LMFDB - Embedded newform 483.2.bc.a.389.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(11,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([33, 44, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bc (of order $66$, degree $20$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			389.19
Character	$\chi$	$=$	483.389
Dual form			483.2.bc.a.149.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15201 - 0.0548771i) q^{2} +(1.67535 - 0.439554i) q^{3} +(-0.666821 - 0.0636737i) q^{4} +(0.0676965 + 0.279049i) q^{5} +(-1.95414 + 0.414434i) q^{6} +(-0.735966 + 2.54133i) q^{7} +(3.04785 + 0.438215i) q^{8} +(2.61358 - 1.47281i) q^{9} +(-0.0626739 - 0.325183i) q^{10} +(-0.210893 - 4.42719i) q^{11} +(-1.14515 + 0.186429i) q^{12} +(0.275755 + 0.318239i) q^{13} +(0.987304 - 2.88726i) q^{14} +(0.236072 + 0.437748i) q^{15} +(-2.17162 - 0.418546i) q^{16} +(2.71335 + 3.81037i) q^{17} +(-3.09171 + 1.55327i) q^{18} +(4.93743 + 3.51593i) q^{19} +(-0.0273734 - 0.190386i) q^{20} +(-0.115947 + 4.58111i) q^{21} +5.11176i q^{22} +(-4.78550 + 0.314622i) q^{23} +(5.29883 - 0.605534i) q^{24} +(4.37089 - 2.25335i) q^{25} +(-0.300210 - 0.381748i) q^{26} +(3.73128 - 3.61629i) q^{27} +(0.652574 - 1.64775i) q^{28} +(4.08752 + 1.86671i) q^{29} +(-0.247936 - 0.517246i) q^{30} +(5.10794 + 4.01693i) q^{31} +(-3.50603 - 0.850553i) q^{32} +(-2.29931 - 7.32439i) q^{33} +(-2.91672 - 4.53850i) q^{34} +(-0.758977 - 0.0333314i) q^{35} +(-1.83657 + 0.815687i) q^{36} +(7.31103 - 7.66759i) q^{37} +(-5.49504 - 4.32135i) q^{38} +(0.601869 + 0.411951i) q^{39} +(0.0840456 + 0.880165i) q^{40} +(-0.411214 + 1.40047i) q^{41} +(0.384971 - 5.27113i) q^{42} +(-8.01887 + 1.15294i) q^{43} +(-0.141268 + 2.96557i) q^{44} +(0.587917 + 0.629613i) q^{45} +(5.53022 - 0.0998337i) q^{46} +(5.95056 - 3.43556i) q^{47} +(-3.82219 + 0.253336i) q^{48} +(-5.91671 - 3.74066i) q^{49} +(-5.15898 + 2.35603i) q^{50} +(6.22068 + 5.19103i) q^{51} +(-0.163616 - 0.229767i) q^{52} +(0.168270 + 0.486183i) q^{53} +(-4.49694 + 3.96125i) q^{54} +(1.22113 - 0.358555i) q^{55} +(-3.35677 + 7.42309i) q^{56} +(9.81735 + 3.72013i) q^{57} +(-4.60644 - 2.37478i) q^{58} +(-0.436125 - 2.26283i) q^{59} +(-0.129545 - 0.306931i) q^{60} +(2.50729 + 6.26290i) q^{61} +(-5.66398 - 4.90787i) q^{62} +(1.81939 + 7.72592i) q^{63} +(8.23632 + 2.41840i) q^{64} +(-0.0701364 + 0.0984928i) q^{65} +(2.24690 + 8.56398i) q^{66} +(-6.12757 - 11.8858i) q^{67} +(-1.56670 - 2.71361i) q^{68} +(-7.87909 + 2.63059i) q^{69} +(0.872522 + 0.0800487i) q^{70} +(-1.29888 + 2.02110i) q^{71} +(8.61123 - 3.34361i) q^{72} +(-3.00356 - 0.286805i) q^{73} +(-8.84318 + 8.43196i) q^{74} +(6.33230 - 5.69639i) q^{75} +(-3.06851 - 2.65888i) q^{76} +(11.4062 + 2.72232i) q^{77} +(-0.670755 - 0.507602i) q^{78} +(15.4573 + 5.34982i) q^{79} +(-0.0302165 - 0.634322i) q^{80} +(4.66164 - 7.69864i) q^{81} +(0.550578 - 1.59079i) q^{82} +(-14.6256 + 4.29447i) q^{83} +(0.369012 - 3.04740i) q^{84} +(-0.879595 + 1.01511i) q^{85} +(9.30111 - 0.888148i) q^{86} +(7.66854 + 1.33070i) q^{87} +(1.29729 - 13.5859i) q^{88} +(-7.38291 + 5.80598i) q^{89} +(-0.642737 - 0.757586i) q^{90} +(-1.01170 + 0.466572i) q^{91} +(3.21111 + 0.0949141i) q^{92} +(10.3232 + 4.48454i) q^{93} +(-7.04365 + 3.63126i) q^{94} +(-0.646869 + 1.61580i) q^{95} +(-6.24768 + 0.116117i) q^{96} +(-1.66982 + 5.68689i) q^{97} +(6.61085 + 4.63399i) q^{98} +(-7.07162 - 11.2602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) $ 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−1.15201	−	0.0548771i	−0.814596	−	0.0388040i	−0.363852	−	0.931457i	$-0.618538\pi$
$2$	−1.15201	−	0.0548771i	−0.814596	−	0.0388040i	−0.450745	+	0.892653i	$0.648842\pi$
$3$	1.67535	−	0.439554i	0.967263	−	0.253777i
$3$	1.67535	−	0.439554i	0.967263	−	0.253777i
$4$	−0.666821	−	0.0636737i	−0.333411	−	0.0318368i
$5$	0.0676965	+	0.279049i	0.0302748	+	0.124794i	0.984944	−	0.172875i	$-0.0553058\pi$
$5$	0.0676965	+	0.279049i	0.0302748	+	0.124794i	−0.954669	+	0.297670i	$0.903791\pi$
$6$	−1.95414	+	0.414434i	−0.797776	+	0.169192i
$7$	−0.735966	+	2.54133i	−0.278169	+	0.960532i
$7$	−0.735966	+	2.54133i	−0.278169	+	0.960532i
$8$	3.04785	+	0.438215i	1.07758	+	0.154932i
$9$	2.61358	−	1.47281i	0.871195	−	0.490938i
$10$	−0.0626739	−	0.325183i	−0.0198192	−	0.102832i
$11$	−0.210893	−	4.42719i	−0.0635867	−	1.33485i	−0.774949	−	0.632024i	$-0.782225\pi$
$11$	−0.210893	−	4.42719i	−0.0635867	−	1.33485i	0.711362	−	0.702825i	$-0.248079\pi$
$12$	−1.14515	+	0.186429i	−0.330575	+	0.0538173i
$13$	0.275755	+	0.318239i	0.0764808	+	0.0882635i	0.792700	−	0.609612i	$-0.208675\pi$
$13$	0.275755	+	0.318239i	0.0764808	+	0.0882635i	−0.716220	+	0.697875i	$0.754129\pi$
$14$	0.987304	−	2.88726i	0.263868	−	0.771652i
$15$	0.236072	+	0.437748i	0.0609536	+	0.113026i
$16$	−2.17162	−	0.418546i	−0.542905	−	0.104636i
$17$	2.71335	+	3.81037i	0.658085	+	0.924151i	0.999878	−	0.0156242i	$-0.00497354\pi$
$17$	2.71335	+	3.81037i	0.658085	+	0.924151i	−0.341793	+	0.939775i	$0.611034\pi$
$18$	−3.09171	+	1.55327i	−0.728722	+	0.366110i
$19$	4.93743	+	3.51593i	1.13272	+	0.806609i	0.983269	−	0.182159i	$-0.0583087\pi$
$19$	4.93743	+	3.51593i	1.13272	+	0.806609i	0.149455	+	0.988769i	$0.452248\pi$
$20$	−0.0273734	−	0.190386i	−0.00612088	−	0.0425716i
$21$	−0.115947	+	4.58111i	−0.0253018	+	0.999680i
$22$			5.11176i			1.08983i
$23$	−4.78550	+	0.314622i	−0.997846	+	0.0656031i
$23$	−4.78550	+	0.314622i	−0.997846	+	0.0656031i
$24$	5.29883	−	0.605534i	1.08162	−	0.123604i
$25$	4.37089	−	2.25335i	0.874178	−	0.450670i
$26$	−0.300210	−	0.381748i	−0.0588760	−	0.0748669i
$27$	3.73128	−	3.61629i	0.718085	−	0.695955i
$28$	0.652574	−	1.64775i	0.123325	−	0.311396i
$29$	4.08752	+	1.86671i	0.759034	+	0.346639i	0.757048	−	0.653359i	$-0.226641\pi$
$29$	4.08752	+	1.86671i	0.759034	+	0.346639i	0.00198556	+	0.999998i	$0.499368\pi$
$30$	−0.247936	−	0.517246i	−0.0452667	−	0.0944358i
$31$	5.10794	+	4.01693i	0.917414	+	0.721462i	0.960697	−	0.277601i	$-0.0895392\pi$
$31$	5.10794	+	4.01693i	0.917414	+	0.721462i	−0.0432829	+	0.999063i	$0.513782\pi$
$32$	−3.50603	−	0.850553i	−0.619784	−	0.150358i
$33$	−2.29931	−	7.32439i	−0.400259	−	1.27501i
$34$	−2.91672	−	4.53850i	−0.500213	−	0.778346i
$35$	−0.758977	−	0.0333314i	−0.128291	−	0.00563403i
$36$	−1.83657	+	0.815687i	−0.306095	+	0.135948i
$37$	7.31103	−	7.66759i	1.20193	−	1.26054i	0.245227	−	0.969466i	$-0.421137\pi$
$37$	7.31103	−	7.66759i	1.20193	−	1.26054i	0.956699	−	0.291078i	$-0.0940140\pi$
$38$	−5.49504	−	4.32135i	−0.891413	−	0.701015i
$39$	0.601869	+	0.411951i	0.0963762	+	0.0659650i
$40$	0.0840456	+	0.880165i	0.0132888	+	0.139166i
$41$	−0.411214	+	1.40047i	−0.0642209	+	0.218716i	−0.985351	−	0.170539i	$-0.945449\pi$
$41$	−0.411214	+	1.40047i	−0.0642209	+	0.218716i	0.921130	+	0.389255i	$0.127267\pi$
$42$	0.384971	−	5.27113i	0.0594023	−	0.813354i
$43$	−8.01887	+	1.15294i	−1.22287	+	0.175822i	−0.723349	−	0.690483i	$-0.757398\pi$
$43$	−8.01887	+	1.15294i	−1.22287	+	0.175822i	−0.499517	+	0.866304i	$0.666489\pi$
$44$	−0.141268	+	2.96557i	−0.0212969	+	0.447077i
$45$	0.587917	+	0.629613i	0.0876415	+	0.0938572i
$46$	5.53022	−	0.0998337i	0.815387	−	0.0147197i
$47$	5.95056	−	3.43556i	0.867978	−	0.501127i	0.00130232	−	0.999999i	$-0.499585\pi$
$47$	5.95056	−	3.43556i	0.867978	−	0.501127i	0.866676	+	0.498872i	$0.166252\pi$
$48$	−3.82219	+	0.253336i	−0.551686	+	0.0365659i
$49$	−5.91671	−	3.74066i	−0.845244	−	0.534381i
$50$	−5.15898	+	2.35603i	−0.729590	+	0.333193i
$51$	6.22068	+	5.19103i	0.871069	+	0.726890i
$52$	−0.163616	−	0.229767i	−0.0226895	−	0.0318629i
$53$	0.168270	+	0.486183i	0.0231136	+	0.0667824i	0.955968	−	0.293473i	$-0.0948109\pi$
$53$	0.168270	+	0.486183i	0.0231136	+	0.0667824i	−0.932854	+	0.360255i	$0.882690\pi$
$54$	−4.49694	+	3.96125i	−0.611956	+	0.539058i
$55$	1.22113	−	0.358555i	0.164657	−	0.0483476i
$56$	−3.35677	+	7.42309i	−0.448567	+	0.991952i
$57$	9.81735	+	3.72013i	1.30034	+	0.492744i
$58$	−4.60644	−	2.37478i	−0.604855	−	0.311825i
$59$	−0.436125	−	2.26283i	−0.0567786	−	0.294596i	0.942429	−	0.334408i	$-0.108536\pi$
$59$	−0.436125	−	2.26283i	−0.0567786	−	0.294596i	−0.999207	+	0.0398120i	$0.987324\pi$
$60$	−0.129545	−	0.306931i	−0.0167242	−	0.0396246i
$61$	2.50729	+	6.26290i	0.321025	+	0.801882i	0.997838	+	0.0657267i	$0.0209366\pi$
$61$	2.50729	+	6.26290i	0.321025	+	0.801882i	−0.676812	+	0.736155i	$0.736639\pi$
$62$	−5.66398	−	4.90787i	−0.719326	−	0.623300i
$63$	1.81939	+	7.72592i	0.229222	+	0.973374i
$64$	8.23632	+	2.41840i	1.02954	+	0.302300i
$65$	−0.0701364	+	0.0984928i	−0.00869935	+	0.0122165i
$66$	2.24690	+	8.56398i	0.276574	+	1.05415i
$67$	−6.12757	−	11.8858i	−0.748601	−	1.45208i	−0.887030	−	0.461712i	$-0.847236\pi$
$67$	−6.12757	−	11.8858i	−0.748601	−	1.45208i	0.138429	−	0.990372i	$-0.455795\pi$
$68$	−1.56670	−	2.71361i	−0.189990	−	0.329073i
$69$	−7.87909	+	2.63059i	−0.948531	+	0.316686i
$70$	0.872522	+	0.0800487i	0.104286	+	0.00956765i
$71$	−1.29888	+	2.02110i	−0.154149	+	0.239861i	−0.909735	−	0.415188i	$-0.863716\pi$
$71$	−1.29888	+	2.02110i	−0.154149	+	0.239861i	0.755586	+	0.655049i	$0.227352\pi$
$72$	8.61123	−	3.34361i	1.01484	−	0.394048i
$73$	−3.00356	−	0.286805i	−0.351540	−	0.0335680i	−0.0822077	−	0.996615i	$-0.526197\pi$
$73$	−3.00356	−	0.286805i	−0.351540	−	0.0335680i	−0.269333	+	0.963047i	$0.586803\pi$
$74$	−8.84318	+	8.43196i	−1.02800	+	0.980195i
$75$	6.33230	−	5.69639i	0.731191	−	0.657763i
$76$	−3.06851	−	2.65888i	−0.351982	−	0.304994i
$77$	11.4062	+	2.72232i	1.29985	+	0.310237i
