781	+	0.0289176i
$582$		0			0
$583$	19.8007			0.820059
$584$		0			0
$585$	−3.14271	−	2.40980i	−0.129935	−	0.0996332i
$586$		0			0
$587$	21.7682	+	9.01668i	0.898470	+	0.372158i	0.783632	−	0.621226i	$-0.213365\pi$
$587$	21.7682	+	9.01668i	0.898470	+	0.372158i	0.114838	+	0.993384i	$0.463365\pi$
$588$		0			0
$589$	−11.2193	+	27.0859i	−0.462284	+	1.11605i
$590$		0			0
$591$	−0.328846	+	0.793904i	−0.0135269	+	0.0326569i
$592$		0			0
$593$	0.607020	−	0.251436i	0.0249273	−	0.0103252i	−0.370185	−	0.928958i	$-0.620706\pi$
$593$	0.607020	−	0.251436i	0.0249273	−	0.0103252i	0.395112	+	0.918633i	$0.370706\pi$
$594$		0			0
$595$	9.25260	−	5.34615i	0.379320	−	0.219171i
$596$		0			0
$597$	16.6307	+	16.6307i	0.680649	+	0.680649i
$598$		0			0
$599$	−37.9198			−1.54936			−0.774680	−	0.632354i	$-0.782089\pi$
$599$	−37.9198			−1.54936			−0.774680	+	0.632354i	$0.782089\pi$
$600$		0			0
$601$	−29.6032	−	12.2620i	−1.20754	−	0.500179i	−0.314112	−	0.949386i	$-0.601707\pi$
$601$	−29.6032	−	12.2620i	−1.20754	−	0.500179i	−0.893428	+	0.449207i	$0.851707\pi$
$602$		0			0
$603$	−0.186002	+	0.449049i	−0.00757459	+	0.0182867i
$604$		0			0
$605$	−49.6504	−	13.2858i	−2.01857	−	0.540146i
$606$		0			0
$607$	−4.70631			−0.191023			−0.0955117	−	0.995428i	$-0.530449\pi$
$607$	−4.70631			−0.191023			−0.0955117	+	0.995428i	$0.530449\pi$
$608$		0			0
$609$	−1.59508	+	3.85086i	−0.0646358	+	0.156045i
$610$		0			0
$611$	−36.4638			−1.47517
$612$		0			0
$613$	−10.5384			−0.425644			−0.212822	−	0.977091i	$-0.568265\pi$
$613$	−10.5384			−0.425644			−0.212822	+	0.977091i	$0.568265\pi$
$614$		0			0
$615$	21.8764	−	1.27907i	0.882143	−	0.0515772i
$616$		0			0
$617$	−16.4990			−0.664224			−0.332112	−	0.943240i	$-0.607761\pi$
$617$	−16.4990			−0.664224			−0.332112	+	0.943240i	$0.607761\pi$
$618$		0			0
$619$	−19.9470			−0.801739			−0.400869	−	0.916135i	$-0.631292\pi$
$619$	−19.9470			−0.801739			−0.400869	+	0.916135i	$0.631292\pi$
$620$		0			0
$621$	−1.98808	+	4.79965i	−0.0797790	+	0.192603i
$622$		0			0
$623$	−23.3922			−0.937187
$624$		0			0
$625$	−12.5292	−	21.6338i	−0.501168	−	0.865350i
$626$		0			0
$627$	−20.1300	+	48.5982i	−0.803916	+	1.94082i
$628$		0			0
$629$	25.9641	+	10.7547i	1.03525	+	0.428817i
$630$		0			0
$631$	32.5474			1.29569			0.647846	−	0.761771i	$-0.275670\pi$
$631$	32.5474			1.29569			0.647846	+	0.761771i	$0.275670\pi$
$632$		0			0
$633$	−2.75231	−	2.75231i	−0.109395	−	0.109395i
$634$		0			0
$635$	7.85578	−	29.3578i	0.311747	−	1.16503i
$636$		0			0
$637$	−12.2803	+	5.08666i	−0.486562	+	0.201541i
$638$		0			0
$639$	−3.84508	+	9.28284i	−0.152109	+	0.367224i
$640$		0			0
