LMFDB - Embedded newform 260.2.o.a.27.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.19
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0221303 - 1.41404i) q^{2} +(-0.798638 - 0.798638i) q^{3} +(-1.99902 - 0.0625863i) q^{4} +(-1.57330 - 1.58893i) q^{5} +(-1.14698 + 1.11163i) q^{6} +(-1.30625 + 1.30625i) q^{7} +(-0.132739 + 2.82531i) q^{8} -1.72435i q^{9} +O(q^{10})$	\(q+(0.0221303 - 1.41404i) q^{2} +(-0.798638 - 0.798638i) q^{3} +(-1.99902 - 0.0625863i) q^{4} +(-1.57330 - 1.58893i) q^{5} +(-1.14698 + 1.11163i) q^{6} +(-1.30625 + 1.30625i) q^{7} +(-0.132739 + 2.82531i) q^{8} -1.72435i q^{9} +(-2.28164 + 2.18955i) q^{10} +3.52160i q^{11} +(1.54651 + 1.64648i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(1.81818 + 1.87599i) q^{14} +(-0.0124834 + 2.52548i) q^{15} +(3.99217 + 0.250223i) q^{16} +(-1.96348 - 1.96348i) q^{17} +(-2.43831 - 0.0381605i) q^{18} -2.70752 q^{19} +(3.04562 + 3.27478i) q^{20} +2.08644 q^{21} +(4.97969 + 0.0779341i) q^{22} +(-4.89998 - 4.89998i) q^{23} +(2.36241 - 2.15039i) q^{24} +(-0.0494285 + 4.99976i) q^{25} +(0.984229 + 1.01553i) q^{26} +(-3.77305 + 3.77305i) q^{27} +(2.69297 - 2.52946i) q^{28} -6.90940i q^{29} +(3.57086 + 0.0735418i) q^{30} +4.15716i q^{31} +(0.442173 - 5.63955i) q^{32} +(2.81248 - 2.81248i) q^{33} +(-2.81989 + 2.73299i) q^{34} +(4.13066 + 0.0204178i) q^{35} +(-0.107921 + 3.44702i) q^{36} +(-6.10784 - 6.10784i) q^{37} +(-0.0599183 + 3.82854i) q^{38} +1.12944 q^{39} +(4.69807 - 4.23416i) q^{40} +8.91075 q^{41} +(0.0461735 - 2.95031i) q^{42} +(-7.58581 - 7.58581i) q^{43} +(0.220404 - 7.03975i) q^{44} +(-2.73989 + 2.71293i) q^{45} +(-7.03720 + 6.82033i) q^{46} +(5.48290 - 5.48290i) q^{47} +(-2.98846 - 3.38813i) q^{48} +3.58744i q^{49} +(7.06876 + 0.180540i) q^{50} +3.13622i q^{51} +(1.45778 - 1.36927i) q^{52} +(-4.55558 + 4.55558i) q^{53} +(5.25175 + 5.41874i) q^{54} +(5.59559 - 5.54055i) q^{55} +(-3.51716 - 3.86394i) q^{56} +(2.16233 + 2.16233i) q^{57} +(-9.77017 - 0.152907i) q^{58} +2.28885 q^{59} +(0.183015 - 5.04771i) q^{60} -7.76763 q^{61} +(5.87839 + 0.0919991i) q^{62} +(2.25243 + 2.25243i) q^{63} +(-7.96476 - 0.750055i) q^{64} +(2.23604 + 0.0110527i) q^{65} +(-3.91473 - 4.03921i) q^{66} +(0.898523 - 0.898523i) q^{67} +(3.80215 + 4.04792i) q^{68} +7.82662i q^{69} +(0.120284 - 5.84047i) q^{70} -14.2978i q^{71} +(4.87184 + 0.228888i) q^{72} +(3.84146 - 3.84146i) q^{73} +(-8.77190 + 8.50156i) q^{74} +(4.03247 - 3.95352i) q^{75} +(5.41239 + 0.169454i) q^{76} +(-4.60008 - 4.60008i) q^{77} +(0.0249950 - 1.59708i) q^{78} +0.766856 q^{79} +(-5.88330 - 6.73697i) q^{80} +0.853540 q^{81} +(0.197198 - 12.6002i) q^{82} +(0.727706 + 0.727706i) q^{83} +(-4.17083 - 0.130582i) q^{84} +(-0.0306909 + 6.20899i) q^{85} +(-10.8945 + 10.5588i) q^{86} +(-5.51811 + 5.51811i) q^{87} +(-9.94962 - 0.467452i) q^{88} +0.442426i q^{89} +(3.77556 + 3.93435i) q^{90} -1.84731i q^{91} +(9.48848 + 10.1018i) q^{92} +(3.32006 - 3.32006i) q^{93} +(-7.63170 - 7.87438i) q^{94} +(4.25975 + 4.30208i) q^{95} +(-4.85709 + 4.15082i) q^{96} +(5.22374 + 5.22374i) q^{97} +(5.07279 + 0.0793912i) q^{98} +6.07249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0221303	−	1.41404i	0.0156485	−	0.999878i
$2$	0.0221303	−	1.41404i	0.0156485	−	0.999878i
$3$	−0.798638	−	0.798638i	−0.461094	−	0.461094i	0.437920	−	0.899014i	$-0.355715\pi$
$3$	−0.798638	−	0.798638i	−0.461094	−	0.461094i	−0.899014	+	0.437920i	$0.855715\pi$
$4$	−1.99902	−	0.0625863i	−0.999510	−	0.0312932i
$5$	−1.57330	−	1.58893i	−0.703603	−	0.710593i
$5$	−1.57330	−	1.58893i	−0.703603	−	0.710593i
$6$	−1.14698	+	1.11163i	−0.468253	+	0.453822i
$7$	−1.30625	+	1.30625i	−0.493715	+	0.493715i	−0.909474	−	0.415760i	$-0.863516\pi$
$7$	−1.30625	+	1.30625i	−0.493715	+	0.493715i	0.415760	+	0.909474i	$0.363516\pi$
$8$	−0.132739	+	2.82531i	−0.0469301	+	0.998898i
$9$		−	1.72435i		−	0.574785i
$10$	−2.28164	+	2.18955i	−0.721517	+	0.692397i
$11$			3.52160i			1.06180i	0.847434	+	0.530901i	$0.178146\pi$
$11$			3.52160i			1.06180i	−0.847434	+	0.530901i	$0.821854\pi$
$12$	1.54651	+	1.64648i	0.446439	+	0.475297i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	1.81818	+	1.87599i	0.485928	+	0.501380i
$15$	−0.0124834	+	2.52548i	−0.00322320	+	0.652077i
$16$	3.99217	+	0.250223i	0.998041	+	0.0625557i
$17$	−1.96348	−	1.96348i	−0.476214	−	0.476214i	0.427705	−	0.903919i	$-0.359322\pi$
$17$	−1.96348	−	1.96348i	−0.476214	−	0.476214i	−0.903919	+	0.427705i	$0.859322\pi$
$18$	−2.43831	−	0.0381605i	−0.574714	−	0.00899451i
$19$	−2.70752			−0.621148			−0.310574	−	0.950549i	$-0.600521\pi$
$19$	−2.70752			−0.621148			−0.310574	+	0.950549i	$0.600521\pi$
$20$	3.04562	+	3.27478i	0.681022	+	0.732263i
$21$	2.08644			0.455298
$22$	4.97969	+	0.0779341i	1.06167	+	0.0166156i
$23$	−4.89998	−	4.89998i	−1.02172	−	1.02172i	−0.999759	−	0.0219567i	$-0.993010\pi$
$23$	−4.89998	−	4.89998i	−1.02172	−	1.02172i	−0.0219567	−	0.999759i	$-0.506990\pi$
$24$	2.36241	−	2.15039i	0.482225	−	0.438947i
$25$	−0.0494285	+	4.99976i	−0.00988571	+	0.999951i
$26$	0.984229	+	1.01553i	0.193023	+	0.199161i
$27$	−3.77305	+	3.77305i	−0.726124	+	0.726124i
$28$	2.69297	−	2.52946i	0.508923	−	0.478023i
$29$		−	6.90940i		−	1.28304i	−0.767105	−	0.641522i	$-0.778303\pi$
$29$		−	6.90940i		−	1.28304i	0.767105	−	0.641522i	$-0.221697\pi$
$30$	3.57086	+	0.0735418i	0.651947	+	0.0134268i
$31$			4.15716i			0.746647i	0.927701	+	0.373324i	$0.121782\pi$
$31$			4.15716i			0.746647i	−0.927701	+	0.373324i	$0.878218\pi$
$32$	0.442173	−	5.63955i	0.0781658	−	0.996940i
$33$	2.81248	−	2.81248i	0.489591	−	0.489591i
$34$	−2.81989	+	2.73299i	−0.483608	+	0.468703i
$35$	4.13066	+	0.0204178i	0.698210	+	0.00345123i
$36$	−0.107921	+	3.44702i	−0.0179868	+	0.574503i
$37$	−6.10784	−	6.10784i	−1.00412	−	1.00412i	−0.999991	−	0.00413068i	$-0.998685\pi$
$37$	−6.10784	−	6.10784i	−1.00412	−	1.00412i	−0.00413068	−	0.999991i	$-0.501315\pi$
$38$	−0.0599183	+	3.82854i	−0.00972003	+	0.621072i
$39$	1.12944			0.180856
$40$	4.69807	−	4.23416i	0.742831	−	0.669479i
$41$	8.91075			1.39162			0.695812	−	0.718224i	$-0.255045\pi$
$41$	8.91075			1.39162			0.695812	+	0.718224i	$0.255045\pi$
$42$	0.0461735	−	2.95031i	0.00712472	−	0.455242i
$43$	−7.58581	−	7.58581i	−1.15683	−	1.15683i	−0.985154	−	0.171671i	$-0.945083\pi$
$43$	−7.58581	−	7.58581i	−1.15683	−	1.15683i	−0.171671	−	0.985154i	$-0.554917\pi$
$44$	0.220404	−	7.03975i	0.0332271	−	1.06128i
$45$	−2.73989	+	2.71293i	−0.408438	+	0.404420i
$46$	−7.03720	+	6.82033i	−1.03758	+	1.00560i
$47$	5.48290	−	5.48290i	0.799763	−	0.799763i	−0.183295	−	0.983058i	$-0.558676\pi$
$47$	5.48290	−	5.48290i	0.799763	−	0.799763i	0.983058	+	0.183295i	$0.0586763\pi$
$48$	−2.98846	−	3.38813i	−0.431347	−	0.489035i
$49$			3.58744i			0.512492i
$50$	7.06876	+	0.180540i	0.999674	+	0.0255322i
$51$			3.13622i			0.439159i
$52$	1.45778	−	1.36927i	0.202157	−	0.189883i
$53$	−4.55558	+	4.55558i	−0.625757	+	0.625757i	−0.946998	−	0.321241i	$-0.895900\pi$
