LMFDB - Embedded newform 260.2.o.a.183.31

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			183.31
Character	$\chi$	$=$	260.183
Dual form			260.2.o.a.27.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18685 + 0.769019i) q^{2} +(0.808783 - 0.808783i) q^{3} +(0.817219 + 1.82542i) q^{4} +(0.885949 - 2.05307i) q^{5} +(1.58187 - 0.337933i) q^{6} +(-0.771151 - 0.771151i) q^{7} +(-0.433867 + 2.79495i) q^{8} +1.69174i q^{9} +O(q^{10})$	\(q+(1.18685 + 0.769019i) q^{2} +(0.808783 - 0.808783i) q^{3} +(0.817219 + 1.82542i) q^{4} +(0.885949 - 2.05307i) q^{5} +(1.58187 - 0.337933i) q^{6} +(-0.771151 - 0.771151i) q^{7} +(-0.433867 + 2.79495i) q^{8} +1.69174i q^{9} +(2.63034 - 1.75537i) q^{10} -0.875946i q^{11} +(2.13732 + 0.815415i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.322210 - 1.50827i) q^{14} +(-0.943948 - 2.37703i) q^{15} +(-2.66431 + 2.98353i) q^{16} +(4.91209 - 4.91209i) q^{17} +(-1.30098 + 2.00784i) q^{18} -6.89579 q^{19} +(4.47173 - 0.0605793i) q^{20} -1.24739 q^{21} +(0.673619 - 1.03962i) q^{22} +(-6.03681 + 6.03681i) q^{23} +(1.90961 + 2.61142i) q^{24} +(-3.43019 - 3.63783i) q^{25} +(0.295450 + 1.38301i) q^{26} +(3.79460 + 3.79460i) q^{27} +(0.777475 - 2.03787i) q^{28} +7.85222i q^{29} +(0.707658 - 3.54709i) q^{30} -5.45839i q^{31} +(-5.45652 + 1.49210i) q^{32} +(-0.708451 - 0.708451i) q^{33} +(9.60741 - 2.05242i) q^{34} +(-2.26643 + 0.900026i) q^{35} +(-3.08813 + 1.38252i) q^{36} +(-2.21989 + 2.21989i) q^{37} +(-8.18426 - 5.30299i) q^{38} +1.14379 q^{39} +(5.35385 + 3.36694i) q^{40} -1.36683 q^{41} +(-1.48046 - 0.959266i) q^{42} +(4.34174 - 4.34174i) q^{43} +(1.59897 - 0.715840i) q^{44} +(3.47326 + 1.49879i) q^{45} +(-11.8072 + 2.52236i) q^{46} +(-3.81120 - 3.81120i) q^{47} +(0.258185 + 4.56788i) q^{48} -5.81065i q^{49} +(-1.27355 - 6.95543i) q^{50} -7.94564i q^{51} +(-0.712905 + 1.86863i) q^{52} +(-2.18578 - 2.18578i) q^{53} +(1.58550 + 7.42174i) q^{54} +(-1.79838 - 0.776043i) q^{55} +(2.48991 - 1.82075i) q^{56} +(-5.57720 + 5.57720i) q^{57} +(-6.03851 + 9.31940i) q^{58} +0.749270 q^{59} +(3.56766 - 3.66565i) q^{60} -4.79700 q^{61} +(4.19761 - 6.47828i) q^{62} +(1.30459 - 1.30459i) q^{63} +(-7.62352 - 2.42528i) q^{64} +(2.07820 - 0.825279i) q^{65} +(-0.296011 - 1.38564i) q^{66} +(10.0709 + 10.0709i) q^{67} +(12.9809 + 4.95237i) q^{68} +9.76494i q^{69} +(-3.38204 - 0.674731i) q^{70} -5.01480i q^{71} +(-4.72833 - 0.733990i) q^{72} +(6.85076 + 6.85076i) q^{73} +(-4.34181 + 0.927534i) q^{74} +(-5.71650 - 0.167936i) q^{75} +(-5.63537 - 12.5877i) q^{76} +(-0.675487 + 0.675487i) q^{77} +(1.35751 + 0.879598i) q^{78} +1.62958 q^{79} +(3.76496 + 8.11327i) q^{80} +1.06280 q^{81} +(-1.62222 - 1.05112i) q^{82} +(2.66989 - 2.66989i) q^{83} +(-1.01939 - 2.27701i) q^{84} +(-5.73301 - 14.4367i) q^{85} +(8.49186 - 1.81410i) q^{86} +(6.35074 + 6.35074i) q^{87} +(2.44823 + 0.380044i) q^{88} -3.68804i q^{89} +(2.96963 + 4.44984i) q^{90} -1.09057i q^{91} +(-15.9531 - 6.08631i) q^{92} +(-4.41465 - 4.41465i) q^{93} +(-1.59243 - 7.45421i) q^{94} +(-6.10932 + 14.1575i) q^{95} +(-3.20636 + 5.61993i) q^{96} +(6.65520 - 6.65520i) q^{97} +(4.46850 - 6.89636i) q^{98} +1.48187 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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.18685	+	0.769019i	0.839229	+	0.543779i
$2$	1.18685	+	0.769019i	0.839229	+	0.543779i
$3$	0.808783	−	0.808783i	0.466951	−	0.466951i	−0.433974	−	0.900925i	$-0.642889\pi$
$3$	0.808783	−	0.808783i	0.466951	−	0.466951i	0.900925	+	0.433974i	$0.142889\pi$
$4$	0.817219	+	1.82542i	0.408609	+	0.912709i
$5$	0.885949	−	2.05307i	0.396208	−	0.918161i
$5$	0.885949	−	2.05307i	0.396208	−	0.918161i
$6$	1.58187	−	0.337933i	0.645797	−	0.137961i
$7$	−0.771151	−	0.771151i	−0.291468	−	0.291468i	0.546192	−	0.837660i	$-0.316077\pi$
$7$	−0.771151	−	0.771151i	−0.291468	−	0.291468i	−0.837660	+	0.546192i	$0.816077\pi$
$8$	−0.433867	+	2.79495i	−0.153395	+	0.988165i
$9$			1.69174i			0.563913i
$10$	2.63034	−	1.75537i	0.831786	−	0.555097i
$11$		−	0.875946i		−	0.264108i	−0.991243	−	0.132054i	$-0.957843\pi$
$11$		−	0.875946i		−	0.264108i	0.991243	−	0.132054i	$-0.0421572\pi$
$12$	2.13732	+	0.815415i	0.616991	+	0.235390i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	−0.322210	−	1.50827i	−0.0861141	−	0.403102i
$15$	−0.943948	−	2.37703i	−0.243726	−	0.613746i
$16$	−2.66431	+	2.98353i	−0.666077	+	0.745883i
$17$	4.91209	−	4.91209i	1.19136	−	1.19136i	0.214671	−	0.976686i	$-0.431132\pi$
$17$	4.91209	−	4.91209i	1.19136	−	1.19136i	0.976686	−	0.214671i	$-0.0688681\pi$
$18$	−1.30098	+	2.00784i	−0.306644	+	0.473252i
$19$	−6.89579			−1.58200			−0.791001	−	0.611815i	$-0.790440\pi$
$19$	−6.89579			−1.58200			−0.791001	+	0.611815i	$0.790440\pi$
$20$	4.47173	−	0.0605793i	0.999908	−	0.0135459i
$21$	−1.24739			−0.272202
$22$	0.673619	−	1.03962i	0.143616	−	0.221647i
$23$	−6.03681	+	6.03681i	−1.25876	+	1.25876i	−0.307077	+	0.951685i	$0.599351\pi$
$23$	−6.03681	+	6.03681i	−1.25876	+	1.25876i	−0.951685	+	0.307077i	$0.900649\pi$
$24$	1.90961	+	2.61142i	0.389797	+	0.533053i
$25$	−3.43019	−	3.63783i	−0.686038	−	0.727566i
$26$	0.295450	+	1.38301i	0.0579425	+	0.271230i
$27$	3.79460	+	3.79460i	0.730271	+	0.730271i
$28$	0.777475	−	2.03787i	0.146929	−	0.385122i
$29$			7.85222i			1.45812i	0.684449	+	0.729060i	$0.260043\pi$
$29$			7.85222i			1.45812i	−0.684449	+	0.729060i	$0.739957\pi$
$30$	0.707658	−	3.54709i	0.129200	−	0.647607i
$31$		−	5.45839i		−	0.980356i	−0.871622	−	0.490178i	$-0.836932\pi$
$31$		−	5.45839i		−	0.980356i	0.871622	−	0.490178i	$-0.163068\pi$
$32$	−5.45652	+	1.49210i	−0.964586	+	0.263768i
$33$	−0.708451	−	0.708451i	−0.123325	−	0.123325i
$34$	9.60741	−	2.05242i	1.64766	−	0.351987i
$35$	−2.26643	+	0.900026i	−0.383096	+	0.152132i
$36$	−3.08813	+	1.38252i	−0.514689	+	0.230420i
$37$	−2.21989	+	2.21989i	−0.364947	+	0.364947i	−0.865631	−	0.500683i	$-0.833082\pi$
$37$	−2.21989	+	2.21989i	−0.364947	+	0.364947i	0.500683	+	0.865631i	$0.333082\pi$
$38$	−8.18426	−	5.30299i	−1.32766	−	0.860259i
$39$	1.14379			0.183153
$40$	5.35385	+	3.36694i	0.846518	+	0.532361i
$41$	−1.36683			−0.213463			−0.106732	−	0.994288i	$-0.534039\pi$
$41$	−1.36683			−0.213463			−0.106732	+	0.994288i	$0.534039\pi$
$42$	−1.48046	−	0.959266i	−0.228440	−	0.148018i
$43$	4.34174	−	4.34174i	0.662109	−	0.662109i	−0.293768	−	0.955877i	$-0.594909\pi$
$43$	4.34174	−	4.34174i	0.662109	−	0.662109i	0.955877	+	0.293768i	$0.0949093\pi$
$44$	1.59897	−	0.715840i	0.241054	−	0.107917i
$45$	3.47326	+	1.49879i	0.517763	+	0.223427i
$46$	−11.8072	+	2.52236i	−1.74088	+	0.371901i
$47$	−3.81120	−	3.81120i	−0.555921	−	0.555921i	0.372222	−	0.928144i	$-0.378596\pi$
$47$	−3.81120	−	3.81120i	−0.555921	−	0.555921i	−0.928144	+	0.372222i	$0.878596\pi$
$48$	0.258185	+	4.56788i	0.0372657	+	0.659317i
$49$		−	5.81065i		−	0.830093i
$50$	−1.27355	−	6.95543i	−0.180108	−	0.983647i
$51$		−	7.94564i		−	1.11261i
$52$	−0.712905	+	1.86863i	−0.0988621	+	0.259132i