$641$	−11.7933	+	28.4715i	−0.465806	+	1.12456i	0.500170	+	0.865927i	$0.333271\pi$
$641$	−11.7933	+	28.4715i	−0.465806	+	1.12456i	−0.965977	+	0.258629i	$0.916729\pi$
$642$		0			0
$643$	−16.0094	−	6.63131i	−0.631349	−	0.261513i	0.0439769	−	0.999033i	$-0.485997\pi$
$643$	−16.0094	−	6.63131i	−0.631349	−	0.261513i	−0.675326	+	0.737519i	$0.735997\pi$
$644$		0			0
$645$	−3.91411	−	29.6533i	−0.154118	−	1.16760i
$646$		0			0
$647$	−28.6753			−1.12734			−0.563671	−	0.826000i	$-0.690611\pi$
$647$	−28.6753			−1.12734			−0.563671	+	0.826000i	$0.690611\pi$
$648$		0			0
$649$	23.2279	+	56.0771i	0.911774	+	2.20122i
$650$		0			0
$651$	−7.73480	−	7.73480i	−0.303151	−	0.303151i
$652$		0			0
$653$	−24.3022	−	10.0663i	−0.951018	−	0.393925i	−0.147405	−	0.989076i	$-0.547092\pi$
$653$	−24.3022	−	10.0663i	−0.951018	−	0.393925i	−0.803614	+	0.595152i	$0.797092\pi$
$654$		0			0
$655$	33.8778	+	9.06528i	1.32371	+	0.354210i
$656$		0			0
$657$	3.57758	−	3.57758i	0.139575	−	0.139575i
$658$		0			0
$659$	28.2022	−	11.6817i	1.09860	−	0.455056i	0.241603	−	0.970375i	$-0.422327\pi$
$659$	28.2022	−	11.6817i	1.09860	−	0.455056i	0.856998	+	0.515320i	$0.172327\pi$
$660$		0			0
$661$	−22.2897	+	22.2897i	−0.866970	+	0.866970i	−0.992136	−	0.125166i	$-0.960054\pi$
$661$	−22.2897	+	22.2897i	−0.866970	+	0.866970i	0.125166	+	0.992136i	$0.460054\pi$
$662$		0			0
$663$	5.24626	−	12.6656i	0.203748	−	0.491891i
$664$		0			0
$665$	−4.89739	+	18.3020i	−0.189913	+	0.709721i
$666$		0			0
$667$	0.672974	−	1.62470i	0.0260577	−	0.0629087i
$668$		0			0
$669$	3.77736	−	1.56463i	0.146041	−	0.0604923i
$670$		0			0
$671$	−8.12030	−	3.36354i	−0.313481	−	0.129848i
$672$		0			0
$673$	24.4991	−	10.1479i	0.944372	−	0.391172i	0.143260	−	0.989685i	$-0.454242\pi$
$673$	24.4991	−	10.1479i	0.944372	−	0.391172i	0.801113	+	0.598513i	$0.204242\pi$
$674$		0			0
$675$	−3.63464	+	27.7524i	−0.139897	+	1.06819i
$676$		0			0
$677$			21.2779i			0.817775i	0.912585	+	0.408888i	$0.134083\pi$
$677$			21.2779i			0.817775i	−0.912585	+	0.408888i	$0.865917\pi$
$678$		0			0
$679$	5.36081			0.205729
$680$		0			0
$681$			23.6141i			0.904896i
$682$		0			0
$683$	8.22586	+	19.8590i	0.314754	+	0.759883i	0.999516	+	0.0311160i	$0.00990614\pi$
$683$	8.22586	+	19.8590i	0.314754	+	0.759883i	−0.684762	+	0.728767i	$0.740094\pi$
$684$		0			0
$685$	14.5226	−	18.9395i	0.554881	−	0.723641i
$686$		0			0
$687$	−14.9409	−	14.9409i	−0.570032	−	0.570032i
$688$		0			0
$689$	6.46946	−	6.46946i	0.246467	−	0.246467i
$690$		0			0
$691$	24.9826	+	10.3481i	0.950385	+	0.393662i	0.803375	−	0.595473i	$-0.203035\pi$
$691$	24.9826	+	10.3481i	0.950385	+	0.393662i	0.147009	+	0.989135i	$0.453035\pi$
