LMFDB - Embedded newform 722.2.e.n.99.1

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.186694177220038656.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 343x^{6} + 117649 $ x^12 + 343*x^6 + 117649
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			99.1
Root			$2.48619 + 0.904900i$ of defining polynomial
Character	$\chi$	$=$	722.99
Dual form			722.2.e.n.423.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.459430 - 2.60556i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.79281 - 2.34344i) q^{5} +(-0.459430 + 2.60556i) q^{6} +(0.822876 - 1.42526i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.75877 + 1.36808i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.459430 - 2.60556i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.79281 - 2.34344i) q^{5} +(-0.459430 + 2.60556i) q^{6} +(0.822876 - 1.42526i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.75877 + 1.36808i) q^{9} +(-3.42589 + 1.24692i) q^{10} +(-0.322876 - 0.559237i) q^{11} +(1.32288 - 2.29129i) q^{12} +(0.347296 - 1.96962i) q^{13} +(-1.26072 + 1.05787i) q^{14} +(-7.38907 - 6.20017i) q^{15} +(0.173648 + 0.984808i) q^{16} +4.00000 q^{18} +3.64575 q^{20} +(-4.09166 - 1.48924i) q^{21} +(0.112134 + 0.635941i) q^{22} +(2.79281 + 2.34344i) q^{23} +(-2.02676 + 1.70066i) q^{24} +(1.43980 - 8.16554i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(1.32288 + 2.29129i) q^{27} +(1.54650 - 0.562880i) q^{28} +(3.42589 - 1.24692i) q^{29} +(4.82288 + 8.35347i) q^{30} +(0.177124 - 0.306788i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-1.30878 + 1.09820i) q^{33} +(-1.04189 - 5.90885i) q^{35} +(-3.75877 - 1.36808i) q^{36} +5.64575 q^{37} -5.29150 q^{39} +(-3.42589 - 1.24692i) q^{40} +(1.78710 + 10.1352i) q^{41} +(3.33555 + 2.79886i) q^{42} +(0.542740 - 0.455413i) q^{43} +(0.112134 - 0.635941i) q^{44} +(-7.29150 + 12.6293i) q^{45} +(-1.82288 - 3.15731i) q^{46} +(-9.06404 + 3.29904i) q^{47} +(2.48619 - 0.904900i) q^{48} +(2.14575 + 3.71655i) q^{49} +(-4.14575 + 7.18065i) q^{50} +(1.53209 - 1.28558i) q^{52} +(6.57496 + 5.51705i) q^{53} +(-0.459430 - 2.60556i) q^{54} +(-2.21227 - 0.805200i) q^{55} -1.64575 q^{56} -3.64575 q^{58} +(-7.45858 - 2.71470i) q^{59} +(-1.67497 - 9.49921i) q^{60} +(-11.4426 - 9.60148i) q^{61} +(-0.271370 + 0.227707i) q^{62} +(-1.14313 + 6.48299i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.64575 - 6.31463i) q^{65} +(1.60546 - 0.584341i) q^{66} +(4.36558 - 1.58894i) q^{67} +(4.82288 - 8.35347i) q^{69} +(-1.04189 + 5.90885i) q^{70} +(-10.1819 + 8.54361i) q^{71} +(3.06418 + 2.57115i) q^{72} +(2.13440 + 12.1048i) q^{73} +(-5.30527 - 1.93096i) q^{74} -21.9373 q^{75} -1.06275 q^{77} +(4.97239 + 1.80980i) q^{78} +(-0.694593 - 3.93923i) q^{79} +(2.79281 + 2.34344i) q^{80} +(-3.83022 + 3.21394i) q^{81} +(1.78710 - 10.1352i) q^{82} +(3.96863 - 6.87386i) q^{83} +(-2.17712 - 3.77089i) q^{84} +(-0.665770 + 0.242320i) q^{86} +(-4.82288 - 8.35347i) q^{87} +(-0.322876 + 0.559237i) q^{88} +(11.1712 - 9.37378i) q^{90} +(-2.52144 - 2.11574i) q^{91} +(0.633078 + 3.59036i) q^{92} +(-0.880731 - 0.320560i) q^{93} +9.64575 q^{94} -2.64575 q^{96} +(13.4296 + 4.88798i) q^{97} +(-0.745212 - 4.22631i) q^{98} +(1.97870 + 1.66032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8	$ 12 q - 6 q^{7} - 6 q^{8} + 12 q^{11} + 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} + 18 q^{31} + 36 q^{37} - 24 q^{45} - 6 q^{46} - 6 q^{49} - 18 q^{50} + 12 q^{56} - 12 q^{58} - 6 q^{64} - 12 q^{65} + 42 q^{69} - 168 q^{75} - 108 q^{77} - 42 q^{84} - 42 q^{87} + 12 q^{88} + 84 q^{94}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 12 * q^11 + 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 + 18 * q^31 + 36 * q^37 - 24 * q^45 - 6 * q^46 - 6 * q^49 - 18 * q^50 + 12 * q^56 - 12 * q^58 - 6 * q^64 - 12 * q^65 + 42 * q^69 - 168 * q^75 - 108 * q^77 - 42 * q^84 - 42 * q^87 + 12 * q^88 + 84 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.459430	−	2.60556i	−0.265252	−	1.50432i	−0.768317	−	0.640070i	$-0.778905\pi$
$3$	−0.459430	−	2.60556i	−0.265252	−	1.50432i	0.503065	−	0.864249i	$-0.332206\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	2.79281	−	2.34344i	1.24898	−	1.04802i	0.252215	−	0.967671i	$-0.418841\pi$
$5$	2.79281	−	2.34344i	1.24898	−	1.04802i	0.996767	−	0.0803486i	$-0.0256034\pi$
$6$	−0.459430	+	2.60556i	−0.187561	+	1.06371i
$7$	0.822876	−	1.42526i	0.311018	−	0.538699i	−0.667565	−	0.744551i	$-0.732663\pi$
$7$	0.822876	−	1.42526i	0.311018	−	0.538699i	0.978583	+	0.205853i	$0.0659968\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−3.75877	+	1.36808i	−1.25292	+	0.456027i
$10$	−3.42589	+	1.24692i	−1.08336	+	0.394311i
$11$	−0.322876	−	0.559237i	−0.0973507	−	0.168616i	0.813237	−	0.581933i	$-0.197704\pi$
$11$	−0.322876	−	0.559237i	−0.0973507	−	0.168616i	−0.910587	+	0.413317i	$0.864370\pi$
$12$	1.32288	−	2.29129i	0.381881	−	0.661438i
$13$	0.347296	−	1.96962i	0.0963227	−	0.546273i	−0.898011	−	0.439972i	$-0.854988\pi$
$13$	0.347296	−	1.96962i	0.0963227	−	0.546273i	0.994334	−	0.106301i	$-0.0339006\pi$
$14$	−1.26072	+	1.05787i	−0.336941	+	0.282727i
$15$	−7.38907	−	6.20017i	−1.90785	−	1.60088i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$17$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$18$	4.00000			0.942809
$19$		0			0
$19$		0			0
$20$	3.64575			0.815215
$21$	−4.09166	−	1.48924i	−0.892872	−	0.324979i
$22$	0.112134	+	0.635941i	0.0239070	+	0.135583i
$23$	2.79281	+	2.34344i	0.582341	+	0.488642i	0.885715	−	0.464230i	$-0.153669\pi$
$23$	2.79281	+	2.34344i	0.582341	+	0.488642i	−0.303374	+	0.952871i	$0.598113\pi$
$24$	−2.02676	+	1.70066i	−0.413711	+	0.347145i
$25$	1.43980	−	8.16554i	0.287961	−	1.63311i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	1.32288	+	2.29129i	0.254588	+	0.440959i
$28$	1.54650	−	0.562880i	0.292261	−	0.106374i
$29$	3.42589	−	1.24692i	0.636171	−	0.231547i	−0.00374403	−	0.999993i	$-0.501192\pi$
$29$	3.42589	−	1.24692i	0.636171	−	0.231547i	0.639915	+	0.768446i	$0.278970\pi$
$30$	4.82288	+	8.35347i	0.880533	+	1.52513i
$31$	0.177124	−	0.306788i	0.0318125	−	0.0551008i	−0.849681	−	0.527297i	$-0.823205\pi$
$31$	0.177124	−	0.306788i	0.0318125	−	0.0551008i	0.881493	+	0.472197i	$0.156539\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−1.30878	+	1.09820i	−0.227830	+	0.191172i
$34$		0			0
$35$	−1.04189	−	5.90885i	−0.176111	−	0.998777i
$36$	−3.75877	−	1.36808i	−0.626462	−	0.228013i
$37$	5.64575			0.928156			0.464078	−	0.885794i	$-0.346386\pi$
$37$	5.64575			0.928156			0.464078	+	0.885794i	$0.346386\pi$
$38$		0			0
$39$	−5.29150			−0.847319
$40$	−3.42589	−	1.24692i	−0.541680	−	0.197155i
$41$	1.78710	+	10.1352i	0.279098	+	1.58284i	0.725635	+	0.688080i	$0.241546\pi$
$41$	1.78710	+	10.1352i	0.279098	+	1.58284i	−0.446537	+	0.894765i	$0.647343\pi$
$42$	3.33555	+	2.79886i	0.514686	+	0.431873i
$43$	0.542740	−	0.455413i	0.0827671	−	0.0694499i	−0.600465	−	0.799651i	$-0.705018\pi$
$43$	0.542740	−	0.455413i	0.0827671	−	0.0694499i	0.683233	+	0.730201i	$0.260574\pi$
$44$	0.112134	−	0.635941i	0.0169048	−	0.0958717i
$45$	−7.29150	+	12.6293i	−1.08695	+	1.88266i
$46$	−1.82288	−	3.15731i	−0.268768	−	0.465520i
$47$	−9.06404	+	3.29904i	−1.32213	+	0.481215i	−0.904139	−	0.427238i	$-0.859487\pi$
$47$	−9.06404	+	3.29904i	−1.32213	+	0.481215i	−0.417987	+	0.908453i	$0.637264\pi$
$48$	2.48619	−	0.904900i	0.358851	−	0.130611i
$49$	2.14575	+	3.71655i	0.306536	+	0.530936i
$50$	−4.14575	+	7.18065i	−0.586298	+	1.01550i
$51$		0			0
$52$	1.53209	−	1.28558i	0.212463	−	0.178277i
$53$	6.57496	+	5.51705i	0.903141	+	0.757825i	0.970802	−	0.239883i	$-0.0771092\pi$
$53$	6.57496	+	5.51705i	0.903141	+	0.757825i	−0.0676610	+	0.997708i	$0.521554\pi$
$54$	−0.459430	−	2.60556i	−0.0625205	−	0.354571i
$55$	−2.21227	−	0.805200i	−0.298302	−	0.108573i
$56$	−1.64575			−0.219923
$57$		0			0
$58$	−3.64575			−0.478711
$59$	−7.45858	−	2.71470i	−0.971024	−	0.353424i	−0.192680	−	0.981262i	$-0.561718\pi$
$59$	−7.45858	−	2.71470i	−0.971024	−	0.353424i	−0.778344	+	0.627838i	$0.783940\pi$
$60$	−1.67497	−	9.49921i	−0.216237	−	1.22634i
$61$	−11.4426	−	9.60148i	−1.46507	−	1.22934i	−0.920565	−	0.390589i	$-0.872271\pi$
$61$	−11.4426	−	9.60148i	−1.46507	−	1.22934i	−0.544510	−	0.838754i	$-0.683284\pi$
$62$	−0.271370	+	0.227707i	−0.0344641	+	0.0289188i
$63$	−1.14313	+	6.48299i	−0.144020	+	0.816781i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−3.64575	−	6.31463i	−0.452200	−	0.783233i
$66$	1.60546	−	0.584341i	0.197619	−	0.0719273i
$67$	4.36558	−	1.58894i	0.533340	−	0.194120i	−0.0612889	−	0.998120i	$-0.519521\pi$
$67$	4.36558	−	1.58894i	0.533340	−	0.194120i	0.594629	+	0.804000i	$0.297299\pi$
$68$		0			0
$69$	4.82288	−	8.35347i	0.580606	−	1.00564i
$70$	−1.04189	+	5.90885i	−0.124530	+	0.706242i
$71$	−10.1819	+	8.54361i	−1.20837	+	1.01394i	−0.209016	+	0.977912i	$0.567026\pi$