$53$	−2.18578	−	2.18578i	−0.300240	−	0.300240i	0.540867	−	0.841108i	$-0.318096\pi$
$53$	−2.18578	−	2.18578i	−0.300240	−	0.300240i	−0.841108	+	0.540867i	$0.818096\pi$
$54$	1.58550	+	7.42174i	0.215759	+	1.00997i
$55$	−1.79838	−	0.776043i	−0.242493	−	0.104642i
$56$	2.48991	−	1.82075i	0.332728	−	0.243308i
$57$	−5.57720	+	5.57720i	−0.738718	+	0.738718i
$58$	−6.03851	+	9.31940i	−0.792895	+	1.22370i
$59$	0.749270			0.0975467			0.0487733	−	0.998810i	$-0.484469\pi$
$59$	0.749270			0.0975467			0.0487733	+	0.998810i	$0.484469\pi$
$60$	3.56766	−	3.66565i	0.460583	−	0.473234i
$61$	−4.79700			−0.614193			−0.307097	−	0.951678i	$-0.599357\pi$
$61$	−4.79700			−0.614193			−0.307097	+	0.951678i	$0.599357\pi$
$62$	4.19761	−	6.47828i	0.533096	−	0.822742i
$63$	1.30459	−	1.30459i	0.164362	−	0.164362i
$64$	−7.62352	−	2.42528i	−0.952940	−	0.303160i
$65$	2.07820	−	0.825279i	0.257769	−	0.102363i
$66$	−0.296011	−	1.38564i	−0.0364365	−	0.170560i
$67$	10.0709	+	10.0709i	1.23035	+	1.23035i	0.963828	+	0.266526i	$0.0858757\pi$
$67$	10.0709	+	10.0709i	1.23035	+	1.23035i	0.266526	+	0.963828i	$0.414124\pi$
$68$	12.9809	+	4.95237i	1.57416	+	0.600563i
$69$			9.76494i			1.17556i
$70$	−3.38204	−	0.674731i	−0.404232	−	0.0806458i
$71$		−	5.01480i		−	0.595148i	−0.954699	−	0.297574i	$-0.903823\pi$
$71$		−	5.01480i		−	0.595148i	0.954699	−	0.297574i	$-0.0961775\pi$
$72$	−4.72833	−	0.733990i	−0.557239	−	0.0865016i
$73$	6.85076	+	6.85076i	0.801821	+	0.801821i	0.983380	−	0.181559i	$-0.0581144\pi$
$73$	6.85076	+	6.85076i	0.801821	+	0.801821i	−0.181559	+	0.983380i	$0.558114\pi$
$74$	−4.34181	+	0.927534i	−0.504725	+	0.107824i
$75$	−5.71650	−	0.167936i	−0.660084	−	0.0193916i
$76$	−5.63537	−	12.5877i	−0.646421	−	1.44391i
$77$	−0.675487	+	0.675487i	−0.0769789	+	0.0769789i
$78$	1.35751	+	0.879598i	0.153708	+	0.0995949i
$79$	1.62958			0.183342			0.0916710	−	0.995789i	$-0.470779\pi$
$79$	1.62958			0.183342			0.0916710	+	0.995789i	$0.470779\pi$
$80$	3.76496	+	8.11327i	0.420935	+	0.907091i
$81$	1.06280			0.118089
$82$	−1.62222	−	1.05112i	−0.179144	−	0.116077i
$83$	2.66989	−	2.66989i	0.293058	−	0.293058i	−0.545229	−	0.838287i	$-0.683557\pi$
$83$	2.66989	−	2.66989i	0.293058	−	0.293058i	0.838287	+	0.545229i	$0.183557\pi$
$84$	−1.01939	−	2.27701i	−0.111224	−	0.248442i
$85$	−5.73301	−	14.4367i	−0.621832	−	1.56588i
$86$	8.49186	−	1.81410i	0.915701	−	0.195620i
$87$	6.35074	+	6.35074i	0.680871	+	0.680871i
$88$	2.44823	+	0.380044i	0.260982	+	0.0405129i
$89$		−	3.68804i		−	0.390931i	−0.980711	−	0.195466i	$-0.937378\pi$
$89$		−	3.68804i		−	0.390931i	0.980711	−	0.195466i	$-0.0626218\pi$
$90$	2.96963	+	4.44984i	0.313026	+	0.469055i
$91$		−	1.09057i		−	0.114323i
$92$	−15.9531	−	6.08631i	−1.66323	−	0.634542i
$93$	−4.41465	−	4.41465i	−0.457778	−	0.457778i
$94$	−1.59243	−	7.45421i	−0.164247	−	0.768843i
$95$	−6.10932	+	14.1575i	−0.626803	+	1.45253i
$96$	−3.20636	+	5.61993i	−0.327248	+	0.573582i
$97$	6.65520	−	6.65520i	0.675733	−	0.675733i	−0.283299	−	0.959032i	$-0.591429\pi$
$97$	6.65520	−	6.65520i	0.675733	−	0.675733i	0.959032	+	0.283299i	$0.0914288\pi$
$98$	4.46850	−	6.89636i	0.451387	−	0.696638i
$99$	1.48187			0.148934
$100$	3.83735	−	9.23443i	0.383735	−	0.923443i
$101$	−6.22911			−0.619820			−0.309910	−	0.950766i	$-0.600299\pi$
$101$	−6.22911			−0.619820			−0.309910	+	0.950766i	$0.600299\pi$
$102$	6.11035	−	9.43027i	0.605015	−	0.933736i
$103$	9.05772	−	9.05772i	0.892483	−	0.892483i	−0.102273	−	0.994756i	$-0.532612\pi$
$103$	9.05772	−	9.05772i	0.892483	−	0.892483i	0.994756	+	0.102273i	$0.0326115\pi$
$104$	−2.28312	+	1.66954i	−0.223878	+	0.163712i
$105$	−1.10512	+	2.56098i	−0.107849	+	0.249926i
$106$	−0.913284	−	4.27510i	−0.0887060	−	0.415235i
$107$	6.98064	+	6.98064i	0.674844	+	0.674844i	0.958829	−	0.283985i	$-0.0916565\pi$
$107$	6.98064	+	6.98064i	0.674844	+	0.674844i	−0.283985	+	0.958829i	$0.591656\pi$
$108$	−3.82572	+	10.0278i	−0.368130	+	0.964921i
$109$		−	5.87444i		−	0.562670i	−0.959610	−	0.281335i	$-0.909223\pi$
$109$		−	5.87444i		−	0.562670i	0.959610	−	0.281335i	$-0.0907772\pi$
$110$	−1.53761	−	2.30403i	−0.146605	−	0.219681i
$111$			3.59082i			0.340825i
$112$	4.35534	−	0.246171i	0.411541	−	0.0232610i
$113$	8.29477	+	8.29477i	0.780307	+	0.780307i	0.979882	−	0.199576i	$-0.0639564\pi$
$113$	8.29477	+	8.29477i	0.780307	+	0.780307i	−0.199576	+	0.979882i	$0.563956\pi$
$114$	−10.9083	+	2.33032i	−1.02165	+	0.218254i
$115$	7.04568	+	17.7423i	0.657013	+	1.65448i
$116$	−14.3336	+	6.41698i	−1.33084	+	0.595802i
$117$	−1.19624	+	1.19624i	−0.110592	+	0.110592i
$118$	0.889270	+	0.576203i	0.0818640	+	0.0530438i
$119$	−7.57593			−0.694485
$120$	7.05323	−	1.60697i	0.643869	−	0.146696i
$121$	10.2327			0.930247
$122$	−5.69332	−	3.68899i	−0.515449	−	0.333985i
$123$	−1.10547	+	1.10547i	−0.0996768	+	0.0996768i
$124$	9.96384	−	4.46070i	0.894780	−	0.400582i
$125$	−10.5077	+	3.81949i	−0.939836	+	0.341625i
$126$	2.55160	−	0.545094i	0.227314	−	0.0485609i
$127$	8.46315	+	8.46315i	0.750983	+	0.750983i	0.974663	−	0.223680i	$-0.0718070\pi$
$127$	8.46315	+	8.46315i	0.750983	+	0.750983i	−0.223680	+	0.974663i	$0.571807\pi$
$128$	−7.18288	−	8.74107i	−0.634883	−	0.772609i
$129$		−	7.02305i		−	0.618345i
$130$	3.10116	+	0.618695i	0.271990	+	0.0542631i
$131$			15.5022i			1.35443i	0.735785	+	0.677215i	$0.236813\pi$
$131$			15.5022i			1.35443i	−0.735785	+	0.677215i	$0.763187\pi$
$132$	0.714260	−	1.87218i	0.0621683	−	0.162952i
$133$	5.31770	+	5.31770i	0.461103	+	0.461103i
$134$	4.20791	+	19.6973i	0.363508	+	1.70159i
$135$	11.1524	−	4.42876i	0.959846	−	0.381167i
$136$	11.5979	+	15.8603i	0.994509	+	1.36001i
$137$	−2.57473	+	2.57473i	−0.219974	+	0.219974i	−0.808487	−	0.588513i	$-0.799713\pi$
$137$	−2.57473	+	2.57473i	−0.219974	+	0.219974i	0.588513	+	0.808487i	$0.299713\pi$
$138$	−7.50943	+	11.5895i	−0.639245	+	0.986564i
$139$	−4.22654			−0.358491			−0.179245	−	0.983804i	$-0.557366\pi$
$139$	−4.22654			−0.358491			−0.179245	+	0.983804i	$0.557366\pi$
$140$	−3.49509	−	3.40166i	−0.295389	−	0.287493i
$141$	−6.16488			−0.519176
$142$	3.85648	−	5.95181i	0.323629	−	0.499465i
$143$	0.619387	−	0.619387i	0.0517958	−	0.0517958i
$144$	−5.04736	−	4.50731i	−0.420613	−	0.375609i
$145$	16.1212	+	6.95667i	1.33879	+	0.577720i
$146$	2.86245	+	13.3992i	0.236898	+	1.10892i
$147$	−4.69956	−	4.69956i	−0.387613	−	0.387613i
$148$	−5.86636	−	2.23809i	−0.482212	−	0.183970i
$149$		−	1.00491i		−	0.0823258i	−0.999152	−	0.0411629i	$-0.986894\pi$
$149$		−	1.00491i		−	0.0823258i	0.999152	−	0.0411629i	$-0.0131063\pi$
$150$	−6.65547	−	4.59541i	−0.543417	−	0.375214i
$151$		−	16.2847i		−	1.32523i	−0.748960	−	0.662615i	$-0.769446\pi$
$151$		−	16.2847i		−	1.32523i	0.748960	−	0.662615i	$-0.230554\pi$
$152$	2.99186	−	19.2734i	0.242672	−	1.56328i
$153$	8.30998	+	8.30998i	0.671822	+	0.671822i
$154$	−1.32116	+	0.282238i	−0.106462	+	0.0227434i
$155$	−11.2065	−	4.83585i	−0.900124	−	0.388425i
$156$	0.934729	+	2.08790i	0.0748382	+	0.167166i