$692$		0			0
$693$	3.89525	+	3.89525i	0.147968	+	0.147968i
$694$		0			0
$695$	32.8591	−	18.9860i	1.24642	−	0.720180i
$696$		0			0
$697$	−6.69492	−	20.2118i	−0.253588	−	0.765576i
$698$		0			0
$699$	26.4767	−	26.4767i	1.00144	−	1.00144i
$700$		0			0
$701$		−	19.4459i		−	0.734460i	−0.930130	−	0.367230i	$-0.880306\pi$
$701$		−	19.4459i		−	0.734460i	0.930130	−	0.367230i	$-0.119694\pi$
$702$		0			0
$703$	−46.0331	+	19.0675i	−1.73617	+	0.719146i
$704$		0			0
$705$	23.1772	+	40.1128i	0.872902	+	1.51073i
$706$		0			0
$707$	0.491271	−	0.491271i	0.0184762	−	0.0184762i
$708$		0			0
$709$	−10.9281	−	26.3827i	−0.410412	−	0.990821i	−0.985027	−	0.172398i	$-0.944848\pi$
$709$	−10.9281	−	26.3827i	−0.410412	−	0.990821i	0.574616	−	0.818423i	$-0.305152\pi$
$710$		0			0
$711$	−0.727705	+	1.75684i	−0.0272911	+	0.0658865i
$712$		0			0
$713$	3.26337	+	3.26337i	0.122214	+	0.122214i
$714$		0			0
$715$	−30.4038	+	17.5673i	−1.13704	+	0.656981i
$716$		0			0
$717$	1.02304			0.0382060
$718$		0			0
$719$	7.05679	−	17.0366i	0.263174	−	0.635358i	−0.735957	−	0.677028i	$-0.763268\pi$
$719$	7.05679	−	17.0366i	0.263174	−	0.635358i	0.999131	+	0.0416695i	$0.0132677\pi$
$720$		0			0
$721$	13.7371	+	5.69011i	0.511598	+	0.211911i
$722$		0			0
$723$	−26.7851	+	11.0947i	−0.996148	+	0.412618i
$724$		0			0
$725$	1.23034	−	9.39431i	0.0456937	−	0.348896i
$726$		0			0
$727$	−46.3246	−	19.1883i	−1.71809	−	0.711654i	−0.999875	−	0.0158289i	$-0.994961\pi$
$727$	−46.3246	−	19.1883i	−1.71809	−	0.711654i	−0.718211	−	0.695825i	$-0.755039\pi$
$728$		0			0
$729$	21.2411	−	21.2411i	0.786707	−	0.786707i
$730$		0			0
$731$	−26.8493	+	11.1213i	−0.993057	+	0.411338i
$732$		0			0
$733$		−	9.28292i		−	0.342872i	−0.985195	−	0.171436i	$-0.945159\pi$
$733$		−	9.28292i		−	0.342872i	0.985195	−	0.171436i	$-0.0548407\pi$
$734$		0			0
$735$	13.4013	+	10.2760i	0.494314	+	0.379036i
$736$		0			0
$737$	3.04733	+	3.04733i	0.112250	+	0.112250i
$738$		0			0
$739$			35.4342i			1.30347i	0.758447	+	0.651734i	$0.225958\pi$
$739$			35.4342i			1.30347i	−0.758447	+	0.651734i	$0.774042\pi$
$740$		0			0
$741$	9.30139	+	22.4555i	0.341695	+	0.824925i
$742$		0			0
$743$	−23.3023			−0.854879			−0.427440	−	0.904044i	$-0.640584\pi$
$743$	−23.3023			−0.854879			−0.427440	+	0.904044i	$0.640584\pi$
$744$		0			0
$745$	3.41075	+	25.8398i	0.124960	+	0.946699i
$746$		0			0
$747$			0.345153i			0.0126285i
$748$		0			0
$749$	7.19219	+	17.3635i	0.262797	+	0.634448i
$750$		0			0
$751$	6.44172	+	15.5517i	0.235062	+	0.567489i	0.996759	−	0.0804437i	$-0.0256337\pi$
$751$	6.44172	+	15.5517i	0.235062	+	0.567489i	−0.761697	+	0.647933i	$0.775634\pi$
