LMFDB - Embedded newform 722.2.e.n.245.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$12$
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			245.1
Root			$-0.459430 + 2.60556i$ of defining polynomial
Character	$\chi$	$=$	722.245
Dual form			722.2.e.n.389.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-2.02676 - 1.70066i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.42589 + 1.24692i) q^{5} +(-2.02676 + 1.70066i) q^{6} +(0.822876 + 1.42526i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.694593 + 3.93923i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-2.02676 - 1.70066i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.42589 + 1.24692i) q^{5} +(-2.02676 + 1.70066i) q^{6} +(0.822876 + 1.42526i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.694593 + 3.93923i) q^{9} +(0.633078 + 3.59036i) q^{10} +(-0.322876 + 0.559237i) q^{11} +(1.32288 + 2.29129i) q^{12} +(1.53209 - 1.28558i) q^{13} +(1.54650 - 0.562880i) q^{14} +(9.06404 + 3.29904i) q^{15} +(0.766044 + 0.642788i) q^{16} +4.00000 q^{18} +3.64575 q^{20} +(0.756107 - 4.28810i) q^{21} +(0.494674 + 0.415081i) q^{22} +(-3.42589 - 1.24692i) q^{23} +(2.48619 - 0.904900i) q^{24} +(6.35166 - 5.32968i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(1.32288 - 2.29129i) q^{27} +(-0.285782 - 1.62075i) q^{28} +(-0.633078 - 3.59036i) q^{29} +(4.82288 - 8.35347i) q^{30} +(0.177124 + 0.306788i) q^{31} +(0.766044 - 0.642788i) q^{32} +(1.60546 - 0.584341i) q^{33} +(-4.59627 - 3.85673i) q^{35} +(0.694593 - 3.93923i) q^{36} +5.64575 q^{37} -5.29150 q^{39} +(0.633078 - 3.59036i) q^{40} +(7.88375 + 6.61525i) q^{41} +(-4.09166 - 1.48924i) q^{42} +(-0.665770 + 0.242320i) q^{43} +(0.494674 - 0.415081i) q^{44} +(-7.29150 - 12.6293i) q^{45} +(-1.82288 + 3.15731i) q^{46} +(1.67497 + 9.49921i) q^{47} +(-0.459430 - 2.60556i) q^{48} +(2.14575 - 3.71655i) q^{49} +(-4.14575 - 7.18065i) q^{50} +(-1.87939 + 0.684040i) q^{52} +(-8.06539 - 2.93556i) q^{53} +(-2.02676 - 1.70066i) q^{54} +(0.408811 - 2.31848i) q^{55} -1.64575 q^{56} -3.64575 q^{58} +(1.37829 - 7.81667i) q^{59} +(-7.38907 - 6.20017i) q^{60} +(14.0364 + 5.10884i) q^{61} +(0.332885 - 0.121160i) q^{62} +(-5.04287 + 4.23147i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.64575 + 6.31463i) q^{65} +(-0.296677 - 1.68254i) q^{66} +(-0.806726 - 4.57517i) q^{67} +(4.82288 + 8.35347i) q^{69} +(-4.59627 + 3.85673i) q^{70} +(12.4899 - 4.54596i) q^{71} +(-3.75877 - 1.36808i) q^{72} +(9.41584 + 7.90083i) q^{73} +(0.980374 - 5.55998i) q^{74} -21.9373 q^{75} -1.06275 q^{77} +(-0.918860 + 5.21111i) q^{78} +(-3.06418 - 2.57115i) q^{79} +(-3.42589 - 1.24692i) q^{80} +(4.69846 - 1.71010i) q^{81} +(7.88375 - 6.61525i) q^{82} +(3.96863 + 6.87386i) q^{83} +(-2.17712 + 3.77089i) q^{84} +(0.123029 + 0.697734i) q^{86} +(-4.82288 + 8.35347i) q^{87} +(-0.322876 - 0.559237i) q^{88} +(-13.7035 + 4.98768i) q^{90} +(3.09300 + 1.12576i) q^{91} +(2.79281 + 2.34344i) q^{92} +(0.162752 - 0.923015i) q^{93} +9.64575 q^{94} -2.64575 q^{96} +(-2.48169 + 14.0744i) q^{97} +(-3.28748 - 2.75852i) q^{98} +(-2.42723 - 0.883440i) 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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−2.02676	−	1.70066i	−1.17015	−	0.981874i	−0.170158	−	0.985417i	$-0.554428\pi$
$3$	−2.02676	−	1.70066i	−1.17015	−	0.981874i	−0.999994	+	0.00354242i	$0.998872\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−3.42589	+	1.24692i	−1.53210	+	0.557640i	−0.964135	−	0.265411i	$-0.914492\pi$
$5$	−3.42589	+	1.24692i	−1.53210	+	0.557640i	−0.567967	+	0.823051i	$0.692270\pi$
$6$	−2.02676	+	1.70066i	−0.827423	+	0.694290i
$7$	0.822876	+	1.42526i	0.311018	+	0.538699i	0.978583	−	0.205853i	$-0.0659968\pi$
$7$	0.822876	+	1.42526i	0.311018	+	0.538699i	−0.667565	+	0.744551i	$0.732663\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.694593	+	3.93923i	0.231531	+	1.31308i
$10$	0.633078	+	3.59036i	0.200197	+	1.13537i
$11$	−0.322876	+	0.559237i	−0.0973507	+	0.168616i	−0.910587	−	0.413317i	$-0.864370\pi$
$11$	−0.322876	+	0.559237i	−0.0973507	+	0.168616i	0.813237	+	0.581933i	$0.197704\pi$
$12$	1.32288	+	2.29129i	0.381881	+	0.661438i
$13$	1.53209	−	1.28558i	0.424925	−	0.356554i	−0.405108	−	0.914269i	$-0.632766\pi$
$13$	1.53209	−	1.28558i	0.424925	−	0.356554i	0.830033	+	0.557714i	$0.188322\pi$
$14$	1.54650	−	0.562880i	0.413320	−	0.150436i
$15$	9.06404	+	3.29904i	2.34033	+	0.851809i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$17$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$18$	4.00000			0.942809
$19$		0			0
$19$		0			0
$20$	3.64575			0.815215
$21$	0.756107	−	4.28810i	0.164996	−	0.935740i
$22$	0.494674	+	0.415081i	0.105465	+	0.0884956i
$23$	−3.42589	−	1.24692i	−0.714347	−	0.260001i	−0.0408227	−	0.999166i	$-0.512998\pi$
$23$	−3.42589	−	1.24692i	−0.714347	−	0.260001i	−0.673524	+	0.739166i	$0.735220\pi$
$24$	2.48619	−	0.904900i	0.507492	−	0.184712i
$25$	6.35166	−	5.32968i	1.27033	−	1.06594i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	1.32288	−	2.29129i	0.254588	−	0.440959i
$28$	−0.285782	−	1.62075i	−0.0540077	−	0.306293i
$29$	−0.633078	−	3.59036i	−0.117560	−	0.666714i	−0.985451	−	0.169960i	$-0.945636\pi$
$29$	−0.633078	−	3.59036i	−0.117560	−	0.666714i	0.867891	−	0.496754i	$-0.165475\pi$
$30$	4.82288	−	8.35347i	0.880533	−	1.52513i
$31$	0.177124	+	0.306788i	0.0318125	+	0.0551008i	0.881493	−	0.472197i	$-0.156539\pi$
$31$	0.177124	+	0.306788i	0.0318125	+	0.0551008i	−0.849681	+	0.527297i	$0.823205\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	1.60546	−	0.584341i	0.279475	−	0.101721i
$34$		0			0
$35$	−4.59627	−	3.85673i	−0.776911	−	0.651906i
$36$	0.694593	−	3.93923i	0.115765	−	0.656539i
$37$	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
$40$	0.633078	−	3.59036i	0.100098	−	0.567686i
$41$	7.88375	+	6.61525i	1.23123	+	1.03313i	0.998158	+	0.0606702i	$0.0193238\pi$
$41$	7.88375	+	6.61525i	1.23123	+	1.03313i	0.233077	+	0.972458i	$0.425121\pi$
$42$	−4.09166	−	1.48924i	−0.631356	−	0.229795i
$43$	−0.665770	+	0.242320i	−0.101529	+	0.0369535i	−0.392285	−	0.919844i	$-0.628315\pi$
$43$	−0.665770	+	0.242320i	−0.101529	+	0.0369535i	0.290756	+	0.956797i	$0.406093\pi$
$44$	0.494674	−	0.415081i	0.0745749	−	0.0625758i
$45$	−7.29150	−	12.6293i	−1.08695	−	1.88266i
$46$	−1.82288	+	3.15731i	−0.268768	+	0.465520i
$47$	1.67497	+	9.49921i	0.244319	+	1.38560i	0.822069	+	0.569388i	$0.192820\pi$
$47$	1.67497	+	9.49921i	0.244319	+	1.38560i	−0.577750	+	0.816214i	$0.696069\pi$
$48$	−0.459430	−	2.60556i	−0.0663130	−	0.376080i
$49$	2.14575	−	3.71655i	0.306536	−	0.530936i
$50$	−4.14575	−	7.18065i	−0.586298	−	1.01550i
$51$		0			0
$52$	−1.87939	+	0.684040i	−0.260624	+	0.0948593i
$53$	−8.06539	−	2.93556i	−1.10787	−	0.403230i	−0.277656	−	0.960681i	$-0.589557\pi$
$53$	−8.06539	−	2.93556i	−1.10787	−	0.403230i	−0.830210	+	0.557450i	$0.811780\pi$
$54$	−2.02676	−	1.70066i	−0.275808	−	0.231430i
$55$	0.408811	−	2.31848i	0.0551241	−	0.312624i
$56$	−1.64575			−0.219923
$57$		0			0
$58$	−3.64575			−0.478711
$59$	1.37829	−	7.81667i	0.179438	−	1.01764i	−0.753458	−	0.657497i	$-0.771615\pi$
$59$	1.37829	−	7.81667i	0.179438	−	1.01764i	0.932896	−	0.360147i	$-0.117273\pi$
$60$	−7.38907	−	6.20017i	−0.953925	−	0.800438i
$61$	14.0364	+	5.10884i	1.79718	+	0.654120i	0.998638	+	0.0521821i	$0.0166176\pi$
$61$	14.0364	+	5.10884i	1.79718	+	0.654120i	0.798543	+	0.601938i	$0.205605\pi$
$62$	0.332885	−	0.121160i	0.0422764	−	0.0153874i
$63$	−5.04287	+	4.23147i	−0.635342	+	0.533116i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−3.64575	+	6.31463i	−0.452200	+	0.783233i
$66$	−0.296677	−	1.68254i	−0.0365185	−	0.207107i
$67$	−0.806726	−	4.57517i	−0.0985573	−	0.558946i	−0.993599	−	0.112964i	$-0.963966\pi$
$67$	−0.806726	−	4.57517i	−0.0985573	−	0.558946i	0.895042	−	0.445982i	$-0.147146\pi$
$68$		0			0
$69$	4.82288	+	8.35347i	0.580606	+	1.00564i
$70$	−4.59627	+	3.85673i	−0.549359	+	0.460967i
$71$	12.4899	−	4.54596i	1.48228	−	0.539506i	0.530877	−	0.847449i	$-0.321863\pi$
$71$	12.4899	−	4.54596i	1.48228	−	0.539506i	0.951405	+	0.307943i	$0.0996405\pi$
$72$	−3.75877	−	1.36808i	−0.442975	−	0.161230i
$73$	9.41584	+	7.90083i	1.10204	+	0.924722i	0.997561	−	0.0698053i	$-0.0222378\pi$
$73$	9.41584	+	7.90083i	1.10204	+	0.924722i	0.104480	+	0.994527i	$0.466682\pi$
$74$	0.980374	−	5.55998i	0.113966	−	0.646335i
$75$	−21.9373			−2.53310
$76$		0			0
$77$	−1.06275			−0.121111
$78$	−0.918860	+	5.21111i	−0.104040	+	0.590042i
