LMFDB - Embedded newform 260.2.o.a.27.6

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			27.6
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26622 + 0.629837i) q^{2} +(2.21225 + 2.21225i) q^{3} +(1.20661 - 1.59502i) q^{4} +(1.36305 - 1.77259i) q^{5} +(-4.19454 - 1.40783i) q^{6} +(-2.47925 + 2.47925i) q^{7} +(-0.523229 + 2.77961i) q^{8} +6.78807i q^{9} +O(q^{10})$	\(q+(-1.26622 + 0.629837i) q^{2} +(2.21225 + 2.21225i) q^{3} +(1.20661 - 1.59502i) q^{4} +(1.36305 - 1.77259i) q^{5} +(-4.19454 - 1.40783i) q^{6} +(-2.47925 + 2.47925i) q^{7} +(-0.523229 + 2.77961i) q^{8} +6.78807i q^{9} +(-0.609477 + 3.10299i) q^{10} -1.32751i q^{11} +(6.19790 - 0.859257i) q^{12} +(0.707107 - 0.707107i) q^{13} +(1.57775 - 4.70080i) q^{14} +(6.93682 - 0.906002i) q^{15} +(-1.08818 - 3.84914i) q^{16} +(4.38472 + 4.38472i) q^{17} +(-4.27537 - 8.59516i) q^{18} +0.135619 q^{19} +(-1.18265 - 4.31293i) q^{20} -10.9694 q^{21} +(0.836114 + 1.68091i) q^{22} +(0.621580 + 0.621580i) q^{23} +(-7.30669 + 4.99167i) q^{24} +(-1.28417 - 4.83228i) q^{25} +(-0.449989 + 1.34071i) q^{26} +(-8.38013 + 8.38013i) q^{27} +(0.962965 + 6.94596i) q^{28} -2.54775i q^{29} +(-8.21289 + 5.51626i) q^{30} -3.33827i q^{31} +(3.80220 + 4.18847i) q^{32} +(2.93678 - 2.93678i) q^{33} +(-8.31366 - 2.79035i) q^{34} +(1.01535 + 7.77406i) q^{35} +(10.8271 + 8.19056i) q^{36} +(-6.56388 - 6.56388i) q^{37} +(-0.171723 + 0.0854176i) q^{38} +3.12859 q^{39} +(4.21393 + 4.71623i) q^{40} +3.69287 q^{41} +(13.8897 - 6.90896i) q^{42} +(-4.48096 - 4.48096i) q^{43} +(-2.11740 - 1.60179i) q^{44} +(12.0325 + 9.25250i) q^{45} +(-1.17855 - 0.395561i) q^{46} +(0.681313 - 0.681313i) q^{47} +(6.10792 - 10.9226i) q^{48} -5.29340i q^{49} +(4.66958 + 5.30989i) q^{50} +19.4001i q^{51} +(-0.274647 - 1.98105i) q^{52} +(7.99063 - 7.99063i) q^{53} +(5.33295 - 15.8892i) q^{54} +(-2.35313 - 1.80947i) q^{55} +(-5.59414 - 8.18858i) q^{56} +(0.300022 + 0.300022i) q^{57} +(1.60467 + 3.22601i) q^{58} -3.78272 q^{59} +(6.92495 - 12.1576i) q^{60} -11.8592 q^{61} +(2.10256 + 4.22697i) q^{62} +(-16.8293 - 16.8293i) q^{63} +(-7.45246 - 2.90874i) q^{64} +(-0.289588 - 2.21724i) q^{65} +(-1.86891 + 5.56828i) q^{66} +(5.75276 - 5.75276i) q^{67} +(12.2844 - 1.70306i) q^{68} +2.75018i q^{69} +(-6.18205 - 9.20415i) q^{70} -4.51098i q^{71} +(-18.8682 - 3.55171i) q^{72} +(-3.49731 + 3.49731i) q^{73} +(12.4455 + 4.17712i) q^{74} +(7.84929 - 13.5311i) q^{75} +(0.163639 - 0.216315i) q^{76} +(3.29123 + 3.29123i) q^{77} +(-3.96147 + 1.97050i) q^{78} +12.6798 q^{79} +(-8.30620 - 3.31768i) q^{80} -16.7136 q^{81} +(-4.67598 + 2.32591i) q^{82} +(2.19005 + 2.19005i) q^{83} +(-13.2358 + 17.4965i) q^{84} +(13.7489 - 1.79571i) q^{85} +(8.49614 + 2.85159i) q^{86} +(5.63626 - 5.63626i) q^{87} +(3.68996 + 0.694591i) q^{88} +5.56362i q^{89} +(-21.0633 - 4.13717i) q^{90} +3.50619i q^{91} +(1.74144 - 0.241428i) q^{92} +(7.38507 - 7.38507i) q^{93} +(-0.433574 + 1.29181i) q^{94} +(0.184856 - 0.240397i) q^{95} +(-0.854520 + 17.6773i) q^{96} +(-0.789152 - 0.789152i) q^{97} +(3.33398 + 6.70259i) q^{98} +9.01122 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 $

$2$	−1.26622	+	0.629837i	−0.895351	+	0.445362i
$2$	−1.26622	+	0.629837i	−0.895351	+	0.445362i
$3$	2.21225	+	2.21225i	1.27724	+	1.27724i	0.942206	+	0.335035i	$0.108748\pi$
$3$	2.21225	+	2.21225i	1.27724	+	1.27724i	0.335035	+	0.942206i	$0.391252\pi$
$4$	1.20661	−	1.59502i	0.603306	−	0.797510i
$5$	1.36305	−	1.77259i	0.609576	−	0.792728i
$5$	1.36305	−	1.77259i	0.609576	−	0.792728i
$6$	−4.19454	−	1.40783i	−1.71241	−	0.574744i
$7$	−2.47925	+	2.47925i	−0.937070	+	0.937070i	−0.998134	−	0.0610640i	$-0.980551\pi$
$7$	−2.47925	+	2.47925i	−0.937070	+	0.937070i	0.0610640	+	0.998134i	$0.480551\pi$
$8$	−0.523229	+	2.77961i	−0.184989	+	0.982741i
$9$			6.78807i			2.26269i
$10$	−0.609477	+	3.10299i	−0.192734	+	0.981251i
$11$		−	1.32751i		−	0.400259i	−0.979769	−	0.200129i	$-0.935864\pi$
$11$		−	1.32751i		−	0.400259i	0.979769	−	0.200129i	$-0.0641363\pi$
$12$	6.19790	−	0.859257i	1.78918	−	0.248046i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	1.57775	−	4.70080i	0.421671	−	1.25634i
$15$	6.93682	−	0.906002i	1.79108	−	0.233929i
$16$	−1.08818	−	3.84914i	−0.272045	−	0.962285i
$17$	4.38472	+	4.38472i	1.06345	+	1.06345i	0.997846	+	0.0656042i	$0.0208975\pi$
$17$	4.38472	+	4.38472i	1.06345	+	1.06345i	0.0656042	+	0.997846i	$0.479103\pi$
$18$	−4.27537	−	8.59516i	−1.00772	−	2.02590i
$19$	0.135619			0.0311131			0.0155565	−	0.999879i	$-0.495048\pi$
$19$	0.135619			0.0311131			0.0155565	+	0.999879i	$0.495048\pi$
$20$	−1.18265	−	4.31293i	−0.264448	−	0.964400i
$21$	−10.9694			−2.39373
$22$	0.836114	+	1.68091i	0.178260	+	0.358372i
$23$	0.621580	+	0.621580i	0.129608	+	0.129608i	0.768935	−	0.639327i	$-0.220787\pi$
$23$	0.621580	+	0.621580i	0.129608	+	0.129608i	−0.639327	+	0.768935i	$0.720787\pi$
$24$	−7.30669	+	4.99167i	−1.49147	+	1.01892i
$25$	−1.28417	−	4.83228i	−0.256834	−	0.966456i
$26$	−0.449989	+	1.34071i	−0.0882500	+	0.262935i
$27$	−8.38013	+	8.38013i	−1.61276	+	1.61276i
$28$	0.962965	+	6.94596i	0.181983	+	1.31266i
$29$		−	2.54775i		−	0.473106i	−0.971619	−	0.236553i	$-0.923982\pi$
$29$		−	2.54775i		−	0.473106i	0.971619	−	0.236553i	$-0.0760177\pi$
$30$	−8.21289	+	5.51626i	−1.49946	+	1.00713i
$31$		−	3.33827i		−	0.599571i	−0.954007	−	0.299785i	$-0.903085\pi$
$31$		−	3.33827i		−	0.599571i	0.954007	−	0.299785i	$-0.0969150\pi$
$32$	3.80220	+	4.18847i	0.672140	+	0.740424i
$33$	2.93678	−	2.93678i	0.511227	−	0.511227i
$34$	−8.31366	−	2.79035i	−1.42578	−	0.478540i
$35$	1.01535	+	7.77406i	0.171626	+	1.31406i
$36$	10.8271	+	8.19056i	1.80452	+	1.36509i
$37$	−6.56388	−	6.56388i	−1.07909	−	1.07909i	−0.996591	−	0.0825042i	$-0.973708\pi$
$37$	−6.56388	−	6.56388i	−1.07909	−	1.07909i	−0.0825042	−	0.996591i	$-0.526292\pi$
$38$	−0.171723	+	0.0854176i	−0.0278571	+	0.0138566i
$39$	3.12859			0.500975
$40$	4.21393	+	4.71623i	0.666280	+	0.745701i
$41$	3.69287			0.576730			0.288365	−	0.957521i	$-0.406888\pi$
$41$	3.69287			0.576730			0.288365	+	0.957521i	$0.406888\pi$
$42$	13.8897	−	6.90896i	2.14323	−	1.06608i
$43$	−4.48096	−	4.48096i	−0.683340	−	0.683340i	0.277411	−	0.960751i	$-0.410523\pi$
$43$	−4.48096	−	4.48096i	−0.683340	−	0.683340i	−0.960751	+	0.277411i	$0.910523\pi$
$44$	−2.11740	−	1.60179i	−0.319211	−	0.241478i
$45$	12.0325	+	9.25250i	1.79370	+	1.37928i
$46$	−1.17855	−	0.395561i	−0.173768	−	0.0583223i
$47$	0.681313	−	0.681313i	0.0993797	−	0.0993797i	−0.655669	−	0.755049i	$-0.727613\pi$
$47$	0.681313	−	0.681313i	0.0993797	−	0.0993797i	0.755049	+	0.655669i	$0.227613\pi$
$48$	6.10792	−	10.9226i	0.881602	−	1.57654i
$49$		−	5.29340i		−	0.756200i
$50$	4.66958	+	5.30989i	0.660379	+	0.750932i
$51$			19.4001i			2.71656i
$52$	−0.274647	−	1.98105i	−0.0380867	−	0.274723i
$53$	7.99063	−	7.99063i	1.09760	−	1.09760i	0.102906	−	0.994691i	$-0.467186\pi$
