LMFDB - Embedded newform 570.2.m.a.493.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(37,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 $ x^20 + 153x^16 + 6416x^12 + 78648x^8 + 19120x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.8
Root			$1.75036 + 1.75036i$ of defining polynomial
Character	$\chi$	$=$	570.493
Dual form			570.2.m.a.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.253765 + 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.253765 + 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-1.75036 + 1.39149i) q^{10} +2.74367 q^{11} +(0.707107 + 0.707107i) q^{12} +(-1.20178 + 1.20178i) q^{13} -3.50073 q^{14} +(1.39149 + 1.75036i) q^{15} -1.00000 q^{16} +(-4.87121 + 4.87121i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.94007 - 3.90335i) q^{19} +(-2.22162 - 0.253765i) q^{20} +3.50073i q^{21} +(1.94007 + 1.94007i) q^{22} +(0.0321428 + 0.0321428i) q^{23} +1.00000i q^{24} +(-4.87121 - 1.12754i) q^{25} -1.69957 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.47539 - 2.47539i) q^{28} +6.50952 q^{29} +(-0.253765 + 2.22162i) q^{30} +6.50952i q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.94007 - 1.94007i) q^{33} -6.88893 q^{34} +(-4.87121 - 6.12754i) q^{35} +1.00000 q^{36} +(4.58998 + 4.58998i) q^{37} +(4.13192 - 1.38825i) q^{38} +1.69957i q^{39} +(-1.39149 - 1.75036i) q^{40} -5.96665i q^{41} +(-2.47539 + 2.47539i) q^{42} +(5.39582 + 5.39582i) q^{43} +2.74367i q^{44} +(2.22162 + 0.253765i) q^{45} +0.0454567i q^{46} +(3.66743 - 3.66743i) q^{47} +(-0.707107 + 0.707107i) q^{48} -5.25508i q^{49} +(-2.64717 - 4.24175i) q^{50} +6.88893i q^{51} +(-1.20178 - 1.20178i) q^{52} +(8.97544 - 8.97544i) q^{53} -1.00000i q^{54} +(-0.696246 + 6.09540i) q^{55} -3.50073i q^{56} +(-1.38825 - 4.13192i) q^{57} +(4.60292 + 4.60292i) q^{58} +4.42301 q^{59} +(-1.75036 + 1.39149i) q^{60} -2.95077 q^{61} +(-4.60292 + 4.60292i) q^{62} +(2.47539 + 2.47539i) q^{63} -1.00000i q^{64} +(-2.36493 - 2.97487i) q^{65} +2.74367 q^{66} +(7.00145 + 7.00145i) q^{67} +(-4.87121 - 4.87121i) q^{68} +0.0454567 q^{69} +(0.888360 - 7.77729i) q^{70} -5.56594i q^{71} +(0.707107 + 0.707107i) q^{72} +(-2.19205 - 2.19205i) q^{73} +6.49122i q^{74} +(-4.24175 + 2.64717i) q^{75} +(3.90335 + 1.94007i) q^{76} +(-6.79164 + 6.79164i) q^{77} +(-1.20178 + 1.20178i) q^{78} -0.225823 q^{79} +(0.253765 - 2.22162i) q^{80} -1.00000 q^{81} +(4.21906 - 4.21906i) q^{82} +(-3.87246 - 3.87246i) q^{83} -3.50073 q^{84} +(-9.58584 - 12.0581i) q^{85} +7.63084i q^{86} +(4.60292 - 4.60292i) q^{87} +(-1.94007 + 1.94007i) q^{88} -9.13628 q^{89} +(1.39149 + 1.75036i) q^{90} -5.94974i q^{91} +(-0.0321428 + 0.0321428i) q^{92} +(4.60292 + 4.60292i) q^{93} +5.18653 q^{94} +(8.17945 + 5.30063i) q^{95} -1.00000 q^{96} +(-8.76663 - 8.76663i) q^{97} +(3.71590 - 3.71590i) q^{98} -2.74367i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7	$ 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} + 4 q^{17} + 44 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{30} + 4 q^{35} + 20 q^{36} - 4 q^{38} - 4 q^{42} + 52 q^{43} + 4 q^{47} + 16 q^{55} - 4 q^{57} + 8 q^{58} + 32 q^{61} - 8 q^{62} + 4 q^{63} - 8 q^{66} + 4 q^{68} - 20 q^{73} + 20 q^{76} - 24 q^{77} + 4 q^{80} - 20 q^{81} - 24 q^{82} - 116 q^{83} - 60 q^{85} + 8 q^{87} - 44 q^{92} + 8 q^{93} - 32 q^{95} - 20 q^{96}+O(q^{100}) $ 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 + 4 * q^17 + 44 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^30 + 4 * q^35 + 20 * q^36 - 4 * q^38 - 4 * q^42 + 52 * q^43 + 4 * q^47 + 16 * q^55 - 4 * q^57 + 8 * q^58 + 32 * q^61 - 8 * q^62 + 4 * q^63 - 8 * q^66 + 4 * q^68 - 20 * q^73 + 20 * q^76 - 24 * q^77 + 4 * q^80 - 20 * q^81 - 24 * q^82 - 116 * q^83 - 60 * q^85 + 8 * q^87 - 44 * q^92 + 8 * q^93 - 32 * q^95 - 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	−0.253765	+	2.22162i	−0.113487	+	0.993539i
$5$	−0.253765	+	2.22162i	−0.113487	+	0.993539i
$6$	1.00000			0.408248
$7$	−2.47539	+	2.47539i	−0.935608	+	0.935608i	−0.998049	−	0.0624406i	$-0.980112\pi$
$7$	−2.47539	+	2.47539i	−0.935608	+	0.935608i	0.0624406	+	0.998049i	$0.480112\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−1.75036	+	1.39149i	−0.553513	+	0.440026i
$11$	2.74367			0.827247			0.413624	−	0.910448i	$-0.364263\pi$
$11$	2.74367			0.827247			0.413624	+	0.910448i	$0.364263\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−1.20178	+	1.20178i	−0.333314	+	0.333314i	−0.853844	−	0.520530i	$-0.825735\pi$
$13$	−1.20178	+	1.20178i	−0.333314	+	0.333314i	0.520530	+	0.853844i	$0.325735\pi$
$14$	−3.50073			−0.935608
$15$	1.39149	+	1.75036i	0.359280	+	0.451942i
$16$	−1.00000			−0.250000
$17$	−4.87121	+	4.87121i	−1.18144	+	1.18144i	−0.202070	+	0.979371i	$0.564767\pi$
$17$	−4.87121	+	4.87121i	−1.18144	+	1.18144i	−0.979371	+	0.202070i	$0.935233\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	1.94007	−	3.90335i	0.445082	−	0.895490i
$19$	1.94007	−	3.90335i	0.445082	−	0.895490i
$20$	−2.22162	−	0.253765i	−0.496770	−	0.0567435i
$21$			3.50073i			0.763921i
$22$	1.94007	+	1.94007i	0.413624	+	0.413624i
$23$	0.0321428	+	0.0321428i	0.00670223	+	0.00670223i	0.710450	−	0.703748i	$-0.248491\pi$
$23$	0.0321428	+	0.0321428i	0.00670223	+	0.00670223i	−0.703748	+	0.710450i	$0.748491\pi$
$24$			1.00000i			0.204124i
$25$	−4.87121	−	1.12754i	−0.974241	−	0.225508i
$26$	−1.69957			−0.333314
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.47539	−	2.47539i	−0.467804	−	0.467804i
$29$	6.50952			1.20879			0.604394	−	0.796686i	$-0.293415\pi$
$29$	6.50952			1.20879			0.604394	+	0.796686i	$0.293415\pi$
$30$	−0.253765	+	2.22162i	−0.0463309	+	0.405611i
$31$			6.50952i			1.16914i	0.811342	+	0.584572i	$0.198738\pi$
$31$			6.50952i			1.16914i	−0.811342	+	0.584572i	$0.801262\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.94007	−	1.94007i	0.337722	−	0.337722i
$34$	−6.88893			−1.18144
$35$	−4.87121	−	6.12754i	−0.823384	−	1.03574i
$36$	1.00000			0.166667
$37$	4.58998	+	4.58998i	0.754589	+	0.754589i	0.975332	−	0.220743i	$-0.0708483\pi$
$37$	4.58998	+	4.58998i	0.754589	+	0.754589i	−0.220743	+	0.975332i	$0.570848\pi$
$38$	4.13192	−	1.38825i	0.670286	−	0.225204i
$39$			1.69957i			0.272150i
$40$	−1.39149	−	1.75036i	−0.220013	−	0.276757i
$41$		−	5.96665i		−	0.931833i	−0.884829	−	0.465917i	$-0.845725\pi$
$41$		−	5.96665i		−	0.931833i	0.884829	−	0.465917i	$-0.154275\pi$
$42$	−2.47539	+	2.47539i	−0.381960	+	0.381960i
$43$	5.39582	+	5.39582i	0.822855	+	0.822855i	0.986517	−	0.163662i	$-0.0523305\pi$
$43$	5.39582	+	5.39582i	0.822855	+	0.822855i	−0.163662	+	0.986517i	$0.552331\pi$
$44$			2.74367i			0.413624i
$45$	2.22162	+	0.253765i	0.331180	+	0.0378290i
$46$			0.0454567i			0.00670223i
$47$	3.66743	−	3.66743i	0.534950	−	0.534950i	−0.387091	−	0.922041i	$-0.626520\pi$
$47$	3.66743	−	3.66743i	0.534950	−	0.534950i	0.922041	+	0.387091i	$0.126520\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	5.25508i		−	0.750725i
$50$	−2.64717	−	4.24175i	−0.374367	−	0.599875i
$51$			6.88893i			0.964643i
$52$	−1.20178	−	1.20178i	−0.166657	−	0.166657i
$53$	8.97544	−	8.97544i	1.23287	−	1.23287i	0.270015	−	0.962856i	$-0.412971\pi$
$53$	8.97544	−	8.97544i	1.23287	−	1.23287i	0.962856	−	0.270015i	$-0.0870288\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−0.696246	+	6.09540i	−0.0938818	+	0.821903i
$56$		−	3.50073i		−	0.467804i
$57$	−1.38825	−	4.13192i	−0.183878	−	0.547286i
$58$	4.60292	+	4.60292i	0.604394	+	0.604394i
$59$	4.42301			0.575826			0.287913	−	0.957657i	$-0.407039\pi$
$59$	4.42301			0.575826			0.287913	+	0.957657i	$0.407039\pi$
$60$	−1.75036	+	1.39149i	−0.225971	+	0.179640i
$61$	−2.95077			−0.377808			−0.188904	−	0.981996i	$-0.560493\pi$
$61$	−2.95077			−0.377808			−0.188904	+	0.981996i	$0.560493\pi$
$62$	−4.60292	+	4.60292i	−0.584572	+	0.584572i
$63$	2.47539	+	2.47539i	0.311869	+	0.311869i
$64$		−	1.00000i		−	0.125000i
$65$	−2.36493	−	2.97487i	−0.293334	−	0.368987i
$66$	2.74367			0.337722
$67$	7.00145	+	7.00145i	0.855363	+	0.855363i	0.990788	−	0.135424i	$-0.0432398\pi$
$67$	7.00145	+	7.00145i	0.855363	+	0.855363i	−0.135424	+	0.990788i	$0.543240\pi$
$68$	−4.87121	−	4.87121i	−0.590721	−	0.590721i
$69$	0.0454567			0.00547235
$70$	0.888360	−	7.77729i	0.106179	−	0.929564i
$71$		−	5.56594i		−	0.660556i	−0.943884	−	0.330278i	$-0.892858\pi$
$71$		−	5.56594i		−	0.660556i	0.943884	−	0.330278i	$-0.107142\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−2.19205	−	2.19205i	−0.256560	−	0.256560i	0.567094	−	0.823653i	$-0.308068\pi$