$79$	−3.06418	−	2.57115i	−0.344747	−	0.289277i	0.453930	−	0.891038i	$-0.350022\pi$
$79$	−3.06418	−	2.57115i	−0.344747	−	0.289277i	−0.798677	+	0.601760i	$0.794466\pi$
$80$	−3.42589	−	1.24692i	−0.383026	−	0.139410i
$81$	4.69846	−	1.71010i	0.522051	−	0.190011i
$82$	7.88375	−	6.61525i	0.870614	−	0.730532i
$83$	3.96863	+	6.87386i	0.435613	+	0.754505i	0.997345	−	0.0728147i	$-0.0231982\pi$
$83$	3.96863	+	6.87386i	0.435613	+	0.754505i	−0.561732	+	0.827319i	$0.689865\pi$
$84$	−2.17712	+	3.77089i	−0.237544	+	0.411438i
$85$		0			0
$86$	0.123029	+	0.697734i	0.0132666	+	0.0752386i
$87$	−4.82288	+	8.35347i	−0.517067	+	0.895586i
$88$	−0.322876	−	0.559237i	−0.0344187	−	0.0596149i
$89$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$89$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$90$	−13.7035	+	4.98768i	−1.44448	+	0.525748i
$91$	3.09300	+	1.12576i	0.324235	+	0.118012i
$92$	2.79281	+	2.34344i	0.291170	+	0.244321i
$93$	0.162752	−	0.923015i	0.0168766	−	0.0957122i
$94$	9.64575			0.994883
$95$		0			0
$96$	−2.64575			−0.270031
$97$	−2.48169	+	14.0744i	−0.251978	+	1.42904i	0.551735	+	0.834020i	$0.313966\pi$
$97$	−2.48169	+	14.0744i	−0.251978	+	1.42904i	−0.803713	+	0.595018i	$0.797145\pi$
$98$	−3.28748	−	2.75852i	−0.332086	−	0.278653i
$99$	−2.42723	−	0.883440i	−0.243946	−	0.0887890i
$100$	−7.79146	+	2.83586i	−0.779146	+	0.283586i
$101$	−6.39973	+	5.37001i	−0.636797	+	0.534336i	−0.903033	−	0.429572i	$-0.858664\pi$
$101$	−6.39973	+	5.37001i	−0.636797	+	0.534336i	0.266236	+	0.963908i	$0.414220\pi$
$102$		0			0
$103$	1.35425	−	2.34563i	0.133438	−	0.231122i	−0.791562	−	0.611089i	$-0.790732\pi$
$103$	1.35425	−	2.34563i	0.133438	−	0.231122i	0.925000	+	0.379968i	$0.124065\pi$
$104$	0.347296	+	1.96962i	0.0340552	+	0.193137i
$105$	2.75658	+	15.6333i	0.269015	+	1.52566i
$106$	−4.29150	+	7.43310i	−0.416828	+	0.721967i
$107$	−2.35425	−	4.07768i	−0.227594	−	0.394204i	0.729501	−	0.683980i	$-0.239753\pi$
$107$	−2.35425	−	4.07768i	−0.227594	−	0.394204i	−0.957094	+	0.289776i	$0.906419\pi$
$108$	−2.02676	+	1.70066i	−0.195025	+	0.163646i
$109$	6.18600	−	2.25152i	0.592511	−	0.215657i	−0.0283222	−	0.999599i	$-0.509016\pi$
$109$	6.18600	−	2.25152i	0.592511	−	0.215657i	0.620834	+	0.783942i	$0.286794\pi$
$110$	−2.21227	−	0.805200i	−0.210932	−	0.0767729i
$111$	−11.4426	−	9.60148i	−1.08608	−	0.911332i
$112$	−0.285782	+	1.62075i	−0.0270038	+	0.153146i
$113$	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
$116$	−0.633078	+	3.59036i	−0.0587798	+	0.333357i
$117$	6.12836	+	5.14230i	0.566567	+	0.475406i
$118$	−7.45858	−	2.71470i	−0.686618	−	0.249908i
$119$		0			0
$120$	−7.38907	+	6.20017i	−0.674527	+	0.565995i
$121$	5.29150	+	9.16515i	0.481046	+	0.833196i
$122$	7.46863	−	12.9360i	0.676178	−	1.17117i
$123$	−4.72822	−	26.8151i	−0.426330	−	2.41784i
$124$	−0.0615146	−	0.348867i	−0.00552418	−	0.0313292i
$125$	−6.00000	+	10.3923i	−0.536656	+	0.929516i
$126$	3.29150	+	5.70105i	0.293230	+	0.507890i
$127$	−2.07483	+	1.74099i	−0.184111	+	0.154488i	−0.730185	−	0.683249i	$-0.760566\pi$
$127$	−2.07483	+	1.74099i	−0.184111	+	0.154488i	0.546074	+	0.837737i	$0.316122\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	1.76146	+	0.641119i	0.155088	+	0.0564474i
$130$	5.58562	+	4.68689i	0.489891	+	0.411067i
$131$	−2.42018	+	13.7255i	−0.211452	+	1.19920i	0.675506	+	0.737354i	$0.263925\pi$
$131$	−2.42018	+	13.7255i	−0.211452	+	1.19920i	−0.886958	+	0.461850i	$0.847186\pi$
$132$	−1.70850			−0.148706
$133$		0			0
$134$	−4.64575			−0.401332
$135$	−1.67497	+	9.49921i	−0.144158	+	0.817562i
$136$		0			0
$137$	5.24631	+	1.90950i	0.448222	+	0.163140i	0.556262	−	0.831007i	$-0.312235\pi$
$137$	5.24631	+	1.90950i	0.448222	+	0.163140i	−0.108040	+	0.994147i	$0.534457\pi$
$138$	9.06404	−	3.29904i	0.771582	−	0.280833i
$139$	10.2299	−	8.58395i	0.867693	−	0.728081i	−0.0959181	−	0.995389i	$-0.530579\pi$
$139$	10.2299	−	8.58395i	0.867693	−	0.728081i	0.963611	+	0.267308i	$0.0861343\pi$
$140$	3.00000	+	5.19615i	0.253546	+	0.439155i
$141$	12.7601	−	22.1012i	1.07460	−	1.86126i
$142$	−2.30805	−	13.0896i	−0.193687	−	1.09845i
$143$	0.224267	+	1.27188i	0.0187542	+	0.106360i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	6.64575	+	11.5108i	0.551900	+	0.955918i
$146$	9.41584	−	7.90083i	0.779260	−	0.653877i
$147$	−10.6695	+	3.88338i	−0.880006	+	0.320296i
$148$	−5.30527	−	1.93096i	−0.436091	−	0.158724i
$149$	−3.78216	−	3.17361i	−0.309846	−	0.259992i	0.474582	−	0.880211i	$-0.342599\pi$
$149$	−3.78216	−	3.17361i	−0.309846	−	0.259992i	−0.784428	+	0.620219i	$0.787044\pi$
$150$	−3.80936	+	21.6040i	−0.311033	+	1.76396i
$151$	−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
$154$	−0.184544	+	1.04660i	−0.0148710	+	0.0843375i
$155$	−0.989348	−	0.830162i	−0.0794664	−	0.0666802i
$156$	4.97239	+	1.80980i	0.398109	+	0.144900i
$157$	−9.94477	+	3.61960i	−0.793679	+	0.288876i	−0.706865	−	0.707349i	$-0.749891\pi$
$157$	−9.94477	+	3.61960i	−0.793679	+	0.288876i	−0.0868146	+	0.996224i	$0.527669\pi$
$158$	−3.06418	+	2.57115i	−0.243773	+	0.204550i
$159$	11.3542	+	19.6661i	0.900450	+	1.55963i
$160$	−1.82288	+	3.15731i	−0.144111	+	0.249608i
$161$	−1.04189	−	5.90885i	−0.0821124	−	0.465682i
$162$	−0.868241	−	4.92404i	−0.0682154	−	0.386869i
$163$	5.96863	−	10.3380i	0.467499	−	0.809732i	−0.531811	−	0.846863i	$-0.678489\pi$
$163$	5.96863	−	10.3380i	0.467499	−	0.809732i	0.999310	+	0.0371309i	$0.0118218\pi$
$164$	−5.14575	−	8.91270i	−0.401816	−	0.695965i
$165$	−4.77150	+	4.00377i	−0.371461	+	0.311693i
$166$	7.45858	−	2.71470i	0.578898	−	0.210702i
$167$	11.2763	+	4.10424i	0.872587	+	0.317596i	0.739214	−	0.673470i	$-0.235197\pi$
$167$	11.2763	+	4.10424i	0.872587	+	0.317596i	0.133373	+	0.991066i	$0.457419\pi$
$168$	3.33555	+	2.79886i	0.257343	+	0.215937i
$169$	−1.56283	+	8.86327i	−0.120218	+	0.681790i
$170$		0			0
$171$		0			0
$172$	0.708497			0.0540224
$173$	−1.04189	+	5.90885i	−0.0792134	+	0.449241i	0.919243	+	0.393692i	$0.128802\pi$
$173$	−1.04189	+	5.90885i	−0.0792134	+	0.449241i	−0.998456	+	0.0555496i	$0.982309\pi$
$174$	7.38907	+	6.20017i	0.560164	+	0.470034i
$175$	12.8228	+	4.66712i	0.969313	+	0.352801i
$176$	−0.606808	+	0.220860i	−0.0457399	+	0.0166479i
$177$	−16.0869	+	13.4985i	−1.20917	+	1.01461i
$178$		0			0
$179$	−9.96863	+	17.2662i	−0.745090	+	1.29053i	0.205062	+	0.978749i	$0.434260\pi$
$179$	−9.96863	+	17.2662i	−0.745090	+	1.29053i	−0.950153	+	0.311785i	$0.899073\pi$
$180$	2.53231	+	14.3615i	0.188747	+	1.07044i
$181$	−0.734316	−	4.16451i	−0.0545813	−	0.309546i	0.945279	−	0.326263i	$-0.105790\pi$
$181$	−0.734316	−	4.16451i	−0.0545813	−	0.309546i	−0.999860	+	0.0167174i	$0.994678\pi$
$182$	1.64575	−	2.85052i	0.121991	−	0.211295i
$183$	−19.7601	−	34.2255i	−1.46071	−	2.53003i
$184$	2.79281	−	2.34344i	0.205889	−	0.172761i
$185$	−19.3417	+	7.03980i	−1.42203	+	0.517577i
$186$	−0.880731	−	0.320560i	−0.0645783	−	0.0235046i
$187$		0			0
$188$	1.67497	−	9.49921i	0.122160	−	0.692801i
$189$	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	$0.676906\pi$
$192$	−0.459430	+	2.60556i	−0.0331565	+	0.188040i
$193$	−5.04287	−	4.23147i	−0.362994	−	0.304588i	0.442989	−	0.896527i	$-0.353918\pi$
$193$	−5.04287	−	4.23147i	−0.362994	−	0.304588i	−0.805983	+	0.591939i	$0.798363\pi$
$194$	13.4296	+	4.88798i	0.964190	+	0.350937i
$195$	18.1281	−	6.59808i	1.29818	−	0.472499i
$196$	−3.28748	+	2.75852i	−0.234820	+	0.197037i
$197$	1.17712	+	2.03884i	0.0838666	+	0.145261i	0.904908	−	0.425608i	$-0.139940\pi$
$197$	1.17712	+	2.03884i	0.0838666	+	0.145261i	−0.821041	+	0.570869i	$0.806606\pi$
$198$	−1.29150	+	2.23695i	−0.0917831	+	0.158973i
$199$	2.06199	+	11.6941i	0.146170	+	0.828973i	0.966420	+	0.256968i	$0.0827234\pi$
$199$	2.06199	+	11.6941i	0.146170	+	0.828973i	−0.820250	+	0.572006i	$0.806166\pi$
$200$	1.43980	+	8.16554i	0.101810	+	0.577391i
$201$	−6.14575	+	10.6448i	−0.433488	+	0.750823i
$202$	4.17712	+	7.23499i	0.293901	+	0.509052i
$203$	4.59627	−	3.85673i	0.322595	−	0.270689i
$204$		0			0
$205$	−35.2575	−	12.8327i	−2.46249	−	0.896274i
$206$	−2.07483	−	1.74099i	−0.144560	−	0.121300i
$207$	2.53231	−	14.3615i	0.176008	−	0.998190i
$208$	2.00000			0.138675
$209$		0			0
$210$	15.8745			1.09545
$211$	−0.470326	+	2.66735i	−0.0323786	+	0.183628i	−0.996708	−	0.0810779i	$-0.974164\pi$
$211$	−0.470326	+	2.66735i	−0.0323786	+	0.183628i	0.964329	+	0.264706i	$0.0852748\pi$
$212$	6.57496	+	5.51705i	0.451570	+	0.378913i
$213$	−33.0452	−	12.0275i	−2.26422	−	0.824110i
$214$	−4.42454	+	1.61040i	−0.302455	+	0.110085i
