LMFDB - Embedded newform 260.2.o.a.27.1

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			27.1
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41404 + 0.0221303i) q^{2} +(0.798638 + 0.798638i) q^{3} +(1.99902 - 0.0625863i) q^{4} +(-1.57330 - 1.58893i) q^{5} +(-1.14698 - 1.11163i) q^{6} +(1.30625 - 1.30625i) q^{7} +(-2.82531 + 0.132739i) q^{8} -1.72435i q^{9} +O(q^{10})$	\(q+(-1.41404 + 0.0221303i) 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} +(-2.82531 + 0.132739i) q^{8} -1.72435i q^{9} +(2.25988 + 2.21200i) q^{10} -3.52160i q^{11} +(1.64648 + 1.54651i) 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} +(0.0381605 + 2.43831i) q^{18} +2.70752 q^{19} +(-3.24451 - 3.07785i) q^{20} +2.08644 q^{21} +(0.0779341 + 4.97969i) 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} +(2.52946 - 2.69297i) q^{28} -6.90940i q^{29} +(0.0382377 + 3.57141i) q^{30} -4.15716i q^{31} +(-5.63955 + 0.442173i) 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} +(-3.82854 + 0.0599183i) q^{38} -1.12944 q^{39} +(4.65599 + 4.28040i) q^{40} +8.91075 q^{41} +(-2.95031 + 0.0461735i) 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} +(3.38813 + 2.98846i) q^{48} +3.58744i q^{49} +(-0.0407522 - 7.07095i) q^{50} -3.13622i q^{51} +(-1.36927 + 1.45778i) 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} +(0.152907 + 9.77017i) q^{58} -2.28885 q^{59} +(-0.133106 - 5.04928i) q^{60} -7.76763 q^{61} +(0.0919991 + 5.87839i) 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} +(-4.04792 - 3.80215i) q^{68} +7.82662i q^{69} +(5.84138 - 0.0625413i) q^{70} +14.2978i q^{71} +(0.228888 + 4.87184i) 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} +(1.59708 - 0.0249950i) q^{78} -0.766856 q^{79} +(-6.67848 - 5.94962i) q^{80} +0.853540 q^{81} +(-12.6002 + 0.197198i) 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} +(0.467452 + 9.94962i) q^{88} +0.442426i q^{89} +(3.81427 - 3.89683i) q^{90} +1.84731i q^{91} +(10.1018 + 9.48848i) 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} +(-0.0793912 - 5.07279i) 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 $

$2$	−1.41404	+	0.0221303i	−0.999878	+	0.0156485i
$2$	−1.41404	+	0.0221303i	−0.999878	+	0.0156485i
$3$	0.798638	+	0.798638i	0.461094	+	0.461094i	0.899014	−	0.437920i	$-0.144285\pi$
$3$	0.798638	+	0.798638i	0.461094	+	0.461094i	−0.437920	+	0.899014i	$0.644285\pi$
$4$	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	−0.415760	−	0.909474i	$-0.636484\pi$
$7$	1.30625	−	1.30625i	0.493715	−	0.493715i	0.909474	+	0.415760i	$0.136484\pi$
$8$	−2.82531	+	0.132739i	−0.998898	+	0.0469301i
$9$		−	1.72435i		−	0.574785i
$10$	2.25988	+	2.21200i	0.714637	+	0.699496i
$11$		−	3.52160i		−	1.06180i	−0.847434	−	0.530901i	$-0.821854\pi$
$11$		−	3.52160i		−	1.06180i	0.847434	−	0.530901i	$-0.178146\pi$
$12$	1.64648	+	1.54651i	0.475297	+	0.446439i
$13$	−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	$0.859322\pi$
$18$	0.0381605	+	2.43831i	0.00899451	+	0.574714i
$19$	2.70752			0.621148			0.310574	−	0.950549i	$-0.399479\pi$
$19$	2.70752			0.621148			0.310574	+	0.950549i	$0.399479\pi$
$20$	−3.24451	−	3.07785i	−0.725495	−	0.688227i
$21$	2.08644			0.455298
$22$	0.0779341	+	4.97969i	0.0166156	+	1.06167i
$23$	4.89998	+	4.89998i	1.02172	+	1.02172i	0.999759	+	0.0219567i	$0.00698959\pi$
$23$	4.89998	+	4.89998i	1.02172	+	1.02172i	0.0219567	+	0.999759i	$0.493010\pi$
$24$	−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
$28$	2.52946	−	2.69297i	0.478023	−	0.508923i
$29$		−	6.90940i		−	1.28304i	−0.767105	−	0.641522i	$-0.778303\pi$
$29$		−	6.90940i		−	1.28304i	0.767105	−	0.641522i	$-0.221697\pi$
$30$	0.0382377	+	3.57141i	0.00698122	+	0.652048i
$31$		−	4.15716i		−	0.746647i	−0.927701	−	0.373324i	$-0.878218\pi$
$31$		−	4.15716i		−	0.746647i	0.927701	−	0.373324i	$-0.121782\pi$
$32$	−5.63955	+	0.442173i	−0.996940	+	0.0781658i
$33$	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	$-0.501315\pi$
$38$	−3.82854	+	0.0599183i	−0.621072	+	0.00972003i
$39$	−1.12944			−0.180856
$40$	4.65599	+	4.28040i	0.736176	+	0.676790i
$41$	8.91075			1.39162			0.695812	−	0.718224i	$-0.255045\pi$
$41$	8.91075			1.39162			0.695812	+	0.718224i	$0.255045\pi$
$42$	−2.95031	+	0.0461735i	−0.455242	+	0.00712472i
$43$	7.58581	+	7.58581i	1.15683	+	1.15683i	0.985154	+	0.171671i	$0.0549166\pi$
$43$	7.58581	+	7.58581i	1.15683	+	1.15683i	0.171671	+	0.985154i	$0.445083\pi$
$44$	−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	−0.983058	−	0.183295i	$-0.941324\pi$
$47$	−5.48290	+	5.48290i	−0.799763	+	0.799763i	0.183295	+	0.983058i	$0.441324\pi$
