LMFDB - Embedded newform 722.2.e.c.245.1

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			245.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	722.245
Dual form			722.2.e.c.389.1

$q$-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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	$-0.370993\pi$
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i	−0.836560	+	0.547875i	$0.815437\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	3.75877	−	1.36808i	1.68097	−	0.611824i	0.687531	−	0.726155i	$-0.258695\pi$
$5$	3.75877	−	1.36808i	1.68097	−	0.611824i	0.993443	+	0.114331i	$0.0364725\pi$
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−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	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.766044	+	0.642788i	−0.212463	+	0.178277i	−0.742808	−	0.669504i	$-0.766507\pi$
$13$	−0.766044	+	0.642788i	−0.212463	+	0.178277i	0.530346	+	0.847781i	$0.322062\pi$
$14$	−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	−0.854151	−	0.520026i	$-0.825922\pi$
$17$	0.520945	−	2.95442i	0.126348	−	0.716553i	0.980498	−	0.196527i	$-0.0629665\pi$
$18$	−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	0.438126	−	0.898914i	$-0.355642\pi$
$23$	0.939693	+	0.342020i	0.195939	+	0.0713161i	−0.242187	+	0.970230i	$0.577865\pi$
$24$	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	−0.952869	−	0.303384i	$-0.901884\pi$
$29$	−0.868241	−	4.92404i	−0.161228	−	0.914371i	0.791640	−	0.610988i	$-0.209227\pi$
$30$	−2.00000	+	3.46410i	−0.365148	+	0.632456i
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	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	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		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	$-0.492554\pi$
$41$	−6.12836	−	5.14230i	−0.957088	−	0.803092i	−0.980477	+	0.196634i	$0.936999\pi$
$42$	2.81908	+	1.02606i	0.434993	+	0.158325i
$43$	−3.75877	+	1.36808i	−0.573207	+	0.208630i	−0.612328	−	0.790604i	$-0.709767\pi$
$43$	−3.75877	+	1.36808i	−0.573207	+	0.208630i	0.0391204	+	0.999235i	$0.487544\pi$
$44$	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	0.901120	+	0.433569i	$0.142746\pi$
$47$	1.38919	+	7.87846i	0.202634	+	1.14919i	−0.698487	+	0.715623i	$0.746143\pi$
$48$	−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	$-0.367010\pi$
$53$	0.939693	+	0.342020i	0.129077	+	0.0469801i	−0.276674	+	0.960964i	$0.589232\pi$
$54$	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	−0.0430610	−	0.999072i	$-0.513711\pi$
$59$	2.60472	−	14.7721i	0.339106	−	1.92317i	0.382167	−	0.924093i	$-0.375178\pi$
$60$	3.06418	+	2.57115i	0.395584	+	0.331934i
$61$	−1.87939	−	0.684040i	−0.240631	−	0.0875824i	0.218890	−	0.975750i	$-0.429756\pi$
$61$	−1.87939	−	0.684040i	−0.240631	−	0.0875824i	−0.459520	+	0.888167i	$0.651979\pi$
$62$	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	0.999952	+	0.00976258i	$0.00310757\pi$
$67$	0.520945	+	2.95442i	0.0636435	+	0.360940i	−0.936309	+	0.351178i	$0.885781\pi$
$68$	−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	$-0.648977\pi$
$71$	−1.87939	+	0.684040i	−0.223042	+	0.0811806i	0.228082	+	0.973642i	$0.426755\pi$
$72$	1.87939	+	0.684040i	0.221488	+	0.0806149i
$73$	6.89440	+	5.78509i	0.806928	+	0.677093i	0.949873	−	0.312637i	$-0.101212\pi$
$73$	6.89440	+	5.78509i	0.806928	+	0.677093i	−0.142944	+	0.989731i	$0.545657\pi$
$74$	−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	$-0.467955\pi$
$79$	−7.66044	−	6.42788i	−0.861867	−	0.723193i	−0.962369	+	0.271744i	$0.912400\pi$
$80$	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	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$	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	$-0.722222\pi$
