LMFDB - Embedded newform 260.2.o.a.27.10

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			27.10
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.942648 + 1.05424i) q^{2} +(0.158208 + 0.158208i) q^{3} +(-0.222831 - 1.98755i) q^{4} +(-2.23604 + 0.0111104i) q^{5} +(-0.315922 + 0.0176543i) q^{6} +(-2.20671 + 2.20671i) q^{7} +(2.30540 + 1.63864i) q^{8} -2.94994i q^{9} +O(q^{10})$	\(q+(-0.942648 + 1.05424i) q^{2} +(0.158208 + 0.158208i) q^{3} +(-0.222831 - 1.98755i) q^{4} +(-2.23604 + 0.0111104i) q^{5} +(-0.315922 + 0.0176543i) q^{6} +(-2.20671 + 2.20671i) q^{7} +(2.30540 + 1.63864i) q^{8} -2.94994i q^{9} +(2.09608 - 2.36779i) q^{10} -3.71929i q^{11} +(0.279192 - 0.349699i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-0.246246 - 4.40655i) q^{14} +(-0.355516 - 0.352001i) q^{15} +(-3.90069 + 0.885776i) q^{16} +(-3.39861 - 3.39861i) q^{17} +(3.10994 + 2.78075i) q^{18} -3.95131 q^{19} +(0.520342 + 4.44176i) q^{20} -0.698237 q^{21} +(3.92101 + 3.50597i) q^{22} +(-5.15484 - 5.15484i) q^{23} +(0.105486 + 0.623977i) q^{24} +(4.99975 - 0.0496864i) q^{25} +(0.0789057 + 1.41201i) q^{26} +(0.941326 - 0.941326i) q^{27} +(4.87767 + 3.89422i) q^{28} +2.61015i q^{29} +(0.706219 - 0.0429858i) q^{30} -1.82398i q^{31} +(2.74316 - 4.94723i) q^{32} +(0.588419 - 0.588419i) q^{33} +(6.78664 - 0.379250i) q^{34} +(4.90978 - 4.95881i) q^{35} +(-5.86315 + 0.657339i) q^{36} +(7.13984 + 7.13984i) q^{37} +(3.72469 - 4.16562i) q^{38} +0.223739 q^{39} +(-5.17317 - 3.63845i) q^{40} -3.88345 q^{41} +(0.658191 - 0.736107i) q^{42} +(0.0375960 + 0.0375960i) q^{43} +(-7.39226 + 0.828773i) q^{44} +(0.0327749 + 6.59619i) q^{45} +(10.2936 - 0.575226i) q^{46} +(-6.34114 + 6.34114i) q^{47} +(-0.757256 - 0.476983i) q^{48} -2.73915i q^{49} +(-4.66062 + 5.31776i) q^{50} -1.07537i q^{51} +(-1.56297 - 1.24784i) q^{52} +(-0.298805 + 0.298805i) q^{53} +(0.105042 + 1.87972i) q^{54} +(0.0413226 + 8.31647i) q^{55} +(-8.70335 + 1.47134i) q^{56} +(-0.625127 - 0.625127i) q^{57} +(-2.75172 - 2.46046i) q^{58} -1.09335 q^{59} +(-0.620399 + 0.785043i) q^{60} -8.96596 q^{61} +(1.92291 + 1.71937i) q^{62} +(6.50967 + 6.50967i) q^{63} +(2.62972 + 7.55543i) q^{64} +(-1.57326 + 1.58898i) q^{65} +(0.0656614 + 1.17501i) q^{66} +(-7.47449 + 7.47449i) q^{67} +(-5.99759 + 7.51222i) q^{68} -1.63107i q^{69} +(0.599574 + 9.85048i) q^{70} -12.5380i q^{71} +(4.83389 - 6.80079i) q^{72} +(6.19988 - 6.19988i) q^{73} +(-14.2574 + 0.796731i) q^{74} +(0.798860 + 0.783139i) q^{75} +(0.880476 + 7.85342i) q^{76} +(8.20739 + 8.20739i) q^{77} +(-0.210907 + 0.235874i) q^{78} +16.4253 q^{79} +(8.71226 - 2.02397i) q^{80} -8.55197 q^{81} +(3.66072 - 4.09408i) q^{82} +(1.62581 + 1.62581i) q^{83} +(0.155589 + 1.38778i) q^{84} +(7.63720 + 7.56168i) q^{85} +(-0.0750748 + 0.00419532i) q^{86} +(-0.412946 + 0.412946i) q^{87} +(6.09457 - 8.57443i) q^{88} -1.23447i q^{89} +(-6.98484 - 6.18333i) q^{90} +3.12076i q^{91} +(-9.09683 + 11.3942i) q^{92} +(0.288568 - 0.288568i) q^{93} +(-0.707605 - 12.6625i) q^{94} +(8.83529 - 0.0439004i) q^{95} +(1.21668 - 0.348701i) q^{96} +(-11.5096 - 11.5096i) q^{97} +(2.88771 + 2.58205i) q^{98} -10.9717 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 $

$2$	−0.942648	+	1.05424i	−0.666552	+	0.745458i
$2$	−0.942648	+	1.05424i	−0.666552	+	0.745458i
$3$	0.158208	+	0.158208i	0.0913412	+	0.0913412i	0.751301	−	0.659960i	$-0.229427\pi$
$3$	0.158208	+	0.158208i	0.0913412	+	0.0913412i	−0.659960	+	0.751301i	$0.729427\pi$
$4$	−0.222831	−	1.98755i	−0.111416	−	0.993774i
$5$	−2.23604	+	0.0111104i	−0.999988	+	0.00496870i
$5$	−2.23604	+	0.0111104i	−0.999988	+	0.00496870i
$6$	−0.315922	+	0.0176543i	−0.128975	+	0.00720734i
$7$	−2.20671	+	2.20671i	−0.834058	+	0.834058i	−0.988069	−	0.154011i	$-0.950781\pi$
$7$	−2.20671	+	2.20671i	−0.834058	+	0.834058i	0.154011	+	0.988069i	$0.450781\pi$
$8$	2.30540	+	1.63864i	0.815081	+	0.579347i
$9$		−	2.94994i		−	0.983314i
$10$	2.09608	−	2.36779i	0.662840	−	0.748761i
$11$		−	3.71929i		−	1.12141i	−0.828017	−	0.560703i	$-0.810531\pi$
$11$		−	3.71929i		−	1.12141i	0.828017	−	0.560703i	$-0.189469\pi$
$12$	0.279192	−	0.349699i	0.0805957	−	0.100949i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	−0.246246	−	4.40655i	−0.0658120	−	1.17770i
$15$	−0.355516	−	0.352001i	−0.0917940	−	0.0908863i
$16$	−3.90069	+	0.885776i	−0.975173	+	0.221444i
$17$	−3.39861	−	3.39861i	−0.824285	−	0.824285i	0.162435	−	0.986719i	$-0.448065\pi$
$17$	−3.39861	−	3.39861i	−0.824285	−	0.824285i	−0.986719	+	0.162435i	$0.948065\pi$
$18$	3.10994	+	2.78075i	0.733019	+	0.655430i
$19$	−3.95131			−0.906493			−0.453246	−	0.891385i	$-0.649734\pi$
$19$	−3.95131			−0.906493			−0.453246	+	0.891385i	$0.649734\pi$
$20$	0.520342	+	4.44176i	0.116352	+	0.993208i
$21$	−0.698237			−0.152368
$22$	3.92101	+	3.50597i	0.835962	+	0.747476i
$23$	−5.15484	−	5.15484i	−1.07486	−	1.07486i	−0.996961	−	0.0778972i	$-0.975179\pi$
$23$	−5.15484	−	5.15484i	−1.07486	−	1.07486i	−0.0778972	−	0.996961i	$-0.524821\pi$
$24$	0.105486	+	0.623977i	0.0215323	+	0.127369i
$25$	4.99975	−	0.0496864i	0.999951	−	0.00993728i
$26$	0.0789057	+	1.41201i	0.0154747	+	0.276918i
$27$	0.941326	−	0.941326i	0.181158	−	0.181158i
$28$	4.87767	+	3.89422i	0.921793	+	0.735938i
$29$			2.61015i			0.484693i	0.970190	+	0.242347i	$0.0779172\pi$
$29$			2.61015i			0.484693i	−0.970190	+	0.242347i	$0.922083\pi$
$30$	0.706219	−	0.0429858i	0.128937	−	0.00784809i
$31$		−	1.82398i		−	0.327597i	−0.986494	−	0.163798i	$-0.947625\pi$
$31$		−	1.82398i		−	0.327597i	0.986494	−	0.163798i	$-0.0523747\pi$
$32$	2.74316	−	4.94723i	0.484927	−	0.874555i
$33$	0.588419	−	0.588419i	0.102431	−	0.102431i
$34$	6.78664	−	0.379250i	1.16390	−	0.0650408i
$35$	4.90978	−	4.95881i	0.829904	−	0.838192i
$36$	−5.86315	+	0.657339i	−0.977191	+	0.109557i
$37$	7.13984	+	7.13984i	1.17378	+	1.17378i	0.981300	+	0.192482i	$0.0616538\pi$
$37$	7.13984	+	7.13984i	1.17378	+	1.17378i	0.192482	+	0.981300i	$0.438346\pi$
$38$	3.72469	−	4.16562i	0.604225	−	0.675752i
$39$	0.223739			0.0358270
$40$	−5.17317	−	3.63845i	−0.817950	−	0.575290i
$41$	−3.88345			−0.606493			−0.303246	−	0.952912i	$-0.598071\pi$
$41$	−3.88345			−0.606493			−0.303246	+	0.952912i	$0.598071\pi$
$42$	0.658191	−	0.736107i	0.101561	−	0.113584i
$43$	0.0375960	+	0.0375960i	0.00573333	+	0.00573333i	0.709968	−	0.704234i	$-0.248710\pi$
$43$	0.0375960	+	0.0375960i	0.00573333	+	0.00573333i	−0.704234	+	0.709968i	$0.748710\pi$
$44$	−7.39226	+	0.828773i	−1.11442	+	0.124942i
$45$	0.0327749	+	6.59619i	0.00488579	+	0.983301i
$46$	10.2936	−	0.575226i	1.51771	−	0.0848125i
$47$	−6.34114	+	6.34114i	−0.924951	+	0.924951i	−0.997374	−	0.0724230i	$-0.976927\pi$
$47$	−6.34114	+	6.34114i	−0.924951	+	0.924951i	0.0724230	+	0.997374i	$0.476927\pi$
$48$	−0.757256	−	0.476983i	−0.109300	−	0.0688465i
$49$		−	2.73915i		−	0.391306i
$50$	−4.66062	+	5.31776i	−0.659112	+	0.752045i
$51$		−	1.07537i		−	0.150582i
$52$	−1.56297	−	1.24784i	−0.216746	−	0.173045i
$53$	−0.298805	+	0.298805i	−0.0410440	+	0.0410440i	−0.727331	−	0.686287i	$-0.759239\pi$