$71$	−10.1819	+	8.54361i	−1.20837	+	1.01394i	−0.999351	+	0.0360282i	$0.988529\pi$
$72$	3.06418	+	2.57115i	0.361117	+	0.303013i
$73$	2.13440	+	12.1048i	0.249812	+	1.41676i	0.809046	+	0.587746i	$0.199984\pi$
$73$	2.13440	+	12.1048i	0.249812	+	1.41676i	−0.559233	+	0.829010i	$0.688904\pi$
$74$	−5.30527	−	1.93096i	−0.616725	−	0.224470i
$75$	−21.9373			−2.53310
$76$		0			0
$77$	−1.06275			−0.121111
$78$	4.97239	+	1.80980i	0.563012	+	0.204920i
$79$	−0.694593	−	3.93923i	−0.0781478	−	0.443198i	−0.998626	−	0.0524041i	$-0.983312\pi$
$79$	−0.694593	−	3.93923i	−0.0781478	−	0.443198i	0.920478	−	0.390794i	$-0.127800\pi$
$80$	2.79281	+	2.34344i	0.312245	+	0.262005i
$81$	−3.83022	+	3.21394i	−0.425580	+	0.357104i
$82$	1.78710	−	10.1352i	0.197352	−	1.11924i
$83$	3.96863	−	6.87386i	0.435613	−	0.754505i	−0.561732	−	0.827319i	$-0.689865\pi$
$83$	3.96863	−	6.87386i	0.435613	−	0.754505i	0.997345	+	0.0728147i	$0.0231982\pi$
$84$	−2.17712	−	3.77089i	−0.237544	−	0.411438i
$85$		0			0
$86$	−0.665770	+	0.242320i	−0.0717918	+	0.0261301i
$87$	−4.82288	−	8.35347i	−0.517067	−	0.895586i
$88$	−0.322876	+	0.559237i	−0.0344187	+	0.0596149i
$89$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$89$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$90$	11.1712	−	9.37378i	1.17755	−	0.988083i
$91$	−2.52144	−	2.11574i	−0.264318	−	0.221790i
$92$	0.633078	+	3.59036i	0.0660030	+	0.374321i
$93$	−0.880731	−	0.320560i	−0.0913275	−	0.0332405i
$94$	9.64575			0.994883
$95$		0			0
$96$	−2.64575			−0.270031
$97$	13.4296	+	4.88798i	1.36357	+	0.496299i	0.917157	−	0.398527i	$-0.130478\pi$
$97$	13.4296	+	4.88798i	1.36357	+	0.496299i	0.446415	+	0.894826i	$0.352701\pi$
$98$	−0.745212	−	4.22631i	−0.0752777	−	0.426921i
$99$	1.97870	+	1.66032i	0.198867	+	0.166869i
$100$	6.35166	−	5.32968i	0.635166	−	0.532968i
$101$	−1.45070	+	8.22733i	−0.144350	+	0.818650i	0.823537	+	0.567263i	$0.191998\pi$
$101$	−1.45070	+	8.22733i	−0.144350	+	0.818650i	−0.967887	+	0.251387i	$0.919113\pi$
$102$		0			0
$103$	1.35425	+	2.34563i	0.133438	+	0.231122i	0.925000	−	0.379968i	$-0.124065\pi$
$103$	1.35425	+	2.34563i	0.133438	+	0.231122i	−0.791562	+	0.611089i	$0.790732\pi$
$104$	−1.87939	+	0.684040i	−0.184289	+	0.0670757i
$105$	−14.9172	+	5.42940i	−1.45577	+	0.529855i
$106$	−4.29150	−	7.43310i	−0.416828	−	0.721967i
$107$	−2.35425	+	4.07768i	−0.227594	+	0.394204i	−0.957094	−	0.289776i	$-0.906419\pi$
$107$	−2.35425	+	4.07768i	−0.227594	+	0.394204i	0.729501	+	0.683980i	$0.239753\pi$
$108$	−0.459430	+	2.60556i	−0.0442087	+	0.250720i
$109$	−5.04287	+	4.23147i	−0.483020	+	0.405302i	−0.851517	−	0.524327i	$-0.824317\pi$
$109$	−5.04287	+	4.23147i	−0.483020	+	0.405302i	0.368497	+	0.929629i	$0.379872\pi$
$110$	1.80346	+	1.51328i	0.171953	+	0.144286i
$111$	−2.59383	−	14.7103i	−0.246195	−	1.39624i
$112$	1.54650	+	0.562880i	0.146131	+	0.0531872i
$113$	5.58301			0.525205			0.262602	−	0.964904i	$-0.415419\pi$
$113$	5.58301			0.525205			0.262602	+	0.964904i	$0.415419\pi$
$114$		0			0
$115$	13.2915			1.23944
$116$	3.42589	+	1.24692i	0.318085	+	0.115774i
$117$	1.38919	+	7.87846i	0.128430	+	0.728364i
$118$	6.08029	+	5.10197i	0.559736	+	0.469674i
$119$		0			0
$120$	−1.67497	+	9.49921i	−0.152903	+	0.867155i
$121$	5.29150	−	9.16515i	0.481046	−	0.833196i
$122$	7.46863	+	12.9360i	0.676178	+	1.17117i
$123$	25.5867	−	9.31278i	2.30707	−	0.839705i
$124$	0.332885	−	0.121160i	0.0298939	−	0.0108805i
$125$	−6.00000	−	10.3923i	−0.536656	−	0.929516i
$126$	3.29150	−	5.70105i	0.293230	−	0.507890i
$127$	−0.470326	+	2.66735i	−0.0417347	+	0.236689i	−0.998538	−	0.0540453i	$-0.982788\pi$
$127$	−0.470326	+	2.66735i	−0.0417347	+	0.236689i	0.956804	+	0.290734i	$0.0938996\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−1.43596	−	1.20491i	−0.126429	−	0.106086i
$130$	1.26616	+	7.18073i	0.111049	+	0.629792i
$131$	13.0967	+	4.76682i	1.14427	+	0.416479i	0.843453	−	0.537204i	$-0.180519\pi$
$131$	13.0967	+	4.76682i	1.14427	+	0.416479i	0.300814	+	0.953683i	$0.402742\pi$
$132$	−1.70850			−0.148706
$133$		0			0
$134$	−4.64575			−0.401332
$135$	9.06404	+	3.29904i	0.780108	+	0.283936i
$136$		0			0
$137$	−4.27683	−	3.58869i	−0.365394	−	0.306602i	0.441542	−	0.897241i	$-0.354432\pi$
$137$	−4.27683	−	3.58869i	−0.365394	−	0.306602i	−0.806936	+	0.590638i	$0.798876\pi$
$138$	−7.38907	+	6.20017i	−0.629000	+	0.527793i
$139$	2.31894	−	13.1514i	0.196690	−	1.11548i	−0.713301	−	0.700857i	$-0.752801\pi$
$139$	2.31894	−	13.1514i	0.196690	−	1.11548i	0.909991	−	0.414627i	$-0.136088\pi$
$140$	3.00000	−	5.19615i	0.253546	−	0.439155i
$141$	12.7601	+	22.1012i	1.07460	+	1.86126i
$142$	12.4899	−	4.54596i	1.04813	−	0.381489i
$143$	−1.21362	+	0.441720i	−0.101488	+	0.0369385i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	6.64575	−	11.5108i	0.551900	−	0.955918i
$146$	2.13440	−	12.1048i	0.176644	−	1.00180i
$147$	8.69786	−	7.29837i	0.717387	−	0.601959i
$148$	4.32490	+	3.62902i	0.355504	+	0.298304i
$149$	−0.857345	−	4.86225i	−0.0702365	−	0.398331i	−0.999576	−	0.0291054i	$-0.990734\pi$
$149$	−0.857345	−	4.86225i	−0.0702365	−	0.398331i	0.929340	−	0.369225i	$-0.120377\pi$
$150$	20.6143	+	7.50298i	1.68315	+	0.612616i
$151$	−2.93725			−0.239030			−0.119515	−	0.992832i	$-0.538134\pi$
$151$	−2.93725			−0.239030			−0.119515	+	0.992832i	$0.538134\pi$
$152$		0			0
$153$		0			0
$154$	0.998655	+	0.363481i	0.0804739	+	0.0292901i
$155$	−0.224267	−	1.27188i	−0.0180136	−	0.102160i
$156$	−4.05353	−	3.40131i	−0.324542	−	0.272323i
$157$	8.10705	−	6.80262i	0.647013	−	0.542909i	−0.259150	−	0.965837i	$-0.583442\pi$
$157$	8.10705	−	6.80262i	0.647013	−	0.542909i	0.906163	+	0.422929i	$0.138998\pi$
$158$	−0.694593	+	3.93923i	−0.0552588	+	0.313388i
$159$	11.3542	−	19.6661i	0.900450	−	1.55963i
$160$	−1.82288	−	3.15731i	−0.144111	−	0.249608i
$161$	5.63816	−	2.05212i	0.444349	−	0.161730i
$162$	4.69846	−	1.71010i	0.369146	−	0.134358i
$163$	5.96863	+	10.3380i	0.467499	+	0.809732i	0.999310	−	0.0371309i	$-0.0118218\pi$
$163$	5.96863	+	10.3380i	0.467499	+	0.809732i	−0.531811	+	0.846863i	$0.678489\pi$
$164$	−5.14575	+	8.91270i	−0.401816	+	0.695965i
$165$	−1.08161	+	6.13413i	−0.0842034	+	0.477541i
$166$	−6.08029	+	5.10197i	−0.471922	+	0.395990i
$167$	−9.19253	−	7.71345i	−0.711340	−	0.596885i	0.213635	−	0.976914i	$-0.431470\pi$
$167$	−9.19253	−	7.71345i	−0.711340	−	0.596885i	−0.924975	+	0.380029i	$0.875914\pi$
$168$	0.756107	+	4.28810i	0.0583349	+	0.330834i
$169$	8.45723	+	3.07818i	0.650556	+	0.236783i
$170$		0			0
$171$		0			0
$172$	0.708497			0.0540224
$173$	5.63816	+	2.05212i	0.428661	+	0.156020i	0.547335	−	0.836913i	$-0.315642\pi$
$173$	5.63816	+	2.05212i	0.428661	+	0.156020i	−0.118674	+	0.992933i	$0.537864\pi$
$174$	1.67497	+	9.49921i	0.126979	+	0.720133i
$175$	−10.4533	−	8.77132i	−0.790192	−	0.663049i
$176$	0.494674	−	0.415081i	0.0372875	−	0.0312879i
$177$	−3.64661	+	20.6810i	−0.274096	+	1.55448i
$178$		0			0
$179$	−9.96863	−	17.2662i	−0.745090	−	1.29053i	−0.950153	−	0.311785i	$-0.899073\pi$
$179$	−9.96863	−	17.2662i	−0.745090	−	1.29053i	0.205062	−	0.978749i	$-0.434260\pi$
$180$	−13.7035	+	4.98768i	−1.02140	+	0.371760i
$181$	3.97373	−	1.44632i	0.295365	−	0.107504i	−0.190087	−	0.981767i	$-0.560877\pi$
$181$	3.97373	−	1.44632i	0.295365	−	0.107504i	0.485452	+	0.874263i	$0.338655\pi$
$182$	1.64575	+	2.85052i	0.121991	+	0.211295i
$183$	−19.7601	+	34.2255i	−1.46071	+	2.53003i
$184$	0.633078	−	3.59036i	0.0466711	−	0.264685i
$185$	15.7675	−	13.2305i	1.15925	−	0.972726i
$186$	0.717978	+	0.602455i	0.0526447	+	0.0441742i
$187$		0			0
$188$	−9.06404	−	3.29904i	−0.661063	−	0.240607i
$189$	4.35425			0.316725
$190$		0			0
$191$	−14.5830			−1.05519			−0.527595	−	0.849496i	$-0.676906\pi$
$191$	−14.5830			−1.05519			−0.527595	+	0.849496i	$0.676906\pi$
$192$	2.48619	+	0.904900i	0.179426	+	0.0653055i
$193$	−1.14313	−	6.48299i	−0.0822841	−	0.466656i	−0.997910	−	0.0646241i	$-0.979415\pi$
$193$	−1.14313	−	6.48299i	−0.0822841	−	0.466656i	0.915626	−	0.402032i	$-0.131696\pi$
$194$	−10.9479	−	9.18640i	−0.786015	−	0.659545i
$195$	−14.7781	+	12.4003i	−1.05829	+	0.888007i
$196$	−0.745212	+	4.22631i	−0.0532294	+	0.301879i
$197$	1.17712	−	2.03884i	0.0838666	−	0.145261i	−0.821041	−	0.570869i	$-0.806606\pi$
$197$	1.17712	−	2.03884i	0.0838666	−	0.145261i	0.904908	+	0.425608i	$0.139940\pi$
$198$	−1.29150	−	2.23695i	−0.0917831	−	0.158973i
$199$	−11.1584	+	4.06132i	−0.790997	+	0.287899i	−0.705750	−	0.708460i	$-0.749390\pi$
$199$	−11.1584	+	4.06132i	−0.790997	+	0.287899i	−0.0852466	+	0.996360i	$0.527168\pi$
$200$	−7.79146	+	2.83586i	−0.550940	+	0.200526i
$201$	−6.14575	−	10.6448i	−0.433488	−	0.750823i
$202$	4.17712	−	7.23499i	0.293901	−	0.509052i
$203$	1.04189	−	5.90885i	0.0731263	−	0.414720i
$204$		0			0
$205$	28.7422	+	24.1176i	2.00744	+	1.68444i
$206$	−0.470326	−	2.66735i	−0.0327691	−	0.185843i
$207$	−13.7035	−	4.98768i	−0.952462	−	0.346668i
$208$	2.00000			0.138675
$209$		0			0
$210$	15.8745			1.09545
