LMFDB - Embedded newform 570.2.m.a.493.5

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			493.5
Root			$0.498616 + 0.498616i$ of defining polynomial
Character	$\chi$	$=$	570.493
Dual form			570.2.m.a.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.89390 + 1.18875i) q^{5} +1.00000 q^{6} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.89390 + 1.18875i) q^{5} +1.00000 q^{6} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-0.498616 - 2.17977i) q^{10} +1.32903 q^{11} +(-0.707107 - 0.707107i) q^{12} +(0.741383 - 0.741383i) q^{13} -0.997232 q^{14} +(-2.17977 + 0.498616i) q^{15} -1.00000 q^{16} +(2.17373 - 2.17373i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-0.939768 + 4.25639i) q^{19} +(-1.18875 + 1.89390i) q^{20} +0.997232i q^{21} +(-0.939768 - 0.939768i) q^{22} +(-1.08266 - 1.08266i) q^{23} +1.00000i q^{24} +(2.17373 + 4.50276i) q^{25} -1.04847 q^{26} +(0.707107 + 0.707107i) q^{27} +(0.705149 + 0.705149i) q^{28} +5.95089 q^{29} +(1.89390 + 1.18875i) q^{30} +5.95089i q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.939768 + 0.939768i) q^{33} -3.07412 q^{34} +(2.17373 - 0.497236i) q^{35} +1.00000 q^{36} +(1.33551 + 1.33551i) q^{37} +(3.67424 - 2.34520i) q^{38} +1.04847i q^{39} +(2.17977 - 0.498616i) q^{40} -0.531910i q^{41} +(0.705149 - 0.705149i) q^{42} +(1.53142 + 1.53142i) q^{43} +1.32903i q^{44} +(1.18875 - 1.89390i) q^{45} +1.53111i q^{46} +(4.13113 - 4.13113i) q^{47} +(0.707107 - 0.707107i) q^{48} +6.00553i q^{49} +(1.64687 - 4.72100i) q^{50} +3.07412i q^{51} +(0.741383 + 0.741383i) q^{52} +(5.48557 - 5.48557i) q^{53} -1.00000i q^{54} +(2.51706 + 1.57989i) q^{55} -0.997232i q^{56} +(-2.34520 - 3.67424i) q^{57} +(-4.20791 - 4.20791i) q^{58} +3.53944 q^{59} +(-0.498616 - 2.17977i) q^{60} +3.41030 q^{61} +(4.20791 - 4.20791i) q^{62} +(-0.705149 - 0.705149i) q^{63} -1.00000i q^{64} +(2.28543 - 0.522786i) q^{65} +1.32903 q^{66} +(1.99446 + 1.99446i) q^{67} +(2.17373 + 2.17373i) q^{68} +1.53111 q^{69} +(-1.88866 - 1.18546i) q^{70} +8.71907i q^{71} +(-0.707107 - 0.707107i) q^{72} +(-5.83628 - 5.83628i) q^{73} -1.88869i q^{74} +(-4.72100 - 1.64687i) q^{75} +(-4.25639 - 0.939768i) q^{76} +(0.937166 - 0.937166i) q^{77} +(0.741383 - 0.741383i) q^{78} -9.31319 q^{79} +(-1.89390 - 1.18875i) q^{80} -1.00000 q^{81} +(-0.376117 + 0.376117i) q^{82} +(-9.50276 - 9.50276i) q^{83} -0.997232 q^{84} +(6.70087 - 1.53281i) q^{85} -2.16575i q^{86} +(-4.20791 + 4.20791i) q^{87} +(0.939768 - 0.939768i) q^{88} +16.7874 q^{89} +(-2.17977 + 0.498616i) q^{90} -1.04557i q^{91} +(1.08266 - 1.08266i) q^{92} +(-4.20791 - 4.20791i) q^{93} -5.84230 q^{94} +(-6.83962 + 6.94403i) q^{95} -1.00000 q^{96} +(-1.11691 - 1.11691i) q^{97} +(4.24655 - 4.24655i) q^{98} -1.32903i 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
$5$	1.89390	+	1.18875i	0.846979	+	0.531627i
$5$	1.89390	+	1.18875i	0.846979	+	0.531627i
$6$	1.00000			0.408248
$7$	0.705149	−	0.705149i	0.266521	−	0.266521i	−0.561175	−	0.827697i	$-0.689651\pi$
$7$	0.705149	−	0.705149i	0.266521	−	0.266521i	0.827697	+	0.561175i	$0.189651\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−0.498616	−	2.17977i	−0.157676	−	0.689303i
$11$	1.32903			0.400718			0.200359	−	0.979723i	$-0.435789\pi$
$11$	1.32903			0.400718			0.200359	+	0.979723i	$0.435789\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	0.741383	−	0.741383i	0.205623	−	0.205623i	−0.596781	−	0.802404i	$-0.703554\pi$
$13$	0.741383	−	0.741383i	0.205623	−	0.205623i	0.802404	+	0.596781i	$0.203554\pi$
$14$	−0.997232			−0.266521
$15$	−2.17977	+	0.498616i	−0.562813	+	0.128742i
$16$	−1.00000			−0.250000
$17$	2.17373	−	2.17373i	0.527208	−	0.527208i	−0.392531	−	0.919739i	$-0.628400\pi$
$17$	2.17373	−	2.17373i	0.527208	−	0.527208i	0.919739	+	0.392531i	$0.128400\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−0.939768	+	4.25639i	−0.215597	+	0.976482i
$19$	−0.939768	+	4.25639i	−0.215597	+	0.976482i
$20$	−1.18875	+	1.89390i	−0.265813	+	0.423489i
$21$			0.997232i			0.217614i
$22$	−0.939768	−	0.939768i	−0.200359	−	0.200359i
$23$	−1.08266	−	1.08266i	−0.225749	−	0.225749i	0.585165	−	0.810914i	$-0.301030\pi$
$23$	−1.08266	−	1.08266i	−0.225749	−	0.225749i	−0.810914	+	0.585165i	$0.801030\pi$
$24$			1.00000i			0.204124i
$25$	2.17373	+	4.50276i	0.434746	+	0.900553i
$26$	−1.04847			−0.205623
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.705149	+	0.705149i	0.133261	+	0.133261i
$29$	5.95089			1.10505			0.552526	−	0.833496i	$-0.313664\pi$
$29$	5.95089			1.10505			0.552526	+	0.833496i	$0.313664\pi$
$30$	1.89390	+	1.18875i	0.345778	+	0.217036i
$31$			5.95089i			1.06881i	0.845228	+	0.534406i	$0.179464\pi$
$31$			5.95089i			1.06881i	−0.845228	+	0.534406i	$0.820536\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.939768	+	0.939768i	−0.163593	+	0.163593i
$34$	−3.07412			−0.527208
$35$	2.17373	−	0.497236i	0.367428	−	0.0840481i
$36$	1.00000			0.166667
$37$	1.33551	+	1.33551i	0.219556	+	0.219556i	0.808311	−	0.588755i	$-0.200382\pi$
$37$	1.33551	+	1.33551i	0.219556	+	0.219556i	−0.588755	+	0.808311i	$0.700382\pi$
$38$	3.67424	−	2.34520i	0.596040	−	0.380442i
$39$			1.04847i			0.167890i
$40$	2.17977	−	0.498616i	0.344651	−	0.0788381i
$41$		−	0.531910i		−	0.0830704i	−0.999137	−	0.0415352i	$-0.986775\pi$
$41$		−	0.531910i		−	0.0830704i	0.999137	−	0.0415352i	$-0.0132249\pi$
$42$	0.705149	−	0.705149i	0.108807	−	0.108807i
$43$	1.53142	+	1.53142i	0.233539	+	0.233539i	0.814168	−	0.580629i	$-0.197193\pi$
$43$	1.53142	+	1.53142i	0.233539	+	0.233539i	−0.580629	+	0.814168i	$0.697193\pi$
$44$			1.32903i			0.200359i
$45$	1.18875	−	1.89390i	0.177209	−	0.282326i
$46$			1.53111i			0.225749i
$47$	4.13113	−	4.13113i	0.602587	−	0.602587i	−0.338411	−	0.940998i	$-0.609889\pi$
$47$	4.13113	−	4.13113i	0.602587	−	0.602587i	0.940998	+	0.338411i	$0.109889\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			6.00553i			0.857933i
$50$	1.64687	−	4.72100i	0.232903	−	0.667650i
$51$			3.07412i			0.430463i
$52$	0.741383	+	0.741383i	0.102811	+	0.102811i
$53$	5.48557	−	5.48557i	0.753501	−	0.753501i	−0.221630	−	0.975131i	$-0.571138\pi$
$53$	5.48557	−	5.48557i	0.753501	−	0.753501i	0.975131	+	0.221630i	$0.0711378\pi$
$54$		−	1.00000i		−	0.136083i
$55$	2.51706	+	1.57989i	0.339400	+	0.213032i
$56$		−	0.997232i		−	0.133261i
$57$	−2.34520	−	3.67424i	−0.310630	−	0.486665i
$58$	−4.20791	−	4.20791i	−0.552526	−	0.552526i
$59$	3.53944			0.460796			0.230398	−	0.973096i	$-0.425997\pi$
$59$	3.53944			0.460796			0.230398	+	0.973096i	$0.425997\pi$
$60$	−0.498616	−	2.17977i	−0.0643710	−	0.281407i
$61$	3.41030			0.436644			0.218322	−	0.975877i	$-0.429942\pi$
$61$	3.41030			0.436644			0.218322	+	0.975877i	$0.429942\pi$
$62$	4.20791	−	4.20791i	0.534406	−	0.534406i
$63$	−0.705149	−	0.705149i	−0.0888405	−	0.0888405i
$64$		−	1.00000i		−	0.125000i
$65$	2.28543	−	0.522786i	0.283473	−	0.0648436i
$66$	1.32903			0.163593
$67$	1.99446	+	1.99446i	0.243662	+	0.243662i	0.818363	−	0.574701i	$-0.194882\pi$
$67$	1.99446	+	1.99446i	0.243662	+	0.243662i	−0.574701	+	0.818363i	$0.694882\pi$
$68$	2.17373	+	2.17373i	0.263604	+	0.263604i
$69$	1.53111			0.184323
$70$	−1.88866	−	1.18546i	−0.225738	−	0.141690i
$71$			8.71907i			1.03476i	0.855755	+	0.517381i	$0.173093\pi$
$71$			8.71907i			1.03476i	−0.855755	+	0.517381i	$0.826907\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−5.83628	−	5.83628i	−0.683085	−	0.683085i	0.277609	−	0.960694i	$-0.410458\pi$
$73$	−5.83628	−	5.83628i	−0.683085	−	0.683085i	−0.960694	+	0.277609i	$0.910458\pi$
$74$		−	1.88869i		−	0.219556i
$75$	−4.72100	−	1.64687i	−0.545134	−	0.190165i
$76$	−4.25639	−	0.939768i	−0.488241	−	0.107799i
$77$	0.937166	−	0.937166i	0.106800	−	0.106800i
$78$	0.741383	−	0.741383i	0.0839451	−	0.0839451i
$79$	−9.31319			−1.04782			−0.523908	−	0.851775i	$-0.675526\pi$
$79$	−9.31319			−1.04782			−0.523908	+	0.851775i	$0.675526\pi$
$80$	−1.89390	−	1.18875i	−0.211745	−	0.132907i
$81$	−1.00000			−0.111111
$82$	−0.376117	+	0.376117i	−0.0415352	+	0.0415352i
$83$	−9.50276	−	9.50276i	−1.04306	−	1.04306i	−0.999030	−	0.0440339i	$-0.985979\pi$
$83$	−9.50276	−	9.50276i	−1.04306	−	1.04306i	−0.0440339	−	0.999030i	$-0.514021\pi$
$84$	−0.997232			−0.108807