$53$	7.99063	−	7.99063i	1.09760	−	1.09760i	0.994691	−	0.102906i	$-0.0328142\pi$
$54$	5.33295	−	15.8892i	0.725723	−	2.16224i
$55$	−2.35313	−	1.80947i	−0.317296	−	0.243988i
$56$	−5.59414	−	8.18858i	−0.747549	−	1.09424i
$57$	0.300022	+	0.300022i	0.0397389	+	0.0397389i
$58$	1.60467	+	3.22601i	0.210703	+	0.423596i
$59$	−3.78272			−0.492468			−0.246234	−	0.969210i	$-0.579193\pi$
$59$	−3.78272			−0.492468			−0.246234	+	0.969210i	$0.579193\pi$
$60$	6.92495	−	12.1576i	0.894008	−	1.56953i
$61$	−11.8592			−1.51841			−0.759206	−	0.650850i	$-0.774413\pi$
$61$	−11.8592			−1.51841			−0.759206	+	0.650850i	$0.774413\pi$
$62$	2.10256	+	4.22697i	0.267026	+	0.536826i
$63$	−16.8293	−	16.8293i	−2.12030	−	2.12030i
$64$	−7.45246	−	2.90874i	−0.931558	−	0.363593i
$65$	−0.289588	−	2.21724i	−0.0359190	−	0.275014i
$66$	−1.86891	+	5.56828i	−0.230046	+	0.685408i
$67$	5.75276	−	5.75276i	0.702811	−	0.702811i	−0.262202	−	0.965013i	$-0.584449\pi$
$67$	5.75276	−	5.75276i	0.702811	−	0.702811i	0.965013	+	0.262202i	$0.0844486\pi$
$68$	12.2844	−	1.70306i	1.48970	−	0.206527i
$69$			2.75018i			0.331082i
$70$	−6.18205	−	9.20415i	−0.738896	−	1.10011i
$71$		−	4.51098i		−	0.535355i	−0.963509	−	0.267678i	$-0.913744\pi$
$71$		−	4.51098i		−	0.535355i	0.963509	−	0.267678i	$-0.0862562\pi$
$72$	−18.8682	−	3.55171i	−2.22364	−	0.418573i
$73$	−3.49731	+	3.49731i	−0.409329	+	0.409329i	−0.881504	−	0.472176i	$-0.843469\pi$
$73$	−3.49731	+	3.49731i	−0.409329	+	0.409329i	0.472176	+	0.881504i	$0.343469\pi$
$74$	12.4455	+	4.17712i	1.44676	+	0.485581i
$75$	7.84929	−	13.5311i	0.906358	−	1.56244i
$76$	0.163639	−	0.216315i	0.0187707	−	0.0248130i
$77$	3.29123	+	3.29123i	0.375071	+	0.375071i
$78$	−3.96147	+	1.97050i	−0.448548	+	0.223115i
$79$	12.6798			1.42658			0.713292	−	0.700867i	$-0.247203\pi$
$79$	12.6798			1.42658			0.713292	+	0.700867i	$0.247203\pi$
$80$	−8.30620	−	3.31768i	−0.928662	−	0.370928i
$81$	−16.7136			−1.85707
$82$	−4.67598	+	2.32591i	−0.516375	+	0.256854i
$83$	2.19005	+	2.19005i	0.240390	+	0.240390i	0.817011	−	0.576622i	$-0.195629\pi$
$83$	2.19005	+	2.19005i	0.240390	+	0.240390i	−0.576622	+	0.817011i	$0.695629\pi$
$84$	−13.2358	+	17.4965i	−1.44415	+	1.90902i
$85$	13.7489	−	1.79571i	1.49128	−	0.194772i
$86$	8.49614	+	2.85159i	0.916162	+	0.307495i
$87$	5.63626	−	5.63626i	0.604270	−	0.604270i
$88$	3.68996	+	0.694591i	0.393351	+	0.0740436i
$89$			5.56362i			0.589742i	0.955537	+	0.294871i	$0.0952767\pi$
$89$			5.56362i			0.589742i	−0.955537	+	0.294871i	$0.904723\pi$
$90$	−21.0633	−	4.13717i	−2.22027	−	0.436096i
$91$			3.50619i			0.367549i
$92$	1.74144	−	0.241428i	0.181558	−	0.0251706i
$93$	7.38507	−	7.38507i	0.765796	−	0.765796i
$94$	−0.433574	+	1.29181i	−0.0447197	+	0.133240i
$95$	0.184856	−	0.240397i	0.0189658	−	0.0246642i
$96$	−0.854520	+	17.6773i	−0.0872141	+	1.80418i
$97$	−0.789152	−	0.789152i	−0.0801262	−	0.0801262i	0.665908	−	0.746034i	$-0.268044\pi$
$97$	−0.789152	−	0.789152i	−0.0801262	−	0.0801262i	−0.746034	+	0.665908i	$0.768044\pi$
$98$	3.33398	+	6.70259i	0.336783	+	0.677064i
$99$	9.01122			0.905661
$100$	−9.25707	−	3.78240i	−0.925707	−	0.378240i
$101$	15.9336			1.58546			0.792728	−	0.609576i	$-0.208660\pi$
$101$	15.9336			1.58546			0.792728	+	0.609576i	$0.208660\pi$
$102$	−12.2189	−	24.5648i	−1.20985	−	2.43228i
$103$	−3.40973	−	3.40973i	−0.335970	−	0.335970i	0.518878	−	0.854848i	$-0.326350\pi$
$103$	−3.40973	−	3.40973i	−0.335970	−	0.335970i	−0.854848	+	0.518878i	$0.826350\pi$
$104$	1.59550	+	2.33546i	0.156452	+	0.229011i
$105$	−14.9519	+	19.4443i	−1.45916	+	1.89757i
$106$	−5.08508	+	15.1507i	−0.493906	+	1.47156i
$107$	−3.76190	+	3.76190i	−0.363677	+	0.363677i	−0.865165	−	0.501488i	$-0.832786\pi$
$107$	−3.76190	+	3.76190i	−0.363677	+	0.363677i	0.501488	+	0.865165i	$0.332786\pi$
$108$	3.25492	+	23.4780i	0.313205	+	2.25918i
$109$			2.01777i			0.193268i	0.995320	+	0.0966338i	$0.0308076\pi$
$109$			2.01777i			0.193268i	−0.995320	+	0.0966338i	$0.969192\pi$
$110$	4.11924	+	0.809086i	0.392754	+	0.0771434i
$111$		−	29.0418i		−	2.75653i
$112$	12.2409	+	6.84512i	1.15665	+	0.646803i
$113$	−7.84449	+	7.84449i	−0.737948	+	0.737948i	−0.972181	−	0.234233i	$-0.924742\pi$
$113$	−7.84449	+	7.84449i	−0.737948	+	0.737948i	0.234233	+	0.972181i	$0.424742\pi$
$114$	−0.568858	−	0.190928i	−0.0532784	−	0.0178820i
$115$	1.94906	−	0.254562i	0.181750	−	0.0237380i
$116$	−4.06372	−	3.07415i	−0.377307	−	0.285427i
$117$	4.79989	+	4.79989i	0.443750	+	0.443750i
$118$	4.78974	−	2.38250i	0.440932	−	0.219326i
$119$	−21.7417			−1.99305
$120$	−1.11121	+	19.7557i	−0.101440	+	1.80344i
$121$	9.23772			0.839793
$122$	15.0163	−	7.46935i	1.35951	−	0.676243i
$123$	8.16954	+	8.16954i	0.736623	+	0.736623i
$124$	−5.32460	−	4.02799i	−0.478164	−	0.361724i
$125$	−10.3161	−	4.31034i	−0.922696	−	0.385529i
$126$	31.9093	+	10.7099i	2.84271	+	0.954110i
$127$	−14.4150	+	14.4150i	−1.27913	+	1.27913i	−0.337973	+	0.941156i	$0.609741\pi$
$127$	−14.4150	+	14.4150i	−1.27913	+	1.27913i	−0.941156	+	0.337973i	$0.890259\pi$
$128$	11.2685	−	1.01073i	0.996001	−	0.0893371i
$129$		−	19.8260i		−	1.74558i
$130$	1.76318	+	2.62511i	0.154641	+	0.230237i
$131$		−	21.0027i		−	1.83502i	−0.397714	−	0.917509i	$-0.630196\pi$
$131$		−	21.0027i		−	1.83502i	0.397714	−	0.917509i	$-0.369804\pi$
$132$	−1.14067	−	8.22776i	−0.0992826	−	0.716135i
$133$	−0.336233	+	0.336233i	−0.0291551	+	0.0291551i
$134$	−3.66094	+	10.9075i	−0.316257	+	0.942268i
$135$	3.43199	+	26.2771i	0.295379	+	2.26158i
$136$	−14.4820	+	9.89359i	−1.24182	+	0.848368i
$137$	4.47775	+	4.47775i	0.382560	+	0.382560i	0.872024	−	0.489464i	$-0.162807\pi$
$137$	4.47775	+	4.47775i	0.382560	+	0.382560i	−0.489464	+	0.872024i	$0.662807\pi$
$138$	−1.73216	−	3.48232i	−0.147452	−	0.296435i
$139$	−18.6728			−1.58381			−0.791903	−	0.610646i	$-0.790910\pi$
$139$	−18.6728			−1.58381			−0.791903	+	0.610646i	$0.790910\pi$
$140$	13.6249	+	7.76076i	1.15152	+	0.655904i
$141$	3.01446			0.253864
$142$	2.84118	+	5.71189i	0.238427	+	0.479331i
$143$	−0.938690	−	0.938690i	−0.0784972	−	0.0784972i
$144$	26.1282	−	7.38663i	2.17735	−	0.615553i
$145$	−4.51613	−	3.47272i	−0.375044	−	0.288394i
$146$	2.22562	−	6.63108i	0.184193	−	0.548792i
$147$	11.7103	−	11.7103i	0.965850	−	0.965850i
$148$	−18.3896	+	2.54947i	−1.51161	+	0.209565i
$149$			2.16250i			0.177159i	0.996069	+	0.0885794i	$0.0282327\pi$
$149$			2.16250i			0.177159i	−0.996069	+	0.0885794i	$0.971767\pi$
$150$	−1.41652	+	22.0771i	−0.115659	+	1.80258i
$151$			11.4939i			0.935359i	0.883898	+	0.467679i	$0.154910\pi$
$151$			11.4939i			0.935359i	−0.883898	+	0.467679i	$0.845090\pi$
$152$	−0.0709596	+	0.376967i	−0.00575558	+	0.0305761i
$153$	−29.7637	+	29.7637i	−2.40626	+	2.40626i
$154$	−6.24035	−	2.09447i	−0.502862	−	0.168778i
$155$	−5.91739	−	4.55024i	−0.475296	−	0.365484i
$156$	3.77499	−	4.99016i	0.302241	−	0.399533i
$157$	−3.26515	−	3.26515i	−0.260587	−	0.260587i	0.564705	−	0.825293i	$-0.308990\pi$
