LMFDB - Embedded newform 726.2.h.j.215.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,2,Mod(161,726)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("726.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.h (of order $10$, degree $4$, 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:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			215.2
Root			$1.55470 + 0.763481i$ of defining polynomial
Character	$\chi$	$=$	726.215
Dual form			726.2.h.j.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(1.70654 + 0.296161i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.01556 - 0.654895i) q^{5} +(-0.245684 - 1.71454i) q^{6} +(2.01556 + 2.77418i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.82458 + 1.01082i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(1.70654 + 0.296161i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.01556 - 0.654895i) q^{5} +(-0.245684 - 1.71454i) q^{6} +(2.01556 + 2.77418i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.82458 + 1.01082i) q^{9} +2.11929i q^{10} +(-1.55470 + 0.763481i) q^{12} +(1.79505 - 0.583248i) q^{13} +(2.01556 - 2.77418i) q^{14} +(-3.24568 - 1.71454i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.59384 + 4.90534i) q^{17} +(0.0885088 - 2.99869i) q^{18} +(0.141616 - 0.194917i) q^{19} +(2.01556 - 0.654895i) q^{20} +(2.61803 + 5.33119i) q^{21} +4.97072i q^{23} +(1.20654 + 1.24268i) q^{24} +(-0.411491 - 0.298966i) q^{25} +(-1.10940 - 1.52696i) q^{26} +(4.52089 + 2.56155i) q^{27} +(-3.26124 - 1.05964i) q^{28} +(3.37235 - 2.45016i) q^{29} +(-0.627650 + 3.61665i) q^{30} +(2.02518 + 6.23285i) q^{31} -1.00000 q^{32} +5.15778 q^{34} +(-2.24568 - 6.91151i) q^{35} +(-2.87928 + 0.842471i) q^{36} +(7.14052 - 5.18789i) q^{37} +(-0.229139 - 0.0744518i) q^{38} +(3.23607 - 0.463712i) q^{39} +(-1.24568 - 1.71454i) q^{40} +(6.42001 + 4.66441i) q^{41} +(4.26124 - 4.13733i) q^{42} -6.51583i q^{43} +(-5.03112 - 3.88718i) q^{45} +(4.72744 - 1.53604i) q^{46} +(1.98077 - 2.72629i) q^{47} +(0.809017 - 1.53150i) q^{48} +(-1.47047 + 4.52566i) q^{49} +(-0.157176 + 0.483737i) q^{50} +(-4.17274 + 7.89915i) q^{51} +(-1.10940 + 1.52696i) q^{52} +(5.91040 - 1.92040i) q^{53} +(1.03914 - 5.09119i) q^{54} +3.42908i q^{56} +(0.299400 - 0.290694i) q^{57} +(-3.37235 - 2.45016i) q^{58} +(-1.62931 - 2.24256i) q^{59} +(3.63359 - 0.520675i) q^{60} +(-1.53975 - 0.500295i) q^{61} +(5.30198 - 3.85211i) q^{62} +(2.88889 + 9.87326i) q^{63} +(0.309017 + 0.951057i) q^{64} -4.00000 q^{65} -9.98396 q^{67} +(-1.59384 - 4.90534i) q^{68} +(-1.47214 + 8.48275i) q^{69} +(-5.87928 + 4.27155i) q^{70} +(-9.47214 - 3.07768i) q^{71} +(1.69098 + 2.47802i) q^{72} +(1.45756 + 2.00616i) q^{73} +(-7.14052 - 5.18789i) q^{74} +(-0.613685 - 0.632066i) q^{75} +0.240931i q^{76} +(-1.44102 - 2.93439i) q^{78} +(-10.7741 + 3.50072i) q^{79} +(-1.24568 + 1.71454i) q^{80} +(6.95647 + 5.71030i) q^{81} +(2.45223 - 7.54718i) q^{82} +(-2.12232 + 6.53182i) q^{83} +(-5.25163 - 2.77418i) q^{84} +(6.42497 - 8.84322i) q^{85} +(-6.19693 + 2.01350i) q^{86} +(6.48070 - 3.18254i) q^{87} +2.47254i q^{89} +(-2.14222 + 5.98608i) q^{90} +(5.23607 + 3.80423i) q^{91} +(-2.92172 - 4.02140i) q^{92} +(1.61012 + 11.2364i) q^{93} +(-3.20495 - 1.04135i) q^{94} +(-0.413086 + 0.300124i) q^{95} +(-1.70654 - 0.296161i) q^{96} +(-4.08582 - 12.5749i) q^{97} +4.75856 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 3 * q^6 + 2 * q^8 + 2 * q^9	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{8} + 2 q^{9} - 3 q^{12} - 21 q^{15} - 2 q^{16} - 10 q^{17} - 2 q^{18} + 15 q^{19} + 12 q^{21} - 2 q^{24} - 6 q^{25} + 10 q^{26} + 20 q^{27} - 5 q^{28} + 23 q^{29} - 9 q^{30} + 13 q^{31} - 8 q^{32} + 10 q^{34} - 13 q^{35} + 7 q^{36} + 6 q^{37} - 10 q^{38} + 8 q^{39} - 5 q^{40} + 2 q^{41} + 13 q^{42} - 8 q^{45} + 10 q^{46} - 10 q^{47} + 2 q^{48} - 18 q^{49} + q^{50} - 15 q^{51} + 10 q^{52} - 15 q^{53} + 15 q^{54} - 15 q^{57} - 23 q^{58} + 25 q^{59} + 4 q^{60} + 10 q^{61} + 2 q^{62} + 6 q^{63} - 2 q^{64} - 32 q^{65} - 2 q^{67} - 10 q^{68} + 24 q^{69} - 17 q^{70} - 40 q^{71} + 18 q^{72} - 5 q^{73} - 6 q^{74} + q^{75} - 8 q^{78} - 10 q^{79} - 5 q^{80} - 26 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} - 30 q^{85} - 25 q^{86} + 42 q^{87} - 2 q^{90} + 24 q^{91} - 10 q^{92} + 27 q^{93} - 40 q^{94} + 20 q^{95} - 2 q^{96} + 9 q^{97} - 22 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 3 * q^6 + 2 * q^8 + 2 * q^9 - 3 * q^12 - 21 * q^15 - 2 * q^16 - 10 * q^17 - 2 * q^18 + 15 * q^19 + 12 * q^21 - 2 * q^24 - 6 * q^25 + 10 * q^26 + 20 * q^27 - 5 * q^28 + 23 * q^29 - 9 * q^30 + 13 * q^31 - 8 * q^32 + 10 * q^34 - 13 * q^35 + 7 * q^36 + 6 * q^37 - 10 * q^38 + 8 * q^39 - 5 * q^40 + 2 * q^41 + 13 * q^42 - 8 * q^45 + 10 * q^46 - 10 * q^47 + 2 * q^48 - 18 * q^49 + q^50 - 15 * q^51 + 10 * q^52 - 15 * q^53 + 15 * q^54 - 15 * q^57 - 23 * q^58 + 25 * q^59 + 4 * q^60 + 10 * q^61 + 2 * q^62 + 6 * q^63 - 2 * q^64 - 32 * q^65 - 2 * q^67 - 10 * q^68 + 24 * q^69 - 17 * q^70 - 40 * q^71 + 18 * q^72 - 5 * q^73 - 6 * q^74 + q^75 - 8 * q^78 - 10 * q^79 - 5 * q^80 - 26 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 - 30 * q^85 - 25 * q^86 + 42 * q^87 - 2 * q^90 + 24 * q^91 - 10 * q^92 + 27 * q^93 - 40 * q^94 + 20 * q^95 - 2 * q^96 + 9 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	1.70654	+	0.296161i	0.985273	+	0.170989i
$3$	1.70654	+	0.296161i	0.985273	+	0.170989i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−2.01556	−	0.654895i	−0.901386	−	0.292878i	−0.178577	−	0.983926i	$-0.557149\pi$
$5$	−2.01556	−	0.654895i	−0.901386	−	0.292878i	−0.722809	+	0.691048i	$0.757149\pi$
$6$	−0.245684	−	1.71454i	−0.100300	−	0.699957i
$7$	2.01556	+	2.77418i	0.761810	+	1.04854i	0.997061	+	0.0766070i	$0.0244087\pi$
$7$	2.01556	+	2.77418i	0.761810	+	1.04854i	−0.235251	+	0.971935i	$0.575591\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.82458	+	1.01082i	0.941526	+	0.336941i
$10$			2.11929i			0.670177i
$11$		0			0
$11$		0			0
$12$	−1.55470	+	0.763481i	−0.448804	+	0.220398i
$13$	1.79505	−	0.583248i	0.497858	−	0.161764i	−0.0493154	−	0.998783i	$-0.515704\pi$
$13$	1.79505	−	0.583248i	0.497858	−	0.161764i	0.547173	+	0.837019i	$0.315704\pi$
$14$	2.01556	−	2.77418i	0.538681	−	0.741431i
$15$	−3.24568	−	1.71454i	−0.838032	−	0.442692i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.59384	+	4.90534i	−0.386564	+	1.18972i	0.548776	+	0.835970i	$0.315094\pi$
$17$	−1.59384	+	4.90534i	−0.386564	+	1.18972i	−0.935340	+	0.353751i	$0.884906\pi$
$18$	0.0885088	−	2.99869i	0.0208617	−	0.706799i
$19$	0.141616	−	0.194917i	0.0324889	−	0.0447171i	−0.792464	−	0.609919i	$-0.791202\pi$
$19$	0.141616	−	0.194917i	0.0324889	−	0.0447171i	0.824952	+	0.565202i	$0.191202\pi$
$20$	2.01556	−	0.654895i	0.450693	−	0.146439i
$21$	2.61803	+	5.33119i	0.571302	+	1.16336i
$22$		0			0
$23$			4.97072i			1.03647i	0.855239	+	0.518234i	$0.173410\pi$
$23$			4.97072i			1.03647i	−0.855239	+	0.518234i	$0.826590\pi$
$24$	1.20654	+	1.24268i	0.246285	+	0.253661i
$25$	−0.411491	−	0.298966i	−0.0822982	−	0.0597932i
$26$	−1.10940	−	1.52696i	−0.217572	−	0.299462i
$27$	4.52089	+	2.56155i	0.870046	+	0.492970i
$28$	−3.26124	−	1.05964i	−0.616317	−	0.200254i
$29$	3.37235	−	2.45016i	0.626230	−	0.454982i	−0.228862	−	0.973459i	$-0.573501\pi$
$29$	3.37235	−	2.45016i	0.626230	−	0.454982i	0.855092	+	0.518476i	$0.173501\pi$
$30$	−0.627650	+	3.61665i	−0.114593	+	0.660307i
$31$	2.02518	+	6.23285i	0.363732	+	1.11945i	0.950771	+	0.309894i	$0.100294\pi$
$31$	2.02518	+	6.23285i	0.363732	+	1.11945i	−0.587039	+	0.809559i	$0.699706\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	5.15778			0.884553
$35$	−2.24568	−	6.91151i	−0.379590	−	1.16826i
$36$	−2.87928	+	0.842471i	−0.479880	+	0.140412i
$37$	7.14052	−	5.18789i	1.17389	−	0.852884i	0.182425	−	0.983220i	$-0.441605\pi$
$37$	7.14052	−	5.18789i	1.17389	−	0.852884i	0.991470	+	0.130335i	$0.0416054\pi$
$38$	−0.229139	−	0.0744518i	−0.0371713	−	0.0120777i
$39$	3.23607	−	0.463712i	0.518186	−	0.0742533i
$40$	−1.24568	−	1.71454i	−0.196960	−	0.271092i
$41$	6.42001	+	4.66441i	1.00264	+	0.728459i	0.962652	−	0.270741i	$-0.0872688\pi$
$41$	6.42001	+	4.66441i	1.00264	+	0.728459i	0.0399856	+	0.999200i	$0.487269\pi$
$42$	4.26124	−	4.13733i	0.657524	−	0.638403i
$43$		−	6.51583i		−	0.993655i	−0.867849	−	0.496828i	$-0.834498\pi$
$43$		−	6.51583i		−	0.993655i	0.867849	−	0.496828i	$-0.165502\pi$
$44$		0			0
$45$	−5.03112	−	3.88718i	−0.749995	−	0.579466i
$46$	4.72744	−	1.53604i	0.697023	−	0.226476i
$47$	1.98077	−	2.72629i	0.288925	−	0.397671i	−0.639740	−	0.768591i	$-0.720958\pi$
$47$	1.98077	−	2.72629i	0.288925	−	0.397671i	0.928664	+	0.370921i	$0.120958\pi$
$48$	0.809017	−	1.53150i	0.116772	−	0.221053i
$49$	−1.47047	+	4.52566i	−0.210068	+	0.646522i
$50$	−0.157176	+	0.483737i	−0.0222280	+	0.0684107i
$51$	−4.17274	+	7.89915i	−0.584300	+	1.10610i
$52$	−1.10940	+	1.52696i	−0.153847	+	0.211752i
$53$	5.91040	−	1.92040i	0.811856	−	0.263788i	0.126472	−	0.991970i	$-0.459635\pi$
$53$	5.91040	−	1.92040i	0.811856	−	0.263788i	0.685384	+	0.728182i	$0.259635\pi$
$54$	1.03914	−	5.09119i	0.141409	−	0.692823i
$55$		0			0
$56$			3.42908i			0.458229i
$57$	0.299400	−	0.290694i	0.0396566	−	0.0385033i