$752$		0			0
$753$	8.11304	+	19.5866i	0.295655	+	0.713775i
$754$		0			0
$755$	14.0659	+	10.7856i	0.511909	+	0.392527i
$756$		0			0
$757$	−10.5266	−	25.4135i	−0.382597	−	0.923671i	−0.991462	−	0.130397i	$-0.958375\pi$
$757$	−10.5266	−	25.4135i	−0.382597	−	0.923671i	0.608865	−	0.793274i	$-0.291625\pi$
$758$		0			0
$759$	5.85522	+	5.85522i	0.212531	+	0.212531i
$760$		0			0
$761$			39.0404i			1.41521i	0.706607	+	0.707607i	$0.250225\pi$
$761$			39.0404i			1.41521i	−0.706607	+	0.707607i	$0.749775\pi$
$762$		0			0
$763$	15.6544	−	15.6544i	0.566728	−	0.566728i
$764$		0			0
$765$	4.84667	−	0.639739i	0.175232	−	0.0231298i
$766$		0			0
$767$	25.9113	+	10.7328i	0.935602	+	0.387539i
$768$		0			0
$769$	−17.2515			−0.622106			−0.311053	−	0.950393i	$-0.600682\pi$
$769$	−17.2515			−0.622106			−0.311053	+	0.950393i	$0.600682\pi$
$770$		0			0
$771$	1.77530	+	1.77530i	0.0639360	+	0.0639360i
$772$		0			0
$773$	11.7358	+	28.3328i	0.422109	+	1.01906i	0.981724	+	0.190308i	$0.0609488\pi$
$773$	11.7358	+	28.3328i	0.422109	+	1.01906i	−0.559616	+	0.828752i	$0.689051\pi$
$774$		0			0
$775$	21.5417	+	12.4177i	0.773800	+	0.446058i
$776$		0			0
$777$		−	18.5905i		−	0.666932i
$778$		0			0
$779$	33.7321	+	16.9457i	1.20858	+	0.607142i
$780$		0			0
$781$	62.9952	+	62.9952i	2.25415	+	2.25415i
$782$		0			0
$783$	−7.50061	+	7.50061i	−0.268050	+	0.268050i
$784$		0			0
$785$	52.7011	−	6.95631i	1.88098	−	0.248281i
$786$		0			0
$787$			2.33956i			0.0833964i	0.999130	+	0.0416982i	$0.0132768\pi$
$787$			2.33956i			0.0833964i	−0.999130	+	0.0416982i	$0.986723\pi$
$788$		0			0
$789$			43.1940i			1.53775i
$790$		0			0
$791$	−3.10521	+	1.28622i	−0.110408	+	0.0457327i
$792$		0			0
$793$	−3.75211	+	1.55417i	−0.133241	+	0.0551904i
$794$		0			0
$795$	−11.2290	−	3.00474i	−0.398252	−	0.106567i
$796$		0			0
$797$	−20.0151	+	20.0151i	−0.708971	+	0.708971i	−0.966319	−	0.257348i	$-0.917151\pi$
$797$	−20.0151	+	20.0151i	−0.708971	+	0.708971i	0.257348	+	0.966319i	$0.417151\pi$
$798$		0			0
$799$	31.8284	−	31.8284i	1.12601	−	1.12601i
$800$		0			0
$801$	−9.88695	−	4.09531i	−0.349338	−	0.144701i
$802$		0			0
$803$	−17.1673	−	41.4454i	−0.605819	−	1.46258i
$804$		0			0
$805$	2.36673	+	1.81479i	0.0834162	+	0.0639628i
$806$		0			0
$807$	8.16607	−	19.7146i	0.287459	−	0.693988i
$808$		0			0
$809$	−5.52468	+	2.28840i	−0.194237	+	0.0804558i	−0.477682	−	0.878533i	$-0.658523\pi$
$809$	−5.52468	+	2.28840i	−0.194237	+	0.0804558i	0.283444	+	0.958989i	$0.408523\pi$
$810$		0			0
$811$	−20.8391	−	20.8391i	−0.731761	−	0.731761i	0.239207	−	0.970969i	$-0.423112\pi$
$811$	−20.8391	−	20.8391i	−0.731761	−	0.731761i	−0.970969	+	0.239207i	$0.923112\pi$
