LMFDB - Embedded newform 260.2.o.a.27.12

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			27.12
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.769019 + 1.18685i) q^{2} +(-0.808783 - 0.808783i) q^{3} +(-0.817219 - 1.82542i) q^{4} +(0.885949 + 2.05307i) q^{5} +(1.58187 - 0.337933i) q^{6} +(0.771151 - 0.771151i) q^{7} +(2.79495 + 0.433867i) q^{8} -1.69174i q^{9} +O(q^{10})$	\(q+(-0.769019 + 1.18685i) 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} +(2.79495 + 0.433867i) q^{8} -1.69174i q^{9} +(-3.11799 - 0.527363i) q^{10} -0.875946i q^{11} +(-0.815415 + 2.13732i) 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} +(2.00784 + 1.30098i) q^{18} +6.89579 q^{19} +(3.02370 - 3.29503i) q^{20} -1.24739 q^{21} +(1.03962 + 0.673619i) 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} +(-2.03787 - 0.777475i) q^{28} -7.85222i q^{29} +(2.09526 + 2.94830i) q^{30} -5.45839i q^{31} +(-1.49210 - 5.45652i) 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} +(-5.30299 + 8.18426i) q^{38} -1.14379 q^{39} +(1.58543 + 6.12262i) q^{40} -1.36683 q^{41} +(0.959266 - 1.48046i) 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} +(4.56788 - 0.258185i) q^{48} +5.81065i q^{49} +(-1.67967 - 6.86868i) q^{50} -7.94564i q^{51} +(-1.86863 - 0.712905i) 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} +(9.31940 + 6.03851i) q^{58} -0.749270 q^{59} +(-5.11049 + 0.219453i) q^{60} -4.79700 q^{61} +(6.47828 + 4.19761i) 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} +(4.95237 - 12.9809i) q^{68} -9.76494i q^{69} +(-2.81112 + 1.99777i) q^{70} -5.01480i q^{71} +(0.733990 - 4.72833i) 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} +(0.879598 - 1.35751i) q^{78} -1.62958 q^{79} +(-8.48584 - 2.82675i) q^{80} +1.06280 q^{81} +(1.05112 - 1.62222i) 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} +(0.380044 - 2.44823i) q^{88} +3.68804i q^{89} +(-0.892160 + 5.27483i) q^{90} -1.09057i q^{91} +(6.08631 - 15.9531i) 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} +(-6.89636 - 4.46850i) 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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.769019	+	1.18685i	−0.543779	+	0.839229i
$2$	−0.769019	+	1.18685i	−0.543779	+	0.839229i
$3$	−0.808783	−	0.808783i	−0.466951	−	0.466951i	0.433974	−	0.900925i	$-0.357111\pi$
$3$	−0.808783	−	0.808783i	−0.466951	−	0.466951i	−0.900925	+	0.433974i	$0.857111\pi$
$4$	−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	$-0.683923\pi$
$7$	0.771151	−	0.771151i	0.291468	−	0.291468i	0.837660	+	0.546192i	$0.183923\pi$
$8$	2.79495	+	0.433867i	0.988165	+	0.153395i
$9$		−	1.69174i		−	0.563913i
$10$	−3.11799	−	0.527363i	−0.985996	−	0.166767i
$11$		−	0.875946i		−	0.264108i	−0.991243	−	0.132054i	$-0.957843\pi$
$11$		−	0.875946i		−	0.264108i	0.991243	−	0.132054i	$-0.0421572\pi$
$12$	−0.815415	+	2.13732i	−0.235390	+	0.616991i
$13$	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	0.976686	+	0.214671i	$0.0688681\pi$
$17$	4.91209	+	4.91209i	1.19136	+	1.19136i	0.214671	+	0.976686i	$0.431132\pi$
$18$	2.00784	+	1.30098i	0.473252	+	0.306644i
$19$	6.89579			1.58200			0.791001	−	0.611815i	$-0.209560\pi$
$19$	6.89579			1.58200			0.791001	+	0.611815i	$0.209560\pi$
$20$	3.02370	−	3.29503i	0.676119	−	0.736792i
$21$	−1.24739			−0.272202
$22$	1.03962	+	0.673619i	0.221647	+	0.143616i
$23$	6.03681	+	6.03681i	1.25876	+	1.25876i	0.951685	+	0.307077i	$0.0993509\pi$
$23$	6.03681	+	6.03681i	1.25876	+	1.25876i	0.307077	+	0.951685i	$0.400649\pi$
$24$	−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
$28$	−2.03787	−	0.777475i	−0.385122	−	0.146929i
$29$		−	7.85222i		−	1.45812i	−0.684449	−	0.729060i	$-0.739957\pi$
$29$		−	7.85222i		−	1.45812i	0.684449	−	0.729060i	$-0.260043\pi$
$30$	2.09526	+	2.94830i	0.382540	+	0.538284i
$31$		−	5.45839i		−	0.980356i	−0.871622	−	0.490178i	$-0.836932\pi$
$31$		−	5.45839i		−	0.980356i	0.871622	−	0.490178i	$-0.163068\pi$
$32$	−1.49210	−	5.45652i	−0.263768	−	0.964586i
$33$	−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	0.500683	−	0.865631i	$-0.333082\pi$
$37$	−2.21989	−	2.21989i	−0.364947	−	0.364947i	−0.865631	+	0.500683i	$0.833082\pi$
$38$	−5.30299	+	8.18426i	−0.860259	+	1.32766i
$39$	−1.14379			−0.183153
$40$	1.58543	+	6.12262i	0.250678	+	0.968071i
$41$	−1.36683			−0.213463			−0.106732	−	0.994288i	$-0.534039\pi$
$41$	−1.36683			−0.213463			−0.106732	+	0.994288i	$0.534039\pi$
$42$	0.959266	−	1.48046i	0.148018	−	0.228440i
$43$	−4.34174	−	4.34174i	−0.662109	−	0.662109i	0.293768	−	0.955877i	$-0.405091\pi$
$43$	−4.34174	−	4.34174i	−0.662109	−	0.662109i	−0.955877	+	0.293768i	$0.905091\pi$
$44$	−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	$-0.621404\pi$
$47$	3.81120	−	3.81120i	0.555921	−	0.555921i	0.928144	+	0.372222i	$0.121404\pi$
$48$	4.56788	−	0.258185i	0.659317	−	0.0372657i
$49$			5.81065i			0.830093i
$50$	−1.67967	−	6.86868i	−0.237541	−	0.971377i
$51$		−	7.94564i		−	1.11261i
$52$	−1.86863	−	0.712905i	−0.259132	−	0.0988621i
$53$	−2.18578	+	2.18578i	−0.300240	+	0.300240i	−0.841108	−	0.540867i	$-0.818096\pi$