$78$	−0.670755	−	0.507602i	−0.0759480	−	0.0574746i
$79$	15.4573	+	5.34982i	1.73908	+	0.601902i	0.997611	−	0.0690845i	$-0.0220078\pi$
$79$	15.4573	+	5.34982i	1.73908	+	0.601902i	0.741470	+	0.670986i	$0.234129\pi$
$80$	−0.0302165	−	0.634322i	−0.00337831	−	0.0709194i
$81$	4.66164	−	7.69864i	0.517960	−	0.855405i
$82$	0.550578	−	1.59079i	0.0608012	−	0.175673i
$83$	−14.6256	+	4.29447i	−1.60537	+	0.471379i	−0.957034	−	0.289976i	$-0.906353\pi$
$83$	−14.6256	+	4.29447i	−1.60537	+	0.471379i	−0.648335	+	0.761355i	$0.724535\pi$
$84$	0.369012	−	3.04740i	0.0402625	−	0.332498i
$85$	−0.879595	+	1.01511i	−0.0954055	+	0.110104i
$86$	9.30111	−	0.888148i	1.00296	−	0.0957715i
$87$	7.66854	+	1.33070i	0.822154	+	0.142666i
$88$	1.29729	−	13.5859i	0.138292	−	1.44826i
$89$	−7.38291	+	5.80598i	−0.782587	+	0.615433i	−0.927419	−	0.374023i	$-0.877978\pi$
$89$	−7.38291	+	5.80598i	−0.782587	+	0.615433i	0.144833	+	0.989456i	$0.453736\pi$
$90$	−0.642737	−	0.757586i	−0.0677504	−	0.0798565i
$91$	−1.01170	+	0.466572i	−0.106055	+	0.0489101i
$92$	3.21111	+	0.0949141i	0.334781	+	0.00989548i
$93$	10.3232	+	4.48454i	1.07047	+	0.465025i
$94$	−7.04365	+	3.63126i	−0.726498	+	0.374536i
$95$	−0.646869	+	1.61580i	−0.0663673	+	0.165778i
$96$	−6.24768	+	0.116117i	−0.637651	+	0.0118512i
$97$	−1.66982	+	5.68689i	−0.169545	+	0.577416i	0.830255	+	0.557384i	$0.188195\pi$
$97$	−1.66982	+	5.68689i	−0.169545	+	0.577416i	−0.999799	+	0.0200318i	$0.993623\pi$
$98$	6.61085	+	4.63399i	0.667796	+	0.468103i
$99$	−7.07162	−	11.2602i	−0.710724	−	1.13170i
$100$	−3.05808	+	1.22427i	−0.305808	+	0.122427i
$101$	−10.0855	−	2.44671i	−1.00354	−	0.243457i	−0.299870	−	0.953980i	$-0.596943\pi$
$101$	−10.0855	−	2.44671i	−1.00354	−	0.243457i	−0.703674	+	0.710523i	$0.748458\pi$
$102$	−6.88143	−	6.32151i	−0.681364	−	0.625923i
$103$	−3.63296	+	7.04696i	−0.357966	+	0.694357i	−0.997210	−	0.0746467i	$-0.976217\pi$
$103$	−3.63296	+	7.04696i	−0.357966	+	0.694357i	0.639244	+	0.769004i	$0.279247\pi$
$104$	0.701005	+	1.09078i	0.0687392	+	0.106960i
$105$	−1.28620	+	0.277770i	−0.125520	+	0.0271076i
$106$	−0.167168	−	0.569323i	−0.0162368	−	0.0552976i
$107$	−6.48752	+	2.59721i	−0.627172	+	0.251082i	−0.663404	−	0.748262i	$-0.730889\pi$
$107$	−6.48752	+	2.59721i	−0.627172	+	0.251082i	0.0362318	+	0.999343i	$0.488465\pi$
$108$	−2.71836	+	2.17383i	−0.261574	+	0.209177i
$109$	−5.11467	+	3.64214i	−0.489896	+	0.348854i	−0.798158	−	0.602448i	$-0.794192\pi$
$109$	−5.11467	+	3.64214i	−0.489896	+	0.348854i	0.308262	+	0.951302i	$0.400253\pi$
$110$	−1.42643	+	0.346048i	−0.136005	+	0.0329944i
$111$	8.87820	−	16.0595i	0.842682	−	1.52430i
$112$	2.66190	−	5.21077i	0.251526	−	0.492371i
$113$	−11.8467	−	7.61341i	−1.11444	−	0.716210i	−0.152187	−	0.988352i	$-0.548632\pi$
$113$	−11.8467	−	7.61341i	−1.11444	−	0.716210i	−0.962257	+	0.272142i	$0.912268\pi$
$114$	−11.1056	−	4.82439i	−1.04013	−	0.451846i
$115$	−0.411756	−	1.31409i	−0.0383965	−	0.122539i
$116$	−2.60679	−	1.50503i	−0.242034	−	0.139738i
$117$	1.18942	+	0.425607i	0.109962	+	0.0393474i
$118$	0.378244	+	2.63074i	0.0348202	+	0.242180i
$119$	−11.6803	+	4.09122i	−1.07074	+	0.375042i
$120$	0.527686	+	1.43764i	0.0481709	+	0.131238i
$121$	−8.60538	+	0.821714i	−0.782307	+	0.0747013i
$122$	−2.54474	−	7.35254i	−0.230390	−	0.665667i
$123$	−0.0733456	+	2.52702i	−0.00661335	+	0.227854i
$124$	−3.15031	−	3.00382i	−0.282906	−	0.269751i
$125$	1.86488	+	2.15219i	0.166800	+	0.192498i
$126$	−1.67199	−	9.00020i	−0.148953	−	0.801802i
$127$	−5.53279	+	3.55571i	−0.490955	+	0.315518i	−0.762589	−	0.646883i	$-0.776072\pi$
$127$	−5.53279	+	3.55571i	−0.490955	+	0.315518i	0.271634	+	0.962401i	$0.412436\pi$
$128$	−2.53703	−	0.878074i	−0.224244	−	0.0776115i
$129$	−12.9276	+	5.45630i	−1.13821	+	0.480401i
$130$	0.0862031	−	0.109616i	0.00756051	−	0.00961397i
$131$	3.39910	−	17.6362i	0.296981	−	1.54088i	−0.460283	−	0.887772i	$-0.652252\pi$
$131$	3.39910	−	17.6362i	0.296981	−	1.54088i	0.757263	−	0.653110i	$-0.226536\pi$
$132$	1.06686	+	5.03047i	0.0928581	+	0.437846i
$133$	−12.5689	+	9.96003i	−1.08986	+	0.863644i
$134$	6.40678	+	14.0289i	0.553461	+	1.21191i
$135$	1.26172	+	0.796399i	0.108591	+	0.0685432i
$136$	6.60014	+	12.8025i	0.565957	+	1.09780i
$137$	−5.61743	+	9.72967i	−0.479929	+	0.831261i	−0.999735	−	0.0230229i	$-0.992671\pi$
$137$	−5.61743	+	9.72967i	−0.479929	+	0.831261i	0.519806	+	0.854284i	$0.326004\pi$
$138$	9.22117	−	2.59809i	0.784958	−	0.221164i
$139$	−13.1963			−1.11930			−0.559648	−	0.828730i	$-0.689064\pi$
$139$	−13.1963			−1.11930			−0.559648	+	0.828730i	$0.689064\pi$
$140$	0.503980	+	0.0705530i	0.0425941	+	0.00596281i
$141$	8.45914	−	8.37135i	0.712388	−	0.704995i
$142$	1.60724	−	2.25706i	0.134877	−	0.189408i
$143$	1.35075	−	1.28794i	0.112955	−	0.107703i
$144$	−6.29215	+	2.10449i	−0.524346	+	0.175374i
$145$	−0.244192	+	1.26699i	−0.0202790	+	0.105218i
$146$	3.44440	+	0.495231i	0.285061	+	0.0409856i
$147$	−11.5568	−	3.66620i	−0.953186	−	0.302383i
$148$	−5.36337	+	4.64739i	−0.440867	+	0.382013i
$149$	6.57743	+	3.39090i	0.538844	+	0.277793i	0.706090	−	0.708122i	$-0.250457\pi$
$149$	6.57743	+	3.39090i	0.538844	+	0.277793i	−0.167246	+	0.985915i	$0.553488\pi$
$150$	−7.60749	+	6.21482i	−0.621149	+	0.507438i
$151$	−12.6254	+	2.43334i	−1.02744	+	0.198023i	−0.675004	−	0.737814i	$-0.735858\pi$
$151$	−12.6254	+	2.43334i	−1.02744	+	0.198023i	−0.352435	+	0.935836i	$0.614646\pi$
$152$	13.5078	+	12.8797i	1.09563	+	1.04468i
$153$	12.7035	+	5.96246i	1.02702	+	0.482037i
$154$	−12.9907	−	3.76208i	−1.04682	−	0.303157i
$155$	−0.775130	+	1.69730i	−0.0622599	+	0.136330i
$156$	−0.375109	−	0.313021i	−0.0300327	−	0.0250617i
$157$	1.52375	−	15.9575i	0.121609	−	1.27355i	−0.704365	−	0.709838i	$-0.748768\pi$
$157$	1.52375	−	15.9575i	0.121609	−	1.27355i	0.825974	−	0.563708i	$-0.190626\pi$
$158$	−17.5134	−	7.01131i	−1.39329	−	0.557790i
$159$	0.495614	+	0.740562i	0.0393047	+	0.0587304i
$160$		−	1.03593i		−	0.0818976i
$161$	2.72241	−	12.3931i	0.214556	−	0.976712i
$162$	−5.79275	+	8.61312i	−0.455121	+	0.676711i
$163$	0.419884	−	8.81446i	0.0328879	−	0.690401i	−0.920878	−	0.389851i	$-0.872527\pi$
$163$	0.419884	−	8.81446i	0.0328879	−	0.690401i	0.953766	−	0.300551i	$-0.0971704\pi$
$164$	0.363379	−	0.907678i	0.0283752	−	0.0708777i
$165$	1.88821	−	1.13746i	0.146997	−	0.0885508i
$166$	17.0846	−	4.14467i	1.32602	−	0.321689i
$167$	3.55709	+	1.62447i	0.275256	+	0.125705i	0.548261	−	0.836308i	$-0.315290\pi$
$167$	3.55709	+	1.62447i	0.275256	+	0.125705i	−0.273005	+	0.962013i	$0.588017\pi$
$168$	−2.36090	+	13.9117i	−0.182148	+	1.07331i
$169$	1.82486	−	12.6922i	0.140374	−	0.976321i
$170$	1.06901	−	1.12115i	0.0819894	−	0.0859880i
$171$	18.0827	+	1.91726i	1.38282	+	0.146616i
$172$	5.42056	−	0.258213i	0.413314	−	0.0196886i
$173$	11.2791	−	21.8784i	0.857533	−	1.66338i	0.115210	−	0.993341i	$-0.463246\pi$
$173$	11.2791	−	21.8784i	0.857533	−	1.66338i	0.742323	−	0.670042i	$-0.233724\pi$
$174$	−8.76124	−	1.95381i	−0.664188	−	0.148118i
$175$	2.50968	+	12.7663i	0.189714	+	0.965039i
$176$	−1.39500	+	9.70245i	−0.105152	+	0.731350i
$177$	−1.72530	−	3.59933i	−0.129681	−	0.270542i
$178$	8.82382	−	6.28342i	0.661374	−	0.470962i
$179$	11.3423	+	11.8955i	0.847767	+	0.889112i	0.994988	−	0.0999913i	$-0.0318815\pi$
$179$	11.3423	+	11.8955i	0.847767	+	0.889112i	−0.147221	+	0.989104i	$0.547033\pi$
$180$	−0.351946	−	0.457274i	−0.0262325	−	0.0340832i
$181$	3.63240	−	0.522261i	0.269994	−	0.0388193i	−0.00598785	−	0.999982i	$-0.501906\pi$
$181$	3.63240	−	0.522261i	0.269994	−	0.0388193i	0.275982	+	0.961163i	$0.410997\pi$
$182$	1.19109	−	0.481978i	0.0882895	−	0.0357266i
$183$	6.95346	+	9.39045i	0.514015	+	0.694162i
$184$	−14.7234	−	1.13816i	−1.08542	−	0.0839061i
$185$	2.63456	+	1.52107i	0.193697	+	0.111831i
$186$	−11.6464	−	5.73276i	−0.853956	−	0.420346i
$187$	16.2970	−	12.8161i	1.19176	−	0.937208i
$188$	−4.18671	+	1.91201i	−0.305347	+	0.139447i
$189$	6.44408	+	12.1439i	0.468738	+	0.883337i
$190$	0.833872	−	1.82592i	0.0604954	−	0.132466i
$191$	−3.28574	−	0.633274i	−0.237748	−	0.0458221i	0.0689855	−	0.997618i	$-0.478024\pi$
$191$	−3.28574	−	0.633274i	−0.237748	−	0.0458221i	−0.306733	+	0.951796i	$0.599236\pi$
$192$	14.8617	+	0.431354i	1.07255	+	0.0311303i
$193$	−0.185210	+	0.763447i	−0.0133317	+	0.0549541i	−0.978089	−	0.208188i	$-0.933244\pi$
$193$	−0.185210	+	0.763447i	−0.0133317	+	0.0549541i	0.964757	+	0.263142i	$0.0847587\pi$
$194$	2.23574	−	6.45974i	0.160516	−	0.463782i
$195$	−0.0742100	+	0.195839i	−0.00531429	+	0.0140243i
$196$	3.70720	+	2.87109i	0.264800	+	0.205078i
$197$	−10.5458	+	9.13801i	−0.751359	+	0.651057i	−0.943900	−	0.330233i	$-0.892873\pi$
$197$	−10.5458	+	9.13801i	−0.751359	+	0.651057i	0.192540	+	0.981289i	$0.438327\pi$
$198$	7.52867	+	13.3600i	0.535039	+	0.949455i
$199$	2.95413	−	3.75648i	0.209413	−	0.266290i	−0.669988	−	0.742372i	$-0.733701\pi$
$199$	2.95413	−	3.75648i	0.209413	−	0.266290i	0.879401	+	0.476082i	$0.157943\pi$
$200$	14.3093	−	4.95249i	1.01182	−	0.350194i
$201$	−15.4903	−	17.2195i	−1.09260	−	1.21457i
$202$	11.4844	+	3.37211i	0.808036	+	0.237261i
$203$	−7.75220	+	9.01391i	−0.544098	+	0.632652i
$204$	−3.81755	−	3.85759i	−0.267282	−	0.270085i
$205$	−0.418637	−	0.0199421i	−0.0292388	−	0.00139282i
$206$	4.57193	−	7.91882i	0.318542	−	0.551730i
$207$	−12.0439	+	7.87044i	−0.837111	+	0.547033i
$208$	−0.465639	−	0.806510i	−0.0322862	−	0.0559214i
$209$	14.5244	−	22.6004i	1.00468	−	1.56331i
$210$	1.49696	−	0.249412i	0.103300	−	0.0172110i
