LMFDB - Embedded newform 820.2.y.a.137.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] 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, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (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			137.7
Character	$\chi$	$=$	820.137
Dual form			820.2.y.a.413.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41402 - 0.585707i) q^{3} +(1.93611 + 1.11869i) q^{5} +(-0.549988 + 1.32779i) q^{7} +(-0.464917 - 0.464917i) q^{9} +(5.38595 - 2.23093i) q^{11} +(-2.48866 - 1.03084i) q^{13} +(-2.08248 - 2.71584i) q^{15} +(-3.07210 + 1.27250i) q^{17} +(5.44669 + 2.25609i) q^{19} +(1.55539 - 1.55539i) q^{21} +(0.656229 + 0.656229i) q^{23} +(2.49708 + 4.33181i) q^{25} +(2.14222 + 5.17177i) q^{27} +(1.75067 - 0.725150i) q^{29} -4.97291i q^{31} -8.92252 q^{33} +(-2.55022 + 1.95549i) q^{35} +(5.97617 + 5.97617i) q^{37} +(2.91525 + 2.91525i) q^{39} +(-6.38615 - 0.465961i) q^{41} +8.73974 q^{43} +(-0.380036 - 1.42023i) q^{45} +(12.5062 - 5.18025i) q^{47} +(3.48921 + 3.48921i) q^{49} +5.08932 q^{51} +(1.29979 - 3.13796i) q^{53} +(12.9235 + 1.70585i) q^{55} +(-6.38032 - 6.38032i) q^{57} -10.4117i q^{59} +(-1.06609 - 1.06609i) q^{61} +(0.873010 - 0.361612i) q^{63} +(-3.66515 - 4.77985i) q^{65} +(-0.682973 + 0.282897i) q^{67} +(-0.543564 - 1.31228i) q^{69} +(5.84810 + 14.1186i) q^{71} -7.69510 q^{73} +(-0.993751 - 7.58783i) q^{75} +8.37839i q^{77} +(-1.10679 - 2.67203i) q^{79} -6.59523i q^{81} +(0.371199 - 0.371199i) q^{83} +(-7.37146 - 0.973000i) q^{85} -2.90020 q^{87} +(15.0374 - 6.22868i) q^{89} +(2.73747 - 2.73747i) q^{91} +(-2.91266 + 7.03179i) q^{93} +(8.02155 + 10.4612i) q^{95} +(1.42744 + 3.44613i) q^{97} +(-3.54122 - 1.46682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

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

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

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
$3$	−1.41402	−	0.585707i	−0.816386	−	0.338158i	−0.0648869	−	0.997893i	$-0.520669\pi$
$3$	−1.41402	−	0.585707i	−0.816386	−	0.338158i	−0.751499	+	0.659735i	$0.770669\pi$
$4$		0			0
$5$	1.93611	+	1.11869i	0.865857	+	0.500292i
$5$	1.93611	+	1.11869i	0.865857	+	0.500292i
$6$		0			0
$7$	−0.549988	+	1.32779i	−0.207876	+	0.501857i	−0.993088	−	0.117370i	$-0.962554\pi$
$7$	−0.549988	+	1.32779i	−0.207876	+	0.501857i	0.785212	+	0.619227i	$0.212554\pi$
$8$		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
$13$	−2.48866	−	1.03084i	−0.690230	−	0.285903i	0.00986577	−	0.999951i	$-0.496860\pi$
$13$	−2.48866	−	1.03084i	−0.690230	−	0.285903i	−0.700096	+	0.714049i	$0.746860\pi$
$14$		0			0
$15$	−2.08248	−	2.71584i	−0.537695	−	0.701228i
$16$		0			0
$17$	−3.07210	+	1.27250i	−0.745093	+	0.308627i	−0.722737	−	0.691123i	$-0.757116\pi$
$17$	−3.07210	+	1.27250i	−0.745093	+	0.308627i	−0.0223550	+	0.999750i	$0.507116\pi$
$18$		0			0
$19$	5.44669	+	2.25609i	1.24956	+	0.517583i	0.906688	−	0.421801i	$-0.138602\pi$
$19$	5.44669	+	2.25609i	1.24956	+	0.517583i	0.342867	+	0.939384i	$0.388602\pi$
$20$		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	$-0.219153\pi$
$23$	0.656229	+	0.656229i	0.136833	+	0.136833i	−0.635373	+	0.772206i	$0.719153\pi$
$24$		0			0
$25$	2.49708	+	4.33181i	0.499416	+	0.866362i
$26$		0			0
$27$	2.14222	+	5.17177i	0.412270	+	0.995308i
$28$		0			0
$29$	1.75067	−	0.725150i	0.325090	−	0.134657i	−0.214169	−	0.976797i	$-0.568704\pi$
$29$	1.75067	−	0.725150i	0.325090	−	0.134657i	0.539259	+	0.842140i	$0.318704\pi$
$30$		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
$33$	−8.92252			−1.55321
$34$		0			0
$35$	−2.55022	+	1.95549i	−0.431066	+	0.330538i
$36$		0			0
$37$	5.97617	+	5.97617i	0.982476	+	0.982476i	0.999849	−	0.0173729i	$-0.00553025\pi$
$37$	5.97617	+	5.97617i	0.982476	+	0.982476i	−0.0173729	+	0.999849i	$0.505530\pi$
$38$		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
$43$	8.73974			1.33280			0.666399	−	0.745596i	$-0.267835\pi$
$43$	8.73974			1.33280			0.666399	+	0.745596i	$0.267835\pi$
$44$		0			0
$45$	−0.380036	−	1.42023i	−0.0566524	−	0.211715i
$46$		0			0
$47$	12.5062	−	5.18025i	1.82422	−	0.755617i	0.851223	−	0.524803i	$-0.175861\pi$
$47$	12.5062	−	5.18025i	1.82422	−	0.755617i	0.972998	−	0.230814i	$-0.0741388\pi$
$48$		0			0
$49$	3.48921	+	3.48921i	0.498459	+	0.498459i
$50$		0			0
$51$	5.08932			0.712648
$52$		0			0
$53$	1.29979	−	3.13796i	0.178539	−	0.431032i	−0.809121	−	0.587642i	$-0.800056\pi$
$53$	1.29979	−	3.13796i	0.178539	−	0.431032i	0.987661	+	0.156610i	$0.0500564\pi$
$54$		0			0
$55$	12.9235	+	1.70585i	1.74261	+	0.230017i
$56$		0			0
$57$	−6.38032	−	6.38032i	−0.845094	−	0.845094i
$58$		0			0
$59$		−	10.4117i		−	1.35549i	−0.735296	−	0.677746i	$-0.762957\pi$
$59$		−	10.4117i		−	1.35549i	0.735296	−	0.677746i	$-0.237043\pi$
$60$		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
$63$	0.873010	−	0.361612i	0.109989	−	0.0455589i
$64$		0			0
$65$	−3.66515	−	4.77985i	−0.454606	−	0.592868i
$66$		0			0
$67$	−0.682973	+	0.282897i	−0.0834384	+	0.0345613i	−0.424012	−	0.905656i	$-0.639379\pi$
$67$	−0.682973	+	0.282897i	−0.0834384	+	0.0345613i	0.340574	+	0.940218i	$0.389379\pi$