$53$	−4.55558	+	4.55558i	−0.625757	+	0.625757i	0.321241	+	0.946998i	$0.395900\pi$
$54$	5.25175	+	5.41874i	0.714672	+	0.737398i
$55$	5.59559	−	5.54055i	0.754510	−	0.747087i
$56$	−3.51716	−	3.86394i	−0.470001	−	0.516341i
$57$	2.16233	+	2.16233i	0.286408	+	0.286408i
$58$	−9.77017	−	0.152907i	−1.28289	−	0.0200777i
$59$	2.28885			0.297982			0.148991	−	0.988839i	$-0.452397\pi$
$59$	2.28885			0.297982			0.148991	+	0.988839i	$0.452397\pi$
$60$	0.183015	−	5.04771i	0.0236272	−	0.651657i
$61$	−7.76763			−0.994543			−0.497272	−	0.867595i	$-0.665665\pi$
$61$	−7.76763			−0.994543			−0.497272	+	0.867595i	$0.665665\pi$
$62$	5.87839	+	0.0919991i	0.746556	+	0.0116839i
$63$	2.25243	+	2.25243i	0.283780	+	0.283780i
$64$	−7.96476	−	0.750055i	−0.995595	−	0.0937569i
$65$	2.23604	+	0.0110527i	0.277347	+	0.00137092i
$66$	−3.91473	−	4.03921i	−0.481869	−	0.497192i
$67$	0.898523	−	0.898523i	0.109772	−	0.109772i	−0.650087	−	0.759859i	$-0.725268\pi$
$67$	0.898523	−	0.898523i	0.109772	−	0.109772i	0.759859	+	0.650087i	$0.225268\pi$
$68$	3.80215	+	4.04792i	0.461078	+	0.490883i
$69$			7.82662i			0.942214i
$70$	0.120284	−	5.84047i	0.0143767	−	0.698070i
$71$		−	14.2978i		−	1.69683i	−0.529331	−	0.848416i	$-0.677557\pi$
$71$		−	14.2978i		−	1.69683i	0.529331	−	0.848416i	$-0.322443\pi$
$72$	4.87184	+	0.228888i	0.574151	+	0.0269747i
$73$	3.84146	−	3.84146i	0.449609	−	0.449609i	−0.445616	−	0.895224i	$-0.647015\pi$
$73$	3.84146	−	3.84146i	0.449609	−	0.449609i	0.895224	+	0.445616i	$0.147015\pi$
$74$	−8.77190	+	8.50156i	−1.01971	+	0.988286i
$75$	4.03247	−	3.95352i	0.465630	−	0.456513i
$76$	5.41239	+	0.169454i	0.620844	+	0.0194377i
$77$	−4.60008	−	4.60008i	−0.524228	−	0.524228i
$78$	0.0249950	−	1.59708i	0.00283012	−	0.180834i
$79$	0.766856			0.0862780			0.0431390	−	0.999069i	$-0.486264\pi$
$79$	0.766856			0.0862780			0.0431390	+	0.999069i	$0.486264\pi$
$80$	−5.88330	−	6.73697i	−0.657773	−	0.753216i
$81$	0.853540			0.0948378
$82$	0.197198	−	12.6002i	0.0217768	−	1.39145i
$83$	0.727706	+	0.727706i	0.0798761	+	0.0798761i	0.745916	−	0.666040i	$-0.232012\pi$
$83$	0.727706	+	0.727706i	0.0798761	+	0.0798761i	−0.666040	+	0.745916i	$0.732012\pi$
$84$	−4.17083	−	0.130582i	−0.455075	−	0.0142477i
$85$	−0.0306909	+	6.20899i	−0.00332889	+	0.673460i
$86$	−10.8945	+	10.5588i	−1.17479	+	1.13858i
$87$	−5.51811	+	5.51811i	−0.591603	+	0.591603i
$88$	−9.94962	−	0.467452i	−1.06063	−	0.0498305i
$89$			0.442426i			0.0468970i	0.999725	+	0.0234485i	$0.00746458\pi$
$89$			0.442426i			0.0468970i	−0.999725	+	0.0234485i	$0.992535\pi$
$90$	3.77556	+	3.93435i	0.397979	+	0.414717i
$91$		−	1.84731i		−	0.193651i
$92$	9.48848	+	10.1018i	0.989243	+	1.05319i
$93$	3.32006	−	3.32006i	0.344274	−	0.344274i
$94$	−7.63170	−	7.87438i	−0.787150	−	0.812180i
$95$	4.25975	+	4.30208i	0.437042	+	0.441384i
$96$	−4.85709	+	4.15082i	−0.495725	+	0.423641i
$97$	5.22374	+	5.22374i	0.530390	+	0.530390i	0.920688	−	0.390298i	$-0.127628\pi$
$97$	5.22374	+	5.22374i	0.530390	+	0.530390i	−0.390298	+	0.920688i	$0.627628\pi$
$98$	5.07279	+	0.0793912i	0.512429	+	0.00801972i
$99$	6.07249			0.610308
$100$	0.411725	−	9.99152i	0.0411725	−	0.999152i
$101$	3.42179			0.340481			0.170240	−	0.985403i	$-0.445546\pi$
$101$	3.42179			0.340481			0.170240	+	0.985403i	$0.445546\pi$
$102$	4.43474	+	0.0694055i	0.439105	+	0.00687217i
$103$	9.11709	+	9.11709i	0.898333	+	0.898333i	0.995289	−	0.0969555i	$-0.0309104\pi$
$103$	9.11709	+	9.11709i	0.898333	+	0.898333i	−0.0969555	+	0.995289i	$0.530910\pi$
$104$	−1.90394	−	2.09166i	−0.186696	−	0.205104i
$105$	−3.28260	−	3.31521i	−0.320349	−	0.323532i
$106$	6.34096	+	6.54259i	0.615888	+	0.635473i
$107$	−0.884982	+	0.884982i	−0.0855545	+	0.0855545i	−0.748589	−	0.663034i	$-0.769268\pi$
$107$	−0.884982	+	0.884982i	−0.0855545	+	0.0855545i	0.663034	+	0.748589i	$0.269268\pi$
$108$	7.77854	−	7.30626i	0.748491	−	0.703045i
$109$			1.15044i			0.110192i	0.998481	+	0.0550959i	$0.0175465\pi$
$109$			1.15044i			0.110192i	−0.998481	+	0.0550959i	$0.982454\pi$
$110$	−7.71073	−	8.03501i	−0.735189	−	0.766108i
$111$			9.75590i			0.925989i
$112$	−5.54160	+	4.88790i	−0.523632	+	0.461863i
$113$	2.17872	−	2.17872i	0.204956	−	0.204956i	−0.597163	−	0.802120i	$-0.703706\pi$
$113$	2.17872	−	2.17872i	0.204956	−	0.204956i	0.802120	+	0.597163i	$0.203706\pi$
$114$	3.10547	−	3.00977i	0.290854	−	0.281891i
$115$	−0.0765909	+	15.4949i	−0.00714214	+	1.44491i
$116$	−0.432434	+	13.8120i	−0.0401505	+	1.28241i
$117$	1.21930	+	1.21930i	0.112725	+	0.112725i
$118$	0.0506529	−	3.23652i	0.00466298	−	0.297946i
$119$	5.12958			0.470228
$120$	−7.13362	−	0.370499i	−0.651208	−	0.0338217i
$121$	−1.40167			−0.127425
$122$	−0.171900	+	10.9837i	−0.0155631	+	0.994422i
$123$	−7.11646	−	7.11646i	−0.641670	−	0.641670i
$124$	0.260181	−	8.31024i	0.0233649	−	0.746282i
$125$	8.02205	−	7.78760i	0.717514	−	0.696544i
$126$	3.23488	−	3.13518i	0.288186	−	0.279304i
$127$	−7.30276	+	7.30276i	−0.648015	+	0.648015i	−0.952513	−	0.304498i	$-0.901511\pi$
$127$	−7.30276	+	7.30276i	−0.648015	+	0.648015i	0.304498	+	0.952513i	$0.401511\pi$
$128$	−1.23687	+	11.2459i	−0.109325	+	0.994006i
$129$			12.1166i			1.06681i
$130$	0.0651132	−	3.16161i	0.00571081	−	0.277291i
$131$			4.60019i			0.401920i	0.979599	+	0.200960i	$0.0644061\pi$
$131$			4.60019i			0.401920i	−0.979599	+	0.200960i	$0.935594\pi$
$132$	−5.79824	+	5.44619i	−0.504672	+	0.474030i
$133$	3.53669	−	3.53669i	0.306670	−	0.306670i
$134$	−1.25066	−	1.29043i	−0.108041	−	0.111476i
$135$	11.9313	+	0.0589760i	1.02688	+	0.00507585i
$136$	5.80807	−	5.28681i	0.498038	−	0.453340i
$137$	11.8882	+	11.8882i	1.01568	+	1.01568i	0.999875	+	0.0158002i	$0.00502957\pi$
$137$	11.8882	+	11.8882i	1.01568	+	1.01568i	0.0158002	+	0.999875i	$0.494970\pi$
$138$	11.0672	+	0.173205i	0.942098	+	0.0147442i
$139$	−10.1337			−0.859532			−0.429766	−	0.902940i	$-0.641404\pi$
$139$	−10.1337			−0.859532			−0.429766	+	0.902940i	$0.641404\pi$
$140$	−8.25600	−	0.299338i	−0.697760	−	0.0252987i
$141$	−8.75771			−0.737532
$142$	−20.2176	−	0.316414i	−1.69662	−	0.0265528i
$143$	−2.49015	−	2.49015i	−0.208237	−	0.208237i
$144$	0.431472	−	6.88391i	0.0359560	−	0.573659i
$145$	−10.9786	+	10.8706i	−0.911722	+	0.902753i
$146$	−5.34696	−	5.51699i	−0.442518	−	0.456589i
$147$	2.86507	−	2.86507i	0.236307	−	0.236307i
$148$	11.8274	+	12.5920i	0.972208	+	1.03505i
$149$			13.1713i			1.07904i	0.841974	+	0.539519i	$0.181394\pi$
$149$			13.1713i			1.07904i	−0.841974	+	0.539519i	$0.818606\pi$
$150$	−5.50120	−	5.78957i	−0.449171	−	0.472716i
$151$		−	19.6586i		−	1.59979i	−0.600137	−	0.799897i	$-0.704887\pi$
$151$		−	19.6586i		−	1.59979i	0.600137	−	0.799897i	$-0.295113\pi$
$152$	0.359392	−	7.64959i	0.0291506	−	0.620464i
$153$	−3.38573	+	3.38573i	−0.273720	+	0.273720i
$154$	−6.60650	+	6.40290i	−0.532367	+	0.515960i
$155$	6.60545	−	6.54047i	0.530562	−	0.525343i
$156$	−2.25778	−	0.0706878i	−0.180767	−	0.00565955i
$157$	−10.9745	−	10.9745i	−0.875863	−	0.875863i	0.117241	−	0.993104i	$-0.462595\pi$
$157$	−10.9745	−	10.9745i	−0.875863	−	0.875863i	−0.993104	+	0.117241i	$0.962595\pi$
