LMFDB - Embedded newform 722.2.e.d.389.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			389.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	722.389
Dual form			722.2.e.d.245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(3.75877 + 1.36808i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(3.75877 + 1.36808i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +(0.694593 - 3.93923i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.766044 + 0.642788i) q^{13} +(2.81908 + 1.02606i) q^{14} +(3.75877 - 1.36808i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.520945 + 2.95442i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(0.520945 + 2.95442i) q^{21} +(-1.53209 + 1.28558i) q^{22} +(0.939693 - 0.342020i) q^{23} +(0.939693 + 0.342020i) q^{24} +(8.42649 + 7.07066i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 + 4.33013i) q^{27} +(0.520945 - 2.95442i) q^{28} +(0.868241 - 4.92404i) q^{29} +(-2.00000 - 3.46410i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.87939 - 0.684040i) q^{33} +(2.81908 - 1.02606i) q^{34} +(-9.19253 + 7.71345i) q^{35} +(-0.347296 - 1.96962i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(0.694593 + 3.93923i) q^{40} +(6.12836 - 5.14230i) q^{41} +(2.81908 - 1.02606i) q^{42} +(-3.75877 - 1.36808i) q^{43} +(1.53209 + 1.28558i) q^{44} +(-4.00000 + 6.92820i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.38919 - 7.87846i) q^{47} +(0.173648 - 0.984808i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(5.50000 - 9.52628i) q^{50} +(2.29813 + 1.92836i) q^{51} +(-0.939693 - 0.342020i) q^{52} +(-0.939693 + 0.342020i) q^{53} +(3.83022 - 3.21394i) q^{54} +(-1.38919 - 7.87846i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(-2.60472 - 14.7721i) q^{59} +(-3.06418 + 2.57115i) q^{60} +(-1.87939 + 0.684040i) q^{61} +(7.51754 + 2.73616i) q^{62} +(-4.59627 - 3.85673i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.00000 + 3.46410i) q^{65} +(-0.347296 + 1.96962i) q^{66} +(-0.520945 + 2.95442i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(0.500000 - 0.866025i) q^{69} +(9.19253 + 7.71345i) q^{70} +(1.87939 + 0.684040i) q^{71} +(-1.87939 + 0.684040i) q^{72} +(6.89440 - 5.78509i) q^{73} +(-0.347296 - 1.96962i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(-0.173648 - 0.984808i) q^{78} +(7.66044 - 6.42788i) q^{79} +(3.75877 - 1.36808i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-6.12836 - 5.14230i) q^{82} +(3.00000 - 5.19615i) q^{83} +(-1.50000 - 2.59808i) q^{84} +(-2.08378 + 11.8177i) q^{85} +(-0.694593 + 3.93923i) q^{86} +(-2.50000 - 4.33013i) q^{87} +(1.00000 - 1.73205i) q^{88} +(7.51754 + 2.73616i) q^{90} +(-2.81908 + 1.02606i) q^{91} +(-0.766044 + 0.642788i) q^{92} +(1.38919 + 7.87846i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(0.347296 + 1.96962i) q^{97} +(-1.53209 + 1.28558i) q^{98} +(3.75877 - 1.36808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 9 * q^7 + 3 * q^8	$ 6 q - 9 q^{7} + 3 q^{8} - 6 q^{11} - 3 q^{12} + 12 q^{18} - 24 q^{20} + 3 q^{26} + 15 q^{27} - 12 q^{30} - 24 q^{31} + 12 q^{37} + 6 q^{39} - 24 q^{45} - 3 q^{46} - 6 q^{49} + 33 q^{50} - 18 q^{56} - 30 q^{58} - 3 q^{64} + 12 q^{65} - 9 q^{68} + 3 q^{69} + 66 q^{75} + 36 q^{77} + 18 q^{83} - 9 q^{84} - 15 q^{87} + 6 q^{88} - 48 q^{94} - 6 q^{96}+O(q^{100}) $ 6 * q - 9 * q^7 + 3 * q^8 - 6 * q^11 - 3 * q^12 + 12 * q^18 - 24 * q^20 + 3 * q^26 + 15 * q^27 - 12 * q^30 - 24 * q^31 + 12 * q^37 + 6 * q^39 - 24 * q^45 - 3 * q^46 - 6 * q^49 + 33 * q^50 - 18 * q^56 - 30 * q^58 - 3 * q^64 + 12 * q^65 - 9 * q^68 + 3 * q^69 + 66 * q^75 + 36 * q^77 + 18 * q^83 - 9 * q^84 - 15 * q^87 + 6 * q^88 - 48 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i	−0.394284	−	0.918989i	$-0.629007\pi$
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i	0.836560	+	0.547875i	$0.184563\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	3.75877	+	1.36808i	1.68097	+	0.611824i	0.993443	−	0.114331i	$-0.0364725\pi$
$5$	3.75877	+	1.36808i	1.68097	+	0.611824i	0.687531	+	0.726155i	$0.258695\pi$
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.347296	+	1.96962i	−0.115765	+	0.656539i
$10$	0.694593	−	3.93923i	0.219650	−	1.24569i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.766044	+	0.642788i	0.212463	+	0.178277i	0.742808	−	0.669504i	$-0.233493\pi$
$13$	0.766044	+	0.642788i	0.212463	+	0.178277i	−0.530346	+	0.847781i	$0.677938\pi$
$14$	2.81908	+	1.02606i	0.753430	+	0.274226i
$15$	3.75877	−	1.36808i	0.970510	−	0.353237i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.520945	+	2.95442i	0.126348	+	0.716553i	0.980498	+	0.196527i	$0.0629665\pi$
$17$	0.520945	+	2.95442i	0.126348	+	0.716553i	−0.854151	+	0.520026i	$0.825922\pi$
$18$	2.00000			0.471405
$19$		0			0
$19$		0			0
$20$	−4.00000			−0.894427
$21$	0.520945	+	2.95442i	0.113679	+	0.644708i
$22$	−1.53209	+	1.28558i	−0.326642	+	0.274086i
$23$	0.939693	−	0.342020i	0.195939	−	0.0713161i	−0.242187	−	0.970230i	$-0.577865\pi$
$23$	0.939693	−	0.342020i	0.195939	−	0.0713161i	0.438126	+	0.898914i	$0.355642\pi$
$24$	0.939693	+	0.342020i	0.191814	+	0.0698146i
$25$	8.42649	+	7.07066i	1.68530	+	1.41413i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	2.50000	+	4.33013i	0.481125	+	0.833333i
$28$	0.520945	−	2.95442i	0.0984493	−	0.558334i
$29$	0.868241	−	4.92404i	0.161228	−	0.914371i	−0.791640	−	0.610988i	$-0.790773\pi$
$29$	0.868241	−	4.92404i	0.161228	−	0.914371i	0.952869	−	0.303384i	$-0.0981163\pi$
$30$	−2.00000	−	3.46410i	−0.365148	−	0.632456i
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−1.87939	−	0.684040i	−0.327159	−	0.119076i
$34$	2.81908	−	1.02606i	0.483468	−	0.175968i
$35$	−9.19253	+	7.71345i	−1.55382	+	1.30381i
$36$	−0.347296	−	1.96962i	−0.0578827	−	0.328269i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	1.00000			0.160128
$40$	0.694593	+	3.93923i	0.109825	+	0.622847i
$41$	6.12836	−	5.14230i	0.957088	−	0.803092i	−0.0233886	−	0.999726i	$-0.507446\pi$
$41$	6.12836	−	5.14230i	0.957088	−	0.803092i	0.980477	+	0.196634i	$0.0630011\pi$
$42$	2.81908	−	1.02606i	0.434993	−	0.158325i
$43$	−3.75877	−	1.36808i	−0.573207	−	0.208630i	0.0391204	−	0.999235i	$-0.487544\pi$
$43$	−3.75877	−	1.36808i	−0.573207	−	0.208630i	−0.612328	+	0.790604i	$0.709767\pi$
$44$	1.53209	+	1.28558i	0.230971	+	0.193808i
$45$	−4.00000	+	6.92820i	−0.596285	+	1.03280i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	1.38919	−	7.87846i	0.202634	−	1.14919i	−0.698487	−	0.715623i	$-0.746143\pi$
$47$	1.38919	−	7.87846i	0.202634	−	1.14919i	0.901120	−	0.433569i	$-0.142746\pi$
$48$	0.173648	−	0.984808i	0.0250640	−	0.142145i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	5.50000	−	9.52628i	0.777817	−	1.34722i
$51$	2.29813	+	1.92836i	0.321803	+	0.270025i
$52$	−0.939693	−	0.342020i	−0.130312	−	0.0474297i
$53$	−0.939693	+	0.342020i	−0.129077	+	0.0469801i	−0.405751	−	0.913984i	$-0.632990\pi$
$53$	−0.939693	+	0.342020i	−0.129077	+	0.0469801i	0.276674	+	0.960964i	$0.410768\pi$
$54$	3.83022	−	3.21394i	0.521227	−	0.437362i
$55$	−1.38919	−	7.87846i	−0.187318	−	1.06233i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	−5.00000			−0.656532
$59$	−2.60472	−	14.7721i	−0.339106	−	1.92317i	−0.382167	−	0.924093i	$-0.624822\pi$
$59$	−2.60472	−	14.7721i	−0.339106	−	1.92317i	0.0430610	−	0.999072i	$-0.486289\pi$
$60$	−3.06418	+	2.57115i	−0.395584	+	0.331934i
$61$	−1.87939	+	0.684040i	−0.240631	+	0.0875824i	−0.459520	−	0.888167i	$-0.651979\pi$
$61$	−1.87939	+	0.684040i	−0.240631	+	0.0875824i	0.218890	+	0.975750i	$0.429756\pi$
$62$	7.51754	+	2.73616i	0.954729	+	0.347493i
$63$	−4.59627	−	3.85673i	−0.579075	−	0.485902i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$	−0.347296	+	1.96962i	−0.0427492	+	0.242443i
$67$	−0.520945	+	2.95442i	−0.0636435	+	0.360940i	0.936309	+	0.351178i	$0.114219\pi$
$67$	−0.520945	+	2.95442i	−0.0636435	+	0.360940i	−0.999952	+	0.00976258i	$0.996892\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	0.500000	−	0.866025i	0.0601929	−	0.104257i
$70$	9.19253	+	7.71345i	1.09872	+	0.921934i
$71$	1.87939	+	0.684040i	0.223042	+	0.0811806i	0.451124	−	0.892461i	$-0.351023\pi$
$71$	1.87939	+	0.684040i	0.223042	+	0.0811806i	−0.228082	+	0.973642i	$0.573245\pi$
$72$	−1.87939	+	0.684040i	−0.221488	+	0.0806149i
$73$	6.89440	−	5.78509i	0.806928	−	0.677093i	−0.142944	−	0.989731i	$-0.545657\pi$
$73$	6.89440	−	5.78509i	0.806928	−	0.677093i	0.949873	+	0.312637i	$0.101212\pi$
$74$	−0.347296	−	1.96962i	−0.0403724	−	0.228963i
$75$	11.0000			1.27017
$76$		0			0
$77$	6.00000			0.683763
$78$	−0.173648	−	0.984808i	−0.0196618	−	0.111508i
$79$	7.66044	−	6.42788i	0.861867	−	0.723193i	−0.100502	−	0.994937i	$-0.532045\pi$