$211$	−2.89832	−	6.34645i	−0.199529	−	0.436907i	0.783247	−	0.621711i	$-0.213562\pi$
$211$	−2.89832	−	6.34645i	−0.199529	−	0.436907i	−0.982775	+	0.184804i	$0.940835\pi$
$212$	−0.0812486	−	0.334911i	−0.00558018	−	0.0230018i
$213$	−1.28770	+	3.95698i	−0.0882315	+	0.271128i
$214$	7.61623	−	2.63600i	0.520635	−	0.180193i
$215$	−0.864575	−	2.15961i	−0.0589636	−	0.147284i
$216$	12.9571	−	9.38681i	0.881620	−	0.638692i
$217$	−13.9676	+	10.0246i	−0.948184	+	0.680517i
$218$	6.09203	−	3.91511i	0.412605	−	0.265165i
$219$	−5.15808	+	0.839730i	−0.348551	+	0.0567437i
$220$	−0.837103	+	0.161338i	−0.0564375	+	0.0108774i
$221$	−0.464386	+	1.91422i	−0.0312380	+	0.128765i
$222$	−11.1091	+	18.0135i	−0.745594	+	1.20899i
$223$	−12.6397	+	14.5869i	−0.846414	+	0.976814i	−0.999936	−	0.0113310i	$-0.996393\pi$
$223$	−12.6397	+	14.5869i	−0.846414	+	0.976814i	0.153521	+	0.988145i	$0.450939\pi$
$224$	4.74185	−	8.28399i	0.316828	−	0.553498i
$225$	8.10493	−	12.3268i	0.540328	−	0.821789i
$226$	13.2298	+	9.42087i	0.880030	+	0.626667i
$227$	−7.54743	−	3.02153i	−0.500940	−	0.200546i	0.107410	−	0.994215i	$-0.465744\pi$
$227$	−7.54743	−	3.02153i	−0.500940	−	0.200546i	−0.608350	+	0.793669i	$0.708168\pi$
$228$	−6.30955	−	3.10577i	−0.417860	−	0.205685i
$229$	−7.60424	+	4.39031i	−0.502503	+	0.290120i	−0.729746	−	0.683718i	$-0.760362\pi$
$229$	−7.60424	+	4.39031i	−0.502503	+	0.290120i	0.227244	+	0.973838i	$0.427029\pi$
$230$	0.402235	+	1.53644i	0.0265226	+	0.101310i
$231$	20.3059	−	0.452804i	1.33603	−	0.0297923i
$232$	11.6401	+	7.48067i	0.764213	+	0.491130i
$233$	−4.08132	−	5.18981i	−0.267376	−	0.339996i	0.633762	−	0.773528i	$-0.281510\pi$
$233$	−4.08132	−	5.18981i	−0.267376	−	0.339996i	−0.901138	+	0.433532i	$0.857267\pi$
$234$	−1.34687	−	0.555577i	−0.0880474	−	0.0363192i
$235$	1.36152	+	1.42792i	0.0888158	+	0.0931473i
$236$	0.146735	+	1.53667i	0.00955160	+	0.100029i
$237$	28.2479	+	2.16849i	1.83490	+	0.140859i
$238$	13.6804	−	4.07215i	0.886770	−	0.263959i
$239$	0.953470	+	3.24722i	0.0616749	+	0.210045i	0.984565	−	0.175017i	$-0.0559981\pi$
$239$	0.953470	+	3.24722i	0.0616749	+	0.210045i	−0.922891	+	0.385062i	$0.874180\pi$
$240$	−0.329442	−	1.04943i	−0.0212654	−	0.0677403i
$241$	3.82891	−	0.182393i	0.246642	−	0.0117490i	0.0761029	−	0.997100i	$-0.475752\pi$
$241$	3.82891	−	0.182393i	0.246642	−	0.0117490i	0.170539	+	0.985351i	$0.445449\pi$
$242$	9.95860	−	0.474387i	0.640163	−	0.0304947i
$243$	4.42590	−	14.9470i	0.283922	−	0.958848i
$244$	−1.27313	−	4.33588i	−0.0815038	−	0.277576i
$245$	0.643288	−	1.90428i	0.0410981	−	0.121660i
$246$	0.223171	−	2.90714i	0.0142289	−	0.185352i
$247$	0.242619	+	2.54082i	0.0154374	+	0.161668i
$248$	13.8080	+	14.4814i	0.876808	+	0.919569i
$249$	−22.6153	+	13.6235i	−1.43319	+	0.863353i
$250$	−2.03026	−	2.58169i	−0.128405	−	0.163280i
$251$	0.651145	+	0.418466i	0.0410999	+	0.0264133i	0.561029	−	0.827796i	$-0.310405\pi$
$251$	0.651145	+	0.418466i	0.0410999	+	0.0264133i	−0.519930	+	0.854209i	$0.674042\pi$
$252$	−0.721273	−	5.26765i	−0.0454359	−	0.331831i
$253$	2.40212	+	21.1200i	0.151020	+	1.32780i
$254$	6.56897	−	3.79260i	0.412174	−	0.237969i
$255$	−1.02743	+	2.08729i	−0.0643404	+	0.130711i
$256$	−13.0638	−	5.22995i	−0.816486	−	0.326872i
$257$	18.3898	+	13.0953i	1.14712	+	0.816862i	0.985447	−	0.169982i	$-0.0543709\pi$
$257$	18.3898	+	13.0953i	1.14712	+	0.816862i	0.161675	+	0.986844i	$0.448310\pi$
$258$	15.1922	−	5.57630i	0.945826	−	0.347165i
$259$	14.1052	+	24.2228i	0.876454	+	1.50513i
$260$	0.0530399	−	0.0612113i	0.00328939	−	0.00379616i
$261$	13.4324	−	1.14136i	0.831445	−	0.0706483i
$262$	−4.88363	+	20.1306i	−0.301712	+	1.24367i
$263$	−15.7346	+	3.03260i	−0.970237	+	0.186998i	−0.649660	−	0.760225i	$-0.725089\pi$
$263$	−15.7346	+	3.03260i	−0.970237	+	0.186998i	−0.320577	+	0.947223i	$0.603877\pi$
$264$	−3.79831	−	23.3313i	−0.233770	−	1.43594i
$265$	−0.124277	+	0.0798683i	−0.00763431	+	0.00490627i
$266$	15.0261	−	10.7843i	0.921311	−	0.661230i
$267$	−9.81690	+	12.9722i	−0.600784	+	0.793888i
$268$	3.32918	+	8.31588i	0.203362	+	0.507973i
$269$	25.5583	−	8.84583i	1.55832	−	0.539340i	0.594088	−	0.804400i	$-0.297513\pi$
$269$	25.5583	−	8.84583i	1.55832	−	0.539340i	0.964232	+	0.265061i	$0.0853919\pi$
$270$	−1.40981	−	0.986702i	−0.0857982	−	0.0600488i
$271$	3.25036	+	13.3982i	0.197446	+	0.813882i	0.981229	+	0.192847i	$0.0617722\pi$
$271$	3.25036	+	13.3982i	0.197446	+	0.813882i	−0.783783	+	0.621034i	$0.786713\pi$
$272$	−4.29756	−	9.41035i	−0.260578	−	0.570586i
$273$	−1.48986	+	1.22637i	−0.0901704	+	0.0742231i
$274$	7.00528	−	10.9004i	0.423205	−	0.658519i
$275$	−10.8978	−	18.8756i	−0.657163	−	1.13824i
$276$	5.42144	−	1.25244i	0.326332	−	0.0753881i
$277$	6.72138	−	11.6418i	0.403849	−	0.699486i	−0.590338	−	0.807156i	$-0.701006\pi$
$277$	6.72138	−	11.6418i	0.403849	−	0.699486i	0.994187	+	0.107670i	$0.0343389\pi$
$278$	15.2023	+	0.724176i	0.911774	+	0.0434332i
$279$	19.2662	+	2.97554i	1.15344	+	0.178141i
$280$	−2.29864	−	0.434184i	−0.137370	−	0.0259475i
$281$	22.5613	+	6.62460i	1.34590	+	0.395191i	0.873770	−	0.486340i	$-0.161668\pi$
$281$	22.5613	+	6.62460i	1.34590	+	0.395191i	0.472127	+	0.881531i	$0.343487\pi$
$282$	−10.2044	+	9.17969i	−0.607666	+	0.546643i
$283$	13.2836	−	4.59750i	0.789629	−	0.273293i	0.0976595	−	0.995220i	$-0.468864\pi$
$283$	13.2836	−	4.59750i	0.789629	−	0.273293i	0.691970	+	0.721927i	$0.256743\pi$
$284$	0.994813	−	1.26501i	0.0590313	−	0.0750644i
$285$	−0.373498	+	2.99136i	−0.0221241	+	0.177193i
$286$	−1.62676	+	1.40959i	−0.0961923	+	0.0833511i
$287$	−3.25641	−	2.07573i	−0.192220	−	0.122526i
$288$	−10.4160	+	2.94073i	−0.613769	+	0.173284i
$289$	−1.59649	+	4.61277i	−0.0939114	+	0.271339i
$290$	0.350841	−	1.44619i	0.0206021	−	0.0849230i
$291$	−0.297835	+	10.2615i	−0.0174594	+	0.601540i
$292$	1.98458	+	0.382496i	0.116139	+	0.0223839i
$293$	−0.890807	+	1.95059i	−0.0520415	+	0.113955i	−0.933867	−	0.357622i	$-0.883588\pi$
$293$	−0.890807	+	1.95059i	−0.0520415	+	0.113955i	0.881825	+	0.471577i	$0.156315\pi$
$294$	13.1124	+	4.85771i	0.764728	+	0.283308i
$295$	0.601916	−	0.274886i	0.0350449	−	0.0160045i
$296$	25.6430	−	20.1659i	1.49047	−	1.17212i
$297$	−16.7969	−	15.7565i	−0.974656	−	0.914282i
$298$	−7.39120	−	4.26731i	−0.428161	−	0.247199i
$299$	−1.41975	−	1.43617i	−0.0821064	−	0.0830560i
$300$	−4.58522	+	3.39527i	−0.264728	+	0.196026i
$301$	2.97162	−	21.2271i	0.171281	−	1.22351i
$302$	14.6781	−	2.11040i	0.844632	−	0.121440i
$303$	−17.9722	+	0.334025i	−1.03247	+	0.0191892i
$304$	−9.25065	−	9.70180i	−0.530561	−	0.556436i
$305$	−1.57792	+	1.12363i	−0.0903514	+	0.0643390i
$306$	−14.3074	−	7.56597i	−0.817902	−	0.432518i
$307$	4.10423	−	28.5455i	0.234241	−	1.62918i	−0.445188	−	0.895437i	$-0.646863\pi$
$307$	4.10423	−	28.5455i	0.234241	−	1.62918i	0.679429	−	0.733741i	$-0.262228\pi$
$308$	−7.43253	−	2.54157i	−0.423508	−	0.144819i
$309$	−2.98895	+	13.4030i	−0.170035	+	0.762469i
$310$	0.986103	−	1.91277i	0.0560069	−	0.108638i
$311$	−7.71966	+	0.367733i	−0.437742	+	0.0208522i	−0.265296	−	0.964167i	$-0.585470\pi$
$311$	−7.71966	+	0.367733i	−0.437742	+	0.0208522i	−0.172445	+	0.985019i	$0.555167\pi$
$312$	1.65389	+	1.51931i	0.0936329	+	0.0860142i
$313$	−11.3656	+	11.9199i	−0.642424	+	0.673755i	−0.961762	−	0.273886i	$-0.911691\pi$
$313$	−11.3656	+	11.9199i	−0.642424	+	0.673755i	0.319338	+	0.947641i	$0.396539\pi$
$314$	−2.63109	+	18.2996i	−0.148481	+	1.03271i
$315$	−2.03274	+	1.03072i	−0.114532	+	0.0580743i
$316$	−9.96660	−	4.55160i	−0.560665	−	0.256047i
$317$	−29.3688	+	7.12480i	−1.64952	+	0.400169i	−0.949453	−	0.313911i	$-0.898361\pi$
$317$	−29.3688	+	7.12480i	−1.64952	+	0.400169i	−0.700065	+	0.714079i	$0.746846\pi$
$318$	−0.530314	−	0.880335i	−0.0297385	−	0.0493667i
$319$	7.40225	−	18.4899i	0.414447	−	1.03524i
$320$	−0.117282	+	2.46205i	−0.00655626	+	0.137633i
$321$	−9.72723	+	7.20285i	−0.542921	+	0.402024i
$322$	−3.81635	+	14.1276i	−0.212677	+	0.787300i
$323$			28.3534i			1.57763i
$324$	−3.59868	+	4.83679i	−0.199927	+	0.268711i
$325$	1.92240	+	0.769613i	0.106636	+	0.0426904i
$326$	−0.967424	+	10.1313i	−0.0535807	+	0.561122i
$327$	−6.96793	+	8.35003i	−0.385328	+	0.461757i
$328$	−1.86703	+	4.08822i	−0.103089	+	0.225734i
$329$	4.35147	+	17.6508i	0.239904	+	0.973119i
$330$	−2.23766	+	1.20674i	−0.123179	+	0.0664291i
$331$	−8.89540	−	8.48175i	−0.488936	−	0.466199i	0.405050	−	0.914294i	$-0.367254\pi$
$331$	−8.89540	−	8.48175i	−0.488936	−	0.466199i	−0.893986	+	0.448095i	$0.852103\pi$
$332$	10.0261	−	1.93237i	0.550254	−	0.106053i
$333$	7.81507	−	30.8077i	0.428263	−	1.68825i
$334$	−4.00867	−	2.06661i	−0.219345	−	0.113080i
$335$	2.90191	−	2.51452i	0.158548	−	0.137383i
$336$	2.16920	−	9.89990i	0.118339	−	0.540084i
$337$	20.2322	+	2.90896i	1.10212	+	0.158461i	0.669281	−	0.743010i	$-0.266602\pi$
$337$	20.2322	+	2.90896i	1.10212	+	0.158461i	0.432840	+	0.901471i	$0.357512\pi$
$338$	−2.79877	+	14.5214i	−0.152233	+	0.789860i
$339$	−23.1939	−	7.54785i	−1.25972	−	0.409943i
$340$	0.651168	−	0.620888i	0.0353146	−	0.0336724i
$341$	16.7065	−	23.4610i	0.904708	−	1.27048i
$342$	−20.7263	−	3.20103i	−1.12075	−	0.173092i
$343$	13.8608	−	12.2833i	0.748411	−	0.663236i
$344$	−24.9456			−1.34497
$345$	−1.26745	−	2.02057i	−0.0682372	−	0.108784i
$346$	−14.1943	+	24.5852i	−0.763090	+	1.32171i
$347$	−1.07964	−	2.09421i	−0.0579580	−	0.112423i	0.858077	−	0.513521i	$-0.171659\pi$
$347$	−1.07964	−	2.09421i	−0.0579580	−	0.112423i	−0.916035	+	0.401098i	$0.868629\pi$
$348$	−5.02882	−	1.37562i	−0.269573	−	0.0737411i