$68$		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
$73$	−7.69510			−0.900643			−0.450322	−	0.892866i	$-0.648691\pi$
$73$	−7.69510			−0.900643			−0.450322	+	0.892866i	$0.648691\pi$
$74$		0			0
$75$	−0.993751	−	7.58783i	−0.114749	−	0.876167i
$76$		0			0
$77$			8.37839i			0.954806i
$78$		0			0
$79$	−1.10679	−	2.67203i	−0.124524	−	0.300627i	0.849308	−	0.527898i	$-0.177020\pi$
$79$	−1.10679	−	2.67203i	−0.124524	−	0.300627i	−0.973831	+	0.227271i	$0.927020\pi$
$80$		0			0
$81$		−	6.59523i		−	0.732803i
$82$		0			0
$83$	0.371199	−	0.371199i	0.0407444	−	0.0407444i	−0.686441	−	0.727185i	$-0.740828\pi$
$83$	0.371199	−	0.371199i	0.0407444	−	0.0407444i	0.727185	+	0.686441i	$0.240828\pi$
$84$		0			0
$85$	−7.37146	−	0.973000i	−0.799547	−	0.105537i
$86$		0			0
$87$	−2.90020			−0.310934
$88$		0			0
$89$	15.0374	−	6.22868i	1.59396	−	0.660239i	0.603414	−	0.797428i	$-0.293807\pi$
$89$	15.0374	−	6.22868i	1.59396	−	0.660239i	0.990545	+	0.137189i	$0.0438068\pi$
$90$		0			0
$91$	2.73747	−	2.73747i	0.286965	−	0.286965i
$92$		0			0
$93$	−2.91266	+	7.03179i	−0.302029	+	0.729163i
$94$		0			0
$95$	8.02155	+	10.4612i	0.822994	+	1.07330i
$96$		0			0
$97$	1.42744	+	3.44613i	0.144934	+	0.349902i	0.979631	−	0.200809i	$-0.0643569\pi$
$97$	1.42744	+	3.44613i	0.144934	+	0.349902i	−0.834696	+	0.550710i	$0.814357\pi$
$98$		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
$103$		−	10.3459i		−	1.01941i	−0.860349	−	0.509705i	$-0.829755\pi$
$103$		−	10.3459i		−	1.01941i	0.860349	−	0.509705i	$-0.170245\pi$
$104$		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	$-0.967807\pi$
$107$	−9.24683	+	9.24683i	−0.893925	+	0.893925i	0.100965	+	0.994890i	$0.467807\pi$
$108$		0			0
$109$	−5.89492	+	14.2316i	−0.564631	+	1.36314i	0.341396	+	0.939919i	$0.389100\pi$
$109$	−5.89492	+	14.2316i	−0.564631	+	1.36314i	−0.906027	+	0.423220i	$0.860900\pi$
$110$		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	$-0.214915\pi$
$113$	1.65366	+	1.65366i	0.155563	+	0.155563i	−0.625034	+	0.780597i	$0.714915\pi$
$114$		0			0
$115$	0.536420	+	2.00465i	0.0500214	+	0.186935i
$116$		0			0
$117$	0.677767	+	1.63627i	0.0626596	+	0.151274i
$118$		0			0
$119$		−	4.77895i		−	0.438086i
$120$		0			0
$121$	16.2532	−	16.2532i	1.47757	−	1.47757i
$122$		0			0
$123$	8.75723	+	4.39929i	0.789613	+	0.396671i
$124$		0			0
$125$	−0.0113103	+	11.1803i	−0.00101163	+	0.999999i
$126$		0			0
$127$	−9.61037	+	9.61037i	−0.852782	+	0.852782i	−0.990475	−	0.137693i	$-0.956031\pi$
$127$	−9.61037	+	9.61037i	−0.852782	+	0.852782i	0.137693	+	0.990475i	$0.456031\pi$
$128$		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
$135$	−1.63801	+	12.4096i	−0.140978	+	1.06805i
$136$		0			0
$137$	−9.86097	+	4.08455i	−0.842480	+	0.348966i	−0.761831	−	0.647776i	$-0.775699\pi$
$137$	−9.86097	+	4.08455i	−0.842480	+	0.348966i	−0.0806488	+	0.996743i	$0.525699\pi$
$138$		0			0
$139$		−	16.9717i		−	1.43952i	−0.694224	−	0.719759i	$-0.744252\pi$
$139$		−	16.9717i		−	1.43952i	0.694224	−	0.719759i	$-0.255748\pi$
$140$		0			0
$141$	−20.7182			−1.74479
$142$		0			0
$143$	−15.7035			−1.31320
$144$		0			0
$145$	4.20070	+	0.554474i	0.348850	+	0.0460466i
$146$		0			0
$147$	−2.89016	−	6.97747i	−0.238377	−	0.575492i
$148$		0			0
$149$	10.7689	+	4.46062i	0.882222	+	0.365428i	0.777358	−	0.629058i	$-0.216559\pi$
$149$	10.7689	+	4.46062i	0.882222	+	0.365428i	0.104864	+	0.994487i	$0.466559\pi$
$150$		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
$153$	2.01988	+	0.836660i	0.163297	+	0.0676400i
$154$		0			0
$155$	5.56312	−	9.62811i	0.446841	−	0.773349i
$156$		0			0
$157$	−21.9634	−	9.09755i	−1.75287	−	0.726064i	−0.997492	−	0.0707784i	$-0.977452\pi$
$157$	−21.9634	−	9.09755i	−1.75287	−	0.726064i	−0.755381	−	0.655286i	$-0.772548\pi$
$158$		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	−0.974085	−	0.226182i	$-0.927376\pi$
$163$	−15.3240	−	15.3240i	−1.20027	−	1.20027i	−0.226182	−	0.974085i	$-0.572624\pi$
$164$		0			0
$165$	−17.2750	−	9.98151i	−1.34486	−	0.777059i
$166$		0			0
$167$	−4.94027	+	11.9269i	−0.382290	+	0.922929i	0.609233	+	0.792991i	$0.291478\pi$
$167$	−4.94027	+	11.9269i	−0.382290	+	0.922929i	−0.991522	+	0.129937i	$0.958522\pi$
$168$		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
$173$		−	12.8991i		−	0.980699i	−0.871526	−	0.490349i	$-0.836869\pi$
$173$		−	12.8991i		−	0.980699i	0.871526	−	0.490349i	$-0.163131\pi$
$174$		0			0
$175$	−7.12509	+	0.933148i	−0.538606	+	0.0705394i
$176$		0			0
$177$	−6.09822	+	14.7224i	−0.458370	+	1.10660i
$178$		0			0
$179$	−4.82469	+	11.6478i	−0.360615	+	0.870601i	0.634596	+	0.772844i	$0.281167\pi$
$179$	−4.82469	+	11.6478i	−0.360615	+	0.870601i	−0.995210	+	0.0977565i	$0.968833\pi$
$180$		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
$183$	0.883060	+	2.13189i	0.0652776	+	0.157594i
$184$		0			0
$185$	4.88509	+	18.2560i	0.359159	+	1.34221i
$186$		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
$193$	−2.72011	−	1.12671i	−0.195798	−	0.0811020i	0.282630	−	0.959229i	$-0.408793\pi$
$193$	−2.72011	−	1.12671i	−0.195798	−	0.0811020i	−0.478428	+	0.878127i	$0.658793\pi$