$53$	−0.298805	+	0.298805i	−0.0410440	+	0.0410440i	0.686287	+	0.727331i	$0.259239\pi$
$54$	0.105042	+	1.87972i	0.0142944	+	0.255797i
$55$	0.0413226	+	8.31647i	0.00557193	+	1.12139i
$56$	−8.70335	+	1.47134i	−1.16303	+	0.196616i
$57$	−0.625127	−	0.625127i	−0.0828002	−	0.0828002i
$58$	−2.75172	−	2.46046i	−0.361319	−	0.323074i
$59$	−1.09335			−0.142342			−0.0711711	−	0.997464i	$-0.522674\pi$
$59$	−1.09335			−0.142342			−0.0711711	+	0.997464i	$0.522674\pi$
$60$	−0.620399	+	0.785043i	−0.0800931	+	0.101349i
$61$	−8.96596			−1.14797			−0.573987	−	0.818865i	$-0.694604\pi$
$61$	−8.96596			−1.14797			−0.573987	+	0.818865i	$0.694604\pi$
$62$	1.92291	+	1.71937i	0.244210	+	0.218361i
$63$	6.50967	+	6.50967i	0.820141	+	0.820141i
$64$	2.62972	+	7.55543i	0.328715	+	0.944429i
$65$	−1.57326	+	1.58898i	−0.195139	+	0.197088i
$66$	0.0656614	+	1.17501i	0.00808236	+	0.144633i
$67$	−7.47449	+	7.47449i	−0.913155	+	0.913155i	−0.996519	−	0.0833645i	$-0.973433\pi$
$67$	−7.47449	+	7.47449i	−0.913155	+	0.913155i	0.0833645	+	0.996519i	$0.473433\pi$
$68$	−5.99759	+	7.51222i	−0.727314	+	0.910991i
$69$		−	1.63107i		−	0.196358i
$70$	0.599574	+	9.85048i	0.0716628	+	1.17736i
$71$		−	12.5380i		−	1.48799i	−0.668184	−	0.743996i	$-0.732928\pi$
$71$		−	12.5380i		−	1.48799i	0.668184	−	0.743996i	$-0.267072\pi$
$72$	4.83389	−	6.80079i	0.569679	−	0.801480i
$73$	6.19988	−	6.19988i	0.725641	−	0.725641i	−0.244107	−	0.969748i	$-0.578495\pi$
$73$	6.19988	−	6.19988i	0.725641	−	0.725641i	0.969748	+	0.244107i	$0.0784949\pi$
$74$	−14.2574	+	0.796731i	−1.65739	+	0.0926181i
$75$	0.798860	+	0.783139i	0.0922444	+	0.0904290i
$76$	0.880476	+	7.85342i	0.100997	+	0.900849i
$77$	8.20739	+	8.20739i	0.935319	+	0.935319i
$78$	−0.210907	+	0.235874i	−0.0238806	+	0.0267075i
$79$	16.4253			1.84799			0.923994	−	0.382406i	$-0.124904\pi$
$79$	16.4253			1.84799			0.923994	+	0.382406i	$0.124904\pi$
$80$	8.71226	−	2.02397i	0.974061	−	0.226287i
$81$	−8.55197			−0.950219
$82$	3.66072	−	4.09408i	0.404259	−	0.452115i
$83$	1.62581	+	1.62581i	0.178455	+	0.178455i	0.790682	−	0.612227i	$-0.209726\pi$
$83$	1.62581	+	1.62581i	0.178455	+	0.178455i	−0.612227	+	0.790682i	$0.709726\pi$
$84$	0.155589	+	1.38778i	0.0169762	+	0.151419i
$85$	7.63720	+	7.56168i	0.828370	+	0.820179i
$86$	−0.0750748	+	0.00419532i	−0.00809553	+	0.000452393i
$87$	−0.412946	+	0.412946i	−0.0442725	+	0.0442725i
$88$	6.09457	−	8.57443i	0.649683	−	0.914038i
$89$		−	1.23447i		−	0.130854i	−0.997857	−	0.0654269i	$-0.979159\pi$
$89$		−	1.23447i		−	0.130854i	0.997857	−	0.0654269i	$-0.0208409\pi$
$90$	−6.98484	−	6.18333i	−0.736267	−	0.651780i
$91$			3.12076i			0.327145i
$92$	−9.09683	+	11.3942i	−0.948410	+	1.18792i
$93$	0.288568	−	0.288568i	0.0299231	−	0.0299231i
$94$	−0.707605	−	12.6625i	−0.0729839	−	1.30604i
$95$	8.83529	−	0.0439004i	0.906481	−	0.00450409i
$96$	1.21668	−	0.348701i	0.124177	−	0.0355891i
$97$	−11.5096	−	11.5096i	−1.16863	−	1.16863i	−0.982532	−	0.186093i	$-0.940417\pi$
$97$	−11.5096	−	11.5096i	−1.16863	−	1.16863i	−0.186093	−	0.982532i	$-0.559583\pi$
$98$	2.88771	+	2.58205i	0.291703	+	0.260826i
$99$	−10.9717			−1.10269
$100$	−1.21286	−	9.92618i	−0.121286	−	0.992618i
$101$	5.53619			0.550872			0.275436	−	0.961319i	$-0.411178\pi$
$101$	5.53619			0.550872			0.275436	+	0.961319i	$0.411178\pi$
$102$	1.13370	+	1.01370i	0.112253	+	0.100371i
$103$	−8.21473	−	8.21473i	−0.809421	−	0.809421i	0.175125	−	0.984546i	$-0.443967\pi$
$103$	−8.21473	−	8.21473i	−0.809421	−	0.809421i	−0.984546	+	0.175125i	$0.943967\pi$
$104$	2.78886	−	0.471469i	0.273470	−	0.0462314i
$105$	1.56129	−	0.00775766i	0.152366	−	0.000757070i
$106$	−0.0333435	−	0.596679i	−0.00323861	−	0.0579546i
$107$	0.375597	−	0.375597i	0.0363104	−	0.0363104i	−0.688718	−	0.725029i	$-0.741826\pi$
$107$	0.375597	−	0.375597i	0.0363104	−	0.0363104i	0.725029	+	0.688718i	$0.241826\pi$
$108$	−2.08069	−	1.66117i	−0.200214	−	0.159847i
$109$			6.37721i			0.610826i	0.952220	+	0.305413i	$0.0987946\pi$
$109$			6.37721i			0.610826i	−0.952220	+	0.305413i	$0.901205\pi$
$110$	−8.80648	−	7.79594i	−0.839665	−	0.743313i
$111$			2.25916i			0.214430i
$112$	6.65305	−	10.5624i	0.628654	−	0.998048i
$113$	3.29961	−	3.29961i	0.310401	−	0.310401i	−0.534664	−	0.845065i	$-0.679562\pi$
$113$	3.29961	−	3.29961i	0.310401	−	0.310401i	0.845065	+	0.534664i	$0.179562\pi$
$114$	1.24831	−	0.0697577i	0.116915	−	0.00653340i
$115$	11.5837	+	11.4692i	1.08019	+	1.06950i
$116$	5.18781	−	0.581624i	0.481676	−	0.0540025i
$117$	−2.08592	−	2.08592i	−0.192844	−	0.192844i
$118$	1.03065	−	1.15265i	0.0948786	−	0.106110i
$119$	14.9995			1.37500
$120$	−0.242804	−	1.39407i	−0.0221649	−	0.127260i
$121$	−2.83308			−0.257553
$122$	8.45174	−	9.45225i	0.765185	−	0.855766i
$123$	−0.614392	−	0.614392i	−0.0553978	−	0.0553978i
$124$	−3.62525	+	0.406441i	−0.325557	+	0.0364994i
$125$	−11.1791	+	0.166650i	−0.999889	+	0.0149056i
$126$	−12.9991	+	0.726410i	−1.15805	+	0.0647138i
$127$	1.95951	−	1.95951i	0.173878	−	0.173878i	−0.614803	−	0.788681i	$-0.710764\pi$
$127$	1.95951	−	1.95951i	0.173878	−	0.173878i	0.788681	+	0.614803i	$0.210764\pi$
$128$	−10.4441	−	4.34976i	−0.923138	−	0.384468i
$129$			0.0118959i			0.00104738i
$130$	−0.192124	−	3.15644i	−0.0168504	−	0.276838i
$131$		−	1.31295i		−	0.114713i	−0.998354	−	0.0573563i	$-0.981733\pi$
$131$		−	1.31295i		−	0.114713i	0.998354	−	0.0573563i	$-0.0182671\pi$
$132$	−1.30063	−	1.03839i	−0.113205	−	0.0903805i
$133$	8.71940	−	8.71940i	0.756068	−	0.756068i
$134$	−0.834075	−	14.9257i	−0.0720531	−	1.28938i
$135$	−2.09438	+	2.11530i	−0.180256	+	0.182056i
$136$	−2.26605	−	13.4043i	−0.194312	−	1.14941i
$137$	3.17187	+	3.17187i	0.270992	+	0.270992i	0.829499	−	0.558508i	$-0.188626\pi$
$137$	3.17187	+	3.17187i	0.270992	+	0.270992i	−0.558508	+	0.829499i	$0.688626\pi$
$138$	1.71954	+	1.53752i	0.146377	+	0.130883i
$139$	18.9854			1.61032			0.805160	−	0.593058i	$-0.202080\pi$
$139$	18.9854			1.61032			0.805160	+	0.593058i	$0.202080\pi$
$140$	−10.9499	−	8.65344i	−0.925438	−	0.731349i
$141$	−2.00644			−0.168972
$142$	13.2181	+	11.8190i	1.10924	+	0.991824i
$143$	−2.62993	−	2.62993i	−0.219926	−	0.219926i
$144$	2.61299	+	11.5068i	0.217749	+	0.958901i
$145$	−0.0289997	−	5.83641i	−0.00240830	−	0.484687i
$146$	0.691841	+	12.3804i	0.0572572	+	1.02461i
$147$	0.433354	−	0.433354i	0.0357424	−	0.0357424i
$148$	12.5998	−	15.7818i	1.03570	−	1.29725i
$149$		−	20.4040i		−	1.67156i	−0.549061	−	0.835782i	$-0.685015\pi$
$149$		−	20.4040i		−	1.67156i	0.549061	−	0.835782i	$-0.314985\pi$
$150$	−1.57866	+	0.103964i	−0.128897	+	0.00848865i
$151$			5.45100i			0.443596i	0.975093	+	0.221798i	$0.0711926\pi$
$151$			5.45100i			0.443596i	−0.975093	+	0.221798i	$0.928807\pi$
$152$	−9.10934	−	6.47477i	−0.738865	−	0.525173i
$153$	−10.0257	+	10.0257i	−0.810530	+	0.810530i
$154$	−16.3892	+	0.915858i	−1.32068	+	0.0738020i
$155$	0.0202651	+	4.07850i	0.00162773	+	0.327593i
$156$	−0.0498562	−	0.444693i	−0.00399169	−	0.0356039i
$157$	−8.11693	−	8.11693i	−0.647801	−	0.647801i	0.304660	−	0.952461i	$-0.401457\pi$