$89$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$90$	−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	$-0.976820\pi$
$97$	−0.347296	+	1.96962i	−0.0352626	+	0.199984i	0.962087	+	0.272743i	$0.0879308\pi$
$98$	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	−0.563373	−	0.826202i	$-0.690497\pi$
$101$	1.53209	−	1.28558i	0.152449	−	0.127920i	0.715822	+	0.698283i	$0.246052\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	−0.679525	−	0.733652i	$-0.737814\pi$
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	0.975124	+	0.221660i	$0.0711475\pi$
$104$	−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	$-0.0567953\pi$
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	−0.645766	+	0.763535i	$0.723462\pi$
$108$	3.83022	−	3.21394i	0.368563	−	0.309261i
$109$	14.0954	−	5.13030i	1.35009	−	0.491394i	0.437116	−	0.899405i	$-0.356000\pi$
$109$	14.0954	−	5.13030i	1.35009	−	0.491394i	0.912977	+	0.408011i	$0.133778\pi$
$110$	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	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		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	0.224927	−	0.974376i	$-0.427786\pi$
$127$	13.7888	−	11.5702i	1.22356	−	1.02669i	0.998631	−	0.0523116i	$-0.0166589\pi$
$128$	−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	−0.747614	−	0.664134i	$-0.768800\pi$
$131$	2.08378	−	11.8177i	0.182061	−	1.03252i	0.929674	−	0.368383i	$-0.120088\pi$
$132$	−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	0.917540	−	0.397643i	$-0.130172\pi$
$137$	15.9748	+	5.81434i	1.36482	+	0.496753i	0.447277	+	0.894396i	$0.352394\pi$
$138$	−0.939693	+	0.342020i	−0.0799919	+	0.0291147i
$139$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$139$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$140$	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	$-0.277778\pi$
$149$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$150$	−1.91013	+	10.8329i	−0.155961	+	0.884501i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		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	−0.265934	−	0.963991i	$-0.585680\pi$
$157$	1.87939	−	0.684040i	0.149991	−	0.0545924i	0.415925	+	0.909399i	$0.363458\pi$
$158$	−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	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	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	$-0.235197\pi$
$167$	11.2763	+	4.10424i	0.872587	+	0.317596i	0.133373	+	0.991066i	$0.457419\pi$
$168$	−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	0.919243	+	0.393692i	$0.128802\pi$
$173$	−1.04189	+	5.90885i	−0.0792134	+	0.449241i	−0.998456	+	0.0555496i	$0.982309\pi$
$174$	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	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	1.38919	+	7.87846i	0.103544	+	0.587226i
$181$	3.82026	+	21.6658i	0.283958	+	1.61040i	0.708985	+	0.705224i	$0.249153\pi$
$181$	3.82026	+	21.6658i	0.283958	+	1.61040i	−0.425027	+	0.905181i	$0.639736\pi$
$182$	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	$-0.347061\pi$
$193$	−4.59627	−	3.85673i	−0.330847	−	0.277613i	−0.793045	+	0.609163i	$0.791505\pi$
$194$	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	0.687618	−	0.726073i	$-0.258656\pi$
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	−0.972606	+	0.232458i	$0.925323\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	−4.34120	−	24.6202i	−0.307740	−	1.74528i	−0.610320	−	0.792155i	$-0.708959\pi$
$199$	−4.34120	−	24.6202i	−0.307740	−	1.74528i	0.302580	−	0.953124i	$-0.402152\pi$
$200$	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	−0.202136	−	0.979357i	$-0.564788\pi$
$211$	4.68850	−	26.5898i	0.322770	−	1.83052i	0.524906	−	0.851160i	$-0.324101\pi$
$212$	−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	$-0.766408\pi$