$194$		0			0
$195$	2.38301	+	8.90551i	0.170651	+	0.637737i
$196$		0			0
$197$		−	0.561451i		−	0.0400018i	−0.999800	−	0.0200009i	$-0.993633\pi$
$197$		−	0.561451i		−	0.0400018i	0.999800	−	0.0200009i	$-0.00636690\pi$
$198$		0			0
$199$	5.88064	−	14.1971i	0.416868	−	1.00641i	−0.566382	−	0.824143i	$-0.691657\pi$
$199$	5.88064	−	14.1971i	0.416868	−	1.00641i	0.983250	−	0.182265i	$-0.0583428\pi$
$200$		0			0
$201$	1.13143			0.0798051
$202$		0			0
$203$			2.72334i			0.191141i
$204$		0			0
$205$	−11.8430	−	8.04625i	−0.827154	−	0.561975i
$206$		0			0
$207$		−	0.610184i		−	0.0424107i
$208$		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
$213$		−	23.3892i		−	1.60260i
$214$		0			0
$215$	16.9211	+	9.77703i	1.15401	+	0.666788i
$216$		0			0
$217$	6.60297	+	2.73504i	0.448239	+	0.185666i
$218$		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	−0.641026	−	0.767519i	$-0.721491\pi$
$223$	1.88894	−	1.88894i	0.126493	−	0.126493i	0.767519	+	0.641026i	$0.221491\pi$
$224$		0			0
$225$	0.852998	−	3.17487i	0.0568665	−	0.211658i
$226$		0			0
$227$	−5.90434	−	14.2543i	−0.391885	−	0.946094i	−0.989529	−	0.144332i	$-0.953897\pi$
$227$	−5.90434	−	14.2543i	−0.391885	−	0.946094i	0.597644	−	0.801761i	$-0.296103\pi$
$228$		0			0
$229$	−5.28313	+	12.7546i	−0.349119	+	0.842848i	0.647605	+	0.761976i	$0.275771\pi$
$229$	−5.28313	+	12.7546i	−0.349119	+	0.842848i	−0.996724	+	0.0808722i	$0.974229\pi$
$230$		0			0
$231$	4.90728	−	11.8472i	0.322875	−	0.779490i
$232$		0			0
$233$	9.36219	−	22.6023i	0.613337	−	1.48073i	−0.245975	−	0.969276i	$-0.579108\pi$
$233$	9.36219	−	22.6023i	0.613337	−	1.48073i	0.859312	−	0.511451i	$-0.170892\pi$
$234$		0			0
$235$	30.0086	+	3.96100i	1.95754	+	0.258387i
$236$		0			0
$237$			4.42656i			0.287536i
$238$		0			0
$239$	−0.255794	−	0.617540i	−0.0165459	−	0.0399454i	0.915391	−	0.402567i	$-0.131882\pi$
$239$	−0.255794	−	0.617540i	−0.0165459	−	0.0399454i	−0.931937	+	0.362621i	$0.881882\pi$
$240$		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
$243$	2.56378	−	6.18952i	0.164467	−	0.397058i
$244$		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
$253$	4.99842	+	2.07041i	0.314248	+	0.130166i
$254$		0			0
$255$	9.85351	+	5.69336i	0.617051	+	0.356532i
$256$		0			0
$257$	−1.51552	−	0.627750i	−0.0945358	−	0.0391580i	0.334914	−	0.942249i	$-0.391293\pi$
$257$	−1.51552	−	0.627750i	−0.0945358	−	0.0391580i	−0.429450	+	0.903091i	$0.641293\pi$
$258$		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
$263$	10.8000	+	26.0735i	0.665955	+	1.60776i	0.788315	+	0.615272i	$0.210954\pi$
$263$	10.8000	+	26.0735i	0.665955	+	1.60776i	−0.122359	+	0.992486i	$0.539046\pi$
$264$		0			0
$265$	6.02693	−	4.62140i	0.370232	−	0.283890i
$266$		0			0
$267$	−24.9113			−1.52455
$268$		0			0
$269$	−13.9422			−0.850074			−0.425037	−	0.905176i	$-0.639739\pi$
$269$	−13.9422			−0.850074			−0.425037	+	0.905176i	$0.639739\pi$
$270$		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
$273$	−5.47419	+	2.26748i	−0.331313	+	0.137234i
$274$		0			0
$275$	23.1131	+	17.7601i	1.39377	+	1.07097i
$276$		0			0
$277$	1.89578	−	1.89578i	0.113907	−	0.113907i	−0.647856	−	0.761763i	$-0.724334\pi$
$277$	1.89578	−	1.89578i	0.113907	−	0.113907i	0.761763	+	0.647856i	$0.224334\pi$
$278$		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	−0.420689	−	0.907205i	$-0.638212\pi$
$283$	8.18447	−	8.18447i	0.486516	−	0.486516i	0.907205	+	0.420689i	$0.138212\pi$
$284$		0			0
$285$	−5.21545	−	19.4906i	−0.308937	−	1.15452i
$286$		0			0
$287$	4.13100	−	8.22318i	0.243845	−	0.485399i
$288$		0			0
$289$	−4.20231	+	4.20231i	−0.247195	+	0.247195i
$290$		0			0
$291$		−	5.70896i		−	0.334665i
$292$		0			0
$293$	5.60255	+	13.5257i	0.327304	+	0.790182i	0.998791	+	0.0491655i	$0.0156562\pi$
$293$	5.60255	+	13.5257i	0.327304	+	0.790182i	−0.671486	+	0.741017i	$0.734344\pi$
$294$		0			0
$295$	11.6475	−	20.1583i	0.678142	−	1.17366i
$296$		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
$307$		−	20.0709i		−	1.14551i	−0.819728	−	0.572753i	$-0.805875\pi$
$307$		−	20.0709i		−	1.14551i	0.819728	−	0.572753i	$-0.194125\pi$
$308$		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
$313$	1.86232	+	4.49605i	0.105265	+	0.254132i	0.967732	−	0.251981i	$-0.0810820\pi$
$313$	1.86232	+	4.49605i	0.105265	+	0.254132i	−0.862467	+	0.506113i	$0.831082\pi$
$314$		0			0
$315$	2.09478	+	0.276501i	0.118027	+	0.0155791i
$316$		0			0
$317$	5.71595	−	13.7995i	0.321040	−	0.775058i	−0.678155	−	0.734919i	$-0.737220\pi$
$317$	5.71595	−	13.7995i	0.321040	−	0.775058i	0.999194	−	0.0401387i	$-0.0127800\pi$
$318$		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
$323$	−19.6036			−1.09077
$324$		0			0
$325$	−1.74899	−	13.3545i	−0.0970166	−	0.740774i
$326$		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
$333$		−	5.55684i		−	0.304513i
$334$		0			0
$335$	−1.63879	−	0.216313i	−0.0895365	−	0.0118184i
$336$		0			0
$337$	−24.1931			−1.31788			−0.658941	−	0.752194i	$-0.728996\pi$
$337$	−24.1931			−1.31788			−0.658941	+	0.752194i	$0.728996\pi$
$338$		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
$343$	−15.8465	+	6.56383i	−0.855629	+	0.354413i