$48$	3.38813	+	2.98846i	0.489035	+	0.431347i
$49$			3.58744i			0.512492i
$50$	−0.0407522	−	7.07095i	−0.00576323	−	0.999983i
$51$		−	3.13622i		−	0.439159i
$52$	−1.36927	+	1.45778i	−0.189883	+	0.202157i
$53$	−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
$58$	0.152907	+	9.77017i	0.0200777	+	1.28289i
$59$	−2.28885			−0.297982			−0.148991	−	0.988839i	$-0.547603\pi$
$59$	−2.28885			−0.297982			−0.148991	+	0.988839i	$0.547603\pi$
$60$	−0.133106	−	5.04928i	−0.0171839	−	0.651859i
$61$	−7.76763			−0.994543			−0.497272	−	0.867595i	$-0.665665\pi$
$61$	−7.76763			−0.994543			−0.497272	+	0.867595i	$0.665665\pi$
$62$	0.0919991	+	5.87839i	0.0116839	+	0.746556i
$63$	−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	−0.759859	−	0.650087i	$-0.774732\pi$
$67$	−0.898523	+	0.898523i	−0.109772	+	0.109772i	0.650087	+	0.759859i	$0.274732\pi$
$68$	−4.04792	−	3.80215i	−0.490883	−	0.461078i
$69$			7.82662i			0.942214i
$70$	5.84138	−	0.0625413i	0.698178	−	0.00747512i
$71$			14.2978i			1.69683i	0.529331	+	0.848416i	$0.322443\pi$
$71$			14.2978i			1.69683i	−0.529331	+	0.848416i	$0.677557\pi$
$72$	0.228888	+	4.87184i	0.0269747	+	0.574151i
$73$	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
$78$	1.59708	−	0.0249950i	0.180834	−	0.00283012i
$79$	−0.766856			−0.0862780			−0.0431390	−	0.999069i	$-0.513736\pi$
$79$	−0.766856			−0.0862780			−0.0431390	+	0.999069i	$0.513736\pi$
$80$	−6.67848	−	5.94962i	−0.746677	−	0.665187i
$81$	0.853540			0.0948378
$82$	−12.6002	+	0.197198i	−1.39145	+	0.0217768i
$83$	−0.727706	−	0.727706i	−0.0798761	−	0.0798761i	0.666040	−	0.745916i	$-0.267988\pi$
$83$	−0.727706	−	0.727706i	−0.0798761	−	0.0798761i	−0.745916	+	0.666040i	$0.767988\pi$
$84$	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
$88$	0.467452	+	9.94962i	0.0498305	+	1.06063i
$89$			0.442426i			0.0468970i	0.999725	+	0.0234485i	$0.00746458\pi$
$89$			0.442426i			0.0468970i	−0.999725	+	0.0234485i	$0.992535\pi$
$90$	3.81427	−	3.89683i	0.402060	−	0.410762i
$91$			1.84731i			0.193651i
$92$	10.1018	+	9.48848i	1.05319	+	0.989243i
$93$	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	$0.627628\pi$
$98$	−0.0793912	−	5.07279i	−0.00801972	−	0.512429i
$99$	−6.07249			−0.610308
$100$	0.214108	+	9.99771i	0.0214108	+	0.999771i
$101$	3.42179			0.340481			0.170240	−	0.985403i	$-0.445546\pi$
$101$	3.42179			0.340481			0.170240	+	0.985403i	$0.445546\pi$
$102$	0.0694055	+	4.43474i	0.00687217	+	0.439105i
$103$	−9.11709	−	9.11709i	−0.898333	−	0.898333i	0.0969555	−	0.995289i	$-0.469090\pi$
$103$	−9.11709	−	9.11709i	−0.898333	−	0.898333i	−0.995289	+	0.0969555i	$0.969090\pi$
$104$	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	−0.663034	−	0.748589i	$-0.730732\pi$
$107$	0.884982	−	0.884982i	0.0855545	−	0.0855545i	0.748589	+	0.663034i	$0.230732\pi$
$108$	7.30626	−	7.77854i	0.703045	−	0.748491i
$109$			1.15044i			0.110192i	0.998481	+	0.0550959i	$0.0175465\pi$
$109$			1.15044i			0.110192i	−0.998481	+	0.0550959i	$0.982454\pi$
$110$	7.78978	−	7.95839i	0.742727	−	0.758803i
$111$		−	9.75590i		−	0.925989i
$112$	4.88790	−	5.54160i	0.461863	−	0.523632i
$113$	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
$118$	3.23652	−	0.0506529i	0.297946	−	0.00466298i
$119$	−5.12958			−0.470228
$120$	0.299960	+	7.13694i	0.0273824	+	0.651510i
$121$	−1.40167			−0.127425
$122$	10.9837	−	0.171900i	0.994422	−	0.0155631i
$123$	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	−0.304498	−	0.952513i	$-0.598489\pi$
$127$	7.30276	−	7.30276i	0.648015	−	0.648015i	0.952513	+	0.304498i	$0.0984887\pi$
$128$	−11.2459	+	1.23687i	−0.994006	+	0.109325i
$129$			12.1166i			1.06681i
$130$	−3.16210	+	0.0338553i	−0.277334	+	0.00296931i
$131$		−	4.60019i		−	0.401920i	−0.979599	−	0.200960i	$-0.935594\pi$
$131$		−	4.60019i		−	0.401920i	0.979599	−	0.200960i	$-0.0644061\pi$
$132$	5.44619	−	5.79824i	0.474030	−	0.504672i
$133$	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	$0.494970\pi$
$138$	−0.173205	−	11.0672i	−0.0147442	−	0.942098i
$139$	10.1337			0.859532			0.429766	−	0.902940i	$-0.358596\pi$
$139$	10.1337			0.859532			0.429766	+	0.902940i	$0.358596\pi$
$140$	−8.25856	+	0.217707i	−0.697976	+	0.0183996i
$141$	−8.75771			−0.737532
$142$	−0.316414	−	20.2176i	−0.0265528	−	1.69662i
$143$	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
$148$	−12.5920	−	11.8274i	−1.03505	−	0.972208i
$149$			13.1713i			1.07904i	0.841974	+	0.539519i	$0.181394\pi$
$149$			13.1713i			1.07904i	−0.841974	+	0.539519i	$0.818606\pi$
$150$	5.61458	−	5.67968i	0.458429	−	0.463744i
$151$			19.6586i			1.59979i	0.600137	+	0.799897i	$0.295113\pi$