$812$		0			0
$813$	15.0163	+	6.21994i	0.526643	+	0.218143i
$814$		0			0
$815$	−46.8117	−	12.5262i	−1.63974	−	0.438775i
$816$		0			0
$817$	19.7176	−	47.6026i	0.689833	−	1.66540i
$818$		0			0
$819$	2.54539			0.0889431
$820$		0			0
$821$	1.58381			0.0552754			0.0276377	−	0.999618i	$-0.491202\pi$
$821$	1.58381			0.0552754			0.0276377	+	0.999618i	$0.491202\pi$
$822$		0			0
$823$	10.5445	−	25.4567i	0.367558	−	0.887364i	−0.626591	−	0.779348i	$-0.715550\pi$
$823$	10.5445	−	25.4567i	0.367558	−	0.887364i	0.994149	−	0.108016i	$-0.0344497\pi$
$824$		0			0
$825$	38.6507	+	22.2802i	1.34564	+	0.775698i
$826$		0			0
$827$	33.4723	+	13.8647i	1.16395	+	0.482123i	0.879187	−	0.476476i	$-0.158086\pi$
$827$	33.4723	+	13.8647i	1.16395	+	0.482123i	0.284760	+	0.958599i	$0.408086\pi$
$828$		0			0
$829$	−16.2629	−	16.2629i	−0.564834	−	0.564834i	0.365842	−	0.930677i	$-0.380781\pi$
$829$	−16.2629	−	16.2629i	−0.564834	−	0.564834i	−0.930677	+	0.365842i	$0.880781\pi$
$830$		0			0
$831$	−3.79105	+	1.57031i	−0.131510	+	0.0544733i
$832$		0			0
$833$	6.27916	−	15.1592i	0.217560	−	0.525236i
$834$		0			0
$835$	−3.77750	−	28.6184i	−0.130726	−	0.990380i
$836$		0			0
$837$	−10.6530	−	25.7187i	−0.368223	−	0.888969i
$838$		0			0
$839$	44.0247	+	18.2356i	1.51990	+	0.629564i	0.977572	−	0.210601i	$-0.0675420\pi$
$839$	44.0247	+	18.2356i	1.51990	+	0.629564i	0.542331	+	0.840165i	$0.317542\pi$
$840$		0			0
$841$	−17.9671	+	17.9671i	−0.619555	+	0.619555i
$842$		0			0
$843$	−26.3567	+	26.3567i	−0.907772	+	0.907772i
$844$		0			0
$845$	3.32005	−	12.4073i	0.114213	−	0.426825i
$846$		0			0
$847$	30.5199	−	12.6418i	1.04868	−	0.434376i
$848$		0			0
$849$	16.3667	−	6.77932i	0.561704	−	0.232666i
$850$		0			0
$851$			7.84348i			0.268871i
$852$		0			0
$853$		−	13.8733i		−	0.475014i	−0.971386	−	0.237507i	$-0.923670\pi$
$853$		−	13.8733i		−	0.475014i	0.971386	−	0.237507i	$-0.0763303\pi$
$854$		0			0
$855$	−5.27410	+	6.87814i	−0.180370	+	0.235228i
$856$		0			0
$857$	−21.4899	+	21.4899i	−0.734080	+	0.734080i	−0.971425	−	0.237346i	$-0.923723\pi$
$857$	−21.4899	+	21.4899i	−0.734080	+	0.734080i	0.237346	+	0.971425i	$0.423723\pi$
$858$		0			0
$859$	1.68959	+	1.68959i	0.0576479	+	0.0576479i	0.735343	−	0.677695i	$-0.237021\pi$
$859$	1.68959	+	1.68959i	0.0576479	+	0.0576479i	−0.677695	+	0.735343i	$0.737021\pi$
$860$		0			0
$861$	−10.6577	+	9.20819i	−0.363213	+	0.313814i
$862$		0			0
$863$			0.485392i			0.0165229i	0.999966	+	0.00826147i	$0.00262974\pi$
$863$			0.485392i			0.0165229i	−0.999966	+	0.00826147i	$0.997370\pi$
$864$		0			0
$865$	−14.4300	−	24.9741i	−0.490636	−	0.849145i