$157$	−8.11693	−	8.11693i	−0.647801	−	0.647801i	−0.952461	+	0.304660i	$0.901457\pi$
$158$	−15.4833	+	17.3161i	−1.23178	+	1.37760i
$159$	−0.0945465			−0.00749803
$160$	−6.07885	+	11.0927i	−0.480575	+	0.876953i
$161$	22.7505			1.79299
$162$	8.06149	−	9.01581i	0.633371	−	0.708349i
$163$	−6.14842	−	6.14842i	−0.481581	−	0.481581i	0.424055	−	0.905636i	$-0.360606\pi$
$163$	−6.14842	−	6.14842i	−0.481581	−	0.481581i	−0.905636	+	0.424055i	$0.860606\pi$
$164$	0.865355	+	7.71854i	0.0675728	+	0.602717i
$165$	−1.30919	+	1.32227i	−0.101920	+	0.102938i
$166$	−3.24655	+	0.181423i	−0.251981	+	0.0140812i
$167$	14.9835	−	14.9835i	1.15946	−	1.15946i	0.174864	−	0.984593i	$-0.444051\pi$
$167$	14.9835	−	14.9835i	1.15946	−	1.15946i	0.984593	−	0.174864i	$-0.0559487\pi$
$168$	−1.60971	−	1.14416i	−0.124192	−	0.0882738i
$169$		−	1.00000i		−	0.0769231i
$170$	−15.1710	+	0.923419i	−1.16356	+	0.0708230i
$171$			11.6561i			0.891366i
$172$	0.0663462	−	0.0831014i	0.00505885	−	0.00633642i
$173$	−14.1569	+	14.1569i	−1.07633	+	1.07633i	−0.0794964	+	0.996835i	$0.525331\pi$
$173$	−14.1569	+	14.1569i	−1.07633	+	1.07633i	−0.996835	+	0.0794964i	$0.974669\pi$
$174$	−0.0460805	−	0.824606i	−0.00349335	−	0.0625132i
$175$	−10.9234	+	11.1427i	−0.825729	+	0.842305i
$176$	3.29445	+	14.5078i	0.248329	+	1.09357i
$177$	−0.172977	−	0.172977i	−0.0130017	−	0.0130017i
$178$	1.30143	+	1.16367i	0.0975460	+	0.0872209i
$179$	13.8558			1.03563			0.517817	−	0.855492i	$-0.326745\pi$
$179$	13.8558			1.03563			0.517817	+	0.855492i	$0.326745\pi$
$180$	13.1029	−	1.53498i	0.976635	−	0.114411i
$181$	8.60220			0.639397			0.319698	−	0.947519i	$-0.396418\pi$
$181$	8.60220			0.639397			0.319698	+	0.947519i	$0.396418\pi$
$182$	−3.29002	−	2.94178i	−0.243873	−	0.218059i
$183$	−1.41848	−	1.41848i	−0.104857	−	0.104857i
$184$	−3.43703	−	20.3309i	−0.253381	−	1.49881i
$185$	−16.0443	−	15.8856i	−1.17960	−	1.16794i
$186$	0.0322012	+	0.576237i	0.00236110	+	0.0422518i
$187$	−12.6404	+	12.6404i	−0.924358	+	0.924358i
$188$	14.0163	+	11.1903i	1.02225	+	0.816138i
$189$			4.15447i			0.302193i
$190$	−8.28228	+	9.35587i	−0.600860	+	0.678746i
$191$			0.459773i			0.0332680i	0.999862	+	0.0166340i	$0.00529501\pi$
$191$			0.459773i			0.0332680i	−0.999862	+	0.0166340i	$0.994705\pi$
$192$	−0.779286	+	1.61137i	−0.0562401	+	0.116291i
$193$	4.92125	−	4.92125i	0.354239	−	0.354239i	−0.507445	−	0.861684i	$-0.669410\pi$
$193$	4.92125	−	4.92125i	0.354239	−	0.354239i	0.861684	+	0.507445i	$0.169410\pi$
$194$	22.9834	−	1.28435i	1.65011	−	0.0922112i
$195$	−0.500290	+	0.00248582i	−0.0358265	+	0.000178014i
$196$	−5.44418	+	0.610368i	−0.388870	+	0.0435977i
$197$	13.8739	+	13.8739i	0.988476	+	0.988476i	0.999934	−	0.0114581i	$-0.00364731\pi$
$197$	13.8739	+	13.8739i	0.988476	+	0.988476i	−0.0114581	+	0.999934i	$0.503647\pi$
$198$	10.3424	−	11.5667i	0.735004	−	0.822012i
$199$	−14.3199			−1.01511			−0.507554	−	0.861620i	$-0.669450\pi$
$199$	−14.3199			−1.01511			−0.507554	+	0.861620i	$0.669450\pi$
$200$	11.6078	+	8.07825i	0.820798	+	0.571218i
$201$	−2.36504			−0.166817
$202$	−5.21868	+	5.83646i	−0.367185	+	0.410652i
$203$	−5.75986	−	5.75986i	−0.404263	−	0.404263i
$204$	−2.13736	+	0.239627i	−0.149645	+	0.0167772i
$205$	8.68355	−	0.0431465i	0.606485	−	0.00301348i
$206$	16.4039	−	0.916678i	1.14291	−	0.0638680i
$207$	−15.2065	+	15.2065i	−1.05692	+	1.05692i
$208$	−2.13187	+	3.38454i	−0.147818	+	0.234676i
$209$			14.6960i			1.01655i
$210$	−1.46356	+	1.65328i	−0.100996	+	0.114087i
$211$		−	21.8019i		−	1.50091i	−0.660924	−	0.750453i	$-0.729836\pi$
$211$		−	21.8019i		−	1.50091i	0.660924	−	0.750453i	$-0.270164\pi$
$212$	0.660473	+	0.527306i	0.0453615	+	0.0362155i
$213$	1.98361	−	1.98361i	0.135915	−	0.135915i
$214$	0.0419127	+	0.750024i	0.00286509	+	0.0512706i
$215$	−0.0844838	−	0.0836484i	−0.00576175	−	0.00570478i
$216$	3.71263	−	0.627637i	0.252612	−	0.0427053i
$217$	4.02500	+	4.02500i	0.273235	+	0.273235i
$218$	−6.72309	−	6.01146i	−0.455345	−	0.407148i
$219$	1.96174			0.132562
$220$	16.5202	−	1.93530i	1.11379	−	0.130478i
$221$	−4.80636			−0.323311
$222$	−2.38169	−	2.12959i	−0.159848	−	0.142929i
$223$	−12.5947	−	12.5947i	−0.843404	−	0.843404i	0.145896	−	0.989300i	$-0.453394\pi$
$223$	−12.5947	−	12.5947i	−0.843404	−	0.843404i	−0.989300	+	0.145896i	$0.953394\pi$
$224$	4.86374	+	16.9705i	0.324972	+	1.13389i
$225$	−0.146572	−	14.7490i	−0.00977146	−	0.983265i
$226$	0.368202	+	6.58894i	0.0244924	+	0.438290i
$227$	−8.00497	+	8.00497i	−0.531309	+	0.531309i	−0.920962	−	0.389653i	$-0.872595\pi$
$227$	−8.00497	+	8.00497i	−0.531309	+	0.531309i	0.389653	+	0.920962i	$0.372595\pi$
$228$	−1.10317	+	1.38177i	−0.0730594	+	0.0915099i
$229$			20.4753i			1.35305i	0.736421	+	0.676523i	$0.236514\pi$
$229$			20.4753i			1.35305i	−0.736421	+	0.676523i	$0.763486\pi$
$230$	−23.0106	+	1.40059i	−1.51727	+	0.0923525i
$231$			2.59694i			0.170866i
$232$	−4.27710	+	6.01744i	−0.280806	+	0.395065i
$233$	−4.88720	+	4.88720i	−0.320171	+	0.320171i	−0.848833	−	0.528662i	$-0.822694\pi$
$233$	−4.88720	+	4.88720i	−0.320171	+	0.320171i	0.528662	+	0.848833i	$0.322694\pi$
$234$	4.16535	−	0.232767i	0.272297	−	0.0152165i
$235$	14.1086	−	14.2495i	0.920344	−	0.929535i
$236$	0.243633	+	2.17309i	0.0158592	+	0.141456i
$237$	2.59861	+	2.59861i	0.168798	+	0.168798i
$238$	−14.1393	+	15.8130i	−0.916512	+	1.02501i
$239$	−12.4349			−0.804347			−0.402174	−	0.915563i	$-0.631745\pi$
$239$	−12.4349			−0.804347			−0.402174	+	0.915563i	$0.631745\pi$
$240$	1.69855	+	1.05814i	0.109641	+	0.0683026i
$241$	16.7919			1.08166			0.540830	−	0.841132i	$-0.318110\pi$
$241$	16.7919			1.08166			0.540830	+	0.841132i	$0.318110\pi$
$242$	2.67060	−	2.98674i	0.171672	−	0.191995i
$243$	−4.17697	−	4.17697i	−0.267953	−	0.267953i
$244$	1.99790	+	17.8203i	0.127902	+	1.14083i
$245$	0.0304329	+	6.12484i	0.00194428	+	0.391302i
$246$	1.22687	−	0.0685597i	0.0782223	−	0.00437120i
$247$	−2.79400	+	2.79400i	−0.177778	+	0.177778i
$248$	2.98885	−	4.20501i	0.189792	−	0.267018i
$249$			0.514430i			0.0326007i
$250$	10.3623	−	11.9425i	0.655367	−	0.755311i
$251$		−	12.8842i		−	0.813244i	−0.913596	−	0.406622i	$-0.866707\pi$
$251$		−	12.8842i		−	0.813244i	0.913596	−	0.406622i	$-0.133293\pi$
$252$	11.4877	−	14.3888i	0.723658	−	0.906411i
$253$	−19.1723	+	19.1723i	−1.20535	+	1.20535i
$254$	0.218660	+	3.91291i	0.0137200	+	0.245518i
$255$	0.0119478	+	2.40458i	0.000748199	+	0.150581i
$256$	14.4308	−	6.91028i	0.901925	−	0.431892i
$257$	−15.0887	−	15.0887i	−0.941207	−	0.941207i	0.0571585	−	0.998365i	$-0.481796\pi$
$257$	−15.0887	−	15.0887i	−0.941207	−	0.941207i	−0.998365	+	0.0571585i	$0.981796\pi$
$258$	−0.0125411	−	0.0112137i	−0.000780778	−	0.000698133i
$259$	−31.5111			−1.95801
$260$	3.50874	+	2.77286i	0.217603	+	0.171966i
$261$	7.69980			0.476606
$262$	1.38416	+	1.23765i	0.0855135	+	0.0764620i
$263$	9.72534	+	9.72534i	0.599690	+	0.599690i	0.940230	−	0.340540i	$-0.110610\pi$
$263$	9.72534	+	9.72534i	0.599690	+	0.599690i	−0.340540	+	0.940230i	$0.610610\pi$