$157$	−3.26515	−	3.26515i	−0.260587	−	0.260587i	−0.825293	+	0.564705i	$0.808990\pi$
$158$	−16.0553	+	7.98618i	−1.27729	+	0.635346i
$159$	35.3545			2.80379
$160$	12.6071	−	1.03065i	0.996675	−	0.0814797i
$161$	−3.08211			−0.242904
$162$	21.1631	−	10.5269i	1.66273	−	0.827069i
$163$	15.9970	+	15.9970i	1.25299	+	1.25299i	0.954375	+	0.298610i	$0.0965231\pi$
$163$	15.9970	+	15.9970i	1.25299	+	1.25299i	0.298610	+	0.954375i	$0.403477\pi$
$164$	4.45586	−	5.89021i	0.347944	−	0.459948i
$165$	−1.20272	−	9.20869i	−0.0936320	−	0.716895i
$166$	−4.15246	−	1.39371i	−0.322293	−	0.108173i
$167$	−10.7952	+	10.7952i	−0.835357	+	0.835357i	−0.988244	−	0.152887i	$-0.951143\pi$
$167$	−10.7952	+	10.7952i	−0.835357	+	0.835357i	0.152887	+	0.988244i	$0.451143\pi$
$168$	5.73953	−	30.4908i	0.442814	−	2.35241i
$169$		−	1.00000i		−	0.0769231i
$170$	−16.2781	+	10.9333i	−1.24847	+	0.838549i
$171$			0.920589i			0.0703992i
$172$	−12.5540	+	1.74045i	−0.957233	+	0.132708i
$173$	−8.75163	+	8.75163i	−0.665374	+	0.665374i	−0.956642	−	0.291268i	$-0.905923\pi$
$173$	−8.75163	+	8.75163i	−0.665374	+	0.665374i	0.291268	+	0.956642i	$0.405923\pi$
$174$	−3.58680	+	10.6866i	−0.271915	+	0.810152i
$175$	15.1642	+	8.79666i	1.14631	+	0.664965i
$176$	−5.10976	+	1.44457i	−0.385163	+	0.108888i
$177$	−8.36830	−	8.36830i	−0.629000	−	0.629000i
$178$	−3.50417	−	7.04475i	−0.262649	−	0.528026i
$179$	−10.6924			−0.799191			−0.399595	−	0.916692i	$-0.630849\pi$
$179$	−10.6924			−0.799191			−0.399595	+	0.916692i	$0.630849\pi$
$180$	29.2764	−	8.02788i	2.18214	−	0.598363i
$181$	−5.27363			−0.391986			−0.195993	−	0.980605i	$-0.562793\pi$
$181$	−5.27363			−0.391986			−0.195993	+	0.980605i	$0.562793\pi$
$182$	−2.20833	−	4.43960i	−0.163692	−	0.329085i
$183$	−26.2354	−	26.2354i	−1.93938	−	1.93938i
$184$	−2.05298	+	1.40252i	−0.151348	+	0.103395i
$185$	−20.5820	+	2.68817i	−1.51322	+	0.197638i
$186$	−4.69971	+	14.0025i	−0.344600	+	1.02671i
$187$	5.82075	−	5.82075i	0.425655	−	0.425655i
$188$	−0.264628	−	1.90879i	−0.0193000	−	0.139213i
$189$		−	41.5530i		−	3.02253i
$190$	−0.0826565	+	0.420823i	−0.00599653	+	0.0305297i
$191$		−	9.08353i		−	0.657261i	−0.944459	−	0.328631i	$-0.893413\pi$
$191$		−	9.08353i		−	0.657261i	0.944459	−	0.328631i	$-0.106587\pi$
$192$	−10.0518	−	22.9215i	−0.725428	−	1.65422i
$193$	7.15737	−	7.15737i	0.515199	−	0.515199i	−0.400916	−	0.916115i	$-0.631308\pi$
$193$	7.15737	−	7.15737i	0.515199	−	0.515199i	0.916115	+	0.400916i	$0.131308\pi$
$194$	1.49627	+	0.502201i	0.107426	+	0.0360559i
$195$	4.26443	−	5.54571i	0.305382	−	0.397137i
$196$	−8.44308	−	6.38707i	−0.603077	−	0.456220i
$197$	−3.65263	−	3.65263i	−0.260239	−	0.260239i	0.564912	−	0.825151i	$-0.308910\pi$
$197$	−3.65263	−	3.65263i	−0.260239	−	0.260239i	−0.825151	+	0.564912i	$0.808910\pi$
$198$	−11.4102	+	5.67560i	−0.810884	+	0.403347i
$199$	6.66227			0.472276			0.236138	−	0.971720i	$-0.424118\pi$
$199$	6.66227			0.472276			0.236138	+	0.971720i	$0.424118\pi$
$200$	14.1038	−	1.04111i	0.997287	−	0.0736172i
$201$	25.4530			1.79532
$202$	−20.1754	+	10.0356i	−1.41954	+	0.706101i
$203$	6.31653	+	6.31653i	0.443333	+	0.443333i
$204$	30.9436	+	23.4084i	2.16649	+	1.63892i
$205$	5.03358	−	6.54596i	0.351561	−	0.457190i
$206$	6.46502	+	2.16988i	0.450439	+	0.151183i
$207$	−4.21933	+	4.21933i	−0.293264	+	0.293264i
$208$	−3.49121	−	1.95229i	−0.242072	−	0.135367i
$209$		−	0.180035i		−	0.0124533i
$210$	6.68562	−	34.0380i	0.461352	−	2.34885i
$211$		−	9.87309i		−	0.679692i	−0.940481	−	0.339846i	$-0.889625\pi$
$211$		−	9.87309i		−	0.679692i	0.940481	−	0.339846i	$-0.110375\pi$
$212$	−3.10363	−	22.3868i	−0.213158	−	1.53753i
$213$	9.97941	−	9.97941i	0.683778	−	0.683778i
$214$	2.39400	−	7.13277i	0.163650	−	0.487586i
$215$	−14.0507	+	1.83513i	−0.958250	+	0.125155i
$216$	−18.9088	−	27.6782i	−1.28658	−	1.88327i
$217$	8.27641	+	8.27641i	0.561839	+	0.561839i
$218$	−1.27087	−	2.55494i	−0.0860740	−	0.173042i
$219$	−15.4738			−1.04562
$220$	−5.72545	+	1.56997i	−0.386010	+	0.105848i
$221$	6.20093			0.417119
$222$	18.2916	+	36.7733i	1.22765	+	2.46806i
$223$	3.26129	+	3.26129i	0.218392	+	0.218392i	0.807821	−	0.589429i	$-0.200647\pi$
$223$	3.26129	+	3.26129i	0.218392	+	0.218392i	−0.589429	+	0.807821i	$0.700647\pi$
$224$	−19.8109	−	0.957657i	−1.32367	−	0.0639862i
$225$	32.8018	−	8.71703i	2.18679	−	0.581135i
$226$	4.99208	−	14.8736i	0.332068	−	0.989376i
$227$	−6.50040	+	6.50040i	−0.431446	+	0.431446i	−0.889120	−	0.457674i	$-0.848683\pi$
$227$	−6.50040	+	6.50040i	−0.431446	+	0.431446i	0.457674	+	0.889120i	$0.348683\pi$
$228$	0.840551	−	0.116531i	0.0556668	−	0.00771747i
$229$			13.3363i			0.881290i	0.897681	+	0.440645i	$0.145250\pi$
$229$			13.3363i			0.881290i	−0.897681	+	0.440645i	$0.854750\pi$
$230$	−2.30760	+	1.54992i	−0.152158	+	0.102199i
$231$			14.5620i			0.958111i
$232$	7.08176	+	1.33306i	0.464940	+	0.0875195i
$233$	−0.823071	+	0.823071i	−0.0539212	+	0.0539212i	−0.733553	−	0.679632i	$-0.762139\pi$
$233$	−0.823071	+	0.823071i	−0.0539212	+	0.0539212i	0.679632	+	0.733553i	$0.262139\pi$
$234$	−9.10085	−	3.05455i	−0.594941	−	0.199682i
$235$	−0.279024	−	2.13636i	−0.0182015	−	0.139360i
$236$	−4.56427	+	6.03351i	−0.297109	+	0.392748i
$237$	28.0507	+	28.0507i	1.82209	+	1.82209i
$238$	27.5296	−	13.6937i	1.78448	−	0.887630i
$239$	−8.16814			−0.528353			−0.264177	−	0.964474i	$-0.585100\pi$
$239$	−8.16814			−0.528353			−0.264177	+	0.964474i	$0.585100\pi$
$240$	−11.0358	−	25.7149i	−0.712360	−	1.65989i
$241$	−17.3321			−1.11646			−0.558231	−	0.829686i	$-0.688520\pi$
$241$	−17.3321			−1.11646			−0.558231	+	0.829686i	$0.688520\pi$
$242$	−11.6970	+	5.81826i	−0.751909	+	0.374012i
$243$	−11.8343	−	11.8343i	−0.759170	−	0.759170i
$244$	−14.3094	+	18.9156i	−0.916066	+	1.21095i
$245$	−9.38304	−	7.21519i	−0.599461	−	0.460961i
$246$	−15.4899	−	5.19894i	−0.987600	−	0.331472i
$247$	0.0958969	−	0.0958969i	0.00610177	−	0.00610177i
$248$	9.27908	+	1.74668i	0.589222	+	0.110914i
$249$			9.68988i			0.614071i
$250$	15.7772	−	1.03960i	0.997836	−	0.0657502i
$251$		−	1.59327i		−	0.100566i	−0.998735	−	0.0502831i	$-0.983988\pi$
$251$		−	1.59327i		−	0.100566i	0.998735	−	0.0502831i	$-0.0160124\pi$
$252$	−47.1496	+	6.53667i	−2.97015	+	0.411772i
$253$	0.825153	−	0.825153i	0.0518769	−	0.0518769i
$254$	9.17345	−	27.3317i	0.575593	−	1.71494i
$255$	34.3886	+	26.4434i	2.15349	+	1.65595i
$256$	−13.6317	+	8.37711i	−0.851983	+	0.523569i
$257$	9.75097	+	9.75097i	0.608249	+	0.608249i	0.942488	−	0.334239i	$-0.108479\pi$
$257$	9.75097	+	9.75097i	0.608249	+	0.608249i	−0.334239	+	0.942488i	$0.608479\pi$
$258$	12.4871	+	25.1040i	0.777414	+	1.56291i
$259$	32.5470			2.02237
$260$	−3.88596	−	2.21344i	−0.240997	−	0.137272i
$261$	17.2943			1.07049
$262$	13.2283	+	26.5940i	0.817247	+	1.64299i
$263$	3.41329	+	3.41329i	0.210472	+	0.210472i	0.804468	−	0.593996i	$-0.202450\pi$
$263$	3.41329	+	3.41329i	0.210472	+	0.210472i	−0.593996	+	0.804468i	$0.702450\pi$