$85$	6.70087	−	1.53281i	0.726811	−	0.166256i
$86$		−	2.16575i		−	0.233539i
$87$	−4.20791	+	4.20791i	−0.451136	+	0.451136i
$88$	0.939768	−	0.939768i	0.100180	−	0.100180i
$89$	16.7874			1.77946			0.889729	−	0.456490i	$-0.150894\pi$
$89$	16.7874			1.77946			0.889729	+	0.456490i	$0.150894\pi$
$90$	−2.17977	+	0.498616i	−0.229768	+	0.0525587i
$91$		−	1.04557i		−	0.109606i
$92$	1.08266	−	1.08266i	0.112875	−	0.112875i
$93$	−4.20791	−	4.20791i	−0.436340	−	0.436340i
$94$	−5.84230			−0.602587
$95$	−6.83962	+	6.94403i	−0.701730	+	0.712443i
$96$	−1.00000			−0.102062
$97$	−1.11691	−	1.11691i	−0.113405	−	0.113405i	0.648127	−	0.761532i	$-0.275553\pi$
$97$	−1.11691	−	1.11691i	−0.113405	−	0.113405i	−0.761532	+	0.648127i	$0.775553\pi$
$98$	4.24655	−	4.24655i	0.428966	−	0.428966i
$99$		−	1.32903i		−	0.133573i
$100$	−4.50276	+	2.17373i	−0.450276	+	0.217373i
$101$	−15.7109			−1.56329			−0.781645	−	0.623723i	$-0.785619\pi$
$101$	−15.7109			−1.56329			−0.781645	+	0.623723i	$0.785619\pi$
$102$	2.17373	−	2.17373i	0.215232	−	0.215232i
$103$	−10.7950	+	10.7950i	−1.06367	+	1.06367i	−0.0658345	+	0.997831i	$0.520971\pi$
$103$	−10.7950	+	10.7950i	−1.06367	+	1.06367i	−0.997831	+	0.0658345i	$0.979029\pi$
$104$		−	1.04847i		−	0.102811i
$105$	−1.18546	+	1.88866i	−0.115689	+	0.184314i
$106$	−7.75776			−0.753501
$107$	2.65129	+	2.65129i	0.256309	+	0.256309i	0.823551	−	0.567242i	$-0.191990\pi$
$107$	2.65129	+	2.65129i	0.256309	+	0.256309i	−0.567242	+	0.823551i	$0.691990\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	5.83596			0.558984			0.279492	−	0.960148i	$-0.409834\pi$
$109$	5.83596			0.558984			0.279492	+	0.960148i	$0.409834\pi$
$110$	−0.662676	−	2.89698i	−0.0631837	−	0.276216i
$111$	−1.88869			−0.179267
$112$	−0.705149	+	0.705149i	−0.0666303	+	0.0666303i
$113$	0.463357	−	0.463357i	0.0435890	−	0.0435890i	−0.684976	−	0.728565i	$-0.740187\pi$
$113$	0.463357	−	0.463357i	0.0435890	−	0.0435890i	0.728565	+	0.684976i	$0.240187\pi$
$114$	−0.939768	+	4.25639i	−0.0880173	+	0.398647i
$115$	−0.763434	−	3.33745i	−0.0711906	−	0.311219i
$116$			5.95089i			0.552526i
$117$	−0.741383	−	0.741383i	−0.0685409	−	0.0685409i
$118$	−2.50276	−	2.50276i	−0.230398	−	0.230398i
$119$		−	3.06561i		−	0.281024i
$120$	−1.18875	+	1.89390i	−0.108518	+	0.172889i
$121$	−9.23367			−0.839425
$122$	−2.41145	−	2.41145i	−0.218322	−	0.218322i
$123$	0.376117	+	0.376117i	0.0339133	+	0.0339133i
$124$	−5.95089			−0.534406
$125$	−1.23584	+	11.1118i	−0.110537	+	0.993872i
$126$			0.997232i			0.0888405i
$127$	−7.75499	−	7.75499i	−0.688144	−	0.688144i	0.273678	−	0.961821i	$-0.411760\pi$
$127$	−7.75499	−	7.75499i	−0.688144	−	0.688144i	−0.961821	+	0.273678i	$0.911760\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−2.16575			−0.190684
$130$	−1.98571	−	1.24638i	−0.174158	−	0.109314i
$131$	−13.2521			−1.15784			−0.578921	−	0.815384i	$-0.696526\pi$
$131$	−13.2521			−1.15784			−0.578921	+	0.815384i	$0.696526\pi$
$132$	−0.939768	−	0.939768i	−0.0817963	−	0.0817963i
$133$	2.33871	+	3.66407i	0.202792	+	0.317715i
$134$		−	2.82060i		−	0.243662i
$135$	0.498616	+	2.17977i	0.0429140	+	0.187604i
$136$		−	3.07412i		−	0.263604i
$137$	4.42031	−	4.42031i	0.377653	−	0.377653i	−0.492602	−	0.870255i	$-0.663954\pi$
$137$	4.42031	−	4.42031i	0.377653	−	0.377653i	0.870255	+	0.492602i	$0.163954\pi$
$138$	−1.08266	−	1.08266i	−0.0921617	−	0.0921617i
$139$			2.68665i			0.227879i	0.993488	+	0.113939i	$0.0363469\pi$
$139$			2.68665i			0.227879i	−0.993488	+	0.113939i	$0.963653\pi$
$140$	0.497236	+	2.17373i	0.0420241	+	0.183714i
$141$			5.84230i			0.492010i
$142$	6.16531	−	6.16531i	0.517381	−	0.517381i
$143$	0.985322	−	0.985322i	0.0823968	−	0.0823968i
$144$			1.00000i			0.0833333i
$145$	11.2704	+	7.07414i	0.935956	+	0.587475i
$146$			8.25374i			0.683085i
$147$	−4.24655	−	4.24655i	−0.350250	−	0.350250i
$148$	−1.33551	+	1.33551i	−0.109778	+	0.109778i
$149$		−	14.1380i		−	1.15823i	−0.815244	−	0.579117i	$-0.803397\pi$
$149$		−	14.1380i		−	1.15823i	0.815244	−	0.579117i	$-0.196603\pi$
$150$	2.17373	+	4.50276i	0.177485	+	0.367649i
$151$		−	9.45030i		−	0.769054i	−0.923114	−	0.384527i	$-0.874365\pi$
$151$		−	9.45030i		−	0.769054i	0.923114	−	0.384527i	$-0.125635\pi$
$152$	2.34520	+	3.67424i	0.190221	+	0.298020i
$153$	−2.17373	−	2.17373i	−0.175736	−	0.175736i
$154$	−1.32535			−0.106800
$155$	−7.07414	+	11.2704i	−0.568208	+	0.905260i
$156$	−1.04847			−0.0839451
$157$	13.7650	−	13.7650i	1.09857	−	1.09857i	0.103990	−	0.994578i	$-0.466839\pi$
$157$	13.7650	−	13.7650i	1.09857	−	1.09857i	0.994578	−	0.103990i	$-0.0331610\pi$
$158$	6.58542	+	6.58542i	0.523908	+	0.523908i
$159$			7.75776i			0.615231i
$160$	0.498616	+	2.17977i	0.0394190	+	0.172326i
$161$	−1.52687			−0.120334
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	0.792086	+	0.792086i	0.0620410	+	0.0620410i	0.737447	−	0.675406i	$-0.236031\pi$
$163$	0.792086	+	0.792086i	0.0620410	+	0.0620410i	−0.675406	+	0.737447i	$0.736031\pi$
$164$	0.531910			0.0415352
$165$	−2.89698	+	0.662676i	−0.225530	+	0.0515893i
$166$			13.4389i			1.04306i
$167$	−11.1325	−	11.1325i	−0.861457	−	0.861457i	0.130051	−	0.991507i	$-0.458486\pi$
$167$	−11.1325	−	11.1325i	−0.861457	−	0.861457i	−0.991507	+	0.130051i	$0.958486\pi$
$168$	0.705149	+	0.705149i	0.0544035	+	0.0544035i
$169$			11.9007i			0.915439i
$170$	−5.82209	−	3.65437i	−0.446534	−	0.280278i
$171$	4.25639	+	0.939768i	0.325494	+	0.0718658i
$172$	−1.53142	+	1.53142i	−0.116769	+	0.116769i
$173$	−5.42532	+	5.42532i	−0.412479	+	0.412479i	−0.882601	−	0.470122i	$-0.844210\pi$
$173$	−5.42532	+	5.42532i	−0.412479	+	0.412479i	0.470122	+	0.882601i	$0.344210\pi$
$174$	5.95089			0.451136
$175$	4.70793	+	1.64232i	0.355886	+	0.124147i
$176$	−1.32903			−0.100180
$177$	−2.50276	+	2.50276i	−0.188119	+	0.188119i
$178$	−11.8705	−	11.8705i	−0.889729	−	0.889729i
$179$	0.963050			0.0719817			0.0359909	−	0.999352i	$-0.488541\pi$
$179$	0.963050			0.0719817			0.0359909	+	0.999352i	$0.488541\pi$
$180$	1.89390	+	1.18875i	0.141163	+	0.0886044i
$181$		−	20.4214i		−	1.51791i	−0.651141	−	0.758956i	$-0.725710\pi$
$181$		−	20.4214i		−	1.51791i	0.651141	−	0.758956i	$-0.274290\pi$
$182$	−0.739331	+	0.739331i	−0.0548028	+	0.0548028i
$183$	−2.41145	+	2.41145i	−0.178259	+	0.178259i
$184$	−1.53111			−0.112875
$185$	0.941732	+	4.11691i	0.0692375	+	0.302681i
$186$			5.95089i			0.436340i
$187$	2.88896	−	2.88896i	0.211262	−	0.211262i
$188$	4.13113	+	4.13113i	0.301294	+	0.301294i
$189$	0.997232			0.0725379
$190$	9.74651	−	0.0738284i	0.707086	−	0.00535608i
$191$	−7.34773			−0.531663			−0.265832	−	0.964019i	$-0.585647\pi$
$191$	−7.34773			−0.531663			−0.265832	+	0.964019i	$0.585647\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−9.32428	+	9.32428i	−0.671176	+	0.671176i	−0.957987	−	0.286811i	$-0.907405\pi$
$193$	−9.32428	+	9.32428i	−0.671176	+	0.671176i	0.286811	+	0.957987i	$0.407405\pi$
$194$			1.57955i			0.113405i
$195$	−1.24638	+	1.98571i	−0.0892549	+	0.142199i
$196$	−6.00553			−0.428966
$197$	5.43012	−	5.43012i	0.386880	−	0.386880i	−0.486693	−	0.873573i	$-0.661797\pi$
$197$	5.43012	−	5.43012i	0.386880	−	0.386880i	0.873573	+	0.486693i	$0.161797\pi$
$198$	−0.939768	+	0.939768i	−0.0667864	+	0.0667864i
$199$		−	23.4987i		−	1.66578i	−0.553440	−	0.832889i	$-0.686685\pi$
$199$		−	23.4987i		−	1.66578i	0.553440	−	0.832889i	$-0.313315\pi$
$200$	4.72100	+	1.64687i	0.333825	+	0.116452i
$201$	−2.82060			−0.198950
$202$	11.1093	+	11.1093i	0.781645	+	0.781645i
$203$	4.19627	−	4.19627i	0.294520	−	0.294520i
$204$	−3.07412			−0.215232
$205$	0.632310	−	1.00739i	0.0441624	−	0.0703589i
$206$	15.2665			1.06367
$207$	−1.08266	+	1.08266i	−0.0752498	+	0.0752498i
$208$	−0.741383	+	0.741383i	−0.0514057	+	0.0514057i
$209$	−1.24898	+	5.65688i	−0.0863938	+	0.391294i
$210$	2.17373	−	0.497236i	0.150002	−	0.0343125i
$211$		−	8.16488i		−	0.562094i	−0.959694	−	0.281047i	$-0.909318\pi$
$211$		−	8.16488i		−	0.562094i	0.959694	−	0.281047i	$-0.0906816\pi$
$212$	5.48557	+	5.48557i	0.376750	+	0.376750i
$213$	−6.16531	−	6.16531i	−0.422440	−	0.422440i
$214$		−	3.74948i		−	0.256309i
$215$	1.07988	+	4.72083i	0.0736470	+	0.321958i
$216$	1.00000			0.0680414
$217$	4.19627	+	4.19627i	0.284861	+	0.284861i