$151$			19.6586i			1.59979i	−0.600137	+	0.799897i	$0.704887\pi$
$152$	−7.64959	+	0.359392i	−0.620464	+	0.0291506i
$153$	−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	$0.962595\pi$
$158$	1.08437	−	0.0169708i	0.0862675	−	0.00135012i
$159$	−7.27652			−0.577066
$160$	9.57531	+	8.26520i	0.756994	+	0.653421i
$161$	12.8012			1.00887
$162$	−1.20694	+	0.0188891i	−0.0948261	+	0.00148407i
$163$	4.24886	+	4.24886i	0.332796	+	0.332796i	0.853648	−	0.520851i	$-0.174385\pi$
$163$	4.24886	+	4.24886i	0.332796	+	0.332796i	−0.520851	+	0.853648i	$0.674385\pi$
$164$	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	−0.00829711	−	0.999966i	$-0.502641\pi$
$167$	12.8152	−	12.8152i	0.991668	−	0.991668i	0.999966	+	0.00829711i	$0.00264108\pi$
$168$	−5.89483	+	0.276950i	−0.454796	+	0.0213672i
$169$		−	1.00000i		−	0.0769231i
$170$	−0.0940088	−	8.78045i	−0.00721014	−	0.673429i
$171$		−	4.66873i		−	0.357026i
$172$	15.6390	+	14.6894i	1.19246	+	1.12006i
$173$	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
$178$	−0.00979101	−	0.625608i	−0.000733868	−	0.0468913i
$179$	2.63043			0.196608			0.0983039	−	0.995156i	$-0.468658\pi$
$179$	2.63043			0.196608			0.0983039	+	0.995156i	$0.468658\pi$
$180$	−5.30730	+	5.59469i	−0.395583	+	0.417004i
$181$	18.4843			1.37393			0.686963	−	0.726692i	$-0.258943\pi$
$181$	18.4843			1.37393			0.686963	+	0.726692i	$0.258943\pi$
$182$	−0.0408816	−	2.61217i	−0.00303034	−	0.193627i
$183$	−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
$188$	−10.6173	+	11.3036i	−0.774344	+	0.824398i
$189$		−	9.85706i		−	0.716996i
$190$	6.11867	+	5.98904i	0.443895	+	0.434491i
$191$			23.2986i			1.68582i	0.538051	+	0.842912i	$0.319161\pi$
$191$			23.2986i			1.68582i	−0.538051	+	0.842912i	$0.680839\pi$
$192$	6.95998	+	5.76194i	0.502294	+	0.415832i
$193$	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	$0.971242\pi$
$198$	8.58674	−	0.134386i	0.610233	−	0.00955040i
$199$	7.65179			0.542421			0.271211	−	0.962520i	$-0.412576\pi$
$199$	7.65179			0.542421			0.271211	+	0.962520i	$0.412576\pi$
$200$	−0.524009	−	14.1324i	−0.0370530	−	0.999313i
$201$	−1.43519			−0.101230
$202$	−4.83855	+	0.0757252i	−0.340439	+	0.00532801i
$203$	−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
$208$	−2.64595	+	2.99982i	−0.183464	+	0.208000i
$209$		−	9.53481i		−	0.659537i
$210$	4.71509	+	4.61520i	0.325372	+	0.318479i
$211$			0.696850i			0.0479731i	0.999712	+	0.0239866i	$0.00763589\pi$
$211$			0.696850i			0.0479731i	−0.999712	+	0.0239866i	$0.992364\pi$
$212$	−8.82158	+	9.39182i	−0.605869	+	0.645033i
$213$	−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
$218$	−0.0254595	−	1.62676i	−0.00172434	−	0.110178i
$219$	6.13587			0.414624
$220$	−10.8389	+	11.4259i	−0.730762	+	0.770333i
$221$	2.77678			0.186786
$222$	0.215901	+	13.7952i	0.0144903	+	0.925876i
$223$	8.11155	+	8.11155i	0.543190	+	0.543190i	0.924463	−	0.381273i	$-0.124514\pi$
$223$	8.11155	+	8.11155i	0.543190	+	0.543190i	−0.381273	+	0.924463i	$0.624514\pi$
$224$	−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	$0.528262\pi$
$227$	−16.3431	+	16.3431i	−1.08473	+	1.08473i	−0.996061	+	0.0886719i	$0.971738\pi$
$228$	4.45787	+	4.18721i	0.295230	+	0.277305i
$229$			23.0298i			1.52185i	0.648838	+	0.760926i	$0.275255\pi$
$229$			23.0298i			1.52185i	−0.648838	+	0.760926i	$0.724745\pi$
$230$	0.234604	+	21.9121i	0.0154693	+	1.44484i
$231$		−	7.34760i		−	0.483436i
$232$	0.917143	+	19.5212i	0.0602134	+	1.28163i
$233$	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
$238$	7.25343	−	0.113519i	0.470170	−	0.00735835i
$239$	12.2710			0.793744			0.396872	−	0.917874i	$-0.370096\pi$
$239$	12.2710			0.793744			0.396872	+	0.917874i	$0.370096\pi$
$240$	−0.582098	−	10.0853i	−0.0375742	−	0.651002i
$241$	−25.1592			−1.62065			−0.810325	−	0.585981i	$-0.800709\pi$
$241$	−25.1592			−1.62065			−0.810325	+	0.585981i	$0.800709\pi$
$242$	1.98202	−	0.0310194i	0.127409	−	0.00199400i
$243$	−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
$248$	0.551815	+	11.7453i	0.0350403	+	0.745825i
$249$		−	1.16235i		−	0.0736608i
$250$	−11.1712	+	11.1895i	−0.706526	+	0.707687i
$251$			21.2328i			1.34020i	0.742269	+	0.670102i	$0.233750\pi$
$251$			21.2328i			1.34020i	−0.742269	+	0.670102i	$0.766250\pi$
$252$	−4.64363	−	4.36169i	−0.292521	−	0.274760i
$253$	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	$0.765311\pi$
$258$	−0.268145	−	17.1334i	−0.0166940	−	1.06668i
$259$	−15.9567			−0.991500
$260$	4.47058	−	0.117851i	0.277254	−	0.00730881i
$261$	−11.9143			−0.737474
$262$	0.101804	+	6.50485i	0.00628944	+	0.401871i