$215$	1.97870	−	1.66032i	0.134946	−	0.113233i
$216$	1.32288	+	2.29129i	0.0900103	+	0.155902i
$217$	−0.291503	+	0.504897i	−0.0197885	+	0.0342747i
$218$	−1.14313	−	6.48299i	−0.0774223	−	0.439084i
$219$	−5.64708	−	32.0262i	−0.381595	−	2.16413i
$220$	−1.17712	+	2.03884i	−0.0793617	+	0.137459i
$221$		0			0
$222$	−11.4426	+	9.60148i	−0.767977	+	0.644409i
$223$	−27.0742	+	9.85420i	−1.81302	+	0.659886i	−0.816426	+	0.577450i	$0.804048\pi$
$223$	−27.0742	+	9.85420i	−1.81302	+	0.659886i	−0.996596	+	0.0824365i	$0.973730\pi$
$224$	1.54650	+	0.562880i	0.103330	+	0.0376090i
$225$	25.4066	+	21.3187i	1.69378	+	1.42125i
$226$	0.969479	−	5.49819i	0.0644888	−	0.365734i
$227$	−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	$0.270209\pi$
$230$	2.30805	−	13.0896i	0.152188	−	0.863101i
$231$	2.15393	+	1.80737i	0.141718	+	0.118916i
$232$	3.42589	+	1.24692i	0.224920	+	0.0818643i
$233$	12.0981	−	4.40334i	0.792572	−	0.288472i	0.0861670	−	0.996281i	$-0.472538\pi$
$233$	12.0981	−	4.40334i	0.792572	−	0.288472i	0.706405	+	0.707808i	$0.250316\pi$
$234$	6.12836	−	5.14230i	0.400623	−	0.336163i
$235$	−17.5830	−	30.4547i	−1.14699	−	1.98664i
$236$	−3.96863	+	6.87386i	−0.258336	+	0.447450i
$237$	1.83772	+	10.4222i	0.119373	+	0.676996i
$238$		0			0
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$	4.82288	+	8.35347i	0.311315	+	0.539214i
$241$	10.4052	−	8.73099i	0.670257	−	0.562412i	−0.242885	−	0.970055i	$-0.578094\pi$
$241$	10.4052	−	8.73099i	0.670257	−	0.562412i	0.913141	+	0.407643i	$0.133649\pi$
$242$	9.94477	−	3.61960i	0.639274	−	0.232677i
$243$	−19.8895	−	7.23920i	−1.27591	−	0.464395i
$244$	−11.4426	−	9.60148i	−0.732537	−	0.614672i
$245$	−2.71686	+	15.4081i	−0.173574	+	0.984385i
$246$	−27.2288			−1.73604
$247$		0			0
$248$	−0.354249			−0.0224948
$249$	3.64661	−	20.6810i	0.231095	−	1.31060i
$250$	9.19253	+	7.71345i	0.581387	+	0.487841i
$251$	−2.60412	−	0.947821i	−0.164370	−	0.0598259i	0.258524	−	0.966005i	$-0.416764\pi$
$251$	−2.60412	−	0.947821i	−0.164370	−	0.0598259i	−0.422895	+	0.906179i	$0.638986\pi$
$252$	6.18600	−	2.25152i	0.389681	−	0.141832i
$253$	1.80346	−	1.51328i	0.113383	−	0.0951392i
$254$	1.35425	+	2.34563i	0.0849731	+	0.147178i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	0.296677	+	1.68254i	0.0185062	+	0.104954i	0.992662	−	0.120924i	$-0.0385859\pi$
$257$	0.296677	+	1.68254i	0.0185062	+	0.104954i	−0.974155	+	0.225878i	$0.927475\pi$
$258$	0.937254	−	1.62337i	0.0583509	−	0.101067i
$259$	4.64575	+	8.04668i	0.288673	+	0.499996i
$260$	5.58562	−	4.68689i	0.346405	−	0.290668i
$261$	13.7035	−	4.98768i	0.848228	−	0.308730i
$262$	13.0967	+	4.76682i	0.809119	+	0.294495i
$263$	3.78216	+	3.17361i	0.233218	+	0.195693i	0.751906	−	0.659271i	$-0.229135\pi$
$263$	3.78216	+	3.17361i	0.233218	+	0.195693i	−0.518688	+	0.854964i	$0.673579\pi$
$264$	−0.296677	+	1.68254i	−0.0182592	+	0.103553i
$265$	31.2915			1.92222
$266$		0			0
$267$		0			0
$268$	−0.806726	+	4.57517i	−0.0492786	+	0.279473i
$269$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$269$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$270$	9.06404	+	3.29904i	0.551620	+	0.200773i
$271$	−16.5816	+	6.03520i	−1.00726	+	0.366612i	−0.792380	−	0.610028i	$-0.791158\pi$
$271$	−16.5816	+	6.03520i	−1.00726	+	0.366612i	−0.214880	+	0.976641i	$0.568936\pi$
$272$		0			0
$273$	−4.35425	−	7.54178i	−0.263531	−	0.456449i
$274$	2.79150	−	4.83502i	0.168641	−	0.292095i
$275$	0.929756	+	5.27291i	0.0560664	+	0.317968i
$276$	−1.67497	−	9.49921i	−0.100821	−	0.571785i
$277$	−4.76013	+	8.24479i	−0.286008	+	0.495381i	−0.972853	−	0.231423i	$-0.925662\pi$
$277$	−4.76013	+	8.24479i	−0.286008	+	0.495381i	0.686845	+	0.726804i	$0.258995\pi$
$278$	−6.67712	−	11.5651i	−0.400467	−	0.693630i
$279$	−1.08548	+	0.910827i	−0.0649860	+	0.0545298i
$280$	5.63816	−	2.05212i	0.336944	−	0.122638i
$281$	25.8016	+	9.39102i	1.53920	+	0.560221i	0.965852	−	0.259094i	$-0.0834238\pi$
$281$	25.8016	+	9.39102i	1.53920	+	0.560221i	0.573344	+	0.819315i	$0.305646\pi$
$282$	−19.5497	−	16.4041i	−1.16416	−	0.976850i
$283$	4.40272	−	24.9691i	0.261714	−	1.48426i	−0.516516	−	0.856278i	$-0.672771\pi$
$283$	4.40272	−	24.9691i	0.261714	−	1.48426i	0.778230	−	0.627979i	$-0.216118\pi$
$284$	−13.2915			−0.788706
$285$		0			0
$286$	1.29150			0.0763682
$287$	−2.94112	+	16.6799i	−0.173609	+	0.984586i
$288$	3.06418	+	2.57115i	0.180558	+	0.151506i
$289$	15.9748	+	5.81434i	0.939693	+	0.342020i
$290$	12.4899	−	4.54596i	0.733434	−	0.266948i
$291$	28.9655	−	24.3049i	1.69799	−	1.42478i
$292$	−6.14575	−	10.6448i	−0.359653	−	0.622937i
$293$	−6.53137	+	11.3127i	−0.381567	+	0.660893i	−0.991286	−	0.131724i	$-0.957949\pi$
$293$	−6.53137	+	11.3127i	−0.381567	+	0.660893i	0.609720	+	0.792617i	$0.291282\pi$
$294$	1.97164	+	11.1818i	0.114989	+	0.652133i
$295$	5.02490	+	28.4976i	0.292561	+	1.65920i
$296$	−2.82288	+	4.88936i	−0.164076	+	0.284189i
$297$	0.854249	+	1.47960i	0.0495685	+	0.0858552i
$298$	−3.78216	+	3.17361i	−0.219094	+	0.183842i
$299$	−6.85177	+	2.49384i	−0.396248	+	0.144223i
$300$	20.6143	+	7.50298i	1.19017	+	0.433185i
$301$	−0.893216	−	0.749497i	−0.0514841	−	0.0432003i
$302$	−0.510049	+	2.89263i	−0.0293500	+	0.166452i
$303$	22.1033			1.26980
$304$		0			0
$305$	−54.4575			−3.11823
$306$		0			0
$307$	−3.55885	−	2.98623i	−0.203114	−	0.170433i	0.535557	−	0.844499i	$-0.320102\pi$
$307$	−3.55885	−	2.98623i	−0.203114	−	0.170433i	−0.738671	+	0.674066i	$0.764546\pi$
$308$	0.998655	+	0.363481i	0.0569036	+	0.0207112i
$309$	−6.73385	+	2.45092i	−0.383075	+	0.139428i
$310$	−0.989348	+	0.830162i	−0.0561912	+	0.0471500i
$311$	−4.17712	−	7.23499i	−0.236863	−	0.410259i	0.722949	−	0.690901i	$-0.242786\pi$
$311$	−4.17712	−	7.23499i	−0.236863	−	0.410259i	−0.959812	+	0.280642i	$0.909453\pi$
$312$	2.64575	−	4.58258i	0.149786	−	0.259437i
$313$	−3.97212	−	22.5270i	−0.224517	−	1.27330i	−0.863606	−	0.504168i	$-0.831799\pi$
$313$	−3.97212	−	22.5270i	−0.224517	−	1.27330i	0.639088	−	0.769133i	$-0.279312\pi$
$314$	1.83772	+	10.4222i	0.103709	+	0.588160i
$315$	12.0000	−	20.7846i	0.676123	−	1.17108i
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	−4.59627	+	3.85673i	−0.258152	+	0.216615i	−0.762673	−	0.646784i	$-0.776114\pi$
$317$	−4.59627	+	3.85673i	−0.258152	+	0.216615i	0.504521	+	0.863399i	$0.331669\pi$
$318$	21.3390	−	7.76676i	1.19663	−	0.435538i
$319$	2.21227	+	0.805200i	0.123863	+	0.0450826i
$320$	2.79281	+	2.34344i	0.156123	+	0.131002i
$321$	−2.16322	+	12.2683i	−0.120739	+	0.684747i
$322$	−6.00000			−0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$	2.87961	−	16.3311i	0.159732	−	0.905885i
$326$	−9.14447	−	7.67312i	−0.506465	−	0.424975i
$327$	−16.3666	−	5.95696i	−0.905076	−	0.329421i
$328$	−9.67085	+	3.51990i	−0.533983	+	0.194354i
$329$	−12.1606	+	10.2039i	−0.670434	+	0.562561i
$330$	3.11438	+	5.39426i	0.171441	+	0.296944i
$331$	13.9059	−	24.0857i	0.764336	−	1.32387i	−0.176260	−	0.984344i	$-0.556400\pi$
$331$	13.9059	−	24.0857i	0.764336	−	1.32387i	0.940597	−	0.339526i	$-0.110267\pi$
$332$	−1.37829	−	7.81667i	−0.0756435	−	0.428995i
$333$	3.92150	+	22.2399i	0.214897	+	1.21874i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	8.46863	+	14.6681i	0.462691	+	0.801403i
$336$	3.33555	−	2.79886i	0.181969	−	0.152690i
$337$	19.0678	−	6.94010i	1.03869	−	0.378051i	0.234305	−	0.972163i	$-0.424718\pi$
$337$	19.0678	−	6.94010i	1.03869	−	0.378051i	0.804383	+	0.594112i	$0.202496\pi$
$338$	8.45723	+	3.07818i	0.460013	+	0.167431i
$339$	−11.3154	−	9.49477i	−0.614570	−	0.515685i
$340$		0			0
$341$	−0.228757			−0.0123879
$342$		0			0
$343$	18.5830			1.00339
$344$	0.123029	−	0.697734i	0.00663329	−	0.0376193i
$345$	−26.9387	−	22.6043i	−1.45033	−	1.21697i
$346$	5.63816	+	2.05212i	0.303109	+	0.110323i
$347$	−3.03404	+	1.10430i	−0.162876	+	0.0592819i	−0.422171	−	0.906516i	$-0.638732\pi$
$347$	−3.03404	+	1.10430i	−0.162876	+	0.0592819i	0.259295	+	0.965798i	$0.416510\pi$
$348$	7.38907	−	6.20017i	0.396096	−	0.332364i
$349$	10.5830	+	18.3303i	0.566495	+	0.981199i	0.996909	+	0.0785668i	$0.0250344\pi$
$349$	10.5830	+	18.3303i	0.566495	+	0.981199i	−0.430414	+	0.902632i	$0.641632\pi$
$350$	6.82288	−	11.8176i	0.364698	−	0.631676i
$351$	−0.918860	−	5.21111i	−0.0490451	−	0.278149i
$352$	0.112134	+	0.635941i	0.00597674	+	0.0338958i
$353$	9.43725	−	16.3458i	0.502294	−	0.869999i	−0.497702	−	0.867348i	$-0.665823\pi$
$353$	9.43725	−	16.3458i	0.502294	−	0.869999i	0.999996	−	0.00265131i	$-0.000843939\pi$
$354$	10.5000	+	18.1865i	0.558069	+	0.966603i
$355$	−37.1206	+	31.1479i	−1.97016	+	1.65316i