$73$	−2.19205	−	2.19205i	−0.256560	−	0.256560i	−0.823653	+	0.567094i	$0.808068\pi$
$74$			6.49122i			0.754589i
$75$	−4.24175	+	2.64717i	−0.489795	+	0.305669i
$76$	3.90335	+	1.94007i	0.447745	+	0.222541i
$77$	−6.79164	+	6.79164i	−0.773979	+	0.773979i
$78$	−1.20178	+	1.20178i	−0.136075	+	0.136075i
$79$	−0.225823			−0.0254070			−0.0127035	−	0.999919i	$-0.504044\pi$
$79$	−0.225823			−0.0254070			−0.0127035	+	0.999919i	$0.504044\pi$
$80$	0.253765	−	2.22162i	0.0283717	−	0.248385i
$81$	−1.00000			−0.111111
$82$	4.21906	−	4.21906i	0.465917	−	0.465917i
$83$	−3.87246	−	3.87246i	−0.425058	−	0.425058i	0.461883	−	0.886941i	$-0.347174\pi$
$83$	−3.87246	−	3.87246i	−0.425058	−	0.425058i	−0.886941	+	0.461883i	$0.847174\pi$
$84$	−3.50073			−0.381960
$85$	−9.58584	−	12.0581i	−1.03973	−	1.30789i
$86$			7.63084i			0.822855i
$87$	4.60292	−	4.60292i	0.493485	−	0.493485i
$88$	−1.94007	+	1.94007i	−0.206812	+	0.206812i
$89$	−9.13628			−0.968444			−0.484222	−	0.874945i	$-0.660897\pi$
$89$	−9.13628			−0.968444			−0.484222	+	0.874945i	$0.660897\pi$
$90$	1.39149	+	1.75036i	0.146675	+	0.184504i
$91$		−	5.94974i		−	0.623703i
$92$	−0.0321428	+	0.0321428i	−0.00335112	+	0.00335112i
$93$	4.60292	+	4.60292i	0.477301	+	0.477301i
$94$	5.18653			0.534950
$95$	8.17945	+	5.30063i	0.839194	+	0.543833i
$96$	−1.00000			−0.102062
$97$	−8.76663	−	8.76663i	−0.890117	−	0.890117i	0.104417	−	0.994534i	$-0.466702\pi$
$97$	−8.76663	−	8.76663i	−0.890117	−	0.890117i	−0.994534	+	0.104417i	$0.966702\pi$
$98$	3.71590	−	3.71590i	0.375363	−	0.375363i
$99$		−	2.74367i		−	0.275749i
$100$	1.12754	−	4.87121i	0.112754	−	0.487121i
$101$	11.2650			1.12091			0.560455	−	0.828185i	$-0.310626\pi$
$101$	11.2650			1.12091			0.560455	+	0.828185i	$0.310626\pi$
$102$	−4.87121	+	4.87121i	−0.482321	+	0.482321i
$103$	0.762447	−	0.762447i	0.0751262	−	0.0751262i	−0.668545	−	0.743671i	$-0.733083\pi$
$103$	0.762447	−	0.762447i	0.0751262	−	0.0751262i	0.743671	+	0.668545i	$0.233083\pi$
$104$		−	1.69957i		−	0.166657i
$105$	−7.77729	−	0.888360i	−0.758986	−	0.0866951i
$106$	12.6932			1.23287
$107$	−13.5351	−	13.5351i	−1.30849	−	1.30849i	−0.922505	−	0.385985i	$-0.873861\pi$
$107$	−13.5351	−	13.5351i	−1.30849	−	1.30849i	−0.385985	−	0.922505i	$-0.626139\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−4.37207			−0.418768			−0.209384	−	0.977833i	$-0.567146\pi$
$109$	−4.37207			−0.418768			−0.209384	+	0.977833i	$0.567146\pi$
$110$	−4.80242	+	3.81777i	−0.457892	+	0.364011i
$111$	6.49122			0.616119
$112$	2.47539	−	2.47539i	0.233902	−	0.233902i
$113$	6.95599	−	6.95599i	0.654365	−	0.654365i	−0.299676	−	0.954041i	$-0.596879\pi$
$113$	6.95599	−	6.95599i	0.654365	−	0.654365i	0.954041	+	0.299676i	$0.0968786\pi$
$114$	1.94007	−	3.90335i	0.181704	−	0.365582i
$115$	−0.0795658	+	0.0632524i	−0.00741955	+	0.00589832i
$116$			6.50952i			0.604394i
$117$	1.20178	+	1.20178i	0.111105	+	0.111105i
$118$	3.12754	+	3.12754i	0.287913	+	0.287913i
$119$		−	24.1162i		−	2.21073i
$120$	−2.22162	−	0.253765i	−0.202805	−	0.0231654i
$121$	−3.47228			−0.315662
$122$	−2.08651	−	2.08651i	−0.188904	−	0.188904i
$123$	−4.21906	−	4.21906i	−0.380419	−	0.380419i
$124$	−6.50952			−0.584572
$125$	3.74110	−	10.5359i	0.334614	−	0.942355i
$126$			3.50073i			0.311869i
$127$	13.7136	+	13.7136i	1.21689	+	1.21689i	0.968716	+	0.248173i	$0.0798302\pi$
$127$	13.7136	+	13.7136i	1.21689	+	1.21689i	0.248173	+	0.968716i	$0.420170\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	7.63084			0.671858
$130$	0.431292	−	3.77581i	0.0378268	−	0.331161i
$131$	8.01380			0.700169			0.350085	−	0.936718i	$-0.386153\pi$
$131$	8.01380			0.700169			0.350085	+	0.936718i	$0.386153\pi$
$132$	1.94007	+	1.94007i	0.168861	+	0.168861i
$133$	4.85988	+	14.4647i	0.421405	+	1.25425i
$134$			9.90155i			0.855363i
$135$	1.75036	−	1.39149i	0.150647	−	0.119760i
$136$		−	6.88893i		−	0.590721i
$137$	−12.6299	+	12.6299i	−1.07905	+	1.07905i	−0.0824532	+	0.996595i	$0.526275\pi$
$137$	−12.6299	+	12.6299i	−1.07905	+	1.07905i	−0.996595	+	0.0824532i	$0.973725\pi$
$138$	0.0321428	+	0.0321428i	0.00273617	+	0.00273617i
$139$			10.3499i			0.877869i	0.898519	+	0.438934i	$0.144644\pi$
$139$			10.3499i			0.877869i	−0.898519	+	0.438934i	$0.855356\pi$
$140$	6.12754	−	4.87121i	0.517871	−	0.411692i
$141$		−	5.18653i		−	0.436785i
$142$	3.93571	−	3.93571i	0.330278	−	0.330278i
$143$	−3.29729	+	3.29729i	−0.275733	+	0.275733i
$144$			1.00000i			0.0833333i
$145$	−1.65189	+	14.4617i	−0.137182	+	1.20098i
$146$		−	3.10002i		−	0.256560i
$147$	−3.71590	−	3.71590i	−0.306482	−	0.306482i
$148$	−4.58998	+	4.58998i	−0.377294	+	0.377294i
$149$		−	9.07466i		−	0.743425i	−0.928348	−	0.371712i	$-0.878771\pi$
$149$		−	9.07466i		−	0.743425i	0.928348	−	0.371712i	$-0.121229\pi$
$150$	−4.87121	−	1.12754i	−0.397732	−	0.0920631i
$151$			1.75287i			0.142647i	0.997453	+	0.0713234i	$0.0227222\pi$
$151$			1.75287i			0.142647i	−0.997453	+	0.0713234i	$0.977278\pi$
$152$	1.38825	+	4.13192i	0.112602	+	0.335143i
$153$	4.87121	+	4.87121i	0.393814	+	0.393814i
$154$	−9.60483			−0.773979
$155$	−14.4617	−	1.65189i	−1.16159	−	0.132683i
$156$	−1.69957			−0.136075
$157$	7.20733	−	7.20733i	0.575207	−	0.575207i	−0.358372	−	0.933579i	$-0.616668\pi$
$157$	7.20733	−	7.20733i	0.575207	−	0.575207i	0.933579	+	0.358372i	$0.116668\pi$
$158$	−0.159681	−	0.159681i	−0.0127035	−	0.0127035i
$159$		−	12.6932i		−	1.00664i
$160$	1.75036	−	1.39149i	0.138378	−	0.110007i
$161$	−0.159132			−0.0125413
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	9.60292	+	9.60292i	0.752159	+	0.752159i	0.974882	−	0.222723i	$-0.0714945\pi$
$163$	9.60292	+	9.60292i	0.752159	+	0.752159i	−0.222723	+	0.974882i	$0.571494\pi$
$164$	5.96665			0.465917
$165$	3.81777	+	4.80242i	0.297213	+	0.373868i
$166$		−	5.47649i		−	0.425058i
$167$	12.9013	+	12.9013i	0.998336	+	0.998336i	0.999999	−	0.00166271i	$-0.000529259\pi$
$167$	12.9013	+	12.9013i	0.998336	+	0.998336i	−0.00166271	+	0.999999i	$0.500529\pi$
$168$	−2.47539	−	2.47539i	−0.190980	−	0.190980i
$169$			10.1114i			0.777804i
$170$	1.74817	−	15.3046i	0.134078	−	1.17381i
$171$	−3.90335	−	1.94007i	−0.298497	−	0.148361i
$172$	−5.39582	+	5.39582i	−0.411427	+	0.411427i
$173$	0.271593	−	0.271593i	0.0206488	−	0.0206488i	−0.696707	−	0.717356i	$-0.745352\pi$
$173$	0.271593	−	0.271593i	0.0206488	−	0.0206488i	0.717356	+	0.696707i	$0.245352\pi$
$174$	6.50952			0.493485
$175$	14.8492	−	9.26703i	1.12249	−	0.700521i
$176$	−2.74367			−0.206812
$177$	3.12754	−	3.12754i	0.235080	−	0.235080i
$178$	−6.46033	−	6.46033i	−0.484222	−	0.484222i
$179$	16.1543			1.20743			0.603715	−	0.797200i	$-0.293686\pi$
$179$	16.1543			1.20743			0.603715	+	0.797200i	$0.293686\pi$
$180$	−0.253765	+	2.22162i	−0.0189145	+	0.165590i
$181$		−	16.1980i		−	1.20399i	−0.798501	−	0.601994i	$-0.794373\pi$
$181$		−	16.1980i		−	1.20399i	0.798501	−	0.601994i	$-0.205627\pi$
$182$	4.20710	−	4.20710i	0.311851	−	0.311851i
$183$	−2.08651	+	2.08651i	−0.154239	+	0.154239i
$184$	−0.0454567			−0.00335112
$185$	−11.3620	+	9.03243i	−0.835349	+	0.664078i
$186$			6.50952i			0.477301i
$187$	−13.3650	+	13.3650i	−0.977344	+	0.977344i
$188$	3.66743	+	3.66743i	0.267475	+	0.267475i
$189$	3.50073			0.254640
$190$	2.03563	+	9.53185i	0.147680	+	0.691513i
$191$	14.6162			1.05759			0.528795	−	0.848750i	$-0.322644\pi$
$191$	14.6162			1.05759			0.528795	+	0.848750i	$0.322644\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	6.20432	−	6.20432i	0.446597	−	0.446597i	−0.447625	−	0.894221i	$-0.647730\pi$
$193$	6.20432	−	6.20432i	0.446597	−	0.446597i	0.894221	+	0.447625i	$0.147730\pi$
$194$		−	12.3979i		−	0.890117i
$195$	−3.77581	−	0.431292i	−0.270392	−	0.0308855i
$196$	5.25508			0.375363
$197$	−9.77456	+	9.77456i	−0.696408	+	0.696408i	−0.963634	−	0.267226i	$-0.913893\pi$
$197$	−9.77456	+	9.77456i	−0.696408	+	0.696408i	0.267226	+	0.963634i	$0.413893\pi$
$198$	1.94007	−	1.94007i	0.137875	−	0.137875i
$199$			7.77253i			0.550980i	0.961304	+	0.275490i	$0.0888401\pi$
$199$			7.77253i			0.550980i	−0.961304	+	0.275490i	$0.911160\pi$
$200$	4.24175	−	2.64717i	0.299937	−	0.187183i
$201$	9.90155			0.698401
$202$	7.96556	+	7.96556i	0.560455	+	0.560455i
$203$	−16.1136	+	16.1136i	−1.13095	+	1.13095i
$204$	−6.88893			−0.482321
$205$	13.2556	+	1.51412i	0.925813	+	0.105751i
$206$	1.07826			0.0751262
$207$	0.0321428	−	0.0321428i	0.00223408	−	0.00223408i