$79$	7.66044	−	6.42788i	0.861867	−	0.723193i	0.962369	+	0.271744i	$0.0876005\pi$
$80$	3.75877	−	1.36808i	0.420243	−	0.152956i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−6.12836	−	5.14230i	−0.676764	−	0.567872i
$83$	3.00000	−	5.19615i	0.329293	−	0.570352i	−0.653079	−	0.757290i	$-0.726523\pi$
$83$	3.00000	−	5.19615i	0.329293	−	0.570352i	0.982372	+	0.186938i	$0.0598564\pi$
$84$	−1.50000	−	2.59808i	−0.163663	−	0.283473i
$85$	−2.08378	+	11.8177i	−0.226017	+	1.28181i
$86$	−0.694593	+	3.93923i	−0.0748999	+	0.424778i
$87$	−2.50000	−	4.33013i	−0.268028	−	0.464238i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$89$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$90$	7.51754	+	2.73616i	0.792418	+	0.288417i
$91$	−2.81908	+	1.02606i	−0.295520	+	0.107560i
$92$	−0.766044	+	0.642788i	−0.0798657	+	0.0670152i
$93$	1.38919	+	7.87846i	0.144052	+	0.816958i
$94$	−8.00000			−0.825137
$95$		0			0
$96$	−1.00000			−0.102062
$97$	0.347296	+	1.96962i	0.0352626	+	0.199984i	0.997350	−	0.0727587i	$-0.0231803\pi$
$97$	0.347296	+	1.96962i	0.0352626	+	0.199984i	−0.962087	+	0.272743i	$0.912069\pi$
$98$	−1.53209	+	1.28558i	−0.154764	+	0.129863i
$99$	3.75877	−	1.36808i	0.377771	−	0.137497i
$100$	−10.3366	−	3.76222i	−1.03366	−	0.376222i
$101$	1.53209	+	1.28558i	0.152449	+	0.127920i	0.715822	−	0.698283i	$-0.246052\pi$
$101$	1.53209	+	1.28558i	0.152449	+	0.127920i	−0.563373	+	0.826202i	$0.690497\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	0.679525	−	0.733652i	$-0.262186\pi$
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	−0.975124	+	0.221660i	$0.928852\pi$
$104$	−0.173648	+	0.984808i	−0.0170276	+	0.0965683i
$105$	−2.08378	+	11.8177i	−0.203356	+	1.15329i
$106$	0.500000	+	0.866025i	0.0485643	+	0.0841158i
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	−0.984124	−	0.177482i	$-0.943205\pi$
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	0.645766	+	0.763535i	$0.276538\pi$
$108$	−3.83022	−	3.21394i	−0.368563	−	0.309261i
$109$	−14.0954	−	5.13030i	−1.35009	−	0.491394i	−0.437116	−	0.899405i	$-0.644000\pi$
$109$	−14.0954	−	5.13030i	−1.35009	−	0.491394i	−0.912977	+	0.408011i	$0.866222\pi$
$110$	−7.51754	+	2.73616i	−0.716769	+	0.260883i
$111$	1.53209	−	1.28558i	0.145419	−	0.122021i
$112$	0.520945	+	2.95442i	0.0492246	+	0.279167i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	4.00000			0.373002
$116$	0.868241	+	4.92404i	0.0806141	+	0.457186i
$117$	−1.53209	+	1.28558i	−0.141642	+	0.118851i
$118$	−14.0954	+	5.13030i	−1.29759	+	0.472283i
$119$	−8.45723	−	3.07818i	−0.775273	−	0.282176i
$120$	3.06418	+	2.57115i	0.279720	+	0.234713i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$	1.38919	−	7.87846i	0.125259	−	0.710377i
$124$	1.38919	−	7.87846i	0.124753	−	0.707507i
$125$	12.0000	+	20.7846i	1.07331	+	1.85903i
$126$	−3.00000	+	5.19615i	−0.267261	+	0.462910i
$127$	−13.7888	−	11.5702i	−1.22356	−	1.02669i	−0.998631	−	0.0523116i	$-0.983341\pi$
$127$	−13.7888	−	11.5702i	−1.22356	−	1.02669i	−0.224927	−	0.974376i	$-0.572214\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−3.75877	+	1.36808i	−0.330941	+	0.120453i
$130$	3.06418	−	2.57115i	0.268746	−	0.225505i
$131$	2.08378	+	11.8177i	0.182061	+	1.03252i	0.929674	+	0.368383i	$0.120088\pi$
$131$	2.08378	+	11.8177i	0.182061	+	1.03252i	−0.747614	+	0.664134i	$0.768800\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	3.00000			0.259161
$135$	3.47296	+	19.6962i	0.298905	+	1.69518i
$136$	−2.29813	+	1.92836i	−0.197063	+	0.165356i
$137$	15.9748	−	5.81434i	1.36482	−	0.496753i	0.447277	−	0.894396i	$-0.352394\pi$
$137$	15.9748	−	5.81434i	1.36482	−	0.496753i	0.917540	+	0.397643i	$0.130172\pi$
$138$	−0.939693	−	0.342020i	−0.0799919	−	0.0291147i
$139$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$139$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$140$	6.00000	−	10.3923i	0.507093	−	0.878310i
$141$	−4.00000	−	6.92820i	−0.336861	−	0.583460i
$142$	0.347296	−	1.96962i	0.0291445	−	0.165286i
$143$	0.347296	−	1.96962i	0.0290424	−	0.164708i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	10.0000	−	17.3205i	0.830455	−	1.43839i
$146$	−6.89440	−	5.78509i	−0.570585	−	0.478777i
$147$	−1.87939	−	0.684040i	−0.155009	−	0.0564187i
$148$	−1.87939	+	0.684040i	−0.154485	+	0.0562278i
$149$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$149$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$150$	−1.91013	−	10.8329i	−0.155961	−	0.884501i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	−1.04189	−	5.90885i	−0.0839578	−	0.476148i
$155$	−24.5134	+	20.5692i	−1.96897	+	1.65216i
$156$	−0.939693	+	0.342020i	−0.0752356	+	0.0273835i
$157$	1.87939	+	0.684040i	0.149991	+	0.0545924i	0.415925	−	0.909399i	$-0.363458\pi$
$157$	1.87939	+	0.684040i	0.149991	+	0.0545924i	−0.265934	+	0.963991i	$0.585680\pi$
$158$	−7.66044	−	6.42788i	−0.609432	−	0.511374i
$159$	−0.500000	+	0.866025i	−0.0396526	+	0.0686803i
$160$	−2.00000	−	3.46410i	−0.158114	−	0.273861i
$161$	−0.520945	+	2.95442i	−0.0410562	+	0.232841i
$162$	−0.173648	+	0.984808i	−0.0136431	+	0.0773738i
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	−4.00000	+	6.92820i	−0.312348	+	0.541002i
$165$	−6.12836	−	5.14230i	−0.477092	−	0.400328i
$166$	−5.63816	−	2.05212i	−0.437606	−	0.159275i
$167$	−11.2763	+	4.10424i	−0.872587	+	0.317596i	−0.739214	−	0.673470i	$-0.764803\pi$
$167$	−11.2763	+	4.10424i	−0.872587	+	0.317596i	−0.133373	+	0.991066i	$0.542581\pi$
$168$	−2.29813	+	1.92836i	−0.177305	+	0.148776i
$169$	−2.08378	−	11.8177i	−0.160291	−	0.909053i
$170$	12.0000			0.920358
$171$		0			0
$172$	4.00000			0.304997
$173$	1.04189	+	5.90885i	0.0792134	+	0.449241i	0.998456	+	0.0555496i	$0.0176911\pi$
$173$	1.04189	+	5.90885i	0.0792134	+	0.449241i	−0.919243	+	0.393692i	$0.871198\pi$
$174$	−3.83022	+	3.21394i	−0.290368	+	0.243648i
$175$	−31.0099	+	11.2867i	−2.34412	+	0.853192i
$176$	−1.87939	−	0.684040i	−0.141664	−	0.0515615i
$177$	−11.4907	−	9.64181i	−0.863691	−	0.724723i
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	1.38919	−	7.87846i	0.103544	−	0.587226i
$181$	−3.82026	+	21.6658i	−0.283958	+	1.61040i	0.425027	+	0.905181i	$0.360264\pi$
$181$	−3.82026	+	21.6658i	−0.283958	+	1.61040i	−0.708985	+	0.705224i	$0.750847\pi$
$182$	1.50000	+	2.59808i	0.111187	+	0.192582i
$183$	−1.00000	+	1.73205i	−0.0739221	+	0.128037i
$184$	0.766044	+	0.642788i	0.0564735	+	0.0473869i
$185$	7.51754	+	2.73616i	0.552701	+	0.201167i
$186$	7.51754	−	2.73616i	0.551213	−	0.200625i
$187$	4.59627	−	3.85673i	0.336112	−	0.282032i
$188$	1.38919	+	7.87846i	0.101317	+	0.574596i
$189$	−15.0000			−1.09109
$190$		0			0
$191$	7.00000			0.506502			0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000			0.506502			0.253251	+	0.967401i	$0.418500\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	4.59627	−	3.85673i	0.330847	−	0.277613i	−0.462198	−	0.886777i	$-0.652939\pi$
$193$	4.59627	−	3.85673i	0.330847	−	0.277613i	0.793045	+	0.609163i	$0.208495\pi$
$194$	1.87939	−	0.684040i	0.134932	−	0.0491112i
$195$	3.75877	+	1.36808i	0.269171	+	0.0979703i
$196$	1.53209	+	1.28558i	0.109435	+	0.0918268i
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	−0.972606	−	0.232458i	$-0.925323\pi$
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	0.687618	+	0.726073i	$0.258656\pi$
$198$	−2.00000	−	3.46410i	−0.142134	−	0.246183i
$199$	−4.34120	+	24.6202i	−0.307740	+	1.74528i	0.302580	+	0.953124i	$0.402152\pi$
$199$	−4.34120	+	24.6202i	−0.307740	+	1.74528i	−0.610320	+	0.792155i	$0.708959\pi$
$200$	−1.91013	+	10.8329i	−0.135067	+	0.766001i
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$	1.00000	−	1.73205i	0.0703598	−	0.121867i
$203$	11.4907	+	9.64181i	0.806487	+	0.676723i
$204$	−2.81908	−	1.02606i	−0.197375	−	0.0718386i
$205$	30.0702	−	10.9446i	2.10019	−	0.764407i
$206$	−4.59627	+	3.85673i	−0.320237	+	0.268711i
$207$	0.347296	+	1.96962i	0.0241388	+	0.136898i
$208$	1.00000			0.0693375
$209$		0			0
$210$	12.0000			0.828079
$211$	−4.68850	−	26.5898i	−0.322770	−	1.83052i	−0.524906	−	0.851160i	$-0.675899\pi$
$211$	−4.68850	−	26.5898i	−0.322770	−	1.83052i	0.202136	−	0.979357i	$-0.435212\pi$
$212$	0.766044	−	0.642788i	0.0526121	−	0.0441468i
$213$	1.87939	−	0.684040i	0.128773	−	0.0468697i
$214$	6.57785	+	2.39414i	0.449652	+	0.163660i
$215$	−12.2567	−	10.2846i	−0.835901	−	0.701404i
$216$	−2.50000	+	4.33013i	−0.170103	+	0.294628i
$217$	−12.0000	−	20.7846i	−0.814613	−	1.41095i
$218$	−2.60472	+	14.7721i	−0.176414	+	1.00049i
$219$	1.56283	−	8.86327i	0.105607	−	0.598924i
$220$	4.00000	+	6.92820i	0.269680	+	0.467099i
$221$	−1.50000	+	2.59808i	−0.100901	+	0.174766i
$222$	−1.53209	−	1.28558i	−0.102827	−	0.0862822i
$223$	13.1557	+	4.78828i	0.880971	+	0.320647i	0.742601	−	0.669734i	$-0.233592\pi$