$356$		0			0
$357$		0			0
$358$	15.2728	+	12.8154i	0.807194	+	0.677316i
$359$	1.89923	−	10.7711i	0.100238	−	0.568477i	−0.892778	−	0.450496i	$-0.851247\pi$
$359$	1.89923	−	10.7711i	0.100238	−	0.568477i	0.993016	−	0.117980i	$-0.0376419\pi$
$360$	14.5830			0.768592
$361$		0			0
$362$	−4.22876			−0.222259
$363$	4.86215	−	27.5746i	0.255197	−	1.44729i
$364$	−2.52144	−	2.11574i	−0.132159	−	0.110895i
$365$	−42.1093	−	15.3265i	−2.20410	−	0.802227i
$366$	−37.1369	+	13.5167i	−1.94118	+	0.706531i
$367$	−7.83568	+	6.57492i	−0.409019	+	0.343208i	−0.823967	−	0.566637i	$-0.808244\pi$
$367$	−7.83568	+	6.57492i	−0.409019	+	0.343208i	0.414948	+	0.909845i	$0.363800\pi$
$368$	−1.82288	−	3.15731i	−0.0950240	−	0.164586i
$369$	−20.5830	+	35.6508i	−1.07151	+	1.85591i
$370$	3.57420	+	20.2703i	0.185814	+	1.05380i
$371$	−2.45287	−	13.9109i	−0.127346	−	0.722218i
$372$	−0.468627	+	0.811686i	−0.0242972	+	0.0420839i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	29.8343	−	10.8588i	1.54064	−	0.560746i
$376$	−9.06404	−	3.29904i	−0.467442	−	0.170135i
$377$	−5.58562	−	4.68689i	−0.287674	−	0.241387i
$378$	0.756107	−	4.28810i	0.0388900	−	0.220556i
$379$	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
$382$	−2.53231	+	14.3615i	−0.129564	+	0.734796i
$383$	−24.1459	−	20.2608i	−1.23380	−	1.03528i	−0.997983	−	0.0634824i	$-0.979779\pi$
$383$	−24.1459	−	20.2608i	−1.23380	−	1.03528i	−0.235816	−	0.971798i	$-0.575776\pi$
$384$	2.48619	+	0.904900i	0.126873	+	0.0461780i
$385$	3.64085	−	1.32516i	0.185555	−	0.0675364i
$386$	−5.04287	+	4.23147i	−0.256676	+	0.215376i
$387$	−1.41699	−	2.45431i	−0.0720299	−	0.124759i
$388$	7.14575	−	12.3768i	0.362771	−	0.628337i
$389$	2.08378	+	11.8177i	0.105652	+	0.599181i	0.990958	+	0.134172i	$0.0428376\pi$
$389$	2.08378	+	11.8177i	0.105652	+	0.599181i	−0.885306	+	0.465008i	$0.846051\pi$
$390$	−3.34993	−	18.9984i	−0.169631	−	0.962022i
$391$		0			0
$392$	2.14575	+	3.71655i	0.108377	+	0.187714i
$393$	28.2475	−	23.7025i	1.42490	−	1.19563i
$394$	2.21227	−	0.805200i	0.111453	−	0.0405654i
$395$	13.7035	+	4.98768i	0.689500	+	0.250957i
$396$	1.97870	+	1.66032i	0.0994333	+	0.0834344i
$397$	6.41409	−	36.3761i	0.321914	−	1.82566i	−0.208616	−	0.977998i	$-0.566896\pi$
$397$	6.41409	−	36.3761i	0.321914	−	1.82566i	0.530530	−	0.847666i	$-0.321993\pi$
$398$	11.8745			0.595215
$399$		0			0
$400$	8.29150			0.414575
$401$	1.11430	−	6.31951i	0.0556455	−	0.315581i	−0.944262	−	0.329195i	$-0.893223\pi$
$401$	1.11430	−	6.31951i	0.0556455	−	0.315581i	0.999907	+	0.0136142i	$0.00433367\pi$
$402$	9.41584	+	7.90083i	0.469619	+	0.394057i
$403$	0.665770	+	0.242320i	0.0331644	+	0.0120708i
$404$	7.85043	−	2.85732i	0.390573	−	0.142157i
$405$	−13.9640	+	11.7172i	−0.693879	+	0.582233i
$406$	−3.00000	−	5.19615i	−0.148888	−	0.257881i
$407$	−1.82288	+	3.15731i	−0.0903566	+	0.156502i
$408$		0			0
$409$	2.35866	+	13.3766i	0.116628	+	0.661433i	0.985931	+	0.167152i	$0.0534572\pi$
$409$	2.35866	+	13.3766i	0.116628	+	0.661433i	−0.869303	+	0.494280i	$0.835432\pi$
$410$	−18.7601	+	32.4935i	−0.926497	+	1.60474i
$411$	−7.38562	−	12.7923i	−0.364306	−	0.630996i
$412$	−2.07483	+	1.74099i	−0.102220	+	0.0857723i
$413$	12.2750	−	4.46772i	0.604012	−	0.219842i
$414$	−13.7035	−	4.98768i	−0.673492	−	0.245131i
$415$	−22.1672	−	18.6005i	−1.08815	−	0.913063i
$416$	0.347296	−	1.96962i	0.0170276	−	0.0965683i
$417$	−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	$0.217488\pi$
$420$	2.75658	−	15.6333i	0.134507	−	0.762829i
$421$	17.4748	+	14.6631i	0.851671	+	0.714637i	0.960157	−	0.279461i	$-0.0901559\pi$
$421$	17.4748	+	14.6631i	0.851671	+	0.714637i	−0.108486	+	0.994098i	$0.534600\pi$
$422$	2.54515	+	0.926361i	0.123896	+	0.0450945i
$423$	−36.2562	+	13.1962i	−1.76284	+	0.641619i
$424$	6.57496	−	5.51705i	0.319308	−	0.267932i
$425$		0			0
$426$	−17.5830	+	30.4547i	−0.851899	+	1.47553i
$427$	4.26879	+	24.2095i	0.206581	+	1.17158i
$428$	0.817622	+	4.63696i	0.0395213	+	0.224136i
$429$	1.70850	−	2.95920i	0.0824870	−	0.142872i
$430$	−1.29150	−	2.23695i	−0.0622818	−	0.107875i
$431$	−2.96805	+	2.49049i	−0.142966	+	0.119962i	−0.711466	−	0.702721i	$-0.751968\pi$
$431$	−2.96805	+	2.49049i	−0.142966	+	0.119962i	0.568500	+	0.822683i	$0.307524\pi$
$432$	2.48619	−	0.904900i	0.119617	−	0.0435370i
$433$	13.0378	+	4.74536i	0.626555	+	0.228048i	0.635731	−	0.771910i	$-0.280699\pi$
$433$	13.0378	+	4.74536i	0.626555	+	0.228048i	−0.00917597	+	0.999958i	$0.502921\pi$
$434$	0.446608	+	0.374749i	0.0214379	+	0.0179885i
$435$	6.10651	−	34.6318i	0.292785	−	1.66047i
$436$	−6.58301			−0.315269
$437$		0			0
$438$	−32.5203			−1.55388
$439$	−6.39230	+	36.2525i	−0.305088	+	1.73024i	0.318004	+	0.948089i	$0.396987\pi$
$439$	−6.39230	+	36.2525i	−0.305088	+	1.73024i	−0.623092	+	0.782149i	$0.714124\pi$
$440$	1.80346	+	1.51328i	0.0859765	+	0.0721429i
$441$	16.1308	+	5.87112i	0.768132	+	0.279577i
$442$		0			0
$443$	4.10159	−	3.44164i	0.194873	−	0.163517i	−0.540131	−	0.841581i	$-0.681625\pi$
$443$	4.10159	−	3.44164i	0.194873	−	0.163517i	0.735003	+	0.678064i	$0.237181\pi$
$444$	7.46863	+	12.9360i	0.354445	+	0.613917i
$445$		0			0
$446$	5.00311	+	28.3740i	0.236904	+	1.34355i
$447$	2.26832	+	12.8643i	0.107288	+	0.608460i
$448$	0.822876	−	1.42526i	0.0388772	−	0.0673373i
$449$	6.85425	+	11.8719i	0.323472	+	0.560270i	0.981202	−	0.192984i	$-0.0618165\pi$
$449$	6.85425	+	11.8719i	0.323472	+	0.560270i	−0.657730	+	0.753254i	$0.728483\pi$
$450$	25.4066	−	21.3187i	1.19768	−	1.00497i
$451$	−6.24496	+	2.27298i	−0.294064	+	0.107030i
$452$	−5.24631	−	1.90950i	−0.246766	−	0.0898153i
$453$	5.95312	+	4.99526i	0.279702	+	0.234698i
$454$	−2.19591	+	12.4536i	−0.103059	+	0.584478i
$455$	−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	$0.491620\pi$
$458$	3.47296	−	19.6962i	0.162281	−	0.920341i
$459$		0			0
$460$	−12.4899	−	4.54596i	−0.582346	−	0.211957i
$461$	21.7689	−	7.92324i	1.01388	−	0.369022i	0.218958	−	0.975734i	$-0.429734\pi$
$461$	21.7689	−	7.92324i	1.01388	−	0.369022i	0.794922	+	0.606712i	$0.207512\pi$
$462$	2.15393	−	1.80737i	0.100210	−	0.0840863i
$463$	−7.22876	−	12.5206i	−0.335949	−	0.581880i	0.647718	−	0.761880i	$-0.275724\pi$
$463$	−7.22876	−	12.5206i	−0.335949	−	0.581880i	−0.983667	+	0.180000i	$0.942390\pi$
$464$	1.82288	−	3.15731i	0.0846249	−	0.146575i
$465$	0.593355	+	3.36508i	0.0275162	+	0.156052i
$466$	−2.23563	−	12.6789i	−0.103564	−	0.587339i
$467$	12.3229	−	21.3438i	0.570235	−	0.987675i	−0.426307	−	0.904579i	$-0.640186\pi$
$467$	12.3229	−	21.3438i	0.570235	−	0.987675i	0.996541	−	0.0830968i	$-0.0264811\pi$
$468$	−4.00000	−	6.92820i	−0.184900	−	0.320256i
$469$	5.85699	−	4.91459i	0.270450	−	0.226935i
$470$	−33.0452	+	12.0275i	−1.52426	+	0.554786i
$471$	26.3114	+	9.57656i	1.21237	+	0.441265i
$472$	6.08029	+	5.10197i	0.279868	+	0.234837i
$473$	0.0794463	−	0.450562i	0.00365295	−	0.0207169i
$474$	10.5830			0.486094
$475$		0			0
$476$		0			0
$477$	5.96169	−	33.8104i	0.272967	−	1.54807i
$478$	−9.19253	−	7.71345i	−0.420457	−	0.352805i
$479$	13.7035	+	4.98768i	0.626131	+	0.227893i	0.635546	−	0.772063i	$-0.280775\pi$
$479$	13.7035	+	4.98768i	0.626131	+	0.227893i	−0.00941555	+	0.999956i	$0.502997\pi$
$480$	9.06404	−	3.29904i	0.413715	−	0.150580i
$481$	8.64979	−	7.25804i	0.394397	−	0.330938i
$482$	−6.79150	−	11.7632i	−0.309344	−	0.535800i
$483$	−7.93725	+	13.7477i	−0.361158	+	0.625543i
$484$	−1.83772	−	10.4222i	−0.0835327	−	0.473738i
$485$	−9.04764	−	51.3117i	−0.410832	−	2.32994i
$486$	−10.5830	+	18.3303i	−0.480055	+	0.831479i
$487$	11.1144	+	19.2507i	0.503641	+	0.872331i	0.999991	+	0.00420886i	$0.00133973\pi$
$487$	11.1144	+	19.2507i	0.503641	+	0.872331i	−0.496351	+	0.868122i	$0.665327\pi$
$488$	−11.4426	+	9.60148i	−0.517982	+	0.434639i
$489$	−29.6783	+	10.8020i	−1.34210	+	0.488484i
$490$	14.7022	+	5.35116i	0.664178	+	0.241741i
$491$	21.9920	+	18.4535i	0.992484	+	0.832793i	0.985926	−	0.167185i	$-0.0534678\pi$
$491$	21.9920	+	18.4535i	0.992484	+	0.832793i	0.00655888	+	0.999978i	$0.497912\pi$
$492$	−4.72822	+	26.8151i	−0.213165	+	1.20892i
$493$		0			0
$494$		0			0
$495$	9.41699			0.423262
$496$	−0.0615146	+	0.348867i	−0.00276209	+	0.0156646i
$497$	16.7568	+	14.0607i	0.751647	+	0.630707i
$498$	−19.7335	−	7.18242i	−0.884281	−	0.321852i
$499$	29.3454	−	10.6809i	1.31368	−	0.478141i	0.412253	−	0.911069i	$-0.364742\pi$
$499$	29.3454	−	10.6809i	1.31368	−	0.478141i	0.901428	+	0.432928i	$0.142520\pi$
$500$	9.19253	−	7.71345i	0.411103	−	0.344956i
$501$	−15.8745	−	27.4955i	−0.709221	−	1.22841i
