LMFDB - Embedded newform 260.2.o.a.27.31

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			27.31
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.31

$q$-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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.18685	−	0.769019i	0.839229	−	0.543779i
$2$	1.18685	−	0.769019i	0.839229	−	0.543779i
$3$	0.808783	+	0.808783i	0.466951	+	0.466951i	0.900925	−	0.433974i	$-0.142889\pi$
$3$	0.808783	+	0.808783i	0.466951	+	0.466951i	−0.433974	+	0.900925i	$0.642889\pi$
$4$	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	−0.837660	−	0.546192i	$-0.816077\pi$
$7$	−0.771151	+	0.771151i	−0.291468	+	0.291468i	0.546192	+	0.837660i	$0.316077\pi$
$8$	−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	$0.0421572\pi$
$11$			0.875946i			0.264108i	−0.991243	+	0.132054i	$0.957843\pi$
$12$	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	0.976686	+	0.214671i	$0.0688681\pi$
$17$	4.91209	+	4.91209i	1.19136	+	1.19136i	0.214671	+	0.976686i	$0.431132\pi$
$18$	−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	−0.951685	−	0.307077i	$-0.900649\pi$
$23$	−6.03681	−	6.03681i	−1.25876	−	1.25876i	−0.307077	−	0.951685i	$-0.599351\pi$
$24$	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	$-0.739957\pi$
$29$		−	7.85222i		−	1.45812i	0.684449	−	0.729060i	$-0.260043\pi$
$30$	0.707658	+	3.54709i	0.129200	+	0.647607i
$31$			5.45839i			0.980356i	0.871622	+	0.490178i	$0.163068\pi$
$31$			5.45839i			0.980356i	−0.871622	+	0.490178i	$0.836932\pi$
$32$	−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	0.500683	−	0.865631i	$-0.333082\pi$
$37$	−2.21989	−	2.21989i	−0.364947	−	0.364947i	−0.865631	+	0.500683i	$0.833082\pi$
$38$	−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	0.955877	−	0.293768i	$-0.0949093\pi$
$43$	4.34174	+	4.34174i	0.662109	+	0.662109i	−0.293768	+	0.955877i	$0.594909\pi$
$44$	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	−0.928144	−	0.372222i	$-0.878596\pi$
$47$	−3.81120	+	3.81120i	−0.555921	+	0.555921i	0.372222	+	0.928144i	$0.378596\pi$
$48$	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	−0.841108	−	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
$58$	−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	0.266526	−	0.963828i	$-0.414124\pi$
$67$	10.0709	−	10.0709i	1.23035	−	1.23035i	0.963828	−	0.266526i	$-0.0858757\pi$
$68$	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	$0.0961775\pi$
$71$			5.01480i			0.595148i	−0.954699	+	0.297574i	$0.903823\pi$
$72$	−4.72833	+	0.733990i	−0.557239	+	0.0865016i
$73$	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
$78$	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	0.838287	−	0.545229i	$-0.183557\pi$
$83$	2.66989	+	2.66989i	0.293058	+	0.293058i	−0.545229	+	0.838287i	$0.683557\pi$
$84$	−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	$0.0626218\pi$
$89$			3.68804i			0.390931i	−0.980711	+	0.195466i	$0.937378\pi$
$90$	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	0.959032	−	0.283299i	$-0.0914288\pi$
$97$	6.65520	+	6.65520i	0.675733	+	0.675733i	−0.283299	+	0.959032i	$0.591429\pi$
$98$	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	0.994756	−	0.102273i	$-0.0326115\pi$
$103$	9.05772	+	9.05772i	0.892483	+	0.892483i	−0.102273	+	0.994756i	$0.532612\pi$
$104$	−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	−0.283985	−	0.958829i	$-0.591656\pi$
$107$	6.98064	−	6.98064i	0.674844	−	0.674844i	0.958829	+	0.283985i	$0.0916565\pi$
$108$	−3.82572	−	10.0278i	−0.368130	−	0.964921i
$109$			5.87444i			0.562670i	0.959610	+	0.281335i	$0.0907772\pi$
$109$			5.87444i			0.562670i	−0.959610	+	0.281335i	$0.909223\pi$
$110$	−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	−0.199576	−	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