$58$	−3.37235	−	2.45016i	−0.442811	−	0.321721i
$59$	−1.62931	−	2.24256i	−0.212118	−	0.291956i	0.689679	−	0.724115i	$-0.257752\pi$
$59$	−1.62931	−	2.24256i	−0.212118	−	0.291956i	−0.901797	+	0.432160i	$0.857752\pi$
$60$	3.63359	−	0.520675i	0.469095	−	0.0672189i
$61$	−1.53975	−	0.500295i	−0.197145	−	0.0640563i	0.208780	−	0.977963i	$-0.433051\pi$
$61$	−1.53975	−	0.500295i	−0.197145	−	0.0640563i	−0.405925	+	0.913906i	$0.633051\pi$
$62$	5.30198	−	3.85211i	0.673352	−	0.489219i
$63$	2.88889	+	9.87326i	0.363967	+	1.24391i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−4.00000			−0.496139
$66$		0			0
$67$	−9.98396			−1.21973			−0.609867	−	0.792504i	$-0.708777\pi$
$67$	−9.98396			−1.21973			−0.609867	+	0.792504i	$0.708777\pi$
$68$	−1.59384	−	4.90534i	−0.193282	−	0.594860i
$69$	−1.47214	+	8.48275i	−0.177224	+	1.02120i
$70$	−5.87928	+	4.27155i	−0.702708	+	0.510547i
$71$	−9.47214	−	3.07768i	−1.12414	−	0.365254i	−0.312791	−	0.949822i	$-0.601264\pi$
$71$	−9.47214	−	3.07768i	−1.12414	−	0.365254i	−0.811345	+	0.584568i	$0.801264\pi$
$72$	1.69098	+	2.47802i	0.199284	+	0.292037i
$73$	1.45756	+	2.00616i	0.170595	+	0.234803i	0.885751	−	0.464162i	$-0.153644\pi$
$73$	1.45756	+	2.00616i	0.170595	+	0.234803i	−0.715156	+	0.698965i	$0.753644\pi$
$74$	−7.14052	−	5.18789i	−0.830069	−	0.603080i
$75$	−0.613685	−	0.632066i	−0.0708623	−	0.0729847i
$76$			0.240931i			0.0276367i
$77$		0			0
$78$	−1.44102	−	2.93439i	−0.163163	−	0.332254i
$79$	−10.7741	+	3.50072i	−1.21218	+	0.393862i	−0.844229	−	0.535982i	$-0.819941\pi$
$79$	−10.7741	+	3.50072i	−1.21218	+	0.393862i	−0.367953	+	0.929844i	$0.619941\pi$
$80$	−1.24568	+	1.71454i	−0.139272	+	0.191691i
$81$	6.95647	+	5.71030i	0.772941	+	0.634478i
$82$	2.45223	−	7.54718i	0.270803	−	0.833447i
$83$	−2.12232	+	6.53182i	−0.232954	+	0.716960i	0.764432	+	0.644705i	$0.223020\pi$
$83$	−2.12232	+	6.53182i	−0.232954	+	0.716960i	−0.997386	+	0.0722554i	$0.976980\pi$
$84$	−5.25163	−	2.77418i	−0.573000	−	0.302688i
$85$	6.42497	−	8.84322i	0.696886	−	0.959181i
$86$	−6.19693	+	2.01350i	−0.668232	+	0.217122i
$87$	6.48070	−	3.18254i	0.694804	−	0.341204i
$88$		0			0
$89$			2.47254i			0.262088i	0.991377	+	0.131044i	$0.0418330\pi$
$89$			2.47254i			0.262088i	−0.991377	+	0.131044i	$0.958167\pi$
$90$	−2.14222	+	5.98608i	−0.225810	+	0.630989i
$91$	5.23607	+	3.80423i	0.548889	+	0.398791i
$92$	−2.92172	−	4.02140i	−0.304610	−	0.419260i
$93$	1.61012	+	11.2364i	0.166962	+	1.16516i
$94$	−3.20495	−	1.04135i	−0.330565	−	0.107407i
$95$	−0.413086	+	0.300124i	−0.0423817	+	0.0307921i
$96$	−1.70654	−	0.296161i	−0.174173	−	0.0302268i
$97$	−4.08582	−	12.5749i	−0.414852	−	1.27678i	−0.912383	−	0.409338i	$-0.865760\pi$
$97$	−4.08582	−	12.5749i	−0.414852	−	1.27678i	0.497531	−	0.867446i	$-0.334240\pi$
$98$	4.75856			0.480687
$99$		0			0
$100$	0.508631			0.0508631
$101$	−0.760259	−	2.33984i	−0.0756486	−	0.232822i	0.906081	−	0.423105i	$-0.139060\pi$
$101$	−0.760259	−	2.33984i	−0.0756486	−	0.232822i	−0.981729	+	0.190282i	$0.939060\pi$
$102$	8.80198	+	1.52754i	0.871526	+	0.151249i
$103$	3.72914	−	2.70938i	0.367443	−	0.266963i	−0.388707	−	0.921361i	$-0.627078\pi$
$103$	3.72914	−	2.70938i	0.367443	−	0.266963i	0.756150	+	0.654399i	$0.227078\pi$
$104$	1.79505	+	0.583248i	0.176019	+	0.0571921i
$105$	−1.78544	−	12.4599i	−0.174241	−	1.21596i
$106$	−3.65283	−	5.02768i	−0.354794	−	0.488332i
$107$	−14.6716	−	10.6596i	−1.41836	−	1.03050i	−0.992039	−	0.125928i	$-0.959809\pi$
$107$	−14.6716	−	10.6596i	−1.41836	−	1.03050i	−0.426322	−	0.904572i	$-0.640191\pi$
$108$	−5.16312	+	0.584981i	−0.496821	+	0.0562898i
$109$			0.702783i			0.0673144i	0.999433	+	0.0336572i	$0.0107154\pi$
$109$			0.702783i			0.0673144i	−0.999433	+	0.0336572i	$0.989285\pi$
$110$		0			0
$111$	13.7221	−	6.73861i	1.30244	−	0.639601i
$112$	3.26124	−	1.05964i	0.308159	−	0.100127i
$113$	2.51821	−	3.46601i	0.236893	−	0.326055i	−0.673974	−	0.738755i	$-0.735414\pi$
$113$	2.51821	−	3.46601i	0.236893	−	0.326055i	0.910867	+	0.412700i	$0.135414\pi$
$114$	−0.368986	−	0.194917i	−0.0345587	−	0.0182557i
$115$	3.25530	−	10.0188i	0.303558	−	0.934257i
$116$	−1.28812	+	3.96443i	−0.119599	+	0.368089i
$117$	5.65982	+	0.167054i	0.523251	+	0.0154442i
$118$	−1.62931	+	2.24256i	−0.149990	+	0.206444i
$119$	−16.8208	+	5.46541i	−1.54196	+	0.501013i
$120$	−1.61803	−	3.29486i	−0.147706	−	0.300778i
$121$		0			0
$122$			1.61899i			0.146576i
$123$	9.57461	+	9.86138i	0.863314	+	0.889171i
$124$	−5.30198	−	3.85211i	−0.476132	−	0.345930i
$125$	6.86202	+	9.44475i	0.613757	+	0.844765i
$126$	8.49731	−	5.79851i	0.757001	−	0.516572i
$127$	16.6803	+	5.41975i	1.48013	+	0.480925i	0.934153	−	0.356872i	$-0.116157\pi$
$127$	16.6803	+	5.41975i	1.48013	+	0.480925i	0.545982	+	0.837797i	$0.316157\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	1.92974	−	11.1195i	0.169904	−	0.979022i
$130$	1.23607	+	3.80423i	0.108410	+	0.333653i
$131$	−4.82298			−0.421386			−0.210693	−	0.977552i	$-0.567572\pi$
$131$	−4.82298			−0.421386			−0.210693	+	0.977552i	$0.567572\pi$
$132$		0			0
$133$	0.826171			0.0716381
$134$	3.08521	+	9.49531i	0.266522	+	0.820270i
$135$	−7.43459	−	8.12366i	−0.639868	−	0.699173i
$136$	−4.17274	+	3.03167i	−0.357809	+	0.259964i
$137$	−17.1743	−	5.58026i	−1.46730	−	0.476754i	−0.537008	−	0.843577i	$-0.680445\pi$
$137$	−17.1743	−	5.58026i	−1.46730	−	0.476754i	−0.930291	+	0.366823i	$0.880445\pi$
$138$	8.52249	−	1.22123i	0.725482	−	0.103958i
$139$	−0.581539	−	0.800420i	−0.0493255	−	0.0678907i	0.783642	−	0.621213i	$-0.213360\pi$
$139$	−0.581539	−	0.800420i	−0.0493255	−	0.0678907i	−0.832967	+	0.553322i	$0.813360\pi$
$140$	5.87928	+	4.27155i	0.496890	+	0.361012i
$141$	4.18769	−	4.06591i	0.352667	−	0.342411i
$142$			9.95959i			0.835790i
$143$		0			0
$144$	1.83419	−	2.37397i	0.152849	−	0.197831i
$145$	−8.40177	+	2.72990i	−0.697729	+	0.226706i
$146$	1.45756	−	2.00616i	0.120629	−	0.166031i
$147$	−3.84975	+	7.28773i	−0.317522	+	0.601082i
$148$	−2.72744	+	8.39419i	−0.224194	+	0.689998i
$149$	4.32227	−	13.3026i	0.354094	−	1.08979i	−0.602439	−	0.798165i	$-0.705804\pi$
$149$	4.32227	−	13.3026i	0.354094	−	1.08979i	0.956533	−	0.291624i	$-0.0941956\pi$
$150$	−0.411491	+	0.778968i	−0.0335981	+	0.0636025i
$151$	3.71979	−	5.11985i	0.302712	−	0.416648i	−0.630379	−	0.776288i	$-0.717100\pi$
$151$	3.71979	−	5.11985i	0.302712	−	0.416648i	0.933091	+	0.359640i	$0.117100\pi$
$152$	0.229139	−	0.0744518i	0.0185856	−	0.00603884i
$153$	−9.46037	+	12.2444i	−0.764826	+	0.989903i
$154$		0			0
$155$		−	13.8890i		−	1.11559i
$156$	−2.34547	+	2.27726i	−0.187788	+	0.182327i
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$	6.65877	+	9.16501i	0.529743	+	0.729129i
$159$	10.6551	−	1.52682i	0.845004	−	0.121085i
$160$	2.01556	+	0.654895i	0.159344	+	0.0517740i
$161$	−13.7897	+	10.0188i	−1.08678	+	0.789591i
$162$	3.28115	−	8.38057i	0.257792	−	0.658440i
$163$	2.64222	+	8.13193i	0.206955	+	0.636942i	0.999627	+	0.0272943i	$0.00868912\pi$
$163$	2.64222	+	8.13193i	0.206955	+	0.636942i	−0.792672	+	0.609648i	$0.791311\pi$
$164$	−7.93557			−0.619664
$165$		0			0
$166$	6.86796			0.533057
$167$	−0.508631	−	1.56541i	−0.0393591	−	0.121135i	0.929446	−	0.368957i	$-0.120285\pi$
$167$	−0.508631	−	1.56541i	−0.0393591	−	0.121135i	−0.968805	+	0.247822i	$0.920285\pi$
$168$	−1.01556	+	5.85186i	−0.0783521	+	0.451481i
$169$	−7.63519	+	5.54729i	−0.587322	+	0.426715i
$170$	−10.3958	−	3.37781i	−0.797323	−	0.259066i
$171$	0.597032	−	0.407411i	0.0456562	−	0.0311555i
$172$	3.82991	+	5.27142i	0.292028	+	0.401942i
$173$	−2.83854	−	2.06232i	−0.215810	−	0.156795i	0.474628	−	0.880186i	$-0.342582\pi$
$173$	−2.83854	−	2.06232i	−0.215810	−	0.156795i	−0.690439	+	0.723391i	$0.742582\pi$
$174$	−5.02942	−	5.18005i	−0.381279	−	0.392699i
$175$		−	1.74413i		−	0.131844i
$176$		0			0
$177$	−2.11633	−	4.30956i	−0.159073	−	0.323926i
$178$	2.35152	−	0.764056i	0.176254	−	0.0572684i
$179$	−7.80160	+	10.7380i	−0.583119	+	0.802595i	−0.994033	−	0.109079i	$-0.965210\pi$
$179$	−7.80160	+	10.7380i	−0.583119	+	0.802595i	0.410914	+	0.911674i	$0.365210\pi$
$180$	6.35509	+	0.187575i	0.473680	+	0.0139810i
$181$	−2.29709	+	7.06971i	−0.170741	+	0.525488i	−0.999413	−	0.0342467i	$-0.989097\pi$
$181$	−2.29709	+	7.06971i	−0.170741	+	0.525488i	0.828672	+	0.559734i	$0.189097\pi$
$182$	2.00000	−	6.15537i	0.148250	−	0.456266i
$183$	−2.47948	−	1.30979i	−0.183289	−	0.0968225i
$184$	−2.92172	+	4.02140i	−0.215392	+	0.296461i
$185$	−17.7897	+	5.78022i	−1.30792	+	0.424970i
$186$	10.1889	−	5.00356i	0.747087	−	0.366879i
$187$		0			0
$188$			3.36988i			0.245774i
$189$	2.00594	+	17.7047i	0.145911	+	1.28783i
$190$	0.413086	+	0.300124i	0.0299684	+	0.0217733i
$191$	−1.52249	−	2.09553i	−0.110163	−	0.151627i	0.750375	−	0.661012i	$-0.229873\pi$
$191$	−1.52249	−	2.09553i	−0.110163	−	0.151627i	−0.860539	+	0.509385i	$0.829873\pi$
$192$	0.245684	+	1.71454i	0.0177307	+	0.123736i
$193$	−18.5702	−	6.03383i	−1.33671	−	0.434325i	−0.448511	−	0.893777i	$-0.648046\pi$
$193$	−18.5702	−	6.03383i	−1.33671	−	0.434325i	−0.888202	+	0.459453i	$0.848046\pi$
$194$	−10.6968	+	7.77169i	−0.767987	+	0.557975i
$195$	−6.82617	−	1.18465i	−0.488832	−	0.0848342i
$196$	−1.47047	−	4.52566i	−0.105034	−	0.323261i
$197$	−5.38713			−0.383817			−0.191908	−	0.981413i	$-0.561468\pi$