$502$	−1.38562	+	2.39997i	−0.0618433	+	0.107116i
$503$	−4.35210	−	24.6820i	−0.194051	−	1.10052i	−0.913764	−	0.406245i	$-0.866838\pi$
$503$	−4.35210	−	24.6820i	−0.194051	−	1.10052i	0.719714	−	0.694271i	$-0.244273\pi$
$504$	−1.14313	−	6.48299i	−0.0509189	−	0.288776i
$505$	15.2288	−	26.3770i	0.677671	−	1.17376i
$506$	−1.17712	−	2.03884i	−0.0523296	−	0.0906375i
$507$	18.2409	−	15.3059i	0.810105	−	0.679759i
$508$	2.54515	−	0.926361i	0.112923	−	0.0411006i
$509$	−29.8343	−	10.8588i	−1.32238	−	0.481308i	−0.418162	−	0.908373i	$-0.637325\pi$
$509$	−29.8343	−	10.8588i	−1.32238	−	0.481308i	−0.904221	+	0.427065i	$0.859548\pi$
$510$		0			0
$511$	−3.51269	+	19.9214i	−0.155392	+	0.881272i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.70850			0.0753586
$515$	−1.71469	+	9.72449i	−0.0755583	+	0.428512i
$516$	−1.43596	−	1.20491i	−0.0632145	−	0.0530432i
$517$	−5.85312	−	2.13036i	−0.257420	−	0.0936931i
$518$	8.73116	−	3.17788i	0.383625	−	0.139628i
$519$	12.1606	−	10.2039i	0.533790	−	0.447903i
$520$	−3.64575	−	6.31463i	−0.159877	−	0.276915i
$521$	11.1458	−	19.3050i	0.488304	−	0.845768i	−0.511605	−	0.859221i	$-0.670949\pi$
$521$	11.1458	−	19.3050i	0.488304	−	0.845768i	0.999910	+	0.0134529i	$0.00428231\pi$
$522$	−2.53231	−	14.3615i	−0.110836	−	0.628584i
$523$	5.18765	+	29.4206i	0.226840	+	1.28648i	0.859136	+	0.511748i	$0.171002\pi$
$523$	5.18765	+	29.4206i	0.226840	+	1.28648i	−0.632295	+	0.774727i	$0.717887\pi$
$524$	6.96863	−	12.0700i	0.304426	−	0.527281i
$525$	−18.0516	−	31.2663i	−0.787838	−	1.36458i
$526$	3.78216	−	3.17361i	0.164910	−	0.138376i
$527$		0			0
$528$	1.60546	+	0.584341i	0.0698688	+	0.0254302i
$529$	−7.43714	−	6.24050i	−0.323354	−	0.271326i
$530$	5.43371	−	30.8161i	0.236025	−	1.33857i
$531$	31.7490			1.37779
$532$		0			0
$533$	20.5830			0.891549
$534$		0			0
$535$	13.1499	+	11.0341i	0.568521	+	0.477046i
$536$	4.36558	+	1.58894i	0.188564	+	0.0686318i
$537$	49.5679	−	18.0412i	2.13901	−	0.778536i
$538$		0			0
$539$	1.38562	+	2.39997i	0.0596830	+	0.103374i
$540$	4.82288	−	8.35347i	0.207544	−	0.359476i
$541$	1.38919	+	7.87846i	0.0597257	+	0.338722i	0.999999	−	0.00170033i	$-0.000541231\pi$
$541$	1.38919	+	7.87846i	0.0597257	+	0.338722i	−0.940273	+	0.340422i	$0.889430\pi$
$542$	3.06415	+	17.3777i	0.131617	+	0.746435i
$543$	−5.59412	+	9.68930i	−0.240067	+	0.415808i
$544$		0			0
$545$	−18.3851	+	15.4269i	−0.787530	+	0.660816i
$546$	−8.18331	+	2.97848i	−0.350213	+	0.127467i
$547$	−0.665770	−	0.242320i	−0.0284663	−	0.0103609i	0.327748	−	0.944765i	$-0.393710\pi$
$547$	−0.665770	−	0.242320i	−0.0284663	−	0.0103609i	−0.356214	+	0.934404i	$0.615933\pi$
$548$	−4.27683	−	3.58869i	−0.182697	−	0.153301i
$549$	−10.3753	+	58.8413i	−0.442807	+	2.51129i
$550$	5.35425			0.228306
$551$		0			0
$552$	−9.64575			−0.410550
$553$	1.14313	−	6.48299i	0.0486107	−	0.275685i
$554$	7.29294	+	6.11950i	0.309847	+	0.259993i
$555$	51.1733	+	18.6256i	2.17219	+	0.790611i
$556$	−12.5489	+	4.56742i	−0.532191	+	0.193702i
$557$	−20.3638	+	17.0872i	−0.862840	+	0.724009i	−0.962578	−	0.271005i	$-0.912644\pi$
$557$	−20.3638	+	17.0872i	−0.862840	+	0.724009i	0.0997377	+	0.995014i	$0.468200\pi$
$558$	0.708497	+	1.22715i	0.0299931	+	0.0519495i
$559$	−0.708497	+	1.22715i	−0.0299662	+	0.0519031i
$560$	−1.04189	−	5.90885i	−0.0440278	−	0.249694i
$561$		0			0
$562$	13.7288	−	23.7789i	0.579113	−	1.00305i
$563$	−12.9686	−	22.4623i	−0.546562	−	0.946674i	−0.998507	−	0.0546278i	$-0.982603\pi$
$563$	−12.9686	−	22.4623i	−0.546562	−	0.946674i	0.451944	−	0.892046i	$-0.350731\pi$
$564$	−19.5497	+	16.4041i	−0.823189	+	0.690737i
$565$	−19.1267	+	6.96156i	−0.804668	+	0.292875i
$566$	−23.8252	−	8.67166i	−1.00145	−	0.364497i
$567$	6.30359	+	5.28934i	0.264726	+	0.222132i
$568$	−2.30805	+	13.0896i	−0.0968434	+	0.549226i
$569$	−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	$0.813399\pi$
$572$	0.224267	−	1.27188i	0.00937708	−	0.0531800i
$573$	29.5563	+	24.8007i	1.23473	+	1.03606i
$574$	15.9158	+	5.79288i	0.664313	+	0.241790i
$575$	−28.4057	+	10.3388i	−1.18460	+	0.431160i
$576$	3.06418	−	2.57115i	0.127674	−	0.107131i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	3.02443	+	17.1524i	0.125691	+	0.712829i
$580$	−2.30805	−	13.0896i	−0.0958364	−	0.543515i
$581$	−6.53137	+	11.3127i	−0.270967	+	0.469329i
$582$	−18.9059	−	32.7459i	−0.783674	−	1.35736i
$583$	4.24579	−	3.56264i	0.175843	−	0.147550i
$584$	−11.5502	+	4.20394i	−0.477952	+	0.173960i
$585$	−27.4071	−	9.97536i	−1.13314	−	0.412431i
$586$	10.0066	+	8.39657i	0.413371	+	0.346859i
$587$	−7.96602	+	45.1776i	−0.328793	+	1.86468i	0.152763	+	0.988263i	$0.451183\pi$
$587$	−7.96602	+	45.1776i	−0.328793	+	1.86468i	−0.481556	+	0.876415i	$0.659928\pi$
$588$	11.3542			0.468241
$589$		0			0
$590$	28.9373			1.19133
$591$	1.08161	−	6.13413i	0.0444916	−	0.252324i
$592$	4.32490	+	3.62902i	0.177752	+	0.149152i
$593$	−37.8616	−	13.7805i	−1.55479	−	0.565898i	−0.585255	−	0.810849i	$-0.699006\pi$
$593$	−37.8616	−	13.7805i	−1.55479	−	0.565898i	−0.969535	+	0.244951i	$0.921228\pi$
$594$	1.60546	−	0.584341i	0.0658729	−	0.0239758i
$595$		0			0
$596$	2.46863	+	4.27579i	0.101119	+	0.175143i
$597$	15.7085	−	27.2079i	0.642906	−	1.11355i
$598$	1.26616	+	7.18073i	0.0517770	+	0.293642i
$599$	−0.184544	−	1.04660i	−0.00754026	−	0.0427629i	0.980805	−	0.194989i	$-0.0624670\pi$
$599$	−0.184544	−	1.04660i	−0.00754026	−	0.0427629i	−0.988346	+	0.152226i	$0.951356\pi$
$600$	10.9686	−	18.9982i	0.447792	−	0.775599i
$601$	−15.7915	−	27.3517i	−0.644149	−	1.11570i	−0.984497	−	0.175399i	$-0.943878\pi$
$601$	−15.7915	−	27.3517i	−0.644149	−	1.11570i	0.340349	−	0.940299i	$-0.389455\pi$
$602$	−0.893216	+	0.749497i	−0.0364048	+	0.0305472i
$603$	17.4623	−	6.35576i	0.711120	−	0.258827i
$604$	2.76012	+	1.00460i	0.112308	+	0.0408766i
$605$	−29.5563	−	24.8007i	−1.20163	−	1.00829i
$606$	3.83819	−	21.7675i	0.155916	−	0.884243i
$607$	−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
$610$	−9.45645	+	53.6302i	−0.382880	+	2.17142i
$611$	14.7781	+	12.4003i	0.597860	+	0.501664i
$612$		0			0
$613$	−26.8592	+	9.77596i	−1.08483	+	0.394847i	−0.821705	−	0.569913i	$-0.806977\pi$
$613$	−26.8592	+	9.77596i	−1.08483	+	0.394847i	−0.263129	+	0.964761i	$0.584755\pi$
$614$	−3.55885	+	2.98623i	−0.143624	+	0.120514i
$615$	49.6346	+	85.9697i	2.00146	+	3.46663i
$616$	0.531373	−	0.920365i	0.0214096	−	0.0370826i
$617$	0.151857	+	0.861222i	0.00611352	+	0.0346715i	0.987712	−	0.156286i	$-0.0499520\pi$
$617$	0.151857	+	0.861222i	0.00611352	+	0.0346715i	−0.981598	+	0.190957i	$0.938841\pi$
$618$	1.24436	+	7.05714i	0.0500557	+	0.283880i
$619$	−22.2288	+	38.5013i	−0.893449	+	1.54750i	−0.0577369	+	0.998332i	$0.518388\pi$
$619$	−22.2288	+	38.5013i	−0.893449	+	1.54750i	−0.835712	+	0.549168i	$0.814945\pi$
$620$	0.645751	+	1.11847i	0.0259340	+	0.0449190i
$621$	−7.38907	+	6.20017i	−0.296513	+	0.248804i
$622$	−7.85043	+	2.85732i	−0.314773	+	0.114568i
$623$		0			0
$624$	−4.05353	−	3.40131i	−0.162271	−	0.136161i
$625$	0.397915	−	2.25669i	0.0159166	−	0.0902676i
$626$	−22.8745			−0.914249
$627$		0			0
$628$	10.5830			0.422308
$629$		0			0
$630$	−18.3851	−	15.4269i	−0.732479	−	0.614623i
$631$	−21.4360	−	7.80208i	−0.853355	−	0.310596i	−0.121948	−	0.992537i	$-0.538914\pi$
$631$	−21.4360	−	7.80208i	−0.853355	−	0.310596i	−0.731408	+	0.681941i	$0.761136\pi$
$632$	3.75877	−	1.36808i	0.149516	−	0.0544193i
$633$	5.48948	−	4.60622i	0.218187	−	0.183081i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	4.93725	−	8.55157i	0.195929	−	0.339359i
$636$	−3.94329	−	22.3635i	−0.156362	−	0.886771i
$637$	−1.49042	−	8.45261i	−0.0590527	−	0.334905i
$638$	1.17712	−	2.03884i	0.0466028	−	0.0807184i
$639$	26.5830	+	46.0431i	1.05161	+	1.82144i
$640$	2.79281	−	2.34344i	0.110395	−	0.0926327i
$641$	17.7362	−	6.45546i	0.700539	−	0.254975i	0.0328981	−	0.999459i	$-0.489526\pi$
$641$	17.7362	−	6.45546i	0.700539	−	0.254975i	0.667641	+	0.744483i	$0.267304\pi$
$642$	11.7062	+	4.26072i	0.462008	+	0.168157i
$643$	23.3799	+	19.6180i	0.922012	+	0.773660i	0.974366	−	0.224968i	$-0.0722279\pi$
$643$	23.3799	+	19.6180i	0.922012	+	0.773660i	−0.0523538	+	0.998629i	$0.516672\pi$
$644$	−1.04189	+	5.90885i	−0.0410562	+	0.232841i
$645$	−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	$0.295683\pi$
$648$	−0.868241	+	4.92404i	−0.0341077	+	0.193435i
$649$	3.92635	+	3.29460i	0.154123	+	0.129324i
$650$	−15.5829	−	5.67172i	−0.611213	−	0.222463i
$651$	1.44946	−	0.527562i	0.0568090	−	0.0206768i