$349$	6.61194	+	14.4781i	0.353929	+	0.774996i	0.999932	+	0.0116614i	$0.00371202\pi$
$349$	6.61194	+	14.4781i	0.353929	+	0.774996i	−0.646003	+	0.763335i	$0.723561\pi$
$350$	−2.19061	−	14.8446i	−0.117093	−	0.793479i
$351$	2.17976	+	0.190227i	0.116347	+	0.0101536i
$352$	−3.02617	+	15.7012i	−0.161295	+	0.836879i
$353$	12.1957	−	15.5081i	0.649113	−	0.825414i	−0.344437	−	0.938809i	$-0.611930\pi$
$353$	12.1957	−	15.5081i	0.649113	−	0.825414i	0.993550	+	0.113395i	$0.0361727\pi$
$354$	1.79005	+	4.24115i	0.0951399	+	0.225415i
$355$	−0.651916	−	0.225630i	−0.0346001	−	0.0119752i
$356$	5.29277	−	3.40146i	0.280516	−	0.180277i
$357$	−17.7703	+	11.9884i	−0.940506	+	0.634492i
$358$	−12.4137	−	14.3262i	−0.656087	−	0.757164i
$359$	−1.29292	−	1.23279i	−0.0682376	−	0.0650644i	0.655193	−	0.755462i	$-0.272587\pi$
$359$	−1.29292	−	1.23279i	−0.0682376	−	0.0650644i	−0.723431	+	0.690397i	$0.757436\pi$
$360$	1.51598	+	2.17660i	0.0798991	+	0.114717i
$361$	5.80217	+	16.7643i	0.305377	+	0.882330i
$362$	−4.21324	+	0.402315i	−0.221443	+	0.0211452i
$363$	−14.0558	+	5.15919i	−0.737739	+	0.270787i
$364$	0.704328	−	0.246702i	0.0369168	−	0.0129307i
$365$	−0.123298	−	0.857556i	−0.00645371	−	0.0448865i
$366$	−7.49516	−	11.1995i	−0.391778	−	0.585408i
$367$	−22.4521	−	12.9627i	−1.17199	−	0.676649i	−0.217842	−	0.975984i	$-0.569902\pi$
$367$	−22.4521	−	12.9627i	−1.17199	−	0.676649i	−0.954148	+	0.299335i	$0.903235\pi$
$368$	10.5240	+	1.31971i	0.548600	+	0.0687947i
$369$	0.987884	+	4.26588i	0.0514272	+	0.222073i
$370$	−2.95158	−	1.89686i	−0.153445	−	0.0986133i
$371$	−1.35939	+	0.0698141i	−0.0705761	+	0.00362457i
$372$	−6.59821	−	3.64770i	−0.342101	−	0.189125i
$373$	−8.66534	+	2.10219i	−0.448674	+	0.108847i	−0.453728	−	0.891140i	$-0.649906\pi$
$373$	−8.66534	+	2.10219i	−0.448674	+	0.108847i	0.00505422	+	0.999987i	$0.498391\pi$
$374$	−19.4777	+	13.8700i	−1.00717	+	0.717201i
$375$	4.07033	+	2.78595i	0.210191	+	0.143866i
$376$	19.6419	−	7.86345i	1.01296	−	0.405526i
$377$	0.533097	+	1.81556i	0.0274559	+	0.0935062i
$378$	−6.75724	−	14.3435i	−0.347555	−	0.737752i
$379$	−16.1419	−	25.1172i	−0.829152	−	1.29019i	−0.954541	−	0.298078i	$-0.903654\pi$
$379$	−16.1419	−	25.1172i	−0.829152	−	1.29019i	0.125389	−	0.992108i	$-0.459982\pi$
$380$	0.534230	−	1.03626i	0.0274054	−	0.0531591i
$381$	−7.70642	+	8.38901i	−0.394812	+	0.429782i
$382$	3.75046	+	0.909852i	0.191890	+	0.0465521i
$383$	−26.5780	+	10.6402i	−1.35807	+	0.543690i	−0.932479	−	0.361225i	$-0.882359\pi$
$383$	−26.5780	+	10.6402i	−1.35807	+	0.543690i	−0.425592	+	0.904915i	$0.639934\pi$
$384$	−4.63636	−	0.355918i	−0.236599	−	0.0181628i
$385$	0.0124986	+	3.36717i	0.000636988	+	0.171607i
$386$	0.255261	−	0.869337i	0.0129924	−	0.0442481i
$387$	−19.2599	+	14.8236i	−0.979037	+	0.753526i
$388$	1.47558	−	3.68581i	0.0749111	−	0.187119i
$389$	−12.3235	+	6.35319i	−0.624824	+	0.322119i	−0.741401	−	0.671062i	$-0.765838\pi$
$389$	−12.3235	+	6.35319i	−0.624824	+	0.322119i	0.116577	+	0.993182i	$0.462808\pi$
$390$	0.0962379	−	0.221536i	0.00487320	−	0.0112179i
$391$	−14.1836	−	17.3809i	−0.717295	−	0.878988i
$392$	−16.3940	−	13.9938i	−0.828024	−	0.706793i
$393$	−2.05740	−	31.0409i	−0.103782	−	1.56580i
$394$	12.6504	−	9.94839i	0.637318	−	0.501193i
$395$	−0.446456	+	4.67550i	−0.0224637	+	0.235250i
$396$	3.99852	+	7.95884i	0.200933	+	0.399947i
$397$	6.20572	−	0.592574i	0.311456	−	0.0297405i	0.0618424	−	0.998086i	$-0.480302\pi$
$397$	6.20572	−	0.592574i	0.311456	−	0.0297405i	0.249614	+	0.968345i	$0.419696\pi$
$398$	−3.60934	+	4.16540i	−0.180920	+	0.208793i
$399$	−16.6793	+	22.2112i	−0.835011	+	1.11195i
$400$	−10.4350	+	3.06401i	−0.521752	+	0.153200i
$401$	2.11165	−	6.10120i	0.105451	−	0.304679i	−0.879916	−	0.475130i	$-0.842401\pi$
$401$	2.11165	−	6.10120i	0.105451	−	0.304679i	0.985366	+	0.170450i	$0.0545223\pi$
$402$	16.9000	+	20.6871i	0.842897	+	1.03178i
$403$	0.130200	+	2.73323i	0.00648573	+	0.136152i
$404$	6.56943	+	2.27370i	0.326841	+	0.113121i
$405$	2.46387	+	0.779654i	0.122431	+	0.0387413i
$406$	9.42529	−	9.95872i	0.467770	−	0.494243i
$407$	−35.4878	−	30.7503i	−1.75906	−	1.52424i
$408$	16.6849	+	18.5475i	0.826027	+	0.918238i
$409$	9.53042	−	9.08723i	0.471249	−	0.449335i	−0.416858	−	0.908971i	$-0.636869\pi$
$409$	9.53042	−	9.08723i	0.471249	−	0.449335i	0.888107	+	0.459637i	$0.152020\pi$
$410$	0.481180	+	0.0459472i	0.0237638	+	0.00226917i
$411$	−5.13443	+	18.7697i	−0.253263	+	0.925843i
$412$	2.87124	−	4.46774i	0.141456	−	0.220110i
$413$	6.07157	+	0.557030i	0.298763	+	0.0274097i
$414$	14.3067	−	8.40591i	0.703134	−	0.413128i
$415$	−2.18847	−	3.79054i	−0.107428	−	0.186070i
$416$	−0.696127	−	1.35030i	−0.0341304	−	0.0662038i
$417$	−22.1084	+	5.80049i	−1.08265	+	0.284051i
$418$	−17.9726	+	25.2389i	−0.879067	+	1.23448i
$419$	−10.2543	−	3.01092i	−0.500953	−	0.147093i	0.0214870	−	0.999769i	$-0.493160\pi$
$419$	−10.2543	−	3.01092i	−0.500953	−	0.147093i	−0.522440	+	0.852676i	$0.674978\pi$
$420$	0.875353	−	0.103326i	0.0427129	−	0.00504178i
$421$	15.0142	+	13.0099i	0.731749	+	0.634064i	0.938878	−	0.344250i	$-0.111867\pi$
$421$	15.0142	+	13.0099i	0.731749	+	0.634064i	−0.207129	+	0.978314i	$0.566412\pi$
$422$	2.99063	+	7.47024i	0.145582	+	0.363646i
$423$	10.4923	−	17.7432i	0.510155	−	0.862703i
$424$	0.299808	+	1.55555i	0.0145600	+	0.0755443i
$425$	20.4459	+	10.5406i	0.991771	+	0.511294i
$426$	1.70059	−	4.48782i	0.0823939	−	0.217436i
$427$	−17.7614	+	1.76256i	−0.859533	+	0.0852962i
$428$	4.49139	−	1.31879i	0.217099	−	0.0637461i
$429$	1.69686	−	2.75147i	0.0819250	−	0.132842i
$430$	0.877489	+	2.53534i	0.0423163	+	0.122265i
$431$	21.9141	+	30.7740i	1.05556	+	1.48233i	0.865726	+	0.500518i	$0.166857\pi$
$431$	21.9141	+	30.7740i	1.05556	+	1.48233i	0.189838	+	0.981815i	$0.439204\pi$
$432$	−9.61651	+	6.29149i	−0.462674	+	0.302700i
$433$	20.8391	−	9.51690i	1.00146	−	0.457353i	0.153922	−	0.988083i	$-0.450809\pi$
$433$	20.8391	−	9.51690i	1.00146	−	0.457353i	0.847541	+	0.530730i	$0.178082\pi$
$434$	16.6410	−	10.7820i	0.798794	−	0.517553i
$435$	0.147804	+	2.22998i	0.00708664	+	0.106919i
$436$	3.64248	−	2.10299i	0.174443	−	0.100715i
$437$	−24.7343	−	15.2720i	−1.18320	−	0.730561i
$438$	5.98826	−	0.684319i	0.286130	−	0.0326980i
$439$	0.228238	−	4.79130i	0.0108932	−	0.228676i	−0.986855	−	0.161607i	$-0.948332\pi$
$439$	0.228238	−	4.79130i	0.0108932	−	0.228676i	0.997748	−	0.0670689i	$-0.0213647\pi$
$440$	3.87894	−	0.557707i	0.184921	−	0.0265876i
$441$	−20.9731	−	1.06233i	−0.998720	−	0.0505874i
$442$	0.640026	−	2.17973i	0.0304429	−	0.103679i
$443$	−0.520060	−	5.44632i	−0.0247088	−	0.258762i	−0.999383	−	0.0351315i	$-0.988815\pi$
$443$	−0.520060	−	5.44632i	−0.0247088	−	0.258762i	0.974674	−	0.223631i	$-0.0717911\pi$
$444$	−6.94274	+	10.1435i	−0.329488	+	0.481389i
$445$	−2.11995	−	1.66715i	−0.100495	−	0.0790304i
$446$	15.3615	−	16.1107i	0.727390	−	0.762865i
$447$	12.5100	+	2.78980i	0.591701	+	0.131953i
$448$	−12.2076	+	19.1513i	−0.576755	+	0.904815i
$449$	−3.24535	−	5.04987i	−0.153158	−	0.238318i	0.756193	−	0.654349i	$-0.227057\pi$
$449$	−3.24535	−	5.04987i	−0.153158	−	0.238318i	−0.909351	+	0.416031i	$0.863421\pi$
$450$	−10.0134	+	13.7559i	−0.472038	+	0.648459i
$451$	6.28686	+	1.52518i	0.296037	+	0.0718178i
$452$	7.41486	+	5.83111i	0.348766	+	0.274272i
$453$	−20.0823	+	9.62624i	−0.943550	+	0.452280i
$454$	8.52892	+	3.89503i	0.400282	+	0.182803i
$455$	−0.198685	−	0.250727i	−0.00931448	−	0.0117543i
$456$	28.2916	+	15.6405i	1.32488	+	0.732435i
$457$	3.34263	+	4.25050i	0.156362	+	0.198830i	0.857922	−	0.513780i	$-0.171755\pi$
$457$	3.34263	+	4.25050i	0.156362	+	0.198830i	−0.701560	+	0.712610i	$0.747513\pi$
$458$	9.00112	−	4.64040i	0.420595	−	0.216832i
$459$	23.9037	+	4.40530i	1.11573	+	0.205622i
$460$	0.190895	+	0.902481i	0.00890052	+	0.0420784i
$461$			8.49024i			0.395430i	0.980260	+	0.197715i	$0.0633520\pi$
$461$			8.49024i			0.395430i	−0.980260	+	0.197715i	$0.936648\pi$
$462$	−23.4175	−	0.592695i	−1.08948	−	0.0275747i
$463$	−0.781934	−	5.43847i	−0.0363396	−	0.252747i	0.963551	−	0.267524i	$-0.0862054\pi$
$463$	−0.781934	−	5.43847i	−0.0363396	−	0.252747i	−0.999891	+	0.0147766i	$0.995296\pi$
$464$	−8.09524	−	5.76460i	−0.375812	−	0.267615i
$465$	−0.552558	+	3.18428i	−0.0256243	+	0.147667i
$466$	4.41693	+	6.20271i	0.204610	+	0.287335i
$467$	8.51557	+	1.64124i	0.394054	+	0.0759476i	0.382429	−	0.923985i	$-0.375088\pi$
$467$	8.51557	+	1.64124i	0.394054	+	0.0759476i	0.0116246	+	0.999932i	$0.496300\pi$
$468$	−0.766028	−	0.359538i	−0.0354096	−	0.0166197i
$469$	34.7155	−	6.82460i	1.60301	−	0.315131i
$470$	−1.49013	−	1.71970i	−0.0687345	−	0.0793238i
$471$	−4.46136	−	27.4041i	−0.205569	−	1.26272i
$472$	−0.337638	−	7.08789i	−0.0155410	−	0.326247i
$473$	6.79541	+	35.2579i	0.312453	+	1.62116i
$474$	−32.4229	−	4.04829i	−1.48923	−	0.185944i
$475$	29.5036	+	4.24198i	1.35372	+	0.194635i
$476$	8.04921	−	1.98438i	0.368935	−	0.0909540i
$477$	1.15584	+	1.02285i	0.0529224	+	0.0468331i
$478$	−0.920212	−	3.79317i	−0.0420895	−	0.173495i
$479$	−24.7537	−	2.36369i	−1.13103	−	0.108000i	−0.487285	−	0.873243i	$-0.662013\pi$
$479$	−24.7537	−	2.36369i	−1.13103	−	0.108000i	−0.643741	+	0.765243i	$0.722619\pi$
$480$	−0.455349	−	1.73555i	−0.0207837	−	0.0792165i
$481$	4.45618	+	0.212274i	0.203184	+	0.00967886i
$482$	−4.42096			−0.201369
$483$	−0.886450	−	21.9594i	−0.0403349	−	0.999186i
$484$	5.79057			0.263208
$485$	−1.69996	−	0.0809791i	−0.0771912	−	0.00367707i
$486$	−5.91894	+	16.9762i	−0.268489	+	0.770056i
$487$	5.37503	+	0.513254i	0.243566	+	0.0232577i	0.216125	−	0.976366i	$-0.430658\pi$