$264$	2.32075	−	0.392333i	0.142832	−	0.0241464i
$265$	0.664821	−	0.671460i	0.0408396	−	0.0412475i
$266$	0.972993	+	17.4116i	0.0596581	+	1.06758i
$267$	0.195303	−	0.195303i	0.0119523	−	0.0119523i
$268$	16.5215	+	13.1904i	1.00921	+	0.805729i
$269$			4.39890i			0.268205i	0.990967	+	0.134103i	$0.0428152\pi$
$269$			4.39890i			0.268205i	−0.990967	+	0.134103i	$0.957185\pi$
$270$	−0.255763	−	4.20196i	−0.0155652	−	0.255723i
$271$		−	25.4419i		−	1.54548i	−0.634720	−	0.772742i	$-0.718884\pi$
$271$		−	25.4419i		−	1.54548i	0.634720	−	0.772742i	$-0.281116\pi$
$272$	16.2674	+	10.2465i	0.986353	+	0.621287i
$273$	−0.493728	+	0.493728i	−0.0298818	+	0.0298818i
$274$	−6.33387	+	0.353948i	−0.382643	+	0.0213828i
$275$	−0.184798	−	18.5955i	−0.0111437	−	1.12135i
$276$	−3.24183	+	0.363454i	−0.195135	+	0.0218773i
$277$	1.56210	+	1.56210i	0.0938575	+	0.0938575i	0.752477	−	0.658619i	$-0.228859\pi$
$277$	1.56210	+	1.56210i	0.0938575	+	0.0938575i	−0.658619	+	0.752477i	$0.728859\pi$
$278$	−17.8965	+	20.0151i	−1.07336	+	1.20043i
$279$	−5.38064			−0.322131
$280$	19.4447	−	3.38668i	1.16204	−	0.202393i
$281$	−2.00740			−0.119751			−0.0598757	−	0.998206i	$-0.519070\pi$
$281$	−2.00740			−0.119751			−0.0598757	+	0.998206i	$0.519070\pi$
$282$	1.89136	−	2.11526i	0.112629	−	0.125962i
$283$	12.4458	+	12.4458i	0.739827	+	0.739827i	0.972544	−	0.232717i	$-0.0747616\pi$
$283$	12.4458	+	12.4458i	0.739827	+	0.739827i	−0.232717	+	0.972544i	$0.574762\pi$
$284$	−24.9200	+	2.79387i	−1.47873	+	0.165786i
$285$	1.40476	+	1.39086i	0.0832105	+	0.0823877i
$286$	5.25167	−	0.293473i	0.310538	−	0.0173534i
$287$	8.56965	−	8.56965i	0.505850	−	0.505850i
$288$	−14.5940	−	8.09216i	−0.859962	−	0.476835i
$289$			6.10114i			0.358891i
$290$	6.18030	+	5.47111i	0.362919	+	0.321274i
$291$		−	3.64182i		−	0.213487i
$292$	−13.7041	−	10.9410i	−0.801971	−	0.640275i
$293$	−2.07145	+	2.07145i	−0.121016	+	0.121016i	−0.765021	−	0.644005i	$-0.777271\pi$
$293$	−2.07145	+	2.07145i	−0.121016	+	0.121016i	0.644005	+	0.765021i	$0.277271\pi$
$294$	0.0483577	+	0.865357i	0.00282028	+	0.0504687i
$295$	2.44478	−	0.0121475i	0.142341	−	0.000707256i
$296$	4.76055	+	28.1598i	0.276701	+	1.63676i
$297$	−3.50106	−	3.50106i	−0.203152	−	0.203152i
$298$	21.5107	+	19.2338i	1.24608	+	1.11419i
$299$	−7.29005			−0.421594
$300$	1.37851	−	1.76228i	0.0795885	−	0.101745i
$301$	−0.165927			−0.00956387
$302$	−5.74665	−	5.13837i	−0.330682	−	0.295680i
$303$	0.875868	+	0.875868i	0.0503173	+	0.0503173i
$304$	15.4128	−	3.49998i	0.883987	−	0.200737i
$305$	20.0483	−	0.0996150i	1.14796	−	0.00570394i
$306$	−1.11876	−	20.0202i	−0.0639555	−	1.14448i
$307$	6.28267	−	6.28267i	0.358571	−	0.358571i	−0.504715	−	0.863286i	$-0.668402\pi$
$307$	6.28267	−	6.28267i	0.358571	−	0.358571i	0.863286	+	0.504715i	$0.168402\pi$
$308$	14.4837	−	18.1414i	0.825286	−	1.03370i
$309$		−	2.59927i		−	0.147867i
$310$	−4.31881	−	3.82322i	−0.245292	−	0.217144i
$311$			18.7418i			1.06275i	0.847137	+	0.531375i	$0.178324\pi$
$311$			18.7418i			1.06275i	−0.847137	+	0.531375i	$0.821676\pi$
$312$	0.515808	+	0.366628i	0.0292019	+	0.0207562i
$313$	4.09503	−	4.09503i	0.231465	−	0.231465i	−0.581839	−	0.813304i	$-0.697667\pi$
$313$	4.09503	−	4.09503i	0.231465	−	0.231465i	0.813304	+	0.581839i	$0.197667\pi$
$314$	16.2086	−	0.905764i	0.914703	−	0.0511152i
$315$	−14.6282	−	14.4836i	−0.824206	−	0.816056i
$316$	−3.66007	−	32.6460i	−0.205895	−	1.83648i
$317$	−10.4527	−	10.4527i	−0.587080	−	0.587080i	0.349760	−	0.936840i	$-0.386263\pi$
$317$	−10.4527	−	10.4527i	−0.587080	−	0.587080i	−0.936840	+	0.349760i	$0.886263\pi$
$318$	0.0891241	−	0.0996745i	0.00499783	−	0.00558947i
$319$	9.70791			0.543538
$320$	−5.96410	−	16.8650i	−0.333403	−	0.942784i
$321$	0.118845			0.00663327
$322$	−21.4457	+	23.9844i	−1.19512	+	1.33660i
$323$	13.4290	+	13.4290i	0.747208	+	0.747208i
$324$	1.90565	+	16.9975i	0.105869	+	0.944303i
$325$	3.50023	−	3.57049i	0.194158	−	0.198055i
$326$	12.2777	−	0.686099i	0.679998	−	0.0379995i
$327$	−1.00892	+	1.00892i	−0.0557936	+	0.0557936i
$328$	−8.95290	−	6.36358i	−0.494341	−	0.351370i
$329$		−	27.9861i		−	1.54293i
$330$	−0.159876	−	2.62663i	−0.00880090	−	0.144591i
$331$			12.5857i			0.691771i	0.938277	+	0.345886i	$0.112421\pi$
$331$			12.5857i			0.691771i	−0.938277	+	0.345886i	$0.887579\pi$
$332$	2.86909	−	3.59365i	0.157462	−	0.197227i
$333$	21.0621	−	21.0621i	1.15420	−	1.15420i
$334$	1.67200	+	29.9203i	0.0914878	+	1.63717i
$335$	16.6302	−	16.7963i	0.908606	−	0.917681i
$336$	2.72361	−	0.618482i	0.148585	−	0.0337409i
$337$	−3.63810	−	3.63810i	−0.198180	−	0.198180i	0.601039	−	0.799219i	$-0.294753\pi$
$337$	−3.63810	−	3.63810i	−0.198180	−	0.198180i	−0.799219	+	0.601039i	$0.794753\pi$
$338$	1.05424	+	0.942648i	0.0573429	+	0.0512733i
$339$	1.04405			0.0567049
$340$	13.3274	−	16.8643i	0.722779	−	0.914593i
$341$	−6.78391			−0.367369
$342$	−12.2883	−	10.9876i	−0.664476	−	0.594142i
$343$	−9.40247	−	9.40247i	−0.507686	−	0.507686i
$344$	0.0250674	+	0.148280i	0.00135154	+	0.00799472i
$345$	0.0181218	+	3.64714i	0.000975643	+	0.196355i
$346$	−1.57977	−	28.2698i	−0.0849287	−	1.51979i
$347$	8.53370	−	8.53370i	0.458113	−	0.458113i	−0.439923	−	0.898036i	$-0.644994\pi$
$347$	8.53370	−	8.53370i	0.458113	−	0.458113i	0.898036	+	0.439923i	$0.144994\pi$
$348$	0.912768	+	0.728733i	0.0489295	+	0.0390642i
$349$			13.3317i			0.713630i	0.934175	+	0.356815i	$0.116137\pi$
$349$			13.3317i			0.713630i	−0.934175	+	0.356815i	$0.883863\pi$
$350$	−1.45011	−	22.0194i	−0.0775118	−	1.17699i
$351$		−	1.33124i		−	0.0710561i
$352$	−18.4002	−	10.2026i	−0.980732	−	0.543800i
$353$	−6.89939	+	6.89939i	−0.367217	+	0.367217i	−0.866461	−	0.499244i	$-0.833611\pi$
$353$	−6.89939	+	6.89939i	−0.367217	+	0.367217i	0.499244	+	0.866461i	$0.333611\pi$
$354$	0.345414	−	0.0193024i	0.0183586	−	0.00102591i
$355$	0.139302	+	28.0356i	0.00739338	+	1.48797i
$356$	−2.45357	+	0.275079i	−0.130039	+	0.0145792i
$357$	2.37304	+	2.37304i	0.125594	+	0.125594i
$358$	−13.0612	+	14.6073i	−0.690304	+	0.772021i
$359$	−36.9920			−1.95236			−0.976181	−	0.216959i	$-0.930386\pi$
$359$	−36.9920			−1.95236			−0.976181	+	0.216959i	$0.930386\pi$
$360$	−10.7332	+	15.2605i	−0.565690	+	0.804301i
$361$	−3.38715			−0.178271
$362$	−8.10885	+	9.06876i	−0.426192	+	0.476644i
$363$	−0.448215	−	0.448215i	−0.0235252	−	0.0235252i
$364$	6.20266	−	0.695403i	0.325108	−	0.0364490i
$365$	−13.7943	+	13.9321i	−0.722026	+	0.729237i
$366$	2.83255	−	0.158288i	0.148060	−	0.00827384i
$367$	−19.5766	+	19.5766i	−1.02189	+	1.02189i	−0.0221373	+	0.999755i	$0.507047\pi$
$367$	−19.5766	+	19.5766i	−1.02189	+	1.02189i	−0.999755	+	0.0221373i	$0.992953\pi$
$368$	24.6735	+	15.5414i	1.28619	+	0.810152i
$369$			11.4559i			0.596373i
$370$	31.8714	−	1.93993i	1.65691	−	0.100852i
$371$		−	1.31875i		−	0.0684663i
$372$	−0.637845	−	0.509241i	−0.0330707	−	0.0264029i
$373$	7.21316	−	7.21316i	0.373483	−	0.373483i	−0.495261	−	0.868744i	$-0.664928\pi$
$373$	7.21316	−	7.21316i	0.373483	−	0.373483i	0.868744	+	0.495261i	$0.164928\pi$
$374$	−1.41054	−	25.2414i	−0.0729372	−	1.30520i