$157$	−0.171561	+	0.171561i	−0.0136920	+	0.0136920i	−0.713920	−	0.700228i	$-0.753082\pi$
$157$	−0.171561	+	0.171561i	−0.0136920	+	0.0136920i	0.700228	+	0.713920i	$0.253082\pi$
$158$	1.93406	+	1.25318i	0.153866	+	0.0996975i
$159$	−3.53565			−0.280395
$160$	−1.77082	+	12.5245i	−0.139996	+	0.990152i
$161$	9.31058			0.733777
$162$	1.26139	+	0.817316i	0.0991038	+	0.0642144i
$163$	8.52729	−	8.52729i	0.667909	−	0.667909i	−0.289323	−	0.957232i	$-0.593430\pi$
$163$	8.52729	−	8.52729i	0.667909	−	0.667909i	0.957232	+	0.289323i	$0.0934301\pi$
$164$	−1.11700	−	2.49504i	−0.0872230	−	0.194830i
$165$	−2.08215	+	0.826847i	−0.162095	+	0.0643700i
$166$	5.22195	−	1.11556i	0.405302	−	0.0865841i
$167$	8.81617	+	8.81617i	0.682216	+	0.682216i	0.960499	−	0.278283i	$-0.0897654\pi$
$167$	8.81617	+	8.81617i	0.682216	+	0.682216i	−0.278283	+	0.960499i	$0.589765\pi$
$168$	0.541201	−	3.48639i	0.0417546	−	0.268981i
$169$			1.00000i			0.0769231i
$170$	4.29792	−	21.5430i	0.329635	−	1.65227i
$171$		−	11.6659i		−	0.892112i
$172$	11.4736	+	4.37734i	0.874857	+	0.333769i
$173$	0.914606	+	0.914606i	0.0695362	+	0.0695362i	0.741020	−	0.671483i	$-0.234343\pi$
$173$	0.914606	+	0.914606i	0.0695362	+	0.0695362i	−0.671483	+	0.741020i	$0.734343\pi$
$174$	2.65353	+	12.4212i	0.201163	+	0.941650i
$175$	−0.160122	+	5.45051i	−0.0121041	+	0.412020i
$176$	2.61341	+	2.33379i	0.196993	+	0.175916i
$177$	0.605997	−	0.605997i	0.0455496	−	0.0455496i
$178$	2.83617	−	4.37714i	0.212580	−	0.328081i
$179$	−4.85523			−0.362897			−0.181449	−	0.983400i	$-0.558079\pi$
$179$	−4.85523			−0.362897			−0.181449	+	0.983400i	$0.558079\pi$
$180$	0.102484	+	7.56499i	0.00763873	+	0.563861i
$181$	−16.5488			−1.23006			−0.615031	−	0.788503i	$-0.710857\pi$
$181$	−16.5488			−1.23006			−0.615031	+	0.788503i	$0.710857\pi$
$182$	0.838671	−	1.29434i	0.0621664	−	0.0959432i
$183$	−3.87974	+	3.87974i	−0.286798	+	0.286798i
$184$	−14.2534	−	19.4918i	−1.05078	−	1.43695i
$185$	2.59088	+	6.52429i	0.190485	+	0.479676i
$186$	−1.84457	−	8.63448i	−0.135251	−	0.633111i
$187$	−4.30273	−	4.30273i	−0.314647	−	0.314647i
$188$	3.84246	−	10.0716i	0.280240	−	0.734549i
$189$		−	5.85242i		−	0.425701i
$190$	−18.1382	+	12.1047i	−1.31589	+	0.878165i
$191$			19.6388i			1.42102i	0.703690	+	0.710508i	$0.251535\pi$
$191$			19.6388i			1.42102i	−0.703690	+	0.710508i	$0.748465\pi$
$192$	−8.12730	+	4.20425i	−0.586537	+	0.303416i
$193$	−13.0800	−	13.0800i	−0.941517	−	0.941517i	0.0568651	−	0.998382i	$-0.481890\pi$
$193$	−13.0800	−	13.0800i	−0.941517	−	0.941517i	−0.998382	+	0.0568651i	$0.981890\pi$
$194$	13.0167	−	2.78074i	0.934544	−	0.199645i
$195$	1.01334	−	2.34829i	0.0725669	−	0.168164i
$196$	10.6069	−	4.74857i	0.757634	−	0.339184i
$197$	−0.774201	+	0.774201i	−0.0551596	+	0.0551596i	−0.734149	−	0.678989i	$-0.762418\pi$
$197$	−0.774201	+	0.774201i	−0.0551596	+	0.0551596i	0.678989	+	0.734149i	$0.262418\pi$
$198$	1.75876	+	1.13959i	0.124989	+	0.0809870i
$199$	3.72024			0.263721			0.131860	−	0.991268i	$-0.457905\pi$
$199$	3.72024			0.263721			0.131860	+	0.991268i	$0.457905\pi$
$200$	11.6558	−	8.00888i	0.824190	−	0.566313i
$201$	16.2903			1.14903
$202$	−7.39301	−	4.79031i	−0.520171	−	0.337045i
$203$	6.05525	−	6.05525i	0.424995	−	0.424995i
$204$	14.5041	−	6.49333i	1.01549	−	0.454624i
$205$	−1.21094	+	2.80620i	−0.0845758	+	0.195993i
$206$	17.7157	−	3.78458i	1.23431	−	0.263684i
$207$	−10.2127	−	10.2127i	−0.709832	−	0.709832i
$208$	−3.99363	+	0.225727i	−0.276908	+	0.0156513i
$209$			6.04034i			0.417819i
$210$	−3.28105	+	2.18963i	−0.226414	+	0.151099i
$211$		−	10.1014i		−	0.695411i	−0.937604	−	0.347706i	$-0.886961\pi$
$211$		−	10.1014i		−	0.695411i	0.937604	−	0.347706i	$-0.113039\pi$
$212$	2.20371	−	5.77623i	0.151351	−	0.396713i
$213$	−4.05589	−	4.05589i	−0.277905	−	0.277905i
$214$	2.91672	+	13.6532i	0.199383	+	0.933314i
$215$	−5.06733	−	12.7604i	−0.345589	−	0.870255i
$216$	−12.2521	+	8.95937i	−0.833648	+	0.609608i
$217$	−4.20924	+	4.20924i	−0.285742	+	0.285742i
$218$	4.51756	−	6.97208i	0.305968	−	0.472209i
$219$	11.0816			0.748822
$220$	−0.0530642	−	3.91699i	−0.00357759	−	0.264083i
$221$	6.94675			0.467289
$222$	−2.76141	+	4.26176i	−0.185334	+	0.286030i
$223$	10.9738	−	10.9738i	0.734860	−	0.734860i	−0.236718	−	0.971578i	$-0.576072\pi$
$223$	10.9738	−	10.9738i	0.734860	−	0.734860i	0.971578	+	0.236718i	$0.0760719\pi$
$224$	5.35844	+	3.05717i	0.358026	+	0.204266i
$225$	6.15426	−	5.80298i	0.410284	−	0.386866i
$226$	3.46580	+	16.2235i	0.230541	+	1.07917i
$227$	−5.10770	−	5.10770i	−0.339010	−	0.339010i	0.516985	−	0.855995i	$-0.327054\pi$
$227$	−5.10770	−	5.10770i	−0.339010	−	0.339010i	−0.855995	+	0.516985i	$0.827054\pi$
$228$	−14.7385	−	5.62293i	−0.976082	−	0.372388i
$229$			1.18140i			0.0780689i	0.999238	+	0.0390345i	$0.0124282\pi$
$229$			1.18140i			0.0780689i	−0.999238	+	0.0390345i	$0.987572\pi$
$230$	−5.28200	+	26.4757i	−0.348285	+	1.74575i
$231$			1.09265i			0.0718908i
$232$	−21.9466	−	3.40682i	−1.44086	−	0.223669i
$233$	−12.0874	−	12.0874i	−0.791870	−	0.791870i	0.189928	−	0.981798i	$-0.439175\pi$
$233$	−12.0874	−	12.0874i	−0.791870	−	0.791870i	−0.981798	+	0.189928i	$0.939175\pi$
$234$	−2.33969	+	0.499824i	−0.152950	+	0.0326745i
$235$	−11.2012	+	4.44814i	−0.730686	+	0.290164i
$236$	0.612318	+	1.36773i	0.0398585	+	0.0890318i
$237$	1.31798	−	1.31798i	0.0856118	−	0.0856118i
$238$	−8.99149	−	5.82604i	−0.582831	−	0.377646i
$239$	−19.0528			−1.23242			−0.616211	−	0.787581i	$-0.711333\pi$
$239$	−19.0528			−1.23242			−0.616211	+	0.787581i	$0.711333\pi$
$240$	9.60691	+	3.51684i	0.620123	+	0.227011i
$241$	−0.866695			−0.0558287			−0.0279144	−	0.999610i	$-0.508887\pi$
$241$	−0.866695			−0.0558287			−0.0279144	+	0.999610i	$0.508887\pi$
$242$	12.1447	+	7.86916i	0.780690	+	0.505849i
$243$	−10.5242	+	10.5242i	−0.675129	+	0.675129i
$244$	−3.92020	−	8.75654i	−0.250965	−	0.560580i
$245$	−11.9297	−	5.14794i	−0.762159	−	0.328890i
$246$	−2.16215	+	0.461898i	−0.137854	+	0.0294495i
$247$	−4.87606	−	4.87606i	−0.310256	−	0.310256i
$248$	15.2559	+	2.36822i	0.968753	+	0.150382i
$249$		−	4.31872i		−	0.273688i
$250$	−15.4083	−	3.54746i	−0.974506	−	0.224361i
$251$			11.9952i			0.757128i	0.925575	+	0.378564i	$0.123582\pi$
$251$			11.9952i			0.757128i	−0.925575	+	0.378564i	$0.876418\pi$
$252$	3.44755	+	1.31528i	0.217175	+	0.0828551i
$253$	5.28792	+	5.28792i	0.332449	+	0.332449i
$254$	3.53615	+	16.5528i	0.221878	+	1.03861i
$255$	−16.3130	−	7.03943i	−1.02156	−	0.440826i
$256$	−1.80294	−	15.8981i	−0.112684	−	0.993631i
$257$	−9.55086	+	9.55086i	−0.595766	+	0.595766i	−0.939183	−	0.343417i	$-0.888416\pi$
$257$	−9.55086	+	9.55086i	−0.595766	+	0.595766i	0.343417	+	0.939183i	$0.388416\pi$
$258$	5.40086	−	8.33530i	0.336243	−	0.518933i
$259$	3.42374			0.212741
$260$	3.20482	+	3.11915i	0.198755	+	0.193442i
$261$	−13.2839			−0.822253
$262$	−11.9215	+	18.3987i	−0.736510	+	1.13668i
$263$	−8.00268	+	8.00268i	−0.493467	+	0.493467i	−0.909397	−	0.415930i	$-0.863456\pi$