$158$	0.0169708	−	1.08437i	0.00135012	−	0.0862675i
$159$	7.27652			0.577066
$160$	−9.65654	+	8.17014i	−0.763417	+	0.645906i
$161$	12.8012			1.00887
$162$	0.0188891	−	1.20694i	0.00148407	−	0.0948261i
$163$	−4.24886	−	4.24886i	−0.332796	−	0.332796i	0.520851	−	0.853648i	$-0.325615\pi$
$163$	−4.24886	−	4.24886i	−0.332796	−	0.332796i	−0.853648	+	0.520851i	$0.825615\pi$
$164$	−17.8128	−	0.557691i	−1.39094	−	0.0435483i
$165$	−8.89375	−	0.0439616i	−0.692377	−	0.00342240i
$166$	1.04511	−	1.01290i	0.0811163	−	0.0786164i
$167$	−12.8152	+	12.8152i	−0.991668	+	0.991668i	−0.999966	−	0.00829711i	$-0.997359\pi$
$167$	−12.8152	+	12.8152i	−0.991668	+	0.991668i	0.00829711	+	0.999966i	$0.497359\pi$
$168$	−0.276950	+	5.89483i	−0.0213672	+	0.454796i
$169$		−	1.00000i		−	0.0769231i
$170$	8.77909	+	0.180805i	0.673325	+	0.0138671i
$171$			4.66873i			0.357026i
$172$	14.6894	+	15.6390i	1.12006	+	1.19246i
$173$	3.57993	−	3.57993i	0.272177	−	0.272177i	−0.557799	−	0.829976i	$-0.688354\pi$
$173$	3.57993	−	3.57993i	0.272177	−	0.272177i	0.829976	+	0.557799i	$0.188354\pi$
$174$	7.68071	+	7.92495i	0.582273	+	0.600789i
$175$	−6.46635	−	6.59548i	−0.488810	−	0.498571i
$176$	−0.881184	+	14.0588i	−0.0664217	+	1.05972i
$177$	−1.82796	−	1.82796i	−0.137398	−	0.137398i
$178$	0.625608	+	0.00979101i	0.0468913	+	0.000733868i
$179$	−2.63043			−0.196608			−0.0983039	−	0.995156i	$-0.531342\pi$
$179$	−2.63043			−0.196608			−0.0983039	+	0.995156i	$0.531342\pi$
$180$	5.64688	−	5.25173i	0.420894	−	0.391441i
$181$	18.4843			1.37393			0.686963	−	0.726692i	$-0.258943\pi$
$181$	18.4843			1.37393			0.686963	+	0.726692i	$0.258943\pi$
$182$	−2.61217	−	0.0408816i	−0.193627	−	0.00303034i
$183$	6.20353	+	6.20353i	0.458578	+	0.458578i
$184$	14.4944	−	13.1935i	1.06854	−	0.972641i
$185$	−0.0954708	+	19.3144i	−0.00701915	+	1.42003i
$186$	−4.62123	−	4.76818i	−0.338845	−	0.349620i
$187$	6.91459	−	6.91459i	0.505645	−	0.505645i
$188$	−11.3036	+	10.6173i	−0.824398	+	0.774344i
$189$		−	9.85706i		−	0.716996i
$190$	6.17758	−	5.92826i	0.448169	−	0.430081i
$191$		−	23.2986i		−	1.68582i	−0.538051	−	0.842912i	$-0.680839\pi$
$191$		−	23.2986i		−	1.68582i	0.538051	−	0.842912i	$-0.319161\pi$
$192$	5.76194	+	6.95998i	0.415832	+	0.502294i
$193$	2.67458	−	2.67458i	0.192520	−	0.192520i	−0.604264	−	0.796784i	$-0.706533\pi$
$193$	2.67458	−	2.67458i	0.192520	−	0.192520i	0.796784	+	0.604264i	$0.206533\pi$
$194$	7.50218	−	7.27097i	0.538625	−	0.522025i
$195$	−1.77696	−	1.79461i	−0.127251	−	0.128515i
$196$	0.224525	−	7.17137i	0.0160375	−	0.512241i
$197$	−12.7121	−	12.7121i	−0.905697	−	0.905697i	0.0902242	−	0.995921i	$-0.471242\pi$
$197$	−12.7121	−	12.7121i	−0.905697	−	0.905697i	−0.995921	+	0.0902242i	$0.971242\pi$
$198$	0.134386	−	8.58674i	0.00955040	−	0.610233i
$199$	−7.65179			−0.542421			−0.271211	−	0.962520i	$-0.587424\pi$
$199$	−7.65179			−0.542421			−0.271211	+	0.962520i	$0.587424\pi$
$200$	−14.1193	−	0.803311i	−0.998385	−	0.0568027i
$201$	−1.43519			−0.101230
$202$	0.0757252	−	4.83855i	0.00532801	−	0.340439i
$203$	9.02538	+	9.02538i	0.633457	+	0.633457i
$204$	0.196284	−	6.26937i	0.0137427	−	0.438944i
$205$	−14.0193	−	14.1586i	−0.979151	−	0.988879i
$206$	13.0937	−	12.6902i	0.912281	−	0.884166i
$207$	−8.44929	+	8.44929i	−0.587267	+	0.587267i
$208$	−2.99982	+	2.64595i	−0.208000	+	0.183464i
$209$		−	9.53481i		−	0.659537i
$210$	−4.76049	+	4.56836i	−0.328505	+	0.315247i
$211$		−	0.696850i		−	0.0479731i	−0.999712	−	0.0239866i	$-0.992364\pi$
$211$		−	0.696850i		−	0.0479731i	0.999712	−	0.0239866i	$-0.00763589\pi$
$212$	9.39182	−	8.82158i	0.645033	−	0.605869i
$213$	−11.4187	+	11.4187i	−0.782399	+	0.782399i
$214$	1.23182	+	1.27099i	0.0842052	+	0.0868828i
$215$	−0.118573	+	23.9881i	−0.00808660	+	1.63598i
$216$	−10.1592	−	11.1609i	−0.691247	−	0.759401i
$217$	−5.43027	−	5.43027i	−0.368631	−	0.368631i
$218$	1.62676	+	0.0254595i	0.110178	+	0.00172434i
$219$	−6.13587			−0.414624
$220$	−11.5325	+	10.7255i	−0.777519	+	0.723111i
$221$	2.77678			0.186786
$222$	13.7952	+	0.215901i	0.925876	+	0.0144903i
$223$	−8.11155	−	8.11155i	−0.543190	−	0.543190i	0.381273	−	0.924463i	$-0.375486\pi$
$223$	−8.11155	−	8.11155i	−0.543190	−	0.543190i	−0.924463	+	0.381273i	$0.875486\pi$
$224$	6.78905	+	7.94422i	0.453613	+	0.530796i
$225$	8.62135	+	0.0852323i	0.574757	+	0.00568215i
$226$	−3.03258	−	3.12901i	−0.201724	−	0.208139i
$227$	16.3431	−	16.3431i	1.08473	−	1.08473i	0.0886719	−	0.996061i	$-0.471738\pi$
$227$	16.3431	−	16.3431i	1.08473	−	1.08473i	0.996061	−	0.0886719i	$-0.0282623\pi$
$228$	−4.18721	−	4.45787i	−0.277305	−	0.295230i
$229$			23.0298i			1.52185i	0.648838	+	0.760926i	$0.275255\pi$
$229$			23.0298i			1.52185i	−0.648838	+	0.760926i	$0.724745\pi$
$230$	21.9087	+	0.451209i	1.44462	+	0.0297519i
$231$			7.34760i			0.483436i
$232$	19.5212	+	0.917143i	1.28163	+	0.0602134i
$233$	12.3099	−	12.3099i	0.806449	−	0.806449i	−0.177645	−	0.984095i	$-0.556848\pi$
$233$	12.3099	−	12.3099i	0.806449	−	0.806449i	0.984095	+	0.177645i	$0.0568480\pi$
$234$	1.75113	−	1.69716i	0.114475	−	0.110947i
$235$	−17.3382	−	0.0857025i	−1.13102	−	0.00559061i
$236$	−4.57545	−	0.143250i	−0.297837	−	0.00932481i
$237$	−0.612440	−	0.612440i	−0.0397823	−	0.0397823i
$238$	0.113519	−	7.25343i	0.00735835	−	0.470170i
$239$	−12.2710			−0.793744			−0.396872	−	0.917874i	$-0.629904\pi$
$239$	−12.2710			−0.793744			−0.396872	+	0.917874i	$0.629904\pi$
$240$	−0.681769	+	10.0790i	−0.0440080	+	0.650599i
$241$	−25.1592			−1.62065			−0.810325	−	0.585981i	$-0.800709\pi$
$241$	−25.1592			−1.62065			−0.810325	+	0.585981i	$0.800709\pi$
$242$	−0.0310194	+	1.98202i	−0.00199400	+	0.127409i
$243$	10.6375	+	10.6375i	0.682395	+	0.682395i
$244$	15.5277	+	0.486147i	0.994056	+	0.0311224i
$245$	5.70021	−	5.64413i	0.364173	−	0.360591i
$246$	−10.2205	+	9.90547i	−0.651632	+	0.631550i
$247$	1.91451	−	1.91451i	0.121817	−	0.121817i
$248$	−11.7453	−	0.551815i	−0.745825	−	0.0350403i
$249$		−	1.16235i		−	0.0736608i
$250$	−10.8344	−	11.5158i	−0.685231	−	0.728326i
$251$		−	21.2328i		−	1.34020i	−0.742269	−	0.670102i	$-0.766250\pi$
$251$		−	21.2328i		−	1.34020i	0.742269	−	0.670102i	$-0.233750\pi$
$252$	−4.36169	−	4.64363i	−0.274760	−	0.292521i
$253$	17.2558	−	17.2558i	1.08486	−	1.08486i
$254$	10.1648	+	10.4880i	0.637795	+	0.658076i
$255$	4.98325	−	4.93423i	0.312063	−	0.308993i
$256$	15.8748	+	1.99786i	0.992174	+	0.124866i
$257$	−1.09013	−	1.09013i	−0.0680006	−	0.0680006i	0.672289	−	0.740289i	$-0.265311\pi$
$257$	−1.09013	−	1.09013i	−0.0680006	−	0.0680006i	−0.740289	+	0.672289i	$0.765311\pi$
$258$	17.1334	+	0.268145i	1.06668	+	0.0166940i
$259$	15.9567			0.991500
$260$	−4.46920	−	0.162040i	−0.277168	−	0.0100493i
$261$	−11.9143			−0.737474
$262$	6.50485	+	0.101804i	0.401871	+	0.00628944i
$263$	−12.5796	−	12.5796i	−0.775689	−	0.775689i	0.203405	−	0.979095i	$-0.434799\pi$
$263$	−12.5796	−	12.5796i	−0.775689	−	0.775689i	−0.979095	+	0.203405i	$0.934799\pi$
$264$	7.57282	+	8.31947i	0.466075	+	0.512028i