$218$	−4.12665	−	4.12665i	−0.279492	−	0.279492i
$219$	8.25374			0.557736
$220$	−1.57989	+	2.51706i	−0.106516	+	0.169700i
$221$		−	3.22314i		−	0.216812i
$222$	1.33551	+	1.33551i	0.0896334	+	0.0896334i
$223$	−0.212542	+	0.212542i	−0.0142329	+	0.0142329i	−0.714187	−	0.699955i	$-0.753204\pi$
$223$	−0.212542	+	0.212542i	−0.0142329	+	0.0142329i	0.699955	+	0.714187i	$0.253204\pi$
$224$	0.997232			0.0666303
$225$	4.50276	−	2.17373i	0.300184	−	0.144915i
$226$	−0.655286			−0.0435890
$227$	−16.9240	−	16.9240i	−1.12328	−	1.12328i	−0.991244	−	0.132040i	$-0.957847\pi$
$227$	−16.9240	−	16.9240i	−1.12328	−	1.12328i	−0.132040	−	0.991244i	$-0.542153\pi$
$228$	3.67424	−	2.34520i	0.243332	−	0.155315i
$229$			7.59523i			0.501907i	0.967999	+	0.250953i	$0.0807441\pi$
$229$			7.59523i			0.501907i	−0.967999	+	0.250953i	$0.919256\pi$
$230$	−1.82011	+	2.89977i	−0.120014	+	0.191205i
$231$			1.32535i			0.0872018i
$232$	4.20791	−	4.20791i	0.276263	−	0.276263i
$233$	0.816115	+	0.816115i	0.0534655	+	0.0534655i	0.733334	−	0.679869i	$-0.237963\pi$
$233$	0.816115	+	0.816115i	0.0534655	+	0.0534655i	−0.679869	+	0.733334i	$0.737963\pi$
$234$			1.04847i			0.0685409i
$235$	12.7348	−	2.91306i	0.830730	−	0.190027i
$236$			3.53944i			0.230398i
$237$	6.58542	−	6.58542i	0.427769	−	0.427769i
$238$	−2.16771	+	2.16771i	−0.140512	+	0.140512i
$239$			4.21103i			0.272389i	0.990682	+	0.136195i	$0.0434872\pi$
$239$			4.21103i			0.272389i	−0.990682	+	0.136195i	$0.956513\pi$
$240$	2.17977	−	0.498616i	0.140703	−	0.0321855i
$241$		−	24.8896i		−	1.60328i	−0.597809	−	0.801638i	$-0.703962\pi$
$241$		−	24.8896i		−	1.60328i	0.597809	−	0.801638i	$-0.296038\pi$
$242$	6.52919	+	6.52919i	0.419712	+	0.419712i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$			3.41030i			0.218322i
$245$	−7.13909	+	11.3739i	−0.456100	+	0.726651i
$246$		−	0.531910i		−	0.0339133i
$247$	2.45889	+	3.85234i	0.156455	+	0.245119i
$248$	4.20791	+	4.20791i	0.267203	+	0.267203i
$249$	13.4389			0.851658
$250$	8.73112	−	6.98338i	0.552204	−	0.441668i
$251$	−0.952848			−0.0601432			−0.0300716	−	0.999548i	$-0.509574\pi$
$251$	−0.952848			−0.0601432			−0.0300716	+	0.999548i	$0.509574\pi$
$252$	0.705149	−	0.705149i	0.0444202	−	0.0444202i
$253$	−1.43888	−	1.43888i	−0.0904619	−	0.0904619i
$254$			10.9672i			0.688144i
$255$	−3.65437	+	5.82209i	−0.228846	+	0.364593i
$256$	1.00000			0.0625000
$257$	−12.4298	−	12.4298i	−0.775349	−	0.775349i	0.203687	−	0.979036i	$-0.434708\pi$
$257$	−12.4298	−	12.4298i	−0.775349	−	0.775349i	−0.979036	+	0.203687i	$0.934708\pi$
$258$	1.53142	+	1.53142i	0.0953419	+	0.0953419i
$259$	1.88346			0.117033
$260$	0.522786	+	2.28543i	0.0324218	+	0.141736i
$261$		−	5.95089i		−	0.368351i
$262$	9.37065	+	9.37065i	0.578921	+	0.578921i
$263$	3.37612	+	3.37612i	0.208180	+	0.208180i	0.803494	−	0.595313i	$-0.202972\pi$
$263$	3.37612	+	3.37612i	0.208180	+	0.208180i	−0.595313	+	0.803494i	$0.702972\pi$
$264$			1.32903i			0.0817963i
$265$	16.9101	−	3.86814i	1.03878	−	0.237618i
$266$	0.937166	−	4.24460i	0.0574613	−	0.260253i
$267$	−11.8705	+	11.8705i	−0.726460	+	0.726460i
$268$	−1.99446	+	1.99446i	−0.121831	+	0.121831i
$269$	−1.10025			−0.0670834			−0.0335417	−	0.999437i	$-0.510679\pi$
$269$	−1.10025			−0.0670834			−0.0335417	+	0.999437i	$0.510679\pi$
$270$	1.18875	−	1.89390i	0.0723452	−	0.115259i
$271$	18.3193			1.11282			0.556409	−	0.830909i	$-0.312179\pi$
$271$	18.3193			1.11282			0.556409	+	0.830909i	$0.312179\pi$
$272$	−2.17373	+	2.17373i	−0.131802	+	0.131802i
$273$	0.739331	+	0.739331i	0.0447463	+	0.0447463i
$274$	−6.25126			−0.377653
$275$	2.88896	+	5.98432i	0.174211	+	0.360868i
$276$			1.53111i			0.0921617i
$277$	−6.48039	+	6.48039i	−0.389369	+	0.389369i	−0.874462	−	0.485093i	$-0.838786\pi$
$277$	−6.48039	+	6.48039i	−0.389369	+	0.389369i	0.485093	+	0.874462i	$0.338786\pi$
$278$	1.89975	−	1.89975i	0.113939	−	0.113939i
$279$	5.95089			0.356270
$280$	1.18546	−	1.88866i	0.0708449	−	0.112869i
$281$		−	12.6675i		−	0.755678i	−0.925871	−	0.377839i	$-0.876667\pi$
$281$		−	12.6675i		−	0.755678i	0.925871	−	0.377839i	$-0.123333\pi$
$282$	4.13113	−	4.13113i	0.246005	−	0.246005i
$283$	11.2107	+	11.2107i	0.666406	+	0.666406i	0.956882	−	0.290476i	$-0.0938136\pi$
$283$	11.2107	+	11.2107i	0.666406	+	0.666406i	−0.290476	+	0.956882i	$0.593814\pi$
$284$	−8.71907			−0.517381
$285$	−0.0738284	−	9.74651i	−0.00437322	−	0.577334i
$286$	−1.39346			−0.0823968
$287$	−0.375076	−	0.375076i	−0.0221400	−	0.0221400i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			7.54978i			0.444104i
$290$	−2.96721	−	12.9715i	−0.174240	−	0.761716i
$291$	1.57955			0.0925948
$292$	5.83628	−	5.83628i	0.341542	−	0.341542i
$293$	−0.128802	+	0.128802i	−0.00752471	+	0.00752471i	−0.710859	−	0.703334i	$-0.751694\pi$
$293$	−0.128802	+	0.128802i	−0.00752471	+	0.00752471i	0.703334	+	0.710859i	$0.251694\pi$
$294$			6.00553i			0.350250i
$295$	6.70336	+	4.20752i	0.390285	+	0.244972i
$296$	1.88869			0.109778
$297$	0.939768	+	0.939768i	0.0545308	+	0.0545308i
$298$	−9.99711	+	9.99711i	−0.579117	+	0.579117i
$299$	−1.60532			−0.0928383
$300$	1.64687	−	4.72100i	0.0950823	−	0.272567i
$301$	2.15976			0.124486
$302$	−6.68237	+	6.68237i	−0.384527	+	0.384527i
$303$	11.1093	−	11.1093i	0.638211	−	0.638211i
$304$	0.939768	−	4.25639i	0.0538994	−	0.244121i
$305$	6.45877	+	4.05400i	0.369828	+	0.232132i
$306$			3.07412i			0.175736i
$307$	−15.7940	−	15.7940i	−0.901413	−	0.901413i	0.0941458	−	0.995558i	$-0.469988\pi$
$307$	−15.7940	−	15.7940i	−0.901413	−	0.901413i	−0.995558	+	0.0941458i	$0.969988\pi$
$308$	0.937166	+	0.937166i	0.0534000	+	0.0534000i
$309$		−	15.2665i		−	0.868479i
$310$	12.9715	−	2.96721i	0.736734	−	0.168526i
$311$	14.6924			0.833132			0.416566	−	0.909105i	$-0.363233\pi$
$311$	14.6924			0.833132			0.416566	+	0.909105i	$0.363233\pi$
$312$	0.741383	+	0.741383i	0.0419726	+	0.0419726i
$313$	−1.77069	−	1.77069i	−0.100086	−	0.100086i	0.655291	−	0.755377i	$-0.272546\pi$
$313$	−1.77069	−	1.77069i	−0.100086	−	0.100086i	−0.755377	+	0.655291i	$0.772546\pi$
$314$	−19.4667			−1.09857
$315$	−0.497236	−	2.17373i	−0.0280160	−	0.122476i
$316$		−	9.31319i		−	0.523908i
$317$	4.63384	+	4.63384i	0.260262	+	0.260262i	0.825161	−	0.564898i	$-0.191085\pi$
$317$	4.63384	+	4.63384i	0.260262	+	0.260262i	−0.564898	+	0.825161i	$0.691085\pi$
$318$	5.48557	−	5.48557i	0.307615	−	0.307615i
$319$	7.90892			0.442815
$320$	1.18875	−	1.89390i	0.0664533	−	0.105872i
$321$	−3.74948			−0.209276
$322$	1.07966	+	1.07966i	0.0601670	+	0.0601670i
$323$	7.20944	+	11.2951i	0.401144	+	0.628473i
$324$		−	1.00000i		−	0.0555556i
$325$	4.94984	+	1.72670i	0.274568	+	0.0957804i
$326$		−	1.12018i		−	0.0620410i
$327$	−4.12665	+	4.12665i	−0.228204	+	0.228204i
$328$	−0.376117	−	0.376117i	−0.0207676	−	0.0207676i
$329$		−	5.82613i		−	0.321205i
$330$	2.51706	+	1.57989i	0.138559	+	0.0869701i
$331$		−	10.5075i		−	0.577544i	−0.957398	−	0.288772i	$-0.906753\pi$
$331$		−	10.5075i		−	0.577544i	0.957398	−	0.288772i	$-0.0932470\pi$
$332$	9.50276	−	9.50276i	0.521532	−	0.521532i
$333$	1.33551	−	1.33551i	0.0731853	−	0.0731853i
$334$			15.7437i			0.861457i
$335$	1.40639	+	6.14824i	0.0768395	+	0.335914i
$336$		−	0.997232i		−	0.0544035i
$337$	18.8126	+	18.8126i	1.02479	+	1.02479i	0.999685	+	0.0251053i	$0.00799212\pi$
$337$	18.8126	+	18.8126i	1.02479	+	1.02479i	0.0251053	+	0.999685i	$0.492008\pi$
$338$	8.41507	−	8.41507i	0.457719	−	0.457719i
$339$			0.655286i			0.0355903i
$340$	1.53281	+	6.70087i	0.0831281	+	0.363406i
$341$			7.90892i			0.428292i
$342$	−2.34520	−	3.67424i	−0.126814	−	0.198680i
$343$	9.17084	+	9.17084i	0.495179	+	0.495179i
$344$	2.16575			0.116769
$345$	2.89977	+	1.82011i	0.156118	+	0.0979913i
$346$	7.67256			0.412479
$347$	16.9775	−	16.9775i	0.911399	−	0.911399i	−0.0849832	−	0.996382i	$-0.527084\pi$
$347$	16.9775	−	16.9775i	0.911399	−	0.911399i	0.996382	+	0.0849832i	$0.0270836\pi$
$348$	−4.20791	−	4.20791i	−0.225568	−	0.225568i
$349$			16.3106i			0.873086i	0.899683	+	0.436543i	$0.143797\pi$
$349$			16.3106i			0.873086i	−0.899683	+	0.436543i	$0.856203\pi$
$350$	−2.16771	−	4.49030i	−0.115869	−	0.240017i
$351$	1.04847			0.0559634
$352$	0.939768	+	0.939768i	0.0500898	+	0.0500898i
$353$	7.93890	+	7.93890i	0.422545	+	0.422545i	0.886079	−	0.463534i	$-0.153419\pi$