$375$	−1.79498	−	1.74225i	−0.0926926	−	0.0899696i
$376$	−25.0097	+	4.22801i	−1.28978	+	0.218043i
$377$	1.84566	+	1.84566i	0.0950562	+	0.0950562i
$378$	−4.37980	−	3.91620i	−0.225272	−	0.201428i
$379$	8.59778			0.441638			0.220819	−	0.975315i	$-0.429127\pi$
$379$	8.59778			0.441638			0.220819	+	0.975315i	$0.429127\pi$
$380$	−2.05603	−	17.5508i	−0.105472	−	0.900336i
$381$	0.620018			0.0317645
$382$	−0.484709	−	0.433403i	−0.0247999	−	0.0221748i
$383$	4.02733	+	4.02733i	0.205787	+	0.205787i	0.802474	−	0.596687i	$-0.203517\pi$
$383$	4.02733	+	4.02733i	0.205787	+	0.205787i	−0.596687	+	0.802474i	$0.703517\pi$
$384$	−0.964173	−	2.34051i	−0.0492028	−	0.119438i
$385$	−18.4432	−	18.2609i	−0.939954	−	0.930660i
$386$	0.549160	+	9.82717i	0.0279515	+	0.500190i
$387$	0.110906	−	0.110906i	0.00563766	−	0.00563766i
$388$	−20.3112	+	25.4406i	−1.03115	+	1.29155i
$389$		−	0.970610i		−	0.0492119i	−0.999697	−	0.0246059i	$-0.992167\pi$
$389$		−	0.970610i		−	0.0492119i	0.999697	−	0.0246059i	$-0.00783310\pi$
$390$	0.468977	−	0.529768i	0.0237476	−	0.0268258i
$391$			35.0386i			1.77198i
$392$	4.48847	−	6.31482i	0.226702	−	0.318947i
$393$	0.207718	−	0.207718i	0.0104780	−	0.0104780i
$394$	−27.7046	+	1.54818i	−1.39574	+	0.0779964i
$395$	−36.7276	+	0.182491i	−1.84797	+	0.00918210i
$396$	2.44483	+	21.8067i	0.122857	+	1.09583i
$397$	−12.3155	−	12.3155i	−0.618095	−	0.618095i	0.326947	−	0.945043i	$-0.393980\pi$
$397$	−12.3155	−	12.3155i	−0.618095	−	0.618095i	−0.945043	+	0.326947i	$0.893980\pi$
$398$	13.4986	−	15.0965i	0.676623	−	0.756721i
$399$	2.75895			0.138120
$400$	−19.4585	+	4.62247i	−0.972924	+	0.231124i
$401$	25.2740			1.26212			0.631062	−	0.775732i	$-0.282619\pi$
$401$	25.2740			1.26212			0.631062	+	0.775732i	$0.282619\pi$
$402$	2.22940	−	2.49332i	0.111193	−	0.124355i
$403$	−1.28975	−	1.28975i	−0.0642471	−	0.0642471i
$404$	−1.23364	−	11.0035i	−0.0613758	−	0.547442i
$405$	19.1226	−	0.0950154i	0.950207	−	0.00472135i
$406$	11.5018	−	0.642740i	0.570823	−	0.0318986i
$407$	26.5551	−	26.5551i	1.31629	−	1.31629i
$408$	1.76215	−	2.47916i	0.0872394	−	0.122737i
$409$			4.10429i			0.202944i	0.994838	+	0.101472i	$0.0323552\pi$
$409$			4.10429i			0.202944i	−0.994838	+	0.101472i	$0.967645\pi$
$410$	−8.14004	+	9.19519i	−0.402008	+	0.454118i
$411$			1.00363i			0.0495054i
$412$	−14.4967	+	18.1577i	−0.714199	+	0.894564i
$413$	2.41271	−	2.41271i	0.118722	−	0.118722i
$414$	−1.69688	−	30.3656i	−0.0833973	−	1.49239i
$415$	−3.65343	−	3.61731i	−0.179340	−	0.177567i
$416$	−1.55851	−	5.43793i	−0.0764123	−	0.266616i
$417$	3.00363	+	3.00363i	0.147089	+	0.147089i
$418$	−15.4931	−	13.8532i	−0.757793	−	0.677582i
$419$	17.3311			0.846680			0.423340	−	0.905971i	$-0.360858\pi$
$419$	17.3311			0.846680			0.423340	+	0.905971i	$0.360858\pi$
$420$	−0.363322	−	3.10140i	−0.0177283	−	0.151333i
$421$	−34.0343			−1.65873			−0.829364	−	0.558708i	$-0.811297\pi$
$421$	−34.0343			−1.65873			−0.829364	+	0.558708i	$0.811297\pi$
$422$	22.9844	+	20.5515i	1.11886	+	1.00043i
$423$	18.7060	+	18.7060i	0.909517	+	0.909517i
$424$	−1.17850	+	0.199231i	−0.0572330	+	0.00967550i
$425$	−17.1611	−	16.8234i	−0.832435	−	0.816053i
$426$	0.221351	+	3.96105i	0.0107245	+	0.191913i
$427$	19.7853	−	19.7853i	0.957477	−	0.957477i
$428$	−0.830212	−	0.662823i	−0.0401298	−	0.0320387i
$429$		−	0.832151i		−	0.0401766i
$430$	0.167824	−	0.0102150i	0.00809318	−	0.000492611i
$431$		−	11.8497i		−	0.570781i	−0.958411	−	0.285390i	$-0.907877\pi$
$431$		−	11.8497i		−	0.570781i	0.958411	−	0.285390i	$-0.0921232\pi$
$432$	−2.83802	+	4.50563i	−0.136544	+	0.216777i
$433$	−9.87468	+	9.87468i	−0.474547	+	0.474547i	−0.903382	−	0.428836i	$-0.858924\pi$
$433$	−9.87468	+	9.87468i	−0.474547	+	0.474547i	0.428836	+	0.903382i	$0.358924\pi$
$434$	−8.03746	+	0.449148i	−0.385811	+	0.0215598i
$435$	0.918777	−	0.927953i	0.0440520	−	0.0444919i
$436$	12.6750	−	1.42104i	0.607023	−	0.0680556i
$437$	20.3684	+	20.3684i	0.974351	+	0.974351i
$438$	−1.84923	+	2.06814i	−0.0883594	+	0.0988193i
$439$	13.8583			0.661418			0.330709	−	0.943733i	$-0.392712\pi$
$439$	13.8583			0.661418			0.330709	+	0.943733i	$0.392712\pi$
$440$	−13.5324	+	19.2405i	−0.645134	+	0.917254i
$441$	−8.08032			−0.384777
$442$	4.53071	−	5.06705i	0.215504	−	0.241015i
$443$	7.77783	+	7.77783i	0.369536	+	0.369536i	0.867308	−	0.497772i	$-0.165848\pi$
$443$	7.77783	+	7.77783i	0.369536	+	0.369536i	−0.497772	+	0.867308i	$0.665848\pi$
$444$	4.49018	−	0.503411i	0.213094	−	0.0238908i
$445$	0.0137154	+	2.76033i	0.000650173	+	0.130852i
$446$	25.1502	−	1.40544i	1.19090	−	0.0665494i
$447$	3.22808	−	3.22808i	0.152683	−	0.152683i
$448$	−22.4757	−	10.8696i	−1.06188	−	0.513542i
$449$		−	27.3178i		−	1.28921i	−0.764516	−	0.644604i	$-0.777022\pi$
$449$		−	27.3178i		−	1.28921i	0.764516	−	0.644604i	$-0.222978\pi$
$450$	15.6871	+	13.7486i	0.739496	+	0.648113i
$451$			14.4437i			0.680125i
$452$	−7.29339	−	5.82288i	−0.343052	−	0.273885i
$453$	−0.862390	+	0.862390i	−0.0405186	+	0.0405186i
$454$	−0.893271	−	15.9850i	−0.0419233	−	0.750213i
$455$	−0.0346727	−	6.97815i	−0.00162548	−	0.327141i
$456$	−0.416809	−	2.46553i	−0.0195189	−	0.115459i
$457$	−29.4423	−	29.4423i	−1.37725	−	1.37725i	−0.849234	−	0.528016i	$-0.822936\pi$
$457$	−29.4423	−	29.4423i	−1.37725	−	1.37725i	−0.528016	−	0.849234i	$-0.677064\pi$
$458$	−21.5858	−	19.3010i	−1.00864	−	0.901876i
$459$	−6.39841			−0.298652
$460$	20.2143	−	25.5789i	0.942496	−	1.19262i
$461$	11.5928			0.539932			0.269966	−	0.962870i	$-0.412988\pi$
$461$	11.5928			0.539932			0.269966	+	0.962870i	$0.412988\pi$
$462$	−2.73779	−	2.44800i	−0.127374	−	0.113891i
$463$	−14.0309	−	14.0309i	−0.652069	−	0.652069i	0.301422	−	0.953491i	$-0.402539\pi$
$463$	−14.0309	−	14.0309i	−0.652069	−	0.652069i	−0.953491	+	0.301422i	$0.902539\pi$
$464$	−2.31201	−	10.1814i	−0.107332	−	0.472660i
$465$	−0.642044	+	0.648456i	−0.0297741	+	0.0300714i
$466$	−0.545360	−	9.75917i	−0.0252633	−	0.452085i
$467$	1.57290	−	1.57290i	0.0727851	−	0.0727851i	−0.669777	−	0.742562i	$-0.733610\pi$
$467$	1.57290	−	1.57290i	0.0727851	−	0.0727851i	0.742562	+	0.669777i	$0.233610\pi$
$468$	−3.68106	+	4.61068i	−0.170157	+	0.213129i
$469$		−	32.9881i		−	1.52325i
$470$	1.72292	+	28.3061i	0.0794723	+	1.30566i
$471$		−	2.56832i		−	0.118342i
$472$	−2.52061	−	1.79161i	−0.116021	−	0.0824655i
$473$	0.139830	−	0.139830i	0.00642940	−	0.00642940i
$474$	−5.18912	+	0.289977i	−0.238344	+	0.0133191i
$475$	−19.7556	+	0.196326i	−0.906448	+	0.00900807i
$476$	−3.34236	−	29.8122i	−0.153197	−	1.36644i
$477$	0.881457	+	0.881457i	0.0403592	+	0.0403592i
$478$	11.7217	−	13.1093i	0.536139	−	0.599607i
$479$	20.3724			0.930838			0.465419	−	0.885091i	$-0.345904\pi$
$479$	20.3724			0.930838			0.465419	+	0.885091i	$0.345904\pi$
$480$	−2.71667	+	0.793226i	−0.123998	+	0.0362057i
$481$	10.0973			0.460395
$482$	−15.8288	+	17.7026i	−0.720984	+	0.806333i
$483$	3.59930	+	3.59930i	0.163774	+	0.163774i
$484$	0.631299	+	5.63088i	0.0286954	+	0.255949i
$485$	25.8639	+	25.6081i	1.17442	+	1.16280i