$652$	−9.14447	+	7.67312i	−0.358125	+	0.300503i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	−8.70850	+	15.0836i	−0.340529	+	0.589814i
$655$	−8.82337	−	50.0398i	−0.344758	−	1.95522i
$656$	1.78710	+	10.1352i	0.0697746	+	0.395711i
$657$	−24.5830	+	42.5790i	−0.959074	+	1.66117i
$658$	7.93725	+	13.7477i	0.309426	+	0.535942i
$659$	1.97870	−	1.66032i	0.0770791	−	0.0646770i	−0.603434	−	0.797413i	$-0.706201\pi$
$659$	1.97870	−	1.66032i	0.0770791	−	0.0646770i	0.680513	+	0.732736i	$0.261757\pi$
$660$	5.85312	−	2.13036i	0.227832	−	0.0829242i
$661$	9.61189	+	3.49844i	0.373859	+	0.136074i	0.522114	−	0.852876i	$-0.325143\pi$
$661$	9.61189	+	3.49844i	0.373859	+	0.136074i	−0.148255	+	0.988949i	$0.547366\pi$
$662$	−21.3050	−	17.8771i	−0.828044	−	0.694812i
$663$		0			0
$664$	−7.93725			−0.308025
$665$		0			0
$666$	22.5830			0.875074
$667$	−2.30805	+	13.0896i	−0.0893679	+	0.506830i
$668$	−9.19253	−	7.71345i	−0.355670	−	0.298442i
$669$	71.6316	+	26.0718i	2.76944	+	1.00799i
$670$	15.9158	−	5.79288i	0.614881	−	0.223799i
$671$	−7.38907	+	6.20017i	−0.285252	+	0.239355i
$672$	−2.17712	−	3.77089i	−0.0839844	−	0.145465i
$673$	−8.93725	+	15.4798i	−0.344506	+	0.596702i	−0.985264	−	0.171041i	$-0.945287\pi$
$673$	−8.93725	+	15.4798i	−0.344506	+	0.596702i	0.640758	+	0.767743i	$0.278620\pi$
$674$	−3.52358	−	19.9832i	−0.135723	−	0.769725i
$675$	−3.80936	−	21.6040i	−0.146622	−	0.831537i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	16.2915	+	28.2177i	0.626133	+	1.08449i	0.988321	+	0.152389i	$0.0486968\pi$
$677$	16.2915	+	28.2177i	0.626133	+	1.08449i	−0.362187	+	0.932105i	$0.617970\pi$
$678$	−11.3154	+	9.49477i	−0.434566	+	0.364645i
$679$	−22.1018	+	8.04440i	−0.848190	+	0.308716i
$680$		0			0
$681$	25.6299	+	21.5061i	0.982142	+	0.824115i
$682$	−0.0397232	+	0.225281i	−0.00152108	+	0.00862646i
$683$	−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
$686$	3.22690	−	18.3007i	0.123204	−	0.698724i
$687$	−40.5353	−	34.0131i	−1.54652	−	1.29768i
$688$	−0.665770	−	0.242320i	−0.0253822	−	0.00923838i
$689$	−16.1308	+	5.87112i	−0.614534	+	0.223672i
$690$	−26.9387	+	22.6043i	−1.02554	+	0.860530i
$691$	9.29150	+	16.0934i	0.353465	+	0.612220i	0.986854	−	0.161614i	$-0.0516699\pi$
$691$	9.29150	+	16.0934i	0.353465	+	0.612220i	−0.633389	+	0.773834i	$0.718337\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$	−0.738176	−	4.18640i	−0.0280410	−	0.159028i
$694$	0.560668	+	3.17970i	0.0212827	+	0.120700i
$695$	−24.3431	+	42.1635i	−0.923388	+	1.59935i
$696$	−4.82288	−	8.35347i	−0.182811	−	0.316637i
$697$		0			0
$698$	19.8895	−	7.23920i	0.752830	−	0.274008i
$699$	−32.0085	−	11.6501i	−1.21067	−	0.440649i
$700$	−10.4533	−	8.77132i	−0.395096	−	0.331525i
$701$	2.71686	−	15.4081i	0.102614	−	0.581954i	−0.889532	−	0.456872i	$-0.848970\pi$
$701$	2.71686	−	15.4081i	0.102614	−	0.581954i	0.992146	−	0.125082i	$-0.0399193\pi$
$702$	−5.29150			−0.199715
$703$		0			0
$704$	0.645751			0.0243377
$705$	−16.1563	+	91.6270i	−0.608482	+	3.45087i
$706$	−14.4587	−	12.1323i	−0.544161	−	0.456605i
$707$	−12.9198	−	4.70244i	−0.485901	−	0.176853i
$708$	19.7335	−	7.18242i	0.741632	−	0.269932i
$709$	−1.26072	+	1.05787i	−0.0473473	+	0.0397291i	−0.666154	−	0.745814i	$-0.732061\pi$
$709$	−1.26072	+	1.05787i	−0.0473473	+	0.0397291i	0.618807	+	0.785543i	$0.287616\pi$
$710$	24.2288	+	41.9654i	0.909289	+	1.57493i
$711$	8.00000	−	13.8564i	0.300023	−	0.519656i
$712$		0			0
$713$	−0.224267	−	1.27188i	−0.00839887	−	0.0476323i
$714$		0			0
$715$	−2.35425	−	4.07768i	−0.0880439	−	0.152497i
$716$	15.2728	−	12.8154i	0.570772	−	0.478935i
$717$	−29.8343	+	10.8588i	−1.11418	+	0.405529i
$718$	−10.2777	−	3.74076i	−0.383559	−	0.139604i
$719$	10.1819	+	8.54361i	0.379720	+	0.318623i	0.812593	−	0.582832i	$-0.198056\pi$
$719$	10.1819	+	8.54361i	0.379720	+	0.318623i	−0.432872	+	0.901455i	$0.642500\pi$
$720$	2.53231	−	14.3615i	0.0943737	−	0.535220i
$721$	4.45751			0.166006
$722$		0			0
$723$	−35.9373			−1.33652
$724$	−0.734316	+	4.16451i	−0.0272906	+	0.154773i
$725$	−23.1566	−	19.4307i	−0.860013	−	0.721637i
$726$	−26.3114	−	9.57656i	−0.976507	−	0.355420i
$727$	−21.2211	+	7.72384i	−0.787046	+	0.286461i	−0.704108	−	0.710093i	$-0.748653\pi$
$727$	−21.2211	+	7.72384i	−0.787046	+	0.286461i	−0.0829387	+	0.996555i	$0.526431\pi$
$728$	−2.52144	+	2.11574i	−0.0934507	+	0.0784144i
$729$	20.5000	+	35.5070i	0.759259	+	1.31508i
$730$	−22.4059	+	38.8081i	−0.829279	+	1.43635i
$731$		0			0
$732$	6.86262	+	38.9199i	0.253650	+	1.43852i
$733$	−21.0516	+	36.4625i	−0.777560	+	1.34677i	0.155785	+	0.987791i	$0.450209\pi$
$733$	−21.0516	+	36.4625i	−0.777560	+	1.34677i	−0.933344	+	0.358982i	$0.883124\pi$
$734$	5.11438	+	8.85836i	0.188775	+	0.326968i
$735$	31.7102	−	26.6080i	1.16965	−	0.981452i
$736$	−3.42589	+	1.24692i	−0.126280	+	0.0459621i
$737$	2.81908	+	1.02606i	0.103842	+	0.0377954i
$738$	31.5350	+	26.4610i	1.16082	+	0.974043i
$739$	2.39839	−	13.6019i	0.0882261	−	0.500355i	−0.908388	−	0.418129i	$-0.862686\pi$
$739$	2.39839	−	13.6019i	0.0882261	−	0.500355i	0.996614	−	0.0822260i	$-0.0262029\pi$
$740$	20.5830			0.756646
$741$		0			0
$742$	−14.1255			−0.518563
$743$	−1.81979	+	10.3205i	−0.0667615	+	0.378624i	0.933060	+	0.359721i	$0.117128\pi$
$743$	−1.81979	+	10.3205i	−0.0667615	+	0.378624i	−0.999821	+	0.0189022i	$0.993983\pi$
$744$	0.717978	+	0.602455i	0.0263224	+	0.0220871i
$745$	16.9145	+	6.15636i	0.619698	+	0.225552i
$746$	3.75877	−	1.36808i	0.137618	−	0.0500890i
$747$	−24.3212	+	20.4079i	−0.889865	+	0.746685i
$748$		0			0
$749$	3.87451	−	6.71084i	0.141571	−	0.245209i
$750$	−5.51316	−	31.2667i	−0.201312	−	1.14170i
$751$	4.14576	+	23.5118i	0.151281	+	0.857958i	0.962107	+	0.272671i	$0.0879070\pi$
$751$	4.14576	+	23.5118i	0.151281	+	0.857958i	−0.810826	+	0.585287i	$0.800982\pi$
$752$	−4.82288	+	8.35347i	−0.175872	+	0.304620i
$753$	3.66601	+	6.34972i	0.133597	+	0.231397i
$754$	−5.58562	+	4.68689i	−0.203416	+	0.170686i
$755$	10.0627	−	3.66252i	0.366219	−	0.133293i
$756$	−4.09166	−	1.48924i	−0.148812	−	0.0541632i
$757$	12.7033	+	10.6594i	0.461710	+	0.387421i	0.843760	−	0.536721i	$-0.180337\pi$
$757$	12.7033	+	10.6594i	0.461710	+	0.387421i	−0.382050	+	0.924142i	$0.624782\pi$
$758$	3.69723	−	20.9680i	0.134289	−	0.761593i
$759$	−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	$0.435370\pi$
$762$	1.24436	−	7.05714i	0.0450786	−	0.255653i
$763$	8.29932	+	6.96395i	0.300455	+	0.252112i
$764$	13.7035	+	4.98768i	0.495777	+	0.180448i
$765$		0			0
$766$	−24.1459	+	20.2608i	−0.872428	+	0.732054i
$767$	−7.93725	−	13.7477i	−0.286598	−	0.496402i
$768$	1.32288	−	2.29129i	0.0477352	−	0.0826797i
$769$	4.29059	+	24.3331i	0.154722	+	0.877475i	0.959039	+	0.283274i	$0.0914205\pi$
$769$	4.29059	+	24.3331i	0.154722	+	0.877475i	−0.804317	+	0.594201i	$0.797468\pi$
$770$	−0.672801	−	3.81565i	−0.0242461	−	0.137506i
$771$	2.26013	−	3.91466i	0.0813966	−	0.140983i
$772$	3.29150	+	5.70105i	0.118464	+	0.205185i
$773$	8.37842	−	7.03033i	0.301351	−	0.252863i	−0.479555	−	0.877512i	$-0.659202\pi$
$773$	8.37842	−	7.03033i	0.301351	−	0.252863i	0.780906	+	0.624648i	$0.214758\pi$
$774$	−2.66308	+	0.969281i	−0.0957224	+	0.0348401i
$775$	2.76012	+	1.00460i	0.0991463	+	0.0360863i
$776$	−10.9479	−	9.18640i	−0.393008	−	0.329773i
$777$	4.26879	−	24.2095i	0.153142	−	0.868512i
$778$	12.0000			0.430221
$779$		0			0
$780$	−19.2915			−0.690747
$781$	−1.49042	+	8.45261i	−0.0533315	+	0.302458i
$782$		0			0
$783$	−9.06404	−	3.29904i	−0.323922	−	0.117898i
$784$	4.03269	−	1.46778i	0.144025	−	0.0524207i
$785$	29.5563	−	24.8007i	1.05491	−	0.885174i
$786$	−18.4373	−	31.9343i	−0.657635	−	1.13906i
$787$	2.73987	−	4.74559i	0.0976658	−	0.169162i	−0.813052	−	0.582191i	$-0.802196\pi$
$787$	2.73987	−	4.74559i	0.0976658	−	0.169162i	0.910718	+	0.413029i	$0.135529\pi$
$788$	−0.408811	−	2.31848i	−0.0145633	−	0.0825925i
$789$	−2.26832	−	12.8643i	−0.0807544	−	0.457981i
$790$	7.29150	−	12.6293i	0.259420	−	0.449329i
$791$	4.59412	+	7.95725i	0.163348	+	0.282927i
$792$	1.97870	−	1.66032i	0.0703099	−	0.0589970i
$793$	28.0729	−	10.2177i	0.996896	−	0.362841i
$794$	−34.7097	−	12.6333i	−1.23180	−	0.448339i
$795$	−63.4205	−	53.2161i	−2.24929	−	1.88738i
$796$	2.06199	−	11.6941i	0.0730852	−	0.414487i
$797$	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
$800$	1.43980	−	8.16554i	0.0509048	−	0.288695i
$801$		0			0
$802$	−6.03000	−	2.19474i	−0.212927	−	0.0774990i
$803$	−7.45858	+	2.71470i	−0.263208	+	0.0957997i
$804$	9.41584	−	7.90083i	0.332071	−	0.278641i
$805$	10.9373	+	18.9439i	0.385488	+	0.667684i