$263$	−8.00268	+	8.00268i	−0.493467	+	0.493467i	0.415930	+	0.909397i	$0.363456\pi$
$264$	2.28746	−	1.67271i	0.140783	−	0.102948i
$265$	−6.42406	+	2.55107i	−0.394627	+	0.156711i
$266$	2.22189	+	10.4007i	0.136233	+	0.637708i
$267$	−2.98282	−	2.98282i	−0.182546	−	0.182546i
$268$	−10.1535	+	26.6137i	−0.620221	+	1.62569i
$269$		−	7.28829i		−	0.444375i	−0.975004	−	0.222188i	$-0.928680\pi$
$269$		−	7.28829i		−	0.444375i	0.975004	−	0.222188i	$-0.0713197\pi$
$270$	16.6420	+	3.32015i	1.01280	+	0.202058i
$271$			4.92513i			0.299181i	0.988748	+	0.149590i	$0.0477955\pi$
$271$			4.92513i			0.299181i	−0.988748	+	0.149590i	$0.952205\pi$
$272$	1.56807	+	27.7427i	0.0950781	+	1.68215i
$273$	−0.882037	−	0.882037i	−0.0533833	−	0.0533833i
$274$	−5.03583	+	1.07580i	−0.304226	+	0.0649913i
$275$	−3.18654	+	3.00466i	−0.192156	+	0.181188i
$276$	−17.8251	+	7.98009i	−1.07295	+	0.480345i
$277$	−13.6222	+	13.6222i	−0.818482	+	0.818482i	−0.985888	−	0.167406i	$-0.946461\pi$
$277$	−13.6222	+	13.6222i	−0.818482	+	0.818482i	0.167406	+	0.985888i	$0.446461\pi$
$278$	−5.01627	−	3.25029i	−0.300856	−	0.194940i
$279$	9.23417			0.552835
$280$	−1.53220	−	6.72505i	−0.0915666	−	0.401899i
$281$	11.2668			0.672120			0.336060	−	0.941841i	$-0.390905\pi$
$281$	11.2668			0.672120			0.336060	+	0.941841i	$0.390905\pi$
$282$	−7.31678	−	4.74091i	−0.435708	−	0.282317i
$283$	11.8154	−	11.8154i	0.702350	−	0.702350i	−0.262565	−	0.964914i	$-0.584568\pi$
$283$	11.8154	−	11.8154i	0.702350	−	0.702350i	0.964914	+	0.262565i	$0.0845683\pi$
$284$	9.15412	−	4.09819i	0.543197	−	0.243183i
$285$	6.50926	+	16.3915i	0.385576	+	0.970948i
$286$	1.21144	−	0.258798i	0.0716339	−	0.0153031i
$287$	1.05403	+	1.05403i	0.0622176	+	0.0622176i
$288$	−2.52424	−	9.23101i	−0.148742	−	0.543943i
$289$		−	31.2573i		−	1.83867i
$290$	13.7836	+	20.6540i	0.809398	+	1.21284i
$291$		−	10.7652i		−	0.631069i
$292$	−6.90693	+	18.1041i	−0.404198	+	1.05946i
$293$	−7.28832	−	7.28832i	−0.425788	−	0.425788i	0.461403	−	0.887191i	$-0.347346\pi$
$293$	−7.28832	−	7.28832i	−0.425788	−	0.425788i	−0.887191	+	0.461403i	$0.847346\pi$
$294$	−1.96361	−	9.19172i	−0.114520	−	0.536072i
$295$	0.663815	−	1.53830i	0.0386488	−	0.0895635i
$296$	−5.24135	−	7.16762i	−0.304647	−	0.416609i
$297$	3.32387	−	3.32387i	0.192870	−	0.192870i
$298$	0.772798	−	1.19268i	0.0447670	−	0.0690901i
$299$	−8.53734			−0.493727
$300$	−4.36507	−	10.5722i	−0.252018	−	0.610388i
$301$	−6.69627			−0.385967
$302$	12.5233	−	19.3275i	0.720632	−	1.11217i
$303$	−5.03800	+	5.03800i	−0.289426	+	0.289426i
$304$	18.3725	−	20.5738i	1.05373	−	1.17999i
$305$	−4.24990	+	9.84858i	−0.243349	+	0.563928i
$306$	3.47215	+	16.2532i	0.198490	+	0.929135i
$307$	−16.3497	−	16.3497i	−0.933128	−	0.933128i	0.0647718	−	0.997900i	$-0.479368\pi$
$307$	−16.3497	−	16.3497i	−0.933128	−	0.933128i	−0.997900	+	0.0647718i	$0.979368\pi$
$308$	−1.78507	−	0.681026i	−0.101714	−	0.0388050i
$309$		−	14.6515i		−	0.833493i
$310$	−9.58150	−	14.3574i	−0.544192	−	0.815446i
$311$		−	21.7219i		−	1.23174i	−0.787850	−	0.615868i	$-0.788806\pi$
$311$		−	21.7219i		−	1.23174i	0.787850	−	0.615868i	$-0.211194\pi$
$312$	−0.496254	+	3.19685i	−0.0280949	+	0.180986i
$313$	−1.17273	−	1.17273i	−0.0662866	−	0.0662866i	0.673186	−	0.739473i	$-0.264925\pi$
$313$	−1.17273	−	1.17273i	−0.0662866	−	0.0662866i	−0.739473	+	0.673186i	$0.764925\pi$
$314$	−0.335550	+	0.0716830i	−0.0189362	+	0.00404531i
$315$	−1.52261	−	3.83420i	−0.0857893	−	0.216033i
$316$	1.33172	+	2.97467i	0.0749153	+	0.167338i
$317$	6.45087	−	6.45087i	0.362317	−	0.362317i	−0.502348	−	0.864665i	$-0.667530\pi$
$317$	6.45087	−	6.45087i	0.362317	−	0.362317i	0.864665	+	0.502348i	$0.167530\pi$
$318$	−4.19628	−	2.71898i	−0.235316	−	0.152473i
$319$	6.87812			0.385101
$320$	−11.7333	+	13.5029i	−0.655912	+	0.754837i
$321$	11.2917			0.630239
$322$	11.0503	+	7.16002i	0.615807	+	0.399012i
$323$	−33.8728	+	33.8728i	−1.88473	+	1.88473i
$324$	0.868542	+	1.94006i	0.0482523	+	0.107781i
$325$	0.146824	−	4.99784i	0.00814433	−	0.277230i
$326$	16.6783	−	3.56295i	0.923723	−	0.197334i
$327$	−4.75115	−	4.75115i	−0.262739	−	0.262739i
$328$	0.593023	−	3.82023i	0.0327442	−	0.210937i
$329$			5.87803i			0.324066i
$330$	−3.10706	−	0.619870i	−0.171038	−	0.0341227i
$331$		−	32.7431i		−	1.79973i	−0.436173	−	0.899863i	$-0.643666\pi$
$331$		−	32.7431i		−	1.79973i	0.436173	−	0.899863i	$-0.356334\pi$
$332$	7.05555	+	2.69178i	0.387224	+	0.147731i
$333$	−3.75547	−	3.75547i	−0.205799	−	0.205799i
$334$	3.68365	+	17.2433i	0.201561	+	0.943510i
$335$	29.5985	−	11.7539i	1.61714	−	0.642186i
$336$	3.32343	−	3.72162i	0.181308	−	0.203031i
$337$	17.0557	−	17.0557i	0.929083	−	0.929083i	−0.0685633	−	0.997647i	$-0.521842\pi$
$337$	17.0557	−	17.0557i	0.929083	−	0.929083i	0.997647	+	0.0685633i	$0.0218415\pi$
$338$	−0.769019	+	1.18685i	−0.0418291	+	0.0645560i
$339$	13.4173			0.728730
$340$	21.6680	−	22.2631i	1.17511	−	1.20739i
$341$	−4.78125			−0.258919
$342$	8.97128	−	13.8456i	0.485111	−	0.748686i
$343$	−9.87895	+	9.87895i	−0.533413	+	0.533413i
$344$	10.2512	+	14.0187i	0.552708	+	0.755837i
$345$	20.0481	+	8.65124i	1.07935	+	0.465767i
$346$	0.382149	+	1.78885i	0.0205445	+	0.0961690i
$347$	12.2761	+	12.2761i	0.659016	+	0.659016i	0.955147	−	0.296131i	$-0.0956966\pi$
$347$	12.2761	+	12.2761i	0.659016	+	0.659016i	−0.296131	+	0.955147i	$0.595697\pi$
$348$	−6.40282	+	16.7827i	−0.343227	+	0.899648i
$349$			30.2444i			1.61895i	0.587156	+	0.809474i	$0.300248\pi$
$349$			30.2444i			1.61895i	−0.587156	+	0.809474i	$0.699752\pi$
$350$	−4.38159	+	6.34579i	−0.234206	+	0.339197i
$351$			5.36638i			0.286436i
$352$	1.30700	+	4.77962i	0.0696632	+	0.254755i
$353$	−15.7099	−	15.7099i	−0.836152	−	0.836152i	0.152198	−	0.988350i	$-0.451365\pi$
$353$	−15.7099	−	15.7099i	−0.836152	−	0.836152i	−0.988350	+	0.152198i	$0.951365\pi$
$354$	1.18525	−	0.253203i	0.0629954	−	0.0134576i
$355$	−10.2957	−	4.44286i	−0.546441	−	0.235803i
$356$	6.73221	−	3.01393i	0.356807	−	0.159738i
$357$	−6.12729	+	6.12729i	−0.324291	+	0.324291i
$358$	−5.76243	−	3.73377i	−0.304554	−	0.197336i
$359$	35.6895			1.88362			0.941809	−	0.336149i	$-0.109125\pi$
$359$	35.6895			1.88362			0.941809	+	0.336149i	$0.109125\pi$
$360$	−5.69599	+	9.05731i	−0.300205	+	0.477362i
$361$	28.5519			1.50273
$362$	−19.6409	−	12.7263i	−1.03230	−	0.668882i
$363$	8.27605	−	8.27605i	0.434380	−	0.434380i
$364$	1.99075	−	0.891236i	0.104344	−	0.0467135i
$365$	20.1345	−	7.99566i	1.05389	−	0.418512i
$366$	−7.58825	+	1.62107i	−0.396644	+	0.0847345i
$367$	−4.41082	−	4.41082i	−0.230243	−	0.230243i	0.582551	−	0.812794i	$-0.302055\pi$
$367$	−4.41082	−	4.41082i	−0.230243	−	0.230243i	−0.812794	+	0.582551i	$0.802055\pi$
$368$	−1.92711	−	34.0949i	−0.100457	−	1.77732i
$369$		−	2.31232i		−	0.120375i
$370$	−1.94233	+	9.73578i	−0.100977	+	0.506139i
$371$			3.37114i			0.175021i
$372$	4.45085	−	11.6663i	0.230766	−	0.604871i
$373$	16.1225	+	16.1225i	0.834792	+	0.834792i	0.988168	−	0.153376i	$-0.0490145\pi$