$866$		0			0
$867$	−3.48084	−	8.40348i	−0.118215	−	0.285397i
$868$		0			0
$869$	11.9222	+	11.9222i	0.404434	+	0.404434i
$870$		0			0
$871$	1.99131			0.0674729
$872$		0			0
$873$	2.26580	+	0.938526i	0.0766858	+	0.0317643i
$874$		0			0
$875$	14.8513	+	6.13403i	0.502067	+	0.207368i
$876$		0			0
$877$	−27.6825	+	27.6825i	−0.934770	+	0.934770i	−0.997999	−	0.0632291i	$-0.979860\pi$
$877$	−27.6825	+	27.6825i	−0.934770	+	0.934770i	0.0632291	+	0.997999i	$0.479860\pi$
$878$		0			0
$879$			22.4071i			0.755774i
$880$		0			0
$881$	6.18484	+	6.18484i	0.208372	+	0.208372i	0.803575	−	0.595203i	$-0.202928\pi$
$881$	6.18484	+	6.18484i	0.208372	+	0.208372i	−0.595203	+	0.803575i	$0.702928\pi$
$882$		0			0
$883$	−18.2934	−	44.1642i	−0.615623	−	1.48625i	−0.856740	−	0.515749i	$-0.827514\pi$
$883$	−18.2934	−	44.1642i	−0.615623	−	1.48625i	0.241117	−	0.970496i	$-0.422486\pi$
$884$		0			0
$885$	−4.66291	−	35.3263i	−0.156742	−	1.18748i
$886$		0			0
$887$	−12.8819	−	31.0997i	−0.432533	−	1.04423i	−0.978468	−	0.206399i	$-0.933825\pi$
$887$	−12.8819	−	31.0997i	−0.432533	−	1.04423i	0.545935	−	0.837828i	$-0.316175\pi$
$888$		0			0
$889$	7.47495	+	18.0461i	0.250702	+	0.605248i
$890$		0			0
$891$	−14.7135	−	35.5216i	−0.492921	−	1.19002i
$892$		0			0
$893$			79.8046i			2.67056i
$894$		0			0
$895$	−27.9489	+	3.68913i	−0.934228	+	0.123314i
$896$		0			0
$897$	3.82615			0.127751
$898$		0			0
$899$	3.60610	+	8.70590i	0.120270	+	0.290358i
$900$		0			0
$901$			11.2941i			0.376261i
$902$		0			0
$903$	13.5937	+	13.5937i	0.452370	+	0.452370i
$904$		0			0
$905$	−14.7956	+	1.95295i	−0.491821	+	0.0649182i
$906$		0			0
$907$			24.6015i			0.816880i	0.912785	+	0.408440i	$0.133927\pi$
$907$			24.6015i			0.816880i	−0.912785	+	0.408440i	$0.866073\pi$
$908$		0			0
$909$	0.293649	−	0.121633i	0.00973972	−	0.00403432i
$910$		0			0
$911$	−2.49076	+	2.49076i	−0.0825224	+	0.0825224i	−0.747163	−	0.664641i	$-0.768585\pi$
$911$	−2.49076	+	2.49076i	−0.0825224	+	0.0825224i	0.664641	+	0.747163i	$0.268585\pi$
$912$		0			0
$913$	2.82738	+	1.17114i	0.0935726	+	0.0387590i
$914$		0			0
$915$	4.09463	+	3.13972i	0.135364	+	0.103796i
$916$		0			0
$917$	−20.8246	+	8.62582i	−0.687688	+	0.284850i
$918$		0			0
$919$	−11.1991	−	4.63883i	−0.369425	−	0.153021i	0.190245	−	0.981737i	$-0.439072\pi$
$919$	−11.1991	−	4.63883i	−0.369425	−	0.153021i	−0.559669	+	0.828716i	$0.689072\pi$
$920$		0			0
$921$	−11.7557	+	28.3807i	−0.387362	+	0.935175i
$922$		0			0
$923$	41.1648			1.35496
$924$		0			0
$925$	10.9647	+	40.8106i	0.360516	+	1.34184i
$926$		0			0
$927$	4.80997	+	4.80997i	0.157980	+	0.157980i
$928$		0			0