$208$	1.20178	−	1.20178i	0.0833285	−	0.0833285i
$209$	5.32290	−	10.7095i	0.368193	−	0.740792i
$210$	−4.87121	−	6.12754i	−0.336145	−	0.422840i
$211$		−	7.91902i		−	0.545168i	−0.962132	−	0.272584i	$-0.912122\pi$
$211$		−	7.91902i		−	0.545168i	0.962132	−	0.272584i	$-0.0878783\pi$
$212$	8.97544	+	8.97544i	0.616436	+	0.616436i
$213$	−3.93571	−	3.93571i	−0.269671	−	0.269671i
$214$		−	19.1416i		−	1.30849i
$215$	−13.3567	+	10.6182i	−0.910922	+	0.724156i
$216$	1.00000			0.0680414
$217$	−16.1136	−	16.1136i	−1.09386	−	1.09386i
$218$	−3.09152	−	3.09152i	−0.209384	−	0.209384i
$219$	−3.10002			−0.209480
$220$	−6.09540	−	0.696246i	−0.410951	−	0.0469409i
$221$		−	11.7082i		−	0.787582i
$222$	4.58998	+	4.58998i	0.308059	+	0.308059i
$223$	−14.3643	+	14.3643i	−0.961907	+	0.961907i	−0.999301	−	0.0373940i	$-0.988094\pi$
$223$	−14.3643	+	14.3643i	−0.961907	+	0.961907i	0.0373940	+	0.999301i	$0.488094\pi$
$224$	3.50073			0.233902
$225$	−1.12754	+	4.87121i	−0.0751692	+	0.324747i
$226$	9.83726			0.654365
$227$	−15.0385	−	15.0385i	−0.998139	−	0.998139i	0.00185921	−	0.999998i	$-0.499408\pi$
$227$	−15.0385	−	15.0385i	−0.998139	−	0.998139i	−0.999998	+	0.00185921i	$0.999408\pi$
$228$	4.13192	−	1.38825i	0.273643	−	0.0919391i
$229$			2.69570i			0.178137i	0.996026	+	0.0890683i	$0.0283890\pi$
$229$			2.69570i			0.178137i	−0.996026	+	0.0890683i	$0.971611\pi$
$230$	−0.100988	−	0.0115353i	−0.00665893	−	0.000760616i
$231$			9.60483i			0.631951i
$232$	−4.60292	+	4.60292i	−0.302197	+	0.302197i
$233$	−12.4775	−	12.4775i	−0.817426	−	0.817426i	0.168309	−	0.985734i	$-0.446169\pi$
$233$	−12.4775	−	12.4775i	−0.817426	−	0.817426i	−0.985734	+	0.168309i	$0.946169\pi$
$234$			1.69957i			0.111105i
$235$	7.21698	+	9.07831i	0.470784	+	0.592204i
$236$			4.42301i			0.287913i
$237$	−0.159681	+	0.159681i	−0.0103724	+	0.0103724i
$238$	17.0528	−	17.0528i	1.10537	−	1.10537i
$239$			27.2150i			1.76039i	0.474613	+	0.880195i	$0.342588\pi$
$239$			27.2150i			1.76039i	−0.474613	+	0.880195i	$0.657412\pi$
$240$	−1.39149	−	1.75036i	−0.0898200	−	0.112985i
$241$		−	25.1111i		−	1.61755i	−0.588120	−	0.808774i	$-0.700132\pi$
$241$		−	25.1111i		−	1.61755i	0.588120	−	0.808774i	$-0.299868\pi$
$242$	−2.45527	−	2.45527i	−0.157831	−	0.157831i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		−	2.95077i		−	0.188904i
$245$	11.6748	+	1.33355i	0.745875	+	0.0851975i
$246$		−	5.96665i		−	0.380419i
$247$	2.35944	+	7.02251i	0.150127	+	0.446831i
$248$	−4.60292	−	4.60292i	−0.292286	−	0.292286i
$249$	−5.47649			−0.347058
$250$	10.0953	−	4.80461i	0.638485	−	0.303870i
$251$	−2.30195			−0.145298			−0.0726489	−	0.997358i	$-0.523145\pi$
$251$	−2.30195			−0.145298			−0.0726489	+	0.997358i	$0.523145\pi$
$252$	−2.47539	+	2.47539i	−0.155935	+	0.155935i
$253$	0.0881891	+	0.0881891i	0.00554440	+	0.00554440i
$254$			19.3940i			1.21689i
$255$	−15.3046	−	1.74817i	−0.958411	−	0.109474i
$256$	1.00000			0.0625000
$257$	15.7752	+	15.7752i	0.984032	+	0.984032i	0.999874	−	0.0158429i	$-0.00504315\pi$
$257$	15.7752	+	15.7752i	0.984032	+	0.984032i	−0.0158429	+	0.999874i	$0.505043\pi$
$258$	5.39582	+	5.39582i	0.335929	+	0.335929i
$259$	−22.7240			−1.41200
$260$	2.97487	−	2.36493i	0.184494	−	0.146667i
$261$		−	6.50952i		−	0.402929i
$262$	5.66661	+	5.66661i	0.350085	+	0.350085i
$263$	−1.21906	−	1.21906i	−0.0751702	−	0.0751702i	0.668522	−	0.743692i	$-0.266927\pi$
$263$	−1.21906	−	1.21906i	−0.0751702	−	0.0751702i	−0.743692	+	0.668522i	$0.766927\pi$
$264$			2.74367i			0.168861i
$265$	17.6624	+	22.2177i	1.08499	+	1.36482i
$266$	−6.79164	+	13.6646i	−0.416422	+	0.837828i
$267$	−6.46033	+	6.46033i	−0.395366	+	0.395366i
$268$	−7.00145	+	7.00145i	−0.427682	+	0.427682i
$269$	−7.58430			−0.462423			−0.231211	−	0.972904i	$-0.574269\pi$
$269$	−7.58430			−0.462423			−0.231211	+	0.972904i	$0.574269\pi$
$270$	2.22162	+	0.253765i	0.135204	+	0.0154436i
$271$	−25.6741			−1.55959			−0.779795	−	0.626036i	$-0.784676\pi$
$271$	−25.6741			−1.55959			−0.779795	+	0.626036i	$0.784676\pi$
$272$	4.87121	−	4.87121i	0.295360	−	0.295360i
$273$	−4.20710	−	4.20710i	−0.254626	−	0.254626i
$274$	−17.8614			−1.07905
$275$	−13.3650	−	3.09359i	−0.805939	−	0.186551i
$276$			0.0454567i			0.00273617i
$277$	−21.7414	+	21.7414i	−1.30631	+	1.30631i	−0.382257	+	0.924056i	$0.624853\pi$
$277$	−21.7414	+	21.7414i	−1.30631	+	1.30631i	−0.924056	+	0.382257i	$0.875147\pi$
$278$	−7.31850	+	7.31850i	−0.438934	+	0.438934i
$279$	6.50952			0.389715
$280$	7.77729	+	0.888360i	0.464782	+	0.0530897i
$281$		−	21.9050i		−	1.30674i	−0.757037	−	0.653372i	$-0.773354\pi$
$281$		−	21.9050i		−	1.30674i	0.757037	−	0.653372i	$-0.226646\pi$
$282$	3.66743	−	3.66743i	0.218392	−	0.218392i
$283$	15.7217	+	15.7217i	0.934557	+	0.934557i	0.997986	−	0.0634298i	$-0.0202039\pi$
$283$	15.7217	+	15.7217i	0.934557	+	0.934557i	−0.0634298	+	0.997986i	$0.520204\pi$
$284$	5.56594			0.330278
$285$	9.53185	−	2.03563i	0.564618	−	0.120580i
$286$	−4.66307			−0.275733
$287$	14.7698	+	14.7698i	0.871831	+	0.871831i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$		−	30.4573i		−	1.79161i
$290$	−11.3940	+	9.05790i	−0.669080	+	0.531898i
$291$	−12.3979			−0.726777
$292$	2.19205	−	2.19205i	0.128280	−	0.128280i
$293$	−8.25768	+	8.25768i	−0.482419	+	0.482419i	−0.905903	−	0.423484i	$-0.860807\pi$
$293$	−8.25768	+	8.25768i	−0.482419	+	0.482419i	0.423484	+	0.905903i	$0.360807\pi$
$294$		−	5.25508i		−	0.306482i
$295$	−1.12240	+	9.82625i	−0.0653488	+	0.572106i
$296$	−6.49122			−0.377294
$297$	−1.94007	−	1.94007i	−0.112574	−	0.112574i
$298$	6.41675	−	6.41675i	0.371712	−	0.371712i
$299$	−0.0772571			−0.00446790
$300$	−2.64717	−	4.24175i	−0.152835	−	0.244898i
$301$	−26.7135			−1.53974
$302$	−1.23947	+	1.23947i	−0.0713234	+	0.0713234i
$303$	7.96556	−	7.96556i	0.457609	−	0.457609i
$304$	−1.94007	+	3.90335i	−0.111270	+	0.223872i
$305$	0.748802	−	6.55550i	0.0428763	−	0.375367i
$306$			6.88893i			0.393814i
$307$	−22.1239	−	22.1239i	−1.26268	−	1.26268i	−0.949790	−	0.312887i	$-0.898704\pi$
$307$	−22.1239	−	22.1239i	−1.26268	−	1.26268i	−0.312887	−	0.949790i	$-0.601296\pi$
$308$	−6.79164	−	6.79164i	−0.386990	−	0.386990i
$309$		−	1.07826i		−	0.0613403i
$310$	−9.05790	−	11.3940i	−0.514454	−	0.647137i
$311$	3.22108			0.182651			0.0913254	−	0.995821i	$-0.470890\pi$
$311$	3.22108			0.182651			0.0913254	+	0.995821i	$0.470890\pi$
$312$	−1.20178	−	1.20178i	−0.0680374	−	0.0680374i
$313$	−14.9801	−	14.9801i	−0.846724	−	0.846724i	0.142999	−	0.989723i	$-0.454326\pi$
$313$	−14.9801	−	14.9801i	−0.846724	−	0.846724i	−0.989723	+	0.142999i	$0.954326\pi$
$314$	10.1927			0.575207
$315$	−6.12754	+	4.87121i	−0.345248	+	0.274461i
$316$		−	0.225823i		−	0.0127035i
$317$	−13.3317	−	13.3317i	−0.748782	−	0.748782i	0.225468	−	0.974251i	$-0.427609\pi$
$317$	−13.3317	−	13.3317i	−0.748782	−	0.748782i	−0.974251	+	0.225468i	$0.927609\pi$
$318$	8.97544	−	8.97544i	0.503318	−	0.503318i
$319$	17.8600			0.999966
$320$	2.22162	+	0.253765i	0.124192	+	0.0141859i
$321$	−19.1416			−1.06838
$322$	−0.112523	−	0.112523i	−0.00627066	−	0.00627066i
$323$	9.56356	+	28.4645i	0.532131	+	1.58381i
$324$		−	1.00000i		−	0.0555556i
$325$	7.20918	−	4.49907i	0.399893	−	0.249563i
$326$			13.5806i			0.752159i
$327$	−3.09152	+	3.09152i	−0.170961	+	0.170961i
$328$	4.21906	+	4.21906i	0.232958	+	0.232958i
$329$			18.1566i			1.00101i
$330$	−0.696246	+	6.09540i	−0.0383271	+	0.335540i
$331$			6.73163i			0.370004i	0.982738	+	0.185002i	$0.0592292\pi$
$331$			6.73163i			0.370004i	−0.982738	+	0.185002i	$0.940771\pi$
$332$	3.87246	−	3.87246i	0.212529	−	0.212529i
$333$	4.58998	−	4.58998i	0.251530	−	0.251530i
$334$			18.2453i			0.998336i
$335$	−17.3313	+	13.7779i	−0.946910	+	0.752765i
$336$		−	3.50073i		−	0.190980i
$337$	14.1501	+	14.1501i	0.770806	+	0.770806i	0.978247	−	0.207441i	$-0.0665136\pi$
$337$	14.1501	+	14.1501i	0.770806	+	0.770806i	−0.207441	+	0.978247i	$0.566514\pi$
$338$	−7.14987	+	7.14987i	−0.388902	+	0.388902i
$339$		−	9.83726i		−	0.534287i
$340$	12.0581	−	9.58584i	0.653943	−	0.519865i
$341$			17.8600i			0.967171i
$342$	−1.38825	−	4.13192i	−0.0750680	−	0.223429i
$343$	−4.31936	−	4.31936i	−0.233224	−	0.233224i
$344$	−7.63084			−0.411427
$345$	−0.0115353	+	0.100988i	−0.000621040	+	0.00543700i
$346$	0.384091			0.0206488
$347$	6.84109	−	6.84109i	0.367249	−	0.367249i	−0.499224	−	0.866473i	$-0.666382\pi$
$347$	6.84109	−	6.84109i	0.367249	−	0.367249i	0.866473	+	0.499224i	$0.166382\pi$
$348$	4.60292	+	4.60292i	0.246743	+	0.246743i