$486$	8.34092	−	0.466106i	0.378352	−	0.0211430i
$487$	−4.34315	+	4.34315i	−0.196807	+	0.196807i	−0.798630	−	0.601823i	$-0.794441\pi$
$487$	−4.34315	+	4.34315i	−0.196807	+	0.196807i	0.601823	+	0.798630i	$0.294441\pi$
$488$	−20.6701	−	14.6920i	−0.935692	−	0.665075i
$489$		−	1.94545i		−	0.0879765i
$490$	−6.48572	−	5.74148i	−0.292995	−	0.259374i
$491$			15.6199i			0.704915i	0.935828	+	0.352457i	$0.114654\pi$
$491$			15.6199i			0.704915i	−0.935828	+	0.352457i	$0.885346\pi$
$492$	−1.08423	+	1.35804i	−0.0488807	+	0.0612251i
$493$	8.87090	−	8.87090i	0.399525	−	0.399525i
$494$	−0.311781	−	5.57929i	−0.0140277	−	0.251024i
$495$	24.5331	−	0.121899i	1.10268	−	0.00547896i
$496$	1.61564	+	7.11480i	0.0725444	+	0.319464i
$497$	27.6678	+	27.6678i	1.24107	+	1.24107i
$498$	−0.542331	−	0.484926i	−0.0243024	−	0.0217301i
$499$	30.6893			1.37384			0.686921	−	0.726732i	$-0.258962\pi$
$499$	30.6893			1.37384			0.686921	+	0.726732i	$0.258962\pi$
$500$	2.82228	+	22.1819i	0.126216	+	0.992003i
$501$	4.74100			0.211812
$502$	13.5830	+	12.1453i	0.606239	+	0.542070i
$503$	27.4226	+	27.4226i	1.22272	+	1.22272i	0.966663	+	0.256052i	$0.0824219\pi$
$503$	27.4226	+	27.4226i	1.22272	+	1.22272i	0.256052	+	0.966663i	$0.417578\pi$
$504$	4.34037	+	25.6744i	0.193336	+	1.14363i
$505$	−12.3792	+	0.0615091i	−0.550865	+	0.00273712i
$506$	−2.13943	−	38.2849i	−0.0951093	−	1.70197i
$507$	0.158208	−	0.158208i	0.00702625	−	0.00702625i
$508$	−4.33125	−	3.45797i	−0.192168	−	0.153423i
$509$		−	0.576260i		−	0.0255423i	−0.999918	−	0.0127711i	$-0.995935\pi$
$509$		−	0.576260i		−	0.0255423i	0.999918	−	0.0127711i	$-0.00406529\pi$
$510$	−2.54626	−	2.25407i	−0.112750	−	0.0998121i
$511$			27.3627i			1.21045i
$512$	−6.31809	+	21.7274i	−0.279223	+	0.960226i
$513$	−3.71947	+	3.71947i	−0.164219	+	0.164219i
$514$	30.1304	−	1.68374i	1.32899	−	0.0742666i
$515$	18.4597	+	18.2772i	0.813433	+	0.805389i
$516$	0.0236438	−	0.00265079i	0.00104086	−	0.000116695i
$517$	23.5845	+	23.5845i	1.03725	+	1.03725i
$518$	29.7039	−	33.2202i	1.30511	−	1.45961i
$519$	−4.47947			−0.196627
$520$	−6.23076	+	1.08521i	−0.273237	+	0.0475896i
$521$	9.21378			0.403663			0.201832	−	0.979420i	$-0.435311\pi$
$521$	9.21378			0.403663			0.201832	+	0.979420i	$0.435311\pi$
$522$	−7.25820	+	8.11741i	−0.317683	+	0.355290i
$523$	4.26927	+	4.26927i	0.186682	+	0.186682i	0.794260	−	0.607578i	$-0.207859\pi$
$523$	4.26927	+	4.26927i	0.186682	+	0.186682i	−0.607578	+	0.794260i	$0.707859\pi$
$524$	−2.60954	+	0.292566i	−0.113998	+	0.0127808i
$525$	−3.49101	+	0.0346929i	−0.152360	+	0.00151412i
$526$	−19.4204	+	1.08525i	−0.846769	+	0.0473190i
$527$	−6.19901	+	6.19901i	−0.270033	+	0.270033i
$528$	−1.77404	+	2.81645i	−0.0772050	+	0.122570i
$529$			30.1448i			1.31064i
$530$	0.0811868	+	1.33383i	0.00352653	+	0.0579378i
$531$			3.22532i			0.139967i
$532$	−19.2732	−	15.3873i	−0.835598	−	0.667122i
$533$	−2.74601	+	2.74601i	−0.118943	+	0.118943i
$534$	0.0217938	+	0.389997i	0.000943108	+	0.0168768i
$535$	−0.835678	+	0.844024i	−0.0361295	+	0.0364903i
$536$	−29.4797	+	4.98368i	−1.27333	+	0.215262i
$537$	2.19210	+	2.19210i	0.0945960	+	0.0945960i
$538$	−4.63748	−	4.14661i	−0.199936	−	0.178773i
$539$	−10.1877			−0.438814
$540$	4.67096	+	3.69133i	0.201006	+	0.158850i
$541$	−27.1373			−1.16672			−0.583362	−	0.812212i	$-0.698263\pi$
$541$	−27.1373			−1.16672			−0.583362	+	0.812212i	$0.698263\pi$
$542$	26.8218	+	23.9827i	1.15209	+	1.03015i
$543$	1.36093	+	1.36093i	0.0584033	+	0.0584033i
$544$	−26.1367	+	7.49078i	−1.12060	+	0.321164i
$545$	−0.0708531	−	14.2597i	−0.00303501	−	0.610819i
$546$	−0.0550949	−	0.985918i	−0.00235784	−	0.0421934i
$547$	24.4699	−	24.4699i	1.04626	−	1.04626i	0.0473783	−	0.998877i	$-0.484913\pi$
$547$	24.4699	−	24.4699i	1.04626	−	1.04626i	0.998877	−	0.0473783i	$-0.0150866\pi$
$548$	5.59746	−	7.01104i	0.239112	−	0.299497i
$549$			26.4491i			1.12882i
$550$	19.7783	+	17.3342i	0.843348	+	0.739132i
$551$		−	10.3135i		−	0.439371i
$552$	2.67274	−	3.76027i	0.113759	−	0.160048i
$553$	−36.2459	+	36.2459i	−1.54133	+	1.54133i
$554$	−3.11933	+	0.174314i	−0.132528	+	0.00740590i
$555$	−0.0251000	−	5.05156i	−0.00106544	−	0.214427i
$556$	−4.23054	−	37.7344i	−0.179415	−	1.60029i
$557$	−12.4542	−	12.4542i	−0.527702	−	0.527702i	0.392185	−	0.919886i	$-0.371719\pi$
$557$	−12.4542	−	12.4542i	−0.527702	−	0.527702i	−0.919886	+	0.392185i	$0.871719\pi$
$558$	5.07205	−	5.67247i	0.214717	−	0.240135i
$559$	0.0531687			0.00224880
$560$	−14.7591	+	23.6918i	−0.623687	+	1.00116i
$561$	−3.99962			−0.168864
$562$	1.89227	−	2.11628i	0.0798206	−	0.0892697i
$563$	−10.1639	−	10.1639i	−0.428355	−	0.428355i	0.459712	−	0.888068i	$-0.347952\pi$
$563$	−10.1639	−	10.1639i	−0.428355	−	0.428355i	−0.888068	+	0.459712i	$0.847952\pi$
$564$	0.447097	+	3.98789i	0.0188262	+	0.167920i
$565$	−7.34140	+	7.41472i	−0.308855	+	0.311940i
$566$	−24.8529	+	1.38882i	−1.04464	+	0.0583766i
$567$	18.8717	−	18.8717i	0.792538	−	0.792538i
$568$	20.5453	−	28.9052i	0.862063	−	1.21283i
$569$			22.9141i			0.960611i	0.877101	+	0.480305i	$0.159474\pi$
$569$			22.9141i			0.960611i	−0.877101	+	0.480305i	$0.840526\pi$
$570$	−2.79049	+	0.169850i	−0.116881	+	0.00711424i
$571$			9.44141i			0.395111i	0.980292	+	0.197555i	$0.0633002\pi$
$571$			9.44141i			0.395111i	−0.980292	+	0.197555i	$0.936700\pi$
$572$	−4.64108	+	5.81315i	−0.194053	+	0.243060i
$573$	−0.0727395	+	0.0727395i	−0.00303874	+	0.00303874i
$574$	0.956283	+	17.1126i	0.0399145	+	0.714266i
$575$	−26.0291	−	25.5168i	−1.08549	−	1.06412i
$576$	22.2881	−	7.75751i	0.928670	−	0.323230i
$577$	19.0322	+	19.0322i	0.792322	+	0.792322i	0.981871	−	0.189549i	$-0.0607027\pi$
$577$	19.0322	+	19.0322i	0.792322	+	0.792322i	−0.189549	+	0.981871i	$0.560703\pi$
$578$	−6.43205	−	5.75123i	−0.267538	−	0.239219i
$579$	1.55716			0.0647133
$580$	−11.5937	+	1.35817i	−0.481401	+	0.0563951i
$581$	−7.17537			−0.297684
$582$	3.83934	+	3.43295i	0.159146	+	0.142301i
$583$	1.11134	+	1.11134i	0.0460271	+	0.0460271i
$584$	24.4526	−	4.13382i	1.01185	−	0.171059i
$585$	4.68738	+	4.64103i	0.193799	+	0.191883i
$586$	−0.231153	−	4.13646i	−0.00954883	−	0.170875i
$587$	5.91988	−	5.91988i	0.244340	−	0.244340i	−0.574303	−	0.818643i	$-0.694727\pi$
$587$	5.91988	−	5.91988i	0.244340	−	0.244340i	0.818643	+	0.574303i	$0.194727\pi$
$588$	−0.957876	−	0.764747i	−0.0395021	−	0.0315376i
$589$			7.20712i			0.296964i
$590$	−2.29176	+	2.58883i	−0.0943502	+	0.106580i
$591$			4.38992i			0.180577i
$592$	−34.1746	−	21.5260i	−1.40457	−	0.884714i
$593$	0.153391	−	0.153391i	0.00629903	−	0.00629903i	−0.703950	−	0.710249i	$-0.748582\pi$
$593$	0.153391	−	0.153391i	0.00629903	−	0.00629903i	0.710249	+	0.703950i	$0.248582\pi$
$594$	6.99121	−	0.390682i	0.286853	−	0.0160299i
$595$	−33.5395	+	0.166650i	−1.37499	+	0.00683198i
$596$	−40.5540	+	4.54666i	−1.66116	+	0.186238i
$597$	−2.26551	−	2.26551i	−0.0927212	−	0.0927212i
$598$	6.87194	−	7.68544i	0.281015	−	0.314281i
$599$	−10.5262			−0.430090			−0.215045	−	0.976604i	$-0.568990\pi$
$599$	−10.5262			−0.430090			−0.215045	+	0.976604i	$0.568990\pi$