$344$		0			0
$345$	0.415628	−	3.14880i	0.0223767	−	0.169526i
$346$		0			0
$347$	5.77758	−	2.39315i	0.310157	−	0.128471i	−0.222175	−	0.975007i	$-0.571316\pi$
$347$	5.77758	−	2.39315i	0.310157	−	0.128471i	0.532332	+	0.846536i	$0.321316\pi$
$348$		0			0
$349$	10.7368	+	10.7368i	0.574726	+	0.574726i	0.933445	−	0.358719i	$-0.116786\pi$
$349$	10.7368	+	10.7368i	0.574726	+	0.574726i	−0.358719	+	0.933445i	$0.616786\pi$
$350$		0			0
$351$		−	15.0791i		−	0.804861i
$352$		0			0
$353$	14.8910	+	14.8910i	0.792566	+	0.792566i	0.981911	−	0.189344i	$-0.0606362\pi$
$353$	14.8910	+	14.8910i	0.792566	+	0.792566i	−0.189344	+	0.981911i	$0.560636\pi$
$354$		0			0
$355$	−4.47166	+	33.8774i	−0.237331	+	1.79802i
$356$		0			0
$357$	−2.79907	+	6.75754i	−0.148142	+	0.357647i
$358$		0			0
$359$	18.7718			0.990736			0.495368	−	0.868683i	$-0.335033\pi$
$359$	18.7718			0.990736			0.495368	+	0.868683i	$0.335033\pi$
$360$		0			0
$361$	11.1414	+	11.1414i	0.586390	+	0.586390i
$362$		0			0
$363$	−32.5020	+	13.4628i	−1.70591	+	0.706613i
$364$		0			0
$365$	−14.8986	−	8.60841i	−0.779828	−	0.450585i
$366$		0			0
$367$	13.7074			0.715520			0.357760	−	0.933814i	$-0.383541\pi$
$367$	13.7074			0.715520			0.357760	+	0.933814i	$0.383541\pi$
$368$		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	$-0.288880\pi$
$373$	−3.32790	−	3.32790i	−0.172312	−	0.172312i	−0.787994	+	0.615682i	$0.788880\pi$
$374$		0			0
$375$	6.56439	−	15.8026i	0.338984	−	0.816043i
$376$		0			0
$377$	−5.10433			−0.262886
$378$		0			0
$379$			7.57513i			0.389108i	0.980892	+	0.194554i	$0.0623260\pi$
$379$			7.57513i			0.389108i	−0.980892	+	0.194554i	$0.937674\pi$
$380$		0			0
$381$	19.2181	−	7.96041i	0.984574	−	0.407824i
$382$		0			0
$383$	1.79142	+	4.32487i	0.0915372	+	0.220990i	0.963017	−	0.269441i	$-0.0868391\pi$
$383$	1.79142	+	4.32487i	0.0915372	+	0.220990i	−0.871480	+	0.490432i	$0.836839\pi$
$384$		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	$0.601649\pi$
$389$	−24.9178	+	24.9178i	−1.26338	+	1.26338i	−0.949443	+	0.313939i	$0.898351\pi$
$390$		0			0
$391$	−2.85105	−	1.18094i	−0.144184	−	0.0597230i
$392$		0			0
$393$	22.1770	−	9.18602i	1.11868	−	0.463373i
$394$		0			0
$395$	0.846290	−	6.41150i	0.0425815	−	0.322598i
$396$		0			0
$397$	19.1455	+	7.93034i	0.960887	+	0.398012i	0.807312	−	0.590125i	$-0.200921\pi$
$397$	19.1455	+	7.93034i	0.960887	+	0.398012i	0.153575	+	0.988137i	$0.450921\pi$
$398$		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
$403$	−5.12626	+	12.3759i	−0.255357	+	0.616486i
$404$		0			0
$405$	7.37800	−	12.7691i	0.366616	−	0.634503i
$406$		0			0
$407$	45.5198	+	18.8549i	2.25633	+	0.934603i
$408$		0			0
$409$	3.74666			0.185261			0.0926303	−	0.995701i	$-0.470473\pi$
$409$	3.74666			0.185261			0.0926303	+	0.995701i	$0.470473\pi$
$410$		0			0
$411$	16.3360			0.805794
$412$		0			0
$413$	13.8246	+	5.72633i	0.680263	+	0.281774i
$414$		0			0
$415$	1.13394	−	0.303428i	0.0556629	−	0.0148947i
$416$		0			0
$417$	−9.94042	+	23.9983i	−0.486785	+	1.17520i
$418$		0			0
$419$	−26.1687	−	26.1687i	−1.27842	−	1.27842i	−0.941550	−	0.336873i	$-0.890631\pi$
$419$	−26.1687	−	26.1687i	−1.27842	−	1.27842i	−0.336873	−	0.941550i	$-0.609369\pi$
$420$		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
$423$	−8.22274	−	3.40597i	−0.399803	−	0.165604i
$424$		0			0
$425$	−13.1835	−	10.1302i	−0.639494	−	0.491387i
$426$		0			0
$427$	2.00188	−	0.829207i	0.0968779	−	0.0401281i
$428$		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	−0.963991	−	0.265937i	$-0.914319\pi$
$433$	−25.5931	−	25.5931i	−1.22993	−	1.22993i	−0.265937	−	0.963991i	$-0.585681\pi$
$434$		0			0
$435$	−5.61513	−	3.24442i	−0.269225	−	0.155558i
$436$		0			0
$437$	2.09376	+	5.05479i	0.100158	+	0.241803i
$438$		0			0
$439$	−5.83888	+	2.41854i	−0.278674	+	0.115431i	−0.517643	−	0.855596i	$-0.673191\pi$
$439$	−5.83888	+	2.41854i	−0.278674	+	0.115431i	0.238969	+	0.971027i	$0.423191\pi$
$440$		0			0
$441$		−	3.24439i		−	0.154495i
$442$		0			0
$443$	−7.14463			−0.339452			−0.169726	−	0.985491i	$-0.554288\pi$
$443$	−7.14463			−0.339452			−0.169726	+	0.985491i	$0.554288\pi$
$444$		0			0
$445$	36.0820	+	4.76267i	1.71045	+	0.225772i
$446$		0			0
$447$	−12.6148	−	12.6148i	−0.596661	−	0.596661i
$448$		0			0
$449$	−5.03157	−	5.03157i	−0.237454	−	0.237454i	0.578341	−	0.815795i	$-0.303700\pi$
$449$	−5.03157	−	5.03157i	−0.237454	−	0.237454i	−0.815795	+	0.578341i	$0.803700\pi$
$450$		0			0
$451$	−35.4350	+	11.7374i	−1.66857	+	0.552694i
$452$		0			0
$453$	12.1323			0.570025
$454$		0			0
$455$	8.36242	−	2.23768i	0.392036	−	0.104904i
$456$		0			0
$457$	20.0430	−	8.30209i	0.937572	−	0.388355i	0.139026	−	0.990289i	$-0.455603\pi$
$457$	20.0430	−	8.30209i	0.937572	−	0.388355i	0.798546	+	0.601934i	$0.205603\pi$
$458$		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
$463$	5.03680	−	12.1599i	0.234080	−	0.565119i	−0.762570	−	0.646906i	$-0.776063\pi$
$463$	5.03680	−	12.1599i	0.234080	−	0.565119i	0.996650	+	0.0817870i	$0.0260627\pi$
$464$		0			0
$465$	−13.5056	+	10.3560i	−0.626308	+	0.480248i
$466$		0			0
$467$	−2.08551	−	2.08551i	−0.0965060	−	0.0965060i	0.657205	−	0.753711i	$-0.271738\pi$