$264$	6.62648	+	9.69970i	0.407832	+	0.596975i
$265$	−3.27248	−	25.0558i	−0.201027	−	1.53916i
$266$	0.213972	−	0.637516i	0.0131195	−	0.0390886i
$267$	−12.3081	+	12.3081i	−0.753243	+	0.753243i
$268$	−2.23442	−	16.1171i	−0.136489	−	0.984509i
$269$		−	0.814410i		−	0.0496555i	−0.999692	−	0.0248277i	$-0.992096\pi$
$269$		−	0.814410i		−	0.0496555i	0.999692	−	0.0248277i	$-0.00790372\pi$
$270$	−20.8960	−	31.1110i	−1.27169	−	1.89335i
$271$			5.38145i			0.326900i	0.986552	+	0.163450i	$0.0522622\pi$
$271$			5.38145i			0.326900i	−0.986552	+	0.163450i	$0.947738\pi$
$272$	12.1060	−	21.6487i	0.734035	−	1.31265i
$273$	−7.75657	+	7.75657i	−0.469449	+	0.469449i
$274$	−8.49006	−	2.84955i	−0.512903	−	0.172148i
$275$	−6.41489	+	1.70475i	−0.386832	+	0.102800i
$276$	4.38659	+	3.31839i	0.264042	+	0.199744i
$277$	2.08106	+	2.08106i	0.125039	+	0.125039i	0.766857	−	0.641818i	$-0.221820\pi$
$277$	2.08106	+	2.08106i	0.125039	+	0.125039i	−0.641818	+	0.766857i	$0.721820\pi$
$278$	23.6438	−	11.7608i	1.41806	−	0.705367i
$279$	22.6604			1.35664
$280$	−22.1401	−	1.24533i	−1.32313	−	0.0744229i
$281$	31.3093			1.86776			0.933878	−	0.357592i	$-0.116402\pi$
$281$	31.3093			1.86776			0.933878	+	0.357592i	$0.116402\pi$
$282$	−3.81696	+	1.89862i	−0.227297	+	0.113061i
$283$	−13.3242	−	13.3242i	−0.792041	−	0.792041i	0.189785	−	0.981826i	$-0.439221\pi$
$283$	−13.3242	−	13.3242i	−0.792041	−	0.792041i	−0.981826	+	0.189785i	$0.939221\pi$
$284$	−7.19511	−	5.44300i	−0.426951	−	0.322983i
$285$	0.940763	−	0.122871i	0.0557260	−	0.00727824i
$286$	1.77981	+	0.597364i	0.105242	+	0.0353229i
$287$	−9.15557	+	9.15557i	−0.540436	+	0.540436i
$288$	−28.4316	+	25.8096i	−1.67535	+	1.52084i
$289$			21.4515i			1.26185i
$290$	7.90565	+	1.55280i	0.464236	+	0.0911834i
$291$		−	3.49160i		−	0.204681i
$292$	1.35839	+	9.79816i	0.0794935	+	0.573394i
$293$	−9.96476	+	9.96476i	−0.582148	+	0.582148i	−0.935493	−	0.353345i	$-0.885044\pi$
$293$	−9.96476	+	9.96476i	−0.582148	+	0.582148i	0.353345	+	0.935493i	$0.385044\pi$
$294$	−7.45220	+	22.2034i	−0.434621	+	1.29493i
$295$	−5.15605	+	6.70522i	−0.300197	+	0.390393i
$296$	21.6794	−	14.8106i	1.26009	−	0.860849i
$297$	11.1247	+	11.1247i	0.645521	+	0.645521i
$298$	−1.36202	−	2.73819i	−0.0788998	−	0.158619i
$299$	0.879047			0.0508366
$300$	−12.1113	−	28.8465i	−0.699248	−	1.66546i
$301$	22.2189			1.28067
$302$	−7.23927	−	14.5538i	−0.416573	−	0.837474i
$303$	35.2491	+	35.2491i	2.02501	+	2.02501i
$304$	−0.147577	−	0.522015i	−0.00846415	−	0.0299396i
$305$	−16.1647	+	21.0215i	−0.925588	+	1.20369i
$306$	18.9411	−	56.4337i	1.08279	−	3.22610i
$307$	−3.75196	+	3.75196i	−0.214136	+	0.214136i	−0.806022	−	0.591886i	$-0.798384\pi$
$307$	−3.75196	+	3.75196i	−0.214136	+	0.214136i	0.591886	+	0.806022i	$0.298384\pi$
$308$	9.22081	−	1.27834i	0.525405	−	0.0728404i
$309$		−	15.0863i		−	0.858230i
$310$	10.3586	+	2.03460i	0.588329	+	0.115557i
$311$		−	11.3949i		−	0.646146i	−0.946374	−	0.323073i	$-0.895284\pi$
$311$		−	11.3949i		−	0.646146i	0.946374	−	0.323073i	$-0.104716\pi$
$312$	−1.63697	+	8.69626i	−0.0926751	+	0.492329i
$313$	−13.6506	+	13.6506i	−0.771575	+	0.771575i	−0.978382	−	0.206807i	$-0.933693\pi$
$313$	−13.6506	+	13.6506i	−0.771575	+	0.771575i	0.206807	+	0.978382i	$0.433693\pi$
$314$	6.19090	+	2.07788i	0.349373	+	0.117261i
$315$	−52.7709	+	6.89227i	−2.97330	+	0.388336i
$316$	15.2995	−	20.2245i	0.860666	−	1.13772i
$317$	−13.2138	−	13.2138i	−0.742160	−	0.742160i	0.230833	−	0.972993i	$-0.425855\pi$
$317$	−13.2138	−	13.2138i	−0.742160	−	0.742160i	−0.972993	+	0.230833i	$0.925855\pi$
$318$	−44.7664	+	22.2676i	−2.51038	+	1.24870i
$319$	−3.38216			−0.189365
$320$	−15.3141	+	9.24541i	−0.856086	+	0.516834i
$321$	−16.6445			−0.929005
$322$	3.90262	−	1.94123i	0.217485	−	0.108180i
$323$	0.594649	+	0.594649i	0.0330872	+	0.0330872i
$324$	−20.1669	+	26.6586i	−1.12038	+	1.48103i
$325$	−4.32498	−	2.50889i	−0.239907	−	0.139168i
$326$	−30.3313	−	10.1802i	−1.67989	−	0.563829i
$327$	−4.46381	+	4.46381i	−0.246849	+	0.246849i
$328$	−1.93222	+	10.2647i	−0.106689	+	0.566776i
$329$			3.37829i			0.186251i
$330$	7.32288	+	10.9027i	0.403111	+	0.600173i
$331$		−	14.3131i		−	0.786717i	−0.919385	−	0.393358i	$-0.871313\pi$
$331$		−	14.3131i		−	0.786717i	0.919385	−	0.393358i	$-0.128687\pi$
$332$	6.13572	−	0.850637i	0.336742	−	0.0466848i
$333$	44.5560	−	44.5560i	2.44166	−	2.44166i
$334$	6.86985	−	20.4683i	0.375901	−	1.11997i
$335$	−2.35598	−	18.0386i	−0.128721	−	0.985555i
$336$	11.9367	+	42.2229i	0.651201	+	2.30345i
$337$	−16.1524	−	16.1524i	−0.879878	−	0.879878i	0.113644	−	0.993522i	$-0.463748\pi$
$337$	−16.1524	−	16.1524i	−0.879878	−	0.879878i	−0.993522	+	0.113644i	$0.963748\pi$
$338$	0.629837	+	1.26622i	0.0342586	+	0.0688731i
$339$	−34.7079			−1.88507
$340$	13.7254	−	24.0965i	0.744364	−	1.30682i
$341$	−4.43158			−0.239983
$342$	−0.579821	−	1.16566i	−0.0313531	−	0.0630319i
$343$	−4.23109	−	4.23109i	−0.228458	−	0.228458i
$344$	14.7999	−	10.1108i	0.797956	−	0.545135i
$345$	4.87494	+	3.74864i	0.262458	+	0.201820i
$346$	5.56936	−	16.5936i	0.299411	−	0.892075i
$347$	21.6981	−	21.6981i	1.16481	−	1.16481i	0.181404	−	0.983409i	$-0.441936\pi$
$347$	21.6981	−	21.6981i	1.16481	−	1.16481i	0.983409	−	0.181404i	$-0.0580641\pi$
$348$	−2.18917	−	15.7907i	−0.117352	−	0.846471i
$349$			16.4301i			0.879483i	0.898124	+	0.439742i	$0.144930\pi$
$349$			16.4301i			0.879483i	−0.898124	+	0.439742i	$0.855070\pi$
$350$	−24.7417	−	1.58749i	−1.32250	−	0.0848549i
$351$			11.8513i			0.632576i
$352$	5.56023	−	5.04745i	0.296361	−	0.269030i
$353$	−10.5205	+	10.5205i	−0.559948	+	0.559948i	−0.929292	−	0.369345i	$-0.879582\pi$
$353$	−10.5205	+	10.5205i	−0.559948	+	0.559948i	0.369345	+	0.929292i	$0.379582\pi$
$354$	15.8668	+	5.32542i	0.843309	+	0.283043i
$355$	−7.99614	−	6.14871i	−0.424391	−	0.326340i
$356$	8.87408	+	6.71312i	0.470325	+	0.355795i
$357$	−48.0979	−	48.0979i	−2.54561	−	2.54561i
$358$	13.5390	−	6.73450i	0.715556	−	0.355929i
$359$	−6.26986			−0.330910			−0.165455	−	0.986217i	$-0.552909\pi$
$359$	−6.26986			−0.330910			−0.165455	+	0.986217i	$0.552909\pi$
$360$	−32.0141	+	28.6044i	−1.68729	+	1.50759i
$361$	−18.9816			−0.999032
$362$	6.67756	−	3.32153i	0.350965	−	0.174576i
$363$	20.4361	+	20.4361i	1.07262	+	1.07262i
$364$	5.59245	+	4.23061i	0.293124	+	0.221744i
$365$	1.43228	+	10.9663i	0.0749692	+	0.574003i
$366$	49.7438	+	16.6957i	2.60015	+	0.872698i
$367$	−10.4070	+	10.4070i	−0.543240	+	0.543240i	−0.924477	−	0.381238i	$-0.875498\pi$
$367$	−10.4070	+	10.4070i	−0.543240	+	0.543240i	0.381238	+	0.924477i	$0.375498\pi$
$368$	1.71616	−	3.06894i	0.0894609	−	0.159980i
$369$			25.0675i			1.30496i
$370$	24.3682	−	16.3671i	1.26684	−	0.850885i
$371$			39.6216i			2.05705i
$372$	−2.86843	−	20.6902i	−0.148721	−	1.07274i
$373$	−4.94834	+	4.94834i	−0.256215	+	0.256215i	−0.823513	−	0.567298i	$-0.807989\pi$
$373$	−4.94834	+	4.94834i	−0.256215	+	0.256215i	0.567298	+	0.823513i	$0.307989\pi$