$211$	2.54515	+	0.926361i	0.175216	+	0.0637733i	0.428138	−	0.903713i	$-0.359170\pi$
$211$	2.54515	+	0.926361i	0.175216	+	0.0637733i	−0.252923	+	0.967487i	$0.581392\pi$
$212$	1.49042	+	8.45261i	0.102363	+	0.580528i
$213$	26.9387	+	22.6043i	1.84581	+	1.54882i
$214$	3.60692	−	3.02656i	0.246564	−	0.206892i
$215$	0.448534	−	2.54376i	0.0305898	−	0.173483i
$216$	1.32288	−	2.29129i	0.0900103	−	0.155902i
$217$	−0.291503	−	0.504897i	−0.0197885	−	0.0342747i
$218$	6.18600	−	2.25152i	0.418969	−	0.152492i
$219$	30.5590	−	11.1226i	2.06499	−	0.751595i
$220$	−1.17712	−	2.03884i	−0.0793617	−	0.137459i
$221$		0			0
$222$	−2.59383	+	14.7103i	−0.174086	+	0.987292i
$223$	22.0711	−	18.5198i	1.47799	−	1.24018i	0.569690	−	0.821860i	$-0.307063\pi$
$223$	22.0711	−	18.5198i	1.47799	−	1.24018i	0.908299	−	0.418321i	$-0.137381\pi$
$224$	−1.26072	−	1.05787i	−0.0842353	−	0.0706818i
$225$	5.75922	+	32.6621i	0.383948	+	2.17748i
$226$	−5.24631	−	1.90950i	−0.348979	−	0.127018i
$227$	−12.6458			−0.839328			−0.419664	−	0.907680i	$-0.637852\pi$
$227$	−12.6458			−0.839328			−0.419664	+	0.907680i	$0.637852\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	−12.4899	−	4.54596i	−0.823561	−	0.299752i
$231$	0.488257	+	2.76904i	0.0321250	+	0.182190i
$232$	−2.79281	−	2.34344i	−0.183357	−	0.153855i
$233$	−9.86245	+	8.27557i	−0.646110	+	0.542151i	−0.905888	−	0.423518i	$-0.860795\pi$
$233$	−9.86245	+	8.27557i	−0.646110	+	0.542151i	0.259778	+	0.965668i	$0.416351\pi$
$234$	1.38919	−	7.87846i	0.0908139	−	0.515031i
$235$	−17.5830	+	30.4547i	−1.14699	+	1.98664i
$236$	−3.96863	−	6.87386i	−0.258336	−	0.447450i
$237$	−9.94477	+	3.61960i	−0.645982	+	0.235118i
$238$		0			0
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$	4.82288	−	8.35347i	0.311315	−	0.539214i
$241$	2.35866	−	13.3766i	0.151935	−	0.861666i	−0.809600	−	0.586982i	$-0.800316\pi$
$241$	2.35866	−	13.3766i	0.151935	−	0.861666i	0.961535	−	0.274683i	$-0.0885731\pi$
$242$	−8.10705	+	6.80262i	−0.521141	+	0.437289i
$243$	16.2141	+	13.6052i	1.04014	+	0.872777i
$244$	−2.59383	−	14.7103i	−0.166053	−	0.941732i
$245$	14.7022	+	5.35116i	0.939289	+	0.341873i
$246$	−27.2288			−1.73604
$247$		0			0
$248$	−0.354249			−0.0224948
$249$	−19.7335	−	7.18242i	−1.25056	−	0.455168i
$250$	2.08378	+	11.8177i	0.131790	+	0.747417i
$251$	2.12290	+	1.78132i	0.133996	+	0.112436i	0.707322	−	0.706891i	$-0.249903\pi$
$251$	2.12290	+	1.78132i	0.133996	+	0.112436i	−0.573326	+	0.819327i	$0.694347\pi$
$252$	−5.04287	+	4.23147i	−0.317671	+	0.266558i
$253$	0.408811	−	2.31848i	0.0257017	−	0.145762i
$254$	1.35425	−	2.34563i	0.0849731	−	0.147178i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−1.60546	+	0.584341i	−0.100146	+	0.0364502i	−0.391607	−	0.920132i	$-0.628081\pi$
$257$	−1.60546	+	0.584341i	−0.100146	+	0.0364502i	0.291461	+	0.956583i	$0.405859\pi$
$258$	0.937254	+	1.62337i	0.0583509	+	0.101067i
$259$	4.64575	−	8.04668i	0.288673	−	0.499996i
$260$	1.26616	−	7.18073i	0.0785237	−	0.445330i
$261$	−11.1712	+	9.37378i	−0.691482	+	0.580222i
$262$	−10.6766	−	8.95869i	−0.659600	−	0.553470i
$263$	0.857345	+	4.86225i	0.0528662	+	0.299819i	0.999764	−	0.0217151i	$-0.00691267\pi$
$263$	0.857345	+	4.86225i	0.0528662	+	0.299819i	−0.946898	+	0.321534i	$0.895802\pi$
$264$	1.60546	+	0.584341i	0.0988094	+	0.0359637i
$265$	31.2915			1.92222
$266$		0			0
$267$		0			0
$268$	4.36558	+	1.58894i	0.266670	+	0.0970600i
$269$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$269$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$270$	−7.38907	−	6.20017i	−0.449685	−	0.377330i
$271$	13.5174	−	11.3425i	0.821125	−	0.689006i	−0.132110	−	0.991235i	$-0.542175\pi$
$271$	13.5174	−	11.3425i	0.821125	−	0.689006i	0.953235	+	0.302229i	$0.0977308\pi$
$272$		0			0
$273$	−4.35425	+	7.54178i	−0.263531	+	0.456449i
$274$	2.79150	+	4.83502i	0.168641	+	0.292095i
$275$	−5.03135	+	1.83126i	−0.303402	+	0.110429i
$276$	9.06404	−	3.29904i	0.545591	−	0.198579i
$277$	−4.76013	−	8.24479i	−0.286008	−	0.495381i	0.686845	−	0.726804i	$-0.258995\pi$
$277$	−4.76013	−	8.24479i	−0.286008	−	0.495381i	−0.972853	+	0.231423i	$0.925662\pi$
$278$	−6.67712	+	11.5651i	−0.400467	+	0.693630i
$279$	−0.246059	+	1.39547i	−0.0147311	+	0.0835444i
$280$	−4.59627	+	3.85673i	−0.274679	+	0.230483i
$281$	−21.0337	−	17.6493i	−1.25476	−	1.05287i	−0.996219	−	0.0868725i	$-0.972313\pi$
$281$	−21.0337	−	17.6493i	−1.25476	−	1.05287i	−0.258544	−	0.965999i	$-0.583243\pi$
$282$	−4.43155	−	25.1325i	−0.263895	−	1.49662i
$283$	−23.8252	−	8.67166i	−1.41626	−	0.515477i	−0.483300	−	0.875455i	$-0.660562\pi$
$283$	−23.8252	−	8.67166i	−1.41626	−	0.515477i	−0.932961	+	0.359978i	$0.882784\pi$
$284$	−13.2915			−0.788706
$285$		0			0
$286$	1.29150			0.0763682
$287$	15.9158	+	5.79288i	0.939481	+	0.341943i
$288$	0.694593	+	3.93923i	0.0409293	+	0.232121i
$289$	−13.0228	−	10.9274i	−0.766044	−	0.642788i
$290$	−10.1819	+	8.54361i	−0.597901	+	0.501698i
$291$	6.56594	−	37.2373i	0.384902	−	2.18289i
$292$	−6.14575	+	10.6448i	−0.359653	+	0.622937i
$293$	−6.53137	−	11.3127i	−0.381567	−	0.660893i	0.609720	−	0.792617i	$-0.291282\pi$
$293$	−6.53137	−	11.3127i	−0.381567	−	0.660893i	−0.991286	+	0.131724i	$0.957949\pi$
$294$	−10.6695	+	3.88338i	−0.622258	+	0.226483i
$295$	−27.1921	+	9.89712i	−1.58319	+	0.576233i
$296$	−2.82288	−	4.88936i	−0.164076	−	0.284189i
$297$	0.854249	−	1.47960i	0.0495685	−	0.0858552i
$298$	−0.857345	+	4.86225i	−0.0496647	+	0.281662i
$299$	5.58562	−	4.68689i	0.323024	−	0.271050i
$300$	−16.8049	−	14.1010i	−0.970232	−	0.814121i
$301$	−0.202476	−	1.14830i	−0.0116705	−	0.0661867i
$302$	2.76012	+	1.00460i	0.158827	+	0.0578082i
$303$	22.1033			1.26980
$304$		0			0
$305$	−54.4575			−3.11823
$306$		0			0
$307$	−0.806726	−	4.57517i	−0.0460423	−	0.261119i	0.953094	−	0.302675i	$-0.0978796\pi$
$307$	−0.806726	−	4.57517i	−0.0460423	−	0.261119i	−0.999136	+	0.0415560i	$0.986769\pi$
$308$	−0.814111	−	0.683120i	−0.0463883	−	0.0389244i
$309$	5.48948	−	4.60622i	0.312286	−	0.262039i
$310$	−0.224267	+	1.27188i	−0.0127375	+	0.0722380i
$311$	−4.17712	+	7.23499i	−0.236863	+	0.410259i	−0.959812	−	0.280642i	$-0.909453\pi$
$311$	−4.17712	+	7.23499i	−0.236863	+	0.410259i	0.722949	+	0.690901i	$0.242786\pi$
$312$	2.64575	+	4.58258i	0.149786	+	0.259437i
$313$	21.4950	−	7.82354i	1.21497	−	0.442213i	0.346545	−	0.938033i	$-0.387355\pi$
$313$	21.4950	−	7.82354i	1.21497	−	0.442213i	0.868425	+	0.495821i	$0.165133\pi$
$314$	−9.94477	+	3.61960i	−0.561216	+	0.204266i
$315$	12.0000	+	20.7846i	0.676123	+	1.17108i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−1.04189	+	5.90885i	−0.0585183	+	0.331874i	−0.999986	−	0.00522845i	$-0.998336\pi$
$317$	−1.04189	+	5.90885i	−0.0585183	+	0.331874i	0.941468	+	0.337102i	$0.109447\pi$
$318$	−17.3957	+	14.5967i	−0.975503	+	0.818545i
$319$	−1.80346	−	1.51328i	−0.100974	−	0.0847275i
$320$	0.633078	+	3.59036i	0.0353901	+	0.200707i
$321$	11.7062	+	4.26072i	0.653378	+	0.237810i
$322$	−6.00000			−0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$	−15.5829	−	5.67172i	−0.864385	−	0.314611i
$326$	−2.07288	−	11.7559i	−0.114806	−	0.651099i
$327$	13.3422	+	11.1954i	0.737825	+	0.619109i
$328$	7.88375	−	6.61525i	0.435307	−	0.365266i
$329$	−2.75658	+	15.6333i	−0.151975	+	0.861894i
$330$	3.11438	−	5.39426i	0.171441	−	0.296944i
$331$	13.9059	+	24.0857i	0.764336	+	1.32387i	0.940597	+	0.339526i	$0.110267\pi$
$331$	13.9059	+	24.0857i	0.764336	+	1.32387i	−0.176260	+	0.984344i	$0.556400\pi$
$332$	7.45858	−	2.71470i	0.409343	−	0.148989i
$333$	−21.2211	+	7.72384i	−1.16291	+	0.423264i
$334$	6.00000	+	10.3923i	0.328305	+	0.568642i
$335$	8.46863	−	14.6681i	0.462691	−	0.801403i
$336$	0.756107	−	4.28810i	0.0412490	−	0.233935i
$337$	−15.5442	+	13.0431i	−0.846746	+	0.710504i	−0.959071	−	0.283167i	$-0.908615\pi$
$337$	−15.5442	+	13.0431i	−0.846746	+	0.710504i	0.112324	+	0.993672i	$0.464170\pi$
$338$	−6.89440	−	5.78509i	−0.375006	−	0.314667i
$339$	−2.56500	−	14.5468i	−0.139312	−	0.790076i
$340$		0			0
$341$	−0.228757			−0.0123879
$342$		0			0
$343$	18.5830			1.00339
$344$	−0.665770	−	0.242320i	−0.0358959	−	0.0130650i
$345$	−6.10651	−	34.6318i	−0.328764	−	1.86451i
$346$	−4.59627	−	3.85673i	−0.247097	−	0.207339i
$347$	2.47337	−	2.07540i	0.132778	−	0.111414i	−0.573980	−	0.818869i	$-0.694601\pi$
$347$	2.47337	−	2.07540i	0.132778	−	0.111414i	0.706758	+	0.707455i	$0.250157\pi$
$348$	1.67497	−	9.49921i	0.0897877	−	0.509211i
$349$	10.5830	−	18.3303i	0.566495	−	0.981199i	−0.430414	−	0.902632i	$-0.641632\pi$
$349$	10.5830	−	18.3303i	0.566495	−	0.981199i	0.996909	−	0.0785668i	$-0.0250344\pi$
$350$	6.82288	+	11.8176i	0.364698	+	0.631676i
$351$	4.97239	−	1.80980i	0.265406	−	0.0966000i
$352$	−0.606808	+	0.220860i	−0.0323430	+	0.0117719i
$353$	9.43725	+	16.3458i	0.502294	+	0.869999i	0.999996	+	0.00265131i	$0.000843939\pi$
$353$	9.43725	+	16.3458i	0.502294	+	0.869999i	−0.497702	+	0.867348i	$0.665823\pi$
$354$	10.5000	−	18.1865i	0.558069	−	0.966603i