$487$	5.37503	+	0.513254i	0.243566	+	0.0232577i	0.0274410	+	0.999623i	$0.491264\pi$
$488$	4.89735	+	20.1871i	0.221692	+	0.913828i
$489$	−3.17098	−	14.9518i	−0.143397	−	0.676146i
$490$	−0.845577	+	2.15845i	−0.0381993	+	0.0975090i
$491$	−17.6516	−	2.53792i	−0.796608	−	0.114535i	−0.268020	−	0.963413i	$-0.586369\pi$
$491$	−17.6516	−	2.53792i	−0.796608	−	0.114535i	−0.528588	+	0.848879i	$0.677278\pi$
$492$	0.209813	−	1.68040i	0.00945911	−	0.0757583i
$493$	3.97804	+	20.6400i	0.179162	+	0.929580i
$494$	−0.140067	−	2.94037i	−0.00630191	−	0.132293i
$495$	2.66343	−	2.73560i	0.119712	−	0.122956i
$496$	−9.41124	−	10.8612i	−0.422577	−	0.487680i
$497$	−4.18035	−	4.78835i	−0.187514	−	0.214787i
$498$	26.8008	−	14.4534i	1.20097	−	0.647671i
$499$	−41.6644	−	8.03015i	−1.86515	−	0.359479i	−0.873334	−	0.487121i	$-0.838047\pi$
$499$	−41.6644	−	8.03015i	−1.86515	−	0.359479i	−0.991820	+	0.127642i	$0.959259\pi$
$500$	−1.10650	−	1.55387i	−0.0494844	−	0.0694911i
$501$	6.67341	+	1.15802i	0.298146	+	0.0517364i
$502$	−0.727164	−	0.517811i	−0.0324549	−	0.0231110i
$503$	1.41693	+	9.85493i	0.0631776	+	0.439410i	0.996719	+	0.0809401i	$0.0257923\pi$
$503$	1.41693	+	9.85493i	0.0631776	+	0.439410i	−0.933541	+	0.358470i	$0.883299\pi$
$504$	2.15963	+	24.3447i	0.0961977	+	1.08440i
$505$		−	2.97998i		−	0.132607i
$506$	−1.60827	−	24.4623i	−0.0714963	−	1.08748i
$507$	−2.52163	−	22.0659i	−0.111989	−	0.979982i
$508$	3.91578	−	2.01873i	0.173735	−	0.0895665i
$509$	18.3110	+	23.2843i	0.811619	+	1.03206i	0.998763	+	0.0497253i	$0.0158346\pi$
$509$	18.3110	+	23.2843i	0.811619	+	1.03206i	−0.187144	+	0.982333i	$0.559923\pi$
$510$	1.29816	−	2.34820i	0.0574836	−	0.103980i
$511$	2.93939	−	7.42196i	0.130031	−	0.328328i
$512$	19.6468	+	8.97239i	0.868273	+	0.396527i
$513$	31.1375	−	4.73625i	1.37476	−	0.209111i
$514$	−20.4666	−	16.0951i	−0.902744	−	0.709926i
$515$	−2.21238	−	0.536718i	−0.0974893	−	0.0236506i
$516$	8.96783	−	2.81523i	0.394787	−	0.123934i
$517$	−16.4648	−	25.6197i	−0.724121	−	1.12675i
$518$	−14.9201	−	28.6791i	−0.655551	−	1.26009i
$519$	9.27967	−	41.6117i	0.407332	−	1.82655i
$520$	−0.256927	+	0.269457i	−0.0112670	+	0.0118165i
$521$	6.97014	+	5.48137i	0.305367	+	0.240143i	0.759069	−	0.651010i	$-0.225654\pi$
$521$	6.97014	+	5.48137i	0.305367	+	0.240143i	−0.453702	+	0.891154i	$0.649897\pi$
$522$	−15.5369	+	0.577728i	−0.680033	+	0.0252865i
$523$	−0.816114	−	8.54674i	−0.0356862	−	0.373723i	−0.995620	−	0.0934950i	$-0.970196\pi$
$523$	−0.816114	−	8.54674i	−0.0356862	−	0.373723i	0.959934	−	0.280228i	$-0.0904100\pi$
$524$	−3.38955	+	11.5438i	−0.148073	+	0.504291i
$525$	9.81605	+	20.2848i	0.428408	+	0.885301i
$526$	18.2929	−	2.63012i	0.797608	−	0.114679i
$527$	−1.44635	+	30.3625i	−0.0630038	+	1.32261i
$528$	1.92764	+	16.8682i	0.0838898	+	0.734093i
$529$	22.8020	−	3.01124i	0.991392	−	0.130924i
$530$	0.147552	−	0.0851893i	0.00640926	−	0.00370039i
$531$	−4.47258	−	5.27177i	−0.194093	−	0.228775i
$532$	9.01541	−	5.84125i	0.390867	−	0.253250i
$533$	−0.559077	+	0.255322i	−0.0242163	+	0.0110592i
$534$	12.0211	−	14.4055i	0.520203	−	0.623385i
$535$	−1.16393	−	1.63451i	−0.0503211	−	0.0706661i
$536$	−13.4674	−	38.9114i	−0.581702	−	1.68072i
$537$	24.2311	+	14.9435i	1.04565	+	0.644862i
$538$	−29.9290	+	8.78794i	−1.29033	+	0.378875i
$539$	−15.3129	+	26.9833i	−0.659571	+	1.16225i
$540$	−0.790629	−	0.611394i	−0.0340232	−	0.0263102i
$541$	−1.16013	−	0.598089i	−0.0498779	−	0.0257138i	0.433107	−	0.901342i	$-0.357417\pi$
$541$	−1.16013	−	0.598089i	−0.0498779	−	0.0257138i	−0.482985	+	0.875629i	$0.660447\pi$
$542$	−3.00921	−	15.6133i	−0.129257	−	0.670647i
$543$	5.85598	−	2.47161i	0.251304	−	0.106067i
$544$	−6.27217	−	15.6671i	−0.268917	−	0.671722i
$545$	−1.36258	−	1.18068i	−0.0583665	−	0.0505749i
$546$	1.78364	−	1.33103i	0.0763326	−	0.0569629i
$547$	−3.28124	−	0.963459i	−0.140296	−	0.0411945i	0.210831	−	0.977523i	$-0.432383\pi$
$547$	−3.28124	−	0.963459i	−0.140296	−	0.0411945i	−0.351126	+	0.936328i	$0.614201\pi$
$548$	4.36534	−	6.13026i	0.186478	−	0.261872i
$549$	15.7771	+	12.6758i	0.673350	+	0.540992i
$550$	11.5186	+	22.3429i	0.491154	+	0.952706i
$551$	13.6186	+	23.5882i	0.580174	+	1.00489i
$552$	−25.1671	+	4.56491i	−1.07118	+	0.194296i
$553$	−24.9717	+	35.3448i	−1.06190	+	1.50301i
$554$	−8.38199	+	13.0426i	−0.356117	+	0.554128i
$555$	5.08240	+	1.39028i	0.215736	+	0.0590141i
$556$	8.79958	+	0.840258i	0.373185	+	0.0356349i
$557$	23.0701	−	21.9973i	0.977513	−	0.932057i	−0.0201898	−	0.999796i	$-0.506427\pi$
$557$	23.0701	−	21.9973i	0.977513	−	0.932057i	0.997703	+	0.0677392i	$0.0215786\pi$
$558$	−22.0317	−	4.48513i	−0.932674	−	0.189871i
$559$	−2.57816	−	2.23398i	−0.109044	−	0.0944875i
$560$	1.63426	+	0.390050i	0.0690601	+	0.0164826i
$561$	21.6698	−	28.6349i	0.914900	−	1.20897i
$562$	−25.6274	−	8.86973i	−1.08103	−	0.374147i
$563$	0.777054	+	16.3124i	0.0327489	+	0.687484i	0.954232	+	0.299067i	$0.0966753\pi$
$563$	0.777054	+	16.3124i	0.0327489	+	0.687484i	−0.921483	+	0.388418i	$0.873022\pi$
$564$	−6.17377	+	5.04357i	−0.259963	+	0.212372i
$565$	1.32253	−	3.82121i	0.0556394	−	0.160760i
$566$	−15.5552	+	4.56742i	−0.653834	+	0.191983i
$567$	16.1340	+	17.5127i	0.677563	+	0.735464i
$568$	−4.84448	+	5.59083i	−0.203270	+	0.234586i
$569$	−7.91317	+	0.755616i	−0.331737	+	0.0316771i	−0.259596	−	0.965717i	$-0.583589\pi$
$569$	−7.91317	+	0.755616i	−0.331737	+	0.0316771i	−0.0721415	+	0.997394i	$0.522983\pi$
$570$	0.594432	−	3.42559i	0.0248980	−	0.143482i
$571$	0.0402907	−	0.421943i	0.00168611	−	0.0176578i	−0.994590	−	0.103881i	$-0.966874\pi$
$571$	0.0402907	−	0.421943i	0.00168611	−	0.0176578i	0.996276	+	0.0862234i	$0.0274799\pi$
$572$	−0.982716	+	0.772816i	−0.0410894	+	0.0323131i
$573$	−5.78311	+	0.383306i	−0.241593	+	0.0160128i
$574$	3.63752	+	2.56997i	0.151827	+	0.107268i
$575$	−20.2080	+	12.1586i	−0.842730	+	0.507048i
$576$	25.0882	−	5.80987i	1.04534	−	0.242078i
$577$	−3.47115	+	1.78950i	−0.144506	+	0.0744979i	−0.528963	−	0.848645i	$-0.677419\pi$
$577$	−3.47115	+	1.78950i	−0.144506	+	0.0744979i	0.384457	+	0.923143i	$0.374389\pi$
$578$	2.09232	−	5.22636i	0.0870289	−	0.217388i
$579$	0.0252849	+	1.36045i	0.00105080	+	0.0565384i
$580$	0.243506	−	0.829306i	0.0101110	−	0.0344350i
$581$	−0.149698	−	40.3291i	−0.00621051	−	1.67313i
$582$	0.906231	−	11.8050i	0.0375645	−	0.489334i
$583$	2.11694	−	0.847495i	0.0876747	−	0.0350996i
$584$	−9.02874	−	2.19035i	−0.373612	−	0.0906372i
$585$	−0.0382459	+	0.360717i	−0.00158127	+	0.0149138i
$586$	1.13326	−	2.19823i	0.0468147	−	0.0908079i
$587$	6.86837	+	10.6874i	0.283488	+	0.441116i	0.953570	−	0.301171i	$-0.0973775\pi$
$587$	6.86837	+	10.6874i	0.283488	+	0.441116i	−0.670082	+	0.742287i	$0.733741\pi$
$588$	7.47286	+	3.18056i	0.308176	+	0.131164i
$589$	11.0969	+	37.7925i	0.457239	+	1.55721i
$590$	−0.708500	+	0.283641i	−0.0291685	+	0.0116773i
$591$	−13.6513	+	19.9448i	−0.561539	+	0.820420i
$592$	−19.0860	+	13.5911i	−0.784431	+	0.558591i
$593$	−37.1903	+	9.02226i	−1.52722	+	0.370500i	−0.909435	−	0.415846i	$-0.863486\pi$
$593$	−37.1903	+	9.02226i	−1.52722	+	0.370500i	−0.617787	+	0.786346i	$0.711970\pi$
$594$	18.4856	+	19.0734i	0.758473	+	0.782591i
$595$	−1.93237	−	2.98243i	−0.0792194	−	0.122268i
$596$	−4.17006	−	2.67993i	−0.170812	−	0.109774i
$597$	3.29802	−	7.59191i	0.134979	−	0.310716i
$598$	1.55676	+	1.73240i	0.0636606	+	0.0708432i
$599$	−11.0218	−	6.36343i	−0.450338	−	0.260003i	0.257635	−	0.966242i	$-0.417057\pi$
$599$	−11.0218	−	6.36343i	−0.450338	−	0.260003i	−0.707973	+	0.706240i	$0.750390\pi$
$600$	21.7962	−	14.5869i	0.889824	−	0.595506i
$601$	−1.26235	−	8.77984i	−0.0514924	−	0.358137i	−0.999235	−	0.0391020i	$-0.987550\pi$
$601$	−1.26235	−	8.77984i	−0.0514924	−	0.358137i	0.947743	−	0.319035i	$-0.103359\pi$
$602$	−4.58823	+	24.2908i	−0.187002	+	0.990020i
$603$	−33.5205	−	22.0398i	−1.36506	−	0.897531i
$604$	8.57381	−	0.818700i	0.348863	−	0.0333124i
$605$	−0.811852	−	2.34569i	−0.0330065	−	0.0953660i
$606$	20.7225	+	0.601461i	0.841795	+	0.0244327i
$607$	−17.7601	−	16.9342i	−0.720859	−	0.687338i	0.237986	−	0.971269i	$-0.423513\pi$
$607$	−17.7601	−	16.9342i	−0.720859	−	0.687338i	−0.958845	+	0.283931i	$0.908361\pi$
$608$	−14.3203	−	16.5265i	−0.580764	−	0.670237i
$609$	−9.02553	+	18.5089i	−0.365733	+	0.750020i
$610$	1.87945	−	1.20785i	0.0760966	−	0.0489043i
$611$	2.73422	+	0.946324i	0.110615	+	0.0382842i
$612$	−8.09134	−	4.78478i	−0.327073	−	0.193413i
$613$	−23.3360	+	29.6742i	−0.942533	+	1.19853i	0.0374203	+	0.999300i	$0.488086\pi$
$613$	−23.3360	+	29.6742i	−0.942533	+	1.19853i	−0.979953	+	0.199228i	$0.936156\pi$
$614$	−6.29462	+	32.6596i	−0.254030	+	1.31803i
$615$	−0.710128	+	0.150604i	−0.0286351	+	0.00607292i
$616$	33.5714	+	13.2956i	1.35263	+	0.535694i
$617$	9.55855	+	20.9303i	0.384813	+	0.842623i	0.998587	+	0.0531411i	$0.0169233\pi$
$617$	9.55855	+	20.9303i	0.384813	+	0.842623i	−0.613774	+	0.789482i	$0.710349\pi$
$618$	4.17883	−	15.2764i	0.168097	−	0.614507i
$619$	−18.4923	−	35.8700i	−0.743267	−	1.44174i	−0.891612	−	0.452801i	$-0.850425\pi$
$619$	−18.4923	−	35.8700i	−0.743267	−	1.44174i	0.148345	−	0.988936i	$-0.452605\pi$
$620$	0.624946	−	1.08244i	0.0250984	−	0.0434718i
$621$	−16.7183	+	18.4797i	−0.670882	+	0.741564i
$622$	8.91333			0.357392
$623$	−9.32134	−	23.0354i	−0.373452	−	0.922894i
$624$	−1.13461	−	1.14651i	−0.0454208	−	0.0458972i
$625$	13.7880	−	19.3625i	0.551519	−	0.774500i
$626$	13.7475	−	13.1082i	0.549461	−	0.523910i
$627$	14.3993	−	44.2479i	0.575054	−	1.76709i
$628$	−2.03214	+	10.5438i	−0.0810914	+	0.420742i