$118$	0.889270	−	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	−0.223680	−	0.974663i	$-0.571807\pi$
$127$	8.46315	−	8.46315i	0.750983	−	0.750983i	0.974663	+	0.223680i	$0.0718070\pi$
$128$	−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	$-0.763187\pi$
$131$		−	15.5022i		−	1.35443i	0.735785	−	0.677215i	$-0.236813\pi$
$132$	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	0.588513	−	0.808487i	$-0.299713\pi$
$137$	−2.57473	−	2.57473i	−0.219974	−	0.219974i	−0.808487	+	0.588513i	$0.799713\pi$
$138$	−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	$0.0131063\pi$
$149$			1.00491i			0.0823258i	−0.999152	+	0.0411629i	$0.986894\pi$
$150$	−6.65547	+	4.59541i	−0.543417	+	0.375214i
$151$			16.2847i			1.32523i	0.748960	+	0.662615i	$0.230554\pi$
$151$			16.2847i			1.32523i	−0.748960	+	0.662615i	$0.769446\pi$
$152$	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	0.700228	−	0.713920i	$-0.253082\pi$
$157$	−0.171561	−	0.171561i	−0.0136920	−	0.0136920i	−0.713920	+	0.700228i	$0.753082\pi$
$158$	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	0.957232	−	0.289323i	$-0.0934301\pi$
$163$	8.52729	+	8.52729i	0.667909	+	0.667909i	−0.289323	+	0.957232i	$0.593430\pi$
$164$	−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	−0.278283	−	0.960499i	$-0.589765\pi$
$167$	8.81617	−	8.81617i	0.682216	−	0.682216i	0.960499	+	0.278283i	$0.0897654\pi$
$168$	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	−0.671483	−	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
$178$	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	$-0.748465\pi$
$191$		−	19.6388i		−	1.42102i	0.703690	−	0.710508i	$-0.251535\pi$
$192$	−8.12730	−	4.20425i	−0.586537	−	0.303416i
$193$	−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	$0.762418\pi$
$198$	1.75876	−	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	$0.113039\pi$
$211$			10.1014i			0.695411i	−0.937604	+	0.347706i	$0.886961\pi$
$212$	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	0.971578	−	0.236718i	$-0.0760719\pi$
$223$	10.9738	+	10.9738i	0.734860	+	0.734860i	−0.236718	+	0.971578i	$0.576072\pi$
$224$	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	−0.855995	−	0.516985i	$-0.827054\pi$
$227$	−5.10770	+	5.10770i	−0.339010	+	0.339010i	0.516985	+	0.855995i	$0.327054\pi$
$228$	−14.7385	+	5.62293i	−0.976082	+	0.372388i
$229$		−	1.18140i		−	0.0780689i	−0.999238	−	0.0390345i	$-0.987572\pi$
$229$		−	1.18140i		−	0.0780689i	0.999238	−	0.0390345i	$-0.0124282\pi$
$230$	−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	−0.981798	−	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
$238$	−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	$-0.876418\pi$
$251$		−	11.9952i		−	0.757128i	0.925575	−	0.378564i	$-0.123582\pi$
$252$	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	0.343417	−	0.939183i	$-0.388416\pi$
$257$	−9.55086	−	9.55086i	−0.595766	−	0.595766i	−0.939183	+	0.343417i	$0.888416\pi$
$258$	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	0.415930	−	0.909397i	$-0.363456\pi$
$263$	−8.00268	−	8.00268i	−0.493467	−	0.493467i	−0.909397	+	0.415930i	$0.863456\pi$
$264$	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	$0.0713197\pi$
$269$			7.28829i			0.444375i	−0.975004	+	0.222188i	$0.928680\pi$
$270$	16.6420	−	3.32015i	1.01280	−	0.202058i
$271$		−	4.92513i		−	0.299181i	−0.988748	−	0.149590i	$-0.952205\pi$
$271$		−	4.92513i		−	0.299181i	0.988748	−	0.149590i	$-0.0477955\pi$
$272$	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	0.167406	−	0.985888i	$-0.446461\pi$
$277$	−13.6222	−	13.6222i	−0.818482	−	0.818482i	−0.985888	+	0.167406i	$0.946461\pi$
$278$	−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	0.964914	−	0.262565i	$-0.0845683\pi$