$353$	7.93890	+	7.93890i	0.422545	+	0.422545i	−0.463534	+	0.886079i	$0.653419\pi$
$354$	3.53944			0.188119
$355$	−10.3648	+	16.5131i	−0.550107	+	0.876422i
$356$			16.7874i			0.889729i
$357$	2.16771	+	2.16771i	0.114728	+	0.114728i
$358$	−0.680979	−	0.680979i	−0.0359909	−	0.0359909i
$359$			26.2304i			1.38439i	0.721712	+	0.692193i	$0.243355\pi$
$359$			26.2304i			1.38439i	−0.721712	+	0.692193i	$0.756645\pi$
$360$	−0.498616	−	2.17977i	−0.0262794	−	0.114884i
$361$	−17.2337	−	8.00003i	−0.907035	−	0.421054i
$362$	−14.4401	+	14.4401i	−0.758956	+	0.758956i
$363$	6.52919	−	6.52919i	0.342694	−	0.342694i
$364$	1.04557			0.0548028
$365$	−4.11545	−	17.9912i	−0.215412	−	0.941704i
$366$	3.41030			0.178259
$367$	−1.62269	+	1.62269i	−0.0847040	+	0.0847040i	−0.748189	−	0.663485i	$-0.769077\pi$
$367$	−1.62269	+	1.62269i	−0.0847040	+	0.0847040i	0.663485	+	0.748189i	$0.269077\pi$
$368$	1.08266	+	1.08266i	0.0564373	+	0.0564373i
$369$	−0.531910			−0.0276901
$370$	2.24519	−	3.57700i	0.116722	−	0.185959i
$371$		−	7.73629i		−	0.401648i
$372$	4.20791	−	4.20791i	0.218170	−	0.218170i
$373$	−9.00900	+	9.00900i	−0.466468	+	0.466468i	−0.900768	−	0.434300i	$-0.856996\pi$
$373$	−9.00900	+	9.00900i	−0.466468	+	0.466468i	0.434300	+	0.900768i	$0.356996\pi$
$374$	−4.08561			−0.211262
$375$	−6.98338	−	8.73112i	−0.360620	−	0.450873i
$376$		−	5.84230i		−	0.301294i
$377$	4.41189	−	4.41189i	0.227224	−	0.227224i
$378$	−0.705149	−	0.705149i	−0.0362690	−	0.0362690i
$379$	−4.49635			−0.230962			−0.115481	−	0.993310i	$-0.536841\pi$
$379$	−4.49635			−0.230962			−0.115481	+	0.993310i	$0.536841\pi$
$380$	−6.94403	−	6.83962i	−0.356221	−	0.350865i
$381$	10.9672			0.561867
$382$	5.19563	+	5.19563i	0.265832	+	0.265832i
$383$	−22.5064	+	22.5064i	−1.15003	+	1.15003i	−0.163478	+	0.986547i	$0.552271\pi$
$383$	−22.5064	+	22.5064i	−1.15003	+	1.15003i	−0.986547	+	0.163478i	$0.947729\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	2.88896	−	0.660842i	0.147235	−	0.0336796i
$386$	13.1865			0.671176
$387$	1.53142	−	1.53142i	0.0778463	−	0.0778463i
$388$	1.11691	−	1.11691i	0.0567025	−	0.0567025i
$389$		−	26.1672i		−	1.32673i	−0.748297	−	0.663364i	$-0.769128\pi$
$389$		−	26.1672i		−	1.32673i	0.748297	−	0.663364i	$-0.230872\pi$
$390$	2.28543	−	0.522786i	0.115727	−	0.0264723i
$391$	−4.70681			−0.238033
$392$	4.24655	+	4.24655i	0.214483	+	0.214483i
$393$	9.37065	−	9.37065i	0.472687	−	0.472687i
$394$	−7.67935			−0.386880
$395$	−17.6383	−	11.0711i	−0.887478	−	0.557047i
$396$	1.32903			0.0667864
$397$	−15.5911	+	15.5911i	−0.782497	+	0.782497i	−0.980252	−	0.197754i	$-0.936635\pi$
$397$	−15.5911	+	15.5911i	−0.782497	+	0.782497i	0.197754	+	0.980252i	$0.436635\pi$
$398$	−16.6161	+	16.6161i	−0.832889	+	0.832889i
$399$	−4.24460	−	0.937166i	−0.212496	−	0.0469170i
$400$	−2.17373	−	4.50276i	−0.108687	−	0.225138i
$401$			13.8440i			0.691337i	0.938357	+	0.345668i	$0.112348\pi$
$401$			13.8440i			0.691337i	−0.938357	+	0.345668i	$0.887652\pi$
$402$	1.99446	+	1.99446i	0.0994748	+	0.0994748i
$403$	4.41189	+	4.41189i	0.219772	+	0.219772i
$404$		−	15.7109i		−	0.781645i
$405$	−1.89390	−	1.18875i	−0.0941088	−	0.0590696i
$406$	−5.93441			−0.294520
$407$	1.77493	+	1.77493i	0.0879801	+	0.0879801i
$408$	2.17373	+	2.17373i	0.107616	+	0.107616i
$409$	9.17657			0.453752			0.226876	−	0.973924i	$-0.427149\pi$
$409$	9.17657			0.453752			0.226876	+	0.973924i	$0.427149\pi$
$410$	−1.15944	+	0.265219i	−0.0572606	+	0.0130982i
$411$			6.25126i			0.308352i
$412$	−10.7950	−	10.7950i	−0.531833	−	0.531833i
$413$	2.49584	−	2.49584i	0.122812	−	0.122812i
$414$	1.53111			0.0752498
$415$	−6.70087	−	29.2937i	−0.328933	−	1.43797i
$416$	1.04847			0.0514057
$417$	−1.89975	−	1.89975i	−0.0930311	−	0.0930311i
$418$	4.88318	−	3.11685i	0.238844	−	0.152450i
$419$			21.8535i			1.06762i	0.845606	+	0.533808i	$0.179239\pi$
$419$			21.8535i			1.06762i	−0.845606	+	0.533808i	$0.820761\pi$
$420$	−1.88866	−	1.18546i	−0.0921571	−	0.0578446i
$421$		−	29.4223i		−	1.43396i	−0.697095	−	0.716978i	$-0.745525\pi$
$421$		−	29.4223i		−	1.43396i	0.697095	−	0.716978i	$-0.254475\pi$
$422$	−5.77344	+	5.77344i	−0.281047	+	0.281047i
$423$	−4.13113	−	4.13113i	−0.200862	−	0.200862i
$424$		−	7.75776i		−	0.376750i
$425$	14.5129	+	5.06269i	0.703980	+	0.245577i
$426$			8.71907i			0.422440i
$427$	2.40477	−	2.40477i	0.116375	−	0.116375i
$428$	−2.65129	+	2.65129i	−0.128155	+	0.128155i
$429$			1.39346i			0.0672767i
$430$	2.57454	−	4.10172i	0.124155	−	0.197803i
$431$			36.4149i			1.75404i	0.480452	+	0.877021i	$0.340473\pi$
$431$			36.4149i			1.75404i	−0.480452	+	0.877021i	$0.659527\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−16.4903	+	16.4903i	−0.792475	+	0.792475i	−0.981896	−	0.189421i	$-0.939339\pi$
$433$	−16.4903	+	16.4903i	−0.792475	+	0.792475i	0.189421	+	0.981896i	$0.439339\pi$
$434$		−	5.93441i		−	0.284861i
$435$	−12.9715	+	2.96721i	−0.621938	+	0.142267i
$436$			5.83596i			0.279492i
$437$	5.62565	−	3.59076i	0.269111	−	0.171769i
$438$	−5.83628	−	5.83628i	−0.278868	−	0.278868i
$439$	−13.3446			−0.636903			−0.318452	−	0.947939i	$-0.603163\pi$
$439$	−13.3446			−0.636903			−0.318452	+	0.947939i	$0.603163\pi$
$440$	2.89698	−	0.662676i	0.138108	−	0.0315919i
$441$	6.00553			0.285978
$442$	−2.27910	+	2.27910i	−0.108406	+	0.108406i
$443$	−17.4215	−	17.4215i	−0.827720	−	0.827720i	0.159481	−	0.987201i	$-0.449018\pi$
$443$	−17.4215	−	17.4215i	−0.827720	−	0.827720i	−0.987201	+	0.159481i	$0.949018\pi$
$444$		−	1.88869i		−	0.0896334i
$445$	31.7936	+	19.9560i	1.50716	+	0.946007i
$446$	0.300580			0.0142329
$447$	9.99711	+	9.99711i	0.472847	+	0.472847i
$448$	−0.705149	−	0.705149i	−0.0333152	−	0.0333152i
$449$	−39.0761			−1.84412			−0.922058	−	0.387051i	$-0.873494\pi$
$449$	−39.0761			−1.84412			−0.922058	+	0.387051i	$0.873494\pi$
$450$	−4.72100	−	1.64687i	−0.222550	−	0.0776344i
$451$		−	0.706926i		−	0.0332878i
$452$	0.463357	+	0.463357i	0.0217945	+	0.0217945i
$453$	6.68237	+	6.68237i	0.313965	+	0.313965i
$454$			23.9341i			1.12328i
$455$	1.24293	−	1.98021i	0.0582693	−	0.0928337i
$456$	−4.25639	−	0.939768i	−0.199324	−	0.0440087i
$457$	−25.9258	+	25.9258i	−1.21276	+	1.21276i	−0.242643	+	0.970116i	$0.578014\pi$
$457$	−25.9258	+	25.9258i	−1.21276	+	1.21276i	−0.970116	+	0.242643i	$0.921986\pi$
$458$	5.37064	−	5.37064i	0.250953	−	0.250953i
$459$	3.07412			0.143488
$460$	3.33745	−	0.763434i	0.155610	−	0.0355953i
$461$	−16.3202			−0.760108			−0.380054	−	0.924964i	$-0.624095\pi$
$461$	−16.3202			−0.760108			−0.380054	+	0.924964i	$0.624095\pi$
$462$	0.937166	−	0.937166i	0.0436009	−	0.0436009i
$463$	−4.26074	−	4.26074i	−0.198013	−	0.198013i	0.601135	−	0.799148i	$-0.294716\pi$
$463$	−4.26074	−	4.26074i	−0.198013	−	0.198013i	−0.799148	+	0.601135i	$0.794716\pi$
$464$	−5.95089			−0.276263
$465$	−2.96721	−	12.9715i	−0.137601	−	0.601541i
$466$		−	1.15416i		−	0.0534655i
$467$	−24.0643	+	24.0643i	−1.11356	+	1.11356i	−0.120897	+	0.992665i	$0.538577\pi$
$467$	−24.0643	+	24.0643i	−1.11356	+	1.11356i	−0.992665	+	0.120897i	$0.961423\pi$
$468$	0.741383	−	0.741383i	0.0342704	−	0.0342704i
$469$	2.81279			0.129883
$470$	−11.0647	−	6.94505i	−0.510379	−	0.320351i
$471$			19.4667i			0.896977i
$472$	2.50276	−	2.50276i	0.115199	−	0.115199i
$473$	2.03530	+	2.03530i	0.0935833	+	0.0935833i
$474$	−9.31319			−0.427769
$475$	−21.2083	+	5.02070i	−0.973104	+	0.230365i
$476$	3.06561			0.140512
$477$	−5.48557	−	5.48557i	−0.251167	−	0.251167i
$478$	2.97765	−	2.97765i	0.136195	−	0.136195i
$479$		−	19.7176i		−	0.900920i	−0.892797	−	0.450460i	$-0.851260\pi$
$479$		−	19.7176i		−	0.900920i	0.892797	−	0.450460i	$-0.148740\pi$
$480$	−1.89390	−	1.18875i	−0.0864444	−	0.0542589i
$481$	1.98024			0.0902914
$482$	−17.5996	+	17.5996i	−0.801638	+	0.801638i
$483$	1.07966	−	1.07966i	0.0491262	−	0.0491262i
$484$		−	9.23367i		−	0.419712i
$485$	−0.787588	−	3.44305i	−0.0357625	−	0.156341i
$486$	−1.00000			−0.0453609
$487$	23.8855	+	23.8855i	1.08236	+	1.08236i	0.996289	+	0.0860674i	$0.0274300\pi$
$487$	23.8855	+	23.8855i	1.08236	+	1.08236i	0.0860674	+	0.996289i	$0.472570\pi$
$488$	2.41145	−	2.41145i	0.109161	−	0.109161i
$489$	−1.12018			−0.0506563
$490$	13.0907	−	2.99445i	0.591375	−	0.135276i