$806$	0.354249	−	0.613577i	0.0124779	−	0.0216123i
$807$		0			0
$808$	−1.45070	−	8.22733i	−0.0510355	−	0.289436i
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	9.11438	+	15.7866i	0.320247	+	0.554683i
$811$	−15.8636	+	13.3112i	−0.557047	+	0.467418i	−0.877319	−	0.479907i	$-0.840670\pi$
$811$	−15.8636	+	13.3112i	−0.557047	+	0.467418i	0.320272	+	0.947326i	$0.396226\pi$
$812$	−5.63816	+	2.05212i	−0.197860	+	0.0720153i
$813$	43.8707	+	15.9676i	1.53861	+	0.560010i
$814$	2.79281	+	2.34344i	0.0978879	+	0.0821377i
$815$	−7.55721	+	42.8591i	−0.264718	+	1.50129i
$816$		0			0
$817$		0			0
$818$	13.5830			0.474919
$819$	−2.28625	+	12.9660i	−0.0798882	+	0.453068i
$820$	28.7422	+	24.1176i	1.00372	+	0.842222i
$821$	5.63816	+	2.05212i	0.196773	+	0.0716195i	0.438527	−	0.898718i	$-0.355500\pi$
$821$	5.63816	+	2.05212i	0.196773	+	0.0716195i	−0.241754	+	0.970338i	$0.577723\pi$
$822$	−13.8804	+	5.05206i	−0.484136	+	0.176211i
$823$	−0.0961326	+	0.0806648i	−0.00335097	+	0.00281180i	−0.644462	−	0.764637i	$-0.722918\pi$
$823$	−0.0961326	+	0.0806648i	−0.00335097	+	0.00281180i	0.641111	+	0.767449i	$0.278474\pi$
$824$	1.35425	+	2.34563i	0.0471775	+	0.0817138i
$825$	7.08301	−	12.2681i	0.246599	−	0.427121i
$826$	−2.26832	−	12.8643i	−0.0789250	−	0.447606i
$827$	−8.22298	−	46.6348i	−0.285941	−	1.62165i	−0.701905	−	0.712271i	$-0.747667\pi$
$827$	−8.22298	−	46.6348i	−0.285941	−	1.62165i	0.415964	−	0.909381i	$-0.363444\pi$
$828$	−7.29150	+	12.6293i	−0.253397	+	0.438897i
$829$	−12.5830	−	21.7944i	−0.437026	−	0.756951i	0.560433	−	0.828200i	$-0.310635\pi$
$829$	−12.5830	−	21.7944i	−0.437026	−	0.756951i	−0.997459	+	0.0712490i	$0.977302\pi$
$830$	−22.1672	+	18.6005i	−0.769436	+	0.645633i
$831$	23.6692	−	8.61488i	0.821076	−	0.298847i
$832$	−1.87939	−	0.684040i	−0.0651560	−	0.0237148i
$833$		0			0
$834$	−6.13534	+	34.7952i	−0.212449	+	1.20486i
$835$	−43.7490			−1.51400
$836$		0			0
$837$	0.937254			0.0323962
$838$	5.51316	−	31.2667i	0.190449	−	1.08009i
$839$	−3.43168	−	2.87952i	−0.118475	−	0.0994121i	0.581625	−	0.813457i	$-0.302417\pi$
$839$	−3.43168	−	2.87952i	−0.118475	−	0.0994121i	−0.700100	+	0.714045i	$0.746861\pi$
$840$	−14.9172	−	5.42940i	−0.514691	−	0.187332i
$841$	14.7612	−	5.37262i	0.509005	−	0.185263i
$842$	17.4748	−	14.6631i	0.602222	−	0.505324i
$843$	−36.3229	−	62.9131i	−1.25103	−	2.16684i
$844$	1.35425	−	2.34563i	0.0466152	−	0.0807398i
$845$	−5.69770	−	32.3133i	−0.196007	−	1.11161i
$846$	6.69987	+	37.9968i	0.230346	+	1.30636i
$847$	−8.70850	+	15.0836i	−0.299228	+	0.518277i
$848$	−4.29150	−	7.43310i	−0.147371	−	0.255254i
$849$	−51.3871	+	43.1189i	−1.76360	+	1.47984i
$850$		0			0
$851$	−19.3417	−	7.03980i	−0.663025	−	0.241321i
$852$	26.9387	+	22.6043i	0.922906	+	0.774410i
$853$	−2.18502	+	12.3918i	−0.0748135	+	0.424289i	0.924280	+	0.381716i	$0.124667\pi$
$853$	−2.18502	+	12.3918i	−0.0748135	+	0.424289i	−0.999093	+	0.0425730i	$0.986445\pi$
$854$	24.5830			0.841213
$855$		0			0
$856$	4.70850			0.160933
$857$	3.64661	−	20.6810i	0.124566	−	0.706448i	−0.856999	−	0.515318i	$-0.827674\pi$
$857$	3.64661	−	20.6810i	0.124566	−	0.706448i	0.981565	−	0.191130i	$-0.0612152\pi$
$858$	−2.61757	−	2.19640i	−0.0893624	−	0.0749839i
$859$	12.4310	+	4.52450i	0.424139	+	0.154374i	0.545266	−	0.838263i	$-0.316429\pi$
$859$	12.4310	+	4.52450i	0.424139	+	0.154374i	−0.121127	+	0.992637i	$0.538651\pi$
$860$	−2.42723	+	0.883440i	−0.0827679	+	0.0301250i
$861$	34.3278	−	28.8044i	1.16989	−	0.981653i
$862$	1.93725	+	3.35542i	0.0659831	+	0.114286i
$863$	23.4686	−	40.6489i	0.798881	−	1.38370i	−0.121464	−	0.992596i	$-0.538759\pi$
$863$	23.4686	−	40.6489i	0.798881	−	1.38370i	0.920345	−	0.391107i	$-0.127908\pi$
$864$	−0.459430	−	2.60556i	−0.0156301	−	0.0886428i
$865$	−3.79847	−	21.5422i	−0.129152	−	0.732456i
$866$	6.93725	−	12.0157i	0.235737	−	0.408309i
$867$	−22.4889	−	38.9519i	−0.763763	−	1.32288i
$868$	0.446608	−	0.374749i	0.0151589	−	0.0127198i
$869$	2.42723	−	0.883440i	0.0823382	−	0.0299686i
$870$	−33.0452	−	12.0275i	−1.12034	−	0.407770i
$871$	−7.11770	−	5.97246i	−0.241174	−	0.202369i
$872$	−1.14313	+	6.48299i	−0.0387112	+	0.219542i
$873$	−57.1660			−1.93478
$874$		0			0
$875$	−19.7490			−0.667639
$876$	−5.64708	+	32.0262i	−0.190797	+	1.08207i
$877$	−27.8490	−	23.3681i	−0.940393	−	0.789083i	0.0372607	−	0.999306i	$-0.488137\pi$
$877$	−27.8490	−	23.3681i	−0.940393	−	0.789083i	−0.977654	+	0.210222i	$0.932581\pi$
$878$	34.5917	+	12.5904i	1.16741	+	0.424904i
$879$	32.4765	−	11.8205i	1.09541	−	0.398695i
$880$	1.80346	−	1.51328i	0.0607946	−	0.0510127i
$881$	2.56275	+	4.43881i	0.0863411	+	0.149547i	0.905962	−	0.423359i	$-0.139149\pi$
$881$	2.56275	+	4.43881i	0.0863411	+	0.149547i	−0.819621	+	0.572906i	$0.805816\pi$
$882$	8.58301	−	14.8662i	0.289005	−	0.500571i
$883$	7.01448	+	39.7811i	0.236056	+	1.33874i	0.840378	+	0.542000i	$0.182333\pi$
$883$	7.01448	+	39.7811i	0.236056	+	1.33874i	−0.604322	+	0.796740i	$0.706556\pi$
$884$		0			0
$885$	38.2804	−	66.3036i	1.28678	−	2.22877i
$886$	−2.67712	−	4.63692i	−0.0899398	−	0.155780i
$887$	−29.5563	+	24.8007i	−0.992403	+	0.832725i	−0.985914	−	0.167254i	$-0.946510\pi$
$887$	−29.5563	+	24.8007i	−0.992403	+	0.832725i	−0.00648943	+	0.999979i	$0.502066\pi$
$888$	14.0364	−	5.10884i	0.471032	−	0.171442i
$889$	−4.18869	−	1.52456i	−0.140484	−	0.0511321i
$890$		0			0
$891$	−0.560668	+	3.17970i	−0.0187831	+	0.106524i
$892$	28.8118			0.964689
$893$		0			0
$894$	13.0627			0.436884
$895$	12.6218	−	71.5820i	0.421902	−	2.39272i
$896$	−1.26072	−	1.05787i	−0.0421177	−	0.0353409i
$897$	18.1281	+	6.59808i	0.605279	+	0.220304i
$898$	12.8818	−	4.68858i	0.429870	−	0.156460i
$899$	0.989348	−	0.830162i	0.0329966	−	0.0276874i
$900$	−16.5830	−	28.7226i	−0.552767	−	0.957420i
$901$		0			0
$902$	1.15402	+	6.54479i	0.0384247	+	0.217918i
$903$	0.535700	+	3.03811i	0.0178270	+	0.101102i
$904$	−2.79150	+	4.83502i	−0.0928440	+	0.160811i
$905$	7.70850	+	13.3515i	0.256239	+	0.443819i
$906$	5.95312	−	4.99526i	0.197779	−	0.165956i
$907$	−22.6116	+	8.22994i	−0.750805	+	0.273271i	−0.688945	−	0.724814i	$-0.741926\pi$
$907$	−22.6116	+	8.22994i	−0.750805	+	0.273271i	−0.0618607	+	0.998085i	$0.519703\pi$
$908$	11.8831	+	4.32510i	0.394355	+	0.143534i
$909$	−25.5989	−	21.4800i	−0.849062	−	0.712448i
$910$	−2.08378	+	11.8177i	−0.0690766	+	0.391753i
$911$	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
$914$	0.195440	−	1.10839i	0.00646457	−	0.0366624i
$915$	110.372	+	92.6135i	3.64880	+	3.06171i
$916$	−18.7939	−	6.84040i	−0.620966	−	0.226013i
$917$	−21.5540	+	7.84500i	−0.711775	+	0.259065i
$918$		0			0
$919$	−5.93725	−	10.2836i	−0.195852	−	0.339226i	0.751328	−	0.659929i	$-0.229414\pi$
$919$	−5.93725	−	10.2836i	−0.195852	−	0.339226i	−0.947179	+	0.320704i	$0.896081\pi$
$920$	−6.64575	+	11.5108i	−0.219104	+	0.379499i
$921$	2.13440	+	12.1048i	0.0703308	+	0.398866i
$922$	−4.02274	−	22.8141i	−0.132482	−	0.751341i
$923$	13.2915	−	23.0216i	0.437495	−	0.757764i
$924$	−1.40588	−	2.43506i	−0.0462501	−	0.0801075i
$925$	35.8599	−	30.0900i	1.17907	−	0.989354i
$926$	−13.5856	+	4.94476i	−0.446451	+	0.162495i
$927$	10.1806	+	3.70544i	0.334375	+	0.121703i
$928$	−2.79281	−	2.34344i	−0.0916784	−	0.0769273i
$929$	2.01137	−	11.4070i	0.0659908	−	0.374253i	−0.933871	−	0.357611i	$-0.883591\pi$
$929$	2.01137	−	11.4070i	0.0659908	−	0.374253i	0.999862	−	0.0166417i	$-0.00529747\pi$
$930$	3.41699			0.112048
$931$		0			0
$932$	−12.8745			−0.421719
$933$	−3.83819	+	21.7675i	−0.125657	+	0.712635i
$934$	−18.8797	−	15.8420i	−0.617764	−	0.518366i
$935$		0			0
$936$	−7.51754	+	2.73616i	−0.245719	+	0.0894342i
$937$	29.7796	−	24.9881i	0.972857	−	0.816324i	−0.0101393	−	0.999949i	$-0.503227\pi$
$937$	29.7796	−	24.9881i	0.972857	−	0.816324i	0.982996	+	0.183625i	$0.0587831\pi$
$938$	−3.82288	−	6.62141i	−0.124821	−	0.216197i
$939$	−30.2601	+	52.4121i	−0.987502	+	1.71040i
$940$	6.10651	+	34.6318i	0.199173	+	1.12956i
$941$	10.2741	+	58.2671i	0.334925	+	1.89945i	0.427970	+	0.903793i	$0.359229\pi$
$941$	10.2741	+	58.2671i	0.334925	+	1.89945i	−0.0930452	+	0.995662i	$0.529660\pi$
$942$	14.0000	−	24.2487i	0.456145	−	0.790066i
$943$	−18.7601	−	32.4935i	−0.610914	−	1.05813i
$944$	6.08029	−	5.10197i	0.197897	−	0.166055i
$945$	−14.9172	+	5.42940i	−0.485255	+	0.176618i
$946$	−0.429922	−	0.156479i	−0.0139780	−	0.00508756i
$947$	42.7062	+	35.8348i	1.38777	+	1.16447i	0.966236	+	0.257659i	$0.0829512\pi$
$947$	42.7062	+	35.8348i	1.38777	+	1.16447i	0.421530	+	0.906814i	$0.361493\pi$