$283$	11.8154	+	11.8154i	0.702350	+	0.702350i	−0.262565	+	0.964914i	$0.584568\pi$
$284$	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	−0.887191	−	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
$298$	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	−0.997900	−	0.0647718i	$-0.979368\pi$
$307$	−16.3497	+	16.3497i	−0.933128	+	0.933128i	0.0647718	+	0.997900i	$0.479368\pi$
$308$	−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	$0.211194\pi$
$311$			21.7219i			1.23174i	−0.787850	+	0.615868i	$0.788806\pi$
$312$	−0.496254	−	3.19685i	−0.0280949	−	0.180986i
$313$	−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	$0.667530\pi$
$318$	−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	$0.356334\pi$
$331$			32.7431i			1.79973i	−0.436173	+	0.899863i	$0.643666\pi$
$332$	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	0.997647	−	0.0685633i	$-0.0218415\pi$
$337$	17.0557	+	17.0557i	0.929083	+	0.929083i	−0.0685633	+	0.997647i	$0.521842\pi$
$338$	−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	−0.296131	−	0.955147i	$-0.595697\pi$
$347$	12.2761	−	12.2761i	0.659016	−	0.659016i	0.955147	+	0.296131i	$0.0956966\pi$
$348$	−6.40282	−	16.7827i	−0.343227	−	0.899648i
$349$		−	30.2444i		−	1.61895i	−0.587156	−	0.809474i	$-0.699752\pi$
$349$		−	30.2444i		−	1.61895i	0.587156	−	0.809474i	$-0.300248\pi$
$350$	−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	−0.988350	−	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
$358$	−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	−0.812794	−	0.582551i	$-0.802055\pi$
$367$	−4.41082	+	4.41082i	−0.230243	+	0.230243i	0.582551	+	0.812794i	$0.302055\pi$
$368$	−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	−0.153376	−	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
$378$	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	0.754193	−	0.656652i	$-0.228028\pi$
$383$	1.90891	+	1.90891i	0.0975409	+	0.0975409i	−0.656652	+	0.754193i	$0.728028\pi$
$384$	−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	$-0.983158\pi$
$389$		−	2.08615i		−	0.105772i	0.998601	−	0.0528859i	$-0.0168420\pi$
$390$	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	−0.983033	−	0.183431i	$-0.941280\pi$
$397$	−23.2416	−	23.2416i	−1.16646	−	1.16646i	−0.183431	−	0.983033i	$-0.558720\pi$
$398$	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	$-0.594953\pi$
$409$		−	38.6612i		−	1.91167i	0.293898	−	0.955837i	$-0.405047\pi$
$410$	−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	$-0.694561\pi$
$431$		−	34.0034i		−	1.63788i	0.573876	−	0.818942i	$-0.305439\pi$
$432$	−21.4313	−	1.21134i	−1.03111	−	0.0582804i
$433$	−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
$438$	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	0.983618	−	0.180266i	$-0.0576959\pi$
$443$	16.9086	+	16.9086i	0.803352	+	0.803352i	−0.180266	+	0.983618i	$0.557696\pi$
$444$	−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	$-0.882859\pi$
$449$		−	15.2463i		−	0.719516i	0.933046	−	0.359758i	$-0.117141\pi$
$450$	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	0.859431	−	0.511252i	$-0.170818\pi$
$457$	7.44322	+	7.44322i	0.348179	+	0.348179i	−0.511252	+	0.859431i	$0.670818\pi$
$458$	−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	0.572614	−	0.819825i	$-0.305930\pi$
$463$	−5.31937	−	5.31937i	−0.247212	−	0.247212i	−0.819825	+	0.572614i	$0.805930\pi$
$464$	−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	−0.372210	−	0.928149i	$-0.621400\pi$
$467$	12.0139	−	12.0139i	0.555939	−	0.555939i	0.928149	+	0.372210i	$0.121400\pi$
$468$	−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	−0.827172	−	0.561949i	$-0.810052\pi$
$487$	−5.85296	+	5.85296i	−0.265223	+	0.265223i	0.561949	+	0.827172i	$0.310052\pi$