$600$	0.558408	+	3.11449i	0.0227969	+	0.127149i
$601$	8.71802			0.355615			0.177808	−	0.984065i	$-0.443100\pi$
$601$	8.71802			0.355615			0.177808	+	0.984065i	$0.443100\pi$
$602$	0.156411	−	0.174926i	0.00637482	−	0.00712946i
$603$	22.0493	+	22.0493i	0.897917	+	0.897917i
$604$	10.8341	−	1.21465i	0.440834	−	0.0494236i
$605$	6.33488	−	0.0314765i	0.257550	−	0.00127970i
$606$	−1.74901	+	0.0977377i	−0.0710486	+	0.00397032i
$607$	11.7759	−	11.7759i	0.477969	−	0.477969i	−0.426512	−	0.904482i	$-0.640258\pi$
$607$	11.7759	−	11.7759i	0.477969	−	0.477969i	0.904482	+	0.426512i	$0.140258\pi$
$608$	−10.8391	+	19.5480i	−0.439583	+	0.792777i
$609$		−	1.82251i		−	0.0738517i
$610$	−18.7934	+	21.2295i	−0.760923	+	0.859558i
$611$			8.96773i			0.362796i
$612$	22.1606	+	17.6925i	0.895790	+	0.715178i
$613$	11.0213	−	11.0213i	0.445145	−	0.445145i	−0.448592	−	0.893737i	$-0.648074\pi$
$613$	11.0213	−	11.0213i	0.445145	−	0.445145i	0.893737	+	0.448592i	$0.148074\pi$
$614$	0.701080	+	12.5458i	0.0282933	+	0.506306i
$615$	1.38063	+	1.36698i	0.0556724	+	0.0551219i
$616$	5.47234	+	32.3702i	0.220487	+	1.30423i
$617$	−7.98214	−	7.98214i	−0.321349	−	0.321349i	0.527936	−	0.849284i	$-0.322966\pi$
$617$	−7.98214	−	7.98214i	−0.321349	−	0.321349i	−0.849284	+	0.527936i	$0.822966\pi$
$618$	2.74024	+	2.45019i	0.110229	+	0.0985612i
$619$	−36.9943			−1.48693			−0.743464	−	0.668776i	$-0.766819\pi$
$619$	−36.9943			−1.48693			−0.743464	+	0.668776i	$0.766819\pi$
$620$	8.10170	−	0.949095i	0.325372	−	0.0381166i
$621$	−9.70477			−0.389439
$622$	−19.7583	−	17.6669i	−0.792235	−	0.708378i
$623$	2.72412	+	2.72412i	0.109140	+	0.109140i
$624$	−0.872739	+	0.198183i	−0.0349375	+	0.00793367i
$625$	24.9951	−	0.496839i	0.999803	−	0.0198736i
$626$	0.456962	+	8.17730i	0.0182639	+	0.326831i
$627$	−2.32503	+	2.32503i	−0.0928526	+	0.0928526i
$628$	−14.3241	+	17.9415i	−0.571593	+	0.715943i
$629$		−	48.5311i		−	1.93506i
$630$	29.0583	−	1.76871i	1.15771	−	0.0704670i
$631$		−	16.5387i		−	0.658396i	−0.944261	−	0.329198i	$-0.893222\pi$
$631$		−	16.5387i		−	0.658396i	0.944261	−	0.329198i	$-0.106778\pi$
$632$	37.8668	+	26.9151i	1.50626	+	1.07063i
$633$	3.44923	−	3.44923i	0.137095	−	0.137095i
$634$	20.8728	−	1.16641i	0.828963	−	0.0463240i
$635$	−4.35976	+	4.40331i	−0.173012	+	0.174740i
$636$	0.0210679	+	0.187916i	0.000835398	+	0.00745134i
$637$	−1.93687	−	1.93687i	−0.0767415	−	0.0767415i
$638$	−9.15114	+	10.2344i	−0.362297	+	0.405185i
$639$	−36.9865			−1.46316
$640$	23.4018	+	9.61021i	0.925037	+	0.379877i
$641$	31.3698			1.23903			0.619516	−	0.784984i	$-0.287329\pi$
$641$	31.3698			1.23903			0.619516	+	0.784984i	$0.287329\pi$
$642$	−0.112029	+	0.125291i	−0.00442142	+	0.00494482i
$643$	6.29933	+	6.29933i	0.248421	+	0.248421i	0.820323	−	0.571901i	$-0.193794\pi$
$643$	6.29933	+	6.29933i	0.248421	+	0.248421i	−0.571901	+	0.820323i	$0.693794\pi$
$644$	−5.06952	−	45.2177i	−0.199767	−	1.78183i
$645$	−0.000132168	−	0.0265998i	−5.20411e−6	−	0.00104737i
$646$	−26.8161	+	1.49853i	−1.05507	+	0.0589590i
$647$	−21.4178	+	21.4178i	−0.842019	+	0.842019i	−0.989121	−	0.147102i	$-0.953005\pi$
$647$	−21.4178	+	21.4178i	−0.842019	+	0.842019i	0.147102	+	0.989121i	$0.453005\pi$
$648$	−19.7157	−	14.0136i	−0.774506	−	0.550506i
$649$			4.06649i			0.159624i
$650$	0.464667	+	7.05578i	0.0182257	+	0.276751i
$651$			1.27357i			0.0499152i
$652$	−10.8502	+	13.5903i	−0.424927	+	0.532239i
$653$	20.3186	−	20.3186i	0.795129	−	0.795129i	−0.187194	−	0.982323i	$-0.559939\pi$
$653$	20.3186	−	20.3186i	0.795129	−	0.795129i	0.982323	+	0.187194i	$0.0599393\pi$
$654$	−0.112585	−	2.01470i	−0.00440244	−	0.0787812i
$655$	0.0145873	+	2.93580i	0.000569973	+	0.114711i
$656$	15.1481	−	3.43987i	0.591436	−	0.134304i
$657$	−18.2893	−	18.2893i	−0.713533	−	0.713533i
$658$	29.5040	+	26.3811i	1.15019	+	1.02844i
$659$	−8.42213			−0.328080			−0.164040	−	0.986454i	$-0.552453\pi$
$659$	−8.42213			−0.328080			−0.164040	+	0.986454i	$0.552453\pi$
$660$	2.91980	+	2.30744i	0.113653	+	0.0898169i
$661$	−37.3044			−1.45097			−0.725487	−	0.688236i	$-0.758385\pi$
$661$	−37.3044			−1.45097			−0.725487	+	0.688236i	$0.758385\pi$
$662$	−13.2683	−	11.8639i	−0.515687	−	0.461102i
$663$	−0.760404	−	0.760404i	−0.0295316	−	0.0295316i
$664$	1.08402	+	6.41224i	0.0420681	+	0.248843i
$665$	−19.4000	+	19.5938i	−0.752302	+	0.759815i
$666$	2.35031	+	42.0586i	0.0910727	+	1.62974i
$667$	13.4549	−	13.4549i	0.520977	−	0.520977i
$668$	−33.1192	−	26.4416i	−1.28142	−	1.02306i
$669$		−	3.98516i		−	0.154075i
$670$	2.03086	+	33.3652i	0.0784588	+	1.28901i
$671$			33.3470i			1.28735i
$672$	−1.91538	+	3.45434i	−0.0738872	+	0.133254i
$673$	25.8606	−	25.8606i	0.996852	−	0.996852i	−0.00314279	−	0.999995i	$-0.501000\pi$
$673$	25.8606	−	25.8606i	0.996852	−	0.996852i	0.999995	+	0.00314279i	$0.00100038\pi$
$674$	7.26487	−	0.405974i	0.279832	−	0.0156375i
$675$	4.65963	−	4.75317i	0.179349	−	0.182950i
$676$	−1.98755	+	0.222831i	−0.0764441	+	0.00857044i
$677$	−5.32981	−	5.32981i	−0.204841	−	0.204841i	0.597229	−	0.802071i	$-0.296268\pi$
$677$	−5.32981	−	5.32981i	−0.204841	−	0.204841i	−0.802071	+	0.597229i	$0.796268\pi$
$678$	−0.984168	+	1.10067i	−0.0377968	+	0.0422711i
$679$	50.7968			1.94940
$680$	5.21591	+	29.9473i	0.200021	+	1.14843i
$681$	−2.53290			−0.0970608
$682$	6.39484	−	7.15185i	0.244871	−	0.273859i
$683$	−27.1424	−	27.1424i	−1.03858	−	1.03858i	−0.999225	−	0.0393508i	$-0.987471\pi$
$683$	−27.1424	−	27.1424i	−1.03858	−	1.03858i	−0.0393508	−	0.999225i	$-0.512529\pi$
$684$	23.1671	−	2.59735i	0.885817	−	0.0993122i
$685$	−7.12768	−	7.05720i	−0.272335	−	0.269642i
$686$	18.7757	−	1.04922i	0.716858	−	0.0400593i
$687$	−3.23935	+	3.23935i	−0.123589	+	0.123589i
$688$	−0.179952	−	0.113349i	−0.00686060	−	0.00432138i
$689$			0.422574i			0.0160988i
$690$	−3.86203	−	3.41886i	−0.147025	−	0.130154i
$691$			37.3273i			1.42000i	0.704203	+	0.709999i	$0.251305\pi$
$691$			37.3273i			1.42000i	−0.704203	+	0.709999i	$0.748695\pi$
$692$	31.2922	+	24.9830i	1.18955	+	0.949710i
$693$	24.2113	−	24.2113i	0.919711	−	0.919711i
$694$	0.952272	+	17.0408i	0.0361477	+	0.646861i
$695$	−42.4521	+	0.210934i	−1.61030	+	0.00800119i
$696$	−1.62868	+	0.275335i	−0.0617348	+	0.0104366i
$697$	13.1983	+	13.1983i	0.499923	+	0.499923i
$698$	−14.0548	−	12.5671i	−0.531981	−	0.475672i
$699$	−1.54638			−0.0584896
$700$	24.5806	+	19.2278i	0.929060	+	0.726742i
$701$	−50.6132			−1.91164			−0.955818	−	0.293960i	$-0.905027\pi$
$701$	−50.6132			−1.91164			−0.955818	+	0.293960i	$0.905027\pi$
$702$	1.40344	+	1.25489i	0.0529694	+	0.0473626i
$703$	−28.2117	−	28.2117i	−1.06403	−	1.06403i
$704$	28.1008	−	9.78067i	1.05909	−	0.368623i
$705$	4.48647	−	0.0222922i	0.168970	−	0.000839573i
$706$	−0.769900	−	13.7773i	−0.0289756	−	0.518515i
$707$	−12.2168	+	12.2168i	−0.459459	+	0.459459i
$708$	−0.305255	+	0.382344i	−0.0114722	+	0.0143694i
$709$		−	22.5087i		−	0.845331i	−0.906286	−	0.422665i	$-0.861095\pi$
$709$		−	22.5087i		−	0.845331i	0.906286	−	0.422665i	$-0.138905\pi$