$265$	14.4058	+	0.0712077i	0.884943	+	0.00437425i
$266$	−4.92275	−	5.07929i	−0.301833	−	0.311431i
$267$	0.353338	−	0.353338i	0.0216239	−	0.0216239i
$268$	−1.85240	+	1.73993i	−0.113153	+	0.106283i
$269$		−	19.7683i		−	1.20529i	−0.798008	−	0.602647i	$-0.794113\pi$
$269$		−	19.7683i		−	1.20529i	0.798008	−	0.602647i	$-0.205887\pi$
$270$	0.347438	−	16.8700i	0.0211444	−	1.02668i
$271$			21.2849i			1.29296i	0.762929	+	0.646482i	$0.223761\pi$
$271$			21.2849i			1.29296i	−0.762929	+	0.646482i	$0.776239\pi$
$272$	−7.34723	−	8.32984i	−0.445491	−	0.505071i
$273$	−1.47533	+	1.47533i	−0.0892912	+	0.0892912i
$274$	17.0734	−	16.5473i	1.03144	−	0.999657i
$275$	−17.6071	−	0.174068i	−1.06175	−	0.0104967i
$276$	0.489839	−	15.6456i	0.0294848	−	0.941752i
$277$	−13.0098	−	13.0098i	−0.781685	−	0.781685i	0.198430	−	0.980115i	$-0.436416\pi$
$277$	−13.0098	−	13.0098i	−0.781685	−	0.781685i	−0.980115	+	0.198430i	$0.936416\pi$
$278$	−0.224263	+	14.3295i	−0.0134504	+	0.859426i
$279$	7.16841			0.429161
$280$	−0.605985	+	11.6677i	−0.0362145	+	0.697278i
$281$	12.4347			0.741790			0.370895	−	0.928675i	$-0.379051\pi$
$281$	12.4347			0.741790			0.370895	+	0.928675i	$0.379051\pi$
$282$	−0.193811	+	12.3837i	−0.0115413	+	0.737442i
$283$	13.2718	+	13.2718i	0.788926	+	0.788926i	0.981318	−	0.192393i	$-0.0616247\pi$
$283$	13.2718	+	13.2718i	0.788926	+	0.788926i	−0.192393	+	0.981318i	$0.561625\pi$
$284$	−0.894843	+	28.5815i	−0.0530992	+	1.69600i
$285$	0.0337991	−	6.83780i	0.00200209	−	0.405037i
$286$	−3.57628	+	3.46606i	−0.211470	+	0.204953i
$287$	−11.6396	+	11.6396i	−0.687066	+	0.687066i
$288$	−9.72458	−	0.762462i	−0.573026	−	0.0449285i
$289$		−	9.28949i		−	0.546441i
$290$	15.1285	+	15.7647i	0.888375	+	0.925737i
$291$		−	8.34375i		−	0.489119i
$292$	−7.91957	+	7.43873i	−0.463458	+	0.435319i
$293$	−6.94563	+	6.94563i	−0.405768	+	0.405768i	−0.880260	−	0.474492i	$-0.842632\pi$
$293$	−6.94563	+	6.94563i	−0.405768	+	0.405768i	0.474492	+	0.880260i	$0.342632\pi$
$294$	−3.98792	−	4.11473i	−0.232580	−	0.239976i
$295$	−3.60105	−	3.63683i	−0.209661	−	0.211744i
$296$	18.0673	−	16.4458i	1.05014	−	0.955892i
$297$	−13.2872	−	13.2872i	−0.771000	−	0.771000i
$298$	18.6248	+	0.291486i	1.07891	+	0.0168853i
$299$	6.92961			0.400750
$300$	−8.30843	+	7.65079i	−0.479687	+	0.441719i
$301$	19.8179			1.14228
$302$	−27.7981	−	0.435051i	−1.59960	−	0.0250344i
$303$	−2.73277	−	2.73277i	−0.156994	−	0.156994i
$304$	−10.8089	−	0.677483i	−0.619931	−	0.0388563i
$305$	12.2208	+	12.3423i	0.699764	+	0.706716i
$306$	4.71264	+	4.86249i	0.269404	+	0.277970i
$307$	−4.02072	+	4.02072i	−0.229474	+	0.229474i	−0.812473	−	0.582999i	$-0.801879\pi$
$307$	−4.02072	+	4.02072i	−0.229474	+	0.229474i	0.582999	+	0.812473i	$0.301879\pi$
$308$	8.90775	+	9.48355i	0.507566	+	0.540376i
$309$		−	14.5625i		−	0.828432i
$310$	−9.10231	−	9.48512i	−0.516976	−	0.538718i
$311$		−	25.4676i		−	1.44413i	−0.691823	−	0.722067i	$-0.743192\pi$
$311$		−	25.4676i		−	1.44413i	0.691823	−	0.722067i	$-0.256808\pi$
$312$	−0.149921	+	3.19103i	−0.00848760	+	0.180657i
$313$	8.61361	−	8.61361i	0.486870	−	0.486870i	−0.420447	−	0.907317i	$-0.638127\pi$
$313$	8.61361	−	8.61361i	0.486870	−	0.486870i	0.907317	+	0.420447i	$0.138127\pi$
$314$	−15.7613	+	15.2756i	−0.889461	+	0.862050i
$315$	0.0352075	−	7.12273i	0.00198372	−	0.401320i
$316$	−1.53296	−	0.0479947i	−0.0862358	−	0.00269991i
$317$	13.0464	+	13.0464i	0.732757	+	0.732757i	0.971165	−	0.238408i	$-0.0766257\pi$
$317$	13.0464	+	13.0464i	0.732757	+	0.732757i	−0.238408	+	0.971165i	$0.576626\pi$
$318$	0.161032	−	10.2893i	0.00903021	−	0.576995i
$319$	24.3321			1.36234
$320$	11.3392	+	13.8356i	0.633881	+	0.773431i
$321$	1.41356			0.0788973
$322$	0.283293	−	18.1013i	0.0157873	−	1.00875i
$323$	5.31616	+	5.31616i	0.295799	+	0.295799i
$324$	−1.70624	−	0.0534199i	−0.0947913	−	0.00296777i
$325$	−3.50041	−	3.57031i	−0.194168	−	0.198045i
$326$	−6.10209	+	5.91403i	−0.337963	+	0.327548i
$327$	0.918783	−	0.918783i	0.0508088	−	0.0508088i
$328$	−1.18280	+	25.1756i	−0.0653092	+	1.39009i
$329$			14.3240i			0.789710i
$330$	−0.258985	+	12.5751i	−0.0142566	+	0.692239i
$331$			22.5223i			1.23794i	0.785415	+	0.618970i	$0.212450\pi$
$331$			22.5223i			1.23794i	−0.785415	+	0.618970i	$0.787550\pi$
$332$	−1.40916	−	1.50024i	−0.0773374	−	0.0823366i
$333$	−10.5321	+	10.5321i	−0.577154	+	0.577154i
$334$	17.8376	+	18.4048i	0.976029	+	1.00707i
$335$	−2.84134	−	0.0140447i	−0.155239	−	0.000767343i
$336$	8.32940	+	0.522074i	0.454406	+	0.0284814i
$337$	18.5334	+	18.5334i	1.00958	+	1.00958i	0.999954	+	0.00962269i	$0.00306304\pi$
$337$	18.5334	+	18.5334i	1.00958	+	1.00958i	0.00962269	+	0.999954i	$0.496937\pi$
$338$	−1.41404	−	0.0221303i	−0.0769137	−	0.00120373i
$339$	−3.48001			−0.189008
$340$	0.449950	−	12.4100i	0.0244019	−	0.673026i
$341$	−14.6398			−0.792792
$342$	6.60177	+	0.103320i	0.356983	+	0.00558692i
$343$	−13.8298	−	13.8298i	−0.746739	−	0.746739i
$344$	22.4392	−	20.4253i	1.20984	−	1.10126i
$345$	12.4360	−	12.3136i	0.669531	−	0.662944i
$346$	−4.98295	−	5.14140i	−0.267885	−	0.276403i
$347$	−19.0075	+	19.0075i	−1.02038	+	1.02038i	−0.0205887	+	0.999788i	$0.506554\pi$
$347$	−19.0075	+	19.0075i	−1.02038	+	1.02038i	−0.999788	+	0.0205887i	$0.993446\pi$
$348$	11.3762	−	10.6855i	0.609827	−	0.572801i
$349$			7.56368i			0.404874i	0.979295	+	0.202437i	$0.0648862\pi$
$349$			7.56368i			0.404874i	−0.979295	+	0.202437i	$0.935114\pi$
$350$	−9.46938	+	8.99772i	−0.506159	+	0.480948i
$351$		−	5.33590i		−	0.284809i
$352$	19.8602	+	1.55716i	1.05855	+	0.0829967i
$353$	−21.5167	+	21.5167i	−1.14522	+	1.14522i	−0.157740	+	0.987481i	$0.550421\pi$
$353$	−21.5167	+	21.5167i	−1.14522	+	1.14522i	−0.987481	+	0.157740i	$0.949579\pi$
$354$	−2.62526	+	2.54436i	−0.139531	+	0.135231i
$355$	−22.7182	+	22.4947i	−1.20576	+	1.19390i
$356$	0.0276898	−	0.884418i	0.00146756	−	0.0468740i
$357$	−4.09668	−	4.09668i	−0.216819	−	0.216819i
$358$	−0.0582123	+	3.71954i	−0.00307661	+	0.196584i
$359$	−25.3560			−1.33824			−0.669120	−	0.743155i	$-0.733329\pi$
$359$	−25.3560			−1.33824			−0.669120	+	0.743155i	$0.733329\pi$
$360$	−7.30119	−	8.10114i	−0.384807	−	0.426968i
$361$	−11.6693			−0.614175
$362$	0.409063	−	26.1375i	0.0214999	−	1.37376i
$363$	1.11943	+	1.11943i	0.0587547	+	0.0587547i
$364$	−0.115616	+	3.69281i	−0.00605995	+	0.193556i
$365$	−12.1476	−	0.0600453i	−0.635835	−	0.00314292i
$366$	8.90932	−	8.63475i	0.465698	−	0.451346i
$367$	−0.233912	+	0.233912i	−0.0122101	+	0.0122101i	−0.713185	−	0.700975i	$-0.752748\pi$
$367$	−0.233912	+	0.233912i	−0.0122101	+	0.0122101i	0.700975	+	0.713185i	$0.252748\pi$
$368$	−18.3354	−	20.7876i	−0.955800	−	1.08363i
$369$		−	15.3653i		−	0.799885i
$370$	27.3093	+	0.562434i	1.41974	+	0.0292396i
$371$		−	11.9014i		−	0.617891i
$372$	−6.84466	+	6.42908i	−0.354879	+	0.333332i
$373$	−13.6778	+	13.6778i	−0.708208	+	0.708208i	−0.966158	−	0.257950i	$-0.916953\pi$
$373$	−13.6778	+	13.6778i	−0.708208	+	0.708208i	0.257950	+	0.966158i	$0.416953\pi$