$488$	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	$-0.762323\pi$
$491$		−	30.1005i		−	1.35842i	0.733945	−	0.679209i	$-0.237677\pi$
$492$	−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	0.551343	−	0.834279i	$-0.314116\pi$
$503$	−6.34559	−	6.34559i	−0.282936	−	0.282936i	−0.834279	+	0.551343i	$0.814116\pi$
$504$	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	$-0.643319\pi$
$509$		−	40.6251i		−	1.80068i	0.435190	−	0.900338i	$-0.356681\pi$
$510$	−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	0.592793	−	0.805355i	$-0.298025\pi$
$523$	−4.86113	−	4.86113i	−0.212563	−	0.212563i	−0.805355	+	0.592793i	$0.798025\pi$
$524$	−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	−0.517806	−	0.855498i	$-0.673251\pi$
$547$	7.89796	−	7.89796i	0.337692	−	0.337692i	0.855498	+	0.517806i	$0.173251\pi$
$548$	−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	0.847887	−	0.530176i	$-0.177874\pi$
$557$	7.49825	+	7.49825i	0.317711	+	0.317711i	−0.530176	+	0.847887i	$0.677874\pi$
$558$	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	0.680440	−	0.732804i	$-0.261789\pi$
$563$	−1.24248	−	1.24248i	−0.0523644	−	0.0523644i	−0.732804	+	0.680440i	$0.761789\pi$
$564$	−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	$-0.844876\pi$
$569$		−	22.3401i		−	0.936548i	0.883583	−	0.468274i	$-0.155124\pi$
$570$	−4.87986	−	24.4600i	−0.204395	−	1.02452i
$571$		−	40.7031i		−	1.70337i	−0.524052	−	0.851686i	$-0.675580\pi$
$571$		−	40.7031i		−	1.70337i	0.524052	−	0.851686i	$-0.324420\pi$
$572$	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	0.581897	−	0.813263i	$-0.302311\pi$
$577$	−5.55759	−	5.55759i	−0.231366	−	0.231366i	−0.813263	+	0.581897i	$0.802311\pi$
$578$	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	−0.811957	−	0.583717i	$-0.801598\pi$
$587$	−5.52984	+	5.52984i	−0.228241	+	0.228241i	0.583717	+	0.811957i	$0.301598\pi$
$588$	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	0.0666872	−	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
$598$	−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	−0.848108	−	0.529823i	$-0.822258\pi$
$607$	−7.84172	+	7.84172i	−0.318286	+	0.318286i	0.529823	+	0.848108i	$0.322258\pi$
$608$	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	−0.692523	−	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	$0.587027\pi$
$618$	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	$-0.949665\pi$
$631$		−	7.91135i		−	0.314946i	0.987523	−	0.157473i	$-0.0503347\pi$
$632$	−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	0.736078	−	0.676897i	$-0.236676\pi$
$643$	1.50067	+	1.50067i	0.0591807	+	0.0591807i	−0.676897	+	0.736078i	$0.736676\pi$
$644$	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	−0.939488	−	0.342582i	$-0.888699\pi$
$647$	−15.1830	+	15.1830i	−0.596906	+	0.596906i	0.342582	+	0.939488i	$0.388699\pi$
$648$	−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	−0.900084	−	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
$658$	−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	−0.677801	−	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	$0.547032\pi$
$678$	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	0.150037	−	0.988680i	$-0.452061\pi$
$683$	−21.9173	−	21.9173i	−0.838644	−	0.838644i	−0.988680	+	0.150037i	$0.952061\pi$
$684$	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	$-0.988205\pi$
$691$		−	1.94770i		−	0.0740939i	0.999314	−	0.0370470i	$-0.0117951\pi$
$692$	−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	$-0.940389\pi$
$709$		−	9.91483i		−	0.372359i	0.982516	−	0.186180i	$-0.0596106\pi$
$710$	−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	−0.303642	+	0.952786i	$0.598203\pi$
$727$	−33.8770	+	33.8770i	−1.25643	+	1.25643i	−0.952786	+	0.303642i	$0.901797\pi$