$467$	−2.08551	−	2.08551i	−0.0965060	−	0.0965060i	−0.753711	+	0.657205i	$0.771738\pi$
$468$		0			0
$469$		−	1.06243i		−	0.0490586i
$470$		0			0
$471$	25.7283	+	25.7283i	1.18550	+	1.18550i
$472$		0			0
$473$	47.0718	−	19.4978i	2.16436	−	0.896508i
$474$		0			0
$475$	3.82784	+	29.2277i	0.175633	+	1.34106i
$476$		0			0
$477$	−2.06318	+	0.854599i	−0.0944667	+	0.0391294i
$478$		0			0
$479$	1.23851	+	2.99002i	0.0565889	+	0.136618i	0.949645	−	0.313327i	$-0.101444\pi$
$479$	1.23851	+	2.99002i	0.0565889	+	0.136618i	−0.893056	+	0.449945i	$0.851444\pi$
$480$		0			0
$481$	−8.71220	−	21.0331i	−0.397242	−	0.959028i
$482$		0			0
$483$	2.04138			0.0928862
$484$		0			0
$485$	−1.09147	+	8.26896i	−0.0495609	+	0.375474i
$486$		0			0
$487$			2.77307i			0.125660i	0.998024	+	0.0628299i	$0.0200126\pi$
$487$			2.77307i			0.125660i	−0.998024	+	0.0628299i	$0.979987\pi$
$488$		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
$495$	−5.21529	−	6.80144i	−0.234410	−	0.305702i
$496$		0			0
$497$	−21.9629			−0.985169
$498$		0			0
$499$	16.2476	−	6.72999i	0.727344	−	0.301276i	0.0118841	−	0.999929i	$-0.496217\pi$
$499$	16.2476	−	6.72999i	0.727344	−	0.301276i	0.715460	+	0.698654i	$0.246217\pi$
$500$		0			0
$501$	13.9713	−	13.9713i	0.624191	−	0.624191i
$502$		0			0
$503$	4.44424	−	10.7293i	0.198159	−	0.478398i	−0.793298	−	0.608834i	$-0.791638\pi$
$503$	4.44424	−	10.7293i	0.198159	−	0.478398i	0.991457	+	0.130436i	$0.0416376\pi$
$504$		0			0
$505$	0.857802	−	0.657755i	0.0381717	−	0.0292697i
$506$		0			0
$507$	3.36426	+	8.12205i	0.149412	+	0.360713i
$508$		0			0
$509$	−8.20280	−	3.39771i	−0.363583	−	0.150601i	0.193410	−	0.981118i	$-0.438045\pi$
$509$	−8.20280	−	3.39771i	−0.363583	−	0.150601i	−0.556993	+	0.830517i	$0.688045\pi$
$510$		0			0
$511$	4.23221	−	10.2175i	0.187222	−	0.451994i
$512$		0			0
$513$			33.0021i			1.45708i
$514$		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	−0.934671	−	0.355515i	$-0.884305\pi$
$523$	−29.5055	−	29.5055i	−1.29019	−	1.29019i	−0.355515	−	0.934671i	$-0.615695\pi$
$524$		0			0
$525$	10.6216	+	2.85372i	0.463564	+	0.124547i
$526$		0			0
$527$	6.32804	+	15.2772i	0.275654	+	0.665487i
$528$		0			0
$529$		−	22.1387i		−	0.962553i
$530$		0			0
$531$	−4.84059	+	4.84059i	−0.210064	+	0.210064i
$532$		0			0
$533$	15.4126	+	7.74270i	0.667595	+	0.335374i
$534$		0			0
$535$	−28.2472	+	7.55862i	−1.22123	+	0.326788i
$536$		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
$545$	−27.3339	+	20.9594i	−1.17086	+	0.897803i
$546$		0			0
$547$	−28.2153	+	11.6872i	−1.20640	+	0.499707i	−0.893061	−	0.449935i	$-0.851447\pi$
$547$	−28.2153	+	11.6872i	−1.20640	+	0.499707i	−0.313338	+	0.949642i	$0.601447\pi$
$548$		0			0
$549$			0.991288i			0.0423072i
$550$		0			0
$551$	11.1713			0.475915
$552$		0			0
$553$	4.15661			0.176757
$554$		0			0
$555$	3.78505	−	28.6756i	0.160667	−	1.21721i
$556$		0			0
$557$	12.3702	+	29.8644i	0.524143	+	1.26539i	0.935309	+	0.353833i	$0.115122\pi$
$557$	12.3702	+	29.8644i	0.524143	+	1.26539i	−0.411165	+	0.911561i	$0.634878\pi$
$558$		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
$563$	22.8528	+	9.46592i	0.963129	+	0.398941i	0.808150	−	0.588977i	$-0.200469\pi$
$563$	22.8528	+	9.46592i	0.963129	+	0.398941i	0.154979	+	0.987918i	$0.450469\pi$
$564$		0			0
$565$	1.35175	+	5.05161i	0.0568685	+	0.212523i
$566$		0			0
$567$	8.75707	+	3.62730i	0.367762	+	0.152332i
$568$		0			0
$569$	29.4293	−	29.4293i	1.23374	−	1.23374i	0.271225	−	0.962516i	$-0.412571\pi$
$569$	29.4293	−	29.4293i	1.23374	−	1.23374i	0.962516	−	0.271225i	$-0.0874287\pi$
$570$		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
$577$	−7.22036	+	17.4315i	−0.300588	+	0.725683i	0.699353	+	0.714777i	$0.253472\pi$
$577$	−7.22036	+	17.4315i	−0.300588	+	0.725683i	−0.999941	+	0.0109063i	$0.996528\pi$
$578$		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
$583$		−	19.8007i		−	0.820059i
$584$		0			0
$585$	−0.518244	+	3.92622i	−0.0214268	+	0.162329i
$586$		0			0
$587$	−9.01668	+	21.7682i	−0.372158	+	0.898470i	0.621226	+	0.783632i	$0.286635\pi$
$587$	−9.01668	+	21.7682i	−0.372158	+	0.898470i	−0.993384	+	0.114838i	$0.963365\pi$
$588$		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
$593$	−0.251436	−	0.607020i	−0.0103252	−	0.0249273i	0.918633	−	0.395112i	$-0.129294\pi$
$593$	−0.251436	−	0.607020i	−0.0103252	−	0.0249273i	−0.928958	+	0.370185i	$0.879294\pi$
$594$		0			0
$595$	5.34615	−	9.25260i	0.219171	−	0.379320i
$596$		0			0
$597$	−16.6307	+	16.6307i	−0.680649	+	0.680649i
$598$		0			0
$599$	37.9198			1.54936			0.774680	−	0.632354i	$-0.217911\pi$
$599$	37.9198			1.54936			0.774680	+	0.632354i	$0.217911\pi$
$600$		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
$603$	0.449049	+	0.186002i	0.0182867	+	0.00757459i
$604$		0			0
$605$	49.6504	−	13.2858i	2.01857	−	0.540146i
$606$		0			0
$607$		−	4.70631i		−	0.191023i	−0.995428	−	0.0955117i	$-0.969551\pi$
$607$		−	4.70631i		−	0.191023i	0.995428	−	0.0955117i	$-0.0304487\pi$
$608$		0			0
$609$	1.59508	−	3.85086i	0.0646358	−	0.156045i
$610$		0			0
$611$	−36.4638			−1.47517
$612$		0			0