$710$	−29.6874	−	26.2808i	−1.11415	−	0.986301i
$711$		−	48.4536i		−	1.81715i
$712$	2.02286	−	2.84595i	0.0758097	−	0.106656i
$713$	−9.40234	+	9.40234i	−0.352120	+	0.352120i
$714$	−4.73868	+	0.264806i	−0.177341	+	0.00991012i
$715$	5.90985	+	5.85141i	0.221016	+	0.218830i
$716$	−3.08751	−	27.5391i	−0.115386	−	1.02919i
$717$	−1.96730	−	1.96730i	−0.0734701	−	0.0734701i
$718$	34.8704	−	38.9983i	1.30135	−	1.45540i
$719$	−30.0831			−1.12191			−0.560955	−	0.827847i	$-0.689566\pi$
$719$	−30.0831			−1.12191			−0.560955	+	0.827847i	$0.689566\pi$
$720$	−5.97059	−	25.7007i	−0.222511	−	0.957807i
$721$	36.2551			1.35021
$722$	3.19289	−	3.57086i	0.118827	−	0.132894i
$723$	2.65661	+	2.65661i	0.0988002	+	0.0988002i
$724$	−1.91684	−	17.0973i	−0.0712388	−	0.635416i
$725$	0.129689	+	13.0501i	0.00481653	+	0.484670i
$726$	0.895034	−	0.0500161i	0.0332178	−	0.00185627i
$727$	25.6595	−	25.6595i	0.951656	−	0.951656i	−0.0472278	−	0.998884i	$-0.515039\pi$
$727$	25.6595	−	25.6595i	0.951656	−	0.951656i	0.998884	+	0.0472278i	$0.0150387\pi$
$728$	−5.11380	+	7.19459i	−0.189530	+	0.266649i
$729$			24.3343i			0.901269i
$730$	−1.68454	−	27.6755i	−0.0623475	−	1.02432i
$731$		−	0.255548i		−	0.00945180i
$732$	−2.50322	+	3.13539i	−0.0925217	+	0.115887i
$733$	−0.867465	+	0.867465i	−0.0320406	+	0.0320406i	−0.722946	−	0.690905i	$-0.757212\pi$
$733$	−0.867465	+	0.867465i	−0.0320406	+	0.0320406i	0.690905	+	0.722946i	$0.257212\pi$
$734$	−2.18455	−	39.0923i	−0.0806331	−	1.44292i
$735$	−0.964182	+	0.973811i	−0.0355644	+	0.0359196i
$736$	−39.6427	+	11.3616i	−1.46125	+	0.418795i
$737$	27.7998	+	27.7998i	1.02402	+	1.02402i
$738$	−12.0773	−	10.7989i	−0.444571	−	0.397514i
$739$	2.05358			0.0755423			0.0377712	−	0.999286i	$-0.487974\pi$
$739$	2.05358			0.0755423			0.0377712	+	0.999286i	$0.487974\pi$
$740$	−27.9983	+	35.4286i	−1.02924	+	1.30238i
$741$	−0.884064			−0.0324769
$742$	1.39028	+	1.24312i	0.0510387	+	0.0456363i
$743$	10.3809	+	10.3809i	0.380838	+	0.380838i	0.871404	−	0.490566i	$-0.163210\pi$
$743$	10.3809	+	10.3809i	0.380838	+	0.380838i	−0.490566	+	0.871404i	$0.663210\pi$
$744$	1.13812	−	0.192405i	0.0417256	−	0.00705391i
$745$	0.226696	+	45.6243i	0.00830550	+	1.67154i
$746$	0.804913	+	14.4038i	0.0294699	+	0.527362i
$747$	4.79603	−	4.79603i	0.175478	−	0.175478i
$748$	27.9401	+	22.3067i	1.02159	+	0.815615i
$749$			1.65767i			0.0605699i
$750$	3.52879	−	0.250008i	0.128853	−	0.00912899i
$751$		−	4.09706i		−	0.149504i	−0.997202	−	0.0747519i	$-0.976184\pi$
$751$		−	4.09706i		−	0.149504i	0.997202	−	0.0747519i	$-0.0238165\pi$
$752$	19.1180	−	30.3517i	0.697162	−	1.10681i
$753$	2.03838	−	2.03838i	0.0742827	−	0.0742827i
$754$	−3.68557	+	0.205956i	−0.134220	+	0.00750048i
$755$	−0.0605625	−	12.1887i	−0.00220410	−	0.443591i
$756$	8.25721	−	0.925746i	0.300312	−	0.0336691i
$757$	−21.0913	−	21.0913i	−0.766576	−	0.766576i	0.210926	−	0.977502i	$-0.432352\pi$
$757$	−21.0913	−	21.0913i	−0.766576	−	0.766576i	−0.977502	+	0.210926i	$0.932352\pi$
$758$	−8.10468	+	9.06410i	−0.294375	+	0.329223i
$759$	−6.06642			−0.220197
$760$	20.4408	+	14.3766i	0.741465	+	0.521496i
$761$	−32.9641			−1.19495			−0.597474	−	0.801888i	$-0.703829\pi$
$761$	−32.9641			−1.19495			−0.597474	+	0.801888i	$0.703829\pi$
$762$	−0.584458	+	0.653646i	−0.0211727	+	0.0236791i
$763$	−14.0727	−	14.0727i	−0.509465	−	0.509465i
$764$	0.913820	−	0.102452i	0.0330608	−	0.00370657i
$765$	22.3065	−	22.5293i	0.806493	−	0.814548i
$766$	−8.04212	+	0.449408i	−0.290574	+	0.0162378i
$767$	−0.773117	+	0.773117i	−0.0279156	+	0.0279156i
$768$	3.37632	+	1.18980i	0.121833	+	0.0429334i
$769$		−	23.4118i		−	0.844250i	−0.906538	−	0.422125i	$-0.861284\pi$
$769$		−	23.4118i		−	0.844250i	0.906538	−	0.422125i	$-0.138716\pi$
$770$	36.6367	−	2.22999i	1.32030	−	0.0803631i
$771$		−	4.77429i		−	0.171942i
$772$	−10.8778	−	8.68461i

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)

\(f(q)\)	\(=\)	\(q+(-0.942648 + 1.05424i) q^{2} +(0.158208 + 0.158208i) q^{3} +(-0.222831 - 1.98755i) q^{4} +(-2.23604 + 0.0111104i) q^{5} +(-0.315922 + 0.0176543i) q^{6} +(-2.20671 + 2.20671i) q^{7} +(2.30540 + 1.63864i) q^{8} -2.94994i q^{9} +O(q^{10})\)	\(q+(-0.942648 + 1.05424i) q^{2} +(0.158208 + 0.158208i) q^{3} +(-0.222831 - 1.98755i) q^{4} +(-2.23604 + 0.0111104i) q^{5} +(-0.315922 + 0.0176543i) q^{6} +(-2.20671 + 2.20671i) q^{7} +(2.30540 + 1.63864i) q^{8} -2.94994i q^{9} +(2.09608 - 2.36779i) q^{10} -3.71929i q^{11} +(0.279192 - 0.349699i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-0.246246 - 4.40655i) q^{14} +(-0.355516 - 0.352001i) q^{15} +(-3.90069 + 0.885776i) q^{16} +(-3.39861 - 3.39861i) q^{17} +(3.10994 + 2.78075i) q^{18} -3.95131 q^{19} +(0.520342 + 4.44176i) q^{20} -0.698237 q^{21} +(3.92101 + 3.50597i) q^{22} +(-5.15484 - 5.15484i) q^{23} +(0.105486 + 0.623977i) q^{24} +(4.99975 - 0.0496864i) q^{25} +(0.0789057 + 1.41201i) q^{26} +(0.941326 - 0.941326i) q^{27} +(4.87767 + 3.89422i) q^{28} +2.61015i q^{29} +(0.706219 - 0.0429858i) q^{30} -1.82398i q^{31} +(2.74316 - 4.94723i) q^{32} +(0.588419 - 0.588419i) q^{33} +(6.78664 - 0.379250i) q^{34} +(4.90978 - 4.95881i) q^{35} +(-5.86315 + 0.657339i) q^{36} +(7.13984 + 7.13984i) q^{37} +(3.72469 - 4.16562i) q^{38} +0.223739 q^{39} +(-5.17317 - 3.63845i) q^{40} -3.88345 q^{41} +(0.658191 - 0.736107i) q^{42} +(0.0375960 + 0.0375960i) q^{43} +(-7.39226 + 0.828773i) q^{44} +(0.0327749 + 6.59619i) q^{45} +(10.2936 - 0.575226i) q^{46} +(-6.34114 + 6.34114i) q^{47} +(-0.757256 - 0.476983i) q^{48} -2.73915i q^{49} +(-4.66062 + 5.31776i) q^{50} -1.07537i q^{51} +(-1.56297 - 1.24784i) q^{52} +(-0.298805 + 0.298805i) q^{53} +(0.105042 + 1.87972i) q^{54} +(0.0413226 + 8.31647i) q^{55} +(-8.70335 + 1.47134i) q^{56} +(-0.625127 - 0.625127i) q^{57} +(-2.75172 - 2.46046i) q^{58} -1.09335 q^{59} +(-0.620399 + 0.785043i) q^{60} -8.96596 q^{61} +(1.92291 + 1.71937i) q^{62} +(6.50967 + 6.50967i) q^{63} +(2.62972 + 7.55543i) q^{64} +(-1.57326 + 1.58898i) q^{65} +(0.0656614 + 1.17501i) q^{66} +(-7.47449 + 7.47449i) q^{67} +(-5.99759 + 7.51222i) q^{68} -1.63107i q^{69} +(0.599574 + 9.85048i) q^{70} -12.5380i q^{71} +(4.83389 - 6.80079i) q^{72} +(6.19988 - 6.19988i) q^{73} +(-14.2574 + 0.796731i) q^{74} +(0.798860 + 0.783139i) q^{75} +(0.880476 + 7.85342i) q^{76} +(8.20739 + 8.20739i) q^{77} +(-0.210907 + 0.235874i) q^{78} +16.4253 q^{79} +(8.71226 - 2.02397i) q^{80} -8.55197 q^{81} +(3.66072 - 4.09408i) q^{82} +(1.62581 + 1.62581i) q^{83} +(0.155589 + 1.38778i) q^{84} +(7.63720 + 7.56168i) q^{85} +(-0.0750748 + 0.00419532i) q^{86} +(-0.412946 + 0.412946i) q^{87} +(6.09457 - 8.57443i) q^{88} -1.23447i q^{89} +(-6.98484 - 6.18333i) q^{90} +3.12076i q^{91} +(-9.09683 + 11.3942i) q^{92} +(0.288568 - 0.288568i) q^{93} +(-0.707605 - 12.6625i) q^{94} +(8.83529 - 0.0439004i) q^{95} +(1.21668 - 0.348701i) q^{96} +(-11.5096 - 11.5096i) q^{97} +(2.88771 + 2.58205i) q^{98} -10.9717 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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