$728$	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	−0.0993880	−	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
$738$	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	0.413281	−	0.910604i	$-0.364383\pi$
$743$	−13.5560	−	13.5560i	−0.497323	−	0.497323i	−0.910604	+	0.413281i	$0.864383\pi$
$744$	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	$-0.997175\pi$
$751$		−	0.486430i		−	0.0177501i	0.999961	−	0.00887505i	$-0.00282505\pi$
$752$	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	0.986729	−	0.162379i	$-0.0519166\pi$
$757$	22.6809	+	22.6809i	0.824350	+	0.824350i	−0.162379	+	0.986729i	$0.551917\pi$
$758$	−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	$0.219416\pi$
$769$			35.2742i			1.27202i	−0.771681	+	0.636010i	$0.780584\pi$
$770$	−0.591028	−	2.96249i	−0.0212992	−	0.106761i
$771$		−	15.4491i		−	0.556387i
$772$	13.1872	+	34.5656i	0.474619	+	1.24404i
$773$	−26.9007	+	26.9007i	−0.967551	+	0.967551i	−0.999490	−	0.0319390i	$-0.989832\pi$
$773$	−26.9007	+	26.9007i	−0.967551	+	0.967551i	0.0319390	+	0.999490i	$0.489832\pi$
$774$	3.06899	−	14.3660i	0.110313	−	0.516376i
$775$	−19.8567	−	18.7233i	−0.713273	−	0.672561i
$776$	15.7135	−	21.4884i	0.564081	−	0.771390i
$777$	2.76906	+	2.76906i	0.0993396	+	0.0993396i
$778$	−1.60429	−	2.47594i	−0.0575164	−	0.0887667i
$779$	9.42537			0.337699
$780$	5.11473	+	0.0692901i	0.183137	+	0.00248098i
$781$	−4.39270			−0.157183
$782$	−45.6080	−	70.3881i	−1.63094	−	2.51707i
$783$	−29.7960	−	29.7960i	−1.06482	−	1.06482i
$784$	17.3363	−	15.4814i	0.619153	−	0.552906i
$785$	0.200232	−	0.504220i	0.00714658	−	0.0179964i
$786$	5.23870	−	24.5225i	0.186858	−	0.874687i
$787$	19.9522	−	19.9522i	0.711220	−	0.711220i	−0.255570	−	0.966791i	$-0.582263\pi$
$787$	19.9522	−	19.9522i	0.711220	−	0.711220i	0.966791	+	0.255570i	$0.0822632\pi$
$788$	−2.04593	+	0.780550i	−0.0728834	+	0.0278059i
$789$		−	12.9449i		−	0.460850i
$790$	4.28634	+	2.86052i	0.152501	+	0.101773i
$791$			12.7930i			0.454868i
$792$	−0.642936	−	4.14176i	−0.0228457	−	0.147171i
$793$	−3.39199	+	3.39199i	−0.120453	+	0.120453i
$794$	−45.4575	−	9.71103i	−1.61323	−	0.344631i
$795$	−3.13241	−	7.25894i	−0.111095	−	0.257448i
$796$	3.04025	−	6.79100i	0.107759	−	0.240701i
$797$	0.641383	+	0.641383i	0.0227190	+	0.0227190i	0.718375	−	0.695656i	$-0.244886\pi$
$797$	0.641383	+	0.641383i	0.0227190	+	0.0227190i	−0.695656	+	0.718375i	$0.744886\pi$
$798$	10.2089	−	6.61489i	0.361393	−	0.234165i
$799$	−37.4420			−1.32460
$800$	24.1449	−	14.7317i	0.853651	−	0.520845i
$801$	6.23920			0.220451
$802$	19.0338	−	12.3330i	0.672108	−	0.435493i
$803$	6.00090	+	6.00090i	0.211767	+	0.211767i
$804$	13.3128	−	29.7366i	0.469505	−	1.04873i
$805$	8.24870	+	19.1153i	0.290729	+	0.673725i
$806$	7.54899	+	1.61268i	0.265902	+	0.0568042i
$807$	−5.89465	+	5.89465i	−0.207502	+	0.207502i
$808$	2.70261	+	17.4101i	0.0950774	+	0.612484i
$809$			13.2680i			0.466478i	0.972419	+	0.233239i	$0.0749325\pi$
$809$			13.2680i			0.466478i	−0.972419	+	0.233239i	$0.925067\pi$
$810$	2.79553	+	1.86561i	0.0982249	+	0.0655509i
$811$		−	10.2936i		−	0.361458i	−0.983533	−	0.180729i	$-0.942154\pi$
$811$		−	10.2936i		−	0.361458i	0.983533	−	0.180729i	$-0.0578458\pi$
$812$	16.0018	−	6.10490i	0.561554	−	0.214240i
$813$	3.98337	−	3.98337i	0.139703	−	0.139703i
$814$	0.812470	−	3.80319i	0.0284771	−	0.133302i
$815$	−9.95238	+	25.0619i	−0.348617	+	0.877879i
$816$	23.7061	−	21.1696i	0.829879	−	0.741085i
$817$	−29.9397	−	29.9397i	−1.04746	−	1.04746i
$818$	−29.7312	−	45.8850i	−1.03953	−	1.60433i
$819$	1.84496			0.0644683
$820$	−6.11209	−	0.0828016i	−0.213443	−	0.00289156i
$821$	−1.68106			−0.0586694			−0.0293347	−	0.999570i	$-0.509339\pi$
$821$	−1.68106			−0.0586694			−0.0293347	+	0.999570i	$0.509339\pi$