$929$	11.0654	−	26.7142i	0.363043	−	0.876463i	−0.631809	−	0.775124i	$-0.717687\pi$
$929$	11.0654	−	26.7142i	0.363043	−	0.876463i	0.994852	−	0.101339i	$-0.0323127\pi$
$930$		0			0
$931$	11.1327	+	26.8766i	0.364858	+	0.880846i
$932$		0			0
$933$	11.6491	−	11.6491i	0.381375	−	0.381375i
$934$		0			0
$935$	11.2047	−	41.8730i	0.366433	−	1.36939i
$936$		0			0
$937$	13.8347	−	5.73053i	0.451960	−	0.187208i	−0.145079	−	0.989420i	$-0.546344\pi$
$937$	13.8347	−	5.73053i	0.451960	−	0.187208i	0.597039	+	0.802212i	$0.296344\pi$
$938$		0			0
$939$			7.44829i			0.243066i
$940$		0			0
$941$	−32.4676	+	32.4676i	−1.05841	+	1.05841i	−0.0602288	+	0.998185i	$0.519183\pi$
$941$	−32.4676	+	32.4676i	−1.05841	+	1.05841i	−0.998185	+	0.0602288i	$0.980817\pi$
$942$		0			0
$943$	4.49656	−	3.88500i	0.146428	−	0.126513i
$944$		0			0
$945$	−9.00007	−	15.5765i	−0.292772	−	0.506702i
$946$		0			0
$947$	1.08203	+	1.08203i	0.0351612	+	0.0351612i	0.724469	−	0.689308i	$-0.242085\pi$
$947$	1.08203	+	1.08203i	0.0351612	+	0.0351612i	−0.689308	+	0.724469i	$0.742085\pi$
$948$		0			0
$949$	−19.1505	−	7.93239i	−0.621651	−	0.257496i
$950$		0			0
$951$	−16.1649	+	16.1649i	−0.524184	+	0.524184i
$952$		0			0
$953$	−19.2185	−	19.2185i	−0.622550	−	0.622550i	0.323633	−	0.946183i	$-0.395096\pi$
$953$	−19.2185	−	19.2185i	−0.622550	−	0.622550i	−0.946183	+	0.323633i	$0.895096\pi$
$954$		0			0
$955$	−1.88325	−	14.2675i	−0.0609406	−	0.461686i
$956$		0			0
$957$	6.47016	+	15.6204i	0.209151	+	0.504934i
$958$		0			0
$959$			15.3397i			0.495346i
$960$		0			0
$961$	6.27021			0.202265
$962$		0			0
$963$			8.59802i			0.277067i
$964$		0			0
$965$	−6.52687	+	0.861518i	−0.210107	+	0.0277332i
$966$		0			0
$967$	−52.8978	+	21.9110i	−1.70108	+	0.704610i	−0.999964	−	0.00843938i	$-0.997314\pi$
$967$	−52.8978	+	21.9110i	−1.70108	+	0.704610i	−0.701114	+	0.713049i	$0.747314\pi$
$968$		0			0
$969$	−27.7199	−	11.4820i	−0.890493	−	0.368854i
$970$		0			0
$971$	27.4755	−	11.3807i	0.881730	−	0.365225i	0.104563	−	0.994518i	$-0.466656\pi$
$971$	27.4755	−	11.3807i	0.881730	−	0.365225i	0.777168	+	0.629294i	$0.216656\pi$
$972$		0			0
$973$	−9.33422	+	22.5348i	−0.299241	+	0.722432i
$974$		0			0
$975$	19.9079	−	5.34871i	0.637564	−	0.171296i
$976$		0			0
$977$	22.6795	−	54.7532i	0.725582	−	1.75171i	0.0687971	−	0.997631i	$-0.478084\pi$
$977$	22.6795	−	54.7532i	0.725582	−	1.75171i	0.656785	−	0.754078i	$-0.271916\pi$
$978$		0			0
$979$	−67.0948	+	67.0948i	−2.14436	+	2.14436i
$980$		0			0
$981$	9.35715	−	3.87586i	0.298751	−	0.123747i
$982$		0			0
$983$	−9.04938	+	9.04938i	−0.288630	+	0.288630i	−0.836539	−	0.547908i	$-0.815424\pi$