$223$	−13.1557	+	4.78828i	−0.880971	+	0.320647i	−0.138369	+	0.990381i	$0.544186\pi$
$224$	−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	$-0.690802\pi$
$227$	−17.0000			−1.12833			−0.564165	+	0.825662i	$0.690802\pi$
$228$		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	−0.150666	−	0.988585i	$-0.548142\pi$
$233$	5.63816	−	2.05212i	0.369368	−	0.134439i	0.520033	+	0.854146i	$0.325919\pi$
$234$	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	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$	−2.00000	−	3.46410i	−0.129099	−	0.223607i
$241$	−6.12836	+	5.14230i	−0.394762	+	0.331245i	−0.818465	−	0.574557i	$-0.805175\pi$
$241$	−6.12836	+	5.14230i	−0.394762	+	0.331245i	0.423703	+	0.905801i	$0.360730\pi$
$242$	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	0.282025	−	0.959407i	$-0.408994\pi$
$251$	−1.87939	−	0.684040i	−0.118626	−	0.0431762i	−0.400651	+	0.916231i	$0.631216\pi$
$252$	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	0.996987	+	0.0775665i	$0.0247150\pi$
$257$	1.38919	+	7.87846i	0.0866550	+	0.491445i	−0.910332	+	0.413878i	$0.864174\pi$
$258$	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	0.999213	−	0.0396557i	$-0.0126261\pi$
$263$	18.3851	+	15.4269i	1.13367	+	0.951264i	0.134458	+	0.990919i	$0.457071\pi$
$264$	−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	0.960565	+	0.278056i	$0.0896899\pi$
$269$	22.9813	+	19.2836i	1.40120	+	1.17574i	0.440632	+	0.897688i	$0.354755\pi$
$270$	18.7939	+	6.84040i	1.14376	+	0.416294i
$271$	−6.57785	+	2.39414i	−0.399576	+	0.145434i	−0.533989	−	0.845492i	$-0.679307\pi$
$271$	−6.57785	+	2.39414i	−0.399576	+	0.145434i	0.134413	+	0.990925i	$0.457085\pi$
$272$	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	0.0477206	+	0.998861i	$0.484804\pi$
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	−0.888899	+	0.458103i	$0.848529\pi$
$278$		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	$-0.312194\pi$
$281$	7.51754	+	2.73616i	0.448459	+	0.163226i	−0.107911	+	0.994161i	$0.534416\pi$
$282$	−6.12836	−	5.14230i	−0.364938	−	0.306220i
$283$	−1.04189	+	5.90885i	−0.0619339	+	0.351244i	0.938055	+	0.346487i	$0.112625\pi$
$283$	−1.04189	+	5.90885i	−0.0619339	+	0.351244i	−0.999989	+	0.00475755i	$0.998486\pi$
$284$	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	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$	−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	$-0.389030\pi$
$307$	−9.19253	−	7.71345i	−0.524646	−	0.440230i	−0.866248	+	0.499615i	$0.833475\pi$
$308$	−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	0.749565	−	0.661931i	$-0.230263\pi$
$311$	−3.50000	−	6.06218i	−0.198467	−	0.343755i	−0.948031	+	0.318177i	$0.896930\pi$
$312$	−0.500000	+	0.866025i	−0.0283069	+	0.0490290i
$313$	5.03580	+	28.5594i	0.284640	+	1.61427i	0.706568	+	0.707645i	$0.250242\pi$
$313$	5.03580	+	28.5594i	0.284640	+	1.61427i	−0.421928	+	0.906629i	$0.638647\pi$
$314$	−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	$-0.996161\pi$
$317$	−20.6832	+	17.3553i	−1.16168	+	0.974769i	−0.161757	+	0.986831i	$0.551716\pi$
$318$	−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	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$	−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	$-0.274210\pi$
$337$	30.0702	−	10.9446i	1.63803	−	0.596193i	0.986692	+	0.162598i	$0.0519875\pi$
$338$	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	−0.291082	−	0.956698i	$-0.594015\pi$
$347$	1.87939	−	0.684040i	0.100891	−	0.0367212i	0.391972	+	0.919977i	$0.371793\pi$
$348$	3.83022	−	3.21394i	0.205321	−	0.172285i
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	0.700609	−	0.713545i	$-0.252912\pi$
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	−0.968253	+	0.249973i	$0.919578\pi$