$53$	−2.18578	+	2.18578i	−0.300240	+	0.300240i	0.540867	+	0.841108i	$0.318096\pi$
$54$	−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
$58$	9.31940	+	6.03851i	1.22370	+	0.792895i
$59$	−0.749270			−0.0975467			−0.0487733	−	0.998810i	$-0.515531\pi$
$59$	−0.749270			−0.0975467			−0.0487733	+	0.998810i	$0.515531\pi$
$60$	−5.11049	+	0.219453i	−0.659761	+	0.0283313i
$61$	−4.79700			−0.614193			−0.307097	−	0.951678i	$-0.599357\pi$
$61$	−4.79700			−0.614193			−0.307097	+	0.951678i	$0.599357\pi$
$62$	6.47828	+	4.19761i	0.822742	+	0.533096i
$63$	−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	−0.266526	+	0.963828i	$0.585876\pi$
$67$	−10.0709	+	10.0709i	−1.23035	+	1.23035i	−0.963828	+	0.266526i	$0.914124\pi$
$68$	4.95237	−	12.9809i	0.600563	−	1.57416i
$69$		−	9.76494i		−	1.17556i
$70$	−2.81112	+	1.99777i	−0.335993	+	0.238779i
$71$		−	5.01480i		−	0.595148i	−0.954699	−	0.297574i	$-0.903823\pi$
$71$		−	5.01480i		−	0.595148i	0.954699	−	0.297574i	$-0.0961775\pi$
$72$	0.733990	−	4.72833i	0.0865016	−	0.557239i
$73$	6.85076	−	6.85076i	0.801821	−	0.801821i	−0.181559	−	0.983380i	$-0.558114\pi$
$73$	6.85076	−	6.85076i	0.801821	−	0.801821i	0.983380	+	0.181559i	$0.0581144\pi$
$74$	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
$78$	0.879598	−	1.35751i	0.0995949	−	0.153708i
$79$	−1.62958			−0.183342			−0.0916710	−	0.995789i	$-0.529221\pi$
$79$	−1.62958			−0.183342			−0.0916710	+	0.995789i	$0.529221\pi$
$80$	−8.48584	−	2.82675i	−0.948746	−	0.316040i
$81$	1.06280			0.118089
$82$	1.05112	−	1.62222i	0.116077	−	0.179144i
$83$	−2.66989	−	2.66989i	−0.293058	−	0.293058i	0.545229	−	0.838287i	$-0.316443\pi$
$83$	−2.66989	−	2.66989i	−0.293058	−	0.293058i	−0.838287	+	0.545229i	$0.816443\pi$
$84$	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
$88$	0.380044	−	2.44823i	0.0405129	−	0.260982i
$89$			3.68804i			0.390931i	0.980711	+	0.195466i	$0.0626218\pi$
$89$			3.68804i			0.390931i	−0.980711	+	0.195466i	$0.937378\pi$
$90$	−0.892160	+	5.27483i	−0.0940419	+	0.556016i
$91$		−	1.09057i		−	0.114323i
$92$	6.08631	−	15.9531i	0.634542	−	1.66323i
$93$	−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	0.959032	−	0.283299i	$-0.0914288\pi$
$97$	6.65520	+	6.65520i	0.675733	+	0.675733i	−0.283299	+	0.959032i	$0.591429\pi$
$98$	−6.89636	−	4.46850i	−0.696638	−	0.451387i
$99$	−1.48187			−0.148934
$100$	9.44378	+	3.28863i	0.944378	+	0.328863i
$101$	−6.22911			−0.619820			−0.309910	−	0.950766i	$-0.600299\pi$
$101$	−6.22911			−0.619820			−0.309910	+	0.950766i	$0.600299\pi$
$102$	9.43027	+	6.11035i	0.933736	+	0.605015i
$103$	−9.05772	−	9.05772i	−0.892483	−	0.892483i	0.102273	−	0.994756i	$-0.467388\pi$
$103$	−9.05772	−	9.05772i	−0.892483	−	0.892483i	−0.994756	+	0.102273i	$0.967388\pi$
$104$	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	$-0.908344\pi$
$107$	−6.98064	+	6.98064i	−0.674844	+	0.674844i	0.283985	+	0.958829i	$0.408344\pi$
$108$	10.0278	+	3.82572i	0.964921	+	0.368130i
$109$			5.87444i			0.562670i	0.959610	+	0.281335i	$0.0907772\pi$
$109$			5.87444i			0.562670i	−0.959610	+	0.281335i	$0.909223\pi$
$110$	−0.461941	+	2.73119i	−0.0440444	+	0.260409i
$111$			3.59082i			0.340825i
$112$	0.246171	+	4.35534i	0.0232610	+	0.411541i
$113$	8.29477	−	8.29477i	0.780307	−	0.780307i	−0.199576	−	0.979882i	$-0.563956\pi$
$113$	8.29477	−	8.29477i	0.780307	−	0.780307i	0.979882	+	0.199576i	$0.0639564\pi$
$114$	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
$118$	0.576203	−	0.889270i	0.0530438	−	0.0818640i
$119$	7.57593			0.694485
$120$	3.66960	−	6.23414i	0.334987	−	0.569096i
$121$	10.2327			0.930247
$122$	3.68899	−	5.69332i	0.333985	−	0.515449i
$123$	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	$-0.928193\pi$
$127$	−8.46315	+	8.46315i	−0.750983	+	0.750983i	0.223680	+	0.974663i	$0.428193\pi$
$128$	−8.74107	+	7.18288i	−0.772609	+	0.634883i
$129$			7.02305i			0.618345i
$130$	−2.57766	+	1.83185i	−0.226075	+	0.160664i
$131$			15.5022i			1.35443i	0.735785	+	0.677215i	$0.236813\pi$
$131$			15.5022i			1.35443i	−0.735785	+	0.677215i	$0.763187\pi$
$132$	1.87218	+	0.714260i	0.162952	+	0.0621683i
$133$	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	0.588513	−	0.808487i	$-0.299713\pi$
$137$	−2.57473	−	2.57473i	−0.219974	−	0.219974i	−0.808487	+	0.588513i	$0.799713\pi$
$138$	11.5895	+	7.50943i	0.986564	+	0.639245i
$139$	4.22654			0.358491			0.179245	−	0.983804i	$-0.442634\pi$
$139$	4.22654			0.358491			0.179245	+	0.983804i	$0.442634\pi$
$140$	−0.209242	−	4.87270i	−0.0176842	−	0.411818i
$141$	−6.16488			−0.519176
$142$	5.95181	+	3.85648i	0.499465	+	0.323629i
$143$	−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
$148$	−2.23809	+	5.86636i	−0.183970	+	0.482212i
$149$			1.00491i			0.0823258i	0.999152	+	0.0411629i	$0.0131063\pi$
$149$			1.00491i			0.0823258i	−0.999152	+	0.0411629i	$0.986894\pi$
$150$	−4.19678	+	6.91376i	−0.342666	+	0.564506i
$151$		−	16.2847i		−	1.32523i	−0.748960	−	0.662615i	$-0.769446\pi$
$151$		−	16.2847i		−	1.32523i	0.748960	−	0.662615i	$-0.230554\pi$
$152$	19.2734	+	2.99186i	1.56328	+	0.242672i
$153$	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	0.700228	−	0.713920i	$-0.253082\pi$