$374$	−9.62449	−	9.93053i	−0.497671	−	0.513496i
$375$	−12.6262	−	0.187245i	−0.652014	−	0.00966929i
$376$	14.7631	+	16.2187i	0.761349	+	0.836415i
$377$	4.88568	+	4.88568i	0.251625	+	0.251625i
$378$	−13.9383	−	0.218140i	−0.716908	−	0.0112199i
$379$	27.2977			1.40219			0.701093	−	0.713070i	$-0.252696\pi$
$379$	27.2977			1.40219			0.701093	+	0.713070i	$0.252696\pi$
$380$	−8.24609	−	8.86654i	−0.423015	−	0.454844i
$381$	11.6645			0.597591
$382$	−32.9451	−	0.515604i	−1.68562	−	0.0263806i
$383$	10.7069	+	10.7069i	0.547095	+	0.547095i	0.925599	−	0.378505i	$-0.123562\pi$
$383$	10.7069	+	10.7069i	0.547095	+	0.547095i	−0.378505	+	0.925599i	$0.623562\pi$
$384$	9.96921	−	7.99359i	0.508739	−	0.407921i
$385$	−0.0719032	+	14.5465i	−0.00366453	+	0.741361i
$386$	−3.72277	−	3.84115i	−0.189484	−	0.195509i
$387$	−13.0806	+	13.0806i	−0.664926	+	0.664926i
$388$	−10.1154	−	10.7693i	−0.513533	−	0.546728i
$389$		−	1.85990i		−	0.0943006i	−0.998888	−	0.0471503i	$-0.984986\pi$
$389$		−	1.85990i		−	0.0943006i	0.998888	−	0.0471503i	$-0.0150140\pi$
$390$	−2.57698	+	2.47298i	−0.130491	+	0.125224i
$391$			19.2420i			0.973110i
$392$	−10.1356	−	0.476191i	−0.511927	−	0.0240513i
$393$	3.67388	−	3.67388i	0.185323	−	0.185323i
$394$	−18.2567	+	17.6941i	−0.919759	+	0.891414i
$395$	−1.20650	−	1.21848i	−0.0607055	−	0.0613086i
$396$	−12.1390	−	0.380054i	−0.610009	−	0.0190985i
$397$	1.54829	+	1.54829i	0.0777066	+	0.0777066i	0.744892	−	0.667185i	$-0.232501\pi$
$397$	1.54829	+	1.54829i	0.0777066	+	0.0777066i	−0.667185	+	0.744892i	$0.732501\pi$
$398$	−0.169337	+	10.8199i	−0.00848807	+	0.542355i
$399$	−5.64907			−0.282807
$400$	−1.44838	+	19.9475i	−0.0724189	+	0.997374i
$401$	−25.1569			−1.25628			−0.628139	−	0.778101i	$-0.716183\pi$
$401$	−25.1569			−1.25628			−0.628139	+	0.778101i	$0.716183\pi$
$402$	−0.0317612	+	2.02941i	−0.00158410	+	0.101218i
$403$	−2.93955	−	2.93955i	−0.146430	−	0.146430i
$404$	−6.84023	−	0.214157i	−0.340314	−	0.0106547i
$405$	−1.34288	−	1.35622i	−0.0667281	−	0.0673911i
$406$	12.9620	−	12.5625i	0.643292	−	0.623467i
$407$	21.5094	−	21.5094i	1.06618	−	1.06618i
$408$	−8.86079	−	0.416297i	−0.438675	−	0.0206098i
$409$		−	17.0509i		−	0.843112i	−0.906802	−	0.421556i	$-0.861484\pi$
$409$		−	17.0509i		−	0.843112i	0.906802	−	0.421556i	$-0.138516\pi$
$410$	−20.3311	+	19.5105i	−1.00408	+	0.963557i
$411$		−	18.9887i		−	0.936644i
$412$	−17.6546	−	18.7958i	−0.869782	−	0.926005i
$413$	−2.98980	+	2.98980i	−0.147118	+	0.147118i
$414$	11.7607	+	12.1346i	0.578005	+	0.596384i
$415$	0.0113747	−	2.30118i	0.000558361	−	0.112961i
$416$	3.67510	+	4.30042i	0.180187	+	0.210846i
$417$	8.09318	+	8.09318i	0.396325	+	0.396325i
$418$	−13.4826	−	0.211008i	−0.659456	−	0.0103208i
$419$	−33.8791			−1.65510			−0.827551	−	0.561391i	$-0.810266\pi$
$419$	−33.8791			−1.65510			−0.827551	+	0.561391i	$0.810266\pi$
$420$	6.35450	+	6.83262i	0.310068	+	0.333398i
$421$	−25.0338			−1.22007			−0.610036	−	0.792374i	$-0.708845\pi$
$421$	−25.0338			−1.22007			−0.610036	+	0.792374i	$0.708845\pi$
$422$	−0.985374	−	0.0154215i	−0.0479672	−	0.000750707i
$423$	−9.45446	−	9.45446i	−0.459692	−	0.459692i
$424$	−12.2662	−	13.4756i	−0.595701	−	0.654434i
$425$	9.91397	−	9.71987i	0.480898	−	0.471483i
$426$	15.8938	+	16.3992i	0.770059	+	0.794546i
$427$	10.1464	−	10.1464i	0.491021	−	0.491021i
$428$	1.82449	−	1.71371i	0.0881898	−	0.0828353i
$429$			3.97745i			0.192033i
$430$	33.9176	+	0.698532i	1.63565	+	0.0336862i
$431$			15.0689i			0.725844i	0.931820	+	0.362922i	$0.118221\pi$
$431$			15.0689i			0.725844i	−0.931820	+	0.362922i	$0.881779\pi$
$432$	−16.0067	+	14.1185i	−0.770125	+	0.679278i
$433$	−5.58575	+	5.58575i	−0.268434	+	0.268434i	−0.828469	−	0.560035i	$-0.810788\pi$
$433$	−5.58575	+	5.58575i	−0.268434	+	0.268434i	0.560035	+	0.828469i	$0.310788\pi$
$434$	−7.79879	+	7.55845i	−0.374354	+	0.362817i
$435$	17.4496	+	0.0862528i	0.836643	+	0.00413551i
$436$	0.0720016	−	2.29975i	0.00344825	−	0.110138i
$437$	13.2668	+	13.2668i	0.634637	+	0.634637i
$438$	−0.135789	+	8.67637i	−0.00648823	+	0.414573i
$439$	29.6737			1.41625			0.708124	−	0.706088i	$-0.249542\pi$
$439$	29.6737			1.41625			0.708124	+	0.706088i	$0.249542\pi$
$440$	14.9110	+	16.5447i	0.710855	+	0.788739i
$441$	6.18602			0.294572
$442$	0.0614510	−	3.92648i	0.00292293	−	0.186764i
$443$	1.89262	+	1.89262i	0.0899213	+	0.0899213i	0.750637	−	0.660715i	$-0.229747\pi$
$443$	1.89262	+	1.89262i	0.0899213	+	0.0899213i	−0.660715	+	0.750637i	$0.729747\pi$
$444$	0.610586	−	19.5022i	0.0289771	−	0.925536i
$445$	0.702985	−	0.696070i	0.0333247	−	0.0329969i
$446$	−11.6496	+	11.2906i	−0.551623	+	0.534623i
$447$	10.5191	−	10.5191i	0.497538	−	0.497538i
$448$	11.3837	−	9.42418i	0.537829	−	0.445251i
$449$		−	12.5398i		−	0.591791i	−0.955220	−	0.295895i	$-0.904382\pi$
$449$		−	12.5398i		−	0.591791i	0.955220	−	0.295895i	$-0.0956180\pi$
$450$	0.311315	−	12.1891i	0.0146755	−	0.574597i
$451$			31.3801i			1.47763i
$452$	−4.49166	+	4.21894i	−0.211270	+	0.198442i
$453$	−15.7001	+	15.7001i	−0.737655	+	0.737655i
$454$	−22.7482	−	23.4715i	−1.06763	−	1.10157i
$455$	−2.93526	+	2.90638i	−0.137607	+	0.136253i
$456$	−6.39628	+	5.82223i	−0.299533	+	0.272651i
$457$	12.2710	+	12.2710i	0.574015	+	0.574015i	0.933248	−	0.359233i	$-0.116962\pi$
$457$	12.2710	+	12.2710i	0.574015	+	0.574015i	−0.359233	+	0.933248i	$0.616962\pi$
$458$	32.5651	+	0.509657i	1.52167	+	0.0238147i
$459$	14.8166			0.691580
$460$	1.12287	−	30.9698i	0.0523543	−	1.44398i
$461$	6.10051			0.284129			0.142065	−	0.989857i	$-0.454626\pi$
$461$	6.10051			0.284129			0.142065	+	0.989857i	$0.454626\pi$
$462$	10.3898	+	0.162605i	0.483377	+	0.00756505i
$463$	23.1386	+	23.1386i	1.07534	+	1.07534i	0.996920	+	0.0784197i	$0.0249874\pi$
$463$	23.1386	+	23.1386i	1.07534	+	1.07534i	0.0784197	+	0.996920i	$0.475013\pi$
$464$	1.72889	−	27.5835i	0.0802616	−	1.28053i
$465$	−10.4988	−	0.0518955i	−0.486872	−	0.00240659i
$466$	−17.1343	−	17.6791i	−0.793731	−	0.818970i
$467$	12.2124	−	12.2124i	0.565122	−	0.565122i	−0.365636	−	0.930758i	$-0.619149\pi$
$467$	12.2124	−	12.2124i	0.565122	−	0.565122i	0.930758	+	0.365636i	$0.119149\pi$
$468$	−2.36110	−	2.51372i	−0.109142	−	0.116197i
$469$			2.34738i			0.108392i
$470$	−0.504887	+	24.5151i	−0.0232887	+	1.13080i
$471$			17.5294i			0.807710i
$472$	−0.303818	+	6.46670i	−0.0139844	+	0.297654i
$473$	26.7142	−	26.7142i	1.22832	−	1.22832i
$474$	−0.879569	+	0.852462i	−0.0403999	+	0.0391549i
$475$	0.133829	−	13.5369i	0.00614049	−	0.621118i
$476$	−10.2541	−	0.321041i	−0.469997	−	0.0147149i
$477$	7.85543	+	7.85543i	0.359676	+	0.359676i
$478$	−0.271561	+	17.3517i	−0.0124209	+	0.793646i
$479$	−21.9564			−1.00321			−0.501607	−	0.865096i	$-0.667258\pi$
$479$	−21.9564			−1.00321			−0.501607	+	0.865096i	$0.667258\pi$
$480$	14.2371	+	1.18710i	0.649830	+	0.0541835i
$481$	8.63779			0.393849
$482$	−0.556782	+	35.5762i	−0.0253607	+	1.62045i
$483$	−10.2235	−	10.2235i	−0.465185	−	0.465185i
$484$	2.80197	+	0.0877254i	0.127362	+	0.00398752i
$485$	0.0816515	−	16.5187i	0.00370760	−	0.750076i