$374$	−3.70421	+	11.0365i	−0.191540	+	0.570681i
$375$	−13.2861	−	32.3572i	−0.686092	−	1.67092i
$376$	1.53730	+	2.25027i	0.0792803	+	0.116049i
$377$	−1.80153	−	1.80153i	−0.0927837	−	0.0927837i
$378$	26.1716	+	52.6151i	1.34612	+	2.70623i
$379$	23.0953			1.18633			0.593164	−	0.805082i	$-0.297879\pi$
$379$	23.0953			1.18633			0.593164	+	0.805082i	$0.297879\pi$
$380$	−0.160389	−	0.584914i	−0.00822778	−	0.0300054i
$381$	−63.7793			−3.26751
$382$	5.72114	+	11.5017i	0.292719	+	0.588479i
$383$	24.4550	+	24.4550i	1.24959	+	1.24959i	0.955899	+	0.293694i	$0.0948847\pi$
$383$	24.4550	+	24.4550i	1.24959	+	1.24959i	0.293694	+	0.955899i	$0.405115\pi$
$384$	27.1646	+	22.6926i	1.38624	+	1.15803i
$385$	10.3201	−	1.34789i	0.525963	−	0.0686947i
$386$	−4.55481	+	13.5708i	−0.231834	+	0.690734i
$387$	30.4170	−	30.4170i	1.54619	−	1.54619i
$388$	−2.21091	+	0.306514i	−0.112242	+	0.0155609i
$389$			7.99677i			0.405453i	0.979235	+	0.202726i	$0.0649802\pi$
$389$			7.99677i			0.405453i	−0.979235	+	0.202726i	$0.935020\pi$
$390$	−1.90680	+	9.70797i	−0.0965548	+	0.491582i
$391$			5.45091i			0.275664i
$392$	14.7136	+	2.76966i	0.743148	+	0.139889i
$393$	46.4633	−	46.4633i	2.34376	−	2.34376i
$394$	6.92558	+	2.32446i	0.348906	+	0.117105i
$395$	17.2832	−	22.4760i	0.869611	−	1.13089i
$396$	10.8730	−	14.3731i	0.546390	−	0.722274i
$397$	21.6665	+	21.6665i	1.08741	+	1.08741i	0.995795	+	0.0916143i	$0.0292027\pi$
$397$	21.6665	+	21.6665i	1.08741	+	1.08741i	0.0916143	+	0.995795i	$0.470797\pi$
$398$	−8.43588	+	4.19614i	−0.422852	+	0.210334i
$399$	−1.48766			−0.0744762
$400$	−17.2027	+	10.2013i	−0.860135	+	0.510067i
$401$	−15.6161			−0.779829			−0.389915	−	0.920851i	$-0.627495\pi$
$401$	−15.6161			−0.779829			−0.389915	+	0.920851i	$0.627495\pi$
$402$	−32.2291	+	16.0313i	−1.60744	+	0.799567i
$403$	−2.36051	−	2.36051i	−0.117585	−	0.117585i
$404$	19.2257	−	25.4145i	0.956514	−	1.26442i
$405$	−22.7816	+	29.6265i	−1.13203	+	1.47215i
$406$	−11.9765	−	4.01971i	−0.594382	−	0.199495i
$407$	−8.71360	+	8.71360i	−0.431917	+	0.431917i
$408$	−53.9248	−	10.1507i	−2.66968	−	0.502535i
$409$		−	8.44385i		−	0.417521i	−0.977967	−	0.208761i	$-0.933057\pi$
$409$		−	8.44385i		−	0.417521i	0.977967	−	0.208761i	$-0.0669430\pi$
$410$	−2.25072	+	11.4589i	−0.111155	+	0.565917i
$411$			19.8118i			0.977243i
$412$	−9.55279	+	1.32437i	−0.470632	+	0.0652470i
$413$	9.37832	−	9.37832i	0.461477	−	0.461477i
$414$	2.68510	−	8.00007i	0.131965	−	0.393182i
$415$	6.86723	−	0.896913i	0.337099	−	0.0440277i
$416$	5.65026	+	0.273133i	0.277027	+	0.0133914i
$417$	−41.3089	−	41.3089i	−2.02290	−	2.02290i
$418$	0.113393	+	0.227963i	0.00554622	+	0.0111501i
$419$	18.9187			0.924238			0.462119	−	0.886818i	$-0.347089\pi$
$419$	18.9187			0.924238			0.462119	+	0.886818i	$0.347089\pi$
$420$	12.9730	+	47.3104i	0.633016	+	2.30851i
$421$	18.8621			0.919280			0.459640	−	0.888105i	$-0.347978\pi$
$421$	18.8621			0.919280			0.459640	+	0.888105i	$0.347978\pi$
$422$	6.21844	+	12.5015i	0.302709	+	0.608563i
$423$	4.62480	+	4.62480i	0.224865	+	0.224865i
$424$	18.0299	+	26.3918i	0.875610	+	1.28170i
$425$	15.5574	−	26.8189i	0.754647	−	1.30091i
$426$	−6.35070	+	18.9215i	−0.307692	+	0.916750i
$427$	29.4019	−	29.4019i	1.42286	−	1.42286i
$428$	1.46116	+	10.5395i	0.0706277	+	0.509444i
$429$		−	4.15323i		−	0.200520i
$430$	16.6354	−	11.1733i	0.802231	−	0.538825i
$431$			2.12748i			0.102477i	0.998686	+	0.0512386i	$0.0163169\pi$
$431$			2.12748i			0.102477i	−0.998686	+	0.0512386i	$0.983683\pi$
$432$	41.3754	+	23.1372i	1.99067	+	1.11319i
$433$	−3.83254	+	3.83254i	−0.184180	+	0.184180i	−0.793175	−	0.608994i	$-0.791573\pi$
$433$	−3.83254	+	3.83254i	−0.184180	+	0.184180i	0.608994	+	0.793175i	$0.291573\pi$
$434$	−15.6925	−	5.26694i	−0.753265	−	0.252821i
$435$	−2.30827	−	17.6733i	−0.110673	−	0.847370i
$436$	3.21839	+	2.43467i	0.154133	+	0.116599i
$437$	0.0842979	+	0.0842979i	0.00403252	+	0.00403252i
$438$	19.5932	−	9.74597i	0.936199	−	0.465681i
$439$	14.4981			0.691955			0.345978	−	0.938243i	$-0.387547\pi$
$439$	14.4981			0.691955			0.345978	+	0.938243i	$0.387547\pi$
$440$	6.26083	−	5.59402i	0.298474	−	0.266685i
$441$	35.9319			1.71105
$442$	−7.85172	+	3.90557i	−0.373468	+	0.185769i
$443$	2.81674	+	2.81674i	0.133827	+	0.133827i	0.770847	−	0.637020i	$-0.219833\pi$
$443$	2.81674	+	2.81674i	0.133827	+	0.133827i	−0.637020	+	0.770847i	$0.719833\pi$
$444$	−46.3223	−	35.0422i	−2.19836	−	1.66303i
$445$	9.86203	+	7.58351i	0.467505	+	0.359493i
$446$	−6.18358	−	2.07542i	−0.292801	−	0.0982739i
$447$	−4.78398	+	4.78398i	−0.226275	+	0.226275i
$448$	25.6881	−	11.2650i	1.21365	−	0.532223i
$449$			24.0157i			1.13337i	0.823934	+	0.566686i	$0.191775\pi$
$449$			24.0157i			1.13337i	−0.823934	+	0.566686i	$0.808225\pi$
$450$	−36.0439	+	31.6974i	−1.69913	+	1.49423i
$451$		−	4.90232i		−	0.230841i
$452$	3.04687	+	21.9774i	0.143313	+	1.03373i
$453$	−25.4273	+	25.4273i	−1.19468	+	1.19468i
$454$	4.13672	−	12.3251i	0.194146	−	0.578446i
$455$	6.21506	+	4.77913i	0.291366	+	0.224049i
$456$	−0.990924	+	0.676964i	−0.0464043	+	0.0317017i
$457$	−20.4343	−	20.4343i	−0.955877	−	0.955877i	0.0431895	−	0.999067i	$-0.486248\pi$
$457$	−20.4343	−	20.4343i	−0.955877	−	0.955877i	−0.999067	+	0.0431895i	$0.986248\pi$
$458$	−8.39972	−	16.8867i	−0.392493	−	0.789064i
$459$	−73.4890			−3.43017
$460$	1.94572	−	3.41594i	0.0907197	−	0.159269i
$461$	1.23760			0.0576406			0.0288203	−	0.999585i	$-0.490825\pi$
$461$	1.23760			0.0576406			0.0288203	+	0.999585i	$0.490825\pi$
$462$	−9.17170	−	18.4387i	−0.426706	−	0.857845i
$463$	−21.8154	−	21.8154i	−1.01385	−	1.01385i	−0.999903	−	0.0139434i	$-0.995562\pi$
$463$	−21.8154	−	21.8154i	−1.01385	−	1.01385i	−0.0139434	−	0.999903i	$-0.504438\pi$
$464$	−9.80665	+	2.77241i	−0.455262	+	0.128706i
$465$	−3.02448	−	23.1570i	−0.140257	−	1.07388i
$466$	0.523786	−	1.56059i	0.0242639	−	0.0722928i
$467$	12.6950	−	12.6950i	0.587455	−	0.587455i	−0.349487	−	0.936941i	$-0.613644\pi$
$467$	12.6950	−	12.6950i	0.587455	−	0.587455i	0.936941	+	0.349487i	$0.113644\pi$
$468$	13.4475	−	1.86432i	0.621612	−	0.0861783i
$469$			28.5251i			1.31717i
$470$	1.69886	+	2.52935i	0.0783626	+	0.116670i
$471$		−	14.4466i		−	0.665665i
$472$	1.97923	−	10.5145i	0.0911013	−	0.483968i
$473$	−5.94851	+	5.94851i	−0.273513	+	0.273513i
$474$	−53.1857	−	17.8509i	−2.44290	−	0.819921i
$475$	−0.174157	−	0.655347i	−0.00799089	−	0.0300694i
$476$	−26.2337	+	34.6784i	−1.20242	+	1.58948i
$477$	54.2409	+	54.2409i	2.48352	+	2.48352i
$478$	10.3426	−	5.14460i	0.473061	−	0.235308i
$479$	−36.2989			−1.65854			−0.829269	−	0.558850i	$-0.811243\pi$
$479$	−36.2989			−1.65854			−0.829269	+	0.558850i	$0.811243\pi$
$480$	30.1699	+	25.6099i	1.37706	+	1.16892i
$481$	−9.28273			−0.423256
$482$	21.9463	−	10.9164i	0.999625	−	0.497230i
$483$	−6.81839	−	6.81839i	−0.310247	−	0.310247i
$484$	11.1463	−	14.7344i	0.506652	−	0.669743i
$485$	−2.47450	+	0.323189i	−0.112361	+	0.0146752i