$223$	13.1557	+	4.78828i	0.880971	+	0.320647i	0.138369	+	0.990381i	$0.455814\pi$
$224$	2.81908	−	1.02606i	0.188358	−	0.0685565i
$225$	−16.8530	+	14.1413i	−1.12353	+	0.942755i
$226$	2.43107	+	13.7873i	0.161713	+	0.917118i
$227$	17.0000			1.12833			0.564165	−	0.825662i	$-0.309198\pi$
$227$	17.0000			1.12833			0.564165	+	0.825662i	$0.309198\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	−0.694593	−	3.93923i	−0.0458001	−	0.259745i
$231$	4.59627	−	3.85673i	0.302412	−	0.253754i
$232$	4.69846	−	1.71010i	0.308469	−	0.112274i
$233$	5.63816	+	2.05212i	0.369368	+	0.134439i	0.520033	−	0.854146i	$-0.325919\pi$
$233$	5.63816	+	2.05212i	0.369368	+	0.134439i	−0.150666	+	0.988585i	$0.548142\pi$
$234$	1.53209	+	1.28558i	0.100156	+	0.0840407i
$235$	16.0000	−	27.7128i	1.04372	−	1.80778i
$236$	7.50000	+	12.9904i	0.488208	+	0.845602i
$237$	1.73648	−	9.84808i	0.112797	−	0.639701i
$238$	−1.56283	+	8.86327i	−0.101303	+	0.574520i
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$	2.00000	−	3.46410i	0.129099	−	0.223607i
$241$	6.12836	+	5.14230i	0.394762	+	0.331245i	0.818465	−	0.574557i	$-0.194825\pi$
$241$	6.12836	+	5.14230i	0.394762	+	0.331245i	−0.423703	+	0.905801i	$0.639270\pi$
$242$	−6.57785	−	2.39414i	−0.422840	−	0.153901i
$243$	−15.0351	+	5.47232i	−0.964501	+	0.351050i
$244$	1.53209	−	1.28558i	0.0980819	−	0.0823005i
$245$	−1.38919	−	7.87846i	−0.0887518	−	0.503336i
$246$	−8.00000			−0.510061
$247$		0			0
$248$	−8.00000			−0.508001
$249$	−1.04189	−	5.90885i	−0.0660270	−	0.374458i
$250$	18.3851	−	15.4269i	1.16277	−	0.975683i
$251$	−1.87939	+	0.684040i	−0.118626	+	0.0431762i	−0.400651	−	0.916231i	$-0.631216\pi$
$251$	−1.87939	+	0.684040i	−0.118626	+	0.0431762i	0.282025	+	0.959407i	$0.408994\pi$
$252$	5.63816	+	2.05212i	0.355170	+	0.129271i
$253$	−1.53209	−	1.28558i	−0.0963216	−	0.0808234i
$254$	−9.00000	+	15.5885i	−0.564710	+	0.978107i
$255$	6.00000	+	10.3923i	0.375735	+	0.650791i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.38919	+	7.87846i	−0.0866550	+	0.491445i	0.910332	+	0.413878i	$0.135826\pi$
$257$	−1.38919	+	7.87846i	−0.0866550	+	0.491445i	−0.996987	+	0.0775665i	$0.975285\pi$
$258$	2.00000	+	3.46410i	0.124515	+	0.215666i
$259$	−3.00000	+	5.19615i	−0.186411	+	0.322873i
$260$	−3.06418	−	2.57115i	−0.190032	−	0.159456i
$261$	9.39693	+	3.42020i	0.581655	+	0.211705i
$262$	11.2763	−	4.10424i	0.696653	−	0.253561i
$263$	18.3851	−	15.4269i	1.13367	−	0.951264i	0.134458	−	0.990919i	$-0.457071\pi$
$263$	18.3851	−	15.4269i	1.13367	−	0.951264i	0.999213	+	0.0396557i	$0.0126261\pi$
$264$	−0.347296	−	1.96962i	−0.0213746	−	0.121221i
$265$	−4.00000			−0.245718
$266$		0			0
$267$		0			0
$268$	−0.520945	−	2.95442i	−0.0318218	−	0.180470i
$269$	−22.9813	+	19.2836i	−1.40120	+	1.17574i	−0.440632	+	0.897688i	$0.645245\pi$
$269$	−22.9813	+	19.2836i	−1.40120	+	1.17574i	−0.960565	+	0.278056i	$0.910310\pi$
$270$	18.7939	−	6.84040i	1.14376	−	0.416294i
$271$	−6.57785	−	2.39414i	−0.399576	−	0.145434i	0.134413	−	0.990925i	$-0.457085\pi$
$271$	−6.57785	−	2.39414i	−0.399576	−	0.145434i	−0.533989	+	0.845492i	$0.679307\pi$
$272$	2.29813	+	1.92836i	0.139345	+	0.116924i
$273$	−1.50000	+	2.59808i	−0.0907841	+	0.157243i
$274$	−8.50000	−	14.7224i	−0.513504	−	0.889415i
$275$	3.82026	−	21.6658i	0.230370	−	1.30650i
$276$	−0.173648	+	0.984808i	−0.0104524	+	0.0592785i
$277$	−14.0000	−	24.2487i	−0.841178	−	1.45696i	−0.888899	−	0.458103i	$-0.848529\pi$
$277$	−14.0000	−	24.2487i	−0.841178	−	1.45696i	0.0477206	−	0.998861i	$-0.484804\pi$
$278$		0			0
$279$	−12.2567	−	10.2846i	−0.733790	−	0.615723i
$280$	−11.2763	−	4.10424i	−0.673889	−	0.245275i
$281$	−7.51754	+	2.73616i	−0.448459	+	0.163226i	−0.556370	−	0.830935i	$-0.687806\pi$
$281$	−7.51754	+	2.73616i	−0.448459	+	0.163226i	0.107911	+	0.994161i	$0.465584\pi$
$282$	−6.12836	+	5.14230i	−0.364938	+	0.306220i
$283$	−1.04189	−	5.90885i	−0.0619339	−	0.351244i	−0.999989	−	0.00475755i	$-0.998486\pi$
$283$	−1.04189	−	5.90885i	−0.0619339	−	0.351244i	0.938055	−	0.346487i	$-0.112625\pi$
$284$	−2.00000			−0.118678
$285$		0			0
$286$	−2.00000			−0.118262
$287$	4.16756	+	23.6354i	0.246003	+	1.39515i
$288$	1.53209	−	1.28558i	0.0902792	−	0.0757532i
$289$	7.51754	−	2.73616i	0.442208	−	0.160951i
$290$	−18.7939	−	6.84040i	−1.10361	−	0.401682i
$291$	1.53209	+	1.28558i	0.0898126	+	0.0753618i
$292$	−4.50000	+	7.79423i	−0.263343	+	0.456123i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$	−0.347296	+	1.96962i	−0.0202547	+	0.114870i
$295$	10.4189	−	59.0885i	0.606611	−	3.44026i
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	5.00000	−	8.66025i	0.290129	−	0.502519i
$298$		0			0
$299$	0.939693	+	0.342020i	0.0543438	+	0.0197795i
$300$	−10.3366	+	3.76222i	−0.596785	+	0.217212i
$301$	9.19253	−	7.71345i	0.529849	−	0.444596i
$302$	0.347296	+	1.96962i	0.0199847	+	0.113339i
$303$	2.00000			0.114897
$304$		0			0
$305$	−8.00000			−0.458079
$306$	1.04189	+	5.90885i	0.0595608	+	0.337786i
$307$	9.19253	−	7.71345i	0.524646	−	0.440230i	−0.341602	−	0.939845i	$-0.610970\pi$
$307$	9.19253	−	7.71345i	0.524646	−	0.440230i	0.866248	+	0.499615i	$0.166525\pi$
$308$	−5.63816	+	2.05212i	−0.321264	+	0.116930i
$309$	−5.63816	−	2.05212i	−0.320743	−	0.116741i
$310$	24.5134	+	20.5692i	1.39227	+	1.16825i
$311$	−3.50000	+	6.06218i	−0.198467	+	0.343755i	−0.948031	−	0.318177i	$-0.896930\pi$
$311$	−3.50000	+	6.06218i	−0.198467	+	0.343755i	0.749565	+	0.661931i	$0.230263\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	5.03580	−	28.5594i	0.284640	−	1.61427i	−0.421928	−	0.906629i	$-0.638647\pi$
$313$	5.03580	−	28.5594i	0.284640	−	1.61427i	0.706568	−	0.707645i	$-0.250242\pi$
$314$	0.347296	−	1.96962i	0.0195991	−	0.111152i
$315$	−12.0000	−	20.7846i	−0.676123	−	1.17108i
$316$	−5.00000	+	8.66025i	−0.281272	+	0.487177i
$317$	20.6832	+	17.3553i	1.16168	+	0.974769i	0.999927	−	0.0120618i	$-0.00383948\pi$
$317$	20.6832	+	17.3553i	1.16168	+	0.974769i	0.161757	+	0.986831i	$0.448284\pi$
$318$	0.939693	+	0.342020i	0.0526953	+	0.0191795i
$319$	−9.39693	+	3.42020i	−0.526127	+	0.191495i
$320$	−3.06418	+	2.57115i	−0.171293	+	0.143732i
$321$	1.21554	+	6.89365i	0.0678447	+	0.384766i
$322$	3.00000			0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	1.91013	+	10.8329i	0.105955	+	0.600900i
$326$	12.2567	−	10.2846i	0.678836	−	0.569611i
$327$	−14.0954	+	5.13030i	−0.779477	+	0.283706i
$328$	7.51754	+	2.73616i	0.415087	+	0.151079i
$329$	18.3851	+	15.4269i	1.01360	+	0.850513i
$330$	−4.00000	+	6.92820i	−0.220193	+	0.381385i
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	0.999298	−	0.0374662i	$-0.0119287\pi$
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	−0.532096	+	0.846684i	$0.678595\pi$
$332$	−1.04189	+	5.90885i	−0.0571811	+	0.324290i
$333$	−0.694593	+	3.93923i	−0.0380634	+	0.215869i
$334$	6.00000	+	10.3923i	0.328305	+	0.568642i
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$	2.29813	+	1.92836i	0.125373	+	0.105201i
$337$	−30.0702	−	10.9446i	−1.63803	−	0.596193i	−0.651334	−	0.758791i	$-0.725790\pi$
$337$	−30.0702	−	10.9446i	−1.63803	−	0.596193i	−0.986692	+	0.162598i	$0.948012\pi$
$338$	−11.2763	+	4.10424i	−0.613350	+	0.223241i
$339$	−10.7246	+	8.99903i	−0.582482	+	0.488760i
$340$	−2.08378	−	11.8177i	−0.113009	−	0.640904i
$341$	16.0000			0.866449
$342$		0			0
$343$	−15.0000			−0.809924
$344$	−0.694593	−	3.93923i	−0.0374499	−	0.212389i
$345$	3.06418	−	2.57115i	0.164970	−	0.138426i
$346$	5.63816	−	2.05212i	0.303109	−	0.110323i
$347$	1.87939	+	0.684040i	0.100891	+	0.0367212i	0.391972	−	0.919977i	$-0.371793\pi$
$347$	1.87939	+	0.684040i	0.100891	+	0.0367212i	−0.291082	+	0.956698i	$0.594015\pi$
$348$	3.83022	+	3.21394i	0.205321	+	0.172285i
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$	16.5000	+	28.5788i	0.881962	+	1.52760i
$351$	−0.868241	+	4.92404i	−0.0463433	+	0.262826i
$352$	−0.347296	+	1.96962i	−0.0185110	+	0.104981i
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$	−7.50000	+	12.9904i	−0.398621	+	0.690431i
$355$	6.12836	+	5.14230i	0.325259	+	0.272925i
$356$		0			0
$357$	−8.45723	+	3.07818i	−0.447604	+	0.162915i
$358$		0			0
$359$	−2.60472	−	14.7721i	−0.137472	−	0.779642i	−0.973106	−	0.230356i	$-0.926011\pi$
$359$	−2.60472	−	14.7721i	−0.137472	−	0.779642i	0.835634	−	0.549286i	$-0.185100\pi$
$360$	−8.00000			−0.421637
$361$		0			0
$362$	22.0000			1.15629
$363$	−1.21554	−	6.89365i	−0.0637992	−	0.361823i
$364$	2.29813	−	1.92836i	0.120455	−	0.101074i
$365$	33.8289	−	12.3127i	1.77069	−	0.644477i
$366$	1.87939	+	0.684040i	0.0982370	+	0.0357554i
$367$	21.4492	+	17.9981i	1.11964	+	0.939491i	0.998586	−	0.0531551i	$-0.0169278\pi$
$367$	21.4492	+	17.9981i	1.11964	+	0.939491i	0.121055	+	0.992646i	$0.461372\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	8.00000	+	13.8564i	0.416463	+	0.721336i