$355$	−8.41456	+	47.7213i	−0.446598	+	2.53279i
$356$		0			0
$357$		0			0
$358$	3.46207	+	19.6344i	0.182976	+	1.03771i
$359$	−10.2777	−	3.74076i	−0.542434	−	0.197430i	0.0562477	−	0.998417i	$-0.482086\pi$
$359$	−10.2777	−	3.74076i	−0.542434	−	0.197430i	−0.598682	+	0.800987i	$0.704309\pi$
$360$	14.5830			0.768592
$361$		0			0
$362$	−4.22876			−0.222259
$363$	−26.3114	−	9.57656i	−1.38099	−	0.502639i
$364$	−0.571563	−	3.24150i	−0.0299581	−	0.169901i
$365$	34.3278	+	28.8044i	1.79680	+	1.50769i
$366$	30.2743	−	25.4031i	1.58246	−	1.32784i
$367$	−1.77620	+	10.0734i	−0.0927171	+	0.525825i	0.902706	+	0.430258i	$0.141577\pi$
$367$	−1.77620	+	10.0734i	−0.0927171	+	0.525825i	−0.995423	+	0.0955669i	$0.969534\pi$
$368$	−1.82288	+	3.15731i	−0.0950240	+	0.164586i
$369$	−20.5830	−	35.6508i	−1.07151	−	1.85591i
$370$	−19.3417	+	7.03980i	−1.00553	+	0.365982i
$371$	13.2736	−	4.83120i	0.689132	−	0.250824i
$372$	−0.468627	−	0.811686i	−0.0242972	−	0.0420839i
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	−24.3212	+	20.4079i	−1.25594	+	1.05386i
$376$	7.38907	+	6.20017i	0.381062	+	0.319749i
$377$	−1.26616	−	7.18073i	−0.0652104	−	0.369826i
$378$	−4.09166	−	1.48924i	−0.210452	−	0.0765983i
$379$	21.2915			1.09367			0.546836	−	0.837240i	$-0.315832\pi$
$379$	21.2915			1.09367			0.546836	+	0.837240i	$0.315832\pi$
$380$		0			0
$381$	7.16601			0.367126
$382$	13.7035	+	4.98768i	0.701134	+	0.255192i
$383$	−5.47344	−	31.0414i	−0.279679	−	1.58614i	−0.723694	−	0.690121i	$-0.757557\pi$
$383$	−5.47344	−	31.0414i	−0.279679	−	1.58614i	0.444014	−	0.896020i	$-0.353554\pi$
$384$	−2.02676	−	1.70066i	−0.103428	−	0.0867862i
$385$	−2.96805	+	2.49049i	−0.151266	+	0.126927i
$386$	−1.14313	+	6.48299i	−0.0581836	+	0.329976i
$387$	−1.41699	+	2.45431i	−0.0720299	+	0.124759i
$388$	7.14575	+	12.3768i	0.362771	+	0.628337i
$389$	−11.2763	+	4.10424i	−0.571732	+	0.208093i	−0.611676	−	0.791109i	$-0.709504\pi$
$389$	−11.2763	+	4.10424i	−0.571732	+	0.208093i	0.0399440	+	0.999202i	$0.487282\pi$
$390$	18.1281	−	6.59808i	0.917951	−	0.334107i
$391$		0			0
$392$	2.14575	−	3.71655i	0.108377	−	0.187714i
$393$	6.40319	−	36.3143i	0.322998	−	1.83181i
$394$	−1.80346	+	1.51328i	−0.0908570	+	0.0762380i
$395$	−11.1712	−	9.37378i	−0.562086	−	0.471646i
$396$	0.448534	+	2.54376i	0.0225397	+	0.127829i
$397$	−34.7097	−	12.6333i	−1.74203	−	0.634046i	−0.742663	−	0.669666i	$-0.766437\pi$
$397$	−34.7097	−	12.6333i	−1.74203	−	0.634046i	−0.999365	+	0.0356193i	$0.988660\pi$
$398$	11.8745			0.595215
$399$		0			0
$400$	8.29150			0.414575
$401$	−6.03000	−	2.19474i	−0.301124	−	0.109600i	0.187039	−	0.982352i	$-0.440111\pi$
$401$	−6.03000	−	2.19474i	−0.301124	−	0.109600i	−0.488163	+	0.872752i	$0.662333\pi$
$402$	2.13440	+	12.1048i	0.106454	+	0.603731i
$403$	−0.542740	−	0.455413i	−0.0270358	−	0.0226858i
$404$	−6.39973	+	5.37001i	−0.318398	+	0.267168i
$405$	−3.16539	+	17.9518i	−0.157290	+	0.892033i
$406$	−3.00000	+	5.19615i	−0.148888	+	0.257881i
$407$	−1.82288	−	3.15731i	−0.0903566	−	0.156502i
$408$		0			0
$409$	−12.7638	+	4.64566i	−0.631132	+	0.229713i	−0.637724	−	0.770265i	$-0.720124\pi$
$409$	−12.7638	+	4.64566i	−0.631132	+	0.229713i	0.00659207	+	0.999978i	$0.497902\pi$
$410$	−18.7601	−	32.4935i	−0.926497	−	1.60474i
$411$	−7.38562	+	12.7923i	−0.364306	+	0.630996i
$412$	−0.470326	+	2.66735i	−0.0231713	+	0.131411i
$413$	−10.0066	+	8.39657i	−0.492395	+	0.413168i
$414$	11.1712	+	9.37378i	0.549036	+	0.460696i
$415$	−5.02490	−	28.4976i	−0.246663	−	1.39889i
$416$	−1.87939	−	0.684040i	−0.0921444	−	0.0335378i
$417$	−35.3320			−1.73022
$418$		0			0
$419$	31.7490			1.55104			0.775520	−	0.631322i	$-0.217488\pi$
$419$	31.7490			1.55104			0.775520	+	0.631322i	$0.217488\pi$
$420$	−14.9172	−	5.42940i	−0.727883	−	0.264928i
$421$	3.96122	+	22.4652i	0.193058	+	1.09489i	0.915157	+	0.403097i	$0.132066\pi$
$421$	3.96122	+	22.4652i	0.193058	+	1.09489i	−0.722099	+	0.691790i	$0.756823\pi$
$422$	−2.07483	−	1.74099i	−0.101001	−	0.0847500i
$423$	29.5563	−	24.8007i	1.43708	−	1.20585i
$424$	1.49042	−	8.45261i	0.0723814	−	0.410495i
$425$		0			0
$426$	−17.5830	−	30.4547i	−0.851899	−	1.47553i
$427$	−23.1005	+	8.40788i	−1.11791	+	0.406886i
$428$	−4.42454	+	1.61040i	−0.213868	+	0.0778417i
$429$	1.70850	+	2.95920i	0.0824870	+	0.142872i
$430$	−1.29150	+	2.23695i	−0.0622818	+	0.107875i
$431$	−0.672801	+	3.81565i	−0.0324077	+	0.183793i	−0.996715	−	0.0809939i	$-0.974191\pi$
$431$	−0.672801	+	3.81565i	−0.0324077	+	0.183793i	0.964307	+	0.264787i	$0.0853017\pi$
$432$	−2.02676	+	1.70066i	−0.0975127	+	0.0818229i
$433$	−10.6285	−	8.91836i	−0.510773	−	0.428589i	0.350628	−	0.936515i	$-0.385968\pi$
$433$	−10.6285	−	8.91836i	−0.510773	−	0.428589i	−0.861401	+	0.507926i	$0.830412\pi$
$434$	0.101238	+	0.574148i	0.00485957	+	0.0275600i
$435$	−33.0452	−	12.0275i	−1.58440	−	0.576674i
$436$	−6.58301			−0.315269
$437$		0			0
$438$	−32.5203			−1.55388
$439$	34.5917	+	12.5904i	1.65097	+	0.600905i	0.988907	−	0.148539i	$-0.0474571\pi$
$439$	34.5917	+	12.5904i	1.65097	+	0.600905i	0.662067	+	0.749444i	$0.269679\pi$
$440$	0.408811	+	2.31848i	0.0194893	+	0.110529i
$441$	−13.1499	−	11.0341i	−0.626187	−	0.525433i
$442$		0			0
$443$	0.929756	−	5.27291i	0.0441740	−	0.250523i	−0.954722	−	0.297499i	$-0.903847\pi$
$443$	0.929756	−	5.27291i	0.0441740	−	0.250523i	0.998896	+	0.0469761i	$0.0149585\pi$
$444$	7.46863	−	12.9360i	0.354445	−	0.613917i
$445$		0			0
$446$	−27.0742	+	9.85420i	−1.28200	+	0.466610i
$447$	−12.2750	+	4.46772i	−0.580586	+	0.211316i
$448$	0.822876	+	1.42526i	0.0388772	+	0.0673373i
$449$	6.85425	−	11.8719i	0.323472	−	0.560270i	−0.657730	−	0.753254i	$-0.728483\pi$
$449$	6.85425	−	11.8719i	0.323472	−	0.560270i	0.981202	+	0.192984i	$0.0618165\pi$
$450$	5.75922	−	32.6621i	0.271492	−	1.53971i
$451$	5.09094	−	4.27181i	0.239723	−	0.201152i
$452$	4.27683	+	3.58869i	0.201165	+	0.168798i
$453$	1.34946	+	7.65318i	0.0634033	+	0.359578i
$454$	11.8831	+	4.32510i	0.557702	+	0.202987i
$455$	−12.0000			−0.562569
$456$		0			0
$457$	1.12549			0.0526483			0.0263242	−	0.999653i	$-0.491620\pi$
$457$	1.12549			0.0526483			0.0263242	+	0.999653i	$0.491620\pi$
$458$	−18.7939	−	6.84040i	−0.878179	−	0.319631i
$459$		0			0
$460$	10.1819	+	8.54361i	0.474733	+	0.398348i
$461$	−17.7462	+	14.8908i	−0.826523	+	0.693535i	−0.954490	−	0.298244i	$-0.903599\pi$
$461$	−17.7462	+	14.8908i	−0.826523	+	0.693535i	0.127967	+	0.991778i	$0.459155\pi$
$462$	0.488257	−	2.76904i	0.0227158	−	0.128828i
$463$	−7.22876	+	12.5206i	−0.335949	+	0.581880i	−0.983667	−	0.180000i	$-0.942390\pi$
$463$	−7.22876	+	12.5206i	−0.335949	+	0.581880i	0.647718	+	0.761880i	$0.275724\pi$
$464$	1.82288	+	3.15731i	0.0846249	+	0.146575i
$465$	−3.21092	+	1.16868i	−0.148903	+	0.0541963i
$466$	12.0981	−	4.40334i	0.560433	−	0.203981i
$467$	12.3229	+	21.3438i	0.570235	+	0.987675i	0.996541	+	0.0830968i	$0.0264811\pi$
$467$	12.3229	+	21.3438i	0.570235	+	0.987675i	−0.426307	+	0.904579i	$0.640186\pi$
$468$	−4.00000	+	6.92820i	−0.184900	+	0.320256i
$469$	1.32767	−	7.52960i	0.0613061	−	0.347684i
$470$	26.9387	−	22.6043i	1.24259	−	1.04266i
$471$	−21.4492	−	17.9981i	−0.988329	−	0.829307i
$472$	1.37829	+	7.81667i	0.0634409	+	0.359791i
$473$	−0.429922	−	0.156479i	−0.0197678	−	0.00719490i
$474$	10.5830			0.486094
$475$		0			0
$476$		0			0
$477$	−32.2615	−	11.7422i	−1.47715	−	0.537640i
$478$	−2.08378	−	11.8177i	−0.0953098	−	0.540529i
$479$	−11.1712	−	9.37378i	−0.510427	−	0.428299i	0.350853	−	0.936431i	$-0.385892\pi$
$479$	−11.1712	−	9.37378i	−0.510427	−	0.428299i	−0.861279	+	0.508132i	$0.830336\pi$
$480$	−7.38907	+	6.20017i	−0.337264	+	0.282998i
$481$	1.96075	−	11.1200i	0.0894025	−	0.507027i
$482$	−6.79150	+	11.7632i	−0.309344	+	0.535800i
$483$	−7.93725	−	13.7477i	−0.361158	−	0.625543i
$484$	9.94477	−	3.61960i	0.452035	−	0.164527i
$485$	48.9611	−	17.8204i	2.22321	−	0.809181i
$486$	−10.5830	−	18.3303i	−0.480055	−	0.831479i
$487$	11.1144	−	19.2507i	0.503641	−	0.872331i	−0.496351	−	0.868122i	$-0.665327\pi$
$487$	11.1144	−	19.2507i	0.503641	−	0.872331i	0.999991	−	0.00420886i	$-0.00133973\pi$
$488$	−2.59383	+	14.7103i	−0.117417	+	0.665905i
$489$	24.1940	−	20.3012i	1.09409	−	0.918050i
$490$	−11.9853	−	10.0569i	−0.541443	−	0.454324i
$491$	4.98518	+	28.2724i	0.224978	+	1.27591i	0.862727	+	0.505669i	$0.168754\pi$
$491$	4.98518	+	28.2724i	0.224978	+	1.27591i	−0.637749	+	0.770244i	$0.720134\pi$
$492$	25.5867	+	9.31278i	1.15354	+	0.419853i
$493$		0			0
$494$		0			0
$495$	9.41699			0.423262
$496$	0.332885	+	0.121160i	0.0149470	+	0.00544025i
$497$	3.79847	+	21.5422i	0.170385	+	0.966299i
$498$	16.0869	+	13.4985i	0.720873	+	0.604884i
$499$	−23.9226	+	20.0735i	−1.07092	+	0.898611i	−0.995136	−	0.0985126i	$-0.968592\pi$
$499$	−23.9226	+	20.0735i	−1.07092	+	0.898611i	−0.0757875	+	0.997124i	$0.524147\pi$
$500$	2.08378	−	11.8177i	0.0931894	−	0.528503i
$501$	−15.8745	+	27.4955i	−0.709221	+	1.22841i
$502$	−1.38562	−	2.39997i	−0.0618433	−	0.107116i