$157$	−0.171561	−	0.171561i	−0.0136920	−	0.0136920i	−0.713920	+	0.700228i	$0.753082\pi$
$158$	1.25318	−	1.93406i	0.0996975	−	0.153866i
$159$	3.53565			0.280395
$160$	9.88070	−	7.89758i	0.781138	−	0.624359i
$161$	9.31058			0.733777
$162$	−0.817316	+	1.26139i	−0.0642144	+	0.0991038i
$163$	−8.52729	−	8.52729i	−0.667909	−	0.667909i	0.289323	−	0.957232i	$-0.406570\pi$
$163$	−8.52729	−	8.52729i	−0.667909	−	0.667909i	−0.957232	+	0.289323i	$0.906570\pi$
$164$	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	$-0.910235\pi$
$167$	−8.81617	+	8.81617i	−0.682216	+	0.682216i	0.278283	+	0.960499i	$0.410235\pi$
$168$	−3.48639	−	0.541201i	−0.268981	−	0.0417546i
$169$		−	1.00000i		−	0.0769231i
$170$	−12.7254	−	17.9063i	−0.975996	−	1.37335i
$171$		−	11.6659i		−	0.892112i
$172$	−4.37734	+	11.4736i	−0.333769	+	0.874857i
$173$	0.914606	−	0.914606i	0.0695362	−	0.0695362i	−0.671483	−	0.741020i	$-0.734343\pi$
$173$	0.914606	−	0.914606i	0.0695362	−	0.0695362i	0.741020	+	0.671483i	$0.234343\pi$
$174$	−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
$178$	−4.37714	−	2.83617i	−0.328081	−	0.212580i
$179$	4.85523			0.362897			0.181449	−	0.983400i	$-0.441921\pi$
$179$	4.85523			0.362897			0.181449	+	0.983400i	$0.441921\pi$
$180$	−5.57434	−	5.11531i	−0.415487	−	0.381272i
$181$	−16.5488			−1.23006			−0.615031	−	0.788503i	$-0.710857\pi$
$181$	−16.5488			−1.23006			−0.615031	+	0.788503i	$0.710857\pi$
$182$	1.29434	+	0.838671i	0.0959432	+	0.0621664i
$183$	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
$188$	−10.0716	−	3.84246i	−0.734549	−	0.280240i
$189$			5.85242i			0.425701i
$190$	−21.5010	−	3.63658i	−1.55985	−	0.263825i
$191$			19.6388i			1.42102i	0.703690	+	0.710508i	$0.251535\pi$
$191$			19.6388i			1.42102i	−0.703690	+	0.710508i	$0.748465\pi$
$192$	−4.20425	−	8.12730i	−0.303416	−	0.586537i
$193$	−13.0800	+	13.0800i	−0.941517	+	0.941517i	−0.998382	−	0.0568651i	$-0.981890\pi$
$193$	−13.0800	+	13.0800i	−0.941517	+	0.941517i	0.0568651	+	0.998382i	$0.481890\pi$
$194$	−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	0.678989	−	0.734149i	$-0.262418\pi$
$197$	−0.774201	−	0.774201i	−0.0551596	−	0.0551596i	−0.734149	+	0.678989i	$0.762418\pi$
$198$	1.13959	−	1.75876i	0.0809870	−	0.124989i
$199$	−3.72024			−0.263721			−0.131860	−	0.991268i	$-0.542095\pi$
$199$	−3.72024			−0.263721			−0.131860	+	0.991268i	$0.542095\pi$
$200$	−11.1656	+	8.67931i	−0.789524	+	0.613720i
$201$	16.2903			1.14903
$202$	4.79031	−	7.39301i	0.337045	−	0.520171i
$203$	−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
$208$	0.225727	+	3.99363i	0.0156513	+	0.276908i
$209$		−	6.04034i		−	0.417819i
$210$	3.88935	+	0.657826i	0.268391	+	0.0453943i
$211$		−	10.1014i		−	0.695411i	−0.937604	−	0.347706i	$-0.886961\pi$
$211$		−	10.1014i		−	0.695411i	0.937604	−	0.347706i	$-0.113039\pi$
$212$	5.77623	+	2.20371i	0.396713	+	0.151351i
$213$	−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
$218$	−6.97208	−	4.51756i	−0.472209	−	0.305968i
$219$	−11.0816			−0.748822
$220$	−2.88627	−	2.64860i	−0.194592	−	0.178568i
$221$	6.94675			0.467289
$222$	−4.26176	−	2.76141i	−0.286030	−	0.185334i
$223$	−10.9738	−	10.9738i	−0.734860	−	0.734860i	0.236718	−	0.971578i	$-0.423928\pi$
$223$	−10.9738	−	10.9738i	−0.734860	−	0.734860i	−0.971578	+	0.236718i	$0.923928\pi$
$224$	−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	$-0.672946\pi$
$227$	5.10770	−	5.10770i	0.339010	−	0.339010i	0.855995	+	0.516985i	$0.172946\pi$
$228$	−5.62293	+	14.7385i	−0.372388	+	0.976082i
$229$		−	1.18140i		−	0.0780689i	−0.999238	−	0.0390345i	$-0.987572\pi$
$229$		−	1.18140i		−	0.0780689i	0.999238	−	0.0390345i	$-0.0124282\pi$
$230$	−15.6391	−	22.0063i	−1.03121	−	1.45105i
$231$			1.09265i			0.0718908i
$232$	3.40682	−	21.9466i	0.223669	−	1.44086i
$233$	−12.0874	+	12.0874i	−0.791870	+	0.791870i	−0.981798	−	0.189928i	$-0.939175\pi$
$233$	−12.0874	+	12.0874i	−0.791870	+	0.791870i	0.189928	+	0.981798i	$0.439175\pi$
$234$	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
$238$	−5.82604	+	8.99149i	−0.377646	+	0.582831i
$239$	19.0528			1.23242			0.616211	−	0.787581i	$-0.288667\pi$
$239$	19.0528			1.23242			0.616211	+	0.787581i	$0.288667\pi$
$240$	4.57698	+	9.14943i	0.295443	+	0.590593i
$241$	−0.866695			−0.0558287			−0.0279144	−	0.999610i	$-0.508887\pi$
$241$	−0.866695			−0.0558287			−0.0279144	+	0.999610i	$0.508887\pi$
$242$	−7.86916	+	12.1447i	−0.505849	+	0.780690i
$243$	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
$248$	2.36822	−	15.2559i	0.150382	−	0.968753i
$249$			4.31872i			0.273688i
$250$	12.6138	−	9.53378i	0.797765	−	0.602969i
$251$			11.9952i			0.757128i	0.925575	+	0.378564i	$0.123582\pi$
$251$			11.9952i			0.757128i	−0.925575	+	0.378564i	$0.876418\pi$
$252$	−1.31528	+	3.44755i	−0.0828551	+	0.217175i
$253$	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	0.343417	−	0.939183i	$-0.388416\pi$
$257$	−9.55086	−	9.55086i	−0.595766	−	0.595766i	−0.939183	+	0.343417i	$0.888416\pi$
$258$	−8.33530	−	5.40086i	−0.518933	−	0.336243i
$259$	−3.42374			−0.212741