$349$			33.2298i			1.77875i	0.457181	+	0.889374i	$0.348859\pi$
$349$			33.2298i			1.77875i	−0.457181	+	0.889374i	$0.651141\pi$
$350$	17.0528	+	3.94720i	0.911508	+	0.210987i
$351$	1.69957			0.0907166
$352$	−1.94007	−	1.94007i	−0.103406	−	0.103406i
$353$	25.3639	+	25.3639i	1.34999	+	1.34999i	0.885668	+	0.464318i	$0.153701\pi$
$353$	25.3639	+	25.3639i	1.34999	+	1.34999i	0.464318	+	0.885668i	$0.346299\pi$
$354$	4.42301			0.235080
$355$	12.3654	+	1.41244i	0.656288	+	0.0749645i
$356$		−	9.13628i		−	0.484222i
$357$	−17.0528	−	17.0528i	−0.902528	−	0.902528i
$358$	11.4228	+	11.4228i	0.603715	+	0.603715i
$359$		−	9.12994i		−	0.481860i	−0.970543	−	0.240930i	$-0.922548\pi$
$359$		−	9.12994i		−	0.481860i	0.970543	−	0.240930i	$-0.0774524\pi$
$360$	−1.75036	+	1.39149i	−0.0922522	+	0.0733377i
$361$	−11.4723	−	15.1455i	−0.603804	−	0.797133i
$362$	11.4537	−	11.4537i	0.601994	−	0.601994i
$363$	−2.45527	+	2.45527i	−0.128868	+	0.128868i
$364$	5.94974			0.311851
$365$	5.42616	−	4.31363i	0.284018	−	0.225786i
$366$	−2.95077			−0.154239
$367$	12.9778	−	12.9778i	0.677435	−	0.677435i	−0.281984	−	0.959419i	$-0.590993\pi$
$367$	12.9778	−	12.9778i	0.677435	−	0.677435i	0.959419	+	0.281984i	$0.0909926\pi$
$368$	−0.0321428	−	0.0321428i	−0.00167556	−	0.00167556i
$369$	−5.96665			−0.310611
$370$	−14.4210	−	1.64724i	−0.749713	−	0.0856360i
$371$			44.4354i			2.30697i
$372$	−4.60292	+	4.60292i	−0.238651	+	0.238651i
$373$	6.92570	−	6.92570i	0.358599	−	0.358599i	−0.504697	−	0.863296i	$-0.668396\pi$
$373$	6.92570	−	6.92570i	0.358599	−	0.358599i	0.863296	+	0.504697i	$0.168396\pi$
$374$	−18.9009			−0.977344
$375$	−4.80461	−	10.0953i	−0.248109	−	0.521321i
$376$			5.18653i			0.267475i
$377$	−7.82301	+	7.82301i	−0.402906	+	0.402906i
$378$	2.47539	+	2.47539i	0.127320	+	0.127320i
$379$	22.4882			1.15514			0.577570	−	0.816341i	$-0.304001\pi$
$379$	22.4882			1.15514			0.577570	+	0.816341i	$0.304001\pi$
$380$	−5.30063	+	8.17945i	−0.271916	+	0.419597i
$381$	19.3940			0.993586
$382$	10.3352	+	10.3352i	0.528795	+	0.528795i
$383$	14.9680	−	14.9680i	0.764830	−	0.764830i	−0.212361	−	0.977191i	$-0.568115\pi$
$383$	14.9680	−	14.9680i	0.764830	−	0.764830i	0.977191	+	0.212361i	$0.0681153\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−13.3650	−	16.8119i	−0.681142	−	0.856816i
$386$	8.77423			0.446597
$387$	5.39582	−	5.39582i	0.274285	−	0.274285i
$388$	8.76663	−	8.76663i	0.445058	−	0.445058i
$389$		−	10.1897i		−	0.516639i	−0.966060	−	0.258319i	$-0.916831\pi$
$389$		−	10.1897i		−	0.516639i	0.966060	−	0.258319i	$-0.0831687\pi$
$390$	−2.36493	−	2.97487i	−0.119753	−	0.150638i
$391$	−0.313148			−0.0158366
$392$	3.71590	+	3.71590i	0.187681	+	0.187681i
$393$	5.66661	−	5.66661i	0.285843	−	0.285843i
$394$	−13.8233			−0.696408
$395$	0.0573058	−	0.501693i	0.00288337	−	0.0252429i
$396$	2.74367			0.137875
$397$	14.9493	−	14.9493i	0.750284	−	0.750284i	−0.224248	−	0.974532i	$-0.571993\pi$
$397$	14.9493	−	14.9493i	0.750284	−	0.750284i	0.974532	+	0.224248i	$0.0719927\pi$
$398$	−5.49601	+	5.49601i	−0.275490	+	0.275490i
$399$	13.6646	+	6.79164i	0.684083	+	0.340007i
$400$	4.87121	+	1.12754i	0.243560	+	0.0563769i
$401$		−	17.1894i		−	0.858400i	−0.903210	−	0.429200i	$-0.858796\pi$
$401$		−	17.1894i		−	0.858400i	0.903210	−	0.429200i	$-0.141204\pi$
$402$	7.00145	+	7.00145i	0.349201	+	0.349201i
$403$	−7.82301	−	7.82301i	−0.389692	−	0.389692i
$404$			11.2650i			0.560455i
$405$	0.253765	−	2.22162i	0.0126097	−	0.110393i
$406$	−22.7880			−1.13095
$407$	12.5934	+	12.5934i	0.624231	+	0.624231i
$408$	−4.87121	−	4.87121i	−0.241161	−	0.241161i
$409$	−23.9489			−1.18420			−0.592099	−	0.805865i	$-0.701701\pi$
$409$	−23.9489			−1.18420			−0.592099	+	0.805865i	$0.701701\pi$
$410$	8.30250	+	10.4438i	0.410031	+	0.515782i
$411$			17.8614i			0.881039i
$412$	0.762447	+	0.762447i	0.0375631	+	0.0375631i
$413$	−10.9487	+	10.9487i	−0.538748	+	0.538748i
$414$	0.0454567			0.00223408
$415$	9.58584	−	7.62045i	0.470550	−	0.374073i
$416$	1.69957			0.0833285
$417$	7.31850	+	7.31850i	0.358388	+	0.358388i
$418$	11.3366	−	3.80890i	0.554492	−	0.186299i
$419$			21.4134i			1.04611i	0.852298	+	0.523056i	$0.175208\pi$
$419$			21.4134i			1.04611i	−0.852298	+	0.523056i	$0.824792\pi$
$420$	0.888360	−	7.77729i	0.0433475	−	0.379493i
$421$			1.72609i			0.0841246i	0.999115	+	0.0420623i	$0.0133928\pi$
$421$			1.72609i			0.0841246i	−0.999115	+	0.0420623i	$0.986607\pi$
$422$	5.59960	−	5.59960i	0.272584	−	0.272584i
$423$	−3.66743	−	3.66743i	−0.178317	−	0.178317i
$424$			12.6932i			0.616436i
$425$	29.2211	−	18.2362i	1.41743	−	0.884585i
$426$		−	5.56594i		−	0.269671i
$427$	7.30430	−	7.30430i	0.353480	−	0.353480i
$428$	13.5351	−	13.5351i	0.654245	−	0.654245i
$429$			4.66307i			0.225135i
$430$	−16.9528	−	1.93644i	−0.817539	−	0.0933833i
$431$			29.5770i			1.42467i	0.701838	+	0.712337i	$0.252363\pi$
$431$			29.5770i			1.42467i	−0.701838	+	0.712337i	$0.747637\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−18.7711	+	18.7711i	−0.902081	+	0.902081i	−0.995616	−	0.0935354i	$-0.970183\pi$
$433$	−18.7711	+	18.7711i	−0.902081	+	0.902081i	0.0935354	+	0.995616i	$0.470183\pi$
$434$		−	22.7880i		−	1.09386i
$435$	9.05790	+	11.3940i	0.434293	+	0.546301i
$436$		−	4.37207i		−	0.209384i
$437$	0.187824	−	0.0631054i	0.00898482	−	0.00301874i
$438$	−2.19205	−	2.19205i	−0.104740	−	0.104740i
$439$	8.66125			0.413379			0.206690	−	0.978407i	$-0.433731\pi$
$439$	8.66125			0.413379			0.206690	+	0.978407i	$0.433731\pi$
$440$	−3.81777	−	4.80242i	−0.182005	−	0.228946i
$441$	−5.25508			−0.250242
$442$	8.27898	−	8.27898i	0.393791	−	0.393791i
$443$	−19.5669	−	19.5669i	−0.929652	−	0.929652i	0.0680315	−	0.997683i	$-0.478328\pi$
$443$	−19.5669	−	19.5669i	−0.929652	−	0.929652i	−0.997683	+	0.0680315i	$0.978328\pi$
$444$			6.49122i			0.308059i
$445$	2.31847	−	20.2974i	0.109906	−	0.962187i
$446$	−20.3142			−0.961907
$447$	−6.41675	−	6.41675i	−0.303502	−	0.303502i
$448$	2.47539	+	2.47539i	0.116951	+	0.116951i
$449$	21.3429			1.00724			0.503618	−	0.863927i	$-0.332002\pi$
$449$	21.3429			1.00724			0.503618	+	0.863927i	$0.332002\pi$
$450$	−4.24175	+	2.64717i	−0.199958	+	0.124789i
$451$		−	16.3705i		−	0.770857i
$452$	6.95599	+	6.95599i	0.327182	+	0.327182i
$453$	1.23947	+	1.23947i	0.0582353	+	0.0582353i
$454$		−	21.2676i		−	0.998139i
$455$	13.2181	+	1.50983i	0.619673	+	0.0707821i
$456$	3.90335	+	1.94007i	0.182791	+	0.0908520i
$457$	21.3371	−	21.3371i	0.998110	−	0.998110i	−0.00188859	−	0.999998i	$-0.500601\pi$
$457$	21.3371	−	21.3371i	0.998110	−	0.998110i	0.999998	+	0.00188859i	$0.000601157\pi$
$458$	−1.90615	+	1.90615i	−0.0890683	+	0.0890683i
$459$	6.88893			0.321548
$460$	−0.0632524	−	0.0795658i	−0.00294916	−	0.00370977i
$461$	0.603474			0.0281066			0.0140533	−	0.999901i	$-0.495527\pi$
$461$	0.603474			0.0281066			0.0140533	+	0.999901i	$0.495527\pi$
$462$	−6.79164	+	6.79164i	−0.315976	+	0.315976i
$463$	−13.8679	−	13.8679i	−0.644495	−	0.644495i	0.307162	−	0.951657i	$-0.400621\pi$
$463$	−13.8679	−	13.8679i	−0.644495	−	0.644495i	−0.951657	+	0.307162i	$0.900621\pi$
$464$	−6.50952			−0.302197
$465$	−11.3940	+	9.05790i	−0.528385	+	0.420050i
$466$		−	17.6458i		−	0.817426i
$467$	5.10843	−	5.10843i	0.236390	−	0.236390i	−0.578964	−	0.815353i	$-0.696543\pi$
$467$	5.10843	−	5.10843i	0.236390	−	0.236390i	0.815353	+	0.578964i	$0.196543\pi$
$468$	−1.20178	+	1.20178i	−0.0555523	+	0.0555523i
$469$	−34.6626			−1.60057
$470$	−1.31616	+	11.5225i	−0.0607098	+	0.531494i
$471$		−	10.1927i		−	0.469655i
$472$	−3.12754	+	3.12754i	−0.143957	+	0.143957i
$473$	14.8043	+	14.8043i	0.680705	+	0.680705i
$474$	−0.225823			−0.0103724
$475$	−13.8516	+	16.8265i	−0.635557	+	0.772054i
$476$	24.1162			1.10537
$477$	−8.97544	−	8.97544i	−0.410957	−	0.410957i
$478$	−19.2439	+	19.2439i	−0.880195	+	0.880195i
$479$		−	0.676761i		−	0.0309220i	−0.999880	−	0.0154610i	$-0.995078\pi$
$479$		−	0.676761i		−	0.0309220i	0.999880	−	0.0154610i	$-0.00492158\pi$
$480$	0.253765	−	2.22162i	0.0115827	−	0.101403i
$481$	−11.0323			−0.503030
$482$	17.7562	−	17.7562i	0.808774	−	0.808774i
$483$	−0.112523	+	0.112523i	−0.00511997	+	0.00511997i
$484$		−	3.47228i		−	0.157831i
$485$	21.7008	−	17.2515i	0.985383	−	0.783350i
$486$	−1.00000			−0.0453609
$487$	−2.31334	−	2.31334i	−0.104828	−	0.104828i	0.652748	−	0.757575i	$-0.273616\pi$
$487$	−2.31334	−	2.31334i	−0.104828	−	0.104828i	−0.757575	+	0.652748i	$0.773616\pi$
$488$	2.08651	−	2.08651i	0.0944519	−	0.0944519i