$503$	23.5513	−	8.57196i	1.05010	−	0.382205i	0.241399	−	0.970426i	$-0.422394\pi$
$503$	23.5513	−	8.57196i	1.05010	−	0.382205i	0.808700	+	0.588221i	$0.200171\pi$
$504$	6.18600	−	2.25152i	0.275546	−	0.100291i
$505$	15.2288	+	26.3770i	0.677671	+	1.17376i
$506$	−1.17712	+	2.03884i	−0.0523296	+	0.0906375i
$507$	4.13487	−	23.4500i	0.183636	−	1.04145i
$508$	−2.07483	+	1.74099i	−0.0920557	+	0.0772439i
$509$	24.3212	+	20.4079i	1.07802	+	0.904563i	0.995755	−	0.0920477i	$-0.0293412\pi$
$509$	24.3212	+	20.4079i	1.07802	+	0.904563i	0.0822617	+	0.996611i	$0.473786\pi$
$510$		0			0
$511$	19.0088	+	6.91864i	0.840900	+	0.306063i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.70850			0.0753586
$515$	9.27900	+	3.37728i	0.408882	+	0.148821i
$516$	−0.325505	−	1.84603i	−0.0143296	−	0.0812669i
$517$	4.77150	+	4.00377i	0.209851	+	0.176085i
$518$	−7.11770	+	5.97246i	−0.312734	+	0.262415i
$519$	2.75658	−	15.6333i	0.121000	−	0.686227i
$520$	−3.64575	+	6.31463i	−0.159877	+	0.276915i
$521$	11.1458	+	19.3050i	0.488304	+	0.845768i	0.999910	−	0.0134529i	$-0.00428231\pi$
$521$	11.1458	+	19.3050i	0.488304	+	0.845768i	−0.511605	+	0.859221i	$0.670949\pi$
$522$	13.7035	−	4.98768i	0.599788	−	0.218305i
$523$	−28.0729	+	10.2177i	−1.22754	+	0.446788i	−0.872754	−	0.488160i	$-0.837668\pi$
$523$	−28.0729	+	10.2177i	−1.22754	+	0.446788i	−0.354786	+	0.934948i	$0.615446\pi$
$524$	6.96863	+	12.0700i	0.304426	+	0.527281i
$525$	−18.0516	+	31.2663i	−0.787838	+	1.36458i
$526$	0.857345	−	4.86225i	0.0373820	−	0.212004i
$527$		0			0
$528$	−1.30878	−	1.09820i	−0.0569576	−	0.0477931i
$529$	−1.68586	−	9.56100i	−0.0732984	−	0.415696i
$530$	−29.4044	−	10.7023i	−1.27725	−	0.464879i
$531$	31.7490			1.37779
$532$		0			0
$533$	20.5830			0.891549
$534$		0			0
$535$	2.98085	+	16.9052i	0.128873	+	0.730876i
$536$	−3.55885	−	2.98623i	−0.153719	−	0.128986i
$537$	−40.4081	+	33.9064i	−1.74374	+	1.46317i
$538$		0			0
$539$	1.38562	−	2.39997i	0.0596830	−	0.103374i
$540$	4.82288	+	8.35347i	0.207544	+	0.359476i
$541$	−7.51754	+	2.73616i	−0.323204	+	0.117637i	−0.498527	−	0.866874i	$-0.666125\pi$
$541$	−7.51754	+	2.73616i	−0.323204	+	0.117637i	0.175322	+	0.984511i	$0.443903\pi$
$542$	−16.5816	+	6.03520i	−0.712240	+	0.259234i
$543$	−5.59412	−	9.68930i	−0.240067	−	0.415808i
$544$		0			0
$545$	−4.16756	+	23.6354i	−0.178518	+	1.01243i
$546$	6.67110	−	5.59771i	0.285497	−	0.239560i
$547$	0.542740	+	0.455413i	0.0232059	+	0.0194721i	0.654317	−	0.756221i	$-0.272956\pi$
$547$	0.542740	+	0.455413i	0.0232059	+	0.0194721i	−0.631111	+	0.775693i	$0.717401\pi$
$548$	−0.969479	−	5.49819i	−0.0414141	−	0.234871i
$549$	56.1457	+	20.4354i	2.39624	+	0.872160i
$550$	5.35425			0.228306
$551$		0			0
$552$	−9.64575			−0.410550
$553$	−6.18600	−	2.25152i	−0.263056	−	0.0957444i
$554$	1.65318	+	9.37563i	0.0702367	+	0.398332i
$555$	−41.7169	−	35.0046i	−1.77078	−	1.48586i
$556$	10.2299	−	8.58395i	0.433846	−	0.364040i
$557$	−4.61609	+	26.1791i	−0.195590	+	1.10925i	0.715986	+	0.698115i	$0.245977\pi$
$557$	−4.61609	+	26.1791i	−0.195590	+	1.10925i	−0.911576	+	0.411132i	$0.865134\pi$
$558$	0.708497	−	1.22715i	0.0299931	−	0.0519495i
$559$	−0.708497	−	1.22715i	−0.0299662	−	0.0519031i
$560$	5.63816	−	2.05212i	0.238256	−	0.0867179i
$561$		0			0
$562$	13.7288	+	23.7789i	0.579113	+	1.00305i
$563$	−12.9686	+	22.4623i	−0.546562	+	0.946674i	0.451944	+	0.892046i	$0.350731\pi$
$563$	−12.9686	+	22.4623i	−0.546562	+	0.946674i	−0.998507	+	0.0546278i	$0.982603\pi$
$564$	−4.43155	+	25.1325i	−0.186602	+	1.05827i
$565$	15.5923	−	13.0835i	0.655971	−	0.550425i
$566$	19.4225	+	16.2974i	0.816388	+	0.685031i
$567$	1.42891	+	8.10374i	0.0600085	+	0.340325i
$568$	12.4899	+	4.54596i	0.524066	+	0.190744i
$569$	−14.5830			−0.611351			−0.305676	−	0.952136i	$-0.598882\pi$
$569$	−14.5830			−0.611351			−0.305676	+	0.952136i	$0.598882\pi$
$570$		0			0
$571$	−39.8118			−1.66607			−0.833035	−	0.553220i	$-0.813399\pi$
$571$	−39.8118			−1.66607			−0.833035	+	0.553220i	$0.813399\pi$
$572$	−1.21362	−	0.441720i	−0.0507438	−	0.0184692i
$573$	6.69987	+	37.9968i	0.279891	+	1.58734i
$574$	−12.9747	−	10.8871i	−0.541553	−	0.454417i
$575$	23.1566	−	19.4307i	0.965696	−	0.810315i
$576$	0.694593	−	3.93923i	0.0289414	−	0.164135i
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	−16.3666	+	5.95696i	−0.680174	+	0.247563i
$580$	12.4899	−	4.54596i	0.518616	−	0.188761i
$581$	−6.53137	−	11.3127i	−0.270967	−	0.469329i
$582$	−18.9059	+	32.7459i	−0.783674	+	1.35736i
$583$	0.962443	−	5.45828i	0.0398603	−	0.226059i
$584$	9.41584	−	7.90083i	0.389630	−	0.326938i
$585$	22.3425	+	18.7476i	0.923747	+	0.775116i
$586$	2.26832	+	12.8643i	0.0937035	+	0.531419i
$587$	43.1079	+	15.6900i	1.77925	+	0.647596i	0.999776	+	0.0211675i	$0.00673833\pi$
$587$	43.1079	+	15.6900i	1.77925	+	0.647596i	0.779479	+	0.626428i	$0.215484\pi$
$588$	11.3542			0.468241
$589$		0			0
$590$	28.9373			1.19133
$591$	−5.85312	−	2.13036i	−0.240765	−	0.0876313i
$592$	0.980374	+	5.55998i	0.0402931	+	0.228514i
$593$	30.8651	+	25.8989i	1.26748	+	1.06354i	0.994844	+	0.101421i	$0.0323391\pi$
$593$	30.8651	+	25.8989i	1.26748	+	1.06354i	0.272633	+	0.962118i	$0.412105\pi$
$594$	−1.30878	+	1.09820i	−0.0537001	+	0.0450597i
$595$		0			0
$596$	2.46863	−	4.27579i	0.101119	−	0.175143i
$597$	15.7085	+	27.2079i	0.642906	+	1.11355i
$598$	−6.85177	+	2.49384i	−0.280190	+	0.101981i
$599$	0.998655	−	0.363481i	0.0408039	−	0.0148514i	−0.321538	−	0.946897i	$-0.604200\pi$
$599$	0.998655	−	0.363481i	0.0408039	−	0.0148514i	0.362341	+	0.932045i	$0.381977\pi$
$600$	10.9686	+	18.9982i	0.447792	+	0.775599i
$601$	−15.7915	+	27.3517i	−0.644149	+	1.11570i	0.340349	+	0.940299i	$0.389455\pi$
$601$	−15.7915	+	27.3517i	−0.644149	+	1.11570i	−0.984497	+	0.175399i	$0.943878\pi$
$602$	−0.202476	+	1.14830i	−0.00825229	+	0.0468011i
$603$	−14.2354	+	11.9449i	−0.579711	+	0.486435i
$604$	−2.25007	−	1.88803i	−0.0915539	−	0.0768229i
$605$	−6.69987	−	37.9968i	−0.272388	−	1.54479i
$606$	−20.7703	−	7.55976i	−0.843735	−	0.307094i
$607$	−8.93725			−0.362752			−0.181376	−	0.983414i	$-0.558055\pi$
$607$	−8.93725			−0.362752			−0.181376	+	0.983414i	$0.558055\pi$
$608$		0			0
$609$	−15.8745			−0.643268
$610$	51.1733	+	18.6256i	2.07195	+	0.754127i
$611$	3.34993	+	18.9984i	0.135524	+	0.768594i
$612$		0			0
$613$	21.8959	−	18.3728i	0.884365	−	0.742070i	−0.0827067	−	0.996574i	$-0.526356\pi$
$613$	21.8959	−	18.3728i	0.884365	−	0.742070i	0.967072	+	0.254503i	$0.0819120\pi$
$614$	−0.806726	+	4.57517i	−0.0325568	+	0.184639i
$615$	49.6346	−	85.9697i	2.00146	−	3.46663i
$616$	0.531373	+	0.920365i	0.0214096	+	0.0370826i
$617$	−0.821769	+	0.299099i	−0.0330832	+	0.0120413i	−0.358509	−	0.933526i	$-0.616715\pi$
$617$	−0.821769	+	0.299099i	−0.0330832	+	0.0120413i	0.325426	+	0.945568i	$0.394492\pi$
$618$	−6.73385	+	2.45092i	−0.270875	+	0.0985905i
$619$	−22.2288	−	38.5013i	−0.893449	−	1.54750i	−0.835712	−	0.549168i	$-0.814945\pi$
$619$	−22.2288	−	38.5013i	−0.893449	−	1.54750i	−0.0577369	−	0.998332i	$-0.518388\pi$
$620$	0.645751	−	1.11847i	0.0259340	−	0.0449190i
$621$	−1.67497	+	9.49921i	−0.0672141	+	0.381190i
$622$	6.39973	−	5.37001i	0.256606	−	0.215318i
$623$		0			0
$624$	−0.918860	−	5.21111i	−0.0367838	−	0.208611i
$625$	−2.15331	−	0.783740i	−0.0861323	−	0.0313496i
$626$	−22.8745			−0.914249
$627$		0			0
$628$	10.5830			0.422308
$629$		0			0
$630$	−4.16756	−	23.6354i	−0.166039	−	0.941656i
$631$	17.4748	+	14.6631i	0.695662	+	0.583730i	0.920536	−	0.390658i	$-0.127753\pi$
$631$	17.4748	+	14.6631i	0.695662	+	0.583730i	−0.224874	+	0.974388i	$0.572197\pi$
$632$	−3.06418	+	2.57115i	−0.121886	+	0.102275i
$633$	1.24436	−	7.05714i	0.0494591	−	0.280496i
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$	4.93725	+	8.55157i	0.195929	+	0.339359i
$636$	21.3390	−	7.76676i	0.846147	−	0.307972i
$637$	8.06539	−	2.93556i	0.319562	−	0.116311i
$638$	1.17712	+	2.03884i	0.0466028	+	0.0807184i
$639$	26.5830	−	46.0431i	1.05161	−	1.82144i
$640$	0.633078	−	3.59036i	0.0250246	−	0.141922i
$641$	−14.4587	+	12.1323i	−0.571085	+	0.479197i	−0.882006	−	0.471239i	$-0.843807\pi$
$641$	−14.4587	+	12.1323i	−0.571085	+	0.479197i	0.310921	+	0.950436i	$0.399363\pi$
$642$	−9.54301	−	8.00754i	−0.376633	−	0.316032i
$643$	5.29979	+	30.0566i	0.209003	+	1.18532i	0.891015	+	0.453975i	$0.149994\pi$
$643$	5.29979	+	30.0566i	0.209003	+	1.18532i	−0.682011	+	0.731342i	$0.738895\pi$
$644$	5.63816	+	2.05212i	0.222174	+	0.0808649i
$645$	−6.83399			−0.269088
$646$		0			0
$647$	30.4575			1.19741			0.598704	−	0.800970i	$-0.295683\pi$
$647$	30.4575			1.19741			0.598704	+	0.800970i	$0.295683\pi$
$648$	4.69846	+	1.71010i	0.184573	+	0.0671791i
$649$	0.890032	+	5.04762i	0.0349368	+	0.198137i
$650$	12.7033	+	10.6594i	0.498265	+	0.418094i
$651$	−1.18161	+	0.991491i	−0.0463111	+	0.0388596i
$652$	−2.07288	+	11.7559i	−0.0811803	+	0.460397i
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	−0.999396	−	0.0347583i	$-0.988934\pi$