$263$	12.5796	+	12.5796i	0.775689	+	0.775689i	0.979095	−	0.203405i	$-0.0652009\pi$
$263$	12.5796	+	12.5796i	0.775689	+	0.775689i	−0.203405	+	0.979095i	$0.565201\pi$
$264$	−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
$268$	−1.73993	+	1.85240i	−0.106283	+	0.113153i
$269$		−	19.7683i		−	1.20529i	−0.798008	−	0.602647i	$-0.794113\pi$
$269$		−	19.7683i		−	1.20529i	0.798008	−	0.602647i	$-0.205887\pi$
$270$	16.8726	−	0.180649i	1.02684	−	0.0109939i
$271$		−	21.2849i		−	1.29296i	−0.762929	−	0.646482i	$-0.776239\pi$
$271$		−	21.2849i		−	1.29296i	0.762929	−	0.646482i	$-0.223761\pi$
$272$	−8.32984	−	7.34723i	−0.505071	−	0.445491i
$273$	−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	$0.936416\pi$
$278$	−14.3295	+	0.224263i	−0.859426	+	0.0134504i
$279$	−7.16841			−0.429161
$280$	11.6731	−	0.490612i	0.697602	−	0.0293196i
$281$	12.4347			0.741790			0.370895	−	0.928675i	$-0.379051\pi$
$281$	12.4347			0.741790			0.370895	+	0.928675i	$0.379051\pi$
$282$	12.3837	−	0.193811i	0.737442	−	0.0115413i
$283$	−13.2718	−	13.2718i	−0.788926	−	0.788926i	0.192393	−	0.981318i	$-0.438375\pi$
$283$	−13.2718	−	13.2718i	−0.788926	−	0.788926i	−0.981318	+	0.192393i	$0.938375\pi$
$284$	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
$288$	0.762462	+	9.72458i	0.0449285	+	0.573026i
$289$		−	9.28949i		−	0.546441i
$290$	15.2836	−	15.6144i	0.897484	−	0.916910i
$291$			8.34375i			0.489119i
$292$	7.43873	−	7.91957i	0.435319	−	0.463458i
$293$	−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
$298$	−0.291486	−	18.6248i	−0.0168853	−	1.07891i
$299$	−6.92961			−0.400750
$300$	−7.81356	+	8.15555i	−0.451116	+	0.470861i
$301$	19.8179			1.14228
$302$	−0.435051	−	27.7981i	−0.0250344	−	1.59960i
$303$	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	−0.582999	−	0.812473i	$-0.698121\pi$
$307$	4.02072	−	4.02072i	0.229474	−	0.229474i	0.812473	+	0.582999i	$0.198121\pi$
$308$	−9.48355	−	8.90775i	−0.540376	−	0.507566i
$309$		−	14.5625i		−	0.828432i
$310$	9.19563	−	9.39467i	0.522277	−	0.533581i
$311$			25.4676i			1.44413i	0.691823	+	0.722067i	$0.256808\pi$
$311$			25.4676i			1.44413i	−0.691823	+	0.722067i	$0.743192\pi$
$312$	3.19103	−	0.149921i	0.180657	−	0.00848760i
$313$	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	$0.576626\pi$
$318$	10.2893	−	0.161032i	0.576995	−	0.00903021i
$319$	−24.3321			−1.36234
$320$	−13.7228	−	11.4754i	−0.767127	−	0.641496i
$321$	1.41356			0.0788973
$322$	−18.1013	+	0.283293i	−1.00875	+	0.0157873i
$323$	−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
$328$	−25.1756	+	1.18280i	−1.39009	+	0.0653092i
$329$			14.3240i			0.789710i
$330$	12.5771	−	0.134658i	0.692346	−	0.00741268i
$331$		−	22.5223i		−	1.23794i	−0.785415	−	0.618970i	$-0.787550\pi$
$331$		−	22.5223i		−	1.23794i	0.785415	−	0.618970i	$-0.212450\pi$
$332$	−1.50024	−	1.40916i	−0.0823366	−	0.0773374i
$333$	−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	$0.496937\pi$
$338$	0.0221303	+	1.41404i	0.00120373	+	0.0769137i
$339$	3.48001			0.189008
$340$	0.327246	+	12.4138i	0.0177474	+	0.673234i
$341$	−14.6398			−0.792792
$342$	0.103320	+	6.60177i	0.00558692	+	0.356983i
$343$	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	$-0.493446\pi$
$347$	19.0075	−	19.0075i	1.02038	−	1.02038i	0.999788	−	0.0205887i	$-0.00655405\pi$
$348$	10.6855	−	11.3762i	0.572801	−	0.609827i
$349$			7.56368i			0.404874i	0.979295	+	0.202437i	$0.0648862\pi$
$349$			7.56368i			0.404874i	−0.979295	+	0.202437i	$0.935114\pi$
$350$	−9.28964	−	9.18317i	−0.496552	−	0.490861i
$351$			5.33590i			0.284809i
$352$	1.55716	+	19.8602i	0.0829967	+	1.05855i
$353$	−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
$358$	−3.71954	+	0.0582123i	−0.196584	+	0.00307661i
$359$	25.3560			1.33824			0.669120	−	0.743155i	$-0.266671\pi$
$359$	25.3560			1.33824			0.669120	+	0.743155i	$0.266671\pi$
$360$	7.38092	−	8.02857i	0.389009	−	0.423143i
$361$	−11.6693			−0.614175
$362$	−26.1375	+	0.409063i	−1.37376	+	0.0214999i
$363$	−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	−0.700975	−	0.713185i	$-0.747252\pi$
$367$	0.233912	−	0.233912i	0.0122101	−	0.0122101i	0.713185	+	0.700975i	$0.247252\pi$
$368$	20.7876	+	18.3354i	1.08363	+	0.955800i
$369$		−	15.3653i		−	0.799885i
$370$	−0.292435	−	27.3135i	−0.0152030	−	1.41996i
$371$			11.9014i			0.617891i
$372$	6.42908	−	6.84466i	0.333332	−	0.354879i
$373$	−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
$378$	0.218140	+	13.9383i	0.0112199	+	0.716908i
$379$	−27.2977			−1.40219			−0.701093	−	0.713070i	$-0.747304\pi$
$379$	−27.2977			−1.40219			−0.701093	+	0.713070i	$0.747304\pi$
$380$	−8.78459	−	8.33333i	−0.450640	−	0.427491i