$486$	22.4385	+	7.53111i	1.01783	+	0.341618i
$487$	−16.4587	+	16.4587i	−0.745816	+	0.745816i	−0.973691	−	0.227874i	$-0.926823\pi$
$487$	−16.4587	+	16.4587i	−0.745816	+	0.745816i	0.227874	+	0.973691i	$0.426823\pi$
$488$	6.20506	−	32.9639i	0.280890	−	1.49221i
$489$			70.7788i			3.20073i
$490$	16.4254	+	3.22621i	0.742022	+	0.145745i
$491$			21.7615i			0.982081i	0.871137	+	0.491040i	$0.163383\pi$
$491$			21.7615i			0.982081i	−0.871137	+	0.491040i	$0.836617\pi$
$492$	22.8881	−	3.17313i	1.03187	−	0.143056i
$493$	11.1712	−	11.1712i	0.503124	−	0.503124i
$494$	−0.0610269	+	0.181826i	−0.00274573	+	0.00818072i
$495$	12.2828	−	15.9732i	0.552069	−	0.717943i
$496$	−12.8495	+	3.63263i	−0.576957	+	0.163110i
$497$	11.1839	+	11.1839i	0.501665	+	0.501665i
$498$	−6.10304	−	12.2695i	−0.273484	−	0.549809i
$499$	37.8103			1.69262			0.846310	−	0.532690i	$-0.178819\pi$
$499$	37.8103			1.69262			0.846310	+	0.532690i	$0.178819\pi$
$500$	−19.3225	+	11.2534i	−0.864131	+	0.503268i
$501$	−47.7633			−2.13390
$502$	1.00350	+	2.01742i	0.0447884	+	0.0900421i
$503$	−6.85634	−	6.85634i	−0.305709	−	0.305709i	0.537533	−	0.843242i	$-0.319356\pi$
$503$	−6.85634	−	6.85634i	−0.305709	−	0.305709i	−0.843242	+	0.537533i	$0.819356\pi$
$504$	55.5846	−	37.9734i	2.47593	−	1.69147i
$505$	21.7184	−	28.2438i	0.966456	−	1.25683i
$506$	−0.525111	+	1.56453i	−0.0233440	+	0.0695521i
$507$	2.21225	−	2.21225i	0.0982493	−	0.0982493i
$508$	5.59894	+	40.3857i	0.248413	+	1.79182i
$509$		−	2.43094i		−	0.107749i	−0.998548	−	0.0538747i	$-0.982843\pi$
$509$		−	2.43094i		−	0.107749i	0.998548	−	0.0538747i	$-0.0171572\pi$
$510$	−60.1984	−	11.8239i	−2.66563	−	0.523573i
$511$		−	17.3414i		−	0.767139i
$512$	11.9845	−	19.1930i	0.529646	−	0.848219i
$513$	−1.13650	+	1.13650i	−0.0501778	+	0.0501778i
$514$	−18.4884	−	6.20532i	−0.815487	−	0.273705i
$515$	−10.6917	+	1.39642i	−0.471132	+	0.0615335i
$516$	−31.6228	−	23.9222i	−1.39212	−	1.05312i
$517$	−0.904448	−	0.904448i	−0.0397776	−	0.0397776i
$518$	−41.2116	+	20.4993i	−1.81073	+	0.900689i
$519$	−38.7215			−1.69969
$520$	6.31457	+	0.355181i	0.276912	+	0.0155757i
$521$	29.6911			1.30079			0.650395	−	0.759596i	$-0.274603\pi$
$521$	29.6911			1.30079			0.650395	+	0.759596i	$0.274603\pi$
$522$	−21.8984	+	10.8926i	−0.958465	+	0.476756i
$523$	0.894603	+	0.894603i	0.0391183	+	0.0391183i	0.726395	−	0.687277i	$-0.241194\pi$
$523$	0.894603	+	0.894603i	0.0391183	+	0.0391183i	−0.687277	+	0.726395i	$0.741194\pi$
$524$	−33.4998	−	25.3421i	−1.46345	−	1.10708i
$525$	14.0866	+	53.0074i	0.614791	+	2.31343i
$526$	−6.47178	−	2.17215i	−0.282183	−	0.0947102i
$527$	14.6374	−	14.6374i	0.637613	−	0.637613i
$528$	−14.4998	−	8.10832i	−0.631023	−	0.352869i
$529$		−	22.2273i		−	0.966403i
$530$	19.9247	+	29.6649i	0.865475	+	1.28856i
$531$		−	25.6773i		−	1.11430i
$532$	0.130596	+	0.942001i	0.00566206	+	0.0408409i
$533$	2.61126	−	2.61126i	0.113106	−	0.113106i
$534$	7.83262	−	23.3368i	0.338951	−	1.00988i
$535$	1.54065	+	11.7960i	0.0666079	+	0.509985i
$536$	12.9804	+	19.0004i	0.560669	+	0.820694i
$537$	−23.6543	−	23.6543i	−1.02076	−	1.02076i
$538$	0.512945	+	1.03122i	0.0221146	+	0.0444590i
$539$	−7.02703			−0.302676
$540$	46.0537	+	26.2322i	1.98183	+	1.12885i
$541$	11.2665			0.484383			0.242192	−	0.970228i	$-0.422134\pi$
$541$	11.2665			0.484383			0.242192	+	0.970228i	$0.422134\pi$
$542$	−3.38943	−	6.81408i	−0.145589	−	0.292690i
$543$	−11.6666	−	11.6666i	−0.500660	−	0.500660i
$544$	−1.69368	+	35.0368i	−0.0726158	+	1.50219i
$545$	3.57669	+	2.75033i	0.153209	+	0.117811i
$546$	4.93612	−	14.7069i	0.211247	−	0.629396i
$547$	14.6898	−	14.6898i	0.628091	−	0.628091i	−0.319497	−	0.947587i	$-0.603514\pi$
$547$	14.6898	−	14.6898i	0.628091	−	0.628091i	0.947587	+	0.319497i	$0.103514\pi$
$548$	12.5450	−	1.73920i	0.535896	−	0.0742950i
$549$		−	80.5009i		−	3.43569i
$550$	7.04893	−	6.19891i	0.300567	−	0.264323i
$551$		−	0.345523i		−	0.0147198i
$552$	−7.64442	−	1.43897i	−0.325368	−	0.0612467i
$553$	−31.4363	+	31.4363i	−1.33681	+	1.33681i
$554$	−3.94580	−	1.32435i	−0.167641	−	0.0562660i
$555$	−51.4793	−	39.5856i	−2.18518	−	1.68031i
$556$	−22.5308	+	29.7835i	−0.955520	+	1.26310i
$557$	−22.2763	−	22.2763i	−0.943878	−	0.943878i	0.0546285	−	0.998507i	$-0.482603\pi$
$557$	−22.2763	−	22.2763i	−0.943878	−	0.943878i	−0.998507	+	0.0546285i	$0.982603\pi$
$558$	−28.6930	+	14.2723i	−1.21467	+	0.604196i
$559$	−6.33703			−0.268028
$560$	28.8186	−	12.3678i	1.21781	−	0.522635i
$561$	25.7539			1.08733
$562$	−39.6444	+	19.7197i	−1.67230	+	0.831827i
$563$	−8.60324	−	8.60324i	−0.362583	−	0.362583i	0.502180	−	0.864763i	$-0.332532\pi$
$563$	−8.60324	−	8.60324i	−0.362583	−	0.362583i	−0.864763	+	0.502180i	$0.832532\pi$
$564$	3.63728	−	4.80813i	0.153157	−	0.202459i
$565$	3.21263	+	24.5976i	0.135156	+	1.03483i
$566$	25.2634	+	8.47925i	1.06190	+	0.356409i
$567$	41.4374	−	41.4374i	1.74021	−	1.74021i
$568$	12.5388	+	2.36028i	0.526115	+	0.0990350i
$569$		−	11.6798i		−	0.489641i	−0.969568	−	0.244820i	$-0.921271\pi$
$569$		−	11.6798i		−	0.489641i	0.969568	−	0.244820i	$-0.0787290\pi$
$570$	−1.11382	+	0.748108i	−0.0466528	+	0.0313348i
$571$			28.7228i			1.20201i	0.799244	+	0.601006i	$0.205233\pi$
$571$			28.7228i			1.20201i	−0.799244	+	0.601006i	$0.794767\pi$
$572$	−2.62986	+	0.364596i	−0.109960	+	0.0152445i
$573$	20.0950	−	20.0950i	0.839481	−	0.839481i
$574$	5.82642	−	17.3595i	0.243190	−	0.724570i
$575$	2.20543	−	3.80186i	0.0919729	−	0.158549i
$576$	19.7447	−	50.5878i	0.822698	−	2.10783i
$577$	15.5910	+	15.5910i	0.649061	+	0.649061i	0.952766	−	0.303705i	$-0.0982236\pi$
$577$	15.5910	+	15.5910i	0.649061	+	0.649061i	−0.303705	+	0.952766i	$0.598224\pi$
$578$	−13.5109	−	27.1622i	−0.561981	−	1.12980i
$579$	31.6677			1.31607
$580$	−10.9883	+	3.01309i	−0.456263	+	0.125112i
$581$	−10.8594			−0.450524
$582$	2.19914	+	4.42112i	0.0911571	+	0.183261i
$583$	−10.6076	−	10.6076i	−0.439323	−	0.439323i
$584$	−7.89126	−	11.5510i	−0.326542	−	0.477985i
$585$	15.0507	−	1.96574i	0.622272	−	0.0812734i
$586$	6.34138	−	18.8937i	0.261960	−	0.780493i
$587$	−14.7415	+	14.7415i	−0.608445	+	0.608445i	−0.942540	−	0.334095i	$-0.891569\pi$
$587$	−14.7415	+	14.7415i	−0.608445	+	0.608445i	0.334095	+	0.942540i	$0.391569\pi$
$588$	−4.54839	−	32.8080i	−0.187572	−	1.35298i
$589$		−	0.452731i		−	0.0186545i
$590$	2.30548	−	11.7377i	0.0949152	−	0.483235i
$591$		−	16.1610i		−	0.664776i
$592$	−18.1226	+	32.4080i	−0.744834	+	1.33196i
$593$	19.9137	−	19.9137i	0.817758	−	0.817758i	−0.168025	−	0.985783i	$-0.553739\pi$
$593$	19.9137	−	19.9137i	0.817758	−	0.817758i	0.985783	+	0.168025i	$0.0537389\pi$
$594$	−21.0930	−	7.07954i	−0.865458	−	0.290477i
$595$	−29.6350	+	38.5391i	−1.21492	+	1.57995i
$596$	3.44923	+	2.60930i	0.141286	+	0.106881i
$597$	14.7386	+	14.7386i	0.603210	+	0.603210i
$598$	−1.11306	+	0.553656i	−0.0455166	+	0.0226407i
$599$	8.74117			0.357155			0.178577	−	0.983926i	$-0.442851\pi$