$491$	21.2521			0.959094			0.479547	−	0.877516i	$-0.340801\pi$
$491$	21.2521			0.959094			0.479547	+	0.877516i	$0.340801\pi$
$492$	−0.376117	+	0.376117i	−0.0169567	+	0.0169567i
$493$	12.9356	−	12.9356i	0.582592	−	0.582592i
$494$	0.985322	−	4.46271i	0.0443317	−	0.200787i
$495$	1.57989	−	2.51706i	0.0710108	−	0.113133i
$496$		−	5.95089i		−	0.267203i
$497$	6.14824	+	6.14824i	0.275786	+	0.275786i
$498$	−9.50276	−	9.50276i	−0.425829	−	0.425829i
$499$		−	39.2906i		−	1.75889i	−0.476002	−	0.879444i	$-0.657915\pi$
$499$		−	39.2906i		−	1.75889i	0.476002	−	0.879444i	$-0.342085\pi$
$500$	−11.1118	−	1.23584i	−0.496936	−	0.0552684i
$501$	15.7437			0.703377
$502$	0.673765	+	0.673765i	0.0300716	+	0.0300716i
$503$	7.92010	+	7.92010i	0.353140	+	0.353140i	0.861276	−	0.508137i	$-0.169666\pi$
$503$	7.92010	+	7.92010i	0.353140	+	0.353140i	−0.508137	+	0.861276i	$0.669666\pi$
$504$	−0.997232			−0.0444202
$505$	−29.7549	−	18.6764i	−1.32407	−	0.831087i
$506$			2.03489i			0.0904619i
$507$	−8.41507	−	8.41507i	−0.373726	−	0.373726i
$508$	7.75499	−	7.75499i	0.344072	−	0.344072i
$509$	−19.7948			−0.877389			−0.438695	−	0.898636i	$-0.644559\pi$
$509$	−19.7948			−0.877389			−0.438695	+	0.898636i	$0.644559\pi$
$510$	6.70087	−	1.53281i	0.296719	−	0.0678738i
$511$	−8.23090			−0.364113
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.67424	+	2.34520i	−0.162222	+	0.103543i
$514$			17.5784i			0.775349i
$515$	−33.2773	+	7.61210i	−1.46637	+	0.335429i
$516$		−	2.16575i		−	0.0953419i
$517$	5.49040	−	5.49040i	0.241468	−	0.241468i
$518$	−1.33181	−	1.33181i	−0.0585164	−	0.0585164i
$519$		−	7.67256i		−	0.336788i
$520$	1.24638	−	1.98571i	0.0546572	−	0.0870790i
$521$		−	32.9001i		−	1.44138i	−0.693257	−	0.720691i	$-0.743825\pi$
$521$		−	32.9001i		−	1.44138i	0.693257	−	0.720691i	$-0.256175\pi$
$522$	−4.20791	+	4.20791i	−0.184175	+	0.184175i
$523$	5.26214	−	5.26214i	0.230098	−	0.230098i	−0.582636	−	0.812733i	$-0.697979\pi$
$523$	5.26214	−	5.26214i	0.230098	−	0.230098i	0.812733	+	0.582636i	$0.197979\pi$
$524$		−	13.2521i		−	0.578921i
$525$	−4.49030	+	2.16771i	−0.195973	+	0.0946068i
$526$		−	4.77455i		−	0.208180i
$527$	12.9356	+	12.9356i	0.563485	+	0.563485i
$528$	0.939768	−	0.939768i	0.0408981	−	0.0408981i
$529$		−	20.6557i		−	0.898075i
$530$	−14.6924	−	9.22206i	−0.638199	−	0.400581i
$531$		−	3.53944i		−	0.153599i
$532$	−3.66407	+	2.33871i	−0.158857	+	0.101396i
$533$	−0.394349	−	0.394349i	−0.0170812	−	0.0170812i
$534$	16.7874			0.726460
$535$	1.86955	+	8.17300i	0.0808278	+	0.353350i
$536$	2.82060			0.121831
$537$	−0.680979	+	0.680979i	−0.0293864	+	0.0293864i
$538$	0.777994	+	0.777994i	0.0335417	+	0.0335417i
$539$			7.98154i			0.343789i
$540$	−2.17977	+	0.498616i	−0.0938022	+	0.0214570i
$541$	−3.97998			−0.171113			−0.0855563	−	0.996333i	$-0.527267\pi$
$541$	−3.97998			−0.171113			−0.0855563	+	0.996333i	$0.527267\pi$
$542$	−12.9537	−	12.9537i	−0.556409	−	0.556409i
$543$	14.4401	+	14.4401i	0.619685	+	0.619685i
$544$	3.07412			0.131802
$545$	11.0527	+	6.93752i	0.473447	+	0.297171i
$546$		−	1.04557i		−	0.0447463i
$547$	−17.5769	−	17.5769i	−0.751533	−	0.751533i	0.223232	−	0.974765i	$-0.428339\pi$
$547$	−17.5769	−	17.5769i	−0.751533	−	0.751533i	−0.974765	+	0.223232i	$0.928339\pi$
$548$	4.42031	+	4.42031i	0.188826	+	0.188826i
$549$		−	3.41030i		−	0.145548i
$550$	2.18875	−	6.27436i	0.0933286	−	0.267539i
$551$	−5.59245	+	25.3293i	−0.238246	+	1.07906i
$552$	1.08266	−	1.08266i	0.0460809	−	0.0460809i
$553$	−6.56719	+	6.56719i	−0.279265	+	0.279265i
$554$	9.16466			0.389369
$555$	−3.57700	−	2.24519i	−0.151835	−	0.0953029i
$556$	−2.68665			−0.113939
$557$	10.5795	−	10.5795i	0.448267	−	0.448267i	−0.446511	−	0.894778i	$-0.647334\pi$
$557$	10.5795	−	10.5795i	0.448267	−	0.448267i	0.894778	+	0.446511i	$0.147334\pi$
$558$	−4.20791	−	4.20791i	−0.178135	−	0.178135i
$559$	2.27073			0.0960418
$560$	−2.17373	+	0.497236i	−0.0918570	+	0.0210120i
$561$			4.08561i			0.172494i
$562$	−8.95726	+	8.95726i	−0.377839	+	0.377839i
$563$	1.06530	−	1.06530i	0.0448971	−	0.0448971i	−0.684302	−	0.729199i	$-0.739893\pi$
$563$	1.06530	−	1.06530i	0.0448971	−	0.0448971i	0.729199	+	0.684302i	$0.239893\pi$
$564$	−5.84230			−0.246005
$565$	1.42837	−	0.326736i	0.0600920	−	0.0137459i
$566$		−	15.8543i		−	0.666406i
$567$	−0.705149	+	0.705149i	−0.0296135	+	0.0296135i
$568$	6.16531	+	6.16531i	0.258691	+	0.258691i
$569$	17.2827			0.724528			0.362264	−	0.932076i	$-0.382004\pi$
$569$	17.2827			0.724528			0.362264	+	0.932076i	$0.382004\pi$
$570$	−6.83962	+	6.94403i	−0.286480	+	0.290853i
$571$	10.3420			0.432798			0.216399	−	0.976305i	$-0.430569\pi$
$571$	10.3420			0.432798			0.216399	+	0.976305i	$0.430569\pi$
$572$	0.985322	+	0.985322i	0.0411984	+	0.0411984i
$573$	5.19563	−	5.19563i	0.217051	−	0.217051i
$574$			0.530438i			0.0221400i
$575$	2.52154	−	7.22835i	0.105155	−	0.301443i
$576$	−1.00000			−0.0416667
$577$	−25.5328	+	25.5328i	−1.06294	+	1.06294i	−0.0650631	+	0.997881i	$0.520725\pi$
$577$	−25.5328	+	25.5328i	−1.06294	+	1.06294i	−0.997881	+	0.0650631i	$0.979275\pi$
$578$	5.33850	−	5.33850i	0.222052	−	0.222052i
$579$		−	13.1865i		−	0.548013i
$580$	−7.07414	+	11.2704i	−0.293738	+	0.467978i
$581$	−13.4017			−0.555998
$582$	−1.11691	−	1.11691i	−0.0462974	−	0.0462974i
$583$	7.29049	−	7.29049i	0.301941	−	0.301941i
$584$	−8.25374			−0.341542
$585$	−0.522786	−	2.28543i	−0.0216145	−	0.0944908i
$586$	0.182154			0.00752471
$587$	−25.3120	+	25.3120i	−1.04474	+	1.04474i	−0.0457889	+	0.998951i	$0.514580\pi$
$587$	−25.3120	+	25.3120i	−1.04474	+	1.04474i	−0.998951	+	0.0457889i	$0.985420\pi$
$588$	4.24655	−	4.24655i	0.175125	−	0.175125i
$589$	−25.3293	−	5.59245i	−1.04368	−	0.230433i
$590$	−1.76482	−	7.71516i	−0.0726566	−	0.317628i
$591$			7.67935i			0.315886i
$592$	−1.33551	−	1.33551i	−0.0548890	−	0.0548890i
$593$	−9.66808	−	9.66808i	−0.397020	−	0.397020i	0.480160	−	0.877181i	$-0.340578\pi$
$593$	−9.66808	−	9.66808i	−0.397020	−	0.397020i	−0.877181	+	0.480160i	$0.840578\pi$
$594$		−	1.32903i		−	0.0545308i
$595$	3.64426	−	5.80597i	0.149400	−	0.238022i
$596$	14.1380			0.579117
$597$	16.6161	+	16.6161i	0.680051	+	0.680051i
$598$	1.13514	+	1.13514i	0.0464192	+	0.0464192i
$599$	28.5298			1.16569			0.582847	−	0.812582i	$-0.301939\pi$
$599$	28.5298			1.16569			0.582847	+	0.812582i	$0.301939\pi$
$600$	−4.50276	+	2.17373i	−0.183825	+	0.0887423i
$601$		−	24.3760i		−	0.994317i	−0.867660	−	0.497159i	$-0.834377\pi$
$601$		−	24.3760i		−	0.994317i	0.867660	−	0.497159i	$-0.165623\pi$
$602$	−1.52718	−	1.52718i	−0.0622431	−	0.0622431i
$603$	1.99446	−	1.99446i	0.0812208	−	0.0812208i
$604$	9.45030			0.384527
$605$	−17.4877	−	10.9766i	−0.710975	−	0.446261i
$606$	−15.7109			−0.638211
$607$	27.0140	+	27.0140i	1.09647	+	1.09647i	0.994821	+	0.101646i	$0.0324108\pi$
$607$	27.0140	+	27.0140i	1.09647	+	1.09647i	0.101646	+	0.994821i	$0.467589\pi$
$608$	−3.67424	+	2.34520i	−0.149010	+	0.0951106i
$609$			5.93441i			0.240475i
$610$	−1.70043	−	7.43365i	−0.0688484	−	0.300980i
$611$		−	6.12550i		−	0.247811i
$612$	2.17373	−	2.17373i	0.0878679	−	0.0878679i
$613$	17.2695	+	17.2695i	0.697508	+	0.697508i	0.963872	−	0.266364i	$-0.0858224\pi$
$613$	17.2695	+	17.2695i	0.697508	+	0.697508i	−0.266364	+	0.963872i	$0.585822\pi$
$614$			22.3361i			0.901413i
$615$	0.265219	+	1.15944i	0.0106947	+	0.0467531i
$616$		−	1.32535i		−	0.0534000i
$617$	34.2253	−	34.2253i	1.37786	−	1.37786i	0.529625	−	0.848232i	$-0.322333\pi$
$617$	34.2253	−	34.2253i	1.37786	−	1.37786i	0.848232	−	0.529625i	$-0.177667\pi$
$618$	−10.7950	+	10.7950i	−0.434239	+	0.434239i
$619$		−	34.9000i		−	1.40275i	−0.712792	−	0.701375i	$-0.752570\pi$
$619$		−	34.9000i		−	1.40275i	0.712792	−	0.701375i	$-0.247430\pi$
$620$	−11.2704	−	7.07414i	−0.452630	−	0.284104i
$621$		−	1.53111i		−	0.0614412i
$622$	−10.3891	−	10.3891i	−0.416566	−	0.416566i
$623$	11.8376	−	11.8376i	0.474263	−	0.474263i
$624$		−	1.04847i		−	0.0419726i
$625$	−15.5498	+	19.5756i	−0.621991	+	0.783024i
$626$			2.50414i			0.100086i
$627$	−3.11685	−	4.88318i	−0.124475	−	0.195015i
$628$	13.7650	+	13.7650i	0.549284	+	0.549284i
$629$	5.80607			0.231503
$630$	−1.18546	+	1.88866i	−0.0472299	+	0.0752460i
$631$	33.8489			1.34750			0.673752	−	0.738957i	$-0.264682\pi$