$373$	16.1225	+	16.1225i	0.834792	+	0.834792i	−0.153376	+	0.988168i	$0.549015\pi$
$374$	−1.79781	−	8.41557i	−0.0929624	−	0.435159i
$375$	−5.40931	+	11.5876i	−0.279335	+	0.598380i
$376$	12.3057	−	8.99858i	0.634618	−	0.464066i
$377$	−5.55236	+	5.55236i	−0.285961	+	0.285961i
$378$	4.50062	−	6.94594i	0.231487	−	0.357260i
$379$	−33.3029			−1.71066			−0.855328	−	0.518086i	$-0.826645\pi$
$379$	−33.3029			−1.71066			−0.855328	+	0.518086i	$0.826645\pi$
$380$	−30.8361	+	0.417742i	−1.58186	+	0.0214297i
$381$	13.6897			0.701345
$382$	−15.1026	+	23.3083i	−0.772718	+	1.19256i
$383$	1.90891	−	1.90891i	0.0975409	−	0.0975409i	−0.656652	−	0.754193i	$-0.728028\pi$
$383$	1.90891	−	1.90891i	0.0975409	−	0.0975409i	0.754193	+	0.656652i	$0.228028\pi$
$384$	−12.8790	−	1.26024i	−0.657230	−	0.0643113i
$385$	0.788375	+	1.98527i	0.0401793	+	0.101179i
$386$	−5.46519	−	25.5827i	−0.278171	−	1.30212i
$387$	7.34509	+	7.34509i	0.373372	+	0.373372i
$388$	17.5873	+	6.70977i	0.892859	+	0.340637i
$389$			2.08615i			0.105772i	0.998601	+	0.0528859i	$0.0168420\pi$
$389$			2.08615i			0.105772i	−0.998601	+	0.0528859i	$0.983158\pi$
$390$	3.00856	−	2.00778i	0.152344	−	0.101668i
$391$			59.3067i			2.99927i
$392$	16.2405	+	2.52105i	0.820269	+	0.127332i
$393$	12.5379	+	12.5379i	0.632453	+	0.632453i
$394$	−1.51424	+	0.323484i	−0.0762861	+	0.0162969i
$395$	1.44372	−	3.34564i	0.0726417	−	0.168337i
$396$	1.21101	+	2.70504i	0.0608557	+	0.135933i
$397$	−23.2416	+	23.2416i	−1.16646	+	1.16646i	−0.183431	+	0.983033i	$0.558720\pi$
$397$	−23.2416	+	23.2416i	−1.16646	+	1.16646i	−0.983033	+	0.183431i	$0.941280\pi$
$398$	4.41536	+	2.86094i	0.221322	+	0.143406i
$399$	8.60173			0.430625
$400$	19.9927	−	0.541788i	0.999633	−	0.0270894i
$401$	16.0373			0.800865			0.400432	−	0.916326i	$-0.368860\pi$
$401$	16.0373			0.800865			0.400432	+	0.916326i	$0.368860\pi$
$402$	19.3341	+	12.5276i	0.964299	+	0.624818i
$403$	3.85966	−	3.85966i	0.192264	−	0.192264i
$404$	−5.09055	−	11.3707i	−0.253264	−	0.565715i
$405$	0.941589	−	2.18201i	0.0467879	−	0.108425i
$406$	11.8433	−	2.53006i	0.587771	−	0.125565i
$407$	1.94450	+	1.94450i	0.0963854	+	0.0963854i
$408$	22.2077	+	3.44735i	1.09944	+	0.170669i
$409$			38.6612i			1.91167i	0.293898	+	0.955837i	$0.405047\pi$
$409$			38.6612i			1.91167i	−0.293898	+	0.955837i	$0.594953\pi$
$410$	−3.59522	+	2.39929i	−0.177555	+	0.118493i
$411$			4.16480i			0.205434i
$412$	23.9363	+	9.13199i	1.17925	+	0.449901i
$413$	−0.577801	−	0.577801i	−0.0284317	−	0.0284317i
$414$	−4.26717	−	19.9747i	−0.209720	−	0.981703i
$415$	−3.11608	−	7.84685i	−0.152962	−	0.385187i
$416$	−4.91342	−	2.80327i	−0.240900	−	0.137442i
$417$	−3.41836	+	3.41836i	−0.167398	+	0.167398i
$418$	−4.64514	+	7.16897i	−0.227201	+	0.350646i
$419$	−15.9101			−0.777261			−0.388630	−	0.921394i	$-0.627052\pi$
$419$	−15.9101			−0.777261			−0.388630	+	0.921394i	$0.627052\pi$
$420$	−5.57798	+	0.0755659i	−0.272177	+	0.00368724i
$421$	3.52390			0.171744			0.0858721	−	0.996306i	$-0.472632\pi$
$421$	3.52390			0.171744			0.0858721	+	0.996306i	$0.472632\pi$
$422$	7.76819	−	11.9889i	0.378150	−	0.583609i
$423$	6.44756	−	6.44756i	0.313491	−	0.313491i
$424$	7.05750	−	5.16082i	0.342743	−	0.250632i
$425$	−34.7188	−	1.01995i	−1.68411	−	0.0494748i
$426$	−1.69467	−	7.93279i	−0.0821070	−	0.384345i
$427$	3.69921	+	3.69921i	0.179018	+	0.179018i
$428$	−7.03788	+	18.4473i	−0.340189	+	0.891684i
$429$		−	1.00190i		−	0.0483722i
$430$	3.79887	−	19.0416i	0.183198	−	0.918267i
$431$			34.0034i			1.63788i	0.573876	+	0.818942i	$0.305439\pi$
$431$			34.0034i			1.63788i	−0.573876	+	0.818942i	$0.694561\pi$
$432$	−21.4313	+	1.21134i	−1.03111	+	0.0582804i
$433$	−20.4386	−	20.4386i	−0.982216	−	0.982216i	0.0176285	−	0.999845i	$-0.494388\pi$
$433$	−20.4386	−	20.4386i	−0.982216	−	0.982216i	−0.999845	+	0.0176285i	$0.994388\pi$
$434$	−8.23272	+	1.75874i	−0.395183	+	0.0844224i
$435$	18.6650	−	7.41209i	0.894916	−	0.355382i
$436$	10.7233	−	4.80071i	0.513554	−	0.229912i
$437$	41.6286	−	41.6286i	1.99136	−	1.99136i
$438$	13.1521	+	8.52193i	0.628433	+	0.407194i
$439$	−4.50397			−0.214963			−0.107481	−	0.994207i	$-0.534279\pi$
$439$	−4.50397			−0.214963			−0.107481	+	0.994207i	$0.534279\pi$
$440$	2.94926	−	4.68968i	0.140601	−	0.223572i
$441$	9.83011			0.468100
$442$	8.24474	+	5.34218i	0.392162	+	0.254102i
$443$	16.9086	−	16.9086i	0.803352	−	0.803352i	−0.180266	−	0.983618i	$-0.557696\pi$
$443$	16.9086	−	16.9086i	0.803352	−	0.803352i	0.983618	+	0.180266i	$0.0576959\pi$
$444$	−6.55475	+	2.93448i	−0.311074	+	0.139264i
$445$	−7.57180	−	3.26741i	−0.358938	−	0.154890i
$446$	21.4633	−	4.58517i	1.01632	−	0.217114i
$447$	−0.812758	−	0.812758i	−0.0384421	−	0.0384421i
$448$	4.00863	+	7.74914i	0.189390	+	0.366112i
$449$			15.2463i			0.719516i	0.933046	+	0.359758i	$0.117141\pi$
$449$			15.2463i			0.719516i	−0.933046	+	0.359758i	$0.882859\pi$
$450$	11.7668	−	2.15452i	0.554691	−	0.101565i
$451$			1.19727i			0.0563772i
$452$	−8.36279	+	21.9201i	−0.393353	+	1.03103i
$453$	−13.1708	−	13.1708i	−0.618818	−	0.618818i
$454$	−2.13415	−	9.98999i	−0.100160	−	0.468853i
$455$	−2.23902	−	0.966191i	−0.104967	−	0.0452958i
$456$	−13.1682	−	18.0078i	−0.616659	−	0.843291i
$457$	7.44322	−	7.44322i	0.348179	−	0.348179i	−0.511252	−	0.859431i	$-0.670818\pi$
$457$	7.44322	−	7.44322i	0.348179	−	0.348179i	0.859431	+	0.511252i	$0.170818\pi$
$458$	−0.908517	+	1.40214i	−0.0424522	+	0.0655177i
$459$	37.2789			1.74003
$460$	−26.6292	+	27.3607i	−1.24160	+	1.27570i
$461$	−21.5904			−1.00556			−0.502782	−	0.864413i	$-0.667690\pi$
$461$	−21.5904			−1.00556			−0.502782	+	0.864413i	$0.667690\pi$
$462$	−0.840265	+	1.29680i	−0.0390927	+	0.0603328i
$463$	−5.31937	+	5.31937i	−0.247212	+	0.247212i	−0.819825	−	0.572614i	$-0.805930\pi$
$463$	−5.31937	+	5.31937i	−0.247212	+	0.247212i	0.572614	+	0.819825i	$0.305930\pi$
$464$	−23.4274	−	20.9207i	−1.08759	−	0.971220i
$465$	−12.9747	+	5.15243i	−0.601690	+	0.238938i
$466$	−5.05046	−	23.6413i	−0.233958	−	1.09516i
$467$	12.0139	+	12.0139i	0.555939	+	0.555939i	0.928149	−	0.372210i	$-0.121400\pi$
$467$	12.0139	+	12.0139i	0.555939	+	0.555939i	−0.372210	+	0.928149i	$0.621400\pi$
$468$	−3.16123	−	1.20605i	−0.146128	−	0.0557496i
$469$		−	15.5323i		−	0.717217i
$470$	−16.7148	−	3.33468i	−0.770998	−	0.153817i
$471$			0.277511i			0.0127870i
$472$	−0.325084	+	2.09417i	−0.0149632	+	0.0963922i
$473$	−3.80313	−	3.80313i	−0.174868	−	0.174868i
$474$	2.57779	−	0.550689i	0.118402	−	0.0252940i
$475$	23.6539	+	25.0857i	1.08531	+	1.15101i
$476$	−6.19120	−	13.8293i	−0.283773	−	0.633863i
$477$	3.69777	−	3.69777i	0.169309	−	0.169309i
$478$	−22.6128	−	14.6520i	−1.03428	−	0.670165i
$479$	6.77238			0.309438			0.154719	−	0.987959i	$-0.450553\pi$
$479$	6.77238			0.309438			0.154719	+	0.987959i	$0.450553\pi$
$480$	8.69743	+	11.5619i	0.396982	+	0.527724i
$481$	−3.13940			−0.143144
$482$	−1.02864	−	0.666505i	−0.0468531	−	0.0303585i
$483$	7.53025	−	7.53025i	0.342638	−	0.342638i
$484$	8.36237	+	18.6790i	0.380108	+	0.849045i