$260$	−0.191864	−	4.46802i	−0.0118989	−	0.277095i
$261$	−13.2839			−0.822253
$262$	−18.3987	−	11.9215i	−1.13668	−	0.736510i
$263$	8.00268	+	8.00268i	0.493467	+	0.493467i	0.909397	−	0.415930i	$-0.136544\pi$
$263$	8.00268	+	8.00268i	0.493467	+	0.493467i	−0.415930	+	0.909397i	$0.636544\pi$
$264$	−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
$268$	26.6137	+	10.1535i	1.62569	+	0.620221i
$269$			7.28829i			0.444375i	0.975004	+	0.222188i	$0.0713197\pi$
$269$			7.28829i			0.444375i	−0.975004	+	0.222188i	$0.928680\pi$
$270$	13.8327	−	9.83041i	0.841830	−	0.598260i
$271$			4.92513i			0.299181i	0.988748	+	0.149590i	$0.0477955\pi$
$271$			4.92513i			0.299181i	−0.988748	+	0.149590i	$0.952205\pi$
$272$	−27.7427	+	1.56807i	−1.68215	+	0.0950781i
$273$	−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	0.167406	−	0.985888i	$-0.446461\pi$
$277$	−13.6222	−	13.6222i	−0.818482	−	0.818482i	−0.985888	+	0.167406i	$0.946461\pi$
$278$	−3.25029	+	5.01627i	−0.194940	+	0.300856i
$279$	−9.23417			−0.552835
$280$	5.94406	+	3.49886i	0.355226	+	0.209097i
$281$	11.2668			0.672120			0.336060	−	0.941841i	$-0.390905\pi$
$281$	11.2668			0.672120			0.336060	+	0.941841i	$0.390905\pi$
$282$	4.74091	−	7.31678i	0.282317	−	0.435708i
$283$	−11.8154	−	11.8154i	−0.702350	−	0.702350i	0.262565	−	0.964914i	$-0.415432\pi$
$283$	−11.8154	−	11.8154i	−0.702350	−	0.702350i	−0.964914	+	0.262565i	$0.915432\pi$
$284$	−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
$288$	−9.23101	+	2.52424i	−0.543943	+	0.148742i
$289$			31.2573i			1.83867i
$290$	−4.14097	+	24.4832i	−0.243166	+	1.43770i
$291$		−	10.7652i		−	0.631069i
$292$	−18.1041	−	6.90693i	−1.05946	−	0.404198i
$293$	−7.28832	+	7.28832i	−0.425788	+	0.425788i	−0.887191	−	0.461403i	$-0.847346\pi$
$293$	−7.28832	+	7.28832i	−0.425788	+	0.425788i	0.461403	+	0.887191i	$0.347346\pi$
$294$	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
$298$	−1.19268	−	0.772798i	−0.0690901	−	0.0447670i
$299$	8.53734			0.493727
$300$	−4.97818	−	10.2978i	−0.287415	−	0.594541i
$301$	−6.69627			−0.385967
$302$	19.3275	+	12.5233i	1.11217	+	0.720632i
$303$	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	$-0.520632\pi$
$307$	16.3497	−	16.3497i	0.933128	−	0.933128i	0.997900	+	0.0647718i	$0.0206319\pi$
$308$	−0.681026	+	1.78507i	−0.0388050	+	0.101714i
$309$			14.6515i			0.833493i
$310$	−2.87855	+	17.0192i	−0.163491	+	0.966627i
$311$		−	21.7219i		−	1.23174i	−0.787850	−	0.615868i	$-0.788806\pi$
$311$		−	21.7219i		−	1.23174i	0.787850	−	0.615868i	$-0.211194\pi$
$312$	−3.19685	−	0.496254i	−0.180986	−	0.0280949i
$313$	−1.17273	+	1.17273i	−0.0662866	+	0.0662866i	−0.739473	−	0.673186i	$-0.764925\pi$
$313$	−1.17273	+	1.17273i	−0.0662866	+	0.0662866i	0.673186	+	0.739473i	$0.264925\pi$
$314$	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	0.864665	−	0.502348i	$-0.167530\pi$
$317$	6.45087	+	6.45087i	0.362317	+	0.362317i	−0.502348	+	0.864665i	$0.667530\pi$
$318$	−2.71898	+	4.19628i	−0.152473	+	0.235316i
$319$	−6.87812			−0.385101
$320$	1.77479	+	17.8003i	0.0992136	+	0.995066i
$321$	11.2917			0.630239
$322$	−7.16002	+	11.0503i	−0.399012	+	0.615807i
$323$	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
$328$	−3.82023	−	0.593023i	−0.210937	−	0.0327442i
$329$		−	5.87803i		−	0.324066i
$330$	2.58256	−	1.83533i	0.142165	−	0.101032i
$331$		−	32.7431i		−	1.79973i	−0.436173	−	0.899863i	$-0.643666\pi$
$331$		−	32.7431i		−	1.79973i	0.436173	−	0.899863i	$-0.356334\pi$
$332$	−2.69178	+	7.05555i	−0.147731	+	0.387224i
$333$	−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	0.997647	−	0.0685633i	$-0.0218415\pi$
$337$	17.0557	+	17.0557i	0.929083	+	0.929083i	−0.0685633	+	0.997647i	$0.521842\pi$
$338$	1.18685	+	0.769019i	0.0645560	+	0.0418291i
$339$	−13.4173			−0.728730
$340$	31.0382	−	1.33283i	1.68328	−	0.0722831i
$341$	−4.78125			−0.258919
$342$	13.8456	+	8.97128i	0.748686	+	0.485111i
$343$	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	$-0.904303\pi$
$347$	−12.2761	+	12.2761i	−0.659016	+	0.659016i	0.296131	+	0.955147i	$0.404303\pi$
$348$	16.7827	+	6.40282i	0.899648	+	0.343227i
$349$		−	30.2444i		−	1.61895i	−0.587156	−	0.809474i	$-0.699752\pi$
$349$		−	30.2444i		−	1.61895i	0.587156	−	0.809474i	$-0.300248\pi$
$350$	−6.59207	−	4.00151i	−0.352361	−	0.213890i
$351$			5.36638i			0.286436i
$352$	−4.77962	+	1.30700i	−0.254755	+	0.0696632i
$353$	−15.7099	+	15.7099i	−0.836152	+	0.836152i	−0.988350	−	0.152198i	$-0.951365\pi$
$353$	−15.7099	+	15.7099i	−0.836152	+	0.836152i	0.152198	+	0.988350i	$0.451365\pi$
$354$	−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
$358$	−3.73377	+	5.76243i	−0.197336	+	0.304554i
$359$	−35.6895			−1.88362			−0.941809	−	0.336149i	$-0.890875\pi$
$359$	−35.6895			−1.88362			−0.941809	+	0.336149i	$0.890875\pi$
$360$	10.3579	−	2.68213i	0.545908	−	0.141360i
$361$	28.5519			1.50273
$362$	12.7263	−	19.6409i	0.668882	−	1.03230i
$363$	−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	$-0.697945\pi$
$367$	4.41082	−	4.41082i	0.230243	−	0.230243i	0.812794	+	0.582551i	$0.197945\pi$
$368$	−34.0949	+	1.92711i	−1.77732	+	0.100457i
$369$			2.31232i			0.120375i