$197$	−5.38713			−0.383817			−0.191908	+	0.981413i	$0.561468\pi$
$198$		0			0
$199$	7.38713			0.523659			0.261830	−	0.965114i	$-0.415674\pi$
$199$	7.38713			0.523659			0.261830	+	0.965114i	$0.415674\pi$
$200$	−0.157176	−	0.483737i	−0.0111140	−	0.0342054i
$201$	−17.0380	−	2.95686i	−1.20177	−	0.208561i
$202$	−1.99038	+	1.44610i	−0.140043	+	0.101747i
$203$	13.5943	+	4.41707i	0.954136	+	0.310018i
$204$	−1.26719	−	8.84322i	−0.0887209	−	0.619149i
$205$	−9.88522	−	13.6058i	−0.690414	−	0.950273i
$206$	−3.72914	−	2.70938i	−0.259821	−	0.188771i
$207$	−5.02453	+	14.0402i	−0.349229	+	0.975860i
$208$		−	1.88743i		−	0.130870i
$209$		0			0
$210$	−11.2983	+	5.54836i	−0.779657	+	0.382873i
$211$	8.14317	−	2.64588i	0.560599	−	0.182150i	−0.0149917	−	0.999888i	$-0.504772\pi$
$211$	8.14317	−	2.64588i	0.560599	−	0.182150i	0.575591	+	0.817738i	$0.304772\pi$
$212$	−3.65283	+	5.02768i	−0.250877	+	0.345303i
$213$	−15.2531	−	8.05748i	−1.04513	−	0.552089i
$214$	−5.60407	+	17.2475i	−0.383086	+	1.17902i
$215$	−4.26719	+	13.1331i	−0.291020	+	0.895667i
$216$	2.15184	+	4.72965i	0.146414	+	0.321812i
$217$	−13.2092	+	18.1809i	−0.896698	+	1.23420i
$218$	0.668387	−	0.217172i	0.0452689	−	0.0147087i
$219$	1.89324	+	3.85527i	0.127934	+	0.260515i
$220$		0			0
$221$			9.73495i			0.654844i
$222$	−10.6492	−	10.9681i	−0.714724	−	0.736131i
$223$	−0.0407361	−	0.0295965i	−0.00272789	−	0.00198193i	0.586420	−	0.810007i	$-0.300537\pi$
$223$	−0.0407361	−	0.0295965i	−0.00272789	−	0.00198193i	−0.589148	+	0.808025i	$0.700537\pi$
$224$	−2.01556	−	2.77418i	−0.134670	−	0.185358i
$225$	−0.860086	−	1.26040i	−0.0573391	−	0.0840265i
$226$	−4.07454	−	1.32390i	−0.271035	−	0.0880645i
$227$	11.5589	−	8.39806i	0.767194	−	0.557399i	−0.133914	−	0.990993i	$-0.542755\pi$
$227$	11.5589	−	8.39806i	0.767194	−	0.557399i	0.901108	+	0.433594i	$0.142755\pi$
$228$	−0.0713545	+	0.411159i	−0.00472557	+	0.0272297i
$229$	−9.34547	−	28.7624i	−0.617566	−	1.90067i	−0.345783	−	0.938314i	$-0.612387\pi$
$229$	−9.34547	−	28.7624i	−0.617566	−	1.90067i	−0.271783	−	0.962359i	$-0.587613\pi$
$230$	−10.5344			−0.694616
$231$		0			0
$232$	4.16845			0.273672
$233$	0.874011	+	2.68993i	0.0572583	+	0.176223i	0.975595	−	0.219576i	$-0.0704675\pi$
$233$	0.874011	+	2.68993i	0.0572583	+	0.176223i	−0.918337	+	0.395799i	$0.870468\pi$
$234$	−1.59010	−	5.43443i	−0.103948	−	0.355260i
$235$	−5.77779	+	4.19781i	−0.376901	+	0.273835i
$236$	2.63628	+	0.856580i	0.171607	+	0.0557586i
$237$	−19.4233	+	2.78326i	−1.26168	+	0.180792i
$238$	10.3958	+	14.3086i	0.673861	+	0.927490i
$239$	0.918528	+	0.667349i	0.0594146	+	0.0431672i	0.617096	−	0.786888i	$-0.288309\pi$
$239$	0.918528	+	0.667349i	0.0594146	+	0.0431672i	−0.557682	+	0.830055i	$0.688309\pi$
$240$	−2.63359	+	2.55701i	−0.169998	+	0.165054i
$241$		−	15.0464i		−	0.969223i	−0.874730	−	0.484611i	$-0.838961\pi$
$241$		−	15.0464i		−	0.969223i	0.874730	−	0.484611i	$-0.161039\pi$
$242$		0			0
$243$	10.1803	+	11.8051i	0.653069	+	0.757298i
$244$	1.53975	−	0.500295i	0.0985724	−	0.0320281i
$245$	5.92766	−	8.15872i	0.378704	−	0.521242i
$246$	6.42001	−	12.1533i	0.409325	−	0.774868i
$247$	0.140523	−	0.432484i	0.00894124	−	0.0275183i
$248$	−2.02518	+	6.23285i	−0.128599	+	0.395786i
$249$	−5.55630	+	10.5183i	−0.352116	+	0.666569i
$250$	6.86202	−	9.44475i	0.433992	−	0.597339i
$251$	9.16478	−	2.97782i	0.578476	−	0.187958i	−0.00514185	−	0.999987i	$-0.501637\pi$
$251$	9.16478	−	2.97782i	0.578476	−	0.187958i	0.583618	+	0.812029i	$0.301637\pi$
$252$	−8.14052	−	6.28959i	−0.512805	−	0.396207i
$253$		0			0
$254$		−	17.5387i		−	1.10047i
$255$	13.5835	−	13.1885i	0.850632	−	0.825896i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−7.85036	−	10.8051i	−0.489692	−	0.674003i	0.490639	−	0.871363i	$-0.336763\pi$
$257$	−7.85036	−	10.8051i	−0.489692	−	0.674003i	−0.980331	+	0.197360i	$0.936763\pi$
$258$	−11.1716	+	1.60084i	−0.695516	+	0.0996639i
$259$	28.7843	+	9.35259i	1.78857	+	0.581141i
$260$	3.23607	−	2.35114i	0.200692	−	0.145812i
$261$	12.0021	−	3.51180i	0.742914	−	0.217375i
$262$	1.49038	+	4.58693i	0.0920762	+	0.283381i
$263$	9.33677			0.575730			0.287865	−	0.957671i	$-0.407055\pi$
$263$	9.33677			0.575730			0.287865	+	0.957671i	$0.407055\pi$
$264$		0			0
$265$	−13.1704			−0.809053
$266$	−0.255301	−	0.785736i	−0.0156535	−	0.0481765i
$267$	−0.732270	+	4.21949i	−0.0448142	+	0.258229i
$268$	8.07719	−	5.86842i	0.493393	−	0.358471i
$269$	12.9581	+	4.21035i	0.790071	+	0.256710i	0.676134	−	0.736778i	$-0.263654\pi$
$269$	12.9581	+	4.21035i	0.790071	+	0.256710i	0.113937	+	0.993488i	$0.463654\pi$
$270$	−5.42865	+	9.58106i	−0.330377	+	0.583085i
$271$	−2.75734	−	3.79515i	−0.167496	−	0.230539i	0.717015	−	0.697058i	$-0.245508\pi$
$271$	−2.75734	−	3.79515i	−0.167496	−	0.230539i	−0.884511	+	0.466519i	$0.845508\pi$
$272$	4.17274	+	3.03167i	0.253009	+	0.183822i
$273$	7.80891	+	8.04280i	0.472617	+	0.486772i
$274$			18.0581i			1.09093i
$275$		0			0
$276$	−3.79505	−	7.72799i	−0.228435	−	0.465170i
$277$	7.87652	−	2.55924i	0.473254	−	0.153770i	−0.0626723	−	0.998034i	$-0.519962\pi$
$277$	7.87652	−	2.55924i	0.473254	−	0.153770i	0.535927	+	0.844264i	$0.319962\pi$
$278$	−0.581539	+	0.800420i	−0.0348784	+	0.0480060i
$279$	−0.580052	+	19.6523i	−0.0347268	+	1.17655i
$280$	2.24568	−	6.91151i	0.134205	−	0.413041i
$281$	3.91369	−	12.0451i	0.233471	−	0.718551i	−0.763849	−	0.645395i	$-0.776693\pi$
$281$	3.91369	−	12.0451i	0.233471	−	0.718551i	0.997320	−	0.0731563i	$-0.0233072\pi$
$282$	−5.16097	−	2.72629i	−0.307332	−	0.162348i
$283$	−13.2896	+	18.2916i	−0.789985	+	1.08732i	0.204125	+	0.978945i	$0.434565\pi$
$283$	−13.2896	+	18.2916i	−0.789985	+	1.08732i	−0.994110	+	0.108377i	$0.965435\pi$
$284$	9.47214	−	3.07768i	0.562068	−	0.182627i
$285$	−0.793834	+	0.389835i	−0.0470226	+	0.0230918i
$286$		0			0
$287$			27.2117i			1.60625i
$288$	−2.82458	−	1.01082i	−0.166440	−	0.0595634i
$289$	−7.76878	−	5.64435i	−0.456987	−	0.332021i
$290$	5.19258	+	7.14697i	0.304919	+	0.419685i
$291$	−3.24844	−	22.6696i	−0.190427	−	1.32892i
$292$	−2.35838	−	0.766285i	−0.138014	−	0.0448435i
$293$	20.2998	−	14.7487i	1.18593	−	0.861626i	0.193099	−	0.981179i	$-0.438146\pi$
$293$	20.2998	−	14.7487i	1.18593	−	0.861626i	0.992828	+	0.119553i	$0.0381462\pi$
$294$	8.12068	+	1.40930i	0.473608	+	0.0821921i
$295$	1.81534	+	5.58703i	0.105693	+	0.325290i
$296$	8.82617			0.513011
$297$		0			0
$298$	−13.9871			−0.810254
$299$	2.89916	+	8.92270i	0.167663	+	0.516013i
$300$	0.868001	+	0.150637i	0.0501140	+	0.00869703i
$301$	18.0761	−	13.1331i	1.04189	−	0.756977i
$302$	−6.01875	−	1.95561i	−0.346340	−	0.112533i
$303$	−0.604445	−	4.21819i	−0.0347245	−	0.242329i
$304$	−0.141616	−	0.194917i	−0.00812222	−	0.0111793i
$305$	2.77582	+	2.01675i	0.158943	+	0.115479i
$306$	14.5686	+	5.21361i	0.832829	+	0.298042i
$307$		−	16.0682i		−	0.917058i	−0.888679	−	0.458529i	$-0.848377\pi$
$307$		−	16.0682i		−	0.917058i	0.888679	−	0.458529i	$-0.151623\pi$
$308$		0			0
$309$	7.16635	−	3.51924i	0.407679	−	0.200203i
$310$	−13.2092	+	4.29193i	−0.750232	+	0.243765i
$311$	5.65772	−	7.78718i	0.320820	−	0.441571i	−0.617897	−	0.786259i	$-0.712015\pi$
$311$	5.65772	−	7.78718i	0.320820	−	0.441571i	0.938717	+	0.344688i	$0.112015\pi$
$312$	2.89060	+	1.52696i	0.163648	+	0.0864472i
$313$	6.21555	−	19.1295i	0.351324	−	1.08126i	−0.606787	−	0.794865i	$-0.707542\pi$
$313$	6.21555	−	19.1295i	0.351324	−	1.08126i	0.958111	−	0.286399i	$-0.0924581\pi$
$314$	1.14590	−	3.52671i	0.0646668	−	0.199024i
$315$	0.643210	−	21.7921i	0.0362408	−	1.22784i
$316$	6.65877	−	9.16501i	0.374585	−	0.515572i
$317$	17.5481	−	5.70172i	0.985599	−	0.320241i	0.228503	−	0.973543i	$-0.426617\pi$
$317$	17.5481	−	5.70172i	0.985599	−	0.320241i	0.757097	+	0.653303i	$0.226617\pi$
$318$	−4.74470	−	9.66179i	−0.266070	−	0.541806i
$319$		0			0
$320$		−	2.11929i		−	0.118472i
$321$	−21.8808	−	22.5362i	−1.22127	−	1.25785i
$322$	13.7897	+	10.0188i	0.768469	+	0.558325i
$323$	0.730424	+	1.00534i	0.0406419	+	0.0559387i
$324$	−8.98433	−	0.530822i	−0.499130	−	0.0294901i
$325$	−0.913019	−	0.296658i	−0.0506452	−	0.0164556i
$326$	6.91743	−	5.02581i	0.383121	−	0.278354i
$327$	−0.208137	+	1.19933i	−0.0115100	+	0.0663231i
$328$	2.45223	+	7.54718i	0.135402	+	0.416723i
$329$	11.5556			0.637080
$330$		0			0
$331$	−5.03641			−0.276826			−0.138413	−	0.990375i	$-0.544200\pi$
$331$	−5.03641			−0.276826			−0.138413	+	0.990375i	$0.544200\pi$
$332$	−2.12232	−	6.53182i	−0.116477	−	0.358480i
$333$	25.4130	−	7.43579i	1.39262	−	0.407479i
$334$	−1.33161	+	0.967474i	−0.0728626	+	0.0529378i
$335$	20.1233	+	6.53844i	1.09945	+	0.357233i
$336$	5.87928	−	0.842471i	0.320741	−	0.0459605i
$337$	−10.3769	−	14.2826i	−0.565267	−	0.778024i	0.426717	−	0.904385i	$-0.359670\pi$
$337$	−10.3769	−	14.2826i	−0.565267	−	0.778024i	−0.991984	+	0.126361i	$0.959670\pi$
$338$	7.63519	+	5.54729i	0.415299	+	0.301733i
$339$	5.32393	−	5.16911i	0.289156	−	0.280747i
$340$			10.9308i			0.592807i
$341$		0			0
$342$	−0.571964	−	0.441914i	−0.0309282	−	0.0238960i
$343$	7.30989	−	2.37513i	0.394697	−	0.128245i
$344$	3.82991	−	5.27142i	0.206495	−	0.284216i
$345$	8.52249	−	16.1334i	0.458835	−	0.868593i
$346$	−1.08423	+	3.33691i	−0.0582884	+	0.179393i
$347$	−4.64355	+	14.2914i	−0.249279	+	0.767201i	0.745625	+	0.666366i	$0.232151\pi$