$370$	1.38919	−	7.87846i	0.0722203	−	0.409582i
$371$	0.520945	−	2.95442i	0.0270461	−	0.153386i
$372$	−4.00000	−	6.92820i	−0.207390	−	0.359211i
$373$	14.5000	−	25.1147i	0.750782	−	1.30039i	−0.196663	−	0.980471i	$-0.563010\pi$
$373$	14.5000	−	25.1147i	0.750782	−	1.30039i	0.947444	−	0.319921i	$-0.103656\pi$
$374$	−4.59627	−	3.85673i	−0.237667	−	0.199427i
$375$	22.5526	+	8.20848i	1.16461	+	0.423884i
$376$	7.51754	−	2.73616i	0.387688	−	0.141107i
$377$	3.83022	−	3.21394i	0.197266	−	0.165526i
$378$	2.60472	+	14.7721i	0.133972	+	0.759796i
$379$	−15.0000			−0.770498			−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000			−0.770498			−0.385249	+	0.922813i	$0.625884\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$	−1.21554	−	6.89365i	−0.0621923	−	0.352710i
$383$	19.9172	−	16.7125i	1.01772	−	0.853968i	0.0283799	−	0.999597i	$-0.490965\pi$
$383$	19.9172	−	16.7125i	1.01772	−	0.853968i	0.989339	+	0.145629i	$0.0465207\pi$
$384$	0.939693	−	0.342020i	0.0479535	−	0.0174536i
$385$	22.5526	+	8.20848i	1.14939	+	0.418343i
$386$	−4.59627	−	3.85673i	−0.233944	−	0.196302i
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−5.20945	+	29.5442i	−0.264129	+	1.49795i	0.507374	+	0.861726i	$0.330616\pi$
$389$	−5.20945	+	29.5442i	−0.264129	+	1.49795i	−0.771503	+	0.636226i	$0.780495\pi$
$390$	0.694593	−	3.93923i	0.0351721	−	0.199471i
$391$	1.50000	+	2.59808i	0.0758583	+	0.131390i
$392$	1.00000	−	1.73205i	0.0505076	−	0.0874818i
$393$	9.19253	+	7.71345i	0.463702	+	0.389092i
$394$	7.51754	+	2.73616i	0.378728	+	0.137846i
$395$	37.5877	−	13.6808i	1.89124	−	0.688356i
$396$	−3.06418	+	2.57115i	−0.153981	+	0.129205i
$397$	1.38919	+	7.87846i	0.0697212	+	0.395409i	0.999619	+	0.0275914i	$0.00878372\pi$
$397$	1.38919	+	7.87846i	0.0697212	+	0.395409i	−0.929898	+	0.367817i	$0.880105\pi$
$398$	25.0000			1.25314
$399$		0			0
$400$	11.0000			0.550000
$401$	1.38919	+	7.87846i	0.0693726	+	0.393432i	0.999647	+	0.0265672i	$0.00845760\pi$
$401$	1.38919	+	7.87846i	0.0693726	+	0.393432i	−0.930274	+	0.366864i	$0.880431\pi$
$402$	2.29813	−	1.92836i	0.114620	−	0.0961780i
$403$	−7.51754	+	2.73616i	−0.374475	+	0.136298i
$404$	−1.87939	−	0.684040i	−0.0935029	−	0.0340323i
$405$	−3.06418	−	2.57115i	−0.152260	−	0.127761i
$406$	7.50000	−	12.9904i	0.372219	−	0.644702i
$407$	−2.00000	−	3.46410i	−0.0991363	−	0.171709i
$408$	−0.520945	+	2.95442i	−0.0257906	+	0.146266i
$409$	3.47296	−	19.6962i	0.171727	−	0.973912i	−0.770127	−	0.637890i	$-0.779807\pi$
$409$	3.47296	−	19.6962i	0.171727	−	0.973912i	0.941854	−	0.336022i	$-0.109082\pi$
$410$	−16.0000	−	27.7128i	−0.790184	−	1.36864i
$411$	8.50000	−	14.7224i	0.419274	−	0.726204i
$412$	4.59627	+	3.85673i	0.226442	+	0.190007i
$413$	42.2862	+	15.3909i	2.08077	+	0.757337i
$414$	1.87939	−	0.684040i	0.0923667	−	0.0336187i
$415$	18.3851	−	15.4269i	0.902487	−	0.757277i
$416$	−0.173648	−	0.984808i	−0.00851380	−	0.0482842i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−2.08378	−	11.8177i	−0.101678	−	0.576644i
$421$	9.95858	−	8.35624i	0.485351	−	0.407258i	−0.367005	−	0.930219i	$-0.619617\pi$
$421$	9.95858	−	8.35624i	0.485351	−	0.407258i	0.852357	+	0.522961i	$0.175173\pi$
$422$	−25.3717	+	9.23454i	−1.23508	+	0.449531i
$423$	15.0351	+	5.47232i	0.731031	+	0.266073i
$424$	−0.766044	−	0.642788i	−0.0372024	−	0.0312165i
$425$	−16.5000	+	28.5788i	−0.800368	+	1.38628i
$426$	−1.00000	−	1.73205i	−0.0484502	−	0.0839181i
$427$	1.04189	−	5.90885i	0.0504205	−	0.285949i
$428$	1.21554	−	6.89365i	0.0587552	−	0.333217i
$429$	−1.00000	−	1.73205i	−0.0482805	−	0.0836242i
$430$	−8.00000	+	13.8564i	−0.385794	+	0.668215i
$431$	13.7888	+	11.5702i	0.664183	+	0.557316i	0.911337	−	0.411660i	$-0.135051\pi$
$431$	13.7888	+	11.5702i	0.664183	+	0.557316i	−0.247154	+	0.968976i	$0.579495\pi$
$432$	4.69846	+	1.71010i	0.226055	+	0.0822773i
$433$	13.1557	−	4.78828i	0.632222	−	0.230110i	−0.00597589	−	0.999982i	$-0.501902\pi$
$433$	13.1557	−	4.78828i	0.632222	−	0.230110i	0.638198	+	0.769872i	$0.279680\pi$
$434$	−18.3851	+	15.4269i	−0.882511	+	0.740515i
$435$	−3.47296	−	19.6962i	−0.166516	−	0.944358i
$436$	15.0000			0.718370
$437$		0			0
$438$	−9.00000			−0.430037
$439$	−3.47296	−	19.6962i	−0.165756	−	0.940046i	−0.948282	−	0.317429i	$-0.897180\pi$
$439$	−3.47296	−	19.6962i	−0.165756	−	0.940046i	0.782527	−	0.622617i	$-0.213931\pi$
$440$	6.12836	−	5.14230i	0.292158	−	0.245150i
$441$	3.75877	−	1.36808i	0.178989	−	0.0651467i
$442$	2.81908	+	1.02606i	0.134090	+	0.0488047i
$443$	−19.9172	−	16.7125i	−0.946293	−	0.794034i	0.0323767	−	0.999476i	$-0.489692\pi$
$443$	−19.9172	−	16.7125i	−0.946293	−	0.794034i	−0.978669	+	0.205442i	$0.934137\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$		0			0
$446$	2.43107	−	13.7873i	0.115115	−	0.652848i
$447$		0			0
$448$	−1.50000	−	2.59808i	−0.0708683	−	0.122748i
$449$	5.00000	−	8.66025i	0.235965	−	0.408703i	−0.723588	−	0.690232i	$-0.757508\pi$
$449$	5.00000	−	8.66025i	0.235965	−	0.408703i	0.959553	+	0.281529i	$0.0908417\pi$
$450$	16.8530	+	14.1413i	0.794457	+	0.666629i
$451$	−15.0351	−	5.47232i	−0.707974	−	0.257682i
$452$	13.1557	−	4.78828i	0.618792	−	0.225222i
$453$	−1.53209	+	1.28558i	−0.0719838	+	0.0604016i
$454$	−2.95202	−	16.7417i	−0.138545	−	0.785728i
$455$	−12.0000			−0.562569
$456$		0			0
$457$	−7.00000			−0.327446			−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000			−0.327446			−0.163723	+	0.986506i	$0.552350\pi$
$458$	1.73648	+	9.84808i	0.0811405	+	0.460170i
$459$	−11.4907	+	9.64181i	−0.536338	+	0.450041i
$460$	−3.75877	+	1.36808i	−0.175254	+	0.0637871i
$461$	26.3114	+	9.57656i	1.22544	+	0.446025i	0.872035	−	0.489444i	$-0.162800\pi$
$461$	26.3114	+	9.57656i	1.22544	+	0.446025i	0.353409	+	0.935469i	$0.385022\pi$
$462$	−4.59627	−	3.85673i	−0.213838	−	0.179431i
$463$	−2.00000	+	3.46410i	−0.0929479	+	0.160990i	−0.908750	−	0.417340i	$-0.862962\pi$
$463$	−2.00000	+	3.46410i	−0.0929479	+	0.160990i	0.815802	+	0.578331i	$0.196296\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$	−5.55674	+	31.5138i	−0.257688	+	1.46142i
$466$	1.04189	−	5.90885i	0.0482646	−	0.273722i
$467$	1.00000	+	1.73205i	0.0462745	+	0.0801498i	0.888235	−	0.459390i	$-0.151932\pi$
$467$	1.00000	+	1.73205i	0.0462745	+	0.0801498i	−0.841960	+	0.539539i	$0.818598\pi$
$468$	1.00000	−	1.73205i	0.0462250	−	0.0800641i
$469$	−6.89440	−	5.78509i	−0.318354	−	0.267131i
$470$	−30.0702	−	10.9446i	−1.38703	−	0.504839i
$471$	1.87939	−	0.684040i	0.0865975	−	0.0315189i
$472$	11.4907	−	9.64181i	0.528901	−	0.443800i
$473$	1.38919	+	7.87846i	0.0638748	+	0.362252i
$474$	−10.0000			−0.459315
$475$		0			0
$476$	9.00000			0.412514
$477$	−0.347296	−	1.96962i	−0.0159016	−	0.0901825i
$478$	−11.4907	+	9.64181i	−0.525571	+	0.441006i
$479$	18.7939	−	6.84040i	0.858713	−	0.312546i	0.125125	−	0.992141i	$-0.460067\pi$
$479$	18.7939	−	6.84040i	0.858713	−	0.312546i	0.733588	+	0.679595i	$0.237844\pi$
$480$	−3.75877	−	1.36808i	−0.171564	−	0.0624440i
$481$	1.53209	+	1.28558i	0.0698572	+	0.0586172i
$482$	4.00000	−	6.92820i	0.182195	−	0.315571i
$483$	1.50000	+	2.59808i	0.0682524	+	0.118217i
$484$	−1.21554	+	6.89365i	−0.0552517	+	0.313348i
$485$	−1.38919	+	7.87846i	−0.0630797	+	0.357743i
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	−0.887793	−	0.460243i	$-0.847762\pi$
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	0.842479	+	0.538730i	$0.181096\pi$
$488$	−1.53209	−	1.28558i	−0.0693544	−	0.0581953i
$489$	15.0351	+	5.47232i	0.679910	+	0.247467i
$490$	−7.51754	+	2.73616i	−0.339608	+	0.123607i
$491$	−21.4492	+	17.9981i	−0.967991	+	0.812241i	−0.982234	−	0.187658i	$-0.939910\pi$
$491$	−21.4492	+	17.9981i	−0.967991	+	0.812241i	0.0142436	+	0.999899i	$0.495466\pi$
$492$	1.38919	+	7.87846i	0.0626293	+	0.355188i
$493$	15.0000			0.675566
$494$		0			0
$495$	16.0000			0.719147
$496$	1.38919	+	7.87846i	0.0623763	+	0.353753i
$497$	−4.59627	+	3.85673i	−0.206171	+	0.172998i
$498$	−5.63816	+	2.05212i	−0.252652	+	0.0919577i
$499$	−37.5877	−	13.6808i	−1.68266	−	0.612437i	−0.688987	−	0.724774i	$-0.741944\pi$
$499$	−37.5877	−	13.6808i	−1.68266	−	0.612437i	−0.993670	+	0.112337i	$0.964166\pi$
$500$	−18.3851	−	15.4269i	−0.822205	−	0.689912i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$	1.00000	+	1.73205i	0.0446322	+	0.0773052i
$503$	6.77228	−	38.4075i	0.301961	−	1.71251i	−0.335514	−	0.942035i	$-0.608910\pi$
$503$	6.77228	−	38.4075i	0.301961	−	1.71251i	0.637475	−	0.770471i	$-0.279979\pi$
$504$	1.04189	−	5.90885i	0.0464094	−	0.263201i
$505$	4.00000	+	6.92820i	0.177998	+	0.308301i
$506$	−1.00000	+	1.73205i	−0.0444554	+	0.0769991i
$507$	−9.19253	−	7.71345i	−0.408255	−	0.342566i
$508$	16.9145	+	6.15636i	0.750458	+	0.273144i