$983$	−9.04938	+	9.04938i	−0.288630	+	0.288630i	0.547908	+	0.836539i	$0.315424\pi$
$984$		0			0
$985$	0.628088	+	1.08703i	0.0200126	+	0.0346358i
$986$		0			0
$987$	−27.5094	−	11.3948i	−0.875633	−	0.362699i
$988$		0			0
$989$	−5.73527	−	5.73527i	−0.182371	−	0.182371i
$990$		0			0
$991$	−19.5253	−	47.1382i	−0.620241	−	1.49739i	−0.851421	−	0.524483i	$-0.824258\pi$
$991$	−19.5253	−	47.1382i	−0.620241	−	1.49739i	0.231180	−	0.972911i	$-0.425742\pi$
$992$		0			0
$993$	7.63701			0.242353
$994$		0			0
$995$	34.0659	−	4.49654i	1.07996	−	0.142550i
$996$		0			0
$997$	16.8034	+	6.96020i	0.532170	+	0.220432i	0.632553	−	0.774517i	$-0.282007\pi$
$997$	16.8034	+	6.96020i	0.532170	+	0.220432i	−0.100384	+	0.994949i	$0.532007\pi$
$998$		0			0
$999$	18.1051	−	43.7096i	0.572821	−	1.38291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.793.15	yes	84
5.2	odd	4		820.2.y.a.137.7	yes	84
41.3	odd	8		820.2.y.a.413.7	yes	84
205.167	even	8	inner	820.2.x.a.577.15	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.15	✓	84	205.167	even	8	inner
820.2.x.a.793.15	yes	84	1.1	even	1	trivial
820.2.y.a.137.7	yes	84	5.2	odd	4
820.2.y.a.413.7	yes	84	41.3	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.585707 - 1.41402i) q^{3} +(-1.11869 - 1.93611i) q^{5} +(1.32779 + 0.549988i) q^{7} +(0.464917 + 0.464917i) q^{9} +(5.38595 - 2.23093i) q^{11} +(1.03084 - 2.48866i) q^{13} +(-3.39293 + 0.447852i) q^{15} +(1.27250 + 3.07210i) q^{17} +(-5.44669 - 2.25609i) q^{19} +(1.55539 - 1.55539i) q^{21} +(-0.656229 + 0.656229i) q^{23} +(-2.49708 + 4.33181i) q^{25} +(5.17177 - 2.14222i) q^{27} +(-1.75067 + 0.725150i) q^{29} -4.97291i q^{31} -8.92252i q^{33} +(-0.420540 - 3.18602i) q^{35} +(5.97617 - 5.97617i) q^{37} +(-2.91525 - 2.91525i) q^{39} +(-6.38615 - 0.465961i) q^{41} +8.73974i q^{43} +(0.380036 - 1.42023i) q^{45} +(-5.18025 - 12.5062i) q^{47} +(-3.48921 - 3.48921i) q^{49} +5.08932 q^{51} +(3.13796 + 1.29979i) q^{53} +(-10.3445 - 7.93210i) q^{55} +(-6.38032 + 6.38032i) q^{57} +10.4117i q^{59} +(-1.06609 - 1.06609i) q^{61} +(0.361612 + 0.873010i) q^{63} +(-5.97152 + 0.788214i) q^{65} +(0.282897 + 0.682973i) q^{67} +(0.543564 + 1.31228i) q^{69} +(5.84810 + 14.1186i) q^{71} -7.69510i q^{73} +(4.66272 + 6.06809i) q^{75} +8.37839 q^{77} +(1.10679 + 2.67203i) q^{79} -6.59523i q^{81} +(0.371199 + 0.371199i) q^{83} +(4.52440 - 5.90043i) q^{85} +2.90020i q^{87} +(-15.0374 + 6.22868i) q^{89} +(2.73747 - 2.73747i) q^{91} +(-7.03179 - 2.91266i) q^{93} +(1.72509 + 13.0693i) q^{95} +(3.44613 - 1.42744i) q^{97} +(3.54122 + 1.46682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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