$489$	13.5806			0.614135
$490$	7.31236	+	9.19829i	0.330339	+	0.415536i
$491$	−0.0138034			−0.000622939			−0.000311469	−	1.00000i	$-0.500099\pi$
$491$	−0.0138034			−0.000622939			−0.000311469		1.00000i	$0.500099\pi$
$492$	4.21906	−	4.21906i	0.190210	−	0.190210i
$493$	−31.7092	+	31.7092i	−1.42811	+	1.42811i
$494$	−3.29729	+	6.63403i	−0.148352	+	0.298479i
$495$	6.09540	+	0.696246i	0.273968	+	0.0312939i
$496$		−	6.50952i		−	0.292286i
$497$	13.7779	+	13.7779i	0.618021	+	0.618021i
$498$	−3.87246	−	3.87246i	−0.173529	−	0.173529i
$499$		−	19.0461i		−	0.852619i	−0.904577	−	0.426309i	$-0.859813\pi$
$499$		−	19.0461i		−	0.852619i	0.904577	−	0.426309i	$-0.140187\pi$
$500$	10.5359	+	3.74110i	0.471178	+	0.167307i
$501$	18.2453			0.815138
$502$	−1.62772	−	1.62772i	−0.0726489	−	0.0726489i
$503$	−15.5475	−	15.5475i	−0.693230	−	0.693230i	0.269711	−	0.962941i	$-0.413072\pi$
$503$	−15.5475	−	15.5475i	−0.693230	−	0.693230i	−0.962941	+	0.269711i	$0.913072\pi$
$504$	−3.50073			−0.155935
$505$	−2.85866	+	25.0266i	−0.127209	+	1.11367i
$506$			0.124718i			0.00554440i
$507$	7.14987	+	7.14987i	0.317537	+	0.317537i
$508$	−13.7136	+	13.7136i	−0.608444	+	0.608444i
$509$	4.08859			0.181224			0.0906118	−	0.995886i	$-0.471118\pi$
$509$	4.08859			0.181224			0.0906118	+	0.995886i	$0.471118\pi$
$510$	−9.58584	−	12.0581i	−0.424468	−	0.533943i
$511$	10.8523			0.480078
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.13192	+	1.38825i	−0.182429	+	0.0612928i
$514$			22.3095i			0.984032i
$515$	1.50039	+	1.88735i	0.0661150	+	0.0831667i
$516$			7.63084i			0.335929i
$517$	10.0622	−	10.0622i	0.442536	−	0.442536i
$518$	−16.0683	−	16.0683i	−0.705999	−	0.705999i
$519$		−	0.384091i		−	0.0168597i
$520$	3.77581	+	0.431292i	0.165580	+	0.0189134i
$521$			29.8730i			1.30876i	0.756166	+	0.654380i	$0.227070\pi$
$521$			29.8730i			1.30876i	−0.756166	+	0.654380i	$0.772930\pi$
$522$	4.60292	−	4.60292i	0.201465	−	0.201465i
$523$	−20.1935	+	20.1935i	−0.883001	+	0.883001i	−0.993839	−	0.110837i	$-0.964647\pi$
$523$	−20.1935	+	20.1935i	−0.883001	+	0.883001i	0.110837	+	0.993839i	$0.464647\pi$
$524$			8.01380i			0.350085i
$525$	3.94720	−	17.0528i	0.172270	−	0.744243i
$526$		−	1.72400i		−	0.0751702i
$527$	−31.7092	−	31.7092i	−1.38127	−	1.38127i
$528$	−1.94007	+	1.94007i	−0.0844306	+	0.0844306i
$529$		−	22.9979i		−	0.999910i
$530$	−3.22108	+	28.1995i	−0.139915	+	1.22491i
$531$		−	4.42301i		−	0.191942i
$532$	−14.4647	+	4.85988i	−0.627125	+	0.210703i
$533$	7.17060	+	7.17060i	0.310593	+	0.310593i
$534$	−9.13628			−0.395366
$535$	33.5047	−	26.6352i	1.44853	−	1.15154i
$536$	−9.90155			−0.427682
$537$	11.4228	−	11.4228i	0.492932	−	0.492932i
$538$	−5.36291	−	5.36291i	−0.231211	−	0.231211i
$539$		−	14.4182i		−	0.621035i
$540$	1.39149	+	1.75036i	0.0598800	+	0.0753236i
$541$	−25.3583			−1.09024			−0.545120	−	0.838358i	$-0.683516\pi$
$541$	−25.3583			−1.09024			−0.545120	+	0.838358i	$0.683516\pi$
$542$	−18.1543	−	18.1543i	−0.779795	−	0.779795i
$543$	−11.4537	−	11.4537i	−0.491526	−	0.491526i
$544$	6.88893			0.295360
$545$	1.10948	−	9.71308i	0.0475247	−	0.416063i
$546$		−	5.94974i		−	0.254626i
$547$	−13.3457	−	13.3457i	−0.570622	−	0.570622i	0.361680	−	0.932302i	$-0.382203\pi$
$547$	−13.3457	−	13.3457i	−0.570622	−	0.570622i	−0.932302	+	0.361680i	$0.882203\pi$
$548$	−12.6299	−	12.6299i	−0.539524	−	0.539524i
$549$			2.95077i			0.125936i
$550$	−7.26297	−	11.6380i	−0.309694	−	0.496245i
$551$	12.6289	−	25.4089i	0.538009	−	1.08246i
$552$	−0.0321428	+	0.0321428i	−0.00136809	+	0.00136809i
$553$	0.558998	−	0.558998i	0.0237710	−	0.0237710i
$554$	−30.7470			−1.30631
$555$	−1.64724	+	14.4210i	−0.0699215	+	0.612138i
$556$	−10.3499			−0.438934
$557$	−8.05867	+	8.05867i	−0.341457	+	0.341457i	−0.856915	−	0.515458i	$-0.827622\pi$
$557$	−8.05867	+	8.05867i	−0.341457	+	0.341457i	0.515458	+	0.856915i	$0.327622\pi$
$558$	4.60292	+	4.60292i	0.194857	+	0.194857i
$559$	−12.9692			−0.548538
$560$	4.87121	+	6.12754i	0.205846	+	0.258936i
$561$			18.9009i			0.797998i
$562$	15.4892	−	15.4892i	0.653372	−	0.653372i
$563$	28.6648	−	28.6648i	1.20808	−	1.20808i	0.236430	−	0.971648i	$-0.424022\pi$
$563$	28.6648	−	28.6648i	1.20808	−	1.20808i	0.971648	−	0.236430i	$-0.0759775\pi$
$564$	5.18653			0.218392
$565$	13.6884	+	17.2188i	0.575875	+	0.724399i
$566$			22.2338i			0.934557i
$567$	2.47539	−	2.47539i	0.103956	−	0.103956i
$568$	3.93571	+	3.93571i	0.165139	+	0.165139i
$569$	−8.54540			−0.358242			−0.179121	−	0.983827i	$-0.557325\pi$
$569$	−8.54540			−0.358242			−0.179121	+	0.983827i	$0.557325\pi$
$570$	8.17945	+	5.30063i	0.342599	+	0.222019i
$571$	45.4169			1.90064			0.950320	−	0.311275i	$-0.100756\pi$
$571$	45.4169			1.90064			0.950320	+	0.311275i	$0.100756\pi$
$572$	−3.29729	−	3.29729i	−0.137867	−	0.137867i
$573$	10.3352	−	10.3352i	0.431759	−	0.431759i
$574$			20.8876i			0.871831i
$575$	−0.120332	−	0.192816i	−0.00501819	−	0.00804100i
$576$	−1.00000			−0.0416667
$577$	12.1650	−	12.1650i	0.506437	−	0.506437i	−0.406994	−	0.913431i	$-0.633423\pi$
$577$	12.1650	−	12.1650i	0.506437	−	0.506437i	0.913431	+	0.406994i	$0.133423\pi$
$578$	21.5366	−	21.5366i	0.895803	−	0.895803i
$579$		−	8.77423i		−	0.364645i
$580$	−14.4617	−	1.65189i	−0.600489	−	0.0685908i
$581$	19.1717			0.795375
$582$	−8.76663	−	8.76663i	−0.363389	−	0.363389i
$583$	24.6256	−	24.6256i	1.01989	−	1.01989i
$584$	3.10002			0.128280
$585$	−2.97487	+	2.36493i	−0.122996	+	0.0977779i
$586$	−11.6781			−0.482419
$587$	−5.32968	+	5.32968i	−0.219980	+	0.219980i	−0.808490	−	0.588510i	$-0.799715\pi$
$587$	−5.32968	+	5.32968i	−0.219980	+	0.219980i	0.588510	+	0.808490i	$0.299715\pi$
$588$	3.71590	−	3.71590i	0.153241	−	0.153241i
$589$	25.4089	+	12.6289i	1.04696	+	0.520365i
$590$	−7.74186	+	6.15455i	−0.318728	+	0.253379i
$591$			13.8233i			0.568615i
$592$	−4.58998	−	4.58998i	−0.188647	−	0.188647i
$593$	−1.80818	−	1.80818i	−0.0742529	−	0.0742529i	0.669005	−	0.743258i	$-0.266720\pi$
$593$	−1.80818	−	1.80818i	−0.0742529	−	0.0742529i	−0.743258	+	0.669005i	$0.766720\pi$
$594$		−	2.74367i		−	0.112574i
$595$	53.5772	+	6.11985i	2.19645	+	0.250889i
$596$	9.07466			0.371712
$597$	5.49601	+	5.49601i	0.224937	+	0.224937i
$598$	−0.0546290	−	0.0546290i	−0.00223395	−	0.00223395i
$599$	25.3131			1.03426			0.517132	−	0.855906i	$-0.327000\pi$
$599$	25.3131			1.03426			0.517132	+	0.855906i	$0.327000\pi$
$600$	1.12754	−	4.87121i	0.0460315	−	0.198866i
$601$		−	18.5367i		−	0.756126i	−0.925780	−	0.378063i	$-0.876590\pi$
$601$		−	18.5367i		−	0.756126i	0.925780	−	0.378063i	$-0.123410\pi$
$602$	−18.8893	−	18.8893i	−0.769870	−	0.769870i
$603$	7.00145	−	7.00145i	0.285121	−	0.285121i
$604$	−1.75287			−0.0713234
$605$	0.881142	−	7.71409i	0.0358235	−	0.313622i
$606$	11.2650			0.457609
$607$	−11.5164	−	11.5164i	−0.467435	−	0.467435i	0.433647	−	0.901083i	$-0.357226\pi$
$607$	−11.5164	−	11.5164i	−0.467435	−	0.467435i	−0.901083	+	0.433647i	$0.857226\pi$
$608$	−4.13192	+	1.38825i	−0.167571	+	0.0563010i
$609$			22.7880i			0.923418i
$610$	5.16492	−	4.10596i	0.209122	−	0.166245i
$611$			8.81490i			0.356613i
$612$	−4.87121	+	4.87121i	−0.196907	+	0.196907i
$613$	−7.66890	−	7.66890i	−0.309744	−	0.309744i	0.535066	−	0.844810i	$-0.320287\pi$
$613$	−7.66890	−	7.66890i	−0.309744	−	0.309744i	−0.844810	+	0.535066i	$0.820287\pi$
$614$		−	31.2879i		−	1.26268i
$615$	10.4438	−	8.30250i	0.421134	−	0.334789i
$616$		−	9.60483i		−	0.386990i
$617$	33.2792	−	33.2792i	1.33977	−	1.33977i	0.443492	−	0.896278i	$-0.353740\pi$
$617$	33.2792	−	33.2792i	1.33977	−	1.33977i	0.896278	−	0.443492i	$-0.146260\pi$
$618$	0.762447	−	0.762447i	0.0306701	−	0.0306701i
$619$			3.87513i			0.155755i	0.996963	+	0.0778774i	$0.0248143\pi$
$619$			3.87513i			0.155755i	−0.996963	+	0.0778774i	$0.975186\pi$
$620$	1.65189	−	14.4617i	0.0663413	−	0.580795i
$621$		−	0.0454567i		−	0.00182412i
$622$	2.27765	+	2.27765i	0.0913254	+	0.0913254i
$623$	22.6158	−	22.6158i	0.906084	−	0.906084i
$624$		−	1.69957i		−	0.0680374i
$625$	22.4573	+	10.9849i	0.898293	+	0.439398i
$626$		−	21.1850i		−	0.846724i
$627$	−3.80890	−	11.3366i	−0.152113	−	0.452741i
$628$	7.20733	+	7.20733i	0.287604	+	0.287604i
$629$	−44.7175			−1.78300
$630$	−7.77729	−	0.888360i	−0.309855	−	0.0353931i
$631$	1.80965			0.0720412			0.0360206	−	0.999351i	$-0.488532\pi$
$631$	1.80965			0.0720412			0.0360206	+	0.999351i	$0.488532\pi$
$632$	0.159681	−	0.159681i	0.00635176	−	0.00635176i
$633$	−5.59960	−	5.59960i	−0.222564	−	0.222564i