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	0.529799	+	0.848123i	$0.322267\pi$
$654$	−8.70850	−	15.0836i	−0.340529	−	0.589814i
$655$	47.7474	−	17.3786i	1.86565	−	0.679040i
$656$	−9.67085	+	3.51990i	−0.377583	+	0.137429i
$657$	−24.5830	−	42.5790i	−0.959074	−	1.66117i
$658$	7.93725	−	13.7477i	0.309426	−	0.535942i
$659$	0.448534	−	2.54376i	0.0174724	−	0.0990910i	−0.974824	−	0.222974i	$-0.928424\pi$
$659$	0.448534	−	2.54376i	0.0174724	−	0.0990910i	0.992297	+	0.123883i	$0.0395347\pi$
$660$	−4.77150	+	4.00377i	−0.185731	+	0.155846i
$661$	−7.83568	−	6.57492i	−0.304773	−	0.255735i	0.477555	−	0.878602i	$-0.341523\pi$
$661$	−7.83568	−	6.57492i	−0.304773	−	0.255735i	−0.782328	+	0.622867i	$0.785968\pi$
$662$	−4.82946	−	27.3892i	−0.187702	−	1.06451i
$663$		0			0
$664$	−7.93725			−0.308025
$665$		0			0
$666$	22.5830			0.875074
$667$	12.4899	+	4.54596i	0.483612	+	0.176020i
$668$	−2.08378	−	11.8177i	−0.0806238	−	0.457240i
$669$	−58.3946	−	48.9989i	−2.25767	−	1.89441i
$670$	−12.9747	+	10.8871i	−0.501256	+	0.420604i
$671$	−1.67497	+	9.49921i	−0.0646614	+	0.366713i
$672$	−2.17712	+	3.77089i	−0.0839844	+	0.145465i
$673$	−8.93725	−	15.4798i	−0.344506	−	0.596702i	0.640758	−	0.767743i	$-0.278620\pi$
$673$	−8.93725	−	15.4798i	−0.344506	−	0.596702i	−0.985264	+	0.171041i	$0.945287\pi$
$674$	19.0678	−	6.94010i	0.734463	−	0.267323i
$675$	20.6143	−	7.50298i	0.793444	−	0.288790i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	16.2915	−	28.2177i	0.626133	−	1.08449i	−0.362187	−	0.932105i	$-0.617970\pi$
$677$	16.2915	−	28.2177i	0.626133	−	1.08449i	0.988321	−	0.152389i	$-0.0486968\pi$
$678$	−2.56500	+	14.5468i	−0.0985082	+	0.558668i
$679$	18.0176	−	15.1185i	0.691451	−	0.580196i
$680$		0			0
$681$	5.80984	+	32.9492i	0.222633	+	1.26262i
$682$	0.214961	+	0.0782393i	0.00823128	+	0.00299594i
$683$	−26.5830			−1.01717			−0.508585	−	0.861012i	$-0.669831\pi$
$683$	−26.5830			−1.01717			−0.508585	+	0.861012i	$0.669831\pi$
$684$		0			0
$685$	−20.3542			−0.777696
$686$	−17.4623	−	6.35576i	−0.666714	−	0.242664i
$687$	−9.18860	−	52.1111i	−0.350567	−	1.98816i
$688$	0.542740	+	0.455413i	0.0206918	+	0.0173625i
$689$	13.1499	−	11.0341i	0.500972	−	0.420366i
$690$	−6.10651	+	34.6318i	−0.232471	+	1.31841i
$691$	9.29150	−	16.0934i	0.353465	−	0.612220i	−0.633389	−	0.773834i	$-0.718337\pi$
$691$	9.29150	−	16.0934i	0.353465	−	0.612220i	0.986854	+	0.161614i	$0.0516699\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$	3.99462	−	1.45392i	0.151743	−	0.0552299i
$694$	−3.03404	+	1.10430i	−0.115171	+	0.0419186i
$695$	−24.3431	−	42.1635i	−0.923388	−	1.59935i
$696$	−4.82288	+	8.35347i	−0.182811	+	0.316637i
$697$		0			0
$698$	−16.2141	+	13.6052i	−0.613713	+	0.514966i
$699$	26.0936	+	21.8951i	0.986950	+	0.828149i
$700$	−2.36956	−	13.4384i	−0.0895609	−	0.507925i
$701$	−14.7022	−	5.35116i	−0.555294	−	0.202111i	0.0491029	−	0.998794i	$-0.484364\pi$
$701$	−14.7022	−	5.35116i	−0.555294	−	0.202111i	−0.604397	+	0.796683i	$0.706586\pi$
$702$	−5.29150			−0.199715
$703$		0			0
$704$	0.645751			0.0243377
$705$	87.4295	+	31.8217i	3.29279	+	1.19848i
$706$	−3.27752	−	18.5878i	−0.123351	−	0.699560i
$707$	10.5324	+	8.83770i	0.396110	+	0.332376i
$708$	−16.0869	+	13.4985i	−0.604584	+	0.507306i
$709$	−0.285782	+	1.62075i	−0.0107328	+	0.0608685i	−0.989704	−	0.143131i	$-0.954283\pi$
$709$	−0.285782	+	1.62075i	−0.0107328	+	0.0608685i	0.978971	+	0.203999i	$0.0653941\pi$
$710$	24.2288	−	41.9654i	0.909289	−	1.57493i
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$		0			0
$713$	1.21362	−	0.441720i	0.0454503	−	0.0165425i
$714$		0			0
$715$	−2.35425	+	4.07768i	−0.0880439	+	0.152497i
$716$	3.46207	−	19.6344i	0.129384	−	0.733771i
$717$	24.3212	−	20.4079i	0.908290	−	0.762146i
$718$	8.37842	+	7.03033i	0.312680	+	0.262370i
$719$	2.30805	+	13.0896i	0.0860756	+	0.488159i	0.997119	+	0.0758491i	$0.0241667\pi$
$719$	2.30805	+	13.0896i	0.0860756	+	0.488159i	−0.911044	+	0.412310i	$0.864722\pi$
$720$	−13.7035	−	4.98768i	−0.510701	−	0.185880i
$721$	4.45751			0.166006
$722$		0			0
$723$	−35.9373			−1.33652
$724$	3.97373	+	1.44632i	0.147683	+	0.0537521i
$725$	−5.24917	−	29.7695i	−0.194949	−	1.10561i
$726$	21.4492	+	17.9981i	0.796056	+	0.667970i
$727$	17.2996	−	14.5161i	0.641606	−	0.538371i	−0.262905	−	0.964822i	$-0.584681\pi$
$727$	17.2996	−	14.5161i	0.641606	−	0.538371i	0.904511	+	0.426450i	$0.140236\pi$
$728$	−0.571563	+	3.24150i	−0.0211836	+	0.120138i
$729$	20.5000	−	35.5070i	0.759259	−	1.31508i
$730$	−22.4059	−	38.8081i	−0.829279	−	1.43635i
$731$		0			0
$732$	−37.1369	+	13.5167i	−1.37262	+	0.499593i
$733$	−21.0516	−	36.4625i	−0.777560	−	1.34677i	−0.933344	−	0.358982i	$-0.883124\pi$
$733$	−21.0516	−	36.4625i	−0.777560	−	1.34677i	0.155785	−	0.987791i	$-0.450209\pi$
$734$	5.11438	−	8.85836i	0.188775	−	0.326968i
$735$	7.18813	−	40.7659i	0.265138	−	1.50367i
$736$	2.79281	−	2.34344i	0.102944	−	0.0863805i
$737$	−2.29813	−	1.92836i	−0.0846528	−	0.0710322i
$738$	7.14840	+	40.5406i	0.263136	+	1.49232i
$739$	−12.9788	−	4.72390i	−0.477433	−	0.173771i	0.0920834	−	0.995751i	$-0.470647\pi$
$739$	−12.9788	−	4.72390i	−0.477433	−	0.173771i	−0.569517	+	0.821980i	$0.692870\pi$
$740$	20.5830			0.756646
$741$		0			0
$742$	−14.1255			−0.518563
$743$	9.84774	+	3.58428i	0.361278	+	0.131495i	0.516280	−	0.856420i	$-0.327316\pi$
$743$	9.84774	+	3.58428i	0.361278	+	0.131495i	−0.155002	+	0.987914i	$0.549538\pi$
$744$	0.162752	+	0.923015i	0.00596679	+	0.0338394i
$745$	−13.7888	−	11.5702i	−0.505183	−	0.423898i
$746$	−3.06418	+	2.57115i	−0.112188	+	0.0941365i
$747$	−5.51316	+	31.2667i	−0.201716	+	1.14399i
$748$		0			0
$749$	3.87451	+	6.71084i	0.141571	+	0.245209i
$750$	29.8343	−	10.8588i	1.08940	−	0.396507i
$751$	−22.4347	+	8.16556i	−0.818654	+	0.297966i	−0.717194	−	0.696874i	$-0.754574\pi$
$751$	−22.4347	+	8.16556i	−0.818654	+	0.297966i	−0.101460	+	0.994840i	$0.532351\pi$
$752$	−4.82288	−	8.35347i	−0.175872	−	0.304620i
$753$	3.66601	−	6.34972i	0.133597	−	0.231397i
$754$	−1.26616	+	7.18073i	−0.0461107	+	0.261507i
$755$	−8.20318	+	6.88329i	−0.298544	+	0.250509i
$756$	3.33555	+	2.79886i	0.121313	+	0.101793i
$757$	2.87961	+	16.3311i	0.104661	+	0.593563i	0.991355	+	0.131206i	$0.0418850\pi$
$757$	2.87961	+	16.3311i	0.104661	+	0.593563i	−0.886694	+	0.462357i	$0.847004\pi$
$758$	−20.0075	−	7.28212i	−0.726704	−	0.264499i
$759$	−6.22876			−0.226090
$760$		0			0
$761$	11.1255			0.403299			0.201649	−	0.979458i	$-0.435370\pi$
$761$	11.1255			0.403299			0.201649	+	0.979458i	$0.435370\pi$
$762$	−6.73385	−	2.45092i	−0.243942	−	0.0887875i
$763$	1.88130	+	10.6694i	0.0681077	+	0.386258i
$764$	−11.1712	−	9.37378i	−0.404161	−	0.339131i
$765$		0			0
$766$	−5.47344	+	31.0414i	−0.197763	+	1.12157i
$767$	−7.93725	+	13.7477i	−0.286598	+	0.496402i
$768$	1.32288	+	2.29129i	0.0477352	+	0.0826797i
$769$	−23.2184	+	8.45080i	−0.837277	+	0.304744i	−0.724842	−	0.688915i	$-0.758087\pi$
$769$	−23.2184	+	8.45080i	−0.837277	+	0.304744i	−0.112435	+	0.993659i	$0.535865\pi$
$770$	3.64085	−	1.32516i	0.131207	−	0.0477554i
$771$	2.26013	+	3.91466i	0.0813966	+	0.140983i
$772$	3.29150	−	5.70105i	0.118464	−	0.205185i
$773$	1.89923	−	10.7711i	0.0683107	−	0.387409i	−0.931414	−	0.363961i	$-0.881424\pi$
$773$	1.89923	−	10.7711i	0.0683107	−	0.387409i	0.999725	−	0.0234486i	$-0.00746462\pi$
$774$	2.17096	−	1.82165i	0.0780336	−	0.0654780i
$775$	−2.25007	−	1.88803i	−0.0808248	−	0.0678201i
$776$	−2.48169	−	14.0744i	−0.0890876	−	0.505241i
$777$	−23.1005	−	8.40788i	−0.828725	−	0.301631i
$778$	12.0000			0.430221
$779$		0			0
$780$	−19.2915			−0.690747
$781$	8.06539	+	2.93556i	0.288602	+	0.105043i
$782$		0			0
$783$	7.38907	+	6.20017i	0.264064	+	0.221576i
$784$	−3.28748	+	2.75852i	−0.117410	+	0.0985187i
$785$	6.69987	−	37.9968i	0.239129	−	1.35617i
$786$	−18.4373	+	31.9343i	−0.657635	+	1.13906i
$787$	2.73987	+	4.74559i	0.0976658	+	0.169162i	0.910718	−	0.413029i	$-0.135529\pi$
$787$	2.73987	+	4.74559i	0.0976658	+	0.169162i	−0.813052	+	0.582191i	$0.802196\pi$
$788$	2.21227	−	0.805200i	0.0788089	−	0.0286841i
$789$	12.2750	−	4.46772i	0.437000	−	0.159055i
$790$	7.29150	+	12.6293i	0.259420	+	0.449329i
$791$	4.59412	−	7.95725i	0.163348	−	0.282927i
$792$	0.448534	−	2.54376i	0.0159380	−	0.0903887i
$793$	−22.8852	+	19.2030i	−0.812677	+	0.681917i
$794$	28.2956	+	23.7428i	1.00417	+	0.842601i
$795$	−14.3763	−	81.5318i	−0.509873	−	2.89163i
$796$	−11.1584	−	4.06132i	−0.395499	−	0.143950i
$797$	2.81176			0.0995977			0.0497989	−	0.998759i	$-0.484142\pi$
$797$	2.81176			0.0995977			0.0497989	+	0.998759i	$0.484142\pi$
$798$		0			0
$799$		0			0
$800$	−7.79146	−	2.83586i	−0.275470	−	0.100263i
$801$		0			0
$802$	4.91570	+	4.12476i	0.173580	+	0.145651i
$803$	6.08029	−	5.10197i	0.214569	−	0.180045i
$804$	2.13440	−	12.1048i	0.0752744	−	0.426902i
$805$	10.9373	−	18.9439i	0.385488	−	0.667684i
$806$	0.354249	+	0.613577i	0.0124779	+	0.0216123i