$347$	−4.64355	+	14.2914i	−0.249279	+	0.767201i	−0.994903	+	0.100834i	$0.967849\pi$
$348$	−3.37235	+	6.38399i	−0.180777	+	0.342218i
$349$	−2.05443	+	2.82768i	−0.109971	+	0.151362i	−0.860455	−	0.509527i	$-0.829821\pi$
$349$	−2.05443	+	2.82768i	−0.109971	+	0.151362i	0.750484	+	0.660889i	$0.229821\pi$
$350$	−1.65877	+	0.538967i	−0.0886650	+	0.0288090i
$351$	9.60925	+	1.96131i	0.512904	+	0.104687i
$352$		0			0
$353$		−	25.2674i		−	1.34485i	−0.740167	−	0.672423i	$-0.765253\pi$
$353$		−	25.2674i		−	1.34485i	0.740167	−	0.672423i	$-0.234747\pi$
$354$	−3.44465	+	3.34448i	−0.183081	+	0.177757i
$355$	17.0761	+	12.4065i	0.906305	+	0.658469i
$356$	−1.45332	−	2.00032i	−0.0770258	−	0.106017i
$357$	−30.3241	+	4.34528i	−1.60492	+	0.229977i
$358$	12.6233	+	4.10155i	0.667160	+	0.216773i
$359$	−15.6095	+	11.3409i	−0.823836	+	0.598552i	−0.917809	−	0.397023i	$-0.870043\pi$
$359$	−15.6095	+	11.3409i	−0.823836	+	0.598552i	0.0939725	+	0.995575i	$0.470043\pi$
$360$	−1.78544	−	6.10201i	−0.0941007	−	0.321604i
$361$	5.85339	+	18.0149i	0.308073	+	0.948151i
$362$	7.43354			0.390698
$363$		0			0
$364$	−6.47214			−0.339232
$365$	−1.62398	−	4.99809i	−0.0850029	−	0.261612i
$366$	−0.479482	+	2.76288i	−0.0250629	+	0.144418i
$367$	0.726385	−	0.527749i	0.0379170	−	0.0275483i	−0.568665	−	0.822569i	$-0.692540\pi$
$367$	0.726385	−	0.527749i	0.0379170	−	0.0275483i	0.606582	+	0.795021i	$0.292540\pi$
$368$	4.72744	+	1.53604i	0.246435	+	0.0800715i
$369$	13.4189	+	19.6645i	0.698561	+	1.02369i
$370$	10.9946	+	15.1328i	0.571583	+	0.786717i
$371$	17.2403	+	12.5258i	0.895072	+	0.650308i
$372$	−7.90721	−	8.14404i	−0.409970	−	0.422249i
$373$			26.3407i			1.36387i	0.731413	+	0.681935i	$0.238861\pi$
$373$			26.3407i			1.36387i	−0.731413	+	0.681935i	$0.761139\pi$
$374$		0			0
$375$	8.91315	+	18.1501i	0.460273	+	0.937269i
$376$	3.20495	−	1.04135i	0.165283	−	0.0537036i
$377$	4.62449	−	6.36507i	0.238174	−	0.327818i
$378$	16.2183	−	7.37883i	0.834180	−	0.379526i
$379$	−0.823525	+	2.53455i	−0.0423016	+	0.130191i	−0.969977	−	0.243197i	$-0.921804\pi$
$379$	−0.823525	+	2.53455i	−0.0423016	+	0.130191i	0.927675	+	0.373388i	$0.121804\pi$
$380$	0.157785	−	0.485611i	0.00809418	−	0.0249113i
$381$	26.8605	+	14.1891i	1.37610	+	0.726929i
$382$	−1.52249	+	2.09553i	−0.0778973	+	0.107216i
$383$	31.1072	−	10.1073i	1.58950	−	0.516461i	0.625022	−	0.780607i	$-0.285090\pi$
$383$	31.1072	−	10.1073i	1.58950	−	0.516461i	0.964483	+	0.264146i	$0.0850901\pi$
$384$	1.55470	−	0.763481i	0.0793380	−	0.0389612i
$385$		0			0
$386$			19.5259i			0.993841i
$387$	6.58636	−	18.4045i	0.334804	−	0.935552i
$388$	10.6968	+	7.77169i	0.543049	+	0.394548i
$389$	−0.990218	−	1.36292i	−0.0502060	−	0.0691027i	0.783176	−	0.621800i	$-0.213598\pi$
$389$	−0.990218	−	1.36292i	−0.0502060	−	0.0691027i	−0.833382	+	0.552698i	$0.813598\pi$
$390$	0.982738	+	6.85815i	0.0497629	+	0.347276i
$391$	−24.3831	−	7.92255i	−1.23311	−	0.400661i
$392$	−3.84975	+	2.79701i	−0.194442	+	0.141270i
$393$	−8.23063	−	1.42838i	−0.415180	−	0.0720523i
$394$	1.66471	+	5.12346i	0.0838671	+	0.258116i
$395$	24.0085			1.20800
$396$		0			0
$397$	−8.89235			−0.446294			−0.223147	−	0.974785i	$-0.571633\pi$
$397$	−8.89235			−0.446294			−0.223147	+	0.974785i	$0.571633\pi$
$398$	−2.28275	−	7.02557i	−0.114424	−	0.352160i
$399$	1.40990	+	0.244680i	0.0705831	+	0.0122493i
$400$	−0.411491	+	0.298966i	−0.0205746	+	0.0149483i
$401$	18.6014	+	6.04398i	0.928912	+	0.301822i	0.734118	−	0.679022i	$-0.237596\pi$
$401$	18.6014	+	6.04398i	0.928912	+	0.301822i	0.194794	+	0.980844i	$0.437596\pi$
$402$	2.45290	+	17.1179i	0.122340	+	0.853762i
$403$	7.27059	+	10.0071i	0.362174	+	0.498490i
$404$	1.99038	+	1.44610i	0.0990253	+	0.0719461i
$405$	−10.2815	−	16.0652i	−0.510893	−	0.798287i
$406$		−	14.2939i		−	0.709396i
$407$		0			0
$408$	−8.01882	+	3.93787i	−0.396991	+	0.194954i
$409$	−23.5359	+	7.64727i	−1.16377	+	0.378133i	−0.826315	−	0.563208i	$-0.809567\pi$
$409$	−23.5359	+	7.64727i	−1.16377	+	0.378133i	−0.337458	+	0.941341i	$0.609567\pi$
$410$	−9.88522	+	13.6058i	−0.488196	+	0.671945i
$411$	−27.6560	−	14.6093i	−1.36417	−	0.720625i
$412$	−1.42440	+	4.38387i	−0.0701754	+	0.215978i
$413$	2.93728	−	9.04001i	0.144534	−	0.444830i
$414$	14.9057	+	0.439953i	0.732574	+	0.0216225i
$415$	8.55531	−	11.7754i	0.419964	−	0.578030i
$416$	−1.79505	+	0.583248i	−0.0880096	+	0.0285961i
$417$	−0.755368	−	1.53818i	−0.0369905	−	0.0753250i
$418$		0			0
$419$		−	34.8462i		−	1.70235i	−0.524883	−	0.851174i	$-0.675891\pi$
$419$		−	34.8462i		−	1.70235i	0.524883	−	0.851174i	$-0.324109\pi$
$420$	8.76817	+	9.03079i	0.427843	+	0.440657i
$421$	−14.1996	−	10.3166i	−0.692045	−	0.502800i	0.185287	−	0.982684i	$-0.440679\pi$
$421$	−14.1996	−	10.3166i	−0.692045	−	0.502800i	−0.877332	+	0.479884i	$0.840679\pi$
$422$	−5.03276	−	6.92699i	−0.244991	−	0.337201i
$423$	8.35063	−	5.69841i	0.406022	−	0.277066i
$424$	5.91040	+	1.92040i	0.287034	+	0.0932631i
$425$	2.12238	−	1.54200i	0.102951	−	0.0747981i
$426$	−2.94965	+	16.9965i	−0.142911	+	0.823482i
$427$	−1.71555	−	5.27992i	−0.0830213	−	0.255513i
$428$	18.1351			0.876595
$429$		0			0
$430$	13.8089			0.665925
$431$	10.3275	+	31.7846i	0.497456	+	1.53101i	0.813094	+	0.582133i	$0.197782\pi$
$431$	10.3275	+	31.7846i	0.497456	+	1.53101i	−0.315638	+	0.948880i	$0.602218\pi$
$432$	3.83321	−	3.50806i	0.184425	−	0.168782i
$433$	−21.9952	+	15.9805i	−1.05702	+	0.767973i	−0.973535	−	0.228536i	$-0.926606\pi$
$433$	−21.9952	+	15.9805i	−1.05702	+	0.767973i	−0.0834881	+	0.996509i	$0.526606\pi$
$434$	21.3729	+	6.94448i	1.02593	+	0.333346i
$435$	−15.1465	+	2.17041i	−0.726217	+	0.104063i
$436$	−0.413086	−	0.568564i	−0.0197832	−	0.0272293i
$437$	0.968880	+	0.703933i	0.0463478	+	0.0336737i
$438$	3.08154	−	2.99193i	0.147242	−	0.142960i
$439$		−	13.4068i		−	0.639873i	−0.947439	−	0.319936i	$-0.896338\pi$
$439$		−	13.4068i		−	0.639873i	0.947439	−	0.319936i	$-0.103662\pi$
$440$		0			0
$441$	−8.72811	+	11.2967i	−0.415624	+	0.537937i
$442$	9.25849	−	3.00827i	0.440381	−	0.143089i
$443$	−10.8348	+	14.9128i	−0.514777	+	0.708530i	−0.984716	−	0.174169i	$-0.944276\pi$
$443$	−10.8348	+	14.9128i	−0.514777	+	0.708530i	0.469939	+	0.882699i	$0.344276\pi$
$444$	−7.14052	+	13.5173i	−0.338874	+	0.641502i
$445$	1.61925	−	4.98355i	0.0767599	−	0.236243i
$446$	−0.0155598	+	0.0478882i	−0.000736779	+	0.00226757i
$447$	11.3158	−	21.4213i	0.535221	−	1.01319i
$448$	−2.01556	+	2.77418i	−0.0952263	+	0.131068i
$449$	28.8836	−	9.38485i	1.36310	−	0.442898i	0.466024	−	0.884772i	$-0.345686\pi$
$449$	28.8836	−	9.38485i	1.36310	−	0.442898i	0.897077	+	0.441874i	$0.145686\pi$
$450$	−0.932928	+	1.20748i	−0.0439786	+	0.0569209i
$451$		0			0
$452$			4.28423i			0.201513i
$453$	7.86429	−	7.63559i	0.369496	−	0.358751i
$454$	−11.5589	−	8.39806i	−0.542488	−	0.394141i
$455$	−8.06224	−	11.0967i	−0.377964	−	0.520222i
$456$	0.413086	−	0.0591931i	0.0193445	−	0.00277197i
$457$	−32.9901	−	10.7191i	−1.54321	−	0.501419i	−0.590950	−	0.806708i	$-0.701247\pi$
$457$	−32.9901	−	10.7191i	−1.54321	−	0.501419i	−0.952260	+	0.305289i	$0.901247\pi$
$458$	−24.4668	+	17.7761i	−1.14326	+	0.830625i
$459$	−19.7709	+	18.0938i	−0.922825	+	0.844548i
$460$	3.25530	+	10.0188i	0.151779	+	0.467128i
$461$	−20.8777			−0.972370			−0.486185	−	0.873856i	$-0.661612\pi$
$461$	−20.8777			−0.972370			−0.486185	+	0.873856i	$0.661612\pi$
$462$		0			0
$463$	6.14371			0.285522			0.142761	−	0.989757i	$-0.454402\pi$
$463$	6.14371			0.285522			0.142761	+	0.989757i	$0.454402\pi$
$464$	−1.28812	−	3.96443i	−0.0597996	−	0.184044i
$465$	4.11338	−	23.7021i	0.190753	−	1.09916i
$466$	2.28819	−	1.66247i	0.105998	−	0.0770123i
$467$	−33.1013	−	10.7553i	−1.53174	−	0.497694i	−0.582660	−	0.812716i	$-0.697988\pi$
$467$	−33.1013	−	10.7553i	−1.53174	−	0.497694i	−0.949084	+	0.315022i	$0.897988\pi$
$468$	−4.67708	+	3.19161i	−0.216198	+	0.147532i
$469$	−20.1233	−	27.6973i	−0.929206	−	1.27894i
$470$	5.77779	+	4.19781i	0.266510	+	0.193631i
$471$	4.47411	+	4.60811i	0.206156	+	0.212331i
$472$		−	2.77195i		−	0.127589i
$473$		0			0
$474$	8.64915	+	17.6126i	0.397269	+	0.808971i
$475$	−0.116547	+	0.0378685i	−0.00534756	+	0.00173753i
$476$	10.3958	−	14.3086i	0.476492	−	0.655835i
$477$	18.6356	+	0.550043i	0.853264	+	0.0251848i
$478$	0.350846	−	1.07979i	0.0160473	−	0.0493886i
$479$	10.7639	−	33.1280i	0.491817	−	1.51366i	−0.330043	−	0.943966i	$-0.607063\pi$
$479$	10.7639	−	33.1280i	0.491817	−	1.51366i	0.821860	−	0.569690i	$-0.192937\pi$
$480$	3.24568	+	1.71454i	0.148145	+	0.0782576i
$481$	9.79178	−	13.4772i	0.446467	−	0.614509i
$482$	−14.3100	+	4.64959i	−0.651801	+	0.211783i
$483$	−26.4999	+	13.0135i	−1.20578	+	0.592136i
$484$		0			0
$485$			28.0212i			1.27238i
$486$	8.08143	−	13.3301i	0.366581	−	0.604664i
$487$	4.66471	+	3.38911i	0.211378	+	0.153575i	0.688437	−	0.725296i	$-0.258297\pi$
$487$	4.66471	+	3.38911i	0.211378	+	0.153575i	−0.477059	+	0.878871i	$0.658297\pi$
$488$	−0.951618	−	1.30979i	−0.0430777	−	0.0592914i
$489$	2.10071	+	14.6600i	0.0949972	+	0.662949i
$490$	−9.59116	−	3.11636i	−0.433284	−	0.140783i
$491$	8.42871	−	6.12382i	0.380382	−	0.276364i	−0.381121	−	0.924525i	$-0.624462\pi$
$491$	8.42871	−	6.12382i	0.380382	−	0.276364i	0.761503	+	0.648161i	$0.224462\pi$
$492$	−13.5424	−	2.35021i	−0.610538	−	0.105956i