$486$	15.2772	−	14.8064i	0.692989	−	0.671633i
$487$	19.5227	−	19.5227i	0.884659	−	0.884659i	−0.109345	−	0.994004i	$-0.534875\pi$
$487$	19.5227	−	19.5227i	0.884659	−	0.884659i	0.994004	+	0.109345i	$0.0348753\pi$
$488$	1.03106	−	21.9460i	0.0466741	−	0.993448i
$489$			6.78660i			0.306901i
$490$	−7.85489	−	8.18523i	−0.354848	−	0.369771i
$491$			5.37843i			0.242725i	0.992608	+	0.121363i	$0.0387264\pi$
$491$			5.37843i			0.242725i	−0.992608	+	0.121363i	$0.961274\pi$
$492$	13.7806	+	14.6713i	0.621276	+	0.661435i
$493$	−13.5665	+	13.5665i	−0.611003	+	0.611003i
$494$	−2.66482	−	2.74956i	−0.119896	−	0.123708i
$495$	−9.55387	−	9.64879i	−0.429414	−	0.433681i
$496$	−1.04021	+	16.5961i	−0.0467070	+	0.745185i
$497$	18.6764	+	18.6764i	0.837750	+	0.837750i
$498$	−1.64361	−	0.0257231i	−0.0736518	−	0.00115268i
$499$	25.0685			1.12222			0.561111	−	0.827740i	$-0.310374\pi$
$499$	25.0685			1.12222			0.561111	+	0.827740i	$0.310374\pi$
$500$	−16.5236	+	15.0655i	−0.738960	+	0.673749i
$501$	20.4694			0.914505
$502$	−30.0241	−	0.469889i	−1.34004	−	0.0209722i
$503$	16.4098	+	16.4098i	0.731676	+	0.731676i	0.970952	−	0.239276i	$-0.0769099\pi$
$503$	16.4098	+	16.4098i	0.731676	+	0.731676i	−0.239276	+	0.970952i	$0.576910\pi$
$504$	−6.66280	+	6.06483i	−0.296785	+	0.270149i
$505$	−5.38351	−	5.43700i	−0.239563	−	0.241943i
$506$	−24.0185	−	24.7822i	−1.06775	−	1.10170i
$507$	−0.798638	+	0.798638i	−0.0354688	+	0.0354688i
$508$	15.0554	−	14.1413i	0.667976	−	0.627419i
$509$		−	14.9919i		−	0.664503i	−0.943191	−	0.332252i	$-0.892192\pi$
$509$		−	14.9919i		−	0.664503i	0.943191	−	0.332252i	$-0.107808\pi$
$510$	−6.86692	−	7.15571i	−0.304072	−	0.316860i
$511$			10.0358i			0.443957i
$512$	3.17637	−	22.4034i	0.140377	−	0.990098i
$513$	10.2156	−	10.2156i	0.451030	−	0.451030i
$514$	−1.56562	+	1.51737i	−0.0690564	+	0.0669282i
$515$	0.142508	−	28.8304i	0.00627965	−	1.27042i
$516$	0.758335	−	24.2214i	0.0333839	−	1.06629i
$517$	19.3086	+	19.3086i	0.849190	+	0.849190i
$518$	0.353126	−	22.5634i	0.0155155	−	0.991378i
$519$	−5.71814			−0.250999
$520$	−0.328036	+	6.31604i	−0.0143853	+	0.276977i
$521$	13.2279			0.579524			0.289762	−	0.957099i	$-0.406424\pi$
$521$	13.2279			0.579524			0.289762	+	0.957099i	$0.406424\pi$
$522$	−0.263666	+	16.8472i	−0.0115404	+	0.737383i
$523$	13.5227	+	13.5227i	0.591304	+	0.591304i	0.937984	−	0.346679i	$-0.112691\pi$
$523$	13.5227	+	13.5227i	0.591304	+	0.591304i	−0.346679	+	0.937984i	$0.612691\pi$
$524$	0.287909	−	9.19586i	0.0125773	−	0.401723i
$525$	−0.103130	+	10.4317i	−0.00450094	+	0.455276i
$526$	−18.0664	+	17.5096i	−0.787733	+	0.763456i
$527$	8.16249	−	8.16249i	0.355564	−	0.355564i
$528$	11.9317	−	10.5242i	0.519259	−	0.458005i
$529$			25.0195i			1.08781i
$530$	0.419496	−	20.3689i	0.0182217	−	0.884767i
$531$		−	3.94678i		−	0.171276i
$532$	−7.29126	+	6.84857i	−0.316116	+	0.296923i
$533$	−6.30085	+	6.30085i	−0.272920	+	0.272920i
$534$	−0.491815	−	0.507454i	−0.0212829	−	0.0219597i
$535$	2.79853	+	0.0138330i	0.120991	+	0.000598055i
$536$	2.41934	+	2.65787i	0.104499	+	0.114803i
$537$	2.10076	+	2.10076i	0.0906546	+	0.0906546i
$538$	−27.9532	−	0.437479i	−1.20515	−	0.0188610i
$539$	−12.6335			−0.544165
$540$	−23.8472	−	0.864629i	−1.02622	−	0.0372077i
$541$	18.3005			0.786799			0.393400	−	0.919368i	$-0.371299\pi$
$541$	18.3005			0.786799			0.393400	+	0.919368i	$0.371299\pi$
$542$	30.0977	+	0.471041i	1.29281	+	0.0202330i
$543$	−14.7623	−	14.7623i	−0.633509	−	0.633509i
$544$	−11.9413	+	10.2049i	−0.511980	+	0.437533i
$545$	1.82797	−	1.80999i	0.0783016	−	0.0775313i
$546$	2.05353	+	2.11883i	0.0878830	+	0.0906776i
$547$	23.1342	−	23.1342i	0.989147	−	0.989147i	−0.0107946	−	0.999942i	$-0.503436\pi$
$547$	23.1342	−	23.1342i	0.989147	−	0.989147i	0.999942	+	0.0107946i	$0.00343608\pi$
$548$	−23.0207	−	24.5087i	−0.983394	−	1.04696i
$549$			13.3941i			0.571648i
$550$	−0.635790	+	24.8934i	−0.0271102	+	1.06146i
$551$			18.7073i			0.796960i
$552$	−22.1126	−	1.03889i	−0.941176	−	0.0442182i
$553$	−1.00170	+	1.00170i	−0.0425967	+	0.0425967i
$554$	−18.6844	+	18.1085i	−0.793822	+	0.769358i
$555$	15.5015	−	15.3490i	0.658002	−	0.651529i
$556$	20.2575	+	0.634233i	0.859111	+	0.0268975i
$557$	−12.7940	−	12.7940i	−0.542100	−	0.542100i	0.382044	−	0.924144i	$-0.375220\pi$
$557$	−12.7940	−	12.7940i	−0.542100	−	0.542100i	−0.924144	+	0.382044i	$0.875220\pi$
$558$	0.158639	−	10.1364i	0.00671573	−	0.429109i
$559$	10.7280			0.453744
$560$	16.4852	+	1.11510i	0.696626	+	0.0471214i
$561$	−11.0445			−0.466300
$562$	0.275183	−	17.5831i	0.0116079	−	0.741699i
$563$	25.0765	+	25.0765i	1.05685	+	1.05685i	0.998284	+	0.0585642i	$0.0186522\pi$
$563$	25.0765	+	25.0765i	1.05685	+	1.05685i	0.0585642	+	0.998284i	$0.481348\pi$
$564$	17.5068	+	0.548112i	0.737171	+	0.0230797i
$565$	−6.88962	−	0.0340552i	−0.289849	−	0.00143271i
$566$	19.0605	−	18.4731i	0.801174	−	0.776483i
$567$	−1.11493	+	1.11493i	−0.0468228	+	0.0468228i
$568$	40.3956	+	1.89786i	1.69496	+	0.0796325i
$569$		−	3.78598i		−	0.158716i	−0.996846	−	0.0793582i	$-0.974713\pi$
$569$		−	3.78598i		−	0.158716i	0.996846	−	0.0793582i	$-0.0252871\pi$
$570$	−9.66818	−	0.199116i	−0.404956	−	0.00834005i
$571$		−	25.5130i		−	1.06769i	−0.845583	−	0.533843i	$-0.820747\pi$
$571$		−	25.5130i		−	1.06769i	0.845583	−	0.533843i	$-0.179253\pi$
$572$	4.82201	+	5.13371i	0.201618	+	0.214651i
$573$	−18.6071	+	18.6071i	−0.777324	+	0.777324i
$574$	16.2013	+	16.7165i	0.676230	+	0.697733i
$575$	24.7409	−	24.2565i	1.03177	−	1.01157i
$576$	−1.29336	+	13.7341i	−0.0538900	+	0.572253i
$577$	4.42706	+	4.42706i	0.184301	+	0.184301i	0.793227	−	0.608926i	$-0.208399\pi$
$577$	4.42706	+	4.42706i	0.184301	+	0.184301i	−0.608926	+	0.793227i	$0.708399\pi$
$578$	−13.1357	−	0.205579i	−0.546374	−	0.00855098i
$579$	−4.27204			−0.177540
$580$	22.6268	−	21.0434i	0.939525	−	0.873780i
$581$	−1.90113			−0.0788721
$582$	−11.7984	−	0.184650i	−0.489059	−	0.00765398i
$583$	−16.0429	−	16.0429i	−0.664430	−	0.664430i
$584$	10.3434	+	11.3632i	0.428013	+	0.470213i
$585$	0.0190588	−	3.85573i	0.000787983	−	0.159415i
$586$	9.66769	+	9.97511i	0.399369	+	0.412068i
$587$	23.6571	−	23.6571i	0.976431	−	0.976431i	−0.0232972	−	0.999729i	$-0.507416\pi$
$587$	23.6571	−	23.6571i	0.976431	−	0.976431i	0.999729	+	0.0232972i	$0.00741642\pi$
$588$	−5.90664	+	5.54801i	−0.243586	+	0.228796i
$589$		−	11.2556i		−	0.463778i
$590$	−5.22232	+	5.01155i	−0.214999	+	0.206322i
$591$			20.3047i			0.835223i
$592$	−22.8552	−	25.9118i	−0.939342	−	1.06497i
$593$	−9.21789	+	9.21789i	−0.378534	+	0.378534i	−0.870573	−	0.492039i	$-0.836252\pi$
$593$	−9.21789	+	9.21789i	−0.378534	+	0.378534i	0.492039	+	0.870573i	$0.336252\pi$
$594$	−19.0826	+	18.4946i	−0.782971	+	0.758841i
$595$	−8.07038	−	8.15056i	−0.330853	−	0.334141i
$596$	0.824345	−	26.3298i	0.0337665	−	1.07851i
$597$	6.11101	+	6.11101i	0.250107	+	0.250107i
$598$	0.153354	−	9.79875i	0.00627113	−	0.400701i
$599$	2.77755			0.113488			0.0567438	−	0.998389i	$-0.481928\pi$