$634$		−	18.8539i		−	0.748782i
$635$	−33.9466	+	26.9865i	−1.34713	+	1.07093i
$636$	12.6932			0.503318
$637$	6.31545	+	6.31545i	0.250227	+	0.250227i
$638$	12.6289	+	12.6289i	0.499983	+	0.499983i
$639$	−5.56594			−0.220185
$640$	1.39149	+	1.75036i	0.0550033	+	0.0691892i
$641$		−	6.61503i		−	0.261278i	−0.991430	−	0.130639i	$-0.958297\pi$
$641$		−	6.61503i		−	0.261278i	0.991430	−	0.130639i	$-0.0417029\pi$
$642$	−13.5351	−	13.5351i	−0.534189	−	0.534189i
$643$	−30.3608	−	30.3608i	−1.19731	−	1.19731i	−0.974968	−	0.222347i	$-0.928628\pi$
$643$	−30.3608	−	30.3608i	−1.19731	−	1.19731i	−0.222347	−	0.974968i	$-0.571372\pi$
$644$		−	0.159132i		−	0.00627066i
$645$	−1.93644	+	16.9528i	−0.0762472	+	0.667518i
$646$	−13.3650	+	26.8899i	−0.525838	+	1.05797i
$647$	5.83884	−	5.83884i	0.229549	−	0.229549i	−0.582956	−	0.812504i	$-0.698104\pi$
$647$	5.83884	−	5.83884i	0.229549	−	0.229549i	0.812504	+	0.582956i	$0.198104\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	12.1353			0.476351
$650$	8.27898	+	1.91633i	0.324728	+	0.0751648i
$651$	−22.7880			−0.893133
$652$	−9.60292	+	9.60292i	−0.376080	+	0.376080i
$653$	−19.7797	−	19.7797i	−0.774039	−	0.774039i	0.204771	−	0.978810i	$-0.434355\pi$
$653$	−19.7797	−	19.7797i	−0.774039	−	0.774039i	−0.978810	+	0.204771i	$0.934355\pi$
$654$	−4.37207			−0.170961
$655$	−2.03362	+	17.8036i	−0.0794601	+	0.695646i
$656$			5.96665i			0.232958i
$657$	−2.19205	+	2.19205i	−0.0855198	+	0.0855198i
$658$	−12.8387	+	12.8387i	−0.500503	+	0.500503i
$659$	8.44761			0.329072			0.164536	−	0.986371i	$-0.447387\pi$
$659$	8.44761			0.329072			0.164536	+	0.986371i	$0.447387\pi$
$660$	−4.80242	+	3.81777i	−0.186934	+	0.148607i
$661$		−	23.8283i		−	0.926814i	−0.886146	−	0.463407i	$-0.846627\pi$
$661$		−	23.8283i		−	0.926814i	0.886146	−	0.463407i	$-0.153373\pi$
$662$	−4.75998	+	4.75998i	−0.185002	+	0.185002i
$663$	−8.27898	−	8.27898i	−0.321529	−	0.321529i
$664$	5.47649			0.212529
$665$	−33.3684	+	7.12619i	−1.29397	+	0.276342i
$666$	6.49122			0.251530
$667$	0.209234	+	0.209234i	0.00810157	+	0.00810157i
$668$	−12.9013	+	12.9013i	−0.499168	+	0.499168i
$669$			20.3142i			0.785393i
$670$	−21.9975	−	2.51266i	−0.849837	−	0.0970726i
$671$	−8.09594			−0.312540
$672$	2.47539	−	2.47539i	0.0954901	−	0.0954901i
$673$	−31.9422	+	31.9422i	−1.23128	+	1.23128i	−0.267812	+	0.963471i	$0.586300\pi$
$673$	−31.9422	+	31.9422i	−1.23128	+	1.23128i	−0.963471	+	0.267812i	$0.913700\pi$
$674$			20.0113i			0.770806i
$675$	2.64717	+	4.24175i	0.101890	+	0.163265i
$676$	−10.1114			−0.388902
$677$	−11.7115	−	11.7115i	−0.450111	−	0.450111i	0.445280	−	0.895391i	$-0.353104\pi$
$677$	−11.7115	−	11.7115i	−0.450111	−	0.450111i	−0.895391	+	0.445280i	$0.853104\pi$
$678$	6.95599	−	6.95599i	0.267143	−	0.267143i
$679$	43.4016			1.66560
$680$	15.3046	+	1.74817i	0.586904	+	0.0670391i
$681$	−21.2676			−0.814977
$682$	−12.6289	+	12.6289i	−0.483586	+	0.483586i
$683$	−3.55375	+	3.55375i	−0.135981	+	0.135981i	−0.771821	−	0.635840i	$-0.780654\pi$
$683$	−3.55375	+	3.55375i	−0.135981	+	0.135981i	0.635840	+	0.771821i	$0.280654\pi$
$684$	1.94007	−	3.90335i	0.0741803	−	0.149248i
$685$	−24.8539	−	31.2640i	−0.949619	−	1.19453i
$686$		−	6.10850i		−	0.233224i
$687$	1.90615	+	1.90615i	0.0727240	+	0.0727240i
$688$	−5.39582	−	5.39582i	−0.205714	−	0.205714i
$689$			21.5730i			0.821867i
$690$	−0.0795658	+	0.0632524i	−0.00302902	+	0.00240798i
$691$	9.74241			0.370619			0.185309	−	0.982680i	$-0.440671\pi$
$691$	9.74241			0.370619			0.185309	+	0.982680i	$0.440671\pi$
$692$	0.271593	+	0.271593i	0.0103244	+	0.0103244i
$693$	6.79164	+	6.79164i	0.257993	+	0.257993i
$694$	9.67476			0.367249
$695$	−22.9936	−	2.62644i	−0.872197	−	0.0996267i
$696$			6.50952i			0.246743i
$697$	29.0648	+	29.0648i	1.10091	+	1.10091i
$698$	−23.4970	+	23.4970i	−0.889374	+	0.889374i
$699$	−17.6458			−0.667425
$700$	9.26703	+	14.8492i	0.350261	+	0.561247i
$701$	−10.3224			−0.389873			−0.194936	−	0.980816i	$-0.562450\pi$
$701$	−10.3224			−0.389873			−0.194936	+	0.980816i	$0.562450\pi$
$702$	1.20178	+	1.20178i	0.0453583	+	0.0453583i
$703$	26.8212	−	9.01143i	1.01158	−	0.339873i
$704$		−	2.74367i		−	0.103406i
$705$	11.5225	+	1.31616i	0.433963	+	0.0495694i
$706$			35.8700i			1.34999i
$707$	−27.8852	+	27.8852i	−1.04873	+	1.04873i
$708$	3.12754	+	3.12754i	0.117540	+	0.117540i
$709$			10.3223i			0.387663i	0.981035	+	0.193831i	$0.0620915\pi$
$709$			10.3223i			0.387663i	−0.981035	+	0.193831i	$0.937909\pi$
$710$	7.74492	+	9.74241i	0.290662	+	0.365626i
$711$			0.225823i			0.00846901i
$712$	6.46033	−	6.46033i	0.242111	−	0.242111i
$713$	−0.209234	+	0.209234i	−0.00783587	+	0.00783587i
$714$		−	24.1162i		−	0.902528i
$715$	−6.48859	−	8.16206i	−0.242660	−	0.305244i
$716$			16.1543i			0.603715i
$717$	19.2439	+	19.2439i	0.718676	+	0.718676i
$718$	6.45584	−	6.45584i	0.240930	−	0.240930i
$719$		−	34.9029i		−	1.30166i	−0.759224	−	0.650830i	$-0.774421\pi$
$719$		−	34.9029i		−	1.30166i	0.759224	−	0.650830i	$-0.225579\pi$
$720$	−2.22162	−	0.253765i	−0.0827950	−	0.00945725i
$721$			3.77470i			0.140577i
$722$	2.59737	−	18.8216i	0.0966642	−	0.700468i
$723$	−17.7562	−	17.7562i	−0.660361	−	0.660361i
$724$	16.1980			0.601994
$725$	−31.7092	−	7.33973i	−1.17765	−	0.272591i
$726$	−3.47228			−0.128868
$727$	12.8595	−	12.8595i	0.476932	−	0.476932i	−0.427217	−	0.904149i	$-0.640506\pi$
$727$	12.8595	−	12.8595i	0.476932	−	0.476932i	0.904149	+	0.427217i	$0.140506\pi$
$728$	4.20710	+	4.20710i	0.155926	+	0.155926i
$729$			1.00000i			0.0370370i
$730$	6.88707	+	0.786675i	0.254902	+	0.0291162i
$731$	−52.5683			−1.94431
$732$	−2.08651	−	2.08651i	−0.0771197	−	0.0771197i
$733$	11.1047	+	11.1047i	0.410162	+	0.410162i	0.881795	−	0.471633i	$-0.156335\pi$
$733$	11.1047	+	11.1047i	0.410162	+	0.410162i	−0.471633	+	0.881795i	$0.656335\pi$
$734$	18.3534			0.677435
$735$	9.19829	−	7.31236i	0.339284	−	0.269720i
$736$		−	0.0454567i		−	0.00167556i
$737$	19.2097	+	19.2097i	0.707597	+	0.707597i
$738$	−4.21906	−	4.21906i	−0.155306	−	0.155306i
$739$			18.1001i			0.665823i	0.942958	+	0.332911i	$0.108031\pi$
$739$			18.1001i			0.665823i	−0.942958	+	0.332911i	$0.891969\pi$
$740$	−9.03243	−	11.3620i	−0.332039	−	0.417675i
$741$	6.63403	+	3.29729i	0.243707	+	0.121129i
$742$	−31.4205	+	31.4205i	−1.15348	+	1.15348i
$743$	26.9208	−	26.9208i	0.987630	−	0.987630i	−0.0122949	−	0.999924i	$-0.503914\pi$
$743$	26.9208	−	26.9208i	0.987630	−	0.987630i	0.999924	+	0.0122949i	$0.00391368\pi$
$744$	−6.50952			−0.238651
$745$	20.1605	+	2.30283i	0.738622	+	0.0843690i
$746$	9.79442			0.358599
$747$	−3.87246	+	3.87246i	−0.141686	+	0.141686i
$748$	−13.3650	−	13.3650i	−0.488672	−	0.488672i
$749$	67.0093			2.44847
$750$	3.74110	−	10.5359i	0.136606	−	0.384715i
$751$		−	9.91849i		−	0.361931i	−0.983489	−	0.180965i	$-0.942078\pi$
$751$		−	9.91849i		−	0.361931i	0.983489	−	0.180965i	$-0.0579222\pi$
$752$	−3.66743	+	3.66743i	−0.133737	+	0.133737i
$753$	−1.62772	+	1.62772i	−0.0593176	+	0.0593176i
$754$	−11.0634			−0.402906
$755$	−3.89422	−	0.444817i	−0.141725	−	0.0161886i
$756$			3.50073i			0.127320i
$757$	3.01763	−	3.01763i	0.109678	−	0.109678i	−0.650138	−	0.759816i	$-0.725289\pi$
$757$	3.01763	−	3.01763i	0.109678	−	0.109678i	0.759816	+	0.650138i	$0.225289\pi$
$758$	15.9015	+	15.9015i	0.577570	+	0.577570i
$759$	0.124718			0.00452699
$760$	−9.53185	+	2.03563i	−0.345757	+	0.0738402i
$761$	−11.1416			−0.403881			−0.201941	−	0.979398i	$-0.564725\pi$
$761$	−11.1416			−0.403881			−0.201941	+	0.979398i	$0.564725\pi$
$762$	13.7136	+	13.7136i	0.496793	+	0.496793i
$763$	10.8226	−	10.8226i	0.391803	−	0.391803i
$764$			14.6162i			0.528795i
$765$	−12.0581	+	9.58584i	−0.435962	+	0.346577i
$766$	21.1680			0.764830
$767$	−5.31548	+	5.31548i	−0.191931	+	0.191931i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$		−	32.8840i		−	1.18583i	−0.805266	−	0.592913i	$-0.797978\pi$
$769$		−	32.8840i		−	1.18583i	0.805266	−	0.592913i	$-0.202022\pi$
$770$	2.43737	−	21.3383i	0.0878366	−	0.768979i
$771$	22.3095			0.803458
$772$	6.20432	+	6.20432i	0.223298	+	0.223298i
$773$	−31.2573	+	31.2573i	−1.12425	+	1.12425i	−0.133152	+	0.991096i	$0.542510\pi$
$773$	−31.2573	+	31.2573i	−1.12425	+	1.12425i	−0.991096	+	0.133152i	$0.957490\pi$
$774$	7.63084			0.274285
$775$	7.33973	−	31.7092i	0.263651	−	1.13903i
$776$	12.3979			0.445058
$777$	−16.0683	+	16.0683i	−0.576446	+	0.576446i
$778$	7.20521	−	7.20521i	0.258319	−	0.258319i
$779$	−23.2899	−	11.5757i	−0.834447	−	0.414742i