$948$	1.83772	−	10.4222i	0.0596864	−	0.338498i
$949$	24.5830			0.797998
$950$		0			0
$951$	15.8745			0.514766
$952$		0			0
$953$	30.2262	+	25.3628i	0.979123	+	0.821582i	0.983957	−	0.178407i	$-0.0570942\pi$
$953$	30.2262	+	25.3628i	0.979123	+	0.821582i	−0.00483391	+	0.999988i	$0.501539\pi$
$954$	−32.2615	−	11.7422i	−1.04451	−	0.380169i
$955$	49.9597	−	18.1838i	1.61666	−	0.588415i
$956$	−9.19253	+	7.71345i	−0.297308	+	0.249471i
$957$	−3.11438	−	5.39426i	−0.100674	−	0.174372i
$958$	7.29150	−	12.6293i	0.235578	−	0.408033i
$959$	1.59552	+	9.04865i	0.0515221	+	0.292196i
$960$	−1.67497	−	9.49921i	−0.0540593	−	0.306586i
$961$	15.4373	−	26.7381i	0.497976	−	0.862520i
$962$	−5.64575	−	9.77873i	−0.182026	−	0.315279i
$963$	14.4277	−	12.1063i	0.464925	−	0.390119i
$964$	−12.7638	+	4.64566i	−0.411096	+	0.149627i
$965$	22.5526	+	8.20848i	0.725995	+	0.264240i
$966$	12.1606	+	10.2039i	0.391260	+	0.328306i
$967$	−0.470326	+	2.66735i	−0.0151247	+	0.0857762i	−0.991436	−	0.130595i	$-0.958311\pi$
$967$	−0.470326	+	2.66735i	−0.0151247	+	0.0857762i	0.976311	+	0.216372i	$0.0694222\pi$
$968$	−10.5830			−0.340151
$969$		0			0
$970$	−52.1033			−1.67293
$971$	2.49963	−	14.1761i	0.0802168	−	0.454932i	−0.918070	−	0.396419i	$-0.870253\pi$
$971$	2.49963	−	14.1761i	0.0802168	−	0.454932i	0.998287	−	0.0585133i	$-0.0186360\pi$
$972$	16.2141	+	13.6052i	0.520068	+	0.436389i
$973$	20.6524	+	7.51684i	0.662084	+	0.240979i
$974$	20.8882	−	7.60268i	0.669301	−	0.243606i
$975$	−33.6098	+	28.2020i	−1.07638	+	0.903187i
$976$	7.46863	+	12.9360i	0.239065	+	0.414073i
$977$	−22.7288	+	39.3674i	−0.727157	+	1.25947i	0.230923	+	0.972972i	$0.425826\pi$
$977$	−22.7288	+	39.3674i	−0.727157	+	1.25947i	−0.958080	+	0.286501i	$0.907508\pi$
$978$	5.48433	+	31.1032i	0.175370	+	0.994570i
$979$		0			0
$980$	7.82288	−	13.5496i	0.249893	−	0.432827i
$981$	13.1660	+	22.8042i	0.420358	+	0.728082i
$982$	21.9920	−	18.4535i	0.701792	−	0.588874i
$983$	29.8343	−	10.8588i	0.951567	−	0.346342i	0.180843	−	0.983512i	$-0.442117\pi$
$983$	29.8343	−	10.8588i	0.951567	−	0.346342i	0.770723	+	0.637170i	$0.219895\pi$
$984$	25.5867	+	9.31278i	0.815673	+	0.296881i
$985$	−6.57496	−	5.51705i	−0.209496	−	0.175788i
$986$		0			0
$987$	42.0000			1.33687
$988$		0			0
$989$	2.58301			0.0821348
$990$	1.63524	−	9.27393i	0.0519715	−	0.294745i
$991$	−34.5992	−	29.0322i	−1.09908	−	0.922237i	−0.101716	−	0.994813i	$-0.532433\pi$
$991$	−34.5992	−	29.0322i	−1.09908	−	0.922237i	−0.997363	+	0.0725768i	$0.976878\pi$
$992$	0.332885	+	0.121160i	0.0105691	+	0.00384684i
$993$	−69.1454	+	25.1669i	−2.19426	+	0.798646i
$994$	16.7568	−	14.0607i	0.531495	−	0.445977i
$995$	−21.6458	−	37.4915i	−0.686216	−	1.18856i
$996$	−10.5000	+	18.1865i	−0.332705	+	0.576262i
$997$	−1.77620	−	10.0734i	−0.0562530	−	0.319026i	0.943677	−	0.330868i	$-0.107342\pi$
$997$	−1.77620	−	10.0734i	−0.0562530	−	0.319026i	−0.999930	+	0.0118419i	$0.996231\pi$
$998$	−5.42282	−	30.7543i	−0.171656	−	0.973511i
$999$	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.245.1		12
19.2	odd	18		722.2.c.j.429.1		4
19.3	odd	18		722.2.a.g.1.2		2
19.4	even	9	inner	722.2.e.n.595.2		12
19.5	even	9		38.2.c.b.7.2	✓	4
19.6	even	9	inner	722.2.e.n.99.1		12
19.7	even	3	inner	722.2.e.n.415.2		12
19.8	odd	6		722.2.e.o.423.2		12
19.9	even	9	inner	722.2.e.n.389.1		12
19.10	odd	18		722.2.e.o.389.2		12
19.11	even	3	inner	722.2.e.n.423.1		12
19.12	odd	6		722.2.e.o.415.1		12
19.13	odd	18		722.2.e.o.99.2		12
19.14	odd	18		722.2.c.j.653.1		4
19.15	odd	18		722.2.e.o.595.1		12
19.16	even	9		722.2.a.j.1.1		2
19.17	even	9		38.2.c.b.11.2	yes	4
19.18	odd	2		722.2.e.o.245.2		12
57.5	odd	18		342.2.g.f.235.2		4
57.17	odd	18		342.2.g.f.163.2		4
57.35	odd	18		6498.2.a.ba.1.1		2
57.41	even	18		6498.2.a.bg.1.1		2
76.3	even	18		5776.2.a.z.1.1		2
76.35	odd	18		5776.2.a.ba.1.2		2
76.43	odd	18		304.2.i.e.273.1		4
76.55	odd	18		304.2.i.e.49.1		4
95.17	odd	36		950.2.j.g.49.1		8
95.24	even	18		950.2.e.k.501.1		4
95.43	odd	36		950.2.j.g.349.1		8
95.62	odd	36		950.2.j.g.349.4		8
95.74	even	18		950.2.e.k.201.1		4
95.93	odd	36		950.2.j.g.49.4		8
152.5	even	18		1216.2.i.l.577.1		4
152.43	odd	18		1216.2.i.k.577.2		4
152.93	even	18		1216.2.i.l.961.1		4
152.131	odd	18		1216.2.i.k.961.2		4
228.119	even	18		2736.2.s.v.577.2		4
228.131	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	19.5	even	9
38.2.c.b.11.2	yes	4	19.17	even	9
304.2.i.e.49.1		4	76.55	odd	18
304.2.i.e.273.1		4	76.43	odd	18
342.2.g.f.163.2		4	57.17	odd	18
342.2.g.f.235.2		4	57.5	odd	18
722.2.a.g.1.2		2	19.3	odd	18
722.2.a.j.1.1		2	19.16	even	9
722.2.c.j.429.1		4	19.2	odd	18
722.2.c.j.653.1		4	19.14	odd	18
722.2.e.n.99.1		12	19.6	even	9	inner
722.2.e.n.245.1		12	1.1	even	1	trivial
722.2.e.n.389.1		12	19.9	even	9	inner
722.2.e.n.415.2		12	19.7	even	3	inner
722.2.e.n.423.1		12	19.11	even	3	inner
722.2.e.n.595.2		12	19.4	even	9	inner
722.2.e.o.99.2		12	19.13	odd	18
722.2.e.o.245.2		12	19.18	odd	2
722.2.e.o.389.2		12	19.10	odd	18
722.2.e.o.415.1		12	19.12	odd	6
722.2.e.o.423.2		12	19.8	odd	6
722.2.e.o.595.1		12	19.15	odd	18
950.2.e.k.201.1		4	95.74	even	18
950.2.e.k.501.1		4	95.24	even	18
950.2.j.g.49.1		8	95.17	odd	36
950.2.j.g.49.4		8	95.93	odd	36
950.2.j.g.349.1		8	95.43	odd	36
950.2.j.g.349.4		8	95.62	odd	36
1216.2.i.k.577.2		4	152.43	odd	18
1216.2.i.k.961.2		4	152.131	odd	18
1216.2.i.l.577.1		4	152.5	even	18
1216.2.i.l.961.1		4	152.93	even	18
2736.2.s.v.577.2		4	228.119	even	18
2736.2.s.v.1873.2		4	228.131	even	18
5776.2.a.z.1.1		2	76.3	even	18
5776.2.a.ba.1.2		2	76.35	odd	18
6498.2.a.ba.1.1		2	57.35	odd	18
6498.2.a.bg.1.1		2	57.41	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-2.02676 - 1.70066i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.42589 + 1.24692i) q^{5} +(-2.02676 + 1.70066i) q^{6} +(0.822876 + 1.42526i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.694593 + 3.93923i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-2.02676 - 1.70066i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.42589 + 1.24692i) q^{5} +(-2.02676 + 1.70066i) q^{6} +(0.822876 + 1.42526i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.694593 + 3.93923i) q^{9} +(0.633078 + 3.59036i) q^{10} +(-0.322876 + 0.559237i) q^{11} +(1.32288 + 2.29129i) q^{12} +(1.53209 - 1.28558i) q^{13} +(1.54650 - 0.562880i) q^{14} +(9.06404 + 3.29904i) q^{15} +(0.766044 + 0.642788i) q^{16} +4.00000 q^{18} +3.64575 q^{20} +(0.756107 - 4.28810i) q^{21} +(0.494674 + 0.415081i) q^{22} +(-3.42589 - 1.24692i) q^{23} +(2.48619 - 0.904900i) q^{24} +(6.35166 - 5.32968i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(1.32288 - 2.29129i) q^{27} +(-0.285782 - 1.62075i) q^{28} +(-0.633078 - 3.59036i) q^{29} +(4.82288 - 8.35347i) q^{30} +(0.177124 + 0.306788i) q^{31} +(0.766044 - 0.642788i) q^{32} +(1.60546 - 0.584341i) q^{33} +(-4.59627 - 3.85673i) q^{35} +(0.694593 - 3.93923i) q^{36} +5.64575 q^{37} -5.29150 q^{39} +(0.633078 - 3.59036i) q^{40} +(7.88375 + 6.61525i) q^{41} +(-4.09166 - 1.48924i) q^{42} +(-0.665770 + 0.242320i) q^{43} +(0.494674 - 0.415081i) q^{44} +(-7.29150 - 12.6293i) q^{45} +(-1.82288 + 3.15731i) q^{46} +(1.67497 + 9.49921i) q^{47} +(-0.459430 - 2.60556i) q^{48} +(2.14575 - 3.71655i) q^{49} +(-4.14575 - 7.18065i) q^{50} +(-1.87939 + 0.684040i) q^{52} +(-8.06539 - 2.93556i) q^{53} +(-2.02676 - 1.70066i) q^{54} +(0.408811 - 2.31848i) q^{55} -1.64575 q^{56} -3.64575 q^{58} +(1.37829 - 7.81667i) q^{59} +(-7.38907 - 6.20017i) q^{60} +(14.0364 + 5.10884i) q^{61} +(0.332885 - 0.121160i) q^{62} +(-5.04287 + 4.23147i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.64575 + 6.31463i) q^{65} +(-0.296677 - 1.68254i) q^{66} +(-0.806726 - 4.57517i) q^{67} +(4.82288 + 8.35347i) q^{69} +(-4.59627 + 3.85673i) q^{70} +(12.4899 - 4.54596i) q^{71} +(-3.75877 - 1.36808i) q^{72} +(9.41584 + 7.90083i) q^{73} +(0.980374 - 5.55998i) q^{74} -21.9373 q^{75} -1.06275 q^{77} +(-0.918860 + 5.21111i) q^{78} +(-3.06418 - 2.57115i) q^{79} +(-3.42589 - 1.24692i) q^{80} +(4.69846 - 1.71010i) q^{81} +(7.88375 - 6.61525i) q^{82} +(3.96863 + 6.87386i) q^{83} +(-2.17712 + 3.77089i) q^{84} +(0.123029 + 0.697734i) q^{86} +(-4.82288 + 8.35347i) q^{87} +(-0.322876 - 0.559237i) q^{88} +(-13.7035 + 4.98768i) q^{90} +(3.09300 + 1.12576i) q^{91} +(2.79281 + 2.34344i) q^{92} +(0.162752 - 0.923015i) q^{93} +9.64575 q^{94} -2.64575 q^{96} +(-2.48169 + 14.0744i) q^{97} +(-3.28748 - 2.75852i) q^{98} +(-2.42723 - 0.883440i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more