$381$	11.6645			0.597591
$382$	−0.515604	−	32.9451i	−0.0263806	−	1.68562i
$383$	−10.7069	−	10.7069i	−0.547095	−	0.547095i	0.378505	−	0.925599i	$-0.376438\pi$
$383$	−10.7069	−	10.7069i	−0.547095	−	0.547095i	−0.925599	+	0.378505i	$0.876438\pi$
$384$	−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
$388$	10.7693	+	10.1154i	0.546728	+	0.513533i
$389$		−	1.85990i		−	0.0943006i	−0.998888	−	0.0471503i	$-0.984986\pi$
$389$		−	1.85990i		−	0.0943006i	0.998888	−	0.0471503i	$-0.0150140\pi$
$390$	−2.55241	−	2.49833i	−0.129246	−	0.126508i
$391$		−	19.2420i		−	0.973110i
$392$	−0.476191	−	10.1356i	−0.0240513	−	0.511927i
$393$	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	$0.732501\pi$
$398$	−10.8199	+	0.169337i	−0.542355	+	0.00848807i
$399$	5.64907			0.282807
$400$	1.05372	+	19.9722i	0.0526862	+	0.998611i
$401$	−25.1569			−1.25628			−0.628139	−	0.778101i	$-0.716183\pi$
$401$	−25.1569			−1.25628			−0.628139	+	0.778101i	$0.716183\pi$
$402$	2.02941	−	0.0317612i	0.101218	−	0.00158410i
$403$	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
$408$	0.416297	+	8.86079i	0.0206098	+	0.438675i
$409$		−	17.0509i		−	0.843112i	−0.906802	−	0.421556i	$-0.861484\pi$
$409$		−	17.0509i		−	0.843112i	0.906802	−	0.421556i	$-0.138516\pi$
$410$	20.1372	+	19.7106i	0.994506	+	0.973436i
$411$			18.9887i			0.936644i
$412$	−18.7958	−	17.6546i	−0.926005	−	0.869782i
$413$	−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
$418$	0.211008	+	13.4826i	0.0103208	+	0.659456i
$419$	33.8791			1.65510			0.827551	−	0.561391i	$-0.189734\pi$
$419$	33.8791			1.65510			0.827551	+	0.561391i	$0.189734\pi$
$420$	−6.76947	−	6.42173i	−0.330316	−	0.313348i
$421$	−25.0338			−1.22007			−0.610036	−	0.792374i	$-0.708845\pi$
$421$	−25.0338			−1.22007			−0.610036	+	0.792374i	$0.708845\pi$
$422$	−0.0154215	−	0.985374i	−0.000750707	−	0.0479672i
$423$	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
$428$	1.71371	−	1.82449i	0.0828353	−	0.0881898i
$429$			3.97745i			0.192033i
$430$	0.363198	+	33.9228i	0.0175150	+	1.63590i
$431$		−	15.0689i		−	0.725844i	−0.931820	−	0.362922i	$-0.881779\pi$
$431$		−	15.0689i		−	0.725844i	0.931820	−	0.362922i	$-0.118221\pi$
$432$	14.1185	−	16.0067i	0.679278	−	0.770125i
$433$	−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
$438$	−8.67637	+	0.135789i	−0.414573	+	0.00648823i
$439$	−29.6737			−1.41625			−0.708124	−	0.706088i	$-0.750458\pi$
$439$	−29.6737			−1.41625			−0.708124	+	0.706088i	$0.750458\pi$
$440$	15.0738	−	16.3965i	0.718618	−	0.781674i
$441$	6.18602			0.294572
$442$	−3.92648	+	0.0614510i	−0.186764	+	0.00292293i
$443$	−1.89262	−	1.89262i	−0.0899213	−	0.0899213i	0.660715	−	0.750637i	$-0.270253\pi$
$443$	−1.89262	−	1.89262i	−0.0899213	−	0.0899213i	−0.750637	+	0.660715i	$0.770253\pi$
$444$	−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
$448$	9.42418	−	11.3837i	0.445251	−	0.537829i
$449$		−	12.5398i		−	0.591791i	−0.955220	−	0.295895i	$-0.904382\pi$
$449$		−	12.5398i		−	0.591791i	0.955220	−	0.295895i	$-0.0956180\pi$
$450$	−12.1928	+	0.0702712i	−0.574775	+	0.00331262i
$451$		−	31.3801i		−	1.47763i
$452$	4.21894	−	4.49166i	0.198442	−	0.211270i
$453$	−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	$0.616962\pi$
$458$	−0.509657	−	32.5651i	−0.0238147	−	1.52167i
$459$	−14.8166			−0.691580
$460$	−0.816661	−	30.9794i	−0.0380770	−	1.44442i
$461$	6.10051			0.284129			0.142065	−	0.989857i	$-0.454626\pi$
$461$	6.10051			0.284129			0.142065	+	0.989857i	$0.454626\pi$
$462$	0.162605	+	10.3898i	0.00756505	+	0.483377i
$463$	−23.1386	−	23.1386i	−1.07534	−	1.07534i	−0.996920	−	0.0784197i	$-0.975013\pi$
$463$	−23.1386	−	23.1386i	−1.07534	−	1.07534i	−0.0784197	−	0.996920i	$-0.524987\pi$
$464$	−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	−0.930758	−	0.365636i	$-0.880851\pi$
$467$	−12.2124	+	12.2124i	−0.565122	+	0.565122i	0.365636	+	0.930758i	$0.380851\pi$
$468$	2.51372	+	2.36110i	0.116197	+	0.109142i
$469$			2.34738i			0.108392i
$470$	−24.5189	+	0.262514i	−1.13097	+	0.0121089i
$471$		−	17.5294i		−	0.807710i
$472$	6.46670	−	0.303818i	0.297654	−	0.0139844i
$473$	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
$478$	−17.3517	+	0.271561i	−0.793646	+	0.0124209i
$479$	21.9564			1.00321			0.501607	−	0.865096i	$-0.332742\pi$
$479$	21.9564			1.00321			0.501607	+	0.865096i	$0.332742\pi$
$480$	1.04630	+	14.2481i	0.0477568	+	0.650334i
$481$	8.63779			0.393849
$482$	35.5762	−	0.556782i	1.62045	−	0.0253607i
$483$	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	−0.994004	−	0.109345i	$-0.965125\pi$
$487$	−19.5227	+	19.5227i	−0.884659	+	0.884659i	0.109345	+	0.994004i	$0.465125\pi$