$599$	8.74117			0.357155			0.178577	+	0.983926i	$0.442851\pi$
$600$	33.5042	+	28.8978i	1.36780	+	1.17975i
$601$	18.7621			0.765321			0.382661	−	0.923889i	$-0.375008\pi$
$601$	18.7621			0.765321			0.382661	+	0.923889i	$0.375008\pi$
$602$	−28.1339	+	13.9943i	−1.14665	+	0.570364i
$603$	39.0501	+	39.0501i	1.59024	+	1.59024i
$604$	18.3330	+	13.8686i	0.745958	+	0.564307i
$605$	12.5915	−	16.3747i	0.511918	−	0.665727i
$606$	−66.8342	−	22.4318i	−2.71495	−	0.911231i
$607$	5.46201	−	5.46201i	0.221696	−	0.221696i	−0.587516	−	0.809212i	$-0.699894\pi$
$607$	5.46201	−	5.46201i	0.221696	−	0.221696i	0.809212	+	0.587516i	$0.199894\pi$
$608$	0.515649	+	0.568035i	0.0209123	+	0.0230368i
$609$			27.9474i			1.13249i
$610$	7.22790	−	36.7989i	0.292649	−	1.48994i
$611$		−	0.963522i		−	0.0389799i
$612$	11.5605	+	83.3870i	0.467306	+	3.37072i
$613$	−4.77650	+	4.77650i	−0.192921	+	0.192921i	−0.796957	−	0.604036i	$-0.793558\pi$
$613$	−4.77650	+	4.77650i	−0.192921	+	0.192921i	0.604036	+	0.796957i	$0.293558\pi$
$614$	2.38767	−	7.11392i	0.0963586	−	0.287094i
$615$	25.6168	−	3.34575i	1.03297	−	0.134914i
$616$	−10.8704	+	7.42627i	−0.437981	+	0.299213i
$617$	−21.1816	−	21.1816i	−0.852740	−	0.852740i	0.137730	−	0.990470i	$-0.456019\pi$
$617$	−21.1816	−	21.1816i	−0.852740	−	0.852740i	−0.990470	+	0.137730i	$0.956019\pi$
$618$	9.50191	+	19.1025i	0.382223	+	0.768417i
$619$	15.8026			0.635159			0.317579	−	0.948232i	$-0.397130\pi$
$619$	15.8026			0.635159			0.317579	+	0.948232i	$0.397130\pi$
$620$	−14.3977	+	3.94799i	−0.578226	+	0.158555i
$621$	−10.4179			−0.418054
$622$	7.17693	+	14.4284i	0.287769	+	0.578527i
$623$	−13.7936	−	13.7936i	−0.552630	−	0.552630i
$624$	−3.40447	−	12.0424i	−0.136288	−	0.482081i
$625$	−21.7018	+	12.4109i	−0.868073	+	0.496437i
$626$	8.68694	−	25.8822i	0.347200	−	1.03446i
$627$	0.398282	−	0.398282i	0.0159058	−	0.0159058i
$628$	−9.14774	+	1.26821i	−0.365035	+	0.0506072i
$629$		−	57.5615i		−	2.29513i
$630$	62.4783	−	41.9641i	2.48920	−	1.67189i
$631$		−	33.2454i		−	1.32348i	−0.749734	−	0.661739i	$-0.769819\pi$
$631$		−	33.2454i		−	1.32348i	0.749734	−	0.661739i	$-0.230181\pi$
$632$	−6.63441	+	35.2448i	−0.263903	+	1.40196i
$633$	21.8417	−	21.8417i	0.868130	−	0.868130i
$634$	25.0540	+	8.40899i	0.995023	+	0.333964i
$635$	5.90353	+	45.2005i	0.234274	+	1.79373i
$636$	42.6591	−	56.3911i	1.69154	−	2.23605i
$637$	−3.74300	−	3.74300i	−0.148303	−	0.148303i
$638$	4.28255	−	2.13021i	0.169548	−	0.0843359i
$639$	30.6209			1.21134
$640$	13.5679	−	21.3521i	0.536319	−	0.844016i
$641$	−3.03323			−0.119805			−0.0599026	−	0.998204i	$-0.519079\pi$
$641$	−3.03323			−0.119805			−0.0599026	+	0.998204i	$0.519079\pi$
$642$	21.0756	−	10.4833i	0.831786	−	0.413744i
$643$	−26.6548	−	26.6548i	−1.05116	−	1.05116i	−0.998619	−	0.0525441i	$-0.983267\pi$
$643$	−26.6548	−	26.6548i	−1.05116	−	1.05116i	−0.0525441	−	0.998619i	$-0.516733\pi$
$644$	−3.71891	+	4.91603i	−0.146546	+	0.193719i
$645$	−35.1434	−	27.0239i	−1.38377	−	1.06406i
$646$	−1.12749	−	0.378423i	−0.0443604	−	0.0148889i
$647$	12.5256	−	12.5256i	0.492433	−	0.492433i	−0.416639	−	0.909072i	$-0.636792\pi$
$647$	12.5256	−	12.5256i	0.492433	−	0.492433i	0.909072	+	0.416639i	$0.136792\pi$
$648$	8.74506	−	46.4574i	0.343538	−	1.82502i
$649$			5.02159i			0.197115i
$650$	7.05656	+	0.452767i	0.276781	+	0.0177590i
$651$			36.6189i			1.43521i
$652$	44.8178	−	6.21340i	1.75520	−	0.243336i
$653$	−30.1826	+	30.1826i	−1.18114	+	1.18114i	−0.201685	+	0.979450i	$0.564642\pi$
$653$	−30.1826	+	30.1826i	−1.18114	+	1.18114i	−0.979450	+	0.201685i	$0.935358\pi$
$654$	2.84068	−	8.46362i	0.111079	−	0.330954i
$655$	−37.2293	−	28.6279i	−1.45467	−	1.11858i
$656$	−4.01851	−	14.2144i	−0.156896	−	0.554978i
$657$	−23.7399	−	23.7399i	−0.926184	−	0.926184i
$658$	−2.12777	−	4.27765i	−0.0829493	−	0.166760i
$659$	11.6711			0.454642			0.227321	−	0.973820i	$-0.427003\pi$
$659$	11.6711			0.454642			0.227321	+	0.973820i	$0.427003\pi$
$660$	−16.1393	−	9.19294i	−0.628220	−	0.357835i
$661$	5.29802			0.206069			0.103035	−	0.994678i	$-0.467145\pi$
$661$	5.29802			0.206069			0.103035	+	0.994678i	$0.467145\pi$
$662$	9.01489	+	18.1234i	0.350374	+	0.704387i
$663$	13.7180	+	13.7180i	0.532762	+	0.532762i
$664$	−7.23339	+	4.94160i	−0.280710	+	0.191771i
$665$	0.137701	+	1.05431i	0.00533980	+	0.0408843i
$666$	−28.3546	+	84.4807i	−1.09872	+	3.27356i
$667$	1.58363	−	1.58363i	0.0613185	−	0.0613185i
$668$	4.19295	+	30.2442i	0.162230	+	1.17018i
$669$			14.4295i			0.557878i
$670$	14.3446	+	21.3569i	0.554179	+	0.825090i
$671$			15.7432i			0.607758i
$672$	−41.7080	−	45.9452i	−1.60892	−	1.77237i
$673$	2.21557	−	2.21557i	0.0854038	−	0.0854038i	−0.663114	−	0.748518i	$-0.730766\pi$
$673$	2.21557	−	2.21557i	0.0854038	−	0.0854038i	0.748518	+	0.663114i	$0.230766\pi$
$674$	30.6258	+	10.2791i	1.17966	+	0.395935i
$675$	51.2567	+	29.7336i	1.97287	+	1.14445i
$676$	−1.59502	−	1.20661i	−0.0613469	−	0.0464081i
$677$	13.6763	+	13.6763i	0.525623	+	0.525623i	0.919264	−	0.393641i	$-0.128785\pi$
$677$	13.6763	+	13.6763i	0.525623	+	0.525623i	−0.393641	+	0.919264i	$0.628785\pi$
$678$	43.9477	−	21.8603i	1.68780	−	0.839540i
$679$	3.91302			0.150168
$680$	−2.20245	+	39.1562i	−0.0844601	+	1.50157i
$681$	−28.7610			−1.10212
$682$	5.61134	−	2.79117i	0.214869	−	0.106879i
$683$	19.4605	+	19.4605i	0.744634	+	0.744634i	0.973466	−	0.228832i	$-0.0734905\pi$
$683$	19.4605	+	19.4605i	0.744634	+	0.744634i	−0.228832	+	0.973466i	$0.573491\pi$
$684$	1.46836	+	1.11079i	0.0561441	+	0.0424722i
$685$	14.0406	−	1.83382i	0.536466	−	0.0700665i
$686$	8.02238	+	2.69258i	0.306296	+	0.102803i
$687$	−29.5033	+	29.5033i	−1.12562	+	1.12562i
$688$	−12.3717	+	22.1239i	−0.471668	+	0.843466i
$689$		−	11.3005i		−	0.430513i
$690$	−8.53377	−	1.67617i	−0.324875	−	0.0638107i
$691$			44.9970i			1.71177i	0.517169	+	0.855884i	$0.326986\pi$
$691$			44.9970i			1.71177i	−0.517169	+	0.855884i	$0.673014\pi$
$692$	3.39921	+	24.5188i	0.129219	+	0.932066i
$693$	−22.3411	+	22.3411i	−0.848668	+	0.848668i
$694$	−13.8082	+	41.1407i	−0.524152	+	1.56168i
$695$	−25.4520	+	33.0993i	−0.965451	+	1.25553i
$696$	12.7175	+	18.6156i	0.482057	+	0.705624i
$697$	16.1922	+	16.1922i	0.613323	+	0.613323i
$698$	−10.3483	−	20.8041i	−0.391688	−	0.787446i
$699$	−3.64167			−0.137741
$700$	32.3282	−	13.5731i	1.22189	−	0.513015i
$701$	−30.8529			−1.16530			−0.582648	−	0.812725i	$-0.697983\pi$
$701$	−30.8529			−1.16530			−0.582648	+	0.812725i	$0.697983\pi$
$702$	−7.46439	−	15.0063i	−0.281725	−	0.566377i
$703$	−0.890185	−	0.890185i	−0.0335739	−	0.0335739i
$704$	−3.86138	+	9.89321i	−0.145531	+	0.372864i
$705$	4.10887	−	5.34342i	0.154749	−	0.201245i
$706$	6.69502	−	19.9474i	0.251970	−	0.750729i
$707$	−39.5035	+	39.5035i	−1.48568	+	1.48568i
$708$	−23.4449	+	3.25033i	−0.881113	+	0.122155i
$709$		−	29.0128i		−	1.08960i	−0.838567	−	0.544799i	$-0.816606\pi$
$709$		−	29.0128i		−	1.08960i	0.838567	−	0.544799i	$-0.183394\pi$