$370$	5.75091	+	8.09229i	0.298976	+	0.420698i
$371$			3.37114i			0.175021i
$372$	11.6663	+	4.45085i	0.604871	+	0.230766i
$373$	16.1225	−	16.1225i	0.834792	−	0.834792i	−0.153376	−	0.988168i	$-0.549015\pi$
$373$	16.1225	−	16.1225i	0.834792	−	0.834792i	0.988168	+	0.153376i	$0.0490145\pi$
$374$	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
$378$	−6.94594	−	4.50062i	−0.357260	−	0.231487i
$379$	33.3029			1.71066			0.855328	−	0.518086i	$-0.173355\pi$
$379$	33.3029			1.71066			0.855328	+	0.518086i	$0.173355\pi$
$380$	20.8508	−	22.7219i	1.06962	−	1.16561i
$381$	13.6897			0.701345
$382$	−23.3083	−	15.1026i	−1.19256	−	0.772718i
$383$	−1.90891	−	1.90891i	−0.0975409	−	0.0975409i	0.656652	−	0.754193i	$-0.271972\pi$
$383$	−1.90891	−	1.90891i	−0.0975409	−	0.0975409i	−0.754193	+	0.656652i	$0.771972\pi$
$384$	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
$388$	6.70977	−	17.5873i	0.340637	−	0.892859i
$389$		−	2.08615i		−	0.105772i	−0.998601	−	0.0528859i	$-0.983158\pi$
$389$		−	2.08615i		−	0.105772i	0.998601	−	0.0528859i	$-0.0168420\pi$
$390$	3.56634	+	0.603194i	0.180589	+	0.0305439i
$391$			59.3067i			2.99927i
$392$	−2.52105	+	16.2405i	−0.127332	+	0.820269i
$393$	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	−0.983033	−	0.183431i	$-0.941280\pi$
$397$	−23.2416	−	23.2416i	−1.16646	−	1.16646i	−0.183431	−	0.983033i	$-0.558720\pi$
$398$	2.86094	−	4.41536i	0.143406	−	0.221322i
$399$	−8.60173			−0.430625
$400$	−1.71451	−	19.9264i	−0.0857254	−	0.996319i
$401$	16.0373			0.800865			0.400432	−	0.916326i	$-0.368860\pi$
$401$	16.0373			0.800865			0.400432	+	0.916326i	$0.368860\pi$
$402$	−12.5276	+	19.3341i	−0.624818	+	0.964299i
$403$	−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
$408$	3.44735	−	22.2077i	0.170669	−	1.09944i
$409$		−	38.6612i		−	1.91167i	−0.293898	−	0.955837i	$-0.594953\pi$
$409$		−	38.6612i		−	1.91167i	0.293898	−	0.955837i	$-0.405047\pi$
$410$	4.26177	+	0.720816i	0.210474	+	0.0355985i
$411$			4.16480i			0.205434i
$412$	−9.13199	+	23.9363i	−0.449901	+	1.17925i
$413$	−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
$418$	7.16897	+	4.64514i	0.350646	+	0.227201i
$419$	15.9101			0.777261			0.388630	−	0.921394i	$-0.372948\pi$
$419$	15.9101			0.777261			0.388630	+	0.921394i	$0.372948\pi$
$420$	−3.77173	+	4.11019i	−0.184041	+	0.200557i
$421$	3.52390			0.171744			0.0858721	−	0.996306i	$-0.472632\pi$
$421$	3.52390			0.171744			0.0858721	+	0.996306i	$0.472632\pi$
$422$	11.9889	+	7.76819i	0.583609	+	0.378150i
$423$	−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
$428$	18.4473	+	7.03788i	0.891684	+	0.340189i
$429$			1.00190i			0.0483722i
$430$	11.2478	+	15.8272i	0.542419	+	0.763255i
$431$			34.0034i			1.63788i	0.573876	+	0.818942i	$0.305439\pi$
$431$			34.0034i			1.63788i	−0.573876	+	0.818942i	$0.694561\pi$
$432$	−1.21134	−	21.4313i	−0.0582804	−	1.03111i
$433$	−20.4386	+	20.4386i	−0.982216	+	0.982216i	−0.999845	−	0.0176285i	$-0.994388\pi$
$433$	−20.4386	+	20.4386i	−0.982216	+	0.982216i	0.0176285	+	0.999845i	$0.494388\pi$
$434$	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
$438$	8.52193	−	13.1521i	0.407194	−	0.628433i
$439$	4.50397			0.214963			0.107481	−	0.994207i	$-0.465721\pi$
$439$	4.50397			0.214963			0.107481	+	0.994207i	$0.465721\pi$
$440$	5.36308	−	1.38875i	0.255675	−	0.0662059i
$441$	9.83011			0.468100
$442$	−5.34218	+	8.24474i	−0.254102	+	0.392162i
$443$	−16.9086	−	16.9086i	−0.803352	−	0.803352i	0.180266	−	0.983618i	$-0.442304\pi$
$443$	−16.9086	−	16.9086i	−0.803352	−	0.803352i	−0.983618	+	0.180266i	$0.942304\pi$
$444$	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
$448$	7.74914	−	4.00863i	0.366112	−	0.189390i
$449$		−	15.2463i		−	0.719516i	−0.933046	−	0.359758i	$-0.882859\pi$
$449$		−	15.2463i		−	0.719516i	0.933046	−	0.359758i	$-0.117141\pi$
$450$	−11.6200	+	2.84156i	−0.547772	+	0.133953i
$451$			1.19727i			0.0563772i
$452$	−21.9201	−	8.36279i	−1.03103	−	0.393353i
$453$	−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	0.859431	−	0.511252i	$-0.170818\pi$
$457$	7.44322	+	7.44322i	0.348179	+	0.348179i	−0.511252	+	0.859431i	$0.670818\pi$
$458$	1.40214	+	0.908517i	0.0655177	+	0.0424522i
$459$	−37.2789			−1.74003
$460$	38.1450	−	1.63801i	1.77852	−	0.0763727i
$461$	−21.5904			−1.00556			−0.502782	−	0.864413i	$-0.667690\pi$
$461$	−21.5904			−1.00556			−0.502782	+	0.864413i	$0.667690\pi$
$462$	−1.29680	−	0.840265i	−0.0603328	−	0.0390927i
$463$	5.31937	+	5.31937i	0.247212	+	0.247212i	0.819825	−	0.572614i	$-0.194070\pi$
$463$	5.31937	+	5.31937i	0.247212	+	0.247212i	−0.572614	+	0.819825i	$0.694070\pi$
$464$	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	$-0.878600\pi$
$467$	−12.0139	+	12.0139i	−0.555939	+	0.555939i	0.372210	+	0.928149i	$0.378600\pi$
$468$	−1.20605	+	3.16123i	−0.0557496	+	0.146128i
$469$			15.5323i			0.717217i
$470$	−13.8932	+	9.87343i	−0.640846	+	0.455427i
$471$			0.277511i			0.0127870i
$472$	−2.09417	−	0.325084i	−0.0963922	−	0.0149632i
$473$	−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
$478$	−14.6520	+	22.6128i	−0.670165	+	1.03428i