$488$	21.9460	−	1.03106i	0.993448	−	0.0466741i
$489$			6.78660i			0.306901i
$490$	−7.93542	+	8.10718i	−0.358486	+	0.366245i
$491$		−	5.37843i		−	0.242725i	−0.992608	−	0.121363i	$-0.961274\pi$
$491$		−	5.37843i		−	0.242725i	0.992608	−	0.121363i	$-0.0387264\pi$
$492$	14.6713	+	13.7806i	0.661435	+	0.621276i
$493$	−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
$498$	0.0257231	+	1.64361i	0.00115268	+	0.0736518i
$499$	−25.0685			−1.12222			−0.561111	−	0.827740i	$-0.689626\pi$
$499$	−25.0685			−1.12222			−0.561111	+	0.827740i	$0.689626\pi$
$500$	15.5489	−	16.0696i	0.695366	−	0.718656i
$501$	20.4694			0.914505
$502$	−0.469889	−	30.0241i	−0.0209722	−	1.34004i
$503$	−16.4098	−	16.4098i	−0.731676	−	0.731676i	0.239276	−	0.970952i	$-0.423090\pi$
$503$	−16.4098	−	16.4098i	−0.731676	−	0.731676i	−0.970952	+	0.239276i	$0.923090\pi$
$504$	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
$508$	14.1413	−	15.0554i	0.627419	−	0.667976i
$509$		−	14.9919i		−	0.664503i	−0.943191	−	0.332252i	$-0.892192\pi$
$509$		−	14.9919i		−	0.664503i	0.943191	−	0.332252i	$-0.107808\pi$
$510$	6.93732	−	7.08748i	0.307190	−	0.313839i
$511$		−	10.0358i		−	0.443957i
$512$	−22.4034	+	3.17637i	−0.990098	+	0.140377i
$513$	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
$518$	22.5634	−	0.353126i	0.991378	−	0.0155155i
$519$	5.71814			0.250999
$520$	−6.31898	+	0.265581i	−0.277105	+	0.0116465i
$521$	13.2279			0.579524			0.289762	−	0.957099i	$-0.406424\pi$
$521$	13.2279			0.579524			0.289762	+	0.957099i	$0.406424\pi$
$522$	16.8472	−	0.263666i	0.737383	−	0.0115404i
$523$	−13.5227	−	13.5227i	−0.591304	−	0.591304i	0.346679	−	0.937984i	$-0.387309\pi$
$523$	−13.5227	−	13.5227i	−0.591304	−	0.591304i	−0.937984	+	0.346679i	$0.887309\pi$
$524$	−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
$528$	10.5242	−	11.9317i	0.458005	−	0.519259i
$529$			25.0195i			1.08781i
$530$	−20.3720	+	0.218115i	−0.884903	+	0.00947431i
$531$			3.94678i			0.171276i
$532$	6.84857	−	7.29126i	0.296923	−	0.316116i
$533$	−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
$538$	0.437479	+	27.9532i	0.0188610	+	1.20515i
$539$	12.6335			0.544165
$540$	−23.8546	+	0.628841i	−1.02654	+	0.0270610i
$541$	18.3005			0.786799			0.393400	−	0.919368i	$-0.371299\pi$
$541$	18.3005			0.786799			0.393400	+	0.919368i	$0.371299\pi$
$542$	0.471041	+	30.0977i	0.0202330	+	1.29281i
$543$	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	−0.999942	−	0.0107946i	$-0.996564\pi$
$547$	−23.1342	+	23.1342i	−0.989147	+	0.989147i	0.0107946	+	0.999942i	$0.496564\pi$
$548$	24.5087	+	23.0207i	1.04696	+	0.983394i
$549$			13.3941i			0.571648i
$550$	−24.9011	+	0.143513i	−1.06178	+	0.00611941i
$551$		−	18.7073i		−	0.796960i
$552$	−1.03889	−	22.1126i	−0.0442182	−	0.941176i
$553$	−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	$0.875220\pi$
$558$	10.1364	−	0.158639i	0.429109	−	0.00671573i
$559$	−10.7280			−0.453744
$560$	−16.4954	+	0.952074i	−0.697058	+	0.0402325i
$561$	−11.0445			−0.466300
$562$	−17.5831	+	0.275183i	−0.741699	+	0.0116079i
$563$	−25.0765	−	25.0765i	−1.05685	−	1.05685i	−0.998284	−	0.0585642i	$-0.981348\pi$
$563$	−25.0765	−	25.0765i	−1.05685	−	1.05685i	−0.0585642	−	0.998284i	$-0.518652\pi$
$564$	−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
$568$	−1.89786	−	40.3956i	−0.0796325	−	1.69496i
$569$		−	3.78598i		−	0.158716i	−0.996846	−	0.0793582i	$-0.974713\pi$
$569$		−	3.78598i		−	0.158716i	0.996846	−	0.0793582i	$-0.0252871\pi$
$570$	0.103529	+	9.66968i	0.00433637	+	0.405018i
$571$			25.5130i			1.06769i	0.845583	+	0.533843i	$0.179253\pi$
$571$			25.5130i			1.06769i	−0.845583	+	0.533843i	$0.820747\pi$
$572$	5.13371	+	4.82201i	0.214651	+	0.201618i
$573$	−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	$0.708399\pi$
$578$	0.205579	+	13.1357i	0.00855098	+	0.546374i
$579$	4.27204			0.177540
$580$	−21.2661	+	22.4176i	−0.883025	+	0.930842i
$581$	−1.90113			−0.0788721
$582$	−0.184650	−	11.7984i	−0.00765398	−	0.489059i
$583$	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	−0.999729	−	0.0232972i	$-0.992584\pi$
$587$	−23.6571	+	23.6571i	−0.976431	+	0.976431i	0.0232972	+	0.999729i	$0.492584\pi$
$588$	−5.54801	+	5.90664i	−0.228796	+	0.243586i
$589$		−	11.2556i		−	0.463778i
$590$	−5.17252	−	5.06293i	−0.212949	−	0.208438i
$591$		−	20.3047i		−	0.835223i
$592$	−25.9118	−	22.8552i	−1.06497	−	0.939342i
$593$	−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
$598$	9.79875	−	0.153354i	0.400701	−	0.00627113i
$599$	−2.77755			−0.113488			−0.0567438	−	0.998389i	$-0.518072\pi$