$613$			10.5384i			0.425644i	0.977091	+	0.212822i	$0.0682654\pi$
$613$			10.5384i			0.425644i	−0.977091	+	0.212822i	$0.931735\pi$
$614$		0			0
$615$	12.0336	+	18.3141i	0.485241	+	0.738497i
$616$		0			0
$617$		−	16.4990i		−	0.664224i	−0.943240	−	0.332112i	$-0.892239\pi$
$617$		−	16.4990i		−	0.664224i	0.943240	−	0.332112i	$-0.107761\pi$
$618$		0			0
$619$	19.9470			0.801739			0.400869	−	0.916135i	$-0.368708\pi$
$619$	19.9470			0.801739			0.400869	+	0.916135i	$0.368708\pi$
$620$		0			0
$621$	−1.98808	+	4.79965i	−0.0797790	+	0.192603i
$622$		0			0
$623$			23.3922i			0.937187i
$624$		0			0
$625$	−12.5292	+	21.6338i	−0.501168	+	0.865350i
$626$		0			0
$627$	−48.5982	−	20.1300i	−1.94082	−	0.803916i
$628$		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
$635$	−29.3578	+	7.85578i	−1.16503	+	0.311747i
$636$		0			0
$637$	−5.08666	−	12.2803i	−0.201541	−	0.486562i
$638$		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
$643$	−6.63131	+	16.0094i	−0.261513	+	0.631349i	−0.999033	−	0.0439769i	$-0.985997\pi$
$643$	−6.63131	+	16.0094i	−0.261513	+	0.631349i	0.737519	+	0.675326i	$0.235997\pi$
$644$		0			0
$645$	−18.2004	−	23.7357i	−0.716639	−	0.934594i
$646$		0			0
$647$		−	28.6753i		−	1.12734i	−0.826000	−	0.563671i	$-0.809389\pi$
$647$		−	28.6753i		−	1.12734i	0.826000	−	0.563671i	$-0.190611\pi$
$648$		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
$653$	−10.0663	+	24.3022i	−0.393925	+	0.951018i	0.595152	+	0.803614i	$0.297092\pi$
$653$	−10.0663	+	24.3022i	−0.393925	+	0.951018i	−0.989076	+	0.147405i	$0.952908\pi$
$654$		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	−0.856998	−	0.515320i	$-0.827673\pi$
$659$	−28.2022	+	11.6817i	−1.09860	+	0.455056i	−0.241603	+	0.970375i	$0.577673\pi$
$660$		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
$663$	−12.6656	−	5.24626i	−0.491891	−	0.203748i
$664$		0			0
$665$	−18.3020	+	4.89739i	−0.709721	+	0.189913i
$666$		0			0
$667$	1.62470	+	0.672974i	0.0629087	+	0.0260577i
$668$		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
$673$	−10.1479	−	24.4991i	−0.391172	−	0.944372i	−0.989685	−	0.143260i	$-0.954242\pi$
$673$	−10.1479	−	24.4991i	−0.391172	−	0.944372i	0.598513	−	0.801113i	$-0.295758\pi$
$674$		0			0
$675$	−17.0539	+	22.1940i	−0.656403	+	0.854248i
$676$		0			0
$677$	−21.2779			−0.817775			−0.408888	−	0.912585i	$-0.634083\pi$
$677$	−21.2779			−0.817775			−0.408888	+	0.912585i	$0.634083\pi$
$678$		0			0
$679$	−5.36081			−0.205729
$680$		0			0
$681$			23.6141i			0.904896i
$682$		0			0
$683$	19.8590	−	8.22586i	0.759883	−	0.314754i	0.0311160	−	0.999516i	$-0.490094\pi$
$683$	19.8590	−	8.22586i	0.759883	−	0.314754i	0.728767	+	0.684762i	$0.240094\pi$
$684$		0			0
$685$	−23.6613	−	3.12319i	−0.904052	−	0.119331i
$686$		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
$695$	18.9860	−	32.8591i	0.720180	−	1.24642i
$696$		0			0
$697$	20.2118	−	6.69492i	0.765576	−	0.253588i
$698$		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
$703$	19.0675	+	46.0331i	0.719146	+	1.73617i
$704$		0			0
$705$	−40.1128	−	23.1772i	−1.51073	−	0.872902i
$706$		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	$0.0551515\pi$
$709$	10.9281	+	26.3827i	0.410412	+	0.990821i	−0.574616	+	0.818423i	$0.694848\pi$
$710$		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
$717$			1.02304i			0.0382060i
$718$		0			0
$719$	−7.05679	+	17.0366i	−0.263174	+	0.635358i	−0.999131	−	0.0416695i	$-0.986732\pi$
$719$	−7.05679	+	17.0366i	−0.263174	+	0.635358i	0.735957	+	0.677028i	$0.236732\pi$
$720$		0			0
$721$	13.7371	+	5.69011i	0.511598	+	0.211911i
$722$		0			0
$723$	11.0947	+	26.7851i	0.412618	+	0.996148i
$724$		0			0
$725$	7.51276	+	5.77280i	0.279017	+	0.214396i
$726$		0			0
$727$	19.1883	−	46.3246i	0.711654	−	1.71809i	0.0158289	−	0.999875i	$-0.494961\pi$
$727$	19.1883	−	46.3246i	0.711654	−	1.71809i	0.695825	−	0.718211i	$-0.255039\pi$
$728$		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
$733$	−9.28292			−0.342872			−0.171436	−	0.985195i	$-0.554841\pi$
$733$	−9.28292			−0.342872			−0.171436	+	0.985195i	$0.554841\pi$
$734$		0			0
$735$	2.20992	−	16.7424i	0.0815141	−	0.617552i
$736$		0			0
$737$	−3.04733	+	3.04733i	−0.112250	+	0.112250i
$738$		0			0
$739$		−	35.4342i		−	1.30347i	−0.758447	−	0.651734i	$-0.774042\pi$
$739$		−	35.4342i		−	1.30347i	0.758447	−	0.651734i	$-0.225958\pi$
$740$		0			0
$741$	9.30139	+	22.4555i	0.341695	+	0.824925i
$742$		0			0
$743$			23.3023i			0.854879i	0.904044	+	0.427440i	$0.140584\pi$
$743$			23.3023i			0.854879i	−0.904044	+	0.427440i	$0.859416\pi$
$744$		0			0
$745$	15.8598	+	20.6833i	0.581057	+	0.757777i
$746$		0			0
$747$	−0.345153			−0.0126285
$748$		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
$753$	19.5866	−	8.11304i	0.713775	−	0.295655i
$754$		0			0
$755$	−17.5726	−	2.31951i	−0.639533	−	0.0844155i
$756$		0			0
$757$	25.4135	−	10.5266i	0.923671	−	0.382597i	0.130397	−	0.991462i	$-0.458375\pi$
$757$	25.4135	−	10.5266i	0.923671	−	0.382597i	0.793274	+	0.608865i	$0.208375\pi$
$758$		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
$765$	2.97475	+	3.87948i	0.107552	+	0.140263i
$766$		0			0