$485$	−7.76742	−	19.5598i	−0.352700	−	0.888163i
$486$	−20.5840	+	4.39733i	−0.933709	+	0.199467i
$487$	−5.85296	−	5.85296i	−0.265223	−	0.265223i	0.561949	−	0.827172i	$-0.310052\pi$
$487$	−5.85296	−	5.85296i	−0.265223	−	0.265223i	−0.827172	+	0.561949i	$0.810052\pi$
$488$	2.08126	−	13.4074i	0.0942143	−	0.606924i
$489$		−	13.7935i		−	0.623762i
$490$	−10.1998	−	15.2840i	−0.460782	−	0.690460i
$491$			30.1005i			1.35842i	0.733945	+	0.679209i	$0.237677\pi$
$491$			30.1005i			1.35842i	−0.733945	+	0.679209i	$0.762323\pi$
$492$	−2.92136	−	1.11453i	−0.131705	−	0.0502471i
$493$	38.5708	+	38.5708i	1.73714	+	1.73714i
$494$	−2.03736	−	9.53693i	−0.0916652	−	0.429087i
$495$	1.31286	−	3.04239i	0.0590088	−	0.136745i
$496$	16.2853	+	14.5428i	0.731231	+	0.652992i
$497$	−3.86717	+	3.86717i	−0.173466	+	0.173466i
$498$	3.32118	−	5.12567i	0.148826	−	0.229687i
$499$	4.19308			0.187708			0.0938541	−	0.995586i	$-0.470081\pi$
$499$	4.19308			0.187708			0.0938541	+	0.995586i	$0.470081\pi$
$500$	−15.5592	−	16.0596i	−0.695830	−	0.718206i
$501$	14.2607			0.637123
$502$	−9.22451	+	14.2364i	−0.411710	+	0.635404i
$503$	−6.34559	+	6.34559i	−0.282936	+	0.282936i	−0.834279	−	0.551343i	$-0.814116\pi$
$503$	−6.34559	+	6.34559i	−0.282936	+	0.282936i	0.551343	+	0.834279i	$0.314116\pi$
$504$	3.08024	+	4.21227i	0.137205	+	0.187630i
$505$	−5.51867	+	12.7888i	−0.245578	+	0.569094i
$506$	2.20945	+	10.3425i	0.0982219	+	0.459779i
$507$	0.808783	+	0.808783i	0.0359193	+	0.0359193i
$508$	−8.53254	+	22.3650i	−0.378570	+	0.992288i
$509$			40.6251i			1.80068i	0.435190	+	0.900338i	$0.356681\pi$
$509$			40.6251i			1.80068i	−0.435190	+	0.900338i	$0.643319\pi$
$510$	−13.9475	−	20.8997i	−0.617608	−	0.925455i
$511$		−	10.5659i		−	0.467410i
$512$	10.0861	−	20.2551i	0.445748	−	0.895158i
$513$	−26.1668	−	26.1668i	−1.15529	−	1.15529i
$514$	−18.6802	+	3.99063i	−0.823949	+	0.176019i
$515$	−10.5714	−	26.6208i	−0.465834	−	1.17305i
$516$	12.8200	−	5.73937i	0.564369	−	0.252662i
$517$	−3.33841	+	3.33841i	−0.146823	+	0.146823i
$518$	4.06346	+	2.63292i	0.178538	+	0.115684i
$519$	1.47944			0.0649400
$520$	1.40495	+	6.16653i	0.0616112	+	0.270420i
$521$	−37.7559			−1.65412			−0.827058	−	0.562116i	$-0.809987\pi$
$521$	−37.7559			−1.65412			−0.827058	+	0.562116i	$0.809987\pi$
$522$	−15.7660	−	10.2156i	−0.690058	−	0.447124i
$523$	−4.86113	+	4.86113i	−0.212563	+	0.212563i	−0.805355	−	0.592793i	$-0.798025\pi$
$523$	−4.86113	+	4.86113i	−0.212563	+	0.212563i	0.592793	+	0.805355i	$0.298025\pi$
$524$	−28.2979	+	12.6687i	−1.23620	+	0.553433i
$525$	4.27878	+	4.53779i	0.186741	+	0.198045i
$526$	−15.6522	+	3.34376i	−0.682468	+	0.145795i
$527$	−26.8121	−	26.8121i	−1.16795	−	1.16795i
$528$	4.00122	−	0.226156i	0.174131	−	0.00984217i
$529$		−	49.8861i		−	2.16896i
$530$	−9.58621	−	1.91249i	−0.416398	−	0.0830731i
$531$			1.26757i			0.0550078i
$532$	−5.36130	+	14.0527i	−0.232442	+	0.609264i
$533$	−0.966495	−	0.966495i	−0.0418635	−	0.0418635i
$534$	−1.24631	−	5.83401i	−0.0539331	−	0.252462i
$535$	20.5162	−	8.14725i	0.886994	−	0.352236i
$536$	−32.5170	+	23.7782i	−1.40452	+	1.02706i
$537$	−3.92683	+	3.92683i	−0.169455	+	0.169455i
$538$	5.60484	−	8.65010i	0.241642	−	0.372932i
$539$	−5.08982			−0.219234
$540$	17.1983	+	16.7385i	0.740096	+	0.720312i
$541$	−38.2350			−1.64385			−0.821925	−	0.569596i	$-0.807100\pi$
$541$	−38.2350			−1.64385			−0.821925	+	0.569596i	$0.807100\pi$
$542$	−3.78752	+	5.84539i	−0.162688	+	0.251081i
$543$	−13.3844	+	13.3844i	−0.574379	+	0.574379i
$544$	−19.4736	+	34.1323i	−0.834925	+	1.46341i
$545$	−12.0606	−	5.20446i	−0.516621	−	0.222934i
$546$	−0.368541	−	1.72515i	−0.0157721	−	0.0738295i
$547$	7.89796	+	7.89796i	0.337692	+	0.337692i	0.855498	−	0.517806i	$-0.173251\pi$
$547$	7.89796	+	7.89796i	0.337692	+	0.337692i	−0.517806	+	0.855498i	$0.673251\pi$
$548$	−6.80408	−	2.59584i	−0.290656	−	0.110889i
$549$		−	8.11528i		−	0.346352i
$550$	−6.09259	+	1.11556i	−0.259789	+	0.0475678i
$551$		−	54.1472i		−	2.30675i
$552$	−27.2925	−	4.23669i	−1.16165	−	0.180325i
$553$	−1.25665	−	1.25665i	−0.0534383	−	0.0534383i
$554$	−26.6433	+	5.69177i	−1.13197	+	0.241820i
$555$	7.37220	+	3.18128i	0.312932	+	0.135038i
$556$	−3.45401	−	7.71521i	−0.146483	−	0.327198i
$557$	7.49825	−	7.49825i	0.317711	−	0.317711i	−0.530176	−	0.847887i	$-0.677874\pi$
$557$	7.49825	−	7.49825i	0.317711	−	0.317711i	0.847887	+	0.530176i	$0.177874\pi$
$558$	10.9596	+	7.10125i	0.463955	+	0.300620i
$559$	6.14014			0.259700
$560$	3.35320	−	9.15991i	0.141699	−	0.387077i
$561$	−6.95995			−0.293849
$562$	13.3720	+	8.66438i	0.564062	+	0.365485i
$563$	−1.24248	+	1.24248i	−0.0523644	+	0.0523644i	−0.732804	−	0.680440i	$-0.761789\pi$
$563$	−1.24248	+	1.24248i	−0.0523644	+	0.0523644i	0.680440	+	0.732804i	$0.261789\pi$
$564$	−5.03805	−	11.2535i	−0.212140	−	0.473857i
$565$	24.3785	−	9.68100i	1.02561	−	0.407283i
$566$	23.1093	−	4.93680i	0.971355	−	0.207509i
$567$	−0.819581	−	0.819581i	−0.0344192	−	0.0344192i
$568$	14.0161	+	2.17576i	0.588104	+	0.0912928i
$569$			22.3401i			0.936548i	0.883583	+	0.468274i	$0.155124\pi$
$569$			22.3401i			0.936548i	−0.883583	+	0.468274i	$0.844876\pi$
$570$	−4.87986	+	24.4600i	−0.204395	+	1.02452i
$571$			40.7031i			1.70337i	0.524052	+	0.851686i	$0.324420\pi$
$571$			40.7031i			1.70337i	−0.524052	+	0.851686i	$0.675580\pi$
$572$	1.63682	+	0.624466i	0.0684387	+	0.0261103i
$573$	15.8836	+	15.8836i	0.663545	+	0.663545i
$574$	0.440406	+	2.06155i	0.0183822	+	0.0860474i
$575$	42.6683	+	1.25349i	1.77939	+	0.0522740i
$576$	4.10293	−	12.8970i	0.170956	−	0.537375i
$577$	−5.55759	+	5.55759i	−0.231366	+	0.231366i	−0.813263	−	0.581897i	$-0.802311\pi$
$577$	−5.55759	+	5.55759i	−0.231366	+	0.231366i	0.581897	+	0.813263i	$0.302311\pi$
$578$	24.0375	−	37.0977i	0.999828	−	1.54306i
$579$	−21.1577			−0.879285
$580$	0.475682	+	35.1130i	0.0197516	+	1.45799i
$581$	−4.11778			−0.170834
$582$	8.27867	−	12.7767i	0.343162	−	0.529611i
$583$	−1.91463	+	1.91463i	−0.0792958	+	0.0792958i
$584$	−22.1199	+	16.1752i	−0.915327	+	0.669336i
$585$	1.39616	+	3.51577i	0.0577240	+	0.145359i
$586$	−3.04527	−	14.2550i	−0.125799	−	0.588868i
$587$	−5.52984	−	5.52984i	−0.228241	−	0.228241i	0.583717	−	0.811957i	$-0.301598\pi$
$587$	−5.52984	−	5.52984i	−0.228241	−	0.228241i	−0.811957	+	0.583717i	$0.801598\pi$
$588$	4.73809	−	12.4192i	0.195396	−	0.512160i
$589$			37.6399i			1.55092i
$590$	1.97083	−	1.31525i	0.0811379	−	0.0541479i
$591$			1.25232i			0.0515137i
$592$	−0.708646	−	12.5376i	−0.0291252	−	0.515291i
$593$	25.9213	+	25.9213i	1.06446	+	1.06446i	0.997774	+	0.0666872i	$0.0212429\pi$
$593$	25.9213	+	25.9213i	1.06446	+	1.06446i	0.0666872	+	0.997774i	$0.478757\pi$
$594$	6.50104	−	1.38881i	0.266741	−	0.0569835i
$595$	−6.71189	+	15.5539i	−0.275161	+	0.637649i
$596$	1.83439	−	0.821235i	0.0751395	−	0.0336391i
$597$	3.00887	−	3.00887i	0.123145	−	0.123145i
$598$	−10.1325	−	6.56538i	−0.414350	−	0.268478i
$599$	−12.5925			−0.514515			−0.257257	−	0.966343i	$-0.582819\pi$