$350$	−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	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$	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	0.835634	+	0.549286i	$0.185100\pi$
$359$	−2.60472	+	14.7721i	−0.137472	+	0.779642i	−0.973106	+	0.230356i	$0.926011\pi$
$360$	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	0.121055	−	0.992646i	$-0.461372\pi$
$367$	21.4492	−	17.9981i	1.11964	−	0.939491i	0.998586	+	0.0531551i	$0.0169278\pi$
$368$	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	−0.947444	−	0.319921i	$-0.896344\pi$
$373$	−14.5000	−	25.1147i	−0.750782	−	1.30039i	0.196663	−	0.980471i	$-0.436990\pi$
$374$	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	$-0.374116\pi$
$379$	15.0000			0.770498			0.385249	+	0.922813i	$0.374116\pi$
$380$		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	$-0.509035\pi$
$383$	−19.9172	−	16.7125i	−1.01772	−	0.853968i	−0.989339	+	0.145629i	$0.953479\pi$
$384$	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	−0.771503	−	0.636226i	$-0.780495\pi$
$389$	−5.20945	−	29.5442i	−0.264129	−	1.49795i	0.507374	−	0.861726i	$-0.330616\pi$
$390$	−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	−0.929898	−	0.367817i	$-0.880105\pi$
$397$	1.38919	−	7.87846i	0.0697212	−	0.395409i	0.999619	−	0.0275914i	$-0.00878372\pi$
$398$	−25.0000			−1.25314
$399$		0			0
$400$	11.0000			0.550000
$401$	−1.38919	+	7.87846i	−0.0693726	+	0.393432i	0.930274	+	0.366864i	$0.119569\pi$
$401$	−1.38919	+	7.87846i	−0.0693726	+	0.393432i	−0.999647	+	0.0265672i	$0.991542\pi$
$402$	−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	−0.941854	−	0.336022i	$-0.890918\pi$
$409$	−3.47296	−	19.6962i	−0.171727	−	0.973912i	0.770127	−	0.637890i	$-0.220193\pi$
$410$	−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	$-0.380383\pi$
$421$	−9.95858	−	8.35624i	−0.485351	−	0.407258i	−0.852357	+	0.522961i	$0.824827\pi$
$422$	−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	$-0.864949\pi$
$431$	−13.7888	+	11.5702i	−0.664183	+	0.557316i	0.247154	+	0.968976i	$0.420505\pi$
$432$	−4.69846	+	1.71010i	−0.226055	+	0.0822773i
$433$	−13.1557	−	4.78828i	−0.632222	−	0.230110i	0.00597589	−	0.999982i	$-0.498098\pi$
$433$	−13.1557	−	4.78828i	−0.632222	−	0.230110i	−0.638198	+	0.769872i	$0.720320\pi$
$434$	−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	−0.782527	−	0.622617i	$-0.786069\pi$
$439$	3.47296	−	19.6962i	0.165756	−	0.940046i	0.948282	−	0.317429i	$-0.102820\pi$
$440$	−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	−0.978669	−	0.205442i	$-0.934137\pi$
$443$	−19.9172	+	16.7125i	−0.946293	+	0.794034i	0.0323767	+	0.999476i	$0.489692\pi$
$444$	−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	$-0.242492\pi$
$449$	−5.00000	−	8.66025i	−0.235965	−	0.408703i	−0.959553	+	0.281529i	$0.909158\pi$
$450$	−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	0.353409	−	0.935469i	$-0.385022\pi$
$461$	26.3114	−	9.57656i	1.22544	−	0.446025i	0.872035	+	0.489444i	$0.162800\pi$
$462$	−4.59627	+	3.85673i	−0.213838	+	0.179431i
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	0.815802	−	0.578331i	$-0.196296\pi$
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	−0.908750	+	0.417340i	$0.862962\pi$
$464$	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	−0.841960	−	0.539539i	$-0.818598\pi$
$467$	1.00000	−	1.73205i	0.0462745	−	0.0801498i	0.888235	+	0.459390i	$0.151932\pi$
$468$	−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	0.733588	−	0.679595i	$-0.237844\pi$
$479$	18.7939	+	6.84040i	0.858713	+	0.312546i	0.125125	+	0.992141i	$0.460067\pi$
$480$	−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	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$	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	0.0142436	−	0.999899i	$-0.495466\pi$