$807$		0			0
$808$	7.85043	−	2.85732i	0.276177	−	0.100520i
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$	9.11438	−	15.7866i	0.320247	−	0.554683i
$811$	−3.59599	+	20.3939i	−0.126272	+	0.716126i	0.854272	+	0.519827i	$0.174004\pi$
$811$	−3.59599	+	20.3939i	−0.126272	+	0.716126i	−0.980544	+	0.196299i	$0.937108\pi$
$812$	4.59627	−	3.85673i	0.161297	−	0.135345i
$813$	−35.7638	−	30.0094i	−1.25429	−	1.05247i
$814$	0.633078	+	3.59036i	0.0221894	+	0.125842i
$815$	40.8957	+	14.8848i	1.43251	+	0.521392i
$816$		0			0
$817$		0			0
$818$	13.5830			0.474919
$819$	12.3720	+	4.50304i	0.432313	+	0.157349i
$820$	6.51532	+	36.9502i	0.227525	+	1.29036i
$821$	−4.59627	−	3.85673i	−0.160411	−	0.134601i	0.559049	−	0.829134i	$-0.311166\pi$
$821$	−4.59627	−	3.85673i	−0.160411	−	0.134601i	−0.719460	+	0.694534i	$0.755611\pi$
$822$	11.3154	−	9.49477i	0.394671	−	0.331168i
$823$	−0.0217915	+	0.123586i	−0.000759603	+	0.00430792i	−0.985185	−	0.171494i	$-0.945141\pi$
$823$	−0.0217915	+	0.123586i	−0.000759603	+	0.00430792i	0.984426	+	0.175802i	$0.0562518\pi$
$824$	1.35425	−	2.34563i	0.0471775	−	0.0817138i
$825$	7.08301	+	12.2681i	0.246599	+	0.427121i
$826$	12.2750	−	4.46772i	0.427101	−	0.155452i
$827$	44.4984	−	16.1961i	1.54736	−	0.563194i	0.579565	−	0.814926i	$-0.303222\pi$
$827$	44.4984	−	16.1961i	1.54736	−	0.563194i	0.967797	+	0.251732i	$0.0810001\pi$
$828$	−7.29150	−	12.6293i	−0.253397	−	0.438897i
$829$	−12.5830	+	21.7944i	−0.437026	+	0.756951i	−0.997459	−	0.0712490i	$-0.977302\pi$
$829$	−12.5830	+	21.7944i	−0.437026	+	0.756951i	0.560433	+	0.828200i	$0.310635\pi$
$830$	−5.02490	+	28.4976i	−0.174417	+	0.989167i
$831$	−19.2953	+	16.1907i	−0.669347	+	0.561649i
$832$	1.53209	+	1.28558i	0.0531156	+	0.0445693i
$833$		0			0
$834$	33.2012	+	12.0843i	1.14966	+	0.418444i
$835$	−43.7490			−1.51400
$836$		0			0
$837$	0.937254			0.0323962
$838$	−29.8343	−	10.8588i	−1.03061	−	0.375111i
$839$	−0.777899	−	4.41168i	−0.0268561	−	0.152308i	0.968431	−	0.249282i	$-0.0801947\pi$
$839$	−0.777899	−	4.41168i	−0.0268561	−	0.152308i	−0.995287	+	0.0969741i	$0.969084\pi$
$840$	12.1606	+	10.2039i	0.419580	+	0.352069i
$841$	−12.0334	+	10.0972i	−0.414945	+	0.348180i
$842$	3.96122	−	22.4652i	0.136513	−	0.774202i
$843$	−36.3229	+	62.9131i	−1.25103	+	2.16684i
$844$	1.35425	+	2.34563i	0.0466152	+	0.0807398i
$845$	30.8330	−	11.2223i	1.06069	−	0.386058i
$846$	−36.2562	+	13.1962i	−1.24651	+	0.453693i
$847$	−8.70850	−	15.0836i	−0.299228	−	0.518277i
$848$	−4.29150	+	7.43310i	−0.147371	+	0.255254i
$849$	−11.6485	+	66.0619i	−0.399775	+	2.26724i
$850$		0			0
$851$	15.7675	+	13.2305i	0.540503	+	0.453536i
$852$	6.10651	+	34.6318i	0.209206	+	1.18646i
$853$	11.8242	+	4.30364i	0.404851	+	0.147354i	0.536416	−	0.843954i	$-0.319778\pi$
$853$	11.8242	+	4.30364i	0.404851	+	0.147354i	−0.131565	+	0.991308i	$0.542000\pi$
$854$	24.5830			0.841213
$855$		0			0
$856$	4.70850			0.160933
$857$	−19.7335	−	7.18242i	−0.674085	−	0.245347i	−0.0177793	−	0.999842i	$-0.505660\pi$
$857$	−19.7335	−	7.18242i	−0.674085	−	0.245347i	−0.656306	+	0.754495i	$0.727882\pi$
$858$	−0.593355	−	3.36508i	−0.0202568	−	0.114882i
$859$	−10.1338	−	8.50328i	−0.345761	−	0.290128i	0.453324	−	0.891346i	$-0.350238\pi$
$859$	−10.1338	−	8.50328i	−0.345761	−	0.290128i	−0.799085	+	0.601218i	$0.794682\pi$
$860$	1.97870	−	1.66032i	0.0674730	−	0.0566166i
$861$	7.78148	−	44.1310i	0.265192	−	1.50398i
$862$	1.93725	−	3.35542i	0.0659831	−	0.114286i
$863$	23.4686	+	40.6489i	0.798881	+	1.38370i	0.920345	+	0.391107i	$0.127908\pi$
$863$	23.4686	+	40.6489i	0.798881	+	1.38370i	−0.121464	+	0.992596i	$0.538759\pi$
$864$	2.48619	−	0.904900i	0.0845820	−	0.0307853i
$865$	20.5553	−	7.48152i	0.698902	−	0.254379i
$866$	6.93725	+	12.0157i	0.235737	+	0.408309i
$867$	−22.4889	+	38.9519i	−0.763763	+	1.32288i
$868$	0.101238	−	0.574148i	0.00343623	−	0.0194879i
$869$	−1.97870	+	1.66032i	−0.0671227	+	0.0563226i
$870$	26.9387	+	22.6043i	0.913308	+	0.766357i
$871$	−1.61345	−	9.15034i	−0.0546698	−	0.310048i
$872$	6.18600	+	2.25152i	0.209484	+	0.0762461i
$873$	−57.1660			−1.93478
$874$		0			0
$875$	−19.7490			−0.667639
$876$	30.5590	+	11.1226i	1.03249	+	0.375797i
$877$	−6.31285	−	35.8019i	−0.213170	−	1.20895i	−0.884054	−	0.467384i	$-0.845197\pi$
$877$	−6.31285	−	35.8019i	−0.213170	−	1.20895i	0.670885	−	0.741562i	$-0.265915\pi$
$878$	−28.1994	−	23.6621i	−0.951685	−	0.798559i
$879$	−26.4751	+	22.2152i	−0.892983	+	0.749301i
$880$	0.408811	−	2.31848i	0.0137810	−	0.0781560i
$881$	2.56275	−	4.43881i	0.0863411	−	0.149547i	−0.819621	−	0.572906i	$-0.805816\pi$
$881$	2.56275	−	4.43881i	0.0863411	−	0.149547i	0.905962	+	0.423359i	$0.139149\pi$
$882$	8.58301	+	14.8662i	0.289005	+	0.500571i
$883$	−37.9587	+	13.8158i	−1.27741	+	0.464939i	−0.889575	−	0.456789i	$-0.848999\pi$
$883$	−37.9587	+	13.8158i	−1.27741	+	0.464939i	−0.387836	+	0.921729i	$0.626777\pi$
$884$		0			0
$885$	38.2804	+	66.3036i	1.28678	+	2.22877i
$886$	−2.67712	+	4.63692i	−0.0899398	+	0.155780i
$887$	−6.69987	+	37.9968i	−0.224960	+	1.27581i	0.637803	+	0.770200i	$0.279843\pi$
$887$	−6.69987	+	37.9968i	−0.224960	+	1.27581i	−0.862762	+	0.505609i	$0.831268\pi$
$888$	−11.4426	+	9.60148i	−0.383989	+	0.322205i
$889$	3.41465	+	2.86523i	0.114524	+	0.0960969i
$890$		0			0
$891$	3.03404	+	1.10430i	0.101644	+	0.0369954i
$892$	28.8118			0.964689
$893$		0			0
$894$	13.0627			0.436884
$895$	−68.3028	−	24.8602i	−2.28311	−	0.830984i
$896$	−0.285782	−	1.62075i	−0.00954730	−	0.0541454i
$897$	−14.7781	−	12.4003i	−0.493428	−	0.414035i
$898$	−10.5013	+	8.81165i	−0.350434	+	0.294049i
$899$	0.224267	−	1.27188i	0.00747973	−	0.0424196i
$900$	−16.5830	+	28.7226i	−0.552767	+	0.957420i
$901$		0			0
$902$	−6.24496	+	2.27298i	−0.207935	+	0.0756820i
$903$	−2.89893	+	1.05512i	−0.0964703	+	0.0351123i
$904$	−2.79150	−	4.83502i	−0.0928440	−	0.160811i
$905$	7.70850	−	13.3515i	0.256239	−	0.443819i
$906$	1.34946	−	7.65318i	0.0448329	−	0.254260i
$907$	18.4331	−	15.4672i	0.612062	−	0.513581i	−0.283235	−	0.959051i	$-0.591408\pi$
$907$	18.4331	−	15.4672i	0.612062	−	0.513581i	0.895297	+	0.445469i	$0.146963\pi$
$908$	−9.68721	−	8.12853i	−0.321481	−	0.269755i
$909$	−5.80280	−	32.9093i	−0.192467	−	1.09153i
$910$	11.2763	+	4.10424i	0.373806	+	0.136054i
$911$	1.06275			0.0352103			0.0176052	−	0.999845i	$-0.494396\pi$
$911$	1.06275			0.0352103			0.0176052	+	0.999845i	$0.494396\pi$
$912$		0			0
$913$	−5.12549			−0.169629
$914$	−1.05762	−	0.384941i	−0.0349828	−	0.0127327i
$915$	25.0194	+	141.892i	0.827116	+	4.69081i
$916$	15.3209	+	12.8558i	0.506216	+	0.424766i
$917$	17.5710	−	14.7438i	0.580244	−	0.486883i
$918$		0			0
$919$	−5.93725	+	10.2836i	−0.195852	+	0.339226i	−0.947179	−	0.320704i	$-0.896081\pi$
$919$	−5.93725	+	10.2836i	−0.195852	+	0.339226i	0.751328	+	0.659929i	$0.229414\pi$
$920$	−6.64575	−	11.5108i	−0.219104	−	0.379499i
$921$	−11.5502	+	4.20394i	−0.380593	+	0.138525i
$922$	21.7689	−	7.92324i	0.716921	−	0.260938i
$923$	13.2915	+	23.0216i	0.437495	+	0.757764i
$924$	−1.40588	+	2.43506i	−0.0462501	+	0.0801075i
$925$	8.12878	−	46.1006i	0.267273	−	1.51578i
$926$	11.0751	−	9.29311i	0.363950	−	0.305391i
$927$	−8.29932	−	6.96395i	−0.272585	−	0.228726i
$928$	−0.633078	−	3.59036i	−0.0207818	−	0.117859i
$929$	−10.8845	−	3.96162i	−0.357108	−	0.129977i	0.157235	−	0.987561i	$-0.449742\pi$
$929$	−10.8845	−	3.96162i	−0.357108	−	0.129977i	−0.514343	+	0.857585i	$0.671964\pi$
$930$	3.41699			0.112048
$931$		0			0
$932$	−12.8745			−0.421719
$933$	20.7703	+	7.55976i	0.679988	+	0.247495i
$934$	−4.27969	−	24.2713i	−0.140036	−	0.794182i
$935$		0			0
$936$	6.12836	−	5.14230i	0.200312	−	0.168081i
$937$	6.75049	−	38.2839i	0.220529	−	1.25068i	−0.650522	−	0.759488i	$-0.725450\pi$
$937$	6.75049	−	38.2839i	0.220529	−	1.25068i	0.871051	−	0.491193i	$-0.163439\pi$
$938$	−3.82288	+	6.62141i	−0.124821	+	0.216197i
$939$	−30.2601	−	52.4121i	−0.987502	−	1.71040i
$940$	−33.0452	+	12.0275i	−1.07782	+	0.392293i
$941$	−55.5979	+	20.2360i	−1.81244	+	0.659674i	−0.815746	+	0.578410i	$0.803673\pi$
$941$	−55.5979	+	20.2360i	−1.81244	+	0.659674i	−0.996693	+	0.0812632i	$0.974105\pi$
$942$	14.0000	+	24.2487i	0.456145	+	0.790066i
$943$	−18.7601	+	32.4935i	−0.610914	+	1.05813i
$944$	1.37829	−	7.81667i	0.0448595	−	0.254411i
$945$	12.1606	−	10.2039i	0.395584	−	0.331934i
$946$	0.350475	+	0.294084i	0.0113949	+	0.00956149i
$947$	9.68071	+	54.9021i	0.314581	+	1.78408i	0.574559	+	0.818463i	$0.305173\pi$
$947$	9.68071	+	54.9021i	0.314581	+	1.78408i	−0.259978	+	0.965614i	$0.583715\pi$
$948$	−9.94477	−	3.61960i	−0.322991	−	0.117559i
$949$	24.5830			0.797998
$950$		0			0
$951$	15.8745			0.514766
$952$		0			0
$953$	6.85173	+	38.8581i	0.221949	+	1.25874i	0.868432	+	0.495808i	$0.165128\pi$
$953$	6.85173	+	38.8581i	0.221949	+	1.25874i	−0.646483	+	0.762928i	$0.723761\pi$
$954$	26.2999	+	22.0682i	0.851489	+	0.714484i
$955$	−40.7275	+	34.1745i	−1.31791	+	1.10586i