$631$	33.8489			1.34750			0.673752	+	0.738957i	$0.264682\pi$
$632$	−6.58542	+	6.58542i	−0.261954	+	0.261954i
$633$	5.77344	+	5.77344i	0.229474	+	0.229474i
$634$		−	6.55324i		−	0.260262i
$635$	−5.46842	−	23.9060i	−0.217008	−	0.948679i
$636$	−7.75776			−0.307615
$637$	4.45240	+	4.45240i	0.176410	+	0.176410i
$638$	−5.59245	−	5.59245i	−0.221407	−	0.221407i
$639$	8.71907			0.344921
$640$	−2.17977	+	0.498616i	−0.0861628	+	0.0197095i
$641$			38.3389i			1.51429i	0.653245	+	0.757147i	$0.273407\pi$
$641$			38.3389i			1.51429i	−0.653245	+	0.757147i	$0.726593\pi$
$642$	2.65129	+	2.65129i	0.104638	+	0.104638i
$643$	−21.8777	−	21.8777i	−0.862773	−	0.862773i	0.128886	−	0.991659i	$-0.458860\pi$
$643$	−21.8777	−	21.8777i	−0.862773	−	0.862773i	−0.991659	+	0.128886i	$0.958860\pi$
$644$		−	1.52687i		−	0.0601670i
$645$	−4.10172	−	2.57454i	−0.161505	−	0.101373i
$646$	2.88896	−	13.0847i	0.113665	−	0.514809i
$647$	−11.5954	+	11.5954i	−0.455863	+	0.455863i	−0.897295	−	0.441432i	$-0.854471\pi$
$647$	−11.5954	+	11.5954i	−0.455863	+	0.455863i	0.441432	+	0.897295i	$0.354471\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	4.70403			0.184649
$650$	−2.27910	−	4.72103i	−0.0893937	−	0.185174i
$651$	−5.93441			−0.232588
$652$	−0.792086	+	0.792086i	−0.0310205	+	0.0310205i
$653$	−11.6996	−	11.6996i	−0.457842	−	0.457842i	0.440105	−	0.897946i	$-0.354941\pi$
$653$	−11.6996	−	11.6996i	−0.457842	−	0.457842i	−0.897946	+	0.440105i	$0.854941\pi$
$654$	5.83596			0.228204
$655$	−25.0982	−	15.7535i	−0.980668	−	0.615539i
$656$			0.531910i			0.0207676i
$657$	−5.83628	+	5.83628i	−0.227695	+	0.227695i
$658$	−4.11969	+	4.11969i	−0.160602	+	0.160602i
$659$	44.6662			1.73995			0.869974	−	0.493097i	$-0.164135\pi$
$659$	44.6662			1.73995			0.869974	+	0.493097i	$0.164135\pi$
$660$	−0.662676	−	2.89698i	−0.0257946	−	0.112765i
$661$			46.5099i			1.80902i	0.426447	+	0.904512i	$0.359765\pi$
$661$			46.5099i			1.80902i	−0.426447	+	0.904512i	$0.640235\pi$
$662$	−7.42992	+	7.42992i	−0.288772	+	0.288772i
$663$	2.27910	+	2.27910i	0.0885130	+	0.0885130i
$664$	−13.4389			−0.521532
$665$	0.0736241	+	9.71953i	0.00285502	+	0.376907i
$666$	−1.88869			−0.0731853
$667$	−6.44276	−	6.44276i	−0.249465	−	0.249465i
$668$	11.1325	−	11.1325i	0.430728	−	0.430728i
$669$		−	0.300580i		−	0.0116211i
$670$	3.35299	−	5.34194i	0.129537	−	0.206377i
$671$	4.53240			0.174971
$672$	−0.705149	+	0.705149i	−0.0272017	+	0.0272017i
$673$	−17.8598	+	17.8598i	−0.688446	+	0.688446i	−0.961888	−	0.273443i	$-0.911838\pi$
$673$	−17.8598	+	17.8598i	−0.688446	+	0.688446i	0.273443	+	0.961888i	$0.411838\pi$
$674$		−	26.6051i		−	1.02479i
$675$	−1.64687	+	4.72100i	−0.0633882	+	0.181711i
$676$	−11.9007			−0.457719
$677$	−20.6616	−	20.6616i	−0.794092	−	0.794092i	0.188065	−	0.982157i	$-0.439778\pi$
$677$	−20.6616	−	20.6616i	−0.794092	−	0.794092i	−0.982157	+	0.188065i	$0.939778\pi$
$678$	0.463357	−	0.463357i	0.0177951	−	0.0177951i
$679$	−1.57518			−0.0604497
$680$	3.65437	−	5.82209i	0.140139	−	0.223267i
$681$	23.9341			0.917158
$682$	5.59245	−	5.59245i	0.214146	−	0.214146i
$683$	23.8243	−	23.8243i	0.911610	−	0.911610i	−0.0847893	−	0.996399i	$-0.527022\pi$
$683$	23.8243	−	23.8243i	0.911610	−	0.911610i	0.996399	+	0.0847893i	$0.0270217\pi$
$684$	−0.939768	+	4.25639i	−0.0359329	+	0.162747i
$685$	13.6263	−	3.11698i	0.520634	−	0.119094i
$686$		−	12.9695i		−	0.495179i
$687$	−5.37064	−	5.37064i	−0.204903	−	0.204903i
$688$	−1.53142	−	1.53142i	−0.0583847	−	0.0583847i
$689$		−	8.13381i		−	0.309874i
$690$	−0.763434	−	3.33745i	−0.0290634	−	0.127055i
$691$	−4.34746			−0.165385			−0.0826927	−	0.996575i	$-0.526352\pi$
$691$	−4.34746			−0.165385			−0.0826927	+	0.996575i	$0.526352\pi$
$692$	−5.42532	−	5.42532i	−0.206240	−	0.206240i
$693$	−0.937166	−	0.937166i	−0.0356000	−	0.0356000i
$694$	−24.0098			−0.911399
$695$	−3.19376	+	5.08825i	−0.121146	+	0.193008i
$696$			5.95089i			0.225568i
$697$	−1.15623	−	1.15623i	−0.0437953	−	0.0437953i
$698$	11.5333	−	11.5333i	0.436543	−	0.436543i
$699$	−1.15416			−0.0436544
$700$	−1.64232	+	4.70793i	−0.0620737	+	0.177943i
$701$	−1.61462			−0.0609832			−0.0304916	−	0.999535i	$-0.509707\pi$
$701$	−1.61462			−0.0609832			−0.0304916	+	0.999535i	$0.509707\pi$
$702$	−0.741383	−	0.741383i	−0.0279817	−	0.0279817i
$703$	−6.93950	+	4.42937i	−0.261728	+	0.167057i
$704$		−	1.32903i		−	0.0500898i
$705$	−6.94505	+	11.0647i	−0.261566	+	0.416722i
$706$		−	11.2273i		−	0.422545i
$707$	−11.0785	+	11.0785i	−0.416650	+	0.416650i
$708$	−2.50276	−	2.50276i	−0.0940596	−	0.0940596i
$709$			45.1909i			1.69718i	0.529052	+	0.848589i	$0.322548\pi$
$709$			45.1909i			1.69718i	−0.529052	+	0.848589i	$0.677452\pi$
$710$	19.0055	−	4.34746i	0.713265	−	0.163157i
$711$			9.31319i			0.349272i
$712$	11.8705	−	11.8705i	0.444864	−	0.444864i
$713$	6.44276	−	6.44276i	0.241283	−	0.241283i
$714$		−	3.06561i		−	0.114728i
$715$	3.03741	−	0.694799i	0.113593	−	0.0259840i
$716$			0.963050i			0.0359909i
$717$	−2.97765	−	2.97765i	−0.111202	−	0.111202i
$718$	18.5477	−	18.5477i	0.692193	−	0.692193i
$719$			8.72035i			0.325214i	0.986691	+	0.162607i	$0.0519903\pi$
$719$			8.72035i			0.325214i	−0.986691	+	0.162607i	$0.948010\pi$
$720$	−1.18875	+	1.89390i	−0.0443022	+	0.0705816i
$721$			15.2242i			0.566979i
$722$	6.52917	+	17.8429i	0.242991	+	0.664045i
$723$	17.5996	+	17.5996i	0.654535	+	0.654535i
$724$	20.4214			0.758956
$725$	12.9356	+	26.7955i	0.480418	+	0.995158i
$726$	−9.23367			−0.342694
$727$	16.9674	−	16.9674i	0.629286	−	0.629286i	−0.318602	−	0.947889i	$-0.603213\pi$
$727$	16.9674	−	16.9674i	0.629286	−	0.629286i	0.947889	+	0.318602i	$0.103213\pi$
$728$	−0.739331	−	0.739331i	−0.0274014	−	0.0274014i
$729$			1.00000i			0.0370370i
$730$	−9.81166	+	15.6318i	−0.363146	+	0.578558i
$731$	6.65778			0.246247
$732$	−2.41145	−	2.41145i	−0.0891296	−	0.0891296i
$733$	25.1664	+	25.1664i	0.929541	+	0.929541i	0.997676	−	0.0681355i	$-0.0217050\pi$
$733$	25.1664	+	25.1664i	0.929541	+	0.929541i	−0.0681355	+	0.997676i	$0.521705\pi$
$734$	2.29484			0.0847040
$735$	−2.99445	−	13.0907i	−0.110452	−	0.482856i
$736$		−	1.53111i		−	0.0564373i
$737$	2.65071	+	2.65071i	0.0976400	+	0.0976400i
$738$	0.376117	+	0.376117i	0.0138451	+	0.0138451i
$739$		−	14.7543i		−	0.542747i	−0.962474	−	0.271373i	$-0.912522\pi$
$739$		−	14.7543i		−	0.542747i	0.962474	−	0.271373i	$-0.0874778\pi$
$740$	−4.11691	+	0.941732i	−0.151341	+	0.0346188i
$741$	−4.46271	−	0.985322i	−0.163942	−	0.0361967i
$742$	−5.47038	+	5.47038i	−0.200824	+	0.200824i
$743$	8.61240	−	8.61240i	0.315958	−	0.315958i	−0.531254	−	0.847213i	$-0.678279\pi$
$743$	8.61240	−	8.61240i	0.315958	−	0.315958i	0.847213	+	0.531254i	$0.178279\pi$
$744$	−5.95089			−0.218170
$745$	16.8066	−	26.7761i	0.615748	−	0.981000i
$746$	12.7407			0.466468
$747$	−9.50276	+	9.50276i	−0.347688	+	0.347688i
$748$	2.88896	+	2.88896i	0.105631	+	0.105631i
$749$	3.73910			0.136624
$750$	−1.23584	+	11.1118i	−0.0451264	+	0.405747i
$751$			44.6100i			1.62784i	0.580974	+	0.813922i	$0.302672\pi$
$751$			44.6100i			1.62784i	−0.580974	+	0.813922i	$0.697328\pi$
$752$	−4.13113	+	4.13113i	−0.150647	+	0.150647i
$753$	0.673765	−	0.673765i	0.0245534	−	0.0245534i
$754$	−6.23935			−0.227224
$755$	11.2341	−	17.8979i	0.408850	−	0.651373i
$756$			0.997232i			0.0362690i
$757$	2.38067	−	2.38067i	0.0865268	−	0.0865268i	−0.662519	−	0.749045i	$-0.730512\pi$
$757$	2.38067	−	2.38067i	0.0865268	−	0.0865268i	0.749045	+	0.662519i	$0.230512\pi$
$758$	3.17940	+	3.17940i	0.115481	+	0.115481i
$759$	2.03489			0.0738618
$760$	0.0738284	+	9.74651i	0.00267804	+	0.353543i
$761$	4.25052			0.154081			0.0770406	−	0.997028i	$-0.475453\pi$
$761$	4.25052			0.154081			0.0770406	+	0.997028i	$0.475453\pi$
$762$	−7.75499	−	7.75499i	−0.280934	−	0.280934i
$763$	4.11522	−	4.11522i	0.148981	−	0.148981i
$764$		−	7.34773i		−	0.265832i
$765$	−1.53281	−	6.70087i	−0.0554187	−	0.242270i
$766$	31.8289			1.15003
$767$	2.62408	−	2.62408i	0.0947502	−	0.0947502i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$		−	3.40202i		−	0.122680i	−0.998117	−	0.0613400i	$-0.980463\pi$
$769$		−	3.40202i		−	0.122680i	0.998117	−	0.0613400i	$-0.0195374\pi$
$770$	−2.51009	−	1.57552i	−0.0904573	−	0.0567777i