$822$	−3.20281	−	4.94298i	−0.111711	−	0.172406i
$823$	30.8205	+	30.8205i	1.07434	+	1.07434i	0.997006	+	0.0773299i	$0.0246395\pi$
$823$	30.8205	+	30.8205i	1.07434	+	1.07434i	0.0773299	+	0.997006i	$0.475361\pi$
$824$	21.3860	−	29.2457i	0.745018	−	1.01882i
$825$	−0.147103	−	5.00734i	−0.00512147	−	0.174333i
$826$	−0.241422	+	1.13010i	−0.00840015	+	0.0393213i
$827$	−2.18949	+	2.18949i	−0.0761362	+	0.0761362i	−0.744149	−	0.668013i	$-0.767145\pi$
$827$	−2.18949	+	2.18949i	−0.0761362	+	0.0761362i	0.668013	+	0.744149i	$0.267145\pi$
$828$	10.2964	+	26.9885i	0.357826	+	0.937914i
$829$			44.9575i			1.56144i	0.624881	+	0.780720i	$0.285147\pi$
$829$			44.9575i			1.56144i	−0.624881	+	0.780720i	$0.714853\pi$
$830$	2.33606	+	11.7094i	0.0810859	+	0.406438i
$831$		−	22.0349i		−	0.764382i
$832$	−3.67571	+	7.10557i	−0.127432	+	0.246341i
$833$	−28.5425	+	28.5425i	−0.988938	+	0.988938i
$834$	−6.68586	−	1.42829i	−0.231512	−	0.0494577i
$835$	25.9109	+	10.2895i	0.896683	+	0.356084i
$836$	−11.0261	−	4.93628i	−0.381347	−	0.170725i
$837$	20.7124	+	20.7124i	0.715925	+	0.715925i
$838$	−18.8829	+	12.2352i	−0.652299	+	0.422658i
$839$	−20.4522			−0.706088			−0.353044	−	0.935607i	$-0.614853\pi$
$839$	−20.4522			−0.706088			−0.353044	+	0.935607i	$0.614853\pi$
$840$	−6.67833	+	4.19989i	−0.230424	+	0.144910i
$841$	−32.6574			−1.12612
$842$	4.18233	−	2.70994i	0.144133	−	0.0933908i
$843$	9.11239	+	9.11239i	0.313847	+	0.313847i
$844$	18.4393	+	8.25508i	0.634708	+	0.284151i
$845$	2.05307	−	0.885949i	0.0706277	−	0.0304776i
$846$	12.6106	+	2.69398i	0.433561	+	0.0926210i
$847$	−7.89097	+	7.89097i	−0.271137	+	0.271137i
$848$	12.3450	+	0.697759i	0.423927	+	0.0239611i
$849$			19.1121i			0.655926i
$850$	−40.4216	+	27.9099i	−1.38645	+	0.957303i
$851$			26.8021i			0.918764i
$852$	4.08915	+	10.7182i	0.140092	+	0.367201i
$853$	10.9833	−	10.9833i	0.376062	−	0.376062i	−0.493618	−	0.869679i	$-0.664326\pi$
$853$	10.9833	−	10.9833i	0.376062	−	0.376062i	0.869679	+	0.493618i	$0.164326\pi$
$854$	1.54564	−	7.23517i	0.0528907	−	0.247583i
$855$	−23.9508	+	10.3354i	−0.819102	+	0.353462i
$856$	−22.5392	−	16.4819i	−0.770375	−	0.563339i
$857$	−26.6753	−	26.6753i	−0.911212	−	0.911212i	0.0851556	−	0.996368i	$-0.472861\pi$
$857$	−26.6753	−	26.6753i	−0.911212	−	0.911212i	−0.996368	+	0.0851556i	$0.972861\pi$
$858$	0.770481	+	1.18910i	0.0263038	+	0.0405953i
$859$	11.5130			0.392817			0.196409	−	0.980522i	$-0.437072\pi$
$859$	11.5130			0.392817			0.196409	+	0.980522i	$0.437072\pi$
$860$	19.1520	+	19.6781i	0.653079	+	0.671017i
$861$	1.70497			0.0581052
$862$	−26.1492	−	40.3568i	−0.890646	−	1.37456i
$863$	−2.48286	−	2.48286i	−0.0845177	−	0.0845177i	0.663584	−	0.748102i	$-0.269034\pi$
$863$	−2.48286	−	2.48286i	−0.0845177	−	0.0845177i	−0.748102	+	0.663584i	$0.769034\pi$
$864$	−26.3672	+	15.0434i	−0.897032	+	0.511787i
$865$	2.68804	+	1.06745i	0.0913962	+	0.0362946i
$866$	−8.53984	+	39.9752i	−0.290196	+	1.35841i
$867$	−25.2804	+	25.2804i	−0.858568	+	0.858568i
$868$	−11.1235	+	4.24376i	−0.377556	+	0.144043i
$869$			1.42742i			0.0484220i
$870$	27.8525	−	5.55669i	0.944289	−	0.188389i
$871$		−	14.2424i		−	0.482584i
$872$	16.4188	−	2.54873i	0.556010	−	0.0863108i
$873$	11.2589	−	11.2589i	0.381055	−	0.381055i
$874$	81.4200	+	17.3936i	2.75407	+	0.588348i
$875$	11.0484	−	5.15762i	0.373505	−	0.174359i
$876$	9.05606	−	20.2285i	0.305976	−	0.683457i
$877$	−9.52846	−	9.52846i	−0.321753	−	0.321753i	0.527686	−	0.849439i	$-0.323060\pi$
$877$	−9.52846	−	9.52846i	−0.321753	−	0.321753i	−0.849439	+	0.527686i	$0.823060\pi$
$878$	−5.34553	+	3.46364i	−0.180403	+	0.116892i
$879$	−11.7893			−0.397645
$880$	7.10678	+	3.29790i	0.239570	+	0.111172i
$881$	23.8353			0.803030			0.401515	−	0.915852i	$-0.368484\pi$
$881$	23.8353			0.803030			0.401515	+	0.915852i	$0.368484\pi$