$599$	2.77755			0.113488			0.0567438	+	0.998389i	$0.481928\pi$
$600$	10.6347	+	11.9178i	0.434158	+	0.486541i
$601$	−40.0680			−1.63441			−0.817205	−	0.576348i	$-0.804477\pi$
$601$	−40.0680			−1.63441			−0.817205	+	0.576348i	$0.804477\pi$
$602$	0.438576	−	28.0233i	0.0178750	−	1.14214i
$603$	−1.54937	−	1.54937i	−0.0630953	−	0.0630953i
$604$	−1.23036	+	39.2979i	−0.0500626	+	1.59901i
$605$	2.20525	+	2.22716i	0.0896563	+	0.0905471i
$606$	−3.92473	+	3.80377i	−0.159431	+	0.154518i
$607$	−15.4132	+	15.4132i	−0.625602	+	0.625602i	−0.946958	−	0.321356i	$-0.895861\pi$
$607$	−15.4132	+	15.4132i	−0.625602	+	0.625602i	0.321356	+	0.946958i	$0.395861\pi$
$608$	−1.19719	+	15.2692i	−0.0485526	+	0.619248i
$609$		−	14.4160i		−	0.584167i
$610$	17.7229	−	17.0076i	0.717580	−	0.688619i
$611$			7.75399i			0.313693i
$612$	6.98005	−	6.55625i	0.282152	−	0.265021i
$613$	24.1149	−	24.1149i	0.973991	−	0.973991i	−0.0256796	−	0.999670i	$-0.508175\pi$
$613$	24.1149	−	24.1149i	0.973991	−	0.973991i	0.999670	+	0.0256796i	$0.00817496\pi$
$614$	5.59647	+	5.77443i	0.225855	+	0.233037i
$615$	−0.111236	+	22.5040i	−0.00448549	+	0.907447i
$616$	13.6073	−	12.3860i	0.548252	−	0.499048i
$617$	−9.31246	−	9.31246i	−0.374905	−	0.374905i	0.494355	−	0.869260i	$-0.335404\pi$
$617$	−9.31246	−	9.31246i	−0.374905	−	0.374905i	−0.869260	+	0.494355i	$0.835404\pi$
$618$	−20.5920	−	0.322273i	−0.828331	−	0.0129637i
$619$	−20.6325			−0.829290			−0.414645	−	0.909983i	$-0.636094\pi$
$619$	−20.6325			−0.829290			−0.414645	+	0.909983i	$0.636094\pi$
$620$	−13.6138	+	12.6611i	−0.546742	+	0.508483i
$621$	36.9757			1.48378
$622$	−36.0122	−	0.563605i	−1.44396	−	0.0225985i
$623$	−0.577917	−	0.577917i	−0.0231537	−	0.0231537i
$624$	4.50893	+	0.282613i	0.180502	+	0.0113136i
$625$	−24.9951	−	0.494261i	−0.999805	−	0.0197705i
$626$	−11.9894	−	12.3706i	−0.479192	−	0.494429i
$627$	−7.61486	+	7.61486i	−0.304108	+	0.304108i
$628$	21.2515	+	22.6252i	0.848025	+	0.902842i
$629$			23.9852i			0.956354i
$630$	−10.0710	−	0.207413i	−0.401240	−	0.00826353i
$631$		−	0.761372i		−	0.0303098i	−0.999885	−	0.0151549i	$-0.995176\pi$
$631$		−	0.761372i		−	0.0303098i	0.999885	−	0.0151549i	$-0.00482413\pi$
$632$	−0.101791	+	2.16661i	−0.00404904	+	0.0861830i
$633$	−0.556531	+	0.556531i	−0.0221201	+	0.0221201i
$634$	18.7368	−	18.1594i	0.744133	−	0.721200i
$635$	23.0931	+	0.114148i	0.916420	+	0.00452984i
$636$	−14.5459	−	0.455410i	−0.576783	−	0.0180582i
$637$	−2.53670	−	2.53670i	−0.100508	−	0.100508i
$638$	0.538478	−	34.4066i	0.0213185	−	1.36217i
$639$	−24.6544			−0.975313
$640$	19.8150	−	15.7279i	0.783255	−	0.621700i
$641$	−46.1859			−1.82423			−0.912117	−	0.409930i	$-0.865553\pi$
$641$	−46.1859			−1.82423			−0.912117	+	0.409930i	$0.865553\pi$
$642$	0.0312825	−	1.99883i	0.00123462	−	0.0788876i
$643$	−24.2799	−	24.2799i	−0.957507	−	0.957507i	0.0416264	−	0.999133i	$-0.486746\pi$
$643$	−24.2799	−	24.2799i	−0.957507	−	0.957507i	−0.999133	+	0.0416264i	$0.986746\pi$
$644$	−25.5898	−	0.801177i	−1.00838	−	0.0315708i
$645$	19.2525	−	19.0632i	0.758068	−	0.750611i
$646$	7.63492	−	7.39962i	0.300392	−	0.291134i
$647$	−0.561905	+	0.561905i	−0.0220907	+	0.0220907i	−0.718066	−	0.695975i	$-0.754972\pi$
$647$	−0.561905	+	0.561905i	−0.0220907	+	0.0220907i	0.695975	+	0.718066i	$0.254972\pi$
$648$	−0.113298	+	2.41152i	−0.00445075	+	0.0947333i
$649$			8.06040i			0.316399i
$650$	−5.12603	+	4.87071i	−0.201059	+	0.191045i
$651$			8.67364i			0.339947i
$652$	8.22764	+	8.75948i	0.322219	+	0.343048i
$653$	9.91131	−	9.91131i	0.387860	−	0.387860i	−0.486064	−	0.873923i	$-0.661568\pi$
$653$	9.91131	−	9.91131i	0.387860	−	0.387860i	0.873923	+	0.486064i	$0.161568\pi$
$654$	−1.27886	−	1.31953i	−0.0500075	−	0.0515977i
$655$	7.30940	−	7.23749i	0.285602	−	0.282792i
$656$	35.5732	+	2.22967i	1.38890	+	0.0870540i
$657$	−6.62403	−	6.62403i	−0.258428	−	0.258428i
$658$	20.2548	+	0.316995i	0.789613	+	0.0123578i
$659$	−30.2716			−1.17922			−0.589608	−	0.807690i	$-0.700718\pi$
$659$	−30.2716			−1.17922			−0.589608	+	0.807690i	$0.700718\pi$
$660$	17.7760	+	0.644507i	0.691931	+	0.0250874i
$661$	1.99460			0.0775808			0.0387904	−	0.999247i	$-0.487650\pi$
$661$	1.99460			0.0775808			0.0387904	+	0.999247i	$0.487650\pi$
$662$	31.8475	+	0.498426i	1.23779	+	0.0193719i
$663$	−2.21764	−	2.21764i	−0.0861261	−	0.0861261i
$664$	−2.15259	+	1.95940i	−0.0835367	+	0.0760395i
$665$	−11.1839	−	0.0552815i	−0.433691	−	0.00214373i
$666$	14.6597	+	15.1259i	0.568052	+	0.586115i
$667$	−33.8559	+	33.8559i	−1.31091	+	1.31091i
$668$	26.4199	−	24.8158i	1.02222	−	0.960150i
$669$			12.9564i			0.500923i
$670$	−0.0827396	+	4.01746i	−0.00319651	+	0.155208i
$671$		−	27.3545i		−	1.05601i
$672$	0.922565	−	11.7666i	0.0355887	−	0.453905i
$673$	−4.18463	+	4.18463i	−0.161306	+	0.161306i	−0.783145	−	0.621839i	$-0.786386\pi$
$673$	−4.18463	+	4.18463i	−0.161306	+	0.161306i	0.621839	+	0.783145i	$0.286386\pi$
$674$	26.6171	−	25.7968i	1.02525	−	0.993654i
$675$	−18.6778	−	19.0508i	−0.718910	−	0.733266i
$676$	−0.0625863	+	1.99902i	−0.00240717	+	0.0768854i
$677$	−21.7743	−	21.7743i	−0.836853	−	0.836853i	0.151590	−	0.988443i	$-0.451561\pi$
$677$	−21.7743	−	21.7743i	−0.836853	−	0.836853i	−0.988443	+	0.151590i	$0.951561\pi$
$678$	−0.0770138	+	4.92088i	−0.00295770	+	0.188985i
$679$	−13.6470			−0.523723
$680$	−17.5383	−	0.910884i	−0.672562	−	0.0349308i
$681$	−26.1045			−1.00033
$682$	−0.323984	+	20.7013i	−0.0124060	+	0.792695i
$683$	−23.8214	−	23.8214i	−0.911500	−	0.911500i	0.0848900	−	0.996390i	$-0.472946\pi$
$683$	−23.8214	−	23.8214i	−0.911500	−	0.911500i	−0.996390	+	0.0848900i	$0.972946\pi$
$684$	0.292198	−	9.33288i	0.0111725	−	0.356852i
$685$	0.185823	−	37.5933i	0.00709991	−	1.43636i
$686$	−19.8620	+	19.2498i	−0.758333	+	0.734963i
$687$	18.3925	−	18.3925i	0.701717	−	0.701717i
$688$	−28.3857	−	32.1820i	−1.08219	−	1.22693i
$689$		−	6.44256i		−	0.245442i
$690$	−17.1368	−	17.8575i	−0.652386	−	0.679823i
$691$			22.6733i			0.862534i	0.902224	+	0.431267i	$0.141933\pi$
$691$			22.6733i			0.862534i	−0.902224	+	0.431267i	$0.858067\pi$
$692$	−7.38042	+	6.93231i	−0.280561	+	0.263527i
$693$	−7.93216	+	7.93216i	−0.301318	+	0.301318i
$694$	26.4567	+	27.2980i	1.00428	+	1.03622i
$695$	15.9434	+	16.1018i	0.604769	+	0.610777i
$696$	−14.8579	−	16.3228i	−0.563188	−	0.618716i
$697$	−17.4961	−	17.4961i	−0.662711	−	0.662711i
$698$	10.6953	+	0.167387i	0.404825	+	0.00633567i
$699$	−19.6623			−0.743698
$700$	12.5136	+	13.5892i	0.472969	+	0.513624i
$701$	−4.26882			−0.161231			−0.0806155	−	0.996745i	$-0.525689\pi$
$701$	−4.26882			−0.161231			−0.0806155	+	0.996745i	$0.525689\pi$
$702$	−7.54518	−	0.118085i	−0.284774	−	0.00445683i
$703$	16.5371	+	16.5371i	0.623708	+	0.623708i
$704$	2.64139	−	28.0487i	0.0995513	−	1.05713i
$705$	13.7785	+	13.9154i	0.518930	+	0.524085i
$706$	29.9494	+	30.9017i	1.12716	+	1.16300i
$707$	−4.46970	+	4.46970i	−0.168100	+	0.168100i
$708$	3.53973	+	3.76854i	0.133031	+	0.141630i
$709$			25.6567i			0.963558i	0.876293	+	0.481779i	$0.160009\pi$