$599$	−12.5925			−0.514515			−0.257257	+	0.966343i	$0.582819\pi$
$600$	2.94957	−	15.9045i	0.120416	−	0.649297i
$601$	−8.34802			−0.340523			−0.170261	−	0.985399i	$-0.554461\pi$
$601$	−8.34802			−0.340523			−0.170261	+	0.985399i	$0.554461\pi$
$602$	−7.94746	−	5.14956i	−0.323914	−	0.209880i
$603$	−17.0373	+	17.0373i	−0.693812	+	0.693812i
$604$	29.7264	−	13.3082i	1.20955	−	0.541502i
$605$	9.06567	−	21.0085i	0.368572	−	0.854116i
$606$	−9.85367	+	2.10502i	−0.400278	+	0.0855108i
$607$	−7.84172	−	7.84172i	−0.318286	−	0.318286i	0.529823	−	0.848108i	$-0.322258\pi$
$607$	−7.84172	−	7.84172i	−0.318286	−	0.318286i	−0.848108	+	0.529823i	$0.822258\pi$
$608$	37.6270	−	10.2892i	1.52598	−	0.417282i
$609$		−	9.79477i		−	0.396904i
$610$	−12.6177	+	8.42052i	−0.510877	+	0.340937i
$611$		−	5.38986i		−	0.218050i
$612$	−8.37812	+	21.9603i	−0.338666	+	0.887691i
$613$	0.714872	+	0.714872i	0.0288734	+	0.0288734i	0.721396	−	0.692523i	$-0.243501\pi$
$613$	0.714872	+	0.714872i	0.0288734	+	0.0288734i	−0.692523	+	0.721396i	$0.743501\pi$
$614$	−6.83140	−	31.9779i	−0.275693	−	1.29052i
$615$	1.29022	+	3.24900i	0.0520265	+	0.131012i
$616$	−1.59488	−	2.18103i	−0.0642596	−	0.0878760i
$617$	17.2100	−	17.2100i	0.692847	−	0.692847i	−0.270011	−	0.962857i	$-0.587027\pi$
$617$	17.2100	−	17.2100i	0.692847	−	0.692847i	0.962857	+	0.270011i	$0.0870272\pi$
$618$	11.2673	−	17.3891i	0.453236	−	0.699491i
$619$	0.361036			0.0145113			0.00725564	−	0.999974i	$-0.497690\pi$
$619$	0.361036			0.0145113			0.00725564	+	0.999974i	$0.497690\pi$
$620$	−0.330665	−	24.4084i	−0.0132798	−	0.980266i
$621$	−45.8146			−1.83847
$622$	16.7046	−	25.7806i	0.669792	−	1.03371i
$623$	−2.84403	+	2.84403i	−0.113944	+	0.113944i
$624$	−3.04741	+	3.41254i	−0.121994	+	0.136611i
$625$	−1.46761	+	24.9569i	−0.0587042	+	0.998275i
$626$	−0.490001	−	2.29370i	−0.0195844	−	0.0916748i
$627$	4.88533	+	4.88533i	0.195101	+	0.195101i
$628$	−0.453372	−	0.172967i	−0.0180915	−	0.00690215i
$629$			21.8086i			0.869566i
$630$	1.14147	−	5.72153i	0.0454772	−	0.227951i
$631$			7.91135i			0.314946i	0.987523	+	0.157473i	$0.0503347\pi$
$631$			7.91135i			0.314946i	−0.987523	+	0.157473i	$0.949665\pi$
$632$	−0.707021	+	4.55460i	−0.0281238	+	0.181172i
$633$	−8.16987	−	8.16987i	−0.324723	−	0.324723i
$634$	12.6171	−	2.69536i	0.501087	−	0.107047i
$635$	24.8733	−	9.87751i	0.987068	−	0.391977i
$636$	−2.88940	−	6.45404i	−0.114572	−	0.255919i
$637$	4.10875	−	4.10875i	0.162795	−	0.162795i
$638$	8.16329	+	5.28941i	0.323188	+	0.209410i
$639$	8.48374			0.335612
$640$	−24.3097	+	7.00281i	−0.960925	+	0.276810i
$641$	−12.3758			−0.488813			−0.244407	−	0.969673i	$-0.578593\pi$
$641$	−12.3758			−0.488813			−0.244407	+	0.969673i	$0.578593\pi$
$642$	13.4015	+	8.68350i	0.528914	+	0.342710i
$643$	1.50067	−	1.50067i	0.0591807	−	0.0591807i	−0.676897	−	0.736078i	$-0.736676\pi$
$643$	1.50067	−	1.50067i	0.0591807	−	0.0591807i	0.736078	+	0.676897i	$0.236676\pi$
$644$	7.60878	+	16.9957i	0.299828	+	0.669725i
$645$	−14.4188	−	6.22206i	−0.567740	−	0.244994i
$646$	−66.2506	+	14.1530i	−2.60660	+	0.556844i
$647$	−15.1830	−	15.1830i	−0.596906	−	0.596906i	0.342582	−	0.939488i	$-0.388699\pi$
$647$	−15.1830	−	15.1830i	−0.596906	−	0.596906i	−0.939488	+	0.342582i	$0.888699\pi$
$648$	−0.461115	+	2.97048i	−0.0181143	+	0.116692i
$649$		−	0.656320i		−	0.0257628i
$650$	4.01770	−	5.81877i	0.157587	−	0.228231i
$651$			6.80873i			0.266855i
$652$	22.5345	+	8.59721i	0.882520	+	0.336693i
$653$	−11.8664	−	11.8664i	−0.464369	−	0.464369i	0.435716	−	0.900084i	$-0.356495\pi$
$653$	−11.8664	−	11.8664i	−0.464369	−	0.464369i	−0.900084	+	0.435716i	$0.856495\pi$
$654$	−1.98517	−	9.29263i	−0.0776263	−	0.363370i
$655$	31.8270	+	13.7341i	1.24358	+	0.536637i
$656$	3.64166	−	4.07798i	0.142183	−	0.159219i
$657$	−11.5897	+	11.5897i	−0.452157	+	0.452157i
$658$	−4.52032	+	6.97633i	−0.176220	+	0.271966i
$659$	46.7405			1.82075			0.910376	−	0.413782i	$-0.135792\pi$
$659$	46.7405			1.82075			0.910376	+	0.413782i	$0.135792\pi$
$660$	−3.21091	−	3.12508i	−0.124985	−	0.121644i
$661$	23.7102			0.922219			0.461109	−	0.887343i	$-0.347452\pi$
$661$	23.7102			0.922219			0.461109	+	0.887343i	$0.347452\pi$
$662$	25.1801	−	38.8612i	0.978653	−	1.51038i
$663$	5.61842	−	5.61842i	0.218201	−	0.218201i
$664$	6.30384	+	8.62059i	0.244636	+	0.334544i
$665$	15.6288	−	6.20639i	0.606059	−	0.240674i
$666$	−1.56915	−	7.34521i	−0.0608032	−	0.284621i
$667$	−47.4024	−	47.4024i	−1.83543	−	1.83543i
$668$	−8.88846	+	23.2979i	−0.343905	+	0.901425i
$669$		−	17.7509i		−	0.686288i
$670$	44.1679	+	8.81168i	1.70636	+	0.340425i
$671$			4.20192i			0.162213i
$672$	6.80640	−	1.86123i	0.262563	−	0.0717984i
$673$	1.49025	+	1.49025i	0.0574448	+	0.0574448i	0.735246	−	0.677801i	$-0.237067\pi$
$673$	1.49025	+	1.49025i	0.0574448	+	0.0574448i	−0.677801	+	0.735246i	$0.737067\pi$
$674$	33.3587	−	7.12637i	1.28493	−	0.274498i
$675$	0.787912	−	26.8203i	0.0303268	−	1.03231i
$676$	−1.82542	+	0.817219i	−0.0702084	+	0.0314315i
$677$	21.9052	−	21.9052i	0.841884	−	0.841884i	−0.147219	−	0.989104i	$-0.547032\pi$
$677$	21.9052	−	21.9052i	0.841884	−	0.841884i	0.989104	+	0.147219i	$0.0470323\pi$
$678$	15.9244	+	10.3182i	0.611571	+	0.396268i
$679$	−10.2643			−0.393909
$680$	42.8374	−	9.75985i	1.64274	−	0.374273i
$681$	−8.26205			−0.316602
$682$	−5.67462	−	3.67688i	−0.217293	−	0.140795i
$683$	−21.9173	+	21.9173i	−0.838644	+	0.838644i	−0.988680	−	0.150037i	$-0.952061\pi$
$683$	−21.9173	+	21.9173i	−0.838644	+	0.838644i	0.150037	+	0.988680i	$0.452061\pi$
$684$	21.2951	−	9.53357i	0.814239	−	0.364525i
$685$	3.00502	+	7.56718i	0.114816	+	0.289127i
$686$	−19.3219	+	4.12771i	−0.737714	+	0.157597i
$687$	0.955494	+	0.955494i	0.0364544	+	0.0364544i
$688$	1.38600	+	24.5214i	0.0528406	+	0.934871i
$689$		−	3.09116i		−	0.117764i
$690$	17.1411	+	25.6851i	0.652550	+	0.977815i
$691$			1.94770i			0.0740939i	0.999314	+	0.0370470i	$0.0117951\pi$
$691$			1.94770i			0.0740939i	−0.999314	+	0.0370470i	$0.988205\pi$
$692$	−0.922105	+	2.41697i	−0.0350532	+	0.0918794i
$693$	−1.14275	−	1.14275i	−0.0434094	−	0.0434094i
$694$	5.12932	+	24.0104i	0.194706	+	0.911424i
$695$	−3.74450	+	8.67739i	−0.142037	+	0.329152i
$696$	−20.5054	+	14.9946i	−0.777256	+	0.568371i
$697$	−6.71400	+	6.71400i	−0.254311	+	0.254311i
$698$	−23.2586	+	35.8956i	−0.880349	+	1.35867i
$699$	−19.5521			−0.739529
$700$	−10.0803	+	4.16197i	−0.381000	+	0.157308i
$701$	16.3253			0.616597			0.308299	−	0.951290i	$-0.400240\pi$
$701$	16.3253			0.616597			0.308299	+	0.951290i	$0.400240\pi$
$702$	−4.12685	+	6.36907i	−0.155758	+	0.240385i
$703$	15.3079	−	15.3079i	0.577348	−	0.577348i
$704$	−2.12441	+	6.67779i	−0.0800668	+	0.251679i
$705$	−5.46177	+	12.6569i	−0.205702	+	0.476687i
$706$	−6.56404	−	30.7264i	−0.247041	−	1.15640i
$707$	4.80359	+	4.80359i	0.180657	+	0.180657i
$708$	1.60143	+	0.610967i	0.0601855	+	0.0229615i
$709$			9.91483i			0.372359i	0.982516	+	0.186180i	$0.0596106\pi$
$709$			9.91483i			0.372359i	−0.982516	+	0.186180i	$0.940389\pi$