$491$	−21.4492	−	17.9981i	−0.967991	−	0.812241i	−0.982234	+	0.187658i	$0.939910\pi$
$492$	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	−0.993670	−	0.112337i	$-0.964166\pi$
$499$	−37.5877	+	13.6808i	−1.68266	+	0.612437i	−0.688987	+	0.724774i	$0.741944\pi$
$500$	−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	0.637475	+	0.770471i	$0.279979\pi$
$503$	6.77228	+	38.4075i	0.301961	+	1.71251i	−0.335514	+	0.942035i	$0.608910\pi$
$504$	−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	$-0.157379\pi$
$509$	28.1908	+	10.2606i	1.24953	+	0.454793i	0.369290	+	0.929314i	$0.379601\pi$
$510$	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	−0.377320	−	0.926083i	$-0.623154\pi$
$521$	14.0000	−	24.2487i	0.613351	−	1.06236i	0.990671	−	0.136272i	$-0.0435123\pi$
$522$	1.73648	+	9.84808i	0.0760037	+	0.431039i
$523$	5.03580	+	28.5594i	0.220200	+	1.24882i	0.871652	+	0.490126i	$0.163049\pi$
$523$	5.03580	+	28.5594i	0.220200	+	1.24882i	−0.651451	+	0.758690i	$0.725840\pi$
$524$	−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	0.991363	−	0.131147i	$-0.0418661\pi$
$541$	0.347296	+	1.96962i	0.0149314	+	0.0846804i	−0.976431	+	0.215828i	$0.930755\pi$
$542$	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	$-0.593164\pi$
$547$	−26.3114	−	9.57656i	−1.12499	−	0.409464i	−0.836472	+	0.548009i	$0.815386\pi$
$548$	−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	−0.0630631	−	0.998010i	$-0.520087\pi$
$557$	21.4492	−	17.9981i	0.908834	−	0.762602i	0.971897	+	0.235408i	$0.0756425\pi$
$558$	−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	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−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	$-0.183466\pi$
$569$	40.0000			1.67689			0.838444	+	0.544988i	$0.183466\pi$
$570$		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	0.937472	+	0.348060i	$0.113160\pi$
$577$	18.5000	+	32.0429i	0.770165	+	1.33397i	−0.167307	+	0.985905i	$0.553507\pi$
$578$	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	0.911128	+	0.412123i	$0.135213\pi$
$587$	−2.08378	+	11.8177i	−0.0860067	+	0.487768i	−0.997135	+	0.0756451i	$0.975898\pi$
$588$	−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	−0.411121	−	0.911581i	$-0.634863\pi$
$593$	−31.9495	−	11.6287i	−1.31201	−	0.477533i	−0.900890	+	0.434048i	$0.857085\pi$
$594$	−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	$-0.0555556\pi$
$599$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$600$	5.50000	−	9.52628i	0.224537	−	0.388909i
$601$	4.00000	+	6.92820i	0.163163	+	0.282607i	0.936002	−	0.351996i	$-0.114497\pi$
$601$	4.00000	+	6.92820i	0.163163	+	0.282607i	−0.772838	+	0.634603i	$0.781164\pi$
$602$	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	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$		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	−0.893868	−	0.448330i	$-0.852019\pi$
$613$	−31.9495	+	11.6287i	−1.29043	+	0.469678i	−0.396562	+	0.918008i	$0.629797\pi$
$614$	−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	0.980809	+	0.194973i	$0.0624619\pi$
$617$	3.12567	+	17.7265i	0.125835	+	0.713644i	−0.854974	+	0.518671i	$0.826427\pi$
$618$	1.04189	+	5.90885i	0.0419109	+	0.237689i
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$	−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	−0.334872	−	0.942264i	$-0.608693\pi$
$631$	−30.0702	−	10.9446i	−1.19707	−	0.435699i	−0.862202	+	0.506564i	$0.830915\pi$
$632$	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	$-0.922457\pi$
$641$	−39.4671	+	14.3648i	−1.55886	+	0.567377i	−0.588382	+	0.808583i	$0.700235\pi$
$642$	−6.57785	−	2.39414i	−0.259607	−	0.0944892i
$643$	−19.9172	−	16.7125i	−0.785456	−	0.659076i	0.159160	−	0.987253i	$-0.449121\pi$