$771$	17.5784			0.633070
$772$	−9.32428	−	9.32428i	−0.335588	−	0.335588i
$773$	−21.7310	+	21.7310i	−0.781611	+	0.781611i	−0.980103	−	0.198491i	$-0.936396\pi$
$773$	−21.7310	+	21.7310i	−0.781611	+	0.781611i	0.198491	+	0.980103i	$0.436396\pi$
$774$	−2.16575			−0.0778463
$775$	−26.7955	+	12.9356i	−0.962521	+	0.464662i
$776$	−1.57955			−0.0567025
$777$	−1.33181	+	1.33181i	−0.0477784	+	0.0477784i
$778$	−18.5030	+	18.5030i	−0.663364	+	0.663364i
$779$	2.26402	+	0.499872i	0.0811168	+	0.0179098i
$780$	−1.98571	−	1.24638i	−0.0710997	−	0.0446274i
$781$			11.5879i			0.414648i
$782$	3.32821	+	3.32821i	0.119017	+	0.119017i
$783$	4.20791	+	4.20791i	0.150379	+	0.150379i
$784$		−	6.00553i		−	0.214483i
$785$	42.4328	−	9.70640i	1.51449	−	0.346436i
$786$	−13.2521			−0.472687
$787$	8.02221	+	8.02221i	0.285961	+	0.285961i	0.835481	−	0.549520i	$-0.185189\pi$
$787$	8.02221	+	8.02221i	0.285961	+	0.285961i	−0.549520	+	0.835481i	$0.685189\pi$
$788$	5.43012	+	5.43012i	0.193440	+	0.193440i
$789$	−4.77455			−0.169979
$790$	4.64370	+	20.3006i	0.165216	+	0.722262i
$791$		−	0.653472i		−	0.0232348i
$792$	−0.939768	−	0.939768i	−0.0333932	−	0.0333932i
$793$	2.52834	−	2.52834i	0.0897839	−	0.0897839i
$794$	22.0492			0.782497
$795$	−9.22206	+	14.6924i	−0.327073	+	0.521087i
$796$	23.4987			0.832889
$797$	29.0862	+	29.0862i	1.03029	+	1.03029i	0.999527	+	0.0307591i	$0.00979247\pi$
$797$	29.0862	+	29.0862i	1.03029	+	1.03029i	0.0307591	+	0.999527i	$0.490208\pi$
$798$	2.33871	+	3.66407i	0.0827895	+	0.129707i
$799$		−	17.9599i		−	0.635377i
$800$	−1.64687	+	4.72100i	−0.0582258	+	0.166912i
$801$		−	16.7874i		−	0.593152i
$802$	9.78919	−	9.78919i	0.345668	−	0.345668i
$803$	−7.75660	−	7.75660i	−0.273725	−	0.273725i
$804$		−	2.82060i		−	0.0994748i
$805$	−2.89174	−	1.81507i	−0.101920	−	0.0639728i
$806$		−	6.23935i		−	0.219772i
$807$	0.777994	−	0.777994i	0.0273867	−	0.0273867i
$808$	−11.1093	+	11.1093i	−0.390823	+	0.390823i
$809$			26.9228i			0.946556i	0.880913	+	0.473278i	$0.156929\pi$
$809$			26.9228i			0.946556i	−0.880913	+	0.473278i	$0.843071\pi$
$810$	0.498616	+	2.17977i	0.0175196	+	0.0765892i
$811$		−	38.9518i		−	1.36778i	−0.729584	−	0.683891i	$-0.760286\pi$
$811$		−	38.9518i		−	1.36778i	0.729584	−	0.683891i	$-0.239714\pi$
$812$	4.19627	+	4.19627i	0.147260	+	0.147260i
$813$	−12.9537	+	12.9537i	−0.454306	+	0.454306i
$814$		−	2.51013i		−	0.0879801i
$815$	0.558539	+	2.44173i	0.0195648	+	0.0855300i
$816$		−	3.07412i		−	0.107616i
$817$	−7.95748	+	5.07913i	−0.278397	+	0.177696i
$818$	−6.48881	−	6.48881i	−0.226876	−	0.226876i
$819$	−1.04557			−0.0365352
$820$	1.00739	+	0.632310i	0.0351794	+	0.0220812i
$821$	27.0500			0.944053			0.472026	−	0.881584i	$-0.343523\pi$
$821$	27.0500			0.944053			0.472026	+	0.881584i	$0.343523\pi$
$822$	4.42031	−	4.42031i	0.154176	−	0.154176i
$823$	−7.85319	−	7.85319i	−0.273745	−	0.273745i	0.556861	−	0.830606i	$-0.312006\pi$
$823$	−7.85319	−	7.85319i	−0.273745	−	0.273745i	−0.830606	+	0.556861i	$0.812006\pi$
$824$			15.2665i			0.531833i
$825$	−6.27436	−	2.18875i	−0.218445	−	0.0762025i
$826$	−3.52965			−0.122812
$827$	−13.3020	−	13.3020i	−0.462557	−	0.462557i	0.436936	−	0.899493i	$-0.356064\pi$
$827$	−13.3020	−	13.3020i	−0.462557	−	0.462557i	−0.899493	+	0.436936i	$0.856064\pi$
$828$	−1.08266	−	1.08266i	−0.0376249	−	0.0376249i
$829$	−53.6495			−1.86332			−0.931662	−	0.363326i	$-0.881641\pi$
$829$	−53.6495			−1.86332			−0.931662	+	0.363326i	$0.881641\pi$
$830$	−15.9756	+	25.4520i	−0.554520	+	0.883453i
$831$		−	9.16466i		−	0.317918i
$832$	−0.741383	−	0.741383i	−0.0257028	−	0.0257028i
$833$	13.0544	+	13.0544i	0.452309	+	0.452309i
$834$			2.68665i			0.0930311i
$835$	−7.85006	−	34.3176i	−0.271662	−	1.18761i
$836$	−5.65688	−	1.24898i	−0.195647	−	0.0431969i
$837$	−4.20791	+	4.20791i	−0.145447	+	0.145447i
$838$	15.4528	−	15.4528i	0.533808	−	0.533808i
$839$	32.8129			1.13283			0.566413	−	0.824122i	$-0.308331\pi$
$839$	32.8129			1.13283			0.566413	+	0.824122i	$0.308331\pi$
$840$	0.497236	+	2.17373i	0.0171563	+	0.0750009i
$841$	6.41308			0.221141
$842$	−20.8047	+	20.8047i	−0.716978	+	0.716978i
$843$	8.95726	+	8.95726i	0.308504	+	0.308504i
$844$	8.16488			0.281047
$845$	−14.1470	+	22.5388i	−0.486671	+	0.775357i
$846$			5.84230i			0.200862i
$847$	−6.51112	+	6.51112i	−0.223725	+	0.223725i
$848$	−5.48557	+	5.48557i	−0.188375	+	0.188375i
$849$	−15.8543			−0.544119
$850$	−6.68232	−	13.8420i	−0.229202	−	0.474778i
$851$		−	2.89179i		−	0.0991292i
$852$	6.16531	−	6.16531i	0.211220	−	0.211220i
$853$	23.9591	+	23.9591i	0.820342	+	0.820342i	0.986157	−	0.165815i	$-0.0530253\pi$
$853$	23.9591	+	23.9591i	0.820342	+	0.820342i	−0.165815	+	0.986157i	$0.553025\pi$
$854$	−3.40086			−0.116375
$855$	6.94403	+	6.83962i	0.237481	+	0.233910i
$856$	3.74948			0.128155
$857$	−24.8412	−	24.8412i	−0.848560	−	0.848560i	0.141394	−	0.989953i	$-0.454842\pi$
$857$	−24.8412	−	24.8412i	−0.848560	−	0.848560i	−0.989953	+	0.141394i	$0.954842\pi$
$858$	0.985322	−	0.985322i	0.0336383	−	0.0336383i
$859$			20.5100i			0.699792i	0.936789	+	0.349896i	$0.113783\pi$
$859$			20.5100i			0.699792i	−0.936789	+	0.349896i	$0.886217\pi$
$860$	−4.72083	+	1.07988i	−0.160979	+	0.0368235i
$861$	0.530438			0.0180773
$862$	25.7492	−	25.7492i	0.877021	−	0.877021i
$863$	36.4695	−	36.4695i	1.24144	−	1.24144i	0.282033	−	0.959405i	$-0.408991\pi$
$863$	36.4695	−	36.4695i	1.24144	−	1.24144i	0.959405	−	0.282033i	$-0.0910088\pi$
$864$			1.00000i			0.0340207i
$865$	−16.7244	+	3.82566i	−0.568646	+	0.130076i
$866$	23.3209			0.792475
$867$	−5.33850	−	5.33850i	−0.181305	−	0.181305i
$868$	−4.19627	+	4.19627i	−0.142431	+	0.142431i
$869$	−12.3775			−0.419879
$870$	11.2704	+	7.07414i	0.382102	+	0.239836i
$871$	2.95732			0.100205
$872$	4.12665	−	4.12665i	0.139746	−	0.139746i
$873$	−1.11691	+	1.11691i	−0.0378017	+	0.0378017i
$874$	−6.51698	−	1.43888i	−0.220440	−	0.0486710i
$875$	6.96405	+	8.70695i	0.235428	+	0.294349i
$876$			8.25374i			0.278868i
$877$	−4.63012	−	4.63012i	−0.156348	−	0.156348i	0.624598	−	0.780946i	$-0.285263\pi$
$877$	−4.63012	−	4.63012i	−0.156348	−	0.156348i	−0.780946	+	0.624598i	$0.785263\pi$
$878$	9.43606	+	9.43606i	0.318452	+	0.318452i
$879$		−	0.182154i		−	0.00614390i
$880$	−2.51706	−	1.57989i	−0.0848500	−	0.0532581i
$881$	24.1826			0.814731			0.407365	−	0.913265i	$-0.366448\pi$
$881$	24.1826			0.814731			0.407365	+	0.913265i	$0.366448\pi$
$882$	−4.24655	−	4.24655i	−0.142989	−	0.142989i
$883$	4.73940	+	4.73940i	0.159494	+	0.159494i	0.782342	−	0.622849i	$-0.214025\pi$
$883$	4.73940	+	4.73940i	0.159494	+	0.159494i	−0.622849	+	0.782342i	$0.714025\pi$
$884$	3.22314			0.108406
$885$	−7.71516	+	1.76482i	−0.259342	+	0.0593239i
$886$			24.6377i			0.827720i
$887$	17.0631	+	17.0631i	0.572921	+	0.572921i	0.932944	−	0.360022i	$-0.117231\pi$
$887$	17.0631	+	17.0631i	0.572921	+	0.572921i	−0.360022	+	0.932944i	$0.617231\pi$
$888$	−1.33551	+	1.33551i	−0.0448167	+	0.0448167i
$889$	−10.9368			−0.366810
$890$	−8.37045	−	36.5925i	−0.280578	−	1.22658i
$891$	−1.32903			−0.0445243
$892$	−0.212542	−	0.212542i	−0.00711644	−	0.00711644i
$893$	13.7014	+	21.4660i	0.458499	+	0.718332i
$894$		−	14.1380i		−	0.472847i
$895$	1.82392	+	1.14483i	0.0609670	+	0.0382674i
$896$			0.997232i			0.0333152i
$897$	1.13514	−	1.13514i	0.0379011	−	0.0379011i
$898$	27.6310	+	27.6310i	0.922058	+	0.922058i
$899$			35.4131i			1.18109i
$900$	2.17373	+	4.50276i	0.0724577	+	0.150092i
$901$		−	23.8483i		−	0.794502i
$902$	−0.499872	+	0.499872i	−0.0166439	+	0.0166439i
$903$	−1.52718	+	1.52718i	−0.0508213	+	0.0508213i
$904$		−	0.655286i		−	0.0217945i
$905$	24.2760	−	38.6762i	0.806963	−	1.28564i
$906$		−	9.45030i		−	0.313965i
$907$	−40.9598	−	40.9598i	−1.36005	−	1.36005i	−0.873845	−	0.486204i	$-0.838381\pi$
$907$	−40.9598	−	40.9598i	−1.36005	−	1.36005i	−0.486204	−	0.873845i	$-0.661619\pi$
$908$	16.9240	−	16.9240i	0.561642	−	0.561642i
$909$			15.7109i			0.521097i
$910$	−2.27910	+	0.521339i	−0.0755515	+	0.0172822i
$911$			30.8795i			1.02308i	0.859259	+	0.511541i	$0.170925\pi$
$911$			30.8795i			1.02308i	−0.859259	+	0.511541i	$0.829075\pi$
$912$	2.34520	+	3.67424i	0.0776575	+	0.121666i
$913$	−12.6295	−	12.6295i	−0.417975	−	0.417975i
$914$	36.6647			1.21276