$629$	49.0538	+	7.05287i	1.95590	+	0.281216i
$630$	2.39831	−	1.07585i	0.0955509	−	0.0428628i
$631$	−13.7675	+	11.9296i	−0.548076	+	0.474910i	−0.884331	−	0.466861i	$-0.845385\pi$
$631$	−13.7675	+	11.9296i	−0.548076	+	0.474910i	0.336255	+	0.941771i	$0.390840\pi$
$632$	44.7672	+	23.0791i	1.78074	+	0.918036i
$633$	−7.64531	−	9.35854i	−0.303874	−	0.371968i
$634$	34.2243	−	6.59619i	1.35922	−	0.261968i
$635$	−1.36677	−	1.30321i	−0.0542384	−	0.0517162i
$636$	−0.283332	−	0.525380i	−0.0112348	−	0.0208327i
$637$	−0.441140	−	2.91443i	−0.0174786	−	0.115474i
$638$	−9.54217	+	20.8944i	−0.377778	+	0.827218i
$639$	−0.418034	+	7.19533i	−0.0165372	+	0.284643i
$640$	0.0732775	−	0.767397i	0.00289655	−	0.0303340i
$641$	5.53712	+	2.21673i	0.218703	+	0.0875555i	0.478427	−	0.878127i	$-0.341207\pi$
$641$	5.53712	+	2.21673i	0.218703	+	0.0875555i	−0.259724	+	0.965683i	$0.583631\pi$
$642$	11.6012	−	7.76397i	0.457862	−	0.306420i
$643$			22.9687i			0.905798i	0.891562	+	0.452899i	$0.149610\pi$
$643$			22.9687i			0.905798i	−0.891562	+	0.452899i	$0.850390\pi$
$644$	−2.60447	+	8.09062i	−0.102631	+	0.318815i
$645$	−2.39773	−	3.23806i	−0.0944105	−	0.127499i
$646$	1.55595	−	32.6635i	0.0612182	−	1.28513i
$647$	11.5890	−	28.9480i	0.455611	−	1.13806i	−0.505727	−	0.862693i	$-0.668776\pi$
$647$	11.5890	−	28.9480i	0.455611	−	1.13806i	0.961339	−	0.275369i	$-0.0887999\pi$
$648$	17.5817	−	21.4215i	0.690673	−	0.841517i
$649$	−9.92602	+	2.40803i	−0.389630	+	0.0945233i
$650$	−2.17240	−	0.992100i	−0.0852084	−	0.0389134i
$651$	−18.9942	+	22.9343i	−0.744443	+	0.898866i
$652$	−0.841237	+	5.85093i	−0.0329454	+	0.229140i
$653$	−23.3827	+	24.5231i	−0.915037	+	0.959663i	−0.999323	−	0.0367788i	$-0.988290\pi$
$653$	−23.3827	+	24.5231i	−0.915037	+	0.959663i	0.0842868	+	0.996442i	$0.473139\pi$
$654$	8.48537	−	9.23696i	0.331804	−	0.361194i
$655$	5.15147	−	0.245395i	0.201285	−	0.00958836i
$656$	1.47916	−	2.86917i	0.0577515	−	0.112022i
$657$	−8.27247	+	3.67410i	−0.322740	+	0.143340i
$658$	−4.04433	−	20.5727i	−0.157664	−	0.802008i
$659$	1.37540	−	9.56608i	0.0535778	−	0.372642i	−0.945338	−	0.326092i	$-0.894268\pi$
$659$	1.37540	−	9.56608i	0.0535778	−	0.372642i	0.998916	−	0.0465501i	$-0.0148227\pi$
$660$	−1.33152	+	0.638251i	−0.0518294	+	0.0248439i
$661$	−7.63731	+	5.43850i	−0.297057	+	0.211533i	−0.718861	−	0.695154i	$-0.755336\pi$
$661$	−7.63731	+	5.43850i	−0.297057	+	0.211533i	0.421804	+	0.906687i	$0.361397\pi$
$662$	9.78217	+	10.2592i	0.380195	+	0.398737i
$663$	0.0633978	+	3.41112i	0.00246217	+	0.132477i
$664$	−46.4586	+	6.67974i	−1.80294	+	0.259224i
$665$	−3.63021	−	2.83308i	−0.140773	−	0.109862i
$666$	−10.6937	+	35.0620i	−0.414372	+	1.35862i
$667$	−20.1481	−	7.64711i	−0.780139	−	0.296097i
$668$	−2.26851	−	1.30972i	−0.0877712	−	0.0506747i
$669$	−14.7641	+	29.9940i	−0.570812	+	1.15964i
$670$	−3.48103	+	2.73751i	−0.134484	+	0.105759i
$671$	27.1983	−	12.4210i	1.04998	−	0.479509i
$672$	4.30299	−	15.9629i	0.165991	−	0.615781i
$673$	7.61121	−	16.6662i	0.293390	−	0.642436i	−0.704333	−	0.709869i	$-0.748754\pi$
$673$	7.61121	−	16.6662i	0.293390	−	0.642436i	0.997724	+	0.0674339i	$0.0214812\pi$
$674$	−23.1482	−	4.46144i	−0.891634	−	0.171848i
$675$	8.16026	−	24.2143i	0.314089	−	0.932009i
$676$	−2.02501	+	8.34721i	−0.0778850	+	0.321047i
$677$	4.10628	−	11.8643i	0.157817	−	0.455982i	−0.838177	−	0.545398i	$-0.816379\pi$
$677$	4.10628	−	11.8643i	0.157817	−	0.455982i	0.995994	+	0.0894154i	$0.0284999\pi$
$678$	26.3054	+	9.96804i	1.01025	+	0.382820i
$679$	−13.2233	−	8.42892i	−0.507465	−	0.323472i
$680$	−3.12571	+	2.70845i	−0.119866	+	0.103864i
$681$	−13.9727	−	1.74462i	−0.535435	−	0.0668539i
$682$	−20.5336	+	26.1106i	−0.786271	+	0.999825i
$683$	−0.0542618	+	0.0187802i	−0.00207627	+	0.000718604i	−0.328106	−	0.944641i	$-0.606410\pi$
$683$	−0.0542618	+	0.0187802i	−0.00207627	+	0.000718604i	0.326030	+	0.945360i	$0.394289\pi$
$684$	−11.9358	−	2.42986i	−0.456378	−	0.0929080i
$685$	−3.09533	−	0.908871i	−0.118267	−	0.0347262i
$686$	−16.6418	+	13.3899i	−0.635389	+	0.511228i
$687$	−10.8100	+	10.6978i	−0.412426	+	0.408146i
$688$	17.8965	+	0.852515i	0.682297	+	0.0325018i
$689$	−0.108321	+	0.187617i	−0.00412670	+	0.00714765i
$690$	1.34924	+	2.39727i	0.0513645	+	0.0912627i
$691$	8.11783	+	14.0605i	0.308817	+	0.534886i	0.978104	−	0.208118i	$-0.0667337\pi$
$691$	8.11783	+	14.0605i	0.308817	+	0.534886i	−0.669287	+	0.743004i	$0.733400\pi$
$692$	−8.91421	+	13.8708i	−0.338868	+	0.527288i
$693$	33.8204	−	9.68416i	1.28473	−	0.367871i
$694$	1.12883	+	2.47180i	0.0428499	+	0.0938283i
$695$	−0.893344	−	3.68241i	−0.0338865	−	0.139682i
$696$	22.7895	+	7.41625i	0.863832	+	0.281112i
$697$	−6.45207	+	2.23308i	−0.244390	+	0.0845841i
$698$	−6.82252	−	17.0418i	−0.258236	−	0.645043i
$699$	−9.11883	−	6.90079i	−0.344906	−	0.261012i
$700$	−0.860631	−	8.67262i	−0.0325288	−	0.327794i
$701$	29.7859	−	19.1422i	1.12500	−	0.722992i	0.160487	−	0.987038i	$-0.448693\pi$
$701$	29.7859	−	19.1422i	1.12500	−	0.722992i	0.964510	+	0.264046i	$0.0850571\pi$
$702$	−2.50068	−	0.338763i	−0.0943820	−	0.0127858i
$703$	63.0564	−	12.1531i	2.37822	−	0.458364i
$704$	8.96975	−	36.9738i	0.338060	−	1.39350i
$705$	2.90867	+	1.79380i	0.109547	+	0.0675585i
$706$	−14.9007	+	17.1963i	−0.560794	+	0.647191i
$707$	13.6405	−	23.8299i	0.513003	−	0.896214i
$708$	0.921283	+	2.50997i	0.0346239	+	0.0943303i
$709$	21.5762	+	15.3643i	0.810310	+	0.577019i	0.908373	−	0.418161i	$-0.137325\pi$
$709$	21.5762	+	15.3643i	0.810310	+	0.577019i	−0.0980631	+	0.995180i	$0.531265\pi$
$710$	0.738633	+	0.295704i	0.0277204	+	0.0110976i
$711$	48.2782	−	8.78350i	1.81057	−	0.329407i
$712$	−25.0463	+	14.4605i	−0.938650	+	0.541930i
$713$	−25.7079	−	17.6160i	−0.962768	−	0.659723i
$714$	21.1295	−	12.8356i	0.790753	−	0.480359i
$715$	0.450838	+	0.289736i	0.0168604	+	0.0108355i
$716$	−6.80589	−	8.65439i	−0.254348	−	0.323430i
$717$	3.02473	+	5.02113i	0.112960	+	0.187517i
$718$	1.42181	+	1.49115i	0.0530613	+	0.0556491i
$719$	−4.01161	−	42.0114i	−0.149608	−	1.56676i	−0.689034	−	0.724729i	$-0.741965\pi$
$719$	−4.01161	−	42.0114i	−0.149608	−	1.56676i	0.539426	−	0.842033i	$-0.318641\pi$
$720$	−1.01321	−	1.61335i	−0.0377602	−	0.0601260i
$721$	−15.2349	−	14.4189i	−0.567377	−	0.536987i
$722$	−5.76420	−	19.6311i	−0.214521	−	0.730593i
$723$	6.33458	−	1.98859i	0.235586	−	0.0739563i
$724$	−2.45542	+	0.116966i	−0.0912549	+	0.00434700i
$725$	22.0725	−	1.05144i	0.819751	−	0.0390496i
$726$	16.4756	−	5.17211i	0.611467	−	0.191955i
$727$	2.39096	+	8.14286i	0.0886758	+	0.302002i	0.991874	−	0.127221i	$-0.0406057\pi$
$727$	2.39096	+	8.14286i	0.0886758	+	0.302002i	−0.903199	+	0.429223i	$0.858788\pi$
$728$	−3.28796	+	0.978703i	−0.121860	+	0.0362731i
$729$	0.844923	−	26.9868i	0.0312934	−	0.999510i
$730$	0.0949806	+	0.994682i	0.00351539	+	0.0368148i
$731$	−26.1512	−	27.4265i	−0.967235	−	1.01441i
$732$	−4.03879	−	6.70450i	−0.149278	−	0.247806i
$733$	−12.7628	−	16.2292i	−0.471404	−	0.599439i	0.490967	−	0.871178i	$-0.336644\pi$
$733$	−12.7628	−	16.2292i	−0.471404	−	0.599439i	−0.962371	+	0.271739i	$0.912401\pi$
$734$	25.1538	+	16.1653i	0.928442	+	0.596674i
$735$	0.240696	−	3.47309i	0.00887821	−	0.128107i
$736$	17.0457	+	2.96725i	0.628313	+	0.109374i
$737$	−51.3286	+	29.6346i	−1.89071	+	1.09160i
$738$	−0.903956	−	4.96856i	−0.0332751	−	0.182895i
$739$	0.314436	+	0.125881i	0.0115667	+	0.00463062i	0.377439	−	0.926035i	$-0.376805\pi$
$739$	0.314436	+	0.125881i	0.0115667	+	0.00463062i	−0.365872	+	0.930665i	$0.619229\pi$
$740$	−1.65993	−	1.18203i	−0.0610203	−	0.0434523i
$741$	1.52330	+	4.15011i	0.0559597	+	0.152458i
$742$	1.56987	−	0.00582720i	0.0576317	−	0.000213923i
$743$	−21.6070	+	24.9358i	−0.792684	+	0.914807i	−0.997956	−	0.0638984i	$-0.979647\pi$
$743$	−21.6070	+	24.9358i	−0.792684	+	0.914807i	0.205272	+	0.978705i	$0.434192\pi$
$744$	29.4985	+	18.1920i	1.08147	+	0.666952i
$745$	−0.500958	+	2.06498i	−0.0183537	+	0.0756549i
$746$	10.0979	−	1.94622i	0.369712	−	0.0712561i
$747$	−31.9003	+	32.7647i	−1.16717	+	1.19880i
$748$	−11.6833	+	7.50837i	−0.427182	+	0.274533i
$749$	−1.82577	−	18.3984i	−0.0667123	−	0.672262i
$750$	−4.53619	−	3.43282i	−0.165638	−	0.125349i
$751$	12.1039	+	30.2340i	0.441676	+	1.10325i	0.967547	+	0.252690i	$0.0813152\pi$
$751$	12.1039	+	30.2340i	0.441676	+	1.10325i	−0.525871	+	0.850564i	$0.676261\pi$
$752$	−14.3603	+	4.97014i	−0.523666	+	0.181243i
$753$	1.27483	+	0.414862i	0.0464575	+	0.0151184i
$754$	−0.514502	−	2.12081i	−0.0187371	−	0.0772352i
$755$	−1.53372	−	3.35837i	−0.0558176	−	0.122224i
$756$	−3.52380	−	8.50811i	−0.128159	−	0.309437i
$757$	−25.1349	+	39.1107i	−0.913543	+	1.42150i	−0.00672556	+	0.999977i	$0.502141\pi$
$757$	−25.1349	+	39.1107i	−0.913543	+	1.42150i	−0.906818	+	0.421523i	$0.861496\pi$
$758$	17.2173	+	29.8212i	0.625360	+	1.08315i
$759$	13.3078	+	34.3275i	0.483042	+	1.24601i
$760$	−2.67963	+	4.64125i	−0.0972003	+	0.168356i
$761$	0.445653	+	0.0212291i	0.0161549	+	0.000769554i	0.0556578	−	0.998450i	$-0.482274\pi$
$761$	0.445653	+	0.0212291i	0.0161549	+	0.000769554i	−0.0395029	+	0.999219i	$0.512577\pi$
$762$	9.33826	−	9.24134i	0.338289	−	0.334778i
$763$	−5.49165	−	15.6785i	−0.198811	−	0.567601i
$764$	2.15068	+	0.631496i	0.0778088	+	0.0228467i
$765$	−0.803833	+	3.94855i	−0.0290626	+	0.142760i
$766$	31.2021	−	10.7991i	1.12738	−	0.390189i
$767$	0.599856	−	0.762780i	0.0216596	−	0.0275424i
$768$	−24.1852	−	3.01974i	−0.872709	−	0.108966i
$769$	18.0063	−	15.6025i	0.649322	−	0.562641i	−0.266694	−	0.963781i	$-0.585931\pi$