$509$	−28.1908	+	10.2606i	−1.24953	+	0.454793i	−0.880244	−	0.474521i	$-0.842621\pi$
$509$	−28.1908	+	10.2606i	−1.24953	+	0.454793i	−0.369290	+	0.929314i	$0.620399\pi$
$510$	9.19253	−	7.71345i	0.407052	−	0.341557i
$511$	4.68850	+	26.5898i	0.207407	+	1.17626i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	8.00000			0.352865
$515$	−4.16756	−	23.6354i	−0.183644	−	1.04150i
$516$	3.06418	−	2.57115i	0.134893	−	0.113189i
$517$	−15.0351	+	5.47232i	−0.661242	+	0.240672i
$518$	5.63816	+	2.05212i	0.247726	+	0.0901650i
$519$	4.59627	+	3.85673i	0.201754	+	0.169291i
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	−0.990671	−	0.136272i	$-0.956488\pi$
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	0.377320	−	0.926083i	$-0.376846\pi$
$522$	1.73648	−	9.84808i	0.0760037	−	0.431039i
$523$	−5.03580	+	28.5594i	−0.220200	+	1.24882i	0.651451	+	0.758690i	$0.274160\pi$
$523$	−5.03580	+	28.5594i	−0.220200	+	1.24882i	−0.871652	+	0.490126i	$0.836951\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$	−16.5000	+	28.5788i	−0.720119	+	1.24728i
$526$	−18.3851	−	15.4269i	−0.801627	−	0.672645i
$527$	−22.5526	−	8.20848i	−0.982408	−	0.357567i
$528$	−1.87939	+	0.684040i	−0.0817897	+	0.0297690i
$529$	−16.8530	+	14.1413i	−0.732738	+	0.614840i
$530$	0.694593	+	3.93923i	0.0301712	+	0.171109i
$531$	30.0000			1.30189
$532$		0			0
$533$	8.00000			0.346518
$534$		0			0
$535$	−21.4492	+	17.9981i	−0.927332	+	0.778124i
$536$	−2.81908	+	1.02606i	−0.121766	+	0.0443191i
$537$		0			0
$538$	22.9813	+	19.2836i	0.990796	+	0.831376i
$539$	−2.00000	+	3.46410i	−0.0861461	+	0.149209i
$540$	−10.0000	−	17.3205i	−0.430331	−	0.745356i
$541$	0.347296	−	1.96962i	0.0149314	−	0.0846804i	−0.976431	−	0.215828i	$-0.930755\pi$
$541$	0.347296	−	1.96962i	0.0149314	−	0.0846804i	0.991363	+	0.131147i	$0.0418661\pi$
$542$	−1.21554	+	6.89365i	−0.0522118	+	0.296108i
$543$	11.0000	+	19.0526i	0.472055	+	0.817624i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	−45.9627	−	38.5673i	−1.96882	−	1.65204i
$546$	2.81908	+	1.02606i	0.120645	+	0.0439113i
$547$	26.3114	−	9.57656i	1.12499	−	0.409464i	0.288522	−	0.957473i	$-0.406836\pi$
$547$	26.3114	−	9.57656i	1.12499	−	0.409464i	0.836472	+	0.548009i	$0.184614\pi$
$548$	−13.0228	+	10.9274i	−0.556305	+	0.466795i
$549$	−0.694593	−	3.93923i	−0.0296445	−	0.168122i
$550$	−22.0000			−0.938083
$551$		0			0
$552$	1.00000			0.0425628
$553$	5.20945	+	29.5442i	0.221528	+	1.25635i
$554$	−21.4492	+	17.9981i	−0.911291	+	0.764664i
$555$	7.51754	−	2.73616i	0.319102	−	0.116144i
$556$		0			0
$557$	21.4492	+	17.9981i	0.908834	+	0.762602i	0.971897	−	0.235408i	$-0.0756425\pi$
$557$	21.4492	+	17.9981i	0.908834	+	0.762602i	−0.0630631	+	0.998010i	$0.520087\pi$
$558$	−8.00000	+	13.8564i	−0.338667	+	0.586588i
$559$	−2.00000	−	3.46410i	−0.0845910	−	0.146516i
$560$	−2.08378	+	11.8177i	−0.0880557	+	0.499389i
$561$	1.04189	−	5.90885i	0.0439886	−	0.249472i
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	6.12836	+	5.14230i	0.258050	+	0.216530i
$565$	−52.6228	−	19.1531i	−2.21386	−	0.805778i
$566$	−5.63816	+	2.05212i	−0.236989	+	0.0862571i
$567$	2.29813	−	1.92836i	0.0965125	−	0.0809836i
$568$	0.347296	+	1.96962i	0.0145722	+	0.0826432i
$569$	−40.0000			−1.67689			−0.838444	−	0.544988i	$-0.816534\pi$
$569$	−40.0000			−1.67689			−0.838444	+	0.544988i	$0.816534\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$	0.347296	+	1.96962i	0.0145212	+	0.0823538i
$573$	5.36231	−	4.49951i	0.224014	−	0.187970i
$574$	22.5526	−	8.20848i	0.941328	−	0.342615i
$575$	10.3366	+	3.76222i	0.431067	+	0.156895i
$576$	−1.53209	−	1.28558i	−0.0638370	−	0.0535656i
$577$	18.5000	−	32.0429i	0.770165	−	1.33397i	−0.167307	−	0.985905i	$-0.553507\pi$
$577$	18.5000	−	32.0429i	0.770165	−	1.33397i	0.937472	−	0.348060i	$-0.113160\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	1.04189	−	5.90885i	0.0432994	−	0.245563i
$580$	−3.47296	+	19.6962i	−0.144207	+	0.817838i
$581$	9.00000	+	15.5885i	0.373383	+	0.646718i
$582$	1.00000	−	1.73205i	0.0414513	−	0.0717958i
$583$	1.53209	+	1.28558i	0.0634526	+	0.0532431i
$584$	8.45723	+	3.07818i	0.349963	+	0.127376i
$585$	−7.51754	+	2.73616i	−0.310812	+	0.113126i
$586$	6.89440	−	5.78509i	0.284805	−	0.238980i
$587$	−2.08378	−	11.8177i	−0.0860067	−	0.487768i	−0.997135	−	0.0756451i	$-0.975898\pi$
$587$	−2.08378	−	11.8177i	−0.0860067	−	0.487768i	0.911128	−	0.412123i	$-0.135213\pi$
$588$	2.00000			0.0824786
$589$		0			0
$590$	−60.0000			−2.47016
$591$	1.38919	+	7.87846i	0.0571435	+	0.324077i
$592$	1.53209	−	1.28558i	0.0629685	−	0.0528368i
$593$	−31.9495	+	11.6287i	−1.31201	+	0.477533i	−0.900890	−	0.434048i	$-0.857085\pi$
$593$	−31.9495	+	11.6287i	−1.31201	+	0.477533i	−0.411121	+	0.911581i	$0.634863\pi$
$594$	−9.39693	−	3.42020i	−0.385561	−	0.140333i
$595$	−27.5776	−	23.1404i	−1.13057	−	0.948662i
$596$		0			0
$597$	12.5000	+	21.6506i	0.511591	+	0.886102i
$598$	0.173648	−	0.984808i	0.00710100	−	0.0402718i
$599$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$599$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$600$	5.50000	+	9.52628i	0.224537	+	0.388909i
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	−0.936002	−	0.351996i	$-0.885503\pi$
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	0.772838	+	0.634603i	$0.218836\pi$
$602$	−9.19253	−	7.71345i	−0.374660	−	0.314377i
$603$	−5.63816	−	2.05212i	−0.229603	−	0.0835688i
$604$	1.87939	−	0.684040i	0.0764711	−	0.0278332i
$605$	21.4492	−	17.9981i	0.872036	−	0.731725i
$606$	−0.347296	−	1.96962i	−0.0141080	−	0.0800102i
$607$	22.0000			0.892952			0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000			0.892952			0.446476	+	0.894795i	$0.352679\pi$
$608$		0			0
$609$	15.0000			0.607831
$610$	1.38919	+	7.87846i	0.0562465	+	0.318990i
$611$	6.12836	−	5.14230i	0.247927	−	0.208035i
$612$	5.63816	−	2.05212i	0.227909	−	0.0829521i
$613$	−31.9495	−	11.6287i	−1.29043	−	0.469678i	−0.396562	−	0.918008i	$-0.629797\pi$
$613$	−31.9495	−	11.6287i	−1.29043	−	0.469678i	−0.893868	+	0.448330i	$0.852019\pi$
$614$	−9.19253	−	7.71345i	−0.370980	−	0.311290i
$615$	16.0000	−	27.7128i	0.645182	−	1.11749i
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	3.12567	−	17.7265i	0.125835	−	0.713644i	−0.854974	−	0.518671i	$-0.826427\pi$
$617$	3.12567	−	17.7265i	0.125835	−	0.713644i	0.980809	−	0.194973i	$-0.0624619\pi$
$618$	−1.04189	+	5.90885i	−0.0419109	+	0.237689i
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$	16.0000	−	27.7128i	0.642575	−	1.11297i
$621$	3.83022	+	3.21394i	0.153702	+	0.128971i
$622$	6.57785	+	2.39414i	0.263748	+	0.0959963i
$623$		0			0
$624$	0.766044	−	0.642788i	0.0306663	−	0.0257321i
$625$	7.11958	+	40.3771i	0.284783	+	1.61508i
$626$	−29.0000			−1.15907
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	1.04189	+	5.90885i	0.0415428	+	0.235601i
$630$	−18.3851	+	15.4269i	−0.732479	+	0.614623i
$631$	−30.0702	+	10.9446i	−1.19707	+	0.435699i	−0.862202	−	0.506564i	$-0.830915\pi$
$631$	−30.0702	+	10.9446i	−1.19707	+	0.435699i	−0.334872	+	0.942264i	$0.608693\pi$
$632$	9.39693	+	3.42020i	0.373790	+	0.136048i
$633$	−20.6832	−	17.3553i	−0.822083	−	0.689810i
$634$	13.5000	−	23.3827i	0.536153	−	0.928645i
$635$	−36.0000	−	62.3538i	−1.42862	−	2.47444i
$636$	0.173648	−	0.984808i	0.00688560	−	0.0390502i
$637$	0.347296	−	1.96962i	0.0137604	−	0.0780390i
$638$	5.00000	+	8.66025i	0.197952	+	0.342863i
$639$	−2.00000	+	3.46410i	−0.0791188	+	0.137038i
$640$	3.06418	+	2.57115i	0.121122	+	0.101634i
$641$	39.4671	+	14.3648i	1.55886	+	0.567377i	0.970474	−	0.241206i	$-0.0775428\pi$
$641$	39.4671	+	14.3648i	1.55886	+	0.567377i	0.588382	+	0.808583i	$0.299765\pi$
$642$	6.57785	−	2.39414i	0.259607	−	0.0944892i
$643$	−19.9172	+	16.7125i	−0.785456	+	0.659076i	−0.944616	−	0.328177i	$-0.893566\pi$
$643$	−19.9172	+	16.7125i	−0.785456	+	0.659076i	0.159160	+	0.987253i	$0.449121\pi$
$644$	−0.520945	−	2.95442i	−0.0205281	−	0.116421i
$645$	−16.0000			−0.629999
$646$		0			0
$647$	23.0000			0.904223			0.452112	−	0.891961i	$-0.350671\pi$
$647$	23.0000			0.904223			0.452112	+	0.891961i	$0.350671\pi$
$648$	−0.173648	−	0.984808i	−0.00682154	−	0.0386869i
$649$	−22.9813	+	19.2836i	−0.902096	+	0.756949i
$650$	10.3366	−	3.76222i	0.405436	−	0.147566i
$651$	−22.5526	−	8.20848i	−0.883907	−	0.321716i
$652$	−12.2567	−	10.2846i	−0.480010	−	0.402776i
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	7.50000	+	12.9904i	0.293273	+	0.507964i
$655$	−8.33511	+	47.2708i	−0.325680	+	1.84702i
$656$	1.38919	−	7.87846i	0.0542386	−	0.307602i
$657$	9.00000	+	15.5885i	0.351123	+	0.608164i
$658$	12.0000	−	20.7846i	0.467809	−	0.810268i
$659$	−3.83022	−	3.21394i	−0.149204	−	0.125197i	0.565130	−	0.825002i	$-0.308826\pi$