$780$	0.431292	−	3.77581i	0.0154427	−	0.135196i
$781$		−	15.2711i		−	0.546443i
$782$	−0.221429	−	0.221429i	−0.00791829	−	0.00791829i
$783$	−4.60292	−	4.60292i	−0.164495	−	0.164495i
$784$			5.25508i			0.187681i
$785$	14.1830	+	17.8409i	0.506213	+	0.636770i
$786$	8.01380			0.285843
$787$	2.28524	+	2.28524i	0.0814600	+	0.0814600i	0.746663	−	0.665203i	$-0.231655\pi$
$787$	2.28524	+	2.28524i	0.0814600	+	0.0814600i	−0.665203	+	0.746663i	$0.731655\pi$
$788$	−9.77456	−	9.77456i	−0.348204	−	0.348204i
$789$	−1.72400			−0.0613762
$790$	0.395271	−	0.314229i	0.0140631	−	0.0111798i
$791$			34.4375i			1.22446i
$792$	1.94007	+	1.94007i	0.0689373	+	0.0689373i
$793$	3.54618	−	3.54618i	0.125929	−	0.125929i
$794$	21.1415			0.750284
$795$	28.1995	+	3.22108i	1.00013	+	0.114240i
$796$	−7.77253			−0.275490
$797$	20.1327	+	20.1327i	0.713137	+	0.713137i	0.967190	−	0.254054i	$-0.0817639\pi$
$797$	20.1327	+	20.1327i	0.713137	+	0.713137i	−0.254054	+	0.967190i	$0.581764\pi$
$798$	4.85988	+	14.4647i	0.172038	+	0.512045i
$799$			35.7296i			1.26402i
$800$	2.64717	+	4.24175i	0.0935917	+	0.149969i
$801$			9.13628i			0.322815i
$802$	12.1548	−	12.1548i	0.429200	−	0.429200i
$803$	−6.01425	−	6.01425i	−0.212238	−	0.212238i
$804$			9.90155i			0.349201i
$805$	0.0403820	−	0.353530i	0.00142328	−	0.0124603i
$806$		−	11.0634i		−	0.389692i
$807$	−5.36291	+	5.36291i	−0.188783	+	0.188783i
$808$	−7.96556	+	7.96556i	−0.280227	+	0.280227i
$809$		−	19.9089i		−	0.699958i	−0.936758	−	0.349979i	$-0.886189\pi$
$809$		−	19.9089i		−	0.699958i	0.936758	−	0.349979i	$-0.113811\pi$
$810$	1.75036	−	1.39149i	0.0615015	−	0.0488918i
$811$			27.5845i			0.968623i	0.874896	+	0.484312i	$0.160930\pi$
$811$			27.5845i			0.968623i	−0.874896	+	0.484312i	$0.839070\pi$
$812$	−16.1136	−	16.1136i	−0.565476	−	0.565476i
$813$	−18.1543	+	18.1543i	−0.636700	+	0.636700i
$814$			17.8097i			0.624231i
$815$	−23.7709	+	18.8972i	−0.832660	+	0.661939i
$816$		−	6.88893i		−	0.241161i
$817$	31.5300	−	10.5935i	1.10310	−	0.370620i
$818$	−16.9345	−	16.9345i	−0.592099	−	0.592099i
$819$	−5.94974			−0.207901
$820$	−1.51412	+	13.2556i	−0.0528755	+	0.462907i
$821$	−16.0769			−0.561089			−0.280545	−	0.959841i	$-0.590515\pi$
$821$	−16.0769			−0.561089			−0.280545	+	0.959841i	$0.590515\pi$
$822$	−12.6299	+	12.6299i	−0.440520	+	0.440520i
$823$	0.761023	+	0.761023i	0.0265276	+	0.0265276i	0.720246	−	0.693719i	$-0.244029\pi$
$823$	0.761023	+	0.761023i	0.0265276	+	0.0265276i	−0.693719	+	0.720246i	$0.744029\pi$
$824$			1.07826i			0.0375631i
$825$	−11.6380	+	7.26297i	−0.405182	+	0.252864i
$826$	−15.4837			−0.538748
$827$	−20.8201	−	20.8201i	−0.723984	−	0.723984i	0.245430	−	0.969414i	$-0.421071\pi$
$827$	−20.8201	−	20.8201i	−0.723984	−	0.723984i	−0.969414	+	0.245430i	$0.921071\pi$
$828$	0.0321428	+	0.0321428i	0.00111704	+	0.00111704i
$829$	31.8887			1.10754			0.553771	−	0.832669i	$-0.313188\pi$
$829$	31.8887			1.10754			0.553771	+	0.832669i	$0.313188\pi$
$830$	12.1667	+	1.38974i	0.422312	+	0.0482385i
$831$			30.7470i			1.06660i
$832$	1.20178	+	1.20178i	0.0416642	+	0.0416642i
$833$	25.5986	+	25.5986i	0.886938	+	0.886938i
$834$			10.3499i			0.358388i
$835$	−31.9358	+	25.3880i	−1.10518	+	0.878588i
$836$	10.7095	+	5.32290i	0.370396	+	0.184096i
$837$	4.60292	−	4.60292i	0.159100	−	0.159100i
$838$	−15.1416	+	15.1416i	−0.523056	+	0.523056i
$839$	−39.4110			−1.36062			−0.680310	−	0.732924i	$-0.738155\pi$
$839$	−39.4110			−1.36062			−0.680310	+	0.732924i	$0.738155\pi$
$840$	6.12754	−	4.87121i	0.211420	−	0.168073i
$841$	13.3738			0.461166
$842$	−1.22053	+	1.22053i	−0.0420623	+	0.0420623i
$843$	−15.4892	−	15.4892i	−0.533476	−	0.533476i
$844$	7.91902			0.272584
$845$	−22.4638	−	2.56593i	−0.772779	−	0.0882706i
$846$		−	5.18653i		−	0.178317i
$847$	8.59523	−	8.59523i	0.295336	−	0.295336i
$848$	−8.97544	+	8.97544i	−0.308218	+	0.308218i
$849$	22.2338			0.763062
$850$	33.5574	+	7.76753i	1.15101	+	0.266424i
$851$			0.295070i			0.0101149i
$852$	3.93571	−	3.93571i	0.134835	−	0.134835i
$853$	29.3272	+	29.3272i	1.00414	+	1.00414i	0.999991	+	0.00415191i	$0.00132160\pi$
$853$	29.3272	+	29.3272i	1.00414	+	1.00414i	0.00415191	+	0.999991i	$0.498678\pi$
$854$	10.3298			0.353480
$855$	5.30063	−	8.17945i	0.181278	−	0.279731i
$856$	19.1416			0.654245
$857$	−22.6621	−	22.6621i	−0.774121	−	0.774121i	0.204703	−	0.978824i	$-0.434377\pi$
$857$	−22.6621	−	22.6621i	−0.774121	−	0.774121i	−0.978824	+	0.204703i	$0.934377\pi$
$858$	−3.29729	+	3.29729i	−0.112568	+	0.112568i
$859$		−	9.13130i		−	0.311556i	−0.987792	−	0.155778i	$-0.950212\pi$
$859$		−	9.13130i		−	0.311556i	0.987792	−	0.155778i	$-0.0497884\pi$
$860$	−10.6182	−	13.3567i	−0.362078	−	0.455461i
$861$	20.8876			0.711847
$862$	−20.9141	+	20.9141i	−0.712337	+	0.712337i
$863$	31.2115	−	31.2115i	1.06245	−	1.06245i	0.0645382	−	0.997915i	$-0.479443\pi$
$863$	31.2115	−	31.2115i	1.06245	−	1.06245i	0.997915	−	0.0645382i	$-0.0205574\pi$
$864$			1.00000i			0.0340207i
$865$	0.534456	+	0.672298i	0.0181721	+	0.0228588i
$866$	−26.5463			−0.902081
$867$	−21.5366	−	21.5366i	−0.731420	−	0.731420i
$868$	16.1136	−	16.1136i	0.546930	−	0.546930i
$869$	−0.619583			−0.0210179
$870$	−1.65189	+	14.4617i	−0.0560042	+	0.490297i
$871$	−16.8284			−0.570209
$872$	3.09152	−	3.09152i	0.104692	−	0.104692i
$873$	−8.76663	+	8.76663i	−0.296706	+	0.296706i
$874$	0.177434	+	0.0881891i	0.00600178	+	0.00298304i
$875$	16.8196	+	35.3410i	0.568607	+	1.19474i
$876$		−	3.10002i		−	0.104740i
$877$	15.7226	+	15.7226i	0.530916	+	0.530916i	0.920845	−	0.389929i	$-0.127500\pi$
$877$	15.7226	+	15.7226i	0.530916	+	0.530916i	−0.389929	+	0.920845i	$0.627500\pi$
$878$	6.12443	+	6.12443i	0.206690	+	0.206690i
$879$			11.6781i			0.393894i
$880$	0.696246	−	6.09540i	0.0234705	−	0.205476i
$881$	−12.7472			−0.429464			−0.214732	−	0.976673i	$-0.568888\pi$
$881$	−12.7472			−0.429464			−0.214732	+	0.976673i	$0.568888\pi$
$882$	−3.71590	−	3.71590i	−0.125121	−	0.125121i
$883$	26.1600	+	26.1600i	0.880352	+	0.880352i	0.993570	−	0.113218i	$-0.0361158\pi$
$883$	26.1600	+	26.1600i	0.880352	+	0.880352i	−0.113218	+	0.993570i	$0.536116\pi$
$884$	11.7082			0.393791
$885$	6.15455	+	7.74186i	0.206883	+	0.260240i
$886$		−	27.6718i		−	0.929652i
$887$	3.63787	+	3.63787i	0.122148	+	0.122148i	0.765538	−	0.643390i	$-0.222473\pi$
$887$	3.63787	+	3.63787i	0.122148	+	0.122148i	−0.643390	+	0.765538i	$0.722473\pi$
$888$	−4.58998	+	4.58998i	−0.154030	+	0.154030i
$889$	−67.8931			−2.27706
$890$	15.9918	−	12.7130i	0.536047	−	0.426141i
$891$	−2.74367			−0.0919164
$892$	−14.3643	−	14.3643i	−0.480953	−	0.480953i
$893$	−7.20021	−	21.4303i	−0.240946	−	0.717139i
$894$		−	9.07466i		−	0.303502i
$895$	−4.09940	+	35.8888i	−0.137028	+	1.19963i
$896$			3.50073i			0.116951i
$897$	−0.0546290	+	0.0546290i	−0.00182401	+	0.00182401i
$898$	15.0917	+	15.0917i	0.503618	+	0.503618i
$899$			42.3738i			1.41325i
$900$	−4.87121	−	1.12754i	−0.162374	−	0.0375846i
$901$			87.4424i			2.91313i
$902$	11.5757	−	11.5757i	0.385428	−	0.385428i
$903$	−18.8893	+	18.8893i	−0.628596	+	0.628596i
$904$			9.83726i			0.327182i
$905$	35.9858	+	4.11048i	1.19621	+	0.136637i
$906$			1.75287i			0.0582353i
$907$	−27.2643	−	27.2643i	−0.905298	−	0.905298i	0.0905904	−	0.995888i	$-0.471125\pi$
$907$	−27.2643	−	27.2643i	−0.905298	−	0.905298i	−0.995888	+	0.0905904i	$0.971125\pi$
$908$	15.0385	−	15.0385i	0.499070	−	0.499070i
$909$		−	11.2650i		−	0.373637i
$910$	8.27898	+	10.4142i	0.274445	+	0.345228i
$911$			1.42099i			0.0470796i	0.999723	+	0.0235398i	$0.00749364\pi$
$911$			1.42099i			0.0470796i	−0.999723	+	0.0235398i	$0.992506\pi$
$912$	1.38825	+	4.13192i	0.0459696	+	0.136822i
$913$	−10.6248	−	10.6248i	−0.351628	−	0.351628i
$914$	30.1753			0.998110
$915$	−4.10596	−	5.16492i	−0.135739	−	0.170747i
$916$	−2.69570			−0.0890683
$917$	−19.8373	+	19.8373i	−0.655084	+	0.655084i
$918$	4.87121	+	4.87121i	0.160774	+	0.160774i
$919$			38.9380i			1.28445i	0.766518	+	0.642223i	$0.221988\pi$
$919$			38.9380i			1.28445i	−0.766518	+	0.642223i	$0.778012\pi$
$920$	0.0115353	−	0.100988i	0.000380308	−	0.00332947i
$921$	−31.2879			−1.03097
$922$	0.426720	+	0.426720i	0.0140533	+	0.0140533i
$923$	6.68904	+	6.68904i	0.220172	+	0.220172i
$924$	−9.60483			−0.315976
$925$	−17.1834	−	27.5341i	−0.564986	−	0.905317i
$926$		−	19.6121i		−	0.644495i
$927$	−0.762447	−	0.762447i	−0.0250421	−	0.0250421i
$928$	−4.60292	−	4.60292i	−0.151098	−	0.151098i
$929$			23.8414i			0.782211i	0.920346	+	0.391106i	$0.127907\pi$