$710$	13.9975	+	2.74934i	0.525318	+	0.103181i
$711$			86.0710i			3.22792i
$712$	−15.4647	−	2.91105i	−0.579564	−	0.109096i
$713$	2.07500	−	2.07500i	0.0777094	−	0.0777094i
$714$	91.1962	+	30.6085i	3.41293	+	1.14550i
$715$	−2.94340	+	0.384430i	−0.110077	+	0.0143769i
$716$	−12.9016	+	17.0547i	−0.482156	+	0.637363i
$717$	−18.0699	−	18.0699i	−0.674834	−	0.674834i
$718$	7.93900	−	3.94899i	0.296281	−	0.147375i
$719$	−11.0483			−0.412031			−0.206015	−	0.978549i	$-0.566050\pi$
$719$	−11.0483			−0.412031			−0.206015	+	0.978549i	$0.566050\pi$
$720$	22.5206	−	56.3830i	0.839295	−	2.10127i
$721$	16.9071			0.629655
$722$	24.0348	−	11.9553i	0.894484	−	0.444931i
$723$	−38.3430	−	38.3430i	−1.42599	−	1.42599i
$724$	−6.36322	+	8.41155i	−0.236487	+	0.312613i
$725$	−12.3114	+	3.27175i	−0.457236	+	0.121510i
$726$	−38.7480	−	13.0051i	−1.43807	−	0.482666i
$727$	25.4507	−	25.4507i	0.943914	−	0.943914i	−0.0545947	−	0.998509i	$-0.517387\pi$
$727$	25.4507	−	25.4507i	0.943914	−	0.943914i	0.998509	+	0.0545947i	$0.0173867\pi$
$728$	−9.74585	−	1.83454i	−0.361205	−	0.0679927i
$729$		−	2.21979i		−	0.0822146i
$730$	−8.72057	−	12.9836i	−0.322763	−	0.480546i
$731$		−	39.2955i		−	1.45340i
$732$	−73.5020	+	10.1901i	−2.71671	+	0.376636i
$733$	−28.6191	+	28.6191i	−1.05707	+	1.05707i	−0.0587996	+	0.998270i	$0.518727\pi$
$733$	−28.6191	+	28.6191i	−1.05707	+	1.05707i	−0.998270	+	0.0587996i	$0.981273\pi$
$734$	6.62279	−	19.7322i	0.244452	−	0.728328i
$735$	−4.79583	−	36.7194i	−0.176897	−	1.35441i
$736$	−0.240097	+	4.96684i	−0.00885008	+	0.183080i
$737$	−7.63684	−	7.63684i	−0.281306	−	0.281306i
$738$	−15.7884	−	31.7409i	−0.581180	−	1.16840i
$739$	−15.7301			−0.578643			−0.289321	−	0.957232i	$-0.593430\pi$
$739$	−15.7301			−0.578643			−0.289321	+	0.957232i	$0.593430\pi$
$740$	−20.5468	+	36.0723i	−0.755315	+	1.32604i
$741$	0.424295			0.0155869
$742$	−24.9551	−	50.1695i	−0.916132	−	1.84178i
$743$	−10.0819	−	10.0819i	−0.369868	−	0.369868i	0.497561	−	0.867429i	$-0.334229\pi$
$743$	−10.0819	−	10.0819i	−0.369868	−	0.369868i	−0.867429	+	0.497561i	$0.834229\pi$
$744$	16.6635	+	24.3917i	0.610915	+	0.894243i
$745$	3.83323	+	2.94760i	0.140439	+	0.107992i
$746$	3.14903	−	9.38232i	0.115294	−	0.343511i
$747$	−14.8662	+	14.8662i	−0.543927	+	0.543927i
$748$	−2.26083	−	16.3076i	−0.0826642	−	0.596265i
$749$		−	18.6534i		−	0.681581i
$750$	37.2028	+	32.6031i	1.35846	+	1.19050i
$751$			6.72265i			0.245313i	0.992449	+	0.122656i	$0.0391413\pi$
$751$			6.72265i			0.245313i	−0.992449	+	0.122656i	$0.960859\pi$
$752$	−3.36386	−	1.88108i	−0.122667	−	0.0685958i
$753$	3.52470	−	3.52470i	0.128447	−	0.128447i
$754$	3.41580	+	1.14646i	0.124396	+	0.0417516i
$755$	20.3740	+	15.6668i	0.741485	+	0.570172i
$756$	−66.2778	−	50.1383i	−2.41050	−	1.82351i
$757$	−9.77504	−	9.77504i	−0.355280	−	0.355280i	0.506790	−	0.862070i	$-0.330832\pi$
$757$	−9.77504	−	9.77504i	−0.355280	−	0.355280i	−0.862070	+	0.506790i	$0.830832\pi$
$758$	−29.2437	+	14.5463i	−1.06218	+	0.528345i
$759$	3.65088			0.132519
$760$	0.571487	+	0.639609i	0.0207300	+	0.0232010i
$761$	33.6933			1.22138			0.610690	−	0.791870i	$-0.290892\pi$
$761$	33.6933			1.22138			0.610690	+	0.791870i	$0.290892\pi$
$762$	80.7584	−	40.1705i	2.92557	−	1.45522i
$763$	−5.00257	−	5.00257i	−0.181105	−	0.181105i
$764$	−14.4884	−	10.9603i	−0.524172	−	0.396529i
$765$	12.1894	+	93.3286i	0.440709	+	3.37430i
$766$	−46.3681	−	15.5627i	−1.67535	−	0.562303i
$767$	−2.67479	+	2.67479i	−0.0965809	+	0.0965809i
$768$	−48.6890	−	11.6245i	−1.75691	−	0.419464i
$769$		−	27.1271i		−	0.978229i	−0.872220	−	0.489114i	$-0.837320\pi$
$769$		−	27.1271i		−	0.978229i	0.872220	−	0.489114i	$-0.162680\pi$
$770$	−12.2186	+	8.20672i	−0.440327	+	0.295750i
$771$			43.1431i			1.55376i
$772$	−2.77999	−	20.0523i	−0.100054	−	0.721699i
$773$

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)

\(f(q)\)	\(=\)	\(q+(-1.26622 + 0.629837i) q^{2} +(2.21225 + 2.21225i) q^{3} +(1.20661 - 1.59502i) q^{4} +(1.36305 - 1.77259i) q^{5} +(-4.19454 - 1.40783i) q^{6} +(-2.47925 + 2.47925i) q^{7} +(-0.523229 + 2.77961i) q^{8} +6.78807i q^{9} +O(q^{10})\)	\(q+(-1.26622 + 0.629837i) q^{2} +(2.21225 + 2.21225i) q^{3} +(1.20661 - 1.59502i) q^{4} +(1.36305 - 1.77259i) q^{5} +(-4.19454 - 1.40783i) q^{6} +(-2.47925 + 2.47925i) q^{7} +(-0.523229 + 2.77961i) q^{8} +6.78807i q^{9} +(-0.609477 + 3.10299i) q^{10} -1.32751i q^{11} +(6.19790 - 0.859257i) q^{12} +(0.707107 - 0.707107i) q^{13} +(1.57775 - 4.70080i) q^{14} +(6.93682 - 0.906002i) q^{15} +(-1.08818 - 3.84914i) q^{16} +(4.38472 + 4.38472i) q^{17} +(-4.27537 - 8.59516i) q^{18} +0.135619 q^{19} +(-1.18265 - 4.31293i) q^{20} -10.9694 q^{21} +(0.836114 + 1.68091i) q^{22} +(0.621580 + 0.621580i) q^{23} +(-7.30669 + 4.99167i) q^{24} +(-1.28417 - 4.83228i) q^{25} +(-0.449989 + 1.34071i) q^{26} +(-8.38013 + 8.38013i) q^{27} +(0.962965 + 6.94596i) q^{28} -2.54775i q^{29} +(-8.21289 + 5.51626i) q^{30} -3.33827i q^{31} +(3.80220 + 4.18847i) q^{32} +(2.93678 - 2.93678i) q^{33} +(-8.31366 - 2.79035i) q^{34} +(1.01535 + 7.77406i) q^{35} +(10.8271 + 8.19056i) q^{36} +(-6.56388 - 6.56388i) q^{37} +(-0.171723 + 0.0854176i) q^{38} +3.12859 q^{39} +(4.21393 + 4.71623i) q^{40} +3.69287 q^{41} +(13.8897 - 6.90896i) q^{42} +(-4.48096 - 4.48096i) q^{43} +(-2.11740 - 1.60179i) q^{44} +(12.0325 + 9.25250i) q^{45} +(-1.17855 - 0.395561i) q^{46} +(0.681313 - 0.681313i) q^{47} +(6.10792 - 10.9226i) q^{48} -5.29340i q^{49} +(4.66958 + 5.30989i) q^{50} +19.4001i q^{51} +(-0.274647 - 1.98105i) q^{52} +(7.99063 - 7.99063i) q^{53} +(5.33295 - 15.8892i) q^{54} +(-2.35313 - 1.80947i) q^{55} +(-5.59414 - 8.18858i) q^{56} +(0.300022 + 0.300022i) q^{57} +(1.60467 + 3.22601i) q^{58} -3.78272 q^{59} +(6.92495 - 12.1576i) q^{60} -11.8592 q^{61} +(2.10256 + 4.22697i) q^{62} +(-16.8293 - 16.8293i) q^{63} +(-7.45246 - 2.90874i) q^{64} +(-0.289588 - 2.21724i) q^{65} +(-1.86891 + 5.56828i) q^{66} +(5.75276 - 5.75276i) q^{67} +(12.2844 - 1.70306i) q^{68} +2.75018i q^{69} +(-6.18205 - 9.20415i) q^{70} -4.51098i q^{71} +(-18.8682 - 3.55171i) q^{72} +(-3.49731 + 3.49731i) q^{73} +(12.4455 + 4.17712i) q^{74} +(7.84929 - 13.5311i) q^{75} +(0.163639 - 0.216315i) q^{76} +(3.29123 + 3.29123i) q^{77} +(-3.96147 + 1.97050i) q^{78} +12.6798 q^{79} +(-8.30620 - 3.31768i) q^{80} -16.7136 q^{81} +(-4.67598 + 2.32591i) q^{82} +(2.19005 + 2.19005i) q^{83} +(-13.2358 + 17.4965i) q^{84} +(13.7489 - 1.79571i) q^{85} +(8.49614 + 2.85159i) q^{86} +(5.63626 - 5.63626i) q^{87} +(3.68996 + 0.694591i) q^{88} +5.56362i q^{89} +(-21.0633 - 4.13717i) q^{90} +3.50619i q^{91} +(1.74144 - 0.241428i) q^{92} +(7.38507 - 7.38507i) q^{93} +(-0.433574 + 1.29181i) q^{94} +(0.184856 - 0.240397i) q^{95} +(-0.854520 + 17.6773i) q^{96} +(-0.789152 - 0.789152i) q^{97} +(3.33398 + 6.70259i) q^{98} +9.01122 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

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