$643$	−19.9172	−	16.7125i	−0.785456	−	0.659076i	−0.944616	+	0.328177i	$0.893566\pi$
$644$	−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	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$	−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	$-0.691174\pi$
$659$	3.83022	−	3.21394i	0.149204	−	0.125197i	0.714334	+	0.699805i	$0.246730\pi$
$660$	−7.51754	+	2.73616i	−0.292620	+	0.106505i
$661$	21.6129	+	7.86646i	0.840646	+	0.305970i	0.726220	−	0.687462i	$-0.241275\pi$
$661$	21.6129	+	7.86646i	0.840646	+	0.305970i	0.114425	+	0.993432i	$0.463497\pi$
$662$	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	0.0349191	+	0.999390i	$0.488883\pi$
$673$	−22.0000	+	38.1051i	−0.848038	+	1.46884i	−0.882957	+	0.469454i	$0.844451\pi$
$674$	−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	$-0.247037\pi$
$677$	−6.50000	−	11.2583i	−0.249815	−	0.432693i	−0.963474	+	0.267800i	$0.913703\pi$
$678$	−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	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$		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	−0.920348	−	0.391102i	$-0.872094\pi$
$691$	−21.0000	−	36.3731i	−0.798878	−	1.38370i	0.121470	−	0.992595i	$-0.461239\pi$
$692$	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	0.744048	+	0.668126i	$0.232903\pi$
$701$	−4.86215	+	27.5746i	−0.183641	+	1.04148i	−0.927689	+	0.373353i	$0.878208\pi$
$702$	−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	−0.962630	−	0.270821i	$-0.912705\pi$
$709$	−22.9813	+	19.2836i	−0.863082	+	0.724212i	0.0995477	+	0.995033i	$0.468260\pi$
$710$	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	0.568566	−	0.822638i	$-0.307498\pi$
$719$	−3.83022	−	3.21394i	−0.142843	−	0.119860i	−0.711409	+	0.702778i	$0.751943\pi$
$720$	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	−0.0283446	−	0.999598i	$-0.509024\pi$
$727$	15.9748	−	5.81434i	0.592472	−	0.215642i	0.620816	+	0.783956i	$0.286801\pi$
$728$	−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	−0.314482	−	0.949263i	$-0.601831\pi$
$733$	18.0000	−	31.1769i	0.664845	−	1.15155i	0.979327	−	0.202282i	$-0.0648358\pi$
$734$	−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	0.539250	+	0.842146i	$0.318708\pi$
$739$	−6.94593	+	39.3923i	−0.255510	+	1.44907i	−0.794760	+	0.606924i	$0.792403\pi$
$740$	8.00000			0.294086
$741$		0			0
$742$	−3.00000			−0.110133
$743$	−2.77837	+	15.7569i	−0.101929	+	0.578065i	0.890474	+	0.455034i	$0.150373\pi$
$743$	−2.77837	+	15.7569i	−0.101929	+	0.578065i	−0.992403	+	0.123032i	$0.960738\pi$
$744$	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	0.900913	+	0.434000i	$0.142898\pi$
$751$	5.55674	+	31.5138i	0.202768	+	1.14996i	−0.698145	+	0.715957i	$0.745991\pi$
$752$	−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	0.614521	−	0.788901i	$-0.289349\pi$
$757$	−1.53209	−	1.28558i	−0.0556847	−	0.0467250i	−0.670205	+	0.742176i	$0.733794\pi$
$758$	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	−0.873527	−	0.486775i	$-0.838173\pi$
$769$	−6.07769	−	34.4683i	−0.219167	−	1.24296i	0.654360	−	0.756183i	$-0.272938\pi$
$770$	−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	$-0.670475\pi$
$773$	6.89440	−	5.78509i	0.247974	−	0.208075i	0.758299	+	0.651906i	$0.226030\pi$
$774$	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	$-0.735348\pi$
$787$	8.50000	−	14.7224i	0.302992	−	0.524798i	0.976812	+	0.214097i	$0.0686810\pi$
$788$	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	$-0.483079\pi$
$797$	3.00000			0.106265			0.0531327	+	0.998587i	$0.483079\pi$
$798$		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	−0.703533	−	0.710663i	$-0.748395\pi$
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	0.967219	+	0.253946i	$0.0817284\pi$