$709$			25.6567i			0.963558i	−0.876293	+	0.481779i	$0.839991\pi$
$710$	31.3057	+	32.6223i	1.17488	+	1.22429i
$711$		−	1.32233i		−	0.0495913i
$712$	−1.24999	−	0.0587269i	−0.0468453	−	0.00220088i
$713$	20.3700	−	20.3700i	0.762861	−	0.762861i
$714$	−5.88353	+	5.70220i	−0.220185	+	0.213400i
$715$	−0.0389232	+	7.87444i	−0.00145564	+	0.294487i
$716$	5.25829	+	0.164629i	0.196511	+	0.00615248i
$717$	9.80007	+	9.80007i	0.365990	+	0.365990i
$718$	−0.561137	+	35.8544i	−0.0209414	+	1.33808i
$719$	44.8441			1.67240			0.836201	−	0.548422i	$-0.184771\pi$
$719$	44.8441			1.67240			0.836201	+	0.548422i	$0.184771\pi$
$720$	−11.6169	+	10.1449i	−0.432937	+	0.378078i
$721$	−23.8183			−0.887041
$722$	−0.258246	+	16.5009i	−0.00961091	+	0.614100i
$723$	20.0931	+	20.0931i	0.747272	+	0.747272i
$724$	−36.9505	−	1.15686i	−1.37325	−	0.0429945i
$725$	34.5453	+	0.341522i	1.28298	+	0.0126838i
$726$	1.60769	−	1.55814i	0.0596669	−	0.0578281i
$727$	4.22306	−	4.22306i	0.156625	−	0.156625i	−0.624444	−	0.781069i	$-0.714675\pi$
$727$	4.22306	−	4.22306i	0.156625	−	0.156625i	0.781069	+	0.624444i	$0.214675\pi$
$728$	5.21923	+	0.245209i	0.193437	+	0.00908806i
$729$		−	19.5516i		−	0.724134i
$730$	−0.353737	+	17.1759i	−0.0130924	+	0.635708i
$731$			29.7892i			1.10179i
$732$	−12.0127	−	12.7892i	−0.444003	−	0.472704i
$733$	10.7917	−	10.7917i	0.398601	−	0.398601i	−0.479139	−	0.877739i	$-0.659051\pi$
$733$	10.7917	−	10.7917i	0.398601	−	0.398601i	0.877739	+	0.479139i	$0.159051\pi$
$734$	0.325584	+	0.335937i	0.0120175	+	0.0123997i
$735$	−9.06003	−	0.0447835i	−0.334184	−	0.00165186i
$736$	−29.8003	+	25.4670i	−1.09845	+	0.938726i
$737$	3.16424	+	3.16424i	0.116556	+	0.116556i
$738$	−21.7271	−	0.340038i	−0.799787	−	0.0125170i
$739$	−40.5731			−1.49250			−0.746252	−	0.665663i	$-0.768149\pi$
$739$	−40.5731			−1.49250			−0.746252	+	0.665663i	$0.768149\pi$
$740$	1.39967	−	38.6040i	0.0514528	−	1.41911i
$741$	−3.05800			−0.112338
$742$	−16.8291	−	0.263382i	−0.617815	−	0.00966906i
$743$	2.78875	+	2.78875i	0.102309	+	0.102309i	0.756409	−	0.654099i	$-0.226952\pi$
$743$	2.78875	+	2.78875i	0.102309	+	0.102309i	−0.654099	+	0.756409i	$0.726952\pi$
$744$	8.93951	+	9.82091i	0.327738	+	0.360052i
$745$	20.9284	−	20.7225i	0.766757	−	0.759214i
$746$	19.0382	+	19.6436i	0.697039	+	0.719203i
$747$	1.25482	−	1.25482i	0.0459116	−	0.0459116i
$748$	−14.2552	+	13.3897i	−0.521221	+	0.489574i
$749$		−	2.31201i		−	0.0844790i
$750$	−0.544194	+	17.8498i	−0.0198711	+	0.651782i
$751$		−	17.6843i		−	0.645308i	−0.946517	−	0.322654i	$-0.895425\pi$
$751$		−	17.6843i		−	0.645308i	0.946517	−	0.322654i	$-0.104575\pi$
$752$	23.2606	−	20.5167i	0.848226	−	0.748167i
$753$	−16.9573	+	16.9573i	−0.617960	+	0.617960i
$754$	7.01667	−	6.80043i	0.255532	−	0.247657i
$755$	−31.2362	+	30.9290i	−1.13680	+	1.12562i
$756$	−0.616917	+	19.7045i	−0.0224371	+	0.716645i
$757$	21.2020	+	21.2020i	0.770600	+	0.770600i	0.978211	−	0.207611i	$-0.0665689\pi$
$757$	21.2020	+	21.2020i	0.770600	+	0.770600i	−0.207611	+	0.978211i	$0.566569\pi$
$758$	0.604106	−	38.6000i	0.0219421	−	1.40201i
$759$	−27.5622			−1.00044
$760$	−12.7201	+	11.4641i	−0.461408	+	0.415846i
$761$	−10.5601			−0.382804			−0.191402	−	0.981512i	$-0.561303\pi$
$761$	−10.5601			−0.382804			−0.191402	+	0.981512i	$0.561303\pi$
$762$	0.258139	−	16.4941i	0.00935141	−	0.597518i
$763$	−1.50275	−	1.50275i	−0.0544033	−	0.0544033i
$764$	−1.45817	+	46.5743i	−0.0527548	+	1.68500i
$765$	10.7065	+	0.0529220i	0.387094	+	0.00191340i
$766$	15.3769	−	14.9030i	0.555589	−	0.538466i
$767$	−1.61846	+	1.61846i	−0.0584392	+	0.0584392i
$768$	−11.0826	−	14.2738i	−0.399910	−	0.515060i
$769$			1.08776i			0.0392255i	0.999808	+	0.0196128i	$0.00624333\pi$
$769$			1.08776i			0.0392255i	−0.999808	+	0.0196128i	$0.993757\pi$
$770$	20.5678	+	0.423594i	0.741213	+	0.0152653i
$771$			1.74124i			0.0627094i
$772$	−5.51393	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0221303 - 1.41404i) q^{2} +(-0.798638 - 0.798638i) q^{3} +(-1.99902 - 0.0625863i) q^{4} +(-1.57330 - 1.58893i) q^{5} +(-1.14698 + 1.11163i) q^{6} +(-1.30625 + 1.30625i) q^{7} +(-0.132739 + 2.82531i) q^{8} -1.72435i q^{9} +O(q^{10})\)	\(q+(0.0221303 - 1.41404i) q^{2} +(-0.798638 - 0.798638i) q^{3} +(-1.99902 - 0.0625863i) q^{4} +(-1.57330 - 1.58893i) q^{5} +(-1.14698 + 1.11163i) q^{6} +(-1.30625 + 1.30625i) q^{7} +(-0.132739 + 2.82531i) q^{8} -1.72435i q^{9} +(-2.28164 + 2.18955i) q^{10} +3.52160i q^{11} +(1.54651 + 1.64648i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(1.81818 + 1.87599i) q^{14} +(-0.0124834 + 2.52548i) q^{15} +(3.99217 + 0.250223i) q^{16} +(-1.96348 - 1.96348i) q^{17} +(-2.43831 - 0.0381605i) q^{18} -2.70752 q^{19} +(3.04562 + 3.27478i) q^{20} +2.08644 q^{21} +(4.97969 + 0.0779341i) q^{22} +(-4.89998 - 4.89998i) q^{23} +(2.36241 - 2.15039i) q^{24} +(-0.0494285 + 4.99976i) q^{25} +(0.984229 + 1.01553i) q^{26} +(-3.77305 + 3.77305i) q^{27} +(2.69297 - 2.52946i) q^{28} -6.90940i q^{29} +(3.57086 + 0.0735418i) q^{30} +4.15716i q^{31} +(0.442173 - 5.63955i) q^{32} +(2.81248 - 2.81248i) q^{33} +(-2.81989 + 2.73299i) q^{34} +(4.13066 + 0.0204178i) q^{35} +(-0.107921 + 3.44702i) q^{36} +(-6.10784 - 6.10784i) q^{37} +(-0.0599183 + 3.82854i) q^{38} +1.12944 q^{39} +(4.69807 - 4.23416i) q^{40} +8.91075 q^{41} +(0.0461735 - 2.95031i) q^{42} +(-7.58581 - 7.58581i) q^{43} +(0.220404 - 7.03975i) q^{44} +(-2.73989 + 2.71293i) q^{45} +(-7.03720 + 6.82033i) q^{46} +(5.48290 - 5.48290i) q^{47} +(-2.98846 - 3.38813i) q^{48} +3.58744i q^{49} +(7.06876 + 0.180540i) q^{50} +3.13622i q^{51} +(1.45778 - 1.36927i) q^{52} +(-4.55558 + 4.55558i) q^{53} +(5.25175 + 5.41874i) q^{54} +(5.59559 - 5.54055i) q^{55} +(-3.51716 - 3.86394i) q^{56} +(2.16233 + 2.16233i) q^{57} +(-9.77017 - 0.152907i) q^{58} +2.28885 q^{59} +(0.183015 - 5.04771i) q^{60} -7.76763 q^{61} +(5.87839 + 0.0919991i) q^{62} +(2.25243 + 2.25243i) q^{63} +(-7.96476 - 0.750055i) q^{64} +(2.23604 + 0.0110527i) q^{65} +(-3.91473 - 4.03921i) q^{66} +(0.898523 - 0.898523i) q^{67} +(3.80215 + 4.04792i) q^{68} +7.82662i q^{69} +(0.120284 - 5.84047i) q^{70} -14.2978i q^{71} +(4.87184 + 0.228888i) q^{72} +(3.84146 - 3.84146i) q^{73} +(-8.77190 + 8.50156i) q^{74} +(4.03247 - 3.95352i) q^{75} +(5.41239 + 0.169454i) q^{76} +(-4.60008 - 4.60008i) q^{77} +(0.0249950 - 1.59708i) q^{78} +0.766856 q^{79} +(-5.88330 - 6.73697i) q^{80} +0.853540 q^{81} +(0.197198 - 12.6002i) q^{82} +(0.727706 + 0.727706i) q^{83} +(-4.17083 - 0.130582i) q^{84} +(-0.0306909 + 6.20899i) q^{85} +(-10.8945 + 10.5588i) q^{86} +(-5.51811 + 5.51811i) q^{87} +(-9.94962 - 0.467452i) q^{88} +0.442426i q^{89} +(3.77556 + 3.93435i) q^{90} -1.84731i q^{91} +(9.48848 + 10.1018i) q^{92} +(3.32006 - 3.32006i) q^{93} +(-7.63170 - 7.87438i) q^{94} +(4.25975 + 4.30208i) q^{95} +(-4.85709 + 4.15082i) q^{96} +(5.22374 + 5.22374i) q^{97} +(5.07279 + 0.0793912i) q^{98} +6.07249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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