$929$			23.8414i			0.782211i	−0.920346	+	0.391106i	$0.872093\pi$
$930$	−14.4617	−	1.65189i	−0.474217	−	0.0541675i
$931$	−20.5124	−	10.1952i	−0.672267	−	0.334134i
$932$	12.4775	−	12.4775i	0.408713	−	0.408713i
$933$	2.27765	−	2.27765i	0.0745669	−	0.0745669i
$934$	7.22441			0.236390
$935$	−26.3004	−	33.0835i	−0.860114	−	1.08195i
$936$	−1.69957			−0.0555523
$937$	−13.2718	+	13.2718i	−0.433572	+	0.433572i	−0.889842	−	0.456270i	$-0.849185\pi$
$937$	−13.2718	+	13.2718i	−0.433572	+	0.433572i	0.456270	+	0.889842i	$0.349185\pi$
$938$	−24.5102	−	24.5102i	−0.800285	−	0.800285i
$939$	−21.1850			−0.691347
$940$	−9.07831	+	7.21698i	−0.296102	+	0.235392i
$941$		−	27.1173i		−	0.884000i	−0.897015	−	0.442000i	$-0.854269\pi$
$941$		−	27.1173i		−	0.884000i	0.897015	−	0.442000i	$-0.145731\pi$
$942$	7.20733	−	7.20733i	0.234827	−	0.234827i
$943$	0.191785	−	0.191785i	0.00624536	−	0.00624536i
$944$	−4.42301			−0.143957
$945$	−0.888360	+	7.77729i	−0.0288984	+	0.252995i
$946$			20.9365i			0.680705i
$947$	−12.0469	+	12.0469i	−0.391473	+	0.391473i	−0.875212	−	0.483739i	$-0.839278\pi$
$947$	−12.0469	+	12.0469i	−0.391473	+	0.391473i	0.483739	+	0.875212i	$0.339278\pi$
$948$	−0.159681	−	0.159681i	−0.00518619	−	0.00518619i
$949$	5.26872			0.171030
$950$	−21.6927	+	2.10356i	−0.703805	+	0.0682485i
$951$	−18.8539			−0.611378
$952$	17.0528	+	17.0528i	0.552683	+	0.552683i
$953$	33.0593	−	33.0593i	1.07090	−	1.07090i	0.0736082	−	0.997287i	$-0.476549\pi$
$953$	33.0593	−	33.0593i	1.07090	−	1.07090i	0.997287	−	0.0736082i	$-0.0234514\pi$
$954$		−	12.6932i		−	0.410957i
$955$	−3.70907	+	32.4716i	−0.120023	+	1.05076i
$956$	−27.2150			−0.880195
$957$	12.6289	−	12.6289i	0.408234	−	0.408234i
$958$	0.478542	−	0.478542i	0.0154610	−	0.0154610i
$959$		−	62.5279i		−	2.01913i
$960$	1.75036	−	1.39149i	0.0564927	−	0.0449100i
$961$	−11.3738			−0.366898
$962$	−7.80102	−	7.80102i	−0.251515	−	0.251515i
$963$	−13.5351	+	13.5351i	−0.436163	+	0.436163i
$964$	25.1111			0.808774
$965$	12.2092	+	15.3581i	0.393028	+	0.494394i
$966$	−0.159132			−0.00511997
$967$	4.66093	−	4.66093i	0.149885	−	0.149885i	−0.628181	−	0.778067i	$-0.716200\pi$
$967$	4.66093	−	4.66093i	0.149885	−	0.149885i	0.778067	+	0.628181i	$0.216200\pi$
$968$	2.45527	−	2.45527i	0.0789155	−	0.0789155i
$969$	26.8899	+	13.3650i	0.863828	+	0.429345i
$970$	27.5434	+	3.14615i	0.884366	+	0.101017i
$971$		−	11.8515i		−	0.380332i	−0.981752	−	0.190166i	$-0.939097\pi$
$971$		−	11.8515i		−	0.380332i	0.981752	−	0.190166i	$-0.0609026\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−25.6201	−	25.6201i	−0.821341	−	0.821341i
$974$		−	3.27156i		−	0.104828i
$975$	1.91633	−	8.27898i	0.0613718	−	0.265140i
$976$	2.95077			0.0944519
$977$	26.7920	+	26.7920i	0.857153	+	0.857153i	0.991002	−	0.133849i	$-0.0427336\pi$
$977$	26.7920	+	26.7920i	0.857153	+	0.857153i	−0.133849	+	0.991002i	$0.542734\pi$
$978$	9.60292	+	9.60292i	0.307068	+	0.307068i
$979$	−25.0669			−0.801143
$980$	−1.33355	+	11.6748i	−0.0425988	+	0.372938i
$981$			4.37207i			0.139589i
$982$	−0.00976048	−	0.00976048i	−0.000311469	−	0.000311469i
$983$	−11.6066	+	11.6066i	−0.370193	+	0.370193i	−0.867547	−	0.497354i	$-0.834305\pi$
$983$	−11.6066	+	11.6066i	−0.370193	+	0.370193i	0.497354	+	0.867547i	$0.334305\pi$
$984$	5.96665			0.190210
$985$	−19.2349	−	24.1958i	−0.612876	−	0.770942i
$986$	−44.8436			−1.42811
$987$	12.8387	+	12.8387i	0.408659	+	0.408659i
$988$	−7.02251	+	2.35944i	−0.223416	+	0.0750636i
$989$			0.346873i			0.0110299i
$990$	3.81777	+	4.80242i	0.121337	+	0.152631i
$991$			58.1707i			1.84785i	0.382568	+	0.923927i	$0.375040\pi$
$991$			58.1707i			1.84785i	−0.382568	+	0.923927i	$0.624960\pi$
$992$	4.60292	−	4.60292i	0.146143	−	0.146143i
$993$	4.75998	+	4.75998i	0.151053	+	0.151053i
$994$			19.4848i			0.618021i
$995$	−17.2676	−	1.97239i	−0.547420	−	0.0625291i
$996$		−	5.47649i		−	0.173529i
$997$	−21.5242	+	21.5242i	−0.681678	+	0.681678i	−0.960378	−	0.278701i	$-0.910096\pi$
$997$	−21.5242	+	21.5242i	−0.681678	+	0.681678i	0.278701	+	0.960378i	$0.410096\pi$
$998$	13.4676	−	13.4676i	0.426309	−	0.426309i
$999$		−	6.49122i		−	0.205373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.a.493.8	yes	20
3.2	odd	2		1710.2.p.d.1063.3		20
5.2	odd	4	inner	570.2.m.a.37.3	✓	20
15.2	even	4		1710.2.p.d.37.8		20
19.18	odd	2	inner	570.2.m.a.493.3	yes	20
57.56	even	2		1710.2.p.d.1063.8		20
95.37	even	4	inner	570.2.m.a.37.8	yes	20
285.227	odd	4		1710.2.p.d.37.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.3	✓	20	5.2	odd	4	inner
570.2.m.a.37.8	yes	20	95.37	even	4	inner
570.2.m.a.493.3	yes	20	19.18	odd	2	inner
570.2.m.a.493.8	yes	20	1.1	even	1	trivial
1710.2.p.d.37.3		20	285.227	odd	4
1710.2.p.d.37.8		20	15.2	even	4
1710.2.p.d.1063.3		20	3.2	odd	2
1710.2.p.d.1063.8		20	57.56	even	2

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.253765 + 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.253765 + 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-1.75036 + 1.39149i) q^{10} +2.74367 q^{11} +(0.707107 + 0.707107i) q^{12} +(-1.20178 + 1.20178i) q^{13} -3.50073 q^{14} +(1.39149 + 1.75036i) q^{15} -1.00000 q^{16} +(-4.87121 + 4.87121i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.94007 - 3.90335i) q^{19} +(-2.22162 - 0.253765i) q^{20} +3.50073i q^{21} +(1.94007 + 1.94007i) q^{22} +(0.0321428 + 0.0321428i) q^{23} +1.00000i q^{24} +(-4.87121 - 1.12754i) q^{25} -1.69957 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.47539 - 2.47539i) q^{28} +6.50952 q^{29} +(-0.253765 + 2.22162i) q^{30} +6.50952i q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.94007 - 1.94007i) q^{33} -6.88893 q^{34} +(-4.87121 - 6.12754i) q^{35} +1.00000 q^{36} +(4.58998 + 4.58998i) q^{37} +(4.13192 - 1.38825i) q^{38} +1.69957i q^{39} +(-1.39149 - 1.75036i) q^{40} -5.96665i q^{41} +(-2.47539 + 2.47539i) q^{42} +(5.39582 + 5.39582i) q^{43} +2.74367i q^{44} +(2.22162 + 0.253765i) q^{45} +0.0454567i q^{46} +(3.66743 - 3.66743i) q^{47} +(-0.707107 + 0.707107i) q^{48} -5.25508i q^{49} +(-2.64717 - 4.24175i) q^{50} +6.88893i q^{51} +(-1.20178 - 1.20178i) q^{52} +(8.97544 - 8.97544i) q^{53} -1.00000i q^{54} +(-0.696246 + 6.09540i) q^{55} -3.50073i q^{56} +(-1.38825 - 4.13192i) q^{57} +(4.60292 + 4.60292i) q^{58} +4.42301 q^{59} +(-1.75036 + 1.39149i) q^{60} -2.95077 q^{61} +(-4.60292 + 4.60292i) q^{62} +(2.47539 + 2.47539i) q^{63} -1.00000i q^{64} +(-2.36493 - 2.97487i) q^{65} +2.74367 q^{66} +(7.00145 + 7.00145i) q^{67} +(-4.87121 - 4.87121i) q^{68} +0.0454567 q^{69} +(0.888360 - 7.77729i) q^{70} -5.56594i q^{71} +(0.707107 + 0.707107i) q^{72} +(-2.19205 - 2.19205i) q^{73} +6.49122i q^{74} +(-4.24175 + 2.64717i) q^{75} +(3.90335 + 1.94007i) q^{76} +(-6.79164 + 6.79164i) q^{77} +(-1.20178 + 1.20178i) q^{78} -0.225823 q^{79} +(0.253765 - 2.22162i) q^{80} -1.00000 q^{81} +(4.21906 - 4.21906i) q^{82} +(-3.87246 - 3.87246i) q^{83} -3.50073 q^{84} +(-9.58584 - 12.0581i) q^{85} +7.63084i q^{86} +(4.60292 - 4.60292i) q^{87} +(-1.94007 + 1.94007i) q^{88} -9.13628 q^{89} +(1.39149 + 1.75036i) q^{90} -5.94974i q^{91} +(-0.0321428 + 0.0321428i) q^{92} +(4.60292 + 4.60292i) q^{93} +5.18653 q^{94} +(8.17945 + 5.30063i) q^{95} -1.00000 q^{96} +(-8.76663 - 8.76663i) q^{97} +(3.71590 - 3.71590i) q^{98} -2.74367i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7	\( 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} + 4 q^{17} + 44 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{30} + 4 q^{35} + 20 q^{36} - 4 q^{38} - 4 q^{42} + 52 q^{43} + 4 q^{47} + 16 q^{55} - 4 q^{57} + 8 q^{58} + 32 q^{61} - 8 q^{62} + 4 q^{63} - 8 q^{66} + 4 q^{68} - 20 q^{73} + 20 q^{76} - 24 q^{77} + 4 q^{80} - 20 q^{81} - 24 q^{82} - 116 q^{83} - 60 q^{85} + 8 q^{87} - 44 q^{92} + 8 q^{93} - 32 q^{95} - 20 q^{96}+O(q^{100}) \) 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 + 4 * q^17 + 44 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^30 + 4 * q^35 + 20 * q^36 - 4 * q^38 - 4 * q^42 + 52 * q^43 + 4 * q^47 + 16 * q^55 - 4 * q^57 + 8 * q^58 + 32 * q^61 - 8 * q^62 + 4 * q^63 - 8 * q^66 + 4 * q^68 - 20 * q^73 + 20 * q^76 - 24 * q^77 + 4 * q^80 - 20 * q^81 - 24 * q^82 - 116 * q^83 - 60 * q^85 + 8 * q^87 - 44 * q^92 + 8 * q^93 - 32 * q^95 - 20 * q^96

Introduction

L-functions

Modular forms

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Database

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