$769$	18.0063	−	15.6025i	0.649322	−	0.562641i	0.916017	+	0.401140i	$0.131386\pi$
$770$	0.170382	−	3.87971i	0.00614014	−	0.139815i
$771$	36.5654	+	13.8559i	1.31687	+	0.499007i
$772$	0.172114	−	0.497290i	0.00619451	−	0.0178979i
$773$	−4.22175	+	17.4023i	−0.151846	+	0.625917i	0.844118	+	0.536158i	$0.180125\pi$
$773$	−4.22175	+	17.4023i	−0.151846	+	0.625917i	−0.995964	+	0.0897592i	$0.971390\pi$
$774$	23.0012	−	16.0201i	0.826759	−	0.575829i
$775$	31.3778	+	6.04758i	1.12712	+	0.217235i
$776$	−7.58145	+	16.6011i	−0.272158	+	0.595943i
$777$	34.2784	+	34.3817i	1.22973	+	1.23344i
$778$	14.5454	−	6.64268i	0.521479	−	0.238152i
$779$	−6.95428	+	5.46891i	−0.249163	+	0.195944i
$780$	0.0619546	−	0.125864i	0.00221833	−	0.00450666i
$781$	9.22173	+	5.32417i	0.329979	+	0.190514i
$782$	15.3859	+	20.8013i	0.550197	+	0.743854i
$783$	22.0023	−	7.81644i	0.786296	−	0.279337i
$784$	11.2832	+	10.5997i	0.402972	+	0.378561i
$785$	4.55607	−	0.655064i	0.162613	−	0.0233802i
$786$	0.666712	+	35.8724i	0.0237808	+	1.27953i
$787$	17.0516	+	17.8832i	0.607824	+	0.637468i	0.953681	−	0.300819i	$-0.0972602\pi$
$787$	17.0516	+	17.8832i	0.607824	+	0.637468i	−0.345857	+	0.938287i	$0.612412\pi$
$788$	7.61403	−	5.42193i	0.271239	−	0.193148i
$789$	−25.0279	+	11.9969i	−0.891018	+	0.427100i
$790$	0.770902	−	5.36174i	0.0274274	−	0.190762i
$791$	28.0670	−	24.5032i	0.997946	−	0.871232i
$792$	−16.6188	−	37.4184i	−0.590525	−	1.32961i
$793$	−1.30170	+	2.52494i	−0.0462247	+	0.0896634i
$794$	−7.18159	+	0.342101i	−0.254865	+	0.0121407i
$795$	−0.173102	+	0.188434i	−0.00613928	+	0.00668306i
$796$	−2.20906	+	2.31680i	−0.0782982	+	0.0821168i
$797$	0.942859	−	6.55773i	0.0333978	−	0.232287i	−0.966285	−	0.257475i	$-0.917109\pi$
$797$	0.942859	−	6.55773i	0.0333978	−	0.232287i	0.999683	+	0.0251884i	$0.00801856\pi$
$798$	20.4337	−	24.6723i	0.723345	−	0.873391i
$799$	29.2367	+	13.3520i	1.03432	+	0.472359i
$800$	−17.2411	+	4.18264i	−0.609564	+	0.147879i
$801$	−10.7447	+	26.0481i	−0.379646	+	0.920363i
$802$	−2.76746	+	6.91278i	−0.0977224	+	0.244099i
$803$	−0.636312	+	13.3578i	−0.0224550	+	0.471388i
$804$	9.23281	+	12.4686i	0.325616	+	0.439735i
$805$	3.64257	−	0.0792833i	0.128384	−	0.00279437i
$806$		−	3.15587i		−	0.111161i
$807$	38.9309	−	26.0541i	1.37043	−	0.917149i
$808$	−29.6669	−	11.8768i	−1.04368	−	0.417826i
$809$	4.77487	−	50.0047i	0.167875	−	1.75807i	−0.383246	−	0.923646i	$-0.625194\pi$
$809$	4.77487	−	50.0047i	0.167875	−	1.75807i	0.551121	−	0.834425i	$-0.314200\pi$
$810$	−2.79563	−	1.03338i	−0.0982284	−	0.0363093i
$811$	−20.7846	+	45.5119i	−0.729846	+	1.59814i	0.0697240	+	0.997566i	$0.477788\pi$
$811$	−20.7846	+	45.5119i	−0.729846	+	1.59814i	−0.799570	+	0.600573i	$0.794939\pi$
$812$	5.74328	−	5.51705i	0.201550	−	0.193611i
$813$	11.3347	+	21.0179i	0.397526	+	0.737130i
$814$	39.1949	+	37.3722i	1.37378	+	1.30990i
$815$	2.48809	−	0.479540i	0.0871539	−	0.0167975i
$816$	−11.3363	−	13.8766i	−0.396849	−	0.485778i
$817$	−43.6462	−	22.5012i	−1.52699	−	0.787217i
$818$	−11.4778	+	9.94561i	−0.401313	+	0.347740i
$819$	−1.95698	+	2.70946i	−0.0683823	+	0.0946764i
$820$	0.277886	+	0.0399540i	0.00970420	+	0.00139525i
$821$	5.21575	−	27.0619i	0.182031	−	0.944465i	−0.769903	−	0.638161i	$-0.779695\pi$
$821$	5.21575	−	27.0619i	0.182031	−	0.944465i	0.951934	−	0.306304i	$-0.0990925\pi$
$822$	6.94496	−	21.3412i	0.242233	−	0.744361i
$823$	−17.5335	+	16.7181i	−0.611179	+	0.582758i	−0.931135	−	0.364674i	$-0.881180\pi$
$823$	−17.5335	+	16.7181i	−0.611179	+	0.582758i	0.319956	+	0.947432i	$0.396332\pi$
$824$	−14.1608	+	19.8861i	−0.493315	+	0.692764i
$825$	−26.5545	−	26.8330i	−0.924508	−	0.934204i
$826$	−6.96396	−	0.974897i	−0.242307	−	0.0339210i
$827$	−39.7940			−1.38377			−0.691886	−	0.722006i	$-0.743220\pi$
$827$	−39.7940			−1.38377			−0.691886	+	0.722006i	$0.743220\pi$
$828$	8.53229	−	4.48129i	0.296517	−	0.155736i
$829$	8.19746	−	14.1984i	0.284710	−	0.493131i	−0.687829	−	0.725873i	$-0.741436\pi$
$829$	8.19746	−	14.1984i	0.284710	−	0.493131i	0.972539	+	0.232741i	$0.0747695\pi$
$830$	2.31313	+	4.48685i	0.0802899	+	0.155741i
$831$	6.14346	−	22.4584i	0.213114	−	0.779075i
$832$	1.50158	+	3.28800i	0.0520579	+	0.113991i
$833$	−1.80079	−	32.6946i	−0.0623938	−	1.13280i
$834$	25.7875	−	5.46900i	0.892948	−	0.189376i
$835$	−0.212504	+	1.10257i	−0.00735399	+	0.0381561i
$836$	−11.1242	+	14.1456i	−0.384740	+	0.489237i
$837$	33.5856	−	3.48349i	1.16089	−	0.120407i
$838$	11.6478	+	4.03134i	0.402367	+	0.139260i
$839$	−10.0737	+	6.47396i	−0.347782	+	0.223506i	−0.702856	−	0.711332i	$-0.748092\pi$
$839$	−10.0737	+	6.47396i	−0.347782	+	0.223506i	0.355074	+	0.934838i	$0.384456\pi$
$840$	−4.04188	+	0.282969i	−0.139458	+	0.00976336i
$841$	−5.76772	−	6.65631i	−0.198887	−	0.229528i
$842$	−16.5826	−	15.8115i	−0.571476	−	0.544901i
$843$	40.7100	+	1.18159i	1.40213	+	0.0406960i
$844$	1.52856	+	4.41649i	0.0526153	+	0.152022i
$845$	3.66527	−	0.349991i	0.126089	−	0.0120401i
$846$	−13.0610	+	19.8646i	−0.449047	+	0.682958i
$847$	4.24502	−	22.4739i	0.145861	−	0.772211i
$848$	−0.161928	−	1.12623i	−0.00556063	−	0.0386750i
$849$	20.2338	−	13.5413i	0.694423	−	0.464736i
$850$	−22.9755	−	13.2649i	−0.788053	−	0.454983i
$851$	−32.5746	+	38.9935i	−1.11664	+	1.33668i
$852$	1.11062	−	2.55660i	0.0380492	−	0.0875878i
$853$	20.1805	+	12.9692i	0.690966	+	0.444057i	0.838429	−	0.545010i	$-0.183474\pi$
$853$	20.1805	+	12.9692i	0.690966	+	0.444057i	−0.147463	+	0.989068i	$0.547111\pi$
$854$	20.5581	−	1.05580i	0.703482	−	0.0361286i
$855$	0.689126	+	5.17574i	0.0235676	+	0.177007i
$856$	−20.9111	+	5.07299i	−0.714728	+	0.173391i
$857$	−41.9604	+	29.8798i	−1.43334	+	1.02068i	−0.440950	+	0.897532i	$0.645358\pi$
$857$	−41.9604	+	29.8798i	−1.43334	+	1.02068i	−0.992389	+	0.123144i	$0.960702\pi$
$858$	−2.10579	+	3.07661i	−0.0718906	+	0.105034i
$859$	−1.10325	+	0.441674i	−0.0376423	+	0.0150697i	−0.390407	−	0.920642i	$-0.627666\pi$
$859$	−1.10325	+	0.441674i	−0.0376423	+	0.0150697i	0.352765	+	0.935712i	$0.385242\pi$
$860$	0.439007	+	1.49512i	0.0149700	+	0.0509832i
$861$	−6.36801	−	2.04620i	−0.217021	−	0.0697342i
$862$	−23.5565	−	36.6547i	−0.802339	−	1.24846i
$863$	−10.8328	+	21.0126i	−0.368752	+	0.715279i	−0.998085	−	0.0618567i	$-0.980298\pi$
$863$	−10.8328	+	21.0126i	−0.368752	+	0.715279i	0.629333	+	0.777136i	$0.283328\pi$
$864$	−16.1578	+	9.50515i	−0.549700	+	0.323372i
$865$	6.86869	+	1.66633i	0.233543	+	0.0566568i
$866$	−24.5292	+	9.82000i	−0.833535	+	0.333697i
$867$	−0.647122	+	8.42974i	−0.0219774	+	0.286289i
$868$	9.95221	−	5.79527i	0.337800	−	0.196704i
$869$	20.4248	−	69.5606i	0.692866	−	2.35968i
$870$	−0.0478967	−	2.57708i	−0.00162385	−	0.0873712i
$871$	2.09282	−	5.22761i	0.0709124	−	0.177131i
$872$	−17.1848	+	8.85938i	−0.581951	+	0.300016i
$873$	4.01151	+	17.3225i	0.135769	+	0.586278i
$874$	27.6561	+	18.9509i	0.935482	+	0.641025i
$875$	−6.84191	+	3.15534i	−0.231299	+	0.106670i
$876$	3.49299	−	0.231516i	0.118017	−	0.00782219i
$877$	−4.19781	+	3.30119i	−0.141750	+	0.111473i	−0.686516	−	0.727115i	$-0.740861\pi$
$877$	−4.19781	+	3.30119i	−0.141750	+	0.111473i	0.544766	+	0.838588i	$0.316618\pi$
$878$	−0.525866	+	5.50711i	−0.0177471	+	0.185856i
$879$	−0.635019	+	3.65948i	−0.0214187	+	0.123431i
$880$	−2.80189	+	0.267548i	−0.0944518	+	0.00901906i
$881$	8.35655	−	9.64397i	0.281539	−	0.324914i	−0.597312	−	0.802009i	$-0.703765\pi$
$881$	8.35655	−	9.64397i	0.281539	−	0.324914i	0.878852	+	0.477095i	$0.158310\pi$
$882$	24.1030	+	2.37477i	0.811590	+	0.0799626i
$883$	−29.0280	+	8.52340i	−0.976871	+	0.286835i	−0.730932	−	0.682450i	$-0.760914\pi$
$883$	−29.0280	+	8.52340i	−0.976871	+	0.286835i	−0.245939	+	0.969285i	$0.579096\pi$
$884$	0.431548	−	1.24688i	0.0145145	−	0.0419370i
$885$	0.887592	−	0.725105i	0.0298361	−	0.0243741i
$886$	0.300238	+	6.30277i	0.0100867	+	0.211746i
$887$	51.6192	+	17.8656i	1.73320	+	0.599867i	0.997036	−	0.0769334i	$-0.0245129\pi$
$887$	51.6192	+	17.8656i	1.73320	+	0.599867i	0.736166	+	0.676801i	$0.236634\pi$
$888$	34.0970	−	45.0564i	1.14422	−	1.51199i
$889$	−4.96427	−	16.6775i	−0.166496	−	0.559346i
$890$	2.35072	+	2.03691i	0.0787964	+	0.0682774i
$891$	−35.0665	−	19.0144i	−1.17477	−	0.637006i
$892$	9.35720	−	8.92207i	0.313302	−	0.298733i
$893$	41.4596	+	3.95891i	1.38739	+	0.132480i
$894$	−14.2586	−	3.90040i	−0.476877	−	0.130449i
$895$	−2.55159	+	3.97035i	−0.0852903	+	0.132714i
$896$	4.09864	−	5.80119i	0.136926	−	0.193804i
$897$	−3.00985	−	1.78203i	−0.100496	−	0.0595003i
$898$	3.46157	+	5.99561i	0.115514	+	0.200076i
$899$	13.3804	+	25.9543i	0.446261	+	0.865626i
$900$	−6.18943	+	7.70372i	−0.206314	+	0.256791i
$901$	−1.39596	+	1.96036i	−0.0465063	+	0.0653089i
$902$	−7.15885	−	2.10203i	−0.238364	−	0.0699899i
$903$	−4.35197	−	36.8690i	−0.144825	−	1.22692i
$904$	−32.7707	−	28.3960i	−1.08994	−	0.944436i
$905$	0.391637	+	0.978262i	0.0130185	+	0.0325185i
$906$	23.6634	−	9.98749i	0.786163	−	0.331812i
$907$	1.91365	+	9.92895i	0.0635417	+	0.329685i	0.999764	−	0.0217227i	$-0.00691509\pi$
$907$	1.91365	+	9.92895i	0.0635417	+	0.329685i	−0.936222	+	0.351408i	$0.885703\pi$
$908$	4.84039	+	2.49540i	0.160634	+	0.0828126i
$909$	−29.9628	+	8.45936i	−0.993805	+	0.280579i
$910$	0.215128	+	0.299744i	0.00713143	+	0.00993642i
$911$	−11.3657	+	3.33728i	−0.376563	+	0.110569i	−0.464537	−	0.885554i	$-0.653779\pi$
$911$	−11.3657	+	3.33728i	−0.376563	+	0.110569i	0.0879735	+	0.996123i	$0.471961\pi$
$912$	−19.7625	−	12.1877i	−0.654403	−	0.403576i
$913$	22.0969	+	63.8447i	0.731300	+	2.11295i