$915$	−7.43365	+	1.70043i	−0.245749	+	0.0562144i
$916$	−7.59523			−0.250953
$917$	−9.34471	+	9.34471i	−0.308590	+	0.308590i
$918$	−2.17373	−	2.17373i	−0.0717439	−	0.0717439i
$919$		−	7.02277i		−	0.231660i	−0.993269	−	0.115830i	$-0.963047\pi$
$919$		−	7.02277i		−	0.231660i	0.993269	−	0.115830i	$-0.0369528\pi$
$920$	−2.89977	−	1.82011i	−0.0956024	−	0.0600071i
$921$	22.3361			0.736000
$922$	11.5401	+	11.5401i	0.380054	+	0.380054i
$923$	6.46417	+	6.46417i	0.212771	+	0.212771i
$924$	−1.32535			−0.0436009
$925$	−3.11044	+	8.91651i	−0.102271	+	0.293173i
$926$			6.02559i			0.198013i
$927$	10.7950	+	10.7950i	0.354555	+	0.354555i
$928$	4.20791	+	4.20791i	0.138132	+	0.138132i
$929$		−	6.87722i		−	0.225634i	−0.993616	−	0.112817i	$-0.964013\pi$
$929$		−	6.87722i		−	0.225634i	0.993616	−	0.112817i	$-0.0359874\pi$
$930$	−7.07414	+	11.2704i	−0.231970	+	0.369571i
$931$	−25.5619	−	5.64380i	−0.837756	−	0.184968i
$932$	−0.816115	+	0.816115i	−0.0267327	+	0.0267327i
$933$	−10.3891	+	10.3891i	−0.340125	+	0.340125i
$934$	34.0320			1.11356
$935$	8.90567	−	2.03715i	0.291247	−	0.0666219i
$936$	−1.04847			−0.0342704
$937$	−29.1041	+	29.1041i	−0.950788	+	0.950788i	−0.998845	−	0.0480562i	$-0.984697\pi$
$937$	−29.1041	+	29.1041i	−0.950788	+	0.950788i	0.0480562	+	0.998845i	$0.484697\pi$
$938$	−1.98894	−	1.98894i	−0.0649413	−	0.0649413i
$939$	2.50414			0.0817195
$940$	2.91306	+	12.7348i	0.0950136	+	0.415365i
$941$		−	56.1970i		−	1.83197i	−0.401213	−	0.915985i	$-0.631411\pi$
$941$		−	56.1970i		−	1.83197i	0.401213	−	0.915985i	$-0.368589\pi$
$942$	13.7650	−	13.7650i	0.448489	−	0.448489i
$943$	−0.575875	+	0.575875i	−0.0187531	+	0.0187531i
$944$	−3.53944			−0.115199
$945$	1.88866	+	1.18546i	0.0614381	+	0.0385631i
$946$		−	2.87835i		−	0.0935833i
$947$	−4.56166	+	4.56166i	−0.148234	+	0.148234i	−0.777329	−	0.629095i	$-0.783426\pi$
$947$	−4.56166	+	4.56166i	−0.148234	+	0.148234i	0.629095	+	0.777329i	$0.283426\pi$
$948$	6.58542	+	6.58542i	0.213884	+	0.213884i
$949$	−8.65384			−0.280915
$950$	18.5467	+	11.4464i	0.601735	+	0.371369i
$951$	−6.55324			−0.212503
$952$	−2.16771	−	2.16771i	−0.0702560	−	0.0702560i
$953$	2.55998	−	2.55998i	0.0829258	−	0.0829258i	−0.664427	−	0.747353i	$-0.731324\pi$
$953$	2.55998	−	2.55998i	0.0829258	−	0.0829258i	0.747353	+	0.664427i	$0.231324\pi$
$954$			7.75776i			0.251167i
$955$	−13.9159	−	8.73464i	−0.450308	−	0.282646i
$956$	−4.21103			−0.136195
$957$	−5.59245	+	5.59245i	−0.180778	+	0.180778i
$958$	−13.9424	+	13.9424i	−0.450460	+	0.450460i
$959$		−	6.23396i		−	0.201305i
$960$	0.498616	+	2.17977i	0.0160928	+	0.0703517i
$961$	−4.41308			−0.142357
$962$	−1.40024	−	1.40024i	−0.0451457	−	0.0451457i
$963$	2.65129	−	2.65129i	0.0854365	−	0.0854365i
$964$	24.8896			0.801638
$965$	−28.7435	+	6.57501i	−0.925287	+	0.211657i
$966$	−1.52687			−0.0491262
$967$	28.9011	−	28.9011i	0.929398	−	0.929398i	−0.0682690	−	0.997667i	$-0.521748\pi$
$967$	28.9011	−	28.9011i	0.929398	−	0.929398i	0.997667	+	0.0682690i	$0.0217476\pi$
$968$	−6.52919	+	6.52919i	−0.209856	+	0.209856i
$969$	−13.0847	−	2.88896i	−0.420340	−	0.0928068i
$970$	−1.87769	+	2.99151i	−0.0602891	+	0.0960516i
$971$		−	7.01480i		−	0.225116i	−0.993645	−	0.112558i	$-0.964096\pi$
$971$		−	7.01480i		−	0.225116i	0.993645	−	0.112558i	$-0.0359044\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	1.89449	+	1.89449i	0.0607345	+	0.0607345i
$974$		−	33.7792i		−	1.08236i
$975$	−4.72103	+	2.27910i	−0.151194	+	0.0729897i
$976$	−3.41030			−0.109161
$977$	−22.3335	−	22.3335i	−0.714512	−	0.714512i	0.252964	−	0.967476i	$-0.418595\pi$
$977$	−22.3335	−	22.3335i	−0.714512	−	0.714512i	−0.967476	+	0.252964i	$0.918595\pi$
$978$	0.792086	+	0.792086i	0.0253281	+	0.0253281i
$979$	22.3109			0.713061
$980$	−11.3739	−	7.13909i	−0.363325	−	0.228050i
$981$		−	5.83596i		−	0.186328i
$982$	−15.0275	−	15.0275i	−0.479547	−	0.479547i
$983$	4.61128	−	4.61128i	0.147077	−	0.147077i	−0.629734	−	0.776811i	$-0.716836\pi$
$983$	4.61128	−	4.61128i	0.147077	−	0.147077i	0.776811	+	0.629734i	$0.216836\pi$
$984$	0.531910			0.0169567
$985$	16.7392	−	3.82905i	0.533355	−	0.122004i
$986$	−18.2938			−0.582592
$987$	4.11969	+	4.11969i	0.131131	+	0.131131i
$988$	−3.85234	+	2.45889i	−0.122559	+	0.0782276i
$989$		−	3.31599i		−	0.105442i
$990$	−2.89698	+	0.662676i	−0.0920721	+	0.0210612i
$991$			30.5890i			0.971691i	0.874045	+	0.485845i	$0.161488\pi$
$991$			30.5890i			0.971691i	−0.874045	+	0.485845i	$0.838512\pi$
$992$	−4.20791	+	4.20791i	−0.133601	+	0.133601i
$993$	7.42992	+	7.42992i	0.235781	+	0.235781i
$994$		−	8.69493i		−	0.275786i
$995$	27.9341	−	44.5042i	0.885572	−	1.41088i
$996$			13.4389i			0.425829i
$997$	10.7588	−	10.7588i	0.340735	−	0.340735i	−0.515909	−	0.856644i	$-0.672546\pi$
$997$	10.7588	−	10.7588i	0.340735	−	0.340735i	0.856644	+	0.515909i	$0.172546\pi$
$998$	−27.7826	+	27.7826i	−0.879444	+	0.879444i
$999$			1.88869i			0.0597556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.a.493.5	yes	20
3.2	odd	2		1710.2.p.d.1063.6		20
5.2	odd	4	inner	570.2.m.a.37.10	yes	20
15.2	even	4		1710.2.p.d.37.1		20
19.18	odd	2	inner	570.2.m.a.493.10	yes	20
57.56	even	2		1710.2.p.d.1063.1		20
95.37	even	4	inner	570.2.m.a.37.5	✓	20
285.227	odd	4		1710.2.p.d.37.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.5	✓	20	95.37	even	4	inner
570.2.m.a.37.10	yes	20	5.2	odd	4	inner
570.2.m.a.493.5	yes	20	1.1	even	1	trivial
570.2.m.a.493.10	yes	20	19.18	odd	2	inner
1710.2.p.d.37.1		20	15.2	even	4
1710.2.p.d.37.6		20	285.227	odd	4
1710.2.p.d.1063.1		20	57.56	even	2
1710.2.p.d.1063.6		20	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.89390 + 1.18875i) q^{5} +1.00000 q^{6} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.89390 + 1.18875i) q^{5} +1.00000 q^{6} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-0.498616 - 2.17977i) q^{10} +1.32903 q^{11} +(-0.707107 - 0.707107i) q^{12} +(0.741383 - 0.741383i) q^{13} -0.997232 q^{14} +(-2.17977 + 0.498616i) q^{15} -1.00000 q^{16} +(2.17373 - 2.17373i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-0.939768 + 4.25639i) q^{19} +(-1.18875 + 1.89390i) q^{20} +0.997232i q^{21} +(-0.939768 - 0.939768i) q^{22} +(-1.08266 - 1.08266i) q^{23} +1.00000i q^{24} +(2.17373 + 4.50276i) q^{25} -1.04847 q^{26} +(0.707107 + 0.707107i) q^{27} +(0.705149 + 0.705149i) q^{28} +5.95089 q^{29} +(1.89390 + 1.18875i) q^{30} +5.95089i q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.939768 + 0.939768i) q^{33} -3.07412 q^{34} +(2.17373 - 0.497236i) q^{35} +1.00000 q^{36} +(1.33551 + 1.33551i) q^{37} +(3.67424 - 2.34520i) q^{38} +1.04847i q^{39} +(2.17977 - 0.498616i) q^{40} -0.531910i q^{41} +(0.705149 - 0.705149i) q^{42} +(1.53142 + 1.53142i) q^{43} +1.32903i q^{44} +(1.18875 - 1.89390i) q^{45} +1.53111i q^{46} +(4.13113 - 4.13113i) q^{47} +(0.707107 - 0.707107i) q^{48} +6.00553i q^{49} +(1.64687 - 4.72100i) q^{50} +3.07412i q^{51} +(0.741383 + 0.741383i) q^{52} +(5.48557 - 5.48557i) q^{53} -1.00000i q^{54} +(2.51706 + 1.57989i) q^{55} -0.997232i q^{56} +(-2.34520 - 3.67424i) q^{57} +(-4.20791 - 4.20791i) q^{58} +3.53944 q^{59} +(-0.498616 - 2.17977i) q^{60} +3.41030 q^{61} +(4.20791 - 4.20791i) q^{62} +(-0.705149 - 0.705149i) q^{63} -1.00000i q^{64} +(2.28543 - 0.522786i) q^{65} +1.32903 q^{66} +(1.99446 + 1.99446i) q^{67} +(2.17373 + 2.17373i) q^{68} +1.53111 q^{69} +(-1.88866 - 1.18546i) q^{70} +8.71907i q^{71} +(-0.707107 - 0.707107i) q^{72} +(-5.83628 - 5.83628i) q^{73} -1.88869i q^{74} +(-4.72100 - 1.64687i) q^{75} +(-4.25639 - 0.939768i) q^{76} +(0.937166 - 0.937166i) q^{77} +(0.741383 - 0.741383i) q^{78} -9.31319 q^{79} +(-1.89390 - 1.18875i) q^{80} -1.00000 q^{81} +(-0.376117 + 0.376117i) q^{82} +(-9.50276 - 9.50276i) q^{83} -0.997232 q^{84} +(6.70087 - 1.53281i) q^{85} -2.16575i q^{86} +(-4.20791 + 4.20791i) q^{87} +(0.939768 - 0.939768i) q^{88} +16.7874 q^{89} +(-2.17977 + 0.498616i) q^{90} -1.04557i q^{91} +(1.08266 - 1.08266i) q^{92} +(-4.20791 - 4.20791i) q^{93} -5.84230 q^{94} +(-6.83962 + 6.94403i) q^{95} -1.00000 q^{96} +(-1.11691 - 1.11691i) q^{97} +(4.24655 - 4.24655i) q^{98} -1.32903i 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

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