$882$	11.6668	−	7.55954i	0.392843	−	0.254543i
$883$	−18.1255	−	18.1255i	−0.609973	−	0.609973i	0.332966	−	0.942939i	$-0.391951\pi$
$883$	−18.1255	−	18.1255i	−0.609973	−	0.609973i	−0.942939	+	0.332966i	$0.891951\pi$
$884$	5.67701	−	12.6807i	0.190939	−	0.426499i
$885$	−0.707272	+	1.78104i	−0.0237747	+	0.0598689i
$886$	33.0710	+	7.06491i	1.11104	+	0.237350i
$887$	40.7732	−	40.7732i	1.36903	−	1.36903i	0.507202	−	0.861827i	$-0.330680\pi$
$887$	40.7732	−	40.7732i	1.36903	−	1.36903i	0.861827	−	0.507202i	$-0.169320\pi$
$888$	−10.0362	+	1.55794i	−0.336792	+	0.0522810i
$889$			13.0527i			0.437774i
$890$	−6.47387	+	9.70078i	−0.217005	+	0.325171i
$891$			0.930958i			0.0311883i
$892$	28.9998	−	11.0638i	0.970984	−	0.370443i
$893$	26.2813	−	26.2813i	0.879469	−	0.879469i
$894$	−0.339594	+	1.58965i	−0.0113577	+	0.0531657i
$895$	−4.30149	−	9.96813i	−0.143783	−	0.333198i
$896$	−1.20160	−	12.2798i	−0.0401427	−	0.410238i
$897$	−6.90486	−	6.90486i	−0.230546	−	0.230546i
$898$	−11.7247	−	18.0950i	−0.391258	−	0.603839i
$899$	42.8605			1.42948
$900$	15.6223	−	6.49179i	0.520742	−	0.216393i
$901$	−21.4735			−0.715388
$902$	−0.920723	−	1.42098i	−0.0306567	−	0.0473134i
$903$	−5.41583	−	5.41583i	−0.180228	−	0.180228i
$904$	−26.7823	−	19.5847i	−0.890767	−	0.651376i
$905$	−14.6614	−	33.9758i	−0.487361	−	1.12939i
$906$	−5.50315	+	25.7603i	−0.182830	+	0.855830i
$907$	4.06624	−	4.06624i	0.135017	−	0.135017i	−0.636368	−	0.771385i	$-0.719564\pi$
$907$	4.06624	−	4.06624i	0.135017	−	0.135017i	0.771385	+	0.636368i	$0.219564\pi$
$908$	5.14958	+	13.4978i	0.170895	+	0.447940i
$909$			10.5380i			0.349524i
$910$	−1.91436	+	2.86857i	−0.0634604	+	0.0950923i
$911$			39.9899i			1.32492i	0.749095	+	0.662462i	$0.230489\pi$
$911$			39.9899i			1.32492i	−0.749095	+	0.662462i	$0.769511\pi$
$912$	−1.78039	+	31.4991i	−0.0589545	+	1.04304i
$913$	−2.33868	+	2.33868i	−0.0773990	+	0.0773990i
$914$	14.5580	+	3.11000i	0.481534	+	0.102869i
$915$	4.52812	−	11.4026i	0.149695	−	0.376959i
$916$	−2.15654	−	0.965460i	−0.0712542	−	0.0318997i
$917$	11.9545	+	11.9545i	0.394773	+	0.394773i
$918$	44.2444	−	28.6682i	1.46028	−	0.946190i
$919$	−11.6349			−0.383799			−0.191899	−	0.981415i	$-0.561465\pi$
$919$	−11.6349			−0.383799			−0.191899	+	0.981415i	$0.561465\pi$
$920$	−52.6458	−	11.9946i	−1.73568	−	0.395449i
$921$	−26.4468			−0.871451
$922$	−25.6245	+	16.6034i	−0.843898	+	0.546804i
$923$	3.54600	+	3.54600i	0.116718	+	0.116718i
$924$	−1.99453	−	0.892930i	−0.0656154	−	0.0293752i
$925$	15.6902	−	0.460939i	0.515891	−	0.0151556i
$926$	−10.4040	−	2.22259i	−0.341896	−	0.0730387i
$927$	15.3233	−	15.3233i	0.503283	−	0.503283i
$928$	−11.7163	+	42.8458i	−0.384606	+	1.40648i
$929$			8.92800i			0.292918i	0.989217	+	0.146459i	$0.0467877\pi$
$929$			8.92800i			0.292918i	−0.989217	+	0.146459i	$0.953212\pi$
$930$	−19.3614	+	3.86267i	−0.634885	+	0.126662i
$931$		−	40.0690i		−	1.31321i
$932$	12.1865	+	31.9425i	0.399182	+	1.04631i
$933$	−17.5683	+	17.5683i	−0.575160	+	0.575160i
$934$	5.01977	−	23.4977i	0.164252	−	0.768867i
$935$	−12.6458	−	5.02180i	−0.413562	−	0.164231i
$936$	−2.82442	+	3.86244i	−0.0923192	+	0.126248i
$937$	24.2793	+	24.2793i	0.793171	+	0.793171i	0.982008	−	0.188837i	$-0.0604718\pi$
$937$	24.2793	+	24.2793i	0.793171	+	0.793171i	−0.188837	+	0.982008i	$0.560472\pi$
$938$	11.9447	+	18.4345i	0.390007	+	0.601909i
$939$	−1.89697			−0.0619052
$940$	−17.2735	+	16.8118i	−0.563401	+	0.548340i
$941$	36.8409			1.20098			0.600490	−	0.799632i	$-0.294972\pi$
$941$	36.8409			1.20098			0.600490	+	0.799632i	$0.294972\pi$
$942$	−0.213411	−	0.329363i	−0.00695331	−	0.0107312i
$943$	8.25129	+	8.25129i	0.268699	+	0.268699i
$944$	−1.99629	−	2.23547i	−0.0649736	−	0.0727584i
$945$	−12.0154	+	5.18495i	−0.390862	+	0.168666i
$946$	−1.58906	+	7.43842i	−0.0516647	+	0.241844i