$810$	2.00000	+	3.46410i	0.0702728	+	0.121716i
$811$	−2.29813	+	1.92836i	−0.0806984	+	0.0677140i	−0.682245	−	0.731124i	$-0.738996\pi$
$811$	−2.29813	+	1.92836i	−0.0806984	+	0.0677140i	0.601546	+	0.798838i	$0.294552\pi$
$812$	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	0.137664	−	0.990479i	$-0.456040\pi$
$821$	−11.2763	−	4.10424i	−0.393546	−	0.143239i	−0.531210	+	0.847240i	$0.678263\pi$
$822$	−15.9748	+	5.81434i	−0.557184	+	0.202798i
$823$	22.2153	−	18.6408i	0.774376	−	0.649779i	−0.167449	−	0.985881i	$-0.553553\pi$
$823$	22.2153	−	18.6408i	0.774376	−	0.649779i	0.941826	+	0.336102i	$0.109109\pi$
$824$	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	0.972078	+	0.234660i	$0.0753976\pi$
$827$	3.99391	+	22.6506i	0.138882	+	0.787638i	−0.833196	+	0.552978i	$0.813491\pi$
$828$	−1.00000	+	1.73205i	−0.0347524	+	0.0601929i
$829$	7.50000	+	12.9904i	0.260486	+	0.451175i	0.966371	−	0.257152i	$-0.0827840\pi$
$829$	7.50000	+	12.9904i	0.260486	+	0.451175i	−0.705885	+	0.708326i	$0.749451\pi$
$830$	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	$-0.165576\pi$
$839$	15.3209	+	12.8558i	0.528936	+	0.443830i	−0.338798	+	0.940859i	$0.610020\pi$
$840$	−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	−0.997435	−	0.0715721i	$-0.977198\pi$
$853$	−1.04189	+	5.90885i	−0.0356736	+	0.202315i	0.961762	+	0.273887i	$0.0883095\pi$
$854$	6.00000			0.205316
$855$		0			0
$856$	−7.00000			−0.239255
$857$	−2.08378	+	11.8177i	−0.0711805	+	0.403685i	0.928311	+	0.371804i	$0.121261\pi$
$857$	−2.08378	+	11.8177i	−0.0711805	+	0.403685i	−0.999492	+	0.0318805i	$0.989850\pi$
$858$	1.53209	+	1.28558i	0.0523047	+	0.0438888i
$859$	46.9846	+	17.1010i	1.60309	+	0.583479i	0.980058	−	0.198713i	$-0.0636763\pi$
$859$	46.9846	+	17.1010i	1.60309	+	0.583479i	0.623037	+	0.782192i	$0.285898\pi$
$860$	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	−0.118291	+	0.992979i	$0.537742\pi$
$863$	−27.0000	+	46.7654i	−0.919091	+	1.59191i	−0.800799	+	0.598933i	$0.795592\pi$
$864$	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	$-0.207339\pi$
$877$	9.95858	+	8.35624i	0.336277	+	0.282170i	−0.458975	+	0.888449i	$0.651783\pi$
$878$	−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	0.976863	−	0.213866i	$-0.0686057\pi$
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	−0.673645	+	0.739055i	$0.735272\pi$
$882$	2.00000	−	3.46410i	0.0673435	−	0.116642i
$883$	5.90404	+	33.4835i	0.198687	+	1.12681i	0.907070	+	0.420980i	$0.138314\pi$
$883$	5.90404	+	33.4835i	0.198687	+	1.12681i	−0.708383	+	0.705828i	$0.750575\pi$
$884$	−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	$-0.732912\pi$
$887$	−1.53209	+	1.28558i	−0.0514425	+	0.0431654i	0.616704	+	0.787195i	$0.288468\pi$
$888$	−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	$-0.953514\pi$
$907$	−49.8037	+	18.1271i	−1.65371	+	0.601899i	−0.664350	+	0.747422i	$0.731292\pi$
$908$	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	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		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	0.821842	−	0.569716i	$-0.192947\pi$
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	−0.904309	+	0.426878i	$0.859613\pi$
$920$	−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	0.267998	+	0.963420i	$0.413638\pi$
$929$	−9.55065	+	54.1644i	−0.313347	+	1.77708i	−0.581344	+	0.813658i	$0.697473\pi$
$930$	−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	−0.726162	−	0.687524i	$-0.758698\pi$
$937$	−5.36231	+	4.49951i	−0.175179	+	0.146993i	0.550982	+	0.834517i	$0.314253\pi$
$938$	−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	$-0.0191582\pi$
$941$	1.21554	+	6.89365i	0.0396254	+	0.224727i	−0.958564	+	0.284878i	$0.908047\pi$