$493$	6.64386	+	20.4477i	0.299224	+	0.920918i
$494$	−0.454741			−0.0204597
$495$		0			0
$496$	6.55361			0.294266
$497$	−10.5536	−	32.4807i	−0.473394	−	1.45696i
$498$	11.7205	+	2.03402i	0.525207	+	0.0911468i
$499$	17.7151	−	12.8708i	0.793038	−	0.576176i	−0.115825	−	0.993270i	$-0.536951\pi$
$499$	17.7151	−	12.8708i	0.793038	−	0.576176i	0.908864	+	0.417094i	$0.136951\pi$
$500$	−11.1030	−	3.60758i	−0.496540	−	0.161336i
$501$	−0.404388	−	2.82207i	−0.0180667	−	0.126081i
$502$	−5.66415	−	7.79603i	−0.252803	−	0.347954i
$503$	15.8347	+	11.5045i	0.706032	+	0.512962i	0.881891	−	0.471453i	$-0.156270\pi$
$503$	15.8347	+	11.5045i	0.706032	+	0.512962i	−0.175859	+	0.984415i	$0.556270\pi$
$504$	−3.46619	+	9.68569i	−0.154396	+	0.431435i
$505$			5.21397i			0.232019i
$506$		0			0
$507$	−14.6727	+	7.20544i	−0.651636	+	0.320005i
$508$	−16.6803	+	5.41975i	−0.740067	+	0.240462i
$509$	−21.3064	+	29.3257i	−0.944389	+	1.29984i	0.00958605	+	0.999954i	$0.496949\pi$
$509$	−21.3064	+	29.3257i	−0.944389	+	1.29984i	−0.953975	+	0.299886i	$0.903051\pi$
$510$	−16.7405	−	8.84322i	−0.741284	−	0.391584i
$511$	−2.62765	+	8.08708i	−0.116240	+	0.357751i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	1.13952	−	0.518446i	0.0503110	−	0.0228899i
$514$	−7.85036	+	10.8051i	−0.346265	+	0.476592i
$515$	−9.29066	+	3.01872i	−0.409395	+	0.133021i
$516$	4.97472	+	10.1302i	0.219000	+	0.445956i
$517$		0			0
$518$		−	30.2656i		−	1.32979i
$519$	−4.23331	−	4.36011i	−0.185822	−	0.191387i
$520$	−3.23607	−	2.35114i	−0.141911	−	0.103104i
$521$	10.6363	+	14.6396i	0.465985	+	0.641373i	0.975736	−	0.218948i	$-0.0702626\pi$
$521$	10.6363	+	14.6396i	0.465985	+	0.641373i	−0.509751	+	0.860322i	$0.670263\pi$
$522$	−7.04878	−	10.3295i	−0.308517	−	0.452110i
$523$	23.8450	+	7.74771i	1.04267	+	0.338784i	0.779787	−	0.626045i	$-0.215327\pi$
$523$	23.8450	+	7.74771i	1.04267	+	0.338784i	0.262881	+	0.964828i	$0.415327\pi$
$524$	3.90187	−	2.83488i	0.170454	−	0.123842i
$525$	0.516545	−	2.97644i	0.0225439	−	0.129902i
$526$	−2.88522	−	8.87980i	−0.125802	−	0.387178i
$527$	−33.8021			−1.47244
$528$		0			0
$529$	−1.70807			−0.0742639
$530$	4.06988	+	12.5258i	0.176785	+	0.544087i
$531$	−2.33529	−	7.98122i	−0.101343	−	0.346355i
$532$	−0.668387	+	0.485611i	−0.0289782	+	0.0210539i
$533$	14.2448	+	4.62840i	0.617009	+	0.200478i
$534$	4.23926	−	0.607464i	0.183451	−	0.0262875i
$535$	22.5907	+	31.0934i	0.976680	+	1.34428i
$536$	−8.07719	−	5.86842i	−0.348881	−	0.253477i
$537$	−16.4939	+	16.0143i	−0.711766	+	0.691068i
$538$		−	13.6250i		−	0.587415i
$539$		0			0
$540$	10.7897	+	2.20224i	0.464314	+	0.0947692i
$541$	37.4648	−	12.1730i	1.61074	−	0.523360i	0.641006	−	0.767536i	$-0.278517\pi$
$541$	37.4648	−	12.1730i	1.61074	−	0.523360i	0.969731	+	0.244176i	$0.0785173\pi$
$542$	−2.75734	+	3.79515i	−0.118438	+	0.163016i
$543$	−6.01386	+	11.3845i	−0.258079	+	0.488554i
$544$	1.59384	−	4.90534i	0.0683355	−	0.210315i
$545$	0.460249	−	1.41650i	0.0197149	−	0.0606763i
$546$	5.23607	−	9.91207i	0.224083	−	0.424198i
$547$	−1.05599	+	1.45344i	−0.0451507	+	0.0621446i	−0.830995	−	0.556279i	$-0.812228\pi$
$547$	−1.05599	+	1.45344i	−0.0451507	+	0.0621446i	0.785845	+	0.618424i	$0.212228\pi$
$548$	17.1743	−	5.58026i	0.733649	−	0.238377i
$549$	−3.84343	−	2.96954i	−0.164034	−	0.126737i
$550$		0			0
$551$		−	1.00431i		−	0.0427851i
$552$	−6.17702	+	5.99739i	−0.262911	+	0.255266i
$553$	−31.4275	−	22.8334i	−1.33643	−	0.970976i
$554$	−4.86796	−	6.70017i	−0.206820	−	0.284663i
$555$	−32.0707	+	4.59557i	−1.36133	+	0.195071i
$556$	0.940950	+	0.305733i	0.0399052	+	0.0129660i
$557$	−34.6574	+	25.1801i	−1.46848	+	1.06691i	−0.487429	+	0.873163i	$0.662065\pi$
$557$	−34.6574	+	25.1801i	−1.46848	+	1.06691i	−0.981051	+	0.193750i	$0.937935\pi$
$558$	18.8697	−	5.52122i	0.798816	−	0.233732i
$559$	−3.80034	−	11.6963i	−0.160737	−	0.494699i
$560$	−7.26719			−0.307095
$561$		0			0
$562$	−12.6650			−0.534240
$563$	5.33623	+	16.4232i	0.224895	+	0.692157i	0.998302	+	0.0582467i	$0.0185510\pi$
$563$	5.33623	+	16.4232i	0.224895	+	0.692157i	−0.773407	+	0.633910i	$0.781449\pi$
$564$	−0.998029	+	5.75085i	−0.0420246	+	0.242154i
$565$	−7.34547	+	5.33680i	−0.309026	+	0.224521i
$566$	21.5030	+	6.98676i	0.903840	+	0.293675i
$567$	−1.82023	+	30.8080i	−0.0764424	+	1.29381i
$568$	−5.85410	−	8.05748i	−0.245633	−	0.338084i
$569$	4.41418	+	3.20709i	0.185052	+	0.134448i	0.676454	−	0.736484i	$-0.263516\pi$
$569$	4.41418	+	3.20709i	0.185052	+	0.134448i	−0.491402	+	0.870933i	$0.663516\pi$
$570$	0.616063	+	0.634515i	0.0258040	+	0.0265769i
$571$			18.8259i			0.787838i	0.919145	+	0.393919i	$0.128881\pi$
$571$			18.8259i			0.787838i	−0.919145	+	0.393919i	$0.871119\pi$
$572$		0			0
$573$	−1.97758	−	4.02701i	−0.0826145	−	0.168231i
$574$	25.8798	−	8.40887i	1.08020	−	0.350980i
$575$	1.48608	−	2.04541i	0.0619736	−	0.0852994i
$576$	−0.0885088	+	2.99869i	−0.00368787	+	0.124946i
$577$	4.84849	−	14.9221i	0.201845	−	0.621216i	−0.797983	−	0.602680i	$-0.794099\pi$
$577$	4.84849	−	14.9221i	0.201845	−	0.621216i	0.999828	−	0.0185361i	$-0.00590056\pi$
$578$	−2.96741	+	9.13275i	−0.123428	+	0.379872i
$579$	−29.9039	−	15.7968i	−1.24276	−	0.656491i
$580$	5.19258	−	7.14697i	0.215610	−	0.296762i
$581$	−22.3981	+	7.27758i	−0.929230	+	0.301925i
$582$	−20.5563	+	10.0947i	−0.852084	+	0.418441i
$583$		0			0
$584$			2.47975i			0.102613i
$585$	−11.2983	−	4.04330i	−0.467128	−	0.167170i
$586$	−20.2998	−	14.7487i	−0.838577	−	0.609262i
$587$	−1.74399	−	2.40039i	−0.0719821	−	0.0990748i	0.771508	−	0.636220i	$-0.219503\pi$
$587$	−1.74399	−	2.40039i	−0.0719821	−	0.0990748i	−0.843490	+	0.537145i	$0.819503\pi$
$588$	−1.16910	−	8.15872i	−0.0482130	−	0.336460i
$589$	1.50169	+	0.487928i	0.0618760	+	0.0201047i
$590$	4.75261	−	3.45298i	0.195662	−	0.142157i
$591$	−9.19336	−	1.59546i	−0.378164	−	0.0656284i
$592$	−2.72744	−	8.39419i	−0.112097	−	0.344999i
$593$	43.4839			1.78567			0.892836	−	0.450383i	$-0.148712\pi$
$593$	43.4839			1.78567			0.892836	+	0.450383i	$0.148712\pi$
$594$		0			0
$595$	37.4826			1.53664
$596$	4.32227	+	13.3026i	0.177047	+	0.544894i
$597$	12.6064	+	2.18778i	0.515948	+	0.0895399i
$598$	7.59010	−	5.51453i	0.310382	−	0.225506i
$599$	24.7770	+	8.05055i	1.01236	+	0.328936i	0.767795	−	0.640696i	$-0.221354\pi$
$599$	24.7770	+	8.05055i	1.01236	+	0.328936i	0.244567	+	0.969632i	$0.421354\pi$
$600$	−0.124963	−	0.872067i	−0.00510158	−	0.0356020i
$601$	27.1211	+	37.3290i	1.10629	+	1.52268i	0.826766	+	0.562546i	$0.190178\pi$
$601$	27.1211	+	37.3290i	1.10629	+	1.52268i	0.279529	+	0.960137i	$0.409822\pi$
$602$	−18.0761	−	13.1331i	−0.736727	−	0.535263i
$603$	−28.2005	−	10.0920i	−1.14841	−	0.410979i
$604$			6.32849i			0.257502i
$605$		0			0
$606$	−3.82495	+	1.87835i	−0.155378	+	0.0763029i
$607$	9.07413	−	2.94836i	0.368307	−	0.119670i	−0.119015	−	0.992892i	$-0.537974\pi$
$607$	9.07413	−	2.94836i	0.368307	−	0.119670i	0.487322	+	0.873222i	$0.337974\pi$
$608$	−0.141616	+	0.194917i	−0.00574328	+	0.00790495i
$609$	21.8912	+	11.5640i	0.887075	+	0.468599i
$610$	1.06027	−	3.26317i	0.0429290	−	0.132122i
$611$	1.96548	−	6.04911i	0.0795146	−	0.244721i
$612$	0.456510	−	15.4666i	0.0184533	−	0.625201i
$613$	6.16173	−	8.48089i	0.248870	−	0.342540i	−0.666245	−	0.745733i	$-0.732100\pi$
$613$	6.16173	−	8.48089i	0.248870	−	0.342540i	0.915115	+	0.403193i	$0.132100\pi$
$614$	−15.2817	+	4.96533i	−0.616720	+	0.200384i
$615$	−12.8400	−	26.1466i	−0.517760	−	1.05433i
$616$		0			0
$617$		−	26.7867i		−	1.07839i	−0.842180	−	0.539196i	$-0.818728\pi$
$617$		−	26.7867i		−	1.07839i	0.842180	−	0.539196i	$-0.181272\pi$
$618$	−5.56152	−	5.72810i	−0.223717	−	0.230418i
$619$	6.51821	+	4.73575i	0.261989	+	0.190346i	0.711023	−	0.703168i	$-0.248232\pi$
$619$	6.51821	+	4.73575i	0.261989	+	0.190346i	−0.449035	+	0.893514i	$0.648232\pi$
$620$	8.16373	+	11.2364i	0.327863	+	0.451265i
$621$	−12.7327	+	22.4721i	−0.510947	+	0.901775i
$622$	−9.15438	−	2.97444i	−0.367057	−	0.119264i
$623$	−6.85926	+	4.98355i	−0.274811	+	0.199662i
$624$	0.558984	−	3.22098i	0.0223773	−	0.128942i
$625$	−6.85960	−	21.1117i	−0.274384	−	0.844467i
$626$	−20.1139			−0.803915
$627$		0			0
$628$	−3.70820			−0.147973
$629$	14.0675	+	43.2954i	0.560909	+	1.72630i
$630$	−20.9243	+	6.12239i	−0.833642	+	0.243922i
$631$	16.5719	−	12.0402i	0.659718	−	0.479313i	−0.206850	−	0.978373i	$-0.566321\pi$
$631$	16.5719	−	12.0402i	0.659718	−	0.479313i	0.866568	+	0.499060i	$0.166321\pi$
$632$	−10.7741	−	3.50072i	−0.428571	−	0.139251i
$633$	14.6803	−	2.10361i	0.583488	−	0.0836109i
$634$	−10.8453	−	14.9273i	−0.430723	−	0.592839i
$635$	−30.0707	−	21.8477i	−1.19332	−	0.866998i
$636$	−7.72271	+	7.49813i	−0.306225	+	0.297320i
$637$			8.98144i			0.355858i
$638$		0			0
$639$	−23.6438	−	18.2678i	−0.935333	−	0.722664i
$640$	−2.01556	+	0.654895i	−0.0796720	+	0.0258870i
$641$	1.82529	−	2.51229i	0.0720946	−	0.0992296i	−0.771447	−	0.636294i	$-0.780467\pi$
$641$	1.82529	−	2.51229i	0.0720946	−	0.0992296i	0.843541	+	0.537064i	$0.180467\pi$
$642$	−14.6716	+	27.7740i	−0.579044	+	1.09615i
$643$	−12.1432	+	37.3728i	−0.478880	+	1.47384i	0.361773	+	0.932266i	$0.382172\pi$
$643$	−12.1432	+	37.3728i	−0.478880	+	1.47384i	−0.840653	+	0.541574i	$0.817828\pi$
$644$	5.26719	−	16.2107i	0.207556	−	0.638793i
$645$	−11.1716	+	21.1483i	−0.439883	+	0.832715i