$956$	−2.08378	+	11.8177i	−0.0673942	+	0.382212i
$957$	−3.11438	+	5.39426i	−0.100674	+	0.174372i
$958$	7.29150	+	12.6293i	0.235578	+	0.408033i
$959$	−8.63412	+	3.14256i	−0.278810	+	0.101479i
$960$	9.06404	−	3.29904i	0.292541	−	0.106476i
$961$	15.4373	+	26.7381i	0.497976	+	0.862520i
$962$	−5.64575	+	9.77873i	−0.182026	+	0.315279i
$963$	3.27049	−	18.5479i	0.105390	−	0.597696i
$964$	10.4052	−	8.73099i	0.335128	−	0.281206i
$965$	−18.3851	−	15.4269i	−0.591836	−	0.496610i
$966$	2.75658	+	15.6333i	0.0886915	+	0.502994i
$967$	2.54515	+	0.926361i	0.0818467	+	0.0297898i	0.382619	−	0.923906i	$-0.375022\pi$
$967$	2.54515	+	0.926361i	0.0818467	+	0.0297898i	−0.300772	+	0.953696i	$0.597244\pi$
$968$	−10.5830			−0.340151
$969$		0			0
$970$	−52.1033			−1.67293
$971$	−13.5267	−	4.92330i	−0.434091	−	0.157996i	0.115726	−	0.993281i	$-0.463080\pi$
$971$	−13.5267	−	4.92330i	−0.434091	−	0.157996i	−0.549817	+	0.835285i	$0.685303\pi$
$972$	3.67544	+	20.8445i	0.117890	+	0.668586i
$973$	−16.8360	−	14.1270i	−0.539736	−	0.452892i
$974$	−17.0282	+	14.2884i	−0.545619	+	0.457829i
$975$	−7.61873	+	43.2080i	−0.243995	+	1.38376i
$976$	7.46863	−	12.9360i	0.239065	−	0.414073i
$977$	−22.7288	−	39.3674i	−0.727157	−	1.25947i	−0.958080	−	0.286501i	$-0.907508\pi$
$977$	−22.7288	−	39.3674i	−0.727157	−	1.25947i	0.230923	−	0.972972i	$-0.425826\pi$
$978$	−29.6783	+	10.8020i	−0.949008	+	0.345411i
$979$		0			0
$980$	7.82288	+	13.5496i	0.249893	+	0.432827i
$981$	13.1660	−	22.8042i	0.420358	−	0.728082i
$982$	4.98518	−	28.2724i	0.159083	−	0.902207i
$983$	−24.3212	+	20.4079i	−0.775724	+	0.650910i	−0.942168	−	0.335141i	$-0.891216\pi$
$983$	−24.3212	+	20.4079i	−0.775724	+	0.650910i	0.166444	+	0.986051i	$0.446772\pi$
$984$	−20.8584	−	17.5023i	−0.664943	−	0.557953i
$985$	−1.49042	−	8.45261i	−0.0474888	−	0.269323i
$986$		0			0
$987$	42.0000			1.33687
$988$		0			0
$989$	2.58301			0.0821348
$990$	−8.84908	−	3.22080i	−0.281242	−	0.102364i
$991$	−7.84300	−	44.4798i	−0.249141	−	1.41295i	−0.810676	−	0.585495i	$-0.800900\pi$
$991$	−7.84300	−	44.4798i	−0.249141	−	1.41295i	0.561535	−	0.827453i	$-0.310211\pi$
$992$	−0.271370	−	0.227707i	−0.00861601	−	0.00722969i
$993$	56.3679	−	47.2982i	1.78878	−	1.50096i
$994$	3.79847	−	21.5422i	0.120480	−	0.683277i
$995$	−21.6458	+	37.4915i	−0.686216	+	1.18856i
$996$	−10.5000	−	18.1865i	−0.332705	−	0.576262i
$997$	9.61189	−	3.49844i	0.304412	−	0.110797i	−0.185298	−	0.982682i	$-0.559325\pi$
$997$	9.61189	−	3.49844i	0.304412	−	0.110797i	0.489710	+	0.871886i	$0.337103\pi$
$998$	29.3454	−	10.6809i	0.928913	−	0.338097i
$999$	7.46863	+	12.9360i	0.236297	+	0.409278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.n.99.1		12
19.2	odd	18		722.2.e.o.415.1		12
19.3	odd	18		722.2.e.o.245.2		12
19.4	even	9		38.2.c.b.7.2	✓	4
19.5	even	9	inner	722.2.e.n.423.1		12
19.6	even	9		38.2.c.b.11.2	yes	4
19.7	even	3	inner	722.2.e.n.595.2		12
19.8	odd	6		722.2.e.o.389.2		12
19.9	even	9		722.2.a.j.1.1		2
19.10	odd	18		722.2.a.g.1.2		2
19.11	even	3	inner	722.2.e.n.389.1		12
19.12	odd	6		722.2.e.o.595.1		12
19.13	odd	18		722.2.c.j.429.1		4
19.14	odd	18		722.2.e.o.423.2		12
19.15	odd	18		722.2.c.j.653.1		4
19.16	even	9	inner	722.2.e.n.245.1		12
19.17	even	9	inner	722.2.e.n.415.2		12
19.18	odd	2		722.2.e.o.99.2		12
57.23	odd	18		342.2.g.f.235.2		4
57.29	even	18		6498.2.a.bg.1.1		2
57.44	odd	18		342.2.g.f.163.2		4
57.47	odd	18		6498.2.a.ba.1.1		2
76.23	odd	18		304.2.i.e.273.1		4
76.47	odd	18		5776.2.a.ba.1.2		2
76.63	odd	18		304.2.i.e.49.1		4
76.67	even	18		5776.2.a.z.1.1		2
95.4	even	18		950.2.e.k.501.1		4
95.23	odd	36		950.2.j.g.349.1		8
95.42	odd	36		950.2.j.g.349.4		8
95.44	even	18		950.2.e.k.201.1		4
95.63	odd	36		950.2.j.g.49.4		8
95.82	odd	36		950.2.j.g.49.1		8
152.61	even	18		1216.2.i.l.577.1		4
152.99	odd	18		1216.2.i.k.577.2		4
152.101	even	18		1216.2.i.l.961.1		4
152.139	odd	18		1216.2.i.k.961.2		4
228.23	even	18		2736.2.s.v.577.2		4
228.215	even	18		2736.2.s.v.1873.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.2	✓	4	19.4	even	9
38.2.c.b.11.2	yes	4	19.6	even	9
304.2.i.e.49.1		4	76.63	odd	18
304.2.i.e.273.1		4	76.23	odd	18
342.2.g.f.163.2		4	57.44	odd	18
342.2.g.f.235.2		4	57.23	odd	18
722.2.a.g.1.2		2	19.10	odd	18
722.2.a.j.1.1		2	19.9	even	9
722.2.c.j.429.1		4	19.13	odd	18
722.2.c.j.653.1		4	19.15	odd	18
722.2.e.n.99.1		12	1.1	even	1	trivial
722.2.e.n.245.1		12	19.16	even	9	inner
722.2.e.n.389.1		12	19.11	even	3	inner
722.2.e.n.415.2		12	19.17	even	9	inner
722.2.e.n.423.1		12	19.5	even	9	inner
722.2.e.n.595.2		12	19.7	even	3	inner
722.2.e.o.99.2		12	19.18	odd	2
722.2.e.o.245.2		12	19.3	odd	18
722.2.e.o.389.2		12	19.8	odd	6
722.2.e.o.415.1		12	19.2	odd	18
722.2.e.o.423.2		12	19.14	odd	18
722.2.e.o.595.1		12	19.12	odd	6
950.2.e.k.201.1		4	95.44	even	18
950.2.e.k.501.1		4	95.4	even	18
950.2.j.g.49.1		8	95.82	odd	36
950.2.j.g.49.4		8	95.63	odd	36
950.2.j.g.349.1		8	95.23	odd	36
950.2.j.g.349.4		8	95.42	odd	36
1216.2.i.k.577.2		4	152.99	odd	18
1216.2.i.k.961.2		4	152.139	odd	18
1216.2.i.l.577.1		4	152.61	even	18
1216.2.i.l.961.1		4	152.101	even	18
2736.2.s.v.577.2		4	228.23	even	18
2736.2.s.v.1873.2		4	228.215	even	18
5776.2.a.z.1.1		2	76.67	even	18
5776.2.a.ba.1.2		2	76.47	odd	18
6498.2.a.ba.1.1		2	57.47	odd	18
6498.2.a.bg.1.1		2	57.29	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.459430 - 2.60556i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.79281 - 2.34344i) q^{5} +(-0.459430 + 2.60556i) q^{6} +(0.822876 - 1.42526i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.75877 + 1.36808i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.459430 - 2.60556i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.79281 - 2.34344i) q^{5} +(-0.459430 + 2.60556i) q^{6} +(0.822876 - 1.42526i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.75877 + 1.36808i) q^{9} +(-3.42589 + 1.24692i) q^{10} +(-0.322876 - 0.559237i) q^{11} +(1.32288 - 2.29129i) q^{12} +(0.347296 - 1.96962i) q^{13} +(-1.26072 + 1.05787i) q^{14} +(-7.38907 - 6.20017i) q^{15} +(0.173648 + 0.984808i) q^{16} +4.00000 q^{18} +3.64575 q^{20} +(-4.09166 - 1.48924i) q^{21} +(0.112134 + 0.635941i) q^{22} +(2.79281 + 2.34344i) q^{23} +(-2.02676 + 1.70066i) q^{24} +(1.43980 - 8.16554i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(1.32288 + 2.29129i) q^{27} +(1.54650 - 0.562880i) q^{28} +(3.42589 - 1.24692i) q^{29} +(4.82288 + 8.35347i) q^{30} +(0.177124 - 0.306788i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-1.30878 + 1.09820i) q^{33} +(-1.04189 - 5.90885i) q^{35} +(-3.75877 - 1.36808i) q^{36} +5.64575 q^{37} -5.29150 q^{39} +(-3.42589 - 1.24692i) q^{40} +(1.78710 + 10.1352i) q^{41} +(3.33555 + 2.79886i) q^{42} +(0.542740 - 0.455413i) q^{43} +(0.112134 - 0.635941i) q^{44} +(-7.29150 + 12.6293i) q^{45} +(-1.82288 - 3.15731i) q^{46} +(-9.06404 + 3.29904i) q^{47} +(2.48619 - 0.904900i) q^{48} +(2.14575 + 3.71655i) q^{49} +(-4.14575 + 7.18065i) q^{50} +(1.53209 - 1.28558i) q^{52} +(6.57496 + 5.51705i) q^{53} +(-0.459430 - 2.60556i) q^{54} +(-2.21227 - 0.805200i) q^{55} -1.64575 q^{56} -3.64575 q^{58} +(-7.45858 - 2.71470i) q^{59} +(-1.67497 - 9.49921i) q^{60} +(-11.4426 - 9.60148i) q^{61} +(-0.271370 + 0.227707i) q^{62} +(-1.14313 + 6.48299i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.64575 - 6.31463i) q^{65} +(1.60546 - 0.584341i) q^{66} +(4.36558 - 1.58894i) q^{67} +(4.82288 - 8.35347i) q^{69} +(-1.04189 + 5.90885i) q^{70} +(-10.1819 + 8.54361i) q^{71} +(3.06418 + 2.57115i) q^{72} +(2.13440 + 12.1048i) q^{73} +(-5.30527 - 1.93096i) q^{74} -21.9373 q^{75} -1.06275 q^{77} +(4.97239 + 1.80980i) q^{78} +(-0.694593 - 3.93923i) q^{79} +(2.79281 + 2.34344i) q^{80} +(-3.83022 + 3.21394i) q^{81} +(1.78710 - 10.1352i) q^{82} +(3.96863 - 6.87386i) q^{83} +(-2.17712 - 3.77089i) q^{84} +(-0.665770 + 0.242320i) q^{86} +(-4.82288 - 8.35347i) q^{87} +(-0.322876 + 0.559237i) q^{88} +(11.1712 - 9.37378i) q^{90} +(-2.52144 - 2.11574i) q^{91} +(0.633078 + 3.59036i) q^{92} +(-0.880731 - 0.320560i) q^{93} +9.64575 q^{94} -2.64575 q^{96} +(13.4296 + 4.88798i) q^{97} +(-0.745212 - 4.22631i) q^{98} +(1.97870 + 1.66032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8	\( 12 q - 6 q^{7} - 6 q^{8} + 12 q^{11} + 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} + 18 q^{31} + 36 q^{37} - 24 q^{45} - 6 q^{46} - 6 q^{49} - 18 q^{50} + 12 q^{56} - 12 q^{58} - 6 q^{64} - 12 q^{65} + 42 q^{69} - 168 q^{75} - 108 q^{77} - 42 q^{84} - 42 q^{87} + 12 q^{88} + 84 q^{94}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 12 * q^11 + 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 + 18 * q^31 + 36 * q^37 - 24 * q^45 - 6 * q^46 - 6 * q^49 - 18 * q^50 + 12 * q^56 - 12 * q^58 - 6 * q^64 - 12 * q^65 + 42 * q^69 - 168 * q^75 - 108 * q^77 - 42 * q^84 - 42 * q^87 + 12 * q^88 + 84 * q^94

Introduction

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