$659$	−3.83022	−	3.21394i	−0.149204	−	0.125197i	−0.714334	+	0.699805i	$0.753270\pi$
$660$	7.51754	+	2.73616i	0.292620	+	0.106505i
$661$	−21.6129	+	7.86646i	−0.840646	+	0.305970i	−0.726220	−	0.687462i	$-0.758725\pi$
$661$	−21.6129	+	7.86646i	−0.840646	+	0.305970i	−0.114425	+	0.993432i	$0.536503\pi$
$662$	13.0228	−	10.9274i	0.506144	−	0.424705i
$663$	0.520945	+	2.95442i	0.0202318	+	0.114740i
$664$	6.00000			0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	−0.868241	−	4.92404i	−0.0336184	−	0.190660i
$668$	9.19253	−	7.71345i	0.355670	−	0.298442i
$669$	13.1557	−	4.78828i	0.508629	−	0.185126i
$670$	11.2763	+	4.10424i	0.435642	+	0.158561i
$671$	3.06418	+	2.57115i	0.118291	+	0.0992582i
$672$	1.50000	−	2.59808i	0.0578638	−	0.100223i
$673$	22.0000	+	38.1051i	0.848038	+	1.46884i	0.882957	+	0.469454i	$0.155549\pi$
$673$	22.0000	+	38.1051i	0.848038	+	1.46884i	−0.0349191	+	0.999390i	$0.511117\pi$
$674$	−5.55674	+	31.5138i	−0.214038	+	1.21387i
$675$	−9.55065	+	54.1644i	−0.367605	+	2.08479i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	6.50000	−	11.2583i	0.249815	−	0.432693i	−0.713659	−	0.700493i	$-0.752963\pi$
$677$	6.50000	−	11.2583i	0.249815	−	0.432693i	0.963474	+	0.267800i	$0.0862968\pi$
$678$	10.7246	+	8.99903i	0.411877	+	0.345606i
$679$	−5.63816	−	2.05212i	−0.216373	−	0.0787532i
$680$	−11.2763	+	4.10424i	−0.432427	+	0.157390i
$681$	13.0228	−	10.9274i	0.499033	−	0.418738i
$682$	−2.77837	−	15.7569i	−0.106389	−	0.603364i
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$	68.0000			2.59815
$686$	2.60472	+	14.7721i	0.0994488	+	0.564002i
$687$	−7.66044	+	6.42788i	−0.292264	+	0.245239i
$688$	−3.75877	+	1.36808i	−0.143302	+	0.0521576i
$689$	−0.939693	−	0.342020i	−0.0357994	−	0.0130299i
$690$	−3.06418	−	2.57115i	−0.116651	−	0.0978820i
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	0.121470	+	0.992595i	$0.461239\pi$
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	−0.920348	+	0.391102i	$0.872094\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$	−2.08378	+	11.8177i	−0.0791562	+	0.448917i
$694$	0.347296	−	1.96962i	0.0131832	−	0.0747656i
$695$		0			0
$696$	2.50000	−	4.33013i	0.0947623	−	0.164133i
$697$	18.3851	+	15.4269i	0.696384	+	0.584336i
$698$	9.39693	+	3.42020i	0.355679	+	0.129457i
$699$	5.63816	−	2.05212i	0.213255	−	0.0776183i
$700$	25.2795	−	21.2120i	0.955474	−	0.801738i
$701$	−4.86215	−	27.5746i	−0.183641	−	1.04148i	−0.927689	−	0.373353i	$-0.878208\pi$
$701$	−4.86215	−	27.5746i	−0.183641	−	1.04148i	0.744048	−	0.668126i	$-0.232903\pi$
$702$	5.00000			0.188713
$703$		0			0
$704$	2.00000			0.0753778
$705$	−5.55674	−	31.5138i	−0.209279	−	1.18688i
$706$	−6.89440	+	5.78509i	−0.259474	+	0.217725i
$707$	−5.63816	+	2.05212i	−0.212045	+	0.0771779i
$708$	14.0954	+	5.13030i	0.529737	+	0.192809i
$709$	−22.9813	−	19.2836i	−0.863082	−	0.724212i	0.0995477	−	0.995033i	$-0.468260\pi$
$709$	−22.9813	−	19.2836i	−0.863082	−	0.724212i	−0.962630	+	0.270821i	$0.912705\pi$
$710$	4.00000	−	6.92820i	0.150117	−	0.260011i
$711$	10.0000	+	17.3205i	0.375029	+	0.649570i
$712$		0			0
$713$	−1.38919	+	7.87846i	−0.0520254	+	0.295051i
$714$	4.50000	+	7.79423i	0.168408	+	0.291692i
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$		0			0
$717$	−14.0954	−	5.13030i	−0.526402	−	0.191595i
$718$	−14.0954	+	5.13030i	−0.526035	+	0.191461i
$719$	−3.83022	+	3.21394i	−0.142843	+	0.119860i	−0.711409	−	0.702778i	$-0.751943\pi$
$719$	−3.83022	+	3.21394i	−0.142843	+	0.119860i	0.568566	+	0.822638i	$0.307498\pi$
$720$	1.38919	+	7.87846i	0.0517719	+	0.293613i
$721$	18.0000			0.670355
$722$		0			0
$723$	8.00000			0.297523
$724$	−3.82026	−	21.6658i	−0.141979	−	0.805202i
$725$	42.1324	−	35.3533i	1.56476	−	1.31299i
$726$	−6.57785	+	2.39414i	−0.244127	+	0.0888549i
$727$	15.9748	+	5.81434i	0.592472	+	0.215642i	0.620816	−	0.783956i	$-0.286801\pi$
$727$	15.9748	+	5.81434i	0.592472	+	0.215642i	−0.0283446	+	0.999598i	$0.509024\pi$
$728$	−2.29813	−	1.92836i	−0.0851745	−	0.0714699i
$729$	−6.50000	+	11.2583i	−0.240741	+	0.416975i
$730$	−18.0000	−	31.1769i	−0.666210	−	1.15391i
$731$	2.08378	−	11.8177i	0.0770713	−	0.437093i
$732$	0.347296	−	1.96962i	0.0128364	−	0.0727991i
$733$	18.0000	+	31.1769i	0.664845	+	1.15155i	0.979327	+	0.202282i	$0.0648358\pi$
$733$	18.0000	+	31.1769i	0.664845	+	1.15155i	−0.314482	+	0.949263i	$0.601831\pi$
$734$	14.0000	−	24.2487i	0.516749	−	0.895036i
$735$	−6.12836	−	5.14230i	−0.226048	−	0.189677i
$736$	−0.939693	−	0.342020i	−0.0346375	−	0.0126070i
$737$	5.63816	−	2.05212i	0.207684	−	0.0755908i
$738$	12.2567	−	10.2846i	0.451176	−	0.378581i
$739$	−6.94593	−	39.3923i	−0.255510	−	1.44907i	−0.794760	−	0.606924i	$-0.792403\pi$
$739$	−6.94593	−	39.3923i	−0.255510	−	1.44907i	0.539250	−	0.842146i	$-0.318708\pi$
$740$	−8.00000			−0.294086
$741$		0			0
$742$	−3.00000			−0.110133
$743$	2.77837	+	15.7569i	0.101929	+	0.578065i	0.992403	+	0.123032i	$0.0392617\pi$
$743$	2.77837	+	15.7569i	0.101929	+	0.578065i	−0.890474	+	0.455034i	$0.849627\pi$
$744$	−6.12836	+	5.14230i	−0.224676	+	0.188526i
$745$		0			0
$746$	−27.2511	−	9.91858i	−0.997733	−	0.363145i
$747$	9.19253	+	7.71345i	0.336337	+	0.282220i
$748$	−3.00000	+	5.19615i	−0.109691	+	0.189990i
$749$	−10.5000	−	18.1865i	−0.383662	−	0.664521i
$750$	4.16756	−	23.6354i	0.152178	−	0.863042i
$751$	−5.55674	+	31.5138i	−0.202768	+	1.14996i	0.698145	+	0.715957i	$0.254009\pi$
$751$	−5.55674	+	31.5138i	−0.202768	+	1.14996i	−0.900913	+	0.434000i	$0.857102\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	−1.00000	+	1.73205i	−0.0364420	+	0.0631194i
$754$	−3.83022	−	3.21394i	−0.139488	−	0.117045i
$755$	−7.51754	−	2.73616i	−0.273591	−	0.0995791i
$756$	14.0954	−	5.13030i	0.512644	−	0.186587i
$757$	−1.53209	+	1.28558i	−0.0556847	+	0.0467250i	−0.670205	−	0.742176i	$-0.733794\pi$
$757$	−1.53209	+	1.28558i	−0.0556847	+	0.0467250i	0.614521	+	0.788901i	$0.289349\pi$
$758$	2.60472	+	14.7721i	0.0946078	+	0.536547i
$759$	−2.00000			−0.0725954
$760$		0			0
$761$	27.0000			0.978749			0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000			0.978749			0.489375	+	0.872074i	$0.337225\pi$
$762$	3.12567	+	17.7265i	0.113231	+	0.642165i
$763$	34.4720	−	28.9254i	1.24797	−	1.04717i
$764$	−6.57785	+	2.39414i	−0.237978	+	0.0866170i
$765$	−22.5526	−	8.20848i	−0.815392	−	0.296778i
$766$	−19.9172	−	16.7125i	−0.719636	−	0.603846i
$767$	7.50000	−	12.9904i	0.270809	−	0.469055i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−6.07769	+	34.4683i	−0.219167	+	1.24296i	0.654360	+	0.756183i	$0.272938\pi$
$769$	−6.07769	+	34.4683i	−0.219167	+	1.24296i	−0.873527	+	0.486775i	$0.838173\pi$
$770$	4.16756	−	23.6354i	0.150188	−	0.851760i
$771$	4.00000	+	6.92820i	0.144056	+	0.249513i
$772$	−3.00000	+	5.19615i	−0.107972	+	0.187014i
$773$	−6.89440	−	5.78509i	−0.247974	−	0.208075i	0.510325	−	0.859982i	$-0.329525\pi$
$773$	−6.89440	−	5.78509i	−0.247974	−	0.208075i	−0.758299	+	0.651906i	$0.773970\pi$
$774$	−7.51754	−	2.73616i	−0.270212	−	0.0983493i
$775$	−82.6930	+	30.0978i	−2.97042	+	1.08114i
$776$	−1.53209	+	1.28558i	−0.0549988	+	0.0461495i
$777$	1.04189	+	5.90885i	0.0373776	+	0.211979i
$778$	30.0000			1.07555
$779$		0			0
$780$	−4.00000			−0.143223
$781$	−0.694593	−	3.93923i	−0.0248545	−	0.140957i
$782$	2.29813	−	1.92836i	0.0821811	−	0.0689581i
$783$	23.4923	−	8.55050i	0.839547	−	0.305570i
$784$	−1.87939	−	0.684040i	−0.0671209	−	0.0244300i
$785$	6.12836	+	5.14230i	0.218730	+	0.183537i
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	0.673820	−	0.738896i	$-0.264652\pi$
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	−0.976812	+	0.214097i	$0.931319\pi$
$788$	1.38919	−	7.87846i	0.0494877	−	0.280659i
$789$	4.16756	−	23.6354i	0.148369	−	0.841442i
$790$	−20.0000	−	34.6410i	−0.711568	−	1.23247i
$791$	21.0000	−	36.3731i	0.746674	−	1.29328i
$792$	3.06418	+	2.57115i	0.108881	+	0.0913619i
$793$	−1.87939	−	0.684040i	−0.0667389	−	0.0242910i
$794$	7.51754	−	2.73616i	0.266788	−	0.0971027i
$795$	−3.06418	+	2.57115i	−0.108675	+	0.0911893i
$796$	−4.34120	−	24.6202i	−0.153870	−	0.872640i
$797$	−3.00000			−0.106265			−0.0531327	−	0.998587i	$-0.516921\pi$
$797$	−3.00000			−0.106265			−0.0531327	+	0.998587i	$0.516921\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	−1.91013	−	10.8329i	−0.0675333	−	0.383000i
$801$		0			0
$802$	7.51754	−	2.73616i	0.265454	−	0.0966172i
$803$	−16.9145	−	6.15636i	−0.596899	−	0.217253i
$804$	−2.29813	−	1.92836i	−0.0810489	−	0.0680081i
$805$	−6.00000	+	10.3923i	−0.211472	+	0.366281i
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$	−5.20945	+	29.5442i	−0.183381	+	1.04001i
$808$	−0.347296	+	1.96962i	−0.0122178	+	0.0692908i
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	0.967219	−	0.253946i	$-0.0817284\pi$