$646$	0.730424	−	1.00534i	0.0287381	−	0.0395547i
$647$	−34.1070	+	11.0820i	−1.34088	+	0.435680i	−0.889616	−	0.456709i	$-0.849028\pi$
$647$	−34.1070	+	11.0820i	−1.34088	+	0.435680i	−0.451268	+	0.892388i	$0.649028\pi$
$648$	2.27147	+	8.70864i	0.0892318	+	0.342108i
$649$		0			0
$650$			0.960005i			0.0376545i
$651$	−27.9265	+	27.1144i	−1.09453	+	1.06270i
$652$	−6.91743	−	5.02581i	−0.270908	−	0.196826i
$653$	1.38621	+	1.90795i	0.0542465	+	0.0746639i	0.835278	−	0.549827i	$-0.185306\pi$
$653$	1.38621	+	1.90795i	0.0542465	+	0.0746639i	−0.781032	+	0.624491i	$0.785306\pi$
$654$	1.20495	−	0.172663i	0.0471172	−	0.00675166i
$655$	9.72101	+	3.15855i	0.379831	+	0.123415i
$656$	6.42001	−	4.66441i	0.250659	−	0.182115i
$657$	2.08912	+	7.13990i	0.0815043	+	0.278554i
$658$	−3.57087	−	10.9900i	−0.139207	−	0.428435i
$659$	8.51039			0.331518			0.165759	−	0.986166i	$-0.446993\pi$
$659$	8.51039			0.331518			0.165759	+	0.986166i	$0.446993\pi$
$660$		0			0
$661$	42.4546			1.65129			0.825646	−	0.564189i	$-0.190811\pi$
$661$	42.4546			1.65129			0.825646	+	0.564189i	$0.190811\pi$
$662$	1.55634	+	4.78991i	0.0604888	+	0.186165i
$663$	−2.88312	+	16.6131i	−0.111971	+	0.645200i
$664$	−5.55630	+	4.03689i	−0.215626	+	0.156662i
$665$	−1.66520	−	0.541056i	−0.0645736	−	0.0209812i
$666$	−14.9249	−	21.8714i	−0.578328	−	0.847500i
$667$	12.1790	+	16.7630i	0.471574	+	0.649066i
$668$	1.33161	+	0.967474i	0.0515217	+	0.0374327i
$669$	−0.0607526	−	0.0625722i	−0.00234883	−	0.00241918i
$670$		−	21.1588i		−	0.817438i
$671$		0			0
$672$	−2.61803	−	5.33119i	−0.100993	−	0.205655i
$673$	−45.4817	+	14.7779i	−1.75319	+	0.569646i	−0.996459	−	0.0840801i	$-0.973205\pi$
$673$	−45.4817	+	14.7779i	−1.75319	+	0.569646i	−0.756731	+	0.653726i	$0.773205\pi$
$674$	−10.3769	+	14.2826i	−0.399704	+	0.550146i
$675$	−1.09449	−	2.40565i	−0.0421271	−	0.0925934i
$676$	2.91638	−	8.97570i	0.112169	−	0.345219i
$677$	−1.70016	+	5.23254i	−0.0653423	+	0.201103i	−0.978397	−	0.206734i	$-0.933717\pi$
$677$	−1.70016	+	5.23254i	−0.0653423	+	0.201103i	0.913055	+	0.407837i	$0.133717\pi$
$678$	−6.56130	−	3.46601i	−0.251985	−	0.133111i
$679$	26.6497	−	36.6802i	1.02272	−	1.40766i
$680$	10.3958	−	3.37781i	0.398662	−	0.129533i
$681$	22.2130	−	10.9083i	0.851205	−	0.418009i
$682$		0			0
$683$			40.1110i			1.53480i	0.641166	+	0.767402i	$0.278451\pi$
$683$			40.1110i			1.53480i	−0.641166	+	0.767402i	$0.721549\pi$
$684$	−0.243539	+	0.680529i	−0.00931195	+	0.0260207i
$685$	30.9613	+	22.4947i	1.18297	+	0.859479i
$686$	−4.51776	−	6.21817i	−0.172489	−	0.237411i
$687$	−7.43013	−	51.8520i	−0.283477	−	1.97828i
$688$	−6.19693	−	2.01350i	−0.236256	−	0.0767641i
$689$	9.48940	−	6.89445i	0.361517	−	0.262658i
$690$	−17.9774	−	3.11988i	−0.684386	−	0.118772i
$691$	9.77418	+	30.0818i	0.371827	+	1.14437i	0.945594	+	0.325348i	$0.105482\pi$
$691$	9.77418	+	30.0818i	0.371827	+	1.14437i	−0.573767	+	0.819019i	$0.694518\pi$
$692$	3.50863			0.133378
$693$		0			0
$694$	15.0268			0.570411
$695$	0.647936	+	1.99414i	0.0245776	+	0.0756421i
$696$	7.11364	+	1.23454i	0.269642	+	0.0467949i
$697$	−33.1131	+	24.0580i	−1.25425	+	0.911263i
$698$	3.32413	+	1.08008i	0.125820	+	0.0408815i
$699$	0.694884	+	4.84933i	0.0262829	+	0.183418i
$700$	1.02518	+	1.41103i	0.0387480	+	0.0533321i
$701$	−12.7136	−	9.23696i	−0.480185	−	0.348875i	0.321212	−	0.947007i	$-0.395910\pi$
$701$	−12.7136	−	9.23696i	−0.480185	−	0.348875i	−0.801397	+	0.598132i	$0.795910\pi$
$702$	−1.10411	−	9.74502i	−0.0416719	−	0.367802i
$703$		−	2.12650i		−	0.0802025i
$704$		0			0
$705$	−11.1033	+	5.45258i	−0.418174	+	0.205356i
$706$	−24.0307	+	7.80805i	−0.904407	+	0.293860i
$707$	4.95878	−	6.82517i	0.186494	−	0.256687i
$708$	4.24524	+	2.24256i	0.159546	+	0.0842804i
$709$	1.83617	−	5.65115i	0.0689588	−	0.212233i	−0.910638	−	0.413204i	$-0.864410\pi$
$709$	1.83617	−	5.65115i	0.0689588	−	0.212233i	0.979597	+	0.200971i	$0.0644096\pi$
$710$	6.52249	−	20.0742i	0.244785	−	0.753370i
$711$	−33.9709	−	1.00268i	−1.27401	−	0.0376034i
$712$	−1.45332	+	2.00032i	−0.0544655	+	0.0749653i
$713$	−30.9818	+	10.0666i	−1.16028	+	0.376997i
$714$	13.5033	+	27.4971i	0.505347	+	1.02905i
$715$		0			0
$716$		−	13.2729i		−	0.496031i
$717$	1.36986	+	1.41089i	0.0511585	+	0.0526908i
$718$	15.6095	+	11.3409i	0.582540	+	0.423240i
$719$	18.1483	+	24.9789i	0.676816	+	0.931557i	0.999890	−	0.0148168i	$-0.00471649\pi$
$719$	18.1483	+	24.9789i	0.676816	+	0.931557i	−0.323075	+	0.946373i	$0.604716\pi$
$720$	−5.25163	+	3.58367i	−0.195717	+	0.133556i
$721$	15.0326	+	4.88439i	0.559844	+	0.181904i
$722$	15.3244	−	11.1338i	0.570314	−	0.414357i
$723$	4.45616	−	25.6773i	0.165726	−	0.954949i
$724$	−2.29709	−	7.06971i	−0.0853706	−	0.262744i
$725$	−2.12020			−0.0787424
$726$		0			0
$727$	−23.3566			−0.866249			−0.433124	−	0.901334i	$-0.642589\pi$
$727$	−23.3566			−0.866249			−0.433124	+	0.901334i	$0.642589\pi$
$728$	2.00000	+	6.15537i	0.0741249	+	0.228133i
$729$	13.8770	+	23.1610i	0.513962	+	0.857813i
$730$	−4.25163	+	3.08899i	−0.157360	+	0.114329i
$731$	31.9624	+	10.3852i	1.18217	+	0.384111i
$732$	2.77582	−	0.397761i	0.102597	−	0.0147017i
$733$	−24.3752	−	33.5495i	−0.900317	−	1.23918i	−0.970367	−	0.241636i	$-0.922316\pi$
$733$	−24.3752	−	33.5495i	−0.900317	−	1.23918i	0.0700499	−	0.997543i	$-0.477684\pi$
$734$	−0.726385	−	0.527749i	−0.0268114	−	0.0194796i
$735$	12.5321	−	12.1677i	0.462254	−	0.448811i
$736$		−	4.97072i		−	0.183223i
$737$		0			0
$738$	14.5554	−	18.8388i	0.535791	−	0.693466i
$739$	−29.5635	+	9.60577i	−1.08751	+	0.353354i	−0.797284	−	0.603604i	$-0.793731\pi$
$739$	−29.5635	+	9.60577i	−1.08751	+	0.353354i	−0.290227	+	0.956958i	$0.593731\pi$
$740$	10.9946	−	15.1328i	0.404170	−	0.556293i
$741$	0.367893	−	0.696435i	0.0135149	−	0.0255842i
$742$	6.58521	−	20.2672i	0.241751	−	0.744032i
$743$	9.47940	−	29.1746i	0.347765	−	1.07031i	−0.612321	−	0.790609i	$-0.709764\pi$
$743$	9.47940	−	29.1746i	0.347765	−	1.07031i	0.960087	−	0.279703i	$-0.0902360\pi$
$744$	−5.30198	+	10.0368i	−0.194380	+	0.367969i
$745$	−17.4236	+	23.9815i	−0.638350	+	0.878614i
$746$	25.0515	−	8.13972i	0.917200	−	0.298016i
$747$	−12.5972	+	16.3043i	−0.460906	+	0.596544i
$748$		0			0
$749$		−	62.1868i		−	2.27226i
$750$	14.5075	−	14.0856i	0.529739	−	0.514334i
$751$	6.03982	+	4.38818i	0.220396	+	0.160127i	0.692505	−	0.721413i	$-0.256507\pi$
$751$	6.03982	+	4.38818i	0.220396	+	0.160127i	−0.472109	+	0.881540i	$0.656507\pi$
$752$	−1.98077	−	2.72629i	−0.0722311	−	0.0994176i
$753$	16.5220	−	2.36752i	0.602095	−	0.0862772i
$754$	−7.48259	−	2.43124i	−0.272500	−	0.0885406i
$755$	−10.8504	+	7.88330i	−0.394888	+	0.286903i
$756$	−12.0294	−	13.1444i	−0.437506	−	0.478056i
$757$	−7.21548	−	22.2070i	−0.262251	−	0.807126i	−0.992314	−	0.123746i	$-0.960509\pi$
$757$	−7.21548	−	22.2070i	−0.262251	−	0.807126i	0.730063	−	0.683380i	$-0.239491\pi$
$758$	2.66498			0.0967965
$759$		0			0
$760$	−0.510602			−0.0185215
$761$	2.97052	+	9.14231i	0.107681	+	0.331408i	0.990350	−	0.138586i	$-0.0442558\pi$
$761$	2.97052	+	9.14231i	0.107681	+	0.331408i	−0.882669	+	0.469995i	$0.844256\pi$
$762$	5.19428	−	29.9305i	0.188169	−	1.08427i
$763$	−1.94965	+	1.41650i	−0.0705820	+	0.0512808i
$764$	2.46344	+	0.800420i	0.0891241	+	0.0289582i
$765$	27.0868	−	18.4838i	0.979324	−	0.668284i
$766$	−19.2253	−	26.4614i	−0.694639	−	0.956088i
$767$	−4.23266	−	3.07521i	−0.152833	−	0.111039i
$768$	−1.20654	−	1.24268i	−0.0435374	−	0.0448414i
$769$		−	34.6298i		−	1.24878i	−0.781112	−	0.624391i	$-0.785347\pi$
$769$		−	34.6298i		−	1.24878i	0.781112	−	0.624391i	$-0.214653\pi$
$770$		0			0
$771$	−10.1969	−	20.7643i	−0.367233	−	0.747809i
$772$	18.5702	−	6.03383i	0.668357	−	0.217162i
$773$	−7.96896	+	10.9683i	−0.286624	+	0.394504i	−0.927914	−	0.372795i	$-0.878400\pi$
$773$	−7.96896	+	10.9683i	−0.286624	+	0.394504i	0.641290	+	0.767299i	$0.278400\pi$
$774$	−19.5390	−	0.576709i	−0.702315	−	0.0207294i
$775$	1.03007	−	3.17022i	0.0370011	−	0.113878i
$776$	4.08582	−	12.5749i	0.146672	−	0.451411i
$777$	46.3518	+	24.4854i	1.66286	+	0.878408i
$778$	−0.990218	+	1.36292i	−0.0355010	+	0.0488630i
$779$	1.81835	−	0.590818i	0.0651492	−	0.0211683i
$780$	6.21881	−	3.05392i	0.222669	−	0.109348i
$781$		0			0
$782$			25.6379i			0.916810i
$783$	21.5222	−	2.43847i	0.769141	−	0.0871436i
$784$	3.84975	+	2.79701i	0.137491	+	0.0998932i
$785$	−4.61925	−	6.35786i	−0.164868	−	0.226922i
$786$	1.18493	+	8.26918i	0.0422651	+	0.294952i
$787$	17.6164	+	5.72391i	0.627957	+	0.204036i	0.605670	−	0.795716i	$-0.292905\pi$
$787$	17.6164	+	5.72391i	0.627957	+	0.204036i	0.0222870	+	0.999752i	$0.492905\pi$
$788$	4.35828	−	3.16647i	0.155257	−	0.112801i
$789$	15.9336	+	2.76519i	0.567251	+	0.0984434i
$790$	−7.41903	−	22.8334i	−0.263957	−	0.812377i
$791$	14.6909			0.522350
$792$		0			0
$793$	−3.05573			−0.108512
$794$	2.74789	+	8.45713i	0.0975189	+	0.300132i
$795$	−22.4759	−	3.90057i	−0.797138	−	0.138339i
$796$	−5.97631	+	4.34204i	−0.211825	+	0.153900i
$797$	−49.0135	−	15.9254i	−1.73615	−	0.564108i	−0.741831	−	0.670587i	$-0.766042\pi$
$797$	−49.0135	−	15.9254i	−1.73615	−	0.564108i	−0.994315	+	0.106479i	$0.966042\pi$
$798$	−0.202977	−	1.41650i	−0.00718532	−	0.0501436i
$799$	10.2164	+	14.0616i	0.361429	+	0.497465i
$800$	0.411491	+	0.298966i	0.0145484	+	0.0105700i