$479$	−6.77238			−0.309438			−0.154719	−	0.987959i	$-0.549447\pi$
$479$	−6.77238			−0.309438			−0.154719	+	0.987959i	$0.549447\pi$
$480$	−14.3788	−	1.60391i	−0.656298	−	0.0732082i
$481$	−3.13940			−0.143144
$482$	0.666505	−	1.02864i	0.0303585	−	0.0468531i
$483$	−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	$-0.689948\pi$
$487$	5.85296	−	5.85296i	0.265223	−	0.265223i	0.827172	+	0.561949i	$0.189948\pi$
$488$	−13.4074	−	2.08126i	−0.606924	−	0.0942143i
$489$			13.7935i			0.623762i
$490$	3.06432	−	18.1176i	0.138432	−	0.818469i
$491$			30.1005i			1.35842i	0.733945	+	0.679209i	$0.237677\pi$
$491$			30.1005i			1.35842i	−0.733945	+	0.679209i	$0.762323\pi$
$492$	1.11453	−	2.92136i	0.0502471	−	0.131705i
$493$	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
$498$	−5.12567	−	3.32118i	−0.229687	−	0.148826i
$499$	−4.19308			−0.187708			−0.0938541	−	0.995586i	$-0.529919\pi$
$499$	−4.19308			−0.187708			−0.0938541	+	0.995586i	$0.529919\pi$
$500$	1.61492	+	22.3023i	0.0722214	+	0.997389i
$501$	14.2607			0.637123
$502$	−14.2364	−	9.22451i	−0.635404	−	0.411710i
$503$	6.34559	+	6.34559i	0.282936	+	0.282936i	0.834279	−	0.551343i	$-0.185884\pi$
$503$	6.34559	+	6.34559i	0.282936	+	0.282936i	−0.551343	+	0.834279i	$0.685884\pi$
$504$	−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
$508$	22.3650	+	8.53254i	0.992288	+	0.378570i
$509$		−	40.6251i		−	1.80068i	−0.435190	−	0.900338i	$-0.643319\pi$
$509$		−	40.6251i		−	1.80068i	0.435190	−	0.900338i	$-0.356681\pi$
$510$	−4.19024	+	24.7745i	−0.185547	+	1.09703i
$511$		−	10.5659i		−	0.467410i
$512$	20.2551	+	10.0861i	0.895158	+	0.445748i
$513$	−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
$518$	2.63292	−	4.06346i	0.115684	−	0.178538i
$519$	−1.47944			−0.0649400
$520$	5.45041	+	3.20828i	0.239016	+	0.140692i
$521$	−37.7559			−1.65412			−0.827058	−	0.562116i	$-0.809987\pi$
$521$	−37.7559			−1.65412			−0.827058	+	0.562116i	$0.809987\pi$
$522$	10.2156	−	15.7660i	0.447124	−	0.690058i
$523$	4.86113	+	4.86113i	0.212563	+	0.212563i	0.805355	−	0.592793i	$-0.201975\pi$
$523$	4.86113	+	4.86113i	0.212563	+	0.212563i	−0.592793	+	0.805355i	$0.701975\pi$
$524$	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
$528$	−0.226156	−	4.00122i	−0.00984217	−	0.174131i
$529$			49.8861i			2.16896i
$530$	7.96796	−	5.66256i	0.346106	−	0.245966i
$531$			1.26757i			0.0550078i
$532$	−14.0527	−	5.36130i	−0.609264	−	0.232442i
$533$	−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
$538$	−8.65010	−	5.60484i	−0.372932	−	0.241642i
$539$	5.08982			0.219234
$540$	1.02962	+	23.9771i	0.0443076	+	1.03181i
$541$	−38.2350			−1.64385			−0.821925	−	0.569596i	$-0.807100\pi$
$541$	−38.2350			−1.64385			−0.821925	+	0.569596i	$0.807100\pi$
$542$	−5.84539	−	3.78752i	−0.251081	−	0.162688i
$543$	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	$-0.826749\pi$
$547$	−7.89796	+	7.89796i	−0.337692	+	0.337692i	0.517806	+	0.855498i	$0.326749\pi$
$548$	−2.59584	+	6.80408i	−0.110889	+	0.290656i
$549$			8.11528i			0.346352i
$550$	−6.01659	+	1.47130i	−0.256548	+	0.0627365i
$551$		−	54.1472i		−	2.30675i
$552$	4.23669	−	27.2925i	0.180325	−	1.16165i
$553$	−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	0.847887	−	0.530176i	$-0.177874\pi$
$557$	7.49825	+	7.49825i	0.317711	+	0.317711i	−0.530176	+	0.847887i	$0.677874\pi$
$558$	7.10125	−	10.9596i	0.300620	−	0.463955i
$559$	−6.14014			−0.259700
$560$	−8.72372	+	4.36401i	−0.368644	+	0.184413i
$561$	−6.95995			−0.293849
$562$	−8.66438	+	13.3720i	−0.365485	+	0.564062i
$563$	1.24248	+	1.24248i	0.0523644	+	0.0523644i	0.732804	−	0.680440i	$-0.238211\pi$
$563$	1.24248	+	1.24248i	0.0523644	+	0.0523644i	−0.680440	+	0.732804i	$0.738211\pi$
$564$	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
$568$	2.17576	−	14.0161i	0.0912928	−	0.588104i
$569$		−	22.3401i		−	0.936548i	−0.883583	−	0.468274i	$-0.844876\pi$
$569$		−	22.3401i		−	0.936548i	0.883583	−	0.468274i	$-0.155124\pi$
$570$	14.4485	+	20.3309i	0.605180	+	0.851567i
$571$			40.7031i			1.70337i	0.524052	+	0.851686i	$0.324420\pi$
$571$			40.7031i			1.70337i	−0.524052	+	0.851686i	$0.675580\pi$
$572$	−0.624466	+	1.63682i	−0.0261103	+	0.0684387i
$573$	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	0.581897	−	0.813263i	$-0.302311\pi$
$577$	−5.55759	−	5.55759i	−0.231366	−	0.231366i	−0.813263	+	0.581897i	$0.802311\pi$
$578$	−37.0977	−	24.0375i	−1.54306	−	0.999828i
$579$	21.1577			0.879285
$580$	−25.8733	−	23.7427i	−1.07433	−	0.985864i
$581$	−4.11778			−0.170834
$582$	12.7767	+	8.27867i	0.529611	+	0.343162i
$583$	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	$-0.698402\pi$
$587$	5.52984	−	5.52984i	0.228241	−	0.228241i	0.811957	+	0.583717i	$0.198402\pi$
$588$	−12.4192	−	4.73809i	−0.512160	−	0.195396i
$589$		−	37.6399i		−	1.55092i
$590$	2.33622	+	0.395137i	0.0961807	+	0.0162675i
$591$			1.25232i			0.0515137i
$592$	12.5376	−	0.708646i	0.515291	−	0.0291252i
$593$	25.9213	−	25.9213i	1.06446	−	1.06446i	0.0666872	−	0.997774i	$-0.478757\pi$
$593$	25.9213	−	25.9213i	1.06446	−	1.06446i	0.997774	−	0.0666872i	$-0.0212429\pi$
$594$	−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