$942$	−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	0.481093	−	0.876670i	$-0.340240\pi$
$947$	−9.19253	−	7.71345i	−0.298717	−	0.250653i	−0.779810	+	0.626016i	$0.784684\pi$
$948$	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	$-0.545349\pi$
$953$	−35.2380	−	29.5682i	−1.14147	−	0.957809i	−0.999486	+	0.0320597i	$0.989793\pi$
$954$	−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	−0.492200	−	0.870482i	$-0.663807\pi$
$967$	8.33511	−	47.2708i	0.268039	−	1.52013i	0.760239	−	0.649643i	$-0.225082\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	8.00000			0.256865
$971$	−4.86215	+	27.5746i	−0.156034	+	0.884912i	0.801801	+	0.597591i	$0.203875\pi$
$971$	−4.86215	+	27.5746i	−0.156034	+	0.884912i	−0.957835	+	0.287320i	$0.907236\pi$
$972$	−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	$-0.874180\pi$
$977$	−4.00000	+	6.92820i	−0.127971	+	0.221653i	0.794919	+	0.606715i	$0.207513\pi$
$978$	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	$-0.580607\pi$
$983$	5.63816	−	2.05212i	0.179829	−	0.0654525i	0.430365	+	0.902655i	$0.358385\pi$
$984$	−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	$-0.318333\pi$
$991$	−6.12836	−	5.14230i	−0.194674	−	0.163351i	−0.734914	+	0.678160i	$0.762778\pi$
$992$	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	0.959707	+	0.281002i	$0.0906668\pi$
$997$	4.86215	+	27.5746i	0.153986	+	0.873297i	−0.805721	+	0.592295i	$0.798222\pi$
$998$	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.c.245.1		6
19.2	odd	18		722.2.c.f.429.1		2
19.3	odd	18		722.2.a.b.1.1		1
19.4	even	9	inner	722.2.e.c.595.1		6
19.5	even	9		722.2.c.d.653.1		2
19.6	even	9	inner	722.2.e.c.99.1		6
19.7	even	3	inner	722.2.e.c.415.1		6
19.8	odd	6		722.2.e.d.423.1		6
19.9	even	9	inner	722.2.e.c.389.1		6
19.10	odd	18		722.2.e.d.389.1		6
19.11	even	3	inner	722.2.e.c.423.1		6
19.12	odd	6		722.2.e.d.415.1		6
19.13	odd	18		722.2.e.d.99.1		6
19.14	odd	18		722.2.c.f.653.1		2
19.15	odd	18		722.2.e.d.595.1		6
19.16	even	9		38.2.a.b.1.1	✓	1
19.17	even	9		722.2.c.d.429.1		2
19.18	odd	2		722.2.e.d.245.1		6
57.35	odd	18		342.2.a.d.1.1		1
57.41	even	18		6498.2.a.y.1.1		1
76.3	even	18		5776.2.a.d.1.1		1
76.35	odd	18		304.2.a.d.1.1		1
95.54	even	18		950.2.a.b.1.1		1
95.73	odd	36		950.2.b.c.799.1		2
95.92	odd	36		950.2.b.c.799.2		2
133.111	odd	18		1862.2.a.f.1.1		1
152.35	odd	18		1216.2.a.g.1.1		1
152.149	even	18		1216.2.a.n.1.1		1
209.54	odd	18		4598.2.a.a.1.1		1
228.35	even	18		2736.2.a.w.1.1		1
247.168	even	18		6422.2.a.b.1.1		1
285.149	odd	18		8550.2.a.u.1.1		1
380.339	odd	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	19.16	even	9
304.2.a.d.1.1		1	76.35	odd	18
342.2.a.d.1.1		1	57.35	odd	18
722.2.a.b.1.1		1	19.3	odd	18
722.2.c.d.429.1		2	19.17	even	9
722.2.c.d.653.1		2	19.5	even	9
722.2.c.f.429.1		2	19.2	odd	18
722.2.c.f.653.1		2	19.14	odd	18
722.2.e.c.99.1		6	19.6	even	9	inner
722.2.e.c.245.1		6	1.1	even	1	trivial
722.2.e.c.389.1		6	19.9	even	9	inner
722.2.e.c.415.1		6	19.7	even	3	inner
722.2.e.c.423.1		6	19.11	even	3	inner
722.2.e.c.595.1		6	19.4	even	9	inner
722.2.e.d.99.1		6	19.13	odd	18
722.2.e.d.245.1		6	19.18	odd	2
722.2.e.d.389.1		6	19.10	odd	18
722.2.e.d.415.1		6	19.12	odd	6
722.2.e.d.423.1		6	19.8	odd	6
722.2.e.d.595.1		6	19.15	odd	18
950.2.a.b.1.1		1	95.54	even	18
950.2.b.c.799.1		2	95.73	odd	36
950.2.b.c.799.2		2	95.92	odd	36
1216.2.a.g.1.1		1	152.35	odd	18
1216.2.a.n.1.1		1	152.149	even	18
1862.2.a.f.1.1		1	133.111	odd	18
2736.2.a.w.1.1		1	228.35	even	18
4598.2.a.a.1.1		1	209.54	odd	18
5776.2.a.d.1.1		1	76.3	even	18
6422.2.a.b.1.1		1	247.168	even	18
6498.2.a.y.1.1		1	57.41	even	18
7600.2.a.h.1.1		1	380.339	odd	18
8550.2.a.u.1.1		1	285.149	odd	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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