$914$	−3.61750	−	5.08006i	−0.119656	−	0.168034i
$915$	−2.14967	+	2.57606i	−0.0710658	+	0.0851618i
$916$	5.35022	−	2.44336i	0.176776	−	0.0807310i
$917$	42.3178	+	21.6179i	1.39746	+	0.713885i
$918$	−27.2956	−	6.38673i	−0.900890	−	0.210794i
$919$	9.91174	−	5.72254i	0.326958	−	0.188769i	−0.327532	−	0.944840i	$-0.606217\pi$
$919$	9.91174	−	5.72254i	0.326958	−	0.188769i	0.654490	+	0.756071i	$0.272883\pi$
$920$	−0.679119	−	4.18559i	−0.0223899	−	0.137995i
$921$	−5.67130	−	49.6277i	−0.186876	−	1.63529i
$922$	0.465920	−	9.78087i	0.0153443	−	0.322116i
$923$	−1.00137	+	0.143975i	−0.0329604	+	0.00473899i
$924$	−13.5692	−	0.991013i	−0.446395	−	0.0326019i
$925$	14.6780	−	49.9885i	0.482608	−	1.64361i
$926$	0.602350	+	6.30810i	0.0197945	+	0.207297i
$927$	0.883811	+	23.7685i	0.0290282	+	0.780659i
$928$	−12.7432	−	10.0214i	−0.418317	−	0.328968i
$929$	−13.1283	+	13.7685i	−0.430724	+	0.451731i	−0.902949	−	0.429747i	$-0.858603\pi$
$929$	−13.1283	+	13.7685i	−0.430724	+	0.451731i	0.472225	+	0.881478i	$0.343451\pi$
$930$	0.811298	−	3.63801i	0.0266035	−	0.119295i
$931$	−16.0614	−	39.2720i	−0.526392	−	1.28709i
$932$	2.39105	+	3.72055i	0.0783215	+	0.121871i
$933$	−12.7715	+	4.00929i	−0.418120	+	0.131258i
$934$	−9.71999	−	2.35804i	−0.318048	−	0.0771575i
$935$	4.67958	+	3.68006i	0.153039	+	0.120351i
$936$	3.43866	+	1.81841i	0.112396	+	0.0594365i
$937$	20.4493	+	9.33889i	0.668050	+	0.305088i	0.720419	−	0.693539i	$-0.243950\pi$
$937$	20.4493	+	9.33889i	0.668050	+	0.305088i	−0.0523683	+	0.998628i	$0.516677\pi$
$938$	−40.3672	+	5.95694i	−1.31804	+	0.194501i
$939$	−13.8019	+	24.9659i	−0.450410	+	0.814731i
$940$	−0.816969	−	1.03886i	−0.0266466	−	0.0338839i
$941$	29.4563	−	15.1858i	0.960247	−	0.495042i	0.0945006	−	0.995525i	$-0.469875\pi$
$941$	29.4563	−	15.1858i	0.960247	−	0.495042i	0.865746	+	0.500483i	$0.166844\pi$
$942$	3.63569	+	31.8147i	0.118457	+	1.03658i
$943$	1.52725	−	6.83131i	0.0497341	−	0.222458i
$944$			5.09655i			0.165879i
$945$	−2.95249	+	2.62031i	−0.0960446	+	0.0852387i
$946$	−5.89355	−	40.9905i	−0.191616	−	1.33272i
$947$	35.1443	+	25.0262i	1.14204	+	0.813241i	0.984692	−	0.174302i	$-0.0557670\pi$
$947$	35.1443	+	25.0262i	1.14204	+	0.813241i	0.157346	+	0.987544i	$0.449706\pi$
$948$	−18.6982	−	3.24464i	−0.607289	−	0.105381i
$949$	−0.736976	−	1.03494i	−0.0239232	−	0.0335955i
$950$	−33.7557	−	6.50588i	−1.09518	−	0.211079i
$951$	−46.0713	+	24.8457i	−1.49396	+	0.805678i
$952$	−37.3928	+	7.35093i	−1.21191	+	0.238245i
$953$	10.8893	+	12.5669i	0.352739	+	0.407083i	0.904194	−	0.427122i	$-0.140473\pi$
$953$	10.8893	+	12.5669i	0.352739	+	0.407083i	−0.551455	+	0.834205i	$0.685927\pi$
$954$	−1.27542	−	1.24177i	−0.0412931	−	0.0402037i
$955$	−0.0457186	−	0.959752i	−0.00147942	−	0.0310568i
$956$	−0.429032	−	2.22603i	−0.0138759	−	0.0719949i
$957$	4.27402	−	34.2308i	0.138159	−	1.10652i
$958$	28.3869	+	4.08142i	0.917138	+	0.131865i
$959$	−20.5920	−	21.4364i	−0.664952	−	0.692218i
$960$	0.885718	+	4.17635i	0.0285864	+	0.134791i
$961$	2.64682	+	10.9104i	0.0853814	+	0.351947i
$962$	−5.12193	−	0.489085i	−0.165138	−	0.0157687i
$963$	−13.1305	+	16.3429i	−0.423123	+	0.526643i
$964$	−2.56481	−	0.122177i	−0.0826070	−	0.00393505i
$965$	−0.225577			−0.00726158
$966$	−0.183866	+	25.3461i	−0.00591579	+	0.815499i
$967$	−4.73146			−0.152154			−0.0760768	−	0.997102i	$-0.524239\pi$
$967$	−4.73146			−0.152154			−0.0760768	+	0.997102i	$0.524239\pi$
$968$	−26.5880	−	1.26654i	−0.854571	−	0.0407082i
$969$	12.4629	+	47.5018i	0.400365	+	1.52598i
$970$	1.95393	+	0.186578i	0.0627370	+	0.00599066i
$971$	9.42960	+	38.8694i	0.302610	+	1.24738i	0.896577	+	0.442887i	$0.146046\pi$
$971$	9.42960	+	38.8694i	0.302610	+	1.24738i	−0.593967	+	0.804490i	$0.702439\pi$
$972$	−3.90301	+	9.68513i	−0.125189	+	0.310651i
$973$	9.71203	−	33.5362i	0.311354	−	1.07512i
$974$	−6.16394	−	0.886241i	−0.197506	−	0.0283970i
$975$	3.55898	+	0.444370i	0.113978	+	0.0142312i
$976$	−2.82357	−	14.6501i	−0.0903802	−	0.468937i
$977$	1.63392	+	34.3001i	0.0522736	+	1.09736i	0.860815	+	0.508919i	$0.169955\pi$
$977$	1.63392	+	34.3001i	0.0522736	+	1.09736i	−0.808541	+	0.588440i	$0.799742\pi$
$978$	2.83250	+	17.3987i	0.0905733	+	0.556350i
$979$	27.2612	+	31.4611i	0.871272	+	1.00550i
$980$	−0.550210	+	1.22885i	−0.0175758	+	0.0392543i
$981$	−8.00342	+	17.0520i	−0.255530	+	0.544428i
$982$	20.1957	+	3.89239i	0.644469	+	0.124211i
$983$	−31.1939	−	43.8057i	−0.994930	−	1.39718i	−0.916396	−	0.400273i	$-0.868915\pi$
$983$	−31.1939	−	43.8057i	−0.994930	−	1.39718i	−0.0785344	−	0.996911i	$-0.525024\pi$
$984$	−1.33093	+	7.66985i	−0.0424284	+	0.244506i
$985$	−3.26387	−	2.32419i	−0.103995	−	0.0740548i
$986$	−3.45009	−	23.9959i	−0.109873	−	0.764185i
$987$	15.0487	+	27.6585i	0.479006	+	0.880380i
$988$		−	1.70972i		−	0.0543934i
$989$	38.0116	−	8.04030i	1.20870	−	0.255667i
$990$	−3.21843	+	3.00529i	−0.102288	+	0.0955144i
$991$	−8.84524	+	4.56004i	−0.280978	+	0.144854i	−0.592956	−	0.805235i	$-0.702039\pi$
$991$	−8.84524	+	4.56004i	−0.280978	+	0.144854i	0.311977	+	0.950090i	$0.399009\pi$
$992$	−14.4920	−	18.4280i	−0.460121	−	0.585091i
$993$	−18.6311	−	10.2999i	−0.591240	−	0.326857i
$994$	4.55305	+	5.74565i	0.144414	+	0.182241i
$995$	1.24823	+	0.570045i	0.0395714	+	0.0180717i
$996$	15.9478	−	7.64442i	0.505327	−	0.242223i
$997$	−13.6800	−	10.7581i	−0.433249	−	0.340711i	0.377597	−	0.925970i	$-0.376750\pi$
$997$	−13.6800	−	10.7581i	−0.433249	−	0.340711i	−0.810846	+	0.585259i	$0.800993\pi$
$998$	47.5573	+	11.5373i	1.50540	+	0.365206i
$999$	−0.448694	−	55.0487i	−0.0141960	−	1.74166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bc.a.389.19	yes	1200
3.2	odd	2	inner	483.2.bc.a.389.42	yes	1200
7.2	even	3	inner	483.2.bc.a.44.42	yes	1200
21.2	odd	6	inner	483.2.bc.a.44.19	yes	1200
23.11	odd	22	inner	483.2.bc.a.11.19	✓	1200
69.11	even	22	inner	483.2.bc.a.11.42	yes	1200
161.149	odd	66	inner	483.2.bc.a.149.42	yes	1200
483.149	even	66	inner	483.2.bc.a.149.19	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bc.a.11.19	✓	1200	23.11	odd	22	inner
483.2.bc.a.11.42	yes	1200	69.11	even	22	inner
483.2.bc.a.44.19	yes	1200	21.2	odd	6	inner
483.2.bc.a.44.42	yes	1200	7.2	even	3	inner
483.2.bc.a.149.19	yes	1200	483.149	even	66	inner
483.2.bc.a.149.42	yes	1200	161.149	odd	66	inner
483.2.bc.a.389.19	yes	1200	1.1	even	1	trivial
483.2.bc.a.389.42	yes	1200	3.2	odd	2	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15201 - 0.0548771i) q^{2} +(1.67535 - 0.439554i) q^{3} +(-0.666821 - 0.0636737i) q^{4} +(0.0676965 + 0.279049i) q^{5} +(-1.95414 + 0.414434i) q^{6} +(-0.735966 + 2.54133i) q^{7} +(3.04785 + 0.438215i) q^{8} +(2.61358 - 1.47281i) q^{9} +(-0.0626739 - 0.325183i) q^{10} +(-0.210893 - 4.42719i) q^{11} +(-1.14515 + 0.186429i) q^{12} +(0.275755 + 0.318239i) q^{13} +(0.987304 - 2.88726i) q^{14} +(0.236072 + 0.437748i) q^{15} +(-2.17162 - 0.418546i) q^{16} +(2.71335 + 3.81037i) q^{17} +(-3.09171 + 1.55327i) q^{18} +(4.93743 + 3.51593i) q^{19} +(-0.0273734 - 0.190386i) q^{20} +(-0.115947 + 4.58111i) q^{21} +5.11176i q^{22} +(-4.78550 + 0.314622i) q^{23} +(5.29883 - 0.605534i) q^{24} +(4.37089 - 2.25335i) q^{25} +(-0.300210 - 0.381748i) q^{26} +(3.73128 - 3.61629i) q^{27} +(0.652574 - 1.64775i) q^{28} +(4.08752 + 1.86671i) q^{29} +(-0.247936 - 0.517246i) q^{30} +(5.10794 + 4.01693i) q^{31} +(-3.50603 - 0.850553i) q^{32} +(-2.29931 - 7.32439i) q^{33} +(-2.91672 - 4.53850i) q^{34} +(-0.758977 - 0.0333314i) q^{35} +(-1.83657 + 0.815687i) q^{36} +(7.31103 - 7.66759i) q^{37} +(-5.49504 - 4.32135i) q^{38} +(0.601869 + 0.411951i) q^{39} +(0.0840456 + 0.880165i) q^{40} +(-0.411214 + 1.40047i) q^{41} +(0.384971 - 5.27113i) q^{42} +(-8.01887 + 1.15294i) q^{43} +(-0.141268 + 2.96557i) q^{44} +(0.587917 + 0.629613i) q^{45} +(5.53022 - 0.0998337i) q^{46} +(5.95056 - 3.43556i) q^{47} +(-3.82219 + 0.253336i) q^{48} +(-5.91671 - 3.74066i) q^{49} +(-5.15898 + 2.35603i) q^{50} +(6.22068 + 5.19103i) q^{51} +(-0.163616 - 0.229767i) q^{52} +(0.168270 + 0.486183i) q^{53} +(-4.49694 + 3.96125i) q^{54} +(1.22113 - 0.358555i) q^{55} +(-3.35677 + 7.42309i) q^{56} +(9.81735 + 3.72013i) q^{57} +(-4.60644 - 2.37478i) q^{58} +(-0.436125 - 2.26283i) q^{59} +(-0.129545 - 0.306931i) q^{60} +(2.50729 + 6.26290i) q^{61} +(-5.66398 - 4.90787i) q^{62} +(1.81939 + 7.72592i) q^{63} +(8.23632 + 2.41840i) q^{64} +(-0.0701364 + 0.0984928i) q^{65} +(2.24690 + 8.56398i) q^{66} +(-6.12757 - 11.8858i) q^{67} +(-1.56670 - 2.71361i) q^{68} +(-7.87909 + 2.63059i) q^{69} +(0.872522 + 0.0800487i) q^{70} +(-1.29888 + 2.02110i) q^{71} +(8.61123 - 3.34361i) q^{72} +(-3.00356 - 0.286805i) q^{73} +(-8.84318 + 8.43196i) q^{74} +(6.33230 - 5.69639i) q^{75} +(-3.06851 - 2.65888i) q^{76} +(11.4062 + 2.72232i) q^{77} +(-0.670755 - 0.507602i) q^{78} +(15.4573 + 5.34982i) q^{79} +(-0.0302165 - 0.634322i) q^{80} +(4.66164 - 7.69864i) q^{81} +(0.550578 - 1.59079i) q^{82} +(-14.6256 + 4.29447i) q^{83} +(0.369012 - 3.04740i) q^{84} +(-0.879595 + 1.01511i) q^{85} +(9.30111 - 0.888148i) q^{86} +(7.66854 + 1.33070i) q^{87} +(1.29729 - 13.5859i) q^{88} +(-7.38291 + 5.80598i) q^{89} +(-0.642737 - 0.757586i) q^{90} +(-1.01170 + 0.466572i) q^{91} +(3.21111 + 0.0949141i) q^{92} +(10.3232 + 4.48454i) q^{93} +(-7.04365 + 3.63126i) q^{94} +(-0.646869 + 1.61580i) q^{95} +(-6.24768 + 0.116117i) q^{96} +(-1.66982 + 5.68689i) q^{97} +(6.61085 + 4.63399i) q^{98} +(-7.07162 - 11.2602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) \) 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more