$598$	−6.56538	+	10.1325i	−0.268478	+	0.414350i
$599$	12.5925			0.514515			0.257257	−	0.966343i	$-0.417181\pi$
$599$	12.5925			0.514515			0.257257	+	0.966343i	$0.417181\pi$
$600$	16.0502	+	2.01083i	0.655247	+	0.0820917i
$601$	−8.34802			−0.340523			−0.170261	−	0.985399i	$-0.554461\pi$
$601$	−8.34802			−0.340523			−0.170261	+	0.985399i	$0.554461\pi$
$602$	5.14956	−	7.94746i	0.209880	−	0.323914i
$603$	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	$-0.677742\pi$
$607$	7.84172	−	7.84172i	0.318286	−	0.318286i	0.848108	+	0.529823i	$0.177742\pi$
$608$	−10.2892	−	37.6270i	−0.417282	−	1.52598i
$609$			9.79477i			0.396904i
$610$	14.9570	+	2.52976i	0.605592	+	0.102427i
$611$		−	5.38986i		−	0.218050i
$612$	−21.9603	−	8.37812i	−0.887691	−	0.338666i
$613$	0.714872	−	0.714872i	0.0288734	−	0.0288734i	−0.692523	−	0.721396i	$-0.743501\pi$
$613$	0.714872	−	0.714872i	0.0288734	−	0.0288734i	0.721396	+	0.692523i	$0.243501\pi$
$614$	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	0.962857	−	0.270011i	$-0.0870272\pi$
$617$	17.2100	+	17.2100i	0.692847	+	0.692847i	−0.270011	+	0.962857i	$0.587027\pi$
$618$	−17.3891	−	11.2673i	−0.699491	−	0.453236i
$619$	−0.361036			−0.0145113			−0.00725564	−	0.999974i	$-0.502310\pi$
$619$	−0.361036			−0.0145113			−0.00725564	+	0.999974i	$0.502310\pi$
$620$	−17.9856	−	16.5045i	−0.722318	−	0.662837i
$621$	−45.8146			−1.83847
$622$	25.7806	+	16.7046i	1.03371	+	0.669792i
$623$	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
$628$	−0.172967	+	0.453372i	−0.00690215	+	0.0180915i
$629$		−	21.8086i		−	0.869566i
$630$	3.37970	+	4.75568i	0.134651	+	0.189471i
$631$			7.91135i			0.314946i	0.987523	+	0.157473i	$0.0503347\pi$
$631$			7.91135i			0.314946i	−0.987523	+	0.157473i	$0.949665\pi$
$632$	−4.55460	−	0.707021i	−0.181172	−	0.0281238i
$633$	−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
$638$	5.28941	−	8.16329i	0.209410	−	0.323188i
$639$	−8.48374			−0.335612
$640$	−22.4911	−	11.5824i	−0.889038	−	0.457833i
$641$	−12.3758			−0.488813			−0.244407	−	0.969673i	$-0.578593\pi$
$641$	−12.3758			−0.488813			−0.244407	+	0.969673i	$0.578593\pi$
$642$	−8.68350	+	13.4015i	−0.342710	+	0.528914i
$643$	−1.50067	−	1.50067i	−0.0591807	−	0.0591807i	0.676897	−	0.736078i	$-0.263324\pi$
$643$	−1.50067	−	1.50067i	−0.0591807	−	0.0591807i	−0.736078	+	0.676897i	$0.763324\pi$
$644$	−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	$-0.611301\pi$
$647$	15.1830	−	15.1830i	0.596906	−	0.596906i	0.939488	+	0.342582i	$0.111301\pi$
$648$	2.97048	+	0.461115i	0.116692	+	0.0181143i
$649$			0.656320i			0.0257628i
$650$	−6.04459	−	3.66918i	−0.237088	−	0.143917i
$651$			6.80873i			0.266855i
$652$	−8.59721	+	22.5345i	−0.336693	+	0.882520i
$653$	−11.8664	+	11.8664i	−0.464369	+	0.464369i	−0.900084	−	0.435716i	$-0.856495\pi$
$653$	−11.8664	+	11.8664i	−0.464369	+	0.464369i	0.435716	+	0.900084i	$0.356495\pi$
$654$	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
$658$	6.97633	+	4.52032i	0.271966	+	0.176220i
$659$	−46.7405			−1.82075			−0.910376	−	0.413782i	$-0.864208\pi$
$659$	−46.7405			−1.82075			−0.910376	+	0.413782i	$0.864208\pi$
$660$	0.192229	+	4.47651i	0.00748251	+	0.174248i
$661$	23.7102			0.922219			0.461109	−	0.887343i	$-0.347452\pi$
$661$	23.7102			0.922219			0.461109	+	0.887343i	$0.347452\pi$
$662$	38.8612	+	25.1801i	1.51038	+	0.978653i
$663$	−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
$668$	23.2979	+	8.88846i	0.901425	+	0.343905i
$669$			17.7509i			0.686288i
$670$	36.7119	−	26.0899i	1.41831	−	1.00794i
$671$			4.20192i			0.162213i
$672$	1.86123	+	6.80640i	0.0717984	+	0.262563i
$673$	1.49025	−	1.49025i	0.0574448	−	0.0574448i	−0.677801	−	0.735246i	$-0.737067\pi$
$673$	1.49025	−	1.49025i	0.0574448	−	0.0574448i	0.735246	+	0.677801i	$0.237067\pi$
$674$	−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	0.989104	−	0.147219i	$-0.0470323\pi$
$677$	21.9052	+	21.9052i	0.841884	+	0.841884i	−0.147219	+	0.989104i	$0.547032\pi$
$678$	10.3182	−	15.9244i	0.396268	−	0.611571i
$679$	10.2643			0.393909
$680$	−22.2871	+	37.8626i	−0.854671	+	1.45197i
$681$	−8.26205			−0.316602
$682$	3.67688	−	5.67462i	0.140795	−	0.217293i
$683$	21.9173	+	21.9173i	0.838644	+	0.838644i	0.988680	−	0.150037i	$-0.0479392\pi$
$683$	21.9173	+	21.9173i	0.838644	+	0.838644i	−0.150037	+	0.988680i	$0.547939\pi$
$684$	−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
$688$	24.5214	−	1.38600i	0.934871	−	0.0528406i
$689$			3.09116i			0.117764i
$690$	−5.14967	+	30.4470i	−0.196044	+	1.15910i
$691$			1.94770i			0.0740939i	0.999314	+	0.0370470i	$0.0117951\pi$
$691$			1.94770i			0.0740939i	−0.999314	+	0.0370470i	$0.988205\pi$
$692$	−2.41697	−	0.922105i	−0.0918794	−	0.0350532i
$693$	−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
$698$	35.8956	+	23.2586i	1.35867	+	0.880349i
$699$	19.5521			0.739529
$700$	9.81861	−	4.74655i	0.371109	−	0.179403i
$701$	16.3253			0.616597			0.308299	−	0.951290i	$-0.400240\pi$
$701$	16.3253			0.616597			0.308299	+	0.951290i	$0.400240\pi$
$702$	−6.36907	−	4.12685i	−0.240385	−	0.155758i