$599$	−2.77755			−0.113488			−0.0567438	+	0.998389i	$0.518072\pi$
$600$	10.8682	−	11.7052i	0.443692	−	0.477862i
$601$	−40.0680			−1.63441			−0.817205	−	0.576348i	$-0.804477\pi$
$601$	−40.0680			−1.63441			−0.817205	+	0.576348i	$0.804477\pi$
$602$	−28.0233	+	0.438576i	−1.14214	+	0.0178750i
$603$	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	−0.321356	−	0.946958i	$-0.604139\pi$
$607$	15.4132	−	15.4132i	0.625602	−	0.625602i	0.946958	+	0.321356i	$0.104139\pi$
$608$	−15.2692	+	1.19719i	−0.619248	+	0.0485526i
$609$		−	14.4160i		−	0.584167i
$610$	−17.5539	−	17.1820i	−0.710737	−	0.695679i
$611$		−	7.75399i		−	0.313693i
$612$	−6.55625	+	6.98005i	−0.265021	+	0.282152i
$613$	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	$0.835404\pi$
$618$	0.322273	+	20.5920i	0.0129637	+	0.828331i
$619$	20.6325			0.829290			0.414645	−	0.909983i	$-0.363906\pi$
$619$	20.6325			0.829290			0.414645	+	0.909983i	$0.363906\pi$
$620$	−12.7951	+	13.4879i	−0.513863	+	0.541689i
$621$	36.9757			1.48378
$622$	−0.563605	−	36.0122i	−0.0225985	−	1.44396i
$623$	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
$628$	−22.6252	−	21.2515i	−0.902842	−	0.848025i
$629$			23.9852i			0.956354i
$630$	−0.107843	−	10.0726i	−0.00429658	−	0.401302i
$631$			0.761372i			0.0303098i	0.999885	+	0.0151549i	$0.00482413\pi$
$631$			0.761372i			0.0303098i	−0.999885	+	0.0151549i	$0.995176\pi$
$632$	2.16661	−	0.101791i	0.0861830	−	0.00404904i
$633$	−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
$638$	34.4066	−	0.538478i	1.36217	−	0.0213185i
$639$	24.6544			0.975313
$640$	19.6585	+	15.9230i	0.777071	+	0.629413i
$641$	−46.1859			−1.82423			−0.912117	−	0.409930i	$-0.865553\pi$
$641$	−46.1859			−1.82423			−0.912117	+	0.409930i	$0.865553\pi$
$642$	−1.99883	+	0.0312825i	−0.0788876	+	0.00123462i
$643$	24.2799	+	24.2799i	0.957507	+	0.957507i	0.999133	−	0.0416264i	$-0.0132539\pi$
$643$	24.2799	+	24.2799i	0.957507	+	0.957507i	−0.0416264	+	0.999133i	$0.513254\pi$
$644$	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	−0.695975	−	0.718066i	$-0.745028\pi$
$647$	0.561905	−	0.561905i	0.0220907	−	0.0220907i	0.718066	+	0.695975i	$0.245028\pi$
$648$	−2.41152	+	0.113298i	−0.0947333	+	0.00445075i
$649$			8.06040i			0.316399i
$650$	5.02873	+	4.97110i	0.197243	+	0.194983i
$651$		−	8.67364i		−	0.339947i
$652$	8.75948	+	8.22764i	0.343048	+	0.322219i
$653$	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
$658$	−0.316995	−	20.2548i	−0.0123578	−	0.789613i
$659$	30.2716			1.17922			0.589608	−	0.807690i	$-0.299282\pi$
$659$	30.2716			1.17922			0.589608	+	0.807690i	$0.299282\pi$
$660$	−17.7815	+	0.468747i	−0.692145	+	0.0182459i
$661$	1.99460			0.0775808			0.0387904	−	0.999247i	$-0.487650\pi$
$661$	1.99460			0.0775808			0.0387904	+	0.999247i	$0.487650\pi$
$662$	0.498426	+	31.8475i	0.0193719	+	1.23779i
$663$	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
$668$	24.8158	−	26.4199i	0.960150	−	1.02222i
$669$			12.9564i			0.500923i
$670$	−4.01808	+	0.0430200i	−0.155232	+	0.00166201i
$671$			27.3545i			1.05601i
$672$	−11.7666	+	0.922565i	−0.453905	+	0.0355887i
$673$	−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	$0.951561\pi$
$678$	−4.92088	+	0.0770138i	−0.188985	+	0.00295770i
$679$	13.6470			0.523723
$680$	−0.737461	−	17.5464i	−0.0282803	−	0.672874i
$681$	−26.1045			−1.00033
$682$	20.7013	−	0.323984i	0.792695	−	0.0124060i
$683$	23.8214	+	23.8214i	0.911500	+	0.911500i	0.996390	−	0.0848900i	$-0.0270539\pi$
$683$	23.8214	+	23.8214i	0.911500	+	0.911500i	−0.0848900	+	0.996390i	$0.527054\pi$
$684$	−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
$688$	32.1820	+	28.3857i	1.22693	+	1.08219i
$689$		−	6.44256i		−	0.245442i
$690$	−17.3125	+	17.6872i	−0.659075	+	0.673340i
$691$		−	22.6733i		−	0.862534i	−0.902224	−	0.431267i	$-0.858067\pi$
$691$		−	22.6733i		−	0.862534i	0.902224	−	0.431267i	$-0.141933\pi$
$692$	6.93231	−	7.38042i	0.263527	−	0.280561i
$693$	−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
$698$	−0.167387	−	10.6953i	−0.00633567	−	0.404825i
$699$	19.6623			0.743698
$700$	13.3391	+	12.7798i	0.504172	+	0.483031i
$701$	−4.26882			−0.161231			−0.0806155	−	0.996745i	$-0.525689\pi$
$701$	−4.26882			−0.161231			−0.0806155	+	0.996745i	$0.525689\pi$
$702$	−0.118085	−	7.54518i	−0.00445683	−	0.284774i
$703$	−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
$708$	−3.76854	−	3.53973i	−0.141630	−	0.133031i
$709$			25.6567i			0.963558i	0.876293	+	0.481779i	$0.160009\pi$
$709$			25.6567i			0.963558i	−0.876293	+	0.481779i	$0.839991\pi$
$710$	−31.6266	+	32.3112i	−1.18693	+	1.21262i
$711$			1.32233i			0.0495913i