$801$	−2.49930	+	6.98387i	−0.0883084	+	0.246763i
$802$		−	19.5587i		−	0.690642i
$803$		0			0
$804$	15.5221	−	7.62256i	0.547421	−	0.268827i
$805$	34.3552	−	11.1627i	1.21086	−	0.393432i
$806$	7.27059	−	10.0071i	0.256096	−	0.352485i
$807$	20.8667	+	11.0228i	0.734541	+	0.388022i
$808$	0.760259	−	2.33984i	0.0267458	−	0.0823151i
$809$	−10.8032	+	33.2488i	−0.379820	+	1.16897i	0.560348	+	0.828257i	$0.310667\pi$
$809$	−10.8032	+	33.2488i	−0.379820	+	1.16897i	−0.940169	+	0.340709i	$0.889333\pi$
$810$	−12.1018	+	14.7427i	−0.425212	+	0.518007i
$811$	10.5779	−	14.5592i	0.371440	−	0.511243i	−0.581852	−	0.813295i	$-0.697672\pi$
$811$	10.5779	−	14.5592i	0.371440	−	0.511243i	0.953291	+	0.302052i	$0.0976716\pi$
$812$	−13.5943	+	4.41707i	−0.477068	+	0.155009i
$813$	−3.58154	−	7.29320i	−0.125610	−	0.255784i
$814$		0			0
$815$		−	18.1208i		−	0.634743i
$816$	6.22309	+	6.40948i	0.217852	+	0.224377i
$817$	−1.27005	−	0.922745i	−0.0444334	−	0.0322828i
$818$	14.5460	+	20.0208i	0.508588	+	0.700011i
$819$	10.9443	+	16.0381i	0.382424	+	0.560416i
$820$	15.9946	+	5.19697i	0.558557	+	0.181486i
$821$	7.34398	−	5.33572i	0.256307	−	0.186218i	−0.452210	−	0.891911i	$-0.649364\pi$
$821$	7.34398	−	5.33572i	0.256307	−	0.186218i	0.708517	+	0.705693i	$0.249364\pi$
$822$	−5.34812	+	30.8169i	−0.186537	+	1.07486i
$823$	−0.237770	−	0.731782i	−0.00828815	−	0.0255083i	0.946827	−	0.321743i	$-0.104269\pi$
$823$	−0.237770	−	0.731782i	−0.00828815	−	0.0255083i	−0.955115	+	0.296235i	$0.904269\pi$
$824$	4.60947			0.160578
$825$		0			0
$826$	−9.50523			−0.330729
$827$	−15.2780	−	47.0207i	−0.531267	−	1.63507i	−0.751581	−	0.659641i	$-0.770708\pi$
$827$	−15.2780	−	47.0207i	−0.531267	−	1.63507i	0.220314	−	0.975429i	$-0.429292\pi$
$828$	−4.18769	−	14.3121i	−0.145532	−	0.497380i
$829$	14.2060	−	10.3212i	0.493393	−	0.358471i	−0.313095	−	0.949722i	$-0.601366\pi$
$829$	14.2060	−	10.3212i	0.493393	−	0.358471i	0.806488	+	0.591251i	$0.201366\pi$
$830$	−13.8428	−	4.49779i	−0.480490	−	0.156121i
$831$	14.1996	−	2.03473i	0.492578	−	0.0705839i
$832$	1.10940	+	1.52696i	0.0384616	+	0.0529379i
$833$	−19.8562	−	14.4264i	−0.687976	−	0.499844i
$834$	−1.22947	+	1.19372i	−0.0425732	+	0.0413352i
$835$			3.48827i			0.120717i
$836$		0			0
$837$	−6.81013	+	33.3656i	−0.235392	+	1.15329i
$838$	−33.1407	+	10.7681i	−1.14483	+	0.371977i
$839$	−0.712228	+	0.980298i	−0.0245888	+	0.0338436i	−0.821134	−	0.570735i	$-0.806658\pi$
$839$	−0.712228	+	0.980298i	−0.0245888	+	0.0338436i	0.796546	+	0.604578i	$0.206658\pi$
$840$	5.87928	−	11.1297i	0.202854	−	0.384011i
$841$	−3.59201	+	11.0551i	−0.123863	+	0.381210i
$842$	−5.42375	+	16.6926i	−0.186915	+	0.575265i
$843$	10.2462	−	19.3964i	0.352897	−	0.668048i
$844$	−5.03276	+	6.92699i	−0.173235	+	0.238437i
$845$	19.0221	−	6.18065i	0.654379	−	0.212621i
$846$	−8.00000	−	6.18102i	−0.275046	−	0.212508i
$847$		0			0
$848$		−	6.21456i		−	0.213409i
$849$	−28.0965	+	27.2795i	−0.964271	+	0.936230i
$850$	−2.12238	−	1.54200i	−0.0727971	−	0.0528902i
$851$	25.7876	+	35.4935i	0.883987	+	1.21670i
$852$	17.0761	−	2.44692i	0.585017	−	0.0838300i
$853$	−2.04187	−	0.663444i	−0.0699123	−	0.0227159i	0.273852	−	0.961772i	$-0.411702\pi$
$853$	−2.04187	−	0.663444i	−0.0699123	−	0.0227159i	−0.343764	+	0.939056i	$0.611702\pi$
$854$	−4.49137	+	3.26317i	−0.153691	+	0.111663i
$855$	−1.47017	+	0.430167i	−0.0502786	+	0.0147114i
$856$	−5.60407	−	17.2475i	−0.191543	−	0.589509i
$857$	−55.7274			−1.90361			−0.951805	−	0.306704i	$-0.900774\pi$
$857$	−55.7274			−1.90361			−0.951805	+	0.306704i	$0.900774\pi$
$858$		0			0
$859$	−36.2927			−1.23829			−0.619146	−	0.785276i	$-0.712521\pi$
$859$	−36.2927			−1.23829			−0.619146	+	0.785276i	$0.712521\pi$
$860$	−4.26719	−	13.1331i	−0.145510	−	0.447833i
$861$	−8.05905	+	46.4379i	−0.274652	+	1.58260i
$862$	27.0376	−	19.6440i	0.920905	−	0.669077i
$863$	−29.6543	−	9.63527i	−1.00944	−	0.327988i	−0.242811	−	0.970074i	$-0.578070\pi$
$863$	−29.6543	−	9.63527i	−1.00944	−	0.327988i	−0.766633	+	0.642085i	$0.778070\pi$
$864$	−4.52089	−	2.56155i	−0.153804	−	0.0871456i
$865$	4.37065	+	6.01568i	0.148606	+	0.204539i
$866$	21.9952	+	15.9805i	0.747428	+	0.543039i
$867$	−11.5861	−	11.9331i	−0.393485	−	0.405271i
$868$		−	22.4728i		−	0.762777i
$869$		0			0
$870$	6.74470	+	13.7345i	0.228667	+	0.465642i
$871$	−17.9217	+	5.82312i	−0.607254	+	0.197309i
$872$	−0.413086	+	0.568564i	−0.0139888	+	0.0192540i
$873$	1.17026	−	39.6487i	0.0396074	−	1.34191i
$874$	0.370079	−	1.13899i	0.0125181	−	0.0385268i
$875$	−12.3706	+	38.0729i	−0.418204	+	1.28710i
$876$	−3.79774	−	2.00616i	−0.128314	−	0.0677819i
$877$	10.8949	−	14.9956i	0.367895	−	0.506365i	−0.584432	−	0.811443i	$-0.698683\pi$
$877$	10.8949	−	14.9956i	0.367895	−	0.506365i	0.952327	+	0.305078i	$0.0986826\pi$
$878$	−12.7506	+	4.14293i	−0.430313	+	0.139817i
$879$	39.0105	−	19.1572i	1.31579	−	0.646157i
$880$		0			0
$881$			22.0893i			0.744207i	0.928191	+	0.372103i	$0.121363\pi$
$881$			22.0893i			0.744207i	−0.928191	+	0.372103i	$0.878637\pi$
$882$	13.4409	+	4.81006i	0.452579	+	0.161963i
$883$	−35.3330	−	25.6709i	−1.18905	−	0.863894i	−0.195885	−	0.980627i	$-0.562758\pi$
$883$	−35.3330	−	25.6709i	−1.18905	−	0.863894i	−0.993163	+	0.116733i	$0.962758\pi$
$884$	−5.72206	−	7.87574i	−0.192454	−	0.264890i
$885$	1.44329	+	10.0721i	0.0485155	+	0.338571i
$886$	17.5311	+	5.69619i	0.588968	+	0.191367i
$887$	−6.82936	+	4.96182i	−0.229307	+	0.166602i	−0.696506	−	0.717551i	$-0.745263\pi$
$887$	−6.82936	+	4.96182i	−0.229307	+	0.166602i	0.467199	+	0.884152i	$0.345263\pi$
$888$	15.0622	+	2.61397i	0.505456	+	0.0877191i
$889$	18.5847	+	57.1979i	0.623312	+	1.91836i
$890$	−5.24001			−0.175646
$891$		0			0
$892$	0.0503526			0.00168593
$893$	−0.250894	−	0.772172i	−0.00839585	−	0.0258398i
$894$	−23.8697	−	4.14245i	−0.798321	−	0.138544i
$895$	22.7569	−	16.5338i	0.760678	−	0.552665i
$896$	3.26124	+	1.05964i	0.108951	+	0.0354002i
$897$	2.30498	+	16.0856i	0.0769611	+	0.537082i
$898$	−17.8510	−	24.5698i	−0.595697	−	0.819906i
$899$	22.1011	+	16.0574i	0.737112	+	0.535543i
$900$	1.43667	+	0.514137i	0.0478889	+	0.0171379i
$901$			32.0534i			1.06785i
$902$		0			0
$903$	34.7371	−	17.0587i	1.15598	−	0.567677i
$904$	4.07454	−	1.32390i	0.135517	−	0.0440322i
$905$	9.25984	−	12.7451i	0.307808	−	0.423661i
$906$	−9.69208	−	5.11985i	−0.321998	−	0.170096i
$907$	−3.70460	+	11.4016i	−0.123009	+	0.378583i	−0.993533	−	0.113543i	$-0.963780\pi$
$907$	−3.70460	+	11.4016i	−0.123009	+	0.378583i	0.870524	+	0.492126i	$0.163780\pi$
$908$	−4.41512	+	13.5884i	−0.146521	+	0.450945i
$909$	0.217754	−	7.37754i	0.00722244	−	0.244697i
$910$	−8.06224	+	11.0967i	−0.267261	+	0.367853i
$911$	−27.1492	+	8.82132i	−0.899494	+	0.292263i	−0.722028	−	0.691864i	$-0.756790\pi$
$911$	−27.1492	+	8.82132i	−0.899494	+	0.292263i	−0.177466	+	0.984127i	$0.556790\pi$
$912$	−0.183946	−	0.374576i	−0.00609108	−	0.0124035i
$913$		0			0
$914$			34.6878i			1.14737i
$915$	4.13977	+	4.26376i	0.136857	+	0.140956i
$916$	24.4668	+	17.7761i	0.808405	+	0.587340i
$917$	−9.72101	−	13.3798i	−0.321016	−	0.441841i
$918$	23.3178	+	13.2119i	0.769602	+	0.436058i
$919$	−52.3547	−	17.0111i	−1.72702	−	0.561143i	−0.734008	−	0.679141i	$-0.762352\pi$
$919$	−52.3547	−	17.0111i	−1.72702	−	0.561143i	−0.993014	+	0.117998i	$0.962352\pi$
$920$	8.52249	−	6.19195i	0.280978	−	0.204143i
$921$	4.75877	−	27.4210i	0.156807	−	0.903552i
$922$	6.45155	+	19.8558i	0.212471	+	0.653917i
$923$	−18.7980			−0.618745
$924$		0			0
$925$	−4.48926			−0.147606
$926$	−1.89851	−	5.84302i	−0.0623890	−	0.192013i
$927$	13.2719	−	3.88334i	0.435908	−	0.127546i
$928$	−3.37235	+	2.45016i	−0.110703	+	0.0804303i
$929$	10.6108	+	3.44764i	0.348128	+	0.113114i	0.477861	−	0.878435i	$-0.341412\pi$
$929$	10.6108	+	3.44764i	0.348128	+	0.113114i	−0.129734	+	0.991549i	$0.541412\pi$
$930$	−23.8132	+	3.41230i	−0.780864	+	0.111894i
$931$	0.673887	+	0.927526i	0.0220858	+	0.0303984i
$932$	−2.28819	−	1.66247i	−0.0749521	−	0.0544559i
$933$	11.9614	−	11.6136i	0.391599	−	0.380211i
$934$			34.8047i			1.13885i
$935$		0			0
$936$	4.48070	+	3.46191i	0.146456	+	0.113156i
$937$	30.0019	−	9.74821i	0.980120	−	0.318460i	0.225225	−	0.974307i	$-0.427688\pi$
$937$	30.0019	−	9.74821i	0.980120	−	0.318460i	0.754894	+	0.655847i	$0.227688\pi$
$938$	−20.1233	+	27.6973i	−0.657048	+	0.904349i
$939$	16.2725	−	30.8045i	0.531034	−	1.00527i
$940$	2.20692	−	6.79220i	0.0719818	−	0.221537i
$941$	−15.7950	+	48.6119i	−0.514901	+	1.58470i	0.268560	+	0.963263i	$0.413452\pi$
$941$	−15.7950	+	48.6119i	−0.514901	+	1.58470i	−0.783462	+	0.621440i	$0.786548\pi$
$942$	3.00000	−	5.67911i	0.0977453	−	0.185036i
$943$	−23.1855	+	31.9121i	−0.755024	+	1.03920i
$944$	−2.63628	+	0.856580i	−0.0858037	+	0.0278793i
$945$	7.55164	−	36.9986i	0.245655	−	1.20356i
$946$		0			0
$947$			23.9467i			0.778162i	0.921204	+	0.389081i	$0.127207\pi$
$947$			23.9467i			0.778162i	−0.921204	+	0.389081i	$0.872793\pi$
$948$	14.0778	−	13.6684i	0.457226	−	0.443929i
$949$	3.78649	+	2.75104i	0.122915	+	0.0893027i
$950$	0.0720302	+	0.0991411i	0.00233697	+	0.00321656i
$951$	31.6352	−	4.53316i	1.02584	−	0.146998i
$952$	−16.8208	−	5.46541i	−0.545165	−	0.177135i
$953$	−16.1924	+	11.7645i	−0.524524	+	0.381089i	−0.818306	−	0.574784i	$-0.805086\pi$