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	−0.703533	+	0.710663i	$0.748395\pi$
$810$	−2.00000	+	3.46410i	−0.0702728	+	0.121716i
$811$	2.29813	+	1.92836i	0.0806984	+	0.0677140i	0.682245	−	0.731124i	$-0.261004\pi$
$811$	2.29813	+	1.92836i	0.0806984	+	0.0677140i	−0.601546	+	0.798838i	$0.705448\pi$
$812$	−14.0954	−	5.13030i	−0.494651	−	0.180038i
$813$	−6.57785	+	2.39414i	−0.230695	+	0.0839662i
$814$	−3.06418	+	2.57115i	−0.107399	+	0.0901188i
$815$	11.1135	+	63.0277i	0.389288	+	2.20776i
$816$	3.00000			0.105021
$817$		0			0
$818$	−20.0000			−0.699284
$819$	−1.04189	−	5.90885i	−0.0364066	−	0.206472i
$820$	−24.5134	+	20.5692i	−0.856046	+	0.718308i
$821$	−11.2763	+	4.10424i	−0.393546	+	0.143239i	−0.531210	−	0.847240i	$-0.678263\pi$
$821$	−11.2763	+	4.10424i	−0.393546	+	0.143239i	0.137664	+	0.990479i	$0.456040\pi$
$822$	−15.9748	−	5.81434i	−0.557184	−	0.202798i
$823$	22.2153	+	18.6408i	0.774376	+	0.649779i	0.941826	−	0.336102i	$-0.109109\pi$
$823$	22.2153	+	18.6408i	0.774376	+	0.649779i	−0.167449	+	0.985881i	$0.553553\pi$
$824$	3.00000	−	5.19615i	0.104510	−	0.181017i
$825$	−11.0000	−	19.0526i	−0.382971	−	0.663325i
$826$	7.81417	−	44.3163i	0.271890	−	1.54196i
$827$	−3.99391	+	22.6506i	−0.138882	+	0.787638i	0.833196	+	0.552978i	$0.186509\pi$
$827$	−3.99391	+	22.6506i	−0.138882	+	0.787638i	−0.972078	+	0.234660i	$0.924602\pi$
$828$	−1.00000	−	1.73205i	−0.0347524	−	0.0601929i
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	−0.966371	−	0.257152i	$-0.917216\pi$
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	0.705885	+	0.708326i	$0.250549\pi$
$830$	−18.3851	−	15.4269i	−0.638155	−	0.535476i
$831$	−26.3114	−	9.57656i	−0.912732	−	0.332207i
$832$	−0.939693	+	0.342020i	−0.0325780	+	0.0118574i
$833$	4.59627	−	3.85673i	0.159251	−	0.133628i
$834$		0			0
$835$	−48.0000			−1.66111
$836$		0			0
$837$	−40.0000			−1.38260
$838$		0			0
$839$	−15.3209	+	12.8558i	−0.528936	+	0.443830i	−0.867734	−	0.497029i	$-0.834424\pi$
$839$	−15.3209	+	12.8558i	−0.528936	+	0.443830i	0.338798	+	0.940859i	$0.389980\pi$
$840$	−11.2763	+	4.10424i	−0.389070	+	0.141610i
$841$	3.75877	+	1.36808i	0.129613	+	0.0471752i
$842$	−9.95858	−	8.35624i	−0.343195	−	0.287975i
$843$	−4.00000	+	6.92820i	−0.137767	+	0.238620i
$844$	13.5000	+	23.3827i	0.464689	+	0.804865i
$845$	8.33511	−	47.2708i	0.286737	−	1.62616i
$846$	2.77837	−	15.7569i	0.0955224	−	0.541734i
$847$	10.5000	+	18.1865i	0.360784	+	0.624897i
$848$	−0.500000	+	0.866025i	−0.0171701	+	0.0297394i
$849$	−4.59627	−	3.85673i	−0.157743	−	0.132362i
$850$	31.0099	+	11.2867i	1.06363	+	0.387129i
$851$	1.87939	−	0.684040i	0.0644245	−	0.0234486i
$852$	−1.53209	+	1.28558i	−0.0524885	+	0.0440431i
$853$	−1.04189	−	5.90885i	−0.0356736	−	0.202315i	0.961762	−	0.273887i	$-0.0883095\pi$
$853$	−1.04189	−	5.90885i	−0.0356736	−	0.202315i	−0.997435	+	0.0715721i	$0.977198\pi$
$854$	−6.00000			−0.205316
$855$		0			0
$856$	−7.00000			−0.239255
$857$	2.08378	+	11.8177i	0.0711805	+	0.403685i	0.999492	+	0.0318805i	$0.0101496\pi$
$857$	2.08378	+	11.8177i	0.0711805	+	0.403685i	−0.928311	+	0.371804i	$0.878739\pi$
$858$	−1.53209	+	1.28558i	−0.0523047	+	0.0438888i
$859$	46.9846	−	17.1010i	1.60309	−	0.583479i	0.623037	−	0.782192i	$-0.285898\pi$
$859$	46.9846	−	17.1010i	1.60309	−	0.583479i	0.980058	+	0.198713i	$0.0636763\pi$
$860$	15.0351	+	5.47232i	0.512692	+	0.186605i
$861$	18.3851	+	15.4269i	0.626561	+	0.525747i
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	27.0000	+	46.7654i	0.919091	+	1.59191i	0.800799	+	0.598933i	$0.204408\pi$
$863$	27.0000	+	46.7654i	0.919091	+	1.59191i	0.118291	+	0.992979i	$0.462258\pi$
$864$	0.868241	−	4.92404i	0.0295382	−	0.167519i
$865$	−4.16756	+	23.6354i	−0.141701	+	0.803627i
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	18.3851	+	15.4269i	0.624030	+	0.523623i
$869$	−18.7939	−	6.84040i	−0.637538	−	0.232045i
$870$	−18.7939	+	6.84040i	−0.637171	+	0.231911i
$871$	−2.29813	+	1.92836i	−0.0778693	+	0.0653401i
$872$	−2.60472	−	14.7721i	−0.0882070	−	0.500247i
$873$	−4.00000			−0.135379
$874$		0			0
$875$	−72.0000			−2.43404
$876$	1.56283	+	8.86327i	0.0528033	+	0.299462i
$877$	−9.95858	+	8.35624i	−0.336277	+	0.282170i	−0.795252	−	0.606279i	$-0.792661\pi$
$877$	−9.95858	+	8.35624i	−0.336277	+	0.282170i	0.458975	+	0.888449i	$0.348217\pi$
$878$	−18.7939	+	6.84040i	−0.634262	+	0.230852i
$879$	8.45723	+	3.07818i	0.285255	+	0.103824i
$880$	−6.12836	−	5.14230i	−0.206587	−	0.173347i
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	−0.673645	−	0.739055i	$-0.735272\pi$
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	0.976863	+	0.213866i	$0.0686057\pi$
$882$	−2.00000	−	3.46410i	−0.0673435	−	0.116642i
$883$	5.90404	−	33.4835i	0.198687	−	1.12681i	−0.708383	−	0.705828i	$-0.750575\pi$
$883$	5.90404	−	33.4835i	0.198687	−	1.12681i	0.907070	−	0.420980i	$-0.138314\pi$
$884$	0.520945	−	2.95442i	0.0175213	−	0.0993680i
$885$	−30.0000	−	51.9615i	−1.00844	−	1.74667i
$886$	−13.0000	+	22.5167i	−0.436744	+	0.756462i
$887$	1.53209	+	1.28558i	0.0514425	+	0.0431654i	0.668146	−	0.744030i	$-0.267088\pi$
$887$	1.53209	+	1.28558i	0.0514425	+	0.0431654i	−0.616704	+	0.787195i	$0.711532\pi$
$888$	1.87939	+	0.684040i	0.0630680	+	0.0229549i
$889$	50.7434	−	18.4691i	1.70188	−	0.619433i
$890$		0			0
$891$	0.347296	+	1.96962i	0.0116349	+	0.0659846i
$892$	−14.0000			−0.468755
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.29813	+	1.92836i	−0.0767752	+	0.0644221i
$897$	0.939693	−	0.342020i	0.0313754	−	0.0114197i
$898$	−9.39693	−	3.42020i	−0.313579	−	0.114134i
$899$	30.6418	+	25.7115i	1.02196	+	0.857527i
$900$	11.0000	−	19.0526i	0.366667	−	0.635085i
$901$	−1.50000	−	2.59808i	−0.0499722	−	0.0865545i
$902$	−2.77837	+	15.7569i	−0.0925096	+	0.524648i
$903$	2.08378	−	11.8177i	0.0693438	−	0.393268i
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	−44.0000	+	76.2102i	−1.46261	+	2.53331i
$906$	1.53209	+	1.28558i	0.0509002	+	0.0427104i
$907$	49.8037	+	18.1271i	1.65371	+	0.601899i	0.989355	−	0.145522i	$-0.0464862\pi$
$907$	49.8037	+	18.1271i	1.65371	+	0.601899i	0.664350	+	0.747422i	$0.268708\pi$
$908$	−15.9748	+	5.81434i	−0.530142	+	0.192956i
$909$	−3.06418	+	2.57115i	−0.101632	+	0.0852797i
$910$	2.08378	+	11.8177i	0.0690766	+	0.391753i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	−12.0000			−0.397142
$914$	1.21554	+	6.89365i	0.0402064	+	0.228022i
$915$	−6.12836	+	5.14230i	−0.202597	+	0.169999i
$916$	9.39693	−	3.42020i	0.310483	−	0.113007i
$917$	−33.8289	−	12.3127i	−1.11713	−	0.406602i
$918$	11.4907	+	9.64181i	0.379249	+	0.318227i
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	−0.904309	−	0.426878i	$-0.859613\pi$
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	0.821842	+	0.569716i	$0.192947\pi$
$920$	2.00000	+	3.46410i	0.0659380	+	0.114208i
$921$	2.08378	−	11.8177i	0.0686628	−	0.389406i
$922$	4.86215	−	27.5746i	0.160126	−	0.908122i
$923$	1.00000	+	1.73205i	0.0329154	+	0.0570111i
$924$	−3.00000	+	5.19615i	−0.0986928	+	0.170941i
$925$	16.8530	+	14.1413i	0.554122	+	0.464964i
$926$	3.75877	+	1.36808i	0.123521	+	0.0449579i
$927$	11.2763	−	4.10424i	0.370363	−	0.134801i
$928$	−3.83022	+	3.21394i	−0.125733	+	0.105503i
$929$	−9.55065	−	54.1644i	−0.313347	−	1.77708i	−0.581344	−	0.813658i	$-0.697473\pi$
$929$	−9.55065	−	54.1644i	−0.313347	−	1.77708i	0.267998	−	0.963420i	$-0.413638\pi$
$930$	32.0000			1.04932
$931$		0			0
$932$	−6.00000			−0.196537
$933$	1.21554	+	6.89365i	0.0397949	+	0.225688i
$934$	1.53209	−	1.28558i	0.0501315	−	0.0420653i
$935$	22.5526	−	8.20848i	0.737550	−	0.268446i
$936$	−1.87939	−	0.684040i	−0.0614296	−	0.0223586i
$937$	−5.36231	−	4.49951i	−0.175179	−	0.146993i	0.550982	−	0.834517i	$-0.314253\pi$
$937$	−5.36231	−	4.49951i	−0.175179	−	0.146993i	−0.726162	+	0.687524i	$0.758698\pi$
$938$	−4.50000	+	7.79423i	−0.146930	+	0.254491i
$939$	−14.5000	−	25.1147i	−0.473190	−	0.819588i
$940$	−5.55674	+	31.5138i	−0.181241	+	1.02787i
$941$	−1.21554	+	6.89365i	−0.0396254	+	0.224727i	−0.998189	−	0.0601508i	$-0.980842\pi$
$941$	−1.21554	+	6.89365i	−0.0396254	+	0.224727i	0.958564	+	0.284878i	$0.0919529\pi$
$942$	−1.00000	−	1.73205i	−0.0325818	−	0.0564333i
$943$	4.00000	−	6.92820i	0.130258	−	0.225613i
$944$	−11.4907	−	9.64181i	−0.373989	−	0.313814i
$945$	−56.3816	−	20.5212i	−1.83409	−	0.667555i
$946$	7.51754	−	2.73616i	0.244416	−	0.0889603i
$947$	−9.19253	+	7.71345i	−0.298717	+	0.250653i	−0.779810	−	0.626016i	$-0.784684\pi$
$947$	−9.19253	+	7.71345i	−0.298717	+	0.250653i	0.481093	+	0.876670i	$0.340240\pi$
$948$	1.73648	+	9.84808i	0.0563983	+	0.319851i
$949$	9.00000			0.292152
$950$		0			0
$951$	27.0000			0.875535
$952$	−1.56283	−	8.86327i	−0.0506517	−	0.287260i