$947$	−7.31295	+	7.31295i	−0.237639	+	0.237639i	−0.815872	−	0.578233i	$-0.803743\pi$
$947$	−7.31295	+	7.31295i	−0.237639	+	0.237639i	0.578233	+	0.815872i	$0.303743\pi$
$948$	3.48294	−	1.32878i	0.113120	−	0.0431569i
$949$		−	9.68844i		−	0.314500i
$950$	8.78216	−	47.9632i	0.284931	−	1.55613i
$951$			10.4347i			0.338369i
$952$	3.28695	+	21.1744i	0.106531	+	0.686265i
$953$	−27.6641	+	27.6641i	−0.896127	+	0.896127i	−0.995091	−	0.0989642i	$-0.968447\pi$
$953$	−27.6641	+	27.6641i	−0.896127	+	0.896127i	0.0989642	+	0.995091i	$0.468447\pi$
$954$	7.23236	+	1.54504i	0.234156	+	0.0500225i
$955$	40.3199	−	17.3990i	1.30472	−	0.563018i
$956$	−15.5703	+	34.7793i	−0.503579	+	1.12484i
$957$	5.56291	+	5.56291i	0.179823	+	0.179823i
$958$	8.03779	−	5.20809i	0.259689	−	0.168266i
$959$	3.97101			0.128231
$960$	1.43125	−	20.4107i	0.0461934	−	0.658751i
$961$	1.20600			0.0389031
$962$	−3.72599	+	2.41426i	−0.120131	+	0.0778387i
$963$	−11.8094	−	11.8094i	−0.380553	−	0.380553i
$964$	−0.708280	+	1.58208i	−0.0228121	+	0.0509554i
$965$	−38.4423	−	15.2659i	−1.23750	−	0.491427i
$966$	14.7282	+	3.14636i	0.473871	+	0.101232i
$967$	18.7603	−	18.7603i	0.603289	−	0.603289i	−0.337895	−	0.941184i	$-0.609715\pi$
$967$	18.7603	−	18.7603i	0.603289	−	0.603289i	0.941184	+	0.337895i	$0.109715\pi$
$968$	−4.43964	−	28.6000i	−0.142695	−	0.919238i
$969$		−	54.7915i		−	1.76015i
$970$	5.82307	+	29.1878i	0.186968	+	0.937162i
$971$			46.5164i			1.49278i	0.665508	+	0.746391i	$0.268215\pi$
$971$			46.5164i			1.49278i	−0.665508	+	0.746391i	$0.731785\pi$
$972$	−27.8117	+	10.6105i	−0.892061	+	0.340333i
$973$	3.25930	−	3.25930i	0.104489	−	0.104489i
$974$	−2.44554	+	11.4476i	−0.0783601	+	0.366805i
$975$	−3.92342	+	4.16092i	−0.125650	+	0.133256i
$976$	12.7807	+	14.3120i	0.409100	+	0.458116i
$977$	−31.9984	−	31.9984i	−1.02372	−	1.02372i	−0.999712	−	0.0240079i	$-0.992357\pi$
$977$	−31.9984	−	31.9984i	−1.02372	−	1.02372i	−0.0240079	−	0.999712i	$-0.507643\pi$
$978$	10.6074	+	16.3707i	0.339188	+	0.523479i
$979$	−3.23052			−0.103248
$980$	−0.352005	+	25.9836i	−0.0112444	+	0.830017i
$981$	9.93803			0.317297
$982$	−23.1479	−	35.7248i	−0.738679	−	1.14002i
$983$	26.0707	+	26.0707i	0.831527	+	0.831527i	0.987726	−	0.156198i	$-0.0499239\pi$
$983$	26.0707	+	26.0707i	0.831527	+	0.831527i	−0.156198	+	0.987726i	$0.549924\pi$
$984$	−2.61011	+	3.56936i	−0.0832072	+	0.113787i
$985$	0.903586	−	2.27539i	0.0287907	−	0.0725000i
$986$	16.1160	−	75.4395i	0.513239	−	2.40248i
$987$	4.75405	−	4.75405i	0.151323	−	0.151323i
$988$	4.91604	+	12.8857i	0.156400	+	0.409947i
$989$		−	52.4205i		−	1.66687i
$990$	3.89782	+	2.60124i	0.123881	+	0.0826727i
$991$			51.6625i			1.64111i	0.571565	+	0.820557i	$0.306337\pi$
$991$			51.6625i			1.64111i	−0.571565	+	0.820557i	$0.693663\pi$
$992$	8.14445	−	29.7838i	0.258587	−	0.945637i
$993$	−26.4821	+	26.4821i	−0.840384	+	0.840384i
$994$	−7.56368	−	1.61582i	−0.239905	−	0.0512506i
$995$	3.29594	+	7.63791i	0.104488	+	0.242138i
$996$	7.88348	+	3.52934i	0.249798	+	0.111831i
$997$	6.73844	+	6.73844i	0.213409	+	0.213409i	0.805714	−	0.592305i	$-0.201782\pi$
$997$	6.73844	+	6.73844i	0.213409	+	0.213409i	−0.592305	+	0.805714i	$0.701782\pi$
$998$	4.97656	−	3.22456i	0.157530	−	0.102072i
$999$	−16.8472			−0.533021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.o.a.27.31	yes	72
4.3	odd	2	inner	260.2.o.a.27.12	✓	72
5.3	odd	4	inner	260.2.o.a.183.12	yes	72
20.3	even	4	inner	260.2.o.a.183.31	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.o.a.27.12	✓	72	4.3	odd	2	inner
260.2.o.a.27.31	yes	72	1.1	even	1	trivial
260.2.o.a.183.12	yes	72	5.3	odd	4	inner
260.2.o.a.183.31	yes	72	20.3	even	4	inner

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

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