$767$	−10.7328	+	25.9113i	−0.387539	+	0.935602i
$768$		0			0
$769$	17.2515			0.622106			0.311053	−	0.950393i	$-0.399318\pi$
$769$	17.2515			0.622106			0.311053	+	0.950393i	$0.399318\pi$
$770$		0			0
$771$	1.77530	+	1.77530i	0.0639360	+	0.0639360i
$772$		0			0
$773$	28.3328	−	11.7358i	1.01906	−	0.422109i	0.190308	−	0.981724i	$-0.439051\pi$
$773$	28.3328	−	11.7358i	1.01906	−	0.422109i	0.828752	+	0.559616i	$0.189051\pi$
$774$		0			0
$775$	21.5417	−	12.4177i	0.773800	−	0.446058i
$776$		0			0
$777$	18.5905			0.666932
$778$		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
$785$	−32.3464	−	42.1841i	−1.15449	−	1.50562i
$786$		0			0
$787$	−2.33956			−0.0833964			−0.0416982	−	0.999130i	$-0.513277\pi$
$787$	−2.33956			−0.0833964			−0.0416982	+	0.999130i	$0.513277\pi$
$788$		0			0
$789$		−	43.1940i		−	1.53775i
$790$		0			0
$791$	−3.10521	+	1.28622i	−0.110408	+	0.0457327i
$792$		0			0
$793$	1.55417	+	3.75211i	0.0551904	+	0.133241i
$794$		0			0
$795$	−11.2290	+	3.00474i	−0.398252	+	0.106567i
$796$		0			0
$797$	−20.0151	−	20.0151i	−0.708971	−	0.708971i	0.257348	−	0.966319i	$-0.417151\pi$
$797$	−20.0151	−	20.0151i	−0.708971	−	0.708971i	−0.966319	+	0.257348i	$0.917151\pi$
$798$		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
$803$	−41.4454	+	17.1673i	−1.46258	+	0.605819i
$804$		0			0
$805$	−2.95678	−	0.390281i	−0.104213	−	0.0137556i
$806$		0			0
$807$	19.7146	+	8.16607i	0.693988	+	0.287459i
$808$		0			0
$809$	5.52468	−	2.28840i	0.194237	−	0.0804558i	−0.283444	−	0.958989i	$-0.591477\pi$
$809$	5.52468	−	2.28840i	0.194237	−	0.0804558i	0.477682	+	0.878533i	$0.341477\pi$
$810$		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
$813$	6.21994	−	15.0163i	0.218143	−	0.526643i
$814$		0			0
$815$	−12.5262	−	46.8117i	−0.438775	−	1.63974i
$816$		0			0
$817$	47.6026	+	19.7176i	1.66540	+	0.689833i
$818$		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
$823$	−25.4567	−	10.5445i	−0.887364	−	0.367558i	−0.108016	−	0.994149i	$-0.534450\pi$
$823$	−25.4567	−	10.5445i	−0.887364	−	0.367558i	−0.779348	+	0.626591i	$0.784450\pi$
$824$		0			0
$825$	−22.2802	−	38.6507i	−0.775698	−	1.34564i
$826$		0			0
$827$	−13.8647	+	33.4723i	−0.482123	+	1.16395i	0.476476	+	0.879187i	$0.341914\pi$
$827$	−13.8647	+	33.4723i	−0.482123	+	1.16395i	−0.958599	+	0.284760i	$0.908086\pi$
$828$		0			0
$829$	16.2629	+	16.2629i	0.564834	+	0.564834i	0.930677	−	0.365842i	$-0.119219\pi$
$829$	16.2629	+	16.2629i	0.564834	+	0.564834i	−0.365842	+	0.930677i	$0.619219\pi$
$830$		0			0
$831$	−3.79105	+	1.57031i	−0.131510	+	0.0544733i
$832$		0			0
$833$	−15.1592	−	6.27916i	−0.525236	−	0.217560i
$834$		0			0
$835$	−22.9074	+	17.5652i	−0.792742	+	0.607868i
$836$		0			0
$837$	25.7187	−	10.6530i	0.888969	−	0.368223i
$838$		0			0
$839$	−44.0247	−	18.2356i	−1.51990	−	0.629564i	−0.542331	−	0.840165i	$-0.682458\pi$
$839$	−44.0247	−	18.2356i	−1.51990	−	0.629564i	−0.977572	+	0.210601i	$0.932458\pi$
$840$		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
$847$	12.6418	+	30.5199i	0.434376	+	1.04868i
$848$		0			0
$849$	−16.3667	+	6.77932i	−0.561704	+	0.232666i
$850$		0			0
$851$			7.84348i			0.268871i
$852$		0			0
$853$	−13.8733			−0.475014			−0.237507	−	0.971386i	$-0.576330\pi$
$853$	−13.8733			−0.475014			−0.237507	+	0.971386i	$0.576330\pi$
$854$		0			0
$855$	1.13423	−	8.59293i	0.0387898	−	0.293872i
$856$		0			0
$857$	−21.4899	−	21.4899i	−0.734080	−	0.734080i	0.237346	−	0.971425i	$-0.423723\pi$
$857$	−21.4899	−	21.4899i	−0.734080	−	0.734080i	−0.971425	+	0.237346i	$0.923723\pi$
$858$		0			0
$859$	−1.68959	−	1.68959i	−0.0576479	−	0.0576479i	0.677695	−	0.735343i	$-0.262979\pi$
$859$	−1.68959	−	1.68959i	−0.0576479	−	0.0576479i	−0.735343	+	0.677695i	$0.762979\pi$
$860$		0			0
$861$	−10.6577	+	9.20819i	−0.363213	+	0.313814i
$862$		0			0
$863$	0.485392			0.0165229			0.00826147	−	0.999966i	$-0.497370\pi$
$863$	0.485392			0.0165229			0.00826147	+	0.999966i	$0.497370\pi$
$864$		0			0
$865$	14.4300	−	24.9741i	0.490636	−	0.849145i
$866$		0			0
$867$	8.40348	−	3.48084i	0.285397	−	0.118215i
$868$		0			0
$869$	−11.9222	−	11.9222i	−0.404434	−	0.404434i
$870$		0			0
$871$	1.99131			0.0674729
$872$		0			0
$873$	0.938526	−	2.26580i	0.0317643	−	0.0766858i
$874$		0			0
$875$	−14.8389	−	6.16407i	−0.501646	−	0.208384i
$876$		0			0
$877$	−27.6825	−	27.6825i	−0.934770	−	0.934770i	0.0632291	−	0.997999i	$-0.479860\pi$
$877$	−27.6825	−	27.6825i	−0.934770	−	0.934770i	−0.997999	+	0.0632291i	$0.979860\pi$
$878$		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
$883$	−44.1642	+	18.2934i	−1.48625	+	0.615623i	−0.970496	−	0.241117i	$-0.922486\pi$
$883$	−44.1642	+	18.2934i	−1.48625	+	0.615623i	−0.515749	+	0.856740i	$0.672486\pi$
$884$		0			0
$885$	−28.2766	+	21.6823i	−0.950508	+	0.728841i
$886$		0			0
$887$	31.0997	−	12.8819i	1.04423	−	0.432533i	0.206399	−	0.978468i	$-0.433825\pi$
$887$	31.0997	−	12.8819i	1.04423	−	0.432533i	0.837828	+	0.545935i	$0.183825\pi$
$888$		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
$893$	79.8046			2.67056
$894$		0			0
$895$	−22.3715	+	17.1542i	−0.747795	+	0.573403i
$896$		0			0
$897$			3.82615i			0.127751i