$710$	−8.80284	−	13.1906i	−0.330365	−	0.495035i
$711$			2.75682i			0.103389i
$712$	10.3079	+	1.60012i	0.386304	+	0.0599670i
$713$	32.9512	+	32.9512i	1.23403	+	1.23403i
$714$	−11.9842	+	2.56016i	−0.448496	+	0.0958116i
$715$	−0.722900	−	1.82039i	−0.0270349	−	0.0680788i
$716$	−3.96779	−	8.86283i	−0.148283	−	0.331220i
$717$	−15.4096	+	15.4096i	−0.575481	+	0.575481i
$718$	42.3580	+	27.4459i	1.58079	+	1.02427i
$719$	−5.89066			−0.219685			−0.109842	−	0.993949i	$-0.535035\pi$
$719$	−5.89066			−0.219685			−0.109842	+	0.993949i	$0.535035\pi$
$720$	−13.7255	+	6.36933i	−0.511520	+	0.237371i
$721$	−13.9697			−0.520260
$722$	33.8868	+	21.9570i	1.26114	+	0.817153i
$723$	−0.700969	+	0.700969i	−0.0260693	+	0.0260693i
$724$	−13.5240	−	30.2085i	−0.502615	−	1.12269i
$725$	28.5650	−	26.9346i	1.06088	−	1.00033i
$726$	16.1869	−	3.45798i	0.600751	−	0.128338i
$727$	−33.8770	−	33.8770i	−1.25643	−	1.25643i	−0.952786	−	0.303642i	$-0.901797\pi$
$727$	−33.8770	−	33.8770i	−1.25643	−	1.25643i	−0.303642	−	0.952786i	$-0.598203\pi$
$728$	3.04810	+	0.473164i	0.112970	+	0.0175366i
$729$			20.2120i			0.748594i
$730$	30.0454	+	5.99418i	1.11203	+	0.221855i
$731$		−	42.6540i		−	1.57762i
$732$	−10.2527	−	3.91155i	−0.378952	−	0.144575i
$733$	24.2491	+	24.2491i	0.895661	+	0.895661i	0.995049	−	0.0993880i	$-0.0316885\pi$
$733$	24.2491	+	24.2491i	0.895661	+	0.895661i	−0.0993880	+	0.995049i	$0.531689\pi$
$734$	−1.84297	−	8.62697i	−0.0680252	−	0.318427i
$735$	−13.8121	+	5.48495i	−0.509467	+	0.202315i
$736$	23.9325	−	41.9475i	0.882163	−	1.54621i
$737$	8.82155	−	8.82155i	0.324946	−	0.324946i
$738$	1.77822	−	2.74437i	0.0654571	−	0.101022i
$739$	−11.3816			−0.418679			−0.209339	−	0.977843i	$-0.567131\pi$
$739$	−11.3816			−0.418679			−0.209339	+	0.977843i	$0.567131\pi$
$740$	−9.79225	+	10.0612i	−0.359970	+	0.369858i
$741$	−7.88735			−0.289749
$742$	−2.59247	+	4.00103i	−0.0951726	+	0.146882i
$743$	−13.5560	+	13.5560i	−0.497323	+	0.497323i	−0.910604	−	0.413281i	$-0.864383\pi$
$743$	−13.5560	+	13.5560i	−0.497323	+	0.497323i	0.413281	+	0.910604i	$0.364383\pi$
$744$	14.2541	−	10.4234i	0.522581	−	0.382139i
$745$	−2.06316	−	0.890303i	−0.0755883	−	0.0326182i
$746$	6.73646	+	31.5335i	0.246639	+	1.15452i
$747$	4.51676	+	4.51676i	0.165259	+	0.165259i
$748$	4.33801	−	11.3706i	0.158613	−	0.415749i
$749$		−	10.7663i		−	0.393391i
$750$	−15.3311	+	9.59284i	−0.559813	+	0.350281i
$751$			0.486430i			0.0177501i	0.999961	+	0.00887505i	$0.00282505\pi$
$751$			0.486430i			0.0177501i	−0.999961	+	0.00887505i	$0.997175\pi$
$752$	21.5251	−	1.21664i	0.784939	−	0.0443661i
$753$	9.70149	+	9.70149i	0.353542	+	0.353542i
$754$	−10.8597	+	2.31994i	−0.395486	+	0.0844871i
$755$	−33.4336	−	14.4274i	−1.21677	−	0.525068i
$756$	10.6831	−	4.78271i	0.388541	−	0.173945i
$757$	22.6809	−	22.6809i	0.824350	−	0.824350i	−0.162379	−	0.986729i	$-0.551917\pi$
$757$	22.6809	−	22.6809i	0.824350	−	0.824350i	0.986729	+	0.162379i	$0.0519166\pi$
$758$	−39.5255	−	25.6106i	−1.43563	−	0.930219i
$759$	8.55356			0.310475
$760$	−36.9190	−	23.2177i	−1.33919	−	0.842196i
$761$	41.2722			1.49612			0.748058	−	0.663633i	$-0.230986\pi$
$761$	41.2722			1.49612			0.748058	+	0.663633i	$0.230986\pi$
$762$	16.2476	+	10.5276i	0.588589	+	0.381376i
$763$	−4.53008	+	4.53008i	−0.164000	+	0.164000i
$764$	−35.8491	+	16.0492i	−1.29697	+	0.580640i
$765$	24.4232	−	9.69875i	0.883022	−	0.350659i
$766$	3.73358	−	0.797600i	0.134900	−	0.0288184i
$767$	0.529814	+	0.529814i	0.0191305	+	0.0191305i
$768$	−14.3163	−	11.3999i	−0.516595	−	0.411359i
$769$		−	35.2742i		−	1.27202i	−0.771681	−	0.636010i	$-0.780584\pi$
$769$		−	35.2742i		−	1.27202i	0.771681	−	0.636010i	$-0.219416\pi$
$770$	−0.591028	+	2.96249i	−0.0212992	+	0.106761i
$771$			15.4491i			0.556387i
$772$	13.1872	−	34.5656i	0.474619	−	1.24404i

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)

\(f(q)\)	\(=\)	\(q+(1.18685 + 0.769019i) q^{2} +(0.808783 - 0.808783i) q^{3} +(0.817219 + 1.82542i) q^{4} +(0.885949 - 2.05307i) q^{5} +(1.58187 - 0.337933i) q^{6} +(-0.771151 - 0.771151i) q^{7} +(-0.433867 + 2.79495i) q^{8} +1.69174i q^{9} +O(q^{10})\)	\(q+(1.18685 + 0.769019i) q^{2} +(0.808783 - 0.808783i) q^{3} +(0.817219 + 1.82542i) q^{4} +(0.885949 - 2.05307i) q^{5} +(1.58187 - 0.337933i) q^{6} +(-0.771151 - 0.771151i) q^{7} +(-0.433867 + 2.79495i) q^{8} +1.69174i q^{9} +(2.63034 - 1.75537i) q^{10} -0.875946i q^{11} +(2.13732 + 0.815415i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.322210 - 1.50827i) q^{14} +(-0.943948 - 2.37703i) q^{15} +(-2.66431 + 2.98353i) q^{16} +(4.91209 - 4.91209i) q^{17} +(-1.30098 + 2.00784i) q^{18} -6.89579 q^{19} +(4.47173 - 0.0605793i) q^{20} -1.24739 q^{21} +(0.673619 - 1.03962i) q^{22} +(-6.03681 + 6.03681i) q^{23} +(1.90961 + 2.61142i) q^{24} +(-3.43019 - 3.63783i) q^{25} +(0.295450 + 1.38301i) q^{26} +(3.79460 + 3.79460i) q^{27} +(0.777475 - 2.03787i) q^{28} +7.85222i q^{29} +(0.707658 - 3.54709i) q^{30} -5.45839i q^{31} +(-5.45652 + 1.49210i) q^{32} +(-0.708451 - 0.708451i) q^{33} +(9.60741 - 2.05242i) q^{34} +(-2.26643 + 0.900026i) q^{35} +(-3.08813 + 1.38252i) q^{36} +(-2.21989 + 2.21989i) q^{37} +(-8.18426 - 5.30299i) q^{38} +1.14379 q^{39} +(5.35385 + 3.36694i) q^{40} -1.36683 q^{41} +(-1.48046 - 0.959266i) q^{42} +(4.34174 - 4.34174i) q^{43} +(1.59897 - 0.715840i) q^{44} +(3.47326 + 1.49879i) q^{45} +(-11.8072 + 2.52236i) q^{46} +(-3.81120 - 3.81120i) q^{47} +(0.258185 + 4.56788i) q^{48} -5.81065i q^{49} +(-1.27355 - 6.95543i) q^{50} -7.94564i q^{51} +(-0.712905 + 1.86863i) q^{52} +(-2.18578 - 2.18578i) q^{53} +(1.58550 + 7.42174i) q^{54} +(-1.79838 - 0.776043i) q^{55} +(2.48991 - 1.82075i) q^{56} +(-5.57720 + 5.57720i) q^{57} +(-6.03851 + 9.31940i) q^{58} +0.749270 q^{59} +(3.56766 - 3.66565i) q^{60} -4.79700 q^{61} +(4.19761 - 6.47828i) q^{62} +(1.30459 - 1.30459i) q^{63} +(-7.62352 - 2.42528i) q^{64} +(2.07820 - 0.825279i) q^{65} +(-0.296011 - 1.38564i) q^{66} +(10.0709 + 10.0709i) q^{67} +(12.9809 + 4.95237i) q^{68} +9.76494i q^{69} +(-3.38204 - 0.674731i) q^{70} -5.01480i q^{71} +(-4.72833 - 0.733990i) q^{72} +(6.85076 + 6.85076i) q^{73} +(-4.34181 + 0.927534i) q^{74} +(-5.71650 - 0.167936i) q^{75} +(-5.63537 - 12.5877i) q^{76} +(-0.675487 + 0.675487i) q^{77} +(1.35751 + 0.879598i) q^{78} +1.62958 q^{79} +(3.76496 + 8.11327i) q^{80} +1.06280 q^{81} +(-1.62222 - 1.05112i) q^{82} +(2.66989 - 2.66989i) q^{83} +(-1.01939 - 2.27701i) q^{84} +(-5.73301 - 14.4367i) q^{85} +(8.49186 - 1.81410i) q^{86} +(6.35074 + 6.35074i) q^{87} +(2.44823 + 0.380044i) q^{88} -3.68804i q^{89} +(2.96963 + 4.44984i) q^{90} -1.09057i q^{91} +(-15.9531 - 6.08631i) q^{92} +(-4.41465 - 4.41465i) q^{93} +(-1.59243 - 7.45421i) q^{94} +(-6.10932 + 14.1575i) q^{95} +(-3.20636 + 5.61993i) q^{96} +(6.65520 - 6.65520i) q^{97} +(4.46850 - 6.89636i) q^{98} +1.48187 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

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