$953$	35.2380	−	29.5682i	1.14147	−	0.957809i	0.141986	−	0.989869i	$-0.454651\pi$
$953$	35.2380	−	29.5682i	1.14147	−	0.957809i	0.999486	+	0.0320597i	$0.0102067\pi$
$954$	−1.87939	+	0.684040i	−0.0608473	+	0.0221466i
$955$	26.3114	+	9.57656i	0.851417	+	0.309890i
$956$	11.4907	+	9.64181i	0.371635	+	0.311839i
$957$	−5.00000	+	8.66025i	−0.161627	+	0.279946i
$958$	−10.0000	−	17.3205i	−0.323085	−	0.559600i
$959$	−8.85606	+	50.2252i	−0.285977	+	1.62186i
$960$	−0.694593	+	3.93923i	−0.0224179	+	0.127138i
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	1.00000	−	1.73205i	0.0322413	−	0.0558436i
$963$	−10.7246	−	8.99903i	−0.345596	−	0.289990i
$964$	−7.51754	−	2.73616i	−0.242124	−	0.0881258i
$965$	22.5526	−	8.20848i	0.725995	−	0.264240i
$966$	2.29813	−	1.92836i	0.0739412	−	0.0620441i
$967$	8.33511	+	47.2708i	0.268039	+	1.52013i	0.760239	+	0.649643i	$0.225082\pi$
$967$	8.33511	+	47.2708i	0.268039	+	1.52013i	−0.492200	+	0.870482i	$0.663807\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	8.00000			0.256865
$971$	4.86215	+	27.5746i	0.156034	+	0.884912i	0.957835	+	0.287320i	$0.0927644\pi$
$971$	4.86215	+	27.5746i	0.156034	+	0.884912i	−0.801801	+	0.597591i	$0.796125\pi$
$972$	12.2567	−	10.2846i	0.393134	−	0.329879i
$973$		0			0
$974$	1.87939	+	0.684040i	0.0602194	+	0.0219181i
$975$	8.42649	+	7.07066i	0.269864	+	0.226442i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	4.00000	+	6.92820i	0.127971	+	0.221653i	0.922890	−	0.385063i	$-0.125820\pi$
$977$	4.00000	+	6.92820i	0.127971	+	0.221653i	−0.794919	+	0.606715i	$0.792487\pi$
$978$	2.77837	−	15.7569i	0.0888425	−	0.503851i
$979$		0			0
$980$	4.00000	+	6.92820i	0.127775	+	0.221313i
$981$	15.0000	−	25.9808i	0.478913	−	0.829502i
$982$	21.4492	+	17.9981i	0.684473	+	0.574341i
$983$	−5.63816	−	2.05212i	−0.179829	−	0.0654525i	0.250536	−	0.968107i	$-0.419393\pi$
$983$	−5.63816	−	2.05212i	−0.179829	−	0.0654525i	−0.430365	+	0.902655i	$0.641615\pi$
$984$	7.51754	−	2.73616i	0.239650	−	0.0872256i
$985$	−24.5134	+	20.5692i	−0.781063	+	0.655389i
$986$	−2.60472	−	14.7721i	−0.0829513	−	0.470440i
$987$	24.0000			0.763928
$988$		0			0
$989$	−4.00000			−0.127193
$990$	−2.77837	−	15.7569i	−0.0883024	−	0.500788i
$991$	6.12836	−	5.14230i	0.194674	−	0.163351i	−0.540241	−	0.841511i	$-0.681667\pi$
$991$	6.12836	−	5.14230i	0.194674	−	0.163351i	0.734914	+	0.678160i	$0.237222\pi$
$992$	7.51754	−	2.73616i	0.238682	−	0.0868732i
$993$	15.9748	+	5.81434i	0.506944	+	0.184513i
$994$	4.59627	+	3.85673i	0.145785	+	0.122328i
$995$	−50.0000	+	86.6025i	−1.58511	+	2.74549i
$996$	3.00000	+	5.19615i	0.0950586	+	0.164646i
$997$	4.86215	−	27.5746i	0.153986	−	0.873297i	−0.805721	−	0.592295i	$-0.798222\pi$
$997$	4.86215	−	27.5746i	0.153986	−	0.873297i	0.959707	−	0.281002i	$-0.0906668\pi$
$998$	−6.94593	+	39.3923i	−0.219869	+	1.24694i
$999$	5.00000	+	8.66025i	0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.d.389.1		6
19.2	odd	18		722.2.e.c.245.1		6
19.3	odd	18		722.2.e.c.423.1		6
19.4	even	9		722.2.c.f.429.1		2
19.5	even	9	inner	722.2.e.d.415.1		6
19.6	even	9		722.2.a.b.1.1		1
19.7	even	3	inner	722.2.e.d.99.1		6
19.8	odd	6		722.2.e.c.595.1		6
19.9	even	9		722.2.c.f.653.1		2
19.10	odd	18		722.2.c.d.653.1		2
19.11	even	3	inner	722.2.e.d.595.1		6
19.12	odd	6		722.2.e.c.99.1		6
19.13	odd	18		38.2.a.b.1.1	✓	1
19.14	odd	18		722.2.e.c.415.1		6
19.15	odd	18		722.2.c.d.429.1		2
19.16	even	9	inner	722.2.e.d.423.1		6
19.17	even	9	inner	722.2.e.d.245.1		6
19.18	odd	2		722.2.e.c.389.1		6
57.32	even	18		342.2.a.d.1.1		1
57.44	odd	18		6498.2.a.y.1.1		1
76.51	even	18		304.2.a.d.1.1		1
76.63	odd	18		5776.2.a.d.1.1		1
95.13	even	36		950.2.b.c.799.1		2
95.32	even	36		950.2.b.c.799.2		2
95.89	odd	18		950.2.a.b.1.1		1
133.13	even	18		1862.2.a.f.1.1		1
152.13	odd	18		1216.2.a.n.1.1		1
152.51	even	18		1216.2.a.g.1.1		1
209.32	even	18		4598.2.a.a.1.1		1
228.203	odd	18		2736.2.a.w.1.1		1
247.51	odd	18		6422.2.a.b.1.1		1
285.89	even	18		8550.2.a.u.1.1		1
380.279	even	18		7600.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.a.b.1.1	✓	1	19.13	odd	18
304.2.a.d.1.1		1	76.51	even	18
342.2.a.d.1.1		1	57.32	even	18
722.2.a.b.1.1		1	19.6	even	9
722.2.c.d.429.1		2	19.15	odd	18
722.2.c.d.653.1		2	19.10	odd	18
722.2.c.f.429.1		2	19.4	even	9
722.2.c.f.653.1		2	19.9	even	9
722.2.e.c.99.1		6	19.12	odd	6
722.2.e.c.245.1		6	19.2	odd	18
722.2.e.c.389.1		6	19.18	odd	2
722.2.e.c.415.1		6	19.14	odd	18
722.2.e.c.423.1		6	19.3	odd	18
722.2.e.c.595.1		6	19.8	odd	6
722.2.e.d.99.1		6	19.7	even	3	inner
722.2.e.d.245.1		6	19.17	even	9	inner
722.2.e.d.389.1		6	1.1	even	1	trivial
722.2.e.d.415.1		6	19.5	even	9	inner
722.2.e.d.423.1		6	19.16	even	9	inner
722.2.e.d.595.1		6	19.11	even	3	inner
950.2.a.b.1.1		1	95.89	odd	18
950.2.b.c.799.1		2	95.13	even	36
950.2.b.c.799.2		2	95.32	even	36
1216.2.a.g.1.1		1	152.51	even	18
1216.2.a.n.1.1		1	152.13	odd	18
1862.2.a.f.1.1		1	133.13	even	18
2736.2.a.w.1.1		1	228.203	odd	18
4598.2.a.a.1.1		1	209.32	even	18
5776.2.a.d.1.1		1	76.63	odd	18
6422.2.a.b.1.1		1	247.51	odd	18
6498.2.a.y.1.1		1	57.44	odd	18
7600.2.a.h.1.1		1	380.279	even	18
8550.2.a.u.1.1		1	285.89	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(3.75877 + 1.36808i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(3.75877 + 1.36808i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +(0.694593 - 3.93923i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.766044 + 0.642788i) q^{13} +(2.81908 + 1.02606i) q^{14} +(3.75877 - 1.36808i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.520945 + 2.95442i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(0.520945 + 2.95442i) q^{21} +(-1.53209 + 1.28558i) q^{22} +(0.939693 - 0.342020i) q^{23} +(0.939693 + 0.342020i) q^{24} +(8.42649 + 7.07066i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 + 4.33013i) q^{27} +(0.520945 - 2.95442i) q^{28} +(0.868241 - 4.92404i) q^{29} +(-2.00000 - 3.46410i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.87939 - 0.684040i) q^{33} +(2.81908 - 1.02606i) q^{34} +(-9.19253 + 7.71345i) q^{35} +(-0.347296 - 1.96962i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(0.694593 + 3.93923i) q^{40} +(6.12836 - 5.14230i) q^{41} +(2.81908 - 1.02606i) q^{42} +(-3.75877 - 1.36808i) q^{43} +(1.53209 + 1.28558i) q^{44} +(-4.00000 + 6.92820i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.38919 - 7.87846i) q^{47} +(0.173648 - 0.984808i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(5.50000 - 9.52628i) q^{50} +(2.29813 + 1.92836i) q^{51} +(-0.939693 - 0.342020i) q^{52} +(-0.939693 + 0.342020i) q^{53} +(3.83022 - 3.21394i) q^{54} +(-1.38919 - 7.87846i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(-2.60472 - 14.7721i) q^{59} +(-3.06418 + 2.57115i) q^{60} +(-1.87939 + 0.684040i) q^{61} +(7.51754 + 2.73616i) q^{62} +(-4.59627 - 3.85673i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.00000 + 3.46410i) q^{65} +(-0.347296 + 1.96962i) q^{66} +(-0.520945 + 2.95442i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(0.500000 - 0.866025i) q^{69} +(9.19253 + 7.71345i) q^{70} +(1.87939 + 0.684040i) q^{71} +(-1.87939 + 0.684040i) q^{72} +(6.89440 - 5.78509i) q^{73} +(-0.347296 - 1.96962i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(-0.173648 - 0.984808i) q^{78} +(7.66044 - 6.42788i) q^{79} +(3.75877 - 1.36808i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-6.12836 - 5.14230i) q^{82} +(3.00000 - 5.19615i) q^{83} +(-1.50000 - 2.59808i) q^{84} +(-2.08378 + 11.8177i) q^{85} +(-0.694593 + 3.93923i) q^{86} +(-2.50000 - 4.33013i) q^{87} +(1.00000 - 1.73205i) q^{88} +(7.51754 + 2.73616i) q^{90} +(-2.81908 + 1.02606i) q^{91} +(-0.766044 + 0.642788i) q^{92} +(1.38919 + 7.87846i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(0.347296 + 1.96962i) q^{97} +(-1.53209 + 1.28558i) q^{98} +(3.75877 - 1.36808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 9 * q^7 + 3 * q^8	\( 6 q - 9 q^{7} + 3 q^{8} - 6 q^{11} - 3 q^{12} + 12 q^{18} - 24 q^{20} + 3 q^{26} + 15 q^{27} - 12 q^{30} - 24 q^{31} + 12 q^{37} + 6 q^{39} - 24 q^{45} - 3 q^{46} - 6 q^{49} + 33 q^{50} - 18 q^{56} - 30 q^{58} - 3 q^{64} + 12 q^{65} - 9 q^{68} + 3 q^{69} + 66 q^{75} + 36 q^{77} + 18 q^{83} - 9 q^{84} - 15 q^{87} + 6 q^{88} - 48 q^{94} - 6 q^{96}+O(q^{100}) \) 6 * q - 9 * q^7 + 3 * q^8 - 6 * q^11 - 3 * q^12 + 12 * q^18 - 24 * q^20 + 3 * q^26 + 15 * q^27 - 12 * q^30 - 24 * q^31 + 12 * q^37 + 6 * q^39 - 24 * q^45 - 3 * q^46 - 6 * q^49 + 33 * q^50 - 18 * q^56 - 30 * q^58 - 3 * q^64 + 12 * q^65 - 9 * q^68 + 3 * q^69 + 66 * q^75 + 36 * q^77 + 18 * q^83 - 9 * q^84 - 15 * q^87 + 6 * q^88 - 48 * q^94 - 6 * q^96

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