$712$	−0.0587269	−	1.24999i	−0.00220088	−	0.0468453i
$713$	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
$718$	−35.8544	+	0.561137i	−1.33808	+	0.0209414i
$719$	−44.8441			−1.67240			−0.836201	−	0.548422i	$-0.815229\pi$
$719$	−44.8441			−1.67240			−0.836201	+	0.548422i	$0.815229\pi$
$720$	−10.2592	+	11.5161i	−0.382339	+	0.429178i
$721$	−23.8183			−0.887041
$722$	16.5009	−	0.258246i	0.614100	−	0.00961091i
$723$	−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	−0.781069	−	0.624444i	$-0.785325\pi$
$727$	−4.22306	+	4.22306i	−0.156625	+	0.156625i	0.624444	+	0.781069i	$0.285325\pi$
$728$	−0.245209	−	5.21923i	−0.00908806	−	0.193437i
$729$		−	19.5516i		−	0.724134i
$730$	17.1785	−	0.183924i	0.635806	−	0.00680732i
$731$		−	29.7892i		−	1.10179i
$732$	−12.7892	−	12.0127i	−0.472704	−	0.444003i
$733$	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
$738$	0.340038	+	21.7271i	0.0125170	+	0.799787i
$739$	40.5731			1.49250			0.746252	−	0.665663i	$-0.231851\pi$
$739$	40.5731			1.49250			0.746252	+	0.665663i	$0.231851\pi$
$740$	1.01797	+	38.6159i	0.0374214	+	1.41955i
$741$	−3.05800			−0.112338
$742$	−0.263382	−	16.8291i	−0.00966906	−	0.617815i
$743$	−2.78875	−	2.78875i	−0.102309	−	0.102309i	0.654099	−	0.756409i	$-0.273048\pi$
$743$	−2.78875	−	2.78875i	−0.102309	−	0.102309i	−0.756409	+	0.654099i	$0.773048\pi$
$744$	−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
$748$	−13.3897	+	14.2552i	−0.489574	+	0.521221i
$749$		−	2.31201i		−	0.0844790i
$750$	−17.8581	+	0.0146495i	−0.652085	+	0.000534922i
$751$			17.6843i			0.645308i	0.946517	+	0.322654i	$0.104575\pi$
$751$			17.6843i			0.645308i	−0.946517	+	0.322654i	$0.895425\pi$
$752$	−20.5167	+	23.2606i	−0.748167	+	0.848226i
$753$	−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	$0.566569\pi$
$758$	38.6000	−	0.604106i	1.40201	−	0.0219421i
$759$	27.5622			1.00044
$760$	12.6062	+	11.5893i	0.457274	+	0.420387i
$761$	−10.5601			−0.382804			−0.191402	−	0.981512i	$-0.561303\pi$
$761$	−10.5601			−0.382804			−0.191402	+	0.981512i	$0.561303\pi$
$762$	−16.4941	+	0.258139i	−0.597518	+	0.00935141i
$763$	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
$768$	14.2738	+	11.0826i	0.515060	+	0.399910i
$769$			1.08776i			0.0392255i	0.999808	+	0.0196128i	$0.00624333\pi$
$769$			1.08776i			0.0392255i	−0.999808	+	0.0196128i	$0.993757\pi$
$770$	−0.220246	−	20.5710i	−0.00793710	−	0.741327i
$771$		−	1.74124i		−	0.0627094i
$772$	5.17914	−	5.51393i	0.186401	−	0.198451i

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)

\(f(q)\)	\(=\)	\(q+(-1.41404 + 0.0221303i) q^{2} +(0.798638 + 0.798638i) q^{3} +(1.99902 - 0.0625863i) q^{4} +(-1.57330 - 1.58893i) q^{5} +(-1.14698 - 1.11163i) q^{6} +(1.30625 - 1.30625i) q^{7} +(-2.82531 + 0.132739i) q^{8} -1.72435i q^{9} +O(q^{10})\)	\(q+(-1.41404 + 0.0221303i) 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} +(-2.82531 + 0.132739i) q^{8} -1.72435i q^{9} +(2.25988 + 2.21200i) q^{10} -3.52160i q^{11} +(1.64648 + 1.54651i) 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} +(0.0381605 + 2.43831i) q^{18} +2.70752 q^{19} +(-3.24451 - 3.07785i) q^{20} +2.08644 q^{21} +(0.0779341 + 4.97969i) 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} +(2.52946 - 2.69297i) q^{28} -6.90940i q^{29} +(0.0382377 + 3.57141i) q^{30} -4.15716i q^{31} +(-5.63955 + 0.442173i) 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} +(-3.82854 + 0.0599183i) q^{38} -1.12944 q^{39} +(4.65599 + 4.28040i) q^{40} +8.91075 q^{41} +(-2.95031 + 0.0461735i) 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} +(3.38813 + 2.98846i) q^{48} +3.58744i q^{49} +(-0.0407522 - 7.07095i) q^{50} -3.13622i q^{51} +(-1.36927 + 1.45778i) 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} +(0.152907 + 9.77017i) q^{58} -2.28885 q^{59} +(-0.133106 - 5.04928i) q^{60} -7.76763 q^{61} +(0.0919991 + 5.87839i) 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} +(-4.04792 - 3.80215i) q^{68} +7.82662i q^{69} +(5.84138 - 0.0625413i) q^{70} +14.2978i q^{71} +(0.228888 + 4.87184i) 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} +(1.59708 - 0.0249950i) q^{78} -0.766856 q^{79} +(-6.67848 - 5.94962i) q^{80} +0.853540 q^{81} +(-12.6002 + 0.197198i) 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} +(0.467452 + 9.94962i) q^{88} +0.442426i q^{89} +(3.81427 - 3.89683i) q^{90} +1.84731i q^{91} +(10.1018 + 9.48848i) 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} +(-0.0793912 - 5.07279i) 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

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