$953$	−16.1924	+	11.7645i	−0.524524	+	0.381089i	0.293781	+	0.955873i	$0.405086\pi$
$954$	−5.23558	−	17.8934i	−0.169508	−	0.579322i
$955$	1.69632	+	5.22073i	0.0548915	+	0.168939i
$956$	−1.13536			−0.0367203
$957$		0			0
$958$	−34.8328			−1.12540
$959$	−19.1351	−	58.8919i	−0.617906	−	1.90172i
$960$	0.627650	−	3.61665i	0.0202573	−	0.116727i
$961$	−9.66758	+	7.02390i	−0.311857	+	0.226578i
$962$	−15.8434	−	5.14784i	−0.510813	−	0.165973i
$963$	−30.6662	−	44.9392i	−0.988205	−	1.44815i
$964$	8.84404	+	12.1728i	0.284847	+	0.392059i
$965$	33.4779	+	24.3231i	1.07769	+	0.782988i
$966$	20.5655	+	21.1815i	0.661684	+	0.681502i
$967$			48.8703i			1.57156i	0.618505	+	0.785781i	$0.287739\pi$
$967$			48.8703i			1.57156i	−0.618505	+	0.785781i	$0.712261\pi$
$968$		0			0
$969$	0.948756	+	1.93198i	0.0304784	+	0.0620642i
$970$	26.6497	−	8.65902i	0.855671	−	0.278024i
$971$	16.0664	−	22.1135i	0.515595	−	0.709656i	−0.469255	−	0.883063i	$-0.655478\pi$
$971$	16.0664	−	22.1135i	0.515595	−	0.709656i	0.984850	+	0.173407i	$0.0554775\pi$
$972$	−15.1749	−	3.56668i	−0.486736	−	0.114401i
$973$	1.04838	−	3.22659i	0.0336096	−	0.103440i
$974$	1.78176	−	5.48370i	0.0570913	−	0.175709i
$975$	−1.47025	−	0.776660i	−0.0470856	−	0.0248730i
$976$	−0.951618	+	1.30979i	−0.0304606	+	0.0419254i
$977$	14.7096	−	4.77945i	0.470603	−	0.152908i	−0.0641084	−	0.997943i	$-0.520420\pi$
$977$	14.7096	−	4.77945i	0.470603	−	0.152908i	0.534711	+	0.845035i	$0.320420\pi$
$978$	13.2933	−	6.52808i	0.425074	−	0.208745i
$979$		0			0
$980$			10.0847i			0.322145i
$981$	−0.710390	+	1.98507i	−0.0226810	+	0.0633783i
$982$	−8.42871	−	6.12382i	−0.268971	−	0.195419i
$983$	−25.9872	−	35.7683i	−0.828863	−	1.14083i	−0.988134	−	0.153597i	$-0.950914\pi$
$983$	−25.9872	−	35.7683i	−0.828863	−	1.14083i	0.159271	−	0.987235i	$-0.449086\pi$
$984$	1.94965	+	13.6058i	0.0621525	+	0.433738i
$985$	10.8581	+	3.52800i	0.345967	+	0.112411i
$986$	17.3939	−	12.6374i	0.553933	−	0.402456i
$987$	19.7201	+	3.42232i	0.627697	+	0.108934i
$988$	0.140523	+	0.432484i	0.00447062	+	0.0137591i
$989$	32.3884			1.02989
$990$		0			0
$991$	−36.1335			−1.14782			−0.573909	−	0.818919i	$-0.694574\pi$
$991$	−36.1335			−1.14782			−0.573909	+	0.818919i	$0.694574\pi$
$992$	−2.02518	−	6.23285i	−0.0642994	−	0.197893i
$993$	−8.59485	−	1.49159i	−0.272749	−	0.0473342i
$994$	−27.6297	+	20.0742i	−0.876361	+	0.636714i
$995$	−14.8892	−	4.83779i	−0.472019	−	0.153368i
$996$	−1.68735	−	11.7754i	−0.0534658	−	0.373117i
$997$	−4.77670	−	6.57457i	−0.151280	−	0.208219i	0.726650	−	0.687007i	$-0.241076\pi$
$997$	−4.77670	−	6.57457i	−0.151280	−	0.208219i	−0.877930	+	0.478789i	$0.841076\pi$
$998$	−17.7151	−	12.8708i	−0.560763	−	0.407418i
$999$	45.5706	−	5.16314i	1.44179	−	0.163355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.h.j.215.2		8
3.2	odd	2		726.2.h.d.215.2		8
11.2	odd	10		726.2.h.d.233.1		8
11.3	even	5		726.2.b.c.725.4		8
11.4	even	5		726.2.h.h.239.1		8
11.5	even	5		726.2.h.f.161.2		8
11.6	odd	10		726.2.h.a.161.2		8
11.7	odd	10		726.2.h.c.239.1		8
11.8	odd	10		726.2.b.e.725.4		8
11.9	even	5		66.2.h.b.35.1	yes	8
11.10	odd	2		66.2.h.a.17.2	✓	8
33.2	even	10	inner	726.2.h.j.233.2		8
33.5	odd	10		726.2.h.c.161.1		8
33.8	even	10		726.2.b.c.725.3		8
33.14	odd	10		726.2.b.e.725.3		8
33.17	even	10		726.2.h.h.161.1		8
33.20	odd	10		66.2.h.a.35.2	yes	8
33.26	odd	10		726.2.h.a.239.2		8
33.29	even	10		726.2.h.f.239.2		8
33.32	even	2		66.2.h.b.17.2	yes	8
44.31	odd	10		528.2.bn.a.497.2		8
44.43	even	2		528.2.bn.b.17.1		8
132.119	even	10		528.2.bn.b.497.1		8
132.131	odd	2		528.2.bn.a.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.h.a.17.2	✓	8	11.10	odd	2
66.2.h.a.35.2	yes	8	33.20	odd	10
66.2.h.b.17.2	yes	8	33.32	even	2
66.2.h.b.35.1	yes	8	11.9	even	5
528.2.bn.a.17.1		8	132.131	odd	2
528.2.bn.a.497.2		8	44.31	odd	10
528.2.bn.b.17.1		8	44.43	even	2
528.2.bn.b.497.1		8	132.119	even	10
726.2.b.c.725.3		8	33.8	even	10
726.2.b.c.725.4		8	11.3	even	5
726.2.b.e.725.3		8	33.14	odd	10
726.2.b.e.725.4		8	11.8	odd	10
726.2.h.a.161.2		8	11.6	odd	10
726.2.h.a.239.2		8	33.26	odd	10
726.2.h.c.161.1		8	33.5	odd	10
726.2.h.c.239.1		8	11.7	odd	10
726.2.h.d.215.2		8	3.2	odd	2
726.2.h.d.233.1		8	11.2	odd	10
726.2.h.f.161.2		8	11.5	even	5
726.2.h.f.239.2		8	33.29	even	10
726.2.h.h.161.1		8	33.17	even	10
726.2.h.h.239.1		8	11.4	even	5
726.2.h.j.215.2		8	1.1	even	1	trivial
726.2.h.j.233.2		8	33.2	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(1.70654 + 0.296161i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.01556 - 0.654895i) q^{5} +(-0.245684 - 1.71454i) q^{6} +(2.01556 + 2.77418i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.82458 + 1.01082i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(1.70654 + 0.296161i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.01556 - 0.654895i) q^{5} +(-0.245684 - 1.71454i) q^{6} +(2.01556 + 2.77418i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.82458 + 1.01082i) q^{9} +2.11929i q^{10} +(-1.55470 + 0.763481i) q^{12} +(1.79505 - 0.583248i) q^{13} +(2.01556 - 2.77418i) q^{14} +(-3.24568 - 1.71454i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.59384 + 4.90534i) q^{17} +(0.0885088 - 2.99869i) q^{18} +(0.141616 - 0.194917i) q^{19} +(2.01556 - 0.654895i) q^{20} +(2.61803 + 5.33119i) q^{21} +4.97072i q^{23} +(1.20654 + 1.24268i) q^{24} +(-0.411491 - 0.298966i) q^{25} +(-1.10940 - 1.52696i) q^{26} +(4.52089 + 2.56155i) q^{27} +(-3.26124 - 1.05964i) q^{28} +(3.37235 - 2.45016i) q^{29} +(-0.627650 + 3.61665i) q^{30} +(2.02518 + 6.23285i) q^{31} -1.00000 q^{32} +5.15778 q^{34} +(-2.24568 - 6.91151i) q^{35} +(-2.87928 + 0.842471i) q^{36} +(7.14052 - 5.18789i) q^{37} +(-0.229139 - 0.0744518i) q^{38} +(3.23607 - 0.463712i) q^{39} +(-1.24568 - 1.71454i) q^{40} +(6.42001 + 4.66441i) q^{41} +(4.26124 - 4.13733i) q^{42} -6.51583i q^{43} +(-5.03112 - 3.88718i) q^{45} +(4.72744 - 1.53604i) q^{46} +(1.98077 - 2.72629i) q^{47} +(0.809017 - 1.53150i) q^{48} +(-1.47047 + 4.52566i) q^{49} +(-0.157176 + 0.483737i) q^{50} +(-4.17274 + 7.89915i) q^{51} +(-1.10940 + 1.52696i) q^{52} +(5.91040 - 1.92040i) q^{53} +(1.03914 - 5.09119i) q^{54} +3.42908i q^{56} +(0.299400 - 0.290694i) q^{57} +(-3.37235 - 2.45016i) q^{58} +(-1.62931 - 2.24256i) q^{59} +(3.63359 - 0.520675i) q^{60} +(-1.53975 - 0.500295i) q^{61} +(5.30198 - 3.85211i) q^{62} +(2.88889 + 9.87326i) q^{63} +(0.309017 + 0.951057i) q^{64} -4.00000 q^{65} -9.98396 q^{67} +(-1.59384 - 4.90534i) q^{68} +(-1.47214 + 8.48275i) q^{69} +(-5.87928 + 4.27155i) q^{70} +(-9.47214 - 3.07768i) q^{71} +(1.69098 + 2.47802i) q^{72} +(1.45756 + 2.00616i) q^{73} +(-7.14052 - 5.18789i) q^{74} +(-0.613685 - 0.632066i) q^{75} +0.240931i q^{76} +(-1.44102 - 2.93439i) q^{78} +(-10.7741 + 3.50072i) q^{79} +(-1.24568 + 1.71454i) q^{80} +(6.95647 + 5.71030i) q^{81} +(2.45223 - 7.54718i) q^{82} +(-2.12232 + 6.53182i) q^{83} +(-5.25163 - 2.77418i) q^{84} +(6.42497 - 8.84322i) q^{85} +(-6.19693 + 2.01350i) q^{86} +(6.48070 - 3.18254i) q^{87} +2.47254i q^{89} +(-2.14222 + 5.98608i) q^{90} +(5.23607 + 3.80423i) q^{91} +(-2.92172 - 4.02140i) q^{92} +(1.61012 + 11.2364i) q^{93} +(-3.20495 - 1.04135i) q^{94} +(-0.413086 + 0.300124i) q^{95} +(-1.70654 - 0.296161i) q^{96} +(-4.08582 - 12.5749i) q^{97} +4.75856 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 3 * q^6 + 2 * q^8 + 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{8} + 2 q^{9} - 3 q^{12} - 21 q^{15} - 2 q^{16} - 10 q^{17} - 2 q^{18} + 15 q^{19} + 12 q^{21} - 2 q^{24} - 6 q^{25} + 10 q^{26} + 20 q^{27} - 5 q^{28} + 23 q^{29} - 9 q^{30} + 13 q^{31} - 8 q^{32} + 10 q^{34} - 13 q^{35} + 7 q^{36} + 6 q^{37} - 10 q^{38} + 8 q^{39} - 5 q^{40} + 2 q^{41} + 13 q^{42} - 8 q^{45} + 10 q^{46} - 10 q^{47} + 2 q^{48} - 18 q^{49} + q^{50} - 15 q^{51} + 10 q^{52} - 15 q^{53} + 15 q^{54} - 15 q^{57} - 23 q^{58} + 25 q^{59} + 4 q^{60} + 10 q^{61} + 2 q^{62} + 6 q^{63} - 2 q^{64} - 32 q^{65} - 2 q^{67} - 10 q^{68} + 24 q^{69} - 17 q^{70} - 40 q^{71} + 18 q^{72} - 5 q^{73} - 6 q^{74} + q^{75} - 8 q^{78} - 10 q^{79} - 5 q^{80} - 26 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} - 30 q^{85} - 25 q^{86} + 42 q^{87} - 2 q^{90} + 24 q^{91} - 10 q^{92} + 27 q^{93} - 40 q^{94} + 20 q^{95} - 2 q^{96} + 9 q^{97} - 22 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 3 * q^6 + 2 * q^8 + 2 * q^9 - 3 * q^12 - 21 * q^15 - 2 * q^16 - 10 * q^17 - 2 * q^18 + 15 * q^19 + 12 * q^21 - 2 * q^24 - 6 * q^25 + 10 * q^26 + 20 * q^27 - 5 * q^28 + 23 * q^29 - 9 * q^30 + 13 * q^31 - 8 * q^32 + 10 * q^34 - 13 * q^35 + 7 * q^36 + 6 * q^37 - 10 * q^38 + 8 * q^39 - 5 * q^40 + 2 * q^41 + 13 * q^42 - 8 * q^45 + 10 * q^46 - 10 * q^47 + 2 * q^48 - 18 * q^49 + q^50 - 15 * q^51 + 10 * q^52 - 15 * q^53 + 15 * q^54 - 15 * q^57 - 23 * q^58 + 25 * q^59 + 4 * q^60 + 10 * q^61 + 2 * q^62 + 6 * q^63 - 2 * q^64 - 32 * q^65 - 2 * q^67 - 10 * q^68 + 24 * q^69 - 17 * q^70 - 40 * q^71 + 18 * q^72 - 5 * q^73 - 6 * q^74 + q^75 - 8 * q^78 - 10 * q^79 - 5 * q^80 - 26 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 - 30 * q^85 - 25 * q^86 + 42 * q^87 - 2 * q^90 + 24 * q^91 - 10 * q^92 + 27 * q^93 - 40 * q^94 + 20 * q^95 - 2 * q^96 + 9 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more