$703$	−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
$708$	0.610967	−	1.60143i	0.0229615	−	0.0601855i
$709$		−	9.91483i		−	0.372359i	−0.982516	−	0.186180i	$-0.940389\pi$
$709$		−	9.91483i		−	0.372359i	0.982516	−	0.186180i	$-0.0596106\pi$
$710$	−2.64462	+	15.6361i	−0.0992509	+	0.586814i
$711$			2.75682i			0.103389i
$712$	−1.60012	+	10.3079i	−0.0599670	+	0.386304i
$713$	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
$718$	27.4459	−	42.3580i	1.02427	−	1.58079i
$719$	5.89066			0.219685			0.109842	−	0.993949i	$-0.464965\pi$
$719$	5.89066			0.219685			0.109842	+	0.993949i	$0.464965\pi$
$720$	−4.78212	+	14.3558i	−0.178219	+	0.535010i
$721$	−13.9697			−0.520260
$722$	−21.9570	+	33.8868i	−0.817153	+	1.26114i
$723$	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	0.303642	−	0.952786i	$-0.401797\pi$
$727$	33.8770	−	33.8770i	1.25643	−	1.25643i	0.952786	−	0.303642i	$-0.0982026\pi$
$728$	0.473164	−	3.04810i	0.0175366	−	0.112970i
$729$		−	20.2120i		−	0.748594i
$730$	−24.9735	+	17.7478i	−0.924309	+	0.656875i
$731$		−	42.6540i		−	1.57762i
$732$	3.91155	−	10.2527i	0.144575	−	0.378952i
$733$	24.2491	−	24.2491i	0.895661	−	0.895661i	−0.0993880	−	0.995049i	$-0.531689\pi$
$733$	24.2491	−	24.2491i	0.895661	−	0.895661i	0.995049	+	0.0993880i	$0.0316885\pi$
$734$	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
$738$	−2.74437	−	1.77822i	−0.101022	−	0.0654571i
$739$	11.3816			0.418679			0.209339	−	0.977843i	$-0.432869\pi$
$739$	11.3816			0.418679			0.209339	+	0.977843i	$0.432869\pi$
$740$	−14.0269	+	0.602338i	−0.515638	+	0.0221424i
$741$	−7.88735			−0.289749
$742$	−4.00103	−	2.59247i	−0.146882	−	0.0951726i
$743$	13.5560	+	13.5560i	0.497323	+	0.497323i	0.910604	−	0.413281i	$-0.135617\pi$
$743$	13.5560	+	13.5560i	0.497323	+	0.497323i	−0.413281	+	0.910604i	$0.635617\pi$
$744$	−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
$748$	−11.3706	−	4.33801i	−0.415749	−	0.158613i
$749$			10.7663i			0.393391i
$750$	−17.9126	−	2.49104i	−0.654074	−	0.0909601i
$751$			0.486430i			0.0177501i	0.999961	+	0.00887505i	$0.00282505\pi$
$751$			0.486430i			0.0177501i	−0.999961	+	0.00887505i	$0.997175\pi$
$752$	1.21664	+	21.5251i	0.0443661	+	0.784939i
$753$	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	0.986729	−	0.162379i	$-0.0519166\pi$
$757$	22.6809	+	22.6809i	0.824350	+	0.824350i	−0.162379	+	0.986729i	$0.551917\pi$
$758$	−25.6106	+	39.5255i	−0.930219	+	1.43563i
$759$	−8.55356			−0.310475
$760$	10.9328	+	42.2203i	0.396573	+	1.53149i
$761$	41.2722			1.49612			0.748058	−	0.663633i	$-0.230986\pi$
$761$	41.2722			1.49612			0.748058	+	0.663633i	$0.230986\pi$
$762$	−10.5276	+	16.2476i	−0.381376	+	0.588589i
$763$	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
$768$	−11.3999	+	14.3163i	−0.411359	+	0.516595i
$769$			35.2742i			1.27202i	0.771681	+	0.636010i	$0.219416\pi$
$769$			35.2742i			1.27202i	−0.771681	+	0.636010i	$0.780584\pi$
$770$	1.74994	+	2.46239i	0.0630634	+	0.0887384i
$771$			15.4491i			0.556387i
$772$	34.5656	+	13.1872i	1.24404	+	0.474619i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.769019 + 1.18685i) q^{2} +(-0.808783 - 0.808783i) q^{3} +(-0.817219 - 1.82542i) q^{4} +(0.885949 + 2.05307i) q^{5} +(1.58187 - 0.337933i) q^{6} +(0.771151 - 0.771151i) q^{7} +(2.79495 + 0.433867i) q^{8} -1.69174i q^{9} +O(q^{10})\)	\(q+(-0.769019 + 1.18685i) 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} +(2.79495 + 0.433867i) q^{8} -1.69174i q^{9} +(-3.11799 - 0.527363i) q^{10} -0.875946i q^{11} +(-0.815415 + 2.13732i) 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} +(2.00784 + 1.30098i) q^{18} +6.89579 q^{19} +(3.02370 - 3.29503i) q^{20} -1.24739 q^{21} +(1.03962 + 0.673619i) 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} +(-2.03787 - 0.777475i) q^{28} -7.85222i q^{29} +(2.09526 + 2.94830i) q^{30} -5.45839i q^{31} +(-1.49210 - 5.45652i) 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} +(-5.30299 + 8.18426i) q^{38} -1.14379 q^{39} +(1.58543 + 6.12262i) q^{40} -1.36683 q^{41} +(0.959266 - 1.48046i) 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} +(4.56788 - 0.258185i) q^{48} +5.81065i q^{49} +(-1.67967 - 6.86868i) q^{50} -7.94564i q^{51} +(-1.86863 - 0.712905i) 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} +(9.31940 + 6.03851i) q^{58} -0.749270 q^{59} +(-5.11049 + 0.219453i) q^{60} -4.79700 q^{61} +(6.47828 + 4.19761i) 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} +(4.95237 - 12.9809i) q^{68} -9.76494i q^{69} +(-2.81112 + 1.99777i) q^{70} -5.01480i q^{71} +(0.733990 - 4.72833i) 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} +(0.879598 - 1.35751i) q^{78} -1.62958 q^{79} +(-8.48584 - 2.82675i) q^{80} +1.06280 q^{81} +(1.05112 - 1.62222i) 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} +(0.380044 - 2.44823i) q^{88} +3.68804i q^{89} +(-0.892160 + 5.27483i) q^{90} -1.09057i q^{91} +(6.08631 - 15.9531i) 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} +(-6.89636 - 4.46850i) 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

Varieties

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