$898$		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
$905$	11.8430	−	9.08110i	0.393674	−	0.301866i
$906$		0			0
$907$	−24.6015			−0.816880			−0.408440	−	0.912785i	$-0.633927\pi$
$907$	−24.6015			−0.816880			−0.408440	+	0.912785i	$0.633927\pi$
$908$		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
$913$	1.17114	−	2.82738i	0.0387590	−	0.0935726i
$914$		0			0
$915$	−0.675218	+	5.11546i	−0.0223220	+	0.169112i
$916$		0			0
$917$	−8.62582	−	20.8246i	−0.284850	−	0.687688i
$918$		0			0
$919$	11.1991	+	4.63883i	0.369425	+	0.153021i	0.559669	−	0.828716i	$-0.310928\pi$
$919$	11.1991	+	4.63883i	0.369425	+	0.153021i	−0.190245	+	0.981737i	$0.560928\pi$
$920$		0			0
$921$	−11.7557	+	28.3807i	−0.387362	+	0.935175i
$922$		0			0
$923$		−	41.1648i		−	1.35496i
$924$		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	$0.282313\pi$
$929$	−11.0654	+	26.7142i	−0.363043	+	0.876463i	−0.994852	+	0.101339i	$0.967687\pi$
$930$		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
$935$	−41.8730	+	11.2047i	−1.36939	+	0.366433i
$936$		0			0
$937$	5.73053	+	13.8347i	0.187208	+	0.451960i	0.989420	−	0.145079i	$-0.0463436\pi$
$937$	5.73053	+	13.8347i	0.187208	+	0.451960i	−0.802212	+	0.597039i	$0.796344\pi$
$938$		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
$943$	−3.88500	−	4.49656i	−0.126513	−	0.146428i
$944$		0			0
$945$	−15.5765	−	9.00007i	−0.506702	−	0.292772i
$946$		0			0
$947$	−1.08203	+	1.08203i	−0.0351612	+	0.0351612i	−0.724469	−	0.689308i	$-0.757915\pi$
$947$	−1.08203	+	1.08203i	−0.0351612	+	0.0351612i	0.689308	+	0.724469i	$0.257915\pi$
$948$		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	−0.946183	−	0.323633i	$-0.895096\pi$
$953$	−19.2185	+	19.2185i	−0.622550	+	0.622550i	0.323633	+	0.946183i	$0.395096\pi$
$954$		0			0
$955$	8.75701	+	11.4203i	0.283370	+	0.369553i
$956$		0			0
$957$	−15.6204	+	6.47016i	−0.504934	+	0.209151i
$958$		0			0
$959$		−	15.3397i		−	0.495346i
$960$		0			0
$961$	6.27021			0.202265
$962$		0			0
$963$	8.59802			0.277067
$964$		0			0
$965$	−4.00601	−	5.22438i	−0.128958	−	0.168179i
$966$		0			0
$967$	−21.9110	−	52.8978i	−0.704610	−	1.70108i	−0.713049	−	0.701114i	$-0.752686\pi$
$967$	−21.9110	−	52.8978i	−0.704610	−	1.70108i	0.00843938	−	0.999964i	$-0.497314\pi$
$968$		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
$973$	22.5348	+	9.33422i	0.722432	+	0.299241i
$974$		0			0
$975$	−5.34871	+	19.9079i	−0.171296	+	0.637564i
$976$		0			0
$977$	54.7532	+	22.6795i	1.75171	+	0.725582i	0.997631	+	0.0687971i	$0.0219161\pi$
$977$	54.7532	+	22.6795i	1.75171	+	0.725582i	0.754078	+	0.656785i	$0.228084\pi$
$978$		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	$-0.184576\pi$
$983$	9.04938	+	9.04938i	0.288630	+	0.288630i	−0.547908	+	0.836539i	$0.684576\pi$
$984$		0			0
$985$	0.628088	−	1.08703i	0.0200126	−	0.0346358i
$986$		0			0
$987$	11.3948	−	27.5094i	0.362699	−	0.875633i
$988$		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
$993$		−	7.63701i		−	0.242353i
$994$		0			0
$995$	27.2677	−	20.9087i	0.864445	−	0.662849i
$996$		0			0
$997$	−6.96020	+	16.8034i	−0.220432	+	0.532170i	−0.994949	−	0.100384i	$-0.967993\pi$
$997$	−6.96020	+	16.8034i	−0.220432	+	0.532170i	0.774517	+	0.632553i	$0.217993\pi$
$998$		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.y.a.137.7	yes	84
5.3	odd	4		820.2.x.a.793.15	yes	84
41.3	odd	8		820.2.x.a.577.15	✓	84
205.3	even	8	inner	820.2.y.a.413.7	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.15	✓	84	41.3	odd	8
820.2.x.a.793.15	yes	84	5.3	odd	4
820.2.y.a.137.7	yes	84	1.1	even	1	trivial
820.2.y.a.413.7	yes	84	205.3	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41402 - 0.585707i) q^{3} +(1.93611 + 1.11869i) q^{5} +(-0.549988 + 1.32779i) q^{7} +(-0.464917 - 0.464917i) q^{9} +(5.38595 - 2.23093i) q^{11} +(-2.48866 - 1.03084i) q^{13} +(-2.08248 - 2.71584i) q^{15} +(-3.07210 + 1.27250i) q^{17} +(5.44669 + 2.25609i) q^{19} +(1.55539 - 1.55539i) q^{21} +(0.656229 + 0.656229i) q^{23} +(2.49708 + 4.33181i) q^{25} +(2.14222 + 5.17177i) q^{27} +(1.75067 - 0.725150i) q^{29} -4.97291i q^{31} -8.92252 q^{33} +(-2.55022 + 1.95549i) q^{35} +(5.97617 + 5.97617i) q^{37} +(2.91525 + 2.91525i) q^{39} +(-6.38615 - 0.465961i) q^{41} +8.73974 q^{43} +(-0.380036 - 1.42023i) q^{45} +(12.5062 - 5.18025i) q^{47} +(3.48921 + 3.48921i) q^{49} +5.08932 q^{51} +(1.29979 - 3.13796i) q^{53} +(12.9235 + 1.70585i) q^{55} +(-6.38032 - 6.38032i) q^{57} -10.4117i q^{59} +(-1.06609 - 1.06609i) q^{61} +(0.873010 - 0.361612i) q^{63} +(-3.66515 - 4.77985i) q^{65} +(-0.682973 + 0.282897i) q^{67} +(-0.543564 - 1.31228i) q^{69} +(5.84810 + 14.1186i) q^{71} -7.69510 q^{73} +(-0.993751 - 7.58783i) q^{75} +8.37839i q^{77} +(-1.10679 - 2.67203i) q^{79} -6.59523i q^{81} +(0.371199 - 0.371199i) q^{83} +(-7.37146 - 0.973000i) q^{85} -2.90020 q^{87} +(15.0374 - 6.22868i) q^{89} +(2.73747 - 2.73747i) q^{91} +(-2.91266 + 7.03179i) q^{93} +(8.02155 + 10.4612i) q^{95} +(1.42744 + 3.44613i) q^{97} +(-3.54122 - 1.46682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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